Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,24,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(33.5204037345\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{219241}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 54810 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-233.616\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2048.00 | −0.707107 | ||||||||
\(3\) | 229540. | 0.748108 | 0.374054 | − | 0.927407i | \(-0.377967\pi\) | ||||
0.374054 | + | 0.927407i | \(0.377967\pi\) | |||||||
\(4\) | 4.19430e6 | 0.500000 | ||||||||
\(5\) | 4.88281e7 | 0.447214 | ||||||||
\(6\) | −4.70098e8 | −0.528992 | ||||||||
\(7\) | 1.11945e9 | 0.213982 | 0.106991 | − | 0.994260i | \(-0.465878\pi\) | ||||
0.106991 | + | 0.994260i | \(0.465878\pi\) | |||||||
\(8\) | −8.58993e9 | −0.353553 | ||||||||
\(9\) | −4.14545e10 | −0.440334 | ||||||||
\(10\) | −1.00000e11 | −0.316228 | ||||||||
\(11\) | −9.54047e11 | −1.00822 | −0.504108 | − | 0.863640i | \(-0.668179\pi\) | ||||
−0.504108 | + | 0.863640i | \(0.668179\pi\) | |||||||
\(12\) | 9.62761e11 | 0.374054 | ||||||||
\(13\) | −2.42139e12 | −0.374728 | −0.187364 | − | 0.982291i | \(-0.559994\pi\) | ||||
−0.187364 | + | 0.982291i | \(0.559994\pi\) | |||||||
\(14\) | −2.29263e12 | −0.151308 | ||||||||
\(15\) | 1.12080e13 | 0.334564 | ||||||||
\(16\) | 1.75922e13 | 0.250000 | ||||||||
\(17\) | −1.35256e14 | −0.957179 | −0.478589 | − | 0.878039i | \(-0.658852\pi\) | ||||
−0.478589 | + | 0.878039i | \(0.658852\pi\) | |||||||
\(18\) | 8.48988e13 | 0.311363 | ||||||||
\(19\) | 8.28157e14 | 1.63097 | 0.815485 | − | 0.578778i | \(-0.196470\pi\) | ||||
0.815485 | + | 0.578778i | \(0.196470\pi\) | |||||||
\(20\) | 2.04800e14 | 0.223607 | ||||||||
\(21\) | 2.56958e14 | 0.160081 | ||||||||
\(22\) | 1.95389e15 | 0.712917 | ||||||||
\(23\) | −7.88972e13 | −0.0172660 | −0.00863300 | − | 0.999963i | \(-0.502748\pi\) | ||||
−0.00863300 | + | 0.999963i | \(0.502748\pi\) | |||||||
\(24\) | −1.97174e15 | −0.264496 | ||||||||
\(25\) | 2.38419e15 | 0.200000 | ||||||||
\(26\) | 4.95901e15 | 0.264973 | ||||||||
\(27\) | −3.11251e16 | −1.07753 | ||||||||
\(28\) | 4.69531e15 | 0.106991 | ||||||||
\(29\) | −3.21917e16 | −0.489967 | −0.244983 | − | 0.969527i | \(-0.578783\pi\) | ||||
−0.244983 | + | 0.969527i | \(0.578783\pi\) | |||||||
\(30\) | −2.29540e16 | −0.236573 | ||||||||
\(31\) | −1.85689e17 | −1.31258 | −0.656291 | − | 0.754508i | \(-0.727876\pi\) | ||||
−0.656291 | + | 0.754508i | \(0.727876\pi\) | |||||||
\(32\) | −3.60288e16 | −0.176777 | ||||||||
\(33\) | −2.18992e17 | −0.754255 | ||||||||
\(34\) | 2.77004e17 | 0.676827 | ||||||||
\(35\) | 5.46606e16 | 0.0956955 | ||||||||
\(36\) | −1.73873e17 | −0.220167 | ||||||||
\(37\) | −3.74188e17 | −0.345756 | −0.172878 | − | 0.984943i | \(-0.555307\pi\) | ||||
−0.172878 | + | 0.984943i | \(0.555307\pi\) | |||||||
\(38\) | −1.69607e18 | −1.15327 | ||||||||
\(39\) | −5.55806e17 | −0.280337 | ||||||||
\(40\) | −4.19430e17 | −0.158114 | ||||||||
\(41\) | −3.22679e18 | −0.915707 | −0.457853 | − | 0.889028i | \(-0.651382\pi\) | ||||
−0.457853 | + | 0.889028i | \(0.651382\pi\) | |||||||
\(42\) | −5.26251e17 | −0.113195 | ||||||||
\(43\) | −2.74344e18 | −0.450203 | −0.225102 | − | 0.974335i | \(-0.572271\pi\) | ||||
−0.225102 | + | 0.974335i | \(0.572271\pi\) | |||||||
\(44\) | −4.00156e18 | −0.504108 | ||||||||
\(45\) | −2.02414e18 | −0.196923 | ||||||||
\(46\) | 1.61582e17 | 0.0122089 | ||||||||
\(47\) | 5.25271e17 | 0.0309926 | 0.0154963 | − | 0.999880i | \(-0.495067\pi\) | ||||
0.0154963 | + | 0.999880i | \(0.495067\pi\) | |||||||
\(48\) | 4.03811e18 | 0.187027 | ||||||||
\(49\) | −2.61156e19 | −0.954212 | ||||||||
\(50\) | −4.88281e18 | −0.141421 | ||||||||
\(51\) | −3.10466e19 | −0.716073 | ||||||||
\(52\) | −1.01560e19 | −0.187364 | ||||||||
\(53\) | −4.40675e19 | −0.653050 | −0.326525 | − | 0.945189i | \(-0.605878\pi\) | ||||
−0.326525 | + | 0.945189i | \(0.605878\pi\) | |||||||
\(54\) | 6.37442e19 | 0.761926 | ||||||||
\(55\) | −4.65843e19 | −0.450888 | ||||||||
\(56\) | −9.61599e18 | −0.0756539 | ||||||||
\(57\) | 1.90095e20 | 1.22014 | ||||||||
\(58\) | 6.59286e19 | 0.346459 | ||||||||
\(59\) | 1.56115e20 | 0.673979 | 0.336989 | − | 0.941508i | \(-0.390591\pi\) | ||||
0.336989 | + | 0.941508i | \(0.390591\pi\) | |||||||
\(60\) | 4.70098e19 | 0.167282 | ||||||||
\(61\) | 5.13552e20 | 1.51109 | 0.755546 | − | 0.655095i | \(-0.227372\pi\) | ||||
0.755546 | + | 0.655095i | \(0.227372\pi\) | |||||||
\(62\) | 3.80291e20 | 0.928136 | ||||||||
\(63\) | −4.64061e19 | −0.0942235 | ||||||||
\(64\) | 7.37870e19 | 0.125000 | ||||||||
\(65\) | −1.18232e20 | −0.167583 | ||||||||
\(66\) | 4.48496e20 | 0.533339 | ||||||||
\(67\) | −7.59236e19 | −0.0759480 | −0.0379740 | − | 0.999279i | \(-0.512090\pi\) | ||||
−0.0379740 | + | 0.999279i | \(0.512090\pi\) | |||||||
\(68\) | −5.67304e20 | −0.478589 | ||||||||
\(69\) | −1.81101e19 | −0.0129168 | ||||||||
\(70\) | −1.11945e20 | −0.0676669 | ||||||||
\(71\) | −4.54949e20 | −0.233610 | −0.116805 | − | 0.993155i | \(-0.537265\pi\) | ||||
−0.116805 | + | 0.993155i | \(0.537265\pi\) | |||||||
\(72\) | 3.56091e20 | 0.155682 | ||||||||
\(73\) | −4.50124e21 | −1.67927 | −0.839633 | − | 0.543154i | \(-0.817230\pi\) | ||||
−0.839633 | + | 0.543154i | \(0.817230\pi\) | |||||||
\(74\) | 7.66337e20 | 0.244487 | ||||||||
\(75\) | 5.47267e20 | 0.149622 | ||||||||
\(76\) | 3.47354e21 | 0.815485 | ||||||||
\(77\) | −1.06801e21 | −0.215740 | ||||||||
\(78\) | 1.13829e21 | 0.198228 | ||||||||
\(79\) | −1.03553e22 | −1.55759 | −0.778794 | − | 0.627280i | \(-0.784168\pi\) | ||||
−0.778794 | + | 0.627280i | \(0.784168\pi\) | |||||||
\(80\) | 8.58993e20 | 0.111803 | ||||||||
\(81\) | −3.24181e21 | −0.365771 | ||||||||
\(82\) | 6.60847e21 | 0.647503 | ||||||||
\(83\) | −5.91206e21 | −0.503895 | −0.251948 | − | 0.967741i | \(-0.581071\pi\) | ||||
−0.251948 | + | 0.967741i | \(0.581071\pi\) | |||||||
\(84\) | 1.07776e21 | 0.0800407 | ||||||||
\(85\) | −6.60428e21 | −0.428063 | ||||||||
\(86\) | 5.61857e21 | 0.318342 | ||||||||
\(87\) | −7.38929e21 | −0.366548 | ||||||||
\(88\) | 8.19520e21 | 0.356458 | ||||||||
\(89\) | −2.39717e22 | −0.915617 | −0.457808 | − | 0.889051i | \(-0.651365\pi\) | ||||
−0.457808 | + | 0.889051i | \(0.651365\pi\) | |||||||
\(90\) | 4.14545e21 | 0.139246 | ||||||||
\(91\) | −2.71062e21 | −0.0801849 | ||||||||
\(92\) | −3.30919e20 | −0.00863300 | ||||||||
\(93\) | −4.26231e22 | −0.981954 | ||||||||
\(94\) | −1.07575e21 | −0.0219151 | ||||||||
\(95\) | 4.04373e22 | 0.729392 | ||||||||
\(96\) | −8.27006e21 | −0.132248 | ||||||||
\(97\) | 1.24537e23 | 1.76776 | 0.883878 | − | 0.467717i | \(-0.154923\pi\) | ||||
0.883878 | + | 0.467717i | \(0.154923\pi\) | |||||||
\(98\) | 5.34847e22 | 0.674730 | ||||||||
\(99\) | 3.95495e22 | 0.443952 | ||||||||
\(100\) | 1.00000e22 | 0.100000 | ||||||||
\(101\) | −1.49773e23 | −1.33579 | −0.667893 | − | 0.744257i | \(-0.732804\pi\) | ||||
−0.667893 | + | 0.744257i | \(0.732804\pi\) | |||||||
\(102\) | 6.35835e22 | 0.506340 | ||||||||
\(103\) | 2.00999e23 | 1.43076 | 0.715380 | − | 0.698736i | \(-0.246254\pi\) | ||||
0.715380 | + | 0.698736i | \(0.246254\pi\) | |||||||
\(104\) | 2.07996e22 | 0.132486 | ||||||||
\(105\) | 1.25468e22 | 0.0715906 | ||||||||
\(106\) | 9.02503e22 | 0.461776 | ||||||||
\(107\) | 1.12988e23 | 0.518943 | 0.259471 | − | 0.965751i | \(-0.416452\pi\) | ||||
0.259471 | + | 0.965751i | \(0.416452\pi\) | |||||||
\(108\) | −1.30548e23 | −0.538763 | ||||||||
\(109\) | −2.77607e23 | −1.03045 | −0.515224 | − | 0.857056i | \(-0.672291\pi\) | ||||
−0.515224 | + | 0.857056i | \(0.672291\pi\) | |||||||
\(110\) | 9.54047e22 | 0.318826 | ||||||||
\(111\) | −8.58912e22 | −0.258663 | ||||||||
\(112\) | 1.96935e22 | 0.0534954 | ||||||||
\(113\) | 5.91159e22 | 0.144978 | 0.0724890 | − | 0.997369i | \(-0.476906\pi\) | ||||
0.0724890 | + | 0.997369i | \(0.476906\pi\) | |||||||
\(114\) | −3.89315e23 | −0.862771 | ||||||||
\(115\) | −3.85240e21 | −0.00772159 | ||||||||
\(116\) | −1.35022e23 | −0.244983 | ||||||||
\(117\) | 1.00377e23 | 0.165006 | ||||||||
\(118\) | −3.19723e23 | −0.476575 | ||||||||
\(119\) | −1.51412e23 | −0.204819 | ||||||||
\(120\) | −9.62761e22 | −0.118286 | ||||||||
\(121\) | 1.47751e22 | 0.0165006 | ||||||||
\(122\) | −1.05175e24 | −1.06850 | ||||||||
\(123\) | −7.40678e23 | −0.685048 | ||||||||
\(124\) | −7.78836e23 | −0.656291 | ||||||||
\(125\) | 1.16415e23 | 0.0894427 | ||||||||
\(126\) | 9.50398e22 | 0.0666261 | ||||||||
\(127\) | 1.52582e24 | 0.976696 | 0.488348 | − | 0.872649i | \(-0.337600\pi\) | ||||
0.488348 | + | 0.872649i | \(0.337600\pi\) | |||||||
\(128\) | −1.51116e23 | −0.0883883 | ||||||||
\(129\) | −6.29730e23 | −0.336801 | ||||||||
\(130\) | 2.42139e23 | 0.118499 | ||||||||
\(131\) | 1.92350e24 | 0.861930 | 0.430965 | − | 0.902369i | \(-0.358173\pi\) | ||||
0.430965 | + | 0.902369i | \(0.358173\pi\) | |||||||
\(132\) | −9.18519e23 | −0.377127 | ||||||||
\(133\) | 9.27079e23 | 0.348998 | ||||||||
\(134\) | 1.55492e23 | 0.0537034 | ||||||||
\(135\) | −1.51978e24 | −0.481884 | ||||||||
\(136\) | 1.16184e24 | 0.338414 | ||||||||
\(137\) | 3.29993e24 | 0.883525 | 0.441762 | − | 0.897132i | \(-0.354353\pi\) | ||||
0.441762 | + | 0.897132i | \(0.354353\pi\) | |||||||
\(138\) | 3.70895e22 | 0.00913358 | ||||||||
\(139\) | 6.17390e24 | 1.39923 | 0.699616 | − | 0.714519i | \(-0.253355\pi\) | ||||
0.699616 | + | 0.714519i | \(0.253355\pi\) | |||||||
\(140\) | 2.29263e23 | 0.0478478 | ||||||||
\(141\) | 1.20571e23 | 0.0231858 | ||||||||
\(142\) | 9.31735e23 | 0.165187 | ||||||||
\(143\) | 2.31012e24 | 0.377807 | ||||||||
\(144\) | −7.29275e23 | −0.110084 | ||||||||
\(145\) | −1.57186e24 | −0.219120 | ||||||||
\(146\) | 9.21854e24 | 1.18742 | ||||||||
\(147\) | −5.99458e24 | −0.713854 | ||||||||
\(148\) | −1.56946e24 | −0.172878 | ||||||||
\(149\) | −4.79152e24 | −0.488462 | −0.244231 | − | 0.969717i | \(-0.578536\pi\) | ||||
−0.244231 | + | 0.969717i | \(0.578536\pi\) | |||||||
\(150\) | −1.12080e24 | −0.105798 | ||||||||
\(151\) | −1.17176e25 | −1.02472 | −0.512358 | − | 0.858772i | \(-0.671228\pi\) | ||||
−0.512358 | + | 0.858772i | \(0.671228\pi\) | |||||||
\(152\) | −7.11381e24 | −0.576635 | ||||||||
\(153\) | 5.60695e24 | 0.421479 | ||||||||
\(154\) | 2.18728e24 | 0.152551 | ||||||||
\(155\) | −9.06684e24 | −0.587005 | ||||||||
\(156\) | −2.33122e24 | −0.140169 | ||||||||
\(157\) | 1.45572e24 | 0.0813263 | 0.0406631 | − | 0.999173i | \(-0.487053\pi\) | ||||
0.0406631 | + | 0.999173i | \(0.487053\pi\) | |||||||
\(158\) | 2.12077e25 | 1.10138 | ||||||||
\(159\) | −1.01153e25 | −0.488552 | ||||||||
\(160\) | −1.75922e24 | −0.0790569 | ||||||||
\(161\) | −8.83214e22 | −0.00369461 | ||||||||
\(162\) | 6.63923e24 | 0.258639 | ||||||||
\(163\) | 3.81476e25 | 1.38455 | 0.692277 | − | 0.721632i | \(-0.256608\pi\) | ||||
0.692277 | + | 0.721632i | \(0.256608\pi\) | |||||||
\(164\) | −1.35341e25 | −0.457853 | ||||||||
\(165\) | −1.06930e25 | −0.337313 | ||||||||
\(166\) | 1.21079e25 | 0.356308 | ||||||||
\(167\) | −6.46554e25 | −1.77568 | −0.887842 | − | 0.460149i | \(-0.847796\pi\) | ||||
−0.887842 | + | 0.460149i | \(0.847796\pi\) | |||||||
\(168\) | −2.20726e24 | −0.0565973 | ||||||||
\(169\) | −3.58908e25 | −0.859579 | ||||||||
\(170\) | 1.35256e25 | 0.302686 | ||||||||
\(171\) | −3.43308e25 | −0.718172 | ||||||||
\(172\) | −1.15068e25 | −0.225102 | ||||||||
\(173\) | −2.31249e25 | −0.423203 | −0.211602 | − | 0.977356i | \(-0.567868\pi\) | ||||
−0.211602 | + | 0.977356i | \(0.567868\pi\) | |||||||
\(174\) | 1.51333e25 | 0.259189 | ||||||||
\(175\) | 2.66897e24 | 0.0427963 | ||||||||
\(176\) | −1.67838e25 | −0.252054 | ||||||||
\(177\) | 3.58347e25 | 0.504209 | ||||||||
\(178\) | 4.90941e25 | 0.647439 | ||||||||
\(179\) | −9.97940e25 | −1.23394 | −0.616971 | − | 0.786986i | \(-0.711640\pi\) | ||||
−0.616971 | + | 0.786986i | \(0.711640\pi\) | |||||||
\(180\) | −8.48988e24 | −0.0984617 | ||||||||
\(181\) | 1.18405e26 | 1.28845 | 0.644224 | − | 0.764837i | \(-0.277180\pi\) | ||||
0.644224 | + | 0.764837i | \(0.277180\pi\) | |||||||
\(182\) | 5.55135e24 | 0.0566993 | ||||||||
\(183\) | 1.17881e26 | 1.13046 | ||||||||
\(184\) | 6.77722e23 | 0.00610445 | ||||||||
\(185\) | −1.82709e25 | −0.154627 | ||||||||
\(186\) | 8.72921e25 | 0.694346 | ||||||||
\(187\) | 1.29040e26 | 0.965043 | ||||||||
\(188\) | 2.20315e24 | 0.0154963 | ||||||||
\(189\) | −3.48430e25 | −0.230571 | ||||||||
\(190\) | −8.28157e25 | −0.515758 | ||||||||
\(191\) | 2.47442e26 | 1.45074 | 0.725369 | − | 0.688360i | \(-0.241669\pi\) | ||||
0.725369 | + | 0.688360i | \(0.241669\pi\) | |||||||
\(192\) | 1.69371e25 | 0.0935135 | ||||||||
\(193\) | 2.80515e26 | 1.45897 | 0.729486 | − | 0.683996i | \(-0.239760\pi\) | ||||
0.729486 | + | 0.683996i | \(0.239760\pi\) | |||||||
\(194\) | −2.55051e26 | −1.24999 | ||||||||
\(195\) | −2.71390e25 | −0.125371 | ||||||||
\(196\) | −1.09537e26 | −0.477106 | ||||||||
\(197\) | 2.28927e26 | 0.940451 | 0.470226 | − | 0.882546i | \(-0.344173\pi\) | ||||
0.470226 | + | 0.882546i | \(0.344173\pi\) | |||||||
\(198\) | −8.09974e25 | −0.313922 | ||||||||
\(199\) | −3.84077e26 | −1.40478 | −0.702390 | − | 0.711792i | \(-0.747884\pi\) | ||||
−0.702390 | + | 0.711792i | \(0.747884\pi\) | |||||||
\(200\) | −2.04800e25 | −0.0707107 | ||||||||
\(201\) | −1.74275e25 | −0.0568173 | ||||||||
\(202\) | 3.06735e26 | 0.944543 | ||||||||
\(203\) | −3.60369e25 | −0.104844 | ||||||||
\(204\) | −1.30219e26 | −0.358037 | ||||||||
\(205\) | −1.57558e26 | −0.409517 | ||||||||
\(206\) | −4.11647e26 | −1.01170 | ||||||||
\(207\) | 3.27064e24 | 0.00760281 | ||||||||
\(208\) | −4.25975e25 | −0.0936820 | ||||||||
\(209\) | −7.90100e26 | −1.64437 | ||||||||
\(210\) | −2.56958e25 | −0.0506222 | ||||||||
\(211\) | 5.46973e26 | 1.02028 | 0.510138 | − | 0.860092i | \(-0.329594\pi\) | ||||
0.510138 | + | 0.860092i | \(0.329594\pi\) | |||||||
\(212\) | −1.84833e26 | −0.326525 | ||||||||
\(213\) | −1.04429e26 | −0.174766 | ||||||||
\(214\) | −2.31400e26 | −0.366948 | ||||||||
\(215\) | −1.33957e26 | −0.201337 | ||||||||
\(216\) | 2.67363e26 | 0.380963 | ||||||||
\(217\) | −2.07869e26 | −0.280869 | ||||||||
\(218\) | 5.68539e26 | 0.728636 | ||||||||
\(219\) | −1.03322e27 | −1.25627 | ||||||||
\(220\) | −1.95389e26 | −0.225444 | ||||||||
\(221\) | 3.27507e26 | 0.358682 | ||||||||
\(222\) | 1.75905e26 | 0.182902 | ||||||||
\(223\) | 8.07759e26 | 0.797583 | 0.398792 | − | 0.917042i | \(-0.369430\pi\) | ||||
0.398792 | + | 0.917042i | \(0.369430\pi\) | |||||||
\(224\) | −4.03324e25 | −0.0378270 | ||||||||
\(225\) | −9.88352e25 | −0.0880669 | ||||||||
\(226\) | −1.21069e26 | −0.102515 | ||||||||
\(227\) | 7.29025e26 | 0.586739 | 0.293370 | − | 0.955999i | \(-0.405223\pi\) | ||||
0.293370 | + | 0.955999i | \(0.405223\pi\) | |||||||
\(228\) | 7.97317e26 | 0.610071 | ||||||||
\(229\) | −1.53114e26 | −0.111406 | −0.0557028 | − | 0.998447i | \(-0.517740\pi\) | ||||
−0.0557028 | + | 0.998447i | \(0.517740\pi\) | |||||||
\(230\) | 7.88972e24 | 0.00545999 | ||||||||
\(231\) | −2.45150e26 | −0.161397 | ||||||||
\(232\) | 2.76525e26 | 0.173229 | ||||||||
\(233\) | 2.78414e27 | 1.65996 | 0.829981 | − | 0.557791i | \(-0.188351\pi\) | ||||
0.829981 | + | 0.557791i | \(0.188351\pi\) | |||||||
\(234\) | −2.05573e26 | −0.116677 | ||||||||
\(235\) | 2.56480e25 | 0.0138603 | ||||||||
\(236\) | 6.54794e26 | 0.336989 | ||||||||
\(237\) | −2.37696e27 | −1.16524 | ||||||||
\(238\) | 3.10091e26 | 0.144829 | ||||||||
\(239\) | −1.57931e27 | −0.702896 | −0.351448 | − | 0.936207i | \(-0.614311\pi\) | ||||
−0.351448 | + | 0.936207i | \(0.614311\pi\) | |||||||
\(240\) | 1.97174e26 | 0.0836410 | ||||||||
\(241\) | 1.98820e27 | 0.804013 | 0.402006 | − | 0.915637i | \(-0.368313\pi\) | ||||
0.402006 | + | 0.915637i | \(0.368313\pi\) | |||||||
\(242\) | −3.02595e25 | −0.0116677 | ||||||||
\(243\) | 2.18609e27 | 0.803889 | ||||||||
\(244\) | 2.15399e27 | 0.755546 | ||||||||
\(245\) | −1.27517e27 | −0.426737 | ||||||||
\(246\) | 1.51691e27 | 0.484402 | ||||||||
\(247\) | −2.00529e27 | −0.611170 | ||||||||
\(248\) | 1.59506e27 | 0.464068 | ||||||||
\(249\) | −1.35705e27 | −0.376968 | ||||||||
\(250\) | −2.38419e26 | −0.0632456 | ||||||||
\(251\) | −3.79632e27 | −0.961866 | −0.480933 | − | 0.876757i | \(-0.659702\pi\) | ||||
−0.480933 | + | 0.876757i | \(0.659702\pi\) | |||||||
\(252\) | −1.94641e26 | −0.0471117 | ||||||||
\(253\) | 7.52716e25 | 0.0174079 | ||||||||
\(254\) | −3.12487e27 | −0.690628 | ||||||||
\(255\) | −1.51595e27 | −0.320238 | ||||||||
\(256\) | 3.09485e26 | 0.0625000 | ||||||||
\(257\) | 3.87160e27 | 0.747583 | 0.373791 | − | 0.927513i | \(-0.378058\pi\) | ||||
0.373791 | + | 0.927513i | \(0.378058\pi\) | |||||||
\(258\) | 1.28969e27 | 0.238154 | ||||||||
\(259\) | −4.18884e26 | −0.0739855 | ||||||||
\(260\) | −4.95901e26 | −0.0837917 | ||||||||
\(261\) | 1.33449e27 | 0.215749 | ||||||||
\(262\) | −3.93933e27 | −0.609477 | ||||||||
\(263\) | −1.11317e28 | −1.64842 | −0.824212 | − | 0.566281i | \(-0.808382\pi\) | ||||
−0.824212 | + | 0.566281i | \(0.808382\pi\) | |||||||
\(264\) | 1.88113e27 | 0.266669 | ||||||||
\(265\) | −2.15173e27 | −0.292053 | ||||||||
\(266\) | −1.89866e27 | −0.246779 | ||||||||
\(267\) | −5.50247e27 | −0.684980 | ||||||||
\(268\) | −3.18447e26 | −0.0379740 | ||||||||
\(269\) | 1.52514e28 | 1.74244 | 0.871220 | − | 0.490893i | \(-0.163329\pi\) | ||||
0.871220 | + | 0.490893i | \(0.163329\pi\) | |||||||
\(270\) | 3.11251e27 | 0.340744 | ||||||||
\(271\) | −1.10913e27 | −0.116369 | −0.0581843 | − | 0.998306i | \(-0.518531\pi\) | ||||
−0.0581843 | + | 0.998306i | \(0.518531\pi\) | |||||||
\(272\) | −2.37944e27 | −0.239295 | ||||||||
\(273\) | −6.22196e26 | −0.0599870 | ||||||||
\(274\) | −6.75826e27 | −0.624746 | ||||||||
\(275\) | −2.27462e27 | −0.201643 | ||||||||
\(276\) | −7.59592e25 | −0.00645841 | ||||||||
\(277\) | 1.90865e28 | 1.55671 | 0.778356 | − | 0.627824i | \(-0.216054\pi\) | ||||
0.778356 | + | 0.627824i | \(0.216054\pi\) | |||||||
\(278\) | −1.26442e28 | −0.989406 | ||||||||
\(279\) | 7.69764e27 | 0.577975 | ||||||||
\(280\) | −4.69531e26 | −0.0338335 | ||||||||
\(281\) | −5.75634e27 | −0.398129 | −0.199064 | − | 0.979986i | \(-0.563790\pi\) | ||||
−0.199064 | + | 0.979986i | \(0.563790\pi\) | |||||||
\(282\) | −2.46929e26 | −0.0163948 | ||||||||
\(283\) | −9.14645e27 | −0.583054 | −0.291527 | − | 0.956563i | \(-0.594163\pi\) | ||||
−0.291527 | + | 0.956563i | \(0.594163\pi\) | |||||||
\(284\) | −1.90819e27 | −0.116805 | ||||||||
\(285\) | 9.28200e27 | 0.545664 | ||||||||
\(286\) | −4.73112e27 | −0.267150 | ||||||||
\(287\) | −3.61223e27 | −0.195945 | ||||||||
\(288\) | 1.49355e27 | 0.0778408 | ||||||||
\(289\) | −1.67346e27 | −0.0838091 | ||||||||
\(290\) | 3.21917e27 | 0.154941 | ||||||||
\(291\) | 2.85862e28 | 1.32247 | ||||||||
\(292\) | −1.88796e28 | −0.839633 | ||||||||
\(293\) | 1.07789e28 | 0.460889 | 0.230445 | − | 0.973085i | \(-0.425982\pi\) | ||||
0.230445 | + | 0.973085i | \(0.425982\pi\) | |||||||
\(294\) | 1.22769e28 | 0.504771 | ||||||||
\(295\) | 7.62280e27 | 0.301413 | ||||||||
\(296\) | 3.21425e27 | 0.122243 | ||||||||
\(297\) | 2.96948e28 | 1.08638 | ||||||||
\(298\) | 9.81303e27 | 0.345395 | ||||||||
\(299\) | 1.91041e26 | 0.00647005 | ||||||||
\(300\) | 2.29540e27 | 0.0748108 | ||||||||
\(301\) | −3.07114e27 | −0.0963353 | ||||||||
\(302\) | 2.39977e28 | 0.724584 | ||||||||
\(303\) | −3.43789e28 | −0.999312 | ||||||||
\(304\) | 1.45691e28 | 0.407743 | ||||||||
\(305\) | 2.50758e28 | 0.675781 | ||||||||
\(306\) | −1.14830e28 | −0.298030 | ||||||||
\(307\) | 1.06872e28 | 0.267161 | 0.133581 | − | 0.991038i | \(-0.457352\pi\) | ||||
0.133581 | + | 0.991038i | \(0.457352\pi\) | |||||||
\(308\) | −4.47954e27 | −0.107870 | ||||||||
\(309\) | 4.61375e28 | 1.07036 | ||||||||
\(310\) | 1.85689e28 | 0.415075 | ||||||||
\(311\) | −8.23745e28 | −1.77439 | −0.887194 | − | 0.461397i | \(-0.847348\pi\) | ||||
−0.887194 | + | 0.461397i | \(0.847348\pi\) | |||||||
\(312\) | 4.77434e27 | 0.0991141 | ||||||||
\(313\) | −7.21679e28 | −1.44406 | −0.722028 | − | 0.691863i | \(-0.756790\pi\) | ||||
−0.722028 | + | 0.691863i | \(0.756790\pi\) | |||||||
\(314\) | −2.98131e27 | −0.0575064 | ||||||||
\(315\) | −2.26592e27 | −0.0421380 | ||||||||
\(316\) | −4.34334e28 | −0.778794 | ||||||||
\(317\) | −8.73563e28 | −1.51047 | −0.755236 | − | 0.655453i | \(-0.772478\pi\) | ||||
−0.755236 | + | 0.655453i | \(0.772478\pi\) | |||||||
\(318\) | 2.07161e28 | 0.345458 | ||||||||
\(319\) | 3.07124e28 | 0.493993 | ||||||||
\(320\) | 3.60288e27 | 0.0559017 | ||||||||
\(321\) | 2.59353e28 | 0.388225 | ||||||||
\(322\) | 1.80882e26 | 0.00261248 | ||||||||
\(323\) | −1.12013e29 | −1.56113 | ||||||||
\(324\) | −1.35971e28 | −0.182886 | ||||||||
\(325\) | −5.77304e27 | −0.0749456 | ||||||||
\(326\) | −7.81263e28 | −0.979027 | ||||||||
\(327\) | −6.37220e28 | −0.770886 | ||||||||
\(328\) | 2.77179e28 | 0.323751 | ||||||||
\(329\) | 5.88014e26 | 0.00663185 | ||||||||
\(330\) | 2.18992e28 | 0.238516 | ||||||||
\(331\) | −4.91673e28 | −0.517195 | −0.258597 | − | 0.965985i | \(-0.583260\pi\) | ||||
−0.258597 | + | 0.965985i | \(0.583260\pi\) | |||||||
\(332\) | −2.47970e28 | −0.251948 | ||||||||
\(333\) | 1.55118e28 | 0.152248 | ||||||||
\(334\) | 1.32414e29 | 1.25560 | ||||||||
\(335\) | −3.70721e27 | −0.0339650 | ||||||||
\(336\) | 4.52046e27 | 0.0400204 | ||||||||
\(337\) | 1.56219e29 | 1.33656 | 0.668280 | − | 0.743910i | \(-0.267031\pi\) | ||||
0.668280 | + | 0.743910i | \(0.267031\pi\) | |||||||
\(338\) | 7.35043e28 | 0.607814 | ||||||||
\(339\) | 1.35695e28 | 0.108459 | ||||||||
\(340\) | −2.77004e28 | −0.214032 | ||||||||
\(341\) | 1.77156e29 | 1.32337 | ||||||||
\(342\) | 7.03095e28 | 0.507825 | ||||||||
\(343\) | −5.98729e28 | −0.418166 | ||||||||
\(344\) | 2.35660e28 | 0.159171 | ||||||||
\(345\) | −8.84281e26 | −0.00577658 | ||||||||
\(346\) | 4.73597e28 | 0.299250 | ||||||||
\(347\) | −1.50078e29 | −0.917335 | −0.458668 | − | 0.888608i | \(-0.651673\pi\) | ||||
−0.458668 | + | 0.888608i | \(0.651673\pi\) | |||||||
\(348\) | −3.09929e28 | −0.183274 | ||||||||
\(349\) | 2.61518e29 | 1.49627 | 0.748134 | − | 0.663548i | \(-0.230950\pi\) | ||||
0.748134 | + | 0.663548i | \(0.230950\pi\) | |||||||
\(350\) | −5.46606e27 | −0.0302616 | ||||||||
\(351\) | 7.53660e28 | 0.403779 | ||||||||
\(352\) | 3.43732e28 | 0.178229 | ||||||||
\(353\) | −2.25089e29 | −1.12965 | −0.564827 | − | 0.825209i | \(-0.691057\pi\) | ||||
−0.564827 | + | 0.825209i | \(0.691057\pi\) | |||||||
\(354\) | −7.33894e28 | −0.356530 | ||||||||
\(355\) | −2.22143e28 | −0.104474 | ||||||||
\(356\) | −1.00545e29 | −0.457808 | ||||||||
\(357\) | −3.47551e28 | −0.153227 | ||||||||
\(358\) | 2.04378e29 | 0.872528 | ||||||||
\(359\) | −4.75724e28 | −0.196684 | −0.0983420 | − | 0.995153i | \(-0.531354\pi\) | ||||
−0.0983420 | + | 0.995153i | \(0.531354\pi\) | |||||||
\(360\) | 1.73873e28 | 0.0696230 | ||||||||
\(361\) | 4.28014e29 | 1.66007 | ||||||||
\(362\) | −2.42494e29 | −0.911070 | ||||||||
\(363\) | 3.39149e27 | 0.0123442 | ||||||||
\(364\) | −1.13692e28 | −0.0400925 | ||||||||
\(365\) | −2.19787e29 | −0.750991 | ||||||||
\(366\) | −2.41420e29 | −0.799356 | ||||||||
\(367\) | 1.94572e29 | 0.624339 | 0.312170 | − | 0.950026i | \(-0.398944\pi\) | ||||
0.312170 | + | 0.950026i | \(0.398944\pi\) | |||||||
\(368\) | −1.38797e27 | −0.00431650 | ||||||||
\(369\) | 1.33765e29 | 0.403217 | ||||||||
\(370\) | 3.74188e28 | 0.109338 | ||||||||
\(371\) | −4.93313e28 | −0.139741 | ||||||||
\(372\) | −1.78774e29 | −0.490977 | ||||||||
\(373\) | 5.99622e29 | 1.59671 | 0.798355 | − | 0.602187i | \(-0.205704\pi\) | ||||
0.798355 | + | 0.602187i | \(0.205704\pi\) | |||||||
\(374\) | −2.64274e29 | −0.682389 | ||||||||
\(375\) | 2.67220e28 | 0.0669128 | ||||||||
\(376\) | −4.51204e27 | −0.0109575 | ||||||||
\(377\) | 7.79486e28 | 0.183604 | ||||||||
\(378\) | 7.13584e28 | 0.163038 | ||||||||
\(379\) | −6.46441e29 | −1.43277 | −0.716387 | − | 0.697703i | \(-0.754206\pi\) | ||||
−0.716387 | + | 0.697703i | \(0.754206\pi\) | |||||||
\(380\) | 1.69607e29 | 0.364696 | ||||||||
\(381\) | 3.50236e29 | 0.730674 | ||||||||
\(382\) | −5.06761e29 | −1.02583 | ||||||||
\(383\) | −8.91098e29 | −1.75041 | −0.875205 | − | 0.483752i | \(-0.839274\pi\) | ||||
−0.875205 | + | 0.483752i | \(0.839274\pi\) | |||||||
\(384\) | −3.46871e28 | −0.0661240 | ||||||||
\(385\) | −5.21487e28 | −0.0964818 | ||||||||
\(386\) | −5.74494e29 | −1.03165 | ||||||||
\(387\) | 1.13728e29 | 0.198240 | ||||||||
\(388\) | 5.22345e29 | 0.883878 | ||||||||
\(389\) | −3.75725e29 | −0.617233 | −0.308617 | − | 0.951187i | \(-0.599866\pi\) | ||||
−0.308617 | + | 0.951187i | \(0.599866\pi\) | |||||||
\(390\) | 5.55806e28 | 0.0886504 | ||||||||
\(391\) | 1.06713e28 | 0.0165266 | ||||||||
\(392\) | 2.24331e29 | 0.337365 | ||||||||
\(393\) | 4.41520e29 | 0.644817 | ||||||||
\(394\) | −4.68843e29 | −0.664999 | ||||||||
\(395\) | −5.05631e29 | −0.696574 | ||||||||
\(396\) | 1.65883e29 | 0.221976 | ||||||||
\(397\) | 7.49782e29 | 0.974640 | 0.487320 | − | 0.873223i | \(-0.337975\pi\) | ||||
0.487320 | + | 0.873223i | \(0.337975\pi\) | |||||||
\(398\) | 7.86590e29 | 0.993329 | ||||||||
\(399\) | 2.12802e29 | 0.261088 | ||||||||
\(400\) | 4.19430e28 | 0.0500000 | ||||||||
\(401\) | −8.25665e29 | −0.956409 | −0.478205 | − | 0.878248i | \(-0.658712\pi\) | ||||
−0.478205 | + | 0.878248i | \(0.658712\pi\) | |||||||
\(402\) | 3.56916e28 | 0.0401759 | ||||||||
\(403\) | 4.49625e29 | 0.491861 | ||||||||
\(404\) | −6.28192e29 | −0.667893 | ||||||||
\(405\) | −1.58291e29 | −0.163578 | ||||||||
\(406\) | 7.38036e28 | 0.0741359 | ||||||||
\(407\) | 3.56993e29 | 0.348597 | ||||||||
\(408\) | 2.66688e29 | 0.253170 | ||||||||
\(409\) | −2.03509e30 | −1.87830 | −0.939149 | − | 0.343509i | \(-0.888384\pi\) | ||||
−0.939149 | + | 0.343509i | \(0.888384\pi\) | |||||||
\(410\) | 3.22679e29 | 0.289572 | ||||||||
\(411\) | 7.57467e29 | 0.660972 | ||||||||
\(412\) | 8.43053e29 | 0.715380 | ||||||||
\(413\) | 1.74763e29 | 0.144219 | ||||||||
\(414\) | −6.69828e27 | −0.00537600 | ||||||||
\(415\) | −2.88675e29 | −0.225349 | ||||||||
\(416\) | 8.72398e28 | 0.0662432 | ||||||||
\(417\) | 1.41716e30 | 1.04678 | ||||||||
\(418\) | 1.61813e30 | 1.16275 | ||||||||
\(419\) | −1.17686e30 | −0.822742 | −0.411371 | − | 0.911468i | \(-0.634950\pi\) | ||||
−0.411371 | + | 0.911468i | \(0.634950\pi\) | |||||||
\(420\) | 5.26251e28 | 0.0357953 | ||||||||
\(421\) | 1.99473e30 | 1.32020 | 0.660100 | − | 0.751178i | \(-0.270514\pi\) | ||||
0.660100 | + | 0.751178i | \(0.270514\pi\) | |||||||
\(422\) | −1.12020e30 | −0.721444 | ||||||||
\(423\) | −2.17748e28 | −0.0136471 | ||||||||
\(424\) | 3.78537e29 | 0.230888 | ||||||||
\(425\) | −3.22475e29 | −0.191436 | ||||||||
\(426\) | 2.13871e29 | 0.123578 | ||||||||
\(427\) | 5.74894e29 | 0.323346 | ||||||||
\(428\) | 4.73907e29 | 0.259471 | ||||||||
\(429\) | 5.30265e29 | 0.282640 | ||||||||
\(430\) | 2.74344e29 | 0.142367 | ||||||||
\(431\) | 9.01027e29 | 0.455249 | 0.227625 | − | 0.973749i | \(-0.426904\pi\) | ||||
0.227625 | + | 0.973749i | \(0.426904\pi\) | |||||||
\(432\) | −5.47559e29 | −0.269381 | ||||||||
\(433\) | −3.28011e30 | −1.57137 | −0.785685 | − | 0.618627i | \(-0.787689\pi\) | ||||
−0.785685 | + | 0.618627i | \(0.787689\pi\) | |||||||
\(434\) | 4.25716e29 | 0.198604 | ||||||||
\(435\) | −3.60805e29 | −0.163925 | ||||||||
\(436\) | −1.16437e30 | −0.515224 | ||||||||
\(437\) | −6.53393e28 | −0.0281603 | ||||||||
\(438\) | 2.11603e30 | 0.888319 | ||||||||
\(439\) | 1.34681e30 | 0.550763 | 0.275382 | − | 0.961335i | \(-0.411196\pi\) | ||||
0.275382 | + | 0.961335i | \(0.411196\pi\) | |||||||
\(440\) | 4.00156e29 | 0.159413 | ||||||||
\(441\) | 1.08261e30 | 0.420172 | ||||||||
\(442\) | −6.70734e29 | −0.253626 | ||||||||
\(443\) | −2.42126e30 | −0.892068 | −0.446034 | − | 0.895016i | \(-0.647164\pi\) | ||||
−0.446034 | + | 0.895016i | \(0.647164\pi\) | |||||||
\(444\) | −3.60254e29 | −0.129331 | ||||||||
\(445\) | −1.17049e30 | −0.409476 | ||||||||
\(446\) | −1.65429e30 | −0.563977 | ||||||||
\(447\) | −1.09985e30 | −0.365423 | ||||||||
\(448\) | 8.26007e28 | 0.0267477 | ||||||||
\(449\) | −3.10296e30 | −0.979361 | −0.489681 | − | 0.871902i | \(-0.662887\pi\) | ||||
−0.489681 | + | 0.871902i | \(0.662887\pi\) | |||||||
\(450\) | 2.02414e29 | 0.0622727 | ||||||||
\(451\) | 3.07851e30 | 0.923231 | ||||||||
\(452\) | 2.47950e29 | 0.0724890 | ||||||||
\(453\) | −2.68966e30 | −0.766599 | ||||||||
\(454\) | −1.49304e30 | −0.414887 | ||||||||
\(455\) | −1.32355e29 | −0.0358598 | ||||||||
\(456\) | −1.63291e30 | −0.431385 | ||||||||
\(457\) | −5.07608e30 | −1.30765 | −0.653826 | − | 0.756645i | \(-0.726837\pi\) | ||||
−0.653826 | + | 0.756645i | \(0.726837\pi\) | |||||||
\(458\) | 3.13578e29 | 0.0787757 | ||||||||
\(459\) | 4.20985e30 | 1.03138 | ||||||||
\(460\) | −1.61582e28 | −0.00386079 | ||||||||
\(461\) | 4.69993e29 | 0.109530 | 0.0547648 | − | 0.998499i | \(-0.482559\pi\) | ||||
0.0547648 | + | 0.998499i | \(0.482559\pi\) | |||||||
\(462\) | 5.02068e29 | 0.114125 | ||||||||
\(463\) | −3.39682e29 | −0.0753166 | −0.0376583 | − | 0.999291i | \(-0.511990\pi\) | ||||
−0.0376583 | + | 0.999291i | \(0.511990\pi\) | |||||||
\(464\) | −5.66322e29 | −0.122492 | ||||||||
\(465\) | −2.08121e30 | −0.439143 | ||||||||
\(466\) | −5.70192e30 | −1.17377 | ||||||||
\(467\) | 1.07622e30 | 0.216150 | 0.108075 | − | 0.994143i | \(-0.465531\pi\) | ||||
0.108075 | + | 0.994143i | \(0.465531\pi\) | |||||||
\(468\) | 4.21013e29 | 0.0825028 | ||||||||
\(469\) | −8.49926e28 | −0.0162515 | ||||||||
\(470\) | −5.25271e28 | −0.00980072 | ||||||||
\(471\) | 3.34145e29 | 0.0608408 | ||||||||
\(472\) | −1.34102e30 | −0.238288 | ||||||||
\(473\) | 2.61737e30 | 0.453902 | ||||||||
\(474\) | 4.86802e30 | 0.823952 | ||||||||
\(475\) | 1.97448e30 | 0.326194 | ||||||||
\(476\) | −6.35067e29 | −0.102409 | ||||||||
\(477\) | 1.82680e30 | 0.287560 | ||||||||
\(478\) | 3.23442e30 | 0.497022 | ||||||||
\(479\) | 1.27284e31 | 1.90949 | 0.954744 | − | 0.297429i | \(-0.0961293\pi\) | ||||
0.954744 | + | 0.297429i | \(0.0961293\pi\) | |||||||
\(480\) | −4.03811e29 | −0.0591431 | ||||||||
\(481\) | 9.06055e29 | 0.129565 | ||||||||
\(482\) | −4.07182e30 | −0.568523 | ||||||||
\(483\) | −2.02733e28 | −0.00276397 | ||||||||
\(484\) | 6.19714e28 | 0.00825030 | ||||||||
\(485\) | 6.08089e30 | 0.790565 | ||||||||
\(486\) | −4.47712e30 | −0.568436 | ||||||||
\(487\) | 4.08137e30 | 0.506084 | 0.253042 | − | 0.967455i | \(-0.418569\pi\) | ||||
0.253042 | + | 0.967455i | \(0.418569\pi\) | |||||||
\(488\) | −4.41137e30 | −0.534252 | ||||||||
\(489\) | 8.75641e30 | 1.03580 | ||||||||
\(490\) | 2.61156e30 | 0.301748 | ||||||||
\(491\) | 6.22475e30 | 0.702562 | 0.351281 | − | 0.936270i | \(-0.385746\pi\) | ||||
0.351281 | + | 0.936270i | \(0.385746\pi\) | |||||||
\(492\) | −3.10663e30 | −0.342524 | ||||||||
\(493\) | 4.35411e30 | 0.468986 | ||||||||
\(494\) | 4.10683e30 | 0.432163 | ||||||||
\(495\) | 1.93113e30 | 0.198542 | ||||||||
\(496\) | −3.26667e30 | −0.328146 | ||||||||
\(497\) | −5.09292e29 | −0.0499883 | ||||||||
\(498\) | 2.77925e30 | 0.266557 | ||||||||
\(499\) | 6.71277e30 | 0.629137 | 0.314569 | − | 0.949235i | \(-0.398140\pi\) | ||||
0.314569 | + | 0.949235i | \(0.398140\pi\) | |||||||
\(500\) | 4.88281e29 | 0.0447214 | ||||||||
\(501\) | −1.48410e31 | −1.32840 | ||||||||
\(502\) | 7.77485e30 | 0.680142 | ||||||||
\(503\) | −2.13145e31 | −1.82240 | −0.911200 | − | 0.411965i | \(-0.864843\pi\) | ||||
−0.911200 | + | 0.411965i | \(0.864843\pi\) | |||||||
\(504\) | 3.98626e29 | 0.0333130 | ||||||||
\(505\) | −7.31312e30 | −0.597382 | ||||||||
\(506\) | −1.54156e29 | −0.0123092 | ||||||||
\(507\) | −8.23838e30 | −0.643058 | ||||||||
\(508\) | 6.39974e30 | 0.488348 | ||||||||
\(509\) | −3.48709e30 | −0.260141 | −0.130070 | − | 0.991505i | \(-0.541520\pi\) | ||||
−0.130070 | + | 0.991505i | \(0.541520\pi\) | |||||||
\(510\) | 3.10466e30 | 0.226442 | ||||||||
\(511\) | −5.03891e30 | −0.359332 | ||||||||
\(512\) | −6.33825e29 | −0.0441942 | ||||||||
\(513\) | −2.57765e31 | −1.75741 | ||||||||
\(514\) | −7.92903e30 | −0.528621 | ||||||||
\(515\) | 9.81443e30 | 0.639855 | ||||||||
\(516\) | −2.64128e30 | −0.168400 | ||||||||
\(517\) | −5.01133e29 | −0.0312472 | ||||||||
\(518\) | 8.57875e29 | 0.0523156 | ||||||||
\(519\) | −5.30809e30 | −0.316602 | ||||||||
\(520\) | 1.01560e30 | 0.0592497 | ||||||||
\(521\) | 6.35728e30 | 0.362775 | 0.181388 | − | 0.983412i | \(-0.441941\pi\) | ||||
0.181388 | + | 0.983412i | \(0.441941\pi\) | |||||||
\(522\) | −2.73303e30 | −0.152558 | ||||||||
\(523\) | −2.07982e31 | −1.13568 | −0.567842 | − | 0.823138i | \(-0.692221\pi\) | ||||
−0.567842 | + | 0.823138i | \(0.692221\pi\) | |||||||
\(524\) | 8.06774e30 | 0.430965 | ||||||||
\(525\) | 6.12637e29 | 0.0320163 | ||||||||
\(526\) | 2.27977e31 | 1.16561 | ||||||||
\(527\) | 2.51155e31 | 1.25638 | ||||||||
\(528\) | −3.85255e30 | −0.188564 | ||||||||
\(529\) | −2.08742e31 | −0.999702 | ||||||||
\(530\) | 4.40675e30 | 0.206512 | ||||||||
\(531\) | −6.47166e30 | −0.296776 | ||||||||
\(532\) | 3.88845e30 | 0.174499 | ||||||||
\(533\) | 7.81332e30 | 0.343141 | ||||||||
\(534\) | 1.12691e31 | 0.484354 | ||||||||
\(535\) | 5.51700e30 | 0.232078 | ||||||||
\(536\) | 6.52179e29 | 0.0268517 | ||||||||
\(537\) | −2.29067e31 | −0.923122 | ||||||||
\(538\) | −3.12348e31 | −1.23209 | ||||||||
\(539\) | 2.49155e31 | 0.962052 | ||||||||
\(540\) | −6.37442e30 | −0.240942 | ||||||||
\(541\) | −5.19131e30 | −0.192092 | −0.0960458 | − | 0.995377i | \(-0.530620\pi\) | ||||
−0.0960458 | + | 0.995377i | \(0.530620\pi\) | |||||||
\(542\) | 2.27150e30 | 0.0822850 | ||||||||
\(543\) | 2.71787e31 | 0.963899 | ||||||||
\(544\) | 4.87310e30 | 0.169207 | ||||||||
\(545\) | −1.35550e31 | −0.460830 | ||||||||
\(546\) | 1.27426e30 | 0.0424172 | ||||||||
\(547\) | 1.22758e31 | 0.400125 | 0.200063 | − | 0.979783i | \(-0.435885\pi\) | ||||
0.200063 | + | 0.979783i | \(0.435885\pi\) | |||||||
\(548\) | 1.38409e31 | 0.441762 | ||||||||
\(549\) | −2.12890e31 | −0.665386 | ||||||||
\(550\) | 4.65843e30 | 0.142583 | ||||||||
\(551\) | −2.66598e31 | −0.799122 | ||||||||
\(552\) | 1.55564e29 | 0.00456679 | ||||||||
\(553\) | −1.15923e31 | −0.333295 | ||||||||
\(554\) | −3.90891e31 | −1.10076 | ||||||||
\(555\) | −4.19390e30 | −0.115678 | ||||||||
\(556\) | 2.58952e31 | 0.699616 | ||||||||
\(557\) | 3.14791e31 | 0.833081 | 0.416540 | − | 0.909117i | \(-0.363242\pi\) | ||||
0.416540 | + | 0.909117i | \(0.363242\pi\) | |||||||
\(558\) | −1.57648e31 | −0.408690 | ||||||||
\(559\) | 6.64294e30 | 0.168704 | ||||||||
\(560\) | 9.61599e29 | 0.0239239 | ||||||||
\(561\) | 2.96199e31 | 0.721957 | ||||||||
\(562\) | 1.17890e31 | 0.281520 | ||||||||
\(563\) | 4.85033e31 | 1.13481 | 0.567407 | − | 0.823437i | \(-0.307947\pi\) | ||||
0.567407 | + | 0.823437i | \(0.307947\pi\) | |||||||
\(564\) | 5.05711e29 | 0.0115929 | ||||||||
\(565\) | 2.88652e30 | 0.0648362 | ||||||||
\(566\) | 1.87319e31 | 0.412281 | ||||||||
\(567\) | −3.62904e30 | −0.0782684 | ||||||||
\(568\) | 3.90798e30 | 0.0825936 | ||||||||
\(569\) | 1.58999e31 | 0.329309 | 0.164654 | − | 0.986351i | \(-0.447349\pi\) | ||||
0.164654 | + | 0.986351i | \(0.447349\pi\) | |||||||
\(570\) | −1.90095e31 | −0.385843 | ||||||||
\(571\) | −3.92722e31 | −0.781214 | −0.390607 | − | 0.920557i | \(-0.627735\pi\) | ||||
−0.390607 | + | 0.920557i | \(0.627735\pi\) | |||||||
\(572\) | 9.68934e30 | 0.188903 | ||||||||
\(573\) | 5.67978e31 | 1.08531 | ||||||||
\(574\) | 7.39784e30 | 0.138554 | ||||||||
\(575\) | −1.88106e29 | −0.00345320 | ||||||||
\(576\) | −3.05880e30 | −0.0550418 | ||||||||
\(577\) | 5.05036e30 | 0.0890841 | 0.0445420 | − | 0.999008i | \(-0.485817\pi\) | ||||
0.0445420 | + | 0.999008i | \(0.485817\pi\) | |||||||
\(578\) | 3.42725e30 | 0.0592620 | ||||||||
\(579\) | 6.43894e31 | 1.09147 | ||||||||
\(580\) | −6.59286e30 | −0.109560 | ||||||||
\(581\) | −6.61824e30 | −0.107824 | ||||||||
\(582\) | −5.85445e31 | −0.935130 | ||||||||
\(583\) | 4.20425e31 | 0.658415 | ||||||||
\(584\) | 3.86654e31 | 0.593710 | ||||||||
\(585\) | 4.90124e30 | 0.0737927 | ||||||||
\(586\) | −2.20752e31 | −0.325898 | ||||||||
\(587\) | −3.04905e31 | −0.441394 | −0.220697 | − | 0.975342i | \(-0.570833\pi\) | ||||
−0.220697 | + | 0.975342i | \(0.570833\pi\) | |||||||
\(588\) | −2.51431e31 | −0.356927 | ||||||||
\(589\) | −1.53780e32 | −2.14078 | ||||||||
\(590\) | −1.56115e31 | −0.213131 | ||||||||
\(591\) | 5.25481e31 | 0.703559 | ||||||||
\(592\) | −6.58278e30 | −0.0864390 | ||||||||
\(593\) | 1.36625e32 | 1.75955 | 0.879777 | − | 0.475387i | \(-0.157692\pi\) | ||||
0.879777 | + | 0.475387i | \(0.157692\pi\) | |||||||
\(594\) | −6.08150e31 | −0.768186 | ||||||||
\(595\) | −7.39315e30 | −0.0915977 | ||||||||
\(596\) | −2.00971e31 | −0.244231 | ||||||||
\(597\) | −8.81612e31 | −1.05093 | ||||||||
\(598\) | −3.91252e29 | −0.00457502 | ||||||||
\(599\) | −9.92624e31 | −1.13861 | −0.569307 | − | 0.822125i | \(-0.692788\pi\) | ||||
−0.569307 | + | 0.822125i | \(0.692788\pi\) | |||||||
\(600\) | −4.70098e30 | −0.0528992 | ||||||||
\(601\) | −1.76086e31 | −0.194387 | −0.0971937 | − | 0.995265i | \(-0.530987\pi\) | ||||
−0.0971937 | + | 0.995265i | \(0.530987\pi\) | |||||||
\(602\) | 6.28970e30 | 0.0681193 | ||||||||
\(603\) | 3.14737e30 | 0.0334425 | ||||||||
\(604\) | −4.91472e31 | −0.512358 | ||||||||
\(605\) | 7.21442e29 | 0.00737929 | ||||||||
\(606\) | 7.04079e31 | 0.706621 | ||||||||
\(607\) | −1.39464e32 | −1.37338 | −0.686691 | − | 0.726949i | \(-0.740937\pi\) | ||||
−0.686691 | + | 0.726949i | \(0.740937\pi\) | |||||||
\(608\) | −2.98375e31 | −0.288318 | ||||||||
\(609\) | −8.27193e30 | −0.0784346 | ||||||||
\(610\) | −5.13552e31 | −0.477849 | ||||||||
\(611\) | −1.27189e30 | −0.0116138 | ||||||||
\(612\) | 2.35173e31 | 0.210739 | ||||||||
\(613\) | 1.82366e32 | 1.60380 | 0.801898 | − | 0.597461i | \(-0.203824\pi\) | ||||
0.801898 | + | 0.597461i | \(0.203824\pi\) | |||||||
\(614\) | −2.18874e31 | −0.188912 | ||||||||
\(615\) | −3.61659e31 | −0.306363 | ||||||||
\(616\) | 9.17410e30 | 0.0762756 | ||||||||
\(617\) | 1.13184e32 | 0.923650 | 0.461825 | − | 0.886971i | \(-0.347195\pi\) | ||||
0.461825 | + | 0.886971i | \(0.347195\pi\) | |||||||
\(618\) | −9.44895e31 | −0.756861 | ||||||||
\(619\) | −8.35127e31 | −0.656614 | −0.328307 | − | 0.944571i | \(-0.606478\pi\) | ||||
−0.328307 | + | 0.944571i | \(0.606478\pi\) | |||||||
\(620\) | −3.80291e31 | −0.293502 | ||||||||
\(621\) | 2.45568e30 | 0.0186046 | ||||||||
\(622\) | 1.68703e32 | 1.25468 | ||||||||
\(623\) | −2.68351e31 | −0.195925 | ||||||||
\(624\) | −9.77785e30 | −0.0700843 | ||||||||
\(625\) | 5.68434e30 | 0.0400000 | ||||||||
\(626\) | 1.47800e32 | 1.02110 | ||||||||
\(627\) | −1.81360e32 | −1.23017 | ||||||||
\(628\) | 6.10572e30 | 0.0406631 | ||||||||
\(629\) | 5.06110e31 | 0.330950 | ||||||||
\(630\) | 4.64061e30 | 0.0297961 | ||||||||
\(631\) | −7.94078e31 | −0.500640 | −0.250320 | − | 0.968163i | \(-0.580536\pi\) | ||||
−0.250320 | + | 0.968163i | \(0.580536\pi\) | |||||||
\(632\) | 8.89516e31 | 0.550690 | ||||||||
\(633\) | 1.25552e32 | 0.763277 | ||||||||
\(634\) | 1.78906e32 | 1.06807 | ||||||||
\(635\) | 7.45027e31 | 0.436792 | ||||||||
\(636\) | −4.24265e31 | −0.244276 | ||||||||
\(637\) | 6.32360e31 | 0.357570 | ||||||||
\(638\) | −6.28990e31 | −0.349306 | ||||||||
\(639\) | 1.88597e31 | 0.102867 | ||||||||
\(640\) | −7.37870e30 | −0.0395285 | ||||||||
\(641\) | 1.60774e32 | 0.845955 | 0.422978 | − | 0.906140i | \(-0.360985\pi\) | ||||
0.422978 | + | 0.906140i | \(0.360985\pi\) | |||||||
\(642\) | −5.31155e31 | −0.274517 | ||||||||
\(643\) | −3.25183e32 | −1.65083 | −0.825413 | − | 0.564529i | \(-0.809058\pi\) | ||||
−0.825413 | + | 0.564529i | \(0.809058\pi\) | |||||||
\(644\) | −3.70447e29 | −0.00184730 | ||||||||
\(645\) | −3.07486e31 | −0.150622 | ||||||||
\(646\) | 2.29402e32 | 1.10389 | ||||||||
\(647\) | 2.35559e32 | 1.11353 | 0.556763 | − | 0.830672i | \(-0.312043\pi\) | ||||
0.556763 | + | 0.830672i | \(0.312043\pi\) | |||||||
\(648\) | 2.78469e31 | 0.129320 | ||||||||
\(649\) | −1.48941e32 | −0.679517 | ||||||||
\(650\) | 1.18232e31 | 0.0529945 | ||||||||
\(651\) | −4.77143e31 | −0.210120 | ||||||||
\(652\) | 1.60003e32 | 0.692277 | ||||||||
\(653\) | 1.72242e32 | 0.732215 | 0.366108 | − | 0.930573i | \(-0.380690\pi\) | ||||
0.366108 | + | 0.930573i | \(0.380690\pi\) | |||||||
\(654\) | 1.30503e32 | 0.545099 | ||||||||
\(655\) | 9.39208e31 | 0.385467 | ||||||||
\(656\) | −5.67663e31 | −0.228927 | ||||||||
\(657\) | 1.86597e32 | 0.739438 | ||||||||
\(658\) | −1.20425e30 | −0.00468942 | ||||||||
\(659\) | −2.10755e32 | −0.806483 | −0.403242 | − | 0.915094i | \(-0.632117\pi\) | ||||
−0.403242 | + | 0.915094i | \(0.632117\pi\) | |||||||
\(660\) | −4.48496e31 | −0.168657 | ||||||||
\(661\) | −1.56345e32 | −0.577786 | −0.288893 | − | 0.957361i | \(-0.593287\pi\) | ||||
−0.288893 | + | 0.957361i | \(0.593287\pi\) | |||||||
\(662\) | 1.00695e32 | 0.365712 | ||||||||
\(663\) | 7.51760e31 | 0.268333 | ||||||||
\(664\) | 5.07842e31 | 0.178154 | ||||||||
\(665\) | 4.52675e31 | 0.156077 | ||||||||
\(666\) | −3.17681e31 | −0.107656 | ||||||||
\(667\) | 2.53983e30 | 0.00845977 | ||||||||
\(668\) | −2.71184e32 | −0.887842 | ||||||||
\(669\) | 1.85413e32 | 0.596678 | ||||||||
\(670\) | 7.59236e30 | 0.0240169 | ||||||||
\(671\) | −4.89952e32 | −1.52351 | ||||||||
\(672\) | −9.25790e30 | −0.0282987 | ||||||||
\(673\) | −3.51032e32 | −1.05481 | −0.527405 | − | 0.849614i | \(-0.676835\pi\) | ||||
−0.527405 | + | 0.849614i | \(0.676835\pi\) | |||||||
\(674\) | −3.19936e32 | −0.945091 | ||||||||
\(675\) | −7.42081e31 | −0.215505 | ||||||||
\(676\) | −1.50537e32 | −0.429789 | ||||||||
\(677\) | −5.04787e32 | −1.41690 | −0.708448 | − | 0.705763i | \(-0.750604\pi\) | ||||
−0.708448 | + | 0.705763i | \(0.750604\pi\) | |||||||
\(678\) | −2.77903e31 | −0.0766923 | ||||||||
\(679\) | 1.39412e32 | 0.378268 | ||||||||
\(680\) | 5.67304e31 | 0.151343 | ||||||||
\(681\) | 1.67341e32 | 0.438944 | ||||||||
\(682\) | −3.62815e32 | −0.935762 | ||||||||
\(683\) | 2.13585e32 | 0.541668 | 0.270834 | − | 0.962626i | \(-0.412701\pi\) | ||||
0.270834 | + | 0.962626i | \(0.412701\pi\) | |||||||
\(684\) | −1.43994e32 | −0.359086 | ||||||||
\(685\) | 1.61130e32 | 0.395124 | ||||||||
\(686\) | 1.22620e32 | 0.295688 | ||||||||
\(687\) | −3.51458e31 | −0.0833435 | ||||||||
\(688\) | −4.82632e31 | −0.112551 | ||||||||
\(689\) | 1.06705e32 | 0.244716 | ||||||||
\(690\) | 1.81101e30 | 0.00408466 | ||||||||
\(691\) | −4.74070e32 | −1.05159 | −0.525793 | − | 0.850613i | \(-0.676231\pi\) | ||||
−0.525793 | + | 0.850613i | \(0.676231\pi\) | |||||||
\(692\) | −9.69927e31 | −0.211602 | ||||||||
\(693\) | 4.42736e31 | 0.0949977 | ||||||||
\(694\) | 3.07360e32 | 0.648654 | ||||||||
\(695\) | 3.01460e32 | 0.625755 | ||||||||
\(696\) | 6.34735e31 | 0.129594 | ||||||||
\(697\) | 4.36442e32 | 0.876495 | ||||||||
\(698\) | −5.35589e32 | −1.05802 | ||||||||
\(699\) | 6.39073e32 | 1.24183 | ||||||||
\(700\) | 1.11945e31 | 0.0213982 | ||||||||
\(701\) | −4.92407e32 | −0.925906 | −0.462953 | − | 0.886383i | \(-0.653210\pi\) | ||||
−0.462953 | + | 0.886383i | \(0.653210\pi\) | |||||||
\(702\) | −1.54350e32 | −0.285515 | ||||||||
\(703\) | −3.09886e32 | −0.563918 | ||||||||
\(704\) | −7.03962e31 | −0.126027 | ||||||||
\(705\) | 5.88725e30 | 0.0103690 | ||||||||
\(706\) | 4.60983e32 | 0.798786 | ||||||||
\(707\) | −1.67663e32 | −0.285834 | ||||||||
\(708\) | 1.50301e32 | 0.252105 | ||||||||
\(709\) | 8.64776e32 | 1.42716 | 0.713578 | − | 0.700575i | \(-0.247073\pi\) | ||||
0.713578 | + | 0.700575i | \(0.247073\pi\) | |||||||
\(710\) | 4.54949e31 | 0.0738740 | ||||||||
\(711\) | 4.29275e32 | 0.685859 | ||||||||
\(712\) | 2.05915e32 | 0.323719 | ||||||||
\(713\) | 1.46503e31 | 0.0226630 | ||||||||
\(714\) | 7.11784e31 | 0.108348 | ||||||||
\(715\) | 1.12799e32 | 0.168960 | ||||||||
\(716\) | −4.18566e32 | −0.616971 | ||||||||
\(717\) | −3.62515e32 | −0.525842 | ||||||||
\(718\) | 9.74283e31 | 0.139077 | ||||||||
\(719\) | −6.11269e31 | −0.0858717 | −0.0429359 | − | 0.999078i | \(-0.513671\pi\) | ||||
−0.0429359 | + | 0.999078i | \(0.513671\pi\) | |||||||
\(720\) | −3.56091e31 | −0.0492309 | ||||||||
\(721\) | 2.25009e32 | 0.306156 | ||||||||
\(722\) | −8.76573e32 | −1.17384 | ||||||||
\(723\) | 4.56371e32 | 0.601489 | ||||||||
\(724\) | 4.96627e32 | 0.644224 | ||||||||
\(725\) | −7.67510e31 | −0.0979934 | ||||||||
\(726\) | −6.94577e30 | −0.00872869 | ||||||||
\(727\) | 3.03244e30 | 0.00375099 | 0.00187550 | − | 0.999998i | \(-0.499403\pi\) | ||||
0.00187550 | + | 0.999998i | \(0.499403\pi\) | |||||||
\(728\) | 2.32841e31 | 0.0283497 | ||||||||
\(729\) | 8.06990e32 | 0.967167 | ||||||||
\(730\) | 4.50124e32 | 0.531031 | ||||||||
\(731\) | 3.71066e32 | 0.430925 | ||||||||
\(732\) | 4.94428e32 | 0.565230 | ||||||||
\(733\) | −5.01686e32 | −0.564595 | −0.282297 | − | 0.959327i | \(-0.591096\pi\) | ||||
−0.282297 | + | 0.959327i | \(0.591096\pi\) | |||||||
\(734\) | −3.98484e32 | −0.441475 | ||||||||
\(735\) | −2.92704e32 | −0.319245 | ||||||||
\(736\) | 2.84257e30 | 0.00305223 | ||||||||
\(737\) | 7.24347e31 | 0.0765721 | ||||||||
\(738\) | −2.73951e32 | −0.285118 | ||||||||
\(739\) | 7.88978e32 | 0.808451 | 0.404226 | − | 0.914659i | \(-0.367541\pi\) | ||||
0.404226 | + | 0.914659i | \(0.367541\pi\) | |||||||
\(740\) | −7.66337e31 | −0.0773134 | ||||||||
\(741\) | −4.60295e32 | −0.457221 | ||||||||
\(742\) | 1.01031e32 | 0.0988116 | ||||||||
\(743\) | −1.01205e33 | −0.974609 | −0.487304 | − | 0.873232i | \(-0.662020\pi\) | ||||
−0.487304 | + | 0.873232i | \(0.662020\pi\) | |||||||
\(744\) | 3.66129e32 | 0.347173 | ||||||||
\(745\) | −2.33961e32 | −0.218447 | ||||||||
\(746\) | −1.22803e33 | −1.12904 | ||||||||
\(747\) | 2.45081e32 | 0.221882 | ||||||||
\(748\) | 5.41234e32 | 0.482522 | ||||||||
\(749\) | 1.26484e32 | 0.111044 | ||||||||
\(750\) | −5.47267e31 | −0.0473145 | ||||||||
\(751\) | 9.01052e32 | 0.767169 | 0.383584 | − | 0.923506i | \(-0.374690\pi\) | ||||
0.383584 | + | 0.923506i | \(0.374690\pi\) | |||||||
\(752\) | 9.24066e30 | 0.00774815 | ||||||||
\(753\) | −8.71407e32 | −0.719580 | ||||||||
\(754\) | −1.59639e32 | −0.129828 | ||||||||
\(755\) | −5.72149e32 | −0.458267 | ||||||||
\(756\) | −1.46142e32 | −0.115285 | ||||||||
\(757\) | 3.32781e32 | 0.258557 | 0.129279 | − | 0.991608i | \(-0.458734\pi\) | ||||
0.129279 | + | 0.991608i | \(0.458734\pi\) | |||||||
\(758\) | 1.32391e33 | 1.01312 | ||||||||
\(759\) | 1.72779e31 | 0.0130230 | ||||||||
\(760\) | −3.47354e32 | −0.257879 | ||||||||
\(761\) | −3.01945e32 | −0.220803 | −0.110401 | − | 0.993887i | \(-0.535214\pi\) | ||||
−0.110401 | + | 0.993887i | \(0.535214\pi\) | |||||||
\(762\) | −7.17284e32 | −0.516665 | ||||||||
\(763\) | −3.10767e32 | −0.220497 | ||||||||
\(764\) | 1.03785e33 | 0.725369 | ||||||||
\(765\) | 2.73777e32 | 0.188491 | ||||||||
\(766\) | 1.82497e33 | 1.23773 | ||||||||
\(767\) | −3.78015e32 | −0.252559 | ||||||||
\(768\) | 7.10393e31 | 0.0467568 | ||||||||
\(769\) | −2.38000e33 | −1.54320 | −0.771602 | − | 0.636106i | \(-0.780544\pi\) | ||||
−0.771602 | + | 0.636106i | \(0.780544\pi\) | |||||||
\(770\) | 1.06801e32 | 0.0682229 | ||||||||
\(771\) | 8.88687e32 | 0.559273 | ||||||||
\(772\) | 1.17656e33 | 0.729486 | ||||||||
\(773\) | −1.65561e33 | −1.01133 | −0.505666 | − | 0.862729i | \(-0.668753\pi\) | ||||
−0.505666 | + | 0.862729i | \(0.668753\pi\) | |||||||
\(774\) | −2.32915e32 | −0.140177 | ||||||||
\(775\) | −4.42717e32 | −0.262516 | ||||||||
\(776\) | −1.06976e33 | −0.624996 | ||||||||
\(777\) | −9.61507e31 | −0.0553491 | ||||||||
\(778\) | 7.69484e32 | 0.436450 | ||||||||
\(779\) | −2.67229e33 | −1.49349 | ||||||||
\(780\) | −1.13829e32 | −0.0626853 | ||||||||
\(781\) | 4.34043e32 | 0.235530 | ||||||||
\(782\) | −2.18548e31 | −0.0116861 | ||||||||
\(783\) | 1.00197e33 | 0.527952 | ||||||||
\(784\) | −4.59430e32 | −0.238553 | ||||||||
\(785\) | 7.10799e31 | 0.0363702 | ||||||||
\(786\) | −9.04234e32 | −0.455954 | ||||||||
\(787\) | −1.04035e33 | −0.516974 | −0.258487 | − | 0.966015i | \(-0.583224\pi\) | ||||
−0.258487 | + | 0.966015i | \(0.583224\pi\) | |||||||
\(788\) | 9.60191e32 | 0.470226 | ||||||||
\(789\) | −2.55517e33 | −1.23320 | ||||||||
\(790\) | 1.03553e33 | 0.492552 | ||||||||
\(791\) | 6.61772e31 | 0.0310227 | ||||||||
\(792\) | −3.39728e32 | −0.156961 | ||||||||
\(793\) | −1.24351e33 | −0.566249 | ||||||||
\(794\) | −1.53555e33 | −0.689175 | ||||||||
\(795\) | −4.93910e32 | −0.218487 | ||||||||
\(796\) | −1.61094e33 | −0.702390 | ||||||||
\(797\) | 2.16453e32 | 0.0930238 | 0.0465119 | − | 0.998918i | \(-0.485189\pi\) | ||||
0.0465119 | + | 0.998918i | \(0.485189\pi\) | |||||||
\(798\) | −4.35818e32 | −0.184617 | ||||||||
\(799\) | −7.10459e31 | −0.0296655 | ||||||||
\(800\) | −8.58993e31 | −0.0353553 | ||||||||
\(801\) | 9.93734e32 | 0.403178 | ||||||||
\(802\) | 1.69096e33 | 0.676283 | ||||||||
\(803\) | 4.29440e33 | 1.69306 | ||||||||
\(804\) | −7.30963e31 | −0.0284087 | ||||||||
\(805\) | −4.31257e30 | −0.00165228 | ||||||||
\(806\) | −9.20833e32 | −0.347799 | ||||||||
\(807\) | 3.50080e33 | 1.30353 | ||||||||
\(808\) | 1.28654e33 | 0.472272 | ||||||||
\(809\) | 2.79297e33 | 1.01078 | 0.505392 | − | 0.862890i | \(-0.331348\pi\) | ||||
0.505392 | + | 0.862890i | \(0.331348\pi\) | |||||||
\(810\) | 3.24181e32 | 0.115667 | ||||||||
\(811\) | 2.01537e33 | 0.708948 | 0.354474 | − | 0.935066i | \(-0.384660\pi\) | ||||
0.354474 | + | 0.935066i | \(0.384660\pi\) | |||||||
\(812\) | −1.51150e32 | −0.0524220 | ||||||||
\(813\) | −2.54590e32 | −0.0870562 | ||||||||
\(814\) | −7.31121e32 | −0.246495 | ||||||||
\(815\) | 1.86268e33 | 0.619191 | ||||||||
\(816\) | −5.46178e32 | −0.179018 | ||||||||
\(817\) | −2.27200e33 | −0.734268 | ||||||||
\(818\) | 4.16786e33 | 1.32816 | ||||||||
\(819\) | 1.12367e32 | 0.0353082 | ||||||||
\(820\) | −6.60847e32 | −0.204758 | ||||||||
\(821\) | 4.42385e33 | 1.35162 | 0.675808 | − | 0.737077i | \(-0.263795\pi\) | ||||
0.675808 | + | 0.737077i | \(0.263795\pi\) | |||||||
\(822\) | −1.55129e33 | −0.467378 | ||||||||
\(823\) | −6.10731e31 | −0.0181448 | −0.00907239 | − | 0.999959i | \(-0.502888\pi\) | ||||
−0.00907239 | + | 0.999959i | \(0.502888\pi\) | |||||||
\(824\) | −1.72657e33 | −0.505850 | ||||||||
\(825\) | −5.22118e32 | −0.150851 | ||||||||
\(826\) | −3.57914e32 | −0.101978 | ||||||||
\(827\) | 4.78632e33 | 1.34489 | 0.672447 | − | 0.740145i | \(-0.265243\pi\) | ||||
0.672447 | + | 0.740145i | \(0.265243\pi\) | |||||||
\(828\) | 1.37181e31 | 0.00380140 | ||||||||
\(829\) | −3.13389e33 | −0.856459 | −0.428230 | − | 0.903670i | \(-0.640863\pi\) | ||||
−0.428230 | + | 0.903670i | \(0.640863\pi\) | |||||||
\(830\) | 5.91206e32 | 0.159346 | ||||||||
\(831\) | 4.38111e33 | 1.16459 | ||||||||
\(832\) | −1.78667e32 | −0.0468410 | ||||||||
\(833\) | 3.53228e33 | 0.913351 | ||||||||
\(834\) | −2.90234e33 | −0.740183 | ||||||||
\(835\) | −3.15700e33 | −0.794110 | ||||||||
\(836\) | −3.31392e33 | −0.822186 | ||||||||
\(837\) | 5.77959e33 | 1.41434 | ||||||||
\(838\) | 2.41021e33 | 0.581767 | ||||||||
\(839\) | −4.05251e33 | −0.964855 | −0.482427 | − | 0.875936i | \(-0.660245\pi\) | ||||
−0.482427 | + | 0.875936i | \(0.660245\pi\) | |||||||
\(840\) | −1.07776e32 | −0.0253111 | ||||||||
\(841\) | −3.28042e33 | −0.759932 | ||||||||
\(842\) | −4.08520e33 | −0.933522 | ||||||||
\(843\) | −1.32131e33 | −0.297843 | ||||||||
\(844\) | 2.29417e33 | 0.510138 | ||||||||
\(845\) | −1.75248e33 | −0.384415 | ||||||||
\(846\) | 4.45948e31 | 0.00964996 | ||||||||
\(847\) | 1.65400e31 | 0.00353083 | ||||||||
\(848\) | −7.75244e32 | −0.163262 | ||||||||
\(849\) | −2.09948e33 | −0.436187 | ||||||||
\(850\) | 6.60428e32 | 0.135365 | ||||||||
\(851\) | 2.95224e31 | 0.00596982 | ||||||||
\(852\) | −4.38007e32 | −0.0873828 | ||||||||
\(853\) | −4.75268e33 | −0.935459 | −0.467729 | − | 0.883872i | \(-0.654928\pi\) | ||||
−0.467729 | + | 0.883872i | \(0.654928\pi\) | |||||||
\(854\) | −1.17738e33 | −0.228640 | ||||||||
\(855\) | −1.67631e33 | −0.321176 | ||||||||
\(856\) | −9.70561e32 | −0.183474 | ||||||||
\(857\) | −9.71517e33 | −1.81205 | −0.906027 | − | 0.423221i | \(-0.860900\pi\) | ||||
−0.906027 | + | 0.423221i | \(0.860900\pi\) | |||||||
\(858\) | −1.08598e33 | −0.199857 | ||||||||
\(859\) | −8.89769e32 | −0.161568 | −0.0807841 | − | 0.996732i | \(-0.525742\pi\) | ||||
−0.0807841 | + | 0.996732i | \(0.525742\pi\) | |||||||
\(860\) | −5.61857e32 | −0.100669 | ||||||||
\(861\) | −8.29151e32 | −0.146588 | ||||||||
\(862\) | −1.84530e33 | −0.321910 | ||||||||
\(863\) | 4.93774e33 | 0.849972 | 0.424986 | − | 0.905200i | \(-0.360279\pi\) | ||||
0.424986 | + | 0.905200i | \(0.360279\pi\) | |||||||
\(864\) | 1.12140e33 | 0.190481 | ||||||||
\(865\) | −1.12914e33 | −0.189262 | ||||||||
\(866\) | 6.71768e33 | 1.11113 | ||||||||
\(867\) | −3.84127e32 | −0.0626983 | ||||||||
\(868\) | −8.71867e32 | −0.140434 | ||||||||
\(869\) | 9.87947e33 | 1.57039 | ||||||||
\(870\) | 7.38929e32 | 0.115913 | ||||||||
\(871\) | 1.83841e32 | 0.0284599 | ||||||||
\(872\) | 2.38463e33 | 0.364318 | ||||||||
\(873\) | −5.16260e33 | −0.778404 | ||||||||
\(874\) | 1.33815e32 | 0.0199124 | ||||||||
\(875\) | 1.30321e32 | 0.0191391 | ||||||||
\(876\) | −4.33362e33 | −0.628136 | ||||||||
\(877\) | 8.97071e32 | 0.128331 | 0.0641655 | − | 0.997939i | \(-0.479561\pi\) | ||||
0.0641655 | + | 0.997939i | \(0.479561\pi\) | |||||||
\(878\) | −2.75827e33 | −0.389448 | ||||||||
\(879\) | 2.47419e33 | 0.344795 | ||||||||
\(880\) | −8.19520e32 | −0.112722 | ||||||||
\(881\) | −1.00868e34 | −1.36940 | −0.684699 | − | 0.728826i | \(-0.740066\pi\) | ||||
−0.684699 | + | 0.728826i | \(0.740066\pi\) | |||||||
\(882\) | −2.21718e33 | −0.297107 | ||||||||
\(883\) | −9.65735e33 | −1.27735 | −0.638675 | − | 0.769476i | \(-0.720517\pi\) | ||||
−0.638675 | + | 0.769476i | \(0.720517\pi\) | |||||||
\(884\) | 1.37366e33 | 0.179341 | ||||||||
\(885\) | 1.74974e33 | 0.225489 | ||||||||
\(886\) | 4.95873e33 | 0.630787 | ||||||||
\(887\) | 5.68517e33 | 0.713874 | 0.356937 | − | 0.934128i | \(-0.383821\pi\) | ||||
0.356937 | + | 0.934128i | \(0.383821\pi\) | |||||||
\(888\) | 7.37800e32 | 0.0914512 | ||||||||
\(889\) | 1.70807e33 | 0.208995 | ||||||||
\(890\) | 2.39717e33 | 0.289544 | ||||||||
\(891\) | 3.09284e33 | 0.368777 | ||||||||
\(892\) | 3.38799e33 | 0.398792 | ||||||||
\(893\) | 4.35007e32 | 0.0505480 | ||||||||
\(894\) | 2.25249e33 | 0.258393 | ||||||||
\(895\) | −4.87275e33 | −0.551835 | ||||||||
\(896\) | −1.69166e32 | −0.0189135 | ||||||||
\(897\) | 4.38516e31 | 0.00484030 | ||||||||
\(898\) | 6.35486e33 | 0.692513 | ||||||||
\(899\) | 5.97764e33 | 0.643122 | ||||||||
\(900\) | −4.14545e32 | −0.0440334 | ||||||||
\(901\) | 5.96038e33 | 0.625085 | ||||||||
\(902\) | −6.30479e33 | −0.652823 | ||||||||
\(903\) | −7.04951e32 | −0.0720692 | ||||||||
\(904\) | −5.07802e32 | −0.0512575 | ||||||||
\(905\) | 5.78150e33 | 0.576212 | ||||||||
\(906\) | 5.50843e33 | 0.542067 | ||||||||
\(907\) | −1.49169e34 | −1.44942 | −0.724712 | − | 0.689052i | \(-0.758027\pi\) | ||||
−0.724712 | + | 0.689052i | \(0.758027\pi\) | |||||||
\(908\) | 3.05775e33 | 0.293370 | ||||||||
\(909\) | 6.20875e33 | 0.588192 | ||||||||
\(910\) | 2.71062e32 | 0.0253567 | ||||||||
\(911\) | 1.98559e33 | 0.183412 | 0.0917062 | − | 0.995786i | \(-0.470768\pi\) | ||||
0.0917062 | + | 0.995786i | \(0.470768\pi\) | |||||||
\(912\) | 3.34419e33 | 0.305036 | ||||||||
\(913\) | 5.64038e33 | 0.508036 | ||||||||
\(914\) | 1.03958e34 | 0.924650 | ||||||||
\(915\) | 5.75590e33 | 0.505557 | ||||||||
\(916\) | −6.42207e32 | −0.0557028 | ||||||||
\(917\) | 2.15326e33 | 0.184437 | ||||||||
\(918\) | −8.62177e33 | −0.729299 | ||||||||
\(919\) | −2.72785e32 | −0.0227873 | −0.0113936 | − | 0.999935i | \(-0.503627\pi\) | ||||
−0.0113936 | + | 0.999935i | \(0.503627\pi\) | |||||||
\(920\) | 3.30919e31 | 0.00272999 | ||||||||
\(921\) | 2.45315e33 | 0.199866 | ||||||||
\(922\) | −9.62547e32 | −0.0774491 | ||||||||
\(923\) | 1.10161e33 | 0.0875402 | ||||||||
\(924\) | −1.02824e33 | −0.0806984 | ||||||||
\(925\) | −8.92133e32 | −0.0691512 | ||||||||
\(926\) | 6.95668e32 | 0.0532569 | ||||||||
\(927\) | −8.33233e33 | −0.630013 | ||||||||
\(928\) | 1.15983e33 | 0.0866147 | ||||||||
\(929\) | 1.45553e34 | 1.07360 | 0.536798 | − | 0.843711i | \(-0.319634\pi\) | ||||
0.536798 | + | 0.843711i | \(0.319634\pi\) | |||||||
\(930\) | 4.26231e33 | 0.310521 | ||||||||
\(931\) | −2.16278e34 | −1.55629 | ||||||||
\(932\) | 1.16775e34 | 0.829981 | ||||||||
\(933\) | −1.89083e34 | −1.32743 | ||||||||
\(934\) | −2.20409e33 | −0.152841 | ||||||||
\(935\) | 6.30079e33 | 0.431580 | ||||||||
\(936\) | −8.62236e32 | −0.0583383 | ||||||||
\(937\) | 1.67847e34 | 1.12178 | 0.560889 | − | 0.827891i | \(-0.310459\pi\) | ||||
0.560889 | + | 0.827891i | \(0.310459\pi\) | |||||||
\(938\) | 1.74065e32 | 0.0114915 | ||||||||
\(939\) | −1.65654e34 | −1.08031 | ||||||||
\(940\) | 1.07575e32 | 0.00693016 | ||||||||
\(941\) | −1.26349e34 | −0.804064 | −0.402032 | − | 0.915626i | \(-0.631696\pi\) | ||||
−0.402032 | + | 0.915626i | \(0.631696\pi\) | |||||||
\(942\) | −6.84330e32 | −0.0430210 | ||||||||
\(943\) | 2.54585e32 | 0.0158106 | ||||||||
\(944\) | 2.74640e33 | 0.168495 | ||||||||
\(945\) | −1.70132e33 | −0.103114 | ||||||||
\(946\) | −5.36038e33 | −0.320957 | ||||||||
\(947\) | −1.44322e34 | −0.853703 | −0.426851 | − | 0.904322i | \(-0.640377\pi\) | ||||
−0.426851 | + | 0.904322i | \(0.640377\pi\) | |||||||
\(948\) | −9.96971e33 | −0.582622 | ||||||||
\(949\) | 1.08993e34 | 0.629268 | ||||||||
\(950\) | −4.04373e33 | −0.230654 | ||||||||
\(951\) | −2.00518e34 | −1.13000 | ||||||||
\(952\) | 1.30062e33 | 0.0724143 | ||||||||
\(953\) | 1.65674e34 | 0.911350 | 0.455675 | − | 0.890146i | \(-0.349398\pi\) | ||||
0.455675 | + | 0.890146i | \(0.349398\pi\) | |||||||
\(954\) | −3.74128e33 | −0.203336 | ||||||||
\(955\) | 1.20821e34 | 0.648790 | ||||||||
\(956\) | −6.62409e33 | −0.351448 | ||||||||
\(957\) | 7.04973e33 | 0.369560 | ||||||||
\(958\) | −2.60678e34 | −1.35021 | ||||||||
\(959\) | 3.69411e33 | 0.189058 | ||||||||
\(960\) | 8.27006e32 | 0.0418205 | ||||||||
\(961\) | 1.44671e34 | 0.722873 | ||||||||
\(962\) | −1.85560e33 | −0.0916159 | ||||||||
\(963\) | −4.68386e33 | −0.228508 | ||||||||
\(964\) | 8.33909e33 | 0.402006 | ||||||||
\(965\) | 1.36970e34 | 0.652472 | ||||||||
\(966\) | 4.15197e31 | 0.00195442 | ||||||||
\(967\) | 1.67020e33 | 0.0776896 | 0.0388448 | − | 0.999245i | \(-0.487632\pi\) | ||||
0.0388448 | + | 0.999245i | \(0.487632\pi\) | |||||||
\(968\) | −1.26917e32 | −0.00583384 | ||||||||
\(969\) | −2.57115e34 | −1.16789 | ||||||||
\(970\) | −1.24537e34 | −0.559014 | ||||||||
\(971\) | −1.89959e34 | −0.842633 | −0.421317 | − | 0.906914i | \(-0.638432\pi\) | ||||
−0.421317 | + | 0.906914i | \(0.638432\pi\) | |||||||
\(972\) | 9.16913e33 | 0.401945 | ||||||||
\(973\) | 6.91137e33 | 0.299410 | ||||||||
\(974\) | −8.35865e33 | −0.357856 | ||||||||
\(975\) | −1.32515e33 | −0.0560674 | ||||||||
\(976\) | 9.03450e33 | 0.377773 | ||||||||
\(977\) | 1.78605e34 | 0.738086 | 0.369043 | − | 0.929412i | \(-0.379686\pi\) | ||||
0.369043 | + | 0.929412i | \(0.379686\pi\) | |||||||
\(978\) | −1.79331e34 | −0.732418 | ||||||||
\(979\) | 2.28701e34 | 0.923140 | ||||||||
\(980\) | −5.34847e33 | −0.213368 | ||||||||
\(981\) | 1.15081e34 | 0.453741 | ||||||||
\(982\) | −1.27483e34 | −0.496786 | ||||||||
\(983\) | 9.74109e33 | 0.375182 | 0.187591 | − | 0.982247i | \(-0.439932\pi\) | ||||
0.187591 | + | 0.982247i | \(0.439932\pi\) | |||||||
\(984\) | 6.36238e33 | 0.242201 | ||||||||
\(985\) | 1.11781e34 | 0.420583 | ||||||||
\(986\) | −8.91722e33 | −0.331623 | ||||||||
\(987\) | 1.34973e32 | 0.00496134 | ||||||||
\(988\) | −8.41080e33 | −0.305585 | ||||||||
\(989\) | 2.16450e32 | 0.00777321 | ||||||||
\(990\) | −3.95495e33 | −0.140390 | ||||||||
\(991\) | 1.52559e34 | 0.535292 | 0.267646 | − | 0.963517i | \(-0.413754\pi\) | ||||
0.267646 | + | 0.963517i | \(0.413754\pi\) | |||||||
\(992\) | 6.69015e33 | 0.232034 | ||||||||
\(993\) | −1.12859e34 | −0.386918 | ||||||||
\(994\) | 1.04303e33 | 0.0353471 | ||||||||
\(995\) | −1.87538e34 | −0.628237 | ||||||||
\(996\) | −5.69190e33 | −0.188484 | ||||||||
\(997\) | −9.21743e33 | −0.301728 | −0.150864 | − | 0.988555i | \(-0.548206\pi\) | ||||
−0.150864 | + | 0.988555i | \(0.548206\pi\) | |||||||
\(998\) | −1.37477e34 | −0.444867 | ||||||||
\(999\) | 1.16466e34 | 0.372561 |
(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 | 10.24.a.a.1.2 | ✓ | 2 | |
5.2 | odd | 4 | 50.24.b.d.49.1 | 4 | |||
5.3 | odd | 4 | 50.24.b.d.49.4 | 4 | |||
5.4 | even | 2 | 50.24.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.24.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.24.a.d.1.1 | 2 | 5.4 | even | 2 | |||
50.24.b.d.49.1 | 4 | 5.2 | odd | 4 | |||
50.24.b.d.49.4 | 4 | 5.3 | odd | 4 |