Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,7,Mod(73,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.73");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.z (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(57.9736290722\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 6586 x^{10} - 4380 x^{9} + 29743412 x^{8} - 22316460 x^{7} + 72097469286 x^{6} + \cdots + 78\!\cdots\!61 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{9}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.2 | ||
Root | \(21.5222 - 37.2775i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.73 |
Dual form | 252.7.z.f.145.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −136.035 | + | 78.5400i | −1.08828 | + | 0.628320i | −0.933119 | − | 0.359569i | \(-0.882924\pi\) |
−0.155164 | + | 0.987889i | \(0.549590\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 334.768 | − | 74.6948i | 0.976000 | − | 0.217769i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1305.52 | + | 2261.23i | −0.980859 | + | 1.69890i | −0.321798 | + | 0.946808i | \(0.604287\pi\) |
−0.659061 | + | 0.752090i | \(0.729046\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3315.82i | − | 1.50925i | −0.656157 | − | 0.754625i | \(-0.727819\pi\) | ||
0.656157 | − | 0.754625i | \(-0.272181\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 445.584 | + | 257.258i | 0.0906948 | + | 0.0523627i | 0.544661 | − | 0.838656i | \(-0.316658\pi\) |
−0.453967 | + | 0.891019i | \(0.649991\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5768.65 | + | 3330.53i | −0.841034 | + | 0.485571i | −0.857615 | − | 0.514292i | \(-0.828055\pi\) |
0.0165818 | + | 0.999863i | \(0.494722\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5395.61 | + | 9345.47i | 0.443462 | + | 0.768099i | 0.997944 | − | 0.0640968i | \(-0.0204166\pi\) |
−0.554481 | + | 0.832196i | \(0.687083\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4524.57 | − | 7836.78i | 0.289572 | − | 0.501554i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6779.56 | −0.277976 | −0.138988 | − | 0.990294i | \(-0.544385\pi\) | ||||
−0.138988 | + | 0.990294i | \(0.544385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 23619.9 | + | 13636.9i | 0.792853 | + | 0.457754i | 0.840966 | − | 0.541088i | \(-0.181987\pi\) |
−0.0481129 | + | 0.998842i | \(0.515321\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −39673.7 | + | 36453.8i | −0.925335 | + | 0.850235i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 256.702 | + | 444.621i | 0.00506785 | + | 0.00877778i | 0.868548 | − | 0.495605i | \(-0.165054\pi\) |
−0.863480 | + | 0.504382i | \(0.831720\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 69543.2i | − | 1.00903i | −0.863403 | − | 0.504514i | \(-0.831672\pi\) | ||
0.863403 | − | 0.504514i | \(-0.168328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −146154. | −1.83826 | −0.919129 | − | 0.393956i | \(-0.871106\pi\) | ||||
−0.919129 | + | 0.393956i | \(0.871106\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 150738. | − | 87028.8i | 1.45188 | − | 0.838242i | 0.453290 | − | 0.891363i | \(-0.350250\pi\) |
0.998588 | + | 0.0531205i | \(0.0169167\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 106490. | − | 50010.9i | 0.905153 | − | 0.425085i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 75787.0 | − | 131267.i | 0.509057 | − | 0.881713i | −0.490887 | − | 0.871223i | \(-0.663327\pi\) |
0.999945 | − | 0.0104904i | \(-0.00333927\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 410143.i | − | 2.46517i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −202049. | − | 116653.i | −0.983788 | − | 0.567990i | −0.0803766 | − | 0.996765i | \(-0.525612\pi\) |
−0.903412 | + | 0.428774i | \(0.858946\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 74423.8 | − | 42968.6i | 0.327886 | − | 0.189305i | −0.327016 | − | 0.945019i | \(-0.606043\pi\) |
0.654902 | + | 0.755714i | \(0.272710\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 260425. | + | 451069.i | 0.948292 | + | 1.64249i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 55530.5 | − | 96181.6i | 0.184632 | − | 0.319792i | −0.758820 | − | 0.651300i | \(-0.774224\pi\) |
0.943452 | + | 0.331508i | \(0.107557\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −501154. | −1.40022 | −0.700110 | − | 0.714035i | \(-0.746866\pi\) | ||||
−0.700110 | + | 0.714035i | \(0.746866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −393637. | − | 227266.i | −1.01188 | − | 0.584207i | −0.100135 | − | 0.994974i | \(-0.531928\pi\) |
−0.911740 | + | 0.410767i | \(0.865261\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −268145. | + | 854505.i | −0.587351 | + | 1.87173i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −136941. | − | 237189.i | −0.277749 | − | 0.481075i | 0.693076 | − | 0.720864i | \(-0.256255\pi\) |
−0.970825 | + | 0.239789i | \(0.922922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 186596.i | − | 0.326338i | −0.986598 | − | 0.163169i | \(-0.947828\pi\) | ||
0.986598 | − | 0.163169i | \(-0.0521716\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −80820.1 | −0.131602 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 245350. | − | 141653.i | 0.348029 | − | 0.200935i | −0.315788 | − | 0.948830i | \(-0.602269\pi\) |
0.663817 | + | 0.747895i | \(0.268935\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −247675. | − | 1.11003e6i | −0.328668 | − | 1.47303i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 523160. | − | 906140.i | 0.610188 | − | 1.05688i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 892059.i | − | 0.977413i | −0.872448 | − | 0.488707i | \(-0.837469\pi\) | ||
0.872448 | − | 0.488707i | \(-0.162531\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.08150e6 | + | 624407.i | 1.04970 | + | 0.606043i | 0.922565 | − | 0.385843i | \(-0.126089\pi\) |
0.127133 | + | 0.991886i | \(0.459423\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 594482. | − | 343225.i | 0.544036 | − | 0.314099i | −0.202677 | − | 0.979246i | \(-0.564964\pi\) |
0.746713 | + | 0.665146i | \(0.231631\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −788845. | − | 1.36632e6i | −0.643932 | − | 1.11532i | −0.984547 | − | 0.175120i | \(-0.943969\pi\) |
0.340615 | − | 0.940203i | \(-0.389365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 987760. | − | 1.71085e6i | 0.762732 | − | 1.32109i | −0.178706 | − | 0.983903i | \(-0.557191\pi\) |
0.941437 | − | 0.337188i | \(-0.109476\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −646680. | −0.448182 | −0.224091 | − | 0.974568i | \(-0.571941\pi\) | ||||
−0.224091 | + | 0.974568i | \(0.571941\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.46799e6 | − | 847542.i | −0.965225 | − | 0.557273i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 168383. | + | 52838.9i | 0.0999211 | + | 0.0313555i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.52300e6 | − | 4.36997e6i | −1.42417 | − | 2.46673i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.03294e6i | − | 0.528864i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.81072e6 | 0.883977 | 0.441989 | − | 0.897021i | \(-0.354273\pi\) | ||||
0.441989 | + | 0.897021i | \(0.354273\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.78012e6 | + | 1.60510e6i | −1.23666 | + | 0.713984i | −0.968409 | − | 0.249365i | \(-0.919778\pi\) |
−0.268248 | + | 0.963350i | \(0.586445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.68239e6 | + | 1.54584e6i | −0.715107 | + | 0.657069i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 997578. | − | 1.72786e6i | 0.387958 | − | 0.671964i | −0.604216 | − | 0.796820i | \(-0.706514\pi\) |
0.992175 | + | 0.124857i | \(0.0398471\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 787049.i | 0.293061i | 0.989206 | + | 0.146530i | \(0.0468106\pi\) | ||||
−0.989206 | + | 0.146530i | \(0.953189\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.49784e6 | + | 4.32888e6i | 2.56406 | + | 1.48036i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 922260. | − | 532467.i | 0.302517 | − | 0.174658i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.82668e6 | − | 4.89595e6i | −0.854511 | − | 1.48006i | −0.877098 | − | 0.480311i | \(-0.840524\pi\) |
0.0225871 | − | 0.999745i | \(-0.492810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.22152e6 | − | 2.11573e6i | 0.354788 | − | 0.614510i | −0.632294 | − | 0.774729i | \(-0.717886\pi\) |
0.987082 | + | 0.160218i | \(0.0512198\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.28418e6 | −1.15046 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.46414e6 | + | 845323.i | 0.378342 | + | 0.218436i | 0.677097 | − | 0.735894i | \(-0.263238\pi\) |
−0.298755 | + | 0.954330i | \(0.596571\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.50434e6 | + | 2.72554e6i | 0.600088 | + | 0.653093i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.41898e6 | + | 4.18980e6i | 0.558560 | + | 0.967454i | 0.997617 | + | 0.0689948i | \(0.0219792\pi\) |
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.91269e6i | 1.48422i | 0.670279 | + | 0.742109i | \(0.266174\pi\) | ||||
−0.670279 | + | 0.742109i | \(0.733826\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.16785e6 | −1.27783 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.48120e6 | + | 4.89662e6i | −1.63802 | + | 0.945711i | −0.656505 | + | 0.754321i | \(0.727966\pi\) |
−0.981514 | + | 0.191390i | \(0.938701\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 929314. | − | 2.96147e6i | 0.173400 | − | 0.552577i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.28687e6 | − | 5.69302e6i | 0.573090 | − | 0.992621i | −0.423156 | − | 0.906057i | \(-0.639078\pi\) |
0.996246 | − | 0.0865646i | \(-0.0275889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 848673.i | − | 0.143121i | −0.997436 | − | 0.0715607i | \(-0.977202\pi\) | ||
0.997436 | − | 0.0715607i | \(-0.0227980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −69841.1 | − | 40322.8i | −0.0110305 | − | 0.00636847i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.16344e6 | + | 671712.i | −0.177918 | + | 0.102721i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −784687. | − | 1.35912e6i | −0.112615 | − | 0.195055i | 0.804209 | − | 0.594347i | \(-0.202589\pi\) |
−0.916824 | + | 0.399292i | \(0.869256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.76124e6 | + | 6.51466e6i | −0.523190 | + | 0.906191i | 0.476446 | + | 0.879204i | \(0.341925\pi\) |
−0.999636 | + | 0.0269875i | \(0.991409\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.53944e6 | 0.462952 | 0.231476 | − | 0.972841i | \(-0.425644\pi\) | ||||
0.231476 | + | 0.972841i | \(0.425644\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.80694e6 | + | 1.62059e6i | 0.356184 | + | 0.205643i | 0.667405 | − | 0.744695i | \(-0.267405\pi\) |
−0.311222 | + | 0.950337i | \(0.600738\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.26958e6 | + | 506398.i | −0.271305 | + | 0.0605346i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.46193e6 | + | 9.46033e6i | 0.633993 | + | 1.09811i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.73923e7i | − | 1.90511i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.69821e6 | 0.713036 | 0.356518 | − | 0.934288i | \(-0.383964\pi\) | ||||
0.356518 | + | 0.934288i | \(0.383964\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.98822e7 | − | 1.14790e7i | 2.00054 | − | 1.15501i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.92579e6 | + | 2.80093e6i | 0.873510 | + | 0.274109i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 853021. | − | 1.47748e6i | 0.0790283 | − | 0.136881i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.16194e7i | 1.04777i | 0.851788 | + | 0.523887i | \(0.175518\pi\) | ||||
−0.851788 | + | 0.523887i | \(0.824482\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.41747e6 | − | 1.97308e6i | −0.292165 | − | 0.168681i | 0.346753 | − | 0.937956i | \(-0.387284\pi\) |
−0.638918 | + | 0.769275i | \(0.720618\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.09592e6 | + | 4.09683e6i | −0.590884 | + | 0.341147i | −0.765447 | − | 0.643499i | \(-0.777482\pi\) |
0.174563 | + | 0.984646i | \(0.444149\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.01788e6 | + | 1.38874e7i | 0.633857 | + | 1.09787i | 0.986756 | + | 0.162212i | \(0.0518627\pi\) |
−0.352899 | + | 0.935662i | \(0.614804\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.36705e7 | + | 2.36780e7i | −1.05337 | + | 1.82449i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.92440e7 | −1.40962 | −0.704810 | − | 0.709396i | \(-0.748968\pi\) | ||||
−0.704810 | + | 0.709396i | \(0.748968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.24933e7 | + | 7.21304e6i | 0.892540 | + | 0.515308i | 0.874772 | − | 0.484534i | \(-0.161011\pi\) |
0.0177675 | + | 0.999842i | \(0.494344\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.05586e7 | + | 1.51670e7i | −0.717973 | + | 1.03134i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.10434e7 | + | 1.91278e7i | 0.732848 | + | 1.26933i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.10219e7i | 0.697006i | 0.937308 | + | 0.348503i | \(0.113310\pi\) | ||||
−0.937308 | + | 0.348503i | \(0.886690\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.81764e7 | −1.73990 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.81591e6 | + | 1.04842e6i | −0.106978 | + | 0.0617639i | −0.552535 | − | 0.833490i | \(-0.686339\pi\) |
0.445556 | + | 0.895254i | \(0.353006\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 119147. | + | 129671.i | 0.00685776 | + | 0.00746349i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.04524e7 | + | 1.81040e7i | −0.574576 | + | 0.995196i | 0.421511 | + | 0.906823i | \(0.361500\pi\) |
−0.996088 | + | 0.0883723i | \(0.971833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.38092e7i | 1.27940i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.24934e7 | − | 1.29866e7i | −1.15557 | − | 0.667171i | −0.205335 | − | 0.978692i | \(-0.565828\pi\) |
−0.950239 | + | 0.311520i | \(0.899162\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.92603e7 | − | 1.11199e7i | 0.967732 | − | 0.558720i | 0.0691881 | − | 0.997604i | \(-0.477959\pi\) |
0.898544 | + | 0.438883i | \(0.144626\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.18139e7 | + | 2.04622e7i | 0.568059 | + | 0.983907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.81089e7 | − | 3.13655e7i | 0.852024 | − | 1.47575i | −0.0273547 | − | 0.999626i | \(-0.508708\pi\) |
0.879379 | − | 0.476123i | \(-0.157958\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.23536e7 | 1.90885 | 0.954423 | − | 0.298457i | \(-0.0964720\pi\) | ||||
0.954423 | + | 0.298457i | \(0.0964720\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.16240e7 | + | 6.71110e6i | 0.512855 | + | 0.296097i | 0.734006 | − | 0.679142i | \(-0.237648\pi\) |
−0.221151 | + | 0.975239i | \(0.570981\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.19452e6 | − | 2.32809e7i | −0.219735 | − | 0.984812i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.19364e7 | − | 2.06745e7i | −0.494516 | − | 0.856527i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.03857e6i | − | 0.160555i | −0.996773 | − | 0.0802777i | \(-0.974419\pi\) | ||
0.996773 | − | 0.0802777i | \(-0.0255807\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.66478e7 | 1.42752 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.09879e7 | − | 1.78909e7i | 1.15925 | − | 0.669295i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.89278e7 | + | 1.09170e7i | −1.79414 | + | 0.400316i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.74951e6 | + | 1.16905e7i | −0.237888 | + | 0.412034i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.90517e7i | 1.00405i | 0.864852 | + | 0.502027i | \(0.167412\pi\) | ||||
−0.864852 | + | 0.502027i | \(0.832588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.72721e7 | − | 2.15191e7i | −1.23909 | − | 0.715389i | −0.270182 | − | 0.962809i | \(-0.587084\pi\) |
−0.968908 | + | 0.247420i | \(0.920417\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.60034e7 | + | 9.23959e6i | −0.521891 | + | 0.301314i | −0.737708 | − | 0.675120i | \(-0.764092\pi\) |
0.215817 | + | 0.976434i | \(0.430759\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.37222e6 | − | 4.10881e6i | −0.0744694 | − | 0.128985i | 0.826386 | − | 0.563104i | \(-0.190393\pi\) |
−0.900855 | + | 0.434119i | \(0.857060\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.85088e6 | − | 1.53302e7i | 0.272656 | − | 0.472253i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.42722e6 | −0.101703 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.59853e7 | − | 1.50026e7i | −0.756970 | − | 0.437037i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.39618e7 | − | 4.03939e7i | 1.23449 | − | 1.13430i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.02878e6 | − | 5.24600e6i | −0.0835187 | − | 0.144659i | 0.821240 | − | 0.570582i | \(-0.193282\pi\) |
−0.904759 | + | 0.425924i | \(0.859949\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.74455e7i | 0.464032i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.38677e7 | −0.884905 | −0.442452 | − | 0.896792i | \(-0.645891\pi\) | ||||
−0.442452 | + | 0.896792i | \(0.645891\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.16726e7 | + | 3.56067e7i | −1.55535 | + | 0.897984i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.19140e7 | − | 2.46963e7i | 0.790859 | − | 0.611998i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.36100e6 | + | 9.28552e6i | −0.128309 | + | 0.222238i | −0.923022 | − | 0.384748i | \(-0.874288\pi\) |
0.794713 | + | 0.606986i | \(0.207622\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.76316e7i | − | 0.414779i | −0.978258 | − | 0.207389i | \(-0.933503\pi\) | ||
0.978258 | − | 0.207389i | \(-0.0664967\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.65852e7 | + | 1.53490e7i | 0.604387 | + | 0.348943i | 0.770766 | − | 0.637119i | \(-0.219874\pi\) |
−0.166378 | + | 0.986062i | \(0.553207\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.81747e7 | − | 3.93607e7i | 1.52384 | − | 0.879787i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.25102e7 | − | 5.63093e7i | −0.702646 | − | 1.21702i | −0.967534 | − | 0.252739i | \(-0.918669\pi\) |
0.264889 | − | 0.964279i | \(-0.414665\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.33806e6 | + | 2.31759e6i | −0.0284417 | + | 0.0492624i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.13980e7 | 1.46827 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.04636e7 | + | 1.18147e7i | 0.413985 | + | 0.239014i | 0.692501 | − | 0.721417i | \(-0.256509\pi\) |
−0.278515 | + | 0.960432i | \(0.589842\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.55661e7 | − | 4.96048e7i | 0.304830 | − | 0.971410i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.68038e7 | − | 6.37461e7i | −0.709197 | − | 1.22836i | −0.965156 | − | 0.261677i | \(-0.915725\pi\) |
0.255959 | − | 0.966688i | \(-0.417609\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.24798e7i | 0.419535i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.68460e7 | −1.22788 | −0.613942 | − | 0.789351i | \(-0.710417\pi\) | ||||
−0.613942 | + | 0.789351i | \(0.710417\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.12881e7 | + | 6.51719e6i | −0.200921 | + | 0.116002i | −0.597085 | − | 0.802178i | \(-0.703674\pi\) |
0.396164 | + | 0.918180i | \(0.370341\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.06356e7 | − | 1.37303e8i | −0.536839 | − | 2.40601i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.65342e7 | + | 8.05995e7i | −0.790539 | + | 1.36925i | 0.135095 | + | 0.990833i | \(0.456866\pi\) |
−0.925634 | + | 0.378420i | \(0.876467\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.55225e6i | 0.0928835i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.72576e7 | + | 2.15107e7i | 0.604538 | + | 0.349030i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.08901e7 | − | 2.36079e7i | 0.653502 | − | 0.377300i | −0.136294 | − | 0.990668i | \(-0.543519\pi\) |
0.789797 | + | 0.613369i | \(0.210186\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.68261e7 | + | 2.91437e7i | 0.260946 | + | 0.451972i | 0.966494 | − | 0.256691i | \(-0.0826322\pi\) |
−0.705547 | + | 0.708663i | \(0.749299\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.52177e7 | − | 7.83193e7i | 0.690865 | − | 1.19661i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.34052e6 | −0.0198834 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.08078e7 | − | 5.24279e7i | −1.32725 | − | 0.766289i | −0.342378 | − | 0.939562i | \(-0.611232\pi\) |
−0.984874 | + | 0.173273i | \(0.944566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.63531e7 | − | 2.39598e7i | −1.08387 | − | 0.340120i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.46553e7 | + | 2.53836e7i | 0.205045 | + | 0.355148i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.27931e7i | 0.989574i | 0.869014 | + | 0.494787i | \(0.164754\pi\) | ||||
−0.869014 | + | 0.494787i | \(0.835246\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.33984e7 | −1.11766 | −0.558832 | − | 0.829281i | \(-0.688750\pi\) | ||||
−0.558832 | + | 0.829281i | \(0.688750\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.03215e6 | − | 2.32796e6i | 0.0525254 | − | 0.0303256i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.17052e7 | − | 1.99436e7i | 0.278792 | − | 0.256165i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.49649e7 | + | 4.32405e7i | −0.311816 | + | 0.540081i | −0.978756 | − | 0.205031i | \(-0.934271\pi\) |
0.666940 | + | 0.745112i | \(0.267604\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.20837e7i | − | 1.13428i | −0.823623 | − | 0.567138i | \(-0.808050\pi\) | ||
0.823623 | − | 0.567138i | \(-0.191950\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.22507e7 | − | 3.59405e7i | −0.745934 | − | 0.430665i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.97213e7 | − | 1.71596e7i | 0.351297 | − | 0.202822i | −0.313959 | − | 0.949436i | \(-0.601656\pi\) |
0.665257 | + | 0.746615i | \(0.268322\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.55571e7 | − | 4.42661e7i | −0.293968 | − | 0.509167i | 0.680776 | − | 0.732491i | \(-0.261643\pi\) |
−0.974744 | + | 0.223324i | \(0.928309\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.22508e7 | + | 3.85395e7i | −0.252503 | + | 0.437347i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.46829e7 | −0.714580 | −0.357290 | − | 0.933994i | \(-0.616299\pi\) | ||||
−0.357290 | + | 0.933994i | \(0.616299\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.57253e8 | + | 9.07903e7i | 1.71424 | + | 0.989714i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.20874e8 | + | 1.31551e8i | 1.28322 | + | 1.39656i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.66510e7 | + | 9.81224e7i | 0.593552 | + | 1.02806i | 0.993749 | + | 0.111633i | \(0.0356082\pi\) |
−0.400197 | + | 0.916429i | \(0.631058\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.87367e8i | − | 1.91245i | −0.292638 | − | 0.956223i | \(-0.594533\pi\) | ||
0.292638 | − | 0.956223i | \(-0.405467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.52237e8 | −1.53383 | −0.766914 | − | 0.641750i | \(-0.778209\pi\) | ||||
−0.766914 | + | 0.641750i | \(0.778209\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.93113e7 | − | 5.15639e7i | 0.876912 | − | 0.506285i | 0.00727296 | − | 0.999974i | \(-0.497685\pi\) |
0.869639 | + | 0.493688i | \(0.164352\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.14056e7 | − | 3.63464e7i | 0.110560 | − | 0.352324i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.90808e8 | − | 3.30489e8i | 1.80307 | − | 3.12301i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.02768e7i | 0.562431i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.88344e7 | + | 2.81946e7i | 0.444344 | + | 0.256542i | 0.705439 | − | 0.708771i | \(-0.250750\pi\) |
−0.261094 | + | 0.965313i | \(0.584083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.47428e6 | − | 851178.i | 0.0132479 | − | 0.00764865i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.00623e7 | + | 1.21351e8i | 0.614128 | + | 1.06370i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.68754e7 | − | 9.85111e7i | 0.492422 | − | 0.852900i | −0.507540 | − | 0.861628i | \(-0.669445\pi\) |
0.999962 | + | 0.00872796i | \(0.00277823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.26412e7 | −0.529195 | −0.264598 | − | 0.964359i | \(-0.585239\pi\) | ||||
−0.264598 | + | 0.964359i | \(0.585239\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.02086e6 | − | 1.74410e6i | −0.0252110 | − | 0.0145556i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.67770e8 | + | 3.74336e7i | −1.36662 | + | 0.304925i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.83524e6 | + | 3.17873e6i | 0.0147704 | + | 0.0255830i | 0.873316 | − | 0.487154i | \(-0.161965\pi\) |
−0.858546 | + | 0.512737i | \(0.828632\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 8.33034e7i | − | 0.654574i | −0.944925 | − | 0.327287i | \(-0.893866\pi\) | ||
0.944925 | − | 0.327287i | \(-0.106134\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.96164e8 | −1.52316 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.61652e6 | − | 2.66535e6i | 0.0350075 | − | 0.0202116i | −0.482394 | − | 0.875954i | \(-0.660233\pi\) |
0.517402 | + | 0.855743i | \(0.326899\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.48753e8 | − | 4.66789e7i | −1.11481 | − | 0.349831i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.39137e7 | + | 9.33813e7i | −0.394710 | + | 0.683657i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.54473e8i | 3.28879i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.72901e7 | + | 9.98245e6i | 0.122260 | + | 0.0705869i | 0.559883 | − | 0.828572i | \(-0.310846\pi\) |
−0.437623 | + | 0.899159i | \(0.644179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.33047e8 | − | 1.34550e8i | 1.62906 | − | 0.940541i | 0.644693 | − | 0.764442i | \(-0.276985\pi\) |
0.984372 | − | 0.176099i | \(-0.0563479\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.01642e6 | + | 1.21528e7i | 0.0479384 | + | 0.0830318i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.57928e7 | − | 2.73539e7i | 0.106682 | − | 0.184779i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.30593e8 | −1.52287 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.14621e8 | + | 1.23912e8i | 1.40156 | + | 0.809191i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.59394e7 | + | 3.06090e8i | −0.165651 | + | 1.95471i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.53414e7 | − | 1.30495e8i | −0.475819 | − | 0.824143i | 0.523797 | − | 0.851843i | \(-0.324515\pi\) |
−0.999616 | + | 0.0277000i | \(0.991182\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.10315e8i | 1.91696i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.63897e8 | 1.00140 | 0.500701 | − | 0.865620i | \(-0.333076\pi\) | ||||
0.500701 | + | 0.865620i | \(0.333076\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.91089e7 | − | 2.25795e7i | 0.233787 | − | 0.134977i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.35602e7 | − | 6.91744e7i | −0.375846 | − | 0.409044i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.84031e7 | − | 1.01157e8i | 0.337964 | − | 0.585371i | −0.646086 | − | 0.763265i | \(-0.723595\pi\) |
0.984050 | + | 0.177894i | \(0.0569285\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.84622e8i | 2.77439i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.33717e8 | − | 7.72016e7i | −0.749311 | − | 0.432615i | 0.0761341 | − | 0.997098i | \(-0.475742\pi\) |
−0.825445 | + | 0.564483i | \(0.809076\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.79713e7 | − | 5.07903e7i | 0.487748 | − | 0.281602i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.29301e7 | + | 1.26319e8i | 0.395886 | + | 0.685694i | 0.993214 | − | 0.116303i | \(-0.0371043\pi\) |
−0.597328 | + | 0.801997i | \(0.703771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.14722e7 | + | 1.41114e8i | −0.437624 | + | 0.757987i | −0.997506 | − | 0.0705858i | \(-0.977513\pi\) |
0.559882 | + | 0.828572i | \(0.310846\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.76511e7 | 0.513658 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.68759e7 | − | 1.55168e7i | −0.139906 | − | 0.0807746i | 0.428413 | − | 0.903583i | \(-0.359073\pi\) |
−0.568319 | + | 0.822808i | \(0.692406\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.39378e7 | − | 6.24664e7i | −0.0710664 | − | 0.318506i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.97883e8 | + | 3.42744e8i | 0.998627 | + | 1.72967i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 3.59531e8i | − | 1.77755i | −0.458344 | − | 0.888775i | \(-0.651557\pi\) | ||
0.458344 | − | 0.888775i | \(-0.348443\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.81673e8 | −0.889088 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.10349e7 | + | 5.25590e7i | −0.436560 | + | 0.252048i | −0.702137 | − | 0.712042i | \(-0.747771\pi\) |
0.265577 | + | 0.964090i | \(0.414437\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.70560e7 | + | 6.03684e6i | −0.128444 | + | 0.0286589i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.67005e7 | − | 1.15529e8i | 0.310348 | − | 0.537538i | −0.668090 | − | 0.744081i | \(-0.732888\pi\) |
0.978438 | + | 0.206542i | \(0.0662212\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.19336e8i | 1.01038i | 0.863007 | + | 0.505192i | \(0.168578\pi\) | ||||
−0.863007 | + | 0.505192i | \(0.831422\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.86435e8 | + | 3.96313e8i | 3.09980 | + | 1.78967i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.98185e8 | + | 1.14422e8i | −0.886143 | + | 0.511615i | −0.872679 | − | 0.488294i | \(-0.837619\pi\) |
−0.0134642 | + | 0.999909i | \(0.504286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.88572e8 | − | 4.99821e8i | −1.26512 | − | 2.19125i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.08106e8 | + | 1.87246e8i | −0.469321 | + | 0.812887i | −0.999385 | − | 0.0350704i | \(-0.988834\pi\) |
0.530064 | + | 0.847957i | \(0.322168\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.65273e8 | −0.703634 | −0.351817 | − | 0.936069i | \(-0.614436\pi\) | ||||
−0.351817 | + | 0.936069i | \(0.614436\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.14104e8 | + | 1.23613e8i | 0.902718 | + | 0.521185i | 0.878081 | − | 0.478512i | \(-0.158824\pi\) |
0.0246372 | + | 0.999696i | \(0.492157\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.15545e7 | − | 6.57471e7i | 0.295919 | − | 0.271902i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.51823e8 | + | 2.62966e8i | 0.621868 | + | 1.07711i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 264154.i | 0.00106147i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.97554e8 | −0.786317 | −0.393158 | − | 0.919471i | \(-0.628618\pi\) | ||||
−0.393158 | + | 0.919471i | \(0.628618\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.46322e8 | + | 1.42214e8i | −0.962017 | + | 0.555421i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.65827e8 | − | 3.53103e8i | −0.641560 | − | 1.36610i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.13429e7 | + | 1.96465e7i | −0.0430675 | + | 0.0745951i | −0.886756 | − | 0.462239i | \(-0.847046\pi\) |
0.843688 | + | 0.536834i | \(0.180380\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.36606e8i | 1.26616i | 0.774085 | + | 0.633081i | \(0.218210\pi\) | ||||
−0.774085 | + | 0.633081i | \(0.781790\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.80996e7 | + | 2.19968e7i | 0.140672 | + | 0.0812171i | 0.568684 | − | 0.822556i | \(-0.307453\pi\) |
−0.428012 | + | 0.903773i | \(0.640786\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.27561e8 | − | 3.04587e8i | 1.92992 | − | 1.11424i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.36808e7 | − | 9.29779e7i | −0.192788 | − | 0.333918i | 0.753385 | − | 0.657579i | \(-0.228420\pi\) |
−0.946173 | + | 0.323661i | \(0.895086\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.52129e8 | − | 4.36701e8i | 0.897222 | − | 1.55403i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.96679e7 | 0.173548 | 0.0867739 | − | 0.996228i | \(-0.472344\pi\) | ||||
0.0867739 | + | 0.996228i | \(0.472344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.62080e7 | + | 5.55457e7i | 0.333125 | + | 0.192330i | 0.657228 | − | 0.753692i | \(-0.271729\pi\) |
−0.324103 | + | 0.946022i | \(0.605062\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.07453e8 | − | 3.42424e8i | 0.365389 | − | 1.16439i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.65799e7 | − | 6.33582e7i | −0.123272 | − | 0.213513i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.24386e8i | 0.742726i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.29393e8 | −1.40867 | −0.704337 | − | 0.709866i | \(-0.748755\pi\) | ||||
−0.704337 | + | 0.709866i | \(0.748755\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.11122e8 | + | 6.41564e7i | −0.358125 | + | 0.206764i | −0.668258 | − | 0.743930i | \(-0.732960\pi\) |
0.310133 | + | 0.950693i | \(0.399626\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.66322e7 | − | 2.98633e8i | −0.212850 | − | 0.953956i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.16965e7 | + | 1.58823e8i | −0.287800 | + | 0.498484i | −0.973284 | − | 0.229603i | \(-0.926257\pi\) |
0.685484 | + | 0.728087i | \(0.259590\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.13399e8i | 0.975048i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.35257e8 | − | 2.51296e8i | −1.33073 | − | 0.768295i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.78059e8 | − | 2.76008e8i | 1.44893 | − | 0.836540i | 0.450512 | − | 0.892770i | \(-0.351241\pi\) |
0.998418 | + | 0.0562298i | \(0.0179080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.18148e7 | − | 1.07066e8i | −0.184136 | − | 0.318933i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.78905e7 | − | 3.09873e7i | 0.0528354 | − | 0.0915136i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.32955e8 | 1.83746 | 0.918732 | − | 0.394882i | \(-0.129214\pi\) | ||||
0.918732 | + | 0.394882i | \(0.129214\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.96165e6 | − | 1.70991e6i | −0.00852447 | − | 0.00492161i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.08693e8 | + | 1.28249e8i | 1.15648 | + | 0.362906i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.44154e6 | + | 9.42503e6i | 0.0152680 | + | 0.0264450i | 0.873558 | − | 0.486719i | \(-0.161807\pi\) |
−0.858290 | + | 0.513164i | \(0.828473\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.94318e8i | 0.811987i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.35996e9 | −3.72056 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.00684e8 | − | 5.81301e7i | 0.270879 | − | 0.156392i | −0.358408 | − | 0.933565i | \(-0.616680\pi\) |
0.629287 | + | 0.777173i | \(0.283347\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.73377e8 | − | 1.59305e8i | 0.462578 | − | 0.425035i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.06746e7 | + | 5.31299e7i | −0.0804942 | + | 0.139420i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.51443e8i | − | 1.43515i | −0.696482 | − | 0.717575i | \(-0.745252\pi\) | ||
0.696482 | − | 0.717575i | \(-0.254748\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.51240e7 | − | 3.75994e7i | −0.166721 | − | 0.0962561i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.55500e8 | + | 8.97781e7i | −0.394838 | + | 0.227960i | −0.684254 | − | 0.729243i | \(-0.739872\pi\) |
0.289416 | + | 0.957203i | \(0.406539\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.44993e8 | + | 2.51135e8i | 0.362196 | + | 0.627342i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.19983e7 | + | 1.42025e8i | −0.203176 | + | 0.351911i | −0.949550 | − | 0.313616i | \(-0.898460\pi\) |
0.746374 | + | 0.665526i | \(0.231793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.60076e8 | −0.390265 | −0.195133 | − | 0.980777i | \(-0.562514\pi\) | ||||
−0.195133 | + | 0.980777i | \(0.562514\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.69056e8 | + | 4.44015e8i | 1.85990 | + | 1.07381i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.66137e8 | − | 3.98477e8i | −0.871361 | − | 0.948327i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.23458e7 | − | 3.87040e7i | −0.0527564 | − | 0.0913768i | 0.838441 | − | 0.544992i | \(-0.183467\pi\) |
−0.891198 | + | 0.453615i | \(0.850134\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.83752e8i | 0.891681i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.30985e8 | −0.532471 | −0.266235 | − | 0.963908i | \(-0.585780\pi\) | ||||
−0.266235 | + | 0.963908i | \(0.585780\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.03174e8 | + | 2.32773e8i | −0.914826 | + | 0.528175i | −0.881981 | − | 0.471286i | \(-0.843790\pi\) |
−0.0328451 | + | 0.999460i | \(0.510457\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.02879e8 | − | 6.46519e8i | 0.456734 | − | 1.45548i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.86801e8 | + | 6.69960e8i | −0.857239 | + | 1.48478i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.46426e7i | 0.208117i | 0.994571 | + | 0.104059i | \(0.0331829\pi\) | ||||
−0.994571 | + | 0.104059i | \(0.966817\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.89489e7 | − | 5.13547e7i | −0.192576 | − | 0.111184i | 0.400612 | − | 0.916248i | \(-0.368798\pi\) |
−0.593188 | + | 0.805064i | \(0.702131\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.13740e8 | − | 1.23403e8i | 0.459177 | − | 0.265106i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.31616e8 | + | 4.01170e8i | 0.489955 | + | 0.848626i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.54269e8 | − | 1.13323e9i | 1.37342 | − | 2.37883i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.65567e8 | −0.548990 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.07077e8 | − | 4.08231e8i | −1.45058 | − | 0.837495i | −0.452069 | − | 0.891983i | \(-0.649314\pi\) |
−0.998514 | + | 0.0544879i | \(0.982647\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.16488e8 | + | 4.83037e7i | −0.437426 | + | 0.0976002i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.42476e8 | − | 2.46776e8i | −0.285708 | − | 0.494861i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 6.56026e8i | − | 1.29582i | −0.761715 | − | 0.647912i | \(-0.775642\pi\) | ||
0.761715 | − | 0.647912i | \(-0.224358\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.95554e7 | 0.175570 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.02780e9 | − | 5.93403e8i | 1.98501 | − | 1.14605i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.54742e8 | − | 1.74079e8i | −1.06342 | − | 0.333702i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.57816e8 | − | 2.73345e8i | 0.298061 | − | 0.516257i | −0.677631 | − | 0.735402i | \(-0.736993\pi\) |
0.975692 | + | 0.219145i | \(0.0703268\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.28556e8i | 0.990898i | 0.868637 | + | 0.495449i | \(0.164996\pi\) | ||||
−0.868637 | + | 0.495449i | \(0.835004\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.58134e8 | − | 3.79974e8i | −1.21574 | − | 0.701909i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.43114e8 | − | 4.86772e8i | 1.54604 | − | 0.892605i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.53350e8 | + | 4.38816e8i | 0.457817 | + | 0.792963i | 0.998845 | − | 0.0480419i | \(-0.0152981\pi\) |
−0.541028 | + | 0.841004i | \(0.681965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.42861e8 | + | 4.20647e8i | −0.435670 | + | 0.754603i | −0.997350 | − | 0.0727515i | \(-0.976822\pi\) |
0.561680 | + | 0.827355i | \(0.310155\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.86017e8 | 1.03608 | 0.518041 | − | 0.855356i | \(-0.326662\pi\) | ||||
0.518041 | + | 0.855356i | \(0.326662\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.32195e7 | + | 1.34058e7i | 0.0407557 | + | 0.0235303i | 0.520239 | − | 0.854020i | \(-0.325843\pi\) |
−0.479484 | + | 0.877551i | \(0.659176\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.03161e7 | + | 5.11145e6i | 0.104351 | + | 0.00884320i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.42923e8 | − | 9.40370e8i | −0.932564 | − | 1.61525i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 8.56330e8i | − | 1.44996i | −0.688771 | − | 0.724979i | \(-0.741849\pi\) | ||
0.688771 | − | 0.724979i | \(-0.258151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.48861e8 | −0.922729 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.39046e8 | − | 4.84423e8i | 1.39064 | − | 0.802888i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.17103e9 | − | 1.27447e9i | −1.92717 | − | 2.09739i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.77013e6 | + | 4.79800e6i | −0.00449481 | + | 0.00778523i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.93083e8i | 1.11670i | 0.829604 | + | 0.558352i | \(0.188566\pi\) | ||||
−0.829604 | + | 0.558352i | \(0.811434\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.03661e9 | − | 5.98489e8i | −1.64693 | − | 0.950854i | −0.978283 | − | 0.207271i | \(-0.933542\pi\) |
−0.668644 | − | 0.743583i | \(-0.733125\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.54077e8 | − | 3.77632e8i | 1.03193 | − | 0.595784i | 0.114392 | − | 0.993436i | \(-0.463508\pi\) |
0.917536 | + | 0.397652i | \(0.130175\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.37317e8 | + | 4.11045e8i | 0.369230 | + | 0.639525i | 0.989445 | − | 0.144907i | \(-0.0462882\pi\) |
−0.620216 | + | 0.784431i | \(0.712955\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.69162e8 | − | 1.33223e9i | 1.18842 | − | 2.05840i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.15119e8 | 1.08973 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.18921e8 | − | 1.84129e8i | −0.482646 | − | 0.278656i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.71551e7 | − | 3.45794e8i | −0.115170 | − | 0.516171i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.10023e8 | + | 7.10181e8i | 0.607869 | + | 1.05286i | 0.991591 | + | 0.129411i | \(0.0413086\pi\) |
−0.383723 | + | 0.923448i | \(0.625358\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.24754e8i | 0.182443i | 0.995831 | + | 0.0912216i | \(0.0290772\pi\) | ||||
−0.995831 | + | 0.0912216i | \(0.970923\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.94702e7 | −0.129956 | −0.0649780 | − | 0.997887i | \(-0.520698\pi\) | ||||
−0.0649780 | + | 0.997887i | \(0.520698\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.75975e8 | − | 2.17069e8i | 0.538751 | − | 0.311048i | −0.205821 | − | 0.978590i | \(-0.565987\pi\) |
0.744573 | + | 0.667541i | \(0.232653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.06172e8 | − | 1.35252e8i | 0.862762 | − | 0.192503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.79705e8 | + | 1.00408e9i | −0.814052 | + | 1.40998i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.03260e9i | 1.44034i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.60133e8 | − | 9.24525e7i | −0.220394 | − | 0.127245i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.75388e7 | − | 3.89936e7i | 0.0923377 | − | 0.0533112i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.66548e7 | + | 1.15450e8i | 0.0899261 | + | 0.155757i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.93196e8 | + | 5.07830e8i | −0.392949 | + | 0.680607i | −0.992837 | − | 0.119477i | \(-0.961878\pi\) |
0.599888 | + | 0.800084i | \(0.295212\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.05258e8 | −0.932809 | −0.466405 | − | 0.884572i | \(-0.654451\pi\) | ||||
−0.466405 | + | 0.884572i | \(0.654451\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.21937e8 | + | 2.43605e8i | 0.554416 | + | 0.320092i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.10802e8 | + | 7.44997e8i | −1.05149 | + | 0.966155i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.63656e8 | + | 2.83461e8i | 0.210856 | + | 0.365213i | 0.951983 | − | 0.306152i | \(-0.0990416\pi\) |
−0.741127 | + | 0.671365i | \(0.765708\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.66174e9i | 2.11328i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.64586e6 | 0.00587004 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.04221e9 | + | 6.01721e8i | −1.29990 | + | 0.750496i | −0.980386 | − | 0.197087i | \(-0.936852\pi\) |
−0.319511 | + | 0.947583i | \(0.603519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.47743e8 | + | 6.43165e8i | −0.554855 | + | 0.797027i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.05513e8 | − | 1.82753e8i | 0.129083 | − | 0.223578i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.77788e8i | 0.459230i | 0.973282 | + | 0.229615i | \(0.0737466\pi\) | ||||
−0.973282 | + | 0.229615i | \(0.926253\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.66347e8 | + | 3.84716e8i | 0.799709 | + | 0.461712i | 0.843369 | − | 0.537334i | \(-0.180569\pi\) |
−0.0436607 | + | 0.999046i | \(0.513902\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.49914e8 | − | 3.75228e8i | 0.775034 | − | 0.447466i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.53429e8 | + | 2.65747e8i | 0.180658 | + | 0.312910i | 0.942105 | − | 0.335318i | \(-0.108844\pi\) |
−0.761447 | + | 0.648228i | \(0.775510\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.53574e8 | + | 1.30523e9i | −0.881713 | + | 1.52717i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.56965e7 | −0.0181352 | −0.00906761 | − | 0.999959i | \(-0.502886\pi\) | ||||
−0.00906761 | + | 0.999959i | \(0.502886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.13490e8 | + | 1.23259e8i | 0.245114 | + | 0.141517i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.04895e8 | − | 6.52945e8i | 0.232315 | − | 0.740322i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.18191e7 | − | 1.24394e8i | −0.0809226 | − | 0.140162i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.18163e9i | − | 1.31492i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.01121e9 | −1.11831 | −0.559157 | − | 0.829062i | \(-0.688875\pi\) | ||||
−0.559157 | + | 0.829062i | \(0.688875\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.06493e9 | + | 6.14839e8i | −1.16323 | + | 0.671590i | −0.952075 | − | 0.305864i | \(-0.901055\pi\) |
−0.211152 | + | 0.977453i | \(0.567721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.87885e7 | + | 2.63479e8i | 0.0638195 | + | 0.286027i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.38788e8 | − | 7.60003e8i | 0.470512 | − | 0.814951i | −0.528919 | − | 0.848672i | \(-0.677402\pi\) |
0.999431 | + | 0.0337210i | \(0.0107358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.39724e8i | 0.788354i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.20614e9 | + | 6.96367e8i | 1.26981 | + | 0.733125i | 0.974952 | − | 0.222417i | \(-0.0713946\pi\) |
0.294857 | + | 0.955541i | \(0.404728\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.81489e8 | + | 2.77988e8i | −0.503823 | + | 0.290882i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.88592e8 | − | 1.36588e9i | −0.815199 | − | 1.41197i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.53175e8 | − | 9.58126e8i | 0.568383 | − | 0.984469i | −0.428343 | − | 0.903616i | \(-0.640902\pi\) |
0.996726 | − | 0.0808523i | \(-0.0257642\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.09124e8 | −0.516838 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.44428e8 | + | 4.87530e8i | 0.852073 | + | 0.491945i | 0.861350 | − | 0.508012i | \(-0.169620\pi\) |
−0.00927664 | + | 0.999957i | \(0.502953\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.7.z.f.73.2 | ✓ | 12 | |
3.2 | odd | 2 | inner | 252.7.z.f.73.5 | yes | 12 | |
7.5 | odd | 6 | inner | 252.7.z.f.145.2 | yes | 12 | |
21.5 | even | 6 | inner | 252.7.z.f.145.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.7.z.f.73.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
252.7.z.f.73.5 | yes | 12 | 3.2 | odd | 2 | inner | |
252.7.z.f.145.2 | yes | 12 | 7.5 | odd | 6 | inner | |
252.7.z.f.145.5 | yes | 12 | 21.5 | even | 6 | inner |