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: | \(8\) |
Coefficient field: | 8.0.17284886784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.3 | ||
Root | \(3.17270 + 3.17270i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.ba.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 | ||||||||
\(7\) | 2.32258i | 0.877853i | 0.898523 | + | 0.438926i | \(0.144641\pi\) | ||||
−0.898523 | + | 0.438926i | \(0.855359\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 5.34541i | 1.61170i | 0.592119 | + | 0.805850i | \(0.298291\pi\) | ||||
−0.592119 | + | 0.805850i | \(0.701709\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.32258 | 0.620736 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | 4.02283i | 0.922900i | 0.887166 | + | 0.461450i | \(0.152671\pi\) | ||||
−0.887166 | + | 0.461450i | \(0.847329\pi\) | |||||||
\(20\) | − 1.00000i | − 0.223607i | ||||||||
\(21\) | 2.32258i | 0.506828i | ||||||||
\(22\) | 5.34541 | 1.13964 | ||||||||
\(23\) | 4.93593 | 1.02921 | 0.514607 | − | 0.857426i | \(-0.327938\pi\) | ||||
0.514607 | + | 0.857426i | \(0.327938\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − 2.32258i | − 0.438926i | ||||||||
\(29\) | 4.29078 | 0.796777 | 0.398388 | − | 0.917217i | \(-0.369570\pi\) | ||||
0.398388 | + | 0.917217i | \(0.369570\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | − 3.47183i | − 0.623560i | −0.950154 | − | 0.311780i | \(-0.899075\pi\) | ||||
0.950154 | − | 0.311780i | \(-0.100925\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 5.34541i | 0.930516i | ||||||||
\(34\) | 4.00000i | 0.685994i | ||||||||
\(35\) | −2.32258 | −0.392588 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 3.14925i | − 0.517734i | −0.965913 | − | 0.258867i | \(-0.916651\pi\) | ||||
0.965913 | − | 0.258867i | \(-0.0833491\pi\) | |||||||
\(38\) | 4.02283 | 0.652589 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 2.64516i | 0.413104i | 0.978436 | + | 0.206552i | \(0.0662243\pi\) | ||||
−0.978436 | + | 0.206552i | \(0.933776\pi\) | |||||||
\(42\) | 2.32258 | 0.358382 | ||||||||
\(43\) | −12.2508 | −1.86823 | −0.934113 | − | 0.356976i | \(-0.883808\pi\) | ||||
−0.934113 | + | 0.356976i | \(0.883808\pi\) | |||||||
\(44\) | − 5.34541i | − 0.805850i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | − 4.93593i | − 0.727764i | ||||||||
\(47\) | 1.81894i | 0.265320i | 0.991162 | + | 0.132660i | \(0.0423518\pi\) | ||||
−0.991162 | + | 0.132660i | \(0.957648\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.60562 | 0.229375 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.48693 | −0.753687 | −0.376844 | − | 0.926277i | \(-0.622991\pi\) | ||||
−0.376844 | + | 0.926277i | \(0.622991\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | −5.34541 | −0.720774 | ||||||||
\(56\) | −2.32258 | −0.310368 | ||||||||
\(57\) | 4.02283i | 0.532836i | ||||||||
\(58\) | − 4.29078i | − 0.563406i | ||||||||
\(59\) | − 6.78668i | − 0.883551i | −0.897126 | − | 0.441775i | \(-0.854349\pi\) | ||||
0.897126 | − | 0.441775i | \(-0.145651\pi\) | |||||||
\(60\) | − 1.00000i | − 0.129099i | ||||||||
\(61\) | 0.535898 | 0.0686148 | 0.0343074 | − | 0.999411i | \(-0.489077\pi\) | ||||
0.0343074 | + | 0.999411i | \(0.489077\pi\) | |||||||
\(62\) | −3.47183 | −0.440923 | ||||||||
\(63\) | 2.32258i | 0.292618i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.34541 | 0.657974 | ||||||||
\(67\) | 4.10926i | 0.502026i | 0.967984 | + | 0.251013i | \(0.0807637\pi\) | ||||
−0.967984 | + | 0.251013i | \(0.919236\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | 4.93593 | 0.594217 | ||||||||
\(70\) | 2.32258i | 0.277601i | ||||||||
\(71\) | − 15.8719i | − 1.88364i | −0.336112 | − | 0.941822i | \(-0.609112\pi\) | ||||
0.336112 | − | 0.941822i | \(-0.390888\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 13.5734i | 1.58864i | 0.607498 | + | 0.794321i | \(0.292173\pi\) | ||||
−0.607498 | + | 0.794321i | \(0.707827\pi\) | |||||||
\(74\) | −3.14925 | −0.366093 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | − 4.02283i | − 0.461450i | ||||||||
\(77\) | −12.4151 | −1.41484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.96774 | −0.896441 | −0.448220 | − | 0.893923i | \(-0.647942\pi\) | ||||
−0.448220 | + | 0.893923i | \(0.647942\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.64516 | 0.292109 | ||||||||
\(83\) | 11.3360i | 1.24428i | 0.782904 | + | 0.622142i | \(0.213737\pi\) | ||||
−0.782904 | + | 0.622142i | \(0.786263\pi\) | |||||||
\(84\) | − 2.32258i | − 0.253414i | ||||||||
\(85\) | − 4.00000i | − 0.433861i | ||||||||
\(86\) | 12.2508i | 1.32104i | ||||||||
\(87\) | 4.29078 | 0.460019 | ||||||||
\(88\) | −5.34541 | −0.569822 | ||||||||
\(89\) | − 1.73978i | − 0.184417i | −0.995740 | − | 0.0922083i | \(-0.970607\pi\) | ||||
0.995740 | − | 0.0922083i | \(-0.0293926\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.93593 | −0.514607 | ||||||||
\(93\) | − 3.47183i | − 0.360012i | ||||||||
\(94\) | 1.81894 | 0.187610 | ||||||||
\(95\) | −4.02283 | −0.412733 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | 16.1093i | 1.63565i | 0.575469 | + | 0.817824i | \(0.304820\pi\) | ||||
−0.575469 | + | 0.817824i | \(0.695180\pi\) | |||||||
\(98\) | − 1.60562i | − 0.162192i | ||||||||
\(99\) | 5.34541i | 0.537233i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −12.6908 | −1.26278 | −0.631391 | − | 0.775464i | \(-0.717516\pi\) | ||||
−0.631391 | + | 0.775464i | \(0.717516\pi\) | |||||||
\(102\) | 4.00000i | 0.396059i | ||||||||
\(103\) | −4.79612 | −0.472575 | −0.236288 | − | 0.971683i | \(-0.575931\pi\) | ||||
−0.236288 | + | 0.971683i | \(0.575931\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.32258 | −0.226661 | ||||||||
\(106\) | 5.48693i | 0.532938i | ||||||||
\(107\) | 3.07180 | 0.296962 | 0.148481 | − | 0.988915i | \(-0.452562\pi\) | ||||
0.148481 | + | 0.988915i | \(0.452562\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 6.69081i | 0.640864i | 0.947272 | + | 0.320432i | \(0.103828\pi\) | ||||
−0.947272 | + | 0.320432i | \(0.896172\pi\) | |||||||
\(110\) | 5.34541i | 0.509664i | ||||||||
\(111\) | − 3.14925i | − 0.298914i | ||||||||
\(112\) | 2.32258i | 0.219463i | ||||||||
\(113\) | −7.10972 | −0.668826 | −0.334413 | − | 0.942427i | \(-0.608538\pi\) | ||||
−0.334413 | + | 0.942427i | \(0.608538\pi\) | |||||||
\(114\) | 4.02283 | 0.376772 | ||||||||
\(115\) | 4.93593i | 0.460278i | ||||||||
\(116\) | −4.29078 | −0.398388 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.78668 | −0.624765 | ||||||||
\(119\) | − 9.29032i | − 0.851642i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −17.5734 | −1.59758 | ||||||||
\(122\) | − 0.535898i | − 0.0485180i | ||||||||
\(123\) | 2.64516i | 0.238506i | ||||||||
\(124\) | 3.47183i | 0.311780i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 2.32258 | 0.206912 | ||||||||
\(127\) | 2.13209 | 0.189192 | 0.0945961 | − | 0.995516i | \(-0.469844\pi\) | ||||
0.0945961 | + | 0.995516i | \(0.469844\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −12.2508 | −1.07862 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.25851 | 0.109957 | 0.0549785 | − | 0.998488i | \(-0.482491\pi\) | ||||
0.0549785 | + | 0.998488i | \(0.482491\pi\) | |||||||
\(132\) | − 5.34541i | − 0.465258i | ||||||||
\(133\) | −9.34333 | −0.810170 | ||||||||
\(134\) | 4.10926 | 0.354986 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | − 4.00000i | − 0.342997i | ||||||||
\(137\) | − 19.7149i | − 1.68436i | −0.539199 | − | 0.842178i | \(-0.681273\pi\) | ||||
0.539199 | − | 0.842178i | \(-0.318727\pi\) | |||||||
\(138\) | − 4.93593i | − 0.420175i | ||||||||
\(139\) | 5.67742 | 0.481553 | 0.240776 | − | 0.970581i | \(-0.422598\pi\) | ||||
0.240776 | + | 0.970581i | \(0.422598\pi\) | |||||||
\(140\) | 2.32258 | 0.196294 | ||||||||
\(141\) | 1.81894i | 0.153183i | ||||||||
\(142\) | −15.8719 | −1.33194 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.29078i | 0.356329i | ||||||||
\(146\) | 13.5734 | 1.12334 | ||||||||
\(147\) | 1.60562 | 0.132430 | ||||||||
\(148\) | 3.14925i | 0.258867i | ||||||||
\(149\) | 19.4775i | 1.59566i | 0.602884 | + | 0.797829i | \(0.294018\pi\) | ||||
−0.602884 | + | 0.797829i | \(0.705982\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | − 14.5170i | − 1.18138i | −0.806899 | − | 0.590690i | \(-0.798856\pi\) | ||||
0.806899 | − | 0.590690i | \(-0.201144\pi\) | |||||||
\(152\) | −4.02283 | −0.326294 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 12.4151i | 1.00044i | ||||||||
\(155\) | 3.47183 | 0.278864 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.3829 | 1.94596 | 0.972982 | − | 0.230879i | \(-0.0741602\pi\) | ||||
0.972982 | + | 0.230879i | \(0.0741602\pi\) | |||||||
\(158\) | 7.96774i | 0.633879i | ||||||||
\(159\) | −5.48693 | −0.435142 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 11.4641i | 0.903498i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 23.6267i | − 1.85059i | −0.379249 | − | 0.925295i | \(-0.623818\pi\) | ||||
0.379249 | − | 0.925295i | \(-0.376182\pi\) | |||||||
\(164\) | − 2.64516i | − 0.206552i | ||||||||
\(165\) | −5.34541 | −0.416139 | ||||||||
\(166\) | 11.3360 | 0.879842 | ||||||||
\(167\) | 16.7471i | 1.29593i | 0.761669 | + | 0.647967i | \(0.224380\pi\) | ||||
−0.761669 | + | 0.647967i | \(0.775620\pi\) | |||||||
\(168\) | −2.32258 | −0.179191 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 4.02283i | 0.307633i | ||||||||
\(172\) | 12.2508 | 0.934113 | ||||||||
\(173\) | −16.1321 | −1.22650 | −0.613250 | − | 0.789889i | \(-0.710138\pi\) | ||||
−0.613250 | + | 0.789889i | \(0.710138\pi\) | |||||||
\(174\) | − 4.29078i | − 0.325283i | ||||||||
\(175\) | − 2.32258i | − 0.175571i | ||||||||
\(176\) | 5.34541i | 0.402925i | ||||||||
\(177\) | − 6.78668i | − 0.510118i | ||||||||
\(178\) | −1.73978 | −0.130402 | ||||||||
\(179\) | −7.32824 | −0.547738 | −0.273869 | − | 0.961767i | \(-0.588304\pi\) | ||||
−0.273869 | + | 0.961767i | \(0.588304\pi\) | |||||||
\(180\) | − 1.00000i | − 0.0745356i | ||||||||
\(181\) | −19.5734 | −1.45488 | −0.727438 | − | 0.686173i | \(-0.759289\pi\) | ||||
−0.727438 | + | 0.686173i | \(0.759289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.535898 | 0.0396147 | ||||||||
\(184\) | 4.93593i | 0.363882i | ||||||||
\(185\) | 3.14925 | 0.231538 | ||||||||
\(186\) | −3.47183 | −0.254567 | ||||||||
\(187\) | − 21.3816i | − 1.56358i | ||||||||
\(188\) | − 1.81894i | − 0.132660i | ||||||||
\(189\) | 2.32258i | 0.168943i | ||||||||
\(190\) | 4.02283i | 0.291846i | ||||||||
\(191\) | −17.0375 | −1.23279 | −0.616394 | − | 0.787438i | \(-0.711407\pi\) | ||||
−0.616394 | + | 0.787438i | \(0.711407\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 6.15491i | 0.443040i | 0.975156 | + | 0.221520i | \(0.0711019\pi\) | ||||
−0.975156 | + | 0.221520i | \(0.928898\pi\) | |||||||
\(194\) | 16.1093 | 1.15658 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.60562 | −0.114687 | ||||||||
\(197\) | − 13.7867i | − 0.982260i | −0.871086 | − | 0.491130i | \(-0.836584\pi\) | ||||
0.871086 | − | 0.491130i | \(-0.163416\pi\) | |||||||
\(198\) | 5.34541 | 0.379881 | ||||||||
\(199\) | −2.28304 | −0.161841 | −0.0809203 | − | 0.996721i | \(-0.525786\pi\) | ||||
−0.0809203 | + | 0.996721i | \(0.525786\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | 4.10926i | 0.289845i | ||||||||
\(202\) | 12.6908i | 0.892922i | ||||||||
\(203\) | 9.96567i | 0.699453i | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | −2.64516 | −0.184746 | ||||||||
\(206\) | 4.79612i | 0.334161i | ||||||||
\(207\) | 4.93593 | 0.343071 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.5036 | −1.48744 | ||||||||
\(210\) | 2.32258i | 0.160273i | ||||||||
\(211\) | 22.4775 | 1.54741 | 0.773707 | − | 0.633543i | \(-0.218400\pi\) | ||||
0.773707 | + | 0.633543i | \(0.218400\pi\) | |||||||
\(212\) | 5.48693 | 0.376844 | ||||||||
\(213\) | − 15.8719i | − 1.08752i | ||||||||
\(214\) | − 3.07180i | − 0.209984i | ||||||||
\(215\) | − 12.2508i | − 0.835496i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 8.06361 | 0.547393 | ||||||||
\(218\) | 6.69081 | 0.453159 | ||||||||
\(219\) | 13.5734i | 0.917203i | ||||||||
\(220\) | 5.34541 | 0.360387 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.14925 | −0.211364 | ||||||||
\(223\) | 1.37891i | 0.0923389i | 0.998934 | + | 0.0461694i | \(0.0147014\pi\) | ||||
−0.998934 | + | 0.0461694i | \(0.985299\pi\) | |||||||
\(224\) | 2.32258 | 0.155184 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 7.10972i | 0.472931i | ||||||||
\(227\) | 19.3205i | 1.28235i | 0.767396 | + | 0.641174i | \(0.221552\pi\) | ||||
−0.767396 | + | 0.641174i | \(0.778448\pi\) | |||||||
\(228\) | − 4.02283i | − 0.266418i | ||||||||
\(229\) | 15.7626i | 1.04162i | 0.853672 | + | 0.520811i | \(0.174370\pi\) | ||||
−0.853672 | + | 0.520811i | \(0.825630\pi\) | |||||||
\(230\) | 4.93593 | 0.325466 | ||||||||
\(231\) | −12.4151 | −0.816856 | ||||||||
\(232\) | 4.29078i | 0.281703i | ||||||||
\(233\) | −16.5549 | −1.08455 | −0.542275 | − | 0.840201i | \(-0.682437\pi\) | ||||
−0.542275 | + | 0.840201i | \(0.682437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.81894 | −0.118655 | ||||||||
\(236\) | 6.78668i | 0.441775i | ||||||||
\(237\) | −7.96774 | −0.517560 | ||||||||
\(238\) | −9.29032 | −0.602202 | ||||||||
\(239\) | − 26.2006i | − 1.69477i | −0.530976 | − | 0.847387i | \(-0.678175\pi\) | ||||
0.530976 | − | 0.847387i | \(-0.321825\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | 15.6496i | 1.00808i | 0.863681 | + | 0.504039i | \(0.168153\pi\) | ||||
−0.863681 | + | 0.504039i | \(0.831847\pi\) | |||||||
\(242\) | 17.5734i | 1.12966i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.535898 | −0.0343074 | ||||||||
\(245\) | 1.60562i | 0.102580i | ||||||||
\(246\) | 2.64516 | 0.168649 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.47183 | 0.220462 | ||||||||
\(249\) | 11.3360i | 0.718388i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 28.3416 | 1.78891 | 0.894454 | − | 0.447160i | \(-0.147565\pi\) | ||||
0.894454 | + | 0.447160i | \(0.147565\pi\) | |||||||
\(252\) | − 2.32258i | − 0.146309i | ||||||||
\(253\) | 26.3846i | 1.65878i | ||||||||
\(254\) | − 2.13209i | − 0.133779i | ||||||||
\(255\) | − 4.00000i | − 0.250490i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.5093 | 0.780309 | 0.390154 | − | 0.920750i | \(-0.372422\pi\) | ||||
0.390154 | + | 0.920750i | \(0.372422\pi\) | |||||||
\(258\) | 12.2508i | 0.762700i | ||||||||
\(259\) | 7.31439 | 0.454494 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.29078 | 0.265592 | ||||||||
\(262\) | − 1.25851i | − 0.0777513i | ||||||||
\(263\) | −10.7059 | −0.660154 | −0.330077 | − | 0.943954i | \(-0.607075\pi\) | ||||
−0.330077 | + | 0.943954i | \(0.607075\pi\) | |||||||
\(264\) | −5.34541 | −0.328987 | ||||||||
\(265\) | − 5.48693i | − 0.337059i | ||||||||
\(266\) | 9.34333i | 0.572877i | ||||||||
\(267\) | − 1.73978i | − 0.106473i | ||||||||
\(268\) | − 4.10926i | − 0.251013i | ||||||||
\(269\) | 7.52522 | 0.458821 | 0.229410 | − | 0.973330i | \(-0.426320\pi\) | ||||
0.229410 | + | 0.973330i | \(0.426320\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 9.84868i | 0.598264i | 0.954212 | + | 0.299132i | \(0.0966972\pi\) | ||||
−0.954212 | + | 0.299132i | \(0.903303\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.7149 | −1.19102 | ||||||||
\(275\) | − 5.34541i | − 0.322340i | ||||||||
\(276\) | −4.93593 | −0.297108 | ||||||||
\(277\) | −0.953101 | −0.0572663 | −0.0286331 | − | 0.999590i | \(-0.509115\pi\) | ||||
−0.0286331 | + | 0.999590i | \(0.509115\pi\) | |||||||
\(278\) | − 5.67742i | − 0.340509i | ||||||||
\(279\) | − 3.47183i | − 0.207853i | ||||||||
\(280\) | − 2.32258i | − 0.138801i | ||||||||
\(281\) | 5.57336i | 0.332479i | 0.986085 | + | 0.166239i | \(0.0531625\pi\) | ||||
−0.986085 | + | 0.166239i | \(0.946838\pi\) | |||||||
\(282\) | 1.81894 | 0.108316 | ||||||||
\(283\) | −22.0134 | −1.30856 | −0.654280 | − | 0.756252i | \(-0.727028\pi\) | ||||
−0.654280 | + | 0.756252i | \(0.727028\pi\) | |||||||
\(284\) | 15.8719i | 0.941822i | ||||||||
\(285\) | −4.02283 | −0.238292 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.14359 | −0.362645 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 4.29078 | 0.251963 | ||||||||
\(291\) | 16.1093i | 0.944342i | ||||||||
\(292\) | − 13.5734i | − 0.794321i | ||||||||
\(293\) | − 6.84302i | − 0.399773i | −0.979819 | − | 0.199887i | \(-0.935943\pi\) | ||||
0.979819 | − | 0.199887i | \(-0.0640574\pi\) | |||||||
\(294\) | − 1.60562i | − 0.0936419i | ||||||||
\(295\) | 6.78668 | 0.395136 | ||||||||
\(296\) | 3.14925 | 0.183047 | ||||||||
\(297\) | 5.34541i | 0.310172i | ||||||||
\(298\) | 19.4775 | 1.12830 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | − 28.4534i | − 1.64003i | ||||||||
\(302\) | −14.5170 | −0.835361 | ||||||||
\(303\) | −12.6908 | −0.729068 | ||||||||
\(304\) | 4.02283i | 0.230725i | ||||||||
\(305\) | 0.535898i | 0.0306855i | ||||||||
\(306\) | 4.00000i | 0.228665i | ||||||||
\(307\) | 4.75442i | 0.271349i | 0.990753 | + | 0.135675i | \(0.0433202\pi\) | ||||
−0.990753 | + | 0.135675i | \(0.956680\pi\) | |||||||
\(308\) | 12.4151 | 0.707418 | ||||||||
\(309\) | −4.79612 | −0.272842 | ||||||||
\(310\) | − 3.47183i | − 0.197187i | ||||||||
\(311\) | 1.93639 | 0.109803 | 0.0549013 | − | 0.998492i | \(-0.482516\pi\) | ||||
0.0549013 | + | 0.998492i | \(0.482516\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.5545 | 1.44443 | 0.722213 | − | 0.691671i | \(-0.243125\pi\) | ||||
0.722213 | + | 0.691671i | \(0.243125\pi\) | |||||||
\(314\) | − 24.3829i | − 1.37600i | ||||||||
\(315\) | −2.32258 | −0.130863 | ||||||||
\(316\) | 7.96774 | 0.448220 | ||||||||
\(317\) | 12.6667i | 0.711435i | 0.934594 | + | 0.355717i | \(0.115763\pi\) | ||||
−0.934594 | + | 0.355717i | \(0.884237\pi\) | |||||||
\(318\) | 5.48693i | 0.307692i | ||||||||
\(319\) | 22.9359i | 1.28417i | ||||||||
\(320\) | − 1.00000i | − 0.0559017i | ||||||||
\(321\) | 3.07180 | 0.171451 | ||||||||
\(322\) | 11.4641 | 0.638869 | ||||||||
\(323\) | − 16.0913i | − 0.895344i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.6267 | −1.30856 | ||||||||
\(327\) | 6.69081i | 0.370003i | ||||||||
\(328\) | −2.64516 | −0.146054 | ||||||||
\(329\) | −4.22464 | −0.232912 | ||||||||
\(330\) | 5.34541i | 0.294255i | ||||||||
\(331\) | 23.6981i | 1.30256i | 0.758836 | + | 0.651282i | \(0.225769\pi\) | ||||
−0.758836 | + | 0.651282i | \(0.774231\pi\) | |||||||
\(332\) | − 11.3360i | − 0.622142i | ||||||||
\(333\) | − 3.14925i | − 0.172578i | ||||||||
\(334\) | 16.7471 | 0.916363 | ||||||||
\(335\) | −4.10926 | −0.224513 | ||||||||
\(336\) | 2.32258i | 0.126707i | ||||||||
\(337\) | 19.5554 | 1.06525 | 0.532625 | − | 0.846351i | \(-0.321205\pi\) | ||||
0.532625 | + | 0.846351i | \(0.321205\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.10972 | −0.386147 | ||||||||
\(340\) | 4.00000i | 0.216930i | ||||||||
\(341\) | 18.5584 | 1.00499 | ||||||||
\(342\) | 4.02283 | 0.217530 | ||||||||
\(343\) | 19.9872i | 1.07921i | ||||||||
\(344\) | − 12.2508i | − 0.660518i | ||||||||
\(345\) | 4.93593i | 0.265742i | ||||||||
\(346\) | 16.1321i | 0.867266i | ||||||||
\(347\) | −23.0375 | −1.23672 | −0.618358 | − | 0.785897i | \(-0.712202\pi\) | ||||
−0.618358 | + | 0.785897i | \(0.712202\pi\) | |||||||
\(348\) | −4.29078 | −0.230010 | ||||||||
\(349\) | 15.3205i | 0.820088i | 0.912066 | + | 0.410044i | \(0.134487\pi\) | ||||
−0.912066 | + | 0.410044i | \(0.865513\pi\) | |||||||
\(350\) | −2.32258 | −0.124147 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.34541 | 0.284911 | ||||||||
\(353\) | 28.4078i | 1.51199i | 0.654576 | + | 0.755996i | \(0.272847\pi\) | ||||
−0.654576 | + | 0.755996i | \(0.727153\pi\) | |||||||
\(354\) | −6.78668 | −0.360708 | ||||||||
\(355\) | 15.8719 | 0.842391 | ||||||||
\(356\) | 1.73978i | 0.0922083i | ||||||||
\(357\) | − 9.29032i | − 0.491696i | ||||||||
\(358\) | 7.32824i | 0.387309i | ||||||||
\(359\) | − 23.5734i | − 1.24415i | −0.782956 | − | 0.622077i | \(-0.786289\pi\) | ||||
0.782956 | − | 0.622077i | \(-0.213711\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 2.81687 | 0.148256 | ||||||||
\(362\) | 19.5734i | 1.02875i | ||||||||
\(363\) | −17.5734 | −0.922362 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.5734 | −0.710462 | ||||||||
\(366\) | − 0.535898i | − 0.0280119i | ||||||||
\(367\) | 27.4909 | 1.43501 | 0.717506 | − | 0.696552i | \(-0.245283\pi\) | ||||
0.717506 | + | 0.696552i | \(0.245283\pi\) | |||||||
\(368\) | 4.93593 | 0.257303 | ||||||||
\(369\) | 2.64516i | 0.137701i | ||||||||
\(370\) | − 3.14925i | − 0.163722i | ||||||||
\(371\) | − 12.7438i | − 0.661627i | ||||||||
\(372\) | 3.47183i | 0.180006i | ||||||||
\(373\) | 26.3421 | 1.36394 | 0.681971 | − | 0.731379i | \(-0.261123\pi\) | ||||
0.681971 | + | 0.731379i | \(0.261123\pi\) | |||||||
\(374\) | −21.3816 | −1.10562 | ||||||||
\(375\) | − 1.00000i | − 0.0516398i | ||||||||
\(376\) | −1.81894 | −0.0938048 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.32258 | 0.119461 | ||||||||
\(379\) | 0.448551i | 0.0230405i | 0.999934 | + | 0.0115202i | \(0.00366709\pi\) | ||||
−0.999934 | + | 0.0115202i | \(0.996333\pi\) | |||||||
\(380\) | 4.02283 | 0.206367 | ||||||||
\(381\) | 2.13209 | 0.109230 | ||||||||
\(382\) | 17.0375i | 0.871713i | ||||||||
\(383\) | − 12.1227i | − 0.619439i | −0.950828 | − | 0.309719i | \(-0.899765\pi\) | ||||
0.950828 | − | 0.309719i | \(-0.100235\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | − 12.4151i | − 0.632734i | ||||||||
\(386\) | 6.15491 | 0.313277 | ||||||||
\(387\) | −12.2508 | −0.622742 | ||||||||
\(388\) | − 16.1093i | − 0.817824i | ||||||||
\(389\) | 18.6195 | 0.944045 | 0.472022 | − | 0.881587i | \(-0.343524\pi\) | ||||
0.472022 | + | 0.881587i | \(0.343524\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.7437 | −0.998484 | ||||||||
\(392\) | 1.60562i | 0.0810962i | ||||||||
\(393\) | 1.25851 | 0.0634837 | ||||||||
\(394\) | −13.7867 | −0.694563 | ||||||||
\(395\) | − 7.96774i | − 0.400900i | ||||||||
\(396\) | − 5.34541i | − 0.268617i | ||||||||
\(397\) | − 11.3042i | − 0.567340i | −0.958922 | − | 0.283670i | \(-0.908448\pi\) | ||||
0.958922 | − | 0.283670i | \(-0.0915520\pi\) | |||||||
\(398\) | 2.28304i | 0.114439i | ||||||||
\(399\) | −9.34333 | −0.467752 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 1.50580i | − 0.0751959i | −0.999293 | − | 0.0375980i | \(-0.988029\pi\) | ||||
0.999293 | − | 0.0375980i | \(-0.0119706\pi\) | |||||||
\(402\) | 4.10926 | 0.204951 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12.6908 | 0.631391 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 9.96567 | 0.494588 | ||||||||
\(407\) | 16.8340 | 0.834432 | ||||||||
\(408\) | − 4.00000i | − 0.198030i | ||||||||
\(409\) | − 11.1394i | − 0.550806i | −0.961329 | − | 0.275403i | \(-0.911189\pi\) | ||||
0.961329 | − | 0.275403i | \(-0.0888113\pi\) | |||||||
\(410\) | 2.64516i | 0.130635i | ||||||||
\(411\) | − 19.7149i | − 0.972464i | ||||||||
\(412\) | 4.79612 | 0.236288 | ||||||||
\(413\) | 15.7626 | 0.775627 | ||||||||
\(414\) | − 4.93593i | − 0.242588i | ||||||||
\(415\) | −11.3360 | −0.556461 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.67742 | 0.278024 | ||||||||
\(418\) | 21.5036i | 1.05178i | ||||||||
\(419\) | −15.5098 | −0.757701 | −0.378851 | − | 0.925458i | \(-0.623681\pi\) | ||||
−0.378851 | + | 0.925458i | \(0.623681\pi\) | |||||||
\(420\) | 2.32258 | 0.113330 | ||||||||
\(421\) | 39.4452i | 1.92244i | 0.275778 | + | 0.961221i | \(0.411065\pi\) | ||||
−0.275778 | + | 0.961221i | \(0.588935\pi\) | |||||||
\(422\) | − 22.4775i | − 1.09419i | ||||||||
\(423\) | 1.81894i | 0.0884400i | ||||||||
\(424\) | − 5.48693i | − 0.266469i | ||||||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | −15.8719 | −0.768995 | ||||||||
\(427\) | 1.24467i | 0.0602336i | ||||||||
\(428\) | −3.07180 | −0.148481 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.2508 | −0.590785 | ||||||||
\(431\) | 2.15491i | 0.103799i | 0.998652 | + | 0.0518993i | \(0.0165275\pi\) | ||||
−0.998652 | + | 0.0518993i | \(0.983473\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −1.33938 | −0.0643664 | −0.0321832 | − | 0.999482i | \(-0.510246\pi\) | ||||
−0.0321832 | + | 0.999482i | \(0.510246\pi\) | |||||||
\(434\) | − 8.06361i | − 0.387066i | ||||||||
\(435\) | 4.29078i | 0.205727i | ||||||||
\(436\) | − 6.69081i | − 0.320432i | ||||||||
\(437\) | 19.8564i | 0.949861i | ||||||||
\(438\) | 13.5734 | 0.648560 | ||||||||
\(439\) | 31.6981 | 1.51287 | 0.756434 | − | 0.654071i | \(-0.226940\pi\) | ||||
0.756434 | + | 0.654071i | \(0.226940\pi\) | |||||||
\(440\) | − 5.34541i | − 0.254832i | ||||||||
\(441\) | 1.60562 | 0.0764583 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.0904 | −1.33461 | −0.667307 | − | 0.744782i | \(-0.732553\pi\) | ||||
−0.667307 | + | 0.744782i | \(0.732553\pi\) | |||||||
\(444\) | 3.14925i | 0.149457i | ||||||||
\(445\) | 1.73978 | 0.0824736 | ||||||||
\(446\) | 1.37891 | 0.0652935 | ||||||||
\(447\) | 19.4775i | 0.921254i | ||||||||
\(448\) | − 2.32258i | − 0.109732i | ||||||||
\(449\) | − 28.9167i | − 1.36466i | −0.731043 | − | 0.682332i | \(-0.760966\pi\) | ||||
0.731043 | − | 0.682332i | \(-0.239034\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −14.1395 | −0.665801 | ||||||||
\(452\) | 7.10972 | 0.334413 | ||||||||
\(453\) | − 14.5170i | − 0.682070i | ||||||||
\(454\) | 19.3205 | 0.906756 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.02283 | −0.188386 | ||||||||
\(457\) | 9.69900i | 0.453700i | 0.973930 | + | 0.226850i | \(0.0728427\pi\) | ||||
−0.973930 | + | 0.226850i | \(0.927157\pi\) | |||||||
\(458\) | 15.7626 | 0.736538 | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | − 4.93593i | − 0.230139i | ||||||||
\(461\) | − 11.9979i | − 0.558799i | −0.960175 | − | 0.279400i | \(-0.909865\pi\) | ||||
0.960175 | − | 0.279400i | \(-0.0901354\pi\) | |||||||
\(462\) | 12.4151i | 0.577604i | ||||||||
\(463\) | − 6.42664i | − 0.298671i | −0.988787 | − | 0.149336i | \(-0.952287\pi\) | ||||
0.988787 | − | 0.149336i | \(-0.0477135\pi\) | |||||||
\(464\) | 4.29078 | 0.199194 | ||||||||
\(465\) | 3.47183 | 0.161002 | ||||||||
\(466\) | 16.5549i | 0.766893i | ||||||||
\(467\) | 26.2642 | 1.21536 | 0.607681 | − | 0.794182i | \(-0.292100\pi\) | ||||
0.607681 | + | 0.794182i | \(0.292100\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.54409 | −0.440705 | ||||||||
\(470\) | 1.81894i | 0.0839015i | ||||||||
\(471\) | 24.3829 | 1.12350 | ||||||||
\(472\) | 6.78668 | 0.312382 | ||||||||
\(473\) | − 65.4854i | − 3.01102i | ||||||||
\(474\) | 7.96774i | 0.365970i | ||||||||
\(475\) | − 4.02283i | − 0.184580i | ||||||||
\(476\) | 9.29032i | 0.425821i | ||||||||
\(477\) | −5.48693 | −0.251229 | ||||||||
\(478\) | −26.2006 | −1.19839 | ||||||||
\(479\) | − 25.6826i | − 1.17347i | −0.809779 | − | 0.586735i | \(-0.800413\pi\) | ||||
0.809779 | − | 0.586735i | \(-0.199587\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 15.6496 | 0.712818 | ||||||||
\(483\) | 11.4641i | 0.521635i | ||||||||
\(484\) | 17.5734 | 0.798789 | ||||||||
\(485\) | −16.1093 | −0.731484 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | 9.37891i | 0.424999i | 0.977161 | + | 0.212500i | \(0.0681604\pi\) | ||||
−0.977161 | + | 0.212500i | \(0.931840\pi\) | |||||||
\(488\) | 0.535898i | 0.0242590i | ||||||||
\(489\) | − 23.6267i | − 1.06844i | ||||||||
\(490\) | 1.60562 | 0.0725347 | ||||||||
\(491\) | 7.73854 | 0.349235 | 0.174618 | − | 0.984636i | \(-0.444131\pi\) | ||||
0.174618 | + | 0.984636i | \(0.444131\pi\) | |||||||
\(492\) | − 2.64516i | − 0.119253i | ||||||||
\(493\) | −17.1631 | −0.772987 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.34541 | −0.240258 | ||||||||
\(496\) | − 3.47183i | − 0.155890i | ||||||||
\(497\) | 36.8637 | 1.65356 | ||||||||
\(498\) | 11.3360 | 0.507977 | ||||||||
\(499\) | − 3.18106i | − 0.142404i | −0.997462 | − | 0.0712019i | \(-0.977317\pi\) | ||||
0.997462 | − | 0.0712019i | \(-0.0226834\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 16.7471i | 0.748207i | ||||||||
\(502\) | − 28.3416i | − 1.26495i | ||||||||
\(503\) | −35.0758 | −1.56395 | −0.781975 | − | 0.623309i | \(-0.785788\pi\) | ||||
−0.781975 | + | 0.623309i | \(0.785788\pi\) | |||||||
\(504\) | −2.32258 | −0.103456 | ||||||||
\(505\) | − 12.6908i | − 0.564734i | ||||||||
\(506\) | 26.3846 | 1.17294 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.13209 | −0.0945961 | ||||||||
\(509\) | − 18.7867i | − 0.832705i | −0.909203 | − | 0.416353i | \(-0.863308\pi\) | ||||
0.909203 | − | 0.416353i | \(-0.136692\pi\) | |||||||
\(510\) | −4.00000 | −0.177123 | ||||||||
\(511\) | −31.5252 | −1.39459 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 4.02283i | 0.177612i | ||||||||
\(514\) | − 12.5093i | − 0.551761i | ||||||||
\(515\) | − 4.79612i | − 0.211342i | ||||||||
\(516\) | 12.2508 | 0.539311 | ||||||||
\(517\) | −9.72298 | −0.427616 | ||||||||
\(518\) | − 7.31439i | − 0.321376i | ||||||||
\(519\) | −16.1321 | −0.708120 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.28512 | 0.231545 | 0.115773 | − | 0.993276i | \(-0.463066\pi\) | ||||
0.115773 | + | 0.993276i | \(0.463066\pi\) | |||||||
\(522\) | − 4.29078i | − 0.187802i | ||||||||
\(523\) | −20.7523 | −0.907437 | −0.453718 | − | 0.891145i | \(-0.649903\pi\) | ||||
−0.453718 | + | 0.891145i | \(0.649903\pi\) | |||||||
\(524\) | −1.25851 | −0.0549785 | ||||||||
\(525\) | − 2.32258i | − 0.101366i | ||||||||
\(526\) | 10.7059i | 0.466800i | ||||||||
\(527\) | 13.8873i | 0.604942i | ||||||||
\(528\) | 5.34541i | 0.232629i | ||||||||
\(529\) | 1.36345 | 0.0592805 | ||||||||
\(530\) | −5.48693 | −0.238337 | ||||||||
\(531\) | − 6.78668i | − 0.294517i | ||||||||
\(532\) | 9.34333 | 0.405085 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.73978 | −0.0752877 | ||||||||
\(535\) | 3.07180i | 0.132805i | ||||||||
\(536\) | −4.10926 | −0.177493 | ||||||||
\(537\) | −7.32824 | −0.316237 | ||||||||
\(538\) | − 7.52522i | − 0.324435i | ||||||||
\(539\) | 8.58271i | 0.369683i | ||||||||
\(540\) | − 1.00000i | − 0.0430331i | ||||||||
\(541\) | 28.7365i | 1.23548i | 0.786384 | + | 0.617739i | \(0.211951\pi\) | ||||
−0.786384 | + | 0.617739i | \(0.788049\pi\) | |||||||
\(542\) | 9.84868 | 0.423037 | ||||||||
\(543\) | −19.5734 | −0.839973 | ||||||||
\(544\) | 4.00000i | 0.171499i | ||||||||
\(545\) | −6.69081 | −0.286603 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.3768 | 0.785737 | 0.392869 | − | 0.919595i | \(-0.371483\pi\) | ||||
0.392869 | + | 0.919595i | \(0.371483\pi\) | |||||||
\(548\) | 19.7149i | 0.842178i | ||||||||
\(549\) | 0.535898 | 0.0228716 | ||||||||
\(550\) | −5.34541 | −0.227929 | ||||||||
\(551\) | 17.2610i | 0.735345i | ||||||||
\(552\) | 4.93593i | 0.210087i | ||||||||
\(553\) | − 18.5057i | − 0.786943i | ||||||||
\(554\) | 0.953101i | 0.0404934i | ||||||||
\(555\) | 3.14925 | 0.133678 | ||||||||
\(556\) | −5.67742 | −0.240776 | ||||||||
\(557\) | 26.5386i | 1.12448i | 0.826975 | + | 0.562238i | \(0.190060\pi\) | ||||
−0.826975 | + | 0.562238i | \(0.809940\pi\) | |||||||
\(558\) | −3.47183 | −0.146974 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.32258 | −0.0981469 | ||||||||
\(561\) | − 21.3816i | − 0.902733i | ||||||||
\(562\) | 5.57336 | 0.235098 | ||||||||
\(563\) | 6.06111 | 0.255446 | 0.127723 | − | 0.991810i | \(-0.459233\pi\) | ||||
0.127723 | + | 0.991810i | \(0.459233\pi\) | |||||||
\(564\) | − 1.81894i | − 0.0765913i | ||||||||
\(565\) | − 7.10972i | − 0.299108i | ||||||||
\(566\) | 22.0134i | 0.925292i | ||||||||
\(567\) | 2.32258i | 0.0975392i | ||||||||
\(568\) | 15.8719 | 0.665969 | ||||||||
\(569\) | 14.4964 | 0.607719 | 0.303860 | − | 0.952717i | \(-0.401725\pi\) | ||||
0.303860 | + | 0.952717i | \(0.401725\pi\) | |||||||
\(570\) | 4.02283i | 0.168498i | ||||||||
\(571\) | −2.90413 | −0.121534 | −0.0607670 | − | 0.998152i | \(-0.519355\pi\) | ||||
−0.0607670 | + | 0.998152i | \(0.519355\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.0375 | −0.711750 | ||||||||
\(574\) | 6.14359i | 0.256429i | ||||||||
\(575\) | −4.93593 | −0.205843 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 18.8180i | 0.783405i | 0.920092 | + | 0.391702i | \(0.128114\pi\) | ||||
−0.920092 | + | 0.391702i | \(0.871886\pi\) | |||||||
\(578\) | 1.00000i | 0.0415945i | ||||||||
\(579\) | 6.15491i | 0.255789i | ||||||||
\(580\) | − 4.29078i | − 0.178165i | ||||||||
\(581\) | −26.3287 | −1.09230 | ||||||||
\(582\) | 16.1093 | 0.667750 | ||||||||
\(583\) | − 29.3299i | − 1.21472i | ||||||||
\(584\) | −13.5734 | −0.561670 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.84302 | −0.282682 | ||||||||
\(587\) | − 3.93639i | − 0.162472i | −0.996695 | − | 0.0812361i | \(-0.974113\pi\) | ||||
0.996695 | − | 0.0812361i | \(-0.0258868\pi\) | |||||||
\(588\) | −1.60562 | −0.0662148 | ||||||||
\(589\) | 13.9666 | 0.575483 | ||||||||
\(590\) | − 6.78668i | − 0.279403i | ||||||||
\(591\) | − 13.7867i | − 0.567108i | ||||||||
\(592\) | − 3.14925i | − 0.129434i | ||||||||
\(593\) | − 20.1227i | − 0.826338i | −0.910654 | − | 0.413169i | \(-0.864422\pi\) | ||||
0.910654 | − | 0.413169i | \(-0.135578\pi\) | |||||||
\(594\) | 5.34541 | 0.219325 | ||||||||
\(595\) | 9.29032 | 0.380866 | ||||||||
\(596\) | − 19.4775i | − 0.797829i | ||||||||
\(597\) | −2.28304 | −0.0934388 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 48.1172 | 1.96601 | 0.983007 | − | 0.183567i | \(-0.0587644\pi\) | ||||
0.983007 | + | 0.183567i | \(0.0587644\pi\) | |||||||
\(600\) | − 1.00000i | − 0.0408248i | ||||||||
\(601\) | −4.24217 | −0.173042 | −0.0865209 | − | 0.996250i | \(-0.527575\pi\) | ||||
−0.0865209 | + | 0.996250i | \(0.527575\pi\) | |||||||
\(602\) | −28.4534 | −1.15967 | ||||||||
\(603\) | 4.10926i | 0.167342i | ||||||||
\(604\) | 14.5170i | 0.590690i | ||||||||
\(605\) | − 17.5734i | − 0.714459i | ||||||||
\(606\) | 12.6908i | 0.515529i | ||||||||
\(607\) | 12.0685 | 0.489844 | 0.244922 | − | 0.969543i | \(-0.421238\pi\) | ||||
0.244922 | + | 0.969543i | \(0.421238\pi\) | |||||||
\(608\) | 4.02283 | 0.163147 | ||||||||
\(609\) | 9.96567i | 0.403829i | ||||||||
\(610\) | 0.535898 | 0.0216979 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | 41.7421i | 1.68595i | 0.537954 | + | 0.842974i | \(0.319197\pi\) | ||||
−0.537954 | + | 0.842974i | \(0.680803\pi\) | |||||||
\(614\) | 4.75442 | 0.191873 | ||||||||
\(615\) | −2.64516 | −0.106663 | ||||||||
\(616\) | − 12.4151i | − 0.500220i | ||||||||
\(617\) | 33.4586i | 1.34699i | 0.739190 | + | 0.673497i | \(0.235208\pi\) | ||||
−0.739190 | + | 0.673497i | \(0.764792\pi\) | |||||||
\(618\) | 4.79612i | 0.192928i | ||||||||
\(619\) | − 38.0978i | − 1.53128i | −0.643270 | − | 0.765639i | \(-0.722423\pi\) | ||||
0.643270 | − | 0.765639i | \(-0.277577\pi\) | |||||||
\(620\) | −3.47183 | −0.139432 | ||||||||
\(621\) | 4.93593 | 0.198072 | ||||||||
\(622\) | − 1.93639i | − 0.0776422i | ||||||||
\(623\) | 4.04078 | 0.161891 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 25.5545i | − 1.02136i | ||||||||
\(627\) | −21.5036 | −0.858773 | ||||||||
\(628\) | −24.3829 | −0.972982 | ||||||||
\(629\) | 12.5970i | 0.502276i | ||||||||
\(630\) | 2.32258i | 0.0925338i | ||||||||
\(631\) | 24.8001i | 0.987275i | 0.869668 | + | 0.493638i | \(0.164333\pi\) | ||||
−0.869668 | + | 0.493638i | \(0.835667\pi\) | |||||||
\(632\) | − 7.96774i | − 0.316940i | ||||||||
\(633\) | 22.4775 | 0.893400 | ||||||||
\(634\) | 12.6667 | 0.503060 | ||||||||
\(635\) | 2.13209i | 0.0846093i | ||||||||
\(636\) | 5.48693 | 0.217571 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.9359 | 0.908042 | ||||||||
\(639\) | − 15.8719i | − 0.627881i | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −4.08519 | −0.161355 | −0.0806776 | − | 0.996740i | \(-0.525708\pi\) | ||||
−0.0806776 | + | 0.996740i | \(0.525708\pi\) | |||||||
\(642\) | − 3.07180i | − 0.121234i | ||||||||
\(643\) | 36.5816i | 1.44264i | 0.692604 | + | 0.721318i | \(0.256463\pi\) | ||||
−0.692604 | + | 0.721318i | \(0.743537\pi\) | |||||||
\(644\) | − 11.4641i | − 0.451749i | ||||||||
\(645\) | − 12.2508i | − 0.482374i | ||||||||
\(646\) | −16.0913 | −0.633104 | ||||||||
\(647\) | −17.2341 | −0.677541 | −0.338771 | − | 0.940869i | \(-0.610011\pi\) | ||||
−0.338771 | + | 0.940869i | \(0.610011\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 36.2776 | 1.42402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.06361 | 0.316038 | ||||||||
\(652\) | 23.6267i | 0.925295i | ||||||||
\(653\) | −21.9274 | −0.858085 | −0.429042 | − | 0.903284i | \(-0.641149\pi\) | ||||
−0.429042 | + | 0.903284i | \(0.641149\pi\) | |||||||
\(654\) | 6.69081 | 0.261631 | ||||||||
\(655\) | 1.25851i | 0.0491742i | ||||||||
\(656\) | 2.64516i | 0.103276i | ||||||||
\(657\) | 13.5734i | 0.529547i | ||||||||
\(658\) | 4.22464i | 0.164694i | ||||||||
\(659\) | −48.4759 | −1.88835 | −0.944176 | − | 0.329441i | \(-0.893140\pi\) | ||||
−0.944176 | + | 0.329441i | \(0.893140\pi\) | |||||||
\(660\) | 5.34541 | 0.208070 | ||||||||
\(661\) | − 29.8221i | − 1.15994i | −0.814636 | − | 0.579972i | \(-0.803063\pi\) | ||||
0.814636 | − | 0.579972i | \(-0.196937\pi\) | |||||||
\(662\) | 23.6981 | 0.921052 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.3360 | −0.439921 | ||||||||
\(665\) | − 9.34333i | − 0.362319i | ||||||||
\(666\) | −3.14925 | −0.122031 | ||||||||
\(667\) | 21.1790 | 0.820054 | ||||||||
\(668\) | − 16.7471i | − 0.647967i | ||||||||
\(669\) | 1.37891i | 0.0533119i | ||||||||
\(670\) | 4.10926i | 0.158755i | ||||||||
\(671\) | 2.86459i | 0.110586i | ||||||||
\(672\) | 2.32258 | 0.0895955 | ||||||||
\(673\) | 30.6719 | 1.18232 | 0.591158 | − | 0.806556i | \(-0.298671\pi\) | ||||
0.591158 | + | 0.806556i | \(0.298671\pi\) | |||||||
\(674\) | − 19.5554i | − 0.753246i | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.0831 | 0.810290 | 0.405145 | − | 0.914252i | \(-0.367221\pi\) | ||||
0.405145 | + | 0.914252i | \(0.367221\pi\) | |||||||
\(678\) | 7.10972i | 0.273047i | ||||||||
\(679\) | −37.4150 | −1.43586 | ||||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | 19.3205i | 0.740363i | ||||||||
\(682\) | − 18.5584i | − 0.710636i | ||||||||
\(683\) | 13.3360i | 0.510287i | 0.966903 | + | 0.255143i | \(0.0821227\pi\) | ||||
−0.966903 | + | 0.255143i | \(0.917877\pi\) | |||||||
\(684\) | − 4.02283i | − 0.153817i | ||||||||
\(685\) | 19.7149 | 0.753267 | ||||||||
\(686\) | 19.9872 | 0.763117 | ||||||||
\(687\) | 15.7626i | 0.601381i | ||||||||
\(688\) | −12.2508 | −0.467057 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.93593 | 0.187908 | ||||||||
\(691\) | − 34.9054i | − 1.32786i | −0.747793 | − | 0.663932i | \(-0.768887\pi\) | ||||
0.747793 | − | 0.663932i | \(-0.231113\pi\) | |||||||
\(692\) | 16.1321 | 0.613250 | ||||||||
\(693\) | −12.4151 | −0.471612 | ||||||||
\(694\) | 23.0375i | 0.874490i | ||||||||
\(695\) | 5.67742i | 0.215357i | ||||||||
\(696\) | 4.29078i | 0.162641i | ||||||||
\(697\) | − 10.5806i | − 0.400770i | ||||||||
\(698\) | 15.3205 | 0.579890 | ||||||||
\(699\) | −16.5549 | −0.626166 | ||||||||
\(700\) | 2.32258i | 0.0877853i | ||||||||
\(701\) | 39.6715 | 1.49837 | 0.749186 | − | 0.662360i | \(-0.230445\pi\) | ||||
0.749186 | + | 0.662360i | \(0.230445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.6689 | 0.477817 | ||||||||
\(704\) | − 5.34541i | − 0.201463i | ||||||||
\(705\) | −1.81894 | −0.0685053 | ||||||||
\(706\) | 28.4078 | 1.06914 | ||||||||
\(707\) | − 29.4754i | − 1.10854i | ||||||||
\(708\) | 6.78668i | 0.255059i | ||||||||
\(709\) | − 2.83441i | − 0.106448i | −0.998583 | − | 0.0532242i | \(-0.983050\pi\) | ||||
0.998583 | − | 0.0532242i | \(-0.0169498\pi\) | |||||||
\(710\) | − 15.8719i | − 0.595661i | ||||||||
\(711\) | −7.96774 | −0.298814 | ||||||||
\(712\) | 1.73978 | 0.0652011 | ||||||||
\(713\) | − 17.1367i | − 0.641776i | ||||||||
\(714\) | −9.29032 | −0.347681 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.32824 | 0.273869 | ||||||||
\(717\) | − 26.2006i | − 0.978478i | ||||||||
\(718\) | −23.5734 | −0.879750 | ||||||||
\(719\) | 43.7128 | 1.63021 | 0.815106 | − | 0.579311i | \(-0.196678\pi\) | ||||
0.815106 | + | 0.579311i | \(0.196678\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | − 11.1394i | − 0.414852i | ||||||||
\(722\) | − 2.81687i | − 0.104833i | ||||||||
\(723\) | 15.6496i | 0.582014i | ||||||||
\(724\) | 19.5734 | 0.727438 | ||||||||
\(725\) | −4.29078 | −0.159355 | ||||||||
\(726\) | 17.5734i | 0.652209i | ||||||||
\(727\) | −16.2568 | −0.602932 | −0.301466 | − | 0.953477i | \(-0.597476\pi\) | ||||
−0.301466 | + | 0.953477i | \(0.597476\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.5734i | 0.502373i | ||||||||
\(731\) | 49.0031 | 1.81245 | ||||||||
\(732\) | −0.535898 | −0.0198074 | ||||||||
\(733\) | − 4.96774i | − 0.183488i | −0.995783 | − | 0.0917438i | \(-0.970756\pi\) | ||||
0.995783 | − | 0.0917438i | \(-0.0292441\pi\) | |||||||
\(734\) | − 27.4909i | − 1.01471i | ||||||||
\(735\) | 1.60562i | 0.0592243i | ||||||||
\(736\) | − 4.93593i | − 0.181941i | ||||||||
\(737\) | −21.9657 | −0.809116 | ||||||||
\(738\) | 2.64516 | 0.0973697 | ||||||||
\(739\) | 49.6875i | 1.82778i | 0.405957 | + | 0.913892i | \(0.366938\pi\) | ||||
−0.405957 | + | 0.913892i | \(0.633062\pi\) | |||||||
\(740\) | −3.14925 | −0.115769 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.7438 | −0.467841 | ||||||||
\(743\) | 21.5420i | 0.790300i | 0.918617 | + | 0.395150i | \(0.129307\pi\) | ||||
−0.918617 | + | 0.395150i | \(0.870693\pi\) | |||||||
\(744\) | 3.47183 | 0.127284 | ||||||||
\(745\) | −19.4775 | −0.713600 | ||||||||
\(746\) | − 26.3421i | − 0.964452i | ||||||||
\(747\) | 11.3360i | 0.414761i | ||||||||
\(748\) | 21.3816i | 0.781790i | ||||||||
\(749\) | 7.13449i | 0.260689i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 6.34872 | 0.231668 | 0.115834 | − | 0.993269i | \(-0.463046\pi\) | ||||
0.115834 | + | 0.993269i | \(0.463046\pi\) | |||||||
\(752\) | 1.81894i | 0.0663300i | ||||||||
\(753\) | 28.3416 | 1.03283 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.5170 | 0.528329 | ||||||||
\(756\) | − 2.32258i | − 0.0844714i | ||||||||
\(757\) | −48.1107 | −1.74861 | −0.874307 | − | 0.485373i | \(-0.838684\pi\) | ||||
−0.874307 | + | 0.485373i | \(0.838684\pi\) | |||||||
\(758\) | 0.448551 | 0.0162921 | ||||||||
\(759\) | 26.3846i | 0.957699i | ||||||||
\(760\) | − 4.02283i | − 0.145923i | ||||||||
\(761\) | − 33.6866i | − 1.22114i | −0.791963 | − | 0.610569i | \(-0.790941\pi\) | ||||
0.791963 | − | 0.610569i | \(-0.209059\pi\) | |||||||
\(762\) | − 2.13209i | − 0.0772374i | ||||||||
\(763\) | −15.5399 | −0.562584 | ||||||||
\(764\) | 17.0375 | 0.616394 | ||||||||
\(765\) | − 4.00000i | − 0.144620i | ||||||||
\(766\) | −12.1227 | −0.438009 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | − 5.98886i | − 0.215964i | −0.994153 | − | 0.107982i | \(-0.965561\pi\) | ||||
0.994153 | − | 0.107982i | \(-0.0344389\pi\) | |||||||
\(770\) | −12.4151 | −0.447410 | ||||||||
\(771\) | 12.5093 | 0.450511 | ||||||||
\(772\) | − 6.15491i | − 0.221520i | ||||||||
\(773\) | − 13.4882i | − 0.485136i | −0.970134 | − | 0.242568i | \(-0.922010\pi\) | ||||
0.970134 | − | 0.242568i | \(-0.0779897\pi\) | |||||||
\(774\) | 12.2508i | 0.440345i | ||||||||
\(775\) | 3.47183i | 0.124712i | ||||||||
\(776\) | −16.1093 | −0.578289 | ||||||||
\(777\) | 7.31439 | 0.262402 | ||||||||
\(778\) | − 18.6195i | − 0.667540i | ||||||||
\(779\) | −10.6410 | −0.381254 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 84.8416 | 3.03587 | ||||||||
\(782\) | 19.7437i | 0.706035i | ||||||||
\(783\) | 4.29078 | 0.153340 | ||||||||
\(784\) | 1.60562 | 0.0573437 | ||||||||
\(785\) | 24.3829i | 0.870262i | ||||||||
\(786\) | − 1.25851i | − 0.0448897i | ||||||||
\(787\) | 54.6487i | 1.94802i | 0.226510 | + | 0.974009i | \(0.427268\pi\) | ||||
−0.226510 | + | 0.974009i | \(0.572732\pi\) | |||||||
\(788\) | 13.7867i | 0.491130i | ||||||||
\(789\) | −10.7059 | −0.381140 | ||||||||
\(790\) | −7.96774 | −0.283479 | ||||||||
\(791\) | − 16.5129i | − 0.587131i | ||||||||
\(792\) | −5.34541 | −0.189941 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −11.3042 | −0.401170 | ||||||||
\(795\) | − 5.48693i | − 0.194601i | ||||||||
\(796\) | 2.28304 | 0.0809203 | ||||||||
\(797\) | 38.3244 | 1.35752 | 0.678760 | − | 0.734361i | \(-0.262518\pi\) | ||||
0.678760 | + | 0.734361i | \(0.262518\pi\) | |||||||
\(798\) | 9.34333i | 0.330750i | ||||||||
\(799\) | − 7.27577i | − 0.257398i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − 1.73978i | − 0.0614722i | ||||||||
\(802\) | −1.50580 | −0.0531716 | ||||||||
\(803\) | −72.5551 | −2.56041 | ||||||||
\(804\) | − 4.10926i | − 0.144922i | ||||||||
\(805\) | −11.4641 | −0.404056 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.52522 | 0.264900 | ||||||||
\(808\) | − 12.6908i | − 0.446461i | ||||||||
\(809\) | 11.3816 | 0.400157 | 0.200078 | − | 0.979780i | \(-0.435880\pi\) | ||||
0.200078 | + | 0.979780i | \(0.435880\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 10.8899i | 0.382397i | 0.981551 | + | 0.191198i | \(0.0612374\pi\) | ||||
−0.981551 | + | 0.191198i | \(0.938763\pi\) | |||||||
\(812\) | − 9.96567i | − 0.349726i | ||||||||
\(813\) | 9.84868i | 0.345408i | ||||||||
\(814\) | − 16.8340i | − 0.590033i | ||||||||
\(815\) | 23.6267 | 0.827609 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | − 49.2828i | − 1.72419i | ||||||||
\(818\) | −11.1394 | −0.389479 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.64516 | 0.0923730 | ||||||||
\(821\) | − 1.68810i | − 0.0589152i | −0.999566 | − | 0.0294576i | \(-0.990622\pi\) | ||||
0.999566 | − | 0.0294576i | \(-0.00937800\pi\) | |||||||
\(822\) | −19.7149 | −0.687636 | ||||||||
\(823\) | −6.77816 | −0.236272 | −0.118136 | − | 0.992997i | \(-0.537692\pi\) | ||||
−0.118136 | + | 0.992997i | \(0.537692\pi\) | |||||||
\(824\) | − 4.79612i | − 0.167081i | ||||||||
\(825\) | − 5.34541i | − 0.186103i | ||||||||
\(826\) | − 15.7626i | − 0.548451i | ||||||||
\(827\) | 30.2298i | 1.05119i | 0.850733 | + | 0.525597i | \(0.176158\pi\) | ||||
−0.850733 | + | 0.525597i | \(0.823842\pi\) | |||||||
\(828\) | −4.93593 | −0.171536 | ||||||||
\(829\) | 10.4405 | 0.362612 | 0.181306 | − | 0.983427i | \(-0.441968\pi\) | ||||
0.181306 | + | 0.983427i | \(0.441968\pi\) | |||||||
\(830\) | 11.3360i | 0.393477i | ||||||||
\(831\) | −0.953101 | −0.0330627 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.42249 | −0.222526 | ||||||||
\(834\) | − 5.67742i | − 0.196593i | ||||||||
\(835\) | −16.7471 | −0.579559 | ||||||||
\(836\) | 21.5036 | 0.743719 | ||||||||
\(837\) | − 3.47183i | − 0.120004i | ||||||||
\(838\) | 15.5098i | 0.535776i | ||||||||
\(839\) | − 11.1965i | − 0.386547i | −0.981145 | − | 0.193273i | \(-0.938090\pi\) | ||||
0.981145 | − | 0.193273i | \(-0.0619104\pi\) | |||||||
\(840\) | − 2.32258i | − 0.0801366i | ||||||||
\(841\) | −10.5892 | −0.365146 | ||||||||
\(842\) | 39.4452 | 1.35937 | ||||||||
\(843\) | 5.57336i | 0.191957i | ||||||||
\(844\) | −22.4775 | −0.773707 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.81894 | 0.0625365 | ||||||||
\(847\) | − 40.8155i | − 1.40244i | ||||||||
\(848\) | −5.48693 | −0.188422 | ||||||||
\(849\) | −22.0134 | −0.755498 | ||||||||
\(850\) | − 4.00000i | − 0.137199i | ||||||||
\(851\) | − 15.5445i | − 0.532859i | ||||||||
\(852\) | 15.8719i | 0.543761i | ||||||||
\(853\) | − 21.8185i | − 0.747051i | −0.927620 | − | 0.373525i | \(-0.878149\pi\) | ||||
0.927620 | − | 0.373525i | \(-0.121851\pi\) | |||||||
\(854\) | 1.24467 | 0.0425916 | ||||||||
\(855\) | −4.02283 | −0.137578 | ||||||||
\(856\) | 3.07180i | 0.104992i | ||||||||
\(857\) | −9.42369 | −0.321907 | −0.160954 | − | 0.986962i | \(-0.551457\pi\) | ||||
−0.160954 | + | 0.986962i | \(0.551457\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.4775 | 0.835161 | 0.417581 | − | 0.908640i | \(-0.362878\pi\) | ||||
0.417581 | + | 0.908640i | \(0.362878\pi\) | |||||||
\(860\) | 12.2508i | 0.417748i | ||||||||
\(861\) | −6.14359 | −0.209373 | ||||||||
\(862\) | 2.15491 | 0.0733966 | ||||||||
\(863\) | 29.7873i | 1.01397i | 0.861954 | + | 0.506986i | \(0.169240\pi\) | ||||
−0.861954 | + | 0.506986i | \(0.830760\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | − 16.1321i | − 0.548507i | ||||||||
\(866\) | 1.33938i | 0.0455139i | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −8.06361 | −0.273697 | ||||||||
\(869\) | − 42.5908i | − 1.44479i | ||||||||
\(870\) | 4.29078 | 0.145471 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.69081 | −0.226579 | ||||||||
\(873\) | 16.1093i | 0.545216i | ||||||||
\(874\) | 19.8564 | 0.671653 | ||||||||
\(875\) | 2.32258 | 0.0785175 | ||||||||
\(876\) | − 13.5734i | − 0.458601i | ||||||||
\(877\) | − 1.90979i | − 0.0644890i | −0.999480 | − | 0.0322445i | \(-0.989734\pi\) | ||||
0.999480 | − | 0.0322445i | \(-0.0102655\pi\) | |||||||
\(878\) | − 31.6981i | − 1.06976i | ||||||||
\(879\) | − 6.84302i | − 0.230809i | ||||||||
\(880\) | −5.34541 | −0.180194 | ||||||||
\(881\) | −6.36823 | −0.214551 | −0.107276 | − | 0.994229i | \(-0.534213\pi\) | ||||
−0.107276 | + | 0.994229i | \(0.534213\pi\) | |||||||
\(882\) | − 1.60562i | − 0.0540642i | ||||||||
\(883\) | −34.9897 | −1.17750 | −0.588749 | − | 0.808316i | \(-0.700379\pi\) | ||||
−0.588749 | + | 0.808316i | \(0.700379\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.78668 | 0.228132 | ||||||||
\(886\) | 28.0904i | 0.943715i | ||||||||
\(887\) | 21.4001 | 0.718546 | 0.359273 | − | 0.933233i | \(-0.383025\pi\) | ||||
0.359273 | + | 0.933233i | \(0.383025\pi\) | |||||||
\(888\) | 3.14925 | 0.105682 | ||||||||
\(889\) | 4.95194i | 0.166083i | ||||||||
\(890\) | − 1.73978i | − 0.0583176i | ||||||||
\(891\) | 5.34541i | 0.179078i | ||||||||
\(892\) | − 1.37891i | − 0.0461694i | ||||||||
\(893\) | −7.31729 | −0.244864 | ||||||||
\(894\) | 19.4775 | 0.651425 | ||||||||
\(895\) | − 7.32824i | − 0.244956i | ||||||||
\(896\) | −2.32258 | −0.0775919 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.9167 | −0.964963 | ||||||||
\(899\) | − 14.8969i | − 0.496838i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 21.9477 | 0.731184 | ||||||||
\(902\) | 14.1395i | 0.470792i | ||||||||
\(903\) | − 28.4534i | − 0.946871i | ||||||||
\(904\) | − 7.10972i | − 0.236466i | ||||||||
\(905\) | − 19.5734i | − 0.650641i | ||||||||
\(906\) | −14.5170 | −0.482296 | ||||||||
\(907\) | −32.4693 | −1.07813 | −0.539063 | − | 0.842266i | \(-0.681221\pi\) | ||||
−0.539063 | + | 0.842266i | \(0.681221\pi\) | |||||||
\(908\) | − 19.3205i | − 0.641174i | ||||||||
\(909\) | −12.6908 | −0.420928 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.4380 | 1.14098 | 0.570490 | − | 0.821304i | \(-0.306753\pi\) | ||||
0.570490 | + | 0.821304i | \(0.306753\pi\) | |||||||
\(912\) | 4.02283i | 0.133209i | ||||||||
\(913\) | −60.5954 | −2.00541 | ||||||||
\(914\) | 9.69900 | 0.320814 | ||||||||
\(915\) | 0.535898i | 0.0177163i | ||||||||
\(916\) | − 15.7626i | − 0.520811i | ||||||||
\(917\) | 2.92300i | 0.0965260i | ||||||||
\(918\) | 4.00000i | 0.132020i | ||||||||
\(919\) | 36.4827 | 1.20345 | 0.601727 | − | 0.798702i | \(-0.294480\pi\) | ||||
0.601727 | + | 0.798702i | \(0.294480\pi\) | |||||||
\(920\) | −4.93593 | −0.162733 | ||||||||
\(921\) | 4.75442i | 0.156663i | ||||||||
\(922\) | −11.9979 | −0.395131 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.4151 | 0.408428 | ||||||||
\(925\) | 3.14925i | 0.103547i | ||||||||
\(926\) | −6.42664 | −0.211192 | ||||||||
\(927\) | −4.79612 | −0.157525 | ||||||||
\(928\) | − 4.29078i | − 0.140852i | ||||||||
\(929\) | − 49.9100i | − 1.63749i | −0.574155 | − | 0.818747i | \(-0.694669\pi\) | ||||
0.574155 | − | 0.818747i | \(-0.305331\pi\) | |||||||
\(930\) | − 3.47183i | − 0.113846i | ||||||||
\(931\) | 6.45914i | 0.211690i | ||||||||
\(932\) | 16.5549 | 0.542275 | ||||||||
\(933\) | 1.93639 | 0.0633946 | ||||||||
\(934\) | − 26.2642i | − 0.859390i | ||||||||
\(935\) | 21.3816 | 0.699254 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.8873 | −0.519017 | −0.259508 | − | 0.965741i | \(-0.583560\pi\) | ||||
−0.259508 | + | 0.965741i | \(0.583560\pi\) | |||||||
\(938\) | 9.54409i | 0.311625i | ||||||||
\(939\) | 25.5545 | 0.833939 | ||||||||
\(940\) | 1.81894 | 0.0593274 | ||||||||
\(941\) | − 6.99273i | − 0.227956i | −0.993483 | − | 0.113978i | \(-0.963641\pi\) | ||||
0.993483 | − | 0.113978i | \(-0.0363594\pi\) | |||||||
\(942\) | − 24.3829i | − 0.794437i | ||||||||
\(943\) | 13.0563i | 0.425173i | ||||||||
\(944\) | − 6.78668i | − 0.220888i | ||||||||
\(945\) | −2.32258 | −0.0755535 | ||||||||
\(946\) | −65.4854 | −2.12911 | ||||||||
\(947\) | − 52.3064i | − 1.69973i | −0.527000 | − | 0.849865i | \(-0.676683\pi\) | ||||
0.527000 | − | 0.849865i | \(-0.323317\pi\) | |||||||
\(948\) | 7.96774 | 0.258780 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.02283 | −0.130518 | ||||||||
\(951\) | 12.6667i | 0.410747i | ||||||||
\(952\) | 9.29032 | 0.301101 | ||||||||
\(953\) | −28.8827 | −0.935603 | −0.467802 | − | 0.883833i | \(-0.654954\pi\) | ||||
−0.467802 | + | 0.883833i | \(0.654954\pi\) | |||||||
\(954\) | 5.48693i | 0.177646i | ||||||||
\(955\) | − 17.0375i | − 0.551319i | ||||||||
\(956\) | 26.2006i | 0.847387i | ||||||||
\(957\) | 22.9359i | 0.741413i | ||||||||
\(958\) | −25.6826 | −0.829768 | ||||||||
\(959\) | 45.7894 | 1.47862 | ||||||||
\(960\) | − 1.00000i | − 0.0322749i | ||||||||
\(961\) | 18.9464 | 0.611173 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.07180 | 0.0989873 | ||||||||
\(964\) | − 15.6496i | − 0.504039i | ||||||||
\(965\) | −6.15491 | −0.198134 | ||||||||
\(966\) | 11.4641 | 0.368851 | ||||||||
\(967\) | − 10.8610i | − 0.349265i | −0.984634 | − | 0.174633i | \(-0.944126\pi\) | ||||
0.984634 | − | 0.174633i | \(-0.0558738\pi\) | |||||||
\(968\) | − 17.5734i | − 0.564829i | ||||||||
\(969\) | − 16.0913i | − 0.516927i | ||||||||
\(970\) | 16.1093i | 0.517237i | ||||||||
\(971\) | −24.9979 | −0.802222 | −0.401111 | − | 0.916030i | \(-0.631376\pi\) | ||||
−0.401111 | + | 0.916030i | \(0.631376\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 13.1863i | 0.422732i | ||||||||
\(974\) | 9.37891 | 0.300520 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.535898 | 0.0171537 | ||||||||
\(977\) | − 42.7653i | − 1.36818i | −0.729396 | − | 0.684092i | \(-0.760199\pi\) | ||||
0.729396 | − | 0.684092i | \(-0.239801\pi\) | |||||||
\(978\) | −23.6267 | −0.755500 | ||||||||
\(979\) | 9.29984 | 0.297224 | ||||||||
\(980\) | − 1.60562i | − 0.0512898i | ||||||||
\(981\) | 6.69081i | 0.213621i | ||||||||
\(982\) | − 7.73854i | − 0.246947i | ||||||||
\(983\) | 10.1288i | 0.323058i | 0.986868 | + | 0.161529i | \(0.0516425\pi\) | ||||
−0.986868 | + | 0.161529i | \(0.948358\pi\) | |||||||
\(984\) | −2.64516 | −0.0843246 | ||||||||
\(985\) | 13.7867 | 0.439280 | ||||||||
\(986\) | 17.1631i | 0.546584i | ||||||||
\(987\) | −4.22464 | −0.134472 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −60.4691 | −1.92280 | ||||||||
\(990\) | 5.34541i | 0.169888i | ||||||||
\(991\) | 20.2483 | 0.643208 | 0.321604 | − | 0.946874i | \(-0.395778\pi\) | ||||
0.321604 | + | 0.946874i | \(0.395778\pi\) | |||||||
\(992\) | −3.47183 | −0.110231 | ||||||||
\(993\) | 23.6981i | 0.752036i | ||||||||
\(994\) | − 36.8637i | − 1.16924i | ||||||||
\(995\) | − 2.28304i | − 0.0723774i | ||||||||
\(996\) | − 11.3360i | − 0.359194i | ||||||||
\(997\) | −20.7961 | −0.658620 | −0.329310 | − | 0.944222i | \(-0.606816\pi\) | ||||
−0.329310 | + | 0.944222i | \(0.606816\pi\) | |||||||
\(998\) | −3.18106 | −0.100695 | ||||||||
\(999\) | − 3.14925i | − 0.0996380i |
(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.ba.1351.3 | 8 | ||
13.5 | odd | 4 | 5070.2.a.bz.1.2 | 4 | |||
13.8 | odd | 4 | 5070.2.a.ca.1.3 | 4 | |||
13.9 | even | 3 | 390.2.bb.c.361.1 | yes | 8 | ||
13.10 | even | 6 | 390.2.bb.c.121.1 | ✓ | 8 | ||
13.12 | even | 2 | inner | 5070.2.b.ba.1351.6 | 8 | ||
39.23 | odd | 6 | 1170.2.bs.f.901.3 | 8 | |||
39.35 | odd | 6 | 1170.2.bs.f.361.3 | 8 | |||
65.9 | even | 6 | 1950.2.bc.g.751.4 | 8 | |||
65.22 | odd | 12 | 1950.2.y.j.49.2 | 8 | |||
65.23 | odd | 12 | 1950.2.y.j.199.2 | 8 | |||
65.48 | odd | 12 | 1950.2.y.k.49.3 | 8 | |||
65.49 | even | 6 | 1950.2.bc.g.901.4 | 8 | |||
65.62 | odd | 12 | 1950.2.y.k.199.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.c.121.1 | ✓ | 8 | 13.10 | even | 6 | ||
390.2.bb.c.361.1 | yes | 8 | 13.9 | even | 3 | ||
1170.2.bs.f.361.3 | 8 | 39.35 | odd | 6 | |||
1170.2.bs.f.901.3 | 8 | 39.23 | odd | 6 | |||
1950.2.y.j.49.2 | 8 | 65.22 | odd | 12 | |||
1950.2.y.j.199.2 | 8 | 65.23 | odd | 12 | |||
1950.2.y.k.49.3 | 8 | 65.48 | odd | 12 | |||
1950.2.y.k.199.3 | 8 | 65.62 | odd | 12 | |||
1950.2.bc.g.751.4 | 8 | 65.9 | even | 6 | |||
1950.2.bc.g.901.4 | 8 | 65.49 | even | 6 | |||
5070.2.a.bz.1.2 | 4 | 13.5 | odd | 4 | |||
5070.2.a.ca.1.3 | 4 | 13.8 | odd | 4 | |||
5070.2.b.ba.1351.3 | 8 | 1.1 | even | 1 | trivial | ||
5070.2.b.ba.1351.6 | 8 | 13.12 | even | 2 | inner |