Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(379,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 13x^{8} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 379.10 | ||
Root | \(0.203022 + 1.39956i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.379 |
Dual form | 380.2.d.a.379.9 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.203022 | + | 1.39956i | 0.143559 | + | 0.989642i | ||||
\(3\) | − | 1.12228i | − | 0.647951i | −0.946065 | − | 0.323976i | \(-0.894980\pi\) | ||
0.946065 | − | 0.323976i | \(-0.105020\pi\) | |||||||
\(4\) | −1.91756 | + | 0.568286i | −0.958782 | + | 0.284143i | ||||
\(5\) | −2.23607 | −1.00000 | ||||||||
\(6\) | 1.57071 | − | 0.227849i | 0.641239 | − | 0.0930189i | ||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | −1.18466 | − | 2.56838i | −0.418841 | − | 0.908060i | ||||
\(9\) | 1.74048 | 0.580159 | ||||||||
\(10\) | −0.453972 | − | 3.12952i | −0.143559 | − | 0.989642i | ||||
\(11\) | − | 5.95117i | − | 1.79434i | −0.441680 | − | 0.897172i | \(-0.645618\pi\) | ||
0.441680 | − | 0.897172i | \(-0.354382\pi\) | |||||||
\(12\) | 0.637778 | + | 2.15205i | 0.184111 | + | 0.621244i | ||||
\(13\) | −6.51610 | −1.80724 | −0.903621 | − | 0.428333i | \(-0.859101\pi\) | ||||
−0.903621 | + | 0.428333i | \(0.859101\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.50950i | 0.647951i | ||||||||
\(16\) | 3.35410 | − | 2.17945i | 0.838525 | − | 0.544862i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0.353356 | + | 2.43591i | 0.0832868 | + | 0.574150i | ||||
\(19\) | − | 4.35890i | − | 1.00000i | ||||||
\(20\) | 4.28780 | − | 1.27073i | 0.958782 | − | 0.284143i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.32905 | − | 1.20822i | 1.77576 | − | 0.257593i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | −2.88245 | + | 1.32953i | −0.588378 | + | 0.271389i | ||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | −1.32291 | − | 9.11971i | −0.259445 | − | 1.78852i | ||||
\(27\) | − | 5.32016i | − | 1.02387i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | −3.51221 | + | 0.509485i | −0.641239 | + | 0.0930189i | ||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 3.73124 | + | 4.25181i | 0.659596 | + | 0.751620i | ||||
\(33\) | −6.67890 | −1.16265 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.33748 | + | 0.989090i | −0.556246 | + | 0.164848i | ||||
\(37\) | −8.01591 | −1.31781 | −0.658904 | − | 0.752227i | \(-0.728980\pi\) | ||||
−0.658904 | + | 0.752227i | \(0.728980\pi\) | |||||||
\(38\) | 6.10056 | − | 0.884954i | 0.989642 | − | 0.143559i | ||||
\(39\) | 7.31292i | 1.17100i | ||||||||
\(40\) | 2.64898 | + | 5.74307i | 0.418841 | + | 0.908060i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 3.38197 | + | 11.4117i | 0.509851 | + | 1.72039i | ||||
\(45\) | −3.89183 | −0.580159 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −2.44596 | − | 3.76426i | −0.353044 | − | 0.543323i | ||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 1.01511 | + | 6.99782i | 0.143559 | + | 0.989642i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12.4950 | − | 3.70301i | 1.73275 | − | 0.513515i | ||||
\(53\) | 5.09315 | 0.699599 | 0.349799 | − | 0.936825i | \(-0.386250\pi\) | ||||
0.349799 | + | 0.936825i | \(0.386250\pi\) | |||||||
\(54\) | 7.44591 | − | 1.08011i | 1.01326 | − | 0.146985i | ||||
\(55\) | 13.3072i | 1.79434i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.89192 | −0.647951 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | −1.42612 | − | 4.81213i | −0.184111 | − | 0.621244i | ||||
\(61\) | 1.11908 | 0.143283 | 0.0716414 | − | 0.997430i | \(-0.477176\pi\) | ||||
0.0716414 | + | 0.997430i | \(0.477176\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.19315 | + | 6.08532i | −0.649144 | + | 0.760665i | ||||
\(65\) | 14.5704 | 1.80724 | ||||||||
\(66\) | −1.35597 | − | 9.34756i | −0.166908 | − | 1.15060i | ||||
\(67\) | 13.7060i | 1.67446i | 0.546853 | + | 0.837229i | \(0.315826\pi\) | ||||
−0.546853 | + | 0.837229i | \(0.684174\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −2.06188 | − | 4.47021i | −0.242995 | − | 0.526819i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | −1.62741 | − | 11.2188i | −0.189183 | − | 1.30416i | ||||
\(75\) | − | 5.61142i | − | 0.647951i | ||||||
\(76\) | 2.47710 | + | 8.35847i | 0.284143 | + | 0.958782i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −10.2349 | + | 1.48469i | −1.15887 | + | 0.168108i | ||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −7.50000 | + | 4.87340i | −0.838525 | + | 0.544862i | ||||
\(81\) | −0.749299 | −0.0832555 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.2849 | + | 7.05012i | −1.62937 | + | 0.751545i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −0.790128 | − | 5.44687i | −0.0832868 | − | 0.574150i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.74679i | 1.00000i | ||||||||
\(96\) | 4.77173 | − | 4.18751i | 0.487013 | − | 0.427386i | ||||
\(97\) | −11.6477 | −1.18264 | −0.591322 | − | 0.806436i | \(-0.701394\pi\) | ||||
−0.591322 | + | 0.806436i | \(0.701394\pi\) | |||||||
\(98\) | −1.42116 | − | 9.79695i | −0.143559 | − | 0.989642i | ||||
\(99\) | − | 10.3579i | − | 1.04101i | ||||||
\(100\) | −9.58782 | + | 2.84143i | −0.958782 | + | 0.284143i | ||||
\(101\) | 20.0810 | 1.99813 | 0.999067 | − | 0.0431977i | \(-0.0137545\pi\) | ||||
0.999067 | + | 0.0431977i | \(0.0137545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 19.8835i | − | 1.95918i | −0.200999 | − | 0.979591i | \(-0.564419\pi\) | ||
0.200999 | − | 0.979591i | \(-0.435581\pi\) | |||||||
\(104\) | 7.71938 | + | 16.7358i | 0.756947 | + | 1.64108i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.03402 | + | 7.12820i | 0.100433 | + | 0.692352i | ||||
\(107\) | 3.66801i | 0.354600i | 0.984157 | + | 0.177300i | \(0.0567363\pi\) | ||||
−0.984157 | + | 0.177300i | \(0.943264\pi\) | |||||||
\(108\) | 3.02337 | + | 10.2018i | 0.290924 | + | 0.981664i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | −18.6243 | + | 2.70166i | −1.77576 | + | 0.257593i | ||||
\(111\) | 8.99613i | 0.853875i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 21.1725 | 1.99174 | 0.995870 | − | 0.0907914i | \(-0.0289396\pi\) | ||||
0.995870 | + | 0.0907914i | \(0.0289396\pi\) | |||||||
\(114\) | −0.993170 | − | 6.84656i | −0.0930189 | − | 0.641239i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.3411 | −1.04849 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.44536 | − | 2.97291i | 0.588378 | − | 0.271389i | ||||
\(121\) | −24.4164 | −2.21967 | ||||||||
\(122\) | 0.227197 | + | 1.56622i | 0.0205695 | + | 0.141799i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 21.6693i | − | 1.92284i | −0.275082 | − | 0.961421i | \(-0.588705\pi\) | ||
0.275082 | − | 0.961421i | \(-0.411295\pi\) | |||||||
\(128\) | −9.57113 | − | 6.03270i | −0.845976 | − | 0.533220i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.95813 | + | 20.3923i | 0.259445 | + | 1.78852i | ||||
\(131\) | − | 19.4936i | − | 1.70316i | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||
0.524222 | − | 0.851581i | \(-0.324356\pi\) | |||||||
\(132\) | 12.8072 | − | 3.79553i | 1.11473 | − | 0.330358i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −19.1825 | + | 2.78263i | −1.65711 | + | 0.240383i | ||||
\(135\) | 11.8962i | 1.02387i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.76093i | 0.743092i | 0.928414 | + | 0.371546i | \(0.121172\pi\) | ||||
−0.928414 | + | 0.371546i | \(0.878828\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 38.7784i | 3.24281i | ||||||||
\(144\) | 5.83774 | − | 3.79328i | 0.486479 | − | 0.316107i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.85599i | 0.647951i | ||||||||
\(148\) | 15.3710 | − | 4.55533i | 1.26349 | − | 0.374446i | ||||
\(149\) | 8.36188 | 0.685032 | 0.342516 | − | 0.939512i | \(-0.388721\pi\) | ||||
0.342516 | + | 0.939512i | \(0.388721\pi\) | |||||||
\(150\) | 7.85355 | − | 1.13924i | 0.641239 | − | 0.0930189i | ||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | −11.1953 | + | 5.16382i | −0.908060 | + | 0.418841i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.15583 | − | 14.0230i | −0.332733 | − | 1.12274i | ||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 5.71597i | − | 0.453306i | ||||||
\(160\) | −8.34330 | − | 9.50733i | −0.659596 | − | 0.751620i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.152125 | − | 1.04869i | −0.0119520 | − | 0.0823931i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.9345 | 1.16265 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.1802i | − | 1.32944i | −0.747091 | − | 0.664721i | \(-0.768550\pi\) | ||
0.747091 | − | 0.664721i | \(-0.231450\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.4596 | 2.26612 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 7.58657i | − | 0.580159i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.7967 | 1.73320 | 0.866599 | − | 0.499005i | \(-0.166301\pi\) | ||||
0.866599 | + | 0.499005i | \(0.166301\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.9703 | − | 19.9608i | −0.977671 | − | 1.50460i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 7.46283 | − | 2.21167i | 0.556246 | − | 0.164848i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.25592i | − | 0.0928403i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.9241 | 1.31781 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.6413 | + | 1.97882i | −0.989642 | + | 0.143559i | ||||
\(191\) | − | 26.1534i | − | 1.89239i | −0.323592 | − | 0.946197i | \(-0.604891\pi\) | ||
0.323592 | − | 0.946197i | \(-0.395109\pi\) | |||||||
\(192\) | 6.82946 | + | 5.82819i | 0.492874 | + | 0.420614i | ||||
\(193\) | 27.6795 | 1.99242 | 0.996208 | − | 0.0870089i | \(-0.0277309\pi\) | ||||
0.996208 | + | 0.0870089i | \(0.0277309\pi\) | |||||||
\(194\) | −2.36474 | − | 16.3017i | −0.169779 | − | 1.17039i | ||||
\(195\) | − | 16.3522i | − | 1.17100i | ||||||
\(196\) | 13.4229 | − | 3.97800i | 0.958782 | − | 0.284143i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 14.4965 | − | 2.10288i | 1.03022 | − | 0.149445i | ||||
\(199\) | 8.71780i | 0.617988i | 0.951064 | + | 0.308994i | \(0.0999924\pi\) | ||||
−0.951064 | + | 0.308994i | \(0.900008\pi\) | |||||||
\(200\) | −5.92331 | − | 12.8419i | −0.418841 | − | 0.908060i | ||||
\(201\) | 15.3821 | 1.08497 | ||||||||
\(202\) | 4.07689 | + | 28.1046i | 0.286849 | + | 1.97744i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 27.8283 | − | 4.03680i | 1.93889 | − | 0.281257i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −21.8557 | + | 14.2015i | −1.51542 | + | 0.984698i | ||||
\(209\) | −25.9405 | −1.79434 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | −9.76645 | + | 2.89437i | −0.670762 | + | 0.198786i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.13362 | + | 0.744688i | −0.350927 | + | 0.0509058i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −13.6642 | + | 6.30259i | −0.929731 | + | 0.428837i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.56231 | − | 25.5174i | −0.509851 | − | 1.72039i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −12.5907 | + | 1.82642i | −0.845030 | + | 0.122581i | ||||
\(223\) | 14.9356i | 1.00016i | 0.865978 | + | 0.500082i | \(0.166697\pi\) | ||||
−0.865978 | + | 0.500082i | \(0.833303\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.70239 | 0.580159 | ||||||||
\(226\) | 4.29849 | + | 29.6323i | 0.285931 | + | 1.97111i | ||||
\(227\) | − | 18.7250i | − | 1.24282i | −0.783484 | − | 0.621412i | \(-0.786559\pi\) | ||
0.783484 | − | 0.621412i | \(-0.213441\pi\) | |||||||
\(228\) | 9.38057 | − | 2.78001i | 0.621244 | − | 0.184111i | ||||
\(229\) | −29.5619 | −1.95351 | −0.976754 | − | 0.214362i | \(-0.931233\pi\) | ||||
−0.976754 | + | 0.214362i | \(0.931233\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | −2.30250 | − | 15.8727i | −0.150519 | − | 1.03763i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.4936i | 1.26094i | 0.776215 | + | 0.630468i | \(0.217137\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 5.46934 | + | 8.41713i | 0.353044 | + | 0.543323i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −4.95708 | − | 34.1723i | −0.318653 | − | 2.19668i | ||||
\(243\) | − | 15.1196i | − | 0.969920i | ||||||
\(244\) | −2.14590 | + | 0.635955i | −0.137377 | + | 0.0407128i | ||||
\(245\) | 15.6525 | 1.00000 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.4030i | 1.80724i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.26986 | − | 15.6476i | −0.143559 | − | 0.989642i | ||||
\(251\) | 26.1534i | 1.65079i | 0.564557 | + | 0.825394i | \(0.309047\pi\) | ||||
−0.564557 | + | 0.825394i | \(0.690953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 30.3276 | − | 4.39936i | 1.90292 | − | 0.276040i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.50000 | − | 14.6202i | 0.406250 | − | 0.913762i | ||||
\(257\) | −24.7568 | −1.54428 | −0.772142 | − | 0.635450i | \(-0.780815\pi\) | ||||
−0.772142 | + | 0.635450i | \(0.780815\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −27.9398 | + | 8.28018i | −1.73275 | + | 0.513515i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 27.2825 | − | 3.95764i | 1.68552 | − | 0.244504i | ||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 7.91224 | + | 17.1540i | 0.486965 | + | 1.05575i | ||||
\(265\) | −11.3886 | −0.699599 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.78894 | − | 26.2822i | −0.475785 | − | 1.60544i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | −16.6496 | + | 2.41520i | −1.01326 | + | 0.146985i | ||||
\(271\) | 22.3998i | 1.36069i | 0.732892 | + | 0.680345i | \(0.238170\pi\) | ||||
−0.732892 | + | 0.680345i | \(0.761830\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 29.7558i | − | 1.79434i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | −12.2615 | + | 1.77866i | −0.735395 | + | 0.106677i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.9387 | 0.647951 | ||||||||
\(286\) | −54.2729 | + | 7.87289i | −3.20922 | + | 0.465534i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.49414 | + | 7.40018i | 0.382671 | + | 0.436060i | ||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.0720i | 0.766295i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −34.2340 | −1.99997 | −0.999987 | − | 0.00505234i | \(-0.998392\pi\) | ||||
−0.999987 | + | 0.00505234i | \(0.998392\pi\) | |||||||
\(294\) | −10.9950 | + | 1.59494i | −0.641239 | + | 0.0930189i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.49614 | + | 20.5879i | 0.551952 | + | 1.19665i | ||||
\(297\) | −31.6612 | −1.83717 | ||||||||
\(298\) | 1.69765 | + | 11.7030i | 0.0983422 | + | 0.677936i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.18889 | + | 10.7603i | 0.184111 | + | 0.621244i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 22.5366i | − | 1.29469i | ||||||
\(304\) | −9.50000 | − | 14.6202i | −0.544862 | − | 0.838525i | ||||
\(305\) | −2.50233 | −0.143283 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.35100i | 0.0771055i | 0.999257 | + | 0.0385528i | \(0.0122748\pi\) | ||||
−0.999257 | + | 0.0385528i | \(0.987725\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.3150 | −1.26945 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 16.1170i | − | 0.913910i | −0.889490 | − | 0.456955i | \(-0.848940\pi\) | ||
0.889490 | − | 0.456955i | \(-0.151060\pi\) | |||||||
\(312\) | 18.7824 | − | 8.66333i | 1.06334 | − | 0.490465i | ||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.2999 | 0.915496 | 0.457748 | − | 0.889082i | \(-0.348656\pi\) | ||||
0.457748 | + | 0.889082i | \(0.348656\pi\) | |||||||
\(318\) | 7.99987 | − | 1.16047i | 0.448610 | − | 0.0650759i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 11.6122 | − | 13.6072i | 0.649144 | − | 0.760665i | ||||
\(321\) | 4.11655 | 0.229763 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.43683 | − | 0.425816i | 0.0798239 | − | 0.0236565i | ||||
\(325\) | −32.5805 | −1.80724 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.03203 | + | 20.9018i | 0.166908 | + | 1.15060i | ||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.9515 | −0.764539 | ||||||||
\(334\) | 24.0448 | − | 3.48796i | 1.31567 | − | 0.190853i | ||||
\(335\) | − | 30.6476i | − | 1.67446i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.64356 | −0.0895307 | −0.0447653 | − | 0.998998i | \(-0.514254\pi\) | ||||
−0.0447653 | + | 0.998998i | \(0.514254\pi\) | |||||||
\(338\) | 5.98096 | + | 41.2306i | 0.325321 | + | 2.24265i | ||||
\(339\) | − | 23.7615i | − | 1.29055i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 10.6179 | − | 1.54024i | 0.574150 | − | 0.0832868i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.62823 | + | 31.9054i | 0.248815 | + | 1.71525i | ||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.4164 | 0.718164 | 0.359082 | − | 0.933306i | \(-0.383090\pi\) | ||||
0.359082 | + | 0.933306i | \(0.383090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 34.6667i | 1.85037i | ||||||||
\(352\) | 25.3032 | − | 22.2052i | 1.34867 | − | 1.18354i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.0193i | 1.47880i | 0.673265 | + | 0.739401i | \(0.264891\pi\) | ||||
−0.673265 | + | 0.739401i | \(0.735109\pi\) | |||||||
\(360\) | 4.61050 | + | 9.99569i | 0.242995 | + | 0.526819i | ||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 27.4021i | 1.43824i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.75774 | − | 0.254980i | 0.0918786 | − | 0.0133280i | ||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.63900 | + | 25.0860i | 0.189183 | + | 1.30416i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.3113 | 1.62124 | 0.810619 | − | 0.585575i | \(-0.199131\pi\) | ||||
0.810619 | + | 0.585575i | \(0.199131\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.5475i | 0.647951i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | −5.53897 | − | 18.6901i | −0.284143 | − | 0.958782i | ||||
\(381\) | −24.3191 | −1.24591 | ||||||||
\(382\) | 36.6034 | − | 5.30972i | 1.87279 | − | 0.271669i | ||||
\(383\) | − | 29.9215i | − | 1.52892i | −0.644671 | − | 0.764460i | \(-0.723006\pi\) | ||
0.644671 | − | 0.764460i | \(-0.276994\pi\) | |||||||
\(384\) | −6.77040 | + | 10.7415i | −0.345501 | + | 0.548151i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.61956 | + | 38.7393i | 0.286028 | + | 1.97178i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 22.3352 | − | 6.61922i | 1.13390 | − | 0.336040i | ||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 22.8859 | − | 3.31986i | 1.15887 | − | 0.168108i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 8.29263 | + | 17.9787i | 0.418841 | + | 0.908060i | ||||
\(393\) | −21.8773 | −1.10357 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.88624 | + | 19.8619i | 0.295795 | + | 0.998098i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | −12.2011 | + | 1.76991i | −0.611587 | + | 0.0887175i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.7705 | − | 10.8972i | 0.838525 | − | 0.544862i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 3.12290 | + | 21.5282i | 0.155756 | + | 1.07373i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −38.5066 | + | 11.4117i | −1.91577 | + | 0.567756i | ||||
\(405\) | 1.67548 | 0.0832555 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 47.7041i | 2.36460i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.2995 | + | 38.1279i | 0.556688 | + | 1.87843i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −24.3131 | − | 27.7052i | −1.19205 | − | 1.35836i | ||||
\(417\) | 9.83225 | 0.481487 | ||||||||
\(418\) | −5.26651 | − | 36.3055i | −0.257593 | − | 1.77576i | ||||
\(419\) | − | 19.4936i | − | 0.952324i | −0.879358 | − | 0.476162i | \(-0.842028\pi\) | ||
0.879358 | − | 0.476162i | \(-0.157972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.03366 | − | 13.0812i | −0.293021 | − | 0.635277i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.08448 | − | 7.03364i | −0.100757 | − | 0.339984i | ||||
\(429\) | 43.5204 | 2.10118 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −11.5950 | − | 17.8444i | −0.557866 | − | 0.858538i | ||||
\(433\) | −37.4530 | −1.79988 | −0.899939 | − | 0.436015i | \(-0.856389\pi\) | ||||
−0.899939 | + | 0.436015i | \(0.856389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 34.1780 | − | 15.7645i | 1.62937 | − | 0.751545i | ||||
\(441\) | −12.1833 | −0.580159 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | −5.11238 | − | 17.2507i | −0.242623 | − | 0.818680i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −20.9034 | + | 3.03227i | −0.989803 | + | 0.143582i | ||||
\(447\) | − | 9.38441i | − | 0.443867i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 1.76678 | + | 12.1796i | 0.0832868 | + | 0.574150i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −40.5996 | + | 12.0320i | −1.90964 | + | 0.565939i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26.2069 | − | 3.80160i | 1.22995 | − | 0.178418i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.79527 | + | 12.5643i | 0.271389 | + | 0.588378i | ||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | −6.00174 | − | 41.3739i | −0.280443 | − | 1.93327i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 21.7474 | − | 6.44501i | 1.00527 | − | 0.297921i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 21.7945i | − | 1.00000i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.86453 | 0.405879 | ||||||||
\(478\) | −27.2825 | + | 3.95764i | −1.24787 | + | 0.181018i | ||||
\(479\) | 7.68770i | 0.351260i | 0.984456 | + | 0.175630i | \(0.0561962\pi\) | ||||
−0.984456 | + | 0.175630i | \(0.943804\pi\) | |||||||
\(480\) | −10.6699 | + | 9.36356i | −0.487013 | + | 0.427386i | ||||
\(481\) | 52.2325 | 2.38160 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 46.8200 | − | 13.8755i | 2.12818 | − | 0.630705i | ||||
\(485\) | 26.0450 | 1.18264 | ||||||||
\(486\) | 21.1608 | − | 3.06961i | 0.959874 | − | 0.139240i | ||||
\(487\) | − | 32.2386i | − | 1.46087i | −0.682983 | − | 0.730434i | \(-0.739318\pi\) | ||
0.682983 | − | 0.730434i | \(-0.260682\pi\) | |||||||
\(488\) | −1.32573 | − | 2.87421i | −0.0600128 | − | 0.130109i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.17780 | + | 21.9067i | 0.143559 | + | 0.989642i | ||||
\(491\) | 26.1534i | 1.18029i | 0.807299 | + | 0.590143i | \(0.200929\pi\) | ||||
−0.807299 | + | 0.590143i | \(0.799071\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −39.7519 | + | 5.76645i | −1.78852 | + | 0.259445i | ||||
\(495\) | 23.1609i | 1.04101i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 44.4679i | − | 1.99066i | −0.0965389 | − | 0.995329i | \(-0.530777\pi\) | ||
0.0965389 | − | 0.995329i | \(-0.469223\pi\) | |||||||
\(500\) | 21.4390 | − | 6.35363i | 0.958782 | − | 0.284143i | ||||
\(501\) | −19.2811 | −0.861414 | ||||||||
\(502\) | −36.6034 | + | 5.30972i | −1.63369 | + | 0.236985i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −44.9025 | −1.99813 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 33.0620i | − | 1.46834i | ||||||
\(508\) | 12.3144 | + | 41.5523i | 0.546362 | + | 1.84359i | ||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 21.7816 | + | 6.12895i | 0.962618 | + | 0.270864i | ||||
\(513\) | −23.1901 | −1.02387 | ||||||||
\(514\) | −5.02618 | − | 34.6487i | −0.221695 | − | 1.52829i | ||||
\(515\) | 44.4609i | 1.95918i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 25.5843i | − | 1.12303i | ||||||
\(520\) | −17.2610 | − | 37.4224i | −0.756947 | − | 1.64108i | ||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.9718i | 1.74784i | 0.486066 | + | 0.873922i | \(0.338432\pi\) | ||||
−0.486066 | + | 0.873922i | \(0.661568\pi\) | |||||||
\(524\) | 11.0779 | + | 37.3802i | 0.483942 | + | 1.63296i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −22.4017 | + | 14.5563i | −0.974910 | + | 0.633483i | ||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | −2.31215 | − | 15.9391i | −0.100433 | − | 0.692352i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 8.20192i | − | 0.354600i | ||||||
\(536\) | 35.2023 | − | 16.2370i | 1.52051 | − | 0.701332i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41.6582i | 1.79434i | ||||||||
\(540\) | −6.76047 | − | 22.8118i | −0.290924 | − | 0.981664i | ||||
\(541\) | 27.3238 | 1.17474 | 0.587371 | − | 0.809318i | \(-0.300163\pi\) | ||||
0.587371 | + | 0.809318i | \(0.300163\pi\) | |||||||
\(542\) | −31.3500 | + | 4.54766i | −1.34660 | + | 0.195339i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 46.7055i | − | 1.99698i | −0.0549052 | − | 0.998492i | \(-0.517486\pi\) | ||
0.0549052 | − | 0.998492i | \(-0.482514\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.94773 | 0.0831269 | ||||||||
\(550\) | 41.6452 | − | 6.04110i | 1.77576 | − | 0.257593i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 20.1160i | − | 0.853875i | ||||||
\(556\) | −4.97871 | − | 16.7996i | −0.211144 | − | 0.712463i | ||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 37.7272i | − | 1.59001i | −0.606601 | − | 0.795007i | \(-0.707467\pi\) | ||
0.606601 | − | 0.795007i | \(-0.292533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −47.3431 | −1.99174 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 2.22080 | + | 15.3094i | 0.0930189 | + | 0.641239i | ||||
\(571\) | 26.9461i | 1.12766i | 0.825891 | + | 0.563829i | \(0.190672\pi\) | ||||
−0.825891 | + | 0.563829i | \(0.809328\pi\) | |||||||
\(572\) | −22.0372 | − | 74.3601i | −0.921423 | − | 3.10915i | ||||
\(573\) | −29.3515 | −1.22618 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −9.03857 | + | 10.5914i | −0.376607 | + | 0.441307i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 3.45138 | + | 23.7926i | 0.143559 | + | 0.989642i | ||||
\(579\) | − | 31.0643i | − | 1.29099i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −18.2951 | + | 2.65391i | −0.758358 | + | 0.110008i | ||||
\(583\) | − | 30.3102i | − | 1.25532i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 25.3595 | 1.04849 | ||||||||
\(586\) | −6.95028 | − | 47.9128i | −0.287113 | − | 1.97926i | ||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −4.46445 | − | 15.0644i | −0.184111 | − | 0.621244i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −26.8862 | + | 17.4703i | −1.10502 | + | 0.718024i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | −6.42793 | − | 44.3119i | −0.263741 | − | 1.81814i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.0344 | + | 4.75194i | −0.656796 | + | 0.194647i | ||||
\(597\) | 9.78385 | 0.400426 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | −14.4123 | + | 6.64763i | −0.588378 | + | 0.271389i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.8550i | 0.971452i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 54.5967 | 2.21967 | ||||||||
\(606\) | 31.5414 | − | 4.57543i | 1.28128 | − | 0.185864i | ||||
\(607\) | 47.2956i | 1.91967i | 0.280568 | + | 0.959834i | \(0.409477\pi\) | ||||
−0.280568 | + | 0.959834i | \(0.590523\pi\) | |||||||
\(608\) | 18.5332 | − | 16.2641i | 0.751620 | − | 0.659596i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.508029 | − | 3.50217i | −0.0205695 | − | 0.141799i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | −1.89081 | + | 0.274283i | −0.0763069 | + | 0.0110692i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | −4.53044 | − | 31.2313i | −0.182241 | − | 1.25631i | ||||
\(619\) | − | 35.3754i | − | 1.42186i | −0.703265 | − | 0.710928i | \(-0.748275\pi\) | ||
0.703265 | − | 0.710928i | \(-0.251725\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.5568 | − | 3.27211i | 0.904444 | − | 0.131200i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 15.9381 | + | 24.5283i | 0.638036 | + | 0.981917i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29.1127i | 1.16265i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 49.0142i | − | 1.95123i | −0.219499 | − | 0.975613i | \(-0.570442\pi\) | ||
0.219499 | − | 0.975613i | \(-0.429558\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.30925 | + | 22.8128i | 0.131427 | + | 0.906013i | ||||
\(635\) | 48.4541i | 1.92284i | ||||||||
\(636\) | 3.24830 | + | 10.9607i | 0.128804 | + | 0.434621i | ||||
\(637\) | 45.6127 | 1.80724 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 21.4017 | + | 13.4895i | 0.845976 | + | 0.533220i | ||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0.835751 | + | 5.76138i | 0.0329845 | + | 0.227383i | ||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0.887666 | + | 1.92449i | 0.0348708 | + | 0.0756009i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −6.61457 | − | 45.5985i | −0.259445 | − | 1.78852i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.5890i | 1.70316i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | −28.6378 | + | 8.48706i | −1.11473 | + | 0.330358i | ||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.83247 | − | 19.5261i | −0.109756 | − | 0.756620i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 9.76326 | + | 32.9441i | 0.377752 | + | 1.27465i | ||||
\(669\) | 16.7620 | 0.648057 | ||||||||
\(670\) | 42.8933 | − | 6.22215i | 1.65711 | − | 0.240383i | ||||
\(671\) | − | 6.65980i | − | 0.257099i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.4853 | 1.94606 | 0.973032 | − | 0.230671i | \(-0.0740922\pi\) | ||||
0.973032 | + | 0.230671i | \(0.0740922\pi\) | |||||||
\(674\) | −0.333680 | − | 2.30028i | −0.0128529 | − | 0.0886033i | ||||
\(675\) | − | 26.6008i | − | 1.02387i | ||||||
\(676\) | −56.4906 | + | 16.7415i | −2.17272 | + | 0.643903i | ||||
\(677\) | 44.4204 | 1.70721 | 0.853607 | − | 0.520918i | \(-0.174410\pi\) | ||||
0.853607 | + | 0.520918i | \(0.174410\pi\) | |||||||
\(678\) | 33.2558 | − | 4.82413i | 1.27718 | − | 0.185269i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.0148 | −0.805289 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 51.1946i | − | 1.95891i | −0.201667 | − | 0.979454i | \(-0.564636\pi\) | ||
0.201667 | − | 0.979454i | \(-0.435364\pi\) | |||||||
\(684\) | 4.31134 | + | 14.5477i | 0.164848 | + | 0.556246i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.1769i | 1.26578i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.1875 | −1.26434 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 0.331647i | − | 0.0126165i | −0.999980 | − | 0.00630823i | \(-0.997992\pi\) | ||
0.999980 | − | 0.00630823i | \(-0.00200798\pi\) | |||||||
\(692\) | −43.7141 | + | 12.9550i | −1.66176 | + | 0.492476i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 19.5900i | − | 0.743092i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2.72383 | + | 18.7771i | 0.103099 | + | 0.710725i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.5239 | −1.83272 | −0.916360 | − | 0.400354i | \(-0.868887\pi\) | ||||
−0.916360 | + | 0.400354i | \(0.868887\pi\) | |||||||
\(702\) | −48.5183 | + | 7.03812i | −1.83121 | + | 0.265637i | ||||
\(703\) | 34.9406i | 1.31781i | ||||||||
\(704\) | 36.2148 | + | 30.9053i | 1.36490 | + | 1.16479i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.2492 | −1.51159 | −0.755796 | − | 0.654808i | \(-0.772750\pi\) | ||||
−0.755796 | + | 0.654808i | \(0.772750\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 86.7112i | − | 3.24281i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.8773 | 0.817024 | ||||||||
\(718\) | −39.2149 | + | 5.68855i | −1.46349 | + | 0.212295i | ||||
\(719\) | 51.8240i | 1.93271i | 0.257214 | + | 0.966354i | \(0.417195\pi\) | ||||
−0.257214 | + | 0.966354i | \(0.582805\pi\) | |||||||
\(720\) | −13.0536 | + | 8.48204i | −0.486479 | + | 0.316107i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.85743 | − | 26.5917i | −0.143559 | − | 0.989642i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −38.3511 | + | 5.56325i | −1.42334 | + | 0.206472i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.2163 | −0.711716 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.713722 | + | 2.40831i | 0.0263799 | + | 0.0890136i | ||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 17.5665i | − | 0.647951i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 81.5669 | 3.00455 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 8.71780i | − | 0.320689i | −0.987061 | − | 0.160345i | \(-0.948739\pi\) | ||
0.987061 | − | 0.160345i | \(-0.0512606\pi\) | |||||||
\(740\) | −34.3707 | + | 10.1860i | −1.26349 | + | 0.374446i | ||||
\(741\) | 31.8763 | 1.17100 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.3813i | 1.37139i | 0.727890 | + | 0.685693i | \(0.240501\pi\) | ||||
−0.727890 | + | 0.685693i | \(0.759499\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.6977 | −0.685032 | ||||||||
\(746\) | 6.35689 | + | 43.8222i | 0.232742 | + | 1.60444i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −17.5611 | + | 2.54743i | −0.641239 | + | 0.0930189i | ||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.3515 | 1.06963 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 25.0335 | − | 11.5467i | 0.908060 | − | 0.418841i | ||||
\(761\) | 54.3834 | 1.97140 | 0.985699 | − | 0.168518i | \(-0.0538981\pi\) | ||||
0.985699 | + | 0.168518i | \(0.0538981\pi\) | |||||||
\(762\) | −4.93733 | − | 34.0362i | −0.178861 | − | 1.23300i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 14.8626 | + | 50.1508i | 0.537710 | + | 1.81439i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 41.8771 | − | 6.07474i | 1.51308 | − | 0.219489i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −16.4080 | − | 7.29485i | −0.592073 | − | 0.263230i | ||||
\(769\) | 47.1406 | 1.69993 | 0.849967 | − | 0.526836i | \(-0.176622\pi\) | ||||
0.849967 | + | 0.526836i | \(0.176622\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.7841i | 1.00062i | ||||||||
\(772\) | −53.0772 | + | 15.7299i | −1.91029 | + | 0.566131i | ||||
\(773\) | 13.0516 | 0.469433 | 0.234717 | − | 0.972064i | \(-0.424584\pi\) | ||||
0.234717 | + | 0.972064i | \(0.424584\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.7986 | + | 29.9157i | 0.495340 | + | 1.07391i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.21813 | + | 8.39739i | 0.0436722 | + | 0.301061i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 9.29272 | + | 31.3564i | 0.332733 | + | 1.12274i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −23.4787 | + | 15.2561i | −0.838525 | + | 0.544862i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.44159 | − | 30.6188i | −0.158426 | − | 1.09214i | ||||
\(787\) | 53.4392i | 1.90490i | 0.304692 | + | 0.952451i | \(0.401447\pi\) | ||||
−0.304692 | + | 0.952451i | \(0.598553\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −26.6030 | + | 12.2706i | −0.945296 | + | 0.436016i | ||||
\(793\) | −7.29201 | −0.258947 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.7813i | 0.453306i | ||||||||
\(796\) | −4.95420 | − | 16.7169i | −0.175597 | − | 0.592516i | ||||
\(797\) | −13.8614 | −0.490997 | −0.245499 | − | 0.969397i | \(-0.578952\pi\) | ||||
−0.245499 | + | 0.969397i | \(0.578952\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 18.6562 | + | 21.2590i | 0.659596 | + | 0.751620i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −29.4961 | + | 8.74140i | −1.04025 | + | 0.308286i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23.7892 | − | 51.5756i | −0.836900 | − | 1.81442i | ||||
\(809\) | 22.3607 | 0.786160 | 0.393080 | − | 0.919504i | \(-0.371410\pi\) | ||||
0.393080 | + | 0.919504i | \(0.371410\pi\) | |||||||
\(810\) | 0.340161 | + | 2.34495i | 0.0119520 | + | 0.0823931i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.1389 | 0.881661 | ||||||||
\(814\) | −66.7649 | + | 9.68499i | −2.34011 | + | 0.339459i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.0000 | −1.46581 | −0.732905 | − | 0.680331i | \(-0.761836\pi\) | ||||
−0.732905 | + | 0.680331i | \(0.761836\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | −51.0685 | + | 23.5553i | −1.77905 | + | 0.820586i | ||||
\(825\) | −33.3945 | −1.16265 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.9935i | 1.07775i | 0.842386 | + | 0.538875i | \(0.181151\pi\) | ||||
−0.842386 | + | 0.538875i | \(0.818849\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 33.8391 | − | 39.6526i | 1.17316 | − | 1.37471i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.99617 | + | 13.7609i | 0.0691216 | + | 0.476500i | ||||
\(835\) | 38.4161i | 1.32944i | ||||||||
\(836\) | 49.7426 | − | 14.7416i | 1.72039 | − | 0.509851i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.2825 | − | 3.95764i | 0.942460 | − | 0.136714i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −65.8736 | −2.26612 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17.0830 | − | 11.1003i | 0.586631 | − | 0.381185i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.9641i | 0.580159i | ||||||||
\(856\) | 9.42084 | − | 4.34535i | 0.321998 | − | 0.148521i | ||||
\(857\) | 33.5250 | 1.14519 | 0.572597 | − | 0.819837i | \(-0.305936\pi\) | ||||
0.572597 | + | 0.819837i | \(0.305936\pi\) | |||||||
\(858\) | 8.83562 | + | 60.9096i | 0.301643 | + | 2.07942i | ||||
\(859\) | 58.4808i | 1.99534i | 0.0682391 | + | 0.997669i | \(0.478262\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 3.71278i | − | 0.126385i | −0.998001 | − | 0.0631923i | \(-0.979872\pi\) | ||
0.998001 | − | 0.0631923i | \(-0.0201281\pi\) | |||||||
\(864\) | 22.6203 | − | 19.8508i | 0.769558 | − | 0.675338i | ||||
\(865\) | −50.9749 | −1.73320 | ||||||||
\(866\) | −7.60381 | − | 52.4180i | −0.258388 | − | 1.78124i | ||||
\(867\) | − | 19.0788i | − | 0.647951i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 89.3098i | − | 3.02615i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.2726 | −0.686122 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.752363 | −0.0254055 | −0.0127028 | − | 0.999919i | \(-0.504044\pi\) | ||||
−0.0127028 | + | 0.999919i | \(0.504044\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.4203i | 1.29589i | ||||||||
\(880\) | 29.0024 | + | 44.6338i | 0.977671 | + | 1.50460i | ||||
\(881\) | 9.21678 | 0.310521 | 0.155261 | − | 0.987874i | \(-0.450378\pi\) | ||||
0.155261 | + | 0.987874i | \(0.450378\pi\) | |||||||
\(882\) | −2.47349 | − | 17.0514i | −0.0832868 | − | 0.574150i | ||||
\(883\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 52.3146i | − | 1.75655i | −0.478154 | − | 0.878276i | \(-0.658694\pi\) | ||
0.478154 | − | 0.878276i | \(-0.341306\pi\) | |||||||
\(888\) | 23.1055 | − | 10.6574i | 0.775369 | − | 0.357638i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.45921i | 0.149389i | ||||||||
\(892\) | −8.48771 | − | 28.6400i | −0.284189 | − | 0.958938i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 13.1341 | − | 1.90524i | 0.439270 | − | 0.0637209i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −16.6874 | + | 4.94545i | −0.556246 | + | 0.164848i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −25.0822 | − | 54.3790i | −0.834223 | − | 1.80862i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 28.7630i | − | 0.955061i | −0.878615 | − | 0.477531i | \(-0.841532\pi\) | ||
0.878615 | − | 0.477531i | \(-0.158468\pi\) | |||||||
\(908\) | 10.6412 | + | 35.9064i | 0.353140 | + | 1.19160i | ||||
\(909\) | 34.9505 | 1.15924 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | −16.4080 | + | 10.6617i | −0.543323 | + | 0.353044i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.80832i | 0.0928403i | ||||||||
\(916\) | 56.6869 | − | 16.7996i | 1.87299 | − | 0.555076i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 58.4808i | − | 1.92910i | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||
0.263896 | − | 0.964551i | \(-0.414993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.51620 | 0.0499606 | ||||||||
\(922\) | −3.65440 | − | 25.1922i | −0.120351 | − | 0.829660i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.0796 | −1.31781 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 34.6069i | − | 1.13664i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.3050 | −1.02708 | −0.513541 | − | 0.858065i | \(-0.671667\pi\) | ||||
−0.513541 | + | 0.858065i | \(0.671667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.5123i | 1.00000i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.0878 | −0.592169 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13.4354 | + | 29.1283i | 0.439150 | + | 0.952090i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 30.5028 | − | 4.42477i | 0.989642 | − | 0.143559i | ||||
\(951\) | − | 18.2932i | − | 0.593197i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.80217 | −0.187951 | −0.0939754 | − | 0.995575i | \(-0.529957\pi\) | ||||
−0.0939754 | + | 0.995575i | \(0.529957\pi\) | |||||||
\(954\) | 1.79970 | + | 12.4065i | 0.0582673 | + | 0.401675i | ||||
\(955\) | 58.4808i | 1.89239i | ||||||||
\(956\) | −11.0779 | − | 37.3802i | −0.358286 | − | 1.20896i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.7594 | + | 1.56077i | −0.347621 | + | 0.0504263i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −15.2711 | − | 13.0322i | −0.492874 | − | 0.420614i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 10.6044 | + | 73.1028i | 0.341899 | + | 2.35693i | ||||
\(963\) | 6.38409i | 0.205724i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −61.8933 | −1.99242 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(968\) | 28.9252 | + | 62.7106i | 0.929691 | + | 2.01560i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.28772 | + | 36.4517i | 0.169779 | + | 1.17039i | ||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 8.59224 | + | 28.9927i | 0.275596 | + | 0.929942i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 45.1200 | − | 6.54515i | 1.44574 | − | 0.209720i | ||||
\(975\) | 36.5646i | 1.17100i | ||||||||
\(976\) | 3.75349 | − | 2.43897i | 0.120146 | − | 0.0780695i | ||||
\(977\) | −60.2691 | −1.92818 | −0.964090 | − | 0.265577i | \(-0.914438\pi\) | ||||
−0.964090 | + | 0.265577i | \(0.914438\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −30.0146 | + | 8.89508i | −0.958782 | + | 0.284143i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −36.6034 | + | 5.30972i | −1.16806 | + | 0.169440i | ||||
\(983\) | 0.192493i | 0.00613957i | 0.999995 | + | 0.00306979i | \(0.000977145\pi\) | ||||
−0.999995 | + | 0.00306979i | \(0.999023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.1410 | − | 54.4646i | −0.513515 | − | 1.73275i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −32.4152 | + | 4.70219i | −1.03022 | + | 0.149445i | ||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 19.4936i | − | 0.617988i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 62.2358 | − | 9.02799i | 1.97004 | − | 0.285776i | ||||
\(999\) | 42.6460i | 1.34926i |
(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 | 380.2.d.a.379.10 | yes | 16 | |
4.3 | odd | 2 | inner | 380.2.d.a.379.9 | yes | 16 | |
5.4 | even | 2 | inner | 380.2.d.a.379.7 | ✓ | 16 | |
19.18 | odd | 2 | inner | 380.2.d.a.379.7 | ✓ | 16 | |
20.19 | odd | 2 | inner | 380.2.d.a.379.8 | yes | 16 | |
76.75 | even | 2 | inner | 380.2.d.a.379.8 | yes | 16 | |
95.94 | odd | 2 | CM | 380.2.d.a.379.10 | yes | 16 | |
380.379 | even | 2 | inner | 380.2.d.a.379.9 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.d.a.379.7 | ✓ | 16 | 5.4 | even | 2 | inner | |
380.2.d.a.379.7 | ✓ | 16 | 19.18 | odd | 2 | inner | |
380.2.d.a.379.8 | yes | 16 | 20.19 | odd | 2 | inner | |
380.2.d.a.379.8 | yes | 16 | 76.75 | even | 2 | inner | |
380.2.d.a.379.9 | yes | 16 | 4.3 | odd | 2 | inner | |
380.2.d.a.379.9 | yes | 16 | 380.379 | even | 2 | inner | |
380.2.d.a.379.10 | yes | 16 | 1.1 | even | 1 | trivial | |
380.2.d.a.379.10 | yes | 16 | 95.94 | odd | 2 | CM |