Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(106,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.i (of order \(3\), degree \(2\), 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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 2 x^{10} - x^{9} - 4 x^{8} + 20 x^{7} - 38 x^{6} + 60 x^{5} - 36 x^{4} - 27 x^{3} + 162 x^{2} - 243 x + 729 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.5 | ||
Root | \(1.65373 + 0.514941i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.211 |
Dual form | 315.2.i.e.106.5 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.09108 | + | 1.88981i | 0.771511 | + | 1.33630i | 0.936735 | + | 0.350040i | \(0.113832\pi\) |
−0.165224 | + | 0.986256i | \(0.552835\pi\) | |||||||
\(3\) | 1.65373 | − | 0.514941i | 0.954784 | − | 0.297301i | ||||
\(4\) | −1.38091 | + | 2.39181i | −0.690457 | + | 1.19591i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 2.77750 | + | 2.56340i | 1.13391 | + | 1.04650i | ||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | −1.66244 | −0.587760 | ||||||||
\(9\) | 2.46967 | − | 1.70315i | 0.823224 | − | 0.567717i | ||||
\(10\) | 2.18216 | 0.690060 | ||||||||
\(11\) | 0.754827 | + | 1.30740i | 0.227589 | + | 0.394196i | 0.957093 | − | 0.289781i | \(-0.0935824\pi\) |
−0.729504 | + | 0.683976i | \(0.760249\pi\) | |||||||
\(12\) | −1.05202 | + | 4.66651i | −0.303692 | + | 1.34711i | ||||
\(13\) | −1.12609 | + | 1.95044i | −0.312321 | + | 0.540955i | −0.978864 | − | 0.204511i | \(-0.934440\pi\) |
0.666544 | + | 0.745466i | \(0.267773\pi\) | |||||||
\(14\) | 1.09108 | − | 1.88981i | 0.291604 | − | 0.505072i | ||||
\(15\) | 0.380915 | − | 1.68965i | 0.0983518 | − | 0.436265i | ||||
\(16\) | 0.947978 | + | 1.64195i | 0.236995 | + | 0.410487i | ||||
\(17\) | −6.96525 | −1.68932 | −0.844661 | − | 0.535301i | \(-0.820198\pi\) | ||||
−0.844661 | + | 0.535301i | \(0.820198\pi\) | |||||||
\(18\) | 5.91324 | + | 2.80893i | 1.39376 | + | 0.662070i | ||||
\(19\) | −5.73716 | −1.31619 | −0.658097 | − | 0.752933i | \(-0.728638\pi\) | ||||
−0.658097 | + | 0.752933i | \(0.728638\pi\) | |||||||
\(20\) | 1.38091 | + | 2.39181i | 0.308782 | + | 0.534826i | ||||
\(21\) | −1.27282 | − | 1.17470i | −0.277752 | − | 0.256342i | ||||
\(22\) | −1.64715 | + | 2.85296i | −0.351175 | + | 0.608252i | ||||
\(23\) | 2.03268 | − | 3.52071i | 0.423844 | − | 0.734119i | −0.572468 | − | 0.819927i | \(-0.694014\pi\) |
0.996312 | + | 0.0858084i | \(0.0273473\pi\) | |||||||
\(24\) | −2.74923 | + | 0.856056i | −0.561183 | + | 0.174742i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −4.91461 | −0.963834 | ||||||||
\(27\) | 3.20716 | − | 4.08829i | 0.617217 | − | 0.786793i | ||||
\(28\) | 2.76183 | 0.521937 | ||||||||
\(29\) | −2.65373 | − | 4.59640i | −0.492786 | − | 0.853530i | 0.507179 | − | 0.861840i | \(-0.330688\pi\) |
−0.999965 | + | 0.00831007i | \(0.997355\pi\) | |||||||
\(30\) | 3.60871 | − | 1.12368i | 0.658858 | − | 0.205156i | ||||
\(31\) | −1.40659 | + | 2.43629i | −0.252632 | + | 0.437571i | −0.964250 | − | 0.264996i | \(-0.914629\pi\) |
0.711618 | + | 0.702567i | \(0.247963\pi\) | |||||||
\(32\) | −3.73108 | + | 6.46242i | −0.659568 | + | 1.14240i | ||||
\(33\) | 1.92152 | + | 1.77340i | 0.334493 | + | 0.308709i | ||||
\(34\) | −7.59966 | − | 13.1630i | −1.30333 | − | 2.25743i | ||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0.663217 | + | 8.25890i | 0.110536 | + | 1.37648i | ||||
\(37\) | 11.6509 | 1.91540 | 0.957700 | − | 0.287770i | \(-0.0929138\pi\) | ||||
0.957700 | + | 0.287770i | \(0.0929138\pi\) | |||||||
\(38\) | −6.25970 | − | 10.8421i | −1.01546 | − | 1.75882i | ||||
\(39\) | −0.857887 | + | 3.80538i | −0.137372 | + | 0.609348i | ||||
\(40\) | −0.831218 | + | 1.43971i | −0.131427 | + | 0.227638i | ||||
\(41\) | 0.815937 | − | 1.41324i | 0.127428 | − | 0.220712i | −0.795251 | − | 0.606280i | \(-0.792661\pi\) |
0.922679 | + | 0.385568i | \(0.125994\pi\) | |||||||
\(42\) | 0.831218 | − | 3.68708i | 0.128260 | − | 0.568929i | ||||
\(43\) | 0.539685 | + | 0.934761i | 0.0823011 | + | 0.142550i | 0.904238 | − | 0.427029i | \(-0.140440\pi\) |
−0.821937 | + | 0.569579i | \(0.807106\pi\) | |||||||
\(44\) | −4.16941 | −0.628562 | ||||||||
\(45\) | −0.240137 | − | 2.99037i | −0.0357975 | − | 0.445779i | ||||
\(46\) | 8.87128 | 1.30800 | ||||||||
\(47\) | −2.18138 | − | 3.77826i | −0.318187 | − | 0.551116i | 0.661923 | − | 0.749572i | \(-0.269741\pi\) |
−0.980110 | + | 0.198456i | \(0.936407\pi\) | |||||||
\(48\) | 2.41321 | + | 2.22719i | 0.348317 | + | 0.321467i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 1.09108 | − | 1.88981i | 0.154302 | − | 0.267259i | ||||
\(51\) | −11.5187 | + | 3.58670i | −1.61294 | + | 0.502238i | ||||
\(52\) | −3.11006 | − | 5.38679i | −0.431288 | − | 0.747013i | ||||
\(53\) | −10.2968 | −1.41437 | −0.707187 | − | 0.707027i | \(-0.750036\pi\) | ||||
−0.707187 | + | 0.707027i | \(0.750036\pi\) | |||||||
\(54\) | 11.2254 | + | 1.60025i | 1.52758 | + | 0.217766i | ||||
\(55\) | 1.50965 | 0.203562 | ||||||||
\(56\) | 0.831218 | + | 1.43971i | 0.111076 | + | 0.192389i | ||||
\(57\) | −9.48773 | + | 2.95430i | −1.25668 | + | 0.391306i | ||||
\(58\) | 5.79088 | − | 10.0301i | 0.760379 | − | 1.31702i | ||||
\(59\) | −2.65183 | + | 4.59311i | −0.345239 | + | 0.597972i | −0.985397 | − | 0.170271i | \(-0.945536\pi\) |
0.640158 | + | 0.768243i | \(0.278869\pi\) | |||||||
\(60\) | 3.51531 | + | 3.24433i | 0.453824 | + | 0.418842i | ||||
\(61\) | 2.28577 | + | 3.95908i | 0.292663 | + | 0.506908i | 0.974439 | − | 0.224654i | \(-0.0721251\pi\) |
−0.681775 | + | 0.731562i | \(0.738792\pi\) | |||||||
\(62\) | −6.13883 | −0.779633 | ||||||||
\(63\) | −2.70981 | − | 1.28722i | −0.341404 | − | 0.162175i | ||||
\(64\) | −12.4917 | −1.56146 | ||||||||
\(65\) | 1.12609 | + | 1.95044i | 0.139674 | + | 0.241922i | ||||
\(66\) | −1.25485 | + | 5.56622i | −0.154462 | + | 0.685154i | ||||
\(67\) | 2.01492 | − | 3.48995i | 0.246162 | − | 0.426365i | −0.716296 | − | 0.697797i | \(-0.754164\pi\) |
0.962458 | + | 0.271432i | \(0.0874972\pi\) | |||||||
\(68\) | 9.61842 | − | 16.6596i | 1.16640 | − | 2.02027i | ||||
\(69\) | 1.54856 | − | 6.86903i | 0.186424 | − | 0.826934i | ||||
\(70\) | −1.09108 | − | 1.88981i | −0.130409 | − | 0.225875i | ||||
\(71\) | 0.400307 | 0.0475077 | 0.0237539 | − | 0.999718i | \(-0.492438\pi\) | ||||
0.0237539 | + | 0.999718i | \(0.492438\pi\) | |||||||
\(72\) | −4.10567 | + | 2.83138i | −0.483858 | + | 0.333681i | ||||
\(73\) | 14.2573 | 1.66870 | 0.834348 | − | 0.551238i | \(-0.185844\pi\) | ||||
0.834348 | + | 0.551238i | \(0.185844\pi\) | |||||||
\(74\) | 12.7121 | + | 22.0180i | 1.47775 | + | 2.55954i | ||||
\(75\) | −1.27282 | − | 1.17470i | −0.146972 | − | 0.135643i | ||||
\(76\) | 7.92252 | − | 13.7222i | 0.908776 | − | 1.57405i | ||||
\(77\) | 0.754827 | − | 1.30740i | 0.0860205 | − | 0.148992i | ||||
\(78\) | −8.12746 | + | 2.53074i | −0.920253 | + | 0.286549i | ||||
\(79\) | 7.28217 | + | 12.6131i | 0.819309 | + | 1.41908i | 0.906192 | + | 0.422866i | \(0.138976\pi\) |
−0.0868836 | + | 0.996218i | \(0.527691\pi\) | |||||||
\(80\) | 1.89596 | 0.211974 | ||||||||
\(81\) | 3.19855 | − | 8.41245i | 0.355395 | − | 0.934716i | ||||
\(82\) | 3.56101 | 0.393248 | ||||||||
\(83\) | −3.07603 | − | 5.32784i | −0.337638 | − | 0.584807i | 0.646350 | − | 0.763041i | \(-0.276295\pi\) |
−0.983988 | + | 0.178235i | \(0.942961\pi\) | |||||||
\(84\) | 4.56733 | − | 1.42218i | 0.498337 | − | 0.155173i | ||||
\(85\) | −3.48263 | + | 6.03209i | −0.377744 | + | 0.654272i | ||||
\(86\) | −1.17768 | + | 2.03980i | −0.126992 | + | 0.219957i | ||||
\(87\) | −6.75545 | − | 6.23471i | −0.724260 | − | 0.668431i | ||||
\(88\) | −1.25485 | − | 2.17347i | −0.133768 | − | 0.231692i | ||||
\(89\) | 9.94438 | 1.05410 | 0.527051 | − | 0.849834i | \(-0.323298\pi\) | ||||
0.527051 | + | 0.849834i | \(0.323298\pi\) | |||||||
\(90\) | 5.38922 | − | 3.71655i | 0.568074 | − | 0.391759i | ||||
\(91\) | 2.25218 | 0.236092 | ||||||||
\(92\) | 5.61392 | + | 9.72360i | 0.585292 | + | 1.01376i | ||||
\(93\) | −1.07159 | + | 4.75329i | −0.111118 | + | 0.492894i | ||||
\(94\) | 4.76012 | − | 8.24478i | 0.490969 | − | 0.850384i | ||||
\(95\) | −2.86858 | + | 4.96852i | −0.294310 | + | 0.509760i | ||||
\(96\) | −2.84244 | + | 12.6084i | −0.290106 | + | 1.28684i | ||||
\(97\) | −7.24949 | − | 12.5565i | −0.736074 | − | 1.27492i | −0.954250 | − | 0.299009i | \(-0.903344\pi\) |
0.218176 | − | 0.975909i | \(-0.429989\pi\) | |||||||
\(98\) | −2.18216 | −0.220432 | ||||||||
\(99\) | 4.09087 | + | 1.94326i | 0.411148 | + | 0.195305i | ||||
\(100\) | 2.76183 | 0.276183 | ||||||||
\(101\) | 4.09072 | + | 7.08534i | 0.407042 | + | 0.705018i | 0.994557 | − | 0.104196i | \(-0.0332269\pi\) |
−0.587515 | + | 0.809214i | \(0.699894\pi\) | |||||||
\(102\) | −19.3460 | − | 17.8547i | −1.91554 | − | 1.76788i | ||||
\(103\) | −4.28577 | + | 7.42318i | −0.422290 | + | 0.731428i | −0.996163 | − | 0.0875166i | \(-0.972107\pi\) |
0.573873 | + | 0.818944i | \(0.305440\pi\) | |||||||
\(104\) | 1.87205 | − | 3.24248i | 0.183569 | − | 0.317951i | ||||
\(105\) | −1.65373 | + | 0.514941i | −0.161388 | + | 0.0502531i | ||||
\(106\) | −11.2346 | − | 19.4590i | −1.09120 | − | 1.89002i | ||||
\(107\) | 4.41335 | 0.426654 | 0.213327 | − | 0.976981i | \(-0.431570\pi\) | ||||
0.213327 | + | 0.976981i | \(0.431570\pi\) | |||||||
\(108\) | 5.34963 | + | 13.3165i | 0.514769 | + | 1.28138i | ||||
\(109\) | −10.9433 | −1.04818 | −0.524088 | − | 0.851664i | \(-0.675594\pi\) | ||||
−0.524088 | + | 0.851664i | \(0.675594\pi\) | |||||||
\(110\) | 1.64715 | + | 2.85296i | 0.157050 | + | 0.272019i | ||||
\(111\) | 19.2675 | − | 5.99954i | 1.82879 | − | 0.569451i | ||||
\(112\) | 0.947978 | − | 1.64195i | 0.0895755 | − | 0.155149i | ||||
\(113\) | −1.31168 | + | 2.27190i | −0.123393 | + | 0.213722i | −0.921104 | − | 0.389318i | \(-0.872711\pi\) |
0.797711 | + | 0.603040i | \(0.206044\pi\) | |||||||
\(114\) | −15.9349 | − | 14.7066i | −1.49244 | − | 1.37740i | ||||
\(115\) | −2.03268 | − | 3.52071i | −0.189549 | − | 0.328308i | ||||
\(116\) | 14.6583 | 1.36099 | ||||||||
\(117\) | 0.540830 | + | 6.73485i | 0.0499998 | + | 0.622637i | ||||
\(118\) | −11.5735 | −1.06542 | ||||||||
\(119\) | 3.48263 | + | 6.03209i | 0.319252 | + | 0.552960i | ||||
\(120\) | −0.633246 | + | 2.80893i | −0.0578072 | + | 0.256419i | ||||
\(121\) | 4.36047 | − | 7.55256i | 0.396407 | − | 0.686596i | ||||
\(122\) | −4.98793 | + | 8.63935i | −0.451586 | + | 0.782170i | ||||
\(123\) | 0.621605 | − | 2.75729i | 0.0560482 | − | 0.248617i | ||||
\(124\) | −3.88477 | − | 6.72863i | −0.348863 | − | 0.604249i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.524017 | − | 6.52548i | −0.0466832 | − | 0.581336i | ||||
\(127\) | 1.83032 | 0.162415 | 0.0812073 | − | 0.996697i | \(-0.474122\pi\) | ||||
0.0812073 | + | 0.996697i | \(0.474122\pi\) | |||||||
\(128\) | −6.16732 | − | 10.6821i | −0.545119 | − | 0.944173i | ||||
\(129\) | 1.37384 | + | 1.26794i | 0.120960 | + | 0.111636i | ||||
\(130\) | −2.45731 | + | 4.25618i | −0.215520 | + | 0.373291i | ||||
\(131\) | 8.82154 | − | 15.2794i | 0.770741 | − | 1.33496i | −0.166416 | − | 0.986056i | \(-0.553219\pi\) |
0.937157 | − | 0.348907i | \(-0.113447\pi\) | |||||||
\(132\) | −6.89509 | + | 2.14700i | −0.600141 | + | 0.186872i | ||||
\(133\) | 2.86858 | + | 4.96852i | 0.248737 | + | 0.430826i | ||||
\(134\) | 8.79377 | 0.759666 | ||||||||
\(135\) | −1.93699 | − | 4.82163i | −0.166709 | − | 0.414979i | ||||
\(136\) | 11.5793 | 0.992915 | ||||||||
\(137\) | −8.21586 | − | 14.2303i | −0.701928 | − | 1.21578i | −0.967789 | − | 0.251764i | \(-0.918989\pi\) |
0.265860 | − | 0.964012i | \(-0.414344\pi\) | |||||||
\(138\) | 14.6707 | − | 4.56819i | 1.24886 | − | 0.388870i | ||||
\(139\) | −8.16323 | + | 14.1391i | −0.692396 | + | 1.19926i | 0.278655 | + | 0.960391i | \(0.410111\pi\) |
−0.971051 | + | 0.238873i | \(0.923222\pi\) | |||||||
\(140\) | 1.38091 | − | 2.39181i | 0.116709 | − | 0.202145i | ||||
\(141\) | −5.55300 | − | 5.12496i | −0.467647 | − | 0.431599i | ||||
\(142\) | 0.436767 | + | 0.756503i | 0.0366527 | + | 0.0634844i | ||||
\(143\) | −3.40001 | −0.284323 | ||||||||
\(144\) | 5.13768 | + | 2.44052i | 0.428140 | + | 0.203376i | ||||
\(145\) | −5.30747 | −0.440761 | ||||||||
\(146\) | 15.5559 | + | 26.9436i | 1.28742 | + | 2.22987i | ||||
\(147\) | −0.380915 | + | 1.68965i | −0.0314173 | + | 0.139360i | ||||
\(148\) | −16.0889 | + | 27.8668i | −1.32250 | + | 2.29064i | ||||
\(149\) | −7.65407 | + | 13.2572i | −0.627046 | + | 1.08607i | 0.361096 | + | 0.932529i | \(0.382403\pi\) |
−0.988141 | + | 0.153546i | \(0.950931\pi\) | |||||||
\(150\) | 0.831218 | − | 3.68708i | 0.0678686 | − | 0.301049i | ||||
\(151\) | 6.59239 | + | 11.4184i | 0.536481 | + | 0.929213i | 0.999090 | + | 0.0426501i | \(0.0135801\pi\) |
−0.462609 | + | 0.886562i | \(0.653087\pi\) | |||||||
\(152\) | 9.53765 | 0.773606 | ||||||||
\(153\) | −17.2019 | + | 11.8629i | −1.39069 | + | 0.959057i | ||||
\(154\) | 3.29431 | 0.265463 | ||||||||
\(155\) | 1.40659 | + | 2.43629i | 0.112980 | + | 0.195688i | ||||
\(156\) | −7.91709 | − | 7.30681i | −0.633875 | − | 0.585013i | ||||
\(157\) | −4.56785 | + | 7.91174i | −0.364554 | + | 0.631426i | −0.988704 | − | 0.149878i | \(-0.952112\pi\) |
0.624151 | + | 0.781304i | \(0.285445\pi\) | |||||||
\(158\) | −15.8909 | + | 27.5238i | −1.26421 | + | 2.18968i | ||||
\(159\) | −17.0282 | + | 5.30225i | −1.35042 | + | 0.420495i | ||||
\(160\) | 3.73108 | + | 6.46242i | 0.294968 | + | 0.510899i | ||||
\(161\) | −4.06536 | −0.320396 | ||||||||
\(162\) | 19.3878 | − | 3.13401i | 1.52325 | − | 0.246231i | ||||
\(163\) | −4.25754 | −0.333476 | −0.166738 | − | 0.986001i | \(-0.553323\pi\) | ||||
−0.166738 | + | 0.986001i | \(0.553323\pi\) | |||||||
\(164\) | 2.25348 | + | 3.90314i | 0.175967 | + | 0.304784i | ||||
\(165\) | 2.49657 | − | 0.777383i | 0.194357 | − | 0.0605192i | ||||
\(166\) | 6.71240 | − | 11.6262i | 0.520983 | − | 0.902369i | ||||
\(167\) | −4.55777 | + | 7.89429i | −0.352691 | + | 0.610879i | −0.986720 | − | 0.162430i | \(-0.948067\pi\) |
0.634029 | + | 0.773309i | \(0.281400\pi\) | |||||||
\(168\) | 2.11598 | + | 1.95287i | 0.163251 | + | 0.150667i | ||||
\(169\) | 3.96385 | + | 6.86560i | 0.304912 | + | 0.528123i | ||||
\(170\) | −15.1993 | −1.16573 | ||||||||
\(171\) | −14.1689 | + | 9.77124i | −1.08352 | + | 0.747226i | ||||
\(172\) | −2.98103 | −0.227302 | ||||||||
\(173\) | −4.72807 | − | 8.18925i | −0.359468 | − | 0.622617i | 0.628404 | − | 0.777887i | \(-0.283709\pi\) |
−0.987872 | + | 0.155270i | \(0.950375\pi\) | |||||||
\(174\) | 4.41166 | − | 19.5691i | 0.334447 | − | 1.48353i | ||||
\(175\) | −0.500000 | + | 0.866025i | −0.0377964 | + | 0.0654654i | ||||
\(176\) | −1.43112 | + | 2.47877i | −0.107875 | + | 0.186844i | ||||
\(177\) | −2.02024 | + | 8.96132i | −0.151851 | + | 0.673574i | ||||
\(178\) | 10.8501 | + | 18.7930i | 0.813251 | + | 1.40859i | ||||
\(179\) | −12.0166 | −0.898164 | −0.449082 | − | 0.893491i | \(-0.648249\pi\) | ||||
−0.449082 | + | 0.893491i | \(0.648249\pi\) | |||||||
\(180\) | 7.48403 | + | 3.55509i | 0.557826 | + | 0.264981i | ||||
\(181\) | 16.2695 | 1.20930 | 0.604652 | − | 0.796490i | \(-0.293312\pi\) | ||||
0.604652 | + | 0.796490i | \(0.293312\pi\) | |||||||
\(182\) | 2.45731 | + | 4.25618i | 0.182148 | + | 0.315489i | ||||
\(183\) | 5.81876 | + | 5.37022i | 0.430135 | + | 0.396978i | ||||
\(184\) | −3.37920 | + | 5.85295i | −0.249118 | + | 0.431485i | ||||
\(185\) | 5.82546 | − | 10.0900i | 0.428296 | − | 0.741831i | ||||
\(186\) | −10.1520 | + | 3.16114i | −0.744381 | + | 0.231786i | ||||
\(187\) | −5.25756 | − | 9.10637i | −0.384471 | − | 0.665923i | ||||
\(188\) | 12.0492 | 0.878778 | ||||||||
\(189\) | −5.14414 | − | 0.733331i | −0.374181 | − | 0.0533420i | ||||
\(190\) | −12.5194 | −0.908253 | ||||||||
\(191\) | 0.805501 | + | 1.39517i | 0.0582840 | + | 0.100951i | 0.893695 | − | 0.448675i | \(-0.148104\pi\) |
−0.835411 | + | 0.549625i | \(0.814770\pi\) | |||||||
\(192\) | −20.6580 | + | 6.43250i | −1.49086 | + | 0.464226i | ||||
\(193\) | 6.93614 | − | 12.0137i | 0.499274 | − | 0.864768i | −0.500726 | − | 0.865606i | \(-0.666933\pi\) |
1.00000 | 0.000838059i | \(0.000266763\pi\) | ||||||||
\(194\) | 15.8196 | − | 27.4003i | 1.13578 | − | 1.96723i | ||||
\(195\) | 2.86661 | + | 2.64564i | 0.205282 | + | 0.189458i | ||||
\(196\) | −1.38091 | − | 2.39181i | −0.0986368 | − | 0.170844i | ||||
\(197\) | 26.5726 | 1.89322 | 0.946609 | − | 0.322383i | \(-0.104484\pi\) | ||||
0.946609 | + | 0.322383i | \(0.104484\pi\) | |||||||
\(198\) | 0.791085 | + | 9.85122i | 0.0562200 | + | 0.700096i | ||||
\(199\) | 1.74626 | 0.123789 | 0.0618946 | − | 0.998083i | \(-0.480286\pi\) | ||||
0.0618946 | + | 0.998083i | \(0.480286\pi\) | |||||||
\(200\) | 0.831218 | + | 1.43971i | 0.0587760 | + | 0.101803i | ||||
\(201\) | 1.53503 | − | 6.80901i | 0.108272 | − | 0.480271i | ||||
\(202\) | −8.92662 | + | 15.4614i | −0.628075 | + | 1.08786i | ||||
\(203\) | −2.65373 | + | 4.59640i | −0.186256 | + | 0.322604i | ||||
\(204\) | 7.32760 | − | 32.5035i | 0.513034 | − | 2.27570i | ||||
\(205\) | −0.815937 | − | 1.41324i | −0.0569875 | − | 0.0987053i | ||||
\(206\) | −18.7045 | −1.30320 | ||||||||
\(207\) | −0.976243 | − | 12.1570i | −0.0678536 | − | 0.844967i | ||||
\(208\) | −4.27003 | −0.296073 | ||||||||
\(209\) | −4.33056 | − | 7.50075i | −0.299551 | − | 0.518838i | ||||
\(210\) | −2.77750 | − | 2.56340i | −0.191666 | − | 0.176891i | ||||
\(211\) | −9.32245 | + | 16.1470i | −0.641784 | + | 1.11160i | 0.343250 | + | 0.939244i | \(0.388472\pi\) |
−0.985034 | + | 0.172359i | \(0.944861\pi\) | |||||||
\(212\) | 14.2190 | − | 24.6280i | 0.976565 | − | 1.69146i | ||||
\(213\) | 0.662001 | − | 0.206135i | 0.0453596 | − | 0.0141241i | ||||
\(214\) | 4.81532 | + | 8.34037i | 0.329168 | + | 0.570136i | ||||
\(215\) | 1.07937 | 0.0736124 | ||||||||
\(216\) | −5.33169 | + | 6.79652i | −0.362775 | + | 0.462445i | ||||
\(217\) | 2.81319 | 0.190972 | ||||||||
\(218\) | −11.9400 | − | 20.6807i | −0.808679 | − | 1.40067i | ||||
\(219\) | 23.5779 | − | 7.34169i | 1.59324 | − | 0.496106i | ||||
\(220\) | −2.08470 | + | 3.61081i | −0.140551 | + | 0.243441i | ||||
\(221\) | 7.84349 | − | 13.5853i | 0.527610 | − | 0.913847i | ||||
\(222\) | 32.3604 | + | 29.8659i | 2.17189 | + | 2.00447i | ||||
\(223\) | 10.3101 | + | 17.8576i | 0.690417 | + | 1.19584i | 0.971701 | + | 0.236212i | \(0.0759061\pi\) |
−0.281285 | + | 0.959624i | \(0.590761\pi\) | |||||||
\(224\) | 7.46215 | 0.498586 | ||||||||
\(225\) | −2.70981 | − | 1.28722i | −0.180654 | − | 0.0858148i | ||||
\(226\) | −5.72461 | −0.380795 | ||||||||
\(227\) | −9.97409 | − | 17.2756i | −0.662003 | − | 1.14662i | −0.980088 | − | 0.198561i | \(-0.936373\pi\) |
0.318085 | − | 0.948062i | \(-0.396960\pi\) | |||||||
\(228\) | 6.03561 | − | 26.7725i | 0.399718 | − | 1.77305i | ||||
\(229\) | 2.26958 | − | 3.93103i | 0.149978 | − | 0.259770i | −0.781241 | − | 0.624230i | \(-0.785413\pi\) |
0.931219 | + | 0.364460i | \(0.118746\pi\) | |||||||
\(230\) | 4.43564 | − | 7.68276i | 0.292478 | − | 0.506586i | ||||
\(231\) | 0.575050 | − | 2.55078i | 0.0378355 | − | 0.167829i | ||||
\(232\) | 4.41166 | + | 7.64122i | 0.289640 | + | 0.501671i | ||||
\(233\) | 13.5757 | 0.889375 | 0.444688 | − | 0.895686i | \(-0.353315\pi\) | ||||
0.444688 | + | 0.895686i | \(0.353315\pi\) | |||||||
\(234\) | −12.1375 | + | 8.37033i | −0.793451 | + | 0.547185i | ||||
\(235\) | −4.36276 | −0.284595 | ||||||||
\(236\) | −7.32391 | − | 12.6854i | −0.476746 | − | 0.825748i | ||||
\(237\) | 18.5378 | + | 17.1088i | 1.20416 | + | 1.11134i | ||||
\(238\) | −7.59966 | + | 13.1630i | −0.492612 | + | 0.853230i | ||||
\(239\) | −14.1388 | + | 24.4891i | −0.914564 | + | 1.58407i | −0.107025 | + | 0.994256i | \(0.534132\pi\) |
−0.807539 | + | 0.589814i | \(0.799201\pi\) | |||||||
\(240\) | 3.13541 | − | 0.976306i | 0.202390 | − | 0.0630203i | ||||
\(241\) | 3.10501 | + | 5.37804i | 0.200012 | + | 0.346430i | 0.948532 | − | 0.316682i | \(-0.102569\pi\) |
−0.748520 | + | 0.663112i | \(0.769235\pi\) | |||||||
\(242\) | 19.0305 | 1.22333 | ||||||||
\(243\) | 0.957636 | − | 15.5590i | 0.0614324 | − | 0.998111i | ||||
\(244\) | −12.6258 | −0.808287 | ||||||||
\(245\) | 0.500000 | + | 0.866025i | 0.0319438 | + | 0.0553283i | ||||
\(246\) | 5.88897 | − | 1.83371i | 0.375467 | − | 0.116913i | ||||
\(247\) | 6.46054 | − | 11.1900i | 0.411074 | − | 0.712002i | ||||
\(248\) | 2.33837 | − | 4.05018i | 0.148487 | − | 0.257187i | ||||
\(249\) | −7.83046 | − | 7.22686i | −0.496236 | − | 0.457984i | ||||
\(250\) | −1.09108 | − | 1.88981i | −0.0690060 | − | 0.119522i | ||||
\(251\) | 25.6455 | 1.61873 | 0.809365 | − | 0.587307i | \(-0.199812\pi\) | ||||
0.809365 | + | 0.587307i | \(0.199812\pi\) | |||||||
\(252\) | 6.82081 | − | 4.70381i | 0.429671 | − | 0.296312i | ||||
\(253\) | 6.13730 | 0.385848 | ||||||||
\(254\) | 1.99703 | + | 3.45895i | 0.125305 | + | 0.217034i | ||||
\(255\) | −2.65317 | + | 11.7688i | −0.166148 | + | 0.736992i | ||||
\(256\) | 0.966365 | − | 1.67379i | 0.0603978 | − | 0.104612i | ||||
\(257\) | 4.79108 | − | 8.29839i | 0.298859 | − | 0.517639i | −0.677016 | − | 0.735968i | \(-0.736727\pi\) |
0.975875 | + | 0.218329i | \(0.0700606\pi\) | |||||||
\(258\) | −0.897191 | + | 3.97972i | −0.0558567 | + | 0.247767i | ||||
\(259\) | −5.82546 | − | 10.0900i | −0.361976 | − | 0.626962i | ||||
\(260\) | −6.22012 | −0.385756 | ||||||||
\(261\) | −14.3822 | − | 6.83189i | −0.890237 | − | 0.422883i | ||||
\(262\) | 38.5000 | 2.37854 | ||||||||
\(263\) | −3.53980 | − | 6.13112i | −0.218274 | − | 0.378061i | 0.736007 | − | 0.676974i | \(-0.236709\pi\) |
−0.954280 | + | 0.298913i | \(0.903376\pi\) | |||||||
\(264\) | −3.19440 | − | 2.94816i | −0.196602 | − | 0.181447i | ||||
\(265\) | −5.14840 | + | 8.91729i | −0.316264 | + | 0.547785i | ||||
\(266\) | −6.25970 | + | 10.8421i | −0.383807 | + | 0.664773i | ||||
\(267\) | 16.4454 | − | 5.12077i | 1.00644 | − | 0.313386i | ||||
\(268\) | 5.56487 | + | 9.63864i | 0.339929 | + | 0.588774i | ||||
\(269\) | 6.53680 | 0.398556 | 0.199278 | − | 0.979943i | \(-0.436140\pi\) | ||||
0.199278 | + | 0.979943i | \(0.436140\pi\) | |||||||
\(270\) | 6.99853 | − | 8.92132i | 0.425917 | − | 0.542934i | ||||
\(271\) | −9.56585 | −0.581084 | −0.290542 | − | 0.956862i | \(-0.593836\pi\) | ||||
−0.290542 | + | 0.956862i | \(0.593836\pi\) | |||||||
\(272\) | −6.60291 | − | 11.4366i | −0.400360 | − | 0.693444i | ||||
\(273\) | 3.72450 | − | 1.15974i | 0.225417 | − | 0.0701905i | ||||
\(274\) | 17.9283 | − | 31.0528i | 1.08309 | − | 1.87597i | ||||
\(275\) | 0.754827 | − | 1.30740i | 0.0455178 | − | 0.0788391i | ||||
\(276\) | 14.2910 | + | 13.1894i | 0.860218 | + | 0.793909i | ||||
\(277\) | −4.62684 | − | 8.01392i | −0.278000 | − | 0.481510i | 0.692888 | − | 0.721045i | \(-0.256338\pi\) |
−0.970888 | + | 0.239536i | \(0.923005\pi\) | |||||||
\(278\) | −35.6270 | −2.13676 | ||||||||
\(279\) | 0.675550 | + | 8.41249i | 0.0404441 | + | 0.503642i | ||||
\(280\) | 1.66244 | 0.0993495 | ||||||||
\(281\) | −5.26343 | − | 9.11652i | −0.313990 | − | 0.543846i | 0.665232 | − | 0.746636i | \(-0.268332\pi\) |
−0.979222 | + | 0.202790i | \(0.934999\pi\) | |||||||
\(282\) | 3.62640 | − | 16.0858i | 0.215949 | − | 0.957898i | ||||
\(283\) | −9.09363 | + | 15.7506i | −0.540560 | + | 0.936278i | 0.458312 | + | 0.888792i | \(0.348454\pi\) |
−0.998872 | + | 0.0474862i | \(0.984879\pi\) | |||||||
\(284\) | −0.552790 | + | 0.957460i | −0.0328021 | + | 0.0568148i | ||||
\(285\) | −2.18537 | + | 9.69376i | −0.129450 | + | 0.574209i | ||||
\(286\) | −3.70968 | − | 6.42536i | −0.219358 | − | 0.379939i | ||||
\(287\) | −1.63187 | −0.0963265 | ||||||||
\(288\) | 1.79194 | + | 22.3146i | 0.105591 | + | 1.31490i | ||||
\(289\) | 31.5148 | 1.85381 | ||||||||
\(290\) | −5.79088 | − | 10.0301i | −0.340052 | − | 0.588987i | ||||
\(291\) | −18.4546 | − | 17.0320i | −1.08183 | − | 0.998435i | ||||
\(292\) | −19.6882 | + | 34.1009i | −1.15216 | + | 1.99561i | ||||
\(293\) | 15.3521 | − | 26.5906i | 0.896879 | − | 1.55344i | 0.0654166 | − | 0.997858i | \(-0.479162\pi\) |
0.831462 | − | 0.555581i | \(-0.187504\pi\) | |||||||
\(294\) | −3.60871 | + | 1.12368i | −0.210465 | + | 0.0655346i | ||||
\(295\) | 2.65183 | + | 4.59311i | 0.154396 | + | 0.267421i | ||||
\(296\) | −19.3689 | −1.12579 | ||||||||
\(297\) | 7.76588 | + | 1.10708i | 0.450622 | + | 0.0642391i | ||||
\(298\) | −33.4048 | −1.93509 | ||||||||
\(299\) | 4.57796 | + | 7.92925i | 0.264750 | + | 0.458561i | ||||
\(300\) | 4.56733 | − | 1.42218i | 0.263695 | − | 0.0821096i | ||||
\(301\) | 0.539685 | − | 0.934761i | 0.0311069 | − | 0.0538787i | ||||
\(302\) | −14.3857 | + | 24.9167i | −0.827802 | + | 1.43379i | ||||
\(303\) | 10.4135 | + | 9.61078i | 0.598240 | + | 0.552125i | ||||
\(304\) | −5.43870 | − | 9.42010i | −0.311931 | − | 0.540280i | ||||
\(305\) | 4.57155 | 0.261766 | ||||||||
\(306\) | −41.1872 | − | 19.5649i | −2.35452 | − | 1.11845i | ||||
\(307\) | −18.2136 | −1.03951 | −0.519754 | − | 0.854316i | \(-0.673976\pi\) | ||||
−0.519754 | + | 0.854316i | \(0.673976\pi\) | |||||||
\(308\) | 2.08470 | + | 3.61081i | 0.118787 | + | 0.205745i | ||||
\(309\) | −3.26503 | + | 14.4829i | −0.185741 | + | 0.823903i | ||||
\(310\) | −3.06942 | + | 5.31639i | −0.174331 | + | 0.301950i | ||||
\(311\) | −7.66394 | + | 13.2743i | −0.434582 | + | 0.752718i | −0.997261 | − | 0.0739571i | \(-0.976437\pi\) |
0.562679 | + | 0.826675i | \(0.309771\pi\) | |||||||
\(312\) | 1.42618 | − | 6.32620i | 0.0807416 | − | 0.358150i | ||||
\(313\) | −10.6445 | − | 18.4369i | −0.601665 | − | 1.04211i | −0.992569 | − | 0.121682i | \(-0.961171\pi\) |
0.390905 | − | 0.920431i | \(-0.372162\pi\) | |||||||
\(314\) | −19.9356 | −1.12503 | ||||||||
\(315\) | −2.46967 | + | 1.70315i | −0.139150 | + | 0.0959617i | ||||
\(316\) | −40.2243 | −2.26279 | ||||||||
\(317\) | 5.97807 | + | 10.3543i | 0.335762 | + | 0.581557i | 0.983631 | − | 0.180195i | \(-0.0576729\pi\) |
−0.647869 | + | 0.761752i | \(0.724340\pi\) | |||||||
\(318\) | −28.5993 | − | 26.3948i | −1.60377 | − | 1.48015i | ||||
\(319\) | 4.00622 | − | 6.93898i | 0.224305 | − | 0.388508i | ||||
\(320\) | −6.24586 | + | 10.8181i | −0.349154 | + | 0.604752i | ||||
\(321\) | 7.29850 | − | 2.27261i | 0.407362 | − | 0.126845i | ||||
\(322\) | −4.43564 | − | 7.68276i | −0.247189 | − | 0.428143i | ||||
\(323\) | 39.9607 | 2.22348 | ||||||||
\(324\) | 15.7041 | + | 19.2672i | 0.872449 | + | 1.07040i | ||||
\(325\) | 2.25218 | 0.124928 | ||||||||
\(326\) | −4.64532 | − | 8.04593i | −0.257281 | − | 0.445623i | ||||
\(327\) | −18.0973 | + | 5.63514i | −1.00078 | + | 0.311624i | ||||
\(328\) | −1.35644 | + | 2.34943i | −0.0748970 | + | 0.129725i | ||||
\(329\) | −2.18138 | + | 3.77826i | −0.120263 | + | 0.208302i | ||||
\(330\) | 4.19306 | + | 3.86984i | 0.230820 | + | 0.213028i | ||||
\(331\) | −7.76081 | − | 13.4421i | −0.426573 | − | 0.738846i | 0.569993 | − | 0.821650i | \(-0.306946\pi\) |
−0.996566 | + | 0.0828036i | \(0.973613\pi\) | |||||||
\(332\) | 16.9910 | 0.932500 | ||||||||
\(333\) | 28.7739 | − | 19.8433i | 1.57680 | − | 1.08740i | ||||
\(334\) | −19.8916 | −1.08842 | ||||||||
\(335\) | −2.01492 | − | 3.48995i | −0.110087 | − | 0.190676i | ||||
\(336\) | 0.722198 | − | 3.20350i | 0.0393991 | − | 0.174765i | ||||
\(337\) | −2.02012 | + | 3.49895i | −0.110043 | + | 0.190600i | −0.915787 | − | 0.401663i | \(-0.868432\pi\) |
0.805744 | + | 0.592263i | \(0.201766\pi\) | |||||||
\(338\) | −8.64977 | + | 14.9818i | −0.470485 | + | 0.814905i | ||||
\(339\) | −0.999279 | + | 4.43256i | −0.0542734 | + | 0.240744i | ||||
\(340\) | −9.61842 | − | 16.6596i | −0.521632 | − | 0.903493i | ||||
\(341\) | −4.24694 | −0.229985 | ||||||||
\(342\) | −33.9252 | − | 16.1153i | −1.83446 | − | 0.871413i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −0.897191 | − | 1.55398i | −0.0483733 | − | 0.0837850i | ||||
\(345\) | −5.17447 | − | 4.77560i | −0.278584 | − | 0.257110i | ||||
\(346\) | 10.3174 | − | 17.8703i | 0.554667 | − | 0.960712i | ||||
\(347\) | 0.993330 | − | 1.72050i | 0.0533248 | − | 0.0923612i | −0.838131 | − | 0.545469i | \(-0.816351\pi\) |
0.891456 | + | 0.453108i | \(0.149685\pi\) | |||||||
\(348\) | 24.2410 | − | 7.54817i | 1.29945 | − | 0.404625i | ||||
\(349\) | 16.6038 | + | 28.7587i | 0.888783 | + | 1.53942i | 0.841316 | + | 0.540544i | \(0.181782\pi\) |
0.0474671 | + | 0.998873i | \(0.484885\pi\) | |||||||
\(350\) | −2.18216 | −0.116641 | ||||||||
\(351\) | 4.36244 | + | 10.8591i | 0.232850 | + | 0.579618i | ||||
\(352\) | −11.2653 | −0.600441 | ||||||||
\(353\) | −15.2884 | − | 26.4802i | −0.813717 | − | 1.40940i | −0.910245 | − | 0.414069i | \(-0.864107\pi\) |
0.0965280 | − | 0.995330i | \(-0.469226\pi\) | |||||||
\(354\) | −19.1394 | + | 5.95965i | −1.01725 | + | 0.316752i | ||||
\(355\) | 0.200154 | − | 0.346676i | 0.0106230 | − | 0.0183997i | ||||
\(356\) | −13.7323 | + | 23.7851i | −0.727813 | + | 1.26061i | ||||
\(357\) | 8.86551 | + | 8.18212i | 0.469212 | + | 0.433044i | ||||
\(358\) | −13.1111 | − | 22.7091i | −0.692943 | − | 1.20021i | ||||
\(359\) | −15.4672 | −0.816327 | −0.408163 | − | 0.912909i | \(-0.633831\pi\) | ||||
−0.408163 | + | 0.912909i | \(0.633831\pi\) | |||||||
\(360\) | 0.399212 | + | 4.97130i | 0.0210403 | + | 0.262011i | ||||
\(361\) | 13.9150 | 0.732366 | ||||||||
\(362\) | 17.7514 | + | 30.7463i | 0.932991 | + | 1.61599i | ||||
\(363\) | 3.32194 | − | 14.7353i | 0.174356 | − | 0.773403i | ||||
\(364\) | −3.11006 | + | 5.38679i | −0.163012 | + | 0.282344i | ||||
\(365\) | 7.12867 | − | 12.3472i | 0.373132 | − | 0.646283i | ||||
\(366\) | −3.79995 | + | 16.8557i | −0.198627 | + | 0.881060i | ||||
\(367\) | −12.7930 | − | 22.1581i | −0.667788 | − | 1.15664i | −0.978521 | − | 0.206145i | \(-0.933908\pi\) |
0.310734 | − | 0.950497i | \(-0.399425\pi\) | |||||||
\(368\) | 7.70776 | 0.401795 | ||||||||
\(369\) | −0.391873 | − | 4.87991i | −0.0204001 | − | 0.254038i | ||||
\(370\) | 25.4242 | 1.32174 | ||||||||
\(371\) | 5.14840 | + | 8.91729i | 0.267292 | + | 0.462963i | ||||
\(372\) | −9.88923 | − | 9.12693i | −0.512733 | − | 0.473209i | ||||
\(373\) | 9.53784 | − | 16.5200i | 0.493850 | − | 0.855374i | −0.506124 | − | 0.862460i | \(-0.668922\pi\) |
0.999975 | + | 0.00708638i | \(0.00225568\pi\) | |||||||
\(374\) | 11.4729 | − | 19.8716i | 0.593247 | − | 1.02753i | ||||
\(375\) | −1.65373 | + | 0.514941i | −0.0853984 | + | 0.0265914i | ||||
\(376\) | 3.62640 | + | 6.28111i | 0.187017 | + | 0.323924i | ||||
\(377\) | 11.9533 | 0.615629 | ||||||||
\(378\) | −4.22682 | − | 10.5216i | −0.217404 | − | 0.541171i | ||||
\(379\) | 0.226342 | 0.0116264 | 0.00581321 | − | 0.999983i | \(-0.498150\pi\) | ||||
0.00581321 | + | 0.999983i | \(0.498150\pi\) | |||||||
\(380\) | −7.92252 | − | 13.7222i | −0.406417 | − | 0.703935i | ||||
\(381\) | 3.02686 | − | 0.942507i | 0.155071 | − | 0.0482861i | ||||
\(382\) | −1.75773 | + | 3.04448i | −0.0899335 | + | 0.155769i | ||||
\(383\) | −16.4392 | + | 28.4735i | −0.840003 | + | 1.45493i | 0.0498884 | + | 0.998755i | \(0.484113\pi\) |
−0.889891 | + | 0.456173i | \(0.849220\pi\) | |||||||
\(384\) | −15.6998 | − | 14.4896i | −0.801175 | − | 0.739417i | ||||
\(385\) | −0.754827 | − | 1.30740i | −0.0384696 | − | 0.0666312i | ||||
\(386\) | 30.2715 | 1.54078 | ||||||||
\(387\) | 2.92488 | + | 1.38939i | 0.148680 | + | 0.0706266i | ||||
\(388\) | 40.0437 | 2.03291 | ||||||||
\(389\) | 0.919683 | + | 1.59294i | 0.0466298 | + | 0.0807651i | 0.888398 | − | 0.459074i | \(-0.151819\pi\) |
−0.841768 | + | 0.539839i | \(0.818485\pi\) | |||||||
\(390\) | −1.87205 | + | 8.30395i | −0.0947948 | + | 0.420487i | ||||
\(391\) | −14.1581 | + | 24.5226i | −0.716008 | + | 1.24016i | ||||
\(392\) | 0.831218 | − | 1.43971i | 0.0419828 | − | 0.0727164i | ||||
\(393\) | 6.72051 | − | 29.8106i | 0.339005 | − | 1.50374i | ||||
\(394\) | 28.9928 | + | 50.2171i | 1.46064 | + | 2.52990i | ||||
\(395\) | 14.5643 | 0.732812 | ||||||||
\(396\) | −10.2971 | + | 7.10113i | −0.517447 | + | 0.356845i | ||||
\(397\) | 34.5990 | 1.73647 | 0.868237 | − | 0.496150i | \(-0.165253\pi\) | ||||
0.868237 | + | 0.496150i | \(0.165253\pi\) | |||||||
\(398\) | 1.90531 | + | 3.30010i | 0.0955047 | + | 0.165419i | ||||
\(399\) | 7.30236 | + | 6.73946i | 0.365575 | + | 0.337395i | ||||
\(400\) | 0.947978 | − | 1.64195i | 0.0473989 | − | 0.0820973i | ||||
\(401\) | 1.75214 | − | 3.03479i | 0.0874977 | − | 0.151550i | −0.818955 | − | 0.573858i | \(-0.805446\pi\) |
0.906453 | + | 0.422307i | \(0.138780\pi\) | |||||||
\(402\) | 14.5426 | − | 4.52828i | 0.725317 | − | 0.225850i | ||||
\(403\) | −3.16790 | − | 5.48696i | −0.157804 | − | 0.273325i | ||||
\(404\) | −22.5958 | −1.12418 | ||||||||
\(405\) | −5.68612 | − | 6.97625i | −0.282545 | − | 0.346653i | ||||
\(406\) | −11.5818 | −0.574793 | ||||||||
\(407\) | 8.79443 | + | 15.2324i | 0.435924 | + | 0.755042i | ||||
\(408\) | 19.1491 | − | 5.96265i | 0.948019 | − | 0.295195i | ||||
\(409\) | 5.41258 | − | 9.37487i | 0.267635 | − | 0.463557i | −0.700616 | − | 0.713539i | \(-0.747091\pi\) |
0.968251 | + | 0.249982i | \(0.0804245\pi\) | |||||||
\(410\) | 1.78051 | − | 3.08393i | 0.0879330 | − | 0.152304i | ||||
\(411\) | −20.9146 | − | 19.3024i | −1.03164 | − | 0.952119i | ||||
\(412\) | −11.8366 | − | 20.5016i | −0.583146 | − | 1.01004i | ||||
\(413\) | 5.30367 | 0.260976 | ||||||||
\(414\) | 21.9092 | − | 15.1091i | 1.07678 | − | 0.742574i | ||||
\(415\) | −6.15206 | −0.301993 | ||||||||
\(416\) | −8.40304 | − | 14.5545i | −0.411993 | − | 0.713593i | ||||
\(417\) | −6.21899 | + | 27.5859i | −0.304545 | + | 1.35089i | ||||
\(418\) | 9.44998 | − | 16.3679i | 0.462214 | − | 0.800578i | ||||
\(419\) | 6.49695 | − | 11.2531i | 0.317397 | − | 0.549748i | −0.662547 | − | 0.749020i | \(-0.730525\pi\) |
0.979944 | + | 0.199273i | \(0.0638579\pi\) | |||||||
\(420\) | 1.05202 | − | 4.66651i | 0.0513334 | − | 0.227703i | ||||
\(421\) | −16.6224 | − | 28.7908i | −0.810124 | − | 1.40318i | −0.912777 | − | 0.408459i | \(-0.866066\pi\) |
0.102653 | − | 0.994717i | \(-0.467267\pi\) | |||||||
\(422\) | −40.6862 | −1.98057 | ||||||||
\(423\) | −11.8222 | − | 5.61584i | −0.574817 | − | 0.273052i | ||||
\(424\) | 17.1178 | 0.831312 | ||||||||
\(425\) | 3.48263 | + | 6.03209i | 0.168932 | + | 0.292599i | ||||
\(426\) | 1.11185 | + | 1.02615i | 0.0538694 | + | 0.0497169i | ||||
\(427\) | 2.28577 | − | 3.95908i | 0.110616 | − | 0.191593i | ||||
\(428\) | −6.09445 | + | 10.5559i | −0.294587 | + | 0.510239i | ||||
\(429\) | −5.62270 | + | 1.75080i | −0.271467 | + | 0.0845296i | ||||
\(430\) | 1.17768 | + | 2.03980i | 0.0567927 | + | 0.0983679i | ||||
\(431\) | 22.6025 | 1.08873 | 0.544363 | − | 0.838850i | \(-0.316771\pi\) | ||||
0.544363 | + | 0.838850i | \(0.316771\pi\) | |||||||
\(432\) | 9.75308 | + | 1.39036i | 0.469245 | + | 0.0668939i | ||||
\(433\) | −13.9768 | −0.671683 | −0.335842 | − | 0.941918i | \(-0.609021\pi\) | ||||
−0.335842 | + | 0.941918i | \(0.609021\pi\) | |||||||
\(434\) | 3.06942 | + | 5.31639i | 0.147337 | + | 0.255195i | ||||
\(435\) | −8.77714 | + | 2.73303i | −0.420832 | + | 0.131039i | ||||
\(436\) | 15.1117 | − | 26.1743i | 0.723721 | − | 1.25352i | ||||
\(437\) | −11.6618 | + | 20.1989i | −0.557860 | + | 0.966242i | ||||
\(438\) | 39.5997 | + | 36.5472i | 1.89215 | + | 1.74629i | ||||
\(439\) | −8.76798 | − | 15.1866i | −0.418473 | − | 0.724817i | 0.577313 | − | 0.816523i | \(-0.304101\pi\) |
−0.995786 | + | 0.0917063i | \(0.970768\pi\) | |||||||
\(440\) | −2.50970 | −0.119645 | ||||||||
\(441\) | 0.240137 | + | 2.99037i | 0.0114351 | + | 0.142399i | ||||
\(442\) | 34.2315 | 1.62823 | ||||||||
\(443\) | 15.0793 | + | 26.1182i | 0.716441 | + | 1.24091i | 0.962401 | + | 0.271632i | \(0.0875634\pi\) |
−0.245960 | + | 0.969280i | \(0.579103\pi\) | |||||||
\(444\) | −12.2570 | + | 54.3692i | −0.581692 | + | 2.58025i | ||||
\(445\) | 4.97219 | − | 8.61209i | 0.235704 | − | 0.408252i | ||||
\(446\) | −22.4983 | + | 38.9683i | −1.06533 | + | 1.84520i | ||||
\(447\) | −5.83109 | + | 25.8653i | −0.275801 | + | 1.22339i | ||||
\(448\) | 6.24586 | + | 10.8181i | 0.295089 | + | 0.511109i | ||||
\(449\) | −9.06230 | −0.427676 | −0.213838 | − | 0.976869i | \(-0.568597\pi\) | ||||
−0.213838 | + | 0.976869i | \(0.568597\pi\) | |||||||
\(450\) | −0.524017 | − | 6.52548i | −0.0247024 | − | 0.307614i | ||||
\(451\) | 2.46357 | 0.116005 | ||||||||
\(452\) | −3.62264 | − | 6.27460i | −0.170395 | − | 0.295133i | ||||
\(453\) | 16.7818 | + | 15.4882i | 0.788480 | + | 0.727700i | ||||
\(454\) | 21.7651 | − | 37.6982i | 1.02149 | − | 1.76926i | ||||
\(455\) | 1.12609 | − | 1.95044i | 0.0527918 | − | 0.0914381i | ||||
\(456\) | 15.7727 | − | 4.91133i | 0.738626 | − | 0.229994i | ||||
\(457\) | −10.2326 | − | 17.7234i | −0.478662 | − | 0.829066i | 0.521039 | − | 0.853533i | \(-0.325545\pi\) |
−0.999701 | + | 0.0244665i | \(0.992211\pi\) | |||||||
\(458\) | 9.90519 | 0.462839 | ||||||||
\(459\) | −22.3387 | + | 28.4760i | −1.04268 | + | 1.32915i | ||||
\(460\) | 11.2278 | 0.523501 | ||||||||
\(461\) | 2.29576 | + | 3.97638i | 0.106924 | + | 0.185198i | 0.914523 | − | 0.404534i | \(-0.132566\pi\) |
−0.807598 | + | 0.589733i | \(0.799233\pi\) | |||||||
\(462\) | 5.44791 | − | 1.69638i | 0.253460 | − | 0.0789225i | ||||
\(463\) | 20.7405 | − | 35.9236i | 0.963892 | − | 1.66951i | 0.251331 | − | 0.967901i | \(-0.419132\pi\) |
0.712562 | − | 0.701609i | \(-0.247535\pi\) | |||||||
\(464\) | 5.03136 | − | 8.71458i | 0.233575 | − | 0.404564i | ||||
\(465\) | 3.58068 | + | 3.30467i | 0.166050 | + | 0.153250i | ||||
\(466\) | 14.8122 | + | 25.6555i | 0.686162 | + | 1.18847i | ||||
\(467\) | 6.36603 | 0.294585 | 0.147292 | − | 0.989093i | \(-0.452944\pi\) | ||||
0.147292 | + | 0.989093i | \(0.452944\pi\) | |||||||
\(468\) | −16.8553 | − | 8.00668i | −0.779138 | − | 0.370109i | ||||
\(469\) | −4.02984 | −0.186081 | ||||||||
\(470\) | −4.76012 | − | 8.24478i | −0.219568 | − | 0.380303i | ||||
\(471\) | −3.47992 | + | 15.4361i | −0.160346 | + | 0.711257i | ||||
\(472\) | 4.40850 | − | 7.63575i | 0.202918 | − | 0.351464i | ||||
\(473\) | −0.814737 | + | 1.41117i | −0.0374617 | + | 0.0648855i | ||||
\(474\) | −12.1061 | + | 53.6999i | −0.556054 | + | 2.46652i | ||||
\(475\) | 2.86858 | + | 4.96852i | 0.131619 | + | 0.227971i | ||||
\(476\) | −19.2368 | −0.881719 | ||||||||
\(477\) | −25.4297 | + | 17.5370i | −1.16435 | + | 0.802964i | ||||
\(478\) | −61.7063 | −2.82238 | ||||||||
\(479\) | −10.5752 | − | 18.3169i | −0.483195 | − | 0.836918i | 0.516619 | − | 0.856216i | \(-0.327190\pi\) |
−0.999814 | + | 0.0192973i | \(0.993857\pi\) | |||||||
\(480\) | 9.49797 | + | 8.76583i | 0.433521 | + | 0.400104i | ||||
\(481\) | −13.1200 | + | 22.7244i | −0.598218 | + | 1.03614i | ||||
\(482\) | −6.77564 | + | 11.7358i | −0.308622 | + | 0.534549i | ||||
\(483\) | −6.72303 | + | 2.09342i | −0.305909 | + | 0.0952541i | ||||
\(484\) | 12.0429 | + | 20.8589i | 0.547404 | + | 0.948131i | ||||
\(485\) | −14.4990 | −0.658365 | ||||||||
\(486\) | 30.4484 | − | 15.1664i | 1.38117 | − | 0.687962i | ||||
\(487\) | 5.09422 | 0.230841 | 0.115421 | − | 0.993317i | \(-0.463178\pi\) | ||||
0.115421 | + | 0.993317i | \(0.463178\pi\) | |||||||
\(488\) | −3.79995 | − | 6.58171i | −0.172016 | − | 0.297940i | ||||
\(489\) | −7.04084 | + | 2.19238i | −0.318398 | + | 0.0991430i | ||||
\(490\) | −1.09108 | + | 1.88981i | −0.0492900 | + | 0.0853728i | ||||
\(491\) | −11.8110 | + | 20.4572i | −0.533023 | + | 0.923222i | 0.466234 | + | 0.884662i | \(0.345611\pi\) |
−0.999256 | + | 0.0385605i | \(0.987723\pi\) | |||||||
\(492\) | 5.73654 | + | 5.29435i | 0.258623 | + | 0.238688i | ||||
\(493\) | 18.4839 | + | 32.0151i | 0.832474 | + | 1.44189i | ||||
\(494\) | 28.1959 | 1.26859 | ||||||||
\(495\) | 3.72835 | − | 2.57117i | 0.167577 | − | 0.115565i | ||||
\(496\) | −5.33369 | −0.239490 | ||||||||
\(497\) | −0.200154 | − | 0.346676i | −0.00897811 | − | 0.0155506i | ||||
\(498\) | 5.11370 | − | 22.6832i | 0.229151 | − | 1.01646i | ||||
\(499\) | 1.60691 | − | 2.78326i | 0.0719354 | − | 0.124596i | −0.827814 | − | 0.561003i | \(-0.810416\pi\) |
0.899749 | + | 0.436407i | \(0.143749\pi\) | |||||||
\(500\) | 1.38091 | − | 2.39181i | 0.0617564 | − | 0.106965i | ||||
\(501\) | −3.47225 | + | 15.4020i | −0.155129 | + | 0.688113i | ||||
\(502\) | 27.9813 | + | 48.4650i | 1.24887 | + | 2.16310i | ||||
\(503\) | −13.1848 | −0.587883 | −0.293942 | − | 0.955823i | \(-0.594967\pi\) | ||||
−0.293942 | + | 0.955823i | \(0.594967\pi\) | |||||||
\(504\) | 4.50488 | + | 2.13992i | 0.200663 | + | 0.0953198i | ||||
\(505\) | 8.18145 | 0.364070 | ||||||||
\(506\) | 6.69629 | + | 11.5983i | 0.297686 | + | 0.515608i | ||||
\(507\) | 10.0905 | + | 9.31272i | 0.448136 | + | 0.413592i | ||||
\(508\) | −2.52752 | + | 4.37779i | −0.112140 | + | 0.194233i | ||||
\(509\) | 11.4102 | − | 19.7630i | 0.505747 | − | 0.875979i | −0.494231 | − | 0.869330i | \(-0.664550\pi\) |
0.999978 | − | 0.00664837i | \(-0.00211626\pi\) | |||||||
\(510\) | −25.1356 | + | 7.82675i | −1.11302 | + | 0.346574i | ||||
\(511\) | −7.12867 | − | 12.3472i | −0.315354 | − | 0.546209i | ||||
\(512\) | −20.4517 | −0.903847 | ||||||||
\(513\) | −18.4000 | + | 23.4552i | −0.812378 | + | 1.03557i | ||||
\(514\) | 20.9098 | 0.922292 | ||||||||
\(515\) | 4.28577 | + | 7.42318i | 0.188854 | + | 0.327104i | ||||
\(516\) | −4.92984 | + | 1.53506i | −0.217024 | + | 0.0675771i | ||||
\(517\) | 3.29313 | − | 5.70387i | 0.144832 | − | 0.250856i | ||||
\(518\) | 12.7121 | − | 22.0180i | 0.558537 | − | 0.967415i | ||||
\(519\) | −12.0359 | − | 11.1082i | −0.528319 | − | 0.487594i | ||||
\(520\) | −1.87205 | − | 3.24248i | −0.0820947 | − | 0.142192i | ||||
\(521\) | 11.5314 | 0.505201 | 0.252600 | − | 0.967571i | \(-0.418714\pi\) | ||||
0.252600 | + | 0.967571i | \(0.418714\pi\) | |||||||
\(522\) | −2.78120 | − | 34.6338i | −0.121730 | − | 1.51588i | ||||
\(523\) | 7.50782 | 0.328294 | 0.164147 | − | 0.986436i | \(-0.447513\pi\) | ||||
0.164147 | + | 0.986436i | \(0.447513\pi\) | |||||||
\(524\) | 24.3636 | + | 42.1990i | 1.06433 | + | 1.84347i | ||||
\(525\) | −0.380915 | + | 1.68965i | −0.0166245 | + | 0.0737422i | ||||
\(526\) | 7.72443 | − | 13.3791i | 0.336801 | − | 0.583356i | ||||
\(527\) | 9.79729 | − | 16.9694i | 0.426777 | − | 0.739199i | ||||
\(528\) | −1.09027 | + | 4.83617i | −0.0474479 | + | 0.210467i | ||||
\(529\) | 3.23641 | + | 5.60562i | 0.140713 | + | 0.243723i | ||||
\(530\) | −22.4693 | −0.976003 | ||||||||
\(531\) | 1.27361 | + | 15.8599i | 0.0552698 | + | 0.688263i | ||||
\(532\) | −15.8450 | −0.686970 | ||||||||
\(533\) | 1.83763 | + | 3.18288i | 0.0795968 | + | 0.137866i | ||||
\(534\) | 27.6205 | + | 25.4914i | 1.19526 | + | 1.10312i | ||||
\(535\) | 2.20667 | − | 3.82207i | 0.0954028 | − | 0.165242i | ||||
\(536\) | −3.34968 | + | 5.80181i | −0.144684 | + | 0.250600i | ||||
\(537\) | −19.8723 | + | 6.18785i | −0.857552 | + | 0.267025i | ||||
\(538\) | 7.13217 | + | 12.3533i | 0.307490 | + | 0.532588i | ||||
\(539\) | −1.50965 | −0.0650254 | ||||||||
\(540\) | 14.2073 | + | 2.02534i | 0.611383 | + | 0.0871566i | ||||
\(541\) | −17.9217 | −0.770513 | −0.385256 | − | 0.922810i | \(-0.625887\pi\) | ||||
−0.385256 | + | 0.922810i | \(0.625887\pi\) | |||||||
\(542\) | −10.4371 | − | 18.0776i | −0.448313 | − | 0.776500i | ||||
\(543\) | 26.9054 | − | 8.37784i | 1.15462 | − | 0.359528i | ||||
\(544\) | 25.9879 | − | 45.0124i | 1.11422 | − | 1.92989i | ||||
\(545\) | −5.47164 | + | 9.47715i | −0.234379 | + | 0.405957i | ||||
\(546\) | 6.25541 | + | 5.77322i | 0.267707 | + | 0.247071i | ||||
\(547\) | −7.36929 | − | 12.7640i | −0.315088 | − | 0.545749i | 0.664368 | − | 0.747406i | \(-0.268701\pi\) |
−0.979456 | + | 0.201657i | \(0.935367\pi\) | |||||||
\(548\) | 45.3816 | 1.93861 | ||||||||
\(549\) | 12.3880 | + | 5.88460i | 0.528708 | + | 0.251149i | ||||
\(550\) | 3.29431 | 0.140470 | ||||||||
\(551\) | 15.2249 | + | 26.3703i | 0.648602 | + | 1.12341i | ||||
\(552\) | −2.57438 | + | 11.4193i | −0.109573 | + | 0.486038i | ||||
\(553\) | 7.28217 | − | 12.6131i | 0.309670 | − | 0.536363i | ||||
\(554\) | 10.0965 | − | 17.4877i | 0.428960 | − | 0.742980i | ||||
\(555\) | 4.43801 | − | 19.6859i | 0.188383 | − | 0.835621i | ||||
\(556\) | −22.5454 | − | 39.0498i | −0.956139 | − | 1.65608i | ||||
\(557\) | −21.8306 | −0.924992 | −0.462496 | − | 0.886621i | \(-0.653046\pi\) | ||||
−0.462496 | + | 0.886621i | \(0.653046\pi\) | |||||||
\(558\) | −15.1609 | + | 10.4554i | −0.641812 | + | 0.442611i | ||||
\(559\) | −2.43093 | −0.102817 | ||||||||
\(560\) | −0.947978 | − | 1.64195i | −0.0400594 | − | 0.0693849i | ||||
\(561\) | −13.3839 | − | 12.3522i | −0.565067 | − | 0.521509i | ||||
\(562\) | 11.4856 | − | 19.8937i | 0.484493 | − | 0.839166i | ||||
\(563\) | −14.8302 | + | 25.6867i | −0.625018 | + | 1.08256i | 0.363519 | + | 0.931587i | \(0.381575\pi\) |
−0.988537 | + | 0.150977i | \(0.951758\pi\) | |||||||
\(564\) | 19.9262 | − | 6.20463i | 0.839043 | − | 0.261262i | ||||
\(565\) | 1.31168 | + | 2.27190i | 0.0551829 | + | 0.0955796i | ||||
\(566\) | −39.6875 | −1.66819 | ||||||||
\(567\) | −8.88467 | + | 1.43620i | −0.373121 | + | 0.0603146i | ||||
\(568\) | −0.665485 | −0.0279231 | ||||||||
\(569\) | −19.0696 | − | 33.0295i | −0.799439 | − | 1.38467i | −0.919982 | − | 0.391961i | \(-0.871797\pi\) |
0.120543 | − | 0.992708i | \(-0.461536\pi\) | |||||||
\(570\) | −20.7038 | + | 6.44676i | −0.867185 | + | 0.270025i | ||||
\(571\) | −17.9601 | + | 31.1078i | −0.751608 | + | 1.30182i | 0.195436 | + | 0.980717i | \(0.437388\pi\) |
−0.947043 | + | 0.321106i | \(0.895945\pi\) | |||||||
\(572\) | 4.69512 | − | 8.13218i | 0.196313 | − | 0.340024i | ||||
\(573\) | 2.05052 | + | 1.89245i | 0.0856615 | + | 0.0790584i | ||||
\(574\) | −1.78051 | − | 3.08393i | −0.0743169 | − | 0.128721i | ||||
\(575\) | −4.06536 | −0.169537 | ||||||||
\(576\) | −30.8504 | + | 21.2753i | −1.28543 | + | 0.886470i | ||||
\(577\) | 22.0851 | 0.919415 | 0.459708 | − | 0.888070i | \(-0.347954\pi\) | ||||
0.459708 | + | 0.888070i | \(0.347954\pi\) | |||||||
\(578\) | 34.3852 | + | 59.5568i | 1.43023 | + | 2.47724i | ||||
\(579\) | 5.28415 | − | 23.4392i | 0.219602 | − | 0.974101i | ||||
\(580\) | 7.32916 | − | 12.6945i | 0.304327 | − | 0.527110i | ||||
\(581\) | −3.07603 | + | 5.32784i | −0.127615 | + | 0.221036i | ||||
\(582\) | 12.0518 | − | 53.4589i | 0.499564 | − | 2.21594i | ||||
\(583\) | −7.77230 | − | 13.4620i | −0.321896 | − | 0.557540i | ||||
\(584\) | −23.7019 | −0.980792 | ||||||||
\(585\) | 6.10296 | + | 2.89905i | 0.252326 | + | 0.119861i | ||||
\(586\) | 67.0015 | 2.76781 | ||||||||
\(587\) | −2.50433 | − | 4.33763i | −0.103365 | − | 0.179033i | 0.809704 | − | 0.586838i | \(-0.199628\pi\) |
−0.913069 | + | 0.407805i | \(0.866294\pi\) | |||||||
\(588\) | −3.51531 | − | 3.24433i | −0.144969 | − | 0.133794i | ||||
\(589\) | 8.06985 | − | 13.9774i | 0.332512 | − | 0.575929i | ||||
\(590\) | −5.78673 | + | 10.0229i | −0.238236 | + | 0.412637i | ||||
\(591\) | 43.9440 | − | 13.6833i | 1.80761 | − | 0.562857i | ||||
\(592\) | 11.0448 | + | 19.1302i | 0.453939 | + | 0.786246i | ||||
\(593\) | 0.443763 | 0.0182231 | 0.00911157 | − | 0.999958i | \(-0.497100\pi\) | ||||
0.00911157 | + | 0.999958i | \(0.497100\pi\) | |||||||
\(594\) | 6.38104 | + | 15.8839i | 0.261817 | + | 0.651725i | ||||
\(595\) | 6.96525 | 0.285548 | ||||||||
\(596\) | −21.1392 | − | 36.6142i | −0.865896 | − | 1.49978i | ||||
\(597\) | 2.88785 | − | 0.899222i | 0.118192 | − | 0.0368027i | ||||
\(598\) | −9.98984 | + | 17.3029i | −0.408515 | + | 0.707569i | ||||
\(599\) | 7.62637 | − | 13.2093i | 0.311605 | − | 0.539716i | −0.667105 | − | 0.744964i | \(-0.732467\pi\) |
0.978710 | + | 0.205248i | \(0.0658001\pi\) | |||||||
\(600\) | 2.11598 | + | 1.95287i | 0.0863845 | + | 0.0797256i | ||||
\(601\) | −12.5895 | − | 21.8057i | −0.513538 | − | 0.889474i | −0.999877 | − | 0.0157036i | \(-0.995001\pi\) |
0.486339 | − | 0.873770i | \(-0.338332\pi\) | |||||||
\(602\) | 2.35536 | 0.0959972 | ||||||||
\(603\) | −0.967714 | − | 12.0507i | −0.0394083 | − | 0.490744i | ||||
\(604\) | −36.4141 | −1.48167 | ||||||||
\(605\) | −4.36047 | − | 7.55256i | −0.177278 | − | 0.307055i | ||||
\(606\) | −6.80056 | + | 30.1657i | −0.276254 | + | 1.22540i | ||||
\(607\) | −4.51571 | + | 7.82144i | −0.183287 | + | 0.317462i | −0.942998 | − | 0.332799i | \(-0.892007\pi\) |
0.759711 | + | 0.650261i | \(0.225340\pi\) | |||||||
\(608\) | 21.4058 | − | 37.0759i | 0.868119 | − | 1.50363i | ||||
\(609\) | −2.02169 | + | 8.96774i | −0.0819231 | + | 0.363391i | ||||
\(610\) | 4.98793 | + | 8.63935i | 0.201955 | + | 0.349797i | ||||
\(611\) | 9.82570 | 0.397505 | ||||||||
\(612\) | −4.61947 | − | 57.5254i | −0.186731 | − | 2.32532i | ||||
\(613\) | −40.6655 | −1.64246 | −0.821231 | − | 0.570596i | \(-0.806712\pi\) | ||||
−0.821231 | + | 0.570596i | \(0.806712\pi\) | |||||||
\(614\) | −19.8725 | − | 34.4203i | −0.801991 | − | 1.38909i | ||||
\(615\) | −2.07708 | − | 1.91697i | −0.0837560 | − | 0.0772997i | ||||
\(616\) | −1.25485 | + | 2.17347i | −0.0505594 | + | 0.0875714i | ||||
\(617\) | −22.1187 | + | 38.3108i | −0.890467 | + | 1.54233i | −0.0511506 | + | 0.998691i | \(0.516289\pi\) |
−0.839316 | + | 0.543643i | \(0.817044\pi\) | |||||||
\(618\) | −30.9323 | + | 9.63172i | −1.24428 | + | 0.387445i | ||||
\(619\) | −9.57864 | − | 16.5907i | −0.384998 | − | 0.666836i | 0.606771 | − | 0.794877i | \(-0.292465\pi\) |
−0.991769 | + | 0.128041i | \(0.959131\pi\) | |||||||
\(620\) | −7.76955 | −0.312033 | ||||||||
\(621\) | −7.87457 | − | 19.6017i | −0.315995 | − | 0.786588i | ||||
\(622\) | −33.4479 | −1.34114 | ||||||||
\(623\) | −4.97219 | − | 8.61209i | −0.199207 | − | 0.345036i | ||||
\(624\) | −7.06149 | + | 2.19881i | −0.282686 | + | 0.0880230i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 23.2281 | − | 40.2322i | 0.928381 | − | 1.60800i | ||||
\(627\) | −11.0240 | − | 10.1743i | −0.440258 | − | 0.406321i | ||||
\(628\) | −12.6156 | − | 21.8509i | −0.503418 | − | 0.871945i | ||||
\(629\) | −81.1516 | −3.23573 | ||||||||
\(630\) | −5.91324 | − | 2.80893i | −0.235589 | − | 0.111910i | ||||
\(631\) | −39.5474 | −1.57436 | −0.787179 | − | 0.616725i | \(-0.788459\pi\) | ||||
−0.787179 | + | 0.616725i | \(0.788459\pi\) | |||||||
\(632\) | −12.1061 | − | 20.9685i | −0.481557 | − | 0.834080i | ||||
\(633\) | −7.10212 | + | 31.5033i | −0.282284 | + | 1.25214i | ||||
\(634\) | −13.0451 | + | 22.5948i | −0.518088 | + | 0.897355i | ||||
\(635\) | 0.915160 | − | 1.58510i | 0.0363170 | − | 0.0629029i | ||||
\(636\) | 10.8325 | − | 48.0502i | 0.429535 | − | 1.90531i | ||||
\(637\) | −1.12609 | − | 1.95044i | −0.0446172 | − | 0.0772793i | ||||
\(638\) | 17.4844 | 0.692216 | ||||||||
\(639\) | 0.988627 | − | 0.681784i | 0.0391095 | − | 0.0269709i | ||||
\(640\) | −12.3346 | −0.487569 | ||||||||
\(641\) | −14.2408 | − | 24.6658i | −0.562478 | − | 0.974240i | −0.997279 | − | 0.0737136i | \(-0.976515\pi\) |
0.434802 | − | 0.900526i | \(-0.356818\pi\) | |||||||
\(642\) | 12.2581 | + | 11.3132i | 0.483787 | + | 0.446495i | ||||
\(643\) | −3.38899 | + | 5.86990i | −0.133649 | + | 0.231486i | −0.925080 | − | 0.379771i | \(-0.876003\pi\) |
0.791432 | + | 0.611258i | \(0.209336\pi\) | |||||||
\(644\) | 5.61392 | − | 9.72360i | 0.221220 | − | 0.383163i | ||||
\(645\) | 1.78499 | − | 0.555812i | 0.0702839 | − | 0.0218851i | ||||
\(646\) | 43.6004 | + | 75.5181i | 1.71543 | + | 2.97122i | ||||
\(647\) | −4.88796 | −0.192165 | −0.0960827 | − | 0.995373i | \(-0.530631\pi\) | ||||
−0.0960827 | + | 0.995373i | \(0.530631\pi\) | |||||||
\(648\) | −5.31738 | + | 13.9851i | −0.208887 | + | 0.549389i | ||||
\(649\) | −8.00670 | −0.314291 | ||||||||
\(650\) | 2.45731 | + | 4.25618i | 0.0963834 | + | 0.166941i | ||||
\(651\) | 4.65227 | − | 1.44863i | 0.182337 | − | 0.0567762i | ||||
\(652\) | 5.87930 | − | 10.1832i | 0.230251 | − | 0.398807i | ||||
\(653\) | −2.84057 | + | 4.92001i | −0.111160 | + | 0.192535i | −0.916238 | − | 0.400634i | \(-0.868790\pi\) |
0.805078 | + | 0.593169i | \(0.202123\pi\) | |||||||
\(654\) | −30.3949 | − | 28.0519i | −1.18854 | − | 1.09692i | ||||
\(655\) | −8.82154 | − | 15.2794i | −0.344686 | − | 0.597014i | ||||
\(656\) | 3.09396 | 0.120799 | ||||||||
\(657\) | 35.2110 | − | 24.2824i | 1.37371 | − | 0.947347i | ||||
\(658\) | −9.52025 | −0.371138 | ||||||||
\(659\) | −4.77505 | − | 8.27063i | −0.186009 | − | 0.322178i | 0.757907 | − | 0.652363i | \(-0.226222\pi\) |
−0.943916 | + | 0.330185i | \(0.892889\pi\) | |||||||
\(660\) | −1.58819 | + | 7.04482i | −0.0618202 | + | 0.274219i | ||||
\(661\) | −1.92056 | + | 3.32651i | −0.0747013 | + | 0.129386i | −0.900956 | − | 0.433910i | \(-0.857134\pi\) |
0.826255 | + | 0.563296i | \(0.190467\pi\) | |||||||
\(662\) | 16.9354 | − | 29.3329i | 0.658211 | − | 1.14006i | ||||
\(663\) | 5.97540 | − | 26.5054i | 0.232065 | − | 1.02939i | ||||
\(664\) | 5.11370 | + | 8.85720i | 0.198450 | + | 0.343726i | ||||
\(665\) | 5.73716 | 0.222477 | ||||||||
\(666\) | 68.8947 | + | 32.7266i | 2.66961 | + | 1.26813i | ||||
\(667\) | −21.5768 | −0.835457 | ||||||||
\(668\) | −12.5878 | − | 21.8027i | −0.487036 | − | 0.843572i | ||||
\(669\) | 26.2458 | + | 24.2227i | 1.01472 | + | 0.936503i | ||||
\(670\) | 4.39689 | − | 7.61563i | 0.169867 | − | 0.294217i | ||||
\(671\) | −3.45073 | + | 5.97684i | −0.133214 | + | 0.230733i | ||||
\(672\) | 12.3404 | − | 3.84257i | 0.476042 | − | 0.148230i | ||||
\(673\) | 14.7759 | + | 25.5926i | 0.569569 | + | 0.986522i | 0.996609 | + | 0.0822890i | \(0.0262230\pi\) |
−0.427040 | + | 0.904233i | \(0.640444\pi\) | |||||||
\(674\) | −8.81646 | −0.339597 | ||||||||
\(675\) | −5.14414 | − | 0.733331i | −0.197998 | − | 0.0282259i | ||||
\(676\) | −21.8950 | −0.842114 | ||||||||
\(677\) | 14.8529 | + | 25.7260i | 0.570844 | + | 0.988730i | 0.996480 | + | 0.0838357i | \(0.0267171\pi\) |
−0.425636 | + | 0.904894i | \(0.639950\pi\) | |||||||
\(678\) | −9.46698 | + | 2.94784i | −0.363577 | + | 0.113211i | ||||
\(679\) | −7.24949 | + | 12.5565i | −0.278210 | + | 0.481874i | ||||
\(680\) | 5.78964 | − | 10.0280i | 0.222023 | − | 0.384554i | ||||
\(681\) | −25.3904 | − | 23.4332i | −0.972963 | − | 0.897963i | ||||
\(682\) | −4.63376 | − | 8.02591i | −0.177436 | − | 0.307328i | ||||
\(683\) | −44.2805 | −1.69435 | −0.847174 | − | 0.531316i | \(-0.821698\pi\) | ||||
−0.847174 | + | 0.531316i | \(0.821698\pi\) | |||||||
\(684\) | −3.80498 | − | 47.3826i | −0.145487 | − | 1.81172i | ||||
\(685\) | −16.4317 | −0.627824 | ||||||||
\(686\) | 1.09108 | + | 1.88981i | 0.0416577 | + | 0.0721532i | ||||
\(687\) | 1.72904 | − | 7.66958i | 0.0659668 | − | 0.292613i | ||||
\(688\) | −1.02322 | + | 1.77227i | −0.0390099 | + | 0.0675670i | ||||
\(689\) | 11.5951 | − | 20.0833i | 0.441738 | − | 0.765113i | ||||
\(690\) | 3.37920 | − | 14.9893i | 0.128644 | − | 0.570634i | ||||
\(691\) | 16.1568 | + | 27.9843i | 0.614632 | + | 1.06457i | 0.990449 | + | 0.137880i | \(0.0440288\pi\) |
−0.375817 | + | 0.926694i | \(0.622638\pi\) | |||||||
\(692\) | 26.1162 | 0.992790 | ||||||||
\(693\) | −0.362523 | − | 4.51443i | −0.0137711 | − | 0.171489i | ||||
\(694\) | 4.33521 | 0.164562 | ||||||||
\(695\) | 8.16323 | + | 14.1391i | 0.309649 | + | 0.536327i | ||||
\(696\) | 11.2305 | + | 10.3648i | 0.425691 | + | 0.392877i | ||||
\(697\) | −5.68321 | + | 9.84361i | −0.215267 | + | 0.372853i | ||||
\(698\) | −36.2322 | + | 62.7561i | −1.37141 | + | 2.37535i | ||||
\(699\) | 22.4506 | − | 6.99070i | 0.849161 | − | 0.264413i | ||||
\(700\) | −1.38091 | − | 2.39181i | −0.0521937 | − | 0.0904021i | ||||
\(701\) | 31.3623 | 1.18454 | 0.592269 | − | 0.805740i | \(-0.298232\pi\) | ||||
0.592269 | + | 0.805740i | \(0.298232\pi\) | |||||||
\(702\) | −15.7619 | + | 20.0924i | −0.594895 | + | 0.758338i | ||||
\(703\) | −66.8431 | −2.52104 | ||||||||
\(704\) | −9.42908 | − | 16.3317i | −0.355372 | − | 0.615522i | ||||
\(705\) | −7.21484 | + | 2.24656i | −0.271727 | + | 0.0846105i | ||||
\(706\) | 33.3617 | − | 57.7841i | 1.25558 | − | 2.17473i | ||||
\(707\) | 4.09072 | − | 7.08534i | 0.153847 | − | 0.266472i | ||||
\(708\) | −18.6440 | − | 17.2069i | −0.700685 | − | 0.646674i | ||||
\(709\) | −17.7983 | − | 30.8276i | −0.668429 | − | 1.15775i | −0.978343 | − | 0.206989i | \(-0.933634\pi\) |
0.309914 | − | 0.950765i | \(-0.399700\pi\) | |||||||
\(710\) | 0.873535 | 0.0327832 | ||||||||
\(711\) | 39.4666 | + | 18.7476i | 1.48011 | + | 0.703088i | ||||
\(712\) | −16.5319 | −0.619559 | ||||||||
\(713\) | 5.71832 | + | 9.90442i | 0.214153 | + | 0.370923i | ||||
\(714\) | −5.78964 | + | 25.6815i | −0.216672 | + | 0.961104i | ||||
\(715\) | −1.70000 | + | 2.94449i | −0.0635765 | + | 0.110118i | ||||
\(716\) | 16.5939 | − | 28.7415i | 0.620144 | − | 1.07412i | ||||
\(717\) | −10.7714 | + | 47.7792i | −0.402264 | + | 1.78435i | ||||
\(718\) | −16.8759 | − | 29.2300i | −0.629805 | − | 1.09085i | ||||
\(719\) | −3.70852 | −0.138304 | −0.0691522 | − | 0.997606i | \(-0.522029\pi\) | ||||
−0.0691522 | + | 0.997606i | \(0.522029\pi\) | |||||||
\(720\) | 4.68239 | − | 3.22910i | 0.174502 | − | 0.120341i | ||||
\(721\) | 8.57155 | 0.319221 | ||||||||
\(722\) | 15.1823 | + | 26.2966i | 0.565028 | + | 0.978658i | ||||
\(723\) | 7.90424 | + | 7.29495i | 0.293962 | + | 0.271302i | ||||
\(724\) | −22.4668 | + | 38.9137i | −0.834973 | + | 1.44622i | ||||
\(725\) | −2.65373 | + | 4.59640i | −0.0985572 | + | 0.170706i | ||||
\(726\) | 31.4714 | − | 9.79959i | 1.16801 | − | 0.363697i | ||||
\(727\) | 10.6288 | + | 18.4096i | 0.394199 | + | 0.682773i | 0.992999 | − | 0.118126i | \(-0.0376887\pi\) |
−0.598800 | + | 0.800899i | \(0.704355\pi\) | |||||||
\(728\) | −3.74410 | −0.138765 | ||||||||
\(729\) | −6.42830 | − | 26.2236i | −0.238085 | − | 0.971244i | ||||
\(730\) | 31.1118 | 1.15150 | ||||||||
\(731\) | −3.75904 | − | 6.51085i | −0.139033 | − | 0.240812i | ||||
\(732\) | −20.8798 | + | 6.50157i | −0.771739 | + | 0.240305i | ||||
\(733\) | −14.2601 | + | 24.6992i | −0.526707 | + | 0.912284i | 0.472808 | + | 0.881165i | \(0.343240\pi\) |
−0.999516 | + | 0.0311188i | \(0.990093\pi\) | |||||||
\(734\) | 27.9163 | − | 48.3525i | 1.03041 | − | 1.78472i | ||||
\(735\) | 1.27282 | + | 1.17470i | 0.0469486 | + | 0.0433296i | ||||
\(736\) | 15.1682 | + | 26.2721i | 0.559107 | + | 0.968402i | ||||
\(737\) | 6.08367 | 0.224095 | ||||||||
\(738\) | 8.79453 | − | 6.06495i | 0.323731 | − | 0.223254i | ||||
\(739\) | −5.88760 | −0.216579 | −0.108289 | − | 0.994119i | \(-0.534537\pi\) | ||||
−0.108289 | + | 0.994119i | \(0.534537\pi\) | |||||||
\(740\) | 16.0889 | + | 27.8668i | 0.591441 | + | 1.02441i | ||||
\(741\) | 4.92183 | − | 21.8321i | 0.180808 | − | 0.802020i | ||||
\(742\) | −11.2346 | + | 19.4590i | −0.412437 | + | 0.714361i | ||||
\(743\) | 18.8798 | − | 32.7008i | 0.692633 | − | 1.19967i | −0.278340 | − | 0.960483i | \(-0.589784\pi\) |
0.970972 | − | 0.239192i | \(-0.0768826\pi\) | |||||||
\(744\) | 1.78144 | − | 7.90204i | 0.0653108 | − | 0.289703i | ||||
\(745\) | 7.65407 | + | 13.2572i | 0.280423 | + | 0.485707i | ||||
\(746\) | 41.6262 | 1.52404 | ||||||||
\(747\) | −16.6709 | − | 7.91907i | −0.609957 | − | 0.289744i | ||||
\(748\) | 29.0410 | 1.06184 | ||||||||
\(749\) | −2.20667 | − | 3.82207i | −0.0806301 | − | 0.139655i | ||||
\(750\) | −2.77750 | − | 2.56340i | −0.101420 | − | 0.0936020i | ||||
\(751\) | 7.63491 | − | 13.2241i | 0.278602 | − | 0.482552i | −0.692436 | − | 0.721480i | \(-0.743462\pi\) |
0.971037 | + | 0.238927i | \(0.0767957\pi\) | |||||||
\(752\) | 4.13580 | − | 7.16342i | 0.150817 | − | 0.261223i | ||||
\(753\) | 42.4108 | − | 13.2059i | 1.54554 | − | 0.481250i | ||||
\(754\) | 13.0421 | + | 22.5895i | 0.474964 | + | 0.822662i | ||||
\(755\) | 13.1848 | 0.479843 | ||||||||
\(756\) | 8.85762 | − | 11.2912i | 0.322148 | − | 0.410656i | ||||
\(757\) | 17.2984 | 0.628720 | 0.314360 | − | 0.949304i | \(-0.398210\pi\) | ||||
0.314360 | + | 0.949304i | \(0.398210\pi\) | |||||||
\(758\) | 0.246958 | + | 0.427743i | 0.00896990 | + | 0.0155363i | ||||
\(759\) | 10.1495 | − | 3.16035i | 0.368402 | − | 0.114713i | ||||
\(760\) | 4.76882 | − | 8.25985i | 0.172983 | − | 0.299616i | ||||
\(761\) | 12.3241 | − | 21.3460i | 0.446749 | − | 0.773791i | −0.551424 | − | 0.834225i | \(-0.685915\pi\) |
0.998172 | + | 0.0604342i | \(0.0192485\pi\) | |||||||
\(762\) | 5.08371 | + | 4.69184i | 0.184163 | + | 0.169967i | ||||
\(763\) | 5.47164 | + | 9.47715i | 0.198087 | + | 0.343096i | ||||
\(764\) | −4.44931 | −0.160971 | ||||||||
\(765\) | 1.67261 | + | 20.8287i | 0.0604735 | + | 0.753064i | ||||
\(766\) | −71.7459 | −2.59228 | ||||||||
\(767\) | −5.97239 | − | 10.3445i | −0.215651 | − | 0.373518i | ||||
\(768\) | 0.736205 | − | 3.26563i | 0.0265655 | − | 0.117838i | ||||
\(769\) | −8.50238 | + | 14.7266i | −0.306604 | + | 0.531053i | −0.977617 | − | 0.210392i | \(-0.932526\pi\) |
0.671013 | + | 0.741445i | \(0.265859\pi\) | |||||||
\(770\) | 1.64715 | − | 2.85296i | 0.0593593 | − | 0.102813i | ||||
\(771\) | 3.64998 | − | 16.1905i | 0.131451 | − | 0.583085i | ||||
\(772\) | 19.1564 | + | 33.1799i | 0.689455 | + | 1.19417i | ||||
\(773\) | 13.6622 | 0.491396 | 0.245698 | − | 0.969346i | \(-0.420983\pi\) | ||||
0.245698 | + | 0.969346i | \(0.420983\pi\) | |||||||
\(774\) | 0.565608 | + | 7.04340i | 0.0203304 | + | 0.253170i | ||||
\(775\) | 2.81319 | 0.101053 | ||||||||
\(776\) | 12.0518 | + | 20.8743i | 0.432635 | + | 0.749345i | ||||
\(777\) | −14.8295 | − | 13.6864i | −0.532006 | − | 0.490997i | ||||
\(778\) | −2.00690 | + | 3.47605i | −0.0719507 | + | 0.124622i | ||||
\(779\) | −4.68116 | + | 8.10801i | −0.167720 | + | 0.290499i | ||||
\(780\) | −10.2864 | + | 3.20300i | −0.368313 | + | 0.114686i | ||||
\(781\) | 0.302163 | + | 0.523361i | 0.0108122 | + | 0.0187273i | ||||
\(782\) | −61.7907 | −2.20963 | ||||||||
\(783\) | −27.3024 | − | 3.89213i | −0.975708 | − | 0.139093i | ||||
\(784\) | −1.89596 | −0.0677127 | ||||||||
\(785\) | 4.56785 | + | 7.91174i | 0.163033 | + | 0.282382i | ||||
\(786\) | 63.6688 | − | 19.8253i | 2.27099 | − | 0.707144i | ||||
\(787\) | 20.0360 | − | 34.7034i | 0.714208 | − | 1.23704i | −0.249057 | − | 0.968489i | \(-0.580121\pi\) |
0.963264 | − | 0.268555i | \(-0.0865461\pi\) | |||||||
\(788\) | −36.6945 | + | 63.5567i | −1.30719 | + | 2.26411i | ||||
\(789\) | −9.01106 | − | 8.31645i | −0.320802 | − | 0.296074i | ||||
\(790\) | 15.8909 | + | 27.5238i | 0.565372 | + | 0.979253i | ||||
\(791\) | 2.62337 | 0.0932761 | ||||||||
\(792\) | −6.80081 | − | 3.23054i | −0.241656 | − | 0.114792i | ||||
\(793\) | −10.2959 | −0.365619 | ||||||||
\(794\) | 37.7503 | + | 65.3854i | 1.33971 | + | 2.32044i | ||||
\(795\) | −3.92220 | + | 17.3979i | −0.139106 | + | 0.617042i | ||||
\(796\) | −2.41144 | + | 4.17673i | −0.0854712 | + | 0.148040i | ||||
\(797\) | −22.6210 | + | 39.1807i | −0.801277 | + | 1.38785i | 0.117500 | + | 0.993073i | \(0.462512\pi\) |
−0.918776 | + | 0.394779i | \(0.870821\pi\) | |||||||
\(798\) | −4.76882 | + | 21.1534i | −0.168815 | + | 0.748821i | ||||
\(799\) | 15.1939 | + | 26.3165i | 0.537520 | + | 0.931013i | ||||
\(800\) | 7.46215 | 0.263827 | ||||||||
\(801\) | 24.5594 | − | 16.9368i | 0.867762 | − | 0.598432i | ||||
\(802\) | 7.64690 | 0.270022 | ||||||||
\(803\) | 10.7618 | + | 18.6400i | 0.379777 | + | 0.657793i | ||||
\(804\) | 14.1661 | + | 13.0742i | 0.499602 | + | 0.461090i | ||||
\(805\) | −2.03268 | + | 3.52071i | −0.0716426 | + | 0.124089i | ||||
\(806\) | 6.91286 | − | 11.9734i | 0.243495 | − | 0.421746i | ||||
\(807\) | 10.8101 | − | 3.36607i | 0.380534 | − | 0.118491i | ||||
\(808\) | −6.80056 | − | 11.7789i | −0.239243 | − | 0.414381i | ||||
\(809\) | −27.0132 | −0.949734 | −0.474867 | − | 0.880058i | \(-0.657504\pi\) | ||||
−0.474867 | + | 0.880058i | \(0.657504\pi\) | |||||||
\(810\) | 6.97976 | − | 18.3573i | 0.245244 | − | 0.645010i | ||||
\(811\) | 10.1468 | 0.356301 | 0.178150 | − | 0.984003i | \(-0.442989\pi\) | ||||
0.178150 | + | 0.984003i | \(0.442989\pi\) | |||||||
\(812\) | −7.32916 | − | 12.6945i | −0.257203 | − | 0.445489i | ||||
\(813\) | −15.8194 | + | 4.92585i | −0.554810 | + | 0.172757i | ||||
\(814\) | −19.1909 | + | 33.2396i | −0.672640 | + | 1.16505i | ||||
\(815\) | −2.12877 | + | 3.68714i | −0.0745676 | + | 0.129155i | ||||
\(816\) | −16.8086 | − | 15.5129i | −0.588419 | − | 0.543062i | ||||
\(817\) | −3.09625 | − | 5.36287i | −0.108324 | − | 0.187623i | ||||
\(818\) | 23.6223 | 0.825933 | ||||||||
\(819\) | 5.56213 | − | 3.83580i | 0.194357 | − | 0.134034i | ||||
\(820\) | 4.50696 | 0.157390 | ||||||||
\(821\) | −12.0032 | − | 20.7902i | −0.418915 | − | 0.725582i | 0.576916 | − | 0.816804i | \(-0.304256\pi\) |
−0.995831 | + | 0.0912220i | \(0.970923\pi\) | |||||||
\(822\) | 13.6583 | − | 60.5851i | 0.476389 | − | 2.11315i | ||||
\(823\) | 9.50147 | − | 16.4570i | 0.331200 | − | 0.573656i | −0.651547 | − | 0.758608i | \(-0.725880\pi\) |
0.982747 | + | 0.184952i | \(0.0592131\pi\) | |||||||
\(824\) | 7.12482 | − | 12.3406i | 0.248205 | − | 0.429904i | ||||
\(825\) | 0.575050 | − | 2.55078i | 0.0200207 | − | 0.0888068i | ||||
\(826\) | 5.78673 | + | 10.0229i | 0.201346 | + | 0.348742i | ||||
\(827\) | −23.6824 | −0.823518 | −0.411759 | − | 0.911293i | \(-0.635085\pi\) | ||||
−0.411759 | + | 0.911293i | \(0.635085\pi\) | |||||||
\(828\) | 30.4253 | + | 14.4527i | 1.05735 | + | 0.502267i | ||||
\(829\) | 29.1824 | 1.01355 | 0.506774 | − | 0.862079i | \(-0.330838\pi\) | ||||
0.506774 | + | 0.862079i | \(0.330838\pi\) | |||||||
\(830\) | −6.71240 | − | 11.6262i | −0.232991 | − | 0.403552i | ||||
\(831\) | −11.7783 | − | 10.8703i | −0.408583 | − | 0.377088i | ||||
\(832\) | 14.0668 | − | 24.3644i | 0.487677 | − | 0.844682i | ||||
\(833\) | 3.48263 | − | 6.03209i | 0.120666 | − | 0.208999i | ||||
\(834\) | −58.9175 | + | 18.3458i | −2.04015 | + | 0.635263i | ||||
\(835\) | 4.55777 | + | 7.89429i | 0.157728 | + | 0.273193i | ||||
\(836\) | 23.9205 | 0.827309 | ||||||||
\(837\) | 5.44912 | + | 13.5641i | 0.188349 | + | 0.468845i | ||||
\(838\) | 28.3548 | 0.979501 | ||||||||
\(839\) | 3.81234 | + | 6.60317i | 0.131617 | + | 0.227967i | 0.924300 | − | 0.381667i | \(-0.124650\pi\) |
−0.792683 | + | 0.609634i | \(0.791317\pi\) | |||||||
\(840\) | 2.74923 | − | 0.856056i | 0.0948573 | − | 0.0295368i | ||||
\(841\) | 0.415394 | − | 0.719483i | 0.0143239 | − | 0.0248097i | ||||
\(842\) | 36.2727 | − | 62.8261i | 1.25004 | − | 2.16513i | ||||
\(843\) | −13.3988 | − | 12.3659i | −0.461479 | − | 0.425906i | ||||
\(844\) | −25.7470 | − | 44.5952i | −0.886249 | − | 1.53503i | ||||
\(845\) | 7.92771 | 0.272721 | ||||||||
\(846\) | −2.28616 | − | 28.4691i | −0.0785998 | − | 0.978788i | ||||
\(847\) | −8.72094 | −0.299655 | ||||||||
\(848\) | −9.76114 | − | 16.9068i | −0.335199 | − | 0.580582i | ||||
\(849\) | −6.92780 | + | 30.7300i | −0.237761 | + | 1.05465i | ||||
\(850\) | −7.59966 | + | 13.1630i | −0.260666 | + | 0.451487i | ||||
\(851\) | 23.6826 | − | 41.0195i | 0.811830 | − | 1.40613i | ||||
\(852\) | −0.421132 | + | 1.86804i | −0.0144277 | + | 0.0639980i | ||||
\(853\) | −11.9125 | − | 20.6330i | −0.407876 | − | 0.706462i | 0.586776 | − | 0.809750i | \(-0.300397\pi\) |
−0.994652 | + | 0.103288i | \(0.967064\pi\) | |||||||
\(854\) | 9.97586 | 0.341367 | ||||||||
\(855\) | 1.37770 | + | 17.1562i | 0.0471164 | + | 0.586731i | ||||
\(856\) | −7.33690 | −0.250770 | ||||||||
\(857\) | 7.85857 | + | 13.6114i | 0.268444 | + | 0.464958i | 0.968460 | − | 0.249169i | \(-0.0801574\pi\) |
−0.700016 | + | 0.714127i | \(0.746824\pi\) | |||||||
\(858\) | −9.44351 | − | 8.71556i | −0.322396 | − | 0.297544i | ||||
\(859\) | 11.3041 | − | 19.5792i | 0.385689 | − | 0.668033i | −0.606175 | − | 0.795331i | \(-0.707297\pi\) |
0.991865 | + | 0.127298i | \(0.0406303\pi\) | |||||||
\(860\) | −1.49052 | + | 2.58165i | −0.0508262 | + | 0.0880336i | ||||
\(861\) | −2.69869 | + | 0.840319i | −0.0919710 | + | 0.0286380i | ||||
\(862\) | 24.6612 | + | 42.7144i | 0.839964 | + | 1.45486i | ||||
\(863\) | −44.0266 | −1.49868 | −0.749342 | − | 0.662183i | \(-0.769630\pi\) | ||||
−0.749342 | + | 0.662183i | \(0.769630\pi\) | |||||||
\(864\) | 14.4541 | + | 35.9797i | 0.491739 | + | 1.22405i | ||||
\(865\) | −9.45613 | −0.321518 | ||||||||
\(866\) | −15.2498 | − | 26.4135i | −0.518211 | − | 0.897568i | ||||
\(867\) | 52.1170 | − | 16.2282i | 1.76999 | − | 0.551140i | ||||
\(868\) | −3.88477 | + | 6.72863i | −0.131858 | + | 0.228384i | ||||
\(869\) | −10.9936 | + | 19.0414i | −0.372931 | + | 0.645936i | ||||
\(870\) | −14.7415 | − | 13.6051i | −0.499783 | − | 0.461257i | ||||
\(871\) | 4.53796 | + | 7.85997i | 0.153763 | + | 0.266325i | ||||
\(872\) | 18.1925 | 0.616075 | ||||||||
\(873\) | −39.2895 | − | 18.6634i | −1.32975 | − | 0.631661i | ||||
\(874\) | −50.8959 | −1.72158 | ||||||||
\(875\) | 0.500000 | + | 0.866025i | 0.0169031 | + | 0.0292770i | ||||
\(876\) | −14.9990 | + | 66.5321i | −0.506770 | + | 2.24791i | ||||
\(877\) | −23.9138 | + | 41.4199i | −0.807512 | + | 1.39865i | 0.107070 | + | 0.994252i | \(0.465853\pi\) |
−0.914582 | + | 0.404401i | \(0.867480\pi\) | |||||||
\(878\) | 19.1332 | − | 33.1396i | 0.645713 | − | 1.11841i | ||||
\(879\) | 11.6957 | − | 51.8792i | 0.394485 | − | 1.74984i | ||||
\(880\) | 1.43112 | + | 2.47877i | 0.0482430 | + | 0.0835594i | ||||
\(881\) | −45.3688 | −1.52851 | −0.764257 | − | 0.644912i | \(-0.776894\pi\) | ||||
−0.764257 | + | 0.644912i | \(0.776894\pi\) | |||||||
\(882\) | −5.38922 | + | 3.71655i | −0.181465 | + | 0.125143i | ||||
\(883\) | 38.8987 | 1.30905 | 0.654523 | − | 0.756042i | \(-0.272870\pi\) | ||||
0.654523 | + | 0.756042i | \(0.272870\pi\) | |||||||
\(884\) | 21.6624 | + | 37.5203i | 0.728584 | + | 1.26195i | ||||
\(885\) | 6.75061 | + | 6.23024i | 0.226919 | + | 0.209427i | ||||
\(886\) | −32.9056 | + | 56.9941i | −1.10548 | + | 1.91475i | ||||
\(887\) | 13.3319 | − | 23.0915i | 0.447641 | − | 0.775336i | −0.550591 | − | 0.834775i | \(-0.685598\pi\) |
0.998232 | + | 0.0594387i | \(0.0189311\pi\) | |||||||
\(888\) | −32.0310 | + | 9.97384i | −1.07489 | + | 0.334700i | ||||
\(889\) | −0.915160 | − | 1.58510i | −0.0306935 | − | 0.0531627i | ||||
\(890\) | 21.7002 | 0.727394 | ||||||||
\(891\) | 13.4128 | − | 2.16816i | 0.449345 | − | 0.0726361i | ||||
\(892\) | −56.9496 | −1.90681 | ||||||||
\(893\) | 12.5149 | + | 21.6765i | 0.418796 | + | 0.725375i | ||||
\(894\) | −55.2427 | + | 17.2015i | −1.84759 | + | 0.575305i | ||||
\(895\) | −6.00831 | + | 10.4067i | −0.200836 | + | 0.347857i | ||||
\(896\) | −6.16732 | + | 10.6821i | −0.206036 | + | 0.356864i | ||||
\(897\) | 11.6538 | + | 10.7555i | 0.389110 | + | 0.359116i | ||||
\(898\) | −9.88770 | − | 17.1260i | −0.329957 | − | 0.571502i | ||||
\(899\) | 14.9309 | 0.497974 | ||||||||
\(900\) | 6.82081 | − | 4.70381i | 0.227360 | − | 0.156794i | ||||
\(901\) | 71.7198 | 2.38933 | ||||||||
\(902\) | 2.68795 | + | 4.65567i | 0.0894990 | + | 0.155017i | ||||
\(903\) | 0.411148 | − | 1.82375i | 0.0136821 | − | 0.0606907i | ||||
\(904\) | 2.18059 | − | 3.77689i | 0.0725253 | − | 0.125617i | ||||
\(905\) | 8.13476 | − | 14.0898i | 0.270409 | − | 0.468361i | ||||
\(906\) | −10.9594 | + | 48.6134i | −0.364102 | + | 1.61507i | ||||
\(907\) | −16.1330 | − | 27.9431i | −0.535686 | − | 0.927836i | −0.999130 | − | 0.0417093i | \(-0.986720\pi\) |
0.463444 | − | 0.886126i | \(-0.346614\pi\) | |||||||
\(908\) | 55.0935 | 1.82834 | ||||||||
\(909\) | 22.1701 | + | 10.5313i | 0.735337 | + | 0.349302i | ||||
\(910\) | 4.91461 | 0.162918 | ||||||||
\(911\) | 8.06651 | + | 13.9716i | 0.267255 | + | 0.462900i | 0.968152 | − | 0.250363i | \(-0.0805499\pi\) |
−0.700897 | + | 0.713263i | \(0.747217\pi\) | |||||||
\(912\) | −13.8450 | − | 12.7777i | −0.458452 | − | 0.423113i | ||||
\(913\) | 4.64375 | − | 8.04320i | 0.153686 | − | 0.266191i | ||||
\(914\) | 22.3292 | − | 38.6754i | 0.738585 | − | 1.27927i | ||||
\(915\) | 7.56013 | − | 2.35408i | 0.249930 | − | 0.0778235i | ||||
\(916\) | 6.26820 | + | 10.8568i | 0.207107 | + | 0.358720i | ||||
\(917\) | −17.6431 | −0.582626 | ||||||||
\(918\) | −78.1875 | − | 11.1461i | −2.58057 | − | 0.367877i | ||||
\(919\) | 47.4357 | 1.56476 | 0.782380 | − | 0.622802i | \(-0.214006\pi\) | ||||
0.782380 | + | 0.622802i | \(0.214006\pi\) | |||||||
\(920\) | 3.37920 | + | 5.85295i | 0.111409 | + | 0.192966i | ||||
\(921\) | −30.1205 | + | 9.37895i | −0.992504 | + | 0.309047i | ||||
\(922\) | −5.00972 | + | 8.67710i | −0.164986 | + | 0.285765i | ||||
\(923\) | −0.450781 | + | 0.780775i | −0.0148376 | + | 0.0256995i | ||||
\(924\) | 5.30690 | + | 4.89782i | 0.174584 | + | 0.161127i | ||||
\(925\) | −5.82546 | − | 10.0900i | −0.191540 | − | 0.331757i | ||||
\(926\) | 90.5182 | 2.97461 | ||||||||
\(927\) | 2.05834 | + | 25.6321i | 0.0676049 | + | 0.841870i | ||||
\(928\) | 39.6051 | 1.30010 | ||||||||
\(929\) | 16.9992 | + | 29.4435i | 0.557726 | + | 0.966010i | 0.997686 | + | 0.0679924i | \(0.0216594\pi\) |
−0.439960 | + | 0.898017i | \(0.645007\pi\) | |||||||
\(930\) | −2.33837 | + | 10.3725i | −0.0766783 | + | 0.340126i | ||||
\(931\) | 2.86858 | − | 4.96852i | 0.0940138 | − | 0.162837i | ||||
\(932\) | −18.7469 | + | 32.4706i | −0.614076 | + | 1.06361i | ||||
\(933\) | −5.83861 | + | 25.8987i | −0.191148 | + | 0.847885i | ||||
\(934\) | 6.94585 | + | 12.0306i | 0.227275 | + | 0.393652i | ||||
\(935\) | −10.5151 | −0.343881 | ||||||||
\(936\) | −0.899095 | − | 11.1962i | −0.0293878 | − | 0.365961i | ||||
\(937\) | −17.3685 | −0.567405 | −0.283703 | − | 0.958912i | \(-0.591563\pi\) | ||||
−0.283703 | + | 0.958912i | \(0.591563\pi\) | |||||||
\(938\) | −4.39689 | − | 7.61563i | −0.143563 | − | 0.248659i | ||||
\(939\) | −27.0971 | − | 25.0084i | −0.884281 | − | 0.816117i | ||||
\(940\) | 6.02460 | − | 10.4349i | 0.196501 | − | 0.340349i | ||||
\(941\) | −20.8360 | + | 36.0891i | −0.679235 | + | 1.17647i | 0.295976 | + | 0.955195i | \(0.404355\pi\) |
−0.975212 | + | 0.221275i | \(0.928978\pi\) | |||||||
\(942\) | −32.9681 | + | 10.2656i | −1.07416 | + | 0.334473i | ||||
\(943\) | −3.31708 | − | 5.74536i | −0.108019 | − | 0.187095i | ||||
\(944\) | −10.0555 | −0.327279 | ||||||||
\(945\) | −3.20716 | + | 4.08829i | −0.104329 | + | 0.132992i | ||||
\(946\) | −3.55578 | −0.115608 | ||||||||
\(947\) | 24.1437 | + | 41.8181i | 0.784565 | + | 1.35891i | 0.929258 | + | 0.369430i | \(0.120447\pi\) |
−0.144693 | + | 0.989477i | \(0.546220\pi\) | |||||||
\(948\) | −66.5202 | + | 20.7131i | −2.16048 | + | 0.672731i | ||||
\(949\) | −16.0550 | + | 27.8081i | −0.521168 | + | 0.902689i | ||||
\(950\) | −6.25970 | + | 10.8421i | −0.203092 | + | 0.351765i | ||||
\(951\) | 15.2180 | + | 14.0449i | 0.493478 | + | 0.455439i | ||||
\(952\) | −5.78964 | − | 10.0280i | −0.187643 | − | 0.325008i | ||||
\(953\) | −22.7274 | −0.736213 | −0.368106 | − | 0.929784i | \(-0.619994\pi\) | ||||
−0.368106 | + | 0.929784i | \(0.619994\pi\) | |||||||
\(954\) | −60.8874 | − | 28.9230i | −1.97130 | − | 0.936415i | ||||
\(955\) | 1.61100 | 0.0521308 | ||||||||
\(956\) | −39.0490 | − | 67.6348i | −1.26293 | − | 2.18747i | ||||
\(957\) | 3.05206 | − | 13.5382i | 0.0986590 | − | 0.437628i | ||||
\(958\) | 23.0769 | − | 39.9703i | 0.745580 | − | 1.29138i | ||||
\(959\) | −8.21586 | + | 14.2303i | −0.265304 | + | 0.459520i | ||||
\(960\) | −4.75828 | + | 21.1066i | −0.153573 | + | 0.681212i | ||||
\(961\) | 11.5430 | + | 19.9930i | 0.372354 | + | 0.644937i | ||||
\(962\) | −57.2597 | −1.84613 | ||||||||
\(963\) | 10.8995 | − | 7.51660i | 0.351232 | − | 0.242219i | ||||
\(964\) | −17.1510 | −0.552398 | ||||||||
\(965\) | −6.93614 | − | 12.0137i | −0.223282 | − | 0.386736i | ||||
\(966\) | −11.2915 | − | 10.4211i | −0.363299 | − | 0.335295i | ||||
\(967\) | 16.0398 | − | 27.7818i | 0.515805 | − | 0.893401i | −0.484026 | − | 0.875053i | \(-0.660826\pi\) |
0.999832 | − | 0.0183477i | \(-0.00584058\pi\) | |||||||
\(968\) | −7.24900 | + | 12.5556i | −0.232992 | + | 0.403554i | ||||
\(969\) | 66.0844 | − | 20.5774i | 2.12294 | − | 0.661042i | ||||
\(970\) | −15.8196 | − | 27.4003i | −0.507936 | − | 0.879770i | ||||
\(971\) | −19.7116 | −0.632575 | −0.316288 | − | 0.948663i | \(-0.602437\pi\) | ||||
−0.316288 | + | 0.948663i | \(0.602437\pi\) | |||||||
\(972\) | 35.8919 | + | 23.7762i | 1.15123 | + | 0.762621i | ||||
\(973\) | 16.3265 | 0.523402 | ||||||||
\(974\) | 5.55820 | + | 9.62709i | 0.178096 | + | 0.308472i | ||||
\(975\) | 3.72450 | − | 1.15974i | 0.119279 | − | 0.0371413i | ||||
\(976\) | −4.33373 | + | 7.50624i | −0.138719 | + | 0.240269i | ||||
\(977\) | 21.2412 | − | 36.7909i | 0.679567 | − | 1.17704i | −0.295544 | − | 0.955329i | \(-0.595501\pi\) |
0.975111 | − | 0.221716i | \(-0.0711657\pi\) | |||||||
\(978\) | −11.8253 | − | 10.9138i | −0.378132 | − | 0.348984i | ||||
\(979\) | 7.50629 | + | 13.0013i | 0.239902 | + | 0.415523i | ||||
\(980\) | −2.76183 | −0.0882234 | ||||||||
\(981\) | −27.0263 | + | 18.6381i | −0.862883 | + | 0.595067i | ||||
\(982\) | −51.5470 | −1.64493 | ||||||||
\(983\) | 5.38194 | + | 9.32179i | 0.171657 | + | 0.297319i | 0.938999 | − | 0.343919i | \(-0.111755\pi\) |
−0.767342 | + | 0.641238i | \(0.778421\pi\) | |||||||
\(984\) | −1.03338 | + | 4.58382i | −0.0329429 | + | 0.146127i | ||||
\(985\) | 13.2863 | − | 23.0125i | 0.423336 | − | 0.733240i | ||||
\(986\) | −40.3349 | + | 69.8621i | −1.28453 | + | 2.22486i | ||||
\(987\) | −1.66184 | + | 7.37152i | −0.0528969 | + | 0.234638i | ||||
\(988\) | 17.8429 | + | 30.9048i | 0.567659 | + | 0.983213i | ||||
\(989\) | 4.38803 | 0.139531 | ||||||||
\(990\) | 8.92695 | + | 4.24051i | 0.283717 | + | 0.134772i | ||||
\(991\) | 16.2759 | 0.517022 | 0.258511 | − | 0.966008i | \(-0.416768\pi\) | ||||
0.258511 | + | 0.966008i | \(0.416768\pi\) | |||||||
\(992\) | −10.4962 | − | 18.1800i | −0.333256 | − | 0.577216i | ||||
\(993\) | −19.7562 | − | 18.2333i | −0.626945 | − | 0.578617i | ||||
\(994\) | 0.436767 | − | 0.756503i | 0.0138534 | − | 0.0239948i | ||||
\(995\) | 0.873131 | − | 1.51231i | 0.0276801 | − | 0.0479434i | ||||
\(996\) | 28.0985 | − | 8.74934i | 0.890335 | − | 0.277234i | ||||
\(997\) | −2.26128 | − | 3.91664i | −0.0716153 | − | 0.124041i | 0.827994 | − | 0.560737i | \(-0.189482\pi\) |
−0.899609 | + | 0.436695i | \(0.856149\pi\) | |||||||
\(998\) | 7.01310 | 0.221996 | ||||||||
\(999\) | 37.3663 | − | 47.6324i | 1.18222 | − | 1.50702i |
(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.i.e.211.5 | yes | 12 | |
3.2 | odd | 2 | 945.2.i.e.631.2 | 12 | |||
9.2 | odd | 6 | 945.2.i.e.316.2 | 12 | |||
9.4 | even | 3 | 2835.2.a.u.1.2 | 6 | |||
9.5 | odd | 6 | 2835.2.a.v.1.5 | 6 | |||
9.7 | even | 3 | inner | 315.2.i.e.106.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.i.e.106.5 | ✓ | 12 | 9.7 | even | 3 | inner | |
315.2.i.e.211.5 | yes | 12 | 1.1 | even | 1 | trivial | |
945.2.i.e.316.2 | 12 | 9.2 | odd | 6 | |||
945.2.i.e.631.2 | 12 | 3.2 | odd | 2 | |||
2835.2.a.u.1.2 | 6 | 9.4 | even | 3 | |||
2835.2.a.v.1.5 | 6 | 9.5 | odd | 6 |