Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,3,Mod(721,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("722.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.b (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: | \(19.6730750868\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 38) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.4 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.721 |
Dual form | 722.3.b.b.721.1 |
$q$-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 \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).
\(n\) | \(363\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | 0.317837i | 0.105946i | 0.998596 | + | 0.0529729i | \(0.0168697\pi\) | ||||
−0.998596 | + | 0.0529729i | \(0.983130\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.200000 | −0.100000 | − | 0.994987i | \(-0.531884\pi\) | ||||
−0.100000 | + | 0.994987i | \(0.531884\pi\) | |||||||
\(6\) | −0.449490 | −0.0749150 | ||||||||
\(7\) | −2.89898 | −0.414140 | −0.207070 | − | 0.978326i | \(-0.566393\pi\) | ||||
−0.207070 | + | 0.978326i | \(0.566393\pi\) | |||||||
\(8\) | − 2.82843i | − 0.353553i | ||||||||
\(9\) | 8.89898 | 0.988775 | ||||||||
\(10\) | − 1.41421i | − 0.141421i | ||||||||
\(11\) | −5.10102 | −0.463729 | −0.231865 | − | 0.972748i | \(-0.574483\pi\) | ||||
−0.231865 | + | 0.972748i | \(0.574483\pi\) | |||||||
\(12\) | − 0.635674i | − 0.0529729i | ||||||||
\(13\) | 0.174973i | 0.0134594i | 0.999977 | + | 0.00672972i | \(0.00214215\pi\) | ||||
−0.999977 | + | 0.00672972i | \(0.997858\pi\) | |||||||
\(14\) | − 4.09978i | − 0.292841i | ||||||||
\(15\) | − 0.317837i | − 0.0211891i | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −11.8990 | −0.699940 | −0.349970 | − | 0.936761i | \(-0.613808\pi\) | ||||
−0.349970 | + | 0.936761i | \(0.613808\pi\) | |||||||
\(18\) | 12.5851i | 0.699170i | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.00000 | 0.100000 | ||||||||
\(21\) | − 0.921404i | − 0.0438764i | ||||||||
\(22\) | − 7.21393i | − 0.327906i | ||||||||
\(23\) | −17.0454 | −0.741105 | −0.370552 | − | 0.928812i | \(-0.620832\pi\) | ||||
−0.370552 | + | 0.928812i | \(0.620832\pi\) | |||||||
\(24\) | 0.898979 | 0.0374575 | ||||||||
\(25\) | −24.0000 | −0.960000 | ||||||||
\(26\) | −0.247449 | −0.00951726 | ||||||||
\(27\) | 5.68896i | 0.210702i | ||||||||
\(28\) | 5.79796 | 0.207070 | ||||||||
\(29\) | − 44.5084i | − 1.53477i | −0.641185 | − | 0.767386i | \(-0.721557\pi\) | ||||
0.641185 | − | 0.767386i | \(-0.278443\pi\) | |||||||
\(30\) | 0.449490 | 0.0149830 | ||||||||
\(31\) | − 31.1769i | − 1.00571i | −0.864372 | − | 0.502853i | \(-0.832284\pi\) | ||||
0.864372 | − | 0.502853i | \(-0.167716\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | − 1.62129i | − 0.0491301i | ||||||||
\(34\) | − 16.8277i | − 0.494932i | ||||||||
\(35\) | 2.89898 | 0.0828280 | ||||||||
\(36\) | −17.7980 | −0.494388 | ||||||||
\(37\) | 21.9917i | 0.594371i | 0.954820 | + | 0.297186i | \(0.0960480\pi\) | ||||
−0.954820 | + | 0.297186i | \(0.903952\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0556128 | −0.00142597 | ||||||||
\(40\) | 2.82843i | 0.0707107i | ||||||||
\(41\) | − 54.2008i | − 1.32197i | −0.750399 | − | 0.660986i | \(-0.770138\pi\) | ||||
0.750399 | − | 0.660986i | \(-0.229862\pi\) | |||||||
\(42\) | 1.30306 | 0.0310253 | ||||||||
\(43\) | 37.3383 | 0.868332 | 0.434166 | − | 0.900833i | \(-0.357043\pi\) | ||||
0.434166 | + | 0.900833i | \(0.357043\pi\) | |||||||
\(44\) | 10.2020 | 0.231865 | ||||||||
\(45\) | −8.89898 | −0.197755 | ||||||||
\(46\) | − 24.1058i | − 0.524040i | ||||||||
\(47\) | 81.5403 | 1.73490 | 0.867450 | − | 0.497524i | \(-0.165757\pi\) | ||||
0.867450 | + | 0.497524i | \(0.165757\pi\) | |||||||
\(48\) | 1.27135i | 0.0264864i | ||||||||
\(49\) | −40.5959 | −0.828488 | ||||||||
\(50\) | − 33.9411i | − 0.678823i | ||||||||
\(51\) | − 3.78194i | − 0.0741557i | ||||||||
\(52\) | − 0.349945i | − 0.00672972i | ||||||||
\(53\) | − 55.7579i | − 1.05204i | −0.850474 | − | 0.526018i | \(-0.823684\pi\) | ||||
0.850474 | − | 0.526018i | \(-0.176316\pi\) | |||||||
\(54\) | −8.04541 | −0.148989 | ||||||||
\(55\) | 5.10102 | 0.0927458 | ||||||||
\(56\) | 8.19955i | 0.146421i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 62.9444 | 1.08525 | ||||||||
\(59\) | − 34.5447i | − 0.585503i | −0.956189 | − | 0.292752i | \(-0.905429\pi\) | ||||
0.956189 | − | 0.292752i | \(-0.0945709\pi\) | |||||||
\(60\) | 0.635674i | 0.0105946i | ||||||||
\(61\) | −76.1918 | −1.24905 | −0.624523 | − | 0.781006i | \(-0.714707\pi\) | ||||
−0.624523 | + | 0.781006i | \(0.714707\pi\) | |||||||
\(62\) | 44.0908 | 0.711142 | ||||||||
\(63\) | −25.7980 | −0.409491 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − 0.174973i | − 0.00269189i | ||||||||
\(66\) | 2.29286 | 0.0347402 | ||||||||
\(67\) | − 118.540i | − 1.76926i | −0.466295 | − | 0.884629i | \(-0.654412\pi\) | ||||
0.466295 | − | 0.884629i | \(-0.345588\pi\) | |||||||
\(68\) | 23.7980 | 0.349970 | ||||||||
\(69\) | − 5.41767i | − 0.0785169i | ||||||||
\(70\) | 4.09978i | 0.0585682i | ||||||||
\(71\) | 75.6067i | 1.06488i | 0.846467 | + | 0.532441i | \(0.178725\pi\) | ||||
−0.846467 | + | 0.532441i | \(0.821275\pi\) | |||||||
\(72\) | − 25.1701i | − 0.349585i | ||||||||
\(73\) | 29.3837 | 0.402516 | 0.201258 | − | 0.979538i | \(-0.435497\pi\) | ||||
0.201258 | + | 0.979538i | \(0.435497\pi\) | |||||||
\(74\) | −31.1010 | −0.420284 | ||||||||
\(75\) | − 7.62809i | − 0.101708i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.7878 | 0.192049 | ||||||||
\(78\) | − 0.0786484i | − 0.00100831i | ||||||||
\(79\) | − 66.0716i | − 0.836349i | −0.908367 | − | 0.418174i | \(-0.862670\pi\) | ||||
0.908367 | − | 0.418174i | \(-0.137330\pi\) | |||||||
\(80\) | −4.00000 | −0.0500000 | ||||||||
\(81\) | 78.2827 | 0.966452 | ||||||||
\(82\) | 76.6515 | 0.934775 | ||||||||
\(83\) | −30.6969 | −0.369843 | −0.184921 | − | 0.982753i | \(-0.559203\pi\) | ||||
−0.184921 | + | 0.982753i | \(0.559203\pi\) | |||||||
\(84\) | 1.84281i | 0.0219382i | ||||||||
\(85\) | 11.8990 | 0.139988 | ||||||||
\(86\) | 52.8043i | 0.614003i | ||||||||
\(87\) | 14.1464 | 0.162603 | ||||||||
\(88\) | 14.4279i | 0.163953i | ||||||||
\(89\) | 10.2173i | 0.114801i | 0.998351 | + | 0.0574007i | \(0.0182813\pi\) | ||||
−0.998351 | + | 0.0574007i | \(0.981719\pi\) | |||||||
\(90\) | − 12.5851i | − 0.139834i | ||||||||
\(91\) | − 0.507242i | − 0.00557409i | ||||||||
\(92\) | 34.0908 | 0.370552 | ||||||||
\(93\) | 9.90918 | 0.106550 | ||||||||
\(94\) | 115.315i | 1.22676i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.79796 | −0.0187287 | ||||||||
\(97\) | − 148.781i | − 1.53383i | −0.641749 | − | 0.766914i | \(-0.721791\pi\) | ||||
0.641749 | − | 0.766914i | \(-0.278209\pi\) | |||||||
\(98\) | − 57.4113i | − 0.585830i | ||||||||
\(99\) | −45.3939 | −0.458524 | ||||||||
\(100\) | 48.0000 | 0.480000 | ||||||||
\(101\) | −140.485 | −1.39094 | −0.695469 | − | 0.718556i | \(-0.744803\pi\) | ||||
−0.695469 | + | 0.718556i | \(0.744803\pi\) | |||||||
\(102\) | 5.34847 | 0.0524360 | ||||||||
\(103\) | 113.965i | 1.10646i | 0.833028 | + | 0.553230i | \(0.186605\pi\) | ||||
−0.833028 | + | 0.553230i | \(0.813395\pi\) | |||||||
\(104\) | 0.494897 | 0.00475863 | ||||||||
\(105\) | 0.921404i | 0.00877527i | ||||||||
\(106\) | 78.8536 | 0.743902 | ||||||||
\(107\) | 113.965i | 1.06510i | 0.846399 | + | 0.532549i | \(0.178766\pi\) | ||||
−0.846399 | + | 0.532549i | \(0.821234\pi\) | |||||||
\(108\) | − 11.3779i | − 0.105351i | ||||||||
\(109\) | 68.4072i | 0.627589i | 0.949491 | + | 0.313794i | \(0.101600\pi\) | ||||
−0.949491 | + | 0.313794i | \(0.898400\pi\) | |||||||
\(110\) | 7.21393i | 0.0655812i | ||||||||
\(111\) | −6.98979 | −0.0629711 | ||||||||
\(112\) | −11.5959 | −0.103535 | ||||||||
\(113\) | − 81.9313i | − 0.725056i | −0.931973 | − | 0.362528i | \(-0.881914\pi\) | ||||
0.931973 | − | 0.362528i | \(-0.118086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.0454 | 0.148221 | ||||||||
\(116\) | 89.0168i | 0.767386i | ||||||||
\(117\) | 1.55708i | 0.0133084i | ||||||||
\(118\) | 48.8536 | 0.414013 | ||||||||
\(119\) | 34.4949 | 0.289873 | ||||||||
\(120\) | −0.898979 | −0.00749150 | ||||||||
\(121\) | −94.9796 | −0.784955 | ||||||||
\(122\) | − 107.752i | − 0.883209i | ||||||||
\(123\) | 17.2270 | 0.140057 | ||||||||
\(124\) | 62.3538i | 0.502853i | ||||||||
\(125\) | 49.0000 | 0.392000 | ||||||||
\(126\) | − 36.4838i | − 0.289554i | ||||||||
\(127\) | − 134.146i | − 1.05627i | −0.849160 | − | 0.528136i | \(-0.822891\pi\) | ||||
0.849160 | − | 0.528136i | \(-0.177109\pi\) | |||||||
\(128\) | − 11.3137i | − 0.0883883i | ||||||||
\(129\) | 11.8675i | 0.0919961i | ||||||||
\(130\) | 0.247449 | 0.00190345 | ||||||||
\(131\) | 82.7526 | 0.631699 | 0.315849 | − | 0.948809i | \(-0.397711\pi\) | ||||
0.315849 | + | 0.948809i | \(0.397711\pi\) | |||||||
\(132\) | 3.24259i | 0.0245651i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 167.641 | 1.25105 | ||||||||
\(135\) | − 5.68896i | − 0.0421405i | ||||||||
\(136\) | 33.6554i | 0.247466i | ||||||||
\(137\) | −11.8990 | −0.0868539 | −0.0434269 | − | 0.999057i | \(-0.513828\pi\) | ||||
−0.0434269 | + | 0.999057i | \(0.513828\pi\) | |||||||
\(138\) | 7.66174 | 0.0555198 | ||||||||
\(139\) | 41.7423 | 0.300305 | 0.150152 | − | 0.988663i | \(-0.452024\pi\) | ||||
0.150152 | + | 0.988663i | \(0.452024\pi\) | |||||||
\(140\) | −5.79796 | −0.0414140 | ||||||||
\(141\) | 25.9165i | 0.183805i | ||||||||
\(142\) | −106.924 | −0.752986 | ||||||||
\(143\) | − 0.892539i | − 0.00624153i | ||||||||
\(144\) | 35.5959 | 0.247194 | ||||||||
\(145\) | 44.5084i | 0.306955i | ||||||||
\(146\) | 41.5548i | 0.284622i | ||||||||
\(147\) | − 12.9029i | − 0.0877748i | ||||||||
\(148\) | − 43.9835i | − 0.297186i | ||||||||
\(149\) | −35.6765 | −0.239440 | −0.119720 | − | 0.992808i | \(-0.538200\pi\) | ||||
−0.119720 | + | 0.992808i | \(0.538200\pi\) | |||||||
\(150\) | 10.7878 | 0.0719184 | ||||||||
\(151\) | − 85.5527i | − 0.566574i | −0.959035 | − | 0.283287i | \(-0.908575\pi\) | ||||
0.959035 | − | 0.283287i | \(-0.0914249\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −105.889 | −0.692083 | ||||||||
\(154\) | 20.9130i | 0.135799i | ||||||||
\(155\) | 31.1769i | 0.201141i | ||||||||
\(156\) | 0.111226 | 0.000712985 0 | ||||||||
\(157\) | −200.151 | −1.27485 | −0.637424 | − | 0.770514i | \(-0.720000\pi\) | ||||
−0.637424 | + | 0.770514i | \(0.720000\pi\) | |||||||
\(158\) | 93.4393 | 0.591388 | ||||||||
\(159\) | 17.7219 | 0.111459 | ||||||||
\(160\) | − 5.65685i | − 0.0353553i | ||||||||
\(161\) | 49.4143 | 0.306921 | ||||||||
\(162\) | 110.708i | 0.683385i | ||||||||
\(163\) | −127.303 | −0.781000 | −0.390500 | − | 0.920603i | \(-0.627698\pi\) | ||||
−0.390500 | + | 0.920603i | \(0.627698\pi\) | |||||||
\(164\) | 108.402i | 0.660986i | ||||||||
\(165\) | 1.62129i | 0.00982603i | ||||||||
\(166\) | − 43.4120i | − 0.261518i | ||||||||
\(167\) | 183.501i | 1.09881i | 0.835557 | + | 0.549404i | \(0.185145\pi\) | ||||
−0.835557 | + | 0.549404i | \(0.814855\pi\) | |||||||
\(168\) | −2.60612 | −0.0155126 | ||||||||
\(169\) | 168.969 | 0.999819 | ||||||||
\(170\) | 16.8277i | 0.0989865i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −74.6765 | −0.434166 | ||||||||
\(173\) | − 66.5355i | − 0.384598i | −0.981336 | − | 0.192299i | \(-0.938406\pi\) | ||||
0.981336 | − | 0.192299i | \(-0.0615944\pi\) | |||||||
\(174\) | 20.0061i | 0.114977i | ||||||||
\(175\) | 69.5755 | 0.397574 | ||||||||
\(176\) | −20.4041 | −0.115932 | ||||||||
\(177\) | 10.9796 | 0.0620316 | ||||||||
\(178\) | −14.4495 | −0.0811769 | ||||||||
\(179\) | − 24.2134i | − 0.135270i | −0.997710 | − | 0.0676351i | \(-0.978455\pi\) | ||||
0.997710 | − | 0.0676351i | \(-0.0215454\pi\) | |||||||
\(180\) | 17.7980 | 0.0988775 | ||||||||
\(181\) | − 35.6732i | − 0.197089i | −0.995133 | − | 0.0985447i | \(-0.968581\pi\) | ||||
0.995133 | − | 0.0985447i | \(-0.0314187\pi\) | |||||||
\(182\) | 0.717349 | 0.00394148 | ||||||||
\(183\) | − 24.2166i | − 0.132331i | ||||||||
\(184\) | 48.2117i | 0.262020i | ||||||||
\(185\) | − 21.9917i | − 0.118874i | ||||||||
\(186\) | 14.0137i | 0.0753425i | ||||||||
\(187\) | 60.6969 | 0.324583 | ||||||||
\(188\) | −163.081 | −0.867450 | ||||||||
\(189\) | − 16.4922i | − 0.0872602i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −180.252 | −0.943728 | −0.471864 | − | 0.881671i | \(-0.656419\pi\) | ||||
−0.471864 | + | 0.881671i | \(0.656419\pi\) | |||||||
\(192\) | − 2.54270i | − 0.0132432i | ||||||||
\(193\) | 218.221i | 1.13068i | 0.824859 | + | 0.565339i | \(0.191255\pi\) | ||||
−0.824859 | + | 0.565339i | \(0.808745\pi\) | |||||||
\(194\) | 210.409 | 1.08458 | ||||||||
\(195\) | 0.0556128 | 0.000285194 0 | ||||||||
\(196\) | 81.1918 | 0.414244 | ||||||||
\(197\) | 340.091 | 1.72635 | 0.863175 | − | 0.504905i | \(-0.168473\pi\) | ||||
0.863175 | + | 0.504905i | \(0.168473\pi\) | |||||||
\(198\) | − 64.1966i | − 0.324225i | ||||||||
\(199\) | −333.388 | −1.67532 | −0.837659 | − | 0.546194i | \(-0.816076\pi\) | ||||
−0.837659 | + | 0.546194i | \(0.816076\pi\) | |||||||
\(200\) | 67.8823i | 0.339411i | ||||||||
\(201\) | 37.6765 | 0.187445 | ||||||||
\(202\) | − 198.675i | − 0.983541i | ||||||||
\(203\) | 129.029i | 0.635611i | ||||||||
\(204\) | 7.56388i | 0.0370778i | ||||||||
\(205\) | 54.2008i | 0.264394i | ||||||||
\(206\) | −161.171 | −0.782386 | ||||||||
\(207\) | −151.687 | −0.732786 | ||||||||
\(208\) | 0.699891i | 0.00336486i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.30306 | −0.00620505 | ||||||||
\(211\) | 349.585i | 1.65680i | 0.560135 | + | 0.828401i | \(0.310749\pi\) | ||||
−0.560135 | + | 0.828401i | \(0.689251\pi\) | |||||||
\(212\) | 111.516i | 0.526018i | ||||||||
\(213\) | −24.0306 | −0.112820 | ||||||||
\(214\) | −161.171 | −0.753138 | ||||||||
\(215\) | −37.3383 | −0.173666 | ||||||||
\(216\) | 16.0908 | 0.0744945 | ||||||||
\(217\) | 90.3812i | 0.416503i | ||||||||
\(218\) | −96.7423 | −0.443772 | ||||||||
\(219\) | 9.33923i | 0.0426449i | ||||||||
\(220\) | −10.2020 | −0.0463729 | ||||||||
\(221\) | − 2.08200i | − 0.00942080i | ||||||||
\(222\) | − 9.88506i | − 0.0445273i | ||||||||
\(223\) | − 31.7805i | − 0.142513i | −0.997458 | − | 0.0712567i | \(-0.977299\pi\) | ||||
0.997458 | − | 0.0712567i | \(-0.0227009\pi\) | |||||||
\(224\) | − 16.3991i | − 0.0732103i | ||||||||
\(225\) | −213.576 | −0.949224 | ||||||||
\(226\) | 115.868 | 0.512692 | ||||||||
\(227\) | − 249.730i | − 1.10013i | −0.835121 | − | 0.550066i | \(-0.814603\pi\) | ||||
0.835121 | − | 0.550066i | \(-0.185397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −259.687 | −1.13400 | −0.567002 | − | 0.823717i | \(-0.691897\pi\) | ||||
−0.567002 | + | 0.823717i | \(0.691897\pi\) | |||||||
\(230\) | 24.1058i | 0.104808i | ||||||||
\(231\) | 4.70010i | 0.0203467i | ||||||||
\(232\) | −125.889 | −0.542624 | ||||||||
\(233\) | −390.283 | −1.67503 | −0.837516 | − | 0.546412i | \(-0.815993\pi\) | ||||
−0.837516 | + | 0.546412i | \(0.815993\pi\) | |||||||
\(234\) | −2.20204 | −0.00941043 | ||||||||
\(235\) | −81.5403 | −0.346980 | ||||||||
\(236\) | 69.0894i | 0.292752i | ||||||||
\(237\) | 21.0000 | 0.0886076 | ||||||||
\(238\) | 48.7832i | 0.204971i | ||||||||
\(239\) | −296.677 | −1.24132 | −0.620662 | − | 0.784078i | \(-0.713136\pi\) | ||||
−0.620662 | + | 0.784078i | \(0.713136\pi\) | |||||||
\(240\) | − 1.27135i | − 0.00529729i | ||||||||
\(241\) | 115.155i | 0.477821i | 0.971042 | + | 0.238911i | \(0.0767903\pi\) | ||||
−0.971042 | + | 0.238911i | \(0.923210\pi\) | |||||||
\(242\) | − 134.321i | − 0.555047i | ||||||||
\(243\) | 76.0818i | 0.313094i | ||||||||
\(244\) | 152.384 | 0.624523 | ||||||||
\(245\) | 40.5959 | 0.165698 | ||||||||
\(246\) | 24.3627i | 0.0990354i | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −88.1816 | −0.355571 | ||||||||
\(249\) | − 9.75663i | − 0.0391833i | ||||||||
\(250\) | 69.2965i | 0.277186i | ||||||||
\(251\) | 489.924 | 1.95189 | 0.975944 | − | 0.218021i | \(-0.0699600\pi\) | ||||
0.975944 | + | 0.218021i | \(0.0699600\pi\) | |||||||
\(252\) | 51.5959 | 0.204746 | ||||||||
\(253\) | 86.9490 | 0.343672 | ||||||||
\(254\) | 189.712 | 0.746897 | ||||||||
\(255\) | 3.78194i | 0.0148311i | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 227.913i | 0.886822i | 0.896319 | + | 0.443411i | \(0.146232\pi\) | ||||
−0.896319 | + | 0.443411i | \(0.853768\pi\) | |||||||
\(258\) | −16.7832 | −0.0650510 | ||||||||
\(259\) | − 63.7536i | − 0.246153i | ||||||||
\(260\) | 0.349945i | 0.00134594i | ||||||||
\(261\) | − 396.079i | − 1.51755i | ||||||||
\(262\) | 117.030i | 0.446679i | ||||||||
\(263\) | 135.924 | 0.516821 | 0.258411 | − | 0.966035i | \(-0.416801\pi\) | ||||
0.258411 | + | 0.966035i | \(0.416801\pi\) | |||||||
\(264\) | −4.58571 | −0.0173701 | ||||||||
\(265\) | 55.7579i | 0.210407i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.24745 | −0.0121627 | ||||||||
\(268\) | 237.081i | 0.884629i | ||||||||
\(269\) | 259.912i | 0.966215i | 0.875561 | + | 0.483108i | \(0.160492\pi\) | ||||
−0.875561 | + | 0.483108i | \(0.839508\pi\) | |||||||
\(270\) | 8.04541 | 0.0297978 | ||||||||
\(271\) | −232.984 | −0.859720 | −0.429860 | − | 0.902896i | \(-0.641437\pi\) | ||||
−0.429860 | + | 0.902896i | \(0.641437\pi\) | |||||||
\(272\) | −47.5959 | −0.174985 | ||||||||
\(273\) | 0.161220 | 0.000590551 0 | ||||||||
\(274\) | − 16.8277i | − 0.0614150i | ||||||||
\(275\) | 122.424 | 0.445180 | ||||||||
\(276\) | 10.8353i | 0.0392584i | ||||||||
\(277\) | −9.44387 | −0.0340934 | −0.0170467 | − | 0.999855i | \(-0.505426\pi\) | ||||
−0.0170467 | + | 0.999855i | \(0.505426\pi\) | |||||||
\(278\) | 59.0326i | 0.212347i | ||||||||
\(279\) | − 277.443i | − 0.994418i | ||||||||
\(280\) | − 8.19955i | − 0.0292841i | ||||||||
\(281\) | − 156.567i | − 0.557177i | −0.960411 | − | 0.278589i | \(-0.910133\pi\) | ||||
0.960411 | − | 0.278589i | \(-0.0898666\pi\) | |||||||
\(282\) | −36.6515 | −0.129970 | ||||||||
\(283\) | 2.93418 | 0.0103681 | 0.00518407 | − | 0.999987i | \(-0.498350\pi\) | ||||
0.00518407 | + | 0.999987i | \(0.498350\pi\) | |||||||
\(284\) | − 151.213i | − 0.532441i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.26224 | 0.00441343 | ||||||||
\(287\) | 157.127i | 0.547481i | ||||||||
\(288\) | 50.3402i | 0.174792i | ||||||||
\(289\) | −147.414 | −0.510084 | ||||||||
\(290\) | −62.9444 | −0.217050 | ||||||||
\(291\) | 47.2883 | 0.162503 | ||||||||
\(292\) | −58.7673 | −0.201258 | ||||||||
\(293\) | − 332.361i | − 1.13434i | −0.823601 | − | 0.567169i | \(-0.808039\pi\) | ||||
0.823601 | − | 0.567169i | \(-0.191961\pi\) | |||||||
\(294\) | 18.2474 | 0.0620662 | ||||||||
\(295\) | 34.5447i | 0.117101i | ||||||||
\(296\) | 62.2020 | 0.210142 | ||||||||
\(297\) | − 29.0195i | − 0.0977088i | ||||||||
\(298\) | − 50.4542i | − 0.169309i | ||||||||
\(299\) | − 2.98248i | − 0.00997485i | ||||||||
\(300\) | 15.2562i | 0.0508540i | ||||||||
\(301\) | −108.243 | −0.359611 | ||||||||
\(302\) | 120.990 | 0.400628 | ||||||||
\(303\) | − 44.6513i | − 0.147364i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 76.1918 | 0.249809 | ||||||||
\(306\) | − 149.749i | − 0.489377i | ||||||||
\(307\) | 257.454i | 0.838613i | 0.907845 | + | 0.419307i | \(0.137727\pi\) | ||||
−0.907845 | + | 0.419307i | \(0.862273\pi\) | |||||||
\(308\) | −29.5755 | −0.0960244 | ||||||||
\(309\) | −36.2225 | −0.117225 | ||||||||
\(310\) | −44.0908 | −0.142228 | ||||||||
\(311\) | 217.666 | 0.699892 | 0.349946 | − | 0.936770i | \(-0.386200\pi\) | ||||
0.349946 | + | 0.936770i | \(0.386200\pi\) | |||||||
\(312\) | 0.157297i | 0 0.000504157i | ||||||||
\(313\) | −310.242 | −0.991188 | −0.495594 | − | 0.868554i | \(-0.665050\pi\) | ||||
−0.495594 | + | 0.868554i | \(0.665050\pi\) | |||||||
\(314\) | − 283.056i | − 0.901453i | ||||||||
\(315\) | 25.7980 | 0.0818983 | ||||||||
\(316\) | 132.143i | 0.418174i | ||||||||
\(317\) | 345.185i | 1.08891i | 0.838789 | + | 0.544456i | \(0.183264\pi\) | ||||
−0.838789 | + | 0.544456i | \(0.816736\pi\) | |||||||
\(318\) | 25.0626i | 0.0788132i | ||||||||
\(319\) | 227.038i | 0.711719i | ||||||||
\(320\) | 8.00000 | 0.0250000 | ||||||||
\(321\) | −36.2225 | −0.112843 | ||||||||
\(322\) | 69.8824i | 0.217026i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −156.565 | −0.483226 | ||||||||
\(325\) | − 4.19934i | − 0.0129211i | ||||||||
\(326\) | − 180.034i | − 0.552251i | ||||||||
\(327\) | −21.7423 | −0.0664904 | ||||||||
\(328\) | −153.303 | −0.467387 | ||||||||
\(329\) | −236.384 | −0.718491 | ||||||||
\(330\) | −2.29286 | −0.00694805 | ||||||||
\(331\) | 487.318i | 1.47226i | 0.676841 | + | 0.736130i | \(0.263349\pi\) | ||||
−0.676841 | + | 0.736130i | \(0.736651\pi\) | |||||||
\(332\) | 61.3939 | 0.184921 | ||||||||
\(333\) | 195.704i | 0.587700i | ||||||||
\(334\) | −259.510 | −0.776975 | ||||||||
\(335\) | 118.540i | 0.353852i | ||||||||
\(336\) | − 3.68561i | − 0.0109691i | ||||||||
\(337\) | 166.731i | 0.494751i | 0.968920 | + | 0.247376i | \(0.0795681\pi\) | ||||
−0.968920 | + | 0.247376i | \(0.920432\pi\) | |||||||
\(338\) | 238.959i | 0.706979i | ||||||||
\(339\) | 26.0408 | 0.0768166 | ||||||||
\(340\) | −23.7980 | −0.0699940 | ||||||||
\(341\) | 159.034i | 0.466376i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 259.737 | 0.757250 | ||||||||
\(344\) | − 105.609i | − 0.307002i | ||||||||
\(345\) | 5.41767i | 0.0157034i | ||||||||
\(346\) | 94.0954 | 0.271952 | ||||||||
\(347\) | 377.742 | 1.08859 | 0.544297 | − | 0.838892i | \(-0.316796\pi\) | ||||
0.544297 | + | 0.838892i | \(0.316796\pi\) | |||||||
\(348\) | −28.2929 | −0.0813013 | ||||||||
\(349\) | −586.434 | −1.68033 | −0.840163 | − | 0.542334i | \(-0.817541\pi\) | ||||
−0.840163 | + | 0.542334i | \(0.817541\pi\) | |||||||
\(350\) | 98.3946i | 0.281128i | ||||||||
\(351\) | −0.995413 | −0.00283593 | ||||||||
\(352\) | − 28.8557i | − 0.0819765i | ||||||||
\(353\) | 476.817 | 1.35076 | 0.675379 | − | 0.737471i | \(-0.263980\pi\) | ||||
0.675379 | + | 0.737471i | \(0.263980\pi\) | |||||||
\(354\) | 15.5275i | 0.0438630i | ||||||||
\(355\) | − 75.6067i | − 0.212977i | ||||||||
\(356\) | − 20.4347i | − 0.0574007i | ||||||||
\(357\) | 10.9638i | 0.0307108i | ||||||||
\(358\) | 34.2429 | 0.0956505 | ||||||||
\(359\) | −247.409 | −0.689161 | −0.344580 | − | 0.938757i | \(-0.611979\pi\) | ||||
−0.344580 | + | 0.938757i | \(0.611979\pi\) | |||||||
\(360\) | 25.1701i | 0.0699170i | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 50.4495 | 0.139363 | ||||||||
\(363\) | − 30.1881i | − 0.0831627i | ||||||||
\(364\) | 1.01448i | 0.00278704i | ||||||||
\(365\) | −29.3837 | −0.0805032 | ||||||||
\(366\) | 34.2474 | 0.0935723 | ||||||||
\(367\) | 483.924 | 1.31859 | 0.659297 | − | 0.751883i | \(-0.270854\pi\) | ||||
0.659297 | + | 0.751883i | \(0.270854\pi\) | |||||||
\(368\) | −68.1816 | −0.185276 | ||||||||
\(369\) | − 482.332i | − 1.30713i | ||||||||
\(370\) | 31.1010 | 0.0840568 | ||||||||
\(371\) | 161.641i | 0.435690i | ||||||||
\(372\) | −19.8184 | −0.0532752 | ||||||||
\(373\) | − 140.908i | − 0.377768i | −0.981999 | − | 0.188884i | \(-0.939513\pi\) | ||||
0.981999 | − | 0.188884i | \(-0.0604871\pi\) | |||||||
\(374\) | 85.8384i | 0.229515i | ||||||||
\(375\) | 15.5740i | 0.0415307i | ||||||||
\(376\) | − 230.631i | − 0.613380i | ||||||||
\(377\) | 7.78775 | 0.0206572 | ||||||||
\(378\) | 23.3235 | 0.0617023 | ||||||||
\(379\) | 468.633i | 1.23650i | 0.785982 | + | 0.618249i | \(0.212158\pi\) | ||||
−0.785982 | + | 0.618249i | \(0.787842\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.6367 | 0.111907 | ||||||||
\(382\) | − 254.915i | − 0.667316i | ||||||||
\(383\) | − 557.203i | − 1.45484i | −0.686193 | − | 0.727420i | \(-0.740719\pi\) | ||||
0.686193 | − | 0.727420i | \(-0.259281\pi\) | |||||||
\(384\) | 3.59592 | 0.00936437 | ||||||||
\(385\) | −14.7878 | −0.0384098 | ||||||||
\(386\) | −308.611 | −0.799510 | ||||||||
\(387\) | 332.272 | 0.858585 | ||||||||
\(388\) | 297.563i | 0.766914i | ||||||||
\(389\) | 93.1204 | 0.239384 | 0.119692 | − | 0.992811i | \(-0.461809\pi\) | ||||
0.119692 | + | 0.992811i | \(0.461809\pi\) | |||||||
\(390\) | 0.0786484i | 0 0.000201663i | ||||||||
\(391\) | 202.823 | 0.518729 | ||||||||
\(392\) | 114.823i | 0.292915i | ||||||||
\(393\) | 26.3018i | 0.0669258i | ||||||||
\(394\) | 480.961i | 1.22071i | ||||||||
\(395\) | 66.0716i | 0.167270i | ||||||||
\(396\) | 90.7878 | 0.229262 | ||||||||
\(397\) | 259.363 | 0.653308 | 0.326654 | − | 0.945144i | \(-0.394079\pi\) | ||||
0.326654 | + | 0.945144i | \(0.394079\pi\) | |||||||
\(398\) | − 471.482i | − 1.18463i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −96.0000 | −0.240000 | ||||||||
\(401\) | − 449.738i | − 1.12154i | −0.827972 | − | 0.560770i | \(-0.810505\pi\) | ||||
0.827972 | − | 0.560770i | \(-0.189495\pi\) | |||||||
\(402\) | 53.2827i | 0.132544i | ||||||||
\(403\) | 5.45511 | 0.0135362 | ||||||||
\(404\) | 280.969 | 0.695469 | ||||||||
\(405\) | −78.2827 | −0.193290 | ||||||||
\(406\) | −182.474 | −0.449445 | ||||||||
\(407\) | − 112.180i | − 0.275627i | ||||||||
\(408\) | −10.6969 | −0.0262180 | ||||||||
\(409\) | − 104.885i | − 0.256441i | −0.991746 | − | 0.128221i | \(-0.959073\pi\) | ||||
0.991746 | − | 0.128221i | \(-0.0409266\pi\) | |||||||
\(410\) | −76.6515 | −0.186955 | ||||||||
\(411\) | − 3.78194i | − 0.00920180i | ||||||||
\(412\) | − 227.931i | − 0.553230i | ||||||||
\(413\) | 100.144i | 0.242480i | ||||||||
\(414\) | − 214.517i | − 0.518158i | ||||||||
\(415\) | 30.6969 | 0.0739685 | ||||||||
\(416\) | −0.989795 | −0.00237931 | ||||||||
\(417\) | 13.2673i | 0.0318160i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 463.121 | 1.10530 | 0.552651 | − | 0.833413i | \(-0.313616\pi\) | ||||
0.552651 | + | 0.833413i | \(0.313616\pi\) | |||||||
\(420\) | − 1.84281i | − 0.00438764i | ||||||||
\(421\) | − 483.486i | − 1.14842i | −0.818707 | − | 0.574211i | \(-0.805309\pi\) | ||||
0.818707 | − | 0.574211i | \(-0.194691\pi\) | |||||||
\(422\) | −494.388 | −1.17154 | ||||||||
\(423\) | 725.626 | 1.71543 | ||||||||
\(424\) | −157.707 | −0.371951 | ||||||||
\(425\) | 285.576 | 0.671942 | ||||||||
\(426\) | − 33.9844i | − 0.0797756i | ||||||||
\(427\) | 220.879 | 0.517280 | ||||||||
\(428\) | − 227.931i | − 0.532549i | ||||||||
\(429\) | 0.283682 | 0.000661264 0 | ||||||||
\(430\) | − 52.8043i | − 0.122801i | ||||||||
\(431\) | − 453.158i | − 1.05141i | −0.850666 | − | 0.525706i | \(-0.823801\pi\) | ||||
0.850666 | − | 0.525706i | \(-0.176199\pi\) | |||||||
\(432\) | 22.7558i | 0.0526756i | ||||||||
\(433\) | − 751.307i | − 1.73512i | −0.497332 | − | 0.867560i | \(-0.665687\pi\) | ||||
0.497332 | − | 0.867560i | \(-0.334313\pi\) | |||||||
\(434\) | −127.818 | −0.294512 | ||||||||
\(435\) | −14.1464 | −0.0325205 | ||||||||
\(436\) | − 136.814i | − 0.313794i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −13.2077 | −0.0301545 | ||||||||
\(439\) | 627.378i | 1.42911i | 0.699581 | + | 0.714553i | \(0.253370\pi\) | ||||
−0.699581 | + | 0.714553i | \(0.746630\pi\) | |||||||
\(440\) | − 14.4279i | − 0.0327906i | ||||||||
\(441\) | −361.262 | −0.819189 | ||||||||
\(442\) | 2.94439 | 0.00666151 | ||||||||
\(443\) | 441.257 | 0.996065 | 0.498032 | − | 0.867158i | \(-0.334056\pi\) | ||||
0.498032 | + | 0.867158i | \(0.334056\pi\) | |||||||
\(444\) | 13.9796 | 0.0314856 | ||||||||
\(445\) | − 10.2173i | − 0.0229603i | ||||||||
\(446\) | 44.9444 | 0.100772 | ||||||||
\(447\) | − 11.3393i | − 0.0253676i | ||||||||
\(448\) | 23.1918 | 0.0517675 | ||||||||
\(449\) | 347.932i | 0.774904i | 0.921890 | + | 0.387452i | \(0.126645\pi\) | ||||
−0.921890 | + | 0.387452i | \(0.873355\pi\) | |||||||
\(450\) | − 302.041i | − 0.671203i | ||||||||
\(451\) | 276.479i | 0.613037i | ||||||||
\(452\) | 163.863i | 0.362528i | ||||||||
\(453\) | 27.1918 | 0.0600261 | ||||||||
\(454\) | 353.171 | 0.777911 | ||||||||
\(455\) | 0.507242i | 0.00111482i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 443.576 | 0.970625 | 0.485312 | − | 0.874341i | \(-0.338706\pi\) | ||||
0.485312 | + | 0.874341i | \(0.338706\pi\) | |||||||
\(458\) | − 367.253i | − 0.801861i | ||||||||
\(459\) | − 67.6928i | − 0.147479i | ||||||||
\(460\) | −34.0908 | −0.0741105 | ||||||||
\(461\) | 195.615 | 0.424328 | 0.212164 | − | 0.977234i | \(-0.431949\pi\) | ||||
0.212164 | + | 0.977234i | \(0.431949\pi\) | |||||||
\(462\) | −6.64694 | −0.0143873 | ||||||||
\(463\) | −720.958 | −1.55715 | −0.778573 | − | 0.627555i | \(-0.784056\pi\) | ||||
−0.778573 | + | 0.627555i | \(0.784056\pi\) | |||||||
\(464\) | − 178.034i | − 0.383693i | ||||||||
\(465\) | −9.90918 | −0.0213101 | ||||||||
\(466\) | − 551.943i | − 1.18443i | ||||||||
\(467\) | 271.889 | 0.582203 | 0.291101 | − | 0.956692i | \(-0.405978\pi\) | ||||
0.291101 | + | 0.956692i | \(0.405978\pi\) | |||||||
\(468\) | − 3.11416i | − 0.00665418i | ||||||||
\(469\) | 343.646i | 0.732721i | ||||||||
\(470\) | − 115.315i | − 0.245352i | ||||||||
\(471\) | − 63.6154i | − 0.135065i | ||||||||
\(472\) | −97.7071 | −0.207007 | ||||||||
\(473\) | −190.463 | −0.402671 | ||||||||
\(474\) | 29.6985i | 0.0626550i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −68.9898 | −0.144937 | ||||||||
\(477\) | − 496.188i | − 1.04023i | ||||||||
\(478\) | − 419.564i | − 0.877749i | ||||||||
\(479\) | 347.197 | 0.724838 | 0.362419 | − | 0.932015i | \(-0.381951\pi\) | ||||
0.362419 | + | 0.932015i | \(0.381951\pi\) | |||||||
\(480\) | 1.79796 | 0.00374575 | ||||||||
\(481\) | −3.84795 | −0.00799990 | ||||||||
\(482\) | −162.854 | −0.337870 | ||||||||
\(483\) | 15.7057i | 0.0325170i | ||||||||
\(484\) | 189.959 | 0.392478 | ||||||||
\(485\) | 148.781i | 0.306766i | ||||||||
\(486\) | −107.596 | −0.221391 | ||||||||
\(487\) | − 495.960i | − 1.01840i | −0.860648 | − | 0.509200i | \(-0.829942\pi\) | ||||
0.860648 | − | 0.509200i | \(-0.170058\pi\) | |||||||
\(488\) | 215.503i | 0.441605i | ||||||||
\(489\) | − 40.4617i | − 0.0827437i | ||||||||
\(490\) | 57.4113i | 0.117166i | ||||||||
\(491\) | 534.348 | 1.08829 | 0.544143 | − | 0.838992i | \(-0.316855\pi\) | ||||
0.544143 | + | 0.838992i | \(0.316855\pi\) | |||||||
\(492\) | −34.4541 | −0.0700286 | ||||||||
\(493\) | 529.605i | 1.07425i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 45.3939 | 0.0917048 | ||||||||
\(496\) | − 124.708i | − 0.251427i | ||||||||
\(497\) | − 219.182i | − 0.441010i | ||||||||
\(498\) | 13.7980 | 0.0277067 | ||||||||
\(499\) | 790.914 | 1.58500 | 0.792499 | − | 0.609874i | \(-0.208780\pi\) | ||||
0.792499 | + | 0.609874i | \(0.208780\pi\) | |||||||
\(500\) | −98.0000 | −0.196000 | ||||||||
\(501\) | −58.3235 | −0.116414 | ||||||||
\(502\) | 692.857i | 1.38019i | ||||||||
\(503\) | 419.681 | 0.834356 | 0.417178 | − | 0.908825i | \(-0.363019\pi\) | ||||
0.417178 | + | 0.908825i | \(0.363019\pi\) | |||||||
\(504\) | 72.9676i | 0.144777i | ||||||||
\(505\) | 140.485 | 0.278188 | ||||||||
\(506\) | 122.964i | 0.243013i | ||||||||
\(507\) | 53.7048i | 0.105927i | ||||||||
\(508\) | 268.293i | 0.528136i | ||||||||
\(509\) | − 803.111i | − 1.57782i | −0.614508 | − | 0.788911i | \(-0.710645\pi\) | ||||
0.614508 | − | 0.788911i | \(-0.289355\pi\) | |||||||
\(510\) | −5.34847 | −0.0104872 | ||||||||
\(511\) | −85.1827 | −0.166698 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −322.318 | −0.627078 | ||||||||
\(515\) | − 113.965i | − 0.221292i | ||||||||
\(516\) | − 23.7350i | − 0.0459980i | ||||||||
\(517\) | −415.939 | −0.804524 | ||||||||
\(518\) | 90.1612 | 0.174056 | ||||||||
\(519\) | 21.1475 | 0.0407465 | ||||||||
\(520\) | −0.494897 | −0.000951726 0 | ||||||||
\(521\) | − 413.663i | − 0.793979i | −0.917823 | − | 0.396990i | \(-0.870055\pi\) | ||||
0.917823 | − | 0.396990i | \(-0.129945\pi\) | |||||||
\(522\) | 560.141 | 1.07307 | ||||||||
\(523\) | − 501.306i | − 0.958520i | −0.877673 | − | 0.479260i | \(-0.840905\pi\) | ||||
0.877673 | − | 0.479260i | \(-0.159095\pi\) | |||||||
\(524\) | −165.505 | −0.315849 | ||||||||
\(525\) | 22.1137i | 0.0421213i | ||||||||
\(526\) | 192.226i | 0.365448i | ||||||||
\(527\) | 370.973i | 0.703934i | ||||||||
\(528\) | − 6.48518i | − 0.0122825i | ||||||||
\(529\) | −238.454 | −0.450764 | ||||||||
\(530\) | −78.8536 | −0.148780 | ||||||||
\(531\) | − 307.413i | − 0.578931i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.48366 | 0.0177930 | ||||||||
\(534\) | − 4.59259i | − 0.00860035i | ||||||||
\(535\) | − 113.965i | − 0.213019i | ||||||||
\(536\) | −335.283 | −0.625527 | ||||||||
\(537\) | 7.69591 | 0.0143313 | ||||||||
\(538\) | −367.571 | −0.683217 | ||||||||
\(539\) | 207.081 | 0.384194 | ||||||||
\(540\) | 11.3779i | 0.0210702i | ||||||||
\(541\) | −393.152 | −0.726714 | −0.363357 | − | 0.931650i | \(-0.618369\pi\) | ||||
−0.363357 | + | 0.931650i | \(0.618369\pi\) | |||||||
\(542\) | − 329.489i | − 0.607914i | ||||||||
\(543\) | 11.3383 | 0.0208808 | ||||||||
\(544\) | − 67.3108i | − 0.123733i | ||||||||
\(545\) | − 68.4072i | − 0.125518i | ||||||||
\(546\) | 0.228000i | 0 0.000417583i | ||||||||
\(547\) | 482.849i | 0.882722i | 0.897330 | + | 0.441361i | \(0.145504\pi\) | ||||
−0.897330 | + | 0.441361i | \(0.854496\pi\) | |||||||
\(548\) | 23.7980 | 0.0434269 | ||||||||
\(549\) | −678.030 | −1.23503 | ||||||||
\(550\) | 173.134i | 0.314790i | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −15.3235 | −0.0277599 | ||||||||
\(553\) | 191.540i | 0.346365i | ||||||||
\(554\) | − 13.3557i | − 0.0241077i | ||||||||
\(555\) | 6.98979 | 0.0125942 | ||||||||
\(556\) | −83.4847 | −0.150152 | ||||||||
\(557\) | −151.706 | −0.272363 | −0.136181 | − | 0.990684i | \(-0.543483\pi\) | ||||
−0.136181 | + | 0.990684i | \(0.543483\pi\) | |||||||
\(558\) | 392.363 | 0.703160 | ||||||||
\(559\) | 6.53318i | 0.0116873i | ||||||||
\(560\) | 11.5959 | 0.0207070 | ||||||||
\(561\) | 19.2917i | 0.0343881i | ||||||||
\(562\) | 221.419 | 0.393984 | ||||||||
\(563\) | − 176.634i | − 0.313737i | −0.987620 | − | 0.156868i | \(-0.949860\pi\) | ||||
0.987620 | − | 0.156868i | \(-0.0501399\pi\) | |||||||
\(564\) | − 51.8331i | − 0.0919026i | ||||||||
\(565\) | 81.9313i | 0.145011i | ||||||||
\(566\) | 4.14956i | 0.00733138i | ||||||||
\(567\) | −226.940 | −0.400247 | ||||||||
\(568\) | 213.848 | 0.376493 | ||||||||
\(569\) | 957.928i | 1.68353i | 0.539844 | + | 0.841765i | \(0.318483\pi\) | ||||
−0.539844 | + | 0.841765i | \(0.681517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 833.242 | 1.45927 | 0.729634 | − | 0.683838i | \(-0.239691\pi\) | ||||
0.729634 | + | 0.683838i | \(0.239691\pi\) | |||||||
\(572\) | 1.78508i | 0.00312077i | ||||||||
\(573\) | − 57.2908i | − 0.0999840i | ||||||||
\(574\) | −222.211 | −0.387128 | ||||||||
\(575\) | 409.090 | 0.711460 | ||||||||
\(576\) | −71.1918 | −0.123597 | ||||||||
\(577\) | −484.595 | −0.839852 | −0.419926 | − | 0.907558i | \(-0.637944\pi\) | ||||
−0.419926 | + | 0.907558i | \(0.637944\pi\) | |||||||
\(578\) | − 208.475i | − 0.360684i | ||||||||
\(579\) | −69.3587 | −0.119790 | ||||||||
\(580\) | − 89.0168i | − 0.153477i | ||||||||
\(581\) | 88.9898 | 0.153167 | ||||||||
\(582\) | 66.8757i | 0.114907i | ||||||||
\(583\) | 284.422i | 0.487860i | ||||||||
\(584\) | − 83.1096i | − 0.142311i | ||||||||
\(585\) | − 1.55708i | − 0.00266167i | ||||||||
\(586\) | 470.030 | 0.802098 | ||||||||
\(587\) | −618.864 | −1.05428 | −0.527141 | − | 0.849778i | \(-0.676736\pi\) | ||||
−0.527141 | + | 0.849778i | \(0.676736\pi\) | |||||||
\(588\) | 25.8058i | 0.0438874i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −48.8536 | −0.0828027 | ||||||||
\(591\) | 108.094i | 0.182899i | ||||||||
\(592\) | 87.9670i | 0.148593i | ||||||||
\(593\) | −187.940 | −0.316931 | −0.158465 | − | 0.987365i | \(-0.550655\pi\) | ||||
−0.158465 | + | 0.987365i | \(0.550655\pi\) | |||||||
\(594\) | 41.0398 | 0.0690906 | ||||||||
\(595\) | −34.4949 | −0.0579746 | ||||||||
\(596\) | 71.3531 | 0.119720 | ||||||||
\(597\) | − 105.963i | − 0.177493i | ||||||||
\(598\) | 4.21786 | 0.00705328 | ||||||||
\(599\) | 80.3133i | 0.134079i | 0.997750 | + | 0.0670394i | \(0.0213553\pi\) | ||||
−0.997750 | + | 0.0670394i | \(0.978645\pi\) | |||||||
\(600\) | −21.5755 | −0.0359592 | ||||||||
\(601\) | − 665.929i | − 1.10804i | −0.832505 | − | 0.554018i | \(-0.813094\pi\) | ||||
0.832505 | − | 0.554018i | \(-0.186906\pi\) | |||||||
\(602\) | − 153.079i | − 0.254283i | ||||||||
\(603\) | − 1054.89i | − 1.74940i | ||||||||
\(604\) | 171.105i | 0.283287i | ||||||||
\(605\) | 94.9796 | 0.156991 | ||||||||
\(606\) | 63.1464 | 0.104202 | ||||||||
\(607\) | 105.952i | 0.174550i | 0.996184 | + | 0.0872751i | \(0.0278159\pi\) | ||||
−0.996184 | + | 0.0872751i | \(0.972184\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −41.0102 | −0.0673402 | ||||||||
\(610\) | 107.752i | 0.176642i | ||||||||
\(611\) | 14.2673i | 0.0233508i | ||||||||
\(612\) | 211.778 | 0.346042 | ||||||||
\(613\) | −1138.34 | −1.85700 | −0.928501 | − | 0.371331i | \(-0.878902\pi\) | ||||
−0.928501 | + | 0.371331i | \(0.878902\pi\) | |||||||
\(614\) | −364.095 | −0.592989 | ||||||||
\(615\) | −17.2270 | −0.0280114 | ||||||||
\(616\) | − 41.8261i | − 0.0678995i | ||||||||
\(617\) | 918.262 | 1.48827 | 0.744135 | − | 0.668030i | \(-0.232862\pi\) | ||||
0.744135 | + | 0.668030i | \(0.232862\pi\) | |||||||
\(618\) | − 51.2263i | − 0.0828904i | ||||||||
\(619\) | −1123.85 | −1.81559 | −0.907793 | − | 0.419418i | \(-0.862234\pi\) | ||||
−0.907793 | + | 0.419418i | \(0.862234\pi\) | |||||||
\(620\) | − 62.3538i | − 0.100571i | ||||||||
\(621\) | − 96.9707i | − 0.156152i | ||||||||
\(622\) | 307.827i | 0.494898i | ||||||||
\(623\) | − 29.6198i | − 0.0475439i | ||||||||
\(624\) | −0.222451 | −0.000356492 0 | ||||||||
\(625\) | 551.000 | 0.881600 | ||||||||
\(626\) | − 438.748i | − 0.700876i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 400.302 | 0.637424 | ||||||||
\(629\) | − 261.679i | − 0.416024i | ||||||||
\(630\) | 36.4838i | 0.0579108i | ||||||||
\(631\) | 80.5505 | 0.127655 | 0.0638277 | − | 0.997961i | \(-0.479669\pi\) | ||||
0.0638277 | + | 0.997961i | \(0.479669\pi\) | |||||||
\(632\) | −186.879 | −0.295694 | ||||||||
\(633\) | −111.111 | −0.175531 | ||||||||
\(634\) | −488.166 | −0.769978 | ||||||||
\(635\) | 134.146i | 0.211254i | ||||||||
\(636\) | −35.4439 | −0.0557294 | ||||||||
\(637\) | − 7.10318i | − 0.0111510i | ||||||||
\(638\) | −321.081 | −0.503261 | ||||||||
\(639\) | 672.822i | 1.05293i | ||||||||
\(640\) | 11.3137i | 0.0176777i | ||||||||
\(641\) | − 495.243i | − 0.772610i | −0.922371 | − | 0.386305i | \(-0.873751\pi\) | ||||
0.922371 | − | 0.386305i | \(-0.126249\pi\) | |||||||
\(642\) | − 51.2263i | − 0.0797917i | ||||||||
\(643\) | 490.246 | 0.762436 | 0.381218 | − | 0.924485i | \(-0.375505\pi\) | ||||
0.381218 | + | 0.924485i | \(0.375505\pi\) | |||||||
\(644\) | −98.8286 | −0.153461 | ||||||||
\(645\) | − 11.8675i | − 0.0183992i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −494.132 | −0.763727 | −0.381864 | − | 0.924219i | \(-0.624718\pi\) | ||||
−0.381864 | + | 0.924219i | \(0.624718\pi\) | |||||||
\(648\) | − 221.417i | − 0.341693i | ||||||||
\(649\) | 176.213i | 0.271515i | ||||||||
\(650\) | 5.93877 | 0.00913657 | ||||||||
\(651\) | −28.7265 | −0.0441268 | ||||||||
\(652\) | 254.606 | 0.390500 | ||||||||
\(653\) | 475.383 | 0.727998 | 0.363999 | − | 0.931399i | \(-0.381411\pi\) | ||||
0.363999 | + | 0.931399i | \(0.381411\pi\) | |||||||
\(654\) | − 30.7483i | − 0.0470158i | ||||||||
\(655\) | −82.7526 | −0.126340 | ||||||||
\(656\) | − 216.803i | − 0.330493i | ||||||||
\(657\) | 261.485 | 0.397998 | ||||||||
\(658\) | − 334.297i | − 0.508050i | ||||||||
\(659\) | − 570.517i | − 0.865732i | −0.901458 | − | 0.432866i | \(-0.857502\pi\) | ||||
0.901458 | − | 0.432866i | \(-0.142498\pi\) | |||||||
\(660\) | − 3.24259i | − 0.00491301i | ||||||||
\(661\) | 21.5888i | 0.0326608i | 0.999867 | + | 0.0163304i | \(0.00519835\pi\) | ||||
−0.999867 | + | 0.0163304i | \(0.994802\pi\) | |||||||
\(662\) | −689.171 | −1.04104 | ||||||||
\(663\) | 0.661736 | 0.000998093 0 | ||||||||
\(664\) | 86.8241i | 0.130759i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −276.767 | −0.415567 | ||||||||
\(667\) | 758.664i | 1.13743i | ||||||||
\(668\) | − 367.002i | − 0.549404i | ||||||||
\(669\) | 10.1010 | 0.0150987 | ||||||||
\(670\) | −167.641 | −0.250211 | ||||||||
\(671\) | 388.656 | 0.579219 | ||||||||
\(672\) | 5.21225 | 0.00775632 | ||||||||
\(673\) | 256.395i | 0.380973i | 0.981690 | + | 0.190486i | \(0.0610065\pi\) | ||||
−0.981690 | + | 0.190486i | \(0.938993\pi\) | |||||||
\(674\) | −235.793 | −0.349842 | ||||||||
\(675\) | − 136.535i | − 0.202274i | ||||||||
\(676\) | −337.939 | −0.499909 | ||||||||
\(677\) | − 662.815i | − 0.979048i | −0.871990 | − | 0.489524i | \(-0.837171\pi\) | ||||
0.871990 | − | 0.489524i | \(-0.162829\pi\) | |||||||
\(678\) | 36.8273i | 0.0543175i | ||||||||
\(679\) | 431.314i | 0.635220i | ||||||||
\(680\) | − 33.6554i | − 0.0494932i | ||||||||
\(681\) | 79.3735 | 0.116554 | ||||||||
\(682\) | −224.908 | −0.329777 | ||||||||
\(683\) | − 310.334i | − 0.454369i | −0.973852 | − | 0.227184i | \(-0.927048\pi\) | ||||
0.973852 | − | 0.227184i | \(-0.0729520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.8990 | 0.0173708 | ||||||||
\(686\) | 367.323i | 0.535457i | ||||||||
\(687\) | − 82.5381i | − 0.120143i | ||||||||
\(688\) | 149.353 | 0.217083 | ||||||||
\(689\) | 9.75611 | 0.0141598 | ||||||||
\(690\) | −7.66174 | −0.0111040 | ||||||||
\(691\) | 187.789 | 0.271764 | 0.135882 | − | 0.990725i | \(-0.456613\pi\) | ||||
0.135882 | + | 0.990725i | \(0.456613\pi\) | |||||||
\(692\) | 133.071i | 0.192299i | ||||||||
\(693\) | 131.596 | 0.189893 | ||||||||
\(694\) | 534.208i | 0.769753i | ||||||||
\(695\) | −41.7423 | −0.0600609 | ||||||||
\(696\) | − 40.0121i | − 0.0574887i | ||||||||
\(697\) | 644.934i | 0.925300i | ||||||||
\(698\) | − 829.342i | − 1.18817i | ||||||||
\(699\) | − 124.046i | − 0.177463i | ||||||||
\(700\) | −139.151 | −0.198787 | ||||||||
\(701\) | 541.636 | 0.772661 | 0.386331 | − | 0.922360i | \(-0.373742\pi\) | ||||
0.386331 | + | 0.922360i | \(0.373742\pi\) | |||||||
\(702\) | − 1.40773i | − 0.00200531i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 40.8082 | 0.0579661 | ||||||||
\(705\) | − 25.9165i | − 0.0367611i | ||||||||
\(706\) | 674.322i | 0.955130i | ||||||||
\(707\) | 407.262 | 0.576043 | ||||||||
\(708\) | −21.9592 | −0.0310158 | ||||||||
\(709\) | −491.243 | −0.692867 | −0.346434 | − | 0.938074i | \(-0.612607\pi\) | ||||
−0.346434 | + | 0.938074i | \(0.612607\pi\) | |||||||
\(710\) | 106.924 | 0.150597 | ||||||||
\(711\) | − 587.969i | − 0.826961i | ||||||||
\(712\) | 28.8990 | 0.0405885 | ||||||||
\(713\) | 531.423i | 0.745334i | ||||||||
\(714\) | −15.5051 | −0.0217158 | ||||||||
\(715\) | 0.892539i | 0.00124831i | ||||||||
\(716\) | 48.4267i | 0.0676351i | ||||||||
\(717\) | − 94.2949i | − 0.131513i | ||||||||
\(718\) | − 349.889i | − 0.487310i | ||||||||
\(719\) | −575.468 | −0.800373 | −0.400186 | − | 0.916434i | \(-0.631055\pi\) | ||||
−0.400186 | + | 0.916434i | \(0.631055\pi\) | |||||||
\(720\) | −35.5959 | −0.0494388 | ||||||||
\(721\) | − 330.383i | − 0.458229i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36.6005 | −0.0506231 | ||||||||
\(724\) | 71.3464i | 0.0985447i | ||||||||
\(725\) | 1068.20i | 1.47338i | ||||||||
\(726\) | 42.6924 | 0.0588049 | ||||||||
\(727\) | −819.105 | −1.12669 | −0.563346 | − | 0.826221i | \(-0.690486\pi\) | ||||
−0.563346 | + | 0.826221i | \(0.690486\pi\) | |||||||
\(728\) | −1.43470 | −0.00197074 | ||||||||
\(729\) | 680.362 | 0.933282 | ||||||||
\(730\) | − 41.5548i | − 0.0569244i | ||||||||
\(731\) | −444.287 | −0.607780 | ||||||||
\(732\) | 48.4332i | 0.0661656i | ||||||||
\(733\) | 804.332 | 1.09731 | 0.548657 | − | 0.836047i | \(-0.315139\pi\) | ||||
0.548657 | + | 0.836047i | \(0.315139\pi\) | |||||||
\(734\) | 684.372i | 0.932387i | ||||||||
\(735\) | 12.9029i | 0.0175550i | ||||||||
\(736\) | − 96.4234i | − 0.131010i | ||||||||
\(737\) | 604.677i | 0.820457i | ||||||||
\(738\) | 682.120 | 0.924282 | ||||||||
\(739\) | 75.8627 | 0.102656 | 0.0513280 | − | 0.998682i | \(-0.483655\pi\) | ||||
0.0513280 | + | 0.998682i | \(0.483655\pi\) | |||||||
\(740\) | 43.9835i | 0.0594371i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −228.595 | −0.308079 | ||||||||
\(743\) | 584.059i | 0.786082i | 0.919521 | + | 0.393041i | \(0.128577\pi\) | ||||
−0.919521 | + | 0.393041i | \(0.871423\pi\) | |||||||
\(744\) | − 28.0274i | − 0.0376712i | ||||||||
\(745\) | 35.6765 | 0.0478880 | ||||||||
\(746\) | 199.273 | 0.267123 | ||||||||
\(747\) | −273.171 | −0.365691 | ||||||||
\(748\) | −121.394 | −0.162291 | ||||||||
\(749\) | − 330.383i | − 0.441099i | ||||||||
\(750\) | −22.0250 | −0.0293667 | ||||||||
\(751\) | − 593.437i | − 0.790196i | −0.918639 | − | 0.395098i | \(-0.870711\pi\) | ||||
0.918639 | − | 0.395098i | \(-0.129289\pi\) | |||||||
\(752\) | 326.161 | 0.433725 | ||||||||
\(753\) | 155.716i | 0.206794i | ||||||||
\(754\) | 11.0135i | 0.0146068i | ||||||||
\(755\) | 85.5527i | 0.113315i | ||||||||
\(756\) | 32.9844i | 0.0436301i | ||||||||
\(757\) | −556.514 | −0.735158 | −0.367579 | − | 0.929992i | \(-0.619813\pi\) | ||||
−0.367579 | + | 0.929992i | \(0.619813\pi\) | |||||||
\(758\) | −662.747 | −0.874336 | ||||||||
\(759\) | 27.6356i | 0.0364106i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1211.85 | −1.59244 | −0.796219 | − | 0.605008i | \(-0.793170\pi\) | ||||
−0.796219 | + | 0.605008i | \(0.793170\pi\) | |||||||
\(762\) | 60.2975i | 0.0791305i | ||||||||
\(763\) | − 198.311i | − 0.259910i | ||||||||
\(764\) | 360.504 | 0.471864 | ||||||||
\(765\) | 105.889 | 0.138417 | ||||||||
\(766\) | 788.005 | 1.02873 | ||||||||
\(767\) | 6.04438 | 0.00788054 | ||||||||
\(768\) | 5.08540i | 0.00662161i | ||||||||
\(769\) | −958.231 | −1.24607 | −0.623037 | − | 0.782193i | \(-0.714101\pi\) | ||||
−0.623037 | + | 0.782193i | \(0.714101\pi\) | |||||||
\(770\) | − 20.9130i | − 0.0271598i | ||||||||
\(771\) | −72.4393 | −0.0939550 | ||||||||
\(772\) | − 436.441i | − 0.565339i | ||||||||
\(773\) | 466.972i | 0.604103i | 0.953292 | + | 0.302051i | \(0.0976714\pi\) | ||||
−0.953292 | + | 0.302051i | \(0.902329\pi\) | |||||||
\(774\) | 469.904i | 0.607111i | ||||||||
\(775\) | 748.246i | 0.965479i | ||||||||
\(776\) | −420.817 | −0.542290 | ||||||||
\(777\) | 20.2633 | 0.0260789 | ||||||||
\(778\) | 131.692i | 0.169270i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.111226 | −0.000142597 0 | ||||||||
\(781\) | − 385.671i | − 0.493817i | ||||||||
\(782\) | 286.835i | 0.366797i | ||||||||
\(783\) | 253.207 | 0.323380 | ||||||||
\(784\) | −162.384 | −0.207122 | ||||||||
\(785\) | 200.151 | 0.254969 | ||||||||
\(786\) | −37.1964 | −0.0473237 | ||||||||
\(787\) | 1410.48i | 1.79223i | 0.443824 | + | 0.896114i | \(0.353621\pi\) | ||||
−0.443824 | + | 0.896114i | \(0.646379\pi\) | |||||||
\(788\) | −680.182 | −0.863175 | ||||||||
\(789\) | 43.2017i | 0.0547550i | ||||||||
\(790\) | −93.4393 | −0.118278 | ||||||||
\(791\) | 237.517i | 0.300275i | ||||||||
\(792\) | 128.393i | 0.162113i | ||||||||
\(793\) | − 13.3315i | − 0.0168115i | ||||||||
\(794\) | 366.795i | 0.461958i | ||||||||
\(795\) | −17.7219 | −0.0222917 | ||||||||
\(796\) | 666.777 | 0.837659 | ||||||||
\(797\) | − 774.540i | − 0.971819i | −0.874009 | − | 0.485909i | \(-0.838489\pi\) | ||||
0.874009 | − | 0.485909i | \(-0.161511\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −970.246 | −1.21433 | ||||||||
\(800\) | − 135.765i | − 0.169706i | ||||||||
\(801\) | 90.9238i | 0.113513i | ||||||||
\(802\) | 636.025 | 0.793049 | ||||||||
\(803\) | −149.887 | −0.186658 | ||||||||
\(804\) | −75.3531 | −0.0937227 | ||||||||
\(805\) | −49.4143 | −0.0613842 | ||||||||
\(806\) | 7.71469i | 0.00957157i | ||||||||
\(807\) | −82.6097 | −0.102366 | ||||||||
\(808\) | 397.351i | 0.491771i | ||||||||
\(809\) | −1114.09 | −1.37712 | −0.688559 | − | 0.725180i | \(-0.741756\pi\) | ||||
−0.688559 | + | 0.725180i | \(0.741756\pi\) | |||||||
\(810\) | − 110.708i | − 0.136677i | ||||||||
\(811\) | 15.8951i | 0.0195994i | 0.999952 | + | 0.00979970i | \(0.00311939\pi\) | ||||
−0.999952 | + | 0.00979970i | \(0.996881\pi\) | |||||||
\(812\) | − 258.058i | − 0.317805i | ||||||||
\(813\) | − 74.0510i | − 0.0910837i | ||||||||
\(814\) | 158.647 | 0.194898 | ||||||||
\(815\) | 127.303 | 0.156200 | ||||||||
\(816\) | − 15.1278i | − 0.0185389i | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 148.329 | 0.181331 | ||||||||
\(819\) | − 4.51394i | − 0.00551152i | ||||||||
\(820\) | − 108.402i | − 0.132197i | ||||||||
\(821\) | −204.889 | −0.249560 | −0.124780 | − | 0.992184i | \(-0.539823\pi\) | ||||
−0.124780 | + | 0.992184i | \(0.539823\pi\) | |||||||
\(822\) | 5.34847 | 0.00650665 | ||||||||
\(823\) | 1242.10 | 1.50924 | 0.754619 | − | 0.656163i | \(-0.227822\pi\) | ||||
0.754619 | + | 0.656163i | \(0.227822\pi\) | |||||||
\(824\) | 322.343 | 0.391193 | ||||||||
\(825\) | 38.9111i | 0.0471649i | ||||||||
\(826\) | −141.626 | −0.171459 | ||||||||
\(827\) | 1143.30i | 1.38247i | 0.722631 | + | 0.691234i | \(0.242933\pi\) | ||||
−0.722631 | + | 0.691234i | \(0.757067\pi\) | |||||||
\(828\) | 303.373 | 0.366393 | ||||||||
\(829\) | 1080.66i | 1.30357i | 0.758404 | + | 0.651784i | \(0.225979\pi\) | ||||
−0.758404 | + | 0.651784i | \(0.774021\pi\) | |||||||
\(830\) | 43.4120i | 0.0523036i | ||||||||
\(831\) | − 3.00161i | − 0.00361205i | ||||||||
\(832\) | − 1.39978i | − 0.00168243i | ||||||||
\(833\) | 483.050 | 0.579892 | ||||||||
\(834\) | −18.7628 | −0.0224973 | ||||||||
\(835\) | − 183.501i | − 0.219762i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 177.364 | 0.211905 | ||||||||
\(838\) | 654.953i | 0.781566i | ||||||||
\(839\) | 672.726i | 0.801819i | 0.916118 | + | 0.400909i | \(0.131306\pi\) | ||||
−0.916118 | + | 0.400909i | \(0.868694\pi\) | |||||||
\(840\) | 2.60612 | 0.00310253 | ||||||||
\(841\) | −1140.00 | −1.35553 | ||||||||
\(842\) | 683.753 | 0.812058 | ||||||||
\(843\) | 49.7628 | 0.0590306 | ||||||||
\(844\) | − 699.171i | − 0.828401i | ||||||||
\(845\) | −168.969 | −0.199964 | ||||||||
\(846\) | 1026.19i | 1.21299i | ||||||||
\(847\) | 275.344 | 0.325081 | ||||||||
\(848\) | − 223.032i | − 0.263009i | ||||||||
\(849\) | 0.932592i | 0.00109846i | ||||||||
\(850\) | 403.865i | 0.475135i | ||||||||
\(851\) | − 374.858i | − 0.440491i | ||||||||
\(852\) | 48.0612 | 0.0564099 | ||||||||
\(853\) | 247.241 | 0.289849 | 0.144924 | − | 0.989443i | \(-0.453706\pi\) | ||||
0.144924 | + | 0.989443i | \(0.453706\pi\) | |||||||
\(854\) | 312.369i | 0.365772i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 322.343 | 0.376569 | ||||||||
\(857\) | − 710.402i | − 0.828941i | −0.910063 | − | 0.414470i | \(-0.863967\pi\) | ||||
0.910063 | − | 0.414470i | \(-0.136033\pi\) | |||||||
\(858\) | 0.401187i | 0 0.000467584i | ||||||||
\(859\) | 1010.37 | 1.17621 | 0.588106 | − | 0.808784i | \(-0.299874\pi\) | ||||
0.588106 | + | 0.808784i | \(0.299874\pi\) | |||||||
\(860\) | 74.6765 | 0.0868332 | ||||||||
\(861\) | −49.9408 | −0.0580033 | ||||||||
\(862\) | 640.863 | 0.743460 | ||||||||
\(863\) | − 455.826i | − 0.528188i | −0.964497 | − | 0.264094i | \(-0.914927\pi\) | ||||
0.964497 | − | 0.264094i | \(-0.0850729\pi\) | |||||||
\(864\) | −32.1816 | −0.0372473 | ||||||||
\(865\) | 66.5355i | 0.0769196i | ||||||||
\(866\) | 1062.51 | 1.22692 | ||||||||
\(867\) | − 46.8538i | − 0.0540412i | ||||||||
\(868\) | − 180.762i | − 0.208252i | ||||||||
\(869\) | 337.032i | 0.387839i | ||||||||
\(870\) | − 20.0061i | − 0.0229955i | ||||||||
\(871\) | 20.7413 | 0.0238132 | ||||||||
\(872\) | 193.485 | 0.221886 | ||||||||
\(873\) | − 1324.00i | − 1.51661i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −142.050 | −0.162343 | ||||||||
\(876\) | − 18.6785i | − 0.0213224i | ||||||||
\(877\) | 651.320i | 0.742668i | 0.928499 | + | 0.371334i | \(0.121100\pi\) | ||||
−0.928499 | + | 0.371334i | \(0.878900\pi\) | |||||||
\(878\) | −887.246 | −1.01053 | ||||||||
\(879\) | 105.637 | 0.120178 | ||||||||
\(880\) | 20.4041 | 0.0231865 | ||||||||
\(881\) | −518.293 | −0.588301 | −0.294150 | − | 0.955759i | \(-0.595037\pi\) | ||||
−0.294150 | + | 0.955759i | \(0.595037\pi\) | |||||||
\(882\) | − 510.902i | − 0.579254i | ||||||||
\(883\) | −673.064 | −0.762247 | −0.381123 | − | 0.924524i | \(-0.624463\pi\) | ||||
−0.381123 | + | 0.924524i | \(0.624463\pi\) | |||||||
\(884\) | 4.16399i | 0.00471040i | ||||||||
\(885\) | −10.9796 | −0.0124063 | ||||||||
\(886\) | 624.031i | 0.704324i | ||||||||
\(887\) | − 1496.87i | − 1.68756i | −0.536688 | − | 0.843781i | \(-0.680325\pi\) | ||||
0.536688 | − | 0.843781i | \(-0.319675\pi\) | |||||||
\(888\) | 19.7701i | 0.0222637i | ||||||||
\(889\) | 388.888i | 0.437444i | ||||||||
\(890\) | 14.4495 | 0.0162354 | ||||||||
\(891\) | −399.321 | −0.448172 | ||||||||
\(892\) | 63.5610i | 0.0712567i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 16.0362 | 0.0179376 | ||||||||
\(895\) | 24.2134i | 0.0270540i | ||||||||
\(896\) | 32.7982i | 0.0366051i | ||||||||
\(897\) | 0.947943 | 0.00105679 | ||||||||
\(898\) | −492.050 | −0.547940 | ||||||||
\(899\) | −1387.63 | −1.54353 | ||||||||
\(900\) | 427.151 | 0.474612 | ||||||||
\(901\) | 663.462i | 0.736362i | ||||||||
\(902\) | −391.001 | −0.433482 | ||||||||
\(903\) | − 34.4036i | − 0.0380992i | ||||||||
\(904\) | −231.737 | −0.256346 | ||||||||
\(905\) | 35.6732i | 0.0394179i | ||||||||
\(906\) | 38.4551i | 0.0424449i | ||||||||
\(907\) | 280.724i | 0.309508i | 0.987953 | + | 0.154754i | \(0.0494585\pi\) | ||||
−0.987953 | + | 0.154754i | \(0.950541\pi\) | |||||||
\(908\) | 499.460i | 0.550066i | ||||||||
\(909\) | −1250.17 | −1.37532 | ||||||||
\(910\) | −0.717349 | −0.000788295 0 | ||||||||
\(911\) | − 783.689i | − 0.860252i | −0.902769 | − | 0.430126i | \(-0.858469\pi\) | ||||
0.902769 | − | 0.430126i | \(-0.141531\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 156.586 | 0.171507 | ||||||||
\(914\) | 627.310i | 0.686335i | ||||||||
\(915\) | 24.2166i | 0.0264662i | ||||||||
\(916\) | 519.373 | 0.567002 | ||||||||
\(917\) | −239.898 | −0.261612 | ||||||||
\(918\) | 95.7321 | 0.104283 | ||||||||
\(919\) | −220.334 | −0.239754 | −0.119877 | − | 0.992789i | \(-0.538250\pi\) | ||||
−0.119877 | + | 0.992789i | \(0.538250\pi\) | |||||||
\(920\) | − 48.2117i | − 0.0524040i | ||||||||
\(921\) | −81.8286 | −0.0888475 | ||||||||
\(922\) | 276.642i | 0.300045i | ||||||||
\(923\) | −13.2291 | −0.0143327 | ||||||||
\(924\) | − 9.40020i | − 0.0101734i | ||||||||
\(925\) | − 527.802i | − 0.570597i | ||||||||
\(926\) | − 1019.59i | − 1.10107i | ||||||||
\(927\) | 1014.18i | 1.09404i | ||||||||
\(928\) | 251.778 | 0.271312 | ||||||||
\(929\) | 1229.48 | 1.32345 | 0.661724 | − | 0.749747i | \(-0.269825\pi\) | ||||
0.661724 | + | 0.749747i | \(0.269825\pi\) | |||||||
\(930\) | − 14.0137i | − 0.0150685i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 780.565 | 0.837516 | ||||||||
\(933\) | 69.1825i | 0.0741506i | ||||||||
\(934\) | 384.509i | 0.411680i | ||||||||
\(935\) | −60.6969 | −0.0649165 | ||||||||
\(936\) | 4.40408 | 0.00470522 | ||||||||
\(937\) | −134.212 | −0.143236 | −0.0716181 | − | 0.997432i | \(-0.522816\pi\) | ||||
−0.0716181 | + | 0.997432i | \(0.522816\pi\) | |||||||
\(938\) | −485.989 | −0.518112 | ||||||||
\(939\) | − 98.6064i | − 0.105012i | ||||||||
\(940\) | 163.081 | 0.173490 | ||||||||
\(941\) | 598.537i | 0.636064i | 0.948080 | + | 0.318032i | \(0.103022\pi\) | ||||
−0.948080 | + | 0.318032i | \(0.896978\pi\) | |||||||
\(942\) | 89.9658 | 0.0955051 | ||||||||
\(943\) | 923.875i | 0.979719i | ||||||||
\(944\) | − 138.179i | − 0.146376i | ||||||||
\(945\) | 16.4922i | 0.0174520i | ||||||||
\(946\) | − 269.356i | − 0.284731i | ||||||||
\(947\) | 820.530 | 0.866452 | 0.433226 | − | 0.901285i | \(-0.357375\pi\) | ||||
0.433226 | + | 0.901285i | \(0.357375\pi\) | |||||||
\(948\) | −42.0000 | −0.0443038 | ||||||||
\(949\) | 5.14134i | 0.00541764i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −109.713 | −0.115366 | ||||||||
\(952\) | − 97.5663i | − 0.102486i | ||||||||
\(953\) | − 78.6775i | − 0.0825577i | −0.999148 | − | 0.0412789i | \(-0.986857\pi\) | ||||
0.999148 | − | 0.0412789i | \(-0.0131432\pi\) | |||||||
\(954\) | 701.716 | 0.735552 | ||||||||
\(955\) | 180.252 | 0.188746 | ||||||||
\(956\) | 593.353 | 0.620662 | ||||||||
\(957\) | −72.1612 | −0.0754036 | ||||||||
\(958\) | 491.011i | 0.512538i | ||||||||
\(959\) | 34.4949 | 0.0359697 | ||||||||
\(960\) | 2.54270i | 0.00264864i | ||||||||
\(961\) | −11.0000 | −0.0114464 | ||||||||
\(962\) | − 5.44183i | − 0.00565679i | ||||||||
\(963\) | 1014.18i | 1.05314i | ||||||||
\(964\) | − 230.310i | − 0.238911i | ||||||||
\(965\) | − 218.221i | − 0.226135i | ||||||||
\(966\) | −22.2112 | −0.0229930 | ||||||||
\(967\) | 1329.26 | 1.37462 | 0.687310 | − | 0.726365i | \(-0.258792\pi\) | ||||
0.687310 | + | 0.726365i | \(0.258792\pi\) | |||||||
\(968\) | 268.643i | 0.277524i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −210.409 | −0.216916 | ||||||||
\(971\) | − 568.787i | − 0.585774i | −0.956147 | − | 0.292887i | \(-0.905384\pi\) | ||||
0.956147 | − | 0.292887i | \(-0.0946160\pi\) | |||||||
\(972\) | − 152.164i | − 0.156547i | ||||||||
\(973\) | −121.010 | −0.124368 | ||||||||
\(974\) | 701.394 | 0.720117 | ||||||||
\(975\) | 1.33471 | 0.00136893 | ||||||||
\(976\) | −304.767 | −0.312262 | ||||||||
\(977\) | 884.903i | 0.905735i | 0.891578 | + | 0.452867i | \(0.149599\pi\) | ||||
−0.891578 | + | 0.452867i | \(0.850401\pi\) | |||||||
\(978\) | 57.2214 | 0.0585086 | ||||||||
\(979\) | − 52.1188i | − 0.0532368i | ||||||||
\(980\) | −81.1918 | −0.0828488 | ||||||||
\(981\) | 608.754i | 0.620544i | ||||||||
\(982\) | 755.683i | 0.769534i | ||||||||
\(983\) | 335.835i | 0.341643i | 0.985302 | + | 0.170821i | \(0.0546421\pi\) | ||||
−0.985302 | + | 0.170821i | \(0.945358\pi\) | |||||||
\(984\) | − 48.7254i | − 0.0495177i | ||||||||
\(985\) | −340.091 | −0.345270 | ||||||||
\(986\) | −748.974 | −0.759608 | ||||||||
\(987\) | − 75.1315i | − 0.0761211i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −636.446 | −0.643525 | ||||||||
\(990\) | 64.1966i | 0.0648451i | ||||||||
\(991\) | − 567.458i | − 0.572611i | −0.958138 | − | 0.286306i | \(-0.907573\pi\) | ||||
0.958138 | − | 0.286306i | \(-0.0924273\pi\) | |||||||
\(992\) | 176.363 | 0.177786 | ||||||||
\(993\) | −154.888 | −0.155980 | ||||||||
\(994\) | 309.970 | 0.311841 | ||||||||
\(995\) | 333.388 | 0.335064 | ||||||||
\(996\) | 19.5133i | 0.0195916i | ||||||||
\(997\) | −434.757 | −0.436065 | −0.218033 | − | 0.975941i | \(-0.569964\pi\) | ||||
−0.218033 | + | 0.975941i | \(0.569964\pi\) | |||||||
\(998\) | 1118.52i | 1.12076i | ||||||||
\(999\) | −125.110 | −0.125235 |
(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 | 722.3.b.b.721.4 | 4 | ||
19.11 | even | 3 | 38.3.d.a.31.2 | yes | 4 | ||
19.12 | odd | 6 | 38.3.d.a.27.2 | ✓ | 4 | ||
19.18 | odd | 2 | inner | 722.3.b.b.721.1 | 4 | ||
57.11 | odd | 6 | 342.3.m.a.145.1 | 4 | |||
57.50 | even | 6 | 342.3.m.a.217.1 | 4 | |||
76.11 | odd | 6 | 304.3.r.a.145.2 | 4 | |||
76.31 | even | 6 | 304.3.r.a.65.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.3.d.a.27.2 | ✓ | 4 | 19.12 | odd | 6 | ||
38.3.d.a.31.2 | yes | 4 | 19.11 | even | 3 | ||
304.3.r.a.65.2 | 4 | 76.31 | even | 6 | |||
304.3.r.a.145.2 | 4 | 76.11 | odd | 6 | |||
342.3.m.a.145.1 | 4 | 57.11 | odd | 6 | |||
342.3.m.a.217.1 | 4 | 57.50 | even | 6 | |||
722.3.b.b.721.1 | 4 | 19.18 | odd | 2 | inner | ||
722.3.b.b.721.4 | 4 | 1.1 | even | 1 | trivial |