Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.6");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.c (of order \(3\), degree \(2\), 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: | \(6.89650425196\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 36.7 | ||
Character | \(\chi\) | \(=\) | 43.36 |
Dual form | 43.6.c.a.6.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.30883 | −0.584925 | −0.292462 | − | 0.956277i | \(-0.594475\pi\) | ||||
−0.292462 | + | 0.956277i | \(0.594475\pi\) | |||||||
\(3\) | −12.3585 | − | 21.4055i | −0.792797 | − | 1.37316i | −0.924229 | − | 0.381840i | \(-0.875291\pi\) |
0.131431 | − | 0.991325i | \(-0.458043\pi\) | |||||||
\(4\) | −21.0516 | −0.657863 | ||||||||
\(5\) | −32.1287 | − | 55.6486i | −0.574736 | − | 0.995472i | −0.996070 | − | 0.0885663i | \(-0.971771\pi\) |
0.421334 | − | 0.906905i | \(-0.361562\pi\) | |||||||
\(6\) | 40.8922 | + | 70.8273i | 0.463727 | + | 0.803198i | ||||
\(7\) | −2.83477 | + | 4.90997i | −0.0218662 | + | 0.0378734i | −0.876751 | − | 0.480944i | \(-0.840294\pi\) |
0.854885 | + | 0.518817i | \(0.173627\pi\) | |||||||
\(8\) | 175.539 | 0.969725 | ||||||||
\(9\) | −183.964 | + | 318.635i | −0.757055 | + | 1.31126i | ||||
\(10\) | 106.309 | + | 184.132i | 0.336177 | + | 0.582276i | ||||
\(11\) | −20.0109 | −0.0498638 | −0.0249319 | − | 0.999689i | \(-0.507937\pi\) | ||||
−0.0249319 | + | 0.999689i | \(0.507937\pi\) | |||||||
\(12\) | 260.166 | + | 450.621i | 0.521552 | + | 0.903355i | ||||
\(13\) | 308.316 | − | 534.019i | 0.505985 | − | 0.876392i | −0.493991 | − | 0.869467i | \(-0.664462\pi\) |
0.999976 | − | 0.00692491i | \(-0.00220428\pi\) | |||||||
\(14\) | 9.37980 | − | 16.2463i | 0.0127901 | − | 0.0221531i | ||||
\(15\) | −794.124 | + | 1375.46i | −0.911298 | + | 1.57841i | ||||
\(16\) | 92.8229 | 0.0906473 | ||||||||
\(17\) | −987.938 | + | 1711.16i | −0.829101 | + | 1.43605i | 0.0696433 | + | 0.997572i | \(0.477814\pi\) |
−0.898744 | + | 0.438473i | \(0.855519\pi\) | |||||||
\(18\) | 608.707 | − | 1054.31i | 0.442820 | − | 0.766987i | ||||
\(19\) | −488.757 | − | 846.552i | −0.310605 | − | 0.537984i | 0.667888 | − | 0.744262i | \(-0.267198\pi\) |
−0.978494 | + | 0.206277i | \(0.933865\pi\) | |||||||
\(20\) | 676.361 | + | 1171.49i | 0.378098 | + | 0.654884i | ||||
\(21\) | 140.134 | 0.0693419 | ||||||||
\(22\) | 66.2128 | 0.0291666 | ||||||||
\(23\) | −165.175 | − | 286.091i | −0.0651065 | − | 0.112768i | 0.831635 | − | 0.555323i | \(-0.187405\pi\) |
−0.896741 | + | 0.442555i | \(0.854072\pi\) | |||||||
\(24\) | −2169.40 | − | 3757.50i | −0.768795 | − | 1.33159i | ||||
\(25\) | −502.008 | + | 869.503i | −0.160642 | + | 0.278241i | ||||
\(26\) | −1020.17 | + | 1766.98i | −0.295963 | + | 0.512623i | ||||
\(27\) | 3087.86 | 0.815169 | ||||||||
\(28\) | 59.6766 | − | 103.363i | 0.0143850 | − | 0.0249155i | ||||
\(29\) | 4087.98 | − | 7080.58i | 0.902638 | − | 1.56341i | 0.0785806 | − | 0.996908i | \(-0.474961\pi\) |
0.824057 | − | 0.566507i | \(-0.191705\pi\) | |||||||
\(30\) | 2627.62 | − | 4551.18i | 0.533040 | − | 0.923253i | ||||
\(31\) | 2161.10 | + | 3743.14i | 0.403897 | + | 0.699571i | 0.994192 | − | 0.107617i | \(-0.0343219\pi\) |
−0.590295 | + | 0.807188i | \(0.700989\pi\) | |||||||
\(32\) | −5924.38 | −1.02275 | ||||||||
\(33\) | 247.305 | + | 428.345i | 0.0395319 | + | 0.0684713i | ||||
\(34\) | 3268.92 | − | 5661.94i | 0.484962 | − | 0.839978i | ||||
\(35\) | 364.311 | 0.0502692 | ||||||||
\(36\) | 3872.75 | − | 6707.79i | 0.498038 | − | 0.862628i | ||||
\(37\) | 3707.25 | + | 6421.15i | 0.445193 | + | 0.771096i | 0.998066 | − | 0.0621694i | \(-0.0198019\pi\) |
−0.552873 | + | 0.833265i | \(0.686469\pi\) | |||||||
\(38\) | 1617.22 | + | 2801.10i | 0.181681 | + | 0.314680i | ||||
\(39\) | −15241.3 | −1.60457 | ||||||||
\(40\) | −5639.84 | − | 9768.49i | −0.557336 | − | 0.965334i | ||||
\(41\) | −18961.8 | −1.76165 | −0.880826 | − | 0.473440i | \(-0.843012\pi\) | ||||
−0.880826 | + | 0.473440i | \(0.843012\pi\) | |||||||
\(42\) | −463.680 | −0.0405598 | ||||||||
\(43\) | −8008.53 | + | 9103.40i | −0.660513 | + | 0.750814i | ||||
\(44\) | 421.263 | 0.0328036 | ||||||||
\(45\) | 23642.1 | 1.74043 | ||||||||
\(46\) | 546.536 | + | 946.628i | 0.0380824 | + | 0.0659606i | ||||
\(47\) | −7983.99 | −0.527200 | −0.263600 | − | 0.964632i | \(-0.584910\pi\) | ||||
−0.263600 | + | 0.964632i | \(0.584910\pi\) | |||||||
\(48\) | −1147.15 | − | 1986.92i | −0.0718649 | − | 0.124474i | ||||
\(49\) | 8387.43 | + | 14527.5i | 0.499044 | + | 0.864369i | ||||
\(50\) | 1661.06 | − | 2877.04i | 0.0939637 | − | 0.162750i | ||||
\(51\) | 48837.7 | 2.62924 | ||||||||
\(52\) | −6490.55 | + | 11242.0i | −0.332869 | + | 0.576546i | ||||
\(53\) | 11296.3 | + | 19565.8i | 0.552393 | + | 0.956772i | 0.998101 | + | 0.0615941i | \(0.0196184\pi\) |
−0.445709 | + | 0.895178i | \(0.647048\pi\) | |||||||
\(54\) | −10217.2 | −0.476812 | ||||||||
\(55\) | 642.925 | + | 1113.58i | 0.0286585 | + | 0.0496380i | ||||
\(56\) | −497.613 | + | 861.892i | −0.0212042 | + | 0.0367268i | ||||
\(57\) | −12080.6 | + | 20924.2i | −0.492494 | + | 0.853025i | ||||
\(58\) | −13526.4 | + | 23428.5i | −0.527975 | + | 0.914480i | ||||
\(59\) | −22587.1 | −0.844753 | −0.422377 | − | 0.906420i | \(-0.638804\pi\) | ||||
−0.422377 | + | 0.906420i | \(0.638804\pi\) | |||||||
\(60\) | 16717.6 | − | 28955.7i | 0.599509 | − | 1.03838i | ||||
\(61\) | 1052.98 | − | 1823.81i | 0.0362321 | − | 0.0627559i | −0.847341 | − | 0.531050i | \(-0.821798\pi\) |
0.883573 | + | 0.468294i | \(0.155131\pi\) | |||||||
\(62\) | −7150.73 | − | 12385.4i | −0.236250 | − | 0.409196i | ||||
\(63\) | −1042.99 | − | 1806.52i | −0.0331078 | − | 0.0573444i | ||||
\(64\) | 16632.5 | 0.507582 | ||||||||
\(65\) | −39623.2 | −1.16323 | ||||||||
\(66\) | −818.290 | − | 1417.32i | −0.0231232 | − | 0.0400505i | ||||
\(67\) | −11191.7 | − | 19384.7i | −0.304586 | − | 0.527559i | 0.672583 | − | 0.740022i | \(-0.265185\pi\) |
−0.977169 | + | 0.212463i | \(0.931852\pi\) | |||||||
\(68\) | 20797.7 | − | 36022.7i | 0.545435 | − | 0.944721i | ||||
\(69\) | −4082.62 | + | 7071.31i | −0.103232 | + | 0.178804i | ||||
\(70\) | −1205.44 | −0.0294037 | ||||||||
\(71\) | 2483.70 | − | 4301.89i | 0.0584727 | − | 0.101278i | −0.835307 | − | 0.549783i | \(-0.814710\pi\) |
0.893780 | + | 0.448506i | \(0.148044\pi\) | |||||||
\(72\) | −32292.9 | + | 55932.9i | −0.734135 | + | 1.27156i | ||||
\(73\) | −16393.1 | + | 28393.7i | −0.360042 | + | 0.623612i | −0.987967 | − | 0.154662i | \(-0.950571\pi\) |
0.627925 | + | 0.778274i | \(0.283904\pi\) | |||||||
\(74\) | −12266.7 | − | 21246.5i | −0.260404 | − | 0.451033i | ||||
\(75\) | 24816.2 | 0.509428 | ||||||||
\(76\) | 10289.1 | + | 17821.3i | 0.204336 | + | 0.353920i | ||||
\(77\) | 56.7265 | − | 98.2532i | 0.00109033 | − | 0.00188851i | ||||
\(78\) | 50430.8 | 0.938555 | ||||||||
\(79\) | 26323.6 | − | 45593.7i | 0.474544 | − | 0.821935i | −0.525031 | − | 0.851083i | \(-0.675946\pi\) |
0.999575 | + | 0.0291484i | \(0.00927953\pi\) | |||||||
\(80\) | −2982.28 | − | 5165.46i | −0.0520983 | − | 0.0902368i | ||||
\(81\) | 6542.10 | + | 11331.3i | 0.110791 | + | 0.191896i | ||||
\(82\) | 62741.5 | 1.03043 | ||||||||
\(83\) | −58362.7 | − | 101087.i | −0.929908 | − | 1.61065i | −0.783471 | − | 0.621428i | \(-0.786553\pi\) |
−0.146437 | − | 0.989220i | \(-0.546781\pi\) | |||||||
\(84\) | −2950.05 | −0.0456175 | ||||||||
\(85\) | 126965. | 1.90606 | ||||||||
\(86\) | 26498.9 | − | 30121.6i | 0.386350 | − | 0.439170i | ||||
\(87\) | −202085. | −2.86243 | ||||||||
\(88\) | −3512.70 | −0.0483542 | ||||||||
\(89\) | 19352.1 | + | 33518.8i | 0.258972 | + | 0.448553i | 0.965967 | − | 0.258666i | \(-0.0832829\pi\) |
−0.706995 | + | 0.707219i | \(0.749950\pi\) | |||||||
\(90\) | −78227.9 | −1.01802 | ||||||||
\(91\) | 1748.01 | + | 3027.65i | 0.0221280 | + | 0.0383267i | ||||
\(92\) | 3477.20 | + | 6022.68i | 0.0428312 | + | 0.0741858i | ||||
\(93\) | 53415.9 | − | 92519.1i | 0.640418 | − | 1.10924i | ||||
\(94\) | 26417.7 | 0.308372 | ||||||||
\(95\) | −31406.3 | + | 54397.3i | −0.357032 | + | 0.618398i | ||||
\(96\) | 73216.4 | + | 126815.i | 0.810831 | + | 1.40440i | ||||
\(97\) | 75843.3 | 0.818442 | 0.409221 | − | 0.912435i | \(-0.365801\pi\) | ||||
0.409221 | + | 0.912435i | \(0.365801\pi\) | |||||||
\(98\) | −27752.6 | − | 48068.9i | −0.291903 | − | 0.505591i | ||||
\(99\) | 3681.30 | − | 6376.19i | 0.0377496 | − | 0.0653843i | ||||
\(100\) | 10568.1 | − | 18304.4i | 0.105681 | − | 0.183044i | ||||
\(101\) | 17528.7 | − | 30360.7i | 0.170981 | − | 0.296147i | −0.767782 | − | 0.640711i | \(-0.778640\pi\) |
0.938763 | + | 0.344564i | \(0.111973\pi\) | |||||||
\(102\) | −161596. | −1.53790 | ||||||||
\(103\) | 30269.3 | − | 52428.0i | 0.281131 | − | 0.486934i | −0.690532 | − | 0.723302i | \(-0.742624\pi\) |
0.971664 | + | 0.236368i | \(0.0759570\pi\) | |||||||
\(104\) | 54121.5 | − | 93741.2i | 0.490666 | − | 0.849859i | ||||
\(105\) | −4502.33 | − | 7798.26i | −0.0398533 | − | 0.0690279i | ||||
\(106\) | −37377.7 | − | 64740.1i | −0.323108 | − | 0.559640i | ||||
\(107\) | −212499. | −1.79431 | −0.897155 | − | 0.441716i | \(-0.854370\pi\) | ||||
−0.897155 | + | 0.441716i | \(0.854370\pi\) | |||||||
\(108\) | −65004.4 | −0.536270 | ||||||||
\(109\) | 95684.1 | + | 165730.i | 0.771390 | + | 1.33609i | 0.936801 | + | 0.349861i | \(0.113771\pi\) |
−0.165412 | + | 0.986225i | \(0.552895\pi\) | |||||||
\(110\) | −2127.33 | − | 3684.65i | −0.0167631 | − | 0.0290345i | ||||
\(111\) | 91632.0 | − | 158711.i | 0.705895 | − | 1.22265i | ||||
\(112\) | −263.132 | + | 455.758i | −0.00198211 | + | 0.00343312i | ||||
\(113\) | −8628.08 | −0.0635650 | −0.0317825 | − | 0.999495i | \(-0.510118\pi\) | ||||
−0.0317825 | + | 0.999495i | \(0.510118\pi\) | |||||||
\(114\) | 39972.7 | − | 69234.7i | 0.288072 | − | 0.498955i | ||||
\(115\) | −10613.7 | + | 18383.5i | −0.0748381 | + | 0.129623i | ||||
\(116\) | −86058.6 | + | 149058.i | −0.593812 | + | 1.02851i | ||||
\(117\) | 113438. | + | 196481.i | 0.766117 | + | 1.32695i | ||||
\(118\) | 74736.8 | 0.494117 | ||||||||
\(119\) | −5601.16 | − | 9701.50i | −0.0362586 | − | 0.0628017i | ||||
\(120\) | −139400. | + | 241447.i | −0.883708 | + | 1.53063i | ||||
\(121\) | −160651. | −0.997514 | ||||||||
\(122\) | −3484.12 | + | 6034.68i | −0.0211931 | + | 0.0367075i | ||||
\(123\) | 234339. | + | 405887.i | 1.39663 | + | 2.41904i | ||||
\(124\) | −45494.7 | − | 78799.2i | −0.265709 | − | 0.460222i | ||||
\(125\) | −136289. | −0.780164 | ||||||||
\(126\) | 3451.10 | + | 5977.47i | 0.0193656 | + | 0.0335422i | ||||
\(127\) | 63460.0 | 0.349133 | 0.174566 | − | 0.984645i | \(-0.444148\pi\) | ||||
0.174566 | + | 0.984645i | \(0.444148\pi\) | |||||||
\(128\) | 134546. | 0.725849 | ||||||||
\(129\) | 293836. | + | 58922.4i | 1.55465 | + | 0.311750i | ||||
\(130\) | 131107. | 0.680402 | ||||||||
\(131\) | 207196. | 1.05488 | 0.527439 | − | 0.849593i | \(-0.323152\pi\) | ||||
0.527439 | + | 0.849593i | \(0.323152\pi\) | |||||||
\(132\) | −5206.17 | − | 9017.35i | −0.0260066 | − | 0.0450447i | ||||
\(133\) | 5542.07 | 0.0271671 | ||||||||
\(134\) | 37031.6 | + | 64140.6i | 0.178160 | + | 0.308582i | ||||
\(135\) | −99208.8 | − | 171835.i | −0.468507 | − | 0.811477i | ||||
\(136\) | −173422. | + | 300375.i | −0.804000 | + | 1.39257i | ||||
\(137\) | −186818. | −0.850387 | −0.425194 | − | 0.905102i | \(-0.639794\pi\) | ||||
−0.425194 | + | 0.905102i | \(0.639794\pi\) | |||||||
\(138\) | 13508.7 | − | 23397.8i | 0.0603832 | − | 0.104587i | ||||
\(139\) | −214739. | − | 371939.i | −0.942702 | − | 1.63281i | −0.760289 | − | 0.649585i | \(-0.774943\pi\) |
−0.182413 | − | 0.983222i | \(-0.558391\pi\) | |||||||
\(140\) | −7669.33 | −0.0330702 | ||||||||
\(141\) | 98670.0 | + | 170901.i | 0.417962 | + | 0.723932i | ||||
\(142\) | −8218.14 | + | 14234.2i | −0.0342021 | + | 0.0592398i | ||||
\(143\) | −6169.69 | + | 10686.2i | −0.0252304 | + | 0.0437003i | ||||
\(144\) | −17076.1 | + | 29576.7i | −0.0686250 | + | 0.118862i | ||||
\(145\) | −525366. | −2.07511 | ||||||||
\(146\) | 54242.0 | − | 93949.9i | 0.210598 | − | 0.364766i | ||||
\(147\) | 207312. | − | 359075.i | 0.791281 | − | 1.37054i | ||||
\(148\) | −78043.7 | − | 135176.i | −0.292876 | − | 0.507276i | ||||
\(149\) | −143722. | − | 248933.i | −0.530343 | − | 0.918580i | −0.999373 | − | 0.0353985i | \(-0.988730\pi\) |
0.469031 | − | 0.883182i | \(-0.344603\pi\) | |||||||
\(150\) | −82112.7 | −0.297977 | ||||||||
\(151\) | 168989. | 0.603136 | 0.301568 | − | 0.953445i | \(-0.402490\pi\) | ||||
0.301568 | + | 0.953445i | \(0.402490\pi\) | |||||||
\(152\) | −85795.9 | − | 148603.i | −0.301202 | − | 0.521697i | ||||
\(153\) | −363491. | − | 629584.i | −1.25535 | − | 2.17433i | ||||
\(154\) | −187.699 | + | 325.103i | −0.000637763 | + | 0.00110464i | ||||
\(155\) | 138867. | − | 240524.i | 0.464269 | − | 0.804137i | ||||
\(156\) | 320854. | 1.05559 | ||||||||
\(157\) | −168011. | + | 291003.i | −0.543986 | + | 0.942212i | 0.454683 | + | 0.890653i | \(0.349752\pi\) |
−0.998670 | + | 0.0515591i | \(0.983581\pi\) | |||||||
\(158\) | −87100.2 | + | 150862.i | −0.277573 | + | 0.480770i | ||||
\(159\) | 279211. | − | 483608.i | 0.875871 | − | 1.51705i | ||||
\(160\) | 190343. | + | 329683.i | 0.587809 | + | 1.01812i | ||||
\(161\) | 1872.93 | 0.00569453 | ||||||||
\(162\) | −21646.7 | − | 37493.2i | −0.0648044 | − | 0.112245i | ||||
\(163\) | −25197.1 | + | 43642.7i | −0.0742818 | + | 0.128660i | −0.900774 | − | 0.434289i | \(-0.857000\pi\) |
0.826492 | + | 0.562949i | \(0.190333\pi\) | |||||||
\(164\) | 399177. | 1.15893 | ||||||||
\(165\) | 15891.2 | − | 27524.3i | 0.0454408 | − | 0.0787058i | ||||
\(166\) | 193112. | + | 334480.i | 0.543926 | + | 0.942108i | ||||
\(167\) | 56790.1 | + | 98363.3i | 0.157573 | + | 0.272924i | 0.933993 | − | 0.357292i | \(-0.116300\pi\) |
−0.776420 | + | 0.630216i | \(0.782966\pi\) | |||||||
\(168\) | 24599.0 | 0.0672425 | ||||||||
\(169\) | −4471.10 | − | 7744.16i | −0.0120420 | − | 0.0208573i | ||||
\(170\) | −420105. | −1.11490 | ||||||||
\(171\) | 359655. | 0.940581 | ||||||||
\(172\) | 168592. | − | 191641.i | 0.434527 | − | 0.493933i | ||||
\(173\) | −665668. | −1.69099 | −0.845497 | − | 0.533980i | \(-0.820696\pi\) | ||||
−0.845497 | + | 0.533980i | \(0.820696\pi\) | |||||||
\(174\) | 668665. | 1.67431 | ||||||||
\(175\) | −2846.16 | − | 4929.69i | −0.00702528 | − | 0.0121681i | ||||
\(176\) | −1857.47 | −0.00452002 | ||||||||
\(177\) | 279142. | + | 483488.i | 0.669718 | + | 1.15999i | ||||
\(178\) | −64032.8 | − | 110908.i | −0.151479 | − | 0.262369i | ||||
\(179\) | −384361. | + | 665733.i | −0.896616 | + | 1.55299i | −0.0648252 | + | 0.997897i | \(0.520649\pi\) |
−0.831791 | + | 0.555089i | \(0.812684\pi\) | |||||||
\(180\) | −497705. | −1.14496 | ||||||||
\(181\) | 172445. | − | 298683.i | 0.391249 | − | 0.677664i | −0.601365 | − | 0.798974i | \(-0.705376\pi\) |
0.992615 | + | 0.121311i | \(0.0387097\pi\) | |||||||
\(182\) | −5783.88 | − | 10018.0i | −0.0129432 | − | 0.0224183i | ||||
\(183\) | −52052.8 | −0.114899 | ||||||||
\(184\) | −28994.6 | − | 50220.2i | −0.0631354 | − | 0.109354i | ||||
\(185\) | 238218. | − | 412606.i | 0.511736 | − | 0.886353i | ||||
\(186\) | −176744. | + | 306130.i | −0.374596 | + | 0.648819i | ||||
\(187\) | 19769.6 | − | 34241.9i | 0.0413422 | − | 0.0716067i | ||||
\(188\) | 168076. | 0.346825 | ||||||||
\(189\) | −8753.38 | + | 15161.3i | −0.0178247 | + | 0.0308732i | ||||
\(190\) | 103918. | − | 179991.i | 0.208837 | − | 0.361716i | ||||
\(191\) | −154690. | − | 267932.i | −0.306817 | − | 0.531423i | 0.670847 | − | 0.741596i | \(-0.265931\pi\) |
−0.977664 | + | 0.210173i | \(0.932597\pi\) | |||||||
\(192\) | −205552. | − | 356027.i | −0.402410 | − | 0.696994i | ||||
\(193\) | 145315. | 0.280813 | 0.140406 | − | 0.990094i | \(-0.455159\pi\) | ||||
0.140406 | + | 0.990094i | \(0.455159\pi\) | |||||||
\(194\) | −250953. | −0.478727 | ||||||||
\(195\) | 489683. | + | 848155.i | 0.922206 | + | 1.59731i | ||||
\(196\) | −176569. | − | 305826.i | −0.328303 | − | 0.568637i | ||||
\(197\) | −8366.37 | + | 14491.0i | −0.0153593 | + | 0.0266031i | −0.873603 | − | 0.486639i | \(-0.838223\pi\) |
0.858244 | + | 0.513243i | \(0.171556\pi\) | |||||||
\(198\) | −12180.8 | + | 21097.8i | −0.0220807 | + | 0.0382449i | ||||
\(199\) | −1.00459e6 | −1.79827 | −0.899134 | − | 0.437674i | \(-0.855802\pi\) | ||||
−0.899134 | + | 0.437674i | \(0.855802\pi\) | |||||||
\(200\) | −88121.9 | + | 152632.i | −0.155779 | + | 0.269817i | ||||
\(201\) | −276626. | + | 479130.i | −0.482950 | + | 0.836495i | ||||
\(202\) | −57999.7 | + | 100458.i | −0.100011 | + | 0.173224i | ||||
\(203\) | 23177.0 | + | 40143.7i | 0.0394745 | + | 0.0683719i | ||||
\(204\) | −1.02811e6 | −1.72968 | ||||||||
\(205\) | 609218. | + | 1.05520e6i | 1.01248 | + | 1.75367i | ||||
\(206\) | −100156. | + | 173475.i | −0.164441 | + | 0.284820i | ||||
\(207\) | 121545. | 0.197157 | ||||||||
\(208\) | 28618.8 | − | 49569.2i | 0.0458662 | − | 0.0794426i | ||||
\(209\) | 9780.49 | + | 16940.3i | 0.0154880 | + | 0.0268260i | ||||
\(210\) | 14897.4 | + | 25803.1i | 0.0233111 | + | 0.0403761i | ||||
\(211\) | 1.06401e6 | 1.64528 | 0.822642 | − | 0.568560i | \(-0.192499\pi\) | ||||
0.822642 | + | 0.568560i | \(0.192499\pi\) | |||||||
\(212\) | −237806. | − | 411892.i | −0.363399 | − | 0.629425i | ||||
\(213\) | −122779. | −0.185428 | ||||||||
\(214\) | 703124. | 1.04954 | ||||||||
\(215\) | 763895. | + | 153182.i | 1.12704 | + | 0.226002i | ||||
\(216\) | 542039. | 0.790490 | ||||||||
\(217\) | −24505.0 | −0.0353268 | ||||||||
\(218\) | −316603. | − | 548372.i | −0.451205 | − | 0.781509i | ||||
\(219\) | 810375. | 1.14176 | ||||||||
\(220\) | −13534.6 | − | 23442.7i | −0.0188534 | − | 0.0326550i | ||||
\(221\) | 609194. | + | 1.05516e6i | 0.839026 | + | 1.45323i | ||||
\(222\) | −303195. | + | 525149.i | −0.412895 | + | 0.715155i | ||||
\(223\) | −1.38680e6 | −1.86746 | −0.933730 | − | 0.357979i | \(-0.883466\pi\) | ||||
−0.933730 | + | 0.357979i | \(0.883466\pi\) | |||||||
\(224\) | 16794.3 | − | 29088.6i | 0.0223636 | − | 0.0387349i | ||||
\(225\) | −184703. | − | 319915.i | −0.243230 | − | 0.421287i | ||||
\(226\) | 28548.9 | 0.0371807 | ||||||||
\(227\) | −241584. | − | 418436.i | −0.311175 | − | 0.538970i | 0.667442 | − | 0.744661i | \(-0.267389\pi\) |
−0.978617 | + | 0.205691i | \(0.934056\pi\) | |||||||
\(228\) | 254316. | − | 440489.i | 0.323994 | − | 0.561174i | ||||
\(229\) | −362471. | + | 627818.i | −0.456756 | + | 0.791125i | −0.998787 | − | 0.0492336i | \(-0.984322\pi\) |
0.542031 | + | 0.840358i | \(0.317655\pi\) | |||||||
\(230\) | 35119.0 | − | 60827.9i | 0.0437746 | − | 0.0758199i | ||||
\(231\) | −2804.21 | −0.00345765 | ||||||||
\(232\) | 717599. | − | 1.24292e6i | 0.875310 | − | 1.51608i | ||||
\(233\) | −391445. | + | 678003.i | −0.472369 | + | 0.818167i | −0.999500 | − | 0.0316168i | \(-0.989934\pi\) |
0.527131 | + | 0.849784i | \(0.323268\pi\) | |||||||
\(234\) | −375348. | − | 650122.i | −0.448121 | − | 0.776168i | ||||
\(235\) | 256515. | + | 444297.i | 0.303001 | + | 0.524812i | ||||
\(236\) | 475494. | 0.555732 | ||||||||
\(237\) | −1.30128e6 | −1.50487 | ||||||||
\(238\) | 18533.3 | + | 32100.6i | 0.0212085 | + | 0.0367343i | ||||
\(239\) | 284193. | + | 492237.i | 0.321824 | + | 0.557416i | 0.980864 | − | 0.194692i | \(-0.0623707\pi\) |
−0.659040 | + | 0.752108i | \(0.729037\pi\) | |||||||
\(240\) | −73712.9 | + | 127674.i | −0.0826067 | + | 0.143079i | ||||
\(241\) | 748065. | − | 1.29569e6i | 0.829654 | − | 1.43700i | −0.0686564 | − | 0.997640i | \(-0.521871\pi\) |
0.898310 | − | 0.439362i | \(-0.144795\pi\) | |||||||
\(242\) | 531566. | 0.583470 | ||||||||
\(243\) | 536875. | − | 929896.i | 0.583254 | − | 1.01023i | ||||
\(244\) | −22166.9 | + | 38394.1i | −0.0238358 | + | 0.0412848i | ||||
\(245\) | 538954. | − | 933496.i | 0.573637 | − | 0.993568i | ||||
\(246\) | −775389. | − | 1.34301e6i | −0.816925 | − | 1.41496i | ||||
\(247\) | −602767. | −0.628647 | ||||||||
\(248\) | 379358. | + | 657067.i | 0.391669 | + | 0.678391i | ||||
\(249\) | −1.44255e6 | + | 2.49857e6i | −1.47446 | + | 2.55383i | ||||
\(250\) | 450958. | 0.456337 | ||||||||
\(251\) | 187754. | − | 325199.i | 0.188107 | − | 0.325810i | −0.756512 | − | 0.653980i | \(-0.773098\pi\) |
0.944619 | + | 0.328169i | \(0.106432\pi\) | |||||||
\(252\) | 21956.7 | + | 38030.2i | 0.0217804 | + | 0.0377248i | ||||
\(253\) | 3305.30 | + | 5724.95i | 0.00324646 | + | 0.00562303i | ||||
\(254\) | −209978. | −0.204216 | ||||||||
\(255\) | −1.56909e6 | − | 2.71775e6i | −1.51112 | − | 2.61733i | ||||
\(256\) | −977430. | −0.932150 | ||||||||
\(257\) | 555146. | 0.524294 | 0.262147 | − | 0.965028i | \(-0.415570\pi\) | ||||
0.262147 | + | 0.965028i | \(0.415570\pi\) | |||||||
\(258\) | −972255. | − | 194965.i | −0.909350 | − | 0.182350i | ||||
\(259\) | −42036.9 | −0.0389387 | ||||||||
\(260\) | 834132. | 0.765247 | ||||||||
\(261\) | 1.50408e6 | + | 2.60515e6i | 1.36669 | + | 2.36718i | ||||
\(262\) | −685576. | −0.617025 | ||||||||
\(263\) | −716292. | − | 1.24065e6i | −0.638559 | − | 1.10602i | −0.985749 | − | 0.168222i | \(-0.946198\pi\) |
0.347190 | − | 0.937795i | \(-0.387136\pi\) | |||||||
\(264\) | 43411.6 | + | 75191.2i | 0.0383351 | + | 0.0663983i | ||||
\(265\) | 725873. | − | 1.25725e6i | 0.634960 | − | 1.09978i | ||||
\(266\) | −18337.8 | −0.0158907 | ||||||||
\(267\) | 478325. | − | 828483.i | 0.410624 | − | 0.711222i | ||||
\(268\) | 235604. | + | 408078.i | 0.200376 | + | 0.347062i | ||||
\(269\) | 83748.1 | 0.0705658 | 0.0352829 | − | 0.999377i | \(-0.488767\pi\) | ||||
0.0352829 | + | 0.999377i | \(0.488767\pi\) | |||||||
\(270\) | 328265. | + | 568572.i | 0.274041 | + | 0.474653i | ||||
\(271\) | −251748. | + | 436040.i | −0.208230 | + | 0.360665i | −0.951157 | − | 0.308708i | \(-0.900104\pi\) |
0.742927 | + | 0.669372i | \(0.233437\pi\) | |||||||
\(272\) | −91703.2 | + | 158835.i | −0.0751558 | + | 0.130174i | ||||
\(273\) | 43205.6 | − | 74834.3i | 0.0350860 | − | 0.0607707i | ||||
\(274\) | 618149. | 0.497413 | ||||||||
\(275\) | 10045.6 | − | 17399.6i | 0.00801025 | − | 0.0138742i | ||||
\(276\) | 85945.8 | − | 148863.i | 0.0679129 | − | 0.117629i | ||||
\(277\) | −91509.1 | − | 158498.i | −0.0716580 | − | 0.124115i | 0.827970 | − | 0.560772i | \(-0.189496\pi\) |
−0.899628 | + | 0.436657i | \(0.856162\pi\) | |||||||
\(278\) | 710536. | + | 1.23068e6i | 0.551409 | + | 0.955069i | ||||
\(279\) | −1.59026e6 | −1.22309 | ||||||||
\(280\) | 63950.7 | 0.0487473 | ||||||||
\(281\) | 870095. | + | 1.50705e6i | 0.657356 | + | 1.13857i | 0.981297 | + | 0.192497i | \(0.0616587\pi\) |
−0.323941 | + | 0.946077i | \(0.605008\pi\) | |||||||
\(282\) | −326482. | − | 565484.i | −0.244477 | − | 0.423446i | ||||
\(283\) | −774855. | + | 1.34209e6i | −0.575114 | + | 0.996127i | 0.420915 | + | 0.907100i | \(0.361709\pi\) |
−0.996029 | + | 0.0890270i | \(0.971624\pi\) | |||||||
\(284\) | −52285.9 | + | 90561.8i | −0.0384670 | + | 0.0666268i | ||||
\(285\) | 1.55254e6 | 1.13222 | ||||||||
\(286\) | 20414.5 | − | 35358.9i | 0.0147579 | − | 0.0255614i | ||||
\(287\) | 53752.5 | − | 93102.0i | 0.0385207 | − | 0.0667197i | ||||
\(288\) | 1.08987e6 | − | 1.88772e6i | 0.774275 | − | 1.34108i | ||||
\(289\) | −1.24211e6 | − | 2.15141e6i | −0.874817 | − | 1.51523i | ||||
\(290\) | 1.73835e6 | 1.21378 | ||||||||
\(291\) | −937308. | − | 1.62347e6i | −0.648858 | − | 1.12386i | ||||
\(292\) | 345101. | − | 597733.i | 0.236859 | − | 0.410251i | ||||
\(293\) | 500405. | 0.340528 | 0.170264 | − | 0.985398i | \(-0.445538\pi\) | ||||
0.170264 | + | 0.985398i | \(0.445538\pi\) | |||||||
\(294\) | −685960. | + | 1.18812e6i | −0.462840 | + | 0.801662i | ||||
\(295\) | 725693. | + | 1.25694e6i | 0.485510 | + | 0.840928i | ||||
\(296\) | 650767. | + | 1.12716e6i | 0.431714 | + | 0.747751i | ||||
\(297\) | −61790.9 | −0.0406474 | ||||||||
\(298\) | 475551. | + | 823678.i | 0.310210 | + | 0.537300i | ||||
\(299\) | −203704. | −0.131772 | ||||||||
\(300\) | −522422. | −0.335134 | ||||||||
\(301\) | −21995.1 | − | 65127.8i | −0.0139930 | − | 0.0414333i | ||||
\(302\) | −559156. | −0.352789 | ||||||||
\(303\) | −866514. | −0.542212 | ||||||||
\(304\) | −45367.8 | − | 78579.4i | −0.0281556 | − | 0.0487669i | ||||
\(305\) | −135323. | −0.0832956 | ||||||||
\(306\) | 1.20273e6 | + | 2.08319e6i | 0.734285 | + | 1.27182i | ||||
\(307\) | −254396. | − | 440627.i | −0.154051 | − | 0.266824i | 0.778662 | − | 0.627444i | \(-0.215899\pi\) |
−0.932713 | + | 0.360619i | \(0.882565\pi\) | |||||||
\(308\) | −1194.18 | + | 2068.39i | −0.000717290 | + | 0.00124238i | ||||
\(309\) | −1.49633e6 | −0.891521 | ||||||||
\(310\) | −459487. | + | 795855.i | −0.271562 | + | 0.470359i | ||||
\(311\) | −1.04160e6 | − | 1.80410e6i | −0.610659 | − | 1.05769i | −0.991130 | − | 0.132899i | \(-0.957571\pi\) |
0.380471 | − | 0.924793i | \(-0.375762\pi\) | |||||||
\(312\) | −2.67544e6 | −1.55600 | ||||||||
\(313\) | 801513. | + | 1.38826e6i | 0.462434 | + | 0.800959i | 0.999082 | − | 0.0428474i | \(-0.0136429\pi\) |
−0.536648 | + | 0.843806i | \(0.680310\pi\) | |||||||
\(314\) | 555920. | − | 962881.i | 0.318191 | − | 0.551123i | ||||
\(315\) | −67020.1 | + | 116082.i | −0.0380565 | + | 0.0659158i | ||||
\(316\) | −554154. | + | 959822.i | −0.312185 | + | 0.540721i | ||||
\(317\) | 649471. | 0.363004 | 0.181502 | − | 0.983391i | \(-0.441904\pi\) | ||||
0.181502 | + | 0.983391i | \(0.441904\pi\) | |||||||
\(318\) | −923863. | + | 1.60018e6i | −0.512318 | + | 0.887361i | ||||
\(319\) | −81804.3 | + | 141689.i | −0.0450090 | + | 0.0779578i | ||||
\(320\) | −534379. | − | 925572.i | −0.291726 | − | 0.505284i | ||||
\(321\) | 2.62617e6 | + | 4.54865e6i | 1.42252 | + | 2.46388i | ||||
\(322\) | −6197.23 | −0.00333087 | ||||||||
\(323\) | 1.93145e6 | 1.03009 | ||||||||
\(324\) | −137722. | − | 238541.i | −0.0728854 | − | 0.126241i | ||||
\(325\) | 309554. | + | 536163.i | 0.162565 | + | 0.281572i | ||||
\(326\) | 83373.1 | − | 144407.i | 0.0434492 | − | 0.0752563i | ||||
\(327\) | 2.36502e6 | − | 4.09634e6i | 1.22311 | − | 2.11849i | ||||
\(328\) | −3.32854e6 | −1.70832 | ||||||||
\(329\) | 22632.8 | − | 39201.2i | 0.0115279 | − | 0.0199668i | ||||
\(330\) | −52581.2 | + | 91073.4i | −0.0265794 | + | 0.0460369i | ||||
\(331\) | −317554. | + | 550020.i | −0.159312 | + | 0.275936i | −0.934621 | − | 0.355646i | \(-0.884261\pi\) |
0.775309 | + | 0.631582i | \(0.217594\pi\) | |||||||
\(332\) | 1.22863e6 | + | 2.12805e6i | 0.611752 | + | 1.05959i | ||||
\(333\) | −2.72801e6 | −1.34814 | ||||||||
\(334\) | −187909. | − | 325468.i | −0.0921682 | − | 0.159640i | ||||
\(335\) | −719152. | + | 1.24561e6i | −0.350113 | + | 0.606414i | ||||
\(336\) | 13007.6 | 0.00628566 | ||||||||
\(337\) | 1.51398e6 | − | 2.62229e6i | 0.726181 | − | 1.25778i | −0.232305 | − | 0.972643i | \(-0.574627\pi\) |
0.958486 | − | 0.285140i | \(-0.0920401\pi\) | |||||||
\(338\) | 14794.1 | + | 25624.1i | 0.00704364 | + | 0.0121999i | ||||
\(339\) | 106630. | + | 184689.i | 0.0503941 | + | 0.0872852i | ||||
\(340\) | −2.67281e6 | −1.25392 | ||||||||
\(341\) | −43245.7 | − | 74903.7i | −0.0201399 | − | 0.0348833i | ||||
\(342\) | −1.19004e6 | −0.550169 | ||||||||
\(343\) | −190394. | −0.0873812 | ||||||||
\(344\) | −1.40581e6 | + | 1.59800e6i | −0.640516 | + | 0.728084i | ||||
\(345\) | 524677. | 0.237326 | ||||||||
\(346\) | 2.20258e6 | 0.989104 | ||||||||
\(347\) | 787223. | + | 1.36351e6i | 0.350973 | + | 0.607903i | 0.986420 | − | 0.164241i | \(-0.0525175\pi\) |
−0.635447 | + | 0.772144i | \(0.719184\pi\) | |||||||
\(348\) | 4.25421e6 | 1.88309 | ||||||||
\(349\) | −1.12178e6 | − | 1.94297e6i | −0.492995 | − | 0.853893i | 0.506972 | − | 0.861962i | \(-0.330765\pi\) |
−0.999967 | + | 0.00806979i | \(0.997431\pi\) | |||||||
\(350\) | 9417.46 | + | 16311.5i | 0.00410926 | + | 0.00711745i | ||||
\(351\) | 952036. | − | 1.64897e6i | 0.412463 | − | 0.714407i | ||||
\(352\) | 118552. | 0.0509981 | ||||||||
\(353\) | −1.09997e6 | + | 1.90520e6i | −0.469832 | + | 0.813773i | −0.999405 | − | 0.0344914i | \(-0.989019\pi\) |
0.529573 | + | 0.848264i | \(0.322352\pi\) | |||||||
\(354\) | −923634. | − | 1.59978e6i | −0.391734 | − | 0.678504i | ||||
\(355\) | −319192. | −0.134425 | ||||||||
\(356\) | −407393. | − | 705625.i | −0.170368 | − | 0.295086i | ||||
\(357\) | −138444. | + | 239792.i | −0.0574914 | + | 0.0995781i | ||||
\(358\) | 1.27179e6 | − | 2.20280e6i | 0.524453 | − | 0.908379i | ||||
\(359\) | 117788. | − | 204014.i | 0.0482351 | − | 0.0835457i | −0.840900 | − | 0.541191i | \(-0.817974\pi\) |
0.889135 | + | 0.457645i | \(0.151307\pi\) | |||||||
\(360\) | 4.15012e6 | 1.68773 | ||||||||
\(361\) | 760282. | − | 1.31685e6i | 0.307048 | − | 0.531824i | ||||
\(362\) | −570591. | + | 988292.i | −0.228851 | + | 0.396382i | ||||
\(363\) | 1.98540e6 | + | 3.43881e6i | 0.790826 | + | 1.36975i | ||||
\(364\) | −36798.5 | − | 63736.9i | −0.0145572 | − | 0.0252138i | ||||
\(365\) | 2.10676e6 | 0.827717 | ||||||||
\(366\) | 172234. | 0.0672072 | ||||||||
\(367\) | −1.59744e6 | − | 2.76684e6i | −0.619096 | − | 1.07231i | −0.989651 | − | 0.143495i | \(-0.954166\pi\) |
0.370555 | − | 0.928811i | \(-0.379168\pi\) | |||||||
\(368\) | −15332.0 | − | 26555.8i | −0.00590173 | − | 0.0102221i | ||||
\(369\) | 3.48830e6 | − | 6.04191e6i | 1.33367 | − | 2.30998i | ||||
\(370\) | −788225. | + | 1.36525e6i | −0.299327 | + | 0.518450i | ||||
\(371\) | −128090. | −0.0483149 | ||||||||
\(372\) | −1.12449e6 | + | 1.94768e6i | −0.421307 | + | 0.729725i | ||||
\(373\) | −558212. | + | 966852.i | −0.207743 | + | 0.359822i | −0.951003 | − | 0.309181i | \(-0.899945\pi\) |
0.743260 | + | 0.669003i | \(0.233279\pi\) | |||||||
\(374\) | −65414.2 | + | 113301.i | −0.0241820 | + | 0.0418845i | ||||
\(375\) | 1.68433e6 | + | 2.91734e6i | 0.618512 | + | 1.07129i | ||||
\(376\) | −1.40150e6 | −0.511239 | ||||||||
\(377\) | −2.52078e6 | − | 4.36612e6i | −0.913443 | − | 1.58213i | ||||
\(378\) | 28963.5 | − | 50166.2i | 0.0104261 | − | 0.0180585i | ||||
\(379\) | −1.69907e6 | −0.607593 | −0.303797 | − | 0.952737i | \(-0.598254\pi\) | ||||
−0.303797 | + | 0.952737i | \(0.598254\pi\) | |||||||
\(380\) | 661153. | − | 1.14515e6i | 0.234878 | − | 0.406821i | ||||
\(381\) | −784269. | − | 1.35839e6i | −0.276791 | − | 0.479417i | ||||
\(382\) | 511845. | + | 886541.i | 0.179465 | + | 0.310842i | ||||
\(383\) | −2.65539e6 | −0.924978 | −0.462489 | − | 0.886625i | \(-0.653044\pi\) | ||||
−0.462489 | + | 0.886625i | \(0.653044\pi\) | |||||||
\(384\) | −1.66279e6 | − | 2.88003e6i | −0.575451 | − | 0.996711i | ||||
\(385\) | −7290.20 | −0.00250661 | ||||||||
\(386\) | −480823. | −0.164254 | ||||||||
\(387\) | −1.42738e6 | − | 4.22650e6i | −0.484466 | − | 1.43451i | ||||
\(388\) | −1.59662e6 | −0.538423 | ||||||||
\(389\) | −4.12416e6 | −1.38185 | −0.690926 | − | 0.722925i | \(-0.742797\pi\) | ||||
−0.690926 | + | 0.722925i | \(0.742797\pi\) | |||||||
\(390\) | −1.62028e6 | − | 2.80640e6i | −0.539421 | − | 0.934305i | ||||
\(391\) | 652730. | 0.215919 | ||||||||
\(392\) | 1.47232e6 | + | 2.55013e6i | 0.483935 | + | 0.838200i | ||||
\(393\) | −2.56063e6 | − | 4.43513e6i | −0.836305 | − | 1.44852i | ||||
\(394\) | 27682.9 | − | 47948.2i | 0.00898404 | − | 0.0155608i | ||||
\(395\) | −3.38297e6 | −1.09095 | ||||||||
\(396\) | −77497.3 | + | 134229.i | −0.0248341 | + | 0.0430139i | ||||
\(397\) | 818075. | + | 1.41695e6i | 0.260506 | + | 0.451209i | 0.966376 | − | 0.257132i | \(-0.0827774\pi\) |
−0.705871 | + | 0.708341i | \(0.749444\pi\) | |||||||
\(398\) | 3.32401e6 | 1.05185 | ||||||||
\(399\) | −68491.5 | − | 118631.i | −0.0215380 | − | 0.0373049i | ||||
\(400\) | −46597.8 | + | 80709.7i | −0.0145618 | + | 0.0252218i | ||||
\(401\) | −931084. | + | 1.61268e6i | −0.289153 | + | 0.500828i | −0.973608 | − | 0.228227i | \(-0.926707\pi\) |
0.684455 | + | 0.729055i | \(0.260040\pi\) | |||||||
\(402\) | 915308. | − | 1.58536e6i | 0.282490 | − | 0.489286i | ||||
\(403\) | 2.66521e6 | 0.817464 | ||||||||
\(404\) | −369008. | + | 639141.i | −0.112482 | + | 0.194824i | ||||
\(405\) | 420379. | − | 728117.i | 0.127351 | − | 0.220579i | ||||
\(406\) | −76688.8 | − | 132829.i | −0.0230896 | − | 0.0399924i | ||||
\(407\) | −74185.6 | − | 128493.i | −0.0221990 | − | 0.0384498i | ||||
\(408\) | 8.57291e6 | 2.54964 | ||||||||
\(409\) | 5.04001e6 | 1.48978 | 0.744892 | − | 0.667185i | \(-0.232501\pi\) | ||||
0.744892 | + | 0.667185i | \(0.232501\pi\) | |||||||
\(410\) | −2.01580e6 | − | 3.49147e6i | −0.592227 | − | 1.02577i | ||||
\(411\) | 2.30878e6 | + | 3.99893e6i | 0.674185 | + | 1.16772i | ||||
\(412\) | −637218. | + | 1.10369e6i | −0.184946 | + | 0.320336i | ||||
\(413\) | 64029.3 | − | 110902.i | 0.0184715 | − | 0.0319937i | ||||
\(414\) | −402172. | −0.115322 | ||||||||
\(415\) | −3.75024e6 | + | 6.49560e6i | −1.06890 | + | 1.85139i | ||||
\(416\) | −1.82658e6 | + | 3.16373e6i | −0.517495 | + | 0.896327i | ||||
\(417\) | −5.30770e6 | + | 9.19321e6i | −1.49474 | + | 2.58897i | ||||
\(418\) | −32362.0 | − | 56052.6i | −0.00905930 | − | 0.0156912i | ||||
\(419\) | 4.75356e6 | 1.32277 | 0.661385 | − | 0.750047i | \(-0.269969\pi\) | ||||
0.661385 | + | 0.750047i | \(0.269969\pi\) | |||||||
\(420\) | 94781.3 | + | 164166.i | 0.0262180 | + | 0.0454109i | ||||
\(421\) | 1.33283e6 | − | 2.30854e6i | 0.366497 | − | 0.634792i | −0.622518 | − | 0.782605i | \(-0.713890\pi\) |
0.989015 | + | 0.147814i | \(0.0472236\pi\) | |||||||
\(422\) | −3.52064e6 | −0.962367 | ||||||||
\(423\) | 1.46877e6 | − | 2.54398e6i | 0.399119 | − | 0.691294i | ||||
\(424\) | 1.98295e6 | + | 3.43457e6i | 0.535669 | + | 0.927806i | ||||
\(425\) | −991905. | − | 1.71803e6i | −0.266378 | − | 0.461380i | ||||
\(426\) | 406255. | 0.108461 | ||||||||
\(427\) | 5969.90 | + | 10340.2i | 0.00158452 | + | 0.00274447i | ||||
\(428\) | 4.47345e6 | 1.18041 | ||||||||
\(429\) | 304992. | 0.0800102 | ||||||||
\(430\) | −2.52760e6 | − | 506855.i | −0.659230 | − | 0.132194i | ||||
\(431\) | 4.96901e6 | 1.28848 | 0.644239 | − | 0.764825i | \(-0.277174\pi\) | ||||
0.644239 | + | 0.764825i | \(0.277174\pi\) | |||||||
\(432\) | 286624. | 0.0738929 | ||||||||
\(433\) | 1.64591e6 | + | 2.85080e6i | 0.421877 | + | 0.730713i | 0.996123 | − | 0.0879702i | \(-0.0280380\pi\) |
−0.574246 | + | 0.818683i | \(0.694705\pi\) | |||||||
\(434\) | 81082.8 | 0.0206635 | ||||||||
\(435\) | 6.49272e6 | + | 1.12457e7i | 1.64514 | + | 2.84947i | ||||
\(436\) | −2.01431e6 | − | 3.48888e6i | −0.507469 | − | 0.878962i | ||||
\(437\) | −161461. | + | 279658.i | −0.0404449 | + | 0.0700526i | ||||
\(438\) | −2.68140e6 | −0.667845 | ||||||||
\(439\) | −330222. | + | 571962.i | −0.0817796 | + | 0.141646i | −0.904014 | − | 0.427502i | \(-0.859394\pi\) |
0.822235 | + | 0.569148i | \(0.192727\pi\) | |||||||
\(440\) | 112858. | + | 195477.i | 0.0277909 | + | 0.0481352i | ||||
\(441\) | −6.17195e6 | −1.51121 | ||||||||
\(442\) | −2.01572e6 | − | 3.49133e6i | −0.490767 | − | 0.850033i | ||||
\(443\) | −485243. | + | 840466.i | −0.117476 | + | 0.203475i | −0.918767 | − | 0.394800i | \(-0.870814\pi\) |
0.801291 | + | 0.598275i | \(0.204147\pi\) | |||||||
\(444\) | −1.92900e6 | + | 3.34113e6i | −0.464382 | + | 0.804334i | ||||
\(445\) | 1.24351e6 | − | 2.15383e6i | 0.297681 | − | 0.515598i | ||||
\(446\) | 4.58868e6 | 1.09232 | ||||||||
\(447\) | −3.55236e6 | + | 6.15287e6i | −0.840908 | + | 1.45650i | ||||
\(448\) | −47149.3 | + | 81664.9i | −0.0110989 | + | 0.0192239i | ||||
\(449\) | −2.13071e6 | − | 3.69050e6i | −0.498779 | − | 0.863911i | 0.501220 | − | 0.865320i | \(-0.332885\pi\) |
−0.999999 | + | 0.00140891i | \(0.999552\pi\) | |||||||
\(450\) | 611151. | + | 1.05855e6i | 0.142271 | + | 0.246421i | ||||
\(451\) | 379444. | 0.0878427 | ||||||||
\(452\) | 181635. | 0.0418171 | ||||||||
\(453\) | −2.08845e6 | − | 3.61729e6i | −0.478165 | − | 0.828206i | ||||
\(454\) | 799362. | + | 1.38454e6i | 0.182014 | + | 0.315257i | ||||
\(455\) | 112323. | − | 194549.i | 0.0254355 | − | 0.0440555i | ||||
\(456\) | −2.12062e6 | + | 3.67301e6i | −0.477584 | + | 0.827200i | ||||
\(457\) | 1.91792e6 | 0.429577 | 0.214788 | − | 0.976661i | \(-0.431094\pi\) | ||||
0.214788 | + | 0.976661i | \(0.431094\pi\) | |||||||
\(458\) | 1.19936e6 | − | 2.07734e6i | 0.267168 | − | 0.462748i | ||||
\(459\) | −3.05061e6 | + | 5.28381e6i | −0.675857 | + | 1.17062i | ||||
\(460\) | 223436. | − | 387002.i | 0.0492332 | − | 0.0852744i | ||||
\(461\) | 358554. | + | 621034.i | 0.0785783 | + | 0.136102i | 0.902637 | − | 0.430403i | \(-0.141629\pi\) |
−0.824058 | + | 0.566505i | \(0.808295\pi\) | |||||||
\(462\) | 9278.68 | 0.00202247 | ||||||||
\(463\) | −2.56030e6 | − | 4.43457e6i | −0.555058 | − | 0.961388i | −0.997899 | − | 0.0647880i | \(-0.979363\pi\) |
0.442841 | − | 0.896600i | \(-0.353970\pi\) | |||||||
\(464\) | 379458. | − | 657240.i | 0.0818217 | − | 0.141719i | ||||
\(465\) | −6.86474e6 | −1.47228 | ||||||||
\(466\) | 1.29523e6 | − | 2.24340e6i | 0.276300 | − | 0.478566i | ||||
\(467\) | −1.83744e6 | − | 3.18254e6i | −0.389871 | − | 0.675276i | 0.602561 | − | 0.798073i | \(-0.294147\pi\) |
−0.992432 | + | 0.122797i | \(0.960814\pi\) | |||||||
\(468\) | −2.38806e6 | − | 4.13624e6i | −0.504000 | − | 0.872954i | ||||
\(469\) | 126904. | 0.0266406 | ||||||||
\(470\) | −848766. | − | 1.47011e6i | −0.177232 | − | 0.306976i | ||||
\(471\) | 8.30544e6 | 1.72508 | ||||||||
\(472\) | −3.96491e6 | −0.819178 | ||||||||
\(473\) | 160258. | − | 182168.i | 0.0329357 | − | 0.0374385i | ||||
\(474\) | 4.30571e6 | 0.880235 | ||||||||
\(475\) | 981439. | 0.199586 | ||||||||
\(476\) | 117914. | + | 204232.i | 0.0238532 | + | 0.0413149i | ||||
\(477\) | −8.31249e6 | −1.67277 | ||||||||
\(478\) | −940347. | − | 1.62873e6i | −0.188243 | − | 0.326046i | ||||
\(479\) | 170737. | + | 295725.i | 0.0340007 | + | 0.0588910i | 0.882525 | − | 0.470265i | \(-0.155842\pi\) |
−0.848524 | + | 0.529156i | \(0.822508\pi\) | |||||||
\(480\) | 4.70470e6 | − | 8.14877e6i | 0.932027 | − | 1.61432i | ||||
\(481\) | 4.57202e6 | 0.901043 | ||||||||
\(482\) | −2.47522e6 | + | 4.28721e6i | −0.485285 | + | 0.840538i | ||||
\(483\) | −23146.6 | − | 40091.1i | −0.00451461 | − | 0.00781953i | ||||
\(484\) | 3.38196e6 | 0.656228 | ||||||||
\(485\) | −2.43675e6 | − | 4.22057e6i | −0.470388 | − | 0.814736i | ||||
\(486\) | −1.77643e6 | + | 3.07687e6i | −0.341160 | + | 0.590906i | ||||
\(487\) | 872489. | − | 1.51120e6i | 0.166701 | − | 0.288734i | −0.770557 | − | 0.637371i | \(-0.780022\pi\) |
0.937258 | + | 0.348637i | \(0.113355\pi\) | |||||||
\(488\) | 184838. | − | 320149.i | 0.0351352 | − | 0.0608560i | ||||
\(489\) | 1.24559e6 | 0.235562 | ||||||||
\(490\) | −1.78331e6 | + | 3.08878e6i | −0.335534 | + | 0.581162i | ||||
\(491\) | 1.80519e6 | − | 3.12668e6i | 0.337924 | − | 0.585301i | −0.646118 | − | 0.763237i | \(-0.723609\pi\) |
0.984042 | + | 0.177936i | \(0.0569420\pi\) | |||||||
\(492\) | −4.93322e6 | − | 8.54459e6i | −0.918793 | − | 1.59140i | ||||
\(493\) | 8.07734e6 | + | 1.39904e7i | 1.49676 | + | 2.59246i | ||||
\(494\) | 1.99445e6 | 0.367711 | ||||||||
\(495\) | −473101. | −0.0867843 | ||||||||
\(496\) | 200600. | + | 347449.i | 0.0366122 | + | 0.0634142i | ||||
\(497\) | 14081.4 | + | 24389.8i | 0.00255715 | + | 0.00442911i | ||||
\(498\) | 4.77315e6 | − | 8.26734e6i | 0.862446 | − | 1.49380i | ||||
\(499\) | 2.79628e6 | − | 4.84329e6i | 0.502723 | − | 0.870742i | −0.497272 | − | 0.867595i | \(-0.665665\pi\) |
0.999995 | − | 0.00314702i | \(-0.00100173\pi\) | |||||||
\(500\) | 2.86910e6 | 0.513241 | ||||||||
\(501\) | 1.40368e6 | − | 2.43124e6i | 0.249847 | − | 0.432747i | ||||
\(502\) | −621246. | + | 1.07603e6i | −0.110028 | + | 0.190575i | ||||
\(503\) | −1.62515e6 | + | 2.81484e6i | −0.286400 | + | 0.496059i | −0.972948 | − | 0.231025i | \(-0.925792\pi\) |
0.686548 | + | 0.727085i | \(0.259125\pi\) | |||||||
\(504\) | −183086. | − | 317115.i | −0.0321055 | − | 0.0556083i | ||||
\(505\) | −2.25270e6 | −0.393075 | ||||||||
\(506\) | −10936.7 | − | 18942.9i | −0.00189893 | − | 0.00328905i | ||||
\(507\) | −110512. | + | 191412.i | −0.0190937 | + | 0.0330712i | ||||
\(508\) | −1.33594e6 | −0.229682 | ||||||||
\(509\) | 4.81431e6 | − | 8.33863e6i | 0.823644 | − | 1.42659i | −0.0793064 | − | 0.996850i | \(-0.525271\pi\) |
0.902951 | − | 0.429744i | \(-0.141396\pi\) | |||||||
\(510\) | 5.19186e6 | + | 8.99257e6i | 0.883889 | + | 1.53094i | ||||
\(511\) | −92941.5 | − | 160979.i | −0.0157455 | − | 0.0272721i | ||||
\(512\) | −1.07133e6 | −0.180612 | ||||||||
\(513\) | −1.50921e6 | − | 2.61403e6i | −0.253196 | − | 0.438548i | ||||
\(514\) | −1.83689e6 | −0.306672 | ||||||||
\(515\) | −3.89006e6 | −0.646305 | ||||||||
\(516\) | −6.18573e6 | − | 1.24041e6i | −1.02274 | − | 0.205089i | ||||
\(517\) | 159767. | 0.0262882 | ||||||||
\(518\) | 139093. | 0.0227762 | ||||||||
\(519\) | 8.22664e6 | + | 1.42490e7i | 1.34062 | + | 2.32201i | ||||
\(520\) | −6.95541e6 | −1.12801 | ||||||||
\(521\) | −2.07104e6 | − | 3.58714e6i | −0.334267 | − | 0.578968i | 0.649077 | − | 0.760723i | \(-0.275155\pi\) |
−0.983344 | + | 0.181755i | \(0.941822\pi\) | |||||||
\(522\) | −4.97676e6 | − | 8.62000e6i | −0.799412 | − | 1.38462i | ||||
\(523\) | 1.10795e6 | − | 1.91903e6i | 0.177120 | − | 0.306781i | −0.763773 | − | 0.645485i | \(-0.776655\pi\) |
0.940893 | + | 0.338704i | \(0.109989\pi\) | |||||||
\(524\) | −4.36181e6 | −0.693966 | ||||||||
\(525\) | −70348.4 | + | 121847.i | −0.0111392 | + | 0.0192937i | ||||
\(526\) | 2.37009e6 | + | 4.10512e6i | 0.373509 | + | 0.646936i | ||||
\(527\) | −8.54014e6 | −1.33949 | ||||||||
\(528\) | 22955.5 | + | 39760.2i | 0.00358346 | + | 0.00620674i | ||||
\(529\) | 3.16361e6 | − | 5.47953e6i | 0.491522 | − | 0.851342i | ||||
\(530\) | −2.40179e6 | + | 4.16003e6i | −0.371404 | + | 0.643290i | ||||
\(531\) | 4.15521e6 | − | 7.19704e6i | 0.639524 | − | 1.10769i | ||||
\(532\) | −116669. | −0.0178722 | ||||||||
\(533\) | −5.84623e6 | + | 1.01260e7i | −0.891370 | + | 1.54390i | ||||
\(534\) | −1.58270e6 | + | 2.74131e6i | −0.240184 | + | 0.416011i | ||||
\(535\) | 6.82732e6 | + | 1.18253e7i | 1.03125 | + | 1.78618i | ||||
\(536\) | −1.96459e6 | − | 3.40276e6i | −0.295365 | − | 0.511587i | ||||
\(537\) | 1.90005e7 | 2.84334 | ||||||||
\(538\) | −277108. | −0.0412757 | ||||||||
\(539\) | −167840. | − | 290708.i | −0.0248842 | − | 0.0431008i | ||||
\(540\) | 2.08851e6 | + | 3.61740e6i | 0.308213 | + | 0.533841i | ||||
\(541\) | 3.62393e6 | − | 6.27684e6i | 0.532337 | − | 0.922036i | −0.466950 | − | 0.884284i | \(-0.654647\pi\) |
0.999287 | − | 0.0377517i | \(-0.0120196\pi\) | |||||||
\(542\) | 832992. | − | 1.44278e6i | 0.121799 | − | 0.210962i | ||||
\(543\) | −8.52462e6 | −1.24073 | ||||||||
\(544\) | 5.85292e6 | − | 1.01376e7i | 0.847960 | − | 1.46871i | ||||
\(545\) | 6.14842e6 | − | 1.06494e7i | 0.886690 | − | 1.53579i | ||||
\(546\) | −142960. | + | 247614.i | −0.0205226 | + | 0.0355463i | ||||
\(547\) | 1.34435e6 | + | 2.32848e6i | 0.192107 | + | 0.332739i | 0.945948 | − | 0.324317i | \(-0.105135\pi\) |
−0.753841 | + | 0.657057i | \(0.771801\pi\) | |||||||
\(548\) | 3.93282e6 | 0.559439 | ||||||||
\(549\) | 387420. | + | 671031.i | 0.0548594 | + | 0.0950193i | ||||
\(550\) | −33239.4 | + | 57572.3i | −0.00468539 | + | 0.00811534i | ||||
\(551\) | −7.99211e6 | −1.12146 | ||||||||
\(552\) | −716659. | + | 1.24129e6i | −0.100107 | + | 0.173391i | ||||
\(553\) | 149243. | + | 258496.i | 0.0207530 | + | 0.0359452i | ||||
\(554\) | 302788. | + | 524444.i | 0.0419145 | + | 0.0725981i | ||||
\(555\) | −1.17761e7 | −1.62281 | ||||||||
\(556\) | 4.52061e6 | + | 7.82992e6i | 0.620169 | + | 1.07416i | ||||
\(557\) | −1.15293e7 | −1.57458 | −0.787291 | − | 0.616582i | \(-0.788517\pi\) | ||||
−0.787291 | + | 0.616582i | \(0.788517\pi\) | |||||||
\(558\) | 5.26191e6 | 0.715415 | ||||||||
\(559\) | 2.39223e6 | + | 7.08343e6i | 0.323798 | + | 0.958769i | ||||
\(560\) | 33816.4 | 0.00455677 | ||||||||
\(561\) | −977288. | −0.131104 | ||||||||
\(562\) | −2.87900e6 | − | 4.98657e6i | −0.384504 | − | 0.665980i | ||||
\(563\) | −1.31124e7 | −1.74346 | −0.871730 | − | 0.489987i | \(-0.837002\pi\) | ||||
−0.871730 | + | 0.489987i | \(0.837002\pi\) | |||||||
\(564\) | −2.07716e6 | − | 3.59775e6i | −0.274962 | − | 0.476248i | ||||
\(565\) | 277209. | + | 480140.i | 0.0365331 | + | 0.0632771i | ||||
\(566\) | 2.56386e6 | − | 4.44074e6i | 0.336398 | − | 0.582659i | ||||
\(567\) | −74181.6 | −0.00969033 | ||||||||
\(568\) | 435986. | − | 755149.i | 0.0567024 | − | 0.0982114i | ||||
\(569\) | −2.58034e6 | − | 4.46928e6i | −0.334115 | − | 0.578705i | 0.649199 | − | 0.760618i | \(-0.275104\pi\) |
−0.983314 | + | 0.181914i | \(0.941771\pi\) | |||||||
\(570\) | −5.13708e6 | −0.662261 | ||||||||
\(571\) | −119016. | − | 206142.i | −0.0152762 | − | 0.0264592i | 0.858286 | − | 0.513171i | \(-0.171529\pi\) |
−0.873562 | + | 0.486712i | \(0.838196\pi\) | |||||||
\(572\) | 129882. | − | 224962.i | 0.0165981 | − | 0.0287488i | ||||
\(573\) | −3.82348e6 | + | 6.62246e6i | −0.486488 | + | 0.842622i | ||||
\(574\) | −177858. | + | 308059.i | −0.0225317 | + | 0.0390260i | ||||
\(575\) | 331676. | 0.0418355 | ||||||||
\(576\) | −3.05978e6 | + | 5.29969e6i | −0.384268 | + | 0.665571i | ||||
\(577\) | 809295. | − | 1.40174e6i | 0.101197 | − | 0.175278i | −0.810981 | − | 0.585072i | \(-0.801066\pi\) |
0.912178 | + | 0.409794i | \(0.134399\pi\) | |||||||
\(578\) | 4.10995e6 | + | 7.11864e6i | 0.511702 | + | 0.886294i | ||||
\(579\) | −1.79587e6 | − | 3.11054e6i | −0.222628 | − | 0.385603i | ||||
\(580\) | 1.10598e7 | 1.36514 | ||||||||
\(581\) | 661780. | 0.0813343 | ||||||||
\(582\) | 3.10140e6 | + | 5.37177e6i | 0.379533 | + | 0.657371i | ||||
\(583\) | −226050. | − | 391531.i | −0.0275444 | − | 0.0477083i | ||||
\(584\) | −2.87763e6 | + | 4.98420e6i | −0.349142 | + | 0.604732i | ||||
\(585\) | 7.28925e6 | − | 1.26254e7i | 0.880630 | − | 1.52530i | ||||
\(586\) | −1.65576e6 | −0.199183 | ||||||||
\(587\) | −2.52945e6 | + | 4.38114e6i | −0.302992 | + | 0.524797i | −0.976812 | − | 0.214098i | \(-0.931319\pi\) |
0.673820 | + | 0.738895i | \(0.264652\pi\) | |||||||
\(588\) | −4.36425e6 | + | 7.55910e6i | −0.520555 | + | 0.901627i | ||||
\(589\) | 2.11251e6 | − | 3.65897e6i | 0.250906 | − | 0.434581i | ||||
\(590\) | −2.40120e6 | − | 4.15900e6i | −0.283987 | − | 0.491879i | ||||
\(591\) | 413583. | 0.0487073 | ||||||||
\(592\) | 344118. | + | 596029.i | 0.0403555 | + | 0.0698978i | ||||
\(593\) | 3.73997e6 | − | 6.47781e6i | 0.436748 | − | 0.756470i | −0.560688 | − | 0.828027i | \(-0.689463\pi\) |
0.997437 | + | 0.0715570i | \(0.0227968\pi\) | |||||||
\(594\) | 204456. | 0.0237757 | ||||||||
\(595\) | −359916. | + | 623393.i | −0.0416782 | + | 0.0721888i | ||||
\(596\) | 3.02557e6 | + | 5.24045e6i | 0.348893 | + | 0.604300i | ||||
\(597\) | 1.24152e7 | + | 2.15037e7i | 1.42566 | + | 2.46932i | ||||
\(598\) | 674023. | 0.0770765 | ||||||||
\(599\) | −3.98643e6 | − | 6.90470e6i | −0.453959 | − | 0.786280i | 0.544668 | − | 0.838651i | \(-0.316655\pi\) |
−0.998628 | + | 0.0523710i | \(0.983322\pi\) | |||||||
\(600\) | 4.35621e6 | 0.494005 | ||||||||
\(601\) | −6.17613e6 | −0.697478 | −0.348739 | − | 0.937220i | \(-0.613390\pi\) | ||||
−0.348739 | + | 0.937220i | \(0.613390\pi\) | |||||||
\(602\) | 72778.1 | + | 215497.i | 0.00818483 | + | 0.0242354i | ||||
\(603\) | 8.23552e6 | 0.922354 | ||||||||
\(604\) | −3.55749e6 | −0.396781 | ||||||||
\(605\) | 5.16149e6 | + | 8.93997e6i | 0.573307 | + | 0.992996i | ||||
\(606\) | 2.86715e6 | 0.317153 | ||||||||
\(607\) | 4.37976e6 | + | 7.58597e6i | 0.482480 | + | 0.835679i | 0.999798 | − | 0.0201139i | \(-0.00640290\pi\) |
−0.517318 | + | 0.855793i | \(0.673070\pi\) | |||||||
\(608\) | 2.89558e6 | + | 5.01530e6i | 0.317671 | + | 0.550222i | ||||
\(609\) | 572865. | − | 992231.i | 0.0625906 | − | 0.108410i | ||||
\(610\) | 447761. | 0.0487217 | ||||||||
\(611\) | −2.46159e6 | + | 4.26360e6i | −0.266755 | + | 0.462034i | ||||
\(612\) | 7.65207e6 | + | 1.32538e7i | 0.825848 | + | 1.43041i | ||||
\(613\) | −1.45170e7 | −1.56036 | −0.780181 | − | 0.625554i | \(-0.784873\pi\) | ||||
−0.780181 | + | 0.625554i | \(0.784873\pi\) | |||||||
\(614\) | 841754. | + | 1.45796e6i | 0.0901082 | + | 0.156072i | ||||
\(615\) | 1.50580e7 | − | 2.60813e7i | 1.60539 | − | 2.78062i | ||||
\(616\) | 9957.71 | − | 17247.3i | 0.00105732 | − | 0.00183134i | ||||
\(617\) | −2.25659e6 | + | 3.90852e6i | −0.238638 | + | 0.413333i | −0.960324 | − | 0.278888i | \(-0.910034\pi\) |
0.721686 | + | 0.692221i | \(0.243368\pi\) | |||||||
\(618\) | 4.95111e6 | 0.521472 | ||||||||
\(619\) | −4.13069e6 | + | 7.15456e6i | −0.433307 | + | 0.750510i | −0.997156 | − | 0.0753682i | \(-0.975987\pi\) |
0.563849 | + | 0.825878i | \(0.309320\pi\) | |||||||
\(620\) | −2.92337e6 | + | 5.06343e6i | −0.305425 | + | 0.529012i | ||||
\(621\) | −510036. | − | 883408.i | −0.0530728 | − | 0.0919248i | ||||
\(622\) | 3.44647e6 | + | 5.96946e6i | 0.357189 | + | 0.618670i | ||||
\(623\) | −219435. | −0.0226509 | ||||||||
\(624\) | −1.41474e6 | −0.145450 | ||||||||
\(625\) | 5.94756e6 | + | 1.03015e7i | 0.609030 | + | 1.05487i | ||||
\(626\) | −2.65207e6 | − | 4.59352e6i | −0.270489 | − | 0.468501i | ||||
\(627\) | 241744. | − | 418713.i | 0.0245577 | − | 0.0425351i | ||||
\(628\) | 3.53690e6 | − | 6.12609e6i | 0.357869 | − | 0.619847i | ||||
\(629\) | −1.46501e7 | −1.47644 | ||||||||
\(630\) | 221758. | − | 384097.i | 0.0222602 | − | 0.0385558i | ||||
\(631\) | −7.10806e6 | + | 1.23115e7i | −0.710685 | + | 1.23094i | 0.253915 | + | 0.967227i | \(0.418282\pi\) |
−0.964600 | + | 0.263717i | \(0.915052\pi\) | |||||||
\(632\) | 4.62081e6 | − | 8.00348e6i | 0.460177 | − | 0.797051i | ||||
\(633\) | −1.31496e7 | − | 2.27758e7i | −1.30438 | − | 2.25925i | ||||
\(634\) | −2.14899e6 | −0.212330 | ||||||||
\(635\) | −2.03889e6 | − | 3.53145e6i | −0.200659 | − | 0.347552i | ||||
\(636\) | −5.87785e6 | + | 1.01807e7i | −0.576203 | + | 0.998013i | ||||
\(637\) | 1.03439e7 | 1.01003 | ||||||||
\(638\) | 270677. | − | 468826.i | 0.0263269 | − | 0.0455995i | ||||
\(639\) | 913823. | + | 1.58279e6i | 0.0885340 | + | 0.153345i | ||||
\(640\) | −4.32280e6 | − | 7.48730e6i | −0.417172 | − | 0.722562i | ||||
\(641\) | −1.85458e6 | −0.178280 | −0.0891398 | − | 0.996019i | \(-0.528412\pi\) | ||||
−0.0891398 | + | 0.996019i | \(0.528412\pi\) | |||||||
\(642\) | −8.68954e6 | − | 1.50507e7i | −0.832069 | − | 1.44119i | ||||
\(643\) | −1.71822e7 | −1.63889 | −0.819446 | − | 0.573157i | \(-0.805719\pi\) | ||||
−0.819446 | + | 0.573157i | \(0.805719\pi\) | |||||||
\(644\) | −39428.3 | −0.00374622 | ||||||||
\(645\) | −6.16163e6 | − | 1.82447e7i | −0.583172 | − | 1.72678i | ||||
\(646\) | −6.39084e6 | −0.602527 | ||||||||
\(647\) | 2.02330e7 | 1.90020 | 0.950102 | − | 0.311938i | \(-0.100978\pi\) | ||||
0.950102 | + | 0.311938i | \(0.100978\pi\) | |||||||
\(648\) | 1.14839e6 | + | 1.98908e6i | 0.107437 | + | 0.186086i | ||||
\(649\) | 451988. | 0.0421226 | ||||||||
\(650\) | −1.02426e6 | − | 1.77408e6i | −0.0950885 | − | 0.164698i | ||||
\(651\) | 302844. | + | 524541.i | 0.0280070 | + | 0.0485096i | ||||
\(652\) | 530441. | − | 918750.i | 0.0488673 | − | 0.0846406i | ||||
\(653\) | 9.41580e6 | 0.864120 | 0.432060 | − | 0.901845i | \(-0.357787\pi\) | ||||
0.432060 | + | 0.901845i | \(0.357787\pi\) | |||||||
\(654\) | −7.82546e6 | + | 1.35541e7i | −0.715428 | + | 1.23916i | ||||
\(655\) | −6.65693e6 | − | 1.15301e7i | −0.606277 | − | 1.05010i | ||||
\(656\) | −1.76009e6 | −0.159689 | ||||||||
\(657\) | −6.03149e6 | − | 1.04468e7i | −0.545144 | − | 0.944217i | ||||
\(658\) | −74888.2 | + | 129710.i | −0.00674293 | + | 0.0116791i | ||||
\(659\) | 3.05362e6 | − | 5.28902e6i | 0.273906 | − | 0.474419i | −0.695953 | − | 0.718088i | \(-0.745018\pi\) |
0.969858 | + | 0.243669i | \(0.0783510\pi\) | |||||||
\(660\) | −334535. | + | 579432.i | −0.0298938 | + | 0.0517776i | ||||
\(661\) | −6.81099e6 | −0.606327 | −0.303163 | − | 0.952939i | \(-0.598043\pi\) | ||||
−0.303163 | + | 0.952939i | \(0.598043\pi\) | |||||||
\(662\) | 1.05073e6 | − | 1.81992e6i | 0.0931854 | − | 0.161402i | ||||
\(663\) | 1.50574e7 | − | 2.60802e7i | 1.33035 | − | 2.30424i | ||||
\(664\) | −1.02449e7 | − | 1.77447e7i | −0.901755 | − | 1.56189i | ||||
\(665\) | −178059. | − | 308408.i | −0.0156139 | − | 0.0270440i | ||||
\(666\) | 9.02652e6 | 0.788560 | ||||||||
\(667\) | −2.70092e6 | −0.235070 | ||||||||
\(668\) | −1.19552e6 | − | 2.07071e6i | −0.103661 | − | 0.179547i | ||||
\(669\) | 1.71387e7 | + | 2.96851e7i | 1.48052 | + | 2.56433i | ||||
\(670\) | 2.37955e6 | − | 4.12151e6i | 0.204790 | − | 0.354706i | ||||
\(671\) | −21071.0 | + | 36496.1i | −0.00180667 | + | 0.00312925i | ||||
\(672\) | −830208. | −0.0709192 | ||||||||
\(673\) | −8.77997e6 | + | 1.52074e7i | −0.747232 | + | 1.29424i | 0.201913 | + | 0.979404i | \(0.435284\pi\) |
−0.949145 | + | 0.314840i | \(0.898049\pi\) | |||||||
\(674\) | −5.00950e6 | + | 8.67671e6i | −0.424761 | + | 0.735708i | ||||
\(675\) | −1.55013e6 | + | 2.68490e6i | −0.130951 | + | 0.226813i | ||||
\(676\) | 94123.8 | + | 163027.i | 0.00792196 | + | 0.0137212i | ||||
\(677\) | 1.05096e6 | 0.0881283 | 0.0440641 | − | 0.999029i | \(-0.485969\pi\) | ||||
0.0440641 | + | 0.999029i | \(0.485969\pi\) | |||||||
\(678\) | −352821. | − | 611103.i | −0.0294768 | − | 0.0510553i | ||||
\(679\) | −214999. | + | 372389.i | −0.0178962 | + | 0.0309972i | ||||
\(680\) | 2.22873e7 | 1.84835 | ||||||||
\(681\) | −5.97123e6 | + | 1.03425e7i | −0.493397 | + | 0.854588i | ||||
\(682\) | 143093. | + | 247844.i | 0.0117803 | + | 0.0204041i | ||||
\(683\) | 1.52242e6 | + | 2.63690e6i | 0.124877 | + | 0.216293i | 0.921685 | − | 0.387940i | \(-0.126813\pi\) |
−0.796808 | + | 0.604233i | \(0.793480\pi\) | |||||||
\(684\) | −7.57133e6 | −0.618774 | ||||||||
\(685\) | 6.00221e6 | + | 1.03961e7i | 0.488748 | + | 0.846537i | ||||
\(686\) | 629982. | 0.0511114 | ||||||||
\(687\) | 1.79184e7 | 1.44846 | ||||||||
\(688\) | −743374. | + | 845004.i | −0.0598738 | + | 0.0680593i | ||||
\(689\) | 1.39314e7 | 1.11801 | ||||||||
\(690\) | −1.73607e6 | −0.138818 | ||||||||
\(691\) | −9.31186e6 | − | 1.61286e7i | −0.741893 | − | 1.28500i | −0.951632 | − | 0.307239i | \(-0.900595\pi\) |
0.209739 | − | 0.977757i | \(-0.432738\pi\) | |||||||
\(692\) | 1.40134e7 | 1.11244 | ||||||||
\(693\) | 20871.3 | + | 36150.2i | 0.00165088 | + | 0.00285941i | ||||
\(694\) | −2.60479e6 | − | 4.51163e6i | −0.205293 | − | 0.355578i | ||||
\(695\) | −1.37986e7 | + | 2.38998e7i | −1.08361 | + | 1.87687i | ||||
\(696\) | −3.54738e7 | −2.77577 | ||||||||
\(697\) | 1.87331e7 | − | 3.24467e7i | 1.46059 | − | 2.52981i | ||||
\(698\) | 3.71177e6 | + | 6.42897e6i | 0.288365 | + | 0.499463i | ||||
\(699\) | 1.93507e7 | 1.49797 | ||||||||
\(700\) | 59916.2 | + | 103778.i | 0.00462168 | + | 0.00800498i | ||||
\(701\) | 6.25541e6 | − | 1.08347e7i | 0.480796 | − | 0.832763i | −0.518961 | − | 0.854798i | \(-0.673681\pi\) |
0.999757 | + | 0.0220348i | \(0.00701447\pi\) | |||||||
\(702\) | −3.15013e6 | + | 5.45618e6i | −0.241260 | + | 0.417874i | ||||
\(703\) | 3.62389e6 | − | 6.27677e6i | 0.276558 | − | 0.479013i | ||||
\(704\) | −332831. | −0.0253100 | ||||||||
\(705\) | 6.34028e6 | − | 1.09817e7i | 0.480436 | − | 0.832139i | ||||
\(706\) | 3.63961e6 | − | 6.30398e6i | 0.274816 | − | 0.475996i | ||||
\(707\) | 99380.0 | + | 172131.i | 0.00747740 | + | 0.0129512i | ||||
\(708\) | −5.87639e6 | − | 1.01782e7i | −0.440583 | − | 0.763112i | ||||
\(709\) | −8.88298e6 | −0.663656 | −0.331828 | − | 0.943340i | \(-0.607665\pi\) | ||||
−0.331828 | + | 0.943340i | \(0.607665\pi\) | |||||||
\(710\) | 1.05615e6 | 0.0786287 | ||||||||
\(711\) | 9.68519e6 | + | 1.67752e7i | 0.718512 | + | 1.24450i | ||||
\(712\) | 3.39704e6 | + | 5.88385e6i | 0.251132 | + | 0.434973i | ||||
\(713\) | 713919. | − | 1.23654e6i | 0.0525927 | − | 0.0910932i | ||||
\(714\) | 458087. | − | 793431.i | 0.0336281 | − | 0.0582456i | ||||
\(715\) | 792897. | 0.0580032 | ||||||||
\(716\) | 8.09142e6 | − | 1.40148e7i | 0.589851 | − | 1.02165i | ||||
\(717\) | 7.02439e6 | − | 1.21666e7i | 0.510282 | − | 0.883835i | ||||
\(718\) | −389739. | + | 675049.i | −0.0282139 | + | 0.0488679i | ||||
\(719\) | 4.89833e6 | + | 8.48416e6i | 0.353367 | + | 0.612050i | 0.986837 | − | 0.161718i | \(-0.0517033\pi\) |
−0.633470 | + | 0.773767i | \(0.718370\pi\) | |||||||
\(720\) | 2.19453e6 | 0.157765 | ||||||||
\(721\) | 171613. | + | 297243.i | 0.0122946 | + | 0.0212948i | ||||
\(722\) | −2.51565e6 | + | 4.35723e6i | −0.179600 | + | 0.311077i | ||||
\(723\) | −3.69798e7 | −2.63099 | ||||||||
\(724\) | −3.63024e6 | + | 6.28776e6i | −0.257389 | + | 0.445810i | ||||
\(725\) | 4.10439e6 | + | 7.10902e6i | 0.290004 | + | 0.502301i | ||||
\(726\) | −6.56935e6 | − | 1.13784e7i | −0.462574 | − | 0.801201i | ||||
\(727\) | 3.22814e6 | 0.226525 | 0.113263 | − | 0.993565i | \(-0.463870\pi\) | ||||
0.113263 | + | 0.993565i | \(0.463870\pi\) | |||||||
\(728\) | 306844. | + | 531470.i | 0.0214580 | + | 0.0371664i | ||||
\(729\) | −2.33604e7 | −1.62803 | ||||||||
\(730\) | −6.97090e6 | −0.484152 | ||||||||
\(731\) | −7.66544e6 | − | 2.26975e7i | −0.530571 | − | 1.57103i | ||||
\(732\) | 1.09580e6 | 0.0755878 | ||||||||
\(733\) | 9.71876e6 | 0.668115 | 0.334057 | − | 0.942553i | \(-0.391582\pi\) | ||||
0.334057 | + | 0.942553i | \(0.391582\pi\) | |||||||
\(734\) | 5.28565e6 | + | 9.15501e6i | 0.362125 | + | 0.627218i | ||||
\(735\) | −2.66426e7 | −1.81911 | ||||||||
\(736\) | 978559. | + | 1.69491e6i | 0.0665875 | + | 0.115333i | ||||
\(737\) | 223957. | + | 387905.i | 0.0151878 | + | 0.0263061i | ||||
\(738\) | −1.15422e7 | + | 1.99917e7i | −0.780095 | + | 1.35116i | ||||
\(739\) | −2.33341e7 | −1.57174 | −0.785868 | − | 0.618394i | \(-0.787783\pi\) | ||||
−0.785868 | + | 0.618394i | \(0.787783\pi\) | |||||||
\(740\) | −5.01489e6 | + | 8.68604e6i | −0.336652 | + | 0.583099i | ||||
\(741\) | 7.44928e6 | + | 1.29025e7i | 0.498390 | + | 0.863236i | ||||
\(742\) | 423829. | 0.0282606 | ||||||||
\(743\) | 1.12089e7 | + | 1.94144e7i | 0.744888 | + | 1.29018i | 0.950247 | + | 0.311497i | \(0.100830\pi\) |
−0.205359 | + | 0.978687i | \(0.565836\pi\) | |||||||
\(744\) | 9.37657e6 | − | 1.62407e7i | 0.621029 | − | 1.07565i | ||||
\(745\) | −9.23518e6 | + | 1.59958e7i | −0.609614 | + | 1.05588i | ||||
\(746\) | 1.84703e6 | − | 3.19915e6i | 0.121514 | − | 0.210469i | ||||
\(747\) | 4.29466e7 | 2.81597 | ||||||||
\(748\) | −416181. | + | 720847.i | −0.0271975 | + | 0.0471074i | ||||
\(749\) | 602387. | − | 1.04336e6i | 0.0392347 | − | 0.0679566i | ||||
\(750\) | −5.57315e6 | − | 9.65298e6i | −0.361783 | − | 0.626626i | ||||
\(751\) | 899178. | + | 1.55742e6i | 0.0581762 | + | 0.100764i | 0.893647 | − | 0.448771i | \(-0.148138\pi\) |
−0.835471 | + | 0.549535i | \(0.814805\pi\) | |||||||
\(752\) | −741097. | −0.0477892 | ||||||||
\(753\) | −9.28141e6 | −0.596522 | ||||||||
\(754\) | 8.34083e6 | + | 1.44467e7i | 0.534295 | + | 0.925426i | ||||
\(755\) | −5.42939e6 | − | 9.40398e6i | −0.346644 | − | 0.600405i | ||||
\(756\) | 184273. | − | 319170.i | 0.0117262 | − | 0.0203103i | ||||
\(757\) | 4.25105e6 | − | 7.36303e6i | 0.269623 | − | 0.467000i | −0.699142 | − | 0.714983i | \(-0.746434\pi\) |
0.968764 | + | 0.247983i | \(0.0797677\pi\) | |||||||
\(758\) | 5.62193e6 | 0.355396 | ||||||||
\(759\) | 81697.1 | − | 141503.i | 0.00514757 | − | 0.00891585i | ||||
\(760\) | −5.51302e6 | + | 9.54884e6i | −0.346223 | + | 0.599676i | ||||
\(761\) | 2.22661e6 | − | 3.85660e6i | 0.139374 | − | 0.241403i | −0.787886 | − | 0.615821i | \(-0.788824\pi\) |
0.927260 | + | 0.374418i | \(0.122158\pi\) | |||||||
\(762\) | 2.59501e6 | + | 4.49470e6i | 0.161902 | + | 0.280423i | ||||
\(763\) | −1.08497e6 | −0.0674695 | ||||||||
\(764\) | 3.25648e6 | + | 5.64040e6i | 0.201844 | + | 0.349604i | ||||
\(765\) | −2.33570e7 | + | 4.04555e7i | −1.44299 | + | 2.49933i | ||||
\(766\) | 8.78624e6 | 0.541042 | ||||||||
\(767\) | −6.96396e6 | + | 1.20619e7i | −0.427433 | + | 0.740335i | ||||
\(768\) | 1.20795e7 | + | 2.09224e7i | 0.739005 | + | 1.28000i | ||||
\(769\) | −1.14312e7 | − | 1.97994e7i | −0.697069 | − | 1.20736i | −0.969478 | − | 0.245178i | \(-0.921154\pi\) |
0.272409 | − | 0.962182i | \(-0.412180\pi\) | |||||||
\(770\) | 24122.0 | 0.00146618 | ||||||||
\(771\) | −6.86077e6 | − | 1.18832e7i | −0.415659 | − | 0.719942i | ||||
\(772\) | −3.05912e6 | −0.184737 | ||||||||
\(773\) | 2.08320e6 | 0.125395 | 0.0626977 | − | 0.998033i | \(-0.480030\pi\) | ||||
0.0626977 | + | 0.998033i | \(0.480030\pi\) | |||||||
\(774\) | 4.72298e6 | + | 1.39848e7i | 0.283376 | + | 0.839080i | ||||
\(775\) | −4.33956e6 | −0.259532 | ||||||||
\(776\) | 1.33135e7 | 0.793663 | ||||||||
\(777\) | 519512. | + | 899822.i | 0.0308705 | + | 0.0534692i | ||||
\(778\) | 1.36462e7 | 0.808279 | ||||||||
\(779\) | 9.26772e6 | + | 1.60522e7i | 0.547179 | + | 0.947742i | ||||
\(780\) | −1.03086e7 | − | 1.78550e7i | −0.606686 | − | 1.05081i | ||||
\(781\) | −49701.1 | + | 86084.8i | −0.00291567 | + | 0.00505009i | ||||
\(782\) | −2.15977e6 | −0.126297 | ||||||||
\(783\) | 1.26231e7 | − | 2.18638e7i | 0.735802 | − | 1.27445i | ||||
\(784\) | 778545. | + | 1.34848e6i | 0.0452370 | + | 0.0783527i | ||||
\(785\) | 2.15919e7 | 1.25059 | ||||||||
\(786\) | 8.47268e6 | + | 1.46751e7i | 0.489175 | + | 0.847277i | ||||
\(787\) | −2.11492e6 | + | 3.66315e6i | −0.121719 | + | 0.210823i | −0.920445 | − | 0.390871i | \(-0.872174\pi\) |
0.798727 | + | 0.601694i | \(0.205507\pi\) | |||||||
\(788\) | 176126. | − | 305059.i | 0.0101043 | − | 0.0175012i | ||||
\(789\) | −1.77046e7 | + | 3.06652e7i | −1.01250 | + | 1.75369i | ||||
\(790\) | 1.11937e7 | 0.638124 | ||||||||
\(791\) | 24458.7 | − | 42363.6i | 0.00138993 | − | 0.00240742i | ||||
\(792\) | 646211. | − | 1.11927e6i | 0.0366068 | − | 0.0634048i | ||||
\(793\) | −649299. | − | 1.12462e6i | −0.0366659 | − | 0.0635071i | ||||
\(794\) | −2.70687e6 | − | 4.68844e6i | −0.152376 | − | 0.263923i | ||||
\(795\) | −3.58828e7 | −2.01358 | ||||||||
\(796\) | 2.11482e7 | 1.18301 | ||||||||
\(797\) | 9.21405e6 | + | 1.59592e7i | 0.513813 | + | 0.889950i | 0.999872 | + | 0.0160238i | \(0.00510074\pi\) |
−0.486059 | + | 0.873926i | \(0.661566\pi\) | |||||||
\(798\) | 226627. | + | 392530.i | 0.0125981 | + | 0.0218205i | ||||
\(799\) | 7.88769e6 | − | 1.36619e7i | 0.437102 | − | 0.757083i | ||||
\(800\) | 2.97409e6 | − | 5.15127e6i | 0.164297 | − | 0.284570i | ||||
\(801\) | −1.42404e7 | −0.784224 | ||||||||
\(802\) | 3.08080e6 | − | 5.33610e6i | 0.169133 | − | 0.292947i | ||||
\(803\) | 328041. | − | 568184.i | 0.0179531 | − | 0.0310957i | ||||
\(804\) | 5.82342e6 | − | 1.00865e7i | 0.317715 | − | 0.550299i | ||||
\(805\) | −60174.9 | − | 104226.i | −0.00327285 | − | 0.00566874i | ||||
\(806\) | −8.81874e6 | −0.478155 | ||||||||
\(807\) | −1.03500e6 | − | 1.79267e6i | −0.0559444 | − | 0.0968985i | ||||
\(808\) | 3.07698e6 | − | 5.32948e6i | 0.165804 | − | 0.287181i | ||||
\(809\) | −2.40046e7 | −1.28950 | −0.644752 | − | 0.764392i | \(-0.723039\pi\) | ||||
−0.644752 | + | 0.764392i | \(0.723039\pi\) | |||||||
\(810\) | −1.39096e6 | + | 2.40922e6i | −0.0744909 | + | 0.129022i | ||||
\(811\) | 390830. | + | 676937.i | 0.0208658 | + | 0.0361407i | 0.876270 | − | 0.481821i | \(-0.160024\pi\) |
−0.855404 | + | 0.517961i | \(0.826691\pi\) | |||||||
\(812\) | −487913. | − | 845091.i | −0.0259688 | − | 0.0449794i | ||||
\(813\) | 1.24449e7 | 0.660336 | ||||||||
\(814\) | 245468. | + | 425163.i | 0.0129847 | + | 0.0224902i | ||||
\(815\) | 3.23821e6 | 0.170770 | ||||||||
\(816\) | 4.53325e6 | 0.238333 | ||||||||
\(817\) | 1.16207e7 | + | 2.33028e6i | 0.609086 | + | 0.122139i | ||||
\(818\) | −1.66766e7 | −0.871412 | ||||||||
\(819\) | −1.28629e6 | −0.0670083 | ||||||||
\(820\) | −1.28250e7 | − | 2.22136e7i | −0.666076 | − | 1.15368i | ||||
\(821\) | 1.88047e7 | 0.973662 | 0.486831 | − | 0.873496i | \(-0.338153\pi\) | ||||
0.486831 | + | 0.873496i | \(0.338153\pi\) | |||||||
\(822\) | −7.63938e6 | − | 1.32318e7i | −0.394347 | − | 0.683029i | ||||
\(823\) | 7.95927e6 | + | 1.37859e7i | 0.409613 | + | 0.709471i | 0.994846 | − | 0.101394i | \(-0.0323304\pi\) |
−0.585233 | + | 0.810865i | \(0.698997\pi\) | |||||||
\(824\) | 5.31344e6 | − | 9.20315e6i | 0.272620 | − | 0.472192i | ||||
\(825\) | −496596. | −0.0254020 | ||||||||
\(826\) | −211862. | + | 366956.i | −0.0108045 | + | 0.0187139i | ||||
\(827\) | −1.31285e6 | − | 2.27393e6i | −0.0667502 | − | 0.115615i | 0.830719 | − | 0.556692i | \(-0.187930\pi\) |
−0.897469 | + | 0.441078i | \(0.854596\pi\) | |||||||
\(828\) | −2.55872e6 | −0.129702 | ||||||||
\(829\) | 1.93539e6 | + | 3.35220e6i | 0.0978098 | + | 0.169412i | 0.910778 | − | 0.412897i | \(-0.135483\pi\) |
−0.812968 | + | 0.582308i | \(0.802150\pi\) | |||||||
\(830\) | 1.24089e7 | − | 2.14929e7i | 0.625228 | − | 1.08293i | ||||
\(831\) | −2.26183e6 | + | 3.91760e6i | −0.113621 | + | 0.196796i | ||||
\(832\) | 5.12805e6 | − | 8.88205e6i | 0.256829 | − | 0.444841i | ||||
\(833\) | −3.31450e7 | −1.65503 | ||||||||
\(834\) | 1.75623e7 | − | 3.04188e7i | 0.874312 | − | 1.51435i | ||||
\(835\) | 3.64918e6 | − | 6.32057e6i | 0.181125 | − | 0.313718i | ||||
\(836\) | −205895. | − | 356621.i | −0.0101890 | − | 0.0176478i | ||||
\(837\) | 6.67317e6 | + | 1.15583e7i | 0.329245 | + | 0.570268i | ||||
\(838\) | −1.57287e7 | −0.773720 | ||||||||
\(839\) | 2.05437e7 | 1.00757 | 0.503783 | − | 0.863830i | \(-0.331941\pi\) | ||||
0.503783 | + | 0.863830i | \(0.331941\pi\) | |||||||
\(840\) | −790334. | − | 1.36890e6i | −0.0386467 | − | 0.0669380i | ||||
\(841\) | −2.31675e7 | − | 4.01274e7i | −1.12951 | − | 1.95637i | ||||
\(842\) | −4.41012e6 | + | 7.63856e6i | −0.214373 | + | 0.371305i | ||||
\(843\) | 2.15061e7 | − | 3.72497e7i | 1.04230 | − | 1.80532i | ||||
\(844\) | −2.23992e7 | −1.08237 | ||||||||
\(845\) | −287301. | + | 497620.i | −0.0138419 | + | 0.0239749i | ||||
\(846\) | −4.85991e6 | + | 8.41761e6i | −0.233455 | + | 0.404355i | ||||
\(847\) | 455408. | − | 788790.i | 0.0218118 | − | 0.0377792i | ||||
\(848\) | 1.04856e6 | + | 1.81616e6i | 0.0500729 | + | 0.0867288i | ||||
\(849\) | 3.83041e7 | 1.82380 | ||||||||
\(850\) | 3.28205e6 | + | 5.68467e6i | 0.155811 | + | 0.269872i | ||||
\(851\) | 1.22469e6 | − | 2.12122e6i | 0.0579698 | − | 0.100407i | ||||
\(852\) | 2.58470e6 | 0.121986 | ||||||||
\(853\) | 8.88789e6 | − | 1.53943e7i | 0.418240 | − | 0.724414i | −0.577522 | − | 0.816375i | \(-0.695980\pi\) |
0.995763 | + | 0.0919614i | \(0.0293136\pi\) | |||||||
\(854\) | −19753.4 | − | 34213.9i | −0.000926824 | − | 0.00160531i | ||||
\(855\) | −1.15553e7 | − | 2.00143e7i | −0.540586 | − | 0.936322i | ||||
\(856\) | −3.73018e7 | −1.73999 | ||||||||
\(857\) | −1.18752e7 | − | 2.05685e7i | −0.552319 | − | 0.956645i | −0.998107 | − | 0.0615061i | \(-0.980410\pi\) |
0.445788 | − | 0.895139i | \(-0.352924\pi\) | |||||||
\(858\) | −1.00917e6 | −0.0468000 | ||||||||
\(859\) | 3.33388e7 | 1.54159 | 0.770793 | − | 0.637086i | \(-0.219860\pi\) | ||||
0.770793 | + | 0.637086i | \(0.219860\pi\) | |||||||
\(860\) | −1.60812e7 | − | 3.22474e6i | −0.741435 | − | 0.148679i | ||||
\(861\) | −2.65720e6 | −0.122156 | ||||||||
\(862\) | −1.64416e7 | −0.753662 | ||||||||
\(863\) | 3.67085e6 | + | 6.35810e6i | 0.167780 | + | 0.290603i | 0.937639 | − | 0.347611i | \(-0.113007\pi\) |
−0.769859 | + | 0.638214i | \(0.779674\pi\) | |||||||
\(864\) | −1.82936e7 | −0.833711 | ||||||||
\(865\) | 2.13870e7 | + | 3.70434e7i | 0.971875 | + | 1.68334i | ||||
\(866\) | −5.44604e6 | − | 9.43281e6i | −0.246766 | − | 0.427412i | ||||
\(867\) | −3.07013e7 | + | 5.31762e7i | −1.38710 | + | 2.40254i | ||||
\(868\) | 515869. | 0.0232402 | ||||||||
\(869\) | −526759. | + | 912373.i | −0.0236626 | + | 0.0409848i | ||||
\(870\) | −2.14833e7 | − | 3.72102e7i | −0.962285 | − | 1.66673i | ||||
\(871\) | −1.38024e7 | −0.616465 | ||||||||
\(872\) | 1.67963e7 | + | 2.90920e7i | 0.748036 | + | 1.29564i | ||||
\(873\) | −1.39525e7 | + | 2.41664e7i | −0.619605 | + | 1.07319i | ||||
\(874\) | 534247. | − | 925342.i | 0.0236572 | − | 0.0409755i | ||||
\(875\) | 386349. | − | 669175.i | 0.0170592 | − | 0.0295474i | ||||
\(876\) | −1.70597e7 | −0.751124 | ||||||||
\(877\) | −1.60719e7 | + | 2.78374e7i | −0.705616 | + | 1.22216i | 0.260852 | + | 0.965379i | \(0.415996\pi\) |
−0.966469 | + | 0.256785i | \(0.917337\pi\) | |||||||
\(878\) | 1.09265e6 | − | 1.89253e6i | 0.0478349 | − | 0.0828525i | ||||
\(879\) | −6.18425e6 | − | 1.07114e7i | −0.269970 | − | 0.467601i | ||||
\(880\) | 59678.2 | + | 103366.i | 0.00259782 | + | 0.00449955i | ||||
\(881\) | 2.94583e7 | 1.27870 | 0.639349 | − | 0.768917i | \(-0.279204\pi\) | ||||
0.639349 | + | 0.768917i | \(0.279204\pi\) | |||||||
\(882\) | 2.04219e7 | 0.883946 | ||||||||
\(883\) | 8.68788e6 | + | 1.50479e7i | 0.374984 | + | 0.649491i | 0.990325 | − | 0.138770i | \(-0.0443150\pi\) |
−0.615341 | + | 0.788261i | \(0.710982\pi\) | |||||||
\(884\) | −1.28245e7 | − | 2.22127e7i | −0.551964 | − | 0.956030i | ||||
\(885\) | 1.79369e7 | − | 3.10677e7i | 0.769822 | − | 1.33337i | ||||
\(886\) | 1.60559e6 | − | 2.78096e6i | 0.0687147 | − | 0.119017i | ||||
\(887\) | −1.56294e7 | −0.667013 | −0.333507 | − | 0.942748i | \(-0.608232\pi\) | ||||
−0.333507 | + | 0.942748i | \(0.608232\pi\) | |||||||
\(888\) | 1.60850e7 | − | 2.78600e7i | 0.684524 | − | 1.18563i | ||||
\(889\) | −179895. | + | 311587.i | −0.00763421 | + | 0.0132228i | ||||
\(890\) | −4.11458e6 | + | 7.12667e6i | −0.174121 | + | 0.301586i | ||||
\(891\) | −130914. | − | 226749.i | −0.00552447 | − | 0.00956866i | ||||
\(892\) | 2.91944e7 | 1.22853 | ||||||||
\(893\) | 3.90223e6 | + | 6.75886e6i | 0.163751 | + | 0.283625i | ||||
\(894\) | 1.17542e7 | − | 2.03588e7i | 0.491868 | − | 0.851940i | ||||
\(895\) | 4.93961e7 | 2.06127 | ||||||||
\(896\) | −381408. | + | 660618.i | −0.0158716 | + | 0.0274904i | ||||
\(897\) | 2.51748e6 | + | 4.36040e6i | 0.104468 | + | 0.180944i | ||||
\(898\) | 7.05016e6 | + | 1.22112e7i | 0.291748 | + | 0.505323i | ||||
\(899\) | 3.53382e7 | 1.45829 | ||||||||
\(900\) | 3.88830e6 | + | 6.73473e6i | 0.160012 | + | 0.277149i | ||||
\(901\) | −4.46403e7 | −1.83196 | ||||||||
\(902\) | −1.25552e6 | −0.0513814 | ||||||||
\(903\) | −1.12227e6 | + | 1.27570e6i | −0.0458012 | + | 0.0520629i | ||||
\(904\) | −1.51456e6 | −0.0616406 | ||||||||
\(905\) | −2.21617e7 | −0.899460 | ||||||||
\(906\) | 6.91032e6 | + | 1.19690e7i | 0.279690 | + | 0.484438i | ||||
\(907\) | 5.27592e6 | 0.212951 | 0.106476 | − | 0.994315i | \(-0.466043\pi\) | ||||
0.106476 | + | 0.994315i | \(0.466043\pi\) | |||||||
\(908\) | 5.08574e6 | + | 8.80876e6i | 0.204710 | + | 0.354569i | ||||
\(909\) | 6.44932e6 | + | 1.11706e7i | 0.258883 | + | 0.448399i | ||||
\(910\) | −371657. | + | 643730.i | −0.0148778 | + | 0.0257691i | ||||
\(911\) | 2.41879e6 | 0.0965613 | 0.0482806 | − | 0.998834i | \(-0.484626\pi\) | ||||
0.0482806 | + | 0.998834i | \(0.484626\pi\) | |||||||
\(912\) | −1.12136e6 | + | 1.94224e6i | −0.0446433 | + | 0.0773244i | ||||
\(913\) | 1.16789e6 | + | 2.02285e6i | 0.0463688 | + | 0.0803131i | ||||
\(914\) | −6.34609e6 | −0.251270 | ||||||||
\(915\) | 1.67239e6 | + | 2.89666e6i | 0.0660365 | + | 0.114379i | ||||
\(916\) | 7.63060e6 | − | 1.32166e7i | 0.300483 | − | 0.520452i | ||||
\(917\) | −587353. | + | 1.01733e6i | −0.0230662 | + | 0.0399518i | ||||
\(918\) | 1.00940e7 | − | 1.74833e7i | 0.395326 | − | 0.684724i | ||||
\(919\) | −3.47967e7 | −1.35909 | −0.679546 | − | 0.733633i | \(-0.737823\pi\) | ||||
−0.679546 | + | 0.733633i | \(0.737823\pi\) | |||||||
\(920\) | −1.86312e6 | + | 3.22702e6i | −0.0725723 | + | 0.125699i | ||||
\(921\) | −6.28790e6 | + | 1.08910e7i | −0.244262 | + | 0.423075i | ||||
\(922\) | −1.18640e6 | − | 2.05490e6i | −0.0459623 | − | 0.0796091i | ||||
\(923\) | −1.53153e6 | − | 2.65268e6i | −0.0591726 | − | 0.102490i | ||||
\(924\) | 59033.3 | 0.00227466 | ||||||||
\(925\) | −7.44428e6 | −0.286067 | ||||||||
\(926\) | 8.47160e6 | + | 1.46732e7i | 0.324667 | + | 0.562339i | ||||
\(927\) | 1.11369e7 | + | 1.92898e7i | 0.425664 | + | 0.737271i | ||||
\(928\) | −2.42187e7 | + | 4.19481e7i | −0.923170 | + | 1.59898i | ||||
\(929\) | −1.06660e7 | + | 1.84741e7i | −0.405473 | + | 0.702301i | −0.994376 | − | 0.105903i | \(-0.966227\pi\) |
0.588903 | + | 0.808204i | \(0.299560\pi\) | |||||||
\(930\) | 2.27143e7 | 0.861175 | ||||||||
\(931\) | 8.19883e6 | − | 1.42008e7i | 0.310011 | − | 0.536956i | ||||
\(932\) | 8.24056e6 | − | 1.42731e7i | 0.310754 | − | 0.538242i | ||||
\(933\) | −2.57451e7 | + | 4.45918e7i | −0.968257 | + | 1.67707i | ||||
\(934\) | 6.07977e6 | + | 1.05305e7i | 0.228045 | + | 0.394985i | ||||
\(935\) | −2.54068e6 | −0.0950433 | ||||||||
\(936\) | 1.99128e7 | + | 3.44901e7i | 0.742923 | + | 1.28678i | ||||
\(937\) | 1.85025e6 | − | 3.20473e6i | 0.0688464 | − | 0.119246i | −0.829547 | − | 0.558436i | \(-0.811401\pi\) |
0.898394 | + | 0.439191i | \(0.144735\pi\) | |||||||
\(938\) | −419905. | −0.0155827 | ||||||||
\(939\) | 1.98110e7 | − | 3.43136e7i | 0.733233 | − | 1.27000i | ||||
\(940\) | −5.40006e6 | − | 9.35318e6i | −0.199333 | − | 0.345255i | ||||
\(941\) | 1.07068e7 | + | 1.85447e7i | 0.394172 | + | 0.682727i | 0.992995 | − | 0.118155i | \(-0.0376980\pi\) |
−0.598823 | + | 0.800882i | \(0.704365\pi\) | |||||||
\(942\) | −2.74813e7 | −1.00904 | ||||||||
\(943\) | 3.13201e6 | + | 5.42481e6i | 0.114695 | + | 0.198658i | ||||
\(944\) | −2.09660e6 | −0.0765746 | ||||||||
\(945\) | 1.12494e6 | 0.0409779 | ||||||||
\(946\) | −530267. | + | 602762.i | −0.0192649 | + | 0.0218987i | ||||
\(947\) | −3.68786e7 | −1.33629 | −0.668144 | − | 0.744032i | \(-0.732911\pi\) | ||||
−0.668144 | + | 0.744032i | \(0.732911\pi\) | |||||||
\(948\) | 2.73940e7 | 0.989998 | ||||||||
\(949\) | 1.01085e7 | + | 1.75084e7i | 0.364352 | + | 0.631077i | ||||
\(950\) | −3.24742e6 | −0.116743 | ||||||||
\(951\) | −8.02648e6 | − | 1.39023e7i | −0.287789 | − | 0.498465i | ||||
\(952\) | −983223. | − | 1.70299e6i | −0.0351609 | − | 0.0609004i | ||||
\(953\) | 6.10821e6 | − | 1.05797e7i | 0.217862 | − | 0.377348i | −0.736292 | − | 0.676664i | \(-0.763425\pi\) |
0.954154 | + | 0.299316i | \(0.0967583\pi\) | |||||||
\(954\) | 2.75046e7 | 0.978442 | ||||||||
\(955\) | −9.94000e6 | + | 1.72166e7i | −0.352678 | + | 0.610856i | ||||
\(956\) | −5.98272e6 | − | 1.03624e7i | −0.211716 | − | 0.366703i | ||||
\(957\) | 4.04391e6 | 0.142732 | ||||||||
\(958\) | −564939. | − | 978503.i | −0.0198879 | − | 0.0344468i | ||||
\(959\) | 529586. | − | 917271.i | 0.0185947 | − | 0.0322071i | ||||
\(960\) | −1.32082e7 | + | 2.28773e7i | −0.462559 | + | 0.801175i | ||||
\(961\) | 4.97385e6 | − | 8.61496e6i | 0.173734 | − | 0.300916i | ||||
\(962\) | −1.51281e7 | −0.527042 | ||||||||
\(963\) | 3.90922e7 | − | 6.77097e7i | 1.35839 | − | 2.35280i | ||||
\(964\) | −1.57480e7 | + | 2.72763e7i | −0.545799 | + | 0.945351i | ||||
\(965\) | −4.66878e6 | − | 8.08657e6i | −0.161393 | − | 0.279541i | ||||
\(966\) | 76588.3 | + | 132655.i | 0.00264070 | + | 0.00457383i | ||||
\(967\) | −1.27923e7 | −0.439929 | −0.219964 | − | 0.975508i | \(-0.570594\pi\) | ||||
−0.219964 | + | 0.975508i | \(0.570594\pi\) | |||||||
\(968\) | −2.82004e7 | −0.967314 | ||||||||
\(969\) | −2.38698e7 | − | 4.13436e7i | −0.816655 | − | 1.41449i | ||||
\(970\) | 8.06279e6 | + | 1.39652e7i | 0.275141 | + | 0.476559i | ||||
\(971\) | 4.83741e6 | − | 8.37864e6i | 0.164651 | − | 0.285184i | −0.771880 | − | 0.635768i | \(-0.780683\pi\) |
0.936531 | + | 0.350584i | \(0.114017\pi\) | |||||||
\(972\) | −1.13021e7 | + | 1.95758e7i | −0.383702 | + | 0.664591i | ||||
\(973\) | 2.43495e6 | 0.0824532 | ||||||||
\(974\) | −2.88692e6 | + | 5.00029e6i | −0.0975074 | + | 0.168888i | ||||
\(975\) | 7.65124e6 | − | 1.32523e7i | 0.257763 | − | 0.446458i | ||||
\(976\) | 97740.3 | − | 169291.i | 0.00328435 | − | 0.00568866i | ||||
\(977\) | −1.79071e7 | − | 3.10160e7i | −0.600190 | − | 1.03956i | −0.992792 | − | 0.119851i | \(-0.961758\pi\) |
0.392601 | − | 0.919709i | \(-0.371575\pi\) | |||||||
\(978\) | −4.12146e6 | −0.137786 | ||||||||
\(979\) | −387253. | − | 670742.i | −0.0129133 | − | 0.0223666i | ||||
\(980\) | −1.13459e7 | + | 1.96516e7i | −0.377374 | + | 0.653632i | ||||
\(981\) | −7.04099e7 | −2.33594 | ||||||||
\(982\) | −5.97307e6 | + | 1.03457e7i | −0.197660 | + | 0.342357i | ||||
\(983\) | −1.24336e6 | − | 2.15357e6i | −0.0410407 | − | 0.0710845i | 0.844775 | − | 0.535121i | \(-0.179734\pi\) |
−0.885816 | + | 0.464036i | \(0.846401\pi\) | |||||||
\(984\) | 4.11357e7 | + | 7.12491e7i | 1.35435 | + | 2.34580i | ||||
\(985\) | 1.07520e6 | 0.0353102 | ||||||||
\(986\) | −2.67266e7 | − | 4.62918e7i | −0.875489 | − | 1.51639i | ||||
\(987\) | −1.11883e6 | −0.0365570 | ||||||||
\(988\) | 1.26892e7 | 0.413564 | ||||||||
\(989\) | 3.92721e6 | + | 787516.i | 0.127671 | + | 0.0256017i | ||||
\(990\) | 1.56541e6 | 0.0507623 | ||||||||
\(991\) | −2.18955e7 | −0.708224 | −0.354112 | − | 0.935203i | \(-0.615217\pi\) | ||||
−0.354112 | + | 0.935203i | \(0.615217\pi\) | |||||||
\(992\) | −1.28032e7 | − | 2.21758e7i | −0.413085 | − | 0.715484i | ||||
\(993\) | 1.56980e7 | 0.505208 | ||||||||
\(994\) | −46593.2 | − | 80701.7i | −0.00149574 | − | 0.00259070i | ||||
\(995\) | 3.22760e7 | + | 5.59037e7i | 1.03353 | + | 1.79012i | ||||
\(996\) | 3.03680e7 | − | 5.25989e7i | 0.969991 | − | 1.68007i | ||||
\(997\) | 5.14835e7 | 1.64033 | 0.820163 | − | 0.572129i | \(-0.193882\pi\) | ||||
0.820163 | + | 0.572129i | \(0.193882\pi\) | |||||||
\(998\) | −9.25241e6 | + | 1.60256e7i | −0.294055 | + | 0.509318i | ||||
\(999\) | 1.14475e7 | + | 1.98276e7i | 0.362907 | + | 0.628573i |
(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 | 43.6.c.a.36.7 | yes | 34 | |
43.6 | even | 3 | inner | 43.6.c.a.6.7 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.7 | ✓ | 34 | 43.6 | even | 3 | inner | |
43.6.c.a.36.7 | yes | 34 | 1.1 | even | 1 | trivial |