Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3750,2,Mod(1249,3750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3750, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3750.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3750 = 2 \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3750.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.9439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.2 | ||
Root | \(-0.705457 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3750.1249 |
Dual form | 3750.2.c.k.1249.15 |
$q$-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 \(\left(\mathbb{Z}/3750\mathbb{Z}\right)^\times\).
\(n\) | \(2501\) | \(3127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | − 3.23143i | − 1.22136i | −0.791876 | − | 0.610682i | \(-0.790895\pi\) | ||||
0.791876 | − | 0.610682i | \(-0.209105\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.30029 | 1.59810 | 0.799048 | − | 0.601267i | \(-0.205337\pi\) | ||||
0.799048 | + | 0.601267i | \(0.205337\pi\) | |||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | 5.90441i | 1.63759i | 0.574087 | + | 0.818795i | \(0.305357\pi\) | ||||
−0.574087 | + | 0.818795i | \(0.694643\pi\) | |||||||
\(14\) | −3.23143 | −0.863635 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 1.02469i | − 0.248525i | −0.992249 | − | 0.124262i | \(-0.960344\pi\) | ||||
0.992249 | − | 0.124262i | \(-0.0396564\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 4.50718 | 1.03402 | 0.517010 | − | 0.855980i | \(-0.327045\pi\) | ||||
0.517010 | + | 0.855980i | \(0.327045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.23143 | 0.705155 | ||||||||
\(22\) | − 5.30029i | − 1.13002i | ||||||||
\(23\) | 1.92827i | 0.402073i | 0.979584 | + | 0.201037i | \(0.0644310\pi\) | ||||
−0.979584 | + | 0.201037i | \(0.935569\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.90441 | 1.15795 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 3.23143i | 0.610682i | ||||||||
\(29\) | 0.260762 | 0.0484222 | 0.0242111 | − | 0.999707i | \(-0.492293\pi\) | ||||
0.0242111 | + | 0.999707i | \(0.492293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.24205 | −0.402684 | −0.201342 | − | 0.979521i | \(-0.564530\pi\) | ||||
−0.201342 | + | 0.979521i | \(0.564530\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 5.30029i | 0.922661i | ||||||||
\(34\) | −1.02469 | −0.175734 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.55354i | 1.57059i | 0.619120 | + | 0.785296i | \(0.287489\pi\) | ||||
−0.619120 | + | 0.785296i | \(0.712511\pi\) | |||||||
\(38\) | − 4.50718i | − 0.731162i | ||||||||
\(39\) | −5.90441 | −0.945463 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.96112 | −1.55567 | −0.777833 | − | 0.628471i | \(-0.783681\pi\) | ||||
−0.777833 | + | 0.628471i | \(0.783681\pi\) | |||||||
\(42\) | − 3.23143i | − 0.498620i | ||||||||
\(43\) | − 5.30164i | − 0.808492i | −0.914650 | − | 0.404246i | \(-0.867534\pi\) | ||||
0.914650 | − | 0.404246i | \(-0.132466\pi\) | |||||||
\(44\) | −5.30029 | −0.799048 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.92827 | 0.284309 | ||||||||
\(47\) | 10.5282i | 1.53569i | 0.640635 | + | 0.767846i | \(0.278671\pi\) | ||||
−0.640635 | + | 0.767846i | \(0.721329\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −3.44213 | −0.491732 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.02469 | 0.143486 | ||||||||
\(52\) | − 5.90441i | − 0.818795i | ||||||||
\(53\) | − 2.31107i | − 0.317450i | −0.987323 | − | 0.158725i | \(-0.949262\pi\) | ||||
0.987323 | − | 0.158725i | \(-0.0507383\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.23143 | 0.431818 | ||||||||
\(57\) | 4.50718i | 0.596991i | ||||||||
\(58\) | − 0.260762i | − 0.0342397i | ||||||||
\(59\) | 6.49202 | 0.845190 | 0.422595 | − | 0.906319i | \(-0.361119\pi\) | ||||
0.422595 | + | 0.906319i | \(0.361119\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.94494 | −0.505098 | −0.252549 | − | 0.967584i | \(-0.581269\pi\) | ||||
−0.252549 | + | 0.967584i | \(0.581269\pi\) | |||||||
\(62\) | 2.24205i | 0.284741i | ||||||||
\(63\) | 3.23143i | 0.407122i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.30029 | 0.652420 | ||||||||
\(67\) | − 9.29210i | − 1.13521i | −0.823301 | − | 0.567605i | \(-0.807870\pi\) | ||||
0.823301 | − | 0.567605i | \(-0.192130\pi\) | |||||||
\(68\) | 1.02469i | 0.124262i | ||||||||
\(69\) | −1.92827 | −0.232137 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.53771 | 1.01324 | 0.506620 | − | 0.862170i | \(-0.330895\pi\) | ||||
0.506620 | + | 0.862170i | \(0.330895\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | 3.95422i | 0.462806i | 0.972858 | + | 0.231403i | \(0.0743316\pi\) | ||||
−0.972858 | + | 0.231403i | \(0.925668\pi\) | |||||||
\(74\) | 9.55354 | 1.11058 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.50718 | −0.517010 | ||||||||
\(77\) | − 17.1275i | − 1.95186i | ||||||||
\(78\) | 5.90441i | 0.668543i | ||||||||
\(79\) | 13.3714 | 1.50440 | 0.752199 | − | 0.658936i | \(-0.228993\pi\) | ||||
0.752199 | + | 0.658936i | \(0.228993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.96112i | 1.10002i | ||||||||
\(83\) | 7.48698i | 0.821803i | 0.911680 | + | 0.410901i | \(0.134786\pi\) | ||||
−0.911680 | + | 0.410901i | \(0.865214\pi\) | |||||||
\(84\) | −3.23143 | −0.352578 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.30164 | −0.571691 | ||||||||
\(87\) | 0.260762i | 0.0279566i | ||||||||
\(88\) | 5.30029i | 0.565012i | ||||||||
\(89\) | 0.733574 | 0.0777587 | 0.0388794 | − | 0.999244i | \(-0.487621\pi\) | ||||
0.0388794 | + | 0.999244i | \(0.487621\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.0797 | 2.00009 | ||||||||
\(92\) | − 1.92827i | − 0.201037i | ||||||||
\(93\) | − 2.24205i | − 0.232490i | ||||||||
\(94\) | 10.5282 | 1.08590 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 17.2567i | 1.75215i | 0.482174 | + | 0.876075i | \(0.339847\pi\) | ||||
−0.482174 | + | 0.876075i | \(0.660153\pi\) | |||||||
\(98\) | 3.44213i | 0.347707i | ||||||||
\(99\) | −5.30029 | −0.532699 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.8454 | 1.17866 | 0.589331 | − | 0.807892i | \(-0.299391\pi\) | ||||
0.589331 | + | 0.807892i | \(0.299391\pi\) | |||||||
\(102\) | − 1.02469i | − 0.101460i | ||||||||
\(103\) | − 7.15084i | − 0.704593i | −0.935888 | − | 0.352297i | \(-0.885401\pi\) | ||||
0.935888 | − | 0.352297i | \(-0.114599\pi\) | |||||||
\(104\) | −5.90441 | −0.578975 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.31107 | −0.224471 | ||||||||
\(107\) | − 3.20058i | − 0.309412i | −0.987961 | − | 0.154706i | \(-0.950557\pi\) | ||||
0.987961 | − | 0.154706i | \(-0.0494430\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −9.89555 | −0.947822 | −0.473911 | − | 0.880573i | \(-0.657158\pi\) | ||||
−0.473911 | + | 0.880573i | \(0.657158\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.55354 | −0.906782 | ||||||||
\(112\) | − 3.23143i | − 0.305341i | ||||||||
\(113\) | − 4.24575i | − 0.399406i | −0.979856 | − | 0.199703i | \(-0.936002\pi\) | ||||
0.979856 | − | 0.199703i | \(-0.0639978\pi\) | |||||||
\(114\) | 4.50718 | 0.422137 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.260762 | −0.0242111 | ||||||||
\(117\) | − 5.90441i | − 0.545863i | ||||||||
\(118\) | − 6.49202i | − 0.597639i | ||||||||
\(119\) | −3.31122 | −0.303539 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.0930 | 1.55391 | ||||||||
\(122\) | 3.94494i | 0.357158i | ||||||||
\(123\) | − 9.96112i | − 0.898164i | ||||||||
\(124\) | 2.24205 | 0.201342 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.23143 | 0.287878 | ||||||||
\(127\) | 9.25090i | 0.820884i | 0.911887 | + | 0.410442i | \(0.134626\pi\) | ||||
−0.911887 | + | 0.410442i | \(0.865374\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 5.30164 | 0.466783 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.86497 | −0.425054 | −0.212527 | − | 0.977155i | \(-0.568169\pi\) | ||||
−0.212527 | + | 0.977155i | \(0.568169\pi\) | |||||||
\(132\) | − 5.30029i | − 0.461331i | ||||||||
\(133\) | − 14.5646i | − 1.26291i | ||||||||
\(134\) | −9.29210 | −0.802715 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.02469 | 0.0878668 | ||||||||
\(137\) | − 6.01666i | − 0.514038i | −0.966406 | − | 0.257019i | \(-0.917260\pi\) | ||||
0.966406 | − | 0.257019i | \(-0.0827403\pi\) | |||||||
\(138\) | 1.92827i | 0.164146i | ||||||||
\(139\) | 5.62720 | 0.477293 | 0.238646 | − | 0.971107i | \(-0.423296\pi\) | ||||
0.238646 | + | 0.971107i | \(0.423296\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.5282 | −0.886632 | ||||||||
\(142\) | − 8.53771i | − 0.716469i | ||||||||
\(143\) | 31.2951i | 2.61703i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.95422 | 0.327253 | ||||||||
\(147\) | − 3.44213i | − 0.283902i | ||||||||
\(148\) | − 9.55354i | − 0.785296i | ||||||||
\(149\) | 11.6556 | 0.954863 | 0.477432 | − | 0.878669i | \(-0.341568\pi\) | ||||
0.477432 | + | 0.878669i | \(0.341568\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.52354 | 0.449499 | 0.224750 | − | 0.974417i | \(-0.427844\pi\) | ||||
0.224750 | + | 0.974417i | \(0.427844\pi\) | |||||||
\(152\) | 4.50718i | 0.365581i | ||||||||
\(153\) | 1.02469i | 0.0828416i | ||||||||
\(154\) | −17.1275 | −1.38017 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.90441 | 0.472731 | ||||||||
\(157\) | 6.84307i | 0.546136i | 0.961995 | + | 0.273068i | \(0.0880384\pi\) | ||||
−0.961995 | + | 0.273068i | \(0.911962\pi\) | |||||||
\(158\) | − 13.3714i | − 1.06377i | ||||||||
\(159\) | 2.31107 | 0.183280 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.23108 | 0.491078 | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 9.38717i | − 0.735260i | −0.929972 | − | 0.367630i | \(-0.880169\pi\) | ||||
0.929972 | − | 0.367630i | \(-0.119831\pi\) | |||||||
\(164\) | 9.96112 | 0.777833 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.48698 | 0.581102 | ||||||||
\(167\) | − 6.82883i | − 0.528431i | −0.964464 | − | 0.264215i | \(-0.914887\pi\) | ||||
0.964464 | − | 0.264215i | \(-0.0851129\pi\) | |||||||
\(168\) | 3.23143i | 0.249310i | ||||||||
\(169\) | −21.8621 | −1.68170 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.50718 | −0.344673 | ||||||||
\(172\) | 5.30164i | 0.404246i | ||||||||
\(173\) | 18.8604i | 1.43393i | 0.697108 | + | 0.716966i | \(0.254470\pi\) | ||||
−0.697108 | + | 0.716966i | \(0.745530\pi\) | |||||||
\(174\) | 0.260762 | 0.0197683 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.30029 | 0.399524 | ||||||||
\(177\) | 6.49202i | 0.487970i | ||||||||
\(178\) | − 0.733574i | − 0.0549837i | ||||||||
\(179\) | −0.941336 | −0.0703588 | −0.0351794 | − | 0.999381i | \(-0.511200\pi\) | ||||
−0.0351794 | + | 0.999381i | \(0.511200\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.1057 | 1.04847 | 0.524235 | − | 0.851573i | \(-0.324351\pi\) | ||||
0.524235 | + | 0.851573i | \(0.324351\pi\) | |||||||
\(182\) | − 19.0797i | − 1.41428i | ||||||||
\(183\) | − 3.94494i | − 0.291618i | ||||||||
\(184\) | −1.92827 | −0.142154 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.24205 | −0.164395 | ||||||||
\(187\) | − 5.43117i | − 0.397166i | ||||||||
\(188\) | − 10.5282i | − 0.767846i | ||||||||
\(189\) | −3.23143 | −0.235052 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.4719 | 1.84308 | 0.921541 | − | 0.388280i | \(-0.126931\pi\) | ||||
0.921541 | + | 0.388280i | \(0.126931\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | − 6.63439i | − 0.477554i | −0.971074 | − | 0.238777i | \(-0.923254\pi\) | ||||
0.971074 | − | 0.238777i | \(-0.0767465\pi\) | |||||||
\(194\) | 17.2567 | 1.23896 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.44213 | 0.245866 | ||||||||
\(197\) | 10.1777i | 0.725133i | 0.931958 | + | 0.362567i | \(0.118100\pi\) | ||||
−0.931958 | + | 0.362567i | \(0.881900\pi\) | |||||||
\(198\) | 5.30029i | 0.376675i | ||||||||
\(199\) | 2.52238 | 0.178807 | 0.0894035 | − | 0.995995i | \(-0.471504\pi\) | ||||
0.0894035 | + | 0.995995i | \(0.471504\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.29210 | 0.655414 | ||||||||
\(202\) | − 11.8454i | − 0.833440i | ||||||||
\(203\) | − 0.842633i | − 0.0591412i | ||||||||
\(204\) | −1.02469 | −0.0717429 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.15084 | −0.498223 | ||||||||
\(207\) | − 1.92827i | − 0.134024i | ||||||||
\(208\) | 5.90441i | 0.409397i | ||||||||
\(209\) | 23.8894 | 1.65246 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7638 | 1.08523 | 0.542613 | − | 0.839983i | \(-0.317435\pi\) | ||||
0.542613 | + | 0.839983i | \(0.317435\pi\) | |||||||
\(212\) | 2.31107i | 0.158725i | ||||||||
\(213\) | 8.53771i | 0.584994i | ||||||||
\(214\) | −3.20058 | −0.218787 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 7.24502i | 0.491824i | ||||||||
\(218\) | 9.89555i | 0.670211i | ||||||||
\(219\) | −3.95422 | −0.267201 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.05021 | 0.406981 | ||||||||
\(222\) | 9.55354i | 0.641192i | ||||||||
\(223\) | − 9.29534i | − 0.622462i | −0.950334 | − | 0.311231i | \(-0.899259\pi\) | ||||
0.950334 | − | 0.311231i | \(-0.100741\pi\) | |||||||
\(224\) | −3.23143 | −0.215909 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.24575 | −0.282423 | ||||||||
\(227\) | 3.63809i | 0.241468i | 0.992685 | + | 0.120734i | \(0.0385249\pi\) | ||||
−0.992685 | + | 0.120734i | \(0.961475\pi\) | |||||||
\(228\) | − 4.50718i | − 0.298496i | ||||||||
\(229\) | −9.93181 | −0.656312 | −0.328156 | − | 0.944623i | \(-0.606427\pi\) | ||||
−0.328156 | + | 0.944623i | \(0.606427\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.1275 | 1.12691 | ||||||||
\(232\) | 0.260762i | 0.0171198i | ||||||||
\(233\) | 18.7893i | 1.23093i | 0.788164 | + | 0.615465i | \(0.211032\pi\) | ||||
−0.788164 | + | 0.615465i | \(0.788968\pi\) | |||||||
\(234\) | −5.90441 | −0.385984 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.49202 | −0.422595 | ||||||||
\(237\) | 13.3714i | 0.868565i | ||||||||
\(238\) | 3.31122i | 0.214635i | ||||||||
\(239\) | 9.75186 | 0.630795 | 0.315398 | − | 0.948960i | \(-0.397862\pi\) | ||||
0.315398 | + | 0.948960i | \(0.397862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.9211 | 1.21881 | 0.609407 | − | 0.792858i | \(-0.291408\pi\) | ||||
0.609407 | + | 0.792858i | \(0.291408\pi\) | |||||||
\(242\) | − 17.0930i | − 1.09878i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 3.94494 | 0.252549 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.96112 | −0.635098 | ||||||||
\(247\) | 26.6123i | 1.69330i | ||||||||
\(248\) | − 2.24205i | − 0.142370i | ||||||||
\(249\) | −7.48698 | −0.474468 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.98608 | −0.125360 | −0.0626801 | − | 0.998034i | \(-0.519965\pi\) | ||||
−0.0626801 | + | 0.998034i | \(0.519965\pi\) | |||||||
\(252\) | − 3.23143i | − 0.203561i | ||||||||
\(253\) | 10.2204i | 0.642551i | ||||||||
\(254\) | 9.25090 | 0.580453 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.2797i | 1.20263i | 0.799010 | + | 0.601317i | \(0.205357\pi\) | ||||
−0.799010 | + | 0.601317i | \(0.794643\pi\) | |||||||
\(258\) | − 5.30164i | − 0.330066i | ||||||||
\(259\) | 30.8716 | 1.91827 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.260762 | −0.0161407 | ||||||||
\(262\) | 4.86497i | 0.300559i | ||||||||
\(263\) | 12.5297i | 0.772613i | 0.922370 | + | 0.386307i | \(0.126249\pi\) | ||||
−0.922370 | + | 0.386307i | \(0.873751\pi\) | |||||||
\(264\) | −5.30029 | −0.326210 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.5646 | −0.893016 | ||||||||
\(267\) | 0.733574i | 0.0448940i | ||||||||
\(268\) | 9.29210i | 0.567605i | ||||||||
\(269\) | −13.4929 | −0.822680 | −0.411340 | − | 0.911482i | \(-0.634939\pi\) | ||||
−0.411340 | + | 0.911482i | \(0.634939\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.8135 | −1.62880 | −0.814402 | − | 0.580301i | \(-0.802935\pi\) | ||||
−0.814402 | + | 0.580301i | \(0.802935\pi\) | |||||||
\(272\) | − 1.02469i | − 0.0621312i | ||||||||
\(273\) | 19.0797i | 1.15475i | ||||||||
\(274\) | −6.01666 | −0.363480 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.92827 | 0.116068 | ||||||||
\(277\) | − 8.16724i | − 0.490722i | −0.969432 | − | 0.245361i | \(-0.921094\pi\) | ||||
0.969432 | − | 0.245361i | \(-0.0789065\pi\) | |||||||
\(278\) | − 5.62720i | − 0.337497i | ||||||||
\(279\) | 2.24205 | 0.134228 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.3418 | 1.86970 | 0.934848 | − | 0.355049i | \(-0.115536\pi\) | ||||
0.934848 | + | 0.355049i | \(0.115536\pi\) | |||||||
\(282\) | 10.5282i | 0.626943i | ||||||||
\(283\) | − 16.3503i | − 0.971927i | −0.873979 | − | 0.485964i | \(-0.838469\pi\) | ||||
0.873979 | − | 0.485964i | \(-0.161531\pi\) | |||||||
\(284\) | −8.53771 | −0.506620 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 31.2951 | 1.85052 | ||||||||
\(287\) | 32.1886i | 1.90004i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 15.9500 | 0.938235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.2567 | −1.01160 | ||||||||
\(292\) | − 3.95422i | − 0.231403i | ||||||||
\(293\) | − 28.1867i | − 1.64669i | −0.567545 | − | 0.823343i | \(-0.692107\pi\) | ||||
0.567545 | − | 0.823343i | \(-0.307893\pi\) | |||||||
\(294\) | −3.44213 | −0.200749 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.55354 | −0.555288 | ||||||||
\(297\) | − 5.30029i | − 0.307554i | ||||||||
\(298\) | − 11.6556i | − 0.675190i | ||||||||
\(299\) | −11.3853 | −0.658431 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.1319 | −0.987464 | ||||||||
\(302\) | − 5.52354i | − 0.317844i | ||||||||
\(303\) | 11.8454i | 0.680501i | ||||||||
\(304\) | 4.50718 | 0.258505 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.02469 | 0.0585778 | ||||||||
\(307\) | 14.5372i | 0.829680i | 0.909894 | + | 0.414840i | \(0.136163\pi\) | ||||
−0.909894 | + | 0.414840i | \(0.863837\pi\) | |||||||
\(308\) | 17.1275i | 0.975929i | ||||||||
\(309\) | 7.15084 | 0.406797 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.4924 | 0.821791 | 0.410896 | − | 0.911682i | \(-0.365216\pi\) | ||||
0.410896 | + | 0.911682i | \(0.365216\pi\) | |||||||
\(312\) | − 5.90441i | − 0.334272i | ||||||||
\(313\) | − 31.5288i | − 1.78211i | −0.453892 | − | 0.891057i | \(-0.649965\pi\) | ||||
0.453892 | − | 0.891057i | \(-0.350035\pi\) | |||||||
\(314\) | 6.84307 | 0.386177 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.3714 | −0.752199 | ||||||||
\(317\) | 14.9810i | 0.841419i | 0.907195 | + | 0.420710i | \(0.138219\pi\) | ||||
−0.907195 | + | 0.420710i | \(0.861781\pi\) | |||||||
\(318\) | − 2.31107i | − 0.129598i | ||||||||
\(319\) | 1.38211 | 0.0773834 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.20058 | 0.178639 | ||||||||
\(322\) | − 6.23108i | − 0.347245i | ||||||||
\(323\) | − 4.61848i | − 0.256979i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.38717 | −0.519907 | ||||||||
\(327\) | − 9.89555i | − 0.547225i | ||||||||
\(328\) | − 9.96112i | − 0.550011i | ||||||||
\(329\) | 34.0210 | 1.87564 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.6174 | −1.18820 | −0.594100 | − | 0.804391i | \(-0.702492\pi\) | ||||
−0.594100 | + | 0.804391i | \(0.702492\pi\) | |||||||
\(332\) | − 7.48698i | − 0.410901i | ||||||||
\(333\) | − 9.55354i | − 0.523531i | ||||||||
\(334\) | −6.82883 | −0.373657 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.23143 | 0.176289 | ||||||||
\(337\) | 7.59495i | 0.413723i | 0.978370 | + | 0.206862i | \(0.0663250\pi\) | ||||
−0.978370 | + | 0.206862i | \(0.933675\pi\) | |||||||
\(338\) | 21.8621i | 1.18914i | ||||||||
\(339\) | 4.24575 | 0.230597 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.8835 | −0.643528 | ||||||||
\(342\) | 4.50718i | 0.243721i | ||||||||
\(343\) | − 11.4970i | − 0.620780i | ||||||||
\(344\) | 5.30164 | 0.285845 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.8604 | 1.01394 | ||||||||
\(347\) | 7.53304i | 0.404395i | 0.979345 | + | 0.202197i | \(0.0648083\pi\) | ||||
−0.979345 | + | 0.202197i | \(0.935192\pi\) | |||||||
\(348\) | − 0.260762i | − 0.0139783i | ||||||||
\(349\) | −18.7527 | −1.00381 | −0.501904 | − | 0.864923i | \(-0.667367\pi\) | ||||
−0.501904 | + | 0.864923i | \(0.667367\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.90441 | 0.315154 | ||||||||
\(352\) | − 5.30029i | − 0.282506i | ||||||||
\(353\) | 4.36607i | 0.232383i | 0.993227 | + | 0.116191i | \(0.0370686\pi\) | ||||
−0.993227 | + | 0.116191i | \(0.962931\pi\) | |||||||
\(354\) | 6.49202 | 0.345047 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.733574 | −0.0388794 | ||||||||
\(357\) | − 3.31122i | − 0.175249i | ||||||||
\(358\) | 0.941336i | 0.0497512i | ||||||||
\(359\) | −0.737212 | −0.0389086 | −0.0194543 | − | 0.999811i | \(-0.506193\pi\) | ||||
−0.0194543 | + | 0.999811i | \(0.506193\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.31471 | 0.0691954 | ||||||||
\(362\) | − 14.1057i | − 0.741381i | ||||||||
\(363\) | 17.0930i | 0.897151i | ||||||||
\(364\) | −19.0797 | −1.00005 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.94494 | −0.206205 | ||||||||
\(367\) | − 18.8600i | − 0.984486i | −0.870458 | − | 0.492243i | \(-0.836177\pi\) | ||||
0.870458 | − | 0.492243i | \(-0.163823\pi\) | |||||||
\(368\) | 1.92827i | 0.100518i | ||||||||
\(369\) | 9.96112 | 0.518555 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.46806 | −0.387722 | ||||||||
\(372\) | 2.24205i | 0.116245i | ||||||||
\(373\) | − 29.8366i | − 1.54488i | −0.635086 | − | 0.772441i | \(-0.719035\pi\) | ||||
0.635086 | − | 0.772441i | \(-0.280965\pi\) | |||||||
\(374\) | −5.43117 | −0.280839 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.5282 | −0.542949 | ||||||||
\(377\) | 1.53964i | 0.0792958i | ||||||||
\(378\) | 3.23143i | 0.166207i | ||||||||
\(379\) | −25.4826 | −1.30895 | −0.654477 | − | 0.756082i | \(-0.727111\pi\) | ||||
−0.654477 | + | 0.756082i | \(0.727111\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.25090 | −0.473938 | ||||||||
\(382\) | − 25.4719i | − 1.30326i | ||||||||
\(383\) | 31.6433i | 1.61690i | 0.588566 | + | 0.808449i | \(0.299693\pi\) | ||||
−0.588566 | + | 0.808449i | \(0.700307\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.63439 | −0.337682 | ||||||||
\(387\) | 5.30164i | 0.269497i | ||||||||
\(388\) | − 17.2567i | − 0.876075i | ||||||||
\(389\) | −12.0480 | −0.610858 | −0.305429 | − | 0.952215i | \(-0.598800\pi\) | ||||
−0.305429 | + | 0.952215i | \(0.598800\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.97589 | 0.0999251 | ||||||||
\(392\) | − 3.44213i | − 0.173854i | ||||||||
\(393\) | − 4.86497i | − 0.245405i | ||||||||
\(394\) | 10.1777 | 0.512747 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.30029 | 0.266349 | ||||||||
\(397\) | − 25.7565i | − 1.29268i | −0.763049 | − | 0.646341i | \(-0.776298\pi\) | ||||
0.763049 | − | 0.646341i | \(-0.223702\pi\) | |||||||
\(398\) | − 2.52238i | − 0.126436i | ||||||||
\(399\) | 14.5646 | 0.729144 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.3196 | 1.31434 | 0.657169 | − | 0.753743i | \(-0.271754\pi\) | ||||
0.657169 | + | 0.753743i | \(0.271754\pi\) | |||||||
\(402\) | − 9.29210i | − 0.463448i | ||||||||
\(403\) | − 13.2380i | − 0.659431i | ||||||||
\(404\) | −11.8454 | −0.589331 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.842633 | −0.0418192 | ||||||||
\(407\) | 50.6365i | 2.50996i | ||||||||
\(408\) | 1.02469i | 0.0507299i | ||||||||
\(409\) | −36.7714 | −1.81823 | −0.909113 | − | 0.416549i | \(-0.863239\pi\) | ||||
−0.909113 | + | 0.416549i | \(0.863239\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.01666 | 0.296780 | ||||||||
\(412\) | 7.15084i | 0.352297i | ||||||||
\(413\) | − 20.9785i | − 1.03229i | ||||||||
\(414\) | −1.92827 | −0.0947695 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.90441 | 0.289488 | ||||||||
\(417\) | 5.62720i | 0.275565i | ||||||||
\(418\) | − 23.8894i | − 1.16847i | ||||||||
\(419\) | 31.7245 | 1.54984 | 0.774922 | − | 0.632057i | \(-0.217789\pi\) | ||||
0.774922 | + | 0.632057i | \(0.217789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.81726 | 0.429727 | 0.214864 | − | 0.976644i | \(-0.431069\pi\) | ||||
0.214864 | + | 0.976644i | \(0.431069\pi\) | |||||||
\(422\) | − 15.7638i | − 0.767371i | ||||||||
\(423\) | − 10.5282i | − 0.511897i | ||||||||
\(424\) | 2.31107 | 0.112236 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.53771 | 0.413653 | ||||||||
\(427\) | 12.7478i | 0.616908i | ||||||||
\(428\) | 3.20058i | 0.154706i | ||||||||
\(429\) | −31.2951 | −1.51094 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.5065 | 1.13227 | 0.566135 | − | 0.824313i | \(-0.308438\pi\) | ||||
0.566135 | + | 0.824313i | \(0.308438\pi\) | |||||||
\(432\) | − 1.00000i | − 0.0481125i | ||||||||
\(433\) | − 8.40312i | − 0.403828i | −0.979403 | − | 0.201914i | \(-0.935284\pi\) | ||||
0.979403 | − | 0.201914i | \(-0.0647162\pi\) | |||||||
\(434\) | 7.24502 | 0.347772 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.89555 | 0.473911 | ||||||||
\(437\) | 8.69109i | 0.415751i | ||||||||
\(438\) | 3.95422i | 0.188940i | ||||||||
\(439\) | −35.6325 | −1.70065 | −0.850324 | − | 0.526260i | \(-0.823594\pi\) | ||||
−0.850324 | + | 0.526260i | \(0.823594\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.44213 | 0.163911 | ||||||||
\(442\) | − 6.05021i | − 0.287779i | ||||||||
\(443\) | − 6.79550i | − 0.322864i | −0.986884 | − | 0.161432i | \(-0.948389\pi\) | ||||
0.986884 | − | 0.161432i | \(-0.0516112\pi\) | |||||||
\(444\) | 9.55354 | 0.453391 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.29534 | −0.440147 | ||||||||
\(447\) | 11.6556i | 0.551291i | ||||||||
\(448\) | 3.23143i | 0.152671i | ||||||||
\(449\) | −8.75011 | −0.412943 | −0.206472 | − | 0.978453i | \(-0.566198\pi\) | ||||
−0.206472 | + | 0.978453i | \(0.566198\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −52.7968 | −2.48610 | ||||||||
\(452\) | 4.24575i | 0.199703i | ||||||||
\(453\) | 5.52354i | 0.259519i | ||||||||
\(454\) | 3.63809 | 0.170744 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.50718 | −0.211068 | ||||||||
\(457\) | − 38.1474i | − 1.78446i | −0.451581 | − | 0.892230i | \(-0.649140\pi\) | ||||
0.451581 | − | 0.892230i | \(-0.350860\pi\) | |||||||
\(458\) | 9.93181i | 0.464083i | ||||||||
\(459\) | −1.02469 | −0.0478286 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.27077 | −0.0591856 | −0.0295928 | − | 0.999562i | \(-0.509421\pi\) | ||||
−0.0295928 | + | 0.999562i | \(0.509421\pi\) | |||||||
\(462\) | − 17.1275i | − 0.796843i | ||||||||
\(463\) | − 8.93349i | − 0.415175i | −0.978216 | − | 0.207587i | \(-0.933439\pi\) | ||||
0.978216 | − | 0.207587i | \(-0.0665611\pi\) | |||||||
\(464\) | 0.260762 | 0.0121056 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.7893 | 0.870399 | ||||||||
\(467\) | − 5.75682i | − 0.266394i | −0.991090 | − | 0.133197i | \(-0.957476\pi\) | ||||
0.991090 | − | 0.133197i | \(-0.0425243\pi\) | |||||||
\(468\) | 5.90441i | 0.272932i | ||||||||
\(469\) | −30.0268 | −1.38651 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.84307 | −0.315312 | ||||||||
\(472\) | 6.49202i | 0.298820i | ||||||||
\(473\) | − 28.1002i | − 1.29205i | ||||||||
\(474\) | 13.3714 | 0.614168 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.31122 | 0.151770 | ||||||||
\(477\) | 2.31107i | 0.105817i | ||||||||
\(478\) | − 9.75186i | − 0.446040i | ||||||||
\(479\) | 4.63051 | 0.211573 | 0.105787 | − | 0.994389i | \(-0.466264\pi\) | ||||
0.105787 | + | 0.994389i | \(0.466264\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −56.4080 | −2.57199 | ||||||||
\(482\) | − 18.9211i | − 0.861832i | ||||||||
\(483\) | 6.23108i | 0.283524i | ||||||||
\(484\) | −17.0930 | −0.776956 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 15.9235i | 0.721564i | 0.932650 | + | 0.360782i | \(0.117490\pi\) | ||||
−0.932650 | + | 0.360782i | \(0.882510\pi\) | |||||||
\(488\) | − 3.94494i | − 0.178579i | ||||||||
\(489\) | 9.38717 | 0.424503 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.38076 | −0.287959 | −0.143980 | − | 0.989581i | \(-0.545990\pi\) | ||||
−0.143980 | + | 0.989581i | \(0.545990\pi\) | |||||||
\(492\) | 9.96112i | 0.449082i | ||||||||
\(493\) | − 0.267201i | − 0.0120341i | ||||||||
\(494\) | 26.6123 | 1.19734 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.24205 | −0.100671 | ||||||||
\(497\) | − 27.5890i | − 1.23754i | ||||||||
\(498\) | 7.48698i | 0.335500i | ||||||||
\(499\) | −12.9135 | −0.578087 | −0.289044 | − | 0.957316i | \(-0.593337\pi\) | ||||
−0.289044 | + | 0.957316i | \(0.593337\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.82883 | 0.305090 | ||||||||
\(502\) | 1.98608i | 0.0886431i | ||||||||
\(503\) | 1.45203i | 0.0647429i | 0.999476 | + | 0.0323714i | \(0.0103059\pi\) | ||||
−0.999476 | + | 0.0323714i | \(0.989694\pi\) | |||||||
\(504\) | −3.23143 | −0.143939 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.2204 | 0.454352 | ||||||||
\(507\) | − 21.8621i | − 0.970929i | ||||||||
\(508\) | − 9.25090i | − 0.410442i | ||||||||
\(509\) | 12.4097 | 0.550051 | 0.275026 | − | 0.961437i | \(-0.411314\pi\) | ||||
0.275026 | + | 0.961437i | \(0.411314\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.7778 | 0.565255 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 4.50718i | − 0.198997i | ||||||||
\(514\) | 19.2797 | 0.850391 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.30164 | −0.233392 | ||||||||
\(517\) | 55.8023i | 2.45418i | ||||||||
\(518\) | − 30.8716i | − 1.35642i | ||||||||
\(519\) | −18.8604 | −0.827881 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.94615 | 0.348127 | 0.174064 | − | 0.984734i | \(-0.444310\pi\) | ||||
0.174064 | + | 0.984734i | \(0.444310\pi\) | |||||||
\(522\) | 0.260762i | 0.0114132i | ||||||||
\(523\) | 34.8305i | 1.52303i | 0.648145 | + | 0.761517i | \(0.275545\pi\) | ||||
−0.648145 | + | 0.761517i | \(0.724455\pi\) | |||||||
\(524\) | 4.86497 | 0.212527 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.5297 | 0.546320 | ||||||||
\(527\) | 2.29741i | 0.100077i | ||||||||
\(528\) | 5.30029i | 0.230665i | ||||||||
\(529\) | 19.2818 | 0.838337 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.49202 | −0.281730 | ||||||||
\(532\) | 14.5646i | 0.631457i | ||||||||
\(533\) | − 58.8146i | − 2.54754i | ||||||||
\(534\) | 0.733574 | 0.0317449 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.29210 | 0.401358 | ||||||||
\(537\) | − 0.941336i | − 0.0406216i | ||||||||
\(538\) | 13.4929i | 0.581722i | ||||||||
\(539\) | −18.2443 | −0.785836 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.1723 | 1.21122 | 0.605610 | − | 0.795762i | \(-0.292929\pi\) | ||||
0.605610 | + | 0.795762i | \(0.292929\pi\) | |||||||
\(542\) | 26.8135i | 1.15174i | ||||||||
\(543\) | 14.1057i | 0.605335i | ||||||||
\(544\) | −1.02469 | −0.0439334 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 19.0797 | 0.816535 | ||||||||
\(547\) | − 27.1778i | − 1.16204i | −0.813890 | − | 0.581019i | \(-0.802654\pi\) | ||||
0.813890 | − | 0.581019i | \(-0.197346\pi\) | |||||||
\(548\) | 6.01666i | 0.257019i | ||||||||
\(549\) | 3.94494 | 0.168366 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.17530 | 0.0500695 | ||||||||
\(552\) | − 1.92827i | − 0.0820728i | ||||||||
\(553\) | − 43.2087i | − 1.83742i | ||||||||
\(554\) | −8.16724 | −0.346993 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.62720 | −0.238646 | ||||||||
\(557\) | 6.74857i | 0.285946i | 0.989727 | + | 0.142973i | \(0.0456663\pi\) | ||||
−0.989727 | + | 0.142973i | \(0.954334\pi\) | |||||||
\(558\) | − 2.24205i | − 0.0949135i | ||||||||
\(559\) | 31.3031 | 1.32398 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.43117 | 0.229304 | ||||||||
\(562\) | − 31.3418i | − 1.32207i | ||||||||
\(563\) | 11.3076i | 0.476561i | 0.971196 | + | 0.238280i | \(0.0765837\pi\) | ||||
−0.971196 | + | 0.238280i | \(0.923416\pi\) | |||||||
\(564\) | 10.5282 | 0.443316 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.3503 | −0.687256 | ||||||||
\(567\) | − 3.23143i | − 0.135707i | ||||||||
\(568\) | 8.53771i | 0.358234i | ||||||||
\(569\) | −25.2185 | −1.05721 | −0.528607 | − | 0.848867i | \(-0.677286\pi\) | ||||
−0.528607 | + | 0.848867i | \(0.677286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.8001 | −1.16340 | −0.581699 | − | 0.813404i | \(-0.697612\pi\) | ||||
−0.581699 | + | 0.813404i | \(0.697612\pi\) | |||||||
\(572\) | − 31.2951i | − 1.30851i | ||||||||
\(573\) | 25.4719i | 1.06410i | ||||||||
\(574\) | 32.1886 | 1.34353 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 11.4935i | 0.478479i | 0.970961 | + | 0.239240i | \(0.0768982\pi\) | ||||
−0.970961 | + | 0.239240i | \(0.923102\pi\) | |||||||
\(578\) | − 15.9500i | − 0.663433i | ||||||||
\(579\) | 6.63439 | 0.275716 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.1936 | 1.00372 | ||||||||
\(582\) | 17.2567i | 0.715313i | ||||||||
\(583\) | − 12.2493i | − 0.507316i | ||||||||
\(584\) | −3.95422 | −0.163627 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.1867 | −1.16438 | ||||||||
\(587\) | − 42.2281i | − 1.74294i | −0.490450 | − | 0.871469i | \(-0.663168\pi\) | ||||
0.490450 | − | 0.871469i | \(-0.336832\pi\) | |||||||
\(588\) | 3.44213i | 0.141951i | ||||||||
\(589\) | −10.1053 | −0.416383 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.1777 | −0.418656 | ||||||||
\(592\) | 9.55354i | 0.392648i | ||||||||
\(593\) | − 0.0131121i | 0 0.000538451i | −1.00000 | 0.000269225i | \(-0.999914\pi\) | |||||
1.00000 | 0.000269225i | \(-8.56971e-5\pi\) | ||||||||
\(594\) | −5.30029 | −0.217473 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.6556 | −0.477432 | ||||||||
\(597\) | 2.52238i | 0.103234i | ||||||||
\(598\) | 11.3853i | 0.465581i | ||||||||
\(599\) | −2.38072 | −0.0972738 | −0.0486369 | − | 0.998817i | \(-0.515488\pi\) | ||||
−0.0486369 | + | 0.998817i | \(0.515488\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6020 | −0.799581 | −0.399790 | − | 0.916607i | \(-0.630917\pi\) | ||||
−0.399790 | + | 0.916607i | \(0.630917\pi\) | |||||||
\(602\) | 17.1319i | 0.698243i | ||||||||
\(603\) | 9.29210i | 0.378404i | ||||||||
\(604\) | −5.52354 | −0.224750 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.8454 | 0.481187 | ||||||||
\(607\) | − 10.7155i | − 0.434930i | −0.976068 | − | 0.217465i | \(-0.930221\pi\) | ||||
0.976068 | − | 0.217465i | \(-0.0697788\pi\) | |||||||
\(608\) | − 4.50718i | − 0.182790i | ||||||||
\(609\) | 0.842633 | 0.0341452 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −62.1627 | −2.51483 | ||||||||
\(612\) | − 1.02469i | − 0.0414208i | ||||||||
\(613\) | 1.16434i | 0.0470273i | 0.999724 | + | 0.0235137i | \(0.00748532\pi\) | ||||
−0.999724 | + | 0.0235137i | \(0.992515\pi\) | |||||||
\(614\) | 14.5372 | 0.586673 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17.1275 | 0.690086 | ||||||||
\(617\) | − 22.6435i | − 0.911594i | −0.890084 | − | 0.455797i | \(-0.849354\pi\) | ||||
0.890084 | − | 0.455797i | \(-0.150646\pi\) | |||||||
\(618\) | − 7.15084i | − 0.287649i | ||||||||
\(619\) | −24.7725 | −0.995689 | −0.497844 | − | 0.867266i | \(-0.665875\pi\) | ||||
−0.497844 | + | 0.867266i | \(0.665875\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.92827 | 0.0773790 | ||||||||
\(622\) | − 14.4924i | − 0.581094i | ||||||||
\(623\) | − 2.37049i | − 0.0949718i | ||||||||
\(624\) | −5.90441 | −0.236366 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −31.5288 | −1.26014 | ||||||||
\(627\) | 23.8894i | 0.954049i | ||||||||
\(628\) | − 6.84307i | − 0.273068i | ||||||||
\(629\) | 9.78945 | 0.390331 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.6515 | −1.29983 | −0.649917 | − | 0.760005i | \(-0.725196\pi\) | ||||
−0.649917 | + | 0.760005i | \(0.725196\pi\) | |||||||
\(632\) | 13.3714i | 0.531885i | ||||||||
\(633\) | 15.7638i | 0.626556i | ||||||||
\(634\) | 14.9810 | 0.594973 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.31107 | −0.0916400 | ||||||||
\(637\) | − 20.3237i | − 0.805256i | ||||||||
\(638\) | − 1.38211i | − 0.0547183i | ||||||||
\(639\) | −8.53771 | −0.337747 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.8543 | −1.06068 | −0.530340 | − | 0.847785i | \(-0.677936\pi\) | ||||
−0.530340 | + | 0.847785i | \(0.677936\pi\) | |||||||
\(642\) | − 3.20058i | − 0.126317i | ||||||||
\(643\) | 17.1051i | 0.674559i | 0.941405 | + | 0.337279i | \(0.109507\pi\) | ||||
−0.941405 | + | 0.337279i | \(0.890493\pi\) | |||||||
\(644\) | −6.23108 | −0.245539 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.61848 | −0.181712 | ||||||||
\(647\) | 45.8135i | 1.80112i | 0.434736 | + | 0.900558i | \(0.356842\pi\) | ||||
−0.434736 | + | 0.900558i | \(0.643158\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 34.4096 | 1.35069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.24502 | −0.283955 | ||||||||
\(652\) | 9.38717i | 0.367630i | ||||||||
\(653\) | − 11.4555i | − 0.448288i | −0.974556 | − | 0.224144i | \(-0.928041\pi\) | ||||
0.974556 | − | 0.224144i | \(-0.0719587\pi\) | |||||||
\(654\) | −9.89555 | −0.386947 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.96112 | −0.388916 | ||||||||
\(657\) | − 3.95422i | − 0.154269i | ||||||||
\(658\) | − 34.0210i | − 1.32628i | ||||||||
\(659\) | −39.9982 | −1.55811 | −0.779054 | − | 0.626957i | \(-0.784300\pi\) | ||||
−0.779054 | + | 0.626957i | \(0.784300\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.69132 | −0.221367 | −0.110683 | − | 0.993856i | \(-0.535304\pi\) | ||||
−0.110683 | + | 0.993856i | \(0.535304\pi\) | |||||||
\(662\) | 21.6174i | 0.840184i | ||||||||
\(663\) | 6.05021i | 0.234971i | ||||||||
\(664\) | −7.48698 | −0.290551 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.55354 | −0.370192 | ||||||||
\(667\) | 0.502820i | 0.0194693i | ||||||||
\(668\) | 6.82883i | 0.264215i | ||||||||
\(669\) | 9.29534 | 0.359379 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.9093 | −0.807194 | ||||||||
\(672\) | − 3.23143i | − 0.124655i | ||||||||
\(673\) | − 48.4527i | − 1.86772i | −0.357645 | − | 0.933858i | \(-0.616420\pi\) | ||||
0.357645 | − | 0.933858i | \(-0.383580\pi\) | |||||||
\(674\) | 7.59495 | 0.292547 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.8621 | 0.840849 | ||||||||
\(677\) | 18.5092i | 0.711367i | 0.934607 | + | 0.355683i | \(0.115752\pi\) | ||||
−0.934607 | + | 0.355683i | \(0.884248\pi\) | |||||||
\(678\) | − 4.24575i | − 0.163057i | ||||||||
\(679\) | 55.7637 | 2.14002 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.63809 | −0.139412 | ||||||||
\(682\) | 11.8835i | 0.455043i | ||||||||
\(683\) | 36.0242i | 1.37843i | 0.724558 | + | 0.689214i | \(0.242044\pi\) | ||||
−0.724558 | + | 0.689214i | \(0.757956\pi\) | |||||||
\(684\) | 4.50718 | 0.172337 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.4970 | −0.438958 | ||||||||
\(687\) | − 9.93181i | − 0.378922i | ||||||||
\(688\) | − 5.30164i | − 0.202123i | ||||||||
\(689\) | 13.6455 | 0.519853 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.4695 | −0.550446 | −0.275223 | − | 0.961380i | \(-0.588752\pi\) | ||||
−0.275223 | + | 0.961380i | \(0.588752\pi\) | |||||||
\(692\) | − 18.8604i | − 0.716966i | ||||||||
\(693\) | 17.1275i | 0.650620i | ||||||||
\(694\) | 7.53304 | 0.285950 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.260762 | −0.00988415 | ||||||||
\(697\) | 10.2071i | 0.386621i | ||||||||
\(698\) | 18.7527i | 0.709799i | ||||||||
\(699\) | −18.7893 | −0.710678 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.31284 | 0.313972 | 0.156986 | − | 0.987601i | \(-0.449822\pi\) | ||||
0.156986 | + | 0.987601i | \(0.449822\pi\) | |||||||
\(702\) | − 5.90441i | − 0.222848i | ||||||||
\(703\) | 43.0596i | 1.62402i | ||||||||
\(704\) | −5.30029 | −0.199762 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.36607 | 0.164319 | ||||||||
\(707\) | − 38.2776i | − 1.43958i | ||||||||
\(708\) | − 6.49202i | − 0.243985i | ||||||||
\(709\) | 8.97215 | 0.336956 | 0.168478 | − | 0.985705i | \(-0.446115\pi\) | ||||
0.168478 | + | 0.985705i | \(0.446115\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.3714 | −0.501466 | ||||||||
\(712\) | 0.733574i | 0.0274919i | ||||||||
\(713\) | − 4.32329i | − 0.161908i | ||||||||
\(714\) | −3.31122 | −0.123919 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.941336 | 0.0351794 | ||||||||
\(717\) | 9.75186i | 0.364190i | ||||||||
\(718\) | 0.737212i | 0.0275125i | ||||||||
\(719\) | −28.1138 | −1.04847 | −0.524234 | − | 0.851574i | \(-0.675648\pi\) | ||||
−0.524234 | + | 0.851574i | \(0.675648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.1074 | −0.860566 | ||||||||
\(722\) | − 1.31471i | − 0.0489286i | ||||||||
\(723\) | 18.9211i | 0.703683i | ||||||||
\(724\) | −14.1057 | −0.524235 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.0930 | 0.634382 | ||||||||
\(727\) | − 24.8767i | − 0.922627i | −0.887237 | − | 0.461314i | \(-0.847378\pi\) | ||||
0.887237 | − | 0.461314i | \(-0.152622\pi\) | |||||||
\(728\) | 19.0797i | 0.707140i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.43256 | −0.200930 | ||||||||
\(732\) | 3.94494i | 0.145809i | ||||||||
\(733\) | − 6.75601i | − 0.249539i | −0.992186 | − | 0.124769i | \(-0.960181\pi\) | ||||
0.992186 | − | 0.124769i | \(-0.0398191\pi\) | |||||||
\(734\) | −18.8600 | −0.696136 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.92827 | 0.0710771 | ||||||||
\(737\) | − 49.2508i | − 1.81418i | ||||||||
\(738\) | − 9.96112i | − 0.366674i | ||||||||
\(739\) | 5.09161 | 0.187298 | 0.0936490 | − | 0.995605i | \(-0.470147\pi\) | ||||
0.0936490 | + | 0.995605i | \(0.470147\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.6123 | −0.977626 | ||||||||
\(742\) | 7.46806i | 0.274161i | ||||||||
\(743\) | 16.0999i | 0.590647i | 0.955397 | + | 0.295324i | \(0.0954274\pi\) | ||||
−0.955397 | + | 0.295324i | \(0.904573\pi\) | |||||||
\(744\) | 2.24205 | 0.0821975 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −29.8366 | −1.09240 | ||||||||
\(747\) | − 7.48698i | − 0.273934i | ||||||||
\(748\) | 5.43117i | 0.198583i | ||||||||
\(749\) | −10.3424 | −0.377905 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.4366 | −0.928196 | −0.464098 | − | 0.885784i | \(-0.653622\pi\) | ||||
−0.464098 | + | 0.885784i | \(0.653622\pi\) | |||||||
\(752\) | 10.5282i | 0.383923i | ||||||||
\(753\) | − 1.98608i | − 0.0723768i | ||||||||
\(754\) | 1.53964 | 0.0560706 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.23143 | 0.117526 | ||||||||
\(757\) | 12.4947i | 0.454129i | 0.973880 | + | 0.227064i | \(0.0729128\pi\) | ||||
−0.973880 | + | 0.227064i | \(0.927087\pi\) | |||||||
\(758\) | 25.4826i | 0.925570i | ||||||||
\(759\) | −10.2204 | −0.370977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.5890 | −0.420101 | −0.210051 | − | 0.977691i | \(-0.567363\pi\) | ||||
−0.210051 | + | 0.977691i | \(0.567363\pi\) | |||||||
\(762\) | 9.25090i | 0.335125i | ||||||||
\(763\) | 31.9768i | 1.15764i | ||||||||
\(764\) | −25.4719 | −0.921541 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.6433 | 1.14332 | ||||||||
\(767\) | 38.3316i | 1.38407i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 23.7516 | 0.856505 | 0.428253 | − | 0.903659i | \(-0.359129\pi\) | ||||
0.428253 | + | 0.903659i | \(0.359129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.2797 | −0.694341 | ||||||||
\(772\) | 6.63439i | 0.238777i | ||||||||
\(773\) | − 12.0949i | − 0.435024i | −0.976058 | − | 0.217512i | \(-0.930206\pi\) | ||||
0.976058 | − | 0.217512i | \(-0.0697941\pi\) | |||||||
\(774\) | 5.30164 | 0.190564 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17.2567 | −0.619479 | ||||||||
\(777\) | 30.8716i | 1.10751i | ||||||||
\(778\) | 12.0480i | 0.431942i | ||||||||
\(779\) | −44.8966 | −1.60859 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.2523 | 1.61925 | ||||||||
\(782\) | − 1.97589i | − 0.0706577i | ||||||||
\(783\) | − 0.260762i | − 0.00931887i | ||||||||
\(784\) | −3.44213 | −0.122933 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.86497 | −0.173528 | ||||||||
\(787\) | − 20.3022i | − 0.723694i | −0.932237 | − | 0.361847i | \(-0.882146\pi\) | ||||
0.932237 | − | 0.361847i | \(-0.117854\pi\) | |||||||
\(788\) | − 10.1777i | − 0.362567i | ||||||||
\(789\) | −12.5297 | −0.446068 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.7198 | −0.487821 | ||||||||
\(792\) | − 5.30029i | − 0.188337i | ||||||||
\(793\) | − 23.2925i | − 0.827142i | ||||||||
\(794\) | −25.7565 | −0.914064 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.52238 | −0.0894035 | ||||||||
\(797\) | − 31.7025i | − 1.12296i | −0.827490 | − | 0.561480i | \(-0.810232\pi\) | ||||
0.827490 | − | 0.561480i | \(-0.189768\pi\) | |||||||
\(798\) | − 14.5646i | − 0.515583i | ||||||||
\(799\) | 10.7881 | 0.381657 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.733574 | −0.0259196 | ||||||||
\(802\) | − 26.3196i | − 0.929378i | ||||||||
\(803\) | 20.9585i | 0.739609i | ||||||||
\(804\) | −9.29210 | −0.327707 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.2380 | −0.466288 | ||||||||
\(807\) | − 13.4929i | − 0.474974i | ||||||||
\(808\) | 11.8454i | 0.416720i | ||||||||
\(809\) | −8.72562 | −0.306777 | −0.153388 | − | 0.988166i | \(-0.549019\pi\) | ||||
−0.153388 | + | 0.988166i | \(0.549019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.2022 | 0.533821 | 0.266911 | − | 0.963721i | \(-0.413997\pi\) | ||||
0.266911 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(812\) | 0.842633i | 0.0295706i | ||||||||
\(813\) | − 26.8135i | − 0.940391i | ||||||||
\(814\) | 50.6365 | 1.77481 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.02469 | 0.0358715 | ||||||||
\(817\) | − 23.8955i | − 0.835997i | ||||||||
\(818\) | 36.7714i | 1.28568i | ||||||||
\(819\) | −19.0797 | −0.666698 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.4595 | 0.574441 | 0.287220 | − | 0.957865i | \(-0.407269\pi\) | ||||
0.287220 | + | 0.957865i | \(0.407269\pi\) | |||||||
\(822\) | − 6.01666i | − 0.209855i | ||||||||
\(823\) | 22.9985i | 0.801676i | 0.916149 | + | 0.400838i | \(0.131281\pi\) | ||||
−0.916149 | + | 0.400838i | \(0.868719\pi\) | |||||||
\(824\) | 7.15084 | 0.249111 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.9785 | −0.729936 | ||||||||
\(827\) | − 24.7319i | − 0.860011i | −0.902826 | − | 0.430006i | \(-0.858512\pi\) | ||||
0.902826 | − | 0.430006i | \(-0.141488\pi\) | |||||||
\(828\) | 1.92827i | 0.0670122i | ||||||||
\(829\) | −20.8634 | −0.724617 | −0.362308 | − | 0.932058i | \(-0.618011\pi\) | ||||
−0.362308 | + | 0.932058i | \(0.618011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.16724 | 0.283318 | ||||||||
\(832\) | − 5.90441i | − 0.204699i | ||||||||
\(833\) | 3.52713i | 0.122208i | ||||||||
\(834\) | 5.62720 | 0.194854 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −23.8894 | −0.826231 | ||||||||
\(837\) | 2.24205i | 0.0774966i | ||||||||
\(838\) | − 31.7245i | − 1.09591i | ||||||||
\(839\) | 23.5963 | 0.814635 | 0.407317 | − | 0.913287i | \(-0.366464\pi\) | ||||
0.407317 | + | 0.913287i | \(0.366464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9320 | −0.997655 | ||||||||
\(842\) | − 8.81726i | − 0.303863i | ||||||||
\(843\) | 31.3418i | 1.07947i | ||||||||
\(844\) | −15.7638 | −0.542613 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.5282 | −0.361966 | ||||||||
\(847\) | − 55.2349i | − 1.89789i | ||||||||
\(848\) | − 2.31107i | − 0.0793625i | ||||||||
\(849\) | 16.3503 | 0.561142 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.4218 | −0.631493 | ||||||||
\(852\) | − 8.53771i | − 0.292497i | ||||||||
\(853\) | − 26.3629i | − 0.902647i | −0.892360 | − | 0.451324i | \(-0.850952\pi\) | ||||
0.892360 | − | 0.451324i | \(-0.149048\pi\) | |||||||
\(854\) | 12.7478 | 0.436220 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.20058 | 0.109394 | ||||||||
\(857\) | 16.0891i | 0.549593i | 0.961502 | + | 0.274797i | \(0.0886105\pi\) | ||||
−0.961502 | + | 0.274797i | \(0.911389\pi\) | |||||||
\(858\) | 31.2951i | 1.06840i | ||||||||
\(859\) | −10.5770 | −0.360882 | −0.180441 | − | 0.983586i | \(-0.557752\pi\) | ||||
−0.180441 | + | 0.983586i | \(0.557752\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.1886 | −1.09699 | ||||||||
\(862\) | − 23.5065i | − 0.800636i | ||||||||
\(863\) | 41.7617i | 1.42158i | 0.703403 | + | 0.710792i | \(0.251663\pi\) | ||||
−0.703403 | + | 0.710792i | \(0.748337\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.40312 | −0.285550 | ||||||||
\(867\) | 15.9500i | 0.541690i | ||||||||
\(868\) | − 7.24502i | − 0.245912i | ||||||||
\(869\) | 70.8721 | 2.40417 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.8644 | 1.85901 | ||||||||
\(872\) | − 9.89555i | − 0.335106i | ||||||||
\(873\) | − 17.2567i | − 0.584050i | ||||||||
\(874\) | 8.69109 | 0.293980 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.95422 | 0.133601 | ||||||||
\(877\) | 31.8267i | 1.07471i | 0.843356 | + | 0.537355i | \(0.180577\pi\) | ||||
−0.843356 | + | 0.537355i | \(0.819423\pi\) | |||||||
\(878\) | 35.6325i | 1.20254i | ||||||||
\(879\) | 28.1867 | 0.950714 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.6324 | −1.67216 | −0.836079 | − | 0.548609i | \(-0.815158\pi\) | ||||
−0.836079 | + | 0.548609i | \(0.815158\pi\) | |||||||
\(882\) | − 3.44213i | − 0.115902i | ||||||||
\(883\) | − 5.06098i | − 0.170316i | −0.996367 | − | 0.0851578i | \(-0.972861\pi\) | ||||
0.996367 | − | 0.0851578i | \(-0.0271394\pi\) | |||||||
\(884\) | −6.05021 | −0.203491 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.79550 | −0.228299 | ||||||||
\(887\) | − 11.0542i | − 0.371164i | −0.982629 | − | 0.185582i | \(-0.940583\pi\) | ||||
0.982629 | − | 0.185582i | \(-0.0594171\pi\) | |||||||
\(888\) | − 9.55354i | − 0.320596i | ||||||||
\(889\) | 29.8936 | 1.00260 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.30029 | 0.177566 | ||||||||
\(892\) | 9.29534i | 0.311231i | ||||||||
\(893\) | 47.4524i | 1.58793i | ||||||||
\(894\) | 11.6556 | 0.389821 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.23143 | 0.107954 | ||||||||
\(897\) | − 11.3853i | − 0.380145i | ||||||||
\(898\) | 8.75011i | 0.291995i | ||||||||
\(899\) | −0.584641 | −0.0194989 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.36814 | −0.0788942 | ||||||||
\(902\) | 52.7968i | 1.75794i | ||||||||
\(903\) | − 17.1319i | − 0.570113i | ||||||||
\(904\) | 4.24575 | 0.141211 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.52354 | 0.183507 | ||||||||
\(907\) | 7.57086i | 0.251386i | 0.992069 | + | 0.125693i | \(0.0401155\pi\) | ||||
−0.992069 | + | 0.125693i | \(0.959885\pi\) | |||||||
\(908\) | − 3.63809i | − 0.120734i | ||||||||
\(909\) | −11.8454 | −0.392887 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.7684 | 1.18506 | 0.592529 | − | 0.805549i | \(-0.298129\pi\) | ||||
0.592529 | + | 0.805549i | \(0.298129\pi\) | |||||||
\(912\) | 4.50718i | 0.149248i | ||||||||
\(913\) | 39.6831i | 1.31332i | ||||||||
\(914\) | −38.1474 | −1.26180 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.93181 | 0.328156 | ||||||||
\(917\) | 15.7208i | 0.519147i | ||||||||
\(918\) | 1.02469i | 0.0338199i | ||||||||
\(919\) | 49.6236 | 1.63693 | 0.818466 | − | 0.574555i | \(-0.194825\pi\) | ||||
0.818466 | + | 0.574555i | \(0.194825\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.5372 | −0.479016 | ||||||||
\(922\) | 1.27077i | 0.0418505i | ||||||||
\(923\) | 50.4101i | 1.65927i | ||||||||
\(924\) | −17.1275 | −0.563453 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.93349 | −0.293573 | ||||||||
\(927\) | 7.15084i | 0.234864i | ||||||||
\(928\) | − 0.260762i | − 0.00855992i | ||||||||
\(929\) | 16.2616 | 0.533527 | 0.266764 | − | 0.963762i | \(-0.414046\pi\) | ||||
0.266764 | + | 0.963762i | \(0.414046\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.5143 | −0.508461 | ||||||||
\(932\) | − 18.7893i | − 0.615465i | ||||||||
\(933\) | 14.4924i | 0.474461i | ||||||||
\(934\) | −5.75682 | −0.188369 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.90441 | 0.192992 | ||||||||
\(937\) | − 0.569874i | − 0.0186170i | −0.999957 | − | 0.00930849i | \(-0.997037\pi\) | ||||
0.999957 | − | 0.00930849i | \(-0.00296303\pi\) | |||||||
\(938\) | 30.0268i | 0.980408i | ||||||||
\(939\) | 31.5288 | 1.02890 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.99538 | 0.228043 | 0.114021 | − | 0.993478i | \(-0.463627\pi\) | ||||
0.114021 | + | 0.993478i | \(0.463627\pi\) | |||||||
\(942\) | 6.84307i | 0.222959i | ||||||||
\(943\) | − 19.2078i | − 0.625491i | ||||||||
\(944\) | 6.49202 | 0.211297 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.1002 | −0.913616 | ||||||||
\(947\) | − 34.4620i | − 1.11987i | −0.828538 | − | 0.559933i | \(-0.810827\pi\) | ||||
0.828538 | − | 0.559933i | \(-0.189173\pi\) | |||||||
\(948\) | − 13.3714i | − 0.434282i | ||||||||
\(949\) | −23.3473 | −0.757886 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.9810 | −0.485794 | ||||||||
\(952\) | − 3.31122i | − 0.107317i | ||||||||
\(953\) | 42.0363i | 1.36169i | 0.732427 | + | 0.680845i | \(0.238387\pi\) | ||||
−0.732427 | + | 0.680845i | \(0.761613\pi\) | |||||||
\(954\) | 2.31107 | 0.0748237 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.75186 | −0.315398 | ||||||||
\(957\) | 1.38211i | 0.0446773i | ||||||||
\(958\) | − 4.63051i | − 0.149605i | ||||||||
\(959\) | −19.4424 | −0.627828 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.9732 | −0.837846 | ||||||||
\(962\) | 56.4080i | 1.81867i | ||||||||
\(963\) | 3.20058i | 0.103137i | ||||||||
\(964\) | −18.9211 | −0.609407 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.23108 | 0.200482 | ||||||||
\(967\) | 11.9686i | 0.384885i | 0.981308 | + | 0.192443i | \(0.0616410\pi\) | ||||
−0.981308 | + | 0.192443i | \(0.938359\pi\) | |||||||
\(968\) | 17.0930i | 0.549391i | ||||||||
\(969\) | 4.61848 | 0.148367 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.35194 | 0.0433858 | 0.0216929 | − | 0.999765i | \(-0.493094\pi\) | ||||
0.0216929 | + | 0.999765i | \(0.493094\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | − 18.1839i | − 0.582949i | ||||||||
\(974\) | 15.9235 | 0.510223 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.94494 | −0.126274 | ||||||||
\(977\) | − 18.5448i | − 0.593300i | −0.954986 | − | 0.296650i | \(-0.904131\pi\) | ||||
0.954986 | − | 0.296650i | \(-0.0958695\pi\) | |||||||
\(978\) | − 9.38717i | − 0.300169i | ||||||||
\(979\) | 3.88815 | 0.124266 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.89555 | 0.315941 | ||||||||
\(982\) | 6.38076i | 0.203618i | ||||||||
\(983\) | − 16.3821i | − 0.522508i | −0.965270 | − | 0.261254i | \(-0.915864\pi\) | ||||
0.965270 | − | 0.261254i | \(-0.0841360\pi\) | |||||||
\(984\) | 9.96112 | 0.317549 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.267201 | −0.00850941 | ||||||||
\(987\) | 34.0210i | 1.08290i | ||||||||
\(988\) | − 26.6123i | − 0.846649i | ||||||||
\(989\) | 10.2230 | 0.325073 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.8303 | 0.629930 | 0.314965 | − | 0.949103i | \(-0.398007\pi\) | ||||
0.314965 | + | 0.949103i | \(0.398007\pi\) | |||||||
\(992\) | 2.24205i | 0.0711851i | ||||||||
\(993\) | − 21.6174i | − 0.686007i | ||||||||
\(994\) | −27.5890 | −0.875070 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.48698 | 0.237234 | ||||||||
\(997\) | 10.4675i | 0.331508i | 0.986167 | + | 0.165754i | \(0.0530057\pi\) | ||||
−0.986167 | + | 0.165754i | \(0.946994\pi\) | |||||||
\(998\) | 12.9135i | 0.408769i | ||||||||
\(999\) | 9.55354 | 0.302261 |
(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 | 3750.2.c.k.1249.2 | 16 | ||
5.2 | odd | 4 | 3750.2.a.v.1.7 | 8 | |||
5.3 | odd | 4 | 3750.2.a.u.1.2 | 8 | |||
5.4 | even | 2 | inner | 3750.2.c.k.1249.15 | 16 | ||
25.2 | odd | 20 | 750.2.g.f.601.4 | 16 | |||
25.9 | even | 10 | 750.2.h.d.349.2 | 16 | |||
25.11 | even | 5 | 750.2.h.d.649.1 | 16 | |||
25.12 | odd | 20 | 750.2.g.f.151.4 | 16 | |||
25.13 | odd | 20 | 750.2.g.g.151.1 | 16 | |||
25.14 | even | 10 | 150.2.h.b.79.3 | yes | 16 | ||
25.16 | even | 5 | 150.2.h.b.19.3 | ✓ | 16 | ||
25.23 | odd | 20 | 750.2.g.g.601.1 | 16 | |||
75.14 | odd | 10 | 450.2.l.c.379.2 | 16 | |||
75.41 | odd | 10 | 450.2.l.c.19.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.h.b.19.3 | ✓ | 16 | 25.16 | even | 5 | ||
150.2.h.b.79.3 | yes | 16 | 25.14 | even | 10 | ||
450.2.l.c.19.2 | 16 | 75.41 | odd | 10 | |||
450.2.l.c.379.2 | 16 | 75.14 | odd | 10 | |||
750.2.g.f.151.4 | 16 | 25.12 | odd | 20 | |||
750.2.g.f.601.4 | 16 | 25.2 | odd | 20 | |||
750.2.g.g.151.1 | 16 | 25.13 | odd | 20 | |||
750.2.g.g.601.1 | 16 | 25.23 | odd | 20 | |||
750.2.h.d.349.2 | 16 | 25.9 | even | 10 | |||
750.2.h.d.649.1 | 16 | 25.11 | even | 5 | |||
3750.2.a.u.1.2 | 8 | 5.3 | odd | 4 | |||
3750.2.a.v.1.7 | 8 | 5.2 | odd | 4 | |||
3750.2.c.k.1249.2 | 16 | 1.1 | even | 1 | trivial | ||
3750.2.c.k.1249.15 | 16 | 5.4 | even | 2 | inner |