Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(17,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 113.7 | ||
Character | \(\chi\) | \(=\) | 128.113 |
Dual form | 128.4.g.a.17.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.998206 | + | 2.40988i | 0.192105 | + | 0.463782i | 0.990357 | − | 0.138542i | \(-0.0442415\pi\) |
−0.798252 | + | 0.602324i | \(0.794242\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 17.4005 | + | 7.20752i | 1.55635 | + | 0.644661i | 0.984450 | − | 0.175664i | \(-0.0562073\pi\) |
0.571898 | + | 0.820325i | \(0.306207\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.37099 | − | 4.37099i | −0.236012 | − | 0.236012i | 0.579185 | − | 0.815196i | \(-0.303371\pi\) |
−0.815196 | + | 0.579185i | \(0.803371\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 14.2808 | − | 14.2808i | 0.528917 | − | 0.528917i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.7977 | + | 28.4821i | −0.323375 | + | 0.780697i | 0.675678 | + | 0.737197i | \(0.263851\pi\) |
−0.999053 | + | 0.0435002i | \(0.986149\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.9230 | + | 5.35288i | −0.275707 | + | 0.114202i | −0.516253 | − | 0.856436i | \(-0.672674\pi\) |
0.240546 | + | 0.970638i | \(0.422674\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 49.1278i | 0.845649i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 72.9239i | 1.04039i | 0.854047 | + | 0.520195i | \(0.174141\pi\) | ||||
−0.854047 | + | 0.520195i | \(0.825859\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 143.136 | − | 59.2889i | 1.72830 | − | 0.715884i | 0.728783 | − | 0.684745i | \(-0.240086\pi\) |
0.999515 | − | 0.0311397i | \(-0.00991368\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.17043 | − | 14.8967i | 0.0641190 | − | 0.154797i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −83.6411 | + | 83.6411i | −0.758278 | + | 0.758278i | −0.976009 | − | 0.217731i | \(-0.930134\pi\) |
0.217731 | + | 0.976009i | \(0.430134\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 162.441 | + | 162.441i | 1.29953 | + | 1.29953i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 113.737 | + | 47.1114i | 0.810692 | + | 0.335800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −39.6554 | − | 95.7367i | −0.253925 | − | 0.613030i | 0.744589 | − | 0.667523i | \(-0.232646\pi\) |
−0.998514 | + | 0.0544937i | \(0.982646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29.0324 | 0.168206 | 0.0841029 | − | 0.996457i | \(-0.473198\pi\) | ||||
0.0841029 | + | 0.996457i | \(0.473198\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −80.4149 | −0.424195 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −44.5534 | − | 107.562i | −0.215169 | − | 0.519463i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −267.681 | − | 110.877i | −1.18936 | − | 0.492650i | −0.301815 | − | 0.953366i | \(-0.597593\pi\) |
−0.887547 | + | 0.460716i | \(0.847593\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −25.7996 | − | 25.7996i | −0.105929 | − | 0.105929i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −124.918 | + | 124.918i | −0.475827 | + | 0.475827i | −0.903794 | − | 0.427968i | \(-0.859230\pi\) |
0.427968 | + | 0.903794i | \(0.359230\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.0156 | − | 65.2215i | 0.0958103 | − | 0.231306i | −0.868707 | − | 0.495326i | \(-0.835048\pi\) |
0.964517 | + | 0.264020i | \(0.0850485\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 351.421 | − | 145.564i | 1.16415 | − | 0.482207i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 282.627i | − | 0.877136i | −0.898698 | − | 0.438568i | \(-0.855486\pi\) | ||
0.898698 | − | 0.438568i | \(-0.144514\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 304.789i | − | 0.888597i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −175.738 | + | 72.7931i | −0.482515 | + | 0.199864i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −51.4343 | + | 124.173i | −0.133303 | + | 0.321821i | −0.976410 | − | 0.215924i | \(-0.930724\pi\) |
0.843107 | + | 0.537745i | \(0.180724\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −410.570 | + | 410.570i | −1.00657 | + | 1.00657i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 285.759 | + | 285.759i | 0.664029 | + | 0.664029i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 222.476 | + | 92.1524i | 0.490913 | + | 0.203343i | 0.614387 | − | 0.789005i | \(-0.289404\pi\) |
−0.123474 | + | 0.992348i | \(0.539404\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −226.809 | − | 547.566i | −0.476065 | − | 1.14932i | −0.961440 | − | 0.275016i | \(-0.911317\pi\) |
0.485374 | − | 0.874306i | \(-0.338683\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −124.842 | −0.249661 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −263.447 | −0.502717 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −356.015 | − | 859.496i | −0.649166 | − | 1.56723i | −0.813975 | − | 0.580900i | \(-0.802701\pi\) |
0.164808 | − | 0.986326i | \(-0.447299\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −285.056 | − | 118.074i | −0.497344 | − | 0.206007i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −690.837 | − | 690.837i | −1.15475 | − | 1.15475i | −0.985588 | − | 0.169163i | \(-0.945894\pi\) |
−0.169163 | − | 0.985588i | \(-0.554106\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 223.345 | − | 223.345i | 0.358089 | − | 0.358089i | −0.505019 | − | 0.863108i | \(-0.668515\pi\) |
0.863108 | + | 0.505019i | \(0.168515\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −229.314 | + | 553.612i | −0.353052 | + | 0.852342i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 176.062 | − | 72.9275i | 0.260574 | − | 0.107933i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 698.000i | 0.994065i | 0.867732 | + | 0.497033i | \(0.165577\pi\) | ||||
−0.867732 | + | 0.497033i | \(0.834423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 224.174i | − | 0.307509i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 915.116 | − | 379.053i | 1.21020 | − | 0.501283i | 0.315922 | − | 0.948785i | \(-0.397686\pi\) |
0.894283 | + | 0.447502i | \(0.147686\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −525.601 | + | 1268.91i | −0.670699 | + | 1.61921i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 191.130 | − | 191.130i | 0.235532 | − | 0.235532i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −163.738 | − | 163.738i | −0.195014 | − | 0.195014i | 0.602845 | − | 0.797859i | \(-0.294034\pi\) |
−0.797859 | + | 0.602845i | \(0.794034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 79.8837 | + | 33.0889i | 0.0920229 | + | 0.0381171i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 28.9803 | + | 69.9647i | 0.0323131 | + | 0.0780108i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2917.97 | 3.15134 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −839.460 | −0.878704 | −0.439352 | − | 0.898315i | \(-0.644792\pi\) | ||||
−0.439352 | + | 0.898315i | \(0.644792\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 238.266 | + | 575.225i | 0.241885 | + | 0.583963i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1561.02 | + | 646.594i | 1.53789 | + | 0.637015i | 0.981076 | − | 0.193622i | \(-0.0620235\pi\) |
0.556814 | + | 0.830637i | \(0.312024\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 80.1481 | + | 80.1481i | 0.0766721 | + | 0.0766721i | 0.744403 | − | 0.667731i | \(-0.232734\pi\) |
−0.667731 | + | 0.744403i | \(0.732734\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 214.737 | − | 214.737i | 0.199583 | − | 0.199583i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −552.814 | + | 1334.61i | −0.499463 | + | 1.20581i | 0.450310 | + | 0.892872i | \(0.351313\pi\) |
−0.949773 | + | 0.312939i | \(0.898687\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 490.666 | − | 203.241i | 0.431168 | − | 0.178596i | −0.156535 | − | 0.987672i | \(-0.550032\pi\) |
0.587703 | + | 0.809077i | \(0.300032\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 755.757i | − | 0.646246i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 109.197i | − | 0.0909060i | −0.998966 | − | 0.0454530i | \(-0.985527\pi\) | ||
0.998966 | − | 0.0454530i | \(-0.0144731\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2058.24 | + | 852.552i | −1.66898 | + | 0.691312i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −108.107 | + | 260.993i | −0.0854230 | + | 0.206229i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 318.750 | − | 318.750i | 0.245544 | − | 0.245544i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 269.116 | + | 269.116i | 0.202191 | + | 0.202191i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −425.731 | − | 176.344i | −0.312088 | − | 0.129271i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 754.814 | + | 1822.28i | 0.540101 | + | 1.30392i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1519.49 | −1.06167 | −0.530837 | − | 0.847474i | \(-0.678122\pi\) | ||||
−0.530837 | + | 0.847474i | \(0.678122\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 184.143 | 0.125681 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −386.047 | − | 932.000i | −0.257474 | − | 0.621597i | 0.741296 | − | 0.671178i | \(-0.234211\pi\) |
−0.998770 | + | 0.0495811i | \(0.984211\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −884.798 | − | 366.495i | −0.576855 | − | 0.238941i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1639.52 | + | 1639.52i | 1.04524 | + | 1.04524i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 121.798 | − | 121.798i | 0.0759557 | − | 0.0759557i | −0.668108 | − | 0.744064i | \(-0.732896\pi\) |
0.744064 | + | 0.668108i | \(0.232896\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.36667 | − | 5.71364i | 0.00144416 | − | 0.00348651i | −0.923156 | − | 0.384426i | \(-0.874399\pi\) |
0.924600 | + | 0.380939i | \(0.124399\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 681.098 | − | 282.120i | 0.406800 | − | 0.168502i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 431.225i | − | 0.252174i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1951.68i | − | 1.11778i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 734.505 | − | 304.242i | 0.412115 | − | 0.170704i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 311.513 | − | 752.060i | 0.171276 | − | 0.413497i | −0.814811 | − | 0.579727i | \(-0.803159\pi\) |
0.986087 | + | 0.166229i | \(0.0531592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −571.254 | + | 571.254i | −0.307868 | + | 0.307868i | −0.844082 | − | 0.536214i | \(-0.819854\pi\) |
0.536214 | + | 0.844082i | \(0.319854\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1041.41 | + | 1041.41i | 0.550281 | + | 0.550281i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 505.179 | + | 209.252i | 0.261787 | + | 0.108436i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −219.641 | − | 530.260i | −0.111651 | − | 0.269550i | 0.858171 | − | 0.513365i | \(-0.171601\pi\) |
−0.969822 | + | 0.243814i | \(0.921601\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −350.585 | −0.174863 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 731.190 | 0.357924 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 570.638 | + | 1377.64i | 0.274207 | + | 0.661995i | 0.999655 | − | 0.0262826i | \(-0.00836698\pi\) |
−0.725447 | + | 0.688278i | \(0.758367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1399.26 | − | 579.593i | −0.660196 | − | 0.273462i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −642.374 | − | 642.374i | −0.297655 | − | 0.297655i | 0.542440 | − | 0.840095i | \(-0.317501\pi\) |
−0.840095 | + | 0.542440i | \(0.817501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1415.16 | + | 1415.16i | −0.644134 | + | 0.644134i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1197.40 | − | 2890.78i | 0.535483 | − | 1.29277i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1861.21 | + | 770.937i | −0.817948 | + | 0.338805i | −0.752120 | − | 0.659026i | \(-0.770969\pi\) |
−0.0658275 | + | 0.997831i | \(0.520969\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1420.06i | − | 0.613406i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 628.127i | 0.266740i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 317.221 | − | 131.397i | 0.132459 | − | 0.0548664i | −0.315469 | − | 0.948936i | \(-0.602162\pi\) |
0.447928 | + | 0.894069i | \(0.352162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 532.578 | − | 1285.76i | 0.218708 | − | 0.528008i | −0.776002 | − | 0.630731i | \(-0.782755\pi\) |
0.994710 | + | 0.102722i | \(0.0327553\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1093.17 | − | 1093.17i | 0.441581 | − | 0.441581i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3858.63 | − | 3858.63i | −1.53347 | − | 1.53347i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2077.02 | − | 860.331i | −0.812230 | − | 0.336437i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −291.220 | − | 703.067i | −0.112080 | − | 0.270585i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3161.63 | −1.19773 | −0.598867 | − | 0.800848i | \(-0.704382\pi\) | ||||
−0.598867 | + | 0.800848i | \(0.704382\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1428.55 | −0.532796 | −0.266398 | − | 0.963863i | \(-0.585834\pi\) | ||||
−0.266398 | + | 0.963863i | \(0.585834\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −262.975 | − | 634.877i | −0.0965744 | − | 0.233151i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1377.48 | + | 570.573i | 0.498181 | + | 0.206353i | 0.617603 | − | 0.786490i | \(-0.288104\pi\) |
−0.119421 | + | 0.992844i | \(0.538104\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1207.72 | − | 1207.72i | −0.430217 | − | 0.430217i | 0.458485 | − | 0.888702i | \(-0.348392\pi\) |
−0.888702 | + | 0.458485i | \(0.848392\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1715.91 | − | 1715.91i | 0.602143 | − | 0.602143i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −245.131 | + | 591.798i | −0.0847528 | + | 0.204611i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3073.98 | + | 1273.28i | −1.04730 | + | 0.433805i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2388.92i | 0.802132i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4776.28i | 1.58078i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 627.654 | − | 259.983i | 0.204784 | − | 0.0848245i | −0.277934 | − | 0.960600i | \(-0.589650\pi\) |
0.482718 | + | 0.875776i | \(0.339650\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 975.239 | − | 2354.43i | 0.313720 | − | 0.757386i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 940.170 | − | 940.170i | 0.298228 | − | 0.298228i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −126.901 | − | 126.901i | −0.0396985 | − | 0.0396985i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 761.178 | + | 315.290i | 0.234866 | + | 0.0972846i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −390.353 | − | 942.394i | −0.118814 | − | 0.286843i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1684.85 | −0.505946 | −0.252973 | − | 0.967473i | \(-0.581408\pi\) | ||||
−0.252973 | + | 0.967473i | \(0.581408\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4639.56 | 1.37468 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1751.96 | + | 4229.60i | 0.512254 | + | 1.23669i | 0.942569 | + | 0.334011i | \(0.108402\pi\) |
−0.430315 | + | 0.902679i | \(0.641598\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1072.62 | + | 444.292i | 0.309521 | + | 0.128208i | 0.532037 | − | 0.846721i | \(-0.321427\pi\) |
−0.222515 | + | 0.974929i | \(0.571427\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 351.493 | + | 351.493i | 0.100115 | + | 0.100115i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −224.008 | + | 224.008i | −0.0629840 | + | 0.0629840i | −0.737897 | − | 0.674913i | \(-0.764181\pi\) |
0.674913 | + | 0.737897i | \(0.264181\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2037.04 | − | 4917.85i | 0.565455 | − | 1.36513i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1682.10 | + | 696.748i | −0.461030 | + | 0.190965i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5695.35i | 1.54143i | 0.637181 | + | 0.770714i | \(0.280101\pi\) | ||||
−0.637181 | + | 0.770714i | \(0.719899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5864.62i | 1.56752i | 0.621061 | + | 0.783762i | \(0.286702\pi\) | ||||
−0.621061 | + | 0.783762i | \(0.713298\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3611.13 | − | 1495.78i | 0.953309 | − | 0.394874i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2196.77 | − | 5303.48i | 0.572844 | − | 1.38297i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1532.38 | + | 1532.38i | −0.394749 | + | 0.394749i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1826.95 | + | 1826.95i | 0.464972 | + | 0.464972i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1284.55 | − | 532.079i | −0.323029 | − | 0.133803i | 0.215276 | − | 0.976553i | \(-0.430935\pi\) |
−0.538305 | + | 0.842750i | \(0.680935\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1395.50 | − | 3369.04i | −0.346777 | − | 0.837193i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3582.59 | −0.879805 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6068.35 | 1.47289 | 0.736446 | − | 0.676497i | \(-0.236503\pi\) | ||||
0.736446 | + | 0.676497i | \(0.236503\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 685.388 | + | 1654.67i | 0.164432 | + | 0.396974i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1933.50 | − | 800.883i | −0.458547 | − | 0.189937i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1919.51 | + | 1919.51i | 0.450046 | + | 0.450046i | 0.895370 | − | 0.445324i | \(-0.146911\pi\) |
−0.445324 | + | 0.895370i | \(0.646911\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1789.97 | + | 1789.97i | −0.414931 | + | 0.414931i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 231.146 | − | 558.035i | 0.0529808 | − | 0.127907i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3969.40 | − | 1644.18i | 0.899697 | − | 0.372667i | 0.115593 | − | 0.993297i | \(-0.463123\pi\) |
0.784103 | + | 0.620630i | \(0.213123\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4538.69i | − | 1.01736i | −0.860954 | − | 0.508682i | \(-0.830133\pi\) | ||
0.860954 | − | 0.508682i | \(-0.169867\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 225.540i | 0.0500011i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6543.07 | + | 2710.23i | −1.43477 | + | 0.594301i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1889.91 | + | 4562.63i | −0.409940 | + | 0.989683i | 0.575213 | + | 0.818004i | \(0.304919\pi\) |
−0.985153 | + | 0.171679i | \(0.945081\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 414.605 | − | 414.605i | 0.0889669 | − | 0.0889669i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.7223 | − | 30.7223i | −0.00652220 | − | 0.00652220i | 0.703838 | − | 0.710360i | \(-0.251468\pi\) |
−0.710360 | + | 0.703838i | \(0.751468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5549.45 | + | 2298.66i | 1.16565 | + | 0.482830i | 0.879754 | − | 0.475429i | \(-0.157707\pi\) |
0.285901 | + | 0.958259i | \(0.407707\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2912.73 | + | 7031.95i | 0.605387 | + | 1.46153i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1092.03 | 0.224601 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −404.895 | −0.0824130 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −837.954 | − | 2023.00i | −0.168803 | − | 0.407527i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2663.79 | + | 1103.38i | 0.531128 | + | 0.220000i | 0.632097 | − | 0.774889i | \(-0.282194\pi\) |
−0.100969 | + | 0.994890i | \(0.532194\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3207.00 | + | 3207.00i | 0.632944 | + | 0.632944i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2683.66 | + | 2683.66i | −0.524316 | + | 0.524316i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 633.173 | − | 1528.61i | 0.122466 | − | 0.295659i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −403.168 | + | 166.998i | −0.0772033 | + | 0.0319787i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4407.30i | 0.835620i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 11162.7i | − | 2.09565i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −401.539 | + | 166.323i | −0.0746484 | + | 0.0309204i | −0.419695 | − | 0.907665i | \(-0.637863\pi\) |
0.345047 | + | 0.938585i | \(0.387863\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −113.143 | + | 273.152i | −0.0208301 | + | 0.0502883i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5345.11 | − | 5345.11i | 0.974577 | − | 0.974577i | −0.0251081 | − | 0.999685i | \(-0.507993\pi\) |
0.999685 | + | 0.0251081i | \(0.00799300\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1787.53 | − | 1787.53i | −0.322803 | − | 0.322803i | 0.527039 | − | 0.849841i | \(-0.323302\pi\) |
−0.849841 | + | 0.527039i | \(0.823302\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2172.32 | − | 899.804i | −0.388560 | − | 0.160947i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2370.77 | + | 5723.55i | 0.420050 | + | 1.01409i | 0.982332 | + | 0.187145i | \(0.0599234\pi\) |
−0.562282 | + | 0.826945i | \(0.690077\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3194.62 | 0.560703 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3768.08 | −0.655183 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4323.58 | + | 10438.0i | 0.744800 | + | 1.79811i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2968.74 | − | 1229.69i | −0.506696 | − | 0.209880i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 979.572 | + | 979.572i | 0.165659 | + | 0.165659i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1235.36 | + | 1235.36i | −0.207014 | + | 0.207014i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1696.86 | + | 4096.57i | −0.281775 | + | 0.680265i | −0.999877 | − | 0.0156724i | \(-0.995011\pi\) |
0.718102 | + | 0.695938i | \(0.245011\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5406.09 | + | 2239.28i | −0.889646 | + | 0.368503i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 17521.6i | − | 2.85764i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 927.470i | 0.149918i | 0.997187 | + | 0.0749592i | \(0.0238826\pi\) | ||||
−0.997187 | + | 0.0749592i | \(0.976117\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 263.152 | − | 109.001i | 0.0421606 | − | 0.0174635i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −342.515 | + | 826.904i | −0.0543936 | + | 0.131318i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2831.48 | + | 2831.48i | −0.445731 | + | 0.445731i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4109.10 | − | 4109.10i | −0.641237 | − | 0.641237i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3765.13 | − | 1559.57i | −0.582487 | − | 0.241274i | 0.0719277 | − | 0.997410i | \(-0.477085\pi\) |
−0.654415 | + | 0.756136i | \(0.727085\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1631.14 | − | 3937.93i | −0.250181 | − | 0.603990i | 0.748037 | − | 0.663657i | \(-0.230996\pi\) |
−0.998218 | + | 0.0596662i | \(0.980996\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1722.00 | −0.261862 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11289.2 | −1.70216 | −0.851080 | − | 0.525037i | \(-0.824052\pi\) | ||||
−0.851080 | + | 0.525037i | \(0.824052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7041.69 | − | 17000.1i | −1.05277 | − | 2.54162i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1086.33 | + | 449.972i | 0.161049 | + | 0.0667088i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2970.97 | − | 2970.97i | −0.436774 | − | 0.436774i | 0.454151 | − | 0.890925i | \(-0.349943\pi\) |
−0.890925 | + | 0.454151i | \(0.849943\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12122.7 | − | 12122.7i | 1.76742 | − | 1.76742i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −379.904 | + | 917.170i | −0.0549306 | + | 0.132614i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5496.07 | − | 2276.55i | 0.788157 | − | 0.326465i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12266.5i | 1.74470i | 0.488882 | + | 0.872350i | \(0.337405\pi\) | ||||
−0.488882 | + | 0.872350i | \(0.662595\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3567.84i | 0.503346i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 767.581 | − | 317.942i | 0.107415 | − | 0.0444926i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −905.804 | + | 2186.80i | −0.125739 | + | 0.303561i | −0.974196 | − | 0.225703i | \(-0.927532\pi\) |
0.848457 | + | 0.529265i | \(0.177532\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3638.03 | + | 3638.03i | −0.500979 | + | 0.500979i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1024.93 | + | 1024.93i | 0.140018 | + | 0.140018i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6881.62 | − | 2850.46i | −0.932679 | − | 0.386328i | −0.135985 | − | 0.990711i | \(-0.543420\pi\) |
−0.796694 | + | 0.604383i | \(0.793420\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1516.76 | − | 3661.78i | −0.203953 | − | 0.492385i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2433.37 | 0.324645 | 0.162323 | − | 0.986738i | \(-0.448101\pi\) | ||||
0.162323 | + | 0.986738i | \(0.448101\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3589.20 | 0.475124 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −545.609 | − | 1317.22i | −0.0716663 | − | 0.173018i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4253.32 | + | 1761.78i | 0.554375 | + | 0.229630i | 0.642241 | − | 0.766503i | \(-0.278005\pi\) |
−0.0878663 | + | 0.996132i | \(0.528005\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6099.44 | − | 6099.44i | −0.788905 | − | 0.788905i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1860.66 | − | 1860.66i | 0.238824 | − | 0.238824i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5030.85 | + | 12145.6i | −0.640835 | + | 1.54711i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −306.541 | + | 126.974i | −0.0387528 | + | 0.0160519i | −0.401976 | − | 0.915650i | \(-0.631676\pi\) |
0.363223 | + | 0.931702i | \(0.381676\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 2498.10i | − | 0.313437i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10975.6i | − | 1.36682i | −0.730036 | − | 0.683409i | \(-0.760497\pi\) | ||
0.730036 | − | 0.683409i | \(-0.239503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −375.186 | + | 155.407i | −0.0463755 | + | 0.0192094i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1615.74 | − | 3900.74i | 0.198239 | − | 0.478591i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6316.01 | − | 6316.01i | 0.769221 | − | 0.769221i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8384.88 | + | 8384.88i | 1.01371 | + | 1.01371i | 0.999905 | + | 0.0138007i | \(0.00439304\pi\) |
0.0138007 | + | 0.999905i | \(0.495607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 415.100 | + | 171.940i | 0.0498184 | + | 0.0206355i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −569.642 | − | 1375.24i | −0.0678698 | − | 0.163852i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18655.5 | 2.20666 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.1316 | 0.00189441 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −533.639 | − | 1288.32i | −0.0622195 | − | 0.150211i | 0.889712 | − | 0.456522i | \(-0.150905\pi\) |
−0.951931 | + | 0.306311i | \(0.900905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1963.49 | + | 813.303i | 0.227303 | + | 0.0941520i | 0.493428 | − | 0.869786i | \(-0.335744\pi\) |
−0.266125 | + | 0.963938i | \(0.585744\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4036.13 | − | 4036.13i | −0.463932 | − | 0.463932i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11845.8 | + | 11845.8i | −1.35201 | + | 1.35201i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1402.03 | + | 3384.79i | −0.158897 | + | 0.383610i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1039.20 | − | 430.451i | 0.116954 | − | 0.0484438i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4521.29i | 0.505297i | 0.967558 | + | 0.252649i | \(0.0813016\pi\) | ||||
−0.967558 | + | 0.252649i | \(0.918698\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2122.80i | − | 0.235601i | −0.993037 | − | 0.117801i | \(-0.962416\pi\) | ||
0.993037 | − | 0.117801i | \(-0.0375844\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4703.33 | − | 1948.18i | 0.518408 | − | 0.214732i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7013.07 | + | 16931.1i | −0.767691 | + | 1.85337i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8028.12 | + | 8028.12i | −0.872805 | + | 0.872805i | −0.992777 | − | 0.119972i | \(-0.961719\pi\) |
0.119972 | + | 0.992777i | \(0.461719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4352.62 | − | 4352.62i | −0.469994 | − | 0.469994i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3136.09 | − | 1299.01i | −0.336343 | − | 0.139318i | 0.208119 | − | 0.978104i | \(-0.433266\pi\) |
−0.544462 | + | 0.838786i | \(0.683266\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1668.98 | − | 4029.28i | −0.177792 | − | 0.429227i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2123.33 | 0.224676 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16955.9 | −1.78218 | −0.891088 | − | 0.453832i | \(-0.850057\pi\) | ||||
−0.891088 | + | 0.453832i | \(0.850057\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2084.18 | − | 5031.66i | −0.217606 | − | 0.525347i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1946.88 | − | 806.426i | −0.201926 | − | 0.0836406i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1151.53 | + | 1151.53i | 0.118647 | + | 0.118647i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6223.46 | − | 6223.46i | 0.637027 | − | 0.637027i | −0.312794 | − | 0.949821i | \(-0.601265\pi\) |
0.949821 | + | 0.312794i | \(0.101265\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3435.55 | + | 8294.14i | −0.349363 | + | 0.843437i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10872.5 | − | 4503.54i | 1.09844 | − | 0.454991i | 0.241501 | − | 0.970401i | \(-0.422360\pi\) |
0.856944 | + | 0.515410i | \(0.172360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13182.5i | − | 1.32320i | −0.749858 | − | 0.661599i | \(-0.769878\pi\) | ||
0.749858 | − | 0.661599i | \(-0.230122\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1426.30i | 0.142243i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7043.25 | + | 2917.41i | −0.697907 | + | 0.289083i | −0.703290 | − | 0.710903i | \(-0.748287\pi\) |
0.00538305 | + | 0.999986i | \(0.498287\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2200.71 | + | 5312.99i | −0.216673 | + | 0.523094i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1058.62 | − | 1058.62i | 0.103564 | − | 0.103564i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1538.92 | + | 1538.92i | 0.149598 | + | 0.149598i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32882.1 | + | 13620.2i | 3.17628 | + | 1.31566i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1038.77 | + | 2507.81i | 0.0997107 | + | 0.240723i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4612.37 | −0.439968 | −0.219984 | − | 0.975503i | \(-0.570601\pi\) | ||||
−0.219984 | + | 0.975503i | \(0.570601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4052.74 | 0.384177 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 729.878 | + | 1762.08i | 0.0687590 | + | 0.165999i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14607.0 | − | 6050.43i | −1.36757 | − | 0.566466i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10988.9 | + | 10988.9i | 1.02249 | + | 1.02249i | 0.999741 | + | 0.0227515i | \(0.00724266\pi\) |
0.0227515 | + | 0.999741i | \(0.492757\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2750.34 | + | 2750.34i | −0.254345 | + | 0.254345i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7836.91 | − | 18920.0i | 0.720316 | − | 1.73900i | 0.0478645 | − | 0.998854i | \(-0.484758\pi\) |
0.672451 | − | 0.740142i | \(-0.265242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6981.49 | − | 2891.83i | 0.637790 | − | 0.264181i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11726.5i | 1.06478i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6039.29i | 0.545069i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6404.45 | − | 2652.81i | 0.574554 | − | 0.237988i | −0.0764356 | − | 0.997075i | \(-0.524354\pi\) |
0.650990 | + | 0.759086i | \(0.274354\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 906.824 | − | 2189.27i | 0.0808661 | − | 0.195228i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2553.60 | + | 2553.60i | −0.226361 | + | 0.226361i | −0.811171 | − | 0.584810i | \(-0.801169\pi\) |
0.584810 | + | 0.811171i | \(0.301169\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22502.1 | + | 22502.1i | 1.98283 | + | 1.98283i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4823.00 | − | 1997.75i | −0.422479 | − | 0.174997i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3141.82 | + | 7585.02i | 0.273593 | + | 0.660511i | 0.999632 | − | 0.0271425i | \(-0.00864080\pi\) |
−0.726039 | + | 0.687654i | \(0.758641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1952.48 | −0.169026 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19073.0 | 1.64151 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 816.948 | + | 1972.29i | 0.0699010 | + | 0.168756i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8049.80 | + | 3334.34i | 0.684777 | + | 0.283644i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3715.74 | − | 3715.74i | −0.314263 | − | 0.314263i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7065.05 | + | 7065.05i | −0.594099 | + | 0.594099i | −0.938736 | − | 0.344637i | \(-0.888002\pi\) |
0.344637 | + | 0.938736i | \(0.388002\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 111.041 | − | 268.077i | 0.00928391 | − | 0.0224134i | −0.919170 | − | 0.393862i | \(-0.871139\pi\) |
0.928454 | + | 0.371449i | \(0.121139\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3422.17 | − | 1417.51i | 0.284487 | − | 0.117838i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2117.16i | 0.175000i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1824.68i | − | 0.149970i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4493.13 | − | 1861.11i | 0.367204 | − | 0.152101i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 945.642 | − | 2282.98i | 0.0768486 | − | 0.185529i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19238.5 | + | 19238.5i | −1.55468 | + | 1.55468i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 633.304 | + | 633.304i | 0.0508921 | + | 0.0508921i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8681.02 | + | 3595.79i | 0.693725 | + | 0.287350i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8420.37 | − | 20328.6i | −0.669168 | − | 1.61552i | −0.783005 | − | 0.622016i | \(-0.786314\pi\) |
0.113837 | − | 0.993499i | \(-0.463686\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3630.14 | 0.286896 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10002.7 | 0.786181 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −646.357 | − | 1560.44i | −0.0505233 | − | 0.121974i | 0.896603 | − | 0.442836i | \(-0.146028\pi\) |
−0.947126 | + | 0.320862i | \(0.896028\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11058.7 | − | 4580.65i | −0.859696 | − | 0.356098i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11352.2 | − | 11352.2i | −0.877717 | − | 0.877717i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3050.95 | − | 3050.95i | 0.234611 | − | 0.234611i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5447.14 | − | 13150.5i | 0.416609 | − | 1.00578i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6482.01 | + | 2684.93i | −0.493091 | + | 0.204245i | −0.615351 | − | 0.788253i | \(-0.710986\pi\) |
0.122260 | + | 0.992498i | \(0.460986\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 987.467i | 0.0747145i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 5864.17i | − | 0.441329i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 945.289 | − | 391.551i | 0.0707623 | − | 0.0293107i | −0.347022 | − | 0.937857i | \(-0.612807\pi\) |
0.417784 | + | 0.908546i | \(0.362807\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 787.039 | − | 1900.08i | 0.0586035 | − | 0.141481i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −979.862 | + | 979.862i | −0.0725756 | + | 0.0725756i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3760.45 | − | 3760.45i | −0.277058 | − | 0.277058i | 0.554875 | − | 0.831934i | \(-0.312766\pi\) |
−0.831934 | + | 0.554875i | \(0.812766\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2056.20 | − | 851.705i | −0.150699 | − | 0.0624216i | 0.306059 | − | 0.952013i | \(-0.400990\pi\) |
−0.456758 | + | 0.889591i | \(0.650990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3155.95 | − | 7619.15i | −0.230091 | − | 0.555488i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27173.5 | −1.97080 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23621.3 | −1.70427 | −0.852137 | − | 0.523318i | \(-0.824694\pi\) | ||||
−0.852137 | + | 0.523318i | \(0.824694\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1425.99 | − | 3442.65i | −0.102353 | − | 0.247101i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5656.80 | − | 2343.13i | −0.403931 | − | 0.167314i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2929.91 | − | 2929.91i | −0.208138 | − | 0.208138i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3762.23 | + | 3762.23i | −0.265896 | + | 0.265896i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7316.12 | + | 17662.7i | −0.514427 | + | 1.24194i | 0.426857 | + | 0.904319i | \(0.359621\pi\) |
−0.941283 | + | 0.337617i | \(0.890379\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4155.59 | − | 1721.30i | 0.290710 | − | 0.120416i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3889.13i | 0.270689i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16542.0i | 1.14553i | 0.819720 | + | 0.572764i | \(0.194129\pi\) | ||||
−0.819720 | + | 0.572764i | \(0.805871\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7843.81 | − | 3249.01i | 0.540445 | − | 0.223860i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1704.91 | − | 4116.02i | 0.116880 | − | 0.282174i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8579.81 | − | 8579.81i | 0.585244 | − | 0.585244i | −0.351095 | − | 0.936340i | \(-0.614191\pi\) |
0.936340 | + | 0.351095i | \(0.114191\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13633.8 | − | 13633.8i | −0.925346 | − | 0.925346i | 0.0720542 | − | 0.997401i | \(-0.477045\pi\) |
−0.997401 | + | 0.0720542i | \(0.977045\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17358.4 | − | 7190.09i | −1.17229 | − | 0.485578i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2743.09 | + | 6622.41i | 0.184335 | + | 0.445023i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23984.1 | 1.60376 | 0.801881 | − | 0.597484i | \(-0.203833\pi\) | ||||
0.801881 | + | 0.597484i | \(0.203833\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1670.86 | −0.111176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1512.87 | + | 3652.38i | 0.100170 | + | 0.241833i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18072.9 | + | 7486.04i | 1.19080 | + | 0.493244i | 0.888014 | − | 0.459816i | \(-0.152085\pi\) |
0.302782 | + | 0.953060i | \(0.402085\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6136.93 | − | 6136.93i | −0.402382 | − | 0.402382i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18674.2 | − | 18674.2i | 1.21847 | − | 1.21847i | 0.250301 | − | 0.968168i | \(-0.419470\pi\) |
0.968168 | − | 0.250301i | \(-0.0805297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3214.09 | + | 7759.51i | −0.208700 | + | 0.503846i | −0.993219 | − | 0.116258i | \(-0.962910\pi\) |
0.784519 | + | 0.620105i | \(0.212910\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13453.5 | + | 5572.64i | −0.869359 | + | 0.360100i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1431.40i | 0.0920511i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8433.25i | 0.539728i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11510.3 | + | 4767.71i | −0.733136 | + | 0.303675i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8085.58 | − | 19520.3i | 0.512549 | − | 1.23740i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20023.0 | − | 20023.0i | 1.26324 | − | 1.26324i | 0.313722 | − | 0.949515i | \(-0.398424\pi\) |
0.949515 | − | 0.313722i | \(-0.101576\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1253.06 | + | 1253.06i | 0.0786801 | + | 0.0786801i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26439.8 | − | 10951.7i | −1.65233 | − | 0.684419i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1631.50 | + | 3938.78i | 0.101479 | + | 0.244992i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19731.4 | −1.22154 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8637.88 | 0.532255 | 0.266128 | − | 0.963938i | \(-0.414256\pi\) | ||||
0.266128 | + | 0.963938i | \(0.414256\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5274.73 | − | 12734.3i | −0.323507 | − | 0.781015i | −0.999045 | − | 0.0436901i | \(-0.986089\pi\) |
0.675538 | − | 0.737325i | \(-0.263911\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3204.18 | + | 1327.22i | 0.195604 | + | 0.0810219i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14785.3 | + | 14785.3i | 0.898406 | + | 0.898406i | 0.995295 | − | 0.0968891i | \(-0.0308892\pi\) |
−0.0968891 | + | 0.995295i | \(0.530889\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5249.38 | + | 5249.38i | −0.317498 | + | 0.317498i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 179.143 | − | 432.488i | 0.0107852 | − | 0.0260377i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25046.7 | + | 10374.7i | −1.50100 | + | 0.621733i | −0.973677 | − | 0.227933i | \(-0.926803\pi\) |
−0.527321 | + | 0.849666i | \(0.676803\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 18999.7i | − | 1.13340i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6379.06i | − | 0.378799i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23962.3 | − | 9925.50i | 1.41645 | − | 0.586711i | 0.462481 | − | 0.886629i | \(-0.346959\pi\) |
0.953965 | + | 0.299918i | \(0.0969594\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −398.063 | + | 961.010i | −0.0234234 | + | 0.0565491i | −0.935158 | − | 0.354230i | \(-0.884743\pi\) |
0.911735 | + | 0.410779i | \(0.134743\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1881.41 | − | 1881.41i | 0.110208 | − | 0.110208i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12754.4 | − | 12754.4i | −0.743752 | − | 0.743752i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11324.4 | + | 4690.70i | 0.657392 | + | 0.272301i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1681.83 | − | 4060.30i | −0.0971948 | − | 0.234649i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18271.6 | 1.05122 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15307.7 | −0.876775 | −0.438387 | − | 0.898786i | \(-0.644450\pi\) | ||||
−0.438387 | + | 0.898786i | \(0.644450\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10822.7 | + | 26128.3i | 0.617135 | + | 1.48990i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1043.10 | − | 432.068i | −0.0592168 | − | 0.0245284i | 0.352878 | − | 0.935669i | \(-0.385203\pi\) |
−0.412095 | + | 0.911141i | \(0.635203\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3669.28 | + | 3669.28i | 0.207384 | + | 0.207384i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8444.03 | + | 8444.03i | −0.475148 | + | 0.475148i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8946.40 | − | 21598.5i | 0.501207 | − | 1.21002i | −0.447619 | − | 0.894224i | \(-0.647728\pi\) |
0.948827 | − | 0.315797i | \(-0.102272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2997.22 | − | 1241.49i | 0.167179 | − | 0.0692479i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3028.37i | 0.168180i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1880.01i | − | 0.103952i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19676.4 | + | 8150.22i | −1.08325 | + | 0.448696i | −0.851647 | − | 0.524115i | \(-0.824396\pi\) |
−0.231600 | + | 0.972811i | \(0.574396\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1472.85 | − | 3555.77i | 0.0807342 | − | 0.194910i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 82.3624 | − | 82.3624i | 0.00449523 | − | 0.00449523i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9109.50 | − | 9109.50i | −0.495046 | − | 0.495046i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −763.440 | − | 316.227i | −0.0413104 | − | 0.0171113i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2739.27 | + | 6613.19i | 0.147591 | + | 0.356315i | 0.980334 | − | 0.197343i | \(-0.0632313\pi\) |
−0.832744 | + | 0.553658i | \(0.813231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44888.5 | −2.40825 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13884.8 | 0.741749 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3996.93 | − | 9649.45i | −0.212617 | − | 0.513303i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2388.26 | − | 989.248i | −0.126506 | − | 0.0524005i | 0.318532 | − | 0.947912i | \(-0.396810\pi\) |
−0.445039 | + | 0.895511i | \(0.646810\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9967.97 | + | 9967.97i | 0.525778 | + | 0.525778i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2428.31 | + | 2428.31i | −0.127547 | + | 0.127547i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3108.06 | − | 7503.53i | 0.162566 | − | 0.392470i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13725.1 | + | 5685.13i | −0.714887 | + | 0.296116i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11843.1i | 0.614288i | 0.951663 | + | 0.307144i | \(0.0993734\pi\) | ||||
−0.951663 | + | 0.307144i | \(0.900627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 700.654i | − | 0.0361910i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14133.0 | + | 5854.10i | −0.726990 | + | 0.301129i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9109.88 | − | 21993.2i | 0.466665 | − | 1.12663i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4691.36 | − | 4691.36i | 0.239330 | − | 0.239330i | −0.577243 | − | 0.816573i | \(-0.695871\pi\) |
0.816573 | + | 0.577243i | \(0.195871\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2929.40 | + | 2929.40i | 0.148829 | + | 0.148829i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4756.20 | + | 1970.08i | 0.240649 | + | 0.0996801i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13224.6 | + | 31927.0i | 0.666386 | + | 1.60880i | 0.787610 | + | 0.616174i | \(0.211318\pi\) |
−0.121224 | + | 0.992625i | \(0.538682\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14973.6 | 0.751441 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28680.4 | 1.43345 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13199.0 | + | 31865.1i | 0.657012 | + | 1.58617i | 0.802396 | + | 0.596793i | \(0.203558\pi\) |
−0.145383 | + | 0.989375i | \(0.546442\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5222.48 | − | 2163.22i | −0.258911 | − | 0.107244i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14307.6 | + | 14307.6i | 0.706452 | + | 0.706452i | 0.965787 | − | 0.259335i | \(-0.0835035\pi\) |
−0.259335 | + | 0.965787i | \(0.583503\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10841.0 | − | 10841.0i | 0.533131 | − | 0.533131i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7655.38 | − | 18481.7i | 0.374961 | − | 0.905235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8249.93 | − | 3417.23i | 0.402464 | − | 0.166706i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 15781.7i | − | 0.766820i | −0.923578 | − | 0.383410i | \(-0.874750\pi\) | ||
0.923578 | − | 0.383410i | \(-0.125250\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 3626.75i | − | 0.175519i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14057.4 | + | 5822.78i | −0.677619 | + | 0.280679i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15069.9 | + | 36382.0i | −0.723548 | + | 1.74680i | −0.0605650 | + | 0.998164i | \(0.519290\pi\) |
−0.662983 | + | 0.748635i | \(0.730710\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6726.00 | − | 6726.00i | 0.321658 | − | 0.321658i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12120.7 | − | 12120.7i | −0.577363 | − | 0.577363i | 0.356813 | − | 0.934176i | \(-0.383863\pi\) |
−0.934176 | + | 0.356813i | \(0.883863\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3033.06 | − | 1256.34i | −0.143911 | − | 0.0596100i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10615.1 | + | 25627.0i | 0.501684 | + | 1.21117i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3368.33 | −0.158570 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5213.88 | 0.244496 | 0.122248 | − | 0.992500i | \(-0.460990\pi\) | ||||
0.122248 | + | 0.992500i | \(0.460990\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6057.46 | + | 14624.0i | 0.282950 | + | 0.683101i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25960.5 | + | 10753.2i | 1.20793 | + | 0.500343i | 0.893555 | − | 0.448954i | \(-0.148203\pi\) |
0.314380 | + | 0.949297i | \(0.398203\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4716.05 | + | 4716.05i | 0.218588 | + | 0.218588i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3303.41 | + | 3303.41i | −0.152521 | + | 0.152521i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10474.0 | + | 25286.5i | −0.481733 | + | 1.16301i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27826.7 | − | 11526.2i | 1.27493 | − | 0.528093i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 12757.0i | − | 0.582246i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 10809.9i | − | 0.491491i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31369.3 | + | 12993.6i | −1.42083 | + | 0.588528i | −0.955069 | − | 0.296382i | \(-0.904220\pi\) |
−0.465762 | + | 0.884910i | \(0.654220\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2709.73 | + | 6541.86i | −0.122267 | + | 0.295179i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −477.299 | + | 477.299i | −0.0214549 | + | 0.0214549i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5862.11 | + | 5862.11i | 0.262509 | + | 0.262509i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6100.36 | − | 2526.85i | −0.272148 | − | 0.112727i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8986.32 | + | 21694.9i | 0.399387 | + | 0.964207i | 0.987812 | + | 0.155654i | \(0.0497485\pi\) |
−0.588424 | + | 0.808552i | \(0.700251\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20610.3 | 0.912564 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4676.62 | −0.206292 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3726.37 | + | 8996.26i | 0.163762 | + | 0.395356i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12723.1 | + | 5270.07i | 0.557055 | + | 0.230740i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7924.55 | + | 7924.55i | 0.345672 | + | 0.345672i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13193.6 | + | 13193.6i | −0.573376 | + | 0.573376i | −0.933070 | − | 0.359694i | \(-0.882881\pi\) |
0.359694 | + | 0.933070i | \(0.382881\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −140.367 | + | 338.877i | −0.00607764 | + | 0.0146727i | −0.926889 | − | 0.375335i | \(-0.877528\pi\) |
0.920812 | + | 0.390008i | \(0.127528\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10937.7 | − | 4530.55i | 0.471835 | − | 0.195441i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28084.5i | 1.20707i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 10937.3i | − | 0.468356i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1613.33 | − | 668.265i | 0.0688333 | − | 0.0285117i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6304.96 | − | 15221.5i | 0.268020 | − | 0.647058i | −0.731370 | − | 0.681981i | \(-0.761119\pi\) |
0.999390 | + | 0.0349231i | \(0.0111186\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 769.291 | − | 769.291i | 0.0325830 | − | 0.0325830i | −0.690628 | − | 0.723211i | \(-0.742666\pi\) |
0.723211 | + | 0.690628i | \(0.242666\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13062.7 | − | 13062.7i | −0.551253 | − | 0.551253i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22898.4 | − | 9484.82i | −0.962823 | − | 0.398815i | −0.154788 | − | 0.987948i | \(-0.549469\pi\) |
−0.808036 | + | 0.589133i | \(0.799469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10844.8 | − | 26181.7i | −0.454350 | − | 1.09690i | −0.970651 | − | 0.240492i | \(-0.922691\pi\) |
0.516301 | − | 0.856407i | \(-0.327309\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12881.9 | −0.537749 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22226.4 | 0.924488 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6547.70 | − | 15807.5i | −0.271368 | − | 0.655141i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3302.06 | + | 1367.76i | 0.136363 | + | 0.0564834i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23945.5 | − | 23945.5i | −0.985327 | − | 0.985327i | 0.0145666 | − | 0.999894i | \(-0.495363\pi\) |
−0.999894 | + | 0.0145666i | \(0.995363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9652.67 | − | 9652.67i | 0.395779 | − | 0.395779i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 43.3699 | − | 104.704i | 0.00177193 | − | 0.00427783i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34824.4 | + | 14424.7i | −1.41775 | + | 0.587249i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2352.61i | − | 0.0954386i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15668.0i | 0.633364i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31663.0 | − | 13115.2i | 1.27543 | − | 0.528302i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8663.21 | − | 20914.8i | 0.347740 | − | 0.839520i | −0.649146 | − | 0.760664i | \(-0.724873\pi\) |
0.996886 | − | 0.0788554i | \(-0.0251266\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 41670.8 | − | 41670.8i | 1.66680 | − | 1.66680i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9119.55 | − | 9119.55i | −0.363498 | − | 0.363498i | 0.501601 | − | 0.865099i | \(-0.332745\pi\) |
−0.865099 | + | 0.501601i | \(0.832745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30582.3 | + | 12667.6i | 1.21473 | + | 0.503159i | 0.895732 | − | 0.444595i | \(-0.146652\pi\) |
0.319002 | + | 0.947754i | \(0.396652\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1090.07 | + | 2631.66i | 0.0431470 | + | 0.104166i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1210.85 | −0.0477612 | −0.0238806 | − | 0.999715i | \(-0.507602\pi\) | ||||
−0.0238806 | + | 0.999715i | \(0.507602\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37942.5 | −1.49143 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −404.169 | − | 975.749i | −0.0158319 | − | 0.0382217i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19880.5 | − | 8234.77i | −0.776064 | − | 0.321456i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9201.55 | + | 9201.55i | 0.357959 | + | 0.357959i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11988.1 | + | 11988.1i | −0.464762 | + | 0.464762i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4665.90 | − | 11264.5i | 0.180270 | − | 0.435210i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36421.4 | + | 15086.2i | −1.40235 | + | 0.580873i | −0.950361 | − | 0.311150i | \(-0.899286\pi\) |
−0.451990 | + | 0.892023i | \(0.649286\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7520.83i | 0.288591i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39286.1i | 1.50236i | 0.660095 | + | 0.751182i | \(0.270516\pi\) | ||||
−0.660095 | + | 0.751182i | \(0.729484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 234.092 | − | 96.9642i | 0.00892167 | − | 0.00369548i | −0.378218 | − | 0.925717i | \(-0.623463\pi\) |
0.387140 | + | 0.922021i | \(0.373463\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4527.24 | + | 10929.7i | −0.171957 | + | 0.415140i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13552.8 | + | 13552.8i | −0.513032 | + | 0.513032i | −0.915454 | − | 0.402422i | \(-0.868168\pi\) |
0.402422 | + | 0.915454i | \(0.368168\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6641.66 | + | 6641.66i | 0.250567 | + | 0.250567i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6384.93 | + | 2644.73i | 0.240071 | + | 0.0994407i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16756.6 | − | 40454.1i | −0.627928 | − | 1.51595i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6466.85 | 0.241523 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4315.82 | 0.160648 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1151.29 | − | 2779.47i | −0.0427117 | − | 0.103115i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9055.21 | − | 3750.79i | −0.334820 | − | 0.138687i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −804.889 | − | 804.889i | −0.0296623 | − | 0.0296623i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18534.2 | − | 18534.2i | 0.680772 | − | 0.680772i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2600.00 | − | 6276.95i | 0.0951835 | − | 0.229793i | −0.869115 | − | 0.494609i | \(-0.835311\pi\) |
0.964299 | + | 0.264816i | \(0.0853112\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31526.4 | − | 13058.6i | 1.15034 | − | 0.476488i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22984.1i | 0.835891i | 0.908472 | + | 0.417946i | \(0.137250\pi\) | ||||
−0.908472 | + | 0.417946i | \(0.862750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30536.3i | 1.10691i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26900.7 | − | 11142.6i | 0.971924 | − | 0.402584i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2386.36 | + | 5761.17i | −0.0859372 | + | 0.207471i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38048.0 | + | 38048.0i | −1.36571 | + | 1.36571i | −0.499258 | + | 0.866453i | \(0.666394\pi\) |
−0.866453 | + | 0.499258i | \(0.833606\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −801.638 | − | 801.638i | −0.0286806 | − | 0.0286806i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12625.6 | + | 5229.71i | 0.450247 | + | 0.186499i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25471.3 | − | 61493.2i | −0.905396 | − | 2.18582i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2289.15 | 0.0811064 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28435.1 | 1.00423 | 0.502113 | − | 0.864802i | \(-0.332556\pi\) | ||||
0.502113 | + | 0.864802i | \(0.332556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18070.6 | − | 43626.3i | −0.636133 | − | 1.53576i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18216.6 | + | 7545.57i | 0.639212 | + | 0.264770i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29940.4 | − | 29940.4i | −1.04723 | − | 1.04723i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10599.3 | − | 10599.3i | 0.369546 | − | 0.369546i | −0.497766 | − | 0.867311i | \(-0.665846\pi\) |
0.867311 | + | 0.497766i | \(0.165846\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2523.42 | − | 6092.07i | 0.0876982 | − | 0.211722i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17446.0 | + | 7226.38i | −0.604383 | + | 0.250344i | −0.663825 | − | 0.747888i | \(-0.731068\pi\) |
0.0594418 | + | 0.998232i | \(0.481068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 20896.5i | − | 0.721617i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 14332.7i | − | 0.493378i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8125.64 | − | 3365.75i | 0.278826 | − | 0.115493i | −0.238889 | − | 0.971047i | \(-0.576783\pi\) |
0.517714 | + | 0.855554i | \(0.326783\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1690.74 | + | 4081.81i | −0.0578333 | + | 0.139622i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11426.6 | + | 11426.6i | −0.389623 | + | 0.389623i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20053.9 | + | 20053.9i | 0.681648 | + | 0.681648i | 0.960371 | − | 0.278723i | \(-0.0899113\pi\) |
−0.278723 | + | 0.960371i | \(0.589911\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −55013.9 | − | 22787.5i | −1.86409 | − | 0.772132i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3188.89 | + | 7698.66i | 0.107714 | + | 0.260044i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1064.76 | −0.0358529 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28948.1 | −0.971707 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11164.7 | + | 26953.9i | 0.373599 | + | 0.901949i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24857.6 | − | 10296.3i | −0.829216 | − | 0.343473i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17483.6 | − | 17483.6i | −0.581421 | − | 0.581421i | 0.353872 | − | 0.935294i | \(-0.384865\pi\) |
−0.935294 | + | 0.353872i | \(0.884865\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20838.6 | + | 20838.6i | −0.690849 | + | 0.690849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2567.45 | + | 6198.36i | −0.0848540 | + | 0.204856i | −0.960611 | − | 0.277896i | \(-0.910363\pi\) |
0.875757 | + | 0.482752i | \(0.160363\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.3190 | + | 14.6296i | −0.00116369 | + | 0.000482018i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 8381.81i | − | 0.275316i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 31111.6i | − | 1.01878i | −0.860536 | − | 0.509390i | \(-0.829871\pi\) | ||
0.860536 | − | 0.509390i | \(-0.170129\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6595.34 | − | 2731.88i | 0.215309 | − | 0.0891841i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4104.66 | − | 9909.52i | 0.133590 | − | 0.322514i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17048.2 | + | 17048.2i | −0.553156 | + | 0.553156i | −0.927350 | − | 0.374194i | \(-0.877919\pi\) |
0.374194 | + | 0.927350i | \(0.377919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19856.5 | + | 19856.5i | 0.642316 | + | 0.642316i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4210.22 | − | 1743.93i | −0.135778 | − | 0.0562410i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3195.58 | + | 7714.81i | 0.102744 | + | 0.248045i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32857.3 | −1.05323 | −0.526613 | − | 0.850105i | \(-0.676538\pi\) | ||||
−0.526613 | + | 0.850105i | \(0.676538\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11566.1 | −0.369625 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12310.3 | − | 29719.7i | −0.392223 | − | 0.946911i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30160.2 | − | 12492.8i | −0.958057 | − | 0.396840i | −0.151804 | − | 0.988411i | \(-0.548508\pi\) |
−0.806253 | + | 0.591570i | \(0.798508\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25221.6 | − | 25221.6i | −0.798775 | − | 0.798775i |
(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 | 128.4.g.a.113.7 | 44 | ||
4.3 | odd | 2 | 32.4.g.a.5.2 | ✓ | 44 | ||
8.3 | odd | 2 | 256.4.g.b.225.7 | 44 | |||
8.5 | even | 2 | 256.4.g.a.225.5 | 44 | |||
32.3 | odd | 8 | 256.4.g.b.33.7 | 44 | |||
32.13 | even | 8 | inner | 128.4.g.a.17.7 | 44 | ||
32.19 | odd | 8 | 32.4.g.a.13.2 | yes | 44 | ||
32.29 | even | 8 | 256.4.g.a.33.5 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.2 | ✓ | 44 | 4.3 | odd | 2 | ||
32.4.g.a.13.2 | yes | 44 | 32.19 | odd | 8 | ||
128.4.g.a.17.7 | 44 | 32.13 | even | 8 | inner | ||
128.4.g.a.113.7 | 44 | 1.1 | even | 1 | trivial | ||
256.4.g.a.33.5 | 44 | 32.29 | even | 8 | |||
256.4.g.a.225.5 | 44 | 8.5 | even | 2 | |||
256.4.g.b.33.7 | 44 | 32.3 | odd | 8 | |||
256.4.g.b.225.7 | 44 | 8.3 | odd | 2 |