Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{9} - 56x^{7} - 27x^{6} + 945x^{5} + 763x^{4} - 4139x^{3} - 2478x^{2} + 63x + 27 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.14324\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.69820 | −1.66106 | −0.830532 | − | 0.556970i | \(-0.811964\pi\) | ||||
−0.830532 | + | 0.556970i | \(0.811964\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 14.0731 | 1.75914 | ||||||||
\(5\) | −4.47249 | −0.400032 | −0.200016 | − | 0.979793i | \(-0.564099\pi\) | ||||
−0.200016 | + | 0.979793i | \(0.564099\pi\) | |||||||
\(6\) | −14.0946 | −0.959016 | ||||||||
\(7\) | −27.2096 | −1.46918 | −0.734589 | − | 0.678512i | \(-0.762625\pi\) | ||||
−0.734589 | + | 0.678512i | \(0.762625\pi\) | |||||||
\(8\) | −28.5326 | −1.26098 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 21.0127 | 0.664479 | ||||||||
\(11\) | 5.99207 | 0.164243 | 0.0821216 | − | 0.996622i | \(-0.473830\pi\) | ||||
0.0821216 | + | 0.996622i | \(0.473830\pi\) | |||||||
\(12\) | 42.2193 | 1.01564 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 127.836 | 2.44040 | ||||||||
\(15\) | −13.4175 | −0.230958 | ||||||||
\(16\) | 21.4672 | 0.335425 | ||||||||
\(17\) | 105.037 | 1.49854 | 0.749268 | − | 0.662267i | \(-0.230406\pi\) | ||||
0.749268 | + | 0.662267i | \(0.230406\pi\) | |||||||
\(18\) | −42.2838 | −0.553688 | ||||||||
\(19\) | 156.462 | 1.88920 | 0.944599 | − | 0.328227i | \(-0.106451\pi\) | ||||
0.944599 | + | 0.328227i | \(0.106451\pi\) | |||||||
\(20\) | −62.9418 | −0.703711 | ||||||||
\(21\) | −81.6287 | −0.848231 | ||||||||
\(22\) | −28.1519 | −0.272819 | ||||||||
\(23\) | −175.423 | −1.59036 | −0.795181 | − | 0.606372i | \(-0.792624\pi\) | ||||
−0.795181 | + | 0.606372i | \(0.792624\pi\) | |||||||
\(24\) | −85.5978 | −0.728024 | ||||||||
\(25\) | −104.997 | −0.839975 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −382.923 | −2.58449 | ||||||||
\(29\) | 204.886 | 1.31195 | 0.655973 | − | 0.754785i | \(-0.272259\pi\) | ||||
0.655973 | + | 0.754785i | \(0.272259\pi\) | |||||||
\(30\) | 63.0380 | 0.383637 | ||||||||
\(31\) | −31.9570 | −0.185150 | −0.0925748 | − | 0.995706i | \(-0.529510\pi\) | ||||
−0.0925748 | + | 0.995706i | \(0.529510\pi\) | |||||||
\(32\) | 127.404 | 0.703813 | ||||||||
\(33\) | 17.9762 | 0.0948259 | ||||||||
\(34\) | −493.483 | −2.48916 | ||||||||
\(35\) | 121.695 | 0.587718 | ||||||||
\(36\) | 126.658 | 0.586379 | ||||||||
\(37\) | −344.140 | −1.52909 | −0.764545 | − | 0.644571i | \(-0.777036\pi\) | ||||
−0.764545 | + | 0.644571i | \(0.777036\pi\) | |||||||
\(38\) | −735.088 | −3.13808 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 127.612 | 0.504430 | ||||||||
\(41\) | −46.5921 | −0.177475 | −0.0887373 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887373 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(42\) | 383.508 | 1.40897 | ||||||||
\(43\) | −173.286 | −0.614554 | −0.307277 | − | 0.951620i | \(-0.599418\pi\) | ||||
−0.307277 | + | 0.951620i | \(0.599418\pi\) | |||||||
\(44\) | 84.3269 | 0.288926 | ||||||||
\(45\) | −40.2524 | −0.133344 | ||||||||
\(46\) | 824.175 | 2.64169 | ||||||||
\(47\) | 265.613 | 0.824334 | 0.412167 | − | 0.911108i | \(-0.364772\pi\) | ||||
0.412167 | + | 0.911108i | \(0.364772\pi\) | |||||||
\(48\) | 64.4016 | 0.193658 | ||||||||
\(49\) | 397.361 | 1.15849 | ||||||||
\(50\) | 493.296 | 1.39525 | ||||||||
\(51\) | 315.110 | 0.865180 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 172.912 | 0.448137 | 0.224068 | − | 0.974573i | \(-0.428066\pi\) | ||||
0.224068 | + | 0.974573i | \(0.428066\pi\) | |||||||
\(54\) | −126.851 | −0.319672 | ||||||||
\(55\) | −26.7995 | −0.0657025 | ||||||||
\(56\) | 776.360 | 1.85260 | ||||||||
\(57\) | 469.385 | 1.09073 | ||||||||
\(58\) | −962.596 | −2.17923 | ||||||||
\(59\) | 137.566 | 0.303551 | 0.151775 | − | 0.988415i | \(-0.451501\pi\) | ||||
0.151775 | + | 0.988415i | \(0.451501\pi\) | |||||||
\(60\) | −188.825 | −0.406288 | ||||||||
\(61\) | −58.9384 | −0.123710 | −0.0618548 | − | 0.998085i | \(-0.519702\pi\) | ||||
−0.0618548 | + | 0.998085i | \(0.519702\pi\) | |||||||
\(62\) | 150.140 | 0.307546 | ||||||||
\(63\) | −244.886 | −0.489726 | ||||||||
\(64\) | −770.306 | −1.50450 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −84.4558 | −0.157512 | ||||||||
\(67\) | −211.668 | −0.385961 | −0.192980 | − | 0.981203i | \(-0.561815\pi\) | ||||
−0.192980 | + | 0.981203i | \(0.561815\pi\) | |||||||
\(68\) | 1478.19 | 2.63613 | ||||||||
\(69\) | −526.270 | −0.918196 | ||||||||
\(70\) | −571.746 | −0.976238 | ||||||||
\(71\) | 436.317 | 0.729314 | 0.364657 | − | 0.931142i | \(-0.381186\pi\) | ||||
0.364657 | + | 0.931142i | \(0.381186\pi\) | |||||||
\(72\) | −256.793 | −0.420325 | ||||||||
\(73\) | −1159.11 | −1.85840 | −0.929199 | − | 0.369579i | \(-0.879502\pi\) | ||||
−0.929199 | + | 0.369579i | \(0.879502\pi\) | |||||||
\(74\) | 1616.84 | 2.53992 | ||||||||
\(75\) | −314.990 | −0.484960 | ||||||||
\(76\) | 2201.90 | 3.32336 | ||||||||
\(77\) | −163.042 | −0.241303 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1017.51 | −1.44910 | −0.724548 | − | 0.689224i | \(-0.757952\pi\) | ||||
−0.724548 | + | 0.689224i | \(0.757952\pi\) | |||||||
\(80\) | −96.0118 | −0.134181 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 218.899 | 0.294797 | ||||||||
\(83\) | 150.251 | 0.198701 | 0.0993504 | − | 0.995053i | \(-0.468324\pi\) | ||||
0.0993504 | + | 0.995053i | \(0.468324\pi\) | |||||||
\(84\) | −1148.77 | −1.49215 | ||||||||
\(85\) | −469.775 | −0.599462 | ||||||||
\(86\) | 814.131 | 1.02081 | ||||||||
\(87\) | 614.659 | 0.757452 | ||||||||
\(88\) | −170.969 | −0.207107 | ||||||||
\(89\) | −565.984 | −0.674092 | −0.337046 | − | 0.941488i | \(-0.609428\pi\) | ||||
−0.337046 | + | 0.941488i | \(0.609428\pi\) | |||||||
\(90\) | 189.114 | 0.221493 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2468.75 | −2.79766 | ||||||||
\(93\) | −95.8709 | −0.106896 | ||||||||
\(94\) | −1247.90 | −1.36927 | ||||||||
\(95\) | −699.773 | −0.755739 | ||||||||
\(96\) | 382.211 | 0.406346 | ||||||||
\(97\) | 286.741 | 0.300145 | 0.150073 | − | 0.988675i | \(-0.452049\pi\) | ||||
0.150073 | + | 0.988675i | \(0.452049\pi\) | |||||||
\(98\) | −1866.88 | −1.92432 | ||||||||
\(99\) | 53.9286 | 0.0547478 | ||||||||
\(100\) | −1477.63 | −1.47763 | ||||||||
\(101\) | −1218.57 | −1.20052 | −0.600258 | − | 0.799807i | \(-0.704935\pi\) | ||||
−0.600258 | + | 0.799807i | \(0.704935\pi\) | |||||||
\(102\) | −1480.45 | −1.43712 | ||||||||
\(103\) | 74.2485 | 0.0710283 | 0.0355142 | − | 0.999369i | \(-0.488693\pi\) | ||||
0.0355142 | + | 0.999369i | \(0.488693\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 365.084 | 0.339319 | ||||||||
\(106\) | −812.374 | −0.744384 | ||||||||
\(107\) | −1253.46 | −1.13249 | −0.566246 | − | 0.824237i | \(-0.691605\pi\) | ||||
−0.566246 | + | 0.824237i | \(0.691605\pi\) | |||||||
\(108\) | 379.973 | 0.338546 | ||||||||
\(109\) | −722.643 | −0.635015 | −0.317507 | − | 0.948256i | \(-0.602846\pi\) | ||||
−0.317507 | + | 0.948256i | \(0.602846\pi\) | |||||||
\(110\) | 125.909 | 0.109136 | ||||||||
\(111\) | −1032.42 | −0.882820 | ||||||||
\(112\) | −584.113 | −0.492799 | ||||||||
\(113\) | −855.913 | −0.712544 | −0.356272 | − | 0.934382i | \(-0.615952\pi\) | ||||
−0.356272 | + | 0.934382i | \(0.615952\pi\) | |||||||
\(114\) | −2205.26 | −1.81177 | ||||||||
\(115\) | 784.580 | 0.636195 | ||||||||
\(116\) | 2883.38 | 2.30789 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −646.310 | −0.504218 | ||||||||
\(119\) | −2858.00 | −2.20162 | ||||||||
\(120\) | 382.836 | 0.291233 | ||||||||
\(121\) | −1295.10 | −0.973024 | ||||||||
\(122\) | 276.905 | 0.205490 | ||||||||
\(123\) | −139.776 | −0.102465 | ||||||||
\(124\) | −449.733 | −0.325703 | ||||||||
\(125\) | 1028.66 | 0.736048 | ||||||||
\(126\) | 1150.52 | 0.813467 | ||||||||
\(127\) | 726.104 | 0.507333 | 0.253667 | − | 0.967292i | \(-0.418363\pi\) | ||||
0.253667 | + | 0.967292i | \(0.418363\pi\) | |||||||
\(128\) | 2599.82 | 1.79526 | ||||||||
\(129\) | −519.857 | −0.354813 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1456.91 | −0.971685 | −0.485843 | − | 0.874046i | \(-0.661487\pi\) | ||||
−0.485843 | + | 0.874046i | \(0.661487\pi\) | |||||||
\(132\) | 252.981 | 0.166812 | ||||||||
\(133\) | −4257.25 | −2.77557 | ||||||||
\(134\) | 994.460 | 0.641106 | ||||||||
\(135\) | −120.757 | −0.0769862 | ||||||||
\(136\) | −2996.97 | −1.88962 | ||||||||
\(137\) | −1806.80 | −1.12675 | −0.563377 | − | 0.826200i | \(-0.690498\pi\) | ||||
−0.563377 | + | 0.826200i | \(0.690498\pi\) | |||||||
\(138\) | 2472.52 | 1.52518 | ||||||||
\(139\) | 1229.28 | 0.750117 | 0.375059 | − | 0.927001i | \(-0.377623\pi\) | ||||
0.375059 | + | 0.927001i | \(0.377623\pi\) | |||||||
\(140\) | 1712.62 | 1.03388 | ||||||||
\(141\) | 796.840 | 0.475929 | ||||||||
\(142\) | −2049.90 | −1.21144 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 193.205 | 0.111808 | ||||||||
\(145\) | −916.352 | −0.524820 | ||||||||
\(146\) | 5445.71 | 3.08692 | ||||||||
\(147\) | 1192.08 | 0.668853 | ||||||||
\(148\) | −4843.12 | −2.68988 | ||||||||
\(149\) | −446.127 | −0.245290 | −0.122645 | − | 0.992451i | \(-0.539138\pi\) | ||||
−0.122645 | + | 0.992451i | \(0.539138\pi\) | |||||||
\(150\) | 1479.89 | 0.805549 | ||||||||
\(151\) | −207.208 | −0.111671 | −0.0558355 | − | 0.998440i | \(-0.517782\pi\) | ||||
−0.0558355 | + | 0.998440i | \(0.517782\pi\) | |||||||
\(152\) | −4464.26 | −2.38223 | ||||||||
\(153\) | 945.329 | 0.499512 | ||||||||
\(154\) | 766.002 | 0.400819 | ||||||||
\(155\) | 142.927 | 0.0740658 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1096.60 | 0.557442 | 0.278721 | − | 0.960372i | \(-0.410089\pi\) | ||||
0.278721 | + | 0.960372i | \(0.410089\pi\) | |||||||
\(158\) | 4780.46 | 2.40704 | ||||||||
\(159\) | 518.735 | 0.258732 | ||||||||
\(160\) | −569.812 | −0.281547 | ||||||||
\(161\) | 4773.20 | 2.33653 | ||||||||
\(162\) | −380.554 | −0.184563 | ||||||||
\(163\) | 3154.25 | 1.51571 | 0.757853 | − | 0.652425i | \(-0.226248\pi\) | ||||
0.757853 | + | 0.652425i | \(0.226248\pi\) | |||||||
\(164\) | −655.694 | −0.312202 | ||||||||
\(165\) | −80.3984 | −0.0379334 | ||||||||
\(166\) | −705.908 | −0.330055 | ||||||||
\(167\) | −3679.65 | −1.70503 | −0.852514 | − | 0.522705i | \(-0.824923\pi\) | ||||
−0.852514 | + | 0.522705i | \(0.824923\pi\) | |||||||
\(168\) | 2329.08 | 1.06960 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2207.10 | 0.995745 | ||||||||
\(171\) | 1408.15 | 0.629733 | ||||||||
\(172\) | −2438.66 | −1.08108 | ||||||||
\(173\) | −3666.99 | −1.61154 | −0.805768 | − | 0.592231i | \(-0.798247\pi\) | ||||
−0.805768 | + | 0.592231i | \(0.798247\pi\) | |||||||
\(174\) | −2887.79 | −1.25818 | ||||||||
\(175\) | 2856.92 | 1.23407 | ||||||||
\(176\) | 128.633 | 0.0550913 | ||||||||
\(177\) | 412.697 | 0.175255 | ||||||||
\(178\) | 2659.11 | 1.11971 | ||||||||
\(179\) | 4173.50 | 1.74269 | 0.871347 | − | 0.490666i | \(-0.163247\pi\) | ||||
0.871347 | + | 0.490666i | \(0.163247\pi\) | |||||||
\(180\) | −566.476 | −0.234570 | ||||||||
\(181\) | −499.197 | −0.205000 | −0.102500 | − | 0.994733i | \(-0.532684\pi\) | ||||
−0.102500 | + | 0.994733i | \(0.532684\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −176.815 | −0.0714238 | ||||||||
\(184\) | 5005.29 | 2.00541 | ||||||||
\(185\) | 1539.16 | 0.611685 | ||||||||
\(186\) | 450.421 | 0.177562 | ||||||||
\(187\) | 629.386 | 0.246124 | ||||||||
\(188\) | 3738.00 | 1.45012 | ||||||||
\(189\) | −734.659 | −0.282744 | ||||||||
\(190\) | 3287.68 | 1.25533 | ||||||||
\(191\) | −3086.68 | −1.16934 | −0.584671 | − | 0.811271i | \(-0.698776\pi\) | ||||
−0.584671 | + | 0.811271i | \(0.698776\pi\) | |||||||
\(192\) | −2310.92 | −0.868625 | ||||||||
\(193\) | −1644.14 | −0.613201 | −0.306601 | − | 0.951838i | \(-0.599192\pi\) | ||||
−0.306601 | + | 0.951838i | \(0.599192\pi\) | |||||||
\(194\) | −1347.17 | −0.498561 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5592.10 | 2.03794 | ||||||||
\(197\) | 1371.21 | 0.495911 | 0.247956 | − | 0.968771i | \(-0.420241\pi\) | ||||
0.247956 | + | 0.968771i | \(0.420241\pi\) | |||||||
\(198\) | −253.367 | −0.0909396 | ||||||||
\(199\) | −4627.33 | −1.64836 | −0.824178 | − | 0.566332i | \(-0.808362\pi\) | ||||
−0.824178 | + | 0.566332i | \(0.808362\pi\) | |||||||
\(200\) | 2995.83 | 1.05919 | ||||||||
\(201\) | −635.004 | −0.222835 | ||||||||
\(202\) | 5725.08 | 1.99413 | ||||||||
\(203\) | −5574.87 | −1.92748 | ||||||||
\(204\) | 4434.57 | 1.52197 | ||||||||
\(205\) | 208.383 | 0.0709955 | ||||||||
\(206\) | −348.834 | −0.117983 | ||||||||
\(207\) | −1578.81 | −0.530121 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 937.528 | 0.310288 | ||||||||
\(210\) | −1715.24 | −0.563631 | ||||||||
\(211\) | 5088.31 | 1.66016 | 0.830080 | − | 0.557644i | \(-0.188294\pi\) | ||||
0.830080 | + | 0.557644i | \(0.188294\pi\) | |||||||
\(212\) | 2433.40 | 0.788334 | ||||||||
\(213\) | 1308.95 | 0.421069 | ||||||||
\(214\) | 5889.01 | 1.88114 | ||||||||
\(215\) | 775.019 | 0.245841 | ||||||||
\(216\) | −770.380 | −0.242675 | ||||||||
\(217\) | 869.535 | 0.272018 | ||||||||
\(218\) | 3395.12 | 1.05480 | ||||||||
\(219\) | −3477.32 | −1.07295 | ||||||||
\(220\) | −377.151 | −0.115580 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4850.52 | 1.46642 | ||||||||
\(223\) | −4744.82 | −1.42483 | −0.712415 | − | 0.701759i | \(-0.752398\pi\) | ||||
−0.712415 | + | 0.701759i | \(0.752398\pi\) | |||||||
\(224\) | −3466.60 | −1.03403 | ||||||||
\(225\) | −944.971 | −0.279992 | ||||||||
\(226\) | 4021.25 | 1.18358 | ||||||||
\(227\) | −1145.52 | −0.334937 | −0.167469 | − | 0.985877i | \(-0.553559\pi\) | ||||
−0.167469 | + | 0.985877i | \(0.553559\pi\) | |||||||
\(228\) | 6605.70 | 1.91874 | ||||||||
\(229\) | −1348.47 | −0.389123 | −0.194561 | − | 0.980890i | \(-0.562328\pi\) | ||||
−0.194561 | + | 0.980890i | \(0.562328\pi\) | |||||||
\(230\) | −3686.12 | −1.05676 | ||||||||
\(231\) | −489.125 | −0.139316 | ||||||||
\(232\) | −5845.94 | −1.65433 | ||||||||
\(233\) | −952.002 | −0.267673 | −0.133836 | − | 0.991003i | \(-0.542730\pi\) | ||||
−0.133836 | + | 0.991003i | \(0.542730\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1187.95 | −0.329760 | ||||||||
\(236\) | 1935.97 | 0.533987 | ||||||||
\(237\) | −3052.52 | −0.836636 | ||||||||
\(238\) | 13427.5 | 3.65703 | ||||||||
\(239\) | 3069.12 | 0.830647 | 0.415323 | − | 0.909674i | \(-0.363668\pi\) | ||||
0.415323 | + | 0.909674i | \(0.363668\pi\) | |||||||
\(240\) | −288.036 | −0.0774692 | ||||||||
\(241\) | −2508.17 | −0.670396 | −0.335198 | − | 0.942148i | \(-0.608803\pi\) | ||||
−0.335198 | + | 0.942148i | \(0.608803\pi\) | |||||||
\(242\) | 6084.62 | 1.61626 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −829.446 | −0.217622 | ||||||||
\(245\) | −1777.19 | −0.463432 | ||||||||
\(246\) | 656.697 | 0.170201 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 911.815 | 0.233469 | ||||||||
\(249\) | 450.752 | 0.114720 | ||||||||
\(250\) | −4832.85 | −1.22262 | ||||||||
\(251\) | 3405.91 | 0.856490 | 0.428245 | − | 0.903663i | \(-0.359132\pi\) | ||||
0.428245 | + | 0.903663i | \(0.359132\pi\) | |||||||
\(252\) | −3446.31 | −0.861495 | ||||||||
\(253\) | −1051.15 | −0.261206 | ||||||||
\(254\) | −3411.38 | −0.842714 | ||||||||
\(255\) | −1409.33 | −0.346100 | ||||||||
\(256\) | −6052.04 | −1.47755 | ||||||||
\(257\) | −4733.95 | −1.14901 | −0.574506 | − | 0.818501i | \(-0.694806\pi\) | ||||
−0.574506 | + | 0.818501i | \(0.694806\pi\) | |||||||
\(258\) | 2442.39 | 0.589367 | ||||||||
\(259\) | 9363.91 | 2.24651 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1843.98 | 0.437315 | ||||||||
\(262\) | 6844.85 | 1.61403 | ||||||||
\(263\) | −1866.11 | −0.437526 | −0.218763 | − | 0.975778i | \(-0.570202\pi\) | ||||
−0.218763 | + | 0.975778i | \(0.570202\pi\) | |||||||
\(264\) | −512.908 | −0.119573 | ||||||||
\(265\) | −773.346 | −0.179269 | ||||||||
\(266\) | 20001.4 | 4.61040 | ||||||||
\(267\) | −1697.95 | −0.389187 | ||||||||
\(268\) | −2978.83 | −0.678958 | ||||||||
\(269\) | 1580.19 | 0.358164 | 0.179082 | − | 0.983834i | \(-0.442687\pi\) | ||||
0.179082 | + | 0.983834i | \(0.442687\pi\) | |||||||
\(270\) | 567.342 | 0.127879 | ||||||||
\(271\) | −4922.09 | −1.10330 | −0.551652 | − | 0.834074i | \(-0.686002\pi\) | ||||
−0.551652 | + | 0.834074i | \(0.686002\pi\) | |||||||
\(272\) | 2254.84 | 0.502646 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8488.71 | 1.87161 | ||||||||
\(275\) | −629.148 | −0.137960 | ||||||||
\(276\) | −7406.25 | −1.61523 | ||||||||
\(277\) | 2687.08 | 0.582856 | 0.291428 | − | 0.956593i | \(-0.405870\pi\) | ||||
0.291428 | + | 0.956593i | \(0.405870\pi\) | |||||||
\(278\) | −5775.41 | −1.24599 | ||||||||
\(279\) | −287.613 | −0.0617165 | ||||||||
\(280\) | −3472.26 | −0.741098 | ||||||||
\(281\) | −883.753 | −0.187617 | −0.0938083 | − | 0.995590i | \(-0.529904\pi\) | ||||
−0.0938083 | + | 0.995590i | \(0.529904\pi\) | |||||||
\(282\) | −3743.71 | −0.790550 | ||||||||
\(283\) | −469.776 | −0.0986759 | −0.0493379 | − | 0.998782i | \(-0.515711\pi\) | ||||
−0.0493379 | + | 0.998782i | \(0.515711\pi\) | |||||||
\(284\) | 6140.33 | 1.28296 | ||||||||
\(285\) | −2099.32 | −0.436326 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1267.75 | 0.260742 | ||||||||
\(288\) | 1146.63 | 0.234604 | ||||||||
\(289\) | 6119.68 | 1.24561 | ||||||||
\(290\) | 4305.20 | 0.871760 | ||||||||
\(291\) | 860.222 | 0.173289 | ||||||||
\(292\) | −16312.2 | −3.26918 | ||||||||
\(293\) | 3403.76 | 0.678668 | 0.339334 | − | 0.940666i | \(-0.389798\pi\) | ||||
0.339334 | + | 0.940666i | \(0.389798\pi\) | |||||||
\(294\) | −5600.65 | −1.11101 | ||||||||
\(295\) | −615.261 | −0.121430 | ||||||||
\(296\) | 9819.22 | 1.92814 | ||||||||
\(297\) | 161.786 | 0.0316086 | ||||||||
\(298\) | 2095.99 | 0.407442 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4432.89 | −0.853110 | ||||||||
\(301\) | 4715.03 | 0.902889 | ||||||||
\(302\) | 973.504 | 0.185493 | ||||||||
\(303\) | −3655.70 | −0.693118 | ||||||||
\(304\) | 3358.79 | 0.633684 | ||||||||
\(305\) | 263.602 | 0.0494878 | ||||||||
\(306\) | −4441.35 | −0.829722 | ||||||||
\(307\) | 888.862 | 0.165244 | 0.0826222 | − | 0.996581i | \(-0.473671\pi\) | ||||
0.0826222 | + | 0.996581i | \(0.473671\pi\) | |||||||
\(308\) | −2294.50 | −0.424484 | ||||||||
\(309\) | 222.745 | 0.0410082 | ||||||||
\(310\) | −671.501 | −0.123028 | ||||||||
\(311\) | −1218.36 | −0.222145 | −0.111072 | − | 0.993812i | \(-0.535429\pi\) | ||||
−0.111072 | + | 0.993812i | \(0.535429\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4870.41 | −0.879526 | −0.439763 | − | 0.898114i | \(-0.644938\pi\) | ||||
−0.439763 | + | 0.898114i | \(0.644938\pi\) | |||||||
\(314\) | −5152.06 | −0.925948 | ||||||||
\(315\) | 1095.25 | 0.195906 | ||||||||
\(316\) | −14319.5 | −2.54916 | ||||||||
\(317\) | −4340.93 | −0.769120 | −0.384560 | − | 0.923100i | \(-0.625647\pi\) | ||||
−0.384560 | + | 0.923100i | \(0.625647\pi\) | |||||||
\(318\) | −2437.12 | −0.429770 | ||||||||
\(319\) | 1227.69 | 0.215478 | ||||||||
\(320\) | 3445.19 | 0.601849 | ||||||||
\(321\) | −3760.38 | −0.653844 | ||||||||
\(322\) | −22425.4 | −3.88112 | ||||||||
\(323\) | 16434.2 | 2.83103 | ||||||||
\(324\) | 1139.92 | 0.195460 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14819.3 | −2.51769 | ||||||||
\(327\) | −2167.93 | −0.366626 | ||||||||
\(328\) | 1329.39 | 0.223791 | ||||||||
\(329\) | −7227.23 | −1.21109 | ||||||||
\(330\) | 377.728 | 0.0630098 | ||||||||
\(331\) | −907.289 | −0.150662 | −0.0753310 | − | 0.997159i | \(-0.524001\pi\) | ||||
−0.0753310 | + | 0.997159i | \(0.524001\pi\) | |||||||
\(332\) | 2114.49 | 0.349542 | ||||||||
\(333\) | −3097.26 | −0.509697 | ||||||||
\(334\) | 17287.7 | 2.83216 | ||||||||
\(335\) | 946.684 | 0.154397 | ||||||||
\(336\) | −1752.34 | −0.284518 | ||||||||
\(337\) | 8660.88 | 1.39997 | 0.699983 | − | 0.714160i | \(-0.253191\pi\) | ||||
0.699983 | + | 0.714160i | \(0.253191\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2567.74 | −0.411388 | ||||||||
\(340\) | −6611.19 | −1.05454 | ||||||||
\(341\) | −191.488 | −0.0304096 | ||||||||
\(342\) | −6615.79 | −1.04603 | ||||||||
\(343\) | −1479.14 | −0.232846 | ||||||||
\(344\) | 4944.29 | 0.774937 | ||||||||
\(345\) | 2353.74 | 0.367308 | ||||||||
\(346\) | 17228.2 | 2.67687 | ||||||||
\(347\) | −347.605 | −0.0537763 | −0.0268882 | − | 0.999638i | \(-0.508560\pi\) | ||||
−0.0268882 | + | 0.999638i | \(0.508560\pi\) | |||||||
\(348\) | 8650.15 | 1.33246 | ||||||||
\(349\) | −10970.2 | −1.68258 | −0.841292 | − | 0.540581i | \(-0.818205\pi\) | ||||
−0.841292 | + | 0.540581i | \(0.818205\pi\) | |||||||
\(350\) | −13422.4 | −2.04988 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 763.411 | 0.115596 | ||||||||
\(353\) | 10384.8 | 1.56580 | 0.782901 | − | 0.622146i | \(-0.213739\pi\) | ||||
0.782901 | + | 0.622146i | \(0.213739\pi\) | |||||||
\(354\) | −1938.93 | −0.291110 | ||||||||
\(355\) | −1951.42 | −0.291749 | ||||||||
\(356\) | −7965.15 | −1.18582 | ||||||||
\(357\) | −8574.00 | −1.27110 | ||||||||
\(358\) | −19608.0 | −2.89473 | ||||||||
\(359\) | 8665.80 | 1.27399 | 0.636996 | − | 0.770867i | \(-0.280177\pi\) | ||||
0.636996 | + | 0.770867i | \(0.280177\pi\) | |||||||
\(360\) | 1148.51 | 0.168143 | ||||||||
\(361\) | 17621.2 | 2.56907 | ||||||||
\(362\) | 2345.33 | 0.340518 | ||||||||
\(363\) | −3885.29 | −0.561776 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5184.09 | 0.743419 | ||||||||
\(366\) | 830.714 | 0.118640 | ||||||||
\(367\) | 1234.22 | 0.175547 | 0.0877734 | − | 0.996140i | \(-0.472025\pi\) | ||||
0.0877734 | + | 0.996140i | \(0.472025\pi\) | |||||||
\(368\) | −3765.85 | −0.533447 | ||||||||
\(369\) | −419.329 | −0.0591582 | ||||||||
\(370\) | −7231.31 | −1.01605 | ||||||||
\(371\) | −4704.85 | −0.658393 | ||||||||
\(372\) | −1349.20 | −0.188045 | ||||||||
\(373\) | −427.483 | −0.0593410 | −0.0296705 | − | 0.999560i | \(-0.509446\pi\) | ||||
−0.0296705 | + | 0.999560i | \(0.509446\pi\) | |||||||
\(374\) | −2956.98 | −0.408829 | ||||||||
\(375\) | 3085.98 | 0.424958 | ||||||||
\(376\) | −7578.64 | −1.03946 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3451.57 | 0.469656 | ||||||||
\(379\) | −124.241 | −0.0168386 | −0.00841929 | − | 0.999965i | \(-0.502680\pi\) | ||||
−0.00841929 | + | 0.999965i | \(0.502680\pi\) | |||||||
\(380\) | −9847.98 | −1.32945 | ||||||||
\(381\) | 2178.31 | 0.292909 | ||||||||
\(382\) | 14501.8 | 1.94235 | ||||||||
\(383\) | −9341.21 | −1.24625 | −0.623125 | − | 0.782122i | \(-0.714137\pi\) | ||||
−0.623125 | + | 0.782122i | \(0.714137\pi\) | |||||||
\(384\) | 7799.46 | 1.03650 | ||||||||
\(385\) | 729.202 | 0.0965288 | ||||||||
\(386\) | 7724.51 | 1.01857 | ||||||||
\(387\) | −1559.57 | −0.204851 | ||||||||
\(388\) | 4035.33 | 0.527997 | ||||||||
\(389\) | 11368.9 | 1.48182 | 0.740908 | − | 0.671607i | \(-0.234396\pi\) | ||||
0.740908 | + | 0.671607i | \(0.234396\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18425.9 | −2.38321 | ||||||||
\(392\) | −11337.7 | −1.46082 | ||||||||
\(393\) | −4370.73 | −0.561003 | ||||||||
\(394\) | −6442.21 | −0.823741 | ||||||||
\(395\) | 4550.80 | 0.579685 | ||||||||
\(396\) | 758.942 | 0.0963088 | ||||||||
\(397\) | 12077.8 | 1.52687 | 0.763436 | − | 0.645883i | \(-0.223511\pi\) | ||||
0.763436 | + | 0.645883i | \(0.223511\pi\) | |||||||
\(398\) | 21740.1 | 2.73802 | ||||||||
\(399\) | −12771.8 | −1.60248 | ||||||||
\(400\) | −2253.99 | −0.281748 | ||||||||
\(401\) | 4856.74 | 0.604823 | 0.302411 | − | 0.953178i | \(-0.402208\pi\) | ||||
0.302411 | + | 0.953178i | \(0.402208\pi\) | |||||||
\(402\) | 2983.38 | 0.370143 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −17149.0 | −2.11187 | ||||||||
\(405\) | −362.272 | −0.0444480 | ||||||||
\(406\) | 26191.8 | 3.20167 | ||||||||
\(407\) | −2062.11 | −0.251143 | ||||||||
\(408\) | −8990.90 | −1.09097 | ||||||||
\(409\) | −2981.80 | −0.360490 | −0.180245 | − | 0.983622i | \(-0.557689\pi\) | ||||
−0.180245 | + | 0.983622i | \(0.557689\pi\) | |||||||
\(410\) | −979.023 | −0.117928 | ||||||||
\(411\) | −5420.40 | −0.650532 | ||||||||
\(412\) | 1044.91 | 0.124949 | ||||||||
\(413\) | −3743.10 | −0.445971 | ||||||||
\(414\) | 7417.57 | 0.880565 | ||||||||
\(415\) | −671.995 | −0.0794866 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3687.84 | 0.433080 | ||||||||
\(418\) | −4404.70 | −0.515409 | ||||||||
\(419\) | 7774.01 | 0.906408 | 0.453204 | − | 0.891407i | \(-0.350281\pi\) | ||||
0.453204 | + | 0.891407i | \(0.350281\pi\) | |||||||
\(420\) | 5137.86 | 0.596909 | ||||||||
\(421\) | −3959.71 | −0.458396 | −0.229198 | − | 0.973380i | \(-0.573610\pi\) | ||||
−0.229198 | + | 0.973380i | \(0.573610\pi\) | |||||||
\(422\) | −23905.9 | −2.75763 | ||||||||
\(423\) | 2390.52 | 0.274778 | ||||||||
\(424\) | −4933.62 | −0.565089 | ||||||||
\(425\) | −11028.5 | −1.25873 | ||||||||
\(426\) | −6149.71 | −0.699424 | ||||||||
\(427\) | 1603.69 | 0.181752 | ||||||||
\(428\) | −17640.1 | −1.99221 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3641.19 | −0.408358 | ||||||||
\(431\) | −4375.12 | −0.488961 | −0.244480 | − | 0.969654i | \(-0.578617\pi\) | ||||
−0.244480 | + | 0.969654i | \(0.578617\pi\) | |||||||
\(432\) | 579.614 | 0.0645525 | ||||||||
\(433\) | 8992.74 | 0.998068 | 0.499034 | − | 0.866582i | \(-0.333688\pi\) | ||||
0.499034 | + | 0.866582i | \(0.333688\pi\) | |||||||
\(434\) | −4085.25 | −0.451839 | ||||||||
\(435\) | −2749.06 | −0.303005 | ||||||||
\(436\) | −10169.8 | −1.11708 | ||||||||
\(437\) | −27447.0 | −3.00451 | ||||||||
\(438\) | 16337.1 | 1.78223 | ||||||||
\(439\) | −195.465 | −0.0212506 | −0.0106253 | − | 0.999944i | \(-0.503382\pi\) | ||||
−0.0106253 | + | 0.999944i | \(0.503382\pi\) | |||||||
\(440\) | 764.659 | 0.0828493 | ||||||||
\(441\) | 3576.25 | 0.386162 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7369.97 | 0.790424 | 0.395212 | − | 0.918590i | \(-0.370671\pi\) | ||||
0.395212 | + | 0.918590i | \(0.370671\pi\) | |||||||
\(444\) | −14529.4 | −1.55300 | ||||||||
\(445\) | 2531.36 | 0.269658 | ||||||||
\(446\) | 22292.1 | 2.36673 | ||||||||
\(447\) | −1338.38 | −0.141618 | ||||||||
\(448\) | 20959.7 | 2.21038 | ||||||||
\(449\) | 164.281 | 0.0172670 | 0.00863351 | − | 0.999963i | \(-0.497252\pi\) | ||||
0.00863351 | + | 0.999963i | \(0.497252\pi\) | |||||||
\(450\) | 4439.67 | 0.465084 | ||||||||
\(451\) | −279.183 | −0.0291490 | ||||||||
\(452\) | −12045.3 | −1.25346 | ||||||||
\(453\) | −621.623 | −0.0644733 | ||||||||
\(454\) | 5381.88 | 0.556352 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13392.8 | −1.37538 | ||||||||
\(457\) | −11687.0 | −1.19627 | −0.598133 | − | 0.801397i | \(-0.704091\pi\) | ||||
−0.598133 | + | 0.801397i | \(0.704091\pi\) | |||||||
\(458\) | 6335.36 | 0.646358 | ||||||||
\(459\) | 2835.99 | 0.288393 | ||||||||
\(460\) | 11041.5 | 1.11915 | ||||||||
\(461\) | −1057.53 | −0.106842 | −0.0534211 | − | 0.998572i | \(-0.517013\pi\) | ||||
−0.0534211 | + | 0.998572i | \(0.517013\pi\) | |||||||
\(462\) | 2298.01 | 0.231413 | ||||||||
\(463\) | −8554.74 | −0.858688 | −0.429344 | − | 0.903141i | \(-0.641255\pi\) | ||||
−0.429344 | + | 0.903141i | \(0.641255\pi\) | |||||||
\(464\) | 4398.33 | 0.440059 | ||||||||
\(465\) | 428.782 | 0.0427619 | ||||||||
\(466\) | 4472.70 | 0.444622 | ||||||||
\(467\) | −7705.26 | −0.763506 | −0.381753 | − | 0.924264i | \(-0.624679\pi\) | ||||
−0.381753 | + | 0.924264i | \(0.624679\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5759.40 | 0.567046 | ||||||||
\(470\) | 5581.24 | 0.547752 | ||||||||
\(471\) | 3289.81 | 0.321839 | ||||||||
\(472\) | −3925.10 | −0.382770 | ||||||||
\(473\) | −1038.34 | −0.100936 | ||||||||
\(474\) | 14341.4 | 1.38971 | ||||||||
\(475\) | −16428.0 | −1.58688 | ||||||||
\(476\) | −40220.9 | −3.87295 | ||||||||
\(477\) | 1556.21 | 0.149379 | ||||||||
\(478\) | −14419.3 | −1.37976 | ||||||||
\(479\) | 4508.59 | 0.430069 | 0.215034 | − | 0.976606i | \(-0.431014\pi\) | ||||
0.215034 | + | 0.976606i | \(0.431014\pi\) | |||||||
\(480\) | −1709.44 | −0.162551 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 11783.9 | 1.11357 | ||||||||
\(483\) | 14319.6 | 1.34899 | ||||||||
\(484\) | −18226.0 | −1.71168 | ||||||||
\(485\) | −1282.45 | −0.120068 | ||||||||
\(486\) | −1141.66 | −0.106557 | ||||||||
\(487\) | −6725.73 | −0.625815 | −0.312908 | − | 0.949784i | \(-0.601303\pi\) | ||||
−0.312908 | + | 0.949784i | \(0.601303\pi\) | |||||||
\(488\) | 1681.67 | 0.155995 | ||||||||
\(489\) | 9462.76 | 0.875094 | ||||||||
\(490\) | 8349.61 | 0.769790 | ||||||||
\(491\) | 11517.5 | 1.05861 | 0.529303 | − | 0.848433i | \(-0.322454\pi\) | ||||
0.529303 | + | 0.848433i | \(0.322454\pi\) | |||||||
\(492\) | −1967.08 | −0.180250 | ||||||||
\(493\) | 21520.5 | 1.96600 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −241.195 | −0.0219008 | ||||||||
\(496\) | −686.026 | −0.0621038 | ||||||||
\(497\) | −11872.0 | −1.07149 | ||||||||
\(498\) | −2117.72 | −0.190557 | ||||||||
\(499\) | −19907.9 | −1.78598 | −0.892988 | − | 0.450080i | \(-0.851395\pi\) | ||||
−0.892988 | + | 0.450080i | \(0.851395\pi\) | |||||||
\(500\) | 14476.4 | 1.29481 | ||||||||
\(501\) | −11038.9 | −0.984398 | ||||||||
\(502\) | −16001.6 | −1.42269 | ||||||||
\(503\) | −5735.48 | −0.508415 | −0.254207 | − | 0.967150i | \(-0.581815\pi\) | ||||
−0.254207 | + | 0.967150i | \(0.581815\pi\) | |||||||
\(504\) | 6987.24 | 0.617533 | ||||||||
\(505\) | 5450.04 | 0.480244 | ||||||||
\(506\) | 4938.51 | 0.433881 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10218.5 | 0.892469 | ||||||||
\(509\) | −9253.84 | −0.805834 | −0.402917 | − | 0.915237i | \(-0.632004\pi\) | ||||
−0.402917 | + | 0.915237i | \(0.632004\pi\) | |||||||
\(510\) | 6621.29 | 0.574894 | ||||||||
\(511\) | 31538.8 | 2.73032 | ||||||||
\(512\) | 7635.12 | 0.659039 | ||||||||
\(513\) | 4224.46 | 0.363576 | ||||||||
\(514\) | 22241.1 | 1.90858 | ||||||||
\(515\) | −332.076 | −0.0284136 | ||||||||
\(516\) | −7315.99 | −0.624164 | ||||||||
\(517\) | 1591.57 | 0.135391 | ||||||||
\(518\) | −43993.5 | −3.73159 | ||||||||
\(519\) | −11001.0 | −0.930421 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3887.42 | 0.326892 | 0.163446 | − | 0.986552i | \(-0.447739\pi\) | ||||
0.163446 | + | 0.986552i | \(0.447739\pi\) | |||||||
\(522\) | −8663.37 | −0.726409 | ||||||||
\(523\) | 4782.27 | 0.399836 | 0.199918 | − | 0.979813i | \(-0.435932\pi\) | ||||
0.199918 | + | 0.979813i | \(0.435932\pi\) | |||||||
\(524\) | −20503.2 | −1.70933 | ||||||||
\(525\) | 8570.76 | 0.712492 | ||||||||
\(526\) | 8767.37 | 0.726759 | ||||||||
\(527\) | −3356.65 | −0.277453 | ||||||||
\(528\) | 385.898 | 0.0318070 | ||||||||
\(529\) | 18606.4 | 1.52925 | ||||||||
\(530\) | 3633.34 | 0.297777 | ||||||||
\(531\) | 1238.09 | 0.101184 | ||||||||
\(532\) | −59912.7 | −4.88261 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 7977.32 | 0.646465 | ||||||||
\(535\) | 5606.09 | 0.453033 | ||||||||
\(536\) | 6039.44 | 0.486687 | ||||||||
\(537\) | 12520.5 | 1.00615 | ||||||||
\(538\) | −7424.06 | −0.594933 | ||||||||
\(539\) | 2381.01 | 0.190274 | ||||||||
\(540\) | −1699.43 | −0.135429 | ||||||||
\(541\) | 14872.6 | 1.18192 | 0.590962 | − | 0.806699i | \(-0.298748\pi\) | ||||
0.590962 | + | 0.806699i | \(0.298748\pi\) | |||||||
\(542\) | 23125.0 | 1.83266 | ||||||||
\(543\) | −1497.59 | −0.118357 | ||||||||
\(544\) | 13382.0 | 1.05469 | ||||||||
\(545\) | 3232.01 | 0.254026 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16965.3 | 1.32611 | 0.663055 | − | 0.748570i | \(-0.269259\pi\) | ||||
0.663055 | + | 0.748570i | \(0.269259\pi\) | |||||||
\(548\) | −25427.3 | −1.98212 | ||||||||
\(549\) | −530.446 | −0.0412366 | ||||||||
\(550\) | 2955.86 | 0.229161 | ||||||||
\(551\) | 32056.8 | 2.47852 | ||||||||
\(552\) | 15015.9 | 1.15782 | ||||||||
\(553\) | 27686.0 | 2.12898 | ||||||||
\(554\) | −12624.5 | −0.968162 | ||||||||
\(555\) | 4617.49 | 0.353156 | ||||||||
\(556\) | 17299.8 | 1.31956 | ||||||||
\(557\) | −1934.05 | −0.147125 | −0.0735623 | − | 0.997291i | \(-0.523437\pi\) | ||||
−0.0735623 | + | 0.997291i | \(0.523437\pi\) | |||||||
\(558\) | 1351.26 | 0.102515 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2612.44 | 0.197135 | ||||||||
\(561\) | 1888.16 | 0.142100 | ||||||||
\(562\) | 4152.05 | 0.311643 | ||||||||
\(563\) | 6592.13 | 0.493473 | 0.246736 | − | 0.969083i | \(-0.420642\pi\) | ||||
0.246736 | + | 0.969083i | \(0.420642\pi\) | |||||||
\(564\) | 11214.0 | 0.837225 | ||||||||
\(565\) | 3828.06 | 0.285040 | ||||||||
\(566\) | 2207.10 | 0.163907 | ||||||||
\(567\) | −2203.98 | −0.163242 | ||||||||
\(568\) | −12449.3 | −0.919646 | ||||||||
\(569\) | −14477.7 | −1.06667 | −0.533336 | − | 0.845903i | \(-0.679062\pi\) | ||||
−0.533336 | + | 0.845903i | \(0.679062\pi\) | |||||||
\(570\) | 9863.03 | 0.724766 | ||||||||
\(571\) | −4998.21 | −0.366320 | −0.183160 | − | 0.983083i | \(-0.558633\pi\) | ||||
−0.183160 | + | 0.983083i | \(0.558633\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9260.04 | −0.675120 | ||||||||
\(574\) | −5956.15 | −0.433109 | ||||||||
\(575\) | 18418.9 | 1.33586 | ||||||||
\(576\) | −6932.75 | −0.501501 | ||||||||
\(577\) | −9291.73 | −0.670398 | −0.335199 | − | 0.942147i | \(-0.608804\pi\) | ||||
−0.335199 | + | 0.942147i | \(0.608804\pi\) | |||||||
\(578\) | −28751.5 | −2.06904 | ||||||||
\(579\) | −4932.42 | −0.354032 | ||||||||
\(580\) | −12895.9 | −0.923230 | ||||||||
\(581\) | −4088.26 | −0.291927 | ||||||||
\(582\) | −4041.50 | −0.287844 | ||||||||
\(583\) | 1036.10 | 0.0736034 | ||||||||
\(584\) | 33072.3 | 2.34339 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15991.5 | −1.12731 | ||||||||
\(587\) | 5602.64 | 0.393945 | 0.196972 | − | 0.980409i | \(-0.436889\pi\) | ||||
0.196972 | + | 0.980409i | \(0.436889\pi\) | |||||||
\(588\) | 16776.3 | 1.17660 | ||||||||
\(589\) | −5000.04 | −0.349784 | ||||||||
\(590\) | 2890.62 | 0.201703 | ||||||||
\(591\) | 4113.62 | 0.286314 | ||||||||
\(592\) | −7387.73 | −0.512895 | ||||||||
\(593\) | 10885.8 | 0.753839 | 0.376919 | − | 0.926246i | \(-0.376983\pi\) | ||||
0.376919 | + | 0.926246i | \(0.376983\pi\) | |||||||
\(594\) | −760.102 | −0.0525040 | ||||||||
\(595\) | 12782.4 | 0.880717 | ||||||||
\(596\) | −6278.38 | −0.431498 | ||||||||
\(597\) | −13882.0 | −0.951678 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20403.2 | 1.39174 | 0.695872 | − | 0.718166i | \(-0.255018\pi\) | ||||
0.695872 | + | 0.718166i | \(0.255018\pi\) | |||||||
\(600\) | 8987.50 | 0.611522 | ||||||||
\(601\) | −6312.19 | −0.428419 | −0.214209 | − | 0.976788i | \(-0.568717\pi\) | ||||
−0.214209 | + | 0.976788i | \(0.568717\pi\) | |||||||
\(602\) | −22152.2 | −1.49976 | ||||||||
\(603\) | −1905.01 | −0.128654 | ||||||||
\(604\) | −2916.05 | −0.196445 | ||||||||
\(605\) | 5792.30 | 0.389241 | ||||||||
\(606\) | 17175.2 | 1.15131 | ||||||||
\(607\) | −21848.6 | −1.46097 | −0.730484 | − | 0.682930i | \(-0.760705\pi\) | ||||
−0.730484 | + | 0.682930i | \(0.760705\pi\) | |||||||
\(608\) | 19933.8 | 1.32964 | ||||||||
\(609\) | −16724.6 | −1.11283 | ||||||||
\(610\) | −1238.45 | −0.0822025 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 13303.7 | 0.878710 | ||||||||
\(613\) | 1335.14 | 0.0879704 | 0.0439852 | − | 0.999032i | \(-0.485995\pi\) | ||||
0.0439852 | + | 0.999032i | \(0.485995\pi\) | |||||||
\(614\) | −4176.05 | −0.274482 | ||||||||
\(615\) | 625.148 | 0.0409893 | ||||||||
\(616\) | 4652.00 | 0.304277 | ||||||||
\(617\) | −18908.3 | −1.23374 | −0.616871 | − | 0.787064i | \(-0.711600\pi\) | ||||
−0.616871 | + | 0.787064i | \(0.711600\pi\) | |||||||
\(618\) | −1046.50 | −0.0681173 | ||||||||
\(619\) | −6722.49 | −0.436510 | −0.218255 | − | 0.975892i | \(-0.570036\pi\) | ||||
−0.218255 | + | 0.975892i | \(0.570036\pi\) | |||||||
\(620\) | 2011.43 | 0.130292 | ||||||||
\(621\) | −4736.43 | −0.306065 | ||||||||
\(622\) | 5724.11 | 0.368997 | ||||||||
\(623\) | 15400.2 | 0.990362 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8523.93 | 0.545532 | ||||||||
\(626\) | 22882.2 | 1.46095 | ||||||||
\(627\) | 2812.59 | 0.179145 | ||||||||
\(628\) | 15432.6 | 0.980617 | ||||||||
\(629\) | −36147.3 | −2.29140 | ||||||||
\(630\) | −5145.71 | −0.325413 | ||||||||
\(631\) | 8098.44 | 0.510925 | 0.255463 | − | 0.966819i | \(-0.417772\pi\) | ||||
0.255463 | + | 0.966819i | \(0.417772\pi\) | |||||||
\(632\) | 29032.2 | 1.82727 | ||||||||
\(633\) | 15264.9 | 0.958494 | ||||||||
\(634\) | 20394.6 | 1.27756 | ||||||||
\(635\) | −3247.50 | −0.202950 | ||||||||
\(636\) | 7300.21 | 0.455145 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5767.94 | −0.357923 | ||||||||
\(639\) | 3926.85 | 0.243105 | ||||||||
\(640\) | −11627.7 | −0.718163 | ||||||||
\(641\) | −10955.9 | −0.675090 | −0.337545 | − | 0.941309i | \(-0.609597\pi\) | ||||
−0.337545 | + | 0.941309i | \(0.609597\pi\) | |||||||
\(642\) | 17667.0 | 1.08608 | ||||||||
\(643\) | 28125.0 | 1.72495 | 0.862473 | − | 0.506104i | \(-0.168915\pi\) | ||||
0.862473 | + | 0.506104i | \(0.168915\pi\) | |||||||
\(644\) | 67173.7 | 4.11027 | ||||||||
\(645\) | 2325.06 | 0.141936 | ||||||||
\(646\) | −77211.1 | −4.70253 | ||||||||
\(647\) | −29001.4 | −1.76223 | −0.881115 | − | 0.472901i | \(-0.843207\pi\) | ||||
−0.881115 | + | 0.472901i | \(0.843207\pi\) | |||||||
\(648\) | −2311.14 | −0.140108 | ||||||||
\(649\) | 824.302 | 0.0498562 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2608.61 | 0.157050 | ||||||||
\(652\) | 44390.1 | 2.66634 | ||||||||
\(653\) | 19506.3 | 1.16898 | 0.584488 | − | 0.811402i | \(-0.301295\pi\) | ||||
0.584488 | + | 0.811402i | \(0.301295\pi\) | |||||||
\(654\) | 10185.4 | 0.608989 | ||||||||
\(655\) | 6516.01 | 0.388705 | ||||||||
\(656\) | −1000.20 | −0.0595294 | ||||||||
\(657\) | −10432.0 | −0.619466 | ||||||||
\(658\) | 33955.0 | 2.01171 | ||||||||
\(659\) | 5985.86 | 0.353833 | 0.176917 | − | 0.984226i | \(-0.443388\pi\) | ||||
0.176917 | + | 0.984226i | \(0.443388\pi\) | |||||||
\(660\) | −1131.45 | −0.0667300 | ||||||||
\(661\) | 280.836 | 0.0165254 | 0.00826268 | − | 0.999966i | \(-0.497370\pi\) | ||||
0.00826268 | + | 0.999966i | \(0.497370\pi\) | |||||||
\(662\) | 4262.63 | 0.250259 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4287.04 | −0.250557 | ||||||||
\(665\) | 19040.5 | 1.11032 | ||||||||
\(666\) | 14551.6 | 0.846639 | ||||||||
\(667\) | −35941.8 | −2.08647 | ||||||||
\(668\) | −51784.0 | −2.99938 | ||||||||
\(669\) | −14234.5 | −0.822626 | ||||||||
\(670\) | −4447.71 | −0.256463 | ||||||||
\(671\) | −353.163 | −0.0203185 | ||||||||
\(672\) | −10399.8 | −0.596996 | ||||||||
\(673\) | −14868.9 | −0.851640 | −0.425820 | − | 0.904808i | \(-0.640014\pi\) | ||||
−0.425820 | + | 0.904808i | \(0.640014\pi\) | |||||||
\(674\) | −40690.6 | −2.32543 | ||||||||
\(675\) | −2834.91 | −0.161653 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20769.5 | −1.17908 | −0.589540 | − | 0.807739i | \(-0.700691\pi\) | ||||
−0.589540 | + | 0.807739i | \(0.700691\pi\) | |||||||
\(678\) | 12063.7 | 0.683341 | ||||||||
\(679\) | −7802.09 | −0.440967 | ||||||||
\(680\) | 13403.9 | 0.755907 | ||||||||
\(681\) | −3436.56 | −0.193376 | ||||||||
\(682\) | 899.650 | 0.0505123 | ||||||||
\(683\) | −14980.8 | −0.839275 | −0.419638 | − | 0.907692i | \(-0.637843\pi\) | ||||
−0.419638 | + | 0.907692i | \(0.637843\pi\) | |||||||
\(684\) | 19817.1 | 1.10779 | ||||||||
\(685\) | 8080.90 | 0.450738 | ||||||||
\(686\) | 6949.30 | 0.386772 | ||||||||
\(687\) | −4045.40 | −0.224660 | ||||||||
\(688\) | −3719.96 | −0.206137 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −11058.3 | −0.610122 | ||||||||
\(691\) | −9472.45 | −0.521489 | −0.260745 | − | 0.965408i | \(-0.583968\pi\) | ||||
−0.260745 | + | 0.965408i | \(0.583968\pi\) | |||||||
\(692\) | −51605.8 | −2.83491 | ||||||||
\(693\) | −1467.37 | −0.0804342 | ||||||||
\(694\) | 1633.12 | 0.0893260 | ||||||||
\(695\) | −5497.95 | −0.300071 | ||||||||
\(696\) | −17537.8 | −0.955128 | ||||||||
\(697\) | −4893.87 | −0.265952 | ||||||||
\(698\) | 51540.3 | 2.79488 | ||||||||
\(699\) | −2856.01 | −0.154541 | ||||||||
\(700\) | 40205.7 | 2.17090 | ||||||||
\(701\) | 1035.34 | 0.0557834 | 0.0278917 | − | 0.999611i | \(-0.491121\pi\) | ||||
0.0278917 | + | 0.999611i | \(0.491121\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −53844.8 | −2.88875 | ||||||||
\(704\) | −4615.72 | −0.247105 | ||||||||
\(705\) | −3563.86 | −0.190387 | ||||||||
\(706\) | −48790.0 | −2.60090 | ||||||||
\(707\) | 33156.7 | 1.76377 | ||||||||
\(708\) | 5807.92 | 0.308298 | ||||||||
\(709\) | −16800.4 | −0.889917 | −0.444958 | − | 0.895551i | \(-0.646781\pi\) | ||||
−0.444958 | + | 0.895551i | \(0.646781\pi\) | |||||||
\(710\) | 9168.18 | 0.484614 | ||||||||
\(711\) | −9157.57 | −0.483032 | ||||||||
\(712\) | 16149.0 | 0.850013 | ||||||||
\(713\) | 5606.00 | 0.294455 | ||||||||
\(714\) | 40282.4 | 2.11139 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 58734.1 | 3.06564 | ||||||||
\(717\) | 9207.35 | 0.479574 | ||||||||
\(718\) | −40713.7 | −2.11618 | ||||||||
\(719\) | 14873.1 | 0.771449 | 0.385724 | − | 0.922614i | \(-0.373952\pi\) | ||||
0.385724 | + | 0.922614i | \(0.373952\pi\) | |||||||
\(720\) | −864.107 | −0.0447269 | ||||||||
\(721\) | −2020.27 | −0.104353 | ||||||||
\(722\) | −82788.1 | −4.26739 | ||||||||
\(723\) | −7524.51 | −0.387053 | ||||||||
\(724\) | −7025.24 | −0.360623 | ||||||||
\(725\) | −21512.4 | −1.10200 | ||||||||
\(726\) | 18253.9 | 0.933146 | ||||||||
\(727\) | −2318.92 | −0.118300 | −0.0591500 | − | 0.998249i | \(-0.518839\pi\) | ||||
−0.0591500 | + | 0.998249i | \(0.518839\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −24355.9 | −1.23487 | ||||||||
\(731\) | −18201.3 | −0.920931 | ||||||||
\(732\) | −2488.34 | −0.125644 | ||||||||
\(733\) | 3350.95 | 0.168854 | 0.0844270 | − | 0.996430i | \(-0.473094\pi\) | ||||
0.0844270 | + | 0.996430i | \(0.473094\pi\) | |||||||
\(734\) | −5798.61 | −0.291595 | ||||||||
\(735\) | −5331.58 | −0.267562 | ||||||||
\(736\) | −22349.6 | −1.11932 | ||||||||
\(737\) | −1268.33 | −0.0633915 | ||||||||
\(738\) | 1970.09 | 0.0982656 | ||||||||
\(739\) | 29348.1 | 1.46088 | 0.730438 | − | 0.682979i | \(-0.239316\pi\) | ||||
0.730438 | + | 0.682979i | \(0.239316\pi\) | |||||||
\(740\) | 21660.8 | 1.07604 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22104.3 | 1.09363 | ||||||||
\(743\) | −23622.2 | −1.16637 | −0.583187 | − | 0.812338i | \(-0.698195\pi\) | ||||
−0.583187 | + | 0.812338i | \(0.698195\pi\) | |||||||
\(744\) | 2735.45 | 0.134793 | ||||||||
\(745\) | 1995.30 | 0.0981236 | ||||||||
\(746\) | 2008.40 | 0.0985693 | ||||||||
\(747\) | 1352.26 | 0.0662336 | ||||||||
\(748\) | 8857.41 | 0.432966 | ||||||||
\(749\) | 34106.1 | 1.66383 | ||||||||
\(750\) | −14498.5 | −0.705882 | ||||||||
\(751\) | 29751.4 | 1.44560 | 0.722798 | − | 0.691059i | \(-0.242856\pi\) | ||||
0.722798 | + | 0.691059i | \(0.242856\pi\) | |||||||
\(752\) | 5701.97 | 0.276502 | ||||||||
\(753\) | 10217.7 | 0.494495 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 926.735 | 0.0446720 | ||||||||
\(756\) | −10338.9 | −0.497385 | ||||||||
\(757\) | −36907.2 | −1.77201 | −0.886006 | − | 0.463673i | \(-0.846531\pi\) | ||||
−0.886006 | + | 0.463673i | \(0.846531\pi\) | |||||||
\(758\) | 583.709 | 0.0279700 | ||||||||
\(759\) | −3153.45 | −0.150807 | ||||||||
\(760\) | 19966.4 | 0.952968 | ||||||||
\(761\) | 20208.2 | 0.962613 | 0.481306 | − | 0.876552i | \(-0.340162\pi\) | ||||
0.481306 | + | 0.876552i | \(0.340162\pi\) | |||||||
\(762\) | −10234.2 | −0.486541 | ||||||||
\(763\) | 19662.8 | 0.932950 | ||||||||
\(764\) | −43439.1 | −2.05703 | ||||||||
\(765\) | −4227.98 | −0.199821 | ||||||||
\(766\) | 43886.9 | 2.07010 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −18156.1 | −0.853063 | ||||||||
\(769\) | −24751.0 | −1.16066 | −0.580329 | − | 0.814382i | \(-0.697076\pi\) | ||||
−0.580329 | + | 0.814382i | \(0.697076\pi\) | |||||||
\(770\) | −3425.94 | −0.160341 | ||||||||
\(771\) | −14201.9 | −0.663382 | ||||||||
\(772\) | −23138.2 | −1.07871 | ||||||||
\(773\) | 30673.4 | 1.42722 | 0.713612 | − | 0.700541i | \(-0.247058\pi\) | ||||
0.713612 | + | 0.700541i | \(0.247058\pi\) | |||||||
\(774\) | 7327.18 | 0.340271 | ||||||||
\(775\) | 3355.38 | 0.155521 | ||||||||
\(776\) | −8181.46 | −0.378476 | ||||||||
\(777\) | 28091.7 | 1.29702 | ||||||||
\(778\) | −53413.4 | −2.46139 | ||||||||
\(779\) | −7289.87 | −0.335285 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2614.44 | 0.119785 | ||||||||
\(782\) | 86568.5 | 3.95867 | ||||||||
\(783\) | 5531.93 | 0.252484 | ||||||||
\(784\) | 8530.23 | 0.388585 | ||||||||
\(785\) | −4904.55 | −0.222995 | ||||||||
\(786\) | 20534.6 | 0.931862 | ||||||||
\(787\) | −29009.9 | −1.31397 | −0.656983 | − | 0.753905i | \(-0.728168\pi\) | ||||
−0.656983 | + | 0.753905i | \(0.728168\pi\) | |||||||
\(788\) | 19297.1 | 0.872375 | ||||||||
\(789\) | −5598.33 | −0.252606 | ||||||||
\(790\) | −21380.6 | −0.962894 | ||||||||
\(791\) | 23289.0 | 1.04685 | ||||||||
\(792\) | −1538.72 | −0.0690355 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −56744.0 | −2.53623 | ||||||||
\(795\) | −2320.04 | −0.103501 | ||||||||
\(796\) | −65120.8 | −2.89968 | ||||||||
\(797\) | 6778.24 | 0.301252 | 0.150626 | − | 0.988591i | \(-0.451871\pi\) | ||||
0.150626 | + | 0.988591i | \(0.451871\pi\) | |||||||
\(798\) | 60004.3 | 2.66182 | ||||||||
\(799\) | 27899.1 | 1.23529 | ||||||||
\(800\) | −13377.0 | −0.591185 | ||||||||
\(801\) | −5093.86 | −0.224697 | ||||||||
\(802\) | −22817.9 | −1.00465 | ||||||||
\(803\) | −6945.44 | −0.305229 | ||||||||
\(804\) | −8936.48 | −0.391997 | ||||||||
\(805\) | −21348.1 | −0.934685 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4740.58 | 0.206786 | ||||||||
\(808\) | 34768.9 | 1.51382 | ||||||||
\(809\) | −34862.9 | −1.51510 | −0.757549 | − | 0.652778i | \(-0.773603\pi\) | ||||
−0.757549 | + | 0.652778i | \(0.773603\pi\) | |||||||
\(810\) | 1702.03 | 0.0738310 | ||||||||
\(811\) | −22665.4 | −0.981370 | −0.490685 | − | 0.871337i | \(-0.663253\pi\) | ||||
−0.490685 | + | 0.871337i | \(0.663253\pi\) | |||||||
\(812\) | −78455.6 | −3.39070 | ||||||||
\(813\) | −14766.3 | −0.636993 | ||||||||
\(814\) | 9688.21 | 0.417164 | ||||||||
\(815\) | −14107.4 | −0.606331 | ||||||||
\(816\) | 6764.52 | 0.290203 | ||||||||
\(817\) | −27112.6 | −1.16101 | ||||||||
\(818\) | 14009.1 | 0.598797 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2932.59 | 0.124891 | ||||||||
\(821\) | −20748.7 | −0.882016 | −0.441008 | − | 0.897503i | \(-0.645379\pi\) | ||||
−0.441008 | + | 0.897503i | \(0.645379\pi\) | |||||||
\(822\) | 25466.1 | 1.08058 | ||||||||
\(823\) | 6141.41 | 0.260117 | 0.130058 | − | 0.991506i | \(-0.458484\pi\) | ||||
0.130058 | + | 0.991506i | \(0.458484\pi\) | |||||||
\(824\) | −2118.50 | −0.0895650 | ||||||||
\(825\) | −1887.44 | −0.0796513 | ||||||||
\(826\) | 17585.8 | 0.740786 | ||||||||
\(827\) | 28383.5 | 1.19346 | 0.596730 | − | 0.802442i | \(-0.296467\pi\) | ||||
0.596730 | + | 0.802442i | \(0.296467\pi\) | |||||||
\(828\) | −22218.8 | −0.932555 | ||||||||
\(829\) | −908.734 | −0.0380720 | −0.0190360 | − | 0.999819i | \(-0.506060\pi\) | ||||
−0.0190360 | + | 0.999819i | \(0.506060\pi\) | |||||||
\(830\) | 3157.17 | 0.132032 | ||||||||
\(831\) | 8061.25 | 0.336512 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 41737.4 | 1.73603 | ||||||||
\(834\) | −17326.2 | −0.719375 | ||||||||
\(835\) | 16457.2 | 0.682065 | ||||||||
\(836\) | 13193.9 | 0.545839 | ||||||||
\(837\) | −862.838 | −0.0356321 | ||||||||
\(838\) | −36523.8 | −1.50560 | ||||||||
\(839\) | 27820.3 | 1.14477 | 0.572385 | − | 0.819985i | \(-0.306018\pi\) | ||||
0.572385 | + | 0.819985i | \(0.306018\pi\) | |||||||
\(840\) | −10416.8 | −0.427873 | ||||||||
\(841\) | 17589.3 | 0.721200 | ||||||||
\(842\) | 18603.5 | 0.761425 | ||||||||
\(843\) | −2651.26 | −0.108321 | ||||||||
\(844\) | 71608.3 | 2.92045 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11231.1 | −0.456424 | ||||||||
\(847\) | 35239.0 | 1.42955 | ||||||||
\(848\) | 3711.93 | 0.150316 | ||||||||
\(849\) | −1409.33 | −0.0569706 | ||||||||
\(850\) | 51814.1 | 2.09084 | ||||||||
\(851\) | 60370.3 | 2.43181 | ||||||||
\(852\) | 18421.0 | 0.740719 | ||||||||
\(853\) | −5802.11 | −0.232896 | −0.116448 | − | 0.993197i | \(-0.537151\pi\) | ||||
−0.116448 | + | 0.993197i | \(0.537151\pi\) | |||||||
\(854\) | −7534.45 | −0.301901 | ||||||||
\(855\) | −6297.96 | −0.251913 | ||||||||
\(856\) | 35764.5 | 1.42804 | ||||||||
\(857\) | −43311.1 | −1.72635 | −0.863173 | − | 0.504909i | \(-0.831526\pi\) | ||||
−0.863173 | + | 0.504909i | \(0.831526\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16698.2 | −0.663254 | −0.331627 | − | 0.943411i | \(-0.607598\pi\) | ||||
−0.331627 | + | 0.943411i | \(0.607598\pi\) | |||||||
\(860\) | 10906.9 | 0.432468 | ||||||||
\(861\) | 3803.25 | 0.150539 | ||||||||
\(862\) | 20555.2 | 0.812196 | ||||||||
\(863\) | −19429.2 | −0.766369 | −0.383185 | − | 0.923672i | \(-0.625173\pi\) | ||||
−0.383185 | + | 0.923672i | \(0.625173\pi\) | |||||||
\(864\) | 3439.90 | 0.135449 | ||||||||
\(865\) | 16400.6 | 0.644666 | ||||||||
\(866\) | −42249.7 | −1.65786 | ||||||||
\(867\) | 18359.0 | 0.719153 | ||||||||
\(868\) | 12237.0 | 0.478517 | ||||||||
\(869\) | −6096.98 | −0.238004 | ||||||||
\(870\) | 12915.6 | 0.503311 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 20618.9 | 0.800738 | ||||||||
\(873\) | 2580.67 | 0.100048 | ||||||||
\(874\) | 128952. | 4.99068 | ||||||||
\(875\) | −27989.4 | −1.08139 | ||||||||
\(876\) | −48936.6 | −1.88746 | ||||||||
\(877\) | −11619.7 | −0.447400 | −0.223700 | − | 0.974658i | \(-0.571814\pi\) | ||||
−0.223700 | + | 0.974658i | \(0.571814\pi\) | |||||||
\(878\) | 918.332 | 0.0352986 | ||||||||
\(879\) | 10211.3 | 0.391829 | ||||||||
\(880\) | −575.309 | −0.0220383 | ||||||||
\(881\) | −51102.0 | −1.95422 | −0.977112 | − | 0.212726i | \(-0.931766\pi\) | ||||
−0.977112 | + | 0.212726i | \(0.931766\pi\) | |||||||
\(882\) | −16801.9 | −0.641441 | ||||||||
\(883\) | −37838.5 | −1.44209 | −0.721046 | − | 0.692888i | \(-0.756338\pi\) | ||||
−0.721046 | + | 0.692888i | \(0.756338\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1845.78 | −0.0701077 | ||||||||
\(886\) | −34625.6 | −1.31295 | ||||||||
\(887\) | −9626.92 | −0.364420 | −0.182210 | − | 0.983260i | \(-0.558325\pi\) | ||||
−0.182210 | + | 0.983260i | \(0.558325\pi\) | |||||||
\(888\) | 29457.7 | 1.11321 | ||||||||
\(889\) | −19757.0 | −0.745364 | ||||||||
\(890\) | −11892.8 | −0.447920 | ||||||||
\(891\) | 485.357 | 0.0182493 | ||||||||
\(892\) | −66774.3 | −2.50647 | ||||||||
\(893\) | 41558.3 | 1.55733 | ||||||||
\(894\) | 6287.98 | 0.235237 | ||||||||
\(895\) | −18666.0 | −0.697133 | ||||||||
\(896\) | −70740.0 | −2.63757 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −771.825 | −0.0286816 | ||||||||
\(899\) | −6547.54 | −0.242906 | ||||||||
\(900\) | −13298.7 | −0.492543 | ||||||||
\(901\) | 18162.0 | 0.671549 | ||||||||
\(902\) | 1311.66 | 0.0484184 | ||||||||
\(903\) | 14145.1 | 0.521283 | ||||||||
\(904\) | 24421.4 | 0.898500 | ||||||||
\(905\) | 2232.65 | 0.0820065 | ||||||||
\(906\) | 2920.51 | 0.107094 | ||||||||
\(907\) | 17066.0 | 0.624772 | 0.312386 | − | 0.949955i | \(-0.398872\pi\) | ||||
0.312386 | + | 0.949955i | \(0.398872\pi\) | |||||||
\(908\) | −16121.0 | −0.589200 | ||||||||
\(909\) | −10967.1 | −0.400172 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37423.9 | −1.36104 | −0.680521 | − | 0.732729i | \(-0.738246\pi\) | ||||
−0.680521 | + | 0.732729i | \(0.738246\pi\) | |||||||
\(912\) | 10076.4 | 0.365858 | ||||||||
\(913\) | 900.312 | 0.0326353 | ||||||||
\(914\) | 54907.7 | 1.98708 | ||||||||
\(915\) | 790.805 | 0.0285718 | ||||||||
\(916\) | −18977.1 | −0.684520 | ||||||||
\(917\) | 39641.9 | 1.42758 | ||||||||
\(918\) | −13324.0 | −0.479040 | ||||||||
\(919\) | −2783.88 | −0.0999256 | −0.0499628 | − | 0.998751i | \(-0.515910\pi\) | ||||
−0.0499628 | + | 0.998751i | \(0.515910\pi\) | |||||||
\(920\) | −22386.1 | −0.802227 | ||||||||
\(921\) | 2666.59 | 0.0954039 | ||||||||
\(922\) | 4968.50 | 0.177472 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −6883.50 | −0.245076 | ||||||||
\(925\) | 36133.6 | 1.28440 | ||||||||
\(926\) | 40191.9 | 1.42634 | ||||||||
\(927\) | 668.236 | 0.0236761 | ||||||||
\(928\) | 26103.3 | 0.923363 | ||||||||
\(929\) | −26585.2 | −0.938894 | −0.469447 | − | 0.882961i | \(-0.655547\pi\) | ||||
−0.469447 | + | 0.882961i | \(0.655547\pi\) | |||||||
\(930\) | −2014.50 | −0.0710303 | ||||||||
\(931\) | 62171.8 | 2.18861 | ||||||||
\(932\) | −13397.6 | −0.470873 | ||||||||
\(933\) | −3655.09 | −0.128255 | ||||||||
\(934\) | 36200.9 | 1.26823 | ||||||||
\(935\) | −2814.92 | −0.0984576 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34474.0 | 1.20194 | 0.600970 | − | 0.799272i | \(-0.294781\pi\) | ||||
0.600970 | + | 0.799272i | \(0.294781\pi\) | |||||||
\(938\) | −27058.8 | −0.941900 | ||||||||
\(939\) | −14611.2 | −0.507795 | ||||||||
\(940\) | −16718.2 | −0.580092 | ||||||||
\(941\) | 41994.3 | 1.45481 | 0.727404 | − | 0.686209i | \(-0.240726\pi\) | ||||
0.727404 | + | 0.686209i | \(0.240726\pi\) | |||||||
\(942\) | −15456.2 | −0.534596 | ||||||||
\(943\) | 8173.34 | 0.282249 | ||||||||
\(944\) | 2953.15 | 0.101819 | ||||||||
\(945\) | 3285.75 | 0.113106 | ||||||||
\(946\) | 4878.32 | 0.167662 | ||||||||
\(947\) | 49352.0 | 1.69348 | 0.846739 | − | 0.532008i | \(-0.178562\pi\) | ||||
0.846739 | + | 0.532008i | \(0.178562\pi\) | |||||||
\(948\) | −42958.5 | −1.47176 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 77181.9 | 2.63591 | ||||||||
\(951\) | −13022.8 | −0.444052 | ||||||||
\(952\) | 81546.2 | 2.77618 | ||||||||
\(953\) | −51144.5 | −1.73844 | −0.869220 | − | 0.494425i | \(-0.835379\pi\) | ||||
−0.869220 | + | 0.494425i | \(0.835379\pi\) | |||||||
\(954\) | −7311.36 | −0.248128 | ||||||||
\(955\) | 13805.2 | 0.467774 | ||||||||
\(956\) | 43192.0 | 1.46122 | ||||||||
\(957\) | 3683.07 | 0.124406 | ||||||||
\(958\) | −21182.3 | −0.714372 | ||||||||
\(959\) | 49162.3 | 1.65540 | ||||||||
\(960\) | 10335.6 | 0.347478 | ||||||||
\(961\) | −28769.8 | −0.965720 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11281.1 | −0.377497 | ||||||||
\(964\) | −35297.7 | −1.17932 | ||||||||
\(965\) | 7353.41 | 0.245300 | ||||||||
\(966\) | −67276.3 | −2.24077 | ||||||||
\(967\) | 24895.1 | 0.827892 | 0.413946 | − | 0.910301i | \(-0.364150\pi\) | ||||
0.413946 | + | 0.910301i | \(0.364150\pi\) | |||||||
\(968\) | 36952.4 | 1.22696 | ||||||||
\(969\) | 49302.6 | 1.63450 | ||||||||
\(970\) | 6025.19 | 0.199440 | ||||||||
\(971\) | 42942.9 | 1.41926 | 0.709630 | − | 0.704574i | \(-0.248862\pi\) | ||||
0.709630 | + | 0.704574i | \(0.248862\pi\) | |||||||
\(972\) | 3419.76 | 0.112849 | ||||||||
\(973\) | −33448.2 | −1.10206 | ||||||||
\(974\) | 31598.8 | 1.03952 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1265.24 | −0.0414953 | ||||||||
\(977\) | −42555.7 | −1.39353 | −0.696764 | − | 0.717301i | \(-0.745377\pi\) | ||||
−0.696764 | + | 0.717301i | \(0.745377\pi\) | |||||||
\(978\) | −44458.0 | −1.45359 | ||||||||
\(979\) | −3391.41 | −0.110715 | ||||||||
\(980\) | −25010.6 | −0.815240 | ||||||||
\(981\) | −6503.78 | −0.211672 | ||||||||
\(982\) | −54111.3 | −1.75841 | ||||||||
\(983\) | 4345.38 | 0.140993 | 0.0704965 | − | 0.997512i | \(-0.477542\pi\) | ||||
0.0704965 | + | 0.997512i | \(0.477542\pi\) | |||||||
\(984\) | 3988.18 | 0.129206 | ||||||||
\(985\) | −6132.71 | −0.198380 | ||||||||
\(986\) | −101108. | −3.26565 | ||||||||
\(987\) | −21681.7 | −0.699225 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30398.4 | 0.977363 | ||||||||
\(990\) | 1133.18 | 0.0363787 | ||||||||
\(991\) | 7934.89 | 0.254349 | 0.127175 | − | 0.991880i | \(-0.459409\pi\) | ||||
0.127175 | + | 0.991880i | \(0.459409\pi\) | |||||||
\(992\) | −4071.43 | −0.130311 | ||||||||
\(993\) | −2721.87 | −0.0869848 | ||||||||
\(994\) | 55777.0 | 1.77982 | ||||||||
\(995\) | 20695.7 | 0.659395 | ||||||||
\(996\) | 6343.48 | 0.201808 | ||||||||
\(997\) | 2725.62 | 0.0865810 | 0.0432905 | − | 0.999063i | \(-0.486216\pi\) | ||||
0.0432905 | + | 0.999063i | \(0.486216\pi\) | |||||||
\(998\) | 93531.5 | 2.96662 | ||||||||
\(999\) | −9291.79 | −0.294273 |
(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 | 507.4.a.o.1.2 | ✓ | 9 | |
3.2 | odd | 2 | 1521.4.a.bi.1.8 | 9 | |||
13.5 | odd | 4 | 507.4.b.k.337.16 | 18 | |||
13.8 | odd | 4 | 507.4.b.k.337.3 | 18 | |||
13.12 | even | 2 | 507.4.a.p.1.8 | yes | 9 | ||
39.38 | odd | 2 | 1521.4.a.bf.1.2 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.2 | ✓ | 9 | 1.1 | even | 1 | trivial | |
507.4.a.p.1.8 | yes | 9 | 13.12 | even | 2 | ||
507.4.b.k.337.3 | 18 | 13.8 | odd | 4 | |||
507.4.b.k.337.16 | 18 | 13.5 | odd | 4 | |||
1521.4.a.bf.1.2 | 9 | 39.38 | odd | 2 | |||
1521.4.a.bi.1.8 | 9 | 3.2 | odd | 2 |