Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1351,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.4 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1351 |
Dual form | 1950.2.b.h.1351.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 5.12311i | 1.93635i | 0.250270 | + | 0.968176i | \(0.419480\pi\) | ||||
−0.250270 | + | 0.968176i | \(0.580520\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.12311i | − | 0.941652i | −0.882226 | − | 0.470826i | \(-0.843956\pi\) | ||
0.882226 | − | 0.470826i | \(-0.156044\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0.561553 | − | 3.56155i | 0.155747 | − | 0.987797i | ||||
\(14\) | −5.12311 | −1.36921 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | − | 6.00000i | − | 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.12311i | − | 1.11795i | ||||||
\(22\) | 3.12311 | 0.665848 | ||||||||
\(23\) | −3.12311 | −0.651213 | −0.325606 | − | 0.945505i | \(-0.605568\pi\) | ||||
−0.325606 | + | 0.945505i | \(0.605568\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.56155 | + | 0.561553i | 0.698478 | + | 0.110130i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | − | 5.12311i | − | 0.968176i | ||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.12311i | − | 0.920137i | −0.887883 | − | 0.460068i | \(-0.847825\pi\) | ||
0.887883 | − | 0.460068i | \(-0.152175\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 3.12311i | 0.543663i | ||||||||
\(34\) | − | 2.00000i | − | 0.342997i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − | 3.12311i | − | 0.513435i | −0.966486 | − | 0.256718i | \(-0.917359\pi\) | ||
0.966486 | − | 0.256718i | \(-0.0826411\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | −0.561553 | + | 3.56155i | −0.0899204 | + | 0.570305i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.12311i | 1.42479i | 0.701779 | + | 0.712395i | \(0.252389\pi\) | ||||
−0.701779 | + | 0.712395i | \(0.747611\pi\) | |||||||
\(42\) | 5.12311 | 0.790512 | ||||||||
\(43\) | 10.2462 | 1.56253 | 0.781266 | − | 0.624198i | \(-0.214574\pi\) | ||||
0.781266 | + | 0.624198i | \(0.214574\pi\) | |||||||
\(44\) | 3.12311i | 0.470826i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 3.12311i | − | 0.460477i | ||||||
\(47\) | − | 10.2462i | − | 1.49456i | −0.664507 | − | 0.747282i | \(-0.731359\pi\) | ||
0.664507 | − | 0.747282i | \(-0.268641\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −19.2462 | −2.74946 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | −0.561553 | + | 3.56155i | −0.0778734 | + | 0.493899i | ||||
\(53\) | −11.3693 | −1.56170 | −0.780848 | − | 0.624721i | \(-0.785213\pi\) | ||||
−0.780848 | + | 0.624721i | \(0.785213\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.12311 | 0.684604 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 2.00000i | 0.262613i | ||||||||
\(59\) | 7.12311i | 0.927349i | 0.886006 | + | 0.463675i | \(0.153469\pi\) | ||||
−0.886006 | + | 0.463675i | \(0.846531\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 5.12311 | 0.650635 | ||||||||
\(63\) | 5.12311i | 0.645451i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.12311 | −0.384428 | ||||||||
\(67\) | − | 13.1231i | − | 1.60324i | −0.597832 | − | 0.801621i | \(-0.703971\pi\) | ||
0.597832 | − | 0.801621i | \(-0.296029\pi\) | |||||||
\(68\) | 2.00000 | 0.242536 | ||||||||
\(69\) | 3.12311 | 0.375978 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.24621i | − | 0.741289i | −0.928775 | − | 0.370644i | \(-0.879137\pi\) | ||
0.928775 | − | 0.370644i | \(-0.120863\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 4.87689i | 0.570797i | 0.958409 | + | 0.285399i | \(0.0921260\pi\) | ||||
−0.958409 | + | 0.285399i | \(0.907874\pi\) | |||||||
\(74\) | 3.12311 | 0.363054 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000i | 0.688247i | ||||||||
\(77\) | 16.0000 | 1.82337 | ||||||||
\(78\) | −3.56155 | − | 0.561553i | −0.403266 | − | 0.0635833i | ||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.12311 | −1.00748 | ||||||||
\(83\) | − | 10.2462i | − | 1.12467i | −0.826910 | − | 0.562334i | \(-0.809904\pi\) | ||
0.826910 | − | 0.562334i | \(-0.190096\pi\) | |||||||
\(84\) | 5.12311i | 0.558977i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.2462i | 1.10488i | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | −3.12311 | −0.332924 | ||||||||
\(89\) | − | 5.12311i | − | 0.543048i | −0.962432 | − | 0.271524i | \(-0.912472\pi\) | ||
0.962432 | − | 0.271524i | \(-0.0875277\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.2462 | + | 2.87689i | 1.91272 | + | 0.301580i | ||||
\(92\) | 3.12311 | 0.325606 | ||||||||
\(93\) | 5.12311i | 0.531241i | ||||||||
\(94\) | 10.2462 | 1.05682 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 4.87689i | 0.495174i | 0.968866 | + | 0.247587i | \(0.0796375\pi\) | ||||
−0.968866 | + | 0.247587i | \(0.920362\pi\) | |||||||
\(98\) | − | 19.2462i | − | 1.94416i | ||||||
\(99\) | − | 3.12311i | − | 0.313884i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.24621 | 0.422514 | 0.211257 | − | 0.977431i | \(-0.432244\pi\) | ||||
0.211257 | + | 0.977431i | \(0.432244\pi\) | |||||||
\(102\) | 2.00000i | 0.198030i | ||||||||
\(103\) | 4.87689 | 0.480535 | 0.240267 | − | 0.970707i | \(-0.422765\pi\) | ||||
0.240267 | + | 0.970707i | \(0.422765\pi\) | |||||||
\(104\) | −3.56155 | − | 0.561553i | −0.349239 | − | 0.0550648i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 11.3693i | − | 1.10429i | ||||||
\(107\) | 8.00000 | 0.773389 | 0.386695 | − | 0.922208i | \(-0.373617\pi\) | ||||
0.386695 | + | 0.922208i | \(0.373617\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 11.1231i | 1.06540i | 0.846304 | + | 0.532700i | \(0.178823\pi\) | ||||
−0.846304 | + | 0.532700i | \(0.821177\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.12311i | 0.296432i | ||||||||
\(112\) | 5.12311i | 0.484088i | ||||||||
\(113\) | 4.24621 | 0.399450 | 0.199725 | − | 0.979852i | \(-0.435995\pi\) | ||||
0.199725 | + | 0.979852i | \(0.435995\pi\) | |||||||
\(114\) | −6.00000 | −0.561951 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 0.561553 | − | 3.56155i | 0.0519156 | − | 0.329266i | ||||
\(118\) | −7.12311 | −0.655735 | ||||||||
\(119\) | − | 10.2462i | − | 0.939269i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.24621 | 0.113292 | ||||||||
\(122\) | 10.0000i | 0.905357i | ||||||||
\(123\) | − | 9.12311i | − | 0.822603i | ||||||
\(124\) | 5.12311i | 0.460068i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.12311 | −0.456403 | ||||||||
\(127\) | 4.87689 | 0.432754 | 0.216377 | − | 0.976310i | \(-0.430576\pi\) | ||||
0.216377 | + | 0.976310i | \(0.430576\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −10.2462 | −0.902129 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | − | 3.12311i | − | 0.271831i | ||||||
\(133\) | 30.7386 | 2.66538 | ||||||||
\(134\) | 13.1231 | 1.13366 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000i | 0.171499i | ||||||||
\(137\) | − | 22.4924i | − | 1.92166i | −0.277143 | − | 0.960829i | \(-0.589388\pi\) | ||
0.277143 | − | 0.960829i | \(-0.410612\pi\) | |||||||
\(138\) | 3.12311i | 0.265856i | ||||||||
\(139\) | 16.4924 | 1.39887 | 0.699435 | − | 0.714697i | \(-0.253435\pi\) | ||||
0.699435 | + | 0.714697i | \(0.253435\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2462i | 0.862887i | ||||||||
\(142\) | 6.24621 | 0.524170 | ||||||||
\(143\) | −11.1231 | − | 1.75379i | −0.930161 | − | 0.146659i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.87689 | −0.403615 | ||||||||
\(147\) | 19.2462 | 1.58740 | ||||||||
\(148\) | 3.12311i | 0.256718i | ||||||||
\(149\) | − | 14.0000i | − | 1.14692i | −0.819232 | − | 0.573462i | \(-0.805600\pi\) | ||
0.819232 | − | 0.573462i | \(-0.194400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.3693i | − | 0.925222i | −0.886561 | − | 0.462611i | \(-0.846913\pi\) | ||
0.886561 | − | 0.462611i | \(-0.153087\pi\) | |||||||
\(152\) | −6.00000 | −0.486664 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 16.0000i | 1.28932i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.561553 | − | 3.56155i | 0.0449602 | − | 0.285152i | ||||
\(157\) | 3.36932 | 0.268901 | 0.134450 | − | 0.990920i | \(-0.457073\pi\) | ||||
0.134450 | + | 0.990920i | \(0.457073\pi\) | |||||||
\(158\) | 8.00000i | 0.636446i | ||||||||
\(159\) | 11.3693 | 0.901645 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 16.0000i | − | 1.26098i | ||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − | 1.12311i | − | 0.0879684i | −0.999032 | − | 0.0439842i | \(-0.985995\pi\) | ||
0.999032 | − | 0.0439842i | \(-0.0140051\pi\) | |||||||
\(164\) | − | 9.12311i | − | 0.712395i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.2462 | 0.795260 | ||||||||
\(167\) | 5.75379i | 0.445242i | 0.974905 | + | 0.222621i | \(0.0714612\pi\) | ||||
−0.974905 | + | 0.222621i | \(0.928539\pi\) | |||||||
\(168\) | −5.12311 | −0.395256 | ||||||||
\(169\) | −12.3693 | − | 4.00000i | −0.951486 | − | 0.307692i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 6.00000i | − | 0.458831i | ||||||
\(172\) | −10.2462 | −0.781266 | ||||||||
\(173\) | −14.8769 | −1.13107 | −0.565535 | − | 0.824725i | \(-0.691330\pi\) | ||||
−0.565535 | + | 0.824725i | \(0.691330\pi\) | |||||||
\(174\) | − | 2.00000i | − | 0.151620i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 3.12311i | − | 0.235413i | ||||||
\(177\) | − | 7.12311i | − | 0.535405i | ||||||
\(178\) | 5.12311 | 0.383993 | ||||||||
\(179\) | −16.4924 | −1.23270 | −0.616351 | − | 0.787472i | \(-0.711390\pi\) | ||||
−0.616351 | + | 0.787472i | \(0.711390\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.75379 | −0.279017 | −0.139508 | − | 0.990221i | \(-0.544552\pi\) | ||||
−0.139508 | + | 0.990221i | \(0.544552\pi\) | |||||||
\(182\) | −2.87689 | + | 18.2462i | −0.213250 | + | 1.35250i | ||||
\(183\) | −10.0000 | −0.739221 | ||||||||
\(184\) | 3.12311i | 0.230238i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.12311 | −0.375644 | ||||||||
\(187\) | 6.24621i | 0.456768i | ||||||||
\(188\) | 10.2462i | 0.747282i | ||||||||
\(189\) | − | 5.12311i | − | 0.372651i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.4924 | −1.19335 | −0.596675 | − | 0.802483i | \(-0.703512\pi\) | ||||
−0.596675 | + | 0.802483i | \(0.703512\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 16.8769i | 1.21483i | 0.794386 | + | 0.607413i | \(0.207793\pi\) | ||||
−0.794386 | + | 0.607413i | \(0.792207\pi\) | |||||||
\(194\) | −4.87689 | −0.350141 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.2462 | 1.37473 | ||||||||
\(197\) | 0.246211i | 0.0175418i | 0.999962 | + | 0.00877091i | \(0.00279190\pi\) | ||||
−0.999962 | + | 0.00877091i | \(0.997208\pi\) | |||||||
\(198\) | 3.12311 | 0.221949 | ||||||||
\(199\) | 1.75379 | 0.124323 | 0.0621614 | − | 0.998066i | \(-0.480201\pi\) | ||||
0.0621614 | + | 0.998066i | \(0.480201\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.1231i | 0.925633i | ||||||||
\(202\) | 4.24621i | 0.298762i | ||||||||
\(203\) | 10.2462i | 0.719143i | ||||||||
\(204\) | −2.00000 | −0.140028 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.87689i | 0.339789i | ||||||||
\(207\) | −3.12311 | −0.217071 | ||||||||
\(208\) | 0.561553 | − | 3.56155i | 0.0389367 | − | 0.246949i | ||||
\(209\) | −18.7386 | −1.29618 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 11.3693 | 0.780848 | ||||||||
\(213\) | 6.24621i | 0.427983i | ||||||||
\(214\) | 8.00000i | 0.546869i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 26.2462 | 1.78171 | ||||||||
\(218\) | −11.1231 | −0.753352 | ||||||||
\(219\) | − | 4.87689i | − | 0.329550i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.12311 | + | 7.12311i | −0.0755483 | + | 0.479152i | ||||
\(222\) | −3.12311 | −0.209609 | ||||||||
\(223\) | 15.3693i | 1.02921i | 0.857429 | + | 0.514603i | \(0.172061\pi\) | ||||
−0.857429 | + | 0.514603i | \(0.827939\pi\) | |||||||
\(224\) | −5.12311 | −0.342302 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.24621i | 0.282454i | ||||||||
\(227\) | − | 8.00000i | − | 0.530979i | −0.964114 | − | 0.265489i | \(-0.914466\pi\) | ||
0.964114 | − | 0.265489i | \(-0.0855335\pi\) | |||||||
\(228\) | − | 6.00000i | − | 0.397360i | ||||||
\(229\) | 3.12311i | 0.206381i | 0.994662 | + | 0.103190i | \(0.0329051\pi\) | ||||
−0.994662 | + | 0.103190i | \(0.967095\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.0000 | −1.05272 | ||||||||
\(232\) | − | 2.00000i | − | 0.131306i | ||||||
\(233\) | 24.2462 | 1.58842 | 0.794211 | − | 0.607642i | \(-0.207884\pi\) | ||||
0.794211 | + | 0.607642i | \(0.207884\pi\) | |||||||
\(234\) | 3.56155 | + | 0.561553i | 0.232826 | + | 0.0367099i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 7.12311i | − | 0.463675i | ||||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 10.2462 | 0.664163 | ||||||||
\(239\) | − | 28.4924i | − | 1.84302i | −0.388353 | − | 0.921511i | \(-0.626956\pi\) | ||
0.388353 | − | 0.921511i | \(-0.373044\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.24621i | 0.144691i | 0.997380 | + | 0.0723456i | \(0.0230485\pi\) | ||||
−0.997380 | + | 0.0723456i | \(0.976952\pi\) | |||||||
\(242\) | 1.24621i | 0.0801095i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.12311 | 0.581668 | ||||||||
\(247\) | −21.3693 | − | 3.36932i | −1.35970 | − | 0.214384i | ||||
\(248\) | −5.12311 | −0.325318 | ||||||||
\(249\) | 10.2462i | 0.649327i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.75379 | 0.615654 | 0.307827 | − | 0.951442i | \(-0.400398\pi\) | ||||
0.307827 | + | 0.951442i | \(0.400398\pi\) | |||||||
\(252\) | − | 5.12311i | − | 0.322725i | ||||||
\(253\) | 9.75379i | 0.613215i | ||||||||
\(254\) | 4.87689i | 0.306004i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.24621 | −0.264871 | −0.132436 | − | 0.991192i | \(-0.542280\pi\) | ||||
−0.132436 | + | 0.991192i | \(0.542280\pi\) | |||||||
\(258\) | − | 10.2462i | − | 0.637901i | ||||||
\(259\) | 16.0000 | 0.994192 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 4.00000i | 0.247121i | ||||||||
\(263\) | 2.63068 | 0.162215 | 0.0811074 | − | 0.996705i | \(-0.474154\pi\) | ||||
0.0811074 | + | 0.996705i | \(0.474154\pi\) | |||||||
\(264\) | 3.12311 | 0.192214 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 30.7386i | 1.88471i | ||||||||
\(267\) | 5.12311i | 0.313529i | ||||||||
\(268\) | 13.1231i | 0.801621i | ||||||||
\(269\) | 0.246211 | 0.0150118 | 0.00750588 | − | 0.999972i | \(-0.497611\pi\) | ||||
0.00750588 | + | 0.999972i | \(0.497611\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.8769i | 0.903707i | 0.892092 | + | 0.451853i | \(0.149237\pi\) | ||||
−0.892092 | + | 0.451853i | \(0.850763\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | −18.2462 | − | 2.87689i | −1.10431 | − | 0.174118i | ||||
\(274\) | 22.4924 | 1.35882 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.12311 | −0.187989 | ||||||||
\(277\) | −27.8617 | −1.67405 | −0.837025 | − | 0.547165i | \(-0.815707\pi\) | ||||
−0.837025 | + | 0.547165i | \(0.815707\pi\) | |||||||
\(278\) | 16.4924i | 0.989150i | ||||||||
\(279\) | − | 5.12311i | − | 0.306712i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.12311i | 0.305619i | 0.988256 | + | 0.152809i | \(0.0488321\pi\) | ||||
−0.988256 | + | 0.152809i | \(0.951168\pi\) | |||||||
\(282\) | −10.2462 | −0.610153 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | 6.24621i | 0.370644i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.75379 | − | 11.1231i | 0.103704 | − | 0.657723i | ||||
\(287\) | −46.7386 | −2.75889 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 4.87689i | − | 0.285889i | ||||||
\(292\) | − | 4.87689i | − | 0.285399i | ||||||
\(293\) | 20.7386i | 1.21156i | 0.795631 | + | 0.605782i | \(0.207140\pi\) | ||||
−0.795631 | + | 0.605782i | \(0.792860\pi\) | |||||||
\(294\) | 19.2462i | 1.12246i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.12311 | −0.181527 | ||||||||
\(297\) | 3.12311i | 0.181221i | ||||||||
\(298\) | 14.0000 | 0.810998 | ||||||||
\(299\) | −1.75379 | + | 11.1231i | −0.101424 | + | 0.643266i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 52.4924i | 3.02561i | ||||||||
\(302\) | 11.3693 | 0.654231 | ||||||||
\(303\) | −4.24621 | −0.243938 | ||||||||
\(304\) | − | 6.00000i | − | 0.344124i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 2.00000i | − | 0.114332i | ||||||
\(307\) | − | 22.8769i | − | 1.30565i | −0.757507 | − | 0.652827i | \(-0.773583\pi\) | ||
0.757507 | − | 0.652827i | \(-0.226417\pi\) | |||||||
\(308\) | −16.0000 | −0.911685 | ||||||||
\(309\) | −4.87689 | −0.277437 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.4924 | −1.38884 | −0.694419 | − | 0.719571i | \(-0.744339\pi\) | ||||
−0.694419 | + | 0.719571i | \(0.744339\pi\) | |||||||
\(312\) | 3.56155 | + | 0.561553i | 0.201633 | + | 0.0317917i | ||||
\(313\) | 0.246211 | 0.0139167 | 0.00695834 | − | 0.999976i | \(-0.497785\pi\) | ||||
0.00695834 | + | 0.999976i | \(0.497785\pi\) | |||||||
\(314\) | 3.36932i | 0.190142i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | − | 6.00000i | − | 0.336994i | −0.985702 | − | 0.168497i | \(-0.946109\pi\) | ||
0.985702 | − | 0.168497i | \(-0.0538913\pi\) | |||||||
\(318\) | 11.3693i | 0.637560i | ||||||||
\(319\) | − | 6.24621i | − | 0.349721i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.00000 | −0.446516 | ||||||||
\(322\) | 16.0000 | 0.891645 | ||||||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.12311 | 0.0622031 | ||||||||
\(327\) | − | 11.1231i | − | 0.615109i | ||||||
\(328\) | 9.12311 | 0.503739 | ||||||||
\(329\) | 52.4924 | 2.89400 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 24.2462i | − | 1.33269i | −0.745643 | − | 0.666346i | \(-0.767857\pi\) | ||
0.745643 | − | 0.666346i | \(-0.232143\pi\) | |||||||
\(332\) | 10.2462i | 0.562334i | ||||||||
\(333\) | − | 3.12311i | − | 0.171145i | ||||||
\(334\) | −5.75379 | −0.314833 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 5.12311i | − | 0.279488i | ||||||
\(337\) | −6.00000 | −0.326841 | −0.163420 | − | 0.986557i | \(-0.552253\pi\) | ||||
−0.163420 | + | 0.986557i | \(0.552253\pi\) | |||||||
\(338\) | 4.00000 | − | 12.3693i | 0.217571 | − | 0.672802i | ||||
\(339\) | −4.24621 | −0.230623 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.0000 | −0.866449 | ||||||||
\(342\) | 6.00000 | 0.324443 | ||||||||
\(343\) | − | 62.7386i | − | 3.38757i | ||||||
\(344\) | − | 10.2462i | − | 0.552439i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 14.8769i | − | 0.799787i | ||||||
\(347\) | −2.24621 | −0.120583 | −0.0602915 | − | 0.998181i | \(-0.519203\pi\) | ||||
−0.0602915 | + | 0.998181i | \(0.519203\pi\) | |||||||
\(348\) | 2.00000 | 0.107211 | ||||||||
\(349\) | − | 5.36932i | − | 0.287413i | −0.989620 | − | 0.143706i | \(-0.954098\pi\) | ||
0.989620 | − | 0.143706i | \(-0.0459021\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.561553 | + | 3.56155i | −0.0299735 | + | 0.190102i | ||||
\(352\) | 3.12311 | 0.166462 | ||||||||
\(353\) | − | 4.24621i | − | 0.226003i | −0.993595 | − | 0.113002i | \(-0.963954\pi\) | ||
0.993595 | − | 0.113002i | \(-0.0360465\pi\) | |||||||
\(354\) | 7.12311 | 0.378589 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.12311i | 0.271524i | ||||||||
\(357\) | 10.2462i | 0.542287i | ||||||||
\(358\) | − | 16.4924i | − | 0.871652i | ||||||
\(359\) | 34.2462i | 1.80745i | 0.428118 | + | 0.903723i | \(0.359177\pi\) | ||||
−0.428118 | + | 0.903723i | \(0.640823\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | − | 3.75379i | − | 0.197295i | ||||||
\(363\) | −1.24621 | −0.0654091 | ||||||||
\(364\) | −18.2462 | − | 2.87689i | −0.956361 | − | 0.150790i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 10.0000i | − | 0.522708i | ||||||
\(367\) | −33.3693 | −1.74186 | −0.870932 | − | 0.491403i | \(-0.836484\pi\) | ||||
−0.870932 | + | 0.491403i | \(0.836484\pi\) | |||||||
\(368\) | −3.12311 | −0.162803 | ||||||||
\(369\) | 9.12311i | 0.474930i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 58.2462i | − | 3.02399i | ||||||
\(372\) | − | 5.12311i | − | 0.265621i | ||||||
\(373\) | 1.12311 | 0.0581522 | 0.0290761 | − | 0.999577i | \(-0.490743\pi\) | ||||
0.0290761 | + | 0.999577i | \(0.490743\pi\) | |||||||
\(374\) | −6.24621 | −0.322984 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.2462 | −0.528408 | ||||||||
\(377\) | 1.12311 | − | 7.12311i | 0.0578429 | − | 0.366859i | ||||
\(378\) | 5.12311 | 0.263504 | ||||||||
\(379\) | − | 6.00000i | − | 0.308199i | −0.988055 | − | 0.154100i | \(-0.950752\pi\) | ||
0.988055 | − | 0.154100i | \(-0.0492477\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.87689 | −0.249851 | ||||||||
\(382\) | − | 16.4924i | − | 0.843826i | ||||||
\(383\) | − | 18.2462i | − | 0.932338i | −0.884696 | − | 0.466169i | \(-0.845634\pi\) | ||
0.884696 | − | 0.466169i | \(-0.154366\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.8769 | −0.859011 | ||||||||
\(387\) | 10.2462 | 0.520844 | ||||||||
\(388\) | − | 4.87689i | − | 0.247587i | ||||||
\(389\) | 16.2462 | 0.823716 | 0.411858 | − | 0.911248i | \(-0.364880\pi\) | ||||
0.411858 | + | 0.911248i | \(0.364880\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.24621 | 0.315884 | ||||||||
\(392\) | 19.2462i | 0.972080i | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | −0.246211 | −0.0124039 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.12311i | 0.156942i | ||||||||
\(397\) | − | 9.36932i | − | 0.470233i | −0.971967 | − | 0.235116i | \(-0.924453\pi\) | ||
0.971967 | − | 0.235116i | \(-0.0755471\pi\) | |||||||
\(398\) | 1.75379i | 0.0879095i | ||||||||
\(399\) | −30.7386 | −1.53886 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.3693i | 1.16701i | 0.812110 | + | 0.583504i | \(0.198319\pi\) | ||||
−0.812110 | + | 0.583504i | \(0.801681\pi\) | |||||||
\(402\) | −13.1231 | −0.654521 | ||||||||
\(403\) | −18.2462 | − | 2.87689i | −0.908909 | − | 0.143308i | ||||
\(404\) | −4.24621 | −0.211257 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.2462 | −0.508511 | ||||||||
\(407\) | −9.75379 | −0.483477 | ||||||||
\(408\) | − | 2.00000i | − | 0.0990148i | ||||||
\(409\) | − | 24.4924i | − | 1.21107i | −0.795818 | − | 0.605536i | \(-0.792959\pi\) | ||
0.795818 | − | 0.605536i | \(-0.207041\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.4924i | 1.10947i | ||||||||
\(412\) | −4.87689 | −0.240267 | ||||||||
\(413\) | −36.4924 | −1.79567 | ||||||||
\(414\) | − | 3.12311i | − | 0.153492i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.56155 | + | 0.561553i | 0.174619 | + | 0.0275324i | ||||
\(417\) | −16.4924 | −0.807637 | ||||||||
\(418\) | − | 18.7386i | − | 0.916537i | ||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 25.3693i | − | 1.23642i | −0.786011 | − | 0.618212i | \(-0.787857\pi\) | ||
0.786011 | − | 0.618212i | \(-0.212143\pi\) | |||||||
\(422\) | 4.00000i | 0.194717i | ||||||||
\(423\) | − | 10.2462i | − | 0.498188i | ||||||
\(424\) | 11.3693i | 0.552143i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.24621 | −0.302630 | ||||||||
\(427\) | 51.2311i | 2.47924i | ||||||||
\(428\) | −8.00000 | −0.386695 | ||||||||
\(429\) | 11.1231 | + | 1.75379i | 0.537029 | + | 0.0846737i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.492423i | 0.0237192i | 0.999930 | + | 0.0118596i | \(0.00377511\pi\) | ||||
−0.999930 | + | 0.0118596i | \(0.996225\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 18.0000 | 0.865025 | 0.432512 | − | 0.901628i | \(-0.357627\pi\) | ||||
0.432512 | + | 0.901628i | \(0.357627\pi\) | |||||||
\(434\) | 26.2462i | 1.25986i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 11.1231i | − | 0.532700i | ||||||
\(437\) | 18.7386i | 0.896390i | ||||||||
\(438\) | 4.87689 | 0.233027 | ||||||||
\(439\) | −3.50758 | −0.167408 | −0.0837038 | − | 0.996491i | \(-0.526675\pi\) | ||||
−0.0837038 | + | 0.996491i | \(0.526675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.2462 | −0.916486 | ||||||||
\(442\) | −7.12311 | − | 1.12311i | −0.338812 | − | 0.0534207i | ||||
\(443\) | 36.4924 | 1.73381 | 0.866904 | − | 0.498476i | \(-0.166107\pi\) | ||||
0.866904 | + | 0.498476i | \(0.166107\pi\) | |||||||
\(444\) | − | 3.12311i | − | 0.148216i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.3693 | −0.727758 | ||||||||
\(447\) | 14.0000i | 0.662177i | ||||||||
\(448\) | − | 5.12311i | − | 0.242044i | ||||||
\(449\) | − | 37.1231i | − | 1.75195i | −0.482359 | − | 0.875974i | \(-0.660220\pi\) | ||
0.482359 | − | 0.875974i | \(-0.339780\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.4924 | 1.34166 | ||||||||
\(452\) | −4.24621 | −0.199725 | ||||||||
\(453\) | 11.3693i | 0.534177i | ||||||||
\(454\) | 8.00000 | 0.375459 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | − | 6.63068i | − | 0.310170i | −0.987901 | − | 0.155085i | \(-0.950435\pi\) | ||
0.987901 | − | 0.155085i | \(-0.0495652\pi\) | |||||||
\(458\) | −3.12311 | −0.145933 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 14.4924i | − | 0.674979i | −0.941329 | − | 0.337490i | \(-0.890422\pi\) | ||
0.941329 | − | 0.337490i | \(-0.109578\pi\) | |||||||
\(462\) | − | 16.0000i | − | 0.744387i | ||||||
\(463\) | − | 35.8617i | − | 1.66664i | −0.552794 | − | 0.833318i | \(-0.686438\pi\) | ||
0.552794 | − | 0.833318i | \(-0.313562\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.2462i | 1.12318i | ||||||||
\(467\) | 5.75379 | 0.266254 | 0.133127 | − | 0.991099i | \(-0.457498\pi\) | ||||
0.133127 | + | 0.991099i | \(0.457498\pi\) | |||||||
\(468\) | −0.561553 | + | 3.56155i | −0.0259578 | + | 0.164633i | ||||
\(469\) | 67.2311 | 3.10444 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.36932 | −0.155250 | ||||||||
\(472\) | 7.12311 | 0.327868 | ||||||||
\(473\) | − | 32.0000i | − | 1.47136i | ||||||
\(474\) | − | 8.00000i | − | 0.367452i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.2462i | 0.469634i | ||||||||
\(477\) | −11.3693 | −0.520565 | ||||||||
\(478\) | 28.4924 | 1.30321 | ||||||||
\(479\) | 20.4924i | 0.936323i | 0.883643 | + | 0.468161i | \(0.155083\pi\) | ||||
−0.883643 | + | 0.468161i | \(0.844917\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.1231 | − | 1.75379i | −0.507170 | − | 0.0799659i | ||||
\(482\) | −2.24621 | −0.102312 | ||||||||
\(483\) | 16.0000i | 0.728025i | ||||||||
\(484\) | −1.24621 | −0.0566460 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 7.36932i | 0.333936i | 0.985962 | + | 0.166968i | \(0.0533976\pi\) | ||||
−0.985962 | + | 0.166968i | \(0.946602\pi\) | |||||||
\(488\) | − | 10.0000i | − | 0.452679i | ||||||
\(489\) | 1.12311i | 0.0507886i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.7386 | −0.484628 | −0.242314 | − | 0.970198i | \(-0.577906\pi\) | ||||
−0.242314 | + | 0.970198i | \(0.577906\pi\) | |||||||
\(492\) | 9.12311i | 0.411301i | ||||||||
\(493\) | −4.00000 | −0.180151 | ||||||||
\(494\) | 3.36932 | − | 21.3693i | 0.151593 | − | 0.961451i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 5.12311i | − | 0.230034i | ||||||
\(497\) | 32.0000 | 1.43540 | ||||||||
\(498\) | −10.2462 | −0.459144 | ||||||||
\(499\) | 1.50758i | 0.0674884i | 0.999431 | + | 0.0337442i | \(0.0107432\pi\) | ||||
−0.999431 | + | 0.0337442i | \(0.989257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 5.75379i | − | 0.257060i | ||||||
\(502\) | 9.75379i | 0.435333i | ||||||||
\(503\) | −10.6307 | −0.473999 | −0.236999 | − | 0.971510i | \(-0.576164\pi\) | ||||
−0.236999 | + | 0.971510i | \(0.576164\pi\) | |||||||
\(504\) | 5.12311 | 0.228201 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.75379 | −0.433609 | ||||||||
\(507\) | 12.3693 | + | 4.00000i | 0.549341 | + | 0.177646i | ||||
\(508\) | −4.87689 | −0.216377 | ||||||||
\(509\) | 15.7538i | 0.698274i | 0.937072 | + | 0.349137i | \(0.113525\pi\) | ||||
−0.937072 | + | 0.349137i | \(0.886475\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.9848 | −1.10526 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 6.00000i | 0.264906i | ||||||||
\(514\) | − | 4.24621i | − | 0.187292i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.2462 | 0.451064 | ||||||||
\(517\) | −32.0000 | −1.40736 | ||||||||
\(518\) | 16.0000i | 0.703000i | ||||||||
\(519\) | 14.8769 | 0.653023 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.2462 | −0.711759 | −0.355880 | − | 0.934532i | \(-0.615819\pi\) | ||||
−0.355880 | + | 0.934532i | \(0.615819\pi\) | |||||||
\(522\) | 2.00000i | 0.0875376i | ||||||||
\(523\) | −22.7386 | −0.994291 | −0.497146 | − | 0.867667i | \(-0.665618\pi\) | ||||
−0.497146 | + | 0.867667i | \(0.665618\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.63068i | 0.114703i | ||||||||
\(527\) | 10.2462i | 0.446332i | ||||||||
\(528\) | 3.12311i | 0.135916i | ||||||||
\(529\) | −13.2462 | −0.575922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.12311i | 0.309116i | ||||||||
\(532\) | −30.7386 | −1.33269 | ||||||||
\(533\) | 32.4924 | + | 5.12311i | 1.40740 | + | 0.221906i | ||||
\(534\) | −5.12311 | −0.221698 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.1231 | −0.566832 | ||||||||
\(537\) | 16.4924 | 0.711701 | ||||||||
\(538\) | 0.246211i | 0.0106149i | ||||||||
\(539\) | 60.1080i | 2.58903i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.1231i | 0.822167i | 0.911598 | + | 0.411083i | \(0.134849\pi\) | ||||
−0.911598 | + | 0.411083i | \(0.865151\pi\) | |||||||
\(542\) | −14.8769 | −0.639017 | ||||||||
\(543\) | 3.75379 | 0.161090 | ||||||||
\(544\) | − | 2.00000i | − | 0.0857493i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.87689 | − | 18.2462i | 0.123120 | − | 0.780866i | ||||
\(547\) | 44.9848 | 1.92341 | 0.961707 | − | 0.274081i | \(-0.0883737\pi\) | ||||
0.961707 | + | 0.274081i | \(0.0883737\pi\) | |||||||
\(548\) | 22.4924i | 0.960829i | ||||||||
\(549\) | 10.0000 | 0.426790 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 12.0000i | − | 0.511217i | ||||||
\(552\) | − | 3.12311i | − | 0.132928i | ||||||
\(553\) | 40.9848i | 1.74285i | ||||||||
\(554\) | − | 27.8617i | − | 1.18373i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.4924 | −0.699435 | ||||||||
\(557\) | − | 28.2462i | − | 1.19683i | −0.801186 | − | 0.598415i | \(-0.795797\pi\) | ||
0.801186 | − | 0.598415i | \(-0.204203\pi\) | |||||||
\(558\) | 5.12311 | 0.216878 | ||||||||
\(559\) | 5.75379 | − | 36.4924i | 0.243359 | − | 1.54347i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 6.24621i | − | 0.263715i | ||||||
\(562\) | −5.12311 | −0.216105 | ||||||||
\(563\) | −32.9848 | −1.39015 | −0.695073 | − | 0.718939i | \(-0.744628\pi\) | ||||
−0.695073 | + | 0.718939i | \(0.744628\pi\) | |||||||
\(564\) | − | 10.2462i | − | 0.431443i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.00000i | 0.168133i | ||||||||
\(567\) | 5.12311i | 0.215150i | ||||||||
\(568\) | −6.24621 | −0.262085 | ||||||||
\(569\) | 36.7386 | 1.54016 | 0.770082 | − | 0.637945i | \(-0.220215\pi\) | ||||
0.770082 | + | 0.637945i | \(0.220215\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.4924 | 1.02498 | 0.512488 | − | 0.858694i | \(-0.328724\pi\) | ||||
0.512488 | + | 0.858694i | \(0.328724\pi\) | |||||||
\(572\) | 11.1231 | + | 1.75379i | 0.465080 | + | 0.0733296i | ||||
\(573\) | 16.4924 | 0.688981 | ||||||||
\(574\) | − | 46.7386i | − | 1.95083i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − | 2.63068i | − | 0.109517i | −0.998500 | − | 0.0547584i | \(-0.982561\pi\) | ||
0.998500 | − | 0.0547584i | \(-0.0174389\pi\) | |||||||
\(578\) | − | 13.0000i | − | 0.540729i | ||||||
\(579\) | − | 16.8769i | − | 0.701380i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 52.4924 | 2.17775 | ||||||||
\(582\) | 4.87689 | 0.202154 | ||||||||
\(583\) | 35.5076i | 1.47057i | ||||||||
\(584\) | 4.87689 | 0.201807 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.7386 | −0.856705 | ||||||||
\(587\) | − | 16.4924i | − | 0.680715i | −0.940296 | − | 0.340358i | \(-0.889452\pi\) | ||
0.940296 | − | 0.340358i | \(-0.110548\pi\) | |||||||
\(588\) | −19.2462 | −0.793700 | ||||||||
\(589\) | −30.7386 | −1.26656 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 0.246211i | − | 0.0101278i | ||||||
\(592\) | − | 3.12311i | − | 0.128359i | ||||||
\(593\) | 38.4924i | 1.58069i | 0.612659 | + | 0.790347i | \(0.290100\pi\) | ||||
−0.612659 | + | 0.790347i | \(0.709900\pi\) | |||||||
\(594\) | −3.12311 | −0.128143 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.0000i | 0.573462i | ||||||||
\(597\) | −1.75379 | −0.0717778 | ||||||||
\(598\) | −11.1231 | − | 1.75379i | −0.454858 | − | 0.0717178i | ||||
\(599\) | −3.50758 | −0.143316 | −0.0716579 | − | 0.997429i | \(-0.522829\pi\) | ||||
−0.0716579 | + | 0.997429i | \(0.522829\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | −52.4924 | −2.13943 | ||||||||
\(603\) | − | 13.1231i | − | 0.534414i | ||||||
\(604\) | 11.3693i | 0.462611i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 4.24621i | − | 0.172491i | ||||||
\(607\) | 9.36932 | 0.380289 | 0.190144 | − | 0.981756i | \(-0.439104\pi\) | ||||
0.190144 | + | 0.981756i | \(0.439104\pi\) | |||||||
\(608\) | 6.00000 | 0.243332 | ||||||||
\(609\) | − | 10.2462i | − | 0.415197i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.4924 | − | 5.75379i | −1.47633 | − | 0.232773i | ||||
\(612\) | 2.00000 | 0.0808452 | ||||||||
\(613\) | − | 14.6307i | − | 0.590928i | −0.955354 | − | 0.295464i | \(-0.904526\pi\) | ||
0.955354 | − | 0.295464i | \(-0.0954742\pi\) | |||||||
\(614\) | 22.8769 | 0.923236 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 16.0000i | − | 0.644658i | ||||||
\(617\) | − | 8.73863i | − | 0.351804i | −0.984408 | − | 0.175902i | \(-0.943716\pi\) | ||
0.984408 | − | 0.175902i | \(-0.0562842\pi\) | |||||||
\(618\) | − | 4.87689i | − | 0.196177i | ||||||
\(619\) | − | 26.9848i | − | 1.08461i | −0.840181 | − | 0.542306i | \(-0.817551\pi\) | ||
0.840181 | − | 0.542306i | \(-0.182449\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.12311 | 0.125326 | ||||||||
\(622\) | − | 24.4924i | − | 0.982057i | ||||||
\(623\) | 26.2462 | 1.05153 | ||||||||
\(624\) | −0.561553 | + | 3.56155i | −0.0224801 | + | 0.142576i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.246211i | 0.00984058i | ||||||||
\(627\) | 18.7386 | 0.748349 | ||||||||
\(628\) | −3.36932 | −0.134450 | ||||||||
\(629\) | 6.24621i | 0.249053i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.61553i | 0.223551i | 0.993734 | + | 0.111775i | \(0.0356537\pi\) | ||||
−0.993734 | + | 0.111775i | \(0.964346\pi\) | |||||||
\(632\) | − | 8.00000i | − | 0.318223i | ||||||
\(633\) | −4.00000 | −0.158986 | ||||||||
\(634\) | 6.00000 | 0.238290 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11.3693 | −0.450823 | ||||||||
\(637\) | −10.8078 | + | 68.5464i | −0.428219 | + | 2.71591i | ||||
\(638\) | 6.24621 | 0.247290 | ||||||||
\(639\) | − | 6.24621i | − | 0.247096i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | − | 8.00000i | − | 0.315735i | ||||||
\(643\) | 7.36932i | 0.290617i | 0.989386 | + | 0.145309i | \(0.0464175\pi\) | ||||
−0.989386 | + | 0.145309i | \(0.953582\pi\) | |||||||
\(644\) | 16.0000i | 0.630488i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | 11.6155 | 0.456654 | 0.228327 | − | 0.973585i | \(-0.426675\pi\) | ||||
0.228327 | + | 0.973585i | \(0.426675\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 22.2462 | 0.873240 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.2462 | −1.02867 | ||||||||
\(652\) | 1.12311i | 0.0439842i | ||||||||
\(653\) | −43.8617 | −1.71644 | −0.858221 | − | 0.513280i | \(-0.828430\pi\) | ||||
−0.858221 | + | 0.513280i | \(0.828430\pi\) | |||||||
\(654\) | 11.1231 | 0.434948 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.12311i | 0.356197i | ||||||||
\(657\) | 4.87689i | 0.190266i | ||||||||
\(658\) | 52.4924i | 2.04637i | ||||||||
\(659\) | −38.2462 | −1.48986 | −0.744930 | − | 0.667142i | \(-0.767517\pi\) | ||||
−0.744930 | + | 0.667142i | \(0.767517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.876894i | 0.0341072i | 0.999855 | + | 0.0170536i | \(0.00542860\pi\) | ||||
−0.999855 | + | 0.0170536i | \(0.994571\pi\) | |||||||
\(662\) | 24.2462 | 0.942356 | ||||||||
\(663\) | 1.12311 | − | 7.12311i | 0.0436178 | − | 0.276638i | ||||
\(664\) | −10.2462 | −0.397630 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.12311 | 0.121018 | ||||||||
\(667\) | −6.24621 | −0.241854 | ||||||||
\(668\) | − | 5.75379i | − | 0.222621i | ||||||
\(669\) | − | 15.3693i | − | 0.594212i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 31.2311i | − | 1.20566i | ||||||
\(672\) | 5.12311 | 0.197628 | ||||||||
\(673\) | 38.9848 | 1.50276 | 0.751378 | − | 0.659872i | \(-0.229390\pi\) | ||||
0.751378 | + | 0.659872i | \(0.229390\pi\) | |||||||
\(674\) | − | 6.00000i | − | 0.231111i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.3693 | + | 4.00000i | 0.475743 | + | 0.153846i | ||||
\(677\) | −21.1231 | −0.811827 | −0.405913 | − | 0.913912i | \(-0.633047\pi\) | ||||
−0.405913 | + | 0.913912i | \(0.633047\pi\) | |||||||
\(678\) | − | 4.24621i | − | 0.163075i | ||||||
\(679\) | −24.9848 | −0.958830 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.00000i | 0.306561i | ||||||||
\(682\) | − | 16.0000i | − | 0.612672i | ||||||
\(683\) | − | 48.9848i | − | 1.87435i | −0.348856 | − | 0.937177i | \(-0.613430\pi\) | ||
0.348856 | − | 0.937177i | \(-0.386570\pi\) | |||||||
\(684\) | 6.00000i | 0.229416i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 62.7386 | 2.39537 | ||||||||
\(687\) | − | 3.12311i | − | 0.119154i | ||||||
\(688\) | 10.2462 | 0.390633 | ||||||||
\(689\) | −6.38447 | + | 40.4924i | −0.243229 | + | 1.54264i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.7386i | − | 0.788935i | −0.918910 | − | 0.394467i | \(-0.870929\pi\) | ||
0.918910 | − | 0.394467i | \(-0.129071\pi\) | |||||||
\(692\) | 14.8769 | 0.565535 | ||||||||
\(693\) | 16.0000 | 0.607790 | ||||||||
\(694\) | − | 2.24621i | − | 0.0852650i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.00000i | 0.0758098i | ||||||||
\(697\) | − | 18.2462i | − | 0.691125i | ||||||
\(698\) | 5.36932 | 0.203232 | ||||||||
\(699\) | −24.2462 | −0.917076 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.0000 | −0.528773 | −0.264386 | − | 0.964417i | \(-0.585169\pi\) | ||||
−0.264386 | + | 0.964417i | \(0.585169\pi\) | |||||||
\(702\) | −3.56155 | − | 0.561553i | −0.134422 | − | 0.0211944i | ||||
\(703\) | −18.7386 | −0.706741 | ||||||||
\(704\) | 3.12311i | 0.117706i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.24621 | 0.159808 | ||||||||
\(707\) | 21.7538i | 0.818135i | ||||||||
\(708\) | 7.12311i | 0.267703i | ||||||||
\(709\) | 39.6155i | 1.48779i | 0.668295 | + | 0.743896i | \(0.267024\pi\) | ||||
−0.668295 | + | 0.743896i | \(0.732976\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | −5.12311 | −0.191997 | ||||||||
\(713\) | 16.0000i | 0.599205i | ||||||||
\(714\) | −10.2462 | −0.383455 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.4924 | 0.616351 | ||||||||
\(717\) | 28.4924i | 1.06407i | ||||||||
\(718\) | −34.2462 | −1.27806 | ||||||||
\(719\) | −20.0000 | −0.745874 | −0.372937 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372937 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.9848i | 0.930484i | ||||||||
\(722\) | − | 17.0000i | − | 0.632674i | ||||||
\(723\) | − | 2.24621i | − | 0.0835375i | ||||||
\(724\) | 3.75379 | 0.139508 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 1.24621i | − | 0.0462512i | ||||||
\(727\) | 37.8617 | 1.40421 | 0.702107 | − | 0.712071i | \(-0.252243\pi\) | ||||
0.702107 | + | 0.712071i | \(0.252243\pi\) | |||||||
\(728\) | 2.87689 | − | 18.2462i | 0.106625 | − | 0.676250i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.4924 | −0.757940 | ||||||||
\(732\) | 10.0000 | 0.369611 | ||||||||
\(733\) | − | 10.6307i | − | 0.392653i | −0.980539 | − | 0.196327i | \(-0.937099\pi\) | ||
0.980539 | − | 0.196327i | \(-0.0629013\pi\) | |||||||
\(734\) | − | 33.3693i | − | 1.23168i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.12311i | − | 0.115119i | ||||||
\(737\) | −40.9848 | −1.50970 | ||||||||
\(738\) | −9.12311 | −0.335826 | ||||||||
\(739\) | 45.2311i | 1.66385i | 0.554887 | + | 0.831926i | \(0.312761\pi\) | ||||
−0.554887 | + | 0.831926i | \(0.687239\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.3693 | + | 3.36932i | 0.785021 | + | 0.123775i | ||||
\(742\) | 58.2462 | 2.13829 | ||||||||
\(743\) | 16.0000i | 0.586983i | 0.955962 | + | 0.293492i | \(0.0948173\pi\) | ||||
−0.955962 | + | 0.293492i | \(0.905183\pi\) | |||||||
\(744\) | 5.12311 | 0.187822 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.12311i | 0.0411198i | ||||||||
\(747\) | − | 10.2462i | − | 0.374889i | ||||||
\(748\) | − | 6.24621i | − | 0.228384i | ||||||
\(749\) | 40.9848i | 1.49755i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.75379 | −0.355921 | −0.177960 | − | 0.984038i | \(-0.556950\pi\) | ||||
−0.177960 | + | 0.984038i | \(0.556950\pi\) | |||||||
\(752\) | − | 10.2462i | − | 0.373641i | ||||||
\(753\) | −9.75379 | −0.355448 | ||||||||
\(754\) | 7.12311 | + | 1.12311i | 0.259408 | + | 0.0409011i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.12311i | 0.186326i | ||||||||
\(757\) | −5.12311 | −0.186202 | −0.0931012 | − | 0.995657i | \(-0.529678\pi\) | ||||
−0.0931012 | + | 0.995657i | \(0.529678\pi\) | |||||||
\(758\) | 6.00000 | 0.217930 | ||||||||
\(759\) | − | 9.75379i | − | 0.354040i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.12311i | 0.185712i | 0.995680 | + | 0.0928562i | \(0.0295997\pi\) | ||||
−0.995680 | + | 0.0928562i | \(0.970400\pi\) | |||||||
\(762\) | − | 4.87689i | − | 0.176671i | ||||||
\(763\) | −56.9848 | −2.06299 | ||||||||
\(764\) | 16.4924 | 0.596675 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.2462 | 0.659262 | ||||||||
\(767\) | 25.3693 | + | 4.00000i | 0.916033 | + | 0.144432i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 32.9848i | 1.18946i | 0.803924 | + | 0.594732i | \(0.202742\pi\) | ||||
−0.803924 | + | 0.594732i | \(0.797258\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.24621 | 0.152924 | ||||||||
\(772\) | − | 16.8769i | − | 0.607413i | ||||||
\(773\) | − | 0.246211i | − | 0.00885560i | −0.999990 | − | 0.00442780i | \(-0.998591\pi\) | ||
0.999990 | − | 0.00442780i | \(-0.00140942\pi\) | |||||||
\(774\) | 10.2462i | 0.368292i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.87689 | 0.175070 | ||||||||
\(777\) | −16.0000 | −0.573997 | ||||||||
\(778\) | 16.2462i | 0.582455i | ||||||||
\(779\) | 54.7386 | 1.96122 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.5076 | −0.698036 | ||||||||
\(782\) | 6.24621i | 0.223364i | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | −19.2462 | −0.687365 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − | 4.00000i | − | 0.142675i | ||||||
\(787\) | 53.6155i | 1.91119i | 0.294688 | + | 0.955594i | \(0.404784\pi\) | ||||
−0.294688 | + | 0.955594i | \(0.595216\pi\) | |||||||
\(788\) | − | 0.246211i | − | 0.00877091i | ||||||
\(789\) | −2.63068 | −0.0936548 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.7538i | 0.773476i | ||||||||
\(792\) | −3.12311 | −0.110975 | ||||||||
\(793\) | 5.61553 | − | 35.6155i | 0.199413 | − | 1.26474i | ||||
\(794\) | 9.36932 | 0.332505 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.75379 | −0.0621614 | ||||||||
\(797\) | 31.8617 | 1.12860 | 0.564300 | − | 0.825570i | \(-0.309146\pi\) | ||||
0.564300 | + | 0.825570i | \(0.309146\pi\) | |||||||
\(798\) | − | 30.7386i | − | 1.08814i | ||||||
\(799\) | 20.4924i | 0.724970i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 5.12311i | − | 0.181016i | ||||||
\(802\) | −23.3693 | −0.825199 | ||||||||
\(803\) | 15.2311 | 0.537492 | ||||||||
\(804\) | − | 13.1231i | − | 0.462816i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.87689 | − | 18.2462i | 0.101334 | − | 0.642695i | ||||
\(807\) | −0.246211 | −0.00866705 | ||||||||
\(808\) | − | 4.24621i | − | 0.149381i | ||||||
\(809\) | −46.4924 | −1.63459 | −0.817293 | − | 0.576222i | \(-0.804526\pi\) | ||||
−0.817293 | + | 0.576222i | \(0.804526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 44.2462i | − | 1.55369i | −0.629689 | − | 0.776847i | \(-0.716818\pi\) | ||
0.629689 | − | 0.776847i | \(-0.283182\pi\) | |||||||
\(812\) | − | 10.2462i | − | 0.359572i | ||||||
\(813\) | − | 14.8769i | − | 0.521755i | ||||||
\(814\) | − | 9.75379i | − | 0.341870i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.00000 | 0.0700140 | ||||||||
\(817\) | − | 61.4773i | − | 2.15082i | ||||||
\(818\) | 24.4924 | 0.856357 | ||||||||
\(819\) | 18.2462 | + | 2.87689i | 0.637574 | + | 0.100527i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.7538i | 0.968614i | 0.874898 | + | 0.484307i | \(0.160928\pi\) | ||||
−0.874898 | + | 0.484307i | \(0.839072\pi\) | |||||||
\(822\) | −22.4924 | −0.784513 | ||||||||
\(823\) | 51.1231 | 1.78204 | 0.891020 | − | 0.453965i | \(-0.149991\pi\) | ||||
0.891020 | + | 0.453965i | \(0.149991\pi\) | |||||||
\(824\) | − | 4.87689i | − | 0.169895i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 36.4924i | − | 1.26973i | ||||||
\(827\) | − | 50.7386i | − | 1.76436i | −0.470917 | − | 0.882178i | \(-0.656077\pi\) | ||
0.470917 | − | 0.882178i | \(-0.343923\pi\) | |||||||
\(828\) | 3.12311 | 0.108535 | ||||||||
\(829\) | −7.75379 | −0.269300 | −0.134650 | − | 0.990893i | \(-0.542991\pi\) | ||||
−0.134650 | + | 0.990893i | \(0.542991\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.8617 | 0.966513 | ||||||||
\(832\) | −0.561553 | + | 3.56155i | −0.0194683 | + | 0.123475i | ||||
\(833\) | 38.4924 | 1.33368 | ||||||||
\(834\) | − | 16.4924i | − | 0.571086i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 18.7386 | 0.648089 | ||||||||
\(837\) | 5.12311i | 0.177080i | ||||||||
\(838\) | − | 28.0000i | − | 0.967244i | ||||||
\(839\) | 2.73863i | 0.0945481i | 0.998882 | + | 0.0472741i | \(0.0150534\pi\) | ||||
−0.998882 | + | 0.0472741i | \(0.984947\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 25.3693 | 0.874284 | ||||||||
\(843\) | − | 5.12311i | − | 0.176449i | ||||||
\(844\) | −4.00000 | −0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.2462 | 0.352272 | ||||||||
\(847\) | 6.38447i | 0.219373i | ||||||||
\(848\) | −11.3693 | −0.390424 | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.75379i | 0.334356i | ||||||||
\(852\) | − | 6.24621i | − | 0.213992i | ||||||
\(853\) | 21.8617i | 0.748532i | 0.927321 | + | 0.374266i | \(0.122105\pi\) | ||||
−0.927321 | + | 0.374266i | \(0.877895\pi\) | |||||||
\(854\) | −51.2311 | −1.75309 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 8.00000i | − | 0.273434i | ||||||
\(857\) | −2.49242 | −0.0851395 | −0.0425698 | − | 0.999093i | \(-0.513554\pi\) | ||||
−0.0425698 | + | 0.999093i | \(0.513554\pi\) | |||||||
\(858\) | −1.75379 | + | 11.1231i | −0.0598734 | + | 0.379737i | ||||
\(859\) | −12.0000 | −0.409435 | −0.204717 | − | 0.978821i | \(-0.565628\pi\) | ||||
−0.204717 | + | 0.978821i | \(0.565628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 46.7386 | 1.59285 | ||||||||
\(862\) | −0.492423 | −0.0167720 | ||||||||
\(863\) | − | 10.2462i | − | 0.348785i | −0.984676 | − | 0.174393i | \(-0.944204\pi\) | ||
0.984676 | − | 0.174393i | \(-0.0557962\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.0000i | 0.611665i | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | −26.2462 | −0.890854 | ||||||||
\(869\) | − | 24.9848i | − | 0.847553i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.7386 | − | 7.36932i | −1.58368 | − | 0.249700i | ||||
\(872\) | 11.1231 | 0.376676 | ||||||||
\(873\) | 4.87689i | 0.165058i | ||||||||
\(874\) | −18.7386 | −0.633844 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.87689i | 0.164775i | ||||||||
\(877\) | 27.1231i | 0.915882i | 0.888983 | + | 0.457941i | \(0.151413\pi\) | ||||
−0.888983 | + | 0.457941i | \(0.848587\pi\) | |||||||
\(878\) | − | 3.50758i | − | 0.118375i | ||||||
\(879\) | − | 20.7386i | − | 0.699497i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.7538 | 0.395995 | 0.197998 | − | 0.980203i | \(-0.436556\pi\) | ||||
0.197998 | + | 0.980203i | \(0.436556\pi\) | |||||||
\(882\) | − | 19.2462i | − | 0.648054i | ||||||
\(883\) | 26.2462 | 0.883255 | 0.441628 | − | 0.897198i | \(-0.354401\pi\) | ||||
0.441628 | + | 0.897198i | \(0.354401\pi\) | |||||||
\(884\) | 1.12311 | − | 7.12311i | 0.0377741 | − | 0.239576i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.4924i | 1.22599i | ||||||||
\(887\) | 27.1231 | 0.910705 | 0.455352 | − | 0.890311i | \(-0.349513\pi\) | ||||
0.455352 | + | 0.890311i | \(0.349513\pi\) | |||||||
\(888\) | 3.12311 | 0.104805 | ||||||||
\(889\) | 24.9848i | 0.837965i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 3.12311i | − | 0.104628i | ||||||
\(892\) | − | 15.3693i | − | 0.514603i | ||||||
\(893\) | −61.4773 | −2.05726 | ||||||||
\(894\) | −14.0000 | −0.468230 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.12311 | 0.171151 | ||||||||
\(897\) | 1.75379 | − | 11.1231i | 0.0585573 | − | 0.371390i | ||||
\(898\) | 37.1231 | 1.23881 | ||||||||
\(899\) | − | 10.2462i | − | 0.341730i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.7386 | 0.757534 | ||||||||
\(902\) | 28.4924i | 0.948694i | ||||||||
\(903\) | − | 52.4924i | − | 1.74684i | ||||||
\(904\) | − | 4.24621i | − | 0.141227i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.3693 | −0.377720 | ||||||||
\(907\) | −42.2462 | −1.40276 | −0.701381 | − | 0.712786i | \(-0.747433\pi\) | ||||
−0.701381 | + | 0.712786i | \(0.747433\pi\) | |||||||
\(908\) | 8.00000i | 0.265489i | ||||||||
\(909\) | 4.24621 | 0.140838 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.00000 | 0.132526 | 0.0662630 | − | 0.997802i | \(-0.478892\pi\) | ||||
0.0662630 | + | 0.997802i | \(0.478892\pi\) | |||||||
\(912\) | 6.00000i | 0.198680i | ||||||||
\(913\) | −32.0000 | −1.05905 | ||||||||
\(914\) | 6.63068 | 0.219324 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 3.12311i | − | 0.103190i | ||||||
\(917\) | 20.4924i | 0.676719i | ||||||||
\(918\) | 2.00000i | 0.0660098i | ||||||||
\(919\) | −38.2462 | −1.26163 | −0.630813 | − | 0.775935i | \(-0.717279\pi\) | ||||
−0.630813 | + | 0.775935i | \(0.717279\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.8769i | 0.753819i | ||||||||
\(922\) | 14.4924 | 0.477283 | ||||||||
\(923\) | −22.2462 | − | 3.50758i | −0.732243 | − | 0.115453i | ||||
\(924\) | 16.0000 | 0.526361 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35.8617 | 1.17849 | ||||||||
\(927\) | 4.87689 | 0.160178 | ||||||||
\(928\) | 2.00000i | 0.0656532i | ||||||||
\(929\) | − | 46.1080i | − | 1.51275i | −0.654137 | − | 0.756376i | \(-0.726968\pi\) | ||
0.654137 | − | 0.756376i | \(-0.273032\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 115.477i | 3.78461i | ||||||||
\(932\) | −24.2462 | −0.794211 | ||||||||
\(933\) | 24.4924 | 0.801846 | ||||||||
\(934\) | 5.75379i | 0.188270i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.56155 | − | 0.561553i | −0.116413 | − | 0.0183549i | ||||
\(937\) | 3.75379 | 0.122631 | 0.0613155 | − | 0.998118i | \(-0.480470\pi\) | ||||
0.0613155 | + | 0.998118i | \(0.480470\pi\) | |||||||
\(938\) | 67.2311i | 2.19517i | ||||||||
\(939\) | −0.246211 | −0.00803480 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 14.0000i | − | 0.456387i | −0.973616 | − | 0.228193i | \(-0.926718\pi\) | ||
0.973616 | − | 0.228193i | \(-0.0732819\pi\) | |||||||
\(942\) | − | 3.36932i | − | 0.109778i | ||||||
\(943\) | − | 28.4924i | − | 0.927841i | ||||||
\(944\) | 7.12311i | 0.231837i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.0000 | 1.04041 | ||||||||
\(947\) | 24.4924i | 0.795897i | 0.917408 | + | 0.397948i | \(0.130278\pi\) | ||||
−0.917408 | + | 0.397948i | \(0.869722\pi\) | |||||||
\(948\) | 8.00000 | 0.259828 | ||||||||
\(949\) | 17.3693 | + | 2.73863i | 0.563832 | + | 0.0888998i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000i | 0.194563i | ||||||||
\(952\) | −10.2462 | −0.332082 | ||||||||
\(953\) | 42.9848 | 1.39242 | 0.696208 | − | 0.717840i | \(-0.254869\pi\) | ||||
0.696208 | + | 0.717840i | \(0.254869\pi\) | |||||||
\(954\) | − | 11.3693i | − | 0.368095i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 28.4924i | 0.921511i | ||||||||
\(957\) | 6.24621i | 0.201911i | ||||||||
\(958\) | −20.4924 | −0.662080 | ||||||||
\(959\) | 115.231 | 3.72100 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.75379 | 0.153348 | ||||||||
\(962\) | 1.75379 | − | 11.1231i | 0.0565444 | − | 0.358623i | ||||
\(963\) | 8.00000 | 0.257796 | ||||||||
\(964\) | − | 2.24621i | − | 0.0723456i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −16.0000 | −0.514792 | ||||||||
\(967\) | 6.38447i | 0.205311i | 0.994717 | + | 0.102655i | \(0.0327339\pi\) | ||||
−0.994717 | + | 0.102655i | \(0.967266\pi\) | |||||||
\(968\) | − | 1.24621i | − | 0.0400547i | ||||||
\(969\) | − | 12.0000i | − | 0.385496i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.2462 | 1.74084 | 0.870422 | − | 0.492307i | \(-0.163846\pi\) | ||||
0.870422 | + | 0.492307i | \(0.163846\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 84.4924i | 2.70870i | ||||||||
\(974\) | −7.36932 | −0.236128 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | − | 44.7386i | − | 1.43132i | −0.698451 | − | 0.715658i | \(-0.746127\pi\) | ||
0.698451 | − | 0.715658i | \(-0.253873\pi\) | |||||||
\(978\) | −1.12311 | −0.0359130 | ||||||||
\(979\) | −16.0000 | −0.511362 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.1231i | 0.355133i | ||||||||
\(982\) | − | 10.7386i | − | 0.342684i | ||||||
\(983\) | 27.5076i | 0.877355i | 0.898644 | + | 0.438678i | \(0.144553\pi\) | ||||
−0.898644 | + | 0.438678i | \(0.855447\pi\) | |||||||
\(984\) | −9.12311 | −0.290834 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 4.00000i | − | 0.127386i | ||||||
\(987\) | −52.4924 | −1.67085 | ||||||||
\(988\) | 21.3693 | + | 3.36932i | 0.679849 | + | 0.107192i | ||||
\(989\) | −32.0000 | −1.01754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.7386 | 0.595252 | 0.297626 | − | 0.954682i | \(-0.403805\pi\) | ||||
0.297626 | + | 0.954682i | \(0.403805\pi\) | |||||||
\(992\) | 5.12311 | 0.162659 | ||||||||
\(993\) | 24.2462i | 0.769430i | ||||||||
\(994\) | 32.0000i | 1.01498i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 10.2462i | − | 0.324664i | ||||||
\(997\) | 52.3542 | 1.65807 | 0.829036 | − | 0.559195i | \(-0.188890\pi\) | ||||
0.829036 | + | 0.559195i | \(0.188890\pi\) | |||||||
\(998\) | −1.50758 | −0.0477215 | ||||||||
\(999\) | 3.12311i | 0.0988107i |
(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 | 1950.2.b.h.1351.4 | 4 | ||
5.2 | odd | 4 | 1950.2.f.l.649.3 | 4 | |||
5.3 | odd | 4 | 1950.2.f.o.649.2 | 4 | |||
5.4 | even | 2 | 390.2.b.d.181.1 | ✓ | 4 | ||
13.12 | even | 2 | inner | 1950.2.b.h.1351.1 | 4 | ||
15.14 | odd | 2 | 1170.2.b.f.181.3 | 4 | |||
20.19 | odd | 2 | 3120.2.g.o.961.4 | 4 | |||
65.12 | odd | 4 | 1950.2.f.o.649.4 | 4 | |||
65.34 | odd | 4 | 5070.2.a.bh.1.1 | 2 | |||
65.38 | odd | 4 | 1950.2.f.l.649.1 | 4 | |||
65.44 | odd | 4 | 5070.2.a.bd.1.2 | 2 | |||
65.64 | even | 2 | 390.2.b.d.181.4 | yes | 4 | ||
195.194 | odd | 2 | 1170.2.b.f.181.2 | 4 | |||
260.259 | odd | 2 | 3120.2.g.o.961.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.b.d.181.1 | ✓ | 4 | 5.4 | even | 2 | ||
390.2.b.d.181.4 | yes | 4 | 65.64 | even | 2 | ||
1170.2.b.f.181.2 | 4 | 195.194 | odd | 2 | |||
1170.2.b.f.181.3 | 4 | 15.14 | odd | 2 | |||
1950.2.b.h.1351.1 | 4 | 13.12 | even | 2 | inner | ||
1950.2.b.h.1351.4 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.f.l.649.1 | 4 | 65.38 | odd | 4 | |||
1950.2.f.l.649.3 | 4 | 5.2 | odd | 4 | |||
1950.2.f.o.649.2 | 4 | 5.3 | odd | 4 | |||
1950.2.f.o.649.4 | 4 | 65.12 | odd | 4 | |||
3120.2.g.o.961.1 | 4 | 260.259 | odd | 2 | |||
3120.2.g.o.961.4 | 4 | 20.19 | odd | 2 | |||
5070.2.a.bd.1.2 | 2 | 65.44 | odd | 4 | |||
5070.2.a.bh.1.1 | 2 | 65.34 | odd | 4 |