Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 152x^{5} + 358x^{4} + 5771x^{3} - 13444x^{2} - 51316x + 92576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.33276\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33276 | −0.412378 | −0.206189 | − | 0.978512i | \(-0.566106\pi\) | ||||
−0.206189 | + | 0.978512i | \(0.566106\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −26.5582 | −0.829944 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 20.9949 | 0.238087 | ||||||||
\(7\) | 146.260 | 1.12818 | 0.564092 | − | 0.825712i | \(-0.309226\pi\) | ||||
0.564092 | + | 0.825712i | \(0.309226\pi\) | |||||||
\(8\) | 136.602 | 0.754629 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 239.024 | 0.479169 | ||||||||
\(13\) | −158.241 | −0.259694 | −0.129847 | − | 0.991534i | \(-0.541449\pi\) | ||||
−0.129847 | + | 0.991534i | \(0.541449\pi\) | |||||||
\(14\) | −341.189 | −0.465238 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 531.202 | 0.518752 | ||||||||
\(17\) | −1926.04 | −1.61638 | −0.808189 | − | 0.588923i | \(-0.799552\pi\) | ||||
−0.808189 | + | 0.588923i | \(0.799552\pi\) | |||||||
\(18\) | −188.954 | −0.137459 | ||||||||
\(19\) | −32.9364 | −0.0209311 | −0.0104656 | − | 0.999945i | \(-0.503331\pi\) | ||||
−0.0104656 | + | 0.999945i | \(0.503331\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1316.34 | −0.651358 | ||||||||
\(22\) | −282.264 | −0.124337 | ||||||||
\(23\) | 2077.06 | 0.818710 | 0.409355 | − | 0.912375i | \(-0.365754\pi\) | ||||
0.409355 | + | 0.912375i | \(0.365754\pi\) | |||||||
\(24\) | −1229.42 | −0.435685 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 369.139 | 0.107092 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −3884.40 | −0.936330 | ||||||||
\(29\) | 1641.87 | 0.362530 | 0.181265 | − | 0.983434i | \(-0.441981\pi\) | ||||
0.181265 | + | 0.983434i | \(0.441981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3563.71 | −0.666036 | −0.333018 | − | 0.942920i | \(-0.608067\pi\) | ||||
−0.333018 | + | 0.942920i | \(0.608067\pi\) | |||||||
\(32\) | −5610.45 | −0.968551 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 4492.99 | 0.666559 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2151.22 | −0.276648 | ||||||||
\(37\) | −5396.83 | −0.648089 | −0.324045 | − | 0.946042i | \(-0.605043\pi\) | ||||
−0.324045 | + | 0.946042i | \(0.605043\pi\) | |||||||
\(38\) | 76.8329 | 0.00863154 | ||||||||
\(39\) | 1424.17 | 0.149934 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2803.48 | 0.260458 | 0.130229 | − | 0.991484i | \(-0.458429\pi\) | ||||
0.130229 | + | 0.991484i | \(0.458429\pi\) | |||||||
\(42\) | 3070.71 | 0.268606 | ||||||||
\(43\) | −1140.23 | −0.0940417 | −0.0470208 | − | 0.998894i | \(-0.514973\pi\) | ||||
−0.0470208 | + | 0.998894i | \(0.514973\pi\) | |||||||
\(44\) | −3213.54 | −0.250238 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4845.29 | −0.337618 | ||||||||
\(47\) | −15797.7 | −1.04316 | −0.521578 | − | 0.853204i | \(-0.674656\pi\) | ||||
−0.521578 | + | 0.853204i | \(0.674656\pi\) | |||||||
\(48\) | −4780.82 | −0.299502 | ||||||||
\(49\) | 4584.95 | 0.272800 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 17334.4 | 0.933216 | ||||||||
\(52\) | 4202.61 | 0.215531 | ||||||||
\(53\) | 24043.7 | 1.17574 | 0.587871 | − | 0.808955i | \(-0.299966\pi\) | ||||
0.587871 | + | 0.808955i | \(0.299966\pi\) | |||||||
\(54\) | 1700.58 | 0.0793622 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 19979.4 | 0.851360 | ||||||||
\(57\) | 296.428 | 0.0120846 | ||||||||
\(58\) | −3830.09 | −0.149499 | ||||||||
\(59\) | 5002.23 | 0.187083 | 0.0935414 | − | 0.995615i | \(-0.470181\pi\) | ||||
0.0935414 | + | 0.995615i | \(0.470181\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4798.86 | −0.165125 | −0.0825626 | − | 0.996586i | \(-0.526310\pi\) | ||||
−0.0825626 | + | 0.996586i | \(0.526310\pi\) | |||||||
\(62\) | 8313.28 | 0.274659 | ||||||||
\(63\) | 11847.0 | 0.376061 | ||||||||
\(64\) | −3910.63 | −0.119343 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2540.38 | 0.0717858 | ||||||||
\(67\) | 34126.4 | 0.928759 | 0.464379 | − | 0.885636i | \(-0.346277\pi\) | ||||
0.464379 | + | 0.885636i | \(0.346277\pi\) | |||||||
\(68\) | 51152.2 | 1.34150 | ||||||||
\(69\) | −18693.6 | −0.472683 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10059.7 | 0.236832 | 0.118416 | − | 0.992964i | \(-0.462218\pi\) | ||||
0.118416 | + | 0.992964i | \(0.462218\pi\) | |||||||
\(72\) | 11064.8 | 0.251543 | ||||||||
\(73\) | 71743.6 | 1.57571 | 0.787855 | − | 0.615861i | \(-0.211192\pi\) | ||||
0.787855 | + | 0.615861i | \(0.211192\pi\) | |||||||
\(74\) | 12589.5 | 0.267258 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 874.733 | 0.0173717 | ||||||||
\(77\) | 17697.4 | 0.340160 | ||||||||
\(78\) | −3322.25 | −0.0618296 | ||||||||
\(79\) | −14305.9 | −0.257899 | −0.128949 | − | 0.991651i | \(-0.541160\pi\) | ||||
−0.128949 | + | 0.991651i | \(0.541160\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −6539.84 | −0.107407 | ||||||||
\(83\) | 66464.5 | 1.05900 | 0.529498 | − | 0.848311i | \(-0.322380\pi\) | ||||
0.529498 | + | 0.848311i | \(0.322380\pi\) | |||||||
\(84\) | 34959.6 | 0.540591 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2659.88 | 0.0387807 | ||||||||
\(87\) | −14776.8 | −0.209307 | ||||||||
\(88\) | 16528.9 | 0.227529 | ||||||||
\(89\) | −11104.6 | −0.148603 | −0.0743017 | − | 0.997236i | \(-0.523673\pi\) | ||||
−0.0743017 | + | 0.997236i | \(0.523673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −23144.4 | −0.292982 | ||||||||
\(92\) | −55163.1 | −0.679484 | ||||||||
\(93\) | 32073.4 | 0.384536 | ||||||||
\(94\) | 36852.3 | 0.430174 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 50494.0 | 0.559193 | ||||||||
\(97\) | 56522.6 | 0.609948 | 0.304974 | − | 0.952361i | \(-0.401352\pi\) | ||||
0.304974 | + | 0.952361i | \(0.401352\pi\) | |||||||
\(98\) | −10695.6 | −0.112497 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −21709.1 | −0.211758 | −0.105879 | − | 0.994379i | \(-0.533766\pi\) | ||||
−0.105879 | + | 0.994379i | \(0.533766\pi\) | |||||||
\(102\) | −40436.9 | −0.384838 | ||||||||
\(103\) | 15441.9 | 0.143419 | 0.0717096 | − | 0.997426i | \(-0.477155\pi\) | ||||
0.0717096 | + | 0.997426i | \(0.477155\pi\) | |||||||
\(104\) | −21616.1 | −0.195972 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −56088.3 | −0.484850 | ||||||||
\(107\) | 33358.3 | 0.281673 | 0.140836 | − | 0.990033i | \(-0.455021\pi\) | ||||
0.140836 | + | 0.990033i | \(0.455021\pi\) | |||||||
\(108\) | 19360.9 | 0.159723 | ||||||||
\(109\) | −94499.4 | −0.761838 | −0.380919 | − | 0.924608i | \(-0.624392\pi\) | ||||
−0.380919 | + | 0.924608i | \(0.624392\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 48571.5 | 0.374174 | ||||||||
\(112\) | 77693.6 | 0.585248 | ||||||||
\(113\) | −150985. | −1.11234 | −0.556170 | − | 0.831069i | \(-0.687730\pi\) | ||||
−0.556170 | + | 0.831069i | \(0.687730\pi\) | |||||||
\(114\) | −691.496 | −0.00498342 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −43605.1 | −0.300879 | ||||||||
\(117\) | −12817.5 | −0.0865646 | ||||||||
\(118\) | −11669.0 | −0.0771488 | ||||||||
\(119\) | −281702. | −1.82357 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 11194.6 | 0.0680940 | ||||||||
\(123\) | −25231.3 | −0.150375 | ||||||||
\(124\) | 94645.7 | 0.552773 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −27636.3 | −0.155079 | ||||||||
\(127\) | 348511. | 1.91737 | 0.958687 | − | 0.284462i | \(-0.0918149\pi\) | ||||
0.958687 | + | 0.284462i | \(0.0918149\pi\) | |||||||
\(128\) | 188657. | 1.01777 | ||||||||
\(129\) | 10262.0 | 0.0542950 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 59482.3 | 0.302837 | 0.151419 | − | 0.988470i | \(-0.451616\pi\) | ||||
0.151419 | + | 0.988470i | \(0.451616\pi\) | |||||||
\(132\) | 28921.9 | 0.144475 | ||||||||
\(133\) | −4817.28 | −0.0236142 | ||||||||
\(134\) | −79608.7 | −0.383000 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −263102. | −1.21977 | ||||||||
\(137\) | −148254. | −0.674848 | −0.337424 | − | 0.941353i | \(-0.609556\pi\) | ||||
−0.337424 | + | 0.941353i | \(0.609556\pi\) | |||||||
\(138\) | 43607.7 | 0.194924 | ||||||||
\(139\) | −196689. | −0.863462 | −0.431731 | − | 0.902002i | \(-0.642097\pi\) | ||||
−0.431731 | + | 0.902002i | \(0.642097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 142179. | 0.602266 | ||||||||
\(142\) | −23467.0 | −0.0976645 | ||||||||
\(143\) | −19147.2 | −0.0783006 | ||||||||
\(144\) | 43027.4 | 0.172917 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −167361. | −0.649788 | ||||||||
\(147\) | −41264.5 | −0.157501 | ||||||||
\(148\) | 143330. | 0.537878 | ||||||||
\(149\) | −305815. | −1.12848 | −0.564239 | − | 0.825611i | \(-0.690830\pi\) | ||||
−0.564239 | + | 0.825611i | \(0.690830\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −220420. | −0.786701 | −0.393350 | − | 0.919389i | \(-0.628684\pi\) | ||||
−0.393350 | + | 0.919389i | \(0.628684\pi\) | |||||||
\(152\) | −4499.20 | −0.0157952 | ||||||||
\(153\) | −156009. | −0.538793 | ||||||||
\(154\) | −41283.9 | −0.140275 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −37823.5 | −0.124437 | ||||||||
\(157\) | −585267. | −1.89498 | −0.947491 | − | 0.319782i | \(-0.896390\pi\) | ||||
−0.947491 | + | 0.319782i | \(0.896390\pi\) | |||||||
\(158\) | 33372.4 | 0.106352 | ||||||||
\(159\) | −216393. | −0.678815 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 303791. | 0.923656 | ||||||||
\(162\) | −15305.3 | −0.0458198 | ||||||||
\(163\) | 109151. | 0.321780 | 0.160890 | − | 0.986972i | \(-0.448564\pi\) | ||||
0.160890 | + | 0.986972i | \(0.448564\pi\) | |||||||
\(164\) | −74455.3 | −0.216165 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −155046. | −0.436707 | ||||||||
\(167\) | −243334. | −0.675168 | −0.337584 | − | 0.941295i | \(-0.609610\pi\) | ||||
−0.337584 | + | 0.941295i | \(0.609610\pi\) | |||||||
\(168\) | −179815. | −0.491533 | ||||||||
\(169\) | −346253. | −0.932559 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2667.85 | −0.00697704 | ||||||||
\(172\) | 30282.4 | 0.0780494 | ||||||||
\(173\) | −398905. | −1.01334 | −0.506669 | − | 0.862141i | \(-0.669123\pi\) | ||||
−0.506669 | + | 0.862141i | \(0.669123\pi\) | |||||||
\(174\) | 34470.8 | 0.0863134 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 64275.5 | 0.156410 | ||||||||
\(177\) | −45020.1 | −0.108012 | ||||||||
\(178\) | 25904.5 | 0.0612808 | ||||||||
\(179\) | 198924. | 0.464039 | 0.232019 | − | 0.972711i | \(-0.425467\pi\) | ||||
0.232019 | + | 0.972711i | \(0.425467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −474113. | −1.07569 | −0.537843 | − | 0.843045i | \(-0.680761\pi\) | ||||
−0.537843 | + | 0.843045i | \(0.680761\pi\) | |||||||
\(182\) | 53990.3 | 0.120819 | ||||||||
\(183\) | 43189.7 | 0.0953350 | ||||||||
\(184\) | 283732. | 0.617822 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −74819.5 | −0.158574 | ||||||||
\(187\) | −233051. | −0.487356 | ||||||||
\(188\) | 419559. | 0.865761 | ||||||||
\(189\) | −106623. | −0.217119 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 201548. | 0.399757 | 0.199878 | − | 0.979821i | \(-0.435945\pi\) | ||||
0.199878 | + | 0.979821i | \(0.435945\pi\) | |||||||
\(192\) | 35195.7 | 0.0689028 | ||||||||
\(193\) | 205191. | 0.396519 | 0.198260 | − | 0.980150i | \(-0.436471\pi\) | ||||
0.198260 | + | 0.980150i | \(0.436471\pi\) | |||||||
\(194\) | −131854. | −0.251529 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −121768. | −0.226409 | ||||||||
\(197\) | −99895.6 | −0.183392 | −0.0916961 | − | 0.995787i | \(-0.529229\pi\) | ||||
−0.0916961 | + | 0.995787i | \(0.529229\pi\) | |||||||
\(198\) | −22863.4 | −0.0414455 | ||||||||
\(199\) | −371365. | −0.664765 | −0.332382 | − | 0.943145i | \(-0.607852\pi\) | ||||
−0.332382 | + | 0.943145i | \(0.607852\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −307137. | −0.536219 | ||||||||
\(202\) | 50642.3 | 0.0873242 | ||||||||
\(203\) | 240139. | 0.409000 | ||||||||
\(204\) | −460370. | −0.774518 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −36022.3 | −0.0591429 | ||||||||
\(207\) | 168242. | 0.272903 | ||||||||
\(208\) | −84058.1 | −0.134717 | ||||||||
\(209\) | −3985.31 | −0.00631097 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −285877. | −0.442052 | −0.221026 | − | 0.975268i | \(-0.570940\pi\) | ||||
−0.221026 | + | 0.975268i | \(0.570940\pi\) | |||||||
\(212\) | −638558. | −0.975800 | ||||||||
\(213\) | −90537.7 | −0.136735 | ||||||||
\(214\) | −77817.0 | −0.116156 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −99583.2 | −0.145228 | ||||||||
\(217\) | −521227. | −0.751412 | ||||||||
\(218\) | 220445. | 0.314165 | ||||||||
\(219\) | −645693. | −0.909737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 304779. | 0.419763 | ||||||||
\(222\) | −113306. | −0.154301 | ||||||||
\(223\) | 1.12395e6 | 1.51351 | 0.756756 | − | 0.653698i | \(-0.226783\pi\) | ||||
0.756756 | + | 0.653698i | \(0.226783\pi\) | |||||||
\(224\) | −820583. | −1.09270 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 352212. | 0.458705 | ||||||||
\(227\) | 998160. | 1.28569 | 0.642844 | − | 0.765997i | \(-0.277754\pi\) | ||||
0.642844 | + | 0.765997i | \(0.277754\pi\) | |||||||
\(228\) | −7872.60 | −0.0100295 | ||||||||
\(229\) | −964804. | −1.21577 | −0.607884 | − | 0.794026i | \(-0.707981\pi\) | ||||
−0.607884 | + | 0.794026i | \(0.707981\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −159277. | −0.196392 | ||||||||
\(232\) | 224283. | 0.273575 | ||||||||
\(233\) | 550785. | 0.664649 | 0.332324 | − | 0.943165i | \(-0.392167\pi\) | ||||
0.332324 | + | 0.943165i | \(0.392167\pi\) | |||||||
\(234\) | 29900.3 | 0.0356973 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −132850. | −0.155268 | ||||||||
\(237\) | 128754. | 0.148898 | ||||||||
\(238\) | 657144. | 0.752001 | ||||||||
\(239\) | −413388. | −0.468127 | −0.234063 | − | 0.972221i | \(-0.575202\pi\) | ||||
−0.234063 | + | 0.972221i | \(0.575202\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 213029. | 0.236263 | 0.118132 | − | 0.992998i | \(-0.462310\pi\) | ||||
0.118132 | + | 0.992998i | \(0.462310\pi\) | |||||||
\(242\) | −34154.0 | −0.0374889 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 127449. | 0.137045 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 58858.6 | 0.0620115 | ||||||||
\(247\) | 5211.90 | 0.00543568 | ||||||||
\(248\) | −486811. | −0.502610 | ||||||||
\(249\) | −598181. | −0.611412 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.62034e6 | 1.62339 | 0.811694 | − | 0.584082i | \(-0.198546\pi\) | ||||
0.811694 | + | 0.584082i | \(0.198546\pi\) | |||||||
\(252\) | −314637. | −0.312110 | ||||||||
\(253\) | 251325. | 0.246850 | ||||||||
\(254\) | −812993. | −0.790683 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −314951. | −0.300361 | ||||||||
\(257\) | −1.03963e6 | −0.981849 | −0.490924 | − | 0.871202i | \(-0.663341\pi\) | ||||
−0.490924 | + | 0.871202i | \(0.663341\pi\) | |||||||
\(258\) | −23938.9 | −0.0223901 | ||||||||
\(259\) | −789340. | −0.731164 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 132991. | 0.120843 | ||||||||
\(262\) | −138758. | −0.124883 | ||||||||
\(263\) | −207828. | −0.185274 | −0.0926372 | − | 0.995700i | \(-0.529530\pi\) | ||||
−0.0926372 | + | 0.995700i | \(0.529530\pi\) | |||||||
\(264\) | −148760. | −0.131364 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11237.6 | 0.00973796 | ||||||||
\(267\) | 99941.6 | 0.0857963 | ||||||||
\(268\) | −906335. | −0.770818 | ||||||||
\(269\) | 302188. | 0.254622 | 0.127311 | − | 0.991863i | \(-0.459365\pi\) | ||||
0.127311 | + | 0.991863i | \(0.459365\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.17189e6 | 0.969310 | 0.484655 | − | 0.874705i | \(-0.338945\pi\) | ||||
0.484655 | + | 0.874705i | \(0.338945\pi\) | |||||||
\(272\) | −1.02312e6 | −0.838499 | ||||||||
\(273\) | 208299. | 0.169153 | ||||||||
\(274\) | 345842. | 0.278292 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 496468. | 0.392300 | ||||||||
\(277\) | −2.15093e6 | −1.68433 | −0.842164 | − | 0.539221i | \(-0.818719\pi\) | ||||
−0.842164 | + | 0.539221i | \(0.818719\pi\) | |||||||
\(278\) | 458829. | 0.356073 | ||||||||
\(279\) | −288660. | −0.222012 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.31245e6 | −1.74705 | −0.873527 | − | 0.486775i | \(-0.838173\pi\) | ||||
−0.873527 | + | 0.486775i | \(0.838173\pi\) | |||||||
\(282\) | −331670. | −0.248361 | ||||||||
\(283\) | 655859. | 0.486793 | 0.243397 | − | 0.969927i | \(-0.421738\pi\) | ||||
0.243397 | + | 0.969927i | \(0.421738\pi\) | |||||||
\(284\) | −267169. | −0.196558 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 44665.9 | 0.0322894 | ||||||||
\(287\) | 410036. | 0.293844 | ||||||||
\(288\) | −454446. | −0.322850 | ||||||||
\(289\) | 2.28977e6 | 1.61268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −508703. | −0.352154 | ||||||||
\(292\) | −1.90538e6 | −1.30775 | ||||||||
\(293\) | −602815. | −0.410218 | −0.205109 | − | 0.978739i | \(-0.565755\pi\) | ||||
−0.205109 | + | 0.978739i | \(0.565755\pi\) | |||||||
\(294\) | 96260.3 | 0.0649500 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −737221. | −0.489067 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 713394. | 0.465360 | ||||||||
\(299\) | −328677. | −0.212614 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −166770. | −0.106096 | ||||||||
\(302\) | 514189. | 0.324418 | ||||||||
\(303\) | 195382. | 0.122258 | ||||||||
\(304\) | −17495.9 | −0.0108581 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 363932. | 0.222186 | ||||||||
\(307\) | −62538.0 | −0.0378703 | −0.0189351 | − | 0.999821i | \(-0.506028\pi\) | ||||
−0.0189351 | + | 0.999821i | \(0.506028\pi\) | |||||||
\(308\) | −470013. | −0.282314 | ||||||||
\(309\) | −138977. | −0.0828031 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.16927e6 | −0.685510 | −0.342755 | − | 0.939425i | \(-0.611360\pi\) | ||||
−0.342755 | + | 0.939425i | \(0.611360\pi\) | |||||||
\(312\) | 194545. | 0.113145 | ||||||||
\(313\) | 2.51021e6 | 1.44827 | 0.724135 | − | 0.689659i | \(-0.242239\pi\) | ||||
0.724135 | + | 0.689659i | \(0.242239\pi\) | |||||||
\(314\) | 1.36529e6 | 0.781449 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 379940. | 0.214041 | ||||||||
\(317\) | −1.58370e6 | −0.885167 | −0.442584 | − | 0.896727i | \(-0.645938\pi\) | ||||
−0.442584 | + | 0.896727i | \(0.645938\pi\) | |||||||
\(318\) | 504794. | 0.279928 | ||||||||
\(319\) | 198666. | 0.109307 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −300225. | −0.162624 | ||||||||
\(322\) | −708672. | −0.380895 | ||||||||
\(323\) | 63436.9 | 0.0338326 | ||||||||
\(324\) | −174248. | −0.0922160 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −254623. | −0.132695 | ||||||||
\(327\) | 850495. | 0.439848 | ||||||||
\(328\) | 382961. | 0.196549 | ||||||||
\(329\) | −2.31057e6 | −1.17687 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.73382e6 | −1.37151 | −0.685757 | − | 0.727831i | \(-0.740529\pi\) | ||||
−0.685757 | + | 0.727831i | \(0.740529\pi\) | |||||||
\(332\) | −1.76518e6 | −0.878908 | ||||||||
\(333\) | −437144. | −0.216030 | ||||||||
\(334\) | 567641. | 0.278424 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −699242. | −0.337893 | ||||||||
\(337\) | −3.08115e6 | −1.47787 | −0.738937 | − | 0.673774i | \(-0.764672\pi\) | ||||
−0.738937 | + | 0.673774i | \(0.764672\pi\) | |||||||
\(338\) | 807725. | 0.384567 | ||||||||
\(339\) | 1.35886e6 | 0.642210 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −431209. | −0.200817 | ||||||||
\(342\) | 6223.46 | 0.00287718 | ||||||||
\(343\) | −1.78760e6 | −0.820416 | ||||||||
\(344\) | −155758. | −0.0709666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 930551. | 0.417878 | ||||||||
\(347\) | −1.31963e6 | −0.588338 | −0.294169 | − | 0.955753i | \(-0.595043\pi\) | ||||
−0.294169 | + | 0.955753i | \(0.595043\pi\) | |||||||
\(348\) | 392446. | 0.173713 | ||||||||
\(349\) | −4.16706e6 | −1.83133 | −0.915664 | − | 0.401944i | \(-0.868335\pi\) | ||||
−0.915664 | + | 0.401944i | \(0.868335\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 115358. | 0.0499781 | ||||||||
\(352\) | −678864. | −0.292029 | ||||||||
\(353\) | 3.56475e6 | 1.52262 | 0.761310 | − | 0.648388i | \(-0.224556\pi\) | ||||
0.761310 | + | 0.648388i | \(0.224556\pi\) | |||||||
\(354\) | 105021. | 0.0445419 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 294919. | 0.123333 | ||||||||
\(357\) | 2.53532e6 | 1.05284 | ||||||||
\(358\) | −464042. | −0.191359 | ||||||||
\(359\) | −402049. | −0.164643 | −0.0823215 | − | 0.996606i | \(-0.526233\pi\) | ||||
−0.0823215 | + | 0.996606i | \(0.526233\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47501e6 | −0.999562 | ||||||||
\(362\) | 1.10599e6 | 0.443589 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | 614673. | 0.243159 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −100751. | −0.0393141 | ||||||||
\(367\) | 1.69899e6 | 0.658455 | 0.329227 | − | 0.944251i | \(-0.393212\pi\) | ||||
0.329227 | + | 0.944251i | \(0.393212\pi\) | |||||||
\(368\) | 1.10334e6 | 0.424708 | ||||||||
\(369\) | 227081. | 0.0868192 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.51663e6 | 1.32645 | ||||||||
\(372\) | −851812. | −0.319144 | ||||||||
\(373\) | −1.78079e6 | −0.662738 | −0.331369 | − | 0.943501i | \(-0.607510\pi\) | ||||
−0.331369 | + | 0.943501i | \(0.607510\pi\) | |||||||
\(374\) | 543652. | 0.200975 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.15800e6 | −0.787195 | ||||||||
\(377\) | −259811. | −0.0941466 | ||||||||
\(378\) | 248727. | 0.0895352 | ||||||||
\(379\) | −2.12968e6 | −0.761580 | −0.380790 | − | 0.924662i | \(-0.624348\pi\) | ||||
−0.380790 | + | 0.924662i | \(0.624348\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.13660e6 | −1.10700 | ||||||||
\(382\) | −470165. | −0.164851 | ||||||||
\(383\) | 3.06780e6 | 1.06864 | 0.534318 | − | 0.845284i | \(-0.320568\pi\) | ||||
0.534318 | + | 0.845284i | \(0.320568\pi\) | |||||||
\(384\) | −1.69791e6 | −0.587607 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −478661. | −0.163516 | ||||||||
\(387\) | −92358.4 | −0.0313472 | ||||||||
\(388\) | −1.50114e6 | −0.506223 | ||||||||
\(389\) | 784173. | 0.262747 | 0.131374 | − | 0.991333i | \(-0.458061\pi\) | ||||
0.131374 | + | 0.991333i | \(0.458061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00051e6 | −1.32335 | ||||||||
\(392\) | 626315. | 0.205863 | ||||||||
\(393\) | −535340. | −0.174843 | ||||||||
\(394\) | 233033. | 0.0756269 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −260297. | −0.0834125 | ||||||||
\(397\) | 4.54374e6 | 1.44690 | 0.723448 | − | 0.690379i | \(-0.242556\pi\) | ||||
0.723448 | + | 0.690379i | \(0.242556\pi\) | |||||||
\(398\) | 866306. | 0.274134 | ||||||||
\(399\) | 43355.5 | 0.0136336 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.45110e6 | 1.07176 | 0.535879 | − | 0.844295i | \(-0.319980\pi\) | ||||
0.535879 | + | 0.844295i | \(0.319980\pi\) | |||||||
\(402\) | 716478. | 0.221125 | ||||||||
\(403\) | 563926. | 0.172965 | ||||||||
\(404\) | 576556. | 0.175747 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −560188. | −0.168663 | ||||||||
\(407\) | −653017. | −0.195406 | ||||||||
\(408\) | 2.36791e6 | 0.704232 | ||||||||
\(409\) | 3.80281e6 | 1.12408 | 0.562039 | − | 0.827111i | \(-0.310017\pi\) | ||||
0.562039 | + | 0.827111i | \(0.310017\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.33429e6 | 0.389624 | ||||||||
\(412\) | −410109. | −0.119030 | ||||||||
\(413\) | 731626. | 0.211064 | ||||||||
\(414\) | −392469. | −0.112539 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 887804. | 0.251527 | ||||||||
\(417\) | 1.77020e6 | 0.498520 | ||||||||
\(418\) | 9296.78 | 0.00260251 | ||||||||
\(419\) | −2.60701e6 | −0.725450 | −0.362725 | − | 0.931896i | \(-0.618153\pi\) | ||||
−0.362725 | + | 0.931896i | \(0.618153\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.05826e6 | −1.39090 | −0.695449 | − | 0.718575i | \(-0.744795\pi\) | ||||
−0.695449 | + | 0.718575i | \(0.744795\pi\) | |||||||
\(422\) | 666883. | 0.182292 | ||||||||
\(423\) | −1.27961e6 | −0.347718 | ||||||||
\(424\) | 3.28443e6 | 0.887248 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 211203. | 0.0563866 | ||||||||
\(427\) | −701880. | −0.186292 | ||||||||
\(428\) | −885937. | −0.233773 | ||||||||
\(429\) | 172325. | 0.0452069 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.62455e6 | −0.939856 | −0.469928 | − | 0.882705i | \(-0.655720\pi\) | ||||
−0.469928 | + | 0.882705i | \(0.655720\pi\) | |||||||
\(432\) | −387246. | −0.0998339 | ||||||||
\(433\) | −6.53089e6 | −1.67399 | −0.836995 | − | 0.547211i | \(-0.815690\pi\) | ||||
−0.836995 | + | 0.547211i | \(0.815690\pi\) | |||||||
\(434\) | 1.21590e6 | 0.309866 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.50974e6 | 0.632283 | ||||||||
\(437\) | −68411.1 | −0.0171365 | ||||||||
\(438\) | 1.50625e6 | 0.375155 | ||||||||
\(439\) | −4.25980e6 | −1.05494 | −0.527471 | − | 0.849573i | \(-0.676860\pi\) | ||||
−0.527471 | + | 0.849573i | \(0.676860\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 371381. | 0.0909333 | ||||||||
\(442\) | −710977. | −0.173101 | ||||||||
\(443\) | 1.87861e6 | 0.454807 | 0.227404 | − | 0.973801i | \(-0.426976\pi\) | ||||
0.227404 | + | 0.973801i | \(0.426976\pi\) | |||||||
\(444\) | −1.28997e6 | −0.310544 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.62191e6 | −0.624139 | ||||||||
\(447\) | 2.75234e6 | 0.651527 | ||||||||
\(448\) | −571969. | −0.134641 | ||||||||
\(449\) | −296649. | −0.0694428 | −0.0347214 | − | 0.999397i | \(-0.511054\pi\) | ||||
−0.0347214 | + | 0.999397i | \(0.511054\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 339220. | 0.0785309 | ||||||||
\(452\) | 4.00989e6 | 0.923180 | ||||||||
\(453\) | 1.98378e6 | 0.454202 | ||||||||
\(454\) | −2.32847e6 | −0.530189 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 40492.8 | 0.00911938 | ||||||||
\(457\) | −2.30010e6 | −0.515177 | −0.257588 | − | 0.966255i | \(-0.582928\pi\) | ||||
−0.257588 | + | 0.966255i | \(0.582928\pi\) | |||||||
\(458\) | 2.25066e6 | 0.501356 | ||||||||
\(459\) | 1.40408e6 | 0.311072 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.72547e6 | 1.69306 | 0.846530 | − | 0.532340i | \(-0.178687\pi\) | ||||
0.846530 | + | 0.532340i | \(0.178687\pi\) | |||||||
\(462\) | 371555. | 0.0809876 | ||||||||
\(463\) | −6.54474e6 | −1.41886 | −0.709430 | − | 0.704776i | \(-0.751048\pi\) | ||||
−0.709430 | + | 0.704776i | \(0.751048\pi\) | |||||||
\(464\) | 872164. | 0.188063 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.28485e6 | −0.274087 | ||||||||
\(467\) | 6.94728e6 | 1.47409 | 0.737043 | − | 0.675846i | \(-0.236222\pi\) | ||||
0.737043 | + | 0.675846i | \(0.236222\pi\) | |||||||
\(468\) | 340411. | 0.0718438 | ||||||||
\(469\) | 4.99132e6 | 1.04781 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.26741e6 | 1.09407 | ||||||||
\(472\) | 683317. | 0.141178 | ||||||||
\(473\) | −137968. | −0.0283546 | ||||||||
\(474\) | −300351. | −0.0614022 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.48151e6 | 1.51346 | ||||||||
\(477\) | 1.94754e6 | 0.391914 | ||||||||
\(478\) | 964336. | 0.193045 | ||||||||
\(479\) | −3.98195e6 | −0.792971 | −0.396485 | − | 0.918041i | \(-0.629770\pi\) | ||||
−0.396485 | + | 0.918041i | \(0.629770\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 854002. | 0.168305 | ||||||||
\(482\) | −496946. | −0.0974298 | ||||||||
\(483\) | −2.73412e6 | −0.533273 | ||||||||
\(484\) | −388839. | −0.0754495 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 137747. | 0.0264541 | ||||||||
\(487\) | 2.10449e6 | 0.402090 | 0.201045 | − | 0.979582i | \(-0.435566\pi\) | ||||
0.201045 | + | 0.979582i | \(0.435566\pi\) | |||||||
\(488\) | −655535. | −0.124608 | ||||||||
\(489\) | −982358. | −0.185779 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.60384e6 | −0.861820 | −0.430910 | − | 0.902395i | \(-0.641807\pi\) | ||||
−0.430910 | + | 0.902395i | \(0.641807\pi\) | |||||||
\(492\) | 670098. | 0.124803 | ||||||||
\(493\) | −3.16230e6 | −0.585985 | ||||||||
\(494\) | −12158.1 | −0.00224156 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.89305e6 | −0.345508 | ||||||||
\(497\) | 1.47134e6 | 0.267191 | ||||||||
\(498\) | 1.39541e6 | 0.252133 | ||||||||
\(499\) | −2.17027e6 | −0.390177 | −0.195089 | − | 0.980786i | \(-0.562499\pi\) | ||||
−0.195089 | + | 0.980786i | \(0.562499\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.19001e6 | 0.389808 | ||||||||
\(502\) | −3.77987e6 | −0.669450 | ||||||||
\(503\) | −1.16557e6 | −0.205409 | −0.102705 | − | 0.994712i | \(-0.532750\pi\) | ||||
−0.102705 | + | 0.994712i | \(0.532750\pi\) | |||||||
\(504\) | 1.61834e6 | 0.283787 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −586281. | −0.101796 | ||||||||
\(507\) | 3.11627e6 | 0.538413 | ||||||||
\(508\) | −9.25583e6 | −1.59131 | ||||||||
\(509\) | 498433. | 0.0852732 | 0.0426366 | − | 0.999091i | \(-0.486424\pi\) | ||||
0.0426366 | + | 0.999091i | \(0.486424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.04932e7 | 1.77769 | ||||||||
\(512\) | −5.30231e6 | −0.893903 | ||||||||
\(513\) | 24010.7 | 0.00402820 | ||||||||
\(514\) | 2.42520e6 | 0.404893 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −272542. | −0.0450618 | ||||||||
\(517\) | −1.91152e6 | −0.314523 | ||||||||
\(518\) | 1.84134e6 | 0.301516 | ||||||||
\(519\) | 3.59015e6 | 0.585051 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.11019e6 | 0.179186 | 0.0895929 | − | 0.995978i | \(-0.471443\pi\) | ||||
0.0895929 | + | 0.995978i | \(0.471443\pi\) | |||||||
\(522\) | −310237. | −0.0498331 | ||||||||
\(523\) | −5.52154e6 | −0.882686 | −0.441343 | − | 0.897338i | \(-0.645498\pi\) | ||||
−0.441343 | + | 0.897338i | \(0.645498\pi\) | |||||||
\(524\) | −1.57974e6 | −0.251338 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 484814. | 0.0764031 | ||||||||
\(527\) | 6.86384e6 | 1.07657 | ||||||||
\(528\) | −578479. | −0.0903031 | ||||||||
\(529\) | −2.12215e6 | −0.329714 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 405181. | 0.0623609 | ||||||||
\(532\) | 127938. | 0.0195984 | ||||||||
\(533\) | −443626. | −0.0676392 | ||||||||
\(534\) | −233140. | −0.0353805 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.66174e6 | 0.700868 | ||||||||
\(537\) | −1.79032e6 | −0.267913 | ||||||||
\(538\) | −704933. | −0.105001 | ||||||||
\(539\) | 554779. | 0.0822523 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.17913e7 | −1.73208 | −0.866039 | − | 0.499977i | \(-0.833342\pi\) | ||||
−0.866039 | + | 0.499977i | \(0.833342\pi\) | |||||||
\(542\) | −2.73373e6 | −0.399722 | ||||||||
\(543\) | 4.26702e6 | 0.621047 | ||||||||
\(544\) | 1.08059e7 | 1.56554 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −485912. | −0.0697552 | ||||||||
\(547\) | −1.11424e7 | −1.59224 | −0.796121 | − | 0.605137i | \(-0.793118\pi\) | ||||
−0.796121 | + | 0.605137i | \(0.793118\pi\) | |||||||
\(548\) | 3.93737e6 | 0.560086 | ||||||||
\(549\) | −388707. | −0.0550417 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −54077.3 | −0.00758815 | ||||||||
\(552\) | −2.55359e6 | −0.356700 | ||||||||
\(553\) | −2.09239e6 | −0.290957 | ||||||||
\(554\) | 5.01761e6 | 0.694580 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.22371e6 | 0.716626 | ||||||||
\(557\) | 8.68222e6 | 1.18575 | 0.592875 | − | 0.805295i | \(-0.297993\pi\) | ||||
0.592875 | + | 0.805295i | \(0.297993\pi\) | |||||||
\(558\) | 673376. | 0.0915529 | ||||||||
\(559\) | 180431. | 0.0244220 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.09746e6 | 0.281375 | ||||||||
\(562\) | 5.39439e6 | 0.720447 | ||||||||
\(563\) | −2.59561e6 | −0.345118 | −0.172559 | − | 0.984999i | \(-0.555204\pi\) | ||||
−0.172559 | + | 0.984999i | \(0.555204\pi\) | |||||||
\(564\) | −3.77603e6 | −0.499847 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.52996e6 | −0.200743 | ||||||||
\(567\) | 959611. | 0.125354 | ||||||||
\(568\) | 1.37419e6 | 0.178721 | ||||||||
\(569\) | 1.43008e7 | 1.85174 | 0.925869 | − | 0.377846i | \(-0.123335\pi\) | ||||
0.925869 | + | 0.377846i | \(0.123335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.13885e6 | 0.402884 | 0.201442 | − | 0.979500i | \(-0.435437\pi\) | ||||
0.201442 | + | 0.979500i | \(0.435437\pi\) | |||||||
\(572\) | 508515. | 0.0649851 | ||||||||
\(573\) | −1.81394e6 | −0.230800 | ||||||||
\(574\) | −956516. | −0.121175 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −316761. | −0.0397810 | ||||||||
\(577\) | −7.88699e6 | −0.986215 | −0.493108 | − | 0.869968i | \(-0.664139\pi\) | ||||
−0.493108 | + | 0.869968i | \(0.664139\pi\) | |||||||
\(578\) | −5.34149e6 | −0.665033 | ||||||||
\(579\) | −1.84671e6 | −0.228930 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.72109e6 | 1.19474 | ||||||||
\(582\) | 1.18668e6 | 0.145220 | ||||||||
\(583\) | 2.90929e6 | 0.354499 | ||||||||
\(584\) | 9.80035e6 | 1.18908 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.40622e6 | 0.169165 | ||||||||
\(587\) | −1.91771e6 | −0.229714 | −0.114857 | − | 0.993382i | \(-0.536641\pi\) | ||||
−0.114857 | + | 0.993382i | \(0.536641\pi\) | |||||||
\(588\) | 1.09591e6 | 0.130717 | ||||||||
\(589\) | 117376. | 0.0139409 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 899061. | 0.105882 | ||||||||
\(592\) | −2.86681e6 | −0.336198 | ||||||||
\(593\) | −1.20632e7 | −1.40872 | −0.704362 | − | 0.709841i | \(-0.748767\pi\) | ||||
−0.704362 | + | 0.709841i | \(0.748767\pi\) | |||||||
\(594\) | 205771. | 0.0239286 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.12190e6 | 0.936574 | ||||||||
\(597\) | 3.34228e6 | 0.383802 | ||||||||
\(598\) | 766726. | 0.0876773 | ||||||||
\(599\) | −5.17336e6 | −0.589123 | −0.294562 | − | 0.955633i | \(-0.595174\pi\) | ||||
−0.294562 | + | 0.955633i | \(0.595174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.40838e6 | 1.06250 | 0.531250 | − | 0.847215i | \(-0.321723\pi\) | ||||
0.531250 | + | 0.847215i | \(0.321723\pi\) | |||||||
\(602\) | 389034. | 0.0437518 | ||||||||
\(603\) | 2.76423e6 | 0.309586 | ||||||||
\(604\) | 5.85398e6 | 0.652918 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −455781. | −0.0504167 | ||||||||
\(607\) | 368372. | 0.0405802 | 0.0202901 | − | 0.999794i | \(-0.493541\pi\) | ||||
0.0202901 | + | 0.999794i | \(0.493541\pi\) | |||||||
\(608\) | 184788. | 0.0202729 | ||||||||
\(609\) | −2.16126e6 | −0.236136 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.49985e6 | 0.270901 | ||||||||
\(612\) | 4.14333e6 | 0.447168 | ||||||||
\(613\) | −6.57960e6 | −0.707210 | −0.353605 | − | 0.935395i | \(-0.615044\pi\) | ||||
−0.353605 | + | 0.935395i | \(0.615044\pi\) | |||||||
\(614\) | 145886. | 0.0156169 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.41751e6 | 0.256695 | ||||||||
\(617\) | 140601. | 0.0148688 | 0.00743441 | − | 0.999972i | \(-0.497634\pi\) | ||||
0.00743441 | + | 0.999972i | \(0.497634\pi\) | |||||||
\(618\) | 324200. | 0.0341462 | ||||||||
\(619\) | 1.69769e7 | 1.78087 | 0.890433 | − | 0.455115i | \(-0.150402\pi\) | ||||
0.890433 | + | 0.455115i | \(0.150402\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.51418e6 | −0.157561 | ||||||||
\(622\) | 2.72763e6 | 0.282689 | ||||||||
\(623\) | −1.62416e6 | −0.167652 | ||||||||
\(624\) | 756523. | 0.0777787 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.85572e6 | −0.597234 | ||||||||
\(627\) | 35867.8 | 0.00364364 | ||||||||
\(628\) | 1.55437e7 | 1.57273 | ||||||||
\(629\) | 1.03945e7 | 1.04756 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.16982e7 | −1.16962 | −0.584811 | − | 0.811170i | \(-0.698831\pi\) | ||||
−0.584811 | + | 0.811170i | \(0.698831\pi\) | |||||||
\(632\) | −1.95423e6 | −0.194618 | ||||||||
\(633\) | 2.57289e6 | 0.255219 | ||||||||
\(634\) | 3.69440e6 | 0.365023 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.74702e6 | 0.563378 | ||||||||
\(637\) | −725528. | −0.0708444 | ||||||||
\(638\) | −463441. | −0.0450757 | ||||||||
\(639\) | 814839. | 0.0789441 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.21774e6 | 0.117060 | 0.0585301 | − | 0.998286i | \(-0.481359\pi\) | ||||
0.0585301 | + | 0.998286i | \(0.481359\pi\) | |||||||
\(642\) | 700353. | 0.0670625 | ||||||||
\(643\) | −1.22181e7 | −1.16541 | −0.582703 | − | 0.812685i | \(-0.698005\pi\) | ||||
−0.582703 | + | 0.812685i | \(0.698005\pi\) | |||||||
\(644\) | −8.06815e6 | −0.766583 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −147983. | −0.0139518 | ||||||||
\(647\) | 1.38354e7 | 1.29936 | 0.649682 | − | 0.760206i | \(-0.274902\pi\) | ||||
0.649682 | + | 0.760206i | \(0.274902\pi\) | |||||||
\(648\) | 896248. | 0.0838476 | ||||||||
\(649\) | 605270. | 0.0564076 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.69105e6 | 0.433828 | ||||||||
\(652\) | −2.89885e6 | −0.267059 | ||||||||
\(653\) | 7.07482e6 | 0.649280 | 0.324640 | − | 0.945838i | \(-0.394757\pi\) | ||||
0.324640 | + | 0.945838i | \(0.394757\pi\) | |||||||
\(654\) | −1.98400e6 | −0.181383 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.48921e6 | 0.135113 | ||||||||
\(657\) | 5.81124e6 | 0.525237 | ||||||||
\(658\) | 5.39001e6 | 0.485316 | ||||||||
\(659\) | −1.42464e7 | −1.27788 | −0.638942 | − | 0.769255i | \(-0.720627\pi\) | ||||
−0.638942 | + | 0.769255i | \(0.720627\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.44156e7 | −1.28330 | −0.641651 | − | 0.766997i | \(-0.721750\pi\) | ||||
−0.641651 | + | 0.766997i | \(0.721750\pi\) | |||||||
\(662\) | 6.37735e6 | 0.565582 | ||||||||
\(663\) | −2.74301e6 | −0.242350 | ||||||||
\(664\) | 9.07921e6 | 0.799149 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.01975e6 | 0.0890859 | ||||||||
\(667\) | 3.41026e6 | 0.296807 | ||||||||
\(668\) | 6.46252e6 | 0.560352 | ||||||||
\(669\) | −1.01156e7 | −0.873826 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −580662. | −0.0497871 | ||||||||
\(672\) | 7.38525e6 | 0.630873 | ||||||||
\(673\) | −4.41234e6 | −0.375519 | −0.187759 | − | 0.982215i | \(-0.560123\pi\) | ||||
−0.187759 | + | 0.982215i | \(0.560123\pi\) | |||||||
\(674\) | 7.18758e6 | 0.609443 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.19586e6 | 0.773972 | ||||||||
\(677\) | 2.15482e7 | 1.80692 | 0.903461 | − | 0.428670i | \(-0.141018\pi\) | ||||
0.903461 | + | 0.428670i | \(0.141018\pi\) | |||||||
\(678\) | −3.16991e6 | −0.264833 | ||||||||
\(679\) | 8.26699e6 | 0.688134 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.98344e6 | −0.742292 | ||||||||
\(682\) | 1.00591e6 | 0.0828127 | ||||||||
\(683\) | −1.93575e7 | −1.58781 | −0.793903 | − | 0.608045i | \(-0.791954\pi\) | ||||
−0.793903 | + | 0.608045i | \(0.791954\pi\) | |||||||
\(684\) | 70853.4 | 0.00579056 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.17004e6 | 0.338321 | ||||||||
\(687\) | 8.68324e6 | 0.701923 | ||||||||
\(688\) | −605691. | −0.0487843 | ||||||||
\(689\) | −3.80471e6 | −0.305333 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.29763e6 | 0.581416 | 0.290708 | − | 0.956812i | \(-0.406109\pi\) | ||||
0.290708 | + | 0.956812i | \(0.406109\pi\) | |||||||
\(692\) | 1.05942e7 | 0.841014 | ||||||||
\(693\) | 1.43349e6 | 0.113387 | ||||||||
\(694\) | 3.07837e6 | 0.242618 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.01855e6 | −0.157949 | ||||||||
\(697\) | −5.39960e6 | −0.420998 | ||||||||
\(698\) | 9.72076e6 | 0.755200 | ||||||||
\(699\) | −4.95707e6 | −0.383735 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.83574e7 | 1.41096 | 0.705481 | − | 0.708729i | \(-0.250731\pi\) | ||||
0.705481 | + | 0.708729i | \(0.250731\pi\) | |||||||
\(702\) | −269103. | −0.0206099 | ||||||||
\(703\) | 177753. | 0.0135652 | ||||||||
\(704\) | −473187. | −0.0359833 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.31570e6 | −0.627895 | ||||||||
\(707\) | −3.17518e6 | −0.238902 | ||||||||
\(708\) | 1.19565e6 | 0.0896442 | ||||||||
\(709\) | 749166. | 0.0559709 | 0.0279855 | − | 0.999608i | \(-0.491091\pi\) | ||||
0.0279855 | + | 0.999608i | \(0.491091\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.15878e6 | −0.0859662 | ||||||||
\(712\) | −1.51692e6 | −0.112140 | ||||||||
\(713\) | −7.40205e6 | −0.545291 | ||||||||
\(714\) | −5.91430e6 | −0.434168 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.28306e6 | −0.385126 | ||||||||
\(717\) | 3.72049e6 | 0.270273 | ||||||||
\(718\) | 937885. | 0.0678951 | ||||||||
\(719\) | 1.65136e7 | 1.19129 | 0.595647 | − | 0.803246i | \(-0.296896\pi\) | ||||
0.595647 | + | 0.803246i | \(0.296896\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.25853e6 | 0.161803 | ||||||||
\(722\) | 5.77362e6 | 0.412197 | ||||||||
\(723\) | −1.91726e6 | −0.136407 | ||||||||
\(724\) | 1.25916e7 | 0.892759 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 307386. | 0.0216442 | ||||||||
\(727\) | −1.79988e7 | −1.26301 | −0.631505 | − | 0.775372i | \(-0.717562\pi\) | ||||
−0.631505 | + | 0.775372i | \(0.717562\pi\) | |||||||
\(728\) | −3.16157e6 | −0.221093 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.19612e6 | 0.152007 | ||||||||
\(732\) | −1.14704e6 | −0.0791228 | ||||||||
\(733\) | −127875. | −0.00879075 | −0.00439537 | − | 0.999990i | \(-0.501399\pi\) | ||||
−0.00439537 | + | 0.999990i | \(0.501399\pi\) | |||||||
\(734\) | −3.96334e6 | −0.271532 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.16533e7 | −0.792962 | ||||||||
\(737\) | 4.12929e6 | 0.280031 | ||||||||
\(738\) | −529727. | −0.0358023 | ||||||||
\(739\) | −7.32976e6 | −0.493718 | −0.246859 | − | 0.969051i | \(-0.579398\pi\) | ||||
−0.246859 | + | 0.969051i | \(0.579398\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −46907.1 | −0.00313829 | ||||||||
\(742\) | −8.20346e6 | −0.547000 | ||||||||
\(743\) | −2.18733e7 | −1.45359 | −0.726797 | − | 0.686852i | \(-0.758992\pi\) | ||||
−0.726797 | + | 0.686852i | \(0.758992\pi\) | |||||||
\(744\) | 4.38130e6 | 0.290182 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.15417e6 | 0.273298 | ||||||||
\(747\) | 5.38363e6 | 0.352999 | ||||||||
\(748\) | 6.18941e6 | 0.404479 | ||||||||
\(749\) | 4.87898e6 | 0.317779 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.28695e7 | −1.47964 | −0.739820 | − | 0.672805i | \(-0.765089\pi\) | ||||
−0.739820 | + | 0.672805i | \(0.765089\pi\) | |||||||
\(752\) | −8.39177e6 | −0.541139 | ||||||||
\(753\) | −1.45831e7 | −0.937264 | ||||||||
\(754\) | 606078. | 0.0388240 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.83173e6 | 0.180197 | ||||||||
\(757\) | −1.68271e7 | −1.06726 | −0.533629 | − | 0.845719i | \(-0.679172\pi\) | ||||
−0.533629 | + | 0.845719i | \(0.679172\pi\) | |||||||
\(758\) | 4.96803e6 | 0.314059 | ||||||||
\(759\) | −2.26192e6 | −0.142519 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.72838e7 | −1.08188 | −0.540938 | − | 0.841062i | \(-0.681931\pi\) | ||||
−0.540938 | + | 0.841062i | \(0.681931\pi\) | |||||||
\(762\) | 7.31694e6 | 0.456501 | ||||||||
\(763\) | −1.38215e7 | −0.859494 | ||||||||
\(764\) | −5.35277e6 | −0.331776 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.15644e6 | −0.440682 | ||||||||
\(767\) | −791560. | −0.0485842 | ||||||||
\(768\) | 2.83456e6 | 0.173413 | ||||||||
\(769\) | 1.11705e7 | 0.681173 | 0.340587 | − | 0.940213i | \(-0.389374\pi\) | ||||
0.340587 | + | 0.940213i | \(0.389374\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.35664e6 | 0.566871 | ||||||||
\(772\) | −5.44950e6 | −0.329089 | ||||||||
\(773\) | 1.77002e7 | 1.06544 | 0.532719 | − | 0.846292i | \(-0.321170\pi\) | ||||
0.532719 | + | 0.846292i | \(0.321170\pi\) | |||||||
\(774\) | 215450. | 0.0129269 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.72112e6 | 0.460284 | ||||||||
\(777\) | 7.10406e6 | 0.422138 | ||||||||
\(778\) | −1.82929e6 | −0.108351 | ||||||||
\(779\) | −92336.5 | −0.00545167 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.21723e6 | 0.0714076 | ||||||||
\(782\) | 9.33223e6 | 0.545718 | ||||||||
\(783\) | −1.19692e6 | −0.0697688 | ||||||||
\(784\) | 2.43553e6 | 0.141515 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.24882e6 | 0.0721015 | ||||||||
\(787\) | 3.55985e6 | 0.204878 | 0.102439 | − | 0.994739i | \(-0.467335\pi\) | ||||
0.102439 | + | 0.994739i | \(0.467335\pi\) | |||||||
\(788\) | 2.65305e6 | 0.152205 | ||||||||
\(789\) | 1.87045e6 | 0.106968 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.20830e7 | −1.25492 | ||||||||
\(792\) | 1.33884e6 | 0.0758430 | ||||||||
\(793\) | 759377. | 0.0428820 | ||||||||
\(794\) | −1.05995e7 | −0.596668 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.86279e6 | 0.551718 | ||||||||
\(797\) | −2.09403e7 | −1.16771 | −0.583857 | − | 0.811856i | \(-0.698457\pi\) | ||||
−0.583857 | + | 0.811856i | \(0.698457\pi\) | |||||||
\(798\) | −101138. | −0.00562222 | ||||||||
\(799\) | 3.04270e7 | 1.68613 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −899475. | −0.0495345 | ||||||||
\(802\) | −8.05060e6 | −0.441970 | ||||||||
\(803\) | 8.68098e6 | 0.475094 | ||||||||
\(804\) | 8.15702e6 | 0.445032 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.31550e6 | −0.0713271 | ||||||||
\(807\) | −2.71969e6 | −0.147006 | ||||||||
\(808\) | −2.96552e6 | −0.159799 | ||||||||
\(809\) | −2.22981e7 | −1.19784 | −0.598918 | − | 0.800810i | \(-0.704402\pi\) | ||||
−0.598918 | + | 0.800810i | \(0.704402\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.95262e6 | −0.424578 | −0.212289 | − | 0.977207i | \(-0.568092\pi\) | ||||
−0.212289 | + | 0.977207i | \(0.568092\pi\) | |||||||
\(812\) | −6.37768e6 | −0.339447 | ||||||||
\(813\) | −1.05470e7 | −0.559631 | ||||||||
\(814\) | 1.52333e6 | 0.0805812 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.20805e6 | 0.484108 | ||||||||
\(817\) | 37555.0 | 0.00196840 | ||||||||
\(818\) | −8.87105e6 | −0.463545 | ||||||||
\(819\) | −1.87469e6 | −0.0976608 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.23384e7 | −0.638852 | −0.319426 | − | 0.947611i | \(-0.603490\pi\) | ||||
−0.319426 | + | 0.947611i | \(0.603490\pi\) | |||||||
\(822\) | −3.11258e6 | −0.160672 | ||||||||
\(823\) | 1.87024e6 | 0.0962493 | 0.0481247 | − | 0.998841i | \(-0.484676\pi\) | ||||
0.0481247 | + | 0.998841i | \(0.484676\pi\) | |||||||
\(824\) | 2.10940e6 | 0.108228 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.70671e6 | −0.0870381 | ||||||||
\(827\) | 2.63791e7 | 1.34121 | 0.670604 | − | 0.741816i | \(-0.266035\pi\) | ||||
0.670604 | + | 0.741816i | \(0.266035\pi\) | |||||||
\(828\) | −4.46821e6 | −0.226495 | ||||||||
\(829\) | 2.85869e7 | 1.44471 | 0.722355 | − | 0.691522i | \(-0.243060\pi\) | ||||
0.722355 | + | 0.691522i | \(0.243060\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.93584e7 | 0.972447 | ||||||||
\(832\) | 618824. | 0.0309926 | ||||||||
\(833\) | −8.83079e6 | −0.440948 | ||||||||
\(834\) | −4.12946e6 | −0.205579 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 105843. | 0.00523776 | ||||||||
\(837\) | 2.59794e6 | 0.128179 | ||||||||
\(838\) | 6.08153e6 | 0.299159 | ||||||||
\(839\) | −1.62633e7 | −0.797634 | −0.398817 | − | 0.917031i | \(-0.630579\pi\) | ||||
−0.398817 | + | 0.917031i | \(0.630579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.78154e7 | −0.868572 | ||||||||
\(842\) | 1.17997e7 | 0.573576 | ||||||||
\(843\) | 2.08120e7 | 1.00866 | ||||||||
\(844\) | 7.59238e6 | 0.366878 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.98503e6 | 0.143391 | ||||||||
\(847\) | 2.14139e6 | 0.102562 | ||||||||
\(848\) | 1.27721e7 | 0.609918 | ||||||||
\(849\) | −5.90273e6 | −0.281050 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.12096e7 | −0.530597 | ||||||||
\(852\) | 2.40452e6 | 0.113483 | ||||||||
\(853\) | −1.29208e6 | −0.0608021 | −0.0304010 | − | 0.999538i | \(-0.509678\pi\) | ||||
−0.0304010 | + | 0.999538i | \(0.509678\pi\) | |||||||
\(854\) | 1.63732e6 | 0.0768225 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.55683e6 | 0.212558 | ||||||||
\(857\) | 8.96034e6 | 0.416747 | 0.208374 | − | 0.978049i | \(-0.433183\pi\) | ||||
0.208374 | + | 0.978049i | \(0.433183\pi\) | |||||||
\(858\) | −401993. | −0.0186423 | ||||||||
\(859\) | −4.85453e6 | −0.224473 | −0.112236 | − | 0.993682i | \(-0.535801\pi\) | ||||
−0.112236 | + | 0.993682i | \(0.535801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.69032e6 | −0.169651 | ||||||||
\(862\) | 8.45522e6 | 0.387576 | ||||||||
\(863\) | −6.39862e6 | −0.292455 | −0.146228 | − | 0.989251i | \(-0.546713\pi\) | ||||
−0.146228 | + | 0.989251i | \(0.546713\pi\) | |||||||
\(864\) | 4.09001e6 | 0.186398 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.52350e7 | 0.690316 | ||||||||
\(867\) | −2.06079e7 | −0.931080 | ||||||||
\(868\) | 1.38429e7 | 0.623630 | ||||||||
\(869\) | −1.73102e6 | −0.0777593 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.40020e6 | −0.241193 | ||||||||
\(872\) | −1.29088e7 | −0.574905 | ||||||||
\(873\) | 4.57833e6 | 0.203316 | ||||||||
\(874\) | 159587. | 0.00706673 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.71485e7 | 0.755031 | ||||||||
\(877\) | −1.53595e7 | −0.674340 | −0.337170 | − | 0.941444i | \(-0.609470\pi\) | ||||
−0.337170 | + | 0.941444i | \(0.609470\pi\) | |||||||
\(878\) | 9.93711e6 | 0.435035 | ||||||||
\(879\) | 5.42533e6 | 0.236840 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.14534e7 | −0.931228 | −0.465614 | − | 0.884988i | \(-0.654167\pi\) | ||||
−0.465614 | + | 0.884988i | \(0.654167\pi\) | |||||||
\(882\) | −866343. | −0.0374989 | ||||||||
\(883\) | 3.30136e6 | 0.142492 | 0.0712460 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712460 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(884\) | −8.09439e6 | −0.348380 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.38235e6 | −0.187553 | ||||||||
\(887\) | 1.34325e7 | 0.573256 | 0.286628 | − | 0.958042i | \(-0.407466\pi\) | ||||
0.286628 | + | 0.958042i | \(0.407466\pi\) | |||||||
\(888\) | 6.63498e6 | 0.282363 | ||||||||
\(889\) | 5.09732e7 | 2.16315 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | −2.98502e7 | −1.25613 | ||||||||
\(893\) | 520320. | 0.0218344 | ||||||||
\(894\) | −6.42054e6 | −0.268675 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.75929e7 | 1.14823 | ||||||||
\(897\) | 2.95809e6 | 0.122753 | ||||||||
\(898\) | 692011. | 0.0286367 | ||||||||
\(899\) | −5.85114e6 | −0.241458 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.63091e7 | −1.90044 | ||||||||
\(902\) | −791321. | −0.0323844 | ||||||||
\(903\) | 1.50093e6 | 0.0612548 | ||||||||
\(904\) | −2.06249e7 | −0.839404 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.62770e6 | −0.187303 | ||||||||
\(907\) | −2.40573e6 | −0.0971023 | −0.0485512 | − | 0.998821i | \(-0.515460\pi\) | ||||
−0.0485512 | + | 0.998821i | \(0.515460\pi\) | |||||||
\(908\) | −2.65093e7 | −1.06705 | ||||||||
\(909\) | −1.75844e6 | −0.0705859 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.38090e7 | −1.74891 | −0.874455 | − | 0.485107i | \(-0.838781\pi\) | ||||
−0.874455 | + | 0.485107i | \(0.838781\pi\) | |||||||
\(912\) | 157463. | 0.00626891 | ||||||||
\(913\) | 8.04221e6 | 0.319300 | ||||||||
\(914\) | 5.36559e6 | 0.212448 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.56235e7 | 1.00902 | ||||||||
\(917\) | 8.69987e6 | 0.341656 | ||||||||
\(918\) | −3.27539e6 | −0.128279 | ||||||||
\(919\) | 4.10650e6 | 0.160392 | 0.0801962 | − | 0.996779i | \(-0.474445\pi\) | ||||
0.0801962 | + | 0.996779i | \(0.474445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 562842. | 0.0218644 | ||||||||
\(922\) | −1.80217e7 | −0.698181 | ||||||||
\(923\) | −1.59187e6 | −0.0615039 | ||||||||
\(924\) | 4.23011e6 | 0.162994 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.52673e7 | 0.585107 | ||||||||
\(927\) | 1.25079e6 | 0.0478064 | ||||||||
\(928\) | −9.21161e6 | −0.351128 | ||||||||
\(929\) | −7.91355e6 | −0.300838 | −0.150419 | − | 0.988622i | \(-0.548062\pi\) | ||||
−0.150419 | + | 0.988622i | \(0.548062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −151012. | −0.00571001 | ||||||||
\(932\) | −1.46279e7 | −0.551622 | ||||||||
\(933\) | 1.05234e7 | 0.395780 | ||||||||
\(934\) | −1.62064e7 | −0.607880 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.75091e6 | −0.0653241 | ||||||||
\(937\) | −5.82636e6 | −0.216795 | −0.108397 | − | 0.994108i | \(-0.534572\pi\) | ||||
−0.108397 | + | 0.994108i | \(0.534572\pi\) | |||||||
\(938\) | −1.16436e7 | −0.432094 | ||||||||
\(939\) | −2.25919e7 | −0.836159 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.94213e7 | −1.81945 | −0.909725 | − | 0.415210i | \(-0.863708\pi\) | ||||
−0.909725 | + | 0.415210i | \(0.863708\pi\) | |||||||
\(942\) | −1.22876e7 | −0.451170 | ||||||||
\(943\) | 5.82300e6 | 0.213239 | ||||||||
\(944\) | 2.65720e6 | 0.0970496 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 321845. | 0.0116928 | ||||||||
\(947\) | −1.11808e7 | −0.405135 | −0.202567 | − | 0.979268i | \(-0.564929\pi\) | ||||
−0.202567 | + | 0.979268i | \(0.564929\pi\) | |||||||
\(948\) | −3.41946e6 | −0.123577 | ||||||||
\(949\) | −1.13528e7 | −0.409202 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.42533e7 | 0.511051 | ||||||||
\(952\) | −3.84812e7 | −1.37612 | ||||||||
\(953\) | 1.89338e7 | 0.675315 | 0.337658 | − | 0.941269i | \(-0.390365\pi\) | ||||
0.337658 | + | 0.941269i | \(0.390365\pi\) | |||||||
\(954\) | −4.54315e6 | −0.161617 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.09789e7 | 0.388519 | ||||||||
\(957\) | −1.78799e6 | −0.0631083 | ||||||||
\(958\) | 9.28894e6 | 0.327004 | ||||||||
\(959\) | −2.16837e7 | −0.761353 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.59291e7 | −0.556396 | ||||||||
\(962\) | −1.99218e6 | −0.0694052 | ||||||||
\(963\) | 2.70202e6 | 0.0938909 | ||||||||
\(964\) | −5.65767e6 | −0.196085 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.37805e6 | 0.219910 | ||||||||
\(967\) | −2.87893e7 | −0.990069 | −0.495034 | − | 0.868873i | \(-0.664845\pi\) | ||||
−0.495034 | + | 0.868873i | \(0.664845\pi\) | |||||||
\(968\) | 2.00000e6 | 0.0686026 | ||||||||
\(969\) | −570932. | −0.0195333 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.23023e7 | 1.78022 | 0.890108 | − | 0.455750i | \(-0.150629\pi\) | ||||
0.890108 | + | 0.455750i | \(0.150629\pi\) | |||||||
\(972\) | 1.56824e6 | 0.0532410 | ||||||||
\(973\) | −2.87677e7 | −0.974145 | ||||||||
\(974\) | −4.90926e6 | −0.165813 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.54916e6 | −0.0856590 | ||||||||
\(977\) | −5.27070e7 | −1.76657 | −0.883286 | − | 0.468834i | \(-0.844674\pi\) | ||||
−0.883286 | + | 0.468834i | \(0.844674\pi\) | |||||||
\(978\) | 2.29161e6 | 0.0766114 | ||||||||
\(979\) | −1.34366e6 | −0.0448056 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.65445e6 | −0.253946 | ||||||||
\(982\) | 1.07397e7 | 0.355396 | ||||||||
\(983\) | 5.51463e7 | 1.82026 | 0.910128 | − | 0.414328i | \(-0.135983\pi\) | ||||
0.910128 | + | 0.414328i | \(0.135983\pi\) | |||||||
\(984\) | −3.44665e6 | −0.113478 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.37690e6 | 0.241647 | ||||||||
\(987\) | 2.07951e7 | 0.679467 | ||||||||
\(988\) | −138419. | −0.00451131 | ||||||||
\(989\) | −2.36833e6 | −0.0769929 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.11719e7 | −1.33173 | −0.665866 | − | 0.746071i | \(-0.731938\pi\) | ||||
−0.665866 | + | 0.746071i | \(0.731938\pi\) | |||||||
\(992\) | 1.99940e7 | 0.645090 | ||||||||
\(993\) | 2.46044e7 | 0.791844 | ||||||||
\(994\) | −3.43228e6 | −0.110184 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.58866e7 | 0.507438 | ||||||||
\(997\) | 4.61912e7 | 1.47171 | 0.735853 | − | 0.677141i | \(-0.236781\pi\) | ||||
0.735853 | + | 0.677141i | \(0.236781\pi\) | |||||||
\(998\) | 5.06272e6 | 0.160900 | ||||||||
\(999\) | 3.93429e6 | 0.124725 |
(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 | 825.6.a.o.1.3 | yes | 7 | |
5.4 | even | 2 | 825.6.a.m.1.5 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.m.1.5 | ✓ | 7 | 5.4 | even | 2 | ||
825.6.a.o.1.3 | yes | 7 | 1.1 | even | 1 | trivial |