Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not 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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.6 | ||
Root | \(-1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.y.1351.1 |
$q$-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 \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 5.04892i | 1.90831i | 0.299311 | + | 0.954156i | \(0.403243\pi\) | ||||
−0.299311 | + | 0.954156i | \(0.596757\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | − 4.74094i | − 1.42945i | −0.699407 | − | 0.714723i | \(-0.746553\pi\) | ||||
0.699407 | − | 0.714723i | \(-0.253447\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −5.04892 | −1.34938 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.08815 | 0.263914 | 0.131957 | − | 0.991255i | \(-0.457874\pi\) | ||||
0.131957 | + | 0.991255i | \(0.457874\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | − 4.44504i | − 1.01976i | −0.860245 | − | 0.509881i | \(-0.829689\pi\) | ||||
0.860245 | − | 0.509881i | \(-0.170311\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 5.04892i | 1.10176i | ||||||||
\(22\) | 4.74094 | 1.01077 | ||||||||
\(23\) | −2.69202 | −0.561325 | −0.280663 | − | 0.959806i | \(-0.590554\pi\) | ||||
−0.280663 | + | 0.959806i | \(0.590554\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − 5.04892i | − 0.954156i | ||||||||
\(29\) | −7.93900 | −1.47424 | −0.737118 | − | 0.675764i | \(-0.763814\pi\) | ||||
−0.737118 | + | 0.675764i | \(0.763814\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | − 7.85086i | − 1.41006i | −0.709180 | − | 0.705028i | \(-0.750935\pi\) | ||||
0.709180 | − | 0.705028i | \(-0.249065\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 4.74094i | − 0.825292i | ||||||||
\(34\) | 1.08815i | 0.186615i | ||||||||
\(35\) | 5.04892 | 0.853423 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 7.14675i | − 1.17492i | −0.809254 | − | 0.587459i | \(-0.800128\pi\) | ||||
0.809254 | − | 0.587459i | \(-0.199872\pi\) | |||||||
\(38\) | 4.44504 | 0.721081 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 0.664874i | 0.103836i | 0.998651 | + | 0.0519180i | \(0.0165334\pi\) | ||||
−0.998651 | + | 0.0519180i | \(0.983467\pi\) | |||||||
\(42\) | −5.04892 | −0.779065 | ||||||||
\(43\) | −4.35690 | −0.664420 | −0.332210 | − | 0.943205i | \(-0.607794\pi\) | ||||
−0.332210 | + | 0.943205i | \(0.607794\pi\) | |||||||
\(44\) | 4.74094i | 0.714723i | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | − 2.69202i | − 0.396917i | ||||||||
\(47\) | 7.00000i | 1.02105i | 0.859861 | + | 0.510527i | \(0.170550\pi\) | ||||
−0.859861 | + | 0.510527i | \(0.829450\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −18.4916 | −2.64165 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | 1.08815 | 0.152371 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.8605 | −1.49181 | −0.745905 | − | 0.666052i | \(-0.767983\pi\) | ||||
−0.745905 | + | 0.666052i | \(0.767983\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −4.74094 | −0.639268 | ||||||||
\(56\) | 5.04892 | 0.674690 | ||||||||
\(57\) | − 4.44504i | − 0.588760i | ||||||||
\(58\) | − 7.93900i | − 1.04244i | ||||||||
\(59\) | 12.2784i | 1.59852i | 0.600988 | + | 0.799258i | \(0.294774\pi\) | ||||
−0.600988 | + | 0.799258i | \(0.705226\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | −11.0707 | −1.41746 | −0.708728 | − | 0.705482i | \(-0.750731\pi\) | ||||
−0.708728 | + | 0.705482i | \(0.750731\pi\) | |||||||
\(62\) | 7.85086 | 0.997060 | ||||||||
\(63\) | 5.04892i | 0.636104i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.74094 | 0.583569 | ||||||||
\(67\) | − 9.58211i | − 1.17064i | −0.810802 | − | 0.585320i | \(-0.800969\pi\) | ||||
0.810802 | − | 0.585320i | \(-0.199031\pi\) | |||||||
\(68\) | −1.08815 | −0.131957 | ||||||||
\(69\) | −2.69202 | −0.324081 | ||||||||
\(70\) | 5.04892i | 0.603461i | ||||||||
\(71\) | − 4.47219i | − 0.530751i | −0.964145 | − | 0.265376i | \(-0.914504\pi\) | ||||
0.964145 | − | 0.265376i | \(-0.0854960\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 8.17390i | − 0.956683i | −0.878174 | − | 0.478341i | \(-0.841238\pi\) | ||||
0.878174 | − | 0.478341i | \(-0.158762\pi\) | |||||||
\(74\) | 7.14675 | 0.830793 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 4.44504i | 0.509881i | ||||||||
\(77\) | 23.9366 | 2.72783 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.1468 | 1.59163 | 0.795817 | − | 0.605537i | \(-0.207042\pi\) | ||||
0.795817 | + | 0.605537i | \(0.207042\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.664874 | −0.0734231 | ||||||||
\(83\) | − 4.86294i | − 0.533777i | −0.963727 | − | 0.266888i | \(-0.914005\pi\) | ||||
0.963727 | − | 0.266888i | \(-0.0859955\pi\) | |||||||
\(84\) | − 5.04892i | − 0.550882i | ||||||||
\(85\) | − 1.08815i | − 0.118026i | ||||||||
\(86\) | − 4.35690i | − 0.469816i | ||||||||
\(87\) | −7.93900 | −0.851150 | ||||||||
\(88\) | −4.74094 | −0.505386 | ||||||||
\(89\) | 14.8877i | 1.57809i | 0.614334 | + | 0.789046i | \(0.289425\pi\) | ||||
−0.614334 | + | 0.789046i | \(0.710575\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.69202 | 0.280663 | ||||||||
\(93\) | − 7.85086i | − 0.814096i | ||||||||
\(94\) | −7.00000 | −0.721995 | ||||||||
\(95\) | −4.44504 | −0.456052 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | − 14.9269i | − 1.51560i | −0.652487 | − | 0.757800i | \(-0.726274\pi\) | ||||
0.652487 | − | 0.757800i | \(-0.273726\pi\) | |||||||
\(98\) | − 18.4916i | − 1.86793i | ||||||||
\(99\) | − 4.74094i | − 0.476482i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −11.4819 | −1.14249 | −0.571245 | − | 0.820780i | \(-0.693539\pi\) | ||||
−0.571245 | + | 0.820780i | \(0.693539\pi\) | |||||||
\(102\) | 1.08815i | 0.107743i | ||||||||
\(103\) | −4.16421 | −0.410312 | −0.205156 | − | 0.978729i | \(-0.565770\pi\) | ||||
−0.205156 | + | 0.978729i | \(0.565770\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.04892 | 0.492724 | ||||||||
\(106\) | − 10.8605i | − 1.05487i | ||||||||
\(107\) | −0.796561 | −0.0770065 | −0.0385032 | − | 0.999258i | \(-0.512259\pi\) | ||||
−0.0385032 | + | 0.999258i | \(0.512259\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | − 0.704103i | − 0.0674408i | −0.999431 | − | 0.0337204i | \(-0.989264\pi\) | ||||
0.999431 | − | 0.0337204i | \(-0.0107356\pi\) | |||||||
\(110\) | − 4.74094i | − 0.452031i | ||||||||
\(111\) | − 7.14675i | − 0.678340i | ||||||||
\(112\) | 5.04892i | 0.477078i | ||||||||
\(113\) | 14.4983 | 1.36388 | 0.681941 | − | 0.731407i | \(-0.261136\pi\) | ||||
0.681941 | + | 0.731407i | \(0.261136\pi\) | |||||||
\(114\) | 4.44504 | 0.416316 | ||||||||
\(115\) | 2.69202i | 0.251032i | ||||||||
\(116\) | 7.93900 | 0.737118 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.2784 | −1.13032 | ||||||||
\(119\) | 5.49396i | 0.503630i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −11.4765 | −1.04332 | ||||||||
\(122\) | − 11.0707i | − 1.00229i | ||||||||
\(123\) | 0.664874i | 0.0599497i | ||||||||
\(124\) | 7.85086i | 0.705028i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −5.04892 | −0.449793 | ||||||||
\(127\) | 2.93900 | 0.260794 | 0.130397 | − | 0.991462i | \(-0.458375\pi\) | ||||
0.130397 | + | 0.991462i | \(0.458375\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −4.35690 | −0.383603 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.56465 | −0.311445 | −0.155722 | − | 0.987801i | \(-0.549771\pi\) | ||||
−0.155722 | + | 0.987801i | \(0.549771\pi\) | |||||||
\(132\) | 4.74094i | 0.412646i | ||||||||
\(133\) | 22.4426 | 1.94602 | ||||||||
\(134\) | 9.58211 | 0.827768 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | − 1.08815i | − 0.0933077i | ||||||||
\(137\) | − 9.47650i | − 0.809632i | −0.914398 | − | 0.404816i | \(-0.867336\pi\) | ||||
0.914398 | − | 0.404816i | \(-0.132664\pi\) | |||||||
\(138\) | − 2.69202i | − 0.229160i | ||||||||
\(139\) | −14.2078 | −1.20509 | −0.602543 | − | 0.798087i | \(-0.705846\pi\) | ||||
−0.602543 | + | 0.798087i | \(0.705846\pi\) | |||||||
\(140\) | −5.04892 | −0.426711 | ||||||||
\(141\) | 7.00000i | 0.589506i | ||||||||
\(142\) | 4.47219 | 0.375298 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.93900i | 0.659298i | ||||||||
\(146\) | 8.17390 | 0.676477 | ||||||||
\(147\) | −18.4916 | −1.52516 | ||||||||
\(148\) | 7.14675i | 0.587459i | ||||||||
\(149\) | − 10.2010i | − 0.835702i | −0.908516 | − | 0.417851i | \(-0.862783\pi\) | ||||
0.908516 | − | 0.417851i | \(-0.137217\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | 3.86294i | 0.314361i | 0.987570 | + | 0.157181i | \(0.0502405\pi\) | ||||
−0.987570 | + | 0.157181i | \(0.949760\pi\) | |||||||
\(152\) | −4.44504 | −0.360541 | ||||||||
\(153\) | 1.08815 | 0.0879714 | ||||||||
\(154\) | 23.9366i | 1.92887i | ||||||||
\(155\) | −7.85086 | −0.630596 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2174 | −0.895249 | −0.447625 | − | 0.894222i | \(-0.647730\pi\) | ||||
−0.447625 | + | 0.894222i | \(0.647730\pi\) | |||||||
\(158\) | 14.1468i | 1.12546i | ||||||||
\(159\) | −10.8605 | −0.861297 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | − 13.5918i | − 1.07118i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − 6.50902i | − 0.509826i | −0.966964 | − | 0.254913i | \(-0.917953\pi\) | ||||
0.966964 | − | 0.254913i | \(-0.0820469\pi\) | |||||||
\(164\) | − 0.664874i | − 0.0519180i | ||||||||
\(165\) | −4.74094 | −0.369082 | ||||||||
\(166\) | 4.86294 | 0.377437 | ||||||||
\(167\) | 9.67456i | 0.748640i | 0.927300 | + | 0.374320i | \(0.122124\pi\) | ||||
−0.927300 | + | 0.374320i | \(0.877876\pi\) | |||||||
\(168\) | 5.04892 | 0.389532 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.08815 | 0.0834570 | ||||||||
\(171\) | − 4.44504i | − 0.339921i | ||||||||
\(172\) | 4.35690 | 0.332210 | ||||||||
\(173\) | 13.8388 | 1.05214 | 0.526071 | − | 0.850441i | \(-0.323665\pi\) | ||||
0.526071 | + | 0.850441i | \(0.323665\pi\) | |||||||
\(174\) | − 7.93900i | − 0.601854i | ||||||||
\(175\) | − 5.04892i | − 0.381662i | ||||||||
\(176\) | − 4.74094i | − 0.357362i | ||||||||
\(177\) | 12.2784i | 0.922904i | ||||||||
\(178\) | −14.8877 | −1.11588 | ||||||||
\(179\) | 14.2078 | 1.06194 | 0.530969 | − | 0.847392i | \(-0.321828\pi\) | ||||
0.530969 | + | 0.847392i | \(0.321828\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | 24.9028 | 1.85101 | 0.925504 | − | 0.378739i | \(-0.123642\pi\) | ||||
0.925504 | + | 0.378739i | \(0.123642\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.0707 | −0.818369 | ||||||||
\(184\) | 2.69202i | 0.198458i | ||||||||
\(185\) | −7.14675 | −0.525440 | ||||||||
\(186\) | 7.85086 | 0.575653 | ||||||||
\(187\) | − 5.15883i | − 0.377251i | ||||||||
\(188\) | − 7.00000i | − 0.510527i | ||||||||
\(189\) | 5.04892i | 0.367255i | ||||||||
\(190\) | − 4.44504i | − 0.322477i | ||||||||
\(191\) | 2.44504 | 0.176917 | 0.0884585 | − | 0.996080i | \(-0.471806\pi\) | ||||
0.0884585 | + | 0.996080i | \(0.471806\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − 15.2959i | − 1.10102i | −0.834828 | − | 0.550511i | \(-0.814433\pi\) | ||||
0.834828 | − | 0.550511i | \(-0.185567\pi\) | |||||||
\(194\) | 14.9269 | 1.07169 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.4916 | 1.32083 | ||||||||
\(197\) | − 3.44935i | − 0.245756i | −0.992422 | − | 0.122878i | \(-0.960788\pi\) | ||||
0.992422 | − | 0.122878i | \(-0.0392124\pi\) | |||||||
\(198\) | 4.74094 | 0.336924 | ||||||||
\(199\) | 9.18598 | 0.651177 | 0.325588 | − | 0.945512i | \(-0.394438\pi\) | ||||
0.325588 | + | 0.945512i | \(0.394438\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | − 9.58211i | − 0.675870i | ||||||||
\(202\) | − 11.4819i | − 0.807862i | ||||||||
\(203\) | − 40.0834i | − 2.81330i | ||||||||
\(204\) | −1.08815 | −0.0761855 | ||||||||
\(205\) | 0.664874 | 0.0464368 | ||||||||
\(206\) | − 4.16421i | − 0.290134i | ||||||||
\(207\) | −2.69202 | −0.187108 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.0737 | −1.45770 | ||||||||
\(210\) | 5.04892i | 0.348408i | ||||||||
\(211\) | −20.7875 | −1.43107 | −0.715534 | − | 0.698578i | \(-0.753817\pi\) | ||||
−0.715534 | + | 0.698578i | \(0.753817\pi\) | |||||||
\(212\) | 10.8605 | 0.745905 | ||||||||
\(213\) | − 4.47219i | − 0.306429i | ||||||||
\(214\) | − 0.796561i | − 0.0544518i | ||||||||
\(215\) | 4.35690i | 0.297138i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | 39.6383 | 2.69082 | ||||||||
\(218\) | 0.704103 | 0.0476879 | ||||||||
\(219\) | − 8.17390i | − 0.552341i | ||||||||
\(220\) | 4.74094 | 0.319634 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.14675 | 0.479659 | ||||||||
\(223\) | − 17.3502i | − 1.16185i | −0.813955 | − | 0.580927i | \(-0.802690\pi\) | ||||
0.813955 | − | 0.580927i | \(-0.197310\pi\) | |||||||
\(224\) | −5.04892 | −0.337345 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 14.4983i | 0.964411i | ||||||||
\(227\) | 13.7573i | 0.913106i | 0.889696 | + | 0.456553i | \(0.150916\pi\) | ||||
−0.889696 | + | 0.456553i | \(0.849084\pi\) | |||||||
\(228\) | 4.44504i | 0.294380i | ||||||||
\(229\) | 1.75541i | 0.116001i | 0.998317 | + | 0.0580005i | \(0.0184725\pi\) | ||||
−0.998317 | + | 0.0580005i | \(0.981528\pi\) | |||||||
\(230\) | −2.69202 | −0.177507 | ||||||||
\(231\) | 23.9366 | 1.57491 | ||||||||
\(232\) | 7.93900i | 0.521221i | ||||||||
\(233\) | 5.49396 | 0.359921 | 0.179961 | − | 0.983674i | \(-0.442403\pi\) | ||||
0.179961 | + | 0.983674i | \(0.442403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.00000 | 0.456630 | ||||||||
\(236\) | − 12.2784i | − 0.799258i | ||||||||
\(237\) | 14.1468 | 0.918930 | ||||||||
\(238\) | −5.49396 | −0.356120 | ||||||||
\(239\) | 17.4004i | 1.12554i | 0.826613 | + | 0.562770i | \(0.190264\pi\) | ||||
−0.826613 | + | 0.562770i | \(0.809736\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | − 3.15452i | − 0.203201i | −0.994825 | − | 0.101600i | \(-0.967604\pi\) | ||||
0.994825 | − | 0.101600i | \(-0.0323963\pi\) | |||||||
\(242\) | − 11.4765i | − 0.737737i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 11.0707 | 0.708728 | ||||||||
\(245\) | 18.4916i | 1.18138i | ||||||||
\(246\) | −0.664874 | −0.0423908 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.85086 | −0.498530 | ||||||||
\(249\) | − 4.86294i | − 0.308176i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −23.9433 | −1.51129 | −0.755644 | − | 0.654982i | \(-0.772676\pi\) | ||||
−0.755644 | + | 0.654982i | \(0.772676\pi\) | |||||||
\(252\) | − 5.04892i | − 0.318052i | ||||||||
\(253\) | 12.7627i | 0.802385i | ||||||||
\(254\) | 2.93900i | 0.184409i | ||||||||
\(255\) | − 1.08815i | − 0.0681423i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.3381 | −0.769630 | −0.384815 | − | 0.922994i | \(-0.625735\pi\) | ||||
−0.384815 | + | 0.922994i | \(0.625735\pi\) | |||||||
\(258\) | − 4.35690i | − 0.271248i | ||||||||
\(259\) | 36.0834 | 2.24211 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.93900 | −0.491412 | ||||||||
\(262\) | − 3.56465i | − 0.220225i | ||||||||
\(263\) | 2.70709 | 0.166926 | 0.0834631 | − | 0.996511i | \(-0.473402\pi\) | ||||
0.0834631 | + | 0.996511i | \(0.473402\pi\) | |||||||
\(264\) | −4.74094 | −0.291785 | ||||||||
\(265\) | 10.8605i | 0.667158i | ||||||||
\(266\) | 22.4426i | 1.37605i | ||||||||
\(267\) | 14.8877i | 0.911112i | ||||||||
\(268\) | 9.58211i | 0.585320i | ||||||||
\(269\) | 20.9681 | 1.27845 | 0.639223 | − | 0.769022i | \(-0.279256\pi\) | ||||
0.639223 | + | 0.769022i | \(0.279256\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | − 7.99761i | − 0.485820i | −0.970049 | − | 0.242910i | \(-0.921898\pi\) | ||||
0.970049 | − | 0.242910i | \(-0.0781020\pi\) | |||||||
\(272\) | 1.08815 | 0.0659785 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.47650 | 0.572496 | ||||||||
\(275\) | 4.74094i | 0.285889i | ||||||||
\(276\) | 2.69202 | 0.162041 | ||||||||
\(277\) | 5.78554 | 0.347620 | 0.173810 | − | 0.984779i | \(-0.444392\pi\) | ||||
0.173810 | + | 0.984779i | \(0.444392\pi\) | |||||||
\(278\) | − 14.2078i | − 0.852124i | ||||||||
\(279\) | − 7.85086i | − 0.470018i | ||||||||
\(280\) | − 5.04892i | − 0.301731i | ||||||||
\(281\) | 19.5579i | 1.16673i | 0.812210 | + | 0.583365i | \(0.198264\pi\) | ||||
−0.812210 | + | 0.583365i | \(0.801736\pi\) | |||||||
\(282\) | −7.00000 | −0.416844 | ||||||||
\(283\) | −31.0726 | −1.84707 | −0.923537 | − | 0.383508i | \(-0.874716\pi\) | ||||
−0.923537 | + | 0.383508i | \(0.874716\pi\) | |||||||
\(284\) | 4.47219i | 0.265376i | ||||||||
\(285\) | −4.44504 | −0.263302 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.35690 | −0.198151 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −15.8159 | −0.930349 | ||||||||
\(290\) | −7.93900 | −0.466194 | ||||||||
\(291\) | − 14.9269i | − 0.875032i | ||||||||
\(292\) | 8.17390i | 0.478341i | ||||||||
\(293\) | − 10.0543i | − 0.587378i | −0.955901 | − | 0.293689i | \(-0.905117\pi\) | ||||
0.955901 | − | 0.293689i | \(-0.0948830\pi\) | |||||||
\(294\) | − 18.4916i | − 1.07845i | ||||||||
\(295\) | 12.2784 | 0.714878 | ||||||||
\(296\) | −7.14675 | −0.415397 | ||||||||
\(297\) | − 4.74094i | − 0.275097i | ||||||||
\(298\) | 10.2010 | 0.590931 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | − 21.9976i | − 1.26792i | ||||||||
\(302\) | −3.86294 | −0.222287 | ||||||||
\(303\) | −11.4819 | −0.659617 | ||||||||
\(304\) | − 4.44504i | − 0.254941i | ||||||||
\(305\) | 11.0707i | 0.633906i | ||||||||
\(306\) | 1.08815i | 0.0622052i | ||||||||
\(307\) | − 23.6872i | − 1.35190i | −0.736947 | − | 0.675951i | \(-0.763733\pi\) | ||||
0.736947 | − | 0.675951i | \(-0.236267\pi\) | |||||||
\(308\) | −23.9366 | −1.36391 | ||||||||
\(309\) | −4.16421 | −0.236894 | ||||||||
\(310\) | − 7.85086i | − 0.445899i | ||||||||
\(311\) | −6.77240 | −0.384027 | −0.192014 | − | 0.981392i | \(-0.561502\pi\) | ||||
−0.192014 | + | 0.981392i | \(0.561502\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.16123 | 0.404776 | 0.202388 | − | 0.979305i | \(-0.435130\pi\) | ||||
0.202388 | + | 0.979305i | \(0.435130\pi\) | |||||||
\(314\) | − 11.2174i | − 0.633037i | ||||||||
\(315\) | 5.04892 | 0.284474 | ||||||||
\(316\) | −14.1468 | −0.795817 | ||||||||
\(317\) | 1.20344i | 0.0675919i | 0.999429 | + | 0.0337959i | \(0.0107596\pi\) | ||||
−0.999429 | + | 0.0337959i | \(0.989240\pi\) | |||||||
\(318\) | − 10.8605i | − 0.609029i | ||||||||
\(319\) | 37.6383i | 2.10734i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −0.796561 | −0.0444597 | ||||||||
\(322\) | 13.5918 | 0.757441 | ||||||||
\(323\) | − 4.83685i | − 0.269130i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.50902 | 0.360502 | ||||||||
\(327\) | − 0.704103i | − 0.0389370i | ||||||||
\(328\) | 0.664874 | 0.0367115 | ||||||||
\(329\) | −35.3424 | −1.94849 | ||||||||
\(330\) | − 4.74094i | − 0.260980i | ||||||||
\(331\) | − 20.9933i | − 1.15390i | −0.816781 | − | 0.576948i | \(-0.804244\pi\) | ||||
0.816781 | − | 0.576948i | \(-0.195756\pi\) | |||||||
\(332\) | 4.86294i | 0.266888i | ||||||||
\(333\) | − 7.14675i | − 0.391640i | ||||||||
\(334\) | −9.67456 | −0.529369 | ||||||||
\(335\) | −9.58211 | −0.523526 | ||||||||
\(336\) | 5.04892i | 0.275441i | ||||||||
\(337\) | 3.01938 | 0.164476 | 0.0822380 | − | 0.996613i | \(-0.473793\pi\) | ||||
0.0822380 | + | 0.996613i | \(0.473793\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.4983 | 0.787438 | ||||||||
\(340\) | 1.08815i | 0.0590130i | ||||||||
\(341\) | −37.2204 | −2.01560 | ||||||||
\(342\) | 4.44504 | 0.240360 | ||||||||
\(343\) | − 58.0200i | − 3.13278i | ||||||||
\(344\) | 4.35690i | 0.234908i | ||||||||
\(345\) | 2.69202i | 0.144934i | ||||||||
\(346\) | 13.8388i | 0.743977i | ||||||||
\(347\) | 11.2610 | 0.604521 | 0.302261 | − | 0.953225i | \(-0.402259\pi\) | ||||
0.302261 | + | 0.953225i | \(0.402259\pi\) | |||||||
\(348\) | 7.93900 | 0.425575 | ||||||||
\(349\) | − 5.84010i | − 0.312613i | −0.987709 | − | 0.156307i | \(-0.950041\pi\) | ||||
0.987709 | − | 0.156307i | \(-0.0499588\pi\) | |||||||
\(350\) | 5.04892 | 0.269876 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.74094 | 0.252693 | ||||||||
\(353\) | − 0.675628i | − 0.0359601i | −0.999838 | − | 0.0179800i | \(-0.994276\pi\) | ||||
0.999838 | − | 0.0179800i | \(-0.00572353\pi\) | |||||||
\(354\) | −12.2784 | −0.652592 | ||||||||
\(355\) | −4.47219 | −0.237359 | ||||||||
\(356\) | − 14.8877i | − 0.789046i | ||||||||
\(357\) | 5.49396i | 0.290771i | ||||||||
\(358\) | 14.2078i | 0.750903i | ||||||||
\(359\) | − 8.52350i | − 0.449853i | −0.974376 | − | 0.224927i | \(-0.927786\pi\) | ||||
0.974376 | − | 0.224927i | \(-0.0722142\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −0.758397 | −0.0399156 | ||||||||
\(362\) | 24.9028i | 1.30886i | ||||||||
\(363\) | −11.4765 | −0.602360 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.17390 | −0.427841 | ||||||||
\(366\) | − 11.0707i | − 0.578674i | ||||||||
\(367\) | −9.40044 | −0.490699 | −0.245349 | − | 0.969435i | \(-0.578903\pi\) | ||||
−0.245349 | + | 0.969435i | \(0.578903\pi\) | |||||||
\(368\) | −2.69202 | −0.140331 | ||||||||
\(369\) | 0.664874i | 0.0346120i | ||||||||
\(370\) | − 7.14675i | − 0.371542i | ||||||||
\(371\) | − 54.8340i | − 2.84684i | ||||||||
\(372\) | 7.85086i | 0.407048i | ||||||||
\(373\) | 23.6582 | 1.22497 | 0.612487 | − | 0.790481i | \(-0.290169\pi\) | ||||
0.612487 | + | 0.790481i | \(0.290169\pi\) | |||||||
\(374\) | 5.15883 | 0.266757 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −5.04892 | −0.259688 | ||||||||
\(379\) | − 16.3437i | − 0.839522i | −0.907635 | − | 0.419761i | \(-0.862114\pi\) | ||||
0.907635 | − | 0.419761i | \(-0.137886\pi\) | |||||||
\(380\) | 4.44504 | 0.228026 | ||||||||
\(381\) | 2.93900 | 0.150570 | ||||||||
\(382\) | 2.44504i | 0.125099i | ||||||||
\(383\) | 4.79656i | 0.245093i | 0.992463 | + | 0.122546i | \(0.0391060\pi\) | ||||
−0.992463 | + | 0.122546i | \(0.960894\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | − 23.9366i | − 1.21992i | ||||||||
\(386\) | 15.2959 | 0.778541 | ||||||||
\(387\) | −4.35690 | −0.221473 | ||||||||
\(388\) | 14.9269i | 0.757800i | ||||||||
\(389\) | −21.4534 | −1.08773 | −0.543865 | − | 0.839173i | \(-0.683040\pi\) | ||||
−0.543865 | + | 0.839173i | \(0.683040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.92931 | −0.148142 | ||||||||
\(392\) | 18.4916i | 0.933965i | ||||||||
\(393\) | −3.56465 | −0.179813 | ||||||||
\(394\) | 3.44935 | 0.173776 | ||||||||
\(395\) | − 14.1468i | − 0.711800i | ||||||||
\(396\) | 4.74094i | 0.238241i | ||||||||
\(397\) | 1.36765i | 0.0686404i | 0.999411 | + | 0.0343202i | \(0.0109266\pi\) | ||||
−0.999411 | + | 0.0343202i | \(0.989073\pi\) | |||||||
\(398\) | 9.18598i | 0.460452i | ||||||||
\(399\) | 22.4426 | 1.12354 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 18.8931i | − 0.943475i | −0.881739 | − | 0.471737i | \(-0.843627\pi\) | ||||
0.881739 | − | 0.471737i | \(-0.156373\pi\) | |||||||
\(402\) | 9.58211 | 0.477912 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 11.4819 | 0.571245 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | 40.0834 | 1.98930 | ||||||||
\(407\) | −33.8823 | −1.67948 | ||||||||
\(408\) | − 1.08815i | − 0.0538713i | ||||||||
\(409\) | 25.9638i | 1.28383i | 0.766778 | + | 0.641913i | \(0.221859\pi\) | ||||
−0.766778 | + | 0.641913i | \(0.778141\pi\) | |||||||
\(410\) | 0.664874i | 0.0328358i | ||||||||
\(411\) | − 9.47650i | − 0.467441i | ||||||||
\(412\) | 4.16421 | 0.205156 | ||||||||
\(413\) | −61.9928 | −3.05047 | ||||||||
\(414\) | − 2.69202i | − 0.132306i | ||||||||
\(415\) | −4.86294 | −0.238712 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.2078 | −0.695757 | ||||||||
\(418\) | − 21.0737i | − 1.03075i | ||||||||
\(419\) | −32.4282 | −1.58422 | −0.792110 | − | 0.610378i | \(-0.791017\pi\) | ||||
−0.792110 | + | 0.610378i | \(0.791017\pi\) | |||||||
\(420\) | −5.04892 | −0.246362 | ||||||||
\(421\) | 33.2868i | 1.62230i | 0.584839 | + | 0.811150i | \(0.301158\pi\) | ||||
−0.584839 | + | 0.811150i | \(0.698842\pi\) | |||||||
\(422\) | − 20.7875i | − 1.01192i | ||||||||
\(423\) | 7.00000i | 0.340352i | ||||||||
\(424\) | 10.8605i | 0.527435i | ||||||||
\(425\) | −1.08815 | −0.0527828 | ||||||||
\(426\) | 4.47219 | 0.216678 | ||||||||
\(427\) | − 55.8950i | − 2.70495i | ||||||||
\(428\) | 0.796561 | 0.0385032 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.35690 | −0.210108 | ||||||||
\(431\) | − 11.1578i | − 0.537451i | −0.963217 | − | 0.268725i | \(-0.913398\pi\) | ||||
0.963217 | − | 0.268725i | \(-0.0866024\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −14.0828 | −0.676775 | −0.338387 | − | 0.941007i | \(-0.609881\pi\) | ||||
−0.338387 | + | 0.941007i | \(0.609881\pi\) | |||||||
\(434\) | 39.6383i | 1.90270i | ||||||||
\(435\) | 7.93900i | 0.380646i | ||||||||
\(436\) | 0.704103i | 0.0337204i | ||||||||
\(437\) | 11.9661i | 0.572418i | ||||||||
\(438\) | 8.17390 | 0.390564 | ||||||||
\(439\) | 28.9933 | 1.38377 | 0.691887 | − | 0.722006i | \(-0.256780\pi\) | ||||
0.691887 | + | 0.722006i | \(0.256780\pi\) | |||||||
\(440\) | 4.74094i | 0.226015i | ||||||||
\(441\) | −18.4916 | −0.880551 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.3080 | 1.58251 | 0.791255 | − | 0.611486i | \(-0.209428\pi\) | ||||
0.791255 | + | 0.611486i | \(0.209428\pi\) | |||||||
\(444\) | 7.14675i | 0.339170i | ||||||||
\(445\) | 14.8877 | 0.705744 | ||||||||
\(446\) | 17.3502 | 0.821555 | ||||||||
\(447\) | − 10.2010i | − 0.482493i | ||||||||
\(448\) | − 5.04892i | − 0.238539i | ||||||||
\(449\) | − 37.7899i | − 1.78341i | −0.452614 | − | 0.891707i | \(-0.649508\pi\) | ||||
0.452614 | − | 0.891707i | \(-0.350492\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | 3.15213 | 0.148428 | ||||||||
\(452\) | −14.4983 | −0.681941 | ||||||||
\(453\) | 3.86294i | 0.181497i | ||||||||
\(454\) | −13.7573 | −0.645664 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.44504 | −0.208158 | ||||||||
\(457\) | 10.5700i | 0.494445i | 0.968959 | + | 0.247222i | \(0.0795178\pi\) | ||||
−0.968959 | + | 0.247222i | \(0.920482\pi\) | |||||||
\(458\) | −1.75541 | −0.0820251 | ||||||||
\(459\) | 1.08815 | 0.0507903 | ||||||||
\(460\) | − 2.69202i | − 0.125516i | ||||||||
\(461\) | 20.1420i | 0.938105i | 0.883170 | + | 0.469052i | \(0.155404\pi\) | ||||
−0.883170 | + | 0.469052i | \(0.844596\pi\) | |||||||
\(462\) | 23.9366i | 1.11363i | ||||||||
\(463\) | 15.9065i | 0.739237i | 0.929184 | + | 0.369618i | \(0.120512\pi\) | ||||
−0.929184 | + | 0.369618i | \(0.879488\pi\) | |||||||
\(464\) | −7.93900 | −0.368559 | ||||||||
\(465\) | −7.85086 | −0.364075 | ||||||||
\(466\) | 5.49396i | 0.254503i | ||||||||
\(467\) | 25.6136 | 1.18525 | 0.592627 | − | 0.805477i | \(-0.298091\pi\) | ||||
0.592627 | + | 0.805477i | \(0.298091\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.3793 | 2.23395 | ||||||||
\(470\) | 7.00000i | 0.322886i | ||||||||
\(471\) | −11.2174 | −0.516872 | ||||||||
\(472\) | 12.2784 | 0.565161 | ||||||||
\(473\) | 20.6558i | 0.949754i | ||||||||
\(474\) | 14.1468i | 0.649782i | ||||||||
\(475\) | 4.44504i | 0.203953i | ||||||||
\(476\) | − 5.49396i | − 0.251815i | ||||||||
\(477\) | −10.8605 | −0.497270 | ||||||||
\(478\) | −17.4004 | −0.795877 | ||||||||
\(479\) | − 7.59658i | − 0.347097i | −0.984825 | − | 0.173548i | \(-0.944477\pi\) | ||||
0.984825 | − | 0.173548i | \(-0.0555233\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.15452 | 0.143685 | ||||||||
\(483\) | − 13.5918i | − 0.618448i | ||||||||
\(484\) | 11.4765 | 0.521659 | ||||||||
\(485\) | −14.9269 | −0.677796 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | − 0.779103i | − 0.0353045i | −0.999844 | − | 0.0176523i | \(-0.994381\pi\) | ||||
0.999844 | − | 0.0176523i | \(-0.00561918\pi\) | |||||||
\(488\) | 11.0707i | 0.501146i | ||||||||
\(489\) | − 6.50902i | − 0.294348i | ||||||||
\(490\) | −18.4916 | −0.835364 | ||||||||
\(491\) | −11.3948 | −0.514240 | −0.257120 | − | 0.966379i | \(-0.582774\pi\) | ||||
−0.257120 | + | 0.966379i | \(0.582774\pi\) | |||||||
\(492\) | − 0.664874i | − 0.0299749i | ||||||||
\(493\) | −8.63879 | −0.389072 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.74094 | −0.213089 | ||||||||
\(496\) | − 7.85086i | − 0.352514i | ||||||||
\(497\) | 22.5797 | 1.01284 | ||||||||
\(498\) | 4.86294 | 0.217913 | ||||||||
\(499\) | − 23.5555i | − 1.05449i | −0.849713 | − | 0.527246i | \(-0.823225\pi\) | ||||
0.849713 | − | 0.527246i | \(-0.176775\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | 9.67456i | 0.432228i | ||||||||
\(502\) | − 23.9433i | − 1.06864i | ||||||||
\(503\) | −12.6165 | −0.562544 | −0.281272 | − | 0.959628i | \(-0.590756\pi\) | ||||
−0.281272 | + | 0.959628i | \(0.590756\pi\) | |||||||
\(504\) | 5.04892 | 0.224897 | ||||||||
\(505\) | 11.4819i | 0.510937i | ||||||||
\(506\) | −12.7627 | −0.567372 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.93900 | −0.130397 | ||||||||
\(509\) | 8.45473i | 0.374749i | 0.982289 | + | 0.187375i | \(0.0599978\pi\) | ||||
−0.982289 | + | 0.187375i | \(0.940002\pi\) | |||||||
\(510\) | 1.08815 | 0.0481839 | ||||||||
\(511\) | 41.2693 | 1.82565 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 4.44504i | − 0.196253i | ||||||||
\(514\) | − 12.3381i | − 0.544211i | ||||||||
\(515\) | 4.16421i | 0.183497i | ||||||||
\(516\) | 4.35690 | 0.191802 | ||||||||
\(517\) | 33.1866 | 1.45954 | ||||||||
\(518\) | 36.0834i | 1.58541i | ||||||||
\(519\) | 13.8388 | 0.607455 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.7254 | 1.52135 | 0.760674 | − | 0.649134i | \(-0.224869\pi\) | ||||
0.760674 | + | 0.649134i | \(0.224869\pi\) | |||||||
\(522\) | − 7.93900i | − 0.347481i | ||||||||
\(523\) | 29.3163 | 1.28191 | 0.640957 | − | 0.767577i | \(-0.278538\pi\) | ||||
0.640957 | + | 0.767577i | \(0.278538\pi\) | |||||||
\(524\) | 3.56465 | 0.155722 | ||||||||
\(525\) | − 5.04892i | − 0.220353i | ||||||||
\(526\) | 2.70709i | 0.118035i | ||||||||
\(527\) | − 8.54288i | − 0.372134i | ||||||||
\(528\) | − 4.74094i | − 0.206323i | ||||||||
\(529\) | −15.7530 | −0.684914 | ||||||||
\(530\) | −10.8605 | −0.471752 | ||||||||
\(531\) | 12.2784i | 0.532839i | ||||||||
\(532\) | −22.4426 | −0.973012 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −14.8877 | −0.644253 | ||||||||
\(535\) | 0.796561i | 0.0344383i | ||||||||
\(536\) | −9.58211 | −0.413884 | ||||||||
\(537\) | 14.2078 | 0.613110 | ||||||||
\(538\) | 20.9681i | 0.903998i | ||||||||
\(539\) | 87.6674i | 3.77610i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | 29.1032i | 1.25124i | 0.780126 | + | 0.625622i | \(0.215155\pi\) | ||||
−0.780126 | + | 0.625622i | \(0.784845\pi\) | |||||||
\(542\) | 7.99761 | 0.343527 | ||||||||
\(543\) | 24.9028 | 1.06868 | ||||||||
\(544\) | 1.08815i | 0.0466539i | ||||||||
\(545\) | −0.704103 | −0.0301605 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.37004 | −0.101336 | −0.0506678 | − | 0.998716i | \(-0.516135\pi\) | ||||
−0.0506678 | + | 0.998716i | \(0.516135\pi\) | |||||||
\(548\) | 9.47650i | 0.404816i | ||||||||
\(549\) | −11.0707 | −0.472485 | ||||||||
\(550\) | −4.74094 | −0.202154 | ||||||||
\(551\) | 35.2892i | 1.50337i | ||||||||
\(552\) | 2.69202i | 0.114580i | ||||||||
\(553\) | 71.4258i | 3.03733i | ||||||||
\(554\) | 5.78554i | 0.245804i | ||||||||
\(555\) | −7.14675 | −0.303363 | ||||||||
\(556\) | 14.2078 | 0.602543 | ||||||||
\(557\) | 28.8364i | 1.22184i | 0.791694 | + | 0.610918i | \(0.209200\pi\) | ||||
−0.791694 | + | 0.610918i | \(0.790800\pi\) | |||||||
\(558\) | 7.85086 | 0.332353 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 5.04892 | 0.213356 | ||||||||
\(561\) | − 5.15883i | − 0.217806i | ||||||||
\(562\) | −19.5579 | −0.825002 | ||||||||
\(563\) | 35.7133 | 1.50514 | 0.752568 | − | 0.658514i | \(-0.228815\pi\) | ||||
0.752568 | + | 0.658514i | \(0.228815\pi\) | |||||||
\(564\) | − 7.00000i | − 0.294753i | ||||||||
\(565\) | − 14.4983i | − 0.609947i | ||||||||
\(566\) | − 31.0726i | − 1.30608i | ||||||||
\(567\) | 5.04892i | 0.212035i | ||||||||
\(568\) | −4.47219 | −0.187649 | ||||||||
\(569\) | −42.1618 | −1.76752 | −0.883758 | − | 0.467945i | \(-0.844995\pi\) | ||||
−0.883758 | + | 0.467945i | \(0.844995\pi\) | |||||||
\(570\) | − 4.44504i | − 0.186182i | ||||||||
\(571\) | −23.1497 | −0.968786 | −0.484393 | − | 0.874850i | \(-0.660960\pi\) | ||||
−0.484393 | + | 0.874850i | \(0.660960\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.44504 | 0.102143 | ||||||||
\(574\) | − 3.35690i | − 0.140114i | ||||||||
\(575\) | 2.69202 | 0.112265 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 41.7318i | 1.73732i | 0.495409 | + | 0.868660i | \(0.335018\pi\) | ||||
−0.495409 | + | 0.868660i | \(0.664982\pi\) | |||||||
\(578\) | − 15.8159i | − 0.657856i | ||||||||
\(579\) | − 15.2959i | − 0.635676i | ||||||||
\(580\) | − 7.93900i | − 0.329649i | ||||||||
\(581\) | 24.5526 | 1.01861 | ||||||||
\(582\) | 14.9269 | 0.618741 | ||||||||
\(583\) | 51.4892i | 2.13246i | ||||||||
\(584\) | −8.17390 | −0.338238 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.0543 | 0.415339 | ||||||||
\(587\) | 3.52648i | 0.145554i | 0.997348 | + | 0.0727768i | \(0.0231861\pi\) | ||||
−0.997348 | + | 0.0727768i | \(0.976814\pi\) | |||||||
\(588\) | 18.4916 | 0.762579 | ||||||||
\(589\) | −34.8974 | −1.43792 | ||||||||
\(590\) | 12.2784i | 0.505495i | ||||||||
\(591\) | − 3.44935i | − 0.141887i | ||||||||
\(592\) | − 7.14675i | − 0.293730i | ||||||||
\(593\) | 7.53617i | 0.309473i | 0.987956 | + | 0.154737i | \(0.0494529\pi\) | ||||
−0.987956 | + | 0.154737i | \(0.950547\pi\) | |||||||
\(594\) | 4.74094 | 0.194523 | ||||||||
\(595\) | 5.49396 | 0.225230 | ||||||||
\(596\) | 10.2010i | 0.417851i | ||||||||
\(597\) | 9.18598 | 0.375957 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.2161 | −1.80662 | −0.903311 | − | 0.428987i | \(-0.858871\pi\) | ||||
−0.903311 | + | 0.428987i | \(0.858871\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | −40.7251 | −1.66121 | −0.830606 | − | 0.556860i | \(-0.812006\pi\) | ||||
−0.830606 | + | 0.556860i | \(0.812006\pi\) | |||||||
\(602\) | 21.9976 | 0.896556 | ||||||||
\(603\) | − 9.58211i | − 0.390213i | ||||||||
\(604\) | − 3.86294i | − 0.157181i | ||||||||
\(605\) | 11.4765i | 0.466586i | ||||||||
\(606\) | − 11.4819i | − 0.466419i | ||||||||
\(607\) | 40.9788 | 1.66328 | 0.831640 | − | 0.555316i | \(-0.187403\pi\) | ||||
0.831640 | + | 0.555316i | \(0.187403\pi\) | |||||||
\(608\) | 4.44504 | 0.180270 | ||||||||
\(609\) | − 40.0834i | − 1.62426i | ||||||||
\(610\) | −11.0707 | −0.448239 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.08815 | −0.0439857 | ||||||||
\(613\) | 40.5491i | 1.63776i | 0.573963 | + | 0.818882i | \(0.305405\pi\) | ||||
−0.573963 | + | 0.818882i | \(0.694595\pi\) | |||||||
\(614\) | 23.6872 | 0.955939 | ||||||||
\(615\) | 0.664874 | 0.0268103 | ||||||||
\(616\) | − 23.9366i | − 0.964433i | ||||||||
\(617\) | 3.06829i | 0.123525i | 0.998091 | + | 0.0617624i | \(0.0196721\pi\) | ||||
−0.998091 | + | 0.0617624i | \(0.980328\pi\) | |||||||
\(618\) | − 4.16421i | − 0.167509i | ||||||||
\(619\) | − 31.0847i | − 1.24940i | −0.780865 | − | 0.624700i | \(-0.785221\pi\) | ||||
0.780865 | − | 0.624700i | \(-0.214779\pi\) | |||||||
\(620\) | 7.85086 | 0.315298 | ||||||||
\(621\) | −2.69202 | −0.108027 | ||||||||
\(622\) | − 6.77240i | − 0.271548i | ||||||||
\(623\) | −75.1667 | −3.01149 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.16123i | 0.286220i | ||||||||
\(627\) | −21.0737 | −0.841601 | ||||||||
\(628\) | 11.2174 | 0.447625 | ||||||||
\(629\) | − 7.77671i | − 0.310078i | ||||||||
\(630\) | 5.04892i | 0.201154i | ||||||||
\(631\) | 23.7101i | 0.943883i | 0.881630 | + | 0.471942i | \(0.156447\pi\) | ||||
−0.881630 | + | 0.471942i | \(0.843553\pi\) | |||||||
\(632\) | − 14.1468i | − 0.562728i | ||||||||
\(633\) | −20.7875 | −0.826227 | ||||||||
\(634\) | −1.20344 | −0.0477947 | ||||||||
\(635\) | − 2.93900i | − 0.116631i | ||||||||
\(636\) | 10.8605 | 0.430649 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −37.6383 | −1.49012 | ||||||||
\(639\) | − 4.47219i | − 0.176917i | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 48.3866 | 1.91115 | 0.955577 | − | 0.294742i | \(-0.0952336\pi\) | ||||
0.955577 | + | 0.294742i | \(0.0952336\pi\) | |||||||
\(642\) | − 0.796561i | − 0.0314378i | ||||||||
\(643\) | − 20.4209i | − 0.805321i | −0.915349 | − | 0.402660i | \(-0.868086\pi\) | ||||
0.915349 | − | 0.402660i | \(-0.131914\pi\) | |||||||
\(644\) | 13.5918i | 0.535592i | ||||||||
\(645\) | 4.35690i | 0.171553i | ||||||||
\(646\) | 4.83685 | 0.190303 | ||||||||
\(647\) | 0.292913 | 0.0115156 | 0.00575780 | − | 0.999983i | \(-0.498167\pi\) | ||||
0.00575780 | + | 0.999983i | \(0.498167\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 58.2113 | 2.28499 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 39.6383 | 1.55355 | ||||||||
\(652\) | 6.50902i | 0.254913i | ||||||||
\(653\) | 21.8323 | 0.854365 | 0.427183 | − | 0.904165i | \(-0.359506\pi\) | ||||
0.427183 | + | 0.904165i | \(0.359506\pi\) | |||||||
\(654\) | 0.704103 | 0.0275326 | ||||||||
\(655\) | 3.56465i | 0.139282i | ||||||||
\(656\) | 0.664874i | 0.0259590i | ||||||||
\(657\) | − 8.17390i | − 0.318894i | ||||||||
\(658\) | − 35.3424i | − 1.37779i | ||||||||
\(659\) | −17.0519 | −0.664248 | −0.332124 | − | 0.943236i | \(-0.607765\pi\) | ||||
−0.332124 | + | 0.943236i | \(0.607765\pi\) | |||||||
\(660\) | 4.74094 | 0.184541 | ||||||||
\(661\) | − 31.8098i | − 1.23726i | −0.785683 | − | 0.618629i | \(-0.787688\pi\) | ||||
0.785683 | − | 0.618629i | \(-0.212312\pi\) | |||||||
\(662\) | 20.9933 | 0.815928 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.86294 | −0.188719 | ||||||||
\(665\) | − 22.4426i | − 0.870289i | ||||||||
\(666\) | 7.14675 | 0.276931 | ||||||||
\(667\) | 21.3720 | 0.827526 | ||||||||
\(668\) | − 9.67456i | − 0.374320i | ||||||||
\(669\) | − 17.3502i | − 0.670797i | ||||||||
\(670\) | − 9.58211i | − 0.370189i | ||||||||
\(671\) | 52.4855i | 2.02618i | ||||||||
\(672\) | −5.04892 | −0.194766 | ||||||||
\(673\) | 4.10513 | 0.158241 | 0.0791206 | − | 0.996865i | \(-0.474789\pi\) | ||||
0.0791206 | + | 0.996865i | \(0.474789\pi\) | |||||||
\(674\) | 3.01938i | 0.116302i | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.0543 | 0.424851 | 0.212426 | − | 0.977177i | \(-0.431864\pi\) | ||||
0.212426 | + | 0.977177i | \(0.431864\pi\) | |||||||
\(678\) | 14.4983i | 0.556803i | ||||||||
\(679\) | 75.3648 | 2.89223 | ||||||||
\(680\) | −1.08815 | −0.0417285 | ||||||||
\(681\) | 13.7573i | 0.527182i | ||||||||
\(682\) | − 37.2204i | − 1.42524i | ||||||||
\(683\) | − 9.06590i | − 0.346897i | −0.984843 | − | 0.173449i | \(-0.944509\pi\) | ||||
0.984843 | − | 0.173449i | \(-0.0554910\pi\) | |||||||
\(684\) | 4.44504i | 0.169960i | ||||||||
\(685\) | −9.47650 | −0.362078 | ||||||||
\(686\) | 58.0200 | 2.21521 | ||||||||
\(687\) | 1.75541i | 0.0669732i | ||||||||
\(688\) | −4.35690 | −0.166105 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.69202 | −0.102484 | ||||||||
\(691\) | 12.4282i | 0.472790i | 0.971657 | + | 0.236395i | \(0.0759659\pi\) | ||||
−0.971657 | + | 0.236395i | \(0.924034\pi\) | |||||||
\(692\) | −13.8388 | −0.526071 | ||||||||
\(693\) | 23.9366 | 0.909277 | ||||||||
\(694\) | 11.2610i | 0.427461i | ||||||||
\(695\) | 14.2078i | 0.538931i | ||||||||
\(696\) | 7.93900i | 0.300927i | ||||||||
\(697\) | 0.723480i | 0.0274038i | ||||||||
\(698\) | 5.84010 | 0.221051 | ||||||||
\(699\) | 5.49396 | 0.207801 | ||||||||
\(700\) | 5.04892i | 0.190831i | ||||||||
\(701\) | 38.5418 | 1.45570 | 0.727852 | − | 0.685734i | \(-0.240519\pi\) | ||||
0.727852 | + | 0.685734i | \(0.240519\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.7676 | −1.19814 | ||||||||
\(704\) | 4.74094i | 0.178681i | ||||||||
\(705\) | 7.00000 | 0.263635 | ||||||||
\(706\) | 0.675628 | 0.0254276 | ||||||||
\(707\) | − 57.9711i | − 2.18023i | ||||||||
\(708\) | − 12.2784i | − 0.461452i | ||||||||
\(709\) | 38.7851i | 1.45660i | 0.685256 | + | 0.728302i | \(0.259690\pi\) | ||||
−0.685256 | + | 0.728302i | \(0.740310\pi\) | |||||||
\(710\) | − 4.47219i | − 0.167838i | ||||||||
\(711\) | 14.1468 | 0.530545 | ||||||||
\(712\) | 14.8877 | 0.557940 | ||||||||
\(713\) | 21.1347i | 0.791500i | ||||||||
\(714\) | −5.49396 | −0.205606 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.2078 | −0.530969 | ||||||||
\(717\) | 17.4004i | 0.649831i | ||||||||
\(718\) | 8.52350 | 0.318094 | ||||||||
\(719\) | 12.1021 | 0.451334 | 0.225667 | − | 0.974205i | \(-0.427544\pi\) | ||||
0.225667 | + | 0.974205i | \(0.427544\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | − 21.0248i | − 0.783003i | ||||||||
\(722\) | − 0.758397i | − 0.0282246i | ||||||||
\(723\) | − 3.15452i | − 0.117318i | ||||||||
\(724\) | −24.9028 | −0.925504 | ||||||||
\(725\) | 7.93900 | 0.294847 | ||||||||
\(726\) | − 11.4765i | − 0.425933i | ||||||||
\(727\) | −40.6088 | −1.50610 | −0.753048 | − | 0.657965i | \(-0.771417\pi\) | ||||
−0.753048 | + | 0.657965i | \(0.771417\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 8.17390i | − 0.302530i | ||||||||
\(731\) | −4.74094 | −0.175350 | ||||||||
\(732\) | 11.0707 | 0.409184 | ||||||||
\(733\) | − 32.6601i | − 1.20633i | −0.797617 | − | 0.603164i | \(-0.793906\pi\) | ||||
0.797617 | − | 0.603164i | \(-0.206094\pi\) | |||||||
\(734\) | − 9.40044i | − 0.346976i | ||||||||
\(735\) | 18.4916i | 0.682072i | ||||||||
\(736\) | − 2.69202i | − 0.0992292i | ||||||||
\(737\) | −45.4282 | −1.67337 | ||||||||
\(738\) | −0.664874 | −0.0244744 | ||||||||
\(739\) | 3.72348i | 0.136970i | 0.997652 | + | 0.0684852i | \(0.0218166\pi\) | ||||
−0.997652 | + | 0.0684852i | \(0.978183\pi\) | |||||||
\(740\) | 7.14675 | 0.262720 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 54.8340 | 2.01302 | ||||||||
\(743\) | 31.3099i | 1.14865i | 0.818628 | + | 0.574324i | \(0.194735\pi\) | ||||
−0.818628 | + | 0.574324i | \(0.805265\pi\) | |||||||
\(744\) | −7.85086 | −0.287826 | ||||||||
\(745\) | −10.2010 | −0.373737 | ||||||||
\(746\) | 23.6582i | 0.866187i | ||||||||
\(747\) | − 4.86294i | − 0.177926i | ||||||||
\(748\) | 5.15883i | 0.188626i | ||||||||
\(749\) | − 4.02177i | − 0.146952i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −2.66296 | −0.0971726 | −0.0485863 | − | 0.998819i | \(-0.515472\pi\) | ||||
−0.0485863 | + | 0.998819i | \(0.515472\pi\) | |||||||
\(752\) | 7.00000i | 0.255264i | ||||||||
\(753\) | −23.9433 | −0.872543 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.86294 | 0.140587 | ||||||||
\(756\) | − 5.04892i | − 0.183627i | ||||||||
\(757\) | 32.2553 | 1.17234 | 0.586170 | − | 0.810188i | \(-0.300635\pi\) | ||||
0.586170 | + | 0.810188i | \(0.300635\pi\) | |||||||
\(758\) | 16.3437 | 0.593632 | ||||||||
\(759\) | 12.7627i | 0.463257i | ||||||||
\(760\) | 4.44504i | 0.161239i | ||||||||
\(761\) | 27.2228i | 0.986826i | 0.869795 | + | 0.493413i | \(0.164251\pi\) | ||||
−0.869795 | + | 0.493413i | \(0.835749\pi\) | |||||||
\(762\) | 2.93900i | 0.106469i | ||||||||
\(763\) | 3.55496 | 0.128698 | ||||||||
\(764\) | −2.44504 | −0.0884585 | ||||||||
\(765\) | − 1.08815i | − 0.0393420i | ||||||||
\(766\) | −4.79656 | −0.173307 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 5.62133i | 0.202710i | 0.994850 | + | 0.101355i | \(0.0323179\pi\) | ||||
−0.994850 | + | 0.101355i | \(0.967682\pi\) | |||||||
\(770\) | 23.9366 | 0.862615 | ||||||||
\(771\) | −12.3381 | −0.444346 | ||||||||
\(772\) | 15.2959i | 0.550511i | ||||||||
\(773\) | − 35.7918i | − 1.28734i | −0.765303 | − | 0.643670i | \(-0.777411\pi\) | ||||
0.765303 | − | 0.643670i | \(-0.222589\pi\) | |||||||
\(774\) | − 4.35690i | − 0.156605i | ||||||||
\(775\) | 7.85086i | 0.282011i | ||||||||
\(776\) | −14.9269 | −0.535845 | ||||||||
\(777\) | 36.0834 | 1.29448 | ||||||||
\(778\) | − 21.4534i | − 0.769142i | ||||||||
\(779\) | 2.95539 | 0.105888 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.2024 | −0.758681 | ||||||||
\(782\) | − 2.92931i | − 0.104752i | ||||||||
\(783\) | −7.93900 | −0.283717 | ||||||||
\(784\) | −18.4916 | −0.660413 | ||||||||
\(785\) | 11.2174i | 0.400368i | ||||||||
\(786\) | − 3.56465i | − 0.127147i | ||||||||
\(787\) | − 18.5442i | − 0.661030i | −0.943801 | − | 0.330515i | \(-0.892778\pi\) | ||||
0.943801 | − | 0.330515i | \(-0.107222\pi\) | |||||||
\(788\) | 3.44935i | 0.122878i | ||||||||
\(789\) | 2.70709 | 0.0963748 | ||||||||
\(790\) | 14.1468 | 0.503319 | ||||||||
\(791\) | 73.2006i | 2.60271i | ||||||||
\(792\) | −4.74094 | −0.168462 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.36765 | −0.0485361 | ||||||||
\(795\) | 10.8605i | 0.385184i | ||||||||
\(796\) | −9.18598 | −0.325588 | ||||||||
\(797\) | 33.0898 | 1.17210 | 0.586050 | − | 0.810275i | \(-0.300682\pi\) | ||||
0.586050 | + | 0.810275i | \(0.300682\pi\) | |||||||
\(798\) | 22.4426i | 0.794461i | ||||||||
\(799\) | 7.61702i | 0.269471i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | 14.8877i | 0.526031i | ||||||||
\(802\) | 18.8931 | 0.667137 | ||||||||
\(803\) | −38.7520 | −1.36753 | ||||||||
\(804\) | 9.58211i | 0.337935i | ||||||||
\(805\) | −13.5918 | −0.479048 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.9681 | 0.738111 | ||||||||
\(808\) | 11.4819i | 0.403931i | ||||||||
\(809\) | 11.4004 | 0.400818 | 0.200409 | − | 0.979712i | \(-0.435773\pi\) | ||||
0.200409 | + | 0.979712i | \(0.435773\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | − 38.9724i | − 1.36851i | −0.729245 | − | 0.684253i | \(-0.760129\pi\) | ||||
0.729245 | − | 0.684253i | \(-0.239871\pi\) | |||||||
\(812\) | 40.0834i | 1.40665i | ||||||||
\(813\) | − 7.99761i | − 0.280488i | ||||||||
\(814\) | − 33.8823i | − 1.18757i | ||||||||
\(815\) | −6.50902 | −0.228001 | ||||||||
\(816\) | 1.08815 | 0.0380927 | ||||||||
\(817\) | 19.3666i | 0.677551i | ||||||||
\(818\) | −25.9638 | −0.907801 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.664874 | −0.0232184 | ||||||||
\(821\) | 7.12498i | 0.248664i | 0.992241 | + | 0.124332i | \(0.0396787\pi\) | ||||
−0.992241 | + | 0.124332i | \(0.960321\pi\) | |||||||
\(822\) | 9.47650 | 0.330531 | ||||||||
\(823\) | −19.1323 | −0.666909 | −0.333455 | − | 0.942766i | \(-0.608214\pi\) | ||||
−0.333455 | + | 0.942766i | \(0.608214\pi\) | |||||||
\(824\) | 4.16421i | 0.145067i | ||||||||
\(825\) | 4.74094i | 0.165058i | ||||||||
\(826\) | − 61.9928i | − 2.15701i | ||||||||
\(827\) | 42.0538i | 1.46235i | 0.682187 | + | 0.731177i | \(0.261029\pi\) | ||||
−0.682187 | + | 0.731177i | \(0.738971\pi\) | |||||||
\(828\) | 2.69202 | 0.0935542 | ||||||||
\(829\) | 17.6364 | 0.612537 | 0.306269 | − | 0.951945i | \(-0.400919\pi\) | ||||
0.306269 | + | 0.951945i | \(0.400919\pi\) | |||||||
\(830\) | − 4.86294i | − 0.168795i | ||||||||
\(831\) | 5.78554 | 0.200698 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.1215 | −0.697169 | ||||||||
\(834\) | − 14.2078i | − 0.491974i | ||||||||
\(835\) | 9.67456 | 0.334802 | ||||||||
\(836\) | 21.0737 | 0.728848 | ||||||||
\(837\) | − 7.85086i | − 0.271365i | ||||||||
\(838\) | − 32.4282i | − 1.12021i | ||||||||
\(839\) | − 44.4905i | − 1.53598i | −0.640460 | − | 0.767991i | \(-0.721256\pi\) | ||||
0.640460 | − | 0.767991i | \(-0.278744\pi\) | |||||||
\(840\) | − 5.04892i | − 0.174204i | ||||||||
\(841\) | 34.0277 | 1.17337 | ||||||||
\(842\) | −33.2868 | −1.14714 | ||||||||
\(843\) | 19.5579i | 0.673611i | ||||||||
\(844\) | 20.7875 | 0.715534 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.00000 | −0.240665 | ||||||||
\(847\) | − 57.9439i | − 1.99098i | ||||||||
\(848\) | −10.8605 | −0.372953 | ||||||||
\(849\) | −31.0726 | −1.06641 | ||||||||
\(850\) | − 1.08815i | − 0.0373231i | ||||||||
\(851\) | 19.2392i | 0.659512i | ||||||||
\(852\) | 4.47219i | 0.153215i | ||||||||
\(853\) | 7.59743i | 0.260131i | 0.991505 | + | 0.130066i | \(0.0415188\pi\) | ||||
−0.991505 | + | 0.130066i | \(0.958481\pi\) | |||||||
\(854\) | 55.8950 | 1.91269 | ||||||||
\(855\) | −4.44504 | −0.152017 | ||||||||
\(856\) | 0.796561i | 0.0272259i | ||||||||
\(857\) | 34.2978 | 1.17159 | 0.585796 | − | 0.810459i | \(-0.300782\pi\) | ||||
0.585796 | + | 0.810459i | \(0.300782\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.8412 | −1.05229 | −0.526144 | − | 0.850396i | \(-0.676363\pi\) | ||||
−0.526144 | + | 0.850396i | \(0.676363\pi\) | |||||||
\(860\) | − 4.35690i | − 0.148569i | ||||||||
\(861\) | −3.35690 | −0.114403 | ||||||||
\(862\) | 11.1578 | 0.380035 | ||||||||
\(863\) | 16.1075i | 0.548306i | 0.961686 | + | 0.274153i | \(0.0883975\pi\) | ||||
−0.961686 | + | 0.274153i | \(0.911602\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | − 13.8388i | − 0.470532i | ||||||||
\(866\) | − 14.0828i | − 0.478552i | ||||||||
\(867\) | −15.8159 | −0.537137 | ||||||||
\(868\) | −39.6383 | −1.34541 | ||||||||
\(869\) | − 67.0689i | − 2.27516i | ||||||||
\(870\) | −7.93900 | −0.269157 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.704103 | −0.0238439 | ||||||||
\(873\) | − 14.9269i | − 0.505200i | ||||||||
\(874\) | −11.9661 | −0.404761 | ||||||||
\(875\) | −5.04892 | −0.170685 | ||||||||
\(876\) | 8.17390i | 0.276170i | ||||||||
\(877\) | 32.7342i | 1.10536i | 0.833395 | + | 0.552678i | \(0.186394\pi\) | ||||
−0.833395 | + | 0.552678i | \(0.813606\pi\) | |||||||
\(878\) | 28.9933i | 0.978476i | ||||||||
\(879\) | − 10.0543i | − 0.339123i | ||||||||
\(880\) | −4.74094 | −0.159817 | ||||||||
\(881\) | 9.32736 | 0.314247 | 0.157123 | − | 0.987579i | \(-0.449778\pi\) | ||||
0.157123 | + | 0.987579i | \(0.449778\pi\) | |||||||
\(882\) | − 18.4916i | − 0.622643i | ||||||||
\(883\) | −45.1135 | −1.51819 | −0.759095 | − | 0.650980i | \(-0.774358\pi\) | ||||
−0.759095 | + | 0.650980i | \(0.774358\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.2784 | 0.412735 | ||||||||
\(886\) | 33.3080i | 1.11900i | ||||||||
\(887\) | −37.4383 | −1.25706 | −0.628528 | − | 0.777787i | \(-0.716342\pi\) | ||||
−0.628528 | + | 0.777787i | \(0.716342\pi\) | |||||||
\(888\) | −7.14675 | −0.239829 | ||||||||
\(889\) | 14.8388i | 0.497676i | ||||||||
\(890\) | 14.8877i | 0.499037i | ||||||||
\(891\) | − 4.74094i | − 0.158827i | ||||||||
\(892\) | 17.3502i | 0.580927i | ||||||||
\(893\) | 31.1153 | 1.04123 | ||||||||
\(894\) | 10.2010 | 0.341174 | ||||||||
\(895\) | − 14.2078i | − 0.474913i | ||||||||
\(896\) | 5.04892 | 0.168672 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 37.7899 | 1.26106 | ||||||||
\(899\) | 62.3279i | 2.07875i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −11.8179 | −0.393710 | ||||||||
\(902\) | 3.15213i | 0.104954i | ||||||||
\(903\) | − 21.9976i | − 0.732035i | ||||||||
\(904\) | − 14.4983i | − 0.482205i | ||||||||
\(905\) | − 24.9028i | − 0.827796i | ||||||||
\(906\) | −3.86294 | −0.128337 | ||||||||
\(907\) | 35.9004 | 1.19205 | 0.596026 | − | 0.802965i | \(-0.296746\pi\) | ||||
0.596026 | + | 0.802965i | \(0.296746\pi\) | |||||||
\(908\) | − 13.7573i | − 0.456553i | ||||||||
\(909\) | −11.4819 | −0.380830 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.0025 | 1.12655 | 0.563277 | − | 0.826268i | \(-0.309541\pi\) | ||||
0.563277 | + | 0.826268i | \(0.309541\pi\) | |||||||
\(912\) | − 4.44504i | − 0.147190i | ||||||||
\(913\) | −23.0549 | −0.763005 | ||||||||
\(914\) | −10.5700 | −0.349625 | ||||||||
\(915\) | 11.0707i | 0.365986i | ||||||||
\(916\) | − 1.75541i | − 0.0580005i | ||||||||
\(917\) | − 17.9976i | − 0.594333i | ||||||||
\(918\) | 1.08815i | 0.0359142i | ||||||||
\(919\) | −27.7778 | −0.916304 | −0.458152 | − | 0.888874i | \(-0.651489\pi\) | ||||
−0.458152 | + | 0.888874i | \(0.651489\pi\) | |||||||
\(920\) | 2.69202 | 0.0887533 | ||||||||
\(921\) | − 23.6872i | − 0.780521i | ||||||||
\(922\) | −20.1420 | −0.663340 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −23.9366 | −0.787457 | ||||||||
\(925\) | 7.14675i | 0.234984i | ||||||||
\(926\) | −15.9065 | −0.522719 | ||||||||
\(927\) | −4.16421 | −0.136771 | ||||||||
\(928\) | − 7.93900i | − 0.260610i | ||||||||
\(929\) | 44.9342i | 1.47424i | 0.675760 | + | 0.737122i | \(0.263816\pi\) | ||||
−0.675760 | + | 0.737122i | \(0.736184\pi\) | |||||||
\(930\) | − 7.85086i | − 0.257440i | ||||||||
\(931\) | 82.1958i | 2.69386i | ||||||||
\(932\) | −5.49396 | −0.179961 | ||||||||
\(933\) | −6.77240 | −0.221718 | ||||||||
\(934\) | 25.6136i | 0.838101i | ||||||||
\(935\) | −5.15883 | −0.168712 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.50843 | −0.147284 | −0.0736421 | − | 0.997285i | \(-0.523462\pi\) | ||||
−0.0736421 | + | 0.997285i | \(0.523462\pi\) | |||||||
\(938\) | 48.3793i | 1.57964i | ||||||||
\(939\) | 7.16123 | 0.233698 | ||||||||
\(940\) | −7.00000 | −0.228315 | ||||||||
\(941\) | 18.4926i | 0.602843i | 0.953491 | + | 0.301421i | \(0.0974610\pi\) | ||||
−0.953491 | + | 0.301421i | \(0.902539\pi\) | |||||||
\(942\) | − 11.2174i | − 0.365484i | ||||||||
\(943\) | − 1.78986i | − 0.0582857i | ||||||||
\(944\) | 12.2784i | 0.399629i | ||||||||
\(945\) | 5.04892 | 0.164241 | ||||||||
\(946\) | −20.6558 | −0.671577 | ||||||||
\(947\) | − 60.3062i | − 1.95969i | −0.199766 | − | 0.979844i | \(-0.564018\pi\) | ||||
0.199766 | − | 0.979844i | \(-0.435982\pi\) | |||||||
\(948\) | −14.1468 | −0.459465 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.44504 | −0.144216 | ||||||||
\(951\) | 1.20344i | 0.0390242i | ||||||||
\(952\) | 5.49396 | 0.178060 | ||||||||
\(953\) | −23.6394 | −0.765755 | −0.382877 | − | 0.923799i | \(-0.625067\pi\) | ||||
−0.382877 | + | 0.923799i | \(0.625067\pi\) | |||||||
\(954\) | − 10.8605i | − 0.351623i | ||||||||
\(955\) | − 2.44504i | − 0.0791197i | ||||||||
\(956\) | − 17.4004i | − 0.562770i | ||||||||
\(957\) | 37.6383i | 1.21667i | ||||||||
\(958\) | 7.59658 | 0.245434 | ||||||||
\(959\) | 47.8461 | 1.54503 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | −30.6359 | −0.988256 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.796561 | −0.0256688 | ||||||||
\(964\) | 3.15452i | 0.101600i | ||||||||
\(965\) | −15.2959 | −0.492392 | ||||||||
\(966\) | 13.5918 | 0.437309 | ||||||||
\(967\) | 22.4910i | 0.723261i | 0.932321 | + | 0.361631i | \(0.117780\pi\) | ||||
−0.932321 | + | 0.361631i | \(0.882220\pi\) | |||||||
\(968\) | 11.4765i | 0.368869i | ||||||||
\(969\) | − 4.83685i | − 0.155382i | ||||||||
\(970\) | − 14.9269i | − 0.479275i | ||||||||
\(971\) | −15.4257 | −0.495033 | −0.247517 | − | 0.968884i | \(-0.579614\pi\) | ||||
−0.247517 | + | 0.968884i | \(0.579614\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | − 71.7338i | − 2.29968i | ||||||||
\(974\) | 0.779103 | 0.0249641 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.0707 | −0.354364 | ||||||||
\(977\) | − 38.5018i | − 1.23178i | −0.787831 | − | 0.615892i | \(-0.788796\pi\) | ||||
0.787831 | − | 0.615892i | \(-0.211204\pi\) | |||||||
\(978\) | 6.50902 | 0.208136 | ||||||||
\(979\) | 70.5816 | 2.25580 | ||||||||
\(980\) | − 18.4916i | − 0.590691i | ||||||||
\(981\) | − 0.704103i | − 0.0224803i | ||||||||
\(982\) | − 11.3948i | − 0.363623i | ||||||||
\(983\) | 3.83340i | 0.122266i | 0.998130 | + | 0.0611332i | \(0.0194714\pi\) | ||||
−0.998130 | + | 0.0611332i | \(0.980529\pi\) | |||||||
\(984\) | 0.664874 | 0.0211954 | ||||||||
\(985\) | −3.44935 | −0.109906 | ||||||||
\(986\) | − 8.63879i | − 0.275115i | ||||||||
\(987\) | −35.3424 | −1.12496 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.7289 | 0.372956 | ||||||||
\(990\) | − 4.74094i | − 0.150677i | ||||||||
\(991\) | −46.7670 | −1.48560 | −0.742802 | − | 0.669512i | \(-0.766503\pi\) | ||||
−0.742802 | + | 0.669512i | \(0.766503\pi\) | |||||||
\(992\) | 7.85086 | 0.249265 | ||||||||
\(993\) | − 20.9933i | − 0.666202i | ||||||||
\(994\) | 22.5797i | 0.716185i | ||||||||
\(995\) | − 9.18598i | − 0.291215i | ||||||||
\(996\) | 4.86294i | 0.154088i | ||||||||
\(997\) | −42.8920 | −1.35840 | −0.679202 | − | 0.733952i | \(-0.737674\pi\) | ||||
−0.679202 | + | 0.733952i | \(0.737674\pi\) | |||||||
\(998\) | 23.5555 | 0.745638 | ||||||||
\(999\) | − 7.14675i | − 0.226113i |
(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 | 5070.2.b.y.1351.6 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bv.1.1 | yes | 3 | ||
13.8 | odd | 4 | 5070.2.a.bq.1.3 | ✓ | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.y.1351.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bq.1.3 | ✓ | 3 | 13.8 | odd | 4 | ||
5070.2.a.bv.1.1 | yes | 3 | 13.5 | odd | 4 | ||
5070.2.b.y.1351.1 | 6 | 13.12 | even | 2 | inner | ||
5070.2.b.y.1351.6 | 6 | 1.1 | even | 1 | trivial |