Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(193,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bs (of order \(12\), degree \(4\), 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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 457.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.457 |
Dual form | 1300.2.bs.a.293.1 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −1.86603 | − | 0.500000i | −1.07735 | − | 0.288675i | −0.323840 | − | 0.946112i | \(-0.604974\pi\) |
−0.753510 | + | 0.657437i | \(0.771641\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.23205 | − | 1.86603i | −1.22160 | − | 0.705291i | −0.256341 | − | 0.966586i | \(-0.582517\pi\) |
−0.965259 | + | 0.261295i | \(0.915850\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.633975 | + | 0.366025i | 0.211325 | + | 0.122008i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.598076 | + | 2.23205i | −0.180327 | + | 0.672989i | 0.815256 | + | 0.579101i | \(0.196596\pi\) |
−0.995583 | + | 0.0938879i | \(0.970070\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 2.00000i | −0.832050 | + | 0.554700i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.13397 | + | 4.23205i | 0.275029 | + | 1.02642i | 0.955822 | + | 0.293947i | \(0.0949689\pi\) |
−0.680793 | + | 0.732476i | \(0.738364\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.866025 | − | 0.232051i | 0.198680 | − | 0.0532361i | −0.158107 | − | 0.987422i | \(-0.550539\pi\) |
0.356787 | + | 0.934186i | \(0.383872\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.09808 | + | 5.09808i | 1.11249 | + | 1.11249i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.86603 | − | 6.96410i | 0.389093 | − | 1.45212i | −0.442519 | − | 0.896759i | \(-0.645915\pi\) |
0.831612 | − | 0.555357i | \(-0.187418\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.09808 | + | 3.09808i | 0.596225 | + | 0.596225i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.96410 | + | 4.59808i | −1.47890 | + | 0.853841i | −0.999715 | − | 0.0238745i | \(-0.992400\pi\) |
−0.479182 | + | 0.877716i | \(0.659066\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.73205 | − | 5.73205i | 1.02951 | − | 1.02951i | 0.0299555 | − | 0.999551i | \(-0.490463\pi\) |
0.999551 | − | 0.0299555i | \(-0.00953655\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.23205 | − | 3.86603i | 0.388550 | − | 0.672989i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.232051 | + | 0.133975i | −0.0381489 | + | 0.0220253i | −0.518953 | − | 0.854803i | \(-0.673678\pi\) |
0.480804 | + | 0.876828i | \(0.340345\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.59808 | − | 2.23205i | 1.05654 | − | 0.357414i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.133975 | − | 0.0358984i | −0.0209233 | − | 0.00560639i | 0.248342 | − | 0.968672i | \(-0.420114\pi\) |
−0.269266 | + | 0.963066i | \(0.586781\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3301 | − | 3.03590i | 1.72783 | − | 0.462970i | 0.748147 | − | 0.663533i | \(-0.230944\pi\) |
0.979681 | + | 0.200563i | \(0.0642770\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.535898i | 0.0781688i | 0.999236 | + | 0.0390844i | \(0.0124441\pi\) | ||||
−0.999236 | + | 0.0390844i | \(0.987556\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.46410 | + | 6.00000i | 0.494872 | + | 0.857143i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 8.46410i | − | 1.18521i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.53590 | − | 1.53590i | 0.210972 | − | 0.210972i | −0.593708 | − | 0.804680i | \(-0.702337\pi\) |
0.804680 | + | 0.593708i | \(0.202337\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.73205 | −0.229416 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.79423 | − | 6.69615i | −0.233589 | − | 0.871765i | −0.978780 | − | 0.204914i | \(-0.934309\pi\) |
0.745191 | − | 0.666851i | \(-0.232358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.36603 | − | 2.36603i | −0.172103 | − | 0.298091i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.76795 | + | 4.79423i | 0.338159 | + | 0.585708i | 0.984086 | − | 0.177690i | \(-0.0568626\pi\) |
−0.645928 | + | 0.763399i | \(0.723529\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.96410 | + | 12.0622i | −0.838379 | + | 1.45212i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.13397 | + | 4.23205i | 0.134578 | + | 0.502252i | 0.999999 | + | 0.00120705i | \(0.000384217\pi\) |
−0.865421 | + | 0.501045i | \(0.832949\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9282 | 1.51313 | 0.756566 | − | 0.653917i | \(-0.226876\pi\) | ||||
0.756566 | + | 0.653917i | \(0.226876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.09808 | − | 6.09808i | 0.694940 | − | 0.694940i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.53590i | 0.510328i | 0.966898 | + | 0.255164i | \(0.0821295\pi\) | ||||
−0.966898 | + | 0.255164i | \(0.917870\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.33013 | − | 9.23205i | −0.592236 | − | 1.02578i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.46410i | 0.380235i | 0.981761 | + | 0.190117i | \(0.0608868\pi\) | ||||
−0.981761 | + | 0.190117i | \(0.939113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.1603 | − | 4.59808i | 1.83977 | − | 0.492966i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.7942 | + | 3.96410i | 1.56819 | + | 0.420194i | 0.935243 | − | 0.354005i | \(-0.115181\pi\) |
0.632942 | + | 0.774199i | \(0.281847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.4282 | − | 0.866025i | 1.40766 | − | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.5622 | + | 7.83013i | −1.40633 | + | 0.811946i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.23205 | − | 3.86603i | 0.226630 | − | 0.392535i | −0.730177 | − | 0.683258i | \(-0.760562\pi\) |
0.956807 | + | 0.290723i | \(0.0938957\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.19615 | + | 1.19615i | −0.120218 | + | 0.120218i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50000 | − | 0.866025i | 0.149256 | − | 0.0861727i | −0.423512 | − | 0.905890i | \(-0.639203\pi\) |
0.572768 | + | 0.819718i | \(0.305870\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.66025 | − | 6.66025i | −0.656254 | − | 0.656254i | 0.298237 | − | 0.954492i | \(-0.403601\pi\) |
−0.954492 | + | 0.298237i | \(0.903601\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.59808 | + | 5.96410i | −0.154492 | + | 0.576571i | 0.844656 | + | 0.535309i | \(0.179805\pi\) |
−0.999148 | + | 0.0412627i | \(0.986862\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.39230 | + | 9.39230i | 0.899620 | + | 0.899620i | 0.995402 | − | 0.0957826i | \(-0.0305354\pi\) |
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.500000 | − | 0.133975i | 0.0474579 | − | 0.0127163i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.52628 | + | 13.1603i | 0.331724 | + | 1.23801i | 0.907377 | + | 0.420318i | \(0.138081\pi\) |
−0.575652 | + | 0.817695i | \(0.695252\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.63397 | + | 0.169873i | −0.243511 | + | 0.0157048i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.23205 | − | 15.7942i | 0.387951 | − | 1.44785i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.90192 | + | 2.83013i | 0.445629 | + | 0.257284i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.232051 | + | 0.133975i | 0.0209233 | + | 0.0120801i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.7942 | − | 4.50000i | −1.49025 | − | 0.399310i | −0.580426 | − | 0.814313i | \(-0.697114\pi\) |
−0.909820 | + | 0.415002i | \(0.863781\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.6603 | −1.99512 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.8564 | 1.21064 | 0.605320 | − | 0.795982i | \(-0.293045\pi\) | ||||
0.605320 | + | 0.795982i | \(0.293045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.23205 | − | 0.866025i | −0.280254 | − | 0.0750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.696152 | + | 0.401924i | 0.0594763 | + | 0.0343387i | 0.529443 | − | 0.848345i | \(-0.322401\pi\) |
−0.469967 | + | 0.882684i | \(0.655734\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.42820 | − | 4.86603i | −0.714871 | − | 0.412731i | 0.0979911 | − | 0.995187i | \(-0.468758\pi\) |
−0.812862 | + | 0.582456i | \(0.802092\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.267949 | − | 1.00000i | 0.0225654 | − | 0.0842152i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.66987 | − | 7.89230i | −0.223266 | − | 0.659988i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.46410 | − | 12.9282i | −0.285714 | − | 1.06630i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.2583 | − | 4.89230i | 1.49578 | − | 0.400793i | 0.584096 | − | 0.811684i | \(-0.301449\pi\) |
0.911684 | + | 0.410891i | \(0.134782\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.803848 | + | 0.803848i | 0.0654162 | + | 0.0654162i | 0.739058 | − | 0.673642i | \(-0.235271\pi\) |
−0.673642 | + | 0.739058i | \(0.735271\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.830127 | + | 3.09808i | −0.0671118 | + | 0.250465i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.39230 | + | 7.39230i | 0.589970 | + | 0.589970i | 0.937623 | − | 0.347653i | \(-0.113021\pi\) |
−0.347653 | + | 0.937623i | \(0.613021\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.63397 | + | 2.09808i | −0.288193 | + | 0.166388i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.0263 | + | 19.0263i | −1.49948 | + | 1.49948i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.767949 | + | 1.33013i | −0.0601504 | + | 0.104184i | −0.894533 | − | 0.447003i | \(-0.852491\pi\) |
0.834382 | + | 0.551186i | \(0.185825\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.76795 | − | 3.33013i | 0.446337 | − | 0.257693i | −0.259945 | − | 0.965623i | \(-0.583704\pi\) |
0.706282 | + | 0.707931i | \(0.250371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | − | 12.0000i | 0.384615 | − | 0.923077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.633975 | + | 0.169873i | 0.0484812 | + | 0.0129905i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.59808 | + | 2.30385i | −0.653700 | + | 0.175158i | −0.570401 | − | 0.821366i | \(-0.693212\pi\) |
−0.0832986 | + | 0.996525i | \(0.526546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.3923i | 1.00663i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.96410 | + | 10.3301i | 0.445778 | + | 0.772110i | 0.998106 | − | 0.0615168i | \(-0.0195938\pi\) |
−0.552328 | + | 0.833627i | \(0.686260\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.9282i | − | 1.10960i | −0.831982 | − | 0.554802i | \(-0.812794\pi\) | ||
0.831982 | − | 0.554802i | \(-0.187206\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.36603 | + | 1.36603i | −0.100980 | + | 0.100980i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.1244 | −0.740366 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.23205 | − | 15.7942i | −0.307836 | − | 1.14886i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.9641 | + | 20.7224i | −0.865692 | + | 1.49942i | 0.000666402 | 1.00000i | \(0.499788\pi\) | |
−0.866358 | + | 0.499423i | \(0.833545\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.1603 | − | 21.0622i | −0.875314 | − | 1.51609i | −0.856428 | − | 0.516267i | \(-0.827321\pi\) |
−0.0188866 | − | 0.999822i | \(-0.506012\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.16025 | + | 12.4019i | 0.510147 | + | 0.883600i | 0.999931 | + | 0.0117566i | \(0.00374234\pi\) |
−0.489784 | + | 0.871844i | \(0.662924\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.96410 | − | 8.59808i | 0.351896 | − | 0.609501i | −0.634686 | − | 0.772770i | \(-0.718870\pi\) |
0.986582 | + | 0.163269i | \(0.0522038\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.76795 | − | 10.3301i | −0.195236 | − | 0.728631i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 34.3205 | 2.40883 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.73205 | − | 3.73205i | 0.259395 | − | 0.259395i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.07180i | 0.143309i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.96410 | + | 3.40192i | 0.135214 | + | 0.234198i | 0.925679 | − | 0.378309i | \(-0.123494\pi\) |
−0.790465 | + | 0.612507i | \(0.790161\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.46410i | − | 0.579951i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.2224 | + | 7.83013i | −1.98375 | + | 0.531544i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.1244 | − | 6.46410i | −1.63017 | − | 0.436804i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.8660 | − | 10.4282i | −0.798195 | − | 0.701477i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.0885 | + | 8.13397i | −0.943433 | + | 0.544691i | −0.891035 | − | 0.453935i | \(-0.850020\pi\) |
−0.0523981 | + | 0.998626i | \(0.516686\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.23205 | − | 5.59808i | 0.214519 | − | 0.371557i | −0.738605 | − | 0.674139i | \(-0.764515\pi\) |
0.953124 | + | 0.302581i | \(0.0978484\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.8564 | + | 16.8564i | −1.11390 | + | 1.11390i | −0.121285 | + | 0.992618i | \(0.538701\pi\) |
−0.992618 | + | 0.121285i | \(0.961299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.4282 | + | 8.33013i | −0.949306 | + | 0.548082i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.0000 | + | 11.0000i | 0.720634 | + | 0.720634i | 0.968734 | − | 0.248100i | \(-0.0798063\pi\) |
−0.248100 | + | 0.968734i | \(0.579806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.26795 | − | 8.46410i | 0.147319 | − | 0.549802i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.19615 | + | 1.19615i | 0.0773727 | + | 0.0773727i | 0.744734 | − | 0.667361i | \(-0.232576\pi\) |
−0.667361 | + | 0.744734i | \(0.732576\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0622 | + | 4.57180i | −1.09907 | + | 0.294495i | −0.762386 | − | 0.647122i | \(-0.775972\pi\) |
−0.336685 | + | 0.941617i | \(0.609306\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.92820 | + | 7.19615i | 0.123694 | + | 0.461633i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.13397 | + | 2.42820i | −0.135782 | + | 0.154503i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.73205 | − | 6.46410i | 0.109764 | − | 0.409646i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.10770 | − | 1.79423i | −0.196156 | − | 0.113251i | 0.398705 | − | 0.917079i | \(-0.369460\pi\) |
−0.594861 | + | 0.803828i | \(0.702793\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.4282 | + | 8.33013i | 0.907093 | + | 0.523711i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.5263 | − | 4.16025i | −0.968503 | − | 0.259510i | −0.260307 | − | 0.965526i | \(-0.583824\pi\) |
−0.708196 | + | 0.706016i | \(0.750490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00000 | 0.0621370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.73205 | −0.416703 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.7942 | − | 2.89230i | −0.665601 | − | 0.178347i | −0.0898284 | − | 0.995957i | \(-0.528632\pi\) |
−0.575772 | + | 0.817610i | \(0.695299\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.6244 | − | 14.7942i | −1.56819 | − | 0.905392i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.57180 | − | 5.52628i | −0.583603 | − | 0.336943i | 0.178961 | − | 0.983856i | \(-0.442726\pi\) |
−0.762564 | + | 0.646913i | \(0.776060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.20577 | + | 15.6962i | −0.255482 | + | 0.953473i | 0.712339 | + | 0.701836i | \(0.247636\pi\) |
−0.967821 | + | 0.251638i | \(0.919031\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.4904 | − | 5.09808i | −1.54275 | − | 0.308550i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.99038 | + | 11.1603i | 0.179675 | + | 0.670555i | 0.995708 | + | 0.0925500i | \(0.0295018\pi\) |
−0.816033 | + | 0.578005i | \(0.803832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.73205 | − | 1.53590i | 0.343169 | − | 0.0919518i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.3923 | + | 13.3923i | 0.798918 | + | 0.798918i | 0.982925 | − | 0.184007i | \(-0.0589069\pi\) |
−0.184007 | + | 0.982925i | \(0.558907\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.52628 | + | 24.3564i | −0.387947 | + | 1.44784i | 0.445522 | + | 0.895271i | \(0.353018\pi\) |
−0.833469 | + | 0.552567i | \(0.813648\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.366025 | + | 0.366025i | 0.0216058 | + | 0.0216058i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.90192 | + | 1.09808i | −0.111878 | + | 0.0645927i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.09808 | + | 6.09808i | −0.357476 | + | 0.357476i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.76795 | + | 13.4545i | −0.453808 | + | 0.786019i | −0.998619 | − | 0.0525400i | \(-0.983268\pi\) |
0.544810 | + | 0.838559i | \(0.316602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.76795 | + | 5.06218i | −0.508768 | + | 0.293737i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.33013 | + | 24.6244i | 0.481744 | + | 1.42406i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.2846 | − | 11.3301i | −2.43724 | − | 0.653058i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.23205 | + | 0.866025i | −0.185676 | + | 0.0497519i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.60770i | 0.548340i | 0.961681 | + | 0.274170i | \(0.0884031\pi\) | ||||
−0.961681 | + | 0.274170i | \(0.911597\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.09808 | + | 15.7583i | 0.517571 | + | 0.896460i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 32.2487i | − | 1.82866i | −0.404974 | − | 0.914328i | \(-0.632719\pi\) | ||
0.404974 | − | 0.914328i | \(-0.367281\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3205 | − | 14.3205i | 0.809443 | − | 0.809443i | −0.175107 | − | 0.984549i | \(-0.556027\pi\) |
0.984549 | + | 0.175107i | \(0.0560270\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.9282 | 0.950783 | 0.475391 | − | 0.879774i | \(-0.342306\pi\) | ||||
0.475391 | + | 0.879774i | \(0.342306\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.50000 | − | 20.5263i | −0.307941 | − | 1.14925i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.96410 | − | 10.3301i | 0.332884 | − | 0.576571i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.96410 | + | 3.40192i | 0.109286 | + | 0.189288i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.8301 | − | 22.2224i | −0.709508 | − | 1.22890i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.00000 | − | 1.73205i | 0.0551318 | − | 0.0954911i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.66987 | + | 6.23205i | 0.0917845 | + | 0.342544i | 0.996512 | − | 0.0834456i | \(-0.0265925\pi\) |
−0.904728 | + | 0.425990i | \(0.859926\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.196152 | −0.0107491 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.9282 | − | 13.9282i | 0.758718 | − | 0.758718i | −0.217371 | − | 0.976089i | \(-0.569748\pi\) |
0.976089 | + | 0.217371i | \(0.0697483\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 26.3205i | − | 1.42953i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.36603 | + | 16.2224i | 0.507199 | + | 0.878494i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.267949i | 0.0144679i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.3301 | − | 4.10770i | 0.822964 | − | 0.220513i | 0.177322 | − | 0.984153i | \(-0.443256\pi\) |
0.645642 | + | 0.763640i | \(0.276590\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.5263 | − | 6.57180i | −1.31286 | − | 0.351780i | −0.466563 | − | 0.884488i | \(-0.654508\pi\) |
−0.846299 | + | 0.532708i | \(0.821174\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.4904 | − | 3.09808i | −0.826815 | − | 0.165363i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.6244 | + | 6.13397i | −0.565477 | + | 0.326479i | −0.755341 | − | 0.655332i | \(-0.772529\pi\) |
0.189864 | + | 0.981810i | \(0.439195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.7942 | + | 27.3564i | −0.835919 | + | 1.44785i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.5885 | − | 23.5885i | 1.24495 | − | 1.24495i | 0.287029 | − | 0.957922i | \(-0.407332\pi\) |
0.957922 | − | 0.287029i | \(-0.0926677\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7583 | + | 9.09808i | −0.829386 | + | 0.478846i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.73205 | − | 7.73205i | −0.405827 | − | 0.405827i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.79423 | − | 17.8923i | 0.250257 | − | 0.933971i | −0.720411 | − | 0.693547i | \(-0.756047\pi\) |
0.970668 | − | 0.240424i | \(-0.0772864\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0717968 | − | 0.0717968i | −0.00373759 | − | 0.00373759i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.83013 | + | 2.09808i | −0.406520 | + | 0.108927i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.00962 | − | 3.76795i | −0.0522761 | − | 0.195097i | 0.934849 | − | 0.355044i | \(-0.115534\pi\) |
−0.987126 | + | 0.159947i | \(0.948868\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.6962 | − | 29.7224i | 0.756890 | − | 1.53078i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.47372 | − | 16.6962i | 0.229800 | − | 0.857624i | −0.750625 | − | 0.660729i | \(-0.770247\pi\) |
0.980425 | − | 0.196895i | \(-0.0630859\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.0885 | + | 16.7942i | 1.49025 | + | 0.860394i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.69615 | + | 5.59808i | 0.495450 | + | 0.286048i | 0.726833 | − | 0.686815i | \(-0.240992\pi\) |
−0.231382 | + | 0.972863i | \(0.574325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.29423 | + | 2.22243i | 0.421619 | + | 0.112973i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.8564 | 1.20957 | 0.604784 | − | 0.796390i | \(-0.293259\pi\) | ||||
0.604784 | + | 0.796390i | \(0.293259\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.5885 | 1.59750 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −25.8564 | − | 6.92820i | −1.30428 | − | 0.349482i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.6244 | + | 18.2583i | 1.58718 | + | 0.916359i | 0.993769 | + | 0.111460i | \(0.0355529\pi\) |
0.593412 | + | 0.804899i | \(0.297780\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.59808 | + | 3.23205i | 0.280254 | + | 0.161805i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.13397 | − | 15.4282i | 0.206441 | − | 0.770448i | −0.782565 | − | 0.622569i | \(-0.786089\pi\) |
0.989006 | − | 0.147878i | \(-0.0472444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.73205 | + | 28.6603i | −0.285534 | + | 1.42767i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.160254 | − | 0.598076i | −0.00794350 | − | 0.0296455i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.06218 | + | 2.42820i | −0.448096 | + | 0.120067i | −0.475808 | − | 0.879549i | \(-0.657844\pi\) |
0.0277124 | + | 0.999616i | \(0.491178\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.09808 | − | 1.09808i | −0.0541641 | − | 0.0541641i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.69615 | + | 24.9904i | −0.329496 | + | 1.22970i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.2942 | + | 13.2942i | 0.651021 | + | 0.651021i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.356406 | + | 0.205771i | −0.0174116 | + | 0.0100526i | −0.508681 | − | 0.860955i | \(-0.669867\pi\) |
0.491269 | + | 0.871008i | \(0.336533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.9282 | − | 27.9282i | 1.36114 | − | 1.36114i | 0.488667 | − | 0.872470i | \(-0.337483\pi\) |
0.872470 | − | 0.488667i | \(-0.162517\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.196152 | + | 0.339746i | −0.00953726 | + | 0.0165190i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.23205 | + | 1.86603i | −0.156410 | + | 0.0903033i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.03590 | + | 16.0622i | 0.0500136 | + | 0.775489i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.5263 | + | 7.37564i | 1.32589 | + | 0.355272i | 0.851183 | − | 0.524869i | \(-0.175886\pi\) |
0.474711 | + | 0.880142i | \(0.342552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.7224 | − | 7.16025i | 1.28420 | − | 0.344100i | 0.448744 | − | 0.893660i | \(-0.351871\pi\) |
0.835454 | + | 0.549560i | \(0.185205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.46410i | − | 0.309220i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.964102 | − | 1.66987i | −0.0460141 | − | 0.0796987i | 0.842101 | − | 0.539320i | \(-0.181319\pi\) |
−0.888115 | + | 0.459621i | \(0.847985\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.07180i | 0.241514i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.0526 | − | 11.0526i | 0.525123 | − | 0.525123i | −0.393991 | − | 0.919114i | \(-0.628906\pi\) |
0.919114 | + | 0.393991i | \(0.128906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36.5167 | −1.72718 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.99038 | + | 7.42820i | 0.0939319 | + | 0.350559i | 0.996855 | − | 0.0792428i | \(-0.0252502\pi\) |
−0.902923 | + | 0.429801i | \(0.858584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.160254 | − | 0.277568i | 0.00754607 | − | 0.0130702i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.09808 | − | 1.90192i | −0.0515921 | − | 0.0893602i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.30385 | − | 7.45448i | −0.201325 | − | 0.348706i | 0.747630 | − | 0.664115i | \(-0.231192\pi\) |
−0.948956 | + | 0.315409i | \(0.897858\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.59808 | + | 16.6244i | −0.448000 | + | 0.775958i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.99038 | + | 7.42820i | 0.0927013 | + | 0.345966i | 0.996661 | − | 0.0816519i | \(-0.0260196\pi\) |
−0.903960 | + | 0.427618i | \(0.859353\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.14359 | 0.0996212 | 0.0498106 | − | 0.998759i | \(-0.484138\pi\) | ||||
0.0498106 | + | 0.998759i | \(0.484138\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.12436 | − | 4.12436i | 0.190852 | − | 0.190852i | −0.605212 | − | 0.796064i | \(-0.706912\pi\) |
0.796064 | + | 0.605212i | \(0.206912\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 20.6603i | − | 0.954002i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0981 | − | 17.4904i | −0.465295 | − | 0.805914i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.1051i | 1.24629i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.53590 | − | 0.411543i | 0.0703240 | − | 0.0188432i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.9904 | + | 7.23205i | 1.23322 | + | 0.330441i | 0.815833 | − | 0.578287i | \(-0.196279\pi\) |
0.417389 | + | 0.908728i | \(0.362945\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.428203 | − | 0.866025i | 0.0195244 | − | 0.0394874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 45.0167 | − | 25.9904i | 2.04833 | − | 1.18260i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.160254 | − | 0.277568i | 0.00726180 | − | 0.0125778i | −0.862372 | − | 0.506276i | \(-0.831022\pi\) |
0.869633 | + | 0.493698i | \(0.164355\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.09808 | − | 2.09808i | 0.0948783 | − | 0.0948783i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.03590 | + | 4.06218i | −0.317526 | + | 0.183324i | −0.650289 | − | 0.759687i | \(-0.725352\pi\) |
0.332763 | + | 0.943010i | \(0.392019\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.4904 | − | 28.4904i | −1.28314 | − | 1.28314i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.23205 | − | 15.7942i | 0.189833 | − | 0.708468i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.19615 | − | 7.19615i | −0.322144 | − | 0.322144i | 0.527445 | − | 0.849589i | \(-0.323150\pi\) |
−0.849589 | + | 0.527445i | \(0.823150\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.4282 | + | 3.33013i | −0.555251 | + | 0.148779i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.93782 | − | 10.9641i | −0.130991 | − | 0.488865i | 0.868991 | − | 0.494828i | \(-0.164769\pi\) |
−0.999982 | + | 0.00596240i | \(0.998102\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.3301 | + | 19.8923i | −0.680835 | + | 0.883448i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.79423 | + | 25.3564i | −0.301149 | + | 1.12390i | 0.635061 | + | 0.772462i | \(0.280975\pi\) |
−0.936210 | + | 0.351441i | \(0.885692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.7846 | − | 24.1244i | −1.84844 | − | 1.06720i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.40192 | + | 1.96410i | 0.150199 | + | 0.0867172i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.19615 | − | 0.320508i | −0.0526067 | − | 0.0140959i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.1962 | 0.754827 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.8564 | −1.04517 | −0.522584 | − | 0.852588i | \(-0.675032\pi\) | ||||
−0.522584 | + | 0.852588i | \(0.675032\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.06218 | + | 0.820508i | 0.133900 | + | 0.0358783i | 0.325146 | − | 0.945664i | \(-0.394586\pi\) |
−0.191247 | + | 0.981542i | \(0.561253\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.7583 | + | 17.7583i | 1.33985 | + | 0.773565i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −25.0981 | − | 14.4904i | −1.09122 | − | 0.630017i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.31347 | − | 4.90192i | 0.0569996 | − | 0.212725i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.473721 | − | 0.160254i | 0.0205191 | − | 0.00694137i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.96410 | − | 22.2583i | −0.257370 | − | 0.960518i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.4641 | + | 4.14359i | −0.666086 | + | 0.178477i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.9282 | + | 27.9282i | 1.20073 | + | 1.20073i | 0.973946 | + | 0.226782i | \(0.0728204\pi\) |
0.226782 | + | 0.973946i | \(0.427180\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.46410 | + | 27.8564i | −0.320315 | + | 1.19543i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.19615 | − | 1.19615i | −0.0511438 | − | 0.0511438i | 0.681072 | − | 0.732216i | \(-0.261514\pi\) |
−0.732216 | + | 0.681072i | \(0.761514\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.633975 | − | 0.366025i | 0.0270574 | − | 0.0156216i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.83013 | + | 5.83013i | −0.248372 | + | 0.248372i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.46410 | − | 14.6603i | 0.359930 | − | 0.623417i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.2321 | − | 12.2583i | 0.899631 | − | 0.519402i | 0.0225505 | − | 0.999746i | \(-0.492821\pi\) |
0.877080 | + | 0.480344i | \(0.159488\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.9186 | + | 31.7679i | −1.18083 | + | 1.34364i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.8923 | + | 5.06218i | 0.797634 | + | 0.213725i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.5263 | + | 2.82051i | −0.443630 | + | 0.118870i | −0.473717 | − | 0.880677i | \(-0.657088\pi\) |
0.0300874 | + | 0.999547i | \(0.490421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 39.7846i | 1.67080i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.4282 | + | 26.7224i | 0.646784 | + | 1.12026i | 0.983886 | + | 0.178795i | \(0.0572198\pi\) |
−0.337102 | + | 0.941468i | \(0.609447\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.1051i | 1.42725i | 0.700525 | + | 0.713627i | \(0.252949\pi\) | ||||
−0.700525 | + | 0.713627i | \(0.747051\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.6865 | − | 32.6865i | 1.36550 | − | 1.36550i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.0718 | 0.627447 | 0.313724 | − | 0.949514i | \(-0.398423\pi\) | ||||
0.313724 | + | 0.949514i | \(0.398423\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.1603 | + | 45.3827i | 0.505363 | + | 1.88604i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.46410 | − | 11.1962i | 0.268176 | − | 0.464495i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.50962 | + | 4.34679i | 0.103938 | + | 0.180026i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.16025 | − | 7.20577i | −0.171712 | − | 0.297414i | 0.767306 | − | 0.641281i | \(-0.221597\pi\) |
−0.939019 | + | 0.343867i | \(0.888263\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.63397 | − | 6.29423i | 0.149735 | − | 0.259349i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.16025 | − | 26.7224i | −0.294533 | − | 1.09921i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.9282 | 0.859418 | 0.429709 | − | 0.902967i | \(-0.358616\pi\) | ||||
0.429709 | + | 0.902967i | \(0.358616\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.5622 | + | 13.5622i | −0.555063 | + | 0.555063i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.3923i | 1.07836i | 0.842190 | + | 0.539180i | \(0.181266\pi\) | ||||
−0.842190 | + | 0.539180i | \(0.818734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.4282 | − | 31.9186i | −0.751702 | − | 1.30199i | −0.946997 | − | 0.321242i | \(-0.895900\pi\) |
0.195295 | − | 0.980745i | \(-0.437434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.05256i | 0.165033i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.0622 | + | 5.64359i | −0.854887 | + | 0.229066i | −0.659542 | − | 0.751668i | \(-0.729250\pi\) |
−0.195346 | + | 0.980734i | \(0.562583\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −64.0429 | − | 17.1603i | −2.59515 | − | 0.695369i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.07180 | − | 1.60770i | −0.0433603 | − | 0.0650404i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.76795 | − | 3.33013i | 0.232965 | − | 0.134503i | −0.378974 | − | 0.925407i | \(-0.623723\pi\) |
0.611939 | + | 0.790905i | \(0.290390\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.0885 | + | 26.1340i | −0.607438 | + | 1.05211i | 0.384223 | + | 0.923240i | \(0.374470\pi\) |
−0.991661 | + | 0.128874i | \(0.958864\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.1244 | − | 30.1244i | 1.21080 | − | 1.21080i | 0.240036 | − | 0.970764i | \(-0.422841\pi\) |
0.970764 | − | 0.240036i | \(-0.0771593\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.3564 | − | 15.7942i | 1.09777 | − | 0.633801i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −40.4186 | − | 40.4186i | −1.61934 | − | 1.61934i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.03590 | − | 3.86603i | 0.0413698 | − | 0.154394i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.830127 | − | 0.830127i | −0.0330993 | − | 0.0330993i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.7942 | − | 5.83975i | 0.867615 | − | 0.232477i | 0.202559 | − | 0.979270i | \(-0.435074\pi\) |
0.665056 | + | 0.746794i | \(0.268408\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.96410 | − | 7.33013i | −0.0780660 | − | 0.291346i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.3923 | − | 11.0718i | −0.887215 | − | 0.438681i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.830127 | + | 3.09808i | −0.0328393 | + | 0.122558i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.28461 | − | 0.741670i | −0.0507390 | − | 0.0292942i | 0.474416 | − | 0.880301i | \(-0.342659\pi\) |
−0.525155 | + | 0.851007i | \(0.675993\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.2321 | − | 22.6506i | −1.54716 | − | 0.893254i | −0.998357 | − | 0.0573029i | \(-0.981750\pi\) |
−0.548804 | − | 0.835951i | \(-0.684917\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.7942 | − | 3.96410i | −0.581621 | − | 0.155845i | −0.0440001 | − | 0.999032i | \(-0.514010\pi\) |
−0.537621 | + | 0.843187i | \(0.680677\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0192 | 0.628810 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 58.4449 | 2.29063 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.1865 | + | 9.69615i | 1.41609 | + | 0.379440i | 0.884094 | − | 0.467308i | \(-0.154776\pi\) |
0.531994 | + | 0.846748i | \(0.321443\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.19615 | + | 4.73205i | 0.319762 | + | 0.184615i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.2128 | + | 15.1340i | 1.02111 | + | 0.589536i | 0.914424 | − | 0.404757i | \(-0.132644\pi\) |
0.106682 | + | 0.994293i | \(0.465977\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.59808 | − | 13.4282i | 0.139949 | − | 0.522297i | −0.859979 | − | 0.510329i | \(-0.829524\pi\) |
0.999928 | − | 0.0119679i | \(-0.00380959\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.9282 | + | 25.3923i | 0.657437 | + | 0.986155i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.1603 | + | 64.0429i | 0.664448 | + | 2.47975i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30.3564 | − | 8.13397i | 1.17365 | − | 0.314478i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.63397 | + | 1.63397i | 0.0630789 | + | 0.0630789i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00962 | + | 3.76795i | −0.0389180 | + | 0.145244i | −0.982651 | − | 0.185465i | \(-0.940621\pi\) |
0.943733 | + | 0.330708i | \(0.107288\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.3205 | − | 24.3205i | −0.934713 | − | 0.934713i | 0.0632826 | − | 0.997996i | \(-0.479843\pi\) |
−0.997996 | + | 0.0632826i | \(0.979843\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.4282 | + | 8.33013i | −0.553704 | + | 0.319681i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.83013 | + | 8.83013i | −0.338371 | + | 0.338371i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.7679 | − | 20.3827i | 0.450288 | − | 0.779922i | −0.548116 | − | 0.836403i | \(-0.684655\pi\) |
0.998404 | + | 0.0564808i | \(0.0179880\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.8827 | − | 23.0263i | 1.52162 | − | 0.878507i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.53590 | + | 7.67949i | −0.0585131 | + | 0.292565i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0622 | + | 3.23205i | 0.458867 | + | 0.122953i | 0.480845 | − | 0.876805i | \(-0.340330\pi\) |
−0.0219785 | + | 0.999758i | \(0.506997\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.09808 | − | 1.63397i | 0.231647 | − | 0.0620696i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.607695i | − | 0.0230181i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.0263 | − | 26.0263i | −0.568346 | − | 0.984404i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.9282i | 1.62138i | 0.585479 | + | 0.810688i | \(0.300907\pi\) | ||||
−0.585479 | + | 0.810688i | \(0.699093\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.169873 | + | 0.169873i | −0.00640688 | + | 0.00640688i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.46410 | −0.243108 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.401924 | − | 1.50000i | −0.0150946 | − | 0.0563337i | 0.957968 | − | 0.286876i | \(-0.0926167\pi\) |
−0.973062 | + | 0.230542i | \(0.925950\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.66025 | + | 2.87564i | −0.0622644 | + | 0.107845i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.2224 | − | 50.6147i | −1.09439 | − | 1.89554i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.63397 | − | 2.83013i | −0.0610219 | − | 0.105693i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.89230 | − | 10.2058i | 0.219746 | − | 0.380611i | −0.734984 | − | 0.678084i | \(-0.762811\pi\) |
0.954730 | + | 0.297473i | \(0.0961438\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.09808 | + | 33.9545i | 0.338830 | + | 1.26453i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.1244 | 1.26910 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.5885 | − | 17.5885i | 0.652320 | − | 0.652320i | −0.301231 | − | 0.953551i | \(-0.597398\pi\) |
0.953551 | + | 0.301231i | \(0.0973976\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.5885i | 0.651424i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.6962 | + | 44.5070i | 0.950407 | + | 1.64615i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.6410i | 1.13175i | 0.824490 | + | 0.565876i | \(0.191462\pi\) | ||||
−0.824490 | + | 0.565876i | \(0.808538\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.3564 | + | 3.31089i | −0.455154 | + | 0.121958i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.2583 | − | 8.91154i | −1.22343 | − | 0.327816i | −0.411410 | − | 0.911450i | \(-0.634964\pi\) |
−0.812017 | + | 0.583634i | \(0.801630\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.19615 | − | 3.46410i | 0.190885 | − | 0.127257i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.4808 | − | 12.4019i | 0.788053 | − | 0.454982i | −0.0512238 | − | 0.998687i | \(-0.516312\pi\) |
0.839277 | + | 0.543705i | \(0.182979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.26795 | + | 2.19615i | −0.0463918 | + | 0.0803530i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.2942 | − | 16.2942i | 0.595378 | − | 0.595378i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.7487 | + | 9.66987i | −0.611169 | + | 0.352859i | −0.773423 | − | 0.633890i | \(-0.781457\pi\) |
0.162254 | + | 0.986749i | \(0.448124\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.90192 | + | 4.90192i | 0.178636 | + | 0.178636i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.93782 | + | 14.6962i | −0.143123 | + | 0.534141i | 0.856709 | + | 0.515800i | \(0.172505\pi\) |
−0.999832 | + | 0.0183410i | \(0.994162\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.7583 | − | 22.7583i | −0.826075 | − | 0.826075i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.3301 | − | 3.03590i | 0.410717 | − | 0.110051i | −0.0475437 | − | 0.998869i | \(-0.515139\pi\) |
0.458261 | + | 0.888818i | \(0.348473\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.8301 | − | 47.8827i | −0.464482 | − | 1.73347i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.7750 | + | 16.5000i | 0.677926 | + | 0.595780i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.33013 | + | 12.4282i | −0.120087 | + | 0.448172i | −0.999617 | − | 0.0276717i | \(-0.991191\pi\) |
0.879530 | + | 0.475844i | \(0.157857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.8923 | + | 15.5263i | 0.968503 | + | 0.559165i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.4808 | + | 8.93782i | 0.556804 | + | 0.321471i | 0.751862 | − | 0.659321i | \(-0.229156\pi\) |
−0.195058 | + | 0.980792i | \(0.562489\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.86603 | − | 0.500000i | −0.0669433 | − | 0.0179374i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.124356 | −0.00445550 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.1244 | −0.362278 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.9186 | − | 10.4282i | −1.39084 | − | 0.372674i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.91154 | + | 3.99038i | 0.246370 | + | 0.142242i | 0.618101 | − | 0.786099i | \(-0.287902\pi\) |
−0.371731 | + | 0.928340i | \(0.621236\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.6962 | + | 10.7942i | 0.665601 | + | 0.384285i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.1603 | − | 49.1147i | 0.467925 | − | 1.74632i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.232051 | + | 3.59808i | 0.00824037 | + | 0.127771i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.72243 | − | 17.6244i | −0.167277 | − | 0.624287i | −0.997739 | − | 0.0672109i | \(-0.978590\pi\) |
0.830462 | − | 0.557076i | \(-0.188077\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.26795 | + | 0.607695i | −0.0802343 | + | 0.0214987i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.92820 | + | 7.92820i | 0.280129 | + | 0.280129i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.73205 | + | 28.8564i | −0.272858 | + | 1.01832i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.0981 | + | 15.0981i | 0.531477 | + | 0.531477i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.10770 | − | 5.25833i | 0.320210 | − | 0.184873i | −0.331276 | − | 0.943534i | \(-0.607479\pi\) |
0.651486 | + | 0.758661i | \(0.274146\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.87564 | − | 7.87564i | 0.276551 | − | 0.276551i | −0.555179 | − | 0.831731i | \(-0.687350\pi\) |
0.831731 | + | 0.555179i | \(0.187350\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.6962 | − | 27.1865i | 0.550488 | − | 0.953473i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.10770 | − | 5.25833i | 0.318638 | − | 0.183966i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.83013 | + | 4.36603i | 0.308550 | + | 0.152561i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.59808 | − | 2.57180i | −0.334975 | − | 0.0897563i | 0.0874109 | − | 0.996172i | \(-0.472141\pi\) |
−0.422386 | + | 0.906416i | \(0.638807\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.9186 | + | 9.35641i | −1.21719 | + | 0.326144i | −0.809577 | − | 0.587013i | \(-0.800304\pi\) |
−0.407608 | + | 0.913157i | \(0.633637\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.4641i | 1.09411i | 0.837095 | + | 0.547057i | \(0.184252\pi\) | ||||
−0.837095 | + | 0.547057i | \(0.815748\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.96410 | + | 13.7942i | 0.276605 | + | 0.479093i | 0.970539 | − | 0.240945i | \(-0.0774574\pi\) |
−0.693934 | + | 0.720039i | \(0.744124\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 22.3205i | − | 0.774290i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.4641 | + | 21.4641i | −0.743687 | + | 0.743687i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 35.5167 | 1.22764 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.47372 | − | 24.1603i | −0.223498 | − | 0.834105i | −0.983001 | − | 0.183601i | \(-0.941225\pi\) |
0.759503 | − | 0.650504i | \(-0.225442\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.7846 | − | 48.1244i | 0.958090 | − | 1.65946i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.2942 | − | 31.6865i | −0.630087 | − | 1.09134i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.5622 | − | 18.2942i | −0.362921 | − | 0.628597i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.3564 | − | 42.1865i | 0.835910 | − | 1.44784i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.500000 | + | 1.86603i | 0.0171398 | + | 0.0639665i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.5692 | −0.943952 | −0.471976 | − | 0.881611i | \(-0.656459\pi\) | ||||
−0.471976 | + | 0.881611i | \(0.656459\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.3923 | + | 29.3923i | −1.00402 | + | 1.00402i | −0.00403013 | + | 0.999992i | \(0.501283\pi\) |
−0.999992 | + | 0.00403013i | \(0.998717\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.1051i | 1.02717i | 0.858038 | + | 0.513587i | \(0.171684\pi\) | ||||
−0.858038 | + | 0.513587i | \(0.828316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.500000 | − | 0.866025i | −0.0170400 | − | 0.0295141i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.2487i | 0.961597i | 0.876831 | + | 0.480799i | \(0.159653\pi\) | ||||
−0.876831 | + | 0.480799i | \(0.840347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.09808 | − | 1.09808i | 0.139178 | − | 0.0372926i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.1244 | − | 2.71281i | −0.343445 | − | 0.0920259i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.8923 | − | 8.84679i | −0.606258 | − | 0.299762i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.83013 | − | 1.63397i | 0.0957853 | − | 0.0553017i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.5526 | − | 30.4019i | 0.592708 | − | 1.02660i | −0.401158 | − | 0.916009i | \(-0.631392\pi\) |
0.993866 | − | 0.110591i | \(-0.0352744\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.2224 | − | 21.2224i | 0.715815 | − | 0.715815i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.96410 | − | 2.86603i | 0.167245 | − | 0.0965588i | −0.414041 | − | 0.910258i | \(-0.635883\pi\) |
0.581286 | + | 0.813699i | \(0.302550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.1962 | + | 27.1962i | 0.915223 | + | 0.915223i | 0.996677 | − | 0.0814537i | \(-0.0259563\pi\) |
−0.0814537 | + | 0.996677i | \(0.525956\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.7942 | − | 47.7487i | 0.429588 | − | 1.60324i | −0.324107 | − | 0.946020i | \(-0.605064\pi\) |
0.753695 | − | 0.657224i | \(-0.228270\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.8827 | + | 45.8827i | 1.53886 | + | 1.53886i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.7942 | − | 6.37564i | 0.797137 | − | 0.213592i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.124356 | + | 0.464102i | 0.00416140 | + | 0.0155306i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.23205 | − | 50.1147i | −0.107915 | − | 1.67328i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.2942 | + | 72.0070i | −0.643499 | + | 2.40157i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.24167 | + | 4.75833i | 0.274570 | + | 0.158523i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 73.2391 | + | 42.2846i | 2.43724 | + | 1.40714i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.5263 | + | 6.03590i | 0.747973 | + | 0.200419i | 0.612619 | − | 0.790379i | \(-0.290116\pi\) |
0.135354 | + | 0.990797i | \(0.456783\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.26795 | 0.0420552 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.9282 | −1.42227 | −0.711137 | − | 0.703053i | \(-0.751820\pi\) | ||||
−0.711137 | + | 0.703053i | \(0.751820\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.73205 | − | 2.07180i | −0.255894 | − | 0.0685665i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.7846 | − | 25.8564i | −1.47892 | − | 0.853854i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.7487 | + | 6.20577i | 0.354567 | + | 0.204710i | 0.666695 | − | 0.745331i | \(-0.267708\pi\) |
−0.312128 | + | 0.950040i | \(0.601042\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.80385 | − | 17.9282i | 0.158292 | − | 0.590754i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.8660 | − | 10.4282i | −0.390575 | − | 0.343248i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.78461 | − | 6.66025i | −0.0586143 | − | 0.218751i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.7942 | − | 3.96410i | 0.485383 | − | 0.130058i | −0.00782508 | − | 0.999969i | \(-0.502491\pi\) |
0.493208 | + | 0.869911i | \(0.335824\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.39230 | + | 4.39230i | 0.143952 | + | 0.143952i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.1244 | + | 60.1769i | −0.527888 | + | 1.97010i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.215390 | − | 0.215390i | −0.00703649 | − | 0.00703649i | 0.703580 | − | 0.710616i | \(-0.251584\pi\) |
−0.710616 | + | 0.703580i | \(0.751584\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33.8827 | + | 19.5622i | −1.10572 | + | 0.638388i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.0000 | + | 19.0000i | −0.619382 | + | 0.619382i | −0.945373 | − | 0.325991i | \(-0.894302\pi\) |
0.325991 | + | 0.945373i | \(0.394302\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.500000 | + | 0.866025i | −0.0162822 | + | 0.0282017i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42.0167 | − | 24.2583i | 1.36536 | − | 0.788290i | 0.375027 | − | 0.927014i | \(-0.377633\pi\) |
0.990331 | + | 0.138724i | \(0.0443001\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.7846 | + | 25.8564i | −1.25900 | + | 0.839334i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.5885 | − | 8.46410i | −1.02433 | − | 0.274467i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.9904 | + | 5.62436i | −0.679945 | + | 0.182191i | −0.582231 | − | 0.813024i | \(-0.697820\pi\) |
−0.0977146 | + | 0.995214i | \(0.531153\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 41.0526i | 1.32704i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.50000 | − | 2.59808i | −0.0484375 | − | 0.0838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 34.7128i | − | 1.11977i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.19615 | + | 3.19615i | −0.102995 | + | 0.102995i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −58.6410 | −1.88577 | −0.942884 | − | 0.333121i | \(-0.891898\pi\) | ||||
−0.942884 | + | 0.333121i | \(0.891898\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.96410 | − | 7.33013i | −0.0630960 | − | 0.235478i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.5000 | + | 28.5788i | −0.529510 | + | 0.917139i | 0.469897 | + | 0.882721i | \(0.344291\pi\) |
−0.999408 | + | 0.0344175i | \(0.989042\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.1603 | + | 31.4545i | 0.582191 | + | 1.00838i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.6244 | + | 42.6506i | 0.787803 | + | 1.36451i | 0.927310 | + | 0.374294i | \(0.122115\pi\) |
−0.139507 | + | 0.990221i | \(0.544552\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.6962 | + | 30.6506i | −0.565571 | + | 0.979599i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.51666 | + | 9.39230i | 0.0803508 | + | 0.299873i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.0718 | 0.927246 | 0.463623 | − | 0.886032i | \(-0.346549\pi\) | ||||
0.463623 | + | 0.886032i | \(0.346549\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.73205 | + | 2.73205i | −0.0869621 | + | 0.0869621i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 84.5692i | − | 2.68914i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.9641 | − | 43.2391i | −0.793011 | − | 1.37354i | −0.924095 | − | 0.382164i | \(-0.875179\pi\) |
0.131084 | − | 0.991371i | \(-0.458154\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 12.4641i | − | 0.395536i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.33013 | − | 1.69615i | 0.200477 | − | 0.0537177i | −0.157183 | − | 0.987569i | \(-0.550241\pi\) |
0.357660 | + | 0.933852i | \(0.383575\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.13397 | − | 0.303848i | −0.0358774 | − | 0.00961331i |
(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 | 1300.2.bs.a.457.1 | 4 | ||
5.2 | odd | 4 | 260.2.bf.a.93.1 | ✓ | 4 | ||
5.3 | odd | 4 | 1300.2.bn.b.93.1 | 4 | |||
5.4 | even | 2 | 260.2.bk.b.197.1 | yes | 4 | ||
13.7 | odd | 12 | 1300.2.bn.b.657.1 | 4 | |||
65.7 | even | 12 | 260.2.bk.b.33.1 | yes | 4 | ||
65.33 | even | 12 | inner | 1300.2.bs.a.293.1 | 4 | ||
65.59 | odd | 12 | 260.2.bf.a.137.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.a.93.1 | ✓ | 4 | 5.2 | odd | 4 | ||
260.2.bf.a.137.1 | yes | 4 | 65.59 | odd | 12 | ||
260.2.bk.b.33.1 | yes | 4 | 65.7 | even | 12 | ||
260.2.bk.b.197.1 | yes | 4 | 5.4 | even | 2 | ||
1300.2.bn.b.93.1 | 4 | 5.3 | odd | 4 | |||
1300.2.bn.b.657.1 | 4 | 13.7 | odd | 12 | |||
1300.2.bs.a.293.1 | 4 | 65.33 | even | 12 | inner | ||
1300.2.bs.a.457.1 | 4 | 1.1 | even | 1 | trivial |