Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(209.608008215\) |
Analytic rank: | \(1\) |
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: | \( x^{10} - 5 x^{9} - 15486550 x^{8} - 930225020 x^{7} + 80619202368510 x^{6} + \cdots + 47\!\cdots\!18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{14}\cdot 5^{24}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1063.71\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 998.710 | 0.689643 | 0.344821 | − | 0.938668i | \(-0.387939\pi\) | ||||
0.344821 | + | 0.938668i | \(0.387939\pi\) | |||||||
\(3\) | 59049.0 | 0.577350 | ||||||||
\(4\) | −1.09973e6 | −0.524393 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.89728e7 | 0.398165 | ||||||||
\(7\) | 1.20991e9 | 1.61892 | 0.809459 | − | 0.587176i | \(-0.199760\pi\) | ||||
0.809459 | + | 0.587176i | \(0.199760\pi\) | |||||||
\(8\) | −3.19276e9 | −1.05129 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.80573e10 | 0.558645 | 0.279323 | − | 0.960197i | \(-0.409890\pi\) | ||||
0.279323 | + | 0.960197i | \(0.409890\pi\) | |||||||
\(12\) | −6.49380e10 | −0.302758 | ||||||||
\(13\) | −1.71413e11 | −0.344857 | −0.172429 | − | 0.985022i | \(-0.555161\pi\) | ||||
−0.172429 | + | 0.985022i | \(0.555161\pi\) | |||||||
\(14\) | 1.20835e12 | 1.11648 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.82334e11 | −0.200619 | ||||||||
\(17\) | −1.14949e13 | −1.38290 | −0.691450 | − | 0.722424i | \(-0.743028\pi\) | ||||
−0.691450 | + | 0.722424i | \(0.743028\pi\) | |||||||
\(18\) | 3.48228e12 | 0.229881 | ||||||||
\(19\) | 7.38155e12 | 0.276207 | 0.138104 | − | 0.990418i | \(-0.455899\pi\) | ||||
0.138104 | + | 0.990418i | \(0.455899\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.14442e13 | 0.934683 | ||||||||
\(22\) | 4.79953e13 | 0.385266 | ||||||||
\(23\) | −2.65776e14 | −1.33775 | −0.668874 | − | 0.743376i | \(-0.733223\pi\) | ||||
−0.668874 | + | 0.743376i | \(0.733223\pi\) | |||||||
\(24\) | −1.88529e14 | −0.606961 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.71192e14 | −0.237828 | ||||||||
\(27\) | 2.05891e14 | 0.192450 | ||||||||
\(28\) | −1.33058e15 | −0.848949 | ||||||||
\(29\) | 3.36415e14 | 0.148489 | 0.0742447 | − | 0.997240i | \(-0.476345\pi\) | ||||
0.0742447 | + | 0.997240i | \(0.476345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.12517e15 | 0.465689 | 0.232845 | − | 0.972514i | \(-0.425197\pi\) | ||||
0.232845 | + | 0.972514i | \(0.425197\pi\) | |||||||
\(32\) | 5.81450e15 | 0.912931 | ||||||||
\(33\) | 2.83774e15 | 0.322534 | ||||||||
\(34\) | −1.14801e16 | −0.953707 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.83453e15 | −0.174798 | ||||||||
\(37\) | −5.00544e16 | −1.71129 | −0.855646 | − | 0.517562i | \(-0.826840\pi\) | ||||
−0.855646 | + | 0.517562i | \(0.826840\pi\) | |||||||
\(38\) | 7.37203e15 | 0.190484 | ||||||||
\(39\) | −1.01218e16 | −0.199103 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.46448e16 | −0.984850 | −0.492425 | − | 0.870355i | \(-0.663889\pi\) | ||||
−0.492425 | + | 0.870355i | \(0.663889\pi\) | |||||||
\(42\) | 7.13520e16 | 0.644598 | ||||||||
\(43\) | −5.45785e16 | −0.385126 | −0.192563 | − | 0.981285i | \(-0.561680\pi\) | ||||
−0.192563 | + | 0.981285i | \(0.561680\pi\) | |||||||
\(44\) | −5.28501e16 | −0.292950 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.65433e17 | −0.922568 | ||||||||
\(47\) | 2.16734e17 | 0.601036 | 0.300518 | − | 0.953776i | \(-0.402841\pi\) | ||||
0.300518 | + | 0.953776i | \(0.402841\pi\) | |||||||
\(48\) | −5.21009e16 | −0.115828 | ||||||||
\(49\) | 9.05346e17 | 1.62090 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.78761e17 | −0.798418 | ||||||||
\(52\) | 1.88508e17 | 0.180841 | ||||||||
\(53\) | −7.54978e17 | −0.592977 | −0.296488 | − | 0.955036i | \(-0.595816\pi\) | ||||
−0.296488 | + | 0.955036i | \(0.595816\pi\) | |||||||
\(54\) | 2.05625e17 | 0.132722 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.86296e18 | −1.70195 | ||||||||
\(57\) | 4.35873e17 | 0.159468 | ||||||||
\(58\) | 3.35980e17 | 0.102405 | ||||||||
\(59\) | 6.39259e18 | 1.62829 | 0.814143 | − | 0.580664i | \(-0.197207\pi\) | ||||
0.814143 | + | 0.580664i | \(0.197207\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.01150e18 | 0.899507 | 0.449754 | − | 0.893153i | \(-0.351512\pi\) | ||||
0.449754 | + | 0.893153i | \(0.351512\pi\) | |||||||
\(62\) | 2.12243e18 | 0.321159 | ||||||||
\(63\) | 4.21871e18 | 0.539640 | ||||||||
\(64\) | 7.65739e18 | 0.830216 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.83407e18 | 0.222433 | ||||||||
\(67\) | 1.05392e19 | 0.706351 | 0.353175 | − | 0.935557i | \(-0.385102\pi\) | ||||
0.353175 | + | 0.935557i | \(0.385102\pi\) | |||||||
\(68\) | 1.26413e19 | 0.725183 | ||||||||
\(69\) | −1.56938e19 | −0.772349 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.86086e19 | −0.678425 | −0.339212 | − | 0.940710i | \(-0.610161\pi\) | ||||
−0.339212 | + | 0.940710i | \(0.610161\pi\) | |||||||
\(72\) | −1.11325e19 | −0.350429 | ||||||||
\(73\) | −3.26224e18 | −0.0888437 | −0.0444218 | − | 0.999013i | \(-0.514145\pi\) | ||||
−0.0444218 | + | 0.999013i | \(0.514145\pi\) | |||||||
\(74\) | −4.99898e19 | −1.18018 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.11772e18 | −0.144841 | ||||||||
\(77\) | 5.81452e19 | 0.904402 | ||||||||
\(78\) | −1.01087e19 | −0.137310 | ||||||||
\(79\) | −1.64810e20 | −1.95839 | −0.979194 | − | 0.202926i | \(-0.934955\pi\) | ||||
−0.979194 | + | 0.202926i | \(0.934955\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | −8.45356e19 | −0.679195 | ||||||||
\(83\) | −3.17359e18 | −0.0224508 | −0.0112254 | − | 0.999937i | \(-0.503573\pi\) | ||||
−0.0112254 | + | 0.999937i | \(0.503573\pi\) | |||||||
\(84\) | −7.85694e19 | −0.490141 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.45080e19 | −0.265599 | ||||||||
\(87\) | 1.98649e19 | 0.0857305 | ||||||||
\(88\) | −1.53435e20 | −0.587296 | ||||||||
\(89\) | 8.25383e19 | 0.280582 | 0.140291 | − | 0.990110i | \(-0.455196\pi\) | ||||
0.140291 | + | 0.990110i | \(0.455196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.07395e20 | −0.558296 | ||||||||
\(92\) | 2.92283e20 | 0.701505 | ||||||||
\(93\) | 1.25489e20 | 0.268866 | ||||||||
\(94\) | 2.16455e20 | 0.414500 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.43341e20 | 0.527081 | ||||||||
\(97\) | −1.37703e21 | −1.89600 | −0.948001 | − | 0.318268i | \(-0.896899\pi\) | ||||
−0.948001 | + | 0.318268i | \(0.896899\pi\) | |||||||
\(98\) | 9.04178e20 | 1.11784 | ||||||||
\(99\) | 1.67565e20 | 0.186215 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.10058e21 | −0.991394 | −0.495697 | − | 0.868495i | \(-0.665087\pi\) | ||||
−0.495697 | + | 0.868495i | \(0.665087\pi\) | |||||||
\(102\) | −6.77885e20 | −0.550623 | ||||||||
\(103\) | −2.30652e21 | −1.69109 | −0.845546 | − | 0.533903i | \(-0.820725\pi\) | ||||
−0.845546 | + | 0.533903i | \(0.820725\pi\) | |||||||
\(104\) | 5.47281e20 | 0.362544 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.54003e20 | −0.408942 | ||||||||
\(107\) | 3.50991e21 | 1.72491 | 0.862455 | − | 0.506134i | \(-0.168926\pi\) | ||||
0.862455 | + | 0.506134i | \(0.168926\pi\) | |||||||
\(108\) | −2.26425e20 | −0.100919 | ||||||||
\(109\) | −1.42742e21 | −0.577531 | −0.288765 | − | 0.957400i | \(-0.593245\pi\) | ||||
−0.288765 | + | 0.957400i | \(0.593245\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.95566e21 | −0.988015 | ||||||||
\(112\) | −1.06755e21 | −0.324787 | ||||||||
\(113\) | 8.18492e20 | 0.226825 | 0.113412 | − | 0.993548i | \(-0.463822\pi\) | ||||
0.113412 | + | 0.993548i | \(0.463822\pi\) | |||||||
\(114\) | 4.35311e20 | 0.109976 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.69966e20 | −0.0778668 | ||||||||
\(117\) | −5.97681e20 | −0.114952 | ||||||||
\(118\) | 6.38434e21 | 1.12294 | ||||||||
\(119\) | −1.39078e22 | −2.23880 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.09075e21 | −0.687915 | ||||||||
\(122\) | 5.00504e21 | 0.620339 | ||||||||
\(123\) | −4.99819e21 | −0.568603 | ||||||||
\(124\) | −2.33712e21 | −0.244204 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.21327e21 | 0.372159 | ||||||||
\(127\) | −1.55268e22 | −1.26225 | −0.631123 | − | 0.775683i | \(-0.717406\pi\) | ||||
−0.631123 | + | 0.775683i | \(0.717406\pi\) | |||||||
\(128\) | −4.54639e21 | −0.340378 | ||||||||
\(129\) | −3.22280e21 | −0.222352 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.80456e22 | 1.05931 | 0.529653 | − | 0.848214i | \(-0.322322\pi\) | ||||
0.529653 | + | 0.848214i | \(0.322322\pi\) | |||||||
\(132\) | −3.12075e21 | −0.169135 | ||||||||
\(133\) | 8.93104e21 | 0.447157 | ||||||||
\(134\) | 1.05256e22 | 0.487130 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.67004e22 | 1.45382 | ||||||||
\(137\) | 3.76764e22 | 1.38199 | 0.690993 | − | 0.722861i | \(-0.257173\pi\) | ||||
0.690993 | + | 0.722861i | \(0.257173\pi\) | |||||||
\(138\) | −1.56736e22 | −0.532645 | ||||||||
\(139\) | −2.07959e22 | −0.655121 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.27979e22 | 0.347008 | ||||||||
\(142\) | −1.85846e22 | −0.467871 | ||||||||
\(143\) | −8.23766e21 | −0.192653 | ||||||||
\(144\) | −3.07651e21 | −0.0668732 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.25803e21 | −0.0612704 | ||||||||
\(147\) | 5.34598e22 | 0.935826 | ||||||||
\(148\) | 5.50464e22 | 0.897389 | ||||||||
\(149\) | −8.31054e22 | −1.26233 | −0.631166 | − | 0.775648i | \(-0.717423\pi\) | ||||
−0.631166 | + | 0.775648i | \(0.717423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.83660e22 | −1.29893 | −0.649467 | − | 0.760390i | \(-0.725008\pi\) | ||||
−0.649467 | + | 0.760390i | \(0.725008\pi\) | |||||||
\(152\) | −2.35675e22 | −0.290373 | ||||||||
\(153\) | −4.00802e22 | −0.460967 | ||||||||
\(154\) | 5.80702e22 | 0.623714 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.11312e22 | 0.104408 | ||||||||
\(157\) | −1.08861e23 | −0.954827 | −0.477414 | − | 0.878679i | \(-0.658426\pi\) | ||||
−0.477414 | + | 0.878679i | \(0.658426\pi\) | |||||||
\(158\) | −1.64597e23 | −1.35059 | ||||||||
\(159\) | −4.45807e22 | −0.342355 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.21567e23 | −2.16570 | ||||||||
\(162\) | 1.21420e22 | 0.0766270 | ||||||||
\(163\) | 3.20827e23 | 1.89802 | 0.949010 | − | 0.315245i | \(-0.102087\pi\) | ||||
0.949010 | + | 0.315245i | \(0.102087\pi\) | |||||||
\(164\) | 9.30866e22 | 0.516448 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.16950e21 | −0.0154830 | ||||||||
\(167\) | −2.16820e23 | −0.994437 | −0.497219 | − | 0.867625i | \(-0.665645\pi\) | ||||
−0.497219 | + | 0.867625i | \(0.665645\pi\) | |||||||
\(168\) | −2.28104e23 | −0.982620 | ||||||||
\(169\) | −2.17682e23 | −0.881074 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.57379e22 | 0.0920690 | ||||||||
\(172\) | 6.00216e22 | 0.201957 | ||||||||
\(173\) | −3.92562e23 | −1.24287 | −0.621433 | − | 0.783468i | \(-0.713449\pi\) | ||||
−0.621433 | + | 0.783468i | \(0.713449\pi\) | |||||||
\(174\) | 1.98393e22 | 0.0591234 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.24026e22 | −0.112075 | ||||||||
\(177\) | 3.77476e23 | 0.940092 | ||||||||
\(178\) | 8.24318e22 | 0.193502 | ||||||||
\(179\) | 2.94913e23 | 0.652735 | 0.326368 | − | 0.945243i | \(-0.394175\pi\) | ||||
0.326368 | + | 0.945243i | \(0.394175\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.84557e23 | 1.15134 | 0.575668 | − | 0.817684i | \(-0.304742\pi\) | ||||
0.575668 | + | 0.817684i | \(0.304742\pi\) | |||||||
\(182\) | −2.07128e23 | −0.385025 | ||||||||
\(183\) | 2.95924e23 | 0.519331 | ||||||||
\(184\) | 8.48560e23 | 1.40636 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.25327e23 | 0.185421 | ||||||||
\(187\) | −5.52413e23 | −0.772551 | ||||||||
\(188\) | −2.38350e23 | −0.315179 | ||||||||
\(189\) | 2.49111e23 | 0.311561 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.13125e24 | 1.26680 | 0.633400 | − | 0.773824i | \(-0.281659\pi\) | ||||
0.633400 | + | 0.773824i | \(0.281659\pi\) | |||||||
\(192\) | 4.52161e23 | 0.479325 | ||||||||
\(193\) | −1.59566e24 | −1.60173 | −0.800866 | − | 0.598843i | \(-0.795627\pi\) | ||||
−0.800866 | + | 0.598843i | \(0.795627\pi\) | |||||||
\(194\) | −1.37525e24 | −1.30756 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.95637e23 | −0.849987 | ||||||||
\(197\) | 2.74899e23 | 0.222473 | 0.111236 | − | 0.993794i | \(-0.464519\pi\) | ||||
0.111236 | + | 0.993794i | \(0.464519\pi\) | |||||||
\(198\) | 1.67349e23 | 0.128422 | ||||||||
\(199\) | −1.12111e24 | −0.816000 | −0.408000 | − | 0.912982i | \(-0.633774\pi\) | ||||
−0.408000 | + | 0.912982i | \(0.633774\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.22327e23 | 0.407812 | ||||||||
\(202\) | −1.09916e24 | −0.683708 | ||||||||
\(203\) | 4.07033e23 | 0.240392 | ||||||||
\(204\) | 7.46455e23 | 0.418685 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.30355e24 | −1.16625 | ||||||||
\(207\) | −9.26705e23 | −0.445916 | ||||||||
\(208\) | 1.51244e23 | 0.0691850 | ||||||||
\(209\) | 3.54737e23 | 0.154302 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.53568e24 | 0.604415 | 0.302208 | − | 0.953242i | \(-0.402276\pi\) | ||||
0.302208 | + | 0.953242i | \(0.402276\pi\) | |||||||
\(212\) | 8.30273e23 | 0.310953 | ||||||||
\(213\) | −1.09882e24 | −0.391689 | ||||||||
\(214\) | 3.50538e24 | 1.18957 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.57361e23 | −0.202320 | ||||||||
\(217\) | 2.57127e24 | 0.753913 | ||||||||
\(218\) | −1.42558e24 | −0.398290 | ||||||||
\(219\) | −1.92632e23 | −0.0512939 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.97038e24 | 0.476903 | ||||||||
\(222\) | −2.95185e24 | −0.681377 | ||||||||
\(223\) | −7.77339e24 | −1.71163 | −0.855814 | − | 0.517284i | \(-0.826943\pi\) | ||||
−0.855814 | + | 0.517284i | \(0.826943\pi\) | |||||||
\(224\) | 7.03505e24 | 1.47796 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.17436e23 | 0.156428 | ||||||||
\(227\) | −2.76707e23 | −0.0505533 | −0.0252766 | − | 0.999680i | \(-0.508047\pi\) | ||||
−0.0252766 | + | 0.999680i | \(0.508047\pi\) | |||||||
\(228\) | −4.79343e23 | −0.0836240 | ||||||||
\(229\) | 5.04294e24 | 0.840255 | 0.420128 | − | 0.907465i | \(-0.361985\pi\) | ||||
0.420128 | + | 0.907465i | \(0.361985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.43342e24 | 0.522156 | ||||||||
\(232\) | −1.07409e24 | −0.156105 | ||||||||
\(233\) | −3.34935e24 | −0.465290 | −0.232645 | − | 0.972562i | \(-0.574738\pi\) | ||||
−0.232645 | + | 0.972562i | \(0.574738\pi\) | |||||||
\(234\) | −5.96910e23 | −0.0792761 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.03013e24 | −0.853862 | ||||||||
\(237\) | −9.73186e24 | −1.13068 | ||||||||
\(238\) | −1.38899e25 | −1.54398 | ||||||||
\(239\) | −3.36899e24 | −0.358362 | −0.179181 | − | 0.983816i | \(-0.557345\pi\) | ||||
−0.179181 | + | 0.983816i | \(0.557345\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.50937e25 | 1.47101 | 0.735505 | − | 0.677519i | \(-0.236945\pi\) | ||||
0.735505 | + | 0.677519i | \(0.236945\pi\) | |||||||
\(242\) | −5.08418e24 | −0.474416 | ||||||||
\(243\) | 7.17898e23 | 0.0641500 | ||||||||
\(244\) | −5.51131e24 | −0.471695 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.99174e24 | −0.392133 | ||||||||
\(247\) | −1.26530e24 | −0.0952520 | ||||||||
\(248\) | −6.78516e24 | −0.489573 | ||||||||
\(249\) | −1.87398e23 | −0.0129620 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.55363e24 | −0.225994 | −0.112997 | − | 0.993595i | \(-0.536045\pi\) | ||||
−0.112997 | + | 0.993595i | \(0.536045\pi\) | |||||||
\(252\) | −4.63945e24 | −0.282983 | ||||||||
\(253\) | −1.27725e25 | −0.747326 | ||||||||
\(254\) | −1.55068e25 | −0.870499 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.05992e25 | −1.06496 | ||||||||
\(257\) | −2.83931e25 | −1.40901 | −0.704506 | − | 0.709698i | \(-0.748831\pi\) | ||||
−0.704506 | + | 0.709698i | \(0.748831\pi\) | |||||||
\(258\) | −3.21864e24 | −0.153344 | ||||||||
\(259\) | −6.05615e25 | −2.77044 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.17300e24 | 0.0494965 | ||||||||
\(262\) | 1.80223e25 | 0.730543 | ||||||||
\(263\) | −3.64456e25 | −1.41941 | −0.709707 | − | 0.704497i | \(-0.751173\pi\) | ||||
−0.709707 | + | 0.704497i | \(0.751173\pi\) | |||||||
\(264\) | −9.06020e24 | −0.339076 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.91952e24 | 0.308379 | ||||||||
\(267\) | 4.87380e24 | 0.161994 | ||||||||
\(268\) | −1.15902e25 | −0.370405 | ||||||||
\(269\) | −1.65928e25 | −0.509943 | −0.254972 | − | 0.966949i | \(-0.582066\pi\) | ||||
−0.254972 | + | 0.966949i | \(0.582066\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.72800e25 | −0.775652 | −0.387826 | − | 0.921733i | \(-0.626774\pi\) | ||||
−0.387826 | + | 0.921733i | \(0.626774\pi\) | |||||||
\(272\) | 1.01423e25 | 0.277437 | ||||||||
\(273\) | −1.22465e25 | −0.322332 | ||||||||
\(274\) | 3.76278e25 | 0.953077 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.72590e25 | 0.405014 | ||||||||
\(277\) | 1.80011e25 | 0.406688 | 0.203344 | − | 0.979107i | \(-0.434819\pi\) | ||||
0.203344 | + | 0.979107i | \(0.434819\pi\) | |||||||
\(278\) | −2.07690e25 | −0.451800 | ||||||||
\(279\) | 7.41001e24 | 0.155230 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.41233e25 | −0.468835 | −0.234418 | − | 0.972136i | \(-0.575318\pi\) | ||||
−0.234418 | + | 0.972136i | \(0.575318\pi\) | |||||||
\(282\) | 1.27814e25 | 0.239312 | ||||||||
\(283\) | −2.76536e25 | −0.498878 | −0.249439 | − | 0.968390i | \(-0.580246\pi\) | ||||
−0.249439 | + | 0.968390i | \(0.580246\pi\) | |||||||
\(284\) | 2.04645e25 | 0.355761 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.22703e24 | −0.132862 | ||||||||
\(287\) | −1.02413e26 | −1.59439 | ||||||||
\(288\) | 2.02739e25 | 0.304310 | ||||||||
\(289\) | 6.30404e25 | 0.912414 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.13120e25 | −1.09466 | ||||||||
\(292\) | 3.58759e24 | 0.0465890 | ||||||||
\(293\) | −8.83764e25 | −1.10720 | −0.553600 | − | 0.832783i | \(-0.686746\pi\) | ||||
−0.553600 | + | 0.832783i | \(0.686746\pi\) | |||||||
\(294\) | 5.33908e25 | 0.645386 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.59811e26 | 1.79906 | ||||||||
\(297\) | 9.89457e24 | 0.107511 | ||||||||
\(298\) | −8.29982e25 | −0.870558 | ||||||||
\(299\) | 4.55576e25 | 0.461332 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.60352e25 | −0.623487 | ||||||||
\(302\) | −9.82390e25 | −0.895800 | ||||||||
\(303\) | −6.49880e25 | −0.572382 | ||||||||
\(304\) | −6.51299e24 | −0.0554125 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.00285e25 | −0.317902 | ||||||||
\(307\) | −7.20639e25 | −0.553050 | −0.276525 | − | 0.961007i | \(-0.589183\pi\) | ||||
−0.276525 | + | 0.961007i | \(0.589183\pi\) | |||||||
\(308\) | −6.39441e25 | −0.474262 | ||||||||
\(309\) | −1.36198e26 | −0.976352 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.91089e26 | −1.28012 | −0.640062 | − | 0.768323i | \(-0.721091\pi\) | ||||
−0.640062 | + | 0.768323i | \(0.721091\pi\) | |||||||
\(312\) | 3.23164e25 | 0.209315 | ||||||||
\(313\) | −1.41091e25 | −0.0883655 | −0.0441827 | − | 0.999023i | \(-0.514068\pi\) | ||||
−0.0441827 | + | 0.999023i | \(0.514068\pi\) | |||||||
\(314\) | −1.08720e26 | −0.658490 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.81247e26 | 1.02696 | ||||||||
\(317\) | 2.75275e26 | 1.50884 | 0.754421 | − | 0.656391i | \(-0.227918\pi\) | ||||
0.754421 | + | 0.656391i | \(0.227918\pi\) | |||||||
\(318\) | −4.45232e25 | −0.236103 | ||||||||
\(319\) | 1.61672e25 | 0.0829530 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.07257e26 | 0.995877 | ||||||||
\(322\) | −3.21152e26 | −1.49356 | ||||||||
\(323\) | −8.48501e25 | −0.381967 | ||||||||
\(324\) | −1.33702e25 | −0.0582659 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.20413e26 | 1.30896 | ||||||||
\(327\) | −8.42880e25 | −0.333437 | ||||||||
\(328\) | 2.70250e26 | 1.03536 | ||||||||
\(329\) | 2.62230e26 | 0.973028 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.91314e26 | 1.01430 | 0.507151 | − | 0.861857i | \(-0.330699\pi\) | ||||
0.507151 | + | 0.861857i | \(0.330699\pi\) | |||||||
\(332\) | 3.49010e24 | 0.0117730 | ||||||||
\(333\) | −1.74529e26 | −0.570430 | ||||||||
\(334\) | −2.16541e26 | −0.685806 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.30376e25 | −0.187516 | ||||||||
\(337\) | 1.20851e26 | 0.348446 | 0.174223 | − | 0.984706i | \(-0.444259\pi\) | ||||
0.174223 | + | 0.984706i | \(0.444259\pi\) | |||||||
\(338\) | −2.17401e26 | −0.607626 | ||||||||
\(339\) | 4.83311e25 | 0.130957 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.02130e26 | 0.260155 | ||||||||
\(342\) | 2.57047e25 | 0.0634948 | ||||||||
\(343\) | 4.19599e26 | 1.00518 | ||||||||
\(344\) | 1.74256e26 | 0.404877 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.92055e26 | −0.857133 | ||||||||
\(347\) | −5.90558e25 | −0.125257 | −0.0626286 | − | 0.998037i | \(-0.519948\pi\) | ||||
−0.0626286 | + | 0.998037i | \(0.519948\pi\) | |||||||
\(348\) | −2.18461e25 | −0.0449564 | ||||||||
\(349\) | 5.09244e26 | 1.01686 | 0.508428 | − | 0.861105i | \(-0.330227\pi\) | ||||
0.508428 | + | 0.861105i | \(0.330227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.52925e25 | −0.0663678 | ||||||||
\(352\) | 2.79429e26 | 0.510005 | ||||||||
\(353\) | 5.10387e26 | 0.904201 | 0.452100 | − | 0.891967i | \(-0.350675\pi\) | ||||
0.452100 | + | 0.891967i | \(0.350675\pi\) | |||||||
\(354\) | 3.76989e26 | 0.648327 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.07700e25 | −0.147135 | ||||||||
\(357\) | −8.21243e26 | −1.29257 | ||||||||
\(358\) | 2.94533e26 | 0.450154 | ||||||||
\(359\) | 4.81726e26 | 0.715004 | 0.357502 | − | 0.933912i | \(-0.383628\pi\) | ||||
0.357502 | + | 0.933912i | \(0.383628\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.59722e26 | −0.923710 | ||||||||
\(362\) | 5.83803e26 | 0.794010 | ||||||||
\(363\) | −3.00603e26 | −0.397168 | ||||||||
\(364\) | 2.28079e26 | 0.292766 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.95542e26 | 0.358153 | ||||||||
\(367\) | 1.68764e27 | 1.98740 | 0.993701 | − | 0.112062i | \(-0.0357456\pi\) | ||||
0.993701 | + | 0.112062i | \(0.0357456\pi\) | |||||||
\(368\) | 2.34504e26 | 0.268378 | ||||||||
\(369\) | −2.95138e26 | −0.328283 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.13458e26 | −0.959981 | ||||||||
\(372\) | −1.38004e26 | −0.140991 | ||||||||
\(373\) | −7.80302e25 | −0.0775033 | −0.0387516 | − | 0.999249i | \(-0.512338\pi\) | ||||
−0.0387516 | + | 0.999249i | \(0.512338\pi\) | |||||||
\(374\) | −5.51700e26 | −0.532784 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.91980e26 | −0.631861 | ||||||||
\(377\) | −5.76659e25 | −0.0512076 | ||||||||
\(378\) | 2.48789e26 | 0.214866 | ||||||||
\(379\) | −1.17814e27 | −0.989656 | −0.494828 | − | 0.868991i | \(-0.664769\pi\) | ||||
−0.494828 | + | 0.868991i | \(0.664769\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.16844e26 | −0.728758 | ||||||||
\(382\) | 1.12979e27 | 0.873640 | ||||||||
\(383\) | 1.32936e27 | 1.00013 | 0.500065 | − | 0.865988i | \(-0.333309\pi\) | ||||
0.500065 | + | 0.865988i | \(0.333309\pi\) | |||||||
\(384\) | −2.68460e26 | −0.196518 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.59361e27 | −1.10462 | ||||||||
\(387\) | −1.90303e26 | −0.128375 | ||||||||
\(388\) | 1.51436e27 | 0.994250 | ||||||||
\(389\) | −3.12812e27 | −1.99900 | −0.999501 | − | 0.0315999i | \(-0.989940\pi\) | ||||
−0.999501 | + | 0.0315999i | \(0.989940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.05507e27 | 1.84997 | ||||||||
\(392\) | −2.89055e27 | −1.70403 | ||||||||
\(393\) | 1.06557e27 | 0.611591 | ||||||||
\(394\) | 2.74544e26 | 0.153427 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.84277e26 | −0.0976499 | ||||||||
\(397\) | 1.58428e27 | 0.817584 | 0.408792 | − | 0.912628i | \(-0.365950\pi\) | ||||
0.408792 | + | 0.912628i | \(0.365950\pi\) | |||||||
\(398\) | −1.11966e27 | −0.562748 | ||||||||
\(399\) | 5.27369e26 | 0.258166 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.23835e27 | 1.50421 | 0.752103 | − | 0.659045i | \(-0.229039\pi\) | ||||
0.752103 | + | 0.659045i | \(0.229039\pi\) | |||||||
\(402\) | 6.21524e26 | 0.281245 | ||||||||
\(403\) | −3.64282e26 | −0.160596 | ||||||||
\(404\) | 1.21034e27 | 0.519880 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.06507e26 | 0.165785 | ||||||||
\(407\) | −2.40548e27 | −0.956005 | ||||||||
\(408\) | 2.16712e27 | 0.839366 | ||||||||
\(409\) | −1.32012e27 | −0.498333 | −0.249166 | − | 0.968461i | \(-0.580157\pi\) | ||||
−0.249166 | + | 0.968461i | \(0.580157\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.22476e27 | 0.797890 | ||||||||
\(412\) | 2.53656e27 | 0.886796 | ||||||||
\(413\) | 7.73449e27 | 2.63606 | ||||||||
\(414\) | −9.25509e26 | −0.307523 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.96683e26 | −0.314831 | ||||||||
\(417\) | −1.22798e27 | −0.378234 | ||||||||
\(418\) | 3.54280e26 | 0.106413 | ||||||||
\(419\) | −4.15945e26 | −0.121840 | −0.0609198 | − | 0.998143i | \(-0.519403\pi\) | ||||
−0.0609198 | + | 0.998143i | \(0.519403\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.74327e27 | −0.485740 | −0.242870 | − | 0.970059i | \(-0.578089\pi\) | ||||
−0.242870 | + | 0.970059i | \(0.578089\pi\) | |||||||
\(422\) | 1.53370e27 | 0.416831 | ||||||||
\(423\) | 7.55706e26 | 0.200345 | ||||||||
\(424\) | 2.41046e27 | 0.623388 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.09740e27 | −0.270125 | ||||||||
\(427\) | 6.06349e27 | 1.45623 | ||||||||
\(428\) | −3.85996e27 | −0.904530 | ||||||||
\(429\) | −4.86425e26 | −0.111228 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.48313e26 | −0.206510 | −0.103255 | − | 0.994655i | \(-0.532926\pi\) | ||||
−0.103255 | + | 0.994655i | \(0.532926\pi\) | |||||||
\(432\) | −1.81665e26 | −0.0386092 | ||||||||
\(433\) | −1.08053e26 | −0.0224137 | −0.0112069 | − | 0.999937i | \(-0.503567\pi\) | ||||
−0.0112069 | + | 0.999937i | \(0.503567\pi\) | |||||||
\(434\) | 2.56796e27 | 0.519931 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.56978e27 | 0.302853 | ||||||||
\(437\) | −1.96184e27 | −0.369495 | ||||||||
\(438\) | −1.92384e26 | −0.0353745 | ||||||||
\(439\) | −5.87233e27 | −1.05422 | −0.527112 | − | 0.849796i | \(-0.676725\pi\) | ||||
−0.527112 | + | 0.849796i | \(0.676725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.15675e27 | 0.540299 | ||||||||
\(442\) | 1.96783e27 | 0.328893 | ||||||||
\(443\) | −1.92716e27 | −0.314541 | −0.157271 | − | 0.987556i | \(-0.550270\pi\) | ||||
−0.157271 | + | 0.987556i | \(0.550270\pi\) | |||||||
\(444\) | 3.25043e27 | 0.518108 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.76335e27 | −1.18041 | ||||||||
\(447\) | −4.90729e27 | −0.728808 | ||||||||
\(448\) | 9.26478e27 | 1.34405 | ||||||||
\(449\) | 9.45588e27 | 1.34003 | 0.670016 | − | 0.742346i | \(-0.266287\pi\) | ||||
0.670016 | + | 0.742346i | \(0.266287\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.06780e27 | −0.550182 | ||||||||
\(452\) | −9.00121e26 | −0.118945 | ||||||||
\(453\) | −5.80841e27 | −0.749940 | ||||||||
\(454\) | −2.76350e26 | −0.0348637 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.39164e27 | −0.167647 | ||||||||
\(457\) | 2.59303e27 | 0.305273 | 0.152636 | − | 0.988282i | \(-0.451224\pi\) | ||||
0.152636 | + | 0.988282i | \(0.451224\pi\) | |||||||
\(458\) | 5.03643e27 | 0.579476 | ||||||||
\(459\) | −2.36669e27 | −0.266139 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.56399e27 | 0.705194 | 0.352597 | − | 0.935775i | \(-0.385299\pi\) | ||||
0.352597 | + | 0.935775i | \(0.385299\pi\) | |||||||
\(462\) | 3.42899e27 | 0.360101 | ||||||||
\(463\) | 9.11873e27 | 0.936125 | 0.468063 | − | 0.883695i | \(-0.344952\pi\) | ||||
0.468063 | + | 0.883695i | \(0.344952\pi\) | |||||||
\(464\) | −2.96830e26 | −0.0297899 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.34503e27 | −0.320884 | ||||||||
\(467\) | 1.69430e28 | 1.58914 | 0.794572 | − | 0.607170i | \(-0.207695\pi\) | ||||
0.794572 | + | 0.607170i | \(0.207695\pi\) | |||||||
\(468\) | 6.57288e26 | 0.0602802 | ||||||||
\(469\) | 1.27515e28 | 1.14352 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.42811e27 | −0.551270 | ||||||||
\(472\) | −2.04100e28 | −1.71180 | ||||||||
\(473\) | −2.62289e27 | −0.215149 | ||||||||
\(474\) | −9.71930e27 | −0.779763 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.52949e28 | 1.17401 | ||||||||
\(477\) | −2.63244e27 | −0.197659 | ||||||||
\(478\) | −3.36465e27 | −0.247142 | ||||||||
\(479\) | −9.99660e27 | −0.718339 | −0.359169 | − | 0.933272i | \(-0.616940\pi\) | ||||
−0.359169 | + | 0.933272i | \(0.616940\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.57998e27 | 0.590151 | ||||||||
\(482\) | 1.50742e28 | 1.01447 | ||||||||
\(483\) | −1.89882e28 | −1.25037 | ||||||||
\(484\) | 5.59845e27 | 0.360738 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.16972e26 | 0.0442406 | ||||||||
\(487\) | −1.13449e28 | −0.685088 | −0.342544 | − | 0.939502i | \(-0.611289\pi\) | ||||
−0.342544 | + | 0.939502i | \(0.611289\pi\) | |||||||
\(488\) | −1.60005e28 | −0.945640 | ||||||||
\(489\) | 1.89445e28 | 1.09582 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.77588e27 | 0.430917 | 0.215459 | − | 0.976513i | \(-0.430875\pi\) | ||||
0.215459 | + | 0.976513i | \(0.430875\pi\) | |||||||
\(492\) | 5.49667e27 | 0.298171 | ||||||||
\(493\) | −3.86705e27 | −0.205346 | ||||||||
\(494\) | −1.26366e27 | −0.0656898 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.87511e27 | −0.0934263 | ||||||||
\(497\) | −2.25148e28 | −1.09832 | ||||||||
\(498\) | −1.87156e26 | −0.00893913 | ||||||||
\(499\) | −4.94546e27 | −0.231287 | −0.115643 | − | 0.993291i | \(-0.536893\pi\) | ||||
−0.115643 | + | 0.993291i | \(0.536893\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.28030e28 | −0.574139 | ||||||||
\(502\) | −3.54904e27 | −0.155855 | ||||||||
\(503\) | 1.49983e27 | 0.0645028 | 0.0322514 | − | 0.999480i | \(-0.489732\pi\) | ||||
0.0322514 | + | 0.999480i | \(0.489732\pi\) | |||||||
\(504\) | −1.34693e28 | −0.567316 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.27560e28 | −0.515388 | ||||||||
\(507\) | −1.28539e28 | −0.508688 | ||||||||
\(508\) | 1.70754e28 | 0.661913 | ||||||||
\(509\) | 3.17947e28 | 1.20731 | 0.603653 | − | 0.797247i | \(-0.293711\pi\) | ||||
0.603653 | + | 0.797247i | \(0.293711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.94704e27 | −0.143831 | ||||||||
\(512\) | −1.10382e28 | −0.394060 | ||||||||
\(513\) | 1.51980e27 | 0.0531561 | ||||||||
\(514\) | −2.83564e28 | −0.971715 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.54422e27 | 0.116600 | ||||||||
\(517\) | 1.04157e28 | 0.335766 | ||||||||
\(518\) | −6.04833e28 | −1.91062 | ||||||||
\(519\) | −2.31804e28 | −0.717568 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.91614e28 | 1.16429 | 0.582147 | − | 0.813084i | \(-0.302213\pi\) | ||||
0.582147 | + | 0.813084i | \(0.302213\pi\) | |||||||
\(522\) | 1.17149e27 | 0.0341349 | ||||||||
\(523\) | −5.01202e28 | −1.43135 | −0.715674 | − | 0.698435i | \(-0.753880\pi\) | ||||
−0.715674 | + | 0.698435i | \(0.753880\pi\) | |||||||
\(524\) | −1.98453e28 | −0.555493 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.63985e28 | −0.978889 | ||||||||
\(527\) | −2.44286e28 | −0.644002 | ||||||||
\(528\) | −2.50383e27 | −0.0647066 | ||||||||
\(529\) | 3.11655e28 | 0.789568 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.22896e28 | 0.542762 | ||||||||
\(532\) | −9.82175e27 | −0.234486 | ||||||||
\(533\) | 1.45092e28 | 0.339632 | ||||||||
\(534\) | 4.86751e27 | 0.111718 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.36490e28 | −0.742577 | ||||||||
\(537\) | 1.74143e28 | 0.376857 | ||||||||
\(538\) | −1.65714e28 | −0.351679 | ||||||||
\(539\) | 4.35085e28 | 0.905507 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.55350e27 | −0.0711352 | −0.0355676 | − | 0.999367i | \(-0.511324\pi\) | ||||
−0.0355676 | + | 0.999367i | \(0.511324\pi\) | |||||||
\(542\) | −2.72448e28 | −0.534923 | ||||||||
\(543\) | 3.45175e28 | 0.664724 | ||||||||
\(544\) | −6.68370e28 | −1.26249 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.22307e28 | −0.222294 | ||||||||
\(547\) | −3.63220e27 | −0.0647594 | −0.0323797 | − | 0.999476i | \(-0.510309\pi\) | ||||
−0.0323797 | + | 0.999476i | \(0.510309\pi\) | |||||||
\(548\) | −4.14339e28 | −0.724704 | ||||||||
\(549\) | 1.74740e28 | 0.299836 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.48326e27 | 0.0410139 | ||||||||
\(552\) | 5.01066e28 | 0.811960 | ||||||||
\(553\) | −1.99406e29 | −3.17047 | ||||||||
\(554\) | 1.79779e28 | 0.280470 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.28699e28 | 0.343541 | ||||||||
\(557\) | −7.81368e27 | −0.115180 | −0.0575899 | − | 0.998340i | \(-0.518342\pi\) | ||||
−0.0575899 | + | 0.998340i | \(0.518342\pi\) | |||||||
\(558\) | 7.40045e27 | 0.107053 | ||||||||
\(559\) | 9.35547e27 | 0.132813 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.26194e28 | −0.446032 | ||||||||
\(562\) | −2.40922e28 | −0.323329 | ||||||||
\(563\) | 4.73621e28 | 0.623868 | 0.311934 | − | 0.950104i | \(-0.399023\pi\) | ||||
0.311934 | + | 0.950104i | \(0.399023\pi\) | |||||||
\(564\) | −1.40743e28 | −0.181969 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.76180e28 | −0.344048 | ||||||||
\(567\) | 1.47097e28 | 0.179880 | ||||||||
\(568\) | 5.94129e28 | 0.713219 | ||||||||
\(569\) | 3.94549e28 | 0.464967 | 0.232484 | − | 0.972600i | \(-0.425315\pi\) | ||||
0.232484 | + | 0.972600i | \(0.425315\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.57091e28 | 1.08711 | 0.543556 | − | 0.839373i | \(-0.317078\pi\) | ||||
0.543556 | + | 0.839373i | \(0.317078\pi\) | |||||||
\(572\) | 9.05921e27 | 0.101026 | ||||||||
\(573\) | 6.67992e28 | 0.731387 | ||||||||
\(574\) | −1.02281e29 | −1.09956 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.66997e28 | 0.276739 | ||||||||
\(577\) | 2.32691e28 | 0.236828 | 0.118414 | − | 0.992964i | \(-0.462219\pi\) | ||||
0.118414 | + | 0.992964i | \(0.462219\pi\) | |||||||
\(578\) | 6.29591e28 | 0.629240 | ||||||||
\(579\) | −9.42224e28 | −0.924761 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.83978e27 | −0.0363460 | ||||||||
\(582\) | −8.12070e28 | −0.754922 | ||||||||
\(583\) | −3.62822e28 | −0.331264 | ||||||||
\(584\) | 1.04156e28 | 0.0934002 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.82623e28 | −0.763573 | ||||||||
\(587\) | 4.21414e28 | 0.358104 | 0.179052 | − | 0.983840i | \(-0.442697\pi\) | ||||
0.179052 | + | 0.983840i | \(0.442697\pi\) | |||||||
\(588\) | −5.87914e28 | −0.490740 | ||||||||
\(589\) | 1.56871e28 | 0.128627 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.62325e28 | 0.128445 | ||||||||
\(592\) | 4.41647e28 | 0.343318 | ||||||||
\(593\) | −6.60899e28 | −0.504732 | −0.252366 | − | 0.967632i | \(-0.581209\pi\) | ||||
−0.252366 | + | 0.967632i | \(0.581209\pi\) | |||||||
\(594\) | 9.88180e27 | 0.0741444 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.13936e28 | 0.661958 | ||||||||
\(597\) | −6.62003e28 | −0.471118 | ||||||||
\(598\) | 4.54988e28 | 0.318154 | ||||||||
\(599\) | −1.39484e29 | −0.958394 | −0.479197 | − | 0.877707i | \(-0.659072\pi\) | ||||
−0.479197 | + | 0.877707i | \(0.659072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.18282e29 | 0.784761 | 0.392380 | − | 0.919803i | \(-0.371652\pi\) | ||||
0.392380 | + | 0.919803i | \(0.371652\pi\) | |||||||
\(602\) | −6.59500e28 | −0.429983 | ||||||||
\(603\) | 3.67478e28 | 0.235450 | ||||||||
\(604\) | 1.08176e29 | 0.681151 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.49042e28 | −0.394739 | ||||||||
\(607\) | −6.52603e28 | −0.390093 | −0.195046 | − | 0.980794i | \(-0.562486\pi\) | ||||
−0.195046 | + | 0.980794i | \(0.562486\pi\) | |||||||
\(608\) | 4.29201e28 | 0.252158 | ||||||||
\(609\) | 2.40349e28 | 0.138791 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.71511e28 | −0.207271 | ||||||||
\(612\) | 4.40774e28 | 0.241728 | ||||||||
\(613\) | −5.95584e28 | −0.321076 | −0.160538 | − | 0.987030i | \(-0.551323\pi\) | ||||
−0.160538 | + | 0.987030i | \(0.551323\pi\) | |||||||
\(614\) | −7.19709e28 | −0.381407 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.85644e29 | −0.950785 | ||||||||
\(617\) | 4.33753e28 | 0.218398 | 0.109199 | − | 0.994020i | \(-0.465171\pi\) | ||||
0.109199 | + | 0.994020i | \(0.465171\pi\) | |||||||
\(618\) | −1.36022e29 | −0.673334 | ||||||||
\(619\) | −2.80609e29 | −1.36568 | −0.682842 | − | 0.730566i | \(-0.739256\pi\) | ||||
−0.682842 | + | 0.730566i | \(0.739256\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.47210e28 | −0.257450 | ||||||||
\(622\) | −1.90843e29 | −0.882828 | ||||||||
\(623\) | 9.98643e28 | 0.454240 | ||||||||
\(624\) | 8.93079e27 | 0.0399440 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.40909e28 | −0.0609406 | ||||||||
\(627\) | 2.09469e28 | 0.0890862 | ||||||||
\(628\) | 1.19718e29 | 0.500704 | ||||||||
\(629\) | 5.75369e29 | 2.36655 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.91070e29 | −0.760124 | −0.380062 | − | 0.924961i | \(-0.624097\pi\) | ||||
−0.380062 | + | 0.924961i | \(0.624097\pi\) | |||||||
\(632\) | 5.26198e29 | 2.05883 | ||||||||
\(633\) | 9.06805e28 | 0.348959 | ||||||||
\(634\) | 2.74919e29 | 1.04056 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.90268e28 | 0.179529 | ||||||||
\(637\) | −1.55188e29 | −0.558978 | ||||||||
\(638\) | 1.61463e28 | 0.0572079 | ||||||||
\(639\) | −6.48843e28 | −0.226142 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.08795e28 | 0.104150 | 0.0520752 | − | 0.998643i | \(-0.483416\pi\) | ||||
0.0520752 | + | 0.998643i | \(0.483416\pi\) | |||||||
\(642\) | 2.06989e29 | 0.686800 | ||||||||
\(643\) | 3.31619e29 | 1.08249 | 0.541245 | − | 0.840865i | \(-0.317953\pi\) | ||||
0.541245 | + | 0.840865i | \(0.317953\pi\) | |||||||
\(644\) | 3.53637e29 | 1.13568 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.47406e28 | −0.263421 | ||||||||
\(647\) | 1.60958e29 | 0.492287 | 0.246143 | − | 0.969233i | \(-0.420837\pi\) | ||||
0.246143 | + | 0.969233i | \(0.420837\pi\) | |||||||
\(648\) | −3.88165e28 | −0.116810 | ||||||||
\(649\) | 3.07211e29 | 0.909635 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.51831e29 | 0.435272 | ||||||||
\(652\) | −3.52823e29 | −0.995308 | ||||||||
\(653\) | 4.10395e29 | 1.13924 | 0.569618 | − | 0.821910i | \(-0.307091\pi\) | ||||
0.569618 | + | 0.821910i | \(0.307091\pi\) | |||||||
\(654\) | −8.41792e28 | −0.229953 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.46850e28 | 0.197580 | ||||||||
\(657\) | −1.13747e28 | −0.0296146 | ||||||||
\(658\) | 2.61891e29 | 0.671042 | ||||||||
\(659\) | 4.59733e29 | 1.15933 | 0.579667 | − | 0.814853i | \(-0.303183\pi\) | ||||
0.579667 | + | 0.814853i | \(0.303183\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.47451e29 | 0.848747 | 0.424374 | − | 0.905487i | \(-0.360494\pi\) | ||||
0.424374 | + | 0.905487i | \(0.360494\pi\) | |||||||
\(662\) | 2.90938e29 | 0.699506 | ||||||||
\(663\) | 1.16349e29 | 0.275340 | ||||||||
\(664\) | 1.01325e28 | 0.0236022 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.74304e29 | −0.393393 | ||||||||
\(667\) | −8.94110e28 | −0.198641 | ||||||||
\(668\) | 2.38444e29 | 0.521476 | ||||||||
\(669\) | −4.59011e29 | −0.988208 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.40839e29 | 0.502506 | ||||||||
\(672\) | 4.15413e29 | 0.853301 | ||||||||
\(673\) | 5.46802e29 | 1.10579 | 0.552894 | − | 0.833252i | \(-0.313524\pi\) | ||||
0.552894 | + | 0.833252i | \(0.313524\pi\) | |||||||
\(674\) | 1.20695e29 | 0.240304 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.39392e29 | 0.462029 | ||||||||
\(677\) | −3.19471e29 | −0.607086 | −0.303543 | − | 0.952818i | \(-0.598170\pi\) | ||||
−0.303543 | + | 0.952818i | \(0.598170\pi\) | |||||||
\(678\) | 4.82688e28 | 0.0903139 | ||||||||
\(679\) | −1.66608e30 | −3.06947 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.63393e28 | −0.0291869 | ||||||||
\(682\) | 1.01998e29 | 0.179414 | ||||||||
\(683\) | −2.97244e29 | −0.514869 | −0.257434 | − | 0.966296i | \(-0.582877\pi\) | ||||
−0.257434 | + | 0.966296i | \(0.582877\pi\) | |||||||
\(684\) | −2.83048e28 | −0.0482803 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.19057e29 | 0.693218 | ||||||||
\(687\) | 2.97780e29 | 0.485121 | ||||||||
\(688\) | 4.81564e28 | 0.0772637 | ||||||||
\(689\) | 1.29413e29 | 0.204492 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.77979e28 | 0.149903 | 0.0749514 | − | 0.997187i | \(-0.476120\pi\) | ||||
0.0749514 | + | 0.997187i | \(0.476120\pi\) | |||||||
\(692\) | 4.31713e29 | 0.651749 | ||||||||
\(693\) | 2.02740e29 | 0.301467 | ||||||||
\(694\) | −5.89796e28 | −0.0863828 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.34239e28 | −0.0901273 | ||||||||
\(697\) | 9.72983e29 | 1.36195 | ||||||||
\(698\) | 5.08587e29 | 0.701267 | ||||||||
\(699\) | −1.97776e29 | −0.268635 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.22259e29 | 0.952037 | 0.476019 | − | 0.879435i | \(-0.342079\pi\) | ||||
0.476019 | + | 0.879435i | \(0.342079\pi\) | |||||||
\(702\) | −3.52469e28 | −0.0457701 | ||||||||
\(703\) | −3.69479e29 | −0.472671 | ||||||||
\(704\) | 3.67993e29 | 0.463796 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.09728e29 | 0.623575 | ||||||||
\(707\) | −1.33160e30 | −1.60499 | ||||||||
\(708\) | −4.15122e29 | −0.492977 | ||||||||
\(709\) | 4.17404e29 | 0.488395 | 0.244197 | − | 0.969726i | \(-0.421475\pi\) | ||||
0.244197 | + | 0.969726i | \(0.421475\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.74657e29 | −0.652796 | ||||||||
\(712\) | −2.63525e29 | −0.294973 | ||||||||
\(713\) | −5.64820e29 | −0.622975 | ||||||||
\(714\) | −8.20183e29 | −0.891414 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.24325e29 | −0.342290 | ||||||||
\(717\) | −1.98936e29 | −0.206900 | ||||||||
\(718\) | 4.81105e29 | 0.493098 | ||||||||
\(719\) | −7.89811e29 | −0.797756 | −0.398878 | − | 0.917004i | \(-0.630600\pi\) | ||||
−0.398878 | + | 0.917004i | \(0.630600\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.79070e30 | −2.73774 | ||||||||
\(722\) | −6.58871e29 | −0.637030 | ||||||||
\(723\) | 8.91266e29 | 0.849288 | ||||||||
\(724\) | −6.42856e29 | −0.603752 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.00216e29 | −0.273904 | ||||||||
\(727\) | 4.46262e29 | 0.401309 | 0.200654 | − | 0.979662i | \(-0.435693\pi\) | ||||
0.200654 | + | 0.979662i | \(0.435693\pi\) | |||||||
\(728\) | 6.62163e29 | 0.586929 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.27373e29 | 0.532590 | ||||||||
\(732\) | −3.25437e29 | −0.272333 | ||||||||
\(733\) | −4.52156e29 | −0.372990 | −0.186495 | − | 0.982456i | \(-0.559713\pi\) | ||||
−0.186495 | + | 0.982456i | \(0.559713\pi\) | |||||||
\(734\) | 1.68546e30 | 1.37060 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.54536e30 | −1.22127 | ||||||||
\(737\) | 5.06484e29 | 0.394600 | ||||||||
\(738\) | −2.94757e29 | −0.226398 | ||||||||
\(739\) | −5.68446e29 | −0.430450 | −0.215225 | − | 0.976564i | \(-0.569049\pi\) | ||||
−0.215225 | + | 0.976564i | \(0.569049\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.47144e28 | −0.0549937 | ||||||||
\(742\) | −9.12279e29 | −0.662044 | ||||||||
\(743\) | −9.68858e29 | −0.693231 | −0.346615 | − | 0.938007i | \(-0.612669\pi\) | ||||
−0.346615 | + | 0.938007i | \(0.612669\pi\) | |||||||
\(744\) | −4.00657e29 | −0.282655 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.79295e28 | −0.0534496 | ||||||||
\(747\) | −1.10656e28 | −0.00748359 | ||||||||
\(748\) | 6.07506e29 | 0.405120 | ||||||||
\(749\) | 4.24669e30 | 2.79249 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.04636e30 | 0.669052 | 0.334526 | − | 0.942387i | \(-0.391424\pi\) | ||||
0.334526 | + | 0.942387i | \(0.391424\pi\) | |||||||
\(752\) | −1.91232e29 | −0.120579 | ||||||||
\(753\) | −2.09838e29 | −0.130478 | ||||||||
\(754\) | −5.75915e28 | −0.0353150 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.73955e29 | −0.163380 | ||||||||
\(757\) | 2.74898e30 | 1.61683 | 0.808415 | − | 0.588612i | \(-0.200326\pi\) | ||||
0.808415 | + | 0.588612i | \(0.200326\pi\) | |||||||
\(758\) | −1.17662e30 | −0.682509 | ||||||||
\(759\) | −7.54203e29 | −0.431469 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.54630e30 | −0.860508 | −0.430254 | − | 0.902708i | \(-0.641576\pi\) | ||||
−0.430254 | + | 0.902708i | \(0.641576\pi\) | |||||||
\(762\) | −9.15661e29 | −0.502583 | ||||||||
\(763\) | −1.72706e30 | −0.934975 | ||||||||
\(764\) | −1.24407e30 | −0.664301 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.32765e30 | 0.689733 | ||||||||
\(767\) | −1.09577e30 | −0.561526 | ||||||||
\(768\) | −1.21636e30 | −0.614852 | ||||||||
\(769\) | −1.67246e30 | −0.833928 | −0.416964 | − | 0.908923i | \(-0.636906\pi\) | ||||
−0.416964 | + | 0.908923i | \(0.636906\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.67658e30 | −0.813493 | ||||||||
\(772\) | 1.75480e30 | 0.839937 | ||||||||
\(773\) | 1.23290e30 | 0.582159 | 0.291080 | − | 0.956699i | \(-0.405986\pi\) | ||||
0.291080 | + | 0.956699i | \(0.405986\pi\) | |||||||
\(774\) | −1.90058e29 | −0.0885330 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.39651e30 | 1.99324 | ||||||||
\(777\) | −3.57610e30 | −1.59952 | ||||||||
\(778\) | −3.12409e30 | −1.37860 | ||||||||
\(779\) | −6.24810e29 | −0.272023 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.94281e29 | −0.378999 | ||||||||
\(782\) | 3.05113e30 | 1.27582 | ||||||||
\(783\) | 6.92648e28 | 0.0285768 | ||||||||
\(784\) | −7.98817e29 | −0.325184 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.06420e30 | 0.421779 | ||||||||
\(787\) | −2.10384e30 | −0.822769 | −0.411385 | − | 0.911462i | \(-0.634955\pi\) | ||||
−0.411385 | + | 0.911462i | \(0.634955\pi\) | |||||||
\(788\) | −3.02315e29 | −0.116663 | ||||||||
\(789\) | −2.15207e30 | −0.819499 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.90305e29 | 0.367211 | ||||||||
\(792\) | −5.34996e29 | −0.195765 | ||||||||
\(793\) | −8.59038e29 | −0.310201 | ||||||||
\(794\) | 1.58224e30 | 0.563841 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.23292e30 | 0.427904 | ||||||||
\(797\) | −4.27207e30 | −1.46327 | −0.731637 | − | 0.681694i | \(-0.761243\pi\) | ||||
−0.731637 | + | 0.681694i | \(0.761243\pi\) | |||||||
\(798\) | 5.26689e29 | 0.178042 | ||||||||
\(799\) | −2.49134e30 | −0.831172 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.87793e29 | 0.0935275 | ||||||||
\(802\) | 3.23417e30 | 1.03737 | ||||||||
\(803\) | −1.56775e29 | −0.0496321 | ||||||||
\(804\) | −6.84392e29 | −0.213854 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.63812e29 | −0.110754 | ||||||||
\(807\) | −9.79791e29 | −0.294416 | ||||||||
\(808\) | 3.51388e30 | 1.04224 | ||||||||
\(809\) | 6.44960e30 | 1.88831 | 0.944154 | − | 0.329503i | \(-0.106881\pi\) | ||||
0.944154 | + | 0.329503i | \(0.106881\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.43726e28 | −0.00980604 | −0.00490302 | − | 0.999988i | \(-0.501561\pi\) | ||||
−0.00490302 | + | 0.999988i | \(0.501561\pi\) | |||||||
\(812\) | −4.47627e29 | −0.126060 | ||||||||
\(813\) | −1.61086e30 | −0.447823 | ||||||||
\(814\) | −2.40237e30 | −0.659302 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.98894e29 | 0.160178 | ||||||||
\(817\) | −4.02874e29 | −0.106374 | ||||||||
\(818\) | −1.31842e30 | −0.343672 | ||||||||
\(819\) | −7.23143e29 | −0.186099 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.56685e30 | −1.14555 | −0.572775 | − | 0.819713i | \(-0.694133\pi\) | ||||
−0.572775 | + | 0.819713i | \(0.694133\pi\) | |||||||
\(822\) | 2.22188e30 | 0.550259 | ||||||||
\(823\) | −7.18647e30 | −1.75718 | −0.878592 | − | 0.477572i | \(-0.841517\pi\) | ||||
−0.878592 | + | 0.477572i | \(0.841517\pi\) | |||||||
\(824\) | 7.36417e30 | 1.77782 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.72450e30 | 1.81794 | ||||||||
\(827\) | 2.77401e30 | 0.644614 | 0.322307 | − | 0.946635i | \(-0.395542\pi\) | ||||
0.322307 | + | 0.946635i | \(0.395542\pi\) | |||||||
\(828\) | 1.01913e30 | 0.233835 | ||||||||
\(829\) | 5.61496e30 | 1.27211 | 0.636054 | − | 0.771644i | \(-0.280565\pi\) | ||||
0.636054 | + | 0.771644i | \(0.280565\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.06295e30 | 0.234801 | ||||||||
\(832\) | −1.31258e30 | −0.286306 | ||||||||
\(833\) | −1.04068e31 | −2.24154 | ||||||||
\(834\) | −1.22639e30 | −0.260847 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.90116e29 | −0.0809148 | ||||||||
\(837\) | 4.37554e29 | 0.0896219 | ||||||||
\(838\) | −4.15408e29 | −0.0840258 | ||||||||
\(839\) | 3.99858e30 | 0.798740 | 0.399370 | − | 0.916790i | \(-0.369229\pi\) | ||||
0.399370 | + | 0.916790i | \(0.369229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.01967e30 | −0.977951 | ||||||||
\(842\) | −1.74102e30 | −0.334987 | ||||||||
\(843\) | −1.42446e30 | −0.270682 | ||||||||
\(844\) | −1.68884e30 | −0.316951 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.54731e29 | 0.138167 | ||||||||
\(847\) | −6.15936e30 | −1.11368 | ||||||||
\(848\) | 6.66142e29 | 0.118963 | ||||||||
\(849\) | −1.63292e30 | −0.288028 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.33033e31 | 2.28928 | ||||||||
\(852\) | 1.20841e30 | 0.205399 | ||||||||
\(853\) | 6.64773e30 | 1.11611 | 0.558057 | − | 0.829803i | \(-0.311547\pi\) | ||||
0.558057 | + | 0.829803i | \(0.311547\pi\) | |||||||
\(854\) | 6.05566e30 | 1.00428 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.12063e31 | −1.81337 | ||||||||
\(857\) | −8.33064e30 | −1.33162 | −0.665809 | − | 0.746122i | \(-0.731914\pi\) | ||||
−0.665809 | + | 0.746122i | \(0.731914\pi\) | |||||||
\(858\) | −4.85798e29 | −0.0767077 | ||||||||
\(859\) | 4.73149e30 | 0.738023 | 0.369012 | − | 0.929425i | \(-0.379696\pi\) | ||||
0.369012 | + | 0.929425i | \(0.379696\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.04738e30 | −0.920523 | ||||||||
\(862\) | −9.47089e29 | −0.142418 | ||||||||
\(863\) | 5.45168e30 | 0.809874 | 0.404937 | − | 0.914345i | \(-0.367294\pi\) | ||||
0.404937 | + | 0.914345i | \(0.367294\pi\) | |||||||
\(864\) | 1.19715e30 | 0.175694 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.07914e29 | −0.0154575 | ||||||||
\(867\) | 3.72247e30 | 0.526782 | ||||||||
\(868\) | −2.82771e30 | −0.395347 | ||||||||
\(869\) | −7.92032e30 | −1.09404 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.80655e30 | −0.243590 | ||||||||
\(872\) | 4.55742e30 | 0.607150 | ||||||||
\(873\) | −4.80139e30 | −0.632001 | ||||||||
\(874\) | −1.95931e30 | −0.254820 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.11844e29 | 0.0268982 | ||||||||
\(877\) | 1.97851e30 | 0.248224 | 0.124112 | − | 0.992268i | \(-0.460392\pi\) | ||||
0.124112 | + | 0.992268i | \(0.460392\pi\) | |||||||
\(878\) | −5.86475e30 | −0.727038 | ||||||||
\(879\) | −5.21854e30 | −0.639242 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.03712e30 | −0.482864 | −0.241432 | − | 0.970418i | \(-0.577617\pi\) | ||||
−0.241432 | + | 0.970418i | \(0.577617\pi\) | |||||||
\(882\) | 3.15267e30 | 0.372614 | ||||||||
\(883\) | 9.81177e30 | 1.14593 | 0.572967 | − | 0.819578i | \(-0.305792\pi\) | ||||
0.572967 | + | 0.819578i | \(0.305792\pi\) | |||||||
\(884\) | −2.16688e30 | −0.250084 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.92467e30 | −0.216921 | ||||||||
\(887\) | −6.61087e30 | −0.736310 | −0.368155 | − | 0.929764i | \(-0.620010\pi\) | ||||
−0.368155 | + | 0.929764i | \(0.620010\pi\) | |||||||
\(888\) | 9.43671e30 | 1.03869 | ||||||||
\(889\) | −1.87861e31 | −2.04347 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.84265e29 | 0.0620717 | ||||||||
\(892\) | 8.54864e30 | 0.897565 | ||||||||
\(893\) | 1.59984e30 | 0.166010 | ||||||||
\(894\) | −4.90096e30 | −0.502617 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.50074e30 | −0.551045 | ||||||||
\(897\) | 2.69013e30 | 0.266350 | ||||||||
\(898\) | 9.44368e30 | 0.924144 | ||||||||
\(899\) | 7.14938e29 | 0.0691500 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.67838e30 | 0.820028 | ||||||||
\(902\) | −4.06255e30 | −0.379429 | ||||||||
\(903\) | −3.89931e30 | −0.359971 | ||||||||
\(904\) | −2.61325e30 | −0.238458 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.80092e30 | −0.517191 | ||||||||
\(907\) | −7.36764e30 | −0.649310 | −0.324655 | − | 0.945833i | \(-0.605248\pi\) | ||||
−0.324655 | + | 0.945833i | \(0.605248\pi\) | |||||||
\(908\) | 3.04304e29 | 0.0265098 | ||||||||
\(909\) | −3.83748e30 | −0.330465 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.51177e30 | 0.295518 | 0.147759 | − | 0.989023i | \(-0.452794\pi\) | ||||
0.147759 | + | 0.989023i | \(0.452794\pi\) | |||||||
\(912\) | −3.84586e29 | −0.0319924 | ||||||||
\(913\) | −1.52514e29 | −0.0125420 | ||||||||
\(914\) | 2.58969e30 | 0.210529 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.54588e30 | −0.440624 | ||||||||
\(917\) | 2.18336e31 | 1.71493 | ||||||||
\(918\) | −2.36364e30 | −0.183541 | ||||||||
\(919\) | −1.76504e31 | −1.35501 | −0.677505 | − | 0.735519i | \(-0.736939\pi\) | ||||
−0.677505 | + | 0.735519i | \(0.736939\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.25530e30 | −0.319304 | ||||||||
\(922\) | 6.55552e30 | 0.486332 | ||||||||
\(923\) | 3.18977e30 | 0.233960 | ||||||||
\(924\) | −3.77584e30 | −0.273815 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.10696e30 | 0.645592 | ||||||||
\(927\) | −8.04235e30 | −0.563697 | ||||||||
\(928\) | 1.95608e30 | 0.135561 | ||||||||
\(929\) | 1.81466e31 | 1.24346 | 0.621729 | − | 0.783232i | \(-0.286430\pi\) | ||||
0.621729 | + | 0.783232i | \(0.286430\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.68286e30 | 0.447704 | ||||||||
\(932\) | 3.68339e30 | 0.243995 | ||||||||
\(933\) | −1.12836e31 | −0.739080 | ||||||||
\(934\) | 1.69211e31 | 1.09594 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.90825e30 | 0.120848 | ||||||||
\(937\) | −1.90377e31 | −1.19220 | −0.596101 | − | 0.802910i | \(-0.703284\pi\) | ||||
−0.596101 | + | 0.802910i | \(0.703284\pi\) | |||||||
\(938\) | 1.27350e31 | 0.788624 | ||||||||
\(939\) | −8.33126e29 | −0.0510178 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.95092e30 | 0.476131 | 0.238065 | − | 0.971249i | \(-0.423487\pi\) | ||||
0.238065 | + | 0.971249i | \(0.423487\pi\) | |||||||
\(942\) | −6.41982e30 | −0.380179 | ||||||||
\(943\) | 2.24966e31 | 1.31748 | ||||||||
\(944\) | −5.64040e30 | −0.326666 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.61951e30 | −0.148376 | ||||||||
\(947\) | 1.53126e31 | 0.857779 | 0.428890 | − | 0.903357i | \(-0.358905\pi\) | ||||
0.428890 | + | 0.903357i | \(0.358905\pi\) | |||||||
\(948\) | 1.07024e31 | 0.592918 | ||||||||
\(949\) | 5.59192e29 | 0.0306384 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.62547e31 | 0.871131 | ||||||||
\(952\) | 4.44043e31 | 2.35362 | ||||||||
\(953\) | 2.71409e31 | 1.42282 | 0.711409 | − | 0.702778i | \(-0.248057\pi\) | ||||
0.711409 | + | 0.702778i | \(0.248057\pi\) | |||||||
\(954\) | −2.62905e30 | −0.136314 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.70499e30 | 0.187923 | ||||||||
\(957\) | 9.54655e29 | 0.0478929 | ||||||||
\(958\) | −9.98369e30 | −0.495397 | ||||||||
\(959\) | 4.55852e31 | 2.23732 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.63092e31 | −0.783134 | ||||||||
\(962\) | 8.56891e30 | 0.406993 | ||||||||
\(963\) | 1.22383e31 | 0.574970 | ||||||||
\(964\) | −1.65990e31 | −0.771387 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.89637e31 | −0.862309 | ||||||||
\(967\) | −3.62577e31 | −1.63088 | −0.815439 | − | 0.578842i | \(-0.803505\pi\) | ||||
−0.815439 | + | 0.578842i | \(0.803505\pi\) | |||||||
\(968\) | 1.62535e31 | 0.723196 | ||||||||
\(969\) | −5.01031e30 | −0.220529 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.06711e29 | −0.0175180 | −0.00875899 | − | 0.999962i | \(-0.502788\pi\) | ||||
−0.00875899 | + | 0.999962i | \(0.502788\pi\) | |||||||
\(972\) | −7.89495e29 | −0.0336398 | ||||||||
\(973\) | −2.51612e31 | −1.06059 | ||||||||
\(974\) | −1.13303e31 | −0.472466 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.42182e30 | −0.180459 | ||||||||
\(977\) | −3.57816e30 | −0.144466 | −0.0722331 | − | 0.997388i | \(-0.523013\pi\) | ||||
−0.0722331 | + | 0.997388i | \(0.523013\pi\) | |||||||
\(978\) | 1.89201e31 | 0.755726 | ||||||||
\(979\) | 3.96657e30 | 0.156746 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.97712e30 | −0.192510 | ||||||||
\(982\) | 7.76585e30 | 0.297179 | ||||||||
\(983\) | 1.79552e31 | 0.679796 | 0.339898 | − | 0.940462i | \(-0.389607\pi\) | ||||
0.339898 | + | 0.940462i | \(0.389607\pi\) | |||||||
\(984\) | 1.59580e31 | 0.597765 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.86206e30 | −0.141616 | ||||||||
\(987\) | 1.54844e31 | 0.561778 | ||||||||
\(988\) | 1.39149e30 | 0.0499494 | ||||||||
\(989\) | 1.45057e31 | 0.515201 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.08018e31 | 0.375599 | 0.187800 | − | 0.982207i | \(-0.439864\pi\) | ||||
0.187800 | + | 0.982207i | \(0.439864\pi\) | |||||||
\(992\) | 1.23568e31 | 0.425142 | ||||||||
\(993\) | 1.72018e31 | 0.585608 | ||||||||
\(994\) | −2.24858e31 | −0.757445 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.06087e29 | 0.00679716 | ||||||||
\(997\) | −3.78917e31 | −1.23664 | −0.618322 | − | 0.785925i | \(-0.712187\pi\) | ||||
−0.618322 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(998\) | −4.93907e30 | −0.159505 | ||||||||
\(999\) | −1.03058e31 | −0.329338 |
(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 | 75.22.a.m.1.7 | 10 | ||
5.2 | odd | 4 | 15.22.b.a.4.13 | yes | 20 | ||
5.3 | odd | 4 | 15.22.b.a.4.8 | ✓ | 20 | ||
5.4 | even | 2 | 75.22.a.n.1.4 | 10 | |||
15.2 | even | 4 | 45.22.b.d.19.8 | 20 | |||
15.8 | even | 4 | 45.22.b.d.19.13 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.22.b.a.4.8 | ✓ | 20 | 5.3 | odd | 4 | ||
15.22.b.a.4.13 | yes | 20 | 5.2 | odd | 4 | ||
45.22.b.d.19.8 | 20 | 15.2 | even | 4 | |||
45.22.b.d.19.13 | 20 | 15.8 | even | 4 | |||
75.22.a.m.1.7 | 10 | 1.1 | even | 1 | trivial | ||
75.22.a.n.1.4 | 10 | 5.4 | even | 2 |