Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (of order \(2\), degree \(1\), 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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.19 | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.d.2155.6 |
$q$-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 \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.313884i | 0.140373i | 0.997534 | + | 0.0701866i | \(0.0223595\pi\) | ||||
−0.997534 | + | 0.0701866i | \(0.977641\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.313884 | −0.0992588 | ||||||||
\(11\) | −0.720050 | − | 3.23752i | −0.217103 | − | 0.976149i | ||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −4.42216 | −1.22649 | −0.613244 | − | 0.789894i | \(-0.710136\pi\) | ||||
−0.613244 | + | 0.789894i | \(0.710136\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.313884 | 0.0810445 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.88254 | 0.941653 | 0.470827 | − | 0.882226i | \(-0.343956\pi\) | ||||
0.470827 | + | 0.882226i | \(0.343956\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −1.19962 | −0.275211 | −0.137606 | − | 0.990487i | \(-0.543941\pi\) | ||||
−0.137606 | + | 0.990487i | \(0.543941\pi\) | |||||||
\(20\) | − | 0.313884i | − | 0.0701866i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.23752 | − | 0.720050i | 0.690241 | − | 0.153515i | ||||
\(23\) | −7.80896 | −1.62828 | −0.814140 | − | 0.580668i | \(-0.802791\pi\) | ||||
−0.814140 | + | 0.580668i | \(0.802791\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 4.90148 | 0.980295 | ||||||||
\(26\) | − | 4.42216i | − | 0.867258i | ||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.32404i | 1.17435i | 0.809462 | + | 0.587173i | \(0.199759\pi\) | ||||
−0.809462 | + | 0.587173i | \(0.800241\pi\) | |||||||
\(30\) | 0.313884i | 0.0573071i | ||||||||
\(31\) | − | 1.97170i | − | 0.354127i | −0.984199 | − | 0.177064i | \(-0.943340\pi\) | ||
0.984199 | − | 0.177064i | \(-0.0566599\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −3.23752 | + | 0.720050i | −0.563580 | + | 0.125345i | ||||
\(34\) | 3.88254i | 0.665849i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.89552 | −0.640420 | −0.320210 | − | 0.947347i | \(-0.603754\pi\) | ||||
−0.320210 | + | 0.947347i | \(0.603754\pi\) | |||||||
\(38\) | − | 1.19962i | − | 0.194604i | ||||||
\(39\) | 4.42216i | 0.708113i | ||||||||
\(40\) | 0.313884 | 0.0496294 | ||||||||
\(41\) | 11.2575 | 1.75813 | 0.879064 | − | 0.476705i | \(-0.158169\pi\) | ||||
0.879064 | + | 0.476705i | \(0.158169\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.06657i | 0.620146i | 0.950713 | + | 0.310073i | \(0.100353\pi\) | ||||
−0.950713 | + | 0.310073i | \(0.899647\pi\) | |||||||
\(44\) | 0.720050 | + | 3.23752i | 0.108552 | + | 0.488074i | ||||
\(45\) | − | 0.313884i | − | 0.0467911i | ||||||
\(46\) | − | 7.80896i | − | 1.15137i | ||||||
\(47\) | 9.92277i | 1.44738i | 0.690123 | + | 0.723692i | \(0.257557\pi\) | ||||
−0.690123 | + | 0.723692i | \(0.742443\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.90148i | 0.693174i | ||||||||
\(51\) | − | 3.88254i | − | 0.543664i | ||||||
\(52\) | 4.42216 | 0.613244 | ||||||||
\(53\) | −11.7453 | −1.61334 | −0.806669 | − | 0.591004i | \(-0.798732\pi\) | ||||
−0.806669 | + | 0.591004i | \(0.798732\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 1.01621 | − | 0.226012i | 0.137025 | − | 0.0304755i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.19962i | 0.158893i | ||||||||
\(58\) | −6.32404 | −0.830387 | ||||||||
\(59\) | 8.87397i | 1.15529i | 0.816287 | + | 0.577646i | \(0.196029\pi\) | ||||
−0.816287 | + | 0.577646i | \(0.803971\pi\) | |||||||
\(60\) | −0.313884 | −0.0405222 | ||||||||
\(61\) | 11.6955 | 1.49746 | 0.748730 | − | 0.662875i | \(-0.230664\pi\) | ||||
0.748730 | + | 0.662875i | \(0.230664\pi\) | |||||||
\(62\) | 1.97170 | 0.250406 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 1.38805i | − | 0.172166i | ||||||
\(66\) | −0.720050 | − | 3.23752i | −0.0886320 | − | 0.398511i | ||||
\(67\) | −12.2415 | −1.49554 | −0.747769 | − | 0.663959i | \(-0.768875\pi\) | ||||
−0.747769 | + | 0.663959i | \(0.768875\pi\) | |||||||
\(68\) | −3.88254 | −0.470827 | ||||||||
\(69\) | 7.80896i | 0.940088i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0331 | 1.19071 | 0.595354 | − | 0.803464i | \(-0.297012\pi\) | ||||
0.595354 | + | 0.803464i | \(0.297012\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 4.85587 | 0.568337 | 0.284168 | − | 0.958774i | \(-0.408283\pi\) | ||||
0.284168 | + | 0.958774i | \(0.408283\pi\) | |||||||
\(74\) | − | 3.89552i | − | 0.452846i | ||||||
\(75\) | − | 4.90148i | − | 0.565974i | ||||||
\(76\) | 1.19962 | 0.137606 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.42216 | −0.500712 | ||||||||
\(79\) | 6.61990i | 0.744797i | 0.928073 | + | 0.372399i | \(0.121465\pi\) | ||||
−0.928073 | + | 0.372399i | \(0.878535\pi\) | |||||||
\(80\) | 0.313884i | 0.0350933i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.2575i | 1.24318i | ||||||||
\(83\) | −13.4283 | −1.47395 | −0.736974 | − | 0.675921i | \(-0.763746\pi\) | ||||
−0.736974 | + | 0.675921i | \(0.763746\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.21867i | 0.132183i | ||||||||
\(86\) | −4.06657 | −0.438509 | ||||||||
\(87\) | 6.32404 | 0.678008 | ||||||||
\(88\) | −3.23752 | + | 0.720050i | −0.345121 | + | 0.0767576i | ||||
\(89\) | − | 11.7289i | − | 1.24326i | −0.783309 | − | 0.621632i | \(-0.786470\pi\) | ||
0.783309 | − | 0.621632i | \(-0.213530\pi\) | |||||||
\(90\) | 0.313884 | 0.0330863 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.80896 | 0.814140 | ||||||||
\(93\) | −1.97170 | −0.204456 | ||||||||
\(94\) | −9.92277 | −1.02346 | ||||||||
\(95\) | − | 0.376541i | − | 0.0386323i | ||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 11.7519i | 1.19322i | 0.802530 | + | 0.596612i | \(0.203487\pi\) | ||||
−0.802530 | + | 0.596612i | \(0.796513\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.720050 | + | 3.23752i | 0.0723678 | + | 0.325383i | ||||
\(100\) | −4.90148 | −0.490148 | ||||||||
\(101\) | 8.27979 | 0.823869 | 0.411935 | − | 0.911213i | \(-0.364853\pi\) | ||||
0.411935 | + | 0.911213i | \(0.364853\pi\) | |||||||
\(102\) | 3.88254 | 0.384428 | ||||||||
\(103\) | 14.5682i | 1.43545i | 0.696329 | + | 0.717723i | \(0.254815\pi\) | ||||
−0.696329 | + | 0.717723i | \(0.745185\pi\) | |||||||
\(104\) | 4.42216i | 0.433629i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 11.7453i | − | 1.14080i | ||||||
\(107\) | 2.86420i | 0.276892i | 0.990370 | + | 0.138446i | \(0.0442108\pi\) | ||||
−0.990370 | + | 0.138446i | \(0.955789\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 2.95882i | 0.283404i | 0.989909 | + | 0.141702i | \(0.0452574\pi\) | ||||
−0.989909 | + | 0.141702i | \(0.954743\pi\) | |||||||
\(110\) | 0.226012 | + | 1.01621i | 0.0215494 | + | 0.0968914i | ||||
\(111\) | 3.89552i | 0.369747i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.597983 | −0.0562535 | −0.0281268 | − | 0.999604i | \(-0.508954\pi\) | ||||
−0.0281268 | + | 0.999604i | \(0.508954\pi\) | |||||||
\(114\) | −1.19962 | −0.112354 | ||||||||
\(115\) | − | 2.45111i | − | 0.228567i | ||||||
\(116\) | − | 6.32404i | − | 0.587173i | ||||||
\(117\) | 4.42216 | 0.408829 | ||||||||
\(118\) | −8.87397 | −0.816915 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 0.313884i | − | 0.0286535i | ||||||
\(121\) | −9.96306 | + | 4.66235i | −0.905732 | + | 0.423850i | ||||
\(122\) | 11.6955i | 1.05886i | ||||||||
\(123\) | − | 11.2575i | − | 1.01506i | ||||||
\(124\) | 1.97170i | 0.177064i | ||||||||
\(125\) | 3.10791i | 0.277980i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.86982i | 0.787069i | 0.919310 | + | 0.393535i | \(0.128748\pi\) | ||||
−0.919310 | + | 0.393535i | \(0.871252\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 4.06657 | 0.358041 | ||||||||
\(130\) | 1.38805 | 0.121740 | ||||||||
\(131\) | 2.87234 | 0.250957 | 0.125479 | − | 0.992096i | \(-0.459953\pi\) | ||||
0.125479 | + | 0.992096i | \(0.459953\pi\) | |||||||
\(132\) | 3.23752 | − | 0.720050i | 0.281790 | − | 0.0626723i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 12.2415i | − | 1.05750i | ||||||
\(135\) | −0.313884 | −0.0270148 | ||||||||
\(136\) | − | 3.88254i | − | 0.332925i | ||||||
\(137\) | −5.10296 | −0.435975 | −0.217988 | − | 0.975952i | \(-0.569949\pi\) | ||||
−0.217988 | + | 0.975952i | \(0.569949\pi\) | |||||||
\(138\) | −7.80896 | −0.664743 | ||||||||
\(139\) | −1.71162 | −0.145177 | −0.0725887 | − | 0.997362i | \(-0.523126\pi\) | ||||
−0.0725887 | + | 0.997362i | \(0.523126\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.92277 | 0.835648 | ||||||||
\(142\) | 10.0331i | 0.841957i | ||||||||
\(143\) | 3.18418 | + | 14.3168i | 0.266275 | + | 1.19723i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −1.98501 | −0.164847 | ||||||||
\(146\) | 4.85587i | 0.401875i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.89552 | 0.320210 | ||||||||
\(149\) | − | 19.5364i | − | 1.60048i | −0.599679 | − | 0.800241i | \(-0.704705\pi\) | ||
0.599679 | − | 0.800241i | \(-0.295295\pi\) | |||||||
\(150\) | 4.90148 | 0.400204 | ||||||||
\(151\) | 6.75468i | 0.549688i | 0.961489 | + | 0.274844i | \(0.0886262\pi\) | ||||
−0.961489 | + | 0.274844i | \(0.911374\pi\) | |||||||
\(152\) | 1.19962i | 0.0973018i | ||||||||
\(153\) | −3.88254 | −0.313884 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.618884 | 0.0497100 | ||||||||
\(156\) | − | 4.42216i | − | 0.354057i | ||||||
\(157\) | 0.904021i | 0.0721487i | 0.999349 | + | 0.0360744i | \(0.0114853\pi\) | ||||
−0.999349 | + | 0.0360744i | \(0.988515\pi\) | |||||||
\(158\) | −6.61990 | −0.526651 | ||||||||
\(159\) | 11.7453i | 0.931461i | ||||||||
\(160\) | −0.313884 | −0.0248147 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 9.98569 | 0.782140 | 0.391070 | − | 0.920361i | \(-0.372105\pi\) | ||||
0.391070 | + | 0.920361i | \(0.372105\pi\) | |||||||
\(164\) | −11.2575 | −0.879064 | ||||||||
\(165\) | −0.226012 | − | 1.01621i | −0.0175950 | − | 0.0791115i | ||||
\(166\) | − | 13.4283i | − | 1.04224i | ||||||
\(167\) | 1.46451 | 0.113327 | 0.0566635 | − | 0.998393i | \(-0.481954\pi\) | ||||
0.0566635 | + | 0.998393i | \(0.481954\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.55554 | 0.504272 | ||||||||
\(170\) | −1.21867 | −0.0934674 | ||||||||
\(171\) | 1.19962 | 0.0917370 | ||||||||
\(172\) | − | 4.06657i | − | 0.310073i | ||||||
\(173\) | 2.11320 | 0.160663 | 0.0803317 | − | 0.996768i | \(-0.474402\pi\) | ||||
0.0803317 | + | 0.996768i | \(0.474402\pi\) | |||||||
\(174\) | 6.32404i | 0.479424i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.720050 | − | 3.23752i | −0.0542758 | − | 0.244037i | ||||
\(177\) | 8.87397 | 0.667008 | ||||||||
\(178\) | 11.7289 | 0.879120 | ||||||||
\(179\) | −25.0586 | −1.87297 | −0.936483 | − | 0.350714i | \(-0.885939\pi\) | ||||
−0.936483 | + | 0.350714i | \(0.885939\pi\) | |||||||
\(180\) | 0.313884i | 0.0233955i | ||||||||
\(181\) | 18.3609i | 1.36475i | 0.731000 | + | 0.682377i | \(0.239054\pi\) | ||||
−0.731000 | + | 0.682377i | \(0.760946\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 11.6955i | − | 0.864559i | ||||||
\(184\) | 7.80896i | 0.575684i | ||||||||
\(185\) | − | 1.22274i | − | 0.0898978i | ||||||
\(186\) | − | 1.97170i | − | 0.144572i | ||||||
\(187\) | −2.79562 | − | 12.5698i | −0.204436 | − | 0.919193i | ||||
\(188\) | − | 9.92277i | − | 0.723692i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.376541 | 0.0273171 | ||||||||
\(191\) | 1.90284 | 0.137684 | 0.0688422 | − | 0.997628i | \(-0.478070\pi\) | ||||
0.0688422 | + | 0.997628i | \(0.478070\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − | 0.0227424i | − | 0.00163703i | −1.00000 | 0.000818516i | \(-0.999739\pi\) | |||
1.00000 | 0.000818516i | \(-0.000260542\pi\) | ||||||||
\(194\) | −11.7519 | −0.843737 | ||||||||
\(195\) | −1.38805 | −0.0994001 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.73950i | − | 0.622663i | −0.950301 | − | 0.311332i | \(-0.899225\pi\) | ||
0.950301 | − | 0.311332i | \(-0.100775\pi\) | |||||||
\(198\) | −3.23752 | + | 0.720050i | −0.230080 | + | 0.0511717i | ||||
\(199\) | − | 3.66906i | − | 0.260093i | −0.991508 | − | 0.130046i | \(-0.958487\pi\) | ||
0.991508 | − | 0.130046i | \(-0.0415126\pi\) | |||||||
\(200\) | − | 4.90148i | − | 0.346587i | ||||||
\(201\) | 12.2415i | 0.863449i | ||||||||
\(202\) | 8.27979i | 0.582564i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.88254i | 0.271832i | ||||||||
\(205\) | 3.53355i | 0.246794i | ||||||||
\(206\) | −14.5682 | −1.01501 | ||||||||
\(207\) | 7.80896 | 0.542760 | ||||||||
\(208\) | −4.42216 | −0.306622 | ||||||||
\(209\) | 0.863785 | + | 3.88378i | 0.0597492 | + | 0.268647i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.2522i | 1.39422i | 0.716966 | + | 0.697108i | \(0.245530\pi\) | ||||
−0.716966 | + | 0.697108i | \(0.754470\pi\) | |||||||
\(212\) | 11.7453 | 0.806669 | ||||||||
\(213\) | − | 10.0331i | − | 0.687455i | ||||||
\(214\) | −2.86420 | −0.195793 | ||||||||
\(215\) | −1.27643 | −0.0870518 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.95882 | −0.200397 | ||||||||
\(219\) | − | 4.85587i | − | 0.328129i | ||||||
\(220\) | −1.01621 | + | 0.226012i | −0.0685125 | + | 0.0152377i | ||||
\(221\) | −17.1692 | −1.15493 | ||||||||
\(222\) | −3.89552 | −0.261451 | ||||||||
\(223\) | 17.5626i | 1.17608i | 0.808833 | + | 0.588038i | \(0.200100\pi\) | ||||
−0.808833 | + | 0.588038i | \(0.799900\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.90148 | −0.326765 | ||||||||
\(226\) | − | 0.597983i | − | 0.0397773i | ||||||
\(227\) | −6.00479 | −0.398552 | −0.199276 | − | 0.979943i | \(-0.563859\pi\) | ||||
−0.199276 | + | 0.979943i | \(0.563859\pi\) | |||||||
\(228\) | − | 1.19962i | − | 0.0794466i | ||||||
\(229\) | 19.7840i | 1.30736i | 0.756769 | + | 0.653682i | \(0.226777\pi\) | ||||
−0.756769 | + | 0.653682i | \(0.773223\pi\) | |||||||
\(230\) | 2.45111 | 0.161621 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.32404 | 0.415194 | ||||||||
\(233\) | − | 5.93788i | − | 0.389004i | −0.980902 | − | 0.194502i | \(-0.937691\pi\) | ||
0.980902 | − | 0.194502i | \(-0.0623090\pi\) | |||||||
\(234\) | 4.42216i | 0.289086i | ||||||||
\(235\) | −3.11460 | −0.203174 | ||||||||
\(236\) | − | 8.87397i | − | 0.577646i | ||||||
\(237\) | 6.61990 | 0.430009 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.7844i | 1.99128i | 0.0932798 | + | 0.995640i | \(0.470265\pi\) | ||||
−0.0932798 | + | 0.995640i | \(0.529735\pi\) | |||||||
\(240\) | 0.313884 | 0.0202611 | ||||||||
\(241\) | −26.6455 | −1.71639 | −0.858195 | − | 0.513324i | \(-0.828414\pi\) | ||||
−0.858195 | + | 0.513324i | \(0.828414\pi\) | |||||||
\(242\) | −4.66235 | − | 9.96306i | −0.299707 | − | 0.640449i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −11.6955 | −0.748730 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.2575 | 0.717752 | ||||||||
\(247\) | 5.30491 | 0.337543 | ||||||||
\(248\) | −1.97170 | −0.125203 | ||||||||
\(249\) | 13.4283i | 0.850985i | ||||||||
\(250\) | −3.10791 | −0.196562 | ||||||||
\(251\) | − | 0.276414i | − | 0.0174471i | −0.999962 | − | 0.00872356i | \(-0.997223\pi\) | ||
0.999962 | − | 0.00872356i | \(-0.00277683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.62284 | + | 25.2816i | 0.353505 | + | 1.58944i | ||||
\(254\) | −8.86982 | −0.556542 | ||||||||
\(255\) | 1.21867 | 0.0763158 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 20.9764i | − | 1.30847i | −0.756290 | − | 0.654236i | \(-0.772990\pi\) | ||
0.756290 | − | 0.654236i | \(-0.227010\pi\) | |||||||
\(258\) | 4.06657i | 0.253173i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.38805i | 0.0860830i | ||||||||
\(261\) | − | 6.32404i | − | 0.391448i | ||||||
\(262\) | 2.87234i | 0.177454i | ||||||||
\(263\) | 3.53926i | 0.218240i | 0.994029 | + | 0.109120i | \(0.0348033\pi\) | ||||
−0.994029 | + | 0.109120i | \(0.965197\pi\) | |||||||
\(264\) | 0.720050 | + | 3.23752i | 0.0443160 | + | 0.199256i | ||||
\(265\) | − | 3.68665i | − | 0.226469i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.7289 | −0.717799 | ||||||||
\(268\) | 12.2415 | 0.747769 | ||||||||
\(269\) | 11.1093i | 0.677347i | 0.940904 | + | 0.338674i | \(0.109978\pi\) | ||||
−0.940904 | + | 0.338674i | \(0.890022\pi\) | |||||||
\(270\) | − | 0.313884i | − | 0.0191024i | ||||||
\(271\) | 14.7241 | 0.894424 | 0.447212 | − | 0.894428i | \(-0.352417\pi\) | ||||
0.447212 | + | 0.894428i | \(0.352417\pi\) | |||||||
\(272\) | 3.88254 | 0.235413 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 5.10296i | − | 0.308281i | ||||||
\(275\) | −3.52931 | − | 15.8686i | −0.212825 | − | 0.956914i | ||||
\(276\) | − | 7.80896i | − | 0.470044i | ||||||
\(277\) | 25.2978i | 1.52000i | 0.649925 | + | 0.759998i | \(0.274800\pi\) | ||||
−0.649925 | + | 0.759998i | \(0.725200\pi\) | |||||||
\(278\) | − | 1.71162i | − | 0.102656i | ||||||
\(279\) | 1.97170i | 0.118042i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.4309i | − | 1.63639i | −0.574939 | − | 0.818196i | \(-0.694974\pi\) | ||
0.574939 | − | 0.818196i | \(-0.305026\pi\) | |||||||
\(282\) | 9.92277i | 0.590892i | ||||||||
\(283\) | −6.31585 | −0.375438 | −0.187719 | − | 0.982223i | \(-0.560109\pi\) | ||||
−0.187719 | + | 0.982223i | \(0.560109\pi\) | |||||||
\(284\) | −10.0331 | −0.595354 | ||||||||
\(285\) | −0.376541 | −0.0223043 | ||||||||
\(286\) | −14.3168 | + | 3.18418i | −0.846573 | + | 0.188285i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −1.92592 | −0.113289 | ||||||||
\(290\) | − | 1.98501i | − | 0.116564i | ||||||
\(291\) | 11.7519 | 0.688908 | ||||||||
\(292\) | −4.85587 | −0.284168 | ||||||||
\(293\) | 5.67806 | 0.331716 | 0.165858 | − | 0.986150i | \(-0.446961\pi\) | ||||
0.165858 | + | 0.986150i | \(0.446961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.78540 | −0.162172 | ||||||||
\(296\) | 3.89552i | 0.226423i | ||||||||
\(297\) | 3.23752 | − | 0.720050i | 0.187860 | − | 0.0417815i | ||||
\(298\) | 19.5364 | 1.13171 | ||||||||
\(299\) | 34.5325 | 1.99707 | ||||||||
\(300\) | 4.90148i | 0.282987i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.75468 | −0.388688 | ||||||||
\(303\) | − | 8.27979i | − | 0.475661i | ||||||
\(304\) | −1.19962 | −0.0688028 | ||||||||
\(305\) | 3.67104i | 0.210203i | ||||||||
\(306\) | − | 3.88254i | − | 0.221950i | ||||||
\(307\) | −19.2444 | −1.09834 | −0.549169 | − | 0.835711i | \(-0.685056\pi\) | ||||
−0.549169 | + | 0.835711i | \(0.685056\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.5682 | 0.828755 | ||||||||
\(310\) | 0.618884i | 0.0351503i | ||||||||
\(311\) | 10.8759i | 0.616717i | 0.951270 | + | 0.308359i | \(0.0997797\pi\) | ||||
−0.951270 | + | 0.308359i | \(0.900220\pi\) | |||||||
\(312\) | 4.42216 | 0.250356 | ||||||||
\(313\) | 16.5392i | 0.934851i | 0.884033 | + | 0.467425i | \(0.154818\pi\) | ||||
−0.884033 | + | 0.467425i | \(0.845182\pi\) | |||||||
\(314\) | −0.904021 | −0.0510169 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 6.61990i | − | 0.372399i | ||||||
\(317\) | −16.6033 | −0.932534 | −0.466267 | − | 0.884644i | \(-0.654401\pi\) | ||||
−0.466267 | + | 0.884644i | \(0.654401\pi\) | |||||||
\(318\) | −11.7453 | −0.658642 | ||||||||
\(319\) | 20.4742 | − | 4.55363i | 1.14634 | − | 0.254954i | ||||
\(320\) | − | 0.313884i | − | 0.0175466i | ||||||
\(321\) | 2.86420 | 0.159864 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.65756 | −0.259153 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −21.6751 | −1.20232 | ||||||||
\(326\) | 9.98569i | 0.553056i | ||||||||
\(327\) | 2.95882 | 0.163623 | ||||||||
\(328\) | − | 11.2575i | − | 0.621592i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.01621 | − | 0.226012i | 0.0559402 | − | 0.0124416i | ||||
\(331\) | −16.9166 | −0.929822 | −0.464911 | − | 0.885357i | \(-0.653914\pi\) | ||||
−0.464911 | + | 0.885357i | \(0.653914\pi\) | |||||||
\(332\) | 13.4283 | 0.736974 | ||||||||
\(333\) | 3.89552 | 0.213473 | ||||||||
\(334\) | 1.46451i | 0.0801343i | ||||||||
\(335\) | − | 3.84241i | − | 0.209933i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.4320i | − | 0.895109i | −0.894257 | − | 0.447554i | \(-0.852295\pi\) | ||
0.894257 | − | 0.447554i | \(-0.147705\pi\) | |||||||
\(338\) | 6.55554i | 0.356574i | ||||||||
\(339\) | 0.597983i | 0.0324780i | ||||||||
\(340\) | − | 1.21867i | − | 0.0660914i | ||||||
\(341\) | −6.38341 | + | 1.41972i | −0.345681 | + | 0.0768822i | ||||
\(342\) | 1.19962i | 0.0648679i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.06657 | 0.219255 | ||||||||
\(345\) | −2.45111 | −0.131963 | ||||||||
\(346\) | 2.11320i | 0.113606i | ||||||||
\(347\) | 10.0447i | 0.539227i | 0.962969 | + | 0.269614i | \(0.0868959\pi\) | ||||
−0.962969 | + | 0.269614i | \(0.913104\pi\) | |||||||
\(348\) | −6.32404 | −0.339004 | ||||||||
\(349\) | 27.7696 | 1.48647 | 0.743236 | − | 0.669029i | \(-0.233290\pi\) | ||||
0.743236 | + | 0.669029i | \(0.233290\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.42216i | − | 0.236038i | ||||||
\(352\) | 3.23752 | − | 0.720050i | 0.172560 | − | 0.0383788i | ||||
\(353\) | 22.0619i | 1.17424i | 0.809501 | + | 0.587118i | \(0.199738\pi\) | ||||
−0.809501 | + | 0.587118i | \(0.800262\pi\) | |||||||
\(354\) | 8.87397i | 0.471646i | ||||||||
\(355\) | 3.14922i | 0.167143i | ||||||||
\(356\) | 11.7289i | 0.621632i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 25.0586i | − | 1.32439i | ||||||
\(359\) | 1.20528i | 0.0636125i | 0.999494 | + | 0.0318062i | \(0.0101259\pi\) | ||||
−0.999494 | + | 0.0318062i | \(0.989874\pi\) | |||||||
\(360\) | −0.313884 | −0.0165431 | ||||||||
\(361\) | −17.5609 | −0.924259 | ||||||||
\(362\) | −18.3609 | −0.965027 | ||||||||
\(363\) | 4.66235 | + | 9.96306i | 0.244710 | + | 0.522925i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.52418i | 0.0797792i | ||||||||
\(366\) | 11.6955 | 0.611335 | ||||||||
\(367\) | − | 18.3216i | − | 0.956381i | −0.878256 | − | 0.478191i | \(-0.841293\pi\) | ||
0.878256 | − | 0.478191i | \(-0.158707\pi\) | |||||||
\(368\) | −7.80896 | −0.407070 | ||||||||
\(369\) | −11.2575 | −0.586042 | ||||||||
\(370\) | 1.22274 | 0.0635674 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.97170 | 0.102228 | ||||||||
\(373\) | − | 20.8069i | − | 1.07734i | −0.842517 | − | 0.538670i | \(-0.818927\pi\) | ||
0.842517 | − | 0.538670i | \(-0.181073\pi\) | |||||||
\(374\) | 12.5698 | − | 2.79562i | 0.649968 | − | 0.144558i | ||||
\(375\) | 3.10791 | 0.160492 | ||||||||
\(376\) | 9.92277 | 0.511728 | ||||||||
\(377\) | − | 27.9660i | − | 1.44032i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.8436 | −0.659729 | −0.329865 | − | 0.944028i | \(-0.607003\pi\) | ||||
−0.329865 | + | 0.944028i | \(0.607003\pi\) | |||||||
\(380\) | 0.376541i | 0.0193161i | ||||||||
\(381\) | 8.86982 | 0.454415 | ||||||||
\(382\) | 1.90284i | 0.0973575i | ||||||||
\(383\) | − | 32.1738i | − | 1.64400i | −0.569486 | − | 0.822001i | \(-0.692858\pi\) | ||
0.569486 | − | 0.822001i | \(-0.307142\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.0227424 | 0.00115756 | ||||||||
\(387\) | − | 4.06657i | − | 0.206715i | ||||||
\(388\) | − | 11.7519i | − | 0.596612i | ||||||
\(389\) | 0.425402 | 0.0215687 | 0.0107844 | − | 0.999942i | \(-0.496567\pi\) | ||||
0.0107844 | + | 0.999942i | \(0.496567\pi\) | |||||||
\(390\) | − | 1.38805i | − | 0.0702865i | ||||||
\(391\) | −30.3186 | −1.53328 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.87234i | − | 0.144890i | ||||||
\(394\) | 8.73950 | 0.440289 | ||||||||
\(395\) | −2.07788 | −0.104550 | ||||||||
\(396\) | −0.720050 | − | 3.23752i | −0.0361839 | − | 0.162691i | ||||
\(397\) | − | 3.56911i | − | 0.179128i | −0.995981 | − | 0.0895642i | \(-0.971453\pi\) | ||
0.995981 | − | 0.0895642i | \(-0.0285474\pi\) | |||||||
\(398\) | 3.66906 | 0.183913 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.90148 | 0.245074 | ||||||||
\(401\) | 32.6415 | 1.63004 | 0.815019 | − | 0.579435i | \(-0.196727\pi\) | ||||
0.815019 | + | 0.579435i | \(0.196727\pi\) | |||||||
\(402\) | −12.2415 | −0.610551 | ||||||||
\(403\) | 8.71917i | 0.434333i | ||||||||
\(404\) | −8.27979 | −0.411935 | ||||||||
\(405\) | 0.313884i | 0.0155970i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.80497 | + | 12.6118i | 0.139037 | + | 0.625145i | ||||
\(408\) | −3.88254 | −0.192214 | ||||||||
\(409\) | 20.9821 | 1.03750 | 0.518750 | − | 0.854926i | \(-0.326398\pi\) | ||||
0.518750 | + | 0.854926i | \(0.326398\pi\) | |||||||
\(410\) | −3.53355 | −0.174510 | ||||||||
\(411\) | 5.10296i | 0.251710i | ||||||||
\(412\) | − | 14.5682i | − | 0.717723i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.80896i | 0.383789i | ||||||||
\(415\) | − | 4.21493i | − | 0.206903i | ||||||
\(416\) | − | 4.42216i | − | 0.216814i | ||||||
\(417\) | 1.71162i | 0.0838182i | ||||||||
\(418\) | −3.88378 | + | 0.863785i | −0.189962 | + | 0.0422491i | ||||
\(419\) | 3.85865i | 0.188507i | 0.995548 | + | 0.0942536i | \(0.0300465\pi\) | ||||
−0.995548 | + | 0.0942536i | \(0.969954\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.02513 | −0.0499618 | −0.0249809 | − | 0.999688i | \(-0.507952\pi\) | ||||
−0.0249809 | + | 0.999688i | \(0.507952\pi\) | |||||||
\(422\) | −20.2522 | −0.985860 | ||||||||
\(423\) | − | 9.92277i | − | 0.482462i | ||||||
\(424\) | 11.7453i | 0.570401i | ||||||||
\(425\) | 19.0302 | 0.923098 | ||||||||
\(426\) | 10.0331 | 0.486104 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 2.86420i | − | 0.138446i | ||||||
\(429\) | 14.3168 | − | 3.18418i | 0.691224 | − | 0.153734i | ||||
\(430\) | − | 1.27643i | − | 0.0615549i | ||||||
\(431\) | − | 38.0689i | − | 1.83371i | −0.399218 | − | 0.916856i | \(-0.630718\pi\) | ||
0.399218 | − | 0.916856i | \(-0.369282\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 13.6047i | − | 0.653798i | −0.945059 | − | 0.326899i | \(-0.893996\pi\) | ||
0.945059 | − | 0.326899i | \(-0.106004\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.98501i | 0.0951742i | ||||||||
\(436\) | − | 2.95882i | − | 0.141702i | ||||||
\(437\) | 9.36776 | 0.448121 | ||||||||
\(438\) | 4.85587 | 0.232023 | ||||||||
\(439\) | −8.72564 | −0.416452 | −0.208226 | − | 0.978081i | \(-0.566769\pi\) | ||||
−0.208226 | + | 0.978081i | \(0.566769\pi\) | |||||||
\(440\) | −0.226012 | − | 1.01621i | −0.0107747 | − | 0.0484457i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 17.1692i | − | 0.816656i | ||||||
\(443\) | 11.8030 | 0.560779 | 0.280390 | − | 0.959886i | \(-0.409536\pi\) | ||||
0.280390 | + | 0.959886i | \(0.409536\pi\) | |||||||
\(444\) | − | 3.89552i | − | 0.184873i | ||||||
\(445\) | 3.68152 | 0.174521 | ||||||||
\(446\) | −17.5626 | −0.831612 | ||||||||
\(447\) | −19.5364 | −0.924038 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.11503 | −0.335779 | −0.167889 | − | 0.985806i | \(-0.553695\pi\) | ||||
−0.167889 | + | 0.985806i | \(0.553695\pi\) | |||||||
\(450\) | − | 4.90148i | − | 0.231058i | ||||||
\(451\) | −8.10597 | − | 36.4464i | −0.381695 | − | 1.71619i | ||||
\(452\) | 0.597983 | 0.0281268 | ||||||||
\(453\) | 6.75468 | 0.317363 | ||||||||
\(454\) | − | 6.00479i | − | 0.281819i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.19962 | 0.0561772 | ||||||||
\(457\) | − | 14.9142i | − | 0.697655i | −0.937187 | − | 0.348828i | \(-0.886580\pi\) | ||
0.937187 | − | 0.348828i | \(-0.113420\pi\) | |||||||
\(458\) | −19.7840 | −0.924446 | ||||||||
\(459\) | 3.88254i | 0.181221i | ||||||||
\(460\) | 2.45111i | 0.114283i | ||||||||
\(461\) | 23.4773 | 1.09345 | 0.546723 | − | 0.837314i | \(-0.315875\pi\) | ||||
0.546723 | + | 0.837314i | \(0.315875\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.7950 | 1.66354 | 0.831768 | − | 0.555124i | \(-0.187329\pi\) | ||||
0.831768 | + | 0.555124i | \(0.187329\pi\) | |||||||
\(464\) | 6.32404i | 0.293586i | ||||||||
\(465\) | − | 0.618884i | − | 0.0287001i | ||||||
\(466\) | 5.93788 | 0.275067 | ||||||||
\(467\) | − | 17.3569i | − | 0.803180i | −0.915819 | − | 0.401590i | \(-0.868458\pi\) | ||
0.915819 | − | 0.401590i | \(-0.131542\pi\) | |||||||
\(468\) | −4.42216 | −0.204415 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 3.11460i | − | 0.143666i | ||||||
\(471\) | 0.904021 | 0.0416551 | ||||||||
\(472\) | 8.87397 | 0.408458 | ||||||||
\(473\) | 13.1656 | − | 2.92813i | 0.605354 | − | 0.134636i | ||||
\(474\) | 6.61990i | 0.304062i | ||||||||
\(475\) | −5.87990 | −0.269788 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.7453 | 0.537779 | ||||||||
\(478\) | −30.7844 | −1.40805 | ||||||||
\(479\) | −29.3682 | −1.34187 | −0.670933 | − | 0.741518i | \(-0.734106\pi\) | ||||
−0.670933 | + | 0.741518i | \(0.734106\pi\) | |||||||
\(480\) | 0.313884i | 0.0143268i | ||||||||
\(481\) | 17.2267 | 0.785468 | ||||||||
\(482\) | − | 26.6455i | − | 1.21367i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.96306 | − | 4.66235i | 0.452866 | − | 0.211925i | ||||
\(485\) | −3.68873 | −0.167497 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 11.7596 | 0.532877 | 0.266439 | − | 0.963852i | \(-0.414153\pi\) | ||||
0.266439 | + | 0.963852i | \(0.414153\pi\) | |||||||
\(488\) | − | 11.6955i | − | 0.529432i | ||||||
\(489\) | − | 9.98569i | − | 0.451569i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 31.4910i | − | 1.42117i | −0.703612 | − | 0.710585i | \(-0.748430\pi\) | ||
0.703612 | − | 0.710585i | \(-0.251570\pi\) | |||||||
\(492\) | 11.2575i | 0.507528i | ||||||||
\(493\) | 24.5533i | 1.10583i | ||||||||
\(494\) | 5.30491i | 0.238679i | ||||||||
\(495\) | −1.01621 | + | 0.226012i | −0.0456750 | + | 0.0101585i | ||||
\(496\) | − | 1.97170i | − | 0.0885319i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −13.4283 | −0.601737 | ||||||||
\(499\) | −2.16815 | −0.0970597 | −0.0485298 | − | 0.998822i | \(-0.515454\pi\) | ||||
−0.0485298 | + | 0.998822i | \(0.515454\pi\) | |||||||
\(500\) | − | 3.10791i | − | 0.138990i | ||||||
\(501\) | − | 1.46451i | − | 0.0654294i | ||||||
\(502\) | 0.276414 | 0.0123370 | ||||||||
\(503\) | −7.07263 | −0.315353 | −0.157677 | − | 0.987491i | \(-0.550400\pi\) | ||||
−0.157677 | + | 0.987491i | \(0.550400\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.59889i | 0.115649i | ||||||||
\(506\) | −25.2816 | + | 5.62284i | −1.12391 | + | 0.249966i | ||||
\(507\) | − | 6.55554i | − | 0.291142i | ||||||
\(508\) | − | 8.86982i | − | 0.393535i | ||||||
\(509\) | 0.538666i | 0.0238759i | 0.999929 | + | 0.0119380i | \(0.00380006\pi\) | ||||
−0.999929 | + | 0.0119380i | \(0.996200\pi\) | |||||||
\(510\) | 1.21867i | 0.0539634i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 1.19962i | − | 0.0529644i | ||||||
\(514\) | 20.9764 | 0.925230 | ||||||||
\(515\) | −4.57272 | −0.201498 | ||||||||
\(516\) | −4.06657 | −0.179021 | ||||||||
\(517\) | 32.1252 | − | 7.14489i | 1.41286 | − | 0.314232i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 2.11320i | − | 0.0927590i | ||||||
\(520\) | −1.38805 | −0.0608699 | ||||||||
\(521\) | − | 26.0419i | − | 1.14092i | −0.821326 | − | 0.570459i | \(-0.806765\pi\) | ||
0.821326 | − | 0.570459i | \(-0.193235\pi\) | |||||||
\(522\) | 6.32404 | 0.276796 | ||||||||
\(523\) | −15.1764 | −0.663617 | −0.331809 | − | 0.943347i | \(-0.607659\pi\) | ||||
−0.331809 | + | 0.943347i | \(0.607659\pi\) | |||||||
\(524\) | −2.87234 | −0.125479 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.53926 | −0.154319 | ||||||||
\(527\) | − | 7.65519i | − | 0.333465i | ||||||
\(528\) | −3.23752 | + | 0.720050i | −0.140895 | + | 0.0313362i | ||||
\(529\) | 37.9798 | 1.65130 | ||||||||
\(530\) | 3.68665 | 0.160138 | ||||||||
\(531\) | − | 8.87397i | − | 0.385097i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −49.7825 | −2.15632 | ||||||||
\(534\) | − | 11.7289i | − | 0.507560i | ||||||
\(535\) | −0.899026 | −0.0388683 | ||||||||
\(536\) | 12.2415i | 0.528752i | ||||||||
\(537\) | 25.0586i | 1.08136i | ||||||||
\(538\) | −11.1093 | −0.478957 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.313884 | 0.0135074 | ||||||||
\(541\) | 33.1237i | 1.42410i | 0.702130 | + | 0.712049i | \(0.252233\pi\) | ||||
−0.702130 | + | 0.712049i | \(0.747767\pi\) | |||||||
\(542\) | 14.7241i | 0.632453i | ||||||||
\(543\) | 18.3609 | 0.787941 | ||||||||
\(544\) | 3.88254i | 0.166462i | ||||||||
\(545\) | −0.928727 | −0.0397823 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0871i | 1.20092i | 0.799656 | + | 0.600459i | \(0.205015\pi\) | ||||
−0.799656 | + | 0.600459i | \(0.794985\pi\) | |||||||
\(548\) | 5.10296 | 0.217988 | ||||||||
\(549\) | −11.6955 | −0.499153 | ||||||||
\(550\) | 15.8686 | − | 3.52931i | 0.676640 | − | 0.150490i | ||||
\(551\) | − | 7.58643i | − | 0.323193i | ||||||
\(552\) | 7.80896 | 0.332371 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −25.2978 | −1.07480 | ||||||||
\(555\) | −1.22274 | −0.0519025 | ||||||||
\(556\) | 1.71162 | 0.0725887 | ||||||||
\(557\) | 7.15504i | 0.303169i | 0.988444 | + | 0.151584i | \(0.0484375\pi\) | ||||
−0.988444 | + | 0.151584i | \(0.951562\pi\) | |||||||
\(558\) | −1.97170 | −0.0834686 | ||||||||
\(559\) | − | 17.9830i | − | 0.760601i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.5698 | + | 2.79562i | −0.530697 | + | 0.118031i | ||||
\(562\) | 27.4309 | 1.15710 | ||||||||
\(563\) | 11.4715 | 0.483464 | 0.241732 | − | 0.970343i | \(-0.422284\pi\) | ||||
0.241732 | + | 0.970343i | \(0.422284\pi\) | |||||||
\(564\) | −9.92277 | −0.417824 | ||||||||
\(565\) | − | 0.187697i | − | 0.00789649i | ||||||
\(566\) | − | 6.31585i | − | 0.265475i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 10.0331i | − | 0.420979i | ||||||
\(569\) | 17.5534i | 0.735878i | 0.929850 | + | 0.367939i | \(0.119936\pi\) | ||||
−0.929850 | + | 0.367939i | \(0.880064\pi\) | |||||||
\(570\) | − | 0.376541i | − | 0.0157716i | ||||||
\(571\) | 36.5396i | 1.52914i | 0.644543 | + | 0.764568i | \(0.277047\pi\) | ||||
−0.644543 | + | 0.764568i | \(0.722953\pi\) | |||||||
\(572\) | −3.18418 | − | 14.3168i | −0.133137 | − | 0.598617i | ||||
\(573\) | − | 1.90284i | − | 0.0794921i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.2754 | −1.59620 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 3.01392i | − | 0.125471i | −0.998030 | − | 0.0627355i | \(-0.980018\pi\) | ||
0.998030 | − | 0.0627355i | \(-0.0199824\pi\) | |||||||
\(578\) | − | 1.92592i | − | 0.0801077i | ||||||
\(579\) | −0.0227424 | −0.000945141 | ||||||||
\(580\) | 1.98501 | 0.0824233 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 11.7519i | 0.487132i | ||||||||
\(583\) | 8.45719 | + | 38.0256i | 0.350261 | + | 1.57486i | ||||
\(584\) | − | 4.85587i | − | 0.200937i | ||||||
\(585\) | 1.38805i | 0.0573887i | ||||||||
\(586\) | 5.67806i | 0.234558i | ||||||||
\(587\) | − | 35.7499i | − | 1.47556i | −0.675042 | − | 0.737779i | \(-0.735875\pi\) | ||
0.675042 | − | 0.737779i | \(-0.264125\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.36528i | 0.0974598i | ||||||||
\(590\) | − | 2.78540i | − | 0.114673i | ||||||
\(591\) | −8.73950 | −0.359495 | ||||||||
\(592\) | −3.89552 | −0.160105 | ||||||||
\(593\) | 27.4252 | 1.12622 | 0.563109 | − | 0.826383i | \(-0.309605\pi\) | ||||
0.563109 | + | 0.826383i | \(0.309605\pi\) | |||||||
\(594\) | 0.720050 | + | 3.23752i | 0.0295440 | + | 0.132837i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.5364i | 0.800241i | ||||||||
\(597\) | −3.66906 | −0.150165 | ||||||||
\(598\) | 34.5325i | 1.41214i | ||||||||
\(599\) | −44.4086 | −1.81449 | −0.907244 | − | 0.420605i | \(-0.861818\pi\) | ||||
−0.907244 | + | 0.420605i | \(0.861818\pi\) | |||||||
\(600\) | −4.90148 | −0.200102 | ||||||||
\(601\) | 44.2914 | 1.80668 | 0.903342 | − | 0.428922i | \(-0.141106\pi\) | ||||
0.903342 | + | 0.428922i | \(0.141106\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.2415 | 0.498512 | ||||||||
\(604\) | − | 6.75468i | − | 0.274844i | ||||||
\(605\) | −1.46344 | − | 3.12724i | −0.0594972 | − | 0.127141i | ||||
\(606\) | 8.27979 | 0.336343 | ||||||||
\(607\) | 1.98763 | 0.0806754 | 0.0403377 | − | 0.999186i | \(-0.487157\pi\) | ||||
0.0403377 | + | 0.999186i | \(0.487157\pi\) | |||||||
\(608\) | − | 1.19962i | − | 0.0486509i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.67104 | −0.148636 | ||||||||
\(611\) | − | 43.8801i | − | 1.77520i | ||||||
\(612\) | 3.88254 | 0.156942 | ||||||||
\(613\) | − | 10.1472i | − | 0.409842i | −0.978779 | − | 0.204921i | \(-0.934306\pi\) | ||
0.978779 | − | 0.204921i | \(-0.0656937\pi\) | |||||||
\(614\) | − | 19.2444i | − | 0.776642i | ||||||
\(615\) | 3.53355 | 0.142486 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.71985 | 0.270531 | 0.135265 | − | 0.990809i | \(-0.456811\pi\) | ||||
0.135265 | + | 0.990809i | \(0.456811\pi\) | |||||||
\(618\) | 14.5682i | 0.586018i | ||||||||
\(619\) | 17.9109i | 0.719899i | 0.932972 | + | 0.359950i | \(0.117206\pi\) | ||||
−0.932972 | + | 0.359950i | \(0.882794\pi\) | |||||||
\(620\) | −0.618884 | −0.0248550 | ||||||||
\(621\) | − | 7.80896i | − | 0.313363i | ||||||
\(622\) | −10.8759 | −0.436085 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.42216i | 0.177028i | ||||||||
\(625\) | 23.5319 | 0.941274 | ||||||||
\(626\) | −16.5392 | −0.661039 | ||||||||
\(627\) | 3.88378 | − | 0.863785i | 0.155103 | − | 0.0344962i | ||||
\(628\) | − | 0.904021i | − | 0.0360744i | ||||||
\(629\) | −15.1245 | −0.603054 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.8544 | −1.42734 | −0.713671 | − | 0.700481i | \(-0.752969\pi\) | ||||
−0.713671 | + | 0.700481i | \(0.752969\pi\) | |||||||
\(632\) | 6.61990 | 0.263326 | ||||||||
\(633\) | 20.2522 | 0.804951 | ||||||||
\(634\) | − | 16.6033i | − | 0.659401i | ||||||
\(635\) | −2.78409 | −0.110483 | ||||||||
\(636\) | − | 11.7453i | − | 0.465731i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.55363 | + | 20.4742i | 0.180280 | + | 0.810581i | ||||
\(639\) | −10.0331 | −0.396902 | ||||||||
\(640\) | 0.313884 | 0.0124074 | ||||||||
\(641\) | −41.4397 | −1.63677 | −0.818384 | − | 0.574671i | \(-0.805130\pi\) | ||||
−0.818384 | + | 0.574671i | \(0.805130\pi\) | |||||||
\(642\) | 2.86420i | 0.113041i | ||||||||
\(643\) | − | 19.6233i | − | 0.773867i | −0.922108 | − | 0.386933i | \(-0.873534\pi\) | ||
0.922108 | − | 0.386933i | \(-0.126466\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.27643i | 0.0502594i | ||||||||
\(646\) | − | 4.65756i | − | 0.183249i | ||||||
\(647\) | − | 2.65766i | − | 0.104484i | −0.998634 | − | 0.0522418i | \(-0.983363\pi\) | ||
0.998634 | − | 0.0522418i | \(-0.0166367\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 28.7296 | − | 6.38970i | 1.12774 | − | 0.250818i | ||||
\(650\) | − | 21.6751i | − | 0.850169i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.98569 | −0.391070 | ||||||||
\(653\) | −22.7849 | −0.891641 | −0.445820 | − | 0.895122i | \(-0.647088\pi\) | ||||
−0.445820 | + | 0.895122i | \(0.647088\pi\) | |||||||
\(654\) | 2.95882i | 0.115699i | ||||||||
\(655\) | 0.901581i | 0.0352277i | ||||||||
\(656\) | 11.2575 | 0.439532 | ||||||||
\(657\) | −4.85587 | −0.189446 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.89032i | − | 0.112591i | −0.998414 | − | 0.0562955i | \(-0.982071\pi\) | ||
0.998414 | − | 0.0562955i | \(-0.0179289\pi\) | |||||||
\(660\) | 0.226012 | + | 1.01621i | 0.00879751 | + | 0.0395557i | ||||
\(661\) | − | 40.6647i | − | 1.58167i | −0.612027 | − | 0.790837i | \(-0.709646\pi\) | ||
0.612027 | − | 0.790837i | \(-0.290354\pi\) | |||||||
\(662\) | − | 16.9166i | − | 0.657484i | ||||||
\(663\) | 17.1692i | 0.666797i | ||||||||
\(664\) | 13.4283i | 0.521120i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.89552i | 0.150949i | ||||||||
\(667\) | − | 49.3842i | − | 1.91216i | ||||||
\(668\) | −1.46451 | −0.0566635 | ||||||||
\(669\) | 17.5626 | 0.679008 | ||||||||
\(670\) | 3.84241 | 0.148445 | ||||||||
\(671\) | −8.42137 | − | 37.8645i | −0.325103 | − | 1.46174i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.76054i | − | 0.183505i | −0.995782 | − | 0.0917526i | \(-0.970753\pi\) | ||
0.995782 | − | 0.0917526i | \(-0.0292469\pi\) | |||||||
\(674\) | 16.4320 | 0.632938 | ||||||||
\(675\) | 4.90148i | 0.188658i | ||||||||
\(676\) | −6.55554 | −0.252136 | ||||||||
\(677\) | 9.85362 | 0.378705 | 0.189353 | − | 0.981909i | \(-0.439361\pi\) | ||||
0.189353 | + | 0.981909i | \(0.439361\pi\) | |||||||
\(678\) | −0.597983 | −0.0229654 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.21867 | 0.0467337 | ||||||||
\(681\) | 6.00479i | 0.230104i | ||||||||
\(682\) | −1.41972 | − | 6.38341i | −0.0543639 | − | 0.244433i | ||||
\(683\) | 32.7366 | 1.25263 | 0.626315 | − | 0.779570i | \(-0.284562\pi\) | ||||
0.626315 | + | 0.779570i | \(0.284562\pi\) | |||||||
\(684\) | −1.19962 | −0.0458685 | ||||||||
\(685\) | − | 1.60174i | − | 0.0611992i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.7840 | 0.754807 | ||||||||
\(688\) | 4.06657i | 0.155036i | ||||||||
\(689\) | 51.9395 | 1.97874 | ||||||||
\(690\) | − | 2.45111i | − | 0.0933120i | ||||||
\(691\) | 20.2918i | 0.771938i | 0.922512 | + | 0.385969i | \(0.126133\pi\) | ||||
−0.922512 | + | 0.385969i | \(0.873867\pi\) | |||||||
\(692\) | −2.11320 | −0.0803317 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.0447 | −0.381291 | ||||||||
\(695\) | − | 0.537249i | − | 0.0203790i | ||||||
\(696\) | − | 6.32404i | − | 0.239712i | ||||||
\(697\) | 43.7077 | 1.65555 | ||||||||
\(698\) | 27.7696i | 1.05109i | ||||||||
\(699\) | −5.93788 | −0.224591 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.3858i | − | 0.883268i | −0.897195 | − | 0.441634i | \(-0.854399\pi\) | ||
0.897195 | − | 0.441634i | \(-0.145601\pi\) | |||||||
\(702\) | 4.42216 | 0.166904 | ||||||||
\(703\) | 4.67314 | 0.176251 | ||||||||
\(704\) | 0.720050 | + | 3.23752i | 0.0271379 | + | 0.122019i | ||||
\(705\) | 3.11460i | 0.117303i | ||||||||
\(706\) | −22.0619 | −0.830310 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.87397 | −0.333504 | ||||||||
\(709\) | 47.0000 | 1.76512 | 0.882561 | − | 0.470198i | \(-0.155817\pi\) | ||||
0.882561 | + | 0.470198i | \(0.155817\pi\) | |||||||
\(710\) | −3.14922 | −0.118188 | ||||||||
\(711\) | − | 6.61990i | − | 0.248266i | ||||||
\(712\) | −11.7289 | −0.439560 | ||||||||
\(713\) | 15.3969i | 0.576619i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.49383 | + | 0.999463i | −0.168060 | + | 0.0373778i | ||||
\(716\) | 25.0586 | 0.936483 | ||||||||
\(717\) | 30.7844 | 1.14967 | ||||||||
\(718\) | −1.20528 | −0.0449808 | ||||||||
\(719\) | 4.12031i | 0.153662i | 0.997044 | + | 0.0768309i | \(0.0244802\pi\) | ||||
−0.997044 | + | 0.0768309i | \(0.975520\pi\) | |||||||
\(720\) | − | 0.313884i | − | 0.0116978i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 17.5609i | − | 0.653550i | ||||||
\(723\) | 26.6455i | 0.990958i | ||||||||
\(724\) | − | 18.3609i | − | 0.682377i | ||||||
\(725\) | 30.9971i | 1.15121i | ||||||||
\(726\) | −9.96306 | + | 4.66235i | −0.369764 | + | 0.173036i | ||||
\(727\) | − | 6.30961i | − | 0.234011i | −0.993131 | − | 0.117005i | \(-0.962671\pi\) | ||
0.993131 | − | 0.117005i | \(-0.0373294\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −1.52418 | −0.0564124 | ||||||||
\(731\) | 15.7886i | 0.583962i | ||||||||
\(732\) | 11.6955i | 0.432279i | ||||||||
\(733\) | −46.1627 | −1.70506 | −0.852528 | − | 0.522681i | \(-0.824932\pi\) | ||||
−0.852528 | + | 0.522681i | \(0.824932\pi\) | |||||||
\(734\) | 18.3216 | 0.676264 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 7.80896i | − | 0.287842i | ||||||
\(737\) | 8.81449 | + | 39.6321i | 0.324686 | + | 1.45987i | ||||
\(738\) | − | 11.2575i | − | 0.414395i | ||||||
\(739\) | − | 47.1589i | − | 1.73477i | −0.497638 | − | 0.867385i | \(-0.665799\pi\) | ||
0.497638 | − | 0.867385i | \(-0.334201\pi\) | |||||||
\(740\) | 1.22274i | 0.0449489i | ||||||||
\(741\) | − | 5.30491i | − | 0.194881i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.18549i | − | 0.0434915i | −0.999764 | − | 0.0217458i | \(-0.993078\pi\) | ||
0.999764 | − | 0.0217458i | \(-0.00692244\pi\) | |||||||
\(744\) | 1.97170i | 0.0722860i | ||||||||
\(745\) | 6.13215 | 0.224665 | ||||||||
\(746\) | 20.8069 | 0.761795 | ||||||||
\(747\) | 13.4283 | 0.491316 | ||||||||
\(748\) | 2.79562 | + | 12.5698i | 0.102218 | + | 0.459597i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.10791i | 0.113485i | ||||||||
\(751\) | 21.2874 | 0.776787 | 0.388393 | − | 0.921494i | \(-0.373030\pi\) | ||||
0.388393 | + | 0.921494i | \(0.373030\pi\) | |||||||
\(752\) | 9.92277i | 0.361846i | ||||||||
\(753\) | −0.276414 | −0.0100731 | ||||||||
\(754\) | 27.9660 | 1.01846 | ||||||||
\(755\) | −2.12019 | −0.0771614 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.3152 | −0.774715 | −0.387357 | − | 0.921930i | \(-0.626612\pi\) | ||||
−0.387357 | + | 0.921930i | \(0.626612\pi\) | |||||||
\(758\) | − | 12.8436i | − | 0.466499i | ||||||
\(759\) | 25.2816 | − | 5.62284i | 0.917666 | − | 0.204096i | ||||
\(760\) | −0.376541 | −0.0136586 | ||||||||
\(761\) | −34.3734 | −1.24604 | −0.623018 | − | 0.782207i | \(-0.714094\pi\) | ||||
−0.623018 | + | 0.782207i | \(0.714094\pi\) | |||||||
\(762\) | 8.86982i | 0.321320i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.90284 | −0.0688422 | ||||||||
\(765\) | − | 1.21867i | − | 0.0440609i | ||||||
\(766\) | 32.1738 | 1.16249 | ||||||||
\(767\) | − | 39.2422i | − | 1.41695i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 43.5831 | 1.57165 | 0.785823 | − | 0.618452i | \(-0.212240\pi\) | ||||
0.785823 | + | 0.618452i | \(0.212240\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.9764 | −0.755447 | ||||||||
\(772\) | 0.0227424i | 0.000818516i | ||||||||
\(773\) | 33.9112i | 1.21970i | 0.792517 | + | 0.609850i | \(0.208770\pi\) | ||||
−0.792517 | + | 0.609850i | \(0.791230\pi\) | |||||||
\(774\) | 4.06657 | 0.146170 | ||||||||
\(775\) | − | 9.66423i | − | 0.347150i | ||||||
\(776\) | 11.7519 | 0.421868 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.425402i | 0.0152514i | ||||||||
\(779\) | −13.5047 | −0.483856 | ||||||||
\(780\) | 1.38805 | 0.0497000 | ||||||||
\(781\) | −7.22432 | − | 32.4823i | −0.258506 | − | 1.16231i | ||||
\(782\) | − | 30.3186i | − | 1.08419i | ||||||
\(783\) | −6.32404 | −0.226003 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.283758 | −0.0101277 | ||||||||
\(786\) | 2.87234 | 0.102453 | ||||||||
\(787\) | −49.6233 | −1.76888 | −0.884440 | − | 0.466654i | \(-0.845459\pi\) | ||||
−0.884440 | + | 0.466654i | \(0.845459\pi\) | |||||||
\(788\) | 8.73950i | 0.311332i | ||||||||
\(789\) | 3.53926 | 0.126001 | ||||||||
\(790\) | − | 2.07788i | − | 0.0739277i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.23752 | − | 0.720050i | 0.115040 | − | 0.0255859i | ||||
\(793\) | −51.7196 | −1.83662 | ||||||||
\(794\) | 3.56911 | 0.126663 | ||||||||
\(795\) | −3.68665 | −0.130752 | ||||||||
\(796\) | 3.66906i | 0.130046i | ||||||||
\(797\) | − | 11.7829i | − | 0.417374i | −0.977983 | − | 0.208687i | \(-0.933081\pi\) | ||
0.977983 | − | 0.208687i | \(-0.0669189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.5255i | 1.36293i | ||||||||
\(800\) | 4.90148i | 0.173293i | ||||||||
\(801\) | 11.7289i | 0.414421i | ||||||||
\(802\) | 32.6415i | 1.15261i | ||||||||
\(803\) | −3.49647 | − | 15.7210i | −0.123388 | − | 0.554781i | ||||
\(804\) | − | 12.2415i | − | 0.431724i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.71917 | −0.307120 | ||||||||
\(807\) | 11.1093 | 0.391067 | ||||||||
\(808\) | − | 8.27979i | − | 0.291282i | ||||||
\(809\) | 43.8765i | 1.54262i | 0.636462 | + | 0.771308i | \(0.280397\pi\) | ||||
−0.636462 | + | 0.771308i | \(0.719603\pi\) | |||||||
\(810\) | −0.313884 | −0.0110288 | ||||||||
\(811\) | 38.1514 | 1.33968 | 0.669839 | − | 0.742506i | \(-0.266363\pi\) | ||||
0.669839 | + | 0.742506i | \(0.266363\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 14.7241i | − | 0.516396i | ||||||
\(814\) | −12.6118 | + | 2.80497i | −0.442045 | + | 0.0983143i | ||||
\(815\) | 3.13435i | 0.109791i | ||||||||
\(816\) | − | 3.88254i | − | 0.135916i | ||||||
\(817\) | − | 4.87833i | − | 0.170671i | ||||||
\(818\) | 20.9821i | 0.733623i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 3.53355i | − | 0.123397i | ||||||
\(821\) | 39.1064i | 1.36482i | 0.730969 | + | 0.682411i | \(0.239068\pi\) | ||||
−0.730969 | + | 0.682411i | \(0.760932\pi\) | |||||||
\(822\) | −5.10296 | −0.177986 | ||||||||
\(823\) | 39.3506 | 1.37168 | 0.685839 | − | 0.727754i | \(-0.259436\pi\) | ||||
0.685839 | + | 0.727754i | \(0.259436\pi\) | |||||||
\(824\) | 14.5682 | 0.507507 | ||||||||
\(825\) | −15.8686 | + | 3.52931i | −0.552475 | + | 0.122875i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.88958i | 0.0657070i | 0.999460 | + | 0.0328535i | \(0.0104595\pi\) | ||||
−0.999460 | + | 0.0328535i | \(0.989541\pi\) | |||||||
\(828\) | −7.80896 | −0.271380 | ||||||||
\(829\) | − | 11.3169i | − | 0.393053i | −0.980499 | − | 0.196526i | \(-0.937034\pi\) | ||
0.980499 | − | 0.196526i | \(-0.0629661\pi\) | |||||||
\(830\) | 4.21493 | 0.146302 | ||||||||
\(831\) | 25.2978 | 0.877570 | ||||||||
\(832\) | 4.42216 | 0.153311 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.71162 | −0.0592684 | ||||||||
\(835\) | 0.459686i | 0.0159081i | ||||||||
\(836\) | −0.863785 | − | 3.88378i | −0.0298746 | − | 0.134323i | ||||
\(837\) | 1.97170 | 0.0681519 | ||||||||
\(838\) | −3.85865 | −0.133295 | ||||||||
\(839\) | − | 36.6681i | − | 1.26592i | −0.774183 | − | 0.632961i | \(-0.781839\pi\) | ||
0.774183 | − | 0.632961i | \(-0.218161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.9935 | −0.379086 | ||||||||
\(842\) | − | 1.02513i | − | 0.0353283i | ||||||
\(843\) | −27.4309 | −0.944771 | ||||||||
\(844\) | − | 20.2522i | − | 0.697108i | ||||||
\(845\) | 2.05768i | 0.0707863i | ||||||||
\(846\) | 9.92277 | 0.341152 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.7453 | −0.403334 | ||||||||
\(849\) | 6.31585i | 0.216759i | ||||||||
\(850\) | 19.0302i | 0.652729i | ||||||||
\(851\) | 30.4200 | 1.04278 | ||||||||
\(852\) | 10.0331i | 0.343728i | ||||||||
\(853\) | −6.33290 | −0.216834 | −0.108417 | − | 0.994105i | \(-0.534578\pi\) | ||||
−0.108417 | + | 0.994105i | \(0.534578\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.376541i | 0.0128774i | ||||||||
\(856\) | 2.86420 | 0.0978963 | ||||||||
\(857\) | −44.7905 | −1.53001 | −0.765007 | − | 0.644022i | \(-0.777265\pi\) | ||||
−0.765007 | + | 0.644022i | \(0.777265\pi\) | |||||||
\(858\) | 3.18418 | + | 14.3168i | 0.108706 | + | 0.488769i | ||||
\(859\) | − | 8.44407i | − | 0.288108i | −0.989570 | − | 0.144054i | \(-0.953986\pi\) | ||
0.989570 | − | 0.144054i | \(-0.0460139\pi\) | |||||||
\(860\) | 1.27643 | 0.0435259 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 38.0689 | 1.29663 | ||||||||
\(863\) | 5.86648 | 0.199697 | 0.0998487 | − | 0.995003i | \(-0.468164\pi\) | ||||
0.0998487 | + | 0.995003i | \(0.468164\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0.663298i | 0.0225528i | ||||||||
\(866\) | 13.6047 | 0.462305 | ||||||||
\(867\) | 1.92592i | 0.0654077i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.4321 | − | 4.76666i | 0.727033 | − | 0.161698i | ||||
\(870\) | −1.98501 | −0.0672983 | ||||||||
\(871\) | 54.1339 | 1.83426 | ||||||||
\(872\) | 2.95882 | 0.100198 | ||||||||
\(873\) | − | 11.7519i | − | 0.397741i | ||||||
\(874\) | 9.36776i | 0.316869i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.85587i | 0.164065i | ||||||||
\(877\) | 46.4196i | 1.56748i | 0.621090 | + | 0.783739i | \(0.286690\pi\) | ||||
−0.621090 | + | 0.783739i | \(0.713310\pi\) | |||||||
\(878\) | − | 8.72564i | − | 0.294476i | ||||||
\(879\) | − | 5.67806i | − | 0.191516i | ||||||
\(880\) | 1.01621 | − | 0.226012i | 0.0342563 | − | 0.00761887i | ||||
\(881\) | 10.4075i | 0.350638i | 0.984512 | + | 0.175319i | \(0.0560957\pi\) | ||||
−0.984512 | + | 0.175319i | \(0.943904\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.2346 | −1.52227 | −0.761133 | − | 0.648596i | \(-0.775356\pi\) | ||||
−0.761133 | + | 0.648596i | \(0.775356\pi\) | |||||||
\(884\) | 17.1692 | 0.577463 | ||||||||
\(885\) | 2.78540i | 0.0936301i | ||||||||
\(886\) | 11.8030i | 0.396531i | ||||||||
\(887\) | 16.8922 | 0.567183 | 0.283591 | − | 0.958945i | \(-0.408474\pi\) | ||||
0.283591 | + | 0.958945i | \(0.408474\pi\) | |||||||
\(888\) | 3.89552 | 0.130725 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.68152i | 0.123405i | ||||||||
\(891\) | −0.720050 | − | 3.23752i | −0.0241226 | − | 0.108461i | ||||
\(892\) | − | 17.5626i | − | 0.588038i | ||||||
\(893\) | − | 11.9035i | − | 0.398336i | ||||||
\(894\) | − | 19.5364i | − | 0.653394i | ||||||
\(895\) | − | 7.86548i | − | 0.262914i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 34.5325i | − | 1.15301i | ||||||
\(898\) | − | 7.11503i | − | 0.237432i | ||||||
\(899\) | 12.4691 | 0.415868 | ||||||||
\(900\) | 4.90148 | 0.163383 | ||||||||
\(901\) | −45.6014 | −1.51920 | ||||||||
\(902\) | 36.4464 | − | 8.10597i | 1.21353 | − | 0.269899i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.597983i | 0.0198886i | ||||||||
\(905\) | −5.76319 | −0.191575 | ||||||||
\(906\) | 6.75468i | 0.224409i | ||||||||
\(907\) | 23.6944 | 0.786760 | 0.393380 | − | 0.919376i | \(-0.371306\pi\) | ||||
0.393380 | + | 0.919376i | \(0.371306\pi\) | |||||||
\(908\) | 6.00479 | 0.199276 | ||||||||
\(909\) | −8.27979 | −0.274623 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.5110 | −1.47472 | −0.737358 | − | 0.675502i | \(-0.763927\pi\) | ||||
−0.737358 | + | 0.675502i | \(0.763927\pi\) | |||||||
\(912\) | 1.19962i | 0.0397233i | ||||||||
\(913\) | 9.66906 | + | 43.4744i | 0.319999 | + | 1.43879i | ||||
\(914\) | 14.9142 | 0.493317 | ||||||||
\(915\) | 3.67104 | 0.121361 | ||||||||
\(916\) | − | 19.7840i | − | 0.653682i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.88254 | −0.128143 | ||||||||
\(919\) | − | 9.49698i | − | 0.313276i | −0.987656 | − | 0.156638i | \(-0.949934\pi\) | ||
0.987656 | − | 0.156638i | \(-0.0500657\pi\) | |||||||
\(920\) | −2.45111 | −0.0808106 | ||||||||
\(921\) | 19.2444i | 0.634125i | ||||||||
\(922\) | 23.4773i | 0.773183i | ||||||||
\(923\) | −44.3679 | −1.46039 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.0938 | −0.627801 | ||||||||
\(926\) | 35.7950i | 1.17630i | ||||||||
\(927\) | − | 14.5682i | − | 0.478482i | ||||||
\(928\) | −6.32404 | −0.207597 | ||||||||
\(929\) | 0.396529i | 0.0130097i | 0.999979 | + | 0.00650484i | \(0.00207057\pi\) | ||||
−0.999979 | + | 0.00650484i | \(0.997929\pi\) | |||||||
\(930\) | 0.618884 | 0.0202940 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.93788i | 0.194502i | ||||||||
\(933\) | 10.8759 | 0.356062 | ||||||||
\(934\) | 17.3569 | 0.567934 | ||||||||
\(935\) | 3.94545 | − | 0.877500i | 0.129030 | − | 0.0286973i | ||||
\(936\) | − | 4.42216i | − | 0.144543i | ||||||
\(937\) | 29.2790 | 0.956504 | 0.478252 | − | 0.878223i | \(-0.341271\pi\) | ||||
0.478252 | + | 0.878223i | \(0.341271\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.5392 | 0.539736 | ||||||||
\(940\) | 3.11460 | 0.101587 | ||||||||
\(941\) | −27.5117 | −0.896854 | −0.448427 | − | 0.893819i | \(-0.648016\pi\) | ||||
−0.448427 | + | 0.893819i | \(0.648016\pi\) | |||||||
\(942\) | 0.904021i | 0.0294546i | ||||||||
\(943\) | −87.9094 | −2.86272 | ||||||||
\(944\) | 8.87397i | 0.288823i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.92813 | + | 13.1656i | 0.0952018 | + | 0.428050i | ||||
\(947\) | 25.4599 | 0.827334 | 0.413667 | − | 0.910428i | \(-0.364248\pi\) | ||||
0.413667 | + | 0.910428i | \(0.364248\pi\) | |||||||
\(948\) | −6.61990 | −0.215004 | ||||||||
\(949\) | −21.4735 | −0.697058 | ||||||||
\(950\) | − | 5.87990i | − | 0.190769i | ||||||
\(951\) | 16.6033i | 0.538399i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.82076i | − | 0.156160i | −0.996947 | − | 0.0780799i | \(-0.975121\pi\) | ||
0.996947 | − | 0.0780799i | \(-0.0248789\pi\) | |||||||
\(954\) | 11.7453i | 0.380267i | ||||||||
\(955\) | 0.597269i | 0.0193272i | ||||||||
\(956\) | − | 30.7844i | − | 0.995640i | ||||||
\(957\) | −4.55363 | − | 20.4742i | −0.147198 | − | 0.661837i | ||||
\(958\) | − | 29.3682i | − | 0.948842i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.313884 | −0.0101306 | ||||||||
\(961\) | 27.1124 | 0.874594 | ||||||||
\(962\) | 17.2267i | 0.555410i | ||||||||
\(963\) | − | 2.86420i | − | 0.0922975i | ||||||
\(964\) | 26.6455 | 0.858195 | ||||||||
\(965\) | 0.00713847 | 0.000229795 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.9375i | 0.930567i | 0.885162 | + | 0.465284i | \(0.154048\pi\) | ||||
−0.885162 | + | 0.465284i | \(0.845952\pi\) | |||||||
\(968\) | 4.66235 | + | 9.96306i | 0.149854 | + | 0.320225i | ||||
\(969\) | 4.65756i | 0.149622i | ||||||||
\(970\) | − | 3.68873i | − | 0.118438i | ||||||
\(971\) | 27.0612i | 0.868435i | 0.900808 | + | 0.434218i | \(0.142975\pi\) | ||||
−0.900808 | + | 0.434218i | \(0.857025\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.7596i | 0.376801i | ||||||||
\(975\) | 21.6751i | 0.694160i | ||||||||
\(976\) | 11.6955 | 0.374365 | ||||||||
\(977\) | −7.23749 | −0.231548 | −0.115774 | − | 0.993276i | \(-0.536935\pi\) | ||||
−0.115774 | + | 0.993276i | \(0.536935\pi\) | |||||||
\(978\) | 9.98569 | 0.319307 | ||||||||
\(979\) | −37.9726 | + | 8.44542i | −1.21361 | + | 0.269917i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2.95882i | − | 0.0944679i | ||||||
\(982\) | 31.4910 | 1.00492 | ||||||||
\(983\) | − | 11.3461i | − | 0.361885i | −0.983494 | − | 0.180942i | \(-0.942085\pi\) | ||
0.983494 | − | 0.180942i | \(-0.0579147\pi\) | |||||||
\(984\) | −11.2575 | −0.358876 | ||||||||
\(985\) | 2.74319 | 0.0874052 | ||||||||
\(986\) | −24.5533 | −0.781937 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.30491 | −0.168772 | ||||||||
\(989\) | − | 31.7557i | − | 1.00977i | ||||||
\(990\) | −0.226012 | − | 1.01621i | −0.00718314 | − | 0.0322971i | ||||
\(991\) | −25.6080 | −0.813464 | −0.406732 | − | 0.913547i | \(-0.633332\pi\) | ||||
−0.406732 | + | 0.913547i | \(0.633332\pi\) | |||||||
\(992\) | 1.97170 | 0.0626015 | ||||||||
\(993\) | 16.9166i | 0.536833i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.15166 | 0.0365100 | ||||||||
\(996\) | − | 13.4283i | − | 0.425492i | ||||||
\(997\) | −43.7341 | −1.38507 | −0.692536 | − | 0.721383i | \(-0.743507\pi\) | ||||
−0.692536 | + | 0.721383i | \(0.743507\pi\) | |||||||
\(998\) | − | 2.16815i | − | 0.0686316i | ||||||
\(999\) | − | 3.89552i | − | 0.123249i |
(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 | 3234.2.e.d.2155.19 | yes | 24 | |
7.6 | odd | 2 | 3234.2.e.c.2155.18 | yes | 24 | ||
11.10 | odd | 2 | 3234.2.e.c.2155.7 | ✓ | 24 | ||
77.76 | even | 2 | inner | 3234.2.e.d.2155.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.e.c.2155.7 | ✓ | 24 | 11.10 | odd | 2 | ||
3234.2.e.c.2155.18 | yes | 24 | 7.6 | odd | 2 | ||
3234.2.e.d.2155.6 | yes | 24 | 77.76 | even | 2 | inner | |
3234.2.e.d.2155.19 | yes | 24 | 1.1 | even | 1 | trivial |