Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,5,Mod(14,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, 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("15.14");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.d (of order \(2\), degree \(1\), 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: | \(1.55054944626\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{10}, \sqrt{-26})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 8x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 14.2 | ||
Root | \(-1.58114 + 2.54951i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.14 |
Dual form | 15.5.d.c.14.1 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.16228 | −0.790569 | −0.395285 | − | 0.918559i | \(-0.629354\pi\) | ||||
−0.395285 | + | 0.918559i | \(0.629354\pi\) | |||||||
\(3\) | −4.74342 | + | 7.64853i | −0.527046 | + | 0.849837i | ||||
\(4\) | −6.00000 | −0.375000 | ||||||||
\(5\) | −6.32456 | + | 24.1868i | −0.252982 | + | 0.967471i | ||||
\(6\) | 15.0000 | − | 24.1868i | 0.416667 | − | 0.671855i | ||||
\(7\) | − | 15.2971i | − | 0.312185i | −0.987742 | − | 0.156092i | \(-0.950110\pi\) | ||
0.987742 | − | 0.156092i | \(-0.0498898\pi\) | |||||||
\(8\) | 69.5701 | 1.08703 | ||||||||
\(9\) | −36.0000 | − | 72.5603i | −0.444444 | − | 0.895806i | ||||
\(10\) | 20.0000 | − | 76.4853i | 0.200000 | − | 0.764853i | ||||
\(11\) | 96.7471i | 0.799563i | 0.916611 | + | 0.399781i | \(0.130914\pi\) | ||||
−0.916611 | + | 0.399781i | \(0.869086\pi\) | |||||||
\(12\) | 28.4605 | − | 45.8912i | 0.197642 | − | 0.318689i | ||||
\(13\) | 244.753i | 1.44824i | 0.689673 | + | 0.724121i | \(0.257754\pi\) | ||||
−0.689673 | + | 0.724121i | \(0.742246\pi\) | |||||||
\(14\) | 48.3735i | 0.246804i | ||||||||
\(15\) | −154.993 | − | 163.101i | −0.688859 | − | 0.724895i | ||||
\(16\) | −124.000 | −0.484375 | ||||||||
\(17\) | −278.280 | −0.962908 | −0.481454 | − | 0.876471i | \(-0.659891\pi\) | ||||
−0.481454 | + | 0.876471i | \(0.659891\pi\) | |||||||
\(18\) | 113.842 | + | 229.456i | 0.351364 | + | 0.708197i | ||||
\(19\) | 308.000 | 0.853186 | 0.426593 | − | 0.904444i | \(-0.359714\pi\) | ||||
0.426593 | + | 0.904444i | \(0.359714\pi\) | |||||||
\(20\) | 37.9473 | − | 145.121i | 0.0948683 | − | 0.362802i | ||||
\(21\) | 117.000 | + | 72.5603i | 0.265306 | + | 0.164536i | ||||
\(22\) | − | 305.941i | − | 0.632110i | ||||||
\(23\) | 414.258 | 0.783097 | 0.391549 | − | 0.920157i | \(-0.371940\pi\) | ||||
0.391549 | + | 0.920157i | \(0.371940\pi\) | |||||||
\(24\) | −330.000 | + | 532.109i | −0.572917 | + | 0.923800i | ||||
\(25\) | −545.000 | − | 305.941i | −0.872000 | − | 0.489506i | ||||
\(26\) | − | 773.977i | − | 1.14494i | ||||||
\(27\) | 725.743 | + | 68.8368i | 0.995532 | + | 0.0944263i | ||||
\(28\) | 91.7824i | 0.117069i | ||||||||
\(29\) | − | 193.494i | − | 0.230076i | −0.993361 | − | 0.115038i | \(-0.963301\pi\) | ||
0.993361 | − | 0.115038i | \(-0.0366990\pi\) | |||||||
\(30\) | 490.132 | + | 515.772i | 0.544591 | + | 0.573080i | ||||
\(31\) | 32.0000 | 0.0332986 | 0.0166493 | − | 0.999861i | \(-0.494700\pi\) | ||||
0.0166493 | + | 0.999861i | \(0.494700\pi\) | |||||||
\(32\) | −720.999 | −0.704101 | ||||||||
\(33\) | −739.973 | − | 458.912i | −0.679498 | − | 0.421407i | ||||
\(34\) | 880.000 | 0.761246 | ||||||||
\(35\) | 369.986 | + | 96.7471i | 0.302030 | + | 0.0789772i | ||||
\(36\) | 216.000 | + | 435.362i | 0.166667 | + | 0.335927i | ||||
\(37\) | 1284.95i | 0.938607i | 0.883037 | + | 0.469303i | \(0.155495\pi\) | ||||
−0.883037 | + | 0.469303i | \(0.844505\pi\) | |||||||
\(38\) | −973.982 | −0.674502 | ||||||||
\(39\) | −1872.00 | − | 1160.97i | −1.23077 | − | 0.763291i | ||||
\(40\) | −440.000 | + | 1682.68i | −0.275000 | + | 1.05167i | ||||
\(41\) | 2080.06i | 1.23740i | 0.785629 | + | 0.618698i | \(0.212340\pi\) | ||||
−0.785629 | + | 0.618698i | \(0.787660\pi\) | |||||||
\(42\) | −369.986 | − | 229.456i | −0.209743 | − | 0.130077i | ||||
\(43\) | − | 2585.20i | − | 1.39816i | −0.715042 | − | 0.699081i | \(-0.753593\pi\) | ||
0.715042 | − | 0.699081i | \(-0.246407\pi\) | |||||||
\(44\) | − | 580.483i | − | 0.299836i | ||||||
\(45\) | 1982.68 | − | 411.812i | 0.979103 | − | 0.203364i | ||||
\(46\) | −1310.00 | −0.619093 | ||||||||
\(47\) | 2444.44 | 1.10658 | 0.553291 | − | 0.832988i | \(-0.313372\pi\) | ||||
0.553291 | + | 0.832988i | \(0.313372\pi\) | |||||||
\(48\) | 588.184 | − | 948.418i | 0.255288 | − | 0.411640i | ||||
\(49\) | 2167.00 | 0.902541 | ||||||||
\(50\) | 1723.44 | + | 967.471i | 0.689377 | + | 0.386988i | ||||
\(51\) | 1320.00 | − | 2128.44i | 0.507497 | − | 0.818315i | ||||
\(52\) | − | 1468.52i | − | 0.543091i | ||||||
\(53\) | −1416.70 | −0.504343 | −0.252172 | − | 0.967683i | \(-0.581145\pi\) | ||||
−0.252172 | + | 0.967683i | \(0.581145\pi\) | |||||||
\(54\) | −2295.00 | − | 217.681i | −0.787037 | − | 0.0746505i | ||||
\(55\) | −2340.00 | − | 611.882i | −0.773554 | − | 0.202275i | ||||
\(56\) | − | 1064.22i | − | 0.339355i | ||||||
\(57\) | −1460.97 | + | 2355.75i | −0.449668 | + | 0.725068i | ||||
\(58\) | 611.882i | 0.181891i | ||||||||
\(59\) | 3966.63i | 1.13951i | 0.821815 | + | 0.569754i | \(0.192962\pi\) | ||||
−0.821815 | + | 0.569754i | \(0.807038\pi\) | |||||||
\(60\) | 929.959 | + | 978.609i | 0.258322 | + | 0.271836i | ||||
\(61\) | −928.000 | −0.249395 | −0.124698 | − | 0.992195i | \(-0.539796\pi\) | ||||
−0.124698 | + | 0.992195i | \(0.539796\pi\) | |||||||
\(62\) | −101.193 | −0.0263249 | ||||||||
\(63\) | −1109.96 | + | 550.694i | −0.279657 | + | 0.138749i | ||||
\(64\) | 4264.00 | 1.04102 | ||||||||
\(65\) | −5919.78 | − | 1547.95i | −1.40113 | − | 0.366380i | ||||
\(66\) | 2340.00 | + | 1451.21i | 0.537190 | + | 0.333151i | ||||
\(67\) | 2585.20i | 0.575897i | 0.957646 | + | 0.287949i | \(0.0929732\pi\) | ||||
−0.957646 | + | 0.287949i | \(0.907027\pi\) | |||||||
\(68\) | 1669.68 | 0.361091 | ||||||||
\(69\) | −1965.00 | + | 3168.47i | −0.412728 | + | 0.665505i | ||||
\(70\) | −1170.00 | − | 305.941i | −0.238776 | − | 0.0624370i | ||||
\(71\) | − | 4643.86i | − | 0.921218i | −0.887603 | − | 0.460609i | \(-0.847631\pi\) | ||
0.887603 | − | 0.460609i | \(-0.152369\pi\) | |||||||
\(72\) | −2504.52 | − | 5048.03i | −0.483126 | − | 0.973771i | ||||
\(73\) | 4221.99i | 0.792266i | 0.918193 | + | 0.396133i | \(0.129648\pi\) | ||||
−0.918193 | + | 0.396133i | \(0.870352\pi\) | |||||||
\(74\) | − | 4063.38i | − | 0.742034i | ||||||
\(75\) | 4925.16 | − | 2717.24i | 0.875584 | − | 0.483065i | ||||
\(76\) | −1848.00 | −0.319945 | ||||||||
\(77\) | 1479.95 | 0.249611 | ||||||||
\(78\) | 5919.78 | + | 3671.29i | 0.973009 | + | 0.603434i | ||||
\(79\) | 8.00000 | 0.00128185 | 0.000640923 | − | 1.00000i | \(-0.499796\pi\) | ||||
0.000640923 | 1.00000i | \(0.499796\pi\) | ||||||||
\(80\) | 784.245 | − | 2999.16i | 0.122538 | − | 0.468619i | ||||
\(81\) | −3969.00 | + | 5224.34i | −0.604938 | + | 0.796272i | ||||
\(82\) | − | 6577.74i | − | 0.978247i | ||||||
\(83\) | 4436.68 | 0.644023 | 0.322012 | − | 0.946736i | \(-0.395641\pi\) | ||||
0.322012 | + | 0.946736i | \(0.395641\pi\) | |||||||
\(84\) | −702.000 | − | 435.362i | −0.0994898 | − | 0.0617010i | ||||
\(85\) | 1760.00 | − | 6730.71i | 0.243599 | − | 0.931586i | ||||
\(86\) | 8175.13i | 1.10534i | ||||||||
\(87\) | 1479.95 | + | 917.824i | 0.195527 | + | 0.121261i | ||||
\(88\) | 6730.71i | 0.869151i | ||||||||
\(89\) | − | 9287.72i | − | 1.17254i | −0.810114 | − | 0.586272i | \(-0.800595\pi\) | ||
0.810114 | − | 0.586272i | \(-0.199405\pi\) | |||||||
\(90\) | −6269.80 | + | 1302.26i | −0.774049 | + | 0.160773i | ||||
\(91\) | 3744.00 | 0.452119 | ||||||||
\(92\) | −2485.55 | −0.293661 | ||||||||
\(93\) | −151.789 | + | 244.753i | −0.0175499 | + | 0.0282984i | ||||
\(94\) | −7730.00 | −0.874830 | ||||||||
\(95\) | −1947.96 | + | 7449.53i | −0.215841 | + | 0.825432i | ||||
\(96\) | 3420.00 | − | 5514.58i | 0.371094 | − | 0.598371i | ||||
\(97\) | 2508.72i | 0.266630i | 0.991074 | + | 0.133315i | \(0.0425621\pi\) | ||||
−0.991074 | + | 0.133315i | \(0.957438\pi\) | |||||||
\(98\) | −6852.66 | −0.713521 | ||||||||
\(99\) | 7020.00 | − | 3482.90i | 0.716253 | − | 0.355361i | ||||
\(100\) | 3270.00 | + | 1835.65i | 0.327000 | + | 0.183565i | ||||
\(101\) | − | 4837.35i | − | 0.474204i | −0.971485 | − | 0.237102i | \(-0.923802\pi\) | ||
0.971485 | − | 0.237102i | \(-0.0761976\pi\) | |||||||
\(102\) | −4174.21 | + | 6730.71i | −0.401212 | + | 0.646934i | ||||
\(103\) | − | 5491.64i | − | 0.517640i | −0.965926 | − | 0.258820i | \(-0.916666\pi\) | ||
0.965926 | − | 0.258820i | \(-0.0833337\pi\) | |||||||
\(104\) | 17027.5i | 1.57429i | ||||||||
\(105\) | −2494.97 | + | 2370.94i | −0.226301 | + | 0.215051i | ||||
\(106\) | 4480.00 | 0.398718 | ||||||||
\(107\) | −2925.11 | −0.255490 | −0.127745 | − | 0.991807i | \(-0.540774\pi\) | ||||
−0.127745 | + | 0.991807i | \(0.540774\pi\) | |||||||
\(108\) | −4354.46 | − | 413.021i | −0.373324 | − | 0.0354099i | ||||
\(109\) | −6352.00 | −0.534635 | −0.267318 | − | 0.963608i | \(-0.586137\pi\) | ||||
−0.267318 | + | 0.963608i | \(0.586137\pi\) | |||||||
\(110\) | 7399.73 | + | 1934.94i | 0.611548 | + | 0.159913i | ||||
\(111\) | −9828.00 | − | 6095.07i | −0.797663 | − | 0.494689i | ||||
\(112\) | 1896.84i | 0.151215i | ||||||||
\(113\) | 8867.03 | 0.694418 | 0.347209 | − | 0.937788i | \(-0.387129\pi\) | ||||
0.347209 | + | 0.937788i | \(0.387129\pi\) | |||||||
\(114\) | 4620.00 | − | 7449.53i | 0.355494 | − | 0.573217i | ||||
\(115\) | −2620.00 | + | 10019.6i | −0.198110 | + | 0.757624i | ||||
\(116\) | 1160.97i | 0.0862786i | ||||||||
\(117\) | 17759.4 | − | 8811.11i | 1.29734 | − | 0.643663i | ||||
\(118\) | − | 12543.6i | − | 0.900861i | ||||||
\(119\) | 4256.87i | 0.300605i | ||||||||
\(120\) | −10782.9 | − | 11347.0i | −0.748812 | − | 0.787985i | ||||
\(121\) | 5281.00 | 0.360699 | ||||||||
\(122\) | 2934.59 | 0.197164 | ||||||||
\(123\) | −15909.4 | − | 9866.60i | −1.05158 | − | 0.652165i | ||||
\(124\) | −192.000 | −0.0124870 | ||||||||
\(125\) | 10846.6 | − | 11246.8i | 0.694183 | − | 0.719798i | ||||
\(126\) | 3510.00 | − | 1741.45i | 0.221088 | − | 0.109691i | ||||
\(127\) | 3808.97i | 0.236156i | 0.993004 | + | 0.118078i | \(0.0376734\pi\) | ||||
−0.993004 | + | 0.118078i | \(0.962327\pi\) | |||||||
\(128\) | −1947.96 | −0.118894 | ||||||||
\(129\) | 19773.0 | + | 12262.7i | 1.18821 | + | 0.736896i | ||||
\(130\) | 18720.0 | + | 4895.06i | 1.10769 | + | 0.289648i | ||||
\(131\) | 8030.01i | 0.467922i | 0.972246 | + | 0.233961i | \(0.0751688\pi\) | ||||
−0.972246 | + | 0.233961i | \(0.924831\pi\) | |||||||
\(132\) | 4439.84 | + | 2753.47i | 0.254812 | + | 0.158027i | ||||
\(133\) | − | 4711.49i | − | 0.266352i | ||||||
\(134\) | − | 8175.13i | − | 0.455287i | ||||||
\(135\) | −6254.94 | + | 17118.0i | −0.343207 | + | 0.939260i | ||||
\(136\) | −19360.0 | −1.04671 | ||||||||
\(137\) | −21263.2 | −1.13289 | −0.566443 | − | 0.824101i | \(-0.691681\pi\) | ||||
−0.566443 | + | 0.824101i | \(0.691681\pi\) | |||||||
\(138\) | 6213.88 | − | 10019.6i | 0.326290 | − | 0.526128i | ||||
\(139\) | −19372.0 | −1.00264 | −0.501320 | − | 0.865262i | \(-0.667152\pi\) | ||||
−0.501320 | + | 0.865262i | \(0.667152\pi\) | |||||||
\(140\) | −2219.92 | − | 580.483i | −0.113261 | − | 0.0296165i | ||||
\(141\) | −11595.0 | + | 18696.4i | −0.583220 | + | 0.940414i | ||||
\(142\) | 14685.2i | 0.728287i | ||||||||
\(143\) | −23679.1 | −1.15796 | ||||||||
\(144\) | 4464.00 | + | 8997.48i | 0.215278 | + | 0.433906i | ||||
\(145\) | 4680.00 | + | 1223.76i | 0.222592 | + | 0.0582052i | ||||
\(146\) | − | 13351.1i | − | 0.626342i | ||||||
\(147\) | −10279.0 | + | 16574.4i | −0.475681 | + | 0.767012i | ||||
\(148\) | − | 7709.72i | − | 0.351978i | ||||||
\(149\) | − | 16205.1i | − | 0.729928i | −0.931022 | − | 0.364964i | \(-0.881081\pi\) | ||
0.931022 | − | 0.364964i | \(-0.118919\pi\) | |||||||
\(150\) | −15574.7 | + | 8592.67i | −0.692210 | + | 0.381897i | ||||
\(151\) | 33272.0 | 1.45923 | 0.729617 | − | 0.683856i | \(-0.239698\pi\) | ||||
0.729617 | + | 0.683856i | \(0.239698\pi\) | |||||||
\(152\) | 21427.6 | 0.927441 | ||||||||
\(153\) | 10018.1 | + | 20192.1i | 0.427959 | + | 0.862579i | ||||
\(154\) | −4680.00 | −0.197335 | ||||||||
\(155\) | −202.386 | + | 773.977i | −0.00842397 | + | 0.0322155i | ||||
\(156\) | 11232.0 | + | 6965.79i | 0.461538 | + | 0.286234i | ||||
\(157\) | − | 29309.2i | − | 1.18906i | −0.804073 | − | 0.594530i | \(-0.797338\pi\) | ||
0.804073 | − | 0.594530i | \(-0.202662\pi\) | |||||||
\(158\) | −25.2982 | −0.00101339 | ||||||||
\(159\) | 6720.00 | − | 10835.7i | 0.265812 | − | 0.428609i | ||||
\(160\) | 4560.00 | − | 17438.6i | 0.178125 | − | 0.681197i | ||||
\(161\) | − | 6336.93i | − | 0.244471i | ||||||
\(162\) | 12551.1 | − | 16520.8i | 0.478246 | − | 0.629509i | ||||
\(163\) | 12252.9i | 0.461174i | 0.973052 | + | 0.230587i | \(0.0740647\pi\) | ||||
−0.973052 | + | 0.230587i | \(0.925935\pi\) | |||||||
\(164\) | − | 12480.4i | − | 0.464023i | ||||||
\(165\) | 15779.6 | − | 14995.1i | 0.579599 | − | 0.550786i | ||||
\(166\) | −14030.0 | −0.509145 | ||||||||
\(167\) | 2520.34 | 0.0903702 | 0.0451851 | − | 0.998979i | \(-0.485612\pi\) | ||||
0.0451851 | + | 0.998979i | \(0.485612\pi\) | |||||||
\(168\) | 8139.70 | + | 5048.03i | 0.288396 | + | 0.178856i | ||||
\(169\) | −31343.0 | −1.09741 | ||||||||
\(170\) | −5565.61 | + | 21284.4i | −0.192582 | + | 0.736483i | ||||
\(171\) | −11088.0 | − | 22348.6i | −0.379194 | − | 0.764289i | ||||
\(172\) | 15511.2i | 0.524311i | ||||||||
\(173\) | 49318.9 | 1.64786 | 0.823931 | − | 0.566690i | \(-0.191776\pi\) | ||||
0.823931 | + | 0.566690i | \(0.191776\pi\) | |||||||
\(174\) | −4680.00 | − | 2902.41i | −0.154578 | − | 0.0958651i | ||||
\(175\) | −4680.00 | + | 8336.90i | −0.152816 | + | 0.272225i | ||||
\(176\) | − | 11996.6i | − | 0.387288i | ||||||
\(177\) | −30338.9 | − | 18815.4i | −0.968396 | − | 0.600574i | ||||
\(178\) | 29370.4i | 0.926977i | ||||||||
\(179\) | 38021.6i | 1.18665i | 0.804961 | + | 0.593327i | \(0.202186\pi\) | ||||
−0.804961 | + | 0.593327i | \(0.797814\pi\) | |||||||
\(180\) | −11896.1 | + | 2470.87i | −0.367164 | + | 0.0762615i | ||||
\(181\) | 20342.0 | 0.620921 | 0.310461 | − | 0.950586i | \(-0.399517\pi\) | ||||
0.310461 | + | 0.950586i | \(0.399517\pi\) | |||||||
\(182\) | −11839.6 | −0.357432 | ||||||||
\(183\) | 4401.89 | − | 7097.84i | 0.131443 | − | 0.211945i | ||||
\(184\) | 28820.0 | 0.851252 | ||||||||
\(185\) | −31078.9 | − | 8126.76i | −0.908075 | − | 0.237451i | ||||
\(186\) | 480.000 | − | 773.977i | 0.0138744 | − | 0.0223719i | ||||
\(187\) | − | 26922.8i | − | 0.769905i | ||||||
\(188\) | −14666.6 | −0.414968 | ||||||||
\(189\) | 1053.00 | − | 11101.7i | 0.0294785 | − | 0.310790i | ||||
\(190\) | 6160.00 | − | 23557.5i | 0.170637 | − | 0.652562i | ||||
\(191\) | 55532.8i | 1.52224i | 0.648611 | + | 0.761120i | \(0.275350\pi\) | ||||
−0.648611 | + | 0.761120i | \(0.724650\pi\) | |||||||
\(192\) | −20225.9 | + | 32613.3i | −0.548663 | + | 0.884693i | ||||
\(193\) | 50725.0i | 1.36178i | 0.732384 | + | 0.680891i | \(0.238407\pi\) | ||||
−0.732384 | + | 0.680891i | \(0.761593\pi\) | |||||||
\(194\) | − | 7933.26i | − | 0.210789i | ||||||
\(195\) | 39919.6 | − | 37935.1i | 1.04982 | − | 0.997634i | ||||
\(196\) | −13002.0 | −0.338453 | ||||||||
\(197\) | 28865.3 | 0.743778 | 0.371889 | − | 0.928277i | \(-0.378710\pi\) | ||||
0.371889 | + | 0.928277i | \(0.378710\pi\) | |||||||
\(198\) | −22199.2 | + | 11013.9i | −0.566248 | + | 0.280938i | ||||
\(199\) | 34328.0 | 0.866847 | 0.433423 | − | 0.901190i | \(-0.357305\pi\) | ||||
0.433423 | + | 0.901190i | \(0.357305\pi\) | |||||||
\(200\) | −37915.7 | − | 21284.4i | −0.947893 | − | 0.532109i | ||||
\(201\) | −19773.0 | − | 12262.7i | −0.489419 | − | 0.303525i | ||||
\(202\) | 15297.1i | 0.374891i | ||||||||
\(203\) | −2959.89 | −0.0718263 | ||||||||
\(204\) | −7920.00 | + | 12770.6i | −0.190311 | + | 0.306868i | ||||
\(205\) | −50310.0 | − | 13155.5i | −1.19714 | − | 0.313039i | ||||
\(206\) | 17366.1i | 0.409230i | ||||||||
\(207\) | −14913.3 | − | 30058.7i | −0.348043 | − | 0.701503i | ||||
\(208\) | − | 30349.4i | − | 0.701492i | ||||||
\(209\) | 29798.1i | 0.682175i | ||||||||
\(210\) | 7889.80 | − | 7497.57i | 0.178907 | − | 0.170013i | ||||
\(211\) | −33268.0 | −0.747243 | −0.373621 | − | 0.927581i | \(-0.621884\pi\) | ||||
−0.373621 | + | 0.927581i | \(0.621884\pi\) | |||||||
\(212\) | 8500.20 | 0.189129 | ||||||||
\(213\) | 35518.7 | + | 22027.8i | 0.782885 | + | 0.485525i | ||||
\(214\) | 9250.00 | 0.201983 | ||||||||
\(215\) | 62527.7 | + | 16350.3i | 1.35268 | + | 0.353710i | ||||
\(216\) | 50490.0 | + | 4788.98i | 1.08218 | + | 0.102644i | ||||
\(217\) | − | 489.506i | − | 0.0103953i | ||||||
\(218\) | 20086.8 | 0.422666 | ||||||||
\(219\) | −32292.0 | − | 20026.6i | −0.673297 | − | 0.417561i | ||||
\(220\) | 14040.0 | + | 3671.29i | 0.290083 | + | 0.0758532i | ||||
\(221\) | − | 68110.0i | − | 1.39452i | ||||||
\(222\) | 31078.9 | + | 19274.3i | 0.630608 | + | 0.391086i | ||||
\(223\) | − | 76011.1i | − | 1.52851i | −0.644916 | − | 0.764253i | \(-0.723108\pi\) | ||
0.644916 | − | 0.764253i | \(-0.276892\pi\) | |||||||
\(224\) | 11029.2i | 0.219810i | ||||||||
\(225\) | −2579.19 | + | 50559.3i | −0.0509469 | + | 0.998701i | ||||
\(226\) | −28040.0 | −0.548986 | ||||||||
\(227\) | 16788.5 | 0.325807 | 0.162904 | − | 0.986642i | \(-0.447914\pi\) | ||||
0.162904 | + | 0.986642i | \(0.447914\pi\) | |||||||
\(228\) | 8765.83 | − | 14134.5i | 0.168626 | − | 0.271901i | ||||
\(229\) | 40298.0 | 0.768445 | 0.384222 | − | 0.923241i | \(-0.374470\pi\) | ||||
0.384222 | + | 0.923241i | \(0.374470\pi\) | |||||||
\(230\) | 8285.17 | − | 31684.7i | 0.156619 | − | 0.598954i | ||||
\(231\) | −7020.00 | + | 11319.4i | −0.131557 | + | 0.212129i | ||||
\(232\) | − | 13461.4i | − | 0.250101i | ||||||
\(233\) | −87253.6 | −1.60721 | −0.803603 | − | 0.595166i | \(-0.797086\pi\) | ||||
−0.803603 | + | 0.595166i | \(0.797086\pi\) | |||||||
\(234\) | −56160.0 | + | 27863.2i | −1.02564 | + | 0.508860i | ||||
\(235\) | −15460.0 | + | 59123.1i | −0.279946 | + | 1.07059i | ||||
\(236\) | − | 23799.8i | − | 0.427316i | ||||||
\(237\) | −37.9473 | + | 61.1882i | −0.000675592 | + | 0.00108936i | ||||
\(238\) | − | 13461.4i | − | 0.237649i | ||||||
\(239\) | − | 88620.3i | − | 1.55145i | −0.631072 | − | 0.775725i | \(-0.717385\pi\) | ||
0.631072 | − | 0.775725i | \(-0.282615\pi\) | |||||||
\(240\) | 19219.2 | + | 20224.6i | 0.333666 | + | 0.351121i | ||||
\(241\) | 72152.0 | 1.24227 | 0.621133 | − | 0.783706i | \(-0.286673\pi\) | ||||
0.621133 | + | 0.783706i | \(0.286673\pi\) | |||||||
\(242\) | −16700.0 | −0.285158 | ||||||||
\(243\) | −21131.9 | − | 55138.2i | −0.357871 | − | 0.933771i | ||||
\(244\) | 5568.00 | 0.0935232 | ||||||||
\(245\) | −13705.3 | + | 52412.7i | −0.228327 | + | 0.873182i | ||||
\(246\) | 50310.0 | + | 31200.9i | 0.831350 | + | 0.515582i | ||||
\(247\) | 75383.9i | 1.23562i | ||||||||
\(248\) | 2226.24 | 0.0361967 | ||||||||
\(249\) | −21045.0 | + | 33934.0i | −0.339430 | + | 0.547314i | ||||
\(250\) | −34300.0 | + | 35565.7i | −0.548800 | + | 0.569051i | ||||
\(251\) | 15963.3i | 0.253381i | 0.991942 | + | 0.126691i | \(0.0404355\pi\) | ||||
−0.991942 | + | 0.126691i | \(0.959564\pi\) | |||||||
\(252\) | 6659.76 | − | 3304.16i | 0.104871 | − | 0.0520308i | ||||
\(253\) | 40078.3i | 0.626135i | ||||||||
\(254\) | − | 12045.0i | − | 0.186698i | ||||||
\(255\) | 43131.6 | + | 45388.0i | 0.663308 | + | 0.698008i | ||||
\(256\) | −62064.0 | −0.947021 | ||||||||
\(257\) | −84938.8 | −1.28600 | −0.642998 | − | 0.765868i | \(-0.722310\pi\) | ||||
−0.642998 | + | 0.765868i | \(0.722310\pi\) | |||||||
\(258\) | −62527.7 | − | 38778.0i | −0.939362 | − | 0.582568i | ||||
\(259\) | 19656.0 | 0.293019 | ||||||||
\(260\) | 35518.7 | + | 9287.72i | 0.525425 | + | 0.137392i | ||||
\(261\) | −14040.0 | + | 6965.79i | −0.206104 | + | 0.102256i | ||||
\(262\) | − | 25393.1i | − | 0.369925i | ||||||
\(263\) | −2849.21 | −0.0411920 | −0.0205960 | − | 0.999788i | \(-0.506556\pi\) | ||||
−0.0205960 | + | 0.999788i | \(0.506556\pi\) | |||||||
\(264\) | −51480.0 | − | 31926.5i | −0.738636 | − | 0.458083i | ||||
\(265\) | 8960.00 | − | 34265.4i | 0.127590 | − | 0.487938i | ||||
\(266\) | 14899.1i | 0.210569i | ||||||||
\(267\) | 71037.4 | + | 44055.5i | 0.996471 | + | 0.617985i | ||||
\(268\) | − | 15511.2i | − | 0.215961i | ||||||
\(269\) | − | 3918.26i | − | 0.0541487i | −0.999633 | − | 0.0270744i | \(-0.991381\pi\) | ||
0.999633 | − | 0.0270744i | \(-0.00861909\pi\) | |||||||
\(270\) | 19779.9 | − | 54131.9i | 0.271329 | − | 0.742550i | ||||
\(271\) | −67048.0 | −0.912951 | −0.456475 | − | 0.889736i | \(-0.650888\pi\) | ||||
−0.456475 | + | 0.889736i | \(0.650888\pi\) | |||||||
\(272\) | 34506.8 | 0.466409 | ||||||||
\(273\) | −17759.4 | + | 28636.1i | −0.238288 | + | 0.384228i | ||||
\(274\) | 67240.0 | 0.895626 | ||||||||
\(275\) | 29598.9 | − | 52727.2i | 0.391391 | − | 0.697219i | ||||
\(276\) | 11790.0 | − | 19010.8i | 0.154773 | − | 0.249564i | ||||
\(277\) | − | 10340.8i | − | 0.134771i | −0.997727 | − | 0.0673853i | \(-0.978534\pi\) | ||
0.997727 | − | 0.0673853i | \(-0.0214657\pi\) | |||||||
\(278\) | 61259.6 | 0.792656 | ||||||||
\(279\) | −1152.00 | − | 2321.93i | −0.0147994 | − | 0.0298291i | ||||
\(280\) | 25740.0 | + | 6730.71i | 0.328316 | + | 0.0858508i | ||||
\(281\) | 22300.2i | 0.282420i | 0.989980 | + | 0.141210i | \(0.0450994\pi\) | ||||
−0.989980 | + | 0.141210i | \(0.954901\pi\) | |||||||
\(282\) | 36666.6 | − | 59123.1i | 0.461076 | − | 0.743463i | ||||
\(283\) | − | 117466.i | − | 1.46669i | −0.679854 | − | 0.733347i | \(-0.737957\pi\) | ||
0.679854 | − | 0.733347i | \(-0.262043\pi\) | |||||||
\(284\) | 27863.2i | 0.345457i | ||||||||
\(285\) | −47737.9 | − | 50235.3i | −0.587724 | − | 0.618470i | ||||
\(286\) | 74880.0 | 0.915448 | ||||||||
\(287\) | 31818.8 | 0.386296 | ||||||||
\(288\) | 25956.0 | + | 52315.9i | 0.312934 | + | 0.630738i | ||||
\(289\) | −6081.00 | −0.0728080 | ||||||||
\(290\) | −14799.5 | − | 3869.88i | −0.175975 | − | 0.0460153i | ||||
\(291\) | −19188.0 | − | 11899.9i | −0.226592 | − | 0.140526i | ||||
\(292\) | − | 25331.9i | − | 0.297100i | ||||||
\(293\) | 57363.7 | 0.668193 | 0.334097 | − | 0.942539i | \(-0.391569\pi\) | ||||
0.334097 | + | 0.942539i | \(0.391569\pi\) | |||||||
\(294\) | 32505.0 | − | 52412.7i | 0.376059 | − | 0.606376i | ||||
\(295\) | −95940.0 | − | 25087.2i | −1.10244 | − | 0.288276i | ||||
\(296\) | 89394.3i | 1.02030i | ||||||||
\(297\) | −6659.76 | + | 70213.5i | −0.0754997 | + | 0.795990i | ||||
\(298\) | 51245.1i | 0.577059i | ||||||||
\(299\) | 101391.i | 1.13411i | ||||||||
\(300\) | −29551.0 | + | 16303.5i | −0.328344 | + | 0.181149i | ||||
\(301\) | −39546.0 | −0.436485 | ||||||||
\(302\) | −105215. | −1.15363 | ||||||||
\(303\) | 36998.6 | + | 22945.6i | 0.402996 | + | 0.249927i | ||||
\(304\) | −38192.0 | −0.413262 | ||||||||
\(305\) | 5869.19 | − | 22445.3i | 0.0630926 | − | 0.241283i | ||||
\(306\) | −31680.0 | − | 63853.1i | −0.338331 | − | 0.681929i | ||||
\(307\) | − | 10417.3i | − | 0.110530i | −0.998472 | − | 0.0552648i | \(-0.982400\pi\) | ||
0.998472 | − | 0.0552648i | \(-0.0176003\pi\) | |||||||
\(308\) | −8879.68 | −0.0936043 | ||||||||
\(309\) | 42003.0 | + | 26049.2i | 0.439910 | + | 0.272820i | ||||
\(310\) | 640.000 | − | 2447.53i | 0.00665973 | − | 0.0254686i | ||||
\(311\) | − | 101971.i | − | 1.05428i | −0.849777 | − | 0.527142i | \(-0.823264\pi\) | ||
0.849777 | − | 0.527142i | \(-0.176736\pi\) | |||||||
\(312\) | −130235. | − | 80768.5i | −1.33789 | − | 0.829722i | ||||
\(313\) | 182586.i | 1.86371i | 0.362832 | + | 0.931854i | \(0.381810\pi\) | ||||
−0.362832 | + | 0.931854i | \(0.618190\pi\) | |||||||
\(314\) | 92683.7i | 0.940035i | ||||||||
\(315\) | −6299.51 | − | 30329.2i | −0.0634872 | − | 0.305661i | ||||
\(316\) | −48.0000 | −0.000480692 | ||||||||
\(317\) | 33494.8 | 0.333319 | 0.166659 | − | 0.986015i | \(-0.446702\pi\) | ||||
0.166659 | + | 0.986015i | \(0.446702\pi\) | |||||||
\(318\) | −21250.5 | + | 34265.4i | −0.210143 | + | 0.338845i | ||||
\(319\) | 18720.0 | 0.183960 | ||||||||
\(320\) | −26967.9 | + | 103132.i | −0.263358 | + | 1.00715i | ||||
\(321\) | 13875.0 | − | 22372.8i | 0.134655 | − | 0.217125i | ||||
\(322\) | 20039.1i | 0.193271i | ||||||||
\(323\) | −85710.4 | −0.821539 | ||||||||
\(324\) | 23814.0 | − | 31346.1i | 0.226852 | − | 0.298602i | ||||
\(325\) | 74880.0 | − | 133390.i | 0.708923 | − | 1.26287i | ||||
\(326\) | − | 38747.2i | − | 0.364590i | ||||||
\(327\) | 30130.2 | − | 48583.5i | 0.281777 | − | 0.454352i | ||||
\(328\) | 144710.i | 1.34509i | ||||||||
\(329\) | − | 37392.8i | − | 0.345458i | ||||||
\(330\) | −49899.5 | + | 47418.8i | −0.458214 | + | 0.435434i | ||||
\(331\) | 204092. | 1.86282 | 0.931408 | − | 0.363977i | \(-0.118581\pi\) | ||||
0.931408 | + | 0.363977i | \(0.118581\pi\) | |||||||
\(332\) | −26620.1 | −0.241509 | ||||||||
\(333\) | 93236.6 | − | 46258.3i | 0.840810 | − | 0.417159i | ||||
\(334\) | −7970.00 | −0.0714439 | ||||||||
\(335\) | −62527.7 | − | 16350.3i | −0.557164 | − | 0.145692i | ||||
\(336\) | −14508.0 | − | 8997.48i | −0.128508 | − | 0.0796971i | ||||
\(337\) | − | 44912.2i | − | 0.395461i | −0.980256 | − | 0.197731i | \(-0.936643\pi\) | ||
0.980256 | − | 0.197731i | \(-0.0633572\pi\) | |||||||
\(338\) | 99115.3 | 0.867575 | ||||||||
\(339\) | −42060.0 | + | 67819.7i | −0.365991 | + | 0.590142i | ||||
\(340\) | −10560.0 | + | 40384.2i | −0.0913495 | + | 0.349345i | ||||
\(341\) | 3095.91i | 0.0266244i | ||||||||
\(342\) | 35063.3 | + | 70672.4i | 0.299779 | + | 0.604224i | ||||
\(343\) | − | 69877.0i | − | 0.593944i | ||||||
\(344\) | − | 179853.i | − | 1.51985i | ||||||
\(345\) | −64207.2 | − | 67566.2i | −0.539443 | − | 0.567664i | ||||
\(346\) | −155960. | −1.30275 | ||||||||
\(347\) | 135260. | 1.12334 | 0.561669 | − | 0.827362i | \(-0.310159\pi\) | ||||
0.561669 | + | 0.827362i | \(0.310159\pi\) | |||||||
\(348\) | −8879.68 | − | 5506.94i | −0.0733227 | − | 0.0454728i | ||||
\(349\) | −228682. | −1.87751 | −0.938753 | − | 0.344592i | \(-0.888017\pi\) | ||||
−0.938753 | + | 0.344592i | \(0.888017\pi\) | |||||||
\(350\) | 14799.5 | − | 26363.6i | 0.120812 | − | 0.215213i | ||||
\(351\) | −16848.0 | + | 177628.i | −0.136752 | + | 1.44177i | ||||
\(352\) | − | 69754.6i | − | 0.562973i | ||||||
\(353\) | 106923. | 0.858067 | 0.429034 | − | 0.903288i | \(-0.358854\pi\) | ||||
0.429034 | + | 0.903288i | \(0.358854\pi\) | |||||||
\(354\) | 95940.0 | + | 59499.5i | 0.765585 | + | 0.474795i | ||||
\(355\) | 112320. | + | 29370.4i | 0.891252 | + | 0.233052i | ||||
\(356\) | 55726.3i | 0.439704i | ||||||||
\(357\) | −32558.8 | − | 20192.1i | −0.255465 | − | 0.158433i | ||||
\(358\) | − | 120235.i | − | 0.938133i | ||||||
\(359\) | − | 176467.i | − | 1.36922i | −0.728909 | − | 0.684611i | \(-0.759972\pi\) | ||
0.728909 | − | 0.684611i | \(-0.240028\pi\) | |||||||
\(360\) | 137936. | − | 28649.8i | 1.06432 | − | 0.221063i | ||||
\(361\) | −35457.0 | −0.272074 | ||||||||
\(362\) | −64327.1 | −0.490881 | ||||||||
\(363\) | −25050.0 | + | 40391.9i | −0.190105 | + | 0.306536i | ||||
\(364\) | −22464.0 | −0.169545 | ||||||||
\(365\) | −102116. | − | 26702.2i | −0.766495 | − | 0.200429i | ||||
\(366\) | −13920.0 | + | 22445.3i | −0.103915 | + | 0.167557i | ||||
\(367\) | 178042.i | 1.32188i | 0.750440 | + | 0.660939i | \(0.229842\pi\) | ||||
−0.750440 | + | 0.660939i | \(0.770158\pi\) | |||||||
\(368\) | −51368.0 | −0.379313 | ||||||||
\(369\) | 150930. | − | 74882.2i | 1.10847 | − | 0.549954i | ||||
\(370\) | 98280.0 | + | 25699.1i | 0.717896 | + | 0.187721i | ||||
\(371\) | 21671.3i | 0.157448i | ||||||||
\(372\) | 910.736 | − | 1468.52i | 0.00658122 | − | 0.0106119i | ||||
\(373\) | − | 77770.2i | − | 0.558979i | −0.960149 | − | 0.279490i | \(-0.909835\pi\) | ||
0.960149 | − | 0.279490i | \(-0.0901653\pi\) | |||||||
\(374\) | 85137.4i | 0.608664i | ||||||||
\(375\) | 34571.9 | + | 136309.i | 0.245844 | + | 0.969309i | ||||
\(376\) | 170060. | 1.20289 | ||||||||
\(377\) | 47358.3 | 0.333206 | ||||||||
\(378\) | −3329.88 | + | 35106.7i | −0.0233048 | + | 0.245701i | ||||
\(379\) | −12292.0 | −0.0855745 | −0.0427872 | − | 0.999084i | \(-0.513624\pi\) | ||||
−0.0427872 | + | 0.999084i | \(0.513624\pi\) | |||||||
\(380\) | 11687.8 | − | 44697.2i | 0.0809403 | − | 0.309537i | ||||
\(381\) | −29133.0 | − | 18067.5i | −0.200694 | − | 0.124465i | ||||
\(382\) | − | 175610.i | − | 1.20344i | ||||||
\(383\) | −246111. | −1.67777 | −0.838886 | − | 0.544308i | \(-0.816792\pi\) | ||||
−0.838886 | + | 0.544308i | \(0.816792\pi\) | |||||||
\(384\) | 9240.00 | − | 14899.1i | 0.0626628 | − | 0.101041i | ||||
\(385\) | −9360.00 | + | 35795.1i | −0.0631472 | + | 0.241492i | ||||
\(386\) | − | 160407.i | − | 1.07658i | ||||||
\(387\) | −187583. | + | 93067.3i | −1.25248 | + | 0.621406i | ||||
\(388\) | − | 15052.3i | − | 0.0999861i | ||||||
\(389\) | 99794.6i | 0.659490i | 0.944070 | + | 0.329745i | \(0.106963\pi\) | ||||
−0.944070 | + | 0.329745i | \(0.893037\pi\) | |||||||
\(390\) | −126237. | + | 119961.i | −0.829959 | + | 0.788699i | ||||
\(391\) | −115280. | −0.754051 | ||||||||
\(392\) | 150758. | 0.981091 | ||||||||
\(393\) | −61417.8 | − | 38089.7i | −0.397657 | − | 0.246617i | ||||
\(394\) | −91280.0 | −0.588008 | ||||||||
\(395\) | −50.5964 | + | 193.494i | −0.000324284 | + | 0.00124015i | ||||
\(396\) | −42120.0 | + | 20897.4i | −0.268595 | + | 0.133260i | ||||
\(397\) | 143548.i | 0.910783i | 0.890291 | + | 0.455391i | \(0.150501\pi\) | ||||
−0.890291 | + | 0.455391i | \(0.849499\pi\) | |||||||
\(398\) | −108555. | −0.685303 | ||||||||
\(399\) | 36036.0 | + | 22348.6i | 0.226355 | + | 0.140380i | ||||
\(400\) | 67580.0 | + | 37936.7i | 0.422375 | + | 0.237104i | ||||
\(401\) | 245738.i | 1.52821i | 0.645092 | + | 0.764105i | \(0.276819\pi\) | ||||
−0.645092 | + | 0.764105i | \(0.723181\pi\) | |||||||
\(402\) | 62527.7 | + | 38778.0i | 0.386919 | + | 0.239957i | ||||
\(403\) | 7832.09i | 0.0482245i | ||||||||
\(404\) | 29024.1i | 0.177826i | ||||||||
\(405\) | −101258. | − | 129039.i | −0.617332 | − | 0.786703i | ||||
\(406\) | 9360.00 | 0.0567837 | ||||||||
\(407\) | −124315. | −0.750475 | ||||||||
\(408\) | 91832.5 | − | 148076.i | 0.551666 | − | 0.889535i | ||||
\(409\) | 34808.0 | 0.208081 | 0.104041 | − | 0.994573i | \(-0.466823\pi\) | ||||
0.104041 | + | 0.994573i | \(0.466823\pi\) | |||||||
\(410\) | 159094. | + | 41601.2i | 0.946426 | + | 0.247479i | ||||
\(411\) | 100860. | − | 162632.i | 0.597084 | − | 0.962769i | ||||
\(412\) | 32949.9i | 0.194115i | ||||||||
\(413\) | 60677.8 | 0.355737 | ||||||||
\(414\) | 47160.0 | + | 95054.0i | 0.275152 | + | 0.554587i | ||||
\(415\) | −28060.0 | + | 107309.i | −0.162926 | + | 0.623074i | ||||
\(416\) | − | 176467.i | − | 1.01971i | ||||||
\(417\) | 91889.5 | − | 148167.i | 0.528437 | − | 0.852080i | ||||
\(418\) | − | 94229.9i | − | 0.539307i | ||||||
\(419\) | 219326.i | 1.24928i | 0.780911 | + | 0.624642i | \(0.214755\pi\) | ||||
−0.780911 | + | 0.624642i | \(0.785245\pi\) | |||||||
\(420\) | 14969.8 | − | 14225.6i | 0.0848630 | − | 0.0806442i | ||||
\(421\) | 168992. | 0.953459 | 0.476729 | − | 0.879050i | \(-0.341822\pi\) | ||||
0.476729 | + | 0.879050i | \(0.341822\pi\) | |||||||
\(422\) | 105203. | 0.590747 | ||||||||
\(423\) | −87999.9 | − | 177369.i | −0.491814 | − | 0.991284i | ||||
\(424\) | −98560.0 | −0.548238 | ||||||||
\(425\) | 151663. | + | 85137.4i | 0.839656 | + | 0.471349i | ||||
\(426\) | −112320. | − | 69657.9i | −0.618925 | − | 0.383841i | ||||
\(427\) | 14195.7i | 0.0778574i | ||||||||
\(428\) | 17550.6 | 0.0958088 | ||||||||
\(429\) | 112320. | − | 181111.i | 0.610299 | − | 0.984077i | ||||
\(430\) | −197730. | − | 51704.1i | −1.06939 | − | 0.279633i | ||||
\(431\) | − | 154989.i | − | 0.834345i | −0.908827 | − | 0.417173i | \(-0.863021\pi\) | ||
0.908827 | − | 0.417173i | \(-0.136979\pi\) | |||||||
\(432\) | −89992.1 | − | 8535.76i | −0.482211 | − | 0.0457377i | ||||
\(433\) | − | 153644.i | − | 0.819481i | −0.912202 | − | 0.409740i | \(-0.865619\pi\) | ||
0.912202 | − | 0.409740i | \(-0.134381\pi\) | |||||||
\(434\) | 1547.95i | 0.00821823i | ||||||||
\(435\) | −31559.2 | + | 29990.3i | −0.166781 | + | 0.158490i | ||||
\(436\) | 38112.0 | 0.200488 | ||||||||
\(437\) | 127592. | 0.668127 | ||||||||
\(438\) | 102116. | + | 63329.8i | 0.532288 | + | 0.330111i | ||||
\(439\) | 65168.0 | 0.338147 | 0.169073 | − | 0.985603i | \(-0.445922\pi\) | ||||
0.169073 | + | 0.985603i | \(0.445922\pi\) | |||||||
\(440\) | −162794. | − | 42568.7i | −0.840878 | − | 0.219880i | ||||
\(441\) | −78012.0 | − | 157238.i | −0.401129 | − | 0.808502i | ||||
\(442\) | 215383.i | 1.10247i | ||||||||
\(443\) | 116514. | 0.593706 | 0.296853 | − | 0.954923i | \(-0.404063\pi\) | ||||
0.296853 | + | 0.954923i | \(0.404063\pi\) | |||||||
\(444\) | 58968.0 | + | 36570.4i | 0.299123 | + | 0.185508i | ||||
\(445\) | 224640. | + | 58740.7i | 1.13440 | + | 0.296633i | ||||
\(446\) | 240368.i | 1.20839i | ||||||||
\(447\) | 123945. | + | 76867.7i | 0.620320 | + | 0.384706i | ||||
\(448\) | − | 65226.7i | − | 0.324989i | ||||||
\(449\) | − | 79090.7i | − | 0.392313i | −0.980573 | − | 0.196157i | \(-0.937154\pi\) | ||
0.980573 | − | 0.196157i | \(-0.0628461\pi\) | |||||||
\(450\) | 8156.11 | − | 159882.i | 0.0402771 | − | 0.789543i | ||||
\(451\) | −201240. | −0.989376 | ||||||||
\(452\) | −53202.2 | −0.260407 | ||||||||
\(453\) | −157823. | + | 254482.i | −0.769084 | + | 1.24011i | ||||
\(454\) | −53090.0 | −0.257573 | ||||||||
\(455\) | −23679.1 | + | 90555.3i | −0.114378 | + | 0.437412i | ||||
\(456\) | −101640. | + | 163890.i | −0.488804 | + | 0.788173i | ||||
\(457\) | − | 389402.i | − | 1.86451i | −0.361797 | − | 0.932257i | \(-0.617836\pi\) | ||
0.361797 | − | 0.932257i | \(-0.382164\pi\) | |||||||
\(458\) | −127433. | −0.607509 | ||||||||
\(459\) | −201960. | − | 19155.9i | −0.958606 | − | 0.0909238i | ||||
\(460\) | 15720.0 | − | 60117.4i | 0.0742911 | − | 0.284109i | ||||
\(461\) | 236643.i | 1.11351i | 0.830678 | + | 0.556753i | \(0.187953\pi\) | ||||
−0.830678 | + | 0.556753i | \(0.812047\pi\) | |||||||
\(462\) | 22199.2 | − | 35795.1i | 0.104005 | − | 0.167703i | ||||
\(463\) | 253793.i | 1.18391i | 0.805971 | + | 0.591955i | \(0.201644\pi\) | ||||
−0.805971 | + | 0.591955i | \(0.798356\pi\) | |||||||
\(464\) | 23993.3i | 0.111443i | ||||||||
\(465\) | −4959.78 | − | 5219.25i | −0.0229381 | − | 0.0241380i | ||||
\(466\) | 275920. | 1.27061 | ||||||||
\(467\) | −365853. | −1.67754 | −0.838771 | − | 0.544485i | \(-0.816725\pi\) | ||||
−0.838771 | + | 0.544485i | \(0.816725\pi\) | |||||||
\(468\) | −106556. | + | 52866.6i | −0.486504 | + | 0.241374i | ||||
\(469\) | 39546.0 | 0.179786 | ||||||||
\(470\) | 48888.8 | − | 186964.i | 0.221316 | − | 0.846373i | ||||
\(471\) | 224172. | + | 139026.i | 1.01051 | + | 0.626690i | ||||
\(472\) | 275959.i | 1.23868i | ||||||||
\(473\) | 250111. | 1.11792 | ||||||||
\(474\) | 120.000 | − | 193.494i | 0.000534102 | − | 0.000861214i | ||||
\(475\) | −167860. | − | 94229.9i | −0.743978 | − | 0.417639i | ||||
\(476\) | − | 25541.2i | − | 0.112727i | ||||||
\(477\) | 51001.2 | + | 102796.i | 0.224153 | + | 0.451794i | ||||
\(478\) | 280242.i | 1.22653i | ||||||||
\(479\) | − | 255606.i | − | 1.11404i | −0.830500 | − | 0.557019i | \(-0.811945\pi\) | ||
0.830500 | − | 0.557019i | \(-0.188055\pi\) | |||||||
\(480\) | 111750. | + | 117596.i | 0.485026 | + | 0.510400i | ||||
\(481\) | −314496. | −1.35933 | ||||||||
\(482\) | −228165. | −0.982097 | ||||||||
\(483\) | 48468.2 | + | 30058.7i | 0.207760 | + | 0.128848i | ||||
\(484\) | −31686.0 | −0.135262 | ||||||||
\(485\) | −60677.8 | − | 15866.5i | −0.257956 | − | 0.0674525i | ||||
\(486\) | 66825.0 | + | 174362.i | 0.282922 | + | 0.738211i | ||||
\(487\) | − | 445925.i | − | 1.88020i | −0.340902 | − | 0.940099i | \(-0.610733\pi\) | ||
0.340902 | − | 0.940099i | \(-0.389267\pi\) | |||||||
\(488\) | −64561.1 | −0.271101 | ||||||||
\(489\) | −93717.0 | − | 58120.8i | −0.391923 | − | 0.243060i | ||||
\(490\) | 43340.0 | − | 165744.i | 0.180508 | − | 0.690311i | ||||
\(491\) | − | 229387.i | − | 0.951495i | −0.879582 | − | 0.475747i | \(-0.842178\pi\) | ||
0.879582 | − | 0.475747i | \(-0.157822\pi\) | |||||||
\(492\) | 95456.5 | + | 59199.6i | 0.394344 | + | 0.244562i | ||||
\(493\) | 53845.6i | 0.221542i | ||||||||
\(494\) | − | 238385.i | − | 0.976843i | ||||||
\(495\) | 39841.6 | + | 191819.i | 0.162602 | + | 0.782854i | ||||
\(496\) | −3968.00 | −0.0161290 | ||||||||
\(497\) | −71037.4 | −0.287590 | ||||||||
\(498\) | 66550.1 | − | 107309.i | 0.268343 | − | 0.432690i | ||||
\(499\) | 157748. | 0.633524 | 0.316762 | − | 0.948505i | \(-0.397404\pi\) | ||||
0.316762 | + | 0.948505i | \(0.397404\pi\) | |||||||
\(500\) | −65079.7 | + | 67481.1i | −0.260319 | + | 0.269924i | ||||
\(501\) | −11955.0 | + | 19276.9i | −0.0476293 | + | 0.0767999i | ||||
\(502\) | − | 50480.3i | − | 0.200315i | ||||||
\(503\) | 499630. | 1.97475 | 0.987377 | − | 0.158390i | \(-0.0506302\pi\) | ||||
0.987377 | + | 0.158390i | \(0.0506302\pi\) | |||||||
\(504\) | −77220.0 | + | 38311.8i | −0.303997 | + | 0.150825i | ||||
\(505\) | 117000. | + | 30594.1i | 0.458779 | + | 0.119965i | ||||
\(506\) | − | 126739.i | − | 0.495003i | ||||||
\(507\) | 148673. | − | 239728.i | 0.578384 | − | 0.932615i | ||||
\(508\) | − | 22853.8i | − | 0.0885587i | ||||||
\(509\) | 153441.i | 0.592251i | 0.955149 | + | 0.296125i | \(0.0956946\pi\) | ||||
−0.955149 | + | 0.296125i | \(0.904305\pi\) | |||||||
\(510\) | −136394. | − | 143529.i | −0.524391 | − | 0.551824i | ||||
\(511\) | 64584.0 | 0.247334 | ||||||||
\(512\) | 227431. | 0.867580 | ||||||||
\(513\) | 223529. | + | 21201.7i | 0.849373 | + | 0.0805631i | ||||
\(514\) | 268600. | 1.01667 | ||||||||
\(515\) | 132825. | + | 34732.2i | 0.500802 | + | 0.130954i | ||||
\(516\) | −118638. | − | 73576.2i | −0.445579 | − | 0.276336i | ||||
\(517\) | 236493.i | 0.884782i | ||||||||
\(518\) | −62157.7 | −0.231652 | ||||||||
\(519\) | −233940. | + | 377217.i | −0.868500 | + | 1.40041i | ||||
\(520\) | −411840. | − | 107691.i | −1.52308 | − | 0.398267i | ||||
\(521\) | − | 242642.i | − | 0.893902i | −0.894558 | − | 0.446951i | \(-0.852510\pi\) | ||
0.894558 | − | 0.446951i | \(-0.147490\pi\) | |||||||
\(522\) | 44398.4 | − | 22027.8i | 0.162939 | − | 0.0808406i | ||||
\(523\) | 133865.i | 0.489398i | 0.969599 | + | 0.244699i | \(0.0786892\pi\) | ||||
−0.969599 | + | 0.244699i | \(0.921311\pi\) | |||||||
\(524\) | − | 48180.1i | − | 0.175471i | ||||||
\(525\) | −41565.8 | − | 75340.5i | −0.150806 | − | 0.273344i | ||||
\(526\) | 9010.00 | 0.0325652 | ||||||||
\(527\) | −8904.97 | −0.0320635 | ||||||||
\(528\) | 91756.6 | + | 56905.1i | 0.329132 | + | 0.204119i | ||||
\(529\) | −108231. | −0.386759 | ||||||||
\(530\) | −28334.0 | + | 108357.i | −0.100869 | + | 0.385748i | ||||
\(531\) | 287820. | − | 142799.i | 1.02078 | − | 0.506448i | ||||
\(532\) | 28269.0i | 0.0998819i | ||||||||
\(533\) | −509101. | −1.79205 | ||||||||
\(534\) | −224640. | − | 139316.i | −0.787779 | − | 0.488560i | ||||
\(535\) | 18500.0 | − | 70748.9i | 0.0646345 | − | 0.247179i | ||||
\(536\) | 179853.i | 0.626019i | ||||||||
\(537\) | −290809. | − | 180352.i | −1.00846 | − | 0.625422i | ||||
\(538\) | 12390.6i | 0.0428083i | ||||||||
\(539\) | 209651.i | 0.721638i | ||||||||
\(540\) | 37529.6 | − | 102708.i | 0.128702 | − | 0.352222i | ||||
\(541\) | −195478. | −0.667888 | −0.333944 | − | 0.942593i | \(-0.608380\pi\) | ||||
−0.333944 | + | 0.942593i | \(0.608380\pi\) | |||||||
\(542\) | 212024. | 0.721751 | ||||||||
\(543\) | −96490.6 | + | 155586.i | −0.327254 | + | 0.527682i | ||||
\(544\) | 200640. | 0.677984 | ||||||||
\(545\) | 40173.6 | − | 153634.i | 0.135253 | − | 0.517244i | ||||
\(546\) | 56160.0 | − | 90555.3i | 0.188383 | − | 0.303759i | ||||
\(547\) | 143165.i | 0.478479i | 0.970961 | + | 0.239239i | \(0.0768981\pi\) | ||||
−0.970961 | + | 0.239239i | \(0.923102\pi\) | |||||||
\(548\) | 127579. | 0.424833 | ||||||||
\(549\) | 33408.0 | + | 67336.0i | 0.110842 | + | 0.223410i | ||||
\(550\) | −93600.0 | + | 166738.i | −0.309421 | + | 0.551200i | ||||
\(551\) | − | 59596.2i | − | 0.196298i | ||||||
\(552\) | −136705. | + | 220431.i | −0.448649 | + | 0.723425i | ||||
\(553\) | − | 122.376i | − | 0.000400173i | ||||||
\(554\) | 32700.5i | 0.106545i | ||||||||
\(555\) | 209578. | − | 199159.i | 0.680392 | − | 0.646568i | ||||
\(556\) | 116232. | 0.375990 | ||||||||
\(557\) | −401799. | −1.29509 | −0.647543 | − | 0.762029i | \(-0.724203\pi\) | ||||
−0.647543 | + | 0.762029i | \(0.724203\pi\) | |||||||
\(558\) | 3642.94 | + | 7342.59i | 0.0117000 | + | 0.0235820i | ||||
\(559\) | 632736. | 2.02488 | ||||||||
\(560\) | −45878.3 | − | 11996.6i | −0.146296 | − | 0.0382546i | ||||
\(561\) | 205920. | + | 127706.i | 0.654294 | + | 0.405776i | ||||
\(562\) | − | 70519.4i | − | 0.223273i | ||||||
\(563\) | −126178. | −0.398077 | −0.199038 | − | 0.979992i | \(-0.563782\pi\) | ||||
−0.199038 | + | 0.979992i | \(0.563782\pi\) | |||||||
\(564\) | 69570.0 | − | 112178.i | 0.218708 | − | 0.352655i | ||||
\(565\) | −56080.0 | + | 214465.i | −0.175675 | + | 0.671829i | ||||
\(566\) | 371460.i | 1.15952i | ||||||||
\(567\) | 79917.1 | + | 60714.0i | 0.248584 | + | 0.188853i | ||||
\(568\) | − | 323074.i | − | 1.00139i | ||||||
\(569\) | 355497.i | 1.09802i | 0.835815 | + | 0.549012i | \(0.184996\pi\) | ||||
−0.835815 | + | 0.549012i | \(0.815004\pi\) | |||||||
\(570\) | 150961. | + | 158858.i | 0.464637 | + | 0.488944i | ||||
\(571\) | −454108. | −1.39279 | −0.696397 | − | 0.717657i | \(-0.745215\pi\) | ||||
−0.696397 | + | 0.717657i | \(0.745215\pi\) | |||||||
\(572\) | 142075. | 0.434235 | ||||||||
\(573\) | −424744. | − | 263415.i | −1.29366 | − | 0.802291i | ||||
\(574\) | −100620. | −0.305394 | ||||||||
\(575\) | −225771. | − | 126739.i | −0.682861 | − | 0.383331i | ||||
\(576\) | −153504. | − | 309397.i | −0.462674 | − | 0.932548i | ||||
\(577\) | 103163.i | 0.309866i | 0.987925 | + | 0.154933i | \(0.0495162\pi\) | ||||
−0.987925 | + | 0.154933i | \(0.950484\pi\) | |||||||
\(578\) | 19229.8 | 0.0575598 | ||||||||
\(579\) | −387972. | − | 240610.i | −1.15729 | − | 0.717723i | ||||
\(580\) | −28080.0 | − | 7342.59i | −0.0834721 | − | 0.0218270i | ||||
\(581\) | − | 67868.1i | − | 0.201054i | ||||||
\(582\) | 60677.8 | + | 37630.8i | 0.179136 | + | 0.111096i | ||||
\(583\) | − | 137062.i | − | 0.403254i | ||||||
\(584\) | 293724.i | 0.861220i | ||||||||
\(585\) | 100792. | + | 485268.i | 0.294520 | + | 1.41798i | ||||
\(586\) | −181400. | −0.528253 | ||||||||
\(587\) | 474661. | 1.37755 | 0.688775 | − | 0.724975i | \(-0.258149\pi\) | ||||
0.688775 | + | 0.724975i | \(0.258149\pi\) | |||||||
\(588\) | 61673.9 | − | 99446.2i | 0.178380 | − | 0.287630i | ||||
\(589\) | 9856.00 | 0.0284099 | ||||||||
\(590\) | 303389. | + | 79332.6i | 0.871557 | + | 0.227902i | ||||
\(591\) | −136920. | + | 220777.i | −0.392005 | + | 0.632090i | ||||
\(592\) | − | 159334.i | − | 0.454638i | ||||||
\(593\) | 173103. | 0.492261 | 0.246130 | − | 0.969237i | \(-0.420841\pi\) | ||||
0.246130 | + | 0.969237i | \(0.420841\pi\) | |||||||
\(594\) | 21060.0 | − | 222035.i | 0.0596878 | − | 0.629285i | ||||
\(595\) | −102960. | − | 26922.8i | −0.290827 | − | 0.0760478i | ||||
\(596\) | 97230.8i | 0.273723i | ||||||||
\(597\) | −162832. | + | 262559.i | −0.456868 | + | 0.736678i | ||||
\(598\) | − | 320626.i | − | 0.896596i | ||||||
\(599\) | − | 587255.i | − | 1.63671i | −0.574710 | − | 0.818357i | \(-0.694885\pi\) | ||
0.574710 | − | 0.818357i | \(-0.305115\pi\) | |||||||
\(600\) | 342644. | − | 189039.i | 0.951789 | − | 0.525108i | ||||
\(601\) | 475352. | 1.31603 | 0.658016 | − | 0.753004i | \(-0.271396\pi\) | ||||
0.658016 | + | 0.753004i | \(0.271396\pi\) | |||||||
\(602\) | 125055. | 0.345072 | ||||||||
\(603\) | 187583. | − | 93067.3i | 0.515892 | − | 0.255954i | ||||
\(604\) | −199632. | −0.547213 | ||||||||
\(605\) | −33400.0 | + | 127730.i | −0.0912505 | + | 0.348966i | ||||
\(606\) | −117000. | − | 72560.3i | −0.318596 | − | 0.197585i | ||||
\(607\) | − | 311310.i | − | 0.844921i | −0.906381 | − | 0.422461i | \(-0.861166\pi\) | ||
0.906381 | − | 0.422461i | \(-0.138834\pi\) | |||||||
\(608\) | −222068. | −0.600729 | ||||||||
\(609\) | 14040.0 | − | 22638.8i | 0.0378558 | − | 0.0610407i | ||||
\(610\) | −18560.0 | + | 70978.4i | −0.0498791 | + | 0.190751i | ||||
\(611\) | 598284.i | 1.60260i | ||||||||
\(612\) | −60108.6 | − | 121153.i | −0.160485 | − | 0.323467i | ||||
\(613\) | − | 224316.i | − | 0.596952i | −0.954417 | − | 0.298476i | \(-0.903522\pi\) | ||
0.954417 | − | 0.298476i | \(-0.0964783\pi\) | |||||||
\(614\) | 32942.4i | 0.0873813i | ||||||||
\(615\) | 339261. | − | 322396.i | 0.896983 | − | 0.852391i | ||||
\(616\) | 102960. | 0.271336 | ||||||||
\(617\) | 200463. | 0.526580 | 0.263290 | − | 0.964717i | \(-0.415192\pi\) | ||||
0.263290 | + | 0.964717i | \(0.415192\pi\) | |||||||
\(618\) | −132825. | − | 82374.7i | −0.347779 | − | 0.215683i | ||||
\(619\) | 22508.0 | 0.0587429 | 0.0293715 | − | 0.999569i | \(-0.490649\pi\) | ||||
0.0293715 | + | 0.999569i | \(0.490649\pi\) | |||||||
\(620\) | 1214.31 | − | 4643.86i | 0.00315899 | − | 0.0120808i | ||||
\(621\) | 300645. | + | 28516.2i | 0.779598 | + | 0.0739450i | ||||
\(622\) | 322462.i | 0.833485i | ||||||||
\(623\) | −142075. | −0.366050 | ||||||||
\(624\) | 232128. | + | 143960.i | 0.596154 | + | 0.369719i | ||||
\(625\) | 203425. | + | 333476.i | 0.520768 | + | 0.853698i | ||||
\(626\) | − | 577387.i | − | 1.47339i | ||||||
\(627\) | −227912. | − | 141345.i | −0.579738 | − | 0.359538i | ||||
\(628\) | 175855.i | 0.445898i | ||||||||
\(629\) | − | 357577.i | − | 0.903792i | ||||||
\(630\) | 19920.8 | + | 95909.5i | 0.0501910 | + | 0.241646i | ||||
\(631\) | −157408. | −0.395338 | −0.197669 | − | 0.980269i | \(-0.563337\pi\) | ||||
−0.197669 | + | 0.980269i | \(0.563337\pi\) | |||||||
\(632\) | 556.561 | 0.00139341 | ||||||||
\(633\) | 157804. | − | 254451.i | 0.393832 | − | 0.635034i | ||||
\(634\) | −105920. | −0.263511 | ||||||||
\(635\) | −92126.6 | − | 24090.0i | −0.228475 | − | 0.0597434i | ||||
\(636\) | −40320.0 | + | 65014.0i | −0.0996796 | + | 0.160729i | ||||
\(637\) | 530380.i | 1.30710i | ||||||||
\(638\) | −59197.8 | −0.145434 | ||||||||
\(639\) | −336960. | + | 167179.i | −0.825233 | + | 0.409430i | ||||
\(640\) | 12320.0 | − | 47114.9i | 0.0300781 | − | 0.115027i | ||||
\(641\) | − | 297836.i | − | 0.724871i | −0.932009 | − | 0.362436i | \(-0.881945\pi\) | ||
0.932009 | − | 0.362436i | \(-0.118055\pi\) | |||||||
\(642\) | −43876.6 | + | 70748.9i | −0.106454 | + | 0.171652i | ||||
\(643\) | 130805.i | 0.316376i | 0.987409 | + | 0.158188i | \(0.0505651\pi\) | ||||
−0.987409 | + | 0.158188i | \(0.949435\pi\) | |||||||
\(644\) | 38021.6i | 0.0916767i | ||||||||
\(645\) | −421650. | + | 400689.i | −1.01352 | + | 0.963137i | ||||
\(646\) | 271040. | 0.649484 | ||||||||
\(647\) | 117520. | 0.280739 | 0.140369 | − | 0.990099i | \(-0.455171\pi\) | ||||
0.140369 | + | 0.990099i | \(0.455171\pi\) | |||||||
\(648\) | −276124. | + | 363458.i | −0.657588 | + | 0.865574i | ||||
\(649\) | −383760. | −0.911109 | ||||||||
\(650\) | −236791. | + | 421817.i | −0.560453 | + | 0.998384i | ||||
\(651\) | 3744.00 | + | 2321.93i | 0.00883433 | + | 0.00547882i | ||||
\(652\) | − | 73517.7i | − | 0.172940i | ||||||
\(653\) | −640829. | −1.50285 | −0.751426 | − | 0.659818i | \(-0.770633\pi\) | ||||
−0.751426 | + | 0.659818i | \(0.770633\pi\) | |||||||
\(654\) | −95280.0 | + | 153634.i | −0.222765 | + | 0.359197i | ||||
\(655\) | −194220. | − | 50786.2i | −0.452701 | − | 0.118376i | ||||
\(656\) | − | 257928.i | − | 0.599364i | ||||||
\(657\) | 306349. | − | 151992.i | 0.709717 | − | 0.352118i | ||||
\(658\) | 118246.i | 0.273109i | ||||||||
\(659\) | − | 121805.i | − | 0.280474i | −0.990118 | − | 0.140237i | \(-0.955214\pi\) | ||
0.990118 | − | 0.140237i | \(-0.0447865\pi\) | |||||||
\(660\) | −94677.6 | + | 89970.9i | −0.217350 | + | 0.206545i | ||||
\(661\) | 5072.00 | 0.0116085 | 0.00580425 | − | 0.999983i | \(-0.498152\pi\) | ||||
0.00580425 | + | 0.999983i | \(0.498152\pi\) | |||||||
\(662\) | −645396. | −1.47269 | ||||||||
\(663\) | 520941. | + | 323074.i | 1.18512 | + | 0.734979i | ||||
\(664\) | 308660. | 0.700074 | ||||||||
\(665\) | 113956. | + | 29798.1i | 0.257687 | + | 0.0673822i | ||||
\(666\) | −294840. | + | 146282.i | −0.664719 | + | 0.329793i | ||||
\(667\) | − | 80156.6i | − | 0.180172i | ||||||
\(668\) | −15122.0 | −0.0338888 | ||||||||
\(669\) | 581373. | + | 360552.i | 1.29898 | + | 0.805593i | ||||
\(670\) | 197730. | + | 51704.1i | 0.440477 | + | 0.115179i | ||||
\(671\) | − | 89781.3i | − | 0.199407i | ||||||
\(672\) | −84356.9 | − | 52315.9i | −0.186802 | − | 0.115850i | ||||
\(673\) | − | 181790.i | − | 0.401366i | −0.979656 | − | 0.200683i | \(-0.935684\pi\) | ||
0.979656 | − | 0.200683i | \(-0.0643161\pi\) | |||||||
\(674\) | 142025.i | 0.312640i | ||||||||
\(675\) | −374470. | − | 259551.i | −0.821882 | − | 0.569658i | ||||
\(676\) | 188058. | 0.411527 | ||||||||
\(677\) | 304666. | 0.664733 | 0.332367 | − | 0.943150i | \(-0.392153\pi\) | ||||
0.332367 | + | 0.943150i | \(0.392153\pi\) | |||||||
\(678\) | 133005. | − | 214465.i | 0.289341 | − | 0.466548i | ||||
\(679\) | 38376.0 | 0.0832377 | ||||||||
\(680\) | 122443. | − | 468256.i | 0.264800 | − | 1.01266i | ||||
\(681\) | −79635.0 | + | 128408.i | −0.171716 | + | 0.276883i | ||||
\(682\) | − | 9790.12i | − | 0.0210484i | ||||||
\(683\) | 627816. | 1.34583 | 0.672917 | − | 0.739718i | \(-0.265041\pi\) | ||||
0.672917 | + | 0.739718i | \(0.265041\pi\) | |||||||
\(684\) | 66528.0 | + | 134091.i | 0.142198 | + | 0.286608i | ||||
\(685\) | 134480. | − | 514287.i | 0.286600 | − | 1.09604i | ||||
\(686\) | 220970.i | 0.469554i | ||||||||
\(687\) | −191150. | + | 308220.i | −0.405006 | + | 0.653052i | ||||
\(688\) | 320565.i | 0.677235i | ||||||||
\(689\) | − | 346742.i | − | 0.730411i | ||||||
\(690\) | 203041. | + | 213663.i | 0.426467 | + | 0.448777i | ||||
\(691\) | −17308.0 | −0.0362486 | −0.0181243 | − | 0.999836i | \(-0.505769\pi\) | ||||
−0.0181243 | + | 0.999836i | \(0.505769\pi\) | |||||||
\(692\) | −295913. | −0.617949 | ||||||||
\(693\) | −53278.1 | − | 107385.i | −0.110938 | − | 0.223603i | ||||
\(694\) | −427730. | −0.888077 | ||||||||
\(695\) | 122519. | − | 468546.i | 0.253650 | − | 0.970025i | ||||
\(696\) | 102960. | + | 63853.1i | 0.212545 | + | 0.131815i | ||||
\(697\) | − | 578841.i | − | 1.19150i | ||||||
\(698\) | 723156. | 1.48430 | ||||||||
\(699\) | 413880. | − | 667361.i | 0.847072 | − | 1.36586i | ||||
\(700\) | 28080.0 | − | 50021.4i | 0.0573061 | − | 0.102084i | ||||
\(701\) | 23944.9i | 0.0487278i | 0.999703 | + | 0.0243639i | \(0.00775604\pi\) | ||||
−0.999703 | + | 0.0243639i | \(0.992244\pi\) | |||||||
\(702\) | 53278.1 | − | 561708.i | 0.108112 | − | 1.13982i | ||||
\(703\) | 395765.i | 0.800806i | ||||||||
\(704\) | 412530.i | 0.832357i | ||||||||
\(705\) | −378872. | − | 398692.i | −0.762279 | − | 0.802157i | ||||
\(706\) | −338120. | −0.678362 | ||||||||
\(707\) | −73997.3 | −0.148039 | ||||||||
\(708\) | 182033. | + | 112892.i | 0.363149 | + | 0.225215i | ||||
\(709\) | −381322. | −0.758577 | −0.379288 | − | 0.925279i | \(-0.623831\pi\) | ||||
−0.379288 | + | 0.925279i | \(0.623831\pi\) | |||||||
\(710\) | −355187. | − | 92877.2i | −0.704596 | − | 0.184244i | ||||
\(711\) | −288.000 | − | 580.483i | −0.000569709 | − | 0.00114829i | ||||
\(712\) | − | 646148.i | − | 1.27459i | ||||||
\(713\) | 13256.3 | 0.0260761 | ||||||||
\(714\) | 102960. | + | 63853.1i | 0.201963 | + | 0.125252i | ||||
\(715\) | 149760. | − | 572722.i | 0.292943 | − | 1.12029i | ||||
\(716\) | − | 228130.i | − | 0.444996i | ||||||
\(717\) | 677815. | + | 420363.i | 1.31848 | + | 0.817686i | ||||
\(718\) | 558037.i | 1.08247i | ||||||||
\(719\) | 927031.i | 1.79323i | 0.442810 | + | 0.896616i | \(0.353982\pi\) | ||||
−0.442810 | + | 0.896616i | \(0.646018\pi\) | |||||||
\(720\) | −245853. | + | 51064.7i | −0.474253 | + | 0.0985044i | ||||
\(721\) | −84006.0 | −0.161599 | ||||||||
\(722\) | 112125. | 0.215094 | ||||||||
\(723\) | −342247. | + | 551857.i | −0.654731 | + | 1.05572i | ||||
\(724\) | −122052. | −0.232845 | ||||||||
\(725\) | −59197.8 | + | 105454.i | −0.112624 | + | 0.200627i | ||||
\(726\) | 79215.0 | − | 127730.i | 0.150291 | − | 0.242338i | ||||
\(727\) | 373998.i | 0.707620i | 0.935317 | + | 0.353810i | \(0.115114\pi\) | ||||
−0.935317 | + | 0.353810i | \(0.884886\pi\) | |||||||
\(728\) | 260470. | 0.491469 | ||||||||
\(729\) | 521964. | + | 99915.6i | 0.982167 | + | 0.188009i | ||||
\(730\) | 322920. | + | 84439.8i | 0.605967 | + | 0.158453i | ||||
\(731\) | 719411.i | 1.34630i | ||||||||
\(732\) | −26411.3 | + | 42587.0i | −0.0492911 | + | 0.0794795i | ||||
\(733\) | − | 318240.i | − | 0.592307i | −0.955140 | − | 0.296153i | \(-0.904296\pi\) | ||
0.955140 | − | 0.296153i | \(-0.0957040\pi\) | |||||||
\(734\) | − | 563020.i | − | 1.04504i | ||||||
\(735\) | −335870. | − | 353441.i | −0.621723 | − | 0.654248i | ||||
\(736\) | −298680. | −0.551379 | ||||||||
\(737\) | −250111. | −0.460466 | ||||||||
\(738\) | −477283. | + | 236798.i | −0.876320 | + | 0.434777i | ||||
\(739\) | 409268. | 0.749409 | 0.374705 | − | 0.927144i | \(-0.377744\pi\) | ||||
0.374705 | + | 0.927144i | \(0.377744\pi\) | |||||||
\(740\) | 186473. | + | 48760.5i | 0.340528 | + | 0.0890441i | ||||
\(741\) | −576576. | − | 357577.i | −1.05007 | − | 0.651229i | ||||
\(742\) | − | 68530.8i | − | 0.124474i | ||||||
\(743\) | 11400.0 | 0.0206504 | 0.0103252 | − | 0.999947i | \(-0.496713\pi\) | ||||
0.0103252 | + | 0.999947i | \(0.496713\pi\) | |||||||
\(744\) | −10560.0 | + | 17027.5i | −0.0190773 | + | 0.0307613i | ||||
\(745\) | 391950. | + | 102490.i | 0.706184 | + | 0.184659i | ||||
\(746\) | 245931.i | 0.441912i | ||||||||
\(747\) | −159720. | − | 321927.i | −0.286233 | − | 0.576920i | ||||
\(748\) | 161537.i | 0.288715i | ||||||||
\(749\) | 44745.5i | 0.0797602i | ||||||||
\(750\) | −109326. | − | 431047.i | −0.194357 | − | 0.766306i | ||||
\(751\) | 347432. | 0.616013 | 0.308007 | − | 0.951384i | \(-0.400338\pi\) | ||||
0.308007 | + | 0.951384i | \(0.400338\pi\) | |||||||
\(752\) | −303111. | −0.536001 | ||||||||
\(753\) | −122096. | − | 75720.4i | −0.215333 | − | 0.133544i | ||||
\(754\) | −149760. | −0.263423 | ||||||||
\(755\) | −210431. | + | 804742.i | −0.369160 | + | 1.41177i | ||||
\(756\) | −6318.00 | + | 66610.4i | −0.0110544 | + | 0.116546i | ||||
\(757\) | 886067.i | 1.54623i | 0.634265 | + | 0.773116i | \(0.281303\pi\) | ||||
−0.634265 | + | 0.773116i | \(0.718697\pi\) | |||||||
\(758\) | 38870.7 | 0.0676525 | ||||||||
\(759\) | −306540. | − | 190108.i | −0.532113 | − | 0.330002i | ||||
\(760\) | −135520. | + | 518264.i | −0.234626 | + | 0.897272i | ||||
\(761\) | − | 261604.i | − | 0.451726i | −0.974159 | − | 0.225863i | \(-0.927480\pi\) | ||
0.974159 | − | 0.225863i | \(-0.0725202\pi\) | |||||||
\(762\) | 92126.6 | + | 57134.5i | 0.158663 | + | 0.0983985i | ||||
\(763\) | 97166.9i | 0.166905i | ||||||||
\(764\) | − | 333197.i | − | 0.570840i | ||||||
\(765\) | −551742. | + | 114599.i | −0.942786 | + | 0.195821i | ||||
\(766\) | 778270. | 1.32639 | ||||||||
\(767\) | −970845. | −1.65029 | ||||||||
\(768\) | 294395. | − | 474698.i | 0.499124 | − | 0.804814i | ||||
\(769\) | −832882. | −1.40842 | −0.704208 | − | 0.709994i | \(-0.748698\pi\) | ||||
−0.704208 | + | 0.709994i | \(0.748698\pi\) | |||||||
\(770\) | 29598.9 | − | 113194.i | 0.0499223 | − | 0.190916i | ||||
\(771\) | 402900. | − | 649657.i | 0.677780 | − | 1.09289i | ||||
\(772\) | − | 304350.i | − | 0.510669i | ||||||
\(773\) | −38529.2 | −0.0644809 | −0.0322404 | − | 0.999480i | \(-0.510264\pi\) | ||||
−0.0322404 | + | 0.999480i | \(0.510264\pi\) | |||||||
\(774\) | 593190. | − | 294305.i | 0.990175 | − | 0.491264i | ||||
\(775\) | −17440.0 | − | 9790.12i | −0.0290364 | − | 0.0162999i | ||||
\(776\) | 174532.i | 0.289835i | ||||||||
\(777\) | −93236.6 | + | 150339.i | −0.154435 | + | 0.249018i | ||||
\(778\) | − | 315578.i | − | 0.521372i | ||||||
\(779\) | 640659.i | 1.05573i | ||||||||
\(780\) | −239517. | + | 227610.i | −0.393684 | + | 0.374113i | ||||
\(781\) | 449280. | 0.736572 | ||||||||
\(782\) | 364547. | 0.596129 | ||||||||
\(783\) | 13319.5 | − | 140427.i | 0.0217253 | − | 0.229048i | ||||
\(784\) | −268708. | −0.437168 | ||||||||
\(785\) | 708894. | + | 185367.i | 1.15038 | + | 0.300811i | ||||
\(786\) | 194220. | + | 120450.i | 0.314376 | + | 0.194967i | ||||
\(787\) | 627164.i | 1.01259i | 0.862362 | + | 0.506293i | \(0.168984\pi\) | ||||
−0.862362 | + | 0.506293i | \(0.831016\pi\) | |||||||
\(788\) | −173192. | −0.278917 | ||||||||
\(789\) | 13515.0 | − | 21792.3i | 0.0217101 | − | 0.0350065i | ||||
\(790\) | 160.000 | − | 611.882i | 0.000256369 | − | 0.000980424i | ||||
\(791\) | − | 135639.i | − | 0.216787i | ||||||
\(792\) | 488382. | − | 242305.i | 0.778591 | − | 0.386289i | ||||
\(793\) | − | 227131.i | − | 0.361185i | ||||||
\(794\) | − | 453937.i | − | 0.720037i | ||||||
\(795\) | 219579. | + | 231066.i | 0.347421 | + | 0.365596i | ||||
\(796\) | −205968. | −0.325068 | ||||||||
\(797\) | 1.09025e6 | 1.71637 | 0.858184 | − | 0.513343i | \(-0.171593\pi\) | ||||
0.858184 | + | 0.513343i | \(0.171593\pi\) | |||||||
\(798\) | −113956. | − | 70672.4i | −0.178950 | − | 0.110980i | ||||
\(799\) | −680240. | −1.06554 | ||||||||
\(800\) | 392945. | + | 220583.i | 0.613976 | + | 0.344662i | ||||
\(801\) | −673920. | + | 334358.i | −1.05037 | + | 0.521131i | ||||
\(802\) | − | 777091.i | − | 1.20816i | ||||||
\(803\) | −408465. | −0.633467 | ||||||||
\(804\) | 118638. | + | 73576.2i | 0.183532 | + | 0.113822i | ||||
\(805\) | 153270. | + | 40078.3i | 0.236519 | + | 0.0618468i | ||||
\(806\) | − | 24767.3i | − | 0.0381248i | ||||||
\(807\) | 29968.9 | + | 18585.9i | 0.0460176 | + | 0.0285389i | ||||
\(808\) | − | 336535.i | − | 0.515475i | ||||||
\(809\) | − | 101004.i | − | 0.154327i | −0.997018 | − | 0.0771634i | \(-0.975414\pi\) | ||
0.997018 | − | 0.0771634i | \(-0.0245863\pi\) | |||||||
\(810\) | 320205. | + | 408057.i | 0.488044 | + | 0.621943i | ||||
\(811\) | −400948. | −0.609602 | −0.304801 | − | 0.952416i | \(-0.598590\pi\) | ||||
−0.304801 | + | 0.952416i | \(0.598590\pi\) | |||||||
\(812\) | 17759.4 | 0.0269349 | ||||||||
\(813\) | 318037. | − | 512819.i | 0.481167 | − | 0.775859i | ||||
\(814\) | 393120. | 0.593303 | ||||||||
\(815\) | −296359. | − | 77494.4i | −0.446173 | − | 0.116669i | ||||
\(816\) | −163680. | + | 263926.i | −0.245819 | + | 0.396371i | ||||
\(817\) | − | 796242.i | − | 1.19289i | ||||||
\(818\) | −110073. | −0.164502 | ||||||||
\(819\) | −134784. | − | 271666.i | −0.200942 | − | 0.405011i | ||||
\(820\) | 301860. | + | 78932.8i | 0.448929 | + | 0.117390i | ||||
\(821\) | − | 777895.i | − | 1.15408i | −0.816717 | − | 0.577038i | \(-0.804208\pi\) | ||
0.816717 | − | 0.577038i | \(-0.195792\pi\) | |||||||
\(822\) | −318947. | + | 514287.i | −0.472036 | + | 0.761136i | ||||
\(823\) | 218457.i | 0.322528i | 0.986911 | + | 0.161264i | \(0.0515570\pi\) | ||||
−0.986911 | + | 0.161264i | \(0.948443\pi\) | |||||||
\(824\) | − | 382054.i | − | 0.562692i | ||||||
\(825\) | 262885. | + | 476495.i | 0.386241 | + | 0.700085i | ||||
\(826\) | −191880. | −0.281235 | ||||||||
\(827\) | 460867. | 0.673852 | 0.336926 | − | 0.941531i | \(-0.390613\pi\) | ||||
0.336926 | + | 0.941531i | \(0.390613\pi\) | |||||||
\(828\) | 89479.8 | + | 180352.i | 0.130516 | + | 0.263064i | ||||
\(829\) | −60352.0 | −0.0878178 | −0.0439089 | − | 0.999036i | \(-0.513981\pi\) | ||||
−0.0439089 | + | 0.999036i | \(0.513981\pi\) | |||||||
\(830\) | 88733.5 | − | 339340.i | 0.128805 | − | 0.492583i | ||||
\(831\) | 79092.0 | + | 49050.8i | 0.114533 | + | 0.0710303i | ||||
\(832\) | 1.04363e6i | 1.50764i | ||||||||
\(833\) | −603034. | −0.869064 | ||||||||
\(834\) | −290580. | + | 468546.i | −0.417767 | + | 0.673628i | ||||
\(835\) | −15940.0 | + | 60958.8i | −0.0228621 | + | 0.0874306i | ||||
\(836\) | − | 178789.i | − | 0.255816i | ||||||
\(837\) | 23223.8 | + | 2202.78i | 0.0331499 | + | 0.00314427i | ||||
\(838\) | − | 693569.i | − | 0.987646i | ||||||
\(839\) | − | 162148.i | − | 0.230350i | −0.993345 | − | 0.115175i | \(-0.963257\pi\) | ||
0.993345 | − | 0.115175i | \(-0.0367429\pi\) | |||||||
\(840\) | −173576. | + | 164947.i | −0.245997 | + | 0.233768i | ||||
\(841\) | 669841. | 0.947065 | ||||||||
\(842\) | −534400. | −0.753775 | ||||||||
\(843\) | −170564. | − | 105779.i | −0.240011 | − | 0.148849i | ||||
\(844\) | 199608. | 0.280216 | ||||||||
\(845\) | 198231. | − | 758086.i | 0.277624 | − | 1.06171i | ||||
\(846\) | 278280. | + | 560891.i | 0.388813 | + | 0.783679i | ||||
\(847\) | − | 80783.8i | − | 0.112605i | ||||||
\(848\) | 175671. | 0.244291 | ||||||||
\(849\) | 898443. | + | 557191.i | 1.24645 | + | 0.773016i | ||||
\(850\) | −479600. | − | 269228.i | −0.663806 | − | 0.372634i | ||||
\(851\) | 532303.i | 0.735020i | ||||||||
\(852\) | −213112. | − | 132167.i | −0.293582 | − | 0.182072i | ||||
\(853\) | − | 1.27675e6i | − | 1.75472i | −0.479828 | − | 0.877362i | \(-0.659301\pi\) | ||
0.479828 | − | 0.877362i | \(-0.340699\pi\) | |||||||
\(854\) | − | 44890.7i | − | 0.0615517i | ||||||
\(855\) | 610667. | − | 126838.i | 0.835357 | − | 0.173507i | ||||
\(856\) | −203500. | −0.277726 | ||||||||
\(857\) | −311105. | −0.423589 | −0.211795 | − | 0.977314i | \(-0.567931\pi\) | ||||
−0.211795 | + | 0.977314i | \(0.567931\pi\) | |||||||
\(858\) | −355187. | + | 572722.i | −0.482484 | + | 0.777981i | ||||
\(859\) | 1.14631e6 | 1.55351 | 0.776757 | − | 0.629801i | \(-0.216863\pi\) | ||||
0.776757 | + | 0.629801i | \(0.216863\pi\) | |||||||
\(860\) | −375166. | − | 98101.6i | −0.507256 | − | 0.132641i | ||||
\(861\) | −150930. | + | 243367.i | −0.203596 | + | 0.328289i | ||||
\(862\) | 490118.i | 0.659608i | ||||||||
\(863\) | −640839. | −0.860453 | −0.430227 | − | 0.902721i | \(-0.641566\pi\) | ||||
−0.430227 | + | 0.902721i | \(0.641566\pi\) | |||||||
\(864\) | −523260. | − | 49631.3i | −0.700955 | − | 0.0664856i | ||||
\(865\) | −311920. | + | 1.19286e6i | −0.416880 | + | 1.59426i | ||||
\(866\) | 485864.i | 0.647857i | ||||||||
\(867\) | 28844.7 | − | 46510.7i | 0.0383732 | − | 0.0618749i | ||||
\(868\) | 2937.04i | 0.00389825i | ||||||||
\(869\) | 773.977i | 0.00102492i | ||||||||
\(870\) | 99798.9 | − | 94837.6i | 0.131852 | − | 0.125297i | ||||
\(871\) | −632736. | −0.834039 | ||||||||
\(872\) | −441909. | −0.581166 | ||||||||
\(873\) | 182033. | − | 90313.8i | 0.238848 | − | 0.118502i | ||||
\(874\) | −403480. | −0.528201 | ||||||||
\(875\) | −172044. | − | 165921.i | −0.224710 | − | 0.216713i | ||||
\(876\) | 193752. | + | 120160.i | 0.252486 | + | 0.156585i | ||||
\(877\) | 447959.i | 0.582424i | 0.956659 | + | 0.291212i | \(0.0940585\pi\) | ||||
−0.956659 | + | 0.291212i | \(0.905942\pi\) | |||||||
\(878\) | −206079. | −0.267329 | ||||||||
\(879\) | −272100. | + | 438748.i | −0.352169 | + | 0.567855i | ||||
\(880\) | 290160. | + | 75873.4i | 0.374690 | + | 0.0979770i | ||||
\(881\) | − | 72995.7i | − | 0.0940471i | −0.998894 | − | 0.0470235i | \(-0.985026\pi\) | ||
0.998894 | − | 0.0470235i | \(-0.0149736\pi\) | |||||||
\(882\) | 246696. | + | 497231.i | 0.317120 | + | 0.639177i | ||||
\(883\) | 797910.i | 1.02337i | 0.859173 | + | 0.511685i | \(0.170978\pi\) | ||||
−0.859173 | + | 0.511685i | \(0.829022\pi\) | |||||||
\(884\) | 408660.i | 0.522947i | ||||||||
\(885\) | 646963. | − | 614801.i | 0.826025 | − | 0.784961i | ||||
\(886\) | −368450. | −0.469365 | ||||||||
\(887\) | 1.04890e6 | 1.33317 | 0.666586 | − | 0.745428i | \(-0.267755\pi\) | ||||
0.666586 | + | 0.745428i | \(0.267755\pi\) | |||||||
\(888\) | −683735. | − | 424034.i | −0.867085 | − | 0.537744i | ||||
\(889\) | 58266.0 | 0.0737245 | ||||||||
\(890\) | −710374. | − | 185754.i | −0.896824 | − | 0.234509i | ||||
\(891\) | −505440. | − | 383989.i | −0.636670 | − | 0.483686i | ||||
\(892\) | 456067.i | 0.573190i | ||||||||
\(893\) | 752888. | 0.944120 | ||||||||
\(894\) | −391950. | − | 243077.i | −0.490406 | − | 0.304137i | ||||
\(895\) | −919620. | − | 240470.i | −1.14805 | − | 0.300203i | ||||
\(896\) | 29798.1i | 0.0371170i | ||||||||
\(897\) | −775492. | − | 480940.i | −0.963812 | − | 0.597731i | ||||
\(898\) | 250107.i | 0.310151i | ||||||||
\(899\) | − | 6191.81i | − | 0.00766123i | ||||||
\(900\) | 15475.1 | − | 303356.i | 0.0191051 | − | 0.374513i | ||||
\(901\) | 394240. | 0.485636 | ||||||||
\(902\) | 636377. | 0.782170 | ||||||||
\(903\) | 187583. | − | 302469.i | 0.230048 | − | 0.370941i | ||||
\(904\) | 616880. | 0.754856 | ||||||||
\(905\) | −128654. | + | 492007.i | −0.157082 | + | 0.600723i | ||||
\(906\) | 499080. | − | 804742.i | 0.608014 | − | 0.980394i | ||||
\(907\) | − | 1.06515e6i | − | 1.29478i | −0.762159 | − | 0.647390i | \(-0.775861\pi\) | ||
0.762159 | − | 0.647390i | \(-0.224139\pi\) | |||||||
\(908\) | −100731. | −0.122178 | ||||||||
\(909\) | −351000. | + | 174145.i | −0.424795 | + | 0.210757i | ||||
\(910\) | 74880.0 | − | 286361.i | 0.0904239 | − | 0.345805i | ||||
\(911\) | − | 1.25520e6i | − | 1.51243i | −0.654324 | − | 0.756215i | \(-0.727047\pi\) | ||
0.654324 | − | 0.756215i | \(-0.272953\pi\) | |||||||
\(912\) | 181161. | − | 292113.i | 0.217808 | − | 0.351205i | ||||
\(913\) | 429235.i | 0.514937i | ||||||||
\(914\) | 1.23140e6i | 1.47403i | ||||||||
\(915\) | 143834. | + | 151358.i | 0.171798 | + | 0.180786i | ||||
\(916\) | −241788. | −0.288167 | ||||||||
\(917\) | 122836. | 0.146078 | ||||||||
\(918\) | 638654. | + | 60576.4i | 0.757844 | + | 0.0718816i | ||||
\(919\) | 552368. | 0.654030 | 0.327015 | − | 0.945019i | \(-0.393957\pi\) | ||||
0.327015 | + | 0.945019i | \(0.393957\pi\) | |||||||
\(920\) | −182274. | + | 697063.i | −0.215352 | + | 0.823562i | ||||
\(921\) | 79677.0 | + | 49413.6i | 0.0939320 | + | 0.0582542i | ||||
\(922\) | − | 748332.i | − | 0.880304i | ||||||
\(923\) | 1.13660e6 | 1.33415 | ||||||||
\(924\) | 42120.0 | − | 67916.5i | 0.0493338 | − | 0.0795483i | ||||
\(925\) | 393120. | − | 700299.i | 0.459454 | − | 0.818465i | ||||
\(926\) | − | 802566.i | − | 0.935963i | ||||||
\(927\) | −398475. | + | 197699.i | −0.463705 | + | 0.230062i | ||||
\(928\) | 139509.i | 0.161997i | ||||||||
\(929\) | − | 748290.i | − | 0.867039i | −0.901144 | − | 0.433520i | \(-0.857271\pi\) | ||
0.901144 | − | 0.433520i | \(-0.142729\pi\) | |||||||
\(930\) | 15684.2 | + | 16504.7i | 0.0181341 | + | 0.0190828i | ||||
\(931\) | 667436. | 0.770035 | ||||||||
\(932\) | 523521. | 0.602702 | ||||||||
\(933\) | 779932. | + | 483693.i | 0.895969 | + | 0.555657i | ||||
\(934\) | 1.15693e6 | 1.32621 | ||||||||
\(935\) | 651176. | + | 170275.i | 0.744861 | + | 0.194772i | ||||
\(936\) | 1.23552e6 | − | 612990.i | 1.41026 | − | 0.699683i | ||||
\(937\) | − | 173102.i | − | 0.197161i | −0.995129 | − | 0.0985807i | \(-0.968570\pi\) | ||
0.995129 | − | 0.0985807i | \(-0.0314302\pi\) | |||||||
\(938\) | −125055. | −0.142134 | ||||||||
\(939\) | −1.39651e6 | − | 866080.i | −1.58385 | − | 0.982261i | ||||
\(940\) | 92760.0 | − | 354739.i | 0.104980 | − | 0.401470i | ||||
\(941\) | 1.74861e6i | 1.97475i | 0.158388 | + | 0.987377i | \(0.449370\pi\) | ||||
−0.158388 | + | 0.987377i | \(0.550630\pi\) | |||||||
\(942\) | −708894. | − | 439637.i | −0.798876 | − | 0.495442i | ||||
\(943\) | 861683.i | 0.969001i | ||||||||
\(944\) | − | 491862.i | − | 0.551950i | ||||||
\(945\) | 261855. | + | 95682.2i | 0.293223 | + | 0.107144i | ||||
\(946\) | −790920. | −0.883792 | ||||||||
\(947\) | −983427. | −1.09658 | −0.548292 | − | 0.836287i | \(-0.684722\pi\) | ||||
−0.548292 | + | 0.836287i | \(0.684722\pi\) | |||||||
\(948\) | 227.684 | − | 367.129i | 0.000253347 | − | 0.000408510i | ||||
\(949\) | −1.03334e6 | −1.14739 | ||||||||
\(950\) | 530820. | + | 297981.i | 0.588166 | + | 0.330173i | ||||
\(951\) | −158880. | + | 256186.i | −0.175674 | + | 0.283266i | ||||
\(952\) | 296151.i | 0.326768i | ||||||||
\(953\) | −894507. | −0.984913 | −0.492457 | − | 0.870337i | \(-0.663901\pi\) | ||||
−0.492457 | + | 0.870337i | \(0.663901\pi\) | |||||||
\(954\) | −161280. | − | 325070.i | −0.177208 | − | 0.357175i | ||||
\(955\) | −1.34316e6 | − | 351220.i | −1.47272 | − | 0.385100i | ||||
\(956\) | 531722.i | 0.581793i | ||||||||
\(957\) | −88796.8 | + | 143180.i | −0.0969557 | + | 0.156336i | ||||
\(958\) | 808297.i | 0.880724i | ||||||||
\(959\) | 325264.i | 0.353670i | ||||||||
\(960\) | −660891. | − | 695465.i | −0.717113 | − | 0.754628i | ||||
\(961\) | −922497. | −0.998891 | ||||||||
\(962\) | 994524. | 1.07464 | ||||||||
\(963\) | 105304. | + | 212247.i | 0.113551 | + | 0.228870i | ||||
\(964\) | −432912. | −0.465849 | ||||||||
\(965\) | −1.22688e6 | − | 320813.i | −1.31749 | − | 0.344507i | ||||
\(966\) | −153270. | − | 95054.0i | −0.164249 | − | 0.101863i | ||||
\(967\) | − | 811983.i | − | 0.868349i | −0.900829 | − | 0.434174i | \(-0.857040\pi\) | ||
0.900829 | − | 0.434174i | \(-0.142960\pi\) | |||||||
\(968\) | 367400. | 0.392092 | ||||||||
\(969\) | 406560. | − | 655558.i | 0.432989 | − | 0.698174i | ||||
\(970\) | 191880. | + | 50174.4i | 0.203932 | + | 0.0533259i | ||||
\(971\) | 333487.i | 0.353705i | 0.984237 | + | 0.176852i | \(0.0565915\pi\) | ||||
−0.984237 | + | 0.176852i | \(0.943409\pi\) | |||||||
\(972\) | 126792. | + | 330829.i | 0.134202 | + | 0.350164i | ||||
\(973\) | 296335.i | 0.313009i | ||||||||
\(974\) | 1.41014e6i | 1.48643i | ||||||||
\(975\) | 665053. | + | 1.20545e6i | 0.699596 | + | 1.26806i | ||||
\(976\) | 115072. | 0.120801 | ||||||||
\(977\) | −1.32479e6 | −1.38790 | −0.693951 | − | 0.720023i | \(-0.744131\pi\) | ||||
−0.693951 | + | 0.720023i | \(0.744131\pi\) | |||||||
\(978\) | 296359. | + | 183794.i | 0.309842 | + | 0.192156i | ||||
\(979\) | 898560. | 0.937522 | ||||||||
\(980\) | 82231.9 | − | 314476.i | 0.0856225 | − | 0.327443i | ||||
\(981\) | 228672. | + | 460903.i | 0.237616 | + | 0.478930i | ||||
\(982\) | 725387.i | 0.752223i | ||||||||
\(983\) | 815276. | 0.843719 | 0.421859 | − | 0.906661i | \(-0.361378\pi\) | ||||
0.421859 | + | 0.906661i | \(0.361378\pi\) | |||||||
\(984\) | −1.10682e6 | − | 686421.i | −1.14311 | − | 0.708925i | ||||
\(985\) | −182560. | + | 698158.i | −0.188163 | + | 0.719583i | ||||
\(986\) | − | 170275.i | − | 0.175145i | ||||||
\(987\) | 286000. | + | 177369.i | 0.293583 | + | 0.182073i | ||||
\(988\) | − | 452303.i | − | 0.463357i | ||||||
\(989\) | − | 1.07094e6i | − | 1.09490i | ||||||
\(990\) | −125990. | − | 606585.i | −0.128548 | − | 0.618901i | ||||
\(991\) | 1.57635e6 | 1.60511 | 0.802557 | − | 0.596575i | \(-0.203472\pi\) | ||||
0.802557 | + | 0.596575i | \(0.203472\pi\) | |||||||
\(992\) | −23072.0 | −0.0234456 | ||||||||
\(993\) | −968093. | + | 1.56100e6i | −0.981790 | + | 1.58309i | ||||
\(994\) | 224640. | 0.227360 | ||||||||
\(995\) | −217109. | + | 830284.i | −0.219297 | + | 0.838649i | ||||
\(996\) | 126270. | − | 203604.i | 0.127286 | − | 0.205243i | ||||
\(997\) | 128251.i | 0.129024i | 0.997917 | + | 0.0645118i | \(0.0205490\pi\) | ||||
−0.997917 | + | 0.0645118i | \(0.979451\pi\) | |||||||
\(998\) | −498843. | −0.500844 | ||||||||
\(999\) | −88452.0 | + | 932545.i | −0.0886292 | + | 0.934413i |
(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 | 15.5.d.c.14.2 | yes | 4 | |
3.2 | odd | 2 | inner | 15.5.d.c.14.4 | yes | 4 | |
4.3 | odd | 2 | 240.5.c.c.209.3 | 4 | |||
5.2 | odd | 4 | 75.5.c.h.26.2 | 4 | |||
5.3 | odd | 4 | 75.5.c.h.26.3 | 4 | |||
5.4 | even | 2 | inner | 15.5.d.c.14.3 | yes | 4 | |
12.11 | even | 2 | 240.5.c.c.209.1 | 4 | |||
15.2 | even | 4 | 75.5.c.h.26.4 | 4 | |||
15.8 | even | 4 | 75.5.c.h.26.1 | 4 | |||
15.14 | odd | 2 | inner | 15.5.d.c.14.1 | ✓ | 4 | |
20.19 | odd | 2 | 240.5.c.c.209.2 | 4 | |||
60.59 | even | 2 | 240.5.c.c.209.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.5.d.c.14.1 | ✓ | 4 | 15.14 | odd | 2 | inner | |
15.5.d.c.14.2 | yes | 4 | 1.1 | even | 1 | trivial | |
15.5.d.c.14.3 | yes | 4 | 5.4 | even | 2 | inner | |
15.5.d.c.14.4 | yes | 4 | 3.2 | odd | 2 | inner | |
75.5.c.h.26.1 | 4 | 15.8 | even | 4 | |||
75.5.c.h.26.2 | 4 | 5.2 | odd | 4 | |||
75.5.c.h.26.3 | 4 | 5.3 | odd | 4 | |||
75.5.c.h.26.4 | 4 | 15.2 | even | 4 | |||
240.5.c.c.209.1 | 4 | 12.11 | even | 2 | |||
240.5.c.c.209.2 | 4 | 20.19 | odd | 2 | |||
240.5.c.c.209.3 | 4 | 4.3 | odd | 2 | |||
240.5.c.c.209.4 | 4 | 60.59 | even | 2 |