Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(2,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(156))
chi = DirichletCharacter(H, H._module([78, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.2");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.x (of order \(156\), degree \(48\), 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{156}]$ |
Embedding invariants
Embedding label | 98.1 | ||
Character | \(\chi\) | \(=\) | 507.98 |
Dual form | 507.2.x.a.119.1 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{59}{156}\right)\) |
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 | −0.373361 | − | 0.927686i | \(-0.621795\pi\) | ||||
0.373361 | + | 0.927686i | \(0.378205\pi\) | |||||||
\(3\) | 1.64291 | − | 0.548485i | 0.948536 | − | 0.316668i | ||||
\(4\) | −1.44240 | + | 1.38545i | −0.721202 | + | 0.692724i | ||||
\(5\) | 0 | 0 | −0.297503 | − | 0.954721i | \(-0.596154\pi\) | ||||
0.297503 | + | 0.954721i | \(0.403846\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.527444 | − | 5.22047i | −0.199355 | − | 1.97315i | −0.228369 | − | 0.973575i | \(-0.573339\pi\) |
0.0290142 | − | 0.999579i | \(-0.490763\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.39833 | − | 1.80223i | 0.799443 | − | 0.600742i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.990080 | − | 0.140502i | \(-0.0448718\pi\) | ||||
−0.990080 | + | 0.140502i | \(0.955128\pi\) | |||||||
\(12\) | −1.60985 | + | 3.06731i | −0.464723 | + | 0.885456i | ||||
\(13\) | 2.59808 | + | 2.50000i | 0.720577 | + | 0.693375i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.161064 | − | 3.99676i | 0.0402659 | − | 0.999189i | ||||
\(17\) | 0 | 0 | −0.774605 | − | 0.632445i | \(-0.782051\pi\) | ||||
0.774605 | + | 0.632445i | \(0.217949\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.98272 | − | 7.39960i | 0.454867 | − | 1.69759i | −0.233613 | − | 0.972330i | \(-0.575055\pi\) |
0.688479 | − | 0.725256i | \(-0.258279\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.72990 | − | 8.28749i | −0.813930 | − | 1.80848i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.11492 | + | 2.84032i | −0.822984 | + | 0.568065i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.95175 | − | 4.27635i | 0.568065 | − | 0.822984i | ||||
\(28\) | 7.99349 | + | 6.79929i | 1.51063 | + | 1.28495i | ||||
\(29\) | 0 | 0 | −0.919979 | − | 0.391967i | \(-0.871795\pi\) | ||||
0.919979 | + | 0.391967i | \(0.128205\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.48545 | − | 0.272220i | 0.266796 | − | 0.0488921i | −0.0451919 | − | 0.998978i | \(-0.514390\pi\) |
0.311987 | + | 0.950086i | \(0.399005\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.962468 | + | 5.92230i | −0.160411 | + | 0.987050i | ||||
\(37\) | 5.91139 | + | 2.10674i | 0.971826 | + | 0.346346i | 0.773504 | − | 0.633791i | \(-0.218502\pi\) |
0.198322 | + | 0.980137i | \(0.436451\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.63963 | + | 2.68228i | 0.903063 | + | 0.429508i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.894635 | − | 0.446798i | \(-0.852564\pi\) | ||||
0.894635 | + | 0.446798i | \(0.147436\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.5365 | + | 5.47415i | 1.75930 | + | 0.834800i | 0.977399 | + | 0.211401i | \(0.0678026\pi\) |
0.781904 | + | 0.623399i | \(0.214249\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.855781 | − | 0.517338i | \(-0.173077\pi\) | ||||
−0.855781 | + | 0.517338i | \(0.826923\pi\) | |||||||
\(48\) | −1.92755 | − | 6.65466i | −0.278217 | − | 0.960518i | ||||
\(49\) | −20.1166 | + | 4.10684i | −2.87380 | + | 0.586691i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.21110 | − | 0.00651091i | −1.00000 | − | 0.000902901i | ||||
\(53\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.801139 | − | 13.2444i | −0.106113 | − | 1.75426i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.735006 | − | 0.678061i | \(-0.762821\pi\) | ||||
0.735006 | + | 0.678061i | \(0.237179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3705 | + | 1.84789i | −1.45585 | + | 0.236598i | −0.836261 | − | 0.548331i | \(-0.815263\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.6735 | − | 11.5698i | −1.34473 | − | 1.45766i | ||||
\(64\) | 5.30498 | + | 5.98809i | 0.663123 | + | 0.748511i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.94094 | + | 0.200222i | −1.21448 | + | 0.0244610i | −0.623237 | − | 0.782033i | \(-0.714183\pi\) |
−0.591242 | + | 0.806494i | \(0.701362\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.834256 | − | 0.551377i | \(-0.185897\pi\) | ||||
−0.834256 | + | 0.551377i | \(0.814103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.09927 | + | 2.67951i | 0.245700 | + | 0.313614i | 0.894258 | − | 0.447552i | \(-0.147704\pi\) |
−0.648557 | + | 0.761166i | \(0.724627\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.20258 | + | 6.92338i | −0.600742 | + | 0.799443i | ||||
\(76\) | 7.39189 | + | 13.4202i | 0.847908 | + | 1.53940i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.441406 | − | 0.108797i | −0.0496620 | − | 0.0122406i | 0.214406 | − | 0.976745i | \(-0.431218\pi\) |
−0.264068 | + | 0.964504i | \(0.585064\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.50396 | − | 8.64466i | 0.278217 | − | 0.960518i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.998176 | − | 0.0603785i | \(-0.980769\pi\) | ||||
0.998176 | + | 0.0603785i | \(0.0192308\pi\) | |||||||
\(84\) | 16.8619 | + | 6.78634i | 1.83979 | + | 0.740450i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.6808 | − | 14.8818i | 1.22449 | − | 1.56004i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.29117 | − | 1.26198i | 0.237583 | − | 0.130862i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.18324 | + | 9.69385i | 0.221674 | + | 0.984261i | 0.953175 | + | 0.302420i | \(0.0977946\pi\) |
−0.731501 | + | 0.681841i | \(0.761180\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00026 | − | 9.79791i | 0.200026 | − | 0.979791i | ||||
\(101\) | 0 | 0 | −0.0804666 | − | 0.996757i | \(-0.525641\pi\) | ||||
0.0804666 | + | 0.996757i | \(0.474359\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.1592 | + | 14.8537i | −1.29661 | + | 1.46358i | −0.490970 | + | 0.871177i | \(0.663357\pi\) |
−0.805645 | + | 0.592399i | \(0.798181\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.845190 | − | 0.534466i | \(-0.179487\pi\) | ||||
−0.845190 | + | 0.534466i | \(0.820513\pi\) | |||||||
\(108\) | 1.66704 | + | 10.2577i | 0.160411 | + | 0.987050i | ||||
\(109\) | −3.73419 | + | 20.3768i | −0.357671 | + | 1.95175i | −0.0556241 | + | 0.998452i | \(0.517715\pi\) |
−0.302046 | + | 0.953293i | \(0.597670\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.8674 | + | 0.218882i | 1.03149 | + | 0.0207754i | ||||
\(112\) | −20.9499 | + | 1.26724i | −1.97958 | + | 0.119743i | ||||
\(113\) | 0 | 0 | −0.948536 | − | 0.316668i | \(-0.897436\pi\) | ||||
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.7366 | + | 1.31350i | 0.992600 | + | 0.121433i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5657 | − | 3.06039i | 0.960518 | − | 0.278217i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.76548 | + | 2.45067i | −0.158545 | + | 0.220077i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.18527 | − | 7.86205i | −0.726325 | − | 0.697644i | 0.235327 | − | 0.971916i | \(-0.424384\pi\) |
−0.961652 | + | 0.274272i | \(0.911563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21.9560 | + | 2.66594i | 1.93312 | + | 0.234723i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.120537 | − | 0.992709i | \(-0.538462\pi\) | ||||
0.120537 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −39.6752 | − | 6.44785i | −3.44028 | − | 0.559099i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.335705 | − | 0.941967i | \(-0.608974\pi\) | ||||
0.335705 | + | 0.941967i | \(0.391026\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.0229 | + | 12.0294i | 1.61351 | + | 1.02032i | 0.966098 | + | 0.258175i | \(0.0831210\pi\) |
0.647407 | + | 0.762144i | \(0.275853\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.81678 | − | 9.87581i | −0.568065 | − | 0.822984i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −30.7973 | + | 17.7808i | −2.54012 | + | 1.46654i | ||||
\(148\) | −11.4454 | + | 5.15115i | −0.940805 | + | 0.423422i | ||||
\(149\) | 0 | 0 | 0.482459 | − | 0.875918i | \(-0.339744\pi\) | ||||
−0.482459 | + | 0.875918i | \(0.660256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.29671 | − | 7.10763i | 0.349662 | − | 0.578411i | −0.630602 | − | 0.776107i | \(-0.717192\pi\) |
0.980263 | + | 0.197696i | \(0.0633457\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.8508 | + | 3.94448i | −0.948822 | + | 0.315811i | ||||
\(157\) | 4.68563 | + | 2.45921i | 0.373954 | + | 0.196266i | 0.641221 | − | 0.767356i | \(-0.278428\pi\) |
−0.267267 | + | 0.963623i | \(0.586121\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.4443 | − | 16.5394i | 1.52300 | − | 1.29547i | 0.746156 | − | 0.665771i | \(-0.231897\pi\) |
0.776842 | − | 0.629696i | \(-0.216821\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.927686 | − | 0.373361i | \(-0.121795\pi\) | ||||
−0.927686 | + | 0.373361i | \(0.878205\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | + | 12.9904i | 0.0384615 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.58056 | − | 21.3200i | −0.656172 | − | 1.63038i | ||||
\(172\) | −24.2245 | + | 8.08732i | −1.84710 | + | 0.616653i | ||||
\(173\) | 0 | 0 | 0.721202 | − | 0.692724i | \(-0.243590\pi\) | ||||
−0.721202 | + | 0.692724i | \(0.756410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.9982 | + | 19.9837i | 1.28495 | + | 1.51063i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.774605 | − | 0.632445i | \(-0.217949\pi\) | ||||
−0.774605 | + | 0.632445i | \(0.782051\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.11496 | − | 15.4618i | 0.603180 | − | 1.14926i | −0.372080 | − | 0.928201i | \(-0.621355\pi\) |
0.975260 | − | 0.221062i | \(-0.0709525\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.6673 | + | 9.27249i | −1.30600 | + | 0.685442i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23.8815 | − | 13.1540i | −1.73712 | − | 0.956813i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 12.0000 | + | 6.92820i | 0.866025 | + | 0.500000i | ||||
\(193\) | 23.5348 | + | 2.37781i | 1.69407 | + | 0.171158i | 0.899770 | − | 0.436365i | \(-0.143734\pi\) |
0.794302 | + | 0.607524i | \(0.207837\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 23.3265 | − | 33.7943i | 1.66618 | − | 2.41388i | ||||
\(197\) | 0 | 0 | −0.761712 | − | 0.647915i | \(-0.775641\pi\) | ||||
0.761712 | + | 0.647915i | \(0.224359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.8515 | + | 17.1602i | −0.769239 | + | 1.21645i | 0.202241 | + | 0.979336i | \(0.435177\pi\) |
−0.971481 | + | 0.237119i | \(0.923797\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.2223 | + | 5.78140i | −1.14423 | + | 0.407789i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.4103 | − | 9.98122i | 0.721828 | − | 0.692073i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.81244 | − | 2.92806i | 0.193616 | − | 0.201576i | −0.617317 | − | 0.786714i | \(-0.711780\pi\) |
0.810933 | + | 0.585139i | \(0.198960\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.20461 | − | 7.61120i | −0.149659 | − | 0.516682i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.91859 | + | 3.25079i | 0.332367 | + | 0.219668i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.4841 | − | 5.96471i | −1.77351 | − | 0.399427i | −0.795159 | − | 0.606401i | \(-0.792613\pi\) |
−0.978346 | + | 0.206974i | \(0.933638\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.75002 | + | 14.2280i | −0.316668 | + | 0.948536i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.0201371 | − | 0.999797i | \(-0.493590\pi\) | ||||
−0.0201371 | + | 0.999797i | \(0.506410\pi\) | |||||||
\(228\) | 19.5050 | + | 17.9939i | 1.29175 | + | 1.19167i | ||||
\(229\) | 14.5776 | + | 2.67145i | 0.963316 | + | 0.176534i | 0.638823 | − | 0.769354i | \(-0.279422\pi\) |
0.324493 | + | 0.945888i | \(0.394806\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.663123 | − | 0.748511i | \(-0.730769\pi\) | ||||
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.784865 | + | 0.0633608i | −0.0509824 | + | 0.00411573i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 30.2023 | − | 6.80213i | 1.94550 | − | 0.438164i | 0.956079 | − | 0.293108i | \(-0.0946894\pi\) |
0.989423 | − | 0.145056i | \(-0.0463362\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.627684 | − | 15.5758i | −0.0402659 | − | 0.999189i | ||||
\(244\) | 13.8407 | − | 18.4187i | 0.886063 | − | 1.17914i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.6503 | − | 14.2679i | 1.50483 | − | 0.907847i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.0804666 | − | 0.996757i | \(-0.474359\pi\) | ||||
−0.0804666 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(252\) | 31.4249 | + | 1.90085i | 1.97958 | + | 0.119743i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9481 | − | 1.28747i | −0.996757 | − | 0.0804666i | ||||
\(257\) | 0 | 0 | −0.960518 | − | 0.278217i | \(-0.910256\pi\) | ||||
0.960518 | + | 0.278217i | \(0.0897436\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.88025 | − | 31.9714i | 0.489655 | − | 1.98661i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.799443 | − | 0.600742i | \(-0.794872\pi\) | ||||
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.0615 | − | 14.0615i | 0.858940 | − | 0.858940i | ||||
\(269\) | 0 | 0 | 0.200026 | − | 0.979791i | \(-0.435897\pi\) | ||||
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.570747 | + | 28.3374i | 0.0346704 | + | 1.72137i | 0.526073 | + | 0.850439i | \(0.323664\pi\) |
−0.491403 | + | 0.870933i | \(0.663516\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.0282 | − | 30.8563i | 0.667455 | − | 1.86751i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.26128 | − | 32.3740i | −0.316120 | − | 1.94516i | −0.326446 | − | 0.945216i | \(-0.605851\pi\) |
0.0103260 | − | 0.999947i | \(-0.496713\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.07201 | − | 3.33000i | 0.183916 | − | 0.199362i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.998176 | − | 0.0603785i | \(-0.0192308\pi\) | ||||
−0.998176 | + | 0.0603785i | \(0.980769\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5454 | + | 5.00387i | −0.626860 | + | 0.297449i | −0.715498 | − | 0.698615i | \(-0.753800\pi\) |
0.0886374 | + | 0.996064i | \(0.471749\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.40044 | + | 16.6564i | 0.200026 | + | 0.979791i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.90380 | + | 14.7287i | 0.521950 | + | 0.863411i | ||||
\(292\) | −6.74032 | − | 0.956520i | −0.394448 | − | 0.0559761i | ||||
\(293\) | 0 | 0 | 0.584522 | − | 0.811378i | \(-0.301282\pi\) | ||||
−0.584522 | + | 0.811378i | \(0.698718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.08776 | − | 17.1942i | −0.120537 | − | 0.992709i | ||||
\(301\) | 22.4928 | − | 63.1134i | 1.29646 | − | 3.63780i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −29.2551 | − | 9.11625i | −1.67789 | − | 0.522853i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.30456 | − | 12.5756i | −0.131528 | − | 0.717726i | −0.981584 | − | 0.191033i | \(-0.938816\pi\) |
0.850056 | − | 0.526693i | \(-0.176568\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.4724 | + | 31.6209i | −0.766419 | + | 1.79885i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.822984 | − | 0.568065i | \(-0.807692\pi\) | ||||
0.822984 | + | 0.568065i | \(0.192308\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.8900 | − | 27.3669i | −1.06773 | − | 1.54687i | −0.815111 | − | 0.579304i | \(-0.803324\pi\) |
−0.252616 | − | 0.967567i | \(-0.581291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.787418 | − | 0.454616i | 0.0442957 | − | 0.0255741i | ||||
\(317\) | 0 | 0 | 0.911900 | − | 0.410413i | \(-0.134615\pi\) | ||||
−0.911900 | + | 0.410413i | \(0.865385\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 8.36502 | + | 15.9382i | 0.464723 | + | 0.885456i | ||||
\(325\) | −17.7917 | − | 2.90792i | −0.986905 | − | 0.161302i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.04143 | + | 35.5255i | 0.278792 | + | 1.96456i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.2052 | − | 2.44554i | 1.33044 | − | 0.134419i | 0.590468 | − | 0.807061i | \(-0.298943\pi\) |
0.739968 | + | 0.672642i | \(0.234841\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.9743 | − | 5.60101i | 0.984984 | − | 0.306933i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −33.7238 | + | 13.5727i | −1.83979 | + | 0.740450i | ||||
\(337\) | 31.3370i | 1.70703i | 0.521065 | + | 0.853517i | \(0.325535\pi\) | ||||
−0.521065 | + | 0.853517i | \(0.674465\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 21.1229 | + | 67.7858i | 1.14053 | + | 3.66009i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.799443 | − | 0.600742i | \(-0.205128\pi\) | ||||
−0.799443 | + | 0.600742i | \(0.794872\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −36.7163 | + | 5.21041i | −1.96538 | + | 0.278907i | −0.965551 | + | 0.260214i | \(0.916207\pi\) |
−0.999825 | + | 0.0186925i | \(0.994050\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.3597 | − | 3.73090i | 0.979971 | − | 0.199141i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.584522 | − | 0.811378i | \(-0.698718\pi\) | ||||
0.584522 | + | 0.811378i | \(0.301282\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.410413 | − | 0.911900i | \(-0.634615\pi\) | ||||
0.410413 | + | 0.911900i | \(0.365385\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −34.3685 | − | 19.8427i | −1.80887 | − | 1.04435i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.6799 | − | 10.8231i | 0.822984 | − | 0.568065i | ||||
\(364\) | 3.76946 | + | 37.6488i | 0.197573 | + | 1.97333i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.0835 | + | 14.9477i | 1.83135 | + | 0.780264i | 0.953554 | + | 0.301222i | \(0.0973945\pi\) |
0.877792 | + | 0.479042i | \(0.159016\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.55637 | + | 4.99458i | −0.0806943 | + | 0.258957i | ||||
\(373\) | −29.6280 | + | 12.6233i | −1.53408 | + | 0.653609i | −0.983456 | − | 0.181146i | \(-0.942019\pi\) |
−0.550622 | + | 0.834755i | \(0.685609\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.3675 | − | 9.67250i | −0.994840 | − | 0.496843i | −0.126050 | − | 0.992024i | \(-0.540230\pi\) |
−0.868790 | + | 0.495181i | \(0.835102\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.7599 | − | 8.42718i | −0.909867 | − | 0.431737i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.811378 | − | 0.584522i | \(-0.801282\pi\) | ||||
0.811378 | + | 0.584522i | \(0.198718\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 37.5340 | − | 7.66263i | 1.90796 | − | 0.389513i | ||||
\(388\) | −16.5794 | − | 10.9577i | −0.841693 | − | 0.556293i | ||||
\(389\) | 0 | 0 | −0.935016 | − | 0.354605i | \(-0.884615\pi\) | ||||
0.935016 | + | 0.354605i | \(0.115385\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.6775 | − | 22.7656i | −1.23853 | − | 1.14257i | −0.984502 | − | 0.175376i | \(-0.943886\pi\) |
−0.254026 | − | 0.967197i | \(-0.581755\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −68.7195 | + | 11.1680i | −3.44028 | + | 0.559099i | ||||
\(400\) | 10.6893 | + | 16.9038i | 0.534466 | + | 0.845190i | ||||
\(401\) | 0 | 0 | −0.678061 | − | 0.735006i | \(-0.737179\pi\) | ||||
0.678061 | + | 0.735006i | \(0.262821\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.53987 | + | 3.00639i | 0.226147 | + | 0.149759i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.99095 | + | 4.62046i | −0.345680 | + | 0.228467i | −0.712254 | − | 0.701922i | \(-0.752326\pi\) |
0.366574 | + | 0.930389i | \(0.380531\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.59810 | − | 39.6564i | −0.0787327 | − | 1.95373i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.8510 | + | 9.32943i | 1.85357 | + | 0.456864i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.278217 | − | 0.960518i | \(-0.410256\pi\) | ||||
−0.278217 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.0205 | + | 1.75542i | 1.41437 | + | 0.0855539i | 0.749798 | − | 0.661667i | \(-0.230151\pi\) |
0.664576 | + | 0.747221i | \(0.268612\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.6442 | + | 58.3849i | 0.757075 | + | 2.82544i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.875918 | − | 0.482459i | \(-0.160256\pi\) | ||||
−0.875918 | + | 0.482459i | \(0.839744\pi\) | |||||||
\(432\) | −16.6161 | − | 12.4862i | −0.799443 | − | 0.600742i | ||||
\(433\) | −26.5497 | + | 1.06992i | −1.27590 | + | 0.0514169i | −0.668940 | − | 0.743317i | \(-0.733252\pi\) |
−0.606958 | + | 0.794734i | \(0.707611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −22.8448 | − | 34.5651i | −1.09407 | − | 1.65537i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.652051 | + | 8.07710i | 0.0311207 | + | 0.385499i | 0.993503 | + | 0.113802i | \(0.0363029\pi\) |
−0.962383 | + | 0.271697i | \(0.912415\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −40.8448 | + | 46.1042i | −1.94499 | + | 2.19544i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(444\) | −15.9785 | + | 14.7405i | −0.758304 | + | 0.699554i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 28.4626 | − | 30.8529i | 1.34473 | − | 1.45766i | ||||
\(449\) | 0 | 0 | −0.999797 | − | 0.0201371i | \(-0.993590\pi\) | ||||
0.999797 | + | 0.0201371i | \(0.00641026\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.16070 | − | 14.0339i | 0.148503 | − | 0.659371i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5940 | − | 29.6466i | 0.916570 | − | 1.38681i | −0.00558406 | − | 0.999984i | \(-0.501777\pi\) |
0.922154 | − | 0.386823i | \(-0.126428\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.990080 | − | 0.140502i | \(-0.955128\pi\) | ||||
0.990080 | + | 0.140502i | \(0.0448718\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.4861 | − | 21.5340i | −1.27739 | − | 1.00077i | −0.999190 | − | 0.0402476i | \(-0.987185\pi\) |
−0.278200 | − | 0.960523i | \(-0.589738\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.992709 | − | 0.120537i | \(-0.961538\pi\) | ||||
0.992709 | + | 0.120537i | \(0.0384615\pi\) | |||||||
\(468\) | −17.3063 | + | 12.9804i | −0.799985 | + | 0.600020i | ||||
\(469\) | 6.28854 | + | 51.7908i | 0.290378 | + | 2.39148i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.04692 | + | 1.47027i | 0.416860 | + | 0.0677464i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.8585 | + | 36.0803i | 0.589991 | + | 1.65548i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.647915 | − | 0.761712i | \(-0.275641\pi\) | ||||
−0.647915 | + | 0.761712i | \(0.724359\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0914 | + | 20.2519i | 0.460128 | + | 0.923409i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0000 | + | 19.0526i | −0.500000 | + | 0.866025i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.4124 | − | 22.5351i | 0.562460 | − | 1.02116i | −0.430486 | − | 0.902597i | \(-0.641658\pi\) |
0.992946 | − | 0.118565i | \(-0.0378293\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.8737 | − | 37.8378i | 1.03439 | − | 1.71108i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.999189 | − | 0.0402659i | \(-0.987179\pi\) | ||||
0.999189 | + | 0.0402659i | \(0.0128205\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.848743 | − | 5.98085i | −0.0381097 | − | 0.268548i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.1232 | − | 35.8243i | 0.721774 | − | 1.60372i | −0.0733768 | − | 0.997304i | \(-0.523378\pi\) |
0.795151 | − | 0.606412i | \(-0.207392\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.692724 | − | 0.721202i | \(-0.743590\pi\) | ||||
0.692724 | + | 0.721202i | \(0.256410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.94649 | + | 21.0678i | 0.352916 | + | 0.935655i | ||||
\(508\) | 22.6989 | 1.00710 | ||||||||
\(509\) | 0 | 0 | −0.373361 | − | 0.927686i | \(-0.621795\pi\) | ||||
0.373361 | + | 0.927686i | \(0.378205\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8811 | − | 12.3725i | 0.569826 | − | 0.547325i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25.7908 | − | 30.3206i | −1.13869 | − | 1.33869i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −35.3630 | + | 26.5735i | −1.55677 | + | 1.16984i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.76126 | + | 43.7052i | −0.0770145 | + | 1.91110i | 0.253567 | + | 0.967318i | \(0.418396\pi\) |
−0.330581 | + | 0.943778i | \(0.607245\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 38.8874 | + | 23.5082i | 1.69718 | + | 1.02598i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 66.1609 | − | 45.6676i | 2.86844 | − | 1.97994i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.65262 | + | 8.51255i | −0.114045 | + | 0.365983i | −0.994042 | − | 0.108996i | \(-0.965237\pi\) |
0.879997 | + | 0.474979i | \(0.157544\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.85163 | − | 29.8533i | 0.208203 | − | 1.28113i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.44792 | + | 44.8677i | −0.232936 | + | 1.91840i | 0.139273 | + | 0.990254i | \(0.455523\pi\) |
−0.372209 | + | 0.928149i | \(0.621400\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.9399 | + | 24.9241i | −1.02173 | + | 1.06374i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.335154 | + | 2.36173i | −0.0142522 | + | 0.100431i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −44.1049 | + | 9.00408i | −1.87046 | + | 0.381858i | ||||
\(557\) | 0 | 0 | −0.834256 | − | 0.551377i | \(-0.814103\pi\) | ||||
0.834256 | + | 0.551377i | \(0.185897\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.2874 | + | 43.0636i | 0.688884 | + | 1.82139i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −46.4499 | − | 8.51227i | −1.95071 | − | 0.357482i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.534466 | − | 0.845190i | \(-0.679487\pi\) | ||||
0.534466 | + | 0.845190i | \(0.320513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.8609 | + | 13.3882i | 0.496363 | + | 0.560279i | 0.942293 | − | 0.334790i | \(-0.108665\pi\) |
−0.445929 | + | 0.895068i | \(0.647127\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 23.5150 | + | 4.80062i | 0.979791 | + | 0.200026i | ||||
\(577\) | −30.2280 | − | 30.2280i | −1.25841 | − | 1.25841i | −0.951853 | − | 0.306554i | \(-0.900824\pi\) |
−0.306554 | − | 0.951853i | \(-0.599176\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.9698 | − | 9.00195i | 1.66109 | − | 0.374108i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(588\) | 19.7878 | − | 68.3153i | 0.816033 | − | 2.81727i | ||||
\(589\) | 0.930920 | − | 11.5315i | 0.0383579 | − | 0.475148i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.37223 | − | 23.2871i | 0.385196 | − | 0.957092i | ||||
\(593\) | 0 | 0 | 0.0603785 | − | 0.998176i | \(-0.480769\pi\) | ||||
−0.0603785 | + | 0.998176i | \(0.519231\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.41588 | + | 34.1446i | −0.344439 | + | 1.39744i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.970942 | − | 0.239316i | \(-0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.65049 | − | 5.74897i | −0.312070 | − | 0.234505i | 0.433154 | − | 0.901320i | \(-0.357401\pi\) |
−0.745223 | + | 0.666815i | \(0.767657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −23.4808 | + | 18.3960i | −0.956211 | + | 0.749144i | ||||
\(604\) | 3.64966 | + | 16.2050i | 0.148503 | + | 0.659371i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.00386 | − | 34.3072i | 0.284278 | − | 1.39248i | −0.547235 | − | 0.836979i | \(-0.684320\pi\) |
0.831513 | − | 0.555506i | \(-0.187475\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.7265 | + | 32.0360i | −1.40259 | + | 1.29392i | −0.498300 | + | 0.867005i | \(0.666042\pi\) |
−0.904290 | + | 0.426919i | \(0.859599\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.678061 | − | 0.735006i | \(-0.262821\pi\) | ||||
−0.678061 | + | 0.735006i | \(0.737179\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.6321 | + | 2.09486i | −1.39198 | + | 0.0841994i | −0.739271 | − | 0.673408i | \(-0.764830\pi\) |
−0.652711 | + | 0.757607i | \(0.726368\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.6287 | − | 22.1082i | 0.465522 | − | 0.885036i | ||||
\(625\) | 8.86512 | − | 23.3754i | 0.354605 | − | 0.935016i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.1657 | + | 2.94453i | −0.405655 | + | 0.117499i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.5337 | + | 36.8316i | −1.05629 | + | 1.46624i | −0.180484 | + | 0.983578i | \(0.557766\pi\) |
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.01459 | − | 6.35312i | 0.119819 | − | 0.252514i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −62.5316 | − | 39.6217i | −2.47759 | − | 1.56987i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.391967 | − | 0.919979i | \(-0.628205\pi\) | ||||
0.391967 | + | 0.919979i | \(0.371795\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.855787 | − | 1.71356i | −0.0337490 | − | 0.0675763i | 0.877122 | − | 0.480268i | \(-0.159461\pi\) |
−0.910871 | + | 0.412692i | \(0.864589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.391967 | − | 0.919979i | \(-0.371795\pi\) | ||||
−0.391967 | + | 0.919979i | \(0.628205\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.79661 | − | 11.2953i | −0.305573 | − | 0.442699i | ||||
\(652\) | −5.13208 | + | 50.7957i | −0.200988 | + | 1.98931i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.86382 | + | 2.64300i | 0.384824 | + | 0.103113i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.632445 | − | 0.774605i | \(-0.282051\pi\) | ||||
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.0968 | + | 28.1656i | −1.52069 | + | 1.09551i | −0.556315 | + | 0.830971i | \(0.687785\pi\) |
−0.964374 | + | 0.264543i | \(0.914779\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −46.7826 | + | 4.72662i | −1.80872 | + | 0.182742i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.00393 | − | 17.9840i | −0.231435 | − | 0.693231i | −0.998655 | − | 0.0518477i | \(-0.983489\pi\) |
0.767220 | − | 0.641384i | \(-0.221639\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.9808i | 1.00000i | ||||||||
\(676\) | −18.7187 | − | 18.0447i | −0.719950 | − | 0.694026i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 49.4549 | − | 16.5105i | 1.89791 | − | 0.633614i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.100522 | − | 0.994935i | \(-0.532051\pi\) | ||||
0.100522 | + | 0.994935i | \(0.467949\pi\) | |||||||
\(684\) | 41.9144 | + | 18.8641i | 1.60264 | + | 0.721288i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.4150 | − | 3.60665i | 0.969643 | − | 0.137602i | ||||
\(688\) | 23.7370 | − | 45.2270i | 0.904963 | − | 1.72426i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.4607 | − | 42.2826i | −1.15878 | − | 1.60851i | −0.686681 | − | 0.726959i | \(-0.740933\pi\) |
−0.472098 | − | 0.881546i | \(-0.656503\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −52.2047 | − | 5.27444i | −1.97315 | − | 0.199355i | ||||
\(701\) | 0 | 0 | 0.822984 | − | 0.568065i | \(-0.192308\pi\) | ||||
−0.822984 | + | 0.568065i | \(0.807692\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.3096 | − | 39.5649i | 1.03000 | − | 1.49222i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.97439 | + | 1.98489i | −0.149262 | + | 0.0745442i | −0.519872 | − | 0.854244i | \(-0.674020\pi\) |
0.370610 | + | 0.928788i | \(0.379149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.25471 | + | 0.534583i | −0.0470554 | + | 0.0200484i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.903450 | − | 0.428693i | \(-0.858974\pi\) | ||||
0.903450 | + | 0.428693i | \(0.141026\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 84.4839 | + | 60.8628i | 3.14635 | + | 2.26665i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 45.8889 | − | 27.7408i | 1.70663 | − | 1.03169i | ||||
\(724\) | 9.71642 | + | 33.5450i | 0.361108 | + | 1.24669i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.43881 | − | 1.30417i | −0.127538 | − | 0.0483689i | 0.290010 | − | 0.957024i | \(-0.406341\pi\) |
−0.417548 | + | 0.908655i | \(0.637111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.57433 | − | 25.2454i | −0.354605 | − | 0.935016i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 12.6368 | − | 37.8518i | 0.467069 | − | 1.39904i | ||||
\(733\) | −1.71595 | − | 28.3680i | −0.0633799 | − | 1.04780i | −0.881329 | − | 0.472504i | \(-0.843350\pi\) |
0.817949 | − | 0.575291i | \(-0.195111\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5392 | + | 26.6001i | 0.902690 | + | 0.978499i | 0.999859 | − | 0.0167685i | \(-0.00533782\pi\) |
−0.0971693 | + | 0.995268i | \(0.530979\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.0296 | − | 36.4128i | 1.13990 | − | 1.33766i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.999797 | − | 0.0201371i | \(-0.00641026\pi\) | ||||
−0.999797 | + | 0.0201371i | \(0.993590\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.7306 | + | 31.5797i | −0.865942 | + | 1.15236i | 0.121218 | + | 0.992626i | \(0.461320\pi\) |
−0.987160 | + | 0.159734i | \(0.948936\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 52.6709 | − | 14.1131i | 1.91562 | − | 0.513290i | ||||
\(757\) | −11.5482 | + | 39.8690i | −0.419727 | + | 1.44906i | 0.420730 | + | 0.907186i | \(0.361774\pi\) |
−0.840457 | + | 0.541879i | \(0.817713\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.373361 | − | 0.927686i | \(-0.378205\pi\) | ||||
−0.373361 | + | 0.927686i | \(0.621795\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 108.346 | + | 8.74661i | 3.92240 | + | 0.316649i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −26.9075 | + | 6.63211i | −0.970942 | + | 0.239316i | ||||
\(769\) | 47.4373 | − | 26.1287i | 1.71063 | − | 0.942224i | 0.751295 | − | 0.659967i | \(-0.229430\pi\) |
0.959339 | − | 0.282257i | \(-0.0910831\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −37.2410 | + | 29.1765i | −1.34033 | + | 1.05008i | ||||
\(773\) | 0 | 0 | −0.219715 | − | 0.975564i | \(-0.570513\pi\) | ||||
0.219715 | + | 0.975564i | \(0.429487\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.33934 | + | 5.33934i | −0.191795 | + | 0.191795i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.58928 | − | 56.8485i | −0.164640 | − | 2.03943i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.1740 | + | 81.0627i | 0.470499 | + | 2.89509i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.92279 | − | 0.179715i | −0.318063 | − | 0.00640615i | −0.139151 | − | 0.990271i | \(-0.544437\pi\) |
−0.178912 | + | 0.983865i | \(0.557258\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.1612 | − | 23.6254i | −1.21310 | − | 0.838961i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.12239 | − | 39.7861i | −0.287890 | − | 1.41018i | ||||
\(797\) | 0 | 0 | 0.960518 | − | 0.278217i | \(-0.0897436\pi\) | ||||
−0.960518 | + | 0.278217i | \(0.910256\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 15.3893 | − | 30.8143i | 0.542737 | − | 1.08674i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.987050 | − | 0.160411i | \(-0.948718\pi\) | ||||
0.987050 | + | 0.160411i | \(0.0512821\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.3352 | − | 5.40187i | −0.608721 | − | 0.189685i | −0.0223803 | − | 0.999750i | \(-0.507124\pi\) |
−0.586341 | + | 0.810064i | \(0.699432\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.4803 | + | 46.2428i | 0.577990 | + | 1.62181i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 63.3802 | − | 74.5120i | 2.21739 | − | 2.60685i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.19412 | − | 56.7430i | 0.0417260 | − | 1.98276i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.100522 | − | 0.994935i | \(-0.467949\pi\) | ||||
−0.100522 | + | 0.994935i | \(0.532051\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.1737 | − | 24.3490i | 1.47008 | − | 0.848753i | 0.470647 | − | 0.882322i | \(-0.344021\pi\) |
0.999436 | + | 0.0335690i | \(0.0106873\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.517338 | − | 0.855781i | \(-0.326923\pi\) | ||||
−0.517338 | + | 0.855781i | \(0.673077\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 57.3466 | + | 2.31099i | 1.99173 | + | 0.0802640i | 0.999147 | − | 0.0412960i | \(-0.0131487\pi\) |
0.992584 | + | 0.121560i | \(0.0387897\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.4005 | − | 50.3019i | −0.915822 | − | 1.74495i | ||||
\(832\) | −1.18747 | + | 28.8200i | −0.0411681 | + | 0.999152i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.22059 | − | 7.15585i | 0.111320 | − | 0.247342i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.761712 | − | 0.647915i | \(-0.224359\pi\) | ||||
−0.761712 | + | 0.647915i | \(0.775641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0890 | + | 20.9149i | 0.692724 | + | 0.721202i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.11993i | 0.279500i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.5495 | − | 53.5438i | −0.740450 | − | 1.83979i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.5807 | + | 14.0049i | −0.500407 | + | 0.480648i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.1585 | − | 19.4240i | −1.47772 | − | 0.665067i | −0.498317 | − | 0.866995i | \(-0.666048\pi\) |
−0.979400 | + | 0.201928i | \(0.935279\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.464723 | − | 0.885456i | \(-0.346154\pi\) | ||||
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.2494 | − | 15.8761i | 1.03210 | − | 0.541686i | 0.138409 | − | 0.990375i | \(-0.455801\pi\) |
0.893688 | + | 0.448689i | \(0.148109\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.855781 | − | 0.517338i | \(-0.826923\pi\) | ||||
0.855781 | + | 0.517338i | \(0.173077\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.7224 | + | 25.5000i | 0.500000 | + | 0.866025i | ||||
\(868\) | 13.7249 | + | 7.92405i | 0.465852 | + | 0.268960i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.3279 | − | 24.3321i | −0.892086 | − | 0.824463i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.7066 | + | 19.3143i | 0.768503 | + | 0.653692i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.5984 | + | 2.12549i | −0.391874 | + | 0.0718135i | ||||
\(877\) | −54.8026 | + | 19.5309i | −1.85055 | + | 0.659511i | −0.862357 | + | 0.506300i | \(0.831013\pi\) |
−0.988193 | + | 0.153211i | \(0.951038\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.160411 | − | 0.987050i | \(-0.448718\pi\) | ||||
−0.160411 | + | 0.987050i | \(0.551282\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.2610 | + | 4.88857i | −1.35489 | + | 0.164514i | −0.765553 | − | 0.643373i | \(-0.777534\pi\) |
−0.589338 | + | 0.807887i | \(0.700611\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.692724 | − | 0.721202i | \(-0.256410\pi\) | ||||
−0.692724 | + | 0.721202i | \(0.743590\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.7264 | + | 46.8778i | −1.23176 | + | 1.57223i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 46.4646 | − | 28.0888i | 1.55575 | − | 0.940483i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −12.8608 | − | 27.1035i | −0.428693 | − | 0.903450i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.33691 | − | 116.027i | 0.0777676 | − | 3.86113i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.9527 | + | 50.5291i | 1.06097 | + | 1.67779i | 0.633446 | + | 0.773787i | \(0.281640\pi\) |
0.427525 | + | 0.904004i | \(0.359386\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(912\) | −53.0637 | + | 1.06876i | −1.75711 | + | 0.0353903i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.7280 | + | 16.3432i | −0.817035 | + | 0.539996i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.43632 | − | 60.4566i | −0.0803667 | − | 1.99428i | −0.104147 | − | 0.994562i | \(-0.533211\pi\) |
0.0237804 | − | 0.999717i | \(-0.492430\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.6837 | − | 19.3966i | −0.352040 | − | 0.639138i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.3087 | + | 8.12119i | −0.996544 | + | 0.267023i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.79041 | + | 59.3398i | −0.157338 | + | 1.94898i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.927686 | − | 0.373361i | \(-0.878205\pi\) | ||||
0.927686 | + | 0.373361i | \(0.121795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.49661 | + | 156.998i | −0.311239 | + | 5.14539i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.5471 | + | 7.77567i | −1.03060 | + | 0.254020i | −0.718131 | − | 0.695908i | \(-0.755002\pi\) |
−0.312469 | + | 0.949928i | \(0.601156\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −46.0450 | − | 34.6006i | −1.50262 | − | 1.12915i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.787183 | − | 0.616719i | \(-0.211538\pi\) | ||||
−0.787183 | + | 0.616719i | \(0.788462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.0201371 | − | 0.999797i | \(-0.506410\pi\) | ||||
0.0201371 | + | 0.999797i | \(0.493590\pi\) | |||||||
\(948\) | 1.04431 | − | 1.17878i | 0.0339176 | − | 0.0382850i | ||||
\(949\) | −1.24473 | + | 12.2097i | −0.0404058 | + | 0.396345i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.160411 | − | 0.987050i | \(-0.551282\pi\) | ||||
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.8530 | + | 10.1840i | −0.866227 | + | 0.328516i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −34.1400 | + | 51.6552i | −1.09957 | + | 1.66370i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.6157 | − | 40.7194i | −0.791588 | − | 1.30945i | −0.946883 | − | 0.321578i | \(-0.895787\pi\) |
0.155295 | − | 0.987868i | \(-0.450367\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.428693 | − | 0.903450i | \(-0.358974\pi\) | ||||
−0.428693 | + | 0.903450i | \(0.641026\pi\) | |||||||
\(972\) | 22.4849 | + | 21.5970i | 0.721202 | + | 0.692724i | ||||
\(973\) | 52.7655 | − | 105.654i | 1.69159 | − | 3.38710i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −30.8251 | + | 4.98101i | −0.987195 | + | 0.159520i | ||||
\(976\) | 5.55419 | + | 45.7429i | 0.177785 | + | 1.46419i | ||||
\(977\) | 0 | 0 | 0.335705 | − | 0.941967i | \(-0.391026\pi\) | ||||
−0.335705 | + | 0.941967i | \(0.608974\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.7678 | + | 55.6002i | 0.886559 | + | 1.77518i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.180255 | − | 0.983620i | \(-0.557692\pi\) | ||||
0.180255 | + | 0.983620i | \(0.442308\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.3458 | + | 53.3464i | −0.456399 | + | 1.69717i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.0043 | + | 43.3087i | −0.794288 | + | 1.37575i | 0.129003 | + | 0.991644i | \(0.458822\pi\) |
−0.923291 | + | 0.384102i | \(0.874511\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38.4256 | − | 17.2940i | 1.21940 | − | 0.548808i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.9167 | − | 40.3156i | 1.04248 | − | 1.27681i | 0.0825460 | − | 0.996587i | \(-0.473695\pi\) |
0.959936 | − | 0.280221i | \(-0.0904077\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.4581 | − | 19.0606i | 0.837097 | − | 0.603050i |
(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 | 507.2.x.a.98.1 | ✓ | 48 | |
3.2 | odd | 2 | CM | 507.2.x.a.98.1 | ✓ | 48 | |
169.119 | odd | 156 | inner | 507.2.x.a.119.1 | yes | 48 | |
507.119 | even | 156 | inner | 507.2.x.a.119.1 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.x.a.98.1 | ✓ | 48 | 1.1 | even | 1 | trivial | |
507.2.x.a.98.1 | ✓ | 48 | 3.2 | odd | 2 | CM | |
507.2.x.a.119.1 | yes | 48 | 169.119 | odd | 156 | inner | |
507.2.x.a.119.1 | yes | 48 | 507.119 | even | 156 | inner |