Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,2,Mod(61,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 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("240.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.s (of order \(4\), 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: | \(1.91640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + 136 x^{10} + 80 x^{9} - 168 x^{8} - 288 x^{7} + 96 x^{6} + 512 x^{5} + 448 x^{4} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 181.9 | ||
Root | \(1.19834 - 0.750988i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.181 |
Dual form | 240.2.s.c.61.9 |
$q$-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 \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.19834 | − | 0.750988i | 0.847354 | − | 0.531029i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0.872033 | − | 1.79988i | 0.436016 | − | 0.899939i | ||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | −0.316325 | + | 1.37838i | −0.129139 | + | 0.562722i | ||||
\(7\) | − | 3.79862i | − | 1.43574i | −0.696176 | − | 0.717871i | \(-0.745117\pi\) | ||
0.696176 | − | 0.717871i | \(-0.254883\pi\) | |||||||
\(8\) | −0.306697 | − | 2.81175i | −0.108434 | − | 0.994104i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.37838 | − | 0.316325i | −0.435883 | − | 0.100031i | ||||
\(11\) | 3.08662 | + | 3.08662i | 0.930650 | + | 0.930650i | 0.997746 | − | 0.0670964i | \(-0.0213735\pi\) |
−0.0670964 | + | 0.997746i | \(0.521374\pi\) | |||||||
\(12\) | 0.656085 | + | 1.88933i | 0.189396 | + | 0.545401i | ||||
\(13\) | 1.54638 | − | 1.54638i | 0.428888 | − | 0.428888i | −0.459361 | − | 0.888249i | \(-0.651922\pi\) |
0.888249 | + | 0.459361i | \(0.151922\pi\) | |||||||
\(14\) | −2.85272 | − | 4.55203i | −0.762420 | − | 1.21658i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −2.47912 | − | 3.13910i | −0.619780 | − | 0.784776i | ||||
\(17\) | 4.32428 | 1.04879 | 0.524396 | − | 0.851474i | \(-0.324291\pi\) | ||||
0.524396 | + | 0.851474i | \(0.324291\pi\) | |||||||
\(18\) | −0.750988 | − | 1.19834i | −0.177010 | − | 0.282451i | ||||
\(19\) | −5.37165 | + | 5.37165i | −1.23234 | + | 1.23234i | −0.269279 | + | 0.963062i | \(0.586785\pi\) |
−0.963062 | + | 0.269279i | \(0.913215\pi\) | |||||||
\(20\) | −1.88933 | + | 0.656085i | −0.422466 | + | 0.146705i | ||||
\(21\) | 2.68603 | + | 2.68603i | 0.586139 | + | 0.586139i | ||||
\(22\) | 6.01683 | + | 1.38080i | 1.28279 | + | 0.294387i | ||||
\(23\) | 3.91059i | 0.815414i | 0.913113 | + | 0.407707i | \(0.133671\pi\) | ||||
−0.913113 | + | 0.407707i | \(0.866329\pi\) | |||||||
\(24\) | 2.20507 | + | 1.77134i | 0.450109 | + | 0.361573i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0.691773 | − | 3.01440i | 0.135668 | − | 0.591172i | ||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | −6.83704 | − | 3.31252i | −1.29208 | − | 0.626007i | ||||
\(29\) | 1.84243 | − | 1.84243i | 0.342131 | − | 0.342131i | −0.515037 | − | 0.857168i | \(-0.672222\pi\) |
0.857168 | + | 0.515037i | \(0.172222\pi\) | |||||||
\(30\) | 1.19834 | − | 0.750988i | 0.218786 | − | 0.137111i | ||||
\(31\) | −9.52790 | −1.71126 | −0.855630 | − | 0.517587i | \(-0.826830\pi\) | ||||
−0.855630 | + | 0.517587i | \(0.826830\pi\) | |||||||
\(32\) | −5.32825 | − | 1.89992i | −0.941911 | − | 0.335862i | ||||
\(33\) | −4.36514 | −0.759873 | ||||||||
\(34\) | 5.18195 | − | 3.24748i | 0.888698 | − | 0.556939i | ||||
\(35\) | −2.68603 | + | 2.68603i | −0.454021 | + | 0.454021i | ||||
\(36\) | −1.79988 | − | 0.872033i | −0.299980 | − | 0.145339i | ||||
\(37\) | 4.55033 | + | 4.55033i | 0.748070 | + | 0.748070i | 0.974116 | − | 0.226047i | \(-0.0725802\pi\) |
−0.226047 | + | 0.974116i | \(0.572580\pi\) | |||||||
\(38\) | −2.40301 | + | 10.4711i | −0.389820 | + | 1.69864i | ||||
\(39\) | 2.18691i | 0.350186i | ||||||||
\(40\) | −1.77134 | + | 2.20507i | −0.280073 | + | 0.348653i | ||||
\(41\) | − | 0.580195i | − | 0.0906112i | −0.998973 | − | 0.0453056i | \(-0.985574\pi\) | ||
0.998973 | − | 0.0453056i | \(-0.0144262\pi\) | |||||||
\(42\) | 5.23595 | + | 1.20160i | 0.807924 | + | 0.185410i | ||||
\(43\) | 0.994741 | + | 0.994741i | 0.151697 | + | 0.151697i | 0.778875 | − | 0.627179i | \(-0.215790\pi\) |
−0.627179 | + | 0.778875i | \(0.715790\pi\) | |||||||
\(44\) | 8.24716 | − | 2.86390i | 1.24331 | − | 0.431749i | ||||
\(45\) | −0.707107 | + | 0.707107i | −0.105409 | + | 0.105409i | ||||
\(46\) | 2.93681 | + | 4.68621i | 0.433008 | + | 0.690944i | ||||
\(47\) | 2.22461 | 0.324492 | 0.162246 | − | 0.986750i | \(-0.448126\pi\) | ||||
0.162246 | + | 0.986750i | \(0.448126\pi\) | |||||||
\(48\) | 3.97268 | + | 0.466680i | 0.573407 | + | 0.0673595i | ||||
\(49\) | −7.42948 | −1.06135 | ||||||||
\(50\) | 0.750988 | + | 1.19834i | 0.106206 | + | 0.169471i | ||||
\(51\) | −3.05773 | + | 3.05773i | −0.428168 | + | 0.428168i | ||||
\(52\) | −1.43480 | − | 4.13178i | −0.198971 | − | 0.572975i | ||||
\(53\) | 4.80257 | + | 4.80257i | 0.659684 | + | 0.659684i | 0.955305 | − | 0.295622i | \(-0.0955267\pi\) |
−0.295622 | + | 0.955305i | \(0.595527\pi\) | |||||||
\(54\) | 1.37838 | + | 0.316325i | 0.187574 | + | 0.0430463i | ||||
\(55\) | − | 4.36514i | − | 0.588595i | ||||||
\(56\) | −10.6808 | + | 1.16502i | −1.42728 | + | 0.155683i | ||||
\(57\) | − | 7.59666i | − | 1.00620i | ||||||
\(58\) | 0.824214 | − | 3.59151i | 0.108225 | − | 0.471588i | ||||
\(59\) | 7.26404 | + | 7.26404i | 0.945698 | + | 0.945698i | 0.998600 | − | 0.0529020i | \(-0.0168471\pi\) |
−0.0529020 | + | 0.998600i | \(0.516847\pi\) | |||||||
\(60\) | 0.872033 | − | 1.79988i | 0.112579 | − | 0.232363i | ||||
\(61\) | 0.301222 | − | 0.301222i | 0.0385676 | − | 0.0385676i | −0.687560 | − | 0.726128i | \(-0.741318\pi\) |
0.726128 | + | 0.687560i | \(0.241318\pi\) | |||||||
\(62\) | −11.4176 | + | 7.15534i | −1.45004 | + | 0.908729i | ||||
\(63\) | −3.79862 | −0.478581 | ||||||||
\(64\) | −7.81187 | + | 1.72471i | −0.976484 | + | 0.215588i | ||||
\(65\) | −2.18691 | −0.271253 | ||||||||
\(66\) | −5.23091 | + | 3.27817i | −0.643881 | + | 0.403514i | ||||
\(67\) | 6.97711 | − | 6.97711i | 0.852389 | − | 0.852389i | −0.138038 | − | 0.990427i | \(-0.544079\pi\) |
0.990427 | + | 0.138038i | \(0.0440795\pi\) | |||||||
\(68\) | 3.77091 | − | 7.78318i | 0.457290 | − | 0.943849i | ||||
\(69\) | −2.76520 | − | 2.76520i | −0.332891 | − | 0.332891i | ||||
\(70\) | −1.20160 | + | 5.23595i | −0.143618 | + | 0.625815i | ||||
\(71\) | − | 0.585051i | − | 0.0694327i | −0.999397 | − | 0.0347164i | \(-0.988947\pi\) | ||
0.999397 | − | 0.0347164i | \(-0.0110528\pi\) | |||||||
\(72\) | −2.81175 | + | 0.306697i | −0.331368 | + | 0.0361445i | ||||
\(73\) | − | 11.9999i | − | 1.40448i | −0.711939 | − | 0.702241i | \(-0.752183\pi\) | ||
0.711939 | − | 0.702241i | \(-0.247817\pi\) | |||||||
\(74\) | 8.87009 | + | 2.03559i | 1.03113 | + | 0.236633i | ||||
\(75\) | −0.707107 | − | 0.707107i | −0.0816497 | − | 0.0816497i | ||||
\(76\) | 4.98406 | + | 14.3526i | 0.571711 | + | 1.64635i | ||||
\(77\) | 11.7249 | − | 11.7249i | 1.33617 | − | 1.33617i | ||||
\(78\) | 1.64234 | + | 2.62066i | 0.185959 | + | 0.296731i | ||||
\(79\) | 12.6436 | 1.42252 | 0.711260 | − | 0.702929i | \(-0.248125\pi\) | ||||
0.711260 | + | 0.702929i | \(0.248125\pi\) | |||||||
\(80\) | −0.466680 | + | 3.97268i | −0.0521765 | + | 0.444159i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −0.435720 | − | 0.695270i | −0.0481172 | − | 0.0767797i | ||||
\(83\) | −11.1632 | + | 11.1632i | −1.22532 | + | 1.22532i | −0.259610 | + | 0.965713i | \(0.583594\pi\) |
−0.965713 | + | 0.259610i | \(0.916406\pi\) | |||||||
\(84\) | 7.17682 | − | 2.49222i | 0.783055 | − | 0.271923i | ||||
\(85\) | −3.05773 | − | 3.05773i | −0.331657 | − | 0.331657i | ||||
\(86\) | 1.93908 | + | 0.444998i | 0.209096 | + | 0.0479854i | ||||
\(87\) | 2.60559i | 0.279349i | ||||||||
\(88\) | 7.73214 | − | 9.62545i | 0.824249 | − | 1.02608i | ||||
\(89\) | 12.9706i | 1.37488i | 0.726241 | + | 0.687440i | \(0.241266\pi\) | ||||
−0.726241 | + | 0.687440i | \(0.758734\pi\) | |||||||
\(90\) | −0.316325 | + | 1.37838i | −0.0333435 | + | 0.145294i | ||||
\(91\) | −5.87409 | − | 5.87409i | −0.615772 | − | 0.615772i | ||||
\(92\) | 7.03858 | + | 3.41016i | 0.733822 | + | 0.355534i | ||||
\(93\) | 6.73724 | − | 6.73724i | 0.698619 | − | 0.698619i | ||||
\(94\) | 2.66583 | − | 1.67065i | 0.274960 | − | 0.172315i | ||||
\(95\) | 7.59666 | 0.779401 | ||||||||
\(96\) | 5.11109 | − | 2.42420i | 0.521649 | − | 0.247419i | ||||
\(97\) | −6.78553 | −0.688966 | −0.344483 | − | 0.938793i | \(-0.611946\pi\) | ||||
−0.344483 | + | 0.938793i | \(0.611946\pi\) | |||||||
\(98\) | −8.90303 | + | 5.57945i | −0.899342 | + | 0.563610i | ||||
\(99\) | 3.08662 | − | 3.08662i | 0.310217 | − | 0.310217i | ||||
\(100\) | 1.79988 | + | 0.872033i | 0.179988 | + | 0.0872033i | ||||
\(101\) | −6.19304 | − | 6.19304i | −0.616231 | − | 0.616231i | 0.328332 | − | 0.944562i | \(-0.393514\pi\) |
−0.944562 | + | 0.328332i | \(0.893514\pi\) | |||||||
\(102\) | −1.36788 | + | 5.96051i | −0.135440 | + | 0.590179i | ||||
\(103\) | − | 11.3519i | − | 1.11854i | −0.828987 | − | 0.559269i | \(-0.811082\pi\) | ||
0.828987 | − | 0.559269i | \(-0.188918\pi\) | |||||||
\(104\) | −4.82230 | − | 3.87376i | −0.472865 | − | 0.379853i | ||||
\(105\) | − | 3.79862i | − | 0.370707i | ||||||
\(106\) | 9.36178 | + | 2.14843i | 0.909296 | + | 0.208674i | ||||
\(107\) | −8.58488 | − | 8.58488i | −0.829932 | − | 0.829932i | 0.157575 | − | 0.987507i | \(-0.449632\pi\) |
−0.987507 | + | 0.157575i | \(0.949632\pi\) | |||||||
\(108\) | 1.88933 | − | 0.656085i | 0.181800 | − | 0.0631318i | ||||
\(109\) | −10.6624 | + | 10.6624i | −1.02127 | + | 1.02127i | −0.0215039 | + | 0.999769i | \(0.506845\pi\) |
−0.999769 | + | 0.0215039i | \(0.993155\pi\) | |||||||
\(110\) | −3.27817 | − | 5.23091i | −0.312561 | − | 0.498748i | ||||
\(111\) | −6.43514 | −0.610797 | ||||||||
\(112\) | −11.9242 | + | 9.41722i | −1.12674 | + | 0.889843i | ||||
\(113\) | −3.11152 | −0.292707 | −0.146354 | − | 0.989232i | \(-0.546754\pi\) | ||||
−0.146354 | + | 0.989232i | \(0.546754\pi\) | |||||||
\(114\) | −5.70500 | − | 9.10337i | −0.534323 | − | 0.852609i | ||||
\(115\) | 2.76520 | − | 2.76520i | 0.257856 | − | 0.257856i | ||||
\(116\) | −1.70949 | − | 4.92282i | −0.158722 | − | 0.457072i | ||||
\(117\) | −1.54638 | − | 1.54638i | −0.142963 | − | 0.142963i | ||||
\(118\) | 14.1600 | + | 3.24957i | 1.30353 | + | 0.299147i | ||||
\(119\) | − | 16.4263i | − | 1.50579i | ||||||
\(120\) | −0.306697 | − | 2.81175i | −0.0279974 | − | 0.256676i | ||||
\(121\) | 8.05441i | 0.732219i | ||||||||
\(122\) | 0.134752 | − | 0.587181i | 0.0121999 | − | 0.0531609i | ||||
\(123\) | 0.410260 | + | 0.410260i | 0.0369919 | + | 0.0369919i | ||||
\(124\) | −8.30864 | + | 17.1490i | −0.746138 | + | 1.54003i | ||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | −4.55203 | + | 2.85272i | −0.405527 | + | 0.254140i | ||||
\(127\) | −7.16390 | −0.635693 | −0.317846 | − | 0.948142i | \(-0.602960\pi\) | ||||
−0.317846 | + | 0.948142i | \(0.602960\pi\) | |||||||
\(128\) | −8.06604 | + | 7.93341i | −0.712944 | + | 0.701221i | ||||
\(129\) | −1.40678 | −0.123860 | ||||||||
\(130\) | −2.62066 | + | 1.64234i | −0.229847 | + | 0.144043i | ||||
\(131\) | −6.55090 | + | 6.55090i | −0.572355 | + | 0.572355i | −0.932786 | − | 0.360431i | \(-0.882630\pi\) |
0.360431 | + | 0.932786i | \(0.382630\pi\) | |||||||
\(132\) | −3.80654 | + | 7.85671i | −0.331317 | + | 0.683839i | ||||
\(133\) | 20.4048 | + | 20.4048i | 1.76932 | + | 1.76932i | ||||
\(134\) | 3.12121 | − | 13.6007i | 0.269632 | − | 1.17492i | ||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | −1.32624 | − | 12.1588i | −0.113724 | − | 1.04261i | ||||
\(137\) | − | 11.0502i | − | 0.944082i | −0.881577 | − | 0.472041i | \(-0.843518\pi\) | ||
0.881577 | − | 0.472041i | \(-0.156482\pi\) | |||||||
\(138\) | −5.39029 | − | 1.23701i | −0.458852 | − | 0.105302i | ||||
\(139\) | −5.17171 | − | 5.17171i | −0.438659 | − | 0.438659i | 0.452902 | − | 0.891561i | \(-0.350389\pi\) |
−0.891561 | + | 0.452902i | \(0.850389\pi\) | |||||||
\(140\) | 2.49222 | + | 7.17682i | 0.210631 | + | 0.606552i | ||||
\(141\) | −1.57304 | + | 1.57304i | −0.132473 | + | 0.132473i | ||||
\(142\) | −0.439366 | − | 0.701089i | −0.0368708 | − | 0.0588341i | ||||
\(143\) | 9.54615 | 0.798289 | ||||||||
\(144\) | −3.13910 | + | 2.47912i | −0.261592 | + | 0.206593i | ||||
\(145\) | −2.60559 | −0.216383 | ||||||||
\(146\) | −9.01178 | − | 14.3799i | −0.745821 | − | 1.19009i | ||||
\(147\) | 5.25343 | − | 5.25343i | 0.433296 | − | 0.433296i | ||||
\(148\) | 12.1581 | − | 4.22200i | 0.999388 | − | 0.347046i | ||||
\(149\) | −5.80335 | − | 5.80335i | −0.475429 | − | 0.475429i | 0.428237 | − | 0.903666i | \(-0.359135\pi\) |
−0.903666 | + | 0.428237i | \(0.859135\pi\) | |||||||
\(150\) | −1.37838 | − | 0.316325i | −0.112544 | − | 0.0258278i | ||||
\(151\) | − | 13.2591i | − | 1.07901i | −0.841982 | − | 0.539505i | \(-0.818611\pi\) | ||
0.841982 | − | 0.539505i | \(-0.181389\pi\) | |||||||
\(152\) | 16.7512 | + | 13.4563i | 1.35870 | + | 1.09145i | ||||
\(153\) | − | 4.32428i | − | 0.349597i | ||||||
\(154\) | 5.24513 | − | 22.8556i | 0.422664 | − | 1.84176i | ||||
\(155\) | 6.73724 | + | 6.73724i | 0.541148 | + | 0.541148i | ||||
\(156\) | 3.93617 | + | 1.90706i | 0.315146 | + | 0.152687i | ||||
\(157\) | 6.83329 | − | 6.83329i | 0.545356 | − | 0.545356i | −0.379738 | − | 0.925094i | \(-0.623986\pi\) |
0.925094 | + | 0.379738i | \(0.123986\pi\) | |||||||
\(158\) | 15.1514 | − | 9.49522i | 1.20538 | − | 0.755399i | ||||
\(159\) | −6.79186 | −0.538629 | ||||||||
\(160\) | 2.42420 | + | 5.11109i | 0.191650 | + | 0.404067i | ||||
\(161\) | 14.8548 | 1.17072 | ||||||||
\(162\) | −1.19834 | + | 0.750988i | −0.0941504 | + | 0.0590032i | ||||
\(163\) | −7.11541 | + | 7.11541i | −0.557322 | + | 0.557322i | −0.928544 | − | 0.371222i | \(-0.878939\pi\) |
0.371222 | + | 0.928544i | \(0.378939\pi\) | |||||||
\(164\) | −1.04428 | − | 0.505949i | −0.0815445 | − | 0.0395080i | ||||
\(165\) | 3.08662 | + | 3.08662i | 0.240293 | + | 0.240293i | ||||
\(166\) | −4.99388 | + | 21.7608i | −0.387600 | + | 1.68896i | ||||
\(167\) | − | 6.14029i | − | 0.475150i | −0.971369 | − | 0.237575i | \(-0.923648\pi\) | ||
0.971369 | − | 0.237575i | \(-0.0763525\pi\) | |||||||
\(168\) | 6.72864 | − | 8.37623i | 0.519126 | − | 0.646240i | ||||
\(169\) | 8.21743i | 0.632110i | ||||||||
\(170\) | −5.96051 | − | 1.36788i | −0.457150 | − | 0.104911i | ||||
\(171\) | 5.37165 | + | 5.37165i | 0.410780 | + | 0.410780i | ||||
\(172\) | 2.65786 | − | 0.922965i | 0.202660 | − | 0.0703754i | ||||
\(173\) | −7.29269 | + | 7.29269i | −0.554453 | + | 0.554453i | −0.927723 | − | 0.373270i | \(-0.878237\pi\) |
0.373270 | + | 0.927723i | \(0.378237\pi\) | |||||||
\(174\) | 1.95677 | + | 3.12239i | 0.148342 | + | 0.236707i | ||||
\(175\) | 3.79862 | 0.287148 | ||||||||
\(176\) | 2.03712 | − | 17.3413i | 0.153554 | − | 1.30715i | ||||
\(177\) | −10.2729 | −0.772159 | ||||||||
\(178\) | 9.74077 | + | 15.5432i | 0.730101 | + | 1.16501i | ||||
\(179\) | 6.22897 | − | 6.22897i | 0.465575 | − | 0.465575i | −0.434902 | − | 0.900478i | \(-0.643217\pi\) |
0.900478 | + | 0.434902i | \(0.143217\pi\) | |||||||
\(180\) | 0.656085 | + | 1.88933i | 0.0489017 | + | 0.140822i | ||||
\(181\) | −1.27302 | − | 1.27302i | −0.0946227 | − | 0.0946227i | 0.658211 | − | 0.752834i | \(-0.271314\pi\) |
−0.752834 | + | 0.658211i | \(0.771314\pi\) | |||||||
\(182\) | −11.4505 | − | 2.62778i | −0.848770 | − | 0.194784i | ||||
\(183\) | 0.425993i | 0.0314903i | ||||||||
\(184\) | 10.9956 | − | 1.19936i | 0.810606 | − | 0.0884182i | ||||
\(185\) | − | 6.43514i | − | 0.473121i | ||||||
\(186\) | 3.01391 | − | 13.1331i | 0.220990 | − | 0.962965i | ||||
\(187\) | 13.3474 | + | 13.3474i | 0.976058 | + | 0.976058i | ||||
\(188\) | 1.93993 | − | 4.00402i | 0.141484 | − | 0.292023i | ||||
\(189\) | 2.68603 | − | 2.68603i | 0.195380 | − | 0.195380i | ||||
\(190\) | 9.10337 | − | 5.70500i | 0.660428 | − | 0.413885i | ||||
\(191\) | 9.63638 | 0.697264 | 0.348632 | − | 0.937260i | \(-0.386646\pi\) | ||||
0.348632 | + | 0.937260i | \(0.386646\pi\) | |||||||
\(192\) | 4.30428 | − | 6.74338i | 0.310634 | − | 0.486662i | ||||
\(193\) | −3.64530 | −0.262394 | −0.131197 | − | 0.991356i | \(-0.541882\pi\) | ||||
−0.131197 | + | 0.991356i | \(0.541882\pi\) | |||||||
\(194\) | −8.13137 | + | 5.09586i | −0.583798 | + | 0.365861i | ||||
\(195\) | 1.54638 | − | 1.54638i | 0.110738 | − | 0.110738i | ||||
\(196\) | −6.47875 | + | 13.3721i | −0.462768 | + | 0.955153i | ||||
\(197\) | −7.55422 | − | 7.55422i | −0.538216 | − | 0.538216i | 0.384789 | − | 0.923005i | \(-0.374274\pi\) |
−0.923005 | + | 0.384789i | \(0.874274\pi\) | |||||||
\(198\) | 1.38080 | − | 6.01683i | 0.0981292 | − | 0.427597i | ||||
\(199\) | 23.7442i | 1.68318i | 0.540116 | + | 0.841591i | \(0.318380\pi\) | ||||
−0.540116 | + | 0.841591i | \(0.681620\pi\) | |||||||
\(200\) | 2.81175 | − | 0.306697i | 0.198821 | − | 0.0216867i | ||||
\(201\) | 9.86712i | 0.695973i | ||||||||
\(202\) | −12.0723 | − | 2.77046i | −0.849402 | − | 0.194929i | ||||
\(203\) | −6.99870 | − | 6.99870i | −0.491212 | − | 0.491212i | ||||
\(204\) | 2.83710 | + | 8.16997i | 0.198637 | + | 0.572013i | ||||
\(205\) | −0.410260 | + | 0.410260i | −0.0286538 | + | 0.0286538i | ||||
\(206\) | −8.52516 | − | 13.6034i | −0.593976 | − | 0.947797i | ||||
\(207\) | 3.91059 | 0.271805 | ||||||||
\(208\) | −8.68789 | − | 1.02059i | −0.602397 | − | 0.0707650i | ||||
\(209\) | −33.1605 | −2.29376 | ||||||||
\(210\) | −2.85272 | − | 4.55203i | −0.196856 | − | 0.314120i | ||||
\(211\) | 14.5856 | − | 14.5856i | 1.00412 | − | 1.00412i | 0.00412399 | − | 0.999991i | \(-0.498687\pi\) |
0.999991 | − | 0.00412399i | \(-0.00131271\pi\) | |||||||
\(212\) | 12.8320 | − | 4.45604i | 0.881308 | − | 0.306042i | ||||
\(213\) | 0.413693 | + | 0.413693i | 0.0283458 | + | 0.0283458i | ||||
\(214\) | −16.7347 | − | 3.84045i | −1.14396 | − | 0.262528i | ||||
\(215\) | − | 1.40678i | − | 0.0959413i | ||||||
\(216\) | 1.77134 | − | 2.20507i | 0.120524 | − | 0.150036i | ||||
\(217\) | 36.1928i | 2.45693i | ||||||||
\(218\) | −4.76983 | + | 20.7845i | −0.323054 | + | 1.40770i | ||||
\(219\) | 8.48521 | + | 8.48521i | 0.573377 | + | 0.573377i | ||||
\(220\) | −7.85671 | − | 3.80654i | −0.529699 | − | 0.256637i | ||||
\(221\) | 6.68697 | − | 6.68697i | 0.449814 | − | 0.449814i | ||||
\(222\) | −7.71148 | + | 4.83272i | −0.517561 | + | 0.324351i | ||||
\(223\) | −13.6893 | −0.916702 | −0.458351 | − | 0.888771i | \(-0.651560\pi\) | ||||
−0.458351 | + | 0.888771i | \(0.651560\pi\) | |||||||
\(224\) | −7.21707 | + | 20.2400i | −0.482211 | + | 1.35234i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −3.72865 | + | 2.33671i | −0.248026 | + | 0.155436i | ||||
\(227\) | −11.9490 | + | 11.9490i | −0.793085 | + | 0.793085i | −0.981994 | − | 0.188910i | \(-0.939505\pi\) |
0.188910 | + | 0.981994i | \(0.439505\pi\) | |||||||
\(228\) | −13.6731 | − | 6.62454i | −0.905520 | − | 0.438721i | ||||
\(229\) | 9.40821 | + | 9.40821i | 0.621712 | + | 0.621712i | 0.945969 | − | 0.324257i | \(-0.105114\pi\) |
−0.324257 | + | 0.945969i | \(0.605114\pi\) | |||||||
\(230\) | 1.23701 | − | 5.39029i | 0.0815663 | − | 0.355425i | ||||
\(231\) | 16.5815i | 1.09098i | ||||||||
\(232\) | −5.74553 | − | 4.61539i | −0.377213 | − | 0.303016i | ||||
\(233\) | 11.8223i | 0.774505i | 0.921974 | + | 0.387253i | \(0.126576\pi\) | ||||
−0.921974 | + | 0.387253i | \(0.873424\pi\) | |||||||
\(234\) | −3.01440 | − | 0.691773i | −0.197057 | − | 0.0452226i | ||||
\(235\) | −1.57304 | − | 1.57304i | −0.102614 | − | 0.102614i | ||||
\(236\) | 19.4089 | − | 6.73990i | 1.26341 | − | 0.438730i | ||||
\(237\) | −8.94040 | + | 8.94040i | −0.580741 | + | 0.580741i | ||||
\(238\) | −12.3359 | − | 19.6842i | −0.799621 | − | 1.27594i | ||||
\(239\) | 11.2115 | 0.725213 | 0.362607 | − | 0.931942i | \(-0.381887\pi\) | ||||
0.362607 | + | 0.931942i | \(0.381887\pi\) | |||||||
\(240\) | −2.47912 | − | 3.13910i | −0.160026 | − | 0.202628i | ||||
\(241\) | 7.89997 | 0.508881 | 0.254441 | − | 0.967088i | \(-0.418109\pi\) | ||||
0.254441 | + | 0.967088i | \(0.418109\pi\) | |||||||
\(242\) | 6.04877 | + | 9.65191i | 0.388830 | + | 0.620448i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −0.279488 | − | 0.804839i | −0.0178924 | − | 0.0515245i | ||||
\(245\) | 5.25343 | + | 5.25343i | 0.335630 | + | 0.335630i | ||||
\(246\) | 0.799730 | + | 0.183530i | 0.0509890 | + | 0.0117014i | ||||
\(247\) | 16.6132i | 1.05707i | ||||||||
\(248\) | 2.92217 | + | 26.7901i | 0.185558 | + | 1.70117i | ||||
\(249\) | − | 15.7872i | − | 1.00047i | ||||||
\(250\) | 0.316325 | − | 1.37838i | 0.0200061 | − | 0.0871766i | ||||
\(251\) | −5.34286 | − | 5.34286i | −0.337238 | − | 0.337238i | 0.518089 | − | 0.855327i | \(-0.326644\pi\) |
−0.855327 | + | 0.518089i | \(0.826644\pi\) | |||||||
\(252\) | −3.31252 | + | 6.83704i | −0.208669 | + | 0.430693i | ||||
\(253\) | −12.0705 | + | 12.0705i | −0.758865 | + | 0.758865i | ||||
\(254\) | −8.58477 | + | 5.38000i | −0.538657 | + | 0.337571i | ||||
\(255\) | 4.32428 | 0.270797 | ||||||||
\(256\) | −3.70795 | + | 15.5644i | −0.231747 | + | 0.972776i | ||||
\(257\) | 15.5250 | 0.968420 | 0.484210 | − | 0.874952i | \(-0.339107\pi\) | ||||
0.484210 | + | 0.874952i | \(0.339107\pi\) | |||||||
\(258\) | −1.68579 | + | 1.05647i | −0.104953 | + | 0.0657731i | ||||
\(259\) | 17.2850 | − | 17.2850i | 1.07404 | − | 1.07404i | ||||
\(260\) | −1.90706 | + | 3.93617i | −0.118271 | + | 0.244111i | ||||
\(261\) | −1.84243 | − | 1.84243i | −0.114044 | − | 0.114044i | ||||
\(262\) | −2.93055 | + | 12.7698i | −0.181050 | + | 0.788924i | ||||
\(263\) | − | 14.3705i | − | 0.886126i | −0.896491 | − | 0.443063i | \(-0.853892\pi\) | ||
0.896491 | − | 0.443063i | \(-0.146108\pi\) | |||||||
\(264\) | 1.33877 | + | 12.2737i | 0.0823957 | + | 0.755392i | ||||
\(265\) | − | 6.79186i | − | 0.417221i | ||||||
\(266\) | 39.7757 | + | 9.12811i | 2.43880 | + | 0.559680i | ||||
\(267\) | −9.17160 | − | 9.17160i | −0.561293 | − | 0.561293i | ||||
\(268\) | −6.47367 | − | 18.6422i | −0.395443 | − | 1.13875i | ||||
\(269\) | −19.0607 | + | 19.0607i | −1.16215 | + | 1.16215i | −0.178145 | + | 0.984004i | \(0.557010\pi\) |
−0.984004 | + | 0.178145i | \(0.942990\pi\) | |||||||
\(270\) | −0.750988 | − | 1.19834i | −0.0457037 | − | 0.0729286i | ||||
\(271\) | −4.66889 | −0.283615 | −0.141808 | − | 0.989894i | \(-0.545291\pi\) | ||||
−0.141808 | + | 0.989894i | \(0.545291\pi\) | |||||||
\(272\) | −10.7204 | − | 13.5744i | −0.650020 | − | 0.823067i | ||||
\(273\) | 8.30722 | 0.502776 | ||||||||
\(274\) | −8.29857 | − | 13.2419i | −0.501335 | − | 0.799971i | ||||
\(275\) | −3.08662 | + | 3.08662i | −0.186130 | + | 0.186130i | ||||
\(276\) | −7.38837 | + | 2.56568i | −0.444728 | + | 0.154436i | ||||
\(277\) | −6.24572 | − | 6.24572i | −0.375269 | − | 0.375269i | 0.494123 | − | 0.869392i | \(-0.335489\pi\) |
−0.869392 | + | 0.494123i | \(0.835489\pi\) | |||||||
\(278\) | −10.0814 | − | 2.31357i | −0.604640 | − | 0.138759i | ||||
\(279\) | 9.52790i | 0.570420i | ||||||||
\(280\) | 8.37623 | + | 6.72864i | 0.500575 | + | 0.402113i | ||||
\(281\) | 29.7389i | 1.77407i | 0.461699 | + | 0.887037i | \(0.347240\pi\) | ||||
−0.461699 | + | 0.887037i | \(0.652760\pi\) | |||||||
\(282\) | −0.703698 | + | 3.06636i | −0.0419046 | + | 0.182599i | ||||
\(283\) | −9.49040 | − | 9.49040i | −0.564146 | − | 0.564146i | 0.366337 | − | 0.930482i | \(-0.380612\pi\) |
−0.930482 | + | 0.366337i | \(0.880612\pi\) | |||||||
\(284\) | −1.05302 | − | 0.510183i | −0.0624852 | − | 0.0302738i | ||||
\(285\) | −5.37165 | + | 5.37165i | −0.318189 | + | 0.318189i | ||||
\(286\) | 11.4395 | − | 7.16905i | 0.676433 | − | 0.423915i | ||||
\(287\) | −2.20394 | −0.130094 | ||||||||
\(288\) | −1.89992 | + | 5.32825i | −0.111954 | + | 0.313970i | ||||
\(289\) | 1.69940 | 0.0999648 | ||||||||
\(290\) | −3.12239 | + | 1.95677i | −0.183353 | + | 0.114906i | ||||
\(291\) | 4.79809 | − | 4.79809i | 0.281269 | − | 0.281269i | ||||
\(292\) | −21.5983 | − | 10.4643i | −1.26395 | − | 0.612377i | ||||
\(293\) | −1.72797 | − | 1.72797i | −0.100949 | − | 0.100949i | 0.654829 | − | 0.755777i | \(-0.272741\pi\) |
−0.755777 | + | 0.654829i | \(0.772741\pi\) | |||||||
\(294\) | 2.35013 | − | 10.2407i | 0.137062 | − | 0.597248i | ||||
\(295\) | − | 10.2729i | − | 0.598112i | ||||||
\(296\) | 11.3988 | − | 14.1900i | 0.662543 | − | 0.824775i | ||||
\(297\) | 4.36514i | 0.253291i | ||||||||
\(298\) | −11.3126 | − | 2.59613i | −0.655323 | − | 0.150390i | ||||
\(299\) | 6.04724 | + | 6.04724i | 0.349721 | + | 0.349721i | ||||
\(300\) | −1.88933 | + | 0.656085i | −0.109080 | + | 0.0378791i | ||||
\(301\) | 3.77864 | − | 3.77864i | 0.217797 | − | 0.217797i | ||||
\(302\) | −9.95743 | − | 15.8889i | −0.572986 | − | 0.914304i | ||||
\(303\) | 8.75828 | 0.503150 | ||||||||
\(304\) | 30.1791 | + | 3.54521i | 1.73089 | + | 0.203332i | ||||
\(305\) | −0.425993 | −0.0243923 | ||||||||
\(306\) | −3.24748 | − | 5.18195i | −0.185646 | − | 0.296233i | ||||
\(307\) | 17.5875 | − | 17.5875i | 1.00377 | − | 1.00377i | 0.00377977 | − | 0.999993i | \(-0.498797\pi\) |
0.999993 | − | 0.00377977i | \(-0.00120314\pi\) | |||||||
\(308\) | −10.8789 | − | 31.3278i | −0.619881 | − | 1.78507i | ||||
\(309\) | 8.02701 | + | 8.02701i | 0.456641 | + | 0.456641i | ||||
\(310\) | 13.1331 | + | 3.01391i | 0.745909 | + | 0.171178i | ||||
\(311\) | 1.71809i | 0.0974241i | 0.998813 | + | 0.0487120i | \(0.0155117\pi\) | ||||
−0.998813 | + | 0.0487120i | \(0.984488\pi\) | |||||||
\(312\) | 6.14904 | − | 0.670717i | 0.348121 | − | 0.0379719i | ||||
\(313\) | − | 16.4421i | − | 0.929363i | −0.885478 | − | 0.464682i | \(-0.846169\pi\) | ||
0.885478 | − | 0.464682i | \(-0.153831\pi\) | |||||||
\(314\) | 3.05687 | − | 13.3203i | 0.172509 | − | 0.751709i | ||||
\(315\) | 2.68603 | + | 2.68603i | 0.151340 | + | 0.151340i | ||||
\(316\) | 11.0257 | − | 22.7570i | 0.620242 | − | 1.28018i | ||||
\(317\) | −7.96065 | + | 7.96065i | −0.447114 | + | 0.447114i | −0.894394 | − | 0.447280i | \(-0.852393\pi\) |
0.447280 | + | 0.894394i | \(0.352393\pi\) | |||||||
\(318\) | −8.13895 | + | 5.10061i | −0.456410 | + | 0.286028i | ||||
\(319\) | 11.3738 | 0.636809 | ||||||||
\(320\) | 6.74338 | + | 4.30428i | 0.376967 | + | 0.240616i | ||||
\(321\) | 12.1409 | 0.677637 | ||||||||
\(322\) | 17.8011 | − | 11.1558i | 0.992017 | − | 0.621688i | ||||
\(323\) | −23.2285 | + | 23.2285i | −1.29247 | + | 1.29247i | ||||
\(324\) | −0.872033 | + | 1.79988i | −0.0484463 | + | 0.0999932i | ||||
\(325\) | 1.54638 | + | 1.54638i | 0.0857776 | + | 0.0857776i | ||||
\(326\) | −3.18308 | + | 13.8703i | −0.176295 | + | 0.768203i | ||||
\(327\) | − | 15.0789i | − | 0.833866i | ||||||
\(328\) | −1.63136 | + | 0.177944i | −0.0900769 | + | 0.00982530i | ||||
\(329\) | − | 8.45043i | − | 0.465887i | ||||||
\(330\) | 6.01683 | + | 1.38080i | 0.331215 | + | 0.0760105i | ||||
\(331\) | 9.02535 | + | 9.02535i | 0.496078 | + | 0.496078i | 0.910215 | − | 0.414137i | \(-0.135916\pi\) |
−0.414137 | + | 0.910215i | \(0.635916\pi\) | |||||||
\(332\) | 10.3577 | + | 29.8271i | 0.568455 | + | 1.63698i | ||||
\(333\) | 4.55033 | − | 4.55033i | 0.249357 | − | 0.249357i | ||||
\(334\) | −4.61128 | − | 7.35814i | −0.252318 | − | 0.402620i | ||||
\(335\) | −9.86712 | −0.539098 | ||||||||
\(336\) | 1.77274 | − | 15.0907i | 0.0967109 | − | 0.823265i | ||||
\(337\) | 7.44173 | 0.405377 | 0.202688 | − | 0.979243i | \(-0.435032\pi\) | ||||
0.202688 | + | 0.979243i | \(0.435032\pi\) | |||||||
\(338\) | 6.17120 | + | 9.84727i | 0.335669 | + | 0.535621i | ||||
\(339\) | 2.20018 | − | 2.20018i | 0.119497 | − | 0.119497i | ||||
\(340\) | −8.16997 | + | 2.83710i | −0.443079 | + | 0.153863i | ||||
\(341\) | −29.4090 | − | 29.4090i | −1.59258 | − | 1.59258i | ||||
\(342\) | 10.4711 | + | 2.40301i | 0.566213 | + | 0.129940i | ||||
\(343\) | 1.63142i | 0.0880882i | ||||||||
\(344\) | 2.49188 | − | 3.10205i | 0.134353 | − | 0.167251i | ||||
\(345\) | 3.91059i | 0.210539i | ||||||||
\(346\) | −3.26239 | + | 14.2158i | −0.175387 | + | 0.764249i | ||||
\(347\) | −0.659315 | − | 0.659315i | −0.0353939 | − | 0.0353939i | 0.689188 | − | 0.724582i | \(-0.257967\pi\) |
−0.724582 | + | 0.689188i | \(0.757967\pi\) | |||||||
\(348\) | 4.68975 | + | 2.27216i | 0.251397 | + | 0.121801i | ||||
\(349\) | 8.04705 | − | 8.04705i | 0.430749 | − | 0.430749i | −0.458134 | − | 0.888883i | \(-0.651482\pi\) |
0.888883 | + | 0.458134i | \(0.151482\pi\) | |||||||
\(350\) | 4.55203 | − | 2.85272i | 0.243316 | − | 0.152484i | ||||
\(351\) | 2.18691 | 0.116729 | ||||||||
\(352\) | −10.5820 | − | 22.3106i | −0.564020 | − | 1.18916i | ||||
\(353\) | 18.3339 | 0.975815 | 0.487907 | − | 0.872895i | \(-0.337760\pi\) | ||||
0.487907 | + | 0.872895i | \(0.337760\pi\) | |||||||
\(354\) | −12.3104 | + | 7.71483i | −0.654292 | + | 0.410039i | ||||
\(355\) | −0.413693 | + | 0.413693i | −0.0219566 | + | 0.0219566i | ||||
\(356\) | 23.3455 | + | 11.3108i | 1.23731 | + | 0.599470i | ||||
\(357\) | 11.6151 | + | 11.6151i | 0.614738 | + | 0.614738i | ||||
\(358\) | 2.78653 | − | 12.1423i | 0.147273 | − | 0.641741i | ||||
\(359\) | 11.8783i | 0.626912i | 0.949603 | + | 0.313456i | \(0.101487\pi\) | ||||
−0.949603 | + | 0.313456i | \(0.898513\pi\) | |||||||
\(360\) | 2.20507 | + | 1.77134i | 0.116218 | + | 0.0933578i | ||||
\(361\) | − | 38.7093i | − | 2.03733i | ||||||
\(362\) | −2.48153 | − | 0.569485i | −0.130426 | − | 0.0299315i | ||||
\(363\) | −5.69533 | − | 5.69533i | −0.298927 | − | 0.298927i | ||||
\(364\) | −15.6951 | + | 5.45025i | −0.822644 | + | 0.285671i | ||||
\(365\) | −8.48521 | + | 8.48521i | −0.444136 | + | 0.444136i | ||||
\(366\) | 0.319916 | + | 0.510484i | 0.0167223 | + | 0.0266834i | ||||
\(367\) | −24.0792 | −1.25692 | −0.628462 | − | 0.777841i | \(-0.716315\pi\) | ||||
−0.628462 | + | 0.777841i | \(0.716315\pi\) | |||||||
\(368\) | 12.2757 | − | 9.69481i | 0.639917 | − | 0.505377i | ||||
\(369\) | −0.580195 | −0.0302037 | ||||||||
\(370\) | −4.83272 | − | 7.71148i | −0.251241 | − | 0.400901i | ||||
\(371\) | 18.2431 | − | 18.2431i | 0.947135 | − | 0.947135i | ||||
\(372\) | −6.25111 | − | 18.0013i | −0.324105 | − | 0.933324i | ||||
\(373\) | 5.50986 | + | 5.50986i | 0.285290 | + | 0.285290i | 0.835214 | − | 0.549925i | \(-0.185344\pi\) |
−0.549925 | + | 0.835214i | \(0.685344\pi\) | |||||||
\(374\) | 26.0184 | + | 5.97097i | 1.34538 | + | 0.308751i | ||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | −0.682279 | − | 6.25504i | −0.0351859 | − | 0.322579i | ||||
\(377\) | − | 5.69820i | − | 0.293472i | ||||||
\(378\) | 1.20160 | − | 5.23595i | 0.0618034 | − | 0.269308i | ||||
\(379\) | −4.41212 | − | 4.41212i | −0.226635 | − | 0.226635i | 0.584650 | − | 0.811285i | \(-0.301232\pi\) |
−0.811285 | + | 0.584650i | \(0.801232\pi\) | |||||||
\(380\) | 6.62454 | − | 13.6731i | 0.339832 | − | 0.701413i | ||||
\(381\) | 5.06564 | − | 5.06564i | 0.259521 | − | 0.259521i | ||||
\(382\) | 11.5477 | − | 7.23681i | 0.590829 | − | 0.370267i | ||||
\(383\) | 12.4394 | 0.635625 | 0.317812 | − | 0.948154i | \(-0.397052\pi\) | ||||
0.317812 | + | 0.948154i | \(0.397052\pi\) | |||||||
\(384\) | 0.0937806 | − | 11.3133i | 0.00478572 | − | 0.577330i | ||||
\(385\) | −16.5815 | −0.845070 | ||||||||
\(386\) | −4.36830 | + | 2.73757i | −0.222341 | + | 0.139339i | ||||
\(387\) | 0.994741 | − | 0.994741i | 0.0505655 | − | 0.0505655i | ||||
\(388\) | −5.91720 | + | 12.2131i | −0.300401 | + | 0.620027i | ||||
\(389\) | −22.7006 | − | 22.7006i | −1.15097 | − | 1.15097i | −0.986359 | − | 0.164609i | \(-0.947364\pi\) |
−0.164609 | − | 0.986359i | \(-0.552636\pi\) | |||||||
\(390\) | 0.691773 | − | 3.01440i | 0.0350293 | − | 0.152640i | ||||
\(391\) | 16.9105i | 0.855199i | ||||||||
\(392\) | 2.27859 | + | 20.8898i | 0.115086 | + | 1.05510i | ||||
\(393\) | − | 9.26437i | − | 0.467326i | ||||||
\(394\) | −14.7257 | − | 3.37939i | −0.741868 | − | 0.170251i | ||||
\(395\) | −8.94040 | − | 8.94040i | −0.449840 | − | 0.449840i | ||||
\(396\) | −2.86390 | − | 8.24716i | −0.143916 | − | 0.414436i | ||||
\(397\) | −23.2641 | + | 23.2641i | −1.16759 | + | 1.16759i | −0.184819 | + | 0.982773i | \(0.559170\pi\) |
−0.982773 | + | 0.184819i | \(0.940830\pi\) | |||||||
\(398\) | 17.8316 | + | 28.4536i | 0.893818 | + | 1.42625i | ||||
\(399\) | −28.8568 | −1.44465 | ||||||||
\(400\) | 3.13910 | − | 2.47912i | 0.156955 | − | 0.123956i | ||||
\(401\) | 31.5965 | 1.57786 | 0.788928 | − | 0.614486i | \(-0.210636\pi\) | ||||
0.788928 | + | 0.614486i | \(0.210636\pi\) | |||||||
\(402\) | 7.41009 | + | 11.8242i | 0.369582 | + | 0.589735i | ||||
\(403\) | −14.7337 | + | 14.7337i | −0.733939 | + | 0.733939i | ||||
\(404\) | −16.5473 | + | 5.74618i | −0.823257 | + | 0.285883i | ||||
\(405\) | 0.707107 | + | 0.707107i | 0.0351364 | + | 0.0351364i | ||||
\(406\) | −13.6428 | − | 3.13087i | −0.677078 | − | 0.155383i | ||||
\(407\) | 28.0903i | 1.39238i | ||||||||
\(408\) | 9.53536 | + | 7.65977i | 0.472071 | + | 0.379215i | ||||
\(409\) | − | 14.4988i | − | 0.716917i | −0.933546 | − | 0.358459i | \(-0.883302\pi\) | ||
0.933546 | − | 0.358459i | \(-0.116698\pi\) | |||||||
\(410\) | −0.183530 | + | 0.799730i | −0.00906390 | + | 0.0394959i | ||||
\(411\) | 7.81367 | + | 7.81367i | 0.385420 | + | 0.385420i | ||||
\(412\) | −20.4321 | − | 9.89924i | −1.00661 | − | 0.487700i | ||||
\(413\) | 27.5933 | − | 27.5933i | 1.35778 | − | 1.35778i | ||||
\(414\) | 4.68621 | − | 2.93681i | 0.230315 | − | 0.144336i | ||||
\(415\) | 15.7872 | 0.774963 | ||||||||
\(416\) | −11.1775 | + | 5.30150i | −0.548022 | + | 0.259927i | ||||
\(417\) | 7.31391 | 0.358164 | ||||||||
\(418\) | −39.7375 | + | 24.9031i | −1.94362 | + | 1.21805i | ||||
\(419\) | 24.0709 | − | 24.0709i | 1.17594 | − | 1.17594i | 0.195169 | − | 0.980770i | \(-0.437475\pi\) |
0.980770 | − | 0.195169i | \(-0.0625254\pi\) | |||||||
\(420\) | −6.83704 | − | 3.31252i | −0.333613 | − | 0.161634i | ||||
\(421\) | −20.1095 | − | 20.1095i | −0.980079 | − | 0.980079i | 0.0197268 | − | 0.999805i | \(-0.493720\pi\) |
−0.999805 | + | 0.0197268i | \(0.993720\pi\) | |||||||
\(422\) | 6.52488 | − | 28.4321i | 0.317626 | − | 1.38406i | ||||
\(423\) | − | 2.22461i | − | 0.108164i | ||||||
\(424\) | 12.0307 | − | 14.9766i | 0.584262 | − | 0.727326i | ||||
\(425\) | 4.32428i | 0.209758i | ||||||||
\(426\) | 0.806424 | + | 0.185066i | 0.0390714 | + | 0.00896647i | ||||
\(427\) | −1.14423 | − | 1.14423i | −0.0553730 | − | 0.0553730i | ||||
\(428\) | −22.9380 | + | 7.96544i | −1.10875 | + | 0.385024i | ||||
\(429\) | −6.75015 | + | 6.75015i | −0.325900 | + | 0.325900i | ||||
\(430\) | −1.05647 | − | 1.68579i | −0.0509476 | − | 0.0812962i | ||||
\(431\) | −29.9026 | −1.44036 | −0.720180 | − | 0.693787i | \(-0.755941\pi\) | ||||
−0.720180 | + | 0.693787i | \(0.755941\pi\) | |||||||
\(432\) | 0.466680 | − | 3.97268i | 0.0224532 | − | 0.191136i | ||||
\(433\) | 17.7487 | 0.852950 | 0.426475 | − | 0.904499i | \(-0.359755\pi\) | ||||
0.426475 | + | 0.904499i | \(0.359755\pi\) | |||||||
\(434\) | 27.1804 | + | 43.3713i | 1.30470 | + | 2.08189i | ||||
\(435\) | 1.84243 | − | 1.84243i | 0.0883379 | − | 0.0883379i | ||||
\(436\) | 9.89305 | + | 28.4890i | 0.473791 | + | 1.36437i | ||||
\(437\) | −21.0063 | − | 21.0063i | −1.00487 | − | 1.00487i | ||||
\(438\) | 16.5405 | + | 3.79586i | 0.790333 | + | 0.181373i | ||||
\(439\) | − | 15.1376i | − | 0.722478i | −0.932473 | − | 0.361239i | \(-0.882354\pi\) | ||
0.932473 | − | 0.361239i | \(-0.117646\pi\) | |||||||
\(440\) | −12.2737 | + | 1.33877i | −0.585124 | + | 0.0638234i | ||||
\(441\) | 7.42948i | 0.353785i | ||||||||
\(442\) | 2.99142 | − | 13.0351i | 0.142287 | − | 0.620016i | ||||
\(443\) | −16.4687 | − | 16.4687i | −0.782451 | − | 0.782451i | 0.197793 | − | 0.980244i | \(-0.436623\pi\) |
−0.980244 | + | 0.197793i | \(0.936623\pi\) | |||||||
\(444\) | −5.61165 | + | 11.5825i | −0.266317 | + | 0.549679i | ||||
\(445\) | 9.17160 | − | 9.17160i | 0.434775 | − | 0.434775i | ||||
\(446\) | −16.4044 | + | 10.2805i | −0.776771 | + | 0.486795i | ||||
\(447\) | 8.20718 | 0.388186 | ||||||||
\(448\) | 6.55150 | + | 29.6743i | 0.309529 | + | 1.40198i | ||||
\(449\) | 35.6078 | 1.68044 | 0.840218 | − | 0.542249i | \(-0.182427\pi\) | ||||
0.840218 | + | 0.542249i | \(0.182427\pi\) | |||||||
\(450\) | 1.19834 | − | 0.750988i | 0.0564902 | − | 0.0354019i | ||||
\(451\) | 1.79084 | − | 1.79084i | 0.0843273 | − | 0.0843273i | ||||
\(452\) | −2.71335 | + | 5.60035i | −0.127625 | + | 0.263418i | ||||
\(453\) | 9.37560 | + | 9.37560i | 0.440504 | + | 0.440504i | ||||
\(454\) | −5.34540 | + | 23.2926i | −0.250872 | + | 1.09317i | ||||
\(455\) | 8.30722i | 0.389449i | ||||||||
\(456\) | −21.3599 | + | 2.32987i | −1.00027 | + | 0.109106i | ||||
\(457\) | − | 1.98064i | − | 0.0926502i | −0.998926 | − | 0.0463251i | \(-0.985249\pi\) | ||
0.998926 | − | 0.0463251i | \(-0.0147510\pi\) | |||||||
\(458\) | 18.3397 | + | 4.20877i | 0.856957 | + | 0.196663i | ||||
\(459\) | 3.05773 | + | 3.05773i | 0.142723 | + | 0.142723i | ||||
\(460\) | −2.56568 | − | 7.38837i | −0.119625 | − | 0.344485i | ||||
\(461\) | −4.13532 | + | 4.13532i | −0.192601 | + | 0.192601i | −0.796819 | − | 0.604218i | \(-0.793486\pi\) |
0.604218 | + | 0.796819i | \(0.293486\pi\) | |||||||
\(462\) | 12.4525 | + | 19.8702i | 0.579342 | + | 0.924446i | ||||
\(463\) | 23.4228 | 1.08855 | 0.544274 | − | 0.838907i | \(-0.316805\pi\) | ||||
0.544274 | + | 0.838907i | \(0.316805\pi\) | |||||||
\(464\) | −10.3512 | − | 1.21598i | −0.480542 | − | 0.0564505i | ||||
\(465\) | −9.52790 | −0.441846 | ||||||||
\(466\) | 8.87842 | + | 14.1671i | 0.411285 | + | 0.656280i | ||||
\(467\) | −4.20786 | + | 4.20786i | −0.194717 | + | 0.194717i | −0.797731 | − | 0.603014i | \(-0.793966\pi\) |
0.603014 | + | 0.797731i | \(0.293966\pi\) | |||||||
\(468\) | −4.13178 | + | 1.43480i | −0.190992 | + | 0.0663236i | ||||
\(469\) | −26.5033 | − | 26.5033i | −1.22381 | − | 1.22381i | ||||
\(470\) | −3.06636 | − | 0.703698i | −0.141441 | − | 0.0324592i | ||||
\(471\) | 9.66373i | 0.445281i | ||||||||
\(472\) | 18.1968 | − | 22.6525i | 0.837576 | − | 1.04267i | ||||
\(473\) | 6.14077i | 0.282353i | ||||||||
\(474\) | −3.99949 | + | 17.4278i | −0.183703 | + | 0.800484i | ||||
\(475\) | −5.37165 | − | 5.37165i | −0.246468 | − | 0.246468i | ||||
\(476\) | −29.5653 | − | 14.3242i | −1.35512 | − | 0.656551i | ||||
\(477\) | 4.80257 | − | 4.80257i | 0.219895 | − | 0.219895i | ||||
\(478\) | 13.4352 | − | 8.41973i | 0.614512 | − | 0.385109i | ||||
\(479\) | 5.52216 | 0.252314 | 0.126157 | − | 0.992010i | \(-0.459736\pi\) | ||||
0.126157 | + | 0.992010i | \(0.459736\pi\) | |||||||
\(480\) | −5.32825 | − | 1.89992i | −0.243200 | − | 0.0867192i | ||||
\(481\) | 14.0731 | 0.641676 | ||||||||
\(482\) | 9.46684 | − | 5.93278i | 0.431203 | − | 0.270231i | ||||
\(483\) | −10.5039 | + | 10.5039i | −0.477946 | + | 0.477946i | ||||
\(484\) | 14.4970 | + | 7.02371i | 0.658952 | + | 0.319259i | ||||
\(485\) | 4.79809 | + | 4.79809i | 0.217870 | + | 0.217870i | ||||
\(486\) | 0.316325 | − | 1.37838i | 0.0143488 | − | 0.0625247i | ||||
\(487\) | 28.0612i | 1.27158i | 0.771864 | + | 0.635788i | \(0.219325\pi\) | ||||
−0.771864 | + | 0.635788i | \(0.780675\pi\) | |||||||
\(488\) | −0.939345 | − | 0.754578i | −0.0425222 | − | 0.0341581i | ||||
\(489\) | − | 10.0627i | − | 0.455051i | ||||||
\(490\) | 10.2407 | + | 2.35013i | 0.462626 | + | 0.106168i | ||||
\(491\) | −1.27407 | − | 1.27407i | −0.0574979 | − | 0.0574979i | 0.677773 | − | 0.735271i | \(-0.262945\pi\) |
−0.735271 | + | 0.677773i | \(0.762945\pi\) | |||||||
\(492\) | 1.09618 | − | 0.380657i | 0.0494195 | − | 0.0171614i | ||||
\(493\) | 7.96720 | − | 7.96720i | 0.358825 | − | 0.358825i | ||||
\(494\) | 12.4763 | + | 19.9082i | 0.561336 | + | 0.895714i | ||||
\(495\) | −4.36514 | −0.196198 | ||||||||
\(496\) | 23.6208 | + | 29.9091i | 1.06060 | + | 1.34296i | ||||
\(497\) | −2.22238 | −0.0996875 | ||||||||
\(498\) | −11.8560 | − | 18.9184i | −0.531280 | − | 0.847754i | ||||
\(499\) | −26.3351 | + | 26.3351i | −1.17892 | + | 1.17892i | −0.198901 | + | 0.980020i | \(0.563737\pi\) |
−0.980020 | + | 0.198901i | \(0.936263\pi\) | |||||||
\(500\) | −0.656085 | − | 1.88933i | −0.0293410 | − | 0.0844932i | ||||
\(501\) | 4.34184 | + | 4.34184i | 0.193979 | + | 0.193979i | ||||
\(502\) | −10.4150 | − | 2.39013i | −0.464843 | − | 0.106677i | ||||
\(503\) | − | 33.2293i | − | 1.48162i | −0.671715 | − | 0.740810i | \(-0.734442\pi\) | ||
0.671715 | − | 0.740810i | \(-0.265558\pi\) | |||||||
\(504\) | 1.16502 | + | 10.6808i | 0.0518942 | + | 0.475759i | ||||
\(505\) | 8.75828i | 0.389739i | ||||||||
\(506\) | −5.39974 | + | 23.5293i | −0.240048 | + | 1.04601i | ||||
\(507\) | −5.81060 | − | 5.81060i | −0.258058 | − | 0.258058i | ||||
\(508\) | −6.24715 | + | 12.8941i | −0.277172 | + | 0.572085i | ||||
\(509\) | −5.03424 | + | 5.03424i | −0.223139 | + | 0.223139i | −0.809819 | − | 0.586680i | \(-0.800435\pi\) |
0.586680 | + | 0.809819i | \(0.300435\pi\) | |||||||
\(510\) | 5.18195 | − | 3.24748i | 0.229461 | − | 0.143801i | ||||
\(511\) | −45.5830 | −2.01647 | ||||||||
\(512\) | 7.24532 | + | 21.4361i | 0.320201 | + | 0.947350i | ||||
\(513\) | −7.59666 | −0.335401 | ||||||||
\(514\) | 18.6042 | − | 11.6591i | 0.820594 | − | 0.514259i | ||||
\(515\) | −8.02701 | + | 8.02701i | −0.353713 | + | 0.353713i | ||||
\(516\) | −1.22675 | + | 2.53202i | −0.0540049 | + | 0.111466i | ||||
\(517\) | 6.86651 | + | 6.86651i | 0.301989 | + | 0.301989i | ||||
\(518\) | 7.73244 | − | 33.6940i | 0.339744 | − | 1.48043i | ||||
\(519\) | − | 10.3134i | − | 0.452709i | ||||||
\(520\) | 0.670717 | + | 6.14904i | 0.0294129 | + | 0.269653i | ||||
\(521\) | 29.6023i | 1.29690i | 0.761257 | + | 0.648450i | \(0.224582\pi\) | ||||
−0.761257 | + | 0.648450i | \(0.775418\pi\) | |||||||
\(522\) | −3.59151 | − | 0.824214i | −0.157196 | − | 0.0360749i | ||||
\(523\) | 6.90122 | + | 6.90122i | 0.301769 | + | 0.301769i | 0.841706 | − | 0.539937i | \(-0.181552\pi\) |
−0.539937 | + | 0.841706i | \(0.681552\pi\) | |||||||
\(524\) | 6.07822 | + | 17.5034i | 0.265528 | + | 0.764640i | ||||
\(525\) | −2.68603 | + | 2.68603i | −0.117228 | + | 0.117228i | ||||
\(526\) | −10.7921 | − | 17.2208i | −0.470559 | − | 0.750862i | ||||
\(527\) | −41.2013 | −1.79476 | ||||||||
\(528\) | 10.8217 | + | 13.7026i | 0.470953 | + | 0.596330i | ||||
\(529\) | 7.70731 | 0.335100 | ||||||||
\(530\) | −5.10061 | − | 8.13895i | −0.221556 | − | 0.353533i | ||||
\(531\) | 7.26404 | − | 7.26404i | 0.315233 | − | 0.315233i | ||||
\(532\) | 54.5199 | − | 18.9325i | 2.36374 | − | 0.820829i | ||||
\(533\) | −0.897200 | − | 0.897200i | −0.0388621 | − | 0.0388621i | ||||
\(534\) | −17.8784 | − | 4.10292i | −0.773676 | − | 0.177551i | ||||
\(535\) | 12.1409i | 0.524895i | ||||||||
\(536\) | −21.7577 | − | 17.4780i | −0.939791 | − | 0.754936i | ||||
\(537\) | 8.80909i | 0.380140i | ||||||||
\(538\) | −8.52680 | + | 37.1555i | −0.367617 | + | 1.60189i | ||||
\(539\) | −22.9319 | − | 22.9319i | −0.987749 | − | 0.987749i | ||||
\(540\) | −1.79988 | − | 0.872033i | −0.0774544 | − | 0.0375263i | ||||
\(541\) | −7.18248 | + | 7.18248i | −0.308799 | + | 0.308799i | −0.844443 | − | 0.535645i | \(-0.820069\pi\) |
0.535645 | + | 0.844443i | \(0.320069\pi\) | |||||||
\(542\) | −5.59492 | + | 3.50628i | −0.240322 | + | 0.150608i | ||||
\(543\) | 1.80032 | 0.0772591 | ||||||||
\(544\) | −23.0409 | − | 8.21579i | −0.987869 | − | 0.352249i | ||||
\(545\) | 15.0789 | 0.645910 | ||||||||
\(546\) | 9.95487 | − | 6.23863i | 0.426029 | − | 0.266989i | ||||
\(547\) | −14.9525 | + | 14.9525i | −0.639323 | + | 0.639323i | −0.950388 | − | 0.311066i | \(-0.899314\pi\) |
0.311066 | + | 0.950388i | \(0.399314\pi\) | |||||||
\(548\) | −19.8890 | − | 9.63613i | −0.849616 | − | 0.411635i | ||||
\(549\) | −0.301222 | − | 0.301222i | −0.0128559 | − | 0.0128559i | ||||
\(550\) | −1.38080 | + | 6.01683i | −0.0588775 | + | 0.256558i | ||||
\(551\) | 19.7938i | 0.843245i | ||||||||
\(552\) | −6.92698 | + | 8.62314i | −0.294832 | + | 0.367025i | ||||
\(553\) | − | 48.0283i | − | 2.04237i | ||||||
\(554\) | −12.1749 | − | 2.79402i | −0.517264 | − | 0.118707i | ||||
\(555\) | 4.55033 | + | 4.55033i | 0.193151 | + | 0.193151i | ||||
\(556\) | −13.8184 | + | 4.79855i | −0.586029 | + | 0.203504i | ||||
\(557\) | 24.8706 | − | 24.8706i | 1.05380 | − | 1.05380i | 0.0553344 | − | 0.998468i | \(-0.482378\pi\) |
0.998468 | − | 0.0553344i | \(-0.0176225\pi\) | |||||||
\(558\) | 7.15534 | + | 11.4176i | 0.302910 | + | 0.483348i | ||||
\(559\) | 3.07649 | 0.130122 | ||||||||
\(560\) | 15.0907 | + | 1.77274i | 0.637698 | + | 0.0749119i | ||||
\(561\) | −18.8761 | −0.796948 | ||||||||
\(562\) | 22.3336 | + | 35.6373i | 0.942085 | + | 1.50327i | ||||
\(563\) | 11.1111 | − | 11.1111i | 0.468277 | − | 0.468277i | −0.433079 | − | 0.901356i | \(-0.642573\pi\) |
0.901356 | + | 0.433079i | \(0.142573\pi\) | |||||||
\(564\) | 1.45953 | + | 4.20301i | 0.0614574 | + | 0.176979i | ||||
\(565\) | 2.20018 | + | 2.20018i | 0.0925621 | + | 0.0925621i | ||||
\(566\) | −18.4999 | − | 4.24554i | −0.777609 | − | 0.178453i | ||||
\(567\) | 3.79862i | 0.159527i | ||||||||
\(568\) | −1.64502 | + | 0.179433i | −0.0690233 | + | 0.00752884i | ||||
\(569\) | 12.9347i | 0.542250i | 0.962544 | + | 0.271125i | \(0.0873956\pi\) | ||||
−0.962544 | + | 0.271125i | \(0.912604\pi\) | |||||||
\(570\) | −2.40301 | + | 10.4711i | −0.100651 | + | 0.438586i | ||||
\(571\) | −14.5979 | − | 14.5979i | −0.610903 | − | 0.610903i | 0.332278 | − | 0.943181i | \(-0.392183\pi\) |
−0.943181 | + | 0.332278i | \(0.892183\pi\) | |||||||
\(572\) | 8.32456 | − | 17.1819i | 0.348067 | − | 0.718411i | ||||
\(573\) | −6.81395 | + | 6.81395i | −0.284657 | + | 0.284657i | ||||
\(574\) | −2.64106 | + | 1.65513i | −0.110236 | + | 0.0690838i | ||||
\(575\) | −3.91059 | −0.163083 | ||||||||
\(576\) | 1.72471 | + | 7.81187i | 0.0718628 | + | 0.325495i | ||||
\(577\) | 15.7906 | 0.657373 | 0.328687 | − | 0.944439i | \(-0.393394\pi\) | ||||
0.328687 | + | 0.944439i | \(0.393394\pi\) | |||||||
\(578\) | 2.03646 | − | 1.27623i | 0.0847055 | − | 0.0530842i | ||||
\(579\) | 2.57761 | − | 2.57761i | 0.107122 | − | 0.107122i | ||||
\(580\) | −2.27216 | + | 4.68975i | −0.0943465 | + | 0.194731i | ||||
\(581\) | 42.4048 | + | 42.4048i | 1.75925 | + | 1.75925i | ||||
\(582\) | 2.14643 | − | 9.35306i | 0.0889724 | − | 0.387697i | ||||
\(583\) | 29.6474i | 1.22787i | ||||||||
\(584\) | −33.7407 | + | 3.68033i | −1.39620 | + | 0.152293i | ||||
\(585\) | 2.18691i | 0.0904175i | ||||||||
\(586\) | −3.36837 | − | 0.773006i | −0.139146 | − | 0.0319326i | ||||
\(587\) | 13.9365 | + | 13.9365i | 0.575221 | + | 0.575221i | 0.933583 | − | 0.358362i | \(-0.116665\pi\) |
−0.358362 | + | 0.933583i | \(0.616665\pi\) | |||||||
\(588\) | −4.87437 | − | 14.0367i | −0.201016 | − | 0.578864i | ||||
\(589\) | 51.1805 | − | 51.1805i | 2.10886 | − | 2.10886i | ||||
\(590\) | −7.71483 | − | 12.3104i | −0.317615 | − | 0.506812i | ||||
\(591\) | 10.6833 | 0.439452 | ||||||||
\(592\) | 3.00315 | − | 25.5648i | 0.123429 | − | 1.05071i | ||||
\(593\) | −47.4176 | −1.94721 | −0.973604 | − | 0.228242i | \(-0.926702\pi\) | ||||
−0.973604 | + | 0.228242i | \(0.926702\pi\) | |||||||
\(594\) | 3.27817 | + | 5.23091i | 0.134505 | + | 0.214627i | ||||
\(595\) | −11.6151 | + | 11.6151i | −0.476174 | + | 0.476174i | ||||
\(596\) | −15.5060 | + | 5.38461i | −0.635152 | + | 0.220562i | ||||
\(597\) | −16.7897 | − | 16.7897i | −0.687156 | − | 0.687156i | ||||
\(598\) | 11.7881 | + | 2.70524i | 0.482050 | + | 0.110625i | ||||
\(599\) | − | 23.5791i | − | 0.963415i | −0.876332 | − | 0.481707i | \(-0.840017\pi\) | ||
0.876332 | − | 0.481707i | \(-0.159983\pi\) | |||||||
\(600\) | −1.77134 | + | 2.20507i | −0.0723147 | + | 0.0900218i | ||||
\(601\) | − | 3.86582i | − | 0.157690i | −0.996887 | − | 0.0788450i | \(-0.974877\pi\) | ||
0.996887 | − | 0.0788450i | \(-0.0251232\pi\) | |||||||
\(602\) | 1.69038 | − | 7.36580i | 0.0688946 | − | 0.300208i | ||||
\(603\) | −6.97711 | − | 6.97711i | −0.284130 | − | 0.284130i | ||||
\(604\) | −23.8648 | − | 11.5624i | −0.971043 | − | 0.470466i | ||||
\(605\) | 5.69533 | − | 5.69533i | 0.231548 | − | 0.231548i | ||||
\(606\) | 10.4954 | − | 6.57737i | 0.426346 | − | 0.267187i | ||||
\(607\) | 32.4306 | 1.31632 | 0.658159 | − | 0.752879i | \(-0.271335\pi\) | ||||
0.658159 | + | 0.752879i | \(0.271335\pi\) | |||||||
\(608\) | 38.8272 | − | 18.4158i | 1.57465 | − | 0.746860i | ||||
\(609\) | 9.89765 | 0.401073 | ||||||||
\(610\) | −0.510484 | + | 0.319916i | −0.0206689 | + | 0.0129530i | ||||
\(611\) | 3.44008 | − | 3.44008i | 0.139171 | − | 0.139171i | ||||
\(612\) | −7.78318 | − | 3.77091i | −0.314616 | − | 0.152430i | ||||
\(613\) | 21.7952 | + | 21.7952i | 0.880298 | + | 0.880298i | 0.993565 | − | 0.113267i | \(-0.0361314\pi\) |
−0.113267 | + | 0.993565i | \(0.536131\pi\) | |||||||
\(614\) | 7.86779 | − | 34.2838i | 0.317518 | − | 1.38358i | ||||
\(615\) | − | 0.580195i | − | 0.0233957i | ||||||
\(616\) | −36.5634 | − | 29.3714i | −1.47318 | − | 1.18341i | ||||
\(617\) | 1.49837i | 0.0603219i | 0.999545 | + | 0.0301610i | \(0.00960199\pi\) | ||||
−0.999545 | + | 0.0301610i | \(0.990398\pi\) | |||||||
\(618\) | 15.6473 | + | 3.59089i | 0.629426 | + | 0.144447i | ||||
\(619\) | 16.7004 | + | 16.7004i | 0.671246 | + | 0.671246i | 0.958003 | − | 0.286757i | \(-0.0925772\pi\) |
−0.286757 | + | 0.958003i | \(0.592577\pi\) | |||||||
\(620\) | 18.0013 | − | 6.25111i | 0.722950 | − | 0.251051i | ||||
\(621\) | −2.76520 | + | 2.76520i | −0.110964 | + | 0.110964i | ||||
\(622\) | 1.29027 | + | 2.05886i | 0.0517350 | + | 0.0825526i | ||||
\(623\) | 49.2703 | 1.97397 | ||||||||
\(624\) | 6.86493 | − | 5.42160i | 0.274817 | − | 0.217038i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | −12.3478 | − | 19.7032i | −0.493519 | − | 0.787499i | ||||
\(627\) | 23.4480 | − | 23.4480i | 0.936422 | − | 0.936422i | ||||
\(628\) | −6.34023 | − | 18.2579i | −0.253003 | − | 0.728571i | ||||
\(629\) | 19.6769 | + | 19.6769i | 0.784570 | + | 0.784570i | ||||
\(630\) | 5.23595 | + | 1.20160i | 0.208605 | + | 0.0478727i | ||||
\(631\) | 28.6304i | 1.13976i | 0.821729 | + | 0.569878i | \(0.193010\pi\) | ||||
−0.821729 | + | 0.569878i | \(0.806990\pi\) | |||||||
\(632\) | −3.87776 | − | 35.5507i | −0.154249 | − | 1.41413i | ||||
\(633\) | 20.6272i | 0.819857i | ||||||||
\(634\) | −3.56120 | + | 15.5179i | −0.141433 | + | 0.616295i | ||||
\(635\) | 5.06564 | + | 5.06564i | 0.201024 | + | 0.201024i | ||||
\(636\) | −5.92272 | + | 12.2245i | −0.234851 | + | 0.484733i | ||||
\(637\) | −11.4888 | + | 11.4888i | −0.455202 | + | 0.455202i | ||||
\(638\) | 13.6296 | − | 8.54157i | 0.539603 | − | 0.338164i | ||||
\(639\) | −0.585051 | −0.0231442 | ||||||||
\(640\) | 11.3133 | + | 0.0937806i | 0.447198 | + | 0.00370700i | ||||
\(641\) | −47.4097 | −1.87257 | −0.936286 | − | 0.351239i | \(-0.885760\pi\) | ||||
−0.936286 | + | 0.351239i | \(0.885760\pi\) | |||||||
\(642\) | 14.5489 | − | 9.11764i | 0.574198 | − | 0.359845i | ||||
\(643\) | 22.0744 | − | 22.0744i | 0.870528 | − | 0.870528i | −0.122002 | − | 0.992530i | \(-0.538931\pi\) |
0.992530 | + | 0.122002i | \(0.0389314\pi\) | |||||||
\(644\) | 12.9539 | − | 26.7368i | 0.510455 | − | 1.05358i | ||||
\(645\) | 0.994741 | + | 0.994741i | 0.0391679 | + | 0.0391679i | ||||
\(646\) | −10.3913 | + | 45.2800i | −0.408840 | + | 1.78152i | ||||
\(647\) | 28.8171i | 1.13292i | 0.824090 | + | 0.566459i | \(0.191687\pi\) | ||||
−0.824090 | + | 0.566459i | \(0.808313\pi\) | |||||||
\(648\) | 0.306697 | + | 2.81175i | 0.0120482 | + | 0.110456i | ||||
\(649\) | 44.8426i | 1.76023i | ||||||||
\(650\) | 3.01440 | + | 0.691773i | 0.118234 | + | 0.0271336i | ||||
\(651\) | −25.5922 | − | 25.5922i | −1.00304 | − | 1.00304i | ||||
\(652\) | 6.60200 | + | 19.0117i | 0.258554 | + | 0.744557i | ||||
\(653\) | −25.1198 | + | 25.1198i | −0.983015 | + | 0.983015i | −0.999858 | − | 0.0168430i | \(-0.994638\pi\) |
0.0168430 | + | 0.999858i | \(0.494638\pi\) | |||||||
\(654\) | −11.3241 | − | 18.0696i | −0.442807 | − | 0.706579i | ||||
\(655\) | 9.26437 | 0.361989 | ||||||||
\(656\) | −1.82129 | + | 1.43837i | −0.0711095 | + | 0.0561590i | ||||
\(657\) | −11.9999 | −0.468161 | ||||||||
\(658\) | −6.34617 | − | 10.1265i | −0.247400 | − | 0.394771i | ||||
\(659\) | 11.3103 | − | 11.3103i | 0.440585 | − | 0.440585i | −0.451623 | − | 0.892209i | \(-0.649155\pi\) |
0.892209 | + | 0.451623i | \(0.149155\pi\) | |||||||
\(660\) | 8.24716 | − | 2.86390i | 0.321020 | − | 0.111477i | ||||
\(661\) | −19.4036 | − | 19.4036i | −0.754713 | − | 0.754713i | 0.220642 | − | 0.975355i | \(-0.429185\pi\) |
−0.975355 | + | 0.220642i | \(0.929185\pi\) | |||||||
\(662\) | 17.5934 | + | 4.03749i | 0.683785 | + | 0.156922i | ||||
\(663\) | 9.45680i | 0.367272i | ||||||||
\(664\) | 34.8119 | + | 27.9645i | 1.35097 | + | 1.08523i | ||||
\(665\) | − | 28.8568i | − | 1.11902i | ||||||
\(666\) | 2.03559 | − | 8.87009i | 0.0788776 | − | 0.343709i | ||||
\(667\) | 7.20500 | + | 7.20500i | 0.278979 | + | 0.278979i | ||||
\(668\) | −11.0518 | − | 5.35453i | −0.427606 | − | 0.207173i | ||||
\(669\) | 9.67978 | − | 9.67978i | 0.374242 | − | 0.374242i | ||||
\(670\) | −11.8242 | + | 7.41009i | −0.456807 | + | 0.286277i | ||||
\(671\) | 1.85952 | 0.0717858 | ||||||||
\(672\) | −9.20859 | − | 19.4151i | −0.355229 | − | 0.748953i | ||||
\(673\) | −6.76645 | −0.260827 | −0.130414 | − | 0.991460i | \(-0.541631\pi\) | ||||
−0.130414 | + | 0.991460i | \(0.541631\pi\) | |||||||
\(674\) | 8.91772 | − | 5.58865i | 0.343498 | − | 0.215267i | ||||
\(675\) | −0.707107 | + | 0.707107i | −0.0272166 | + | 0.0272166i | ||||
\(676\) | 14.7904 | + | 7.16587i | 0.568860 | + | 0.275610i | ||||
\(677\) | −2.12216 | − | 2.12216i | −0.0815613 | − | 0.0815613i | 0.665149 | − | 0.746710i | \(-0.268368\pi\) |
−0.746710 | + | 0.665149i | \(0.768368\pi\) | |||||||
\(678\) | 0.984250 | − | 4.28886i | 0.0377999 | − | 0.164713i | ||||
\(679\) | 25.7756i | 0.989177i | ||||||||
\(680\) | −7.65977 | + | 9.53536i | −0.293739 | + | 0.365664i | ||||
\(681\) | − | 16.8985i | − | 0.647551i | ||||||
\(682\) | −57.3277 | − | 13.1561i | −2.19519 | − | 0.503774i | ||||
\(683\) | 16.9525 | + | 16.9525i | 0.648669 | + | 0.648669i | 0.952671 | − | 0.304002i | \(-0.0983230\pi\) |
−0.304002 | + | 0.952671i | \(0.598323\pi\) | |||||||
\(684\) | 14.3526 | − | 4.98406i | 0.548784 | − | 0.190570i | ||||
\(685\) | −7.81367 | + | 7.81367i | −0.298545 | + | 0.298545i | ||||
\(686\) | 1.22517 | + | 1.95499i | 0.0467774 | + | 0.0746419i | ||||
\(687\) | −13.3052 | −0.507626 | ||||||||
\(688\) | 0.656515 | − | 5.58867i | 0.0250294 | − | 0.213066i | ||||
\(689\) | 14.8532 | 0.565861 | ||||||||
\(690\) | 2.93681 | + | 4.68621i | 0.111802 | + | 0.178401i | ||||
\(691\) | 18.4439 | − | 18.4439i | 0.701640 | − | 0.701640i | −0.263122 | − | 0.964763i | \(-0.584752\pi\) |
0.964763 | + | 0.263122i | \(0.0847523\pi\) | |||||||
\(692\) | 6.76649 | + | 19.4854i | 0.257223 | + | 0.740725i | ||||
\(693\) | −11.7249 | − | 11.7249i | −0.445391 | − | 0.445391i | ||||
\(694\) | −1.28522 | − | 0.294945i | −0.0487863 | − | 0.0111960i | ||||
\(695\) | 7.31391i | 0.277432i | ||||||||
\(696\) | 7.32628 | − | 0.799127i | 0.277702 | − | 0.0302908i | ||||
\(697\) | − | 2.50893i | − | 0.0950323i | ||||||
\(698\) | 3.59985 | − | 15.6863i | 0.136256 | − | 0.593737i | ||||
\(699\) | −8.35964 | − | 8.35964i | −0.316190 | − | 0.316190i | ||||
\(700\) | 3.31252 | − | 6.83704i | 0.125201 | − | 0.258416i | ||||
\(701\) | 6.59102 | − | 6.59102i | 0.248940 | − | 0.248940i | −0.571596 | − | 0.820535i | \(-0.693675\pi\) |
0.820535 | + | 0.571596i | \(0.193675\pi\) | |||||||
\(702\) | 2.62066 | − | 1.64234i | 0.0989103 | − | 0.0619862i | ||||
\(703\) | −48.8856 | −1.84375 | ||||||||
\(704\) | −29.4358 | − | 18.7888i | −1.10940 | − | 0.708128i | ||||
\(705\) | 2.22461 | 0.0837836 | ||||||||
\(706\) | 21.9702 | − | 13.7685i | 0.826860 | − | 0.518186i | ||||
\(707\) | −23.5250 | + | 23.5250i | −0.884748 | + | 0.884748i | ||||
\(708\) | −8.95831 | + | 18.4900i | −0.336674 | + | 0.694896i | ||||
\(709\) | −12.7715 | − | 12.7715i | −0.479642 | − | 0.479642i | 0.425375 | − | 0.905017i | \(-0.360142\pi\) |
−0.905017 | + | 0.425375i | \(0.860142\pi\) | |||||||
\(710\) | −0.185066 | + | 0.806424i | −0.00694540 | + | 0.0302645i | ||||
\(711\) | − | 12.6436i | − | 0.474173i | ||||||
\(712\) | 36.4701 | − | 3.97804i | 1.36677 | − | 0.149083i | ||||
\(713\) | − | 37.2597i | − | 1.39539i | ||||||
\(714\) | 22.6417 | + | 5.19604i | 0.847344 | + | 0.194457i | ||||
\(715\) | −6.75015 | − | 6.75015i | −0.252441 | − | 0.252441i | ||||
\(716\) | −5.77952 | − | 16.6432i | −0.215991 | − | 0.621987i | ||||
\(717\) | −7.92775 | + | 7.92775i | −0.296067 | + | 0.296067i | ||||
\(718\) | 8.92046 | + | 14.2342i | 0.332908 | + | 0.531216i | ||||
\(719\) | 17.1105 | 0.638115 | 0.319057 | − | 0.947735i | \(-0.396634\pi\) | ||||
0.319057 | + | 0.947735i | \(0.396634\pi\) | |||||||
\(720\) | 3.97268 | + | 0.466680i | 0.148053 | + | 0.0173922i | ||||
\(721\) | −43.1215 | −1.60593 | ||||||||
\(722\) | −29.0702 | − | 46.3868i | −1.08188 | − | 1.72634i | ||||
\(723\) | −5.58612 | + | 5.58612i | −0.207750 | + | 0.207750i | ||||
\(724\) | −3.40139 | + | 1.18116i | −0.126412 | + | 0.0438976i | ||||
\(725\) | 1.84243 | + | 1.84243i | 0.0684263 | + | 0.0684263i | ||||
\(726\) | −11.1021 | − | 2.54781i | −0.412036 | − | 0.0945580i | ||||
\(727\) | − | 43.9133i | − | 1.62865i | −0.580407 | − | 0.814327i | \(-0.697107\pi\) | ||
0.580407 | − | 0.814327i | \(-0.302893\pi\) | |||||||
\(728\) | −14.7149 | + | 18.3180i | −0.545371 | + | 0.678912i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −3.79586 | + | 16.5405i | −0.140491 | + | 0.612190i | ||||
\(731\) | 4.30154 | + | 4.30154i | 0.159098 | + | 0.159098i | ||||
\(732\) | 0.766735 | + | 0.371479i | 0.0283393 | + | 0.0137303i | ||||
\(733\) | −16.5301 | + | 16.5301i | −0.610553 | + | 0.610553i | −0.943090 | − | 0.332537i | \(-0.892095\pi\) |
0.332537 | + | 0.943090i | \(0.392095\pi\) | |||||||
\(734\) | −28.8550 | + | 18.0832i | −1.06506 | + | 0.667463i | ||||
\(735\) | −7.42948 | −0.274040 | ||||||||
\(736\) | 7.42981 | − | 20.8366i | 0.273866 | − | 0.768047i | ||||
\(737\) | 43.0713 | 1.58655 | ||||||||
\(738\) | −0.695270 | + | 0.435720i | −0.0255932 | + | 0.0160391i | ||||
\(739\) | −17.2689 | + | 17.2689i | −0.635246 | + | 0.635246i | −0.949379 | − | 0.314133i | \(-0.898286\pi\) |
0.314133 | + | 0.949379i | \(0.398286\pi\) | |||||||
\(740\) | −11.5825 | − | 5.61165i | −0.425780 | − | 0.206288i | ||||
\(741\) | −11.7473 | − | 11.7473i | −0.431548 | − | 0.431548i | ||||
\(742\) | 8.16107 | − | 35.5618i | 0.299602 | − | 1.30551i | ||||
\(743\) | − | 20.9862i | − | 0.769909i | −0.922936 | − | 0.384955i | \(-0.874217\pi\) | ||
0.922936 | − | 0.384955i | \(-0.125783\pi\) | |||||||
\(744\) | −21.0097 | − | 16.8771i | −0.770254 | − | 0.618746i | ||||
\(745\) | 8.20718i | 0.300688i | ||||||||
\(746\) | 10.7405 | + | 2.46484i | 0.393239 | + | 0.0902442i | ||||
\(747\) | 11.1632 | + | 11.1632i | 0.408441 | + | 0.408441i | ||||
\(748\) | 35.6630 | − | 12.3843i | 1.30397 | − | 0.452815i | ||||
\(749\) | −32.6107 | + | 32.6107i | −1.19157 | + | 1.19157i | ||||
\(750\) | 0.750988 | + | 1.19834i | 0.0274222 | + | 0.0437572i | ||||
\(751\) | −1.64813 | −0.0601413 | −0.0300706 | − | 0.999548i | \(-0.509573\pi\) | ||||
−0.0300706 | + | 0.999548i | \(0.509573\pi\) | |||||||
\(752\) | −5.51507 | − | 6.98327i | −0.201114 | − | 0.254654i | ||||
\(753\) | 7.55594 | 0.275354 | ||||||||
\(754\) | −4.27928 | − | 6.82837i | −0.155842 | − | 0.248675i | ||||
\(755\) | −9.37560 | + | 9.37560i | −0.341213 | + | 0.341213i | ||||
\(756\) | −2.49222 | − | 7.17682i | −0.0906410 | − | 0.261018i | ||||
\(757\) | 2.50864 | + | 2.50864i | 0.0911779 | + | 0.0911779i | 0.751225 | − | 0.660047i | \(-0.229464\pi\) |
−0.660047 | + | 0.751225i | \(0.729464\pi\) | |||||||
\(758\) | −8.60066 | − | 1.97376i | −0.312390 | − | 0.0716903i | ||||
\(759\) | − | 17.0702i | − | 0.619611i | ||||||
\(760\) | −2.32987 | − | 21.3599i | −0.0845132 | − | 0.774805i | ||||
\(761\) | 19.9555i | 0.723387i | 0.932297 | + | 0.361693i | \(0.117801\pi\) | ||||
−0.932297 | + | 0.361693i | \(0.882199\pi\) | |||||||
\(762\) | 2.26612 | − | 9.87459i | 0.0820927 | − | 0.357719i | ||||
\(763\) | 40.5024 | + | 40.5024i | 1.46628 | + | 1.46628i | ||||
\(764\) | 8.40324 | − | 17.3443i | 0.304019 | − | 0.627495i | ||||
\(765\) | −3.05773 | + | 3.05773i | −0.110552 | + | 0.110552i | ||||
\(766\) | 14.9066 | − | 9.34187i | 0.538599 | − | 0.337535i | ||||
\(767\) | 22.4659 | 0.811197 | ||||||||
\(768\) | −8.38379 | − | 13.6276i | −0.302524 | − | 0.491744i | ||||
\(769\) | 28.8082 | 1.03885 | 0.519426 | − | 0.854516i | \(-0.326146\pi\) | ||||
0.519426 | + | 0.854516i | \(0.326146\pi\) | |||||||
\(770\) | −19.8702 | + | 12.4525i | −0.716073 | + | 0.448757i | ||||
\(771\) | −10.9778 | + | 10.9778i | −0.395356 | + | 0.395356i | ||||
\(772\) | −3.17882 | + | 6.56109i | −0.114408 | + | 0.236139i | ||||
\(773\) | 33.6461 | + | 33.6461i | 1.21017 | + | 1.21017i | 0.970972 | + | 0.239195i | \(0.0768836\pi\) |
0.239195 | + | 0.970972i | \(0.423116\pi\) | |||||||
\(774\) | 0.444998 | − | 1.93908i | 0.0159951 | − | 0.0696986i | ||||
\(775\) | − | 9.52790i | − | 0.342252i | ||||||
\(776\) | 2.08110 | + | 19.0792i | 0.0747071 | + | 0.684904i | ||||
\(777\) | 24.4446i | 0.876946i | ||||||||
\(778\) | −44.2510 | − | 10.1551i | −1.58647 | − | 0.364080i | ||||
\(779\) | 3.11660 | + | 3.11660i | 0.111664 | + | 0.111664i | ||||
\(780\) | −1.43480 | − | 4.13178i | −0.0513740 | − | 0.147942i | ||||
\(781\) | 1.80583 | − | 1.80583i | 0.0646176 | − | 0.0646176i | ||||
\(782\) | 12.6996 | + | 20.2645i | 0.454136 | + | 0.724656i | ||||
\(783\) | 2.60559 | 0.0931164 | ||||||||
\(784\) | 18.4185 | + | 23.3219i | 0.657805 | + | 0.832925i | ||||
\(785\) | −9.66373 | −0.344913 | ||||||||
\(786\) | −6.95744 | − | 11.1019i | −0.248163 | − | 0.395990i | ||||
\(787\) | −11.0029 | + | 11.0029i | −0.392211 | + | 0.392211i | −0.875475 | − | 0.483264i | \(-0.839451\pi\) |
0.483264 | + | 0.875475i | \(0.339451\pi\) | |||||||
\(788\) | −20.1842 | + | 7.00915i | −0.719033 | + | 0.249691i | ||||
\(789\) | 10.1615 | + | 10.1615i | 0.361759 | + | 0.361759i | ||||
\(790\) | −17.4278 | − | 3.99949i | −0.620052 | − | 0.142296i | ||||
\(791\) | 11.8195i | 0.420252i | ||||||||
\(792\) | −9.62545 | − | 7.73214i | −0.342025 | − | 0.274750i | ||||
\(793\) | − | 0.931607i | − | 0.0330823i | ||||||
\(794\) | −10.4072 | + | 45.3493i | −0.369338 | + | 1.60939i | ||||
\(795\) | 4.80257 | + | 4.80257i | 0.170330 | + | 0.170330i | ||||
\(796\) | 42.7366 | + | 20.7057i | 1.51476 | + | 0.733894i | ||||
\(797\) | 13.3729 | − | 13.3729i | 0.473692 | − | 0.473692i | −0.429415 | − | 0.903107i | \(-0.641280\pi\) |
0.903107 | + | 0.429415i | \(0.141280\pi\) | |||||||
\(798\) | −34.5802 | + | 21.6711i | −1.22413 | + | 0.767149i | ||||
\(799\) | 9.61983 | 0.340325 | ||||||||
\(800\) | 1.89992 | − | 5.32825i | 0.0671724 | − | 0.188382i | ||||
\(801\) | 12.9706 | 0.458293 | ||||||||
\(802\) | 37.8634 | − | 23.7286i | 1.33700 | − | 0.837887i | ||||
\(803\) | 37.0391 | − | 37.0391i | 1.30708 | − | 1.30708i | ||||
\(804\) | 17.7596 | + | 8.60445i | 0.626333 | + | 0.303456i | ||||
\(805\) | −10.5039 | − | 10.5039i | −0.370215 | − | 0.370215i | ||||
\(806\) | −6.59114 | + | 28.7209i | −0.232163 | + | 1.01165i | ||||
\(807\) | − | 26.9559i | − | 0.948891i | ||||||
\(808\) | −15.5139 | + | 19.3127i | −0.545777 | + | 0.679417i | ||||
\(809\) | − | 20.9970i | − | 0.738214i | −0.929387 | − | 0.369107i | \(-0.879664\pi\) | ||
0.929387 | − | 0.369107i | \(-0.120336\pi\) | |||||||
\(810\) | 1.37838 | + | 0.316325i | 0.0484314 | + | 0.0111145i | ||||
\(811\) | 26.7257 | + | 26.7257i | 0.938468 | + | 0.938468i | 0.998214 | − | 0.0597459i | \(-0.0190290\pi\) |
−0.0597459 | + | 0.998214i | \(0.519029\pi\) | |||||||
\(812\) | −18.6999 | + | 6.49370i | −0.656237 | + | 0.227884i | ||||
\(813\) | 3.30141 | − | 3.30141i | 0.115785 | − | 0.115785i | ||||
\(814\) | 21.0955 | + | 33.6617i | 0.739396 | + | 1.17984i | ||||
\(815\) | 10.0627 | 0.352481 | ||||||||
\(816\) | 17.1790 | + | 2.01806i | 0.601385 | + | 0.0706461i | ||||
\(817\) | −10.6868 | −0.373884 | ||||||||
\(818\) | −10.8884 | − | 17.3744i | −0.380704 | − | 0.607482i | ||||
\(819\) | −5.87409 | + | 5.87409i | −0.205257 | + | 0.205257i | ||||
\(820\) | 0.380657 | + | 1.09618i | 0.0132931 | + | 0.0382802i | ||||
\(821\) | −9.81609 | − | 9.81609i | −0.342584 | − | 0.342584i | 0.514754 | − | 0.857338i | \(-0.327883\pi\) |
−0.857338 | + | 0.514754i | \(0.827883\pi\) | |||||||
\(822\) | 15.2314 | + | 3.49545i | 0.531256 | + | 0.121918i | ||||
\(823\) | − | 23.7241i | − | 0.826969i | −0.910511 | − | 0.413484i | \(-0.864312\pi\) | ||
0.910511 | − | 0.413484i | \(-0.135688\pi\) | |||||||
\(824\) | −31.9187 | + | 3.48159i | −1.11194 | + | 0.121287i | ||||
\(825\) | − | 4.36514i | − | 0.151975i | ||||||
\(826\) | 12.3439 | − | 53.7884i | 0.429498 | − | 1.87154i | ||||
\(827\) | 13.8903 | + | 13.8903i | 0.483014 | + | 0.483014i | 0.906093 | − | 0.423079i | \(-0.139051\pi\) |
−0.423079 | + | 0.906093i | \(0.639051\pi\) | |||||||
\(828\) | 3.41016 | − | 7.03858i | 0.118511 | − | 0.244607i | ||||
\(829\) | 34.7927 | − | 34.7927i | 1.20840 | − | 1.20840i | 0.236856 | − | 0.971545i | \(-0.423883\pi\) |
0.971545 | − | 0.236856i | \(-0.0761169\pi\) | |||||||
\(830\) | 18.9184 | − | 11.8560i | 0.656668 | − | 0.411528i | ||||
\(831\) | 8.83278 | 0.306406 | ||||||||
\(832\) | −9.41306 | + | 14.7472i | −0.326339 | + | 0.511266i | ||||
\(833\) | −32.1271 | −1.11314 | ||||||||
\(834\) | 8.76454 | − | 5.49266i | 0.303491 | − | 0.190195i | ||||
\(835\) | −4.34184 | + | 4.34184i | −0.150256 | + | 0.150256i | ||||
\(836\) | −28.9170 | + | 59.6848i | −1.00012 | + | 2.06424i | ||||
\(837\) | −6.73724 | − | 6.73724i | −0.232873 | − | 0.232873i | ||||
\(838\) | 10.7681 | − | 46.9220i | 0.371978 | − | 1.62089i | ||||
\(839\) | − | 41.9136i | − | 1.44702i | −0.690314 | − | 0.723510i | \(-0.742528\pi\) | ||
0.690314 | − | 0.723510i | \(-0.257472\pi\) | |||||||
\(840\) | −10.6808 | + | 1.16502i | −0.368521 | + | 0.0401971i | ||||
\(841\) | 22.2109i | 0.765892i | ||||||||
\(842\) | −39.2001 | − | 8.99601i | −1.35092 | − | 0.310023i | ||||
\(843\) | −21.0286 | − | 21.0286i | −0.724262 | − | 0.724262i | ||||
\(844\) | −13.5332 | − | 38.9715i | −0.465832 | − | 1.34145i | ||||
\(845\) | 5.81060 | − | 5.81060i | 0.199891 | − | 0.199891i | ||||
\(846\) | −1.67065 | − | 2.66583i | −0.0574383 | − | 0.0916533i | ||||
\(847\) | 30.5956 | 1.05128 | ||||||||
\(848\) | 3.16963 | − | 26.9819i | 0.108845 | − | 0.926562i | ||||
\(849\) | 13.4215 | 0.460623 | ||||||||
\(850\) | 3.24748 | + | 5.18195i | 0.111388 | + | 0.177740i | ||||
\(851\) | −17.7945 | + | 17.7945i | −0.609987 | + | 0.609987i | ||||
\(852\) | 1.10535 | − | 0.383843i | 0.0378687 | − | 0.0131503i | ||||
\(853\) | −17.8552 | − | 17.8552i | −0.611349 | − | 0.611349i | 0.331949 | − | 0.943297i | \(-0.392294\pi\) |
−0.943297 | + | 0.331949i | \(0.892294\pi\) | |||||||
\(854\) | −2.23047 | − | 0.511871i | −0.0763252 | − | 0.0175159i | ||||
\(855\) | − | 7.59666i | − | 0.259800i | ||||||
\(856\) | −21.5056 | + | 26.7715i | −0.735046 | + | 0.915031i | ||||
\(857\) | 37.8604i | 1.29328i | 0.762793 | + | 0.646642i | \(0.223827\pi\) | ||||
−0.762793 | + | 0.646642i | \(0.776173\pi\) | |||||||
\(858\) | −3.01968 | + | 13.1582i | −0.103090 | + | 0.449215i | ||||
\(859\) | −33.0486 | − | 33.0486i | −1.12760 | − | 1.12760i | −0.990566 | − | 0.137036i | \(-0.956242\pi\) |
−0.137036 | − | 0.990566i | \(-0.543758\pi\) | |||||||
\(860\) | −2.53202 | − | 1.22675i | −0.0863413 | − | 0.0418320i | ||||
\(861\) | 1.55842 | − | 1.55842i | 0.0531108 | − | 0.0531108i | ||||
\(862\) | −35.8335 | + | 22.4565i | −1.22049 | + | 0.764873i | ||||
\(863\) | 7.90340 | 0.269035 | 0.134518 | − | 0.990911i | \(-0.457052\pi\) | ||||
0.134518 | + | 0.990911i | \(0.457052\pi\) | |||||||
\(864\) | −2.42420 | − | 5.11109i | −0.0824729 | − | 0.173883i | ||||
\(865\) | 10.3134 | 0.350667 | ||||||||
\(866\) | 21.2690 | − | 13.3291i | 0.722750 | − | 0.452941i | ||||
\(867\) | −1.20166 | + | 1.20166i | −0.0408104 | + | 0.0408104i | ||||
\(868\) | 65.1426 | + | 31.5613i | 2.21108 | + | 1.07126i | ||||
\(869\) | 39.0260 | + | 39.0260i | 1.32387 | + | 1.32387i | ||||
\(870\) | 0.824214 | − | 3.59151i | 0.0279435 | − | 0.121763i | ||||
\(871\) | − | 21.5785i | − | 0.731159i | ||||||
\(872\) | 33.2501 | + | 26.7099i | 1.12599 | + | 0.904511i | ||||
\(873\) | 6.78553i | 0.229655i | ||||||||
\(874\) | −40.9482 | − | 9.39718i | −1.38509 | − | 0.317864i | ||||
\(875\) | −2.68603 | − | 2.68603i | −0.0908043 | − | 0.0908043i | ||||
\(876\) | 22.6717 | − | 7.87296i | 0.766006 | − | 0.266003i | ||||
\(877\) | −23.4020 | + | 23.4020i | −0.790229 | + | 0.790229i | −0.981531 | − | 0.191302i | \(-0.938729\pi\) |
0.191302 | + | 0.981531i | \(0.438729\pi\) | |||||||
\(878\) | −11.3682 | − | 18.1400i | −0.383657 | − | 0.612194i | ||||
\(879\) | 2.44371 | 0.0824243 | ||||||||
\(880\) | −13.7026 | + | 10.8217i | −0.461915 | + | 0.364799i | ||||
\(881\) | 4.99400 | 0.168252 | 0.0841261 | − | 0.996455i | \(-0.473190\pi\) | ||||
0.0841261 | + | 0.996455i | \(0.473190\pi\) | |||||||
\(882\) | 5.57945 | + | 8.90303i | 0.187870 | + | 0.299781i | ||||
\(883\) | −22.8573 | + | 22.8573i | −0.769209 | + | 0.769209i | −0.977967 | − | 0.208758i | \(-0.933058\pi\) |
0.208758 | + | 0.977967i | \(0.433058\pi\) | |||||||
\(884\) | −6.20447 | − | 17.8670i | −0.208679 | − | 0.600932i | ||||
\(885\) | 7.26404 | + | 7.26404i | 0.244178 | + | 0.244178i | ||||
\(886\) | −32.1029 | − | 7.36728i | −1.07852 | − | 0.247509i | ||||
\(887\) | − | 20.5245i | − | 0.689146i | −0.938760 | − | 0.344573i | \(-0.888024\pi\) | ||
0.938760 | − | 0.344573i | \(-0.111976\pi\) | |||||||
\(888\) | 1.97364 | + | 18.0940i | 0.0662309 | + | 0.607195i | ||||
\(889\) | 27.2129i | 0.912691i | ||||||||
\(890\) | 4.10292 | − | 17.8784i | 0.137530 | − | 0.599287i | ||||
\(891\) | −3.08662 | − | 3.08662i | −0.103406 | − | 0.103406i | ||||
\(892\) | −11.9375 | + | 24.6390i | −0.399697 | + | 0.824975i | ||||
\(893\) | −11.9498 | + | 11.9498i | −0.399885 | + | 0.399885i | ||||
\(894\) | 9.83499 | − | 6.16350i | 0.328931 | − | 0.206138i | ||||
\(895\) | −8.80909 | −0.294456 | ||||||||
\(896\) | 30.1360 | + | 30.6398i | 1.00677 | + | 1.02360i | ||||
\(897\) | −8.55210 | −0.285546 | ||||||||
\(898\) | 42.6702 | − | 26.7410i | 1.42392 | − | 0.892360i | ||||
\(899\) | −17.5545 | + | 17.5545i | −0.585476 | + | 0.585476i | ||||
\(900\) | 0.872033 | − | 1.79988i | 0.0290678 | − | 0.0599959i | ||||
\(901\) | 20.7677 | + | 20.7677i | 0.691871 | + | 0.691871i | ||||
\(902\) | 0.801133 | − | 3.49093i | 0.0266748 | − | 0.116235i | ||||
\(903\) | 5.34380i | 0.177831i | ||||||||
\(904\) | 0.954292 | + | 8.74881i | 0.0317393 | + | 0.290981i | ||||
\(905\) | 1.80032i | 0.0598446i | ||||||||
\(906\) | 18.2761 | + | 4.19418i | 0.607183 | + | 0.139342i | ||||
\(907\) | −12.1526 | − | 12.1526i | −0.403521 | − | 0.403521i | 0.475951 | − | 0.879472i | \(-0.342104\pi\) |
−0.879472 | + | 0.475951i | \(0.842104\pi\) | |||||||
\(908\) | 11.0868 | + | 31.9267i | 0.367930 | + | 1.05953i | ||||
\(909\) | −6.19304 | + | 6.19304i | −0.205410 | + | 0.205410i | ||||
\(910\) | 6.23863 | + | 9.95487i | 0.206809 | + | 0.330001i | ||||
\(911\) | 26.1222 | 0.865468 | 0.432734 | − | 0.901522i | \(-0.357549\pi\) | ||||
0.432734 | + | 0.901522i | \(0.357549\pi\) | |||||||
\(912\) | −23.8467 | + | 18.8330i | −0.789643 | + | 0.623624i | ||||
\(913\) | −68.9132 | −2.28070 | ||||||||
\(914\) | −1.48743 | − | 2.37347i | −0.0492000 | − | 0.0785075i | ||||
\(915\) | 0.301222 | − | 0.301222i | 0.00995810 | − | 0.00995810i | ||||
\(916\) | 25.1379 | − | 8.72936i | 0.830580 | − | 0.288426i | ||||
\(917\) | 24.8843 | + | 24.8843i | 0.821753 | + | 0.821753i | ||||
\(918\) | 5.96051 | + | 1.36788i | 0.196726 | + | 0.0451466i | ||||
\(919\) | − | 12.3754i | − | 0.408228i | −0.978947 | − | 0.204114i | \(-0.934569\pi\) | ||
0.978947 | − | 0.204114i | \(-0.0654313\pi\) | |||||||
\(920\) | −8.62314 | − | 6.92698i | −0.284296 | − | 0.228376i | ||||
\(921\) | 24.8725i | 0.819577i | ||||||||
\(922\) | −1.84994 | + | 8.06109i | −0.0609244 | + | 0.265478i | ||||
\(923\) | −0.904709 | − | 0.904709i | −0.0297789 | − | 0.0297789i | ||||
\(924\) | 29.8446 | + | 14.4596i | 0.981816 | + | 0.475685i | ||||
\(925\) | −4.55033 | + | 4.55033i | −0.149614 | + | 0.149614i | ||||
\(926\) | 28.0684 | − | 17.5902i | 0.922385 | − | 0.578051i | ||||
\(927\) | −11.3519 | −0.372846 | ||||||||
\(928\) | −13.3174 | + | 6.31648i | −0.437166 | + | 0.207349i | ||||
\(929\) | −14.1300 | −0.463591 | −0.231795 | − | 0.972765i | \(-0.574460\pi\) | ||||
−0.231795 | + | 0.972765i | \(0.574460\pi\) | |||||||
\(930\) | −11.4176 | + | 7.15534i | −0.374399 | + | 0.234633i | ||||
\(931\) | 39.9085 | − | 39.9085i | 1.30795 | − | 1.30795i | ||||
\(932\) | 21.2787 | + | 10.3094i | 0.697007 | + | 0.337697i | ||||
\(933\) | −1.21487 | − | 1.21487i | −0.0397732 | − | 0.0397732i | ||||
\(934\) | −1.88239 | + | 8.20250i | −0.0615937 | + | 0.268394i | ||||
\(935\) | − | 18.8761i | − | 0.617314i | ||||||
\(936\) | −3.87376 | + | 4.82230i | −0.126618 | + | 0.157622i | ||||
\(937\) | − | 39.1538i | − | 1.27910i | −0.768750 | − | 0.639549i | \(-0.779121\pi\) | ||
0.768750 | − | 0.639549i | \(-0.220879\pi\) | |||||||
\(938\) | −51.6637 | − | 11.8563i | −1.68688 | − | 0.387121i | ||||
\(939\) | 11.6263 | + | 11.6263i | 0.379411 | + | 0.379411i | ||||
\(940\) | −4.20301 | + | 1.45953i | −0.137087 | + | 0.0476047i | ||||
\(941\) | −17.1373 | + | 17.1373i | −0.558661 | + | 0.558661i | −0.928926 | − | 0.370265i | \(-0.879267\pi\) |
0.370265 | + | 0.928926i | \(0.379267\pi\) | |||||||
\(942\) | 7.25735 | + | 11.5804i | 0.236457 | + | 0.377310i | ||||
\(943\) | 2.26890 | 0.0738856 | ||||||||
\(944\) | 4.79416 | − | 40.8110i | 0.156037 | − | 1.32828i | ||||
\(945\) | −3.79862 | −0.123569 | ||||||||
\(946\) | 4.61165 | + | 7.35872i | 0.149938 | + | 0.239253i | ||||
\(947\) | 21.7252 | − | 21.7252i | 0.705973 | − | 0.705973i | −0.259713 | − | 0.965686i | \(-0.583628\pi\) |
0.965686 | + | 0.259713i | \(0.0836279\pi\) | |||||||
\(948\) | 8.29530 | + | 23.8879i | 0.269419 | + | 0.775844i | ||||
\(949\) | −18.5564 | − | 18.5564i | −0.602365 | − | 0.602365i | ||||
\(950\) | −10.4711 | − | 2.40301i | −0.339728 | − | 0.0779640i | ||||
\(951\) | − | 11.2581i | − | 0.365067i | ||||||
\(952\) | −46.1866 | + | 5.03788i | −1.49692 | + | 0.163279i | ||||
\(953\) | 6.05956i | 0.196288i | 0.995172 | + | 0.0981442i | \(0.0312906\pi\) | ||||
−0.995172 | + | 0.0981442i | \(0.968709\pi\) | |||||||
\(954\) | 2.14843 | − | 9.36178i | 0.0695580 | − | 0.303099i | ||||
\(955\) | −6.81395 | − | 6.81395i | −0.220494 | − | 0.220494i | ||||
\(956\) | 9.77682 | − | 20.1794i | 0.316205 | − | 0.652648i | ||||
\(957\) | −8.04247 | + | 8.04247i | −0.259976 | + | 0.259976i | ||||
\(958\) | 6.61742 | − | 4.14708i | 0.213799 | − | 0.133986i | ||||
\(959\) | −41.9754 | −1.35546 | ||||||||
\(960\) | −7.81187 | + | 1.72471i | −0.252127 | + | 0.0556647i | ||||
\(961\) | 59.7808 | 1.92841 | ||||||||
\(962\) | 16.8643 | − | 10.5687i | 0.543727 | − | 0.340749i | ||||
\(963\) | −8.58488 | + | 8.58488i | −0.276644 | + | 0.276644i | ||||
\(964\) | 6.88903 | − | 14.2190i | 0.221881 | − | 0.457962i | ||||
\(965\) | 2.57761 | + | 2.57761i | 0.0829763 | + | 0.0829763i | ||||
\(966\) | −4.69894 | + | 20.4756i | −0.151186 | + | 0.658792i | ||||
\(967\) | − | 32.6389i | − | 1.04959i | −0.851227 | − | 0.524797i | \(-0.824141\pi\) | ||
0.851227 | − | 0.524797i | \(-0.175859\pi\) | |||||||
\(968\) | 22.6470 | − | 2.47026i | 0.727902 | − | 0.0793971i | ||||
\(969\) | − | 32.8501i | − | 1.05530i | ||||||
\(970\) | 9.35306 | + | 2.14643i | 0.300309 | + | 0.0689177i | ||||
\(971\) | −4.73662 | − | 4.73662i | −0.152005 | − | 0.152005i | 0.627008 | − | 0.779013i | \(-0.284279\pi\) |
−0.779013 | + | 0.627008i | \(0.784279\pi\) | |||||||
\(972\) | −0.656085 | − | 1.88933i | −0.0210439 | − | 0.0606002i | ||||
\(973\) | −19.6453 | + | 19.6453i | −0.629801 | + | 0.629801i | ||||
\(974\) | 21.0737 | + | 33.6269i | 0.675244 | + | 1.07747i | ||||
\(975\) | −2.18691 | −0.0700371 | ||||||||
\(976\) | −1.69233 | − | 0.198802i | −0.0541703 | − | 0.00636351i | ||||
\(977\) | −31.9605 | −1.02251 | −0.511254 | − | 0.859430i | \(-0.670819\pi\) | ||||
−0.511254 | + | 0.859430i | \(0.670819\pi\) | |||||||
\(978\) | −7.55698 | − | 12.0585i | −0.241645 | − | 0.385589i | ||||
\(979\) | −40.0353 | + | 40.0353i | −1.27953 | + | 1.27953i | ||||
\(980\) | 14.0367 | − | 4.87437i | 0.448386 | − | 0.155706i | ||||
\(981\) | 10.6624 | + | 10.6624i | 0.340424 | + | 0.340424i | ||||
\(982\) | −2.48358 | − | 0.569955i | −0.0792541 | − | 0.0181880i | ||||
\(983\) | 36.1044i | 1.15155i | 0.817607 | + | 0.575776i | \(0.195300\pi\) | ||||
−0.817607 | + | 0.575776i | \(0.804700\pi\) | |||||||
\(984\) | 1.02772 | − | 1.27937i | 0.0327626 | − | 0.0407849i | ||||
\(985\) | 10.6833i | 0.340398i | ||||||||
\(986\) | 3.56413 | − | 15.5307i | 0.113505 | − | 0.494598i | ||||
\(987\) | 5.97536 | + | 5.97536i | 0.190198 | + | 0.190198i | ||||
\(988\) | 29.9017 | + | 14.4873i | 0.951301 | + | 0.460901i | ||||
\(989\) | −3.89002 | + | 3.89002i | −0.123695 | + | 0.123695i | ||||
\(990\) | −5.23091 | + | 3.27817i | −0.166249 | + | 0.104187i | ||||
\(991\) | 19.3054 | 0.613255 | 0.306628 | − | 0.951830i | \(-0.400799\pi\) | ||||
0.306628 | + | 0.951830i | \(0.400799\pi\) | |||||||
\(992\) | 50.7671 | + | 18.1023i | 1.61186 | + | 0.574747i | ||||
\(993\) | −12.7638 | −0.405046 | ||||||||
\(994\) | −2.66317 | + | 1.66898i | −0.0844705 | + | 0.0529369i | ||||
\(995\) | 16.7897 | − | 16.7897i | 0.532269 | − | 0.532269i | ||||
\(996\) | −28.4150 | − | 13.7669i | −0.900364 | − | 0.436222i | ||||
\(997\) | −6.99944 | − | 6.99944i | −0.221674 | − | 0.221674i | 0.587529 | − | 0.809203i | \(-0.300101\pi\) |
−0.809203 | + | 0.587529i | \(0.800101\pi\) | |||||||
\(998\) | −11.7810 | + | 51.3357i | −0.372922 | + | 1.62500i | ||||
\(999\) | 6.43514i | 0.203599i |
(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 | 240.2.s.c.181.9 | yes | 20 | |
3.2 | odd | 2 | 720.2.t.d.181.2 | 20 | |||
4.3 | odd | 2 | 960.2.s.c.241.10 | 20 | |||
8.3 | odd | 2 | 1920.2.s.f.481.5 | 20 | |||
8.5 | even | 2 | 1920.2.s.e.481.6 | 20 | |||
12.11 | even | 2 | 2880.2.t.d.2161.10 | 20 | |||
16.3 | odd | 4 | 960.2.s.c.721.6 | 20 | |||
16.5 | even | 4 | 1920.2.s.e.1441.10 | 20 | |||
16.11 | odd | 4 | 1920.2.s.f.1441.1 | 20 | |||
16.13 | even | 4 | inner | 240.2.s.c.61.9 | ✓ | 20 | |
48.29 | odd | 4 | 720.2.t.d.541.2 | 20 | |||
48.35 | even | 4 | 2880.2.t.d.721.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.s.c.61.9 | ✓ | 20 | 16.13 | even | 4 | inner | |
240.2.s.c.181.9 | yes | 20 | 1.1 | even | 1 | trivial | |
720.2.t.d.181.2 | 20 | 3.2 | odd | 2 | |||
720.2.t.d.541.2 | 20 | 48.29 | odd | 4 | |||
960.2.s.c.241.10 | 20 | 4.3 | odd | 2 | |||
960.2.s.c.721.6 | 20 | 16.3 | odd | 4 | |||
1920.2.s.e.481.6 | 20 | 8.5 | even | 2 | |||
1920.2.s.e.1441.10 | 20 | 16.5 | even | 4 | |||
1920.2.s.f.481.5 | 20 | 8.3 | odd | 2 | |||
1920.2.s.f.1441.1 | 20 | 16.11 | odd | 4 | |||
2880.2.t.d.721.6 | 20 | 48.35 | even | 4 | |||
2880.2.t.d.2161.10 | 20 | 12.11 | even | 2 |