Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,5,Mod(29,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.29");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(6.20219778503\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 110x^{6} + 2705x^{4} + 17000x^{2} + 25600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 5^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 29.4 | ||
Root | \(-4.83397i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.29 |
Dual form | 60.5.b.a.29.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.64318 | + | 8.60312i | −0.293687 | + | 0.955902i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −23.0886 | − | 9.58741i | −0.923542 | − | 0.383496i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 11.6269i | − | 0.237283i | −0.992937 | − | 0.118641i | \(-0.962146\pi\) | ||
0.992937 | − | 0.118641i | \(-0.0378539\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −67.0272 | − | 45.4792i | −0.827496 | − | 0.561471i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 177.001i | − | 1.46282i | −0.681940 | − | 0.731409i | \(-0.738863\pi\) | ||
0.681940 | − | 0.731409i | \(-0.261137\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.7381i | 0.0990421i | 0.998773 | + | 0.0495211i | \(0.0157695\pi\) | ||||
−0.998773 | + | 0.0495211i | \(0.984231\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 143.509 | − | 173.292i | 0.637817 | − | 0.770188i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −294.322 | −1.01841 | −0.509207 | − | 0.860644i | \(-0.670061\pi\) | ||||
−0.509207 | + | 0.860644i | \(0.670061\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −390.163 | −1.08078 | −0.540392 | − | 0.841413i | \(-0.681724\pi\) | ||||
−0.540392 | + | 0.841413i | \(0.681724\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 100.027 | + | 30.7319i | 0.226819 | + | 0.0696868i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −414.194 | −0.782975 | −0.391488 | − | 0.920183i | \(-0.628039\pi\) | ||||
−0.391488 | + | 0.920183i | \(0.628039\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 441.163 | + | 442.719i | 0.705861 | + | 0.708350i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 568.427 | − | 456.433i | 0.779736 | − | 0.626109i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1106.25i | 1.31539i | 0.753282 | + | 0.657697i | \(0.228469\pi\) | ||||
−0.753282 | + | 0.657697i | \(0.771531\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 250.163 | 0.260316 | 0.130158 | − | 0.991493i | \(-0.458452\pi\) | ||||
0.130158 | + | 0.991493i | \(0.458452\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1522.76 | + | 467.845i | 1.39831 | + | 0.429610i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −111.471 | + | 268.447i | −0.0909971 | + | 0.219141i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2261.90i | − | 1.65223i | −0.563504 | − | 0.826113i | \(-0.690547\pi\) | ||
0.563504 | − | 0.826113i | \(-0.309453\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −144.000 | − | 44.2419i | −0.0946746 | − | 0.0290873i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2293.62i | 1.36444i | 0.731148 | + | 0.682219i | \(0.238985\pi\) | ||||
−0.731148 | + | 0.682219i | \(0.761015\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 990.978i | 0.535953i | 0.963425 | + | 0.267977i | \(0.0863550\pi\) | ||||
−0.963425 | + | 0.267977i | \(0.913645\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1111.53 | + | 1692.67i | 0.548906 | + | 0.835884i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3163.39 | −1.43205 | −0.716023 | − | 0.698077i | \(-0.754039\pi\) | ||||
−0.716023 | + | 0.698077i | \(0.754039\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2265.82 | 0.943697 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 777.946 | − | 2532.09i | 0.299095 | − | 0.973505i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1253.30 | −0.446172 | −0.223086 | − | 0.974799i | \(-0.571613\pi\) | ||||
−0.223086 | + | 0.974799i | \(0.571613\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1696.98 | + | 4086.70i | −0.560985 | + | 1.35097i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1031.27 | − | 3356.62i | 0.317412 | − | 1.03312i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4484.01i | − | 1.28814i | −0.764967 | − | 0.644069i | \(-0.777245\pi\) | ||
0.764967 | − | 0.644069i | \(-0.222755\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4439.14 | −1.19300 | −0.596499 | − | 0.802614i | \(-0.703442\pi\) | ||||
−0.596499 | + | 0.802614i | \(0.703442\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −528.780 | + | 779.316i | −0.133227 | + | 0.196351i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 160.475 | − | 386.459i | 0.0379823 | − | 0.0914696i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8074.48i | − | 1.79873i | −0.437203 | − | 0.899363i | \(-0.644031\pi\) | ||
0.437203 | − | 0.899363i | \(-0.355969\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1094.79 | − | 3563.36i | 0.229949 | − | 0.748448i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4395.49i | − | 0.871949i | −0.899959 | − | 0.435974i | \(-0.856404\pi\) | ||
0.899959 | − | 0.435974i | \(-0.143596\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5593.47i | 1.04963i | 0.851217 | + | 0.524814i | \(0.175865\pi\) | ||||
−0.851217 | + | 0.524814i | \(0.824135\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4974.84 | + | 2625.19i | −0.884415 | + | 0.466701i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2057.96 | −0.347101 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 569.510 | 0.0912531 | 0.0456265 | − | 0.998959i | \(-0.485472\pi\) | ||||
0.0456265 | + | 0.998959i | \(0.485472\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2424.29 | + | 6096.68i | 0.369500 | + | 0.929231i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5253.93 | 0.762655 | 0.381328 | − | 0.924440i | \(-0.375467\pi\) | ||||
0.381328 | + | 0.924440i | \(0.375467\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6795.47 | + | 2821.78i | 0.940549 | + | 0.390558i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9517.17 | − | 2924.01i | −1.25739 | − | 0.386314i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7050.54i | 0.890107i | 0.895504 | + | 0.445054i | \(0.146815\pi\) | ||||
−0.895504 | + | 0.445054i | \(0.853185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 194.612 | 0.0235010 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −661.226 | + | 2152.18i | −0.0764512 | + | 0.248836i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9008.31 | + | 3740.65i | 0.998150 | + | 0.414477i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7364.12i | − | 0.782667i | −0.920249 | − | 0.391334i | \(-0.872014\pi\) | ||
0.920249 | − | 0.391334i | \(-0.127986\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8049.85 | + | 11863.9i | −0.821329 | + | 1.21048i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 280.265i | − | 0.0274743i | −0.999906 | − | 0.0137371i | \(-0.995627\pi\) | ||
0.999906 | − | 0.0137371i | \(-0.00437281\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4121.46i | − | 0.388487i | −0.980953 | − | 0.194244i | \(-0.937775\pi\) | ||
0.980953 | − | 0.194244i | \(-0.0622252\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2014.85 | − | 1668.56i | −0.182752 | − | 0.151343i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18817.9 | 1.64363 | 0.821814 | − | 0.569756i | \(-0.192962\pi\) | ||||
0.821814 | + | 0.569756i | \(0.192962\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3096.45 | −0.260622 | −0.130311 | − | 0.991473i | \(-0.541598\pi\) | ||||
−0.130311 | + | 0.991473i | \(0.541598\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19459.4 | + | 5978.60i | 1.57937 | + | 0.485237i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8644.49 | 0.676990 | 0.338495 | − | 0.940968i | \(-0.390082\pi\) | ||||
0.338495 | + | 0.940968i | \(0.390082\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9563.14 | + | 3971.05i | 0.723111 | + | 0.300268i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 761.236 | − | 1121.91i | 0.0556093 | − | 0.0819570i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3422.04i | 0.241652i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16688.3 | −1.13983 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19732.3 | − | 6062.45i | −1.30427 | − | 0.400717i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5941.30 | − | 14451.4i | −0.380243 | − | 0.924887i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16001.4i | 0.992089i | 0.868297 | + | 0.496044i | \(0.165215\pi\) | ||||
−0.868297 | + | 0.496044i | \(0.834785\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8525.50 | − | 2619.33i | −0.512319 | − | 0.157402i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1297.86i | − | 0.0756285i | −0.999285 | − | 0.0378143i | \(-0.987960\pi\) | ||
0.999285 | − | 0.0378143i | \(-0.0120395\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4536.37i | 0.256452i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17500.2 | + | 5088.64i | −0.960229 | + | 0.279212i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18427.4 | −0.981801 | −0.490900 | − | 0.871216i | \(-0.663332\pi\) | ||||
−0.490900 | + | 0.871216i | \(0.663332\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9241.84 | 0.478331 | 0.239166 | − | 0.970979i | \(-0.423126\pi\) | ||||
0.239166 | + | 0.970979i | \(0.423126\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8361.40 | − | 27215.0i | 0.420573 | − | 1.36889i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2962.66 | 0.144881 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10606.0 | − | 25541.7i | 0.504449 | − | 1.21482i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5988.96 | + | 19493.1i | −0.277151 | + | 0.902081i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 36705.5i | − | 1.65333i | −0.562696 | − | 0.826664i | \(-0.690236\pi\) | ||
0.562696 | − | 0.826664i | \(-0.309764\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −29223.8 | −1.28169 | −0.640845 | − | 0.767671i | \(-0.721416\pi\) | ||||
−0.640845 | + | 0.767671i | \(0.721416\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 19727.6 | + | 13385.5i | 0.842735 | + | 0.571811i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5775.91 | − | 2398.42i | −0.240412 | − | 0.0998300i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 28009.5i | 1.13633i | 0.822914 | + | 0.568166i | \(0.192347\pi\) | ||||
−0.822914 | + | 0.568166i | \(0.807653\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3312.69 | − | 10782.3i | 0.131035 | − | 0.426497i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4815.77i | 0.185787i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 39685.6i | − | 1.49368i | −0.665004 | − | 0.746840i | \(-0.731570\pi\) | ||
0.665004 | − | 0.746840i | \(-0.268430\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −30672.9 | − | 25401.2i | −1.12664 | − | 0.933009i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 26386.5 | 0.946126 | 0.473063 | − | 0.881029i | \(-0.343148\pi\) | ||||
0.473063 | + | 0.881029i | \(0.343148\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28280.8 | 0.990191 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26151.6 | + | 17744.3i | 0.894345 | + | 0.606829i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −55622.9 | −1.85849 | −0.929247 | − | 0.369459i | \(-0.879543\pi\) | ||||
−0.929247 | + | 0.369459i | \(0.879543\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5147.43 | − | 5129.34i | 0.168079 | − | 0.167489i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 38576.5 | + | 11852.0i | 1.23133 | + | 0.378309i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25045.7i | 0.781676i | 0.920460 | + | 0.390838i | \(0.127815\pi\) | ||||
−0.920460 | + | 0.390838i | \(0.872185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −31678.3 | −0.966952 | −0.483476 | − | 0.875358i | \(-0.660626\pi\) | ||||
−0.483476 | + | 0.875358i | \(0.660626\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11733.5 | − | 38190.5i | 0.350367 | − | 1.14039i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21685.7 | + | 52224.0i | −0.633623 | + | 1.52590i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 52095.2i | 1.48975i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5306.88 | − | 6609.02i | −0.148565 | − | 0.185018i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17906.2i | 0.490837i | 0.969417 | + | 0.245418i | \(0.0789253\pi\) | ||||
−0.969417 | + | 0.245418i | \(0.921075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26498.7i | 0.711393i | 0.934602 | + | 0.355696i | \(0.115756\pi\) | ||||
−0.934602 | + | 0.355696i | \(0.884244\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2900.59 | + | 2402.07i | 0.0762811 | + | 0.0631707i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17018.7 | −0.438524 | −0.219262 | − | 0.975666i | \(-0.570365\pi\) | ||||
−0.219262 | + | 0.975666i | \(0.570365\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 38402.7 | 0.969739 | 0.484870 | − | 0.874586i | \(-0.338867\pi\) | ||||
0.484870 | + | 0.874586i | \(0.338867\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 69465.7 | + | 21342.3i | 1.71941 | + | 0.528262i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12862.2 | 0.312121 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21989.9 | − | 52956.4i | 0.523257 | − | 1.26012i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 27762.3 | + | 18837.2i | 0.647909 | + | 0.439618i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 69059.2i | 1.58099i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −50216.1 | −1.12792 | −0.563960 | − | 0.825802i | \(-0.690723\pi\) | ||||
−0.563960 | + | 0.825802i | \(0.690723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 37814.9 | + | 11618.1i | 0.833497 | + | 0.256080i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9500.91 | − | 22880.2i | 0.205536 | − | 0.494976i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2908.61i | − | 0.0617684i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −48121.2 | − | 14784.5i | −1.00334 | − | 0.308262i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4926.40i | − | 0.100866i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 49997.2i | − | 1.00539i | −0.864463 | − | 0.502696i | \(-0.832341\pi\) | ||
0.864463 | − | 0.502696i | \(-0.167659\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9435.46 | − | 49737.9i | −0.186379 | − | 0.982478i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −41601.3 | −0.807337 | −0.403669 | − | 0.914905i | \(-0.632265\pi\) | ||||
−0.403669 | + | 0.914905i | \(0.632265\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −42178.2 | −0.804299 | −0.402149 | − | 0.915574i | \(-0.631737\pi\) | ||||
−0.402149 | + | 0.915574i | \(0.631737\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5439.57 | − | 17704.9i | 0.101939 | − | 0.331795i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 30326.6 | 0.558614 | 0.279307 | − | 0.960202i | \(-0.409895\pi\) | ||||
0.279307 | + | 0.960202i | \(0.409895\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 73038.1 | + | 30328.7i | 1.32255 | + | 0.549184i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1505.32 | + | 4899.56i | −0.0267998 | + | 0.0872290i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 60416.0i | − | 1.05768i | −0.848720 | − | 0.528842i | \(-0.822626\pi\) | ||
0.848720 | − | 0.528842i | \(-0.177374\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8045.10 | 0.138515 | 0.0692576 | − | 0.997599i | \(-0.477937\pi\) | ||||
0.0692576 | + | 0.997599i | \(0.477937\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −58858.3 | + | 4741.85i | −0.996770 | + | 0.0803036i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −52314.4 | − | 21723.3i | −0.871544 | − | 0.361904i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6530.60i | − | 0.107043i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13887.1 | + | 45200.2i | −0.223982 | + | 0.729024i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 48910.7i | − | 0.776348i | −0.921586 | − | 0.388174i | \(-0.873106\pi\) | ||
0.921586 | − | 0.388174i | \(-0.126894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 73312.7i | 1.14535i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −42237.8 | + | 51003.7i | −0.649562 | + | 0.784371i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 51287.5 | 0.776507 | 0.388253 | − | 0.921553i | \(-0.373079\pi\) | ||||
0.388253 | + | 0.921553i | \(0.373079\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26298.8 | −0.392045 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 50311.2 | − | 74148.6i | 0.738556 | − | 1.08848i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −102945. | −1.48830 | −0.744152 | − | 0.668010i | \(-0.767146\pi\) | ||||
−0.744152 | + | 0.668010i | \(0.767146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28936.9 | + | 12015.9i | 0.412059 | + | 0.171105i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −60656.6 | − | 18635.8i | −0.850855 | − | 0.261413i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 27899.4i | − | 0.385558i | −0.981242 | − | 0.192779i | \(-0.938250\pi\) | ||
0.981242 | − | 0.192779i | \(-0.0617500\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −91164.7 | −1.24133 | −0.620666 | − | 0.784075i | \(-0.713138\pi\) | ||||
−0.620666 | + | 0.784075i | \(0.713138\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −514.394 | + | 1674.27i | −0.00690193 | + | 0.0224646i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 78361.6 | − | 78086.3i | 1.03619 | − | 1.03255i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 83010.4i | − | 1.08186i | −0.841066 | − | 0.540932i | \(-0.818072\pi\) | ||
0.841066 | − | 0.540932i | \(-0.181928\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −16767.7 | − | 11377.2i | −0.215410 | − | 0.146160i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 37059.2i | 0.469336i | 0.972076 | + | 0.234668i | \(0.0754003\pi\) | ||||
−0.972076 | + | 0.234668i | \(0.924600\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 40545.4i | − | 0.506254i | −0.967433 | − | 0.253127i | \(-0.918541\pi\) | ||
0.967433 | − | 0.253127i | \(-0.0814591\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −55991.9 | + | 67612.3i | −0.689343 | + | 0.832407i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26667.6 | 0.323758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3104.39 | 0.0371689 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 63354.3 | + | 19464.7i | 0.748153 | + | 0.229859i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 162610. | 1.89414 | 0.947068 | − | 0.321032i | \(-0.104030\pi\) | ||||
0.947068 | + | 0.321032i | \(0.104030\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −42990.0 | + | 103529.i | −0.493996 | + | 1.18965i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −80789.1 | − | 100612.i | −0.915883 | − | 1.14061i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 6932.83i | − | 0.0775476i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11522.0 | 0.127173 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2411.15 | + | 740.791i | 0.0262627 | + | 0.00806883i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 102493. | + | 42559.9i | 1.10178 | + | 0.457510i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 50365.0i | − | 0.534383i | −0.963643 | − | 0.267191i | \(-0.913904\pi\) | ||
0.963643 | − | 0.267191i | \(-0.0860956\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35457.4 | + | 10893.8i | 0.371356 | + | 0.114094i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29441.4i | 0.304395i | 0.988350 | + | 0.152198i | \(0.0486350\pi\) | ||||
−0.988350 | + | 0.152198i | \(0.951365\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 108346.i | 1.10592i | 0.833207 | + | 0.552962i | \(0.186503\pi\) | ||||
−0.833207 | + | 0.552962i | \(0.813497\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 19680.4 | − | 12923.7i | 0.198341 | − | 0.130246i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −68136.9 | −0.678054 | −0.339027 | − | 0.940777i | \(-0.610098\pi\) | ||||
−0.339027 | + | 0.940777i | \(0.610098\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 195807. | 1.92418 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −49739.1 | + | 161892.i | −0.482711 | + | 1.57115i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 114834. | 1.10069 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7410.28 | + | 7384.24i | −0.0701565 | + | 0.0699100i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8184.47 | − | 26639.1i | 0.0765412 | − | 0.249129i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36780.3i | 0.339800i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31817.4 | −0.290408 | −0.145204 | − | 0.989402i | \(-0.546384\pi\) | ||||
−0.145204 | + | 0.989402i | \(0.546384\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −102869. | + | 151609.i | −0.927677 | + | 1.36721i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −77413.3 | + | 186428.i | −0.689805 | + | 1.66120i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 217789.i | − | 1.91768i | −0.283942 | − | 0.958842i | \(-0.591642\pi\) | ||
0.283942 | − | 0.958842i | \(-0.408358\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −22848.9 | + | 74369.6i | −0.198823 | + | 0.647136i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 44279.1i | − | 0.380794i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 54260.4i | − | 0.461206i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −59440.5 | + | 71776.6i | −0.499395 | + | 0.603038i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 108878. | 0.904234 | 0.452117 | − | 0.891959i | \(-0.350669\pi\) | ||||
0.452117 | + | 0.891959i | \(0.350669\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27193.2 | 0.223259 | 0.111630 | − | 0.993750i | \(-0.464393\pi\) | ||||
0.111630 | + | 0.993750i | \(0.464393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7639.84 | + | 9514.41i | 0.0620111 | + | 0.0772267i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −53685.5 | −0.430832 | −0.215416 | − | 0.976522i | \(-0.569111\pi\) | ||||
−0.215416 | + | 0.976522i | \(0.569111\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −42141.4 | + | 101486.i | −0.334389 | + | 0.805282i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −29440.2 | − | 9045.06i | −0.230996 | − | 0.0709701i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 63041.9i | − | 0.489148i | −0.969631 | − | 0.244574i | \(-0.921352\pi\) | ||
0.969631 | − | 0.244574i | \(-0.0786482\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21906.4 | 0.168095 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 44110.2 | − | 143571.i | 0.334754 | − | 1.08957i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 53626.9 | − | 129145.i | 0.402528 | − | 0.969376i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18291.7i | − | 0.135807i | −0.997692 | − | 0.0679035i | \(-0.978369\pi\) | ||
0.997692 | − | 0.0679035i | \(-0.0216310\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 104312. | − | 153735.i | 0.766093 | − | 1.12907i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14571.9i | 0.105869i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 75846.7i | 0.545153i | 0.962134 | + | 0.272577i | \(0.0878759\pi\) | ||||
−0.962134 | + | 0.272577i | \(0.912124\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 140031. | − | 12916.2i | 0.995773 | − | 0.0918482i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18516.5 | −0.130280 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −180877. | −1.25923 | −0.629616 | − | 0.776907i | \(-0.716788\pi\) | ||||
−0.629616 | + | 0.776907i | \(0.716788\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −137662. | − | 42294.6i | −0.948340 | − | 0.291363i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −83812.2 | −0.571360 | −0.285680 | − | 0.958325i | \(-0.592219\pi\) | ||||
−0.285680 | + | 0.958325i | \(0.592219\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 47515.4 | + | 19730.5i | 0.320563 | + | 0.133112i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 45068.8 | − | 66422.5i | 0.300922 | − | 0.443499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 48698.1i | − | 0.321820i | −0.986969 | − | 0.160910i | \(-0.948557\pi\) | ||
0.986969 | − | 0.160910i | \(-0.0514429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 121906. | 0.797394 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11165.7 | + | 3430.48i | 0.0722935 | + | 0.0222111i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13149.2 | − | 5460.13i | −0.0842761 | − | 0.0349952i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 92676.0i | 0.588012i | 0.955804 | + | 0.294006i | \(0.0949886\pi\) | ||||
−0.955804 | + | 0.294006i | \(0.905011\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −39026.9 | − | 11990.4i | −0.245143 | − | 0.0753164i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 251104.i | − | 1.56158i | −0.624791 | − | 0.780792i | \(-0.714816\pi\) | ||
0.624791 | − | 0.780792i | \(-0.285184\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4187.26i | 0.0257822i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2477.94 | − | 164006.i | 0.0151071 | − | 0.999886i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −400358. | −2.41691 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −230500. | −1.37792 | −0.688960 | − | 0.724799i | \(-0.741932\pi\) | ||||
−0.688960 | + | 0.724799i | \(0.741932\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 48707.0 | − | 158533.i | 0.288342 | − | 0.938505i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −52135.0 | −0.305653 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −121306. | − | 50371.6i | −0.704345 | − | 0.292476i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24427.8 | + | 79508.6i | −0.140479 | + | 0.457238i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 220779.i | 1.25756i | 0.777583 | + | 0.628781i | \(0.216446\pi\) | ||||
−0.777583 | + | 0.628781i | \(0.783554\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14062.0 | −0.0793382 | −0.0396691 | − | 0.999213i | \(-0.512630\pi\) | ||||
−0.0396691 | + | 0.999213i | \(0.512630\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 212033. | + | 143868.i | 1.18501 | + | 0.804052i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −129844. | − | 130302.i | −0.718860 | − | 0.721394i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 51613.3i | 0.283078i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7830.85 | + | 25488.1i | −0.0425495 | + | 0.138492i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 222578.i | 1.19819i | 0.800677 | + | 0.599097i | \(0.204473\pi\) | ||||
−0.800677 | + | 0.599097i | \(0.795527\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26766.9i | 0.142765i | 0.997449 | + | 0.0713827i | \(0.0227411\pi\) | ||||
−0.997449 | + | 0.0713827i | \(0.977259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 191704. | + | 158756.i | 1.01310 | + | 0.838981i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 161603. | 0.846228 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 95907.3 | 0.497648 | 0.248824 | − | 0.968549i | \(-0.419956\pi\) | ||||
0.248824 | + | 0.968549i | \(0.419956\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −151871. | − | 103047.i | −0.780906 | − | 0.529858i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −277148. | −1.41223 | −0.706113 | − | 0.708099i | \(-0.749553\pi\) | ||||
−0.706113 | + | 0.708099i | \(0.749553\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 67596.4 | − | 162787.i | 0.341353 | − | 0.822052i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 315782. | + | 97019.3i | 1.58042 | + | 0.485560i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 151594.i | − | 0.751950i | −0.926630 | − | 0.375975i | \(-0.877308\pi\) | ||
0.926630 | − | 0.375975i | \(-0.122692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 405973. | 1.99592 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 77243.7 | − | 251416.i | 0.376415 | − | 1.22517i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4493.31 | − | 1865.82i | −0.0217042 | − | 0.00901255i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 132213.i | 0.633057i | 0.948583 | + | 0.316528i | \(0.102517\pi\) | ||||
−0.948583 | + | 0.316528i | \(0.897483\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −167301. | + | 134338.i | −0.794095 | + | 0.637638i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 399652.i | 1.88053i | 0.340446 | + | 0.940264i | \(0.389422\pi\) | ||||
−0.340446 | + | 0.940264i | \(0.610578\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 99054.1i | − | 0.462073i | −0.972945 | − | 0.231036i | \(-0.925788\pi\) | ||
0.972945 | − | 0.231036i | \(-0.0742117\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 35900.6 | − | 43351.4i | 0.166034 | − | 0.200492i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 198490. | 0.910134 | 0.455067 | − | 0.890457i | \(-0.349615\pi\) | ||||
0.455067 | + | 0.890457i | \(0.349615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −93880.8 | −0.426807 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −240969. | − | 74034.0i | −1.08622 | − | 0.333726i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 175404. | 0.784002 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −172126. | − | 172733.i | −0.762884 | − | 0.765574i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 84005.1 | + | 56999.0i | 0.369206 | + | 0.250513i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 289423.i | 1.26143i | 0.776016 | + | 0.630713i | \(0.217238\pi\) | ||||
−0.776016 | + | 0.630713i | \(0.782762\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37859.9 | 0.163640 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −41430.7 | − | 12729.0i | −0.177594 | − | 0.0545630i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −70602.8 | + | 170027.i | −0.300150 | + | 0.722826i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 141256.i | 0.595593i | 0.954629 | + | 0.297796i | \(0.0962516\pi\) | ||||
−0.954629 | + | 0.297796i | \(0.903748\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 341420. | + | 104896.i | 1.42781 | + | 0.438674i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 132986.i | − | 0.551622i | −0.961212 | − | 0.275811i | \(-0.911054\pi\) | ||
0.961212 | − | 0.275811i | \(-0.0889463\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 325593.i | − | 1.33962i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 299603. | − | 196743.i | 1.22275 | − | 0.802949i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −51105.8 | −0.206898 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 107327. | 0.431031 | 0.215515 | − | 0.976500i | \(-0.430857\pi\) | ||||
0.215515 | + | 0.976500i | \(0.430857\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −69744.3 | + | 227006.i | −0.277865 | + | 0.904404i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8472.66 | −0.0334876 | −0.0167438 | − | 0.999860i | \(-0.505330\pi\) | ||||
−0.0167438 | + | 0.999860i | \(0.505330\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2687.02 | + | 6470.92i | −0.0105363 | + | 0.0253737i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −74751.3 | + | 243303.i | −0.290806 | + | 0.946525i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 98517.0i | 0.380256i | 0.981759 | + | 0.190128i | \(0.0608902\pi\) | ||||
−0.981759 | + | 0.190128i | \(0.939110\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 65034.5 | 0.249059 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −221779. | + | 178083.i | −0.842726 | + | 0.676689i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −39514.1 | + | 95158.6i | −0.148983 | + | 0.358785i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 559922.i | 2.09482i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 147021. | − | 478530.i | 0.545815 | − | 1.77654i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 93249.9i | − | 0.343536i | −0.985137 | − | 0.171768i | \(-0.945052\pi\) | ||
0.985137 | − | 0.171768i | \(-0.0549480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 64242.3i | 0.234865i | 0.993081 | + | 0.117432i | \(0.0374663\pi\) | ||||
−0.993081 | + | 0.117432i | \(0.962534\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 30522.7 | + | 57841.7i | 0.110740 | + | 0.209857i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −73628.5 | −0.265109 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −108284. | −0.386950 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −203929. | + | 300551.i | −0.723253 | + | 1.06593i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38390.9 | −0.135137 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −434478. | − | 180415.i | −1.51796 | − | 0.630325i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −215471. | − | 66200.2i | −0.747205 | − | 0.229568i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 401051.i | − | 1.38046i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 370186. | 1.26481 | 0.632406 | − | 0.774638i | \(-0.282068\pi\) | ||||
0.632406 | + | 0.774638i | \(0.282068\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 83731.5 | − | 272532.i | 0.283981 | − | 0.924311i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 71492.5 | + | 29686.9i | 0.240695 | + | 0.0999475i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 120927.i | 0.404155i | 0.979370 | + | 0.202077i | \(0.0647692\pi\) | ||||
−0.979370 | + | 0.202077i | \(0.935231\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 297543. | + | 201888.i | 0.987201 | + | 0.669833i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 431617.i | − | 1.42166i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6621.62i | − | 0.0216528i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −391970. | − | 324602.i | −1.27253 | − | 1.05382i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 416965. | 1.34397 | 0.671985 | − | 0.740565i | \(-0.265442\pi\) | ||||
0.671985 | + | 0.740565i | \(0.265442\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16587.1 | −0.0530820 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −448181. | − | 137697.i | −1.42406 | − | 0.437521i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 244647. | 0.771832 | 0.385916 | − | 0.922534i | \(-0.373885\pi\) | ||||
0.385916 | + | 0.922534i | \(0.373885\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −199589. | − | 82878.3i | −0.625229 | − | 0.259623i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 70885.3 | − | 28186.9i | 0.220490 | − | 0.0876761i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 379067.i | − | 1.17082i | −0.810736 | − | 0.585412i | \(-0.800933\pi\) | ||
0.810736 | − | 0.585412i | \(-0.199067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −231722. | −0.710714 | −0.355357 | − | 0.934731i | \(-0.615641\pi\) | ||||
−0.355357 | + | 0.934731i | \(0.615641\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −154049. | − | 47329.3i | −0.469192 | − | 0.144152i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −182727. | − | 183371.i | −0.552672 | − | 0.554621i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 266901.i | − | 0.801675i | −0.916149 | − | 0.400837i | \(-0.868719\pi\) | ||
0.916149 | − | 0.400837i | \(-0.131281\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −227971. | − | 70040.7i | −0.680021 | − | 0.208926i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 61086.7i | − | 0.180965i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 221835.i | 0.652669i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −28332.0 | + | 18605.0i | −0.0827878 | + | 0.0543648i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 149752. | 0.434605 | 0.217303 | − | 0.976104i | \(-0.430274\pi\) | ||||
0.217303 | + | 0.976104i | \(0.430274\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −97604.5 | −0.281345 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 44983.4 | − | 146414.i | 0.128789 | − | 0.419186i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −83211.3 | −0.236632 | −0.118316 | − | 0.992976i | \(-0.537750\pi\) | ||||
−0.118316 | + | 0.992976i | \(0.537750\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 32808.5 | − | 79010.0i | 0.0926728 | − | 0.223176i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −101505. | + | 330382.i | −0.284799 | + | 0.926976i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 223787.i | − | 0.623709i | −0.950130 | − | 0.311854i | \(-0.899050\pi\) | ||
0.950130 | − | 0.311854i | \(-0.100950\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 523744. | 1.45001 | 0.725004 | − | 0.688745i | \(-0.241838\pi\) | ||||
0.725004 | + | 0.688745i | \(0.241838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −367221. | + | 541210.i | −1.00993 | + | 1.48844i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 385309. | + | 159998.i | 1.05268 | + | 0.437122i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 52257.0i | 0.141830i | 0.997482 | + | 0.0709148i | \(0.0225918\pi\) | ||||
−0.997482 | + | 0.0709148i | \(0.977408\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −33997.0 | + | 110655.i | −0.0916656 | + | 0.298357i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 52949.2i | − | 0.141833i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 563838.i | − | 1.50049i | −0.661159 | − | 0.750246i | \(-0.729935\pi\) | ||
0.661159 | − | 0.750246i | \(-0.270065\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 397467. | + | 329155.i | 1.05087 | + | 0.870262i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −45450.6 | −0.119390 | −0.0596952 | − | 0.998217i | \(-0.519013\pi\) | ||||
−0.0596952 | + | 0.998217i | \(0.519013\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 371405. | 0.969318 | 0.484659 | − | 0.874703i | \(-0.338944\pi\) | ||||
0.484659 | + | 0.874703i | \(0.338944\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −235439. | + | 189052.i | −0.610514 | + | 0.490228i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 81975.6 | 0.211207 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1375.00 | + | 390623.i | −0.00352000 | + | 0.999994i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −594125. | − | 182536.i | −1.51127 | − | 0.464316i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 665726.i | 1.68265i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −146982. | −0.369152 | −0.184576 | − | 0.982818i | \(-0.559091\pi\) | ||||
−0.184576 | + | 0.982818i | \(0.559091\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 132730. | − | 432015.i | 0.331255 | − | 1.07818i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 153412. | − | 369449.i | 0.380462 | − | 0.916236i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37925.5i | 0.0934658i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −199903. | + | 294618.i | −0.489574 | + | 0.721534i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 270894.i | 0.659301i | 0.944103 | + | 0.329651i | \(0.106931\pi\) | ||||
−0.944103 | + | 0.329651i | \(0.893069\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 269824.i | 0.652617i | 0.945263 | + | 0.326308i | \(0.105805\pi\) | ||||
−0.945263 | + | 0.326308i | \(0.894195\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 171729. | + | 142214.i | 0.412785 | + | 0.341840i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −72190.9 | −0.172454 | −0.0862271 | − | 0.996276i | \(-0.527481\pi\) | ||||
−0.0862271 | + | 0.996276i | \(0.527481\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −793674. | −1.88431 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25023.1 | + | 7687.98i | 0.0590445 | + | 0.0181406i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 58611.2 | 0.137453 | 0.0687265 | − | 0.997636i | \(-0.478106\pi\) | ||||
0.0687265 | + | 0.997636i | \(0.478106\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12443.1 | + | 29965.8i | −0.0290033 | + | 0.0698462i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 254386. | − | 374915.i | 0.589336 | − | 0.868563i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 247655.i | 0.570264i | 0.958488 | + | 0.285132i | \(0.0920374\pi\) | ||||
−0.958488 | + | 0.285132i | \(0.907963\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 630440. | 1.44292 | 0.721458 | − | 0.692458i | \(-0.243472\pi\) | ||||
0.721458 | + | 0.692458i | \(0.243472\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 42382.4 | + | 13021.3i | 0.0964180 | + | 0.0296230i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 43492.1 | − | 104738.i | 0.0983482 | − | 0.236844i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 458201.i | − | 1.02992i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 430131. | + | 132151.i | 0.961057 | + | 0.295270i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 785732.i | 1.74514i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 233258.i | 0.515000i | 0.966278 | + | 0.257500i | \(0.0828987\pi\) | ||||
−0.966278 | + | 0.257500i | \(0.917101\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 452841. | + | 50292.0i | 0.993889 | + | 0.110380i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 139465. | 0.304289 | 0.152145 | − | 0.988358i | \(-0.451382\pi\) | ||||
0.152145 | + | 0.988358i | \(0.451382\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −85621.5 | −0.185713 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 109960. | − | 357901.i | 0.237104 | − | 0.771735i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 667760. | 1.43146 | 0.715730 | − | 0.698377i | \(-0.246094\pi\) | ||||
0.715730 | + | 0.698377i | \(0.246094\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 425463. | + | 176671.i | 0.906735 | + | 0.376517i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 111485. | − | 362864.i | 0.236212 | − | 0.768831i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 20977.9i | − | 0.0441899i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −146022. | −0.305816 | −0.152908 | − | 0.988240i | \(-0.548864\pi\) | ||||
−0.152908 | + | 0.988240i | \(0.548864\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 137940. | + | 93594.5i | 0.287225 | + | 0.194887i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −213381. | − | 88605.3i | −0.441759 | − | 0.183438i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 675063.i | − | 1.38956i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −80158.6 | + | 260903.i | −0.164057 | + | 0.533980i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 336887.i | − | 0.685564i | −0.939415 | − | 0.342782i | \(-0.888631\pi\) | ||
0.939415 | − | 0.342782i | \(-0.111369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 882510.i | 1.78570i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −453974. | + | 548191.i | −0.913383 | + | 1.10294i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3258.60 | −0.00651918 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −363926. | −0.723970 | −0.361985 | − | 0.932184i | \(-0.617901\pi\) | ||||
−0.361985 | + | 0.932184i | \(0.617901\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −38172.7 | − | 25900.8i | −0.0755116 | − | 0.0512359i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −103616. | −0.203821 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −68403.6 | − | 28404.2i | −0.133803 | − | 0.0555611i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 519766. | + | 159690.i | 1.01104 | + | 0.310628i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 214672.i | 0.415259i | 0.978208 | + | 0.207629i | \(0.0665748\pi\) | ||||
−0.978208 | + | 0.207629i | \(0.933425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47919.7 | −0.0921814 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21264.6 | + | 69212.9i | −0.0406800 | + | 0.132407i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −489756. | + | 488036.i | −0.931760 | + | 0.928486i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 929982.i | − | 1.75957i | −0.475374 | − | 0.879784i | \(-0.657687\pi\) | ||
0.475374 | − | 0.879784i | \(-0.342313\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 114778. | − | 518898.i | 0.215976 | − | 0.976399i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 291666.i | − | 0.545823i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 459420.i | − | 0.855070i | −0.903999 | − | 0.427535i | \(-0.859382\pi\) | ||
0.903999 | − | 0.427535i | \(-0.140618\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 325165. | − | 392649.i | 0.601906 | − | 0.726824i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.42919e6 | −2.63121 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 422731. | 0.774061 | 0.387030 | − | 0.922067i | \(-0.373501\pi\) | ||||
0.387030 | + | 0.922067i | \(0.373501\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 56183.5 | + | 17261.5i | 0.102323 | + | 0.0314372i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −777990. | −1.40928 | −0.704639 | − | 0.709566i | \(-0.748891\pi\) | ||||
−0.704639 | + | 0.709566i | \(0.748891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −351911. | + | 847478.i | −0.634045 | + | 1.52692i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −352156. | − | 238944.i | −0.631095 | − | 0.428209i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 218793.i | − | 0.390005i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35629.1 | 0.0631720 | 0.0315860 | − | 0.999501i | \(-0.489944\pi\) | ||||
0.0315860 | + | 0.999501i | \(0.489944\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 420785. | + | 129280.i | 0.742113 | + | 0.228003i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 674735. | + | 280180.i | 1.18369 | + | 0.491523i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 654607.i | 1.14232i | 0.820838 | + | 0.571161i | \(0.193507\pi\) | ||||
−0.820838 | + | 0.571161i | \(0.806493\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −630718. | − | 193779.i | −1.09484 | − | 0.336374i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 302702.i | − | 0.522693i | −0.965245 | − | 0.261346i | \(-0.915834\pi\) | ||
0.965245 | − | 0.261346i | \(-0.0841665\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36002.0i | 0.0618411i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −327149. | − | 498189.i | −0.559014 | − | 0.851277i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 75053.9 | 0.127580 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 538991. | 0.911442 | 0.455721 | − | 0.890123i | \(-0.349382\pi\) | ||||
0.455721 | + | 0.890123i | \(0.349382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −135562. | + | 441232.i | −0.228050 | + | 0.742264i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.15999e6 | −1.94131 | −0.970655 | − | 0.240476i | \(-0.922696\pi\) | ||||
−0.970655 | + | 0.240476i | \(0.922696\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 110363. | + | 110752.i | 0.183747 | + | 0.184395i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 69512.4 | − | 226251.i | 0.115138 | − | 0.374757i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 894887.i | − | 1.47466i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −778006. | −1.27550 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 504928. | + | 628821.i | 0.823580 | + | 1.02566i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 268538. | − | 646698.i | 0.435779 | − | 1.04945i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 575186.i | − | 0.928664i | −0.885661 | − | 0.464332i | \(-0.846294\pi\) | ||
0.885661 | − | 0.464332i | \(-0.153706\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 272101. | − | 885644.i | 0.437095 | − | 1.42267i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 100508.i | − | 0.160638i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 74302.9i | − | 0.118157i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −179859. | + | 217187.i | −0.284576 | + | 0.343637i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −534494. | −0.841446 | −0.420723 | − | 0.907189i | \(-0.638224\pi\) | ||||
−0.420723 | + | 0.907189i | \(0.638224\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 931054. | 1.45842 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 320653. | − | 472578.i | 0.499770 | − | 0.736561i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 990049. | 1.53541 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 46170.8 | − | 111189.i | 0.0712485 | − | 0.171582i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 240021. | + | 73743.0i | 0.368555 | + | 0.113233i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 399046.i | 0.609713i | 0.952398 | + | 0.304857i | \(0.0986085\pi\) | ||||
−0.952398 | + | 0.304857i | \(0.901391\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −613273. | −0.932421 | −0.466211 | − | 0.884674i | \(-0.654381\pi\) | ||||
−0.466211 | + | 0.884674i | \(0.654381\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 240965. | − | 784300.i | 0.364563 | − | 1.18659i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −380482. | + | 916283.i | −0.572820 | + | 1.37948i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 386643.i | − | 0.579250i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13044.3 | − | 8850.78i | −0.0194470 | − | 0.0131951i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 425411.i | − | 0.631135i | −0.948903 | − | 0.315568i | \(-0.897805\pi\) | ||
0.948903 | − | 0.315568i | \(-0.102195\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 286394.i | 0.422829i | 0.977397 | + | 0.211414i | \(0.0678069\pi\) | ||||
−0.977397 | + | 0.211414i | \(0.932193\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 464661. | + | 880550.i | 0.682698 | + | 1.29374i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 167100. | 0.244324 | 0.122162 | − | 0.992510i | \(-0.461017\pi\) | ||||
0.122162 | + | 0.992510i | \(0.461017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −872623. | −1.26975 | −0.634874 | − | 0.772616i | \(-0.718948\pi\) | ||||
−0.634874 | + | 0.772616i | \(0.718948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 714148. | + | 219411.i | 1.03416 | + | 0.317729i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −666879. | −0.961075 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −609227. | − | 252978.i | −0.873788 | − | 0.362836i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 142200. | − | 114183.i | 0.202977 | − | 0.162986i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 428726.i | 0.609053i | 0.952504 | + | 0.304527i | \(0.0984983\pi\) | ||||
−0.952504 | + | 0.304527i | \(0.901502\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −516502. | −0.730264 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −318825. | − | 97954.2i | −0.448639 | − | 0.137838i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −652964. | − | 271140.i | −0.914483 | − | 0.379734i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 194033.i | 0.270463i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 348817. | + | 107169.i | 0.483929 | + | 0.148680i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 936865.i | 1.29365i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 199001.i | 0.273500i | 0.990606 | + | 0.136750i | \(0.0436657\pi\) | ||||
−0.990606 | + | 0.136750i | \(0.956334\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −433680. | − | 660416.i | −0.593249 | − | 0.903411i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.10063e6 | 1.49858 | 0.749288 | − | 0.662244i | \(-0.230396\pi\) | ||||
0.749288 | + | 0.662244i | \(0.230396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 900672. | 1.22062 | 0.610310 | − | 0.792163i | \(-0.291045\pi\) | ||||
0.610310 | + | 0.792163i | \(0.291045\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −70487.3 | + | 229424.i | −0.0950833 | + | 0.309481i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 330953. | 0.444370 | 0.222185 | − | 0.975004i | \(-0.428681\pi\) | ||||
0.222185 | + | 0.975004i | \(0.428681\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.28425e6 | + | 533279.i | 1.71640 | + | 0.712725i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8205.45 | + | 26707.4i | −0.0109160 | + | 0.0355298i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 100804.i | − | 0.133487i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 135152. | 0.178150 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −334914. | + | 493596.i | −0.439445 | + | 0.647654i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −168024. | + | 69078.6i | −0.219460 | + | 0.0902251i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 635350.i | 0.826065i | 0.910716 | + | 0.413032i | \(0.135530\pi\) | ||||
−0.910716 | + | 0.413032i | \(0.864470\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −429807. | + | 1.39895e6i | −0.556282 | + | 1.81061i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.39000e6i | 1.79087i | 0.445194 | + | 0.895434i | \(0.353135\pi\) | ||||
−0.445194 | + | 0.895434i | \(0.646865\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 87356.3i | − | 0.112040i | −0.998430 | − | 0.0560200i | \(-0.982159\pi\) | ||
0.998430 | − | 0.0560200i | \(-0.0178410\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −777045. | − | 643495.i | −0.992109 | − | 0.821597i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −450532. | −0.572636 | −0.286318 | − | 0.958135i | \(-0.592431\pi\) | ||||
−0.286318 | + | 0.958135i | \(0.592431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 186046. | 0.235406 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.07912e6 | − | 429102.i | 1.35929 | − | 0.540512i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.23424e6 | 1.54773 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 240123. | − | 578269.i | 0.299770 | − | 0.721911i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 59643.9 | + | 18324.7i | 0.0741278 | + | 0.0227747i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 276742.i | 0.342418i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 368873. | 0.454389 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30454.6 | + | 99124.7i | −0.0373489 | + | 0.121564i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 731407. | + | 303713.i | 0.893022 | + | 0.370823i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.38725e6i | 1.68632i | 0.537665 | + | 0.843158i | \(0.319306\pi\) | ||||
−0.537665 | + | 0.843158i | \(0.680694\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12746.2 | + | 18785.4i | −0.0154260 | + | 0.0227349i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 482647.i | − | 0.581558i | −0.956790 | − | 0.290779i | \(-0.906086\pi\) | ||
0.956790 | − | 0.290779i | \(-0.0939144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 929951.i | − | 1.11563i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −637056. | + | 769269.i | −0.760914 | + | 0.918832i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15090.1 | −0.0179454 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.22708e6 | −1.45292 | −0.726461 | − | 0.687207i | \(-0.758836\pi\) | ||||
−0.726461 | + | 0.687207i | \(0.758836\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 433296. | + | 133124.i | 0.510817 | + | 0.156941i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 73572.3 | 0.0863597 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00139e6 | − | 997866.i | 1.17036 | − | 1.16624i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −187441. | + | 276250.i | −0.218124 | + | 0.321472i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 24692.2i | − | 0.0286107i | −0.999898 | − | 0.0143053i | \(-0.995446\pi\) | ||
0.999898 | − | 0.0143053i | \(-0.00455368\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −884038. | −1.01993 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −253288. | − | 77818.9i | −0.290972 | − | 0.0893968i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 499458. | − | 1.20280e6i | 0.571315 | − | 1.37585i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 955822.i | − | 1.08867i | −0.838867 | − | 0.544337i | \(-0.816781\pi\) | ||
0.838867 | − | 0.544337i | \(-0.183219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −932115. | − | 286379.i | −1.05715 | − | 0.324795i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 286579.i | − | 0.323642i | −0.986820 | − | 0.161821i | \(-0.948263\pi\) | ||
0.986820 | − | 0.161821i | \(-0.0517367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 950004.i | − | 1.06832i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 59164.9 | + | 203472.i | 0.0662522 | + | 0.227846i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.28493e6 | 1.43278 | 0.716388 | − | 0.697702i | \(-0.245794\pi\) | ||||
0.716388 | + | 0.697702i | \(0.245794\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −93624.1 | −0.103957 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 180098. | − | 586190.i | 0.199135 | − | 0.648153i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −130389. | −0.143567 | −0.0717836 | − | 0.997420i | \(-0.522869\pi\) | ||||
−0.0717836 | + | 0.997420i | \(0.522869\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 171674. | − | 413429.i | 0.188234 | − | 0.453309i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −517552. | + | 1.68455e6i | −0.565106 | + | 1.83933i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 214253.i | 0.232964i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −860939. | −0.932236 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.26131e6 | − | 855822.i | −1.36010 | − | 0.922849i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 254053. | − | 611816.i | 0.272816 | − | 0.657001i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.28463e6i | 1.37381i | 0.726749 | + | 0.686904i | \(0.241031\pi\) | ||||
−0.726749 | + | 0.686904i | \(0.758969\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −303526. | + | 987927.i | −0.323257 | + | 1.05215i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.31697e6i | − | 1.39681i | −0.715705 | − | 0.698403i | \(-0.753894\pi\) | ||
0.715705 | − | 0.698403i | \(-0.246106\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 107454.i | − | 0.113500i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −43940.8 | − | 83269.4i | −0.0462231 | − | 0.0875944i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 346834. | 0.363357 | 0.181678 | − | 0.983358i | \(-0.441847\pi\) | ||||
0.181678 | + | 0.983358i | \(0.441847\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.24795e6 | 1.30206 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 207546. | + | 140824.i | 0.215664 | + | 0.146332i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −310815. | −0.321658 | −0.160829 | − | 0.986982i | \(-0.551417\pi\) | ||||
−0.160829 | + | 0.986982i | \(0.551417\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 392937. | + | 163165.i | 0.404996 | + | 0.168172i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −316425. | − | 97216.8i | −0.324815 | − | 0.0997946i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 410457.i | − | 0.419638i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 162102. | 0.165059 | 0.0825296 | − | 0.996589i | \(-0.473700\pi\) | ||||
0.0825296 | + | 0.996589i | \(0.473700\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 84099.2 | − | 273729.i | 0.0852890 | − | 0.277602i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −886662. | − | 368182.i | −0.895595 | − | 0.371891i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.80197e6i | 1.81283i | 0.422388 | + | 0.906415i | \(0.361192\pi\) | ||||
−0.422388 | + | 0.906415i | \(0.638808\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.03241e6 | − | 1.28572e6i | −1.03447 | − | 1.28830i |
(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 | 60.5.b.a.29.4 | yes | 8 | |
3.2 | odd | 2 | inner | 60.5.b.a.29.6 | yes | 8 | |
4.3 | odd | 2 | 240.5.c.e.209.5 | 8 | |||
5.2 | odd | 4 | 300.5.g.h.101.8 | 8 | |||
5.3 | odd | 4 | 300.5.g.h.101.1 | 8 | |||
5.4 | even | 2 | inner | 60.5.b.a.29.5 | yes | 8 | |
12.11 | even | 2 | 240.5.c.e.209.3 | 8 | |||
15.2 | even | 4 | 300.5.g.h.101.7 | 8 | |||
15.8 | even | 4 | 300.5.g.h.101.2 | 8 | |||
15.14 | odd | 2 | inner | 60.5.b.a.29.3 | ✓ | 8 | |
20.19 | odd | 2 | 240.5.c.e.209.4 | 8 | |||
60.59 | even | 2 | 240.5.c.e.209.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.5.b.a.29.3 | ✓ | 8 | 15.14 | odd | 2 | inner | |
60.5.b.a.29.4 | yes | 8 | 1.1 | even | 1 | trivial | |
60.5.b.a.29.5 | yes | 8 | 5.4 | even | 2 | inner | |
60.5.b.a.29.6 | yes | 8 | 3.2 | odd | 2 | inner | |
240.5.c.e.209.3 | 8 | 12.11 | even | 2 | |||
240.5.c.e.209.4 | 8 | 20.19 | odd | 2 | |||
240.5.c.e.209.5 | 8 | 4.3 | odd | 2 | |||
240.5.c.e.209.6 | 8 | 60.59 | even | 2 | |||
300.5.g.h.101.1 | 8 | 5.3 | odd | 4 | |||
300.5.g.h.101.2 | 8 | 15.8 | even | 4 | |||
300.5.g.h.101.7 | 8 | 15.2 | even | 4 | |||
300.5.g.h.101.8 | 8 | 5.2 | odd | 4 |