Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(93,1300)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.93");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bn (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 | 93.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.93 |
Dual form | 1300.2.bn.b.657.1 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 0.500000 | − | 1.86603i | 0.288675 | − | 1.07735i | −0.657437 | − | 0.753510i | \(-0.728359\pi\) |
0.946112 | − | 0.323840i | \(-0.104974\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.86603 | + | 3.23205i | −0.705291 | + | 1.22160i | 0.261295 | + | 0.965259i | \(0.415850\pi\) |
−0.966586 | + | 0.256341i | \(0.917483\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −2.00000 | − | 3.00000i | −0.554700 | − | 0.832050i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.23205 | − | 1.13397i | 1.02642 | − | 0.275029i | 0.293947 | − | 0.955822i | \(-0.405031\pi\) |
0.732476 | + | 0.680793i | \(0.238364\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.866025 | + | 0.232051i | −0.198680 | + | 0.0532361i | −0.356787 | − | 0.934186i | \(-0.616128\pi\) |
0.158107 | + | 0.987422i | \(0.449461\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.09808 | + | 5.09808i | 1.11249 | + | 1.11249i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.96410 | + | 1.86603i | 1.45212 | + | 0.389093i | 0.896759 | − | 0.442519i | \(-0.145915\pi\) |
0.555357 | + | 0.831612i | \(0.312582\pi\) | |||||||
\(24\) | 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 | 0.479182 | − | 0.877716i | \(-0.340934\pi\) |
0.999715 | + | 0.0238745i | \(0.00760020\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 3.86603 | + | 2.23205i | 0.672989 | + | 0.388550i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.133975 | + | 0.232051i | 0.0220253 | + | 0.0381489i | 0.876828 | − | 0.480804i | \(-0.159655\pi\) |
−0.854803 | + | 0.518953i | \(0.826322\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 3.03590 | + | 11.3301i | 0.462970 | + | 1.72783i | 0.663533 | + | 0.748147i | \(0.269056\pi\) |
−0.200563 | + | 0.979681i | \(0.564277\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.535898 | 0.0781688 | 0.0390844 | − | 0.999236i | \(-0.487556\pi\) | ||||
0.0390844 | + | 0.999236i | \(0.487556\pi\) | |||||||
\(48\) | 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 | 0.804680 | − | 0.593708i | \(-0.202337\pi\) |
−0.593708 | + | 0.804680i | \(0.702337\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.73205i | 0.229416i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.79423 | + | 6.69615i | 0.233589 | + | 0.871765i | 0.978780 | + | 0.204914i | \(0.0656915\pi\) |
−0.745191 | + | 0.666851i | \(0.767642\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 2.36603 | − | 1.36603i | 0.298091 | − | 0.172103i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.79423 | − | 2.76795i | 0.585708 | − | 0.338159i | −0.177690 | − | 0.984086i | \(-0.556863\pi\) |
0.763399 | + | 0.645928i | \(0.223529\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 12.9282i | 1.51313i | 0.653917 | + | 0.756566i | \(0.273124\pi\) | ||||
−0.653917 | + | 0.756566i | \(0.726876\pi\) | |||||||
\(74\) | 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 | \(-0.917870\pi\) | ||
0.966898 | − | 0.255164i | \(-0.0821295\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.33013 | − | 9.23205i | −0.592236 | − | 1.02578i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.46410 | −0.380235 | −0.190117 | − | 0.981761i | \(-0.560887\pi\) | ||||
−0.190117 | + | 0.981761i | \(0.560887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.59808 | − | 17.1603i | −0.492966 | − | 1.83977i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7942 | − | 3.96410i | −1.56819 | − | 0.420194i | −0.632942 | − | 0.774199i | \(-0.718153\pi\) |
−0.935243 | + | 0.354005i | \(0.884819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.4282 | − | 0.866025i | 1.40766 | − | 0.0907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.83013 | − | 13.5622i | −0.811946 | − | 1.40633i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.86603 | − | 2.23205i | −0.392535 | − | 0.226630i | 0.290723 | − | 0.956807i | \(-0.406104\pi\) |
−0.683258 | + | 0.730177i | \(0.739438\pi\) | |||||||
\(98\) | 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 | \(-0.596399\pi\) |
0.954492 | + | 0.298237i | \(0.0963987\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.96410 | + | 1.59808i | 0.576571 | + | 0.154492i | 0.535309 | − | 0.844656i | \(-0.320195\pi\) |
0.0412627 | + | 0.999148i | \(0.486862\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.39230 | − | 9.39230i | −0.899620 | − | 0.899620i | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) |
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.500000 | − | 0.133975i | 0.0474579 | − | 0.0127163i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.1603 | + | 3.52628i | −1.23801 | + | 0.331724i | −0.817695 | − | 0.575652i | \(-0.804748\pi\) |
−0.420318 | + | 0.907377i | \(0.638081\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.169873 | + | 2.63397i | 0.0157048 | + | 0.243511i | ||||
\(118\) | 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 | ||||||||
\(123\) | −0.133975 | + | 0.232051i | −0.0120801 | + | 0.0209233i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.50000 | + | 16.7942i | −0.399310 | + | 1.49025i | 0.415002 | + | 0.909820i | \(0.363781\pi\) |
−0.814313 | + | 0.580426i | \(0.802886\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 0.866025 | − | 3.23205i | 0.0750939 | − | 0.280254i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.401924 | − | 0.696152i | 0.0343387 | − | 0.0594763i | −0.848345 | − | 0.529443i | \(-0.822401\pi\) |
0.882684 | + | 0.469967i | \(0.155734\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.42820 | + | 4.86603i | 0.714871 | + | 0.412731i | 0.812862 | − | 0.582456i | \(-0.197908\pi\) |
−0.0979911 | + | 0.995187i | \(0.531242\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.267949 | − | 1.00000i | 0.0225654 | − | 0.0842152i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.89230 | − | 2.66987i | 0.659988 | − | 0.223266i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.9282 | + | 3.46410i | −1.06630 | + | 0.285714i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.2583 | + | 4.89230i | −1.49578 | + | 0.400793i | −0.911684 | − | 0.410891i | \(-0.865218\pi\) |
−0.584096 | + | 0.811684i | \(0.698551\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | −3.09808 | − | 0.830127i | −0.250465 | − | 0.0671118i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.39230 | − | 7.39230i | 0.589970 | − | 0.589970i | −0.347653 | − | 0.937623i | \(-0.613021\pi\) |
0.937623 | + | 0.347653i | \(0.113021\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | −1.33013 | − | 0.767949i | −0.104184 | − | 0.0601504i | 0.447003 | − | 0.894533i | \(-0.352491\pi\) |
−0.551186 | + | 0.834382i | \(0.685825\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.33013 | − | 5.76795i | −0.257693 | − | 0.446337i | 0.707931 | − | 0.706282i | \(-0.249629\pi\) |
−0.965623 | + | 0.259945i | \(0.916296\pi\) | |||||||
\(168\) | 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 | ||||||||
\(173\) | −2.30385 | − | 8.59808i | −0.175158 | − | 0.653700i | −0.996525 | − | 0.0832986i | \(-0.973454\pi\) |
0.821366 | − | 0.570401i | \(-0.193212\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.3923 | 1.00663 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.96410 | − | 10.3301i | −0.445778 | − | 0.772110i | 0.552328 | − | 0.833627i | \(-0.313740\pi\) |
−0.998106 | + | 0.0615168i | \(0.980406\pi\) | |||||||
\(180\) | 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 | ||||||||
\(187\) | 10.1244i | 0.740366i | ||||||||
\(188\) | 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 | ||||||||
\(193\) | 21.0622 | − | 12.1603i | 1.51609 | − | 0.875314i | 0.516267 | − | 0.856428i | \(-0.327321\pi\) |
0.999822 | − | 0.0188866i | \(-0.00601215\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.4019 | − | 7.16025i | 0.883600 | − | 0.510147i | 0.0117566 | − | 0.999931i | \(-0.496258\pi\) |
0.871844 | + | 0.489784i | \(0.162924\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.96410 | + | 8.59808i | −0.351896 | + | 0.609501i | −0.986582 | − | 0.163269i | \(-0.947796\pi\) |
0.634686 | + | 0.772770i | \(0.281130\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.76795 | − | 10.3301i | −0.195236 | − | 0.728631i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 34.3205i | 2.40883i | ||||||||
\(204\) | 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 | ||||||||
\(213\) | 8.46410 | 0.579951 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.83013 | + | 29.2224i | 0.531544 | + | 1.98375i | ||||
\(218\) | 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 | ||||||||
\(223\) | −8.13397 | − | 14.0885i | −0.544691 | − | 0.943433i | −0.998626 | − | 0.0523981i | \(-0.983314\pi\) |
0.453935 | − | 0.891035i | \(-0.350020\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.59808 | − | 3.23205i | −0.371557 | − | 0.214519i | 0.302581 | − | 0.953124i | \(-0.402152\pi\) |
−0.674139 | + | 0.738605i | \(0.735485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.8564 | − | 16.8564i | 1.11390 | − | 1.11390i | 0.121285 | − | 0.992618i | \(-0.461299\pi\) |
0.992618 | − | 0.121285i | \(-0.0387015\pi\) | |||||||
\(230\) | 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 | \(-0.920194\pi\) |
0.248100 | + | 0.968734i | \(0.420194\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.46410 | − | 2.26795i | −0.549802 | − | 0.147319i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.19615 | − | 1.19615i | −0.0773727 | − | 0.0773727i | 0.667361 | − | 0.744734i | \(-0.267424\pi\) |
−0.744734 | + | 0.667361i | \(0.767424\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | −7.19615 | + | 1.92820i | −0.461633 | + | 0.123694i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.42820 | + | 2.13397i | 0.154503 | + | 0.135782i | ||||
\(248\) | 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 | ||||||||
\(253\) | −8.33013 | + | 14.4282i | −0.523711 | + | 0.907093i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.16025 | + | 15.5263i | −0.259510 | + | 0.968503i | 0.706016 | + | 0.708196i | \(0.250490\pi\) |
−0.965526 | + | 0.260307i | \(0.916176\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | −0.0621370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.73205 | −0.416703 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.89230 | − | 10.7942i | 0.178347 | − | 0.665601i | −0.817610 | − | 0.575772i | \(-0.804701\pi\) |
0.995957 | − | 0.0898284i | \(-0.0286319\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.7942 | + | 25.6244i | −0.905392 | + | 1.56819i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.57180 | + | 5.52628i | 0.583603 | + | 0.336943i | 0.762564 | − | 0.646913i | \(-0.223940\pi\) |
−0.178961 | + | 0.983856i | \(0.557274\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 5.09808 | − | 25.4904i | 0.308550 | − | 1.54275i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.1603 | − | 2.99038i | 0.670555 | − | 0.179675i | 0.0925500 | − | 0.995708i | \(-0.470498\pi\) |
0.578005 | + | 0.816033i | \(0.303832\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −24.3564 | − | 6.52628i | −1.44784 | − | 0.387947i | −0.552567 | − | 0.833469i | \(-0.686352\pi\) |
−0.895271 | + | 0.445522i | \(0.853018\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | −13.4545 | − | 7.76795i | −0.786019 | − | 0.453808i | 0.0525400 | − | 0.998619i | \(-0.483268\pi\) |
−0.838559 | + | 0.544810i | \(0.816602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.06218 | + | 8.76795i | 0.293737 | + | 0.508768i | ||||
\(298\) | 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 | ||||||||
\(303\) | −0.866025 | − | 3.23205i | −0.0497519 | − | 0.185676i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.60770 | 0.548340 | 0.274170 | − | 0.961681i | \(-0.411597\pi\) | ||||
0.274170 | + | 0.961681i | \(0.411597\pi\) | |||||||
\(308\) | 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 | 0.984549 | − | 0.175107i | \(-0.0560270\pi\) |
−0.175107 | + | 0.984549i | \(0.556027\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 16.9282i | − | 0.950783i | −0.879774 | − | 0.475391i | \(-0.842306\pi\) | ||
0.879774 | − | 0.475391i | \(-0.157694\pi\) | |||||||
\(318\) | 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 | ||||||||
\(323\) | −3.40192 | + | 1.96410i | −0.189288 | + | 0.109286i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.2224 | + | 12.8301i | −1.22890 | + | 0.709508i | ||||
\(328\) | 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 | ||||||||
\(333\) | − | 0.196152i | − | 0.0107491i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.9282 | − | 13.9282i | −0.758718 | − | 0.758718i | 0.217371 | − | 0.976089i | \(-0.430252\pi\) |
−0.976089 | + | 0.217371i | \(0.930252\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.3205i | 1.42953i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.36603 | + | 16.2224i | 0.507199 | + | 0.878494i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.267949 | −0.0144679 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.10770 | − | 15.3301i | −0.220513 | − | 0.822964i | −0.984153 | − | 0.177322i | \(-0.943256\pi\) |
0.763640 | − | 0.645642i | \(-0.223410\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.5263 | + | 6.57180i | 1.31286 | + | 0.351780i | 0.846299 | − | 0.532708i | \(-0.178826\pi\) |
0.466563 | + | 0.884488i | \(0.345492\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.4904 | − | 3.09808i | −0.826815 | − | 0.165363i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.13397 | − | 10.6244i | −0.326479 | − | 0.565477i | 0.655332 | − | 0.755341i | \(-0.272529\pi\) |
−0.981810 | + | 0.189864i | \(0.939195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27.3564 | + | 15.7942i | 1.44785 | + | 0.835919i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.5885 | + | 23.5885i | −1.24495 | + | 1.24495i | −0.287029 | + | 0.957922i | \(0.592668\pi\) |
−0.957922 | + | 0.287029i | \(0.907332\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | −17.8923 | − | 4.79423i | −0.933971 | − | 0.250257i | −0.240424 | − | 0.970668i | \(-0.577286\pi\) |
−0.693547 | + | 0.720411i | \(0.743953\pi\) | |||||||
\(368\) | 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 | ||||||||
\(373\) | 3.76795 | − | 1.00962i | 0.195097 | − | 0.0522761i | −0.159947 | − | 0.987126i | \(-0.551132\pi\) |
0.355044 | + | 0.934849i | \(0.384466\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −29.7224 | − | 14.6962i | −1.53078 | − | 0.756890i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.47372 | + | 16.6962i | −0.229800 | + | 0.857624i | 0.750625 | + | 0.660729i | \(0.229753\pi\) |
−0.980425 | + | 0.196895i | \(0.936914\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.0885 | + | 16.7942i | 1.49025 | + | 0.860394i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.59808 | + | 9.69615i | −0.286048 | + | 0.495450i | −0.972863 | − | 0.231382i | \(-0.925675\pi\) |
0.686815 | + | 0.726833i | \(0.259008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.22243 | − | 8.29423i | 0.112973 | − | 0.421619i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.8564 | −1.20957 | −0.604784 | − | 0.796390i | \(-0.706741\pi\) | ||||
−0.604784 | + | 0.796390i | \(0.706741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.5885 | 1.59750 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.92820 | − | 25.8564i | 0.349482 | − | 1.30428i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2583 | − | 31.6244i | 0.916359 | − | 1.58718i | 0.111460 | − | 0.993769i | \(-0.464447\pi\) |
0.804899 | − | 0.593412i | \(-0.202220\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | −28.6603 | − | 5.73205i | −1.42767 | − | 0.285534i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.598076 | + | 0.160254i | −0.0296455 | + | 0.00794350i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.06218 | − | 2.42820i | 0.448096 | − | 0.120067i | −0.0277124 | − | 0.999616i | \(-0.508822\pi\) |
0.475808 | + | 0.879549i | \(0.342156\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.09808 | − | 1.09808i | −0.0541641 | − | 0.0541641i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.9904 | − | 6.69615i | −1.22970 | − | 0.329496i | ||||
\(414\) | 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 | −0.491269 | − | 0.871008i | \(-0.663467\pi\) |
0.508681 | + | 0.860955i | \(0.330133\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | −0.339746 | − | 0.196152i | −0.0165190 | − | 0.00953726i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.86603 | + | 3.23205i | 0.0903033 | + | 0.156410i | ||||
\(428\) | 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 | ||||||||
\(433\) | 7.16025 | + | 26.7224i | 0.344100 | + | 1.28420i | 0.893660 | + | 0.448744i | \(0.148129\pi\) |
−0.549560 | + | 0.835454i | \(0.685205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.46410 | −0.309220 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.964102 | + | 1.66987i | 0.0460141 | + | 0.0796987i | 0.888115 | − | 0.459621i | \(-0.152015\pi\) |
−0.842101 | + | 0.539320i | \(0.818681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.07180i | 0.241514i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.0526 | + | 11.0526i | 0.525123 | + | 0.525123i | 0.919114 | − | 0.393991i | \(-0.128906\pi\) |
−0.393991 | + | 0.919114i | \(0.628906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.5167i | 1.72718i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.99038 | − | 7.42820i | −0.0939319 | − | 0.350559i | 0.902923 | − | 0.429801i | \(-0.141416\pi\) |
−0.996855 | + | 0.0792428i | \(0.974750\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.160254 | − | 0.277568i | 0.00754607 | − | 0.0130702i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.90192 | − | 1.09808i | 0.0893602 | − | 0.0515921i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.45448 | + | 4.30385i | −0.348706 | + | 0.201325i | −0.664115 | − | 0.747630i | \(-0.731192\pi\) |
0.315409 | + | 0.948956i | \(0.397858\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 2.14359i | 0.0996212i | 0.998759 | + | 0.0498106i | \(0.0158618\pi\) | ||||
−0.998759 | + | 0.0498106i | \(0.984138\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.12436 | − | 4.12436i | −0.190852 | − | 0.190852i | 0.605212 | − | 0.796064i | \(-0.293088\pi\) |
−0.796064 | + | 0.605212i | \(0.793088\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.6603i | 0.954002i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0981 | − | 17.4904i | −0.465295 | − | 0.805914i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.1051 | −1.24629 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.411543 | − | 1.53590i | −0.0188432 | − | 0.0703240i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.9904 | − | 7.23205i | −1.23322 | − | 0.330441i | −0.417389 | − | 0.908728i | \(-0.637055\pi\) |
−0.815833 | + | 0.578287i | \(0.803721\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.428203 | − | 0.866025i | 0.0195244 | − | 0.0394874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 25.9904 | + | 45.0167i | 1.18260 | + | 2.04833i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.277568 | − | 0.160254i | −0.0125778 | − | 0.00726180i | 0.493698 | − | 0.869633i | \(-0.335645\pi\) |
−0.506276 | + | 0.862372i | \(0.668978\pi\) | |||||||
\(488\) | 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 | ||||||||
\(497\) | −15.7942 | − | 4.23205i | −0.708468 | − | 0.189833i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.19615 | + | 7.19615i | 0.322144 | + | 0.322144i | 0.849589 | − | 0.527445i | \(-0.176850\pi\) |
−0.527445 | + | 0.849589i | \(0.676850\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.4282 | + | 3.33013i | −0.555251 | + | 0.148779i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.9641 | − | 2.93782i | 0.488865 | − | 0.130991i | −0.00596240 | − | 0.999982i | \(-0.501898\pi\) |
0.494828 | + | 0.868991i | \(0.335231\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.8923 | + | 15.3301i | 0.883448 | + | 0.680835i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.79423 | − | 25.3564i | 0.301149 | − | 1.12390i | −0.635061 | − | 0.772462i | \(-0.719025\pi\) |
0.936210 | − | 0.351441i | \(-0.114308\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.7846 | − | 24.1244i | −1.84844 | − | 1.06720i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.96410 | + | 3.40192i | −0.0867172 | + | 0.150199i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.320508 | + | 1.19615i | −0.0140959 | + | 0.0526067i | ||||
\(518\) | 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 | ||||||||
\(523\) | −0.820508 | + | 3.06218i | −0.0358783 | + | 0.133900i | −0.981542 | − | 0.191247i | \(-0.938747\pi\) |
0.945664 | + | 0.325146i | \(0.105414\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.7583 | − | 30.7583i | 0.773565 | − | 1.33985i | ||||
\(528\) | 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 | ||||||||
\(533\) | 0.160254 | + | 0.473721i | 0.00694137 | + | 0.0205191i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.2583 | + | 5.96410i | −0.960518 | + | 0.257370i | ||||
\(538\) | 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 | ||||||||
\(543\) | −27.8564 | − | 7.46410i | −1.19543 | − | 0.320315i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.19615 | + | 1.19615i | −0.0511438 | + | 0.0511438i | −0.732216 | − | 0.681072i | \(-0.761514\pi\) |
0.681072 | + | 0.732216i | \(0.261514\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 14.6603 | + | 8.46410i | 0.623417 | + | 0.359930i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.2583 | − | 21.2321i | −0.519402 | − | 0.899631i | −0.999746 | − | 0.0225505i | \(-0.992821\pi\) |
0.480344 | − | 0.877080i | \(-0.340512\pi\) | |||||||
\(558\) | 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 | ||||||||
\(563\) | −2.82051 | − | 10.5263i | −0.118870 | − | 0.443630i | 0.880677 | − | 0.473717i | \(-0.157088\pi\) |
−0.999547 | + | 0.0300874i | \(0.990421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 39.7846 | 1.67080 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.4282 | − | 26.7224i | −0.646784 | − | 1.12026i | −0.983886 | − | 0.178795i | \(-0.942780\pi\) |
0.337102 | − | 0.941468i | \(-0.390553\pi\) | |||||||
\(570\) | 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 | ||||||||
\(577\) | − | 15.0718i | − | 0.627447i | −0.949514 | − | 0.313724i | \(-0.898423\pi\) | ||
0.949514 | − | 0.313724i | \(-0.101577\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −4.34679 | + | 2.50962i | −0.180026 | + | 0.103938i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.20577 | + | 4.16025i | −0.297414 | + | 0.171712i | −0.641281 | − | 0.767306i | \(-0.721597\pi\) |
0.343867 | + | 0.939019i | \(0.388263\pi\) | |||||||
\(588\) | 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 | ||||||||
\(593\) | 20.9282i | 0.859418i | 0.902967 | + | 0.429709i | \(0.141384\pi\) | ||||
−0.902967 | + | 0.429709i | \(0.858616\pi\) | |||||||
\(594\) | 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 | \(-0.818734\pi\) | ||
0.842190 | − | 0.539180i | \(-0.181266\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | −4.05256 | −0.165033 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.64359 | + | 21.0622i | 0.229066 | + | 0.854887i | 0.980734 | + | 0.195346i | \(0.0625829\pi\) |
−0.751668 | + | 0.659542i | \(0.770750\pi\) | |||||||
\(608\) | 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 | ||||||||
\(613\) | 3.33013 | + | 5.76795i | 0.134503 | + | 0.232965i | 0.925407 | − | 0.378974i | \(-0.123723\pi\) |
−0.790905 | + | 0.611939i | \(0.790390\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.1340 | + | 15.0885i | 1.05211 | + | 0.607438i | 0.923240 | − | 0.384223i | \(-0.125530\pi\) |
0.128874 | + | 0.991661i | \(0.458864\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.1244 | + | 30.1244i | −1.21080 | + | 1.21080i | −0.240036 | + | 0.970764i | \(0.577159\pi\) |
−0.970764 | + | 0.240036i | \(0.922841\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | −3.86603 | − | 1.03590i | −0.154394 | − | 0.0413698i | ||||
\(628\) | 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 | ||||||||
\(633\) | 7.33013 | − | 1.96410i | 0.291346 | − | 0.0780660i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.0718 | + | 22.3923i | −0.438681 | + | 0.887215i | ||||
\(638\) | 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 | ||||||||
\(643\) | 22.6506 | − | 39.2321i | 0.893254 | − | 1.54716i | 0.0573029 | − | 0.998357i | \(-0.481750\pi\) |
0.835951 | − | 0.548804i | \(-0.184917\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.96410 | + | 14.7942i | −0.155845 | + | 0.581621i | 0.843187 | + | 0.537621i | \(0.180677\pi\) |
−0.999032 | + | 0.0440001i | \(0.985990\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.0192 | −0.628810 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 58.4449 | 2.29063 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.69615 | + | 36.1865i | −0.379440 | + | 1.41609i | 0.467308 | + | 0.884094i | \(0.345224\pi\) |
−0.846748 | + | 0.531994i | \(0.821443\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.73205 | − | 8.19615i | 0.184615 | − | 0.319762i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.2128 | − | 15.1340i | −1.02111 | − | 0.589536i | −0.106682 | − | 0.994293i | \(-0.534023\pi\) |
−0.914424 | + | 0.404757i | \(0.867356\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −25.3923 | + | 16.9282i | −0.986155 | + | 0.657437i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 64.0429 | − | 17.1603i | 2.47975 | − | 0.664448i | ||||
\(668\) | 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 | ||||||||
\(673\) | −3.76795 | − | 1.00962i | −0.145244 | − | 0.0389180i | 0.185465 | − | 0.982651i | \(-0.440621\pi\) |
−0.330708 | + | 0.943733i | \(0.607288\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.3205 | + | 24.3205i | −0.934713 | + | 0.934713i | −0.997996 | − | 0.0632826i | \(-0.979843\pi\) |
0.0632826 | + | 0.997996i | \(0.479843\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 20.3827 | + | 11.7679i | 0.779922 | + | 0.450288i | 0.836403 | − | 0.548116i | \(-0.184655\pi\) |
−0.0564808 | + | 0.998404i | \(0.517988\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.0263 | − | 39.8827i | −0.878507 | − | 1.52162i | ||||
\(688\) | 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 | ||||||||
\(693\) | 1.63397 | + | 6.09808i | 0.0620696 | + | 0.231647i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.607695 | −0.0230181 | ||||||||
\(698\) | 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 | ||||||||
\(707\) | 6.46410i | 0.243108i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.401924 | + | 1.50000i | 0.0150946 | + | 0.0563337i | 0.973062 | − | 0.230542i | \(-0.0740500\pi\) |
−0.957968 | + | 0.286876i | \(0.907383\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.66025 | + | 2.87564i | −0.0622644 | + | 0.107845i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50.6147 | − | 29.2224i | 1.89554 | − | 1.09439i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.83013 | + | 1.63397i | −0.105693 | + | 0.0610219i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.89230 | + | 10.2058i | −0.219746 | + | 0.380611i | −0.954730 | − | 0.297473i | \(-0.903856\pi\) |
0.734984 | + | 0.678084i | \(0.237189\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.09808 | + | 33.9545i | 0.338830 | + | 1.26453i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.1244i | 1.26910i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.5885 | − | 17.5885i | −0.652320 | − | 0.652320i | 0.301231 | − | 0.953551i | \(-0.402602\pi\) |
−0.953551 | + | 0.301231i | \(0.902602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 17.5885i | − | 0.651424i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.6962 | + | 44.5070i | 0.950407 | + | 1.64615i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.6410 | −1.13175 | −0.565876 | − | 0.824490i | \(-0.691462\pi\) | ||||
−0.565876 | + | 0.824490i | \(0.691462\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.31089 | + | 12.3564i | 0.121958 | + | 0.455154i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.2583 | + | 8.91154i | 1.22343 | + | 0.327816i | 0.812017 | − | 0.583634i | \(-0.198370\pi\) |
0.411410 | + | 0.911450i | \(0.365036\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.19615 | − | 3.46410i | 0.190885 | − | 0.127257i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.4019 | + | 21.4808i | 0.454982 | + | 0.788053i | 0.998687 | − | 0.0512238i | \(-0.0163122\pi\) |
−0.543705 | + | 0.839277i | \(0.682979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.19615 | + | 1.26795i | 0.0803530 | + | 0.0463918i | ||||
\(748\) | 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 | ||||||||
\(757\) | 14.6962 | + | 3.93782i | 0.534141 | + | 0.143123i | 0.515800 | − | 0.856709i | \(-0.327495\pi\) |
0.0183410 | + | 0.999832i | \(0.494162\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 47.8827 | − | 12.8301i | 1.73347 | − | 0.464482i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.5000 | − | 18.7750i | 0.595780 | − | 0.677926i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.33013 | − | 12.4282i | 0.120087 | − | 0.448172i | −0.879530 | − | 0.475844i | \(-0.842143\pi\) |
0.999617 | + | 0.0276717i | \(0.00880929\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.8923 | + | 15.5263i | 0.968503 | + | 0.559165i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.93782 | + | 15.4808i | −0.321471 | + | 0.556804i | −0.980792 | − | 0.195058i | \(-0.937511\pi\) |
0.659321 | + | 0.751862i | \(0.270844\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.500000 | + | 1.86603i | −0.0179374 | + | 0.0669433i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.124356 | 0.00445550 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.1244 | −0.362278 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.4282 | − | 38.9186i | 0.372674 | − | 1.39084i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.99038 | − | 6.91154i | 0.142242 | − | 0.246370i | −0.786099 | − | 0.618101i | \(-0.787902\pi\) |
0.928340 | + | 0.371731i | \(0.121236\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | −3.59808 | + | 0.232051i | −0.127771 | + | 0.00824037i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.6244 | + | 4.72243i | −0.624287 | + | 0.167277i | −0.557076 | − | 0.830462i | \(-0.688077\pi\) |
−0.0672109 | + | 0.997739i | \(0.521410\pi\) | |||||||
\(798\) | 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 | ||||||||
\(803\) | −28.8564 | − | 7.73205i | −1.01832 | − | 0.272858i | ||||
\(804\) | 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 | −0.651486 | − | 0.758661i | \(-0.725854\pi\) |
0.331276 | + | 0.943534i | \(0.392521\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 27.1865 | + | 15.6962i | 0.953473 | + | 0.550488i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.25833 | − | 9.10770i | −0.183966 | − | 0.318638i | ||||
\(818\) | 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 | ||||||||
\(823\) | −9.35641 | − | 34.9186i | −0.326144 | − | 1.21719i | −0.913157 | − | 0.407608i | \(-0.866363\pi\) |
0.587013 | − | 0.809577i | \(-0.300304\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.4641 | 1.09411 | 0.547057 | − | 0.837095i | \(-0.315748\pi\) | ||||
0.547057 | + | 0.837095i | \(0.315748\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.96410 | − | 13.7942i | −0.276605 | − | 0.479093i | 0.693934 | − | 0.720039i | \(-0.255876\pi\) |
−0.970539 | + | 0.240945i | \(0.922543\pi\) | |||||||
\(830\) | 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 | ||||||||
\(837\) | − | 35.5167i | − | 1.22764i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.47372 | + | 24.1603i | 0.223498 | + | 0.834105i | 0.983001 | + | 0.183601i | \(0.0587754\pi\) |
−0.759503 | + | 0.650504i | \(0.774558\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.7846 | − | 48.1244i | 0.958090 | − | 1.65946i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.6865 | − | 18.2942i | 1.09134 | − | 0.630087i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.2942 | + | 10.5622i | −0.628597 | + | 0.362921i | ||||
\(848\) | 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 | ||||||||
\(853\) | − | 27.5692i | − | 0.943952i | −0.881611 | − | 0.471976i | \(-0.843541\pi\) | ||
0.881611 | − | 0.471976i | \(-0.156459\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.3923 | + | 29.3923i | 1.00402 | + | 1.00402i | 0.999992 | + | 0.00403013i | \(0.00128283\pi\) |
0.00403013 | + | 0.999992i | \(0.498717\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 30.1051i | − | 1.02717i | −0.858038 | − | 0.513587i | \(-0.828316\pi\) | ||
0.858038 | − | 0.513587i | \(-0.171684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.500000 | − | 0.866025i | −0.0170400 | − | 0.0295141i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.2487 | −0.961597 | −0.480799 | − | 0.876831i | \(-0.659653\pi\) | ||||
−0.480799 | + | 0.876831i | \(0.659653\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.09808 | − | 4.09808i | −0.0372926 | − | 0.139178i | ||||
\(868\) | 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 | ||||||||
\(873\) | 1.63397 | + | 2.83013i | 0.0553017 | + | 0.0957853i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.4019 | − | 17.5526i | −1.02660 | − | 0.592708i | −0.110591 | − | 0.993866i | \(-0.535274\pi\) |
−0.916009 | + | 0.401158i | \(0.868608\pi\) | |||||||
\(878\) | 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 | \(-0.974044\pi\) |
0.0814537 | + | 0.996677i | \(0.474044\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −47.7487 | − | 12.7942i | −1.60324 | − | 0.429588i | −0.657224 | − | 0.753695i | \(-0.728270\pi\) |
−0.946020 | + | 0.324107i | \(0.894936\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | −0.464102 | + | 0.124356i | −0.0155306 | + | 0.00416140i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −50.1147 | + | 3.23205i | −1.67328 | + | 0.107915i | ||||
\(898\) | 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 | ||||||||
\(903\) | −42.2846 | + | 73.2391i | −1.40714 | + | 2.43724i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.03590 | − | 22.5263i | 0.200419 | − | 0.747973i | −0.790379 | − | 0.612619i | \(-0.790116\pi\) |
0.990797 | − | 0.135354i | \(-0.0432172\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 2.07180 | − | 7.73205i | 0.0685665 | − | 0.255894i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.8564 | + | 44.7846i | −0.853854 | + | 1.47892i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.7487 | − | 6.20577i | −0.354567 | − | 0.204710i | 0.312128 | − | 0.950040i | \(-0.398958\pi\) |
−0.666695 | + | 0.745331i | \(0.732292\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.80385 | − | 17.9282i | 0.158292 | − | 0.590754i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.4282 | − | 11.8660i | 0.343248 | − | 0.390575i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.66025 | + | 1.78461i | −0.218751 | + | 0.0586143i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.7942 | + | 3.96410i | −0.485383 | + | 0.130058i | −0.493208 | − | 0.869911i | \(-0.664176\pi\) |
0.00782508 | + | 0.999969i | \(0.497509\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.39230 | + | 4.39230i | 0.143952 | + | 0.143952i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −60.1769 | − | 16.1244i | −1.97010 | − | 0.527888i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.215390 | + | 0.215390i | −0.00703649 | + | 0.00703649i | −0.710616 | − | 0.703580i | \(-0.751584\pi\) |
0.703580 | + | 0.710616i | \(0.251584\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | −0.866025 | − | 0.500000i | −0.0282017 | − | 0.0162822i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.2583 | − | 42.0167i | −0.788290 | − | 1.36536i | −0.927014 | − | 0.375027i | \(-0.877633\pi\) |
0.138724 | − | 0.990331i | \(-0.455700\pi\) | |||||||
\(948\) | 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 | ||||||||
\(953\) | −5.62436 | − | 20.9904i | −0.182191 | − | 0.679945i | −0.995214 | − | 0.0977146i | \(-0.968847\pi\) |
0.813024 | − | 0.582231i | \(-0.197820\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 41.0526 | 1.32704 | ||||||||
\(958\) | 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 | ||||||||
\(967\) | 58.6410i | 1.88577i | 0.333121 | + | 0.942884i | \(0.391898\pi\) | ||||
−0.333121 | + | 0.942884i | \(0.608102\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −31.4545 | + | 18.1603i | −1.00838 | + | 0.582191i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.6506 | − | 24.6244i | 1.36451 | − | 0.787803i | 0.374294 | − | 0.927310i | \(-0.377885\pi\) |
0.990221 | + | 0.139507i | \(0.0445519\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 29.0718i | 0.927246i | 0.886032 | + | 0.463623i | \(0.153451\pi\) | ||||
−0.886032 | + | 0.463623i | \(0.846549\pi\) | |||||||
\(984\) | 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 | ||||||||
\(993\) | 12.4641 | 0.395536 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.69615 | − | 6.33013i | −0.0537177 | − | 0.200477i | 0.933852 | − | 0.357660i | \(-0.116425\pi\) |
−0.987569 | + | 0.157183i | \(0.949759\pi\) | |||||||
\(998\) | 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.bn.b.93.1 | 4 | ||
5.2 | odd | 4 | 1300.2.bs.a.457.1 | 4 | |||
5.3 | odd | 4 | 260.2.bk.b.197.1 | yes | 4 | ||
5.4 | even | 2 | 260.2.bf.a.93.1 | ✓ | 4 | ||
13.7 | odd | 12 | 1300.2.bs.a.293.1 | 4 | |||
65.7 | even | 12 | inner | 1300.2.bn.b.657.1 | 4 | ||
65.33 | even | 12 | 260.2.bf.a.137.1 | yes | 4 | ||
65.59 | odd | 12 | 260.2.bk.b.33.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.a.93.1 | ✓ | 4 | 5.4 | even | 2 | ||
260.2.bf.a.137.1 | yes | 4 | 65.33 | even | 12 | ||
260.2.bk.b.33.1 | yes | 4 | 65.59 | odd | 12 | ||
260.2.bk.b.197.1 | yes | 4 | 5.3 | odd | 4 | ||
1300.2.bn.b.93.1 | 4 | 1.1 | even | 1 | trivial | ||
1300.2.bn.b.657.1 | 4 | 65.7 | even | 12 | inner | ||
1300.2.bs.a.293.1 | 4 | 13.7 | odd | 12 | |||
1300.2.bs.a.457.1 | 4 | 5.2 | odd | 4 |