Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + x^{18} + 4x^{16} + 8x^{12} + 4x^{10} + 32x^{8} + 256x^{4} + 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.15 | ||
Root | \(0.885915 - 1.10234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.e.757.16 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.885915 | − | 1.10234i | 0.626437 | − | 0.779472i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.430309 | − | 1.95316i | −0.215154 | − | 0.976580i | ||||
\(5\) | 3.50133i | 1.56584i | 0.622120 | + | 0.782922i | \(0.286272\pi\) | ||||
−0.622120 | + | 0.782922i | \(0.713728\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.53426 | − | 1.25599i | −0.895998 | − | 0.444059i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.85966 | + | 3.10188i | 1.22053 | + | 0.980902i | ||||
\(11\) | − | 3.01331i | − | 0.908547i | −0.890862 | − | 0.454273i | \(-0.849899\pi\) | ||
0.890862 | − | 0.454273i | \(-0.150101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.90632i | 1.08342i | 0.840566 | + | 0.541709i | \(0.182223\pi\) | ||||
−0.840566 | + | 0.541709i | \(0.817777\pi\) | |||||||
\(14\) | −0.885915 | + | 1.10234i | −0.236771 | + | 0.294613i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.62967 | + | 1.68092i | −0.907417 | + | 0.420231i | ||||
\(17\) | 1.38839 | 0.336733 | 0.168367 | − | 0.985724i | \(-0.446151\pi\) | ||||
0.168367 | + | 0.985724i | \(0.446151\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.79460i | 1.09996i | 0.835179 | + | 0.549978i | \(0.185364\pi\) | ||||
−0.835179 | + | 0.549978i | \(0.814636\pi\) | |||||||
\(20\) | 6.83867 | − | 1.50665i | 1.52917 | − | 0.336898i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.32169 | − | 2.66954i | −0.708187 | − | 0.569147i | ||||
\(23\) | −5.06853 | −1.05686 | −0.528431 | − | 0.848976i | \(-0.677219\pi\) | ||||
−0.528431 | + | 0.848976i | \(0.677219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.25934 | −1.45187 | ||||||||
\(26\) | 4.30609 | + | 3.46067i | 0.844495 | + | 0.678693i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.430309 | + | 1.95316i | 0.0813207 | + | 0.369113i | ||||
\(29\) | 4.91070i | 0.911893i | 0.890007 | + | 0.455947i | \(0.150699\pi\) | ||||
−0.890007 | + | 0.455947i | \(0.849301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.13938 | 0.204639 | 0.102320 | − | 0.994752i | \(-0.467374\pi\) | ||||
0.102320 | + | 0.994752i | \(0.467374\pi\) | |||||||
\(32\) | −1.36263 | + | 5.49029i | −0.240881 | + | 0.970555i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.22999 | − | 1.53047i | 0.210942 | − | 0.262474i | ||||
\(35\) | − | 3.50133i | − | 0.591833i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.45610i | 1.55457i | 0.629146 | + | 0.777287i | \(0.283405\pi\) | ||||
−0.629146 | + | 0.777287i | \(0.716595\pi\) | |||||||
\(38\) | 5.28528 | + | 4.24761i | 0.857386 | + | 0.689053i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.39763 | − | 8.87330i | 0.695327 | − | 1.40299i | ||||
\(41\) | 4.11364 | 0.642443 | 0.321222 | − | 0.947004i | \(-0.395907\pi\) | ||||
0.321222 | + | 0.947004i | \(0.395907\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.51868i | − | 0.231597i | −0.993273 | − | 0.115799i | \(-0.963057\pi\) | ||
0.993273 | − | 0.115799i | \(-0.0369427\pi\) | |||||||
\(44\) | −5.88547 | + | 1.29665i | −0.887269 | + | 0.195478i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.49029 | + | 5.58724i | −0.662057 | + | 0.823794i | ||||
\(47\) | −10.7641 | −1.57010 | −0.785051 | − | 0.619431i | \(-0.787363\pi\) | ||||
−0.785051 | + | 0.619431i | \(0.787363\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.43116 | + | 8.00226i | −0.909503 | + | 1.13169i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.62967 | − | 1.68092i | 1.05804 | − | 0.233102i | ||||
\(53\) | 0.431457i | 0.0592651i | 0.999561 | + | 0.0296326i | \(0.00943372\pi\) | ||||
−0.999561 | + | 0.0296326i | \(0.990566\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.5506 | 1.42264 | ||||||||
\(56\) | 2.53426 | + | 1.25599i | 0.338655 | + | 0.167838i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.41326 | + | 4.35046i | 0.710796 | + | 0.571243i | ||||
\(59\) | 7.40936i | 0.964617i | 0.876002 | + | 0.482308i | \(0.160202\pi\) | ||||
−0.876002 | + | 0.482308i | \(0.839798\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9520i | 1.65834i | 0.559000 | + | 0.829168i | \(0.311185\pi\) | ||||
−0.559000 | + | 0.829168i | \(0.688815\pi\) | |||||||
\(62\) | 1.00940 | − | 1.25599i | 0.128193 | − | 0.159511i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.84499 | + | 6.36601i | 0.605624 | + | 0.795751i | ||||
\(65\) | −13.6773 | −1.69646 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.36185i | 0.410715i | 0.978687 | + | 0.205357i | \(0.0658357\pi\) | ||||
−0.978687 | + | 0.205357i | \(0.934164\pi\) | |||||||
\(68\) | −0.597435 | − | 2.71174i | −0.0724496 | − | 0.328847i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.85966 | − | 3.10188i | −0.461318 | − | 0.370746i | ||||
\(71\) | −6.26892 | −0.743984 | −0.371992 | − | 0.928236i | \(-0.621325\pi\) | ||||
−0.371992 | + | 0.928236i | \(0.621325\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0859 | 1.18046 | 0.590230 | − | 0.807235i | \(-0.299037\pi\) | ||||
0.590230 | + | 0.807235i | \(0.299037\pi\) | |||||||
\(74\) | 10.4238 | + | 8.37730i | 1.21175 | + | 0.973842i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.36462 | − | 2.06316i | 1.07420 | − | 0.236660i | ||||
\(77\) | 3.01331i | 0.343398i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9346 | 1.45526 | 0.727631 | − | 0.685969i | \(-0.240622\pi\) | ||||
0.727631 | + | 0.685969i | \(0.240622\pi\) | |||||||
\(80\) | −5.88547 | − | 12.7087i | −0.658016 | − | 1.42087i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.64434 | − | 4.53464i | 0.402450 | − | 0.500767i | ||||
\(83\) | − | 17.4139i | − | 1.91142i | −0.294307 | − | 0.955711i | \(-0.595089\pi\) | ||
0.294307 | − | 0.955711i | \(-0.404911\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.86120i | 0.527272i | ||||||||
\(86\) | −1.67411 | − | 1.34543i | −0.180524 | − | 0.145081i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.78468 | + | 7.63652i | −0.403448 | + | 0.814056i | ||||
\(89\) | −0.818403 | −0.0867506 | −0.0433753 | − | 0.999059i | \(-0.513811\pi\) | ||||
−0.0433753 | + | 0.999059i | \(0.513811\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.90632i | − | 0.409494i | ||||||
\(92\) | 2.18103 | + | 9.89965i | 0.227388 | + | 1.03211i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.53606 | + | 11.8657i | −0.983569 | + | 1.22385i | ||||
\(95\) | −16.7875 | −1.72236 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.4727 | −1.16488 | −0.582441 | − | 0.812873i | \(-0.697902\pi\) | ||||
−0.582441 | + | 0.812873i | \(0.697902\pi\) | |||||||
\(98\) | 0.885915 | − | 1.10234i | 0.0894909 | − | 0.111353i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.12376 | + | 14.1786i | 0.312376 | + | 1.41786i | ||||
\(101\) | 5.38541i | 0.535868i | 0.963437 | + | 0.267934i | \(0.0863410\pi\) | ||||
−0.963437 | + | 0.267934i | \(0.913659\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.82652 | −0.475571 | −0.237785 | − | 0.971318i | \(-0.576421\pi\) | ||||
−0.237785 | + | 0.971318i | \(0.576421\pi\) | |||||||
\(104\) | 4.90629 | − | 9.89965i | 0.481101 | − | 0.970740i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.475612 | + | 0.382234i | 0.0461955 | + | 0.0371258i | ||||
\(107\) | 4.92215i | 0.475842i | 0.971284 | + | 0.237921i | \(0.0764660\pi\) | ||||
−0.971284 | + | 0.237921i | \(0.923534\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 20.1342i | − | 1.92851i | −0.264974 | − | 0.964255i | \(-0.585363\pi\) | ||
0.264974 | − | 0.964255i | \(-0.414637\pi\) | |||||||
\(110\) | 9.34694 | − | 11.6304i | 0.891195 | − | 1.10891i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.62967 | − | 1.68092i | 0.342971 | − | 0.158832i | ||||
\(113\) | −13.2438 | −1.24587 | −0.622937 | − | 0.782272i | \(-0.714061\pi\) | ||||
−0.622937 | + | 0.782272i | \(0.714061\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 17.7466i | − | 1.65488i | ||||||
\(116\) | 9.59137 | − | 2.11311i | 0.890537 | − | 0.196198i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.16764 | + | 6.56407i | 0.751892 | + | 0.604271i | ||||
\(119\) | −1.38839 | −0.127273 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.91997 | 0.174543 | ||||||||
\(122\) | 14.2775 | + | 11.4744i | 1.29263 | + | 1.03884i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.490286 | − | 2.22540i | −0.0440290 | − | 0.199847i | ||||
\(125\) | − | 7.91070i | − | 0.707554i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2252 | 0.907343 | 0.453671 | − | 0.891169i | \(-0.350114\pi\) | ||||
0.453671 | + | 0.891169i | \(0.350114\pi\) | |||||||
\(128\) | 11.3098 | + | 0.298914i | 0.999651 | + | 0.0264205i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.1170 | + | 15.0771i | −1.06273 | + | 1.32235i | ||||
\(131\) | − | 1.54726i | − | 0.135185i | −0.997713 | − | 0.0675924i | \(-0.978468\pi\) | ||
0.997713 | − | 0.0675924i | \(-0.0215317\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 4.79460i | − | 0.415744i | ||||||
\(134\) | 3.70590 | + | 2.97831i | 0.320141 | + | 0.257287i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.51854 | − | 1.74380i | −0.301712 | − | 0.149529i | ||||
\(137\) | 7.46379 | 0.637674 | 0.318837 | − | 0.947809i | \(-0.396708\pi\) | ||||
0.318837 | + | 0.947809i | \(0.396708\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.6383i | 1.41125i | 0.708588 | + | 0.705623i | \(0.249333\pi\) | ||||
−0.708588 | + | 0.705623i | \(0.750667\pi\) | |||||||
\(140\) | −6.83867 | + | 1.50665i | −0.577973 | + | 0.127336i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.55373 | + | 6.91048i | −0.466059 | + | 0.579915i | ||||
\(143\) | 11.7709 | 0.984336 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.1940 | −1.42788 | ||||||||
\(146\) | 8.93521 | − | 11.1180i | 0.739483 | − | 0.920136i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.4693 | − | 4.06904i | 1.51817 | − | 0.334473i | ||||
\(149\) | − | 21.3846i | − | 1.75190i | −0.482405 | − | 0.875948i | \(-0.660237\pi\) | ||
0.482405 | − | 0.875948i | \(-0.339763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.21341 | 0.0987459 | 0.0493730 | − | 0.998780i | \(-0.484278\pi\) | ||||
0.0493730 | + | 0.998780i | \(0.484278\pi\) | |||||||
\(152\) | 6.02196 | − | 12.1508i | 0.488445 | − | 0.985558i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.32169 | + | 2.66954i | 0.267670 | + | 0.215117i | ||||
\(155\) | 3.98936i | 0.320433i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.15645i | − | 0.650955i | −0.945550 | − | 0.325478i | \(-0.894475\pi\) | ||
0.945550 | − | 0.325478i | \(-0.105525\pi\) | |||||||
\(158\) | 11.4590 | − | 14.2584i | 0.911629 | − | 1.13434i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −19.2233 | − | 4.77102i | −1.51974 | − | 0.377182i | ||||
\(161\) | 5.06853 | 0.399456 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 22.8278i | − | 1.78801i | −0.448055 | − | 0.894006i | \(-0.647883\pi\) | ||
0.448055 | − | 0.894006i | \(-0.352117\pi\) | |||||||
\(164\) | −1.77014 | − | 8.03461i | −0.138224 | − | 0.627397i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.1960 | − | 15.4272i | −1.48990 | − | 1.19738i | ||||
\(167\) | 17.3575 | 1.34316 | 0.671581 | − | 0.740931i | \(-0.265616\pi\) | ||||
0.671581 | + | 0.740931i | \(0.265616\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.25934 | −0.173795 | ||||||||
\(170\) | 5.35870 | + | 4.30661i | 0.410994 | + | 0.330302i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.96623 | + | 0.653503i | −0.226173 | + | 0.0498291i | ||||
\(173\) | − | 23.5784i | − | 1.79263i | −0.443415 | − | 0.896316i | \(-0.646233\pi\) | ||
0.443415 | − | 0.896316i | \(-0.353767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.25934 | 0.548754 | ||||||||
\(176\) | 5.06514 | + | 10.9373i | 0.381799 | + | 0.824431i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.725036 | + | 0.902159i | −0.0543437 | + | 0.0676197i | ||||
\(179\) | − | 12.0965i | − | 0.904134i | −0.891984 | − | 0.452067i | \(-0.850687\pi\) | ||
0.891984 | − | 0.452067i | \(-0.149313\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.70662i | 0.275511i | 0.990466 | + | 0.137755i | \(0.0439888\pi\) | ||||
−0.990466 | + | 0.137755i | \(0.956011\pi\) | |||||||
\(182\) | −4.30609 | − | 3.46067i | −0.319189 | − | 0.256522i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.8450 | + | 6.36601i | 0.946945 | + | 0.469308i | ||||
\(185\) | −33.1090 | −2.43422 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.18364i | − | 0.305938i | ||||||
\(188\) | 4.63188 | + | 21.0240i | 0.337814 | + | 1.53333i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.8723 | + | 18.5055i | −1.07895 | + | 1.34253i | ||||
\(191\) | 11.2770 | 0.815977 | 0.407988 | − | 0.912987i | \(-0.366230\pi\) | ||||
0.407988 | + | 0.912987i | \(0.366230\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.15188 | −0.226877 | −0.113439 | − | 0.993545i | \(-0.536187\pi\) | ||||
−0.113439 | + | 0.993545i | \(0.536187\pi\) | |||||||
\(194\) | −10.1639 | + | 12.6469i | −0.729724 | + | 0.907993i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.430309 | − | 1.95316i | −0.0307363 | − | 0.139511i | ||||
\(197\) | 11.4819i | 0.818052i | 0.912523 | + | 0.409026i | \(0.134131\pi\) | ||||
−0.912523 | + | 0.409026i | \(0.865869\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.38405 | −0.239889 | −0.119944 | − | 0.992781i | \(-0.538272\pi\) | ||||
−0.119944 | + | 0.992781i | \(0.538272\pi\) | |||||||
\(200\) | 18.3971 | + | 9.11764i | 1.30087 | + | 0.644714i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.93656 | + | 4.77102i | 0.417695 | + | 0.335688i | ||||
\(203\) | − | 4.91070i | − | 0.344663i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.4032i | 1.00597i | ||||||||
\(206\) | −4.27588 | + | 5.32046i | −0.297915 | + | 0.370694i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.56623 | − | 14.1786i | −0.455286 | − | 0.983112i | ||||
\(209\) | 14.4476 | 0.999362 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0774i | 1.17565i | 0.808987 | + | 0.587827i | \(0.200016\pi\) | ||||
−0.808987 | + | 0.587827i | \(0.799984\pi\) | |||||||
\(212\) | 0.842704 | − | 0.185659i | 0.0578771 | − | 0.0127511i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.42588 | + | 4.36061i | 0.370906 | + | 0.298085i | ||||
\(215\) | 5.31742 | 0.362645 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.13938 | −0.0773463 | ||||||||
\(218\) | −22.1948 | − | 17.8372i | −1.50322 | − | 1.20809i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.54001 | − | 20.6070i | −0.306088 | − | 1.38932i | ||||
\(221\) | 5.42348i | 0.364823i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.1161 | 1.61494 | 0.807468 | − | 0.589912i | \(-0.200837\pi\) | ||||
0.807468 | + | 0.589912i | \(0.200837\pi\) | |||||||
\(224\) | 1.36263 | − | 5.49029i | 0.0910445 | − | 0.366835i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.7329 | + | 14.5992i | −0.780461 | + | 0.971125i | ||||
\(227\) | 7.60050i | 0.504463i | 0.967667 | + | 0.252231i | \(0.0811644\pi\) | ||||
−0.967667 | + | 0.252231i | \(0.918836\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.0017i | 1.58608i | 0.609171 | + | 0.793039i | \(0.291502\pi\) | ||||
−0.609171 | + | 0.793039i | \(0.708498\pi\) | |||||||
\(230\) | −19.5628 | − | 15.7220i | −1.28993 | − | 1.03668i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.16777 | − | 12.4450i | 0.404934 | − | 0.817054i | ||||
\(233\) | −10.6276 | −0.696237 | −0.348118 | − | 0.937451i | \(-0.613179\pi\) | ||||
−0.348118 | + | 0.937451i | \(0.613179\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 37.6886i | − | 2.45853i | ||||||
\(236\) | 14.4717 | − | 3.18831i | 0.942025 | − | 0.207541i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.22999 | + | 1.53047i | −0.0797286 | + | 0.0992059i | ||||
\(239\) | −28.0645 | −1.81534 | −0.907671 | − | 0.419682i | \(-0.862142\pi\) | ||||
−0.907671 | + | 0.419682i | \(0.862142\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.7612 | −1.33734 | −0.668672 | − | 0.743558i | \(-0.733137\pi\) | ||||
−0.668672 | + | 0.743558i | \(0.733137\pi\) | |||||||
\(242\) | 1.70093 | − | 2.11646i | 0.109340 | − | 0.136051i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 25.2974 | − | 5.57336i | 1.61950 | − | 0.356798i | ||||
\(245\) | 3.50133i | 0.223692i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.7292 | −1.19171 | ||||||||
\(248\) | −2.88750 | − | 1.43105i | −0.183356 | − | 0.0908718i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.72028 | − | 7.00820i | −0.551519 | − | 0.443238i | ||||
\(251\) | 21.4352i | 1.35298i | 0.736454 | + | 0.676488i | \(0.236499\pi\) | ||||
−0.736454 | + | 0.676488i | \(0.763501\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.2730i | 0.960208i | ||||||||
\(254\) | 9.05869 | − | 11.2717i | 0.568393 | − | 0.707249i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.3490 | − | 12.2024i | 0.646812 | − | 0.762649i | ||||
\(257\) | −13.6807 | −0.853380 | −0.426690 | − | 0.904398i | \(-0.640320\pi\) | ||||
−0.426690 | + | 0.904398i | \(0.640320\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 9.45610i | − | 0.587574i | ||||||
\(260\) | 5.88547 | + | 26.7140i | 0.365002 | + | 1.65673i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.70561 | − | 1.37074i | −0.105373 | − | 0.0846847i | ||||
\(263\) | −18.8063 | −1.15965 | −0.579823 | − | 0.814743i | \(-0.696878\pi\) | ||||
−0.579823 | + | 0.814743i | \(0.696878\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.51067 | −0.0927999 | ||||||||
\(266\) | −5.28528 | − | 4.24761i | −0.324061 | − | 0.260438i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.56623 | − | 1.44663i | 0.401096 | − | 0.0883671i | ||||
\(269\) | − | 27.1654i | − | 1.65630i | −0.560504 | − | 0.828152i | \(-0.689393\pi\) | ||
0.560504 | − | 0.828152i | \(-0.310607\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.618132 | 0.0375488 | 0.0187744 | − | 0.999824i | \(-0.494024\pi\) | ||||
0.0187744 | + | 0.999824i | \(0.494024\pi\) | |||||||
\(272\) | −5.03938 | + | 2.33377i | −0.305558 | + | 0.141506i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.61228 | − | 8.22763i | 0.399463 | − | 0.497050i | ||||
\(275\) | 21.8746i | 1.31909i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.4479i | 0.988260i | 0.869388 | + | 0.494130i | \(0.164513\pi\) | ||||
−0.869388 | + | 0.494130i | \(0.835487\pi\) | |||||||
\(278\) | 18.3411 | + | 14.7402i | 1.10003 | + | 0.884056i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.39763 | + | 8.87330i | −0.262809 | + | 0.530281i | ||||
\(281\) | 26.6482 | 1.58970 | 0.794849 | − | 0.606807i | \(-0.207550\pi\) | ||||
0.794849 | + | 0.606807i | \(0.207550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5.96019i | − | 0.354297i | −0.984184 | − | 0.177148i | \(-0.943313\pi\) | ||
0.984184 | − | 0.177148i | \(-0.0566872\pi\) | |||||||
\(284\) | 2.69757 | + | 12.2442i | 0.160071 | + | 0.726560i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.4281 | − | 12.9756i | 0.616624 | − | 0.767263i | ||||
\(287\) | −4.11364 | −0.242821 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0724 | −0.886611 | ||||||||
\(290\) | −15.2324 | + | 18.9536i | −0.894478 | + | 1.11300i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.34003 | − | 19.6993i | −0.253981 | − | 1.15281i | ||||
\(293\) | 1.52262i | 0.0889522i | 0.999010 | + | 0.0444761i | \(0.0141619\pi\) | ||||
−0.999010 | + | 0.0444761i | \(0.985838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.9426 | −1.51044 | ||||||||
\(296\) | 11.8767 | − | 23.9643i | 0.690322 | − | 1.39289i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −23.5731 | − | 18.9450i | −1.36556 | − | 1.09745i | ||||
\(299\) | − | 19.7993i | − | 1.14502i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.51868i | 0.0875355i | ||||||||
\(302\) | 1.07498 | − | 1.33759i | 0.0618581 | − | 0.0769697i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.05935 | − | 17.4028i | −0.462236 | − | 0.998119i | ||||
\(305\) | −45.3493 | −2.59669 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.29191i | − | 0.302025i | −0.988532 | − | 0.151013i | \(-0.951747\pi\) | ||
0.988532 | − | 0.151013i | \(-0.0482534\pi\) | |||||||
\(308\) | 5.88547 | − | 1.29665i | 0.335356 | − | 0.0738837i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.39763 | + | 3.53423i | 0.249769 | + | 0.200731i | ||||
\(311\) | 6.95423 | 0.394338 | 0.197169 | − | 0.980370i | \(-0.436825\pi\) | ||||
0.197169 | + | 0.980370i | \(0.436825\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.7834 | −0.666039 | −0.333020 | − | 0.942920i | \(-0.608068\pi\) | ||||
−0.333020 | + | 0.942920i | \(0.608068\pi\) | |||||||
\(314\) | −8.99118 | − | 7.22592i | −0.507402 | − | 0.407782i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.56589 | − | 25.2634i | −0.313106 | − | 1.42118i | ||||
\(317\) | − | 1.74196i | − | 0.0978384i | −0.998803 | − | 0.0489192i | \(-0.984422\pi\) | ||
0.998803 | − | 0.0489192i | \(-0.0155777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.7974 | 0.828498 | ||||||||
\(320\) | −22.2895 | + | 16.9639i | −1.24602 | + | 0.948313i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.49029 | − | 5.58724i | 0.250234 | − | 0.311365i | ||||
\(323\) | 6.65676i | 0.370392i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 28.3573i | − | 1.57298i | ||||||
\(326\) | −25.1640 | − | 20.2235i | −1.39371 | − | 1.12008i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.4251 | − | 5.16669i | −0.575628 | − | 0.285282i | ||||
\(329\) | 10.7641 | 0.593443 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.6068i | 1.24258i | 0.783579 | + | 0.621292i | \(0.213392\pi\) | ||||
−0.783579 | + | 0.621292i | \(0.786608\pi\) | |||||||
\(332\) | −34.0121 | + | 7.49335i | −1.86666 | + | 0.411251i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.3772 | − | 19.1338i | 0.841406 | − | 1.04696i | ||||
\(335\) | −11.7709 | −0.643116 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.7468 | 1.34804 | 0.674021 | − | 0.738712i | \(-0.264566\pi\) | ||||
0.674021 | + | 0.738712i | \(0.264566\pi\) | |||||||
\(338\) | −2.00158 | + | 2.49056i | −0.108872 | + | 0.135469i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.49471 | − | 2.09182i | 0.514923 | − | 0.113445i | ||||
\(341\) | − | 3.43331i | − | 0.185924i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −1.90745 | + | 3.84875i | −0.102843 | + | 0.207511i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.9914 | − | 20.8885i | −1.39731 | − | 1.12297i | ||||
\(347\) | − | 3.17968i | − | 0.170694i | −0.996351 | − | 0.0853471i | \(-0.972800\pi\) | ||
0.996351 | − | 0.0853471i | \(-0.0271999\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0444i | 0.644722i | 0.946617 | + | 0.322361i | \(0.104477\pi\) | ||||
−0.946617 | + | 0.322361i | \(0.895523\pi\) | |||||||
\(350\) | 6.43116 | − | 8.00226i | 0.343760 | − | 0.427739i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.5439 | + | 4.10602i | 0.881794 | + | 0.218852i | ||||
\(353\) | 28.3700 | 1.50998 | 0.754991 | − | 0.655736i | \(-0.227641\pi\) | ||||
0.754991 | + | 0.655736i | \(0.227641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 21.9496i | − | 1.16496i | ||||||
\(356\) | 0.352166 | + | 1.59847i | 0.0186648 | + | 0.0847189i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.3345 | − | 10.7165i | −0.704748 | − | 0.566383i | ||||
\(359\) | 26.2701 | 1.38648 | 0.693241 | − | 0.720706i | \(-0.256182\pi\) | ||||
0.693241 | + | 0.720706i | \(0.256182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.98817 | −0.209904 | ||||||||
\(362\) | 4.08596 | + | 3.28375i | 0.214753 | + | 0.172590i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.62967 | + | 1.68092i | −0.399903 | + | 0.0881043i | ||||
\(365\) | 35.3139i | 1.84842i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.6261 | 0.815678 | 0.407839 | − | 0.913054i | \(-0.366283\pi\) | ||||
0.407839 | + | 0.913054i | \(0.366283\pi\) | |||||||
\(368\) | 18.3971 | − | 8.51981i | 0.959014 | − | 0.444126i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −29.3317 | + | 36.4974i | −1.52488 | + | 1.89741i | ||||
\(371\) | − | 0.431457i | − | 0.0224001i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.63905i | − | 0.188423i | −0.995552 | − | 0.0942113i | \(-0.969967\pi\) | ||
0.995552 | − | 0.0942113i | \(-0.0300329\pi\) | |||||||
\(374\) | −4.61179 | − | 3.70635i | −0.238470 | − | 0.191651i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.2790 | + | 13.5195i | 1.40681 | + | 0.697217i | ||||
\(377\) | −19.1827 | −0.987962 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.66150i | 0.239445i | 0.992807 | + | 0.119723i | \(0.0382005\pi\) | ||||
−0.992807 | + | 0.119723i | \(0.961799\pi\) | |||||||
\(380\) | 7.22380 | + | 32.7887i | 0.370573 | + | 1.68202i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.99049 | − | 12.4311i | 0.511158 | − | 0.636031i | ||||
\(383\) | 11.9040 | 0.608268 | 0.304134 | − | 0.952629i | \(-0.401633\pi\) | ||||
0.304134 | + | 0.952629i | \(0.401633\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.5506 | −0.537708 | ||||||||
\(386\) | −2.79230 | + | 3.47444i | −0.142124 | + | 0.176845i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.93682 | + | 22.4081i | 0.250629 | + | 1.13760i | ||||
\(389\) | 35.6321i | 1.80662i | 0.428987 | + | 0.903311i | \(0.358871\pi\) | ||||
−0.428987 | + | 0.903311i | \(0.641129\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.03708 | −0.355880 | ||||||||
\(392\) | −2.53426 | − | 1.25599i | −0.128000 | − | 0.0634369i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.6570 | + | 10.1720i | 0.637649 | + | 0.512458i | ||||
\(395\) | 45.2885i | 2.27871i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.9738i | − | 0.550760i | −0.961335 | − | 0.275380i | \(-0.911196\pi\) | ||
0.961335 | − | 0.275380i | \(-0.0888037\pi\) | |||||||
\(398\) | −2.99798 | + | 3.73037i | −0.150275 | + | 0.186987i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 26.3490 | − | 12.2024i | 1.31745 | − | 0.610120i | ||||
\(401\) | −6.65382 | −0.332276 | −0.166138 | − | 0.986103i | \(-0.553130\pi\) | ||||
−0.166138 | + | 0.986103i | \(0.553130\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.45079i | 0.221710i | ||||||||
\(404\) | 10.5186 | − | 2.31739i | 0.523318 | − | 0.115294i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.41326 | − | 4.35046i | −0.268655 | − | 0.215910i | ||||
\(407\) | 28.4942 | 1.41240 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.8304 | −1.67281 | −0.836404 | − | 0.548114i | \(-0.815346\pi\) | ||||
−0.836404 | + | 0.548114i | \(0.815346\pi\) | |||||||
\(410\) | 15.8773 | + | 12.7600i | 0.784123 | + | 0.630174i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.07689 | + | 9.42696i | 0.102321 | + | 0.464433i | ||||
\(413\) | − | 7.40936i | − | 0.364591i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 60.9718 | 2.99299 | ||||||||
\(416\) | −21.4468 | − | 5.32286i | −1.05152 | − | 0.260975i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.7994 | − | 15.9262i | 0.626037 | − | 0.778975i | ||||
\(419\) | − | 10.6763i | − | 0.521571i | −0.965397 | − | 0.260786i | \(-0.916018\pi\) | ||
0.965397 | − | 0.260786i | \(-0.0839816\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 15.4063i | − | 0.750855i | −0.926852 | − | 0.375427i | \(-0.877496\pi\) | ||
0.926852 | − | 0.375427i | \(-0.122504\pi\) | |||||||
\(422\) | 18.8251 | + | 15.1291i | 0.916390 | + | 0.736473i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.541904 | − | 1.09342i | 0.0263172 | − | 0.0531014i | ||||
\(425\) | −10.0788 | −0.488892 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 12.9520i | − | 0.626792i | ||||||
\(428\) | 9.61375 | − | 2.11804i | 0.464698 | − | 0.102379i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.71078 | − | 5.86161i | 0.227174 | − | 0.282672i | ||||
\(431\) | −25.7179 | −1.23879 | −0.619393 | − | 0.785081i | \(-0.712621\pi\) | ||||
−0.619393 | + | 0.785081i | \(0.712621\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.26219 | −0.348998 | −0.174499 | − | 0.984657i | \(-0.555831\pi\) | ||||
−0.174499 | + | 0.984657i | \(0.555831\pi\) | |||||||
\(434\) | −1.00940 | + | 1.25599i | −0.0484526 | + | 0.0602893i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −39.3254 | + | 8.66394i | −1.88335 | + | 0.414928i | ||||
\(437\) | − | 24.3016i | − | 1.16250i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.7252 | 1.37098 | 0.685488 | − | 0.728084i | \(-0.259589\pi\) | ||||
0.685488 | + | 0.728084i | \(0.259589\pi\) | |||||||
\(440\) | −26.7380 | − | 13.2514i | −1.27468 | − | 0.631737i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.97852 | + | 4.80475i | 0.284369 | + | 0.228538i | ||||
\(443\) | − | 5.70732i | − | 0.271163i | −0.990766 | − | 0.135582i | \(-0.956710\pi\) | ||
0.990766 | − | 0.135582i | \(-0.0432903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 2.86550i | − | 0.135838i | ||||||
\(446\) | 21.3648 | − | 26.5842i | 1.01165 | − | 1.25880i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.84499 | − | 6.36601i | −0.228904 | − | 0.300766i | ||||
\(449\) | 33.9514 | 1.60227 | 0.801134 | − | 0.598485i | \(-0.204230\pi\) | ||||
0.801134 | + | 0.598485i | \(0.204230\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.3957i | − | 0.583690i | ||||||
\(452\) | 5.69893 | + | 25.8673i | 0.268055 | + | 1.21670i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.37833 | + | 6.73339i | 0.393215 | + | 0.316014i | ||||
\(455\) | 13.6773 | 0.641203 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.4661 | 1.65903 | 0.829517 | − | 0.558482i | \(-0.188616\pi\) | ||||
0.829517 | + | 0.558482i | \(0.188616\pi\) | |||||||
\(458\) | 26.4581 | + | 21.2635i | 1.23630 | + | 0.993578i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −34.6620 | + | 7.63652i | −1.61612 | + | 0.356055i | ||||
\(461\) | 26.3291i | 1.22627i | 0.789979 | + | 0.613134i | \(0.210092\pi\) | ||||
−0.789979 | + | 0.613134i | \(0.789908\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.45714 | −0.253615 | −0.126807 | − | 0.991927i | \(-0.540473\pi\) | ||||
−0.126807 | + | 0.991927i | \(0.540473\pi\) | |||||||
\(464\) | −8.25450 | − | 17.8242i | −0.383206 | − | 0.827468i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.41515 | + | 11.7152i | −0.436148 | + | 0.542697i | ||||
\(467\) | 5.77349i | 0.267165i | 0.991038 | + | 0.133583i | \(0.0426482\pi\) | ||||
−0.991038 | + | 0.133583i | \(0.957352\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3.36185i | − | 0.155236i | ||||||
\(470\) | −41.5457 | − | 33.3889i | −1.91636 | − | 1.54012i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.30607 | − | 18.7773i | 0.428346 | − | 0.864294i | ||||
\(473\) | −4.57626 | −0.210417 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 34.8056i | − | 1.59699i | ||||||
\(476\) | 0.597435 | + | 2.71174i | 0.0273834 | + | 0.124292i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.8628 | + | 30.9366i | −1.13720 | + | 1.41501i | ||||
\(479\) | 31.3044 | 1.43033 | 0.715167 | − | 0.698954i | \(-0.246351\pi\) | ||||
0.715167 | + | 0.698954i | \(0.246351\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.9386 | −1.68425 | ||||||||
\(482\) | −18.3926 | + | 22.8859i | −0.837761 | + | 1.04242i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.826180 | − | 3.75001i | −0.0375536 | − | 0.170455i | ||||
\(485\) | − | 40.1699i | − | 1.82402i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.7136 | −1.16519 | −0.582597 | − | 0.812761i | \(-0.697963\pi\) | ||||
−0.582597 | + | 0.812761i | \(0.697963\pi\) | |||||||
\(488\) | 16.2676 | − | 32.8238i | 0.736398 | − | 1.48586i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.85966 | + | 3.10188i | 0.174362 | + | 0.140129i | ||||
\(491\) | − | 12.7216i | − | 0.574116i | −0.957913 | − | 0.287058i | \(-0.907323\pi\) | ||
0.957913 | − | 0.287058i | \(-0.0926773\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.81794i | 0.307065i | ||||||||
\(494\) | −16.5925 | + | 20.6460i | −0.746533 | + | 0.928907i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.13558 | + | 1.91522i | −0.185693 | + | 0.0859957i | ||||
\(497\) | 6.26892 | 0.281199 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.9382i | 1.69835i | 0.528115 | + | 0.849173i | \(0.322899\pi\) | ||||
−0.528115 | + | 0.849173i | \(0.677101\pi\) | |||||||
\(500\) | −15.4509 | + | 3.40404i | −0.690983 | + | 0.152233i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23.6288 | + | 18.9897i | 1.05461 | + | 0.847554i | ||||
\(503\) | −16.9704 | −0.756674 | −0.378337 | − | 0.925668i | \(-0.623504\pi\) | ||||
−0.378337 | + | 0.925668i | \(0.623504\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.8561 | −0.839086 | ||||||||
\(506\) | 16.8361 | + | 13.5306i | 0.748455 | + | 0.601509i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.40001 | − | 19.9715i | −0.195219 | − | 0.886093i | ||||
\(509\) | − | 11.6789i | − | 0.517656i | −0.965923 | − | 0.258828i | \(-0.916664\pi\) | ||
0.965923 | − | 0.258828i | \(-0.0833363\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0859 | −0.446172 | ||||||||
\(512\) | −4.28286 | − | 22.2184i | −0.189277 | − | 0.981924i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.1200 | + | 15.0808i | −0.534588 | + | 0.665186i | ||||
\(515\) | − | 16.8992i | − | 0.744670i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.4355i | 1.42651i | ||||||||
\(518\) | −10.4238 | − | 8.37730i | −0.457997 | − | 0.368078i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 34.6620 | + | 17.1786i | 1.52003 | + | 0.753330i | ||||
\(521\) | 4.82516 | 0.211394 | 0.105697 | − | 0.994398i | \(-0.466293\pi\) | ||||
0.105697 | + | 0.994398i | \(0.466293\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.7958i | − | 1.08424i | −0.840300 | − | 0.542121i | \(-0.817621\pi\) | ||
0.840300 | − | 0.542121i | \(-0.182379\pi\) | |||||||
\(524\) | −3.02205 | + | 0.665800i | −0.132019 | + | 0.0290856i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.6608 | + | 20.7309i | −0.726444 | + | 0.903911i | ||||
\(527\) | 1.58190 | 0.0689088 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.68998 | 0.116956 | ||||||||
\(530\) | −1.33833 | + | 1.66528i | −0.0581333 | + | 0.0723350i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.36462 | + | 2.06316i | −0.406008 | + | 0.0894492i | ||||
\(533\) | 16.0692i | 0.696035i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.2341 | −0.745095 | ||||||||
\(536\) | 4.22244 | − | 8.51981i | 0.182382 | − | 0.368000i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.9455 | − | 24.0662i | −1.29104 | − | 1.03757i | ||||
\(539\) | − | 3.01331i | − | 0.129792i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0510i | 0.604100i | 0.953292 | + | 0.302050i | \(0.0976709\pi\) | ||||
−0.953292 | + | 0.302050i | \(0.902329\pi\) | |||||||
\(542\) | 0.547613 | − | 0.681392i | 0.0235220 | − | 0.0292683i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.89186 | + | 7.62264i | −0.0811126 | + | 0.326818i | ||||
\(545\) | 70.4967 | 3.01975 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.56879i | 0.366375i | 0.983078 | + | 0.183188i | \(0.0586416\pi\) | ||||
−0.983078 | + | 0.183188i | \(0.941358\pi\) | |||||||
\(548\) | −3.21173 | − | 14.5780i | −0.137198 | − | 0.622740i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 24.1133 | + | 19.3791i | 1.02819 | + | 0.826326i | ||||
\(551\) | −23.5448 | −1.00304 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9346 | −0.550037 | ||||||||
\(554\) | 18.1312 | + | 14.5715i | 0.770321 | + | 0.619082i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 32.4973 | − | 7.15962i | 1.37819 | − | 0.303636i | ||||
\(557\) | 3.47669i | 0.147312i | 0.997284 | + | 0.0736560i | \(0.0234667\pi\) | ||||
−0.997284 | + | 0.0736560i | \(0.976533\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.93247 | 0.250917 | ||||||||
\(560\) | 5.88547 | + | 12.7087i | 0.248707 | + | 0.537040i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.6080 | − | 29.3754i | 0.995845 | − | 1.23913i | ||||
\(563\) | 6.82325i | 0.287566i | 0.989609 | + | 0.143783i | \(0.0459267\pi\) | ||||
−0.989609 | + | 0.143783i | \(0.954073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 46.3711i | − | 1.95085i | ||||||
\(566\) | −6.57016 | − | 5.28023i | −0.276165 | − | 0.221944i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.8871 | + | 7.87368i | 0.666608 | + | 0.330372i | ||||
\(569\) | 25.1322 | 1.05360 | 0.526799 | − | 0.849990i | \(-0.323392\pi\) | ||||
0.526799 | + | 0.849990i | \(0.323392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 14.1758i | − | 0.593238i | −0.954996 | − | 0.296619i | \(-0.904141\pi\) | ||
0.954996 | − | 0.296619i | \(-0.0958591\pi\) | |||||||
\(572\) | −5.06514 | − | 22.9905i | −0.211784 | − | 0.961283i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.64434 | + | 4.53464i | −0.152112 | + | 0.189272i | ||||
\(575\) | 36.7942 | 1.53442 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.3021 | 0.761927 | 0.380963 | − | 0.924590i | \(-0.375592\pi\) | ||||
0.380963 | + | 0.924590i | \(0.375592\pi\) | |||||||
\(578\) | −13.3529 | + | 16.6149i | −0.555405 | + | 0.691089i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.39872 | + | 33.5826i | 0.307215 | + | 1.39444i | ||||
\(581\) | 17.4139i | 0.722450i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.30011 | 0.0538451 | ||||||||
\(584\) | −25.5602 | − | 12.6677i | −1.05769 | − | 0.524193i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.67844 | + | 1.34891i | 0.0693358 | + | 0.0557229i | ||||
\(587\) | − | 6.70640i | − | 0.276803i | −0.990376 | − | 0.138401i | \(-0.955804\pi\) | ||
0.990376 | − | 0.138401i | \(-0.0441964\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.46288i | 0.225094i | ||||||||
\(590\) | −22.9830 | + | 28.5976i | −0.946194 | + | 1.17735i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15.8950 | − | 34.3225i | −0.653280 | − | 1.41065i | ||||
\(593\) | −17.9084 | −0.735411 | −0.367706 | − | 0.929942i | \(-0.619857\pi\) | ||||
−0.367706 | + | 0.929942i | \(0.619857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 4.86120i | − | 0.199290i | ||||||
\(596\) | −41.7676 | + | 9.20199i | −1.71087 | + | 0.376928i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −21.8256 | − | 17.5405i | −0.892514 | − | 0.717284i | ||||
\(599\) | −23.9838 | −0.979953 | −0.489976 | − | 0.871736i | \(-0.662995\pi\) | ||||
−0.489976 | + | 0.871736i | \(0.662995\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.2548 | −0.703840 | −0.351920 | − | 0.936030i | \(-0.614471\pi\) | ||||
−0.351920 | + | 0.936030i | \(0.614471\pi\) | |||||||
\(602\) | 1.67411 | + | 1.34543i | 0.0682315 | + | 0.0548354i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.522141 | − | 2.36998i | −0.0212456 | − | 0.0964333i | ||||
\(605\) | 6.72246i | 0.273307i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.0189 | 1.54314 | 0.771569 | − | 0.636146i | \(-0.219472\pi\) | ||||
0.771569 | + | 0.636146i | \(0.219472\pi\) | |||||||
\(608\) | −26.3237 | − | 6.53326i | −1.06757 | − | 0.264959i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −40.1756 | + | 49.9904i | −1.62666 | + | 2.02405i | ||||
\(611\) | − | 42.0479i | − | 1.70108i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 33.1990i | − | 1.34089i | −0.741957 | − | 0.670447i | \(-0.766102\pi\) | ||
0.741957 | − | 0.670447i | \(-0.233898\pi\) | |||||||
\(614\) | −5.83349 | − | 4.68818i | −0.235420 | − | 0.189200i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.78468 | − | 7.63652i | 0.152489 | − | 0.307684i | ||||
\(617\) | 0.827310 | 0.0333062 | 0.0166531 | − | 0.999861i | \(-0.494699\pi\) | ||||
0.0166531 | + | 0.999861i | \(0.494699\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.3695i | 1.70297i | 0.524377 | + | 0.851486i | \(0.324298\pi\) | ||||
−0.524377 | + | 0.851486i | \(0.675702\pi\) | |||||||
\(620\) | 7.79186 | − | 1.71666i | 0.312928 | − | 0.0689426i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.16085 | − | 7.66593i | 0.247028 | − | 0.307376i | ||||
\(623\) | 0.818403 | 0.0327886 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.59870 | −0.343948 | ||||||||
\(626\) | −10.4391 | + | 12.9894i | −0.417231 | + | 0.519159i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.9308 | + | 3.50979i | −0.635710 | + | 0.140056i | ||||
\(629\) | 13.1287i | 0.523477i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.5333 | −0.737801 | −0.368901 | − | 0.929469i | \(-0.620266\pi\) | ||||
−0.368901 | + | 0.929469i | \(0.620266\pi\) | |||||||
\(632\) | −32.7798 | − | 16.2458i | −1.30391 | − | 0.646221i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.92024 | − | 1.54323i | −0.0762624 | − | 0.0612896i | ||||
\(635\) | 35.8020i | 1.42076i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.90632i | 0.154774i | ||||||||
\(638\) | 13.1093 | − | 16.3118i | 0.519001 | − | 0.645791i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.04660 | + | 39.5992i | −0.0413704 | + | 1.56530i | ||||
\(641\) | 13.3013 | 0.525371 | 0.262686 | − | 0.964881i | \(-0.415392\pi\) | ||||
0.262686 | + | 0.964881i | \(0.415392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12.1885i | − | 0.480668i | −0.970690 | − | 0.240334i | \(-0.922743\pi\) | ||
0.970690 | − | 0.240334i | \(-0.0772570\pi\) | |||||||
\(644\) | −2.18103 | − | 9.89965i | −0.0859447 | − | 0.390101i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.33801 | + | 5.89732i | 0.288710 | + | 0.232027i | ||||
\(647\) | 18.4813 | 0.726576 | 0.363288 | − | 0.931677i | \(-0.381654\pi\) | ||||
0.363288 | + | 0.931677i | \(0.381654\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.3267 | 0.876399 | ||||||||
\(650\) | −31.2594 | − | 25.1222i | −1.22609 | − | 0.985372i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −44.5864 | + | 9.82300i | −1.74614 | + | 0.384699i | ||||
\(653\) | 25.0787i | 0.981405i | 0.871327 | + | 0.490703i | \(0.163260\pi\) | ||||
−0.871327 | + | 0.490703i | \(0.836740\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.41748 | 0.211678 | ||||||||
\(656\) | −14.9312 | + | 6.91472i | −0.582964 | + | 0.269975i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.53606 | − | 11.8657i | 0.371754 | − | 0.462572i | ||||
\(659\) | − | 40.3331i | − | 1.57115i | −0.618764 | − | 0.785577i | \(-0.712366\pi\) | ||
0.618764 | − | 0.785577i | \(-0.287634\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.1566i | 0.822896i | 0.911433 | + | 0.411448i | \(0.134977\pi\) | ||||
−0.911433 | + | 0.411448i | \(0.865023\pi\) | |||||||
\(662\) | 24.9204 | + | 20.0277i | 0.968560 | + | 0.778401i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.8716 | + | 44.1314i | −0.848783 | + | 1.71263i | ||||
\(665\) | 16.7875 | 0.650991 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 24.8900i | − | 0.963745i | ||||||
\(668\) | −7.46907 | − | 33.9019i | −0.288987 | − | 1.31170i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.4281 | + | 12.9756i | −0.402871 | + | 0.501291i | ||||
\(671\) | 39.0284 | 1.50667 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.8540 | 1.76754 | 0.883772 | − | 0.467918i | \(-0.154996\pi\) | ||||
0.883772 | + | 0.467918i | \(0.154996\pi\) | |||||||
\(674\) | 21.9235 | − | 27.2794i | 0.844463 | − | 1.05076i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.972213 | + | 4.41285i | 0.0373928 | + | 0.169725i | ||||
\(677\) | 41.0495i | 1.57766i | 0.614612 | + | 0.788830i | \(0.289313\pi\) | ||||
−0.614612 | + | 0.788830i | \(0.710687\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.4727 | 0.440284 | ||||||||
\(680\) | 6.10561 | − | 12.3196i | 0.234140 | − | 0.472434i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.78468 | − | 3.04162i | −0.144923 | − | 0.116470i | ||||
\(683\) | 7.87089i | 0.301171i | 0.988597 | + | 0.150586i | \(0.0481159\pi\) | ||||
−0.988597 | + | 0.150586i | \(0.951884\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.1332i | 0.998499i | ||||||||
\(686\) | −0.885915 | + | 1.10234i | −0.0338244 | + | 0.0420876i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.55279 | + | 5.51232i | 0.0973243 | + | 0.210155i | ||||
\(689\) | −1.68541 | −0.0642089 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 33.4478i | − | 1.27241i | −0.771519 | − | 0.636207i | \(-0.780503\pi\) | ||
0.771519 | − | 0.636207i | \(-0.219497\pi\) | |||||||
\(692\) | −46.0524 | + | 10.1460i | −1.75065 | + | 0.385693i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.50509 | − | 2.81693i | −0.133051 | − | 0.106929i | ||||
\(695\) | −58.2564 | −2.20979 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.71133 | 0.216332 | ||||||||
\(698\) | 13.2770 | + | 10.6703i | 0.502543 | + | 0.403878i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.12376 | − | 14.1786i | −0.118067 | − | 0.535903i | ||||
\(701\) | − | 19.9716i | − | 0.754317i | −0.926149 | − | 0.377158i | \(-0.876901\pi\) | ||
0.926149 | − | 0.377158i | \(-0.123099\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −45.3382 | −1.70996 | ||||||||
\(704\) | 19.1827 | − | 14.5995i | 0.722977 | − | 0.550238i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.1334 | − | 31.2734i | 0.945907 | − | 1.17699i | ||||
\(707\) | − | 5.38541i | − | 0.202539i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.1379i | 1.43230i | 0.697947 | + | 0.716149i | \(0.254097\pi\) | ||||
−0.697947 | + | 0.716149i | \(0.745903\pi\) | |||||||
\(710\) | −24.1959 | − | 19.4455i | −0.908056 | − | 0.729775i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.07405 | + | 1.02790i | 0.0777283 | + | 0.0385223i | ||||
\(713\) | −5.77499 | −0.216275 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.2140i | 1.54132i | ||||||||
\(716\) | −23.6264 | + | 5.20523i | −0.882960 | + | 0.194528i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 23.2731 | − | 28.9586i | 0.868543 | − | 1.08072i | ||||
\(719\) | 33.8150 | 1.26109 | 0.630543 | − | 0.776155i | \(-0.282832\pi\) | ||||
0.630543 | + | 0.776155i | \(0.282832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.82652 | 0.179749 | ||||||||
\(722\) | −3.53318 | + | 4.39633i | −0.131492 | + | 0.163614i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.23962 | − | 1.59499i | 0.269058 | − | 0.0592774i | ||||
\(725\) | − | 35.6484i | − | 1.32395i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.9720 | −1.44539 | −0.722696 | − | 0.691166i | \(-0.757097\pi\) | ||||
−0.722696 | + | 0.691166i | \(0.757097\pi\) | |||||||
\(728\) | −4.90629 | + | 9.89965i | −0.181839 | + | 0.366905i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 38.9280 | + | 31.2852i | 1.44079 | + | 1.15792i | ||||
\(731\) | − | 2.10852i | − | 0.0779865i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.2978i | 0.491164i | 0.969376 | + | 0.245582i | \(0.0789790\pi\) | ||||
−0.969376 | + | 0.245582i | \(0.921021\pi\) | |||||||
\(734\) | 13.8434 | − | 17.2253i | 0.510970 | − | 0.635798i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.90652 | − | 27.8277i | 0.254578 | − | 1.02574i | ||||
\(737\) | 10.1303 | 0.373154 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.4030i | 1.37589i | 0.725762 | + | 0.687946i | \(0.241487\pi\) | ||||
−0.725762 | + | 0.687946i | \(0.758513\pi\) | |||||||
\(740\) | 14.2471 | + | 64.6671i | 0.523733 | + | 2.37721i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.475612 | − | 0.382234i | −0.0174603 | − | 0.0140322i | ||||
\(743\) | −31.1138 | −1.14145 | −0.570727 | − | 0.821140i | \(-0.693338\pi\) | ||||
−0.570727 | + | 0.821140i | \(0.693338\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 74.8747 | 2.74320 | ||||||||
\(746\) | −4.01147 | − | 3.22389i | −0.146870 | − | 0.118035i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.17131 | + | 1.80026i | −0.298773 | + | 0.0658239i | ||||
\(749\) | − | 4.92215i | − | 0.179851i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.6412 | 0.680227 | 0.340114 | − | 0.940384i | \(-0.389534\pi\) | ||||
0.340114 | + | 0.940384i | \(0.389534\pi\) | |||||||
\(752\) | 39.0700 | − | 18.0936i | 1.42474 | − | 0.659805i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.9943 | + | 21.1459i | −0.618895 | + | 0.770089i | ||||
\(755\) | 4.24855i | 0.154621i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 29.8972i | − | 1.08663i | −0.839528 | − | 0.543317i | \(-0.817168\pi\) | ||
0.839528 | − | 0.543317i | \(-0.182832\pi\) | |||||||
\(758\) | 5.13856 | + | 4.12970i | 0.186641 | + | 0.149997i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 42.5439 | + | 21.0849i | 1.54323 | + | 0.764829i | ||||
\(761\) | 42.6967 | 1.54776 | 0.773878 | − | 0.633335i | \(-0.218315\pi\) | ||||
0.773878 | + | 0.633335i | \(0.218315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.1342i | 0.728909i | ||||||||
\(764\) | −4.85260 | − | 22.0258i | −0.175561 | − | 0.796867i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.5460 | − | 13.1223i | 0.381041 | − | 0.474128i | ||||
\(767\) | −28.9433 | −1.04508 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.5127 | 1.46092 | 0.730462 | − | 0.682953i | \(-0.239305\pi\) | ||||
0.730462 | + | 0.682953i | \(0.239305\pi\) | |||||||
\(770\) | −9.34694 | + | 11.6304i | −0.336840 | + | 0.419129i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.35628 | + | 6.15612i | 0.0488136 | + | 0.221564i | ||||
\(773\) | 14.6650i | 0.527465i | 0.964596 | + | 0.263732i | \(0.0849536\pi\) | ||||
−0.964596 | + | 0.263732i | \(0.915046\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.27116 | −0.297109 | ||||||||
\(776\) | 29.0750 | + | 14.4096i | 1.04373 | + | 0.517276i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39.2787 | + | 31.5671i | 1.40821 | + | 1.13173i | ||||
\(779\) | 19.7233i | 0.706660i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.8902i | 0.675944i | ||||||||
\(782\) | −6.23425 | + | 7.75725i | −0.222936 | + | 0.277399i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.62967 | + | 1.68092i | −0.129631 | + | 0.0600330i | ||||
\(785\) | 28.5584 | 1.01929 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 17.3453i | − | 0.618292i | −0.951015 | − | 0.309146i | \(-0.899957\pi\) | ||
0.951015 | − | 0.309146i | \(-0.100043\pi\) | |||||||
\(788\) | 22.4260 | − | 4.94076i | 0.798893 | − | 0.176007i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 49.9234 | + | 40.1218i | 1.77619 | + | 1.42747i | ||||
\(791\) | 13.2438 | 0.470896 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −50.5947 | −1.79667 | ||||||||
\(794\) | −12.0969 | − | 9.72187i | −0.429302 | − | 0.345016i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.45618 | + | 6.60958i | 0.0516131 | + | 0.234270i | ||||
\(797\) | 21.9239i | 0.776585i | 0.921536 | + | 0.388292i | \(0.126935\pi\) | ||||
−0.921536 | + | 0.388292i | \(0.873065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.9447 | −0.528705 | ||||||||
\(800\) | 9.89178 | − | 39.8558i | 0.349727 | − | 1.40912i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.89472 | + | 7.33477i | −0.208150 | + | 0.259000i | ||||
\(803\) | − | 30.3918i | − | 1.07250i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.7466i | 0.625486i | ||||||||
\(806\) | 4.90629 | + | 3.94303i | 0.172817 | + | 0.138887i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.76401 | − | 13.6481i | 0.237957 | − | 0.480137i | ||||
\(809\) | −19.2482 | −0.676731 | −0.338366 | − | 0.941015i | \(-0.609874\pi\) | ||||
−0.338366 | + | 0.941015i | \(0.609874\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.4354i | 0.436665i | 0.975874 | + | 0.218333i | \(0.0700617\pi\) | ||||
−0.975874 | + | 0.218333i | \(0.929938\pi\) | |||||||
\(812\) | −9.59137 | + | 2.11311i | −0.336591 | + | 0.0741558i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 25.2434 | − | 31.4103i | 0.884781 | − | 1.10093i | ||||
\(815\) | 79.9278 | 2.79975 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.28148 | 0.254747 | ||||||||
\(818\) | −29.9709 | + | 37.2927i | −1.04791 | + | 1.30391i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.1318 | − | 6.19784i | 0.982406 | − | 0.216438i | ||||
\(821\) | 55.1514i | 1.92480i | 0.271640 | + | 0.962399i | \(0.412434\pi\) | ||||
−0.271640 | + | 0.962399i | \(0.587566\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.6639 | 0.546009 | 0.273004 | − | 0.962013i | \(-0.411983\pi\) | ||||
0.273004 | + | 0.962013i | \(0.411983\pi\) | |||||||
\(824\) | 12.2317 | + | 6.06204i | 0.426110 | + | 0.211181i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.16764 | − | 6.56407i | −0.284188 | − | 0.228393i | ||||
\(827\) | 16.1178i | 0.560470i | 0.959931 | + | 0.280235i | \(0.0904124\pi\) | ||||
−0.959931 | + | 0.280235i | \(0.909588\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 42.5904i | − | 1.47923i | −0.673032 | − | 0.739613i | \(-0.735008\pi\) | ||
0.673032 | − | 0.739613i | \(-0.264992\pi\) | |||||||
\(830\) | 54.0159 | − | 67.2117i | 1.87492 | − | 2.33295i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −24.8677 | + | 18.9261i | −0.862131 | + | 0.656144i | ||||
\(833\) | 1.38839 | 0.0481047 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 60.7743i | 2.10318i | ||||||||
\(836\) | −6.21693 | − | 28.2185i | −0.215017 | − | 0.975957i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.7689 | − | 9.45830i | −0.406551 | − | 0.326731i | ||||
\(839\) | 21.1741 | 0.731011 | 0.365505 | − | 0.930809i | \(-0.380896\pi\) | ||||
0.365505 | + | 0.930809i | \(0.380896\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.88507 | 0.168451 | ||||||||
\(842\) | −16.9829 | − | 13.6486i | −0.585271 | − | 0.470363i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 33.3548 | − | 7.34854i | 1.14812 | − | 0.252947i | ||||
\(845\) | − | 7.91070i | − | 0.272136i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.91997 | −0.0659710 | ||||||||
\(848\) | −0.725245 | − | 1.56604i | −0.0249050 | − | 0.0537782i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.92893 | + | 11.1102i | −0.306260 | + | 0.381078i | ||||
\(851\) | − | 47.9285i | − | 1.64297i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.2958i | 0.455240i | 0.973750 | + | 0.227620i | \(0.0730944\pi\) | ||||
−0.973750 | + | 0.227620i | \(0.926906\pi\) | |||||||
\(854\) | −14.2775 | − | 11.4744i | −0.488567 | − | 0.392645i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.18216 | − | 12.4740i | 0.211302 | − | 0.426353i | ||||
\(857\) | 26.1940 | 0.894770 | 0.447385 | − | 0.894341i | \(-0.352355\pi\) | ||||
0.447385 | + | 0.894341i | \(0.352355\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.90287i | − | 0.201403i | −0.994917 | − | 0.100702i | \(-0.967891\pi\) | ||
0.994917 | − | 0.100702i | \(-0.0321088\pi\) | |||||||
\(860\) | −2.28813 | − | 10.3858i | −0.0780247 | − | 0.354152i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.7838 | + | 28.3498i | −0.776021 | + | 0.965599i | ||||
\(863\) | 12.1022 | 0.411964 | 0.205982 | − | 0.978556i | \(-0.433961\pi\) | ||||
0.205982 | + | 0.978556i | \(0.433961\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 82.5558 | 2.80698 | ||||||||
\(866\) | −6.43368 | + | 8.00540i | −0.218625 | + | 0.272035i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.490286 | + | 2.22540i | 0.0166414 | + | 0.0755349i | ||||
\(869\) | − | 38.9761i | − | 1.32217i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.1325 | −0.444976 | ||||||||
\(872\) | −25.2884 | + | 51.0255i | −0.856372 | + | 1.72794i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −26.7886 | − | 21.5291i | −0.906138 | − | 0.728233i | ||||
\(875\) | 7.91070i | 0.267430i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.9450i | 0.943634i | 0.881697 | + | 0.471817i | \(0.156402\pi\) | ||||
−0.881697 | + | 0.471817i | \(0.843598\pi\) | |||||||
\(878\) | 25.4480 | − | 31.6649i | 0.858830 | − | 1.06864i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −38.2952 | + | 17.7348i | −1.29093 | + | 0.597838i | ||||
\(881\) | 26.6503 | 0.897872 | 0.448936 | − | 0.893564i | \(-0.351803\pi\) | ||||
0.448936 | + | 0.893564i | \(0.351803\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.47024i | 0.150435i | 0.997167 | + | 0.0752177i | \(0.0239652\pi\) | ||||
−0.997167 | + | 0.0752177i | \(0.976035\pi\) | |||||||
\(884\) | 10.5929 | − | 2.33377i | 0.356279 | − | 0.0784932i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.29141 | − | 5.05620i | −0.211364 | − | 0.169867i | ||||
\(887\) | −8.53323 | −0.286518 | −0.143259 | − | 0.989685i | \(-0.545758\pi\) | ||||
−0.143259 | + | 0.989685i | \(0.545758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.2252 | −0.342943 | ||||||||
\(890\) | −3.15876 | − | 2.53859i | −0.105882 | − | 0.0850938i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.3774 | − | 47.1027i | −0.347460 | − | 1.57711i | ||||
\(893\) | − | 51.6094i | − | 1.72704i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.3539 | 1.41573 | ||||||||
\(896\) | −11.3098 | − | 0.298914i | −0.377833 | − | 0.00998602i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.0781 | − | 37.4260i | 1.00372 | − | 1.24892i | ||||
\(899\) | 5.59516i | 0.186609i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.599028i | 0.0199565i | ||||||||
\(902\) | −13.6643 | − | 10.9815i | −0.454970 | − | 0.365645i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 33.5634 | + | 16.6341i | 1.11630 | + | 0.553241i | ||||
\(905\) | −12.9781 | −0.431407 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.0969i | 0.999353i | 0.866212 | + | 0.499676i | \(0.166548\pi\) | ||||
−0.866212 | + | 0.499676i | \(0.833452\pi\) | |||||||
\(908\) | 14.8450 | − | 3.27056i | 0.492648 | − | 0.108537i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.1170 | − | 15.0771i | 0.401673 | − | 0.499800i | ||||
\(911\) | −5.93001 | −0.196470 | −0.0982350 | − | 0.995163i | \(-0.531320\pi\) | ||||
−0.0982350 | + | 0.995163i | \(0.531320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.4734 | −1.73662 | ||||||||
\(914\) | 31.4199 | − | 39.0957i | 1.03928 | − | 1.29317i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46.8792 | − | 10.3281i | 1.54893 | − | 0.341252i | ||||
\(917\) | 1.54726i | 0.0510951i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.3264 | 1.29726 | 0.648630 | − | 0.761104i | \(-0.275342\pi\) | ||||
0.648630 | + | 0.761104i | \(0.275342\pi\) | |||||||
\(920\) | −22.2895 | + | 44.9746i | −0.734864 | + | 1.48277i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 29.0236 | + | 23.3254i | 0.955842 | + | 0.768179i | ||||
\(923\) | − | 24.4884i | − | 0.806046i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 68.6450i | − | 2.25704i | ||||||
\(926\) | −4.83457 | + | 6.01563i | −0.158874 | + | 0.197686i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26.9611 | − | 6.69145i | −0.885042 | − | 0.219658i | ||||
\(929\) | −35.9339 | −1.17895 | −0.589476 | − | 0.807786i | \(-0.700666\pi\) | ||||
−0.589476 | + | 0.807786i | \(0.700666\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.79460i | 0.157137i | ||||||||
\(932\) | 4.57315 | + | 20.7574i | 0.149798 | + | 0.679931i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.36435 | + | 5.11482i | 0.208248 | + | 0.167362i | ||||
\(935\) | 14.6483 | 0.479051 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.6365 | −0.804838 | −0.402419 | − | 0.915456i | \(-0.631830\pi\) | ||||
−0.402419 | + | 0.915456i | \(0.631830\pi\) | |||||||
\(938\) | −3.70590 | − | 2.97831i | −0.121002 | − | 0.0972453i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −73.6119 | + | 16.2177i | −2.40096 | + | 0.528964i | ||||
\(941\) | − | 23.2069i | − | 0.756522i | −0.925699 | − | 0.378261i | \(-0.876522\pi\) | ||
0.925699 | − | 0.378261i | \(-0.123478\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.8501 | −0.678973 | ||||||||
\(944\) | −12.4546 | − | 26.8935i | −0.405362 | − | 0.875310i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.05418 | + | 5.04460i | −0.131813 | + | 0.164014i | ||||
\(947\) | − | 19.6763i | − | 0.639394i | −0.947520 | − | 0.319697i | \(-0.896419\pi\) | ||
0.947520 | − | 0.319697i | \(-0.103581\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.3986i | 1.27893i | ||||||||
\(950\) | −38.3676 | − | 30.8348i | −1.24481 | − | 1.00041i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.51854 | + | 1.74380i | 0.114036 | + | 0.0565168i | ||||
\(953\) | 9.96974 | 0.322952 | 0.161476 | − | 0.986877i | \(-0.448375\pi\) | ||||
0.161476 | + | 0.986877i | \(0.448375\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.4846i | 1.27769i | ||||||||
\(956\) | 12.0764 | + | 54.8145i | 0.390579 | + | 1.77283i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.7330 | − | 34.5081i | 0.896013 | − | 1.11491i | ||||
\(959\) | −7.46379 | −0.241018 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7018 | −0.958123 | ||||||||
\(962\) | −32.7244 | + | 40.7189i | −1.05508 | + | 1.31283i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.93371 | + | 40.5499i | 0.287735 | + | 1.30602i | ||||
\(965\) | − | 11.0358i | − | 0.355254i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.20443 | −0.231679 | −0.115839 | − | 0.993268i | \(-0.536956\pi\) | ||||
−0.115839 | + | 0.993268i | \(0.536956\pi\) | |||||||
\(968\) | −4.86571 | − | 2.41146i | −0.156390 | − | 0.0775072i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −44.2809 | − | 35.5871i | −1.42177 | − | 1.14263i | ||||
\(971\) | 32.0495i | 1.02852i | 0.857635 | + | 0.514258i | \(0.171933\pi\) | ||||
−0.857635 | + | 0.514258i | \(0.828067\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 16.6383i | − | 0.533401i | ||||||
\(974\) | −22.7801 | + | 28.3451i | −0.729920 | + | 0.908236i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −21.7713 | − | 47.0115i | −0.696884 | − | 1.50480i | ||||
\(977\) | 8.17655 | 0.261591 | 0.130796 | − | 0.991409i | \(-0.458247\pi\) | ||||
0.130796 | + | 0.991409i | \(0.458247\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.46610i | 0.0788169i | ||||||||
\(980\) | 6.83867 | − | 1.50665i | 0.218453 | − | 0.0481283i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14.0235 | − | 11.2702i | −0.447508 | − | 0.359647i | ||||
\(983\) | −32.2990 | −1.03018 | −0.515089 | − | 0.857137i | \(-0.672241\pi\) | ||||
−0.515089 | + | 0.857137i | \(0.672241\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.2020 | −1.28094 | ||||||||
\(986\) | 7.51569 | + | 6.04012i | 0.239348 | + | 0.192357i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.05935 | + | 36.5812i | 0.256402 | + | 1.16380i | ||||
\(989\) | 7.69749i | 0.244766i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.7283 | −1.38907 | −0.694537 | − | 0.719457i | \(-0.744391\pi\) | ||||
−0.694537 | + | 0.719457i | \(0.744391\pi\) | |||||||
\(992\) | −1.55256 | + | 6.25554i | −0.0492937 | + | 0.198613i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.55373 | − | 6.91048i | 0.176154 | − | 0.219187i | ||||
\(995\) | − | 11.8487i | − | 0.375628i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 4.64199i | − | 0.147013i | −0.997295 | − | 0.0735066i | \(-0.976581\pi\) | ||
0.997295 | − | 0.0735066i | \(-0.0234190\pi\) | |||||||
\(998\) | 41.8208 | + | 33.6100i | 1.32381 | + | 1.06391i | ||||
\(999\) | 0 | 0 |
(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 | 1512.2.c.e.757.15 | yes | 20 | |
3.2 | odd | 2 | inner | 1512.2.c.e.757.6 | yes | 20 | |
4.3 | odd | 2 | 6048.2.c.e.3025.20 | 20 | |||
8.3 | odd | 2 | 6048.2.c.e.3025.1 | 20 | |||
8.5 | even | 2 | inner | 1512.2.c.e.757.16 | yes | 20 | |
12.11 | even | 2 | 6048.2.c.e.3025.2 | 20 | |||
24.5 | odd | 2 | inner | 1512.2.c.e.757.5 | ✓ | 20 | |
24.11 | even | 2 | 6048.2.c.e.3025.19 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.e.757.5 | ✓ | 20 | 24.5 | odd | 2 | inner | |
1512.2.c.e.757.6 | yes | 20 | 3.2 | odd | 2 | inner | |
1512.2.c.e.757.15 | yes | 20 | 1.1 | even | 1 | trivial | |
1512.2.c.e.757.16 | yes | 20 | 8.5 | even | 2 | inner | |
6048.2.c.e.3025.1 | 20 | 8.3 | odd | 2 | |||
6048.2.c.e.3025.2 | 20 | 12.11 | even | 2 | |||
6048.2.c.e.3025.19 | 20 | 24.11 | even | 2 | |||
6048.2.c.e.3025.20 | 20 | 4.3 | odd | 2 |