Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.a (trivial) |
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: | yes |
Analytic conductor: | \(60.8699614608\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 22x^{10} + 181x^{8} - 692x^{6} + 1240x^{4} - 936x^{2} + 244 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.79401\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.79401 | −1.97566 | −0.987832 | − | 0.155524i | \(-0.950293\pi\) | ||||
−0.987832 | + | 0.155524i | \(0.950293\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.80650 | 2.90325 | ||||||||
\(5\) | −1.62657 | −0.727423 | −0.363712 | − | 0.931512i | \(-0.618491\pi\) | ||||
−0.363712 | + | 0.931512i | \(0.618491\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −10.6354 | −3.76018 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.54465 | 1.43714 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.23267 | 1.72863 | 0.864316 | − | 0.502949i | \(-0.167752\pi\) | ||||
0.864316 | + | 0.502949i | \(0.167752\pi\) | |||||||
\(14\) | −2.79401 | −0.746731 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18.1024 | 4.52560 | ||||||||
\(17\) | 6.00681 | 1.45687 | 0.728433 | − | 0.685117i | \(-0.240249\pi\) | ||||
0.728433 | + | 0.685117i | \(0.240249\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.305878 | −0.0701733 | −0.0350866 | − | 0.999384i | \(-0.511171\pi\) | ||||
−0.0350866 | + | 0.999384i | \(0.511171\pi\) | |||||||
\(20\) | −9.44466 | −2.11189 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.84138 | −1.63504 | −0.817521 | − | 0.575899i | \(-0.804652\pi\) | ||||
−0.817521 | + | 0.575899i | \(0.804652\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.35428 | −0.470855 | ||||||||
\(26\) | −17.4141 | −3.41520 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.80650 | 1.09732 | ||||||||
\(29\) | 2.94628 | 0.547111 | 0.273555 | − | 0.961856i | \(-0.411800\pi\) | ||||
0.273555 | + | 0.961856i | \(0.411800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.31322 | −0.954282 | −0.477141 | − | 0.878827i | \(-0.658327\pi\) | ||||
−0.477141 | + | 0.878827i | \(0.658327\pi\) | |||||||
\(32\) | −29.3076 | −5.18089 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.7831 | −2.87828 | ||||||||
\(35\) | −1.62657 | −0.274940 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.41825 | −1.05515 | −0.527577 | − | 0.849507i | \(-0.676899\pi\) | ||||
−0.527577 | + | 0.849507i | \(0.676899\pi\) | |||||||
\(38\) | 0.854627 | 0.138639 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 17.2992 | 2.73524 | ||||||||
\(41\) | 4.04048 | 0.631016 | 0.315508 | − | 0.948923i | \(-0.397825\pi\) | ||||
0.315508 | + | 0.948923i | \(0.397825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.640934 | 0.0977416 | 0.0488708 | − | 0.998805i | \(-0.484438\pi\) | ||||
0.0488708 | + | 0.998805i | \(0.484438\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 21.9089 | 3.23029 | ||||||||
\(47\) | 7.86467 | 1.14718 | 0.573590 | − | 0.819142i | \(-0.305550\pi\) | ||||
0.573590 | + | 0.819142i | \(0.305550\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.57787 | 0.930251 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 36.1900 | 5.01865 | ||||||||
\(53\) | 0.251121 | 0.0344941 | 0.0172471 | − | 0.999851i | \(-0.494510\pi\) | ||||
0.0172471 | + | 0.999851i | \(0.494510\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.6354 | −1.42121 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.23194 | −1.08091 | ||||||||
\(59\) | 5.46616 | 0.711634 | 0.355817 | − | 0.934556i | \(-0.384203\pi\) | ||||
0.355817 | + | 0.934556i | \(0.384203\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.45477 | −0.314301 | −0.157151 | − | 0.987575i | \(-0.550231\pi\) | ||||
−0.157151 | + | 0.987575i | \(0.550231\pi\) | |||||||
\(62\) | 14.8452 | 1.88534 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 45.6808 | 5.71010 | ||||||||
\(65\) | −10.1379 | −1.25745 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.54902 | 0.800090 | 0.400045 | − | 0.916496i | \(-0.368995\pi\) | ||||
0.400045 | + | 0.916496i | \(0.368995\pi\) | |||||||
\(68\) | 34.8785 | 4.22964 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.54465 | 0.543190 | ||||||||
\(71\) | 5.61219 | 0.666045 | 0.333022 | − | 0.942919i | \(-0.391932\pi\) | ||||
0.333022 | + | 0.942919i | \(0.391932\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4714 | 1.22559 | 0.612795 | − | 0.790242i | \(-0.290045\pi\) | ||||
0.612795 | + | 0.790242i | \(0.290045\pi\) | |||||||
\(74\) | 17.9327 | 2.08463 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.77608 | −0.203731 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.16047 | −0.805616 | −0.402808 | − | 0.915285i | \(-0.631966\pi\) | ||||
−0.402808 | + | 0.915285i | \(0.631966\pi\) | |||||||
\(80\) | −29.4448 | −3.29203 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.2891 | −1.24668 | ||||||||
\(83\) | 11.7565 | 1.29045 | 0.645224 | − | 0.763993i | \(-0.276764\pi\) | ||||
0.645224 | + | 0.763993i | \(0.276764\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.77049 | −1.05976 | ||||||||
\(86\) | −1.79078 | −0.193104 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.59605 | 1.01718 | 0.508590 | − | 0.861009i | \(-0.330167\pi\) | ||||
0.508590 | + | 0.861009i | \(0.330167\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.23267 | 0.653361 | ||||||||
\(92\) | −45.5310 | −4.74693 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.9740 | −2.26644 | ||||||||
\(95\) | 0.497532 | 0.0510457 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0963 | 1.63433 | 0.817167 | − | 0.576402i | \(-0.195544\pi\) | ||||
0.817167 | + | 0.576402i | \(0.195544\pi\) | |||||||
\(98\) | −2.79401 | −0.282238 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.6701 | −1.36701 | ||||||||
\(101\) | −11.2701 | −1.12141 | −0.560707 | − | 0.828014i | \(-0.689471\pi\) | ||||
−0.560707 | + | 0.828014i | \(0.689471\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.7879 | −1.26003 | −0.630014 | − | 0.776584i | \(-0.716951\pi\) | ||||
−0.630014 | + | 0.776584i | \(0.716951\pi\) | |||||||
\(104\) | −66.2869 | −6.49997 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.701635 | −0.0681488 | ||||||||
\(107\) | −7.68911 | −0.743335 | −0.371667 | − | 0.928366i | \(-0.621214\pi\) | ||||
−0.371667 | + | 0.928366i | \(0.621214\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1634 | −1.45239 | −0.726196 | − | 0.687487i | \(-0.758714\pi\) | ||||
−0.726196 | + | 0.687487i | \(0.758714\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 18.1024 | 1.71052 | ||||||||
\(113\) | 1.50471 | 0.141551 | 0.0707756 | − | 0.997492i | \(-0.477453\pi\) | ||||
0.0707756 | + | 0.997492i | \(0.477453\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.7545 | 1.18937 | ||||||||
\(116\) | 17.1076 | 1.58840 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.2725 | −1.40595 | ||||||||
\(119\) | 6.00681 | 0.550644 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.85866 | 0.620954 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −30.8512 | −2.77052 | ||||||||
\(125\) | 11.9622 | 1.06993 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.93093 | 0.171342 | 0.0856710 | − | 0.996323i | \(-0.472697\pi\) | ||||
0.0856710 | + | 0.996323i | \(0.472697\pi\) | |||||||
\(128\) | −69.0176 | −6.10035 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 28.3253 | 2.48429 | ||||||||
\(131\) | 12.7038 | 1.10993 | 0.554966 | − | 0.831873i | \(-0.312731\pi\) | ||||
0.554966 | + | 0.831873i | \(0.312731\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.305878 | −0.0265230 | ||||||||
\(134\) | −18.2980 | −1.58071 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −63.8848 | −5.47808 | ||||||||
\(137\) | 0.345262 | 0.0294977 | 0.0147489 | − | 0.999891i | \(-0.495305\pi\) | ||||
0.0147489 | + | 0.999891i | \(0.495305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.0710 | 1.61758 | 0.808790 | − | 0.588097i | \(-0.200123\pi\) | ||||
0.808790 | + | 0.588097i | \(0.200123\pi\) | |||||||
\(140\) | −9.44466 | −0.798220 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.6805 | −1.31588 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.79233 | −0.397981 | ||||||||
\(146\) | −29.2573 | −2.42135 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −37.2676 | −3.06338 | ||||||||
\(149\) | 6.46872 | 0.529938 | 0.264969 | − | 0.964257i | \(-0.414638\pi\) | ||||
0.264969 | + | 0.964257i | \(0.414638\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.36030 | −0.354837 | −0.177418 | − | 0.984136i | \(-0.556775\pi\) | ||||
−0.177418 | + | 0.984136i | \(0.556775\pi\) | |||||||
\(152\) | 3.25314 | 0.263864 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.64231 | 0.694167 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.03397 | −0.481563 | −0.240782 | − | 0.970579i | \(-0.577404\pi\) | ||||
−0.240782 | + | 0.970579i | \(0.577404\pi\) | |||||||
\(158\) | 20.0064 | 1.59163 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 47.6708 | 3.76870 | ||||||||
\(161\) | −7.84138 | −0.617988 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.5925 | −1.37795 | −0.688974 | − | 0.724786i | \(-0.741939\pi\) | ||||
−0.688974 | + | 0.724786i | \(0.741939\pi\) | |||||||
\(164\) | 23.4610 | 1.83200 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −32.8479 | −2.54949 | ||||||||
\(167\) | −0.870792 | −0.0673839 | −0.0336920 | − | 0.999432i | \(-0.510727\pi\) | ||||
−0.0336920 | + | 0.999432i | \(0.510727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.8462 | 1.98817 | ||||||||
\(170\) | 27.2989 | 2.09373 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.72158 | 0.283768 | ||||||||
\(173\) | −0.432174 | −0.0328576 | −0.0164288 | − | 0.999865i | \(-0.505230\pi\) | ||||
−0.0164288 | + | 0.999865i | \(0.505230\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.35428 | −0.177966 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −26.8115 | −2.00960 | ||||||||
\(179\) | −7.87633 | −0.588705 | −0.294352 | − | 0.955697i | \(-0.595104\pi\) | ||||
−0.294352 | + | 0.955697i | \(0.595104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7505 | 1.02207 | 0.511035 | − | 0.859560i | \(-0.329262\pi\) | ||||
0.511035 | + | 0.859560i | \(0.329262\pi\) | |||||||
\(182\) | −17.4141 | −1.29082 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 83.3962 | 6.14805 | ||||||||
\(185\) | 10.4397 | 0.767544 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 45.6662 | 3.33055 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.39011 | −0.100849 | ||||||||
\(191\) | −27.2449 | −1.97137 | −0.985685 | − | 0.168597i | \(-0.946076\pi\) | ||||
−0.985685 | + | 0.168597i | \(0.946076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4927 | 1.47510 | 0.737548 | − | 0.675294i | \(-0.235983\pi\) | ||||
0.737548 | + | 0.675294i | \(0.235983\pi\) | |||||||
\(194\) | −44.9733 | −3.22889 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.80650 | 0.414750 | ||||||||
\(197\) | −12.5543 | −0.894455 | −0.447227 | − | 0.894420i | \(-0.647589\pi\) | ||||
−0.447227 | + | 0.894420i | \(0.647589\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.65670 | 0.400993 | 0.200497 | − | 0.979694i | \(-0.435744\pi\) | ||||
0.200497 | + | 0.979694i | \(0.435744\pi\) | |||||||
\(200\) | 25.0387 | 1.77050 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 31.4887 | 2.21554 | ||||||||
\(203\) | 2.94628 | 0.206788 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.57211 | −0.459016 | ||||||||
\(206\) | 35.7295 | 2.48939 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 112.826 | 7.82310 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.86223 | 0.678944 | 0.339472 | − | 0.940616i | \(-0.389752\pi\) | ||||
0.339472 | + | 0.940616i | \(0.389752\pi\) | |||||||
\(212\) | 1.45813 | 0.100145 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 21.4835 | 1.46858 | ||||||||
\(215\) | −1.04252 | −0.0710995 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.31322 | −0.360685 | ||||||||
\(218\) | 42.3668 | 2.86944 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 37.4385 | 2.51838 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4235 | −0.831936 | −0.415968 | − | 0.909379i | \(-0.636557\pi\) | ||||
−0.415968 | + | 0.909379i | \(0.636557\pi\) | |||||||
\(224\) | −29.3076 | −1.95819 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.20418 | −0.279658 | ||||||||
\(227\) | −8.47261 | −0.562347 | −0.281173 | − | 0.959657i | \(-0.590724\pi\) | ||||
−0.281173 | + | 0.959657i | \(0.590724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.0760 | −0.731920 | −0.365960 | − | 0.930631i | \(-0.619259\pi\) | ||||
−0.365960 | + | 0.930631i | \(0.619259\pi\) | |||||||
\(230\) | −35.6363 | −2.34979 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −31.3349 | −2.05723 | ||||||||
\(233\) | 7.59103 | 0.497305 | 0.248652 | − | 0.968593i | \(-0.420012\pi\) | ||||
0.248652 | + | 0.968593i | \(0.420012\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.7924 | −0.834486 | ||||||||
\(236\) | 31.7393 | 2.06605 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −16.7831 | −1.08789 | ||||||||
\(239\) | −27.8021 | −1.79837 | −0.899184 | − | 0.437571i | \(-0.855839\pi\) | ||||
−0.899184 | + | 0.437571i | \(0.855839\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.242223 | 0.0156030 | 0.00780149 | − | 0.999970i | \(-0.497517\pi\) | ||||
0.00780149 | + | 0.999970i | \(0.497517\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.2536 | −0.912495 | ||||||||
\(245\) | −1.62657 | −0.103918 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.90644 | −0.121304 | ||||||||
\(248\) | 56.5082 | 3.58827 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −33.4226 | −2.11383 | ||||||||
\(251\) | −18.0334 | −1.13826 | −0.569130 | − | 0.822247i | \(-0.692720\pi\) | ||||
−0.569130 | + | 0.822247i | \(0.692720\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.39503 | −0.338514 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 101.474 | 6.34214 | ||||||||
\(257\) | 8.27384 | 0.516108 | 0.258054 | − | 0.966131i | \(-0.416919\pi\) | ||||
0.258054 | + | 0.966131i | \(0.416919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.41825 | −0.398811 | ||||||||
\(260\) | −58.8655 | −3.65068 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −35.4944 | −2.19285 | ||||||||
\(263\) | 3.42958 | 0.211477 | 0.105738 | − | 0.994394i | \(-0.466279\pi\) | ||||
0.105738 | + | 0.994394i | \(0.466279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.408466 | −0.0250918 | ||||||||
\(266\) | 0.854627 | 0.0524006 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 38.0268 | 2.32286 | ||||||||
\(269\) | 10.4629 | 0.637934 | 0.318967 | − | 0.947766i | \(-0.396664\pi\) | ||||
0.318967 | + | 0.947766i | \(0.396664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.4886 | −1.36608 | −0.683042 | − | 0.730380i | \(-0.739343\pi\) | ||||
−0.683042 | + | 0.730380i | \(0.739343\pi\) | |||||||
\(272\) | 108.738 | 6.59320 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.964666 | −0.0582776 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.0639 | 0.965188 | 0.482594 | − | 0.875844i | \(-0.339695\pi\) | ||||
0.482594 | + | 0.875844i | \(0.339695\pi\) | |||||||
\(278\) | −53.2846 | −3.19580 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 17.2992 | 1.03382 | ||||||||
\(281\) | −9.57248 | −0.571046 | −0.285523 | − | 0.958372i | \(-0.592167\pi\) | ||||
−0.285523 | + | 0.958372i | \(0.592167\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.2182 | 0.726296 | 0.363148 | − | 0.931731i | \(-0.381702\pi\) | ||||
0.363148 | + | 0.931731i | \(0.381702\pi\) | |||||||
\(284\) | 32.5872 | 1.93369 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.04048 | 0.238502 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0818 | 1.12246 | ||||||||
\(290\) | 13.3898 | 0.786277 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 60.8024 | 3.55819 | ||||||||
\(293\) | 30.0285 | 1.75428 | 0.877142 | − | 0.480232i | \(-0.159447\pi\) | ||||
0.877142 | + | 0.480232i | \(0.159447\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.89109 | −0.517659 | ||||||||
\(296\) | 68.2607 | 3.96757 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.0737 | −1.04698 | ||||||||
\(299\) | −48.8728 | −2.82638 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.640934 | 0.0369428 | ||||||||
\(302\) | 12.1827 | 0.701038 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.53714 | −0.317577 | ||||||||
\(305\) | 3.99285 | 0.228630 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.5503 | 1.00165 | 0.500825 | − | 0.865549i | \(-0.333030\pi\) | ||||
0.500825 | + | 0.865549i | \(0.333030\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24.1467 | −1.37144 | ||||||||
\(311\) | −17.9991 | −1.02063 | −0.510317 | − | 0.859986i | \(-0.670472\pi\) | ||||
−0.510317 | + | 0.859986i | \(0.670472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.1718 | −1.47932 | −0.739659 | − | 0.672982i | \(-0.765013\pi\) | ||||
−0.739659 | + | 0.672982i | \(0.765013\pi\) | |||||||
\(314\) | 16.8590 | 0.951408 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −41.5772 | −2.33890 | ||||||||
\(317\) | −12.2998 | −0.690824 | −0.345412 | − | 0.938451i | \(-0.612261\pi\) | ||||
−0.345412 | + | 0.938451i | \(0.612261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −74.3030 | −4.15366 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 21.9089 | 1.22094 | ||||||||
\(323\) | −1.83735 | −0.102233 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.6734 | −0.813935 | ||||||||
\(326\) | 49.1536 | 2.72236 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −42.9721 | −2.37274 | ||||||||
\(329\) | 7.86467 | 0.433593 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.1006 | 0.555177 | 0.277589 | − | 0.960700i | \(-0.410465\pi\) | ||||
0.277589 | + | 0.960700i | \(0.410465\pi\) | |||||||
\(332\) | 68.2643 | 3.74649 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.43300 | 0.133128 | ||||||||
\(335\) | −10.6524 | −0.582004 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.1452 | 1.20633 | 0.603163 | − | 0.797618i | \(-0.293907\pi\) | ||||
0.603163 | + | 0.797618i | \(0.293907\pi\) | |||||||
\(338\) | −72.2145 | −3.92795 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −56.7323 | −3.07674 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −6.81659 | −0.367526 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.20750 | 0.0649156 | ||||||||
\(347\) | 10.5620 | 0.567000 | 0.283500 | − | 0.958972i | \(-0.408504\pi\) | ||||
0.283500 | + | 0.958972i | \(0.408504\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.188962 | −0.0101149 | −0.00505746 | − | 0.999987i | \(-0.501610\pi\) | ||||
−0.00505746 | + | 0.999987i | \(0.501610\pi\) | |||||||
\(350\) | 6.57787 | 0.351602 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.2121 | 1.76770 | 0.883851 | − | 0.467768i | \(-0.154942\pi\) | ||||
0.883851 | + | 0.467768i | \(0.154942\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.12862 | −0.484497 | ||||||||
\(356\) | 55.7194 | 2.95312 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.0066 | 1.16308 | ||||||||
\(359\) | 24.7059 | 1.30393 | 0.651965 | − | 0.758249i | \(-0.273945\pi\) | ||||
0.651965 | + | 0.758249i | \(0.273945\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9064 | −0.995076 | ||||||||
\(362\) | −38.4192 | −2.01927 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 36.1900 | 1.89687 | ||||||||
\(365\) | −17.0325 | −0.891523 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.563769 | 0.0294285 | 0.0147143 | − | 0.999892i | \(-0.495316\pi\) | ||||
0.0147143 | + | 0.999892i | \(0.495316\pi\) | |||||||
\(368\) | −141.948 | −7.39955 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −29.1687 | −1.51641 | ||||||||
\(371\) | 0.251121 | 0.0130376 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.5228 | −0.959073 | −0.479536 | − | 0.877522i | \(-0.659195\pi\) | ||||
−0.479536 | + | 0.877522i | \(0.659195\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −83.6439 | −4.31361 | ||||||||
\(377\) | 18.3632 | 0.945753 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.2210 | −1.14141 | −0.570707 | − | 0.821153i | \(-0.693331\pi\) | ||||
−0.570707 | + | 0.821153i | \(0.693331\pi\) | |||||||
\(380\) | 2.88892 | 0.148198 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 76.1225 | 3.89477 | ||||||||
\(383\) | 27.3023 | 1.39508 | 0.697540 | − | 0.716546i | \(-0.254278\pi\) | ||||
0.697540 | + | 0.716546i | \(0.254278\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −57.2568 | −2.91430 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 93.4632 | 4.74488 | ||||||||
\(389\) | −27.9317 | −1.41620 | −0.708098 | − | 0.706115i | \(-0.750446\pi\) | ||||
−0.708098 | + | 0.706115i | \(0.750446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −47.1017 | −2.38204 | ||||||||
\(392\) | −10.6354 | −0.537169 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 35.0768 | 1.76714 | ||||||||
\(395\) | 11.6470 | 0.586024 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.0029 | 0.752975 | 0.376488 | − | 0.926422i | \(-0.377132\pi\) | ||||
0.376488 | + | 0.926422i | \(0.377132\pi\) | |||||||
\(398\) | −15.8049 | −0.792227 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −42.6181 | −2.13090 | ||||||||
\(401\) | 28.5554 | 1.42599 | 0.712996 | − | 0.701169i | \(-0.247338\pi\) | ||||
0.712996 | + | 0.701169i | \(0.247338\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.1155 | −1.64960 | ||||||||
\(404\) | −65.4397 | −3.25575 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.23194 | −0.408544 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.6910 | 1.17145 | 0.585723 | − | 0.810511i | \(-0.300810\pi\) | ||||
0.585723 | + | 0.810511i | \(0.300810\pi\) | |||||||
\(410\) | 18.3626 | 0.906862 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −74.2528 | −3.65817 | ||||||||
\(413\) | 5.46616 | 0.268972 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.1228 | −0.938702 | ||||||||
\(416\) | −182.664 | −8.95586 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.47054 | 0.218400 | 0.109200 | − | 0.994020i | \(-0.465171\pi\) | ||||
0.109200 | + | 0.994020i | \(0.465171\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7968 | 0.672416 | 0.336208 | − | 0.941788i | \(-0.390856\pi\) | ||||
0.336208 | + | 0.941788i | \(0.390856\pi\) | |||||||
\(422\) | −27.5552 | −1.34137 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.67077 | −0.129704 | ||||||||
\(425\) | −14.1417 | −0.685973 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.45477 | −0.118795 | ||||||||
\(428\) | −44.6468 | −2.15809 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.91282 | 0.140469 | ||||||||
\(431\) | −20.1019 | −0.968275 | −0.484137 | − | 0.874992i | \(-0.660866\pi\) | ||||
−0.484137 | + | 0.874992i | \(0.660866\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.4237 | −0.645103 | −0.322552 | − | 0.946552i | \(-0.604541\pi\) | ||||
−0.322552 | + | 0.946552i | \(0.604541\pi\) | |||||||
\(434\) | 14.8452 | 0.712592 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −88.0464 | −4.21666 | ||||||||
\(437\) | 2.39851 | 0.114736 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.3166 | 1.20829 | 0.604147 | − | 0.796873i | \(-0.293514\pi\) | ||||
0.604147 | + | 0.796873i | \(0.293514\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −104.604 | −4.97548 | ||||||||
\(443\) | 14.9425 | 0.709939 | 0.354970 | − | 0.934878i | \(-0.384491\pi\) | ||||
0.354970 | + | 0.934878i | \(0.384491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.6086 | −0.739920 | ||||||||
\(446\) | 34.7113 | 1.64363 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 45.6808 | 2.15822 | ||||||||
\(449\) | −32.4752 | −1.53260 | −0.766300 | − | 0.642482i | \(-0.777905\pi\) | ||||
−0.766300 | + | 0.642482i | \(0.777905\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 8.73709 | 0.410958 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 23.6726 | 1.11101 | ||||||||
\(455\) | −10.1379 | −0.475270 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.97016 | 0.0921603 | 0.0460802 | − | 0.998938i | \(-0.485327\pi\) | ||||
0.0460802 | + | 0.998938i | \(0.485327\pi\) | |||||||
\(458\) | 30.9464 | 1.44603 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 74.0593 | 3.45303 | ||||||||
\(461\) | −31.8240 | −1.48219 | −0.741095 | − | 0.671400i | \(-0.765693\pi\) | ||||
−0.741095 | + | 0.671400i | \(0.765693\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.1084 | 0.516250 | 0.258125 | − | 0.966112i | \(-0.416895\pi\) | ||||
0.258125 | + | 0.966112i | \(0.416895\pi\) | |||||||
\(464\) | 53.3348 | 2.47601 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.2094 | −0.982507 | ||||||||
\(467\) | 27.2112 | 1.25918 | 0.629592 | − | 0.776926i | \(-0.283222\pi\) | ||||
0.629592 | + | 0.776926i | \(0.283222\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.54902 | 0.302405 | ||||||||
\(470\) | 35.7422 | 1.64866 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −58.1348 | −2.67587 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.720122 | 0.0330415 | ||||||||
\(476\) | 34.8785 | 1.59866 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 77.6793 | 3.55297 | ||||||||
\(479\) | 13.3861 | 0.611626 | 0.305813 | − | 0.952092i | \(-0.401072\pi\) | ||||
0.305813 | + | 0.952092i | \(0.401072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.0029 | −1.82397 | ||||||||
\(482\) | −0.676775 | −0.0308262 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.1818 | −1.18885 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.2741 | 0.782762 | 0.391381 | − | 0.920229i | \(-0.371997\pi\) | ||||
0.391381 | + | 0.920229i | \(0.371997\pi\) | |||||||
\(488\) | 26.1075 | 1.18183 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.54465 | 0.205306 | ||||||||
\(491\) | −2.45742 | −0.110902 | −0.0554510 | − | 0.998461i | \(-0.517660\pi\) | ||||
−0.0554510 | + | 0.998461i | \(0.517660\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.6978 | 0.797067 | ||||||||
\(494\) | 5.32661 | 0.239656 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −96.1821 | −4.31870 | ||||||||
\(497\) | 5.61219 | 0.251741 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.5539 | −0.741055 | −0.370527 | − | 0.928822i | \(-0.620823\pi\) | ||||
−0.370527 | + | 0.928822i | \(0.620823\pi\) | |||||||
\(500\) | 69.4587 | 3.10629 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 50.3856 | 2.24882 | ||||||||
\(503\) | −2.75734 | −0.122944 | −0.0614718 | − | 0.998109i | \(-0.519579\pi\) | ||||
−0.0614718 | + | 0.998109i | \(0.519579\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.3316 | 0.815743 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.2119 | 0.497449 | ||||||||
\(509\) | 32.6055 | 1.44522 | 0.722608 | − | 0.691258i | \(-0.242943\pi\) | ||||
0.722608 | + | 0.691258i | \(0.242943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.4714 | 0.463229 | ||||||||
\(512\) | −145.485 | −6.42959 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −23.1172 | −1.01966 | ||||||||
\(515\) | 20.8004 | 0.916574 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 17.9327 | 0.787916 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 107.820 | 4.72823 | ||||||||
\(521\) | 5.53662 | 0.242564 | 0.121282 | − | 0.992618i | \(-0.461300\pi\) | ||||
0.121282 | + | 0.992618i | \(0.461300\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.800091 | −0.0349856 | −0.0174928 | − | 0.999847i | \(-0.505568\pi\) | ||||
−0.0174928 | + | 0.999847i | \(0.505568\pi\) | |||||||
\(524\) | 73.7644 | 3.22241 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.58228 | −0.417807 | ||||||||
\(527\) | −31.9155 | −1.39026 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 38.4873 | 1.67336 | ||||||||
\(530\) | 1.14126 | 0.0495730 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.77608 | −0.0770029 | ||||||||
\(533\) | 25.1830 | 1.09079 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.5069 | 0.540719 | ||||||||
\(536\) | −69.6514 | −3.00848 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.2335 | −1.26034 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.0294 | 1.46304 | 0.731519 | − | 0.681821i | \(-0.238812\pi\) | ||||
0.731519 | + | 0.681821i | \(0.238812\pi\) | |||||||
\(542\) | 62.8333 | 2.69892 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −176.045 | −7.54787 | ||||||||
\(545\) | 24.6643 | 1.05650 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.2897 | 1.12406 | 0.562032 | − | 0.827115i | \(-0.310020\pi\) | ||||
0.562032 | + | 0.827115i | \(0.310020\pi\) | |||||||
\(548\) | 2.00476 | 0.0856392 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.901203 | −0.0383926 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.16047 | −0.304494 | ||||||||
\(554\) | −44.8828 | −1.90689 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 110.736 | 4.69624 | ||||||||
\(557\) | 15.3838 | 0.651832 | 0.325916 | − | 0.945399i | \(-0.394327\pi\) | ||||
0.325916 | + | 0.945399i | \(0.394327\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.99473 | 0.168959 | ||||||||
\(560\) | −29.4448 | −1.24427 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.7456 | 1.12820 | ||||||||
\(563\) | 3.55750 | 0.149931 | 0.0749654 | − | 0.997186i | \(-0.476115\pi\) | ||||
0.0749654 | + | 0.997186i | \(0.476115\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.44751 | −0.102968 | ||||||||
\(566\) | −34.1378 | −1.43492 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −59.6879 | −2.50445 | ||||||||
\(569\) | −4.30125 | −0.180318 | −0.0901590 | − | 0.995927i | \(-0.528738\pi\) | ||||
−0.0901590 | + | 0.995927i | \(0.528738\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.8296 | 0.871692 | 0.435846 | − | 0.900021i | \(-0.356449\pi\) | ||||
0.435846 | + | 0.900021i | \(0.356449\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.2891 | −0.471199 | ||||||||
\(575\) | 18.4608 | 0.769868 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.5025 | −1.18657 | −0.593287 | − | 0.804991i | \(-0.702170\pi\) | ||||
−0.593287 | + | 0.804991i | \(0.702170\pi\) | |||||||
\(578\) | −53.3147 | −2.21760 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −27.8266 | −1.15544 | ||||||||
\(581\) | 11.7565 | 0.487744 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −111.368 | −4.60844 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −83.9000 | −3.46588 | ||||||||
\(587\) | −18.1401 | −0.748721 | −0.374360 | − | 0.927283i | \(-0.622138\pi\) | ||||
−0.374360 | + | 0.927283i | \(0.622138\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.62520 | 0.0669651 | ||||||||
\(590\) | 24.8418 | 1.02272 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −116.186 | −4.77521 | ||||||||
\(593\) | 28.2014 | 1.15809 | 0.579047 | − | 0.815294i | \(-0.303425\pi\) | ||||
0.579047 | + | 0.815294i | \(0.303425\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.77049 | −0.400551 | ||||||||
\(596\) | 37.5606 | 1.53854 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 136.551 | 5.58399 | ||||||||
\(599\) | 3.67415 | 0.150122 | 0.0750608 | − | 0.997179i | \(-0.476085\pi\) | ||||
0.0750608 | + | 0.997179i | \(0.476085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.1861 | −0.537872 | −0.268936 | − | 0.963158i | \(-0.586672\pi\) | ||||
−0.268936 | + | 0.963158i | \(0.586672\pi\) | |||||||
\(602\) | −1.79078 | −0.0729866 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −25.3181 | −1.03018 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.7655 | −0.436958 | −0.218479 | − | 0.975842i | \(-0.570110\pi\) | ||||
−0.218479 | + | 0.975842i | \(0.570110\pi\) | |||||||
\(608\) | 8.96455 | 0.363560 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.1561 | −0.451696 | ||||||||
\(611\) | 49.0179 | 1.98305 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.9610 | 0.483100 | 0.241550 | − | 0.970388i | \(-0.422344\pi\) | ||||
0.241550 | + | 0.970388i | \(0.422344\pi\) | |||||||
\(614\) | −49.0358 | −1.97892 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.0580 | 0.767247 | 0.383623 | − | 0.923490i | \(-0.374676\pi\) | ||||
0.383623 | + | 0.923490i | \(0.374676\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.8089 | 0.715799 | 0.357900 | − | 0.933760i | \(-0.383493\pi\) | ||||
0.357900 | + | 0.933760i | \(0.383493\pi\) | |||||||
\(620\) | 50.1816 | 2.01534 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 50.2896 | 2.01643 | ||||||||
\(623\) | 9.59605 | 0.384458 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.68601 | −0.307440 | ||||||||
\(626\) | 73.1243 | 2.92263 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −35.0362 | −1.39810 | ||||||||
\(629\) | −38.5532 | −1.53722 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.7960 | −0.827874 | −0.413937 | − | 0.910306i | \(-0.635847\pi\) | ||||
−0.413937 | + | 0.910306i | \(0.635847\pi\) | |||||||
\(632\) | 76.1544 | 3.02926 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 34.3657 | 1.36484 | ||||||||
\(635\) | −3.14078 | −0.124638 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.23267 | 0.246947 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 112.262 | 4.43754 | ||||||||
\(641\) | −35.3225 | −1.39515 | −0.697577 | − | 0.716510i | \(-0.745738\pi\) | ||||
−0.697577 | + | 0.716510i | \(0.745738\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.6899 | 1.32860 | 0.664299 | − | 0.747467i | \(-0.268730\pi\) | ||||
0.664299 | + | 0.747467i | \(0.268730\pi\) | |||||||
\(644\) | −45.5310 | −1.79417 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.13359 | 0.201978 | ||||||||
\(647\) | 28.6950 | 1.12812 | 0.564059 | − | 0.825735i | \(-0.309239\pi\) | ||||
0.564059 | + | 0.825735i | \(0.309239\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 40.9977 | 1.60806 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −102.151 | −4.00053 | ||||||||
\(653\) | −1.07891 | −0.0422212 | −0.0211106 | − | 0.999777i | \(-0.506720\pi\) | ||||
−0.0211106 | + | 0.999777i | \(0.506720\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.6635 | −0.807391 | ||||||||
\(656\) | 73.1424 | 2.85573 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −21.9740 | −0.856635 | ||||||||
\(659\) | 4.07523 | 0.158748 | 0.0793742 | − | 0.996845i | \(-0.474708\pi\) | ||||
0.0793742 | + | 0.996845i | \(0.474708\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.3678 | 0.753321 | 0.376660 | − | 0.926351i | \(-0.377072\pi\) | ||||
0.376660 | + | 0.926351i | \(0.377072\pi\) | |||||||
\(662\) | −28.2211 | −1.09684 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −125.035 | −4.85232 | ||||||||
\(665\) | 0.497532 | 0.0192935 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.1029 | −0.894549 | ||||||||
\(668\) | −5.05625 | −0.195632 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 29.7630 | 1.14984 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.39835 | 0.285185 | 0.142593 | − | 0.989781i | \(-0.454456\pi\) | ||||
0.142593 | + | 0.989781i | \(0.454456\pi\) | |||||||
\(674\) | −61.8740 | −2.38330 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 150.076 | 5.77214 | ||||||||
\(677\) | 17.7449 | 0.681990 | 0.340995 | − | 0.940065i | \(-0.389236\pi\) | ||||
0.340995 | + | 0.940065i | \(0.389236\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.0963 | 0.617720 | ||||||||
\(680\) | 103.913 | 3.98488 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.6595 | −1.32621 | −0.663104 | − | 0.748527i | \(-0.730761\pi\) | ||||
−0.663104 | + | 0.748527i | \(0.730761\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.561592 | −0.0214573 | ||||||||
\(686\) | −2.79401 | −0.106676 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.6025 | 0.442340 | ||||||||
\(689\) | 1.56515 | 0.0596276 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.5107 | 0.399845 | 0.199923 | − | 0.979812i | \(-0.435931\pi\) | ||||
0.199923 | + | 0.979812i | \(0.435931\pi\) | |||||||
\(692\) | −2.50942 | −0.0953938 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.5105 | −1.12020 | ||||||||
\(695\) | −31.0203 | −1.17667 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.2704 | 0.919306 | ||||||||
\(698\) | 0.527963 | 0.0199837 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.6701 | −0.516681 | ||||||||
\(701\) | −28.1203 | −1.06209 | −0.531044 | − | 0.847344i | \(-0.678200\pi\) | ||||
−0.531044 | + | 0.847344i | \(0.678200\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.96320 | 0.0740437 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −92.7950 | −3.49239 | ||||||||
\(707\) | −11.2701 | −0.423855 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.44375 | 0.166889 | 0.0834443 | − | 0.996512i | \(-0.473408\pi\) | ||||
0.0834443 | + | 0.996512i | \(0.473408\pi\) | |||||||
\(710\) | 25.5055 | 0.957203 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −102.058 | −3.82478 | ||||||||
\(713\) | 41.6630 | 1.56029 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −45.7339 | −1.70916 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −69.0286 | −2.57613 | ||||||||
\(719\) | −2.11794 | −0.0789857 | −0.0394929 | − | 0.999220i | \(-0.512574\pi\) | ||||
−0.0394929 | + | 0.999220i | \(0.512574\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.7879 | −0.476246 | ||||||||
\(722\) | 52.8248 | 1.96594 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 79.8425 | 2.96732 | ||||||||
\(725\) | −6.93636 | −0.257610 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.3015 | 0.901292 | 0.450646 | − | 0.892703i | \(-0.351194\pi\) | ||||
0.450646 | + | 0.892703i | \(0.351194\pi\) | |||||||
\(728\) | −66.2869 | −2.45676 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 47.5890 | 1.76135 | ||||||||
\(731\) | 3.84997 | 0.142396 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.14483 | −0.0792212 | −0.0396106 | − | 0.999215i | \(-0.512612\pi\) | ||||
−0.0396106 | + | 0.999215i | \(0.512612\pi\) | |||||||
\(734\) | −1.57518 | −0.0581408 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 229.812 | 8.47098 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.4005 | −1.55973 | −0.779864 | − | 0.625949i | \(-0.784712\pi\) | ||||
−0.779864 | + | 0.625949i | \(0.784712\pi\) | |||||||
\(740\) | 60.6183 | 2.22837 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.701635 | −0.0257578 | ||||||||
\(743\) | 11.5589 | 0.424054 | 0.212027 | − | 0.977264i | \(-0.431994\pi\) | ||||
0.212027 | + | 0.977264i | \(0.431994\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.5218 | −0.385489 | ||||||||
\(746\) | 51.7528 | 1.89481 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.68911 | −0.280954 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.5439 | −0.968602 | −0.484301 | − | 0.874902i | \(-0.660926\pi\) | ||||
−0.484301 | + | 0.874902i | \(0.660926\pi\) | |||||||
\(752\) | 142.370 | 5.19168 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −51.3070 | −1.86849 | ||||||||
\(755\) | 7.09233 | 0.258116 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.32802 | 0.229996 | 0.114998 | − | 0.993366i | \(-0.463314\pi\) | ||||
0.114998 | + | 0.993366i | \(0.463314\pi\) | |||||||
\(758\) | 62.0857 | 2.25505 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.29145 | −0.191941 | ||||||||
\(761\) | −11.2562 | −0.408037 | −0.204018 | − | 0.978967i | \(-0.565400\pi\) | ||||
−0.204018 | + | 0.978967i | \(0.565400\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.1634 | −0.548953 | ||||||||
\(764\) | −158.197 | −5.72338 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −76.2828 | −2.75621 | ||||||||
\(767\) | 34.0688 | 1.23015 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.7122 | 1.54024 | 0.770121 | − | 0.637897i | \(-0.220196\pi\) | ||||
0.770121 | + | 0.637897i | \(0.220196\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 118.991 | 4.28257 | ||||||||
\(773\) | −32.6637 | −1.17483 | −0.587415 | − | 0.809286i | \(-0.699854\pi\) | ||||
−0.587415 | + | 0.809286i | \(0.699854\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.5088 | 0.449329 | ||||||||
\(776\) | −171.191 | −6.14539 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 78.0416 | 2.79793 | ||||||||
\(779\) | −1.23589 | −0.0442805 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 131.603 | 4.70610 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.1024 | 0.646515 | ||||||||
\(785\) | 9.81467 | 0.350301 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.5832 | 1.26840 | 0.634201 | − | 0.773168i | \(-0.281329\pi\) | ||||
0.634201 | + | 0.773168i | \(0.281329\pi\) | |||||||
\(788\) | −72.8963 | −2.59682 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.5418 | −1.15779 | ||||||||
\(791\) | 1.50471 | 0.0535013 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.2998 | −0.543311 | ||||||||
\(794\) | −41.9183 | −1.48763 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 32.8456 | 1.16418 | ||||||||
\(797\) | 31.7624 | 1.12508 | 0.562541 | − | 0.826769i | \(-0.309824\pi\) | ||||
0.562541 | + | 0.826769i | \(0.309824\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.2416 | 1.67129 | ||||||||
\(800\) | 68.9981 | 2.43945 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −79.7842 | −2.81728 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.7545 | 0.449539 | ||||||||
\(806\) | 92.5252 | 3.25906 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 119.862 | 4.21672 | ||||||||
\(809\) | 8.48704 | 0.298388 | 0.149194 | − | 0.988808i | \(-0.452332\pi\) | ||||
0.149194 | + | 0.988808i | \(0.452332\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.72728 | −0.271341 | −0.135671 | − | 0.990754i | \(-0.543319\pi\) | ||||
−0.135671 | + | 0.990754i | \(0.543319\pi\) | |||||||
\(812\) | 17.1076 | 0.600358 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.6154 | 1.00235 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.196048 | −0.00685885 | ||||||||
\(818\) | −66.1931 | −2.31439 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −38.1609 | −1.33264 | ||||||||
\(821\) | 7.37351 | 0.257337 | 0.128669 | − | 0.991688i | \(-0.458930\pi\) | ||||
0.128669 | + | 0.991688i | \(0.458930\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.5473 | −0.716232 | −0.358116 | − | 0.933677i | \(-0.616581\pi\) | ||||
−0.358116 | + | 0.933677i | \(0.616581\pi\) | |||||||
\(824\) | 136.004 | 4.73793 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.2725 | −0.531399 | ||||||||
\(827\) | −5.14784 | −0.179008 | −0.0895040 | − | 0.995986i | \(-0.528528\pi\) | ||||
−0.0895040 | + | 0.995986i | \(0.528528\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.86695 | 0.273231 | 0.136615 | − | 0.990624i | \(-0.456378\pi\) | ||||
0.136615 | + | 0.990624i | \(0.456378\pi\) | |||||||
\(830\) | 53.4294 | 1.85456 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 284.713 | 9.87066 | ||||||||
\(833\) | 6.00681 | 0.208124 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.41640 | 0.0490166 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.4907 | −0.431485 | ||||||||
\(839\) | 46.3300 | 1.59949 | 0.799744 | − | 0.600341i | \(-0.204969\pi\) | ||||
0.799744 | + | 0.600341i | \(0.204969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.3194 | −0.700670 | ||||||||
\(842\) | −38.5484 | −1.32847 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 57.2650 | 1.97114 | ||||||||
\(845\) | −42.0406 | −1.44624 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.54590 | 0.156107 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 39.5120 | 1.35525 | ||||||||
\(851\) | 50.3280 | 1.72522 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.9539 | 1.57343 | 0.786715 | − | 0.617316i | \(-0.211780\pi\) | ||||
0.786715 | + | 0.617316i | \(0.211780\pi\) | |||||||
\(854\) | 6.85866 | 0.234698 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 81.7768 | 2.79507 | ||||||||
\(857\) | −10.4781 | −0.357925 | −0.178963 | − | 0.983856i | \(-0.557274\pi\) | ||||
−0.178963 | + | 0.983856i | \(0.557274\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.6385 | −1.38657 | −0.693283 | − | 0.720665i | \(-0.743837\pi\) | ||||
−0.693283 | + | 0.720665i | \(0.743837\pi\) | |||||||
\(860\) | −6.05341 | −0.206420 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 56.1649 | 1.91299 | ||||||||
\(863\) | 40.6737 | 1.38455 | 0.692274 | − | 0.721634i | \(-0.256609\pi\) | ||||
0.692274 | + | 0.721634i | \(0.256609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.702961 | 0.0239014 | ||||||||
\(866\) | 37.5060 | 1.27451 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −30.8512 | −1.04716 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.8179 | 1.38306 | ||||||||
\(872\) | 161.269 | 5.46126 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.70146 | −0.226680 | ||||||||
\(875\) | 11.9622 | 0.404397 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.5951 | 1.06689 | 0.533445 | − | 0.845835i | \(-0.320897\pi\) | ||||
0.533445 | + | 0.845835i | \(0.320897\pi\) | |||||||
\(878\) | −70.7348 | −2.38718 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.1210 | 1.18326 | 0.591628 | − | 0.806211i | \(-0.298485\pi\) | ||||
0.591628 | + | 0.806211i | \(0.298485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.5879 | −1.60146 | −0.800730 | − | 0.599026i | \(-0.795555\pi\) | ||||
−0.800730 | + | 0.599026i | \(0.795555\pi\) | |||||||
\(884\) | 217.386 | 7.31150 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41.7495 | −1.40260 | ||||||||
\(887\) | −1.94873 | −0.0654318 | −0.0327159 | − | 0.999465i | \(-0.510416\pi\) | ||||
−0.0327159 | + | 0.999465i | \(0.510416\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.93093 | 0.0647612 | ||||||||
\(890\) | 43.6107 | 1.46183 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −72.1368 | −2.41532 | ||||||||
\(893\) | −2.40563 | −0.0805014 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.8114 | 0.428238 | ||||||||
\(896\) | −69.0176 | −2.30572 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 90.7362 | 3.02790 | ||||||||
\(899\) | −15.6542 | −0.522098 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.50844 | 0.0502533 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.0032 | −0.532258 | ||||||||
\(905\) | −22.3662 | −0.743478 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.1044 | −0.634351 | −0.317175 | − | 0.948367i | \(-0.602734\pi\) | ||||
−0.317175 | + | 0.948367i | \(0.602734\pi\) | |||||||
\(908\) | −49.1962 | −1.63263 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 28.3253 | 0.938975 | ||||||||
\(911\) | 38.3457 | 1.27045 | 0.635225 | − | 0.772327i | \(-0.280907\pi\) | ||||
0.635225 | + | 0.772327i | \(0.280907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −5.50466 | −0.182078 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −64.3126 | −2.12495 | ||||||||
\(917\) | 12.7038 | 0.419515 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.3891 | −0.474652 | −0.237326 | − | 0.971430i | \(-0.576271\pi\) | ||||
−0.237326 | + | 0.971430i | \(0.576271\pi\) | |||||||
\(920\) | −135.650 | −4.47224 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 88.9166 | 2.92831 | ||||||||
\(923\) | 34.9789 | 1.15135 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.1103 | 0.496825 | ||||||||
\(926\) | −31.0369 | −1.01994 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −86.3483 | −2.83452 | ||||||||
\(929\) | −31.6841 | −1.03952 | −0.519761 | − | 0.854311i | \(-0.673979\pi\) | ||||
−0.519761 | + | 0.854311i | \(0.673979\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.305878 | −0.0100248 | ||||||||
\(932\) | 44.0773 | 1.44380 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −76.0284 | −2.48772 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.41304 | −0.0461620 | −0.0230810 | − | 0.999734i | \(-0.507348\pi\) | ||||
−0.0230810 | + | 0.999734i | \(0.507348\pi\) | |||||||
\(938\) | −18.2980 | −0.597452 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −74.2792 | −2.42272 | ||||||||
\(941\) | −21.9730 | −0.716298 | −0.358149 | − | 0.933664i | \(-0.616592\pi\) | ||||
−0.358149 | + | 0.933664i | \(0.616592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.6829 | −1.03174 | ||||||||
\(944\) | 98.9508 | 3.22057 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 53.5540 | 1.74027 | 0.870136 | − | 0.492812i | \(-0.164031\pi\) | ||||
0.870136 | + | 0.492812i | \(0.164031\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 65.2650 | 2.11859 | ||||||||
\(950\) | −2.01203 | −0.0652788 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −63.8848 | −2.07052 | ||||||||
\(953\) | 16.0586 | 0.520189 | 0.260095 | − | 0.965583i | \(-0.416246\pi\) | ||||
0.260095 | + | 0.965583i | \(0.416246\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.3157 | 1.43402 | ||||||||
\(956\) | −161.433 | −5.22111 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37.4009 | −1.20837 | ||||||||
\(959\) | 0.345262 | 0.0111491 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.76971 | −0.0893456 | ||||||||
\(962\) | 111.768 | 3.60356 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.40647 | 0.0452993 | ||||||||
\(965\) | −33.3328 | −1.07302 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.923832 | 0.0297084 | 0.0148542 | − | 0.999890i | \(-0.495272\pi\) | ||||
0.0148542 | + | 0.999890i | \(0.495272\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 73.1521 | 2.34877 | ||||||||
\(971\) | 15.1444 | 0.486007 | 0.243004 | − | 0.970025i | \(-0.421867\pi\) | ||||
0.243004 | + | 0.970025i | \(0.421867\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.0710 | 0.611388 | ||||||||
\(974\) | −48.2639 | −1.54647 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −44.4373 | −1.42240 | ||||||||
\(977\) | 33.2665 | 1.06429 | 0.532145 | − | 0.846653i | \(-0.321386\pi\) | ||||
0.532145 | + | 0.846653i | \(0.321386\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −9.44466 | −0.301699 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.86607 | 0.219105 | ||||||||
\(983\) | −0.187510 | −0.00598064 | −0.00299032 | − | 0.999996i | \(-0.500952\pi\) | ||||
−0.00299032 | + | 0.999996i | \(0.500952\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.4204 | 0.650647 | ||||||||
\(986\) | −49.4477 | −1.57474 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.0697 | −0.352175 | ||||||||
\(989\) | −5.02581 | −0.159812 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.61914 | 0.114966 | 0.0574829 | − | 0.998346i | \(-0.481693\pi\) | ||||
0.0574829 | + | 0.998346i | \(0.481693\pi\) | |||||||
\(992\) | 155.717 | 4.94403 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −15.6805 | −0.497356 | ||||||||
\(995\) | −9.20101 | −0.291692 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.7426 | −0.403561 | −0.201780 | − | 0.979431i | \(-0.564673\pi\) | ||||
−0.201780 | + | 0.979431i | \(0.564673\pi\) | |||||||
\(998\) | 46.2518 | 1.46408 | ||||||||
\(999\) | 0 | 0 |
(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 | 7623.2.a.da.1.1 | yes | 12 | |
3.2 | odd | 2 | inner | 7623.2.a.da.1.12 | yes | 12 | |
11.10 | odd | 2 | 7623.2.a.cz.1.12 | yes | 12 | ||
33.32 | even | 2 | 7623.2.a.cz.1.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7623.2.a.cz.1.1 | ✓ | 12 | 33.32 | even | 2 | ||
7623.2.a.cz.1.12 | yes | 12 | 11.10 | odd | 2 | ||
7623.2.a.da.1.1 | yes | 12 | 1.1 | even | 1 | trivial | |
7623.2.a.da.1.12 | yes | 12 | 3.2 | odd | 2 | inner |