Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(53,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 22 x^{18} - 72 x^{17} + 236 x^{16} - 556 x^{15} + 1232 x^{14} - 1981 x^{13} + \cdots + 400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 521.2 | ||
Root | \(-0.384533 - 0.279379i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 572.521 |
Dual form | 572.2.n.a.157.2 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.146878 | + | 0.452045i | −0.0848003 | + | 0.260988i | −0.984462 | − | 0.175600i | \(-0.943813\pi\) |
0.899661 | + | 0.436589i | \(0.143813\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.01285 | − | 2.18896i | 1.34739 | − | 0.978933i | 0.348248 | − | 0.937402i | \(-0.386777\pi\) |
0.999137 | − | 0.0415304i | \(-0.0132234\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.736420 | + | 2.26647i | 0.278341 | + | 0.856644i | 0.988316 | + | 0.152418i | \(0.0487060\pi\) |
−0.709976 | + | 0.704226i | \(0.751294\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.24428 | + | 1.63056i | 0.748093 | + | 0.543521i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.05430 | + | 2.60382i | −0.619394 | + | 0.785080i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.809017 | − | 0.587785i | −0.224381 | − | 0.163022i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.546987 | + | 1.68345i | 0.141231 | + | 0.434666i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.68509 | − | 1.22429i | 0.408694 | − | 0.296934i | −0.364379 | − | 0.931251i | \(-0.618719\pi\) |
0.773073 | + | 0.634317i | \(0.218719\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.128120 | − | 0.394314i | 0.0293928 | − | 0.0904618i | −0.935284 | − | 0.353898i | \(-0.884856\pi\) |
0.964677 | + | 0.263436i | \(0.0848559\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.13271 | −0.247178 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.03568 | 0.424469 | 0.212235 | − | 0.977219i | \(-0.431926\pi\) | ||||
0.212235 | + | 0.977219i | \(0.431926\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.74061 | − | 8.43472i | 0.548121 | − | 1.68694i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.22032 | + | 1.61316i | −0.427301 | + | 0.310453i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.36307 | − | 4.19511i | −0.253117 | − | 0.779013i | −0.994195 | − | 0.107594i | \(-0.965685\pi\) |
0.741078 | − | 0.671419i | \(-0.234315\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.681319 | + | 0.495008i | 0.122369 | + | 0.0889060i | 0.647286 | − | 0.762247i | \(-0.275904\pi\) |
−0.524918 | + | 0.851153i | \(0.675904\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.875311 | − | 1.31108i | −0.152372 | − | 0.228230i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.17993 | + | 5.21652i | 1.21363 | + | 0.881753i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.25746 | + | 10.0254i | 0.535523 | + | 1.64817i | 0.742517 | + | 0.669828i | \(0.233632\pi\) |
−0.206994 | + | 0.978342i | \(0.566368\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.384533 | − | 0.279379i | 0.0615745 | − | 0.0447365i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.668949 | − | 2.05881i | 0.104472 | − | 0.321533i | −0.885134 | − | 0.465336i | \(-0.845933\pi\) |
0.989606 | + | 0.143804i | \(0.0459334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.76843 | −0.727179 | −0.363589 | − | 0.931559i | \(-0.618449\pi\) | ||||
−0.363589 | + | 0.931559i | \(0.618449\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.3309 | 1.54004 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.01488 | − | 9.27883i | 0.439765 | − | 1.35346i | −0.448359 | − | 0.893853i | \(-0.647992\pi\) |
0.888124 | − | 0.459603i | \(-0.152008\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.06856 | − | 0.776353i | 0.152651 | − | 0.110908i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.305931 | + | 0.941558i | 0.0428389 | + | 0.131845i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.01337 | + | 2.91588i | 0.551278 | + | 0.400527i | 0.828257 | − | 0.560349i | \(-0.189333\pi\) |
−0.276978 | + | 0.960876i | \(0.589333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.489631 | + | 12.3417i | −0.0660218 | + | 1.66415i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.159430 | + | 0.115832i | 0.0211170 | + | 0.0153424i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.06466 | + | 3.27668i | 0.138606 | + | 0.426587i | 0.996134 | − | 0.0878520i | \(-0.0280002\pi\) |
−0.857527 | + | 0.514439i | \(0.828000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.0723 | + | 8.04449i | −1.41766 | + | 1.02999i | −0.425509 | + | 0.904954i | \(0.639905\pi\) |
−0.992152 | + | 0.125037i | \(0.960095\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.04289 | + | 6.28737i | −0.257380 | + | 0.792134i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.72408 | −0.461915 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00057 | −0.122240 | −0.0611198 | − | 0.998130i | \(-0.519467\pi\) | ||||
−0.0611198 | + | 0.998130i | \(0.519467\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.298998 | + | 0.920220i | −0.0359951 | + | 0.110782i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.70580 | − | 4.87205i | 0.795832 | − | 0.578206i | −0.113857 | − | 0.993497i | \(-0.536320\pi\) |
0.909688 | + | 0.415292i | \(0.136320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.91502 | − | 15.1269i | −0.575259 | − | 1.77047i | −0.635294 | − | 0.772270i | \(-0.719121\pi\) |
0.0600345 | − | 0.998196i | \(-0.480879\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.41034 | + | 2.47775i | 0.393792 | + | 0.286107i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.41429 | − | 2.73850i | −0.844937 | − | 0.312081i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.27431 | − | 2.37892i | −0.368388 | − | 0.267650i | 0.388154 | − | 0.921595i | \(-0.373113\pi\) |
−0.756542 | + | 0.653945i | \(0.773113\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.16861 | + | 6.67430i | 0.240957 | + | 0.741589i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.759221 | + | 0.551607i | −0.0833354 | + | 0.0605467i | −0.628673 | − | 0.777670i | \(-0.716402\pi\) |
0.545337 | + | 0.838217i | \(0.316402\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.39699 | − | 7.37719i | 0.259991 | − | 0.800169i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.09659 | 0.224778 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.1180 | −1.07251 | −0.536253 | − | 0.844057i | \(-0.680161\pi\) | ||||
−0.536253 | + | 0.844057i | \(0.680161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.736420 | − | 2.26647i | 0.0771978 | − | 0.237590i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.323837 | + | 0.235281i | −0.0335803 | + | 0.0243975i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.477131 | − | 1.46846i | −0.0489526 | − | 0.150661i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.95505 | − | 6.50623i | −0.909248 | − | 0.660607i | 0.0315767 | − | 0.999501i | \(-0.489947\pi\) |
−0.940825 | + | 0.338894i | \(0.889947\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.85611 | + | 2.49403i | −0.890072 | + | 0.250659i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.45276 | − | 1.05549i | −0.144555 | − | 0.105025i | 0.513157 | − | 0.858295i | \(-0.328476\pi\) |
−0.657712 | + | 0.753269i | \(0.728476\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.70405 | − | 14.4776i | −0.463504 | − | 1.42652i | −0.860854 | − | 0.508852i | \(-0.830070\pi\) |
0.397350 | − | 0.917667i | \(-0.369930\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.41268 | + | 2.47946i | −0.333043 | + | 0.241970i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.45237 | − | 4.46992i | 0.140405 | − | 0.432124i | −0.855986 | − | 0.516999i | \(-0.827049\pi\) |
0.996392 | + | 0.0848752i | \(0.0270492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.92677 | 0.759247 | 0.379623 | − | 0.925141i | \(-0.376054\pi\) | ||||
0.379623 | + | 0.925141i | \(0.376054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.01040 | −0.475566 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.08380 | + | 3.33559i | −0.101955 | + | 0.313786i | −0.989004 | − | 0.147890i | \(-0.952752\pi\) |
0.887048 | + | 0.461676i | \(0.152752\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.13320 | − | 4.45603i | 0.571923 | − | 0.415527i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.857238 | − | 2.63831i | −0.0792517 | − | 0.243912i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.01575 | + | 2.91761i | 0.368123 | + | 0.267457i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.55972 | − | 10.6980i | −0.232702 | − | 0.972548i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.832423 | + | 0.604791i | 0.0750570 | + | 0.0545321i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.45221 | − | 13.7025i | −0.398218 | − | 1.22559i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1765 | + | 10.2998i | −1.25796 | + | 0.913964i | −0.998656 | − | 0.0518310i | \(-0.983494\pi\) |
−0.259307 | + | 0.965795i | \(0.583494\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.700379 | − | 2.15555i | 0.0616649 | − | 0.189785i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.1407 | −1.06074 | −0.530371 | − | 0.847766i | \(-0.677947\pi\) | ||||
−0.530371 | + | 0.847766i | \(0.677947\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.988050 | 0.0856748 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.15835 | + | 9.72040i | −0.271827 | + | 0.836599i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.28955 | + | 2.39000i | −0.281045 | + | 0.204191i | −0.719373 | − | 0.694624i | \(-0.755571\pi\) |
0.438328 | + | 0.898815i | \(0.355571\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.78965 | − | 11.6634i | −0.321434 | − | 0.989273i | −0.973024 | − | 0.230702i | \(-0.925898\pi\) |
0.651590 | − | 0.758571i | \(-0.274102\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.75163 | + | 2.72572i | 0.315944 | + | 0.229547i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.19245 | − | 0.899046i | 0.266966 | − | 0.0751820i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.2897 | − | 9.65551i | −1.10365 | − | 0.801846i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.193998 | + | 0.597066i | 0.0160007 | + | 0.0492452i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.9230 | + | 8.66255i | −0.976768 | + | 0.709664i | −0.956984 | − | 0.290141i | \(-0.906298\pi\) |
−0.0197843 | + | 0.999804i | \(0.506298\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.49300 | + | 13.8280i | −0.365635 | + | 1.12531i | 0.583948 | + | 0.811791i | \(0.301507\pi\) |
−0.949583 | + | 0.313517i | \(0.898493\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.77809 | 0.467131 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.13626 | 0.251911 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.78117 | − | 11.6372i | 0.301770 | − | 0.928753i | −0.679092 | − | 0.734053i | \(-0.737626\pi\) |
0.980863 | − | 0.194701i | \(-0.0623735\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.90759 | + | 1.38594i | −0.151282 | + | 0.109912i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.49912 | + | 4.61381i | 0.118147 | + | 0.363619i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.17616 | + | 3.76070i | 0.405428 | + | 0.294561i | 0.771748 | − | 0.635928i | \(-0.219383\pi\) |
−0.366320 | + | 0.930489i | \(0.619383\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.50708 | − | 2.03406i | −0.428725 | − | 0.158351i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.5623 | + | 10.5801i | 1.12687 | + | 0.818716i | 0.985236 | − | 0.171204i | \(-0.0547658\pi\) |
0.141630 | + | 0.989920i | \(0.454766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.309017 | + | 0.951057i | 0.0237705 | + | 0.0731582i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.930492 | − | 0.676042i | 0.0711565 | − | 0.0516982i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.74816 | + | 14.6133i | −0.360996 | + | 1.11103i | 0.591455 | + | 0.806338i | \(0.298554\pi\) |
−0.952451 | + | 0.304693i | \(0.901446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.1352 | 1.59767 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.63758 | −0.123088 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.64343 | + | 17.3687i | −0.421810 | + | 1.29820i | 0.484206 | + | 0.874954i | \(0.339109\pi\) |
−0.906016 | + | 0.423244i | \(0.860891\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.54734 | + | 2.57729i | −0.263672 | + | 0.191569i | −0.711764 | − | 0.702419i | \(-0.752104\pi\) |
0.448092 | + | 0.893987i | \(0.352104\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.01019 | − | 6.18674i | −0.148598 | − | 0.457337i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 31.7595 | + | 23.0746i | 2.33500 | + | 1.69648i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.273851 | + | 6.90272i | −0.0200260 | + | 0.504777i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.29126 | − | 3.84433i | −0.384883 | − | 0.279634i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.19913 | − | 19.0790i | −0.448553 | − | 1.38051i | −0.878539 | − | 0.477670i | \(-0.841482\pi\) |
0.429986 | − | 0.902835i | \(-0.358518\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.39675 | − | 6.10059i | 0.604411 | − | 0.439130i | −0.243031 | − | 0.970019i | \(-0.578142\pi\) |
0.847442 | + | 0.530888i | \(0.178142\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.546987 | − | 1.68345i | 0.0391706 | − | 0.120555i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.96244 | −0.211065 | −0.105533 | − | 0.994416i | \(-0.533655\pi\) | ||||
−0.105533 | + | 0.994416i | \(0.533655\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.6041 | −1.81502 | −0.907512 | − | 0.420025i | \(-0.862021\pi\) | ||||
−0.907512 | + | 0.420025i | \(0.862021\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.146963 | − | 0.452305i | 0.0103659 | − | 0.0319031i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.50429 | − | 6.17873i | 0.596884 | − | 0.433662i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.49122 | − | 7.66719i | −0.173994 | − | 0.535500i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.56864 | + | 3.31931i | 0.317542 | + | 0.230708i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.763524 | + | 1.14364i | 0.0528140 | + | 0.0791072i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.31694 | + | 5.31607i | 0.503719 | + | 0.365973i | 0.810436 | − | 0.585827i | \(-0.199230\pi\) |
−0.306717 | + | 0.951801i | \(0.599230\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.21745 | + | 3.74692i | 0.0834182 | + | 0.256735i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.3665 | + | 10.4379i | −0.979790 | + | 0.711859i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.620181 | + | 1.90872i | −0.0421007 | + | 0.129572i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.55994 | 0.510853 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.08289 | −0.140110 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.92375 | − | 18.2314i | 0.396684 | − | 1.22087i | −0.530959 | − | 0.847398i | \(-0.678168\pi\) |
0.927642 | − | 0.373470i | \(-0.121832\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.9040 | − | 14.4611i | 1.32694 | − | 0.964075i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.17122 | + | 22.0708i | 0.475971 | + | 1.46489i | 0.844644 | + | 0.535328i | \(0.179812\pi\) |
−0.368673 | + | 0.929559i | \(0.620188\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.32200 | − | 6.77283i | −0.616015 | − | 0.447561i | 0.235512 | − | 0.971871i | \(-0.424323\pi\) |
−0.851527 | + | 0.524310i | \(0.824323\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.32692 | − | 2.94937i | 0.153100 | − | 0.194054i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.10338 | − | 0.801651i | −0.0722847 | − | 0.0525179i | 0.551056 | − | 0.834468i | \(-0.314225\pi\) |
−0.623341 | + | 0.781950i | \(0.714225\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2276 | − | 34.5551i | −0.732411 | − | 2.25413i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.55631 | − | 1.13072i | 0.101093 | − | 0.0734483i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.18862 | + | 25.2020i | −0.529678 | + | 1.63018i | 0.225198 | + | 0.974313i | \(0.427697\pi\) |
−0.754876 | + | 0.655868i | \(0.772303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.5645 | 1.19584 | 0.597921 | − | 0.801555i | \(-0.295994\pi\) | ||||
0.597921 | + | 0.801555i | \(0.295994\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.5690 | −0.742153 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.51999 | − | 4.67806i | 0.0971089 | − | 0.298870i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.335423 | + | 0.243699i | −0.0213425 | + | 0.0155062i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.137838 | − | 0.424222i | −0.00873512 | − | 0.0268839i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.1412 | − | 7.36801i | −0.640106 | − | 0.465064i | 0.219780 | − | 0.975549i | \(-0.429466\pi\) |
−0.859887 | + | 0.510485i | \(0.829466\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.18190 | + | 5.30054i | −0.262914 | + | 0.333242i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.98276 | + | 2.16710i | 0.186787 | + | 0.135709i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.95707 | − | 15.2563i | −0.309214 | − | 0.951662i | −0.978071 | − | 0.208271i | \(-0.933216\pi\) |
0.668857 | − | 0.743391i | \(-0.266784\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.3234 | + | 14.7658i | −1.26284 | + | 0.917505i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.78128 | − | 11.6376i | 0.234055 | − | 0.720348i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.0633 | 1.42214 | 0.711071 | − | 0.703120i | \(-0.248211\pi\) | ||||
0.711071 | + | 0.703120i | \(0.248211\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.4744 | 1.13487 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.48612 | − | 4.57379i | 0.0909488 | − | 0.279912i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.67937 | + | 1.94668i | −0.163364 | + | 0.118691i | −0.666464 | − | 0.745537i | \(-0.732193\pi\) |
0.503100 | + | 0.864228i | \(0.332193\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.27519 | − | 25.4684i | −0.502682 | − | 1.54710i | −0.804633 | − | 0.593773i | \(-0.797638\pi\) |
0.301951 | − | 0.953324i | \(-0.402362\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.916382 | + | 0.665790i | 0.0554619 | + | 0.0402955i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.3324 | + | 24.4635i | 0.984883 | + | 1.47520i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.29565 | − | 1.66789i | −0.137932 | − | 0.100214i | 0.516679 | − | 0.856179i | \(-0.327168\pi\) |
−0.654612 | + | 0.755965i | \(0.727168\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.721929 | + | 2.22187i | 0.0432208 | + | 0.133020i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.9446 | − | 14.4906i | 1.18980 | − | 0.864438i | 0.196554 | − | 0.980493i | \(-0.437025\pi\) |
0.993243 | + | 0.116055i | \(0.0370250\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.80355 | − | 27.0945i | 0.523317 | − | 1.61060i | −0.244304 | − | 0.969699i | \(-0.578560\pi\) |
0.767621 | − | 0.640904i | \(-0.221440\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.733889 | 0.0434718 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.15886 | 0.304518 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.91265 | + | 12.0419i | −0.230156 | + | 0.708346i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.25641 | − | 3.09246i | 0.249515 | − | 0.181283i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.534224 | − | 1.64417i | −0.0312097 | − | 0.0960535i | 0.934238 | − | 0.356649i | \(-0.116081\pi\) |
−0.965448 | + | 0.260596i | \(0.916081\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.3802 | + | 7.54163i | 0.604356 | + | 0.439091i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.360835 | − | 9.09522i | 0.0209377 | − | 0.527758i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.64690 | − | 1.19654i | −0.0952428 | − | 0.0691979i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.51157 | − | 10.8075i | −0.202403 | − | 0.622933i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.690509 | − | 0.501684i | 0.0396687 | − | 0.0288210i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.7500 | + | 48.4736i | −0.901844 | + | 2.77559i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.0188744 | 0.00107722 | 0.000538610 | − | 1.00000i | \(-0.499829\pi\) | ||||
0.000538610 | 1.00000i | \(0.499829\pi\) | ||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.23545 | 0.411610 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.61018 | + | 17.2664i | −0.318124 | + | 0.979085i | 0.656325 | + | 0.754478i | \(0.272110\pi\) |
−0.974449 | + | 0.224607i | \(0.927890\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.35146 | − | 1.70843i | 0.132912 | − | 0.0965663i | −0.519343 | − | 0.854566i | \(-0.673823\pi\) |
0.652255 | + | 0.758000i | \(0.273823\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.60789 | + | 23.4147i | 0.428656 | + | 1.31927i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.8760 | + | 20.2531i | 1.56567 | + | 1.13753i | 0.931159 | + | 0.364613i | \(0.118799\pi\) |
0.634511 | + | 0.772914i | \(0.281201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.7235 | + | 5.06881i | 0.768366 | + | 0.283799i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.80729 | + | 1.31307i | 0.100873 | + | 0.0732884i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.266860 | − | 0.821311i | −0.0148485 | − | 0.0456989i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.17500 | + | 5.21294i | −0.397997 | + | 0.289162i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.16427 | + | 3.58326i | −0.0643843 | + | 0.198155i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 23.2504 | 1.28184 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.36846 | 0.185147 | 0.0925736 | − | 0.995706i | \(-0.470491\pi\) | ||||
0.0925736 | + | 0.995706i | \(0.470491\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.03646 | + | 27.8114i | −0.495195 | + | 1.52405i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.01457 | + | 2.19022i | −0.164704 | + | 0.119664i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.67846 | − | 8.24345i | −0.145905 | − | 0.449049i | 0.851221 | − | 0.524807i | \(-0.175862\pi\) |
−0.997126 | + | 0.0757575i | \(0.975862\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.34865 | − | 0.979853i | −0.0732488 | − | 0.0532183i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.68854 | + | 0.757138i | −0.145593 | + | 0.0410013i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.0423 | + | 11.6554i | 0.866202 | + | 0.629333i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.11349 | + | 3.42698i | 0.0599484 | + | 0.184502i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.9409 | − | 20.3002i | 1.49994 | − | 1.08977i | 0.529541 | − | 0.848285i | \(-0.322364\pi\) |
0.970404 | − | 0.241489i | \(-0.0776357\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.1483 | + | 34.3109i | −0.596754 | + | 1.83662i | −0.0509625 | + | 0.998701i | \(0.516229\pi\) |
−0.545792 | + | 0.837921i | \(0.683771\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.74447 | 0.146489 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.0990 | 1.12299 | 0.561493 | − | 0.827482i | \(-0.310227\pi\) | ||||
0.561493 | + | 0.827482i | \(0.310227\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.53881 | − | 29.3575i | 0.506268 | − | 1.55813i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.90872 | + | 1.38676i | −0.101020 | + | 0.0733954i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.49492 | − | 4.60088i | −0.0788987 | − | 0.242825i | 0.903826 | − | 0.427901i | \(-0.140747\pi\) |
−0.982724 | + | 0.185076i | \(0.940747\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2323 | + | 11.0669i | 0.801698 | + | 0.582467i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.21196 | + | 0.414200i | 0.273557 | + | 0.0217399i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −47.9203 | − | 34.8162i | −2.50826 | − | 1.82236i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.29461 | − | 7.06208i | −0.119778 | − | 0.368638i | 0.873136 | − | 0.487477i | \(-0.162083\pi\) |
−0.992914 | + | 0.118839i | \(0.962083\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.85834 | − | 3.52979i | 0.252915 | − | 0.183753i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.65323 | + | 11.2435i | −0.189666 | + | 0.583733i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.08926 | −0.159956 | −0.0799778 | − | 0.996797i | \(-0.525485\pi\) | ||||
−0.0799778 | + | 0.996797i | \(0.525485\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.84809 | 0.353634 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.36307 | + | 4.19511i | −0.0702019 | + | 0.216059i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.17954 | + | 4.48970i | −0.317421 | + | 0.230620i | −0.735074 | − | 0.677986i | \(-0.762853\pi\) |
0.417653 | + | 0.908607i | \(0.362853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.57377 | − | 7.92126i | −0.131858 | − | 0.405818i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.6862 | + | 14.3029i | 1.00592 | + | 0.730844i | 0.963349 | − | 0.268250i | \(-0.0864453\pi\) |
0.0425706 | + | 0.999093i | \(0.486445\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −28.3326 | + | 7.97892i | −1.44396 | + | 0.406644i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.7017 | − | 7.77523i | −0.543997 | − | 0.395237i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.84696 | − | 11.8397i | −0.195049 | − | 0.600298i | −0.999976 | − | 0.00692468i | \(-0.997796\pi\) |
0.804927 | − | 0.593373i | \(-0.202204\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.43031 | − | 2.49226i | 0.173478 | − | 0.126039i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.78321 | − | 5.48817i | 0.0899512 | − | 0.276841i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.0723 | −0.758372 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.1554 | −1.51346 | −0.756729 | − | 0.653729i | \(-0.773204\pi\) | ||||
−0.756729 | + | 0.653729i | \(0.773204\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.145123 | + | 0.446643i | −0.00726525 | + | 0.0223601i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.5084 | − | 22.1656i | 1.52352 | − | 1.10690i | 0.563806 | − | 0.825907i | \(-0.309336\pi\) |
0.959710 | − | 0.280992i | \(-0.0906635\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.260241 | − | 0.800939i | −0.0129635 | − | 0.0398976i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.1435 | + | 15.3616i | 1.05063 | + | 0.763326i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −32.7962 | − | 12.1134i | −1.62565 | − | 0.600438i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.3480 | + | 11.1510i | 0.758910 | + | 0.551380i | 0.898576 | − | 0.438818i | \(-0.144603\pi\) |
−0.139666 | + | 0.990199i | \(0.544603\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.597224 | − | 1.83807i | −0.0294589 | − | 0.0906651i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.64245 | + | 4.82602i | −0.326853 | + | 0.237473i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.07997 | + | 3.32381i | −0.0530137 | + | 0.163159i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.82898 | 0.285447 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.2286 | 0.743966 | 0.371983 | − | 0.928240i | \(-0.378678\pi\) | ||||
0.371983 | + | 0.928240i | \(0.378678\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.11146 | + | 6.49841i | −0.102906 | + | 0.316713i | −0.989233 | − | 0.146347i | \(-0.953249\pi\) |
0.886327 | + | 0.463060i | \(0.153249\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.8960 | − | 15.9083i | 1.06462 | − | 0.773490i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.70837 | − | 17.5685i | −0.276896 | − | 0.852200i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.3864 | − | 19.1709i | −1.27693 | − | 0.927743i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.0624921 | + | 1.57518i | −0.00301715 | + | 0.0760504i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.7568 | − | 18.7134i | −1.24066 | − | 0.901392i | −0.243017 | − | 0.970022i | \(-0.578137\pi\) |
−0.997642 | + | 0.0686300i | \(0.978137\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.21764 | + | 9.90288i | 0.154630 | + | 0.475902i | 0.998123 | − | 0.0612377i | \(-0.0195048\pi\) |
−0.843493 | + | 0.537140i | \(0.819505\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.31669 | − | 4.58934i | 0.302862 | − | 0.220042i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.260812 | − | 0.802698i | 0.0124763 | − | 0.0383982i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.5295 | −0.884366 | −0.442183 | − | 0.896925i | \(-0.645796\pi\) | ||||
−0.442183 | + | 0.896925i | \(0.645796\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.66404 | 0.174478 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.2399 | − | 31.5153i | 0.486514 | − | 1.49733i | −0.343263 | − | 0.939239i | \(-0.611532\pi\) |
0.829777 | − | 0.558096i | \(-0.188468\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.4840 | + | 22.1479i | −1.44508 | + | 1.04991i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.16464 | − | 6.66207i | −0.102384 | − | 0.315105i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.2858 | + | 18.3712i | 1.19331 | + | 0.866991i | 0.993610 | − | 0.112865i | \(-0.0360029\pi\) |
0.199701 | + | 0.979857i | \(0.436003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.98655 | + | 5.97124i | 0.187719 | + | 0.281175i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.59097 | − | 4.06208i | −0.262687 | − | 0.190853i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.74249 | − | 8.44051i | −0.128570 | − | 0.395697i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.3247 | + | 19.1260i | −1.23142 | + | 0.894678i | −0.996996 | − | 0.0774566i | \(-0.975320\pi\) |
−0.234423 | + | 0.972135i | \(0.575320\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.76647 | + | 5.43664i | −0.0824518 | + | 0.253760i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.18662 | −0.427864 | −0.213932 | − | 0.976849i | \(-0.568627\pi\) | ||||
−0.213932 | + | 0.976849i | \(0.568627\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.1230 | −0.516932 | −0.258466 | − | 0.966020i | \(-0.583217\pi\) | ||||
−0.258466 | + | 0.966020i | \(0.583217\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.460649 | + | 1.41773i | −0.0213621 | + | 0.0657458i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.793337 | + | 0.576393i | −0.0367113 | + | 0.0266723i | −0.605990 | − | 0.795473i | \(-0.707223\pi\) |
0.569278 | + | 0.822145i | \(0.307223\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.736842 | − | 2.26777i | −0.0340242 | − | 0.104716i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.70519 | + | 3.41852i | 0.216804 | + | 0.157517i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.79577 | − | 12.4161i | 0.450410 | − | 0.570893i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.97480 | − | 2.16132i | −0.136493 | − | 0.0991680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.25258 | + | 13.0881i | 0.194712 | + | 0.599263i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.69896 | + | 2.68745i | −0.169010 | + | 0.122793i | −0.669075 | − | 0.743195i | \(-0.733309\pi\) |
0.500065 | + | 0.865988i | \(0.333309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.25746 | − | 10.0254i | 0.148527 | − | 0.457120i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.30584 | −0.104919 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −41.2221 | −1.87180 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.98284 | − | 27.6463i | 0.407051 | − | 1.25278i | −0.512119 | − | 0.858915i | \(-0.671139\pi\) |
0.919170 | − | 0.393861i | \(-0.128861\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.46027 | + | 1.78749i | −0.111257 | + | 0.0808332i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.87149 | − | 24.2260i | −0.355235 | − | 1.09330i | −0.955873 | − | 0.293781i | \(-0.905087\pi\) |
0.600638 | − | 0.799521i | \(-0.294913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.43293 | − | 5.40034i | −0.334762 | − | 0.243219i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −21.2228 | + | 26.8998i | −0.953892 | + | 1.20906i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.9806 | + | 11.6106i | 0.716829 | + | 0.520807i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.44084 | + | 25.9782i | 0.377864 | + | 1.16295i | 0.941526 | + | 0.336940i | \(0.109392\pi\) |
−0.563662 | + | 0.826005i | \(0.690608\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.92159 | + | 5.02883i | −0.309234 | + | 0.224671i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.2342 | − | 37.6530i | 0.545496 | − | 1.67886i | −0.174313 | − | 0.984690i | \(-0.555770\pi\) |
0.719808 | − | 0.694173i | \(-0.244230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.68737 | −0.297584 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.475308 | −0.0211092 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.92584 | + | 24.3932i | −0.351307 | + | 1.08121i | 0.606814 | + | 0.794844i | \(0.292447\pi\) |
−0.958120 | + | 0.286366i | \(0.907553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.6651 | − | 22.2795i | 1.35654 | − | 0.985585i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.351622 | + | 1.08218i | 0.0155245 | + | 0.0477795i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −45.8634 | − | 33.3217i | −2.02099 | − | 1.46833i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.9669 | + | 26.9117i | 0.790184 | + | 1.18357i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.90848 | − | 4.29276i | −0.259354 | − | 0.188431i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.09668 | + | 18.7637i | 0.267100 | + | 0.822051i | 0.991202 | + | 0.132357i | \(0.0422546\pi\) |
−0.724102 | + | 0.689693i | \(0.757745\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.2992 | + | 7.48280i | −0.450352 | + | 0.327200i | −0.789735 | − | 0.613448i | \(-0.789782\pi\) |
0.339383 | + | 0.940648i | \(0.389782\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.10431 | + | 9.55409i | −0.135483 | + | 0.416975i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.75412 | 0.0764105 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.8560 | −0.819826 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.95344 | + | 9.08977i | −0.128169 | + | 0.394462i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.75133 | + | 1.27242i | −0.0758586 | + | 0.0551145i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.40873 | − | 16.6464i | −0.233840 | − | 0.719685i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.02254 | − | 5.10217i | −0.303045 | − | 0.220175i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.173656 | + | 4.37719i | −0.00747990 | + | 0.188539i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.4628 | + | 10.5079i | 0.621805 | + | 0.451768i | 0.853552 | − | 0.521008i | \(-0.174444\pi\) |
−0.231747 | + | 0.972776i | \(0.574444\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.644025 | − | 1.98211i | −0.0276378 | − | 0.0850603i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.8821 | − | 17.3514i | 1.02300 | − | 0.743251i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.60674 | − | 11.1004i | 0.154213 | − | 0.474619i | −0.843867 | − | 0.536552i | \(-0.819727\pi\) |
0.998080 | + | 0.0619330i | \(0.0197265\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −37.9664 | −1.62036 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.82883 | −0.0779107 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.98049 | − | 9.17299i | 0.126743 | − | 0.390075i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.0956 | + | 10.9676i | −0.640770 | + | 0.465547i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.79199 | + | 8.59286i | 0.118300 | + | 0.364091i | 0.992621 | − | 0.121258i | \(-0.0386927\pi\) |
−0.874321 | + | 0.485349i | \(0.838693\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.85774 | + | 2.80281i | 0.163165 | + | 0.118546i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.08012 | − | 1.13765i | −0.130043 | − | 0.0480318i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.96951 | + | 7.24328i | 0.420165 | + | 0.305268i | 0.777704 | − | 0.628630i | \(-0.216384\pi\) |
−0.357539 | + | 0.933898i | \(0.616384\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.03616 | + | 12.4220i | 0.169803 | + | 0.522599i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.5301 | + | 9.83018i | −0.568210 | + | 0.412829i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.78821 | − | 23.9697i | 0.326499 | − | 1.00486i | −0.644261 | − | 0.764806i | \(-0.722835\pi\) |
0.970759 | − | 0.240054i | \(-0.0771653\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.3451 | −0.851415 | −0.425708 | − | 0.904861i | \(-0.639975\pi\) | ||||
−0.425708 | + | 0.904861i | \(0.639975\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.53507 | 0.398333 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.57900 | − | 17.1704i | 0.232660 | − | 0.716055i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.81656 | − | 5.67906i | 0.325408 | − | 0.236422i | −0.413072 | − | 0.910698i | \(-0.635544\pi\) |
0.738479 | + | 0.674276i | \(0.235544\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.52444 | + | 4.69175i | 0.0633537 | + | 0.194983i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.80930 | − | 1.31454i | −0.0750626 | − | 0.0545362i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.8371 | + | 4.45998i | −0.655905 | + | 0.184714i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.35788 | − | 6.07236i | −0.345556 | − | 0.251061i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.97130 | − | 6.06703i | −0.0813641 | − | 0.250413i | 0.902097 | − | 0.431534i | \(-0.142027\pi\) |
−0.983461 | + | 0.181121i | \(0.942027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.282479 | − | 0.205233i | 0.0116394 | − | 0.00845648i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.435119 | − | 1.33916i | 0.0178984 | − | 0.0550856i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.4444 | 0.757420 | 0.378710 | − | 0.925515i | \(-0.376368\pi\) | ||||
0.378710 | + | 0.925515i | \(0.376368\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.4854 | 0.757826 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.76069 | − | 11.5742i | 0.153915 | − | 0.473700i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.9941 | + | 24.6982i | −1.38896 | + | 1.00914i | −0.392983 | + | 0.919546i | \(0.628557\pi\) |
−0.995978 | + | 0.0895941i | \(0.971443\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0802 | + | 40.2568i | 0.533553 | + | 1.64211i | 0.746754 | + | 0.665100i | \(0.231611\pi\) |
−0.213201 | + | 0.977008i | \(0.568389\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.24557 | − | 1.63150i | −0.0914465 | − | 0.0664398i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31.1296 | − | 26.6284i | −1.26560 | − | 1.08260i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.1376 | + | 16.8104i | 0.939125 | + | 0.682314i | 0.948210 | − | 0.317645i | \(-0.102892\pi\) |
−0.00908495 | + | 0.999959i | \(0.502892\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.54397 | + | 4.75185i | 0.0625647 | + | 0.192554i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.89305 | + | 5.73463i | −0.319318 | + | 0.231998i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.0921 | − | 31.0604i | 0.407618 | − | 1.25452i | −0.511072 | − | 0.859538i | \(-0.670752\pi\) |
0.918690 | − | 0.394980i | \(-0.129248\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.83182 | 0.154514 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.21975 | −0.250398 | −0.125199 | − | 0.992132i | \(-0.539957\pi\) | ||||
−0.125199 | + | 0.992132i | \(0.539957\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.07613 | − | 27.9334i | 0.364800 | − | 1.12274i | −0.585306 | − | 0.810813i | \(-0.699026\pi\) |
0.950106 | − | 0.311927i | \(-0.100974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.51987 | + | 3.28388i | −0.181376 | + | 0.131778i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.45110 | − | 22.9321i | −0.298522 | − | 0.918756i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.53309 | − | 5.47311i | −0.301324 | − | 0.218925i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.629122 | + | 0.177171i | −0.0251247 | + | 0.00707554i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.7631 | + | 12.9057i | 0.708263 | + | 0.514583i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.57122 | + | 10.9911i | 0.142168 | + | 0.437548i | 0.996636 | − | 0.0819559i | \(-0.0261167\pi\) |
−0.854468 | + | 0.519504i | \(0.826117\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.47781 | + | 2.52677i | −0.138230 | + | 0.100430i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.1657 | + | 62.0637i | −0.800252 | + | 2.46292i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.32081 | −0.0523324 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.9939 | 0.909624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.68540 | + | 29.8086i | −0.382550 | + | 1.17737i | 0.555692 | + | 0.831388i | \(0.312453\pi\) |
−0.938242 | + | 0.345980i | \(0.887547\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.8771 | − | 19.5273i | 1.05993 | − | 0.770083i | 0.0858534 | − | 0.996308i | \(-0.472638\pi\) |
0.974075 | + | 0.226225i | \(0.0726383\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.60827 | − | 8.02743i | −0.102701 | − | 0.316080i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.6150 | + | 23.6961i | 1.28223 | + | 0.931592i | 0.999618 | − | 0.0276437i | \(-0.00880038\pi\) |
0.282608 | + | 0.959235i | \(0.408800\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.7190 | − | 3.95910i | −0.420757 | − | 0.155408i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.771737 | − | 0.560700i | −0.0302468 | − | 0.0219756i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.24116 | − | 22.2860i | −0.283368 | − | 0.872118i | −0.986883 | − | 0.161437i | \(-0.948387\pi\) |
0.703515 | − | 0.710681i | \(-0.251613\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.5782 | + | 26.5756i | −1.42923 | + | 1.03840i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.6347 | − | 41.9632i | 0.531939 | − | 1.63714i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.23253 | −0.203830 | −0.101915 | − | 0.994793i | \(-0.532497\pi\) | ||||
−0.101915 | + | 0.994793i | \(0.532497\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.9745 | 0.738023 | 0.369011 | − | 0.929425i | \(-0.379696\pi\) | ||||
0.369011 | + | 0.929425i | \(0.379696\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.305931 | − | 0.941558i | 0.0118814 | − | 0.0365671i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.97684 | − | 2.16280i | 0.115437 | − | 0.0838699i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.77479 | − | 8.53991i | −0.107440 | − | 0.330667i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.37136 | + | 5.35561i | 0.284993 | + | 0.207060i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.79941 | − | 45.3560i | 0.0694653 | − | 1.75095i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3239 | − | 7.50077i | −0.397958 | − | 0.289133i | 0.370751 | − | 0.928732i | \(-0.379100\pi\) |
−0.768709 | + | 0.639599i | \(0.779100\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.52151 | + | 23.1488i | 0.289503 | + | 0.890999i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.278063 | + | 0.202025i | −0.0106868 | + | 0.00776444i | −0.593116 | − | 0.805117i | \(-0.702102\pi\) |
0.582429 | + | 0.812882i | \(0.302102\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.15147 | − | 25.0877i | 0.312825 | − | 0.962776i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.0303 | −0.422681 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.6280 | −0.904100 | −0.452050 | − | 0.891993i | \(-0.649307\pi\) | ||||
−0.452050 | + | 0.891993i | \(0.649307\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.67930 | + | 14.4014i | −0.178787 | + | 0.550249i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.43082 | − | 3.21918i | 0.169047 | − | 0.122819i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.53297 | − | 4.71800i | −0.0584015 | − | 0.179741i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.21932 | + | 0.885886i | 0.0463850 | + | 0.0337007i | 0.610736 | − | 0.791834i | \(-0.290874\pi\) |
−0.564351 | + | 0.825535i | \(0.690874\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.1744 | − | 18.2354i | −0.462469 | − | 0.692707i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36.9483 | − | 26.8445i | −1.40153 | − | 1.01827i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.39334 | − | 4.28827i | −0.0527767 | − | 0.162430i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.524445 | − | 0.381031i | 0.0198363 | − | 0.0144119i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.7754 | − | 39.3186i | 0.482520 | − | 1.48504i | −0.353021 | − | 0.935615i | \(-0.614846\pi\) |
0.835541 | − | 0.549428i | \(-0.185154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.37051 | 0.164837 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.2696 | 0.650410 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.32240 | − | 4.06992i | 0.0497338 | − | 0.153065i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.71042 | − | 3.42232i | 0.176903 | − | 0.128528i | −0.495810 | − | 0.868431i | \(-0.665129\pi\) |
0.672713 | + | 0.739903i | \(0.265129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.46947 | − | 10.6779i | −0.130115 | − | 0.400454i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.38695 | + | 1.00768i | 0.0519417 | + | 0.0377378i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.65037 | − | 9.69683i | 0.286108 | − | 0.362641i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.1897 | − | 7.40325i | −0.380541 | − | 0.276480i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.12394 | + | 28.0806i | 0.340266 | + | 1.04723i | 0.964070 | + | 0.265649i | \(0.0855863\pi\) |
−0.623804 | + | 0.781581i | \(0.714414\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.3488 | − | 21.3232i | 1.09301 | − | 0.794116i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.72672 | + | 8.39198i | −0.101408 | + | 0.312101i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.1202 | −1.45289 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.99681 | −0.370761 | −0.185381 | − | 0.982667i | \(-0.559352\pi\) | ||||
−0.185381 | + | 0.982667i | \(0.559352\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.80660 | + | 14.7932i | −0.178022 | + | 0.547896i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.03523 | + | 5.83794i | −0.297194 | + | 0.215924i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.18448 | + | 3.64546i | 0.0437498 | + | 0.134648i | 0.970546 | − | 0.240918i | \(-0.0774484\pi\) |
−0.926796 | + | 0.375566i | \(0.877448\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.89144 | + | 1.37421i | 0.0697669 | + | 0.0506886i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.05548 | − | 2.60531i | 0.0757144 | − | 0.0959678i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.5091 | + | 25.7989i | 1.30622 | + | 0.949028i | 0.999996 | − | 0.00293044i | \(-0.000932788\pi\) |
0.306229 | + | 0.951958i | \(0.400933\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0608967 | − | 0.187421i | −0.00223710 | − | 0.00688507i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.6943 | + | 26.6600i | −1.34619 | + | 0.978061i | −0.346993 | + | 0.937868i | \(0.612797\pi\) |
−0.999192 | + | 0.0401930i | \(0.987203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.9601 | + | 52.1978i | −0.621370 | + | 1.91238i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.60334 | −0.0952511 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.2005 | 0.409257 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.286404 | − | 0.881460i | 0.0104510 | − | 0.0321649i | −0.945695 | − | 0.325055i | \(-0.894617\pi\) |
0.956146 | + | 0.292890i | \(0.0946171\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.82019 | − | 3.50208i | 0.175658 | − | 0.127623i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.7323 | + | 51.4967i | 0.608950 | + | 1.87416i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.0430 | + | 11.6559i | 0.583091 | + | 0.423641i | 0.839837 | − | 0.542838i | \(-0.182650\pi\) |
−0.256746 | + | 0.966479i | \(0.582650\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.78185 | − | 2.66894i | −0.0646772 | − | 0.0968765i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.6586 | + | 11.3767i | 0.567624 | + | 0.412403i | 0.834241 | − | 0.551399i | \(-0.185906\pi\) |
−0.266617 | + | 0.963803i | \(0.585906\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.83743 | + | 17.9658i | 0.211329 | + | 0.650404i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.4085 | − | 12.6480i | 0.629406 | − | 0.457290i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.06466 | − | 3.27668i | 0.0384425 | − | 0.118314i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.5850 | −1.53566 | −0.767828 | − | 0.640657i | \(-0.778662\pi\) | ||||
−0.767828 | + | 0.640657i | \(0.778662\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.62463 | 0.274594 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.71862 | + | 11.4447i | −0.133750 | + | 0.411639i | −0.995393 | − | 0.0958746i | \(-0.969435\pi\) |
0.861644 | + | 0.507513i | \(0.169435\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.04248 | − | 4.39012i | 0.217052 | − | 0.157698i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.68976 | − | 11.3559i | −0.132369 | − | 0.407391i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.726113 | − | 0.527552i | −0.0260157 | − | 0.0189015i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.08979 | + | 27.4693i | −0.0389957 | + | 0.982929i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.79385 | + | 7.11565i | 0.350004 | + | 0.254292i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0814 | − | 43.3381i | −0.502586 | − | 1.54680i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.42431 | − | 5.39408i | 0.264648 | − | 0.192278i | −0.447546 | − | 0.894261i | \(-0.647702\pi\) |
0.712194 | + | 0.701983i | \(0.247702\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.38750 | + | 10.4256i | −0.120598 | + | 0.371163i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.35815 | −0.297182 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.6861 | 0.486008 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.71349 | + | 8.35127i | −0.0962376 | + | 0.296189i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.1064 | − | 10.2489i | 0.499673 | − | 0.363034i | −0.309219 | − | 0.950991i | \(-0.600068\pi\) |
0.808892 | + | 0.587957i | \(0.200068\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.27964 | − | 19.3267i | −0.222158 | − | 0.683731i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.7076 | − | 16.4981i | −0.802334 | − | 0.582930i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 49.4845 | + | 18.2773i | 1.74627 | + | 0.644992i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.6161 | + | 10.6192i | 0.515148 | + | 0.374277i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.486444 | − | 1.49712i | −0.0171236 | − | 0.0527012i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.20031 | + | 6.68442i | −0.323466 | + | 0.235012i | −0.737653 | − | 0.675180i | \(-0.764066\pi\) |
0.414187 | + | 0.910192i | \(0.364066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.0421 | − | 43.2172i | 0.493086 | − | 1.51756i | −0.326833 | − | 0.945082i | \(-0.605981\pi\) |
0.819919 | − | 0.572480i | \(-0.194019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.7283 | 0.446402 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.8270 | 0.834623 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.610933 | + | 1.88026i | −0.0213738 | + | 0.0657819i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.34835 | − | 3.88581i | 0.186887 | − | 0.135781i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.7953 | + | 33.2247i | 0.376760 | + | 1.15955i | 0.942283 | + | 0.334816i | \(0.108674\pi\) |
−0.565523 | + | 0.824732i | \(0.691326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.5355 | − | 14.1934i | −0.680965 | − | 0.494750i | 0.192713 | − | 0.981255i | \(-0.438271\pi\) |
−0.873678 | + | 0.486505i | \(0.838271\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.4575 | + | 3.78985i | −0.468529 | + | 0.131945i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.9329 | + | 21.7475i | 1.04087 | + | 0.756235i | 0.970455 | − | 0.241282i | \(-0.0775680\pi\) |
0.0704138 | + | 0.997518i | \(0.477568\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.6805 | + | 51.3374i | 0.579338 | + | 1.78302i | 0.620906 | + | 0.783885i | \(0.286765\pi\) |
−0.0415677 | + | 0.999136i | \(0.513235\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.09114 | − | 0.792762i | 0.0378513 | − | 0.0275006i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.850136 | − | 2.61645i | 0.0294555 | − | 0.0906546i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 67.0335 | 2.31979 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.31127 | −0.0798894 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.70232 | − | 5.23920i | 0.0587706 | − | 0.180877i | −0.917361 | − | 0.398055i | \(-0.869685\pi\) |
0.976132 | + | 0.217178i | \(0.0696852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.72050 | − | 5.60927i | 0.266224 | − | 0.193423i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.62098 | + | 11.1442i | 0.124713 | + | 0.383828i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.01285 | + | 2.18896i | 0.103645 | + | 0.0753025i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.3617 | − | 13.6798i | 0.768357 | − | 0.470042i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.9549 | + | 7.95920i | 0.375971 | + | 0.273159i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.63115 | + | 20.4086i | 0.227313 | + | 0.699597i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.9357 | − | 10.1249i | 0.477150 | − | 0.346670i | −0.323071 | − | 0.946375i | \(-0.604715\pi\) |
0.800221 | + | 0.599705i | \(0.204715\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.32360 | − | 4.07362i | 0.0452661 | − | 0.139315i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.1309 | 1.50748 | 0.753741 | − | 0.657172i | \(-0.228247\pi\) | ||||
0.753741 | + | 0.657172i | \(0.228247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.1579 | 0.551299 | 0.275649 | − | 0.961258i | \(-0.411107\pi\) | ||||
0.275649 | + | 0.961258i | \(0.411107\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.757726 | + | 2.33204i | −0.0258232 | + | 0.0794757i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.43483 | − | 2.49555i | 0.116923 | − | 0.0849494i | −0.527787 | − | 0.849377i | \(-0.676978\pi\) |
0.644710 | + | 0.764427i | \(0.276978\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.6825 | + | 54.4212i | 0.601224 | + | 1.85038i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.86879 | − | 3.53739i | −0.165353 | − | 0.120136i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.9207 | − | 3.63868i | 0.438304 | − | 0.123434i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.809481 | + | 0.588122i | 0.0274282 | + | 0.0199278i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.48882 | − | 29.2036i | −0.321148 | − | 0.988391i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.7776 | − | 20.1816i | 0.939054 | − | 0.682263i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.85652 | + | 5.71379i | −0.0626903 | + | 0.192941i | −0.977496 | − | 0.210953i | \(-0.932343\pi\) |
0.914806 | + | 0.403894i | \(0.132343\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.821705 | 0.0277154 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.691967 | −0.0233130 | −0.0116565 | − | 0.999932i | \(-0.503710\pi\) | ||||
−0.0116565 | + | 0.999932i | \(0.503710\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.16056 | − | 15.8826i | 0.173667 | − | 0.534491i | −0.825903 | − | 0.563812i | \(-0.809334\pi\) |
0.999570 | + | 0.0293204i | \(0.00933430\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.93378 | + | 3.58460i | −0.165847 | + | 0.120495i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.05947 | − | 18.6491i | −0.203457 | − | 0.626177i | −0.999773 | − | 0.0212959i | \(-0.993221\pi\) |
0.796316 | − | 0.604881i | \(-0.206779\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.7842 | − | 24.5456i | −1.13308 | − | 0.823234i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.8336 | − | 8.06434i | −0.731454 | − | 0.270165i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.27251 | − | 2.37761i | −0.109510 | − | 0.0795638i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.0166 | + | 64.6825i | 0.702508 | + | 2.16210i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.782786 | − | 0.568728i | 0.0261365 | − | 0.0189893i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.14792 | − | 3.53294i | 0.0382854 | − | 0.117830i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.3328 | 0.344234 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.40125 | 0.179742 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.04599 | + | 15.5300i | −0.167735 | + | 0.516234i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.1475 | + | 29.1688i | −1.33307 | + | 0.968536i | −0.333406 | + | 0.942783i | \(0.608198\pi\) |
−0.999668 | + | 0.0257524i | \(0.991802\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.53935 | − | 4.73763i | −0.0510570 | − | 0.157137i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.1171 | + | 31.3264i | 1.42853 | + | 1.03789i | 0.990287 | + | 0.139036i | \(0.0444005\pi\) |
0.438247 | + | 0.898855i | \(0.355600\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.123384 | − | 3.11004i | 0.00408343 | − | 0.102927i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.5989 | − | 14.2394i | −0.647920 | − | 0.470742i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.94069 | − | 27.5166i | −0.295248 | − | 0.908679i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.8500 | + | 26.0466i | −1.18258 | + | 0.859197i | −0.992461 | − | 0.122563i | \(-0.960889\pi\) |
−0.190122 | + | 0.981760i | \(0.560889\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.00277225 | + | 0.00853209i | −9.13486e−5 | + | 0.000281142i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.28882 | −0.272830 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 93.4890 | 3.07390 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.0494 | − | 40.1620i | 0.428599 | − | 1.31909i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.19873 | − | 5.23018i | 0.236183 | − | 0.171597i | −0.463398 | − | 0.886150i | \(-0.653370\pi\) |
0.699581 | + | 0.714553i | \(0.253370\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.169223 | − | 0.520814i | −0.00554605 | − | 0.0170690i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.98116 | − | 5.07211i | −0.228553 | − | 0.166053i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.2847 | + | 21.3963i | 0.467160 | + | 0.699733i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.67726 | − | 6.30439i | −0.283474 | − | 0.205956i | 0.436957 | − | 0.899482i | \(-0.356056\pi\) |
−0.720431 | + | 0.693527i | \(0.756056\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.426911 | + | 1.31390i | 0.0139317 | + | 0.0428774i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.1940 | − | 17.5780i | 0.788702 | − | 0.573025i | −0.118876 | − | 0.992909i | \(-0.537929\pi\) |
0.907578 | + | 0.419884i | \(0.137929\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.36177 | − | 4.19109i | 0.0443453 | − | 0.136481i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24.3568 | −0.792328 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.2979 | −1.11453 | −0.557265 | − | 0.830335i | \(-0.688149\pi\) | ||||
−0.557265 | + | 0.830335i | \(0.688149\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.91502 | + | 15.1269i | −0.159548 | + | 0.491039i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.2497 | + | 9.62646i | −0.429650 | + | 0.312159i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.45722 | + | 16.7956i | 0.176777 | + | 0.544062i | 0.999710 | − | 0.0240753i | \(-0.00766414\pi\) |
−0.822934 | + | 0.568138i | \(0.807664\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −60.4401 | − | 43.9123i | −1.95580 | − | 1.42097i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.30701 | + | 5.45913i | −0.139226 | + | 0.176468i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.83935 | − | 5.69562i | −0.253146 | − | 0.183921i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.36036 | − | 28.8082i | −0.301947 | − | 0.929298i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.5480 | − | 7.66358i | 0.339905 | − | 0.246955i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.9441 | − | 36.7603i | 0.384496 | − | 1.18336i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 61.0661 | 1.96375 | 0.981876 | − | 0.189523i | \(-0.0606943\pi\) | ||||
0.981876 | + | 0.189523i | \(0.0606943\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.410466 | 0.0131861 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.37660 | + | 7.31443i | −0.0762688 | + | 0.234731i | −0.981921 | − | 0.189289i | \(-0.939382\pi\) |
0.905653 | + | 0.424021i | \(0.139382\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.6438 | − | 17.1783i | 0.757987 | − | 0.550710i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.30263 | − | 4.00909i | −0.0417176 | − | 0.128394i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.4015 | − | 19.1818i | −0.844660 | − | 0.613681i | 0.0790086 | − | 0.996874i | \(-0.474825\pi\) |
−0.923668 | + | 0.383193i | \(0.874825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.7854 | − | 26.3454i | 0.664304 | − | 0.842003i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.7899 | + | 12.9251i | 0.567987 | + | 0.412667i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.37294 | − | 19.6139i | −0.203265 | − | 0.625586i | −0.999780 | − | 0.0209673i | \(-0.993325\pi\) |
0.796515 | − | 0.604619i | \(-0.206675\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.92538 | + | 6.48467i | −0.284386 | + | 0.206619i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.41498 | + | 10.5102i | −0.108700 | + | 0.334544i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.70701 | −0.308665 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.4012 | −1.53752 | −0.768758 | − | 0.639540i | \(-0.779125\pi\) | ||||
−0.768758 | + | 0.639540i | \(0.779125\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.494754 | + | 1.52270i | −0.0157005 | + | 0.0483213i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −77.1411 | + | 56.0463i | −2.44554 | + | 1.77679i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.10636 | + | 24.9488i | 0.256731 | + | 0.790136i | 0.993484 | + | 0.113974i | \(0.0363581\pi\) |
−0.736753 | + | 0.676162i | \(0.763642\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.4052 | − | 17.0049i | −0.740508 | − | 0.538011i |
(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 | 572.2.n.a.521.2 | yes | 20 | |
11.3 | even | 5 | inner | 572.2.n.a.157.2 | ✓ | 20 | |
11.5 | even | 5 | 6292.2.a.w.1.5 | 10 | |||
11.6 | odd | 10 | 6292.2.a.x.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.n.a.157.2 | ✓ | 20 | 11.3 | even | 5 | inner | |
572.2.n.a.521.2 | yes | 20 | 1.1 | even | 1 | trivial | |
6292.2.a.w.1.5 | 10 | 11.5 | even | 5 | |||
6292.2.a.x.1.5 | 10 | 11.6 | odd | 10 |