Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7500,2,Mod(1249,7500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7500, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7500.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7500 = 2^{2} \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7500.d (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: | \(59.8878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.6 | ||
Character | \(\chi\) | \(=\) | 7500.1249 |
Dual form | 7500.2.d.g.1249.19 |
$q$-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 \(\left(\mathbb{Z}/7500\mathbb{Z}\right)^\times\).
\(n\) | \(2501\) | \(3751\) | \(6877\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.595901i | − 0.225229i | −0.993639 | − | 0.112615i | \(-0.964077\pi\) | ||||
0.993639 | − | 0.112615i | \(-0.0359225\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.35561 | 1.01175 | 0.505877 | − | 0.862606i | \(-0.331169\pi\) | ||||
0.505877 | + | 0.862606i | \(0.331169\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.76906i | − 1.32270i | −0.750077 | − | 0.661350i | \(-0.769984\pi\) | ||||
0.750077 | − | 0.661350i | \(-0.230016\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.47993i | 1.81415i | 0.420969 | + | 0.907075i | \(0.361690\pi\) | ||||
−0.420969 | + | 0.907075i | \(0.638310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.18873 | −1.41979 | −0.709896 | − | 0.704307i | \(-0.751258\pi\) | ||||
−0.709896 | + | 0.704307i | \(0.751258\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.595901 | −0.130036 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.40898i | 0.919337i | 0.888091 | + | 0.459668i | \(0.152032\pi\) | ||||
−0.888091 | + | 0.459668i | \(0.847968\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.76048 | 0.512608 | 0.256304 | − | 0.966596i | \(-0.417495\pi\) | ||||
0.256304 | + | 0.966596i | \(0.417495\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.48868 | 0.806191 | 0.403096 | − | 0.915158i | \(-0.367934\pi\) | ||||
0.403096 | + | 0.915158i | \(0.367934\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 3.35561i | − 0.584137i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.30067i | − 0.213828i | −0.994268 | − | 0.106914i | \(-0.965903\pi\) | ||||
0.994268 | − | 0.106914i | \(-0.0340970\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.76906 | −0.763661 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.40875 | −1.46940 | −0.734700 | − | 0.678392i | \(-0.762677\pi\) | ||||
−0.734700 | + | 0.678392i | \(0.762677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.59854i | − 1.15877i | −0.815055 | − | 0.579383i | \(-0.803294\pi\) | ||||
0.815055 | − | 0.579383i | \(-0.196706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 4.40189i | − 0.642082i | −0.947065 | − | 0.321041i | \(-0.895967\pi\) | ||||
0.947065 | − | 0.321041i | \(-0.104033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.64490 | 0.949272 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.47993 | 1.04740 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 8.20731i | − 1.12736i | −0.825993 | − | 0.563680i | \(-0.809385\pi\) | ||||
0.825993 | − | 0.563680i | \(-0.190615\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.18873i | 0.819717i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.22874 | 0.290158 | 0.145079 | − | 0.989420i | \(-0.453656\pi\) | ||||
0.145079 | + | 0.989420i | \(0.453656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.6096 | 1.61450 | 0.807248 | − | 0.590213i | \(-0.200956\pi\) | ||||
0.807248 | + | 0.590213i | \(0.200956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.595901i | 0.0750764i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.35839i | − 1.02114i | −0.859836 | − | 0.510570i | \(-0.829435\pi\) | ||||
0.859836 | − | 0.510570i | \(-0.170565\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.40898 | 0.530779 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.79530 | 0.806454 | 0.403227 | − | 0.915100i | \(-0.367889\pi\) | ||||
0.403227 | + | 0.915100i | \(0.367889\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 7.31221i | − 0.855830i | −0.903819 | − | 0.427915i | \(-0.859248\pi\) | ||||
0.903819 | − | 0.427915i | \(-0.140752\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.99961i | − 0.227877i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.5672 | 1.18891 | 0.594454 | − | 0.804130i | \(-0.297368\pi\) | ||||
0.594454 | + | 0.804130i | \(0.297368\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.18160i | 0.458991i | 0.973310 | + | 0.229495i | \(0.0737076\pi\) | ||||
−0.973310 | + | 0.229495i | \(0.926292\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 2.76048i | − 0.295955i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.25036 | −0.450538 | −0.225269 | − | 0.974297i | \(-0.572326\pi\) | ||||
−0.225269 | + | 0.974297i | \(0.572326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.84189 | −0.297911 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.48868i | − 0.465455i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 12.2752i | − 1.24636i | −0.782078 | − | 0.623180i | \(-0.785840\pi\) | ||||
0.782078 | − | 0.623180i | \(-0.214160\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.35561 | −0.337251 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.00835 | −0.796860 | −0.398430 | − | 0.917199i | \(-0.630445\pi\) | ||||
−0.398430 | + | 0.917199i | \(0.630445\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 5.62521i | − 0.554269i | −0.960831 | − | 0.277134i | \(-0.910615\pi\) | ||||
0.960831 | − | 0.277134i | \(-0.0893847\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7701i | 1.33120i | 0.746308 | + | 0.665601i | \(0.231825\pi\) | ||||
−0.746308 | + | 0.665601i | \(0.768175\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8014 | 1.22616 | 0.613078 | − | 0.790023i | \(-0.289931\pi\) | ||||
0.613078 | + | 0.790023i | \(0.289931\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.30067 | −0.123454 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.6394i | 1.09494i | 0.836825 | + | 0.547471i | \(0.184409\pi\) | ||||
−0.836825 | + | 0.547471i | \(0.815591\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.76906i | 0.440900i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.45730 | 0.408600 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.260113 | 0.0236466 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.40875i | 0.848358i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2.66172i | − 0.236189i | −0.993002 | − | 0.118095i | \(-0.962321\pi\) | ||||
0.993002 | − | 0.118095i | \(-0.0376786\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.59854 | −0.669014 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.71046 | 0.848407 | 0.424203 | − | 0.905567i | \(-0.360554\pi\) | ||||
0.424203 | + | 0.905567i | \(0.360554\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.68787i | 0.319779i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 3.84194i | − 0.328239i | −0.986440 | − | 0.164119i | \(-0.947522\pi\) | ||||
0.986440 | − | 0.164119i | \(-0.0524783\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.92765 | 0.417958 | 0.208979 | − | 0.977920i | \(-0.432986\pi\) | ||||
0.208979 | + | 0.977920i | \(0.432986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.40189 | −0.370706 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 16.0031i | − 1.33825i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 6.64490i | − 0.548062i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.59040 | 0.539907 | 0.269953 | − | 0.962873i | \(-0.412992\pi\) | ||||
0.269953 | + | 0.962873i | \(0.412992\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5433 | −1.59041 | −0.795207 | − | 0.606338i | \(-0.792638\pi\) | ||||
−0.795207 | + | 0.606338i | \(0.792638\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 7.47993i | − 0.604717i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.341995i | 0.0272942i | 0.999907 | + | 0.0136471i | \(0.00434414\pi\) | ||||
−0.999907 | + | 0.0136471i | \(0.995656\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.20731 | −0.650882 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.62732 | 0.207062 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 22.5163i | − 1.76361i | −0.471612 | − | 0.881806i | \(-0.656328\pi\) | ||||
0.471612 | − | 0.881806i | \(-0.343672\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 4.31493i | − 0.333900i | −0.985965 | − | 0.166950i | \(-0.946608\pi\) | ||||
0.985965 | − | 0.166950i | \(-0.0533918\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.74397 | −0.749536 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.18873 | 0.473264 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 17.1688i | − 1.30532i | −0.757652 | − | 0.652659i | \(-0.773653\pi\) | ||||
0.757652 | − | 0.652659i | \(-0.226347\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 2.22874i | − 0.167523i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.06360 | −0.0794970 | −0.0397485 | − | 0.999210i | \(-0.512656\pi\) | ||||
−0.0397485 | + | 0.999210i | \(0.512656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0267 | −0.893936 | −0.446968 | − | 0.894550i | \(-0.647496\pi\) | ||||
−0.446968 | + | 0.894550i | \(0.647496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 12.6096i | − 0.932130i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.0997i | 1.83547i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.595901 | 0.0433454 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.9695 | −1.58966 | −0.794830 | − | 0.606832i | \(-0.792440\pi\) | ||||
−0.794830 | + | 0.606832i | \(0.792440\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4002i | 1.46844i | 0.678912 | + | 0.734220i | \(0.262452\pi\) | ||||
−0.678912 | + | 0.734220i | \(0.737548\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 4.10501i | − 0.292470i | −0.989250 | − | 0.146235i | \(-0.953284\pi\) | ||||
0.989250 | − | 0.146235i | \(-0.0467155\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.5940 | −1.81431 | −0.907156 | − | 0.420795i | \(-0.861751\pi\) | ||||
−0.907156 | + | 0.420795i | \(0.861751\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.35839 | −0.589555 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.64497i | − 0.115454i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 4.40898i | − 0.306446i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.7670 | −1.43648 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.5084 | 1.34301 | 0.671505 | − | 0.741000i | \(-0.265648\pi\) | ||||
0.671505 | + | 0.741000i | \(0.265648\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 6.79530i | − 0.465606i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 2.67481i | − 0.181578i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.31221 | −0.494113 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.6723 | 2.39958 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2.22827i | − 0.149216i | −0.997213 | − | 0.0746081i | \(-0.976229\pi\) | ||||
0.997213 | − | 0.0746081i | \(-0.0237706\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.54796i | 0.301859i | 0.988545 | + | 0.150929i | \(0.0482266\pi\) | ||||
−0.988545 | + | 0.150929i | \(0.951773\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.41511 | −0.225677 | −0.112838 | − | 0.993613i | \(-0.535994\pi\) | ||||
−0.112838 | + | 0.993613i | \(0.535994\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.99961 | −0.131565 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 16.7395i | − 1.09664i | −0.836268 | − | 0.548320i | \(-0.815267\pi\) | ||||
0.836268 | − | 0.548320i | \(-0.184733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 10.5672i | − 0.686417i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.3643 | 1.44663 | 0.723313 | − | 0.690520i | \(-0.242618\pi\) | ||||
0.723313 | + | 0.690520i | \(0.242618\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.265356 | 0.0170931 | 0.00854655 | − | 0.999963i | \(-0.497280\pi\) | ||||
0.00854655 | + | 0.999963i | \(0.497280\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.5144i | 1.87796i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.18160 | 0.264998 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.0694 | 1.83484 | 0.917422 | − | 0.397915i | \(-0.130266\pi\) | ||||
0.917422 | + | 0.397915i | \(0.130266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.7948i | 0.930143i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 7.05952i | − 0.440361i | −0.975459 | − | 0.220180i | \(-0.929335\pi\) | ||||
0.975459 | − | 0.220180i | \(-0.0706646\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.775067 | −0.0481603 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.76048 | −0.170869 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 1.38649i | − 0.0854949i | −0.999086 | − | 0.0427475i | \(-0.986389\pi\) | ||||
0.999086 | − | 0.0427475i | \(-0.0136111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.25036i | 0.260118i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.1752 | 0.864280 | 0.432140 | − | 0.901807i | \(-0.357759\pi\) | ||||
0.432140 | + | 0.901807i | \(0.357759\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.0411 | 0.913681 | 0.456841 | − | 0.889549i | \(-0.348981\pi\) | ||||
0.456841 | + | 0.889549i | \(0.348981\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.84189i | 0.171999i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.7933i | 0.768677i | 0.923192 | + | 0.384338i | \(0.125570\pi\) | ||||
−0.923192 | + | 0.384338i | \(0.874430\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.48868 | −0.268730 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.3058 | −0.913068 | −0.456534 | − | 0.889706i | \(-0.650909\pi\) | ||||
−0.456534 | + | 0.889706i | \(0.650909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 23.3502i | − 1.38802i | −0.719964 | − | 0.694011i | \(-0.755842\pi\) | ||||
0.719964 | − | 0.694011i | \(-0.244158\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.60668i | 0.330952i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −38.9494 | −2.29114 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2752 | −0.719587 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 6.36651i | − 0.371936i | −0.982556 | − | 0.185968i | \(-0.940458\pi\) | ||||
0.982556 | − | 0.185968i | \(-0.0595420\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.35561i | 0.194712i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.0267 | 1.21601 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.52797 | −0.260988 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.00835i | 0.460068i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 27.2317i | − 1.55419i | −0.629382 | − | 0.777096i | \(-0.716692\pi\) | ||||
0.629382 | − | 0.777096i | \(-0.283308\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.62521 | −0.320007 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.1583 | 0.972961 | 0.486480 | − | 0.873692i | \(-0.338281\pi\) | ||||
0.486480 | + | 0.873692i | \(0.338281\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 20.2659i | − 1.14550i | −0.819731 | − | 0.572749i | \(-0.805877\pi\) | ||||
0.819731 | − | 0.572749i | \(-0.194123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 21.0153i | − 1.18034i | −0.807279 | − | 0.590169i | \(-0.799061\pi\) | ||||
0.807279 | − | 0.590169i | \(-0.200939\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.26309 | 0.518634 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.7701 | 0.768570 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 46.2913i | − 2.57572i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 12.8014i | − 0.707921i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.62309 | −0.144616 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.7425 | −0.700391 | −0.350195 | − | 0.936677i | \(-0.613885\pi\) | ||||
−0.350195 | + | 0.936677i | \(0.613885\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.30067i | 0.0712760i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.3467i | 0.672567i | 0.941761 | + | 0.336284i | \(0.109170\pi\) | ||||
−0.941761 | + | 0.336284i | \(0.890830\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.6394 | 0.632165 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0623 | 0.815668 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 8.13100i | − 0.439033i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.1617i | 0.706555i | 0.935519 | + | 0.353277i | \(0.114933\pi\) | ||||
−0.935519 | + | 0.353277i | \(0.885067\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.8060 | −1.11372 | −0.556861 | − | 0.830606i | \(-0.687994\pi\) | ||||
−0.556861 | + | 0.830606i | \(0.687994\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.76906 | 0.254554 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 28.7945i | − 1.53258i | −0.642496 | − | 0.766289i | \(-0.722101\pi\) | ||||
0.642496 | − | 0.766289i | \(-0.277899\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 4.45730i | − 0.235905i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.3278 | 1.75897 | 0.879487 | − | 0.475923i | \(-0.157886\pi\) | ||||
0.879487 | + | 0.475923i | \(0.157886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.3004 | 1.01581 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 0.260113i | − 0.0136524i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.89727i | − 0.0990366i | −0.998773 | − | 0.0495183i | \(-0.984231\pi\) | ||||
0.998773 | − | 0.0495183i | \(-0.0157686\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.40875 | 0.489800 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.89074 | −0.253914 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 30.8908i | − 1.59947i | −0.600355 | − | 0.799733i | \(-0.704974\pi\) | ||||
0.600355 | − | 0.799733i | \(-0.295026\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 13.1649i | − 0.678027i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.5547 | −1.15856 | −0.579279 | − | 0.815129i | \(-0.696666\pi\) | ||||
−0.579279 | + | 0.815129i | \(0.696666\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.66172 | −0.136364 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.34373i | 0.221954i | 0.993823 | + | 0.110977i | \(0.0353980\pi\) | ||||
−0.993823 | + | 0.110977i | \(0.964602\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.59854i | 0.386255i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.5459 | 0.940313 | 0.470156 | − | 0.882583i | \(-0.344198\pi\) | ||||
0.470156 | + | 0.882583i | \(0.344198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.9789 | −1.66782 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 9.71046i | − 0.489828i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.706994i | 0.0354830i | 0.999843 | + | 0.0177415i | \(0.00564759\pi\) | ||||
−0.999843 | + | 0.0177415i | \(0.994352\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.68787 | 0.184624 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.8304 | −1.23997 | −0.619986 | − | 0.784613i | \(-0.712862\pi\) | ||||
−0.619986 | + | 0.784613i | \(0.712862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 21.4068i | − 1.06635i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 4.36453i | − 0.216341i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.730007 | 0.0360965 | 0.0180483 | − | 0.999837i | \(-0.494255\pi\) | ||||
0.0180483 | + | 0.999837i | \(0.494255\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.84194 | −0.189509 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.32811i | − 0.0653520i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 4.92765i | − 0.241308i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.9094 | 0.630666 | 0.315333 | − | 0.948981i | \(-0.397884\pi\) | ||||
0.315333 | + | 0.948981i | \(0.397884\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.1301 | 1.85835 | 0.929173 | − | 0.369644i | \(-0.120520\pi\) | ||||
0.929173 | + | 0.369644i | \(0.120520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.40189i | 0.214027i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 7.51408i | − 0.363632i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.0031 | −0.772638 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.1887 | −1.74315 | −0.871575 | − | 0.490262i | \(-0.836901\pi\) | ||||
−0.871575 | + | 0.490262i | \(0.836901\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 21.7487i | − 1.04518i | −0.852586 | − | 0.522588i | \(-0.824967\pi\) | ||||
0.852586 | − | 0.522588i | \(-0.175033\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 27.2860i | − 1.30527i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.3586 | 1.87848 | 0.939242 | − | 0.343255i | \(-0.111529\pi\) | ||||
0.939242 | + | 0.343255i | \(0.111529\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.64490 | −0.316424 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 27.4919i | − 1.30618i | −0.757281 | − | 0.653089i | \(-0.773473\pi\) | ||||
0.757281 | − | 0.653089i | \(-0.226527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 6.59040i | − 0.311715i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.51087 | −0.165688 | −0.0828441 | − | 0.996563i | \(-0.526400\pi\) | ||||
−0.0828441 | + | 0.996563i | \(0.526400\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.5721 | −1.48667 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.5433i | 0.918226i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.1677i | 0.475624i | 0.971311 | + | 0.237812i | \(0.0764302\pi\) | ||||
−0.971311 | + | 0.237812i | \(0.923570\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.47993 | −0.349133 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.934168 | 0.0435085 | 0.0217543 | − | 0.999763i | \(-0.493075\pi\) | ||||
0.0217543 | + | 0.999763i | \(0.493075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.88586i | 0.227065i | 0.993534 | + | 0.113533i | \(0.0362166\pi\) | ||||
−0.993534 | + | 0.113533i | \(0.963783\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.8046i | 1.19410i | 0.802206 | + | 0.597048i | \(0.203660\pi\) | ||||
−0.802206 | + | 0.597048i | \(0.796340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.98077 | −0.229990 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.341995 | 0.0157583 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 25.4977i | − 1.17239i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.20731i | 0.375787i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.9156 | 0.772893 | 0.386447 | − | 0.922312i | \(-0.373702\pi\) | ||||
0.386447 | + | 0.922312i | \(0.373702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.20296 | −0.282830 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.62732i | − 0.119547i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 16.3876i | − 0.742592i | −0.928515 | − | 0.371296i | \(-0.878914\pi\) | ||||
0.928515 | − | 0.371296i | \(-0.121086\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.5163 | −1.01822 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.2714 | −0.463541 | −0.231771 | − | 0.972770i | \(-0.574452\pi\) | ||||
−0.231771 | + | 0.972770i | \(0.574452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.6482i | 0.929948i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 4.04932i | − 0.181637i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5015 | 0.738707 | 0.369354 | − | 0.929289i | \(-0.379579\pi\) | ||||
0.369354 | + | 0.929289i | \(0.379579\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.31493 | −0.192777 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 7.60033i | − 0.338882i | −0.985540 | − | 0.169441i | \(-0.945804\pi\) | ||||
0.985540 | − | 0.169441i | \(-0.0541962\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.74397i | 0.432745i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.9513 | 0.972976 | 0.486488 | − | 0.873687i | \(-0.338278\pi\) | ||||
0.486488 | + | 0.873687i | \(0.338278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.35735 | −0.192758 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 6.18873i | − 0.273239i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 14.7710i | − 0.649629i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.1688 | −0.753626 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.8379 | −1.61390 | −0.806949 | − | 0.590621i | \(-0.798883\pi\) | ||||
−0.806949 | + | 0.590621i | \(0.798883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.5997i | 1.81903i | 0.415675 | + | 0.909513i | \(0.363545\pi\) | ||||
−0.415675 | + | 0.909513i | \(0.636455\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.5751i | 1.46255i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.56085 | 0.154820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.22874 | −0.0967193 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.8709i | 1.94358i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.06360i | 0.0458976i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.2977 | 0.960430 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5213 | −0.667313 | −0.333656 | − | 0.942695i | \(-0.608283\pi\) | ||||
−0.333656 | + | 0.942695i | \(0.608283\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.0267i | 0.516114i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3039i | 0.996403i | 0.867061 | + | 0.498202i | \(0.166006\pi\) | ||||
−0.867061 | + | 0.498202i | \(0.833994\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.6096 | −0.538165 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.0839 | −0.727797 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 6.29703i | − 0.267777i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 11.0914i | − 0.469959i | −0.972000 | − | 0.234979i | \(-0.924498\pi\) | ||||
0.972000 | − | 0.234979i | \(-0.0755023\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.2379 | −1.53270 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.0997 | 1.05971 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.3052i | 0.602890i | 0.953484 | + | 0.301445i | \(0.0974690\pi\) | ||||
−0.953484 | + | 0.301445i | \(0.902531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 0.595901i | − 0.0250255i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.7743 | 1.20628 | 0.603141 | − | 0.797634i | \(-0.293915\pi\) | ||||
0.603141 | + | 0.797634i | \(0.293915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.0394 | −0.545683 | −0.272842 | − | 0.962059i | \(-0.587963\pi\) | ||||
−0.272842 | + | 0.962059i | \(0.587963\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.9695i | 0.917791i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 1.79973i | − 0.0749239i | −0.999298 | − | 0.0374619i | \(-0.988073\pi\) | ||||
0.999298 | − | 0.0374619i | \(-0.0119273\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.4002 | 0.847804 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.49182 | 0.103378 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 27.5405i | − 1.14061i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.5964i | 1.67559i | 0.545982 | + | 0.837797i | \(0.316157\pi\) | ||||
−0.545982 | + | 0.837797i | \(0.683843\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.7792 | −1.14462 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.10501 | −0.168857 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 29.4991i | − 1.21138i | −0.795700 | − | 0.605690i | \(-0.792897\pi\) | ||||
0.795700 | − | 0.605690i | \(-0.207103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.5940i | 1.04749i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.91418 | 0.364224 | 0.182112 | − | 0.983278i | \(-0.441707\pi\) | ||||
0.182112 | + | 0.983278i | \(0.441707\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.6757 | 0.680217 | 0.340109 | − | 0.940386i | \(-0.389536\pi\) | ||||
0.340109 | + | 0.940386i | \(0.389536\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.35839i | 0.340380i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.9626i | 1.09438i | 0.837008 | + | 0.547190i | \(0.184302\pi\) | ||||
−0.837008 | + | 0.547190i | \(0.815698\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.64497 | −0.0666576 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.9929 | −0.849282 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 16.5230i | − 0.667356i | −0.942687 | − | 0.333678i | \(-0.891710\pi\) | ||||
0.942687 | − | 0.333678i | \(-0.108290\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.9879i | 0.925456i | 0.886500 | + | 0.462728i | \(0.153129\pi\) | ||||
−0.886500 | + | 0.462728i | \(0.846871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −49.3165 | −1.98220 | −0.991099 | − | 0.133124i | \(-0.957499\pi\) | ||||
−0.991099 | + | 0.133124i | \(0.957499\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.40898 | −0.176926 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.53279i | 0.101474i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.7670i | 0.829352i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.72889 | 0.387916 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.1782 | 0.962519 | 0.481260 | − | 0.876578i | \(-0.340179\pi\) | ||||
0.481260 | + | 0.876578i | \(0.340179\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 19.5084i | − 0.775387i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 31.6900i | − 1.25560i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.79530 | −0.268818 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −49.3663 | −1.94985 | −0.974927 | − | 0.222526i | \(-0.928570\pi\) | ||||
−0.974927 | + | 0.222526i | \(0.928570\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3.97743i | − 0.156854i | −0.996920 | − | 0.0784272i | \(-0.975010\pi\) | ||||
0.996920 | − | 0.0784272i | \(-0.0249898\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.01441i | 0.0398807i | 0.999801 | + | 0.0199404i | \(0.00634764\pi\) | ||||
−0.999801 | + | 0.0199404i | \(0.993652\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.47879 | 0.293568 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.67481 | −0.104834 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.17155i | 0.319778i | 0.987135 | + | 0.159889i | \(0.0511136\pi\) | ||||
−0.987135 | + | 0.159889i | \(0.948886\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.31221i | 0.285277i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.68859 | −0.299505 | −0.149752 | − | 0.988724i | \(-0.547848\pi\) | ||||
−0.149752 | + | 0.988724i | \(0.547848\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.2000 | −1.40802 | −0.704008 | − | 0.710192i | \(-0.748608\pi\) | ||||
−0.704008 | + | 0.710192i | \(0.748608\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 35.6723i | − 1.38540i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.1709i | 0.471260i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.22827 | −0.0861500 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.3129 | 1.63347 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.1819i | 1.16343i | 0.813394 | + | 0.581714i | \(0.197618\pi\) | ||||
−0.813394 | + | 0.581714i | \(0.802382\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 47.0154i | − 1.80695i | −0.428644 | − | 0.903473i | \(-0.641009\pi\) | ||||
0.428644 | − | 0.903473i | \(-0.358991\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.31482 | −0.280717 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.54796 | 0.174278 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 2.19204i | − 0.0838762i | −0.999120 | − | 0.0419381i | \(-0.986647\pi\) | ||||
0.999120 | − | 0.0419381i | \(-0.0133532\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.41511i | 0.130295i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.1412 | −1.49116 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.78521 | 0.0679127 | 0.0339563 | − | 0.999423i | \(-0.489189\pi\) | ||||
0.0339563 | + | 0.999423i | \(0.489189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.99961i | 0.0759589i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 70.3768i | − 2.66571i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.7395 | −0.633146 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.0728 | −0.418215 | −0.209107 | − | 0.977893i | \(-0.567056\pi\) | ||||
−0.209107 | + | 0.977893i | \(0.567056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.04947i | 0.303591i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.77218i | 0.179476i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.9129 | −0.747846 | −0.373923 | − | 0.927460i | \(-0.621988\pi\) | ||||
−0.373923 | + | 0.927460i | \(0.621988\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.5672 | −0.396303 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.7905i | 0.741162i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 22.3643i | − 0.835210i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.7804 | −1.29709 | −0.648546 | − | 0.761176i | \(-0.724623\pi\) | ||||
−0.648546 | + | 0.761176i | \(0.724623\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.35207 | −0.124837 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 0.265356i | − 0.00986871i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.9677i | 0.592209i | 0.955156 | + | 0.296105i | \(0.0956877\pi\) | ||||
−0.955156 | + | 0.296105i | \(0.904312\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 56.8365 | 2.10218 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 10.1425i | − 0.374621i | −0.982301 | − | 0.187310i | \(-0.940023\pi\) | ||||
0.982301 | − | 0.187310i | \(-0.0599770\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 28.0475i | − 1.03314i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.27848 | −0.120601 | −0.0603004 | − | 0.998180i | \(-0.519206\pi\) | ||||
−0.0603004 | + | 0.998180i | \(0.519206\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.5144 | 1.08424 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.7278i | 1.42078i | 0.703806 | + | 0.710392i | \(0.251482\pi\) | ||||
−0.703806 | + | 0.710392i | \(0.748518\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4.18160i | − 0.152997i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.20559 | 0.299826 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0211 | 0.475146 | 0.237573 | − | 0.971370i | \(-0.423648\pi\) | ||||
0.237573 | + | 0.971370i | \(0.423648\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 29.0694i | − 1.05935i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 33.4057i | − 1.21415i | −0.794645 | − | 0.607075i | \(-0.792343\pi\) | ||||
0.794645 | − | 0.607075i | \(-0.207657\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.7948 | 0.537018 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.7319 | 1.07778 | 0.538890 | − | 0.842376i | \(-0.318844\pi\) | ||||
0.538890 | + | 0.842376i | \(0.318844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7.62838i | − 0.276166i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 10.6290i | − 0.383792i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.45427 | 0.196686 | 0.0983431 | − | 0.995153i | \(-0.468646\pi\) | ||||
0.0983431 | + | 0.995153i | \(0.468646\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.05952 | −0.254242 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 29.0843i | − 1.04609i | −0.852306 | − | 0.523044i | \(-0.824796\pi\) | ||||
0.852306 | − | 0.523044i | \(-0.175204\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.775067i | 0.0278054i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58.2282 | 2.08624 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.8024 | 0.815933 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.76048i | 0.0986515i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34.1141i | − 1.21604i | −0.793923 | − | 0.608018i | \(-0.791965\pi\) | ||||
0.793923 | − | 0.608018i | \(-0.208035\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.38649 | −0.0493605 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.93592 | 0.246613 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 60.1361i | − 2.13549i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.4560i | 0.866276i | 0.901328 | + | 0.433138i | \(0.142594\pi\) | ||||
−0.901328 | + | 0.433138i | \(0.857406\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.9259 | 1.16483 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.25036 | 0.150179 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 24.5369i | − 0.865889i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 14.1752i | − 0.498992i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.2487 | 1.83697 | 0.918483 | − | 0.395460i | \(-0.129415\pi\) | ||||
0.918483 | + | 0.395460i | \(0.129415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.6487 | 0.619728 | 0.309864 | − | 0.950781i | \(-0.399716\pi\) | ||||
0.309864 | + | 0.950781i | \(0.399716\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 15.0411i | − 0.527514i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47.0253i | 1.64521i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.84189 | 0.0993036 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.1306 | −1.19117 | −0.595584 | − | 0.803293i | \(-0.703079\pi\) | ||||
−0.595584 | + | 0.803293i | \(0.703079\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.5282i | 1.58701i | 0.608562 | + | 0.793506i | \(0.291747\pi\) | ||||
−0.608562 | + | 0.793506i | \(0.708253\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.0967i | 0.664057i | 0.943269 | + | 0.332029i | \(0.107733\pi\) | ||||
−0.943269 | + | 0.332029i | \(0.892267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.3819 | −0.395309 | −0.197654 | − | 0.980272i | \(-0.563332\pi\) | ||||
−0.197654 | + | 0.980272i | \(0.563332\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.7933 | 0.443796 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 49.7034i | 1.72212i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.48868i | 0.155152i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.7924 | −0.890452 | −0.445226 | − | 0.895418i | \(-0.646877\pi\) | ||||
−0.445226 | + | 0.895418i | \(0.646877\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.3798 | −0.737233 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.3058i | 0.527160i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 0.155001i | − 0.00532591i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.3502 | −0.801375 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.73461 | 0.196580 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 15.7410i | − 0.538961i | −0.963006 | − | 0.269480i | \(-0.913148\pi\) | ||||
0.963006 | − | 0.269480i | \(-0.0868519\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 46.4948i | − 1.58823i | −0.607767 | − | 0.794116i | \(-0.707934\pi\) | ||||
0.607767 | − | 0.794116i | \(-0.292066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.1958 | −0.416116 | −0.208058 | − | 0.978116i | \(-0.566714\pi\) | ||||
−0.208058 | + | 0.978116i | \(0.566714\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.60668 | 0.191075 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.3926i | 1.54518i | 0.634904 | + | 0.772591i | \(0.281040\pi\) | ||||
−0.634904 | + | 0.772591i | \(0.718960\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.9494i | 1.32279i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.4596 | 1.20288 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.8617 | −1.35066 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.2752i | 0.415454i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 19.0305i | − 0.642615i | −0.946975 | − | 0.321308i | \(-0.895878\pi\) | ||||
0.946975 | − | 0.321308i | \(-0.104122\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.36651 | −0.214737 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.2097 | −0.512426 | −0.256213 | − | 0.966620i | \(-0.582475\pi\) | ||||
−0.256213 | + | 0.966620i | \(0.582475\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.3181i | 1.62603i | 0.582240 | + | 0.813017i | \(0.302176\pi\) | ||||
−0.582240 | + | 0.813017i | \(0.697824\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 32.4010i | − 1.08792i | −0.839111 | − | 0.543960i | \(-0.816924\pi\) | ||||
0.839111 | − | 0.543960i | \(-0.183076\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.58612 | −0.0531968 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.35561 | 0.112417 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.2421i | 0.911622i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 21.0267i | − 0.702062i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.3909 | 0.413260 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.3901 | 2.04520 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.52797i | 0.150681i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.8525i | 1.02444i | 0.858854 | + | 0.512220i | \(0.171177\pi\) | ||||
−0.858854 | + | 0.512220i | \(0.828823\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.00835 | 0.265620 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.2181 | 1.19996 | 0.599980 | − | 0.800015i | \(-0.295175\pi\) | ||||
0.599980 | + | 0.800015i | \(0.295175\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.0318i | 0.464386i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 5.78647i | − 0.191086i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.9977 | 1.25343 | 0.626715 | − | 0.779249i | \(-0.284399\pi\) | ||||
0.626715 | + | 0.779249i | \(0.284399\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.2317 | −0.897314 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 32.4072i | − 1.06670i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.62521i | 0.184756i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.4600 | 0.343180 | 0.171590 | − | 0.985168i | \(-0.445110\pi\) | ||||
0.171590 | + | 0.985168i | \(0.445110\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.1235 | −1.34777 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 17.1583i | − 0.561739i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 33.7638i | − 1.10301i | −0.834170 | − | 0.551507i | \(-0.814053\pi\) | ||||
0.834170 | − | 0.551507i | \(-0.185947\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.2659 | −0.661354 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.23047 | 0.0727113 | 0.0363556 | − | 0.999339i | \(-0.488425\pi\) | ||||
0.0363556 | + | 0.999339i | \(0.488425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 41.4830i | − 1.35087i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 7.65150i | − 0.248640i | −0.992242 | − | 0.124320i | \(-0.960325\pi\) | ||||
0.992242 | − | 0.124320i | \(-0.0396750\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.8724 | −1.13201 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.0153 | −0.681469 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 11.6526i | − 0.377465i | −0.982029 | − | 0.188733i | \(-0.939562\pi\) | ||||
0.982029 | − | 0.188733i | \(-0.0604380\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 9.26309i | − 0.299433i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.28941 | −0.0739290 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.8517 | −0.350055 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 13.7701i | − 0.443734i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.7782i | 1.08623i | 0.839657 | + | 0.543117i | \(0.182756\pi\) | ||||
−0.839657 | + | 0.543117i | \(0.817244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −46.2913 | −1.48709 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.7855 | 1.08423 | 0.542114 | − | 0.840305i | \(-0.317624\pi\) | ||||
0.542114 | + | 0.840305i | \(0.317624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.93639i | − 0.0941363i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.77099i | 0.120645i | 0.998179 | + | 0.0603223i | \(0.0192128\pi\) | ||||
−0.998179 | + | 0.0603223i | \(0.980787\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.2626 | −0.455833 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.8014 | −0.408718 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.3040i | 1.34929i | 0.738143 | + | 0.674644i | \(0.235703\pi\) | ||||
−0.738143 | + | 0.674644i | \(0.764297\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.62309i | 0.0834939i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.5018 | 1.06530 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.9881 | 1.01614 | 0.508068 | − | 0.861317i | \(-0.330360\pi\) | ||||
0.508068 | + | 0.861317i | \(0.330360\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.7425i | 0.404371i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.7077i | 0.529138i | 0.964367 | + | 0.264569i | \(0.0852296\pi\) | ||||
−0.964367 | + | 0.264569i | \(0.914770\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.30067 | 0.0411512 |
(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 | 7500.2.d.g.1249.6 | 24 | ||
5.2 | odd | 4 | 7500.2.a.m.1.7 | 12 | |||
5.3 | odd | 4 | 7500.2.a.n.1.6 | 12 | |||
5.4 | even | 2 | inner | 7500.2.d.g.1249.19 | 24 | ||
25.3 | odd | 20 | 1500.2.m.c.1201.3 | 24 | |||
25.4 | even | 10 | 300.2.o.a.109.1 | ✓ | 24 | ||
25.6 | even | 5 | 300.2.o.a.289.1 | yes | 24 | ||
25.8 | odd | 20 | 1500.2.m.c.301.3 | 24 | |||
25.17 | odd | 20 | 1500.2.m.d.301.4 | 24 | |||
25.19 | even | 10 | 1500.2.o.c.949.5 | 24 | |||
25.21 | even | 5 | 1500.2.o.c.49.5 | 24 | |||
25.22 | odd | 20 | 1500.2.m.d.1201.4 | 24 | |||
75.29 | odd | 10 | 900.2.w.c.109.6 | 24 | |||
75.56 | odd | 10 | 900.2.w.c.289.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.1 | ✓ | 24 | 25.4 | even | 10 | ||
300.2.o.a.289.1 | yes | 24 | 25.6 | even | 5 | ||
900.2.w.c.109.6 | 24 | 75.29 | odd | 10 | |||
900.2.w.c.289.6 | 24 | 75.56 | odd | 10 | |||
1500.2.m.c.301.3 | 24 | 25.8 | odd | 20 | |||
1500.2.m.c.1201.3 | 24 | 25.3 | odd | 20 | |||
1500.2.m.d.301.4 | 24 | 25.17 | odd | 20 | |||
1500.2.m.d.1201.4 | 24 | 25.22 | odd | 20 | |||
1500.2.o.c.49.5 | 24 | 25.21 | even | 5 | |||
1500.2.o.c.949.5 | 24 | 25.19 | even | 10 | |||
7500.2.a.m.1.7 | 12 | 5.2 | odd | 4 | |||
7500.2.a.n.1.6 | 12 | 5.3 | odd | 4 | |||
7500.2.d.g.1249.6 | 24 | 1.1 | even | 1 | trivial | ||
7500.2.d.g.1249.19 | 24 | 5.4 | even | 2 | inner |