Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1119,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1119");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.n (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1119.2 | ||
Root | \(-2.21837 + 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1119 |
Dual form | 2240.2.n.g.1119.3 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | − | 1.00000i | −0.894427 | − | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.16879 | −1.85996 | −0.929980 | − | 0.367610i | \(-0.880176\pi\) | ||||
−0.929980 | + | 0.367610i | \(0.880176\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.56155i | − | 0.987797i | −0.869520 | − | 0.493899i | \(-0.835571\pi\) | ||
0.869520 | − | 0.493899i | \(-0.164429\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.12311 | + | 1.56155i | 0.806382 | + | 0.403191i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.70469 | −0.655983 | −0.327992 | − | 0.944681i | \(-0.606372\pi\) | ||||
−0.327992 | + | 0.944681i | \(0.606372\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.12311i | − | 1.63415i | −0.576530 | − | 0.817076i | \(-0.695593\pi\) | ||
0.576530 | − | 0.817076i | \(-0.304407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.12311 | − | 2.70469i | 0.681518 | − | 0.590211i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.12311 | −1.48527 | −0.742635 | − | 0.669696i | \(-0.766424\pi\) | ||||
−0.742635 | + | 0.669696i | \(0.766424\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.70469i | − | 0.502248i | −0.967955 | − | 0.251124i | \(-0.919200\pi\) | ||
0.967955 | − | 0.251124i | \(-0.0808002\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.40938 | −0.971553 | −0.485776 | − | 0.874083i | \(-0.661463\pi\) | ||||
−0.485776 | + | 0.874083i | \(0.661463\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.63289 | 1.67687 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.73205 | − | 1.46410i | 0.968893 | − | 0.247478i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.40938 | −0.889296 | −0.444648 | − | 0.895705i | \(-0.646671\pi\) | ||||
−0.444648 | + | 0.895705i | \(0.646671\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.56155i | 0.890561i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.40938i | − | 0.844803i | −0.906409 | − | 0.422401i | \(-0.861187\pi\) | ||
0.906409 | − | 0.422401i | \(-0.138813\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.3376i | 1.88146i | 0.339152 | + | 0.940732i | \(0.389860\pi\) | ||||
−0.339152 | + | 0.940732i | \(0.610140\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.12311 | + | 0.561553i | 0.167423 | + | 0.0837114i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.16879i | 0.899811i | 0.893076 | + | 0.449905i | \(0.148542\pi\) | ||||
−0.893076 | + | 0.449905i | \(0.851458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.22351 | 0.591410 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.3376 | + | 6.16879i | 1.66360 | + | 0.831800i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.1231i | 1.47329i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4.00000i | − | 0.520756i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) | ||
0.965507 | − | 0.260378i | \(-0.0838471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.12311 | −0.912020 | −0.456010 | − | 0.889975i | \(-0.650722\pi\) | ||||
−0.456010 | + | 0.889975i | \(0.650722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.12311 | − | 0.972638i | 0.141498 | − | 0.122541i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.56155 | + | 7.12311i | −0.441756 | + | 0.883513i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.92820i | 0.846415i | 0.906033 | + | 0.423207i | \(0.139096\pi\) | ||||
−0.906033 | + | 0.423207i | \(0.860904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.1231 | 1.33906 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.24621i | − | 0.266576i | −0.991077 | − | 0.133288i | \(-0.957446\pi\) | ||
0.991077 | − | 0.133288i | \(-0.0425536\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92820 | 0.810885 | 0.405442 | − | 0.914121i | \(-0.367117\pi\) | ||||
0.405442 | + | 0.914121i | \(0.367117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.68466 | − | 6.24621i | −0.540938 | − | 0.721250i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.3376 | − | 10.6847i | 1.40600 | − | 1.21763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.68466i | 0.527065i | 0.964650 | + | 0.263533i | \(0.0848877\pi\) | ||||
−0.964650 | + | 0.263533i | \(0.915112\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.40938 | + | 2.70469i | 0.586729 | + | 0.293365i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.22351i | 0.452808i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.40938i | 0.573393i | 0.958021 | + | 0.286696i | \(0.0925571\pi\) | ||||
−0.958021 | + | 0.286696i | \(0.907443\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.16879 | + | 7.12311i | 0.646665 | + | 0.746704i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.44703 | 0.875916 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.12311 | + | 14.2462i | −0.730815 | + | 1.46163i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.5611 | 1.68152 | 0.840762 | − | 0.541405i | \(-0.182107\pi\) | ||||
0.840762 | + | 0.541405i | \(0.182107\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.46410 | 0.348155 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3693 | −1.33030 | −0.665148 | − | 0.746711i | \(-0.731632\pi\) | ||||
−0.665148 | + | 0.746711i | \(0.731632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.68762i | 0.757483i | 0.925502 | + | 0.378742i | \(0.123643\pi\) | ||||
−0.925502 | + | 0.378742i | \(0.876357\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.95090 | + | 2.28627i | −0.873518 | + | 0.223117i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 17.7470i | − | 1.71566i | −0.513931 | − | 0.857832i | \(-0.671811\pi\) | ||
0.513931 | − | 0.857832i | \(-0.328189\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.1517i | − | 1.06814i | −0.845440 | − | 0.534070i | \(-0.820662\pi\) | ||
0.845440 | − | 0.534070i | \(-0.179338\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.44703 | 0.801756 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.36932i | − | 0.881391i | −0.897657 | − | 0.440696i | \(-0.854732\pi\) | ||
0.897657 | − | 0.440696i | \(-0.145268\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.2462 | + | 7.12311i | 1.32847 | + | 0.664233i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000i | 0.184900i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.40938 | − | 4.68466i | 0.495877 | − | 0.429442i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.0540 | 2.45945 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.44703i | 0.761643i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 19.2658i | − | 1.69626i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.36932i | 0.469119i | 0.972102 | + | 0.234560i | \(0.0753648\pi\) | ||||
−0.972102 | + | 0.234560i | \(0.924635\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.3376 | + | 14.2462i | 1.06980 | + | 1.23530i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.1231 | − | 5.56155i | −0.957325 | − | 0.478662i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.87689i | 0.416661i | 0.978058 | + | 0.208331i | \(0.0668030\pi\) | ||||
−0.978058 | + | 0.208331i | \(0.933197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.24621i | 0.190521i | 0.995452 | + | 0.0952606i | \(0.0303684\pi\) | ||||
−0.995452 | + | 0.0952606i | \(0.969632\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.63289i | − | 0.811236i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.9705i | 1.83726i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.70469 | + | 5.40938i | −0.224612 | + | 0.449224i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.56155 | + | 10.8188i | −0.128795 | + | 0.892316i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.7470i | 1.45389i | 0.686697 | + | 0.726944i | \(0.259060\pi\) | ||||
−0.686697 | + | 0.726944i | \(0.740940\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 22.0540i | − | 1.79473i | −0.441292 | − | 0.897364i | \(-0.645480\pi\) | ||
0.441292 | − | 0.897364i | \(-0.354520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.51883 | 0.122790 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.8188 | + | 5.40938i | 0.868983 | + | 0.434492i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.75379i | − | 0.299585i | −0.988717 | − | 0.149792i | \(-0.952139\pi\) | ||
0.988717 | − | 0.149792i | \(-0.0478606\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.2462 | − | 12.3376i | 1.12276 | − | 0.972338i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.89055i | − | 0.304732i | −0.988324 | − | 0.152366i | \(-0.951311\pi\) | ||
0.988324 | − | 0.152366i | \(-0.0486892\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −19.2658 | − | 9.63289i | −1.49984 | − | 0.749920i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 18.5064i | − | 1.43207i | −0.698066 | − | 0.716033i | \(-0.745956\pi\) | ||
0.698066 | − | 0.716033i | \(-0.254044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.315342 | 0.0242570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000i | 0.305888i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.68466i | 0.204111i | 0.994779 | + | 0.102055i | \(0.0325419\pi\) | ||||
−0.994779 | + | 0.102055i | \(0.967458\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.9282 | − | 2.80385i | −0.977280 | − | 0.211951i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.24621i | 0.469494i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.35465 | 0.549713 | 0.274856 | − | 0.961485i | \(-0.411370\pi\) | ||||
0.274856 | + | 0.961485i | \(0.411370\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.24621 | −0.166960 | −0.0834798 | − | 0.996509i | \(-0.526603\pi\) | ||||
−0.0834798 | + | 0.996509i | \(0.526603\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.1231 | 0.822244 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.8188 | + | 5.40938i | 0.795411 | + | 0.397705i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.6847 | 1.22010 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.1231 | + | 9.63289i | −0.809087 | + | 0.700690i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.56155i | 0.691850i | 0.938262 | + | 0.345925i | \(0.112435\pi\) | ||||
−0.938262 | + | 0.345925i | \(0.887565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.3693i | 1.25027i | 0.780516 | + | 0.625135i | \(0.214956\pi\) | ||||
−0.780516 | + | 0.625135i | \(0.785044\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.56155 | − | 11.1231i | 0.398271 | − | 0.796542i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.44703 | −0.601826 | −0.300913 | − | 0.953652i | \(-0.597291\pi\) | ||||
−0.300913 | + | 0.953652i | \(0.597291\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.8188 | 0.766921 | 0.383461 | − | 0.923557i | \(-0.374732\pi\) | ||||
0.383461 | + | 0.923557i | \(0.374732\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 10.8188i | − | 0.763096i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.68466 | + | 5.40938i | 0.328799 | + | 0.379664i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.40938 | + | 10.8188i | −0.377807 | + | 0.755615i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 43.9409i | 3.03946i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.68762 | −0.529237 | −0.264619 | − | 0.964353i | \(-0.585246\pi\) | ||||
−0.264619 | + | 0.964353i | \(0.585246\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.50758i | 0.240335i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.3376 | − | 24.6752i | 0.841416 | − | 1.68283i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.8188 | − | 9.36932i | 0.734425 | − | 0.636031i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.8188 | −0.731064 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.63289i | 0.647978i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.16879i | 0.413093i | 0.978437 | + | 0.206546i | \(0.0662224\pi\) | ||||
−0.978437 | + | 0.206546i | \(0.933778\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.68466 | − | 2.24621i | −0.112311 | − | 0.149747i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.31534 | 0.220047 | 0.110023 | − | 0.993929i | \(-0.464907\pi\) | ||||
0.110023 | + | 0.993929i | \(0.464907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.12311 | 0.470708 | 0.235354 | − | 0.971910i | \(-0.424375\pi\) | ||||
0.235354 | + | 0.971910i | \(0.424375\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.2658 | + | 16.6847i | −1.26760 | + | 1.09777i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.49242i | 0.294308i | 0.989114 | + | 0.147154i | \(0.0470114\pi\) | ||||
−0.989114 | + | 0.147154i | \(0.952989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.16879 | − | 12.3376i | 0.402408 | − | 0.804815i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 7.31534i | − | 0.475182i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.68466i | 0.303025i | 0.988455 | + | 0.151513i | \(0.0484144\pi\) | ||||
−0.988455 | + | 0.151513i | \(0.951586\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 19.2658i | − | 1.24102i | −0.784199 | − | 0.620509i | \(-0.786926\pi\) | ||
0.784199 | − | 0.620509i | \(-0.213074\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.92820 | + | 12.8564i | −0.570402 | + | 0.821366i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.3693 | −1.61421 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.24621 | 0.395838 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 20.0000i | − | 1.26239i | −0.775625 | − | 0.631194i | \(-0.782565\pi\) | ||
0.775625 | − | 0.631194i | \(-0.217435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 43.9409 | 2.76254 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.44703 | − | 4.22351i | −0.528973 | − | 0.264487i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.92820 | −0.432169 | −0.216085 | − | 0.976375i | \(-0.569329\pi\) | ||||
−0.216085 | + | 0.976375i | \(0.569329\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.8188 | − | 9.36932i | 0.672245 | − | 0.582181i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.51883i | 0.0940129i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000 | 0.739952 | 0.369976 | − | 0.929041i | \(-0.379366\pi\) | ||||
0.369976 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 8.44703i | − | 0.516950i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.0000 | −1.21942 | −0.609711 | − | 0.792624i | \(-0.708714\pi\) | ||||
−0.609711 | + | 0.792624i | \(0.708714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.44703 | 0.513120 | 0.256560 | − | 0.966528i | \(-0.417411\pi\) | ||||
0.256560 | + | 0.966528i | \(0.417411\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.63289 | − | 11.1231i | −0.583009 | − | 0.673201i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.5064 | − | 24.6752i | −1.11598 | − | 1.48797i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.8564 | −0.832551 | −0.416275 | − | 0.909239i | \(-0.636665\pi\) | ||||
−0.416275 | + | 0.909239i | \(0.636665\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.03765 | 0.181859 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.3153 | −0.794327 | −0.397163 | − | 0.917748i | \(-0.630005\pi\) | ||||
−0.397163 | + | 0.917748i | \(0.630005\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.56155 | −0.568375 | −0.284188 | − | 0.958769i | \(-0.591724\pi\) | ||||
−0.284188 | + | 0.958769i | \(0.591724\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.1231 | − | 22.2462i | 0.658876 | − | 1.31775i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.36932 | + | 10.8188i | 0.553053 | + | 0.638611i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.68466 | −0.569686 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −25.8610 | −1.51600 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.6847i | 1.55893i | 0.626443 | + | 0.779467i | \(0.284510\pi\) | ||||
−0.626443 | + | 0.779467i | \(0.715490\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | + | 8.00000i | −0.232889 | + | 0.465778i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −34.3081 | −1.99076 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.3693i | 1.46715i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.3693 | − | 24.6752i | −1.23171 | − | 1.42225i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.8769 | 1.19935 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.2462 | + | 7.12311i | 0.815736 | + | 0.407868i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.9309 | −1.08044 | −0.540221 | − | 0.841523i | \(-0.681659\pi\) | ||||
−0.540221 | + | 0.841523i | \(0.681659\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 12.0046i | − | 0.682919i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.1222 | −1.87819 | −0.939094 | − | 0.343662i | \(-0.888333\pi\) | ||||
−0.939094 | + | 0.343662i | \(0.888333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.1517 | 0.630332 | 0.315166 | − | 0.949037i | \(-0.397940\pi\) | ||||
0.315166 | + | 0.949037i | \(0.397940\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.21885 | + | 0.822170i | −0.181362 | + | 0.0463241i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.8188 | −0.607642 | −0.303821 | − | 0.952729i | \(-0.598262\pi\) | ||||
−0.303821 | + | 0.952729i | \(0.598262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.6847i | 0.934162i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.7128i | 1.54678i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.2658i | 1.07198i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.2462 | − | 10.6847i | 0.790238 | − | 0.592678i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.4140i | 0.962996i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.6847 | − | 12.3376i | −0.589064 | − | 0.680193i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3205 | 0.952021 | 0.476011 | − | 0.879440i | \(-0.342082\pi\) | ||||
0.476011 | + | 0.879440i | \(0.342082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.03765 | 0.166462 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.92820 | − | 13.8564i | 0.378528 | − | 0.757056i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 26.7386i | − | 1.45655i | −0.685287 | − | 0.728273i | \(-0.740323\pi\) | ||
0.685287 | − | 0.728273i | \(-0.259677\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.6307i | 0.794630i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.3693 | 1.80705 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −22.2462 | − | 11.1231i | −1.19770 | − | 0.598848i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 1.51883i | − | 0.0815348i | −0.999169 | − | 0.0407674i | \(-0.987020\pi\) | ||
0.999169 | − | 0.0407674i | \(-0.0129803\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.12311 | 0.381291 | 0.190646 | − | 0.981659i | \(-0.438942\pi\) | ||||
0.190646 | + | 0.981659i | \(0.438942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 19.8078i | − | 1.05726i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.1517 | −0.593546 | −0.296773 | − | 0.954948i | \(-0.595910\pi\) | ||||
−0.296773 | + | 0.954948i | \(0.595910\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.24621 | + | 4.49242i | −0.119217 | + | 0.238433i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.44703 | + | 7.31534i | −0.447064 | + | 0.387169i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 12.0000i | − | 0.633336i | −0.948536 | − | 0.316668i | \(-0.897436\pi\) | ||
0.948536 | − | 0.316668i | \(-0.102564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −31.7386 | −1.67045 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −42.2462 | −2.21735 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.8564 | − | 6.92820i | −0.725277 | − | 0.362639i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 27.8063i | − | 1.45148i | −0.687971 | − | 0.725739i | \(-0.741498\pi\) | ||
0.687971 | − | 0.725739i | \(-0.258502\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.03765i | 0.158134i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.2281 | −0.840261 | −0.420130 | − | 0.907464i | \(-0.638016\pi\) | ||||
−0.420130 | + | 0.907464i | \(0.638016\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.12311 | + | 17.1771i | 0.161276 | + | 0.887021i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.63289 | −0.496119 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.426450 | −0.0219053 | −0.0109526 | − | 0.999940i | \(-0.503486\pi\) | ||||
−0.0109526 | + | 0.999940i | \(0.503486\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.7386 | 0.960009 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 28.1393i | − | 1.43785i | −0.695088 | − | 0.718925i | \(-0.744635\pi\) | ||
0.695088 | − | 0.718925i | \(-0.255365\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −35.3598 | + | 9.03174i | −1.80210 | + | 0.460300i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 6.92820i | − | 0.352180i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.9705i | 1.11395i | 0.830530 | + | 0.556974i | \(0.188038\pi\) | ||||
−0.830530 | + | 0.556974i | \(0.811962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.2658 | 0.974313 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 8.38447i | − | 0.422941i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.68466 | − | 9.36932i | 0.235711 | − | 0.471421i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 24.9309i | − | 1.25124i | −0.780126 | − | 0.625622i | \(-0.784845\pi\) | ||
0.780126 | − | 0.625622i | \(-0.215155\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.2658 | − | 22.2462i | −0.964496 | − | 1.11370i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.8078 | 0.889277 | 0.444639 | − | 0.895710i | \(-0.353332\pi\) | ||||
0.444639 | + | 0.895710i | \(0.353332\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.2658i | 0.959697i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.0000 | + | 7.00000i | 0.695666 | + | 0.347833i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.3693 | 1.65406 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.03765i | − | 0.150202i | −0.997176 | − | 0.0751011i | \(-0.976072\pi\) | ||
0.997176 | − | 0.0751011i | \(-0.0239279\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 7.61553i | − | 0.375646i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.92820 | + | 8.00000i | 0.340915 | + | 0.393654i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00000 | + | 4.00000i | 0.392705 | + | 0.196352i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3.50758i | − | 0.171767i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 22.7386i | − | 1.11085i | −0.831565 | − | 0.555427i | \(-0.812555\pi\) | ||
0.831565 | − | 0.555427i | \(-0.187445\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.70469i | 0.131818i | 0.997826 | + | 0.0659092i | \(0.0209948\pi\) | ||||
−0.997826 | + | 0.0659092i | \(0.979005\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.46410i | − | 0.168430i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.11407 | − | 10.8188i | −0.393590 | − | 0.524787i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.2462 | − | 12.3376i | 0.689422 | − | 0.597057i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 34.3081i | − | 1.65641i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 28.6847i | − | 1.38169i | −0.723002 | − | 0.690846i | \(-0.757238\pi\) | ||
0.723002 | − | 0.690846i | \(-0.242762\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.6034 | 1.51876 | 0.759380 | − | 0.650647i | \(-0.225502\pi\) | ||||
0.759380 | + | 0.650647i | \(0.225502\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.22351 | − | 8.44703i | 0.202502 | − | 0.405004i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 50.7386i | 2.42716i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.8564 | 0.661330 | 0.330665 | − | 0.943748i | \(-0.392727\pi\) | ||||
0.330665 | + | 0.943748i | \(0.392727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.561553 | + | 3.89055i | −0.0267406 | + | 0.185264i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.3752i | 0.730499i | 0.930910 | + | 0.365250i | \(0.119016\pi\) | ||||
−0.930910 | + | 0.365250i | \(0.880984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.40938 | − | 10.8188i | 0.256429 | − | 0.512858i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 27.7128i | − | 1.31077i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.05398 | −0.380091 | −0.190045 | − | 0.981775i | \(-0.560863\pi\) | ||||
−0.190045 | + | 0.981775i | \(0.560863\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.3693i | 1.57130i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 34.4384i | 1.61806i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.21448 | − | 20.4150i | −0.244458 | − | 0.957070i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.3693i | 1.18673i | 0.804935 | + | 0.593363i | \(0.202200\pi\) | ||||
−0.804935 | + | 0.593363i | \(0.797800\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.0423 | −0.702113 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.0000 | 0.931493 | 0.465746 | − | 0.884918i | \(-0.345786\pi\) | ||||
0.465746 | + | 0.884918i | \(0.345786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.3693 | 0.621325 | 0.310662 | − | 0.950520i | \(-0.399449\pi\) | ||||
0.310662 | + | 0.950520i | \(0.399449\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.8941 | − | 8.44703i | −0.783443 | − | 0.391722i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.05398 | 0.280145 | 0.140072 | − | 0.990141i | \(-0.455267\pi\) | ||||
0.140072 | + | 0.990141i | \(0.455267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0000 | − | 13.8564i | −0.554109 | − | 0.639829i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.86174i | 0.270095i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 76.1080i | − | 3.49945i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.4924 | − | 21.3693i | 1.30732 | − | 0.980492i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.1222 | −1.51339 | −0.756696 | − | 0.653767i | \(-0.773188\pi\) | ||||
−0.756696 | + | 0.653767i | \(0.773188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.2658i | 0.878444i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.2462 | + | 19.2658i | −1.01224 | + | 0.876624i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −33.1222 | − | 16.5611i | −1.50400 | − | 0.752001i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.0000 | −0.543772 | −0.271886 | − | 0.962329i | \(-0.587647\pi\) | ||||
−0.271886 | + | 0.962329i | \(0.587647\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.07530i | 0.274735i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.5440 | −0.972268 | −0.486134 | − | 0.873884i | \(-0.661593\pi\) | ||||
−0.486134 | + | 0.873884i | \(0.661593\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.31534i | 0.329466i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.92820 | − | 3.46410i | −0.311400 | − | 0.155700i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.89055 | + | 4.49242i | 0.174515 | + | 0.201513i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.68762 | −0.344145 | −0.172072 | − | 0.985084i | \(-0.555046\pi\) | ||||
−0.172072 | + | 0.985084i | \(0.555046\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.8987i | 1.29110i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 9.20644i | − | 0.410495i | −0.978710 | − | 0.205247i | \(-0.934200\pi\) | ||
0.978710 | − | 0.205247i | \(-0.0657999\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.7386 | + | 13.3693i | 1.18985 | + | 0.594927i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.492423 | −0.0218693 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.00000 | 0.177297 | 0.0886484 | − | 0.996063i | \(-0.471745\pi\) | ||||
0.0886484 | + | 0.996063i | \(0.471745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8564 | + | 12.0000i | −0.612971 | + | 0.530849i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 39.6155i | − | 1.74907i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.68762 | − | 15.3752i | 0.338757 | − | 0.677514i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 38.0540i | − | 1.67361i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4.19224i | − | 0.184019i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8.44703i | − | 0.370071i | −0.982732 | − | 0.185036i | \(-0.940760\pi\) | ||
0.982732 | − | 0.185036i | \(-0.0592400\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.4924 | −1.77061 | −0.885305 | − | 0.465011i | \(-0.846050\pi\) | ||||
−0.885305 | + | 0.465011i | \(0.846050\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.1881 | + | 4.37836i | 0.881080 | + | 0.191087i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.6307 | 0.637323 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.7386 | 1.20603 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.24621i | 0.0974773i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.2658 | −0.834494 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.7470 | + | 35.4939i | −0.767268 | + | 1.53454i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.4847 | −0.495601 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.16879 | + | 42.7386i | −0.265709 | + | 1.84088i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.3799i | 1.17715i | 0.808442 | + | 0.588576i | \(0.200311\pi\) | ||||
−0.808442 | + | 0.588576i | \(0.799689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.50758 | 0.150525 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.1517 | + | 22.3034i | −0.477687 | + | 0.955374i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.51883i | − | 0.0649403i | −0.999473 | − | 0.0324701i | \(-0.989663\pi\) | ||
0.999473 | − | 0.0324701i | \(-0.0103374\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.00000 | 0.170716 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.2658 | −0.820750 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.11407 | − | 9.36932i | −0.345045 | − | 0.398424i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.8941 | − | 8.44703i | −0.717113 | − | 0.358556i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.8564 | 0.587115 | 0.293557 | − | 0.955941i | \(-0.405161\pi\) | ||||
0.293557 | + | 0.955941i | \(0.405161\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.9409 | 1.85850 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26.0540 | −1.10000 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.0000 | −0.842900 | −0.421450 | − | 0.906852i | \(-0.638479\pi\) | ||||
−0.421450 | + | 0.906852i | \(0.638479\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.36932 | + | 18.7386i | −0.394170 | + | 0.788340i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.0000 | − | 12.1244i | 0.587945 | − | 0.509175i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.7538 | −0.660433 | −0.330217 | − | 0.943905i | \(-0.607122\pi\) | ||||
−0.330217 | + | 0.943905i | \(0.607122\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.2111 | 0.887655 | 0.443828 | − | 0.896112i | \(-0.353620\pi\) | ||||
0.443828 | + | 0.896112i | \(0.353620\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 14.9309i | − | 0.623746i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.3693 | − | 28.4924i | −0.891162 | − | 1.18822i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.3422 | −1.01338 | −0.506690 | − | 0.862129i | \(-0.669131\pi\) | ||||
−0.506690 | + | 0.862129i | \(0.669131\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 27.1231i | − | 1.12720i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00000 | − | 6.92820i | 0.331896 | − | 0.287430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | − | 4.00000i | 0.0826898 | − | 0.165380i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.0000 | −1.15568 | −0.577842 | − | 0.816149i | \(-0.696105\pi\) | ||||
−0.577842 | + | 0.816149i | \(0.696105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38.5316i | 1.58767i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.1905 | 0.542584 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.9705 | −0.902219 | −0.451110 | − | 0.892469i | \(-0.648972\pi\) | ||||
−0.451110 | + | 0.892469i | \(0.648972\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.5034 | + | 3.95994i | −0.635578 | + | 0.162342i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.8941 | −0.691428 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 9.56155i | − | 0.390674i | −0.980736 | − | 0.195337i | \(-0.937420\pi\) | ||
0.980736 | − | 0.195337i | \(-0.0625801\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.5316i | 1.57174i | 0.618395 | + | 0.785868i | \(0.287783\pi\) | ||||
−0.618395 | + | 0.785868i | \(0.712217\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 3.89055i | − | 0.158436i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −54.1080 | − | 27.0540i | −2.19980 | − | 1.09990i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.64996i | 0.188736i | 0.995537 | + | 0.0943681i | \(0.0300831\pi\) | ||||
−0.995537 | + | 0.0943681i | \(0.969917\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.31534 | − | 8.44703i | −0.296433 | − | 0.342291i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.9705 | 0.888830 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.5316 | 1.55628 | 0.778138 | − | 0.628094i | \(-0.216165\pi\) | ||||
0.778138 | + | 0.628094i | \(0.216165\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.44703 | − | 16.8941i | 0.340617 | − | 0.681234i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.7386i | 0.754389i | 0.926134 | + | 0.377194i | \(0.123111\pi\) | ||||
−0.926134 | + | 0.377194i | \(0.876889\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.6155i | 0.466867i | 0.972373 | + | 0.233434i | \(0.0749962\pi\) | ||||
−0.972373 | + | 0.233434i | \(0.925004\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −39.6155 | −1.58972 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.36932 | − | 10.8188i | −0.375374 | − | 0.433444i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 68.6161i | − | 2.74026i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.6307 | 0.583364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.6847i | 1.14192i | 0.820978 | + | 0.570959i | \(0.193429\pi\) | ||||
−0.820978 | + | 0.570959i | \(0.806571\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0046 | 0.477141 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.0000 | + | 12.0000i | 0.952411 | + | 0.476205i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.6752 | − | 3.56155i | −0.977666 | − | 0.141114i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.26137i | 0.0498989i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.24621 | −0.325706 | −0.162853 | − | 0.986650i | \(-0.552070\pi\) | ||||
−0.162853 | + | 0.986650i | \(0.552070\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.3002 | 1.11605 | 0.558025 | − | 0.829824i | \(-0.311559\pi\) | ||||
0.558025 | + | 0.829824i | \(0.311559\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.2658 | + | 38.5316i | −0.758590 | + | 1.51718i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 25.1016i | − | 0.986846i | −0.869789 | − | 0.493423i | \(-0.835745\pi\) | ||
0.869789 | − | 0.493423i | \(-0.164255\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.6752i | 0.968585i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.8941 | + | 14.6307i | −0.662130 | + | 0.573422i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.0845 | 1.17730 | 0.588649 | − | 0.808388i | \(-0.299660\pi\) | ||||
0.588649 | + | 0.808388i | \(0.299660\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.36932 | − | 10.7386i | 0.209797 | − | 0.419593i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.89055 | −0.151785 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.5064 | 0.720906 | 0.360453 | − | 0.932777i | \(-0.382622\pi\) | ||||
0.360453 | + | 0.932777i | \(0.382622\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.7538 | −0.846124 | −0.423062 | − | 0.906101i | \(-0.639045\pi\) | ||||
−0.423062 | + | 0.906101i | \(0.639045\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 15.0423i | − | 0.584193i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.4290 | − | 40.8300i | −0.404417 | − | 1.58332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.2658i | 0.745974i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 9.63289i | − | 0.372429i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.9409 | 1.69632 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 9.36932i | − | 0.361161i | −0.983560 | − | 0.180580i | \(-0.942202\pi\) | ||
0.983560 | − | 0.180580i | \(-0.0577976\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.6847 | + | 22.2462i | 0.642193 | + | 0.856257i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.31534i | 0.204285i | 0.994770 | + | 0.102143i | \(0.0325698\pi\) | ||||
−0.994770 | + | 0.102143i | \(0.967430\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.1222 | + | 28.6847i | −1.27111 | + | 1.10082i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.17708 | −0.198386 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.3752i | − | 0.588317i | −0.955757 | − | 0.294158i | \(-0.904961\pi\) | ||
0.955757 | − | 0.294158i | \(-0.0950393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.87689 | − | 9.75379i | 0.186337 | − | 0.372673i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.1231 | −0.424373 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 40.4924i | − | 1.54040i | −0.637800 | − | 0.770202i | \(-0.720155\pi\) | ||
0.637800 | − | 0.770202i | \(-0.279845\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.92820 | + | 6.00000i | −0.263181 | + | 0.227921i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.24621 | − | 4.49242i | 0.0852036 | − | 0.170407i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.6307i | 0.554177i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 7.01515i | − | 0.265338i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.5987i | − | 0.740234i | −0.928985 | − | 0.370117i | \(-0.879318\pi\) | ||
0.928985 | − | 0.370117i | \(-0.120682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.5316i | 1.45325i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.63289 | + | 19.2658i | −0.362796 | + | 0.725591i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.7386 | − | 23.1563i | 1.00561 | − | 0.870884i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.9705i | 0.825118i | 0.910931 | + | 0.412559i | \(0.135365\pi\) | ||||
−0.910931 | + | 0.412559i | \(0.864635\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2.63068i | − | 0.0986583i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38.5316 | 1.44302 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.9705 | − | 43.9409i | 0.821649 | − | 1.64330i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 7.31534i | − | 0.273196i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.40938 | 0.201736 | 0.100868 | − | 0.994900i | \(-0.467838\pi\) | ||||
0.100868 | + | 0.994900i | \(0.467838\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.3153 | − | 15.3752i | −0.495889 | − | 0.572604i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.0845i | 1.11886i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.8188 | − | 8.11407i | 0.401798 | − | 0.301349i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 14.2829i | − | 0.529722i | −0.964287 | − | 0.264861i | \(-0.914674\pi\) | ||
0.964287 | − | 0.264861i | \(-0.0853260\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 33.3693i | − | 1.23421i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.3002i | 0.823676i | 0.911257 | + | 0.411838i | \(0.135113\pi\) | ||||
−0.911257 | + | 0.411838i | \(0.864887\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.9419 | − | 20.0760i | 0.514253 | − | 0.740513i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 42.7386i | − | 1.57430i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.3251 | 1.07874 | 0.539371 | − | 0.842068i | \(-0.318662\pi\) | ||||
0.539371 | + | 0.842068i | \(0.318662\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 39.6155 | 1.45531 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.7538 | 0.798069 | 0.399035 | − | 0.916936i | \(-0.369345\pi\) | ||||
0.399035 | + | 0.916936i | \(0.369345\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.7470 | − | 35.4939i | 0.650198 | − | 1.30040i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.24621 | 0.0821846 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.7386 | + | 35.4939i | 1.12317 | + | 1.29692i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.31534i | 0.120979i | 0.998169 | + | 0.0604893i | \(0.0192661\pi\) | ||||
−0.998169 | + | 0.0604893i | \(0.980734\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.2311i | 1.13812i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.0540 | + | 44.1080i | −0.802626 | + | 1.60525i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.8564 | 0.503620 | 0.251810 | − | 0.967777i | \(-0.418974\pi\) | ||||
0.251810 | + | 0.967777i | \(0.418974\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −68.6161 | −2.49061 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.9033i | 1.48274i | 0.671095 | + | 0.741372i | \(0.265824\pi\) | ||||
−0.671095 | + | 0.741372i | \(0.734176\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.3153 | + | 22.3034i | 0.699262 | + | 0.807439i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.03765 | − | 1.51883i | −0.109827 | − | 0.0549133i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.2462 | −0.514401 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 24.6752i | − | 0.889809i | −0.895578 | − | 0.444905i | \(-0.853238\pi\) | ||
0.895578 | − | 0.444905i | \(-0.146762\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.8188 | 0.389628 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.0540i | 1.44064i | 0.693641 | + | 0.720321i | \(0.256005\pi\) | ||||
−0.693641 | + | 0.720321i | \(0.743995\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.2281 | − | 21.6375i | −0.582932 | − | 0.777242i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.8941 | + | 14.6307i | −0.606071 | + | 0.524873i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −38.5316 | −1.38054 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8564i | 0.495821i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 15.0423i | − | 0.537567i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.75379 | + | 7.50758i | −0.133978 | + | 0.267957i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.1922 | 0.862360 | 0.431180 | − | 0.902266i | \(-0.358097\pi\) | ||||
0.431180 | + | 0.902266i | \(0.358097\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.7386 | −0.667113 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.2281 | + | 18.7386i | 0.577006 | + | 0.666269i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.3693i | 0.900891i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.0540i | 0.568661i | 0.958726 | + | 0.284330i | \(0.0917713\pi\) | ||||
−0.958726 | + | 0.284330i | \(0.908229\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 16.6847i | − | 0.590261i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.03765i | − | 0.107330i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −42.7386 | −1.50821 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −40.8300 | + | 10.4290i | −1.43907 | + | 0.367572i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.2311 | 1.09939 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.3002 | −0.784033 | −0.392016 | − | 0.919958i | \(-0.628222\pi\) | ||||
−0.392016 | + | 0.919958i | \(0.628222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.24621i | − | 0.0788751i | −0.999222 | − | 0.0394376i | \(-0.987443\pi\) | ||
0.999222 | − | 0.0394376i | \(-0.0125566\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.1905 | −0.462610 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.89055 | + | 7.78110i | −0.136280 | + | 0.272560i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 87.8819 | 3.07460 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.46410 | − | 4.00000i | −0.121046 | − | 0.139771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1517i | 0.389198i | 0.980883 | + | 0.194599i | \(0.0623405\pi\) | ||||
−0.980883 | + | 0.194599i | \(0.937660\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.6307 | −0.370562 | −0.185281 | − | 0.982686i | \(-0.559320\pi\) | ||||
−0.185281 | + | 0.982686i | \(0.559320\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28.8987 | + | 38.5316i | 1.00612 | + | 1.34150i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.6410i | 1.20459i | 0.798275 | + | 0.602293i | \(0.205746\pi\) | ||||
−0.798275 | + | 0.602293i | \(0.794254\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.6155 | −0.403424 | −0.201712 | − | 0.979445i | \(-0.564650\pi\) | ||||
−0.201712 | + | 0.979445i | \(0.564650\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.6375 | 0.750597 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.70469 | + | 18.7386i | −0.0937119 | + | 0.649255i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.5064 | + | 37.0127i | −0.640439 | + | 1.28088i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.0845 | −1.03987 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.9786 | 1.62188 | 0.810941 | − | 0.585128i | \(-0.198956\pi\) | ||||
0.810941 | + | 0.585128i | \(0.198956\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.6847 | 0.747747 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.7926 | 0.716135 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.630683 | − | 0.315342i | −0.0216962 | − | 0.0108481i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −54.1080 | + | 46.8589i | −1.85917 | + | 1.61009i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.9309 | 0.512426 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.5316 | 1.32085 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.4924i | 0.359254i | 0.983735 | + | 0.179627i | \(0.0574890\pi\) | ||||
−0.983735 | + | 0.179627i | \(0.942511\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | − | 8.00000i | 0.136797 | − | 0.273594i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −53.2409 | −1.81867 | −0.909337 | − | 0.416061i | \(-0.863410\pi\) | ||||
−0.909337 | + | 0.416061i | \(0.863410\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 26.2462i | − | 0.895509i | −0.894156 | − | 0.447755i | \(-0.852224\pi\) | ||
0.894156 | − | 0.447755i | \(-0.147776\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.6307 | − | 16.8941i | −0.498612 | − | 0.575748i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.3693 | 0.727420 | 0.363710 | − | 0.931512i | \(-0.381510\pi\) | ||||
0.363710 | + | 0.931512i | \(0.381510\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.68466 | − | 5.36932i | 0.0912811 | − | 0.182562i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.1231 | 0.513608 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 28.8987i | − | 0.980320i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.6752 | 0.836086 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.29993 | −0.314755 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 23.0526 | + | 18.5359i | 0.779319 | + | 0.626628i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.2281 | 0.547985 | 0.273993 | − | 0.961732i | \(-0.411656\pi\) | ||||
0.273993 | + | 0.961732i | \(0.411656\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 41.6695i | − | 1.40548i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.8564i | 0.466834i | 0.972377 | + | 0.233417i | \(0.0749907\pi\) | ||||
−0.972377 | + | 0.233417i | \(0.925009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.51883i | 0.0511126i | 0.999673 | + | 0.0255563i | \(0.00813570\pi\) | ||||
−0.999673 | + | 0.0255563i | \(0.991864\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.24621 | − | 12.4924i | 0.209964 | − | 0.419928i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.1016i | 0.842830i | 0.906868 | + | 0.421415i | \(0.138466\pi\) | ||||
−0.906868 | + | 0.421415i | \(0.861534\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.0000 | − | 20.7846i | 0.804934 | − | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.1815 | 1.44664 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43.9409 | 1.47043 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.7093 | − | 7.35465i | −0.491678 | − | 0.245839i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 39.6155i | − | 1.32272i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.6307i | 0.487961i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.3693 | + | 38.5316i | 1.11046 | + | 1.28225i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.49242 | + | 2.24621i | 0.149333 | + | 0.0746666i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.29993i | 0.308799i | 0.988008 | + | 0.154400i | \(0.0493443\pi\) | ||||
−0.988008 | + | 0.154400i | \(0.950656\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.50758 | 0.249011 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.7386i | 1.01842i | 0.860643 | + | 0.509208i | \(0.170062\pi\) | ||||
−0.860643 | + | 0.509208i | \(0.829938\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.6752 | 0.816629 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22.2462 | − | 11.1231i | −0.735437 | − | 0.367719i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.29993 | − | 10.7386i | −0.307111 | − | 0.354621i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.68466i | − | 0.154533i | −0.997010 | − | 0.0772663i | \(-0.975381\pi\) | ||
0.997010 | − | 0.0772663i | \(-0.0246192\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.5616 | 0.974086 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.00000 | −0.263323 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.2281 | − | 21.6375i | −0.533578 | − | 0.711437i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 4.31700i | − | 0.141789i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 38.5316i | − | 1.26418i | −0.774895 | − | 0.632090i | \(-0.782197\pi\) | ||
0.774895 | − | 0.632090i | \(-0.217803\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −49.3503 | − | 7.12311i | −1.61739 | − | 0.233450i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 51.7220 | 1.69330 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −33.3693 | − | 16.6847i | −1.09129 | − | 0.545647i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.9328 | −0.618508 | −0.309254 | − | 0.950979i | \(-0.600079\pi\) | ||||
−0.309254 | + | 0.950979i | \(0.600079\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.4140 | −0.568284 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.36932 | −0.175035 | −0.0875174 | − | 0.996163i | \(-0.527893\pi\) | ||||
−0.0875174 | + | 0.996163i | \(0.527893\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.5316i | 1.25476i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 31.8791 | − | 8.14268i | 1.03703 | − | 0.264881i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.1563i | 0.752480i | 0.926522 | + | 0.376240i | \(0.122783\pi\) | ||||
−0.926522 | + | 0.376240i | \(0.877217\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 24.6752i | − | 0.800990i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.8941 | 0.547827 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.6155i | 0.764982i | 0.923959 | + | 0.382491i | \(0.124934\pi\) | ||||
−0.923959 | + | 0.382491i | \(0.875066\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.56155 | − | 19.1231i | 0.309405 | − | 0.618809i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 26.0540i | − | 0.842205i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.44703 | − | 9.75379i | −0.272769 | − | 0.314966i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.73863 | −0.0560850 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.96585i | 0.321145i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.3693 | − | 34.7386i | 0.559138 | − | 1.11828i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.7386 | −1.76028 | −0.880138 | − | 0.474718i | \(-0.842550\pi\) | ||||
−0.880138 | + | 0.474718i | \(0.842550\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 30.0845i | − | 0.966455i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.3693i | 1.19924i | 0.800285 | + | 0.599619i | \(0.204681\pi\) | ||||
−0.800285 | + | 0.599619i | \(0.795319\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.89055 | − | 4.49242i | −0.124725 | − | 0.144020i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.2462 | + | 16.6847i | −0.712449 | + | 0.534337i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 28.8769i | − | 0.923854i | −0.886918 | − | 0.461927i | \(-0.847158\pi\) | ||
0.886918 | − | 0.461927i | \(-0.152842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 33.3693i | − | 1.06649i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.26228i | 0.199939i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.8440i | 0.983769i | 0.870660 | + | 0.491885i | \(0.163692\pi\) | ||||
−0.870660 | + | 0.491885i | \(0.836308\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.8941 | + | 8.44703i | 0.538289 | + | 0.269145i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.6847 | + | 19.2658i | 0.531079 | + | 0.613237i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 87.8819i | − | 2.79448i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.4773i | 1.57170i | 0.618419 | + | 0.785849i | \(0.287774\pi\) | ||||
−0.618419 | + | 0.785849i | \(0.712226\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.0469 | −0.858307 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.6375 | − | 10.8188i | −0.685955 | − | 0.342978i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 8.82292i | − | 0.279425i | −0.990192 | − | 0.139712i | \(-0.955382\pi\) | ||
0.990192 | − | 0.139712i | \(-0.0446178\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.0845 | −0.951833 |
(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 | 2240.2.n.g.1119.2 | yes | 8 | |
4.3 | odd | 2 | 2240.2.n.a.1119.5 | ✓ | 8 | ||
5.4 | even | 2 | 2240.2.n.a.1119.7 | yes | 8 | ||
7.6 | odd | 2 | 2240.2.n.b.1119.7 | yes | 8 | ||
8.3 | odd | 2 | 2240.2.n.h.1119.3 | yes | 8 | ||
8.5 | even | 2 | 2240.2.n.b.1119.8 | yes | 8 | ||
20.19 | odd | 2 | inner | 2240.2.n.g.1119.4 | yes | 8 | |
28.27 | even | 2 | 2240.2.n.h.1119.4 | yes | 8 | ||
35.34 | odd | 2 | 2240.2.n.h.1119.2 | yes | 8 | ||
40.19 | odd | 2 | 2240.2.n.b.1119.6 | yes | 8 | ||
40.29 | even | 2 | 2240.2.n.h.1119.1 | yes | 8 | ||
56.13 | odd | 2 | inner | 2240.2.n.g.1119.1 | yes | 8 | |
56.27 | even | 2 | 2240.2.n.a.1119.6 | yes | 8 | ||
140.139 | even | 2 | 2240.2.n.b.1119.5 | yes | 8 | ||
280.69 | odd | 2 | 2240.2.n.a.1119.8 | yes | 8 | ||
280.139 | even | 2 | inner | 2240.2.n.g.1119.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.n.a.1119.5 | ✓ | 8 | 4.3 | odd | 2 | ||
2240.2.n.a.1119.6 | yes | 8 | 56.27 | even | 2 | ||
2240.2.n.a.1119.7 | yes | 8 | 5.4 | even | 2 | ||
2240.2.n.a.1119.8 | yes | 8 | 280.69 | odd | 2 | ||
2240.2.n.b.1119.5 | yes | 8 | 140.139 | even | 2 | ||
2240.2.n.b.1119.6 | yes | 8 | 40.19 | odd | 2 | ||
2240.2.n.b.1119.7 | yes | 8 | 7.6 | odd | 2 | ||
2240.2.n.b.1119.8 | yes | 8 | 8.5 | even | 2 | ||
2240.2.n.g.1119.1 | yes | 8 | 56.13 | odd | 2 | inner | |
2240.2.n.g.1119.2 | yes | 8 | 1.1 | even | 1 | trivial | |
2240.2.n.g.1119.3 | yes | 8 | 280.139 | even | 2 | inner | |
2240.2.n.g.1119.4 | yes | 8 | 20.19 | odd | 2 | inner | |
2240.2.n.h.1119.1 | yes | 8 | 40.29 | even | 2 | ||
2240.2.n.h.1119.2 | yes | 8 | 35.34 | odd | 2 | ||
2240.2.n.h.1119.3 | yes | 8 | 8.3 | odd | 2 | ||
2240.2.n.h.1119.4 | yes | 8 | 28.27 | even | 2 |