Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.1 | ||
Root | \(-1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.v.1351.6 |
$q$-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 \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | − 4.24698i | − 1.60521i | −0.596513 | − | 0.802604i | \(-0.703447\pi\) | ||||
0.596513 | − | 0.802604i | \(-0.296553\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.91185i | 0.576446i | 0.957563 | + | 0.288223i | \(0.0930644\pi\) | ||||
−0.957563 | + | 0.288223i | \(0.906936\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.24698 | −1.13505 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.33513 | 0.808887 | 0.404443 | − | 0.914563i | \(-0.367465\pi\) | ||||
0.404443 | + | 0.914563i | \(0.367465\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | 4.85086i | 1.11286i | 0.830894 | + | 0.556431i | \(0.187830\pi\) | ||||
−0.830894 | + | 0.556431i | \(0.812170\pi\) | |||||||
\(20\) | − 1.00000i | − 0.223607i | ||||||||
\(21\) | 4.24698i | 0.926767i | ||||||||
\(22\) | 1.91185 | 0.407609 | ||||||||
\(23\) | 0.445042 | 0.0927976 | 0.0463988 | − | 0.998923i | \(-0.485225\pi\) | ||||
0.0463988 | + | 0.998923i | \(0.485225\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.24698i | 0.802604i | ||||||||
\(29\) | −8.56465 | −1.59041 | −0.795207 | − | 0.606337i | \(-0.792638\pi\) | ||||
−0.795207 | + | 0.606337i | \(0.792638\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | − 5.29590i | − 0.951171i | −0.879669 | − | 0.475586i | \(-0.842236\pi\) | ||||
0.879669 | − | 0.475586i | \(-0.157764\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 1.91185i | − 0.332811i | ||||||||
\(34\) | − 3.33513i | − 0.571969i | ||||||||
\(35\) | 4.24698 | 0.717871 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 1.75302i | 0.288195i | 0.989564 | + | 0.144097i | \(0.0460279\pi\) | ||||
−0.989564 | + | 0.144097i | \(0.953972\pi\) | |||||||
\(38\) | 4.85086 | 0.786913 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | − 3.24698i | − 0.507093i | −0.967323 | − | 0.253547i | \(-0.918403\pi\) | ||||
0.967323 | − | 0.253547i | \(-0.0815971\pi\) | |||||||
\(42\) | 4.24698 | 0.655323 | ||||||||
\(43\) | 1.97823 | 0.301677 | 0.150839 | − | 0.988558i | \(-0.451803\pi\) | ||||
0.150839 | + | 0.988558i | \(0.451803\pi\) | |||||||
\(44\) | − 1.91185i | − 0.288223i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | − 0.445042i | − 0.0656178i | ||||||||
\(47\) | 10.3840i | 1.51467i | 0.653028 | + | 0.757334i | \(0.273499\pi\) | ||||
−0.653028 | + | 0.757334i | \(0.726501\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −11.0368 | −1.57669 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | −3.33513 | −0.467011 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.14914 | −0.157847 | −0.0789236 | − | 0.996881i | \(-0.525148\pi\) | ||||
−0.0789236 | + | 0.996881i | \(0.525148\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −1.91185 | −0.257794 | ||||||||
\(56\) | 4.24698 | 0.567527 | ||||||||
\(57\) | − 4.85086i | − 0.642511i | ||||||||
\(58\) | 8.56465i | 1.12459i | ||||||||
\(59\) | 13.4601i | 1.75236i | 0.481987 | + | 0.876178i | \(0.339915\pi\) | ||||
−0.481987 | + | 0.876178i | \(0.660085\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | 1.13169 | 0.144898 | 0.0724488 | − | 0.997372i | \(-0.476919\pi\) | ||||
0.0724488 | + | 0.997372i | \(0.476919\pi\) | |||||||
\(62\) | −5.29590 | −0.672580 | ||||||||
\(63\) | − 4.24698i | − 0.535069i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.91185 | −0.235333 | ||||||||
\(67\) | − 13.5308i | − 1.65305i | −0.562900 | − | 0.826525i | \(-0.690314\pi\) | ||||
0.562900 | − | 0.826525i | \(-0.309686\pi\) | |||||||
\(68\) | −3.33513 | −0.404443 | ||||||||
\(69\) | −0.445042 | −0.0535767 | ||||||||
\(70\) | − 4.24698i | − 0.507611i | ||||||||
\(71\) | 2.14675i | 0.254773i | 0.991853 | + | 0.127386i | \(0.0406588\pi\) | ||||
−0.991853 | + | 0.127386i | \(0.959341\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 5.15883i | 0.603796i | 0.953340 | + | 0.301898i | \(0.0976202\pi\) | ||||
−0.953340 | + | 0.301898i | \(0.902380\pi\) | |||||||
\(74\) | 1.75302 | 0.203784 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | − 4.85086i | − 0.556431i | ||||||||
\(77\) | 8.11960 | 0.925315 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.5526 | −1.63729 | −0.818646 | − | 0.574299i | \(-0.805275\pi\) | ||||
−0.818646 | + | 0.574299i | \(0.805275\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.24698 | −0.358569 | ||||||||
\(83\) | 9.49157i | 1.04183i | 0.853607 | + | 0.520917i | \(0.174410\pi\) | ||||
−0.853607 | + | 0.520917i | \(0.825590\pi\) | |||||||
\(84\) | − 4.24698i | − 0.463383i | ||||||||
\(85\) | 3.33513i | 0.361745i | ||||||||
\(86\) | − 1.97823i | − 0.213318i | ||||||||
\(87\) | 8.56465 | 0.918227 | ||||||||
\(88\) | −1.91185 | −0.203804 | ||||||||
\(89\) | − 1.25667i | − 0.133207i | −0.997780 | − | 0.0666033i | \(-0.978784\pi\) | ||||
0.997780 | − | 0.0666033i | \(-0.0212162\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.445042 | −0.0463988 | ||||||||
\(93\) | 5.29590i | 0.549159i | ||||||||
\(94\) | 10.3840 | 1.07103 | ||||||||
\(95\) | −4.85086 | −0.497687 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 5.01507i | 0.509203i | 0.967046 | + | 0.254601i | \(0.0819443\pi\) | ||||
−0.967046 | + | 0.254601i | \(0.918056\pi\) | |||||||
\(98\) | 11.0368i | 1.11489i | ||||||||
\(99\) | 1.91185i | 0.192149i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −14.8116 | −1.47381 | −0.736906 | − | 0.675995i | \(-0.763714\pi\) | ||||
−0.736906 | + | 0.675995i | \(0.763714\pi\) | |||||||
\(102\) | 3.33513i | 0.330227i | ||||||||
\(103\) | 13.6896 | 1.34888 | 0.674440 | − | 0.738330i | \(-0.264385\pi\) | ||||
0.674440 | + | 0.738330i | \(0.264385\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.24698 | −0.414463 | ||||||||
\(106\) | 1.14914i | 0.111615i | ||||||||
\(107\) | −12.8334 | −1.24065 | −0.620326 | − | 0.784344i | \(-0.713000\pi\) | ||||
−0.620326 | + | 0.784344i | \(0.713000\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | − 10.8726i | − 1.04141i | −0.853737 | − | 0.520704i | \(-0.825669\pi\) | ||||
0.853737 | − | 0.520704i | \(-0.174331\pi\) | |||||||
\(110\) | 1.91185i | 0.182288i | ||||||||
\(111\) | − 1.75302i | − 0.166389i | ||||||||
\(112\) | − 4.24698i | − 0.401302i | ||||||||
\(113\) | −11.2295 | −1.05638 | −0.528192 | − | 0.849125i | \(-0.677130\pi\) | ||||
−0.528192 | + | 0.849125i | \(0.677130\pi\) | |||||||
\(114\) | −4.85086 | −0.454324 | ||||||||
\(115\) | 0.445042i | 0.0415004i | ||||||||
\(116\) | 8.56465 | 0.795207 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.4601 | 1.23910 | ||||||||
\(119\) | − 14.1642i | − 1.29843i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 7.34481 | 0.667710 | ||||||||
\(122\) | − 1.13169i | − 0.102458i | ||||||||
\(123\) | 3.24698i | 0.292770i | ||||||||
\(124\) | 5.29590i | 0.475586i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | −4.24698 | −0.378351 | ||||||||
\(127\) | −20.8267 | −1.84807 | −0.924035 | − | 0.382308i | \(-0.875129\pi\) | ||||
−0.924035 | + | 0.382308i | \(0.875129\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −1.97823 | −0.174173 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.5036 | 1.52930 | 0.764650 | − | 0.644445i | \(-0.222912\pi\) | ||||
0.764650 | + | 0.644445i | \(0.222912\pi\) | |||||||
\(132\) | 1.91185i | 0.166406i | ||||||||
\(133\) | 20.6015 | 1.78638 | ||||||||
\(134\) | −13.5308 | −1.16888 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | 3.33513i | 0.285985i | ||||||||
\(137\) | − 0.929312i | − 0.0793965i | −0.999212 | − | 0.0396983i | \(-0.987360\pi\) | ||||
0.999212 | − | 0.0396983i | \(-0.0126397\pi\) | |||||||
\(138\) | 0.445042i | 0.0378845i | ||||||||
\(139\) | 3.12200 | 0.264804 | 0.132402 | − | 0.991196i | \(-0.457731\pi\) | ||||
0.132402 | + | 0.991196i | \(0.457731\pi\) | |||||||
\(140\) | −4.24698 | −0.358935 | ||||||||
\(141\) | − 10.3840i | − 0.874494i | ||||||||
\(142\) | 2.14675 | 0.180151 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 8.56465i | − 0.711255i | ||||||||
\(146\) | 5.15883 | 0.426948 | ||||||||
\(147\) | 11.0368 | 0.910303 | ||||||||
\(148\) | − 1.75302i | − 0.144097i | ||||||||
\(149\) | − 6.57673i | − 0.538787i | −0.963030 | − | 0.269393i | \(-0.913177\pi\) | ||||
0.963030 | − | 0.269393i | \(-0.0868232\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | 6.29590i | 0.512353i | 0.966630 | + | 0.256176i | \(0.0824628\pi\) | ||||
−0.966630 | + | 0.256176i | \(0.917537\pi\) | |||||||
\(152\) | −4.85086 | −0.393456 | ||||||||
\(153\) | 3.33513 | 0.269629 | ||||||||
\(154\) | − 8.11960i | − 0.654296i | ||||||||
\(155\) | 5.29590 | 0.425377 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.9148 | 1.58938 | 0.794689 | − | 0.607017i | \(-0.207634\pi\) | ||||
0.794689 | + | 0.607017i | \(0.207634\pi\) | |||||||
\(158\) | 14.5526i | 1.15774i | ||||||||
\(159\) | 1.14914 | 0.0911331 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | − 1.89008i | − 0.148959i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 13.1075i | 1.02666i | 0.858191 | + | 0.513330i | \(0.171588\pi\) | ||||
−0.858191 | + | 0.513330i | \(0.828412\pi\) | |||||||
\(164\) | 3.24698i | 0.253547i | ||||||||
\(165\) | 1.91185 | 0.148838 | ||||||||
\(166\) | 9.49157 | 0.736688 | ||||||||
\(167\) | 21.5351i | 1.66644i | 0.552944 | + | 0.833218i | \(0.313504\pi\) | ||||
−0.552944 | + | 0.833218i | \(0.686496\pi\) | |||||||
\(168\) | −4.24698 | −0.327662 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3.33513 | 0.255792 | ||||||||
\(171\) | 4.85086i | 0.370954i | ||||||||
\(172\) | −1.97823 | −0.150839 | ||||||||
\(173\) | 13.9541 | 1.06091 | 0.530454 | − | 0.847714i | \(-0.322021\pi\) | ||||
0.530454 | + | 0.847714i | \(0.322021\pi\) | |||||||
\(174\) | − 8.56465i | − 0.649284i | ||||||||
\(175\) | 4.24698i | 0.321041i | ||||||||
\(176\) | 1.91185i | 0.144111i | ||||||||
\(177\) | − 13.4601i | − 1.01172i | ||||||||
\(178\) | −1.25667 | −0.0941913 | ||||||||
\(179\) | −8.32975 | −0.622595 | −0.311297 | − | 0.950313i | \(-0.600764\pi\) | ||||
−0.311297 | + | 0.950313i | \(0.600764\pi\) | |||||||
\(180\) | − 1.00000i | − 0.0745356i | ||||||||
\(181\) | −17.1371 | −1.27379 | −0.636894 | − | 0.770951i | \(-0.719781\pi\) | ||||
−0.636894 | + | 0.770951i | \(0.719781\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.13169 | −0.0836567 | ||||||||
\(184\) | 0.445042i | 0.0328089i | ||||||||
\(185\) | −1.75302 | −0.128885 | ||||||||
\(186\) | 5.29590 | 0.388314 | ||||||||
\(187\) | 6.37627i | 0.466279i | ||||||||
\(188\) | − 10.3840i | − 0.757334i | ||||||||
\(189\) | 4.24698i | 0.308922i | ||||||||
\(190\) | 4.85086i | 0.351918i | ||||||||
\(191\) | 23.1685 | 1.67642 | 0.838208 | − | 0.545351i | \(-0.183604\pi\) | ||||
0.838208 | + | 0.545351i | \(0.183604\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 6.38942i | 0.459920i | 0.973200 | + | 0.229960i | \(0.0738596\pi\) | ||||
−0.973200 | + | 0.229960i | \(0.926140\pi\) | |||||||
\(194\) | 5.01507 | 0.360061 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.0368 | 0.788345 | ||||||||
\(197\) | 14.8605i | 1.05877i | 0.848382 | + | 0.529385i | \(0.177577\pi\) | ||||
−0.848382 | + | 0.529385i | \(0.822423\pi\) | |||||||
\(198\) | 1.91185 | 0.135870 | ||||||||
\(199\) | −26.3860 | −1.87045 | −0.935226 | − | 0.354052i | \(-0.884803\pi\) | ||||
−0.935226 | + | 0.354052i | \(0.884803\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | 13.5308i | 0.954389i | ||||||||
\(202\) | 14.8116i | 1.04214i | ||||||||
\(203\) | 36.3739i | 2.55295i | ||||||||
\(204\) | 3.33513 | 0.233505 | ||||||||
\(205\) | 3.24698 | 0.226779 | ||||||||
\(206\) | − 13.6896i | − 0.953802i | ||||||||
\(207\) | 0.445042 | 0.0309325 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.27413 | −0.641505 | ||||||||
\(210\) | 4.24698i | 0.293069i | ||||||||
\(211\) | 17.4383 | 1.20050 | 0.600252 | − | 0.799811i | \(-0.295067\pi\) | ||||
0.600252 | + | 0.799811i | \(0.295067\pi\) | |||||||
\(212\) | 1.14914 | 0.0789236 | ||||||||
\(213\) | − 2.14675i | − 0.147093i | ||||||||
\(214\) | 12.8334i | 0.877273i | ||||||||
\(215\) | 1.97823i | 0.134914i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | −22.4916 | −1.52683 | ||||||||
\(218\) | −10.8726 | −0.736387 | ||||||||
\(219\) | − 5.15883i | − 0.348602i | ||||||||
\(220\) | 1.91185 | 0.128897 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.75302 | −0.117655 | ||||||||
\(223\) | 9.95838i | 0.666862i | 0.942774 | + | 0.333431i | \(0.108206\pi\) | ||||
−0.942774 | + | 0.333431i | \(0.891794\pi\) | |||||||
\(224\) | −4.24698 | −0.283763 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 11.2295i | 0.746977i | ||||||||
\(227\) | 19.6112i | 1.30164i | 0.759232 | + | 0.650820i | \(0.225575\pi\) | ||||
−0.759232 | + | 0.650820i | \(0.774425\pi\) | |||||||
\(228\) | 4.85086i | 0.321256i | ||||||||
\(229\) | − 8.72886i | − 0.576819i | −0.957507 | − | 0.288410i | \(-0.906874\pi\) | ||||
0.957507 | − | 0.288410i | \(-0.0931265\pi\) | |||||||
\(230\) | 0.445042 | 0.0293452 | ||||||||
\(231\) | −8.11960 | −0.534231 | ||||||||
\(232\) | − 8.56465i | − 0.562297i | ||||||||
\(233\) | −0.975837 | −0.0639292 | −0.0319646 | − | 0.999489i | \(-0.510176\pi\) | ||||
−0.0319646 | + | 0.999489i | \(0.510176\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.3840 | −0.677380 | ||||||||
\(236\) | − 13.4601i | − 0.876178i | ||||||||
\(237\) | 14.5526 | 0.945291 | ||||||||
\(238\) | −14.1642 | −0.918129 | ||||||||
\(239\) | 7.39373i | 0.478261i | 0.970987 | + | 0.239130i | \(0.0768623\pi\) | ||||
−0.970987 | + | 0.239130i | \(0.923138\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | − 2.11529i | − 0.136258i | −0.997677 | − | 0.0681290i | \(-0.978297\pi\) | ||||
0.997677 | − | 0.0681290i | \(-0.0217029\pi\) | |||||||
\(242\) | − 7.34481i | − 0.472143i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.13169 | −0.0724488 | ||||||||
\(245\) | − 11.0368i | − 0.705118i | ||||||||
\(246\) | 3.24698 | 0.207020 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.29590 | 0.336290 | ||||||||
\(249\) | − 9.49157i | − 0.601504i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 1.62863 | 0.102798 | 0.0513991 | − | 0.998678i | \(-0.483632\pi\) | ||||
0.0513991 | + | 0.998678i | \(0.483632\pi\) | |||||||
\(252\) | 4.24698i | 0.267535i | ||||||||
\(253\) | 0.850855i | 0.0534928i | ||||||||
\(254\) | 20.8267i | 1.30678i | ||||||||
\(255\) | − 3.33513i | − 0.208854i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.87263 | 0.553459 | 0.276730 | − | 0.960948i | \(-0.410749\pi\) | ||||
0.276730 | + | 0.960948i | \(0.410749\pi\) | |||||||
\(258\) | 1.97823i | 0.123159i | ||||||||
\(259\) | 7.44504 | 0.462612 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.56465 | −0.530138 | ||||||||
\(262\) | − 17.5036i | − 1.08138i | ||||||||
\(263\) | 22.4185 | 1.38238 | 0.691192 | − | 0.722672i | \(-0.257086\pi\) | ||||
0.691192 | + | 0.722672i | \(0.257086\pi\) | |||||||
\(264\) | 1.91185 | 0.117666 | ||||||||
\(265\) | − 1.14914i | − 0.0705914i | ||||||||
\(266\) | − 20.6015i | − 1.26316i | ||||||||
\(267\) | 1.25667i | 0.0769068i | ||||||||
\(268\) | 13.5308i | 0.826525i | ||||||||
\(269\) | 26.9071 | 1.64055 | 0.820276 | − | 0.571967i | \(-0.193820\pi\) | ||||
0.820276 | + | 0.571967i | \(0.193820\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 31.7265i | 1.92725i | 0.267266 | + | 0.963623i | \(0.413880\pi\) | ||||
−0.267266 | + | 0.963623i | \(0.586120\pi\) | |||||||
\(272\) | 3.33513 | 0.202222 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.929312 | −0.0561418 | ||||||||
\(275\) | − 1.91185i | − 0.115289i | ||||||||
\(276\) | 0.445042 | 0.0267884 | ||||||||
\(277\) | 30.6069 | 1.83899 | 0.919494 | − | 0.393104i | \(-0.128599\pi\) | ||||
0.919494 | + | 0.393104i | \(0.128599\pi\) | |||||||
\(278\) | − 3.12200i | − 0.187245i | ||||||||
\(279\) | − 5.29590i | − 0.317057i | ||||||||
\(280\) | 4.24698i | 0.253806i | ||||||||
\(281\) | 16.6649i | 0.994143i | 0.867710 | + | 0.497072i | \(0.165591\pi\) | ||||
−0.867710 | + | 0.497072i | \(0.834409\pi\) | |||||||
\(282\) | −10.3840 | −0.618361 | ||||||||
\(283\) | 4.32304 | 0.256978 | 0.128489 | − | 0.991711i | \(-0.458987\pi\) | ||||
0.128489 | + | 0.991711i | \(0.458987\pi\) | |||||||
\(284\) | − 2.14675i | − 0.127386i | ||||||||
\(285\) | 4.85086 | 0.287340 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.7899 | −0.813989 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −5.87694 | −0.345702 | ||||||||
\(290\) | −8.56465 | −0.502933 | ||||||||
\(291\) | − 5.01507i | − 0.293988i | ||||||||
\(292\) | − 5.15883i | − 0.301898i | ||||||||
\(293\) | 5.62804i | 0.328794i | 0.986394 | + | 0.164397i | \(0.0525677\pi\) | ||||
−0.986394 | + | 0.164397i | \(0.947432\pi\) | |||||||
\(294\) | − 11.0368i | − 0.643681i | ||||||||
\(295\) | −13.4601 | −0.783678 | ||||||||
\(296\) | −1.75302 | −0.101892 | ||||||||
\(297\) | − 1.91185i | − 0.110937i | ||||||||
\(298\) | −6.57673 | −0.380980 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | − 8.40150i | − 0.484254i | ||||||||
\(302\) | 6.29590 | 0.362288 | ||||||||
\(303\) | 14.8116 | 0.850906 | ||||||||
\(304\) | 4.85086i | 0.278216i | ||||||||
\(305\) | 1.13169i | 0.0648002i | ||||||||
\(306\) | − 3.33513i | − 0.190656i | ||||||||
\(307\) | 12.6635i | 0.722747i | 0.932421 | + | 0.361373i | \(0.117692\pi\) | ||||
−0.932421 | + | 0.361373i | \(0.882308\pi\) | |||||||
\(308\) | −8.11960 | −0.462657 | ||||||||
\(309\) | −13.6896 | −0.778776 | ||||||||
\(310\) | − 5.29590i | − 0.300787i | ||||||||
\(311\) | −8.49635 | −0.481784 | −0.240892 | − | 0.970552i | \(-0.577440\pi\) | ||||
−0.240892 | + | 0.970552i | \(0.577440\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.2610 | −1.42784 | −0.713918 | − | 0.700230i | \(-0.753081\pi\) | ||||
−0.713918 | + | 0.700230i | \(0.753081\pi\) | |||||||
\(314\) | − 19.9148i | − 1.12386i | ||||||||
\(315\) | 4.24698 | 0.239290 | ||||||||
\(316\) | 14.5526 | 0.818646 | ||||||||
\(317\) | − 4.96615i | − 0.278927i | −0.990227 | − | 0.139463i | \(-0.955462\pi\) | ||||
0.990227 | − | 0.139463i | \(-0.0445377\pi\) | |||||||
\(318\) | − 1.14914i | − 0.0644408i | ||||||||
\(319\) | − 16.3744i | − 0.916788i | ||||||||
\(320\) | − 1.00000i | − 0.0559017i | ||||||||
\(321\) | 12.8334 | 0.716290 | ||||||||
\(322\) | −1.89008 | −0.105330 | ||||||||
\(323\) | 16.1782i | 0.900180i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.1075 | 0.725959 | ||||||||
\(327\) | 10.8726i | 0.601258i | ||||||||
\(328\) | 3.24698 | 0.179284 | ||||||||
\(329\) | 44.1008 | 2.43136 | ||||||||
\(330\) | − 1.91185i | − 0.105244i | ||||||||
\(331\) | 35.3749i | 1.94438i | 0.234188 | + | 0.972191i | \(0.424757\pi\) | ||||
−0.234188 | + | 0.972191i | \(0.575243\pi\) | |||||||
\(332\) | − 9.49157i | − 0.520917i | ||||||||
\(333\) | 1.75302i | 0.0960649i | ||||||||
\(334\) | 21.5351 | 1.17835 | ||||||||
\(335\) | 13.5308 | 0.739266 | ||||||||
\(336\) | 4.24698i | 0.231692i | ||||||||
\(337\) | 4.70171 | 0.256118 | 0.128059 | − | 0.991767i | \(-0.459125\pi\) | ||||
0.128059 | + | 0.991767i | \(0.459125\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.2295 | 0.609904 | ||||||||
\(340\) | − 3.33513i | − 0.180873i | ||||||||
\(341\) | 10.1250 | 0.548299 | ||||||||
\(342\) | 4.85086 | 0.262304 | ||||||||
\(343\) | 17.1444i | 0.925708i | ||||||||
\(344\) | 1.97823i | 0.106659i | ||||||||
\(345\) | − 0.445042i | − 0.0239602i | ||||||||
\(346\) | − 13.9541i | − 0.750175i | ||||||||
\(347\) | 14.9028 | 0.800022 | 0.400011 | − | 0.916510i | \(-0.369006\pi\) | ||||
0.400011 | + | 0.916510i | \(0.369006\pi\) | |||||||
\(348\) | −8.56465 | −0.459113 | ||||||||
\(349\) | 35.2669i | 1.88780i | 0.330237 | + | 0.943898i | \(0.392871\pi\) | ||||
−0.330237 | + | 0.943898i | \(0.607129\pi\) | |||||||
\(350\) | 4.24698 | 0.227011 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.91185 | 0.101902 | ||||||||
\(353\) | − 10.5574i | − 0.561911i | −0.959721 | − | 0.280956i | \(-0.909349\pi\) | ||||
0.959721 | − | 0.280956i | \(-0.0906514\pi\) | |||||||
\(354\) | −13.4601 | −0.715397 | ||||||||
\(355\) | −2.14675 | −0.113938 | ||||||||
\(356\) | 1.25667i | 0.0666033i | ||||||||
\(357\) | 14.1642i | 0.749650i | ||||||||
\(358\) | 8.32975i | 0.440241i | ||||||||
\(359\) | 28.7724i | 1.51855i | 0.650770 | + | 0.759275i | \(0.274446\pi\) | ||||
−0.650770 | + | 0.759275i | \(0.725554\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −4.53079 | −0.238463 | ||||||||
\(362\) | 17.1371i | 0.900704i | ||||||||
\(363\) | −7.34481 | −0.385503 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.15883 | −0.270026 | ||||||||
\(366\) | 1.13169i | 0.0591542i | ||||||||
\(367\) | −24.1511 | −1.26068 | −0.630338 | − | 0.776321i | \(-0.717084\pi\) | ||||
−0.630338 | + | 0.776321i | \(0.717084\pi\) | |||||||
\(368\) | 0.445042 | 0.0231994 | ||||||||
\(369\) | − 3.24698i | − 0.169031i | ||||||||
\(370\) | 1.75302i | 0.0911352i | ||||||||
\(371\) | 4.88040i | 0.253377i | ||||||||
\(372\) | − 5.29590i | − 0.274579i | ||||||||
\(373\) | −21.0664 | −1.09078 | −0.545388 | − | 0.838184i | \(-0.683618\pi\) | ||||
−0.545388 | + | 0.838184i | \(0.683618\pi\) | |||||||
\(374\) | 6.37627 | 0.329709 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | −10.3840 | −0.535516 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.24698 | 0.218441 | ||||||||
\(379\) | 8.42327i | 0.432674i | 0.976319 | + | 0.216337i | \(0.0694111\pi\) | ||||
−0.976319 | + | 0.216337i | \(0.930589\pi\) | |||||||
\(380\) | 4.85086 | 0.248844 | ||||||||
\(381\) | 20.8267 | 1.06698 | ||||||||
\(382\) | − 23.1685i | − 1.18540i | ||||||||
\(383\) | − 10.6377i | − 0.543562i | −0.962359 | − | 0.271781i | \(-0.912387\pi\) | ||||
0.962359 | − | 0.271781i | \(-0.0876127\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | 8.11960i | 0.413813i | ||||||||
\(386\) | 6.38942 | 0.325213 | ||||||||
\(387\) | 1.97823 | 0.100559 | ||||||||
\(388\) | − 5.01507i | − 0.254601i | ||||||||
\(389\) | 25.7429 | 1.30521 | 0.652607 | − | 0.757696i | \(-0.273675\pi\) | ||||
0.652607 | + | 0.757696i | \(0.273675\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.48427 | 0.0750628 | ||||||||
\(392\) | − 11.0368i | − 0.557444i | ||||||||
\(393\) | −17.5036 | −0.882942 | ||||||||
\(394\) | 14.8605 | 0.748663 | ||||||||
\(395\) | − 14.5526i | − 0.732219i | ||||||||
\(396\) | − 1.91185i | − 0.0960743i | ||||||||
\(397\) | 11.4373i | 0.574020i | 0.957928 | + | 0.287010i | \(0.0926613\pi\) | ||||
−0.957928 | + | 0.287010i | \(0.907339\pi\) | |||||||
\(398\) | 26.3860i | 1.32261i | ||||||||
\(399\) | −20.6015 | −1.03136 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 22.1511i | 1.10617i | 0.833124 | + | 0.553086i | \(0.186550\pi\) | ||||
−0.833124 | + | 0.553086i | \(0.813450\pi\) | |||||||
\(402\) | 13.5308 | 0.674855 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.8116 | 0.736906 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 36.3739 | 1.80521 | ||||||||
\(407\) | −3.35152 | −0.166129 | ||||||||
\(408\) | − 3.33513i | − 0.165113i | ||||||||
\(409\) | 22.0965i | 1.09260i | 0.837589 | + | 0.546301i | \(0.183965\pi\) | ||||
−0.837589 | + | 0.546301i | \(0.816035\pi\) | |||||||
\(410\) | − 3.24698i | − 0.160357i | ||||||||
\(411\) | 0.929312i | 0.0458396i | ||||||||
\(412\) | −13.6896 | −0.674440 | ||||||||
\(413\) | 57.1648 | 2.81290 | ||||||||
\(414\) | − 0.445042i | − 0.0218726i | ||||||||
\(415\) | −9.49157 | −0.465923 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.12200 | −0.152885 | ||||||||
\(418\) | 9.27413i | 0.453612i | ||||||||
\(419\) | 9.03444 | 0.441361 | 0.220681 | − | 0.975346i | \(-0.429172\pi\) | ||||
0.220681 | + | 0.975346i | \(0.429172\pi\) | |||||||
\(420\) | 4.24698 | 0.207231 | ||||||||
\(421\) | − 7.17928i | − 0.349896i | −0.984578 | − | 0.174948i | \(-0.944024\pi\) | ||||
0.984578 | − | 0.174948i | \(-0.0559758\pi\) | |||||||
\(422\) | − 17.4383i | − 0.848885i | ||||||||
\(423\) | 10.3840i | 0.504889i | ||||||||
\(424\) | − 1.14914i | − 0.0558074i | ||||||||
\(425\) | −3.33513 | −0.161777 | ||||||||
\(426\) | −2.14675 | −0.104010 | ||||||||
\(427\) | − 4.80625i | − 0.232591i | ||||||||
\(428\) | 12.8334 | 0.620326 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.97823 | 0.0953987 | ||||||||
\(431\) | − 8.36360i | − 0.402860i | −0.979503 | − | 0.201430i | \(-0.935441\pi\) | ||||
0.979503 | − | 0.201430i | \(-0.0645589\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 12.2851 | 0.590386 | 0.295193 | − | 0.955438i | \(-0.404616\pi\) | ||||
0.295193 | + | 0.955438i | \(0.404616\pi\) | |||||||
\(434\) | 22.4916i | 1.07963i | ||||||||
\(435\) | 8.56465i | 0.410643i | ||||||||
\(436\) | 10.8726i | 0.520704i | ||||||||
\(437\) | 2.15883i | 0.103271i | ||||||||
\(438\) | −5.15883 | −0.246499 | ||||||||
\(439\) | −20.4849 | −0.977689 | −0.488845 | − | 0.872371i | \(-0.662581\pi\) | ||||
−0.488845 | + | 0.872371i | \(0.662581\pi\) | |||||||
\(440\) | − 1.91185i | − 0.0911441i | ||||||||
\(441\) | −11.0368 | −0.525564 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.928247 | −0.0441024 | −0.0220512 | − | 0.999757i | \(-0.507020\pi\) | ||||
−0.0220512 | + | 0.999757i | \(0.507020\pi\) | |||||||
\(444\) | 1.75302i | 0.0831947i | ||||||||
\(445\) | 1.25667 | 0.0595718 | ||||||||
\(446\) | 9.95838 | 0.471543 | ||||||||
\(447\) | 6.57673i | 0.311069i | ||||||||
\(448\) | 4.24698i | 0.200651i | ||||||||
\(449\) | − 22.9355i | − 1.08240i | −0.840895 | − | 0.541198i | \(-0.817971\pi\) | ||||
0.840895 | − | 0.541198i | \(-0.182029\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | 6.20775 | 0.292312 | ||||||||
\(452\) | 11.2295 | 0.528192 | ||||||||
\(453\) | − 6.29590i | − 0.295807i | ||||||||
\(454\) | 19.6112 | 0.920398 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.85086 | 0.227162 | ||||||||
\(457\) | − 10.3773i | − 0.485431i | −0.970097 | − | 0.242716i | \(-0.921962\pi\) | ||||
0.970097 | − | 0.242716i | \(-0.0780382\pi\) | |||||||
\(458\) | −8.72886 | −0.407873 | ||||||||
\(459\) | −3.33513 | −0.155670 | ||||||||
\(460\) | − 0.445042i | − 0.0207502i | ||||||||
\(461\) | − 7.69740i | − 0.358504i | −0.983803 | − | 0.179252i | \(-0.942632\pi\) | ||||
0.983803 | − | 0.179252i | \(-0.0573677\pi\) | |||||||
\(462\) | 8.11960i | 0.377758i | ||||||||
\(463\) | − 39.0640i | − 1.81546i | −0.419558 | − | 0.907729i | \(-0.637815\pi\) | ||||
0.419558 | − | 0.907729i | \(-0.362185\pi\) | |||||||
\(464\) | −8.56465 | −0.397604 | ||||||||
\(465\) | −5.29590 | −0.245591 | ||||||||
\(466\) | 0.975837i | 0.0452048i | ||||||||
\(467\) | −0.916166 | −0.0423951 | −0.0211976 | − | 0.999775i | \(-0.506748\pi\) | ||||
−0.0211976 | + | 0.999775i | \(0.506748\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −57.4650 | −2.65349 | ||||||||
\(470\) | 10.3840i | 0.478980i | ||||||||
\(471\) | −19.9148 | −0.917627 | ||||||||
\(472\) | −13.4601 | −0.619552 | ||||||||
\(473\) | 3.78209i | 0.173901i | ||||||||
\(474\) | − 14.5526i | − 0.668421i | ||||||||
\(475\) | − 4.85086i | − 0.222572i | ||||||||
\(476\) | 14.1642i | 0.649216i | ||||||||
\(477\) | −1.14914 | −0.0526157 | ||||||||
\(478\) | 7.39373 | 0.338181 | ||||||||
\(479\) | − 23.1715i | − 1.05873i | −0.848393 | − | 0.529367i | \(-0.822430\pi\) | ||||
0.848393 | − | 0.529367i | \(-0.177570\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2.11529 | −0.0963490 | ||||||||
\(483\) | 1.89008i | 0.0860018i | ||||||||
\(484\) | −7.34481 | −0.333855 | ||||||||
\(485\) | −5.01507 | −0.227722 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 11.9812i | 0.542921i | 0.962450 | + | 0.271460i | \(0.0875066\pi\) | ||||
−0.962450 | + | 0.271460i | \(0.912493\pi\) | |||||||
\(488\) | 1.13169i | 0.0512290i | ||||||||
\(489\) | − 13.1075i | − 0.592743i | ||||||||
\(490\) | −11.0368 | −0.498593 | ||||||||
\(491\) | 24.8745 | 1.12257 | 0.561286 | − | 0.827622i | \(-0.310307\pi\) | ||||
0.561286 | + | 0.827622i | \(0.310307\pi\) | |||||||
\(492\) | − 3.24698i | − 0.146385i | ||||||||
\(493\) | −28.5642 | −1.28647 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.91185 | −0.0859314 | ||||||||
\(496\) | − 5.29590i | − 0.237793i | ||||||||
\(497\) | 9.11721 | 0.408963 | ||||||||
\(498\) | −9.49157 | −0.425327 | ||||||||
\(499\) | 42.0737i | 1.88348i | 0.336347 | + | 0.941738i | \(0.390808\pi\) | ||||
−0.336347 | + | 0.941738i | \(0.609192\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | − 21.5351i | − 0.962118i | ||||||||
\(502\) | − 1.62863i | − 0.0726893i | ||||||||
\(503\) | −20.0151 | −0.892428 | −0.446214 | − | 0.894926i | \(-0.647228\pi\) | ||||
−0.446214 | + | 0.894926i | \(0.647228\pi\) | |||||||
\(504\) | 4.24698 | 0.189176 | ||||||||
\(505\) | − 14.8116i | − 0.659109i | ||||||||
\(506\) | 0.850855 | 0.0378251 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.8267 | 0.924035 | ||||||||
\(509\) | − 25.6907i | − 1.13872i | −0.822088 | − | 0.569360i | \(-0.807191\pi\) | ||||
0.822088 | − | 0.569360i | \(-0.192809\pi\) | |||||||
\(510\) | −3.33513 | −0.147682 | ||||||||
\(511\) | 21.9095 | 0.969217 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 4.85086i | − 0.214170i | ||||||||
\(514\) | − 8.87263i | − 0.391355i | ||||||||
\(515\) | 13.6896i | 0.603237i | ||||||||
\(516\) | 1.97823 | 0.0870867 | ||||||||
\(517\) | −19.8528 | −0.873124 | ||||||||
\(518\) | − 7.44504i | − 0.327116i | ||||||||
\(519\) | −13.9541 | −0.612516 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.7342 | −1.08363 | −0.541813 | − | 0.840499i | \(-0.682262\pi\) | ||||
−0.541813 | + | 0.840499i | \(0.682262\pi\) | |||||||
\(522\) | 8.56465i | 0.374864i | ||||||||
\(523\) | −18.7439 | −0.819615 | −0.409807 | − | 0.912172i | \(-0.634404\pi\) | ||||
−0.409807 | + | 0.912172i | \(0.634404\pi\) | |||||||
\(524\) | −17.5036 | −0.764650 | ||||||||
\(525\) | − 4.24698i | − 0.185353i | ||||||||
\(526\) | − 22.4185i | − 0.977492i | ||||||||
\(527\) | − 17.6625i | − 0.769390i | ||||||||
\(528\) | − 1.91185i | − 0.0832028i | ||||||||
\(529\) | −22.8019 | −0.991389 | ||||||||
\(530\) | −1.14914 | −0.0499157 | ||||||||
\(531\) | 13.4601i | 0.584119i | ||||||||
\(532\) | −20.6015 | −0.893188 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.25667 | 0.0543814 | ||||||||
\(535\) | − 12.8334i | − 0.554836i | ||||||||
\(536\) | 13.5308 | 0.584441 | ||||||||
\(537\) | 8.32975 | 0.359455 | ||||||||
\(538\) | − 26.9071i | − 1.16005i | ||||||||
\(539\) | − 21.1008i | − 0.908877i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | − 43.7434i | − 1.88068i | −0.340239 | − | 0.940339i | \(-0.610508\pi\) | ||||
0.340239 | − | 0.940339i | \(-0.389492\pi\) | |||||||
\(542\) | 31.7265 | 1.36277 | ||||||||
\(543\) | 17.1371 | 0.735422 | ||||||||
\(544\) | − 3.33513i | − 0.142992i | ||||||||
\(545\) | 10.8726 | 0.465732 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.9681 | 0.768259 | 0.384130 | − | 0.923279i | \(-0.374502\pi\) | ||||
0.384130 | + | 0.923279i | \(0.374502\pi\) | |||||||
\(548\) | 0.929312i | 0.0396983i | ||||||||
\(549\) | 1.13169 | 0.0482992 | ||||||||
\(550\) | −1.91185 | −0.0815217 | ||||||||
\(551\) | − 41.5459i | − 1.76991i | ||||||||
\(552\) | − 0.445042i | − 0.0189422i | ||||||||
\(553\) | 61.8044i | 2.62819i | ||||||||
\(554\) | − 30.6069i | − 1.30036i | ||||||||
\(555\) | 1.75302 | 0.0744116 | ||||||||
\(556\) | −3.12200 | −0.132402 | ||||||||
\(557\) | − 8.26981i | − 0.350403i | −0.984533 | − | 0.175202i | \(-0.943942\pi\) | ||||
0.984533 | − | 0.175202i | \(-0.0560577\pi\) | |||||||
\(558\) | −5.29590 | −0.224193 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.24698 | 0.179468 | ||||||||
\(561\) | − 6.37627i | − 0.269206i | ||||||||
\(562\) | 16.6649 | 0.702965 | ||||||||
\(563\) | −19.8984 | −0.838619 | −0.419310 | − | 0.907843i | \(-0.637728\pi\) | ||||
−0.419310 | + | 0.907843i | \(0.637728\pi\) | |||||||
\(564\) | 10.3840i | 0.437247i | ||||||||
\(565\) | − 11.2295i | − 0.472430i | ||||||||
\(566\) | − 4.32304i | − 0.181711i | ||||||||
\(567\) | − 4.24698i | − 0.178356i | ||||||||
\(568\) | −2.14675 | −0.0900757 | ||||||||
\(569\) | −14.6528 | −0.614277 | −0.307139 | − | 0.951665i | \(-0.599371\pi\) | ||||
−0.307139 | + | 0.951665i | \(0.599371\pi\) | |||||||
\(570\) | − 4.85086i | − 0.203180i | ||||||||
\(571\) | 9.47517 | 0.396524 | 0.198262 | − | 0.980149i | \(-0.436470\pi\) | ||||
0.198262 | + | 0.980149i | \(0.436470\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.1685 | −0.967879 | ||||||||
\(574\) | 13.7899i | 0.575577i | ||||||||
\(575\) | −0.445042 | −0.0185595 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 8.79225i | 0.366026i | 0.983110 | + | 0.183013i | \(0.0585851\pi\) | ||||
−0.983110 | + | 0.183013i | \(0.941415\pi\) | |||||||
\(578\) | 5.87694i | 0.244448i | ||||||||
\(579\) | − 6.38942i | − 0.265535i | ||||||||
\(580\) | 8.56465i | 0.355628i | ||||||||
\(581\) | 40.3105 | 1.67236 | ||||||||
\(582\) | −5.01507 | −0.207881 | ||||||||
\(583\) | − 2.19700i | − 0.0909903i | ||||||||
\(584\) | −5.15883 | −0.213474 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.62804 | 0.232492 | ||||||||
\(587\) | 2.38942i | 0.0986219i | 0.998783 | + | 0.0493110i | \(0.0157025\pi\) | ||||
−0.998783 | + | 0.0493110i | \(0.984297\pi\) | |||||||
\(588\) | −11.0368 | −0.455151 | ||||||||
\(589\) | 25.6896 | 1.05852 | ||||||||
\(590\) | 13.4601i | 0.554144i | ||||||||
\(591\) | − 14.8605i | − 0.611281i | ||||||||
\(592\) | 1.75302i | 0.0720487i | ||||||||
\(593\) | 21.4034i | 0.878933i | 0.898259 | + | 0.439467i | \(0.144833\pi\) | ||||
−0.898259 | + | 0.439467i | \(0.855167\pi\) | |||||||
\(594\) | −1.91185 | −0.0784443 | ||||||||
\(595\) | 14.1642 | 0.580676 | ||||||||
\(596\) | 6.57673i | 0.269393i | ||||||||
\(597\) | 26.3860 | 1.07991 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.4765 | 0.509776 | 0.254888 | − | 0.966971i | \(-0.417961\pi\) | ||||
0.254888 | + | 0.966971i | \(0.417961\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | −12.9487 | −0.528188 | −0.264094 | − | 0.964497i | \(-0.585073\pi\) | ||||
−0.264094 | + | 0.964497i | \(0.585073\pi\) | |||||||
\(602\) | −8.40150 | −0.342420 | ||||||||
\(603\) | − 13.5308i | − 0.551017i | ||||||||
\(604\) | − 6.29590i | − 0.256176i | ||||||||
\(605\) | 7.34481i | 0.298609i | ||||||||
\(606\) | − 14.8116i | − 0.601681i | ||||||||
\(607\) | −11.5230 | −0.467705 | −0.233853 | − | 0.972272i | \(-0.575133\pi\) | ||||
−0.233853 | + | 0.972272i | \(0.575133\pi\) | |||||||
\(608\) | 4.85086 | 0.196728 | ||||||||
\(609\) | − 36.3739i | − 1.47394i | ||||||||
\(610\) | 1.13169 | 0.0458206 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.33513 | −0.134814 | ||||||||
\(613\) | 44.9842i | 1.81689i | 0.417999 | + | 0.908447i | \(0.362731\pi\) | ||||
−0.417999 | + | 0.908447i | \(0.637269\pi\) | |||||||
\(614\) | 12.6635 | 0.511059 | ||||||||
\(615\) | −3.24698 | −0.130931 | ||||||||
\(616\) | 8.11960i | 0.327148i | ||||||||
\(617\) | − 24.9318i | − 1.00372i | −0.864950 | − | 0.501859i | \(-0.832650\pi\) | ||||
0.864950 | − | 0.501859i | \(-0.167350\pi\) | |||||||
\(618\) | 13.6896i | 0.550678i | ||||||||
\(619\) | − 11.2929i | − 0.453900i | −0.973906 | − | 0.226950i | \(-0.927125\pi\) | ||||
0.973906 | − | 0.226950i | \(-0.0728755\pi\) | |||||||
\(620\) | −5.29590 | −0.212688 | ||||||||
\(621\) | −0.445042 | −0.0178589 | ||||||||
\(622\) | 8.49635i | 0.340673i | ||||||||
\(623\) | −5.33704 | −0.213824 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 25.2610i | 1.00963i | ||||||||
\(627\) | 9.27413 | 0.370373 | ||||||||
\(628\) | −19.9148 | −0.794689 | ||||||||
\(629\) | 5.84654i | 0.233117i | ||||||||
\(630\) | − 4.24698i | − 0.169204i | ||||||||
\(631\) | − 20.6165i | − 0.820732i | −0.911921 | − | 0.410366i | \(-0.865401\pi\) | ||||
0.911921 | − | 0.410366i | \(-0.134599\pi\) | |||||||
\(632\) | − 14.5526i | − 0.578870i | ||||||||
\(633\) | −17.4383 | −0.693112 | ||||||||
\(634\) | −4.96615 | −0.197231 | ||||||||
\(635\) | − 20.8267i | − 0.826482i | ||||||||
\(636\) | −1.14914 | −0.0455666 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.3744 | −0.648267 | ||||||||
\(639\) | 2.14675i | 0.0849242i | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −47.1487 | −1.86226 | −0.931130 | − | 0.364687i | \(-0.881176\pi\) | ||||
−0.931130 | + | 0.364687i | \(0.881176\pi\) | |||||||
\(642\) | − 12.8334i | − 0.506494i | ||||||||
\(643\) | 8.41981i | 0.332045i | 0.986122 | + | 0.166023i | \(0.0530924\pi\) | ||||
−0.986122 | + | 0.166023i | \(0.946908\pi\) | |||||||
\(644\) | 1.89008i | 0.0744797i | ||||||||
\(645\) | − 1.97823i | − 0.0778927i | ||||||||
\(646\) | 16.1782 | 0.636523 | ||||||||
\(647\) | 43.3836 | 1.70558 | 0.852792 | − | 0.522251i | \(-0.174907\pi\) | ||||
0.852792 | + | 0.522251i | \(0.174907\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −25.7338 | −1.01014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.4916 | 0.881514 | ||||||||
\(652\) | − 13.1075i | − 0.513330i | ||||||||
\(653\) | −21.2862 | −0.832994 | −0.416497 | − | 0.909137i | \(-0.636742\pi\) | ||||
−0.416497 | + | 0.909137i | \(0.636742\pi\) | |||||||
\(654\) | 10.8726 | 0.425153 | ||||||||
\(655\) | 17.5036i | 0.683924i | ||||||||
\(656\) | − 3.24698i | − 0.126773i | ||||||||
\(657\) | 5.15883i | 0.201265i | ||||||||
\(658\) | − 44.1008i | − 1.71923i | ||||||||
\(659\) | 24.9075 | 0.970260 | 0.485130 | − | 0.874442i | \(-0.338772\pi\) | ||||
0.485130 | + | 0.874442i | \(0.338772\pi\) | |||||||
\(660\) | −1.91185 | −0.0744188 | ||||||||
\(661\) | − 17.6209i | − 0.685372i | −0.939450 | − | 0.342686i | \(-0.888663\pi\) | ||||
0.939450 | − | 0.342686i | \(-0.111337\pi\) | |||||||
\(662\) | 35.3749 | 1.37489 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.49157 | −0.368344 | ||||||||
\(665\) | 20.6015i | 0.798891i | ||||||||
\(666\) | 1.75302 | 0.0679282 | ||||||||
\(667\) | −3.81163 | −0.147587 | ||||||||
\(668\) | − 21.5351i | − 0.833218i | ||||||||
\(669\) | − 9.95838i | − 0.385013i | ||||||||
\(670\) | − 13.5308i | − 0.522740i | ||||||||
\(671\) | 2.16362i | 0.0835256i | ||||||||
\(672\) | 4.24698 | 0.163831 | ||||||||
\(673\) | 28.8888 | 1.11358 | 0.556790 | − | 0.830653i | \(-0.312033\pi\) | ||||
0.556790 | + | 0.830653i | \(0.312033\pi\) | |||||||
\(674\) | − 4.70171i | − 0.181103i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.3927 | 0.937486 | 0.468743 | − | 0.883335i | \(-0.344707\pi\) | ||||
0.468743 | + | 0.883335i | \(0.344707\pi\) | |||||||
\(678\) | − 11.2295i | − 0.431267i | ||||||||
\(679\) | 21.2989 | 0.817376 | ||||||||
\(680\) | −3.33513 | −0.127896 | ||||||||
\(681\) | − 19.6112i | − 0.751502i | ||||||||
\(682\) | − 10.1250i | − 0.387706i | ||||||||
\(683\) | 47.6558i | 1.82350i | 0.410748 | + | 0.911749i | \(0.365268\pi\) | ||||
−0.410748 | + | 0.911749i | \(0.634732\pi\) | |||||||
\(684\) | − 4.85086i | − 0.185477i | ||||||||
\(685\) | 0.929312 | 0.0355072 | ||||||||
\(686\) | 17.1444 | 0.654575 | ||||||||
\(687\) | 8.72886i | 0.333027i | ||||||||
\(688\) | 1.97823 | 0.0754193 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.445042 | −0.0169425 | ||||||||
\(691\) | − 50.2180i | − 1.91038i | −0.295987 | − | 0.955192i | \(-0.595649\pi\) | ||||
0.295987 | − | 0.955192i | \(-0.404351\pi\) | |||||||
\(692\) | −13.9541 | −0.530454 | ||||||||
\(693\) | 8.11960 | 0.308438 | ||||||||
\(694\) | − 14.9028i | − 0.565701i | ||||||||
\(695\) | 3.12200i | 0.118424i | ||||||||
\(696\) | 8.56465i | 0.324642i | ||||||||
\(697\) | − 10.8291i | − 0.410181i | ||||||||
\(698\) | 35.2669 | 1.33487 | ||||||||
\(699\) | 0.975837 | 0.0369095 | ||||||||
\(700\) | − 4.24698i | − 0.160521i | ||||||||
\(701\) | 12.8140 | 0.483979 | 0.241989 | − | 0.970279i | \(-0.422200\pi\) | ||||
0.241989 | + | 0.970279i | \(0.422200\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.50365 | −0.320721 | ||||||||
\(704\) | − 1.91185i | − 0.0720557i | ||||||||
\(705\) | 10.3840 | 0.391086 | ||||||||
\(706\) | −10.5574 | −0.397331 | ||||||||
\(707\) | 62.9047i | 2.36577i | ||||||||
\(708\) | 13.4601i | 0.505862i | ||||||||
\(709\) | − 34.5515i | − 1.29761i | −0.760955 | − | 0.648804i | \(-0.775269\pi\) | ||||
0.760955 | − | 0.648804i | \(-0.224731\pi\) | |||||||
\(710\) | 2.14675i | 0.0805662i | ||||||||
\(711\) | −14.5526 | −0.545764 | ||||||||
\(712\) | 1.25667 | 0.0470956 | ||||||||
\(713\) | − 2.35690i | − 0.0882664i | ||||||||
\(714\) | 14.1642 | 0.530082 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.32975 | 0.311297 | ||||||||
\(717\) | − 7.39373i | − 0.276124i | ||||||||
\(718\) | 28.7724 | 1.07378 | ||||||||
\(719\) | −20.8528 | −0.777677 | −0.388839 | − | 0.921306i | \(-0.627124\pi\) | ||||
−0.388839 | + | 0.921306i | \(0.627124\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | − 58.1396i | − 2.16523i | ||||||||
\(722\) | 4.53079i | 0.168619i | ||||||||
\(723\) | 2.11529i | 0.0786686i | ||||||||
\(724\) | 17.1371 | 0.636894 | ||||||||
\(725\) | 8.56465 | 0.318083 | ||||||||
\(726\) | 7.34481i | 0.272592i | ||||||||
\(727\) | −32.7192 | −1.21349 | −0.606743 | − | 0.794898i | \(-0.707524\pi\) | ||||
−0.606743 | + | 0.794898i | \(0.707524\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.15883i | 0.190937i | ||||||||
\(731\) | 6.59764 | 0.244023 | ||||||||
\(732\) | 1.13169 | 0.0418283 | ||||||||
\(733\) | − 52.2737i | − 1.93077i | −0.260826 | − | 0.965386i | \(-0.583995\pi\) | ||||
0.260826 | − | 0.965386i | \(-0.416005\pi\) | |||||||
\(734\) | 24.1511i | 0.891432i | ||||||||
\(735\) | 11.0368i | 0.407100i | ||||||||
\(736\) | − 0.445042i | − 0.0164045i | ||||||||
\(737\) | 25.8689 | 0.952893 | ||||||||
\(738\) | −3.24698 | −0.119523 | ||||||||
\(739\) | − 13.4571i | − 0.495028i | −0.968884 | − | 0.247514i | \(-0.920386\pi\) | ||||
0.968884 | − | 0.247514i | \(-0.0796137\pi\) | |||||||
\(740\) | 1.75302 | 0.0644423 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.88040 | 0.179165 | ||||||||
\(743\) | − 22.9989i | − 0.843749i | −0.906654 | − | 0.421875i | \(-0.861372\pi\) | ||||
0.906654 | − | 0.421875i | \(-0.138628\pi\) | |||||||
\(744\) | −5.29590 | −0.194157 | ||||||||
\(745\) | 6.57673 | 0.240953 | ||||||||
\(746\) | 21.0664i | 0.771295i | ||||||||
\(747\) | 9.49157i | 0.347278i | ||||||||
\(748\) | − 6.37627i | − 0.233140i | ||||||||
\(749\) | 54.5032i | 1.99150i | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −34.1159 | −1.24491 | −0.622453 | − | 0.782657i | \(-0.713864\pi\) | ||||
−0.622453 | + | 0.782657i | \(0.713864\pi\) | |||||||
\(752\) | 10.3840i | 0.378667i | ||||||||
\(753\) | −1.62863 | −0.0593506 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.29590 | −0.229131 | ||||||||
\(756\) | − 4.24698i | − 0.154461i | ||||||||
\(757\) | −38.9004 | −1.41386 | −0.706929 | − | 0.707285i | \(-0.749920\pi\) | ||||
−0.706929 | + | 0.707285i | \(0.749920\pi\) | |||||||
\(758\) | 8.42327 | 0.305947 | ||||||||
\(759\) | − 0.850855i | − 0.0308841i | ||||||||
\(760\) | − 4.85086i | − 0.175959i | ||||||||
\(761\) | − 36.8528i | − 1.33591i | −0.744201 | − | 0.667956i | \(-0.767169\pi\) | ||||
0.744201 | − | 0.667956i | \(-0.232831\pi\) | |||||||
\(762\) | − 20.8267i | − 0.754471i | ||||||||
\(763\) | −46.1758 | −1.67168 | ||||||||
\(764\) | −23.1685 | −0.838208 | ||||||||
\(765\) | 3.33513i | 0.120582i | ||||||||
\(766\) | −10.6377 | −0.384357 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 23.4198i | 0.844540i | 0.906470 | + | 0.422270i | \(0.138767\pi\) | ||||
−0.906470 | + | 0.422270i | \(0.861233\pi\) | |||||||
\(770\) | 8.11960 | 0.292610 | ||||||||
\(771\) | −8.87263 | −0.319540 | ||||||||
\(772\) | − 6.38942i | − 0.229960i | ||||||||
\(773\) | − 0.275192i | − 0.00989795i | −0.999988 | − | 0.00494898i | \(-0.998425\pi\) | ||||
0.999988 | − | 0.00494898i | \(-0.00157531\pi\) | |||||||
\(774\) | − 1.97823i | − 0.0711060i | ||||||||
\(775\) | 5.29590i | 0.190234i | ||||||||
\(776\) | −5.01507 | −0.180030 | ||||||||
\(777\) | −7.44504 | −0.267089 | ||||||||
\(778\) | − 25.7429i | − 0.922926i | ||||||||
\(779\) | 15.7506 | 0.564325 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.10428 | −0.146863 | ||||||||
\(782\) | − 1.48427i | − 0.0530774i | ||||||||
\(783\) | 8.56465 | 0.306076 | ||||||||
\(784\) | −11.0368 | −0.394173 | ||||||||
\(785\) | 19.9148i | 0.710791i | ||||||||
\(786\) | 17.5036i | 0.624334i | ||||||||
\(787\) | 27.2543i | 0.971510i | 0.874095 | + | 0.485755i | \(0.161455\pi\) | ||||
−0.874095 | + | 0.485755i | \(0.838545\pi\) | |||||||
\(788\) | − 14.8605i | − 0.529385i | ||||||||
\(789\) | −22.4185 | −0.798119 | ||||||||
\(790\) | −14.5526 | −0.517757 | ||||||||
\(791\) | 47.6915i | 1.69572i | ||||||||
\(792\) | −1.91185 | −0.0679348 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11.4373 | 0.405894 | ||||||||
\(795\) | 1.14914i | 0.0407560i | ||||||||
\(796\) | 26.3860 | 0.935226 | ||||||||
\(797\) | −14.2819 | −0.505891 | −0.252945 | − | 0.967481i | \(-0.581399\pi\) | ||||
−0.252945 | + | 0.967481i | \(0.581399\pi\) | |||||||
\(798\) | 20.6015i | 0.729285i | ||||||||
\(799\) | 34.6321i | 1.22520i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − 1.25667i | − 0.0444022i | ||||||||
\(802\) | 22.1511 | 0.782181 | ||||||||
\(803\) | −9.86294 | −0.348055 | ||||||||
\(804\) | − 13.5308i | − 0.477194i | ||||||||
\(805\) | 1.89008 | 0.0666167 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.9071 | −0.947174 | ||||||||
\(808\) | − 14.8116i | − 0.521071i | ||||||||
\(809\) | −8.82610 | −0.310309 | −0.155155 | − | 0.987890i | \(-0.549588\pi\) | ||||
−0.155155 | + | 0.987890i | \(0.549588\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | − 6.37196i | − 0.223750i | −0.993722 | − | 0.111875i | \(-0.964314\pi\) | ||||
0.993722 | − | 0.111875i | \(-0.0356856\pi\) | |||||||
\(812\) | − 36.3739i | − 1.27647i | ||||||||
\(813\) | − 31.7265i | − 1.11270i | ||||||||
\(814\) | 3.35152i | 0.117471i | ||||||||
\(815\) | −13.1075 | −0.459137 | ||||||||
\(816\) | −3.33513 | −0.116753 | ||||||||
\(817\) | 9.59611i | 0.335725i | ||||||||
\(818\) | 22.0965 | 0.772586 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.24698 | −0.113389 | ||||||||
\(821\) | − 13.7476i | − 0.479796i | −0.970798 | − | 0.239898i | \(-0.922886\pi\) | ||||
0.970798 | − | 0.239898i | \(-0.0771140\pi\) | |||||||
\(822\) | 0.929312 | 0.0324135 | ||||||||
\(823\) | −47.8587 | −1.66825 | −0.834125 | − | 0.551575i | \(-0.814027\pi\) | ||||
−0.834125 | + | 0.551575i | \(0.814027\pi\) | |||||||
\(824\) | 13.6896i | 0.476901i | ||||||||
\(825\) | 1.91185i | 0.0665622i | ||||||||
\(826\) | − 57.1648i | − 1.98902i | ||||||||
\(827\) | − 29.1317i | − 1.01301i | −0.862238 | − | 0.506504i | \(-0.830938\pi\) | ||||
0.862238 | − | 0.506504i | \(-0.169062\pi\) | |||||||
\(828\) | −0.445042 | −0.0154663 | ||||||||
\(829\) | 25.7748 | 0.895195 | 0.447598 | − | 0.894235i | \(-0.352280\pi\) | ||||
0.447598 | + | 0.894235i | \(0.352280\pi\) | |||||||
\(830\) | 9.49157i | 0.329457i | ||||||||
\(831\) | −30.6069 | −1.06174 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36.8092 | −1.27536 | ||||||||
\(834\) | 3.12200i | 0.108106i | ||||||||
\(835\) | −21.5351 | −0.745253 | ||||||||
\(836\) | 9.27413 | 0.320752 | ||||||||
\(837\) | 5.29590i | 0.183053i | ||||||||
\(838\) | − 9.03444i | − 0.312090i | ||||||||
\(839\) | − 2.91292i | − 0.100565i | −0.998735 | − | 0.0502826i | \(-0.983988\pi\) | ||||
0.998735 | − | 0.0502826i | \(-0.0160122\pi\) | |||||||
\(840\) | − 4.24698i | − 0.146535i | ||||||||
\(841\) | 44.3532 | 1.52942 | ||||||||
\(842\) | −7.17928 | −0.247414 | ||||||||
\(843\) | − 16.6649i | − 0.573969i | ||||||||
\(844\) | −17.4383 | −0.600252 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.3840 | 0.357011 | ||||||||
\(847\) | − 31.1933i | − 1.07181i | ||||||||
\(848\) | −1.14914 | −0.0394618 | ||||||||
\(849\) | −4.32304 | −0.148366 | ||||||||
\(850\) | 3.33513i | 0.114394i | ||||||||
\(851\) | 0.780167i | 0.0267438i | ||||||||
\(852\) | 2.14675i | 0.0735465i | ||||||||
\(853\) | 12.9661i | 0.443952i | 0.975052 | + | 0.221976i | \(0.0712507\pi\) | ||||
−0.975052 | + | 0.221976i | \(0.928749\pi\) | |||||||
\(854\) | −4.80625 | −0.164466 | ||||||||
\(855\) | −4.85086 | −0.165896 | ||||||||
\(856\) | − 12.8334i | − 0.438636i | ||||||||
\(857\) | 9.85623 | 0.336682 | 0.168341 | − | 0.985729i | \(-0.446159\pi\) | ||||
0.168341 | + | 0.985729i | \(0.446159\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.6746 | 1.04660 | 0.523301 | − | 0.852148i | \(-0.324700\pi\) | ||||
0.523301 | + | 0.852148i | \(0.324700\pi\) | |||||||
\(860\) | − 1.97823i | − 0.0674571i | ||||||||
\(861\) | 13.7899 | 0.469957 | ||||||||
\(862\) | −8.36360 | −0.284865 | ||||||||
\(863\) | − 34.1588i | − 1.16278i | −0.813625 | − | 0.581390i | \(-0.802509\pi\) | ||||
0.813625 | − | 0.581390i | \(-0.197491\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 13.9541i | 0.474452i | ||||||||
\(866\) | − 12.2851i | − 0.417466i | ||||||||
\(867\) | 5.87694 | 0.199591 | ||||||||
\(868\) | 22.4916 | 0.763414 | ||||||||
\(869\) | − 27.8224i | − 0.943810i | ||||||||
\(870\) | 8.56465 | 0.290369 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.8726 | 0.368194 | ||||||||
\(873\) | 5.01507i | 0.169734i | ||||||||
\(874\) | 2.15883 | 0.0730236 | ||||||||
\(875\) | −4.24698 | −0.143574 | ||||||||
\(876\) | 5.15883i | 0.174301i | ||||||||
\(877\) | − 20.1588i | − 0.680715i | −0.940296 | − | 0.340358i | \(-0.889452\pi\) | ||||
0.940296 | − | 0.340358i | \(-0.110548\pi\) | |||||||
\(878\) | 20.4849i | 0.691331i | ||||||||
\(879\) | − 5.62804i | − 0.189829i | ||||||||
\(880\) | −1.91185 | −0.0644486 | ||||||||
\(881\) | 2.79550 | 0.0941827 | 0.0470913 | − | 0.998891i | \(-0.485005\pi\) | ||||
0.0470913 | + | 0.998891i | \(0.485005\pi\) | |||||||
\(882\) | 11.0368i | 0.371630i | ||||||||
\(883\) | 16.8605 | 0.567402 | 0.283701 | − | 0.958913i | \(-0.408438\pi\) | ||||
0.283701 | + | 0.958913i | \(0.408438\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.4601 | 0.452457 | ||||||||
\(886\) | 0.928247i | 0.0311851i | ||||||||
\(887\) | −8.71379 | −0.292580 | −0.146290 | − | 0.989242i | \(-0.546733\pi\) | ||||
−0.146290 | + | 0.989242i | \(0.546733\pi\) | |||||||
\(888\) | 1.75302 | 0.0588275 | ||||||||
\(889\) | 88.4505i | 2.96654i | ||||||||
\(890\) | − 1.25667i | − 0.0421236i | ||||||||
\(891\) | 1.91185i | 0.0640495i | ||||||||
\(892\) | − 9.95838i | − 0.333431i | ||||||||
\(893\) | −50.3715 | −1.68562 | ||||||||
\(894\) | 6.57673 | 0.219959 | ||||||||
\(895\) | − 8.32975i | − 0.278433i | ||||||||
\(896\) | 4.24698 | 0.141882 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.9355 | −0.765369 | ||||||||
\(899\) | 45.3575i | 1.51276i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −3.83254 | −0.127681 | ||||||||
\(902\) | − 6.20775i | − 0.206695i | ||||||||
\(903\) | 8.40150i | 0.279584i | ||||||||
\(904\) | − 11.2295i | − 0.373488i | ||||||||
\(905\) | − 17.1371i | − 0.569655i | ||||||||
\(906\) | −6.29590 | −0.209167 | ||||||||
\(907\) | −14.2295 | −0.472483 | −0.236242 | − | 0.971694i | \(-0.575916\pi\) | ||||
−0.236242 | + | 0.971694i | \(0.575916\pi\) | |||||||
\(908\) | − 19.6112i | − 0.650820i | ||||||||
\(909\) | −14.8116 | −0.491271 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.3672 | −0.641663 | −0.320832 | − | 0.947136i | \(-0.603962\pi\) | ||||
−0.320832 | + | 0.947136i | \(0.603962\pi\) | |||||||
\(912\) | − 4.85086i | − 0.160628i | ||||||||
\(913\) | −18.1465 | −0.600561 | ||||||||
\(914\) | −10.3773 | −0.343252 | ||||||||
\(915\) | − 1.13169i | − 0.0374124i | ||||||||
\(916\) | 8.72886i | 0.288410i | ||||||||
\(917\) | − 74.3376i | − 2.45484i | ||||||||
\(918\) | 3.33513i | 0.110076i | ||||||||
\(919\) | −44.1420 | −1.45611 | −0.728055 | − | 0.685519i | \(-0.759575\pi\) | ||||
−0.728055 | + | 0.685519i | \(0.759575\pi\) | |||||||
\(920\) | −0.445042 | −0.0146726 | ||||||||
\(921\) | − 12.6635i | − 0.417278i | ||||||||
\(922\) | −7.69740 | −0.253500 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 8.11960 | 0.267115 | ||||||||
\(925\) | − 1.75302i | − 0.0576390i | ||||||||
\(926\) | −39.0640 | −1.28372 | ||||||||
\(927\) | 13.6896 | 0.449626 | ||||||||
\(928\) | 8.56465i | 0.281148i | ||||||||
\(929\) | − 14.8616i | − 0.487594i | −0.969826 | − | 0.243797i | \(-0.921607\pi\) | ||||
0.969826 | − | 0.243797i | \(-0.0783930\pi\) | |||||||
\(930\) | 5.29590i | 0.173659i | ||||||||
\(931\) | − 53.5381i | − 1.75464i | ||||||||
\(932\) | 0.975837 | 0.0319646 | ||||||||
\(933\) | 8.49635 | 0.278158 | ||||||||
\(934\) | 0.916166i | 0.0299779i | ||||||||
\(935\) | −6.37627 | −0.208526 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.3196 | 1.77454 | 0.887272 | − | 0.461247i | \(-0.152598\pi\) | ||||
0.887272 | + | 0.461247i | \(0.152598\pi\) | |||||||
\(938\) | 57.4650i | 1.87630i | ||||||||
\(939\) | 25.2610 | 0.824361 | ||||||||
\(940\) | 10.3840 | 0.338690 | ||||||||
\(941\) | 14.0121i | 0.456781i | 0.973570 | + | 0.228390i | \(0.0733463\pi\) | ||||
−0.973570 | + | 0.228390i | \(0.926654\pi\) | |||||||
\(942\) | 19.9148i | 0.648860i | ||||||||
\(943\) | − 1.44504i | − 0.0470570i | ||||||||
\(944\) | 13.4601i | 0.438089i | ||||||||
\(945\) | −4.24698 | −0.138154 | ||||||||
\(946\) | 3.78209 | 0.122966 | ||||||||
\(947\) | 56.1831i | 1.82571i | 0.408289 | + | 0.912853i | \(0.366126\pi\) | ||||
−0.408289 | + | 0.912853i | \(0.633874\pi\) | |||||||
\(948\) | −14.5526 | −0.472645 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.85086 | −0.157383 | ||||||||
\(951\) | 4.96615i | 0.161038i | ||||||||
\(952\) | 14.1642 | 0.459065 | ||||||||
\(953\) | −42.9090 | −1.38996 | −0.694979 | − | 0.719030i | \(-0.744586\pi\) | ||||
−0.694979 | + | 0.719030i | \(0.744586\pi\) | |||||||
\(954\) | 1.14914i | 0.0372049i | ||||||||
\(955\) | 23.1685i | 0.749716i | ||||||||
\(956\) | − 7.39373i | − 0.239130i | ||||||||
\(957\) | 16.3744i | 0.529308i | ||||||||
\(958\) | −23.1715 | −0.748637 | ||||||||
\(959\) | −3.94677 | −0.127448 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 2.95348 | 0.0952734 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.8334 | −0.413550 | ||||||||
\(964\) | 2.11529i | 0.0681290i | ||||||||
\(965\) | −6.38942 | −0.205683 | ||||||||
\(966\) | 1.89008 | 0.0608124 | ||||||||
\(967\) | − 2.89977i | − 0.0932504i | −0.998912 | − | 0.0466252i | \(-0.985153\pi\) | ||||
0.998912 | − | 0.0466252i | \(-0.0148466\pi\) | |||||||
\(968\) | 7.34481i | 0.236071i | ||||||||
\(969\) | − 16.1782i | − 0.519719i | ||||||||
\(970\) | 5.01507i | 0.161024i | ||||||||
\(971\) | 32.8146 | 1.05307 | 0.526535 | − | 0.850153i | \(-0.323491\pi\) | ||||
0.526535 | + | 0.850153i | \(0.323491\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | − 13.2591i | − 0.425066i | ||||||||
\(974\) | 11.9812 | 0.383903 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.13169 | 0.0362244 | ||||||||
\(977\) | 13.1806i | 0.421685i | 0.977520 | + | 0.210842i | \(0.0676207\pi\) | ||||
−0.977520 | + | 0.210842i | \(0.932379\pi\) | |||||||
\(978\) | −13.1075 | −0.419132 | ||||||||
\(979\) | 2.40257 | 0.0767864 | ||||||||
\(980\) | 11.0368i | 0.352559i | ||||||||
\(981\) | − 10.8726i | − 0.347136i | ||||||||
\(982\) | − 24.8745i | − 0.793779i | ||||||||
\(983\) | 31.3726i | 1.00063i | 0.865844 | + | 0.500315i | \(0.166782\pi\) | ||||
−0.865844 | + | 0.500315i | \(0.833218\pi\) | |||||||
\(984\) | −3.24698 | −0.103510 | ||||||||
\(985\) | −14.8605 | −0.473496 | ||||||||
\(986\) | 28.5642i | 0.909669i | ||||||||
\(987\) | −44.1008 | −1.40374 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.880395 | 0.0279949 | ||||||||
\(990\) | 1.91185i | 0.0607627i | ||||||||
\(991\) | −44.1842 | −1.40356 | −0.701778 | − | 0.712395i | \(-0.747610\pi\) | ||||
−0.701778 | + | 0.712395i | \(0.747610\pi\) | |||||||
\(992\) | −5.29590 | −0.168145 | ||||||||
\(993\) | − 35.3749i | − 1.12259i | ||||||||
\(994\) | − 9.11721i | − 0.289180i | ||||||||
\(995\) | − 26.3860i | − 0.836491i | ||||||||
\(996\) | 9.49157i | 0.300752i | ||||||||
\(997\) | 50.8254 | 1.60966 | 0.804828 | − | 0.593509i | \(-0.202258\pi\) | ||||
0.804828 | + | 0.593509i | \(0.202258\pi\) | |||||||
\(998\) | 42.0737 | 1.33182 | ||||||||
\(999\) | − 1.75302i | − 0.0554631i |
(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 | 5070.2.b.v.1351.1 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bl.1.3 | ✓ | 3 | ||
13.8 | odd | 4 | 5070.2.a.bs.1.1 | yes | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.v.1351.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bl.1.3 | ✓ | 3 | 13.5 | odd | 4 | ||
5070.2.a.bs.1.1 | yes | 3 | 13.8 | odd | 4 | ||
5070.2.b.v.1351.1 | 6 | 1.1 | even | 1 | trivial | ||
5070.2.b.v.1351.6 | 6 | 13.12 | even | 2 | inner |