Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(157,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([4, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.cg (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 187.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.187 |
Dual form | 315.2.cg.d.283.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.133975 | − | 0.500000i | 0.0947343 | − | 0.353553i | −0.902245 | − | 0.431224i | \(-0.858082\pi\) |
0.996979 | + | 0.0776710i | \(0.0247484\pi\) | |||||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | 1.50000 | + | 0.866025i | 0.750000 | + | 0.433013i | ||||
\(5\) | −1.00000 | + | 2.00000i | −0.447214 | + | 0.894427i | ||||
\(6\) | −0.232051 | − | 0.866025i | −0.0947343 | − | 0.353553i | ||||
\(7\) | 0.500000 | + | 2.59808i | 0.188982 | + | 0.981981i | ||||
\(8\) | 1.36603 | − | 1.36603i | 0.482963 | − | 0.482963i | ||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0.866025 | + | 0.767949i | 0.273861 | + | 0.242847i | ||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 3.00000 | 0.866025 | ||||||||
\(13\) | −0.0980762 | + | 0.366025i | −0.0272014 | + | 0.101517i | −0.978192 | − | 0.207703i | \(-0.933401\pi\) |
0.950991 | + | 0.309220i | \(0.100068\pi\) | |||||||
\(14\) | 1.36603 | + | 0.0980762i | 0.365086 | + | 0.0262120i | ||||
\(15\) | 0.232051 | + | 3.86603i | 0.0599153 | + | 0.998203i | ||||
\(16\) | 1.23205 | + | 2.13397i | 0.308013 | + | 0.533494i | ||||
\(17\) | −2.00000 | − | 0.535898i | −0.485071 | − | 0.129974i | 0.00799174 | − | 0.999968i | \(-0.497456\pi\) |
−0.493063 | + | 0.869994i | \(0.664123\pi\) | |||||||
\(18\) | −1.09808 | − | 1.09808i | −0.258819 | − | 0.258819i | ||||
\(19\) | 0.366025 | − | 0.633975i | 0.0839720 | − | 0.145444i | −0.820981 | − | 0.570956i | \(-0.806573\pi\) |
0.904953 | + | 0.425512i | \(0.139906\pi\) | |||||||
\(20\) | −3.23205 | + | 2.13397i | −0.722709 | + | 0.477171i | ||||
\(21\) | 3.00000 | + | 3.46410i | 0.654654 | + | 0.755929i | ||||
\(22\) | −0.267949 | + | 1.00000i | −0.0571270 | + | 0.213201i | ||||
\(23\) | 4.46410 | − | 4.46410i | 0.930830 | − | 0.930830i | −0.0669283 | − | 0.997758i | \(-0.521320\pi\) |
0.997758 | + | 0.0669283i | \(0.0213199\pi\) | |||||||
\(24\) | 0.866025 | − | 3.23205i | 0.176777 | − | 0.659740i | ||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 0.169873 | + | 0.0980762i | 0.0333148 | + | 0.0192343i | ||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −1.50000 | + | 4.33013i | −0.283473 | + | 0.818317i | ||||
\(29\) | −8.59808 | − | 4.96410i | −1.59662 | − | 0.921811i | −0.992132 | − | 0.125199i | \(-0.960043\pi\) |
−0.604491 | − | 0.796612i | \(-0.706623\pi\) | |||||||
\(30\) | 1.96410 | + | 0.401924i | 0.358594 | + | 0.0733809i | ||||
\(31\) | −4.73205 | − | 2.73205i | −0.849901 | − | 0.490691i | 0.0107162 | − | 0.999943i | \(-0.496589\pi\) |
−0.860618 | + | 0.509252i | \(0.829922\pi\) | |||||||
\(32\) | 4.96410 | − | 1.33013i | 0.877537 | − | 0.235135i | ||||
\(33\) | −3.00000 | + | 1.73205i | −0.522233 | + | 0.301511i | ||||
\(34\) | −0.535898 | + | 0.928203i | −0.0919058 | + | 0.159186i | ||||
\(35\) | −5.69615 | − | 1.59808i | −0.962825 | − | 0.270124i | ||||
\(36\) | 4.50000 | − | 2.59808i | 0.750000 | − | 0.433013i | ||||
\(37\) | 8.83013 | − | 2.36603i | 1.45166 | − | 0.388972i | 0.555062 | − | 0.831809i | \(-0.312695\pi\) |
0.896602 | + | 0.442837i | \(0.146028\pi\) | |||||||
\(38\) | −0.267949 | − | 0.267949i | −0.0434671 | − | 0.0434671i | ||||
\(39\) | 0.169873 | + | 0.633975i | 0.0272014 | + | 0.101517i | ||||
\(40\) | 1.36603 | + | 4.09808i | 0.215988 | + | 0.647963i | ||||
\(41\) | −2.59808 | + | 1.50000i | −0.405751 | + | 0.234261i | −0.688963 | − | 0.724797i | \(-0.741934\pi\) |
0.283211 | + | 0.959058i | \(0.408600\pi\) | |||||||
\(42\) | 2.13397 | − | 1.03590i | 0.329279 | − | 0.159843i | ||||
\(43\) | −0.232051 | − | 0.866025i | −0.0353874 | − | 0.132068i | 0.945972 | − | 0.324247i | \(-0.105111\pi\) |
−0.981360 | + | 0.192180i | \(0.938444\pi\) | |||||||
\(44\) | −3.00000 | − | 1.73205i | −0.452267 | − | 0.261116i | ||||
\(45\) | 3.69615 | + | 5.59808i | 0.550990 | + | 0.834512i | ||||
\(46\) | −1.63397 | − | 2.83013i | −0.240916 | − | 0.417279i | ||||
\(47\) | 4.96410 | + | 1.33013i | 0.724089 | + | 0.194019i | 0.601995 | − | 0.798500i | \(-0.294373\pi\) |
0.122093 | + | 0.992519i | \(0.461039\pi\) | |||||||
\(48\) | 3.69615 | + | 2.13397i | 0.533494 | + | 0.308013i | ||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | −2.40192 | + | 0.964102i | −0.339683 | + | 0.136345i | ||||
\(51\) | −3.46410 | + | 0.928203i | −0.485071 | + | 0.129974i | ||||
\(52\) | −0.464102 | + | 0.464102i | −0.0643593 | + | 0.0643593i | ||||
\(53\) | −1.00000 | − | 0.267949i | −0.137361 | − | 0.0368057i | 0.189484 | − | 0.981884i | \(-0.439319\pi\) |
−0.326844 | + | 0.945078i | \(0.605985\pi\) | |||||||
\(54\) | −2.59808 | − | 0.696152i | −0.353553 | − | 0.0947343i | ||||
\(55\) | 2.00000 | − | 4.00000i | 0.269680 | − | 0.539360i | ||||
\(56\) | 4.23205 | + | 2.86603i | 0.565532 | + | 0.382989i | ||||
\(57\) | − | 1.26795i | − | 0.167944i | ||||||
\(58\) | −3.63397 | + | 3.63397i | −0.477164 | + | 0.477164i | ||||
\(59\) | −4.56218 | + | 7.90192i | −0.593945 | + | 1.02874i | 0.399750 | + | 0.916624i | \(0.369097\pi\) |
−0.993695 | + | 0.112119i | \(0.964236\pi\) | |||||||
\(60\) | −3.00000 | + | 6.00000i | −0.387298 | + | 0.774597i | ||||
\(61\) | 9.46410 | − | 5.46410i | 1.21175 | − | 0.699607i | 0.248613 | − | 0.968603i | \(-0.420025\pi\) |
0.963141 | + | 0.268996i | \(0.0866920\pi\) | |||||||
\(62\) | −2.00000 | + | 2.00000i | −0.254000 | + | 0.254000i | ||||
\(63\) | 7.50000 | + | 2.59808i | 0.944911 | + | 0.327327i | ||||
\(64\) | 2.26795i | 0.283494i | ||||||||
\(65\) | −0.633975 | − | 0.562178i | −0.0786349 | − | 0.0697296i | ||||
\(66\) | 0.464102 | + | 1.73205i | 0.0571270 | + | 0.213201i | ||||
\(67\) | −3.36603 | + | 0.901924i | −0.411225 | + | 0.110188i | −0.458500 | − | 0.888694i | \(-0.651613\pi\) |
0.0472746 | + | 0.998882i | \(0.484946\pi\) | |||||||
\(68\) | −2.53590 | − | 2.53590i | −0.307523 | − | 0.307523i | ||||
\(69\) | 2.83013 | − | 10.5622i | 0.340707 | − | 1.27154i | ||||
\(70\) | −1.56218 | + | 2.63397i | −0.186716 | + | 0.314820i | ||||
\(71\) | 1.26795 | 0.150478 | 0.0752389 | − | 0.997166i | \(-0.476028\pi\) | ||||
0.0752389 | + | 0.997166i | \(0.476028\pi\) | |||||||
\(72\) | −1.50000 | − | 5.59808i | −0.176777 | − | 0.659740i | ||||
\(73\) | −3.46410 | + | 12.9282i | −0.405442 | + | 1.51313i | 0.397796 | + | 0.917474i | \(0.369775\pi\) |
−0.803238 | + | 0.595658i | \(0.796891\pi\) | |||||||
\(74\) | − | 4.73205i | − | 0.550090i | ||||||
\(75\) | −7.96410 | − | 3.40192i | −0.919615 | − | 0.392820i | ||||
\(76\) | 1.09808 | − | 0.633975i | 0.125958 | − | 0.0727219i | ||||
\(77\) | −1.00000 | − | 5.19615i | −0.113961 | − | 0.592157i | ||||
\(78\) | 0.339746 | 0.0384687 | ||||||||
\(79\) | −9.92820 | + | 5.73205i | −1.11701 | + | 0.644906i | −0.940636 | − | 0.339417i | \(-0.889770\pi\) |
−0.176374 | + | 0.984323i | \(0.556437\pi\) | |||||||
\(80\) | −5.50000 | + | 0.330127i | −0.614919 | + | 0.0369093i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0.401924 | + | 1.50000i | 0.0443851 | + | 0.165647i | ||||
\(83\) | −9.96410 | + | 2.66987i | −1.09370 | + | 0.293057i | −0.760198 | − | 0.649692i | \(-0.774898\pi\) |
−0.333505 | + | 0.942748i | \(0.608231\pi\) | |||||||
\(84\) | 1.50000 | + | 7.79423i | 0.163663 | + | 0.850420i | ||||
\(85\) | 3.07180 | − | 3.46410i | 0.333183 | − | 0.375735i | ||||
\(86\) | −0.464102 | −0.0500454 | ||||||||
\(87\) | −17.1962 | −1.84362 | ||||||||
\(88\) | −2.73205 | + | 2.73205i | −0.291238 | + | 0.291238i | ||||
\(89\) | −0.535898 | + | 0.928203i | −0.0568051 | + | 0.0983893i | −0.893030 | − | 0.449998i | \(-0.851425\pi\) |
0.836224 | + | 0.548387i | \(0.184758\pi\) | |||||||
\(90\) | 3.29423 | − | 1.09808i | 0.347242 | − | 0.115747i | ||||
\(91\) | −1.00000 | − | 0.0717968i | −0.104828 | − | 0.00752635i | ||||
\(92\) | 10.5622 | − | 2.83013i | 1.10118 | − | 0.295061i | ||||
\(93\) | −9.46410 | −0.981382 | ||||||||
\(94\) | 1.33013 | − | 2.30385i | 0.137192 | − | 0.237624i | ||||
\(95\) | 0.901924 | + | 1.36603i | 0.0925354 | + | 0.140151i | ||||
\(96\) | 6.29423 | − | 6.29423i | 0.642402 | − | 0.642402i | ||||
\(97\) | 2.43782 | + | 9.09808i | 0.247523 | + | 0.923770i | 0.972098 | + | 0.234574i | \(0.0753694\pi\) |
−0.724575 | + | 0.689196i | \(0.757964\pi\) | |||||||
\(98\) | 0.428203 | + | 3.59808i | 0.0432551 | + | 0.363461i | ||||
\(99\) | −3.00000 | + | 5.19615i | −0.301511 | + | 0.522233i | ||||
\(100\) | −1.03590 | − | 8.59808i | −0.103590 | − | 0.859808i | ||||
\(101\) | 0.267949i | 0.0266619i | 0.999911 | + | 0.0133310i | \(0.00424351\pi\) | ||||
−0.999911 | + | 0.0133310i | \(0.995756\pi\) | |||||||
\(102\) | 1.85641i | 0.183812i | ||||||||
\(103\) | −4.63397 | − | 4.63397i | −0.456599 | − | 0.456599i | 0.440938 | − | 0.897537i | \(-0.354646\pi\) |
−0.897537 | + | 0.440938i | \(0.854646\pi\) | |||||||
\(104\) | 0.366025 | + | 0.633975i | 0.0358917 | + | 0.0621663i | ||||
\(105\) | −9.92820 | + | 2.53590i | −0.968893 | + | 0.247478i | ||||
\(106\) | −0.267949 | + | 0.464102i | −0.0260255 | + | 0.0450775i | ||||
\(107\) | 9.06218 | − | 2.42820i | 0.876074 | − | 0.234743i | 0.207361 | − | 0.978264i | \(-0.433512\pi\) |
0.668712 | + | 0.743521i | \(0.266846\pi\) | |||||||
\(108\) | 4.50000 | − | 7.79423i | 0.433013 | − | 0.750000i | ||||
\(109\) | 8.42820 | − | 4.86603i | 0.807275 | − | 0.466081i | −0.0387334 | − | 0.999250i | \(-0.512332\pi\) |
0.846009 | + | 0.533169i | \(0.178999\pi\) | |||||||
\(110\) | −1.73205 | − | 1.53590i | −0.165145 | − | 0.146442i | ||||
\(111\) | 11.1962 | − | 11.1962i | 1.06269 | − | 1.06269i | ||||
\(112\) | −4.92820 | + | 4.26795i | −0.465671 | + | 0.403283i | ||||
\(113\) | 9.46410 | + | 2.53590i | 0.890308 | + | 0.238557i | 0.674849 | − | 0.737956i | \(-0.264209\pi\) |
0.215459 | + | 0.976513i | \(0.430875\pi\) | |||||||
\(114\) | −0.633975 | − | 0.169873i | −0.0593772 | − | 0.0159101i | ||||
\(115\) | 4.46410 | + | 13.3923i | 0.416280 | + | 1.24884i | ||||
\(116\) | −8.59808 | − | 14.8923i | −0.798311 | − | 1.38272i | ||||
\(117\) | 0.803848 | + | 0.803848i | 0.0743157 | + | 0.0743157i | ||||
\(118\) | 3.33975 | + | 3.33975i | 0.307449 | + | 0.307449i | ||||
\(119\) | 0.392305 | − | 5.46410i | 0.0359625 | − | 0.500893i | ||||
\(120\) | 5.59808 | + | 4.96410i | 0.511032 | + | 0.453158i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −1.46410 | − | 5.46410i | −0.132554 | − | 0.494697i | ||||
\(123\) | −2.59808 | + | 4.50000i | −0.234261 | + | 0.405751i | ||||
\(124\) | −4.73205 | − | 8.19615i | −0.424951 | − | 0.736036i | ||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | 2.30385 | − | 3.40192i | 0.205243 | − | 0.303067i | ||||
\(127\) | 11.3660 | + | 11.3660i | 1.00857 | + | 1.00857i | 0.999963 | + | 0.00860872i | \(0.00274027\pi\) |
0.00860872 | + | 0.999963i | \(0.497260\pi\) | |||||||
\(128\) | 11.0622 | + | 2.96410i | 0.977768 | + | 0.261992i | ||||
\(129\) | −1.09808 | − | 1.09808i | −0.0966802 | − | 0.0966802i | ||||
\(130\) | −0.366025 | + | 0.241670i | −0.0321026 | + | 0.0211958i | ||||
\(131\) | 18.9282i | 1.65376i | 0.562375 | + | 0.826882i | \(0.309888\pi\) | ||||
−0.562375 | + | 0.826882i | \(0.690112\pi\) | |||||||
\(132\) | −6.00000 | −0.522233 | ||||||||
\(133\) | 1.83013 | + | 0.633975i | 0.158692 | + | 0.0549726i | ||||
\(134\) | 1.80385i | 0.155829i | ||||||||
\(135\) | 10.3923 | + | 5.19615i | 0.894427 | + | 0.447214i | ||||
\(136\) | −3.46410 | + | 2.00000i | −0.297044 | + | 0.171499i | ||||
\(137\) | 1.00000 | + | 1.00000i | 0.0854358 | + | 0.0854358i | 0.748533 | − | 0.663097i | \(-0.230758\pi\) |
−0.663097 | + | 0.748533i | \(0.730758\pi\) | |||||||
\(138\) | −4.90192 | − | 2.83013i | −0.417279 | − | 0.240916i | ||||
\(139\) | −9.29423 | − | 16.0981i | −0.788326 | − | 1.36542i | −0.926992 | − | 0.375082i | \(-0.877615\pi\) |
0.138666 | − | 0.990339i | \(-0.455719\pi\) | |||||||
\(140\) | −7.16025 | − | 7.33013i | −0.605152 | − | 0.619509i | ||||
\(141\) | 8.59808 | − | 2.30385i | 0.724089 | − | 0.194019i | ||||
\(142\) | 0.169873 | − | 0.633975i | 0.0142554 | − | 0.0532020i | ||||
\(143\) | 0.196152 | − | 0.732051i | 0.0164031 | − | 0.0612172i | ||||
\(144\) | 7.39230 | 0.616025 | ||||||||
\(145\) | 18.5263 | − | 12.2321i | 1.53852 | − | 1.01582i | ||||
\(146\) | 6.00000 | + | 3.46410i | 0.496564 | + | 0.286691i | ||||
\(147\) | −7.50000 | + | 9.52628i | −0.618590 | + | 0.785714i | ||||
\(148\) | 15.2942 | + | 4.09808i | 1.25718 | + | 0.336860i | ||||
\(149\) | − | 8.53590i | − | 0.699288i | −0.936883 | − | 0.349644i | \(-0.886303\pi\) | ||
0.936883 | − | 0.349644i | \(-0.113697\pi\) | |||||||
\(150\) | −2.76795 | + | 3.52628i | −0.226002 | + | 0.287920i | ||||
\(151\) | −0.339746 | −0.0276481 | −0.0138241 | − | 0.999904i | \(-0.504400\pi\) | ||||
−0.0138241 | + | 0.999904i | \(0.504400\pi\) | |||||||
\(152\) | −0.366025 | − | 1.36603i | −0.0296886 | − | 0.110799i | ||||
\(153\) | −4.39230 | + | 4.39230i | −0.355097 | + | 0.355097i | ||||
\(154\) | −2.73205 | − | 0.196152i | −0.220155 | − | 0.0158064i | ||||
\(155\) | 10.1962 | − | 6.73205i | 0.818975 | − | 0.540731i | ||||
\(156\) | −0.294229 | + | 1.09808i | −0.0235571 | + | 0.0879165i | ||||
\(157\) | −1.16987 | − | 4.36603i | −0.0933660 | − | 0.348447i | 0.903401 | − | 0.428798i | \(-0.141063\pi\) |
−0.996767 | + | 0.0803508i | \(0.974396\pi\) | |||||||
\(158\) | 1.53590 | + | 5.73205i | 0.122190 | + | 0.456017i | ||||
\(159\) | −1.73205 | + | 0.464102i | −0.137361 | + | 0.0368057i | ||||
\(160\) | −2.30385 | + | 11.2583i | −0.182135 | + | 0.890049i | ||||
\(161\) | 13.8301 | + | 9.36603i | 1.08997 | + | 0.738146i | ||||
\(162\) | −4.50000 | + | 1.20577i | −0.353553 | + | 0.0947343i | ||||
\(163\) | −6.29423 | − | 23.4904i | −0.493002 | − | 1.83991i | −0.540944 | − | 0.841059i | \(-0.681933\pi\) |
0.0479421 | − | 0.998850i | \(-0.484734\pi\) | |||||||
\(164\) | −5.19615 | −0.405751 | ||||||||
\(165\) | −0.464102 | − | 7.73205i | −0.0361303 | − | 0.601939i | ||||
\(166\) | 5.33975i | 0.414445i | ||||||||
\(167\) | −6.09808 | − | 1.63397i | −0.471883 | − | 0.126441i | 0.0150374 | − | 0.999887i | \(-0.495213\pi\) |
−0.486921 | + | 0.873446i | \(0.661880\pi\) | |||||||
\(168\) | 8.83013 | + | 0.633975i | 0.681259 | + | 0.0489122i | ||||
\(169\) | 11.1340 | + | 6.42820i | 0.856460 | + | 0.494477i | ||||
\(170\) | −1.32051 | − | 2.00000i | −0.101278 | − | 0.153393i | ||||
\(171\) | −1.09808 | − | 1.90192i | −0.0839720 | − | 0.145444i | ||||
\(172\) | 0.401924 | − | 1.50000i | 0.0306464 | − | 0.114374i | ||||
\(173\) | −5.85641 | + | 21.8564i | −0.445254 | + | 1.66171i | 0.270010 | + | 0.962858i | \(0.412973\pi\) |
−0.715264 | + | 0.698854i | \(0.753694\pi\) | |||||||
\(174\) | −2.30385 | + | 8.59808i | −0.174654 | + | 0.651818i | ||||
\(175\) | 8.89230 | − | 9.79423i | 0.672195 | − | 0.740374i | ||||
\(176\) | −2.46410 | − | 4.26795i | −0.185739 | − | 0.321709i | ||||
\(177\) | 15.8038i | 1.18789i | ||||||||
\(178\) | 0.392305 | + | 0.392305i | 0.0294045 | + | 0.0294045i | ||||
\(179\) | −4.09808 | + | 2.36603i | −0.306305 | + | 0.176845i | −0.645272 | − | 0.763953i | \(-0.723256\pi\) |
0.338967 | + | 0.940798i | \(0.389922\pi\) | |||||||
\(180\) | 0.696152 | + | 11.5981i | 0.0518881 | + | 0.864470i | ||||
\(181\) | 4.12436i | 0.306561i | 0.988183 | + | 0.153280i | \(0.0489838\pi\) | ||||
−0.988183 | + | 0.153280i | \(0.951016\pi\) | |||||||
\(182\) | −0.169873 | + | 0.490381i | −0.0125918 | + | 0.0363495i | ||||
\(183\) | 9.46410 | − | 16.3923i | 0.699607 | − | 1.21175i | ||||
\(184\) | − | 12.1962i | − | 0.899112i | ||||||
\(185\) | −4.09808 | + | 20.0263i | −0.301297 | + | 1.47236i | ||||
\(186\) | −1.26795 | + | 4.73205i | −0.0929705 | + | 0.346971i | ||||
\(187\) | 4.00000 | + | 1.07180i | 0.292509 | + | 0.0783775i | ||||
\(188\) | 6.29423 | + | 6.29423i | 0.459054 | + | 0.459054i | ||||
\(189\) | 13.5000 | − | 2.59808i | 0.981981 | − | 0.188982i | ||||
\(190\) | 0.803848 | − | 0.267949i | 0.0583172 | − | 0.0194391i | ||||
\(191\) | 10.0981 | + | 17.4904i | 0.730671 | + | 1.26556i | 0.956597 | + | 0.291415i | \(0.0941260\pi\) |
−0.225926 | + | 0.974145i | \(0.572541\pi\) | |||||||
\(192\) | 1.96410 | + | 3.40192i | 0.141747 | + | 0.245513i | ||||
\(193\) | −3.73205 | − | 13.9282i | −0.268639 | − | 1.00257i | −0.959985 | − | 0.280051i | \(-0.909649\pi\) |
0.691346 | − | 0.722523i | \(-0.257018\pi\) | |||||||
\(194\) | 4.87564 | 0.350051 | ||||||||
\(195\) | −1.43782 | − | 0.294229i | −0.102965 | − | 0.0210702i | ||||
\(196\) | −12.0000 | − | 1.73205i | −0.857143 | − | 0.123718i | ||||
\(197\) | 4.00000 | + | 4.00000i | 0.284988 | + | 0.284988i | 0.835095 | − | 0.550106i | \(-0.185413\pi\) |
−0.550106 | + | 0.835095i | \(0.685413\pi\) | |||||||
\(198\) | 2.19615 | + | 2.19615i | 0.156074 | + | 0.156074i | ||||
\(199\) | −8.19615 | − | 14.1962i | −0.581010 | − | 1.00634i | −0.995360 | − | 0.0962210i | \(-0.969324\pi\) |
0.414350 | − | 0.910118i | \(-0.364009\pi\) | |||||||
\(200\) | −9.56218 | − | 1.36603i | −0.676148 | − | 0.0965926i | ||||
\(201\) | −4.26795 | + | 4.26795i | −0.301038 | + | 0.301038i | ||||
\(202\) | 0.133975 | + | 0.0358984i | 0.00942642 | + | 0.00252580i | ||||
\(203\) | 8.59808 | − | 24.8205i | 0.603467 | − | 1.74206i | ||||
\(204\) | −6.00000 | − | 1.60770i | −0.420084 | − | 0.112561i | ||||
\(205\) | −0.401924 | − | 6.69615i | −0.0280716 | − | 0.467680i | ||||
\(206\) | −2.93782 | + | 1.69615i | −0.204688 | + | 0.118177i | ||||
\(207\) | −4.90192 | − | 18.2942i | −0.340707 | − | 1.27154i | ||||
\(208\) | −0.901924 | + | 0.241670i | −0.0625372 | + | 0.0167568i | ||||
\(209\) | −0.732051 | + | 1.26795i | −0.0506370 | + | 0.0877059i | ||||
\(210\) | −0.0621778 | + | 5.30385i | −0.00429068 | + | 0.366000i | ||||
\(211\) | −13.4641 | − | 23.3205i | −0.926907 | − | 1.60545i | −0.788465 | − | 0.615079i | \(-0.789124\pi\) |
−0.138442 | − | 0.990371i | \(-0.544209\pi\) | |||||||
\(212\) | −1.26795 | − | 1.26795i | −0.0870831 | − | 0.0870831i | ||||
\(213\) | 1.90192 | − | 1.09808i | 0.130318 | − | 0.0752389i | ||||
\(214\) | − | 4.85641i | − | 0.331977i | ||||||
\(215\) | 1.96410 | + | 0.401924i | 0.133951 | + | 0.0274110i | ||||
\(216\) | −7.09808 | − | 7.09808i | −0.482963 | − | 0.482963i | ||||
\(217\) | 4.73205 | − | 13.6603i | 0.321233 | − | 0.927318i | ||||
\(218\) | −1.30385 | − | 4.86603i | −0.0883077 | − | 0.329569i | ||||
\(219\) | 6.00000 | + | 22.3923i | 0.405442 | + | 1.51313i | ||||
\(220\) | 6.46410 | − | 4.26795i | 0.435810 | − | 0.287745i | ||||
\(221\) | 0.392305 | − | 0.679492i | 0.0263893 | − | 0.0457076i | ||||
\(222\) | −4.09808 | − | 7.09808i | −0.275045 | − | 0.476392i | ||||
\(223\) | −4.96410 | + | 1.33013i | −0.332421 | + | 0.0890719i | −0.421169 | − | 0.906982i | \(-0.638380\pi\) |
0.0887481 | + | 0.996054i | \(0.471713\pi\) | |||||||
\(224\) | 5.93782 | + | 12.2321i | 0.396737 | + | 0.817288i | ||||
\(225\) | −14.8923 | + | 1.79423i | −0.992820 | + | 0.119615i | ||||
\(226\) | 2.53590 | − | 4.39230i | 0.168685 | − | 0.292172i | ||||
\(227\) | 17.5885 | − | 17.5885i | 1.16739 | − | 1.16739i | 0.184567 | − | 0.982820i | \(-0.440912\pi\) |
0.982820 | − | 0.184567i | \(-0.0590883\pi\) | |||||||
\(228\) | 1.09808 | − | 1.90192i | 0.0727219 | − | 0.125958i | ||||
\(229\) | 22.6603 | 1.49743 | 0.748716 | − | 0.662891i | \(-0.230671\pi\) | ||||
0.748716 | + | 0.662891i | \(0.230671\pi\) | |||||||
\(230\) | 7.29423 | − | 0.437822i | 0.480967 | − | 0.0288691i | ||||
\(231\) | −6.00000 | − | 6.92820i | −0.394771 | − | 0.455842i | ||||
\(232\) | −18.5263 | + | 4.96410i | −1.21631 | + | 0.325909i | ||||
\(233\) | 5.53590 | + | 20.6603i | 0.362669 | + | 1.35350i | 0.870554 | + | 0.492073i | \(0.163761\pi\) |
−0.507885 | + | 0.861425i | \(0.669573\pi\) | |||||||
\(234\) | 0.509619 | − | 0.294229i | 0.0333148 | − | 0.0192343i | ||||
\(235\) | −7.62436 | + | 8.59808i | −0.497358 | + | 0.560877i | ||||
\(236\) | −13.6865 | + | 7.90192i | −0.890917 | + | 0.514371i | ||||
\(237\) | −9.92820 | + | 17.1962i | −0.644906 | + | 1.11701i | ||||
\(238\) | −2.67949 | − | 0.928203i | −0.173686 | − | 0.0601665i | ||||
\(239\) | 1.73205 | − | 1.00000i | 0.112037 | − | 0.0646846i | −0.442934 | − | 0.896554i | \(-0.646063\pi\) |
0.554971 | + | 0.831869i | \(0.312729\pi\) | |||||||
\(240\) | −7.96410 | + | 5.25833i | −0.514081 | + | 0.339424i | ||||
\(241\) | 15.5359i | 1.00076i | 0.865807 | + | 0.500378i | \(0.166805\pi\) | ||||
−0.865807 | + | 0.500378i | \(0.833195\pi\) | |||||||
\(242\) | −0.937822 | + | 3.50000i | −0.0602855 | + | 0.224989i | ||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | 18.9282 | 1.21175 | ||||||||
\(245\) | 1.30385 | − | 15.5981i | 0.0832998 | − | 0.996525i | ||||
\(246\) | 1.90192 | + | 1.90192i | 0.121262 | + | 0.121262i | ||||
\(247\) | 0.196152 | + | 0.196152i | 0.0124809 | + | 0.0124809i | ||||
\(248\) | −10.1962 | + | 2.73205i | −0.647456 | + | 0.173485i | ||||
\(249\) | −12.6340 | + | 12.6340i | −0.800646 | + | 0.800646i | ||||
\(250\) | 0.473721 | − | 5.76795i | 0.0299607 | − | 0.364797i | ||||
\(251\) | − | 13.6603i | − | 0.862228i | −0.902298 | − | 0.431114i | \(-0.858121\pi\) | ||
0.902298 | − | 0.431114i | \(-0.141879\pi\) | |||||||
\(252\) | 9.00000 | + | 10.3923i | 0.566947 | + | 0.654654i | ||||
\(253\) | −8.92820 | + | 8.92820i | −0.561311 | + | 0.561311i | ||||
\(254\) | 7.20577 | − | 4.16025i | 0.452130 | − | 0.261038i | ||||
\(255\) | 1.60770 | − | 7.85641i | 0.100678 | − | 0.491987i | ||||
\(256\) | 0.696152 | − | 1.20577i | 0.0435095 | − | 0.0753607i | ||||
\(257\) | 10.1962 | − | 10.1962i | 0.636019 | − | 0.636019i | −0.313552 | − | 0.949571i | \(-0.601519\pi\) |
0.949571 | + | 0.313552i | \(0.101519\pi\) | |||||||
\(258\) | −0.696152 | + | 0.401924i | −0.0433406 | + | 0.0250227i | ||||
\(259\) | 10.5622 | + | 21.7583i | 0.656302 | + | 1.35200i | ||||
\(260\) | −0.464102 | − | 1.39230i | −0.0287824 | − | 0.0863471i | ||||
\(261\) | −25.7942 | + | 14.8923i | −1.59662 | + | 0.921811i | ||||
\(262\) | 9.46410 | + | 2.53590i | 0.584694 | + | 0.156668i | ||||
\(263\) | 9.09808 | − | 9.09808i | 0.561011 | − | 0.561011i | −0.368583 | − | 0.929595i | \(-0.620157\pi\) |
0.929595 | + | 0.368583i | \(0.120157\pi\) | |||||||
\(264\) | −1.73205 | + | 6.46410i | −0.106600 | + | 0.397838i | ||||
\(265\) | 1.53590 | − | 1.73205i | 0.0943495 | − | 0.106399i | ||||
\(266\) | 0.562178 | − | 0.830127i | 0.0344693 | − | 0.0508984i | ||||
\(267\) | 1.85641i | 0.113610i | ||||||||
\(268\) | −5.83013 | − | 1.56218i | −0.356132 | − | 0.0954252i | ||||
\(269\) | 3.80385 | + | 6.58846i | 0.231925 | + | 0.401705i | 0.958374 | − | 0.285514i | \(-0.0921644\pi\) |
−0.726450 | + | 0.687220i | \(0.758831\pi\) | |||||||
\(270\) | 3.99038 | − | 4.50000i | 0.242847 | − | 0.273861i | ||||
\(271\) | 1.22243 | + | 0.705771i | 0.0742574 | + | 0.0428726i | 0.536669 | − | 0.843793i | \(-0.319682\pi\) |
−0.462412 | + | 0.886665i | \(0.653016\pi\) | |||||||
\(272\) | −1.32051 | − | 4.92820i | −0.0800676 | − | 0.298816i | ||||
\(273\) | −1.56218 | + | 0.758330i | −0.0945473 | + | 0.0458962i | ||||
\(274\) | 0.633975 | − | 0.366025i | 0.0382998 | − | 0.0221124i | ||||
\(275\) | 6.00000 | + | 8.00000i | 0.361814 | + | 0.482418i | ||||
\(276\) | 13.3923 | − | 13.3923i | 0.806122 | − | 0.806122i | ||||
\(277\) | 2.19615 | + | 2.19615i | 0.131954 | + | 0.131954i | 0.769999 | − | 0.638045i | \(-0.220257\pi\) |
−0.638045 | + | 0.769999i | \(0.720257\pi\) | |||||||
\(278\) | −9.29423 | + | 2.49038i | −0.557431 | + | 0.149363i | ||||
\(279\) | −14.1962 | + | 8.19615i | −0.849901 | + | 0.490691i | ||||
\(280\) | −9.96410 | + | 5.59808i | −0.595469 | + | 0.334549i | ||||
\(281\) | −12.8660 | + | 22.2846i | −0.767523 | + | 1.32939i | 0.171380 | + | 0.985205i | \(0.445178\pi\) |
−0.938902 | + | 0.344183i | \(0.888156\pi\) | |||||||
\(282\) | − | 4.60770i | − | 0.274384i | ||||||
\(283\) | −15.5263 | + | 4.16025i | −0.922942 | + | 0.247301i | −0.688842 | − | 0.724911i | \(-0.741881\pi\) |
−0.234099 | + | 0.972213i | \(0.575214\pi\) | |||||||
\(284\) | 1.90192 | + | 1.09808i | 0.112858 | + | 0.0651588i | ||||
\(285\) | 2.53590 | + | 1.26795i | 0.150214 | + | 0.0751068i | ||||
\(286\) | −0.339746 | − | 0.196152i | −0.0200896 | − | 0.0115987i | ||||
\(287\) | −5.19615 | − | 6.00000i | −0.306719 | − | 0.354169i | ||||
\(288\) | 3.99038 | − | 14.8923i | 0.235135 | − | 0.877537i | ||||
\(289\) | −11.0096 | − | 6.35641i | −0.647625 | − | 0.373906i | ||||
\(290\) | −3.63397 | − | 10.9019i | −0.213394 | − | 0.640183i | ||||
\(291\) | 11.5359 | + | 11.5359i | 0.676246 | + | 0.676246i | ||||
\(292\) | −16.3923 | + | 16.3923i | −0.959287 | + | 0.959287i | ||||
\(293\) | −3.26795 | + | 12.1962i | −0.190916 | + | 0.712507i | 0.802371 | + | 0.596826i | \(0.203572\pi\) |
−0.993286 | + | 0.115681i | \(0.963095\pi\) | |||||||
\(294\) | 3.75833 | + | 5.02628i | 0.219190 | + | 0.293139i | ||||
\(295\) | −11.2417 | − | 17.0263i | −0.654515 | − | 0.991308i | ||||
\(296\) | 8.83013 | − | 15.2942i | 0.513241 | − | 0.888959i | ||||
\(297\) | 10.3923i | 0.603023i | ||||||||
\(298\) | −4.26795 | − | 1.14359i | −0.247236 | − | 0.0662466i | ||||
\(299\) | 1.19615 | + | 2.07180i | 0.0691753 | + | 0.119815i | ||||
\(300\) | −9.00000 | − | 12.0000i | −0.519615 | − | 0.692820i | ||||
\(301\) | 2.13397 | − | 1.03590i | 0.123000 | − | 0.0597082i | ||||
\(302\) | −0.0455173 | + | 0.169873i | −0.00261923 | + | 0.00977509i | ||||
\(303\) | 0.232051 | + | 0.401924i | 0.0133310 | + | 0.0230899i | ||||
\(304\) | 1.80385 | 0.103458 | ||||||||
\(305\) | 1.46410 | + | 24.3923i | 0.0838342 | + | 1.39670i | ||||
\(306\) | 1.60770 | + | 2.78461i | 0.0919058 | + | 0.159186i | ||||
\(307\) | −3.63397 | + | 3.63397i | −0.207402 | + | 0.207402i | −0.803162 | − | 0.595760i | \(-0.796851\pi\) |
0.595760 | + | 0.803162i | \(0.296851\pi\) | |||||||
\(308\) | 3.00000 | − | 8.66025i | 0.170941 | − | 0.493464i | ||||
\(309\) | −10.9641 | − | 2.93782i | −0.623726 | − | 0.167127i | ||||
\(310\) | −2.00000 | − | 6.00000i | −0.113592 | − | 0.340777i | ||||
\(311\) | −14.8301 | − | 8.56218i | −0.840939 | − | 0.485517i | 0.0166441 | − | 0.999861i | \(-0.494702\pi\) |
−0.857583 | + | 0.514345i | \(0.828035\pi\) | |||||||
\(312\) | 1.09808 | + | 0.633975i | 0.0621663 | + | 0.0358917i | ||||
\(313\) | 8.19615 | − | 30.5885i | 0.463274 | − | 1.72896i | −0.199275 | − | 0.979944i | \(-0.563859\pi\) |
0.662549 | − | 0.749018i | \(-0.269475\pi\) | |||||||
\(314\) | −2.33975 | −0.132040 | ||||||||
\(315\) | −12.6962 | + | 12.4019i | −0.715347 | + | 0.698769i | ||||
\(316\) | −19.8564 | −1.11701 | ||||||||
\(317\) | 0.562178 | − | 2.09808i | 0.0315751 | − | 0.117840i | −0.948340 | − | 0.317257i | \(-0.897238\pi\) |
0.979915 | + | 0.199417i | \(0.0639049\pi\) | |||||||
\(318\) | 0.928203i | 0.0520511i | ||||||||
\(319\) | 17.1962 | + | 9.92820i | 0.962800 | + | 0.555873i | ||||
\(320\) | −4.53590 | − | 2.26795i | −0.253564 | − | 0.126782i | ||||
\(321\) | 11.4904 | − | 11.4904i | 0.641331 | − | 0.641331i | ||||
\(322\) | 6.53590 | − | 5.66025i | 0.364231 | − | 0.315434i | ||||
\(323\) | −1.07180 | + | 1.07180i | −0.0596364 | + | 0.0596364i | ||||
\(324\) | − | 15.5885i | − | 0.866025i | ||||||
\(325\) | 1.75833 | − | 0.705771i | 0.0975346 | − | 0.0391492i | ||||
\(326\) | −12.5885 | −0.697210 | ||||||||
\(327\) | 8.42820 | − | 14.5981i | 0.466081 | − | 0.807275i | ||||
\(328\) | −1.50000 | + | 5.59808i | −0.0828236 | + | 0.309102i | ||||
\(329\) | −0.973721 | + | 13.5622i | −0.0536830 | + | 0.747707i | ||||
\(330\) | −3.92820 | − | 0.803848i | −0.216240 | − | 0.0442504i | ||||
\(331\) | 3.00000 | + | 5.19615i | 0.164895 | + | 0.285606i | 0.936618 | − | 0.350352i | \(-0.113938\pi\) |
−0.771723 | + | 0.635959i | \(0.780605\pi\) | |||||||
\(332\) | −17.2583 | − | 4.62436i | −0.947174 | − | 0.253794i | ||||
\(333\) | 7.09808 | − | 26.4904i | 0.388972 | − | 1.45166i | ||||
\(334\) | −1.63397 | + | 2.83013i | −0.0894071 | + | 0.154858i | ||||
\(335\) | 1.56218 | − | 7.63397i | 0.0853509 | − | 0.417089i | ||||
\(336\) | −3.69615 | + | 10.6699i | −0.201642 | + | 0.582089i | ||||
\(337\) | −5.63397 | + | 21.0263i | −0.306902 | + | 1.14537i | 0.624393 | + | 0.781110i | \(0.285346\pi\) |
−0.931296 | + | 0.364264i | \(0.881320\pi\) | |||||||
\(338\) | 4.70577 | − | 4.70577i | 0.255960 | − | 0.255960i | ||||
\(339\) | 16.3923 | − | 4.39230i | 0.890308 | − | 0.238557i | ||||
\(340\) | 7.60770 | − | 2.53590i | 0.412585 | − | 0.137528i | ||||
\(341\) | 9.46410 | + | 5.46410i | 0.512510 | + | 0.295898i | ||||
\(342\) | −1.09808 | + | 0.294229i | −0.0593772 | + | 0.0159101i | ||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | −1.50000 | − | 0.866025i | −0.0808746 | − | 0.0466930i | ||||
\(345\) | 18.2942 | + | 16.2224i | 0.984928 | + | 0.873386i | ||||
\(346\) | 10.1436 | + | 5.85641i | 0.545323 | + | 0.314842i | ||||
\(347\) | −11.4282 | + | 3.06218i | −0.613498 | + | 0.164386i | −0.552170 | − | 0.833731i | \(-0.686200\pi\) |
−0.0613278 | + | 0.998118i | \(0.519534\pi\) | |||||||
\(348\) | −25.7942 | − | 14.8923i | −1.38272 | − | 0.798311i | ||||
\(349\) | 5.00000 | − | 8.66025i | 0.267644 | − | 0.463573i | −0.700609 | − | 0.713545i | \(-0.747088\pi\) |
0.968253 | + | 0.249973i | \(0.0804216\pi\) | |||||||
\(350\) | −3.70577 | − | 5.75833i | −0.198082 | − | 0.307796i | ||||
\(351\) | 1.90192 | + | 0.509619i | 0.101517 | + | 0.0272014i | ||||
\(352\) | −9.92820 | + | 2.66025i | −0.529175 | + | 0.141792i | ||||
\(353\) | −5.53590 | − | 5.53590i | −0.294646 | − | 0.294646i | 0.544266 | − | 0.838912i | \(-0.316808\pi\) |
−0.838912 | + | 0.544266i | \(0.816808\pi\) | |||||||
\(354\) | 7.90192 | + | 2.11731i | 0.419983 | + | 0.112534i | ||||
\(355\) | −1.26795 | + | 2.53590i | −0.0672958 | + | 0.134592i | ||||
\(356\) | −1.60770 | + | 0.928203i | −0.0852077 | + | 0.0491947i | ||||
\(357\) | −4.14359 | − | 8.53590i | −0.219302 | − | 0.451768i | ||||
\(358\) | 0.633975 | + | 2.36603i | 0.0335066 | + | 0.125048i | ||||
\(359\) | 2.53590 | + | 1.46410i | 0.133840 | + | 0.0772723i | 0.565425 | − | 0.824800i | \(-0.308712\pi\) |
−0.431585 | + | 0.902072i | \(0.642046\pi\) | |||||||
\(360\) | 12.6962 | + | 2.59808i | 0.669146 | + | 0.136931i | ||||
\(361\) | 9.23205 | + | 15.9904i | 0.485897 | + | 0.841599i | ||||
\(362\) | 2.06218 | + | 0.552559i | 0.108386 | + | 0.0290419i | ||||
\(363\) | −10.5000 | + | 6.06218i | −0.551107 | + | 0.318182i | ||||
\(364\) | −1.43782 | − | 0.973721i | −0.0753624 | − | 0.0510368i | ||||
\(365\) | −22.3923 | − | 19.8564i | −1.17207 | − | 1.03933i | ||||
\(366\) | −6.92820 | − | 6.92820i | −0.362143 | − | 0.362143i | ||||
\(367\) | 9.09808 | − | 9.09808i | 0.474916 | − | 0.474916i | −0.428586 | − | 0.903501i | \(-0.640988\pi\) |
0.903501 | + | 0.428586i | \(0.140988\pi\) | |||||||
\(368\) | 15.0263 | + | 4.02628i | 0.783299 | + | 0.209884i | ||||
\(369\) | 9.00000i | 0.468521i | ||||||||
\(370\) | 9.46410 | + | 4.73205i | 0.492015 | + | 0.246008i | ||||
\(371\) | 0.196152 | − | 2.73205i | 0.0101837 | − | 0.141841i | ||||
\(372\) | −14.1962 | − | 8.19615i | −0.736036 | − | 0.424951i | ||||
\(373\) | −12.4641 | + | 12.4641i | −0.645367 | + | 0.645367i | −0.951870 | − | 0.306503i | \(-0.900841\pi\) |
0.306503 | + | 0.951870i | \(0.400841\pi\) | |||||||
\(374\) | 1.07180 | − | 1.85641i | 0.0554213 | − | 0.0959925i | ||||
\(375\) | 14.7679 | − | 12.5263i | 0.762614 | − | 0.646854i | ||||
\(376\) | 8.59808 | − | 4.96410i | 0.443412 | − | 0.256004i | ||||
\(377\) | 2.66025 | − | 2.66025i | 0.137010 | − | 0.137010i | ||||
\(378\) | 0.509619 | − | 7.09808i | 0.0262120 | − | 0.365086i | ||||
\(379\) | 27.5167i | 1.41344i | 0.707495 | + | 0.706718i | \(0.249825\pi\) | ||||
−0.707495 | + | 0.706718i | \(0.750175\pi\) | |||||||
\(380\) | 0.169873 | + | 2.83013i | 0.00871430 | + | 0.145182i | ||||
\(381\) | 26.8923 | + | 7.20577i | 1.37773 | + | 0.369163i | ||||
\(382\) | 10.0981 | − | 2.70577i | 0.516663 | − | 0.138439i | ||||
\(383\) | 14.7583 | + | 14.7583i | 0.754115 | + | 0.754115i | 0.975245 | − | 0.221129i | \(-0.0709742\pi\) |
−0.221129 | + | 0.975245i | \(0.570974\pi\) | |||||||
\(384\) | 19.1603 | − | 5.13397i | 0.977768 | − | 0.261992i | ||||
\(385\) | 11.3923 | + | 3.19615i | 0.580606 | + | 0.162891i | ||||
\(386\) | −7.46410 | −0.379913 | ||||||||
\(387\) | −2.59808 | − | 0.696152i | −0.132068 | − | 0.0353874i | ||||
\(388\) | −4.22243 | + | 15.7583i | −0.214362 | + | 0.800008i | ||||
\(389\) | 29.0526i | 1.47302i | 0.676425 | + | 0.736512i | \(0.263528\pi\) | ||||
−0.676425 | + | 0.736512i | \(0.736472\pi\) | |||||||
\(390\) | −0.339746 | + | 0.679492i | −0.0172037 | + | 0.0344074i | ||||
\(391\) | −11.3205 | + | 6.53590i | −0.572503 | + | 0.330535i | ||||
\(392\) | −5.33013 | + | 12.4282i | −0.269212 | + | 0.627719i | ||||
\(393\) | 16.3923 | + | 28.3923i | 0.826882 | + | 1.43220i | ||||
\(394\) | 2.53590 | − | 1.46410i | 0.127757 | − | 0.0737604i | ||||
\(395\) | −1.53590 | − | 25.5885i | −0.0772794 | − | 1.28750i | ||||
\(396\) | −9.00000 | + | 5.19615i | −0.452267 | + | 0.261116i | ||||
\(397\) | −5.32051 | − | 19.8564i | −0.267029 | − | 0.996564i | −0.960997 | − | 0.276559i | \(-0.910806\pi\) |
0.693968 | − | 0.720006i | \(-0.255861\pi\) | |||||||
\(398\) | −8.19615 | + | 2.19615i | −0.410836 | + | 0.110083i | ||||
\(399\) | 3.29423 | − | 0.633975i | 0.164918 | − | 0.0317384i | ||||
\(400\) | 4.83975 | − | 11.3301i | 0.241987 | − | 0.566506i | ||||
\(401\) | 11.3923 | 0.568905 | 0.284452 | − | 0.958690i | \(-0.408188\pi\) | ||||
0.284452 | + | 0.958690i | \(0.408188\pi\) | |||||||
\(402\) | 1.56218 | + | 2.70577i | 0.0779143 | + | 0.134952i | ||||
\(403\) | 1.46410 | − | 1.46410i | 0.0729321 | − | 0.0729321i | ||||
\(404\) | −0.232051 | + | 0.401924i | −0.0115450 | + | 0.0199965i | ||||
\(405\) | 20.0885 | − | 1.20577i | 0.998203 | − | 0.0599153i | ||||
\(406\) | −11.2583 | − | 7.62436i | −0.558742 | − | 0.378390i | ||||
\(407\) | −17.6603 | + | 4.73205i | −0.875386 | + | 0.234559i | ||||
\(408\) | −3.46410 | + | 6.00000i | −0.171499 | + | 0.297044i | ||||
\(409\) | −6.16025 | + | 10.6699i | −0.304605 | + | 0.527591i | −0.977173 | − | 0.212444i | \(-0.931858\pi\) |
0.672568 | + | 0.740035i | \(0.265191\pi\) | |||||||
\(410\) | −3.40192 | − | 0.696152i | −0.168009 | − | 0.0343805i | ||||
\(411\) | 2.36603 | + | 0.633975i | 0.116707 | + | 0.0312717i | ||||
\(412\) | −2.93782 | − | 10.9641i | −0.144736 | − | 0.540163i | ||||
\(413\) | −22.8109 | − | 7.90192i | −1.12245 | − | 0.388828i | ||||
\(414\) | −9.80385 | −0.481833 | ||||||||
\(415\) | 4.62436 | − | 22.5981i | 0.227001 | − | 1.10930i | ||||
\(416\) | 1.94744i | 0.0954812i | ||||||||
\(417\) | −27.8827 | − | 16.0981i | −1.36542 | − | 0.788326i | ||||
\(418\) | 0.535898 | + | 0.535898i | 0.0262116 | + | 0.0262116i | ||||
\(419\) | −9.83013 | − | 17.0263i | −0.480233 | − | 0.831788i | 0.519510 | − | 0.854465i | \(-0.326115\pi\) |
−0.999743 | + | 0.0226764i | \(0.992781\pi\) | |||||||
\(420\) | −17.0885 | − | 4.79423i | −0.833831 | − | 0.233934i | ||||
\(421\) | −7.59808 | + | 13.1603i | −0.370308 | + | 0.641392i | −0.989613 | − | 0.143759i | \(-0.954081\pi\) |
0.619305 | + | 0.785150i | \(0.287414\pi\) | |||||||
\(422\) | −13.4641 | + | 3.60770i | −0.655422 | + | 0.175620i | ||||
\(423\) | 10.9019 | − | 10.9019i | 0.530070 | − | 0.530070i | ||||
\(424\) | −1.73205 | + | 1.00000i | −0.0841158 | + | 0.0485643i | ||||
\(425\) | 3.85641 | + | 9.60770i | 0.187063 | + | 0.466042i | ||||
\(426\) | −0.294229 | − | 1.09808i | −0.0142554 | − | 0.0532020i | ||||
\(427\) | 18.9282 | + | 21.8564i | 0.916000 | + | 1.05771i | ||||
\(428\) | 15.6962 | + | 4.20577i | 0.758702 | + | 0.203294i | ||||
\(429\) | −0.339746 | − | 1.26795i | −0.0164031 | − | 0.0612172i | ||||
\(430\) | 0.464102 | − | 0.928203i | 0.0223810 | − | 0.0447619i | ||||
\(431\) | 5.29423 | + | 9.16987i | 0.255014 | + | 0.441697i | 0.964899 | − | 0.262620i | \(-0.0845866\pi\) |
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(432\) | 11.0885 | − | 6.40192i | 0.533494 | − | 0.308013i | ||||
\(433\) | 24.1244 | + | 24.1244i | 1.15934 | + | 1.15934i | 0.984617 | + | 0.174725i | \(0.0559037\pi\) |
0.174725 | + | 0.984617i | \(0.444096\pi\) | |||||||
\(434\) | −6.19615 | − | 4.19615i | −0.297425 | − | 0.201422i | ||||
\(435\) | 17.1962 | − | 34.3923i | 0.824492 | − | 1.64898i | ||||
\(436\) | 16.8564 | 0.807275 | ||||||||
\(437\) | −1.19615 | − | 4.46410i | −0.0572197 | − | 0.213547i | ||||
\(438\) | 12.0000 | 0.573382 | ||||||||
\(439\) | 4.07180 | + | 7.05256i | 0.194336 | + | 0.336600i | 0.946683 | − | 0.322167i | \(-0.104411\pi\) |
−0.752346 | + | 0.658768i | \(0.771078\pi\) | |||||||
\(440\) | −2.73205 | − | 8.19615i | −0.130245 | − | 0.390736i | ||||
\(441\) | −3.00000 | + | 20.7846i | −0.142857 | + | 0.989743i | ||||
\(442\) | −0.287187 | − | 0.287187i | −0.0136601 | − | 0.0136601i | ||||
\(443\) | −14.1603 | − | 3.79423i | −0.672774 | − | 0.180269i | −0.0937699 | − | 0.995594i | \(-0.529892\pi\) |
−0.579004 | + | 0.815325i | \(0.696558\pi\) | |||||||
\(444\) | 26.4904 | − | 7.09808i | 1.25718 | − | 0.336860i | ||||
\(445\) | −1.32051 | − | 2.00000i | −0.0625981 | − | 0.0948091i | ||||
\(446\) | 2.66025i | 0.125967i | ||||||||
\(447\) | −7.39230 | − | 12.8038i | −0.349644 | − | 0.605601i | ||||
\(448\) | −5.89230 | + | 1.13397i | −0.278385 | + | 0.0535753i | ||||
\(449\) | − | 24.6603i | − | 1.16379i | −0.813264 | − | 0.581895i | \(-0.802312\pi\) | ||
0.813264 | − | 0.581895i | \(-0.197688\pi\) | |||||||
\(450\) | −1.09808 | + | 7.68653i | −0.0517638 | + | 0.362347i | ||||
\(451\) | 5.19615 | − | 3.00000i | 0.244677 | − | 0.141264i | ||||
\(452\) | 12.0000 | + | 12.0000i | 0.564433 | + | 0.564433i | ||||
\(453\) | −0.509619 | + | 0.294229i | −0.0239440 | + | 0.0138241i | ||||
\(454\) | −6.43782 | − | 11.1506i | −0.302142 | − | 0.523325i | ||||
\(455\) | 1.14359 | − | 1.92820i | 0.0536125 | − | 0.0903956i | ||||
\(456\) | −1.73205 | − | 1.73205i | −0.0811107 | − | 0.0811107i | ||||
\(457\) | 5.50962 | − | 20.5622i | 0.257729 | − | 0.961858i | −0.708823 | − | 0.705387i | \(-0.750773\pi\) |
0.966552 | − | 0.256471i | \(-0.0825600\pi\) | |||||||
\(458\) | 3.03590 | − | 11.3301i | 0.141858 | − | 0.529422i | ||||
\(459\) | −2.78461 | + | 10.3923i | −0.129974 | + | 0.485071i | ||||
\(460\) | −4.90192 | + | 23.9545i | −0.228553 | + | 1.11688i | ||||
\(461\) | 24.2321 | + | 13.9904i | 1.12860 | + | 0.651597i | 0.943582 | − | 0.331138i | \(-0.107433\pi\) |
0.185017 | + | 0.982735i | \(0.440766\pi\) | |||||||
\(462\) | −4.26795 | + | 2.07180i | −0.198563 | + | 0.0963887i | ||||
\(463\) | 21.1603 | + | 5.66987i | 0.983400 | + | 0.263501i | 0.714476 | − | 0.699660i | \(-0.246665\pi\) |
0.268924 | + | 0.963161i | \(0.413332\pi\) | |||||||
\(464\) | − | 24.4641i | − | 1.13572i | ||||||
\(465\) | 9.46410 | − | 18.9282i | 0.438887 | − | 0.877774i | ||||
\(466\) | 11.0718 | 0.512891 | ||||||||
\(467\) | −2.50000 | − | 9.33013i | −0.115686 | − | 0.431747i | 0.883651 | − | 0.468146i | \(-0.155078\pi\) |
−0.999337 | + | 0.0363992i | \(0.988411\pi\) | |||||||
\(468\) | 0.509619 | + | 1.90192i | 0.0235571 | + | 0.0879165i | ||||
\(469\) | −4.02628 | − | 8.29423i | −0.185916 | − | 0.382992i | ||||
\(470\) | 3.27757 | + | 4.96410i | 0.151183 | + | 0.228977i | ||||
\(471\) | −5.53590 | − | 5.53590i | −0.255081 | − | 0.255081i | ||||
\(472\) | 4.56218 | + | 17.0263i | 0.209991 | + | 0.783698i | ||||
\(473\) | 0.464102 | + | 1.73205i | 0.0213394 | + | 0.0796398i | ||||
\(474\) | 7.26795 | + | 7.26795i | 0.333828 | + | 0.333828i | ||||
\(475\) | −3.63397 | + | 0.437822i | −0.166738 | + | 0.0200887i | ||||
\(476\) | 5.32051 | − | 7.85641i | 0.243865 | − | 0.360098i | ||||
\(477\) | −2.19615 | + | 2.19615i | −0.100555 | + | 0.100555i | ||||
\(478\) | −0.267949 | − | 1.00000i | −0.0122557 | − | 0.0457389i | ||||
\(479\) | −20.7321 | −0.947272 | −0.473636 | − | 0.880721i | \(-0.657059\pi\) | ||||
−0.473636 | + | 0.880721i | \(0.657059\pi\) | |||||||
\(480\) | 6.29423 | + | 18.8827i | 0.287291 | + | 0.861873i | ||||
\(481\) | 3.46410i | 0.157949i | ||||||||
\(482\) | 7.76795 | + | 2.08142i | 0.353820 | + | 0.0948059i | ||||
\(483\) | 28.8564 | + | 2.07180i | 1.31301 | + | 0.0942700i | ||||
\(484\) | −10.5000 | − | 6.06218i | −0.477273 | − | 0.275554i | ||||
\(485\) | −20.6340 | − | 4.22243i | −0.936941 | − | 0.191731i | ||||
\(486\) | −5.70577 | + | 5.70577i | −0.258819 | + | 0.258819i | ||||
\(487\) | −7.24167 | + | 27.0263i | −0.328151 | + | 1.22468i | 0.582954 | + | 0.812505i | \(0.301897\pi\) |
−0.911106 | + | 0.412173i | \(0.864770\pi\) | |||||||
\(488\) | 5.46410 | − | 20.3923i | 0.247348 | − | 0.923116i | ||||
\(489\) | −29.7846 | − | 29.7846i | −1.34691 | − | 1.34691i | ||||
\(490\) | −7.62436 | − | 2.74167i | −0.344433 | − | 0.123856i | ||||
\(491\) | −7.29423 | − | 12.6340i | −0.329184 | − | 0.570163i | 0.653166 | − | 0.757215i | \(-0.273440\pi\) |
−0.982350 | + | 0.187051i | \(0.940107\pi\) | |||||||
\(492\) | −7.79423 | + | 4.50000i | −0.351391 | + | 0.202876i | ||||
\(493\) | 14.5359 | + | 14.5359i | 0.654664 | + | 0.654664i | ||||
\(494\) | 0.124356 | − | 0.0717968i | 0.00559503 | − | 0.00323029i | ||||
\(495\) | −7.39230 | − | 11.1962i | −0.332259 | − | 0.503230i | ||||
\(496\) | − | 13.4641i | − | 0.604556i | ||||||
\(497\) | 0.633975 | + | 3.29423i | 0.0284376 | + | 0.147766i | ||||
\(498\) | 4.62436 | + | 8.00962i | 0.207222 | + | 0.358920i | ||||
\(499\) | 38.3923i | 1.71868i | 0.511408 | + | 0.859338i | \(0.329124\pi\) | ||||
−0.511408 | + | 0.859338i | \(0.670876\pi\) | |||||||
\(500\) | 18.2321 | + | 6.52628i | 0.815362 | + | 0.291864i | ||||
\(501\) | −10.5622 | + | 2.83013i | −0.471883 | + | 0.126441i | ||||
\(502\) | −6.83013 | − | 1.83013i | −0.304843 | − | 0.0816826i | ||||
\(503\) | 2.63397 | + | 2.63397i | 0.117443 | + | 0.117443i | 0.763386 | − | 0.645943i | \(-0.223536\pi\) |
−0.645943 | + | 0.763386i | \(0.723536\pi\) | |||||||
\(504\) | 13.7942 | − | 6.69615i | 0.614444 | − | 0.298270i | ||||
\(505\) | −0.535898 | − | 0.267949i | −0.0238472 | − | 0.0119236i | ||||
\(506\) | 3.26795 | + | 5.66025i | 0.145278 | + | 0.251629i | ||||
\(507\) | 22.2679 | 0.988954 | ||||||||
\(508\) | 7.20577 | + | 26.8923i | 0.319704 | + | 1.19315i | ||||
\(509\) | 32.9090 | 1.45866 | 0.729332 | − | 0.684160i | \(-0.239831\pi\) | ||||
0.729332 | + | 0.684160i | \(0.239831\pi\) | |||||||
\(510\) | −3.71281 | − | 1.85641i | −0.164406 | − | 0.0822031i | ||||
\(511\) | −35.3205 | − | 2.53590i | −1.56249 | − | 0.112182i | ||||
\(512\) | 15.6865 | + | 15.6865i | 0.693253 | + | 0.693253i | ||||
\(513\) | −3.29423 | − | 1.90192i | −0.145444 | − | 0.0839720i | ||||
\(514\) | −3.73205 | − | 6.46410i | −0.164614 | − | 0.285119i | ||||
\(515\) | 13.9019 | − | 4.63397i | 0.612592 | − | 0.204197i | ||||
\(516\) | −0.696152 | − | 2.59808i | −0.0306464 | − | 0.114374i | ||||
\(517\) | −9.92820 | − | 2.66025i | −0.436642 | − | 0.116998i | ||||
\(518\) | 12.2942 | − | 2.36603i | 0.540177 | − | 0.103957i | ||||
\(519\) | 10.1436 | + | 37.8564i | 0.445254 | + | 1.66171i | ||||
\(520\) | −1.63397 | + | 0.0980762i | −0.0716545 | + | 0.00430093i | ||||
\(521\) | 21.3564 | − | 12.3301i | 0.935641 | − | 0.540193i | 0.0470499 | − | 0.998893i | \(-0.485018\pi\) |
0.888591 | + | 0.458700i | \(0.151685\pi\) | |||||||
\(522\) | 3.99038 | + | 14.8923i | 0.174654 | + | 0.651818i | ||||
\(523\) | 2.76795 | − | 0.741670i | 0.121034 | − | 0.0324310i | −0.197794 | − | 0.980244i | \(-0.563378\pi\) |
0.318828 | + | 0.947813i | \(0.396711\pi\) | |||||||
\(524\) | −16.3923 | + | 28.3923i | −0.716101 | + | 1.24032i | ||||
\(525\) | 4.85641 | − | 22.3923i | 0.211951 | − | 0.977280i | ||||
\(526\) | −3.33013 | − | 5.76795i | −0.145200 | − | 0.251495i | ||||
\(527\) | 8.00000 | + | 8.00000i | 0.348485 | + | 0.348485i | ||||
\(528\) | −7.39230 | − | 4.26795i | −0.321709 | − | 0.185739i | ||||
\(529\) | − | 16.8564i | − | 0.732887i | ||||||
\(530\) | −0.660254 | − | 1.00000i | −0.0286796 | − | 0.0434372i | ||||
\(531\) | 13.6865 | + | 23.7058i | 0.593945 | + | 1.02874i | ||||
\(532\) | 2.19615 | + | 2.53590i | 0.0952153 | + | 0.109945i | ||||
\(533\) | −0.294229 | − | 1.09808i | −0.0127445 | − | 0.0475630i | ||||
\(534\) | 0.928203 | + | 0.248711i | 0.0401673 | + | 0.0107628i | ||||
\(535\) | −4.20577 | + | 20.5526i | −0.181831 | + | 0.888565i | ||||
\(536\) | −3.36603 | + | 5.83013i | −0.145390 | + | 0.251823i | ||||
\(537\) | −4.09808 | + | 7.09808i | −0.176845 | + | 0.306305i | ||||
\(538\) | 3.80385 | − | 1.01924i | 0.163996 | − | 0.0439425i | ||||
\(539\) | 13.0000 | − | 5.19615i | 0.559950 | − | 0.223814i | ||||
\(540\) | 11.0885 | + | 16.7942i | 0.477171 | + | 0.722709i | ||||
\(541\) | −3.46410 | + | 6.00000i | −0.148933 | + | 0.257960i | −0.930834 | − | 0.365444i | \(-0.880917\pi\) |
0.781900 | + | 0.623404i | \(0.214251\pi\) | |||||||
\(542\) | 0.516660 | − | 0.516660i | 0.0221925 | − | 0.0221925i | ||||
\(543\) | 3.57180 | + | 6.18653i | 0.153280 | + | 0.265490i | ||||
\(544\) | −10.6410 | −0.456230 | ||||||||
\(545\) | 1.30385 | + | 21.7224i | 0.0558507 | + | 0.930487i | ||||
\(546\) | 0.169873 | + | 0.882686i | 0.00726989 | + | 0.0377755i | ||||
\(547\) | −15.5981 | + | 4.17949i | −0.666926 | + | 0.178702i | −0.576370 | − | 0.817189i | \(-0.695531\pi\) |
−0.0905561 | + | 0.995891i | \(0.528864\pi\) | |||||||
\(548\) | 0.633975 | + | 2.36603i | 0.0270821 | + | 0.101072i | ||||
\(549\) | − | 32.7846i | − | 1.39921i | ||||||
\(550\) | 4.80385 | − | 1.92820i | 0.204837 | − | 0.0822189i | ||||
\(551\) | −6.29423 | + | 3.63397i | −0.268143 | + | 0.154813i | ||||
\(552\) | −10.5622 | − | 18.2942i | −0.449556 | − | 0.778654i | ||||
\(553\) | −19.8564 | − | 22.9282i | −0.844380 | − | 0.975006i | ||||
\(554\) | 1.39230 | − | 0.803848i | 0.0591534 | − | 0.0341522i | ||||
\(555\) | 11.1962 | + | 33.5885i | 0.475250 | + | 1.42575i | ||||
\(556\) | − | 32.1962i | − | 1.36542i | ||||||
\(557\) | 6.67949 | − | 24.9282i | 0.283019 | − | 1.05624i | −0.667256 | − | 0.744829i | \(-0.732531\pi\) |
0.950275 | − | 0.311413i | \(-0.100802\pi\) | |||||||
\(558\) | 2.19615 | + | 8.19615i | 0.0929705 | + | 0.346971i | ||||
\(559\) | 0.339746 | 0.0143697 | ||||||||
\(560\) | −3.60770 | − | 14.1244i | −0.152453 | − | 0.596863i | ||||
\(561\) | 6.92820 | − | 1.85641i | 0.292509 | − | 0.0783775i | ||||
\(562\) | 9.41858 | + | 9.41858i | 0.397299 | + | 0.397299i | ||||
\(563\) | 4.09808 | − | 1.09808i | 0.172713 | − | 0.0462784i | −0.171426 | − | 0.985197i | \(-0.554837\pi\) |
0.344139 | + | 0.938919i | \(0.388171\pi\) | |||||||
\(564\) | 14.8923 | + | 3.99038i | 0.627079 | + | 0.168025i | ||||
\(565\) | −14.5359 | + | 16.3923i | −0.611530 | + | 0.689629i | ||||
\(566\) | 8.32051i | 0.349737i | ||||||||
\(567\) | 18.0000 | − | 15.5885i | 0.755929 | − | 0.654654i | ||||
\(568\) | 1.73205 | − | 1.73205i | 0.0726752 | − | 0.0726752i | ||||
\(569\) | 2.53590 | − | 1.46410i | 0.106310 | − | 0.0613783i | −0.445902 | − | 0.895082i | \(-0.647117\pi\) |
0.552212 | + | 0.833703i | \(0.313784\pi\) | |||||||
\(570\) | 0.973721 | − | 1.09808i | 0.0407847 | − | 0.0459934i | ||||
\(571\) | 2.09808 | − | 3.63397i | 0.0878018 | − | 0.152077i | −0.818780 | − | 0.574108i | \(-0.805349\pi\) |
0.906582 | + | 0.422030i | \(0.138682\pi\) | |||||||
\(572\) | 0.928203 | − | 0.928203i | 0.0388101 | − | 0.0388101i | ||||
\(573\) | 30.2942 | + | 17.4904i | 1.26556 | + | 0.730671i | ||||
\(574\) | −3.69615 | + | 1.79423i | −0.154274 | + | 0.0748897i | ||||
\(575\) | −31.2487 | − | 4.46410i | −1.30316 | − | 0.186166i | ||||
\(576\) | 5.89230 | + | 3.40192i | 0.245513 | + | 0.141747i | ||||
\(577\) | 19.1962 | + | 5.14359i | 0.799146 | + | 0.214131i | 0.635209 | − | 0.772340i | \(-0.280914\pi\) |
0.163937 | + | 0.986471i | \(0.447581\pi\) | |||||||
\(578\) | −4.65321 | + | 4.65321i | −0.193548 | + | 0.193548i | ||||
\(579\) | −17.6603 | − | 17.6603i | −0.733935 | − | 0.733935i | ||||
\(580\) | 38.3827 | − | 2.30385i | 1.59375 | − | 0.0956621i | ||||
\(581\) | −11.9186 | − | 24.5526i | −0.494466 | − | 1.01861i | ||||
\(582\) | 7.31347 | − | 4.22243i | 0.303153 | − | 0.175025i | ||||
\(583\) | 2.00000 | + | 0.535898i | 0.0828315 | + | 0.0221946i | ||||
\(584\) | 12.9282 | + | 22.3923i | 0.534973 | + | 0.926600i | ||||
\(585\) | −2.41154 | + | 0.803848i | −0.0997050 | + | 0.0332350i | ||||
\(586\) | 5.66025 | + | 3.26795i | 0.233823 | + | 0.134998i | ||||
\(587\) | −8.83975 | − | 32.9904i | −0.364855 | − | 1.36166i | −0.867617 | − | 0.497234i | \(-0.834349\pi\) |
0.502761 | − | 0.864425i | \(-0.332317\pi\) | |||||||
\(588\) | −19.5000 | + | 7.79423i | −0.804166 | + | 0.321429i | ||||
\(589\) | −3.46410 | + | 2.00000i | −0.142736 | + | 0.0824086i | ||||
\(590\) | −10.0192 | + | 3.33975i | −0.412485 | + | 0.137495i | ||||
\(591\) | 9.46410 | + | 2.53590i | 0.389301 | + | 0.104313i | ||||
\(592\) | 15.9282 | + | 15.9282i | 0.654645 | + | 0.654645i | ||||
\(593\) | −14.7583 | + | 3.95448i | −0.606052 | + | 0.162391i | −0.548779 | − | 0.835967i | \(-0.684907\pi\) |
−0.0572729 | + | 0.998359i | \(0.518241\pi\) | |||||||
\(594\) | 5.19615 | + | 1.39230i | 0.213201 | + | 0.0571270i | ||||
\(595\) | 10.5359 | + | 6.24871i | 0.431930 | + | 0.256172i | ||||
\(596\) | 7.39230 | − | 12.8038i | 0.302801 | − | 0.524466i | ||||
\(597\) | −24.5885 | − | 14.1962i | −1.00634 | − | 0.581010i | ||||
\(598\) | 1.19615 | − | 0.320508i | 0.0489143 | − | 0.0131065i | ||||
\(599\) | −39.7128 | − | 22.9282i | −1.62262 | − | 0.936821i | −0.986215 | − | 0.165467i | \(-0.947087\pi\) |
−0.636406 | − | 0.771354i | \(-0.719580\pi\) | |||||||
\(600\) | −15.5263 | + | 6.23205i | −0.633858 | + | 0.254422i | ||||
\(601\) | −5.32051 | − | 3.07180i | −0.217028 | − | 0.125301i | 0.387545 | − | 0.921851i | \(-0.373323\pi\) |
−0.604573 | + | 0.796549i | \(0.706656\pi\) | |||||||
\(602\) | −0.232051 | − | 1.20577i | −0.00945768 | − | 0.0491436i | ||||
\(603\) | −2.70577 | + | 10.0981i | −0.110188 | + | 0.411225i | ||||
\(604\) | −0.509619 | − | 0.294229i | −0.0207361 | − | 0.0119720i | ||||
\(605\) | 7.00000 | − | 14.0000i | 0.284590 | − | 0.569181i | ||||
\(606\) | 0.232051 | − | 0.0621778i | 0.00942642 | − | 0.00252580i | ||||
\(607\) | 18.2942 | − | 18.2942i | 0.742540 | − | 0.742540i | −0.230526 | − | 0.973066i | \(-0.574045\pi\) |
0.973066 | + | 0.230526i | \(0.0740448\pi\) | |||||||
\(608\) | 0.973721 | − | 3.63397i | 0.0394896 | − | 0.147377i | ||||
\(609\) | −8.59808 | − | 44.6769i | −0.348412 | − | 1.81040i | ||||
\(610\) | 12.3923 | + | 2.53590i | 0.501750 | + | 0.102676i | ||||
\(611\) | −0.973721 | + | 1.68653i | −0.0393925 | + | 0.0682298i | ||||
\(612\) | −10.3923 | + | 2.78461i | −0.420084 | + | 0.112561i | ||||
\(613\) | 0.901924 | + | 0.241670i | 0.0364284 | + | 0.00976095i | 0.276987 | − | 0.960874i | \(-0.410664\pi\) |
−0.240559 | + | 0.970635i | \(0.577331\pi\) | |||||||
\(614\) | 1.33013 | + | 2.30385i | 0.0536796 | + | 0.0929757i | ||||
\(615\) | −6.40192 | − | 9.69615i | −0.258150 | − | 0.390987i | ||||
\(616\) | −8.46410 | − | 5.73205i | −0.341028 | − | 0.230951i | ||||
\(617\) | −8.39230 | + | 31.3205i | −0.337861 | + | 1.26092i | 0.562872 | + | 0.826544i | \(0.309696\pi\) |
−0.900734 | + | 0.434372i | \(0.856970\pi\) | |||||||
\(618\) | −2.93782 | + | 5.08846i | −0.118177 | + | 0.204688i | ||||
\(619\) | 0.784610 | 0.0315361 | 0.0157681 | − | 0.999876i | \(-0.494981\pi\) | ||||
0.0157681 | + | 0.999876i | \(0.494981\pi\) | |||||||
\(620\) | 21.1244 | − | 1.26795i | 0.848375 | − | 0.0509221i | ||||
\(621\) | −23.1962 | − | 23.1962i | −0.930830 | − | 0.930830i | ||||
\(622\) | −6.26795 | + | 6.26795i | −0.251322 | + | 0.251322i | ||||
\(623\) | −2.67949 | − | 0.928203i | −0.107352 | − | 0.0371877i | ||||
\(624\) | −1.14359 | + | 1.14359i | −0.0457804 | + | 0.0457804i | ||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | −14.1962 | − | 8.19615i | −0.567392 | − | 0.327584i | ||||
\(627\) | 2.53590i | 0.101274i | ||||||||
\(628\) | 2.02628 | − | 7.56218i | 0.0808574 | − | 0.301764i | ||||
\(629\) | −18.9282 | −0.754717 | ||||||||
\(630\) | 4.50000 | + | 8.00962i | 0.179284 | + | 0.319111i | ||||
\(631\) | −11.8564 | −0.471996 | −0.235998 | − | 0.971754i | \(-0.575836\pi\) | ||||
−0.235998 | + | 0.971754i | \(0.575836\pi\) | |||||||
\(632\) | −5.73205 | + | 21.3923i | −0.228009 | + | 0.850940i | ||||
\(633\) | −40.3923 | − | 23.3205i | −1.60545 | − | 0.926907i | ||||
\(634\) | −0.973721 | − | 0.562178i | −0.0386714 | − | 0.0223269i | ||||
\(635\) | −34.0981 | + | 11.3660i | −1.35314 | + | 0.451047i | ||||
\(636\) | −3.00000 | − | 0.803848i | −0.118958 | − | 0.0318746i | ||||
\(637\) | −0.313467 | − | 2.63397i | −0.0124200 | − | 0.104362i | ||||
\(638\) | 7.26795 | − | 7.26795i | 0.287741 | − | 0.287741i | ||||
\(639\) | 1.90192 | − | 3.29423i | 0.0752389 | − | 0.130318i | ||||
\(640\) | −16.9904 | + | 19.1603i | −0.671604 | + | 0.757376i | ||||
\(641\) | 17.6077 | 0.695462 | 0.347731 | − | 0.937594i | \(-0.386952\pi\) | ||||
0.347731 | + | 0.937594i | \(0.386952\pi\) | |||||||
\(642\) | −4.20577 | − | 7.28461i | −0.165989 | − | 0.287501i | ||||
\(643\) | 6.65064 | − | 24.8205i | 0.262275 | − | 0.978825i | −0.701622 | − | 0.712550i | \(-0.747540\pi\) |
0.963897 | − | 0.266275i | \(-0.0857931\pi\) | |||||||
\(644\) | 12.6340 | + | 26.0263i | 0.497848 | + | 1.02558i | ||||
\(645\) | 3.29423 | − | 1.09808i | 0.129710 | − | 0.0432367i | ||||
\(646\) | 0.392305 | + | 0.679492i | 0.0154350 | + | 0.0267343i | ||||
\(647\) | −12.5981 | − | 3.37564i | −0.495281 | − | 0.132710i | 0.00252779 | − | 0.999997i | \(-0.499195\pi\) |
−0.497809 | + | 0.867287i | \(0.665862\pi\) | |||||||
\(648\) | −16.7942 | − | 4.50000i | −0.659740 | − | 0.176777i | ||||
\(649\) | 9.12436 | − | 15.8038i | 0.358162 | − | 0.620355i | ||||
\(650\) | −0.117314 | − | 0.973721i | −0.00460144 | − | 0.0381925i | ||||
\(651\) | −4.73205 | − | 24.5885i | −0.185464 | − | 0.963698i | ||||
\(652\) | 10.9019 | − | 40.6865i | 0.426952 | − | 1.59341i | ||||
\(653\) | 14.7321 | − | 14.7321i | 0.576510 | − | 0.576510i | −0.357430 | − | 0.933940i | \(-0.616347\pi\) |
0.933940 | + | 0.357430i | \(0.116347\pi\) | |||||||
\(654\) | −6.16987 | − | 6.16987i | −0.241261 | − | 0.241261i | ||||
\(655\) | −37.8564 | − | 18.9282i | −1.47917 | − | 0.739586i | ||||
\(656\) | −6.40192 | − | 3.69615i | −0.249953 | − | 0.144311i | ||||
\(657\) | 28.3923 | + | 28.3923i | 1.10769 | + | 1.10769i | ||||
\(658\) | 6.65064 | + | 2.30385i | 0.259269 | + | 0.0898133i | ||||
\(659\) | −19.3468 | − | 11.1699i | −0.753644 | − | 0.435116i | 0.0733652 | − | 0.997305i | \(-0.476626\pi\) |
−0.827009 | + | 0.562189i | \(0.809959\pi\) | |||||||
\(660\) | 6.00000 | − | 12.0000i | 0.233550 | − | 0.467099i | ||||
\(661\) | −2.25833 | − | 1.30385i | −0.0878389 | − | 0.0507138i | 0.455437 | − | 0.890268i | \(-0.349483\pi\) |
−0.543276 | + | 0.839554i | \(0.682816\pi\) | |||||||
\(662\) | 3.00000 | − | 0.803848i | 0.116598 | − | 0.0312424i | ||||
\(663\) | − | 1.35898i | − | 0.0527786i | ||||||
\(664\) | −9.96410 | + | 17.2583i | −0.386682 | + | 0.669753i | ||||
\(665\) | −3.09808 | + | 3.02628i | −0.120138 | + | 0.117354i | ||||
\(666\) | −12.2942 | − | 7.09808i | −0.476392 | − | 0.275045i | ||||
\(667\) | −60.5429 | + | 16.2224i | −2.34423 | + | 0.628135i | ||||
\(668\) | −7.73205 | − | 7.73205i | −0.299162 | − | 0.299162i | ||||
\(669\) | −6.29423 | + | 6.29423i | −0.243349 | + | 0.243349i | ||||
\(670\) | −3.60770 | − | 1.80385i | −0.139377 | − | 0.0696887i | ||||
\(671\) | −18.9282 | + | 10.9282i | −0.730715 | + | 0.421879i | ||||
\(672\) | 19.5000 | + | 13.2058i | 0.752229 | + | 0.509424i | ||||
\(673\) | −1.43782 | − | 5.36603i | −0.0554240 | − | 0.206845i | 0.932661 | − | 0.360754i | \(-0.117481\pi\) |
−0.988085 | + | 0.153909i | \(0.950814\pi\) | |||||||
\(674\) | 9.75833 | + | 5.63397i | 0.375877 | + | 0.217013i | ||||
\(675\) | −20.7846 | + | 15.5885i | −0.800000 | + | 0.600000i | ||||
\(676\) | 11.1340 | + | 19.2846i | 0.428230 | + | 0.741716i | ||||
\(677\) | −14.3660 | − | 3.84936i | −0.552131 | − | 0.147943i | −0.0280424 | − | 0.999607i | \(-0.508927\pi\) |
−0.524089 | + | 0.851664i | \(0.675594\pi\) | |||||||
\(678\) | − | 8.78461i | − | 0.337371i | ||||||
\(679\) | −22.4186 | + | 10.8827i | −0.860346 | + | 0.417639i | ||||
\(680\) | −0.535898 | − | 8.92820i | −0.0205508 | − | 0.342381i | ||||
\(681\) | 11.1506 | − | 41.6147i | 0.427293 | − | 1.59468i | ||||
\(682\) | 4.00000 | − | 4.00000i | 0.153168 | − | 0.153168i | ||||
\(683\) | −42.9186 | − | 11.5000i | −1.64223 | − | 0.440035i | −0.684810 | − | 0.728721i | \(-0.740115\pi\) |
−0.957424 | + | 0.288686i | \(0.906782\pi\) | |||||||
\(684\) | − | 3.80385i | − | 0.145444i | ||||||
\(685\) | −3.00000 | + | 1.00000i | −0.114624 | + | 0.0382080i | ||||
\(686\) | −9.13397 | + | 2.91154i | −0.348737 | + | 0.111163i | ||||
\(687\) | 33.9904 | − | 19.6244i | 1.29681 | − | 0.748716i | ||||
\(688\) | 1.56218 | − | 1.56218i | 0.0595575 | − | 0.0595575i | ||||
\(689\) | 0.196152 | − | 0.339746i | 0.00747281 | − | 0.0129433i | ||||
\(690\) | 10.5622 | − | 6.97372i | 0.402095 | − | 0.265485i | ||||
\(691\) | −16.8564 | + | 9.73205i | −0.641248 | + | 0.370225i | −0.785095 | − | 0.619375i | \(-0.787386\pi\) |
0.143847 | + | 0.989600i | \(0.454053\pi\) | |||||||
\(692\) | −27.7128 | + | 27.7128i | −1.05348 | + | 1.05348i | ||||
\(693\) | −15.0000 | − | 5.19615i | −0.569803 | − | 0.197386i | ||||
\(694\) | 6.12436i | 0.232477i | ||||||||
\(695\) | 41.4904 | − | 2.49038i | 1.57382 | − | 0.0944655i | ||||
\(696\) | −23.4904 | + | 23.4904i | −0.890401 | + | 0.890401i | ||||
\(697\) | 6.00000 | − | 1.60770i | 0.227266 | − | 0.0608958i | ||||
\(698\) | −3.66025 | − | 3.66025i | −0.138543 | − | 0.138543i | ||||
\(699\) | 26.1962 | + | 26.1962i | 0.990829 | + | 0.990829i | ||||
\(700\) | 21.8205 | − | 6.99038i | 0.824738 | − | 0.264212i | ||||
\(701\) | 11.0526 | 0.417449 | 0.208725 | − | 0.977974i | \(-0.433069\pi\) | ||||
0.208725 | + | 0.977974i | \(0.433069\pi\) | |||||||
\(702\) | 0.509619 | − | 0.882686i | 0.0192343 | − | 0.0333148i | ||||
\(703\) | 1.73205 | − | 6.46410i | 0.0653255 | − | 0.243798i | ||||
\(704\) | − | 4.53590i | − | 0.170953i | ||||||
\(705\) | −3.99038 | + | 19.5000i | −0.150286 | + | 0.734412i | ||||
\(706\) | −3.50962 | + | 2.02628i | −0.132086 | + | 0.0762600i | ||||
\(707\) | −0.696152 | + | 0.133975i | −0.0261815 | + | 0.00503863i | ||||
\(708\) | −13.6865 | + | 23.7058i | −0.514371 | + | 0.890917i | ||||
\(709\) | 35.1962 | − | 20.3205i | 1.32182 | − | 0.763153i | 0.337801 | − | 0.941218i | \(-0.390317\pi\) |
0.984019 | + | 0.178065i | \(0.0569837\pi\) | |||||||
\(710\) | 1.09808 | + | 0.973721i | 0.0412101 | + | 0.0365431i | ||||
\(711\) | 34.3923i | 1.28981i | ||||||||
\(712\) | 0.535898 | + | 2.00000i | 0.0200836 | + | 0.0749532i | ||||
\(713\) | −33.3205 | + | 8.92820i | −1.24786 | + | 0.334364i | ||||
\(714\) | −4.82309 | + | 0.928203i | −0.180499 | + | 0.0347371i | ||||
\(715\) | 1.26795 | + | 1.12436i | 0.0474186 | + | 0.0420485i | ||||
\(716\) | −8.19615 | −0.306305 | ||||||||
\(717\) | 1.73205 | − | 3.00000i | 0.0646846 | − | 0.112037i | ||||
\(718\) | 1.07180 | − | 1.07180i | 0.0399991 | − | 0.0399991i | ||||
\(719\) | 11.4641 | − | 19.8564i | 0.427539 | − | 0.740519i | −0.569115 | − | 0.822258i | \(-0.692714\pi\) |
0.996654 | + | 0.0817390i | \(0.0260474\pi\) | |||||||
\(720\) | −7.39230 | + | 14.7846i | −0.275495 | + | 0.550990i | ||||
\(721\) | 9.72243 | − | 14.3564i | 0.362082 | − | 0.534661i | ||||
\(722\) | 9.23205 | − | 2.47372i | 0.343581 | − | 0.0920623i | ||||
\(723\) | 13.4545 | + | 23.3038i | 0.500378 | + | 0.866679i | ||||
\(724\) | −3.57180 | + | 6.18653i | −0.132745 | + | 0.229921i | ||||
\(725\) | 5.93782 | + | 49.2846i | 0.220525 | + | 1.83038i | ||||
\(726\) | 1.62436 | + | 6.06218i | 0.0602855 | + | 0.224989i | ||||
\(727\) | 6.75833 | + | 25.2224i | 0.250653 | + | 0.935448i | 0.970458 | + | 0.241272i | \(0.0775646\pi\) |
−0.719805 | + | 0.694176i | \(0.755769\pi\) | |||||||
\(728\) | −1.46410 | + | 1.26795i | −0.0542632 | + | 0.0469933i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −12.9282 | + | 8.53590i | −0.478494 | + | 0.315928i | ||||
\(731\) | 1.85641i | 0.0686617i | ||||||||
\(732\) | 28.3923 | − | 16.3923i | 1.04941 | − | 0.605877i | ||||
\(733\) | −4.32051 | − | 4.32051i | −0.159582 | − | 0.159582i | 0.622800 | − | 0.782381i | \(-0.285995\pi\) |
−0.782381 | + | 0.622800i | \(0.785995\pi\) | |||||||
\(734\) | −3.33013 | − | 5.76795i | −0.122917 | − | 0.212899i | ||||
\(735\) | −11.5526 | − | 24.5263i | −0.426123 | − | 0.904665i | ||||
\(736\) | 16.2224 | − | 28.0981i | 0.597967 | − | 1.03571i | ||||
\(737\) | 6.73205 | − | 1.80385i | 0.247978 | − | 0.0664456i | ||||
\(738\) | 4.50000 | + | 1.20577i | 0.165647 | + | 0.0443851i | ||||
\(739\) | −0.679492 | + | 0.392305i | −0.0249955 | + | 0.0144312i | −0.512446 | − | 0.858720i | \(-0.671260\pi\) |
0.487450 | + | 0.873151i | \(0.337927\pi\) | |||||||
\(740\) | −23.4904 | + | 26.4904i | −0.863524 | + | 0.973806i | ||||
\(741\) | 0.464102 | + | 0.124356i | 0.0170492 | + | 0.00456832i | ||||
\(742\) | −1.33975 | − | 0.464102i | −0.0491836 | − | 0.0170377i | ||||
\(743\) | −34.9186 | − | 9.35641i | −1.28104 | − | 0.343253i | −0.446789 | − | 0.894640i | \(-0.647432\pi\) |
−0.834250 | + | 0.551386i | \(0.814099\pi\) | |||||||
\(744\) | −12.9282 | + | 12.9282i | −0.473971 | + | 0.473971i | ||||
\(745\) | 17.0718 | + | 8.53590i | 0.625462 | + | 0.312731i | ||||
\(746\) | 4.56218 | + | 7.90192i | 0.167033 | + | 0.289310i | ||||
\(747\) | −8.00962 | + | 29.8923i | −0.293057 | + | 1.09370i | ||||
\(748\) | 5.07180 | + | 5.07180i | 0.185443 | + | 0.185443i | ||||
\(749\) | 10.8397 | + | 22.3301i | 0.396076 | + | 0.815925i | ||||
\(750\) | −4.28461 | − | 9.06218i | −0.156452 | − | 0.330904i | ||||
\(751\) | 24.8756 | 0.907725 | 0.453863 | − | 0.891072i | \(-0.350046\pi\) | ||||
0.453863 | + | 0.891072i | \(0.350046\pi\) | |||||||
\(752\) | 3.27757 | + | 12.2321i | 0.119521 | + | 0.446057i | ||||
\(753\) | −11.8301 | − | 20.4904i | −0.431114 | − | 0.746711i | ||||
\(754\) | −0.973721 | − | 1.68653i | −0.0354608 | − | 0.0614199i | ||||
\(755\) | 0.339746 | − | 0.679492i | 0.0123646 | − | 0.0247292i | ||||
\(756\) | 22.5000 | + | 7.79423i | 0.818317 | + | 0.283473i | ||||
\(757\) | −14.3923 | − | 14.3923i | −0.523097 | − | 0.523097i | 0.395408 | − | 0.918505i | \(-0.370603\pi\) |
−0.918505 | + | 0.395408i | \(0.870603\pi\) | |||||||
\(758\) | 13.7583 | + | 3.68653i | 0.499725 | + | 0.133901i | ||||
\(759\) | −5.66025 | + | 21.1244i | −0.205454 | + | 0.766766i | ||||
\(760\) | 3.09808 | + | 0.633975i | 0.112379 | + | 0.0229967i | ||||
\(761\) | − | 9.19615i | − | 0.333360i | −0.986011 | − | 0.166680i | \(-0.946695\pi\) | ||
0.986011 | − | 0.166680i | \(-0.0533047\pi\) | |||||||
\(762\) | 7.20577 | − | 12.4808i | 0.261038 | − | 0.452130i | ||||
\(763\) | 16.8564 | + | 19.4641i | 0.610243 | + | 0.704648i | ||||
\(764\) | 34.9808i | 1.26556i | ||||||||
\(765\) | −4.39230 | − | 13.1769i | −0.158804 | − | 0.476412i | ||||
\(766\) | 9.35641 | − | 5.40192i | 0.338061 | − | 0.195179i | ||||
\(767\) | −2.44486 | − | 2.44486i | −0.0882789 | − | 0.0882789i | ||||
\(768\) | − | 2.41154i | − | 0.0870191i | ||||||
\(769\) | −12.5981 | − | 21.8205i | −0.454298 | − | 0.786868i | 0.544349 | − | 0.838859i | \(-0.316777\pi\) |
−0.998648 | + | 0.0519910i | \(0.983443\pi\) | |||||||
\(770\) | 3.12436 | − | 5.26795i | 0.112594 | − | 0.189844i | ||||
\(771\) | 6.46410 | − | 24.1244i | 0.232799 | − | 0.868817i | ||||
\(772\) | 6.46410 | − | 24.1244i | 0.232648 | − | 0.868255i | ||||
\(773\) | −4.58142 | + | 17.0981i | −0.164782 | + | 0.614975i | 0.833286 | + | 0.552842i | \(0.186457\pi\) |
−0.998068 | + | 0.0621327i | \(0.980210\pi\) | |||||||
\(774\) | −0.696152 | + | 1.20577i | −0.0250227 | + | 0.0433406i | ||||
\(775\) | 3.26795 | + | 27.1244i | 0.117388 | + | 0.974336i | ||||
\(776\) | 15.7583 | + | 9.09808i | 0.565691 | + | 0.326602i | ||||
\(777\) | 34.6865 | + | 23.4904i | 1.24437 | + | 0.842713i | ||||
\(778\) | 14.5263 | + | 3.89230i | 0.520792 | + | 0.139546i | ||||
\(779\) | 2.19615i | 0.0786853i | ||||||||
\(780\) | −1.90192 | − | 1.68653i | −0.0680998 | − | 0.0603876i | ||||
\(781\) | −2.53590 | −0.0907416 | ||||||||
\(782\) | 1.75129 | + | 6.53590i | 0.0626260 | + | 0.233723i | ||||
\(783\) | −25.7942 | + | 44.6769i | −0.921811 | + | 1.59662i | ||||
\(784\) | −13.5526 | − | 10.6699i | −0.484020 | − | 0.381067i | ||||
\(785\) | 9.90192 | + | 2.02628i | 0.353415 | + | 0.0723210i | ||||
\(786\) | 16.3923 | − | 4.39230i | 0.584694 | − | 0.156668i | ||||
\(787\) | −10.6769 | − | 39.8468i | −0.380591 | − | 1.42038i | −0.845001 | − | 0.534764i | \(-0.820400\pi\) |
0.464410 | − | 0.885620i | \(-0.346266\pi\) | |||||||
\(788\) | 2.53590 | + | 9.46410i | 0.0903376 | + | 0.337145i | ||||
\(789\) | 5.76795 | − | 21.5263i | 0.205344 | − | 0.766356i | ||||
\(790\) | −13.0000 | − | 2.66025i | −0.462519 | − | 0.0946476i | ||||
\(791\) | −1.85641 | + | 25.8564i | −0.0660062 | + | 0.919348i | ||||
\(792\) | 3.00000 | + | 11.1962i | 0.106600 | + | 0.397838i | ||||
\(793\) | 1.07180 | + | 4.00000i | 0.0380606 | + | 0.142044i | ||||
\(794\) | −10.6410 | −0.377636 | ||||||||
\(795\) | 0.803848 | − | 3.92820i | 0.0285095 | − | 0.139319i | ||||
\(796\) | − | 28.3923i | − | 1.00634i | ||||||
\(797\) | 34.8827 | + | 9.34679i | 1.23561 | + | 0.331080i | 0.816761 | − | 0.576976i | \(-0.195768\pi\) |
0.418847 | + | 0.908057i | \(0.362434\pi\) | |||||||
\(798\) | 0.124356 | − | 1.73205i | 0.00440214 | − | 0.0613139i | ||||
\(799\) | −9.21539 | − | 5.32051i | −0.326017 | − | 0.188226i | ||||
\(800\) | −20.2128 | − | 15.8660i | −0.714631 | − | 0.560949i | ||||
\(801\) | 1.60770 | + | 2.78461i | 0.0568051 | + | 0.0983893i | ||||
\(802\) | 1.52628 | − | 5.69615i | 0.0538948 | − | 0.201138i | ||||
\(803\) | 6.92820 | − | 25.8564i | 0.244491 | − | 0.912453i | ||||
\(804\) | −10.0981 | + | 2.70577i | −0.356132 | + | 0.0954252i | ||||
\(805\) | −32.5622 | + | 18.2942i | −1.14767 | + | 0.644787i | ||||
\(806\) | −0.535898 | − | 0.928203i | −0.0188762 | − | 0.0326946i | ||||
\(807\) | 11.4115 | + | 6.58846i | 0.401705 | + | 0.231925i | ||||
\(808\) | 0.366025 | + | 0.366025i | 0.0128767 | + | 0.0128767i | ||||
\(809\) | 38.3827 | − | 22.1603i | 1.34946 | − | 0.779113i | 0.361290 | − | 0.932454i | \(-0.382336\pi\) |
0.988173 | + | 0.153340i | \(0.0490031\pi\) | |||||||
\(810\) | 2.08846 | − | 10.2058i | 0.0733809 | − | 0.358594i | ||||
\(811\) | 6.58846i | 0.231352i | 0.993287 | + | 0.115676i | \(0.0369034\pi\) | ||||
−0.993287 | + | 0.115676i | \(0.963097\pi\) | |||||||
\(812\) | 34.3923 | − | 29.7846i | 1.20693 | − | 1.04523i | ||||
\(813\) | 2.44486 | 0.0857451 | ||||||||
\(814\) | 9.46410i | 0.331717i | ||||||||
\(815\) | 53.2750 | + | 10.9019i | 1.86614 | + | 0.381878i | ||||
\(816\) | −6.24871 | − | 6.24871i | −0.218749 | − | 0.218749i | ||||
\(817\) | −0.633975 | − | 0.169873i | −0.0221800 | − | 0.00594310i | ||||
\(818\) | 4.50962 | + | 4.50962i | 0.157675 | + | 0.157675i | ||||
\(819\) | −1.68653 | + | 2.49038i | −0.0589322 | + | 0.0870210i | ||||
\(820\) | 5.19615 | − | 10.3923i | 0.181458 | − | 0.362915i | ||||
\(821\) | −20.7942 | − | 36.0167i | −0.725724 | − | 1.25699i | −0.958675 | − | 0.284502i | \(-0.908172\pi\) |
0.232952 | − | 0.972488i | \(-0.425162\pi\) | |||||||
\(822\) | 0.633975 | − | 1.09808i | 0.0221124 | − | 0.0382998i | ||||
\(823\) | 2.72243 | + | 10.1603i | 0.0948980 | + | 0.354164i | 0.997004 | − | 0.0773504i | \(-0.0246460\pi\) |
−0.902106 | + | 0.431515i | \(0.857979\pi\) | |||||||
\(824\) | −12.6603 | −0.441041 | ||||||||
\(825\) | 15.9282 | + | 6.80385i | 0.554549 | + | 0.236880i | ||||
\(826\) | −7.00704 | + | 10.3468i | −0.243806 | + | 0.360011i | ||||
\(827\) | 14.1699 | + | 14.1699i | 0.492735 | + | 0.492735i | 0.909167 | − | 0.416432i | \(-0.136720\pi\) |
−0.416432 | + | 0.909167i | \(0.636720\pi\) | |||||||
\(828\) | 8.49038 | − | 31.6865i | 0.295061 | − | 1.10118i | ||||
\(829\) | −22.1603 | − | 38.3827i | −0.769657 | − | 1.33309i | −0.937749 | − | 0.347314i | \(-0.887094\pi\) |
0.168091 | − | 0.985771i | \(-0.446240\pi\) | |||||||
\(830\) | −10.6795 | − | 5.33975i | −0.370691 | − | 0.185345i | ||||
\(831\) | 5.19615 | + | 1.39230i | 0.180253 | + | 0.0482985i | ||||
\(832\) | −0.830127 | − | 0.222432i | −0.0287795 | − | 0.00771144i | ||||
\(833\) | 14.3923 | − | 1.71281i | 0.498664 | − | 0.0593455i | ||||
\(834\) | −11.7846 | + | 11.7846i | −0.408068 | + | 0.408068i | ||||
\(835\) | 9.36603 | − | 10.5622i | 0.324125 | − | 0.365519i | ||||
\(836\) | −2.19615 | + | 1.26795i | −0.0759555 | + | 0.0438529i | ||||
\(837\) | −14.1962 | + | 24.5885i | −0.490691 | + | 0.849901i | ||||
\(838\) | −9.83013 | + | 2.63397i | −0.339576 | + | 0.0909891i | ||||
\(839\) | 22.6147 | − | 39.1699i | 0.780747 | − | 1.35229i | −0.150759 | − | 0.988570i | \(-0.548172\pi\) |
0.931507 | − | 0.363724i | \(-0.118495\pi\) | |||||||
\(840\) | −10.0981 | + | 17.0263i | −0.348417 | + | 0.587462i | ||||
\(841\) | 34.7846 | + | 60.2487i | 1.19947 | + | 2.07754i | ||||
\(842\) | 5.56218 | + | 5.56218i | 0.191685 | + | 0.191685i | ||||
\(843\) | 44.5692i | 1.53505i | ||||||||
\(844\) | − | 46.6410i | − | 1.60545i | ||||||
\(845\) | −23.9904 | + | 15.8397i | −0.825294 | + | 0.544904i | ||||
\(846\) | −3.99038 | − | 6.91154i | −0.137192 | − | 0.237624i | ||||
\(847\) | −3.50000 | − | 18.1865i | −0.120261 | − | 0.624897i | ||||
\(848\) | −0.660254 | − | 2.46410i | −0.0226732 | − | 0.0846176i | ||||
\(849\) | −19.6865 | + | 19.6865i | −0.675640 | + | 0.675640i | ||||
\(850\) | 5.32051 | − | 0.641016i | 0.182492 | − | 0.0219867i | ||||
\(851\) | 28.8564 | − | 49.9808i | 0.989185 | − | 1.71332i | ||||
\(852\) | 3.80385 | 0.130318 | ||||||||
\(853\) | −24.1244 | + | 6.46410i | −0.826002 | + | 0.221327i | −0.646969 | − | 0.762516i | \(-0.723964\pi\) |
−0.179033 | + | 0.983843i | \(0.557297\pi\) | |||||||
\(854\) | 13.4641 | − | 6.53590i | 0.460732 | − | 0.223654i | ||||
\(855\) | 4.90192 | − | 0.294229i | 0.167642 | − | 0.0100624i | ||||
\(856\) | 9.06218 | − | 15.6962i | 0.309739 | − | 0.536483i | ||||
\(857\) | −8.92820 | + | 8.92820i | −0.304982 | + | 0.304982i | −0.842959 | − | 0.537978i | \(-0.819189\pi\) |
0.537978 | + | 0.842959i | \(0.319189\pi\) | |||||||
\(858\) | −0.679492 | −0.0231975 | ||||||||
\(859\) | 27.6603 | 0.943756 | 0.471878 | − | 0.881664i | \(-0.343576\pi\) | ||||
0.471878 | + | 0.881664i | \(0.343576\pi\) | |||||||
\(860\) | 2.59808 | + | 2.30385i | 0.0885937 | + | 0.0785606i | ||||
\(861\) | −12.9904 | − | 4.50000i | −0.442711 | − | 0.153360i | ||||
\(862\) | 5.29423 | − | 1.41858i | 0.180322 | − | 0.0483172i | ||||
\(863\) | 12.6147 | + | 47.0788i | 0.429411 | + | 1.60258i | 0.754099 | + | 0.656761i | \(0.228074\pi\) |
−0.324688 | + | 0.945821i | \(0.605259\pi\) | |||||||
\(864\) | −6.91154 | − | 25.7942i | −0.235135 | − | 0.877537i | ||||
\(865\) | −37.8564 | − | 33.5692i | −1.28716 | − | 1.14139i | ||||
\(866\) | 15.2942 | − | 8.83013i | 0.519719 | − | 0.300060i | ||||
\(867\) | −22.0192 | −0.747813 | ||||||||
\(868\) | 18.9282 | − | 16.3923i | 0.642465 | − | 0.556391i | ||||
\(869\) | 19.8564 | − | 11.4641i | 0.673582 | − | 0.388893i | ||||
\(870\) | −14.8923 | − | 13.2058i | −0.504896 | − | 0.447718i | ||||
\(871\) | − | 1.32051i | − | 0.0447437i | ||||||
\(872\) | 4.86603 | − | 18.1603i | 0.164784 | − | 0.614984i | ||||
\(873\) | 27.2942 | + | 7.31347i | 0.923770 | + | 0.247523i | ||||
\(874\) | −2.39230 | −0.0809209 | ||||||||
\(875\) | 10.6962 | + | 27.5788i | 0.361596 | + | 0.932335i | ||||
\(876\) | −10.3923 | + | 38.7846i | −0.351123 | + | 1.31041i | ||||
\(877\) | 1.19615 | + | 1.19615i | 0.0403912 | + | 0.0403912i | 0.727014 | − | 0.686623i | \(-0.240908\pi\) |
−0.686623 | + | 0.727014i | \(0.740908\pi\) | |||||||
\(878\) | 4.07180 | − | 1.09103i | 0.137416 | − | 0.0368206i | ||||
\(879\) | 5.66025 | + | 21.1244i | 0.190916 | + | 0.712507i | ||||
\(880\) | 11.0000 | − | 0.660254i | 0.370810 | − | 0.0222572i | ||||
\(881\) | − | 39.0333i | − | 1.31507i | −0.753426 | − | 0.657533i | \(-0.771600\pi\) | ||
0.753426 | − | 0.657533i | \(-0.228400\pi\) | |||||||
\(882\) | 9.99038 | + | 4.28461i | 0.336394 | + | 0.144270i | ||||
\(883\) | 31.5622 | − | 31.5622i | 1.06215 | − | 1.06215i | 0.0642158 | − | 0.997936i | \(-0.479545\pi\) |
0.997936 | − | 0.0642158i | \(-0.0204546\pi\) | |||||||
\(884\) | 1.17691 | − | 0.679492i | 0.0395839 | − | 0.0228538i | ||||
\(885\) | −31.6077 | − | 15.8038i | −1.06248 | − | 0.531241i | ||||
\(886\) | −3.79423 | + | 6.57180i | −0.127470 | + | 0.220784i | ||||
\(887\) | 19.4904 | − | 19.4904i | 0.654423 | − | 0.654423i | −0.299632 | − | 0.954055i | \(-0.596864\pi\) |
0.954055 | + | 0.299632i | \(0.0968639\pi\) | |||||||
\(888\) | − | 30.5885i | − | 1.02648i | ||||||
\(889\) | −23.8468 | + | 35.2128i | −0.799796 | + | 1.18100i | ||||
\(890\) | −1.17691 | + | 0.392305i | −0.0394503 | + | 0.0131501i | ||||
\(891\) | 9.00000 | + | 15.5885i | 0.301511 | + | 0.522233i | ||||
\(892\) | −8.59808 | − | 2.30385i | −0.287885 | − | 0.0771385i | ||||
\(893\) | 2.66025 | − | 2.66025i | 0.0890220 | − | 0.0890220i | ||||
\(894\) | −7.39230 | + | 1.98076i | −0.247236 | + | 0.0662466i | ||||
\(895\) | −0.633975 | − | 10.5622i | −0.0211914 | − | 0.353055i | ||||
\(896\) | −2.16987 | + | 30.2224i | −0.0724904 | + | 1.00966i | ||||
\(897\) | 3.58846 | + | 2.07180i | 0.119815 | + | 0.0691753i | ||||
\(898\) | −12.3301 | − | 3.30385i | −0.411462 | − | 0.110251i | ||||
\(899\) | 27.1244 | + | 46.9808i | 0.904648 | + | 1.56690i | ||||
\(900\) | −23.8923 | − | 10.2058i | −0.796410 | − | 0.340192i | ||||
\(901\) | 1.85641 | + | 1.07180i | 0.0618459 | + | 0.0357067i | ||||
\(902\) | −0.803848 | − | 3.00000i | −0.0267652 | − | 0.0998891i | ||||
\(903\) | 2.30385 | − | 3.40192i | 0.0766672 | − | 0.113209i | ||||
\(904\) | 16.3923 | − | 9.46410i | 0.545200 | − | 0.314771i | ||||
\(905\) | −8.24871 | − | 4.12436i | −0.274196 | − | 0.137098i | ||||
\(906\) | 0.0788383 | + | 0.294229i | 0.00261923 | + | 0.00977509i | ||||
\(907\) | 7.63397 | + | 7.63397i | 0.253482 | + | 0.253482i | 0.822397 | − | 0.568915i | \(-0.192637\pi\) |
−0.568915 | + | 0.822397i | \(0.692637\pi\) | |||||||
\(908\) | 41.6147 | − | 11.1506i | 1.38103 | − | 0.370047i | ||||
\(909\) | 0.696152 | + | 0.401924i | 0.0230899 | + | 0.0133310i | ||||
\(910\) | −0.810889 | − | 0.830127i | −0.0268807 | − | 0.0275184i | ||||
\(911\) | −2.36603 | + | 4.09808i | −0.0783899 | + | 0.135775i | −0.902555 | − | 0.430574i | \(-0.858311\pi\) |
0.824165 | + | 0.566349i | \(0.191645\pi\) | |||||||
\(912\) | 2.70577 | − | 1.56218i | 0.0895970 | − | 0.0517289i | ||||
\(913\) | 19.9282 | − | 5.33975i | 0.659527 | − | 0.176720i | ||||
\(914\) | −9.54294 | − | 5.50962i | −0.315652 | − | 0.182242i | ||||
\(915\) | 23.3205 | + | 35.3205i | 0.770952 | + | 1.16766i | ||||
\(916\) | 33.9904 | + | 19.6244i | 1.12307 | + | 0.648407i | ||||
\(917\) | −49.1769 | + | 9.46410i | −1.62396 | + | 0.312532i | ||||
\(918\) | 4.82309 | + | 2.78461i | 0.159186 | + | 0.0919058i | ||||
\(919\) | 10.9019 | + | 6.29423i | 0.359621 | + | 0.207627i | 0.668915 | − | 0.743339i | \(-0.266759\pi\) |
−0.309293 | + | 0.950967i | \(0.600092\pi\) | |||||||
\(920\) | 24.3923 | + | 12.1962i | 0.804190 | + | 0.402095i | ||||
\(921\) | −2.30385 | + | 8.59808i | −0.0759144 | + | 0.283316i | ||||
\(922\) | 10.2417 | − | 10.2417i | 0.337291 | − | 0.337291i | ||||
\(923\) | −0.124356 | + | 0.464102i | −0.00409322 | + | 0.0152761i | ||||
\(924\) | −3.00000 | − | 15.5885i | −0.0986928 | − | 0.512823i | ||||
\(925\) | −35.9545 | − | 28.2224i | −1.18218 | − | 0.927948i | ||||
\(926\) | 5.66987 | − | 9.82051i | 0.186324 | − | 0.322722i | ||||
\(927\) | −18.9904 | + | 5.08846i | −0.623726 | + | 0.167127i | ||||
\(928\) | −49.2846 | − | 13.2058i | −1.61785 | − | 0.433501i | ||||
\(929\) | 4.89230 | + | 8.47372i | 0.160511 | + | 0.278014i | 0.935052 | − | 0.354510i | \(-0.115352\pi\) |
−0.774541 | + | 0.632524i | \(0.782019\pi\) | |||||||
\(930\) | −8.19615 | − | 7.26795i | −0.268762 | − | 0.238325i | ||||
\(931\) | −0.732051 | + | 5.07180i | −0.0239920 | + | 0.166221i | ||||
\(932\) | −9.58846 | + | 35.7846i | −0.314080 | + | 1.17216i | ||||
\(933\) | −29.6603 | −0.971033 | ||||||||
\(934\) | −5.00000 | −0.163605 | ||||||||
\(935\) | −6.14359 | + | 6.92820i | −0.200917 | + | 0.226576i | ||||
\(936\) | 2.19615 | 0.0717835 | ||||||||
\(937\) | 12.4641 | − | 12.4641i | 0.407184 | − | 0.407184i | −0.473571 | − | 0.880756i | \(-0.657035\pi\) |
0.880756 | + | 0.473571i | \(0.157035\pi\) | |||||||
\(938\) | −4.68653 | + | 0.901924i | −0.153021 | + | 0.0294489i | ||||
\(939\) | −14.1962 | − | 52.9808i | −0.463274 | − | 1.72896i | ||||
\(940\) | −18.8827 | + | 6.29423i | −0.615885 | + | 0.205295i | ||||
\(941\) | −26.8923 | − | 15.5263i | −0.876664 | − | 0.506142i | −0.00710703 | − | 0.999975i | \(-0.502262\pi\) |
−0.869557 | + | 0.493833i | \(0.835596\pi\) | |||||||
\(942\) | −3.50962 | + | 2.02628i | −0.114350 | + | 0.0660198i | ||||
\(943\) | −4.90192 | + | 18.2942i | −0.159629 | + | 0.595742i | ||||
\(944\) | −22.4833 | −0.731770 | ||||||||
\(945\) | −8.30385 | + | 29.5981i | −0.270124 | + | 0.962825i | ||||
\(946\) | 0.928203 | 0.0301785 | ||||||||
\(947\) | 1.83013 | − | 6.83013i | 0.0594711 | − | 0.221949i | −0.929794 | − | 0.368080i | \(-0.880015\pi\) |
0.989265 | + | 0.146131i | \(0.0466820\pi\) | |||||||
\(948\) | −29.7846 | + | 17.1962i | −0.967359 | + | 0.558505i | ||||
\(949\) | −4.39230 | − | 2.53590i | −0.142580 | − | 0.0823187i | ||||
\(950\) | −0.267949 | + | 1.87564i | −0.00869342 | + | 0.0608539i | ||||
\(951\) | −0.973721 | − | 3.63397i | −0.0315751 | − | 0.117840i | ||||
\(952\) | −6.92820 | − | 8.00000i | −0.224544 | − | 0.259281i | ||||
\(953\) | −16.0526 | + | 16.0526i | −0.519993 | + | 0.519993i | −0.917569 | − | 0.397576i | \(-0.869852\pi\) |
0.397576 | + | 0.917569i | \(0.369852\pi\) | |||||||
\(954\) | 0.803848 | + | 1.39230i | 0.0260255 | + | 0.0450775i | ||||
\(955\) | −45.0788 | + | 2.70577i | −1.45872 | + | 0.0875567i | ||||
\(956\) | 3.46410 | 0.112037 | ||||||||
\(957\) | 34.3923 | 1.11175 | ||||||||
\(958\) | −2.77757 | + | 10.3660i | −0.0897392 | + | 0.334911i | ||||
\(959\) | −2.09808 | + | 3.09808i | −0.0677504 | + | 0.100042i | ||||
\(960\) | −8.76795 | + | 0.526279i | −0.282984 | + | 0.0169856i | ||||
\(961\) | −0.571797 | − | 0.990381i | −0.0184451 | − | 0.0319478i | ||||
\(962\) | 1.73205 | + | 0.464102i | 0.0558436 | + | 0.0149632i | ||||
\(963\) | 7.28461 | − | 27.1865i | 0.234743 | − | 0.876074i | ||||
\(964\) | −13.4545 | + | 23.3038i | −0.433340 | + | 0.750566i | ||||
\(965\) | 31.5885 | + | 6.46410i | 1.01687 | + | 0.208087i | ||||
\(966\) | 4.90192 | − | 14.1506i | 0.157717 | − | 0.455289i | ||||
\(967\) | 6.07884 | − | 22.6865i | 0.195482 | − | 0.729550i | −0.796659 | − | 0.604429i | \(-0.793401\pi\) |
0.992141 | − | 0.125121i | \(-0.0399319\pi\) | |||||||
\(968\) | −9.56218 | + | 9.56218i | −0.307340 | + | 0.307340i | ||||
\(969\) | −0.679492 | + | 2.53590i | −0.0218284 | + | 0.0814648i | ||||
\(970\) | −4.87564 | + | 9.75129i | −0.156548 | + | 0.313095i | ||||
\(971\) | 16.2224 | + | 9.36603i | 0.520603 | + | 0.300570i | 0.737181 | − | 0.675695i | \(-0.236156\pi\) |
−0.216579 | + | 0.976265i | \(0.569490\pi\) | |||||||
\(972\) | −13.5000 | − | 23.3827i | −0.433013 | − | 0.750000i | ||||
\(973\) | 37.1769 | − | 32.1962i | 1.19184 | − | 1.03216i | ||||
\(974\) | 12.5429 | + | 7.24167i | 0.401902 | + | 0.232038i | ||||
\(975\) | 2.02628 | − | 2.58142i | 0.0648929 | − | 0.0826715i | ||||
\(976\) | 23.3205 | + | 13.4641i | 0.746471 | + | 0.430975i | ||||
\(977\) | 24.3205 | − | 6.51666i | 0.778082 | − | 0.208486i | 0.152143 | − | 0.988358i | \(-0.451383\pi\) |
0.625939 | + | 0.779872i | \(0.284716\pi\) | |||||||
\(978\) | −18.8827 | + | 10.9019i | −0.603802 | + | 0.348605i | ||||
\(979\) | 1.07180 | − | 1.85641i | 0.0342548 | − | 0.0593310i | ||||
\(980\) | 15.4641 | − | 22.2679i | 0.493983 | − | 0.711324i | ||||
\(981\) | − | 29.1962i | − | 0.932161i | ||||||
\(982\) | −7.29423 | + | 1.95448i | −0.232768 | + | 0.0623700i | ||||
\(983\) | 40.0263 | + | 40.0263i | 1.27664 | + | 1.27664i | 0.942536 | + | 0.334104i | \(0.108434\pi\) |
0.334104 | + | 0.942536i | \(0.391566\pi\) | |||||||
\(984\) | 2.59808 | + | 9.69615i | 0.0828236 | + | 0.309102i | ||||
\(985\) | −12.0000 | + | 4.00000i | −0.382352 | + | 0.127451i | ||||
\(986\) | 9.21539 | − | 5.32051i | 0.293478 | − | 0.169439i | ||||
\(987\) | 10.2846 | + | 21.1865i | 0.327363 | + | 0.674375i | ||||
\(988\) | 0.124356 | + | 0.464102i | 0.00395628 | + | 0.0147650i | ||||
\(989\) | −4.90192 | − | 2.83013i | −0.155872 | − | 0.0899928i | ||||
\(990\) | −6.58846 | + | 2.19615i | −0.209395 | + | 0.0697983i | ||||
\(991\) | 4.00000 | + | 6.92820i | 0.127064 | + | 0.220082i | 0.922538 | − | 0.385906i | \(-0.126111\pi\) |
−0.795474 | + | 0.605988i | \(0.792778\pi\) | |||||||
\(992\) | −27.1244 | − | 7.26795i | −0.861199 | − | 0.230758i | ||||
\(993\) | 9.00000 | + | 5.19615i | 0.285606 | + | 0.164895i | ||||
\(994\) | 1.73205 | + | 0.124356i | 0.0549373 | + | 0.00394432i | ||||
\(995\) | 36.5885 | − | 2.19615i | 1.15993 | − | 0.0696227i | ||||
\(996\) | −29.8923 | + | 8.00962i | −0.947174 | + | 0.253794i | ||||
\(997\) | 24.8038 | − | 24.8038i | 0.785546 | − | 0.785546i | −0.195215 | − | 0.980761i | \(-0.562540\pi\) |
0.980761 | + | 0.195215i | \(0.0625404\pi\) | |||||||
\(998\) | 19.1962 | + | 5.14359i | 0.607644 | + | 0.162818i | ||||
\(999\) | −12.2942 | − | 45.8827i | −0.388972 | − | 1.45166i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.2.cg.d.187.1 | yes | 4 | |
3.2 | odd | 2 | 945.2.cj.b.397.1 | 4 | |||
5.3 | odd | 4 | 315.2.cg.b.313.1 | yes | 4 | ||
7.3 | odd | 6 | 315.2.bs.d.52.1 | yes | 4 | ||
9.4 | even | 3 | 315.2.bs.a.292.1 | yes | 4 | ||
9.5 | odd | 6 | 945.2.bv.b.712.1 | 4 | |||
15.8 | even | 4 | 945.2.cj.c.208.1 | 4 | |||
21.17 | even | 6 | 945.2.bv.c.262.1 | 4 | |||
35.3 | even | 12 | 315.2.bs.a.178.1 | ✓ | 4 | ||
45.13 | odd | 12 | 315.2.bs.d.103.1 | yes | 4 | ||
45.23 | even | 12 | 945.2.bv.c.523.1 | 4 | |||
63.31 | odd | 6 | 315.2.cg.b.157.1 | yes | 4 | ||
63.59 | even | 6 | 945.2.cj.c.577.1 | 4 | |||
105.38 | odd | 12 | 945.2.bv.b.73.1 | 4 | |||
315.248 | odd | 12 | 945.2.cj.b.388.1 | 4 | |||
315.283 | even | 12 | inner | 315.2.cg.d.283.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bs.a.178.1 | ✓ | 4 | 35.3 | even | 12 | ||
315.2.bs.a.292.1 | yes | 4 | 9.4 | even | 3 | ||
315.2.bs.d.52.1 | yes | 4 | 7.3 | odd | 6 | ||
315.2.bs.d.103.1 | yes | 4 | 45.13 | odd | 12 | ||
315.2.cg.b.157.1 | yes | 4 | 63.31 | odd | 6 | ||
315.2.cg.b.313.1 | yes | 4 | 5.3 | odd | 4 | ||
315.2.cg.d.187.1 | yes | 4 | 1.1 | even | 1 | trivial | |
315.2.cg.d.283.1 | yes | 4 | 315.283 | even | 12 | inner | |
945.2.bv.b.73.1 | 4 | 105.38 | odd | 12 | |||
945.2.bv.b.712.1 | 4 | 9.5 | odd | 6 | |||
945.2.bv.c.262.1 | 4 | 21.17 | even | 6 | |||
945.2.bv.c.523.1 | 4 | 45.23 | even | 12 | |||
945.2.cj.b.388.1 | 4 | 315.248 | odd | 12 | |||
945.2.cj.b.397.1 | 4 | 3.2 | odd | 2 | |||
945.2.cj.c.208.1 | 4 | 15.8 | even | 4 | |||
945.2.cj.c.577.1 | 4 | 63.59 | even | 6 |