Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, 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("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.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: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 18x^{8} + 117x^{6} + 333x^{4} + 396x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.9 | ||
Root | \(2.29544i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.w.4049.2 |
$q$-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 \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.29544i | 1.32527i | 0.748941 | + | 0.662637i | \(0.230563\pi\) | ||||
−0.748941 | + | 0.662637i | \(0.769437\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.61758i | − 0.611388i | −0.952130 | − | 0.305694i | \(-0.901111\pi\) | ||||
0.952130 | − | 0.305694i | \(-0.0988885\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.26905 | −0.756349 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.79255 | −0.841985 | −0.420993 | − | 0.907064i | \(-0.638318\pi\) | ||||
−0.420993 | + | 0.907064i | \(0.638318\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.88663i | − 1.35531i | −0.735381 | − | 0.677653i | \(-0.762997\pi\) | ||||
0.735381 | − | 0.677653i | \(-0.237003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.54388i | 0.859516i | 0.902944 | + | 0.429758i | \(0.141401\pi\) | ||||
−0.902944 | + | 0.429758i | \(0.858599\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.79255 | 0.640655 | 0.320327 | − | 0.947307i | \(-0.396207\pi\) | ||||
0.320327 | + | 0.947307i | \(0.396207\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.71306 | 0.810257 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.67786i | 0.322904i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.36282 | 0.624460 | 0.312230 | − | 0.950007i | \(-0.398924\pi\) | ||||
0.312230 | + | 0.950007i | \(0.398924\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.84564 | −0.870303 | −0.435152 | − | 0.900357i | \(-0.643305\pi\) | ||||
−0.435152 | + | 0.900357i | \(0.643305\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 6.41013i | − 1.11586i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.87204i | 0.636559i | 0.947997 | + | 0.318279i | \(0.103105\pi\) | ||||
−0.947997 | + | 0.318279i | \(0.896895\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.2170 | 1.79615 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.327923 | −0.0512130 | −0.0256065 | − | 0.999672i | \(-0.508152\pi\) | ||||
−0.0256065 | + | 0.999672i | \(0.508152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.38343i | 0.820965i | 0.911868 | + | 0.410483i | \(0.134640\pi\) | ||||
−0.911868 | + | 0.410483i | \(0.865360\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0121087i | 0.00176623i | 1.00000 | 0.000883117i | \(0.000281105\pi\) | |||||
−1.00000 | 0.000883117i | \(0.999719\pi\) | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.38343 | 0.626204 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.13476 | −1.13909 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.866254i | 0.118989i | 0.998229 | + | 0.0594946i | \(0.0189489\pi\) | ||||
−0.998229 | + | 0.0594946i | \(0.981051\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.41013i | 0.849043i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.96752 | −0.386338 | −0.193169 | − | 0.981166i | \(-0.561877\pi\) | ||||
−0.193169 | + | 0.981166i | \(0.561877\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.29816 | −0.934434 | −0.467217 | − | 0.884143i | \(-0.654743\pi\) | ||||
−0.467217 | + | 0.884143i | \(0.654743\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.67037i | 0.462423i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.94082i | 0.847956i | 0.905673 | + | 0.423978i | \(0.139367\pi\) | ||||
−0.905673 | + | 0.423978i | \(0.860633\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.29544 | −0.276339 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.16864 | −0.257370 | −0.128685 | − | 0.991685i | \(-0.541076\pi\) | ||||
−0.128685 | + | 0.991685i | \(0.541076\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.02888i | 0.705627i | 0.935694 | + | 0.352813i | \(0.114775\pi\) | ||||
−0.935694 | + | 0.352813i | \(0.885225\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.51718i | 0.514780i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.50561 | −0.731938 | −0.365969 | − | 0.930627i | \(-0.619262\pi\) | ||||
−0.365969 | + | 0.930627i | \(0.619262\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6586 | −1.18429 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.88030i | 0.864976i | 0.901640 | + | 0.432488i | \(0.142364\pi\) | ||||
−0.901640 | + | 0.432488i | \(0.857636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.71915i | 0.827580i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.71986 | 1.03030 | 0.515151 | − | 0.857099i | \(-0.327736\pi\) | ||||
0.515151 | + | 0.857099i | \(0.327736\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.90452 | −0.828619 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 11.1229i | − 1.15339i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.9952i | 1.21793i | 0.793197 | + | 0.608966i | \(0.208415\pi\) | ||||
−0.793197 | + | 0.608966i | \(0.791585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.33643 | 0.636835 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.4712 | 1.14143 | 0.570713 | − | 0.821150i | \(-0.306667\pi\) | ||||
0.570713 | + | 0.821150i | \(0.306667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.02030i | 0.396132i | 0.980189 | + | 0.198066i | \(0.0634661\pi\) | ||||
−0.980189 | + | 0.198066i | \(0.936534\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.8318i | 1.43385i | 0.697152 | + | 0.716923i | \(0.254450\pi\) | ||||
−0.697152 | + | 0.716923i | \(0.745550\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.3573 | −1.18362 | −0.591809 | − | 0.806078i | \(-0.701586\pi\) | ||||
−0.591809 | + | 0.806078i | \(0.701586\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.88803 | −0.843614 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.48632i | 0.516109i | 0.966130 | + | 0.258055i | \(0.0830815\pi\) | ||||
−0.966130 | + | 0.258055i | \(0.916919\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.0880i | 1.02509i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.73251 | 0.525498 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.20167 | −0.291061 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 0.752728i | − 0.0678712i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.14959i | − 0.279481i | −0.990188 | − | 0.139740i | \(-0.955373\pi\) | ||||
0.990188 | − | 0.139740i | \(-0.0446268\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.3573 | −1.08800 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.93231 | −0.256197 | −0.128099 | − | 0.991761i | \(-0.540887\pi\) | ||||
−0.128099 | + | 0.991761i | \(0.540887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.51718i | − 0.391689i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.4054i | 1.23073i | 0.788241 | + | 0.615366i | \(0.210992\pi\) | ||||
−0.788241 | + | 0.615366i | \(0.789008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.2241 | −1.54575 | −0.772873 | − | 0.634561i | \(-0.781181\pi\) | ||||
−0.772873 | + | 0.634561i | \(0.781181\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0277948 | −0.00234074 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.6462i | 1.14115i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.0619i | 0.829892i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.71986 | 0.468589 | 0.234294 | − | 0.972166i | \(-0.424722\pi\) | ||||
0.234294 | + | 0.972166i | \(0.424722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.43082 | −0.441954 | −0.220977 | − | 0.975279i | \(-0.570925\pi\) | ||||
−0.220977 | + | 0.975279i | \(0.570925\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 8.04122i | − 0.650094i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 24.2004i | − 1.93140i | −0.259657 | − | 0.965701i | \(-0.583610\pi\) | ||||
0.259657 | − | 0.965701i | \(-0.416390\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.98844 | −0.157693 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.61758 | 0.127483 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2970i | 0.884849i | 0.896806 | + | 0.442425i | \(0.145882\pi\) | ||||
−0.896806 | + | 0.442425i | \(0.854118\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.6478i | 1.67516i | 0.546318 | + | 0.837578i | \(0.316029\pi\) | ||||
−0.546318 | + | 0.837578i | \(0.683971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8791 | −0.836857 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.33643 | −0.484559 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.39593i | − 0.106130i | −0.998591 | − | 0.0530652i | \(-0.983101\pi\) | ||||
0.998591 | − | 0.0530652i | \(-0.0168991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 6.81176i | − 0.512003i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.5665 | −1.76144 | −0.880722 | − | 0.473634i | \(-0.842942\pi\) | ||||
−0.880722 | + | 0.473634i | \(0.842942\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.33495 | 0.619532 | 0.309766 | − | 0.950813i | \(-0.399749\pi\) | ||||
0.309766 | + | 0.950813i | \(0.399749\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 16.7525i | − 1.23838i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 9.89645i | − 0.723700i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.71407 | 0.197420 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.3074 | 1.32468 | 0.662340 | − | 0.749204i | \(-0.269564\pi\) | ||||
0.662340 | + | 0.749204i | \(0.269564\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 15.4434i | − 1.11164i | −0.831303 | − | 0.555820i | \(-0.812404\pi\) | ||||
0.831303 | − | 0.555820i | \(-0.187596\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 0.876228i | − 0.0624287i | −0.999513 | − | 0.0312143i | \(-0.990063\pi\) | ||||
0.999513 | − | 0.0312143i | \(-0.00993745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.5818 | 0.962788 | 0.481394 | − | 0.876504i | \(-0.340131\pi\) | ||||
0.481394 | + | 0.876504i | \(0.340131\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.9322 | −1.12377 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 5.43963i | − 0.381787i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 2.26905i | − 0.157710i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.79833 | −0.539422 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9100 | 0.888758 | 0.444379 | − | 0.895839i | \(-0.353424\pi\) | ||||
0.444379 | + | 0.895839i | \(0.353424\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 4.97799i | − 0.341086i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.83822i | 0.532093i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.8389 | −0.935148 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.3176 | 1.16491 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.05527i | 0.539421i | 0.962941 | + | 0.269710i | \(0.0869280\pi\) | ||||
−0.962941 | + | 0.269710i | \(0.913072\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.41490i | 0.293027i | 0.989209 | + | 0.146514i | \(0.0468052\pi\) | ||||
−0.989209 | + | 0.146514i | \(0.953195\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.5197 | −1.15773 | −0.578866 | − | 0.815423i | \(-0.696505\pi\) | ||||
−0.578866 | + | 0.815423i | \(0.696505\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.3689 | −0.682224 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 15.8080i | − 1.03562i | −0.855497 | − | 0.517808i | \(-0.826748\pi\) | ||||
0.855497 | − | 0.517808i | \(-0.173252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 14.9332i | − 0.970018i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.93972 | 0.578263 | 0.289131 | − | 0.957289i | \(-0.406634\pi\) | ||||
0.289131 | + | 0.957289i | \(0.406634\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50992 | 0.226094 | 0.113047 | − | 0.993590i | \(-0.463939\pi\) | ||||
0.113047 | + | 0.993590i | \(0.463939\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 19.4325i | − 1.24660i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 13.6462i | − 0.868284i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.0888 | −1.14633 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.33837 | 0.273836 | 0.136918 | − | 0.990582i | \(-0.456280\pi\) | ||||
0.136918 | + | 0.990582i | \(0.456280\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.79255i | − 0.175566i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 16.6252i | − 1.03705i | −0.855063 | − | 0.518524i | \(-0.826482\pi\) | ||||
0.855063 | − | 0.518524i | \(-0.173518\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.26333 | 0.389185 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.63039 | −0.472310 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 13.0084i | − 0.802134i | −0.916049 | − | 0.401067i | \(-0.868640\pi\) | ||||
0.916049 | − | 0.401067i | \(-0.131360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.3114i | 1.36543i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.30995 | 0.506667 | 0.253333 | − | 0.967379i | \(-0.418473\pi\) | ||||
0.253333 | + | 0.967379i | \(0.418473\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.35009 | −0.507232 | −0.253616 | − | 0.967305i | \(-0.581620\pi\) | ||||
−0.253616 | + | 0.967305i | \(0.581620\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 18.1444i | − 1.09815i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.23195i | 0.374441i | 0.982318 | + | 0.187221i | \(0.0599479\pi\) | ||||
−0.982318 | + | 0.187221i | \(0.940052\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.9950 | 0.658253 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.01836 | 0.478335 | 0.239168 | − | 0.970978i | \(-0.423125\pi\) | ||||
0.239168 | + | 0.970978i | \(0.423125\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.11741i | 0.541974i | 0.962583 | + | 0.270987i | \(0.0873500\pi\) | ||||
−0.962583 | + | 0.270987i | \(0.912650\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.530443i | 0.0313110i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.44094 | 0.261232 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.5343 | −1.61409 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 17.5323i | − 1.02425i | −0.858911 | − | 0.512124i | \(-0.828859\pi\) | ||||
0.858911 | − | 0.512124i | \(-0.171141\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 4.68550i | − 0.271881i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.88663 | 0.282601 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.70814 | 0.501929 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 26.3314i | 1.51270i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.3404i | 1.73162i | 0.500375 | + | 0.865809i | \(0.333196\pi\) | ||||
−0.500375 | + | 0.865809i | \(0.666804\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.22837 | −0.524984 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.7703 | −0.780840 | −0.390420 | − | 0.920637i | \(-0.627670\pi\) | ||||
−0.390420 | + | 0.920637i | \(0.627670\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 14.3715i | − 0.812328i | −0.913800 | − | 0.406164i | \(-0.866866\pi\) | ||||
0.913800 | − | 0.406164i | \(-0.133134\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.5726i | 1.49247i | 0.665685 | + | 0.746233i | \(0.268140\pi\) | ||||
−0.665685 | + | 0.746233i | \(0.731860\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.39084 | −0.525786 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −34.0456 | −1.90024 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.89645i | 0.550653i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 28.3655i | − 1.56862i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.0195868 | 0.00107986 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.2379 | −0.672655 | −0.336327 | − | 0.941745i | \(-0.609185\pi\) | ||||
−0.336327 | + | 0.941745i | \(0.609185\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 8.78583i | − 0.481461i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.7474i | 0.912290i | 0.889906 | + | 0.456145i | \(0.150770\pi\) | ||||
−0.889906 | + | 0.456145i | \(0.849230\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.5935 | −0.683986 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.5317 | 0.732783 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.4136i | − 0.994242i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.6122i | 1.10652i | 0.833008 | + | 0.553260i | \(0.186617\pi\) | ||||
−0.833008 | + | 0.553260i | \(0.813383\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.5885 | −1.90501 | −0.952505 | − | 0.304523i | \(-0.901503\pi\) | ||||
−0.952505 | + | 0.304523i | \(0.901503\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.19907 | 0.437634 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.574309i | 0.0305674i | 0.999883 | + | 0.0152837i | \(0.00486514\pi\) | ||||
−0.999883 | + | 0.0152837i | \(0.995135\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.1586i | 0.696429i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.12882 | −0.217911 | −0.108955 | − | 0.994047i | \(-0.534751\pi\) | ||||
−0.108955 | + | 0.994047i | \(0.534751\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.2017 | −0.589561 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 7.34924i | − 0.385735i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.16724i | 0.217528i | 0.994068 | + | 0.108764i | \(0.0346893\pi\) | ||||
−0.994068 | + | 0.108764i | \(0.965311\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.744073 | 0.0387349 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.40124 | 0.0727486 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.3579i | 1.31298i | 0.754334 | + | 0.656491i | \(0.227960\pi\) | ||||
−0.754334 | + | 0.656491i | \(0.772040\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 16.4328i | − 0.846335i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.2580 | −0.732382 | −0.366191 | − | 0.930540i | \(-0.619338\pi\) | ||||
−0.366191 | + | 0.930540i | \(0.619338\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.22969 | 0.370388 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 16.6805i | − 0.852334i | −0.904645 | − | 0.426167i | \(-0.859864\pi\) | ||||
0.904645 | − | 0.426167i | \(-0.140136\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 12.2153i | − 0.620936i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.3853 | −1.33779 | −0.668894 | − | 0.743358i | \(-0.733232\pi\) | ||||
−0.668894 | + | 0.743358i | \(0.733232\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.54388 | −0.179222 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 6.73095i | − 0.339532i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 6.44231i | − 0.323330i | −0.986846 | − | 0.161665i | \(-0.948314\pi\) | ||||
0.986846 | − | 0.161665i | \(-0.0516864\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.3689 | 0.519095 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.6326 | 1.08028 | 0.540141 | − | 0.841574i | \(-0.318371\pi\) | ||||
0.540141 | + | 0.841574i | \(0.318371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.6789i | 1.17953i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 10.8129i | − 0.535973i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.07200 | −0.399135 | −0.199567 | − | 0.979884i | \(-0.563954\pi\) | ||||
−0.199567 | + | 0.979884i | \(0.563954\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −33.0666 | −1.63106 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.80020i | 0.236202i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 41.8323i | − 2.04853i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.4538 | 1.24350 | 0.621751 | − | 0.783215i | \(-0.286422\pi\) | ||||
0.621751 | + | 0.783215i | \(0.286422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.4111 | 1.53089 | 0.765443 | − | 0.643504i | \(-0.222520\pi\) | ||||
0.765443 | + | 0.643504i | \(0.222520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 0.0274752i | − 0.00133589i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.8054i | 0.571302i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −31.3239 | −1.51233 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.35572 | 0.161639 | 0.0808196 | − | 0.996729i | \(-0.474246\pi\) | ||||
0.0808196 | + | 0.996729i | \(0.474246\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 18.0365i | − 0.866777i | −0.901207 | − | 0.433388i | \(-0.857318\pi\) | ||||
0.901207 | − | 0.433388i | \(-0.142682\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.79255i | 0.133586i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.8080 | −0.945384 | −0.472692 | − | 0.881228i | \(-0.656718\pi\) | ||||
−0.472692 | + | 0.881228i | \(0.656718\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.94621 | −0.473629 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 11.5628i | − 0.549364i | −0.961535 | − | 0.274682i | \(-0.911427\pi\) | ||||
0.961535 | − | 0.274682i | \(-0.0885726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.1296i | 0.621008i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.6506 | 0.927368 | 0.463684 | − | 0.886001i | \(-0.346527\pi\) | ||||
0.463684 | + | 0.886001i | \(0.346527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.915742 | 0.0431206 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 12.4661i | − 0.585710i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 23.0682i | − 1.07908i | −0.841959 | − | 0.539542i | \(-0.818598\pi\) | ||||
0.841959 | − | 0.539542i | \(-0.181402\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.94613 | −0.277541 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.86556 | 0.0868876 | 0.0434438 | − | 0.999056i | \(-0.486167\pi\) | ||||
0.0434438 | + | 0.999056i | \(0.486167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9981i | 0.604071i | 0.953297 | + | 0.302035i | \(0.0976661\pi\) | ||||
−0.953297 | + | 0.302035i | \(0.902334\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.7712i | 1.28510i | 0.766245 | + | 0.642548i | \(0.222123\pi\) | ||||
−0.766245 | + | 0.642548i | \(0.777877\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2273 | 0.518430 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 55.5506 | 2.55963 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 15.0335i | − 0.691241i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1.96557i | − 0.0899974i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.25003 | 0.239880 | 0.119940 | − | 0.992781i | \(-0.461730\pi\) | ||||
0.119940 | + | 0.992781i | \(0.461730\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.9212 | 0.862733 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.71306i | 0.168950i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 9.90856i | − 0.449000i | −0.974474 | − | 0.224500i | \(-0.927925\pi\) | ||||
0.974474 | − | 0.224500i | \(-0.0720748\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.9316 | −1.17267 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.2168 | −1.09289 | −0.546444 | − | 0.837495i | \(-0.684019\pi\) | ||||
−0.546444 | + | 0.837495i | \(0.684019\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.9174i | 0.536733i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.50795i | 0.157353i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.6722 | 1.19401 | 0.597007 | − | 0.802236i | \(-0.296357\pi\) | ||||
0.597007 | + | 0.802236i | \(0.296357\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −49.6912 | −2.22004 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 2.38303i | − 0.106254i | −0.998588 | − | 0.0531271i | \(-0.983081\pi\) | ||||
0.998588 | − | 0.0531271i | \(-0.0169188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 24.9724i | − 1.10906i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.2807 | −1.60811 | −0.804056 | − | 0.594554i | \(-0.797329\pi\) | ||||
−0.804056 | + | 0.594554i | \(0.797329\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.75220 | 0.431412 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.68550i | 0.206870i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 0.0338141i | − 0.00148714i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.20427 | 0.140652 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.8498 | −0.606773 | −0.303386 | − | 0.952868i | \(-0.598117\pi\) | ||||
−0.303386 | + | 0.952868i | \(0.598117\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.3982i | 0.498411i | 0.968451 | + | 0.249205i | \(0.0801694\pi\) | ||||
−0.968451 | + | 0.249205i | \(0.919831\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 17.1724i | − 0.748040i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.73344 | 0.292206 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.60244i | 0.0694094i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 54.0955i | − 2.33439i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.2409 | −0.527255 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.6397 | −0.672402 | −0.336201 | − | 0.941790i | \(-0.609142\pi\) | ||||
−0.336201 | + | 0.941790i | \(0.609142\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.1324i | 0.821050i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 45.7911i | 1.95789i | 0.204131 | + | 0.978944i | \(0.434563\pi\) | ||||
−0.204131 | + | 0.978944i | \(0.565437\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.5599 | 0.706758 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.39084 | 0.400063 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.5234i | 0.447499i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 30.8143i | − 1.30564i | −0.757512 | − | 0.652821i | \(-0.773585\pi\) | ||||
0.757512 | − | 0.652821i | \(-0.226415\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.3068 | 1.11266 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.7167 | 0.959100 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 27.8036i | − 1.17178i | −0.810390 | − | 0.585891i | \(-0.800745\pi\) | ||||
0.810390 | − | 0.585891i | \(-0.199255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.2411i | 0.724058i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.89706 | −0.331062 | −0.165531 | − | 0.986205i | \(-0.552934\pi\) | ||||
−0.165531 | + | 0.986205i | \(0.552934\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.12319 | 0.256248 | 0.128124 | − | 0.991758i | \(-0.459105\pi\) | ||||
0.128124 | + | 0.991758i | \(0.459105\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 42.0236i | 1.75556i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.2174i | 1.13307i | 0.824036 | + | 0.566537i | \(0.191717\pi\) | ||||
−0.824036 | + | 0.566537i | \(0.808283\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35.4494 | 1.47323 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.7470 | 0.528836 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.41906i | − 0.100187i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.7305i | 1.10329i | 0.834080 | + | 0.551644i | \(0.185999\pi\) | ||||
−0.834080 | + | 0.551644i | \(0.814001\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.5317 | −0.557564 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.01133 | 0.0827350 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.0562817i | 0.00231121i | 0.999999 | + | 0.00115561i | \(0.000367841\pi\) | ||||
−0.999999 | + | 0.00115561i | \(0.999632\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.1762i | 1.27596i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.4760 | 1.61295 | 0.806473 | − | 0.591271i | \(-0.201374\pi\) | ||||
0.806473 | + | 0.591271i | \(0.201374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.2118 | 0.946829 | 0.473415 | − | 0.880840i | \(-0.343021\pi\) | ||||
0.473415 | + | 0.880840i | \(0.343021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 15.7490i | − 0.641350i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 19.7212i | − 0.800459i | −0.916415 | − | 0.400230i | \(-0.868930\pi\) | ||||
0.916415 | − | 0.400230i | \(-0.131070\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.4864 | 0.505973 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0591707 | 0.00239379 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.4609i | 0.422512i | 0.977431 | + | 0.211256i | \(0.0677553\pi\) | ||||
−0.977431 | + | 0.211256i | \(0.932245\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 14.4969i | − 0.583622i | −0.956476 | − | 0.291811i | \(-0.905742\pi\) | ||||
0.956476 | − | 0.291811i | \(-0.0942578\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.30293 | 0.0523692 | 0.0261846 | − | 0.999657i | \(-0.491664\pi\) | ||||
0.0261846 | + | 0.999657i | \(0.491664\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.67786 | −0.0673302 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 15.7227i | − 0.629915i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 17.9006i | − 0.714881i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.7220 | −0.547133 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.653161 | −0.0260019 | −0.0130010 | − | 0.999915i | \(-0.504138\pi\) | ||||
−0.0130010 | + | 0.999915i | \(0.504138\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.6340i | 1.17785i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 21.4202i | − 0.848699i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.92075 | 0.194662 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2594 | −0.523714 | −0.261857 | − | 0.965107i | \(-0.584335\pi\) | ||||
−0.261857 | + | 0.965107i | \(0.584335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 45.9135i | − 1.81065i | −0.424716 | − | 0.905326i | \(-0.639626\pi\) | ||||
0.424716 | − | 0.905326i | \(-0.360374\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.36368i | 0.132240i | 0.997812 | + | 0.0661199i | \(0.0210620\pi\) | ||||
−0.997812 | + | 0.0661199i | \(0.978938\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.28694 | 0.325291 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.9922 | −0.705169 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.4704i | 0.996734i | 0.866966 | + | 0.498367i | \(0.166067\pi\) | ||||
−0.866966 | + | 0.498367i | \(0.833933\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 13.6798i | − 0.533700i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.03335 | −0.351890 | −0.175945 | − | 0.984400i | \(-0.556298\pi\) | ||||
−0.175945 | + | 0.984400i | \(0.556298\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.20679 | −0.124730 | −0.0623648 | − | 0.998053i | \(-0.519864\pi\) | ||||
−0.0623648 | + | 0.998053i | \(0.519864\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 39.7515i | 1.54382i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.36282i | 0.130209i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.4904 | −0.714880 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.3805 | 0.786779 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.4923i | 0.635733i | 0.948135 | + | 0.317866i | \(0.102966\pi\) | ||||
−0.948135 | + | 0.317866i | \(0.897034\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.9260i | 1.34232i | 0.741314 | + | 0.671158i | \(0.234203\pi\) | ||||
−0.741314 | + | 0.671158i | \(0.765797\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.4033 | 0.744629 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.1341 | −0.388341 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 23.1448i | − 0.885612i | −0.896618 | − | 0.442806i | \(-0.853983\pi\) | ||||
0.896618 | − | 0.442806i | \(-0.146017\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 40.2153i | − 1.53431i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.23306 | 0.161267 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.24273 | 0.123359 | 0.0616795 | − | 0.998096i | \(-0.480354\pi\) | ||||
0.0616795 | + | 0.998096i | \(0.480354\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 10.2497i | − 0.389353i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.16212i | − 0.0440184i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.2863 | 1.37247 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.9466 | 0.753373 | 0.376686 | − | 0.926341i | \(-0.377063\pi\) | ||||
0.376686 | + | 0.926341i | \(0.377063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.8129i | 0.407814i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 18.5556i | − 0.697854i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.3774 | −0.539955 | −0.269977 | − | 0.962867i | \(-0.587016\pi\) | ||||
−0.269977 | + | 0.962867i | \(0.587016\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.7615 | 0.553601 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4.84564i | − 0.181471i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.5206i | 0.766356i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.4356 | 1.91822 | 0.959111 | − | 0.283029i | \(-0.0913394\pi\) | ||||
0.959111 | + | 0.283029i | \(0.0913394\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.50317 | 0.242191 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.05682i | 0.299636i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.4611i | 0.647597i | 0.946126 | + | 0.323799i | \(0.104960\pi\) | ||||
−0.946126 | + | 0.323799i | \(0.895040\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.6305 | 0.467797 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.0782 | −0.705633 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.6443i | 1.46429i | 0.681147 | + | 0.732147i | \(0.261482\pi\) | ||||
−0.681147 | + | 0.732147i | \(0.738518\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 19.3826i | − 0.713966i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.1149 | 1.58601 | 0.793003 | − | 0.609218i | \(-0.208517\pi\) | ||||
0.793003 | + | 0.609218i | \(0.208517\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.3239 | 1.15071 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.8929i | 0.693112i | 0.938029 | + | 0.346556i | \(0.112649\pi\) | ||||
−0.938029 | + | 0.346556i | \(0.887351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 17.8808i | − 0.654223i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.9917 | 0.876637 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.5146 | 1.00402 | 0.502012 | − | 0.864861i | \(-0.332593\pi\) | ||||
0.502012 | + | 0.864861i | \(0.332593\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.95847i | 0.362907i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.6895i | 0.533899i | 0.963711 | + | 0.266949i | \(0.0860157\pi\) | ||||
−0.963711 | + | 0.266949i | \(0.913984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.41013 | 0.232673 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.5884 | −1.36258 | −0.681289 | − | 0.732015i | \(-0.738580\pi\) | ||||
−0.681289 | + | 0.732015i | \(0.738580\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.9890i | 0.723651i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.5012i | 0.523606i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.6879 | 1.57543 | 0.787713 | − | 0.616042i | \(-0.211265\pi\) | ||||
0.787713 | + | 0.616042i | \(0.211265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.1620 | 1.37437 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 7.01583i | − 0.252342i | −0.992009 | − | 0.126171i | \(-0.959731\pi\) | ||||
0.992009 | − | 0.126171i | \(-0.0402688\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.3771i | 0.515776i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.915742 | −0.0328099 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.05604 | 0.216702 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.64234i | 0.201641i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 23.6386i | − 0.842624i | −0.906916 | − | 0.421312i | \(-0.861570\pi\) | ||||
0.906916 | − | 0.421312i | \(-0.138430\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.8601 | 1.06305 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.87457 | 0.315543 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.6634i | 1.26644i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.9000i | 1.12996i | 0.825106 | + | 0.564978i | \(0.191115\pi\) | ||||
−0.825106 | + | 0.564978i | \(0.808885\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0429117 | −0.00151811 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.0548 | −0.779268 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 16.8359i | − 0.594127i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.0750i | 0.671472i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.68831 | 0.199990 | 0.0999951 | − | 0.994988i | \(-0.468117\pi\) | ||||
0.0999951 | + | 0.994988i | \(0.468117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.1989 | −0.568821 | −0.284410 | − | 0.958703i | \(-0.591798\pi\) | ||||
−0.284410 | + | 0.958703i | \(0.591798\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 19.1671i | − 0.672221i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.0335i | 0.525955i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.9357 | 0.626725 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.9329 | −0.939965 | −0.469982 | − | 0.882676i | \(-0.655740\pi\) | ||||
−0.469982 | + | 0.882676i | \(0.655740\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 42.0280i | − 1.46500i | −0.680765 | − | 0.732502i | \(-0.738352\pi\) | ||||
0.680765 | − | 0.732502i | \(-0.261648\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 11.1311i | − 0.387065i | −0.981094 | − | 0.193532i | \(-0.938006\pi\) | ||||
0.981094 | − | 0.193532i | \(-0.0619945\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.1506 | 0.699859 | 0.349929 | − | 0.936776i | \(-0.386206\pi\) | ||||
0.349929 | + | 0.936776i | \(0.386206\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.3051 | −0.496237 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.5343i | 0.538233i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 8.13031i | − 0.281024i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.5573 | 0.433526 | 0.216763 | − | 0.976224i | \(-0.430450\pi\) | ||||
0.216763 | + | 0.976224i | \(0.430450\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.6914 | −0.610050 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.4057i | 0.633925i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.17896i | 0.177951i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.9285 | −0.718263 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.87204 | −0.132732 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.2016i | 1.71887i | 0.511246 | + | 0.859434i | \(0.329184\pi\) | ||||
−0.511246 | + | 0.859434i | \(0.670816\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 36.9126i | − 1.26091i | −0.776225 | − | 0.630456i | \(-0.782868\pi\) | ||||
0.776225 | − | 0.630456i | \(-0.217132\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.29638 | −0.248949 | −0.124475 | − | 0.992223i | \(-0.539725\pi\) | ||||
−0.124475 | + | 0.992223i | \(0.539725\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.21760 | −0.0414957 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.3903i | 1.78339i | 0.452640 | + | 0.891694i | \(0.350482\pi\) | ||||
−0.452640 | + | 0.891694i | \(0.649518\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.1939i | 0.346203i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.1672 | 0.616281 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.9172 | 1.14924 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 27.2177i | − 0.921181i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 28.1120i | − 0.949276i | −0.880181 | − | 0.474638i | \(-0.842579\pi\) | ||||
0.880181 | − | 0.474638i | \(-0.157421\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 40.2444 | 1.35741 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.3936 | 1.39459 | 0.697293 | − | 0.716787i | \(-0.254388\pi\) | ||||
0.697293 | + | 0.716787i | \(0.254388\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.7906i | 1.23810i | 0.785350 | + | 0.619052i | \(0.212483\pi\) | ||||
−0.785350 | + | 0.619052i | \(0.787517\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43.7836i | 1.47011i | 0.678007 | + | 0.735055i | \(0.262844\pi\) | ||||
−0.678007 | + | 0.735055i | \(0.737156\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.09471 | −0.170871 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.7646 | 0.997151 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.0338141i | 0.00113155i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.2170i | 0.374524i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.2950 | −0.543469 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.06990 | −0.102273 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.9890i | 0.665193i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 20.8370i | − 0.691882i | −0.938256 | − | 0.345941i | \(-0.887560\pi\) | ||||
0.938256 | − | 0.345941i | \(-0.112440\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.0287 | −0.863316 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.8193 | 1.51806 | 0.759031 | − | 0.651054i | \(-0.225673\pi\) | ||||
0.759031 | + | 0.651054i | \(0.225673\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 22.0061i | − 0.728297i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.74326i | 0.156636i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.3282 | −1.00044 | −0.500218 | − | 0.865900i | \(-0.666747\pi\) | ||||
−0.500218 | + | 0.865900i | \(0.666747\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −69.6446 | −2.29487 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.5973i | 0.348816i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 9.12226i | − 0.299614i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.7602 | 1.17325 | 0.586626 | − | 0.809858i | \(-0.300456\pi\) | ||||
0.586626 | + | 0.809858i | \(0.300456\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.2409 | 0.401181 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 31.6088i | − 1.03483i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 26.6768i | − 0.871494i | −0.900069 | − | 0.435747i | \(-0.856484\pi\) | ||||
0.900069 | − | 0.435747i | \(-0.143516\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.9890 | 1.07656 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.52987 | −0.310665 | −0.155332 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155332 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 0.327923i | − 0.0106787i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.5209i | 1.05679i | 0.849000 | + | 0.528393i | \(0.177205\pi\) | ||||
−0.849000 | + | 0.528393i | \(0.822795\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.4609 | 0.956341 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −60.9958 | −1.97793 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 8.80252i | − 0.285141i | −0.989785 | − | 0.142571i | \(-0.954463\pi\) | ||||
0.989785 | − | 0.142571i | \(-0.0455368\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 21.5561i | − 0.696810i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.3018 | 0.752456 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.51974 | −0.242572 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 33.6541i | − 1.08449i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 47.0307i | − 1.51241i | −0.654337 | − | 0.756203i | \(-0.727052\pi\) | ||||
0.654337 | − | 0.756203i | \(-0.272948\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.7167 | −0.729766 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.3450 | 1.07009 | 0.535046 | − | 0.844823i | \(-0.320294\pi\) | ||||
0.535046 | + | 0.844823i | \(0.320294\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.4789i | 0.945050i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 55.8915i | − 1.78813i | −0.447939 | − | 0.894064i | \(-0.647842\pi\) | ||||
0.447939 | − | 0.894064i | \(-0.352158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.1432 | −0.867500 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.0394 | 0.895229 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 44.2540i | − 1.41148i | −0.708469 | − | 0.705742i | \(-0.750614\pi\) | ||||
0.708469 | − | 0.705742i | \(-0.249386\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.0449603i | 0.00143110i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.38343 | −0.171183 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.2426 | −0.897157 | −0.448579 | − | 0.893743i | \(-0.648070\pi\) | ||||
−0.448579 | + | 0.893743i | \(0.648070\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 28.0913i | − 0.891451i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.7730i | 0.626218i | 0.949717 | + | 0.313109i | \(0.101371\pi\) | ||||
−0.949717 | + | 0.313109i | \(0.898629\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.49673 | −0.205547 |
(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 | 4600.2.e.w.4049.9 | 10 | ||
5.2 | odd | 4 | 4600.2.a.bd.1.5 | ✓ | 5 | ||
5.3 | odd | 4 | 4600.2.a.bf.1.1 | yes | 5 | ||
5.4 | even | 2 | inner | 4600.2.e.w.4049.2 | 10 | ||
20.3 | even | 4 | 9200.2.a.ct.1.5 | 5 | |||
20.7 | even | 4 | 9200.2.a.cv.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bd.1.5 | ✓ | 5 | 5.2 | odd | 4 | ||
4600.2.a.bf.1.1 | yes | 5 | 5.3 | odd | 4 | ||
4600.2.e.w.4049.2 | 10 | 5.4 | even | 2 | inner | ||
4600.2.e.w.4049.9 | 10 | 1.1 | even | 1 | trivial | ||
9200.2.a.ct.1.5 | 5 | 20.3 | even | 4 | |||
9200.2.a.cv.1.1 | 5 | 20.7 | even | 4 |