Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,74,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 74, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 74);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 74 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(33.7483973737\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots + 17\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{15}\cdot 5^{6}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-3.13124e9\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.31882e11 | 1.35703 | 0.678516 | − | 0.734586i | \(-0.262624\pi\) | ||||
0.678516 | + | 0.734586i | \(0.262624\pi\) | |||||||
\(3\) | 7.82937e15 | 0.0301163 | 0.0150581 | − | 0.999887i | \(-0.495207\pi\) | ||||
0.0150581 | + | 0.999887i | \(0.495207\pi\) | |||||||
\(4\) | 7.94807e21 | 0.841534 | ||||||||
\(5\) | −7.75470e24 | −0.238320 | −0.119160 | − | 0.992875i | \(-0.538020\pi\) | ||||
−0.119160 | + | 0.992875i | \(0.538020\pi\) | |||||||
\(6\) | 1.03255e27 | 0.0408687 | ||||||||
\(7\) | 1.05974e30 | 0.151050 | 0.0755252 | − | 0.997144i | \(-0.475937\pi\) | ||||
0.0755252 | + | 0.997144i | \(0.475937\pi\) | |||||||
\(8\) | −1.97383e32 | −0.215043 | ||||||||
\(9\) | −6.75239e34 | −0.999093 | ||||||||
\(10\) | −1.02270e36 | −0.323407 | ||||||||
\(11\) | 5.33872e37 | 0.520720 | 0.260360 | − | 0.965512i | \(-0.416159\pi\) | ||||
0.260360 | + | 0.965512i | \(0.416159\pi\) | |||||||
\(12\) | 6.22283e37 | 0.0253439 | ||||||||
\(13\) | −2.33841e40 | −0.512847 | −0.256423 | − | 0.966565i | \(-0.582544\pi\) | ||||
−0.256423 | + | 0.966565i | \(0.582544\pi\) | |||||||
\(14\) | 1.39761e41 | 0.204980 | ||||||||
\(15\) | −6.07144e40 | −0.00717730 | ||||||||
\(16\) | −1.01099e44 | −1.13335 | ||||||||
\(17\) | −3.97117e44 | −0.487004 | −0.243502 | − | 0.969900i | \(-0.578296\pi\) | ||||
−0.243502 | + | 0.969900i | \(0.578296\pi\) | |||||||
\(18\) | −8.90517e45 | −1.35580 | ||||||||
\(19\) | −7.99880e46 | −1.69246 | −0.846230 | − | 0.532817i | \(-0.821133\pi\) | ||||
−0.846230 | + | 0.532817i | \(0.821133\pi\) | |||||||
\(20\) | −6.16349e46 | −0.200554 | ||||||||
\(21\) | 8.29711e45 | 0.00454907 | ||||||||
\(22\) | 7.04080e48 | 0.706633 | ||||||||
\(23\) | 6.65108e49 | 1.31773 | 0.658864 | − | 0.752262i | \(-0.271037\pi\) | ||||
0.658864 | + | 0.752262i | \(0.271037\pi\) | |||||||
\(24\) | −1.54539e48 | −0.00647629 | ||||||||
\(25\) | −9.98656e50 | −0.943204 | ||||||||
\(26\) | −3.08393e51 | −0.695949 | ||||||||
\(27\) | −1.05782e51 | −0.0602052 | ||||||||
\(28\) | 8.42290e51 | 0.127114 | ||||||||
\(29\) | 2.50436e53 | 1.04995 | 0.524977 | − | 0.851117i | \(-0.324074\pi\) | ||||
0.524977 | + | 0.851117i | \(0.324074\pi\) | |||||||
\(30\) | −8.00713e51 | −0.00973982 | ||||||||
\(31\) | −3.03546e54 | −1.11564 | −0.557819 | − | 0.829963i | \(-0.688362\pi\) | ||||
−0.557819 | + | 0.829963i | \(0.688362\pi\) | |||||||
\(32\) | −1.14688e55 | −1.32295 | ||||||||
\(33\) | 4.17988e53 | 0.0156821 | ||||||||
\(34\) | −5.23725e55 | −0.660880 | ||||||||
\(35\) | −8.21799e54 | −0.0359983 | ||||||||
\(36\) | −5.36684e56 | −0.840771 | ||||||||
\(37\) | −2.59488e57 | −1.49539 | −0.747696 | − | 0.664042i | \(-0.768840\pi\) | ||||
−0.747696 | + | 0.664042i | \(0.768840\pi\) | |||||||
\(38\) | −1.05490e58 | −2.29672 | ||||||||
\(39\) | −1.83082e56 | −0.0154450 | ||||||||
\(40\) | 1.53065e57 | 0.0512490 | ||||||||
\(41\) | 1.11326e58 | 0.151352 | 0.0756759 | − | 0.997132i | \(-0.475889\pi\) | ||||
0.0756759 | + | 0.997132i | \(0.475889\pi\) | |||||||
\(42\) | 1.09424e57 | 0.00617323 | ||||||||
\(43\) | −1.82489e58 | −0.0436152 | −0.0218076 | − | 0.999762i | \(-0.506942\pi\) | ||||
−0.0218076 | + | 0.999762i | \(0.506942\pi\) | |||||||
\(44\) | 4.24325e59 | 0.438204 | ||||||||
\(45\) | 5.23628e59 | 0.238104 | ||||||||
\(46\) | 8.77155e60 | 1.78820 | ||||||||
\(47\) | 1.00933e61 | 0.938562 | 0.469281 | − | 0.883049i | \(-0.344513\pi\) | ||||
0.469281 | + | 0.883049i | \(0.344513\pi\) | |||||||
\(48\) | −7.91538e59 | −0.0341324 | ||||||||
\(49\) | −4.80987e61 | −0.977184 | ||||||||
\(50\) | −1.31704e62 | −1.27996 | ||||||||
\(51\) | −3.10917e60 | −0.0146667 | ||||||||
\(52\) | −1.85858e62 | −0.431578 | ||||||||
\(53\) | 9.84119e60 | 0.0114019 | 0.00570096 | − | 0.999984i | \(-0.498185\pi\) | ||||
0.00570096 | + | 0.999984i | \(0.498185\pi\) | |||||||
\(54\) | −1.39507e62 | −0.0817003 | ||||||||
\(55\) | −4.14002e62 | −0.124098 | ||||||||
\(56\) | −2.09175e62 | −0.0324823 | ||||||||
\(57\) | −6.26256e62 | −0.0509706 | ||||||||
\(58\) | 3.30280e64 | 1.42482 | ||||||||
\(59\) | 5.71932e64 | 1.32205 | 0.661023 | − | 0.750366i | \(-0.270123\pi\) | ||||
0.661023 | + | 0.750366i | \(0.270123\pi\) | |||||||
\(60\) | −4.82562e62 | −0.00603994 | ||||||||
\(61\) | −7.84734e64 | −0.537259 | −0.268629 | − | 0.963244i | \(-0.586571\pi\) | ||||
−0.268629 | + | 0.963244i | \(0.586571\pi\) | |||||||
\(62\) | −4.00322e65 | −1.51396 | ||||||||
\(63\) | −7.15579e64 | −0.150913 | ||||||||
\(64\) | −5.57680e65 | −0.661936 | ||||||||
\(65\) | 1.81336e65 | 0.122221 | ||||||||
\(66\) | 5.51250e64 | 0.0212811 | ||||||||
\(67\) | 5.03632e66 | 1.12301 | 0.561505 | − | 0.827474i | \(-0.310223\pi\) | ||||
0.561505 | + | 0.827474i | \(0.310223\pi\) | |||||||
\(68\) | −3.15631e66 | −0.409831 | ||||||||
\(69\) | 5.20737e65 | 0.0396850 | ||||||||
\(70\) | −1.08380e66 | −0.0488508 | ||||||||
\(71\) | 4.24341e67 | 1.13969 | 0.569843 | − | 0.821753i | \(-0.307004\pi\) | ||||
0.569843 | + | 0.821753i | \(0.307004\pi\) | |||||||
\(72\) | 1.33281e67 | 0.214848 | ||||||||
\(73\) | 9.03815e67 | 0.880633 | 0.440317 | − | 0.897843i | \(-0.354866\pi\) | ||||
0.440317 | + | 0.897843i | \(0.354866\pi\) | |||||||
\(74\) | −3.42218e68 | −2.02929 | ||||||||
\(75\) | −7.81884e66 | −0.0284058 | ||||||||
\(76\) | −6.35750e68 | −1.42426 | ||||||||
\(77\) | 5.65767e67 | 0.0786549 | ||||||||
\(78\) | −2.41452e67 | −0.0209594 | ||||||||
\(79\) | 2.30814e69 | 1.25856 | 0.629279 | − | 0.777180i | \(-0.283350\pi\) | ||||
0.629279 | + | 0.777180i | \(0.283350\pi\) | |||||||
\(80\) | 7.83990e68 | 0.270101 | ||||||||
\(81\) | 4.55533e69 | 0.997280 | ||||||||
\(82\) | 1.46819e69 | 0.205389 | ||||||||
\(83\) | −1.28517e70 | −1.15507 | −0.577536 | − | 0.816365i | \(-0.695986\pi\) | ||||
−0.577536 | + | 0.816365i | \(0.695986\pi\) | |||||||
\(84\) | 6.59460e67 | 0.00382820 | ||||||||
\(85\) | 3.07952e69 | 0.116063 | ||||||||
\(86\) | −2.40669e69 | −0.0591871 | ||||||||
\(87\) | 1.96076e69 | 0.0316207 | ||||||||
\(88\) | −1.05377e70 | −0.111977 | ||||||||
\(89\) | −2.21881e71 | −1.56093 | −0.780466 | − | 0.625198i | \(-0.785018\pi\) | ||||
−0.780466 | + | 0.625198i | \(0.785018\pi\) | |||||||
\(90\) | 6.90570e70 | 0.323114 | ||||||||
\(91\) | −2.47811e70 | −0.0774657 | ||||||||
\(92\) | 5.28632e71 | 1.10891 | ||||||||
\(93\) | −2.37658e70 | −0.0335988 | ||||||||
\(94\) | 1.33113e72 | 1.27366 | ||||||||
\(95\) | 6.20284e71 | 0.403347 | ||||||||
\(96\) | −8.97937e70 | −0.0398424 | ||||||||
\(97\) | −2.42972e72 | −0.738564 | −0.369282 | − | 0.929317i | \(-0.620396\pi\) | ||||
−0.369282 | + | 0.929317i | \(0.620396\pi\) | |||||||
\(98\) | −6.34334e72 | −1.32607 | ||||||||
\(99\) | −3.60491e72 | −0.520248 | ||||||||
\(100\) | −7.93738e72 | −0.793738 | ||||||||
\(101\) | 2.33656e73 | 1.62497 | 0.812486 | − | 0.582980i | \(-0.198114\pi\) | ||||
0.812486 | + | 0.582980i | \(0.198114\pi\) | |||||||
\(102\) | −4.10043e71 | −0.0199032 | ||||||||
\(103\) | 5.10135e72 | 0.173431 | 0.0867155 | − | 0.996233i | \(-0.472363\pi\) | ||||
0.0867155 | + | 0.996233i | \(0.472363\pi\) | |||||||
\(104\) | 4.61562e72 | 0.110284 | ||||||||
\(105\) | −6.43416e70 | −0.00108413 | ||||||||
\(106\) | 1.29787e72 | 0.0154728 | ||||||||
\(107\) | 7.28757e73 | 0.616701 | 0.308351 | − | 0.951273i | \(-0.400223\pi\) | ||||
0.308351 | + | 0.951273i | \(0.400223\pi\) | |||||||
\(108\) | −8.40761e72 | −0.0506647 | ||||||||
\(109\) | 1.98778e73 | 0.0855662 | 0.0427831 | − | 0.999084i | \(-0.486378\pi\) | ||||
0.0427831 | + | 0.999084i | \(0.486378\pi\) | |||||||
\(110\) | −5.45993e73 | −0.168405 | ||||||||
\(111\) | −2.03163e73 | −0.0450356 | ||||||||
\(112\) | −1.07138e74 | −0.171194 | ||||||||
\(113\) | −1.41242e75 | −1.63155 | −0.815773 | − | 0.578372i | \(-0.803688\pi\) | ||||
−0.815773 | + | 0.578372i | \(0.803688\pi\) | |||||||
\(114\) | −8.25917e73 | −0.0691687 | ||||||||
\(115\) | −5.15771e74 | −0.314041 | ||||||||
\(116\) | 1.99048e75 | 0.883572 | ||||||||
\(117\) | 1.57898e75 | 0.512381 | ||||||||
\(118\) | 7.54275e75 | 1.79406 | ||||||||
\(119\) | −4.20842e74 | −0.0735622 | ||||||||
\(120\) | 1.19840e73 | 0.00154343 | ||||||||
\(121\) | −7.66134e75 | −0.728851 | ||||||||
\(122\) | −1.03492e76 | −0.729077 | ||||||||
\(123\) | 8.71616e73 | 0.00455815 | ||||||||
\(124\) | −2.41261e76 | −0.938848 | ||||||||
\(125\) | 1.59549e76 | 0.463104 | ||||||||
\(126\) | −9.43718e75 | −0.204794 | ||||||||
\(127\) | 8.09414e75 | 0.131624 | 0.0658120 | − | 0.997832i | \(-0.479036\pi\) | ||||
0.0658120 | + | 0.997832i | \(0.479036\pi\) | |||||||
\(128\) | 3.47722e76 | 0.424686 | ||||||||
\(129\) | −1.42877e74 | −0.00131353 | ||||||||
\(130\) | 2.39150e76 | 0.165858 | ||||||||
\(131\) | −1.61076e75 | −0.00844554 | −0.00422277 | − | 0.999991i | \(-0.501344\pi\) | ||||
−0.00422277 | + | 0.999991i | \(0.501344\pi\) | |||||||
\(132\) | 3.32220e75 | 0.0131971 | ||||||||
\(133\) | −8.47667e76 | −0.255647 | ||||||||
\(134\) | 6.64199e77 | 1.52396 | ||||||||
\(135\) | 8.20307e75 | 0.0143481 | ||||||||
\(136\) | 7.83842e76 | 0.104727 | ||||||||
\(137\) | −1.35087e78 | −1.38138 | −0.690690 | − | 0.723151i | \(-0.742693\pi\) | ||||
−0.690690 | + | 0.723151i | \(0.742693\pi\) | |||||||
\(138\) | 6.86757e76 | 0.0538538 | ||||||||
\(139\) | −2.90894e78 | −1.75265 | −0.876324 | − | 0.481722i | \(-0.840011\pi\) | ||||
−0.876324 | + | 0.481722i | \(0.840011\pi\) | |||||||
\(140\) | −6.53171e76 | −0.0302938 | ||||||||
\(141\) | 7.90244e76 | 0.0282660 | ||||||||
\(142\) | 5.59629e78 | 1.54659 | ||||||||
\(143\) | −1.24841e78 | −0.267049 | ||||||||
\(144\) | 6.82657e78 | 1.13233 | ||||||||
\(145\) | −1.94206e78 | −0.250225 | ||||||||
\(146\) | 1.19197e79 | 1.19505 | ||||||||
\(147\) | −3.76582e77 | −0.0294291 | ||||||||
\(148\) | −2.06243e79 | −1.25842 | ||||||||
\(149\) | −1.05138e79 | −0.501717 | −0.250859 | − | 0.968024i | \(-0.580713\pi\) | ||||
−0.250859 | + | 0.968024i | \(0.580713\pi\) | |||||||
\(150\) | −1.03116e78 | −0.0385475 | ||||||||
\(151\) | −3.34668e79 | −0.981646 | −0.490823 | − | 0.871259i | \(-0.663304\pi\) | ||||
−0.490823 | + | 0.871259i | \(0.663304\pi\) | |||||||
\(152\) | 1.57883e79 | 0.363952 | ||||||||
\(153\) | 2.68149e79 | 0.486563 | ||||||||
\(154\) | 7.46143e78 | 0.106737 | ||||||||
\(155\) | 2.35391e79 | 0.265879 | ||||||||
\(156\) | −1.45515e78 | −0.0129975 | ||||||||
\(157\) | −2.44529e80 | −1.72979 | −0.864894 | − | 0.501955i | \(-0.832614\pi\) | ||||
−0.864894 | + | 0.501955i | \(0.832614\pi\) | |||||||
\(158\) | 3.04401e80 | 1.70790 | ||||||||
\(159\) | 7.70503e76 | 0.000343383 0 | ||||||||
\(160\) | 8.89374e79 | 0.315286 | ||||||||
\(161\) | 7.04842e79 | 0.199043 | ||||||||
\(162\) | 6.00765e80 | 1.35334 | ||||||||
\(163\) | −7.33185e80 | −1.31937 | −0.659684 | − | 0.751543i | \(-0.729310\pi\) | ||||
−0.659684 | + | 0.751543i | \(0.729310\pi\) | |||||||
\(164\) | 8.84830e79 | 0.127368 | ||||||||
\(165\) | −3.24137e78 | −0.00373736 | ||||||||
\(166\) | −1.69490e81 | −1.56747 | ||||||||
\(167\) | −3.20208e80 | −0.237838 | −0.118919 | − | 0.992904i | \(-0.537943\pi\) | ||||
−0.118919 | + | 0.992904i | \(0.537943\pi\) | |||||||
\(168\) | −1.63771e78 | −0.000978246 0 | ||||||||
\(169\) | −1.53223e81 | −0.736988 | ||||||||
\(170\) | 4.06133e80 | 0.157501 | ||||||||
\(171\) | 5.40110e81 | 1.69093 | ||||||||
\(172\) | −1.45043e80 | −0.0367037 | ||||||||
\(173\) | 7.26967e81 | 1.48878 | 0.744392 | − | 0.667743i | \(-0.232739\pi\) | ||||
0.744392 | + | 0.667743i | \(0.232739\pi\) | |||||||
\(174\) | 2.58588e80 | 0.0429102 | ||||||||
\(175\) | −1.05832e81 | −0.142471 | ||||||||
\(176\) | −5.39737e81 | −0.590160 | ||||||||
\(177\) | 4.47787e80 | 0.0398151 | ||||||||
\(178\) | −2.92620e82 | −2.11824 | ||||||||
\(179\) | 1.31256e82 | 0.774431 | 0.387216 | − | 0.921989i | \(-0.373437\pi\) | ||||
0.387216 | + | 0.921989i | \(0.373437\pi\) | |||||||
\(180\) | 4.16183e81 | 0.200372 | ||||||||
\(181\) | 1.94546e81 | 0.0765166 | 0.0382583 | − | 0.999268i | \(-0.487819\pi\) | ||||
0.0382583 | + | 0.999268i | \(0.487819\pi\) | |||||||
\(182\) | −3.26817e81 | −0.105123 | ||||||||
\(183\) | −6.14397e80 | −0.0161802 | ||||||||
\(184\) | −1.31281e82 | −0.283368 | ||||||||
\(185\) | 2.01225e82 | 0.356381 | ||||||||
\(186\) | −3.13427e81 | −0.0455947 | ||||||||
\(187\) | −2.12010e82 | −0.253593 | ||||||||
\(188\) | 8.02225e82 | 0.789832 | ||||||||
\(189\) | −1.12102e81 | −0.00909402 | ||||||||
\(190\) | 8.18041e82 | 0.547354 | ||||||||
\(191\) | −2.93860e82 | −0.162339 | −0.0811695 | − | 0.996700i | \(-0.525866\pi\) | ||||
−0.0811695 | + | 0.996700i | \(0.525866\pi\) | |||||||
\(192\) | −4.36628e81 | −0.0199350 | ||||||||
\(193\) | 2.95820e83 | 1.11734 | 0.558671 | − | 0.829389i | \(-0.311311\pi\) | ||||
0.558671 | + | 0.829389i | \(0.311311\pi\) | |||||||
\(194\) | −3.20436e83 | −1.00225 | ||||||||
\(195\) | 1.41975e81 | 0.00368085 | ||||||||
\(196\) | −3.82291e83 | −0.822334 | ||||||||
\(197\) | −7.95523e83 | −1.42114 | −0.710568 | − | 0.703628i | \(-0.751562\pi\) | ||||
−0.710568 | + | 0.703628i | \(0.751562\pi\) | |||||||
\(198\) | −4.75422e83 | −0.705992 | ||||||||
\(199\) | 6.99041e83 | 0.863704 | 0.431852 | − | 0.901944i | \(-0.357860\pi\) | ||||
0.431852 | + | 0.901944i | \(0.357860\pi\) | |||||||
\(200\) | 1.97118e83 | 0.202829 | ||||||||
\(201\) | 3.94312e82 | 0.0338208 | ||||||||
\(202\) | 3.08149e84 | 2.20514 | ||||||||
\(203\) | 2.65398e83 | 0.158596 | ||||||||
\(204\) | −2.47119e82 | −0.0123426 | ||||||||
\(205\) | −8.63304e82 | −0.0360701 | ||||||||
\(206\) | 6.72775e83 | 0.235351 | ||||||||
\(207\) | −4.49107e84 | −1.31653 | ||||||||
\(208\) | 2.36410e84 | 0.581237 | ||||||||
\(209\) | −4.27034e84 | −0.881298 | ||||||||
\(210\) | −8.48549e81 | −0.00147120 | ||||||||
\(211\) | −5.03036e84 | −0.733313 | −0.366657 | − | 0.930356i | \(-0.619498\pi\) | ||||
−0.366657 | + | 0.930356i | \(0.619498\pi\) | |||||||
\(212\) | 7.82184e82 | 0.00959511 | ||||||||
\(213\) | 3.32232e83 | 0.0343231 | ||||||||
\(214\) | 9.61098e84 | 0.836883 | ||||||||
\(215\) | 1.41515e83 | 0.0103944 | ||||||||
\(216\) | 2.08796e83 | 0.0129467 | ||||||||
\(217\) | −3.21681e84 | −0.168518 | ||||||||
\(218\) | 2.62153e84 | 0.116116 | ||||||||
\(219\) | 7.07630e83 | 0.0265214 | ||||||||
\(220\) | −3.29052e84 | −0.104433 | ||||||||
\(221\) | 9.28621e84 | 0.249759 | ||||||||
\(222\) | −2.67935e84 | −0.0611147 | ||||||||
\(223\) | 7.49686e85 | 1.45128 | 0.725641 | − | 0.688073i | \(-0.241543\pi\) | ||||
0.725641 | + | 0.688073i | \(0.241543\pi\) | |||||||
\(224\) | −1.21540e85 | −0.199833 | ||||||||
\(225\) | 6.74331e85 | 0.942348 | ||||||||
\(226\) | −1.86272e86 | −2.21406 | ||||||||
\(227\) | −2.61202e85 | −0.264261 | −0.132131 | − | 0.991232i | \(-0.542182\pi\) | ||||
−0.132131 | + | 0.991232i | \(0.542182\pi\) | |||||||
\(228\) | −4.97752e84 | −0.0428935 | ||||||||
\(229\) | −1.16589e86 | −0.856369 | −0.428185 | − | 0.903691i | \(-0.640847\pi\) | ||||
−0.428185 | + | 0.903691i | \(0.640847\pi\) | |||||||
\(230\) | −6.80208e85 | −0.426163 | ||||||||
\(231\) | 4.42960e83 | 0.00236879 | ||||||||
\(232\) | −4.94319e85 | −0.225785 | ||||||||
\(233\) | 3.91796e86 | 1.52957 | 0.764783 | − | 0.644288i | \(-0.222846\pi\) | ||||
0.764783 | + | 0.644288i | \(0.222846\pi\) | |||||||
\(234\) | 2.08239e86 | 0.695318 | ||||||||
\(235\) | −7.82708e85 | −0.223678 | ||||||||
\(236\) | 4.54576e86 | 1.11255 | ||||||||
\(237\) | 1.80713e85 | 0.0379030 | ||||||||
\(238\) | −5.55013e85 | −0.0998262 | ||||||||
\(239\) | 1.13004e86 | 0.174409 | 0.0872046 | − | 0.996190i | \(-0.472207\pi\) | ||||
0.0872046 | + | 0.996190i | \(0.472207\pi\) | |||||||
\(240\) | 6.13814e84 | 0.00813442 | ||||||||
\(241\) | −1.12975e87 | −1.28635 | −0.643175 | − | 0.765719i | \(-0.722383\pi\) | ||||
−0.643175 | + | 0.765719i | \(0.722383\pi\) | |||||||
\(242\) | −1.01039e87 | −0.989073 | ||||||||
\(243\) | 1.07158e86 | 0.0902395 | ||||||||
\(244\) | −6.23712e86 | −0.452121 | ||||||||
\(245\) | 3.72991e86 | 0.232882 | ||||||||
\(246\) | 1.14950e85 | 0.00618555 | ||||||||
\(247\) | 1.87045e87 | 0.867973 | ||||||||
\(248\) | 5.99150e86 | 0.239910 | ||||||||
\(249\) | −1.00620e86 | −0.0347864 | ||||||||
\(250\) | 2.10416e87 | 0.628446 | ||||||||
\(251\) | −4.85688e87 | −1.25391 | −0.626955 | − | 0.779055i | \(-0.715699\pi\) | ||||
−0.626955 | + | 0.779055i | \(0.715699\pi\) | |||||||
\(252\) | −5.68747e86 | −0.126999 | ||||||||
\(253\) | 3.55082e87 | 0.686167 | ||||||||
\(254\) | 1.06747e87 | 0.178618 | ||||||||
\(255\) | 2.41107e85 | 0.00349538 | ||||||||
\(256\) | 9.85296e87 | 1.23825 | ||||||||
\(257\) | −5.12068e87 | −0.558173 | −0.279087 | − | 0.960266i | \(-0.590032\pi\) | ||||
−0.279087 | + | 0.960266i | \(0.590032\pi\) | |||||||
\(258\) | −1.88429e85 | −0.00178250 | ||||||||
\(259\) | −2.74991e87 | −0.225879 | ||||||||
\(260\) | 1.44127e87 | 0.102854 | ||||||||
\(261\) | −1.69104e88 | −1.04900 | ||||||||
\(262\) | −2.12429e86 | −0.0114609 | ||||||||
\(263\) | −1.76095e88 | −0.826727 | −0.413364 | − | 0.910566i | \(-0.635646\pi\) | ||||
−0.413364 | + | 0.910566i | \(0.635646\pi\) | |||||||
\(264\) | −8.25038e85 | −0.00337234 | ||||||||
\(265\) | −7.63155e85 | −0.00271730 | ||||||||
\(266\) | −1.11792e88 | −0.346921 | ||||||||
\(267\) | −1.73719e87 | −0.0470095 | ||||||||
\(268\) | 4.00290e88 | 0.945051 | ||||||||
\(269\) | 4.34069e88 | 0.894541 | 0.447271 | − | 0.894399i | \(-0.352396\pi\) | ||||
0.447271 | + | 0.894399i | \(0.352396\pi\) | |||||||
\(270\) | 1.08184e87 | 0.0194708 | ||||||||
\(271\) | 9.76535e88 | 1.53571 | 0.767854 | − | 0.640625i | \(-0.221325\pi\) | ||||
0.767854 | + | 0.640625i | \(0.221325\pi\) | |||||||
\(272\) | 4.01480e88 | 0.551948 | ||||||||
\(273\) | −1.94020e86 | −0.00233298 | ||||||||
\(274\) | −1.78155e89 | −1.87458 | ||||||||
\(275\) | −5.33154e88 | −0.491145 | ||||||||
\(276\) | 4.13885e87 | 0.0333963 | ||||||||
\(277\) | 1.10474e88 | 0.0781172 | 0.0390586 | − | 0.999237i | \(-0.487564\pi\) | ||||
0.0390586 | + | 0.999237i | \(0.487564\pi\) | |||||||
\(278\) | −3.83636e89 | −2.37840 | ||||||||
\(279\) | 2.04966e89 | 1.11463 | ||||||||
\(280\) | 1.62209e87 | 0.00774118 | ||||||||
\(281\) | 1.93794e89 | 0.812006 | 0.406003 | − | 0.913872i | \(-0.366922\pi\) | ||||
0.406003 | + | 0.913872i | \(0.366922\pi\) | |||||||
\(282\) | 1.04219e88 | 0.0383578 | ||||||||
\(283\) | −1.60337e89 | −0.518597 | −0.259298 | − | 0.965797i | \(-0.583491\pi\) | ||||
−0.259298 | + | 0.965797i | \(0.583491\pi\) | |||||||
\(284\) | 3.37269e89 | 0.959085 | ||||||||
\(285\) | 4.85643e87 | 0.0121473 | ||||||||
\(286\) | −1.64642e89 | −0.362395 | ||||||||
\(287\) | 1.17977e88 | 0.0228617 | ||||||||
\(288\) | 7.74420e89 | 1.32175 | ||||||||
\(289\) | −5.07221e89 | −0.762827 | ||||||||
\(290\) | −2.56122e89 | −0.339563 | ||||||||
\(291\) | −1.90232e88 | −0.0222428 | ||||||||
\(292\) | 7.18358e89 | 0.741083 | ||||||||
\(293\) | −2.60962e89 | −0.237635 | −0.118817 | − | 0.992916i | \(-0.537910\pi\) | ||||
−0.118817 | + | 0.992916i | \(0.537910\pi\) | |||||||
\(294\) | −4.96643e88 | −0.0399362 | ||||||||
\(295\) | −4.43517e89 | −0.315070 | ||||||||
\(296\) | 5.12186e89 | 0.321574 | ||||||||
\(297\) | −5.64740e88 | −0.0313500 | ||||||||
\(298\) | −1.38657e90 | −0.680846 | ||||||||
\(299\) | −1.55529e90 | −0.675792 | ||||||||
\(300\) | −6.21447e88 | −0.0239044 | ||||||||
\(301\) | −1.93391e88 | −0.00658809 | ||||||||
\(302\) | −4.41365e90 | −1.33212 | ||||||||
\(303\) | 1.82938e89 | 0.0489381 | ||||||||
\(304\) | 8.08668e90 | 1.91816 | ||||||||
\(305\) | 6.08538e89 | 0.128039 | ||||||||
\(306\) | 3.53639e90 | 0.660281 | ||||||||
\(307\) | 6.88569e90 | 1.14129 | 0.570646 | − | 0.821196i | \(-0.306693\pi\) | ||||
0.570646 | + | 0.821196i | \(0.306693\pi\) | |||||||
\(308\) | 4.49675e89 | 0.0661908 | ||||||||
\(309\) | 3.99404e88 | 0.00522309 | ||||||||
\(310\) | 3.10438e90 | 0.360806 | ||||||||
\(311\) | −1.52167e91 | −1.57242 | −0.786208 | − | 0.617962i | \(-0.787958\pi\) | ||||
−0.786208 | + | 0.617962i | \(0.787958\pi\) | |||||||
\(312\) | 3.61374e88 | 0.00332135 | ||||||||
\(313\) | 2.24817e90 | 0.183849 | 0.0919245 | − | 0.995766i | \(-0.470698\pi\) | ||||
0.0919245 | + | 0.995766i | \(0.470698\pi\) | |||||||
\(314\) | −3.22489e91 | −2.34738 | ||||||||
\(315\) | 5.54911e89 | 0.0359656 | ||||||||
\(316\) | 1.83452e91 | 1.05912 | ||||||||
\(317\) | −1.42898e91 | −0.735129 | −0.367564 | − | 0.929998i | \(-0.619808\pi\) | ||||
−0.367564 | + | 0.929998i | \(0.619808\pi\) | |||||||
\(318\) | 1.01615e88 | 0.000465982 0 | ||||||||
\(319\) | 1.33701e91 | 0.546732 | ||||||||
\(320\) | 4.32464e90 | 0.157752 | ||||||||
\(321\) | 5.70571e89 | 0.0185727 | ||||||||
\(322\) | 9.29559e90 | 0.270108 | ||||||||
\(323\) | 3.17646e91 | 0.824236 | ||||||||
\(324\) | 3.62061e91 | 0.839245 | ||||||||
\(325\) | 2.33526e91 | 0.483719 | ||||||||
\(326\) | −9.66938e91 | −1.79042 | ||||||||
\(327\) | 1.55631e89 | 0.00257693 | ||||||||
\(328\) | −2.19740e90 | −0.0325472 | ||||||||
\(329\) | 1.06963e91 | 0.141770 | ||||||||
\(330\) | −4.27478e89 | −0.00507172 | ||||||||
\(331\) | 1.73204e91 | 0.184007 | 0.0920036 | − | 0.995759i | \(-0.470673\pi\) | ||||
0.0920036 | + | 0.995759i | \(0.470673\pi\) | |||||||
\(332\) | −1.02146e92 | −0.972032 | ||||||||
\(333\) | 1.75217e92 | 1.49403 | ||||||||
\(334\) | −4.22296e91 | −0.322754 | ||||||||
\(335\) | −3.90552e91 | −0.267635 | ||||||||
\(336\) | −8.38826e89 | −0.00515571 | ||||||||
\(337\) | −1.40454e92 | −0.774538 | −0.387269 | − | 0.921967i | \(-0.626582\pi\) | ||||
−0.387269 | + | 0.921967i | \(0.626582\pi\) | |||||||
\(338\) | −2.02074e92 | −1.00012 | ||||||||
\(339\) | −1.10583e91 | −0.0491361 | ||||||||
\(340\) | 2.44763e91 | 0.0976708 | ||||||||
\(341\) | −1.62055e92 | −0.580935 | ||||||||
\(342\) | 7.12307e92 | 2.29464 | ||||||||
\(343\) | −1.03135e92 | −0.298654 | ||||||||
\(344\) | 3.60202e90 | 0.00937914 | ||||||||
\(345\) | −4.03816e90 | −0.00945773 | ||||||||
\(346\) | 9.58736e92 | 2.02033 | ||||||||
\(347\) | −2.50690e92 | −0.475457 | −0.237728 | − | 0.971332i | \(-0.576403\pi\) | ||||
−0.237728 | + | 0.971332i | \(0.576403\pi\) | |||||||
\(348\) | 1.55842e91 | 0.0266099 | ||||||||
\(349\) | −2.05783e92 | −0.316433 | −0.158216 | − | 0.987404i | \(-0.550574\pi\) | ||||
−0.158216 | + | 0.987404i | \(0.550574\pi\) | |||||||
\(350\) | −1.39573e92 | −0.193338 | ||||||||
\(351\) | 2.47361e91 | 0.0308760 | ||||||||
\(352\) | −6.12289e92 | −0.688889 | ||||||||
\(353\) | −1.17187e93 | −1.18879 | −0.594393 | − | 0.804174i | \(-0.702608\pi\) | ||||
−0.594393 | + | 0.804174i | \(0.702608\pi\) | |||||||
\(354\) | 5.90549e91 | 0.0540303 | ||||||||
\(355\) | −3.29064e92 | −0.271610 | ||||||||
\(356\) | −1.76352e93 | −1.31358 | ||||||||
\(357\) | −3.29492e90 | −0.00221542 | ||||||||
\(358\) | 1.73102e93 | 1.05093 | ||||||||
\(359\) | 9.08675e92 | 0.498266 | 0.249133 | − | 0.968469i | \(-0.419854\pi\) | ||||
0.249133 | + | 0.968469i | \(0.419854\pi\) | |||||||
\(360\) | −1.03355e92 | −0.0512025 | ||||||||
\(361\) | 4.16445e93 | 1.86442 | ||||||||
\(362\) | 2.56571e92 | 0.103835 | ||||||||
\(363\) | −5.99834e91 | −0.0219503 | ||||||||
\(364\) | −1.96962e92 | −0.0651900 | ||||||||
\(365\) | −7.00882e92 | −0.209872 | ||||||||
\(366\) | −8.10278e91 | −0.0219571 | ||||||||
\(367\) | 1.48899e93 | 0.365242 | 0.182621 | − | 0.983183i | \(-0.441542\pi\) | ||||
0.182621 | + | 0.983183i | \(0.441542\pi\) | |||||||
\(368\) | −6.72414e93 | −1.49345 | ||||||||
\(369\) | −7.51720e92 | −0.151215 | ||||||||
\(370\) | 2.65380e93 | 0.483621 | ||||||||
\(371\) | 1.04291e91 | 0.00172227 | ||||||||
\(372\) | −1.88892e92 | −0.0282746 | ||||||||
\(373\) | 2.51509e93 | 0.341336 | 0.170668 | − | 0.985329i | \(-0.445408\pi\) | ||||
0.170668 | + | 0.985329i | \(0.445408\pi\) | |||||||
\(374\) | −2.79602e93 | −0.344133 | ||||||||
\(375\) | 1.24917e92 | 0.0139470 | ||||||||
\(376\) | −1.99225e93 | −0.201831 | ||||||||
\(377\) | −5.85621e93 | −0.538465 | ||||||||
\(378\) | −1.47841e92 | −0.0123409 | ||||||||
\(379\) | −2.99096e93 | −0.226714 | −0.113357 | − | 0.993554i | \(-0.536160\pi\) | ||||
−0.113357 | + | 0.993554i | \(0.536160\pi\) | |||||||
\(380\) | 4.93005e93 | 0.339430 | ||||||||
\(381\) | 6.33720e91 | 0.00396402 | ||||||||
\(382\) | −3.87548e93 | −0.220299 | ||||||||
\(383\) | 1.08200e94 | 0.559078 | 0.279539 | − | 0.960134i | \(-0.409818\pi\) | ||||
0.279539 | + | 0.960134i | \(0.409818\pi\) | |||||||
\(384\) | 2.72244e92 | 0.0127900 | ||||||||
\(385\) | −4.38735e92 | −0.0187450 | ||||||||
\(386\) | 3.90133e94 | 1.51627 | ||||||||
\(387\) | 1.23224e93 | 0.0435756 | ||||||||
\(388\) | −1.93116e94 | −0.621527 | ||||||||
\(389\) | 3.46532e94 | 1.01527 | 0.507636 | − | 0.861572i | \(-0.330519\pi\) | ||||
0.507636 | + | 0.861572i | \(0.330519\pi\) | |||||||
\(390\) | 1.87239e92 | 0.00499503 | ||||||||
\(391\) | −2.64125e94 | −0.641739 | ||||||||
\(392\) | 9.49387e93 | 0.210137 | ||||||||
\(393\) | −1.26112e91 | −0.000254348 0 | ||||||||
\(394\) | −1.04915e95 | −1.92853 | ||||||||
\(395\) | −1.78989e94 | −0.299939 | ||||||||
\(396\) | −2.86521e94 | −0.437806 | ||||||||
\(397\) | −1.15711e95 | −1.61258 | −0.806288 | − | 0.591523i | \(-0.798527\pi\) | ||||
−0.806288 | + | 0.591523i | \(0.798527\pi\) | |||||||
\(398\) | 9.21907e94 | 1.17207 | ||||||||
\(399\) | −6.63670e92 | −0.00769912 | ||||||||
\(400\) | 1.00963e95 | 1.06898 | ||||||||
\(401\) | 5.61950e94 | 0.543160 | 0.271580 | − | 0.962416i | \(-0.412454\pi\) | ||||
0.271580 | + | 0.962416i | \(0.412454\pi\) | |||||||
\(402\) | 5.20026e93 | 0.0458959 | ||||||||
\(403\) | 7.09815e94 | 0.572151 | ||||||||
\(404\) | 1.85711e95 | 1.36747 | ||||||||
\(405\) | −3.53253e94 | −0.237672 | ||||||||
\(406\) | 3.50011e94 | 0.215220 | ||||||||
\(407\) | −1.38534e95 | −0.778680 | ||||||||
\(408\) | 6.13699e92 | 0.00315398 | ||||||||
\(409\) | −1.31996e95 | −0.620385 | −0.310192 | − | 0.950674i | \(-0.600393\pi\) | ||||
−0.310192 | + | 0.950674i | \(0.600393\pi\) | |||||||
\(410\) | −1.13854e94 | −0.0489483 | ||||||||
\(411\) | −1.05765e94 | −0.0416020 | ||||||||
\(412\) | 4.05459e94 | 0.145948 | ||||||||
\(413\) | 6.06101e94 | 0.199695 | ||||||||
\(414\) | −5.92290e95 | −1.78658 | ||||||||
\(415\) | 9.96608e94 | 0.275276 | ||||||||
\(416\) | 2.68188e95 | 0.678473 | ||||||||
\(417\) | −2.27752e94 | −0.0527832 | ||||||||
\(418\) | −5.63180e95 | −1.19595 | ||||||||
\(419\) | 5.03533e95 | 0.979978 | 0.489989 | − | 0.871729i | \(-0.337001\pi\) | ||||
0.489989 | + | 0.871729i | \(0.337001\pi\) | |||||||
\(420\) | −5.11392e92 | −0.000912335 0 | ||||||||
\(421\) | 1.06657e96 | 1.74458 | 0.872292 | − | 0.488984i | \(-0.162633\pi\) | ||||
0.872292 | + | 0.488984i | \(0.162633\pi\) | |||||||
\(422\) | −6.63413e95 | −0.995129 | ||||||||
\(423\) | −6.81541e95 | −0.937710 | ||||||||
\(424\) | −1.94248e93 | −0.00245191 | ||||||||
\(425\) | 3.96583e95 | 0.459344 | ||||||||
\(426\) | 4.38154e94 | 0.0465775 | ||||||||
\(427\) | −8.31615e94 | −0.0811531 | ||||||||
\(428\) | 5.79221e95 | 0.518975 | ||||||||
\(429\) | −9.77426e93 | −0.00804253 | ||||||||
\(430\) | 1.86632e94 | 0.0141055 | ||||||||
\(431\) | 2.15593e96 | 1.49697 | 0.748487 | − | 0.663150i | \(-0.230781\pi\) | ||||
0.748487 | + | 0.663150i | \(0.230781\pi\) | |||||||
\(432\) | 1.06944e95 | 0.0682338 | ||||||||
\(433\) | −5.70080e95 | −0.334293 | −0.167147 | − | 0.985932i | \(-0.553455\pi\) | ||||
−0.167147 | + | 0.985932i | \(0.553455\pi\) | |||||||
\(434\) | −4.24238e95 | −0.228684 | ||||||||
\(435\) | −1.52051e94 | −0.00753583 | ||||||||
\(436\) | 1.57990e95 | 0.0720069 | ||||||||
\(437\) | −5.32006e96 | −2.23020 | ||||||||
\(438\) | 9.33235e94 | 0.0359903 | ||||||||
\(439\) | −3.84665e96 | −1.36498 | −0.682492 | − | 0.730893i | \(-0.739104\pi\) | ||||
−0.682492 | + | 0.730893i | \(0.739104\pi\) | |||||||
\(440\) | 8.17170e94 | 0.0266864 | ||||||||
\(441\) | 3.24781e96 | 0.976297 | ||||||||
\(442\) | 1.22468e96 | 0.338930 | ||||||||
\(443\) | −1.87246e96 | −0.477173 | −0.238586 | − | 0.971121i | \(-0.576684\pi\) | ||||
−0.238586 | + | 0.971121i | \(0.576684\pi\) | |||||||
\(444\) | −1.61475e95 | −0.0378990 | ||||||||
\(445\) | 1.72062e96 | 0.372001 | ||||||||
\(446\) | 9.88699e96 | 1.96944 | ||||||||
\(447\) | −8.23161e94 | −0.0151098 | ||||||||
\(448\) | −5.90997e95 | −0.0999857 | ||||||||
\(449\) | 1.04927e96 | 0.163642 | 0.0818211 | − | 0.996647i | \(-0.473926\pi\) | ||||
0.0818211 | + | 0.996647i | \(0.473926\pi\) | |||||||
\(450\) | 8.89320e96 | 1.27880 | ||||||||
\(451\) | 5.94341e95 | 0.0788119 | ||||||||
\(452\) | −1.12260e97 | −1.37300 | ||||||||
\(453\) | −2.62024e95 | −0.0295635 | ||||||||
\(454\) | −3.44478e96 | −0.358611 | ||||||||
\(455\) | 1.92170e95 | 0.0184616 | ||||||||
\(456\) | 1.23612e95 | 0.0109609 | ||||||||
\(457\) | −1.31030e97 | −1.07258 | −0.536291 | − | 0.844033i | \(-0.680175\pi\) | ||||
−0.536291 | + | 0.844033i | \(0.680175\pi\) | |||||||
\(458\) | −1.53759e97 | −1.16212 | ||||||||
\(459\) | 4.20078e95 | 0.0293202 | ||||||||
\(460\) | −4.09938e96 | −0.264276 | ||||||||
\(461\) | 2.03230e97 | 1.21033 | 0.605166 | − | 0.796099i | \(-0.293107\pi\) | ||||
0.605166 | + | 0.796099i | \(0.293107\pi\) | |||||||
\(462\) | 5.84183e94 | 0.00321453 | ||||||||
\(463\) | 2.28467e97 | 1.16176 | 0.580881 | − | 0.813988i | \(-0.302708\pi\) | ||||
0.580881 | + | 0.813988i | \(0.302708\pi\) | |||||||
\(464\) | −2.53187e97 | −1.18997 | ||||||||
\(465\) | 1.84297e95 | 0.00800727 | ||||||||
\(466\) | 5.16707e97 | 2.07567 | ||||||||
\(467\) | −4.33212e97 | −1.60929 | −0.804645 | − | 0.593756i | \(-0.797645\pi\) | ||||
−0.804645 | + | 0.593756i | \(0.797645\pi\) | |||||||
\(468\) | 1.25499e97 | 0.431187 | ||||||||
\(469\) | 5.33721e96 | 0.169631 | ||||||||
\(470\) | −1.03225e97 | −0.303538 | ||||||||
\(471\) | −1.91451e96 | −0.0520947 | ||||||||
\(472\) | −1.12890e97 | −0.284297 | ||||||||
\(473\) | −9.74257e95 | −0.0227113 | ||||||||
\(474\) | 2.38327e96 | 0.0514356 | ||||||||
\(475\) | 7.98805e97 | 1.59634 | ||||||||
\(476\) | −3.34488e96 | −0.0619051 | ||||||||
\(477\) | −6.64515e95 | −0.0113916 | ||||||||
\(478\) | 1.49031e97 | 0.236679 | ||||||||
\(479\) | −8.07458e97 | −1.18816 | −0.594078 | − | 0.804407i | \(-0.702483\pi\) | ||||
−0.594078 | + | 0.804407i | \(0.702483\pi\) | |||||||
\(480\) | 6.96324e95 | 0.00949524 | ||||||||
\(481\) | 6.06789e97 | 0.766906 | ||||||||
\(482\) | −1.48993e98 | −1.74562 | ||||||||
\(483\) | 5.51847e95 | 0.00599444 | ||||||||
\(484\) | −6.08928e97 | −0.613353 | ||||||||
\(485\) | 1.88418e97 | 0.176014 | ||||||||
\(486\) | 1.41322e97 | 0.122458 | ||||||||
\(487\) | −8.36643e97 | −0.672563 | −0.336282 | − | 0.941761i | \(-0.609169\pi\) | ||||
−0.336282 | + | 0.941761i | \(0.609169\pi\) | |||||||
\(488\) | 1.54893e97 | 0.115534 | ||||||||
\(489\) | −5.74038e96 | −0.0397344 | ||||||||
\(490\) | 4.91907e97 | 0.316028 | ||||||||
\(491\) | 2.52751e98 | 1.50736 | 0.753681 | − | 0.657240i | \(-0.228276\pi\) | ||||
0.753681 | + | 0.657240i | \(0.228276\pi\) | |||||||
\(492\) | 6.92766e95 | 0.00383584 | ||||||||
\(493\) | −9.94524e97 | −0.511332 | ||||||||
\(494\) | 2.46678e98 | 1.17787 | ||||||||
\(495\) | 2.79550e97 | 0.123985 | ||||||||
\(496\) | 3.06881e98 | 1.26441 | ||||||||
\(497\) | 4.49692e97 | 0.172150 | ||||||||
\(498\) | −1.32700e97 | −0.0472063 | ||||||||
\(499\) | −4.63850e98 | −1.53358 | −0.766792 | − | 0.641896i | \(-0.778148\pi\) | ||||
−0.766792 | + | 0.641896i | \(0.778148\pi\) | |||||||
\(500\) | 1.26811e98 | 0.389718 | ||||||||
\(501\) | −2.50703e96 | −0.00716279 | ||||||||
\(502\) | −6.40534e98 | −1.70160 | ||||||||
\(503\) | −5.77546e98 | −1.42677 | −0.713387 | − | 0.700770i | \(-0.752840\pi\) | ||||
−0.713387 | + | 0.700770i | \(0.752840\pi\) | |||||||
\(504\) | 1.41243e97 | 0.0324529 | ||||||||
\(505\) | −1.81193e98 | −0.387263 | ||||||||
\(506\) | 4.68289e98 | 0.931151 | ||||||||
\(507\) | −1.19964e97 | −0.0221953 | ||||||||
\(508\) | 6.43328e97 | 0.110766 | ||||||||
\(509\) | 3.98850e98 | 0.639162 | 0.319581 | − | 0.947559i | \(-0.396458\pi\) | ||||
0.319581 | + | 0.947559i | \(0.396458\pi\) | |||||||
\(510\) | 3.17977e96 | 0.00474333 | ||||||||
\(511\) | 9.57811e97 | 0.133020 | ||||||||
\(512\) | 9.71011e98 | 1.25566 | ||||||||
\(513\) | 8.46129e97 | 0.101895 | ||||||||
\(514\) | −6.75325e98 | −0.757458 | ||||||||
\(515\) | −3.95595e97 | −0.0413320 | ||||||||
\(516\) | −1.13560e96 | −0.00110538 | ||||||||
\(517\) | 5.38855e98 | 0.488728 | ||||||||
\(518\) | −3.62663e98 | −0.306525 | ||||||||
\(519\) | 5.69169e97 | 0.0448366 | ||||||||
\(520\) | −3.57928e97 | −0.0262829 | ||||||||
\(521\) | 1.51314e99 | 1.03586 | 0.517932 | − | 0.855422i | \(-0.326702\pi\) | ||||
0.517932 | + | 0.855422i | \(0.326702\pi\) | |||||||
\(522\) | −2.23018e99 | −1.42353 | ||||||||
\(523\) | 8.82515e98 | 0.525303 | 0.262652 | − | 0.964891i | \(-0.415403\pi\) | ||||
0.262652 | + | 0.964891i | \(0.415403\pi\) | |||||||
\(524\) | −1.28024e97 | −0.00710721 | ||||||||
\(525\) | −8.28596e96 | −0.00429070 | ||||||||
\(526\) | −2.32237e99 | −1.12189 | ||||||||
\(527\) | 1.20543e99 | 0.543321 | ||||||||
\(528\) | −4.22580e97 | −0.0177734 | ||||||||
\(529\) | 1.87608e99 | 0.736408 | ||||||||
\(530\) | −1.00646e97 | −0.00368747 | ||||||||
\(531\) | −3.86191e99 | −1.32085 | ||||||||
\(532\) | −6.73731e98 | −0.215136 | ||||||||
\(533\) | −2.60326e98 | −0.0776203 | ||||||||
\(534\) | −2.29103e98 | −0.0637933 | ||||||||
\(535\) | −5.65130e98 | −0.146972 | ||||||||
\(536\) | −9.94086e98 | −0.241495 | ||||||||
\(537\) | 1.02765e98 | 0.0233230 | ||||||||
\(538\) | 5.72458e99 | 1.21392 | ||||||||
\(539\) | −2.56785e99 | −0.508839 | ||||||||
\(540\) | 6.51986e97 | 0.0120744 | ||||||||
\(541\) | 2.12211e99 | 0.367340 | 0.183670 | − | 0.982988i | \(-0.441202\pi\) | ||||
0.183670 | + | 0.982988i | \(0.441202\pi\) | |||||||
\(542\) | 1.28787e100 | 2.08400 | ||||||||
\(543\) | 1.52318e97 | 0.00230439 | ||||||||
\(544\) | 4.55447e99 | 0.644284 | ||||||||
\(545\) | −1.54147e98 | −0.0203921 | ||||||||
\(546\) | −2.55877e97 | −0.00316592 | ||||||||
\(547\) | −7.50110e99 | −0.868136 | −0.434068 | − | 0.900880i | \(-0.642922\pi\) | ||||
−0.434068 | + | 0.900880i | \(0.642922\pi\) | |||||||
\(548\) | −1.07368e100 | −1.16248 | ||||||||
\(549\) | 5.29883e99 | 0.536771 | ||||||||
\(550\) | −7.03134e99 | −0.666499 | ||||||||
\(551\) | −2.00319e100 | −1.77701 | ||||||||
\(552\) | −1.02785e98 | −0.00853399 | ||||||||
\(553\) | 2.44603e99 | 0.190105 | ||||||||
\(554\) | 1.45695e99 | 0.106008 | ||||||||
\(555\) | 1.57547e98 | 0.0107329 | ||||||||
\(556\) | −2.31205e100 | −1.47491 | ||||||||
\(557\) | 1.56973e100 | 0.937801 | 0.468900 | − | 0.883251i | \(-0.344650\pi\) | ||||
0.468900 | + | 0.883251i | \(0.344650\pi\) | |||||||
\(558\) | 2.70313e100 | 1.51258 | ||||||||
\(559\) | 4.26733e98 | 0.0223679 | ||||||||
\(560\) | 8.30827e98 | 0.0407988 | ||||||||
\(561\) | −1.65990e98 | −0.00763727 | ||||||||
\(562\) | 2.55579e100 | 1.10192 | ||||||||
\(563\) | 4.75620e99 | 0.192178 | 0.0960891 | − | 0.995373i | \(-0.469367\pi\) | ||||
0.0960891 | + | 0.995373i | \(0.469367\pi\) | |||||||
\(564\) | 6.28091e98 | 0.0237868 | ||||||||
\(565\) | 1.09529e100 | 0.388830 | ||||||||
\(566\) | −2.11456e100 | −0.703752 | ||||||||
\(567\) | 4.82748e99 | 0.150639 | ||||||||
\(568\) | −8.37578e99 | −0.245082 | ||||||||
\(569\) | 2.04030e100 | 0.559882 | 0.279941 | − | 0.960017i | \(-0.409685\pi\) | ||||
0.279941 | + | 0.960017i | \(0.409685\pi\) | |||||||
\(570\) | 6.40474e98 | 0.0164843 | ||||||||
\(571\) | −5.80730e100 | −1.40203 | −0.701013 | − | 0.713148i | \(-0.747269\pi\) | ||||
−0.701013 | + | 0.713148i | \(0.747269\pi\) | |||||||
\(572\) | −9.92244e99 | −0.224731 | ||||||||
\(573\) | −2.30074e98 | −0.00488904 | ||||||||
\(574\) | 1.55591e99 | 0.0310241 | ||||||||
\(575\) | −6.64213e100 | −1.24289 | ||||||||
\(576\) | 3.76567e100 | 0.661336 | ||||||||
\(577\) | 1.19206e101 | 1.96508 | 0.982539 | − | 0.186059i | \(-0.0595714\pi\) | ||||
0.982539 | + | 0.186059i | \(0.0595714\pi\) | |||||||
\(578\) | −6.68932e100 | −1.03518 | ||||||||
\(579\) | 2.31609e99 | 0.0336502 | ||||||||
\(580\) | −1.54356e100 | −0.210573 | ||||||||
\(581\) | −1.36194e100 | −0.174474 | ||||||||
\(582\) | −2.50881e99 | −0.0301841 | ||||||||
\(583\) | 5.25394e98 | 0.00593721 | ||||||||
\(584\) | −1.78398e100 | −0.189374 | ||||||||
\(585\) | −1.22445e100 | −0.122111 | ||||||||
\(586\) | −3.44162e100 | −0.322478 | ||||||||
\(587\) | −6.02937e100 | −0.530862 | −0.265431 | − | 0.964130i | \(-0.585514\pi\) | ||||
−0.265431 | + | 0.964130i | \(0.585514\pi\) | |||||||
\(588\) | −2.99310e99 | −0.0247656 | ||||||||
\(589\) | 2.42801e101 | 1.88817 | ||||||||
\(590\) | −5.84918e100 | −0.427559 | ||||||||
\(591\) | −6.22845e99 | −0.0427993 | ||||||||
\(592\) | 2.62339e101 | 1.69481 | ||||||||
\(593\) | 7.82421e100 | 0.475274 | 0.237637 | − | 0.971354i | \(-0.423627\pi\) | ||||
0.237637 | + | 0.971354i | \(0.423627\pi\) | |||||||
\(594\) | −7.44789e99 | −0.0425430 | ||||||||
\(595\) | 3.26350e99 | 0.0175313 | ||||||||
\(596\) | −8.35640e100 | −0.422212 | ||||||||
\(597\) | 5.47305e99 | 0.0260115 | ||||||||
\(598\) | −2.05115e101 | −0.917072 | ||||||||
\(599\) | −1.98442e101 | −0.834745 | −0.417372 | − | 0.908736i | \(-0.637049\pi\) | ||||
−0.417372 | + | 0.908736i | \(0.637049\pi\) | |||||||
\(600\) | 1.54331e99 | 0.00610846 | ||||||||
\(601\) | 4.38699e100 | 0.163399 | 0.0816994 | − | 0.996657i | \(-0.473965\pi\) | ||||
0.0816994 | + | 0.996657i | \(0.473965\pi\) | |||||||
\(602\) | −2.55048e99 | −0.00894024 | ||||||||
\(603\) | −3.40072e101 | −1.12199 | ||||||||
\(604\) | −2.65996e101 | −0.826089 | ||||||||
\(605\) | 5.94114e100 | 0.173700 | ||||||||
\(606\) | 2.41261e100 | 0.0664105 | ||||||||
\(607\) | −4.89694e101 | −1.26922 | −0.634611 | − | 0.772832i | \(-0.718840\pi\) | ||||
−0.634611 | + | 0.772832i | \(0.718840\pi\) | |||||||
\(608\) | 9.17369e101 | 2.23905 | ||||||||
\(609\) | 2.07790e99 | 0.00477631 | ||||||||
\(610\) | 8.02550e100 | 0.173753 | ||||||||
\(611\) | −2.36023e101 | −0.481338 | ||||||||
\(612\) | 2.13126e101 | 0.409459 | ||||||||
\(613\) | 5.37584e101 | 0.973058 | 0.486529 | − | 0.873664i | \(-0.338263\pi\) | ||||
0.486529 | + | 0.873664i | \(0.338263\pi\) | |||||||
\(614\) | 9.08097e101 | 1.54877 | ||||||||
\(615\) | −6.75912e98 | −0.00108630 | ||||||||
\(616\) | −1.11673e100 | −0.0169142 | ||||||||
\(617\) | 3.31920e101 | 0.473833 | 0.236916 | − | 0.971530i | \(-0.423863\pi\) | ||||
0.236916 | + | 0.971530i | \(0.423863\pi\) | |||||||
\(618\) | 5.26740e99 | 0.00708790 | ||||||||
\(619\) | −1.13312e102 | −1.43737 | −0.718684 | − | 0.695337i | \(-0.755255\pi\) | ||||
−0.718684 | + | 0.695337i | \(0.755255\pi\) | |||||||
\(620\) | 1.87091e101 | 0.223746 | ||||||||
\(621\) | −7.03563e100 | −0.0793341 | ||||||||
\(622\) | −2.00681e102 | −2.13382 | ||||||||
\(623\) | −2.35136e101 | −0.235779 | ||||||||
\(624\) | 1.85094e100 | 0.0175047 | ||||||||
\(625\) | 9.33642e101 | 0.832837 | ||||||||
\(626\) | 2.96493e101 | 0.249489 | ||||||||
\(627\) | −3.34341e100 | −0.0265414 | ||||||||
\(628\) | −1.94353e102 | −1.45567 | ||||||||
\(629\) | 1.03047e102 | 0.728262 | ||||||||
\(630\) | 7.31826e100 | 0.0488065 | ||||||||
\(631\) | 2.37031e102 | 1.49188 | 0.745938 | − | 0.666015i | \(-0.232001\pi\) | ||||
0.745938 | + | 0.666015i | \(0.232001\pi\) | |||||||
\(632\) | −4.55588e101 | −0.270644 | ||||||||
\(633\) | −3.93845e100 | −0.0220846 | ||||||||
\(634\) | −1.88457e102 | −0.997593 | ||||||||
\(635\) | −6.27677e100 | −0.0313686 | ||||||||
\(636\) | 6.12401e98 | 0.000288969 0 | ||||||||
\(637\) | 1.12474e102 | 0.501145 | ||||||||
\(638\) | 1.76327e102 | 0.741932 | ||||||||
\(639\) | −2.86532e102 | −1.13865 | ||||||||
\(640\) | −2.69648e101 | −0.101211 | ||||||||
\(641\) | 3.06386e102 | 1.08630 | 0.543152 | − | 0.839634i | \(-0.317231\pi\) | ||||
0.543152 | + | 0.839634i | \(0.317231\pi\) | |||||||
\(642\) | 7.52479e100 | 0.0252038 | ||||||||
\(643\) | 5.67273e101 | 0.179511 | 0.0897557 | − | 0.995964i | \(-0.471391\pi\) | ||||
0.0897557 | + | 0.995964i | \(0.471391\pi\) | |||||||
\(644\) | 5.60213e101 | 0.167502 | ||||||||
\(645\) | 1.10797e99 | 0.000313039 0 | ||||||||
\(646\) | 4.18917e102 | 1.11851 | ||||||||
\(647\) | −5.49944e102 | −1.38775 | −0.693876 | − | 0.720094i | \(-0.744099\pi\) | ||||
−0.693876 | + | 0.720094i | \(0.744099\pi\) | |||||||
\(648\) | −8.99146e101 | −0.214458 | ||||||||
\(649\) | 3.05339e102 | 0.688415 | ||||||||
\(650\) | 3.07978e102 | 0.656422 | ||||||||
\(651\) | −2.51856e100 | −0.00507512 | ||||||||
\(652\) | −5.82740e102 | −1.11029 | ||||||||
\(653\) | −5.48029e102 | −0.987353 | −0.493676 | − | 0.869646i | \(-0.664347\pi\) | ||||
−0.493676 | + | 0.869646i | \(0.664347\pi\) | |||||||
\(654\) | 2.05249e100 | 0.00349698 | ||||||||
\(655\) | 1.24909e100 | 0.00201274 | ||||||||
\(656\) | −1.12549e102 | −0.171535 | ||||||||
\(657\) | −6.10291e102 | −0.879835 | ||||||||
\(658\) | 1.41065e102 | 0.192386 | ||||||||
\(659\) | −7.75339e102 | −1.00040 | −0.500200 | − | 0.865910i | \(-0.666740\pi\) | ||||
−0.500200 | + | 0.865910i | \(0.666740\pi\) | |||||||
\(660\) | −2.57627e100 | −0.00314512 | ||||||||
\(661\) | 8.44451e102 | 0.975486 | 0.487743 | − | 0.872987i | \(-0.337820\pi\) | ||||
0.487743 | + | 0.872987i | \(0.337820\pi\) | |||||||
\(662\) | 2.28424e102 | 0.249704 | ||||||||
\(663\) | 7.27051e100 | 0.00752179 | ||||||||
\(664\) | 2.53670e102 | 0.248390 | ||||||||
\(665\) | 6.57341e101 | 0.0609257 | ||||||||
\(666\) | 2.31079e103 | 2.02745 | ||||||||
\(667\) | 1.66567e103 | 1.38355 | ||||||||
\(668\) | −2.54504e102 | −0.200149 | ||||||||
\(669\) | 5.86957e101 | 0.0437072 | ||||||||
\(670\) | −5.15067e102 | −0.363190 | ||||||||
\(671\) | −4.18948e102 | −0.279761 | ||||||||
\(672\) | −9.51582e100 | −0.00601821 | ||||||||
\(673\) | −8.74718e102 | −0.523984 | −0.261992 | − | 0.965070i | \(-0.584379\pi\) | ||||
−0.261992 | + | 0.965070i | \(0.584379\pi\) | |||||||
\(674\) | −1.85233e103 | −1.05107 | ||||||||
\(675\) | 1.05640e102 | 0.0567858 | ||||||||
\(676\) | −1.21783e103 | −0.620201 | ||||||||
\(677\) | −1.30620e103 | −0.630263 | −0.315132 | − | 0.949048i | \(-0.602049\pi\) | ||||
−0.315132 | + | 0.949048i | \(0.602049\pi\) | |||||||
\(678\) | −1.45839e102 | −0.0666792 | ||||||||
\(679\) | −2.57488e102 | −0.111560 | ||||||||
\(680\) | −6.07846e101 | −0.0249585 | ||||||||
\(681\) | −2.04505e101 | −0.00795856 | ||||||||
\(682\) | −2.13721e103 | −0.788347 | ||||||||
\(683\) | 1.16711e103 | 0.408089 | 0.204045 | − | 0.978962i | \(-0.434591\pi\) | ||||
0.204045 | + | 0.978962i | \(0.434591\pi\) | |||||||
\(684\) | 4.29283e103 | 1.42297 | ||||||||
\(685\) | 1.04756e103 | 0.329210 | ||||||||
\(686\) | −1.36016e103 | −0.405283 | ||||||||
\(687\) | −9.12815e101 | −0.0257906 | ||||||||
\(688\) | 1.84494e102 | 0.0494314 | ||||||||
\(689\) | −2.30127e101 | −0.00584744 | ||||||||
\(690\) | −5.32560e101 | −0.0128344 | ||||||||
\(691\) | 4.35029e102 | 0.0994419 | 0.0497209 | − | 0.998763i | \(-0.484167\pi\) | ||||
0.0497209 | + | 0.998763i | \(0.484167\pi\) | |||||||
\(692\) | 5.77798e103 | 1.25286 | ||||||||
\(693\) | −3.82028e102 | −0.0785836 | ||||||||
\(694\) | −3.30614e103 | −0.645210 | ||||||||
\(695\) | 2.25580e103 | 0.417691 | ||||||||
\(696\) | −3.87020e101 | −0.00679981 | ||||||||
\(697\) | −4.42096e102 | −0.0737090 | ||||||||
\(698\) | −2.71390e103 | −0.429409 | ||||||||
\(699\) | 3.06751e102 | 0.0460648 | ||||||||
\(700\) | −8.41158e102 | −0.119894 | ||||||||
\(701\) | −8.51668e103 | −1.15229 | −0.576146 | − | 0.817347i | \(-0.695444\pi\) | ||||
−0.576146 | + | 0.817347i | \(0.695444\pi\) | |||||||
\(702\) | 3.26224e102 | 0.0418997 | ||||||||
\(703\) | 2.07560e104 | 2.53089 | ||||||||
\(704\) | −2.97730e103 | −0.344683 | ||||||||
\(705\) | −6.12811e101 | −0.00673634 | ||||||||
\(706\) | −1.54549e104 | −1.61322 | ||||||||
\(707\) | 2.47615e103 | 0.245453 | ||||||||
\(708\) | 3.55904e102 | 0.0335057 | ||||||||
\(709\) | 6.19940e103 | 0.554322 | 0.277161 | − | 0.960824i | \(-0.410607\pi\) | ||||
0.277161 | + | 0.960824i | \(0.410607\pi\) | |||||||
\(710\) | −4.33975e103 | −0.368583 | ||||||||
\(711\) | −1.55854e104 | −1.25742 | ||||||||
\(712\) | 4.37955e103 | 0.335668 | ||||||||
\(713\) | −2.01891e104 | −1.47011 | ||||||||
\(714\) | −4.34540e101 | −0.00300639 | ||||||||
\(715\) | 9.68105e102 | 0.0636432 | ||||||||
\(716\) | 1.04323e104 | 0.651710 | ||||||||
\(717\) | 8.84748e101 | 0.00525255 | ||||||||
\(718\) | 1.19838e104 | 0.676163 | ||||||||
\(719\) | 2.00289e104 | 1.07412 | 0.537060 | − | 0.843544i | \(-0.319535\pi\) | ||||
0.537060 | + | 0.843544i | \(0.319535\pi\) | |||||||
\(720\) | −5.29380e103 | −0.269856 | ||||||||
\(721\) | 5.40612e102 | 0.0261968 | ||||||||
\(722\) | 5.49215e104 | 2.53008 | ||||||||
\(723\) | −8.84521e102 | −0.0387400 | ||||||||
\(724\) | 1.54627e103 | 0.0643913 | ||||||||
\(725\) | −2.50099e104 | −0.990320 | ||||||||
\(726\) | −7.91072e102 | −0.0297872 | ||||||||
\(727\) | 2.41721e103 | 0.0865582 | 0.0432791 | − | 0.999063i | \(-0.486220\pi\) | ||||
0.0432791 | + | 0.999063i | \(0.486220\pi\) | |||||||
\(728\) | 4.89137e102 | 0.0166585 | ||||||||
\(729\) | −3.07034e104 | −0.994562 | ||||||||
\(730\) | −9.24335e103 | −0.284803 | ||||||||
\(731\) | 7.24694e102 | 0.0212408 | ||||||||
\(732\) | −4.88327e102 | −0.0136162 | ||||||||
\(733\) | −6.29556e104 | −1.67009 | −0.835044 | − | 0.550183i | \(-0.814558\pi\) | ||||
−0.835044 | + | 0.550183i | \(0.814558\pi\) | |||||||
\(734\) | 1.96371e104 | 0.495645 | ||||||||
\(735\) | 2.92028e102 | 0.00701354 | ||||||||
\(736\) | −7.62800e104 | −1.74329 | ||||||||
\(737\) | 2.68875e104 | 0.584774 | ||||||||
\(738\) | −9.91381e103 | −0.205203 | ||||||||
\(739\) | 3.87280e104 | 0.762962 | 0.381481 | − | 0.924377i | \(-0.375414\pi\) | ||||
0.381481 | + | 0.924377i | \(0.375414\pi\) | |||||||
\(740\) | 1.59935e104 | 0.299907 | ||||||||
\(741\) | 1.46444e103 | 0.0261401 | ||||||||
\(742\) | 1.37541e102 | 0.00233717 | ||||||||
\(743\) | 7.35672e104 | 1.19012 | 0.595062 | − | 0.803680i | \(-0.297127\pi\) | ||||
0.595062 | + | 0.803680i | \(0.297127\pi\) | |||||||
\(744\) | 4.69096e102 | 0.00722520 | ||||||||
\(745\) | 8.15311e103 | 0.119569 | ||||||||
\(746\) | 3.31695e104 | 0.463203 | ||||||||
\(747\) | 8.67794e104 | 1.15402 | ||||||||
\(748\) | −1.68507e104 | −0.213407 | ||||||||
\(749\) | 7.72295e103 | 0.0931530 | ||||||||
\(750\) | 1.64742e103 | 0.0189265 | ||||||||
\(751\) | −3.95530e104 | −0.432834 | −0.216417 | − | 0.976301i | \(-0.569437\pi\) | ||||
−0.216417 | + | 0.976301i | \(0.569437\pi\) | |||||||
\(752\) | −1.02042e105 | −1.06372 | ||||||||
\(753\) | −3.80263e103 | −0.0377631 | ||||||||
\(754\) | −7.72328e104 | −0.730714 | ||||||||
\(755\) | 2.59525e104 | 0.233946 | ||||||||
\(756\) | −8.90990e102 | −0.00765292 | ||||||||
\(757\) | 7.45337e104 | 0.610033 | 0.305016 | − | 0.952347i | \(-0.401338\pi\) | ||||
0.305016 | + | 0.952347i | \(0.401338\pi\) | |||||||
\(758\) | −3.94452e104 | −0.307658 | ||||||||
\(759\) | 2.78007e103 | 0.0206648 | ||||||||
\(760\) | −1.22434e104 | −0.0867370 | ||||||||
\(761\) | 3.87339e103 | 0.0261548 | 0.0130774 | − | 0.999914i | \(-0.495837\pi\) | ||||
0.0130774 | + | 0.999914i | \(0.495837\pi\) | |||||||
\(762\) | 8.35762e102 | 0.00537930 | ||||||||
\(763\) | 2.10654e103 | 0.0129248 | ||||||||
\(764\) | −2.33562e104 | −0.136614 | ||||||||
\(765\) | −2.07941e104 | −0.115957 | ||||||||
\(766\) | 1.42696e105 | 0.758686 | ||||||||
\(767\) | −1.33741e105 | −0.678006 | ||||||||
\(768\) | 7.71424e103 | 0.0372914 | ||||||||
\(769\) | −3.13426e105 | −1.44485 | −0.722426 | − | 0.691449i | \(-0.756973\pi\) | ||||
−0.722426 | + | 0.691449i | \(0.756973\pi\) | |||||||
\(770\) | −5.78612e103 | −0.0254376 | ||||||||
\(771\) | −4.00917e103 | −0.0168101 | ||||||||
\(772\) | 2.35120e105 | 0.940282 | ||||||||
\(773\) | −1.54663e105 | −0.589975 | −0.294988 | − | 0.955501i | \(-0.595316\pi\) | ||||
−0.294988 | + | 0.955501i | \(0.595316\pi\) | |||||||
\(774\) | 1.62509e104 | 0.0591335 | ||||||||
\(775\) | 3.03138e105 | 1.05227 | ||||||||
\(776\) | 4.79586e104 | 0.158823 | ||||||||
\(777\) | −2.15300e103 | −0.00680264 | ||||||||
\(778\) | 4.57012e105 | 1.37776 | ||||||||
\(779\) | −8.90478e104 | −0.256157 | ||||||||
\(780\) | 1.12843e103 | 0.00309756 | ||||||||
\(781\) | 2.26544e105 | 0.593458 | ||||||||
\(782\) | −3.48333e105 | −0.870860 | ||||||||
\(783\) | −2.64916e104 | −0.0632126 | ||||||||
\(784\) | 4.86271e105 | 1.10750 | ||||||||
\(785\) | 1.89625e105 | 0.412242 | ||||||||
\(786\) | −1.66319e102 | −0.000345158 0 | ||||||||
\(787\) | −6.10714e105 | −1.20993 | −0.604965 | − | 0.796252i | \(-0.706813\pi\) | ||||
−0.604965 | + | 0.796252i | \(0.706813\pi\) | |||||||
\(788\) | −6.32287e105 | −1.19593 | ||||||||
\(789\) | −1.37871e104 | −0.0248979 | ||||||||
\(790\) | −2.36054e105 | −0.407027 | ||||||||
\(791\) | −1.49680e105 | −0.246446 | ||||||||
\(792\) | 7.11549e104 | 0.111876 | ||||||||
\(793\) | 1.83503e105 | 0.275531 | ||||||||
\(794\) | −1.52601e106 | −2.18832 | ||||||||
\(795\) | −5.97502e101 | −8.18350e−5 0 | ||||||||
\(796\) | 5.55602e105 | 0.726837 | ||||||||
\(797\) | −1.83409e105 | −0.229188 | −0.114594 | − | 0.993412i | \(-0.536557\pi\) | ||||
−0.114594 | + | 0.993412i | \(0.536557\pi\) | |||||||
\(798\) | −8.75259e103 | −0.0104480 | ||||||||
\(799\) | −4.00823e105 | −0.457084 | ||||||||
\(800\) | 1.14534e106 | 1.24782 | ||||||||
\(801\) | 1.49822e106 | 1.55952 | ||||||||
\(802\) | 7.41110e105 | 0.737086 | ||||||||
\(803\) | 4.82522e105 | 0.458563 | ||||||||
\(804\) | 3.13402e104 | 0.0284614 | ||||||||
\(805\) | −5.46584e104 | −0.0474360 | ||||||||
\(806\) | 9.36116e105 | 0.776427 | ||||||||
\(807\) | 3.39849e104 | 0.0269402 | ||||||||
\(808\) | −4.61197e105 | −0.349439 | ||||||||
\(809\) | −2.14223e105 | −0.155147 | −0.0775737 | − | 0.996987i | \(-0.524717\pi\) | ||||
−0.0775737 | + | 0.996987i | \(0.524717\pi\) | |||||||
\(810\) | −4.65876e105 | −0.322528 | ||||||||
\(811\) | −1.90972e106 | −1.26389 | −0.631943 | − | 0.775015i | \(-0.717742\pi\) | ||||
−0.631943 | + | 0.775015i | \(0.717742\pi\) | |||||||
\(812\) | 2.10940e105 | 0.133464 | ||||||||
\(813\) | 7.64565e104 | 0.0462498 | ||||||||
\(814\) | −1.82701e106 | −1.05669 | ||||||||
\(815\) | 5.68563e105 | 0.314432 | ||||||||
\(816\) | 3.14333e104 | 0.0166226 | ||||||||
\(817\) | 1.45969e105 | 0.0738170 | ||||||||
\(818\) | −1.74079e106 | −0.841882 | ||||||||
\(819\) | 1.67331e105 | 0.0773954 | ||||||||
\(820\) | −6.86159e104 | −0.0303542 | ||||||||
\(821\) | 4.47743e106 | 1.89454 | 0.947269 | − | 0.320438i | \(-0.103830\pi\) | ||||
0.947269 | + | 0.320438i | \(0.103830\pi\) | |||||||
\(822\) | −1.39484e105 | −0.0564552 | ||||||||
\(823\) | −3.95023e106 | −1.52942 | −0.764712 | − | 0.644372i | \(-0.777119\pi\) | ||||
−0.764712 | + | 0.644372i | \(0.777119\pi\) | |||||||
\(824\) | −1.00692e105 | −0.0372951 | ||||||||
\(825\) | −4.17426e104 | −0.0147914 | ||||||||
\(826\) | 7.99337e105 | 0.270993 | ||||||||
\(827\) | 2.04734e106 | 0.664108 | 0.332054 | − | 0.943260i | \(-0.392258\pi\) | ||||
0.332054 | + | 0.943260i | \(0.392258\pi\) | |||||||
\(828\) | −3.56953e106 | −1.10791 | ||||||||
\(829\) | 1.25356e106 | 0.372310 | 0.186155 | − | 0.982520i | \(-0.440397\pi\) | ||||
0.186155 | + | 0.982520i | \(0.440397\pi\) | |||||||
\(830\) | 1.31434e106 | 0.373559 | ||||||||
\(831\) | 8.64938e103 | 0.00235260 | ||||||||
\(832\) | 1.30408e106 | 0.339472 | ||||||||
\(833\) | 1.91008e106 | 0.475893 | ||||||||
\(834\) | −3.00363e105 | −0.0716285 | ||||||||
\(835\) | 2.48312e105 | 0.0566815 | ||||||||
\(836\) | −3.39409e106 | −0.741643 | ||||||||
\(837\) | 3.21097e105 | 0.0671672 | ||||||||
\(838\) | 6.64069e106 | 1.32986 | ||||||||
\(839\) | −7.25075e106 | −1.39018 | −0.695090 | − | 0.718922i | \(-0.744636\pi\) | ||||
−0.695090 | + | 0.718922i | \(0.744636\pi\) | |||||||
\(840\) | 1.27000e103 | 0.000233135 0 | ||||||||
\(841\) | 5.82589e105 | 0.102402 | ||||||||
\(842\) | 1.40661e107 | 2.36746 | ||||||||
\(843\) | 1.51728e105 | 0.0244546 | ||||||||
\(844\) | −3.99816e106 | −0.617108 | ||||||||
\(845\) | 1.18820e106 | 0.175639 | ||||||||
\(846\) | −8.98829e106 | −1.27250 | ||||||||
\(847\) | −8.11904e105 | −0.110093 | ||||||||
\(848\) | −9.94930e104 | −0.0129224 | ||||||||
\(849\) | −1.25534e105 | −0.0156182 | ||||||||
\(850\) | 5.23021e106 | 0.623345 | ||||||||
\(851\) | −1.72588e107 | −1.97052 | ||||||||
\(852\) | 2.64060e105 | 0.0288841 | ||||||||
\(853\) | −1.20325e107 | −1.26100 | −0.630502 | − | 0.776187i | \(-0.717151\pi\) | ||||
−0.630502 | + | 0.776187i | \(0.717151\pi\) | |||||||
\(854\) | −1.09675e106 | −0.110127 | ||||||||
\(855\) | −4.18840e106 | −0.402981 | ||||||||
\(856\) | −1.43844e106 | −0.132617 | ||||||||
\(857\) | 1.24387e107 | 1.09894 | 0.549469 | − | 0.835514i | \(-0.314830\pi\) | ||||
0.549469 | + | 0.835514i | \(0.314830\pi\) | |||||||
\(858\) | −1.28905e105 | −0.0109140 | ||||||||
\(859\) | 5.72297e106 | 0.464377 | 0.232189 | − | 0.972671i | \(-0.425411\pi\) | ||||
0.232189 | + | 0.972671i | \(0.425411\pi\) | |||||||
\(860\) | 1.12477e105 | 0.00874721 | ||||||||
\(861\) | 9.23688e103 | 0.000688510 0 | ||||||||
\(862\) | 2.84328e107 | 2.03144 | ||||||||
\(863\) | 2.04897e107 | 1.40327 | 0.701635 | − | 0.712537i | \(-0.252454\pi\) | ||||
0.701635 | + | 0.712537i | \(0.252454\pi\) | |||||||
\(864\) | 1.21319e106 | 0.0796487 | ||||||||
\(865\) | −5.63741e106 | −0.354807 | ||||||||
\(866\) | −7.51831e106 | −0.453646 | ||||||||
\(867\) | −3.97122e105 | −0.0229735 | ||||||||
\(868\) | −2.55674e106 | −0.141813 | ||||||||
\(869\) | 1.23225e107 | 0.655356 | ||||||||
\(870\) | −2.00527e105 | −0.0102264 | ||||||||
\(871\) | −1.17770e107 | −0.575932 | ||||||||
\(872\) | −3.92355e105 | −0.0184004 | ||||||||
\(873\) | 1.64064e107 | 0.737894 | ||||||||
\(874\) | −7.01620e107 | −3.02646 | ||||||||
\(875\) | 1.69081e106 | 0.0699520 | ||||||||
\(876\) | 5.62429e105 | 0.0223186 | ||||||||
\(877\) | 3.53292e107 | 1.34477 | 0.672386 | − | 0.740201i | \(-0.265270\pi\) | ||||
0.672386 | + | 0.740201i | \(0.265270\pi\) | |||||||
\(878\) | −5.07303e107 | −1.85233 | ||||||||
\(879\) | −2.04317e105 | −0.00715666 | ||||||||
\(880\) | 4.18550e106 | 0.140647 | ||||||||
\(881\) | −3.92634e107 | −1.26581 | −0.632903 | − | 0.774231i | \(-0.718137\pi\) | ||||
−0.632903 | + | 0.774231i | \(0.718137\pi\) | |||||||
\(882\) | 4.28327e107 | 1.32487 | ||||||||
\(883\) | 7.97346e106 | 0.236636 | 0.118318 | − | 0.992976i | \(-0.462250\pi\) | ||||
0.118318 | + | 0.992976i | \(0.462250\pi\) | |||||||
\(884\) | 7.38074e106 | 0.210180 | ||||||||
\(885\) | −3.47246e105 | −0.00948871 | ||||||||
\(886\) | −2.46943e107 | −0.647538 | ||||||||
\(887\) | 4.80107e107 | 1.20816 | 0.604082 | − | 0.796922i | \(-0.293540\pi\) | ||||
0.604082 | + | 0.796922i | \(0.293540\pi\) | |||||||
\(888\) | 4.01009e105 | 0.00968459 | ||||||||
\(889\) | 8.57771e105 | 0.0198819 | ||||||||
\(890\) | 2.26918e107 | 0.504817 | ||||||||
\(891\) | 2.43197e107 | 0.519304 | ||||||||
\(892\) | 5.95855e107 | 1.22130 | ||||||||
\(893\) | −8.07346e107 | −1.58848 | ||||||||
\(894\) | −1.08560e106 | −0.0205045 | ||||||||
\(895\) | −1.01785e107 | −0.184562 | ||||||||
\(896\) | 3.68496e106 | 0.0641490 | ||||||||
\(897\) | −1.21769e106 | −0.0203523 | ||||||||
\(898\) | 1.38379e107 | 0.222068 | ||||||||
\(899\) | −7.60190e107 | −1.17137 | ||||||||
\(900\) | 5.35963e107 | 0.793018 | ||||||||
\(901\) | −3.90810e105 | −0.00555279 | ||||||||
\(902\) | 7.83827e106 | 0.106950 | ||||||||
\(903\) | −1.51413e104 | −0.000198408 0 | ||||||||
\(904\) | 2.78787e107 | 0.350853 | ||||||||
\(905\) | −1.50865e106 | −0.0182354 | ||||||||
\(906\) | −3.45561e106 | −0.0401186 | ||||||||
\(907\) | 9.97593e107 | 1.11247 | 0.556234 | − | 0.831026i | \(-0.312246\pi\) | ||||
0.556234 | + | 0.831026i | \(0.312246\pi\) | |||||||
\(908\) | −2.07605e107 | −0.222385 | ||||||||
\(909\) | −1.57773e108 | −1.62350 | ||||||||
\(910\) | 2.53437e106 | 0.0250530 | ||||||||
\(911\) | 6.39729e107 | 0.607541 | 0.303770 | − | 0.952745i | \(-0.401754\pi\) | ||||
0.303770 | + | 0.952745i | \(0.401754\pi\) | |||||||
\(912\) | 6.33136e106 | 0.0577677 | ||||||||
\(913\) | −6.86114e107 | −0.601469 | ||||||||
\(914\) | −1.72805e108 | −1.45553 | ||||||||
\(915\) | 4.76447e105 | 0.00385607 | ||||||||
\(916\) | −9.26654e107 | −0.720664 | ||||||||
\(917\) | −1.70699e105 | −0.00127570 | ||||||||
\(918\) | 5.54006e106 | 0.0397884 | ||||||||
\(919\) | 7.62885e107 | 0.526554 | 0.263277 | − | 0.964720i | \(-0.415197\pi\) | ||||
0.263277 | + | 0.964720i | \(0.415197\pi\) | |||||||
\(920\) | 1.01805e107 | 0.0675323 | ||||||||
\(921\) | 5.39106e106 | 0.0343714 | ||||||||
\(922\) | 2.68024e108 | 1.64246 | ||||||||
\(923\) | −9.92282e107 | −0.584485 | ||||||||
\(924\) | 3.52067e105 | 0.00199342 | ||||||||
\(925\) | 2.59139e108 | 1.41046 | ||||||||
\(926\) | 3.01306e108 | 1.57655 | ||||||||
\(927\) | −3.44463e107 | −0.173274 | ||||||||
\(928\) | −2.87221e108 | −1.38904 | ||||||||
\(929\) | −1.19972e108 | −0.557836 | −0.278918 | − | 0.960315i | \(-0.589976\pi\) | ||||
−0.278918 | + | 0.960315i | \(0.589976\pi\) | |||||||
\(930\) | 2.43053e106 | 0.0108661 | ||||||||
\(931\) | 3.84732e108 | 1.65385 | ||||||||
\(932\) | 3.11402e108 | 1.28718 | ||||||||
\(933\) | −1.19137e107 | −0.0473553 | ||||||||
\(934\) | −5.71328e108 | −2.18386 | ||||||||
\(935\) | 1.64407e107 | 0.0604362 | ||||||||
\(936\) | −3.11665e107 | −0.110184 | ||||||||
\(937\) | −4.93029e108 | −1.67640 | −0.838199 | − | 0.545364i | \(-0.816392\pi\) | ||||
−0.838199 | + | 0.545364i | \(0.816392\pi\) | |||||||
\(938\) | 7.03880e107 | 0.230195 | ||||||||
\(939\) | 1.76018e106 | 0.00553684 | ||||||||
\(940\) | −6.22102e107 | −0.188233 | ||||||||
\(941\) | −2.57654e108 | −0.749922 | −0.374961 | − | 0.927041i | \(-0.622344\pi\) | ||||
−0.374961 | + | 0.927041i | \(0.622344\pi\) | |||||||
\(942\) | −2.52488e107 | −0.0706942 | ||||||||
\(943\) | 7.40441e107 | 0.199441 | ||||||||
\(944\) | −5.78216e108 | −1.49835 | ||||||||
\(945\) | 8.69314e105 | 0.00216728 | ||||||||
\(946\) | −1.28487e107 | −0.0308199 | ||||||||
\(947\) | 5.94015e108 | 1.37095 | 0.685477 | − | 0.728094i | \(-0.259594\pi\) | ||||
0.685477 | + | 0.728094i | \(0.259594\pi\) | |||||||
\(948\) | 1.43632e107 | 0.0318967 | ||||||||
\(949\) | −2.11349e108 | −0.451630 | ||||||||
\(950\) | 1.05348e109 | 2.16628 | ||||||||
\(951\) | −1.11880e107 | −0.0221393 | ||||||||
\(952\) | 8.30670e106 | 0.0158190 | ||||||||
\(953\) | 7.40128e108 | 1.35649 | 0.678244 | − | 0.734837i | \(-0.262741\pi\) | ||||
0.678244 | + | 0.734837i | \(0.262741\pi\) | |||||||
\(954\) | −8.76375e106 | −0.0154587 | ||||||||
\(955\) | 2.27880e107 | 0.0386886 | ||||||||
\(956\) | 8.98161e107 | 0.146771 | ||||||||
\(957\) | 1.04679e107 | 0.0164655 | ||||||||
\(958\) | −1.06489e109 | −1.61237 | ||||||||
\(959\) | −1.43158e108 | −0.208658 | ||||||||
\(960\) | 3.38592e106 | 0.00475091 | ||||||||
\(961\) | 1.81111e108 | 0.244648 | ||||||||
\(962\) | 8.00244e108 | 1.04072 | ||||||||
\(963\) | −4.92085e108 | −0.616142 | ||||||||
\(964\) | −8.97930e108 | −1.08251 | ||||||||
\(965\) | −2.29400e108 | −0.266285 | ||||||||
\(966\) | 7.27786e106 | 0.00813464 | ||||||||
\(967\) | 6.04627e108 | 0.650761 | 0.325381 | − | 0.945583i | \(-0.394508\pi\) | ||||
0.325381 | + | 0.945583i | \(0.394508\pi\) | |||||||
\(968\) | 1.51222e108 | 0.156734 | ||||||||
\(969\) | 2.48697e107 | 0.0248229 | ||||||||
\(970\) | 2.48488e108 | 0.238857 | ||||||||
\(971\) | −1.02330e108 | −0.0947325 | −0.0473663 | − | 0.998878i | \(-0.515083\pi\) | ||||
−0.0473663 | + | 0.998878i | \(0.515083\pi\) | |||||||
\(972\) | 8.51701e107 | 0.0759396 | ||||||||
\(973\) | −3.08273e108 | −0.264738 | ||||||||
\(974\) | −1.10338e109 | −0.912690 | ||||||||
\(975\) | 1.82836e107 | 0.0145678 | ||||||||
\(976\) | 7.93355e108 | 0.608904 | ||||||||
\(977\) | −8.76474e108 | −0.648019 | −0.324009 | − | 0.946054i | \(-0.605031\pi\) | ||||
−0.324009 | + | 0.946054i | \(0.605031\pi\) | |||||||
\(978\) | −7.57051e107 | −0.0539209 | ||||||||
\(979\) | −1.18456e109 | −0.812809 | ||||||||
\(980\) | 2.96456e108 | 0.195978 | ||||||||
\(981\) | −1.34223e108 | −0.0854886 | ||||||||
\(982\) | 3.33332e109 | 2.04554 | ||||||||
\(983\) | −1.92093e109 | −1.13582 | −0.567908 | − | 0.823092i | \(-0.692247\pi\) | ||||
−0.567908 | + | 0.823092i | \(0.692247\pi\) | |||||||
\(984\) | −1.72042e106 | −0.000980199 0 | ||||||||
\(985\) | 6.16905e108 | 0.338685 | ||||||||
\(986\) | −1.31160e109 | −0.693893 | ||||||||
\(987\) | 8.37455e106 | 0.00426958 | ||||||||
\(988\) | 1.48664e109 | 0.730429 | ||||||||
\(989\) | −1.21375e108 | −0.0574729 | ||||||||
\(990\) | 3.68676e108 | 0.168252 | ||||||||
\(991\) | 4.65440e108 | 0.204727 | 0.102363 | − | 0.994747i | \(-0.467360\pi\) | ||||
0.102363 | + | 0.994747i | \(0.467360\pi\) | |||||||
\(992\) | 3.48132e109 | 1.47594 | ||||||||
\(993\) | 1.35607e107 | 0.00554161 | ||||||||
\(994\) | 5.93062e108 | 0.233613 | ||||||||
\(995\) | −5.42085e108 | −0.205838 | ||||||||
\(996\) | −7.99737e107 | −0.0292740 | ||||||||
\(997\) | 4.58521e109 | 1.61803 | 0.809015 | − | 0.587788i | \(-0.200001\pi\) | ||||
0.809015 | + | 0.587788i | \(0.200001\pi\) | |||||||
\(998\) | −6.11733e109 | −2.08112 | ||||||||
\(999\) | 2.74492e108 | 0.0900303 |
(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 | 1.74.a.a.1.5 | ✓ | 5 | |
3.2 | odd | 2 | 9.74.a.a.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.74.a.a.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.74.a.a.1.1 | 5 | 3.2 | odd | 2 |