Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(143,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), not 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 1007.7 | ||
Character | \(\chi\) | \(=\) | 1152.1007 |
Dual form | 1152.2.w.b.143.7 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.11994 | + | 2.70378i | 0.500854 | + | 1.20917i | 0.949019 | + | 0.315218i | \(0.102078\pi\) |
−0.448165 | + | 0.893951i | \(0.647922\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.57144 | − | 1.57144i | −0.593950 | − | 0.593950i | 0.344746 | − | 0.938696i | \(-0.387965\pi\) |
−0.938696 | + | 0.344746i | \(0.887965\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00153 | − | 2.41791i | −0.301973 | − | 0.729027i | −0.999917 | − | 0.0128746i | \(-0.995902\pi\) |
0.697944 | − | 0.716152i | \(-0.254098\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.48559 | − | 2.68642i | −1.79878 | − | 0.745079i | −0.986917 | − | 0.161230i | \(-0.948454\pi\) |
−0.811863 | − | 0.583848i | \(-0.801546\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.520719 | −0.126293 | −0.0631465 | − | 0.998004i | \(-0.520114\pi\) | ||||
−0.0631465 | + | 0.998004i | \(0.520114\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.95774 | + | 7.14062i | −0.678552 | + | 1.63817i | 0.0881038 | + | 0.996111i | \(0.471919\pi\) |
−0.766656 | + | 0.642058i | \(0.778081\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.35340 | − | 1.35340i | −0.282204 | − | 0.282204i | 0.551784 | − | 0.833987i | \(-0.313947\pi\) |
−0.833987 | + | 0.551784i | \(0.813947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.52064 | + | 2.52064i | −0.504128 | + | 0.504128i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.31381 | − | 2.20105i | −0.986750 | − | 0.408725i | −0.169828 | − | 0.985474i | \(-0.554321\pi\) |
−0.816922 | + | 0.576748i | \(0.804321\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.54505i | 0.277498i | 0.990328 | + | 0.138749i | \(0.0443082\pi\) | ||||
−0.990328 | + | 0.138749i | \(0.955692\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.48892 | − | 6.00877i | 0.420704 | − | 1.01567i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.79897 | + | 1.57359i | −0.624548 | + | 0.258696i | −0.672434 | − | 0.740157i | \(-0.734751\pi\) |
0.0478869 | + | 0.998853i | \(0.484751\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.08917 | + | 1.08917i | −0.170100 | + | 0.170100i | −0.787023 | − | 0.616923i | \(-0.788379\pi\) |
0.616923 | + | 0.787023i | \(0.288379\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.71012 | − | 1.12257i | 0.413290 | − | 0.171190i | −0.166343 | − | 0.986068i | \(-0.553196\pi\) |
0.579633 | + | 0.814878i | \(0.303196\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11.1855i | − | 1.63157i | −0.578358 | − | 0.815783i | \(-0.696306\pi\) | ||
0.578358 | − | 0.815783i | \(-0.303694\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 2.06113i | − | 0.294447i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.70104 | − | 1.53302i | 0.508377 | − | 0.210577i | −0.113726 | − | 0.993512i | \(-0.536279\pi\) |
0.622103 | + | 0.782936i | \(0.286279\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.41584 | − | 5.41584i | 0.730272 | − | 0.730272i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.19376 | − | 1.32290i | 0.415792 | − | 0.172227i | −0.164973 | − | 0.986298i | \(-0.552754\pi\) |
0.580765 | + | 0.814071i | \(0.302754\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.78169 | + | 9.12981i | −0.484196 | + | 1.16895i | 0.473403 | + | 0.880846i | \(0.343026\pi\) |
−0.957598 | + | 0.288106i | \(0.906974\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 20.5443i | − | 2.54820i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9492 | − | 4.53532i | −1.33766 | − | 0.554077i | −0.404830 | − | 0.914392i | \(-0.632669\pi\) |
−0.932831 | + | 0.360314i | \(0.882669\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.83579 | + | 6.83579i | −0.811259 | + | 0.811259i | −0.984823 | − | 0.173564i | \(-0.944472\pi\) |
0.173564 | + | 0.984823i | \(0.444472\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.94667 | + | 2.94667i | 0.344882 | + | 0.344882i | 0.858199 | − | 0.513317i | \(-0.171584\pi\) |
−0.513317 | + | 0.858199i | \(0.671584\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.22576 | + | 5.37346i | −0.253649 | + | 0.612362i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.79533 | −0.989552 | −0.494776 | − | 0.869021i | \(-0.664750\pi\) | ||||
−0.494776 | + | 0.869021i | \(0.664750\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.9866 | + | 5.79342i | 1.53522 | + | 0.635911i | 0.980570 | − | 0.196170i | \(-0.0628504\pi\) |
0.554655 | + | 0.832081i | \(0.312850\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.583176 | − | 1.40791i | −0.0632544 | − | 0.152710i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.09089 | − | 7.09089i | −0.751633 | − | 0.751633i | 0.223151 | − | 0.974784i | \(-0.428366\pi\) |
−0.974784 | + | 0.223151i | \(0.928366\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.97019 | + | 14.4133i | 0.625846 | + | 1.51092i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −22.6192 | −2.32068 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.91713 | −0.600793 | −0.300397 | − | 0.953814i | \(-0.597119\pi\) | ||||
−0.300397 | + | 0.953814i | \(0.597119\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.62448 | + | 11.1645i | 0.460153 | + | 1.11091i | 0.968334 | + | 0.249657i | \(0.0803178\pi\) |
−0.508182 | + | 0.861250i | \(0.669682\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0132 | − | 12.0132i | −1.18369 | − | 1.18369i | −0.978780 | − | 0.204913i | \(-0.934309\pi\) |
−0.204913 | − | 0.978780i | \(-0.565691\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.56773 | + | 13.4417i | 0.538253 | + | 1.29946i | 0.925941 | + | 0.377667i | \(0.123274\pi\) |
−0.387688 | + | 0.921791i | \(0.626726\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.97381 | − | 2.47443i | −0.572187 | − | 0.237008i | 0.0777792 | − | 0.996971i | \(-0.475217\pi\) |
−0.649966 | + | 0.759963i | \(0.725217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0445 | 0.944908 | 0.472454 | − | 0.881355i | \(-0.343368\pi\) | ||||
0.472454 | + | 0.881355i | \(0.343368\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.14357 | − | 5.17504i | 0.199889 | − | 0.482575i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.818281 | + | 0.818281i | 0.0750117 | + | 0.0750117i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.93496 | − | 2.93496i | 0.266815 | − | 0.266815i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.88069 | + | 1.60743i | 0.347099 | + | 0.143773i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2276i | 1.08503i | 0.840047 | + | 0.542513i | \(0.182527\pi\) | ||||
−0.840047 | + | 0.542513i | \(0.817473\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.18881 | − | 5.28425i | 0.191237 | − | 0.461687i | −0.798957 | − | 0.601389i | \(-0.794614\pi\) |
0.990194 | + | 0.139702i | \(0.0446144\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.8690 | − | 6.57316i | 1.37602 | − | 0.569965i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.53314 | − | 3.53314i | 0.301856 | − | 0.301856i | −0.539883 | − | 0.841740i | \(-0.681532\pi\) |
0.841740 | + | 0.539883i | \(0.181532\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.17495 | + | 1.72932i | −0.354115 | + | 0.146679i | −0.552648 | − | 0.833415i | \(-0.686382\pi\) |
0.198533 | + | 0.980094i | \(0.436382\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.3721i | 1.53635i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 16.8325i | − | 1.39786i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.4396 | + | 6.39531i | −1.26486 | + | 0.523924i | −0.911399 | − | 0.411524i | \(-0.864997\pi\) |
−0.353465 | + | 0.935448i | \(0.614997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.199339 | + | 0.199339i | −0.0162220 | + | 0.0162220i | −0.715171 | − | 0.698949i | \(-0.753651\pi\) |
0.698949 | + | 0.715171i | \(0.253651\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.17747 | + | 1.73036i | −0.335542 | + | 0.138986i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.24745 | + | 5.42583i | −0.179366 | + | 0.433028i | −0.987834 | − | 0.155512i | \(-0.950297\pi\) |
0.808468 | + | 0.588540i | \(0.200297\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.25359i | 0.335230i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.85740 | − | 2.01200i | −0.380461 | − | 0.157592i | 0.184253 | − | 0.982879i | \(-0.441013\pi\) |
−0.564714 | + | 0.825287i | \(0.691013\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.1373 | − | 14.1373i | 1.09397 | − | 1.09397i | 0.0988739 | − | 0.995100i | \(-0.468476\pi\) |
0.995100 | − | 0.0988739i | \(-0.0315240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.6537 | + | 25.6537i | 1.97336 | + | 1.97336i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.98598 | − | 9.62302i | 0.303049 | − | 0.731625i | −0.696847 | − | 0.717219i | \(-0.745415\pi\) |
0.999896 | − | 0.0144051i | \(-0.00458545\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.92208 | 0.598853 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.3296 | − | 7.17815i | −1.29527 | − | 0.536520i | −0.374721 | − | 0.927138i | \(-0.622261\pi\) |
−0.920553 | + | 0.390618i | \(0.872261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.80823 | − | 4.36545i | −0.134404 | − | 0.324481i | 0.842320 | − | 0.538977i | \(-0.181189\pi\) |
−0.976725 | + | 0.214496i | \(0.931189\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.50928 | − | 8.50928i | −0.625614 | − | 0.625614i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.521516 | + | 1.25905i | 0.0381370 | + | 0.0920709i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.95000 | −0.502885 | −0.251442 | − | 0.967872i | \(-0.580905\pi\) | ||||
−0.251442 | + | 0.967872i | \(0.580905\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.4125 | 0.749511 | 0.374756 | − | 0.927124i | \(-0.377727\pi\) | ||||
0.374756 | + | 0.927124i | \(0.377727\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.52349 | + | 8.50645i | 0.251038 | + | 0.606059i | 0.998288 | − | 0.0584832i | \(-0.0186264\pi\) |
−0.747250 | + | 0.664543i | \(0.768626\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.74862 | + | 5.74862i | 0.407509 | + | 0.407509i | 0.880869 | − | 0.473360i | \(-0.156959\pi\) |
−0.473360 | + | 0.880869i | \(0.656959\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.89153 | + | 11.8092i | 0.343318 | + | 0.828843i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.16470 | − | 1.72507i | −0.290875 | − | 0.120484i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.2276 | 1.39917 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.53929 | + | 8.54461i | −0.243655 | + | 0.588235i | −0.997640 | − | 0.0686560i | \(-0.978129\pi\) |
0.753985 | + | 0.656891i | \(0.228129\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.07037 | + | 6.07037i | 0.413996 | + | 0.413996i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.42795 | − | 2.42795i | 0.164820 | − | 0.164820i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.37717 | + | 1.39887i | 0.227173 | + | 0.0940982i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.5406i | − | 0.772814i | −0.922328 | − | 0.386407i | \(-0.873716\pi\) | ||
0.922328 | − | 0.386407i | \(-0.126284\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.48691 | − | 13.2466i | 0.364179 | − | 0.879205i | −0.630501 | − | 0.776188i | \(-0.717151\pi\) |
0.994680 | − | 0.103017i | \(-0.0328495\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.29256 | − | 1.77804i | 0.283661 | − | 0.117496i | −0.236317 | − | 0.971676i | \(-0.575940\pi\) |
0.519977 | + | 0.854180i | \(0.325940\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.05679 | + | 9.05679i | −0.593330 | + | 0.593330i | −0.938529 | − | 0.345199i | \(-0.887811\pi\) |
0.345199 | + | 0.938529i | \(0.387811\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 30.2430 | − | 12.5271i | 1.97284 | − | 0.817177i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.04485i | 0.520378i | 0.965558 | + | 0.260189i | \(0.0837849\pi\) | ||||
−0.965558 | + | 0.260189i | \(0.916215\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 19.0228i | − | 1.22536i | −0.790329 | − | 0.612682i | \(-0.790091\pi\) | ||
0.790329 | − | 0.612682i | \(-0.209909\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.57284 | − | 2.30835i | 0.356036 | − | 0.147475i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.3654 | − | 38.3654i | 2.44113 | − | 2.44113i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.25290 | − | 3.00425i | 0.457799 | − | 0.189626i | −0.141853 | − | 0.989888i | \(-0.545306\pi\) |
0.599651 | + | 0.800261i | \(0.295306\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.91693 | + | 4.62787i | −0.120516 | + | 0.290952i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.0041i | 1.43496i | 0.696581 | + | 0.717478i | \(0.254703\pi\) | ||||
−0.696581 | + | 0.717478i | \(0.745297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.44268 | + | 3.49707i | 0.524603 | + | 0.217298i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.44247 | + | 1.44247i | −0.0889468 | + | 0.0889468i | −0.750180 | − | 0.661233i | \(-0.770033\pi\) |
0.661233 | + | 0.750180i | \(0.270033\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.28991 | + | 8.28991i | 0.509245 | + | 0.509245i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.77582 | − | 4.28722i | 0.108274 | − | 0.261396i | −0.860451 | − | 0.509533i | \(-0.829818\pi\) |
0.968725 | + | 0.248137i | \(0.0798182\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.52337 | −0.153284 | −0.0766419 | − | 0.997059i | \(-0.524420\pi\) | ||||
−0.0766419 | + | 0.997059i | \(0.524420\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.61916 | + | 3.57017i | 0.519755 | + | 0.215290i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.50691 | − | 8.46643i | −0.210710 | − | 0.508699i | 0.782823 | − | 0.622245i | \(-0.213779\pi\) |
−0.993533 | + | 0.113546i | \(0.963779\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.34778 | + | 5.34778i | 0.319022 | + | 0.319022i | 0.848391 | − | 0.529369i | \(-0.177571\pi\) |
−0.529369 | + | 0.848391i | \(0.677571\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0243 | + | 24.2009i | 0.595885 | + | 1.43859i | 0.877741 | + | 0.479136i | \(0.159050\pi\) |
−0.281856 | + | 0.959457i | \(0.590950\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.42315 | 0.202062 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7289 | −0.984050 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.12975 | + | 14.7985i | 0.358104 | + | 0.864539i | 0.995567 | + | 0.0940580i | \(0.0299839\pi\) |
−0.637463 | + | 0.770481i | \(0.720016\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.15366 | + | 7.15366i | 0.416502 | + | 0.416502i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.14180 | + | 12.4134i | 0.297358 | + | 0.717886i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.02286 | − | 2.49475i | −0.347152 | − | 0.143795i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −28.9203 | −1.65597 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.63881 | − | 16.0275i | 0.378897 | − | 0.914738i | −0.613276 | − | 0.789869i | \(-0.710149\pi\) |
0.992173 | − | 0.124870i | \(-0.0398513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0561 | + | 15.0561i | 0.853754 | + | 0.853754i | 0.990593 | − | 0.136839i | \(-0.0436942\pi\) |
−0.136839 | + | 0.990593i | \(0.543694\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.19455 | − | 4.19455i | 0.237090 | − | 0.237090i | −0.578554 | − | 0.815644i | \(-0.696383\pi\) |
0.815644 | + | 0.578554i | \(0.196383\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.3097 | − | 5.51307i | −0.747549 | − | 0.309645i | −0.0238078 | − | 0.999717i | \(-0.507579\pi\) |
−0.723741 | + | 0.690072i | \(0.757579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.0527i | 0.842791i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.54015 | − | 3.71826i | 0.0856964 | − | 0.206889i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.1193 | − | 9.57633i | 1.28243 | − | 0.531199i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.5773 | + | 17.5773i | −0.969069 | + | 0.969069i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.98959 | + | 2.48097i | −0.329218 | + | 0.136366i | −0.541169 | − | 0.840914i | \(-0.682018\pi\) |
0.211951 | + | 0.977280i | \(0.432018\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 34.6836i | − | 1.89497i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.6988i | 1.61779i | 0.587950 | + | 0.808897i | \(0.299935\pi\) | ||||
−0.587950 | + | 0.808897i | \(0.700065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.73578 | − | 1.54741i | 0.202304 | − | 0.0837969i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2391 | + | 14.2391i | −0.768837 | + | 0.768837i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.8947 | + | 12.3828i | −1.60483 | + | 0.664744i | −0.992089 | − | 0.125537i | \(-0.959935\pi\) |
−0.612745 | + | 0.790281i | \(0.709935\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.37790 | + | 20.2260i | −0.448459 | + | 1.08268i | 0.524441 | + | 0.851447i | \(0.324274\pi\) |
−0.972899 | + | 0.231228i | \(0.925726\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.58104i | 0.137375i | 0.997638 | + | 0.0686874i | \(0.0218811\pi\) | ||||
−0.997638 | + | 0.0686874i | \(0.978119\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.1382 | − | 10.8268i | −1.38727 | − | 0.574627i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3463 | − | 11.3463i | 0.598834 | − | 0.598834i | −0.341168 | − | 0.940002i | \(-0.610823\pi\) |
0.940002 | + | 0.341168i | \(0.110823\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −28.8051 | − | 28.8051i | −1.51606 | − | 1.51606i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.66705 | + | 11.2673i | −0.244285 | + | 0.589755i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.71339 | −0.454835 | −0.227418 | − | 0.973797i | \(-0.573028\pi\) | ||||
−0.227418 | + | 0.973797i | \(0.573028\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.22503 | − | 3.40692i | −0.427022 | − | 0.176878i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.56395 | + | 3.77570i | 0.0809781 | + | 0.195498i | 0.959183 | − | 0.282786i | \(-0.0912587\pi\) |
−0.878205 | + | 0.478285i | \(0.841259\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.5503 | + | 28.5503i | 1.47041 | + | 1.47041i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.85643 | − | 21.3813i | −0.454925 | − | 1.09828i | −0.970427 | − | 0.241397i | \(-0.922395\pi\) |
0.515502 | − | 0.856888i | \(-0.327605\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.90996 | 0.199790 | 0.0998949 | − | 0.994998i | \(-0.468149\pi\) | ||||
0.0998949 | + | 0.994998i | \(0.468149\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.0214 | −0.867490 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.92740 | − | 9.48159i | −0.199127 | − | 0.480736i | 0.792500 | − | 0.609872i | \(-0.208779\pi\) |
−0.991627 | + | 0.129137i | \(0.958779\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.704742 | + | 0.704742i | 0.0356403 | + | 0.0356403i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.85028 | − | 23.7807i | −0.495621 | − | 1.19654i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.8590 | + | 6.56903i | 0.795942 | + | 0.329690i | 0.743330 | − | 0.668925i | \(-0.233245\pi\) |
0.0526124 | + | 0.998615i | \(0.483245\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.8741 | 0.942529 | 0.471265 | − | 0.881992i | \(-0.343798\pi\) | ||||
0.471265 | + | 0.881992i | \(0.343798\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.15064 | − | 10.0205i | 0.206758 | − | 0.499158i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.60957 | + | 7.60957i | 0.377193 | + | 0.377193i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.68899 | + | 9.68899i | −0.479089 | + | 0.479089i | −0.904840 | − | 0.425751i | \(-0.860010\pi\) |
0.425751 | + | 0.904840i | \(0.360010\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.09768 | − | 2.93995i | −0.349254 | − | 0.144666i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 44.3049i | 2.17484i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.8806 | + | 33.5108i | −0.678114 | + | 1.63711i | 0.0893350 | + | 0.996002i | \(0.471526\pi\) |
−0.767449 | + | 0.641110i | \(0.778474\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.7882 | − | 9.85339i | 1.15937 | − | 0.480225i | 0.281702 | − | 0.959502i | \(-0.409101\pi\) |
0.877664 | + | 0.479277i | \(0.159101\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.31254 | − | 1.31254i | 0.0636678 | − | 0.0636678i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.2897 | − | 8.40427i | 0.981887 | − | 0.406711i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.02776i | 0.0495056i | 0.999694 | + | 0.0247528i | \(0.00787987\pi\) | ||||
−0.999694 | + | 0.0247528i | \(0.992120\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 21.3662i | − | 1.02680i | −0.858151 | − | 0.513398i | \(-0.828386\pi\) | ||
0.858151 | − | 0.513398i | \(-0.171614\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.6671 | − | 5.66111i | 0.653787 | − | 0.270807i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.4689 | + | 13.4689i | −0.642835 | + | 0.642835i | −0.951251 | − | 0.308417i | \(-0.900201\pi\) |
0.308417 | + | 0.951251i | \(0.400201\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.92612 | − | 2.04047i | 0.234047 | − | 0.0969454i | −0.262578 | − | 0.964911i | \(-0.584573\pi\) |
0.496625 | + | 0.867965i | \(0.334573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.2308 | − | 27.1136i | 0.532393 | − | 1.28531i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.2980i | − | 1.05231i | −0.850390 | − | 0.526153i | \(-0.823634\pi\) | ||
0.850390 | − | 0.526153i | \(-0.176366\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.72436 | + | 1.54268i | 0.175373 | + | 0.0726419i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −32.2842 | + | 32.2842i | −1.51351 | + | 1.51351i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.58505 | − | 6.58505i | −0.308035 | − | 0.308035i | 0.536112 | − | 0.844147i | \(-0.319893\pi\) |
−0.844147 | + | 0.536112i | \(0.819893\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.3380 | − | 34.6150i | 0.667788 | − | 1.61218i | −0.117515 | − | 0.993071i | \(-0.537493\pi\) |
0.785303 | − | 0.619112i | \(-0.212507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.4728 | 0.672607 | 0.336304 | − | 0.941754i | \(-0.390823\pi\) | ||||
0.336304 | + | 0.941754i | \(0.390823\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.73511 | − | 4.03241i | −0.450487 | − | 0.186598i | 0.145892 | − | 0.989300i | \(-0.453395\pi\) |
−0.596380 | + | 0.802703i | \(0.703395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0791 | + | 24.3331i | 0.465410 | + | 1.12360i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.42854 | − | 5.42854i | −0.249605 | − | 0.249605i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.5435 | − | 25.4543i | −0.483770 | − | 1.16792i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.2779 | 1.38343 | 0.691717 | − | 0.722169i | \(-0.256855\pi\) | ||||
0.691717 | + | 0.722169i | \(0.256855\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.8659 | 1.31617 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.62685 | − | 15.9986i | −0.300910 | − | 0.726461i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.6078 | − | 11.6078i | −0.526000 | − | 0.526000i | 0.393377 | − | 0.919377i | \(-0.371307\pi\) |
−0.919377 | + | 0.393377i | \(0.871307\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.08448 | − | 9.86082i | −0.184330 | − | 0.445012i | 0.804520 | − | 0.593925i | \(-0.202423\pi\) |
−0.988850 | + | 0.148913i | \(0.952423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.76700 | + | 1.14613i | 0.124620 | + | 0.0516191i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.4841 | 0.963695 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5238 | + | 25.4066i | −0.471109 | + | 1.13736i | 0.492565 | + | 0.870276i | \(0.336059\pi\) |
−0.963674 | + | 0.267082i | \(0.913941\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.9786 | − | 16.9786i | −0.757040 | − | 0.757040i | 0.218742 | − | 0.975783i | \(-0.429805\pi\) |
−0.975783 | + | 0.218742i | \(0.929805\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.0072 | + | 25.0072i | −1.11280 | + | 1.11280i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.0892 | − | 10.3923i | −1.11206 | − | 0.460630i | −0.250413 | − | 0.968139i | \(-0.580566\pi\) |
−0.861646 | + | 0.507509i | \(0.830566\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 9.26105i | − | 0.409685i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.0269 | − | 45.9351i | 0.838427 | − | 2.02414i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.0454 | + | 11.2026i | −1.18946 | + | 0.492688i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.51029 | − | 3.51029i | 0.153789 | − | 0.153789i | −0.626019 | − | 0.779808i | \(-0.715317\pi\) |
0.779808 | + | 0.626019i | \(0.215317\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.65762 | − | 1.10082i | 0.116209 | − | 0.0481355i | −0.323821 | − | 0.946118i | \(-0.604968\pi\) |
0.440031 | + | 0.897983i | \(0.354968\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 0.804535i | − | 0.0350461i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 19.3366i | − | 0.840722i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.98990 | − | 4.13795i | 0.432711 | − | 0.179235i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.1079 | + | 30.1079i | −1.30168 | + | 1.30168i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.98361 | + | 2.06428i | −0.214659 | + | 0.0889148i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.33435 | − | 20.1209i | 0.358322 | − | 0.865066i | −0.637214 | − | 0.770687i | \(-0.719913\pi\) |
0.995536 | − | 0.0943790i | \(-0.0300866\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 18.9231i | − | 0.810577i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.3897 | − | 6.37463i | −0.658017 | − | 0.272560i | 0.0285868 | − | 0.999591i | \(-0.490899\pi\) |
−0.686604 | + | 0.727032i | \(0.740899\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.4337 | − | 31.4337i | 1.33912 | − | 1.33912i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.8214 | + | 13.8214i | 0.587744 | + | 0.587744i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.13010 | + | 7.55673i | −0.132627 | + | 0.320189i | −0.976216 | − | 0.216800i | \(-0.930438\pi\) |
0.843590 | + | 0.536989i | \(0.180438\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.5924 | −0.870968 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.345832 | − | 0.143248i | −0.0145751 | − | 0.00603719i | 0.375384 | − | 0.926869i | \(-0.377511\pi\) |
−0.389959 | + | 0.920832i | \(0.627511\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.2493 | + | 27.1582i | 0.473261 | + | 1.14255i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.8289 | − | 31.8289i | −1.33434 | − | 1.33434i | −0.901447 | − | 0.432890i | \(-0.857494\pi\) |
−0.432890 | − | 0.901447i | \(-0.642506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.49818 | − | 18.1022i | −0.313789 | − | 0.757554i | −0.999558 | − | 0.0297343i | \(-0.990534\pi\) |
0.685769 | − | 0.727819i | \(-0.259466\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.82287 | 0.284533 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.6358 | −0.817447 | −0.408724 | − | 0.912658i | \(-0.634026\pi\) | ||||
−0.408724 | + | 0.912658i | \(0.634026\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.8751 | − | 31.0831i | −0.534147 | − | 1.28955i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.41340 | − | 7.41340i | −0.307032 | − | 0.307032i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.01640 | − | 19.3533i | −0.330872 | − | 0.798796i | −0.998523 | − | 0.0543221i | \(-0.982700\pi\) |
0.667651 | − | 0.744474i | \(-0.267300\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.0326 | − | 4.56984i | −0.454589 | − | 0.188297i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.2206 | −1.07675 | −0.538376 | − | 0.842704i | \(-0.680962\pi\) | ||||
−0.538376 | + | 0.842704i | \(0.680962\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.29603 | + | 3.12888i | −0.0531319 | + | 0.128272i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.4497 | + | 13.4497i | 0.549542 | + | 0.549542i | 0.926308 | − | 0.376767i | \(-0.122964\pi\) |
−0.376767 | + | 0.926308i | \(0.622964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.7760 | + | 10.7760i | −0.439562 | + | 0.439562i | −0.891864 | − | 0.452303i | \(-0.850603\pi\) |
0.452303 | + | 0.891864i | \(0.350603\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.2225 | + | 4.64851i | 0.456259 | + | 0.188989i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5.71428i | − | 0.231936i | −0.993253 | − | 0.115968i | \(-0.963003\pi\) | ||
0.993253 | − | 0.115968i | \(-0.0369969\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.0488 | + | 72.5443i | −1.21565 | + | 2.93483i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.0980 | + | 10.3959i | −1.01370 | + | 0.419887i | −0.826802 | − | 0.562493i | \(-0.809842\pi\) |
−0.186895 | + | 0.982380i | \(0.559842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.07388 | + | 7.07388i | −0.284784 | + | 0.284784i | −0.835013 | − | 0.550230i | \(-0.814540\pi\) |
0.550230 | + | 0.835013i | \(0.314540\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.9781 | + | 13.6600i | −1.32550 | + | 0.549041i | −0.929369 | − | 0.369151i | \(-0.879648\pi\) |
−0.396134 | + | 0.918193i | \(0.629648\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.2859i | 0.892865i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30.1164i | 1.20465i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.97820 | − | 0.819397i | 0.0788760 | − | 0.0326715i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.15849 | − | 2.15849i | 0.0859280 | − | 0.0859280i | −0.662836 | − | 0.748764i | \(-0.730647\pi\) |
0.748764 | + | 0.662836i | \(0.230647\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.0608 | + | 13.6943i | −1.31198 | + | 0.543440i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.53705 | + | 13.3676i | −0.219386 | + | 0.529645i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.0487i | 1.50283i | 0.659827 | + | 0.751417i | \(0.270629\pi\) | ||||
−0.659827 | + | 0.751417i | \(0.729371\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.7464 | + | 6.93660i | 0.660414 | + | 0.273553i | 0.687613 | − | 0.726077i | \(-0.258659\pi\) |
−0.0271985 | + | 0.999630i | \(0.508659\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.77745 | − | 1.77745i | 0.0698786 | − | 0.0698786i | −0.671304 | − | 0.741182i | \(-0.734265\pi\) |
0.741182 | + | 0.671304i | \(0.234265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.39729 | − | 6.39729i | −0.251116 | − | 0.251116i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.13694 | − | 19.6443i | 0.318423 | − | 0.768742i | −0.680915 | − | 0.732363i | \(-0.738418\pi\) |
0.999338 | − | 0.0363791i | \(-0.0115824\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.7388 | 0.654039 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.72478 | − | 2.37128i | −0.223006 | − | 0.0923720i | 0.268383 | − | 0.963312i | \(-0.413511\pi\) |
−0.491389 | + | 0.870940i | \(0.663511\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.6754 | − | 35.4296i | −0.570808 | − | 1.37805i | −0.900868 | − | 0.434092i | \(-0.857069\pi\) |
0.330061 | − | 0.943960i | \(-0.392931\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 35.5448 | + | 35.5448i | 1.37837 | + | 1.37837i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.21281 | + | 10.1706i | 0.163121 | + | 0.393808i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.8625 | 0.998411 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.6272 | −1.25768 | −0.628842 | − | 0.777533i | \(-0.716471\pi\) | ||||
−0.628842 | + | 0.777533i | \(0.716471\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.1224 | − | 26.8518i | −0.427468 | − | 1.03200i | −0.980088 | − | 0.198565i | \(-0.936372\pi\) |
0.552620 | − | 0.833433i | \(-0.313628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.29844 | + | 9.29844i | 0.356841 | + | 0.356841i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.38525 | − | 3.34428i | −0.0530050 | − | 0.127965i | 0.895159 | − | 0.445747i | \(-0.147062\pi\) |
−0.948164 | + | 0.317782i | \(0.897062\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.5098 | + | 5.59593i | 0.516181 | + | 0.213809i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.1218 | −1.07135 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4910 | − | 32.5702i | 0.513223 | − | 1.23903i | −0.428775 | − | 0.903411i | \(-0.641055\pi\) |
0.941998 | − | 0.335618i | \(-0.108945\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.35143 | − | 9.35143i | −0.354720 | − | 0.354720i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.567153 | − | 0.567153i | 0.0214825 | − | 0.0214825i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.25729 | + | 1.34921i | 0.123026 | + | 0.0509590i | 0.443347 | − | 0.896350i | \(-0.353791\pi\) |
−0.320321 | + | 0.947309i | \(0.603791\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 31.7813i | − | 1.19865i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.2772 | − | 24.8115i | 0.386515 | − | 0.933131i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.0551 | + | 11.2066i | −1.01607 | + | 0.420872i | −0.827667 | − | 0.561219i | \(-0.810332\pi\) |
−0.188407 | + | 0.982091i | \(0.560332\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.09107 | − | 2.09107i | 0.0783110 | − | 0.0783110i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −49.6742 | + | 20.5757i | −1.85771 | + | 0.769488i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.87831i | 0.256518i | 0.991741 | + | 0.128259i | \(0.0409389\pi\) | ||||
−0.991741 | + | 0.128259i | \(0.959061\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.7561i | 1.40611i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.9422 | − | 7.84614i | 0.703497 | − | 0.291398i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.61474 | + | 8.61474i | −0.319503 | + | 0.319503i | −0.848576 | − | 0.529073i | \(-0.822540\pi\) |
0.529073 | + | 0.848576i | \(0.322540\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.41121 | + | 0.584544i | −0.0521956 | + | 0.0216201i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.86842 | − | 16.5818i | 0.253691 | − | 0.612464i | −0.744806 | − | 0.667282i | \(-0.767458\pi\) |
0.998496 | + | 0.0548178i | \(0.0174578\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.0165i | 1.14251i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.65828 | − | 3.58638i | −0.318500 | − | 0.131927i | 0.217706 | − | 0.976014i | \(-0.430143\pi\) |
−0.536205 | + | 0.844088i | \(0.680143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.87413 | − | 5.87413i | 0.215501 | − | 0.215501i | −0.591098 | − | 0.806599i | \(-0.701306\pi\) |
0.806599 | + | 0.591098i | \(0.201306\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.5830 | − | 34.5830i | −1.26702 | − | 1.26702i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.3735 | − | 29.8723i | 0.452118 | − | 1.09151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.89687 | −0.142199 | −0.0710993 | − | 0.997469i | \(-0.522651\pi\) | ||||
−0.0710993 | + | 0.997469i | \(0.522651\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.762219 | − | 0.315721i | −0.0277400 | − | 0.0114903i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.04702 | − | 9.77036i | −0.147091 | − | 0.355110i | 0.833112 | − | 0.553105i | \(-0.186557\pi\) |
−0.980203 | + | 0.197995i | \(0.936557\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.3848 | + | 13.3848i | 0.485198 | + | 0.485198i | 0.906787 | − | 0.421589i | \(-0.138528\pi\) |
−0.421589 | + | 0.906787i | \(0.638528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.49908 | + | 13.2759i | 0.199080 | + | 0.480621i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.2673 | −0.876241 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.94152 | 0.214257 | 0.107128 | − | 0.994245i | \(-0.465834\pi\) | ||||
0.107128 | + | 0.994245i | \(0.465834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.97648 | − | 9.60006i | −0.143024 | − | 0.345290i | 0.836093 | − | 0.548588i | \(-0.184834\pi\) |
−0.979117 | + | 0.203297i | \(0.934834\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.89450 | − | 3.89450i | −0.139895 | − | 0.139895i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.55587 | − | 10.9988i | −0.163231 | − | 0.394075i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.3746 | + | 9.68206i | 0.836408 | + | 0.346451i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.1873 | −0.613440 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.79001 | + | 16.3925i | −0.242038 | + | 0.584331i | −0.997485 | − | 0.0708787i | \(-0.977420\pi\) |
0.755447 | + | 0.655210i | \(0.227420\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.7844 | − | 15.7844i | −0.561228 | − | 0.561228i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.0530 | − | 49.0530i | 1.74192 | − | 1.74192i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.96338 | + | 3.71275i | 0.317499 | + | 0.131512i | 0.535741 | − | 0.844382i | \(-0.320032\pi\) |
−0.218242 | + | 0.975895i | \(0.570032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.82448i | 0.206055i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.17360 | − | 10.0760i | 0.147283 | − | 0.355573i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.5008 | + | 4.76378i | −0.405349 | + | 0.167901i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.4525 | − | 23.4525i | 0.824546 | − | 0.824546i | −0.162210 | − | 0.986756i | \(-0.551862\pi\) |
0.986756 | + | 0.162210i | \(0.0518622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.8512 | + | 7.39420i | −0.626840 | + | 0.259645i | −0.673410 | − | 0.739270i | \(-0.735171\pi\) |
0.0465700 | + | 0.998915i | \(0.485171\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 15.3867i | − | 0.538972i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.6722i | 0.793201i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.1323 | + | 18.2802i | −1.54023 | + | 0.637984i | −0.981516 | − | 0.191378i | \(-0.938704\pi\) |
−0.558712 | + | 0.829362i | \(0.688704\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.6647 | − | 24.6647i | 0.859758 | − | 0.859758i | −0.131551 | − | 0.991309i | \(-0.541996\pi\) |
0.991309 | + | 0.131551i | \(0.0419958\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.5767 | − | 20.1211i | 1.68918 | − | 0.699680i | 0.689481 | − | 0.724304i | \(-0.257839\pi\) |
0.999697 | + | 0.0246236i | \(0.00783872\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.29929 | + | 17.6220i | −0.253515 | + | 0.612039i | −0.998483 | − | 0.0550611i | \(-0.982465\pi\) |
0.744968 | + | 0.667100i | \(0.232465\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.07327i | 0.0371865i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.0570 | + | 22.3912i | 1.87072 | + | 0.774878i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.24139 | + | 5.24139i | −0.180953 | + | 0.180953i | −0.791771 | − | 0.610818i | \(-0.790841\pi\) |
0.610818 | + | 0.791771i | \(0.290841\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.88586 | + | 2.88586i | 0.0995125 | + | 0.0995125i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.6313 | + | 98.0926i | −1.39776 | + | 3.37449i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.22425 | −0.316949 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.27123 | + | 3.01184i | 0.249255 | + | 0.103245i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.60778 | − | 11.1242i | −0.157767 | − | 0.380884i | 0.825155 | − | 0.564907i | \(-0.191088\pi\) |
−0.982922 | + | 0.184023i | \(0.941088\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.4017 | − | 26.4017i | −0.901866 | − | 0.901866i | 0.0937316 | − | 0.995598i | \(-0.470120\pi\) |
−0.995598 | + | 0.0937316i | \(0.970120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.63668 | + | 8.77971i | 0.124082 | + | 0.299560i | 0.973698 | − | 0.227841i | \(-0.0731666\pi\) |
−0.849617 | + | 0.527401i | \(0.823167\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.7981 | 0.537773 | 0.268887 | − | 0.963172i | \(-0.413344\pi\) | ||||
0.268887 | + | 0.963172i | \(0.413344\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.4826 | 1.03644 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.80879 | + | 21.2663i | 0.298818 | + | 0.721410i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 58.8285 | + | 58.8285i | 1.99333 | + | 1.99333i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.57229 | − | 8.62427i | −0.120765 | − | 0.291554i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.17572 | + | 1.72964i | 0.141004 | + | 0.0584058i | 0.452070 | − | 0.891983i | \(-0.350686\pi\) |
−0.311066 | + | 0.950388i | \(0.600686\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.9005 | 0.805228 | 0.402614 | − | 0.915370i | \(-0.368102\pi\) | ||||
0.402614 | + | 0.915370i | \(0.368102\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.1690 | − | 36.6212i | 0.510477 | − | 1.23240i | −0.433129 | − | 0.901332i | \(-0.642591\pi\) |
0.943606 | − | 0.331069i | \(-0.107409\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.0807 | − | 26.0807i | −0.875704 | − | 0.875704i | 0.117383 | − | 0.993087i | \(-0.462549\pi\) |
−0.993087 | + | 0.117383i | \(0.962549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.2150 | − | 19.2150i | 0.644451 | − | 0.644451i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 79.8710 | + | 33.0837i | 2.67278 | + | 1.10710i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 54.8946i | − | 1.83492i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.40073 | − | 8.21008i | 0.113421 | − | 0.273822i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.92720 | + | 0.798273i | −0.0642044 | + | 0.0265943i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.77811 | − | 9.77811i | 0.325035 | − | 0.325035i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.9974 | − | 16.1532i | 1.29489 | − | 0.536359i | 0.374448 | − | 0.927248i | \(-0.377832\pi\) |
0.920438 | + | 0.390888i | \(0.127832\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 21.6843i | − | 0.718433i | −0.933254 | − | 0.359217i | \(-0.883044\pi\) | ||
0.933254 | − | 0.359217i | \(-0.116956\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 39.6205i | − | 1.31125i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.7435 | + | 4.86431i | −0.387804 | + | 0.160634i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.7214 | + | 31.7214i | −1.04639 | + | 1.04639i | −0.0475231 | + | 0.998870i | \(0.515133\pi\) |
−0.998870 | + | 0.0475231i | \(0.984867\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 62.6980 | − | 25.9703i | 2.06373 | − | 0.854824i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.60940 | − | 13.5423i | 0.184436 | − | 0.445267i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 0.364065i | − | 0.0119446i | −0.999982 | − | 0.00597230i | \(-0.998099\pi\) | ||
0.999982 | − | 0.00597230i | \(-0.00190105\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.7177 | + | 6.09628i | 0.482354 | + | 0.199797i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.82013 | + | 2.82013i | −0.0922282 | + | 0.0922282i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.47325 | + | 1.47325i | 0.0481290 | + | 0.0481290i | 0.730762 | − | 0.682633i | \(-0.239165\pi\) |
−0.682633 | + | 0.730762i | \(0.739165\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.412404 | + | 0.995632i | −0.0134440 | + | 0.0324567i | −0.930459 | − | 0.366396i | \(-0.880592\pi\) |
0.917015 | + | 0.398853i | \(0.130592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.94817 | 0.0960057 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.6561 | − | 20.5682i | −1.61361 | − | 0.668377i | −0.620350 | − | 0.784325i | \(-0.713010\pi\) |
−0.993255 | + | 0.115948i | \(0.963010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.1949 | − | 27.0269i | −0.363402 | − | 0.877330i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.7097 | − | 14.7097i | −0.476493 | − | 0.476493i | 0.427515 | − | 0.904008i | \(-0.359389\pi\) |
−0.904008 | + | 0.427515i | \(0.859389\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.78361 | − | 18.7913i | −0.251872 | − | 0.608072i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.1043 | −0.358575 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.6128 | 0.922995 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.6615 | + | 28.1533i | 0.375396 | + | 0.906285i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.95466 | + | 6.95466i | 0.223647 | + | 0.223647i | 0.810032 | − | 0.586385i | \(-0.199450\pi\) |
−0.586385 | + | 0.810032i | \(0.699450\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.3256 | + | 46.6562i | 0.620189 | + | 1.49727i | 0.851482 | + | 0.524384i | \(0.175704\pi\) |
−0.231293 | + | 0.972884i | \(0.574296\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.27824 | + | 3.84317i | 0.297447 | + | 0.123206i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.2374 | −0.711439 | −0.355720 | − | 0.934593i | \(-0.615764\pi\) | ||||
−0.355720 | + | 0.934593i | \(0.615764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.0434 | + | 24.2469i | −0.320988 | + | 0.774933i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.7122 | + | 37.7122i | 1.20283 | + | 1.20283i | 0.973301 | + | 0.229531i | \(0.0737191\pi\) |
0.229531 | + | 0.973301i | \(0.426281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.0535 | + | 19.0535i | −0.607095 | + | 0.607095i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.18717 | − | 2.14860i | −0.164942 | − | 0.0683214i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 39.0360i | − | 1.24002i | −0.784594 | − | 0.620010i | \(-0.787129\pi\) | ||
0.784594 | − | 0.620010i | \(-0.212871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.10490 | + | 21.9812i | −0.288645 | + | 0.696850i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.9640 | − | 7.02670i | 0.537254 | − | 0.222538i | −0.0975229 | − | 0.995233i | \(-0.531092\pi\) |
0.634777 | + | 0.772695i | \(0.281092\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1152.2.w.b.1007.7 | 32 | ||
3.2 | odd | 2 | 1152.2.w.a.1007.2 | 32 | |||
4.3 | odd | 2 | 288.2.w.a.179.8 | ✓ | 32 | ||
12.11 | even | 2 | 288.2.w.b.179.1 | yes | 32 | ||
32.5 | even | 8 | 288.2.w.b.251.1 | yes | 32 | ||
32.27 | odd | 8 | 1152.2.w.a.143.2 | 32 | |||
96.5 | odd | 8 | 288.2.w.a.251.8 | yes | 32 | ||
96.59 | even | 8 | inner | 1152.2.w.b.143.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.179.8 | ✓ | 32 | 4.3 | odd | 2 | ||
288.2.w.a.251.8 | yes | 32 | 96.5 | odd | 8 | ||
288.2.w.b.179.1 | yes | 32 | 12.11 | even | 2 | ||
288.2.w.b.251.1 | yes | 32 | 32.5 | even | 8 | ||
1152.2.w.a.143.2 | 32 | 32.27 | odd | 8 | |||
1152.2.w.a.1007.2 | 32 | 3.2 | odd | 2 | |||
1152.2.w.b.143.7 | 32 | 96.59 | even | 8 | inner | ||
1152.2.w.b.1007.7 | 32 | 1.1 | even | 1 | trivial |