Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2496,2,Mod(287,2496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2496.287");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2496 = 2^{6} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2496.j (of order \(2\), degree \(1\), 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: | \(19.9306603445\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.18918897714528256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 3x^{10} + 5x^{8} + 4x^{6} + 20x^{4} + 48x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 287.10 | ||
Root | \(0.643948 - 1.25910i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2496.287 |
Dual form | 2496.2.j.c.287.12 |
$q$-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 \(\left(\mathbb{Z}/2496\mathbb{Z}\right)^\times\).
\(n\) | \(703\) | \(769\) | \(833\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.42976 | − | 0.977641i | 0.825473 | − | 0.564441i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.48533 | 1.11147 | 0.555737 | − | 0.831358i | \(-0.312436\pi\) | ||||
0.555737 | + | 0.831358i | \(0.312436\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.85952i | − | 1.83673i | −0.395738 | − | 0.918364i | \(-0.629511\pi\) | ||
0.395738 | − | 0.918364i | \(-0.370489\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.08844 | − | 2.79559i | 0.362812 | − | 0.931862i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.10584i | − | 0.936446i | −0.883610 | − | 0.468223i | \(-0.844894\pi\) | ||
0.883610 | − | 0.468223i | \(-0.155106\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.55343 | − | 2.42976i | 0.917492 | − | 0.627362i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.59117i | 1.35606i | 0.735035 | + | 0.678029i | \(0.237166\pi\) | ||||
−0.735035 | + | 0.678029i | \(0.762834\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.75087 | − | 6.94796i | −1.03672 | − | 1.51617i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.88123 | 1.85186 | 0.925932 | − | 0.377691i | \(-0.123282\pi\) | ||||
0.925932 | + | 0.377691i | \(0.123282\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.17687 | 0.235375 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.17687 | − | 5.06112i | −0.226490 | − | 0.974014i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.06010 | 0.196856 | 0.0984279 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984279 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000i | 0.718421i | 0.933257 | + | 0.359211i | \(0.116954\pi\) | ||||
−0.933257 | + | 0.359211i | \(0.883046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.03640 | − | 4.44061i | −0.528569 | − | 0.773012i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 12.0775i | − | 2.04147i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.5422i | 1.89752i | 0.315995 | + | 0.948761i | \(0.397662\pi\) | ||||
−0.315995 | + | 0.948761i | \(0.602338\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.977641 | − | 1.42976i | −0.156548 | − | 0.228945i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.95630i | − | 0.930218i | −0.885253 | − | 0.465109i | \(-0.846015\pi\) | ||
0.885253 | − | 0.465109i | \(-0.153985\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.21327 | −0.795016 | −0.397508 | − | 0.917599i | \(-0.630125\pi\) | ||||
−0.397508 | + | 0.917599i | \(0.630125\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.70513 | − | 6.94796i | 0.403257 | − | 1.03574i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.15056 | −0.167826 | −0.0839132 | − | 0.996473i | \(-0.526742\pi\) | ||||
−0.0839132 | + | 0.996473i | \(0.526742\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.6150 | −2.37357 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.46616 | + | 7.99405i | 0.765415 | + | 1.11939i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.15158 | 0.707624 | 0.353812 | − | 0.935317i | \(-0.384885\pi\) | ||||
0.353812 | + | 0.935317i | \(0.384885\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.71905i | − | 1.04084i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.01640i | 0.913458i | 0.889606 | + | 0.456729i | \(0.150979\pi\) | ||||
−0.889606 | + | 0.456729i | \(0.849021\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.07279i | − | 1.03362i | −0.856101 | − | 0.516808i | \(-0.827120\pi\) | ||
0.856101 | − | 0.516808i | \(-0.172880\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.5852 | − | 5.28929i | −1.71158 | − | 0.666387i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.48533i | − | 0.308267i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.71905 | −0.698693 | −0.349346 | − | 0.936994i | \(-0.613596\pi\) | ||||
−0.349346 | + | 0.936994i | \(0.613596\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.6980 | − | 8.68265i | 1.52866 | − | 1.04527i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.15056 | −0.136546 | −0.0682732 | − | 0.997667i | \(-0.521749\pi\) | ||||
−0.0682732 | + | 0.997667i | \(0.521749\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.07279 | −0.944849 | −0.472425 | − | 0.881371i | \(-0.656621\pi\) | ||||
−0.472425 | + | 0.881371i | \(0.656621\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.68265 | − | 1.15056i | 0.194296 | − | 0.132855i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.0929 | −1.72000 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.71905i | − | 0.193408i | −0.995313 | − | 0.0967039i | \(-0.969170\pi\) | ||
0.995313 | − | 0.0967039i | \(-0.0308300\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.63061 | − | 6.08564i | −0.736734 | − | 0.676182i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1680i | 1.33561i | 0.744336 | + | 0.667805i | \(0.232766\pi\) | ||||
−0.744336 | + | 0.667805i | \(0.767234\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8959i | 1.50722i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.51569 | − | 1.03640i | 0.162499 | − | 0.111113i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.25742i | 0.875285i | 0.899149 | + | 0.437643i | \(0.144186\pi\) | ||||
−0.899149 | + | 0.437643i | \(0.855814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.85952 | −0.509416 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.91056 | + | 5.71905i | 0.405507 | + | 0.593038i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.71905 | −0.377612 | −0.188806 | − | 0.982014i | \(-0.560462\pi\) | ||||
−0.188806 | + | 0.982014i | \(0.560462\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.68265 | − | 3.38051i | −0.872639 | − | 0.339754i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0328 | 1.39632 | 0.698158 | − | 0.715943i | \(-0.254003\pi\) | ||||
0.698158 | + | 0.715943i | \(0.254003\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.07279i | − | 0.795436i | −0.917508 | − | 0.397718i | \(-0.869802\pi\) | ||
0.917508 | − | 0.397718i | \(-0.130198\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.8075 | − | 17.2680i | −1.15229 | − | 1.68518i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13.8519i | − | 1.33911i | −0.742761 | − | 0.669556i | \(-0.766484\pi\) | ||
0.742761 | − | 0.669556i | \(-0.233516\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.2497i | 1.55644i | 0.627994 | + | 0.778218i | \(0.283876\pi\) | ||||
−0.627994 | + | 0.778218i | \(0.716124\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.2841 | + | 16.5026i | 1.07104 | + | 1.56635i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.9126i | − | 1.12064i | −0.828275 | − | 0.560322i | \(-0.810677\pi\) | ||
0.828275 | − | 0.560322i | \(-0.189323\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 22.0728 | 2.05830 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.79559 | − | 1.08844i | −0.258452 | − | 0.100626i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 27.1704 | 2.49071 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.35375 | 0.123068 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.82313 | − | 8.51610i | −0.525054 | − | 0.767870i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.50174 | −0.849861 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.36530i | − | 0.831036i | −0.909585 | − | 0.415518i | \(-0.863600\pi\) | ||
0.909585 | − | 0.415518i | \(-0.136400\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.45374 | + | 5.09671i | −0.656265 | + | 0.448740i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.1083i | 1.58213i | 0.611733 | + | 0.791064i | \(0.290473\pi\) | ||||
−0.611733 | + | 0.791064i | \(0.709527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.92492 | − | 12.5786i | −0.251737 | − | 1.08259i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.623802i | 0.0532950i | 0.999645 | + | 0.0266475i | \(0.00848317\pi\) | ||||
−0.999645 | + | 0.0266475i | \(0.991517\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.21327 | 0.442184 | 0.221092 | − | 0.975253i | \(-0.429038\pi\) | ||||
0.221092 | + | 0.975253i | \(0.429038\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.64503 | + | 1.12483i | −0.138536 | + | 0.0947281i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.10584 | −0.259724 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.63470 | 0.218800 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −23.7554 | + | 16.2435i | −1.95932 | + | 1.33974i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.65518 | 0.299444 | 0.149722 | − | 0.988728i | \(-0.452162\pi\) | ||||
0.149722 | + | 0.988728i | \(0.452162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.152027i | − | 0.0123718i | −0.999981 | − | 0.00618591i | \(-0.998031\pi\) | ||
0.999981 | − | 0.00618591i | \(-0.00196905\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.6306 | + | 6.08564i | 1.26366 | + | 0.491995i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.94133i | 0.798507i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.71905i | − | 0.456430i | −0.973611 | − | 0.228215i | \(-0.926711\pi\) | ||
0.973611 | − | 0.228215i | \(-0.0732888\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.36554 | − | 5.03640i | 0.584125 | − | 0.399412i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 43.1585i | − | 3.40137i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.0728 | 1.72887 | 0.864437 | − | 0.502741i | \(-0.167675\pi\) | ||||
0.864437 | + | 0.502741i | \(0.167675\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.54645 | − | 11.0364i | −0.587491 | − | 0.859182i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.8061 | 0.913587 | 0.456794 | − | 0.889573i | \(-0.348998\pi\) | ||||
0.456794 | + | 0.889573i | \(0.348998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.7918 | 0.972542 | 0.486271 | − | 0.873808i | \(-0.338357\pi\) | ||||
0.486271 | + | 0.873808i | \(0.338357\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.71905i | − | 0.432319i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.85952 | + | 10.0318i | 0.515593 | + | 0.754035i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.2892i | 1.36700i | 0.729951 | + | 0.683500i | \(0.239543\pi\) | ||||
−0.729951 | + | 0.683500i | \(0.760457\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3537i | 1.21556i | 0.794104 | + | 0.607782i | \(0.207941\pi\) | ||||
−0.794104 | + | 0.607782i | \(0.792059\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.89229 | − | 11.5422i | −0.583415 | − | 0.853222i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 28.6861i | 2.10905i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.3653 | 1.26988 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −24.5946 | + | 5.71905i | −1.78900 | + | 0.415999i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.3961 | 1.83760 | 0.918798 | − | 0.394729i | \(-0.129161\pi\) | ||||
0.918798 | + | 0.394729i | \(0.129161\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.4381 | −0.967295 | −0.483648 | − | 0.875263i | \(-0.660688\pi\) | ||||
−0.483648 | + | 0.875263i | \(0.660688\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.42976 | − | 3.55343i | −0.173999 | − | 0.254467i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.1276 | −1.29154 | −0.645768 | − | 0.763533i | \(-0.723463\pi\) | ||||
−0.645768 | + | 0.763533i | \(0.723463\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.4265i | − | 0.739118i | −0.929207 | − | 0.369559i | \(-0.879509\pi\) | ||
0.929207 | − | 0.369559i | \(-0.120491\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.17687 | + | 5.59117i | −0.576752 | + | 0.394371i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 5.15158i | − | 0.361570i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 14.8034i | − | 1.03391i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.66666 | − | 24.8282i | 0.671879 | − | 1.72568i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.2976 | −0.984289 | −0.492144 | − | 0.870514i | \(-0.663787\pi\) | ||||
−0.492144 | + | 0.870514i | \(0.663787\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.64503 | + | 1.12483i | −0.112715 | + | 0.0770724i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.9567 | −0.883640 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.4381 | 1.31954 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.5422 | + | 7.89229i | −0.779948 | + | 0.533312i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.59117 | 0.376103 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.152027i | 0.0101805i | 0.999987 | + | 0.00509025i | \(0.00162028\pi\) | ||||
−0.999987 | + | 0.00509025i | \(0.998380\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.28095 | − | 3.29005i | 0.0853969 | − | 0.219337i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 9.49844i | − | 0.630434i | −0.949020 | − | 0.315217i | \(-0.897923\pi\) | ||
0.949020 | − | 0.315217i | \(-0.102077\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.5422i | 0.762728i | 0.924425 | + | 0.381364i | \(0.124546\pi\) | ||||
−0.924425 | + | 0.381364i | \(0.875454\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.5793 | + | 14.7554i | −1.41981 | + | 0.970837i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.9237i | 0.715634i | 0.933792 | + | 0.357817i | \(0.116479\pi\) | ||||
−0.933792 | + | 0.357817i | \(0.883521\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.85952 | −0.186535 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.68061 | − | 2.45783i | −0.109167 | − | 0.159653i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.30152 | −0.601666 | −0.300833 | − | 0.953677i | \(-0.597265\pi\) | ||||
−0.300833 | + | 0.953677i | \(0.597265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.7918 | −1.14607 | −0.573037 | − | 0.819530i | \(-0.694235\pi\) | ||||
−0.573037 | + | 0.819530i | \(0.694235\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4298 | − | 2.21866i | −0.989820 | − | 0.142327i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −41.2937 | −2.63816 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.8959 | + | 17.3973i | 0.753873 | + | 1.10251i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.2753i | − | 1.65848i | −0.558893 | − | 0.829240i | \(-0.688774\pi\) | ||
0.558893 | − | 0.829240i | \(-0.311226\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 27.5837i | − | 1.73417i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.5852 | + | 19.8679i | 0.850739 | + | 1.24417i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.9237i | 0.681400i | 0.940172 | + | 0.340700i | \(0.110664\pi\) | ||||
−0.940172 | + | 0.340700i | \(0.889336\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 56.0895 | 3.48523 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.15385 | − | 2.96360i | 0.0714217 | − | 0.183442i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.0950 | −1.42410 | −0.712048 | − | 0.702131i | \(-0.752232\pi\) | ||||
−0.712048 | + | 0.702131i | \(0.752232\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.8034 | 0.786506 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.07279 | + | 11.8061i | 0.494047 | + | 0.722525i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.64021 | 0.465832 | 0.232916 | − | 0.972497i | \(-0.425173\pi\) | ||||
0.232916 | + | 0.972497i | \(0.425173\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 14.5786i | − | 0.885585i | −0.896624 | − | 0.442793i | \(-0.853988\pi\) | ||
0.896624 | − | 0.442793i | \(-0.146012\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.94796 | + | 4.75087i | −0.420510 | + | 0.287536i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 3.65518i | − | 0.220416i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.71905i | − | 0.343624i | −0.985130 | − | 0.171812i | \(-0.945038\pi\) | ||
0.985130 | − | 0.171812i | \(-0.0549622\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.1823 | + | 4.35375i | 0.669470 | + | 0.260652i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 30.6221i | − | 1.82676i | −0.407105 | − | 0.913381i | \(-0.633462\pi\) | ||
0.407105 | − | 0.913381i | \(-0.366538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.08435 | 0.540008 | 0.270004 | − | 0.962859i | \(-0.412975\pi\) | ||||
0.270004 | + | 0.962859i | \(0.412975\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.9448 | −1.70856 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.2612 | −0.838895 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.31735 | + | 3.63589i | −0.311709 | + | 0.213140i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.57681 | −0.384222 | −0.192111 | − | 0.981373i | \(-0.561533\pi\) | ||||
−0.192111 | + | 0.981373i | \(0.561533\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.4381i | 1.01529i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.7190 | + | 3.65518i | −0.912112 | + | 0.212095i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 8.88123i | − | 0.513615i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.3340i | 1.46023i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.0636 | − | 13.7190i | 1.15262 | − | 0.788139i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 20.0636i | − | 1.14884i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.208158 | 0.0118802 | 0.00594011 | − | 0.999982i | \(-0.498109\pi\) | ||||
0.00594011 | + | 0.999982i | \(0.498109\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.89229 | − | 11.5422i | −0.448977 | − | 0.656611i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.9126 | −0.675502 | −0.337751 | − | 0.941235i | \(-0.609666\pi\) | ||||
−0.337751 | + | 0.941235i | \(0.609666\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.90747 | 0.390433 | 0.195217 | − | 0.980760i | \(-0.437459\pi\) | ||||
0.195217 | + | 0.980760i | \(0.437459\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −33.7638 | − | 13.1456i | −1.90237 | − | 0.740672i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.4691 | 0.812666 | 0.406333 | − | 0.913725i | \(-0.366807\pi\) | ||||
0.406333 | + | 0.913725i | \(0.366807\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.29250i | − | 0.184345i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.5422 | − | 19.8049i | −0.755850 | − | 1.10540i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.17687i | − | 0.0652812i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.8863 | + | 23.2332i | 0.878517 | + | 1.28480i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.59117i | 0.308251i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1571 | 0.943042 | 0.471521 | − | 0.881855i | \(-0.343705\pi\) | ||||
0.471521 | + | 0.881855i | \(0.343705\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 32.2671 | + | 12.5629i | 1.76823 | + | 0.688444i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.2137 | −0.776579 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.9687 | 1.52355 | 0.761777 | − | 0.647840i | \(-0.224327\pi\) | ||||
0.761777 | + | 0.647840i | \(0.224327\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.6463 | − | 17.0322i | −0.632538 | − | 0.925062i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.4234 | 0.672763 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 46.7242i | 2.52287i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 31.5588 | − | 21.5793i | 1.69907 | − | 1.16179i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.1382i | 0.544250i | 0.962262 | + | 0.272125i | \(0.0877264\pi\) | ||||
−0.962262 | + | 0.272125i | \(0.912274\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.2497i | 0.869825i | 0.900473 | + | 0.434912i | \(0.143221\pi\) | ||||
−0.900473 | + | 0.434912i | \(0.856779\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.06112 | + | 1.17687i | −0.270143 | + | 0.0628169i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.2896i | 1.34603i | 0.739629 | + | 0.673015i | \(0.235001\pi\) | ||||
−0.739629 | + | 0.673015i | \(0.764999\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.85952 | −0.151768 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 38.8473 | − | 26.5629i | 2.05601 | − | 1.40586i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.4084 | −0.866002 | −0.433001 | − | 0.901394i | \(-0.642545\pi\) | ||||
−0.433001 | + | 0.901394i | \(0.642545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.93554 | − | 1.32348i | 0.101589 | − | 0.0694646i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.0636 | −1.05018 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 0.634701i | − | 0.0331311i | −0.999863 | − | 0.0165656i | \(-0.994727\pi\) | ||
0.999863 | − | 0.0165656i | \(-0.00527323\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.6514 | − | 6.48306i | −0.866835 | − | 0.337495i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 25.0342i | − | 1.29971i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.35375i | 0.121872i | 0.998142 | + | 0.0609362i | \(0.0194086\pi\) | ||||
−0.998142 | + | 0.0609362i | \(0.980591\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.5852 | + | 9.28929i | −0.701538 | + | 0.479697i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.06010i | − | 0.0545979i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.6347 | 0.546268 | 0.273134 | − | 0.961976i | \(-0.411940\pi\) | ||||
0.273134 | + | 0.961976i | \(0.411940\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.15590 | − | 13.3901i | −0.469071 | − | 0.685998i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.9130 | −0.966410 | −0.483205 | − | 0.875507i | \(-0.660527\pi\) | ||||
−0.483205 | + | 0.875507i | \(0.660527\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −37.5109 | −1.91173 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.67432 | + | 14.5742i | −0.288442 | + | 0.740846i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.9762 | 1.62126 | 0.810628 | − | 0.585561i | \(-0.199126\pi\) | ||||
0.810628 | + | 0.585561i | \(0.199126\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 49.6565i | 2.51124i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.7034 | + | 25.8905i | 0.893019 | + | 1.30601i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 4.27240i | − | 0.214968i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.29250i | 0.466377i | 0.972432 | + | 0.233189i | \(0.0749160\pi\) | ||||
−0.972432 | + | 0.233189i | \(0.925084\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 0.623802i | − | 0.0311512i | −0.999879 | − | 0.0155756i | \(-0.995042\pi\) | ||
0.999879 | − | 0.0155756i | \(-0.00495807\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | 0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.4793 | − | 15.1248i | −0.818861 | − | 0.751559i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.8482 | 1.77693 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.1571 | 1.34283 | 0.671417 | − | 0.741080i | \(-0.265686\pi\) | ||||
0.671417 | + | 0.741080i | \(0.265686\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.609855 | + | 0.891889i | 0.0300819 | + | 0.0439936i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.0964 | 1.67777 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.2415i | 1.48450i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.45374 | − | 5.09671i | 0.365011 | − | 0.249587i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.3179i | 0.797183i | 0.917129 | + | 0.398592i | \(0.130501\pi\) | ||||
−0.917129 | + | 0.398592i | \(0.869499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.60342i | − | 0.224357i | −0.993688 | − | 0.112178i | \(-0.964217\pi\) | ||
0.993688 | − | 0.112178i | \(-0.0357828\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.25231 | + | 3.21649i | −0.0608895 | + | 0.156391i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.58011i | 0.319182i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −39.2299 | −1.89847 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.44061 | + | 3.03640i | −0.214395 | + | 0.146599i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.6654 | 0.850913 | 0.425456 | − | 0.904979i | \(-0.360114\pi\) | ||||
0.425456 | + | 0.904979i | \(0.360114\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.46938 | −0.166728 | −0.0833638 | − | 0.996519i | \(-0.526566\pi\) | ||||
−0.0833638 | + | 0.996519i | \(0.526566\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.76699 | − | 2.57579i | 0.180614 | − | 0.123500i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 33.5837i | − | 1.60286i | −0.598087 | − | 0.801431i | \(-0.704072\pi\) | ||
0.598087 | − | 0.801431i | \(-0.295928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.0843 | + | 46.4486i | −0.861159 | + | 2.21184i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0775i | 0.573821i | 0.957957 | + | 0.286910i | \(0.0926282\pi\) | ||||
−0.957957 | + | 0.286910i | \(0.907372\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.5224i | 0.972857i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.22604 | − | 3.57346i | 0.247183 | − | 0.169019i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.9885i | − | 1.08489i | −0.840090 | − | 0.542447i | \(-0.817498\pi\) | ||
0.840090 | − | 0.542447i | \(-0.182502\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.4993 | −0.871100 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.148628 | − | 0.217363i | −0.00698316 | − | 0.0102126i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0775 | −0.566203 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.9374 | 1.58753 | 0.793763 | − | 0.608227i | \(-0.208119\pi\) | ||||
0.793763 | + | 0.608227i | \(0.208119\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.2976 | − | 6.58011i | 1.32082 | − | 0.307133i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.57620 | −0.446008 | −0.223004 | − | 0.974818i | \(-0.571586\pi\) | ||||
−0.223004 | + | 0.974818i | \(0.571586\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 39.5837i | − | 1.83961i | −0.392376 | − | 0.919805i | \(-0.628347\pi\) | ||
0.392376 | − | 0.919805i | \(-0.371653\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.71905 | + | 14.2137i | 0.450710 | + | 0.659146i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.7358i | 1.28346i | 0.766931 | + | 0.641729i | \(0.221783\pi\) | ||||
−0.766931 | + | 0.641729i | \(0.778217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.7918i | 1.28331i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.59117 | − | 8.17687i | −0.257628 | − | 0.376770i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.1916i | 0.744490i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.60717 | − | 14.4017i | 0.256735 | − | 0.659408i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.7620 | −0.491731 | −0.245865 | − | 0.969304i | \(-0.579072\pi\) | ||||
−0.245865 | + | 0.969304i | \(0.579072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.5422 | 0.526278 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −42.1935 | − | 61.7064i | −1.91987 | − | 2.80774i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.24307 | −0.419706 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.56191i | − | 0.206720i | −0.994644 | − | 0.103360i | \(-0.967041\pi\) | ||
0.994644 | − | 0.103360i | \(-0.0329593\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.5588 | − | 21.5793i | 1.42714 | − | 0.975848i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 16.3179i | − | 0.736418i | −0.929743 | − | 0.368209i | \(-0.879971\pi\) | ||
0.929743 | − | 0.368209i | \(-0.120029\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.92721i | 0.266948i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −21.5793 | − | 8.40170i | −0.969916 | − | 0.377628i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.59117i | 0.250798i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.5224 | −1.54544 | −0.772718 | − | 0.634749i | \(-0.781103\pi\) | ||||
−0.772718 | + | 0.634749i | \(0.781103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.8800 | − | 11.5422i | 0.754142 | − | 0.515666i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.84984 | −0.260832 | −0.130416 | − | 0.991459i | \(-0.541631\pi\) | ||||
−0.130416 | + | 0.991459i | \(0.541631\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.8762 | 1.55197 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.42976 | + | 0.977641i | −0.0634979 | + | 0.0434186i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.7395 | 0.476018 | 0.238009 | − | 0.971263i | \(-0.423505\pi\) | ||||
0.238009 | + | 0.971263i | \(0.423505\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.2299i | 1.73543i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 20.0636i | − | 0.884107i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.57346i | 0.157160i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.2892 | − | 12.5058i | 0.802807 | − | 0.548943i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.9015i | 0.565227i | 0.959234 | + | 0.282613i | \(0.0912014\pi\) | ||||
−0.959234 | + | 0.282613i | \(0.908799\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.5837 | −1.20615 | −0.603075 | − | 0.797684i | \(-0.706058\pi\) | ||||
−0.603075 | + | 0.797684i | \(0.706058\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.59117 | − | 8.17687i | −0.244019 | − | 0.356868i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.3647 | −0.974221 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.8762 | 2.42940 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.6150 | + | 7.63691i | 0.851217 | + | 0.331414i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.95630 | −0.257996 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 34.4265i | − | 1.48839i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.8803 | + | 26.1492i | 0.771591 | + | 1.12842i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 51.6035i | 2.22272i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.1259i | 1.68215i | 0.540917 | + | 0.841076i | \(0.318077\pi\) | ||||
−0.540917 | + | 0.841076i | \(0.681923\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.9881 | + | 23.3820i | 0.686115 | + | 1.00342i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.3858i | 1.72994i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.9439 | 1.70788 | 0.853938 | − | 0.520374i | \(-0.174208\pi\) | ||||
0.853938 | + | 0.520374i | \(0.174208\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.5682 | − | 8.78673i | −0.963187 | − | 0.375008i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.35375 | −0.355238 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 28.0447 | + | 41.0143i | 1.19043 | + | 1.74096i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.6096 | 0.873258 | 0.436629 | − | 0.899642i | \(-0.356172\pi\) | ||||
0.436629 | + | 0.899642i | \(0.356172\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.21327i | 0.220498i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.8282 | − | 16.9770i | 1.04825 | − | 0.716771i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 28.2305i | − | 1.18978i | −0.803809 | − | 0.594888i | \(-0.797197\pi\) | ||
0.803809 | − | 0.594888i | \(-0.202803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 29.6068i | − | 1.24557i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.5733 | + | 32.2216i | −1.24196 | + | 1.35318i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 10.9237i | − | 0.457944i | −0.973433 | − | 0.228972i | \(-0.926464\pi\) | ||
0.973433 | − | 0.228972i | \(-0.0735365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.1405 | −1.05210 | −0.526048 | − | 0.850455i | \(-0.676327\pi\) | ||||
−0.526048 | + | 0.850455i | \(0.676327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 36.3103 | − | 24.8282i | 1.51689 | − | 1.03721i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.4521 | 0.435882 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0959 | 0.586820 | 0.293410 | − | 0.955987i | \(-0.405210\pi\) | ||||
0.293410 | + | 0.955987i | \(0.405210\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.2133 | + | 13.1376i | −0.798476 | + | 0.545981i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 59.1306 | 2.45315 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 16.0000i | − | 0.662652i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.94796 | − | 2.70513i | −0.287263 | − | 0.111843i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.8024i | 1.39518i | 0.716500 | + | 0.697588i | \(0.245743\pi\) | ||||
−0.716500 | + | 0.697588i | \(0.754257\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.9181 | + | 17.7223i | −1.06613 | + | 0.728997i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.47365i | − | 0.265841i | −0.991127 | − | 0.132920i | \(-0.957565\pi\) | ||
0.991127 | − | 0.132920i | \(-0.0424355\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 67.5276 | 2.76836 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.1934 | − | 14.9075i | −0.417189 | − | 0.610122i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.4300 | 0.507874 | 0.253937 | − | 0.967221i | \(-0.418274\pi\) | ||||
0.253937 | + | 0.967221i | \(0.418274\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.61497 | 0.310621 | 0.155311 | − | 0.987866i | \(-0.450362\pi\) | ||||
0.155311 | + | 0.987866i | \(0.450362\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.22482 | + | 15.9881i | −0.253494 | + | 0.651085i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.36451 | 0.136787 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.3143i | 1.14924i | 0.818420 | + | 0.574621i | \(0.194850\pi\) | ||||
−0.818420 | + | 0.574621i | \(0.805150\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.03640 | − | 7.36554i | −0.204085 | − | 0.298467i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.15056i | 0.0465467i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.1687i | 1.29928i | 0.760241 | + | 0.649641i | \(0.225081\pi\) | ||||
−0.760241 | + | 0.649641i | \(0.774919\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.4724 | − | 21.1653i | −0.583583 | − | 0.853468i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.4176i | 0.862242i | 0.902294 | + | 0.431121i | \(0.141882\pi\) | ||||
−0.902294 | + | 0.431121i | \(0.858118\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.8149 | −1.19836 | −0.599182 | − | 0.800613i | \(-0.704507\pi\) | ||||
−0.599182 | + | 0.800613i | \(0.704507\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.4521 | − | 44.9490i | −0.419428 | − | 1.80374i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 40.1271 | 1.60766 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.4993 | −1.17997 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −64.5343 | −2.57315 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.56702i | − | 0.0623821i | −0.999513 | − | 0.0311910i | \(-0.990070\pi\) | ||
0.999513 | − | 0.0311910i | \(-0.00993002\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.4422 | + | 13.9779i | −0.812504 | + | 0.555573i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 23.2759i | − | 0.923675i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.6150i | 0.658309i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.25231 | + | 3.21649i | −0.0495407 | + | 0.127242i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.1271i | 1.58493i | 0.609919 | + | 0.792464i | \(0.291202\pi\) | ||||
−0.609919 | + | 0.792464i | \(0.708798\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.5952 | 1.12769 | 0.563843 | − | 0.825882i | \(-0.309322\pi\) | ||||
0.563843 | + | 0.825882i | \(0.309322\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.5250 | + | 12.6670i | −0.729421 | + | 0.498763i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.3426 | −0.957005 | −0.478502 | − | 0.878086i | \(-0.658820\pi\) | ||||
−0.478502 | + | 0.878086i | \(0.658820\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.7918 | 0.855405 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.7918 | − | 19.0035i | 1.08925 | − | 0.744805i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.3132 | −1.14712 | −0.573558 | − | 0.819165i | \(-0.694437\pi\) | ||||
−0.573558 | + | 0.819165i | \(0.694437\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 45.0051i | 1.75850i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.78673 | + | 22.5682i | −0.342803 | + | 0.880469i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 20.0636i | − | 0.781566i | −0.920483 | − | 0.390783i | \(-0.872204\pi\) | ||
0.920483 | − | 0.390783i | \(-0.127796\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.87619i | 0.345244i | 0.984988 | + | 0.172622i | \(0.0552239\pi\) | ||||
−0.984988 | + | 0.172622i | \(0.944776\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.99405 | − | 5.46616i | 0.310463 | − | 0.212288i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.41499 | 0.364550 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.148628 | + | 0.217363i | 0.00574630 | + | 0.00840373i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.0728 | −0.967926 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.5537 | −0.792288 | −0.396144 | − | 0.918188i | \(-0.629652\pi\) | ||||
−0.396144 | + | 0.918188i | \(0.629652\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.38503 | − | 5.95630i | −0.0533099 | − | 0.229258i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.09807 | −0.157502 | −0.0787508 | − | 0.996894i | \(-0.525093\pi\) | ||||
−0.0787508 | + | 0.996894i | \(0.525093\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.0728i | 0.693570i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.28607 | − | 13.5805i | −0.355843 | − | 0.520406i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 3.47427i | − | 0.132939i | −0.997788 | − | 0.0664695i | \(-0.978826\pi\) | ||
0.997788 | − | 0.0664695i | \(-0.0211735\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.55036i | 0.0592360i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.2841 | + | 16.5026i | 0.430515 | + | 0.629612i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 5.15158i | − | 0.196260i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.0218 | −1.48446 | −0.742229 | − | 0.670146i | \(-0.766231\pi\) | ||||
−0.742229 | + | 0.670146i | \(0.766231\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.4277 | + | 42.1935i | −0.624036 | + | 1.60280i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.9567 | 0.491476 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.3027 | 1.26143 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.6794 | + | 15.6183i | 0.403933 | + | 0.590737i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.5522 | 0.851785 | 0.425892 | − | 0.904774i | \(-0.359960\pi\) | ||||
0.425892 | + | 0.904774i | \(0.359960\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.08844 | + | 2.79559i | −0.153979 | + | 0.105288i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 68.1928i | − | 2.56465i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 16.0231i | − | 0.601760i | −0.953662 | − | 0.300880i | \(-0.902720\pi\) | ||
0.953662 | − | 0.300880i | \(-0.0972804\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.80574 | − | 1.87107i | −0.180229 | − | 0.0701708i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35.5249i | 1.33042i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.71905 | −0.288676 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.2990 | + | 9.09355i | −0.496659 | + | 0.339605i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.6658 | −0.919880 | −0.459940 | − | 0.887950i | \(-0.652129\pi\) | ||||
−0.459940 | + | 0.887950i | \(0.652129\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.2299 | −1.46100 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.4381 | + | 17.3940i | −0.946053 | + | 0.646891i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.24760 | 0.0463349 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.8034i | 0.474852i | 0.971406 | + | 0.237426i | \(0.0763036\pi\) | ||||
−0.971406 | + | 0.237426i | \(0.923696\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.2299 | + | 11.9126i | −0.897405 | + | 0.441208i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 29.1483i | − | 1.07809i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 16.4578i | − | 0.607884i | −0.952691 | − | 0.303942i | \(-0.901697\pi\) | ||
0.952691 | − | 0.303942i | \(-0.0983029\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −59.0402 | + | 40.3704i | −2.17773 | + | 1.48909i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.7625i | 0.654288i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.2299 | −0.413100 | −0.206550 | − | 0.978436i | \(-0.566224\pi\) | ||||
−0.206550 | + | 0.978436i | \(0.566224\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.5153 | 0.862691 | 0.431345 | − | 0.902187i | \(-0.358039\pi\) | ||||
0.431345 | + | 0.902187i | \(0.358039\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.08435 | 0.332825 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.0167 | + | 13.2441i | 1.24460 | + | 0.484576i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −67.3136 | −2.45958 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.56191i | 0.239447i | 0.992807 | + | 0.119724i | \(0.0382009\pi\) | ||||
−0.992807 | + | 0.119724i | \(0.961799\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.6878 | − | 37.5674i | −0.936114 | − | 1.36903i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 0.377838i | − | 0.0137509i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.3027i | 1.71925i | 0.510928 | + | 0.859623i | \(0.329302\pi\) | ||||
−0.510928 | + | 0.859623i | \(0.670698\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −26.9669 | − | 39.4381i | −0.978838 | − | 1.43151i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 28.3210i | − | 1.02664i | −0.858199 | − | 0.513318i | \(-0.828416\pi\) | ||
0.858199 | − | 0.513318i | \(-0.171584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 78.9656 | 2.85875 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 38.8473 | + | 15.1248i | 1.40453 | + | 0.546840i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.01640 | 0.253348 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.5224 | −1.31703 | −0.658516 | − | 0.752566i | \(-0.728816\pi\) | ||||
−0.658516 | + | 0.752566i | \(0.728816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.6794 | + | 15.6183i | 0.384610 | + | 0.562478i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.82504 | 0.173545 | 0.0867723 | − | 0.996228i | \(-0.472345\pi\) | ||||
0.0867723 | + | 0.996228i | \(0.472345\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.70750i | 0.169098i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 80.1946 | − | 54.8353i | 2.87696 | − | 1.96721i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.57346i | 0.127868i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.24760 | − | 5.36530i | −0.0445858 | − | 0.191740i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 14.2137i | − | 0.507310i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.4993 | −1.15848 | −0.579238 | − | 0.815158i | \(-0.696650\pi\) | ||||
−0.579238 | + | 0.815158i | \(0.696650\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −33.0203 | + | 22.5786i | −1.17555 | + | 0.803818i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −57.8896 | −2.05832 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.07279 | −0.286673 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.3058 | − | 12.5171i | 0.649240 | − | 0.443936i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.6679 | −1.15715 | −0.578577 | − | 0.815627i | \(-0.696392\pi\) | ||||
−0.578577 | + | 0.815627i | \(0.696392\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.43298i | − | 0.227582i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.0843 | + | 8.98769i | 0.815645 | + | 0.317564i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.0728i | 0.884801i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 107.263i | − | 3.78053i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.9237 | − | 7.46938i | 0.384532 | − | 0.262935i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 35.2662i | − | 1.23989i | −0.784643 | − | 0.619947i | \(-0.787154\pi\) | ||
0.784643 | − | 0.619947i | \(-0.212846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.8531 | 0.732251 | 0.366125 | − | 0.930566i | \(-0.380684\pi\) | ||||
0.366125 | + | 0.930566i | \(0.380684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.2526 | − | 20.8439i | −0.499861 | − | 0.731027i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 54.8582 | 1.92160 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.28929 | + | 13.5852i | −0.184823 | + | 0.474706i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.3715 | −1.44387 | −0.721937 | − | 0.691959i | \(-0.756748\pi\) | ||||
−0.721937 | + | 0.691959i | \(0.756748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.2925i | 0.463348i | 0.972794 | + | 0.231674i | \(0.0744202\pi\) | ||||
−0.972794 | + | 0.231674i | \(0.925580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.57346 | − | 5.22604i | −0.124412 | − | 0.181947i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.7382i | 0.582045i | 0.956716 | + | 0.291023i | \(0.0939955\pi\) | ||||
−0.956716 | + | 0.291023i | \(0.906005\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.87619i | − | 0.308283i | −0.988049 | − | 0.154141i | \(-0.950739\pi\) | ||
0.988049 | − | 0.154141i | \(-0.0492611\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.59117 | − | 8.17687i | −0.193956 | − | 0.283653i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 92.8972i | − | 3.21870i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.3422 | 1.01543 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.2445 | − | 4.70750i | 0.699752 | − | 0.162715i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.1708 | 1.17971 | 0.589854 | − | 0.807510i | \(-0.299185\pi\) | ||||
0.589854 | + | 0.807510i | \(0.299185\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8762 | −0.961248 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −29.9374 | − | 43.7823i | −1.03110 | − | 1.50794i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.48533 | −0.0854980 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.57857i | − | 0.226042i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.9884 | − | 8.88123i | 0.445762 | − | 0.304803i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 102.509i | 3.51395i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 39.3340i | − | 1.34677i | −0.739292 | − | 0.673386i | \(-0.764839\pi\) | ||
0.739292 | − | 0.673386i | \(-0.235161\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.5148i | 0.564136i | 0.959394 | + | 0.282068i | \(0.0910205\pi\) | ||||
−0.959394 | + | 0.282068i | \(0.908980\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.6463 | −0.875039 | −0.437519 | − | 0.899209i | \(-0.644143\pi\) | ||||
−0.437519 | + | 0.899209i | \(0.644143\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −41.3842 | + | 28.2976i | −1.41037 | + | 0.964380i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.4279 | −1.20598 | −0.602989 | − | 0.797749i | \(-0.706024\pi\) | ||||
−0.602989 | + | 0.797749i | \(0.706024\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.7918 | 1.08096 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.3901 | + | 13.9423i | −0.692486 | + | 0.473507i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.33909 | −0.181116 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.71905i | 0.193783i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.04795 | + | 10.3969i | −0.137002 | + | 0.351882i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 46.1739i | 1.56096i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.51907i | 0.321436i | 0.987000 | + | 0.160718i | \(0.0513810\pi\) | ||||
−0.987000 | + | 0.160718i | \(0.948619\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.40328 | + | 6.42976i | −0.317165 | + | 0.216870i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.32144i | 0.212975i | 0.994314 | + | 0.106487i | \(0.0339603\pi\) | ||||
−0.994314 | + | 0.106487i | \(0.966040\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.87107 | 0.130272 | 0.0651360 | − | 0.997876i | \(-0.479252\pi\) | ||||
0.0651360 | + | 0.997876i | \(0.479252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.0482 | + | 24.9323i | 0.573069 | + | 0.838091i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 52.7700 | 1.77184 | 0.885922 | − | 0.463834i | \(-0.153527\pi\) | ||||
0.885922 | + | 0.463834i | \(0.153527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.5109 | −1.52639 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.9010 | + | 20.5936i | −0.633208 | + | 0.689912i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.4548i | 1.51938i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.68265 | − | 12.6980i | −0.289905 | − | 0.423975i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.24040i | 0.141425i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.8034i | 0.959580i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.7676 | + | 36.2216i | 0.824213 | + | 1.20538i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 40.6445i | 1.35107i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.99489 | −0.298670 | −0.149335 | − | 0.988787i | \(-0.547713\pi\) | ||||
−0.149335 | + | 0.988787i | \(0.547713\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.2738 | − | 39.2299i | 0.506601 | − | 1.30117i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.57086 | −0.0520449 | −0.0260224 | − | 0.999661i | \(-0.508284\pi\) | ||||
−0.0260224 | + | 0.999661i | \(0.508284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.7918 | 1.25073 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.6150 | − | 28.6861i | −0.648451 | − | 0.948334i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 87.9977 | 2.90594 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30.8762i | − | 1.01851i | −0.860615 | − | 0.509256i | \(-0.829921\pi\) | ||
0.860615 | − | 0.509256i | \(-0.170079\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.297617 | − | 0.203504i | 0.00980681 | − | 0.00670569i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.15056i | 0.0378711i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.5837i | 0.446629i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.5682 | − | 8.78673i | −0.741237 | − | 0.288594i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.7095i | 0.613839i | 0.951735 | + | 0.306920i | \(0.0992983\pi\) | ||||
−0.951735 | + | 0.306920i | \(0.900702\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.0322 | + | 11.6463i | −0.557609 | + | 0.381281i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 43.1585 | 1.41143 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.6680 | 1.26323 | 0.631615 | − | 0.775282i | \(-0.282392\pi\) | ||||
0.631615 | + | 0.775282i | \(0.282392\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.87604 | − | 6.75303i | 0.322292 | − | 0.220377i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.18688 | −0.169087 | −0.0845436 | − | 0.996420i | \(-0.526943\pi\) | ||||
−0.0845436 | + | 0.996420i | \(0.526943\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 52.8993i | − | 1.72264i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −61.1259 | + | 14.2137i | −1.98842 | + | 0.462373i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 30.2989i | − | 0.984581i | −0.870431 | − | 0.492290i | \(-0.836160\pi\) | ||
0.870431 | − | 0.492290i | \(-0.163840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.07279i | 0.262054i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.6874 | − | 14.1456i | 0.670834 | − | 0.458702i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 6.83878i | − | 0.221530i | −0.993847 | − | 0.110765i | \(-0.964670\pi\) | ||
0.993847 | − | 0.110765i | \(-0.0353301\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63.1177 | 2.04244 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.21889 | − | 4.70750i | −0.104052 | − | 0.152172i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.03138 | 0.0978884 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38.7242 | − | 15.0769i | −1.24787 | − | 0.485847i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.3981 | −1.07512 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.85952i | 0.284903i | 0.989802 | + | 0.142452i | \(0.0454985\pi\) | ||||
−0.989802 | + | 0.142452i | \(0.954501\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.4187i | 0.815724i | 0.913044 | + | 0.407862i | \(0.133725\pi\) | ||||
−0.913044 | + | 0.407862i | \(0.866275\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 25.3340i | − | 0.812171i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.15056 | − | 1.68265i | −0.0368474 | − | 0.0538879i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.1148i | 1.57132i | 0.618657 | + | 0.785661i | \(0.287677\pi\) | ||||
−0.618657 | + | 0.785661i | \(0.712323\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.6463 | 0.819658 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.4274 | + | 17.6867i | 1.45038 | + | 0.564694i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.1175 | −0.896809 | −0.448404 | − | 0.893831i | \(-0.648008\pi\) | ||||
−0.448404 | + | 0.893831i | \(0.648008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −45.0531 | −1.43551 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.46616 | + | 7.99405i | 0.173990 | + | 0.254453i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46.3002 | −1.47226 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 39.2068i | − | 1.24545i | −0.782442 | − | 0.622723i | \(-0.786026\pi\) | ||
0.782442 | − | 0.622723i | \(-0.213974\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.5306 | − | 16.7735i | 0.778456 | − | 0.532292i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 25.9134i | − | 0.821511i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.3653i | 0.549965i | 0.961449 | + | 0.274982i | \(0.0886720\pi\) | ||||
−0.961449 | + | 0.274982i | \(0.911328\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 58.4164 | − | 13.5837i | 1.84821 | − | 0.429769i |
(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 | 2496.2.j.c.287.10 | yes | 12 | |
3.2 | odd | 2 | inner | 2496.2.j.c.287.11 | yes | 12 | |
4.3 | odd | 2 | 2496.2.j.d.287.4 | yes | 12 | ||
8.3 | odd | 2 | inner | 2496.2.j.c.287.9 | ✓ | 12 | |
8.5 | even | 2 | 2496.2.j.d.287.3 | yes | 12 | ||
12.11 | even | 2 | 2496.2.j.d.287.1 | yes | 12 | ||
24.5 | odd | 2 | 2496.2.j.d.287.2 | yes | 12 | ||
24.11 | even | 2 | inner | 2496.2.j.c.287.12 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2496.2.j.c.287.9 | ✓ | 12 | 8.3 | odd | 2 | inner | |
2496.2.j.c.287.10 | yes | 12 | 1.1 | even | 1 | trivial | |
2496.2.j.c.287.11 | yes | 12 | 3.2 | odd | 2 | inner | |
2496.2.j.c.287.12 | yes | 12 | 24.11 | even | 2 | inner | |
2496.2.j.d.287.1 | yes | 12 | 12.11 | even | 2 | ||
2496.2.j.d.287.2 | yes | 12 | 24.5 | odd | 2 | ||
2496.2.j.d.287.3 | yes | 12 | 8.5 | even | 2 | ||
2496.2.j.d.287.4 | yes | 12 | 4.3 | odd | 2 |