Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(119,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.119");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.b (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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 119.74 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.5.b.a.119.5 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.37175i | 1.84294i | 0.388452 | + | 0.921469i | \(0.373010\pi\) | ||||
−0.388452 | + | 0.921469i | \(0.626990\pi\) | |||||||
\(3\) | 8.47141 | + | 3.03895i | 0.941268 | + | 0.337661i | ||||
\(4\) | −38.3427 | −2.39642 | ||||||||
\(5\) | 40.5786i | 1.62314i | 0.584252 | + | 0.811572i | \(0.301388\pi\) | ||||
−0.584252 | + | 0.811572i | \(0.698612\pi\) | |||||||
\(6\) | −22.4024 | + | 62.4491i | −0.622288 | + | 1.73470i | ||||
\(7\) | 39.1148 | 0.798260 | 0.399130 | − | 0.916894i | \(-0.369312\pi\) | ||||
0.399130 | + | 0.916894i | \(0.369312\pi\) | |||||||
\(8\) | − | 164.705i | − | 2.57352i | ||||||
\(9\) | 62.5296 | + | 51.4883i | 0.771970 | + | 0.635659i | ||||
\(10\) | −299.136 | −2.99136 | ||||||||
\(11\) | 101.974i | 0.842764i | 0.906883 | + | 0.421382i | \(0.138455\pi\) | ||||
−0.906883 | + | 0.421382i | \(0.861545\pi\) | |||||||
\(12\) | −324.817 | − | 116.522i | −2.25567 | − | 0.809178i | ||||
\(13\) | −227.096 | −1.34376 | −0.671882 | − | 0.740659i | \(-0.734514\pi\) | ||||
−0.671882 | + | 0.740659i | \(0.734514\pi\) | |||||||
\(14\) | 288.344i | 1.47114i | ||||||||
\(15\) | −123.316 | + | 343.758i | −0.548072 | + | 1.52781i | ||||
\(16\) | 600.682 | 2.34641 | ||||||||
\(17\) | − | 150.341i | − | 0.520212i | −0.965580 | − | 0.260106i | \(-0.916242\pi\) | ||
0.965580 | − | 0.260106i | \(-0.0837576\pi\) | |||||||
\(18\) | −379.559 | + | 460.953i | −1.17148 | + | 1.42269i | ||||
\(19\) | 458.086 | 1.26894 | 0.634468 | − | 0.772949i | \(-0.281219\pi\) | ||||
0.634468 | + | 0.772949i | \(0.281219\pi\) | |||||||
\(20\) | − | 1555.90i | − | 3.88974i | ||||||
\(21\) | 331.357 | + | 118.868i | 0.751377 | + | 0.269541i | ||||
\(22\) | −751.730 | −1.55316 | ||||||||
\(23\) | 193.289i | 0.365385i | 0.983170 | + | 0.182692i | \(0.0584812\pi\) | ||||
−0.983170 | + | 0.182692i | \(0.941519\pi\) | |||||||
\(24\) | 500.530 | − | 1395.28i | 0.868976 | − | 2.42237i | ||||
\(25\) | −1021.62 | −1.63460 | ||||||||
\(26\) | − | 1674.10i | − | 2.47647i | ||||||
\(27\) | 373.243 | + | 626.203i | 0.511994 | + | 0.858989i | ||||
\(28\) | −1499.77 | −1.91297 | ||||||||
\(29\) | − | 1038.06i | − | 1.23431i | −0.786840 | − | 0.617157i | \(-0.788284\pi\) | ||
0.786840 | − | 0.617157i | \(-0.211716\pi\) | |||||||
\(30\) | −2534.10 | − | 909.057i | −2.81567 | − | 1.01006i | ||||
\(31\) | 1462.33 | 1.52168 | 0.760838 | − | 0.648942i | \(-0.224788\pi\) | ||||
0.760838 | + | 0.648942i | \(0.224788\pi\) | |||||||
\(32\) | 1792.79i | 1.75078i | ||||||||
\(33\) | −309.895 | + | 863.867i | −0.284568 | + | 0.793266i | ||||
\(34\) | 1108.28 | 0.958719 | ||||||||
\(35\) | 1587.22i | 1.29569i | ||||||||
\(36\) | −2397.56 | − | 1974.20i | −1.84997 | − | 1.52331i | ||||
\(37\) | −693.059 | −0.506252 | −0.253126 | − | 0.967433i | \(-0.581459\pi\) | ||||
−0.253126 | + | 0.967433i | \(0.581459\pi\) | |||||||
\(38\) | 3376.90i | 2.33857i | ||||||||
\(39\) | −1923.82 | − | 690.133i | −1.26484 | − | 0.453736i | ||||
\(40\) | 6683.51 | 4.17719 | ||||||||
\(41\) | 119.484i | 0.0710789i | 0.999368 | + | 0.0355395i | \(0.0113149\pi\) | ||||
−0.999368 | + | 0.0355395i | \(0.988685\pi\) | |||||||
\(42\) | −876.263 | + | 2442.68i | −0.496748 | + | 1.38474i | ||||
\(43\) | 1666.91 | 0.901520 | 0.450760 | − | 0.892645i | \(-0.351153\pi\) | ||||
0.450760 | + | 0.892645i | \(0.351153\pi\) | |||||||
\(44\) | − | 3909.98i | − | 2.01962i | ||||||
\(45\) | −2089.33 | + | 2537.36i | −1.03177 | + | 1.25302i | ||||
\(46\) | −1424.88 | −0.673382 | ||||||||
\(47\) | − | 2047.53i | − | 0.926905i | −0.886122 | − | 0.463452i | \(-0.846611\pi\) | ||
0.886122 | − | 0.463452i | \(-0.153389\pi\) | |||||||
\(48\) | 5088.62 | + | 1825.44i | 2.20860 | + | 0.792292i | ||||
\(49\) | −871.036 | −0.362780 | ||||||||
\(50\) | − | 7531.16i | − | 3.01246i | ||||||
\(51\) | 456.880 | − | 1273.60i | 0.175655 | − | 0.489659i | ||||
\(52\) | 8707.48 | 3.22022 | ||||||||
\(53\) | − | 0.219985i | − | 7.83144e-5i | −1.00000 | 3.91572e-5i | \(-0.999988\pi\) | |||
1.00000 | 3.91572e-5i | \(-1.24641e-5\pi\) | ||||||||
\(54\) | −4616.21 | + | 2751.46i | −1.58306 | + | 0.943573i | ||||
\(55\) | −4137.98 | −1.36793 | ||||||||
\(56\) | − | 6442.40i | − | 2.05434i | ||||||
\(57\) | 3880.63 | + | 1392.10i | 1.19441 | + | 0.428470i | ||||
\(58\) | 7652.31 | 2.27476 | ||||||||
\(59\) | 453.188i | 0.130189i | ||||||||
\(60\) | 4728.28 | − | 13180.6i | 1.31341 | − | 3.66129i | ||||
\(61\) | 7367.02 | 1.97985 | 0.989925 | − | 0.141594i | \(-0.0452229\pi\) | ||||
0.989925 | + | 0.141594i | \(0.0452229\pi\) | |||||||
\(62\) | 10779.9i | 2.80435i | ||||||||
\(63\) | 2445.83 | + | 2013.95i | 0.616233 | + | 0.507421i | ||||
\(64\) | −3605.13 | −0.880158 | ||||||||
\(65\) | − | 9215.24i | − | 2.18112i | ||||||
\(66\) | −6368.21 | − | 2284.47i | −1.46194 | − | 0.524442i | ||||
\(67\) | −2787.93 | −0.621059 | −0.310530 | − | 0.950564i | \(-0.600506\pi\) | ||||
−0.310530 | + | 0.950564i | \(0.600506\pi\) | |||||||
\(68\) | 5764.50i | 1.24665i | ||||||||
\(69\) | −587.394 | + | 1637.43i | −0.123376 | + | 0.343925i | ||||
\(70\) | −11700.6 | −2.38788 | ||||||||
\(71\) | 8947.65i | 1.77498i | 0.460831 | + | 0.887488i | \(0.347551\pi\) | ||||
−0.460831 | + | 0.887488i | \(0.652449\pi\) | |||||||
\(72\) | 8480.39 | − | 10298.9i | 1.63588 | − | 1.98668i | ||||
\(73\) | −8302.29 | −1.55794 | −0.778972 | − | 0.627058i | \(-0.784259\pi\) | ||||
−0.778972 | + | 0.627058i | \(0.784259\pi\) | |||||||
\(74\) | − | 5109.06i | − | 0.932991i | ||||||
\(75\) | −8654.60 | − | 3104.66i | −1.53860 | − | 0.551940i | ||||
\(76\) | −17564.3 | −3.04090 | ||||||||
\(77\) | 3988.70i | 0.672745i | ||||||||
\(78\) | 5087.49 | − | 14181.9i | 0.836208 | − | 2.33102i | ||||
\(79\) | −1825.77 | −0.292544 | −0.146272 | − | 0.989244i | \(-0.546728\pi\) | ||||
−0.146272 | + | 0.989244i | \(0.546728\pi\) | |||||||
\(80\) | 24374.8i | 3.80857i | ||||||||
\(81\) | 1258.90 | + | 6439.09i | 0.191876 | + | 0.981419i | ||||
\(82\) | −880.804 | −0.130994 | ||||||||
\(83\) | 10928.3i | 1.58634i | 0.608998 | + | 0.793172i | \(0.291572\pi\) | ||||
−0.608998 | + | 0.793172i | \(0.708428\pi\) | |||||||
\(84\) | −12705.1 | − | 4557.71i | −1.80061 | − | 0.645934i | ||||
\(85\) | 6100.64 | 0.844380 | ||||||||
\(86\) | 12288.1i | 1.66145i | ||||||||
\(87\) | 3154.60 | − | 8793.81i | 0.416779 | − | 1.16182i | ||||
\(88\) | 16795.7 | 2.16887 | ||||||||
\(89\) | − | 7604.36i | − | 0.960025i | −0.877262 | − | 0.480013i | \(-0.840632\pi\) | ||
0.877262 | − | 0.480013i | \(-0.159368\pi\) | |||||||
\(90\) | −18704.8 | − | 15402.0i | −2.30924 | − | 1.90148i | ||||
\(91\) | −8882.80 | −1.07267 | ||||||||
\(92\) | − | 7411.21i | − | 0.875616i | ||||||
\(93\) | 12388.0 | + | 4443.95i | 1.43230 | + | 0.513810i | ||||
\(94\) | 15093.9 | 1.70823 | ||||||||
\(95\) | 18588.5i | 2.05967i | ||||||||
\(96\) | −5448.21 | + | 15187.5i | −0.591168 | + | 1.64795i | ||||
\(97\) | −10747.3 | −1.14224 | −0.571119 | − | 0.820867i | \(-0.693490\pi\) | ||||
−0.571119 | + | 0.820867i | \(0.693490\pi\) | |||||||
\(98\) | − | 6421.06i | − | 0.668582i | ||||||
\(99\) | −5250.49 | + | 6376.42i | −0.535710 | + | 0.650589i | ||||
\(100\) | 39171.9 | 3.91719 | ||||||||
\(101\) | 9016.80i | 0.883913i | 0.897037 | + | 0.441956i | \(0.145715\pi\) | ||||
−0.897037 | + | 0.441956i | \(0.854285\pi\) | |||||||
\(102\) | 9388.69 | + | 3368.00i | 0.902412 | + | 0.323722i | ||||
\(103\) | 11441.8 | 1.07850 | 0.539250 | − | 0.842146i | \(-0.318708\pi\) | ||||
0.539250 | + | 0.842146i | \(0.318708\pi\) | |||||||
\(104\) | 37403.9i | 3.45820i | ||||||||
\(105\) | −4823.49 | + | 13446.0i | −0.437504 | + | 1.21959i | ||||
\(106\) | 1.62168 | 0.000144329 | ||||||||
\(107\) | 5080.56i | 0.443755i | 0.975074 | + | 0.221878i | \(0.0712186\pi\) | ||||
−0.975074 | + | 0.221878i | \(0.928781\pi\) | |||||||
\(108\) | −14311.2 | − | 24010.3i | −1.22695 | − | 2.05850i | ||||
\(109\) | −18603.1 | −1.56579 | −0.782893 | − | 0.622157i | \(-0.786257\pi\) | ||||
−0.782893 | + | 0.622157i | \(0.786257\pi\) | |||||||
\(110\) | − | 30504.2i | − | 2.52101i | ||||||
\(111\) | −5871.19 | − | 2106.17i | −0.476519 | − | 0.170942i | ||||
\(112\) | 23495.5 | 1.87305 | ||||||||
\(113\) | − | 20964.8i | − | 1.64185i | −0.571038 | − | 0.820924i | \(-0.693459\pi\) | ||
0.571038 | − | 0.820924i | \(-0.306541\pi\) | |||||||
\(114\) | −10262.2 | + | 28607.1i | −0.789644 | + | 2.20122i | ||||
\(115\) | −7843.38 | −0.593072 | ||||||||
\(116\) | 39802.0i | 2.95794i | ||||||||
\(117\) | −14200.2 | − | 11692.8i | −1.03735 | − | 0.854175i | ||||
\(118\) | −3340.79 | −0.239930 | ||||||||
\(119\) | − | 5880.57i | − | 0.415265i | ||||||
\(120\) | 56618.7 | + | 20310.8i | 3.93186 | + | 1.41047i | ||||
\(121\) | 4242.22 | 0.289749 | ||||||||
\(122\) | 54307.8i | 3.64874i | ||||||||
\(123\) | −363.105 | + | 1012.20i | −0.0240006 | + | 0.0669043i | ||||
\(124\) | −56069.8 | −3.64658 | ||||||||
\(125\) | − | 16094.5i | − | 1.03005i | ||||||
\(126\) | −14846.4 | + | 18030.1i | −0.935146 | + | 1.13568i | ||||
\(127\) | −29996.7 | −1.85980 | −0.929900 | − | 0.367812i | \(-0.880107\pi\) | ||||
−0.929900 | + | 0.367812i | \(0.880107\pi\) | |||||||
\(128\) | 2108.59i | 0.128698i | ||||||||
\(129\) | 14121.1 | + | 5065.66i | 0.848572 | + | 0.304408i | ||||
\(130\) | 67932.5 | 4.01967 | ||||||||
\(131\) | − | 10098.3i | − | 0.588445i | −0.955737 | − | 0.294223i | \(-0.904939\pi\) | ||
0.955737 | − | 0.294223i | \(-0.0950607\pi\) | |||||||
\(132\) | 11882.2 | − | 33123.0i | 0.681945 | − | 1.90100i | ||||
\(133\) | 17917.9 | 1.01294 | ||||||||
\(134\) | − | 20552.0i | − | 1.14457i | ||||||
\(135\) | −25410.5 | + | 15145.7i | −1.39426 | + | 0.831040i | ||||
\(136\) | −24762.0 | −1.33878 | ||||||||
\(137\) | 4692.61i | 0.250019i | 0.992156 | + | 0.125010i | \(0.0398961\pi\) | ||||
−0.992156 | + | 0.125010i | \(0.960104\pi\) | |||||||
\(138\) | −12070.7 | − | 4330.12i | −0.633832 | − | 0.227375i | ||||
\(139\) | 11174.9 | 0.578382 | 0.289191 | − | 0.957271i | \(-0.406614\pi\) | ||||
0.289191 | + | 0.957271i | \(0.406614\pi\) | |||||||
\(140\) | − | 60858.5i | − | 3.10502i | ||||||
\(141\) | 6222.35 | − | 17345.5i | 0.312979 | − | 0.872466i | ||||
\(142\) | −65959.9 | −3.27117 | ||||||||
\(143\) | − | 23158.0i | − | 1.13247i | ||||||
\(144\) | 37560.4 | + | 30928.1i | 1.81136 | + | 1.49152i | ||||
\(145\) | 42123.0 | 2.00347 | ||||||||
\(146\) | − | 61202.4i | − | 2.87120i | ||||||
\(147\) | −7378.90 | − | 2647.03i | −0.341474 | − | 0.122497i | ||||
\(148\) | 26573.8 | 1.21319 | ||||||||
\(149\) | 13264.6i | 0.597476i | 0.954335 | + | 0.298738i | \(0.0965657\pi\) | ||||
−0.954335 | + | 0.298738i | \(0.903434\pi\) | |||||||
\(150\) | 22886.8 | − | 63799.5i | 1.01719 | − | 2.83554i | ||||
\(151\) | 24846.5 | 1.08971 | 0.544856 | − | 0.838529i | \(-0.316584\pi\) | ||||
0.544856 | + | 0.838529i | \(0.316584\pi\) | |||||||
\(152\) | − | 75449.1i | − | 3.26563i | ||||||
\(153\) | 7740.83 | − | 9400.78i | 0.330677 | − | 0.401588i | ||||
\(154\) | −29403.7 | −1.23983 | ||||||||
\(155\) | 59339.4i | 2.46990i | ||||||||
\(156\) | 73764.6 | + | 26461.6i | 3.03109 | + | 1.08734i | ||||
\(157\) | 16104.2 | 0.653342 | 0.326671 | − | 0.945138i | \(-0.394073\pi\) | ||||
0.326671 | + | 0.945138i | \(0.394073\pi\) | |||||||
\(158\) | − | 13459.1i | − | 0.539141i | ||||||
\(159\) | 0.668524 | − | 1.86359i | 2.64437e−5 | − | 7.37149e-5i | ||||
\(160\) | −72749.1 | −2.84176 | ||||||||
\(161\) | 7560.44i | 0.291672i | ||||||||
\(162\) | −47467.4 | + | 9280.30i | −1.80869 | + | 0.353616i | ||||
\(163\) | 16936.7 | 0.637462 | 0.318731 | − | 0.947845i | \(-0.396743\pi\) | ||||
0.318731 | + | 0.947845i | \(0.396743\pi\) | |||||||
\(164\) | − | 4581.33i | − | 0.170335i | ||||||
\(165\) | −35054.5 | − | 12575.1i | −1.28759 | − | 0.461896i | ||||
\(166\) | −80560.9 | −2.92353 | ||||||||
\(167\) | 38560.4i | 1.38264i | 0.722549 | + | 0.691320i | \(0.242970\pi\) | ||||
−0.722549 | + | 0.691320i | \(0.757030\pi\) | |||||||
\(168\) | 19578.1 | − | 54576.2i | 0.693669 | − | 1.93368i | ||||
\(169\) | 23011.6 | 0.805700 | ||||||||
\(170\) | 44972.4i | 1.55614i | ||||||||
\(171\) | 28643.9 | + | 23586.1i | 0.979581 | + | 0.806610i | ||||
\(172\) | −63913.9 | −2.16042 | ||||||||
\(173\) | 10278.6i | 0.343431i | 0.985147 | + | 0.171716i | \(0.0549310\pi\) | ||||
−0.985147 | + | 0.171716i | \(0.945069\pi\) | |||||||
\(174\) | 64825.8 | + | 23255.0i | 2.14116 | + | 0.768099i | ||||
\(175\) | −39960.6 | −1.30484 | ||||||||
\(176\) | 61254.1i | 1.97747i | ||||||||
\(177\) | −1377.21 | + | 3839.14i | −0.0439597 | + | 0.122543i | ||||
\(178\) | 56057.5 | 1.76927 | ||||||||
\(179\) | − | 26311.2i | − | 0.821173i | −0.911822 | − | 0.410587i | \(-0.865324\pi\) | ||
0.911822 | − | 0.410587i | \(-0.134676\pi\) | |||||||
\(180\) | 80110.5 | − | 97289.5i | 2.47255 | − | 3.00276i | ||||
\(181\) | 7323.15 | 0.223533 | 0.111766 | − | 0.993735i | \(-0.464349\pi\) | ||||
0.111766 | + | 0.993735i | \(0.464349\pi\) | |||||||
\(182\) | − | 65481.8i | − | 1.97687i | ||||||
\(183\) | 62409.1 | + | 22388.0i | 1.86357 | + | 0.668518i | ||||
\(184\) | 31835.6 | 0.940324 | ||||||||
\(185\) | − | 28123.4i | − | 0.821720i | ||||||
\(186\) | −32759.7 | + | 91321.3i | −0.946921 | + | 2.63965i | ||||
\(187\) | 15331.0 | 0.438416 | ||||||||
\(188\) | 78508.0i | 2.22125i | ||||||||
\(189\) | 14599.3 | + | 24493.8i | 0.408704 | + | 0.685697i | ||||
\(190\) | −137030. | −3.79584 | ||||||||
\(191\) | − | 22139.5i | − | 0.606878i | −0.952851 | − | 0.303439i | \(-0.901865\pi\) | ||
0.952851 | − | 0.303439i | \(-0.0981349\pi\) | |||||||
\(192\) | −30540.5 | − | 10955.8i | −0.828465 | − | 0.297195i | ||||
\(193\) | 20014.2 | 0.537307 | 0.268654 | − | 0.963237i | \(-0.413421\pi\) | ||||
0.268654 | + | 0.963237i | \(0.413421\pi\) | |||||||
\(194\) | − | 79226.5i | − | 2.10507i | ||||||
\(195\) | 28004.6 | − | 78066.1i | 0.736480 | − | 2.05302i | ||||
\(196\) | 33397.9 | 0.869375 | ||||||||
\(197\) | 5398.39i | 0.139102i | 0.997578 | + | 0.0695508i | \(0.0221566\pi\) | ||||
−0.997578 | + | 0.0695508i | \(0.977843\pi\) | |||||||
\(198\) | −47005.4 | − | 38705.3i | −1.19899 | − | 0.987280i | ||||
\(199\) | 31903.3 | 0.805619 | 0.402810 | − | 0.915284i | \(-0.368034\pi\) | ||||
0.402810 | + | 0.915284i | \(0.368034\pi\) | |||||||
\(200\) | 168267.i | 4.20667i | ||||||||
\(201\) | −23617.7 | − | 8472.39i | −0.584583 | − | 0.209707i | ||||
\(202\) | −66469.6 | −1.62900 | ||||||||
\(203\) | − | 40603.4i | − | 0.985304i | ||||||
\(204\) | −17518.0 | + | 48833.4i | −0.420944 | + | 1.17343i | ||||
\(205\) | −4848.48 | −0.115371 | ||||||||
\(206\) | 84346.1i | 1.98761i | ||||||||
\(207\) | −9952.11 | + | 12086.3i | −0.232260 | + | 0.282066i | ||||
\(208\) | −136412. | −3.15302 | ||||||||
\(209\) | 46713.0i | 1.06941i | ||||||||
\(210\) | −99120.7 | − | 35557.6i | −2.24763 | − | 0.806294i | ||||
\(211\) | 58686.4 | 1.31817 | 0.659087 | − | 0.752067i | \(-0.270943\pi\) | ||||
0.659087 | + | 0.752067i | \(0.270943\pi\) | |||||||
\(212\) | 8.43484i | 0.000187674i | ||||||||
\(213\) | −27191.5 | + | 75799.2i | −0.599340 | + | 1.67073i | ||||
\(214\) | −37452.6 | −0.817814 | ||||||||
\(215\) | 67641.0i | 1.46330i | ||||||||
\(216\) | 103139. | − | 61475.1i | 2.21062 | − | 1.31762i | ||||
\(217\) | 57198.7 | 1.21469 | ||||||||
\(218\) | − | 137137.i | − | 2.88564i | ||||||
\(219\) | −70332.1 | − | 25230.2i | −1.46644 | − | 0.526057i | ||||
\(220\) | 158661. | 3.27813 | ||||||||
\(221\) | 34141.9i | 0.699042i | ||||||||
\(222\) | 15526.2 | − | 43280.9i | 0.315035 | − | 0.878195i | ||||
\(223\) | 59945.6 | 1.20545 | 0.602723 | − | 0.797950i | \(-0.294082\pi\) | ||||
0.602723 | + | 0.797950i | \(0.294082\pi\) | |||||||
\(224\) | 70124.7i | 1.39757i | ||||||||
\(225\) | −63881.7 | − | 52601.7i | −1.26186 | − | 1.03905i | ||||
\(226\) | 154547. | 3.02582 | ||||||||
\(227\) | − | 57698.6i | − | 1.11973i | −0.828584 | − | 0.559865i | \(-0.810853\pi\) | ||
0.828584 | − | 0.559865i | \(-0.189147\pi\) | |||||||
\(228\) | −148794. | − | 53376.9i | −2.86231 | − | 1.02679i | ||||
\(229\) | −38112.5 | −0.726770 | −0.363385 | − | 0.931639i | \(-0.618379\pi\) | ||||
−0.363385 | + | 0.931639i | \(0.618379\pi\) | |||||||
\(230\) | − | 57819.5i | − | 1.09300i | ||||||
\(231\) | −12121.5 | + | 33789.9i | −0.227160 | + | 0.633233i | ||||
\(232\) | −170973. | −3.17653 | ||||||||
\(233\) | − | 101881.i | − | 1.87665i | −0.345755 | − | 0.938325i | \(-0.612377\pi\) | ||
0.345755 | − | 0.938325i | \(-0.387623\pi\) | |||||||
\(234\) | 86196.4 | − | 104680.i | 1.57419 | − | 1.91176i | ||||
\(235\) | 83086.0 | 1.50450 | ||||||||
\(236\) | − | 17376.5i | − | 0.311987i | ||||||
\(237\) | −15466.8 | − | 5548.42i | −0.275363 | − | 0.0987808i | ||||
\(238\) | 43350.1 | 0.765307 | ||||||||
\(239\) | 31516.2i | 0.551745i | 0.961194 | + | 0.275873i | \(0.0889668\pi\) | ||||
−0.961194 | + | 0.275873i | \(0.911033\pi\) | |||||||
\(240\) | −74073.8 | + | 206489.i | −1.28600 | + | 3.58488i | ||||
\(241\) | −3021.93 | −0.0520295 | −0.0260148 | − | 0.999662i | \(-0.508282\pi\) | ||||
−0.0260148 | + | 0.999662i | \(0.508282\pi\) | |||||||
\(242\) | 31272.6i | 0.533990i | ||||||||
\(243\) | −8903.41 | + | 58373.9i | −0.150780 | + | 0.988567i | ||||
\(244\) | −282472. | −4.74455 | ||||||||
\(245\) | − | 35345.4i | − | 0.588845i | ||||||
\(246\) | −7461.65 | − | 2676.72i | −0.123301 | − | 0.0442316i | ||||
\(247\) | −104029. | −1.70515 | ||||||||
\(248\) | − | 240853.i | − | 3.91606i | ||||||
\(249\) | −33210.6 | + | 92578.3i | −0.535646 | + | 1.49317i | ||||
\(250\) | 118644. | 1.89831 | ||||||||
\(251\) | − | 3350.92i | − | 0.0531883i | −0.999646 | − | 0.0265941i | \(-0.991534\pi\) | ||
0.999646 | − | 0.0265941i | \(-0.00846618\pi\) | |||||||
\(252\) | −93779.8 | − | 77220.5i | −1.47675 | − | 1.21599i | ||||
\(253\) | −19710.5 | −0.307933 | ||||||||
\(254\) | − | 221128.i | − | 3.42750i | ||||||
\(255\) | 51681.1 | + | 18539.5i | 0.794788 | + | 0.285114i | ||||
\(256\) | −73226.1 | −1.11734 | ||||||||
\(257\) | − | 96436.2i | − | 1.46007i | −0.683409 | − | 0.730035i | \(-0.739504\pi\) | ||
0.683409 | − | 0.730035i | \(-0.260496\pi\) | |||||||
\(258\) | −37342.8 | + | 104097.i | −0.561005 | + | 1.56387i | ||||
\(259\) | −27108.8 | −0.404121 | ||||||||
\(260\) | 353338.i | 5.22689i | ||||||||
\(261\) | 53447.9 | − | 64909.3i | 0.784602 | − | 0.952854i | ||||
\(262\) | 74442.2 | 1.08447 | ||||||||
\(263\) | 113800.i | 1.64524i | 0.568591 | + | 0.822620i | \(0.307489\pi\) | ||||
−0.568591 | + | 0.822620i | \(0.692511\pi\) | |||||||
\(264\) | 142283. | + | 51041.3i | 2.04148 | + | 0.732342i | ||||
\(265\) | 8.92670 | 0.000127116 | ||||||||
\(266\) | 132086.i | 1.86679i | ||||||||
\(267\) | 23109.3 | − | 64419.7i | 0.324163 | − | 0.903641i | ||||
\(268\) | 106897. | 1.48832 | ||||||||
\(269\) | − | 35924.4i | − | 0.496460i | −0.968701 | − | 0.248230i | \(-0.920151\pi\) | ||
0.968701 | − | 0.248230i | \(-0.0798489\pi\) | |||||||
\(270\) | −111650. | − | 187320.i | −1.53156 | − | 2.56954i | ||||
\(271\) | 57390.3 | 0.781448 | 0.390724 | − | 0.920508i | \(-0.372225\pi\) | ||||
0.390724 | + | 0.920508i | \(0.372225\pi\) | |||||||
\(272\) | − | 90307.3i | − | 1.22063i | ||||||
\(273\) | −75249.9 | − | 26994.4i | −1.00967 | − | 0.362200i | ||||
\(274\) | −34592.7 | −0.460770 | ||||||||
\(275\) | − | 104180.i | − | 1.37758i | ||||||
\(276\) | 22522.3 | − | 62783.4i | 0.295661 | − | 0.824189i | ||||
\(277\) | 9503.14 | 0.123853 | 0.0619266 | − | 0.998081i | \(-0.480276\pi\) | ||||
0.0619266 | + | 0.998081i | \(0.480276\pi\) | |||||||
\(278\) | 82378.7i | 1.06592i | ||||||||
\(279\) | 91438.9 | + | 75293.0i | 1.17469 | + | 0.967267i | ||||
\(280\) | 261424. | 3.33449 | ||||||||
\(281\) | 123020.i | 1.55798i | 0.627037 | + | 0.778989i | \(0.284267\pi\) | ||||
−0.627037 | + | 0.778989i | \(0.715733\pi\) | |||||||
\(282\) | 127867. | + | 45869.6i | 1.60790 | + | 0.576802i | ||||
\(283\) | 76953.7 | 0.960852 | 0.480426 | − | 0.877035i | \(-0.340482\pi\) | ||||
0.480426 | + | 0.877035i | \(0.340482\pi\) | |||||||
\(284\) | − | 343078.i | − | 4.25359i | ||||||
\(285\) | −56489.4 | + | 157471.i | −0.695469 | + | 1.93870i | ||||
\(286\) | 170715. | 2.08708 | ||||||||
\(287\) | 4673.58i | 0.0567395i | ||||||||
\(288\) | −92308.0 | + | 112103.i | −1.11290 | + | 1.35155i | ||||
\(289\) | 60918.5 | 0.729379 | ||||||||
\(290\) | 310520.i | 3.69227i | ||||||||
\(291\) | −91044.9 | − | 32660.5i | −1.07515 | − | 0.385689i | ||||
\(292\) | 318332. | 3.73349 | ||||||||
\(293\) | − | 14637.7i | − | 0.170505i | −0.996359 | − | 0.0852525i | \(-0.972830\pi\) | ||
0.996359 | − | 0.0852525i | \(-0.0271697\pi\) | |||||||
\(294\) | 19513.3 | − | 54395.4i | 0.225754 | − | 0.629315i | ||||
\(295\) | −18389.7 | −0.211315 | ||||||||
\(296\) | 114150.i | 1.30285i | ||||||||
\(297\) | −63856.7 | + | 38061.3i | −0.723925 | + | 0.431490i | ||||
\(298\) | −97783.1 | −1.10111 | ||||||||
\(299\) | − | 43895.1i | − | 0.490991i | ||||||
\(300\) | 331841. | + | 119041.i | 3.68712 | + | 1.32268i | ||||
\(301\) | 65200.8 | 0.719648 | ||||||||
\(302\) | 183163.i | 2.00827i | ||||||||
\(303\) | −27401.6 | + | 76385.0i | −0.298463 | + | 0.831999i | ||||
\(304\) | 275164. | 2.97745 | ||||||||
\(305\) | 298943.i | 3.21358i | ||||||||
\(306\) | 69300.3 | + | 57063.5i | 0.740103 | + | 0.609418i | ||||
\(307\) | 59016.0 | 0.626171 | 0.313086 | − | 0.949725i | \(-0.398637\pi\) | ||||
0.313086 | + | 0.949725i | \(0.398637\pi\) | |||||||
\(308\) | − | 152938.i | − | 1.61218i | ||||||
\(309\) | 96928.2 | + | 34771.0i | 1.01516 | + | 0.364167i | ||||
\(310\) | −437435. | −4.55187 | ||||||||
\(311\) | − | 105910.i | − | 1.09501i | −0.836803 | − | 0.547505i | \(-0.815578\pi\) | ||
0.836803 | − | 0.547505i | \(-0.184422\pi\) | |||||||
\(312\) | −113668. | + | 316864.i | −1.16770 | + | 3.25509i | ||||
\(313\) | −150512. | −1.53632 | −0.768161 | − | 0.640257i | \(-0.778828\pi\) | ||||
−0.768161 | + | 0.640257i | \(0.778828\pi\) | |||||||
\(314\) | 118716.i | 1.20407i | ||||||||
\(315\) | −81723.5 | + | 99248.4i | −0.823618 | + | 1.00024i | ||||
\(316\) | 70005.0 | 0.701059 | ||||||||
\(317\) | − | 140514.i | − | 1.39830i | −0.714974 | − | 0.699151i | \(-0.753561\pi\) | ||
0.714974 | − | 0.699151i | \(-0.246439\pi\) | |||||||
\(318\) | 13.7379 | + | 4.92819i | 0.000135852 | + | 4.87341e-5i | ||||
\(319\) | 105855. | 1.04023 | ||||||||
\(320\) | − | 146291.i | − | 1.42862i | ||||||
\(321\) | −15439.5 | + | 43039.5i | −0.149839 | + | 0.417693i | ||||
\(322\) | −55733.7 | −0.537534 | ||||||||
\(323\) | − | 68869.3i | − | 0.660116i | ||||||
\(324\) | −48269.7 | − | 246892.i | −0.459816 | − | 2.35189i | ||||
\(325\) | 232007. | 2.19651 | ||||||||
\(326\) | 124853.i | 1.17480i | ||||||||
\(327\) | −157594. | − | 56533.8i | −1.47382 | − | 0.528704i | ||||
\(328\) | 19679.6 | 0.182923 | ||||||||
\(329\) | − | 80088.7i | − | 0.739911i | ||||||
\(330\) | 92700.6 | − | 258413.i | 0.851245 | − | 2.37294i | ||||
\(331\) | 39780.2 | 0.363087 | 0.181544 | − | 0.983383i | \(-0.441891\pi\) | ||||
0.181544 | + | 0.983383i | \(0.441891\pi\) | |||||||
\(332\) | − | 419022.i | − | 3.80155i | ||||||
\(333\) | −43336.7 | − | 35684.5i | −0.390812 | − | 0.321803i | ||||
\(334\) | −284258. | −2.54812 | ||||||||
\(335\) | − | 113131.i | − | 1.00807i | ||||||
\(336\) | 199040. | + | 71401.6i | 1.76304 | + | 0.632455i | ||||
\(337\) | 56088.1 | 0.493868 | 0.246934 | − | 0.969032i | \(-0.420577\pi\) | ||||
0.246934 | + | 0.969032i | \(0.420577\pi\) | |||||||
\(338\) | 169636.i | 1.48485i | ||||||||
\(339\) | 63710.8 | − | 177601.i | 0.554388 | − | 1.54542i | ||||
\(340\) | −233915. | −2.02349 | ||||||||
\(341\) | 149120.i | 1.28241i | ||||||||
\(342\) | −173871. | + | 211156.i | −1.48653 | + | 1.80531i | ||||
\(343\) | −127985. | −1.08785 | ||||||||
\(344\) | − | 274549.i | − | 2.32008i | ||||||
\(345\) | −66444.5 | − | 23835.6i | −0.558240 | − | 0.200257i | ||||
\(346\) | −75771.0 | −0.632923 | ||||||||
\(347\) | − | 163511.i | − | 1.35797i | −0.734154 | − | 0.678983i | \(-0.762421\pi\) | ||
0.734154 | − | 0.678983i | \(-0.237579\pi\) | |||||||
\(348\) | −120956. | + | 337179.i | −0.998779 | + | 2.78421i | ||||
\(349\) | −42912.4 | −0.352316 | −0.176158 | − | 0.984362i | \(-0.556367\pi\) | ||||
−0.176158 | + | 0.984362i | \(0.556367\pi\) | |||||||
\(350\) | − | 294579.i | − | 2.40473i | ||||||
\(351\) | −84762.1 | − | 142208.i | −0.687998 | − | 1.15428i | ||||
\(352\) | −182819. | −1.47549 | ||||||||
\(353\) | − | 14104.9i | − | 0.113193i | −0.998397 | − | 0.0565967i | \(-0.981975\pi\) | ||
0.998397 | − | 0.0565967i | \(-0.0180249\pi\) | |||||||
\(354\) | −28301.2 | − | 10152.5i | −0.225838 | − | 0.0810150i | ||||
\(355\) | −363083. | −2.88104 | ||||||||
\(356\) | 291572.i | 2.30062i | ||||||||
\(357\) | 17870.7 | − | 49816.7i | 0.140219 | − | 0.390875i | ||||
\(358\) | 193960. | 1.51337 | ||||||||
\(359\) | 133490.i | 1.03576i | 0.855452 | + | 0.517882i | \(0.173279\pi\) | ||||
−0.855452 | + | 0.517882i | \(0.826721\pi\) | |||||||
\(360\) | 417917. | + | 344123.i | 3.22467 | + | 2.65527i | ||||
\(361\) | 79521.6 | 0.610198 | ||||||||
\(362\) | 53984.5i | 0.411957i | ||||||||
\(363\) | 35937.6 | + | 12891.9i | 0.272732 | + | 0.0978370i | ||||
\(364\) | 340591. | 2.57058 | ||||||||
\(365\) | − | 336895.i | − | 2.52877i | ||||||
\(366\) | −165039. | + | 460064.i | −1.23204 | + | 3.43444i | ||||
\(367\) | 106223. | 0.788652 | 0.394326 | − | 0.918971i | \(-0.370978\pi\) | ||||
0.394326 | + | 0.918971i | \(0.370978\pi\) | |||||||
\(368\) | 116105.i | 0.857343i | ||||||||
\(369\) | −6152.02 | + | 7471.27i | −0.0451819 | + | 0.0548708i | ||||
\(370\) | 207319. | 1.51438 | ||||||||
\(371\) | − | 8.60467i | − | 6.25153e-5i | ||||||
\(372\) | −474990. | − | 170393.i | −3.43241 | − | 1.23131i | ||||
\(373\) | 37218.8 | 0.267513 | 0.133756 | − | 0.991014i | \(-0.457296\pi\) | ||||
0.133756 | + | 0.991014i | \(0.457296\pi\) | |||||||
\(374\) | 113016.i | 0.807974i | ||||||||
\(375\) | 48910.2 | − | 136343.i | 0.347806 | − | 0.969548i | ||||
\(376\) | −337239. | −2.38541 | ||||||||
\(377\) | 235739.i | 1.65863i | ||||||||
\(378\) | −180562. | + | 107623.i | −1.26370 | + | 0.753217i | ||||
\(379\) | 7019.81 | 0.0488705 | 0.0244353 | − | 0.999701i | \(-0.492221\pi\) | ||||
0.0244353 | + | 0.999701i | \(0.492221\pi\) | |||||||
\(380\) | − | 712733.i | − | 4.93583i | ||||||
\(381\) | −254114. | − | 91158.5i | −1.75057 | − | 0.627982i | ||||
\(382\) | 163207. | 1.11844 | ||||||||
\(383\) | − | 27986.2i | − | 0.190786i | −0.995440 | − | 0.0953928i | \(-0.969589\pi\) | ||
0.995440 | − | 0.0953928i | \(-0.0304107\pi\) | |||||||
\(384\) | −6407.90 | + | 17862.7i | −0.0434563 | + | 0.121139i | ||||
\(385\) | −161856. | −1.09196 | ||||||||
\(386\) | 147539.i | 0.990224i | ||||||||
\(387\) | 104231. | + | 85826.5i | 0.695947 | + | 0.573059i | ||||
\(388\) | 412081. | 2.73728 | ||||||||
\(389\) | 71584.3i | 0.473062i | 0.971624 | + | 0.236531i | \(0.0760105\pi\) | ||||
−0.971624 | + | 0.236531i | \(0.923989\pi\) | |||||||
\(390\) | 575484. | + | 206443.i | 3.78359 | + | 1.35729i | ||||
\(391\) | 29059.3 | 0.190078 | ||||||||
\(392\) | 143464.i | 0.933622i | ||||||||
\(393\) | 30688.2 | − | 85546.9i | 0.198695 | − | 0.553885i | ||||
\(394\) | −39795.6 | −0.256356 | ||||||||
\(395\) | − | 74087.2i | − | 0.474842i | ||||||
\(396\) | 201318. | − | 244489.i | 1.28379 | − | 1.55908i | ||||
\(397\) | −84214.2 | −0.534324 | −0.267162 | − | 0.963652i | \(-0.586086\pi\) | ||||
−0.267162 | + | 0.963652i | \(0.586086\pi\) | |||||||
\(398\) | 235183.i | 1.48471i | ||||||||
\(399\) | 151790. | + | 54451.6i | 0.953449 | + | 0.342031i | ||||
\(400\) | −613671. | −3.83544 | ||||||||
\(401\) | 72922.3i | 0.453494i | 0.973954 | + | 0.226747i | \(0.0728091\pi\) | ||||
−0.973954 | + | 0.226747i | \(0.927191\pi\) | |||||||
\(402\) | 62456.3 | − | 174104.i | 0.386478 | − | 1.07735i | ||||
\(403\) | −332089. | −2.04477 | ||||||||
\(404\) | − | 345729.i | − | 2.11823i | ||||||
\(405\) | −261289. | + | 51084.4i | −1.59299 | + | 0.311443i | ||||
\(406\) | 299318. | 1.81585 | ||||||||
\(407\) | − | 70674.3i | − | 0.426651i | ||||||
\(408\) | −209769. | − | 75250.4i | −1.26015 | − | 0.452052i | ||||
\(409\) | −172315. | −1.03009 | −0.515046 | − | 0.857163i | \(-0.672225\pi\) | ||||
−0.515046 | + | 0.857163i | \(0.672225\pi\) | |||||||
\(410\) | − | 35741.8i | − | 0.212622i | ||||||
\(411\) | −14260.6 | + | 39753.0i | −0.0844217 | + | 0.235335i | ||||
\(412\) | −438710. | −2.58454 | ||||||||
\(413\) | 17726.3i | 0.103925i | ||||||||
\(414\) | −89096.9 | − | 73364.5i | −0.519831 | − | 0.428041i | ||||
\(415\) | −443456. | −2.57487 | ||||||||
\(416\) | − | 407136.i | − | 2.35263i | ||||||
\(417\) | 94667.2 | + | 33960.0i | 0.544412 | + | 0.195297i | ||||
\(418\) | −344357. | −1.97086 | ||||||||
\(419\) | − | 19352.7i | − | 0.110233i | −0.998480 | − | 0.0551166i | \(-0.982447\pi\) | ||
0.998480 | − | 0.0551166i | \(-0.0175531\pi\) | |||||||
\(420\) | 184946. | − | 515557.i | 1.04844 | − | 2.92266i | ||||
\(421\) | −34510.7 | −0.194710 | −0.0973552 | − | 0.995250i | \(-0.531038\pi\) | ||||
−0.0973552 | + | 0.995250i | \(0.531038\pi\) | |||||||
\(422\) | 432622.i | 2.42931i | ||||||||
\(423\) | 105424. | − | 128031.i | 0.589195 | − | 0.715543i | ||||
\(424\) | −36.2327 | −0.000201544 | ||||||||
\(425\) | 153592.i | 0.850338i | ||||||||
\(426\) | −558773. | − | 200449.i | −3.07905 | − | 1.10455i | ||||
\(427\) | 288159. | 1.58044 | ||||||||
\(428\) | − | 194802.i | − | 1.06342i | ||||||
\(429\) | 70375.9 | − | 196181.i | 0.382392 | − | 1.06596i | ||||
\(430\) | −498632. | −2.69677 | ||||||||
\(431\) | − | 27612.2i | − | 0.148644i | −0.997234 | − | 0.0743219i | \(-0.976321\pi\) | ||
0.997234 | − | 0.0743219i | \(-0.0236792\pi\) | |||||||
\(432\) | 224200. | + | 376149.i | 1.20135 | + | 2.01554i | ||||
\(433\) | 245311. | 1.30840 | 0.654200 | − | 0.756322i | \(-0.273005\pi\) | ||||
0.654200 | + | 0.756322i | \(0.273005\pi\) | |||||||
\(434\) | 421655.i | 2.23861i | ||||||||
\(435\) | 356841. | + | 128009.i | 1.88580 | + | 0.676493i | ||||
\(436\) | 713293. | 3.75228 | ||||||||
\(437\) | 88542.8i | 0.463650i | ||||||||
\(438\) | 185991. | − | 518471.i | 0.969491 | − | 2.70256i | ||||
\(439\) | 69211.8 | 0.359130 | 0.179565 | − | 0.983746i | \(-0.442531\pi\) | ||||
0.179565 | + | 0.983746i | \(0.442531\pi\) | |||||||
\(440\) | 681546.i | 3.52038i | ||||||||
\(441\) | −54465.5 | − | 44848.2i | −0.280056 | − | 0.230605i | ||||
\(442\) | −251686. | −1.28829 | ||||||||
\(443\) | − | 76359.2i | − | 0.389094i | −0.980893 | − | 0.194547i | \(-0.937676\pi\) | ||
0.980893 | − | 0.194547i | \(-0.0623236\pi\) | |||||||
\(444\) | 225117. | + | 80756.3i | 1.14194 | + | 0.409648i | ||||
\(445\) | 308574. | 1.55826 | ||||||||
\(446\) | 441904.i | 2.22156i | ||||||||
\(447\) | −40310.3 | + | 112370.i | −0.201744 | + | 0.562385i | ||||
\(448\) | −141014. | −0.702595 | ||||||||
\(449\) | − | 327103.i | − | 1.62253i | −0.584681 | − | 0.811263i | \(-0.698780\pi\) | ||
0.584681 | − | 0.811263i | \(-0.301220\pi\) | |||||||
\(450\) | 387767. | − | 470920.i | 1.91490 | − | 2.32553i | ||||
\(451\) | −12184.3 | −0.0599027 | ||||||||
\(452\) | 803846.i | 3.93456i | ||||||||
\(453\) | 210485. | + | 75507.3i | 1.02571 | + | 0.367953i | ||||
\(454\) | 425340. | 2.06359 | ||||||||
\(455\) | − | 360452.i | − | 1.74110i | ||||||
\(456\) | 229286. | − | 639160.i | 1.10267 | − | 3.07383i | ||||
\(457\) | −304096. | −1.45606 | −0.728029 | − | 0.685546i | \(-0.759564\pi\) | ||||
−0.728029 | + | 0.685546i | \(0.759564\pi\) | |||||||
\(458\) | − | 280956.i | − | 1.33939i | ||||||
\(459\) | 94144.2 | − | 56113.9i | 0.446857 | − | 0.266345i | ||||
\(460\) | 300737. | 1.42125 | ||||||||
\(461\) | 130871.i | 0.615802i | 0.951418 | + | 0.307901i | \(0.0996265\pi\) | ||||
−0.951418 | + | 0.307901i | \(0.900373\pi\) | |||||||
\(462\) | −249091. | − | 89356.4i | −1.16701 | − | 0.418641i | ||||
\(463\) | −362078. | −1.68904 | −0.844520 | − | 0.535524i | \(-0.820114\pi\) | ||||
−0.844520 | + | 0.535524i | \(0.820114\pi\) | |||||||
\(464\) | − | 623542.i | − | 2.89621i | ||||||
\(465\) | −180329. | + | 502688.i | −0.833989 | + | 2.32484i | ||||
\(466\) | 751045. | 3.45855 | ||||||||
\(467\) | − | 935.101i | − | 0.00428771i | −0.999998 | − | 0.00214385i | \(-0.999318\pi\) | ||
0.999998 | − | 0.00214385i | \(-0.000682410\pi\) | |||||||
\(468\) | 544475. | + | 448334.i | 2.48592 | + | 2.04696i | ||||
\(469\) | −109049. | −0.495767 | ||||||||
\(470\) | 612490.i | 2.77270i | ||||||||
\(471\) | 136426. | + | 48939.9i | 0.614970 | + | 0.220608i | ||||
\(472\) | 74642.3 | 0.335043 | ||||||||
\(473\) | 169982.i | 0.759769i | ||||||||
\(474\) | 40901.6 | − | 114018.i | 0.182047 | − | 0.507476i | ||||
\(475\) | −467991. | −2.07420 | ||||||||
\(476\) | 225477.i | 0.995149i | ||||||||
\(477\) | 11.3267 | − | 13.7556i | 4.97813e−5 | − | 6.04564e-5i | ||||
\(478\) | −232330. | −1.01683 | ||||||||
\(479\) | − | 3931.82i | − | 0.0171365i | −0.999963 | − | 0.00856825i | \(-0.997273\pi\) | ||
0.999963 | − | 0.00856825i | \(-0.00272739\pi\) | |||||||
\(480\) | −616287. | − | 221081.i | −2.67486 | − | 0.959552i | ||||
\(481\) | 157391. | 0.680283 | ||||||||
\(482\) | − | 22276.9i | − | 0.0958872i | ||||||
\(483\) | −22975.8 | + | 64047.6i | −0.0984863 | + | 0.274542i | ||||
\(484\) | −162658. | −0.694361 | ||||||||
\(485\) | − | 436111.i | − | 1.85402i | ||||||
\(486\) | −430318. | − | 65633.7i | −1.82187 | − | 0.277878i | ||||
\(487\) | −74782.1 | −0.315312 | −0.157656 | − | 0.987494i | \(-0.550394\pi\) | ||||
−0.157656 | + | 0.987494i | \(0.550394\pi\) | |||||||
\(488\) | − | 1.21339e6i | − | 5.09518i | ||||||
\(489\) | 143478. | + | 51469.8i | 0.600023 | + | 0.215246i | ||||
\(490\) | 260558. | 1.08521 | ||||||||
\(491\) | − | 274270.i | − | 1.13767i | −0.822453 | − | 0.568833i | \(-0.807395\pi\) | ||
0.822453 | − | 0.568833i | \(-0.192605\pi\) | |||||||
\(492\) | 13922.4 | − | 38810.3i | 0.0575155 | − | 0.160331i | ||||
\(493\) | −156063. | −0.642105 | ||||||||
\(494\) | − | 766879.i | − | 3.14248i | ||||||
\(495\) | −258746. | − | 213058.i | −1.05600 | − | 0.869535i | ||||
\(496\) | 878395. | 3.57048 | ||||||||
\(497\) | 349985.i | 1.41689i | ||||||||
\(498\) | −682464. | − | 244820.i | −2.75183 | − | 0.987163i | ||||
\(499\) | −15103.7 | −0.0606573 | −0.0303287 | − | 0.999540i | \(-0.509655\pi\) | ||||
−0.0303287 | + | 0.999540i | \(0.509655\pi\) | |||||||
\(500\) | 617105.i | 2.46842i | ||||||||
\(501\) | −117183. | + | 326661.i | −0.466863 | + | 1.30143i | ||||
\(502\) | 24702.1 | 0.0980227 | ||||||||
\(503\) | − | 100739.i | − | 0.398164i | −0.979983 | − | 0.199082i | \(-0.936204\pi\) | ||
0.979983 | − | 0.199082i | \(-0.0637961\pi\) | |||||||
\(504\) | 331709. | − | 402841.i | 1.30586 | − | 1.58589i | ||||
\(505\) | −365889. | −1.43472 | ||||||||
\(506\) | − | 145301.i | − | 0.567502i | ||||||
\(507\) | 194941. | + | 69931.0i | 0.758379 | + | 0.272053i | ||||
\(508\) | 1.15016e6 | 4.45686 | ||||||||
\(509\) | 239942.i | 0.926125i | 0.886326 | + | 0.463063i | \(0.153250\pi\) | ||||
−0.886326 | + | 0.463063i | \(0.846750\pi\) | |||||||
\(510\) | −136669. | + | 380980.i | −0.525448 | + | 1.46474i | ||||
\(511\) | −324742. | −1.24365 | ||||||||
\(512\) | − | 506067.i | − | 1.93049i | ||||||
\(513\) | 170978. | + | 286855.i | 0.649687 | + | 1.09000i | ||||
\(514\) | 710904. | 2.69082 | ||||||||
\(515\) | 464293.i | 1.75056i | ||||||||
\(516\) | −541441. | − | 194231.i | −2.03354 | − | 0.729490i | ||||
\(517\) | 208796. | 0.781162 | ||||||||
\(518\) | − | 199840.i | − | 0.744770i | ||||||
\(519\) | −31236.0 | + | 87073.9i | −0.115963 | + | 0.323261i | ||||
\(520\) | −1.51780e6 | −5.61316 | ||||||||
\(521\) | − | 194196.i | − | 0.715425i | −0.933832 | − | 0.357712i | \(-0.883557\pi\) | ||
0.933832 | − | 0.357712i | \(-0.116443\pi\) | |||||||
\(522\) | 478496. | + | 394005.i | 1.75605 | + | 1.44597i | ||||
\(523\) | 407345. | 1.48922 | 0.744610 | − | 0.667499i | \(-0.232635\pi\) | ||||
0.744610 | + | 0.667499i | \(0.232635\pi\) | |||||||
\(524\) | 387197.i | 1.41016i | ||||||||
\(525\) | −338522. | − | 121438.i | −1.22820 | − | 0.440592i | ||||
\(526\) | −838903. | −3.03208 | ||||||||
\(527\) | − | 219849.i | − | 0.791595i | ||||||
\(528\) | −186148. | + | 518909.i | −0.667715 | + | 1.86133i | ||||
\(529\) | 242481. | 0.866494 | ||||||||
\(530\) | 65.8054i | 0.000234266i | ||||||||
\(531\) | −23333.9 | + | 28337.6i | −0.0827557 | + | 0.100502i | ||||
\(532\) | −687022. | −2.42743 | ||||||||
\(533\) | − | 27134.3i | − | 0.0955133i | ||||||
\(534\) | 474886. | + | 170356.i | 1.66535 | + | 0.597412i | ||||
\(535\) | −206162. | −0.720279 | ||||||||
\(536\) | 459187.i | 1.59831i | ||||||||
\(537\) | 79958.4 | − | 222893.i | 0.277278 | − | 0.772944i | ||||
\(538\) | 264826. | 0.914946 | ||||||||
\(539\) | − | 88823.4i | − | 0.305738i | ||||||
\(540\) | 974306. | − | 580728.i | 3.34124 | − | 1.99152i | ||||
\(541\) | −197440. | −0.674591 | −0.337296 | − | 0.941399i | \(-0.609512\pi\) | ||||
−0.337296 | + | 0.941399i | \(0.609512\pi\) | |||||||
\(542\) | 423067.i | 1.44016i | ||||||||
\(543\) | 62037.4 | + | 22254.7i | 0.210404 | + | 0.0754782i | ||||
\(544\) | 269531. | 0.910775 | ||||||||
\(545\) | − | 754888.i | − | 2.54150i | ||||||
\(546\) | 198996. | − | 554723.i | 0.667512 | − | 1.86076i | ||||
\(547\) | 162871. | 0.544337 | 0.272169 | − | 0.962250i | \(-0.412259\pi\) | ||||
0.272169 | + | 0.962250i | \(0.412259\pi\) | |||||||
\(548\) | − | 179927.i | − | 0.599151i | ||||||
\(549\) | 460657. | + | 379316.i | 1.52838 | + | 1.25851i | ||||
\(550\) | 767986. | 2.53880 | ||||||||
\(551\) | − | 475520.i | − | 1.56626i | ||||||
\(552\) | 269693. | + | 96746.8i | 0.885097 | + | 0.317511i | ||||
\(553\) | −71414.5 | −0.233527 | ||||||||
\(554\) | 70054.8i | 0.228254i | ||||||||
\(555\) | 85465.5 | − | 238245.i | 0.277463 | − | 0.773459i | ||||
\(556\) | −428477. | −1.38605 | ||||||||
\(557\) | 162633.i | 0.524201i | 0.965041 | + | 0.262100i | \(0.0844151\pi\) | ||||
−0.965041 | + | 0.262100i | \(0.915585\pi\) | |||||||
\(558\) | −555041. | + | 674065.i | −1.78261 | + | 2.16488i | ||||
\(559\) | −378549. | −1.21143 | ||||||||
\(560\) | 953415.i | 3.04023i | ||||||||
\(561\) | 129875. | + | 46590.0i | 0.412667 | + | 0.148036i | ||||
\(562\) | −906870. | −2.87126 | ||||||||
\(563\) | 361668.i | 1.14102i | 0.821291 | + | 0.570510i | \(0.193255\pi\) | ||||
−0.821291 | + | 0.570510i | \(0.806745\pi\) | |||||||
\(564\) | −238582. | + | 665074.i | −0.750031 | + | 2.09079i | ||||
\(565\) | 850721. | 2.66496 | ||||||||
\(566\) | 567283.i | 1.77079i | ||||||||
\(567\) | 49241.6 | + | 251863.i | 0.153167 | + | 0.783428i | ||||
\(568\) | 1.47372e6 | 4.56793 | ||||||||
\(569\) | − | 136555.i | − | 0.421776i | −0.977510 | − | 0.210888i | \(-0.932364\pi\) | ||
0.977510 | − | 0.210888i | \(-0.0676356\pi\) | |||||||
\(570\) | −1.16084e6 | − | 416426.i | −3.57290 | − | 1.28171i | ||||
\(571\) | 17778.1 | 0.0545272 | 0.0272636 | − | 0.999628i | \(-0.491321\pi\) | ||||
0.0272636 | + | 0.999628i | \(0.491321\pi\) | |||||||
\(572\) | 887940.i | 2.71389i | ||||||||
\(573\) | 67280.8 | − | 187553.i | 0.204919 | − | 0.571235i | ||||
\(574\) | −34452.4 | −0.104567 | ||||||||
\(575\) | − | 197468.i | − | 0.597258i | ||||||
\(576\) | −225427. | − | 185622.i | −0.679456 | − | 0.559480i | ||||
\(577\) | −108734. | −0.326597 | −0.163298 | − | 0.986577i | \(-0.552213\pi\) | ||||
−0.163298 | + | 0.986577i | \(0.552213\pi\) | |||||||
\(578\) | 449076.i | 1.34420i | ||||||||
\(579\) | 169548. | + | 60822.0i | 0.505750 | + | 0.181428i | ||||
\(580\) | −1.61511e6 | −4.80116 | ||||||||
\(581\) | 427459.i | 1.26632i | ||||||||
\(582\) | 240765. | − | 671161.i | 0.710801 | − | 1.98144i | ||||
\(583\) | 22.4329 | 6.60006e−5 | ||||||||
\(584\) | 1.36743e6i | 4.00940i | ||||||||
\(585\) | 474478. | − | 576225.i | 1.38645 | − | 1.68376i | ||||
\(586\) | 107905. | 0.314230 | ||||||||
\(587\) | − | 586908.i | − | 1.70331i | −0.524102 | − | 0.851655i | \(-0.675599\pi\) | ||
0.524102 | − | 0.851655i | \(-0.324401\pi\) | |||||||
\(588\) | 282927. | + | 101494.i | 0.818314 | + | 0.293554i | ||||
\(589\) | 669873. | 1.93091 | ||||||||
\(590\) | − | 135565.i | − | 0.389441i | ||||||
\(591\) | −16405.4 | + | 45732.0i | −0.0469691 | + | 0.130932i | ||||
\(592\) | −416308. | −1.18788 | ||||||||
\(593\) | − | 137926.i | − | 0.392227i | −0.980581 | − | 0.196113i | \(-0.937168\pi\) | ||
0.980581 | − | 0.196113i | \(-0.0628321\pi\) | |||||||
\(594\) | −280578. | − | 470736.i | −0.795209 | − | 1.33415i | ||||
\(595\) | 238625. | 0.674035 | ||||||||
\(596\) | − | 508600.i | − | 1.43180i | ||||||
\(597\) | 270266. | + | 96952.6i | 0.758304 | + | 0.272026i | ||||
\(598\) | 323584. | 0.904865 | ||||||||
\(599\) | − | 37284.7i | − | 0.103915i | −0.998649 | − | 0.0519574i | \(-0.983454\pi\) | ||
0.998649 | − | 0.0519574i | \(-0.0165460\pi\) | |||||||
\(600\) | −511354. | + | 1.42546e6i | −1.42043 | + | 3.95960i | ||||
\(601\) | 152155. | 0.421248 | 0.210624 | − | 0.977567i | \(-0.432450\pi\) | ||||
0.210624 | + | 0.977567i | \(0.432450\pi\) | |||||||
\(602\) | 480644.i | 1.32627i | ||||||||
\(603\) | −174328. | − | 143546.i | −0.479439 | − | 0.394782i | ||||
\(604\) | −952684. | −2.61141 | ||||||||
\(605\) | 172143.i | 0.470305i | ||||||||
\(606\) | −563091. | − | 201998.i | −1.53332 | − | 0.550048i | ||||
\(607\) | 97390.8 | 0.264326 | 0.132163 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132163 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(608\) | 821253.i | 2.22162i | ||||||||
\(609\) | 123392. | − | 343968.i | 0.332699 | − | 0.927435i | ||||
\(610\) | −2.20374e6 | −5.92243 | ||||||||
\(611\) | 464986.i | 1.24554i | ||||||||
\(612\) | −296805. | + | 360452.i | −0.792442 | + | 0.962375i | ||||
\(613\) | 177806. | 0.473180 | 0.236590 | − | 0.971610i | \(-0.423970\pi\) | ||||
0.236590 | + | 0.971610i | \(0.423970\pi\) | |||||||
\(614\) | 435051.i | 1.15399i | ||||||||
\(615\) | −41073.5 | − | 14734.3i | −0.108595 | − | 0.0389564i | ||||
\(616\) | 656960. | 1.73132 | ||||||||
\(617\) | 16269.5i | 0.0427370i | 0.999772 | + | 0.0213685i | \(0.00680232\pi\) | ||||
−0.999772 | + | 0.0213685i | \(0.993198\pi\) | |||||||
\(618\) | −256324. | + | 714531.i | −0.671138 | + | 1.87087i | ||||
\(619\) | −34352.4 | −0.0896552 | −0.0448276 | − | 0.998995i | \(-0.514274\pi\) | ||||
−0.0448276 | + | 0.998995i | \(0.514274\pi\) | |||||||
\(620\) | − | 2.27523e6i | − | 5.91892i | ||||||
\(621\) | −121038. | + | 72143.7i | −0.313862 | + | 0.187075i | ||||
\(622\) | 780745. | 2.01803 | ||||||||
\(623\) | − | 297443.i | − | 0.766350i | ||||||
\(624\) | −1.15561e6 | − | 414550.i | −2.96784 | − | 1.06465i | ||||
\(625\) | 14575.7 | 0.0373138 | ||||||||
\(626\) | − | 1.10954e6i | − | 2.83135i | ||||||
\(627\) | −141958. | + | 395725.i | −0.361099 | + | 1.00660i | ||||
\(628\) | −617480. | −1.56568 | ||||||||
\(629\) | 104195.i | 0.263359i | ||||||||
\(630\) | −731635. | − | 602445.i | −1.84337 | − | 1.51788i | ||||
\(631\) | −726363. | −1.82429 | −0.912147 | − | 0.409864i | \(-0.865576\pi\) | ||||
−0.912147 | + | 0.409864i | \(0.865576\pi\) | |||||||
\(632\) | 300714.i | 0.752868i | ||||||||
\(633\) | 497157. | + | 178345.i | 1.24075 | + | 0.445096i | ||||
\(634\) | 1.03583e6 | 2.57698 | ||||||||
\(635\) | − | 1.21723e6i | − | 3.01872i | ||||||
\(636\) | −25.6330 | + | 71.4550i | −6.33703e−5 | + | 0.000176652i | ||||
\(637\) | 197809. | 0.487491 | ||||||||
\(638\) | 780339.i | 1.91709i | ||||||||
\(639\) | −460700. | + | 559493.i | −1.12828 | + | 1.37023i | ||||
\(640\) | −85563.7 | −0.208896 | ||||||||
\(641\) | 368854.i | 0.897714i | 0.893604 | + | 0.448857i | \(0.148169\pi\) | ||||
−0.893604 | + | 0.448857i | \(0.851831\pi\) | |||||||
\(642\) | −317276. | − | 113817.i | −0.769782 | − | 0.276144i | ||||
\(643\) | 248032. | 0.599910 | 0.299955 | − | 0.953953i | \(-0.403028\pi\) | ||||
0.299955 | + | 0.953953i | \(0.403028\pi\) | |||||||
\(644\) | − | 289888.i | − | 0.698969i | ||||||
\(645\) | −205557. | + | 573014.i | −0.494098 | + | 1.37736i | ||||
\(646\) | 507687. | 1.21655 | ||||||||
\(647\) | − | 491048.i | − | 1.17305i | −0.809932 | − | 0.586524i | \(-0.800496\pi\) | ||
0.809932 | − | 0.586524i | \(-0.199504\pi\) | |||||||
\(648\) | 1.06055e6 | − | 207347.i | 2.52570 | − | 0.493797i | ||||
\(649\) | −46213.5 | −0.109718 | ||||||||
\(650\) | 1.71030e6i | 4.04804i | ||||||||
\(651\) | 484554. | + | 173824.i | 1.14335 | + | 0.410155i | ||||
\(652\) | −649401. | −1.52763 | ||||||||
\(653\) | 699337.i | 1.64006i | 0.572319 | + | 0.820031i | \(0.306044\pi\) | ||||
−0.572319 | + | 0.820031i | \(0.693956\pi\) | |||||||
\(654\) | 416753. | − | 1.16175e6i | 0.974369 | − | 2.71616i | ||||
\(655\) | 409775. | 0.955132 | ||||||||
\(656\) | 71771.7i | 0.166780i | ||||||||
\(657\) | −519139. | − | 427471.i | −1.20269 | − | 0.990321i | ||||
\(658\) | 590394. | 1.36361 | ||||||||
\(659\) | − | 321977.i | − | 0.741403i | −0.928752 | − | 0.370702i | \(-0.879117\pi\) | ||
0.928752 | − | 0.370702i | \(-0.120883\pi\) | |||||||
\(660\) | 1.34409e6 | + | 482164.i | 3.08560 | + | 1.10690i | ||||
\(661\) | 197653. | 0.452376 | 0.226188 | − | 0.974084i | \(-0.427374\pi\) | ||||
0.226188 | + | 0.974084i | \(0.427374\pi\) | |||||||
\(662\) | 293250.i | 0.669147i | ||||||||
\(663\) | −103756. | + | 289230.i | −0.236039 | + | 0.657986i | ||||
\(664\) | 1.79995e6 | 4.08248 | ||||||||
\(665\) | 727084.i | 1.64415i | ||||||||
\(666\) | 263057. | − | 319467.i | 0.593064 | − | 0.720241i | ||||
\(667\) | 200645. | 0.451000 | ||||||||
\(668\) | − | 1.47851e6i | − | 3.31339i | ||||||
\(669\) | 507824. | + | 182172.i | 1.13465 | + | 0.407032i | ||||
\(670\) | 833970. | 1.85781 | ||||||||
\(671\) | 751248.i | 1.66855i | ||||||||
\(672\) | −213105. | + | 594055.i | −0.471906 | + | 1.31549i | ||||
\(673\) | 430587. | 0.950673 | 0.475337 | − | 0.879804i | \(-0.342326\pi\) | ||||
0.475337 | + | 0.879804i | \(0.342326\pi\) | |||||||
\(674\) | 413468.i | 0.910168i | ||||||||
\(675\) | −381314. | − | 639744.i | −0.836904 | − | 1.40410i | ||||
\(676\) | −882327. | −1.93080 | ||||||||
\(677\) | 74792.4i | 0.163185i | 0.996666 | + | 0.0815925i | \(0.0260006\pi\) | ||||
−0.996666 | + | 0.0815925i | \(0.973999\pi\) | |||||||
\(678\) | 1.30923e6 | + | 469660.i | 2.84811 | + | 1.02170i | ||||
\(679\) | −420379. | −0.911803 | ||||||||
\(680\) | − | 1.00481e6i | − | 2.17303i | ||||||
\(681\) | 175343. | − | 488789.i | 0.378089 | − | 1.05397i | ||||
\(682\) | −1.09928e6 | −2.36341 | ||||||||
\(683\) | − | 424167.i | − | 0.909275i | −0.890677 | − | 0.454637i | \(-0.849769\pi\) | ||
0.890677 | − | 0.454637i | \(-0.150231\pi\) | |||||||
\(684\) | −1.09829e6 | − | 904355.i | −2.34749 | − | 1.93298i | ||||
\(685\) | −190420. | −0.405817 | ||||||||
\(686\) | − | 943473.i | − | 2.00485i | ||||||
\(687\) | −322867. | − | 115822.i | −0.684085 | − | 0.245402i | ||||
\(688\) | 1.00128e6 | 2.11534 | ||||||||
\(689\) | 49.9578i | 0.000105236i | ||||||||
\(690\) | 175710. | − | 489813.i | 0.369062 | − | 1.02880i | ||||
\(691\) | 450906. | 0.944344 | 0.472172 | − | 0.881506i | \(-0.343470\pi\) | ||||
0.472172 | + | 0.881506i | \(0.343470\pi\) | |||||||
\(692\) | − | 394108.i | − | 0.823006i | ||||||
\(693\) | −205372. | + | 249412.i | −0.427636 | + | 0.519339i | ||||
\(694\) | 1.20537e6 | 2.50265 | ||||||||
\(695\) | 453462.i | 0.938797i | ||||||||
\(696\) | −1.44839e6 | − | 519579.i | −2.98996 | − | 1.07259i | ||||
\(697\) | 17963.3 | 0.0369761 | ||||||||
\(698\) | − | 316340.i | − | 0.649296i | ||||||
\(699\) | 309612. | − | 863079.i | 0.633671 | − | 1.76643i | ||||
\(700\) | 1.53220e6 | 3.12693 | ||||||||
\(701\) | − | 183180.i | − | 0.372770i | −0.982477 | − | 0.186385i | \(-0.940323\pi\) | ||
0.982477 | − | 0.186385i | \(-0.0596772\pi\) | |||||||
\(702\) | 1.04832e6 | − | 624845.i | 2.12726 | − | 1.26794i | ||||
\(703\) | −317481. | −0.642401 | ||||||||
\(704\) | − | 367631.i | − | 0.741765i | ||||||
\(705\) | 703856. | + | 252494.i | 1.41614 | + | 0.508011i | ||||
\(706\) | 103978. | 0.208609 | ||||||||
\(707\) | 352690.i | 0.705593i | ||||||||
\(708\) | 52806.1 | − | 147203.i | 0.105346 | − | 0.293664i | ||||
\(709\) | −419548. | −0.834622 | −0.417311 | − | 0.908764i | \(-0.637027\pi\) | ||||
−0.417311 | + | 0.908764i | \(0.637027\pi\) | |||||||
\(710\) | − | 2.67656e6i | − | 5.30958i | ||||||
\(711\) | −114165. | − | 94005.9i | −0.225836 | − | 0.185958i | ||||
\(712\) | −1.25248e6 | −2.47064 | ||||||||
\(713\) | 282652.i | 0.555997i | ||||||||
\(714\) | 367236. | + | 131739.i | 0.720359 | + | 0.258414i | ||||
\(715\) | 939719. | 1.83817 | ||||||||
\(716\) | 1.00884e6i | 1.96788i | ||||||||
\(717\) | −95776.2 | + | 266987.i | −0.186303 | + | 0.519340i | ||||
\(718\) | −984057. | −1.90885 | ||||||||
\(719\) | − | 388924.i | − | 0.752327i | −0.926553 | − | 0.376164i | \(-0.877243\pi\) | ||
0.926553 | − | 0.376164i | \(-0.122757\pi\) | |||||||
\(720\) | −1.25502e6 | + | 1.52415e6i | −2.42095 | + | 2.94010i | ||||
\(721\) | 447543. | 0.860924 | ||||||||
\(722\) | 586214.i | 1.12456i | ||||||||
\(723\) | −25600.0 | − | 9183.47i | −0.0489737 | − | 0.0175683i | ||||
\(724\) | −280790. | −0.535678 | ||||||||
\(725\) | 1.06050e6i | 2.01761i | ||||||||
\(726\) | −95035.8 | + | 264923.i | −0.180308 | + | 0.502628i | ||||
\(727\) | 142364. | 0.269358 | 0.134679 | − | 0.990889i | \(-0.457000\pi\) | ||||
0.134679 | + | 0.990889i | \(0.457000\pi\) | |||||||
\(728\) | 1.46304e6i | 2.76054i | ||||||||
\(729\) | −252820. | + | 467452.i | −0.475725 | + | 0.879594i | ||||
\(730\) | 2.48351e6 | 4.66037 | ||||||||
\(731\) | − | 250606.i | − | 0.468982i | ||||||
\(732\) | −2.39293e6 | − | 858417.i | −4.46589 | − | 1.60205i | ||||
\(733\) | 576062. | 1.07216 | 0.536082 | − | 0.844166i | \(-0.319904\pi\) | ||||
0.536082 | + | 0.844166i | \(0.319904\pi\) | |||||||
\(734\) | 783048.i | 1.45344i | ||||||||
\(735\) | 107413. | − | 299426.i | 0.198830 | − | 0.554261i | ||||
\(736\) | −346527. | −0.639707 | ||||||||
\(737\) | − | 284298.i | − | 0.523406i | ||||||
\(738\) | −55076.3 | − | 45351.2i | −0.101124 | − | 0.0832675i | ||||
\(739\) | −341810. | −0.625887 | −0.312944 | − | 0.949772i | \(-0.601315\pi\) | ||||
−0.312944 | + | 0.949772i | \(0.601315\pi\) | |||||||
\(740\) | 1.07833e6i | 1.96919i | ||||||||
\(741\) | −881276. | − | 316140.i | −1.60500 | − | 0.575762i | ||||
\(742\) | 63.4315 | 0.000115212 | ||||||||
\(743\) | 197408.i | 0.357591i | 0.983886 | + | 0.178795i | \(0.0572200\pi\) | ||||
−0.983886 | + | 0.178795i | \(0.942780\pi\) | |||||||
\(744\) | 731941. | − | 2.04037e6i | 1.32230 | − | 3.68606i | ||||
\(745\) | −538258. | −0.969790 | ||||||||
\(746\) | 274368.i | 0.493009i | ||||||||
\(747\) | −562681. | + | 683344.i | −1.00837 | + | 1.22461i | ||||
\(748\) | −587831. | −1.05063 | ||||||||
\(749\) | 198725.i | 0.354232i | ||||||||
\(750\) | 1.00508e6 | + | 360554.i | 1.78682 | + | 0.640985i | ||||
\(751\) | −297608. | −0.527673 | −0.263836 | − | 0.964567i | \(-0.584988\pi\) | ||||
−0.263836 | + | 0.964567i | \(0.584988\pi\) | |||||||
\(752\) | − | 1.22992e6i | − | 2.17490i | ||||||
\(753\) | 10183.3 | − | 28387.0i | 0.0179596 | − | 0.0500644i | ||||
\(754\) | −1.73781e6 | −3.05674 | ||||||||
\(755\) | 1.00824e6i | 1.76876i | ||||||||
\(756\) | −559778. | − | 939159.i | −0.979427 | − | 1.64322i | ||||
\(757\) | 507520. | 0.885649 | 0.442824 | − | 0.896608i | \(-0.353977\pi\) | ||||
0.442824 | + | 0.896608i | \(0.353977\pi\) | |||||||
\(758\) | 51748.3i | 0.0900654i | ||||||||
\(759\) | −166976. | − | 59899.1i | −0.289847 | − | 0.103977i | ||||
\(760\) | 3.06162e6 | 5.30059 | ||||||||
\(761\) | 291086.i | 0.502635i | 0.967905 | + | 0.251317i | \(0.0808637\pi\) | ||||
−0.967905 | + | 0.251317i | \(0.919136\pi\) | |||||||
\(762\) | 671998. | − | 1.87327e6i | 1.15733 | − | 3.22619i | ||||
\(763\) | −727655. | −1.24990 | ||||||||
\(764\) | 848890.i | 1.45433i | ||||||||
\(765\) | 381471. | + | 314112.i | 0.651836 | + | 0.536737i | ||||
\(766\) | 206307. | 0.351606 | ||||||||
\(767\) | − | 102917.i | − | 0.174943i | ||||||
\(768\) | −620328. | − | 222530.i | −1.05172 | − | 0.377282i | ||||
\(769\) | 173980. | 0.294203 | 0.147102 | − | 0.989121i | \(-0.453006\pi\) | ||||
0.147102 | + | 0.989121i | \(0.453006\pi\) | |||||||
\(770\) | − | 1.19316e6i | − | 2.01242i | ||||||
\(771\) | 293065. | − | 816951.i | 0.493009 | − | 1.37432i | ||||
\(772\) | −767398. | −1.28761 | ||||||||
\(773\) | − | 98287.5i | − | 0.164490i | −0.996612 | − | 0.0822450i | \(-0.973791\pi\) | ||
0.996612 | − | 0.0822450i | \(-0.0262090\pi\) | |||||||
\(774\) | −632692. | + | 768367.i | −1.05611 | + | 1.28259i | ||||
\(775\) | −1.49395e6 | −2.48733 | ||||||||
\(776\) | 1.77014e6i | 2.93957i | ||||||||
\(777\) | −229650. | − | 82382.3i | −0.380386 | − | 0.136456i | ||||
\(778\) | −527702. | −0.871825 | ||||||||
\(779\) | 54733.8i | 0.0901946i | ||||||||
\(780\) | −1.07377e6 | + | 2.99327e6i | −1.76492 | + | 4.91990i | ||||
\(781\) | −912432. | −1.49589 | ||||||||
\(782\) | 214218.i | 0.350301i | ||||||||
\(783\) | 650035. | − | 387448.i | 1.06026 | − | 0.631961i | ||||
\(784\) | −523215. | −0.851233 | ||||||||
\(785\) | 653487.i | 1.06047i | ||||||||
\(786\) | 630631. | + | 226226.i | 1.02077 | + | 0.366182i | ||||
\(787\) | 900591. | 1.45405 | 0.727023 | − | 0.686613i | \(-0.240903\pi\) | ||||
0.727023 | + | 0.686613i | \(0.240903\pi\) | |||||||
\(788\) | − | 206989.i | − | 0.333346i | ||||||
\(789\) | −345831. | + | 964043.i | −0.555533 | + | 1.54861i | ||||
\(790\) | 546152. | 0.875104 | ||||||||
\(791\) | − | 820031.i | − | 1.31062i | ||||||
\(792\) | 1.05023e6 | + | 864783.i | 1.67430 | + | 1.37866i | ||||
\(793\) | −1.67302e6 | −2.66045 | ||||||||
\(794\) | − | 620806.i | − | 0.984726i | ||||||
\(795\) | 75.6217 | + | 27.1278i | 0.000119650 | + | 4.29220e-5i | ||||
\(796\) | −1.22326e6 | −1.93060 | ||||||||
\(797\) | 31498.7i | 0.0495880i | 0.999693 | + | 0.0247940i | \(0.00789298\pi\) | ||||
−0.999693 | + | 0.0247940i | \(0.992107\pi\) | |||||||
\(798\) | −401404. | + | 1.11896e6i | −0.630341 | + | 1.75715i | ||||
\(799\) | −307829. | −0.482187 | ||||||||
\(800\) | − | 1.83156e6i | − | 2.86181i | ||||||
\(801\) | 391536. | − | 475498.i | 0.610248 | − | 0.741111i | ||||
\(802\) | −537565. | −0.835762 | ||||||||
\(803\) | − | 846621.i | − | 1.31298i | ||||||
\(804\) | 905569. | + | 324855.i | 1.40091 | + | 0.502547i | ||||
\(805\) | −306792. | −0.473426 | ||||||||
\(806\) | − | 2.44808e6i | − | 3.76839i | ||||||
\(807\) | 109172. | − | 304330.i | 0.167635 | − | 0.467302i | ||||
\(808\) | 1.48511e6 | 2.27477 | ||||||||
\(809\) | − | 769946.i | − | 1.17642i | −0.808707 | − | 0.588211i | \(-0.799832\pi\) | ||
0.808707 | − | 0.588211i | \(-0.200168\pi\) | |||||||
\(810\) | −376582. | − | 1.92616e6i | −0.573970 | − | 2.93577i | ||||
\(811\) | −964850. | −1.46696 | −0.733480 | − | 0.679711i | \(-0.762105\pi\) | ||||
−0.733480 | + | 0.679711i | \(0.762105\pi\) | |||||||
\(812\) | 1.55684e6i | 2.36120i | ||||||||
\(813\) | 486177. | + | 174406.i | 0.735552 | + | 0.263864i | ||||
\(814\) | 520993. | 0.786291 | ||||||||
\(815\) | 687269.i | 1.03469i | ||||||||
\(816\) | 274439. | − | 765030.i | 0.412160 | − | 1.14894i | ||||
\(817\) | 763588. | 1.14397 | ||||||||
\(818\) | − | 1.27026e6i | − | 1.89840i | ||||||
\(819\) | −555438. | − | 457361.i | −0.828072 | − | 0.681854i | ||||
\(820\) | 185904. | 0.276478 | ||||||||
\(821\) | − | 101347.i | − | 0.150358i | −0.997170 | − | 0.0751788i | \(-0.976047\pi\) | ||
0.997170 | − | 0.0751788i | \(-0.0239528\pi\) | |||||||
\(822\) | −293049. | − | 105126.i | −0.433708 | − | 0.155584i | ||||
\(823\) | 15672.4 | 0.0231385 | 0.0115693 | − | 0.999933i | \(-0.496317\pi\) | ||||
0.0115693 | + | 0.999933i | \(0.496317\pi\) | |||||||
\(824\) | − | 1.88452e6i | − | 2.77554i | ||||||
\(825\) | 316596. | − | 882547.i | 0.465155 | − | 1.29667i | ||||
\(826\) | −130674. | −0.191527 | ||||||||
\(827\) | − | 133176.i | − | 0.194722i | −0.995249 | − | 0.0973610i | \(-0.968960\pi\) | ||
0.995249 | − | 0.0973610i | \(-0.0310401\pi\) | |||||||
\(828\) | 381591. | − | 463420.i | 0.556593 | − | 0.675949i | ||||
\(829\) | 408389. | 0.594245 | 0.297122 | − | 0.954839i | \(-0.403973\pi\) | ||||
0.297122 | + | 0.954839i | \(0.403973\pi\) | |||||||
\(830\) | − | 3.26905e6i | − | 4.74532i | ||||||
\(831\) | 80505.0 | + | 28879.5i | 0.116579 | + | 0.0418204i | ||||
\(832\) | 818710. | 1.18272 | ||||||||
\(833\) | 130953.i | 0.188723i | ||||||||
\(834\) | −250344. | + | 697864.i | −0.359920 | + | 1.00332i | ||||
\(835\) | −1.56473e6 | −2.24422 | ||||||||
\(836\) | − | 1.79111e6i | − | 2.56276i | ||||||
\(837\) | 545805. | + | 915716.i | 0.779089 | + | 1.30710i | ||||
\(838\) | 142663. | 0.203153 | ||||||||
\(839\) | 1.07239e6i | 1.52345i | 0.647902 | + | 0.761723i | \(0.275646\pi\) | ||||
−0.647902 | + | 0.761723i | \(0.724354\pi\) | |||||||
\(840\) | 2.21463e6 | + | 794453.i | 3.13864 | + | 1.12593i | ||||
\(841\) | −370283. | −0.523531 | ||||||||
\(842\) | − | 254404.i | − | 0.358839i | ||||||
\(843\) | −373850. | + | 1.04215e6i | −0.526068 | + | 1.46648i | ||||
\(844\) | −2.25020e6 | −3.15890 | ||||||||
\(845\) | 933778.i | 1.30777i | ||||||||
\(846\) | 943816. | + | 777160.i | 1.31870 | + | 1.08585i | ||||
\(847\) | 165933. | 0.231295 | ||||||||
\(848\) | − | 132.141i | − | 0.000183758i | ||||||
\(849\) | 651906. | + | 233858.i | 0.904419 | + | 0.324442i | ||||
\(850\) | −1.13224e6 | −1.56712 | ||||||||
\(851\) | − | 133960.i | − | 0.184977i | ||||||
\(852\) | 1.04259e6 | − | 2.90635e6i | 1.43627 | − | 4.00377i | ||||
\(853\) | −1.05056e6 | −1.44385 | −0.721926 | − | 0.691970i | \(-0.756743\pi\) | ||||
−0.721926 | + | 0.691970i | \(0.756743\pi\) | |||||||
\(854\) | 2.12424e6i | 2.91264i | ||||||||
\(855\) | −957091. | + | 1.16233e6i | −1.30924 | + | 1.59000i | ||||
\(856\) | 836794. | 1.14201 | ||||||||
\(857\) | 339342.i | 0.462036i | 0.972950 | + | 0.231018i | \(0.0742056\pi\) | ||||
−0.972950 | + | 0.231018i | \(0.925794\pi\) | |||||||
\(858\) | 1.44620e6 | + | 518794.i | 1.96450 | + | 0.704726i | ||||
\(859\) | 1.01922e6 | 1.38128 | 0.690639 | − | 0.723200i | \(-0.257329\pi\) | ||||
0.690639 | + | 0.723200i | \(0.257329\pi\) | |||||||
\(860\) | − | 2.59354e6i | − | 3.50668i | ||||||
\(861\) | −14202.8 | + | 39591.8i | −0.0191587 | + | 0.0534071i | ||||
\(862\) | 203551. | 0.273941 | ||||||||
\(863\) | − | 100127.i | − | 0.134440i | −0.997738 | − | 0.0672201i | \(-0.978587\pi\) | ||
0.997738 | − | 0.0672201i | \(-0.0214130\pi\) | |||||||
\(864\) | −1.12265e6 | + | 669149.i | −1.50390 | + | 0.896386i | ||||
\(865\) | −417090. | −0.557439 | ||||||||
\(866\) | 1.80837e6i | 2.41130i | ||||||||
\(867\) | 516065. | + | 185128.i | 0.686541 | + | 0.246283i | ||||
\(868\) | −2.19315e6 | −2.91092 | ||||||||
\(869\) | − | 186182.i | − | 0.246546i | ||||||
\(870\) | −943654. | + | 2.63054e6i | −1.24674 | + | 3.47542i | ||||
\(871\) | 633129. | 0.834556 | ||||||||
\(872\) | 3.06402e6i | 4.02957i | ||||||||
\(873\) | −672025. | − | 553362.i | −0.881774 | − | 0.726073i | ||||
\(874\) | −652715. | −0.854478 | ||||||||
\(875\) | − | 629531.i | − | 0.822244i | ||||||
\(876\) | 2.69672e6 | + | 967396.i | 3.51422 | + | 1.26065i | ||||
\(877\) | −384649. | −0.500109 | −0.250055 | − | 0.968232i | \(-0.580449\pi\) | ||||
−0.250055 | + | 0.968232i | \(0.580449\pi\) | |||||||
\(878\) | 510212.i | 0.661854i | ||||||||
\(879\) | 44483.2 | − | 124002.i | 0.0575729 | − | 0.160491i | ||||
\(880\) | −2.48561e6 | −3.20972 | ||||||||
\(881\) | 649770.i | 0.837158i | 0.908180 | + | 0.418579i | \(0.137472\pi\) | ||||
−0.908180 | + | 0.418579i | \(0.862528\pi\) | |||||||
\(882\) | 330610. | − | 401506.i | 0.424990 | − | 0.516125i | ||||
\(883\) | −509794. | −0.653843 | −0.326922 | − | 0.945051i | \(-0.606011\pi\) | ||||
−0.326922 | + | 0.945051i | \(0.606011\pi\) | |||||||
\(884\) | − | 1.30909e6i | − | 1.67520i | ||||||
\(885\) | −155787. | − | 55885.4i | −0.198904 | − | 0.0713530i | ||||
\(886\) | 562901. | 0.717076 | ||||||||
\(887\) | − | 345280.i | − | 0.438858i | −0.975628 | − | 0.219429i | \(-0.929581\pi\) | ||
0.975628 | − | 0.219429i | \(-0.0704194\pi\) | |||||||
\(888\) | −346897. | + | 967015.i | −0.439921 | + | 1.22633i | ||||
\(889\) | −1.17331e6 | −1.48460 | ||||||||
\(890\) | 2.27473e6i | 2.87178i | ||||||||
\(891\) | −656622. | + | 128376.i | −0.827104 | + | 0.161706i | ||||
\(892\) | −2.29848e6 | −2.88876 | ||||||||
\(893\) | − | 937946.i | − | 1.17618i | ||||||
\(894\) | −828361. | − | 297158.i | −1.03644 | − | 0.371802i | ||||
\(895\) | 1.06767e6 | 1.33288 | ||||||||
\(896\) | 82477.0i | 0.102735i | ||||||||
\(897\) | 133395. | − | 371853.i | 0.165788 | − | 0.462154i | ||||
\(898\) | 2.41132e6 | 2.99022 | ||||||||
\(899\) | − | 1.51798e6i | − | 1.87823i | ||||||
\(900\) | 2.44940e6 | + | 2.01689e6i | 3.02395 | + | 2.48999i | ||||
\(901\) | −33.0729 | −4.07401e−5 | ||||||||
\(902\) | − | 89819.5i | − | 0.110397i | ||||||
\(903\) | 552343. | + | 198142.i | 0.677382 | + | 0.242997i | ||||
\(904\) | −3.45300e6 | −4.22532 | ||||||||
\(905\) | 297163.i | 0.362826i | ||||||||
\(906\) | −556621. | + | 1.55165e6i | −0.678115 | + | 1.89032i | ||||
\(907\) | 1.14955e6 | 1.39738 | 0.698691 | − | 0.715424i | \(-0.253766\pi\) | ||||
0.698691 | + | 0.715424i | \(0.253766\pi\) | |||||||
\(908\) | 2.21232e6i | 2.68335i | ||||||||
\(909\) | −464260. | + | 563817.i | −0.561867 | + | 0.682354i | ||||
\(910\) | 2.65716e6 | 3.20875 | ||||||||
\(911\) | − | 263358.i | − | 0.317329i | −0.987333 | − | 0.158665i | \(-0.949281\pi\) | ||
0.987333 | − | 0.158665i | \(-0.0507188\pi\) | |||||||
\(912\) | 2.33102e6 | + | 836208.i | 2.80257 | + | 1.00537i | ||||
\(913\) | −1.11441e6 | −1.33691 | ||||||||
\(914\) | − | 2.24172e6i | − | 2.68343i | ||||||
\(915\) | −908474. | + | 2.53247e6i | −1.08510 | + | 3.02484i | ||||
\(916\) | 1.46134e6 | 1.74165 | ||||||||
\(917\) | − | 394993.i | − | 0.469732i | ||||||
\(918\) | 413658. | + | 694008.i | 0.490858 | + | 0.823529i | ||||
\(919\) | 1.68157e6 | 1.99106 | 0.995529 | − | 0.0944589i | \(-0.0301121\pi\) | ||||
0.995529 | + | 0.0944589i | \(0.0301121\pi\) | |||||||
\(920\) | 1.29185e6i | 1.52628i | ||||||||
\(921\) | 499949. | + | 179347.i | 0.589395 | + | 0.211434i | ||||
\(922\) | −964747. | −1.13488 | ||||||||
\(923\) | − | 2.03198e6i | − | 2.38515i | ||||||
\(924\) | 464770. | − | 1.29560e6i | 0.544370 | − | 1.51749i | ||||
\(925\) | 708046. | 0.827519 | ||||||||
\(926\) | − | 2.66915e6i | − | 3.11280i | ||||||
\(927\) | 715451. | + | 589120.i | 0.832570 | + | 0.685558i | ||||
\(928\) | 1.86102e6 | 2.16101 | ||||||||
\(929\) | − | 119186.i | − | 0.138100i | −0.997613 | − | 0.0690500i | \(-0.978003\pi\) | ||
0.997613 | − | 0.0690500i | \(-0.0219968\pi\) | |||||||
\(930\) | −3.70569e6 | − | 1.32934e6i | −4.28453 | − | 1.53699i | ||||
\(931\) | −399009. | −0.460345 | ||||||||
\(932\) | 3.90641e6i | 4.49724i | ||||||||
\(933\) | 321856. | − | 897210.i | 0.369742 | − | 1.03070i | ||||
\(934\) | 6893.34 | 0.00790198 | ||||||||
\(935\) | 622110.i | 0.711613i | ||||||||
\(936\) | −1.92586e6 | + | 2.33885e6i | −2.19823 | + | 2.66963i | ||||
\(937\) | −1.53037e6 | −1.74308 | −0.871538 | − | 0.490328i | \(-0.836877\pi\) | ||||
−0.871538 | + | 0.490328i | \(0.836877\pi\) | |||||||
\(938\) | − | 803885.i | − | 0.913668i | ||||||
\(939\) | −1.27505e6 | − | 457398.i | −1.44609 | − | 0.518756i | ||||
\(940\) | −3.18575e6 | −3.60542 | ||||||||
\(941\) | 340341.i | 0.384357i | 0.981360 | + | 0.192179i | \(0.0615553\pi\) | ||||
−0.981360 | + | 0.192179i | \(0.938445\pi\) | |||||||
\(942\) | −360773. | + | 1.00570e6i | −0.406567 | + | 1.13335i | ||||
\(943\) | −23094.8 | −0.0259712 | ||||||||
\(944\) | 272221.i | 0.305477i | ||||||||
\(945\) | −993924. | + | 592420.i | −1.11299 | + | 0.663386i | ||||
\(946\) | −1.25307e6 | −1.40021 | ||||||||
\(947\) | 383908.i | 0.428082i | 0.976825 | + | 0.214041i | \(0.0686626\pi\) | ||||
−0.976825 | + | 0.214041i | \(0.931337\pi\) | |||||||
\(948\) | 593041. | + | 212742.i | 0.659885 | + | 0.236720i | ||||
\(949\) | 1.88542e6 | 2.09351 | ||||||||
\(950\) | − | 3.44992e6i | − | 3.82262i | ||||||
\(951\) | 427015. | − | 1.19035e6i | 0.472152 | − | 1.31618i | ||||
\(952\) | −968559. | −1.06869 | ||||||||
\(953\) | 126216.i | 0.138972i | 0.997583 | + | 0.0694862i | \(0.0221360\pi\) | ||||
−0.997583 | + | 0.0694862i | \(0.977864\pi\) | |||||||
\(954\) | 101.403 | + | 83.4975i | 0.000111417 | + | 9.17438e-5i | ||||
\(955\) | 898391. | 0.985051 | ||||||||
\(956\) | − | 1.20842e6i | − | 1.32221i | ||||||
\(957\) | 896744. | + | 321689.i | 0.979140 | + | 0.351247i | ||||
\(958\) | 28984.4 | 0.0315815 | ||||||||
\(959\) | 183550.i | 0.199580i | ||||||||
\(960\) | 444571. | − | 1.23929e6i | 0.482390 | − | 1.34472i | ||||
\(961\) | 1.21489e6 | 1.31550 | ||||||||
\(962\) | 1.16025e6i | 1.25372i | ||||||||
\(963\) | −261589. | + | 317685.i | −0.282077 | + | 0.342566i | ||||
\(964\) | 115869. | 0.124685 | ||||||||
\(965\) | 812147.i | 0.872127i | ||||||||
\(966\) | −472143. | − | 169372.i | −0.505963 | − | 0.181504i | ||||
\(967\) | 923991. | 0.988131 | 0.494066 | − | 0.869425i | \(-0.335510\pi\) | ||||
0.494066 | + | 0.869425i | \(0.335510\pi\) | |||||||
\(968\) | − | 698715.i | − | 0.745675i | ||||||
\(969\) | 209290. | − | 583420.i | 0.222895 | − | 0.621346i | ||||
\(970\) | 3.21490e6 | 3.41684 | ||||||||
\(971\) | 336724.i | 0.357137i | 0.983927 | + | 0.178569i | \(0.0571466\pi\) | ||||
−0.983927 | + | 0.178569i | \(0.942853\pi\) | |||||||
\(972\) | 341381. | − | 2.23822e6i | 0.361332 | − | 2.36902i | ||||
\(973\) | 437104. | 0.461699 | ||||||||
\(974\) | − | 551275.i | − | 0.581100i | ||||||
\(975\) | 1.96542e6 | + | 705056.i | 2.06751 | + | 0.741677i | ||||
\(976\) | 4.42523e6 | 4.64554 | ||||||||
\(977\) | 916422.i | 0.960077i | 0.877247 | + | 0.480039i | \(0.159377\pi\) | ||||
−0.877247 | + | 0.480039i | \(0.840623\pi\) | |||||||
\(978\) | −379423. | + | 1.05768e6i | −0.396685 | + | 1.10580i | ||||
\(979\) | 775450. | 0.809074 | ||||||||
\(980\) | 1.35524e6i | 1.41112i | ||||||||
\(981\) | −1.16324e6 | − | 957842.i | −1.20874 | − | 0.995305i | ||||
\(982\) | 2.02185e6 | 2.09665 | ||||||||
\(983\) | 1.44522e6i | 1.49564i | 0.663904 | + | 0.747818i | \(0.268898\pi\) | ||||
−0.663904 | + | 0.747818i | \(0.731102\pi\) | |||||||
\(984\) | 166714. | + | 59805.2i | 0.172179 | + | 0.0617659i | ||||
\(985\) | −219059. | −0.225782 | ||||||||
\(986\) | − | 1.15046e6i | − | 1.18336i | ||||||
\(987\) | 243386. | − | 678465.i | 0.249839 | − | 0.696455i | ||||
\(988\) | 3.98877e6 | 4.08626 | ||||||||
\(989\) | 322195.i | 0.329402i | ||||||||
\(990\) | 1.57061e6 | − | 1.90741e6i | 1.60250 | − | 1.94614i | ||||
\(991\) | 570072. | 0.580474 | 0.290237 | − | 0.956955i | \(-0.406266\pi\) | ||||
0.290237 | + | 0.956955i | \(0.406266\pi\) | |||||||
\(992\) | 2.62166e6i | 2.66411i | ||||||||
\(993\) | 336994. | + | 120890.i | 0.341762 | + | 0.122600i | ||||
\(994\) | −2.58000e6 | −2.61125 | ||||||||
\(995\) | 1.29459e6i | 1.30764i | ||||||||
\(996\) | 1.27339e6 | − | 3.54971e6i | 1.28363 | − | 3.57827i | ||||
\(997\) | 115417. | 0.116112 | 0.0580562 | − | 0.998313i | \(-0.481510\pi\) | ||||
0.0580562 | + | 0.998313i | \(0.481510\pi\) | |||||||
\(998\) | − | 111341.i | − | 0.111788i | ||||||
\(999\) | −258680. | − | 433996.i | −0.259198 | − | 0.434865i |
(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 | 177.5.b.a.119.74 | yes | 78 | |
3.2 | odd | 2 | inner | 177.5.b.a.119.5 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.b.a.119.5 | ✓ | 78 | 3.2 | odd | 2 | inner | |
177.5.b.a.119.74 | yes | 78 | 1.1 | even | 1 | trivial |