Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,10,Mod(1,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.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: | \(18.0262542657\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −14.8284 | −0.655330 | −0.327665 | − | 0.944794i | \(-0.606262\pi\) | ||||
−0.327665 | + | 0.944794i | \(0.606262\pi\) | |||||||
\(3\) | −239.735 | −1.70878 | −0.854390 | − | 0.519633i | \(-0.826069\pi\) | ||||
−0.854390 | + | 0.519633i | \(0.826069\pi\) | |||||||
\(4\) | −292.118 | −0.570542 | ||||||||
\(5\) | 625.000 | 0.447214 | ||||||||
\(6\) | 3554.89 | 1.11981 | ||||||||
\(7\) | 2401.00 | 0.377964 | ||||||||
\(8\) | 11923.8 | 1.02922 | ||||||||
\(9\) | 37789.9 | 1.91993 | ||||||||
\(10\) | −9267.77 | −0.293073 | ||||||||
\(11\) | −16523.6 | −0.340280 | −0.170140 | − | 0.985420i | \(-0.554422\pi\) | ||||
−0.170140 | + | 0.985420i | \(0.554422\pi\) | |||||||
\(12\) | 70030.9 | 0.974931 | ||||||||
\(13\) | 26311.4 | 0.255505 | 0.127752 | − | 0.991806i | \(-0.459224\pi\) | ||||
0.127752 | + | 0.991806i | \(0.459224\pi\) | |||||||
\(14\) | −35603.1 | −0.247691 | ||||||||
\(15\) | −149834. | −0.764189 | ||||||||
\(16\) | −27246.9 | −0.103939 | ||||||||
\(17\) | −144003. | −0.418167 | −0.209084 | − | 0.977898i | \(-0.567048\pi\) | ||||
−0.209084 | + | 0.977898i | \(0.567048\pi\) | |||||||
\(18\) | −560365. | −1.25819 | ||||||||
\(19\) | −159710. | −0.281151 | −0.140576 | − | 0.990070i | \(-0.544895\pi\) | ||||
−0.140576 | + | 0.990070i | \(0.544895\pi\) | |||||||
\(20\) | −182574. | −0.255154 | ||||||||
\(21\) | −575604. | −0.645858 | ||||||||
\(22\) | 245019. | 0.222996 | ||||||||
\(23\) | 2.07393e6 | 1.54533 | 0.772663 | − | 0.634817i | \(-0.218925\pi\) | ||||
0.772663 | + | 0.634817i | \(0.218925\pi\) | |||||||
\(24\) | −2.85855e6 | −1.75872 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | −390156. | −0.167440 | ||||||||
\(27\) | −4.34086e6 | −1.57195 | ||||||||
\(28\) | −701375. | −0.215645 | ||||||||
\(29\) | −4.94938e6 | −1.29945 | −0.649725 | − | 0.760169i | \(-0.725116\pi\) | ||||
−0.649725 | + | 0.760169i | \(0.725116\pi\) | |||||||
\(30\) | 2.22181e6 | 0.500796 | ||||||||
\(31\) | 4.22040e6 | 0.820779 | 0.410389 | − | 0.911910i | \(-0.365393\pi\) | ||||
0.410389 | + | 0.911910i | \(0.365393\pi\) | |||||||
\(32\) | −5.70096e6 | −0.961110 | ||||||||
\(33\) | 3.96128e6 | 0.581464 | ||||||||
\(34\) | 2.13533e6 | 0.274038 | ||||||||
\(35\) | 1.50062e6 | 0.169031 | ||||||||
\(36\) | −1.10391e7 | −1.09540 | ||||||||
\(37\) | −1.29081e7 | −1.13228 | −0.566142 | − | 0.824308i | \(-0.691565\pi\) | ||||
−0.566142 | + | 0.824308i | \(0.691565\pi\) | |||||||
\(38\) | 2.36824e6 | 0.184247 | ||||||||
\(39\) | −6.30776e6 | −0.436601 | ||||||||
\(40\) | 7.45238e6 | 0.460283 | ||||||||
\(41\) | −2.87518e7 | −1.58905 | −0.794525 | − | 0.607231i | \(-0.792280\pi\) | ||||
−0.794525 | + | 0.607231i | \(0.792280\pi\) | |||||||
\(42\) | 8.53530e6 | 0.423250 | ||||||||
\(43\) | 3.54825e7 | 1.58273 | 0.791363 | − | 0.611347i | \(-0.209372\pi\) | ||||
0.791363 | + | 0.611347i | \(0.209372\pi\) | |||||||
\(44\) | 4.82683e6 | 0.194144 | ||||||||
\(45\) | 2.36187e7 | 0.858617 | ||||||||
\(46\) | −3.07532e7 | −1.01270 | ||||||||
\(47\) | 5.95633e7 | 1.78049 | 0.890243 | − | 0.455485i | \(-0.150534\pi\) | ||||
0.890243 | + | 0.455485i | \(0.150534\pi\) | |||||||
\(48\) | 6.53205e6 | 0.177608 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | −5.79235e6 | −0.131066 | ||||||||
\(51\) | 3.45225e7 | 0.714555 | ||||||||
\(52\) | −7.68602e6 | −0.145776 | ||||||||
\(53\) | 2.31161e6 | 0.0402414 | 0.0201207 | − | 0.999798i | \(-0.493595\pi\) | ||||
0.0201207 | + | 0.999798i | \(0.493595\pi\) | |||||||
\(54\) | 6.43681e7 | 1.03015 | ||||||||
\(55\) | −1.03272e7 | −0.152178 | ||||||||
\(56\) | 2.86290e7 | 0.389010 | ||||||||
\(57\) | 3.82880e7 | 0.480425 | ||||||||
\(58\) | 7.33915e7 | 0.851569 | ||||||||
\(59\) | −1.68651e8 | −1.81198 | −0.905992 | − | 0.423296i | \(-0.860873\pi\) | ||||
−0.905992 | + | 0.423296i | \(0.860873\pi\) | |||||||
\(60\) | 4.37693e7 | 0.436002 | ||||||||
\(61\) | −6.70167e7 | −0.619725 | −0.309863 | − | 0.950781i | \(-0.600283\pi\) | ||||
−0.309863 | + | 0.950781i | \(0.600283\pi\) | |||||||
\(62\) | −6.25819e7 | −0.537881 | ||||||||
\(63\) | 9.07336e7 | 0.725664 | ||||||||
\(64\) | 9.84867e7 | 0.733783 | ||||||||
\(65\) | 1.64446e7 | 0.114265 | ||||||||
\(66\) | −5.87395e7 | −0.381051 | ||||||||
\(67\) | −1.56259e8 | −0.947343 | −0.473671 | − | 0.880702i | \(-0.657072\pi\) | ||||
−0.473671 | + | 0.880702i | \(0.657072\pi\) | |||||||
\(68\) | 4.20657e7 | 0.238582 | ||||||||
\(69\) | −4.97195e8 | −2.64062 | ||||||||
\(70\) | −2.22519e7 | −0.110771 | ||||||||
\(71\) | 6.95067e7 | 0.324612 | 0.162306 | − | 0.986740i | \(-0.448107\pi\) | ||||
0.162306 | + | 0.986740i | \(0.448107\pi\) | |||||||
\(72\) | 4.50599e8 | 1.97603 | ||||||||
\(73\) | −7.83438e7 | −0.322888 | −0.161444 | − | 0.986882i | \(-0.551615\pi\) | ||||
−0.161444 | + | 0.986882i | \(0.551615\pi\) | |||||||
\(74\) | 1.91407e8 | 0.742020 | ||||||||
\(75\) | −9.36465e7 | −0.341756 | ||||||||
\(76\) | 4.66540e7 | 0.160409 | ||||||||
\(77\) | −3.96731e7 | −0.128614 | ||||||||
\(78\) | 9.35342e7 | 0.286118 | ||||||||
\(79\) | −4.26957e8 | −1.23328 | −0.616641 | − | 0.787245i | \(-0.711507\pi\) | ||||
−0.616641 | + | 0.787245i | \(0.711507\pi\) | |||||||
\(80\) | −1.70293e7 | −0.0464828 | ||||||||
\(81\) | 2.96838e8 | 0.766190 | ||||||||
\(82\) | 4.26344e8 | 1.04135 | ||||||||
\(83\) | −5.31242e8 | −1.22869 | −0.614343 | − | 0.789039i | \(-0.710579\pi\) | ||||
−0.614343 | + | 0.789039i | \(0.710579\pi\) | |||||||
\(84\) | 1.68144e8 | 0.368489 | ||||||||
\(85\) | −9.00016e7 | −0.187010 | ||||||||
\(86\) | −5.26149e8 | −1.03721 | ||||||||
\(87\) | 1.18654e9 | 2.22047 | ||||||||
\(88\) | −1.97024e8 | −0.350225 | ||||||||
\(89\) | −1.14168e8 | −0.192881 | −0.0964404 | − | 0.995339i | \(-0.530746\pi\) | ||||
−0.0964404 | + | 0.995339i | \(0.530746\pi\) | |||||||
\(90\) | −3.50228e8 | −0.562678 | ||||||||
\(91\) | 6.31736e7 | 0.0965716 | ||||||||
\(92\) | −6.05833e8 | −0.881674 | ||||||||
\(93\) | −1.01178e9 | −1.40253 | ||||||||
\(94\) | −8.83231e8 | −1.16681 | ||||||||
\(95\) | −9.98185e7 | −0.125735 | ||||||||
\(96\) | 1.36672e9 | 1.64232 | ||||||||
\(97\) | −1.46573e9 | −1.68105 | −0.840524 | − | 0.541774i | \(-0.817753\pi\) | ||||
−0.840524 | + | 0.541774i | \(0.817753\pi\) | |||||||
\(98\) | −8.54829e7 | −0.0936186 | ||||||||
\(99\) | −6.24424e8 | −0.653313 | ||||||||
\(100\) | −1.14108e8 | −0.114108 | ||||||||
\(101\) | 7.53733e8 | 0.720728 | 0.360364 | − | 0.932812i | \(-0.382652\pi\) | ||||
0.360364 | + | 0.932812i | \(0.382652\pi\) | |||||||
\(102\) | −5.11914e8 | −0.468270 | ||||||||
\(103\) | −1.32143e9 | −1.15685 | −0.578425 | − | 0.815736i | \(-0.696332\pi\) | ||||
−0.578425 | + | 0.815736i | \(0.696332\pi\) | |||||||
\(104\) | 3.13732e8 | 0.262971 | ||||||||
\(105\) | −3.59752e8 | −0.288836 | ||||||||
\(106\) | −3.42775e7 | −0.0263714 | ||||||||
\(107\) | 1.07364e9 | 0.791831 | 0.395915 | − | 0.918287i | \(-0.370427\pi\) | ||||
0.395915 | + | 0.918287i | \(0.370427\pi\) | |||||||
\(108\) | 1.26804e9 | 0.896864 | ||||||||
\(109\) | 1.08650e9 | 0.737245 | 0.368623 | − | 0.929579i | \(-0.379830\pi\) | ||||
0.368623 | + | 0.929579i | \(0.379830\pi\) | |||||||
\(110\) | 1.53137e8 | 0.0997268 | ||||||||
\(111\) | 3.09453e9 | 1.93482 | ||||||||
\(112\) | −6.54199e7 | −0.0392852 | ||||||||
\(113\) | 2.85559e9 | 1.64757 | 0.823783 | − | 0.566906i | \(-0.191860\pi\) | ||||
0.823783 | + | 0.566906i | \(0.191860\pi\) | |||||||
\(114\) | −5.67751e8 | −0.314837 | ||||||||
\(115\) | 1.29621e9 | 0.691090 | ||||||||
\(116\) | 1.44580e9 | 0.741392 | ||||||||
\(117\) | 9.94305e8 | 0.490550 | ||||||||
\(118\) | 2.50083e9 | 1.18745 | ||||||||
\(119\) | −3.45750e8 | −0.158052 | ||||||||
\(120\) | −1.78660e9 | −0.786522 | ||||||||
\(121\) | −2.08492e9 | −0.884209 | ||||||||
\(122\) | 9.93753e8 | 0.406125 | ||||||||
\(123\) | 6.89281e9 | 2.71534 | ||||||||
\(124\) | −1.23285e9 | −0.468289 | ||||||||
\(125\) | 2.44141e8 | 0.0894427 | ||||||||
\(126\) | −1.34544e9 | −0.475549 | ||||||||
\(127\) | −3.86082e9 | −1.31693 | −0.658465 | − | 0.752611i | \(-0.728794\pi\) | ||||
−0.658465 | + | 0.752611i | \(0.728794\pi\) | |||||||
\(128\) | 1.45849e9 | 0.480240 | ||||||||
\(129\) | −8.50639e9 | −2.70453 | ||||||||
\(130\) | −2.43848e8 | −0.0748814 | ||||||||
\(131\) | 4.01900e8 | 0.119233 | 0.0596166 | − | 0.998221i | \(-0.481012\pi\) | ||||
0.0596166 | + | 0.998221i | \(0.481012\pi\) | |||||||
\(132\) | −1.15716e9 | −0.331750 | ||||||||
\(133\) | −3.83463e8 | −0.106265 | ||||||||
\(134\) | 2.31707e9 | 0.620822 | ||||||||
\(135\) | −2.71304e9 | −0.702997 | ||||||||
\(136\) | −1.71706e9 | −0.430388 | ||||||||
\(137\) | 3.04172e9 | 0.737695 | 0.368847 | − | 0.929490i | \(-0.379753\pi\) | ||||
0.368847 | + | 0.929490i | \(0.379753\pi\) | |||||||
\(138\) | 7.37262e9 | 1.73048 | ||||||||
\(139\) | 8.36421e8 | 0.190046 | 0.0950229 | − | 0.995475i | \(-0.469708\pi\) | ||||
0.0950229 | + | 0.995475i | \(0.469708\pi\) | |||||||
\(140\) | −4.38359e8 | −0.0964393 | ||||||||
\(141\) | −1.42794e10 | −3.04246 | ||||||||
\(142\) | −1.03068e9 | −0.212728 | ||||||||
\(143\) | −4.34758e8 | −0.0869431 | ||||||||
\(144\) | −1.02966e9 | −0.199555 | ||||||||
\(145\) | −3.09336e9 | −0.581132 | ||||||||
\(146\) | 1.16172e9 | 0.211598 | ||||||||
\(147\) | −1.38202e9 | −0.244111 | ||||||||
\(148\) | 3.77069e9 | 0.646016 | ||||||||
\(149\) | −7.76217e9 | −1.29016 | −0.645082 | − | 0.764114i | \(-0.723177\pi\) | ||||
−0.645082 | + | 0.764114i | \(0.723177\pi\) | |||||||
\(150\) | 1.38863e9 | 0.223963 | ||||||||
\(151\) | 8.38042e9 | 1.31181 | 0.655903 | − | 0.754846i | \(-0.272288\pi\) | ||||
0.655903 | + | 0.754846i | \(0.272288\pi\) | |||||||
\(152\) | −1.90435e9 | −0.289367 | ||||||||
\(153\) | −5.44184e9 | −0.802850 | ||||||||
\(154\) | 5.88290e8 | 0.0842845 | ||||||||
\(155\) | 2.63775e9 | 0.367063 | ||||||||
\(156\) | 1.84261e9 | 0.249099 | ||||||||
\(157\) | −8.49699e9 | −1.11613 | −0.558067 | − | 0.829796i | \(-0.688457\pi\) | ||||
−0.558067 | + | 0.829796i | \(0.688457\pi\) | |||||||
\(158\) | 6.33110e9 | 0.808206 | ||||||||
\(159\) | −5.54173e8 | −0.0687636 | ||||||||
\(160\) | −3.56310e9 | −0.429821 | ||||||||
\(161\) | 4.97952e9 | 0.584078 | ||||||||
\(162\) | −4.40163e9 | −0.502107 | ||||||||
\(163\) | 4.25863e9 | 0.472526 | 0.236263 | − | 0.971689i | \(-0.424077\pi\) | ||||
0.236263 | + | 0.971689i | \(0.424077\pi\) | |||||||
\(164\) | 8.39891e9 | 0.906621 | ||||||||
\(165\) | 2.47580e9 | 0.260039 | ||||||||
\(166\) | 7.87749e9 | 0.805195 | ||||||||
\(167\) | 9.23536e8 | 0.0918818 | 0.0459409 | − | 0.998944i | \(-0.485371\pi\) | ||||
0.0459409 | + | 0.998944i | \(0.485371\pi\) | |||||||
\(168\) | −6.86339e9 | −0.664732 | ||||||||
\(169\) | −9.91221e9 | −0.934717 | ||||||||
\(170\) | 1.33458e9 | 0.122553 | ||||||||
\(171\) | −6.03541e9 | −0.539789 | ||||||||
\(172\) | −1.03651e10 | −0.903012 | ||||||||
\(173\) | −4.76006e9 | −0.404022 | −0.202011 | − | 0.979383i | \(-0.564748\pi\) | ||||
−0.202011 | + | 0.979383i | \(0.564748\pi\) | |||||||
\(174\) | −1.75945e10 | −1.45514 | ||||||||
\(175\) | 9.37891e8 | 0.0755929 | ||||||||
\(176\) | 4.50217e8 | 0.0353683 | ||||||||
\(177\) | 4.04315e10 | 3.09628 | ||||||||
\(178\) | 1.69293e9 | 0.126401 | ||||||||
\(179\) | −9.47187e9 | −0.689599 | −0.344800 | − | 0.938676i | \(-0.612053\pi\) | ||||
−0.344800 | + | 0.938676i | \(0.612053\pi\) | |||||||
\(180\) | −6.89944e9 | −0.489877 | ||||||||
\(181\) | −7.85395e9 | −0.543919 | −0.271960 | − | 0.962309i | \(-0.587672\pi\) | ||||
−0.271960 | + | 0.962309i | \(0.587672\pi\) | |||||||
\(182\) | −9.36766e8 | −0.0632863 | ||||||||
\(183\) | 1.60663e10 | 1.05897 | ||||||||
\(184\) | 2.47292e10 | 1.59049 | ||||||||
\(185\) | −8.06758e9 | −0.506373 | ||||||||
\(186\) | 1.50031e10 | 0.919120 | ||||||||
\(187\) | 2.37944e9 | 0.142294 | ||||||||
\(188\) | −1.73995e10 | −1.01584 | ||||||||
\(189\) | −1.04224e10 | −0.594141 | ||||||||
\(190\) | 1.48015e9 | 0.0823976 | ||||||||
\(191\) | 1.78210e10 | 0.968909 | 0.484454 | − | 0.874817i | \(-0.339018\pi\) | ||||
0.484454 | + | 0.874817i | \(0.339018\pi\) | |||||||
\(192\) | −2.36107e10 | −1.25387 | ||||||||
\(193\) | −1.93101e9 | −0.100179 | −0.0500894 | − | 0.998745i | \(-0.515951\pi\) | ||||
−0.0500894 | + | 0.998745i | \(0.515951\pi\) | |||||||
\(194\) | 2.17344e10 | 1.10164 | ||||||||
\(195\) | −3.94235e9 | −0.195254 | ||||||||
\(196\) | −1.68400e9 | −0.0815061 | ||||||||
\(197\) | 3.24598e10 | 1.53549 | 0.767746 | − | 0.640755i | \(-0.221378\pi\) | ||||
0.767746 | + | 0.640755i | \(0.221378\pi\) | |||||||
\(198\) | 9.25923e9 | 0.428136 | ||||||||
\(199\) | −2.75463e10 | −1.24516 | −0.622578 | − | 0.782558i | \(-0.713915\pi\) | ||||
−0.622578 | + | 0.782558i | \(0.713915\pi\) | |||||||
\(200\) | 4.65773e9 | 0.205845 | ||||||||
\(201\) | 3.74606e10 | 1.61880 | ||||||||
\(202\) | −1.11767e10 | −0.472315 | ||||||||
\(203\) | −1.18835e10 | −0.491146 | ||||||||
\(204\) | −1.00846e10 | −0.407684 | ||||||||
\(205\) | −1.79699e10 | −0.710645 | ||||||||
\(206\) | 1.95947e10 | 0.758118 | ||||||||
\(207\) | 7.83738e10 | 2.96691 | ||||||||
\(208\) | −7.16904e8 | −0.0265568 | ||||||||
\(209\) | 2.63897e9 | 0.0956702 | ||||||||
\(210\) | 5.33456e9 | 0.189283 | ||||||||
\(211\) | 1.94450e10 | 0.675362 | 0.337681 | − | 0.941261i | \(-0.390357\pi\) | ||||
0.337681 | + | 0.941261i | \(0.390357\pi\) | |||||||
\(212\) | −6.75261e8 | −0.0229594 | ||||||||
\(213\) | −1.66632e10 | −0.554690 | ||||||||
\(214\) | −1.59204e10 | −0.518911 | ||||||||
\(215\) | 2.21765e10 | 0.707817 | ||||||||
\(216\) | −5.17595e10 | −1.61789 | ||||||||
\(217\) | 1.01332e10 | 0.310225 | ||||||||
\(218\) | −1.61111e10 | −0.483139 | ||||||||
\(219\) | 1.87818e10 | 0.551744 | ||||||||
\(220\) | 3.01677e9 | 0.0868240 | ||||||||
\(221\) | −3.78891e9 | −0.106844 | ||||||||
\(222\) | −4.58870e10 | −1.26795 | ||||||||
\(223\) | −4.90459e10 | −1.32810 | −0.664050 | − | 0.747688i | \(-0.731164\pi\) | ||||
−0.664050 | + | 0.747688i | \(0.731164\pi\) | |||||||
\(224\) | −1.36880e10 | −0.363265 | ||||||||
\(225\) | 1.47617e10 | 0.383985 | ||||||||
\(226\) | −4.23439e10 | −1.07970 | ||||||||
\(227\) | −6.87990e10 | −1.71975 | −0.859876 | − | 0.510503i | \(-0.829459\pi\) | ||||
−0.859876 | + | 0.510503i | \(0.829459\pi\) | |||||||
\(228\) | −1.11846e10 | −0.274103 | ||||||||
\(229\) | −3.08456e9 | −0.0741198 | −0.0370599 | − | 0.999313i | \(-0.511799\pi\) | ||||
−0.0370599 | + | 0.999313i | \(0.511799\pi\) | |||||||
\(230\) | −1.92207e10 | −0.452892 | ||||||||
\(231\) | 9.51103e9 | 0.219773 | ||||||||
\(232\) | −5.90154e10 | −1.33743 | ||||||||
\(233\) | −1.48643e10 | −0.330402 | −0.165201 | − | 0.986260i | \(-0.552827\pi\) | ||||
−0.165201 | + | 0.986260i | \(0.552827\pi\) | |||||||
\(234\) | −1.47440e10 | −0.321472 | ||||||||
\(235\) | 3.72271e10 | 0.796258 | ||||||||
\(236\) | 4.92659e10 | 1.03381 | ||||||||
\(237\) | 1.02357e11 | 2.10741 | ||||||||
\(238\) | 5.12693e9 | 0.103576 | ||||||||
\(239\) | 4.06416e10 | 0.805713 | 0.402857 | − | 0.915263i | \(-0.368017\pi\) | ||||
0.402857 | + | 0.915263i | \(0.368017\pi\) | |||||||
\(240\) | 4.08253e9 | 0.0794289 | ||||||||
\(241\) | −2.09799e10 | −0.400615 | −0.200308 | − | 0.979733i | \(-0.564194\pi\) | ||||
−0.200308 | + | 0.979733i | \(0.564194\pi\) | |||||||
\(242\) | 3.09161e10 | 0.579449 | ||||||||
\(243\) | 1.42788e10 | 0.262701 | ||||||||
\(244\) | 1.95768e10 | 0.353580 | ||||||||
\(245\) | 3.60300e9 | 0.0638877 | ||||||||
\(246\) | −1.02210e11 | −1.77944 | ||||||||
\(247\) | −4.20218e9 | −0.0718354 | ||||||||
\(248\) | 5.03232e10 | 0.844765 | ||||||||
\(249\) | 1.27357e11 | 2.09955 | ||||||||
\(250\) | −3.62022e9 | −0.0586145 | ||||||||
\(251\) | −9.95566e10 | −1.58321 | −0.791605 | − | 0.611034i | \(-0.790754\pi\) | ||||
−0.791605 | + | 0.611034i | \(0.790754\pi\) | |||||||
\(252\) | −2.65049e10 | −0.414022 | ||||||||
\(253\) | −3.42688e10 | −0.525844 | ||||||||
\(254\) | 5.72499e10 | 0.863024 | ||||||||
\(255\) | 2.15765e10 | 0.319559 | ||||||||
\(256\) | −7.20522e10 | −1.04850 | ||||||||
\(257\) | −1.30781e11 | −1.87002 | −0.935009 | − | 0.354624i | \(-0.884609\pi\) | ||||
−0.935009 | + | 0.354624i | \(0.884609\pi\) | |||||||
\(258\) | 1.26136e11 | 1.77236 | ||||||||
\(259\) | −3.09924e10 | −0.427963 | ||||||||
\(260\) | −4.80376e9 | −0.0651931 | ||||||||
\(261\) | −1.87037e11 | −2.49485 | ||||||||
\(262\) | −5.95954e9 | −0.0781371 | ||||||||
\(263\) | −3.27938e10 | −0.422660 | −0.211330 | − | 0.977415i | \(-0.567779\pi\) | ||||
−0.211330 | + | 0.977415i | \(0.567779\pi\) | |||||||
\(264\) | 4.72335e10 | 0.598456 | ||||||||
\(265\) | 1.44475e9 | 0.0179965 | ||||||||
\(266\) | 5.68615e9 | 0.0696387 | ||||||||
\(267\) | 2.73700e10 | 0.329591 | ||||||||
\(268\) | 4.56459e10 | 0.540499 | ||||||||
\(269\) | 7.47690e9 | 0.0870636 | 0.0435318 | − | 0.999052i | \(-0.486139\pi\) | ||||
0.0435318 | + | 0.999052i | \(0.486139\pi\) | |||||||
\(270\) | 4.02301e10 | 0.460695 | ||||||||
\(271\) | 6.72735e9 | 0.0757674 | 0.0378837 | − | 0.999282i | \(-0.487938\pi\) | ||||
0.0378837 | + | 0.999282i | \(0.487938\pi\) | |||||||
\(272\) | 3.92363e9 | 0.0434638 | ||||||||
\(273\) | −1.51449e10 | −0.165020 | ||||||||
\(274\) | −4.51039e10 | −0.483434 | ||||||||
\(275\) | −6.45452e9 | −0.0680561 | ||||||||
\(276\) | 1.45239e11 | 1.50659 | ||||||||
\(277\) | −1.52676e11 | −1.55815 | −0.779077 | − | 0.626928i | \(-0.784312\pi\) | ||||
−0.779077 | + | 0.626928i | \(0.784312\pi\) | |||||||
\(278\) | −1.24028e10 | −0.124543 | ||||||||
\(279\) | 1.59489e11 | 1.57583 | ||||||||
\(280\) | 1.78932e10 | 0.173971 | ||||||||
\(281\) | 3.09796e10 | 0.296413 | 0.148206 | − | 0.988956i | \(-0.452650\pi\) | ||||
0.148206 | + | 0.988956i | \(0.452650\pi\) | |||||||
\(282\) | 2.11741e11 | 1.99381 | ||||||||
\(283\) | −8.92078e10 | −0.826731 | −0.413365 | − | 0.910565i | \(-0.635647\pi\) | ||||
−0.413365 | + | 0.910565i | \(0.635647\pi\) | |||||||
\(284\) | −2.03041e10 | −0.185205 | ||||||||
\(285\) | 2.39300e10 | 0.214853 | ||||||||
\(286\) | 6.44678e9 | 0.0569765 | ||||||||
\(287\) | −6.90331e10 | −0.600605 | ||||||||
\(288\) | −2.15439e11 | −1.84526 | ||||||||
\(289\) | −9.78512e10 | −0.825136 | ||||||||
\(290\) | 4.58697e10 | 0.380833 | ||||||||
\(291\) | 3.51386e11 | 2.87254 | ||||||||
\(292\) | 2.28856e10 | 0.184221 | ||||||||
\(293\) | 6.30090e10 | 0.499457 | 0.249728 | − | 0.968316i | \(-0.419659\pi\) | ||||
0.249728 | + | 0.968316i | \(0.419659\pi\) | |||||||
\(294\) | 2.04933e10 | 0.159973 | ||||||||
\(295\) | −1.05407e11 | −0.810344 | ||||||||
\(296\) | −1.53914e11 | −1.16537 | ||||||||
\(297\) | 7.17265e10 | 0.534904 | ||||||||
\(298\) | 1.15101e11 | 0.845483 | ||||||||
\(299\) | 5.45681e10 | 0.394838 | ||||||||
\(300\) | 2.73558e10 | 0.194986 | ||||||||
\(301\) | 8.51934e10 | 0.598214 | ||||||||
\(302\) | −1.24268e11 | −0.859665 | ||||||||
\(303\) | −1.80696e11 | −1.23157 | ||||||||
\(304\) | 4.35160e9 | 0.0292225 | ||||||||
\(305\) | −4.18855e10 | −0.277150 | ||||||||
\(306\) | 8.06939e10 | 0.526132 | ||||||||
\(307\) | −1.22461e11 | −0.786821 | −0.393411 | − | 0.919363i | \(-0.628705\pi\) | ||||
−0.393411 | + | 0.919363i | \(0.628705\pi\) | |||||||
\(308\) | 1.15892e10 | 0.0733797 | ||||||||
\(309\) | 3.16793e11 | 1.97680 | ||||||||
\(310\) | −3.91137e10 | −0.240548 | ||||||||
\(311\) | 2.77926e11 | 1.68464 | 0.842321 | − | 0.538975i | \(-0.181188\pi\) | ||||
0.842321 | + | 0.538975i | \(0.181188\pi\) | |||||||
\(312\) | −7.52125e10 | −0.449360 | ||||||||
\(313\) | 1.22493e11 | 0.721374 | 0.360687 | − | 0.932687i | \(-0.382542\pi\) | ||||
0.360687 | + | 0.932687i | \(0.382542\pi\) | |||||||
\(314\) | 1.25997e11 | 0.731436 | ||||||||
\(315\) | 5.67085e10 | 0.324527 | ||||||||
\(316\) | 1.24722e11 | 0.703639 | ||||||||
\(317\) | 2.32000e11 | 1.29039 | 0.645197 | − | 0.764016i | \(-0.276775\pi\) | ||||
0.645197 | + | 0.764016i | \(0.276775\pi\) | |||||||
\(318\) | 8.21752e9 | 0.0450628 | ||||||||
\(319\) | 8.17814e10 | 0.442177 | ||||||||
\(320\) | 6.15542e10 | 0.328158 | ||||||||
\(321\) | −2.57390e11 | −1.35306 | ||||||||
\(322\) | −7.38384e10 | −0.382764 | ||||||||
\(323\) | 2.29986e10 | 0.117568 | ||||||||
\(324\) | −8.67115e10 | −0.437144 | ||||||||
\(325\) | 1.02779e10 | 0.0511009 | ||||||||
\(326\) | −6.31487e10 | −0.309660 | ||||||||
\(327\) | −2.60473e11 | −1.25979 | ||||||||
\(328\) | −3.42831e11 | −1.63549 | ||||||||
\(329\) | 1.43012e11 | 0.672961 | ||||||||
\(330\) | −3.67122e10 | −0.170411 | ||||||||
\(331\) | −3.74253e11 | −1.71372 | −0.856859 | − | 0.515551i | \(-0.827587\pi\) | ||||
−0.856859 | + | 0.515551i | \(0.827587\pi\) | |||||||
\(332\) | 1.55185e11 | 0.701018 | ||||||||
\(333\) | −4.87797e11 | −2.17390 | ||||||||
\(334\) | −1.36946e10 | −0.0602129 | ||||||||
\(335\) | −9.76616e10 | −0.423665 | ||||||||
\(336\) | 1.56834e10 | 0.0671297 | ||||||||
\(337\) | 3.35878e11 | 1.41856 | 0.709280 | − | 0.704927i | \(-0.249020\pi\) | ||||
0.709280 | + | 0.704927i | \(0.249020\pi\) | |||||||
\(338\) | 1.46982e11 | 0.612548 | ||||||||
\(339\) | −6.84585e11 | −2.81533 | ||||||||
\(340\) | 2.62911e10 | 0.106697 | ||||||||
\(341\) | −6.97361e10 | −0.279295 | ||||||||
\(342\) | 8.94956e10 | 0.353740 | ||||||||
\(343\) | 1.38413e10 | 0.0539949 | ||||||||
\(344\) | 4.23086e11 | 1.62898 | ||||||||
\(345\) | −3.10747e11 | −1.18092 | ||||||||
\(346\) | 7.05842e10 | 0.264768 | ||||||||
\(347\) | −3.63698e11 | −1.34666 | −0.673331 | − | 0.739341i | \(-0.735137\pi\) | ||||
−0.673331 | + | 0.739341i | \(0.735137\pi\) | |||||||
\(348\) | −3.46609e11 | −1.26687 | ||||||||
\(349\) | 1.08740e11 | 0.392350 | 0.196175 | − | 0.980569i | \(-0.437148\pi\) | ||||
0.196175 | + | 0.980569i | \(0.437148\pi\) | |||||||
\(350\) | −1.39074e10 | −0.0495383 | ||||||||
\(351\) | −1.14214e11 | −0.401640 | ||||||||
\(352\) | 9.42002e10 | 0.327047 | ||||||||
\(353\) | −3.36249e11 | −1.15259 | −0.576296 | − | 0.817241i | \(-0.695502\pi\) | ||||
−0.576296 | + | 0.817241i | \(0.695502\pi\) | |||||||
\(354\) | −5.99535e11 | −2.02908 | ||||||||
\(355\) | 4.34417e10 | 0.145171 | ||||||||
\(356\) | 3.33505e10 | 0.110047 | ||||||||
\(357\) | 8.28884e10 | 0.270077 | ||||||||
\(358\) | 1.40453e11 | 0.451915 | ||||||||
\(359\) | 5.49944e11 | 1.74741 | 0.873703 | − | 0.486460i | \(-0.161712\pi\) | ||||
0.873703 | + | 0.486460i | \(0.161712\pi\) | |||||||
\(360\) | 2.81625e11 | 0.883709 | ||||||||
\(361\) | −2.97181e11 | −0.920954 | ||||||||
\(362\) | 1.16462e11 | 0.356447 | ||||||||
\(363\) | 4.99828e11 | 1.51092 | ||||||||
\(364\) | −1.84541e10 | −0.0550982 | ||||||||
\(365\) | −4.89649e10 | −0.144400 | ||||||||
\(366\) | −2.38237e11 | −0.693977 | ||||||||
\(367\) | −1.32204e11 | −0.380405 | −0.190203 | − | 0.981745i | \(-0.560914\pi\) | ||||
−0.190203 | + | 0.981745i | \(0.560914\pi\) | |||||||
\(368\) | −5.65084e10 | −0.160619 | ||||||||
\(369\) | −1.08653e12 | −3.05086 | ||||||||
\(370\) | 1.19630e11 | 0.331841 | ||||||||
\(371\) | 5.55017e9 | 0.0152098 | ||||||||
\(372\) | 2.95558e11 | 0.800203 | ||||||||
\(373\) | 4.88064e11 | 1.30553 | 0.652765 | − | 0.757560i | \(-0.273609\pi\) | ||||
0.652765 | + | 0.757560i | \(0.273609\pi\) | |||||||
\(374\) | −3.52833e10 | −0.0932496 | ||||||||
\(375\) | −5.85291e10 | −0.152838 | ||||||||
\(376\) | 7.10222e11 | 1.83252 | ||||||||
\(377\) | −1.30225e11 | −0.332015 | ||||||||
\(378\) | 1.54548e11 | 0.389359 | ||||||||
\(379\) | 3.00162e11 | 0.747274 | 0.373637 | − | 0.927575i | \(-0.378111\pi\) | ||||
0.373637 | + | 0.927575i | \(0.378111\pi\) | |||||||
\(380\) | 2.91587e10 | 0.0717369 | ||||||||
\(381\) | 9.25574e11 | 2.25034 | ||||||||
\(382\) | −2.64258e11 | −0.634955 | ||||||||
\(383\) | 7.74202e11 | 1.83848 | 0.919241 | − | 0.393694i | \(-0.128803\pi\) | ||||
0.919241 | + | 0.393694i | \(0.128803\pi\) | |||||||
\(384\) | −3.49651e11 | −0.820623 | ||||||||
\(385\) | −2.47957e10 | −0.0575179 | ||||||||
\(386\) | 2.86338e10 | 0.0656501 | ||||||||
\(387\) | 1.34088e12 | 3.03872 | ||||||||
\(388\) | 4.28165e11 | 0.959109 | ||||||||
\(389\) | −1.70127e11 | −0.376703 | −0.188352 | − | 0.982102i | \(-0.560314\pi\) | ||||
−0.188352 | + | 0.982102i | \(0.560314\pi\) | |||||||
\(390\) | 5.84589e10 | 0.127956 | ||||||||
\(391\) | −2.98652e11 | −0.646204 | ||||||||
\(392\) | 6.87383e10 | 0.147032 | ||||||||
\(393\) | −9.63495e10 | −0.203743 | ||||||||
\(394\) | −4.81327e11 | −1.00625 | ||||||||
\(395\) | −2.66848e11 | −0.551540 | ||||||||
\(396\) | 1.82405e11 | 0.372743 | ||||||||
\(397\) | −5.47242e11 | −1.10566 | −0.552831 | − | 0.833293i | \(-0.686452\pi\) | ||||
−0.552831 | + | 0.833293i | \(0.686452\pi\) | |||||||
\(398\) | 4.08468e11 | 0.815988 | ||||||||
\(399\) | 9.19294e10 | 0.181584 | ||||||||
\(400\) | −1.06433e10 | −0.0207878 | ||||||||
\(401\) | −4.57174e11 | −0.882941 | −0.441471 | − | 0.897276i | \(-0.645543\pi\) | ||||
−0.441471 | + | 0.897276i | \(0.645543\pi\) | |||||||
\(402\) | −5.55483e11 | −1.06085 | ||||||||
\(403\) | 1.11045e11 | 0.209713 | ||||||||
\(404\) | −2.20179e11 | −0.411206 | ||||||||
\(405\) | 1.85523e11 | 0.342650 | ||||||||
\(406\) | 1.76213e11 | 0.321863 | ||||||||
\(407\) | 2.13288e11 | 0.385294 | ||||||||
\(408\) | 4.11639e11 | 0.735437 | ||||||||
\(409\) | 9.42996e10 | 0.166631 | 0.0833153 | − | 0.996523i | \(-0.473449\pi\) | ||||
0.0833153 | + | 0.996523i | \(0.473449\pi\) | |||||||
\(410\) | 2.66465e11 | 0.465707 | ||||||||
\(411\) | −7.29207e11 | −1.26056 | ||||||||
\(412\) | 3.86013e11 | 0.660032 | ||||||||
\(413\) | −4.04930e11 | −0.684865 | ||||||||
\(414\) | −1.16216e12 | −1.94431 | ||||||||
\(415\) | −3.32026e11 | −0.549485 | ||||||||
\(416\) | −1.50000e11 | −0.245568 | ||||||||
\(417\) | −2.00519e11 | −0.324746 | ||||||||
\(418\) | −3.91318e10 | −0.0626955 | ||||||||
\(419\) | 1.66874e11 | 0.264500 | 0.132250 | − | 0.991216i | \(-0.457780\pi\) | ||||
0.132250 | + | 0.991216i | \(0.457780\pi\) | |||||||
\(420\) | 1.05090e11 | 0.164793 | ||||||||
\(421\) | −5.52779e11 | −0.857594 | −0.428797 | − | 0.903401i | \(-0.641062\pi\) | ||||
−0.428797 | + | 0.903401i | \(0.641062\pi\) | |||||||
\(422\) | −2.88339e11 | −0.442585 | ||||||||
\(423\) | 2.25089e12 | 3.41840 | ||||||||
\(424\) | 2.75631e10 | 0.0414174 | ||||||||
\(425\) | −5.62510e10 | −0.0836334 | ||||||||
\(426\) | 2.47089e11 | 0.363505 | ||||||||
\(427\) | −1.60907e11 | −0.234234 | ||||||||
\(428\) | −3.13630e11 | −0.451773 | ||||||||
\(429\) | 1.04227e11 | 0.148567 | ||||||||
\(430\) | −3.28843e11 | −0.463853 | ||||||||
\(431\) | −4.37408e11 | −0.610575 | −0.305288 | − | 0.952260i | \(-0.598753\pi\) | ||||
−0.305288 | + | 0.952260i | \(0.598753\pi\) | |||||||
\(432\) | 1.18275e11 | 0.163387 | ||||||||
\(433\) | 2.79837e11 | 0.382569 | 0.191285 | − | 0.981535i | \(-0.438735\pi\) | ||||
0.191285 | + | 0.981535i | \(0.438735\pi\) | |||||||
\(434\) | −1.50259e11 | −0.203300 | ||||||||
\(435\) | 7.41587e11 | 0.993026 | ||||||||
\(436\) | −3.17387e11 | −0.420630 | ||||||||
\(437\) | −3.31227e11 | −0.434470 | ||||||||
\(438\) | −2.78504e11 | −0.361575 | ||||||||
\(439\) | 8.87150e11 | 1.14000 | 0.570002 | − | 0.821643i | \(-0.306942\pi\) | ||||
0.570002 | + | 0.821643i | \(0.306942\pi\) | |||||||
\(440\) | −1.23140e11 | −0.156625 | ||||||||
\(441\) | 2.17851e11 | 0.274275 | ||||||||
\(442\) | 5.61835e10 | 0.0700178 | ||||||||
\(443\) | −5.87852e11 | −0.725189 | −0.362594 | − | 0.931947i | \(-0.618109\pi\) | ||||
−0.362594 | + | 0.931947i | \(0.618109\pi\) | |||||||
\(444\) | −9.03967e11 | −1.10390 | ||||||||
\(445\) | −7.13549e10 | −0.0862589 | ||||||||
\(446\) | 7.27274e11 | 0.870344 | ||||||||
\(447\) | 1.86086e12 | 2.20460 | ||||||||
\(448\) | 2.36466e11 | 0.277344 | ||||||||
\(449\) | −5.19918e11 | −0.603707 | −0.301854 | − | 0.953354i | \(-0.597605\pi\) | ||||
−0.301854 | + | 0.953354i | \(0.597605\pi\) | |||||||
\(450\) | −2.18892e11 | −0.251637 | ||||||||
\(451\) | 4.75082e11 | 0.540723 | ||||||||
\(452\) | −8.34168e11 | −0.940006 | ||||||||
\(453\) | −2.00908e12 | −2.24159 | ||||||||
\(454\) | 1.02018e12 | 1.12701 | ||||||||
\(455\) | 3.94835e10 | 0.0431881 | ||||||||
\(456\) | 4.56538e11 | 0.494465 | ||||||||
\(457\) | −1.03055e12 | −1.10521 | −0.552607 | − | 0.833442i | \(-0.686367\pi\) | ||||
−0.552607 | + | 0.833442i | \(0.686367\pi\) | |||||||
\(458\) | 4.57392e10 | 0.0485729 | ||||||||
\(459\) | 6.25095e11 | 0.657338 | ||||||||
\(460\) | −3.78646e11 | −0.394296 | ||||||||
\(461\) | 9.37018e11 | 0.966259 | 0.483130 | − | 0.875549i | \(-0.339500\pi\) | ||||
0.483130 | + | 0.875549i | \(0.339500\pi\) | |||||||
\(462\) | −1.41034e11 | −0.144024 | ||||||||
\(463\) | 1.08281e12 | 1.09506 | 0.547529 | − | 0.836787i | \(-0.315569\pi\) | ||||
0.547529 | + | 0.836787i | \(0.315569\pi\) | |||||||
\(464\) | 1.34855e11 | 0.135063 | ||||||||
\(465\) | −6.32361e11 | −0.627230 | ||||||||
\(466\) | 2.20414e11 | 0.216522 | ||||||||
\(467\) | 1.52419e11 | 0.148290 | 0.0741451 | − | 0.997247i | \(-0.476377\pi\) | ||||
0.0741451 | + | 0.997247i | \(0.476377\pi\) | |||||||
\(468\) | −2.90454e11 | −0.279879 | ||||||||
\(469\) | −3.75177e11 | −0.358062 | ||||||||
\(470\) | −5.52019e11 | −0.521812 | ||||||||
\(471\) | 2.03703e12 | 1.90723 | ||||||||
\(472\) | −2.01096e12 | −1.86494 | ||||||||
\(473\) | −5.86297e11 | −0.538570 | ||||||||
\(474\) | −1.51779e12 | −1.38105 | ||||||||
\(475\) | −6.23865e10 | −0.0562302 | ||||||||
\(476\) | 1.01000e11 | 0.0901756 | ||||||||
\(477\) | 8.73554e10 | 0.0772604 | ||||||||
\(478\) | −6.02652e11 | −0.528008 | ||||||||
\(479\) | −2.02244e11 | −0.175535 | −0.0877677 | − | 0.996141i | \(-0.527973\pi\) | ||||
−0.0877677 | + | 0.996141i | \(0.527973\pi\) | |||||||
\(480\) | 8.54200e11 | 0.734470 | ||||||||
\(481\) | −3.39631e11 | −0.289304 | ||||||||
\(482\) | 3.11099e11 | 0.262535 | ||||||||
\(483\) | −1.19376e12 | −0.998060 | ||||||||
\(484\) | 6.09042e11 | 0.504479 | ||||||||
\(485\) | −9.16079e11 | −0.751788 | ||||||||
\(486\) | −2.11732e11 | −0.172156 | ||||||||
\(487\) | 8.35572e11 | 0.673137 | 0.336568 | − | 0.941659i | \(-0.390734\pi\) | ||||
0.336568 | + | 0.941659i | \(0.390734\pi\) | |||||||
\(488\) | −7.99094e11 | −0.637836 | ||||||||
\(489\) | −1.02094e12 | −0.807442 | ||||||||
\(490\) | −5.34268e10 | −0.0418675 | ||||||||
\(491\) | −1.06242e12 | −0.824953 | −0.412476 | − | 0.910968i | \(-0.635336\pi\) | ||||
−0.412476 | + | 0.910968i | \(0.635336\pi\) | |||||||
\(492\) | −2.01351e12 | −1.54921 | ||||||||
\(493\) | 7.12723e11 | 0.543387 | ||||||||
\(494\) | 6.23117e10 | 0.0470759 | ||||||||
\(495\) | −3.90265e11 | −0.292170 | ||||||||
\(496\) | −1.14993e11 | −0.0853108 | ||||||||
\(497\) | 1.66886e11 | 0.122692 | ||||||||
\(498\) | −1.88851e12 | −1.37590 | ||||||||
\(499\) | −3.33938e11 | −0.241109 | −0.120554 | − | 0.992707i | \(-0.538467\pi\) | ||||
−0.120554 | + | 0.992707i | \(0.538467\pi\) | |||||||
\(500\) | −7.13178e10 | −0.0510309 | ||||||||
\(501\) | −2.21404e11 | −0.157006 | ||||||||
\(502\) | 1.47627e12 | 1.03752 | ||||||||
\(503\) | −3.60934e11 | −0.251404 | −0.125702 | − | 0.992068i | \(-0.540118\pi\) | ||||
−0.125702 | + | 0.992068i | \(0.540118\pi\) | |||||||
\(504\) | 1.08189e12 | 0.746870 | ||||||||
\(505\) | 4.71083e11 | 0.322319 | ||||||||
\(506\) | 5.08152e11 | 0.344601 | ||||||||
\(507\) | 2.37630e12 | 1.59723 | ||||||||
\(508\) | 1.12781e12 | 0.751365 | ||||||||
\(509\) | 4.09926e11 | 0.270692 | 0.135346 | − | 0.990798i | \(-0.456785\pi\) | ||||
0.135346 | + | 0.990798i | \(0.456785\pi\) | |||||||
\(510\) | −3.19946e11 | −0.209417 | ||||||||
\(511\) | −1.88104e11 | −0.122040 | ||||||||
\(512\) | 3.21676e11 | 0.206873 | ||||||||
\(513\) | 6.93277e11 | 0.441955 | ||||||||
\(514\) | 1.93928e12 | 1.22548 | ||||||||
\(515\) | −8.25894e11 | −0.517359 | ||||||||
\(516\) | 2.48487e12 | 1.54305 | ||||||||
\(517\) | −9.84199e11 | −0.605865 | ||||||||
\(518\) | 4.59569e11 | 0.280457 | ||||||||
\(519\) | 1.14115e12 | 0.690384 | ||||||||
\(520\) | 1.96082e11 | 0.117604 | ||||||||
\(521\) | −1.09884e12 | −0.653377 | −0.326688 | − | 0.945132i | \(-0.605933\pi\) | ||||
−0.326688 | + | 0.945132i | \(0.605933\pi\) | |||||||
\(522\) | 2.77346e12 | 1.63495 | ||||||||
\(523\) | 2.97552e12 | 1.73902 | 0.869511 | − | 0.493914i | \(-0.164434\pi\) | ||||
0.869511 | + | 0.493914i | \(0.164434\pi\) | |||||||
\(524\) | −1.17402e11 | −0.0680276 | ||||||||
\(525\) | −2.24845e11 | −0.129172 | ||||||||
\(526\) | 4.86280e11 | 0.276982 | ||||||||
\(527\) | −6.07748e11 | −0.343223 | ||||||||
\(528\) | −1.07933e11 | −0.0604367 | ||||||||
\(529\) | 2.50005e12 | 1.38803 | ||||||||
\(530\) | −2.14234e10 | −0.0117936 | ||||||||
\(531\) | −6.37329e12 | −3.47887 | ||||||||
\(532\) | 1.12016e11 | 0.0606288 | ||||||||
\(533\) | −7.56500e11 | −0.406010 | ||||||||
\(534\) | −4.05855e11 | −0.215991 | ||||||||
\(535\) | 6.71026e11 | 0.354118 | ||||||||
\(536\) | −1.86320e12 | −0.975028 | ||||||||
\(537\) | 2.27074e12 | 1.17837 | ||||||||
\(538\) | −1.10871e11 | −0.0570554 | ||||||||
\(539\) | −9.52551e10 | −0.0486115 | ||||||||
\(540\) | 7.92526e11 | 0.401090 | ||||||||
\(541\) | 2.97095e12 | 1.49110 | 0.745551 | − | 0.666449i | \(-0.232187\pi\) | ||||
0.745551 | + | 0.666449i | \(0.232187\pi\) | |||||||
\(542\) | −9.97561e10 | −0.0496527 | ||||||||
\(543\) | 1.88287e12 | 0.929438 | ||||||||
\(544\) | 8.20952e11 | 0.401904 | ||||||||
\(545\) | 6.79065e11 | 0.329706 | ||||||||
\(546\) | 2.24576e11 | 0.108142 | ||||||||
\(547\) | −1.50514e12 | −0.718842 | −0.359421 | − | 0.933176i | \(-0.617026\pi\) | ||||
−0.359421 | + | 0.933176i | \(0.617026\pi\) | |||||||
\(548\) | −8.88540e11 | −0.420886 | ||||||||
\(549\) | −2.53256e12 | −1.18983 | ||||||||
\(550\) | 9.57104e10 | 0.0445992 | ||||||||
\(551\) | 7.90463e11 | 0.365342 | ||||||||
\(552\) | −5.92845e12 | −2.71779 | ||||||||
\(553\) | −1.02512e12 | −0.466136 | ||||||||
\(554\) | 2.26394e12 | 1.02111 | ||||||||
\(555\) | 1.93408e12 | 0.865279 | ||||||||
\(556\) | −2.44333e11 | −0.108429 | ||||||||
\(557\) | −2.17354e12 | −0.956797 | −0.478399 | − | 0.878143i | \(-0.658783\pi\) | ||||
−0.478399 | + | 0.878143i | \(0.658783\pi\) | |||||||
\(558\) | −2.36496e12 | −1.03269 | ||||||||
\(559\) | 9.33593e11 | 0.404394 | ||||||||
\(560\) | −4.08874e10 | −0.0175689 | ||||||||
\(561\) | −5.70434e11 | −0.243149 | ||||||||
\(562\) | −4.59379e11 | −0.194248 | ||||||||
\(563\) | 1.40104e12 | 0.587710 | 0.293855 | − | 0.955850i | \(-0.405062\pi\) | ||||
0.293855 | + | 0.955850i | \(0.405062\pi\) | |||||||
\(564\) | 4.17127e12 | 1.73585 | ||||||||
\(565\) | 1.78474e12 | 0.736814 | ||||||||
\(566\) | 1.32281e12 | 0.541781 | ||||||||
\(567\) | 7.12707e11 | 0.289592 | ||||||||
\(568\) | 8.28784e11 | 0.334098 | ||||||||
\(569\) | −1.81226e12 | −0.724795 | −0.362397 | − | 0.932024i | \(-0.618042\pi\) | ||||
−0.362397 | + | 0.932024i | \(0.618042\pi\) | |||||||
\(570\) | −3.54844e11 | −0.140799 | ||||||||
\(571\) | −3.38885e12 | −1.33410 | −0.667052 | − | 0.745012i | \(-0.732444\pi\) | ||||
−0.667052 | + | 0.745012i | \(0.732444\pi\) | |||||||
\(572\) | 1.27001e11 | 0.0496048 | ||||||||
\(573\) | −4.27233e12 | −1.65565 | ||||||||
\(574\) | 1.02365e12 | 0.393594 | ||||||||
\(575\) | 8.10131e11 | 0.309065 | ||||||||
\(576\) | 3.72180e12 | 1.40881 | ||||||||
\(577\) | 2.86129e12 | 1.07466 | 0.537329 | − | 0.843373i | \(-0.319433\pi\) | ||||
0.537329 | + | 0.843373i | \(0.319433\pi\) | |||||||
\(578\) | 1.45098e12 | 0.540737 | ||||||||
\(579\) | 4.62930e11 | 0.171183 | ||||||||
\(580\) | 9.03626e11 | 0.331560 | ||||||||
\(581\) | −1.27551e12 | −0.464400 | ||||||||
\(582\) | −5.21050e12 | −1.88246 | ||||||||
\(583\) | −3.81960e10 | −0.0136933 | ||||||||
\(584\) | −9.34156e11 | −0.332324 | ||||||||
\(585\) | 6.21440e11 | 0.219381 | ||||||||
\(586\) | −9.34324e11 | −0.327309 | ||||||||
\(587\) | −7.85729e11 | −0.273150 | −0.136575 | − | 0.990630i | \(-0.543609\pi\) | ||||
−0.136575 | + | 0.990630i | \(0.543609\pi\) | |||||||
\(588\) | 4.03714e11 | 0.139276 | ||||||||
\(589\) | −6.74039e11 | −0.230763 | ||||||||
\(590\) | 1.56302e12 | 0.531043 | ||||||||
\(591\) | −7.78174e12 | −2.62382 | ||||||||
\(592\) | 3.51707e11 | 0.117688 | ||||||||
\(593\) | 8.24271e11 | 0.273731 | 0.136865 | − | 0.990590i | \(-0.456297\pi\) | ||||
0.136865 | + | 0.990590i | \(0.456297\pi\) | |||||||
\(594\) | −1.06359e12 | −0.350538 | ||||||||
\(595\) | −2.16094e11 | −0.0706831 | ||||||||
\(596\) | 2.26747e12 | 0.736093 | ||||||||
\(597\) | 6.60380e12 | 2.12770 | ||||||||
\(598\) | −8.09159e11 | −0.258749 | ||||||||
\(599\) | −2.60594e10 | −0.00827073 | −0.00413537 | − | 0.999991i | \(-0.501316\pi\) | ||||
−0.00413537 | + | 0.999991i | \(0.501316\pi\) | |||||||
\(600\) | −1.11662e12 | −0.351743 | ||||||||
\(601\) | 1.90372e11 | 0.0595207 | 0.0297603 | − | 0.999557i | \(-0.490526\pi\) | ||||
0.0297603 | + | 0.999557i | \(0.490526\pi\) | |||||||
\(602\) | −1.26328e12 | −0.392028 | ||||||||
\(603\) | −5.90499e12 | −1.81883 | ||||||||
\(604\) | −2.44807e12 | −0.748441 | ||||||||
\(605\) | −1.30307e12 | −0.395430 | ||||||||
\(606\) | 2.67944e12 | 0.807082 | ||||||||
\(607\) | 1.77675e12 | 0.531222 | 0.265611 | − | 0.964080i | \(-0.414426\pi\) | ||||
0.265611 | + | 0.964080i | \(0.414426\pi\) | |||||||
\(608\) | 9.10497e11 | 0.270217 | ||||||||
\(609\) | 2.84888e12 | 0.839260 | ||||||||
\(610\) | 6.21096e11 | 0.181624 | ||||||||
\(611\) | 1.56719e12 | 0.454922 | ||||||||
\(612\) | 1.58966e12 | 0.458060 | ||||||||
\(613\) | −2.48518e11 | −0.0710863 | −0.0355431 | − | 0.999368i | \(-0.511316\pi\) | ||||
−0.0355431 | + | 0.999368i | \(0.511316\pi\) | |||||||
\(614\) | 1.81591e12 | 0.515628 | ||||||||
\(615\) | 4.30801e12 | 1.21434 | ||||||||
\(616\) | −4.73054e11 | −0.132372 | ||||||||
\(617\) | 3.52347e12 | 0.978786 | 0.489393 | − | 0.872063i | \(-0.337218\pi\) | ||||
0.489393 | + | 0.872063i | \(0.337218\pi\) | |||||||
\(618\) | −4.69755e12 | −1.29546 | ||||||||
\(619\) | −6.69712e12 | −1.83350 | −0.916748 | − | 0.399466i | \(-0.869196\pi\) | ||||
−0.916748 | + | 0.399466i | \(0.869196\pi\) | |||||||
\(620\) | −7.70534e11 | −0.209425 | ||||||||
\(621\) | −9.00266e12 | −2.42917 | ||||||||
\(622\) | −4.12121e12 | −1.10400 | ||||||||
\(623\) | −2.74117e11 | −0.0729021 | ||||||||
\(624\) | 1.71867e11 | 0.0453798 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | −1.81637e12 | −0.472738 | ||||||||
\(627\) | −6.32654e11 | −0.163479 | ||||||||
\(628\) | 2.48212e12 | 0.636802 | ||||||||
\(629\) | 1.85880e12 | 0.473484 | ||||||||
\(630\) | −8.40897e11 | −0.212672 | ||||||||
\(631\) | 6.29917e11 | 0.158180 | 0.0790900 | − | 0.996867i | \(-0.474799\pi\) | ||||
0.0790900 | + | 0.996867i | \(0.474799\pi\) | |||||||
\(632\) | −5.09095e12 | −1.26932 | ||||||||
\(633\) | −4.66165e12 | −1.15404 | ||||||||
\(634\) | −3.44020e12 | −0.845634 | ||||||||
\(635\) | −2.41301e12 | −0.588949 | ||||||||
\(636\) | 1.61884e11 | 0.0392325 | ||||||||
\(637\) | 1.51680e11 | 0.0365006 | ||||||||
\(638\) | −1.21269e12 | −0.289772 | ||||||||
\(639\) | 2.62665e12 | 0.623231 | ||||||||
\(640\) | 9.11555e11 | 0.214770 | ||||||||
\(641\) | 2.82049e12 | 0.659877 | 0.329938 | − | 0.944002i | \(-0.392972\pi\) | ||||
0.329938 | + | 0.944002i | \(0.392972\pi\) | |||||||
\(642\) | 3.81668e12 | 0.886704 | ||||||||
\(643\) | 7.19804e12 | 1.66060 | 0.830300 | − | 0.557317i | \(-0.188169\pi\) | ||||
0.830300 | + | 0.557317i | \(0.188169\pi\) | |||||||
\(644\) | −1.45461e12 | −0.333241 | ||||||||
\(645\) | −5.31649e12 | −1.20950 | ||||||||
\(646\) | −3.41033e11 | −0.0770459 | ||||||||
\(647\) | 7.17803e12 | 1.61041 | 0.805204 | − | 0.592998i | \(-0.202056\pi\) | ||||
0.805204 | + | 0.592998i | \(0.202056\pi\) | |||||||
\(648\) | 3.53943e12 | 0.788580 | ||||||||
\(649\) | 2.78671e12 | 0.616582 | ||||||||
\(650\) | −1.52405e11 | −0.0334880 | ||||||||
\(651\) | −2.42928e12 | −0.530106 | ||||||||
\(652\) | −1.24402e12 | −0.269596 | ||||||||
\(653\) | −1.54599e12 | −0.332734 | −0.166367 | − | 0.986064i | \(-0.553204\pi\) | ||||
−0.166367 | + | 0.986064i | \(0.553204\pi\) | |||||||
\(654\) | 3.86240e12 | 0.825578 | ||||||||
\(655\) | 2.51187e11 | 0.0533227 | ||||||||
\(656\) | 7.83398e11 | 0.165164 | ||||||||
\(657\) | −2.96061e12 | −0.619921 | ||||||||
\(658\) | −2.12064e12 | −0.441011 | ||||||||
\(659\) | 2.38624e12 | 0.492868 | 0.246434 | − | 0.969160i | \(-0.420741\pi\) | ||||
0.246434 | + | 0.969160i | \(0.420741\pi\) | |||||||
\(660\) | −7.23225e11 | −0.148363 | ||||||||
\(661\) | −2.35488e12 | −0.479802 | −0.239901 | − | 0.970797i | \(-0.577115\pi\) | ||||
−0.239901 | + | 0.970797i | \(0.577115\pi\) | |||||||
\(662\) | 5.54958e12 | 1.12305 | ||||||||
\(663\) | 9.08333e11 | 0.182572 | ||||||||
\(664\) | −6.33443e12 | −1.26459 | ||||||||
\(665\) | −2.39664e11 | −0.0475232 | ||||||||
\(666\) | 7.23326e12 | 1.42462 | ||||||||
\(667\) | −1.02647e13 | −2.00807 | ||||||||
\(668\) | −2.69781e11 | −0.0524225 | ||||||||
\(669\) | 1.17580e13 | 2.26943 | ||||||||
\(670\) | 1.44817e12 | 0.277640 | ||||||||
\(671\) | 1.10736e12 | 0.210880 | ||||||||
\(672\) | 3.28149e12 | 0.620740 | ||||||||
\(673\) | −6.32709e12 | −1.18887 | −0.594437 | − | 0.804142i | \(-0.702625\pi\) | ||||
−0.594437 | + | 0.804142i | \(0.702625\pi\) | |||||||
\(674\) | −4.98055e12 | −0.929625 | ||||||||
\(675\) | −1.69565e12 | −0.314390 | ||||||||
\(676\) | 2.89553e12 | 0.533296 | ||||||||
\(677\) | 3.16670e12 | 0.579372 | 0.289686 | − | 0.957122i | \(-0.406449\pi\) | ||||
0.289686 | + | 0.957122i | \(0.406449\pi\) | |||||||
\(678\) | 1.01513e13 | 1.84497 | ||||||||
\(679\) | −3.51921e12 | −0.635376 | ||||||||
\(680\) | −1.07316e12 | −0.192475 | ||||||||
\(681\) | 1.64935e13 | 2.93868 | ||||||||
\(682\) | 1.03408e12 | 0.183030 | ||||||||
\(683\) | −6.06916e12 | −1.06717 | −0.533587 | − | 0.845745i | \(-0.679156\pi\) | ||||
−0.533587 | + | 0.845745i | \(0.679156\pi\) | |||||||
\(684\) | 1.76305e12 | 0.307973 | ||||||||
\(685\) | 1.90107e12 | 0.329907 | ||||||||
\(686\) | −2.05245e11 | −0.0353845 | ||||||||
\(687\) | 7.39478e11 | 0.126654 | ||||||||
\(688\) | −9.66788e11 | −0.164507 | ||||||||
\(689\) | 6.08216e10 | 0.0102818 | ||||||||
\(690\) | 4.60789e12 | 0.773893 | ||||||||
\(691\) | −1.36410e12 | −0.227611 | −0.113806 | − | 0.993503i | \(-0.536304\pi\) | ||||
−0.113806 | + | 0.993503i | \(0.536304\pi\) | |||||||
\(692\) | 1.39050e12 | 0.230512 | ||||||||
\(693\) | −1.49924e12 | −0.246929 | ||||||||
\(694\) | 5.39307e12 | 0.882508 | ||||||||
\(695\) | 5.22763e11 | 0.0849911 | ||||||||
\(696\) | 1.41481e13 | 2.28536 | ||||||||
\(697\) | 4.14033e12 | 0.664489 | ||||||||
\(698\) | −1.61244e12 | −0.257119 | ||||||||
\(699\) | 3.56349e12 | 0.564584 | ||||||||
\(700\) | −2.73974e11 | −0.0431290 | ||||||||
\(701\) | 4.27032e12 | 0.667927 | 0.333964 | − | 0.942586i | \(-0.391614\pi\) | ||||
0.333964 | + | 0.942586i | \(0.391614\pi\) | |||||||
\(702\) | 1.69361e12 | 0.263207 | ||||||||
\(703\) | 2.06155e12 | 0.318343 | ||||||||
\(704\) | −1.62735e12 | −0.249692 | ||||||||
\(705\) | −8.92464e12 | −1.36063 | ||||||||
\(706\) | 4.98605e12 | 0.755328 | ||||||||
\(707\) | 1.80971e12 | 0.272410 | ||||||||
\(708\) | −1.18108e13 | −1.76656 | ||||||||
\(709\) | 4.76449e12 | 0.708122 | 0.354061 | − | 0.935222i | \(-0.384800\pi\) | ||||
0.354061 | + | 0.935222i | \(0.384800\pi\) | |||||||
\(710\) | −6.44172e11 | −0.0951348 | ||||||||
\(711\) | −1.61347e13 | −2.36781 | ||||||||
\(712\) | −1.36132e12 | −0.198517 | ||||||||
\(713\) | 8.75284e12 | 1.26837 | ||||||||
\(714\) | −1.22910e12 | −0.176989 | ||||||||
\(715\) | −2.71724e11 | −0.0388822 | ||||||||
\(716\) | 2.76690e12 | 0.393446 | ||||||||
\(717\) | −9.74323e12 | −1.37679 | ||||||||
\(718\) | −8.15481e12 | −1.14513 | ||||||||
\(719\) | −2.64192e12 | −0.368671 | −0.184336 | − | 0.982863i | \(-0.559013\pi\) | ||||
−0.184336 | + | 0.982863i | \(0.559013\pi\) | |||||||
\(720\) | −6.43537e11 | −0.0892436 | ||||||||
\(721\) | −3.17276e12 | −0.437248 | ||||||||
\(722\) | 4.40672e12 | 0.603529 | ||||||||
\(723\) | 5.02963e12 | 0.684563 | ||||||||
\(724\) | 2.29428e12 | 0.310329 | ||||||||
\(725\) | −1.93335e12 | −0.259890 | ||||||||
\(726\) | −7.41167e12 | −0.990150 | ||||||||
\(727\) | −3.54861e12 | −0.471144 | −0.235572 | − | 0.971857i | \(-0.575696\pi\) | ||||
−0.235572 | + | 0.971857i | \(0.575696\pi\) | |||||||
\(728\) | 7.53270e11 | 0.0993938 | ||||||||
\(729\) | −9.26577e12 | −1.21509 | ||||||||
\(730\) | 7.26072e11 | 0.0946296 | ||||||||
\(731\) | −5.10956e12 | −0.661844 | ||||||||
\(732\) | −4.69324e12 | −0.604189 | ||||||||
\(733\) | −1.34909e13 | −1.72613 | −0.863063 | − | 0.505095i | \(-0.831457\pi\) | ||||
−0.863063 | + | 0.505095i | \(0.831457\pi\) | |||||||
\(734\) | 1.96037e12 | 0.249291 | ||||||||
\(735\) | −8.63766e11 | −0.109170 | ||||||||
\(736\) | −1.18234e13 | −1.48523 | ||||||||
\(737\) | 2.58195e12 | 0.322362 | ||||||||
\(738\) | 1.61115e13 | 1.99932 | ||||||||
\(739\) | −1.33151e13 | −1.64227 | −0.821133 | − | 0.570736i | \(-0.806658\pi\) | ||||
−0.821133 | + | 0.570736i | \(0.806658\pi\) | |||||||
\(740\) | 2.35668e12 | 0.288907 | ||||||||
\(741\) | 1.00741e12 | 0.122751 | ||||||||
\(742\) | −8.23003e10 | −0.00996744 | ||||||||
\(743\) | 1.37811e13 | 1.65896 | 0.829479 | − | 0.558538i | \(-0.188637\pi\) | ||||
0.829479 | + | 0.558538i | \(0.188637\pi\) | |||||||
\(744\) | −1.20642e13 | −1.44352 | ||||||||
\(745\) | −4.85135e12 | −0.576979 | ||||||||
\(746\) | −7.23722e12 | −0.855553 | ||||||||
\(747\) | −2.00756e13 | −2.35899 | ||||||||
\(748\) | −6.95075e11 | −0.0811848 | ||||||||
\(749\) | 2.57781e12 | 0.299284 | ||||||||
\(750\) | 8.67894e11 | 0.100159 | ||||||||
\(751\) | −1.31166e12 | −0.150467 | −0.0752334 | − | 0.997166i | \(-0.523970\pi\) | ||||
−0.0752334 | + | 0.997166i | \(0.523970\pi\) | |||||||
\(752\) | −1.62292e12 | −0.185062 | ||||||||
\(753\) | 2.38672e13 | 2.70535 | ||||||||
\(754\) | 1.93103e12 | 0.217580 | ||||||||
\(755\) | 5.23776e12 | 0.586657 | ||||||||
\(756\) | 3.04457e12 | 0.338983 | ||||||||
\(757\) | 1.31405e13 | 1.45439 | 0.727196 | − | 0.686430i | \(-0.240823\pi\) | ||||
0.727196 | + | 0.686430i | \(0.240823\pi\) | |||||||
\(758\) | −4.45093e12 | −0.489711 | ||||||||
\(759\) | 8.21543e12 | 0.898551 | ||||||||
\(760\) | −1.19022e12 | −0.129409 | ||||||||
\(761\) | 4.85816e12 | 0.525099 | 0.262549 | − | 0.964919i | \(-0.415437\pi\) | ||||
0.262549 | + | 0.964919i | \(0.415437\pi\) | |||||||
\(762\) | −1.37248e13 | −1.47472 | ||||||||
\(763\) | 2.60869e12 | 0.278652 | ||||||||
\(764\) | −5.20584e12 | −0.552804 | ||||||||
\(765\) | −3.40115e12 | −0.359045 | ||||||||
\(766\) | −1.14802e13 | −1.20481 | ||||||||
\(767\) | −4.43743e12 | −0.462970 | ||||||||
\(768\) | 1.72735e13 | 1.79165 | ||||||||
\(769\) | −1.57384e13 | −1.62290 | −0.811452 | − | 0.584420i | \(-0.801322\pi\) | ||||
−0.811452 | + | 0.584420i | \(0.801322\pi\) | |||||||
\(770\) | 3.67681e11 | 0.0376932 | ||||||||
\(771\) | 3.13528e13 | 3.19545 | ||||||||
\(772\) | 5.64081e11 | 0.0571562 | ||||||||
\(773\) | 1.97088e12 | 0.198542 | 0.0992710 | − | 0.995060i | \(-0.468349\pi\) | ||||
0.0992710 | + | 0.995060i | \(0.468349\pi\) | |||||||
\(774\) | −1.98831e13 | −1.99136 | ||||||||
\(775\) | 1.64859e12 | 0.164156 | ||||||||
\(776\) | −1.74770e13 | −1.73017 | ||||||||
\(777\) | 7.42997e12 | 0.731295 | ||||||||
\(778\) | 2.52271e12 | 0.246865 | ||||||||
\(779\) | 4.59194e12 | 0.446763 | ||||||||
\(780\) | 1.15163e12 | 0.111401 | ||||||||
\(781\) | −1.14850e12 | −0.110459 | ||||||||
\(782\) | 4.42854e12 | 0.423477 | ||||||||
\(783\) | 2.14846e13 | 2.04267 | ||||||||
\(784\) | −1.57073e11 | −0.0148484 | ||||||||
\(785\) | −5.31062e12 | −0.499150 | ||||||||
\(786\) | 1.42871e12 | 0.133519 | ||||||||
\(787\) | −1.29627e13 | −1.20451 | −0.602253 | − | 0.798306i | \(-0.705730\pi\) | ||||
−0.602253 | + | 0.798306i | \(0.705730\pi\) | |||||||
\(788\) | −9.48207e12 | −0.876063 | ||||||||
\(789\) | 7.86182e12 | 0.722232 | ||||||||
\(790\) | 3.95694e12 | 0.361441 | ||||||||
\(791\) | 6.85627e12 | 0.622721 | ||||||||
\(792\) | −7.44551e12 | −0.672405 | ||||||||
\(793\) | −1.76330e12 | −0.158343 | ||||||||
\(794\) | 8.11474e12 | 0.724573 | ||||||||
\(795\) | −3.46358e11 | −0.0307520 | ||||||||
\(796\) | 8.04675e12 | 0.710414 | ||||||||
\(797\) | 1.04429e13 | 0.916762 | 0.458381 | − | 0.888756i | \(-0.348429\pi\) | ||||
0.458381 | + | 0.888756i | \(0.348429\pi\) | |||||||
\(798\) | −1.36317e12 | −0.118997 | ||||||||
\(799\) | −8.57727e12 | −0.744541 | ||||||||
\(800\) | −2.22694e12 | −0.192222 | ||||||||
\(801\) | −4.31439e12 | −0.370317 | ||||||||
\(802\) | 6.77917e12 | 0.578618 | ||||||||
\(803\) | 1.29452e12 | 0.109872 | ||||||||
\(804\) | −1.09429e13 | −0.923594 | ||||||||
\(805\) | 3.11220e12 | 0.261208 | ||||||||
\(806\) | −1.64662e12 | −0.137431 | ||||||||
\(807\) | −1.79248e12 | −0.148772 | ||||||||
\(808\) | 8.98737e12 | 0.741791 | ||||||||
\(809\) | −6.99142e12 | −0.573848 | −0.286924 | − | 0.957953i | \(-0.592633\pi\) | ||||
−0.286924 | + | 0.957953i | \(0.592633\pi\) | |||||||
\(810\) | −2.75102e12 | −0.224549 | ||||||||
\(811\) | −1.14380e13 | −0.928442 | −0.464221 | − | 0.885719i | \(-0.653666\pi\) | ||||
−0.464221 | + | 0.885719i | \(0.653666\pi\) | |||||||
\(812\) | 3.47137e12 | 0.280220 | ||||||||
\(813\) | −1.61278e12 | −0.129470 | ||||||||
\(814\) | −3.16273e12 | −0.252495 | ||||||||
\(815\) | 2.66164e12 | 0.211320 | ||||||||
\(816\) | −9.40631e11 | −0.0742700 | ||||||||
\(817\) | −5.66689e12 | −0.444985 | ||||||||
\(818\) | −1.39831e12 | −0.109198 | ||||||||
\(819\) | 2.38733e12 | 0.185410 | ||||||||
\(820\) | 5.24932e12 | 0.405453 | ||||||||
\(821\) | −4.42435e12 | −0.339864 | −0.169932 | − | 0.985456i | \(-0.554355\pi\) | ||||
−0.169932 | + | 0.985456i | \(0.554355\pi\) | |||||||
\(822\) | 1.08130e13 | 0.826081 | ||||||||
\(823\) | 1.71948e13 | 1.30647 | 0.653234 | − | 0.757156i | \(-0.273412\pi\) | ||||
0.653234 | + | 0.757156i | \(0.273412\pi\) | |||||||
\(824\) | −1.57565e13 | −1.19066 | ||||||||
\(825\) | 1.54737e12 | 0.116293 | ||||||||
\(826\) | 6.00448e12 | 0.448813 | ||||||||
\(827\) | 3.04498e12 | 0.226365 | 0.113182 | − | 0.993574i | \(-0.463896\pi\) | ||||
0.113182 | + | 0.993574i | \(0.463896\pi\) | |||||||
\(828\) | −2.28944e13 | −1.69275 | ||||||||
\(829\) | −8.03416e12 | −0.590806 | −0.295403 | − | 0.955373i | \(-0.595454\pi\) | ||||
−0.295403 | + | 0.955373i | \(0.595454\pi\) | |||||||
\(830\) | 4.92343e12 | 0.360094 | ||||||||
\(831\) | 3.66017e13 | 2.66254 | ||||||||
\(832\) | 2.59132e12 | 0.187485 | ||||||||
\(833\) | −8.30146e11 | −0.0597382 | ||||||||
\(834\) | 2.97339e12 | 0.212816 | ||||||||
\(835\) | 5.77210e11 | 0.0410908 | ||||||||
\(836\) | −7.70891e11 | −0.0545839 | ||||||||
\(837\) | −1.83202e13 | −1.29022 | ||||||||
\(838\) | −2.47448e12 | −0.173335 | ||||||||
\(839\) | 1.36209e13 | 0.949020 | 0.474510 | − | 0.880250i | \(-0.342625\pi\) | ||||
0.474510 | + | 0.880250i | \(0.342625\pi\) | |||||||
\(840\) | −4.28962e12 | −0.297277 | ||||||||
\(841\) | 9.98921e12 | 0.688571 | ||||||||
\(842\) | 8.19684e12 | 0.562007 | ||||||||
\(843\) | −7.42689e12 | −0.506504 | ||||||||
\(844\) | −5.68023e12 | −0.385323 | ||||||||
\(845\) | −6.19513e12 | −0.418018 | ||||||||
\(846\) | −3.33772e13 | −2.24018 | ||||||||
\(847\) | −5.00589e12 | −0.334200 | ||||||||
\(848\) | −6.29842e10 | −0.00418264 | ||||||||
\(849\) | 2.13862e13 | 1.41270 | ||||||||
\(850\) | 8.34114e11 | 0.0548075 | ||||||||
\(851\) | −2.67706e13 | −1.74975 | ||||||||
\(852\) | 4.86762e12 | 0.316474 | ||||||||
\(853\) | 3.64211e12 | 0.235549 | 0.117775 | − | 0.993040i | \(-0.462424\pi\) | ||||
0.117775 | + | 0.993040i | \(0.462424\pi\) | |||||||
\(854\) | 2.38600e12 | 0.153501 | ||||||||
\(855\) | −3.77213e12 | −0.241401 | ||||||||
\(856\) | 1.28019e13 | 0.814971 | ||||||||
\(857\) | 1.62518e13 | 1.02917 | 0.514587 | − | 0.857438i | \(-0.327945\pi\) | ||||
0.514587 | + | 0.857438i | \(0.327945\pi\) | |||||||
\(858\) | −1.54552e12 | −0.0973602 | ||||||||
\(859\) | 1.69063e13 | 1.05944 | 0.529722 | − | 0.848171i | \(-0.322296\pi\) | ||||
0.529722 | + | 0.848171i | \(0.322296\pi\) | |||||||
\(860\) | −6.47816e12 | −0.403839 | ||||||||
\(861\) | 1.65496e13 | 1.02630 | ||||||||
\(862\) | 6.48608e12 | 0.400128 | ||||||||
\(863\) | −1.56857e13 | −0.962619 | −0.481310 | − | 0.876551i | \(-0.659839\pi\) | ||||
−0.481310 | + | 0.876551i | \(0.659839\pi\) | |||||||
\(864\) | 2.47471e13 | 1.51082 | ||||||||
\(865\) | −2.97504e12 | −0.180684 | ||||||||
\(866\) | −4.14955e12 | −0.250709 | ||||||||
\(867\) | 2.34584e13 | 1.40998 | ||||||||
\(868\) | −2.96008e12 | −0.176997 | ||||||||
\(869\) | 7.05485e12 | 0.419661 | ||||||||
\(870\) | −1.09966e13 | −0.650760 | ||||||||
\(871\) | −4.11138e12 | −0.242050 | ||||||||
\(872\) | 1.29553e13 | 0.758790 | ||||||||
\(873\) | −5.53897e13 | −3.22749 | ||||||||
\(874\) | 4.91158e12 | 0.284721 | ||||||||
\(875\) | 5.86182e11 | 0.0338062 | ||||||||
\(876\) | −5.48649e12 | −0.314794 | ||||||||
\(877\) | 2.37521e13 | 1.35583 | 0.677914 | − | 0.735141i | \(-0.262884\pi\) | ||||
0.677914 | + | 0.735141i | \(0.262884\pi\) | |||||||
\(878\) | −1.31550e13 | −0.747079 | ||||||||
\(879\) | −1.51055e13 | −0.853462 | ||||||||
\(880\) | 2.81385e11 | 0.0158172 | ||||||||
\(881\) | 1.13698e13 | 0.635858 | 0.317929 | − | 0.948115i | \(-0.397013\pi\) | ||||
0.317929 | + | 0.948115i | \(0.397013\pi\) | |||||||
\(882\) | −3.23039e12 | −0.179741 | ||||||||
\(883\) | −1.21711e12 | −0.0673762 | −0.0336881 | − | 0.999432i | \(-0.510725\pi\) | ||||
−0.0336881 | + | 0.999432i | \(0.510725\pi\) | |||||||
\(884\) | 1.10681e12 | 0.0609588 | ||||||||
\(885\) | 2.52697e13 | 1.38470 | ||||||||
\(886\) | 8.71692e12 | 0.475238 | ||||||||
\(887\) | 3.43743e13 | 1.86457 | 0.932283 | − | 0.361730i | \(-0.117814\pi\) | ||||
0.932283 | + | 0.361730i | \(0.117814\pi\) | |||||||
\(888\) | 3.68986e13 | 1.99137 | ||||||||
\(889\) | −9.26983e12 | −0.497753 | ||||||||
\(890\) | 1.05808e12 | 0.0565281 | ||||||||
\(891\) | −4.90482e12 | −0.260719 | ||||||||
\(892\) | 1.43272e13 | 0.757738 | ||||||||
\(893\) | −9.51284e12 | −0.500586 | ||||||||
\(894\) | −2.75937e13 | −1.44474 | ||||||||
\(895\) | −5.91992e12 | −0.308398 | ||||||||
\(896\) | 3.50183e12 | 0.181513 | ||||||||
\(897\) | −1.30819e13 | −0.674690 | ||||||||
\(898\) | 7.70957e12 | 0.395627 | ||||||||
\(899\) | −2.08884e13 | −1.06656 | ||||||||
\(900\) | −4.31215e12 | −0.219080 | ||||||||
\(901\) | −3.32877e11 | −0.0168276 | ||||||||
\(902\) | −7.04472e12 | −0.354352 | ||||||||
\(903\) | −2.04238e13 | −1.02222 | ||||||||
\(904\) | 3.40495e13 | 1.69571 | ||||||||
\(905\) | −4.90872e12 | −0.243248 | ||||||||
\(906\) | 2.97915e13 | 1.46898 | ||||||||
\(907\) | −3.08586e13 | −1.51406 | −0.757030 | − | 0.653381i | \(-0.773350\pi\) | ||||
−0.757030 | + | 0.653381i | \(0.773350\pi\) | |||||||
\(908\) | 2.00974e13 | 0.981192 | ||||||||
\(909\) | 2.84835e13 | 1.38374 | ||||||||
\(910\) | −5.85478e11 | −0.0283025 | ||||||||
\(911\) | −3.36006e13 | −1.61627 | −0.808136 | − | 0.588996i | \(-0.799523\pi\) | ||||
−0.808136 | + | 0.588996i | \(0.799523\pi\) | |||||||
\(912\) | −1.04323e12 | −0.0499348 | ||||||||
\(913\) | 8.77802e12 | 0.418098 | ||||||||
\(914\) | 1.52814e13 | 0.724280 | ||||||||
\(915\) | 1.00414e13 | 0.473587 | ||||||||
\(916\) | 9.01056e11 | 0.0422885 | ||||||||
\(917\) | 9.64961e11 | 0.0450659 | ||||||||
\(918\) | −9.26917e12 | −0.430773 | ||||||||
\(919\) | −1.46200e13 | −0.676127 | −0.338063 | − | 0.941123i | \(-0.609772\pi\) | ||||
−0.338063 | + | 0.941123i | \(0.609772\pi\) | |||||||
\(920\) | 1.54557e13 | 0.711287 | ||||||||
\(921\) | 2.93583e13 | 1.34450 | ||||||||
\(922\) | −1.38945e13 | −0.633219 | ||||||||
\(923\) | 1.82882e12 | 0.0829398 | ||||||||
\(924\) | −2.77834e12 | −0.125390 | ||||||||
\(925\) | −5.04224e12 | −0.226457 | ||||||||
\(926\) | −1.60563e13 | −0.717625 | ||||||||
\(927\) | −4.99367e13 | −2.22107 | ||||||||
\(928\) | 2.82162e13 | 1.24891 | ||||||||
\(929\) | −1.36244e13 | −0.600130 | −0.300065 | − | 0.953919i | \(-0.597008\pi\) | ||||
−0.300065 | + | 0.953919i | \(0.597008\pi\) | |||||||
\(930\) | 9.37693e12 | 0.411043 | ||||||||
\(931\) | −9.20694e11 | −0.0401644 | ||||||||
\(932\) | 4.34213e12 | 0.188508 | ||||||||
\(933\) | −6.66287e13 | −2.87868 | ||||||||
\(934\) | −2.26013e12 | −0.0971790 | ||||||||
\(935\) | 1.48715e12 | 0.0636358 | ||||||||
\(936\) | 1.18559e13 | 0.504885 | ||||||||
\(937\) | −1.06580e13 | −0.451697 | −0.225848 | − | 0.974162i | \(-0.572515\pi\) | ||||
−0.225848 | + | 0.974162i | \(0.572515\pi\) | |||||||
\(938\) | 5.56328e12 | 0.234649 | ||||||||
\(939\) | −2.93658e13 | −1.23267 | ||||||||
\(940\) | −1.08747e13 | −0.454299 | ||||||||
\(941\) | 1.54253e13 | 0.641328 | 0.320664 | − | 0.947193i | \(-0.396094\pi\) | ||||
0.320664 | + | 0.947193i | \(0.396094\pi\) | |||||||
\(942\) | −3.02059e13 | −1.24986 | ||||||||
\(943\) | −5.96294e13 | −2.45560 | ||||||||
\(944\) | 4.59522e12 | 0.188335 | ||||||||
\(945\) | −6.51400e12 | −0.265708 | ||||||||
\(946\) | 8.69386e12 | 0.352941 | ||||||||
\(947\) | 1.97267e13 | 0.797039 | 0.398519 | − | 0.917160i | \(-0.369524\pi\) | ||||
0.398519 | + | 0.917160i | \(0.369524\pi\) | |||||||
\(948\) | −2.99002e13 | −1.20236 | ||||||||
\(949\) | −2.06133e12 | −0.0824993 | ||||||||
\(950\) | 9.25094e11 | 0.0368493 | ||||||||
\(951\) | −5.56186e13 | −2.20500 | ||||||||
\(952\) | −4.12265e12 | −0.162671 | ||||||||
\(953\) | −1.39214e12 | −0.0546721 | −0.0273361 | − | 0.999626i | \(-0.508702\pi\) | ||||
−0.0273361 | + | 0.999626i | \(0.508702\pi\) | |||||||
\(954\) | −1.29534e12 | −0.0506311 | ||||||||
\(955\) | 1.11381e13 | 0.433309 | ||||||||
\(956\) | −1.18721e13 | −0.459694 | ||||||||
\(957\) | −1.96059e13 | −0.755583 | ||||||||
\(958\) | 2.99895e12 | 0.115034 | ||||||||
\(959\) | 7.30317e12 | 0.278822 | ||||||||
\(960\) | −1.47567e13 | −0.560749 | ||||||||
\(961\) | −8.62783e12 | −0.326322 | ||||||||
\(962\) | 5.03619e12 | 0.189589 | ||||||||
\(963\) | 4.05728e13 | 1.52026 | ||||||||
\(964\) | 6.12861e12 | 0.228568 | ||||||||
\(965\) | −1.20688e12 | −0.0448013 | ||||||||
\(966\) | 1.77017e13 | 0.654059 | ||||||||
\(967\) | 5.29760e12 | 0.194832 | 0.0974160 | − | 0.995244i | \(-0.468942\pi\) | ||||
0.0974160 | + | 0.995244i | \(0.468942\pi\) | |||||||
\(968\) | −2.48602e13 | −0.910049 | ||||||||
\(969\) | −5.51357e12 | −0.200898 | ||||||||
\(970\) | 1.35840e13 | 0.492669 | ||||||||
\(971\) | −7.97890e12 | −0.288042 | −0.144021 | − | 0.989575i | \(-0.546003\pi\) | ||||
−0.144021 | + | 0.989575i | \(0.546003\pi\) | |||||||
\(972\) | −4.17108e12 | −0.149882 | ||||||||
\(973\) | 2.00825e12 | 0.0718306 | ||||||||
\(974\) | −1.23902e13 | −0.441127 | ||||||||
\(975\) | −2.46397e12 | −0.0873202 | ||||||||
\(976\) | 1.82600e12 | 0.0644135 | ||||||||
\(977\) | −6.27831e12 | −0.220454 | −0.110227 | − | 0.993906i | \(-0.535158\pi\) | ||||
−0.110227 | + | 0.993906i | \(0.535158\pi\) | |||||||
\(978\) | 1.51390e13 | 0.529141 | ||||||||
\(979\) | 1.88646e12 | 0.0656335 | ||||||||
\(980\) | −1.05250e12 | −0.0364506 | ||||||||
\(981\) | 4.10589e13 | 1.41546 | ||||||||
\(982\) | 1.57540e13 | 0.540616 | ||||||||
\(983\) | 1.25053e12 | 0.0427173 | 0.0213586 | − | 0.999772i | \(-0.493201\pi\) | ||||
0.0213586 | + | 0.999772i | \(0.493201\pi\) | |||||||
\(984\) | 8.21886e13 | 2.79469 | ||||||||
\(985\) | 2.02874e13 | 0.686692 | ||||||||
\(986\) | −1.05686e13 | −0.356098 | ||||||||
\(987\) | −3.42849e13 | −1.14994 | ||||||||
\(988\) | 1.22753e12 | 0.0409851 | ||||||||
\(989\) | 7.35883e13 | 2.44583 | ||||||||
\(990\) | 5.78702e12 | 0.191468 | ||||||||
\(991\) | 1.89095e13 | 0.622801 | 0.311400 | − | 0.950279i | \(-0.399202\pi\) | ||||
0.311400 | + | 0.950279i | \(0.399202\pi\) | |||||||
\(992\) | −2.40603e13 | −0.788858 | ||||||||
\(993\) | 8.97216e13 | 2.92836 | ||||||||
\(994\) | −2.47465e12 | −0.0804036 | ||||||||
\(995\) | −1.72164e13 | −0.556851 | ||||||||
\(996\) | −3.72034e13 | −1.19788 | ||||||||
\(997\) | −7.17482e12 | −0.229976 | −0.114988 | − | 0.993367i | \(-0.536683\pi\) | ||||
−0.114988 | + | 0.993367i | \(0.536683\pi\) | |||||||
\(998\) | 4.95178e12 | 0.158006 | ||||||||
\(999\) | 5.60324e13 | 1.77989 |
(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 | 35.10.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 315.10.a.b.1.2 | 2 | |||
5.2 | odd | 4 | 175.10.b.c.99.1 | 4 | |||
5.3 | odd | 4 | 175.10.b.c.99.4 | 4 | |||
5.4 | even | 2 | 175.10.a.c.1.2 | 2 | |||
7.6 | odd | 2 | 245.10.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.10.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
175.10.a.c.1.2 | 2 | 5.4 | even | 2 | |||
175.10.b.c.99.1 | 4 | 5.2 | odd | 4 | |||
175.10.b.c.99.4 | 4 | 5.3 | odd | 4 | |||
245.10.a.c.1.1 | 2 | 7.6 | odd | 2 | |||
315.10.a.b.1.2 | 2 | 3.2 | odd | 2 |