Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(305,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.305");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.h (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: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 156x^{10} + 8721x^{8} + 208784x^{6} + 2024760x^{4} + 7117056x^{2} + 6533136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 684) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 305.6 | ||
Root | \(-1.18282i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.305 |
Dual form | 2736.3.h.c.305.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.18282i | − 0.236563i | −0.992980 | − | 0.118282i | \(-0.962261\pi\) | ||||
0.992980 | − | 0.118282i | \(-0.0377386\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.5550 | −1.65072 | −0.825359 | − | 0.564608i | \(-0.809027\pi\) | ||||
−0.825359 | + | 0.564608i | \(0.809027\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 16.8047i | − 1.52770i | −0.645394 | − | 0.763850i | \(-0.723307\pi\) | ||||
0.645394 | − | 0.763850i | \(-0.276693\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14.6782 | −1.12909 | −0.564546 | − | 0.825402i | \(-0.690949\pi\) | ||||
−0.564546 | + | 0.825402i | \(0.690949\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.3981i | 1.37636i | 0.725542 | + | 0.688178i | \(0.241589\pi\) | ||||
−0.725542 | + | 0.688178i | \(0.758411\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.35890 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 11.6340i | − 0.505827i | −0.967489 | − | 0.252913i | \(-0.918611\pi\) | ||||
0.967489 | − | 0.252913i | \(-0.0813888\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.6009 | 0.944038 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 43.4775i | − 1.49922i | −0.661878 | − | 0.749611i | \(-0.730240\pi\) | ||||
0.661878 | − | 0.749611i | \(-0.269760\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00373 | −0.225927 | −0.112963 | − | 0.993599i | \(-0.536034\pi\) | ||||
−0.112963 | + | 0.993599i | \(0.536034\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.6675i | 0.390499i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −71.2290 | −1.92511 | −0.962554 | − | 0.271090i | \(-0.912616\pi\) | ||||
−0.962554 | + | 0.271090i | \(0.912616\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.74273i | 0.140067i | 0.997545 | + | 0.0700334i | \(0.0223106\pi\) | ||||
−0.997545 | + | 0.0700334i | \(0.977689\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −78.3909 | −1.82305 | −0.911523 | − | 0.411250i | \(-0.865092\pi\) | ||||
−0.911523 | + | 0.411250i | \(0.865092\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 59.9521i | − 1.27558i | −0.770211 | − | 0.637789i | \(-0.779849\pi\) | ||||
0.770211 | − | 0.637789i | \(-0.220151\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 84.5187 | 1.72487 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 96.4896i | 1.82056i | 0.413995 | + | 0.910279i | \(0.364133\pi\) | ||||
−0.413995 | + | 0.910279i | \(0.635867\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.8769 | −0.361397 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 20.9608i | − 0.355268i | −0.984097 | − | 0.177634i | \(-0.943156\pi\) | ||||
0.984097 | − | 0.177634i | \(-0.0568444\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 29.1844 | 0.478433 | 0.239216 | − | 0.970966i | \(-0.423109\pi\) | ||||
0.239216 | + | 0.970966i | \(0.423109\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.3616i | 0.267102i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.31239 | 0.0792894 | 0.0396447 | − | 0.999214i | \(-0.487377\pi\) | ||||
0.0396447 | + | 0.999214i | \(0.487377\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 84.5651i | − 1.19106i | −0.803334 | − | 0.595529i | \(-0.796943\pi\) | ||||
0.803334 | − | 0.595529i | \(-0.203057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 61.3966 | 0.841050 | 0.420525 | − | 0.907281i | \(-0.361846\pi\) | ||||
0.420525 | + | 0.907281i | \(0.361846\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 194.179i | 2.52180i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.8583 | −0.213396 | −0.106698 | − | 0.994291i | \(-0.534028\pi\) | ||||
−0.106698 | + | 0.994291i | \(0.534028\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 123.534i | 1.48836i | 0.667980 | + | 0.744179i | \(0.267159\pi\) | ||||
−0.667980 | + | 0.744179i | \(0.732841\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27.6756 | 0.325595 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 129.705i | 1.45736i | 0.684854 | + | 0.728680i | \(0.259866\pi\) | ||||
−0.684854 | + | 0.728680i | \(0.740134\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 169.607 | 1.86381 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.15578i | 0.0542713i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 116.532 | 1.20136 | 0.600681 | − | 0.799489i | \(-0.294896\pi\) | ||||
0.600681 | + | 0.799489i | \(0.294896\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 185.316i | − 1.83481i | −0.397957 | − | 0.917404i | \(-0.630281\pi\) | ||||
0.397957 | − | 0.917404i | \(-0.369719\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 150.646 | 1.46258 | 0.731291 | − | 0.682066i | \(-0.238918\pi\) | ||||
0.731291 | + | 0.682066i | \(0.238918\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 195.599i | 1.82803i | 0.405683 | + | 0.914014i | \(0.367034\pi\) | ||||
−0.405683 | + | 0.914014i | \(0.632966\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 166.873 | 1.53095 | 0.765474 | − | 0.643467i | \(-0.222504\pi\) | ||||
0.765474 | + | 0.643467i | \(0.222504\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 64.2081i | − 0.568213i | −0.958793 | − | 0.284107i | \(-0.908303\pi\) | ||||
0.958793 | − | 0.284107i | \(-0.0916970\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.7609 | −0.119660 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 270.365i | − 2.27198i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −161.398 | −1.33386 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 57.4860i | − 0.459888i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −49.2467 | −0.387770 | −0.193885 | − | 0.981024i | \(-0.562109\pi\) | ||||
−0.193885 | + | 0.981024i | \(0.562109\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 93.9712i | 0.717338i | 0.933465 | + | 0.358669i | \(0.116769\pi\) | ||||
−0.933465 | + | 0.358669i | \(0.883231\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 50.3672 | 0.378701 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 133.054i | 0.971195i | 0.874183 | + | 0.485597i | \(0.161398\pi\) | ||||
−0.874183 | + | 0.485597i | \(0.838602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −122.453 | −0.880956 | −0.440478 | − | 0.897763i | \(-0.645191\pi\) | ||||
−0.440478 | + | 0.897763i | \(0.645191\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 246.662i | 1.72491i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −51.4258 | −0.354661 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 72.6965i | 0.487896i | 0.969788 | + | 0.243948i | \(0.0784426\pi\) | ||||
−0.969788 | + | 0.243948i | \(0.921557\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 241.294 | 1.59797 | 0.798986 | − | 0.601350i | \(-0.205370\pi\) | ||||
0.798986 | + | 0.601350i | \(0.205370\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.28412i | 0.0534460i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 48.6451 | 0.309841 | 0.154921 | − | 0.987927i | \(-0.450488\pi\) | ||||
0.154921 | + | 0.987927i | \(0.450488\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 134.431i | 0.834978i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 94.2841 | 0.578430 | 0.289215 | − | 0.957264i | \(-0.406606\pi\) | ||||
0.289215 | + | 0.957264i | \(0.406606\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 141.605i | 0.847937i | 0.905677 | + | 0.423968i | \(0.139363\pi\) | ||||
−0.905677 | + | 0.423968i | \(0.860637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 46.4492 | 0.274848 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 138.037i | 0.797900i | 0.916973 | + | 0.398950i | \(0.130625\pi\) | ||||
−0.916973 | + | 0.398950i | \(0.869375\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −272.710 | −1.55834 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 68.9735i | 0.385327i | 0.981265 | + | 0.192664i | \(0.0617126\pi\) | ||||
−0.981265 | + | 0.192664i | \(0.938287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −274.416 | −1.51611 | −0.758054 | − | 0.652192i | \(-0.773850\pi\) | ||||
−0.758054 | + | 0.652192i | \(0.773850\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 84.2508i | 0.455410i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 393.197 | 2.10266 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 171.950i | 0.900261i | 0.892963 | + | 0.450130i | \(0.148622\pi\) | ||||
−0.892963 | + | 0.450130i | \(0.851378\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 84.5350 | 0.438005 | 0.219003 | − | 0.975724i | \(-0.429720\pi\) | ||||
0.219003 | + | 0.975724i | \(0.429720\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.7423i | 0.135748i | 0.997694 | + | 0.0678738i | \(0.0216215\pi\) | ||||
−0.997694 | + | 0.0678738i | \(0.978378\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −39.1603 | −0.196786 | −0.0983928 | − | 0.995148i | \(-0.531370\pi\) | ||||
−0.0983928 | + | 0.995148i | \(0.531370\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 502.383i | 2.47479i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.79260 | 0.0331346 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 73.2499i | 0.350478i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −167.542 | −0.794037 | −0.397018 | − | 0.917811i | \(-0.629955\pi\) | ||||
−0.397018 | + | 0.917811i | \(0.629955\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 92.7221i | 0.431265i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 80.9283 | 0.372941 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 343.441i | − 1.55403i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 41.1052 | 0.184328 | 0.0921641 | − | 0.995744i | \(-0.470622\pi\) | ||||
0.0921641 | + | 0.995744i | \(0.470622\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 120.298i | 0.529947i | 0.964256 | + | 0.264974i | \(0.0853633\pi\) | ||||
−0.964256 | + | 0.264974i | \(0.914637\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −54.0963 | −0.236228 | −0.118114 | − | 0.993000i | \(-0.537685\pi\) | ||||
−0.118114 | + | 0.993000i | \(0.537685\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 57.0923i | − 0.245031i | −0.992467 | − | 0.122516i | \(-0.960904\pi\) | ||||
0.992467 | − | 0.122516i | \(-0.0390962\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −70.9123 | −0.301755 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 173.405i | − 0.725543i | −0.931878 | − | 0.362772i | \(-0.881830\pi\) | ||||
0.931878 | − | 0.362772i | \(-0.118170\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −90.7079 | −0.376381 | −0.188191 | − | 0.982133i | \(-0.560262\pi\) | ||||
−0.188191 | + | 0.982133i | \(0.560262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 99.9700i | − 0.408041i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 63.9807 | 0.259031 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 59.5477i | − 0.237242i | −0.992940 | − | 0.118621i | \(-0.962153\pi\) | ||||
0.992940 | − | 0.118621i | \(-0.0378474\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −195.506 | −0.772751 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 425.688i | − 1.65637i | −0.560453 | − | 0.828186i | \(-0.689373\pi\) | ||||
0.560453 | − | 0.828186i | \(-0.310627\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 823.053 | 3.17781 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 162.639i | 0.618400i | 0.950997 | + | 0.309200i | \(0.100061\pi\) | ||||
−0.950997 | + | 0.309200i | \(0.899939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 114.129 | 0.430677 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 184.141i | − 0.684539i | −0.939602 | − | 0.342269i | \(-0.888804\pi\) | ||||
0.939602 | − | 0.342269i | \(-0.111196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 467.251 | 1.72417 | 0.862087 | − | 0.506761i | \(-0.169157\pi\) | ||||
0.862087 | + | 0.506761i | \(0.169157\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 396.607i | − 1.44221i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −108.683 | −0.392359 | −0.196179 | − | 0.980568i | \(-0.562853\pi\) | ||||
−0.196179 | + | 0.980568i | \(0.562853\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 135.042i | − 0.480577i | −0.970701 | − | 0.240289i | \(-0.922758\pi\) | ||||
0.970701 | − | 0.240289i | \(-0.0772421\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 311.236 | 1.09977 | 0.549886 | − | 0.835240i | \(-0.314671\pi\) | ||||
0.549886 | + | 0.835240i | \(0.314671\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 66.3575i | − 0.231211i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −258.469 | −0.894358 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 252.775i | 0.862714i | 0.902181 | + | 0.431357i | \(0.141965\pi\) | ||||
−0.902181 | + | 0.431357i | \(0.858035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.7928 | −0.0840434 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 170.766i | 0.571125i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 905.810 | 3.00933 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 34.5198i | − 0.113180i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −189.189 | −0.616252 | −0.308126 | − | 0.951346i | \(-0.599702\pi\) | ||||
−0.308126 | + | 0.951346i | \(0.599702\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 270.953i | 0.871232i | 0.900133 | + | 0.435616i | \(0.143469\pi\) | ||||
−0.900133 | + | 0.435616i | \(0.856531\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 326.309 | 1.04252 | 0.521260 | − | 0.853398i | \(-0.325462\pi\) | ||||
0.521260 | + | 0.853398i | \(0.325462\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 205.699i | 0.648892i | 0.945904 | + | 0.324446i | \(0.105178\pi\) | ||||
−0.945904 | + | 0.324446i | \(0.894822\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −730.625 | −2.29036 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 101.990i | − 0.315758i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −346.419 | −1.06591 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 692.749i | 2.10562i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −64.7809 | −0.195713 | −0.0978564 | − | 0.995201i | \(-0.531199\pi\) | ||||
−0.0978564 | + | 0.995201i | \(0.531199\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 6.28358i | − 0.0187570i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 189.465 | 0.562212 | 0.281106 | − | 0.959677i | \(-0.409299\pi\) | ||||
0.281106 | + | 0.959677i | \(0.409299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 117.696i | 0.345148i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −410.419 | −1.19656 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 484.445i | 1.39609i | 0.716052 | + | 0.698047i | \(0.245947\pi\) | ||||
−0.716052 | + | 0.698047i | \(0.754053\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −121.051 | −0.346852 | −0.173426 | − | 0.984847i | \(-0.555484\pi\) | ||||
−0.173426 | + | 0.984847i | \(0.555484\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 461.204i | − 1.30653i | −0.757131 | − | 0.653263i | \(-0.773400\pi\) | ||||
0.757131 | − | 0.653263i | \(-0.226600\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −100.025 | −0.281760 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 272.559i | 0.759216i | 0.925147 | + | 0.379608i | \(0.123941\pi\) | ||||
−0.925147 | + | 0.379608i | \(0.876059\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 72.6209i | − 0.198961i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 428.161 | 1.16665 | 0.583325 | − | 0.812239i | \(-0.301751\pi\) | ||||
0.583325 | + | 0.812239i | \(0.301751\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1114.94i | − 3.00523i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 301.903 | 0.809392 | 0.404696 | − | 0.914451i | \(-0.367377\pi\) | ||||
0.404696 | + | 0.914451i | \(0.367377\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 638.170i | 1.69276i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −350.479 | −0.924746 | −0.462373 | − | 0.886686i | \(-0.653002\pi\) | ||||
−0.462373 | + | 0.886686i | \(0.653002\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 680.296i | − 1.77623i | −0.459621 | − | 0.888115i | \(-0.652015\pi\) | ||||
0.459621 | − | 0.888115i | \(-0.347985\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 229.678 | 0.596565 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 41.4655i | 0.106595i | 0.998579 | + | 0.0532976i | \(0.0169732\pi\) | ||||
−0.998579 | + | 0.0532976i | \(0.983027\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 272.213 | 0.696198 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.9402i | 0.0504816i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −636.189 | −1.60249 | −0.801246 | − | 0.598335i | \(-0.795829\pi\) | ||||
−0.801246 | + | 0.598335i | \(0.795829\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 39.3996i | 0.0982535i | 0.998793 | + | 0.0491267i | \(0.0156438\pi\) | ||||
−0.998793 | + | 0.0491267i | \(0.984356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 102.802 | 0.255092 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1196.98i | 2.94099i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 421.712 | 1.03108 | 0.515540 | − | 0.856865i | \(-0.327591\pi\) | ||||
0.515540 | + | 0.856865i | \(0.327591\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 242.203i | 0.586448i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 146.118 | 0.352091 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 25.5688i | − 0.0610235i | −0.999534 | − | 0.0305117i | \(-0.990286\pi\) | ||||
0.999534 | − | 0.0305117i | \(-0.00971369\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −384.575 | −0.913480 | −0.456740 | − | 0.889600i | \(-0.650983\pi\) | ||||
−0.456740 | + | 0.889600i | \(0.650983\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 552.216i | 1.29933i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −337.227 | −0.789758 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 672.168i | 1.55955i | 0.626058 | + | 0.779777i | \(0.284667\pi\) | ||||
−0.626058 | + | 0.779777i | \(0.715333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −537.952 | −1.24238 | −0.621192 | − | 0.783658i | \(-0.713351\pi\) | ||||
−0.621192 | + | 0.783658i | \(0.713351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 50.7115i | 0.116045i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 156.236 | 0.355890 | 0.177945 | − | 0.984040i | \(-0.443055\pi\) | ||||
0.177945 | + | 0.984040i | \(0.443055\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 89.3191i | − 0.201623i | −0.994906 | − | 0.100812i | \(-0.967856\pi\) | ||||
0.994906 | − | 0.100812i | \(-0.0321439\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 153.417 | 0.344758 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.3171i | 0.0229780i | 0.999934 | + | 0.0114890i | \(0.00365715\pi\) | ||||
−0.999934 | + | 0.0114890i | \(0.996343\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 96.5049 | 0.213980 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 200.614i | − 0.440909i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 116.289 | 0.254462 | 0.127231 | − | 0.991873i | \(-0.459391\pi\) | ||||
0.127231 | + | 0.991873i | \(0.459391\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 303.341i | − 0.658007i | −0.944329 | − | 0.329003i | \(-0.893287\pi\) | ||||
0.944329 | − | 0.329003i | \(-0.106713\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −140.485 | −0.303424 | −0.151712 | − | 0.988425i | \(-0.548479\pi\) | ||||
−0.151712 | + | 0.988425i | \(0.548479\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.8034i | 0.0638189i | 0.999491 | + | 0.0319095i | \(0.0101588\pi\) | ||||
−0.999491 | + | 0.0319095i | \(0.989841\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −61.3848 | −0.130884 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1317.34i | 2.78506i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −102.874 | −0.216577 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 285.569i | 0.596177i | 0.954538 | + | 0.298088i | \(0.0963490\pi\) | ||||
−0.954538 | + | 0.298088i | \(0.903651\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1045.51 | 2.17362 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 137.836i | − 0.284198i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −290.413 | −0.596330 | −0.298165 | − | 0.954514i | \(-0.596375\pi\) | ||||
−0.298165 | + | 0.954514i | \(0.596375\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 146.360i | − 0.298086i | −0.988831 | − | 0.149043i | \(-0.952381\pi\) | ||||
0.988831 | − | 0.149043i | \(-0.0476194\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1017.29 | 2.06346 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 977.152i | 1.96610i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −76.5115 | −0.153330 | −0.0766648 | − | 0.997057i | \(-0.524427\pi\) | ||||
−0.0766648 | + | 0.997057i | \(0.524427\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 261.880i | − 0.520636i | −0.965523 | − | 0.260318i | \(-0.916173\pi\) | ||||
0.965523 | − | 0.260318i | \(-0.0838273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −219.194 | −0.434048 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 183.329i | 0.360174i | 0.983651 | + | 0.180087i | \(0.0576380\pi\) | ||||
−0.983651 | + | 0.180087i | \(0.942362\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −709.440 | −1.38834 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 178.186i | − 0.345993i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1007.48 | −1.94870 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 384.597i | − 0.738190i | −0.929392 | − | 0.369095i | \(-0.879668\pi\) | ||||
0.929392 | − | 0.369095i | \(-0.120332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −359.471 | −0.687325 | −0.343663 | − | 0.939093i | \(-0.611668\pi\) | ||||
−0.343663 | + | 0.939093i | \(0.611668\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 163.874i | − 0.310956i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 393.650 | 0.744139 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 84.2930i | − 0.158148i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 231.358 | 0.432444 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1420.31i | − 2.63508i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 562.194 | 1.03918 | 0.519588 | − | 0.854417i | \(-0.326085\pi\) | ||||
0.519588 | + | 0.854417i | \(0.326085\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 197.381i | − 0.362166i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −701.537 | −1.28252 | −0.641259 | − | 0.767325i | \(-0.721588\pi\) | ||||
−0.641259 | + | 0.767325i | \(0.721588\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 189.514i | 0.343945i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 194.798 | 0.352256 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 912.042i | 1.63742i | 0.574208 | + | 0.818709i | \(0.305310\pi\) | ||||
−0.574208 | + | 0.818709i | \(0.694690\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1150.64 | 2.05838 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 563.674i | − 1.00120i | −0.865680 | − | 0.500599i | \(-0.833113\pi\) | ||||
0.865680 | − | 0.500599i | \(-0.166887\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −75.9464 | −0.134418 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 499.895i | 0.878551i | 0.898352 | + | 0.439275i | \(0.144765\pi\) | ||||
−0.898352 | + | 0.439275i | \(0.855235\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.8910 | −0.0295814 | −0.0147907 | − | 0.999891i | \(-0.504708\pi\) | ||||
−0.0147907 | + | 0.999891i | \(0.504708\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 274.574i | − 0.477520i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 642.505 | 1.11353 | 0.556763 | − | 0.830671i | \(-0.312043\pi\) | ||||
0.556763 | + | 0.830671i | \(0.312043\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1427.44i | − 2.45686i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1621.48 | 2.78127 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 547.322i | 0.932406i | 0.884678 | + | 0.466203i | \(0.154378\pi\) | ||||
−0.884678 | + | 0.466203i | \(0.845622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.5286 | 0.0518312 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 739.380i | − 1.24685i | −0.781884 | − | 0.623424i | \(-0.785741\pi\) | ||||
0.781884 | − | 0.623424i | \(-0.214259\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −319.792 | −0.537466 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 435.313i | 0.726733i | 0.931646 | + | 0.363366i | \(0.118373\pi\) | ||||
−0.931646 | + | 0.363366i | \(0.881627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 511.457 | 0.851009 | 0.425505 | − | 0.904956i | \(-0.360097\pi\) | ||||
0.425505 | + | 0.904956i | \(0.360097\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 190.904i | 0.315543i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −739.350 | −1.21804 | −0.609020 | − | 0.793155i | \(-0.708437\pi\) | ||||
−0.609020 | + | 0.793155i | \(0.708437\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 879.989i | 1.44024i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −528.345 | −0.861900 | −0.430950 | − | 0.902376i | \(-0.641821\pi\) | ||||
−0.430950 | + | 0.902376i | \(0.641821\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 653.241i | − 1.05874i | −0.848392 | − | 0.529369i | \(-0.822429\pi\) | ||||
0.848392 | − | 0.529369i | \(-0.177571\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 115.083 | 0.185918 | 0.0929591 | − | 0.995670i | \(-0.470367\pi\) | ||||
0.0929591 | + | 0.995670i | \(0.470367\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1498.75i | − 2.40569i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 522.028 | 0.835245 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1666.62i | − 2.64964i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 894.388 | 1.41741 | 0.708707 | − | 0.705503i | \(-0.249279\pi\) | ||||
0.708707 | + | 0.705503i | \(0.249279\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 58.2498i | 0.0917320i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1240.58 | −1.94754 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1164.18i | 1.81619i | 0.418764 | + | 0.908095i | \(0.362463\pi\) | ||||
−0.418764 | + | 0.908095i | \(0.637537\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.54128 | −0.0148387 | −0.00741934 | − | 0.999972i | \(-0.502362\pi\) | ||||
−0.00741934 | + | 0.999972i | \(0.502362\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 774.112i | − 1.19646i | −0.801323 | − | 0.598232i | \(-0.795870\pi\) | ||||
0.801323 | − | 0.598232i | \(-0.204130\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −352.240 | −0.542743 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 19.3044i | − 0.0295626i | −0.999891 | − | 0.0147813i | \(-0.995295\pi\) | ||||
0.999891 | − | 0.0147813i | \(-0.00470520\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 111.151 | 0.169696 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1089.39i | 1.65309i | 0.562867 | + | 0.826547i | \(0.309698\pi\) | ||||
−0.562867 | + | 0.826547i | \(0.690302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −757.463 | −1.14593 | −0.572967 | − | 0.819578i | \(-0.694208\pi\) | ||||
−0.572967 | + | 0.819578i | \(0.694208\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 59.5751i | − 0.0895867i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −505.817 | −0.758347 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 490.435i | − 0.730902i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −517.955 | −0.769621 | −0.384810 | − | 0.922996i | \(-0.625733\pi\) | ||||
−0.384810 | + | 0.922996i | \(0.625733\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 705.089i | − 1.04149i | −0.853712 | − | 0.520745i | \(-0.825654\pi\) | ||||
0.853712 | − | 0.520745i | \(-0.174346\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1346.53 | −1.98311 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1165.61i | − 1.70661i | −0.521412 | − | 0.853305i | \(-0.674594\pi\) | ||||
0.521412 | − | 0.853305i | \(-0.325406\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 157.378 | 0.229749 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1416.29i | − 2.05558i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −327.194 | −0.473508 | −0.236754 | − | 0.971570i | \(-0.576084\pi\) | ||||
−0.236754 | + | 0.971570i | \(0.576084\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 144.839i | 0.208402i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −134.369 | −0.192782 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 486.285i | − 0.693702i | −0.937920 | − | 0.346851i | \(-0.887251\pi\) | ||||
0.937920 | − | 0.346851i | \(-0.112749\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 310.480 | 0.441650 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2141.33i | 3.02875i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 218.065 | 0.307567 | 0.153783 | − | 0.988105i | \(-0.450854\pi\) | ||||
0.153783 | + | 0.988105i | \(0.450854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 81.4815i | 0.114280i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 291.756 | 0.408051 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 50.2847i | − 0.0699369i | −0.999388 | − | 0.0349685i | \(-0.988867\pi\) | ||||
0.999388 | − | 0.0349685i | \(-0.0111331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1740.72 | −2.41431 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1026.11i | − 1.41532i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −443.742 | −0.610374 | −0.305187 | − | 0.952292i | \(-0.598719\pi\) | ||||
−0.305187 | + | 0.952292i | \(0.598719\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1834.20i | − 2.50916i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −149.384 | −0.203797 | −0.101899 | − | 0.994795i | \(-0.532492\pi\) | ||||
−0.101899 | + | 0.994795i | \(0.532492\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 89.2731i | − 0.121130i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 570.189 | 0.771568 | 0.385784 | − | 0.922589i | \(-0.373931\pi\) | ||||
0.385784 | + | 0.922589i | \(0.373931\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 576.839i | − 0.776364i | −0.921583 | − | 0.388182i | \(-0.873103\pi\) | ||||
0.921583 | − | 0.388182i | \(-0.126897\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 85.9866 | 0.115418 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 2260.15i | − 3.01756i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1245.80 | −1.65885 | −0.829426 | − | 0.558616i | \(-0.811333\pi\) | ||||
−0.829426 | + | 0.558616i | \(0.811333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 285.406i | − 0.378021i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 213.255 | 0.281711 | 0.140855 | − | 0.990030i | \(-0.455015\pi\) | ||||
0.140855 | + | 0.990030i | \(0.455015\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1088.31i | 1.43011i | 0.699068 | + | 0.715055i | \(0.253598\pi\) | ||||
−0.699068 | + | 0.715055i | \(0.746402\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1928.23 | −2.52716 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 307.667i | 0.401130i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −947.668 | −1.23234 | −0.616169 | − | 0.787614i | \(-0.711316\pi\) | ||||
−0.616169 | + | 0.787614i | \(0.711316\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 126.680i | 0.163881i | 0.996637 | + | 0.0819404i | \(0.0261117\pi\) | ||||
−0.996637 | + | 0.0819404i | \(0.973888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −165.295 | −0.213283 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 25.0320i | − 0.0321335i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1421.09 | −1.81958 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 57.5381i | − 0.0732970i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1023.40 | 1.30039 | 0.650194 | − | 0.759769i | \(-0.274688\pi\) | ||||
0.650194 | + | 0.759769i | \(0.274688\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 741.926i | 0.937960i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −428.374 | −0.540195 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 203.733i | 0.255625i | 0.991798 | + | 0.127813i | \(0.0407956\pi\) | ||||
−0.991798 | + | 0.127813i | \(0.959204\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1402.76 | 1.75565 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1031.75i | − 1.28487i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 159.008 | 0.197525 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 405.365i | − 0.501069i | −0.968108 | − | 0.250534i | \(-0.919394\pi\) | ||||
0.968108 | − | 0.250534i | \(-0.0806063\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 248.205 | 0.306049 | 0.153024 | − | 0.988222i | \(-0.451099\pi\) | ||||
0.153024 | + | 0.988222i | \(0.451099\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 111.521i | − 0.136835i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 341.698 | 0.418235 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1275.86i | − 1.55403i | −0.629482 | − | 0.777015i | \(-0.716733\pi\) | ||||
0.629482 | − | 0.777015i | \(-0.283267\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1207.10 | −1.46671 | −0.733355 | − | 0.679845i | \(-0.762047\pi\) | ||||
−0.733355 | + | 0.679845i | \(0.762047\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 689.696i | − 0.833974i | −0.908912 | − | 0.416987i | \(-0.863086\pi\) | ||||
0.908912 | − | 0.416987i | \(-0.136914\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −812.726 | −0.980369 | −0.490184 | − | 0.871619i | \(-0.663071\pi\) | ||||
−0.490184 | + | 0.871619i | \(0.663071\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1977.57i | 2.37404i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 167.493 | 0.200591 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 78.7405i | 0.0938504i | 0.998898 | + | 0.0469252i | \(0.0149422\pi\) | ||||
−0.998898 | + | 0.0469252i | \(0.985058\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1049.29 | −1.24767 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 54.9409i | − 0.0650188i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1864.95 | 2.20183 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 828.679i | 0.973771i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1460.81 | 1.71256 | 0.856280 | − | 0.516511i | \(-0.172770\pi\) | ||||
0.856280 | + | 0.516511i | \(0.172770\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 262.458i | 0.306253i | 0.988207 | + | 0.153126i | \(0.0489341\pi\) | ||||
−0.988207 | + | 0.153126i | \(0.951066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 143.790 | 0.167392 | 0.0836960 | − | 0.996491i | \(-0.473328\pi\) | ||||
0.0836960 | + | 0.996491i | \(0.473328\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1162.82i | 1.34742i | 0.738996 | + | 0.673710i | \(0.235300\pi\) | ||||
−0.738996 | + | 0.673710i | \(0.764700\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 163.272 | 0.188754 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 283.298i | 0.326005i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −77.9763 | −0.0895250 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 664.252i | 0.759145i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 839.844 | 0.957633 | 0.478816 | − | 0.877915i | \(-0.341066\pi\) | ||||
0.478816 | + | 0.877915i | \(0.341066\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1520.31i | − 1.72566i | −0.505491 | − | 0.862832i | \(-0.668688\pi\) | ||||
0.505491 | − | 0.862832i | \(-0.331312\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −966.317 | −1.09436 | −0.547178 | − | 0.837016i | \(-0.684298\pi\) | ||||
−0.547178 | + | 0.837016i | \(0.684298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 363.989i | 0.410359i | 0.978724 | + | 0.205180i | \(0.0657779\pi\) | ||||
−0.978724 | + | 0.205180i | \(0.934222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 569.047 | 0.640098 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 261.325i | 0.292638i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 81.5830 | 0.0911542 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 304.504i | 0.338715i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2257.67 | −2.50574 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 324.583i | 0.358655i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 346.160 | 0.381654 | 0.190827 | − | 0.981624i | \(-0.438883\pi\) | ||||
0.190827 | + | 0.981624i | \(0.438883\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 108.937i | 0.119580i | 0.998211 | + | 0.0597900i | \(0.0190431\pi\) | ||||
−0.998211 | + | 0.0597900i | \(0.980957\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2075.95 | 2.27376 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1085.84i | − 1.18412i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −972.113 | −1.05779 | −0.528897 | − | 0.848686i | \(-0.677394\pi\) | ||||
−0.528897 | + | 0.848686i | \(0.677394\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1241.26i | 1.34481i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1681.07 | −1.81737 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1247.54i | − 1.34289i | −0.741057 | − | 0.671443i | \(-0.765675\pi\) | ||||
0.741057 | − | 0.671443i | \(-0.234325\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −368.408 | −0.395712 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 465.080i | − 0.497412i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 826.848 | 0.882442 | 0.441221 | − | 0.897398i | \(-0.354545\pi\) | ||||
0.441221 | + | 0.897398i | \(0.354545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 995.652i | − 1.05808i | −0.848597 | − | 0.529039i | \(-0.822552\pi\) | ||||
0.848597 | − | 0.529039i | \(-0.177448\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 66.8111 | 0.0708495 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 676.969i | 0.714856i | 0.933941 | + | 0.357428i | \(0.116346\pi\) | ||||
−0.933941 | + | 0.357428i | \(0.883654\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −901.191 | −0.949622 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1047.94i | 1.09962i | 0.835289 | + | 0.549810i | \(0.185300\pi\) | ||||
−0.835289 | + | 0.549810i | \(0.814700\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 203.385 | 0.212969 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1537.44i | − 1.60317i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −911.948 | −0.948957 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 99.9893i | − 0.103616i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −173.455 | −0.179375 | −0.0896874 | − | 0.995970i | \(-0.528587\pi\) | ||||
−0.0896874 | + | 0.995970i | \(0.528587\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 249.875i | 0.257338i | 0.991688 | + | 0.128669i | \(0.0410705\pi\) | ||||
−0.991688 | + | 0.128669i | \(0.958929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1414.95 | 1.45421 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 697.966i | 0.714397i | 0.934029 | + | 0.357198i | \(0.116268\pi\) | ||||
−0.934029 | + | 0.357198i | \(0.883732\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2179.65 | 2.22641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 739.100i | 0.751881i | 0.926644 | + | 0.375941i | \(0.122680\pi\) | ||||
−0.926644 | + | 0.375941i | \(0.877320\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.6312 | 0.0321129 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 912.002i | 0.922145i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −264.660 | −0.267064 | −0.133532 | − | 0.991045i | \(-0.542632\pi\) | ||||
−0.133532 | + | 0.991045i | \(0.542632\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46.3195i | 0.0465522i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.5526 | −0.0356596 | −0.0178298 | − | 0.999841i | \(-0.505676\pi\) | ||||
−0.0178298 | + | 0.999841i | \(0.505676\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.3.h.c.305.6 | 12 | ||
3.2 | odd | 2 | inner | 2736.3.h.c.305.7 | 12 | ||
4.3 | odd | 2 | 684.3.e.a.305.6 | ✓ | 12 | ||
12.11 | even | 2 | 684.3.e.a.305.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.e.a.305.6 | ✓ | 12 | 4.3 | odd | 2 | ||
684.3.e.a.305.7 | yes | 12 | 12.11 | even | 2 | ||
2736.3.h.c.305.6 | 12 | 1.1 | even | 1 | trivial | ||
2736.3.h.c.305.7 | 12 | 3.2 | odd | 2 | inner |