Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(104,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([11, 9, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.104");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.cs (of order \(18\), degree \(6\), 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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 104.4 | ||
Character | \(\chi\) | \(=\) | 945.104 |
Dual form | 945.2.cs.a.209.4 |
$q$-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 \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{11}{18}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(3\) | 1.62968 | + | 0.586627i | 0.940898 | + | 0.338689i | ||||
\(4\) | −1.53209 | − | 1.28558i | −0.766044 | − | 0.642788i | ||||
\(5\) | 2.20210 | + | 0.388289i | 0.984808 | + | 0.173648i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.02676 | + | 1.70066i | −0.766044 | + | 0.642788i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.31174 | + | 1.91203i | 0.770579 | + | 0.637344i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.46437 | − | 0.787188i | 1.34606 | − | 0.237346i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
0.799798 | + | 0.600270i | \(0.204940\pi\) | |||||||
\(12\) | −1.74267 | − | 2.99385i | −0.503065 | − | 0.864249i | ||||
\(13\) | −6.63961 | + | 2.41662i | −1.84150 | + | 0.670250i | −0.852416 | + | 0.522864i | \(0.824864\pi\) |
−0.989079 | + | 0.147386i | \(0.952914\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.36094 | + | 1.92460i | 0.867791 | + | 0.496929i | ||||
\(16\) | 0.694593 | + | 3.93923i | 0.173648 | + | 0.984808i | ||||
\(17\) | 5.90187 | + | 3.40745i | 1.43141 | + | 0.826428i | 0.997229 | − | 0.0743959i | \(-0.0237028\pi\) |
0.434186 | + | 0.900823i | \(0.357036\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(20\) | −2.87463 | − | 3.42585i | −0.642788 | − | 0.766044i | ||||
\(21\) | −4.30063 | + | 1.58258i | −0.938475 | + | 0.345347i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.69846 | + | 1.71010i | 0.939693 | + | 0.342020i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.64575 | + | 4.47214i | 0.509175 | + | 0.860663i | ||||
\(28\) | 5.29150 | 1.00000 | ||||||||
\(29\) | 1.65407 | − | 4.54453i | 0.307154 | − | 0.843898i | −0.686055 | − | 0.727550i | \(-0.740659\pi\) |
0.993208 | − | 0.116348i | \(-0.0371189\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.73729 | + | 1.33605i | 1.34689 | + | 0.232576i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.12348 | + | 2.95804i | −0.866025 | + | 0.500000i | ||||
\(36\) | −1.08373 | − | 5.90132i | −0.180621 | − | 0.983553i | ||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.2381 | + | 0.0433527i | −1.95967 | + | 0.00694200i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(44\) | −7.85180 | − | 4.53324i | −1.18370 | − | 0.683411i | ||||
\(45\) | 4.34825 | + | 5.10810i | 0.648199 | + | 0.761471i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.27240 | + | 7.47515i | 0.914923 | + | 1.09036i | 0.995608 | + | 0.0936230i | \(0.0298448\pi\) |
−0.0806848 | + | 0.996740i | \(0.525711\pi\) | |||||||
\(48\) | −1.17889 | + | 6.82717i | −0.170158 | + | 0.985417i | ||||
\(49\) | 1.21554 | − | 6.89365i | 0.173648 | − | 0.984808i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.61929 | + | 9.01526i | 1.06691 | + | 1.26239i | ||||
\(52\) | 13.2792 | + | 4.83324i | 1.84150 | + | 0.670250i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.1366 | 1.36682 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(60\) | −2.67504 | − | 7.26940i | −0.345347 | − | 0.938475i | ||||
\(61\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.93705 | + | 0.0562338i | −0.999975 | + | 0.00708479i | ||||
\(64\) | 4.00000 | − | 6.92820i | 0.500000 | − | 0.866025i | ||||
\(65\) | −15.5594 | + | 2.74354i | −1.92991 | + | 0.340295i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(68\) | −4.66166 | − | 12.8078i | −0.565310 | − | 1.55318i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.16957 | + | 0.675254i | 0.138803 | + | 0.0801380i | 0.567793 | − | 0.823171i | \(-0.307797\pi\) |
−0.428990 | + | 0.903309i | \(0.641131\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.36548 | − | 14.4894i | −0.979105 | − | 1.69586i | −0.665664 | − | 0.746252i | \(-0.731851\pi\) |
−0.313441 | − | 0.949608i | \(-0.601482\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.65382 | + | 5.54317i | 0.768317 | + | 0.640070i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.70948 | + | 9.18780i | −0.878576 | + | 1.04705i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.58720 | − | 2.39754i | −0.741117 | − | 0.269745i | −0.0562544 | − | 0.998416i | \(-0.517916\pi\) |
−0.684863 | + | 0.728672i | \(0.740138\pi\) | |||||||
\(80\) | 8.94427i | 1.00000i | ||||||||
\(81\) | 1.68826 | + | 8.84024i | 0.187585 | + | 0.982248i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.73160 | − | 13.0000i | 0.519360 | − | 1.42693i | −0.351866 | − | 0.936050i | \(-0.614453\pi\) |
0.871227 | − | 0.490881i | \(-0.163325\pi\) | |||||||
\(84\) | 8.62348 | + | 3.10414i | 0.940898 | + | 0.338689i | ||||
\(85\) | 11.6734 | + | 9.79516i | 1.26616 | + | 1.06243i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.36156 | − | 6.43582i | 0.574820 | − | 0.689993i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.34707 | − | 16.1896i | 0.979839 | − | 1.69713i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.71484 | + | 9.72536i | 0.174116 | + | 0.987461i | 0.939159 | + | 0.343482i | \(0.111606\pi\) |
−0.765043 | + | 0.643979i | \(0.777282\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.8256 | + | 6.71624i | 1.18851 | + | 0.675008i | ||||
\(100\) | −5.00000 | − | 8.66025i | −0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.25613 | + | 18.4664i | −0.320836 | + | 1.81955i | 0.216616 | + | 0.976257i | \(0.430498\pi\) |
−0.537452 | + | 0.843294i | \(0.680613\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.0849 | + | 1.81510i | −0.984186 | + | 0.177136i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 1.69574 | − | 10.2530i | 0.163173 | − | 0.986598i | ||||
\(109\) | −15.5685 | −1.49119 | −0.745595 | − | 0.666400i | \(-0.767834\pi\) | ||||
−0.745595 | + | 0.666400i | \(0.767834\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.10705 | − | 6.80262i | −0.766044 | − | 0.642788i | ||||
\(113\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.37652 | + | 4.83619i | −0.777741 | + | 0.449029i | ||||
\(117\) | −19.9697 | − | 7.10855i | −1.84620 | − | 0.657186i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.7566 | + | 3.13097i | −1.62774 | + | 0.287015i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.97428 | − | 3.26637i | 0.815844 | − | 0.296943i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.68246 | + | 5.59017i | 0.866025 | + | 0.500000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(132\) | −10.1366 | − | 11.9938i | −0.882280 | − | 1.04393i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.08972 | + | 10.8754i | 0.351987 | + | 0.936005i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(140\) | 11.6524 | + | 2.05463i | 0.984808 | + | 0.173648i | ||||
\(141\) | 5.83690 | + | 15.8617i | 0.491555 | + | 1.33579i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −27.7393 | + | 16.0153i | −2.31968 | + | 1.33927i | ||||
\(144\) | −5.92622 | + | 10.4346i | −0.493852 | + | 0.869546i | ||||
\(145\) | 5.40702 | − | 9.36524i | 0.449029 | − | 0.777741i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.02494 | − | 10.5214i | 0.496929 | − | 0.867791i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.42640 | − | 9.41395i | −0.280701 | − | 0.771221i | −0.997279 | − | 0.0737137i | \(-0.976515\pi\) |
0.716578 | − | 0.697507i | \(-0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.71990 | − | 9.75405i | −0.139964 | − | 0.793773i | −0.971274 | − | 0.237964i | \(-0.923520\pi\) |
0.831310 | − | 0.555809i | \(-0.187591\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.12843 | + | 19.1617i | 0.576299 | + | 1.54913i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 18.8056 | + | 15.6666i | 1.50565 | + | 1.25433i | ||||
\(157\) | 4.25060 | − | 24.1063i | 0.339235 | − | 1.92390i | −0.0413387 | − | 0.999145i | \(-0.513162\pi\) |
0.380573 | − | 0.924751i | \(-0.375727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.5195 | + | 5.94642i | 1.28604 | + | 0.462928i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −25.4357 | − | 4.48500i | −1.96827 | − | 0.347060i | −0.990546 | − | 0.137179i | \(-0.956196\pi\) |
−0.977727 | − | 0.209881i | \(-0.932692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.2857 | − | 23.7346i | 2.17583 | − | 1.82574i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.8135 | − | 4.55162i | 1.96257 | − | 0.346054i | 0.966607 | − | 0.256265i | \(-0.0824918\pi\) |
0.995961 | − | 0.0897890i | \(-0.0286193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.4310 | + | 4.52450i | −0.939693 | + | 0.342020i | ||||
\(176\) | 6.20183 | + | 17.0394i | 0.467481 | + | 1.28439i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.6895 | − | 10.7904i | −1.39692 | − | 0.806511i | −0.402849 | − | 0.915267i | \(-0.631980\pi\) |
−0.994068 | + | 0.108756i | \(0.965313\pi\) | |||||||
\(180\) | −0.0950524 | − | 13.4161i | −0.00708479 | − | 0.999975i | ||||
\(181\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.0304 | + | 10.5662i | 2.12291 | + | 0.772678i | ||||
\(188\) | − | 19.5162i | − | 1.42337i | ||||||
\(189\) | −12.9679 | − | 4.56445i | −0.943274 | − | 0.332015i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.02342 | − | 5.55930i | 0.146409 | − | 0.402257i | −0.844711 | − | 0.535222i | \(-0.820228\pi\) |
0.991121 | + | 0.132966i | \(0.0424500\pi\) | |||||||
\(192\) | 10.5830 | − | 8.94427i | 0.763763 | − | 0.645497i | ||||
\(193\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −26.9663 | − | 4.65646i | −1.93110 | − | 0.333456i | ||||
\(196\) | −10.7246 | + | 8.99903i | −0.766044 | + | 0.642788i | ||||
\(197\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.37627 | + | 12.0237i | 0.307154 | + | 0.843898i | ||||
\(204\) | −0.0836275 | − | 23.6073i | −0.00585510 | − | 1.65284i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.1314 | − | 24.4764i | −0.979839 | − | 1.69713i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.04055 | − | 28.5864i | 0.347006 | − | 1.96797i | 0.133226 | − | 0.991086i | \(-0.457467\pi\) |
0.213780 | − | 0.976882i | \(-0.431422\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.50991 | + | 1.78656i | 0.103458 | + | 0.122413i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.13319 | − | 28.5206i | −0.346869 | − | 1.92724i | ||||
\(220\) | −15.5302 | − | 13.0314i | −1.04705 | − | 0.878576i | ||||
\(221\) | −47.4206 | − | 8.36153i | −3.18986 | − | 0.562458i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.3816 | + | 17.1022i | −1.36486 | + | 1.14525i | −0.390406 | + | 0.920643i | \(0.627665\pi\) |
−0.974449 | + | 0.224607i | \(0.927890\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.59185 | + | 12.9369i | 0.506123 | + | 0.862461i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.72684 | + | 0.480816i | −0.180987 | + | 0.0319129i | −0.263407 | − | 0.964685i | \(-0.584846\pi\) |
0.0824200 | + | 0.996598i | \(0.473735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.9538 | + | 10.4506i | −1.18127 | + | 0.687600i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.9099 | + | 18.8965i | 0.711684 | + | 1.23267i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.32858 | − | 7.77146i | −0.605957 | − | 0.504811i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.5170 | + | 17.3007i | −0.939026 | + | 1.11909i | 0.0536837 | + | 0.998558i | \(0.482904\pi\) |
−0.992710 | + | 0.120530i | \(0.961541\pi\) | |||||||
\(240\) | −5.24695 | + | 14.5763i | −0.338689 | + | 0.940898i | ||||
\(241\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.43459 | + | 15.3972i | −0.156179 | + | 0.987729i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.35346 | − | 14.7085i | 0.342020 | − | 0.939693i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.3371 | − | 18.4101i | 0.971951 | − | 1.16670i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(252\) | 12.2326 | + | 10.1175i | 0.770579 | + | 0.637344i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.2779 | + | 22.8110i | 0.831493 | + | 1.42848i | ||||
\(256\) | −15.0351 | + | 5.47232i | −0.939693 | + | 0.342020i | ||||
\(257\) | −10.9594 | − | 30.1108i | −0.683631 | − | 1.87826i | −0.374317 | − | 0.927301i | \(-0.622123\pi\) |
−0.309314 | − | 0.950960i | \(-0.600099\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 27.3654 | + | 15.7994i | 1.69713 | + | 0.979839i | ||||
\(261\) | 12.5131 | − | 7.34312i | 0.774540 | − | 0.454528i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −9.32333 | + | 25.6156i | −0.565310 | + | 1.55318i | ||||
\(273\) | 24.7300 | − | 20.9007i | 1.49673 | − | 1.26497i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.3218 | + | 3.93594i | 1.34606 | + | 0.237346i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.4266 | − | 2.89645i | 0.979929 | − | 0.172788i | 0.339333 | − | 0.940666i | \(-0.389799\pi\) |
0.640596 | + | 0.767878i | \(0.278687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.1641 | + | 8.06706i | −1.31752 | + | 0.479537i | −0.902662 | − | 0.430350i | \(-0.858390\pi\) |
−0.414855 | + | 0.909887i | \(0.636168\pi\) | |||||||
\(284\) | −0.923802 | − | 2.53813i | −0.0548176 | − | 0.150610i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.7214 | + | 25.4982i | 0.865965 | + | 1.49990i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.91051 | + | 16.8552i | −0.170617 | + | 0.988071i | ||||
\(292\) | −5.81060 | + | 32.9535i | −0.340040 | + | 1.92846i | ||||
\(293\) | 21.1605 | − | 25.2182i | 1.23621 | − | 1.47326i | 0.407868 | − | 0.913041i | \(-0.366272\pi\) |
0.828344 | − | 0.560220i | \(-0.189283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.3320 | + | 17.8825i | 0.889654 | + | 1.03765i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.06808 | − | 17.0466i | −0.177136 | − | 0.984186i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3074 | − | 29.9773i | 0.987787 | − | 1.71090i | 0.358957 | − | 0.933354i | \(-0.383132\pi\) |
0.628830 | − | 0.777543i | \(-0.283534\pi\) | |||||||
\(308\) | 23.6232 | − | 4.16541i | 1.34606 | − | 0.237346i | ||||
\(309\) | −16.1394 | + | 28.1843i | −0.918136 | + | 1.60335i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.499550 | − | 2.83309i | −0.0282362 | − | 0.160136i | 0.967429 | − | 0.253141i | \(-0.0814637\pi\) |
−0.995666 | + | 0.0930055i | \(0.970353\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.5000 | − | 2.95804i | −0.986013 | − | 0.166667i | ||||
\(316\) | 7.00995 | + | 12.1416i | 0.394340 | + | 0.683018i | ||||
\(317\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.80699 | − | 21.5905i | 0.213151 | − | 1.20884i | ||||
\(320\) | 11.4985 | − | 13.7034i | 0.642788 | − | 0.766044i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 8.77822 | − | 15.7144i | 0.487679 | − | 0.873023i | ||||
\(325\) | −35.3286 | −1.95968 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −25.3717 | − | 9.13289i | −1.40306 | − | 0.505050i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.4253 | − | 4.48317i | −1.40174 | − | 0.247165i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.7840 | + | 10.7271i | −0.702673 | + | 0.589612i | −0.922533 | − | 0.385919i | \(-0.873884\pi\) |
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | −23.9617 | + | 13.8343i | −1.31507 | + | 0.759254i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −9.22133 | − | 15.8419i | −0.503065 | − | 0.864249i | ||||
\(337\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.29230 | − | 30.0141i | −0.287015 | − | 1.62774i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.26013 | + | 16.0390i | 0.500000 | + | 0.866025i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(348\) | −16.4881 | + | 2.96756i | −0.883856 | + | 0.159078i | ||||
\(349\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.3742 | − | 23.2994i | −1.51450 | − | 1.24363i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.08193 | + | 5.72005i | −0.110810 | + | 0.304447i | −0.982686 | − | 0.185279i | \(-0.940681\pi\) |
0.871876 | + | 0.489726i | \(0.162903\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.31332 | + | 1.94111i | 0.122778 | + | 0.103023i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −30.7743 | − | 5.31401i | −1.62875 | − | 0.281247i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.1235 | − | 18.5465i | 1.69541 | − | 0.978847i | 0.745409 | − | 0.666608i | \(-0.232254\pi\) |
0.950004 | − | 0.312239i | \(-0.101079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.50000 | + | 16.4545i | −0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.5414 | − | 0.0585968i | 0.868197 | − | 0.00307553i | ||||
\(364\) | −35.1335 | + | 12.7875i | −1.84150 | + | 0.670250i | ||||
\(365\) | −12.7955 | − | 35.1554i | −0.669747 | − | 1.84012i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.03002 | − | 5.84153i | −0.0537666 | − | 0.304925i | 0.946051 | − | 0.324017i | \(-0.105034\pi\) |
−0.999818 | + | 0.0190919i | \(0.993923\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.5000 | + | 14.7902i | 0.645497 | + | 0.763763i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.1712i | 1.75990i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.89457 | 0.148684 | 0.0743421 | − | 0.997233i | \(-0.476314\pi\) | ||||
0.0743421 | + | 0.997233i | \(0.476314\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.9416 | − | 2.98725i | −0.865673 | − | 0.152641i | −0.276859 | − | 0.960910i | \(-0.589294\pi\) |
−0.588813 | + | 0.808269i | \(0.700405\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.5445 | + | 17.2389i | −1.04705 | + | 0.878576i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.87539 | − | 17.1047i | 0.501347 | − | 0.868359i | ||||
\(389\) | 36.8123 | − | 6.49100i | 1.86646 | − | 0.329107i | 0.877768 | − | 0.479085i | \(-0.159032\pi\) |
0.988689 | + | 0.149979i | \(0.0479205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.5747 | − | 7.83736i | −0.683018 | − | 0.394340i | ||||
\(396\) | −9.48360 | − | 25.4925i | −0.476569 | − | 1.28105i | ||||
\(397\) | 17.3129 | + | 29.9868i | 0.868910 | + | 1.50500i | 0.863112 | + | 0.505013i | \(0.168512\pi\) |
0.00579782 | + | 0.999983i | \(0.498154\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.47296 | + | 19.6962i | −0.173648 | + | 0.984808i | ||||
\(401\) | 19.0139 | − | 22.6599i | 0.949510 | − | 1.13158i | −0.0416801 | − | 0.999131i | \(-0.513271\pi\) |
0.991190 | − | 0.132450i | \(-0.0422845\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.285150 | + | 20.1226i | 0.0141692 | + | 0.999900i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 28.7287 | − | 24.1062i | 1.41536 | − | 1.18763i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.4672 | − | 26.7899i | 0.759254 | − | 1.31507i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(420\) | 17.7844 | + | 10.1840i | 0.867791 | + | 0.496929i | ||||
\(421\) | 7.09160 | + | 40.2184i | 0.345623 | + | 1.96013i | 0.269360 | + | 0.963039i | \(0.413188\pi\) |
0.0762630 | + | 0.997088i | \(0.475701\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.207402 | + | 29.2736i | 0.0100843 | + | 1.42333i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.9027 | + | 26.1026i | 1.06243 | + | 1.26616i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −54.6013 | + | 9.82724i | −2.63617 | + | 0.474464i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.23679i | 0.204079i | 0.994780 | + | 0.102040i | \(0.0325368\pi\) | ||||
−0.994780 | + | 0.102040i | \(0.967463\pi\) | |||||||
\(432\) | −15.7791 | + | 13.5285i | −0.759170 | + | 0.650892i | ||||
\(433\) | 29.5653 | 1.42082 | 0.710410 | − | 0.703788i | \(-0.248510\pi\) | ||||
0.710410 | + | 0.703788i | \(0.248510\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.3056 | − | 12.0905i | 0.685903 | − | 0.579694i | ||||
\(436\) | 23.8523 | + | 20.0144i | 1.14232 | + | 0.958518i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.9909 | − | 13.6122i | 0.761471 | − | 0.648199i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.0614676 | − | 17.3518i | −0.00290732 | − | 0.820711i | ||||
\(448\) | 3.67544 | + | 20.8445i | 0.173648 | + | 0.984808i | ||||
\(449\) | 11.1822 | + | 6.45603i | 0.527719 | + | 0.304679i | 0.740087 | − | 0.672511i | \(-0.234784\pi\) |
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.91909 | − | 16.9050i | 0.137151 | − | 0.794264i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.8694 | − | 32.0217i | 1.25966 | − | 1.50120i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.376318 | + | 35.4092i | 0.0175650 | + | 1.65276i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(464\) | 19.0509 | + | 3.35918i | 0.884414 | + | 0.155946i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.6038 | + | 18.8238i | −1.50872 | + | 0.871061i | −0.508774 | + | 0.860900i | \(0.669901\pi\) |
−0.999948 | + | 0.0101613i | \(0.996765\pi\) | |||||||
\(468\) | 21.4567 | + | 36.5635i | 0.991838 | + | 1.69015i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.0686 | − | 36.7922i | 0.970788 | − | 1.69530i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 31.2298 | + | 18.0305i | 1.43141 | + | 0.826428i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.9486 | − | 6.53274i | −0.815844 | − | 0.296943i | ||||
\(485\) | 22.0820i | 1.00269i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.9464 | + | 4.75137i | 1.21607 | + | 0.214427i | 0.744635 | − | 0.667472i | \(-0.232624\pi\) |
0.471439 | + | 0.881899i | \(0.343735\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.2474 | − | 21.1851i | 1.13709 | − | 0.954128i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.4332 | + | 19.3816i | 1.05324 | + | 0.871136i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.51883 | + | 0.620464i | −0.157841 | + | 0.0278316i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.2340 | + | 14.6440i | −1.80112 | + | 0.655555i | −0.802890 | + | 0.596127i | \(0.796706\pi\) |
−0.998233 | + | 0.0594285i | \(0.981072\pi\) | |||||||
\(500\) | −7.64780 | − | 21.0122i | −0.342020 | − | 0.939693i | ||||
\(501\) | −38.8211 | − | 22.2304i | −1.73440 | − | 0.993181i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.3190 | + | 19.8141i | 1.53021 | + | 0.883466i | 0.999352 | + | 0.0360049i | \(0.0114632\pi\) |
0.530857 | + | 0.847461i | \(0.321870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 60.0201 | − | 22.0866i | 2.66559 | − | 0.980902i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 41.5964 | + | 15.1398i | 1.84012 | + | 0.669747i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.3406 | + | 39.4005i | −0.631923 | + | 1.73620i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.8866 | + | 28.4342i | 1.49033 | + | 1.25054i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 44.7380 | + | 7.72521i | 1.96378 | + | 0.339099i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.99657 | + | 17.3146i | −0.437120 | + | 0.757113i | −0.997466 | − | 0.0711450i | \(-0.977335\pi\) |
0.560346 | + | 0.828258i | \(0.310668\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.9127 | + | 0.0811669i | −0.999994 | + | 0.00354242i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.111257 | + | 31.4070i | 0.00484185 | + | 1.36681i | ||||
\(529\) | −3.99391 | − | 22.6506i | −0.173648 | − | 0.984808i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.1280 | − | 28.5487i | −1.04120 | − | 1.23197i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 31.7327i | − | 1.36682i | ||||||
\(540\) | 7.71532 | − | 21.9197i | 0.332015 | − | 0.943274i | ||||
\(541\) | −24.9455 | −1.07249 | −0.536245 | − | 0.844062i | \(-0.680158\pi\) | ||||
−0.536245 | + | 0.844062i | \(0.680158\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −34.2833 | − | 6.04507i | −1.46853 | − | 0.258942i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.4281 | − | 6.34330i | 0.741117 | − | 0.269745i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −15.2111 | − | 18.1279i | −0.642788 | − | 0.766044i | ||||
\(561\) | 41.1120 | + | 34.2496i | 1.73575 | + | 1.44602i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.5799 | + | 34.0602i | −1.20450 | + | 1.43547i | −0.334515 | + | 0.942390i | \(0.608573\pi\) |
−0.869985 | + | 0.493078i | \(0.835872\pi\) | |||||||
\(564\) | 11.4487 | − | 31.8053i | 0.482079 | − | 1.33924i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.4559 | − | 15.0459i | −0.775075 | − | 0.631869i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.7193 | + | 37.6935i | −0.575143 | + | 1.58019i | 0.221123 | + | 0.975246i | \(0.429028\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.0355 | + | 26.0419i | 1.29879 | + | 1.08982i | 0.990352 | + | 0.138575i | \(0.0442523\pi\) |
0.308443 | + | 0.951243i | \(0.400192\pi\) | |||||||
\(572\) | 63.0879 | + | 11.1241i | 2.63784 | + | 0.465122i | ||||
\(573\) | 6.55877 | − | 7.87290i | 0.273996 | − | 0.328895i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 22.4939 | − | 8.36806i | 0.937246 | − | 0.348669i | ||||
\(577\) | 13.5294 | − | 23.4337i | 0.563238 | − | 0.975556i | −0.433974 | − | 0.900926i | \(-0.642889\pi\) |
0.997211 | − | 0.0746307i | \(-0.0237778\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20.3238 | + | 7.39724i | −0.843898 | + | 0.307154i | ||||
\(581\) | 12.5186 | + | 34.3947i | 0.519360 | + | 1.42693i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −41.2150 | − | 23.4077i | −1.70403 | − | 0.967791i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.3852 | + | 35.0200i | 1.21286 | + | 1.44543i | 0.860414 | + | 0.509596i | \(0.170205\pi\) |
0.352445 | + | 0.935833i | \(0.385350\pi\) | |||||||
\(588\) | −22.7568 | + | 8.37421i | −0.938475 | + | 0.345347i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.621055i | 0.0255037i | 0.999919 | + | 0.0127518i | \(0.00405915\pi\) | ||||
−0.999919 | + | 0.0127518i | \(0.995941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −40.3175 | −1.65286 | ||||||||
\(596\) | −6.85279 | + | 18.8279i | −0.280701 | + | 0.771221i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.5103 | + | 7.14306i | 1.65521 | + | 0.291858i | 0.921723 | − | 0.387849i | \(-0.126782\pi\) |
0.733484 | + | 0.679706i | \(0.237893\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.90452 | + | 17.1551i | −0.403009 | + | 0.698032i | ||||
\(605\) | 21.0305 | − | 3.70825i | 0.855013 | − | 0.150762i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.75528 | + | 1.73078i | −0.193011 | + | 0.0702502i | −0.436717 | − | 0.899599i | \(-0.643859\pi\) |
0.243706 | + | 0.969849i | \(0.421637\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0785077 | + | 22.1621i | 0.00318129 | + | 0.898052i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −59.7108 | − | 34.4741i | −2.41564 | − | 1.39467i | ||||
\(612\) | 13.7124 | − | 38.5216i | 0.554292 | − | 1.55714i | ||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.67128 | − | 48.1786i | −0.347129 | − | 1.92869i | ||||
\(625\) | 19.1511 | + | 16.0697i | 0.766044 | + | 0.642788i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −37.5028 | + | 31.4686i | −1.49653 | + | 1.25573i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.65857 | − | 8.06888i | 0.185455 | − | 0.321217i | −0.758275 | − | 0.651935i | \(-0.773958\pi\) |
0.943730 | + | 0.330718i | \(0.107291\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.9840 | − | 43.6298i | 0.993027 | − | 1.73413i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.58865 | + | 48.7086i | 0.340295 | + | 1.92991i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.41264 | + | 3.79728i | 0.0558833 | + | 0.150218i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.19106 | + | 6.18647i | 0.205035 | + | 0.244351i | 0.858756 | − | 0.512384i | \(-0.171238\pi\) |
−0.653722 | + | 0.756735i | \(0.726793\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.66297 | − | 15.1025i | 0.105017 | − | 0.595584i | −0.886196 | − | 0.463311i | \(-0.846661\pi\) |
0.991213 | − | 0.132273i | \(-0.0422275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.2989i | 1.26980i | 0.772594 | + | 0.634901i | \(0.218959\pi\) | ||||
−0.772594 | + | 0.634901i | \(0.781041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.36548 | − | 49.4908i | 0.326368 | − | 1.93082i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.6529 | − | 3.99431i | 0.882430 | − | 0.155596i | 0.285970 | − | 0.958239i | \(-0.407684\pi\) |
0.596461 | + | 0.802642i | \(0.296573\pi\) | |||||||
\(660\) | −17.6648 | − | 30.3475i | −0.687600 | − | 1.18127i | ||||
\(661\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −72.3755 | − | 41.4449i | −2.81083 | − | 1.60959i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 33.2039 | + | 39.5709i | 1.28470 | + | 1.53104i | ||||
\(669\) | −43.2483 | + | 15.9148i | −1.67207 | + | 0.615302i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.78316 | + | 25.5367i | 0.184104 | + | 0.982907i | ||||
\(676\) | −73.8488 | −2.84034 | ||||||||
\(677\) | 5.72792 | − | 15.7373i | 0.220142 | − | 0.604835i | −0.779629 | − | 0.626242i | \(-0.784592\pi\) |
0.999771 | + | 0.0214069i | \(0.00681454\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.0151 | − | 16.7946i | −0.768108 | − | 0.644519i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.72595 | − | 0.816062i | −0.181099 | − | 0.0312716i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(692\) | −45.4001 | − | 26.2118i | −1.72585 | − | 0.996422i | ||||
\(693\) | −35.3897 | + | 6.49900i | −1.34434 | + | 0.246877i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 24.8619 | + | 9.04900i | 0.939693 | + | 0.342020i | ||||
\(701\) | − | 50.2017i | − | 1.89609i | −0.318131 | − | 0.948047i | \(-0.603055\pi\) | ||
0.318131 | − | 0.948047i | \(-0.396945\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 12.4037 | − | 34.0788i | 0.467481 | − | 1.28439i | ||||
\(705\) | 6.69449 | + | 37.1954i | 0.252129 | + | 1.40086i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.7063 | − | 29.9612i | 1.34098 | − | 1.12521i | 0.359605 | − | 0.933105i | \(-0.382911\pi\) |
0.981373 | − | 0.192110i | \(-0.0615331\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.6437 | − | 18.1374i | −0.399170 | − | 0.680207i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −67.3032 | + | 24.4964i | −2.51700 | + | 0.916112i | ||||
\(716\) | 14.7621 | + | 40.5585i | 0.551686 | + | 1.51574i | ||||
\(717\) | −33.8071 | + | 19.6786i | −1.26255 | + | 0.734910i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | −17.1017 | + | 20.6768i | −0.637344 | + | 0.770579i | ||||
\(721\) | −24.8056 | − | 42.9646i | −0.923810 | − | 1.60009i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.5432 | − | 18.5237i | 0.577260 | − | 0.687952i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.6062 | − | 10.4118i | −1.06095 | − | 0.386152i | −0.248162 | − | 0.968719i | \(-0.579826\pi\) |
−0.812783 | + | 0.582566i | \(0.802049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | + | 23.6643i | −0.481481 | + | 0.876456i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.6052 | − | 27.3590i | −1.20430 | − | 1.01053i | −0.999497 | − | 0.0317250i | \(-0.989900\pi\) |
−0.204804 | − | 0.978803i | \(-0.565656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.3529 | − | 20.8297i | 0.640070 | − | 0.768317i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.3056 | + | 35.1704i | −0.746955 | + | 1.29376i | 0.202321 | + | 0.979319i | \(0.435152\pi\) |
−0.949276 | + | 0.314445i | \(0.898182\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.88992 | − | 22.0609i | −0.142516 | − | 0.808247i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.7946 | − | 21.0055i | 1.30965 | − | 0.768552i | ||||
\(748\) | −30.8935 | − | 53.5092i | −1.12958 | − | 1.95649i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.13585 | − | 51.8120i | 0.333372 | − | 1.89065i | −0.109376 | − | 0.994000i | \(-0.534885\pi\) |
0.442748 | − | 0.896646i | \(-0.354004\pi\) | |||||||
\(752\) | −25.0896 | + | 29.9006i | −0.914923 | + | 1.09036i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 22.1472i | − | 0.806018i | ||||||
\(756\) | 14.0000 | + | 23.6643i | 0.509175 | + | 0.860663i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.5536 | − | 26.4766i | 1.14232 | − | 0.958518i | ||||
\(764\) | −10.2470 | + | 5.91608i | −0.370722 | + | 0.214036i | ||||
\(765\) | 8.25722 | + | 44.9638i | 0.298540 | + | 1.62567i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −27.7126 | + | 0.0981703i | −0.999994 | + | 0.00354242i | ||||
\(769\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.196606 | − | 55.5002i | −0.00708059 | − | 1.99879i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −47.0498 | − | 27.1642i | −1.69226 | − | 0.977028i | −0.952686 | − | 0.303956i | \(-0.901693\pi\) |
−0.739576 | − | 0.673073i | \(-0.764974\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 35.3286 | + | 41.8014i | 1.26497 | + | 1.49673i | ||||
\(781\) | 5.75296 | + | 2.09391i | 0.205857 | + | 0.0749259i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.7000 | − | 4.62645i | 0.882707 | − | 0.165336i | ||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | 18.7205 | − | 51.4341i | 0.668162 | − | 1.83576i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.87831 | − | 8.28889i | −0.352124 | − | 0.295467i | 0.449518 | − | 0.893271i | \(-0.351596\pi\) |
−0.801642 | + | 0.597804i | \(0.796040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.0380 | − | 46.8115i | −0.603516 | − | 1.65815i | −0.744092 | − | 0.668077i | \(-0.767118\pi\) |
0.140576 | − | 0.990070i | \(-0.455105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.5477 | + | 65.4902i | 0.408528 | + | 2.31688i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48.7525 | − | 58.1009i | −1.72044 | − | 2.05034i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 56.7926i | 1.99672i | 0.0572419 | + | 0.998360i | \(0.481769\pi\) | ||||
−0.0572419 | + | 0.998360i | \(0.518231\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 8.75254 | − | 24.0474i | 0.307154 | − | 0.843898i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −30.2209 | + | 36.2761i | −1.05794 | + | 1.26992i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 52.5630 | − | 19.5542i | 1.83670 | − | 0.683279i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.7241 | + | 2.41994i | −0.478976 | + | 0.0844563i | −0.407923 | − | 0.913016i | \(-0.633747\pi\) |
−0.0710524 | + | 0.997473i | \(0.522636\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 34.0686 | + | 19.5089i | 1.18612 | + | 0.679214i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.81560 | + | 55.6670i | −0.340295 | + | 1.92991i | ||||
\(833\) | 30.6637 | − | 36.5436i | 1.06243 | − | 1.26616i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54.2704 | − | 19.7528i | −1.87810 | − | 0.683574i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.29849 | + | 3.60686i | 0.148224 | + | 0.124374i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.4693 | + | 4.91599i | 0.980535 | + | 0.169316i | ||||
\(844\) | −44.4725 | + | 37.3169i | −1.53081 | + | 1.28450i | ||||
\(845\) | 71.5038 | − | 41.2828i | 2.45981 | − | 1.42017i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.6338 | + | 21.8823i | −0.434101 | + | 0.751886i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40.8528 | + | 0.144718i | −1.40206 | + | 0.00496672i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.0165725 | − | 4.67827i | −0.000567764 | − | 0.160275i | ||||
\(853\) | 2.37739 | + | 13.4828i | 0.0814003 | + | 0.461644i | 0.998075 | + | 0.0620108i | \(0.0197513\pi\) |
−0.916675 | + | 0.399633i | \(0.869138\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.3410 | − | 44.5013i | −1.27554 | − | 1.52013i | −0.733281 | − | 0.679925i | \(-0.762012\pi\) |
−0.542263 | − | 0.840209i | \(-0.682432\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.6113 | 1.99284 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.03329 | + | 50.1900i | 0.306787 | + | 1.70454i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.2950 | − | 5.51815i | −1.06161 | − | 0.187190i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.6309 | + | 25.7613i | −0.495182 | + | 0.871889i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.1310 | + | 5.13658i | −0.984808 | + | 0.173648i | ||||
\(876\) | −28.8009 | + | 50.2952i | −0.973091 | + | 1.69932i | ||||
\(877\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 49.2786 | − | 28.6843i | 1.66213 | − | 0.967496i | ||||
\(880\) | 7.04083 | + | 39.9305i | 0.237346 | + | 1.34606i | ||||
\(881\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(884\) | 61.9032 | + | 73.7734i | 2.08203 | + | 2.48127i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.0091 | + | 45.2975i | −1.27622 | + | 1.52094i | −0.545873 | + | 0.837868i | \(0.683802\pi\) |
−0.730349 | + | 0.683074i | \(0.760642\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.4960 | + | 38.1371i | 0.485633 | + | 1.27764i | ||||
\(892\) | 53.2127 | 1.78169 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.9663 | − | 31.0184i | −1.23565 | − | 1.03683i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.00000 | − | 29.5804i | 0.166667 | − | 0.986013i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(908\) | 4.79589 | + | 2.76891i | 0.159157 | + | 0.0918895i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.992804 | − | 1.18318i | −0.0328931 | − | 0.0392004i | 0.749347 | − | 0.662177i | \(-0.230367\pi\) |
−0.782240 | + | 0.622977i | \(0.785923\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.8902 | − | 61.7612i | 0.360412 | − | 2.04400i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.6113 | 1.04276 | 0.521380 | − | 0.853325i | \(-0.325417\pi\) | ||||
0.521380 | + | 0.853325i | \(0.325417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45.7911 | − | 38.7006i | 1.50887 | − | 1.27523i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.39735 | − | 1.65701i | −0.309318 | − | 0.0545410i | ||||
\(924\) | 40.9419 | + | 7.06971i | 1.34689 | + | 0.232576i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −42.8357 | + | 36.4637i | −1.40691 | + | 1.19763i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 59.8251 | + | 34.5400i | 1.95649 | + | 1.12958i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.4440 | − | 47.5345i | −0.896558 | − | 1.55288i | −0.831864 | − | 0.554979i | \(-0.812726\pi\) |
−0.0646935 | − | 0.997905i | \(-0.520607\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.847857 | − | 4.91009i | 0.0276688 | − | 0.160235i | ||||
\(940\) | 7.57794 | − | 42.9766i | 0.247165 | − | 1.40174i | ||||
\(941\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −26.7842 | − | 15.0866i | −0.871290 | − | 0.490768i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(948\) | 4.30142 | + | 23.8992i | 0.139704 | + | 0.776209i | ||||
\(949\) | 90.5589 | + | 75.9879i | 2.93967 | + | 2.46667i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.61438 | − | 11.4564i | 0.214036 | − | 0.370722i | ||||
\(956\) | 44.4826 | − | 7.84349i | 1.43867 | − | 0.253677i | ||||
\(957\) | 18.8698 | − | 32.9524i | 0.609973 | − | 1.06520i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 26.7778 | − | 15.5869i | 0.864249 | − | 0.503065i | ||||
\(961\) | 5.38309 | + | 30.5290i | 0.173648 | + | 0.984808i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 23.5242 | − | 20.4600i | 0.754540 | − | 0.656254i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −57.5745 | − | 20.7247i | −1.84386 | − | 0.663722i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −27.1109 | + | 15.6525i | −0.866025 | + | 0.500000i | ||||
\(981\) | −35.9902 | − | 29.7674i | −1.14908 | − | 0.950401i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.18662 | + | 1.44352i | −0.261113 | + | 0.0460412i | −0.302672 | − | 0.953095i | \(-0.597879\pi\) |
0.0415592 | + | 0.999136i | \(0.486767\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −38.8053 | − | 22.2213i | −1.23519 | − | 0.707313i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.3618 | − | 31.8035i | −0.583280 | − | 1.01027i | −0.995087 | − | 0.0990001i | \(-0.968436\pi\) |
0.411807 | − | 0.911271i | \(-0.364898\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.1267 | + | 9.98227i | −0.860839 | + | 0.316778i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −47.1655 | + | 8.48893i | −1.49450 | + | 0.268982i | ||||
\(997\) | −17.4034 | − | 6.33430i | −0.551170 | − | 0.200609i | 0.0513964 | − | 0.998678i | \(-0.483633\pi\) |
−0.602566 | + | 0.798069i | \(0.705855\pi\) | |||||||
\(998\) | 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 | 945.2.cs.a.104.4 | yes | 24 | |
5.4 | even | 2 | inner | 945.2.cs.a.104.1 | ✓ | 24 | |
7.6 | odd | 2 | inner | 945.2.cs.a.104.1 | ✓ | 24 | |
27.20 | odd | 18 | inner | 945.2.cs.a.209.4 | yes | 24 | |
35.34 | odd | 2 | CM | 945.2.cs.a.104.4 | yes | 24 | |
135.74 | odd | 18 | inner | 945.2.cs.a.209.1 | yes | 24 | |
189.20 | even | 18 | inner | 945.2.cs.a.209.1 | yes | 24 | |
945.209 | even | 18 | inner | 945.2.cs.a.209.4 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.cs.a.104.1 | ✓ | 24 | 5.4 | even | 2 | inner | |
945.2.cs.a.104.1 | ✓ | 24 | 7.6 | odd | 2 | inner | |
945.2.cs.a.104.4 | yes | 24 | 1.1 | even | 1 | trivial | |
945.2.cs.a.104.4 | yes | 24 | 35.34 | odd | 2 | CM | |
945.2.cs.a.209.1 | yes | 24 | 135.74 | odd | 18 | inner | |
945.2.cs.a.209.1 | yes | 24 | 189.20 | even | 18 | inner | |
945.2.cs.a.209.4 | yes | 24 | 27.20 | odd | 18 | inner | |
945.2.cs.a.209.4 | yes | 24 | 945.209 | even | 18 | inner |