Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,8,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(28.4270373191\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3 x^{9} - 816 x^{8} + 2298 x^{7} + 213848 x^{6} - 507132 x^{5} - 19919976 x^{4} + \cdots - 7335224320 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(17.3557\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −17.3557 | −1.53404 | −0.767022 | − | 0.641621i | \(-0.778262\pi\) | ||||
−0.767022 | + | 0.641621i | \(0.778262\pi\) | |||||||
\(3\) | −89.1399 | −1.90611 | −0.953055 | − | 0.302797i | \(-0.902079\pi\) | ||||
−0.953055 | + | 0.302797i | \(0.902079\pi\) | |||||||
\(4\) | 173.221 | 1.35329 | ||||||||
\(5\) | −9.67118 | −0.0346007 | −0.0173003 | − | 0.999850i | \(-0.505507\pi\) | ||||
−0.0173003 | + | 0.999850i | \(0.505507\pi\) | |||||||
\(6\) | 1547.09 | 2.92406 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | −784.843 | −0.541961 | ||||||||
\(9\) | 5758.93 | 2.63326 | ||||||||
\(10\) | 167.850 | 0.0530789 | ||||||||
\(11\) | −4810.17 | −1.08965 | −0.544824 | − | 0.838551i | \(-0.683403\pi\) | ||||
−0.544824 | + | 0.838551i | \(0.683403\pi\) | |||||||
\(12\) | −15440.9 | −2.57952 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | 5953.01 | 0.579814 | ||||||||
\(15\) | 862.088 | 0.0659527 | ||||||||
\(16\) | −8550.77 | −0.521898 | ||||||||
\(17\) | −13227.6 | −0.652995 | −0.326497 | − | 0.945198i | \(-0.605868\pi\) | ||||
−0.326497 | + | 0.945198i | \(0.605868\pi\) | |||||||
\(18\) | −99950.4 | −4.03953 | ||||||||
\(19\) | −21690.7 | −0.725499 | −0.362749 | − | 0.931887i | \(-0.618162\pi\) | ||||
−0.362749 | + | 0.931887i | \(0.618162\pi\) | |||||||
\(20\) | −1675.25 | −0.0468247 | ||||||||
\(21\) | 30575.0 | 0.720442 | ||||||||
\(22\) | 83484.0 | 1.67157 | ||||||||
\(23\) | −87446.5 | −1.49863 | −0.749316 | − | 0.662212i | \(-0.769618\pi\) | ||||
−0.749316 | + | 0.662212i | \(0.769618\pi\) | |||||||
\(24\) | 69960.9 | 1.03304 | ||||||||
\(25\) | −78031.5 | −0.998803 | ||||||||
\(26\) | 38130.5 | 0.425467 | ||||||||
\(27\) | −318402. | −3.11316 | ||||||||
\(28\) | −59414.8 | −0.511495 | ||||||||
\(29\) | 195594. | 1.48923 | 0.744615 | − | 0.667495i | \(-0.232633\pi\) | ||||
0.744615 | + | 0.667495i | \(0.232633\pi\) | |||||||
\(30\) | −14962.2 | −0.101174 | ||||||||
\(31\) | −166788. | −1.00554 | −0.502768 | − | 0.864421i | \(-0.667685\pi\) | ||||
−0.502768 | + | 0.864421i | \(0.667685\pi\) | |||||||
\(32\) | 248865. | 1.34257 | ||||||||
\(33\) | 428778. | 2.07699 | ||||||||
\(34\) | 229574. | 1.00172 | ||||||||
\(35\) | 3317.21 | 0.0130778 | ||||||||
\(36\) | 997567. | 3.56356 | ||||||||
\(37\) | 52502.8 | 0.170403 | 0.0852013 | − | 0.996364i | \(-0.472847\pi\) | ||||
0.0852013 | + | 0.996364i | \(0.472847\pi\) | |||||||
\(38\) | 376458. | 1.11295 | ||||||||
\(39\) | 195840. | 0.528660 | ||||||||
\(40\) | 7590.36 | 0.0187522 | ||||||||
\(41\) | −440897. | −0.999065 | −0.499532 | − | 0.866295i | \(-0.666495\pi\) | ||||
−0.499532 | + | 0.866295i | \(0.666495\pi\) | |||||||
\(42\) | −530651. | −1.10519 | ||||||||
\(43\) | −697845. | −1.33850 | −0.669252 | − | 0.743036i | \(-0.733385\pi\) | ||||
−0.669252 | + | 0.743036i | \(0.733385\pi\) | |||||||
\(44\) | −833223. | −1.47461 | ||||||||
\(45\) | −55695.6 | −0.0911124 | ||||||||
\(46\) | 1.51770e6 | 2.29897 | ||||||||
\(47\) | −41717.8 | −0.0586109 | −0.0293055 | − | 0.999571i | \(-0.509330\pi\) | ||||
−0.0293055 | + | 0.999571i | \(0.509330\pi\) | |||||||
\(48\) | 762215. | 0.994794 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 1.35429e6 | 1.53221 | ||||||||
\(51\) | 1.17911e6 | 1.24468 | ||||||||
\(52\) | −380567. | −0.375335 | ||||||||
\(53\) | −1.88875e6 | −1.74265 | −0.871324 | − | 0.490709i | \(-0.836738\pi\) | ||||
−0.871324 | + | 0.490709i | \(0.836738\pi\) | |||||||
\(54\) | 5.52609e6 | 4.77573 | ||||||||
\(55\) | 46520.0 | 0.0377025 | ||||||||
\(56\) | 269201. | 0.204842 | ||||||||
\(57\) | 1.93351e6 | 1.38288 | ||||||||
\(58\) | −3.39467e6 | −2.28454 | ||||||||
\(59\) | −3452.66 | −0.00218863 | −0.00109431 | − | 0.999999i | \(-0.500348\pi\) | ||||
−0.00109431 | + | 0.999999i | \(0.500348\pi\) | |||||||
\(60\) | 149332. | 0.0892530 | ||||||||
\(61\) | −164870. | −0.0930011 | −0.0465005 | − | 0.998918i | \(-0.514807\pi\) | ||||
−0.0465005 | + | 0.998918i | \(0.514807\pi\) | |||||||
\(62\) | 2.89472e6 | 1.54254 | ||||||||
\(63\) | −1.97531e6 | −0.995277 | ||||||||
\(64\) | −3.22473e6 | −1.53767 | ||||||||
\(65\) | 21247.6 | 0.00959650 | ||||||||
\(66\) | −7.44176e6 | −3.18619 | ||||||||
\(67\) | −98035.1 | −0.0398217 | −0.0199109 | − | 0.999802i | \(-0.506338\pi\) | ||||
−0.0199109 | + | 0.999802i | \(0.506338\pi\) | |||||||
\(68\) | −2.29130e6 | −0.883691 | ||||||||
\(69\) | 7.79498e6 | 2.85656 | ||||||||
\(70\) | −57572.6 | −0.0200619 | ||||||||
\(71\) | 1.68643e6 | 0.559196 | 0.279598 | − | 0.960117i | \(-0.409799\pi\) | ||||
0.279598 | + | 0.960117i | \(0.409799\pi\) | |||||||
\(72\) | −4.51986e6 | −1.42712 | ||||||||
\(73\) | −6.15276e6 | −1.85114 | −0.925572 | − | 0.378573i | \(-0.876415\pi\) | ||||
−0.925572 | + | 0.378573i | \(0.876415\pi\) | |||||||
\(74\) | −911224. | −0.261405 | ||||||||
\(75\) | 6.95572e6 | 1.90383 | ||||||||
\(76\) | −3.75729e6 | −0.981809 | ||||||||
\(77\) | 1.64989e6 | 0.411848 | ||||||||
\(78\) | −3.39895e6 | −0.810987 | ||||||||
\(79\) | −171958. | −0.0392399 | −0.0196200 | − | 0.999808i | \(-0.506246\pi\) | ||||
−0.0196200 | + | 0.999808i | \(0.506246\pi\) | |||||||
\(80\) | 82696.0 | 0.0180580 | ||||||||
\(81\) | 1.57875e7 | 3.30078 | ||||||||
\(82\) | 7.65209e6 | 1.53261 | ||||||||
\(83\) | −7.99418e6 | −1.53462 | −0.767309 | − | 0.641277i | \(-0.778405\pi\) | ||||
−0.767309 | + | 0.641277i | \(0.778405\pi\) | |||||||
\(84\) | 5.29623e6 | 0.974966 | ||||||||
\(85\) | 127926. | 0.0225940 | ||||||||
\(86\) | 1.21116e7 | 2.05332 | ||||||||
\(87\) | −1.74352e7 | −2.83863 | ||||||||
\(88\) | 3.77523e6 | 0.590546 | ||||||||
\(89\) | 5.25354e6 | 0.789928 | 0.394964 | − | 0.918697i | \(-0.370757\pi\) | ||||
0.394964 | + | 0.918697i | \(0.370757\pi\) | |||||||
\(90\) | 966638. | 0.139770 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | −1.51476e7 | −2.02808 | ||||||||
\(93\) | 1.48674e7 | 1.91666 | ||||||||
\(94\) | 724042. | 0.0899117 | ||||||||
\(95\) | 209775. | 0.0251027 | ||||||||
\(96\) | −2.21838e7 | −2.55909 | ||||||||
\(97\) | −5.31437e6 | −0.591223 | −0.295611 | − | 0.955308i | \(-0.595523\pi\) | ||||
−0.295611 | + | 0.955308i | \(0.595523\pi\) | |||||||
\(98\) | −2.04188e6 | −0.219149 | ||||||||
\(99\) | −2.77014e7 | −2.86932 | ||||||||
\(100\) | −1.35167e7 | −1.35167 | ||||||||
\(101\) | −7.20787e6 | −0.696117 | −0.348058 | − | 0.937473i | \(-0.613159\pi\) | ||||
−0.348058 | + | 0.937473i | \(0.613159\pi\) | |||||||
\(102\) | −2.04642e7 | −1.90939 | ||||||||
\(103\) | −8.59221e6 | −0.774774 | −0.387387 | − | 0.921917i | \(-0.626622\pi\) | ||||
−0.387387 | + | 0.921917i | \(0.626622\pi\) | |||||||
\(104\) | 1.72430e6 | 0.150313 | ||||||||
\(105\) | −295696. | −0.0249278 | ||||||||
\(106\) | 3.27807e7 | 2.67330 | ||||||||
\(107\) | 1.72130e7 | 1.35835 | 0.679176 | − | 0.733975i | \(-0.262337\pi\) | ||||
0.679176 | + | 0.733975i | \(0.262337\pi\) | |||||||
\(108\) | −5.51538e7 | −4.21301 | ||||||||
\(109\) | 925472. | 0.0684496 | 0.0342248 | − | 0.999414i | \(-0.489104\pi\) | ||||
0.0342248 | + | 0.999414i | \(0.489104\pi\) | |||||||
\(110\) | −807388. | −0.0578373 | ||||||||
\(111\) | −4.68010e6 | −0.324806 | ||||||||
\(112\) | 2.93291e6 | 0.197259 | ||||||||
\(113\) | 1.85205e7 | 1.20748 | 0.603738 | − | 0.797183i | \(-0.293677\pi\) | ||||
0.603738 | + | 0.797183i | \(0.293677\pi\) | |||||||
\(114\) | −3.35575e7 | −2.12140 | ||||||||
\(115\) | 845711. | 0.0518537 | ||||||||
\(116\) | 3.38809e7 | 2.01536 | ||||||||
\(117\) | −1.26524e7 | −0.730334 | ||||||||
\(118\) | 59923.5 | 0.00335745 | ||||||||
\(119\) | 4.53706e6 | 0.246809 | ||||||||
\(120\) | −676604. | −0.0357438 | ||||||||
\(121\) | 3.65057e6 | 0.187332 | ||||||||
\(122\) | 2.86144e6 | 0.142668 | ||||||||
\(123\) | 3.93015e7 | 1.90433 | ||||||||
\(124\) | −2.88911e7 | −1.36078 | ||||||||
\(125\) | 1.51022e6 | 0.0691599 | ||||||||
\(126\) | 3.42830e7 | 1.52680 | ||||||||
\(127\) | −1.44961e7 | −0.627970 | −0.313985 | − | 0.949428i | \(-0.601664\pi\) | ||||
−0.313985 | + | 0.949428i | \(0.601664\pi\) | |||||||
\(128\) | 2.41128e7 | 1.01628 | ||||||||
\(129\) | 6.22059e7 | 2.55134 | ||||||||
\(130\) | −368767. | −0.0147214 | ||||||||
\(131\) | 4.29766e7 | 1.67025 | 0.835127 | − | 0.550057i | \(-0.185394\pi\) | ||||
0.835127 | + | 0.550057i | \(0.185394\pi\) | |||||||
\(132\) | 7.42734e7 | 2.81077 | ||||||||
\(133\) | 7.43992e6 | 0.274213 | ||||||||
\(134\) | 1.70147e6 | 0.0610882 | ||||||||
\(135\) | 3.07932e6 | 0.107718 | ||||||||
\(136\) | 1.03816e7 | 0.353898 | ||||||||
\(137\) | 5.36809e7 | 1.78360 | 0.891801 | − | 0.452428i | \(-0.149442\pi\) | ||||
0.891801 | + | 0.452428i | \(0.149442\pi\) | |||||||
\(138\) | −1.35287e8 | −4.38208 | ||||||||
\(139\) | 6.63333e6 | 0.209498 | 0.104749 | − | 0.994499i | \(-0.466596\pi\) | ||||
0.104749 | + | 0.994499i | \(0.466596\pi\) | |||||||
\(140\) | 574611. | 0.0176981 | ||||||||
\(141\) | 3.71872e6 | 0.111719 | ||||||||
\(142\) | −2.92692e7 | −0.857830 | ||||||||
\(143\) | 1.05679e7 | 0.302214 | ||||||||
\(144\) | −4.92433e7 | −1.37429 | ||||||||
\(145\) | −1.89162e6 | −0.0515283 | ||||||||
\(146\) | 1.06786e8 | 2.83973 | ||||||||
\(147\) | −1.04872e7 | −0.272301 | ||||||||
\(148\) | 9.09459e6 | 0.230604 | ||||||||
\(149\) | 4.29602e6 | 0.106393 | 0.0531967 | − | 0.998584i | \(-0.483059\pi\) | ||||
0.0531967 | + | 0.998584i | \(0.483059\pi\) | |||||||
\(150\) | −1.20722e8 | −2.92055 | ||||||||
\(151\) | 3.44589e6 | 0.0814483 | 0.0407242 | − | 0.999170i | \(-0.487034\pi\) | ||||
0.0407242 | + | 0.999170i | \(0.487034\pi\) | |||||||
\(152\) | 1.70238e7 | 0.393192 | ||||||||
\(153\) | −7.61768e7 | −1.71950 | ||||||||
\(154\) | −2.86350e7 | −0.631793 | ||||||||
\(155\) | 1.61303e6 | 0.0347922 | ||||||||
\(156\) | 3.39237e7 | 0.715430 | ||||||||
\(157\) | −996112. | −0.0205428 | −0.0102714 | − | 0.999947i | \(-0.503270\pi\) | ||||
−0.0102714 | + | 0.999947i | \(0.503270\pi\) | |||||||
\(158\) | 2.98446e6 | 0.0601957 | ||||||||
\(159\) | 1.68363e8 | 3.32168 | ||||||||
\(160\) | −2.40681e6 | −0.0464540 | ||||||||
\(161\) | 2.99942e7 | 0.566430 | ||||||||
\(162\) | −2.74004e8 | −5.06354 | ||||||||
\(163\) | 2.16231e7 | 0.391076 | 0.195538 | − | 0.980696i | \(-0.437355\pi\) | ||||
0.195538 | + | 0.980696i | \(0.437355\pi\) | |||||||
\(164\) | −7.63726e7 | −1.35202 | ||||||||
\(165\) | −4.14679e6 | −0.0718652 | ||||||||
\(166\) | 1.38745e8 | 2.35417 | ||||||||
\(167\) | −5.31098e7 | −0.882403 | −0.441201 | − | 0.897408i | \(-0.645448\pi\) | ||||
−0.441201 | + | 0.897408i | \(0.645448\pi\) | |||||||
\(168\) | −2.39966e7 | −0.390451 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | −2.22025e6 | −0.0346602 | ||||||||
\(171\) | −1.24915e8 | −1.91042 | ||||||||
\(172\) | −1.20881e8 | −1.81138 | ||||||||
\(173\) | 2.03323e7 | 0.298556 | 0.149278 | − | 0.988795i | \(-0.452305\pi\) | ||||
0.149278 | + | 0.988795i | \(0.452305\pi\) | |||||||
\(174\) | 3.02600e8 | 4.35459 | ||||||||
\(175\) | 2.67648e7 | 0.377512 | ||||||||
\(176\) | 4.11307e7 | 0.568684 | ||||||||
\(177\) | 307770. | 0.00417177 | ||||||||
\(178\) | −9.11790e7 | −1.21178 | ||||||||
\(179\) | 2.10751e7 | 0.274653 | 0.137326 | − | 0.990526i | \(-0.456149\pi\) | ||||
0.137326 | + | 0.990526i | \(0.456149\pi\) | |||||||
\(180\) | −9.64765e6 | −0.123301 | ||||||||
\(181\) | −7.51426e7 | −0.941914 | −0.470957 | − | 0.882156i | \(-0.656091\pi\) | ||||
−0.470957 | + | 0.882156i | \(0.656091\pi\) | |||||||
\(182\) | −1.30788e7 | −0.160811 | ||||||||
\(183\) | 1.46965e7 | 0.177270 | ||||||||
\(184\) | 6.86318e7 | 0.812200 | ||||||||
\(185\) | −507764. | −0.00589604 | ||||||||
\(186\) | −2.58035e8 | −2.94024 | ||||||||
\(187\) | 6.36270e7 | 0.711534 | ||||||||
\(188\) | −7.22640e6 | −0.0793176 | ||||||||
\(189\) | 1.09212e8 | 1.17667 | ||||||||
\(190\) | −3.64079e6 | −0.0385087 | ||||||||
\(191\) | −5.82631e7 | −0.605030 | −0.302515 | − | 0.953145i | \(-0.597826\pi\) | ||||
−0.302515 | + | 0.953145i | \(0.597826\pi\) | |||||||
\(192\) | 2.87452e8 | 2.93097 | ||||||||
\(193\) | −1.77411e8 | −1.77636 | −0.888179 | − | 0.459498i | \(-0.848029\pi\) | ||||
−0.888179 | + | 0.459498i | \(0.848029\pi\) | |||||||
\(194\) | 9.22348e7 | 0.906961 | ||||||||
\(195\) | −1.89401e6 | −0.0182920 | ||||||||
\(196\) | 2.03793e7 | 0.193327 | ||||||||
\(197\) | 1.07532e8 | 1.00209 | 0.501046 | − | 0.865421i | \(-0.332949\pi\) | ||||
0.501046 | + | 0.865421i | \(0.332949\pi\) | |||||||
\(198\) | 4.80778e8 | 4.40166 | ||||||||
\(199\) | −5.06953e7 | −0.456018 | −0.228009 | − | 0.973659i | \(-0.573222\pi\) | ||||
−0.228009 | + | 0.973659i | \(0.573222\pi\) | |||||||
\(200\) | 6.12425e7 | 0.541312 | ||||||||
\(201\) | 8.73884e6 | 0.0759045 | ||||||||
\(202\) | 1.25098e8 | 1.06787 | ||||||||
\(203\) | −6.70886e7 | −0.562876 | ||||||||
\(204\) | 2.04246e8 | 1.68441 | ||||||||
\(205\) | 4.26399e6 | 0.0345683 | ||||||||
\(206\) | 1.49124e8 | 1.18854 | ||||||||
\(207\) | −5.03598e8 | −3.94628 | ||||||||
\(208\) | 1.87860e7 | 0.144748 | ||||||||
\(209\) | 1.04336e8 | 0.790538 | ||||||||
\(210\) | 5.13202e6 | 0.0382403 | ||||||||
\(211\) | −2.12543e8 | −1.55761 | −0.778804 | − | 0.627267i | \(-0.784173\pi\) | ||||
−0.778804 | + | 0.627267i | \(0.784173\pi\) | |||||||
\(212\) | −3.27172e8 | −2.35831 | ||||||||
\(213\) | −1.50328e8 | −1.06589 | ||||||||
\(214\) | −2.98743e8 | −2.08377 | ||||||||
\(215\) | 6.74899e6 | 0.0463131 | ||||||||
\(216\) | 2.49895e8 | 1.68721 | ||||||||
\(217\) | 5.72082e7 | 0.380057 | ||||||||
\(218\) | −1.60622e7 | −0.105005 | ||||||||
\(219\) | 5.48457e8 | 3.52848 | ||||||||
\(220\) | 8.05824e6 | 0.0510224 | ||||||||
\(221\) | 2.90610e7 | 0.181108 | ||||||||
\(222\) | 8.12264e7 | 0.498267 | ||||||||
\(223\) | 1.28517e8 | 0.776055 | 0.388028 | − | 0.921648i | \(-0.373157\pi\) | ||||
0.388028 | + | 0.921648i | \(0.373157\pi\) | |||||||
\(224\) | −8.53606e7 | −0.507445 | ||||||||
\(225\) | −4.49378e8 | −2.63010 | ||||||||
\(226\) | −3.21437e8 | −1.85232 | ||||||||
\(227\) | 6.92336e7 | 0.392849 | 0.196425 | − | 0.980519i | \(-0.437067\pi\) | ||||
0.196425 | + | 0.980519i | \(0.437067\pi\) | |||||||
\(228\) | 3.34925e8 | 1.87144 | ||||||||
\(229\) | 3.14258e8 | 1.72927 | 0.864634 | − | 0.502402i | \(-0.167550\pi\) | ||||
0.864634 | + | 0.502402i | \(0.167550\pi\) | |||||||
\(230\) | −1.46779e7 | −0.0795458 | ||||||||
\(231\) | −1.47071e8 | −0.785028 | ||||||||
\(232\) | −1.53510e8 | −0.807104 | ||||||||
\(233\) | −1.91790e8 | −0.993302 | −0.496651 | − | 0.867950i | \(-0.665437\pi\) | ||||
−0.496651 | + | 0.867950i | \(0.665437\pi\) | |||||||
\(234\) | 2.19591e8 | 1.12036 | ||||||||
\(235\) | 403460. | 0.00202798 | ||||||||
\(236\) | −598074. | −0.00296185 | ||||||||
\(237\) | 1.53283e7 | 0.0747956 | ||||||||
\(238\) | −7.87440e7 | −0.378615 | ||||||||
\(239\) | 3.66028e8 | 1.73429 | 0.867145 | − | 0.498055i | \(-0.165952\pi\) | ||||
0.867145 | + | 0.498055i | \(0.165952\pi\) | |||||||
\(240\) | −7.37152e6 | −0.0344205 | ||||||||
\(241\) | −9.86705e7 | −0.454075 | −0.227038 | − | 0.973886i | \(-0.572904\pi\) | ||||
−0.227038 | + | 0.973886i | \(0.572904\pi\) | |||||||
\(242\) | −6.33582e7 | −0.287375 | ||||||||
\(243\) | −7.10954e8 | −3.17848 | ||||||||
\(244\) | −2.85590e7 | −0.125857 | ||||||||
\(245\) | −1.13780e6 | −0.00494295 | ||||||||
\(246\) | −6.82107e8 | −2.92132 | ||||||||
\(247\) | 4.76545e7 | 0.201217 | ||||||||
\(248\) | 1.30902e8 | 0.544962 | ||||||||
\(249\) | 7.12600e8 | 2.92515 | ||||||||
\(250\) | −2.62109e7 | −0.106094 | ||||||||
\(251\) | −3.40854e8 | −1.36054 | −0.680268 | − | 0.732963i | \(-0.738137\pi\) | ||||
−0.680268 | + | 0.732963i | \(0.738137\pi\) | |||||||
\(252\) | −3.42166e8 | −1.34690 | ||||||||
\(253\) | 4.20633e8 | 1.63298 | ||||||||
\(254\) | 2.51591e8 | 0.963333 | ||||||||
\(255\) | −1.14034e7 | −0.0430667 | ||||||||
\(256\) | −5.72962e6 | −0.0213445 | ||||||||
\(257\) | −2.76765e8 | −1.01706 | −0.508528 | − | 0.861045i | \(-0.669810\pi\) | ||||
−0.508528 | + | 0.861045i | \(0.669810\pi\) | |||||||
\(258\) | −1.07963e9 | −3.91386 | ||||||||
\(259\) | −1.80085e7 | −0.0644062 | ||||||||
\(260\) | 3.68053e6 | 0.0129868 | ||||||||
\(261\) | 1.12641e9 | 3.92152 | ||||||||
\(262\) | −7.45890e8 | −2.56224 | ||||||||
\(263\) | −4.06428e8 | −1.37765 | −0.688824 | − | 0.724928i | \(-0.741873\pi\) | ||||
−0.688824 | + | 0.724928i | \(0.741873\pi\) | |||||||
\(264\) | −3.36524e8 | −1.12565 | ||||||||
\(265\) | 1.82665e7 | 0.0602967 | ||||||||
\(266\) | −1.29125e8 | −0.420654 | ||||||||
\(267\) | −4.68301e8 | −1.50569 | ||||||||
\(268\) | −1.69817e7 | −0.0538903 | ||||||||
\(269\) | −5.54000e8 | −1.73531 | −0.867654 | − | 0.497168i | \(-0.834373\pi\) | ||||
−0.867654 | + | 0.497168i | \(0.834373\pi\) | |||||||
\(270\) | −5.34438e7 | −0.165243 | ||||||||
\(271\) | −6.27567e8 | −1.91544 | −0.957718 | − | 0.287708i | \(-0.907107\pi\) | ||||
−0.957718 | + | 0.287708i | \(0.907107\pi\) | |||||||
\(272\) | 1.13106e8 | 0.340796 | ||||||||
\(273\) | −6.71733e7 | −0.199815 | ||||||||
\(274\) | −9.31671e8 | −2.73612 | ||||||||
\(275\) | 3.75345e8 | 1.08834 | ||||||||
\(276\) | 1.35025e9 | 3.86575 | ||||||||
\(277\) | 5.81261e8 | 1.64321 | 0.821604 | − | 0.570059i | \(-0.193080\pi\) | ||||
0.821604 | + | 0.570059i | \(0.193080\pi\) | |||||||
\(278\) | −1.15126e8 | −0.321379 | ||||||||
\(279\) | −9.60518e8 | −2.64783 | ||||||||
\(280\) | −2.60349e6 | −0.00708767 | ||||||||
\(281\) | 1.90995e8 | 0.513512 | 0.256756 | − | 0.966476i | \(-0.417346\pi\) | ||||
0.256756 | + | 0.966476i | \(0.417346\pi\) | |||||||
\(282\) | −6.45411e7 | −0.171382 | ||||||||
\(283\) | −1.94383e8 | −0.509808 | −0.254904 | − | 0.966966i | \(-0.582044\pi\) | ||||
−0.254904 | + | 0.966966i | \(0.582044\pi\) | |||||||
\(284\) | 2.92125e8 | 0.756753 | ||||||||
\(285\) | −1.86993e7 | −0.0478486 | ||||||||
\(286\) | −1.83414e8 | −0.463609 | ||||||||
\(287\) | 1.51228e8 | 0.377611 | ||||||||
\(288\) | 1.43319e9 | 3.53534 | ||||||||
\(289\) | −2.35369e8 | −0.573598 | ||||||||
\(290\) | 3.28304e7 | 0.0790467 | ||||||||
\(291\) | 4.73723e8 | 1.12694 | ||||||||
\(292\) | −1.06579e9 | −2.50513 | ||||||||
\(293\) | 6.41323e8 | 1.48950 | 0.744750 | − | 0.667344i | \(-0.232569\pi\) | ||||
0.744750 | + | 0.667344i | \(0.232569\pi\) | |||||||
\(294\) | 1.82013e8 | 0.417722 | ||||||||
\(295\) | 33391.3 | 7.57280e−5 0 | ||||||||
\(296\) | −4.12065e7 | −0.0923516 | ||||||||
\(297\) | 1.53157e9 | 3.39225 | ||||||||
\(298\) | −7.45605e7 | −0.163212 | ||||||||
\(299\) | 1.92120e8 | 0.415646 | ||||||||
\(300\) | 1.20488e9 | 2.57643 | ||||||||
\(301\) | 2.39361e8 | 0.505907 | ||||||||
\(302\) | −5.98059e7 | −0.124945 | ||||||||
\(303\) | 6.42509e8 | 1.32687 | ||||||||
\(304\) | 1.85472e8 | 0.378636 | ||||||||
\(305\) | 1.59449e6 | 0.00321790 | ||||||||
\(306\) | 1.32210e9 | 2.63779 | ||||||||
\(307\) | 6.02627e7 | 0.118868 | 0.0594339 | − | 0.998232i | \(-0.481070\pi\) | ||||
0.0594339 | + | 0.998232i | \(0.481070\pi\) | |||||||
\(308\) | 2.85795e8 | 0.557350 | ||||||||
\(309\) | 7.65909e8 | 1.47680 | ||||||||
\(310\) | −2.79953e7 | −0.0533728 | ||||||||
\(311\) | 8.95977e8 | 1.68902 | 0.844511 | − | 0.535538i | \(-0.179891\pi\) | ||||
0.844511 | + | 0.535538i | \(0.179891\pi\) | |||||||
\(312\) | −1.53704e8 | −0.286513 | ||||||||
\(313\) | 3.18196e7 | 0.0586530 | 0.0293265 | − | 0.999570i | \(-0.490664\pi\) | ||||
0.0293265 | + | 0.999570i | \(0.490664\pi\) | |||||||
\(314\) | 1.72882e7 | 0.0315135 | ||||||||
\(315\) | 1.91036e7 | 0.0344372 | ||||||||
\(316\) | −2.97868e7 | −0.0531029 | ||||||||
\(317\) | −5.00344e8 | −0.882187 | −0.441094 | − | 0.897461i | \(-0.645409\pi\) | ||||
−0.441094 | + | 0.897461i | \(0.645409\pi\) | |||||||
\(318\) | −2.92207e9 | −5.09560 | ||||||||
\(319\) | −9.40838e8 | −1.62273 | ||||||||
\(320\) | 3.11869e7 | 0.0532044 | ||||||||
\(321\) | −1.53436e9 | −2.58917 | ||||||||
\(322\) | −5.20570e8 | −0.868928 | ||||||||
\(323\) | 2.86916e8 | 0.473747 | ||||||||
\(324\) | 2.73473e9 | 4.46691 | ||||||||
\(325\) | 1.71435e8 | 0.277018 | ||||||||
\(326\) | −3.75285e8 | −0.599928 | ||||||||
\(327\) | −8.24966e7 | −0.130472 | ||||||||
\(328\) | 3.46035e8 | 0.541454 | ||||||||
\(329\) | 1.43092e7 | 0.0221529 | ||||||||
\(330\) | 7.19705e7 | 0.110244 | ||||||||
\(331\) | 7.43225e8 | 1.12648 | 0.563238 | − | 0.826294i | \(-0.309555\pi\) | ||||
0.563238 | + | 0.826294i | \(0.309555\pi\) | |||||||
\(332\) | −1.38476e9 | −2.07678 | ||||||||
\(333\) | 3.02360e8 | 0.448714 | ||||||||
\(334\) | 9.21759e8 | 1.35364 | ||||||||
\(335\) | 948115. | 0.00137786 | ||||||||
\(336\) | −2.61440e8 | −0.375997 | ||||||||
\(337\) | 3.82555e8 | 0.544488 | 0.272244 | − | 0.962228i | \(-0.412234\pi\) | ||||
0.272244 | + | 0.962228i | \(0.412234\pi\) | |||||||
\(338\) | −8.37727e7 | −0.118003 | ||||||||
\(339\) | −1.65092e9 | −2.30158 | ||||||||
\(340\) | 2.21595e7 | 0.0305763 | ||||||||
\(341\) | 8.02277e8 | 1.09568 | ||||||||
\(342\) | 2.16800e9 | 2.93067 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | 5.47699e8 | 0.725417 | ||||||||
\(345\) | −7.53866e7 | −0.0988388 | ||||||||
\(346\) | −3.52882e8 | −0.457997 | ||||||||
\(347\) | 1.27004e9 | 1.63179 | 0.815897 | − | 0.578197i | \(-0.196244\pi\) | ||||
0.815897 | + | 0.578197i | \(0.196244\pi\) | |||||||
\(348\) | −3.02014e9 | −3.84149 | ||||||||
\(349\) | 1.01756e9 | 1.28136 | 0.640680 | − | 0.767808i | \(-0.278653\pi\) | ||||
0.640680 | + | 0.767808i | \(0.278653\pi\) | |||||||
\(350\) | −4.64522e8 | −0.579120 | ||||||||
\(351\) | 6.99528e8 | 0.863436 | ||||||||
\(352\) | −1.19708e9 | −1.46293 | ||||||||
\(353\) | 1.01873e9 | 1.23267 | 0.616335 | − | 0.787484i | \(-0.288617\pi\) | ||||
0.616335 | + | 0.787484i | \(0.288617\pi\) | |||||||
\(354\) | −5.34157e6 | −0.00639967 | ||||||||
\(355\) | −1.63097e7 | −0.0193485 | ||||||||
\(356\) | 9.10024e8 | 1.06900 | ||||||||
\(357\) | −4.04434e8 | −0.470445 | ||||||||
\(358\) | −3.65774e8 | −0.421330 | ||||||||
\(359\) | −6.44985e8 | −0.735731 | −0.367865 | − | 0.929879i | \(-0.619911\pi\) | ||||
−0.367865 | + | 0.929879i | \(0.619911\pi\) | |||||||
\(360\) | 4.37123e7 | 0.0493793 | ||||||||
\(361\) | −4.23384e8 | −0.473652 | ||||||||
\(362\) | 1.30415e9 | 1.44494 | ||||||||
\(363\) | −3.25411e8 | −0.357075 | ||||||||
\(364\) | 1.30534e8 | 0.141863 | ||||||||
\(365\) | 5.95044e7 | 0.0640508 | ||||||||
\(366\) | −2.55069e8 | −0.271940 | ||||||||
\(367\) | −1.21524e9 | −1.28331 | −0.641653 | − | 0.766995i | \(-0.721751\pi\) | ||||
−0.641653 | + | 0.766995i | \(0.721751\pi\) | |||||||
\(368\) | 7.47735e8 | 0.782133 | ||||||||
\(369\) | −2.53910e9 | −2.63079 | ||||||||
\(370\) | 8.81261e6 | 0.00904479 | ||||||||
\(371\) | 6.47842e8 | 0.658659 | ||||||||
\(372\) | 2.57535e9 | 2.59380 | ||||||||
\(373\) | 4.76152e8 | 0.475078 | 0.237539 | − | 0.971378i | \(-0.423659\pi\) | ||||
0.237539 | + | 0.971378i | \(0.423659\pi\) | |||||||
\(374\) | −1.10429e9 | −1.09152 | ||||||||
\(375\) | −1.34621e8 | −0.131826 | ||||||||
\(376\) | 3.27419e7 | 0.0317648 | ||||||||
\(377\) | −4.29719e8 | −0.413038 | ||||||||
\(378\) | −1.89545e9 | −1.80506 | ||||||||
\(379\) | 2.05317e9 | 1.93726 | 0.968628 | − | 0.248516i | \(-0.0799428\pi\) | ||||
0.968628 | + | 0.248516i | \(0.0799428\pi\) | |||||||
\(380\) | 3.63374e7 | 0.0339713 | ||||||||
\(381\) | 1.29218e9 | 1.19698 | ||||||||
\(382\) | 1.01120e9 | 0.928142 | ||||||||
\(383\) | −6.47837e8 | −0.589210 | −0.294605 | − | 0.955619i | \(-0.595188\pi\) | ||||
−0.294605 | + | 0.955619i | \(0.595188\pi\) | |||||||
\(384\) | −2.14941e9 | −1.93714 | ||||||||
\(385\) | −1.59564e7 | −0.0142502 | ||||||||
\(386\) | 3.07910e9 | 2.72501 | ||||||||
\(387\) | −4.01884e9 | −3.52462 | ||||||||
\(388\) | −9.20561e8 | −0.800095 | ||||||||
\(389\) | −1.77218e8 | −0.152645 | −0.0763226 | − | 0.997083i | \(-0.524318\pi\) | ||||
−0.0763226 | + | 0.997083i | \(0.524318\pi\) | |||||||
\(390\) | 3.28719e7 | 0.0280607 | ||||||||
\(391\) | 1.15671e9 | 0.978599 | ||||||||
\(392\) | −9.23360e7 | −0.0774230 | ||||||||
\(393\) | −3.83093e9 | −3.18369 | ||||||||
\(394\) | −1.86630e9 | −1.53725 | ||||||||
\(395\) | 1.66304e6 | 0.00135773 | ||||||||
\(396\) | −4.79847e9 | −3.88302 | ||||||||
\(397\) | 1.86008e9 | 1.49199 | 0.745993 | − | 0.665954i | \(-0.231975\pi\) | ||||
0.745993 | + | 0.665954i | \(0.231975\pi\) | |||||||
\(398\) | 8.79854e8 | 0.699552 | ||||||||
\(399\) | −6.63194e8 | −0.522680 | ||||||||
\(400\) | 6.67229e8 | 0.521273 | ||||||||
\(401\) | −1.70783e9 | −1.32263 | −0.661315 | − | 0.750108i | \(-0.730001\pi\) | ||||
−0.661315 | + | 0.750108i | \(0.730001\pi\) | |||||||
\(402\) | −1.51669e8 | −0.116441 | ||||||||
\(403\) | 3.66432e8 | 0.278886 | ||||||||
\(404\) | −1.24855e9 | −0.942047 | ||||||||
\(405\) | −1.52684e8 | −0.114209 | ||||||||
\(406\) | 1.16437e9 | 0.863476 | ||||||||
\(407\) | −2.52547e8 | −0.185679 | ||||||||
\(408\) | −9.25414e8 | −0.674568 | ||||||||
\(409\) | −7.13105e8 | −0.515373 | −0.257687 | − | 0.966229i | \(-0.582960\pi\) | ||||
−0.257687 | + | 0.966229i | \(0.582960\pi\) | |||||||
\(410\) | −7.40047e7 | −0.0530293 | ||||||||
\(411\) | −4.78511e9 | −3.39974 | ||||||||
\(412\) | −1.48835e9 | −1.04849 | ||||||||
\(413\) | 1.18426e6 | 0.000827224 0 | ||||||||
\(414\) | 8.74031e9 | 6.05377 | ||||||||
\(415\) | 7.73131e7 | 0.0530988 | ||||||||
\(416\) | −5.46756e8 | −0.372363 | ||||||||
\(417\) | −5.91295e8 | −0.399326 | ||||||||
\(418\) | −1.81083e9 | −1.21272 | ||||||||
\(419\) | 8.13873e8 | 0.540515 | 0.270257 | − | 0.962788i | \(-0.412891\pi\) | ||||
0.270257 | + | 0.962788i | \(0.412891\pi\) | |||||||
\(420\) | −5.12208e7 | −0.0337345 | ||||||||
\(421\) | −2.10577e9 | −1.37538 | −0.687692 | − | 0.726003i | \(-0.741376\pi\) | ||||
−0.687692 | + | 0.726003i | \(0.741376\pi\) | |||||||
\(422\) | 3.68884e9 | 2.38944 | ||||||||
\(423\) | −2.40250e8 | −0.154338 | ||||||||
\(424\) | 1.48237e9 | 0.944447 | ||||||||
\(425\) | 1.03217e9 | 0.652213 | ||||||||
\(426\) | 2.60905e9 | 1.63512 | ||||||||
\(427\) | 5.65505e7 | 0.0351511 | ||||||||
\(428\) | 2.98165e9 | 1.83824 | ||||||||
\(429\) | −9.42026e8 | −0.576053 | ||||||||
\(430\) | −1.17134e8 | −0.0710463 | ||||||||
\(431\) | 8.75667e8 | 0.526828 | 0.263414 | − | 0.964683i | \(-0.415152\pi\) | ||||
0.263414 | + | 0.964683i | \(0.415152\pi\) | |||||||
\(432\) | 2.72258e9 | 1.62475 | ||||||||
\(433\) | 8.83882e8 | 0.523223 | 0.261611 | − | 0.965173i | \(-0.415746\pi\) | ||||
0.261611 | + | 0.965173i | \(0.415746\pi\) | |||||||
\(434\) | −9.92889e8 | −0.583024 | ||||||||
\(435\) | 1.68619e8 | 0.0982186 | ||||||||
\(436\) | 1.60311e8 | 0.0926321 | ||||||||
\(437\) | 1.89678e9 | 1.08726 | ||||||||
\(438\) | −9.51886e9 | −5.41284 | ||||||||
\(439\) | −7.07932e8 | −0.399361 | −0.199681 | − | 0.979861i | \(-0.563990\pi\) | ||||
−0.199681 | + | 0.979861i | \(0.563990\pi\) | |||||||
\(440\) | −3.65109e7 | −0.0204333 | ||||||||
\(441\) | 6.77532e8 | 0.376179 | ||||||||
\(442\) | −5.04375e8 | −0.277828 | ||||||||
\(443\) | 3.03959e9 | 1.66112 | 0.830561 | − | 0.556928i | \(-0.188020\pi\) | ||||
0.830561 | + | 0.556928i | \(0.188020\pi\) | |||||||
\(444\) | −8.10691e8 | −0.439557 | ||||||||
\(445\) | −5.08080e7 | −0.0273320 | ||||||||
\(446\) | −2.23050e9 | −1.19050 | ||||||||
\(447\) | −3.82947e8 | −0.202797 | ||||||||
\(448\) | 1.10608e9 | 0.581185 | ||||||||
\(449\) | 9.63068e8 | 0.502106 | 0.251053 | − | 0.967973i | \(-0.419223\pi\) | ||||
0.251053 | + | 0.967973i | \(0.419223\pi\) | |||||||
\(450\) | 7.79927e9 | 4.03469 | ||||||||
\(451\) | 2.12079e9 | 1.08863 | ||||||||
\(452\) | 3.20814e9 | 1.63406 | ||||||||
\(453\) | −3.07166e8 | −0.155249 | ||||||||
\(454\) | −1.20160e9 | −0.602648 | ||||||||
\(455\) | −7.28792e6 | −0.00362713 | ||||||||
\(456\) | −1.51750e9 | −0.749467 | ||||||||
\(457\) | 2.02027e8 | 0.0990154 | 0.0495077 | − | 0.998774i | \(-0.484235\pi\) | ||||
0.0495077 | + | 0.998774i | \(0.484235\pi\) | |||||||
\(458\) | −5.45418e9 | −2.65277 | ||||||||
\(459\) | 4.21169e9 | 2.03288 | ||||||||
\(460\) | 1.46495e8 | 0.0701730 | ||||||||
\(461\) | −2.79434e9 | −1.32839 | −0.664196 | − | 0.747558i | \(-0.731226\pi\) | ||||
−0.664196 | + | 0.747558i | \(0.731226\pi\) | |||||||
\(462\) | 2.55252e9 | 1.20427 | ||||||||
\(463\) | 6.87061e8 | 0.321708 | 0.160854 | − | 0.986978i | \(-0.448575\pi\) | ||||
0.160854 | + | 0.986978i | \(0.448575\pi\) | |||||||
\(464\) | −1.67248e9 | −0.777225 | ||||||||
\(465\) | −1.43786e8 | −0.0663178 | ||||||||
\(466\) | 3.32866e9 | 1.52377 | ||||||||
\(467\) | −3.84537e9 | −1.74715 | −0.873573 | − | 0.486693i | \(-0.838203\pi\) | ||||
−0.873573 | + | 0.486693i | \(0.838203\pi\) | |||||||
\(468\) | −2.19166e9 | −0.988352 | ||||||||
\(469\) | 3.36260e7 | 0.0150512 | ||||||||
\(470\) | −7.00234e6 | −0.00311101 | ||||||||
\(471\) | 8.87934e7 | 0.0391568 | ||||||||
\(472\) | 2.70980e6 | 0.00118615 | ||||||||
\(473\) | 3.35676e9 | 1.45850 | ||||||||
\(474\) | −2.66034e8 | −0.114740 | ||||||||
\(475\) | 1.69256e9 | 0.724630 | ||||||||
\(476\) | 7.85915e8 | 0.334004 | ||||||||
\(477\) | −1.08772e10 | −4.58883 | ||||||||
\(478\) | −6.35268e9 | −2.66048 | ||||||||
\(479\) | −3.45060e9 | −1.43457 | −0.717283 | − | 0.696782i | \(-0.754615\pi\) | ||||
−0.717283 | + | 0.696782i | \(0.754615\pi\) | |||||||
\(480\) | 2.14543e8 | 0.0885464 | ||||||||
\(481\) | −1.15349e8 | −0.0472612 | ||||||||
\(482\) | 1.71250e9 | 0.696571 | ||||||||
\(483\) | −2.67368e9 | −1.07968 | ||||||||
\(484\) | 6.32355e8 | 0.253514 | ||||||||
\(485\) | 5.13963e7 | 0.0204567 | ||||||||
\(486\) | 1.23391e10 | 4.87593 | ||||||||
\(487\) | −2.18947e8 | −0.0858989 | −0.0429495 | − | 0.999077i | \(-0.513675\pi\) | ||||
−0.0429495 | + | 0.999077i | \(0.513675\pi\) | |||||||
\(488\) | 1.29397e8 | 0.0504029 | ||||||||
\(489\) | −1.92748e9 | −0.745434 | ||||||||
\(490\) | 1.97474e7 | 0.00758270 | ||||||||
\(491\) | −5.32188e8 | −0.202899 | −0.101449 | − | 0.994841i | \(-0.532348\pi\) | ||||
−0.101449 | + | 0.994841i | \(0.532348\pi\) | |||||||
\(492\) | 6.80785e9 | 2.57711 | ||||||||
\(493\) | −2.58723e9 | −0.972459 | ||||||||
\(494\) | −8.27079e8 | −0.308676 | ||||||||
\(495\) | 2.67905e8 | 0.0992804 | ||||||||
\(496\) | 1.42616e9 | 0.524787 | ||||||||
\(497\) | −5.78445e8 | −0.211356 | ||||||||
\(498\) | −1.23677e10 | −4.48731 | ||||||||
\(499\) | 3.19449e9 | 1.15093 | 0.575466 | − | 0.817826i | \(-0.304821\pi\) | ||||
0.575466 | + | 0.817826i | \(0.304821\pi\) | |||||||
\(500\) | 2.61601e8 | 0.0935933 | ||||||||
\(501\) | 4.73420e9 | 1.68196 | ||||||||
\(502\) | 5.91576e9 | 2.08712 | ||||||||
\(503\) | −3.24820e9 | −1.13803 | −0.569016 | − | 0.822326i | \(-0.692676\pi\) | ||||
−0.569016 | + | 0.822326i | \(0.692676\pi\) | |||||||
\(504\) | 1.55031e9 | 0.539401 | ||||||||
\(505\) | 6.97086e7 | 0.0240861 | ||||||||
\(506\) | −7.30038e9 | −2.50506 | ||||||||
\(507\) | −4.30261e8 | −0.146624 | ||||||||
\(508\) | −2.51103e9 | −0.849825 | ||||||||
\(509\) | −1.11805e9 | −0.375794 | −0.187897 | − | 0.982189i | \(-0.560167\pi\) | ||||
−0.187897 | + | 0.982189i | \(0.560167\pi\) | |||||||
\(510\) | 1.97913e8 | 0.0660662 | ||||||||
\(511\) | 2.11040e9 | 0.699666 | ||||||||
\(512\) | −2.98699e9 | −0.983535 | ||||||||
\(513\) | 6.90636e9 | 2.25860 | ||||||||
\(514\) | 4.80345e9 | 1.56021 | ||||||||
\(515\) | 8.30968e7 | 0.0268077 | ||||||||
\(516\) | 1.07754e10 | 3.45269 | ||||||||
\(517\) | 2.00670e8 | 0.0638653 | ||||||||
\(518\) | 3.12550e8 | 0.0988018 | ||||||||
\(519\) | −1.81242e9 | −0.569080 | ||||||||
\(520\) | −1.66760e7 | −0.00520093 | ||||||||
\(521\) | −2.63448e9 | −0.816138 | −0.408069 | − | 0.912951i | \(-0.633798\pi\) | ||||
−0.408069 | + | 0.912951i | \(0.633798\pi\) | |||||||
\(522\) | −1.95496e10 | −6.01578 | ||||||||
\(523\) | −5.56509e9 | −1.70105 | −0.850523 | − | 0.525938i | \(-0.823714\pi\) | ||||
−0.850523 | + | 0.525938i | \(0.823714\pi\) | |||||||
\(524\) | 7.44445e9 | 2.26034 | ||||||||
\(525\) | −2.38581e9 | −0.719579 | ||||||||
\(526\) | 7.05385e9 | 2.11337 | ||||||||
\(527\) | 2.20620e9 | 0.656610 | ||||||||
\(528\) | −3.66638e9 | −1.08398 | ||||||||
\(529\) | 4.24207e9 | 1.24590 | ||||||||
\(530\) | −3.17028e8 | −0.0924978 | ||||||||
\(531\) | −1.98836e7 | −0.00576322 | ||||||||
\(532\) | 1.28875e9 | 0.371089 | ||||||||
\(533\) | 9.68651e8 | 0.277091 | ||||||||
\(534\) | 8.12769e9 | 2.30979 | ||||||||
\(535\) | −1.66470e8 | −0.0469999 | ||||||||
\(536\) | 7.69422e7 | 0.0215818 | ||||||||
\(537\) | −1.87863e9 | −0.523519 | ||||||||
\(538\) | 9.61506e9 | 2.66204 | ||||||||
\(539\) | −5.65912e8 | −0.155664 | ||||||||
\(540\) | 5.33403e8 | 0.145773 | ||||||||
\(541\) | −1.68303e9 | −0.456985 | −0.228493 | − | 0.973546i | \(-0.573380\pi\) | ||||
−0.228493 | + | 0.973546i | \(0.573380\pi\) | |||||||
\(542\) | 1.08919e10 | 2.93836 | ||||||||
\(543\) | 6.69821e9 | 1.79539 | ||||||||
\(544\) | −3.29188e9 | −0.876694 | ||||||||
\(545\) | −8.95041e6 | −0.00236840 | ||||||||
\(546\) | 1.16584e9 | 0.306524 | ||||||||
\(547\) | −6.60056e9 | −1.72435 | −0.862174 | − | 0.506612i | \(-0.830898\pi\) | ||||
−0.862174 | + | 0.506612i | \(0.830898\pi\) | |||||||
\(548\) | 9.29866e9 | 2.41373 | ||||||||
\(549\) | −9.49476e8 | −0.244896 | ||||||||
\(550\) | −6.51438e9 | −1.66957 | ||||||||
\(551\) | −4.24257e9 | −1.08043 | ||||||||
\(552\) | −6.11783e9 | −1.54814 | ||||||||
\(553\) | 5.89816e7 | 0.0148313 | ||||||||
\(554\) | −1.00882e10 | −2.52075 | ||||||||
\(555\) | 4.52620e7 | 0.0112385 | ||||||||
\(556\) | 1.14903e9 | 0.283511 | ||||||||
\(557\) | 4.97604e9 | 1.22009 | 0.610044 | − | 0.792368i | \(-0.291152\pi\) | ||||
0.610044 | + | 0.792368i | \(0.291152\pi\) | |||||||
\(558\) | 1.66705e10 | 4.06189 | ||||||||
\(559\) | 1.53317e9 | 0.371234 | ||||||||
\(560\) | −2.83647e7 | −0.00682528 | ||||||||
\(561\) | −5.67170e9 | −1.35626 | ||||||||
\(562\) | −3.31486e9 | −0.787750 | ||||||||
\(563\) | 9.88221e8 | 0.233386 | 0.116693 | − | 0.993168i | \(-0.462771\pi\) | ||||
0.116693 | + | 0.993168i | \(0.462771\pi\) | |||||||
\(564\) | 6.44161e8 | 0.151188 | ||||||||
\(565\) | −1.79115e8 | −0.0417795 | ||||||||
\(566\) | 3.37366e9 | 0.782067 | ||||||||
\(567\) | −5.41512e9 | −1.24758 | ||||||||
\(568\) | −1.32358e9 | −0.303062 | ||||||||
\(569\) | −7.44589e9 | −1.69443 | −0.847215 | − | 0.531250i | \(-0.821723\pi\) | ||||
−0.847215 | + | 0.531250i | \(0.821723\pi\) | |||||||
\(570\) | 3.24540e8 | 0.0734018 | ||||||||
\(571\) | 5.47301e9 | 1.23027 | 0.615134 | − | 0.788422i | \(-0.289102\pi\) | ||||
0.615134 | + | 0.788422i | \(0.289102\pi\) | |||||||
\(572\) | 1.83059e9 | 0.408983 | ||||||||
\(573\) | 5.19357e9 | 1.15325 | ||||||||
\(574\) | −2.62467e9 | −0.579272 | ||||||||
\(575\) | 6.82358e9 | 1.49684 | ||||||||
\(576\) | −1.85710e10 | −4.04908 | ||||||||
\(577\) | 1.63003e9 | 0.353248 | 0.176624 | − | 0.984278i | \(-0.443482\pi\) | ||||
0.176624 | + | 0.984278i | \(0.443482\pi\) | |||||||
\(578\) | 4.08501e9 | 0.879924 | ||||||||
\(579\) | 1.58144e10 | 3.38593 | ||||||||
\(580\) | −3.27668e8 | −0.0697327 | ||||||||
\(581\) | 2.74200e9 | 0.580031 | ||||||||
\(582\) | −8.22180e9 | −1.72877 | ||||||||
\(583\) | 9.08522e9 | 1.89887 | ||||||||
\(584\) | 4.82895e9 | 1.00325 | ||||||||
\(585\) | 1.22363e8 | 0.0252700 | ||||||||
\(586\) | −1.11306e10 | −2.28496 | ||||||||
\(587\) | −3.63952e9 | −0.742695 | −0.371347 | − | 0.928494i | \(-0.621104\pi\) | ||||
−0.371347 | + | 0.928494i | \(0.621104\pi\) | |||||||
\(588\) | −1.81661e9 | −0.368503 | ||||||||
\(589\) | 3.61775e9 | 0.729515 | ||||||||
\(590\) | −579530. | −0.000116170 0 | ||||||||
\(591\) | −9.58543e9 | −1.91010 | ||||||||
\(592\) | −4.48939e8 | −0.0889328 | ||||||||
\(593\) | 1.76713e9 | 0.347998 | 0.173999 | − | 0.984746i | \(-0.444331\pi\) | ||||
0.173999 | + | 0.984746i | \(0.444331\pi\) | |||||||
\(594\) | −2.65814e10 | −5.20386 | ||||||||
\(595\) | −4.38788e7 | −0.00853975 | ||||||||
\(596\) | 7.44161e8 | 0.143981 | ||||||||
\(597\) | 4.51898e9 | 0.869221 | ||||||||
\(598\) | −3.33438e9 | −0.637619 | ||||||||
\(599\) | 3.07060e9 | 0.583753 | 0.291877 | − | 0.956456i | \(-0.405720\pi\) | ||||
0.291877 | + | 0.956456i | \(0.405720\pi\) | |||||||
\(600\) | −5.45915e9 | −1.03180 | ||||||||
\(601\) | −7.99662e8 | −0.150261 | −0.0751304 | − | 0.997174i | \(-0.523937\pi\) | ||||
−0.0751304 | + | 0.997174i | \(0.523937\pi\) | |||||||
\(602\) | −4.15428e9 | −0.776083 | ||||||||
\(603\) | −5.64577e8 | −0.104861 | ||||||||
\(604\) | 5.96901e8 | 0.110223 | ||||||||
\(605\) | −3.53053e7 | −0.00648181 | ||||||||
\(606\) | −1.11512e10 | −2.03548 | ||||||||
\(607\) | 4.24468e9 | 0.770344 | 0.385172 | − | 0.922845i | \(-0.374142\pi\) | ||||
0.385172 | + | 0.922845i | \(0.374142\pi\) | |||||||
\(608\) | −5.39806e9 | −0.974036 | ||||||||
\(609\) | 5.98027e9 | 1.07290 | ||||||||
\(610\) | −2.76735e7 | −0.00493640 | ||||||||
\(611\) | 9.16540e7 | 0.0162558 | ||||||||
\(612\) | −1.31954e10 | −2.32698 | ||||||||
\(613\) | 7.49949e8 | 0.131498 | 0.0657492 | − | 0.997836i | \(-0.479056\pi\) | ||||
0.0657492 | + | 0.997836i | \(0.479056\pi\) | |||||||
\(614\) | −1.04590e9 | −0.182348 | ||||||||
\(615\) | −3.80092e8 | −0.0658910 | ||||||||
\(616\) | −1.29490e9 | −0.223206 | ||||||||
\(617\) | 2.47397e9 | 0.424029 | 0.212015 | − | 0.977266i | \(-0.431998\pi\) | ||||
0.212015 | + | 0.977266i | \(0.431998\pi\) | |||||||
\(618\) | −1.32929e10 | −2.26548 | ||||||||
\(619\) | −5.14688e9 | −0.872222 | −0.436111 | − | 0.899893i | \(-0.643645\pi\) | ||||
−0.436111 | + | 0.899893i | \(0.643645\pi\) | |||||||
\(620\) | 2.79411e8 | 0.0470839 | ||||||||
\(621\) | 2.78431e10 | 4.66549 | ||||||||
\(622\) | −1.55503e10 | −2.59103 | ||||||||
\(623\) | −1.80197e9 | −0.298565 | ||||||||
\(624\) | −1.67459e9 | −0.275906 | ||||||||
\(625\) | 6.08160e9 | 0.996410 | ||||||||
\(626\) | −5.52253e8 | −0.0899762 | ||||||||
\(627\) | −9.30052e9 | −1.50685 | ||||||||
\(628\) | −1.72548e8 | −0.0278003 | ||||||||
\(629\) | −6.94486e8 | −0.111272 | ||||||||
\(630\) | −3.31557e8 | −0.0528282 | ||||||||
\(631\) | −1.27962e9 | −0.202758 | −0.101379 | − | 0.994848i | \(-0.532326\pi\) | ||||
−0.101379 | + | 0.994848i | \(0.532326\pi\) | |||||||
\(632\) | 1.34960e8 | 0.0212665 | ||||||||
\(633\) | 1.89461e10 | 2.96897 | ||||||||
\(634\) | 8.68382e9 | 1.35331 | ||||||||
\(635\) | 1.40195e8 | 0.0217282 | ||||||||
\(636\) | 2.91641e10 | 4.49519 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | 1.63289e10 | 2.48935 | ||||||||
\(639\) | 9.71202e9 | 1.47250 | ||||||||
\(640\) | −2.33199e8 | −0.0351639 | ||||||||
\(641\) | 7.63788e9 | 1.14543 | 0.572716 | − | 0.819754i | \(-0.305890\pi\) | ||||
0.572716 | + | 0.819754i | \(0.305890\pi\) | |||||||
\(642\) | 2.66300e10 | 3.97190 | ||||||||
\(643\) | 9.01009e9 | 1.33657 | 0.668283 | − | 0.743907i | \(-0.267029\pi\) | ||||
0.668283 | + | 0.743907i | \(0.267029\pi\) | |||||||
\(644\) | 5.19562e9 | 0.766543 | ||||||||
\(645\) | −6.01604e8 | −0.0882779 | ||||||||
\(646\) | −4.97964e9 | −0.726748 | ||||||||
\(647\) | 1.53382e9 | 0.222644 | 0.111322 | − | 0.993784i | \(-0.464492\pi\) | ||||
0.111322 | + | 0.993784i | \(0.464492\pi\) | |||||||
\(648\) | −1.23907e10 | −1.78889 | ||||||||
\(649\) | 1.66079e7 | 0.00238483 | ||||||||
\(650\) | −2.97538e9 | −0.424958 | ||||||||
\(651\) | −5.09953e9 | −0.724431 | ||||||||
\(652\) | 3.74558e9 | 0.529239 | ||||||||
\(653\) | −9.14623e9 | −1.28542 | −0.642711 | − | 0.766109i | \(-0.722190\pi\) | ||||
−0.642711 | + | 0.766109i | \(0.722190\pi\) | |||||||
\(654\) | 1.43179e9 | 0.200150 | ||||||||
\(655\) | −4.15634e8 | −0.0577919 | ||||||||
\(656\) | 3.77001e9 | 0.521410 | ||||||||
\(657\) | −3.54333e10 | −4.87453 | ||||||||
\(658\) | −2.48346e8 | −0.0339834 | ||||||||
\(659\) | −3.20337e9 | −0.436022 | −0.218011 | − | 0.975946i | \(-0.569957\pi\) | ||||
−0.218011 | + | 0.975946i | \(0.569957\pi\) | |||||||
\(660\) | −7.18311e8 | −0.0972543 | ||||||||
\(661\) | −2.32121e9 | −0.312614 | −0.156307 | − | 0.987708i | \(-0.549959\pi\) | ||||
−0.156307 | + | 0.987708i | \(0.549959\pi\) | |||||||
\(662\) | −1.28992e10 | −1.72806 | ||||||||
\(663\) | −2.59050e9 | −0.345212 | ||||||||
\(664\) | 6.27417e9 | 0.831703 | ||||||||
\(665\) | −7.19528e7 | −0.00948794 | ||||||||
\(666\) | −5.24767e9 | −0.688346 | ||||||||
\(667\) | −1.71040e10 | −2.23181 | ||||||||
\(668\) | −9.19973e9 | −1.19415 | ||||||||
\(669\) | −1.14560e10 | −1.47925 | ||||||||
\(670\) | −1.64552e7 | −0.00211369 | ||||||||
\(671\) | 7.93054e8 | 0.101338 | ||||||||
\(672\) | 7.60904e9 | 0.967247 | ||||||||
\(673\) | 1.45621e9 | 0.184149 | 0.0920747 | − | 0.995752i | \(-0.470650\pi\) | ||||
0.0920747 | + | 0.995752i | \(0.470650\pi\) | |||||||
\(674\) | −6.63951e9 | −0.835269 | ||||||||
\(675\) | 2.48453e10 | 3.10944 | ||||||||
\(676\) | 8.36105e8 | 0.104099 | ||||||||
\(677\) | −6.26351e9 | −0.775814 | −0.387907 | − | 0.921698i | \(-0.626802\pi\) | ||||
−0.387907 | + | 0.921698i | \(0.626802\pi\) | |||||||
\(678\) | 2.86529e10 | 3.53073 | ||||||||
\(679\) | 1.82283e9 | 0.223461 | ||||||||
\(680\) | −1.00402e8 | −0.0122451 | ||||||||
\(681\) | −6.17148e9 | −0.748814 | ||||||||
\(682\) | −1.39241e10 | −1.68082 | ||||||||
\(683\) | 2.56035e9 | 0.307487 | 0.153744 | − | 0.988111i | \(-0.450867\pi\) | ||||
0.153744 | + | 0.988111i | \(0.450867\pi\) | |||||||
\(684\) | −2.16380e10 | −2.58535 | ||||||||
\(685\) | −5.19158e8 | −0.0617138 | ||||||||
\(686\) | 7.00366e8 | 0.0828306 | ||||||||
\(687\) | −2.80130e10 | −3.29618 | ||||||||
\(688\) | 5.96712e9 | 0.698562 | ||||||||
\(689\) | 4.14959e9 | 0.483323 | ||||||||
\(690\) | 1.30839e9 | 0.151623 | ||||||||
\(691\) | 7.27918e9 | 0.839284 | 0.419642 | − | 0.907690i | \(-0.362156\pi\) | ||||
0.419642 | + | 0.907690i | \(0.362156\pi\) | |||||||
\(692\) | 3.52198e9 | 0.404032 | ||||||||
\(693\) | 9.50159e9 | 1.08450 | ||||||||
\(694\) | −2.20425e10 | −2.50324 | ||||||||
\(695\) | −6.41521e7 | −0.00724877 | ||||||||
\(696\) | 1.36839e10 | 1.53843 | ||||||||
\(697\) | 5.83201e9 | 0.652384 | ||||||||
\(698\) | −1.76605e10 | −1.96566 | ||||||||
\(699\) | 1.70962e10 | 1.89334 | ||||||||
\(700\) | 4.63622e9 | 0.510883 | ||||||||
\(701\) | 9.40973e9 | 1.03173 | 0.515863 | − | 0.856671i | \(-0.327471\pi\) | ||||
0.515863 | + | 0.856671i | \(0.327471\pi\) | |||||||
\(702\) | −1.21408e10 | −1.32455 | ||||||||
\(703\) | −1.13882e9 | −0.123627 | ||||||||
\(704\) | 1.55115e10 | 1.67552 | ||||||||
\(705\) | −3.59644e7 | −0.00386555 | ||||||||
\(706\) | −1.76808e10 | −1.89097 | ||||||||
\(707\) | 2.47230e9 | 0.263107 | ||||||||
\(708\) | 5.33123e7 | 0.00564561 | ||||||||
\(709\) | −1.39670e10 | −1.47178 | −0.735889 | − | 0.677103i | \(-0.763235\pi\) | ||||
−0.735889 | + | 0.677103i | \(0.763235\pi\) | |||||||
\(710\) | 2.83067e8 | 0.0296815 | ||||||||
\(711\) | −9.90295e8 | −0.103329 | ||||||||
\(712\) | −4.12321e9 | −0.428110 | ||||||||
\(713\) | 1.45850e10 | 1.50693 | ||||||||
\(714\) | 7.01924e9 | 0.721682 | ||||||||
\(715\) | −1.02204e8 | −0.0104568 | ||||||||
\(716\) | 3.65065e9 | 0.371685 | ||||||||
\(717\) | −3.26277e10 | −3.30575 | ||||||||
\(718\) | 1.11942e10 | 1.12864 | ||||||||
\(719\) | −1.78331e10 | −1.78927 | −0.894633 | − | 0.446801i | \(-0.852563\pi\) | ||||
−0.894633 | + | 0.446801i | \(0.852563\pi\) | |||||||
\(720\) | 4.76241e8 | 0.0475513 | ||||||||
\(721\) | 2.94713e9 | 0.292837 | ||||||||
\(722\) | 7.34813e9 | 0.726602 | ||||||||
\(723\) | 8.79549e9 | 0.865517 | ||||||||
\(724\) | −1.30163e10 | −1.27468 | ||||||||
\(725\) | −1.52625e10 | −1.48745 | ||||||||
\(726\) | 5.64775e9 | 0.547769 | ||||||||
\(727\) | −6.66437e9 | −0.643264 | −0.321632 | − | 0.946865i | \(-0.604231\pi\) | ||||
−0.321632 | + | 0.946865i | \(0.604231\pi\) | |||||||
\(728\) | −5.91435e8 | −0.0568129 | ||||||||
\(729\) | 2.88471e10 | 2.75776 | ||||||||
\(730\) | −1.03274e9 | −0.0982567 | ||||||||
\(731\) | 9.23082e9 | 0.874036 | ||||||||
\(732\) | 2.54575e9 | 0.239898 | ||||||||
\(733\) | −8.90855e9 | −0.835493 | −0.417747 | − | 0.908564i | \(-0.637180\pi\) | ||||
−0.417747 | + | 0.908564i | \(0.637180\pi\) | |||||||
\(734\) | 2.10913e10 | 1.96865 | ||||||||
\(735\) | 1.01424e8 | 0.00942181 | ||||||||
\(736\) | −2.17624e10 | −2.01203 | ||||||||
\(737\) | 4.71566e8 | 0.0433916 | ||||||||
\(738\) | 4.40678e10 | 4.03575 | ||||||||
\(739\) | −6.30362e9 | −0.574559 | −0.287280 | − | 0.957847i | \(-0.592751\pi\) | ||||
−0.287280 | + | 0.957847i | \(0.592751\pi\) | |||||||
\(740\) | −8.79554e7 | −0.00797905 | ||||||||
\(741\) | −4.24792e9 | −0.383542 | ||||||||
\(742\) | −1.12438e10 | −1.01041 | ||||||||
\(743\) | 1.71064e10 | 1.53002 | 0.765011 | − | 0.644017i | \(-0.222733\pi\) | ||||
0.765011 | + | 0.644017i | \(0.222733\pi\) | |||||||
\(744\) | −1.16686e10 | −1.03876 | ||||||||
\(745\) | −4.15476e7 | −0.00368128 | ||||||||
\(746\) | −8.26397e9 | −0.728790 | ||||||||
\(747\) | −4.60379e10 | −4.04104 | ||||||||
\(748\) | 1.10215e10 | 0.962911 | ||||||||
\(749\) | −5.90405e9 | −0.513409 | ||||||||
\(750\) | 2.33644e9 | 0.202227 | ||||||||
\(751\) | −1.59756e9 | −0.137632 | −0.0688158 | − | 0.997629i | \(-0.521922\pi\) | ||||
−0.0688158 | + | 0.997629i | \(0.521922\pi\) | |||||||
\(752\) | 3.56719e8 | 0.0305889 | ||||||||
\(753\) | 3.03837e10 | 2.59333 | ||||||||
\(754\) | 7.45808e9 | 0.633618 | ||||||||
\(755\) | −3.33258e7 | −0.00281817 | ||||||||
\(756\) | 1.89178e10 | 1.59237 | ||||||||
\(757\) | −9.52163e9 | −0.797767 | −0.398883 | − | 0.917002i | \(-0.630602\pi\) | ||||
−0.398883 | + | 0.917002i | \(0.630602\pi\) | |||||||
\(758\) | −3.56342e10 | −2.97183 | ||||||||
\(759\) | −3.74952e10 | −3.11264 | ||||||||
\(760\) | −1.64640e8 | −0.0136047 | ||||||||
\(761\) | 2.92422e9 | 0.240527 | 0.120263 | − | 0.992742i | \(-0.461626\pi\) | ||||
0.120263 | + | 0.992742i | \(0.461626\pi\) | |||||||
\(762\) | −2.24268e10 | −1.83622 | ||||||||
\(763\) | −3.17437e8 | −0.0258715 | ||||||||
\(764\) | −1.00924e10 | −0.818780 | ||||||||
\(765\) | 7.36719e8 | 0.0594959 | ||||||||
\(766\) | 1.12437e10 | 0.903873 | ||||||||
\(767\) | 7.58550e6 | 0.000607017 0 | ||||||||
\(768\) | 5.10738e8 | 0.0406850 | ||||||||
\(769\) | 1.31606e10 | 1.04360 | 0.521799 | − | 0.853069i | \(-0.325261\pi\) | ||||
0.521799 | + | 0.853069i | \(0.325261\pi\) | |||||||
\(770\) | 2.76934e8 | 0.0218604 | ||||||||
\(771\) | 2.46708e10 | 1.93862 | ||||||||
\(772\) | −3.07313e10 | −2.40393 | ||||||||
\(773\) | 2.71953e9 | 0.211770 | 0.105885 | − | 0.994378i | \(-0.466232\pi\) | ||||
0.105885 | + | 0.994378i | \(0.466232\pi\) | |||||||
\(774\) | 6.97499e10 | 5.40692 | ||||||||
\(775\) | 1.30147e10 | 1.00433 | ||||||||
\(776\) | 4.17095e9 | 0.320420 | ||||||||
\(777\) | 1.60527e9 | 0.122765 | ||||||||
\(778\) | 3.07574e9 | 0.234164 | ||||||||
\(779\) | 9.56338e9 | 0.724820 | ||||||||
\(780\) | −3.28082e8 | −0.0247543 | ||||||||
\(781\) | −8.11201e9 | −0.609326 | ||||||||
\(782\) | −2.00755e10 | −1.50121 | ||||||||
\(783\) | −6.22773e10 | −4.63621 | ||||||||
\(784\) | −1.00599e9 | −0.0745568 | ||||||||
\(785\) | 9.63358e6 | 0.000710794 0 | ||||||||
\(786\) | 6.64886e10 | 4.88392 | ||||||||
\(787\) | 5.29011e9 | 0.386859 | 0.193430 | − | 0.981114i | \(-0.438039\pi\) | ||||
0.193430 | + | 0.981114i | \(0.438039\pi\) | |||||||
\(788\) | 1.86269e10 | 1.35612 | ||||||||
\(789\) | 3.62290e10 | 2.62595 | ||||||||
\(790\) | −2.88632e7 | −0.00208281 | ||||||||
\(791\) | −6.35254e9 | −0.456383 | ||||||||
\(792\) | 2.17413e10 | 1.55506 | ||||||||
\(793\) | 3.62220e8 | 0.0257939 | ||||||||
\(794\) | −3.22830e10 | −2.28877 | ||||||||
\(795\) | −1.62827e9 | −0.114932 | ||||||||
\(796\) | −8.78150e9 | −0.617125 | ||||||||
\(797\) | −7.86647e9 | −0.550396 | −0.275198 | − | 0.961388i | \(-0.588743\pi\) | ||||
−0.275198 | + | 0.961388i | \(0.588743\pi\) | |||||||
\(798\) | 1.15102e10 | 0.801813 | ||||||||
\(799\) | 5.51826e8 | 0.0382726 | ||||||||
\(800\) | −1.94193e10 | −1.34097 | ||||||||
\(801\) | 3.02548e10 | 2.08008 | ||||||||
\(802\) | 2.96406e10 | 2.02897 | ||||||||
\(803\) | 2.95958e10 | 2.01709 | ||||||||
\(804\) | 1.51375e9 | 0.102721 | ||||||||
\(805\) | −2.90079e8 | −0.0195988 | ||||||||
\(806\) | −6.35970e9 | −0.427823 | ||||||||
\(807\) | 4.93835e10 | 3.30769 | ||||||||
\(808\) | 5.65705e9 | 0.377268 | ||||||||
\(809\) | −1.81417e10 | −1.20464 | −0.602322 | − | 0.798253i | \(-0.705758\pi\) | ||||
−0.602322 | + | 0.798253i | \(0.705758\pi\) | |||||||
\(810\) | 2.64994e9 | 0.175202 | ||||||||
\(811\) | −9.20902e9 | −0.606234 | −0.303117 | − | 0.952953i | \(-0.598027\pi\) | ||||
−0.303117 | + | 0.952953i | \(0.598027\pi\) | |||||||
\(812\) | −1.16212e10 | −0.761734 | ||||||||
\(813\) | 5.59413e10 | 3.65103 | ||||||||
\(814\) | 4.38314e9 | 0.284839 | ||||||||
\(815\) | −2.09121e8 | −0.0135315 | ||||||||
\(816\) | −1.00823e10 | −0.649595 | ||||||||
\(817\) | 1.51368e10 | 0.971083 | ||||||||
\(818\) | 1.23765e10 | 0.790605 | ||||||||
\(819\) | 4.33976e9 | 0.276040 | ||||||||
\(820\) | 7.38613e8 | 0.0467809 | ||||||||
\(821\) | −7.97270e9 | −0.502811 | −0.251405 | − | 0.967882i | \(-0.580893\pi\) | ||||
−0.251405 | + | 0.967882i | \(0.580893\pi\) | |||||||
\(822\) | 8.30491e10 | 5.21535 | ||||||||
\(823\) | −8.16620e9 | −0.510646 | −0.255323 | − | 0.966856i | \(-0.582182\pi\) | ||||
−0.255323 | + | 0.966856i | \(0.582182\pi\) | |||||||
\(824\) | 6.74354e9 | 0.419897 | ||||||||
\(825\) | −3.34582e10 | −2.07450 | ||||||||
\(826\) | −2.05537e7 | −0.00126900 | ||||||||
\(827\) | 1.34044e10 | 0.824096 | 0.412048 | − | 0.911162i | \(-0.364814\pi\) | ||||
0.412048 | + | 0.911162i | \(0.364814\pi\) | |||||||
\(828\) | −8.72338e10 | −5.34046 | ||||||||
\(829\) | −4.47188e9 | −0.272615 | −0.136307 | − | 0.990667i | \(-0.543523\pi\) | ||||
−0.136307 | + | 0.990667i | \(0.543523\pi\) | |||||||
\(830\) | −1.34182e9 | −0.0814559 | ||||||||
\(831\) | −5.18136e10 | −3.13213 | ||||||||
\(832\) | 7.08473e9 | 0.426473 | ||||||||
\(833\) | −1.55621e9 | −0.0932849 | ||||||||
\(834\) | 1.02623e10 | 0.612584 | ||||||||
\(835\) | 5.13634e8 | 0.0305317 | ||||||||
\(836\) | 1.80732e10 | 1.06983 | ||||||||
\(837\) | 5.31054e10 | 3.13040 | ||||||||
\(838\) | −1.41254e10 | −0.829173 | ||||||||
\(839\) | −1.60884e10 | −0.940474 | −0.470237 | − | 0.882540i | \(-0.655832\pi\) | ||||
−0.470237 | + | 0.882540i | \(0.655832\pi\) | |||||||
\(840\) | 2.32075e8 | 0.0135099 | ||||||||
\(841\) | 2.10070e10 | 1.21780 | ||||||||
\(842\) | 3.65472e10 | 2.10990 | ||||||||
\(843\) | −1.70253e10 | −0.978811 | ||||||||
\(844\) | −3.68169e10 | −2.10789 | ||||||||
\(845\) | −4.66809e7 | −0.00266159 | ||||||||
\(846\) | 4.16971e9 | 0.236761 | ||||||||
\(847\) | −1.25214e9 | −0.0708048 | ||||||||
\(848\) | 1.61503e10 | 0.909483 | ||||||||
\(849\) | 1.73273e10 | 0.971750 | ||||||||
\(850\) | −1.79140e10 | −1.00052 | ||||||||
\(851\) | −4.59119e9 | −0.255371 | ||||||||
\(852\) | −2.60400e10 | −1.44245 | ||||||||
\(853\) | 2.16103e10 | 1.19217 | 0.596086 | − | 0.802920i | \(-0.296722\pi\) | ||||
0.596086 | + | 0.802920i | \(0.296722\pi\) | |||||||
\(854\) | −9.81475e8 | −0.0539233 | ||||||||
\(855\) | 1.20808e9 | 0.0661019 | ||||||||
\(856\) | −1.35095e10 | −0.736174 | ||||||||
\(857\) | 9.29534e9 | 0.504466 | 0.252233 | − | 0.967666i | \(-0.418835\pi\) | ||||
0.252233 | + | 0.967666i | \(0.418835\pi\) | |||||||
\(858\) | 1.63495e10 | 0.883690 | ||||||||
\(859\) | 2.32940e10 | 1.25392 | 0.626959 | − | 0.779053i | \(-0.284300\pi\) | ||||
0.626959 | + | 0.779053i | \(0.284300\pi\) | |||||||
\(860\) | 1.16907e9 | 0.0626750 | ||||||||
\(861\) | −1.34804e10 | −0.719768 | ||||||||
\(862\) | −1.51978e10 | −0.808176 | ||||||||
\(863\) | −2.18333e10 | −1.15633 | −0.578164 | − | 0.815921i | \(-0.696231\pi\) | ||||
−0.578164 | + | 0.815921i | \(0.696231\pi\) | |||||||
\(864\) | −7.92389e10 | −4.17965 | ||||||||
\(865\) | −1.96637e8 | −0.0103302 | ||||||||
\(866\) | −1.53404e10 | −0.802646 | ||||||||
\(867\) | 2.09808e10 | 1.09334 | ||||||||
\(868\) | 9.90965e9 | 0.514327 | ||||||||
\(869\) | 8.27148e8 | 0.0427577 | ||||||||
\(870\) | −2.92650e9 | −0.150672 | ||||||||
\(871\) | 2.15383e8 | 0.0110446 | ||||||||
\(872\) | −7.26351e8 | −0.0370970 | ||||||||
\(873\) | −3.06051e10 | −1.55684 | ||||||||
\(874\) | −3.29200e10 | −1.66790 | ||||||||
\(875\) | −5.18004e8 | −0.0261400 | ||||||||
\(876\) | 9.50042e10 | 4.77506 | ||||||||
\(877\) | −1.93936e9 | −0.0970866 | −0.0485433 | − | 0.998821i | \(-0.515458\pi\) | ||||
−0.0485433 | + | 0.998821i | \(0.515458\pi\) | |||||||
\(878\) | 1.22867e10 | 0.612637 | ||||||||
\(879\) | −5.71675e10 | −2.83915 | ||||||||
\(880\) | −3.97782e8 | −0.0196769 | ||||||||
\(881\) | −2.05356e10 | −1.01180 | −0.505898 | − | 0.862594i | \(-0.668839\pi\) | ||||
−0.505898 | + | 0.862594i | \(0.668839\pi\) | |||||||
\(882\) | −1.17591e10 | −0.577075 | ||||||||
\(883\) | −2.03996e10 | −0.997149 | −0.498574 | − | 0.866847i | \(-0.666143\pi\) | ||||
−0.498574 | + | 0.866847i | \(0.666143\pi\) | |||||||
\(884\) | 5.03398e9 | 0.245092 | ||||||||
\(885\) | −2.97650e6 | −0.000144346 0 | ||||||||
\(886\) | −5.27542e10 | −2.54823 | ||||||||
\(887\) | 1.54254e9 | 0.0742172 | 0.0371086 | − | 0.999311i | \(-0.488185\pi\) | ||||
0.0371086 | + | 0.999311i | \(0.488185\pi\) | |||||||
\(888\) | 3.67314e9 | 0.176032 | ||||||||
\(889\) | 4.97217e9 | 0.237350 | ||||||||
\(890\) | 8.81809e8 | 0.0419285 | ||||||||
\(891\) | −7.59406e10 | −3.59668 | ||||||||
\(892\) | 2.22618e10 | 1.05023 | ||||||||
\(893\) | 9.04889e8 | 0.0425222 | ||||||||
\(894\) | 6.64632e9 | 0.311100 | ||||||||
\(895\) | −2.03821e8 | −0.00950317 | ||||||||
\(896\) | −8.27069e9 | −0.384117 | ||||||||
\(897\) | −1.71256e10 | −0.792267 | ||||||||
\(898\) | −1.67147e10 | −0.770252 | ||||||||
\(899\) | −3.26226e10 | −1.49747 | ||||||||
\(900\) | −7.78417e10 | −3.55929 | ||||||||
\(901\) | 2.49836e10 | 1.13794 | ||||||||
\(902\) | −3.68078e10 | −1.67000 | ||||||||
\(903\) | −2.13366e10 | −0.964314 | ||||||||
\(904\) | −1.45357e10 | −0.654405 | ||||||||
\(905\) | 7.26718e8 | 0.0325909 | ||||||||
\(906\) | 5.33110e9 | 0.238159 | ||||||||
\(907\) | 1.08181e10 | 0.481422 | 0.240711 | − | 0.970597i | \(-0.422619\pi\) | ||||
0.240711 | + | 0.970597i | \(0.422619\pi\) | |||||||
\(908\) | 1.19927e10 | 0.531639 | ||||||||
\(909\) | −4.15096e10 | −1.83305 | ||||||||
\(910\) | 1.26487e8 | 0.00556418 | ||||||||
\(911\) | −5.51610e9 | −0.241723 | −0.120861 | − | 0.992669i | \(-0.538566\pi\) | ||||
−0.120861 | + | 0.992669i | \(0.538566\pi\) | |||||||
\(912\) | −1.65330e10 | −0.721722 | ||||||||
\(913\) | 3.84533e10 | 1.67219 | ||||||||
\(914\) | −3.50632e9 | −0.151894 | ||||||||
\(915\) | −1.42133e8 | −0.00613367 | ||||||||
\(916\) | 5.44361e10 | 2.34020 | ||||||||
\(917\) | −1.47410e10 | −0.631297 | ||||||||
\(918\) | −7.30968e10 | −3.11852 | ||||||||
\(919\) | −3.38328e10 | −1.43792 | −0.718959 | − | 0.695053i | \(-0.755381\pi\) | ||||
−0.718959 | + | 0.695053i | \(0.755381\pi\) | |||||||
\(920\) | −6.63750e8 | −0.0281027 | ||||||||
\(921\) | −5.37181e9 | −0.226575 | ||||||||
\(922\) | 4.84978e10 | 2.03781 | ||||||||
\(923\) | −3.70508e9 | −0.155093 | ||||||||
\(924\) | −2.54758e10 | −1.06237 | ||||||||
\(925\) | −4.09687e9 | −0.170199 | ||||||||
\(926\) | −1.19244e10 | −0.493514 | ||||||||
\(927\) | −4.94820e10 | −2.04018 | ||||||||
\(928\) | 4.86763e10 | 1.99940 | ||||||||
\(929\) | 2.86913e10 | 1.17407 | 0.587037 | − | 0.809560i | \(-0.300294\pi\) | ||||
0.587037 | + | 0.809560i | \(0.300294\pi\) | |||||||
\(930\) | 2.49550e9 | 0.101734 | ||||||||
\(931\) | −2.55189e9 | −0.103643 | ||||||||
\(932\) | −3.32221e10 | −1.34422 | ||||||||
\(933\) | −7.98673e10 | −3.21946 | ||||||||
\(934\) | 6.67392e10 | 2.68020 | ||||||||
\(935\) | −6.15348e8 | −0.0246195 | ||||||||
\(936\) | 9.93012e9 | 0.395812 | ||||||||
\(937\) | 2.33671e10 | 0.927930 | 0.463965 | − | 0.885853i | \(-0.346426\pi\) | ||||
0.463965 | + | 0.885853i | \(0.346426\pi\) | |||||||
\(938\) | −5.83604e8 | −0.0230892 | ||||||||
\(939\) | −2.83640e9 | −0.111799 | ||||||||
\(940\) | 6.98878e7 | 0.00274444 | ||||||||
\(941\) | −2.50407e9 | −0.0979677 | −0.0489839 | − | 0.998800i | \(-0.515598\pi\) | ||||
−0.0489839 | + | 0.998800i | \(0.515598\pi\) | |||||||
\(942\) | −1.54107e9 | −0.0600683 | ||||||||
\(943\) | 3.85549e10 | 1.49723 | ||||||||
\(944\) | 2.95229e7 | 0.00114224 | ||||||||
\(945\) | −1.05621e9 | −0.0407134 | ||||||||
\(946\) | −5.82589e10 | −2.23740 | ||||||||
\(947\) | 2.09057e10 | 0.799906 | 0.399953 | − | 0.916536i | \(-0.369026\pi\) | ||||
0.399953 | + | 0.916536i | \(0.369026\pi\) | |||||||
\(948\) | 2.65519e9 | 0.101220 | ||||||||
\(949\) | 1.35176e10 | 0.513415 | ||||||||
\(950\) | −2.93756e10 | −1.11161 | ||||||||
\(951\) | 4.46006e10 | 1.68155 | ||||||||
\(952\) | −3.56088e9 | −0.133761 | ||||||||
\(953\) | −2.16794e10 | −0.811378 | −0.405689 | − | 0.914011i | \(-0.632968\pi\) | ||||
−0.405689 | + | 0.914011i | \(0.632968\pi\) | |||||||
\(954\) | 1.88781e11 | 7.03947 | ||||||||
\(955\) | 5.63472e8 | 0.0209344 | ||||||||
\(956\) | 6.34038e10 | 2.34700 | ||||||||
\(957\) | 8.38663e10 | 3.09311 | ||||||||
\(958\) | 5.98877e10 | 2.20069 | ||||||||
\(959\) | −1.84126e10 | −0.674138 | ||||||||
\(960\) | −2.78000e9 | −0.101413 | ||||||||
\(961\) | 3.05498e8 | 0.0111039 | ||||||||
\(962\) | 2.00196e9 | 0.0725007 | ||||||||
\(963\) | 9.91282e10 | 3.57689 | ||||||||
\(964\) | −1.70918e10 | −0.614495 | ||||||||
\(965\) | 1.71577e9 | 0.0614631 | ||||||||
\(966\) | 4.64036e10 | 1.65627 | ||||||||
\(967\) | −2.51463e10 | −0.894296 | −0.447148 | − | 0.894460i | \(-0.647560\pi\) | ||||
−0.447148 | + | 0.894460i | \(0.647560\pi\) | |||||||
\(968\) | −2.86512e9 | −0.101527 | ||||||||
\(969\) | −2.55757e10 | −0.903013 | ||||||||
\(970\) | −8.92019e8 | −0.0313815 | ||||||||
\(971\) | −2.13281e10 | −0.747626 | −0.373813 | − | 0.927504i | \(-0.621950\pi\) | ||||
−0.373813 | + | 0.927504i | \(0.621950\pi\) | |||||||
\(972\) | −1.23152e11 | −4.30140 | ||||||||
\(973\) | −2.27523e9 | −0.0791828 | ||||||||
\(974\) | 3.79998e9 | 0.131773 | ||||||||
\(975\) | −1.52817e10 | −0.528027 | ||||||||
\(976\) | 1.40977e9 | 0.0485370 | ||||||||
\(977\) | −6.90646e9 | −0.236933 | −0.118466 | − | 0.992958i | \(-0.537798\pi\) | ||||
−0.118466 | + | 0.992958i | \(0.537798\pi\) | |||||||
\(978\) | 3.34528e10 | 1.14353 | ||||||||
\(979\) | −2.52704e10 | −0.860743 | ||||||||
\(980\) | −1.97092e8 | −0.00668924 | ||||||||
\(981\) | 5.32973e9 | 0.180245 | ||||||||
\(982\) | 9.23650e9 | 0.311256 | ||||||||
\(983\) | 1.84577e10 | 0.619783 | 0.309892 | − | 0.950772i | \(-0.399707\pi\) | ||||
0.309892 | + | 0.950772i | \(0.399707\pi\) | |||||||
\(984\) | −3.08455e10 | −1.03207 | ||||||||
\(985\) | −1.03997e9 | −0.0346730 | ||||||||
\(986\) | 4.49033e10 | 1.49179 | ||||||||
\(987\) | −1.27552e9 | −0.0422258 | ||||||||
\(988\) | 8.25477e9 | 0.272305 | ||||||||
\(989\) | 6.10241e10 | 2.00593 | ||||||||
\(990\) | −4.64969e9 | −0.152300 | ||||||||
\(991\) | 2.34045e10 | 0.763910 | 0.381955 | − | 0.924181i | \(-0.375251\pi\) | ||||
0.381955 | + | 0.924181i | \(0.375251\pi\) | |||||||
\(992\) | −4.15076e10 | −1.35001 | ||||||||
\(993\) | −6.62510e10 | −2.14719 | ||||||||
\(994\) | 1.00393e10 | 0.324229 | ||||||||
\(995\) | 4.90284e8 | 0.0157785 | ||||||||
\(996\) | 1.23437e11 | 3.95858 | ||||||||
\(997\) | 4.84837e10 | 1.54940 | 0.774698 | − | 0.632332i | \(-0.217902\pi\) | ||||
0.774698 | + | 0.632332i | \(0.217902\pi\) | |||||||
\(998\) | −5.54426e10 | −1.76558 | ||||||||
\(999\) | −1.67170e10 | −0.530491 |
(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 | 91.8.a.d.1.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.8.a.d.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial |