Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,5,Mod(174,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.174");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.c (of order \(2\), degree \(1\), 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: | \(18.0897435397\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 174.18 | ||
Character | \(\chi\) | \(=\) | 175.174 |
Dual form | 175.5.c.d.174.17 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.50299i | 1.62575i | 0.582440 | + | 0.812874i | \(0.302098\pi\) | ||||
−0.582440 | + | 0.812874i | \(0.697902\pi\) | |||||||
\(3\) | −5.52807 | −0.614230 | −0.307115 | − | 0.951672i | \(-0.599364\pi\) | ||||
−0.307115 | + | 0.951672i | \(0.599364\pi\) | |||||||
\(4\) | −26.2889 | −1.64305 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 35.9490i | − | 0.998583i | ||||||
\(7\) | −44.7373 | − | 19.9894i | −0.913005 | − | 0.407948i | ||||
\(8\) | − | 66.9085i | − | 1.04545i | ||||||
\(9\) | −50.4404 | −0.622722 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −105.424 | −0.871273 | −0.435636 | − | 0.900123i | \(-0.643477\pi\) | ||||
−0.435636 | + | 0.900123i | \(0.643477\pi\) | |||||||
\(12\) | 145.327 | 1.00921 | ||||||||
\(13\) | 234.089 | 1.38514 | 0.692571 | − | 0.721349i | \(-0.256478\pi\) | ||||
0.692571 | + | 0.721349i | \(0.256478\pi\) | |||||||
\(14\) | 129.991 | − | 290.926i | 0.663220 | − | 1.48432i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.4831 | 0.0565747 | ||||||||
\(17\) | 375.251 | 1.29845 | 0.649224 | − | 0.760597i | \(-0.275094\pi\) | ||||
0.649224 | + | 0.760597i | \(0.275094\pi\) | |||||||
\(18\) | − | 328.014i | − | 1.01239i | ||||||
\(19\) | − | 45.1673i | − | 0.125117i | −0.998041 | − | 0.0625586i | \(-0.980074\pi\) | ||
0.998041 | − | 0.0625586i | \(-0.0199260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 247.311 | + | 110.503i | 0.560795 | + | 0.250574i | ||||
\(22\) | − | 685.571i | − | 1.41647i | ||||||
\(23\) | − | 46.3674i | − | 0.0876510i | −0.999039 | − | 0.0438255i | \(-0.986045\pi\) | ||
0.999039 | − | 0.0438255i | \(-0.0139546\pi\) | |||||||
\(24\) | 369.875i | 0.642144i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1522.28i | 2.25189i | ||||||||
\(27\) | 726.612 | 0.996724 | ||||||||
\(28\) | 1176.09 | + | 525.500i | 1.50012 | + | 0.670280i | ||||
\(29\) | 257.421 | 0.306089 | 0.153045 | − | 0.988219i | \(-0.451092\pi\) | ||||
0.153045 | + | 0.988219i | \(0.451092\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 194.899i | − | 0.202809i | −0.994845 | − | 0.101404i | \(-0.967666\pi\) | ||
0.994845 | − | 0.101404i | \(-0.0323336\pi\) | |||||||
\(32\) | − | 976.352i | − | 0.953469i | ||||||
\(33\) | 582.791 | 0.535162 | ||||||||
\(34\) | 2440.26i | 2.11095i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1326.02 | 1.02317 | ||||||||
\(37\) | 2523.02i | 1.84296i | 0.388421 | + | 0.921482i | \(0.373021\pi\) | ||||
−0.388421 | + | 0.921482i | \(0.626979\pi\) | |||||||
\(38\) | 293.723 | 0.203409 | ||||||||
\(39\) | −1294.06 | −0.850796 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2504.06i | − | 1.48963i | −0.667274 | − | 0.744813i | \(-0.732539\pi\) | ||
0.667274 | − | 0.744813i | \(-0.267461\pi\) | |||||||
\(42\) | −718.600 | + | 1608.26i | −0.407370 | + | 0.911711i | ||||
\(43\) | − | 2288.24i | − | 1.23756i | −0.785565 | − | 0.618779i | \(-0.787628\pi\) | ||
0.785565 | − | 0.618779i | \(-0.212372\pi\) | |||||||
\(44\) | 2771.48 | 1.43155 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 301.527 | 0.142498 | ||||||||
\(47\) | −2624.74 | −1.18820 | −0.594101 | − | 0.804391i | \(-0.702492\pi\) | ||||
−0.594101 | + | 0.804391i | \(0.702492\pi\) | |||||||
\(48\) | −80.0637 | −0.0347499 | ||||||||
\(49\) | 1601.84 | + | 1788.55i | 0.667157 | + | 0.744917i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2074.42 | −0.797545 | ||||||||
\(52\) | −6153.94 | −2.27587 | ||||||||
\(53\) | 358.663i | 0.127683i | 0.997960 | + | 0.0638417i | \(0.0203353\pi\) | ||||
−0.997960 | + | 0.0638417i | \(0.979665\pi\) | |||||||
\(54\) | 4725.15i | 1.62042i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1337.46 | + | 2993.30i | −0.426487 | + | 0.954497i | ||||
\(57\) | 249.688i | 0.0768508i | ||||||||
\(58\) | 1674.01i | 0.497624i | ||||||||
\(59\) | − | 854.723i | − | 0.245540i | −0.992435 | − | 0.122770i | \(-0.960822\pi\) | ||
0.992435 | − | 0.122770i | \(-0.0391777\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2085.25i | − | 0.560400i | −0.959942 | − | 0.280200i | \(-0.909599\pi\) | ||
0.959942 | − | 0.280200i | \(-0.0904007\pi\) | |||||||
\(62\) | 1267.43 | 0.329716 | ||||||||
\(63\) | 2256.57 | + | 1008.28i | 0.568548 | + | 0.254038i | ||||
\(64\) | 6580.94 | 1.60667 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3789.89i | 0.870038i | ||||||||
\(67\) | − | 7558.23i | − | 1.68372i | −0.539693 | − | 0.841862i | \(-0.681460\pi\) | ||
0.539693 | − | 0.841862i | \(-0.318540\pi\) | |||||||
\(68\) | −9864.94 | −2.13342 | ||||||||
\(69\) | 256.322i | 0.0538379i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −282.660 | −0.0560722 | −0.0280361 | − | 0.999607i | \(-0.508925\pi\) | ||||
−0.0280361 | + | 0.999607i | \(0.508925\pi\) | |||||||
\(72\) | 3374.89i | 0.651021i | ||||||||
\(73\) | 9190.85 | 1.72469 | 0.862343 | − | 0.506325i | \(-0.168996\pi\) | ||||
0.862343 | + | 0.506325i | \(0.168996\pi\) | |||||||
\(74\) | −16407.2 | −2.99619 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1187.40i | 0.205575i | ||||||||
\(77\) | 4716.38 | + | 2107.37i | 0.795477 | + | 0.355434i | ||||
\(78\) | − | 8415.27i | − | 1.38318i | ||||||
\(79\) | 7184.60 | 1.15119 | 0.575597 | − | 0.817734i | \(-0.304770\pi\) | ||||
0.575597 | + | 0.817734i | \(0.304770\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 68.9152 | 0.0105038 | ||||||||
\(82\) | 16283.9 | 2.42175 | ||||||||
\(83\) | −5064.74 | −0.735192 | −0.367596 | − | 0.929986i | \(-0.619819\pi\) | ||||
−0.367596 | + | 0.929986i | \(0.619819\pi\) | |||||||
\(84\) | −6501.52 | − | 2905.00i | −0.921417 | − | 0.411706i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14880.4 | 2.01196 | ||||||||
\(87\) | −1423.04 | −0.188009 | ||||||||
\(88\) | 7053.76i | 0.910868i | ||||||||
\(89\) | − | 10243.7i | − | 1.29323i | −0.762817 | − | 0.646614i | \(-0.776184\pi\) | ||
0.762817 | − | 0.646614i | \(-0.223816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10472.5 | − | 4679.31i | −1.26464 | − | 0.565066i | ||||
\(92\) | 1218.95i | 0.144015i | ||||||||
\(93\) | 1077.42i | 0.124571i | ||||||||
\(94\) | − | 17068.6i | − | 1.93172i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5397.34i | 0.585649i | ||||||||
\(97\) | 608.860 | 0.0647104 | 0.0323552 | − | 0.999476i | \(-0.489699\pi\) | ||||
0.0323552 | + | 0.999476i | \(0.489699\pi\) | |||||||
\(98\) | −11630.9 | + | 10416.8i | −1.21105 | + | 1.08463i | ||||
\(99\) | 5317.63 | 0.542560 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 14966.3i | − | 1.46714i | −0.679616 | − | 0.733568i | \(-0.737854\pi\) | ||
0.679616 | − | 0.733568i | \(-0.262146\pi\) | |||||||
\(102\) | − | 13489.9i | − | 1.29661i | ||||||
\(103\) | 18840.1 | 1.77586 | 0.887930 | − | 0.459979i | \(-0.152143\pi\) | ||||
0.887930 | + | 0.459979i | \(0.152143\pi\) | |||||||
\(104\) | − | 15662.5i | − | 1.44809i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2332.38 | −0.207581 | ||||||||
\(107\) | 3903.78i | 0.340971i | 0.985360 | + | 0.170485i | \(0.0545336\pi\) | ||||
−0.985360 | + | 0.170485i | \(0.945466\pi\) | |||||||
\(108\) | −19101.8 | −1.63767 | ||||||||
\(109\) | −16429.7 | −1.38285 | −0.691427 | − | 0.722447i | \(-0.743018\pi\) | ||||
−0.691427 | + | 0.722447i | \(0.743018\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 13947.4i | − | 1.13200i | ||||||
\(112\) | −647.935 | − | 289.510i | −0.0516530 | − | 0.0230795i | ||||
\(113\) | − | 19430.8i | − | 1.52172i | −0.648918 | − | 0.760858i | \(-0.724778\pi\) | ||
0.648918 | − | 0.760858i | \(-0.275222\pi\) | |||||||
\(114\) | −1623.72 | −0.124940 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6767.31 | −0.502922 | ||||||||
\(117\) | −11807.6 | −0.862558 | ||||||||
\(118\) | 5558.26 | 0.399185 | ||||||||
\(119\) | −16787.7 | − | 7501.06i | −1.18549 | − | 0.529699i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3526.78 | −0.240884 | ||||||||
\(122\) | 13560.3 | 0.911068 | ||||||||
\(123\) | 13842.6i | 0.914972i | ||||||||
\(124\) | 5123.68i | 0.333226i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6556.81 | + | 14674.4i | −0.413001 | + | 0.924316i | ||||
\(127\) | − | 3473.63i | − | 0.215365i | −0.994185 | − | 0.107683i | \(-0.965657\pi\) | ||
0.994185 | − | 0.107683i | \(-0.0343431\pi\) | |||||||
\(128\) | 27174.1i | 1.65858i | ||||||||
\(129\) | 12649.6i | 0.760145i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5214.48i | 0.303856i | 0.988392 | + | 0.151928i | \(0.0485482\pi\) | ||||
−0.988392 | + | 0.151928i | \(0.951452\pi\) | |||||||
\(132\) | −15320.9 | −0.879300 | ||||||||
\(133\) | −902.870 | + | 2020.66i | −0.0510413 | + | 0.114233i | ||||
\(134\) | 49151.1 | 2.73731 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 25107.5i | − | 1.35746i | ||||||
\(137\) | 25017.6i | 1.33292i | 0.745540 | + | 0.666461i | \(0.232192\pi\) | ||||
−0.745540 | + | 0.666461i | \(0.767808\pi\) | |||||||
\(138\) | −1666.86 | −0.0875268 | ||||||||
\(139\) | 9723.25i | 0.503248i | 0.967825 | + | 0.251624i | \(0.0809646\pi\) | ||||
−0.967825 | + | 0.251624i | \(0.919035\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14509.7 | 0.729829 | ||||||||
\(142\) | − | 1838.14i | − | 0.0911593i | ||||||
\(143\) | −24678.6 | −1.20684 | ||||||||
\(144\) | −730.535 | −0.0352303 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 59768.0i | 2.80390i | ||||||||
\(147\) | −8855.11 | − | 9887.20i | −0.409788 | − | 0.457550i | ||||
\(148\) | − | 66327.3i | − | 3.02809i | ||||||
\(149\) | −4969.64 | −0.223847 | −0.111924 | − | 0.993717i | \(-0.535701\pi\) | ||||
−0.111924 | + | 0.993717i | \(0.535701\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15572.0 | −0.682954 | −0.341477 | − | 0.939890i | \(-0.610927\pi\) | ||||
−0.341477 | + | 0.939890i | \(0.610927\pi\) | |||||||
\(152\) | −3022.08 | −0.130803 | ||||||||
\(153\) | −18927.8 | −0.808571 | ||||||||
\(154\) | −13704.2 | + | 30670.6i | −0.577845 | + | 1.29324i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 34019.4 | 1.39790 | ||||||||
\(157\) | 2245.97 | 0.0911180 | 0.0455590 | − | 0.998962i | \(-0.485493\pi\) | ||||
0.0455590 | + | 0.998962i | \(0.485493\pi\) | |||||||
\(158\) | 46721.4i | 1.87155i | ||||||||
\(159\) | − | 1982.71i | − | 0.0784270i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −926.858 | + | 2074.35i | −0.0357570 | + | 0.0800259i | ||||
\(162\) | 448.155i | 0.0170765i | ||||||||
\(163\) | − | 27048.4i | − | 1.01804i | −0.860754 | − | 0.509021i | \(-0.830007\pi\) | ||
0.860754 | − | 0.509021i | \(-0.169993\pi\) | |||||||
\(164\) | 65828.9i | 2.44754i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 32936.0i | − | 1.19524i | ||||||
\(167\) | −36693.5 | −1.31570 | −0.657849 | − | 0.753149i | \(-0.728534\pi\) | ||||
−0.657849 | + | 0.753149i | \(0.728534\pi\) | |||||||
\(168\) | 7393.59 | − | 16547.2i | 0.261961 | − | 0.586281i | ||||
\(169\) | 26236.7 | 0.918620 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2278.26i | 0.0779132i | ||||||||
\(172\) | 60155.4i | 2.03338i | ||||||||
\(173\) | 3132.59 | 0.104667 | 0.0523337 | − | 0.998630i | \(-0.483334\pi\) | ||||
0.0523337 | + | 0.998630i | \(0.483334\pi\) | |||||||
\(174\) | − | 9254.03i | − | 0.305656i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1526.87 | −0.0492920 | ||||||||
\(177\) | 4724.97i | 0.150818i | ||||||||
\(178\) | 66614.4 | 2.10246 | ||||||||
\(179\) | 25816.5 | 0.805732 | 0.402866 | − | 0.915259i | \(-0.368014\pi\) | ||||
0.402866 | + | 0.915259i | \(0.368014\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 31614.4i | − | 0.965002i | −0.875895 | − | 0.482501i | \(-0.839728\pi\) | ||
0.875895 | − | 0.482501i | \(-0.160272\pi\) | |||||||
\(182\) | 30429.5 | − | 68102.6i | 0.918654 | − | 2.05599i | ||||
\(183\) | 11527.4i | 0.344214i | ||||||||
\(184\) | −3102.37 | −0.0916343 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7006.43 | −0.202521 | ||||||||
\(187\) | −39560.5 | −1.13130 | ||||||||
\(188\) | 69001.4 | 1.95228 | ||||||||
\(189\) | −32506.6 | − | 14524.6i | −0.910014 | − | 0.406611i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4727.49 | −0.129588 | −0.0647938 | − | 0.997899i | \(-0.520639\pi\) | ||||
−0.0647938 | + | 0.997899i | \(0.520639\pi\) | |||||||
\(192\) | −36379.9 | −0.986867 | ||||||||
\(193\) | 36953.1i | 0.992057i | 0.868306 | + | 0.496028i | \(0.165209\pi\) | ||||
−0.868306 | + | 0.496028i | \(0.834791\pi\) | |||||||
\(194\) | 3959.41i | 0.105203i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −42110.7 | − | 47018.8i | −1.09618 | − | 1.22394i | ||||
\(197\) | − | 3222.40i | − | 0.0830322i | −0.999138 | − | 0.0415161i | \(-0.986781\pi\) | ||
0.999138 | − | 0.0415161i | \(-0.0132188\pi\) | |||||||
\(198\) | 34580.5i | 0.882066i | ||||||||
\(199\) | − | 51984.5i | − | 1.31271i | −0.754453 | − | 0.656354i | \(-0.772098\pi\) | ||
0.754453 | − | 0.656354i | \(-0.227902\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 41782.4i | 1.03419i | ||||||||
\(202\) | 97325.4 | 2.38519 | ||||||||
\(203\) | −11516.3 | − | 5145.70i | −0.279461 | − | 0.124868i | ||||
\(204\) | 54534.1 | 1.31041 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 122517.i | 2.88710i | ||||||||
\(207\) | 2338.79i | 0.0545822i | ||||||||
\(208\) | 3390.34 | 0.0783641 | ||||||||
\(209\) | 4761.72i | 0.109011i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15750.2 | −0.353770 | −0.176885 | − | 0.984232i | \(-0.556602\pi\) | ||||
−0.176885 | + | 0.984232i | \(0.556602\pi\) | |||||||
\(212\) | − | 9428.84i | − | 0.209791i | ||||||
\(213\) | 1562.56 | 0.0344412 | ||||||||
\(214\) | −25386.2 | −0.554333 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 48616.5i | − | 1.04202i | ||||||
\(217\) | −3895.93 | + | 8719.26i | −0.0827354 | + | 0.185165i | ||||
\(218\) | − | 106842.i | − | 2.24817i | ||||||
\(219\) | −50807.7 | −1.05935 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 87842.3 | 1.79854 | ||||||||
\(222\) | 90699.9 | 1.84035 | ||||||||
\(223\) | 11942.3 | 0.240148 | 0.120074 | − | 0.992765i | \(-0.461687\pi\) | ||||
0.120074 | + | 0.992765i | \(0.461687\pi\) | |||||||
\(224\) | −19516.7 | + | 43679.3i | −0.388965 | + | 0.870522i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 126358. | 2.47393 | ||||||||
\(227\) | 79946.4 | 1.55148 | 0.775742 | − | 0.631051i | \(-0.217376\pi\) | ||||
0.775742 | + | 0.631051i | \(0.217376\pi\) | |||||||
\(228\) | − | 6564.02i | − | 0.126270i | ||||||
\(229\) | 40487.1i | 0.772050i | 0.922488 | + | 0.386025i | \(0.126152\pi\) | ||||
−0.922488 | + | 0.386025i | \(0.873848\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −26072.5 | − | 11649.7i | −0.488606 | − | 0.218318i | ||||
\(232\) | − | 17223.7i | − | 0.320000i | ||||||
\(233\) | 40236.2i | 0.741148i | 0.928803 | + | 0.370574i | \(0.120839\pi\) | ||||
−0.928803 | + | 0.370574i | \(0.879161\pi\) | |||||||
\(234\) | − | 76784.4i | − | 1.40230i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 22469.7i | 0.403435i | ||||||||
\(237\) | −39717.0 | −0.707097 | ||||||||
\(238\) | 48779.3 | − | 109170.i | 0.861156 | − | 1.92731i | ||||
\(239\) | 12346.0 | 0.216137 | 0.108069 | − | 0.994143i | \(-0.465533\pi\) | ||||
0.108069 | + | 0.994143i | \(0.465533\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20969.2i | − | 0.361034i | −0.983572 | − | 0.180517i | \(-0.942223\pi\) | ||
0.983572 | − | 0.180517i | \(-0.0577771\pi\) | |||||||
\(242\) | − | 22934.6i | − | 0.391616i | ||||||
\(243\) | −59236.5 | −1.00318 | ||||||||
\(244\) | 54818.8i | 0.920767i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −90018.4 | −1.48751 | ||||||||
\(247\) | − | 10573.2i | − | 0.173305i | ||||||
\(248\) | −13040.4 | −0.212025 | ||||||||
\(249\) | 27998.2 | 0.451577 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 82331.2i | 1.30682i | 0.757003 | + | 0.653411i | \(0.226663\pi\) | ||||
−0.757003 | + | 0.653411i | \(0.773337\pi\) | |||||||
\(252\) | −59322.6 | − | 26506.4i | −0.934156 | − | 0.417398i | ||||
\(253\) | 4888.24i | 0.0763680i | ||||||||
\(254\) | 22589.0 | 0.350130 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −71418.2 | −1.08975 | ||||||||
\(257\) | −6751.23 | −0.102216 | −0.0511078 | − | 0.998693i | \(-0.516275\pi\) | ||||
−0.0511078 | + | 0.998693i | \(0.516275\pi\) | |||||||
\(258\) | −82260.0 | −1.23580 | ||||||||
\(259\) | 50433.7 | − | 112873.i | 0.751833 | − | 1.68264i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12984.4 | −0.190608 | ||||||||
\(262\) | −33909.7 | −0.493994 | ||||||||
\(263\) | − | 23786.1i | − | 0.343884i | −0.985107 | − | 0.171942i | \(-0.944996\pi\) | ||
0.985107 | − | 0.171942i | \(-0.0550042\pi\) | |||||||
\(264\) | − | 38993.7i | − | 0.559482i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −13140.4 | − | 5871.35i | −0.185714 | − | 0.0829803i | ||||
\(267\) | 56627.7i | 0.794340i | ||||||||
\(268\) | 198697.i | 2.76645i | ||||||||
\(269\) | 74052.1i | 1.02337i | 0.859173 | + | 0.511685i | \(0.170979\pi\) | ||||
−0.859173 | + | 0.511685i | \(0.829021\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 61472.9i | − | 0.837037i | −0.908208 | − | 0.418519i | \(-0.862549\pi\) | ||
0.908208 | − | 0.418519i | \(-0.137451\pi\) | |||||||
\(272\) | 5434.81 | 0.0734593 | ||||||||
\(273\) | 57892.7 | + | 25867.5i | 0.776781 | + | 0.347080i | ||||
\(274\) | −162689. | −2.16699 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 6738.42i | − | 0.0884586i | ||||||
\(277\) | − | 73318.6i | − | 0.955552i | −0.878482 | − | 0.477776i | \(-0.841443\pi\) | ||
0.878482 | − | 0.477776i | \(-0.158557\pi\) | |||||||
\(278\) | −63230.2 | −0.818154 | ||||||||
\(279\) | 9830.80i | 0.126293i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −63569.9 | −0.805080 | −0.402540 | − | 0.915403i | \(-0.631872\pi\) | ||||
−0.402540 | + | 0.915403i | \(0.631872\pi\) | |||||||
\(282\) | 94356.6i | 1.18652i | ||||||||
\(283\) | −99674.3 | −1.24454 | −0.622272 | − | 0.782801i | \(-0.713790\pi\) | ||||
−0.622272 | + | 0.782801i | \(0.713790\pi\) | |||||||
\(284\) | 7430.82 | 0.0921298 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 160485.i | − | 1.96201i | ||||||
\(287\) | −50054.7 | + | 112025.i | −0.607689 | + | 1.36004i | ||||
\(288\) | 49247.6i | 0.593746i | ||||||||
\(289\) | 57292.6 | 0.685967 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3365.82 | −0.0397471 | ||||||||
\(292\) | −241617. | −2.83375 | ||||||||
\(293\) | −33390.9 | −0.388949 | −0.194475 | − | 0.980908i | \(-0.562300\pi\) | ||||
−0.194475 | + | 0.980908i | \(0.562300\pi\) | |||||||
\(294\) | 64296.4 | − | 57584.7i | 0.743861 | − | 0.666212i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 168811. | 1.92672 | ||||||||
\(297\) | −76602.3 | −0.868419 | ||||||||
\(298\) | − | 32317.5i | − | 0.363919i | ||||||
\(299\) | − | 10854.1i | − | 0.121409i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −45740.7 | + | 102370.i | −0.504859 | + | 1.12990i | ||||
\(302\) | − | 101265.i | − | 1.11031i | ||||||
\(303\) | 82734.5i | 0.901159i | ||||||||
\(304\) | − | 654.164i | − | 0.00707847i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 123088.i | − | 1.31453i | ||||||
\(307\) | 81081.7 | 0.860292 | 0.430146 | − | 0.902759i | \(-0.358462\pi\) | ||||
0.430146 | + | 0.902759i | \(0.358462\pi\) | |||||||
\(308\) | −123988. | − | 55400.3i | −1.30701 | − | 0.583997i | ||||
\(309\) | −104149. | −1.09079 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 58811.2i | − | 0.608050i | −0.952664 | − | 0.304025i | \(-0.901669\pi\) | ||
0.952664 | − | 0.304025i | \(-0.0983306\pi\) | |||||||
\(312\) | 86583.7i | 0.889461i | ||||||||
\(313\) | 146677. | 1.49718 | 0.748590 | − | 0.663033i | \(-0.230731\pi\) | ||||
0.748590 | + | 0.663033i | \(0.230731\pi\) | |||||||
\(314\) | 14605.5i | 0.148135i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −188875. | −1.89147 | ||||||||
\(317\) | 106159.i | 1.05642i | 0.849114 | + | 0.528210i | \(0.177137\pi\) | ||||
−0.849114 | + | 0.528210i | \(0.822863\pi\) | |||||||
\(318\) | 12893.6 | 0.127502 | ||||||||
\(319\) | −27138.4 | −0.266687 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 21580.3i | − | 0.209435i | ||||||
\(322\) | −13489.5 | − | 6027.35i | −0.130102 | − | 0.0581319i | ||||
\(323\) | − | 16949.1i | − | 0.162458i | ||||||
\(324\) | −1811.70 | −0.0172583 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 175895. | 1.65508 | ||||||||
\(327\) | 90824.4 | 0.849390 | ||||||||
\(328\) | −167543. | −1.55732 | ||||||||
\(329\) | 117424. | + | 52467.0i | 1.08483 | + | 0.484724i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24297.3 | −0.221769 | −0.110885 | − | 0.993833i | \(-0.535368\pi\) | ||||
−0.110885 | + | 0.993833i | \(0.535368\pi\) | |||||||
\(332\) | 133146. | 1.20796 | ||||||||
\(333\) | − | 127262.i | − | 1.14765i | ||||||
\(334\) | − | 238618.i | − | 2.13899i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3581.83 | + | 1600.43i | 0.0317268 | + | 0.0141761i | ||||
\(337\) | − | 170981.i | − | 1.50553i | −0.658292 | − | 0.752763i | \(-0.728721\pi\) | ||
0.658292 | − | 0.752763i | \(-0.271279\pi\) | |||||||
\(338\) | 170617.i | 1.49344i | ||||||||
\(339\) | 107415.i | 0.934684i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20547.1i | 0.176702i | ||||||||
\(342\) | −14815.5 | −0.126667 | ||||||||
\(343\) | −35910.1 | − | 112035.i | −0.305231 | − | 0.952278i | ||||
\(344\) | −153103. | −1.29380 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20371.2i | 0.170163i | ||||||||
\(347\) | − | 202470.i | − | 1.68152i | −0.541406 | − | 0.840761i | \(-0.682108\pi\) | ||
0.541406 | − | 0.840761i | \(-0.317892\pi\) | |||||||
\(348\) | 37410.2 | 0.308910 | ||||||||
\(349\) | − | 90133.9i | − | 0.740009i | −0.929030 | − | 0.370005i | \(-0.879356\pi\) | ||
0.929030 | − | 0.370005i | \(-0.120644\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 170092. | 1.38061 | ||||||||
\(352\) | 102931.i | 0.830732i | ||||||||
\(353\) | 118178. | 0.948388 | 0.474194 | − | 0.880420i | \(-0.342739\pi\) | ||||
0.474194 | + | 0.880420i | \(0.342739\pi\) | |||||||
\(354\) | −30726.4 | −0.245192 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 269294.i | 2.12485i | ||||||||
\(357\) | 92803.7 | + | 41466.4i | 0.728163 | + | 0.325357i | ||||
\(358\) | 167884.i | 1.30992i | ||||||||
\(359\) | −194552. | −1.50955 | −0.754774 | − | 0.655985i | \(-0.772253\pi\) | ||||
−0.754774 | + | 0.655985i | \(0.772253\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 128281. | 0.984346 | ||||||||
\(362\) | 205588. | 1.56885 | ||||||||
\(363\) | 19496.3 | 0.147958 | ||||||||
\(364\) | 275310. | + | 123014.i | 2.07788 | + | 0.928434i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −74962.5 | −0.559605 | ||||||||
\(367\) | 105692. | 0.784710 | 0.392355 | − | 0.919814i | \(-0.371661\pi\) | ||||
0.392355 | + | 0.919814i | \(0.371661\pi\) | |||||||
\(368\) | − | 671.545i | − | 0.00495883i | ||||||
\(369\) | 126306.i | 0.927622i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7169.46 | − | 16045.6i | 0.0520881 | − | 0.116576i | ||||
\(372\) | − | 28324.1i | − | 0.204677i | ||||||
\(373\) | − | 66392.5i | − | 0.477201i | −0.971118 | − | 0.238600i | \(-0.923311\pi\) | ||
0.971118 | − | 0.238600i | \(-0.0766886\pi\) | |||||||
\(374\) | − | 257262.i | − | 1.83921i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 175617.i | 1.24220i | ||||||||
\(377\) | 60259.5 | 0.423978 | ||||||||
\(378\) | 94453.1 | − | 211390.i | 0.661047 | − | 1.47945i | ||||
\(379\) | −175353. | −1.22077 | −0.610387 | − | 0.792103i | \(-0.708986\pi\) | ||||
−0.610387 | + | 0.792103i | \(0.708986\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19202.5i | 0.132284i | ||||||||
\(382\) | − | 30742.8i | − | 0.210677i | ||||||
\(383\) | 4098.21 | 0.0279381 | 0.0139690 | − | 0.999902i | \(-0.495553\pi\) | ||||
0.0139690 | + | 0.999902i | \(0.495553\pi\) | |||||||
\(384\) | − | 150221.i | − | 1.01875i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −240306. | −1.61283 | ||||||||
\(387\) | 115420.i | 0.770654i | ||||||||
\(388\) | −16006.2 | −0.106323 | ||||||||
\(389\) | 207427. | 1.37077 | 0.685387 | − | 0.728179i | \(-0.259633\pi\) | ||||
0.685387 | + | 0.728179i | \(0.259633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 17399.4i | − | 0.113810i | ||||||
\(392\) | 119669. | − | 107177.i | 0.778770 | − | 0.697476i | ||||
\(393\) | − | 28826.0i | − | 0.186638i | ||||||
\(394\) | 20955.2 | 0.134989 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −139795. | −0.891457 | ||||||||
\(397\) | 115680. | 0.733968 | 0.366984 | − | 0.930227i | \(-0.380390\pi\) | ||||
0.366984 | + | 0.930227i | \(0.380390\pi\) | |||||||
\(398\) | 338055. | 2.13413 | ||||||||
\(399\) | 4991.13 | − | 11170.4i | 0.0313511 | − | 0.0701652i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −198641. | −1.23532 | −0.617661 | − | 0.786444i | \(-0.711920\pi\) | ||||
−0.617661 | + | 0.786444i | \(0.711920\pi\) | |||||||
\(402\) | −271711. | −1.68134 | ||||||||
\(403\) | − | 45623.8i | − | 0.280919i | ||||||
\(404\) | 393446.i | 2.41059i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 33462.5 | − | 74890.5i | 0.203005 | − | 0.454333i | ||||
\(407\) | − | 265987.i | − | 1.60572i | ||||||
\(408\) | 138796.i | 0.833790i | ||||||||
\(409\) | − | 39642.8i | − | 0.236983i | −0.992955 | − | 0.118492i | \(-0.962194\pi\) | ||
0.992955 | − | 0.118492i | \(-0.0378059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 138299.i | − | 0.818720i | ||||||
\(412\) | −495285. | −2.91783 | ||||||||
\(413\) | −17085.4 | + | 38238.0i | −0.100167 | + | 0.224179i | ||||
\(414\) | −15209.1 | −0.0887369 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 228553.i | − | 1.32069i | ||||||
\(417\) | − | 53750.8i | − | 0.309110i | ||||||
\(418\) | −30965.4 | −0.177225 | ||||||||
\(419\) | − | 157716.i | − | 0.898354i | −0.893443 | − | 0.449177i | \(-0.851717\pi\) | ||
0.893443 | − | 0.449177i | \(-0.148283\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9811.94 | 0.0553593 | 0.0276797 | − | 0.999617i | \(-0.491188\pi\) | ||||
0.0276797 | + | 0.999617i | \(0.491188\pi\) | |||||||
\(422\) | − | 102423.i | − | 0.575141i | ||||||
\(423\) | 132393. | 0.739919 | ||||||||
\(424\) | 23997.6 | 0.133486 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10161.3i | 0.0559928i | ||||||||
\(427\) | −41682.9 | + | 93288.2i | −0.228614 | + | 0.511648i | ||||
\(428\) | − | 102626.i | − | 0.560234i | ||||||
\(429\) | 136425. | 0.741276 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 223189. | 1.20149 | 0.600743 | − | 0.799442i | \(-0.294872\pi\) | ||||
0.600743 | + | 0.799442i | \(0.294872\pi\) | |||||||
\(432\) | 10523.6 | 0.0563894 | ||||||||
\(433\) | 112634. | 0.600748 | 0.300374 | − | 0.953821i | \(-0.402888\pi\) | ||||
0.300374 | + | 0.953821i | \(0.402888\pi\) | |||||||
\(434\) | −56701.2 | − | 25335.2i | −0.301032 | − | 0.134507i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 431918. | 2.27210 | ||||||||
\(437\) | −2094.29 | −0.0109667 | ||||||||
\(438\) | − | 330402.i | − | 1.72224i | ||||||
\(439\) | 73105.8i | 0.379335i | 0.981848 | + | 0.189667i | \(0.0607410\pi\) | ||||
−0.981848 | + | 0.189667i | \(0.939259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −80797.8 | − | 90215.0i | −0.415453 | − | 0.463876i | ||||
\(442\) | 571237.i | 2.92396i | ||||||||
\(443\) | − | 50089.8i | − | 0.255236i | −0.991823 | − | 0.127618i | \(-0.959267\pi\) | ||
0.991823 | − | 0.127618i | \(-0.0407331\pi\) | |||||||
\(444\) | 366662.i | 1.85994i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 77660.9i | 0.390421i | ||||||||
\(447\) | 27472.5 | 0.137494 | ||||||||
\(448\) | −294413. | − | 131549.i | −1.46690 | − | 0.655439i | ||||
\(449\) | 5042.02 | 0.0250099 | 0.0125049 | − | 0.999922i | \(-0.496019\pi\) | ||||
0.0125049 | + | 0.999922i | \(0.496019\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 263988.i | 1.29787i | ||||||||
\(452\) | 510814.i | 2.50026i | ||||||||
\(453\) | 86083.3 | 0.419491 | ||||||||
\(454\) | 519891.i | 2.52232i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16706.3 | 0.0803433 | ||||||||
\(457\) | − | 38281.4i | − | 0.183297i | −0.995791 | − | 0.0916486i | \(-0.970786\pi\) | ||
0.995791 | − | 0.0916486i | \(-0.0292136\pi\) | |||||||
\(458\) | −263287. | −1.25516 | ||||||||
\(459\) | 272662. | 1.29419 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 37749.3i | − | 0.177626i | −0.996048 | − | 0.0888132i | \(-0.971693\pi\) | ||
0.996048 | − | 0.0888132i | \(-0.0283074\pi\) | |||||||
\(462\) | 75757.7 | − | 169549.i | 0.354930 | − | 0.794349i | ||||
\(463\) | 343927.i | 1.60437i | 0.597075 | + | 0.802185i | \(0.296329\pi\) | ||||
−0.597075 | + | 0.802185i | \(0.703671\pi\) | |||||||
\(464\) | 3728.26 | 0.0173169 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −261656. | −1.20492 | ||||||||
\(467\) | −96841.6 | −0.444046 | −0.222023 | − | 0.975041i | \(-0.571266\pi\) | ||||
−0.222023 | + | 0.975041i | \(0.571266\pi\) | |||||||
\(468\) | 310408. | 1.41723 | ||||||||
\(469\) | −151085. | + | 338135.i | −0.686871 | + | 1.53725i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12415.9 | −0.0559674 | ||||||||
\(472\) | −57188.2 | −0.256698 | ||||||||
\(473\) | 241236.i | 1.07825i | ||||||||
\(474\) | − | 258279.i | − | 1.14956i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 441330. | + | 197195.i | 1.94782 | + | 0.870324i | ||||
\(477\) | − | 18091.1i | − | 0.0795112i | ||||||
\(478\) | 80285.7i | 0.351384i | ||||||||
\(479\) | 41421.1i | 0.180530i | 0.995918 | + | 0.0902652i | \(0.0287715\pi\) | ||||
−0.995918 | + | 0.0902652i | \(0.971229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 590611.i | 2.55277i | ||||||||
\(482\) | 136363. | 0.586951 | ||||||||
\(483\) | 5123.74 | − | 11467.2i | 0.0219630 | − | 0.0491543i | ||||
\(484\) | 92715.0 | 0.395785 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 385215.i | − | 1.63091i | ||||||
\(487\) | − | 29470.2i | − | 0.124258i | −0.998068 | − | 0.0621290i | \(-0.980211\pi\) | ||
0.998068 | − | 0.0621290i | \(-0.0197890\pi\) | |||||||
\(488\) | −139521. | −0.585867 | ||||||||
\(489\) | 149525.i | 0.625312i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −198756. | −0.824437 | −0.412218 | − | 0.911085i | \(-0.635246\pi\) | ||||
−0.412218 | + | 0.911085i | \(0.635246\pi\) | |||||||
\(492\) | − | 363907.i | − | 1.50335i | ||||||
\(493\) | 96597.7 | 0.397441 | ||||||||
\(494\) | 68757.3 | 0.281751 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2822.75i | − | 0.0114738i | ||||||
\(497\) | 12645.4 | + | 5650.22i | 0.0511942 | + | 0.0228745i | ||||
\(498\) | 182072.i | 0.734150i | ||||||||
\(499\) | −62009.6 | −0.249034 | −0.124517 | − | 0.992218i | \(-0.539738\pi\) | ||||
−0.124517 | + | 0.992218i | \(0.539738\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 202844. | 0.808142 | ||||||||
\(502\) | −535399. | −2.12456 | ||||||||
\(503\) | −335191. | −1.32482 | −0.662409 | − | 0.749143i | \(-0.730466\pi\) | ||||
−0.662409 | + | 0.749143i | \(0.730466\pi\) | |||||||
\(504\) | 67462.2 | − | 150984.i | 0.265583 | − | 0.594386i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −31788.2 | −0.124155 | ||||||||
\(507\) | −145038. | −0.564244 | ||||||||
\(508\) | 91317.8i | 0.353857i | ||||||||
\(509\) | − | 27607.7i | − | 0.106560i | −0.998580 | − | 0.0532800i | \(-0.983032\pi\) | ||
0.998580 | − | 0.0532800i | \(-0.0169676\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −411173. | − | 183720.i | −1.57465 | − | 0.703581i | ||||
\(512\) | − | 29645.3i | − | 0.113088i | ||||||
\(513\) | − | 32819.1i | − | 0.124707i | ||||||
\(514\) | − | 43903.2i | − | 0.166177i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 332543.i | − | 1.24896i | ||||||
\(517\) | 276710. | 1.03525 | ||||||||
\(518\) | 734011. | + | 327970.i | 2.73554 | + | 1.22229i | ||||
\(519\) | −17317.2 | −0.0642899 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 73225.7i | 0.269767i | 0.990861 | + | 0.134883i | \(0.0430660\pi\) | ||||
−0.990861 | + | 0.134883i | \(0.956934\pi\) | |||||||
\(522\) | − | 84437.7i | − | 0.309881i | ||||||
\(523\) | −208338. | −0.761668 | −0.380834 | − | 0.924643i | \(-0.624363\pi\) | ||||
−0.380834 | + | 0.924643i | \(0.624363\pi\) | |||||||
\(524\) | − | 137083.i | − | 0.499253i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 154681. | 0.559069 | ||||||||
\(527\) | − | 73136.2i | − | 0.263337i | ||||||
\(528\) | 8440.64 | 0.0302766 | ||||||||
\(529\) | 277691. | 0.992317 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 43112.6i | 0.152903i | ||||||||
\(532\) | 23735.4 | − | 53121.0i | 0.0838637 | − | 0.187691i | ||||
\(533\) | − | 586173.i | − | 2.06334i | ||||||
\(534\) | −368249. | −1.29140 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −505710. | −1.76024 | ||||||||
\(537\) | −142715. | −0.494905 | ||||||||
\(538\) | −481560. | −1.66374 | ||||||||
\(539\) | −168873. | − | 188556.i | −0.581276 | − | 0.649026i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 71741.5 | 0.245118 | 0.122559 | − | 0.992461i | \(-0.460890\pi\) | ||||
0.122559 | + | 0.992461i | \(0.460890\pi\) | |||||||
\(542\) | 399757. | 1.36081 | ||||||||
\(543\) | 174767.i | 0.592733i | ||||||||
\(544\) | − | 366377.i | − | 1.23803i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −168216. | + | 376476.i | −0.564265 | + | 1.26285i | ||||
\(547\) | 184265.i | 0.615839i | 0.951412 | + | 0.307919i | \(0.0996327\pi\) | ||||
−0.951412 | + | 0.307919i | \(0.900367\pi\) | |||||||
\(548\) | − | 657685.i | − | 2.19006i | ||||||
\(549\) | 105181.i | 0.348973i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 11627.0i | − | 0.0382971i | ||||||
\(552\) | 17150.1 | 0.0562846 | ||||||||
\(553\) | −321419. | − | 143616.i | −1.05105 | − | 0.469627i | ||||
\(554\) | 476790. | 1.55349 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 255613.i | − | 0.826864i | ||||||
\(557\) | 386198.i | 1.24480i | 0.782700 | + | 0.622399i | \(0.213842\pi\) | ||||
−0.782700 | + | 0.622399i | \(0.786158\pi\) | |||||||
\(558\) | −63929.6 | −0.205321 | ||||||||
\(559\) | − | 535653.i | − | 1.71419i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 218693. | 0.694880 | ||||||||
\(562\) | − | 413394.i | − | 1.30886i | ||||||
\(563\) | −352409. | −1.11181 | −0.555904 | − | 0.831246i | \(-0.687628\pi\) | ||||
−0.555904 | + | 0.831246i | \(0.687628\pi\) | |||||||
\(564\) | −381445. | −1.19915 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 648181.i | − | 2.02332i | ||||||
\(567\) | −3083.08 | − | 1377.58i | −0.00958999 | − | 0.00428498i | ||||
\(568\) | 18912.4i | 0.0586204i | ||||||||
\(569\) | −265786. | −0.820932 | −0.410466 | − | 0.911876i | \(-0.634634\pi\) | ||||
−0.410466 | + | 0.911876i | \(0.634634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 455939. | 1.39841 | 0.699205 | − | 0.714921i | \(-0.253537\pi\) | ||||
0.699205 | + | 0.714921i | \(0.253537\pi\) | |||||||
\(572\) | 648773. | 1.98290 | ||||||||
\(573\) | 26133.9 | 0.0795966 | ||||||||
\(574\) | −728496. | − | 325505.i | −2.21107 | − | 0.987949i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −331945. | −1.00051 | ||||||||
\(577\) | −211395. | −0.634956 | −0.317478 | − | 0.948266i | \(-0.602836\pi\) | ||||
−0.317478 | + | 0.948266i | \(0.602836\pi\) | |||||||
\(578\) | 372573.i | 1.11521i | ||||||||
\(579\) | − | 204279.i | − | 0.609351i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 226583. | + | 101241.i | 0.671234 | + | 0.299920i | ||||
\(582\) | − | 21887.9i | − | 0.0646187i | ||||||
\(583\) | − | 37811.7i | − | 0.111247i | ||||||
\(584\) | − | 614946.i | − | 1.80306i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 217141.i | − | 0.632333i | ||||||
\(587\) | 158002. | 0.458550 | 0.229275 | − | 0.973362i | \(-0.426365\pi\) | ||||
0.229275 | + | 0.973362i | \(0.426365\pi\) | |||||||
\(588\) | 232791. | + | 259923.i | 0.673304 | + | 0.751780i | ||||
\(589\) | −8803.08 | −0.0253749 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17813.6i | 0.0510009i | ||||||||
\(592\) | 36541.2i | 0.104265i | ||||||||
\(593\) | 239670. | 0.681561 | 0.340780 | − | 0.940143i | \(-0.389309\pi\) | ||||
0.340780 | + | 0.940143i | \(0.389309\pi\) | |||||||
\(594\) | − | 498144.i | − | 1.41183i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 130646. | 0.367794 | ||||||||
\(597\) | 287374.i | 0.806304i | ||||||||
\(598\) | 70584.1 | 0.197381 | ||||||||
\(599\) | −183572. | −0.511626 | −0.255813 | − | 0.966726i | \(-0.582343\pi\) | ||||
−0.255813 | + | 0.966726i | \(0.582343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14783.5i | − | 0.0409287i | −0.999791 | − | 0.0204643i | \(-0.993486\pi\) | ||
0.999791 | − | 0.0204643i | \(-0.00651446\pi\) | |||||||
\(602\) | −665710. | − | 297451.i | −1.83693 | − | 0.820773i | ||||
\(603\) | 381241.i | 1.04849i | ||||||||
\(604\) | 409371. | 1.12213 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −538022. | −1.46506 | ||||||||
\(607\) | 591265. | 1.60474 | 0.802370 | − | 0.596827i | \(-0.203572\pi\) | ||||
0.802370 | + | 0.596827i | \(0.203572\pi\) | |||||||
\(608\) | −44099.2 | −0.119295 | ||||||||
\(609\) | 63663.0 | + | 28445.8i | 0.171653 | + | 0.0766979i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −614422. | −1.64583 | ||||||||
\(612\) | 497592. | 1.32853 | ||||||||
\(613\) | 90639.8i | 0.241212i | 0.992700 | + | 0.120606i | \(0.0384837\pi\) | ||||
−0.992700 | + | 0.120606i | \(0.961516\pi\) | |||||||
\(614\) | 527273.i | 1.39862i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 141001. | − | 315566.i | 0.371586 | − | 0.831627i | ||||
\(617\) | − | 504471.i | − | 1.32515i | −0.748995 | − | 0.662576i | \(-0.769463\pi\) | ||
0.748995 | − | 0.662576i | \(-0.230537\pi\) | |||||||
\(618\) | − | 677282.i | − | 1.77334i | ||||||
\(619\) | − | 732305.i | − | 1.91122i | −0.294634 | − | 0.955610i | \(-0.595198\pi\) | ||
0.294634 | − | 0.955610i | \(-0.404802\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 33691.1i | − | 0.0873639i | ||||||
\(622\) | 382448. | 0.988535 | ||||||||
\(623\) | −204765. | + | 458273.i | −0.527569 | + | 1.18072i | ||||
\(624\) | −18742.1 | −0.0481336 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 953841.i | 2.43404i | ||||||||
\(627\) | − | 26323.1i | − | 0.0669580i | ||||||
\(628\) | −59044.0 | −0.149712 | ||||||||
\(629\) | 946766.i | 2.39299i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 537983. | 1.35117 | 0.675585 | − | 0.737282i | \(-0.263891\pi\) | ||||
0.675585 | + | 0.737282i | \(0.263891\pi\) | |||||||
\(632\) | − | 480711.i | − | 1.20351i | ||||||
\(633\) | 87068.1 | 0.217296 | ||||||||
\(634\) | −690348. | −1.71747 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 52123.3i | 0.128860i | ||||||||
\(637\) | 374974. | + | 418679.i | 0.924108 | + | 1.03182i | ||||
\(638\) | − | 176481.i | − | 0.433566i | ||||||
\(639\) | 14257.5 | 0.0349174 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 226234. | 0.550608 | 0.275304 | − | 0.961357i | \(-0.411221\pi\) | ||||
0.275304 | + | 0.961357i | \(0.411221\pi\) | |||||||
\(642\) | 140337. | 0.340488 | ||||||||
\(643\) | 186548. | 0.451199 | 0.225599 | − | 0.974220i | \(-0.427566\pi\) | ||||
0.225599 | + | 0.974220i | \(0.427566\pi\) | |||||||
\(644\) | 24366.1 | − | 54532.3i | 0.0587508 | − | 0.131487i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 110220. | 0.264116 | ||||||||
\(647\) | −580904. | −1.38770 | −0.693850 | − | 0.720120i | \(-0.744087\pi\) | ||||
−0.693850 | + | 0.720120i | \(0.744087\pi\) | |||||||
\(648\) | − | 4611.01i | − | 0.0109811i | ||||||
\(649\) | 90108.4i | 0.213932i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21536.9 | − | 48200.7i | 0.0508185 | − | 0.113734i | ||||
\(652\) | 711072.i | 1.67270i | ||||||||
\(653\) | − | 242502.i | − | 0.568707i | −0.958720 | − | 0.284354i | \(-0.908221\pi\) | ||
0.958720 | − | 0.284354i | \(-0.0917789\pi\) | |||||||
\(654\) | 590630.i | 1.38089i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 36266.6i | − | 0.0842751i | ||||||
\(657\) | −463591. | −1.07400 | ||||||||
\(658\) | −341192. | + | 763604.i | −0.788039 | + | 1.76367i | ||||
\(659\) | 377939. | 0.870265 | 0.435132 | − | 0.900367i | \(-0.356702\pi\) | ||||
0.435132 | + | 0.900367i | \(0.356702\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 377336.i | 0.863625i | 0.901963 | + | 0.431812i | \(0.142126\pi\) | ||||
−0.901963 | + | 0.431812i | \(0.857874\pi\) | |||||||
\(662\) | − | 158005.i | − | 0.360541i | ||||||
\(663\) | −485598. | −1.10471 | ||||||||
\(664\) | 338874.i | 0.768603i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 827584. | 1.86579 | ||||||||
\(667\) | − | 11936.0i | − | 0.0268291i | ||||||
\(668\) | 964632. | 2.16177 | ||||||||
\(669\) | −66018.1 | −0.147506 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 219835.i | 0.488261i | ||||||||
\(672\) | 107890. | − | 241462.i | 0.238914 | − | 0.534701i | ||||
\(673\) | − | 334342.i | − | 0.738177i | −0.929394 | − | 0.369088i | \(-0.879670\pi\) | ||
0.929394 | − | 0.369088i | \(-0.120330\pi\) | |||||||
\(674\) | 1.11189e6 | 2.44760 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −689734. | −1.50934 | ||||||||
\(677\) | −823510. | −1.79677 | −0.898383 | − | 0.439212i | \(-0.855258\pi\) | ||||
−0.898383 | + | 0.439212i | \(0.855258\pi\) | |||||||
\(678\) | −698517. | −1.51956 | ||||||||
\(679\) | −27238.7 | − | 12170.8i | −0.0590809 | − | 0.0263984i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −441949. | −0.952967 | ||||||||
\(682\) | −133617. | −0.287272 | ||||||||
\(683\) | 821787.i | 1.76164i | 0.473448 | + | 0.880822i | \(0.343009\pi\) | ||||
−0.473448 | + | 0.880822i | \(0.656991\pi\) | |||||||
\(684\) | − | 59892.9i | − | 0.128016i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 728560. | − | 233523.i | 1.54816 | − | 0.496229i | ||||
\(687\) | − | 223815.i | − | 0.474216i | ||||||
\(688\) | − | 33140.9i | − | 0.0700145i | ||||||
\(689\) | 83959.0i | 0.176860i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 744548.i | − | 1.55933i | −0.626200 | − | 0.779663i | \(-0.715391\pi\) | ||
0.626200 | − | 0.779663i | \(-0.284609\pi\) | |||||||
\(692\) | −82352.3 | −0.171974 | ||||||||
\(693\) | −237896. | − | 106297.i | −0.495361 | − | 0.221336i | ||||
\(694\) | 1.31666e6 | 2.73373 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 95213.6i | 0.196553i | ||||||||
\(697\) | − | 939652.i | − | 1.93420i | ||||||
\(698\) | 586140. | 1.20307 | ||||||||
\(699\) | − | 222428.i | − | 0.455235i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 318730. | 0.648616 | 0.324308 | − | 0.945952i | \(-0.394869\pi\) | ||||
0.324308 | + | 0.945952i | \(0.394869\pi\) | |||||||
\(702\) | 1.10611e6i | 2.24452i | ||||||||
\(703\) | 113958. | 0.230587 | ||||||||
\(704\) | −693789. | −1.39985 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 768509.i | 1.54184i | ||||||||
\(707\) | −299167. | + | 669549.i | −0.598515 | + | 1.33950i | ||||
\(708\) | − | 124214.i | − | 0.247802i | ||||||
\(709\) | −150036. | −0.298471 | −0.149235 | − | 0.988802i | \(-0.547681\pi\) | ||||
−0.149235 | + | 0.988802i | \(0.547681\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −362394. | −0.716873 | ||||||||
\(712\) | −685388. | −1.35200 | ||||||||
\(713\) | −9036.97 | −0.0177764 | ||||||||
\(714\) | −269656. | + | 603501.i | −0.528948 | + | 1.18381i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −678686. | −1.32386 | ||||||||
\(717\) | −68249.4 | −0.132758 | ||||||||
\(718\) | − | 1.26517e6i | − | 2.45414i | ||||||
\(719\) | 124427.i | 0.240690i | 0.992732 | + | 0.120345i | \(0.0384001\pi\) | ||||
−0.992732 | + | 0.120345i | \(0.961600\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −842854. | − | 376603.i | −1.62137 | − | 0.724458i | ||||
\(722\) | 834209.i | 1.60030i | ||||||||
\(723\) | 115919.i | 0.221758i | ||||||||
\(724\) | 831108.i | 1.58555i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 126784.i | 0.240542i | ||||||||
\(727\) | −534357. | −1.01103 | −0.505513 | − | 0.862819i | \(-0.668697\pi\) | ||||
−0.505513 | + | 0.862819i | \(0.668697\pi\) | |||||||
\(728\) | −313085. | + | 700700.i | −0.590745 | + | 1.32211i | ||||
\(729\) | 321882. | 0.605677 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 858667.i | − | 1.60690i | ||||||
\(732\) | − | 303042.i | − | 0.565563i | ||||||
\(733\) | 638734. | 1.18881 | 0.594404 | − | 0.804166i | \(-0.297388\pi\) | ||||
0.594404 | + | 0.804166i | \(0.297388\pi\) | |||||||
\(734\) | 687312.i | 1.27574i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −45270.9 | −0.0835725 | ||||||||
\(737\) | 796819.i | 1.46698i | ||||||||
\(738\) | −821366. | −1.50808 | ||||||||
\(739\) | −198812. | −0.364044 | −0.182022 | − | 0.983295i | \(-0.558264\pi\) | ||||
−0.182022 | + | 0.983295i | \(0.558264\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 58449.3i | 0.106449i | ||||||||
\(742\) | 104344. | + | 46623.0i | 0.189523 | + | 0.0846822i | ||||
\(743\) | − | 865398.i | − | 1.56761i | −0.621006 | − | 0.783806i | \(-0.713276\pi\) | ||
0.621006 | − | 0.783806i | \(-0.286724\pi\) | |||||||
\(744\) | 72088.3 | 0.130232 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 431750. | 0.775808 | ||||||||
\(747\) | 255468. | 0.457820 | ||||||||
\(748\) | 1.04000e6 | 1.85879 | ||||||||
\(749\) | 78034.3 | − | 174644.i | 0.139098 | − | 0.311308i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18813.0 | −0.0333564 | −0.0166782 | − | 0.999861i | \(-0.505309\pi\) | ||||
−0.0166782 | + | 0.999861i | \(0.505309\pi\) | |||||||
\(752\) | −38014.4 | −0.0672222 | ||||||||
\(753\) | − | 455132.i | − | 0.802690i | ||||||
\(754\) | 391867.i | 0.689280i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 854563. | + | 381834.i | 1.49520 | + | 0.668085i | ||||
\(757\) | − | 247909.i | − | 0.432614i | −0.976325 | − | 0.216307i | \(-0.930599\pi\) | ||
0.976325 | − | 0.216307i | \(-0.0694012\pi\) | |||||||
\(758\) | − | 1.14032e6i | − | 1.98467i | ||||||
\(759\) | − | 27022.5i | − | 0.0469075i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 882187.i | − | 1.52332i | −0.647976 | − | 0.761661i | \(-0.724384\pi\) | ||
0.647976 | − | 0.761661i | \(-0.275616\pi\) | |||||||
\(762\) | −124873. | −0.215060 | ||||||||
\(763\) | 735019. | + | 328420.i | 1.26255 | + | 0.564132i | ||||
\(764\) | 124280. | 0.212920 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26650.6i | 0.0454202i | ||||||||
\(767\) | − | 200081.i | − | 0.340107i | ||||||
\(768\) | 394805. | 0.669360 | ||||||||
\(769\) | 10006.5i | 0.0169212i | 0.999964 | + | 0.00846060i | \(0.00269312\pi\) | ||||
−0.999964 | + | 0.00846060i | \(0.997307\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37321.3 | 0.0627838 | ||||||||
\(772\) | − | 971456.i | − | 1.63000i | ||||||
\(773\) | 148529. | 0.248573 | 0.124286 | − | 0.992246i | \(-0.460336\pi\) | ||||
0.124286 | + | 0.992246i | \(0.460336\pi\) | |||||||
\(774\) | −750575. | −1.25289 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 40737.9i | − | 0.0676511i | ||||||
\(777\) | −278801. | + | 623969.i | −0.461798 | + | 1.03353i | ||||
\(778\) | 1.34889e6i | 2.22853i | ||||||||
\(779\) | −113102. | −0.186378 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29799.2 | 0.0488542 | ||||||||
\(782\) | 113148. | 0.185027 | ||||||||
\(783\) | 187045. | 0.305087 | ||||||||
\(784\) | 23199.7 | + | 25903.7i | 0.0377442 | + | 0.0421435i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 187455. | 0.303426 | ||||||||
\(787\) | 954103. | 1.54044 | 0.770222 | − | 0.637776i | \(-0.220145\pi\) | ||||
0.770222 | + | 0.637776i | \(0.220145\pi\) | |||||||
\(788\) | 84713.2i | 0.136426i | ||||||||
\(789\) | 131491.i | 0.211224i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −388411. | + | 869281.i | −0.620781 | + | 1.38934i | ||||
\(792\) | − | 355795.i | − | 0.567217i | ||||||
\(793\) | − | 488134.i | − | 0.776233i | ||||||
\(794\) | 752266.i | 1.19325i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.36662e6i | 2.15685i | ||||||||
\(797\) | 105180. | 0.165583 | 0.0827914 | − | 0.996567i | \(-0.473616\pi\) | ||||
0.0827914 | + | 0.996567i | \(0.473616\pi\) | |||||||
\(798\) | 72640.8 | + | 32457.2i | 0.114071 | + | 0.0509690i | ||||
\(799\) | −984936. | −1.54282 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 516695.i | 0.805321i | ||||||||
\(802\) | − | 1.29176e6i | − | 2.00832i | ||||||
\(803\) | −968936. | −1.50267 | ||||||||
\(804\) | − | 1.09841e6i | − | 1.69924i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 296691. | 0.456704 | ||||||||
\(807\) | − | 409365.i | − | 0.628585i | ||||||
\(808\) | −1.00137e6 | −1.53381 | ||||||||
\(809\) | −13264.8 | −0.0202677 | −0.0101338 | − | 0.999949i | \(-0.503226\pi\) | ||||
−0.0101338 | + | 0.999949i | \(0.503226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 68424.4i | 0.104033i | 0.998646 | + | 0.0520163i | \(0.0165648\pi\) | ||||
−0.998646 | + | 0.0520163i | \(0.983435\pi\) | |||||||
\(812\) | 302751. | + | 135275.i | 0.459170 | + | 0.205166i | ||||
\(813\) | 339826.i | 0.514133i | ||||||||
\(814\) | 1.72971e6 | 2.61050 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −30044.0 | −0.0451209 | ||||||||
\(817\) | −103354. | −0.154840 | ||||||||
\(818\) | 257797. | 0.385275 | ||||||||
\(819\) | 528238. | + | 236026.i | 0.787520 | + | 0.351879i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23666.0 | 0.0351107 | 0.0175553 | − | 0.999846i | \(-0.494412\pi\) | ||||
0.0175553 | + | 0.999846i | \(0.494412\pi\) | |||||||
\(822\) | 899357. | 1.33103 | ||||||||
\(823\) | − | 541429.i | − | 0.799358i | −0.916655 | − | 0.399679i | \(-0.869122\pi\) | ||
0.916655 | − | 0.399679i | \(-0.130878\pi\) | |||||||
\(824\) | − | 1.26056e6i | − | 1.85656i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −248661. | − | 111106.i | −0.364458 | − | 0.162847i | ||||
\(827\) | − | 486140.i | − | 0.710805i | −0.934713 | − | 0.355402i | \(-0.884344\pi\) | ||
0.934713 | − | 0.355402i | \(-0.115656\pi\) | |||||||
\(828\) | − | 61484.2i | − | 0.0896815i | ||||||
\(829\) | 199179.i | 0.289824i | 0.989445 | + | 0.144912i | \(0.0462900\pi\) | ||||
−0.989445 | + | 0.144912i | \(0.953710\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 405310.i | 0.586929i | ||||||||
\(832\) | 1.54053e6 | 2.22547 | ||||||||
\(833\) | 601095. | + | 671154.i | 0.866269 | + | 0.967236i | ||||
\(834\) | 349541. | 0.502535 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 125180.i | − | 0.179112i | ||||||
\(837\) | − | 141616.i | − | 0.202144i | ||||||
\(838\) | 1.02562e6 | 1.46050 | ||||||||
\(839\) | − | 1.05803e6i | − | 1.50306i | −0.659701 | − | 0.751528i | \(-0.729317\pi\) | ||
0.659701 | − | 0.751528i | \(-0.270683\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −641015. | −0.906309 | ||||||||
\(842\) | 63806.9i | 0.0900003i | ||||||||
\(843\) | 351419. | 0.494504 | ||||||||
\(844\) | 414055. | 0.581263 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 860950.i | 1.20292i | ||||||||
\(847\) | 157778. | + | 70498.3i | 0.219928 | + | 0.0982679i | ||||
\(848\) | 5194.56i | 0.00722365i | ||||||||
\(849\) | 551007. | 0.764436 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 116986. | 0.161538 | ||||||||
\(852\) | −41078.1 | −0.0565889 | ||||||||
\(853\) | 659921. | 0.906972 | 0.453486 | − | 0.891263i | \(-0.350180\pi\) | ||||
0.453486 | + | 0.891263i | \(0.350180\pi\) | |||||||
\(854\) | −606652. | − | 271064.i | −0.831810 | − | 0.371668i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 261196. | 0.356466 | ||||||||
\(857\) | 776880. | 1.05777 | 0.528886 | − | 0.848693i | \(-0.322610\pi\) | ||||
0.528886 | + | 0.848693i | \(0.322610\pi\) | |||||||
\(858\) | 887171.i | 1.20513i | ||||||||
\(859\) | − | 31227.0i | − | 0.0423198i | −0.999776 | − | 0.0211599i | \(-0.993264\pi\) | ||
0.999776 | − | 0.0211599i | \(-0.00673591\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 276706. | − | 619281.i | 0.373261 | − | 0.835375i | ||||
\(862\) | 1.45140e6i | 1.95331i | ||||||||
\(863\) | − | 197197.i | − | 0.264776i | −0.991198 | − | 0.132388i | \(-0.957736\pi\) | ||
0.991198 | − | 0.132388i | \(-0.0422645\pi\) | |||||||
\(864\) | − | 709429.i | − | 0.950345i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 732456.i | 0.976665i | ||||||||
\(867\) | −316718. | −0.421341 | ||||||||
\(868\) | 102420. | − | 229220.i | 0.135939 | − | 0.304237i | ||||
\(869\) | −757429. | −1.00300 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.76930e6i | − | 2.33220i | ||||||
\(872\) | 1.09929e6i | 1.44570i | ||||||||
\(873\) | −30711.2 | −0.0402965 | ||||||||
\(874\) | − | 13619.2i | − | 0.0178290i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.33568e6 | 1.74058 | ||||||||
\(877\) | − | 1.22846e6i | − | 1.59720i | −0.601860 | − | 0.798602i | \(-0.705573\pi\) | ||
0.601860 | − | 0.798602i | \(-0.294427\pi\) | |||||||
\(878\) | −475406. | −0.616703 | ||||||||
\(879\) | 184587. | 0.238904 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.23726e6i | − | 1.59408i | −0.603927 | − | 0.797040i | \(-0.706398\pi\) | ||
0.603927 | − | 0.797040i | \(-0.293602\pi\) | |||||||
\(882\) | 586667. | − | 525427.i | 0.754145 | − | 0.675422i | ||||
\(883\) | − | 708608.i | − | 0.908835i | −0.890789 | − | 0.454417i | \(-0.849848\pi\) | ||
0.890789 | − | 0.454417i | \(-0.150152\pi\) | |||||||
\(884\) | −2.30927e6 | −2.95509 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 325733. | 0.414949 | ||||||||
\(887\) | 48621.1 | 0.0617984 | 0.0308992 | − | 0.999523i | \(-0.490163\pi\) | ||||
0.0308992 | + | 0.999523i | \(0.490163\pi\) | |||||||
\(888\) | −933201. | −1.18345 | ||||||||
\(889\) | −69435.9 | + | 155401.i | −0.0878578 | + | 0.196630i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7265.31 | −0.00915164 | ||||||||
\(892\) | −313951. | −0.394577 | ||||||||
\(893\) | 118552.i | 0.148665i | ||||||||
\(894\) | 178653.i | 0.223530i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 543196. | − | 1.21570e6i | 0.676613 | − | 1.51429i | ||||
\(897\) | 60002.2i | 0.0745732i | ||||||||
\(898\) | 32788.2i | 0.0406597i | ||||||||
\(899\) | − | 50171.2i | − | 0.0620776i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 134589.i | 0.165790i | ||||||||
\(902\) | −1.71671e6 | −2.11001 | ||||||||
\(903\) | 252858. | − | 565907.i | 0.310099 | − | 0.694016i | ||||
\(904\) | −1.30009e6 | −1.59087 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 559799.i | 0.681986i | ||||||||
\(907\) | 1.42767e6i | 1.73546i | 0.497036 | + | 0.867730i | \(0.334422\pi\) | ||||
−0.497036 | + | 0.867730i | \(0.665578\pi\) | |||||||
\(908\) | −2.10170e6 | −2.54917 | ||||||||
\(909\) | 754905.i | 0.913617i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −583391. | −0.702947 | −0.351474 | − | 0.936198i | \(-0.614319\pi\) | ||||
−0.351474 | + | 0.936198i | \(0.614319\pi\) | |||||||
\(912\) | 3616.27i | 0.00434781i | ||||||||
\(913\) | 533945. | 0.640553 | ||||||||
\(914\) | 248944. | 0.297995 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 1.06436e6i | − | 1.26852i | ||||||
\(917\) | 104234. | − | 233281.i | 0.123957 | − | 0.277422i | ||||
\(918\) | 1.77312e6i | 2.10403i | ||||||||
\(919\) | −911636. | −1.07942 | −0.539710 | − | 0.841851i | \(-0.681466\pi\) | ||||
−0.539710 | + | 0.841851i | \(0.681466\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −448225. | −0.528417 | ||||||||
\(922\) | 245484. | 0.288776 | ||||||||
\(923\) | −66167.7 | −0.0776681 | ||||||||
\(924\) | 685416. | + | 306257.i | 0.802806 | + | 0.358709i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.23656e6 | −2.60830 | ||||||||
\(927\) | −950303. | −1.10587 | ||||||||
\(928\) | − | 251334.i | − | 0.291847i | ||||||
\(929\) | − | 1.18209e6i | − | 1.36968i | −0.728696 | − | 0.684838i | \(-0.759873\pi\) | ||
0.728696 | − | 0.684838i | \(-0.240127\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 80783.8 | − | 72351.1i | 0.0932020 | − | 0.0834729i | ||||
\(932\) | − | 1.05776e6i | − | 1.21775i | ||||||
\(933\) | 325112.i | 0.373482i | ||||||||
\(934\) | − | 629760.i | − | 0.721907i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 790026.i | 0.901757i | ||||||||
\(937\) | −648753. | −0.738925 | −0.369463 | − | 0.929246i | \(-0.620458\pi\) | ||||
−0.369463 | + | 0.929246i | \(0.620458\pi\) | |||||||
\(938\) | −2.19889e6 | − | 982503.i | −2.49918 | − | 1.11668i | ||||
\(939\) | −810842. | −0.919613 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 539679.i | 0.609475i | 0.952436 | + | 0.304738i | \(0.0985688\pi\) | ||||
−0.952436 | + | 0.304738i | \(0.901431\pi\) | |||||||
\(942\) | − | 80740.3i | − | 0.0909889i | ||||||
\(943\) | −116107. | −0.130567 | ||||||||
\(944\) | − | 12379.1i | − | 0.0138913i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.56875e6 | −1.75296 | ||||||||
\(947\) | 380310.i | 0.424071i | 0.977262 | + | 0.212035i | \(0.0680092\pi\) | ||||
−0.977262 | + | 0.212035i | \(0.931991\pi\) | |||||||
\(948\) | 1.04411e6 | 1.16180 | ||||||||
\(949\) | 2.15148e6 | 2.38894 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 586852.i | − | 0.648884i | ||||||
\(952\) | −501885. | + | 1.12324e6i | −0.553771 | + | 1.23936i | ||||
\(953\) | 1.51323e6i | 1.66617i | 0.553147 | + | 0.833084i | \(0.313427\pi\) | ||||
−0.553147 | + | 0.833084i | \(0.686573\pi\) | |||||||
\(954\) | 117646. | 0.129265 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −324562. | −0.355125 | ||||||||
\(957\) | 150023. | 0.163807 | ||||||||
\(958\) | −269361. | −0.293497 | ||||||||
\(959\) | 500088. | − | 1.11922e6i | 0.543762 | − | 1.21696i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 885535. | 0.958869 | ||||||||
\(962\) | −3.84074e6 | −4.15016 | ||||||||
\(963\) | − | 196908.i | − | 0.212330i | ||||||
\(964\) | 551258.i | 0.593199i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 74570.8 | + | 33319.6i | 0.0799125 | + | 0.0357064i | ||||
\(967\) | − | 393218.i | − | 0.420514i | −0.977646 | − | 0.210257i | \(-0.932570\pi\) | ||
0.977646 | − | 0.210257i | \(-0.0674300\pi\) | |||||||
\(968\) | 235971.i | 0.251831i | ||||||||
\(969\) | 93695.8i | 0.0997867i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 957332.i | − | 1.01537i | −0.861543 | − | 0.507685i | \(-0.830502\pi\) | ||
0.861543 | − | 0.507685i | \(-0.169498\pi\) | |||||||
\(972\) | 1.55726e6 | 1.64827 | ||||||||
\(973\) | 194362. | − | 434992.i | 0.205299 | − | 0.459468i | ||||
\(974\) | 191644. | 0.202012 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 30200.9i | − | 0.0317044i | ||||||
\(977\) | 1.33928e6i | 1.40308i | 0.712631 | + | 0.701539i | \(0.247503\pi\) | ||||
−0.712631 | + | 0.701539i | \(0.752497\pi\) | |||||||
\(978\) | −972362. | −1.01660 | ||||||||
\(979\) | 1.07993e6i | 1.12675i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 828721. | 0.861133 | ||||||||
\(982\) | − | 1.29251e6i | − | 1.34033i | ||||||
\(983\) | −1.72782e6 | −1.78810 | −0.894050 | − | 0.447968i | \(-0.852148\pi\) | ||||
−0.894050 | + | 0.447968i | \(0.852148\pi\) | |||||||
\(984\) | 926188. | 0.956553 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 628174.i | 0.646139i | ||||||||
\(987\) | −649126. | − | 290041.i | −0.666338 | − | 0.297732i | ||||
\(988\) | 277957.i | 0.284750i | ||||||||
\(989\) | −106100. | −0.108473 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 946703. | 0.963977 | 0.481988 | − | 0.876178i | \(-0.339915\pi\) | ||||
0.481988 | + | 0.876178i | \(0.339915\pi\) | |||||||
\(992\) | −190290. | −0.193372 | ||||||||
\(993\) | 134317. | 0.136217 | ||||||||
\(994\) | −36743.3 | + | 82233.2i | −0.0371882 | + | 0.0832289i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −736042. | −0.741966 | ||||||||
\(997\) | 552328. | 0.555657 | 0.277829 | − | 0.960631i | \(-0.410385\pi\) | ||||
0.277829 | + | 0.960631i | \(0.410385\pi\) | |||||||
\(998\) | − | 403248.i | − | 0.404866i | ||||||
\(999\) | 1.83325e6i | 1.83693i |
(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 | 175.5.c.d.174.18 | 24 | ||
5.2 | odd | 4 | 175.5.d.i.76.2 | 12 | |||
5.3 | odd | 4 | 35.5.d.a.6.11 | ✓ | 12 | ||
5.4 | even | 2 | inner | 175.5.c.d.174.7 | 24 | ||
7.6 | odd | 2 | inner | 175.5.c.d.174.8 | 24 | ||
15.8 | even | 4 | 315.5.h.a.181.2 | 12 | |||
20.3 | even | 4 | 560.5.f.b.321.8 | 12 | |||
35.13 | even | 4 | 35.5.d.a.6.12 | yes | 12 | ||
35.27 | even | 4 | 175.5.d.i.76.1 | 12 | |||
35.34 | odd | 2 | inner | 175.5.c.d.174.17 | 24 | ||
105.83 | odd | 4 | 315.5.h.a.181.1 | 12 | |||
140.83 | odd | 4 | 560.5.f.b.321.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.d.a.6.11 | ✓ | 12 | 5.3 | odd | 4 | ||
35.5.d.a.6.12 | yes | 12 | 35.13 | even | 4 | ||
175.5.c.d.174.7 | 24 | 5.4 | even | 2 | inner | ||
175.5.c.d.174.8 | 24 | 7.6 | odd | 2 | inner | ||
175.5.c.d.174.17 | 24 | 35.34 | odd | 2 | inner | ||
175.5.c.d.174.18 | 24 | 1.1 | even | 1 | trivial | ||
175.5.d.i.76.1 | 12 | 35.27 | even | 4 | |||
175.5.d.i.76.2 | 12 | 5.2 | odd | 4 | |||
315.5.h.a.181.1 | 12 | 105.83 | odd | 4 | |||
315.5.h.a.181.2 | 12 | 15.8 | even | 4 | |||
560.5.f.b.321.5 | 12 | 140.83 | odd | 4 | |||
560.5.f.b.321.8 | 12 | 20.3 | even | 4 |