Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(33,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, 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("256.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.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: | \(15.1044889615\) |
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 | 33.7 | ||
Character | \(\chi\) | \(=\) | 256.33 |
Dual form | 256.4.g.b.225.7 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 | −0.798252 | − | 0.602324i | \(-0.794242\pi\) |
0.990357 | + | 0.138542i | \(0.0442415\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −17.4005 | + | 7.20752i | −1.55635 | + | 0.644661i | −0.984450 | − | 0.175664i | \(-0.943793\pi\) |
−0.571898 | + | 0.820325i | \(0.693793\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.37099 | − | 4.37099i | 0.236012 | − | 0.236012i | −0.579185 | − | 0.815196i | \(-0.696629\pi\) |
0.815196 | + | 0.579185i | \(0.196629\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 14.2808 | + | 14.2808i | 0.528917 | + | 0.528917i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.7977 | − | 28.4821i | −0.323375 | − | 0.780697i | −0.999053 | − | 0.0435002i | \(-0.986149\pi\) |
0.675678 | − | 0.737197i | \(-0.263851\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.9230 | + | 5.35288i | 0.275707 | + | 0.114202i | 0.516253 | − | 0.856436i | \(-0.327326\pi\) |
−0.240546 | + | 0.970638i | \(0.577326\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 49.1278i | 0.845649i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 72.9239i | − | 1.04039i | −0.854047 | − | 0.520195i | \(-0.825859\pi\) | ||
0.854047 | − | 0.520195i | \(-0.174141\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 143.136 | + | 59.2889i | 1.72830 | + | 0.715884i | 0.999515 | + | 0.0311397i | \(0.00991368\pi\) |
0.728783 | + | 0.684745i | \(0.240086\pi\) | |||||||
\(20\) | 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 | \(-0.0698656\pi\) |
−0.217731 | + | 0.976009i | \(0.569866\pi\) | |||||||
\(24\) | 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 | \(-0.767354\pi\) |
0.998514 | + | 0.0544937i | \(0.0173545\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −29.0324 | −0.168206 | −0.0841029 | − | 0.996457i | \(-0.526802\pi\) | ||||
−0.0841029 | + | 0.996457i | \(0.526802\pi\) | |||||||
\(32\) | 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 | \(-0.402407\pi\) |
0.887547 | + | 0.460716i | \(0.152407\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 25.7996 | − | 25.7996i | 0.105929 | − | 0.105929i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −124.918 | − | 124.918i | −0.475827 | − | 0.475827i | 0.427968 | − | 0.903794i | \(-0.359230\pi\) |
−0.903794 | + | 0.427968i | \(0.859230\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.0156 | + | 65.2215i | 0.0958103 | + | 0.231306i | 0.964517 | − | 0.264020i | \(-0.0850485\pi\) |
−0.868707 | + | 0.495326i | \(0.835048\pi\) | |||||||
\(44\) | 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 | \(-0.0692763\pi\) |
−0.843107 | + | 0.537745i | \(0.819276\pi\) | |||||||
\(54\) | 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 | −0.123474 | − | 0.992348i | \(-0.539404\pi\) |
0.614387 | + | 0.789005i | \(0.289404\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 226.809 | − | 547.566i | 0.476065 | − | 1.14932i | −0.485374 | − | 0.874306i | \(-0.661317\pi\) |
0.961440 | − | 0.275016i | \(-0.0886833\pi\) | |||||||
\(62\) | 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 | 0.164808 | + | 0.986326i | \(0.447299\pi\) |
−0.813975 | + | 0.580900i | \(0.802701\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 285.056 | − | 118.074i | 0.497344 | − | 0.206007i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 690.837 | − | 690.837i | 1.15475 | − | 1.15475i | 0.169163 | − | 0.985588i | \(-0.445894\pi\) |
0.985588 | − | 0.169163i | \(-0.0541063\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 223.345 | + | 223.345i | 0.358089 | + | 0.358089i | 0.863108 | − | 0.505019i | \(-0.168515\pi\) |
−0.505019 | + | 0.863108i | \(0.668515\pi\) | |||||||
\(74\) | 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 | 0.894283 | − | 0.447502i | \(-0.147686\pi\) |
0.315922 | + | 0.948785i | \(0.397686\pi\) | |||||||
\(84\) | 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 | −0.797859 | − | 0.602845i | \(-0.794034\pi\) |
0.602845 | + | 0.797859i | \(0.294034\pi\) | |||||||
\(90\) | 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 | \(-0.937976\pi\) |
−0.556814 | + | 0.830637i | \(0.687976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −80.1481 | + | 80.1481i | −0.0766721 | + | 0.0766721i | −0.744403 | − | 0.667731i | \(-0.767266\pi\) |
0.667731 | + | 0.744403i | \(0.267266\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 214.737 | + | 214.737i | 0.199583 | + | 0.199583i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −552.814 | − | 1334.61i | −0.499463 | − | 1.20581i | −0.949773 | − | 0.312939i | \(-0.898687\pi\) |
0.450310 | − | 0.892872i | \(-0.351313\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −490.666 | − | 203.241i | −0.431168 | − | 0.178596i | 0.156535 | − | 0.987672i | \(-0.449968\pi\) |
−0.587703 | + | 0.809077i | \(0.699968\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 755.757i | − | 0.646246i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 109.197i | 0.0909060i | 0.998966 | + | 0.0454530i | \(0.0144731\pi\) | ||||
−0.998966 | + | 0.0454530i | \(0.985527\pi\) | |||||||
\(114\) | 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 | \(-0.321878\pi\) | ||||
0.530837 | + | 0.847474i | \(0.321878\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 184.143 | 0.125681 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −386.047 | + | 932.000i | −0.257474 | + | 0.621597i | −0.998770 | − | 0.0495811i | \(-0.984211\pi\) |
0.741296 | + | 0.671178i | \(0.234211\pi\) | |||||||
\(132\) | 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 | 0.744064 | − | 0.668108i | \(-0.232896\pi\) |
−0.668108 | + | 0.744064i | \(0.732896\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.36667 | + | 5.71364i | 0.00144416 | + | 0.00348651i | 0.924600 | − | 0.380939i | \(-0.124399\pi\) |
−0.923156 | + | 0.384426i | \(0.874399\pi\) | |||||||
\(140\) | 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 | \(-0.196841\pi\) |
−0.986087 | + | 0.166229i | \(0.946841\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 571.254 | + | 571.254i | 0.307868 | + | 0.307868i | 0.844082 | − | 0.536214i | \(-0.180146\pi\) |
−0.536214 | + | 0.844082i | \(0.680146\pi\) | |||||||
\(152\) | 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 | \(-0.828399\pi\) |
0.969822 | + | 0.243814i | \(0.0783988\pi\) | |||||||
\(158\) | 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 | −0.725447 | − | 0.688278i | \(-0.758367\pi\) |
0.999655 | + | 0.0262826i | \(0.00836698\pi\) | |||||||
\(164\) | 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 | \(-0.682499\pi\) |
0.840095 | + | 0.542440i | \(0.182499\pi\) | |||||||
\(168\) | 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 | \(-0.229031\pi\) |
0.0658275 | + | 0.997831i | \(0.479031\pi\) | |||||||
\(174\) | 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 | 0.447928 | − | 0.894069i | \(-0.352162\pi\) |
−0.315469 | + | 0.948936i | \(0.602162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −532.578 | − | 1285.76i | −0.218708 | − | 0.528008i | 0.776002 | − | 0.630731i | \(-0.217245\pi\) |
−0.994710 | + | 0.102722i | \(0.967245\pi\) | |||||||
\(182\) | 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 | \(-0.295618\pi\) | ||||
0.598867 | + | 0.800848i | \(0.295618\pi\) | |||||||
\(192\) | 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 | \(-0.711896\pi\) |
0.119421 | + | 0.992844i | \(0.461896\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1207.72 | − | 1207.72i | 0.430217 | − | 0.430217i | −0.458485 | − | 0.888702i | \(-0.651608\pi\) |
0.888702 | + | 0.458485i | \(0.151608\pi\) | |||||||
\(200\) | 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 | 0.482718 | − | 0.875776i | \(-0.339650\pi\) |
−0.277934 | + | 0.960600i | \(0.589650\pi\) | |||||||
\(212\) | 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 | \(-0.418592\pi\) | ||||
0.252973 | + | 0.967473i | \(0.418592\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4639.56 | 1.37468 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1751.96 | − | 4229.60i | 0.512254 | − | 1.23669i | −0.430315 | − | 0.902679i | \(-0.641598\pi\) |
0.942569 | − | 0.334011i | \(-0.108402\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1072.62 | + | 444.292i | −0.309521 | + | 0.128208i | −0.532037 | − | 0.846721i | \(-0.678573\pi\) |
0.222515 | + | 0.974929i | \(0.428573\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −351.493 | + | 351.493i | −0.100115 | + | 0.100115i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −224.008 | − | 224.008i | −0.0629840 | − | 0.0629840i | 0.674913 | − | 0.737897i | \(-0.264181\pi\) |
−0.737897 | + | 0.674913i | \(0.764181\pi\) | |||||||
\(234\) | 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 | \(-0.713298\pi\) | ||
0.621061 | − | 0.783762i | \(-0.286702\pi\) | |||||||
\(242\) | 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 | −0.538305 | − | 0.842750i | \(-0.680935\pi\) |
0.215276 | + | 0.976553i | \(0.430935\pi\) | |||||||
\(252\) | 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 | \(-0.853089\pi\) |
0.445324 | + | 0.895370i | \(0.353089\pi\) | |||||||
\(264\) | 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 | \(-0.536877\pi\) |
−0.784103 | + | 0.620630i | \(0.786877\pi\) | |||||||
\(270\) | 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 | 0.985153 | + | 0.171679i | \(0.0549192\pi\) |
−0.575213 | + | 0.818004i | \(0.695081\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −414.605 | − | 414.605i | −0.0889669 | − | 0.0889669i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.7223 | + | 30.7223i | −0.00652220 | + | 0.00652220i | −0.710360 | − | 0.703838i | \(-0.751468\pi\) |
0.703838 | + | 0.710360i | \(0.251468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5549.45 | − | 2298.66i | 1.16565 | − | 0.482830i | 0.285901 | − | 0.958259i | \(-0.407707\pi\) |
0.879754 | + | 0.475429i | \(0.157707\pi\) | |||||||
\(284\) | 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 | \(-0.717806\pi\) |
0.100969 | + | 0.994890i | \(0.467806\pi\) | |||||||
\(294\) | 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 | 0.345047 | − | 0.938585i | \(-0.387863\pi\) |
−0.419695 | + | 0.907665i | \(0.637863\pi\) | |||||||
\(308\) | 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 | \(-0.492007\pi\) |
−0.999685 | + | 0.0251081i | \(0.992007\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1787.53 | + | 1787.53i | −0.322803 | + | 0.322803i | −0.849841 | − | 0.527039i | \(-0.823302\pi\) |
0.527039 | + | 0.849841i | \(0.323302\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2172.32 | + | 899.804i | −0.388560 | + | 0.160947i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2370.77 | + | 5723.55i | −0.420050 | + | 1.01409i | 0.562282 | + | 0.826945i | \(0.309923\pi\) |
−0.982332 | + | 0.187145i | \(0.940077\pi\) | |||||||
\(318\) | 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 | 0.718102 | − | 0.695938i | \(-0.245011\pi\) |
−0.999877 | + | 0.0156724i | \(0.995011\pi\) | |||||||
\(332\) | 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 | \(-0.976117\pi\) | ||
0.997187 | − | 0.0749592i | \(-0.0238826\pi\) | |||||||
\(338\) | 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 | −0.654415 | − | 0.756136i | \(-0.727085\pi\) |
0.0719277 | + | 0.997410i | \(0.477085\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1631.14 | − | 3937.93i | 0.250181 | − | 0.603990i | −0.748037 | − | 0.663657i | \(-0.769004\pi\) |
0.998218 | + | 0.0596662i | \(0.0190036\pi\) | |||||||
\(350\) | 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 | \(-0.650057\pi\) |
0.890925 | + | 0.454151i | \(0.150057\pi\) | |||||||
\(360\) | 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 | \(-0.0724679\pi\) |
−0.848457 | + | 0.529265i | \(0.822468\pi\) | |||||||
\(374\) | 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 | −0.796694 | − | 0.604383i | \(-0.793420\pi\) |
−0.135985 | + | 0.990711i | \(0.543420\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1516.76 | − | 3661.78i | 0.203953 | − | 0.492385i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2433.37 | −0.324645 | −0.162323 | − | 0.986738i | \(-0.551899\pi\) | ||||
−0.162323 | + | 0.986738i | \(0.551899\pi\) | |||||||
\(384\) | 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 | \(-0.721995\pi\) |
0.0878663 | + | 0.996132i | \(0.471995\pi\) | |||||||
\(390\) | 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 | \(-0.368324\pi\) |
−0.363223 | + | 0.931702i | \(0.618324\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 2498.10i | − | 0.313437i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10975.6i | 1.36682i | 0.730036 | + | 0.683409i | \(0.239503\pi\) | ||||
−0.730036 | + | 0.683409i | \(0.760497\pi\) | |||||||
\(402\) | 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 | 0.0138007 | − | 0.999905i | \(-0.495607\pi\) |
0.999905 | − | 0.0138007i | \(-0.00439304\pi\) | |||||||
\(410\) | 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 | −0.951931 | − | 0.306311i | \(-0.900905\pi\) |
0.889712 | + | 0.456522i | \(0.150905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1963.49 | + | 813.303i | −0.227303 | + | 0.0941520i | −0.493428 | − | 0.869786i | \(-0.664256\pi\) |
0.266125 | + | 0.963938i | \(0.414256\pi\) | |||||||
\(422\) | 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 | \(0.0375844\pi\) | ||||
−0.993037 | + | 0.117801i | \(0.962416\pi\) | |||||||
\(434\) | 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 | \(-0.0382806\pi\) |
−0.119972 | + | 0.992777i | \(0.538281\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4352.62 | + | 4352.62i | −0.469994 | + | 0.469994i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3136.09 | + | 1299.01i | −0.336343 | + | 0.139318i | −0.544462 | − | 0.838786i | \(-0.683266\pi\) |
0.208119 | + | 0.978104i | \(0.433266\pi\) | |||||||
\(444\) | 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 | 0.949821 | − | 0.312794i | \(-0.101265\pi\) |
−0.312794 | + | 0.949821i | \(0.601265\pi\) | |||||||
\(458\) | 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 | \(-0.577640\pi\) |
−0.856944 | + | 0.515410i | \(0.827640\pi\) | |||||||
\(462\) | 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 | 0.00538305 | − | 0.999986i | \(-0.498287\pi\) |
−0.703290 | + | 0.710903i | \(0.748287\pi\) | |||||||
\(468\) | 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 | \(-0.429399\pi\) | ||||
0.219984 | + | 0.975503i | \(0.429399\pi\) | |||||||
\(480\) | 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 | −0.0227515 | + | 0.999741i | \(0.507243\pi\) |
−0.999741 | + | 0.0227515i | \(0.992757\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2750.34 | − | 2750.34i | −0.254345 | − | 0.254345i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7836.91 | + | 18920.0i | 0.720316 | + | 1.73900i | 0.672451 | + | 0.740142i | \(0.265242\pi\) |
0.0478645 | + | 0.998854i | \(0.484758\pi\) | |||||||
\(492\) | 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 | 0.650990 | − | 0.759086i | \(-0.274354\pi\) |
−0.0764356 | + | 0.997075i | \(0.524354\pi\) | |||||||
\(500\) | 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 | \(-0.198831\pi\) |
−0.584810 | + | 0.811171i | \(0.698831\pi\) | |||||||
\(504\) | 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 | \(-0.991359\pi\) |
0.726039 | + | 0.687654i | \(0.241359\pi\) | |||||||
\(510\) | 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 | 0.344637 | − | 0.938736i | \(-0.388002\pi\) |
−0.938736 | + | 0.344637i | \(0.888002\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 111.041 | + | 268.077i | 0.00928391 | + | 0.0224134i | 0.928454 | − | 0.371449i | \(-0.121139\pi\) |
−0.919170 | + | 0.393862i | \(0.871139\pi\) | |||||||
\(524\) | 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 | −0.113837 | − | 0.993499i | \(-0.536314\pi\) |
0.783005 | − | 0.622016i | \(-0.213686\pi\) | |||||||
\(542\) | 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 | −0.947126 | − | 0.320862i | \(-0.896028\pi\) |
0.896603 | + | 0.442836i | \(0.146028\pi\) | |||||||
\(548\) | 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 | \(-0.289014\pi\) |
−0.122260 | + | 0.992498i | \(0.539014\pi\) | |||||||
\(558\) | 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 | 0.417784 | − | 0.908546i | \(-0.362807\pi\) |
−0.347022 | + | 0.937857i | \(0.612807\pi\) | |||||||
\(564\) | 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 | −0.831934 | − | 0.554875i | \(-0.812766\pi\) |
0.554875 | + | 0.831934i | \(0.312766\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2056.20 | + | 851.705i | −0.150699 | + | 0.0624216i | −0.456758 | − | 0.889591i | \(-0.650990\pi\) |
0.306059 | + | 0.952013i | \(0.400990\pi\) | |||||||
\(572\) | 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 | −0.941283 | − | 0.337617i | \(-0.890379\pi\) |
0.426857 | − | 0.904319i | \(-0.359621\pi\) | |||||||
\(588\) | 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 | \(-0.805871\pi\) | ||
0.819720 | − | 0.572764i | \(-0.194129\pi\) | |||||||
\(594\) | 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 | \(-0.385809\pi\) |
−0.936340 | + | 0.351095i | \(0.885809\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13633.8 | + | 13633.8i | −0.925346 | + | 0.925346i | −0.997401 | − | 0.0720542i | \(-0.977045\pi\) |
0.0720542 | + | 0.997401i | \(0.477045\pi\) | |||||||
\(602\) | 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 | \(-0.796167\pi\) | ||||
−0.801881 | + | 0.597484i | \(0.796167\pi\) | |||||||
\(608\) | 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 | \(-0.847915\pi\) |
−0.302782 | + | 0.953060i | \(0.597915\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6136.93 | − | 6136.93i | 0.402382 | − | 0.402382i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18674.2 | + | 18674.2i | 1.21847 | + | 1.21847i | 0.968168 | + | 0.250301i | \(0.0805297\pi\) |
0.250301 | + | 0.968168i | \(0.419470\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3214.09 | − | 7759.51i | −0.208700 | − | 0.503846i | 0.784519 | − | 0.620105i | \(-0.212910\pi\) |
−0.993219 | + | 0.116258i | \(0.962910\pi\) | |||||||
\(620\) | 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 | −0.949515 | − | 0.313722i | \(-0.898424\pi\) |
−0.313722 | − | 0.949515i | \(-0.601576\pi\) | |||||||
\(632\) | 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 | 0.675538 | + | 0.737325i | \(0.263911\pi\) |
−0.999045 | + | 0.0436901i | \(0.986089\pi\) | |||||||
\(644\) | 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 | \(-0.969111\pi\) |
0.0968891 | + | 0.995295i | \(0.469111\pi\) | |||||||
\(648\) | 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 | \(-0.0731967\pi\) |
0.527321 | + | 0.849666i | \(0.323197\pi\) | |||||||
\(654\) | 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 | 0.953965 | − | 0.299918i | \(-0.0969594\pi\) |
0.462481 | + | 0.886629i | \(0.346959\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 398.063 | + | 961.010i | 0.0234234 | + | 0.0565491i | 0.935158 | − | 0.354230i | \(-0.115257\pi\) |
−0.911735 | + | 0.410779i | \(0.865257\pi\) | |||||||
\(662\) | 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 | \(-0.614797\pi\) |
0.412095 | + | 0.911141i | \(0.364797\pi\) | |||||||
\(678\) | 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 | 0.948827 | + | 0.315797i | \(0.102272\pi\) |
−0.447619 | + | 0.894224i | \(0.647728\pi\) | |||||||
\(684\) | 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 | −0.231600 | − | 0.972811i | \(-0.574396\pi\) |
−0.851647 | + | 0.524115i | \(0.824396\pi\) | |||||||
\(692\) | 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 | \(-0.936769\pi\) |
0.832744 | + | 0.553658i | \(0.186769\pi\) | |||||||
\(702\) | 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 | \(-0.603190\pi\) |
0.445039 | + | 0.895511i | \(0.353190\pi\) | |||||||
\(710\) | 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 | \(-0.304129\pi\) |
−0.816573 | + | 0.577243i | \(0.804129\pi\) | |||||||
\(728\) | 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 | 0.121224 | + | 0.992625i | \(0.461318\pi\) |
−0.787610 | + | 0.616174i | \(0.788682\pi\) | |||||||
\(734\) | 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 | −0.145383 | − | 0.989375i | \(-0.546442\pi\) |
0.802396 | − | 0.596793i | \(-0.203558\pi\) | |||||||
\(740\) | 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 | \(-0.916497\pi\) |
0.259335 | + | 0.965787i | \(0.416497\pi\) | |||||||
\(744\) | 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 | 0.662983 | + | 0.748635i | \(0.269290\pi\) |
0.0605650 | + | 0.998164i | \(0.480710\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6726.00 | − | 6726.00i | −0.321658 | − | 0.321658i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12120.7 | + | 12120.7i | −0.577363 | + | 0.577363i | −0.934176 | − | 0.356813i | \(-0.883863\pi\) |
0.356813 | + | 0.934176i | \(0.383863\pi\) | |||||||
\(762\) | 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 | \(-0.851797\pi\) |
−0.314380 | + | 0.949297i | \(0.601797\pi\) | |||||||
\(774\) | 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 | −0.465762 | − | 0.884910i | \(-0.654220\pi\) |
−0.955069 | + | 0.296382i | \(0.904220\pi\) | |||||||
\(788\) | 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 | 0.588424 | + | 0.808552i | \(0.299749\pi\) |
−0.987812 | + | 0.155654i | \(0.950251\pi\) | |||||||
\(798\) | 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 | 0.359694 | − | 0.933070i | \(-0.382881\pi\) |
−0.933070 | + | 0.359694i | \(0.882881\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −140.367 | − | 338.877i | −0.00607764 | − | 0.0146727i | 0.920812 | − | 0.390008i | \(-0.127528\pi\) |
−0.926889 | + | 0.375335i | \(0.877528\pi\) | |||||||
\(812\) | 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 | \(-0.238881\pi\) |
−0.999390 | + | 0.0349231i | \(0.988881\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −769.291 | − | 769.291i | −0.0325830 | − | 0.0325830i | 0.690628 | − | 0.723211i | \(-0.257334\pi\) |
−0.723211 | + | 0.690628i | \(0.757334\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13062.7 | + | 13062.7i | −0.551253 | + | 0.551253i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22898.4 | + | 9484.82i | −0.962823 | + | 0.398815i | −0.808036 | − | 0.589133i | \(-0.799469\pi\) |
−0.154788 | + | 0.987948i | \(0.549469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10844.8 | − | 26181.7i | 0.454350 | − | 1.09690i | −0.516301 | − | 0.856407i | \(-0.672691\pi\) |
0.970651 | − | 0.240492i | \(-0.0773087\pi\) | |||||||
\(830\) | 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 | \(-0.504637\pi\) |
0.999894 | + | 0.0145666i | \(0.00463684\pi\) | |||||||
\(840\) | 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 | −0.996886 | − | 0.0788554i | \(-0.974873\pi\) |
0.649146 | − | 0.760664i | \(-0.275127\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −41670.8 | − | 41670.8i | −1.66680 | − | 1.66680i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9119.55 | + | 9119.55i | −0.363498 | + | 0.363498i | −0.865099 | − | 0.501601i | \(-0.832745\pi\) |
0.501601 | + | 0.865099i | \(0.332745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30582.3 | − | 12667.6i | 1.21473 | − | 0.503159i | 0.319002 | − | 0.947754i | \(-0.396652\pi\) |
0.895732 | + | 0.444595i | \(0.146652\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1090.07 | + | 2631.66i | −0.0431470 | + | 0.104166i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1210.85 | 0.0477612 | 0.0238806 | − | 0.999715i | \(-0.492398\pi\) | ||||
0.0238806 | + | 0.999715i | \(0.492398\pi\) | |||||||
\(864\) | 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 | \(-0.100714\pi\) |
0.451990 | + | 0.892023i | \(0.350714\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7520.83i | 0.288591i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 39286.1i | − | 1.50236i | −0.660095 | − | 0.751182i | \(-0.729484\pi\) | ||
0.660095 | − | 0.751182i | \(-0.270516\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 234.092 | + | 96.9642i | 0.00892167 | + | 0.00369548i | 0.387140 | − | 0.922021i | \(-0.373463\pi\) |
−0.378218 | + | 0.925717i | \(0.623463\pi\) | |||||||
\(884\) | 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 | \(-0.131832\pi\) |
−0.402422 | + | 0.915454i | \(0.631832\pi\) | |||||||
\(888\) | 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 | 0.964299 | − | 0.264816i | \(-0.0853112\pi\) |
−0.869115 | + | 0.494609i | \(0.835311\pi\) | |||||||
\(908\) | 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 | 0.866453 | + | 0.499258i | \(0.166394\pi\) |
0.499258 | + | 0.866453i | \(0.333606\pi\) | |||||||
\(920\) | 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 | 0.867311 | − | 0.497766i | \(-0.165846\pi\) |
−0.497766 | + | 0.867311i | \(0.665846\pi\) | |||||||
\(938\) | 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 | \(-0.268932\pi\) |
−0.0594418 | + | 0.998232i | \(0.518932\pi\) | |||||||
\(942\) | 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 | 0.517714 | − | 0.855554i | \(-0.326783\pi\) |
−0.238889 | + | 0.971047i | \(0.576783\pi\) | |||||||
\(948\) | 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 | −0.278723 | − | 0.960371i | \(-0.589911\pi\) |
0.960371 | + | 0.278723i | \(0.0899113\pi\) | |||||||
\(954\) | 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 | \(-0.615135\pi\) |
0.935294 | + | 0.353872i | \(0.115135\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20838.6 | − | 20838.6i | −0.690849 | − | 0.690849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2567.45 | − | 6198.36i | −0.0848540 | − | 0.204856i | 0.875757 | − | 0.482752i | \(-0.160363\pi\) |
−0.960611 | + | 0.277896i | \(0.910363\pi\) | |||||||
\(972\) | 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 | \(0.170129\pi\) | ||||
−0.860536 | + | 0.509390i | \(0.829871\pi\) | |||||||
\(978\) | 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 | \(-0.122081\pi\) |
−0.374194 | + | 0.927350i | \(0.622081\pi\) | |||||||
\(984\) | 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 | \(-0.323462\pi\) | ||||
0.526613 | + | 0.850105i | \(0.323462\pi\) | |||||||
\(992\) | 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 | \(-0.451492\pi\) |
0.806253 | + | 0.591570i | \(0.201492\pi\) | |||||||
\(998\) | 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 | 256.4.g.b.33.7 | 44 | ||
4.3 | odd | 2 | 256.4.g.a.33.5 | 44 | |||
8.3 | odd | 2 | 128.4.g.a.17.7 | 44 | |||
8.5 | even | 2 | 32.4.g.a.13.2 | yes | 44 | ||
32.5 | even | 8 | inner | 256.4.g.b.225.7 | 44 | ||
32.11 | odd | 8 | 128.4.g.a.113.7 | 44 | |||
32.21 | even | 8 | 32.4.g.a.5.2 | ✓ | 44 | ||
32.27 | odd | 8 | 256.4.g.a.225.5 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.2 | ✓ | 44 | 32.21 | even | 8 | ||
32.4.g.a.13.2 | yes | 44 | 8.5 | even | 2 | ||
128.4.g.a.17.7 | 44 | 8.3 | odd | 2 | |||
128.4.g.a.113.7 | 44 | 32.11 | odd | 8 | |||
256.4.g.a.33.5 | 44 | 4.3 | odd | 2 | |||
256.4.g.a.225.5 | 44 | 32.27 | odd | 8 | |||
256.4.g.b.33.7 | 44 | 1.1 | even | 1 | trivial | ||
256.4.g.b.225.7 | 44 | 32.5 | even | 8 | inner |