Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(1,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.a (trivial) |
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: | yes |
Analytic conductor: | \(23.8957735523\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2292.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 13x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.10645\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.174985 | 0.0618664 | 0.0309332 | − | 0.999521i | \(-0.490152\pi\) | ||||
0.0309332 | + | 0.999521i | \(0.490152\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.96938 | −0.996173 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.46371 | 0.456998 | 0.228499 | − | 0.973544i | \(-0.426618\pi\) | ||||
0.228499 | + | 0.973544i | \(0.426618\pi\) | |||||||
\(8\) | −2.79440 | −0.123496 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.874923 | −0.0276675 | ||||||||
\(11\) | 31.5083 | 0.863645 | 0.431823 | − | 0.901959i | \(-0.357871\pi\) | ||||
0.431823 | + | 0.901959i | \(0.357871\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 26.8696 | 0.573252 | 0.286626 | − | 0.958043i | \(-0.407466\pi\) | ||||
0.286626 | + | 0.958043i | \(0.407466\pi\) | |||||||
\(14\) | 1.48102 | 0.0282728 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 63.2661 | 0.988532 | ||||||||
\(17\) | 44.3307 | 0.632457 | 0.316229 | − | 0.948683i | \(-0.397583\pi\) | ||||
0.316229 | + | 0.948683i | \(0.397583\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −90.2082 | −1.08922 | −0.544610 | − | 0.838689i | \(-0.683322\pi\) | ||||
−0.544610 | + | 0.838689i | \(0.683322\pi\) | |||||||
\(20\) | 39.8469 | 0.445502 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.51346 | 0.0534306 | ||||||||
\(23\) | −194.257 | −1.76111 | −0.880553 | − | 0.473947i | \(-0.842829\pi\) | ||||
−0.880553 | + | 0.473947i | \(0.842829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 4.70176 | 0.0354650 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −67.4506 | −0.455248 | ||||||||
\(29\) | −3.74371 | −0.0239721 | −0.0119860 | − | 0.999928i | \(-0.503815\pi\) | ||||
−0.0119860 | + | 0.999928i | \(0.503815\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −251.664 | −1.45807 | −0.729035 | − | 0.684477i | \(-0.760031\pi\) | ||||
−0.729035 | + | 0.684477i | \(0.760031\pi\) | |||||||
\(32\) | 33.4258 | 0.184653 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.75719 | 0.0391278 | ||||||||
\(35\) | −42.3186 | −0.204376 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −62.2293 | −0.276498 | −0.138249 | − | 0.990397i | \(-0.544147\pi\) | ||||
−0.138249 | + | 0.990397i | \(0.544147\pi\) | |||||||
\(38\) | −15.7850 | −0.0673861 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.9720 | 0.0552291 | ||||||||
\(41\) | 204.346 | 0.778376 | 0.389188 | − | 0.921158i | \(-0.372756\pi\) | ||||
0.389188 | + | 0.921158i | \(0.372756\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −527.661 | −1.87134 | −0.935669 | − | 0.352878i | \(-0.885203\pi\) | ||||
−0.935669 | + | 0.352878i | \(0.885203\pi\) | |||||||
\(44\) | −251.101 | −0.860340 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −33.9920 | −0.108953 | ||||||||
\(47\) | −155.727 | −0.483301 | −0.241651 | − | 0.970363i | \(-0.577689\pi\) | ||||
−0.241651 | + | 0.970363i | \(0.577689\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −271.366 | −0.791153 | ||||||||
\(50\) | 4.37462 | 0.0123733 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −214.134 | −0.571058 | ||||||||
\(53\) | 141.694 | 0.367230 | 0.183615 | − | 0.982998i | \(-0.441220\pi\) | ||||
0.183615 | + | 0.982998i | \(0.441220\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −157.541 | −0.386234 | ||||||||
\(56\) | −23.6510 | −0.0564374 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.655092 | −0.00148307 | ||||||||
\(59\) | 493.845 | 1.08971 | 0.544857 | − | 0.838529i | \(-0.316584\pi\) | ||||
0.544857 | + | 0.838529i | \(0.316584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −759.483 | −1.59413 | −0.797065 | − | 0.603894i | \(-0.793615\pi\) | ||||
−0.797065 | + | 0.603894i | \(0.793615\pi\) | |||||||
\(62\) | −44.0373 | −0.0902055 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −500.280 | −0.977108 | ||||||||
\(65\) | −134.348 | −0.256366 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −543.590 | −0.991196 | −0.495598 | − | 0.868552i | \(-0.665051\pi\) | ||||
−0.495598 | + | 0.868552i | \(0.665051\pi\) | |||||||
\(68\) | −353.288 | −0.630036 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.40510 | −0.0126440 | ||||||||
\(71\) | 928.207 | 1.55152 | 0.775760 | − | 0.631028i | \(-0.217367\pi\) | ||||
0.775760 | + | 0.631028i | \(0.217367\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 608.739 | 0.975993 | 0.487997 | − | 0.872845i | \(-0.337728\pi\) | ||||
0.487997 | + | 0.872845i | \(0.337728\pi\) | |||||||
\(74\) | −10.8892 | −0.0171060 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 718.903 | 1.08505 | ||||||||
\(77\) | 266.677 | 0.394684 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 614.840 | 0.875632 | 0.437816 | − | 0.899065i | \(-0.355752\pi\) | ||||
0.437816 | + | 0.899065i | \(0.355752\pi\) | |||||||
\(80\) | −316.330 | −0.442085 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 35.7573 | 0.0481553 | ||||||||
\(83\) | −1075.31 | −1.42206 | −0.711028 | − | 0.703164i | \(-0.751770\pi\) | ||||
−0.711028 | + | 0.703164i | \(0.751770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −221.653 | −0.282843 | ||||||||
\(86\) | −92.3326 | −0.115773 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −88.0466 | −0.106657 | ||||||||
\(89\) | −1505.15 | −1.79265 | −0.896324 | − | 0.443400i | \(-0.853772\pi\) | ||||
−0.896324 | + | 0.443400i | \(0.853772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 227.416 | 0.261975 | ||||||||
\(92\) | 1548.11 | 1.75437 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −27.2499 | −0.0299001 | ||||||||
\(95\) | 451.041 | 0.487114 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −332.738 | −0.348293 | −0.174147 | − | 0.984720i | \(-0.555717\pi\) | ||||
−0.174147 | + | 0.984720i | \(0.555717\pi\) | |||||||
\(98\) | −47.4848 | −0.0489458 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −199.235 | −0.199235 | ||||||||
\(101\) | 494.986 | 0.487653 | 0.243826 | − | 0.969819i | \(-0.421597\pi\) | ||||
0.243826 | + | 0.969819i | \(0.421597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −630.030 | −0.602706 | −0.301353 | − | 0.953513i | \(-0.597438\pi\) | ||||
−0.301353 | + | 0.953513i | \(0.597438\pi\) | |||||||
\(104\) | −75.0842 | −0.0707943 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.7943 | 0.0227192 | ||||||||
\(107\) | 1561.00 | 1.41035 | 0.705175 | − | 0.709034i | \(-0.250869\pi\) | ||||
0.705175 | + | 0.709034i | \(0.250869\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −936.140 | −0.822623 | −0.411311 | − | 0.911495i | \(-0.634929\pi\) | ||||
−0.411311 | + | 0.911495i | \(0.634929\pi\) | |||||||
\(110\) | −27.5673 | −0.0238949 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 535.466 | 0.451757 | ||||||||
\(113\) | −1354.98 | −1.12802 | −0.564008 | − | 0.825770i | \(-0.690741\pi\) | ||||
−0.564008 | + | 0.825770i | \(0.690741\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 971.287 | 0.787591 | ||||||||
\(116\) | 29.8351 | 0.0238803 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 86.4153 | 0.0674167 | ||||||||
\(119\) | 375.202 | 0.289031 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −338.229 | −0.254117 | ||||||||
\(122\) | −132.898 | −0.0986230 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2005.60 | 1.45249 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1182.37 | −0.826126 | −0.413063 | − | 0.910702i | \(-0.635541\pi\) | ||||
−0.413063 | + | 0.910702i | \(0.635541\pi\) | |||||||
\(128\) | −354.947 | −0.245103 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −23.5088 | −0.0158604 | ||||||||
\(131\) | −2253.75 | −1.50314 | −0.751569 | − | 0.659655i | \(-0.770702\pi\) | ||||
−0.751569 | + | 0.659655i | \(0.770702\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −763.496 | −0.497771 | ||||||||
\(134\) | −95.1199 | −0.0613217 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −123.877 | −0.0781059 | ||||||||
\(137\) | −473.711 | −0.295415 | −0.147708 | − | 0.989031i | \(-0.547189\pi\) | ||||
−0.147708 | + | 0.989031i | \(0.547189\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −137.039 | −0.0836220 | −0.0418110 | − | 0.999126i | \(-0.513313\pi\) | ||||
−0.0418110 | + | 0.999126i | \(0.513313\pi\) | |||||||
\(140\) | 337.253 | 0.203593 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 162.422 | 0.0959870 | ||||||||
\(143\) | 846.613 | 0.495086 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.7186 | 0.0107206 | ||||||||
\(146\) | 106.520 | 0.0603812 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 495.929 | 0.275440 | ||||||||
\(149\) | 143.111 | 0.0786851 | 0.0393426 | − | 0.999226i | \(-0.487474\pi\) | ||||
0.0393426 | + | 0.999226i | \(0.487474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 216.841 | 0.116863 | 0.0584314 | − | 0.998291i | \(-0.481390\pi\) | ||||
0.0584314 | + | 0.998291i | \(0.481390\pi\) | |||||||
\(152\) | 252.077 | 0.134514 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 46.6644 | 0.0244177 | ||||||||
\(155\) | 1258.32 | 0.652068 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1348.43 | 0.685455 | 0.342728 | − | 0.939435i | \(-0.388649\pi\) | ||||
0.342728 | + | 0.939435i | \(0.388649\pi\) | |||||||
\(158\) | 107.588 | 0.0541722 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −167.129 | −0.0825793 | ||||||||
\(161\) | −1644.14 | −0.804822 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1039.85 | 0.499676 | 0.249838 | − | 0.968288i | \(-0.419623\pi\) | ||||
0.249838 | + | 0.968288i | \(0.419623\pi\) | |||||||
\(164\) | −1628.51 | −0.775397 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −188.163 | −0.0879774 | ||||||||
\(167\) | 3327.05 | 1.54164 | 0.770822 | − | 0.637051i | \(-0.219846\pi\) | ||||
0.770822 | + | 0.637051i | \(0.219846\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1475.03 | −0.671382 | ||||||||
\(170\) | −38.7859 | −0.0174985 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4205.13 | 1.86418 | ||||||||
\(173\) | 1194.25 | 0.524841 | 0.262420 | − | 0.964954i | \(-0.415479\pi\) | ||||
0.262420 | + | 0.964954i | \(0.415479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 211.593 | 0.0913995 | ||||||||
\(176\) | 1993.40 | 0.853741 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −263.378 | −0.110905 | ||||||||
\(179\) | −2323.70 | −0.970288 | −0.485144 | − | 0.874434i | \(-0.661233\pi\) | ||||
−0.485144 | + | 0.874434i | \(0.661233\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2527.12 | 1.03779 | 0.518893 | − | 0.854839i | \(-0.326344\pi\) | ||||
0.518893 | + | 0.854839i | \(0.326344\pi\) | |||||||
\(182\) | 39.7944 | 0.0162074 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 542.832 | 0.217490 | ||||||||
\(185\) | 311.147 | 0.123654 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1396.78 | 0.546219 | ||||||||
\(188\) | 1241.05 | 0.481452 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 78.9252 | 0.0301360 | ||||||||
\(191\) | −2388.87 | −0.904986 | −0.452493 | − | 0.891768i | \(-0.649465\pi\) | ||||
−0.452493 | + | 0.891768i | \(0.649465\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3547.97 | 1.32326 | 0.661629 | − | 0.749831i | \(-0.269865\pi\) | ||||
0.661629 | + | 0.749831i | \(0.269865\pi\) | |||||||
\(194\) | −58.2241 | −0.0215476 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2162.62 | 0.788125 | ||||||||
\(197\) | 1239.26 | 0.448192 | 0.224096 | − | 0.974567i | \(-0.428057\pi\) | ||||
0.224096 | + | 0.974567i | \(0.428057\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 516.657 | 0.184044 | 0.0920222 | − | 0.995757i | \(-0.470667\pi\) | ||||
0.0920222 | + | 0.995757i | \(0.470667\pi\) | |||||||
\(200\) | −69.8599 | −0.0246992 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 86.6149 | 0.0301693 | ||||||||
\(203\) | −31.6857 | −0.0109552 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1021.73 | −0.348100 | ||||||||
\(206\) | −110.246 | −0.0372873 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1699.93 | 0.566678 | ||||||||
\(209\) | −2842.30 | −0.940700 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8432 | −0.00582169 | −0.00291084 | − | 0.999996i | \(-0.500927\pi\) | ||||
−0.00291084 | + | 0.999996i | \(0.500927\pi\) | |||||||
\(212\) | −1129.21 | −0.365824 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 273.151 | 0.0872532 | ||||||||
\(215\) | 2638.31 | 0.836888 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2130.01 | −0.666334 | ||||||||
\(218\) | −163.810 | −0.0508927 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1255.51 | 0.384756 | ||||||||
\(221\) | 1191.15 | 0.362557 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 989.553 | 0.297154 | 0.148577 | − | 0.988901i | \(-0.452531\pi\) | ||||
0.148577 | + | 0.988901i | \(0.452531\pi\) | |||||||
\(224\) | 282.906 | 0.0843860 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −237.101 | −0.0697863 | ||||||||
\(227\) | 3427.13 | 1.00206 | 0.501028 | − | 0.865431i | \(-0.332955\pi\) | ||||
0.501028 | + | 0.865431i | \(0.332955\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1099.61 | 0.317311 | 0.158656 | − | 0.987334i | \(-0.449284\pi\) | ||||
0.158656 | + | 0.987334i | \(0.449284\pi\) | |||||||
\(230\) | 169.960 | 0.0487254 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.4614 | 0.00296045 | ||||||||
\(233\) | −4459.91 | −1.25399 | −0.626993 | − | 0.779025i | \(-0.715715\pi\) | ||||
−0.626993 | + | 0.779025i | \(0.715715\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 778.637 | 0.216139 | ||||||||
\(236\) | −3935.64 | −1.08554 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 65.6546 | 0.0178813 | ||||||||
\(239\) | −6544.45 | −1.77124 | −0.885618 | − | 0.464414i | \(-0.846265\pi\) | ||||
−0.885618 | + | 0.464414i | \(0.846265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −210.325 | −0.0562167 | −0.0281083 | − | 0.999605i | \(-0.508948\pi\) | ||||
−0.0281083 | + | 0.999605i | \(0.508948\pi\) | |||||||
\(242\) | −59.1849 | −0.0157213 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6052.61 | 1.58803 | ||||||||
\(245\) | 1356.83 | 0.353814 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2423.86 | −0.624398 | ||||||||
\(248\) | 703.248 | 0.180066 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −21.8731 | −0.00553350 | ||||||||
\(251\) | −816.143 | −0.205237 | −0.102618 | − | 0.994721i | \(-0.532722\pi\) | ||||
−0.102618 | + | 0.994721i | \(0.532722\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6120.71 | −1.52097 | ||||||||
\(254\) | −206.896 | −0.0511094 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3940.13 | 0.961945 | ||||||||
\(257\) | 4172.35 | 1.01270 | 0.506350 | − | 0.862328i | \(-0.330995\pi\) | ||||
0.506350 | + | 0.862328i | \(0.330995\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −526.691 | −0.126359 | ||||||||
\(260\) | 1070.67 | 0.255385 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −394.371 | −0.0929937 | ||||||||
\(263\) | 2817.05 | 0.660482 | 0.330241 | − | 0.943897i | \(-0.392870\pi\) | ||||
0.330241 | + | 0.943897i | \(0.392870\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −708.471 | −0.164230 | ||||||||
\(266\) | −133.600 | −0.0307953 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4332.08 | 0.987402 | ||||||||
\(269\) | 102.610 | 0.0232573 | 0.0116287 | − | 0.999932i | \(-0.496298\pi\) | ||||
0.0116287 | + | 0.999932i | \(0.496298\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3337.27 | −0.748061 | −0.374031 | − | 0.927416i | \(-0.622025\pi\) | ||||
−0.374031 | + | 0.927416i | \(0.622025\pi\) | |||||||
\(272\) | 2804.63 | 0.625204 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −82.8922 | −0.0182763 | ||||||||
\(275\) | 787.707 | 0.172729 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 633.883 | 0.137496 | 0.0687479 | − | 0.997634i | \(-0.478100\pi\) | ||||
0.0687479 | + | 0.997634i | \(0.478100\pi\) | |||||||
\(278\) | −23.9796 | −0.00517339 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 118.255 | 0.0252396 | ||||||||
\(281\) | 6202.40 | 1.31674 | 0.658370 | − | 0.752694i | \(-0.271246\pi\) | ||||
0.658370 | + | 0.752694i | \(0.271246\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7480.12 | −1.57119 | −0.785596 | − | 0.618740i | \(-0.787643\pi\) | ||||
−0.785596 | + | 0.618740i | \(0.787643\pi\) | |||||||
\(284\) | −7397.24 | −1.54558 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 148.144 | 0.0306292 | ||||||||
\(287\) | 1729.52 | 0.355716 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2947.79 | −0.599998 | ||||||||
\(290\) | 3.27546 | 0.000663247 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4851.27 | −0.972258 | ||||||||
\(293\) | 4836.51 | 0.964341 | 0.482171 | − | 0.876077i | \(-0.339849\pi\) | ||||
0.482171 | + | 0.876077i | \(0.339849\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2469.23 | −0.487335 | ||||||||
\(296\) | 173.893 | 0.0341464 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 25.0422 | 0.00486796 | ||||||||
\(299\) | −5219.61 | −1.00956 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4465.97 | −0.855197 | ||||||||
\(302\) | 37.9439 | 0.00722989 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5707.12 | −1.07673 | ||||||||
\(305\) | 3797.42 | 0.712916 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5611.86 | −1.04328 | −0.521638 | − | 0.853167i | \(-0.674679\pi\) | ||||
−0.521638 | + | 0.853167i | \(0.674679\pi\) | |||||||
\(308\) | −2125.25 | −0.393173 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 220.186 | 0.0403411 | ||||||||
\(311\) | −10921.4 | −1.99131 | −0.995653 | − | 0.0931416i | \(-0.970309\pi\) | ||||
−0.995653 | + | 0.0931416i | \(0.970309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4980.73 | 0.899449 | 0.449724 | − | 0.893167i | \(-0.351522\pi\) | ||||
0.449724 | + | 0.893167i | \(0.351522\pi\) | |||||||
\(314\) | 235.955 | 0.0424067 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4899.89 | −0.872280 | ||||||||
\(317\) | 3756.12 | 0.665504 | 0.332752 | − | 0.943014i | \(-0.392023\pi\) | ||||
0.332752 | + | 0.943014i | \(0.392023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −117.958 | −0.0207034 | ||||||||
\(320\) | 2501.40 | 0.436976 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −287.699 | −0.0497914 | ||||||||
\(323\) | −3998.99 | −0.688885 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 671.739 | 0.114650 | ||||||||
\(326\) | 181.958 | 0.0309132 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −571.023 | −0.0961264 | ||||||||
\(329\) | −1318.03 | −0.220868 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −906.954 | −0.150606 | −0.0753031 | − | 0.997161i | \(-0.523992\pi\) | ||||
−0.0753031 | + | 0.997161i | \(0.523992\pi\) | |||||||
\(332\) | 8569.55 | 1.41661 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 582.182 | 0.0953759 | ||||||||
\(335\) | 2717.95 | 0.443276 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9878.70 | 1.59682 | 0.798408 | − | 0.602117i | \(-0.205676\pi\) | ||||
0.798408 | + | 0.602117i | \(0.205676\pi\) | |||||||
\(338\) | −258.107 | −0.0415360 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1766.44 | 0.281761 | ||||||||
\(341\) | −7929.49 | −1.25925 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5199.81 | −0.818553 | ||||||||
\(344\) | 1474.49 | 0.231103 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 208.976 | 0.0324700 | ||||||||
\(347\) | 3509.71 | 0.542972 | 0.271486 | − | 0.962442i | \(-0.412485\pi\) | ||||
0.271486 | + | 0.962442i | \(0.412485\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10393.0 | −1.59405 | −0.797024 | − | 0.603947i | \(-0.793594\pi\) | ||||
−0.797024 | + | 0.603947i | \(0.793594\pi\) | |||||||
\(350\) | 37.0255 | 0.00565456 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1053.19 | 0.159475 | ||||||||
\(353\) | −8085.39 | −1.21910 | −0.609550 | − | 0.792748i | \(-0.708650\pi\) | ||||
−0.609550 | + | 0.792748i | \(0.708650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4641.04 | −0.693861 | ||||||||
\(356\) | 11995.1 | 1.78579 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −406.612 | −0.0600282 | ||||||||
\(359\) | 8189.49 | 1.20397 | 0.601984 | − | 0.798508i | \(-0.294377\pi\) | ||||
0.601984 | + | 0.798508i | \(0.294377\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1278.52 | 0.186400 | ||||||||
\(362\) | 442.207 | 0.0642041 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1812.37 | −0.260972 | ||||||||
\(365\) | −3043.70 | −0.436478 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8994.66 | −1.27934 | −0.639669 | − | 0.768650i | \(-0.720929\pi\) | ||||
−0.639669 | + | 0.768650i | \(0.720929\pi\) | |||||||
\(368\) | −12289.9 | −1.74091 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 54.4459 | 0.00765001 | ||||||||
\(371\) | 1199.26 | 0.167823 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −929.867 | −0.129080 | −0.0645398 | − | 0.997915i | \(-0.520558\pi\) | ||||
−0.0645398 | + | 0.997915i | \(0.520558\pi\) | |||||||
\(374\) | 244.415 | 0.0337926 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 435.164 | 0.0596858 | ||||||||
\(377\) | −100.592 | −0.0137420 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3449.71 | 0.467546 | 0.233773 | − | 0.972291i | \(-0.424893\pi\) | ||||
0.233773 | + | 0.972291i | \(0.424893\pi\) | |||||||
\(380\) | −3594.52 | −0.485250 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −418.015 | −0.0559882 | ||||||||
\(383\) | 5346.13 | 0.713249 | 0.356625 | − | 0.934248i | \(-0.383927\pi\) | ||||
0.356625 | + | 0.934248i | \(0.383927\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1333.38 | −0.176508 | ||||||||
\(386\) | 620.841 | 0.0818652 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2651.72 | 0.346960 | ||||||||
\(389\) | −7723.44 | −1.00667 | −0.503334 | − | 0.864092i | \(-0.667894\pi\) | ||||
−0.503334 | + | 0.864092i | \(0.667894\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8611.56 | −1.11382 | ||||||||
\(392\) | 758.303 | 0.0977043 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 216.852 | 0.0277280 | ||||||||
\(395\) | −3074.20 | −0.391594 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7125.03 | 0.900744 | 0.450372 | − | 0.892841i | \(-0.351291\pi\) | ||||
0.450372 | + | 0.892841i | \(0.351291\pi\) | |||||||
\(398\) | 90.4070 | 0.0113862 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1581.65 | 0.197706 | ||||||||
\(401\) | 1793.09 | 0.223299 | 0.111649 | − | 0.993748i | \(-0.464387\pi\) | ||||
0.111649 | + | 0.993748i | \(0.464387\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6762.10 | −0.835841 | ||||||||
\(404\) | −3944.73 | −0.485786 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.54451 | −0.000677757 0 | ||||||||
\(407\) | −1960.74 | −0.238796 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3139.73 | 0.379584 | 0.189792 | − | 0.981824i | \(-0.439219\pi\) | ||||
0.189792 | + | 0.981824i | \(0.439219\pi\) | |||||||
\(410\) | −178.787 | −0.0215357 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5020.95 | 0.600399 | ||||||||
\(413\) | 4179.77 | 0.497997 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5376.55 | 0.635962 | ||||||||
\(416\) | 898.135 | 0.105853 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −497.359 | −0.0581977 | ||||||||
\(419\) | −2457.40 | −0.286520 | −0.143260 | − | 0.989685i | \(-0.545758\pi\) | ||||
−0.143260 | + | 0.989685i | \(0.545758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2678.67 | −0.310096 | −0.155048 | − | 0.987907i | \(-0.549553\pi\) | ||||
−0.155048 | + | 0.987907i | \(0.549553\pi\) | |||||||
\(422\) | −3.12228 | −0.000360167 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −395.949 | −0.0453514 | ||||||||
\(425\) | 1108.27 | 0.126491 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6428.05 | −0.728513 | ||||||||
\(428\) | −12440.2 | −1.40495 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 461.663 | 0.0517752 | ||||||||
\(431\) | 9472.42 | 1.05863 | 0.529316 | − | 0.848425i | \(-0.322449\pi\) | ||||
0.529316 | + | 0.848425i | \(0.322449\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4238.21 | −0.470382 | −0.235191 | − | 0.971949i | \(-0.575572\pi\) | ||||
−0.235191 | + | 0.971949i | \(0.575572\pi\) | |||||||
\(434\) | −372.719 | −0.0412237 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7460.45 | 0.819474 | ||||||||
\(437\) | 17523.6 | 1.91823 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4858.93 | 0.528255 | 0.264128 | − | 0.964488i | \(-0.414916\pi\) | ||||
0.264128 | + | 0.964488i | \(0.414916\pi\) | |||||||
\(440\) | 440.233 | 0.0476984 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 208.432 | 0.0224301 | ||||||||
\(443\) | −2335.75 | −0.250508 | −0.125254 | − | 0.992125i | \(-0.539975\pi\) | ||||
−0.125254 | + | 0.992125i | \(0.539975\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7525.75 | 0.801696 | ||||||||
\(446\) | 173.157 | 0.0183839 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4234.22 | −0.446536 | ||||||||
\(449\) | −13290.5 | −1.39692 | −0.698460 | − | 0.715649i | \(-0.746131\pi\) | ||||
−0.698460 | + | 0.715649i | \(0.746131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6438.58 | 0.672241 | ||||||||
\(452\) | 10798.3 | 1.12370 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 599.695 | 0.0619936 | ||||||||
\(455\) | −1137.08 | −0.117159 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5174.61 | 0.529668 | 0.264834 | − | 0.964294i | \(-0.414683\pi\) | ||||
0.264834 | + | 0.964294i | \(0.414683\pi\) | |||||||
\(458\) | 192.415 | 0.0196309 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7740.55 | −0.784576 | ||||||||
\(461\) | −6340.88 | −0.640617 | −0.320309 | − | 0.947313i | \(-0.603787\pi\) | ||||
−0.320309 | + | 0.947313i | \(0.603787\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3182.79 | 0.319475 | 0.159737 | − | 0.987160i | \(-0.448935\pi\) | ||||
0.159737 | + | 0.987160i | \(0.448935\pi\) | |||||||
\(464\) | −236.850 | −0.0236972 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −780.416 | −0.0775796 | ||||||||
\(467\) | 8576.23 | 0.849808 | 0.424904 | − | 0.905238i | \(-0.360308\pi\) | ||||
0.424904 | + | 0.905238i | \(0.360308\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4600.79 | −0.452974 | ||||||||
\(470\) | 136.249 | 0.0133717 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1380.00 | −0.134575 | ||||||||
\(473\) | −16625.7 | −1.61617 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2255.21 | −0.217844 | ||||||||
\(476\) | −2990.13 | −0.287925 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1145.18 | −0.109580 | ||||||||
\(479\) | −2917.65 | −0.278311 | −0.139155 | − | 0.990271i | \(-0.544439\pi\) | ||||
−0.139155 | + | 0.990271i | \(0.544439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1672.07 | −0.158503 | ||||||||
\(482\) | −36.8036 | −0.00347792 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2695.48 | 0.253144 | ||||||||
\(485\) | 1663.69 | 0.155761 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14061.0 | −1.30834 | −0.654172 | − | 0.756346i | \(-0.726983\pi\) | ||||
−0.654172 | + | 0.756346i | \(0.726983\pi\) | |||||||
\(488\) | 2122.30 | 0.196869 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 237.424 | 0.0218892 | ||||||||
\(491\) | 932.662 | 0.0857239 | 0.0428620 | − | 0.999081i | \(-0.486352\pi\) | ||||
0.0428620 | + | 0.999081i | \(0.486352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −165.961 | −0.0151613 | ||||||||
\(494\) | −424.137 | −0.0386292 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15921.8 | −1.44135 | ||||||||
\(497\) | 7856.08 | 0.709041 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14430.8 | −1.29461 | −0.647305 | − | 0.762231i | \(-0.724104\pi\) | ||||
−0.647305 | + | 0.762231i | \(0.724104\pi\) | |||||||
\(500\) | 996.173 | 0.0891004 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −142.812 | −0.0126973 | ||||||||
\(503\) | 3230.55 | 0.286368 | 0.143184 | − | 0.989696i | \(-0.454266\pi\) | ||||
0.143184 | + | 0.989696i | \(0.454266\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2474.93 | −0.218085 | ||||||||
\(506\) | −1071.03 | −0.0940970 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9422.72 | 0.822964 | ||||||||
\(509\) | 360.756 | 0.0314150 | 0.0157075 | − | 0.999877i | \(-0.495000\pi\) | ||||
0.0157075 | + | 0.999877i | \(0.495000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5152.19 | 0.446027 | ||||||||
\(512\) | 3529.04 | 0.304615 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 730.096 | 0.0626521 | ||||||||
\(515\) | 3150.15 | 0.269538 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4906.70 | −0.417401 | ||||||||
\(518\) | −92.1628 | −0.00781738 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 375.421 | 0.0316602 | ||||||||
\(521\) | 11698.8 | 0.983747 | 0.491873 | − | 0.870667i | \(-0.336312\pi\) | ||||
0.491873 | + | 0.870667i | \(0.336312\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18557.3 | 1.55154 | 0.775770 | − | 0.631015i | \(-0.217362\pi\) | ||||
0.775770 | + | 0.631015i | \(0.217362\pi\) | |||||||
\(524\) | 17961.0 | 1.49738 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 492.940 | 0.0408616 | ||||||||
\(527\) | −11156.4 | −0.922166 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25568.9 | 2.10150 | ||||||||
\(530\) | −123.971 | −0.0101603 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6084.59 | 0.495866 | ||||||||
\(533\) | 5490.68 | 0.446206 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7804.99 | −0.630727 | ||||||||
\(536\) | 1519.01 | 0.122409 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.9551 | 0.00143885 | ||||||||
\(539\) | −8550.26 | −0.683276 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22755.3 | 1.80837 | 0.904185 | − | 0.427140i | \(-0.140479\pi\) | ||||
0.904185 | + | 0.427140i | \(0.140479\pi\) | |||||||
\(542\) | −583.971 | −0.0462799 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1481.79 | 0.116785 | ||||||||
\(545\) | 4680.70 | 0.367888 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5798.09 | 0.453215 | 0.226608 | − | 0.973986i | \(-0.427237\pi\) | ||||
0.226608 | + | 0.973986i | \(0.427237\pi\) | |||||||
\(548\) | 3775.18 | 0.294284 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 137.837 | 0.0106861 | ||||||||
\(551\) | 337.713 | 0.0261108 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5203.83 | 0.400162 | ||||||||
\(554\) | 110.920 | 0.00850637 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1092.11 | 0.0833019 | ||||||||
\(557\) | −15740.3 | −1.19738 | −0.598688 | − | 0.800982i | \(-0.704311\pi\) | ||||
−0.598688 | + | 0.800982i | \(0.704311\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14178.0 | −1.07275 | ||||||||
\(560\) | −2677.33 | −0.202032 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1085.32 | 0.0814620 | ||||||||
\(563\) | −3819.12 | −0.285891 | −0.142946 | − | 0.989731i | \(-0.545657\pi\) | ||||
−0.142946 | + | 0.989731i | \(0.545657\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6774.90 | 0.504464 | ||||||||
\(566\) | −1308.91 | −0.0972040 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2593.78 | −0.191607 | ||||||||
\(569\) | −8891.12 | −0.655070 | −0.327535 | − | 0.944839i | \(-0.606218\pi\) | ||||
−0.327535 | + | 0.944839i | \(0.606218\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8386.63 | 0.614657 | 0.307329 | − | 0.951603i | \(-0.400565\pi\) | ||||
0.307329 | + | 0.951603i | \(0.400565\pi\) | |||||||
\(572\) | −6746.98 | −0.493192 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 302.640 | 0.0220069 | ||||||||
\(575\) | −4856.43 | −0.352221 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16922.3 | 1.22095 | 0.610473 | − | 0.792037i | \(-0.290979\pi\) | ||||
0.610473 | + | 0.792037i | \(0.290979\pi\) | |||||||
\(578\) | −515.818 | −0.0371197 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −149.175 | −0.0106796 | ||||||||
\(581\) | −9101.12 | −0.649876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4464.54 | 0.317156 | ||||||||
\(584\) | −1701.06 | −0.120531 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 846.315 | 0.0596603 | ||||||||
\(587\) | −15238.6 | −1.07149 | −0.535744 | − | 0.844380i | \(-0.679969\pi\) | ||||
−0.535744 | + | 0.844380i | \(0.679969\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22702.1 | 1.58816 | ||||||||
\(590\) | −432.077 | −0.0301497 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3937.00 | −0.273327 | ||||||||
\(593\) | 16960.2 | 1.17449 | 0.587245 | − | 0.809409i | \(-0.300213\pi\) | ||||
0.587245 | + | 0.809409i | \(0.300213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1876.01 | −0.129259 | ||||||||
\(596\) | −1140.50 | −0.0783839 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −913.351 | −0.0624577 | ||||||||
\(599\) | 24912.1 | 1.69930 | 0.849651 | − | 0.527345i | \(-0.176813\pi\) | ||||
0.849651 | + | 0.527345i | \(0.176813\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4351.27 | −0.295328 | −0.147664 | − | 0.989038i | \(-0.547175\pi\) | ||||
−0.147664 | + | 0.989038i | \(0.547175\pi\) | |||||||
\(602\) | −781.476 | −0.0529080 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1728.09 | −0.116416 | ||||||||
\(605\) | 1691.15 | 0.113644 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27823.7 | 1.86051 | 0.930254 | − | 0.366915i | \(-0.119586\pi\) | ||||
0.930254 | + | 0.366915i | \(0.119586\pi\) | |||||||
\(608\) | −3015.28 | −0.201128 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 664.490 | 0.0441056 | ||||||||
\(611\) | −4184.33 | −0.277054 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20034.6 | 1.32005 | 0.660024 | − | 0.751244i | \(-0.270546\pi\) | ||||
0.660024 | + | 0.751244i | \(0.270546\pi\) | |||||||
\(614\) | −981.989 | −0.0645437 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −745.201 | −0.0487419 | ||||||||
\(617\) | −7553.89 | −0.492882 | −0.246441 | − | 0.969158i | \(-0.579261\pi\) | ||||
−0.246441 | + | 0.969158i | \(0.579261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12385.1 | 0.804198 | 0.402099 | − | 0.915596i | \(-0.368281\pi\) | ||||
0.402099 | + | 0.915596i | \(0.368281\pi\) | |||||||
\(620\) | −10028.0 | −0.649573 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1911.08 | −0.123195 | ||||||||
\(623\) | −12739.2 | −0.819236 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 871.551 | 0.0556457 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10746.2 | −0.682832 | ||||||||
\(629\) | −2758.67 | −0.174873 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1325.17 | −0.0836043 | −0.0418022 | − | 0.999126i | \(-0.513310\pi\) | ||||
−0.0418022 | + | 0.999126i | \(0.513310\pi\) | |||||||
\(632\) | −1718.11 | −0.108137 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 657.264 | 0.0411724 | ||||||||
\(635\) | 5911.83 | 0.369455 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7291.47 | −0.453530 | ||||||||
\(638\) | −20.6408 | −0.00128084 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1774.74 | 0.109613 | ||||||||
\(641\) | 22511.6 | 1.38714 | 0.693568 | − | 0.720392i | \(-0.256038\pi\) | ||||
0.693568 | + | 0.720392i | \(0.256038\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5614.61 | 0.344353 | 0.172176 | − | 0.985066i | \(-0.444920\pi\) | ||||
0.172176 | + | 0.985066i | \(0.444920\pi\) | |||||||
\(644\) | 13102.8 | 0.801741 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −699.762 | −0.0426188 | ||||||||
\(647\) | 11753.6 | 0.714188 | 0.357094 | − | 0.934068i | \(-0.383768\pi\) | ||||
0.357094 | + | 0.934068i | \(0.383768\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15560.2 | 0.941127 | ||||||||
\(650\) | 117.544 | 0.00709301 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8286.95 | −0.497764 | ||||||||
\(653\) | 25858.2 | 1.54963 | 0.774816 | − | 0.632187i | \(-0.217843\pi\) | ||||
0.774816 | + | 0.632187i | \(0.217843\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11268.7 | 0.672223 | ||||||||
\(656\) | 12928.1 | 0.769450 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −230.635 | −0.0136643 | ||||||||
\(659\) | 17695.5 | 1.04601 | 0.523004 | − | 0.852330i | \(-0.324811\pi\) | ||||
0.523004 | + | 0.852330i | \(0.324811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6230.09 | 0.366600 | 0.183300 | − | 0.983057i | \(-0.441322\pi\) | ||||
0.183300 | + | 0.983057i | \(0.441322\pi\) | |||||||
\(662\) | −158.703 | −0.00931747 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3004.84 | 0.175618 | ||||||||
\(665\) | 3817.48 | 0.222610 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 727.243 | 0.0422174 | ||||||||
\(668\) | −26514.5 | −1.53574 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 475.600 | 0.0274239 | ||||||||
\(671\) | −23930.0 | −1.37676 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6051.68 | −0.346620 | −0.173310 | − | 0.984867i | \(-0.555446\pi\) | ||||
−0.173310 | + | 0.984867i | \(0.555446\pi\) | |||||||
\(674\) | 1728.62 | 0.0987892 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11755.0 | 0.668812 | ||||||||
\(677\) | −28098.6 | −1.59515 | −0.797576 | − | 0.603218i | \(-0.793885\pi\) | ||||
−0.797576 | + | 0.603218i | \(0.793885\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2816.20 | −0.159169 | ||||||||
\(680\) | 619.387 | 0.0349300 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1387.54 | −0.0779056 | ||||||||
\(683\) | 8335.71 | 0.466994 | 0.233497 | − | 0.972358i | \(-0.424983\pi\) | ||||
0.233497 | + | 0.972358i | \(0.424983\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2368.56 | 0.132114 | ||||||||
\(686\) | −909.888 | −0.0506409 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −33383.0 | −1.84988 | ||||||||
\(689\) | 3807.26 | 0.210515 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16885.1 | −0.929579 | −0.464790 | − | 0.885421i | \(-0.653870\pi\) | ||||
−0.464790 | + | 0.885421i | \(0.653870\pi\) | |||||||
\(692\) | −9517.46 | −0.522832 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 614.146 | 0.0335917 | ||||||||
\(695\) | 685.193 | 0.0373969 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9058.78 | 0.492290 | ||||||||
\(698\) | −1818.61 | −0.0986180 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1686.26 | −0.0910497 | ||||||||
\(701\) | −16875.2 | −0.909226 | −0.454613 | − | 0.890689i | \(-0.650222\pi\) | ||||
−0.454613 | + | 0.890689i | \(0.650222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5613.59 | 0.301167 | ||||||||
\(704\) | −15762.9 | −0.843875 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1414.82 | −0.0754213 | ||||||||
\(707\) | 4189.42 | 0.222856 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19007.4 | −1.00682 | −0.503412 | − | 0.864046i | \(-0.667922\pi\) | ||||
−0.503412 | + | 0.864046i | \(0.667922\pi\) | |||||||
\(710\) | −812.110 | −0.0429267 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4205.99 | 0.221385 | ||||||||
\(713\) | 48887.5 | 2.56782 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4233.07 | −0.221409 | ||||||||
\(716\) | 18518.5 | 0.966574 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1433.03 | 0.0744852 | ||||||||
\(719\) | −17588.1 | −0.912275 | −0.456138 | − | 0.889909i | \(-0.650767\pi\) | ||||
−0.456138 | + | 0.889909i | \(0.650767\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5332.40 | −0.275435 | ||||||||
\(722\) | 223.721 | 0.0115319 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20139.6 | −1.03381 | ||||||||
\(725\) | −93.5928 | −0.00479441 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5605.38 | 0.285959 | 0.142979 | − | 0.989726i | \(-0.454332\pi\) | ||||
0.142979 | + | 0.989726i | \(0.454332\pi\) | |||||||
\(728\) | −635.491 | −0.0323528 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −532.600 | −0.0270033 | ||||||||
\(731\) | −23391.6 | −1.18354 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14920.1 | 0.751823 | 0.375911 | − | 0.926656i | \(-0.377330\pi\) | ||||
0.375911 | + | 0.926656i | \(0.377330\pi\) | |||||||
\(734\) | −1573.93 | −0.0791481 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6493.20 | −0.325194 | ||||||||
\(737\) | −17127.6 | −0.856042 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27418.8 | −1.36484 | −0.682421 | − | 0.730959i | \(-0.739073\pi\) | ||||
−0.682421 | + | 0.730959i | \(0.739073\pi\) | |||||||
\(740\) | −2479.65 | −0.123181 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 209.852 | 0.0103826 | ||||||||
\(743\) | 24544.2 | 1.21190 | 0.605948 | − | 0.795504i | \(-0.292794\pi\) | ||||
0.605948 | + | 0.795504i | \(0.292794\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −715.553 | −0.0351890 | ||||||||
\(746\) | −162.712 | −0.00798569 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11131.5 | −0.544128 | ||||||||
\(749\) | 13211.8 | 0.644526 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1534.57 | 0.0745634 | 0.0372817 | − | 0.999305i | \(-0.488130\pi\) | ||||
0.0372817 | + | 0.999305i | \(0.488130\pi\) | |||||||
\(752\) | −9852.26 | −0.477759 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.6020 | −0.000850170 0 | ||||||||
\(755\) | −1084.21 | −0.0522627 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18051.1 | −0.866681 | −0.433341 | − | 0.901230i | \(-0.642665\pi\) | ||||
−0.433341 | + | 0.901230i | \(0.642665\pi\) | |||||||
\(758\) | 603.647 | 0.0289254 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1260.39 | −0.0601566 | ||||||||
\(761\) | −12924.6 | −0.615658 | −0.307829 | − | 0.951442i | \(-0.599603\pi\) | ||||
−0.307829 | + | 0.951442i | \(0.599603\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7923.22 | −0.375937 | ||||||||
\(764\) | 19037.8 | 0.901522 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 935.491 | 0.0441262 | ||||||||
\(767\) | 13269.4 | 0.624681 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3372.32 | −0.158139 | −0.0790695 | − | 0.996869i | \(-0.525195\pi\) | ||||
−0.0790695 | + | 0.996869i | \(0.525195\pi\) | |||||||
\(770\) | −233.322 | −0.0109199 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −28275.2 | −1.31819 | ||||||||
\(773\) | 27152.6 | 1.26341 | 0.631703 | − | 0.775211i | \(-0.282356\pi\) | ||||
0.631703 | + | 0.775211i | \(0.282356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6291.59 | −0.291614 | ||||||||
\(776\) | 929.802 | 0.0430128 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1351.48 | −0.0622790 | ||||||||
\(779\) | −18433.7 | −0.847823 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29246.2 | 1.33996 | ||||||||
\(782\) | −1506.89 | −0.0689083 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17168.2 | −0.782080 | ||||||||
\(785\) | −6742.15 | −0.306545 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25212.1 | −1.14195 | −0.570974 | − | 0.820968i | \(-0.693434\pi\) | ||||
−0.570974 | + | 0.820968i | \(0.693434\pi\) | |||||||
\(788\) | −9876.16 | −0.446477 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −537.938 | −0.0242265 | ||||||||
\(791\) | −11468.2 | −0.515500 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20407.0 | −0.913838 | ||||||||
\(794\) | 1246.77 | 0.0557258 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4117.44 | −0.183340 | ||||||||
\(797\) | −39176.9 | −1.74118 | −0.870588 | − | 0.492013i | \(-0.836261\pi\) | ||||
−0.870588 | + | 0.492013i | \(0.836261\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6903.50 | −0.305667 | ||||||||
\(800\) | 835.644 | 0.0369306 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 313.764 | 0.0138147 | ||||||||
\(803\) | 19180.3 | 0.842912 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8220.69 | 0.359927 | ||||||||
\(806\) | −1183.26 | −0.0517105 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1383.19 | −0.0602231 | ||||||||
\(809\) | 36739.0 | 1.59663 | 0.798316 | − | 0.602239i | \(-0.205725\pi\) | ||||
0.798316 | + | 0.602239i | \(0.205725\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29660.0 | −1.28422 | −0.642111 | − | 0.766611i | \(-0.721941\pi\) | ||||
−0.642111 | + | 0.766611i | \(0.721941\pi\) | |||||||
\(812\) | 252.515 | 0.0109132 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −343.099 | −0.0147735 | ||||||||
\(815\) | −5199.24 | −0.223462 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47599.4 | 2.03830 | ||||||||
\(818\) | 549.405 | 0.0234835 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8142.54 | 0.346768 | ||||||||
\(821\) | −20113.2 | −0.855002 | −0.427501 | − | 0.904015i | \(-0.640606\pi\) | ||||
−0.427501 | + | 0.904015i | \(0.640606\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5374.05 | 0.227615 | 0.113808 | − | 0.993503i | \(-0.463695\pi\) | ||||
0.113808 | + | 0.993503i | \(0.463695\pi\) | |||||||
\(824\) | 1760.55 | 0.0744318 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 731.395 | 0.0308093 | ||||||||
\(827\) | −27865.2 | −1.17167 | −0.585833 | − | 0.810432i | \(-0.699233\pi\) | ||||
−0.585833 | + | 0.810432i | \(0.699233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24363.1 | 1.02070 | 0.510352 | − | 0.859965i | \(-0.329515\pi\) | ||||
0.510352 | + | 0.859965i | \(0.329515\pi\) | |||||||
\(830\) | 940.813 | 0.0393447 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13442.3 | −0.560129 | ||||||||
\(833\) | −12029.8 | −0.500370 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16635.2 | −0.689444 | ||||||||
\(836\) | 22651.4 | 0.937099 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −430.007 | −0.0177259 | ||||||||
\(839\) | 35530.6 | 1.46204 | 0.731020 | − | 0.682356i | \(-0.239045\pi\) | ||||
0.731020 | + | 0.682356i | \(0.239045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24375.0 | −0.999425 | ||||||||
\(842\) | −468.726 | −0.0191845 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 142.199 | 0.00579940 | ||||||||
\(845\) | 7375.13 | 0.300251 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2862.68 | −0.116131 | ||||||||
\(848\) | 8964.43 | 0.363019 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 193.930 | 0.00782557 | ||||||||
\(851\) | 12088.5 | 0.486943 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34447.5 | 1.38272 | 0.691360 | − | 0.722511i | \(-0.257012\pi\) | ||||
0.691360 | + | 0.722511i | \(0.257012\pi\) | |||||||
\(854\) | −1124.81 | −0.0450705 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4362.05 | −0.174173 | ||||||||
\(857\) | −20006.8 | −0.797457 | −0.398729 | − | 0.917069i | \(-0.630548\pi\) | ||||
−0.398729 | + | 0.917069i | \(0.630548\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1786.38 | 0.0709552 | 0.0354776 | − | 0.999370i | \(-0.488705\pi\) | ||||
0.0354776 | + | 0.999370i | \(0.488705\pi\) | |||||||
\(860\) | −21025.7 | −0.833685 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1657.53 | 0.0654937 | ||||||||
\(863\) | −12151.9 | −0.479322 | −0.239661 | − | 0.970857i | \(-0.577036\pi\) | ||||
−0.239661 | + | 0.970857i | \(0.577036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5971.27 | −0.234716 | ||||||||
\(866\) | −741.621 | −0.0291008 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16974.9 | 0.663784 | ||||||||
\(869\) | 19372.5 | 0.756235 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14606.0 | −0.568205 | ||||||||
\(872\) | 2615.94 | 0.101591 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3066.36 | 0.118674 | ||||||||
\(875\) | −1057.96 | −0.0408751 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18873.3 | −0.726688 | −0.363344 | − | 0.931655i | \(-0.618365\pi\) | ||||
−0.363344 | + | 0.931655i | \(0.618365\pi\) | |||||||
\(878\) | 850.238 | 0.0326813 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9967.02 | −0.381805 | ||||||||
\(881\) | −23587.2 | −0.902014 | −0.451007 | − | 0.892520i | \(-0.648935\pi\) | ||||
−0.451007 | + | 0.892520i | \(0.648935\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29504.5 | −1.12447 | −0.562234 | − | 0.826978i | \(-0.690058\pi\) | ||||
−0.562234 | + | 0.826978i | \(0.690058\pi\) | |||||||
\(884\) | −9492.70 | −0.361170 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −408.721 | −0.0154980 | ||||||||
\(887\) | −2476.04 | −0.0937286 | −0.0468643 | − | 0.998901i | \(-0.514923\pi\) | ||||
−0.0468643 | + | 0.998901i | \(0.514923\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10007.2 | −0.377538 | ||||||||
\(890\) | 1316.89 | 0.0495981 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7886.13 | −0.296017 | ||||||||
\(893\) | 14047.9 | 0.526422 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11618.5 | 0.433926 | ||||||||
\(896\) | −3004.17 | −0.112012 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2325.63 | −0.0864224 | ||||||||
\(899\) | 942.157 | 0.0349529 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6281.40 | 0.232257 | ||||||||
\(902\) | 1126.65 | 0.0415891 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3786.35 | 0.139305 | ||||||||
\(905\) | −12635.6 | −0.464112 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26751.0 | −0.979331 | −0.489666 | − | 0.871910i | \(-0.662881\pi\) | ||||
−0.489666 | + | 0.871910i | \(0.662881\pi\) | |||||||
\(908\) | −27312.1 | −0.998221 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −198.972 | −0.00724819 | ||||||||
\(911\) | −12668.2 | −0.460721 | −0.230360 | − | 0.973105i | \(-0.573990\pi\) | ||||
−0.230360 | + | 0.973105i | \(0.573990\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33881.1 | −1.22815 | ||||||||
\(914\) | 905.478 | 0.0327686 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8763.21 | −0.316097 | ||||||||
\(917\) | −19075.1 | −0.686930 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46565.5 | 1.67144 | 0.835721 | − | 0.549155i | \(-0.185050\pi\) | ||||
0.835721 | + | 0.549155i | \(0.185050\pi\) | |||||||
\(920\) | −2714.16 | −0.0972643 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1109.56 | −0.0396327 | ||||||||
\(923\) | 24940.5 | 0.889412 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1555.73 | −0.0552997 | ||||||||
\(926\) | 556.940 | 0.0197648 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −125.136 | −0.00442651 | ||||||||
\(929\) | −4610.92 | −0.162841 | −0.0814205 | − | 0.996680i | \(-0.525946\pi\) | ||||
−0.0814205 | + | 0.996680i | \(0.525946\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24479.4 | 0.861740 | ||||||||
\(932\) | 35542.8 | 1.24919 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1500.71 | 0.0525746 | ||||||||
\(935\) | −6983.91 | −0.244276 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6625.43 | −0.230996 | −0.115498 | − | 0.993308i | \(-0.536846\pi\) | ||||
−0.115498 | + | 0.993308i | \(0.536846\pi\) | |||||||
\(938\) | −805.068 | −0.0280239 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6205.25 | −0.215312 | ||||||||
\(941\) | 43442.6 | 1.50498 | 0.752491 | − | 0.658602i | \(-0.228852\pi\) | ||||
0.752491 | + | 0.658602i | \(0.228852\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39695.6 | −1.37080 | ||||||||
\(944\) | 31243.7 | 1.07722 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2909.24 | −0.0999868 | ||||||||
\(947\) | −32922.4 | −1.12971 | −0.564855 | − | 0.825190i | \(-0.691068\pi\) | ||||
−0.564855 | + | 0.825190i | \(0.691068\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16356.6 | 0.559490 | ||||||||
\(950\) | −394.626 | −0.0134772 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1048.46 | −0.0356942 | ||||||||
\(953\) | −20253.5 | −0.688430 | −0.344215 | − | 0.938891i | \(-0.611855\pi\) | ||||
−0.344215 | + | 0.938891i | \(0.611855\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11944.3 | 0.404722 | ||||||||
\(956\) | 52155.2 | 1.76446 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −510.544 | −0.0172181 | ||||||||
\(959\) | −4009.36 | −0.135004 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33543.7 | 1.12597 | ||||||||
\(962\) | −292.587 | −0.00980602 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1676.16 | 0.0560015 | ||||||||
\(965\) | −17739.9 | −0.591779 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3237.13 | 0.107651 | 0.0538257 | − | 0.998550i | \(-0.482858\pi\) | ||||
0.0538257 | + | 0.998550i | \(0.482858\pi\) | |||||||
\(968\) | 945.146 | 0.0313824 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 291.120 | 0.00963640 | ||||||||
\(971\) | 1731.06 | 0.0572114 | 0.0286057 | − | 0.999591i | \(-0.490893\pi\) | ||||
0.0286057 | + | 0.999591i | \(0.490893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1159.86 | −0.0382151 | ||||||||
\(974\) | −2460.45 | −0.0809425 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −48049.5 | −1.57585 | ||||||||
\(977\) | −34546.9 | −1.13127 | −0.565636 | − | 0.824655i | \(-0.691369\pi\) | ||||
−0.565636 | + | 0.824655i | \(0.691369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −47424.7 | −1.54821 | ||||||||
\(980\) | −10813.1 | −0.352460 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 163.201 | 0.00530343 | ||||||||
\(983\) | −20453.2 | −0.663637 | −0.331818 | − | 0.943343i | \(-0.607662\pi\) | ||||
−0.331818 | + | 0.943343i | \(0.607662\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6196.32 | −0.200438 | ||||||||
\(986\) | −29.0407 | −0.000937975 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19316.6 | 0.622008 | ||||||||
\(989\) | 102502. | 3.29563 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5387.77 | −0.172703 | −0.0863513 | − | 0.996265i | \(-0.527521\pi\) | ||||
−0.0863513 | + | 0.996265i | \(0.527521\pi\) | |||||||
\(992\) | −8412.05 | −0.269237 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1374.69 | 0.0438658 | ||||||||
\(995\) | −2583.29 | −0.0823072 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21844.9 | −0.693916 | −0.346958 | − | 0.937881i | \(-0.612785\pi\) | ||||
−0.346958 | + | 0.937881i | \(0.612785\pi\) | |||||||
\(998\) | −2525.16 | −0.0800929 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 405.4.a.j.1.2 | 3 | ||
3.2 | odd | 2 | 405.4.a.h.1.2 | 3 | |||
5.4 | even | 2 | 2025.4.a.q.1.2 | 3 | |||
9.2 | odd | 6 | 45.4.e.b.31.2 | yes | 6 | ||
9.4 | even | 3 | 135.4.e.b.46.2 | 6 | |||
9.5 | odd | 6 | 45.4.e.b.16.2 | ✓ | 6 | ||
9.7 | even | 3 | 135.4.e.b.91.2 | 6 | |||
15.14 | odd | 2 | 2025.4.a.s.1.2 | 3 | |||
45.2 | even | 12 | 225.4.k.c.49.3 | 12 | |||
45.14 | odd | 6 | 225.4.e.c.151.2 | 6 | |||
45.23 | even | 12 | 225.4.k.c.124.3 | 12 | |||
45.29 | odd | 6 | 225.4.e.c.76.2 | 6 | |||
45.32 | even | 12 | 225.4.k.c.124.4 | 12 | |||
45.38 | even | 12 | 225.4.k.c.49.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.b.16.2 | ✓ | 6 | 9.5 | odd | 6 | ||
45.4.e.b.31.2 | yes | 6 | 9.2 | odd | 6 | ||
135.4.e.b.46.2 | 6 | 9.4 | even | 3 | |||
135.4.e.b.91.2 | 6 | 9.7 | even | 3 | |||
225.4.e.c.76.2 | 6 | 45.29 | odd | 6 | |||
225.4.e.c.151.2 | 6 | 45.14 | odd | 6 | |||
225.4.k.c.49.3 | 12 | 45.2 | even | 12 | |||
225.4.k.c.49.4 | 12 | 45.38 | even | 12 | |||
225.4.k.c.124.3 | 12 | 45.23 | even | 12 | |||
225.4.k.c.124.4 | 12 | 45.32 | even | 12 | |||
405.4.a.h.1.2 | 3 | 3.2 | odd | 2 | |||
405.4.a.j.1.2 | 3 | 1.1 | even | 1 | trivial | ||
2025.4.a.q.1.2 | 3 | 5.4 | even | 2 | |||
2025.4.a.s.1.2 | 3 | 15.14 | odd | 2 |