Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,5,Mod(31,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.c (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: | \(6.20219778503\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + \cdots + 16777216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{4}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.9 | ||
Root | \(2.77114 + 0.566380i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.5.c.a.31.10 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.264404 | − | 3.99125i | 0.0661009 | − | 0.997813i | ||||
\(3\) | 5.19615i | 0.577350i | ||||||||
\(4\) | −15.8602 | − | 2.11060i | −0.991261 | − | 0.131913i | ||||
\(5\) | −11.1803 | −0.447214 | ||||||||
\(6\) | 20.7392 | + | 1.37388i | 0.576088 | + | 0.0381634i | ||||
\(7\) | 29.5855i | 0.603786i | 0.953342 | + | 0.301893i | \(0.0976185\pi\) | ||||
−0.953342 | + | 0.301893i | \(0.902382\pi\) | |||||||
\(8\) | −12.6174 | + | 62.7439i | −0.197148 | + | 0.980374i | ||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | −2.95612 | + | 44.6236i | −0.0295612 | + | 0.446236i | ||||
\(11\) | 210.571i | 1.74026i | 0.492825 | + | 0.870128i | \(0.335964\pi\) | ||||
−0.492825 | + | 0.870128i | \(0.664036\pi\) | |||||||
\(12\) | 10.9670 | − | 82.4119i | 0.0761599 | − | 0.572305i | ||||
\(13\) | −135.726 | −0.803115 | −0.401558 | − | 0.915834i | \(-0.631531\pi\) | ||||
−0.401558 | + | 0.915834i | \(0.631531\pi\) | |||||||
\(14\) | 118.083 | + | 7.82252i | 0.602465 | + | 0.0399108i | ||||
\(15\) | − | 58.0948i | − | 0.258199i | ||||||
\(16\) | 247.091 | + | 66.9491i | 0.965198 | + | 0.261520i | ||||
\(17\) | −7.65200 | −0.0264775 | −0.0132387 | − | 0.999912i | \(-0.504214\pi\) | ||||
−0.0132387 | + | 0.999912i | \(0.504214\pi\) | |||||||
\(18\) | −7.13890 | + | 107.764i | −0.0220336 | + | 0.332604i | ||||
\(19\) | − | 166.741i | − | 0.461887i | −0.972967 | − | 0.230943i | \(-0.925819\pi\) | ||
0.972967 | − | 0.230943i | \(-0.0741812\pi\) | |||||||
\(20\) | 177.322 | + | 23.5973i | 0.443306 | + | 0.0589932i | ||||
\(21\) | −153.731 | −0.348596 | ||||||||
\(22\) | 840.442 | + | 55.6758i | 1.73645 | + | 0.115033i | ||||
\(23\) | 405.405i | 0.766361i | 0.923674 | + | 0.383180i | \(0.125171\pi\) | ||||
−0.923674 | + | 0.383180i | \(0.874829\pi\) | |||||||
\(24\) | −326.027 | − | 65.5622i | −0.566019 | − | 0.113823i | ||||
\(25\) | 125.000 | 0.200000 | ||||||||
\(26\) | −35.8866 | + | 541.718i | −0.0530867 | + | 0.801359i | ||||
\(27\) | − | 140.296i | − | 0.192450i | ||||||
\(28\) | 62.4433 | − | 469.231i | 0.0796470 | − | 0.598509i | ||||
\(29\) | −1646.13 | −1.95734 | −0.978672 | − | 0.205431i | \(-0.934140\pi\) | ||||
−0.978672 | + | 0.205431i | \(0.934140\pi\) | |||||||
\(30\) | −231.871 | − | 15.3605i | −0.257634 | − | 0.0170672i | ||||
\(31\) | − | 1179.57i | − | 1.22744i | −0.789525 | − | 0.613718i | \(-0.789673\pi\) | ||
0.789525 | − | 0.613718i | \(-0.210327\pi\) | |||||||
\(32\) | 332.543 | − | 968.500i | 0.324749 | − | 0.945800i | ||||
\(33\) | −1094.16 | −1.00474 | ||||||||
\(34\) | −2.02322 | + | 30.5410i | −0.00175019 | + | 0.0264196i | ||||
\(35\) | − | 330.776i | − | 0.270021i | ||||||
\(36\) | 428.225 | + | 56.9863i | 0.330420 | + | 0.0439709i | ||||
\(37\) | 605.018 | 0.441941 | 0.220971 | − | 0.975280i | \(-0.429077\pi\) | ||||
0.220971 | + | 0.975280i | \(0.429077\pi\) | |||||||
\(38\) | −665.506 | − | 44.0870i | −0.460877 | − | 0.0305312i | ||||
\(39\) | − | 705.255i | − | 0.463679i | ||||||
\(40\) | 141.067 | − | 701.498i | 0.0881671 | − | 0.438437i | ||||
\(41\) | −1498.18 | −0.891243 | −0.445621 | − | 0.895222i | \(-0.647017\pi\) | ||||
−0.445621 | + | 0.895222i | \(0.647017\pi\) | |||||||
\(42\) | −40.6470 | + | 613.578i | −0.0230425 | + | 0.347833i | ||||
\(43\) | 1511.90i | 0.817683i | 0.912605 | + | 0.408842i | \(0.134067\pi\) | ||||
−0.912605 | + | 0.408842i | \(0.865933\pi\) | |||||||
\(44\) | 444.432 | − | 3339.69i | 0.229562 | − | 1.72505i | ||||
\(45\) | 301.869 | 0.149071 | ||||||||
\(46\) | 1618.07 | + | 107.191i | 0.764685 | + | 0.0506572i | ||||
\(47\) | 1880.00i | 0.851066i | 0.904943 | + | 0.425533i | \(0.139913\pi\) | ||||
−0.904943 | + | 0.425533i | \(0.860087\pi\) | |||||||
\(48\) | −347.878 | + | 1283.92i | −0.150989 | + | 0.557257i | ||||
\(49\) | 1525.70 | 0.635443 | ||||||||
\(50\) | 33.0505 | − | 498.906i | 0.0132202 | − | 0.199563i | ||||
\(51\) | − | 39.7609i | − | 0.0152868i | ||||||
\(52\) | 2152.65 | + | 286.465i | 0.796097 | + | 0.105941i | ||||
\(53\) | 4955.24 | 1.76406 | 0.882029 | − | 0.471194i | \(-0.156177\pi\) | ||||
0.882029 | + | 0.471194i | \(0.156177\pi\) | |||||||
\(54\) | −559.957 | − | 37.0948i | −0.192029 | − | 0.0127211i | ||||
\(55\) | − | 2354.26i | − | 0.778266i | ||||||
\(56\) | −1856.31 | − | 373.293i | −0.591936 | − | 0.119035i | ||||
\(57\) | 866.413 | 0.266671 | ||||||||
\(58\) | −435.242 | + | 6570.10i | −0.129382 | + | 1.95306i | ||||
\(59\) | − | 500.976i | − | 0.143917i | −0.997408 | − | 0.0719587i | \(-0.977075\pi\) | ||
0.997408 | − | 0.0719587i | \(-0.0229250\pi\) | |||||||
\(60\) | −122.615 | + | 921.393i | −0.0340597 | + | 0.255943i | ||||
\(61\) | −928.887 | −0.249634 | −0.124817 | − | 0.992180i | \(-0.539834\pi\) | ||||
−0.124817 | + | 0.992180i | \(0.539834\pi\) | |||||||
\(62\) | −4707.95 | − | 311.882i | −1.22475 | − | 0.0811347i | ||||
\(63\) | − | 798.809i | − | 0.201262i | ||||||
\(64\) | −3777.60 | − | 1583.34i | −0.922266 | − | 0.386557i | ||||
\(65\) | 1517.47 | 0.359164 | ||||||||
\(66\) | −289.300 | + | 4367.06i | −0.0664141 | + | 1.00254i | ||||
\(67\) | 3041.07i | 0.677450i | 0.940885 | + | 0.338725i | \(0.109996\pi\) | ||||
−0.940885 | + | 0.338725i | \(0.890004\pi\) | |||||||
\(68\) | 121.362 | + | 16.1503i | 0.0262461 | + | 0.00349272i | ||||
\(69\) | −2106.55 | −0.442459 | ||||||||
\(70\) | −1320.21 | − | 87.4584i | −0.269431 | − | 0.0178487i | ||||
\(71\) | 6963.76i | 1.38143i | 0.723129 | + | 0.690713i | \(0.242703\pi\) | ||||
−0.723129 | + | 0.690713i | \(0.757297\pi\) | |||||||
\(72\) | 340.671 | − | 1694.09i | 0.0657159 | − | 0.326791i | ||||
\(73\) | 7810.56 | 1.46567 | 0.732835 | − | 0.680406i | \(-0.238197\pi\) | ||||
0.732835 | + | 0.680406i | \(0.238197\pi\) | |||||||
\(74\) | 159.969 | − | 2414.78i | 0.0292127 | − | 0.440975i | ||||
\(75\) | 649.519i | 0.115470i | ||||||||
\(76\) | −351.925 | + | 2644.55i | −0.0609288 | + | 0.457851i | ||||
\(77\) | −6229.85 | −1.05074 | ||||||||
\(78\) | −2814.85 | − | 186.472i | −0.462665 | − | 0.0306496i | ||||
\(79\) | − | 9433.20i | − | 1.51149i | −0.654867 | − | 0.755744i | \(-0.727275\pi\) | ||
0.654867 | − | 0.755744i | \(-0.272725\pi\) | |||||||
\(80\) | −2762.56 | − | 748.514i | −0.431650 | − | 0.116955i | ||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | −396.124 | + | 5979.61i | −0.0589120 | + | 0.889293i | ||||
\(83\) | 9487.99i | 1.37727i | 0.725110 | + | 0.688633i | \(0.241789\pi\) | ||||
−0.725110 | + | 0.688633i | \(0.758211\pi\) | |||||||
\(84\) | 2438.20 | + | 324.465i | 0.345550 | + | 0.0459842i | ||||
\(85\) | 85.5519 | 0.0118411 | ||||||||
\(86\) | 6034.36 | + | 399.751i | 0.815895 | + | 0.0540496i | ||||
\(87\) | − | 8553.52i | − | 1.13007i | ||||||
\(88\) | −13212.1 | − | 2656.87i | −1.70610 | − | 0.343087i | ||||
\(89\) | 13795.1 | 1.74159 | 0.870794 | − | 0.491648i | \(-0.163605\pi\) | ||||
0.870794 | + | 0.491648i | \(0.163605\pi\) | |||||||
\(90\) | 79.8154 | − | 1204.84i | 0.00985375 | − | 0.148745i | ||||
\(91\) | − | 4015.54i | − | 0.484909i | ||||||
\(92\) | 855.649 | − | 6429.79i | 0.101093 | − | 0.759664i | ||||
\(93\) | 6129.21 | 0.708661 | ||||||||
\(94\) | 7503.57 | + | 497.080i | 0.849204 | + | 0.0562562i | ||||
\(95\) | 1864.22i | 0.206562i | ||||||||
\(96\) | 5032.47 | + | 1727.94i | 0.546058 | + | 0.187494i | ||||
\(97\) | −7695.33 | −0.817869 | −0.408934 | − | 0.912564i | \(-0.634100\pi\) | ||||
−0.408934 | + | 0.912564i | \(0.634100\pi\) | |||||||
\(98\) | 403.400 | − | 6089.45i | 0.0420034 | − | 0.634053i | ||||
\(99\) | − | 5685.42i | − | 0.580085i | ||||||
\(100\) | −1982.52 | − | 263.826i | −0.198252 | − | 0.0263826i | ||||
\(101\) | −4743.34 | −0.464988 | −0.232494 | − | 0.972598i | \(-0.574689\pi\) | ||||
−0.232494 | + | 0.972598i | \(0.574689\pi\) | |||||||
\(102\) | −158.696 | − | 10.5129i | −0.0152534 | − | 0.00101047i | ||||
\(103\) | − | 549.159i | − | 0.0517635i | −0.999665 | − | 0.0258818i | \(-0.991761\pi\) | ||
0.999665 | − | 0.0258818i | \(-0.00823934\pi\) | |||||||
\(104\) | 1712.52 | − | 8516.01i | 0.158332 | − | 0.787353i | ||||
\(105\) | 1718.76 | 0.155897 | ||||||||
\(106\) | 1310.18 | − | 19777.6i | 0.116606 | − | 1.76020i | ||||
\(107\) | 1692.83i | 0.147859i | 0.997263 | + | 0.0739293i | \(0.0235539\pi\) | ||||
−0.997263 | + | 0.0739293i | \(0.976446\pi\) | |||||||
\(108\) | −296.110 | + | 2225.12i | −0.0253866 | + | 0.190768i | ||||
\(109\) | −15885.9 | −1.33708 | −0.668542 | − | 0.743674i | \(-0.733081\pi\) | ||||
−0.668542 | + | 0.743674i | \(0.733081\pi\) | |||||||
\(110\) | −9396.43 | − | 622.474i | −0.776564 | − | 0.0514441i | ||||
\(111\) | 3143.76i | 0.255155i | ||||||||
\(112\) | −1980.72 | + | 7310.30i | −0.157902 | + | 0.582773i | ||||
\(113\) | 8839.42 | 0.692256 | 0.346128 | − | 0.938187i | \(-0.387496\pi\) | ||||
0.346128 | + | 0.938187i | \(0.387496\pi\) | |||||||
\(114\) | 229.083 | − | 3458.07i | 0.0176272 | − | 0.266087i | ||||
\(115\) | − | 4532.56i | − | 0.342727i | ||||||
\(116\) | 26107.8 | + | 3474.32i | 1.94024 | + | 0.258199i | ||||
\(117\) | 3664.61 | 0.267705 | ||||||||
\(118\) | −1999.52 | − | 132.460i | −0.143603 | − | 0.00951308i | ||||
\(119\) | − | 226.388i | − | 0.0159867i | ||||||
\(120\) | 3645.09 | + | 733.007i | 0.253131 | + | 0.0509033i | ||||
\(121\) | −29699.2 | −2.02849 | ||||||||
\(122\) | −245.601 | + | 3707.42i | −0.0165010 | + | 0.249088i | ||||
\(123\) | − | 7784.76i | − | 0.514559i | ||||||
\(124\) | −2489.60 | + | 18708.1i | −0.161915 | + | 1.21671i | ||||
\(125\) | −1397.54 | −0.0894427 | ||||||||
\(126\) | −3188.25 | − | 211.208i | −0.200822 | − | 0.0133036i | ||||
\(127\) | 2789.62i | 0.172957i | 0.996254 | + | 0.0864784i | \(0.0275614\pi\) | ||||
−0.996254 | + | 0.0864784i | \(0.972439\pi\) | |||||||
\(128\) | −7318.30 | + | 14658.7i | −0.446674 | + | 0.894697i | ||||
\(129\) | −7856.04 | −0.472090 | ||||||||
\(130\) | 401.224 | − | 6056.60i | 0.0237411 | − | 0.358379i | ||||
\(131\) | 11818.8i | 0.688701i | 0.938841 | + | 0.344350i | \(0.111901\pi\) | ||||
−0.938841 | + | 0.344350i | \(0.888099\pi\) | |||||||
\(132\) | 17353.6 | + | 2309.34i | 0.995957 | + | 0.132538i | ||||
\(133\) | 4933.12 | 0.278881 | ||||||||
\(134\) | 12137.7 | + | 804.071i | 0.675969 | + | 0.0447801i | ||||
\(135\) | 1568.56i | 0.0860663i | ||||||||
\(136\) | 96.5486 | − | 480.116i | 0.00521997 | − | 0.0259578i | ||||
\(137\) | −29908.7 | −1.59352 | −0.796759 | − | 0.604297i | \(-0.793454\pi\) | ||||
−0.796759 | + | 0.604297i | \(0.793454\pi\) | |||||||
\(138\) | −556.978 | + | 8407.75i | −0.0292469 | + | 0.441491i | ||||
\(139\) | 23947.7i | 1.23947i | 0.784812 | + | 0.619733i | \(0.212759\pi\) | ||||
−0.784812 | + | 0.619733i | \(0.787241\pi\) | |||||||
\(140\) | −698.137 | + | 5246.17i | −0.0356192 | + | 0.267662i | ||||
\(141\) | −9768.79 | −0.491363 | ||||||||
\(142\) | 27794.1 | + | 1841.25i | 1.37840 | + | 0.0913135i | ||||
\(143\) | − | 28580.1i | − | 1.39763i | ||||||
\(144\) | −6671.45 | − | 1807.63i | −0.321733 | − | 0.0871733i | ||||
\(145\) | 18404.2 | 0.875350 | ||||||||
\(146\) | 2065.14 | − | 31173.9i | 0.0968822 | − | 1.46246i | ||||
\(147\) | 7927.76i | 0.366873i | ||||||||
\(148\) | −9595.69 | − | 1276.95i | −0.438079 | − | 0.0582977i | ||||
\(149\) | −4438.67 | −0.199931 | −0.0999656 | − | 0.994991i | \(-0.531873\pi\) | ||||
−0.0999656 | + | 0.994991i | \(0.531873\pi\) | |||||||
\(150\) | 2592.39 | + | 171.735i | 0.115218 | + | 0.00763268i | ||||
\(151\) | − | 7753.12i | − | 0.340034i | −0.985441 | − | 0.170017i | \(-0.945618\pi\) | ||
0.985441 | − | 0.170017i | \(-0.0543823\pi\) | |||||||
\(152\) | 10462.0 | + | 2103.85i | 0.452822 | + | 0.0910599i | ||||
\(153\) | 206.604 | 0.00882583 | ||||||||
\(154\) | −1647.20 | + | 24864.9i | −0.0694550 | + | 1.04844i | ||||
\(155\) | 13188.0i | 0.548926i | ||||||||
\(156\) | −1488.51 | + | 11185.5i | −0.0611651 | + | 0.459627i | ||||
\(157\) | 29000.7 | 1.17655 | 0.588273 | − | 0.808662i | \(-0.299808\pi\) | ||||
0.588273 | + | 0.808662i | \(0.299808\pi\) | |||||||
\(158\) | −37650.3 | − | 2494.17i | −1.50818 | − | 0.0999108i | ||||
\(159\) | 25748.2i | 1.01848i | ||||||||
\(160\) | −3717.94 | + | 10828.2i | −0.145232 | + | 0.422975i | ||||
\(161\) | −11994.1 | −0.462718 | ||||||||
\(162\) | 192.750 | − | 2909.62i | 0.00734455 | − | 0.110868i | ||||
\(163\) | 14916.0i | 0.561406i | 0.959795 | + | 0.280703i | \(0.0905676\pi\) | ||||
−0.959795 | + | 0.280703i | \(0.909432\pi\) | |||||||
\(164\) | 23761.4 | + | 3162.06i | 0.883454 | + | 0.117566i | ||||
\(165\) | 12233.1 | 0.449332 | ||||||||
\(166\) | 37868.9 | + | 2508.66i | 1.37425 | + | 0.0910386i | ||||
\(167\) | − | 26694.7i | − | 0.957178i | −0.878039 | − | 0.478589i | \(-0.841148\pi\) | ||
0.878039 | − | 0.478589i | \(-0.158852\pi\) | |||||||
\(168\) | 1939.69 | − | 9645.67i | 0.0687248 | − | 0.341754i | ||||
\(169\) | −10139.3 | −0.355006 | ||||||||
\(170\) | 22.6203 | − | 341.459i | 0.000782708 | − | 0.0118152i | ||||
\(171\) | 4502.01i | 0.153962i | ||||||||
\(172\) | 3191.01 | − | 23979.0i | 0.107863 | − | 0.810538i | ||||
\(173\) | 41306.9 | 1.38016 | 0.690082 | − | 0.723731i | \(-0.257574\pi\) | ||||
0.690082 | + | 0.723731i | \(0.257574\pi\) | |||||||
\(174\) | −34139.2 | − | 2261.58i | −1.12760 | − | 0.0746989i | ||||
\(175\) | 3698.19i | 0.120757i | ||||||||
\(176\) | −14097.5 | + | 52030.1i | −0.455112 | + | 1.67969i | ||||
\(177\) | 2603.15 | 0.0830907 | ||||||||
\(178\) | 3647.48 | − | 55059.8i | 0.115121 | − | 1.73778i | ||||
\(179\) | 30792.3i | 0.961029i | 0.876987 | + | 0.480515i | \(0.159550\pi\) | ||||
−0.876987 | + | 0.480515i | \(0.840450\pi\) | |||||||
\(180\) | −4787.70 | − | 637.126i | −0.147769 | − | 0.0196644i | ||||
\(181\) | −5864.01 | −0.178994 | −0.0894968 | − | 0.995987i | \(-0.528526\pi\) | ||||
−0.0894968 | + | 0.995987i | \(0.528526\pi\) | |||||||
\(182\) | −16027.0 | − | 1061.72i | −0.483849 | − | 0.0320530i | ||||
\(183\) | − | 4826.64i | − | 0.144126i | ||||||
\(184\) | −25436.7 | − | 5115.17i | −0.751320 | − | 0.151086i | ||||
\(185\) | −6764.31 | −0.197642 | ||||||||
\(186\) | 1620.59 | − | 24463.2i | 0.0468432 | − | 0.707111i | ||||
\(187\) | − | 1611.29i | − | 0.0460776i | ||||||
\(188\) | 3967.94 | − | 29817.2i | 0.112266 | − | 0.843629i | ||||
\(189\) | 4150.73 | 0.116199 | ||||||||
\(190\) | 7440.58 | + | 492.908i | 0.206110 | + | 0.0136540i | ||||
\(191\) | − | 69081.5i | − | 1.89363i | −0.321777 | − | 0.946815i | \(-0.604280\pi\) | ||
0.321777 | − | 0.946815i | \(-0.395720\pi\) | |||||||
\(192\) | 8227.26 | − | 19629.0i | 0.223179 | − | 0.532470i | ||||
\(193\) | 38834.2 | 1.04256 | 0.521279 | − | 0.853387i | \(-0.325455\pi\) | ||||
0.521279 | + | 0.853387i | \(0.325455\pi\) | |||||||
\(194\) | −2034.67 | + | 30714.0i | −0.0540619 | + | 0.816080i | ||||
\(195\) | 7884.99i | 0.207363i | ||||||||
\(196\) | −24197.8 | − | 3220.14i | −0.629890 | − | 0.0838230i | ||||
\(197\) | −26569.0 | −0.684608 | −0.342304 | − | 0.939589i | \(-0.611207\pi\) | ||||
−0.342304 | + | 0.939589i | \(0.611207\pi\) | |||||||
\(198\) | −22691.9 | − | 1503.25i | −0.578817 | − | 0.0383442i | ||||
\(199\) | − | 59241.5i | − | 1.49596i | −0.663721 | − | 0.747980i | \(-0.731024\pi\) | ||
0.663721 | − | 0.747980i | \(-0.268976\pi\) | |||||||
\(200\) | −1577.18 | + | 7842.99i | −0.0394295 | + | 0.196075i | ||||
\(201\) | −15801.9 | −0.391126 | ||||||||
\(202\) | −1254.16 | + | 18931.9i | −0.0307361 | + | 0.463971i | ||||
\(203\) | − | 48701.4i | − | 1.18182i | ||||||
\(204\) | −83.9196 | + | 630.616i | −0.00201652 | + | 0.0151532i | ||||
\(205\) | 16750.1 | 0.398576 | ||||||||
\(206\) | −2191.83 | − | 145.200i | −0.0516503 | − | 0.00342162i | ||||
\(207\) | − | 10945.9i | − | 0.255454i | ||||||
\(208\) | −33536.7 | − | 9086.77i | −0.775165 | − | 0.210031i | ||||
\(209\) | 35110.9 | 0.803802 | ||||||||
\(210\) | 454.447 | − | 6860.01i | 0.0103049 | − | 0.155556i | ||||
\(211\) | 52946.2i | 1.18924i | 0.804007 | + | 0.594620i | \(0.202698\pi\) | ||||
−0.804007 | + | 0.594620i | \(0.797302\pi\) | |||||||
\(212\) | −78591.0 | − | 10458.6i | −1.74864 | − | 0.232702i | ||||
\(213\) | −36184.8 | −0.797566 | ||||||||
\(214\) | 6756.52 | + | 447.591i | 0.147535 | + | 0.00977359i | ||||
\(215\) | − | 16903.5i | − | 0.365679i | ||||||
\(216\) | 8802.73 | + | 1770.18i | 0.188673 | + | 0.0379411i | ||||
\(217\) | 34898.1 | 0.741109 | ||||||||
\(218\) | −4200.29 | + | 63404.6i | −0.0883825 | + | 1.33416i | ||||
\(219\) | 40584.8i | 0.846205i | ||||||||
\(220\) | −4968.90 | + | 37338.9i | −0.102663 | + | 0.771465i | ||||
\(221\) | 1038.58 | 0.0212645 | ||||||||
\(222\) | 12547.6 | + | 831.223i | 0.254597 | + | 0.0168660i | ||||
\(223\) | 12221.6i | 0.245764i | 0.992421 | + | 0.122882i | \(0.0392137\pi\) | ||||
−0.992421 | + | 0.122882i | \(0.960786\pi\) | |||||||
\(224\) | 28653.5 | + | 9838.44i | 0.571061 | + | 0.196079i | ||||
\(225\) | −3375.00 | −0.0666667 | ||||||||
\(226\) | 2337.17 | − | 35280.3i | 0.0457588 | − | 0.690742i | ||||
\(227\) | 52981.1i | 1.02818i | 0.857736 | + | 0.514090i | \(0.171870\pi\) | ||||
−0.857736 | + | 0.514090i | \(0.828130\pi\) | |||||||
\(228\) | −13741.5 | − | 1828.65i | −0.264340 | − | 0.0351772i | ||||
\(229\) | 26289.4 | 0.501315 | 0.250657 | − | 0.968076i | \(-0.419353\pi\) | ||||
0.250657 | + | 0.968076i | \(0.419353\pi\) | |||||||
\(230\) | −18090.6 | − | 1198.43i | −0.341977 | − | 0.0226546i | ||||
\(231\) | − | 32371.2i | − | 0.606646i | ||||||
\(232\) | 20769.9 | − | 103284.i | 0.385885 | − | 1.91893i | ||||
\(233\) | 37894.8 | 0.698020 | 0.349010 | − | 0.937119i | \(-0.386518\pi\) | ||||
0.349010 | + | 0.937119i | \(0.386518\pi\) | |||||||
\(234\) | 968.938 | − | 14626.4i | 0.0176956 | − | 0.267120i | ||||
\(235\) | − | 21019.1i | − | 0.380608i | ||||||
\(236\) | −1057.36 | + | 7945.58i | −0.0189845 | + | 0.142660i | ||||
\(237\) | 49016.3 | 0.872658 | ||||||||
\(238\) | −903.572 | − | 59.8579i | −0.0159518 | − | 0.00105674i | ||||
\(239\) | 7490.41i | 0.131132i | 0.997848 | + | 0.0655662i | \(0.0208853\pi\) | ||||
−0.997848 | + | 0.0655662i | \(0.979115\pi\) | |||||||
\(240\) | 3889.39 | − | 14354.7i | 0.0675242 | − | 0.249213i | ||||
\(241\) | 76034.4 | 1.30911 | 0.654555 | − | 0.756014i | \(-0.272856\pi\) | ||||
0.654555 | + | 0.756014i | \(0.272856\pi\) | |||||||
\(242\) | −7852.57 | + | 118537.i | −0.134085 | + | 2.02406i | ||||
\(243\) | 3788.00i | 0.0641500i | ||||||||
\(244\) | 14732.3 | + | 1960.51i | 0.247452 | + | 0.0329299i | ||||
\(245\) | −17057.8 | −0.284179 | ||||||||
\(246\) | −31071.0 | − | 2058.32i | −0.513434 | − | 0.0340128i | ||||
\(247\) | 22631.2i | 0.370948i | ||||||||
\(248\) | 74010.6 | + | 14883.1i | 1.20335 | + | 0.241986i | ||||
\(249\) | −49301.0 | −0.795165 | ||||||||
\(250\) | −369.516 | + | 5577.94i | −0.00591225 | + | 0.0892471i | ||||
\(251\) | − | 40829.4i | − | 0.648076i | −0.946044 | − | 0.324038i | \(-0.894959\pi\) | ||
0.946044 | − | 0.324038i | \(-0.105041\pi\) | |||||||
\(252\) | −1685.97 | + | 12669.2i | −0.0265490 | + | 0.199503i | ||||
\(253\) | −85366.5 | −1.33366 | ||||||||
\(254\) | 11134.1 | + | 737.587i | 0.172579 | + | 0.0114326i | ||||
\(255\) | 444.541i | 0.00683646i | ||||||||
\(256\) | 56571.6 | + | 33085.0i | 0.863215 | + | 0.504837i | ||||
\(257\) | −89298.5 | −1.35200 | −0.676002 | − | 0.736900i | \(-0.736289\pi\) | ||||
−0.676002 | + | 0.736900i | \(0.736289\pi\) | |||||||
\(258\) | −2077.17 | + | 31355.5i | −0.0312056 | + | 0.471057i | ||||
\(259\) | 17899.8i | 0.266838i | ||||||||
\(260\) | −24067.3 | − | 3202.77i | −0.356025 | − | 0.0473783i | ||||
\(261\) | 44445.4 | 0.652448 | ||||||||
\(262\) | 47171.8 | + | 3124.93i | 0.687195 | + | 0.0455238i | ||||
\(263\) | − | 9881.37i | − | 0.142858i | −0.997446 | − | 0.0714292i | \(-0.977244\pi\) | ||
0.997446 | − | 0.0714292i | \(-0.0227560\pi\) | |||||||
\(264\) | 13805.5 | − | 68651.8i | 0.198082 | − | 0.985018i | ||||
\(265\) | −55401.3 | −0.788911 | ||||||||
\(266\) | 1304.34 | − | 19689.3i | 0.0184343 | − | 0.278271i | ||||
\(267\) | 71681.5i | 1.00551i | ||||||||
\(268\) | 6418.50 | − | 48232.0i | 0.0893643 | − | 0.671530i | ||||
\(269\) | 106250. | 1.46833 | 0.734163 | − | 0.678974i | \(-0.237575\pi\) | ||||
0.734163 | + | 0.678974i | \(0.237575\pi\) | |||||||
\(270\) | 6260.51 | + | 414.733i | 0.0858781 | + | 0.00568906i | ||||
\(271\) | 64500.8i | 0.878267i | 0.898422 | + | 0.439133i | \(0.144714\pi\) | ||||
−0.898422 | + | 0.439133i | \(0.855286\pi\) | |||||||
\(272\) | −1890.74 | − | 512.294i | −0.0255560 | − | 0.00692440i | ||||
\(273\) | 20865.3 | 0.279963 | ||||||||
\(274\) | −7907.98 | + | 119373.i | −0.105333 | + | 1.59003i | ||||
\(275\) | 26321.4i | 0.348051i | ||||||||
\(276\) | 33410.2 | + | 4446.08i | 0.438592 | + | 0.0583659i | ||||
\(277\) | −99154.8 | −1.29227 | −0.646136 | − | 0.763222i | \(-0.723616\pi\) | ||||
−0.646136 | + | 0.763222i | \(0.723616\pi\) | |||||||
\(278\) | 95581.5 | + | 6331.87i | 1.23676 | + | 0.0819299i | ||||
\(279\) | 31848.3i | 0.409146i | ||||||||
\(280\) | 20754.2 | + | 4173.55i | 0.264722 | + | 0.0532340i | ||||
\(281\) | −53023.5 | −0.671515 | −0.335758 | − | 0.941948i | \(-0.608992\pi\) | ||||
−0.335758 | + | 0.941948i | \(0.608992\pi\) | |||||||
\(282\) | −2582.90 | + | 38989.7i | −0.0324796 | + | 0.490288i | ||||
\(283\) | 135026.i | 1.68596i | 0.537949 | + | 0.842978i | \(0.319199\pi\) | ||||
−0.537949 | + | 0.842978i | \(0.680801\pi\) | |||||||
\(284\) | 14697.8 | − | 110447.i | 0.182228 | − | 1.36935i | ||||
\(285\) | −9686.79 | −0.119259 | ||||||||
\(286\) | −114070. | − | 7556.68i | −1.39457 | − | 0.0923844i | ||||
\(287\) | − | 44324.4i | − | 0.538120i | ||||||
\(288\) | −8978.65 | + | 26149.5i | −0.108250 | + | 0.315267i | ||||
\(289\) | −83462.4 | −0.999299 | ||||||||
\(290\) | 4866.15 | − | 73456.0i | 0.0578615 | − | 0.873436i | ||||
\(291\) | − | 39986.1i | − | 0.472197i | ||||||
\(292\) | −123877. | − | 16485.0i | −1.45286 | − | 0.193341i | ||||
\(293\) | −133739. | −1.55784 | −0.778922 | − | 0.627120i | \(-0.784233\pi\) | ||||
−0.778922 | + | 0.627120i | \(0.784233\pi\) | |||||||
\(294\) | 31641.7 | + | 2096.13i | 0.366071 | + | 0.0242507i | ||||
\(295\) | 5601.09i | 0.0643618i | ||||||||
\(296\) | −7633.78 | + | 37961.2i | −0.0871277 | + | 0.433268i | ||||
\(297\) | 29542.3 | 0.334913 | ||||||||
\(298\) | −1173.60 | + | 17715.9i | −0.0132156 | + | 0.199494i | ||||
\(299\) | − | 55024.2i | − | 0.615476i | ||||||
\(300\) | 1370.88 | − | 10301.5i | 0.0152320 | − | 0.114461i | ||||
\(301\) | −44730.2 | −0.493706 | ||||||||
\(302\) | −30944.7 | − | 2049.96i | −0.339291 | − | 0.0224766i | ||||
\(303\) | − | 24647.1i | − | 0.268461i | ||||||
\(304\) | 11163.2 | − | 41200.2i | 0.120793 | − | 0.445812i | ||||
\(305\) | 10385.3 | 0.111640 | ||||||||
\(306\) | 54.6269 | − | 824.608i | 0.000583396 | − | 0.00880653i | ||||
\(307\) | − | 125386.i | − | 1.33037i | −0.746678 | − | 0.665185i | \(-0.768353\pi\) | ||
0.746678 | − | 0.665185i | \(-0.231647\pi\) | |||||||
\(308\) | 98806.5 | + | 13148.7i | 1.04156 | + | 0.138606i | ||||
\(309\) | 2853.51 | 0.0298857 | ||||||||
\(310\) | 52636.4 | + | 3486.95i | 0.547726 | + | 0.0362845i | ||||
\(311\) | 34537.2i | 0.357080i | 0.983933 | + | 0.178540i | \(0.0571375\pi\) | ||||
−0.983933 | + | 0.178540i | \(0.942863\pi\) | |||||||
\(312\) | 44250.5 | + | 8898.52i | 0.454579 | + | 0.0914131i | ||||
\(313\) | −16667.3 | −0.170129 | −0.0850644 | − | 0.996375i | \(-0.527110\pi\) | ||||
−0.0850644 | + | 0.996375i | \(0.527110\pi\) | |||||||
\(314\) | 7667.89 | − | 115749.i | 0.0777708 | − | 1.17397i | ||||
\(315\) | 8930.95i | 0.0900071i | ||||||||
\(316\) | −19909.7 | + | 149612.i | −0.199385 | + | 1.49828i | ||||
\(317\) | 73762.0 | 0.734030 | 0.367015 | − | 0.930215i | \(-0.380380\pi\) | ||||
0.367015 | + | 0.930215i | \(0.380380\pi\) | |||||||
\(318\) | 102768. | + | 6807.92i | 1.01625 | + | 0.0673225i | ||||
\(319\) | − | 346626.i | − | 3.40628i | ||||||
\(320\) | 42234.9 | + | 17702.2i | 0.412450 | + | 0.172873i | ||||
\(321\) | −8796.21 | −0.0853661 | ||||||||
\(322\) | −3171.29 | + | 47871.5i | −0.0305861 | + | 0.461706i | ||||
\(323\) | 1275.90i | 0.0122296i | ||||||||
\(324\) | −11562.1 | − | 1538.63i | −0.110140 | − | 0.0146570i | ||||
\(325\) | −16965.8 | −0.160623 | ||||||||
\(326\) | 59533.5 | + | 3943.85i | 0.560178 | + | 0.0371095i | ||||
\(327\) | − | 82545.6i | − | 0.771966i | ||||||
\(328\) | 18903.2 | − | 94001.6i | 0.175706 | − | 0.873751i | ||||
\(329\) | −55620.9 | −0.513861 | ||||||||
\(330\) | 3234.47 | − | 48825.3i | 0.0297013 | − | 0.448350i | ||||
\(331\) | 122804.i | 1.12088i | 0.828196 | + | 0.560438i | \(0.189367\pi\) | ||||
−0.828196 | + | 0.560438i | \(0.810633\pi\) | |||||||
\(332\) | 20025.4 | − | 150481.i | 0.181679 | − | 1.36523i | ||||
\(333\) | −16335.5 | −0.147314 | ||||||||
\(334\) | −106545. | − | 7058.19i | −0.955085 | − | 0.0632704i | ||||
\(335\) | − | 34000.2i | − | 0.302965i | ||||||
\(336\) | −37985.4 | − | 10292.1i | −0.336464 | − | 0.0911648i | ||||
\(337\) | 93476.4 | 0.823081 | 0.411540 | − | 0.911392i | \(-0.364991\pi\) | ||||
0.411540 | + | 0.911392i | \(0.364991\pi\) | |||||||
\(338\) | −2680.88 | + | 40468.6i | −0.0234662 | + | 0.354230i | ||||
\(339\) | 45931.0i | 0.399674i | ||||||||
\(340\) | −1356.87 | − | 180.566i | −0.0117376 | − | 0.00156199i | ||||
\(341\) | 248383. | 2.13605 | ||||||||
\(342\) | 17968.7 | + | 1190.35i | 0.153626 | + | 0.0101771i | ||||
\(343\) | 116173.i | 0.987457i | ||||||||
\(344\) | −94862.3 | − | 19076.3i | −0.801635 | − | 0.161204i | ||||
\(345\) | 23551.9 | 0.197873 | ||||||||
\(346\) | 10921.7 | − | 164866.i | 0.0912302 | − | 1.37715i | ||||
\(347\) | 16526.2i | 0.137251i | 0.997643 | + | 0.0686253i | \(0.0218613\pi\) | ||||
−0.997643 | + | 0.0686253i | \(0.978139\pi\) | |||||||
\(348\) | −18053.1 | + | 135660.i | −0.149071 | + | 1.12020i | ||||
\(349\) | −78324.9 | −0.643056 | −0.321528 | − | 0.946900i | \(-0.604196\pi\) | ||||
−0.321528 | + | 0.946900i | \(0.604196\pi\) | |||||||
\(350\) | 14760.4 | + | 977.815i | 0.120493 | + | 0.00798216i | ||||
\(351\) | 19041.9i | 0.154560i | ||||||||
\(352\) | 203938. | + | 70023.8i | 1.64594 | + | 0.565146i | ||||
\(353\) | −89837.2 | −0.720953 | −0.360476 | − | 0.932768i | \(-0.617386\pi\) | ||||
−0.360476 | + | 0.932768i | \(0.617386\pi\) | |||||||
\(354\) | 688.283 | − | 10389.8i | 0.00549238 | − | 0.0829090i | ||||
\(355\) | − | 77857.3i | − | 0.617792i | ||||||
\(356\) | −218793. | − | 29116.0i | −1.72637 | − | 0.229738i | ||||
\(357\) | 1176.35 | 0.00922995 | ||||||||
\(358\) | 122900. | + | 8141.61i | 0.958928 | + | 0.0635250i | ||||
\(359\) | 152507.i | 1.18332i | 0.806188 | + | 0.591659i | \(0.201527\pi\) | ||||
−0.806188 | + | 0.591659i | \(0.798473\pi\) | |||||||
\(360\) | −3808.82 | + | 18940.5i | −0.0293890 | + | 0.146146i | ||||
\(361\) | 102518. | 0.786660 | ||||||||
\(362\) | −1550.47 | + | 23404.8i | −0.0118317 | + | 0.178602i | ||||
\(363\) | − | 154321.i | − | 1.17115i | ||||||
\(364\) | −8475.21 | + | 63687.1i | −0.0639657 | + | 0.480672i | ||||
\(365\) | −87324.7 | −0.655468 | ||||||||
\(366\) | −19264.3 | − | 1276.18i | −0.143811 | − | 0.00952687i | ||||
\(367\) | 110809.i | 0.822700i | 0.911477 | + | 0.411350i | \(0.134943\pi\) | ||||
−0.911477 | + | 0.411350i | \(0.865057\pi\) | |||||||
\(368\) | −27141.5 | + | 100172.i | −0.200419 | + | 0.739690i | ||||
\(369\) | 40450.8 | 0.297081 | ||||||||
\(370\) | −1788.51 | + | 26998.0i | −0.0130643 | + | 0.197210i | ||||
\(371\) | 146603.i | 1.06511i | ||||||||
\(372\) | −97210.3 | − | 12936.3i | −0.702468 | − | 0.0934814i | ||||
\(373\) | −146097. | −1.05009 | −0.525043 | − | 0.851076i | \(-0.675951\pi\) | ||||
−0.525043 | + | 0.851076i | \(0.675951\pi\) | |||||||
\(374\) | −6431.06 | − | 426.031i | −0.0459769 | − | 0.00304577i | ||||
\(375\) | − | 7261.84i | − | 0.0516398i | ||||||
\(376\) | −117959. | − | 23720.8i | −0.834363 | − | 0.167786i | ||||
\(377\) | 223423. | 1.57197 | ||||||||
\(378\) | 1097.47 | − | 16566.6i | 0.00768084 | − | 0.115944i | ||||
\(379\) | − | 193663.i | − | 1.34824i | −0.738620 | − | 0.674122i | \(-0.764522\pi\) | ||
0.738620 | − | 0.674122i | \(-0.235478\pi\) | |||||||
\(380\) | 3934.64 | − | 29566.9i | 0.0272482 | − | 0.204757i | ||||
\(381\) | −14495.3 | −0.0998567 | ||||||||
\(382\) | −275722. | − | 18265.4i | −1.88949 | − | 0.125171i | ||||
\(383\) | 144521.i | 0.985223i | 0.870249 | + | 0.492612i | \(0.163958\pi\) | ||||
−0.870249 | + | 0.492612i | \(0.836042\pi\) | |||||||
\(384\) | −76168.9 | − | 38027.0i | −0.516553 | − | 0.257887i | ||||
\(385\) | 69651.8 | 0.469906 | ||||||||
\(386\) | 10267.9 | − | 154997.i | 0.0689140 | − | 1.04028i | ||||
\(387\) | − | 40821.2i | − | 0.272561i | ||||||
\(388\) | 122049. | + | 16241.8i | 0.810722 | + | 0.107887i | ||||
\(389\) | −111547. | −0.737153 | −0.368577 | − | 0.929597i | \(-0.620155\pi\) | ||||
−0.368577 | + | 0.929597i | \(0.620155\pi\) | |||||||
\(390\) | 31471.0 | + | 2084.82i | 0.206910 | + | 0.0137069i | ||||
\(391\) | − | 3102.16i | − | 0.0202913i | ||||||
\(392\) | −19250.4 | + | 95728.3i | −0.125276 | + | 0.622971i | ||||
\(393\) | −61412.3 | −0.397622 | ||||||||
\(394\) | −7024.93 | + | 106043.i | −0.0452533 | + | 0.683111i | ||||
\(395\) | 105466.i | 0.675958i | ||||||||
\(396\) | −11999.7 | + | 90171.8i | −0.0765207 | + | 0.575016i | ||||
\(397\) | 151266. | 0.959756 | 0.479878 | − | 0.877335i | \(-0.340681\pi\) | ||||
0.479878 | + | 0.877335i | \(0.340681\pi\) | |||||||
\(398\) | −236448. | − | 15663.7i | −1.49269 | − | 0.0988844i | ||||
\(399\) | 25633.3i | 0.161012i | ||||||||
\(400\) | 30886.3 | + | 8368.64i | 0.193040 | + | 0.0523040i | ||||
\(401\) | 79502.4 | 0.494415 | 0.247207 | − | 0.968963i | \(-0.420487\pi\) | ||||
0.247207 | + | 0.968963i | \(0.420487\pi\) | |||||||
\(402\) | −4178.08 | + | 63069.3i | −0.0258538 | + | 0.390271i | ||||
\(403\) | 160098.i | 0.985773i | ||||||||
\(404\) | 75230.3 | + | 10011.3i | 0.460925 | + | 0.0613379i | ||||
\(405\) | −8150.47 | −0.0496904 | ||||||||
\(406\) | −194380. | − | 12876.8i | −1.17923 | − | 0.0781191i | ||||
\(407\) | 127399.i | 0.769091i | ||||||||
\(408\) | 2494.76 | + | 501.681i | 0.0149868 | + | 0.00301375i | ||||
\(409\) | 294406. | 1.75995 | 0.879975 | − | 0.475020i | \(-0.157559\pi\) | ||||
0.879975 | + | 0.475020i | \(0.157559\pi\) | |||||||
\(410\) | 4428.80 | − | 66854.1i | 0.0263462 | − | 0.397704i | ||||
\(411\) | − | 155410.i | − | 0.920018i | ||||||
\(412\) | −1159.06 | + | 8709.76i | −0.00682827 | + | 0.0513112i | ||||
\(413\) | 14821.6 | 0.0868953 | ||||||||
\(414\) | −43688.0 | − | 2894.15i | −0.254895 | − | 0.0168857i | ||||
\(415\) | − | 106079.i | − | 0.615932i | ||||||
\(416\) | −45134.8 | + | 131451.i | −0.260811 | + | 0.759587i | ||||
\(417\) | −124436. | −0.715607 | ||||||||
\(418\) | 9283.44 | − | 140136.i | 0.0531321 | − | 0.802044i | ||||
\(419\) | 250549.i | 1.42713i | 0.700587 | + | 0.713567i | \(0.252921\pi\) | ||||
−0.700587 | + | 0.713567i | \(0.747079\pi\) | |||||||
\(420\) | −27259.9 | − | 3627.63i | −0.154534 | − | 0.0205648i | ||||
\(421\) | 171788. | 0.969234 | 0.484617 | − | 0.874726i | \(-0.338959\pi\) | ||||
0.484617 | + | 0.874726i | \(0.338959\pi\) | |||||||
\(422\) | 211322. | + | 13999.2i | 1.18664 | + | 0.0786099i | ||||
\(423\) | − | 50760.1i | − | 0.283689i | ||||||
\(424\) | −62522.5 | + | 310911.i | −0.347780 | + | 1.72944i | ||||
\(425\) | −956.499 | −0.00529550 | ||||||||
\(426\) | −9567.39 | + | 144423.i | −0.0527199 | + | 0.795822i | ||||
\(427\) | − | 27481.6i | − | 0.150725i | ||||||
\(428\) | 3572.90 | − | 26848.6i | 0.0195044 | − | 0.146566i | ||||
\(429\) | 148506. | 0.806920 | ||||||||
\(430\) | −67466.2 | − | 4469.35i | −0.364879 | − | 0.0241717i | ||||
\(431\) | − | 142972.i | − | 0.769658i | −0.922988 | − | 0.384829i | \(-0.874260\pi\) | ||
0.922988 | − | 0.384829i | \(-0.125740\pi\) | |||||||
\(432\) | 9392.70 | − | 34665.9i | 0.0503296 | − | 0.185752i | ||||
\(433\) | 77884.1 | 0.415406 | 0.207703 | − | 0.978192i | \(-0.433401\pi\) | ||||
0.207703 | + | 0.978192i | \(0.433401\pi\) | |||||||
\(434\) | 9227.18 | − | 139287.i | 0.0489880 | − | 0.739488i | ||||
\(435\) | 95631.3i | 0.505384i | ||||||||
\(436\) | 251953. | + | 33528.8i | 1.32540 | + | 0.176379i | ||||
\(437\) | 67597.7 | 0.353972 | ||||||||
\(438\) | 161984. | + | 10730.8i | 0.844354 | + | 0.0559350i | ||||
\(439\) | 45863.6i | 0.237979i | 0.992895 | + | 0.118990i | \(0.0379655\pi\) | ||||
−0.992895 | + | 0.118990i | \(0.962034\pi\) | |||||||
\(440\) | 147715. | + | 29704.7i | 0.762992 | + | 0.153433i | ||||
\(441\) | −41193.8 | −0.211814 | ||||||||
\(442\) | 274.604 | − | 4145.23i | 0.00140560 | − | 0.0212180i | ||||
\(443\) | − | 178266.i | − | 0.908367i | −0.890908 | − | 0.454184i | \(-0.849931\pi\) | ||
0.890908 | − | 0.454184i | \(-0.150069\pi\) | |||||||
\(444\) | 6635.24 | − | 49860.7i | 0.0336582 | − | 0.252925i | ||||
\(445\) | −154234. | −0.778862 | ||||||||
\(446\) | 48779.6 | + | 3231.44i | 0.245227 | + | 0.0162453i | ||||
\(447\) | − | 23064.0i | − | 0.115430i | ||||||
\(448\) | 46843.8 | − | 111762.i | 0.233397 | − | 0.556851i | ||||
\(449\) | −72533.3 | −0.359786 | −0.179893 | − | 0.983686i | \(-0.557575\pi\) | ||||
−0.179893 | + | 0.983686i | \(0.557575\pi\) | |||||||
\(450\) | −892.363 | + | 13470.5i | −0.00440673 | + | 0.0665209i | ||||
\(451\) | − | 315473.i | − | 1.55099i | ||||||
\(452\) | −140195. | − | 18656.5i | −0.686207 | − | 0.0913174i | ||||
\(453\) | 40286.4 | 0.196319 | ||||||||
\(454\) | 211461. | + | 14008.4i | 1.02593 | + | 0.0679637i | ||||
\(455\) | 44895.1i | 0.216858i | ||||||||
\(456\) | −10931.9 | + | 54362.1i | −0.0525734 | + | 0.261437i | ||||
\(457\) | −21324.1 | −0.102103 | −0.0510514 | − | 0.998696i | \(-0.516257\pi\) | ||||
−0.0510514 | + | 0.998696i | \(0.516257\pi\) | |||||||
\(458\) | 6951.03 | − | 104928.i | 0.0331374 | − | 0.500218i | ||||
\(459\) | 1073.55i | 0.00509560i | ||||||||
\(460\) | −9566.45 | + | 71887.3i | −0.0452101 | + | 0.339732i | ||||
\(461\) | −24839.5 | −0.116880 | −0.0584401 | − | 0.998291i | \(-0.518613\pi\) | ||||
−0.0584401 | + | 0.998291i | \(0.518613\pi\) | |||||||
\(462\) | −129202. | − | 8559.08i | −0.605319 | − | 0.0400999i | ||||
\(463\) | − | 64668.0i | − | 0.301667i | −0.988559 | − | 0.150833i | \(-0.951804\pi\) | ||
0.988559 | − | 0.150833i | \(-0.0481957\pi\) | |||||||
\(464\) | −406742. | − | 110207.i | −1.88922 | − | 0.511884i | ||||
\(465\) | −68526.6 | −0.316923 | ||||||||
\(466\) | 10019.5 | − | 151248.i | 0.0461398 | − | 0.696493i | ||||
\(467\) | − | 172892.i | − | 0.792761i | −0.918086 | − | 0.396381i | \(-0.870266\pi\) | ||
0.918086 | − | 0.396381i | \(-0.129734\pi\) | |||||||
\(468\) | −58121.4 | − | 7734.55i | −0.265366 | − | 0.0353137i | ||||
\(469\) | −89971.7 | −0.409035 | ||||||||
\(470\) | −83892.5 | − | 5557.53i | −0.379776 | − | 0.0251586i | ||||
\(471\) | 150692.i | 0.679279i | ||||||||
\(472\) | 31433.2 | + | 6321.04i | 0.141093 | + | 0.0283730i | ||||
\(473\) | −318362. | −1.42298 | ||||||||
\(474\) | 12960.1 | − | 195637.i | 0.0576835 | − | 0.870750i | ||||
\(475\) | − | 20842.6i | − | 0.0923774i | ||||||
\(476\) | −477.816 | + | 3590.56i | −0.00210885 | + | 0.0158470i | ||||
\(477\) | −133792. | −0.588020 | ||||||||
\(478\) | 29896.1 | + | 1980.49i | 0.130846 | + | 0.00866797i | ||||
\(479\) | − | 19930.4i | − | 0.0868652i | −0.999056 | − | 0.0434326i | \(-0.986171\pi\) | ||
0.999056 | − | 0.0434326i | \(-0.0138294\pi\) | |||||||
\(480\) | −56264.7 | − | 19319.0i | −0.244205 | − | 0.0838497i | ||||
\(481\) | −82116.9 | −0.354930 | ||||||||
\(482\) | 20103.8 | − | 303473.i | 0.0865334 | − | 1.30625i | ||||
\(483\) | − | 62323.2i | − | 0.267150i | ||||||
\(484\) | 471034. | + | 62683.2i | 2.01077 | + | 0.267584i | ||||
\(485\) | 86036.4 | 0.365762 | ||||||||
\(486\) | 15118.8 | + | 1001.56i | 0.0640097 | + | 0.00424038i | ||||
\(487\) | 110147.i | 0.464426i | 0.972665 | + | 0.232213i | \(0.0745966\pi\) | ||||
−0.972665 | + | 0.232213i | \(0.925403\pi\) | |||||||
\(488\) | 11720.2 | − | 58282.0i | 0.0492147 | − | 0.244734i | ||||
\(489\) | −77505.8 | −0.324128 | ||||||||
\(490\) | −4510.15 | + | 68082.1i | −0.0187845 | + | 0.283557i | ||||
\(491\) | − | 164562.i | − | 0.682599i | −0.939955 | − | 0.341300i | \(-0.889133\pi\) | ||
0.939955 | − | 0.341300i | \(-0.110867\pi\) | |||||||
\(492\) | −16430.6 | + | 123468.i | −0.0678769 | + | 0.510063i | ||||
\(493\) | 12596.1 | 0.0518255 | ||||||||
\(494\) | 90326.8 | + | 5983.77i | 0.370137 | + | 0.0245200i | ||||
\(495\) | 63564.9i | 0.259422i | ||||||||
\(496\) | 78971.0 | − | 291460.i | 0.320999 | − | 1.18472i | ||||
\(497\) | −206026. | −0.834085 | ||||||||
\(498\) | −13035.4 | + | 196773.i | −0.0525612 | + | 0.793426i | ||||
\(499\) | 104374.i | 0.419169i | 0.977791 | + | 0.209585i | \(0.0672112\pi\) | ||||
−0.977791 | + | 0.209585i | \(0.932789\pi\) | |||||||
\(500\) | 22165.3 | + | 2949.66i | 0.0886611 | + | 0.0117986i | ||||
\(501\) | 138710. | 0.552627 | ||||||||
\(502\) | −162960. | − | 10795.5i | −0.646658 | − | 0.0428384i | ||||
\(503\) | − | 177345.i | − | 0.700945i | −0.936573 | − | 0.350472i | \(-0.886021\pi\) | ||
0.936573 | − | 0.350472i | \(-0.113979\pi\) | |||||||
\(504\) | 50120.4 | + | 10078.9i | 0.197312 | + | 0.0396783i | ||||
\(505\) | 53032.2 | 0.207949 | ||||||||
\(506\) | −22571.2 | + | 340719.i | −0.0881565 | + | 1.33075i | ||||
\(507\) | − | 52685.5i | − | 0.204963i | ||||||
\(508\) | 5887.79 | − | 44243.9i | 0.0228152 | − | 0.171445i | ||||
\(509\) | 68651.6 | 0.264981 | 0.132491 | − | 0.991184i | \(-0.457703\pi\) | ||||
0.132491 | + | 0.991184i | \(0.457703\pi\) | |||||||
\(510\) | 1774.27 | + | 117.538i | 0.00682151 | + | 0.000451896i | ||||
\(511\) | 231079.i | 0.884951i | ||||||||
\(512\) | 147008. | − | 217044.i | 0.560792 | − | 0.827956i | ||||
\(513\) | −23393.1 | −0.0888902 | ||||||||
\(514\) | −23610.9 | + | 356413.i | −0.0893687 | + | 1.34905i | ||||
\(515\) | 6139.79i | 0.0231494i | ||||||||
\(516\) | 124598. | + | 16581.0i | 0.467964 | + | 0.0622747i | ||||
\(517\) | −395874. | −1.48107 | ||||||||
\(518\) | 71442.4 | + | 4732.76i | 0.266254 | + | 0.0176382i | ||||
\(519\) | 214637.i | 0.796838i | ||||||||
\(520\) | −19146.6 | + | 95211.9i | −0.0708083 | + | 0.352115i | ||||
\(521\) | −371672. | −1.36926 | −0.684628 | − | 0.728893i | \(-0.740035\pi\) | ||||
−0.684628 | + | 0.728893i | \(0.740035\pi\) | |||||||
\(522\) | 11751.5 | − | 177393.i | 0.0431274 | − | 0.651021i | ||||
\(523\) | − | 247920.i | − | 0.906376i | −0.891415 | − | 0.453188i | \(-0.850287\pi\) | ||
0.891415 | − | 0.453188i | \(-0.149713\pi\) | |||||||
\(524\) | 24944.8 | − | 187448.i | 0.0908484 | − | 0.682683i | ||||
\(525\) | −19216.3 | −0.0697192 | ||||||||
\(526\) | −39439.1 | − | 2612.67i | −0.142546 | − | 0.00944308i | ||||
\(527\) | 9026.04i | 0.0324994i | ||||||||
\(528\) | −270357. | − | 73253.0i | −0.969771 | − | 0.262759i | ||||
\(529\) | 115488. | 0.412691 | ||||||||
\(530\) | −14648.3 | + | 221120.i | −0.0521478 | + | 0.787186i | ||||
\(531\) | 13526.4i | 0.0479725i | ||||||||
\(532\) | −78240.2 | − | 10411.9i | −0.276444 | − | 0.0367879i | ||||
\(533\) | 203342. | 0.715770 | ||||||||
\(534\) | 286099. | + | 18952.9i | 1.00331 | + | 0.0664649i | ||||
\(535\) | − | 18926.4i | − | 0.0661243i | ||||||
\(536\) | −190809. | − | 38370.6i | −0.664154 | − | 0.133558i | ||||
\(537\) | −160002. | −0.554851 | ||||||||
\(538\) | 28092.8 | − | 424069.i | 0.0970577 | − | 1.46511i | ||||
\(539\) | 321268.i | 1.10583i | ||||||||
\(540\) | 3310.61 | − | 24877.6i | 0.0113532 | − | 0.0853142i | ||||
\(541\) | −283935. | −0.970119 | −0.485059 | − | 0.874481i | \(-0.661202\pi\) | ||||
−0.485059 | + | 0.874481i | \(0.661202\pi\) | |||||||
\(542\) | 257439. | + | 17054.3i | 0.876346 | + | 0.0580543i | ||||
\(543\) | − | 30470.3i | − | 0.103342i | ||||||
\(544\) | −2544.61 | + | 7410.95i | −0.00859853 | + | 0.0250424i | ||||
\(545\) | 177610. | 0.597962 | ||||||||
\(546\) | 5516.87 | − | 83278.8i | 0.0185058 | − | 0.279350i | ||||
\(547\) | 573141.i | 1.91552i | 0.287567 | + | 0.957761i | \(0.407154\pi\) | ||||
−0.287567 | + | 0.957761i | \(0.592846\pi\) | |||||||
\(548\) | 474358. | + | 63125.5i | 1.57959 | + | 0.210205i | ||||
\(549\) | 25080.0 | 0.0832113 | ||||||||
\(550\) | 105055. | + | 6959.47i | 0.347290 | + | 0.0230065i | ||||
\(551\) | 274477.i | 0.904071i | ||||||||
\(552\) | 26579.2 | − | 132173.i | 0.0872296 | − | 0.433775i | ||||
\(553\) | 279086. | 0.912615 | ||||||||
\(554\) | −26216.9 | + | 395752.i | −0.0854204 | + | 1.28945i | ||||
\(555\) | − | 35148.4i | − | 0.114109i | ||||||
\(556\) | 50544.2 | − | 379815.i | 0.163501 | − | 1.22864i | ||||
\(557\) | 148550. | 0.478810 | 0.239405 | − | 0.970920i | \(-0.423048\pi\) | ||||
0.239405 | + | 0.970920i | \(0.423048\pi\) | |||||||
\(558\) | 127115. | + | 8420.81i | 0.408251 | + | 0.0270449i | ||||
\(559\) | − | 205204.i | − | 0.656694i | ||||||
\(560\) | 22145.2 | − | 81731.7i | 0.0706160 | − | 0.260624i | ||||
\(561\) | 8372.50 | 0.0266029 | ||||||||
\(562\) | −14019.6 | + | 211630.i | −0.0443878 | + | 0.670047i | ||||
\(563\) | − | 518103.i | − | 1.63455i | −0.576246 | − | 0.817277i | \(-0.695483\pi\) | ||
0.576246 | − | 0.817277i | \(-0.304517\pi\) | |||||||
\(564\) | 154935. | + | 20618.0i | 0.487069 | + | 0.0648171i | ||||
\(565\) | −98827.7 | −0.309586 | ||||||||
\(566\) | 538925. | + | 35701.5i | 1.68227 | + | 0.111443i | ||||
\(567\) | 21567.8i | 0.0670873i | ||||||||
\(568\) | −436934. | − | 87864.9i | −1.35431 | − | 0.272345i | ||||
\(569\) | −250898. | −0.774948 | −0.387474 | − | 0.921881i | \(-0.626652\pi\) | ||||
−0.387474 | + | 0.921881i | \(0.626652\pi\) | |||||||
\(570\) | −2561.22 | + | 38662.4i | −0.00788311 | + | 0.118998i | ||||
\(571\) | − | 379446.i | − | 1.16380i | −0.813261 | − | 0.581899i | \(-0.802310\pi\) | ||
0.813261 | − | 0.581899i | \(-0.197690\pi\) | |||||||
\(572\) | −60321.2 | + | 453285.i | −0.184365 | + | 1.38541i | ||||
\(573\) | 358958. | 1.09329 | ||||||||
\(574\) | −176910. | − | 11719.5i | −0.536943 | − | 0.0355702i | ||||
\(575\) | 50675.6i | 0.153272i | ||||||||
\(576\) | 101995. | + | 42750.1i | 0.307422 | + | 0.128852i | ||||
\(577\) | −84917.5 | −0.255062 | −0.127531 | − | 0.991835i | \(-0.540705\pi\) | ||||
−0.127531 | + | 0.991835i | \(0.540705\pi\) | |||||||
\(578\) | −22067.8 | + | 333120.i | −0.0660546 | + | 0.997113i | ||||
\(579\) | 201788.i | 0.601921i | ||||||||
\(580\) | −291895. | − | 38844.1i | −0.867701 | − | 0.115470i | ||||
\(581\) | −280707. | −0.831574 | ||||||||
\(582\) | −159595. | − | 10572.5i | −0.471164 | − | 0.0312127i | ||||
\(583\) | 1.04343e6i | 3.06991i | ||||||||
\(584\) | −98549.3 | + | 490065.i | −0.288953 | + | 1.43690i | ||||
\(585\) | −40971.6 | −0.119721 | ||||||||
\(586\) | −35361.2 | + | 533788.i | −0.102975 | + | 1.55444i | ||||
\(587\) | − | 540757.i | − | 1.56937i | −0.619893 | − | 0.784686i | \(-0.712824\pi\) | ||
0.619893 | − | 0.784686i | \(-0.287176\pi\) | |||||||
\(588\) | 16732.4 | − | 125736.i | 0.0483952 | − | 0.363667i | ||||
\(589\) | −196682. | −0.566937 | ||||||||
\(590\) | 22355.3 | + | 1480.95i | 0.0642210 | + | 0.00425438i | ||||
\(591\) | − | 138056.i | − | 0.395259i | ||||||
\(592\) | 149494. | + | 40505.4i | 0.426561 | + | 0.115577i | ||||
\(593\) | 304664. | 0.866386 | 0.433193 | − | 0.901301i | \(-0.357387\pi\) | ||||
0.433193 | + | 0.901301i | \(0.357387\pi\) | |||||||
\(594\) | 7811.10 | − | 117911.i | 0.0221380 | − | 0.334180i | ||||
\(595\) | 2531.10i | 0.00714948i | ||||||||
\(596\) | 70398.2 | + | 9368.28i | 0.198184 | + | 0.0263735i | ||||
\(597\) | 307828. | 0.863693 | ||||||||
\(598\) | −219615. | − | 14548.6i | −0.614130 | − | 0.0406835i | ||||
\(599\) | − | 148036.i | − | 0.412584i | −0.978490 | − | 0.206292i | \(-0.933860\pi\) | ||
0.978490 | − | 0.206292i | \(-0.0661397\pi\) | |||||||
\(600\) | −40753.4 | − | 8195.27i | −0.113204 | − | 0.0227646i | ||||
\(601\) | −149586. | −0.414134 | −0.207067 | − | 0.978327i | \(-0.566392\pi\) | ||||
−0.207067 | + | 0.978327i | \(0.566392\pi\) | |||||||
\(602\) | −11826.8 | + | 178530.i | −0.0326344 | + | 0.492626i | ||||
\(603\) | − | 82109.0i | − | 0.225817i | ||||||
\(604\) | −16363.8 | + | 122966.i | −0.0448549 | + | 0.337063i | ||||
\(605\) | 332047. | 0.907169 | ||||||||
\(606\) | −98372.9 | − | 6516.79i | −0.267874 | − | 0.0177455i | ||||
\(607\) | − | 220755.i | − | 0.599147i | −0.954073 | − | 0.299574i | \(-0.903156\pi\) | ||
0.954073 | − | 0.299574i | \(-0.0968445\pi\) | |||||||
\(608\) | −161489. | − | 55448.5i | −0.436853 | − | 0.149997i | ||||
\(609\) | 253060. | 0.682322 | ||||||||
\(610\) | 2745.91 | − | 41450.2i | 0.00737948 | − | 0.111395i | ||||
\(611\) | − | 255166.i | − | 0.683504i | ||||||
\(612\) | −3276.78 | − | 436.059i | −0.00874871 | − | 0.00116424i | ||||
\(613\) | −15013.9 | −0.0399551 | −0.0199776 | − | 0.999800i | \(-0.506359\pi\) | ||||
−0.0199776 | + | 0.999800i | \(0.506359\pi\) | |||||||
\(614\) | −500447. | − | 33152.6i | −1.32746 | − | 0.0879387i | ||||
\(615\) | 87036.3i | 0.230118i | ||||||||
\(616\) | 78604.8 | − | 390885.i | 0.207151 | − | 1.03012i | ||||
\(617\) | 537682. | 1.41239 | 0.706196 | − | 0.708016i | \(-0.250410\pi\) | ||||
0.706196 | + | 0.708016i | \(0.250410\pi\) | |||||||
\(618\) | 754.480 | − | 11389.1i | 0.00197547 | − | 0.0298203i | ||||
\(619\) | − | 22215.9i | − | 0.0579806i | −0.999580 | − | 0.0289903i | \(-0.990771\pi\) | ||
0.999580 | − | 0.0289903i | \(-0.00922919\pi\) | |||||||
\(620\) | 27834.6 | − | 209163.i | 0.0724104 | − | 0.544129i | ||||
\(621\) | 56876.7 | 0.147486 | ||||||||
\(622\) | 137847. | + | 9131.76i | 0.356299 | + | 0.0236034i | ||||
\(623\) | 408135.i | 1.05155i | ||||||||
\(624\) | 47216.2 | − | 174262.i | 0.121261 | − | 0.447542i | ||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | −4406.91 | + | 66523.6i | −0.0112457 | + | 0.169757i | ||||
\(627\) | 182441.i | 0.464075i | ||||||||
\(628\) | −459956. | − | 61209.0i | −1.16626 | − | 0.155201i | ||||
\(629\) | −4629.59 | −0.0117015 | ||||||||
\(630\) | 35645.7 | + | 2361.38i | 0.0898102 | + | 0.00594955i | ||||
\(631\) | 356750.i | 0.895994i | 0.894035 | + | 0.447997i | \(0.147863\pi\) | ||||
−0.894035 | + | 0.447997i | \(0.852137\pi\) | |||||||
\(632\) | 591876. | + | 119023.i | 1.48182 | + | 0.297986i | ||||
\(633\) | −275116. | −0.686608 | ||||||||
\(634\) | 19502.9 | − | 294403.i | 0.0485201 | − | 0.732425i | ||||
\(635\) | − | 31188.9i | − | 0.0773487i | ||||||
\(636\) | 54344.2 | − | 408371.i | 0.134350 | − | 1.00958i | ||||
\(637\) | −207078. | −0.510334 | ||||||||
\(638\) | −1.38347e6 | − | 91649.3i | −3.39883 | − | 0.225158i | ||||
\(639\) | − | 188022.i | − | 0.460475i | ||||||
\(640\) | 81821.1 | − | 163889.i | 0.199759 | − | 0.400121i | ||||
\(641\) | 41392.0 | 0.100740 | 0.0503698 | − | 0.998731i | \(-0.483960\pi\) | ||||
0.0503698 | + | 0.998731i | \(0.483960\pi\) | |||||||
\(642\) | −2325.75 | + | 35107.9i | −0.00564278 | + | 0.0851794i | ||||
\(643\) | − | 342725.i | − | 0.828940i | −0.910063 | − | 0.414470i | \(-0.863967\pi\) | ||
0.910063 | − | 0.414470i | \(-0.136033\pi\) | |||||||
\(644\) | 190229. | + | 25314.8i | 0.458674 | + | 0.0610384i | ||||
\(645\) | 87833.2 | 0.211125 | ||||||||
\(646\) | 5092.45 | + | 337.354i | 0.0122029 | + | 0.000808389i | ||||
\(647\) | 300662.i | 0.718240i | 0.933291 | + | 0.359120i | \(0.116923\pi\) | ||||
−0.933291 | + | 0.359120i | \(0.883077\pi\) | |||||||
\(648\) | −9198.12 | + | 45740.3i | −0.0219053 | + | 0.108930i | ||||
\(649\) | 105491. | 0.250453 | ||||||||
\(650\) | −4485.82 | + | 67714.8i | −0.0106173 | + | 0.160272i | ||||
\(651\) | 181336.i | 0.427879i | ||||||||
\(652\) | 31481.8 | − | 236571.i | 0.0740567 | − | 0.556500i | ||||
\(653\) | 127668. | 0.299402 | 0.149701 | − | 0.988731i | \(-0.452169\pi\) | ||||
0.149701 | + | 0.988731i | \(0.452169\pi\) | |||||||
\(654\) | −329460. | − | 21825.4i | −0.770278 | − | 0.0510277i | ||||
\(655\) | − | 132138.i | − | 0.307996i | ||||||
\(656\) | −370186. | − | 100302.i | −0.860226 | − | 0.233078i | ||||
\(657\) | −210885. | −0.488557 | ||||||||
\(658\) | −14706.4 | + | 221997.i | −0.0339667 | + | 0.512738i | ||||
\(659\) | − | 387877.i | − | 0.893147i | −0.894747 | − | 0.446574i | \(-0.852644\pi\) | ||
0.894747 | − | 0.446574i | \(-0.147356\pi\) | |||||||
\(660\) | −194019. | − | 25819.2i | −0.445406 | − | 0.0592727i | ||||
\(661\) | 116256. | 0.266079 | 0.133040 | − | 0.991111i | \(-0.457526\pi\) | ||||
0.133040 | + | 0.991111i | \(0.457526\pi\) | |||||||
\(662\) | 490143. | + | 32469.9i | 1.11842 | + | 0.0740910i | ||||
\(663\) | 5396.61i | 0.0122771i | ||||||||
\(664\) | −595314. | − | 119714.i | −1.35024 | − | 0.271525i | ||||
\(665\) | −55154.0 | −0.124719 | ||||||||
\(666\) | −4319.16 | + | 65199.0i | −0.00973758 | + | 0.146992i | ||||
\(667\) | − | 667347.i | − | 1.50003i | ||||||
\(668\) | −56342.0 | + | 423384.i | −0.126264 | + | 0.948814i | ||||
\(669\) | −63505.4 | −0.141892 | ||||||||
\(670\) | −135704. | − | 8989.79i | −0.302302 | − | 0.0200263i | ||||
\(671\) | − | 195597.i | − | 0.434427i | ||||||
\(672\) | −51122.0 | + | 148888.i | −0.113206 | + | 0.329702i | ||||
\(673\) | 764966. | 1.68893 | 0.844466 | − | 0.535609i | \(-0.179918\pi\) | ||||
0.844466 | + | 0.535609i | \(0.179918\pi\) | |||||||
\(674\) | 24715.5 | − | 373088.i | 0.0544064 | − | 0.821281i | ||||
\(675\) | − | 17537.0i | − | 0.0384900i | ||||||
\(676\) | 160812. | + | 21400.1i | 0.351904 | + | 0.0468298i | ||||
\(677\) | 303589. | 0.662382 | 0.331191 | − | 0.943564i | \(-0.392550\pi\) | ||||
0.331191 | + | 0.943564i | \(0.392550\pi\) | |||||||
\(678\) | 183322. | + | 12144.3i | 0.398800 | + | 0.0264188i | ||||
\(679\) | − | 227670.i | − | 0.493818i | ||||||
\(680\) | −1079.45 | + | 5367.86i | −0.00233444 | + | 0.0116087i | ||||
\(681\) | −275298. | −0.593621 | ||||||||
\(682\) | 65673.3 | − | 991357.i | 0.141195 | − | 2.13138i | ||||
\(683\) | − | 541205.i | − | 1.16017i | −0.814557 | − | 0.580083i | \(-0.803020\pi\) | ||
0.814557 | − | 0.580083i | \(-0.196980\pi\) | |||||||
\(684\) | 9501.96 | − | 71402.7i | 0.0203096 | − | 0.152617i | ||||
\(685\) | 334390. | 0.712643 | ||||||||
\(686\) | 463677. | + | 30716.7i | 0.985297 | + | 0.0652718i | ||||
\(687\) | 136604.i | 0.289434i | ||||||||
\(688\) | −101220. | + | 373576.i | −0.213841 | + | 0.789226i | ||||
\(689\) | −672557. | −1.41674 | ||||||||
\(690\) | 6227.21 | − | 94001.5i | 0.0130796 | − | 0.197441i | ||||
\(691\) | 902741.i | 1.89063i | 0.326155 | + | 0.945316i | \(0.394247\pi\) | ||||
−0.326155 | + | 0.945316i | \(0.605753\pi\) | |||||||
\(692\) | −655136. | − | 87182.6i | −1.36810 | − | 0.182061i | ||||
\(693\) | 168206. | 0.350247 | ||||||||
\(694\) | 65960.3 | + | 4369.59i | 0.136950 | + | 0.00907240i | ||||
\(695\) | − | 267744.i | − | 0.554306i | ||||||
\(696\) | 536681. | + | 107924.i | 1.10789 | + | 0.222791i | ||||
\(697\) | 11464.1 | 0.0235979 | ||||||||
\(698\) | −20709.4 | + | 312614.i | −0.0425066 | + | 0.641650i | ||||
\(699\) | 196907.i | 0.403002i | ||||||||
\(700\) | 7805.41 | − | 58653.9i | 0.0159294 | − | 0.119702i | ||||
\(701\) | 16867.4 | 0.0343251 | 0.0171625 | − | 0.999853i | \(-0.494537\pi\) | ||||
0.0171625 | + | 0.999853i | \(0.494537\pi\) | |||||||
\(702\) | 76001.0 | + | 5034.75i | 0.154222 | + | 0.0102165i | ||||
\(703\) | − | 100881.i | − | 0.204127i | ||||||
\(704\) | 333405. | − | 795453.i | 0.672708 | − | 1.60498i | ||||
\(705\) | 109218. | 0.219744 | ||||||||
\(706\) | −23753.3 | + | 358563.i | −0.0476556 | + | 0.719376i | ||||
\(707\) | − | 140334.i | − | 0.280753i | ||||||
\(708\) | −41286.4 | − | 5494.22i | −0.0823646 | − | 0.0109607i | ||||
\(709\) | 231636. | 0.460801 | 0.230400 | − | 0.973096i | \(-0.425996\pi\) | ||||
0.230400 | + | 0.973096i | \(0.425996\pi\) | |||||||
\(710\) | −310748. | − | 20585.8i | −0.616441 | − | 0.0408366i | ||||
\(711\) | 254696.i | 0.503829i | ||||||||
\(712\) | −174059. | + | 865560.i | −0.343350 | + | 1.70741i | ||||
\(713\) | 478202. | 0.940659 | ||||||||
\(714\) | 311.031 | − | 4695.10i | 0.000610108 | − | 0.00920976i | ||||
\(715\) | 319535.i | 0.625037i | ||||||||
\(716\) | 64990.5 | − | 488372.i | 0.126772 | − | 0.952631i | ||||
\(717\) | −38921.3 | −0.0757093 | ||||||||
\(718\) | 608695. | + | 40323.5i | 1.18073 | + | 0.0782185i | ||||
\(719\) | − | 283759.i | − | 0.548898i | −0.961602 | − | 0.274449i | \(-0.911504\pi\) | ||
0.961602 | − | 0.274449i | \(-0.0884955\pi\) | |||||||
\(720\) | 74589.1 | + | 20209.9i | 0.143883 | + | 0.0389851i | ||||
\(721\) | 16247.2 | 0.0312541 | ||||||||
\(722\) | 27106.2 | − | 409177.i | 0.0519990 | − | 0.784940i | ||||
\(723\) | 395087.i | 0.755815i | ||||||||
\(724\) | 93004.3 | + | 12376.6i | 0.177430 | + | 0.0236116i | ||||
\(725\) | −205766. | −0.391469 | ||||||||
\(726\) | −615935. | − | 40803.1i | −1.16859 | − | 0.0774142i | ||||
\(727\) | 70775.4i | 0.133910i | 0.997756 | + | 0.0669551i | \(0.0213284\pi\) | ||||
−0.997756 | + | 0.0669551i | \(0.978672\pi\) | |||||||
\(728\) | 251950. | + | 50665.8i | 0.475393 | + | 0.0955987i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | −23089.0 | + | 348535.i | −0.0433270 | + | 0.654034i | ||||
\(731\) | − | 11569.0i | − | 0.0216502i | ||||||
\(732\) | −10187.1 | + | 76551.4i | −0.0190121 | + | 0.142867i | ||||
\(733\) | −195503. | −0.363870 | −0.181935 | − | 0.983311i | \(-0.558236\pi\) | ||||
−0.181935 | + | 0.983311i | \(0.558236\pi\) | |||||||
\(734\) | 442265. | + | 29298.2i | 0.820901 | + | 0.0543813i | ||||
\(735\) | − | 88635.0i | − | 0.164071i | ||||||
\(736\) | 392634. | + | 134814.i | 0.724824 | + | 0.248875i | ||||
\(737\) | −640362. | −1.17894 | ||||||||
\(738\) | 10695.4 | − | 161449.i | 0.0196373 | − | 0.296431i | ||||
\(739\) | − | 193327.i | − | 0.354001i | −0.984211 | − | 0.177000i | \(-0.943361\pi\) | ||
0.984211 | − | 0.177000i | \(-0.0566394\pi\) | |||||||
\(740\) | 107283. | + | 14276.8i | 0.195915 | + | 0.0260715i | ||||
\(741\) | −117595. | −0.214167 | ||||||||
\(742\) | 585131. | + | 38762.5i | 1.06278 | + | 0.0704050i | ||||
\(743\) | 592034.i | 1.07243i | 0.844082 | + | 0.536215i | \(0.180146\pi\) | ||||
−0.844082 | + | 0.536215i | \(0.819854\pi\) | |||||||
\(744\) | −77334.9 | + | 384571.i | −0.139711 | + | 0.694753i | ||||
\(745\) | 49625.9 | 0.0894120 | ||||||||
\(746\) | −38628.7 | + | 583111.i | −0.0694117 | + | 1.04779i | ||||
\(747\) | − | 256176.i | − | 0.459089i | ||||||
\(748\) | −3400.79 | + | 25555.3i | −0.00607823 | + | 0.0456750i | ||||
\(749\) | −50083.3 | −0.0892749 | ||||||||
\(750\) | −28983.8 | − | 1920.06i | −0.0515268 | − | 0.00341344i | ||||
\(751\) | 488630.i | 0.866363i | 0.901307 | + | 0.433181i | \(0.142609\pi\) | ||||
−0.901307 | + | 0.433181i | \(0.857391\pi\) | |||||||
\(752\) | −125865. | + | 464532.i | −0.222571 | + | 0.821447i | ||||
\(753\) | 212156. | 0.374167 | ||||||||
\(754\) | 59073.8 | − | 891737.i | 0.103909 | − | 1.56853i | ||||
\(755\) | 86682.6i | 0.152068i | ||||||||
\(756\) | −65831.3 | − | 8760.55i | −0.115183 | − | 0.0153281i | ||||
\(757\) | −123002. | −0.214645 | −0.107323 | − | 0.994224i | \(-0.534228\pi\) | ||||
−0.107323 | + | 0.994224i | \(0.534228\pi\) | |||||||
\(758\) | −772959. | − | 51205.3i | −1.34530 | − | 0.0891203i | ||||
\(759\) | − | 443577.i | − | 0.769991i | ||||||
\(760\) | −116969. | − | 23521.7i | −0.202508 | − | 0.0407232i | ||||
\(761\) | 186320. | 0.321729 | 0.160865 | − | 0.986976i | \(-0.448572\pi\) | ||||
0.160865 | + | 0.986976i | \(0.448572\pi\) | |||||||
\(762\) | −3832.61 | + | 57854.4i | −0.00660062 | + | 0.0996383i | ||||
\(763\) | − | 469992.i | − | 0.807313i | ||||||
\(764\) | −145804. | + | 1.09565e6i | −0.249794 | + | 1.87708i | ||||
\(765\) | −2309.90 | −0.00394703 | ||||||||
\(766\) | 576821. | + | 38212.0i | 0.983069 | + | 0.0651242i | ||||
\(767\) | 67995.8i | 0.115582i | ||||||||
\(768\) | −171915. | + | 293955.i | −0.291468 | + | 0.498377i | ||||
\(769\) | 305968. | 0.517396 | 0.258698 | − | 0.965958i | \(-0.416707\pi\) | ||||
0.258698 | + | 0.965958i | \(0.416707\pi\) | |||||||
\(770\) | 18416.2 | − | 277998.i | 0.0310612 | − | 0.468878i | ||||
\(771\) | − | 464009.i | − | 0.780580i | ||||||
\(772\) | −615918. | − | 81963.6i | −1.03345 | − | 0.137527i | ||||
\(773\) | −453241. | −0.758526 | −0.379263 | − | 0.925289i | \(-0.623822\pi\) | ||||
−0.379263 | + | 0.925289i | \(0.623822\pi\) | |||||||
\(774\) | −162928. | − | 10793.3i | −0.271965 | − | 0.0180165i | ||||
\(775\) | − | 147446.i | − | 0.245487i | ||||||
\(776\) | 97095.4 | − | 482835.i | 0.161241 | − | 0.801817i | ||||
\(777\) | −93009.9 | −0.154059 | ||||||||
\(778\) | −29493.4 | + | 445211.i | −0.0487265 | + | 0.735541i | ||||
\(779\) | 249808.i | 0.411653i | ||||||||
\(780\) | 16642.1 | − | 125057.i | 0.0273539 | − | 0.205551i | ||||
\(781\) | −1.46637e6 | −2.40403 | ||||||||
\(782\) | −12381.5 | − | 820.222i | −0.0202469 | − | 0.00134127i | ||||
\(783\) | 230945.i | 0.376691i | ||||||||
\(784\) | 376986. | + | 102144.i | 0.613328 | + | 0.166181i | ||||
\(785\) | −324237. | −0.526167 | ||||||||
\(786\) | −16237.6 | + | 245112.i | −0.0262832 | + | 0.396752i | ||||
\(787\) | 590772.i | 0.953829i | 0.878950 | + | 0.476915i | \(0.158245\pi\) | ||||
−0.878950 | + | 0.476915i | \(0.841755\pi\) | |||||||
\(788\) | 421389. | + | 56076.6i | 0.678626 | + | 0.0903086i | ||||
\(789\) | 51345.1 | 0.0824794 | ||||||||
\(790\) | 420943. | + | 27885.7i | 0.674480 | + | 0.0446815i | ||||
\(791\) | 261519.i | 0.417974i | ||||||||
\(792\) | 356725. | + | 71735.4i | 0.568701 | + | 0.114362i | ||||
\(793\) | 126075. | 0.200485 | ||||||||
\(794\) | 39995.4 | − | 603742.i | 0.0634408 | − | 0.957657i | ||||
\(795\) | − | 287874.i | − | 0.455478i | ||||||
\(796\) | −125035. | + | 939581.i | −0.197336 | + | 1.48289i | ||||
\(797\) | −709741. | −1.11734 | −0.558668 | − | 0.829392i | \(-0.688687\pi\) | ||||
−0.558668 | + | 0.829392i | \(0.688687\pi\) | |||||||
\(798\) | 102309. | + | 6777.53i | 0.160660 | + | 0.0106430i | ||||
\(799\) | − | 14385.8i | − | 0.0225341i | ||||||
\(800\) | 41567.8 | − | 121062.i | 0.0649497 | − | 0.189160i | ||||
\(801\) | −372468. | −0.580529 | ||||||||
\(802\) | 21020.7 | − | 317314.i | 0.0326813 | − | 0.493334i | ||||
\(803\) | 1.64468e6i | 2.55064i | ||||||||
\(804\) | 250621. | + | 33351.5i | 0.387708 | + | 0.0515945i | ||||
\(805\) | 134098. | 0.206934 | ||||||||
\(806\) | 638993. | + | 42330.6i | 0.983617 | + | 0.0651605i | ||||
\(807\) | 552089.i | 0.847738i | ||||||||
\(808\) | 59848.9 | − | 297616.i | 0.0916713 | − | 0.455862i | ||||
\(809\) | 165063. | 0.252204 | 0.126102 | − | 0.992017i | \(-0.459753\pi\) | ||||
0.126102 | + | 0.992017i | \(0.459753\pi\) | |||||||
\(810\) | −2155.01 | + | 32530.6i | −0.00328458 | + | 0.0495817i | ||||
\(811\) | − | 1.10477e6i | − | 1.67969i | −0.542823 | − | 0.839847i | \(-0.682644\pi\) | ||
0.542823 | − | 0.839847i | \(-0.317356\pi\) | |||||||
\(812\) | −102789. | + | 772414.i | −0.155897 | + | 1.17149i | ||||
\(813\) | −335156. | −0.507068 | ||||||||
\(814\) | 508482. | + | 33684.8i | 0.767409 | + | 0.0508377i | ||||
\(815\) | − | 166766.i | − | 0.251069i | ||||||
\(816\) | 2661.96 | − | 9824.56i | 0.00399780 | − | 0.0147548i | ||||
\(817\) | 252095. | 0.377677 | ||||||||
\(818\) | 77842.1 | − | 1.17505e6i | 0.116334 | − | 1.75610i | ||||
\(819\) | 108419.i | 0.161636i | ||||||||
\(820\) | −265660. | − | 35352.9i | −0.395093 | − | 0.0525772i | ||||
\(821\) | −479717. | −0.711703 | −0.355851 | − | 0.934543i | \(-0.615809\pi\) | ||||
−0.355851 | + | 0.934543i | \(0.615809\pi\) | |||||||
\(822\) | −620282. | − | 41091.1i | −0.918006 | − | 0.0608141i | ||||
\(823\) | 462067.i | 0.682190i | 0.940029 | + | 0.341095i | \(0.110798\pi\) | ||||
−0.940029 | + | 0.341095i | \(0.889202\pi\) | |||||||
\(824\) | 34456.4 | + | 6928.99i | 0.0507476 | + | 0.0102051i | ||||
\(825\) | −136770. | −0.200948 | ||||||||
\(826\) | 3918.90 | − | 59156.9i | 0.00574386 | − | 0.0867052i | ||||
\(827\) | 986535.i | 1.44245i | 0.692699 | + | 0.721226i | \(0.256421\pi\) | ||||
−0.692699 | + | 0.721226i | \(0.743579\pi\) | |||||||
\(828\) | −23102.5 | + | 173604.i | −0.0336976 | + | 0.253221i | ||||
\(829\) | −919939. | −1.33860 | −0.669298 | − | 0.742994i | \(-0.733405\pi\) | ||||
−0.669298 | + | 0.742994i | \(0.733405\pi\) | |||||||
\(830\) | −423388. | − | 28047.7i | −0.614585 | − | 0.0407137i | ||||
\(831\) | − | 515223.i | − | 0.746094i | ||||||
\(832\) | 512720. | + | 214901.i | 0.740686 | + | 0.310449i | ||||
\(833\) | −11674.6 | −0.0168249 | ||||||||
\(834\) | −32901.4 | + | 496656.i | −0.0473023 | + | 0.714041i | ||||
\(835\) | 298456.i | 0.428063i | ||||||||
\(836\) | −556865. | − | 74105.1i | −0.796778 | − | 0.106032i | ||||
\(837\) | −165489. | −0.236220 | ||||||||
\(838\) | 1.00000e6 | + | 66246.1i | 1.42401 | + | 0.0943349i | ||||
\(839\) | − | 913352.i | − | 1.29752i | −0.760993 | − | 0.648760i | \(-0.775288\pi\) | ||
0.760993 | − | 0.648760i | \(-0.224712\pi\) | |||||||
\(840\) | −21686.4 | + | 107842.i | −0.0307347 | + | 0.152837i | ||||
\(841\) | 2.00245e6 | 2.83119 | ||||||||
\(842\) | 45421.4 | − | 685649.i | 0.0640673 | − | 0.967114i | ||||
\(843\) | − | 275518.i | − | 0.387699i | ||||||
\(844\) | 111748. | − | 839736.i | 0.156876 | − | 1.17885i | ||||
\(845\) | 113361. | 0.158764 | ||||||||
\(846\) | −202596. | − | 13421.2i | −0.283068 | − | 0.0187521i | ||||
\(847\) | − | 878664.i | − | 1.22477i | ||||||
\(848\) | 1.22439e6 | + | 331749.i | 1.70267 | + | 0.461337i | ||||
\(849\) | −701618. | −0.973387 | ||||||||
\(850\) | −252.902 | + | 3817.63i | −0.000350037 | + | 0.00528392i | ||||
\(851\) | 245277.i | 0.338687i | ||||||||
\(852\) | 573897. | + | 76371.8i | 0.790597 | + | 0.105209i | ||||
\(853\) | 514313. | 0.706854 | 0.353427 | − | 0.935462i | \(-0.385016\pi\) | ||||
0.353427 | + | 0.935462i | \(0.385016\pi\) | |||||||
\(854\) | −109686. | − | 7266.24i | −0.150396 | − | 0.00996309i | ||||
\(855\) | − | 50334.0i | − | 0.0688540i | ||||||
\(856\) | −106215. | − | 21359.2i | −0.144957 | − | 0.0291499i | ||||
\(857\) | −415272. | −0.565420 | −0.282710 | − | 0.959205i | \(-0.591233\pi\) | ||||
−0.282710 | + | 0.959205i | \(0.591233\pi\) | |||||||
\(858\) | 39265.6 | − | 592726.i | 0.0533382 | − | 0.805155i | ||||
\(859\) | 516118.i | 0.699459i | 0.936851 | + | 0.349730i | \(0.113727\pi\) | ||||
−0.936851 | + | 0.349730i | \(0.886273\pi\) | |||||||
\(860\) | −35676.6 | + | 268093.i | −0.0482377 | + | 0.362484i | ||||
\(861\) | 230316. | 0.310683 | ||||||||
\(862\) | −570639. | − | 37802.4i | −0.767975 | − | 0.0508751i | ||||
\(863\) | − | 535169.i | − | 0.718570i | −0.933228 | − | 0.359285i | \(-0.883021\pi\) | ||
0.933228 | − | 0.359285i | \(-0.116979\pi\) | |||||||
\(864\) | −135877. | − | 46654.4i | −0.182019 | − | 0.0624979i | ||||
\(865\) | −461826. | −0.617228 | ||||||||
\(866\) | 20592.9 | − | 310855.i | 0.0274587 | − | 0.414498i | ||||
\(867\) | − | 433684.i | − | 0.576946i | ||||||
\(868\) | −553490. | − | 73656.0i | −0.734632 | − | 0.0977617i | ||||
\(869\) | 1.98636e6 | 2.63038 | ||||||||
\(870\) | 381688. | + | 25285.3i | 0.504279 | + | 0.0334063i | ||||
\(871\) | − | 412754.i | − | 0.544071i | ||||||
\(872\) | 200439. | − | 996744.i | 0.263603 | − | 1.31084i | ||||
\(873\) | 207774. | 0.272623 | ||||||||
\(874\) | 17873.1 | − | 269799.i | 0.0233979 | − | 0.353198i | ||||
\(875\) | − | 41347.0i | − | 0.0540042i | ||||||
\(876\) | 85658.5 | − | 643683.i | 0.111625 | − | 0.838810i | ||||
\(877\) | 70986.4 | 0.0922945 | 0.0461473 | − | 0.998935i | \(-0.485306\pi\) | ||||
0.0461473 | + | 0.998935i | \(0.485306\pi\) | |||||||
\(878\) | 183053. | + | 12126.5i | 0.237459 | + | 0.0157307i | ||||
\(879\) | − | 694930.i | − | 0.899422i | ||||||
\(880\) | 157615. | − | 581715.i | 0.203532 | − | 0.751181i | ||||
\(881\) | −348009. | −0.448372 | −0.224186 | − | 0.974546i | \(-0.571972\pi\) | ||||
−0.224186 | + | 0.974546i | \(0.571972\pi\) | |||||||
\(882\) | −10891.8 | + | 164415.i | −0.0140011 | + | 0.211351i | ||||
\(883\) | − | 1.32985e6i | − | 1.70562i | −0.522222 | − | 0.852810i | \(-0.674897\pi\) | ||
0.522222 | − | 0.852810i | \(-0.325103\pi\) | |||||||
\(884\) | −16472.0 | − | 2192.03i | −0.0210787 | − | 0.00280506i | ||||
\(885\) | −29104.1 | −0.0371593 | ||||||||
\(886\) | −711505. | − | 47134.3i | −0.906381 | − | 0.0600439i | ||||
\(887\) | 633096.i | 0.804678i | 0.915491 | + | 0.402339i | \(0.131803\pi\) | ||||
−0.915491 | + | 0.402339i | \(0.868197\pi\) | |||||||
\(888\) | −197252. | − | 39666.3i | −0.250147 | − | 0.0503032i | ||||
\(889\) | −82532.4 | −0.104429 | ||||||||
\(890\) | −40780.1 | + | 615587.i | −0.0514835 | + | 0.777158i | ||||
\(891\) | 153506.i | 0.193362i | ||||||||
\(892\) | 25795.0 | − | 193837.i | 0.0324195 | − | 0.243617i | ||||
\(893\) | 313474. | 0.393096 | ||||||||
\(894\) | −92054.3 | − | 6098.21i | −0.115178 | − | 0.00763005i | ||||
\(895\) | − | 344269.i | − | 0.429785i | ||||||
\(896\) | −433685. | − | 216516.i | −0.540205 | − | 0.269695i | ||||
\(897\) | 285914. | 0.355345 | ||||||||
\(898\) | −19178.1 | + | 289499.i | −0.0237822 | + | 0.359000i | ||||
\(899\) | 1.94171e6i | 2.40251i | ||||||||
\(900\) | 53528.1 | + | 7123.29i | 0.0660841 | + | 0.00879418i | ||||
\(901\) | −37917.5 | −0.0467079 | ||||||||
\(902\) | −1.25913e6 | − | 83412.3i | −1.54760 | − | 0.102522i | ||||
\(903\) | − | 232425.i | − | 0.285041i | ||||||
\(904\) | −111531. | + | 554620.i | −0.136477 | + | 0.678670i | ||||
\(905\) | 65561.7 | 0.0800484 | ||||||||
\(906\) | 10651.9 | − | 160793.i | 0.0129769 | − | 0.195890i | ||||
\(907\) | − | 375984.i | − | 0.457041i | −0.973539 | − | 0.228520i | \(-0.926611\pi\) | ||
0.973539 | − | 0.228520i | \(-0.0733887\pi\) | |||||||
\(908\) | 111822. | − | 840290.i | 0.135630 | − | 1.01920i | ||||
\(909\) | 128070. | 0.154996 | ||||||||
\(910\) | 179187. | + | 11870.4i | 0.216384 | + | 0.0143345i | ||||
\(911\) | 265425.i | 0.319819i | 0.987132 | + | 0.159910i | \(0.0511203\pi\) | ||||
−0.987132 | + | 0.159910i | \(0.948880\pi\) | |||||||
\(912\) | 214082. | + | 58005.6i | 0.257390 | + | 0.0697397i | ||||
\(913\) | −1.99790e6 | −2.39680 | ||||||||
\(914\) | −5638.16 | + | 85109.7i | −0.00674909 | + | 0.101879i | ||||
\(915\) | 53963.5i | 0.0644552i | ||||||||
\(916\) | −416955. | − | 55486.6i | −0.496934 | − | 0.0661298i | ||||
\(917\) | −349665. | −0.415828 | ||||||||
\(918\) | 4284.79 | + | 283.849i | 0.00508445 | + | 0.000336824i | ||||
\(919\) | 283610.i | 0.335808i | 0.985803 | + | 0.167904i | \(0.0536999\pi\) | ||||
−0.985803 | + | 0.167904i | \(0.946300\pi\) | |||||||
\(920\) | 284391. | + | 57189.4i | 0.336000 | + | 0.0675678i | ||||
\(921\) | 651525. | 0.768090 | ||||||||
\(922\) | −6567.66 | + | 99140.7i | −0.00772589 | + | 0.116625i | ||||
\(923\) | − | 945167.i | − | 1.10944i | ||||||
\(924\) | −68322.9 | + | 513414.i | −0.0800244 | + | 0.601345i | ||||
\(925\) | 75627.2 | 0.0883883 | ||||||||
\(926\) | −258106. | − | 17098.5i | −0.301007 | − | 0.0199405i | ||||
\(927\) | 14827.3i | 0.0172545i | ||||||||
\(928\) | −547407. | + | 1.59427e6i | −0.635644 | + | 1.85126i | ||||
\(929\) | 871065. | 1.00930 | 0.504649 | − | 0.863325i | \(-0.331622\pi\) | ||||
0.504649 | + | 0.863325i | \(0.331622\pi\) | |||||||
\(930\) | −18118.7 | + | 273507.i | −0.0209489 | + | 0.316230i | ||||
\(931\) | − | 254397.i | − | 0.293503i | ||||||
\(932\) | −601018. | − | 79980.9i | −0.691920 | − | 0.0920777i | ||||
\(933\) | −179460. | −0.206160 | ||||||||
\(934\) | −690057. | − | 45713.4i | −0.791027 | − | 0.0524023i | ||||
\(935\) | 18014.8i | 0.0206065i | ||||||||
\(936\) | −46238.1 | + | 229932.i | −0.0527774 | + | 0.262451i | ||||
\(937\) | 981541. | 1.11797 | 0.558984 | − | 0.829178i | \(-0.311191\pi\) | ||||
0.558984 | + | 0.829178i | \(0.311191\pi\) | |||||||
\(938\) | −23788.9 | + | 359100.i | −0.0270376 | + | 0.408140i | ||||
\(939\) | − | 86606.0i | − | 0.0982239i | ||||||
\(940\) | −44363.0 | + | 333367.i | −0.0502071 | + | 0.377282i | ||||
\(941\) | 1.53969e6 | 1.73882 | 0.869409 | − | 0.494094i | \(-0.164500\pi\) | ||||
0.869409 | + | 0.494094i | \(0.164500\pi\) | |||||||
\(942\) | 601449. | + | 39843.5i | 0.677793 | + | 0.0449010i | ||||
\(943\) | − | 607369.i | − | 0.683013i | ||||||
\(944\) | 33539.9 | − | 123787.i | 0.0376373 | − | 0.138909i | ||||
\(945\) | −46406.6 | −0.0519656 | ||||||||
\(946\) | −84176.0 | + | 1.27066e6i | −0.0940602 | + | 1.41987i | ||||
\(947\) | 100610.i | 0.112187i | 0.998426 | + | 0.0560933i | \(0.0178644\pi\) | ||||
−0.998426 | + | 0.0560933i | \(0.982136\pi\) | |||||||
\(948\) | −777408. | − | 103454.i | −0.865032 | − | 0.115115i | ||||
\(949\) | −1.06010e6 | −1.17710 | ||||||||
\(950\) | −83188.3 | − | 5510.87i | −0.0921754 | − | 0.00610623i | ||||
\(951\) | 383279.i | 0.423793i | ||||||||
\(952\) | 14204.5 | + | 2856.44i | 0.0156730 | + | 0.00315175i | ||||
\(953\) | −1.47750e6 | −1.62683 | −0.813415 | − | 0.581683i | \(-0.802394\pi\) | ||||
−0.813415 | + | 0.581683i | \(0.802394\pi\) | |||||||
\(954\) | −35375.0 | + | 533996.i | −0.0388687 | + | 0.586734i | ||||
\(955\) | 772355.i | 0.846857i | ||||||||
\(956\) | 15809.3 | − | 118799.i | 0.0172980 | − | 0.129986i | ||||
\(957\) | 1.80112e6 | 1.96662 | ||||||||
\(958\) | −79547.4 | − | 5269.68i | −0.0866752 | − | 0.00574187i | ||||
\(959\) | − | 884865.i | − | 0.962143i | ||||||
\(960\) | −91983.5 | + | 219459.i | −0.0998085 | + | 0.238128i | ||||
\(961\) | −467856. | −0.506600 | ||||||||
\(962\) | −21712.0 | + | 327749.i | −0.0234612 | + | 0.354154i | ||||
\(963\) | − | 45706.5i | − | 0.0492862i | ||||||
\(964\) | −1.20592e6 | − | 160479.i | −1.29767 | − | 0.172688i | ||||
\(965\) | −434180. | −0.466246 | ||||||||
\(966\) | −248748. | − | 16478.5i | −0.266566 | − | 0.0176589i | ||||
\(967\) | − | 768191.i | − | 0.821517i | −0.911744 | − | 0.410758i | \(-0.865264\pi\) | ||
0.911744 | − | 0.410758i | \(-0.134736\pi\) | |||||||
\(968\) | 374727. | − | 1.86344e6i | 0.399912 | − | 1.98868i | ||||
\(969\) | −6629.79 | −0.00706077 | ||||||||
\(970\) | 22748.3 | − | 343393.i | 0.0241772 | − | 0.364962i | ||||
\(971\) | − | 458094.i | − | 0.485866i | −0.970043 | − | 0.242933i | \(-0.921891\pi\) | ||
0.970043 | − | 0.242933i | \(-0.0781094\pi\) | |||||||
\(972\) | 7994.96 | − | 60078.3i | 0.00846221 | − | 0.0635894i | ||||
\(973\) | −708506. | −0.748372 | ||||||||
\(974\) | 439626. | + | 29123.4i | 0.463410 | + | 0.0306990i | ||||
\(975\) | − | 88156.9i | − | 0.0927357i | ||||||
\(976\) | −229519. | − | 62188.2i | −0.240946 | − | 0.0652842i | ||||
\(977\) | 905743. | 0.948890 | 0.474445 | − | 0.880285i | \(-0.342649\pi\) | ||||
0.474445 | + | 0.880285i | \(0.342649\pi\) | |||||||
\(978\) | −20492.8 | + | 309345.i | −0.0214252 | + | 0.323419i | ||||
\(979\) | 2.90485e6i | 3.03081i | ||||||||
\(980\) | 270540. | + | 36002.3i | 0.281695 | + | 0.0374868i | ||||
\(981\) | 428919. | 0.445695 | ||||||||
\(982\) | −656807. | − | 43510.7i | −0.681106 | − | 0.0451205i | ||||
\(983\) | 776569.i | 0.803661i | 0.915714 | + | 0.401830i | \(0.131626\pi\) | ||||
−0.915714 | + | 0.401830i | \(0.868374\pi\) | |||||||
\(984\) | 488447. | + | 98223.8i | 0.504460 | + | 0.101444i | ||||
\(985\) | 297050. | 0.306166 | ||||||||
\(986\) | 3330.47 | − | 50274.4i | 0.00342572 | − | 0.0517122i | ||||
\(987\) | − | 289015.i | − | 0.296678i | ||||||
\(988\) | 47765.5 | − | 358935.i | 0.0489328 | − | 0.367707i | ||||
\(989\) | −612930. | −0.626640 | ||||||||
\(990\) | 253704. | + | 16806.8i | 0.258855 | + | 0.0171480i | ||||
\(991\) | − | 1.06325e6i | − | 1.08265i | −0.840812 | − | 0.541327i | \(-0.817922\pi\) | ||
0.840812 | − | 0.541327i | \(-0.182078\pi\) | |||||||
\(992\) | −1.14241e6 | − | 392256.i | −1.16091 | − | 0.398608i | ||||
\(993\) | −638110. | −0.647138 | ||||||||
\(994\) | −54474.2 | + | 822304.i | −0.0551338 | + | 0.832261i | ||||
\(995\) | 662340.i | 0.669014i | ||||||||
\(996\) | 781923. | + | 104055.i | 0.788216 | + | 0.104892i | ||||
\(997\) | 1.19772e6 | 1.20494 | 0.602470 | − | 0.798141i | \(-0.294183\pi\) | ||||
0.602470 | + | 0.798141i | \(0.294183\pi\) | |||||||
\(998\) | 416581. | + | 27596.8i | 0.418252 | + | 0.0277075i | ||||
\(999\) | − | 84881.7i | − | 0.0850517i |
(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 | 60.5.c.a.31.9 | ✓ | 16 | |
3.2 | odd | 2 | 180.5.c.c.91.8 | 16 | |||
4.3 | odd | 2 | inner | 60.5.c.a.31.10 | yes | 16 | |
5.2 | odd | 4 | 300.5.f.b.199.32 | 32 | |||
5.3 | odd | 4 | 300.5.f.b.199.1 | 32 | |||
5.4 | even | 2 | 300.5.c.d.151.8 | 16 | |||
8.3 | odd | 2 | 960.5.e.f.511.13 | 16 | |||
8.5 | even | 2 | 960.5.e.f.511.8 | 16 | |||
12.11 | even | 2 | 180.5.c.c.91.7 | 16 | |||
20.3 | even | 4 | 300.5.f.b.199.31 | 32 | |||
20.7 | even | 4 | 300.5.f.b.199.2 | 32 | |||
20.19 | odd | 2 | 300.5.c.d.151.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.5.c.a.31.9 | ✓ | 16 | 1.1 | even | 1 | trivial | |
60.5.c.a.31.10 | yes | 16 | 4.3 | odd | 2 | inner | |
180.5.c.c.91.7 | 16 | 12.11 | even | 2 | |||
180.5.c.c.91.8 | 16 | 3.2 | odd | 2 | |||
300.5.c.d.151.7 | 16 | 20.19 | odd | 2 | |||
300.5.c.d.151.8 | 16 | 5.4 | even | 2 | |||
300.5.f.b.199.1 | 32 | 5.3 | odd | 4 | |||
300.5.f.b.199.2 | 32 | 20.7 | even | 4 | |||
300.5.f.b.199.31 | 32 | 20.3 | even | 4 | |||
300.5.f.b.199.32 | 32 | 5.2 | odd | 4 | |||
960.5.e.f.511.8 | 16 | 8.5 | even | 2 | |||
960.5.e.f.511.13 | 16 | 8.3 | odd | 2 |