Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.a (trivial) |
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: | yes |
Analytic conductor: | \(170.562223914\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 122890x^{3} - 6160660x^{2} + 3465881625x + 278845474950 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-201.135\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −505.603 | −1.80890 | −0.904450 | − | 0.426581i | \(-0.859718\pi\) | ||||
−0.904450 | + | 0.426581i | \(0.859718\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −4044.82 | −1.27908 | ||||||||
\(11\) | −974.645 | −0.220786 | −0.110393 | − | 0.993888i | \(-0.535211\pi\) | ||||
−0.110393 | + | 0.993888i | \(0.535211\pi\) | |||||||
\(12\) | −1728.00 | −0.288675 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | −2744.00 | −0.267261 | ||||||||
\(15\) | 13651.3 | 1.04437 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −5660.27 | −0.279425 | −0.139713 | − | 0.990192i | \(-0.544618\pi\) | ||||
−0.139713 | + | 0.990192i | \(0.544618\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | 15165.4 | 0.507244 | 0.253622 | − | 0.967303i | \(-0.418378\pi\) | ||||
0.253622 | + | 0.967303i | \(0.418378\pi\) | |||||||
\(20\) | −32358.6 | −0.904450 | ||||||||
\(21\) | 9261.00 | 0.218218 | ||||||||
\(22\) | −7797.16 | −0.156119 | ||||||||
\(23\) | 65731.1 | 1.12648 | 0.563240 | − | 0.826293i | \(-0.309555\pi\) | ||||
0.563240 | + | 0.826293i | \(0.309555\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | 177509. | 2.27212 | ||||||||
\(26\) | −17576.0 | −0.196116 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −21952.0 | −0.188982 | ||||||||
\(29\) | 44041.7 | 0.335329 | 0.167665 | − | 0.985844i | \(-0.446377\pi\) | ||||
0.167665 | + | 0.985844i | \(0.446377\pi\) | |||||||
\(30\) | 109210. | 0.738480 | ||||||||
\(31\) | 86262.8 | 0.520065 | 0.260032 | − | 0.965600i | \(-0.416267\pi\) | ||||
0.260032 | + | 0.965600i | \(0.416267\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | 26315.4 | 0.127471 | ||||||||
\(34\) | −45282.2 | −0.197584 | ||||||||
\(35\) | 173422. | 0.683700 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −428960. | −1.39223 | −0.696115 | − | 0.717931i | \(-0.745089\pi\) | ||||
−0.696115 | + | 0.717931i | \(0.745089\pi\) | |||||||
\(38\) | 121323. | 0.358676 | ||||||||
\(39\) | 59319.0 | 0.160128 | ||||||||
\(40\) | −258869. | −0.639542 | ||||||||
\(41\) | 506507. | 1.14773 | 0.573867 | − | 0.818948i | \(-0.305442\pi\) | ||||
0.573867 | + | 0.818948i | \(0.305442\pi\) | |||||||
\(42\) | 74088.0 | 0.154303 | ||||||||
\(43\) | 79953.1 | 0.153354 | 0.0766771 | − | 0.997056i | \(-0.475569\pi\) | ||||
0.0766771 | + | 0.997056i | \(0.475569\pi\) | |||||||
\(44\) | −62377.3 | −0.110393 | ||||||||
\(45\) | −368584. | −0.602966 | ||||||||
\(46\) | 525849. | 0.796541 | ||||||||
\(47\) | 91123.6 | 0.128023 | 0.0640116 | − | 0.997949i | \(-0.479611\pi\) | ||||
0.0640116 | + | 0.997949i | \(0.479611\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 1.42007e6 | 1.60663 | ||||||||
\(51\) | 152827. | 0.161326 | ||||||||
\(52\) | −140608. | −0.138675 | ||||||||
\(53\) | 858983. | 0.792536 | 0.396268 | − | 0.918135i | \(-0.370305\pi\) | ||||
0.396268 | + | 0.918135i | \(0.370305\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | 492783. | 0.399380 | ||||||||
\(56\) | −175616. | −0.133631 | ||||||||
\(57\) | −409467. | −0.292858 | ||||||||
\(58\) | 352334. | 0.237113 | ||||||||
\(59\) | −2.45810e6 | −1.55818 | −0.779089 | − | 0.626914i | \(-0.784318\pi\) | ||||
−0.779089 | + | 0.626914i | \(0.784318\pi\) | |||||||
\(60\) | 873681. | 0.522184 | ||||||||
\(61\) | −46791.0 | −0.0263942 | −0.0131971 | − | 0.999913i | \(-0.504201\pi\) | ||||
−0.0131971 | + | 0.999913i | \(0.504201\pi\) | |||||||
\(62\) | 690102. | 0.367741 | ||||||||
\(63\) | −250047. | −0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 1.11081e6 | 0.501698 | ||||||||
\(66\) | 210523. | 0.0901356 | ||||||||
\(67\) | 771304. | 0.313302 | 0.156651 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156651 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(68\) | −362257. | −0.139713 | ||||||||
\(69\) | −1.77474e6 | −0.650373 | ||||||||
\(70\) | 1.38737e6 | 0.483449 | ||||||||
\(71\) | 381154. | 0.126385 | 0.0631926 | − | 0.998001i | \(-0.479872\pi\) | ||||
0.0631926 | + | 0.998001i | \(0.479872\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | 1.51728e6 | 0.456494 | 0.228247 | − | 0.973603i | \(-0.426701\pi\) | ||||
0.228247 | + | 0.973603i | \(0.426701\pi\) | |||||||
\(74\) | −3.43168e6 | −0.984455 | ||||||||
\(75\) | −4.79274e6 | −1.31181 | ||||||||
\(76\) | 970588. | 0.253622 | ||||||||
\(77\) | 334303. | 0.0834494 | ||||||||
\(78\) | 474552. | 0.113228 | ||||||||
\(79\) | 2.77962e6 | 0.634293 | 0.317147 | − | 0.948377i | \(-0.397275\pi\) | ||||
0.317147 | + | 0.948377i | \(0.397275\pi\) | |||||||
\(80\) | −2.07095e6 | −0.452225 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 4.05205e6 | 0.811571 | ||||||||
\(83\) | 1.80809e6 | 0.347094 | 0.173547 | − | 0.984826i | \(-0.444477\pi\) | ||||
0.173547 | + | 0.984826i | \(0.444477\pi\) | |||||||
\(84\) | 592704. | 0.109109 | ||||||||
\(85\) | 2.86185e6 | 0.505452 | ||||||||
\(86\) | 639625. | 0.108438 | ||||||||
\(87\) | −1.18913e6 | −0.193602 | ||||||||
\(88\) | −499018. | −0.0780597 | ||||||||
\(89\) | 4.66189e6 | 0.700965 | 0.350483 | − | 0.936569i | \(-0.386018\pi\) | ||||
0.350483 | + | 0.936569i | \(0.386018\pi\) | |||||||
\(90\) | −2.94867e6 | −0.426362 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | 4.20679e6 | 0.563240 | ||||||||
\(93\) | −2.32909e6 | −0.300260 | ||||||||
\(94\) | 728989. | 0.0905260 | ||||||||
\(95\) | −7.66768e6 | −0.917554 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | −7.20167e6 | −0.801184 | −0.400592 | − | 0.916256i | \(-0.631196\pi\) | ||||
−0.400592 | + | 0.916256i | \(0.631196\pi\) | |||||||
\(98\) | 941192. | 0.101015 | ||||||||
\(99\) | −710516. | −0.0735954 | ||||||||
\(100\) | 1.13606e7 | 1.13606 | ||||||||
\(101\) | −1.80857e7 | −1.74667 | −0.873336 | − | 0.487118i | \(-0.838048\pi\) | ||||
−0.873336 | + | 0.487118i | \(0.838048\pi\) | |||||||
\(102\) | 1.22262e6 | 0.114075 | ||||||||
\(103\) | −1.84546e7 | −1.66408 | −0.832038 | − | 0.554718i | \(-0.812826\pi\) | ||||
−0.832038 | + | 0.554718i | \(0.812826\pi\) | |||||||
\(104\) | −1.12486e6 | −0.0980581 | ||||||||
\(105\) | −4.68239e6 | −0.394734 | ||||||||
\(106\) | 6.87186e6 | 0.560408 | ||||||||
\(107\) | 1.63646e7 | 1.29141 | 0.645703 | − | 0.763589i | \(-0.276564\pi\) | ||||
0.645703 | + | 0.763589i | \(0.276564\pi\) | |||||||
\(108\) | −1.25971e6 | −0.0962250 | ||||||||
\(109\) | 1.27087e7 | 0.939960 | 0.469980 | − | 0.882677i | \(-0.344261\pi\) | ||||
0.469980 | + | 0.882677i | \(0.344261\pi\) | |||||||
\(110\) | 3.94227e6 | 0.282404 | ||||||||
\(111\) | 1.15819e7 | 0.803804 | ||||||||
\(112\) | −1.40493e6 | −0.0944911 | ||||||||
\(113\) | −1.18485e7 | −0.772483 | −0.386241 | − | 0.922398i | \(-0.626227\pi\) | ||||
−0.386241 | + | 0.922398i | \(0.626227\pi\) | |||||||
\(114\) | −3.27573e6 | −0.207082 | ||||||||
\(115\) | −3.32338e7 | −2.03769 | ||||||||
\(116\) | 2.81867e6 | 0.167665 | ||||||||
\(117\) | −1.60161e6 | −0.0924500 | ||||||||
\(118\) | −1.96648e7 | −1.10180 | ||||||||
\(119\) | 1.94147e6 | 0.105613 | ||||||||
\(120\) | 6.98945e6 | 0.369240 | ||||||||
\(121\) | −1.85372e7 | −0.951253 | ||||||||
\(122\) | −374328. | −0.0186635 | ||||||||
\(123\) | −1.36757e7 | −0.662645 | ||||||||
\(124\) | 5.52082e6 | 0.260032 | ||||||||
\(125\) | −5.02489e7 | −2.30113 | ||||||||
\(126\) | −2.00038e6 | −0.0890871 | ||||||||
\(127\) | −3.61236e7 | −1.56487 | −0.782435 | − | 0.622732i | \(-0.786023\pi\) | ||||
−0.782435 | + | 0.622732i | \(0.786023\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −2.15873e6 | −0.0885391 | ||||||||
\(130\) | 8.88647e6 | 0.354754 | ||||||||
\(131\) | −1.86594e7 | −0.725185 | −0.362593 | − | 0.931948i | \(-0.618108\pi\) | ||||
−0.362593 | + | 0.931948i | \(0.618108\pi\) | |||||||
\(132\) | 1.68419e6 | 0.0637355 | ||||||||
\(133\) | −5.20174e6 | −0.191720 | ||||||||
\(134\) | 6.17043e6 | 0.221538 | ||||||||
\(135\) | 9.95178e6 | 0.348123 | ||||||||
\(136\) | −2.89806e6 | −0.0987918 | ||||||||
\(137\) | 1.13780e7 | 0.378047 | 0.189023 | − | 0.981973i | \(-0.439468\pi\) | ||||
0.189023 | + | 0.981973i | \(0.439468\pi\) | |||||||
\(138\) | −1.41979e7 | −0.459883 | ||||||||
\(139\) | −4.35614e7 | −1.37578 | −0.687892 | − | 0.725813i | \(-0.741464\pi\) | ||||
−0.687892 | + | 0.725813i | \(0.741464\pi\) | |||||||
\(140\) | 1.10990e7 | 0.341850 | ||||||||
\(141\) | −2.46034e6 | −0.0739142 | ||||||||
\(142\) | 3.04923e6 | 0.0893679 | ||||||||
\(143\) | 2.14130e6 | 0.0612351 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | −2.22676e7 | −0.606576 | ||||||||
\(146\) | 1.21382e7 | 0.322790 | ||||||||
\(147\) | −3.17652e6 | −0.0824786 | ||||||||
\(148\) | −2.74534e7 | −0.696115 | ||||||||
\(149\) | 2.60076e7 | 0.644093 | 0.322046 | − | 0.946724i | \(-0.395629\pi\) | ||||
0.322046 | + | 0.946724i | \(0.395629\pi\) | |||||||
\(150\) | −3.83420e7 | −0.927588 | ||||||||
\(151\) | 5.57190e7 | 1.31699 | 0.658497 | − | 0.752583i | \(-0.271192\pi\) | ||||
0.658497 | + | 0.752583i | \(0.271192\pi\) | |||||||
\(152\) | 7.76470e6 | 0.179338 | ||||||||
\(153\) | −4.12634e6 | −0.0931418 | ||||||||
\(154\) | 2.67443e6 | 0.0590076 | ||||||||
\(155\) | −4.36147e7 | −0.940745 | ||||||||
\(156\) | 3.79642e6 | 0.0800641 | ||||||||
\(157\) | 5.82125e7 | 1.20051 | 0.600257 | − | 0.799807i | \(-0.295065\pi\) | ||||
0.600257 | + | 0.799807i | \(0.295065\pi\) | |||||||
\(158\) | 2.22369e7 | 0.448513 | ||||||||
\(159\) | −2.31925e7 | −0.457571 | ||||||||
\(160\) | −1.65676e7 | −0.319771 | ||||||||
\(161\) | −2.25458e7 | −0.425769 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | −5.85066e7 | −1.05815 | −0.529076 | − | 0.848574i | \(-0.677461\pi\) | ||||
−0.529076 | + | 0.848574i | \(0.677461\pi\) | |||||||
\(164\) | 3.24164e7 | 0.573867 | ||||||||
\(165\) | −1.33051e7 | −0.230582 | ||||||||
\(166\) | 1.44647e7 | 0.245432 | ||||||||
\(167\) | 1.10743e8 | 1.83996 | 0.919979 | − | 0.391969i | \(-0.128206\pi\) | ||||
0.919979 | + | 0.391969i | \(0.128206\pi\) | |||||||
\(168\) | 4.74163e6 | 0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 2.28948e7 | 0.357409 | ||||||||
\(171\) | 1.10556e7 | 0.169081 | ||||||||
\(172\) | 5.11700e6 | 0.0766771 | ||||||||
\(173\) | −1.34755e7 | −0.197871 | −0.0989357 | − | 0.995094i | \(-0.531544\pi\) | ||||
−0.0989357 | + | 0.995094i | \(0.531544\pi\) | |||||||
\(174\) | −9.51301e6 | −0.136898 | ||||||||
\(175\) | −6.08856e7 | −0.858779 | ||||||||
\(176\) | −3.99215e6 | −0.0551966 | ||||||||
\(177\) | 6.63686e7 | 0.899614 | ||||||||
\(178\) | 3.72951e7 | 0.495657 | ||||||||
\(179\) | −4.01736e7 | −0.523547 | −0.261773 | − | 0.965129i | \(-0.584307\pi\) | ||||
−0.261773 | + | 0.965129i | \(0.584307\pi\) | |||||||
\(180\) | −2.35894e7 | −0.301483 | ||||||||
\(181\) | −9.67467e7 | −1.21272 | −0.606361 | − | 0.795189i | \(-0.707371\pi\) | ||||
−0.606361 | + | 0.795189i | \(0.707371\pi\) | |||||||
\(182\) | 6.02857e6 | 0.0741249 | ||||||||
\(183\) | 1.26336e6 | 0.0152387 | ||||||||
\(184\) | 3.36543e7 | 0.398271 | ||||||||
\(185\) | 2.16883e8 | 2.51840 | ||||||||
\(186\) | −1.86328e7 | −0.212316 | ||||||||
\(187\) | 5.51676e6 | 0.0616933 | ||||||||
\(188\) | 5.83191e6 | 0.0640116 | ||||||||
\(189\) | 6.75127e6 | 0.0727393 | ||||||||
\(190\) | −6.13415e7 | −0.648809 | ||||||||
\(191\) | −6.13516e7 | −0.637102 | −0.318551 | − | 0.947906i | \(-0.603196\pi\) | ||||
−0.318551 | + | 0.947906i | \(0.603196\pi\) | |||||||
\(192\) | −7.07789e6 | −0.0721688 | ||||||||
\(193\) | −6.42073e7 | −0.642886 | −0.321443 | − | 0.946929i | \(-0.604168\pi\) | ||||
−0.321443 | + | 0.946929i | \(0.604168\pi\) | |||||||
\(194\) | −5.76134e7 | −0.566523 | ||||||||
\(195\) | −2.99918e7 | −0.289656 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | 6.15065e7 | 0.573178 | 0.286589 | − | 0.958054i | \(-0.407479\pi\) | ||||
0.286589 | + | 0.958054i | \(0.407479\pi\) | |||||||
\(198\) | −5.68413e6 | −0.0520398 | ||||||||
\(199\) | −7.73282e7 | −0.695588 | −0.347794 | − | 0.937571i | \(-0.613069\pi\) | ||||
−0.347794 | + | 0.937571i | \(0.613069\pi\) | |||||||
\(200\) | 9.08846e7 | 0.803314 | ||||||||
\(201\) | −2.08252e7 | −0.180885 | ||||||||
\(202\) | −1.44686e8 | −1.23508 | ||||||||
\(203\) | −1.51063e7 | −0.126742 | ||||||||
\(204\) | 9.78095e6 | 0.0806632 | ||||||||
\(205\) | −2.56091e8 | −2.07614 | ||||||||
\(206\) | −1.47636e8 | −1.17668 | ||||||||
\(207\) | 4.79180e7 | 0.375493 | ||||||||
\(208\) | −8.99891e6 | −0.0693375 | ||||||||
\(209\) | −1.47809e7 | −0.111993 | ||||||||
\(210\) | −3.74591e7 | −0.279119 | ||||||||
\(211\) | −1.05409e8 | −0.772480 | −0.386240 | − | 0.922398i | \(-0.626226\pi\) | ||||
−0.386240 | + | 0.922398i | \(0.626226\pi\) | |||||||
\(212\) | 5.49749e7 | 0.396268 | ||||||||
\(213\) | −1.02912e7 | −0.0729686 | ||||||||
\(214\) | 1.30917e8 | 0.913162 | ||||||||
\(215\) | −4.04245e7 | −0.277402 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | −2.95881e7 | −0.196566 | ||||||||
\(218\) | 1.01670e8 | 0.664652 | ||||||||
\(219\) | −4.09665e7 | −0.263557 | ||||||||
\(220\) | 3.15381e7 | 0.199690 | ||||||||
\(221\) | 1.24356e7 | 0.0774987 | ||||||||
\(222\) | 9.26553e7 | 0.568375 | ||||||||
\(223\) | −3.47141e7 | −0.209623 | −0.104811 | − | 0.994492i | \(-0.533424\pi\) | ||||
−0.104811 | + | 0.994492i | \(0.533424\pi\) | |||||||
\(224\) | −1.12394e7 | −0.0668153 | ||||||||
\(225\) | 1.29404e8 | 0.757372 | ||||||||
\(226\) | −9.47880e7 | −0.546228 | ||||||||
\(227\) | −9.94839e7 | −0.564498 | −0.282249 | − | 0.959341i | \(-0.591080\pi\) | ||||
−0.282249 | + | 0.959341i | \(0.591080\pi\) | |||||||
\(228\) | −2.62059e7 | −0.146429 | ||||||||
\(229\) | 1.36235e7 | 0.0749660 | 0.0374830 | − | 0.999297i | \(-0.488066\pi\) | ||||
0.0374830 | + | 0.999297i | \(0.488066\pi\) | |||||||
\(230\) | −2.65871e8 | −1.44086 | ||||||||
\(231\) | −9.02619e6 | −0.0481795 | ||||||||
\(232\) | 2.25494e7 | 0.118557 | ||||||||
\(233\) | 3.58147e8 | 1.85488 | 0.927440 | − | 0.373971i | \(-0.122004\pi\) | ||||
0.927440 | + | 0.373971i | \(0.122004\pi\) | |||||||
\(234\) | −1.28129e7 | −0.0653720 | ||||||||
\(235\) | −4.60723e7 | −0.231581 | ||||||||
\(236\) | −1.57318e8 | −0.779089 | ||||||||
\(237\) | −7.50496e7 | −0.366209 | ||||||||
\(238\) | 1.55318e7 | 0.0746796 | ||||||||
\(239\) | 1.45807e8 | 0.690855 | 0.345428 | − | 0.938445i | \(-0.387734\pi\) | ||||
0.345428 | + | 0.938445i | \(0.387734\pi\) | |||||||
\(240\) | 5.59156e7 | 0.261092 | ||||||||
\(241\) | −1.59927e8 | −0.735974 | −0.367987 | − | 0.929831i | \(-0.619953\pi\) | ||||
−0.367987 | + | 0.929831i | \(0.619953\pi\) | |||||||
\(242\) | −1.48298e8 | −0.672638 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −2.99462e6 | −0.0131971 | ||||||||
\(245\) | −5.94836e7 | −0.258414 | ||||||||
\(246\) | −1.09405e8 | −0.468561 | ||||||||
\(247\) | −3.33185e7 | −0.140684 | ||||||||
\(248\) | 4.41665e7 | 0.183871 | ||||||||
\(249\) | −4.88185e7 | −0.200395 | ||||||||
\(250\) | −4.01991e8 | −1.62714 | ||||||||
\(251\) | −1.33440e7 | −0.0532632 | −0.0266316 | − | 0.999645i | \(-0.508478\pi\) | ||||
−0.0266316 | + | 0.999645i | \(0.508478\pi\) | |||||||
\(252\) | −1.60030e7 | −0.0629941 | ||||||||
\(253\) | −6.40645e7 | −0.248711 | ||||||||
\(254\) | −2.88989e8 | −1.10653 | ||||||||
\(255\) | −7.72699e7 | −0.291823 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −7.72175e7 | −0.283759 | −0.141880 | − | 0.989884i | \(-0.545315\pi\) | ||||
−0.141880 | + | 0.989884i | \(0.545315\pi\) | |||||||
\(258\) | −1.72699e7 | −0.0626066 | ||||||||
\(259\) | 1.47133e8 | 0.526213 | ||||||||
\(260\) | 7.10918e7 | 0.250849 | ||||||||
\(261\) | 3.21064e7 | 0.111776 | ||||||||
\(262\) | −1.49275e8 | −0.512783 | ||||||||
\(263\) | −1.37858e8 | −0.467292 | −0.233646 | − | 0.972322i | \(-0.575066\pi\) | ||||
−0.233646 | + | 0.972322i | \(0.575066\pi\) | |||||||
\(264\) | 1.34735e7 | 0.0450678 | ||||||||
\(265\) | −4.34304e8 | −1.43362 | ||||||||
\(266\) | −4.16140e7 | −0.135567 | ||||||||
\(267\) | −1.25871e8 | −0.404703 | ||||||||
\(268\) | 4.93634e7 | 0.156651 | ||||||||
\(269\) | −4.62689e8 | −1.44929 | −0.724646 | − | 0.689121i | \(-0.757997\pi\) | ||||
−0.724646 | + | 0.689121i | \(0.757997\pi\) | |||||||
\(270\) | 7.96142e7 | 0.246160 | ||||||||
\(271\) | 2.27980e8 | 0.695832 | 0.347916 | − | 0.937526i | \(-0.386889\pi\) | ||||
0.347916 | + | 0.937526i | \(0.386889\pi\) | |||||||
\(272\) | −2.31845e7 | −0.0698564 | ||||||||
\(273\) | −2.03464e7 | −0.0605228 | ||||||||
\(274\) | 9.10243e7 | 0.267319 | ||||||||
\(275\) | −1.73008e8 | −0.501652 | ||||||||
\(276\) | −1.13583e8 | −0.325187 | ||||||||
\(277\) | 3.50662e8 | 0.991309 | 0.495654 | − | 0.868520i | \(-0.334928\pi\) | ||||
0.495654 | + | 0.868520i | \(0.334928\pi\) | |||||||
\(278\) | −3.48491e8 | −0.972826 | ||||||||
\(279\) | 6.28856e7 | 0.173355 | ||||||||
\(280\) | 8.87919e7 | 0.241724 | ||||||||
\(281\) | −2.49198e8 | −0.669996 | −0.334998 | − | 0.942219i | \(-0.608736\pi\) | ||||
−0.334998 | + | 0.942219i | \(0.608736\pi\) | |||||||
\(282\) | −1.96827e7 | −0.0522652 | ||||||||
\(283\) | −2.17582e8 | −0.570651 | −0.285326 | − | 0.958431i | \(-0.592102\pi\) | ||||
−0.285326 | + | 0.958431i | \(0.592102\pi\) | |||||||
\(284\) | 2.43939e7 | 0.0631926 | ||||||||
\(285\) | 2.07027e8 | 0.529750 | ||||||||
\(286\) | 1.71304e7 | 0.0432998 | ||||||||
\(287\) | −1.73732e8 | −0.433803 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | −3.78300e8 | −0.921921 | ||||||||
\(290\) | −1.78141e8 | −0.428914 | ||||||||
\(291\) | 1.94445e8 | 0.462564 | ||||||||
\(292\) | 9.71058e7 | 0.228247 | ||||||||
\(293\) | −8.46928e6 | −0.0196703 | −0.00983513 | − | 0.999952i | \(-0.503131\pi\) | ||||
−0.00983513 | + | 0.999952i | \(0.503131\pi\) | |||||||
\(294\) | −2.54122e7 | −0.0583212 | ||||||||
\(295\) | 1.24282e9 | 2.81859 | ||||||||
\(296\) | −2.19627e8 | −0.492227 | ||||||||
\(297\) | 1.91839e7 | 0.0424903 | ||||||||
\(298\) | 2.08061e8 | 0.455442 | ||||||||
\(299\) | −1.44411e8 | −0.312429 | ||||||||
\(300\) | −3.06736e8 | −0.655903 | ||||||||
\(301\) | −2.74239e7 | −0.0579624 | ||||||||
\(302\) | 4.45752e8 | 0.931256 | ||||||||
\(303\) | 4.88315e8 | 1.00844 | ||||||||
\(304\) | 6.21176e7 | 0.126811 | ||||||||
\(305\) | 2.36576e7 | 0.0477444 | ||||||||
\(306\) | −3.30107e7 | −0.0658612 | ||||||||
\(307\) | −7.95679e8 | −1.56947 | −0.784736 | − | 0.619830i | \(-0.787202\pi\) | ||||
−0.784736 | + | 0.619830i | \(0.787202\pi\) | |||||||
\(308\) | 2.13954e7 | 0.0417247 | ||||||||
\(309\) | 4.98273e8 | 0.960755 | ||||||||
\(310\) | −3.48917e8 | −0.665207 | ||||||||
\(311\) | 7.01044e8 | 1.32155 | 0.660775 | − | 0.750584i | \(-0.270228\pi\) | ||||
0.660775 | + | 0.750584i | \(0.270228\pi\) | |||||||
\(312\) | 3.03713e7 | 0.0566139 | ||||||||
\(313\) | −5.89581e8 | −1.08677 | −0.543386 | − | 0.839483i | \(-0.682858\pi\) | ||||
−0.543386 | + | 0.839483i | \(0.682858\pi\) | |||||||
\(314\) | 4.65700e8 | 0.848892 | ||||||||
\(315\) | 1.26424e8 | 0.227900 | ||||||||
\(316\) | 1.77895e8 | 0.317147 | ||||||||
\(317\) | 1.13340e8 | 0.199837 | 0.0999183 | − | 0.994996i | \(-0.468142\pi\) | ||||
0.0999183 | + | 0.994996i | \(0.468142\pi\) | |||||||
\(318\) | −1.85540e8 | −0.323552 | ||||||||
\(319\) | −4.29250e7 | −0.0740361 | ||||||||
\(320\) | −1.32541e8 | −0.226112 | ||||||||
\(321\) | −4.41845e8 | −0.745594 | ||||||||
\(322\) | −1.80366e8 | −0.301064 | ||||||||
\(323\) | −8.58405e7 | −0.141737 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −3.89987e8 | −0.630172 | ||||||||
\(326\) | −4.68053e8 | −0.748226 | ||||||||
\(327\) | −3.43136e8 | −0.542686 | ||||||||
\(328\) | 2.59331e8 | 0.405786 | ||||||||
\(329\) | −3.12554e7 | −0.0483882 | ||||||||
\(330\) | −1.06441e8 | −0.163046 | ||||||||
\(331\) | 5.33092e7 | 0.0807986 | 0.0403993 | − | 0.999184i | \(-0.487137\pi\) | ||||
0.0403993 | + | 0.999184i | \(0.487137\pi\) | |||||||
\(332\) | 1.15718e8 | 0.173547 | ||||||||
\(333\) | −3.12712e8 | −0.464076 | ||||||||
\(334\) | 8.85942e8 | 1.30105 | ||||||||
\(335\) | −3.89973e8 | −0.566732 | ||||||||
\(336\) | 3.79331e7 | 0.0545545 | ||||||||
\(337\) | 1.04232e9 | 1.48353 | 0.741767 | − | 0.670658i | \(-0.233988\pi\) | ||||
0.741767 | + | 0.670658i | \(0.233988\pi\) | |||||||
\(338\) | 3.86145e7 | 0.0543928 | ||||||||
\(339\) | 3.19910e8 | 0.445993 | ||||||||
\(340\) | 1.83158e8 | 0.252726 | ||||||||
\(341\) | −8.40756e7 | −0.114823 | ||||||||
\(342\) | 8.84448e7 | 0.119559 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | 4.09360e7 | 0.0542189 | ||||||||
\(345\) | 8.97313e8 | 1.17646 | ||||||||
\(346\) | −1.07804e8 | −0.139916 | ||||||||
\(347\) | −9.08973e7 | −0.116788 | −0.0583939 | − | 0.998294i | \(-0.518598\pi\) | ||||
−0.0583939 | + | 0.998294i | \(0.518598\pi\) | |||||||
\(348\) | −7.61041e7 | −0.0968012 | ||||||||
\(349\) | 3.96319e8 | 0.499064 | 0.249532 | − | 0.968367i | \(-0.419723\pi\) | ||||
0.249532 | + | 0.968367i | \(0.419723\pi\) | |||||||
\(350\) | −4.87085e8 | −0.607249 | ||||||||
\(351\) | 4.32436e7 | 0.0533761 | ||||||||
\(352\) | −3.19372e7 | −0.0390299 | ||||||||
\(353\) | −2.06329e8 | −0.249660 | −0.124830 | − | 0.992178i | \(-0.539839\pi\) | ||||
−0.124830 | + | 0.992178i | \(0.539839\pi\) | |||||||
\(354\) | 5.30949e8 | 0.636123 | ||||||||
\(355\) | −1.92713e8 | −0.228618 | ||||||||
\(356\) | 2.98361e8 | 0.350483 | ||||||||
\(357\) | −5.24198e7 | −0.0609756 | ||||||||
\(358\) | −3.21389e8 | −0.370204 | ||||||||
\(359\) | −1.59470e9 | −1.81907 | −0.909534 | − | 0.415630i | \(-0.863561\pi\) | ||||
−0.909534 | + | 0.415630i | \(0.863561\pi\) | |||||||
\(360\) | −1.88715e8 | −0.213181 | ||||||||
\(361\) | −6.63881e8 | −0.742703 | ||||||||
\(362\) | −7.73974e8 | −0.857524 | ||||||||
\(363\) | 5.00505e8 | 0.549206 | ||||||||
\(364\) | 4.82285e7 | 0.0524142 | ||||||||
\(365\) | −7.67140e8 | −0.825752 | ||||||||
\(366\) | 1.01069e7 | 0.0107754 | ||||||||
\(367\) | 8.63511e8 | 0.911878 | 0.455939 | − | 0.890011i | \(-0.349303\pi\) | ||||
0.455939 | + | 0.890011i | \(0.349303\pi\) | |||||||
\(368\) | 2.69235e8 | 0.281620 | ||||||||
\(369\) | 3.69243e8 | 0.382578 | ||||||||
\(370\) | 1.73507e9 | 1.78078 | ||||||||
\(371\) | −2.94631e8 | −0.299551 | ||||||||
\(372\) | −1.49062e8 | −0.150130 | ||||||||
\(373\) | −3.87571e8 | −0.386697 | −0.193349 | − | 0.981130i | \(-0.561935\pi\) | ||||
−0.193349 | + | 0.981130i | \(0.561935\pi\) | |||||||
\(374\) | 4.41340e7 | 0.0436238 | ||||||||
\(375\) | 1.35672e9 | 1.32856 | ||||||||
\(376\) | 4.66553e7 | 0.0452630 | ||||||||
\(377\) | −9.67596e7 | −0.0930036 | ||||||||
\(378\) | 5.40102e7 | 0.0514344 | ||||||||
\(379\) | 6.80121e8 | 0.641725 | 0.320862 | − | 0.947126i | \(-0.396027\pi\) | ||||
0.320862 | + | 0.947126i | \(0.396027\pi\) | |||||||
\(380\) | −4.90732e8 | −0.458777 | ||||||||
\(381\) | 9.75338e8 | 0.903478 | ||||||||
\(382\) | −4.90813e8 | −0.450499 | ||||||||
\(383\) | 1.89713e8 | 0.172545 | 0.0862725 | − | 0.996272i | \(-0.472504\pi\) | ||||
0.0862725 | + | 0.996272i | \(0.472504\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | −1.69025e8 | −0.150952 | ||||||||
\(386\) | −5.13658e8 | −0.454589 | ||||||||
\(387\) | 5.82858e7 | 0.0511181 | ||||||||
\(388\) | −4.60907e8 | −0.400592 | ||||||||
\(389\) | 5.32318e8 | 0.458508 | 0.229254 | − | 0.973367i | \(-0.426371\pi\) | ||||
0.229254 | + | 0.973367i | \(0.426371\pi\) | |||||||
\(390\) | −2.39935e8 | −0.204817 | ||||||||
\(391\) | −3.72056e8 | −0.314767 | ||||||||
\(392\) | 6.02363e7 | 0.0505076 | ||||||||
\(393\) | 5.03805e8 | 0.418686 | ||||||||
\(394\) | 4.92052e8 | 0.405298 | ||||||||
\(395\) | −1.40538e9 | −1.14737 | ||||||||
\(396\) | −4.54730e7 | −0.0367977 | ||||||||
\(397\) | 3.59479e8 | 0.288341 | 0.144171 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144171 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(398\) | −6.18625e8 | −0.491855 | ||||||||
\(399\) | 1.40447e8 | 0.110690 | ||||||||
\(400\) | 7.27077e8 | 0.568029 | ||||||||
\(401\) | 1.86285e9 | 1.44269 | 0.721344 | − | 0.692577i | \(-0.243525\pi\) | ||||
0.721344 | + | 0.692577i | \(0.243525\pi\) | |||||||
\(402\) | −1.66602e8 | −0.127905 | ||||||||
\(403\) | −1.89519e8 | −0.144240 | ||||||||
\(404\) | −1.15749e9 | −0.873336 | ||||||||
\(405\) | −2.68698e8 | −0.200989 | ||||||||
\(406\) | −1.20850e8 | −0.0896205 | ||||||||
\(407\) | 4.18084e8 | 0.307385 | ||||||||
\(408\) | 7.82476e7 | 0.0570375 | ||||||||
\(409\) | 2.16294e9 | 1.56319 | 0.781595 | − | 0.623786i | \(-0.214406\pi\) | ||||
0.781595 | + | 0.623786i | \(0.214406\pi\) | |||||||
\(410\) | −2.04873e9 | −1.46805 | ||||||||
\(411\) | −3.07207e8 | −0.218265 | ||||||||
\(412\) | −1.18109e9 | −0.832038 | ||||||||
\(413\) | 8.43127e8 | 0.588936 | ||||||||
\(414\) | 3.83344e8 | 0.265514 | ||||||||
\(415\) | −9.14176e8 | −0.627858 | ||||||||
\(416\) | −7.19913e7 | −0.0490290 | ||||||||
\(417\) | 1.17616e9 | 0.794309 | ||||||||
\(418\) | −1.18247e8 | −0.0791907 | ||||||||
\(419\) | −1.25174e9 | −0.831312 | −0.415656 | − | 0.909522i | \(-0.636448\pi\) | ||||
−0.415656 | + | 0.909522i | \(0.636448\pi\) | |||||||
\(420\) | −2.99673e8 | −0.197367 | ||||||||
\(421\) | −6.62692e7 | −0.0432837 | −0.0216419 | − | 0.999766i | \(-0.506889\pi\) | ||||
−0.0216419 | + | 0.999766i | \(0.506889\pi\) | |||||||
\(422\) | −8.43268e8 | −0.546226 | ||||||||
\(423\) | 6.64291e7 | 0.0426744 | ||||||||
\(424\) | 4.39799e8 | 0.280204 | ||||||||
\(425\) | −1.00475e9 | −0.634887 | ||||||||
\(426\) | −8.23293e7 | −0.0515966 | ||||||||
\(427\) | 1.60493e7 | 0.00997605 | ||||||||
\(428\) | 1.04734e9 | 0.645703 | ||||||||
\(429\) | −5.78150e7 | −0.0353541 | ||||||||
\(430\) | −3.23396e8 | −0.196153 | ||||||||
\(431\) | 7.93745e8 | 0.477541 | 0.238770 | − | 0.971076i | \(-0.423256\pi\) | ||||
0.238770 | + | 0.971076i | \(0.423256\pi\) | |||||||
\(432\) | −8.06216e7 | −0.0481125 | ||||||||
\(433\) | −1.05627e8 | −0.0625270 | −0.0312635 | − | 0.999511i | \(-0.509953\pi\) | ||||
−0.0312635 | + | 0.999511i | \(0.509953\pi\) | |||||||
\(434\) | −2.36705e8 | −0.138993 | ||||||||
\(435\) | 6.01225e8 | 0.350207 | ||||||||
\(436\) | 8.13358e8 | 0.469980 | ||||||||
\(437\) | 9.96840e8 | 0.571401 | ||||||||
\(438\) | −3.27732e8 | −0.186363 | ||||||||
\(439\) | −3.29223e9 | −1.85723 | −0.928613 | − | 0.371051i | \(-0.878998\pi\) | ||||
−0.928613 | + | 0.371051i | \(0.878998\pi\) | |||||||
\(440\) | 2.52305e8 | 0.141202 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | 9.94849e7 | 0.0547998 | ||||||||
\(443\) | −1.84176e9 | −1.00652 | −0.503258 | − | 0.864136i | \(-0.667866\pi\) | ||||
−0.503258 | + | 0.864136i | \(0.667866\pi\) | |||||||
\(444\) | 7.41243e8 | 0.401902 | ||||||||
\(445\) | −2.35706e9 | −1.26798 | ||||||||
\(446\) | −2.77712e8 | −0.148226 | ||||||||
\(447\) | −7.02205e8 | −0.371867 | ||||||||
\(448\) | −8.99154e7 | −0.0472456 | ||||||||
\(449\) | 1.52557e9 | 0.795369 | 0.397684 | − | 0.917522i | \(-0.369814\pi\) | ||||
0.397684 | + | 0.917522i | \(0.369814\pi\) | |||||||
\(450\) | 1.03523e9 | 0.535543 | ||||||||
\(451\) | −4.93664e8 | −0.253404 | ||||||||
\(452\) | −7.58304e8 | −0.386241 | ||||||||
\(453\) | −1.50441e9 | −0.760367 | ||||||||
\(454\) | −7.95871e8 | −0.399160 | ||||||||
\(455\) | −3.81008e8 | −0.189624 | ||||||||
\(456\) | −2.09647e8 | −0.103541 | ||||||||
\(457\) | 5.43757e8 | 0.266501 | 0.133250 | − | 0.991082i | \(-0.457459\pi\) | ||||
0.133250 | + | 0.991082i | \(0.457459\pi\) | |||||||
\(458\) | 1.08988e8 | 0.0530090 | ||||||||
\(459\) | 1.11411e8 | 0.0537755 | ||||||||
\(460\) | −2.12696e9 | −1.01884 | ||||||||
\(461\) | −2.01615e9 | −0.958449 | −0.479224 | − | 0.877692i | \(-0.659082\pi\) | ||||
−0.479224 | + | 0.877692i | \(0.659082\pi\) | |||||||
\(462\) | −7.22095e7 | −0.0340681 | ||||||||
\(463\) | 2.10963e9 | 0.987811 | 0.493905 | − | 0.869516i | \(-0.335569\pi\) | ||||
0.493905 | + | 0.869516i | \(0.335569\pi\) | |||||||
\(464\) | 1.80395e8 | 0.0838323 | ||||||||
\(465\) | 1.17760e9 | 0.543139 | ||||||||
\(466\) | 2.86518e9 | 1.31160 | ||||||||
\(467\) | −1.87515e9 | −0.851975 | −0.425987 | − | 0.904729i | \(-0.640073\pi\) | ||||
−0.425987 | + | 0.904729i | \(0.640073\pi\) | |||||||
\(468\) | −1.02503e8 | −0.0462250 | ||||||||
\(469\) | −2.64557e8 | −0.118417 | ||||||||
\(470\) | −3.68579e8 | −0.163752 | ||||||||
\(471\) | −1.57174e9 | −0.693117 | ||||||||
\(472\) | −1.25855e9 | −0.550899 | ||||||||
\(473\) | −7.79259e7 | −0.0338585 | ||||||||
\(474\) | −6.00397e8 | −0.258949 | ||||||||
\(475\) | 2.69200e9 | 1.15252 | ||||||||
\(476\) | 1.24254e8 | 0.0528064 | ||||||||
\(477\) | 6.26199e8 | 0.264179 | ||||||||
\(478\) | 1.16646e9 | 0.488508 | ||||||||
\(479\) | 3.61742e7 | 0.0150392 | 0.00751959 | − | 0.999972i | \(-0.497606\pi\) | ||||
0.00751959 | + | 0.999972i | \(0.497606\pi\) | |||||||
\(480\) | 4.47325e8 | 0.184620 | ||||||||
\(481\) | 9.42425e8 | 0.386135 | ||||||||
\(482\) | −1.27942e9 | −0.520412 | ||||||||
\(483\) | 6.08736e8 | 0.245818 | ||||||||
\(484\) | −1.18638e9 | −0.475627 | ||||||||
\(485\) | 3.64119e9 | 1.44926 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | −1.02235e9 | −0.401098 | −0.200549 | − | 0.979684i | \(-0.564273\pi\) | ||||
−0.200549 | + | 0.979684i | \(0.564273\pi\) | |||||||
\(488\) | −2.39570e7 | −0.00933174 | ||||||||
\(489\) | 1.57968e9 | 0.610924 | ||||||||
\(490\) | −4.75869e8 | −0.182726 | ||||||||
\(491\) | −3.26756e9 | −1.24577 | −0.622885 | − | 0.782313i | \(-0.714040\pi\) | ||||
−0.622885 | + | 0.782313i | \(0.714040\pi\) | |||||||
\(492\) | −8.75243e8 | −0.331323 | ||||||||
\(493\) | −2.49288e8 | −0.0936995 | ||||||||
\(494\) | −2.66548e8 | −0.0994788 | ||||||||
\(495\) | 3.59239e8 | 0.133127 | ||||||||
\(496\) | 3.53332e8 | 0.130016 | ||||||||
\(497\) | −1.30736e8 | −0.0477691 | ||||||||
\(498\) | −3.90548e8 | −0.141700 | ||||||||
\(499\) | −5.10252e9 | −1.83837 | −0.919184 | − | 0.393828i | \(-0.871151\pi\) | ||||
−0.919184 | + | 0.393828i | \(0.871151\pi\) | |||||||
\(500\) | −3.21593e9 | −1.15056 | ||||||||
\(501\) | −2.99005e9 | −1.06230 | ||||||||
\(502\) | −1.06752e8 | −0.0376628 | ||||||||
\(503\) | −9.25013e8 | −0.324086 | −0.162043 | − | 0.986784i | \(-0.551808\pi\) | ||||
−0.162043 | + | 0.986784i | \(0.551808\pi\) | |||||||
\(504\) | −1.28024e8 | −0.0445435 | ||||||||
\(505\) | 9.14420e9 | 3.15955 | ||||||||
\(506\) | −5.12516e8 | −0.175865 | ||||||||
\(507\) | −1.30324e8 | −0.0444116 | ||||||||
\(508\) | −2.31191e9 | −0.782435 | ||||||||
\(509\) | 1.28544e9 | 0.432056 | 0.216028 | − | 0.976387i | \(-0.430690\pi\) | ||||
0.216028 | + | 0.976387i | \(0.430690\pi\) | |||||||
\(510\) | −6.18159e8 | −0.206350 | ||||||||
\(511\) | −5.20426e8 | −0.172539 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −2.98501e8 | −0.0976192 | ||||||||
\(514\) | −6.17740e8 | −0.200648 | ||||||||
\(515\) | 9.33067e9 | 3.01015 | ||||||||
\(516\) | −1.38159e8 | −0.0442695 | ||||||||
\(517\) | −8.88132e7 | −0.0282657 | ||||||||
\(518\) | 1.17707e9 | 0.372089 | ||||||||
\(519\) | 3.63838e8 | 0.114241 | ||||||||
\(520\) | 5.68734e8 | 0.177377 | ||||||||
\(521\) | 1.09976e9 | 0.340695 | 0.170348 | − | 0.985384i | \(-0.445511\pi\) | ||||
0.170348 | + | 0.985384i | \(0.445511\pi\) | |||||||
\(522\) | 2.56851e8 | 0.0790378 | ||||||||
\(523\) | −2.00049e8 | −0.0611479 | −0.0305739 | − | 0.999533i | \(-0.509734\pi\) | ||||
−0.0305739 | + | 0.999533i | \(0.509734\pi\) | |||||||
\(524\) | −1.19420e9 | −0.362593 | ||||||||
\(525\) | 1.64391e9 | 0.495816 | ||||||||
\(526\) | −1.10287e9 | −0.330425 | ||||||||
\(527\) | −4.88271e8 | −0.145319 | ||||||||
\(528\) | 1.07788e8 | 0.0318678 | ||||||||
\(529\) | 9.15750e8 | 0.268957 | ||||||||
\(530\) | −3.47443e9 | −1.01372 | ||||||||
\(531\) | −1.79195e9 | −0.519392 | ||||||||
\(532\) | −3.32912e8 | −0.0958602 | ||||||||
\(533\) | −1.11280e9 | −0.318324 | ||||||||
\(534\) | −1.00697e9 | −0.286168 | ||||||||
\(535\) | −8.27400e9 | −2.33602 | ||||||||
\(536\) | 3.94907e8 | 0.110769 | ||||||||
\(537\) | 1.08469e9 | 0.302270 | ||||||||
\(538\) | −3.70151e9 | −1.02480 | ||||||||
\(539\) | −1.14666e8 | −0.0315409 | ||||||||
\(540\) | 6.36914e8 | 0.174061 | ||||||||
\(541\) | −6.34229e9 | −1.72209 | −0.861045 | − | 0.508529i | \(-0.830190\pi\) | ||||
−0.861045 | + | 0.508529i | \(0.830190\pi\) | |||||||
\(542\) | 1.82384e9 | 0.492027 | ||||||||
\(543\) | 2.61216e9 | 0.700166 | ||||||||
\(544\) | −1.85476e8 | −0.0493959 | ||||||||
\(545\) | −6.42557e9 | −1.70029 | ||||||||
\(546\) | −1.62771e8 | −0.0427960 | ||||||||
\(547\) | −2.39009e9 | −0.624395 | −0.312197 | − | 0.950017i | \(-0.601065\pi\) | ||||
−0.312197 | + | 0.950017i | \(0.601065\pi\) | |||||||
\(548\) | 7.28195e8 | 0.189023 | ||||||||
\(549\) | −3.41106e7 | −0.00879805 | ||||||||
\(550\) | −1.38407e9 | −0.354722 | ||||||||
\(551\) | 6.67912e8 | 0.170094 | ||||||||
\(552\) | −9.08667e8 | −0.229942 | ||||||||
\(553\) | −9.53408e8 | −0.239740 | ||||||||
\(554\) | 2.80529e9 | 0.700961 | ||||||||
\(555\) | −5.85585e9 | −1.45400 | ||||||||
\(556\) | −2.78793e9 | −0.687892 | ||||||||
\(557\) | 4.18084e9 | 1.02511 | 0.512554 | − | 0.858655i | \(-0.328699\pi\) | ||||
0.512554 | + | 0.858655i | \(0.328699\pi\) | |||||||
\(558\) | 5.03084e8 | 0.122580 | ||||||||
\(559\) | −1.75657e8 | −0.0425328 | ||||||||
\(560\) | 7.10335e8 | 0.170925 | ||||||||
\(561\) | −1.48952e8 | −0.0356187 | ||||||||
\(562\) | −1.99358e9 | −0.473759 | ||||||||
\(563\) | 2.41789e9 | 0.571027 | 0.285513 | − | 0.958375i | \(-0.407836\pi\) | ||||
0.285513 | + | 0.958375i | \(0.407836\pi\) | |||||||
\(564\) | −1.57462e8 | −0.0369571 | ||||||||
\(565\) | 5.99063e9 | 1.39734 | ||||||||
\(566\) | −1.74066e9 | −0.403511 | ||||||||
\(567\) | −1.82284e8 | −0.0419961 | ||||||||
\(568\) | 1.95151e8 | 0.0446839 | ||||||||
\(569\) | −3.00544e9 | −0.683935 | −0.341968 | − | 0.939712i | \(-0.611093\pi\) | ||||
−0.341968 | + | 0.939712i | \(0.611093\pi\) | |||||||
\(570\) | 1.65622e9 | 0.374590 | ||||||||
\(571\) | 7.47847e9 | 1.68107 | 0.840536 | − | 0.541756i | \(-0.182240\pi\) | ||||
0.840536 | + | 0.541756i | \(0.182240\pi\) | |||||||
\(572\) | 1.37043e8 | 0.0306176 | ||||||||
\(573\) | 1.65649e9 | 0.367831 | ||||||||
\(574\) | −1.38985e9 | −0.306745 | ||||||||
\(575\) | 1.16679e10 | 2.55949 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | −2.03084e8 | −0.0440110 | −0.0220055 | − | 0.999758i | \(-0.507005\pi\) | ||||
−0.0220055 | + | 0.999758i | \(0.507005\pi\) | |||||||
\(578\) | −3.02640e9 | −0.651897 | ||||||||
\(579\) | 1.73360e9 | 0.371170 | ||||||||
\(580\) | −1.42513e9 | −0.303288 | ||||||||
\(581\) | −6.20175e8 | −0.131189 | ||||||||
\(582\) | 1.55556e9 | 0.327082 | ||||||||
\(583\) | −8.37204e8 | −0.174981 | ||||||||
\(584\) | 7.76846e8 | 0.161395 | ||||||||
\(585\) | 8.09780e8 | 0.167233 | ||||||||
\(586\) | −6.77543e7 | −0.0139090 | ||||||||
\(587\) | 5.05213e9 | 1.03096 | 0.515480 | − | 0.856902i | \(-0.327614\pi\) | ||||
0.515480 | + | 0.856902i | \(0.327614\pi\) | |||||||
\(588\) | −2.03297e8 | −0.0412393 | ||||||||
\(589\) | 1.30821e9 | 0.263800 | ||||||||
\(590\) | 9.94256e9 | 1.99304 | ||||||||
\(591\) | −1.66068e9 | −0.330924 | ||||||||
\(592\) | −1.75702e9 | −0.348057 | ||||||||
\(593\) | 2.67099e9 | 0.525993 | 0.262997 | − | 0.964797i | \(-0.415289\pi\) | ||||
0.262997 | + | 0.964797i | \(0.415289\pi\) | |||||||
\(594\) | 1.53472e8 | 0.0300452 | ||||||||
\(595\) | −9.81614e8 | −0.191043 | ||||||||
\(596\) | 1.66449e9 | 0.322046 | ||||||||
\(597\) | 2.08786e9 | 0.401598 | ||||||||
\(598\) | −1.15529e9 | −0.220921 | ||||||||
\(599\) | 3.33264e8 | 0.0633569 | 0.0316785 | − | 0.999498i | \(-0.489915\pi\) | ||||
0.0316785 | + | 0.999498i | \(0.489915\pi\) | |||||||
\(600\) | −2.45389e9 | −0.463794 | ||||||||
\(601\) | −2.40003e9 | −0.450979 | −0.225490 | − | 0.974246i | \(-0.572398\pi\) | ||||
−0.225490 | + | 0.974246i | \(0.572398\pi\) | |||||||
\(602\) | −2.19391e8 | −0.0409856 | ||||||||
\(603\) | 5.62280e8 | 0.104434 | ||||||||
\(604\) | 3.56602e9 | 0.658497 | ||||||||
\(605\) | 9.37248e9 | 1.72072 | ||||||||
\(606\) | 3.90652e9 | 0.713076 | ||||||||
\(607\) | 4.74046e9 | 0.860321 | 0.430160 | − | 0.902752i | \(-0.358457\pi\) | ||||
0.430160 | + | 0.902752i | \(0.358457\pi\) | |||||||
\(608\) | 4.96941e8 | 0.0896690 | ||||||||
\(609\) | 4.07870e8 | 0.0731748 | ||||||||
\(610\) | 1.89261e8 | 0.0337604 | ||||||||
\(611\) | −2.00199e8 | −0.0355072 | ||||||||
\(612\) | −2.64086e8 | −0.0465709 | ||||||||
\(613\) | −1.70938e9 | −0.299727 | −0.149863 | − | 0.988707i | \(-0.547883\pi\) | ||||
−0.149863 | + | 0.988707i | \(0.547883\pi\) | |||||||
\(614\) | −6.36544e9 | −1.10978 | ||||||||
\(615\) | 6.91446e9 | 1.19866 | ||||||||
\(616\) | 1.71163e8 | 0.0295038 | ||||||||
\(617\) | 2.94186e9 | 0.504225 | 0.252113 | − | 0.967698i | \(-0.418875\pi\) | ||||
0.252113 | + | 0.967698i | \(0.418875\pi\) | |||||||
\(618\) | 3.98618e9 | 0.679356 | ||||||||
\(619\) | 6.20627e9 | 1.05175 | 0.525876 | − | 0.850561i | \(-0.323738\pi\) | ||||
0.525876 | + | 0.850561i | \(0.323738\pi\) | |||||||
\(620\) | −2.79134e9 | −0.470372 | ||||||||
\(621\) | −1.29378e9 | −0.216791 | ||||||||
\(622\) | 5.60835e9 | 0.934478 | ||||||||
\(623\) | −1.59903e9 | −0.264940 | ||||||||
\(624\) | 2.42971e8 | 0.0400320 | ||||||||
\(625\) | 1.15381e10 | 1.89040 | ||||||||
\(626\) | −4.71665e9 | −0.768463 | ||||||||
\(627\) | 3.99085e8 | 0.0646590 | ||||||||
\(628\) | 3.72560e9 | 0.600257 | ||||||||
\(629\) | 2.42803e9 | 0.389024 | ||||||||
\(630\) | 1.01140e9 | 0.161150 | ||||||||
\(631\) | −1.37333e7 | −0.00217607 | −0.00108804 | − | 0.999999i | \(-0.500346\pi\) | ||||
−0.00108804 | + | 0.999999i | \(0.500346\pi\) | |||||||
\(632\) | 1.42316e9 | 0.224257 | ||||||||
\(633\) | 2.84603e9 | 0.445991 | ||||||||
\(634\) | 9.06719e8 | 0.141306 | ||||||||
\(635\) | 1.82642e10 | 2.83069 | ||||||||
\(636\) | −1.48432e9 | −0.228785 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −3.43400e8 | −0.0523514 | ||||||||
\(639\) | 2.77861e8 | 0.0421284 | ||||||||
\(640\) | −1.06033e9 | −0.159886 | ||||||||
\(641\) | 6.38161e9 | 0.957034 | 0.478517 | − | 0.878078i | \(-0.341175\pi\) | ||||
0.478517 | + | 0.878078i | \(0.341175\pi\) | |||||||
\(642\) | −3.53476e9 | −0.527214 | ||||||||
\(643\) | 6.94076e9 | 1.02960 | 0.514800 | − | 0.857310i | \(-0.327866\pi\) | ||||
0.514800 | + | 0.857310i | \(0.327866\pi\) | |||||||
\(644\) | −1.44293e9 | −0.212885 | ||||||||
\(645\) | 1.09146e9 | 0.160158 | ||||||||
\(646\) | −6.86724e8 | −0.100223 | ||||||||
\(647\) | −3.89714e9 | −0.565694 | −0.282847 | − | 0.959165i | \(-0.591279\pi\) | ||||
−0.282847 | + | 0.959165i | \(0.591279\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | 2.39577e9 | 0.344024 | ||||||||
\(650\) | −3.11990e9 | −0.445599 | ||||||||
\(651\) | 7.98879e8 | 0.113487 | ||||||||
\(652\) | −3.74442e9 | −0.529076 | ||||||||
\(653\) | 3.80268e9 | 0.534433 | 0.267216 | − | 0.963637i | \(-0.413896\pi\) | ||||
0.267216 | + | 0.963637i | \(0.413896\pi\) | |||||||
\(654\) | −2.74508e9 | −0.383737 | ||||||||
\(655\) | 9.43426e9 | 1.31179 | ||||||||
\(656\) | 2.07465e9 | 0.286934 | ||||||||
\(657\) | 1.10610e9 | 0.152165 | ||||||||
\(658\) | −2.50043e8 | −0.0342156 | ||||||||
\(659\) | 1.47769e9 | 0.201134 | 0.100567 | − | 0.994930i | \(-0.467934\pi\) | ||||
0.100567 | + | 0.994930i | \(0.467934\pi\) | |||||||
\(660\) | −8.51529e8 | −0.115291 | ||||||||
\(661\) | 3.33396e9 | 0.449009 | 0.224505 | − | 0.974473i | \(-0.427924\pi\) | ||||
0.224505 | + | 0.974473i | \(0.427924\pi\) | |||||||
\(662\) | 4.26473e8 | 0.0571332 | ||||||||
\(663\) | −3.35762e8 | −0.0447439 | ||||||||
\(664\) | 9.25743e8 | 0.122716 | ||||||||
\(665\) | 2.63002e9 | 0.346803 | ||||||||
\(666\) | −2.50169e9 | −0.328152 | ||||||||
\(667\) | 2.89491e9 | 0.377741 | ||||||||
\(668\) | 7.08754e9 | 0.919979 | ||||||||
\(669\) | 9.37280e8 | 0.121026 | ||||||||
\(670\) | −3.11979e9 | −0.400740 | ||||||||
\(671\) | 4.56046e7 | 0.00582747 | ||||||||
\(672\) | 3.03464e8 | 0.0385758 | ||||||||
\(673\) | −5.49101e9 | −0.694383 | −0.347192 | − | 0.937794i | \(-0.612865\pi\) | ||||
−0.347192 | + | 0.937794i | \(0.612865\pi\) | |||||||
\(674\) | 8.33858e9 | 1.04902 | ||||||||
\(675\) | −3.49391e9 | −0.437269 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | 1.53710e10 | 1.90389 | 0.951946 | − | 0.306265i | \(-0.0990794\pi\) | ||||
0.951946 | + | 0.306265i | \(0.0990794\pi\) | |||||||
\(678\) | 2.55928e9 | 0.315365 | ||||||||
\(679\) | 2.47017e9 | 0.302819 | ||||||||
\(680\) | 1.46527e9 | 0.178704 | ||||||||
\(681\) | 2.68607e9 | 0.325913 | ||||||||
\(682\) | −6.72605e8 | −0.0811922 | ||||||||
\(683\) | 1.15224e9 | 0.138379 | 0.0691897 | − | 0.997604i | \(-0.477959\pi\) | ||||
0.0691897 | + | 0.997604i | \(0.477959\pi\) | |||||||
\(684\) | 7.07559e8 | 0.0845407 | ||||||||
\(685\) | −5.75277e9 | −0.683849 | ||||||||
\(686\) | −3.22829e8 | −0.0381802 | ||||||||
\(687\) | −3.67835e8 | −0.0432817 | ||||||||
\(688\) | 3.27488e8 | 0.0383385 | ||||||||
\(689\) | −1.88719e9 | −0.219810 | ||||||||
\(690\) | 7.17850e9 | 0.831883 | ||||||||
\(691\) | 3.87769e9 | 0.447095 | 0.223548 | − | 0.974693i | \(-0.428236\pi\) | ||||
0.223548 | + | 0.974693i | \(0.428236\pi\) | |||||||
\(692\) | −8.62431e8 | −0.0989357 | ||||||||
\(693\) | 2.43707e8 | 0.0278165 | ||||||||
\(694\) | −7.27178e8 | −0.0825815 | ||||||||
\(695\) | 2.20248e10 | 2.48865 | ||||||||
\(696\) | −6.08833e8 | −0.0684488 | ||||||||
\(697\) | −2.86696e9 | −0.320706 | ||||||||
\(698\) | 3.17055e9 | 0.352891 | ||||||||
\(699\) | −9.66998e9 | −1.07092 | ||||||||
\(700\) | −3.89668e9 | −0.429390 | ||||||||
\(701\) | −1.12046e10 | −1.22852 | −0.614260 | − | 0.789104i | \(-0.710545\pi\) | ||||
−0.614260 | + | 0.789104i | \(0.710545\pi\) | |||||||
\(702\) | 3.45948e8 | 0.0377426 | ||||||||
\(703\) | −6.50536e9 | −0.706200 | ||||||||
\(704\) | −2.55497e8 | −0.0275983 | ||||||||
\(705\) | 1.24395e9 | 0.133703 | ||||||||
\(706\) | −1.65063e9 | −0.176536 | ||||||||
\(707\) | 6.20341e9 | 0.660180 | ||||||||
\(708\) | 4.24759e9 | 0.449807 | ||||||||
\(709\) | −5.78180e9 | −0.609258 | −0.304629 | − | 0.952471i | \(-0.598532\pi\) | ||||
−0.304629 | + | 0.952471i | \(0.598532\pi\) | |||||||
\(710\) | −1.54170e9 | −0.161657 | ||||||||
\(711\) | 2.02634e9 | 0.211431 | ||||||||
\(712\) | 2.38689e9 | 0.247829 | ||||||||
\(713\) | 5.67014e9 | 0.585842 | ||||||||
\(714\) | −4.19358e8 | −0.0431163 | ||||||||
\(715\) | −1.08264e9 | −0.110768 | ||||||||
\(716\) | −2.57111e9 | −0.261773 | ||||||||
\(717\) | −3.93680e9 | −0.398865 | ||||||||
\(718\) | −1.27576e10 | −1.28627 | ||||||||
\(719\) | 4.57616e8 | 0.0459145 | 0.0229573 | − | 0.999736i | \(-0.492692\pi\) | ||||
0.0229573 | + | 0.999736i | \(0.492692\pi\) | |||||||
\(720\) | −1.50972e9 | −0.150742 | ||||||||
\(721\) | 6.32991e9 | 0.628962 | ||||||||
\(722\) | −5.31105e9 | −0.525170 | ||||||||
\(723\) | 4.31803e9 | 0.424915 | ||||||||
\(724\) | −6.19179e9 | −0.606361 | ||||||||
\(725\) | 7.81780e9 | 0.761907 | ||||||||
\(726\) | 4.00404e9 | 0.388348 | ||||||||
\(727\) | −1.72274e10 | −1.66284 | −0.831419 | − | 0.555646i | \(-0.812471\pi\) | ||||
−0.831419 | + | 0.555646i | \(0.812471\pi\) | |||||||
\(728\) | 3.85828e8 | 0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −6.13712e9 | −0.583895 | ||||||||
\(731\) | −4.52556e8 | −0.0428511 | ||||||||
\(732\) | 8.08548e7 | 0.00761934 | ||||||||
\(733\) | −5.67159e8 | −0.0531913 | −0.0265957 | − | 0.999646i | \(-0.508467\pi\) | ||||
−0.0265957 | + | 0.999646i | \(0.508467\pi\) | |||||||
\(734\) | 6.90809e9 | 0.644795 | ||||||||
\(735\) | 1.60606e9 | 0.149195 | ||||||||
\(736\) | 2.15388e9 | 0.199135 | ||||||||
\(737\) | −7.51747e8 | −0.0691728 | ||||||||
\(738\) | 2.95395e9 | 0.270524 | ||||||||
\(739\) | −6.70030e9 | −0.610715 | −0.305358 | − | 0.952238i | \(-0.598776\pi\) | ||||
−0.305358 | + | 0.952238i | \(0.598776\pi\) | |||||||
\(740\) | 1.38805e10 | 1.25920 | ||||||||
\(741\) | 8.99598e8 | 0.0812241 | ||||||||
\(742\) | −2.35705e9 | −0.211814 | ||||||||
\(743\) | −1.91086e10 | −1.70910 | −0.854552 | − | 0.519366i | \(-0.826168\pi\) | ||||
−0.854552 | + | 0.519366i | \(0.826168\pi\) | |||||||
\(744\) | −1.19250e9 | −0.106158 | ||||||||
\(745\) | −1.31495e10 | −1.16510 | ||||||||
\(746\) | −3.10057e9 | −0.273436 | ||||||||
\(747\) | 1.31810e9 | 0.115698 | ||||||||
\(748\) | 3.53072e8 | 0.0308467 | ||||||||
\(749\) | −5.61307e9 | −0.488106 | ||||||||
\(750\) | 1.08538e10 | 0.939432 | ||||||||
\(751\) | −7.77506e9 | −0.669829 | −0.334914 | − | 0.942249i | \(-0.608707\pi\) | ||||
−0.334914 | + | 0.942249i | \(0.608707\pi\) | |||||||
\(752\) | 3.73242e8 | 0.0320058 | ||||||||
\(753\) | 3.60287e8 | 0.0307515 | ||||||||
\(754\) | −7.74077e8 | −0.0657634 | ||||||||
\(755\) | −2.81717e10 | −2.38231 | ||||||||
\(756\) | 4.32081e8 | 0.0363696 | ||||||||
\(757\) | −5.51645e9 | −0.462194 | −0.231097 | − | 0.972931i | \(-0.574231\pi\) | ||||
−0.231097 | + | 0.972931i | \(0.574231\pi\) | |||||||
\(758\) | 5.44097e9 | 0.453768 | ||||||||
\(759\) | 1.72974e9 | 0.143594 | ||||||||
\(760\) | −3.92585e9 | −0.324404 | ||||||||
\(761\) | 6.54076e9 | 0.537999 | 0.269000 | − | 0.963140i | \(-0.413307\pi\) | ||||
0.269000 | + | 0.963140i | \(0.413307\pi\) | |||||||
\(762\) | 7.80270e9 | 0.638856 | ||||||||
\(763\) | −4.35909e9 | −0.355271 | ||||||||
\(764\) | −3.92650e9 | −0.318551 | ||||||||
\(765\) | 2.08629e9 | 0.168484 | ||||||||
\(766\) | 1.51771e9 | 0.122008 | ||||||||
\(767\) | 5.40044e9 | 0.432161 | ||||||||
\(768\) | −4.52985e8 | −0.0360844 | ||||||||
\(769\) | −2.15875e10 | −1.71183 | −0.855915 | − | 0.517116i | \(-0.827006\pi\) | ||||
−0.855915 | + | 0.517116i | \(0.827006\pi\) | |||||||
\(770\) | −1.35220e9 | −0.106739 | ||||||||
\(771\) | 2.08487e9 | 0.163828 | ||||||||
\(772\) | −4.10927e9 | −0.321443 | ||||||||
\(773\) | −6.96542e8 | −0.0542399 | −0.0271199 | − | 0.999632i | \(-0.508634\pi\) | ||||
−0.0271199 | + | 0.999632i | \(0.508634\pi\) | |||||||
\(774\) | 4.66286e8 | 0.0361459 | ||||||||
\(775\) | 1.53124e10 | 1.18165 | ||||||||
\(776\) | −3.68726e9 | −0.283261 | ||||||||
\(777\) | −3.97260e9 | −0.303809 | ||||||||
\(778\) | 4.25854e9 | 0.324214 | ||||||||
\(779\) | 7.68139e9 | 0.582182 | ||||||||
\(780\) | −1.91948e9 | −0.144828 | ||||||||
\(781\) | −3.71490e8 | −0.0279041 | ||||||||
\(782\) | −2.97645e9 | −0.222574 | ||||||||
\(783\) | −8.66873e8 | −0.0645341 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | −2.94324e10 | −2.17161 | ||||||||
\(786\) | 4.03044e9 | 0.296056 | ||||||||
\(787\) | −2.34452e10 | −1.71452 | −0.857260 | − | 0.514884i | \(-0.827835\pi\) | ||||
−0.857260 | + | 0.514884i | \(0.827835\pi\) | |||||||
\(788\) | 3.93642e9 | 0.286589 | ||||||||
\(789\) | 3.72218e9 | 0.269791 | ||||||||
\(790\) | −1.12431e10 | −0.811315 | ||||||||
\(791\) | 4.06404e9 | 0.291971 | ||||||||
\(792\) | −3.63784e8 | −0.0260199 | ||||||||
\(793\) | 1.02800e8 | 0.00732042 | ||||||||
\(794\) | 2.87583e9 | 0.203888 | ||||||||
\(795\) | 1.17262e10 | 0.827700 | ||||||||
\(796\) | −4.94900e9 | −0.347794 | ||||||||
\(797\) | −3.48843e9 | −0.244077 | −0.122038 | − | 0.992525i | \(-0.538943\pi\) | ||||
−0.122038 | + | 0.992525i | \(0.538943\pi\) | |||||||
\(798\) | 1.12358e9 | 0.0782695 | ||||||||
\(799\) | −5.15784e8 | −0.0357729 | ||||||||
\(800\) | 5.81662e9 | 0.401657 | ||||||||
\(801\) | 3.39851e9 | 0.233655 | ||||||||
\(802\) | 1.49028e10 | 1.02013 | ||||||||
\(803\) | −1.47881e9 | −0.100788 | ||||||||
\(804\) | −1.33281e9 | −0.0904426 | ||||||||
\(805\) | 1.13992e10 | 0.770174 | ||||||||
\(806\) | −1.51615e9 | −0.101993 | ||||||||
\(807\) | 1.24926e10 | 0.836749 | ||||||||
\(808\) | −9.25990e9 | −0.617542 | ||||||||
\(809\) | −9.81709e9 | −0.651873 | −0.325936 | − | 0.945392i | \(-0.605680\pi\) | ||||
−0.325936 | + | 0.945392i | \(0.605680\pi\) | |||||||
\(810\) | −2.14958e9 | −0.142121 | ||||||||
\(811\) | 9.75834e9 | 0.642396 | 0.321198 | − | 0.947012i | \(-0.395914\pi\) | ||||
0.321198 | + | 0.947012i | \(0.395914\pi\) | |||||||
\(812\) | −9.66804e8 | −0.0633712 | ||||||||
\(813\) | −6.15546e9 | −0.401739 | ||||||||
\(814\) | 3.34467e9 | 0.217354 | ||||||||
\(815\) | 2.95811e10 | 1.91409 | ||||||||
\(816\) | 6.25981e8 | 0.0403316 | ||||||||
\(817\) | 1.21252e9 | 0.0777881 | ||||||||
\(818\) | 1.73035e10 | 1.10534 | ||||||||
\(819\) | 5.49353e8 | 0.0349428 | ||||||||
\(820\) | −1.63898e10 | −1.03807 | ||||||||
\(821\) | −1.62521e9 | −0.102496 | −0.0512482 | − | 0.998686i | \(-0.516320\pi\) | ||||
−0.0512482 | + | 0.998686i | \(0.516320\pi\) | |||||||
\(822\) | −2.45766e9 | −0.154337 | ||||||||
\(823\) | 2.42225e10 | 1.51467 | 0.757337 | − | 0.653024i | \(-0.226500\pi\) | ||||
0.757337 | + | 0.653024i | \(0.226500\pi\) | |||||||
\(824\) | −9.44873e9 | −0.588340 | ||||||||
\(825\) | 4.67123e9 | 0.289629 | ||||||||
\(826\) | 6.74502e9 | 0.416440 | ||||||||
\(827\) | −1.15579e10 | −0.710576 | −0.355288 | − | 0.934757i | \(-0.615617\pi\) | ||||
−0.355288 | + | 0.934757i | \(0.615617\pi\) | |||||||
\(828\) | 3.06675e9 | 0.187747 | ||||||||
\(829\) | 1.35985e10 | 0.828991 | 0.414496 | − | 0.910051i | \(-0.363958\pi\) | ||||
0.414496 | + | 0.910051i | \(0.363958\pi\) | |||||||
\(830\) | −7.31341e9 | −0.443963 | ||||||||
\(831\) | −9.46786e9 | −0.572332 | ||||||||
\(832\) | −5.75930e8 | −0.0346688 | ||||||||
\(833\) | −6.65925e8 | −0.0399179 | ||||||||
\(834\) | 9.40926e9 | 0.561661 | ||||||||
\(835\) | −5.59918e10 | −3.32830 | ||||||||
\(836\) | −9.45979e8 | −0.0559963 | ||||||||
\(837\) | −1.69791e9 | −0.100087 | ||||||||
\(838\) | −1.00139e10 | −0.587826 | ||||||||
\(839\) | 2.11117e10 | 1.23412 | 0.617058 | − | 0.786918i | \(-0.288325\pi\) | ||||
0.617058 | + | 0.786918i | \(0.288325\pi\) | |||||||
\(840\) | −2.39738e9 | −0.139560 | ||||||||
\(841\) | −1.53102e10 | −0.887554 | ||||||||
\(842\) | −5.30154e8 | −0.0306062 | ||||||||
\(843\) | 6.72834e9 | 0.386823 | ||||||||
\(844\) | −6.74614e9 | −0.386240 | ||||||||
\(845\) | −2.44045e9 | −0.139146 | ||||||||
\(846\) | 5.31433e8 | 0.0301753 | ||||||||
\(847\) | 6.35827e9 | 0.359540 | ||||||||
\(848\) | 3.51839e9 | 0.198134 | ||||||||
\(849\) | 5.87472e9 | 0.329466 | ||||||||
\(850\) | −8.03800e9 | −0.448933 | ||||||||
\(851\) | −2.81960e10 | −1.56832 | ||||||||
\(852\) | −6.58634e8 | −0.0364843 | ||||||||
\(853\) | −3.53583e10 | −1.95061 | −0.975304 | − | 0.220865i | \(-0.929112\pi\) | ||||
−0.975304 | + | 0.220865i | \(0.929112\pi\) | |||||||
\(854\) | 1.28394e8 | 0.00705413 | ||||||||
\(855\) | −5.58974e9 | −0.305851 | ||||||||
\(856\) | 8.37869e9 | 0.456581 | ||||||||
\(857\) | −7.75588e9 | −0.420919 | −0.210459 | − | 0.977603i | \(-0.567496\pi\) | ||||
−0.210459 | + | 0.977603i | \(0.567496\pi\) | |||||||
\(858\) | −4.62520e8 | −0.0249991 | ||||||||
\(859\) | 2.62466e10 | 1.41285 | 0.706427 | − | 0.707786i | \(-0.250306\pi\) | ||||
0.706427 | + | 0.707786i | \(0.250306\pi\) | |||||||
\(860\) | −2.58717e9 | −0.138701 | ||||||||
\(861\) | 4.69076e9 | 0.250456 | ||||||||
\(862\) | 6.34996e9 | 0.337672 | ||||||||
\(863\) | 8.24013e8 | 0.0436412 | 0.0218206 | − | 0.999762i | \(-0.493054\pi\) | ||||
0.0218206 | + | 0.999762i | \(0.493054\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | 6.81324e9 | 0.357929 | ||||||||
\(866\) | −8.45016e8 | −0.0442132 | ||||||||
\(867\) | 1.02141e10 | 0.532272 | ||||||||
\(868\) | −1.89364e9 | −0.0982830 | ||||||||
\(869\) | −2.70914e9 | −0.140043 | ||||||||
\(870\) | 4.80980e9 | 0.247634 | ||||||||
\(871\) | −1.69455e9 | −0.0868944 | ||||||||
\(872\) | 6.50687e9 | 0.332326 | ||||||||
\(873\) | −5.25002e9 | −0.267061 | ||||||||
\(874\) | 7.97472e9 | 0.404041 | ||||||||
\(875\) | 1.72354e10 | 0.869745 | ||||||||
\(876\) | −2.62186e9 | −0.131778 | ||||||||
\(877\) | −2.28657e10 | −1.14468 | −0.572342 | − | 0.820015i | \(-0.693965\pi\) | ||||
−0.572342 | + | 0.820015i | \(0.693965\pi\) | |||||||
\(878\) | −2.63379e10 | −1.31326 | ||||||||
\(879\) | 2.28671e8 | 0.0113566 | ||||||||
\(880\) | 2.01844e9 | 0.0998450 | ||||||||
\(881\) | −3.19129e10 | −1.57236 | −0.786178 | − | 0.618000i | \(-0.787943\pi\) | ||||
−0.786178 | + | 0.618000i | \(0.787943\pi\) | |||||||
\(882\) | 6.86129e8 | 0.0336718 | ||||||||
\(883\) | 3.33372e10 | 1.62955 | 0.814774 | − | 0.579779i | \(-0.196861\pi\) | ||||
0.814774 | + | 0.579779i | \(0.196861\pi\) | |||||||
\(884\) | 7.95879e8 | 0.0387493 | ||||||||
\(885\) | −3.35561e10 | −1.62731 | ||||||||
\(886\) | −1.47341e10 | −0.711715 | ||||||||
\(887\) | −3.95761e10 | −1.90415 | −0.952073 | − | 0.305872i | \(-0.901052\pi\) | ||||
−0.952073 | + | 0.305872i | \(0.901052\pi\) | |||||||
\(888\) | 5.92994e9 | 0.284188 | ||||||||
\(889\) | 1.23904e10 | 0.591465 | ||||||||
\(890\) | −1.88565e10 | −0.896594 | ||||||||
\(891\) | −5.17966e8 | −0.0245318 | ||||||||
\(892\) | −2.22170e9 | −0.104811 | ||||||||
\(893\) | 1.38193e9 | 0.0649390 | ||||||||
\(894\) | −5.61764e9 | −0.262950 | ||||||||
\(895\) | 2.03119e10 | 0.947044 | ||||||||
\(896\) | −7.19323e8 | −0.0334077 | ||||||||
\(897\) | 3.89910e9 | 0.180381 | ||||||||
\(898\) | 1.22045e10 | 0.562411 | ||||||||
\(899\) | 3.79916e9 | 0.174393 | ||||||||
\(900\) | 8.28186e9 | 0.378686 | ||||||||
\(901\) | −4.86208e9 | −0.221455 | ||||||||
\(902\) | −3.94931e9 | −0.179184 | ||||||||
\(903\) | 7.40446e8 | 0.0334646 | ||||||||
\(904\) | −6.06643e9 | −0.273114 | ||||||||
\(905\) | 4.89154e10 | 2.19369 | ||||||||
\(906\) | −1.20353e10 | −0.537661 | ||||||||
\(907\) | −1.06912e10 | −0.475773 | −0.237886 | − | 0.971293i | \(-0.576455\pi\) | ||||
−0.237886 | + | 0.971293i | \(0.576455\pi\) | |||||||
\(908\) | −6.36697e9 | −0.282249 | ||||||||
\(909\) | −1.31845e10 | −0.582224 | ||||||||
\(910\) | −3.04806e9 | −0.134085 | ||||||||
\(911\) | −9.80586e9 | −0.429706 | −0.214853 | − | 0.976646i | \(-0.568927\pi\) | ||||
−0.214853 | + | 0.976646i | \(0.568927\pi\) | |||||||
\(912\) | −1.67718e9 | −0.0732144 | ||||||||
\(913\) | −1.76225e9 | −0.0766336 | ||||||||
\(914\) | 4.35006e9 | 0.188444 | ||||||||
\(915\) | −6.38756e8 | −0.0275652 | ||||||||
\(916\) | 8.71904e8 | 0.0374830 | ||||||||
\(917\) | 6.40019e9 | 0.274094 | ||||||||
\(918\) | 8.91289e8 | 0.0380250 | ||||||||
\(919\) | 4.41172e10 | 1.87501 | 0.937506 | − | 0.347970i | \(-0.113129\pi\) | ||||
0.937506 | + | 0.347970i | \(0.113129\pi\) | |||||||
\(920\) | −1.70157e10 | −0.720432 | ||||||||
\(921\) | 2.14833e10 | 0.906136 | ||||||||
\(922\) | −1.61292e10 | −0.677725 | ||||||||
\(923\) | −8.37396e8 | −0.0350530 | ||||||||
\(924\) | −5.77676e8 | −0.0240898 | ||||||||
\(925\) | −7.61443e10 | −3.16331 | ||||||||
\(926\) | 1.68771e10 | 0.698488 | ||||||||
\(927\) | −1.34534e10 | −0.554692 | ||||||||
\(928\) | 1.44316e9 | 0.0592784 | ||||||||
\(929\) | 2.93273e9 | 0.120010 | 0.0600050 | − | 0.998198i | \(-0.480888\pi\) | ||||
0.0600050 | + | 0.998198i | \(0.480888\pi\) | |||||||
\(930\) | 9.42077e9 | 0.384057 | ||||||||
\(931\) | 1.78420e9 | 0.0724635 | ||||||||
\(932\) | 2.29214e10 | 0.927440 | ||||||||
\(933\) | −1.89282e10 | −0.762998 | ||||||||
\(934\) | −1.50012e10 | −0.602437 | ||||||||
\(935\) | −2.78929e9 | −0.111597 | ||||||||
\(936\) | −8.20026e8 | −0.0326860 | ||||||||
\(937\) | −3.65235e10 | −1.45039 | −0.725193 | − | 0.688546i | \(-0.758250\pi\) | ||||
−0.725193 | + | 0.688546i | \(0.758250\pi\) | |||||||
\(938\) | −2.11646e9 | −0.0837335 | ||||||||
\(939\) | 1.59187e10 | 0.627448 | ||||||||
\(940\) | −2.94863e9 | −0.115790 | ||||||||
\(941\) | 4.53786e10 | 1.77537 | 0.887683 | − | 0.460455i | \(-0.152314\pi\) | ||||
0.887683 | + | 0.460455i | \(0.152314\pi\) | |||||||
\(942\) | −1.25739e10 | −0.490108 | ||||||||
\(943\) | 3.32932e10 | 1.29290 | ||||||||
\(944\) | −1.00684e10 | −0.389544 | ||||||||
\(945\) | −3.41346e9 | −0.131578 | ||||||||
\(946\) | −6.23407e8 | −0.0239416 | ||||||||
\(947\) | 2.59610e10 | 0.993338 | 0.496669 | − | 0.867940i | \(-0.334556\pi\) | ||||
0.496669 | + | 0.867940i | \(0.334556\pi\) | |||||||
\(948\) | −4.80318e9 | −0.183105 | ||||||||
\(949\) | −3.33346e9 | −0.126609 | ||||||||
\(950\) | 2.15360e10 | 0.814953 | ||||||||
\(951\) | −3.06018e9 | −0.115376 | ||||||||
\(952\) | 9.94034e8 | 0.0373398 | ||||||||
\(953\) | −3.90857e10 | −1.46283 | −0.731414 | − | 0.681934i | \(-0.761139\pi\) | ||||
−0.731414 | + | 0.681934i | \(0.761139\pi\) | |||||||
\(954\) | 5.00959e9 | 0.186803 | ||||||||
\(955\) | 3.10195e10 | 1.15245 | ||||||||
\(956\) | 9.33167e9 | 0.345428 | ||||||||
\(957\) | 1.15898e9 | 0.0427447 | ||||||||
\(958\) | 2.89393e8 | 0.0106343 | ||||||||
\(959\) | −3.90267e9 | −0.142888 | ||||||||
\(960\) | 3.57860e9 | 0.130546 | ||||||||
\(961\) | −2.00713e10 | −0.729533 | ||||||||
\(962\) | 7.53940e9 | 0.273039 | ||||||||
\(963\) | 1.19298e10 | 0.430469 | ||||||||
\(964\) | −1.02353e10 | −0.367987 | ||||||||
\(965\) | 3.24634e10 | 1.16292 | ||||||||
\(966\) | 4.86988e9 | 0.173820 | ||||||||
\(967\) | 2.11853e10 | 0.753429 | 0.376715 | − | 0.926329i | \(-0.377054\pi\) | ||||
0.376715 | + | 0.926329i | \(0.377054\pi\) | |||||||
\(968\) | −9.49107e9 | −0.336319 | ||||||||
\(969\) | 2.31769e9 | 0.0818319 | ||||||||
\(970\) | 2.91295e10 | 1.02478 | ||||||||
\(971\) | −2.09826e10 | −0.735517 | −0.367758 | − | 0.929921i | \(-0.619875\pi\) | ||||
−0.367758 | + | 0.929921i | \(0.619875\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | 1.49416e10 | 0.519997 | ||||||||
\(974\) | −8.17884e9 | −0.283619 | ||||||||
\(975\) | 1.05297e10 | 0.363830 | ||||||||
\(976\) | −1.91656e8 | −0.00659854 | ||||||||
\(977\) | −3.18014e10 | −1.09098 | −0.545488 | − | 0.838118i | \(-0.683656\pi\) | ||||
−0.545488 | + | 0.838118i | \(0.683656\pi\) | |||||||
\(978\) | 1.26374e10 | 0.431989 | ||||||||
\(979\) | −4.54368e9 | −0.154764 | ||||||||
\(980\) | −3.80695e9 | −0.129207 | ||||||||
\(981\) | 9.26466e9 | 0.313320 | ||||||||
\(982\) | −2.61405e10 | −0.880893 | ||||||||
\(983\) | 4.32852e9 | 0.145346 | 0.0726728 | − | 0.997356i | \(-0.476847\pi\) | ||||
0.0726728 | + | 0.997356i | \(0.476847\pi\) | |||||||
\(984\) | −7.00195e9 | −0.234280 | ||||||||
\(985\) | −3.10979e10 | −1.03682 | ||||||||
\(986\) | −1.99430e9 | −0.0662555 | ||||||||
\(987\) | 8.43896e8 | 0.0279369 | ||||||||
\(988\) | −2.13238e9 | −0.0703421 | ||||||||
\(989\) | 5.25540e9 | 0.172750 | ||||||||
\(990\) | 2.87391e9 | 0.0941348 | ||||||||
\(991\) | −3.54394e10 | −1.15672 | −0.578360 | − | 0.815782i | \(-0.696307\pi\) | ||||
−0.578360 | + | 0.815782i | \(0.696307\pi\) | |||||||
\(992\) | 2.82666e9 | 0.0919353 | ||||||||
\(993\) | −1.43935e9 | −0.0466491 | ||||||||
\(994\) | −1.04589e9 | −0.0337779 | ||||||||
\(995\) | 3.90973e10 | 1.25825 | ||||||||
\(996\) | −3.12438e9 | −0.100197 | ||||||||
\(997\) | −3.65554e10 | −1.16820 | −0.584102 | − | 0.811680i | \(-0.698553\pi\) | ||||
−0.584102 | + | 0.811680i | \(0.698553\pi\) | |||||||
\(998\) | −4.08201e10 | −1.29992 | ||||||||
\(999\) | 8.44322e9 | 0.267935 |
(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 | 546.8.a.l.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.l.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial |