Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} + \cdots + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.1 | ||
Root | \(-0.503254 - 0.503254i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.g.369.14 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 2.98707i | − | 1.72458i | −0.506411 | − | 0.862292i | \(-0.669028\pi\) | ||
0.506411 | − | 0.862292i | \(-0.330972\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.274289 | − | 2.21918i | 0.122666 | − | 0.992448i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.980560i | − | 0.370617i | −0.982680 | − | 0.185308i | \(-0.940672\pi\) | ||
0.982680 | − | 0.185308i | \(-0.0593284\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.92257 | −1.97419 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.14721 | 1.85345 | 0.926727 | − | 0.375734i | \(-0.122609\pi\) | ||||
0.926727 | + | 0.375734i | \(0.122609\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.37400i | − | 1.76783i | −0.467649 | − | 0.883914i | \(-0.654899\pi\) | ||
0.467649 | − | 0.883914i | \(-0.345101\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.62885 | − | 0.819321i | −1.71156 | − | 0.211548i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.36098i | − | 0.815157i | −0.913170 | − | 0.407579i | \(-0.866373\pi\) | ||
0.913170 | − | 0.407579i | \(-0.133627\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.08276 | 0.248403 | 0.124202 | − | 0.992257i | \(-0.460363\pi\) | ||||
0.124202 | + | 0.992257i | \(0.460363\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.92900 | −0.639160 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.84953 | − | 1.21740i | −0.969906 | − | 0.243479i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.72993i | 1.68008i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.271042 | 0.0503313 | 0.0251657 | − | 0.999683i | \(-0.491989\pi\) | ||||
0.0251657 | + | 0.999683i | \(0.491989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.77792 | 1.57656 | 0.788280 | − | 0.615316i | \(-0.210972\pi\) | ||||
0.788280 | + | 0.615316i | \(0.210972\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 18.3621i | − | 3.19644i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.17604 | − | 0.268957i | −0.367818 | − | 0.0454621i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.84665i | 1.45438i | 0.686436 | + | 0.727190i | \(0.259174\pi\) | ||||
−0.686436 | + | 0.727190i | \(0.740826\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −19.0396 | −3.04877 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.85308 | −0.757923 | −0.378962 | − | 0.925412i | \(-0.623719\pi\) | ||||
−0.378962 | + | 0.925412i | \(0.623719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.87756i | − | 0.286326i | −0.989699 | − | 0.143163i | \(-0.954273\pi\) | ||
0.989699 | − | 0.143163i | \(-0.0457273\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.62450 | + | 13.1433i | −0.242166 | + | 1.95928i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.196089i | 0.0286026i | 0.999898 | + | 0.0143013i | \(0.00455239\pi\) | ||||
−0.999898 | + | 0.0143013i | \(0.995448\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.03850 | 0.862643 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.0395 | −1.40581 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.93157i | − | 0.265321i | −0.991162 | − | 0.132661i | \(-0.957648\pi\) | ||
0.991162 | − | 0.132661i | \(-0.0423521\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.68612 | − | 13.6418i | 0.227356 | − | 1.83946i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.23429i | − | 0.428392i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.0036 | 1.69293 | 0.846465 | − | 0.532444i | \(-0.178726\pi\) | ||||
0.846465 | + | 0.532444i | \(0.178726\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00189 | 0.768464 | 0.384232 | − | 0.923237i | \(-0.374466\pi\) | ||||
0.384232 | + | 0.923237i | \(0.374466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.80744i | 0.731668i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.1451 | − | 1.74832i | −1.75448 | − | 0.216852i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.26847i | 0.277138i | 0.990353 | + | 0.138569i | \(0.0442503\pi\) | ||||
−0.990353 | + | 0.138569i | \(0.955750\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.98707 | 0.359601 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2677 | −1.21855 | −0.609277 | − | 0.792958i | \(-0.708540\pi\) | ||||
−0.609277 | + | 0.792958i | \(0.708540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.38188i | 0.161737i | 0.996725 | + | 0.0808685i | \(0.0257694\pi\) | ||||
−0.996725 | + | 0.0808685i | \(0.974231\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.63644 | + | 14.4859i | −0.419900 | + | 1.67269i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6.02771i | − | 0.686921i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.67459 | −0.525932 | −0.262966 | − | 0.964805i | \(-0.584701\pi\) | ||||
−0.262966 | + | 0.964805i | \(0.584701\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.30917 | 0.923241 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.7171i | 1.72517i | 0.505909 | + | 0.862587i | \(0.331157\pi\) | ||||
−0.505909 | + | 0.862587i | \(0.668843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.45862 | − | 0.921881i | −0.809001 | − | 0.0999921i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.809622i | − | 0.0868006i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.1548 | 1.18241 | 0.591206 | − | 0.806521i | \(-0.298652\pi\) | ||||
0.591206 | + | 0.806521i | \(0.298652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.25008 | −0.655187 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 26.2202i | − | 2.71891i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.296991 | − | 2.40285i | 0.0304706 | − | 0.246527i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.2868i | 1.04447i | 0.852802 | + | 0.522234i | \(0.174901\pi\) | ||||
−0.852802 | + | 0.522234i | \(0.825099\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −36.4073 | −3.65908 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.2625 | −1.51868 | −0.759339 | − | 0.650695i | \(-0.774478\pi\) | ||||
−0.759339 | + | 0.650695i | \(0.774478\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.60795i | 0.749634i | 0.927099 | + | 0.374817i | \(0.122294\pi\) | ||||
−0.927099 | + | 0.374817i | \(0.877706\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.803394 | + | 6.49998i | −0.0784032 | + | 0.634333i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3081i | 1.09320i | 0.837395 | + | 0.546599i | \(0.184078\pi\) | ||||
−0.837395 | + | 0.546599i | \(0.815922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.45336 | −0.330772 | −0.165386 | − | 0.986229i | \(-0.552887\pi\) | ||||
−0.165386 | + | 0.986229i | \(0.552887\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.4256 | 2.50820 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.6889i | 1.38181i | 0.722944 | + | 0.690907i | \(0.242788\pi\) | ||||
−0.722944 | + | 0.690907i | \(0.757212\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.21918 | + | 0.274289i | 0.206940 | + | 0.0255776i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 37.7505i | 3.49003i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.29564 | −0.302111 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.7882 | 2.43530 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.4965i | 1.30710i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.03180 | + | 10.4281i | −0.360615 | + | 0.932715i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.19312i | − | 0.105873i | −0.998598 | − | 0.0529363i | \(-0.983142\pi\) | ||
0.998598 | − | 0.0529363i | \(-0.0168580\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.60841 | −0.493793 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.7326 | 1.02509 | 0.512543 | − | 0.858662i | \(-0.328704\pi\) | ||||
0.512543 | + | 0.858662i | \(0.328704\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.06171i | − | 0.0920623i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.3733 | + | 2.39453i | 1.66739 | + | 0.206088i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.4665i | 0.894210i | 0.894481 | + | 0.447105i | \(0.147545\pi\) | ||||
−0.894481 | + | 0.447105i | \(0.852455\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.11349 | 0.348902 | 0.174451 | − | 0.984666i | \(-0.444185\pi\) | ||||
0.174451 | + | 0.984666i | \(0.444185\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.585732 | 0.0493275 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 39.1823i | − | 3.27659i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0743441 | − | 0.601492i | 0.00617394 | − | 0.0499512i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 18.0374i | − | 1.48770i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.37793 | −0.112885 | −0.0564424 | − | 0.998406i | \(-0.517976\pi\) | ||||
−0.0564424 | + | 0.998406i | \(0.517976\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.49384 | 0.284325 | 0.142162 | − | 0.989843i | \(-0.454594\pi\) | ||||
0.142162 | + | 0.989843i | \(0.454594\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 19.9057i | 1.60928i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.40769 | − | 19.4798i | 0.193390 | − | 1.56465i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.32373i | 0.265262i | 0.991165 | + | 0.132631i | \(0.0423426\pi\) | ||||
−0.991165 | + | 0.132631i | \(0.957657\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.76973 | −0.457569 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.980560 | 0.0772789 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.52075i | 0.667397i | 0.942680 | + | 0.333698i | \(0.108297\pi\) | ||||
−0.942680 | + | 0.333698i | \(0.891703\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −40.7489 | − | 5.03654i | −3.17230 | − | 0.392094i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.6190i | 1.20864i | 0.796742 | + | 0.604319i | \(0.206555\pi\) | ||||
−0.796742 | + | 0.604319i | \(0.793445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27.6278 | −2.12522 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.41275 | −0.490395 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 8.42727i | − | 0.640713i | −0.947297 | − | 0.320357i | \(-0.896197\pi\) | ||
0.947297 | − | 0.320357i | \(-0.103803\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.19373 | + | 4.75525i | −0.0902375 | + | 0.359463i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 38.8428i | − | 2.91960i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.8047 | 0.807580 | 0.403790 | − | 0.914852i | \(-0.367693\pi\) | ||||
0.403790 | + | 0.914852i | \(0.367693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.4282 | −1.14677 | −0.573385 | − | 0.819286i | \(-0.694370\pi\) | ||||
−0.573385 | + | 0.819286i | \(0.694370\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 17.9281i | − | 1.32528i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.6323 | + | 2.42654i | 1.44340 | + | 0.178403i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 20.6607i | − | 1.51086i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.56022 | 0.622664 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.2634 | 1.61092 | 0.805462 | − | 0.592648i | \(-0.201917\pi\) | ||||
0.805462 | + | 0.592648i | \(0.201917\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.1399i | 1.16178i | 0.813983 | + | 0.580889i | \(0.197295\pi\) | ||||
−0.813983 | + | 0.580889i | \(0.802705\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.22235 | + | 42.2522i | −0.373980 | + | 3.02575i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 13.9936i | − | 0.997004i | −0.866889 | − | 0.498502i | \(-0.833884\pi\) | ||
0.866889 | − | 0.498502i | \(-0.166116\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.91926 | −0.490493 | −0.245246 | − | 0.969461i | \(-0.578869\pi\) | ||||
−0.245246 | + | 0.969461i | \(0.578869\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.77608 | 0.477948 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 0.265773i | − | 0.0186536i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.33115 | + | 10.7699i | −0.0929714 | + | 0.752200i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.92257i | − | 0.411647i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.65598 | 0.460404 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.9170 | −0.889246 | −0.444623 | − | 0.895718i | \(-0.646662\pi\) | ||||
−0.444623 | + | 0.895718i | \(0.646662\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 30.6704i | 2.10150i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.16665 | − | 0.514996i | −0.284164 | − | 0.0351224i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.60728i | − | 0.584300i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.12777 | 0.278929 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.4229 | −1.44106 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 26.6579i | − | 1.78514i | −0.450905 | − | 0.892572i | \(-0.648899\pi\) | ||
0.450905 | − | 0.892572i | \(-0.351101\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 28.7217 | + | 7.21012i | 1.91478 | + | 0.480675i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 9.44407i | − | 0.626825i | −0.949617 | − | 0.313412i | \(-0.898528\pi\) | ||
0.949617 | − | 0.313412i | \(-0.101472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.1994 | −0.938322 | −0.469161 | − | 0.883113i | \(-0.655444\pi\) | ||||
−0.469161 | + | 0.883113i | \(0.655444\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.0052 | −1.18465 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.41134i | − | 0.616557i | −0.951296 | − | 0.308279i | \(-0.900247\pi\) | ||
0.951296 | − | 0.308279i | \(-0.0997529\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.435158 | + | 0.0537852i | 0.0283866 | + | 0.00350856i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.9633i | 0.907014i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.4781 | −1.00119 | −0.500597 | − | 0.865680i | \(-0.666886\pi\) | ||||
−0.500597 | + | 0.865680i | \(0.666886\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.51052 | −0.226133 | −0.113066 | − | 0.993587i | \(-0.536067\pi\) | ||||
−0.113066 | + | 0.993587i | \(0.536067\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.36974i | 0.0878689i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.65630 | − | 13.4005i | 0.105817 | − | 0.856129i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.90153i | − | 0.439134i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 46.9480 | 2.97521 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.6649 | 1.49372 | 0.746859 | − | 0.664982i | \(-0.231561\pi\) | ||||
0.746859 | + | 0.664982i | \(0.231561\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.14721i | 0.386472i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.75372 | + | 22.2794i | −0.172445 | + | 1.39519i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 30.8326i | − | 1.92328i | −0.274311 | − | 0.961641i | \(-0.588450\pi\) | ||
0.274311 | − | 0.961641i | \(-0.411550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.67467 | 0.539018 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.60527 | −0.0993636 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 20.5880i | − | 1.26951i | −0.772714 | − | 0.634755i | \(-0.781101\pi\) | ||
0.772714 | − | 0.634755i | \(-0.218899\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.28650 | − | 0.529809i | −0.263318 | − | 0.0325459i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 33.3203i | − | 2.03917i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.0277 | 1.03820 | 0.519099 | − | 0.854714i | \(-0.326268\pi\) | ||||
0.519099 | + | 0.854714i | \(0.326268\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6709 | −0.830450 | −0.415225 | − | 0.909719i | \(-0.636297\pi\) | ||||
−0.415225 | + | 0.909719i | \(0.636297\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.6694i | 1.12993i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −29.8111 | − | 7.48360i | −1.79768 | − | 0.451278i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 16.2380i | − | 0.975647i | −0.872942 | − | 0.487824i | \(-0.837791\pi\) | ||
0.872942 | − | 0.487824i | \(-0.162209\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −51.9879 | −3.11243 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.362407 | −0.0216194 | −0.0108097 | − | 0.999942i | \(-0.503441\pi\) | ||||
−0.0108097 | + | 0.999942i | \(0.503441\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 6.80039i | − | 0.404241i | −0.979361 | − | 0.202120i | \(-0.935217\pi\) | ||
0.979361 | − | 0.202120i | \(-0.0647833\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.17747 | − | 0.887131i | −0.425157 | − | 0.0525491i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.75873i | 0.280899i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.70382 | 0.335519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 30.7274 | 1.80127 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 26.2172i | − | 1.53162i | −0.643065 | − | 0.765812i | \(-0.722337\pi\) | ||
0.643065 | − | 0.765812i | \(-0.277663\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.56676 | − | 28.8574i | 0.207665 | − | 1.68015i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 53.6647i | 3.11394i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.37400 | 0.368618 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.84106 | −0.106117 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 45.5902i | 2.61909i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.64626 | − | 13.3193i | 0.0942644 | − | 0.762660i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.7146i | 1.12517i | 0.826738 | + | 0.562587i | \(0.190194\pi\) | ||||
−0.826738 | + | 0.562587i | \(0.809806\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.7255 | 1.29281 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.1003 | −0.856258 | −0.428129 | − | 0.903718i | \(-0.640827\pi\) | ||||
−0.428129 | + | 0.903718i | \(0.640827\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9813i | 0.733747i | 0.930271 | + | 0.366874i | \(0.119572\pi\) | ||||
−0.930271 | + | 0.366874i | \(0.880428\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.8878 | + | 1.59292i | 0.726143 | + | 0.0897508i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.3503i | − | 0.974489i | −0.873266 | − | 0.487244i | \(-0.838002\pi\) | ||
0.873266 | − | 0.487244i | \(-0.161998\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.66616 | 0.0932868 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 33.7781 | 1.88531 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.63915i | − | 0.202488i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.75968 | + | 30.9109i | −0.430429 | + | 1.71463i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.3154i | 0.570444i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.192277 | 0.0106006 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.984756 | −0.0541271 | −0.0270635 | − | 0.999634i | \(-0.508616\pi\) | ||||
−0.0270635 | + | 0.999634i | \(0.508616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 52.3950i | − | 2.87123i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.03415 | + | 0.622218i | 0.275045 | + | 0.0339954i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 23.5575i | − | 1.28326i | −0.767015 | − | 0.641629i | \(-0.778259\pi\) | ||
0.767015 | − | 0.641629i | \(-0.221741\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 43.8767 | 2.38305 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 53.9598 | 2.92208 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 12.7850i | − | 0.690327i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.819321 | − | 6.62885i | 0.0441108 | − | 0.356885i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.0916i | 1.40067i | 0.713813 | + | 0.700337i | \(0.246967\pi\) | ||||
−0.713813 | + | 0.700337i | \(0.753033\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.8609 | 0.956070 | 0.478035 | − | 0.878341i | \(-0.341349\pi\) | ||||
0.478035 | + | 0.878341i | \(0.341349\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 55.6445 | 2.97009 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 13.1080i | − | 0.697667i | −0.937185 | − | 0.348833i | \(-0.886578\pi\) | ||
0.937185 | − | 0.348833i | \(-0.113422\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.81633 | + | 22.7859i | −0.149475 | + | 1.20935i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.84430i | 0.521016i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.1119 | 1.16702 | 0.583510 | − | 0.812106i | \(-0.301679\pi\) | ||||
0.583510 | + | 0.812106i | \(0.301679\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8276 | −0.938296 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 80.0183i | − | 4.19987i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.06665 | + | 0.379036i | 0.160516 | + | 0.0198396i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.98495i | 0.416811i | 0.978043 | + | 0.208406i | \(0.0668274\pi\) | ||||
−0.978043 | + | 0.208406i | \(0.933173\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28.7427 | 1.49629 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.89402 | −0.0983326 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.8712i | 1.23600i | 0.786177 | + | 0.618002i | \(0.212058\pi\) | ||||
−0.786177 | + | 0.618002i | \(0.787942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 31.1493 | + | 12.0433i | 1.60855 | + | 0.621911i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.72762i | − | 0.0889771i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.5647 | −1.77547 | −0.887735 | − | 0.460355i | \(-0.847722\pi\) | ||||
−0.887735 | + | 0.460355i | \(0.847722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.56394 | −0.182586 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 12.3139i | − | 0.629211i | −0.949223 | − | 0.314606i | \(-0.898128\pi\) | ||
0.949223 | − | 0.314606i | \(-0.101872\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.3766 | − | 1.65334i | −0.681734 | − | 0.0842619i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.1200i | 0.565262i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.0447 | 1.37122 | 0.685611 | − | 0.727968i | \(-0.259535\pi\) | ||||
0.685611 | + | 0.727968i | \(0.259535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.36098 | 0.169972 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 35.0462i | − | 1.76785i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.28219 | + | 10.3738i | −0.0645140 | + | 0.521960i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.07631i | 0.455527i | 0.973717 | + | 0.227763i | \(0.0731413\pi\) | ||||
−0.973717 | + | 0.227763i | \(0.926859\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.17141 | −0.158769 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.73762 | 0.336461 | 0.168230 | − | 0.985748i | \(-0.446195\pi\) | ||||
0.168230 | + | 0.985748i | \(0.446195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 55.9504i | − | 2.78709i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.27912 | − | 18.4395i | 0.113250 | − | 0.916268i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 54.3823i | 2.69563i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.7205 | −1.27180 | −0.635898 | − | 0.771773i | \(-0.719370\pi\) | ||||
−0.635898 | + | 0.771773i | \(0.719370\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.2640 | 1.54214 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 12.7509i | − | 0.627428i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.8791 | + | 4.31103i | 1.71215 | + | 0.211620i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 12.2873i | − | 0.601711i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.2666 | −0.794676 | −0.397338 | − | 0.917672i | \(-0.630066\pi\) | ||||
−0.397338 | + | 0.917672i | \(0.630066\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.9106 | −0.921645 | −0.460822 | − | 0.887492i | \(-0.652445\pi\) | ||||
−0.460822 | + | 0.887492i | \(0.652445\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.16135i | − | 0.0564669i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.09164 | + | 16.2992i | −0.198474 | + | 0.790626i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.88522i | − | 0.284806i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −117.040 | −5.65076 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.4086 | 0.549535 | 0.274767 | − | 0.961511i | \(-0.411399\pi\) | ||||
0.274767 | + | 0.961511i | \(0.411399\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 23.2756i | − | 1.11856i | −0.828980 | − | 0.559278i | \(-0.811078\pi\) | ||
0.828980 | − | 0.559278i | \(-0.188922\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.79670 | − | 0.222071i | −0.0861451 | − | 0.0106475i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.08276i | 0.0517956i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.0581 | −0.623231 | −0.311615 | − | 0.950208i | \(-0.600870\pi\) | ||||
−0.311615 | + | 0.950208i | \(0.600870\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −35.7635 | −1.70302 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.113844i | 0.00540891i | 0.999996 | + | 0.00270446i | \(0.000860856\pi\) | ||||
−0.999996 | + | 0.00270446i | \(0.999139\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.05966 | − | 24.7546i | 0.145042 | − | 1.17348i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.11598i | 0.194679i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.0371 | 0.520874 | 0.260437 | − | 0.965491i | \(-0.416133\pi\) | ||||
0.260437 | + | 0.965491i | \(0.416133\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.8329 | −1.40478 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 10.4363i | − | 0.490342i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.71433 | + | 13.8701i | −0.0803691 | + | 0.650239i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.1638i | 1.41100i | 0.708709 | + | 0.705501i | \(0.249278\pi\) | ||||
−0.708709 | + | 0.705501i | \(0.750722\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 29.3411 | 1.36953 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.3908 | −1.74146 | −0.870732 | − | 0.491759i | \(-0.836354\pi\) | ||||
−0.870732 | + | 0.491759i | \(0.836354\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.7365i | 0.777810i | 0.921278 | + | 0.388905i | \(0.127147\pi\) | ||||
−0.921278 | + | 0.388905i | \(0.872853\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −58.1875 | − | 7.19194i | −2.69838 | − | 0.333518i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 18.2260i | − | 0.843399i | −0.906736 | − | 0.421699i | \(-0.861434\pi\) | ||
0.906736 | − | 0.421699i | \(-0.138566\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.22437 | 0.102712 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.92820 | 0.457467 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 11.5418i | − | 0.530692i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.25090 | − | 1.31815i | −0.240928 | − | 0.0604810i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.4399i | 0.523795i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.31948 | 0.151671 | 0.0758355 | − | 0.997120i | \(-0.475838\pi\) | ||||
0.0758355 | + | 0.997120i | \(0.475838\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.3885 | 2.57110 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 2.92900i | − | 0.133274i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.8283 | + | 2.82157i | 1.03658 | + | 0.128121i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 19.7412i | − | 0.894558i | −0.894395 | − | 0.447279i | \(-0.852393\pi\) | ||
0.894395 | − | 0.447279i | \(-0.147607\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.4521 | 1.15098 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.1353 | −0.818432 | −0.409216 | − | 0.912437i | \(-0.634198\pi\) | ||||
−0.409216 | + | 0.912437i | \(0.634198\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.910968i | − | 0.0410279i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.98615 | + | 80.7945i | −0.448844 | + | 3.63144i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.0681i | 0.451616i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.9797 | 0.670582 | 0.335291 | − | 0.942115i | \(-0.391165\pi\) | ||||
0.335291 | + | 0.942115i | \(0.391165\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 46.6552 | 2.08440 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 7.90238i | − | 0.352350i | −0.984359 | − | 0.176175i | \(-0.943628\pi\) | ||
0.984359 | − | 0.176175i | \(-0.0563724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.18635 | + | 33.8703i | −0.186290 | + | 1.50721i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 82.5262i | 3.66512i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.1882 | 0.939152 | 0.469576 | − | 0.882892i | \(-0.344407\pi\) | ||||
0.469576 | + | 0.882892i | \(0.344407\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.35502 | 0.0599425 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.45245i | 0.417336i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.8834 | + | 2.08678i | 0.743973 | + | 0.0919546i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.20540i | 0.0530136i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.1728 | −1.10496 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.1210 | −0.487219 | −0.243610 | − | 0.969873i | \(-0.578332\pi\) | ||||
−0.243610 | + | 0.969873i | \(0.578332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.2670i | − | 0.711304i | −0.934618 | − | 0.355652i | \(-0.884259\pi\) | ||
0.934618 | − | 0.355652i | \(-0.115741\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.2043 | + | 3.56575i | 0.619925 | + | 0.155622i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 29.5024i | − | 1.28515i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −77.0151 | −3.34217 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.9335i | 1.33988i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.0948 | + | 3.10170i | 1.08494 | + | 0.134098i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 32.2743i | − | 1.39274i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.1200 | 1.59887 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.8797 | −0.596733 | −0.298367 | − | 0.954451i | \(-0.596442\pi\) | ||||
−0.298367 | + | 0.954451i | \(0.596442\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 46.0851i | 1.97770i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.947220 | + | 7.66363i | −0.0405745 | + | 0.328274i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.91647i | 0.252970i | 0.991969 | + | 0.126485i | \(0.0403696\pi\) | ||||
−0.991969 | + | 0.126485i | \(0.959630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −35.5467 | −1.51709 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.293475 | 0.0125025 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.58371i | 0.194919i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.24825 | − | 58.6431i | 0.307671 | − | 2.48926i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.2857i | 1.19850i | 0.800560 | + | 0.599252i | \(0.204535\pi\) | ||||
−0.800560 | + | 0.599252i | \(0.795465\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.9676 | −0.506175 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −61.7148 | −2.60560 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.7025i | 1.33610i | 0.744117 | + | 0.668050i | \(0.232871\pi\) | ||||
−0.744117 | + | 0.668050i | \(0.767129\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.5973 | + | 4.02900i | 1.37138 | + | 0.169502i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 8.14763i | − | 0.342169i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0702 | 1.00907 | 0.504537 | − | 0.863390i | \(-0.331663\pi\) | ||||
0.504537 | + | 0.863390i | \(0.331663\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.3935 | −0.602349 | −0.301175 | − | 0.953569i | \(-0.597379\pi\) | ||||
−0.301175 | + | 0.953569i | \(0.597379\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 66.5023i | − | 2.77817i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.21740 | − | 4.84953i | 0.0507689 | − | 0.202239i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.77998i | 0.240624i | 0.992736 | + | 0.120312i | \(0.0383895\pi\) | ||||
−0.992736 | + | 0.120312i | \(0.961611\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 48.2111 | 2.00358 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.4115 | 0.639378 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 11.8738i | − | 0.491761i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 83.7751 | + | 10.3546i | 3.46368 | + | 0.428108i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.7897i | 1.14700i | 0.819204 | + | 0.573502i | \(0.194416\pi\) | ||||
−0.819204 | + | 0.573502i | \(0.805584\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.50441 | 0.391623 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −41.7999 | −1.71942 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 22.1872i | − | 0.911118i | −0.890205 | − | 0.455559i | \(-0.849439\pi\) | ||
0.890205 | − | 0.455559i | \(-0.150561\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.903960 | + | 7.31363i | −0.0370587 | + | 0.299829i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.6683i | 0.845897i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.1380 | 0.618521 | 0.309260 | − | 0.950977i | \(-0.399919\pi\) | ||||
0.309260 | + | 0.950977i | \(0.399919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5353 | 0.837652 | 0.418826 | − | 0.908067i | \(-0.362442\pi\) | ||||
0.418826 | + | 0.908067i | \(0.362442\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 13.4352i | − | 0.547123i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.34773 | − | 59.4480i | 0.298728 | − | 2.41690i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.9906i | 1.17669i | 0.808610 | + | 0.588345i | \(0.200220\pi\) | ||||
−0.808610 | + | 0.588345i | \(0.799780\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.793883 | −0.0321698 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.24987 | 0.0505644 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9.03621i | − | 0.364969i | −0.983209 | − | 0.182485i | \(-0.941586\pi\) | ||
0.983209 | − | 0.182485i | \(-0.0584139\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.1703 | + | 3.97623i | 1.29723 | + | 0.160337i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.42741i | 0.178241i | 0.996021 | + | 0.0891203i | \(0.0284056\pi\) | ||||
−0.996021 | + | 0.0891203i | \(0.971594\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.8403 | 0.596483 | 0.298241 | − | 0.954490i | \(-0.403600\pi\) | ||||
0.298241 | + | 0.954490i | \(0.403600\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.72993 | −0.350320 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 10.9380i | − | 0.438222i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.0359 | + | 11.8076i | 0.881436 | + | 0.472304i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 19.8819i | − | 0.794005i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.7334 | 1.18555 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.8369 | −1.66550 | −0.832751 | − | 0.553648i | \(-0.813235\pi\) | ||||
−0.832751 | + | 0.553648i | \(0.813235\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 38.5841i | 1.53358i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.64776 | − | 0.327261i | −0.105073 | − | 0.0129870i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 38.4894i | − | 1.52501i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 60.8113 | 2.40566 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.86478 | 0.231645 | 0.115822 | − | 0.993270i | \(-0.463050\pi\) | ||||
0.115822 | + | 0.993270i | \(0.463050\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.460745i | 0.0181700i | 0.999959 | + | 0.00908500i | \(0.00289188\pi\) | ||||
−0.999959 | + | 0.00908500i | \(0.997108\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.53833 | + | 12.4461i | −0.0605716 | + | 0.490064i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.5690i | 0.612079i | 0.952019 | + | 0.306040i | \(0.0990040\pi\) | ||||
−0.952019 | + | 0.306040i | \(0.900996\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 79.9362 | 3.13777 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.7105 | −1.00767 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.4538i | 1.15262i | 0.817233 | + | 0.576308i | \(0.195507\pi\) | ||||
−0.817233 | + | 0.576308i | \(0.804493\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.21814 | − | 26.0369i | 0.125743 | − | 1.01734i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 8.18430i | − | 0.319300i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.5604 | 0.878829 | 0.439415 | − | 0.898284i | \(-0.355186\pi\) | ||||
0.439415 | + | 0.898284i | \(0.355186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.7530 | −1.54621 | −0.773106 | − | 0.634277i | \(-0.781298\pi\) | ||||
−0.773106 | + | 0.634277i | \(0.781298\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 63.9916i | 2.48523i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.35614 | − | 0.291217i | −0.0913671 | − | 0.0112929i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.271042i | 0.0104948i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −79.6289 | −3.07863 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.8949 | 1.42431 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11.5047i | − | 0.443475i | −0.975106 | − | 0.221737i | \(-0.928827\pi\) | ||
0.975106 | − | 0.221737i | \(-0.0711728\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.6278 | − | 42.3361i | 0.409064 | − | 1.62952i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.7703i | 1.22103i | 0.792005 | + | 0.610515i | \(0.209038\pi\) | ||||
−0.792005 | + | 0.610515i | \(0.790962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0868 | 0.387098 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.2101 | −1.08101 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.22683i | 0.276527i | 0.990395 | + | 0.138264i | \(0.0441521\pi\) | ||||
−0.990395 | + | 0.138264i | \(0.955848\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.2270 | + | 2.87084i | 0.887457 | + | 0.109689i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42.4145i | 1.61822i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.3118 | −0.469043 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.29788 | −0.125457 | −0.0627286 | − | 0.998031i | \(-0.519980\pi\) | ||||
−0.0627286 | + | 0.998031i | \(0.519980\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 35.6996i | 1.35611i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.12829 | − | 9.12859i | 0.0427984 | − | 0.346267i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.3111i | 0.617827i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.1123 | −1.06331 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.7936 | 0.709824 | 0.354912 | − | 0.934900i | \(-0.384511\pi\) | ||||
0.354912 | + | 0.934900i | \(0.384511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.57884i | 0.361273i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.160660 | − | 1.29985i | 0.00605081 | − | 0.0489550i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.9658i | 0.562848i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.1039 | −0.529685 | −0.264842 | − | 0.964292i | \(-0.585320\pi\) | ||||
−0.264842 | + | 0.964292i | \(0.585320\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.6856 | 1.03829 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.77792i | 0.328736i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −86.9527 | − | 10.7473i | −3.25185 | − | 0.401926i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 46.2341i | 1.72664i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.5631 | −0.878754 | −0.439377 | − | 0.898303i | \(-0.644801\pi\) | ||||
−0.439377 | + | 0.898303i | \(0.644801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.46005 | 0.277827 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.4862i | 0.389985i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.31443 | − | 0.329966i | −0.0488166 | − | 0.0122546i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.57021i | 0.132412i | 0.997806 | + | 0.0662059i | \(0.0210894\pi\) | ||||
−0.997806 | + | 0.0662059i | \(0.978911\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0190 | 1.07478 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.31045 | −0.233401 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 10.3158i | − | 0.381022i | −0.981685 | − | 0.190511i | \(-0.938985\pi\) | ||
0.981685 | − | 0.190511i | \(-0.0610145\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −40.0283 | − | 4.94747i | −1.47647 | − | 0.182490i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.9448i | 0.513663i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.2056 | −1.33185 | −0.665923 | − | 0.746021i | \(-0.731962\pi\) | ||||
−0.665923 | + | 0.746021i | \(0.731962\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.6153 | −0.757324 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.24466i | 0.119035i | 0.998227 | + | 0.0595174i | \(0.0189562\pi\) | ||||
−0.998227 | + | 0.0595174i | \(0.981044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.377953 | + | 3.05788i | −0.0138471 | + | 0.112032i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 93.0856i | − | 3.40582i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.0883 | 0.405157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.9796 | −0.984499 | −0.492250 | − | 0.870454i | \(-0.663825\pi\) | ||||
−0.492250 | + | 0.870454i | \(0.663825\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 70.6888i | − | 2.57604i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.958324 | − | 7.75347i | 0.0348770 | − | 0.282178i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 11.7249i | − | 0.426148i | −0.977036 | − | 0.213074i | \(-0.931652\pi\) | ||
0.977036 | − | 0.213074i | \(-0.0683476\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.3621 | 0.666504 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.4303 | −0.885599 | −0.442800 | − | 0.896621i | \(-0.646015\pi\) | ||||
−0.442800 | + | 0.896621i | \(0.646015\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.38623i | 0.122590i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 44.1742 | + | 5.45991i | 1.59712 | + | 0.197403i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 82.8852i | − | 2.99281i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.804588 | −0.0290142 | −0.0145071 | − | 0.999895i | \(-0.504618\pi\) | ||||
−0.0145071 | + | 0.999895i | \(0.504618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −92.0989 | −3.31686 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 6.02477i | − | 0.216696i | −0.994113 | − | 0.108348i | \(-0.965444\pi\) | ||
0.994113 | − | 0.108348i | \(-0.0345561\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.5688 | − | 10.6862i | −1.52912 | − | 0.383860i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 25.9118i | − | 0.929582i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.25474 | −0.188270 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −63.1179 | −2.25853 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.36618i | 0.0845604i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.37596 | + | 0.911664i | 0.263259 | + | 0.0325387i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.9326i | 0.460996i | 0.973073 | + | 0.230498i | \(0.0740356\pi\) | ||||
−0.973073 | + | 0.230498i | \(0.925964\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −61.4977 | −2.18938 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.4033 | 0.512123 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 38.2561i | − | 1.35851i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.58258 | + | 12.8041i | −0.0561282 | + | 0.454114i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.3660i | 1.28815i | 0.764962 | + | 0.644075i | \(0.222758\pi\) | ||||
−0.764962 | + | 0.644075i | \(0.777242\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.659052 | 0.0233156 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −66.0654 | −2.33431 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.49472i | 0.299772i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.268957 | − | 2.17604i | 0.00947950 | − | 0.0766953i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 50.8629i | − | 1.79046i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.5840 | −0.934642 | −0.467321 | − | 0.884088i | \(-0.654781\pi\) | ||||
−0.467321 | + | 0.884088i | \(0.654781\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.7712 | 1.57213 | 0.786064 | − | 0.618145i | \(-0.212116\pi\) | ||||
0.786064 | + | 0.618145i | \(0.212116\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.8360i | 1.43218i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.9091 | + | 2.33715i | 0.662357 | + | 0.0818669i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.03296i | − | 0.0711242i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 37.0166 | 1.29346 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3949 | 0.781587 | 0.390794 | − | 0.920478i | \(-0.372201\pi\) | ||||
0.390794 | + | 0.920478i | \(0.372201\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.18913i | 0.0763081i | 0.999272 | + | 0.0381541i | \(0.0121478\pi\) | ||||
−0.999272 | + | 0.0381541i | \(0.987852\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.3540 | + | 89.0478i | −0.778267 | + | 3.10025i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 39.4367i | − | 1.37135i | −0.727909 | − | 0.685674i | \(-0.759508\pi\) | ||
0.727909 | − | 0.685674i | \(-0.240492\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0629 | 0.384229 | 0.192115 | − | 0.981373i | \(-0.438465\pi\) | ||||
0.192115 | + | 0.981373i | \(0.438465\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −48.5040 | −1.68259 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 20.2953i | − | 0.703190i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.6615 | + | 4.28414i | 1.19951 | + | 0.148259i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 76.6306i | 2.64874i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.8510 | −1.30676 | −0.653381 | − | 0.757030i | \(-0.726650\pi\) | ||||
−0.653381 | + | 0.757030i | \(0.726650\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9265 | −0.997467 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.08254i | 0.0372845i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.57802 | + | 61.3111i | −0.260692 | + | 2.10917i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 26.2675i | − | 0.902561i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.3132 | −0.697148 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.84665 | −0.303259 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 28.9770i | − | 0.992155i | −0.868278 | − | 0.496078i | \(-0.834773\pi\) | ||
0.868278 | − | 0.496078i | \(-0.165227\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.75895 | + | 14.2311i | −0.0601548 | + | 0.486692i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 56.0462i | − | 1.91450i | −0.289261 | − | 0.957250i | \(-0.593410\pi\) | ||
0.289261 | − | 0.957250i | \(-0.406590\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.8866 | 1.49739 | 0.748695 | − | 0.662914i | \(-0.230681\pi\) | ||||
0.748695 | + | 0.662914i | \(0.230681\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.2147 | 0.484434 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.1955i | 0.755542i | 0.925899 | + | 0.377771i | \(0.123309\pi\) | ||||
−0.925899 | + | 0.377771i | \(0.876691\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.7016 | − | 2.31151i | −0.635875 | − | 0.0785937i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 17.0377i | − | 0.578630i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.7357 | −0.974791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.4592 | 0.489932 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 60.9245i | − | 2.06198i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.2253 | + | 3.95342i | 0.345680 | + | 0.133650i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 5.44979i | − | 0.184026i | −0.995758 | − | 0.0920131i | \(-0.970670\pi\) | ||
0.995758 | − | 0.0920131i | \(-0.0293302\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −78.3125 | −2.64141 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.7854 | −0.397060 | −0.198530 | − | 0.980095i | \(-0.563617\pi\) | ||||
−0.198530 | + | 0.980095i | \(0.563617\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.7945i | 0.800748i | 0.916352 | + | 0.400374i | \(0.131120\pi\) | ||||
−0.916352 | + | 0.400374i | \(0.868880\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −86.1991 | − | 10.6542i | −2.89755 | − | 0.358136i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.4300i | 1.49181i | 0.666050 | + | 0.745907i | \(0.267984\pi\) | ||||
−0.666050 | + | 0.745907i | \(0.732016\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.16993 | −0.0392381 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 51.0782 | 1.71119 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.212318i | 0.00710496i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.96361 | − | 23.9775i | 0.0990626 | − | 0.801481i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 19.0396i | − | 0.635712i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.37919 | 0.0793504 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.49196 | −0.216279 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.49938i | 0.183008i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.23180 | + | 34.2380i | −0.140670 | + | 1.13811i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.7542i | 1.35322i | 0.736341 | + | 0.676611i | \(0.236552\pi\) | ||||
−0.736341 | + | 0.676611i | \(0.763448\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 90.3934 | 2.99816 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.71520 | 0.0899587 | 0.0449794 | − | 0.998988i | \(-0.485678\pi\) | ||||
0.0449794 | + | 0.998988i | \(0.485678\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 96.6163i | 3.19753i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −39.7856 | − | 4.91748i | −1.31527 | − | 0.162567i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 11.5046i | − | 0.379914i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.7227 | 0.353708 | 0.176854 | − | 0.984237i | \(-0.443408\pi\) | ||||
0.176854 | + | 0.984237i | \(0.443408\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 58.8890 | 1.94046 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 65.4464i | 2.15419i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.7699 | − | 42.9021i | 0.354112 | − | 1.41061i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 45.0587i | − | 1.47992i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.8670 | −1.27518 | −0.637592 | − | 0.770374i | \(-0.720070\pi\) | ||||
−0.637592 | + | 0.770374i | \(0.720070\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.53827 | 0.214283 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 45.1055i | 1.47669i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −45.8498 | − | 5.66700i | −1.49945 | − | 0.185331i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.6117i | − | 1.26139i | −0.776032 | − | 0.630694i | \(-0.782770\pi\) | ||
0.776032 | − | 0.630694i | \(-0.217230\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.7761 | 1.26541 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.3928 | 0.860381 | 0.430191 | − | 0.902738i | \(-0.358446\pi\) | ||||
0.430191 | + | 0.902738i | \(0.358446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.85308i | − | 0.158038i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.34798 | − | 18.9967i | 0.0763797 | − | 0.617962i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 22.3777i | − | 0.727179i | −0.931559 | − | 0.363589i | \(-0.881551\pi\) | ||
0.931559 | − | 0.363589i | \(-0.118449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.80811 | 0.285923 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −51.8265 | −1.68059 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 17.4362i | − | 0.564815i | −0.959295 | − | 0.282407i | \(-0.908867\pi\) | ||
0.959295 | − | 0.282407i | \(-0.0911330\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.10662 | − | 49.4065i | 0.197605 | − | 1.59876i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 4.97692i | − | 0.160881i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.2630 | 0.331409 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.0519 | 1.48554 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 66.9732i | − | 2.15818i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.8174 | + | 4.42702i | 1.15300 | + | 0.142511i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45.1587i | − | 1.45221i | −0.687586 | − | 0.726103i | \(-0.741330\pi\) | ||
0.687586 | − | 0.726103i | \(-0.258670\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.8704 | −0.349207 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.3123 | 1.10113 | 0.550567 | − | 0.834791i | \(-0.314412\pi\) | ||||
0.550567 | + | 0.834791i | \(0.314412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4.03353i | − | 0.129309i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 92.3329 | + | 23.1787i | 2.95702 | + | 0.742312i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.51320i | 0.0484115i | 0.999707 | + | 0.0242058i | \(0.00770569\pi\) | ||||
−0.999707 | + | 0.0242058i | \(0.992294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68.5713 | 2.19155 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.4528 | 0.653007 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.1715i | 0.483895i | 0.970289 | + | 0.241947i | \(0.0777861\pi\) | ||||
−0.970289 | + | 0.241947i | \(0.922214\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.0544 | − | 3.83830i | −0.989475 | − | 0.122298i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 0.574345i | − | 0.0182816i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.87756 | 0.0597031 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.4470 | 1.25307 | 0.626537 | − | 0.779392i | \(-0.284472\pi\) | ||||
0.626537 | + | 0.779392i | \(0.284472\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.94153i | 0.0933467i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.89788 | + | 15.3551i | −0.0601668 | + | 0.486789i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 2.33319i | − | 0.0738928i | −0.999317 | − | 0.0369464i | \(-0.988237\pi\) | ||
0.999317 | − | 0.0369464i | \(-0.0117631\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −77.2307 | −2.44347 |
(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 | 1840.2.e.g.369.1 | 14 | ||
4.3 | odd | 2 | 920.2.e.b.369.14 | yes | 14 | ||
5.2 | odd | 4 | 9200.2.a.cz.1.1 | 7 | |||
5.3 | odd | 4 | 9200.2.a.dc.1.7 | 7 | |||
5.4 | even | 2 | inner | 1840.2.e.g.369.14 | 14 | ||
20.3 | even | 4 | 4600.2.a.bh.1.1 | 7 | |||
20.7 | even | 4 | 4600.2.a.bi.1.7 | 7 | |||
20.19 | odd | 2 | 920.2.e.b.369.1 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.1 | ✓ | 14 | 20.19 | odd | 2 | ||
920.2.e.b.369.14 | yes | 14 | 4.3 | odd | 2 | ||
1840.2.e.g.369.1 | 14 | 1.1 | even | 1 | trivial | ||
1840.2.e.g.369.14 | 14 | 5.4 | even | 2 | inner | ||
4600.2.a.bh.1.1 | 7 | 20.3 | even | 4 | |||
4600.2.a.bi.1.7 | 7 | 20.7 | even | 4 | |||
9200.2.a.cz.1.1 | 7 | 5.2 | odd | 4 | |||
9200.2.a.dc.1.7 | 7 | 5.3 | odd | 4 |