Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4002,2,Mod(1,4002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4002, 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("4002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4002.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: | \(31.9561308889\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.23252.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.88474\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.82358 | −0.815531 | −0.407765 | − | 0.913087i | \(-0.633692\pi\) | ||||
−0.407765 | + | 0.913087i | \(0.633692\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.70832 | 1.02365 | 0.511824 | − | 0.859090i | \(-0.328970\pi\) | ||||
0.511824 | + | 0.859090i | \(0.328970\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.82358 | 0.576667 | ||||||||
\(11\) | −4.88474 | −1.47280 | −0.736402 | − | 0.676544i | \(-0.763477\pi\) | ||||
−0.736402 | + | 0.676544i | \(0.763477\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.552237 | −0.153163 | −0.0765814 | − | 0.997063i | \(-0.524401\pi\) | ||||
−0.0765814 | + | 0.997063i | \(0.524401\pi\) | |||||||
\(14\) | −2.70832 | −0.723829 | ||||||||
\(15\) | −1.82358 | −0.470847 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.70832 | −0.656864 | −0.328432 | − | 0.944528i | \(-0.606520\pi\) | ||||
−0.328432 | + | 0.944528i | \(0.606520\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.81279 | 1.33355 | 0.666773 | − | 0.745261i | \(-0.267675\pi\) | ||||
0.666773 | + | 0.745261i | \(0.267675\pi\) | |||||||
\(20\) | −1.82358 | −0.407765 | ||||||||
\(21\) | 2.70832 | 0.591004 | ||||||||
\(22\) | 4.88474 | 1.04143 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −1.67455 | −0.334910 | ||||||||
\(26\) | 0.552237 | 0.108303 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.70832 | 0.511824 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 1.82358 | 0.332939 | ||||||||
\(31\) | 0.321712 | 0.0577812 | 0.0288906 | − | 0.999583i | \(-0.490803\pi\) | ||||
0.0288906 | + | 0.999583i | \(0.490803\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.88474 | −0.850324 | ||||||||
\(34\) | 2.70832 | 0.464473 | ||||||||
\(35\) | −4.93884 | −0.834817 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.52816 | −1.23762 | −0.618811 | − | 0.785540i | \(-0.712385\pi\) | ||||
−0.618811 | + | 0.785540i | \(0.712385\pi\) | |||||||
\(38\) | −5.81279 | −0.942960 | ||||||||
\(39\) | −0.552237 | −0.0884286 | ||||||||
\(40\) | 1.82358 | 0.288334 | ||||||||
\(41\) | −1.57007 | −0.245204 | −0.122602 | − | 0.992456i | \(-0.539124\pi\) | ||||
−0.122602 | + | 0.992456i | \(0.539124\pi\) | |||||||
\(42\) | −2.70832 | −0.417903 | ||||||||
\(43\) | 11.6613 | 1.77833 | 0.889163 | − | 0.457591i | \(-0.151288\pi\) | ||||
0.889163 | + | 0.457591i | \(0.151288\pi\) | |||||||
\(44\) | −4.88474 | −0.736402 | ||||||||
\(45\) | −1.82358 | −0.271844 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 9.58227 | 1.39772 | 0.698859 | − | 0.715260i | \(-0.253692\pi\) | ||||
0.698859 | + | 0.715260i | \(0.253692\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0.334998 | 0.0478568 | ||||||||
\(50\) | 1.67455 | 0.236817 | ||||||||
\(51\) | −2.70832 | −0.379241 | ||||||||
\(52\) | −0.552237 | −0.0765814 | ||||||||
\(53\) | −9.70458 | −1.33303 | −0.666513 | − | 0.745493i | \(-0.732214\pi\) | ||||
−0.666513 | + | 0.745493i | \(0.732214\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 8.90772 | 1.20112 | ||||||||
\(56\) | −2.70832 | −0.361914 | ||||||||
\(57\) | 5.81279 | 0.769923 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −7.21724 | −0.939604 | −0.469802 | − | 0.882772i | \(-0.655675\pi\) | ||||
−0.469802 | + | 0.882772i | \(0.655675\pi\) | |||||||
\(60\) | −1.82358 | −0.235423 | ||||||||
\(61\) | −1.11526 | −0.142795 | −0.0713973 | − | 0.997448i | \(-0.522746\pi\) | ||||
−0.0713973 | + | 0.997448i | \(0.522746\pi\) | |||||||
\(62\) | −0.321712 | −0.0408575 | ||||||||
\(63\) | 2.70832 | 0.341216 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00705 | 0.124909 | ||||||||
\(66\) | 4.88474 | 0.601270 | ||||||||
\(67\) | −9.17268 | −1.12062 | −0.560310 | − | 0.828283i | \(-0.689318\pi\) | ||||
−0.560310 | + | 0.828283i | \(0.689318\pi\) | |||||||
\(68\) | −2.70832 | −0.328432 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 4.93884 | 0.590305 | ||||||||
\(71\) | −4.07709 | −0.483862 | −0.241931 | − | 0.970294i | \(-0.577781\pi\) | ||||
−0.241931 | + | 0.970294i | \(0.577781\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −6.58601 | −0.770834 | −0.385417 | − | 0.922742i | \(-0.625942\pi\) | ||||
−0.385417 | + | 0.922742i | \(0.625942\pi\) | |||||||
\(74\) | 7.52816 | 0.875131 | ||||||||
\(75\) | −1.67455 | −0.193360 | ||||||||
\(76\) | 5.81279 | 0.666773 | ||||||||
\(77\) | −13.2294 | −1.50763 | ||||||||
\(78\) | 0.552237 | 0.0625285 | ||||||||
\(79\) | −1.16937 | −0.131564 | −0.0657821 | − | 0.997834i | \(-0.520954\pi\) | ||||
−0.0657821 | + | 0.997834i | \(0.520954\pi\) | |||||||
\(80\) | −1.82358 | −0.203883 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.57007 | 0.173386 | ||||||||
\(83\) | 10.0601 | 1.10424 | 0.552118 | − | 0.833766i | \(-0.313820\pi\) | ||||
0.552118 | + | 0.833766i | \(0.313820\pi\) | |||||||
\(84\) | 2.70832 | 0.295502 | ||||||||
\(85\) | 4.93884 | 0.535693 | ||||||||
\(86\) | −11.6613 | −1.25747 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 4.88474 | 0.520715 | ||||||||
\(89\) | −16.8091 | −1.78176 | −0.890878 | − | 0.454243i | \(-0.849910\pi\) | ||||
−0.890878 | + | 0.454243i | \(0.849910\pi\) | |||||||
\(90\) | 1.82358 | 0.192222 | ||||||||
\(91\) | −1.49563 | −0.156785 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 0.321712 | 0.0333600 | ||||||||
\(94\) | −9.58227 | −0.988336 | ||||||||
\(95\) | −10.6001 | −1.08755 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −12.8091 | −1.30056 | −0.650281 | − | 0.759694i | \(-0.725349\pi\) | ||||
−0.650281 | + | 0.759694i | \(0.725349\pi\) | |||||||
\(98\) | −0.334998 | −0.0338399 | ||||||||
\(99\) | −4.88474 | −0.490935 | ||||||||
\(100\) | −1.67455 | −0.167455 | ||||||||
\(101\) | −7.42619 | −0.738933 | −0.369467 | − | 0.929244i | \(-0.620460\pi\) | ||||
−0.369467 | + | 0.929244i | \(0.620460\pi\) | |||||||
\(102\) | 2.70832 | 0.268164 | ||||||||
\(103\) | −13.4059 | −1.32092 | −0.660459 | − | 0.750862i | \(-0.729638\pi\) | ||||
−0.660459 | + | 0.750862i | \(0.729638\pi\) | |||||||
\(104\) | 0.552237 | 0.0541513 | ||||||||
\(105\) | −4.93884 | −0.481982 | ||||||||
\(106\) | 9.70458 | 0.942592 | ||||||||
\(107\) | 8.45622 | 0.817493 | 0.408747 | − | 0.912648i | \(-0.365966\pi\) | ||||
0.408747 | + | 0.912648i | \(0.365966\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 13.1645 | 1.26093 | 0.630467 | − | 0.776216i | \(-0.282863\pi\) | ||||
0.630467 | + | 0.776216i | \(0.282863\pi\) | |||||||
\(110\) | −8.90772 | −0.849318 | ||||||||
\(111\) | −7.52816 | −0.714542 | ||||||||
\(112\) | 2.70832 | 0.255912 | ||||||||
\(113\) | 9.06380 | 0.852651 | 0.426326 | − | 0.904570i | \(-0.359808\pi\) | ||||
0.426326 | + | 0.904570i | \(0.359808\pi\) | |||||||
\(114\) | −5.81279 | −0.544418 | ||||||||
\(115\) | −1.82358 | −0.170050 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −0.552237 | −0.0510543 | ||||||||
\(118\) | 7.21724 | 0.664401 | ||||||||
\(119\) | −7.33500 | −0.672398 | ||||||||
\(120\) | 1.82358 | 0.166470 | ||||||||
\(121\) | 12.8607 | 1.16915 | ||||||||
\(122\) | 1.11526 | 0.100971 | ||||||||
\(123\) | −1.57007 | −0.141569 | ||||||||
\(124\) | 0.321712 | 0.0288906 | ||||||||
\(125\) | 12.1716 | 1.08866 | ||||||||
\(126\) | −2.70832 | −0.241276 | ||||||||
\(127\) | −13.4262 | −1.19138 | −0.595691 | − | 0.803214i | \(-0.703122\pi\) | ||||
−0.595691 | + | 0.803214i | \(0.703122\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 11.6613 | 1.02672 | ||||||||
\(130\) | −1.00705 | −0.0883240 | ||||||||
\(131\) | −1.64452 | −0.143682 | −0.0718410 | − | 0.997416i | \(-0.522887\pi\) | ||||
−0.0718410 | + | 0.997416i | \(0.522887\pi\) | |||||||
\(132\) | −4.88474 | −0.425162 | ||||||||
\(133\) | 15.7429 | 1.36508 | ||||||||
\(134\) | 9.17268 | 0.792399 | ||||||||
\(135\) | −1.82358 | −0.156949 | ||||||||
\(136\) | 2.70832 | 0.232237 | ||||||||
\(137\) | −6.24727 | −0.533740 | −0.266870 | − | 0.963732i | \(-0.585990\pi\) | ||||
−0.266870 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −4.83063 | −0.409729 | −0.204864 | − | 0.978790i | \(-0.565675\pi\) | ||||
−0.204864 | + | 0.978790i | \(0.565675\pi\) | |||||||
\(140\) | −4.93884 | −0.417409 | ||||||||
\(141\) | 9.58227 | 0.806973 | ||||||||
\(142\) | 4.07709 | 0.342142 | ||||||||
\(143\) | 2.69753 | 0.225579 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.82358 | 0.151440 | ||||||||
\(146\) | 6.58601 | 0.545062 | ||||||||
\(147\) | 0.334998 | 0.0276301 | ||||||||
\(148\) | −7.52816 | −0.618811 | ||||||||
\(149\) | −8.88474 | −0.727866 | −0.363933 | − | 0.931425i | \(-0.618566\pi\) | ||||
−0.363933 | + | 0.931425i | \(0.618566\pi\) | |||||||
\(150\) | 1.67455 | 0.136726 | ||||||||
\(151\) | −5.79105 | −0.471269 | −0.235635 | − | 0.971842i | \(-0.575717\pi\) | ||||
−0.235635 | + | 0.971842i | \(0.575717\pi\) | |||||||
\(152\) | −5.81279 | −0.471480 | ||||||||
\(153\) | −2.70832 | −0.218955 | ||||||||
\(154\) | 13.2294 | 1.06606 | ||||||||
\(155\) | −0.586669 | −0.0471224 | ||||||||
\(156\) | −0.552237 | −0.0442143 | ||||||||
\(157\) | 9.18347 | 0.732920 | 0.366460 | − | 0.930434i | \(-0.380570\pi\) | ||||
0.366460 | + | 0.930434i | \(0.380570\pi\) | |||||||
\(158\) | 1.16937 | 0.0930300 | ||||||||
\(159\) | −9.70458 | −0.769623 | ||||||||
\(160\) | 1.82358 | 0.144167 | ||||||||
\(161\) | 2.70832 | 0.213446 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −18.1372 | −1.42061 | −0.710306 | − | 0.703893i | \(-0.751443\pi\) | ||||
−0.710306 | + | 0.703893i | \(0.751443\pi\) | |||||||
\(164\) | −1.57007 | −0.122602 | ||||||||
\(165\) | 8.90772 | 0.693465 | ||||||||
\(166\) | −10.0601 | −0.780812 | ||||||||
\(167\) | 19.6735 | 1.52238 | 0.761189 | − | 0.648530i | \(-0.224616\pi\) | ||||
0.761189 | + | 0.648530i | \(0.224616\pi\) | |||||||
\(168\) | −2.70832 | −0.208951 | ||||||||
\(169\) | −12.6950 | −0.976541 | ||||||||
\(170\) | −4.93884 | −0.378792 | ||||||||
\(171\) | 5.81279 | 0.444515 | ||||||||
\(172\) | 11.6613 | 0.889163 | ||||||||
\(173\) | −17.5964 | −1.33783 | −0.668913 | − | 0.743340i | \(-0.733240\pi\) | ||||
−0.668913 | + | 0.743340i | \(0.733240\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | −4.53521 | −0.342830 | ||||||||
\(176\) | −4.88474 | −0.368201 | ||||||||
\(177\) | −7.21724 | −0.542481 | ||||||||
\(178\) | 16.8091 | 1.25989 | ||||||||
\(179\) | 4.29059 | 0.320694 | 0.160347 | − | 0.987061i | \(-0.448739\pi\) | ||||
0.160347 | + | 0.987061i | \(0.448739\pi\) | |||||||
\(180\) | −1.82358 | −0.135922 | ||||||||
\(181\) | 15.7019 | 1.16712 | 0.583558 | − | 0.812072i | \(-0.301660\pi\) | ||||
0.583558 | + | 0.812072i | \(0.301660\pi\) | |||||||
\(182\) | 1.49563 | 0.110864 | ||||||||
\(183\) | −1.11526 | −0.0824426 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 13.7282 | 1.00932 | ||||||||
\(186\) | −0.321712 | −0.0235891 | ||||||||
\(187\) | 13.2294 | 0.967432 | ||||||||
\(188\) | 9.58227 | 0.698859 | ||||||||
\(189\) | 2.70832 | 0.197001 | ||||||||
\(190\) | 10.6001 | 0.769013 | ||||||||
\(191\) | 9.36253 | 0.677449 | 0.338725 | − | 0.940886i | \(-0.390005\pi\) | ||||
0.338725 | + | 0.940886i | \(0.390005\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −11.3376 | −0.816102 | −0.408051 | − | 0.912959i | \(-0.633791\pi\) | ||||
−0.408051 | + | 0.912959i | \(0.633791\pi\) | |||||||
\(194\) | 12.8091 | 0.919636 | ||||||||
\(195\) | 1.00705 | 0.0721163 | ||||||||
\(196\) | 0.334998 | 0.0239284 | ||||||||
\(197\) | −10.5070 | −0.748594 | −0.374297 | − | 0.927309i | \(-0.622116\pi\) | ||||
−0.374297 | + | 0.927309i | \(0.622116\pi\) | |||||||
\(198\) | 4.88474 | 0.347143 | ||||||||
\(199\) | −5.78026 | −0.409752 | −0.204876 | − | 0.978788i | \(-0.565679\pi\) | ||||
−0.204876 | + | 0.978788i | \(0.565679\pi\) | |||||||
\(200\) | 1.67455 | 0.118408 | ||||||||
\(201\) | −9.17268 | −0.646991 | ||||||||
\(202\) | 7.42619 | 0.522505 | ||||||||
\(203\) | −2.70832 | −0.190087 | ||||||||
\(204\) | −2.70832 | −0.189620 | ||||||||
\(205\) | 2.86316 | 0.199972 | ||||||||
\(206\) | 13.4059 | 0.934030 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −0.552237 | −0.0382907 | ||||||||
\(209\) | −28.3940 | −1.96405 | ||||||||
\(210\) | 4.93884 | 0.340813 | ||||||||
\(211\) | 17.6708 | 1.21651 | 0.608254 | − | 0.793742i | \(-0.291870\pi\) | ||||
0.608254 | + | 0.793742i | \(0.291870\pi\) | |||||||
\(212\) | −9.70458 | −0.666513 | ||||||||
\(213\) | −4.07709 | −0.279358 | ||||||||
\(214\) | −8.45622 | −0.578055 | ||||||||
\(215\) | −21.2653 | −1.45028 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.871300 | 0.0591477 | ||||||||
\(218\) | −13.1645 | −0.891615 | ||||||||
\(219\) | −6.58601 | −0.445041 | ||||||||
\(220\) | 8.90772 | 0.600558 | ||||||||
\(221\) | 1.49563 | 0.100607 | ||||||||
\(222\) | 7.52816 | 0.505257 | ||||||||
\(223\) | −25.0996 | −1.68080 | −0.840398 | − | 0.541969i | \(-0.817679\pi\) | ||||
−0.840398 | + | 0.541969i | \(0.817679\pi\) | |||||||
\(224\) | −2.70832 | −0.180957 | ||||||||
\(225\) | −1.67455 | −0.111637 | ||||||||
\(226\) | −9.06380 | −0.602915 | ||||||||
\(227\) | 15.8080 | 1.04921 | 0.524606 | − | 0.851345i | \(-0.324213\pi\) | ||||
0.524606 | + | 0.851345i | \(0.324213\pi\) | |||||||
\(228\) | 5.81279 | 0.384962 | ||||||||
\(229\) | −16.4454 | −1.08674 | −0.543372 | − | 0.839492i | \(-0.682853\pi\) | ||||
−0.543372 | + | 0.839492i | \(0.682853\pi\) | |||||||
\(230\) | 1.82358 | 0.120243 | ||||||||
\(231\) | −13.2294 | −0.870433 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −0.276491 | −0.0181135 | −0.00905677 | − | 0.999959i | \(-0.502883\pi\) | ||||
−0.00905677 | + | 0.999959i | \(0.502883\pi\) | |||||||
\(234\) | 0.552237 | 0.0361008 | ||||||||
\(235\) | −17.4741 | −1.13988 | ||||||||
\(236\) | −7.21724 | −0.469802 | ||||||||
\(237\) | −1.16937 | −0.0759587 | ||||||||
\(238\) | 7.33500 | 0.475457 | ||||||||
\(239\) | 14.9002 | 0.963816 | 0.481908 | − | 0.876222i | \(-0.339944\pi\) | ||||
0.481908 | + | 0.876222i | \(0.339944\pi\) | |||||||
\(240\) | −1.82358 | −0.117712 | ||||||||
\(241\) | −21.3111 | −1.37277 | −0.686384 | − | 0.727240i | \(-0.740803\pi\) | ||||
−0.686384 | + | 0.727240i | \(0.740803\pi\) | |||||||
\(242\) | −12.8607 | −0.826715 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.11526 | −0.0713973 | ||||||||
\(245\) | −0.610896 | −0.0390287 | ||||||||
\(246\) | 1.57007 | 0.100104 | ||||||||
\(247\) | −3.21004 | −0.204250 | ||||||||
\(248\) | −0.321712 | −0.0204287 | ||||||||
\(249\) | 10.0601 | 0.637531 | ||||||||
\(250\) | −12.1716 | −0.769799 | ||||||||
\(251\) | −4.05411 | −0.255893 | −0.127946 | − | 0.991781i | \(-0.540839\pi\) | ||||
−0.127946 | + | 0.991781i | \(0.540839\pi\) | |||||||
\(252\) | 2.70832 | 0.170608 | ||||||||
\(253\) | −4.88474 | −0.307101 | ||||||||
\(254\) | 13.4262 | 0.842434 | ||||||||
\(255\) | 4.93884 | 0.309282 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.8091 | −0.923763 | −0.461882 | − | 0.886942i | \(-0.652826\pi\) | ||||
−0.461882 | + | 0.886942i | \(0.652826\pi\) | |||||||
\(258\) | −11.6613 | −0.725998 | ||||||||
\(259\) | −20.3887 | −1.26689 | ||||||||
\(260\) | 1.00705 | 0.0624545 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 1.64452 | 0.101599 | ||||||||
\(263\) | −2.43183 | −0.149953 | −0.0749765 | − | 0.997185i | \(-0.523888\pi\) | ||||
−0.0749765 | + | 0.997185i | \(0.523888\pi\) | |||||||
\(264\) | 4.88474 | 0.300635 | ||||||||
\(265\) | 17.6971 | 1.08712 | ||||||||
\(266\) | −15.7429 | −0.965259 | ||||||||
\(267\) | −16.8091 | −1.02870 | ||||||||
\(268\) | −9.17268 | −0.560310 | ||||||||
\(269\) | −16.9678 | −1.03454 | −0.517272 | − | 0.855821i | \(-0.673052\pi\) | ||||
−0.517272 | + | 0.855821i | \(0.673052\pi\) | |||||||
\(270\) | 1.82358 | 0.110980 | ||||||||
\(271\) | 19.5078 | 1.18502 | 0.592508 | − | 0.805565i | \(-0.298138\pi\) | ||||
0.592508 | + | 0.805565i | \(0.298138\pi\) | |||||||
\(272\) | −2.70832 | −0.164216 | ||||||||
\(273\) | −1.49563 | −0.0905199 | ||||||||
\(274\) | 6.24727 | 0.377411 | ||||||||
\(275\) | 8.17973 | 0.493256 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −22.1728 | −1.33224 | −0.666118 | − | 0.745846i | \(-0.732045\pi\) | ||||
−0.666118 | + | 0.745846i | \(0.732045\pi\) | |||||||
\(278\) | 4.83063 | 0.289722 | ||||||||
\(279\) | 0.321712 | 0.0192604 | ||||||||
\(280\) | 4.93884 | 0.295152 | ||||||||
\(281\) | −8.04332 | −0.479824 | −0.239912 | − | 0.970795i | \(-0.577119\pi\) | ||||
−0.239912 | + | 0.970795i | \(0.577119\pi\) | |||||||
\(282\) | −9.58227 | −0.570616 | ||||||||
\(283\) | 13.1612 | 0.782354 | 0.391177 | − | 0.920315i | \(-0.372068\pi\) | ||||
0.391177 | + | 0.920315i | \(0.372068\pi\) | |||||||
\(284\) | −4.07709 | −0.241931 | ||||||||
\(285\) | −10.6001 | −0.627896 | ||||||||
\(286\) | −2.69753 | −0.159508 | ||||||||
\(287\) | −4.25226 | −0.251003 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −9.66500 | −0.568530 | ||||||||
\(290\) | −1.82358 | −0.107084 | ||||||||
\(291\) | −12.8091 | −0.750880 | ||||||||
\(292\) | −6.58601 | −0.385417 | ||||||||
\(293\) | 14.4129 | 0.842011 | 0.421005 | − | 0.907058i | \(-0.361677\pi\) | ||||
0.421005 | + | 0.907058i | \(0.361677\pi\) | |||||||
\(294\) | −0.334998 | −0.0195375 | ||||||||
\(295\) | 13.1612 | 0.766276 | ||||||||
\(296\) | 7.52816 | 0.437566 | ||||||||
\(297\) | −4.88474 | −0.283441 | ||||||||
\(298\) | 8.88474 | 0.514679 | ||||||||
\(299\) | −0.552237 | −0.0319367 | ||||||||
\(300\) | −1.67455 | −0.0966801 | ||||||||
\(301\) | 31.5824 | 1.82038 | ||||||||
\(302\) | 5.79105 | 0.333238 | ||||||||
\(303\) | −7.42619 | −0.426623 | ||||||||
\(304\) | 5.81279 | 0.333387 | ||||||||
\(305\) | 2.03377 | 0.116453 | ||||||||
\(306\) | 2.70832 | 0.154824 | ||||||||
\(307\) | 23.2632 | 1.32770 | 0.663851 | − | 0.747865i | \(-0.268921\pi\) | ||||
0.663851 | + | 0.747865i | \(0.268921\pi\) | |||||||
\(308\) | −13.2294 | −0.753817 | ||||||||
\(309\) | −13.4059 | −0.762632 | ||||||||
\(310\) | 0.586669 | 0.0333205 | ||||||||
\(311\) | −29.7024 | −1.68427 | −0.842134 | − | 0.539268i | \(-0.818701\pi\) | ||||
−0.842134 | + | 0.539268i | \(0.818701\pi\) | |||||||
\(312\) | 0.552237 | 0.0312642 | ||||||||
\(313\) | −24.2473 | −1.37054 | −0.685268 | − | 0.728291i | \(-0.740315\pi\) | ||||
−0.685268 | + | 0.728291i | \(0.740315\pi\) | |||||||
\(314\) | −9.18347 | −0.518253 | ||||||||
\(315\) | −4.93884 | −0.278272 | ||||||||
\(316\) | −1.16937 | −0.0657821 | ||||||||
\(317\) | 18.4543 | 1.03650 | 0.518249 | − | 0.855230i | \(-0.326584\pi\) | ||||
0.518249 | + | 0.855230i | \(0.326584\pi\) | |||||||
\(318\) | 9.70458 | 0.544206 | ||||||||
\(319\) | 4.88474 | 0.273493 | ||||||||
\(320\) | −1.82358 | −0.101941 | ||||||||
\(321\) | 8.45622 | 0.471980 | ||||||||
\(322\) | −2.70832 | −0.150929 | ||||||||
\(323\) | −15.7429 | −0.875959 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.924747 | 0.0512957 | ||||||||
\(326\) | 18.1372 | 1.00452 | ||||||||
\(327\) | 13.1645 | 0.728001 | ||||||||
\(328\) | 1.57007 | 0.0866929 | ||||||||
\(329\) | 25.9519 | 1.43077 | ||||||||
\(330\) | −8.90772 | −0.490354 | ||||||||
\(331\) | 25.7072 | 1.41300 | 0.706499 | − | 0.707714i | \(-0.250274\pi\) | ||||
0.706499 | + | 0.707714i | \(0.250274\pi\) | |||||||
\(332\) | 10.0601 | 0.552118 | ||||||||
\(333\) | −7.52816 | −0.412541 | ||||||||
\(334\) | −19.6735 | −1.07648 | ||||||||
\(335\) | 16.7271 | 0.913901 | ||||||||
\(336\) | 2.70832 | 0.147751 | ||||||||
\(337\) | 7.17003 | 0.390576 | 0.195288 | − | 0.980746i | \(-0.437436\pi\) | ||||
0.195288 | + | 0.980746i | \(0.437436\pi\) | |||||||
\(338\) | 12.6950 | 0.690519 | ||||||||
\(339\) | 9.06380 | 0.492278 | ||||||||
\(340\) | 4.93884 | 0.267846 | ||||||||
\(341\) | −1.57148 | −0.0851004 | ||||||||
\(342\) | −5.81279 | −0.314320 | ||||||||
\(343\) | −18.0510 | −0.974660 | ||||||||
\(344\) | −11.6613 | −0.628733 | ||||||||
\(345\) | −1.82358 | −0.0981784 | ||||||||
\(346\) | 17.5964 | 0.945987 | ||||||||
\(347\) | 1.74790 | 0.0938321 | 0.0469160 | − | 0.998899i | \(-0.485061\pi\) | ||||
0.0469160 | + | 0.998899i | \(0.485061\pi\) | |||||||
\(348\) | −1.00000 | −0.0536056 | ||||||||
\(349\) | −13.8899 | −0.743508 | −0.371754 | − | 0.928331i | \(-0.621244\pi\) | ||||
−0.371754 | + | 0.928331i | \(0.621244\pi\) | |||||||
\(350\) | 4.53521 | 0.242417 | ||||||||
\(351\) | −0.552237 | −0.0294762 | ||||||||
\(352\) | 4.88474 | 0.260357 | ||||||||
\(353\) | 5.81279 | 0.309384 | 0.154692 | − | 0.987963i | \(-0.450562\pi\) | ||||
0.154692 | + | 0.987963i | \(0.450562\pi\) | |||||||
\(354\) | 7.21724 | 0.383592 | ||||||||
\(355\) | 7.43491 | 0.394604 | ||||||||
\(356\) | −16.8091 | −0.890878 | ||||||||
\(357\) | −7.33500 | −0.388209 | ||||||||
\(358\) | −4.29059 | −0.226765 | ||||||||
\(359\) | −17.0894 | −0.901941 | −0.450971 | − | 0.892539i | \(-0.648922\pi\) | ||||
−0.450971 | + | 0.892539i | \(0.648922\pi\) | |||||||
\(360\) | 1.82358 | 0.0961112 | ||||||||
\(361\) | 14.7886 | 0.778346 | ||||||||
\(362\) | −15.7019 | −0.825275 | ||||||||
\(363\) | 12.8607 | 0.675010 | ||||||||
\(364\) | −1.49563 | −0.0783925 | ||||||||
\(365\) | 12.0101 | 0.628639 | ||||||||
\(366\) | 1.11526 | 0.0582957 | ||||||||
\(367\) | −1.62559 | −0.0848549 | −0.0424275 | − | 0.999100i | \(-0.513509\pi\) | ||||
−0.0424275 | + | 0.999100i | \(0.513509\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −1.57007 | −0.0817348 | ||||||||
\(370\) | −13.7282 | −0.713696 | ||||||||
\(371\) | −26.2831 | −1.36455 | ||||||||
\(372\) | 0.321712 | 0.0166800 | ||||||||
\(373\) | 14.4562 | 0.748515 | 0.374257 | − | 0.927325i | \(-0.377898\pi\) | ||||
0.374257 | + | 0.927325i | \(0.377898\pi\) | |||||||
\(374\) | −13.2294 | −0.684078 | ||||||||
\(375\) | 12.1716 | 0.628538 | ||||||||
\(376\) | −9.58227 | −0.494168 | ||||||||
\(377\) | 0.552237 | 0.0284416 | ||||||||
\(378\) | −2.70832 | −0.139301 | ||||||||
\(379\) | −11.2970 | −0.580287 | −0.290143 | − | 0.956983i | \(-0.593703\pi\) | ||||
−0.290143 | + | 0.956983i | \(0.593703\pi\) | |||||||
\(380\) | −10.6001 | −0.543774 | ||||||||
\(381\) | −13.4262 | −0.687844 | ||||||||
\(382\) | −9.36253 | −0.479029 | ||||||||
\(383\) | −5.02548 | −0.256790 | −0.128395 | − | 0.991723i | \(-0.540983\pi\) | ||||
−0.128395 | + | 0.991723i | \(0.540983\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 24.1250 | 1.22952 | ||||||||
\(386\) | 11.3376 | 0.577071 | ||||||||
\(387\) | 11.6613 | 0.592775 | ||||||||
\(388\) | −12.8091 | −0.650281 | ||||||||
\(389\) | 29.6742 | 1.50454 | 0.752271 | − | 0.658854i | \(-0.228958\pi\) | ||||
0.752271 | + | 0.658854i | \(0.228958\pi\) | |||||||
\(390\) | −1.00705 | −0.0509939 | ||||||||
\(391\) | −2.70832 | −0.136966 | ||||||||
\(392\) | −0.334998 | −0.0169199 | ||||||||
\(393\) | −1.64452 | −0.0829548 | ||||||||
\(394\) | 10.5070 | 0.529336 | ||||||||
\(395\) | 2.13244 | 0.107295 | ||||||||
\(396\) | −4.88474 | −0.245467 | ||||||||
\(397\) | −8.87395 | −0.445371 | −0.222685 | − | 0.974890i | \(-0.571482\pi\) | ||||
−0.222685 | + | 0.974890i | \(0.571482\pi\) | |||||||
\(398\) | 5.78026 | 0.289738 | ||||||||
\(399\) | 15.7429 | 0.788131 | ||||||||
\(400\) | −1.67455 | −0.0837274 | ||||||||
\(401\) | −16.2073 | −0.809352 | −0.404676 | − | 0.914460i | \(-0.632616\pi\) | ||||
−0.404676 | + | 0.914460i | \(0.632616\pi\) | |||||||
\(402\) | 9.17268 | 0.457492 | ||||||||
\(403\) | −0.177661 | −0.00884994 | ||||||||
\(404\) | −7.42619 | −0.369467 | ||||||||
\(405\) | −1.82358 | −0.0906145 | ||||||||
\(406\) | 2.70832 | 0.134412 | ||||||||
\(407\) | 36.7731 | 1.82277 | ||||||||
\(408\) | 2.70832 | 0.134082 | ||||||||
\(409\) | 23.1428 | 1.14434 | 0.572169 | − | 0.820136i | \(-0.306102\pi\) | ||||
0.572169 | + | 0.820136i | \(0.306102\pi\) | |||||||
\(410\) | −2.86316 | −0.141401 | ||||||||
\(411\) | −6.24727 | −0.308155 | ||||||||
\(412\) | −13.4059 | −0.660459 | ||||||||
\(413\) | −19.5466 | −0.961825 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −18.3454 | −0.900538 | ||||||||
\(416\) | 0.552237 | 0.0270756 | ||||||||
\(417\) | −4.83063 | −0.236557 | ||||||||
\(418\) | 28.3940 | 1.38879 | ||||||||
\(419\) | −25.8843 | −1.26453 | −0.632266 | − | 0.774752i | \(-0.717875\pi\) | ||||
−0.632266 | + | 0.774752i | \(0.717875\pi\) | |||||||
\(420\) | −4.93884 | −0.240991 | ||||||||
\(421\) | 4.11417 | 0.200512 | 0.100256 | − | 0.994962i | \(-0.468034\pi\) | ||||
0.100256 | + | 0.994962i | \(0.468034\pi\) | |||||||
\(422\) | −17.6708 | −0.860201 | ||||||||
\(423\) | 9.58227 | 0.465906 | ||||||||
\(424\) | 9.70458 | 0.471296 | ||||||||
\(425\) | 4.53521 | 0.219990 | ||||||||
\(426\) | 4.07709 | 0.197536 | ||||||||
\(427\) | −3.02049 | −0.146172 | ||||||||
\(428\) | 8.45622 | 0.408747 | ||||||||
\(429\) | 2.69753 | 0.130238 | ||||||||
\(430\) | 21.2653 | 1.02550 | ||||||||
\(431\) | 13.4281 | 0.646808 | 0.323404 | − | 0.946261i | \(-0.395173\pi\) | ||||
0.323404 | + | 0.946261i | \(0.395173\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 8.56162 | 0.411445 | 0.205723 | − | 0.978610i | \(-0.434046\pi\) | ||||
0.205723 | + | 0.978610i | \(0.434046\pi\) | |||||||
\(434\) | −0.871300 | −0.0418237 | ||||||||
\(435\) | 1.82358 | 0.0874341 | ||||||||
\(436\) | 13.1645 | 0.630467 | ||||||||
\(437\) | 5.81279 | 0.278064 | ||||||||
\(438\) | 6.58601 | 0.314692 | ||||||||
\(439\) | 8.42700 | 0.402199 | 0.201099 | − | 0.979571i | \(-0.435549\pi\) | ||||
0.201099 | + | 0.979571i | \(0.435549\pi\) | |||||||
\(440\) | −8.90772 | −0.424659 | ||||||||
\(441\) | 0.334998 | 0.0159523 | ||||||||
\(442\) | −1.49563 | −0.0711400 | ||||||||
\(443\) | −9.49563 | −0.451151 | −0.225576 | − | 0.974226i | \(-0.572426\pi\) | ||||
−0.225576 | + | 0.974226i | \(0.572426\pi\) | |||||||
\(444\) | −7.52816 | −0.357271 | ||||||||
\(445\) | 30.6527 | 1.45308 | ||||||||
\(446\) | 25.0996 | 1.18850 | ||||||||
\(447\) | −8.88474 | −0.420234 | ||||||||
\(448\) | 2.70832 | 0.127956 | ||||||||
\(449\) | −11.1165 | −0.524620 | −0.262310 | − | 0.964984i | \(-0.584484\pi\) | ||||
−0.262310 | + | 0.964984i | \(0.584484\pi\) | |||||||
\(450\) | 1.67455 | 0.0789389 | ||||||||
\(451\) | 7.66940 | 0.361138 | ||||||||
\(452\) | 9.06380 | 0.426326 | ||||||||
\(453\) | −5.79105 | −0.272087 | ||||||||
\(454\) | −15.8080 | −0.741904 | ||||||||
\(455\) | 2.72741 | 0.127863 | ||||||||
\(456\) | −5.81279 | −0.272209 | ||||||||
\(457\) | −23.7977 | −1.11321 | −0.556604 | − | 0.830778i | \(-0.687896\pi\) | ||||
−0.556604 | + | 0.830778i | \(0.687896\pi\) | |||||||
\(458\) | 16.4454 | 0.768444 | ||||||||
\(459\) | −2.70832 | −0.126414 | ||||||||
\(460\) | −1.82358 | −0.0850250 | ||||||||
\(461\) | −39.2849 | −1.82968 | −0.914841 | − | 0.403814i | \(-0.867684\pi\) | ||||
−0.914841 | + | 0.403814i | \(0.867684\pi\) | |||||||
\(462\) | 13.2294 | 0.615489 | ||||||||
\(463\) | 22.5163 | 1.04642 | 0.523210 | − | 0.852204i | \(-0.324734\pi\) | ||||
0.523210 | + | 0.852204i | \(0.324734\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −0.586669 | −0.0272061 | ||||||||
\(466\) | 0.276491 | 0.0128082 | ||||||||
\(467\) | −22.2582 | −1.02999 | −0.514994 | − | 0.857194i | \(-0.672206\pi\) | ||||
−0.514994 | + | 0.857194i | \(0.672206\pi\) | |||||||
\(468\) | −0.552237 | −0.0255271 | ||||||||
\(469\) | −24.8425 | −1.14712 | ||||||||
\(470\) | 17.4741 | 0.806018 | ||||||||
\(471\) | 9.18347 | 0.423152 | ||||||||
\(472\) | 7.21724 | 0.332200 | ||||||||
\(473\) | −56.9622 | −2.61913 | ||||||||
\(474\) | 1.16937 | 0.0537109 | ||||||||
\(475\) | −9.73380 | −0.446617 | ||||||||
\(476\) | −7.33500 | −0.336199 | ||||||||
\(477\) | −9.70458 | −0.444342 | ||||||||
\(478\) | −14.9002 | −0.681521 | ||||||||
\(479\) | −12.4859 | −0.570497 | −0.285248 | − | 0.958454i | \(-0.592076\pi\) | ||||
−0.285248 | + | 0.958454i | \(0.592076\pi\) | |||||||
\(480\) | 1.82358 | 0.0832348 | ||||||||
\(481\) | 4.15733 | 0.189558 | ||||||||
\(482\) | 21.3111 | 0.970693 | ||||||||
\(483\) | 2.70832 | 0.123233 | ||||||||
\(484\) | 12.8607 | 0.584576 | ||||||||
\(485\) | 23.3584 | 1.06065 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −16.6942 | −0.756487 | −0.378244 | − | 0.925706i | \(-0.623472\pi\) | ||||
−0.378244 | + | 0.925706i | \(0.623472\pi\) | |||||||
\(488\) | 1.11526 | 0.0504855 | ||||||||
\(489\) | −18.1372 | −0.820190 | ||||||||
\(490\) | 0.610896 | 0.0275975 | ||||||||
\(491\) | 5.82689 | 0.262964 | 0.131482 | − | 0.991319i | \(-0.458026\pi\) | ||||
0.131482 | + | 0.991319i | \(0.458026\pi\) | |||||||
\(492\) | −1.57007 | −0.0707844 | ||||||||
\(493\) | 2.70832 | 0.121977 | ||||||||
\(494\) | 3.21004 | 0.144426 | ||||||||
\(495\) | 8.90772 | 0.400372 | ||||||||
\(496\) | 0.321712 | 0.0144453 | ||||||||
\(497\) | −11.0421 | −0.495304 | ||||||||
\(498\) | −10.0601 | −0.450802 | ||||||||
\(499\) | 22.6359 | 1.01332 | 0.506662 | − | 0.862145i | \(-0.330879\pi\) | ||||
0.506662 | + | 0.862145i | \(0.330879\pi\) | |||||||
\(500\) | 12.1716 | 0.544330 | ||||||||
\(501\) | 19.6735 | 0.878945 | ||||||||
\(502\) | 4.05411 | 0.180944 | ||||||||
\(503\) | 30.6386 | 1.36611 | 0.683054 | − | 0.730368i | \(-0.260651\pi\) | ||||
0.683054 | + | 0.730368i | \(0.260651\pi\) | |||||||
\(504\) | −2.70832 | −0.120638 | ||||||||
\(505\) | 13.5423 | 0.602623 | ||||||||
\(506\) | 4.88474 | 0.217153 | ||||||||
\(507\) | −12.6950 | −0.563806 | ||||||||
\(508\) | −13.4262 | −0.595691 | ||||||||
\(509\) | 0.686742 | 0.0304393 | 0.0152197 | − | 0.999884i | \(-0.495155\pi\) | ||||
0.0152197 | + | 0.999884i | \(0.495155\pi\) | |||||||
\(510\) | −4.93884 | −0.218696 | ||||||||
\(511\) | −17.8370 | −0.789063 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.81279 | 0.256641 | ||||||||
\(514\) | 14.8091 | 0.653199 | ||||||||
\(515\) | 24.4467 | 1.07725 | ||||||||
\(516\) | 11.6613 | 0.513358 | ||||||||
\(517\) | −46.8069 | −2.05856 | ||||||||
\(518\) | 20.3887 | 0.895827 | ||||||||
\(519\) | −17.5964 | −0.772395 | ||||||||
\(520\) | −1.00705 | −0.0441620 | ||||||||
\(521\) | 4.04332 | 0.177141 | 0.0885705 | − | 0.996070i | \(-0.471770\pi\) | ||||
0.0885705 | + | 0.996070i | \(0.471770\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | −1.34844 | −0.0589630 | −0.0294815 | − | 0.999565i | \(-0.509386\pi\) | ||||
−0.0294815 | + | 0.999565i | \(0.509386\pi\) | |||||||
\(524\) | −1.64452 | −0.0718410 | ||||||||
\(525\) | −4.53521 | −0.197933 | ||||||||
\(526\) | 2.43183 | 0.106033 | ||||||||
\(527\) | −0.871300 | −0.0379544 | ||||||||
\(528\) | −4.88474 | −0.212581 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −17.6971 | −0.768713 | ||||||||
\(531\) | −7.21724 | −0.313201 | ||||||||
\(532\) | 15.7429 | 0.682541 | ||||||||
\(533\) | 0.867053 | 0.0375562 | ||||||||
\(534\) | 16.8091 | 0.727399 | ||||||||
\(535\) | −15.4206 | −0.666691 | ||||||||
\(536\) | 9.17268 | 0.396199 | ||||||||
\(537\) | 4.29059 | 0.185153 | ||||||||
\(538\) | 16.9678 | 0.731533 | ||||||||
\(539\) | −1.63638 | −0.0704837 | ||||||||
\(540\) | −1.82358 | −0.0784745 | ||||||||
\(541\) | −28.7442 | −1.23581 | −0.617904 | − | 0.786254i | \(-0.712018\pi\) | ||||
−0.617904 | + | 0.786254i | \(0.712018\pi\) | |||||||
\(542\) | −19.5078 | −0.837933 | ||||||||
\(543\) | 15.7019 | 0.673834 | ||||||||
\(544\) | 2.70832 | 0.116118 | ||||||||
\(545\) | −24.0066 | −1.02833 | ||||||||
\(546\) | 1.49563 | 0.0640072 | ||||||||
\(547\) | 24.0053 | 1.02639 | 0.513196 | − | 0.858271i | \(-0.328461\pi\) | ||||
0.513196 | + | 0.858271i | \(0.328461\pi\) | |||||||
\(548\) | −6.24727 | −0.266870 | ||||||||
\(549\) | −1.11526 | −0.0475982 | ||||||||
\(550\) | −8.17973 | −0.348785 | ||||||||
\(551\) | −5.81279 | −0.247633 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −3.16703 | −0.134676 | ||||||||
\(554\) | 22.1728 | 0.942033 | ||||||||
\(555\) | 13.7282 | 0.582731 | ||||||||
\(556\) | −4.83063 | −0.204864 | ||||||||
\(557\) | −26.5996 | −1.12706 | −0.563531 | − | 0.826095i | \(-0.690557\pi\) | ||||
−0.563531 | + | 0.826095i | \(0.690557\pi\) | |||||||
\(558\) | −0.321712 | −0.0136192 | ||||||||
\(559\) | −6.43978 | −0.272374 | ||||||||
\(560\) | −4.93884 | −0.208704 | ||||||||
\(561\) | 13.2294 | 0.558547 | ||||||||
\(562\) | 8.04332 | 0.339287 | ||||||||
\(563\) | 26.4263 | 1.11374 | 0.556869 | − | 0.830601i | \(-0.312003\pi\) | ||||
0.556869 | + | 0.830601i | \(0.312003\pi\) | |||||||
\(564\) | 9.58227 | 0.403486 | ||||||||
\(565\) | −16.5286 | −0.695363 | ||||||||
\(566\) | −13.1612 | −0.553208 | ||||||||
\(567\) | 2.70832 | 0.113739 | ||||||||
\(568\) | 4.07709 | 0.171071 | ||||||||
\(569\) | 28.8306 | 1.20864 | 0.604321 | − | 0.796741i | \(-0.293444\pi\) | ||||
0.604321 | + | 0.796741i | \(0.293444\pi\) | |||||||
\(570\) | 10.6001 | 0.443990 | ||||||||
\(571\) | −7.98438 | −0.334136 | −0.167068 | − | 0.985945i | \(-0.553430\pi\) | ||||
−0.167068 | + | 0.985945i | \(0.553430\pi\) | |||||||
\(572\) | 2.69753 | 0.112789 | ||||||||
\(573\) | 9.36253 | 0.391125 | ||||||||
\(574\) | 4.25226 | 0.177486 | ||||||||
\(575\) | −1.67455 | −0.0698335 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 13.3761 | 0.556856 | 0.278428 | − | 0.960457i | \(-0.410187\pi\) | ||||
0.278428 | + | 0.960457i | \(0.410187\pi\) | |||||||
\(578\) | 9.66500 | 0.402011 | ||||||||
\(579\) | −11.3376 | −0.471177 | ||||||||
\(580\) | 1.82358 | 0.0757201 | ||||||||
\(581\) | 27.2459 | 1.13035 | ||||||||
\(582\) | 12.8091 | 0.530952 | ||||||||
\(583\) | 47.4043 | 1.96329 | ||||||||
\(584\) | 6.58601 | 0.272531 | ||||||||
\(585\) | 1.00705 | 0.0416363 | ||||||||
\(586\) | −14.4129 | −0.595391 | ||||||||
\(587\) | −7.28903 | −0.300850 | −0.150425 | − | 0.988621i | \(-0.548064\pi\) | ||||
−0.150425 | + | 0.988621i | \(0.548064\pi\) | |||||||
\(588\) | 0.334998 | 0.0138151 | ||||||||
\(589\) | 1.87005 | 0.0770539 | ||||||||
\(590\) | −13.1612 | −0.541839 | ||||||||
\(591\) | −10.5070 | −0.432201 | ||||||||
\(592\) | −7.52816 | −0.309406 | ||||||||
\(593\) | −7.96813 | −0.327212 | −0.163606 | − | 0.986526i | \(-0.552313\pi\) | ||||
−0.163606 | + | 0.986526i | \(0.552313\pi\) | |||||||
\(594\) | 4.88474 | 0.200423 | ||||||||
\(595\) | 13.3760 | 0.548361 | ||||||||
\(596\) | −8.88474 | −0.363933 | ||||||||
\(597\) | −5.78026 | −0.236570 | ||||||||
\(598\) | 0.552237 | 0.0225826 | ||||||||
\(599\) | −38.9367 | −1.59091 | −0.795454 | − | 0.606013i | \(-0.792768\pi\) | ||||
−0.795454 | + | 0.606013i | \(0.792768\pi\) | |||||||
\(600\) | 1.67455 | 0.0683631 | ||||||||
\(601\) | −37.5992 | −1.53370 | −0.766851 | − | 0.641825i | \(-0.778178\pi\) | ||||
−0.766851 | + | 0.641825i | \(0.778178\pi\) | |||||||
\(602\) | −31.5824 | −1.28720 | ||||||||
\(603\) | −9.17268 | −0.373540 | ||||||||
\(604\) | −5.79105 | −0.235635 | ||||||||
\(605\) | −23.4525 | −0.953479 | ||||||||
\(606\) | 7.42619 | 0.301668 | ||||||||
\(607\) | 34.6628 | 1.40692 | 0.703460 | − | 0.710735i | \(-0.251637\pi\) | ||||
0.703460 | + | 0.710735i | \(0.251637\pi\) | |||||||
\(608\) | −5.81279 | −0.235740 | ||||||||
\(609\) | −2.70832 | −0.109747 | ||||||||
\(610\) | −2.03377 | −0.0823450 | ||||||||
\(611\) | −5.29168 | −0.214078 | ||||||||
\(612\) | −2.70832 | −0.109477 | ||||||||
\(613\) | −29.8755 | −1.20666 | −0.603330 | − | 0.797491i | \(-0.706160\pi\) | ||||
−0.603330 | + | 0.797491i | \(0.706160\pi\) | |||||||
\(614\) | −23.2632 | −0.938827 | ||||||||
\(615\) | 2.86316 | 0.115454 | ||||||||
\(616\) | 13.2294 | 0.533029 | ||||||||
\(617\) | 18.2994 | 0.736706 | 0.368353 | − | 0.929686i | \(-0.379922\pi\) | ||||
0.368353 | + | 0.929686i | \(0.379922\pi\) | |||||||
\(618\) | 13.4059 | 0.539262 | ||||||||
\(619\) | −23.3658 | −0.939153 | −0.469576 | − | 0.882892i | \(-0.655593\pi\) | ||||
−0.469576 | + | 0.882892i | \(0.655593\pi\) | |||||||
\(620\) | −0.586669 | −0.0235612 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 29.7024 | 1.19096 | ||||||||
\(623\) | −45.5243 | −1.82389 | ||||||||
\(624\) | −0.552237 | −0.0221072 | ||||||||
\(625\) | −13.8232 | −0.552926 | ||||||||
\(626\) | 24.2473 | 0.969116 | ||||||||
\(627\) | −28.3940 | −1.13395 | ||||||||
\(628\) | 9.18347 | 0.366460 | ||||||||
\(629\) | 20.3887 | 0.812950 | ||||||||
\(630\) | 4.93884 | 0.196768 | ||||||||
\(631\) | −29.2186 | −1.16318 | −0.581588 | − | 0.813484i | \(-0.697568\pi\) | ||||
−0.581588 | + | 0.813484i | \(0.697568\pi\) | |||||||
\(632\) | 1.16937 | 0.0465150 | ||||||||
\(633\) | 17.6708 | 0.702352 | ||||||||
\(634\) | −18.4543 | −0.732914 | ||||||||
\(635\) | 24.4838 | 0.971608 | ||||||||
\(636\) | −9.70458 | −0.384812 | ||||||||
\(637\) | −0.184998 | −0.00732989 | ||||||||
\(638\) | −4.88474 | −0.193389 | ||||||||
\(639\) | −4.07709 | −0.161287 | ||||||||
\(640\) | 1.82358 | 0.0720834 | ||||||||
\(641\) | 35.9162 | 1.41860 | 0.709302 | − | 0.704905i | \(-0.249010\pi\) | ||||
0.709302 | + | 0.704905i | \(0.249010\pi\) | |||||||
\(642\) | −8.45622 | −0.333740 | ||||||||
\(643\) | 22.0026 | 0.867700 | 0.433850 | − | 0.900985i | \(-0.357155\pi\) | ||||
0.433850 | + | 0.900985i | \(0.357155\pi\) | |||||||
\(644\) | 2.70832 | 0.106723 | ||||||||
\(645\) | −21.2653 | −0.837319 | ||||||||
\(646\) | 15.7429 | 0.619396 | ||||||||
\(647\) | 1.65936 | 0.0652361 | 0.0326181 | − | 0.999468i | \(-0.489616\pi\) | ||||
0.0326181 | + | 0.999468i | \(0.489616\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 35.2543 | 1.38385 | ||||||||
\(650\) | −0.924747 | −0.0362715 | ||||||||
\(651\) | 0.871300 | 0.0341489 | ||||||||
\(652\) | −18.1372 | −0.710306 | ||||||||
\(653\) | 9.53705 | 0.373214 | 0.186607 | − | 0.982435i | \(-0.440251\pi\) | ||||
0.186607 | + | 0.982435i | \(0.440251\pi\) | |||||||
\(654\) | −13.1645 | −0.514774 | ||||||||
\(655\) | 2.99891 | 0.117177 | ||||||||
\(656\) | −1.57007 | −0.0613011 | ||||||||
\(657\) | −6.58601 | −0.256945 | ||||||||
\(658\) | −25.9519 | −1.01171 | ||||||||
\(659\) | −39.7699 | −1.54922 | −0.774609 | − | 0.632441i | \(-0.782053\pi\) | ||||
−0.774609 | + | 0.632441i | \(0.782053\pi\) | |||||||
\(660\) | 8.90772 | 0.346733 | ||||||||
\(661\) | −30.1852 | −1.17407 | −0.587034 | − | 0.809562i | \(-0.699704\pi\) | ||||
−0.587034 | + | 0.809562i | \(0.699704\pi\) | |||||||
\(662\) | −25.7072 | −0.999140 | ||||||||
\(663\) | 1.49563 | 0.0580856 | ||||||||
\(664\) | −10.0601 | −0.390406 | ||||||||
\(665\) | −28.7085 | −1.11327 | ||||||||
\(666\) | 7.52816 | 0.291710 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 19.6735 | 0.761189 | ||||||||
\(669\) | −25.0996 | −0.970408 | ||||||||
\(670\) | −16.7271 | −0.646226 | ||||||||
\(671\) | 5.44776 | 0.210309 | ||||||||
\(672\) | −2.70832 | −0.104476 | ||||||||
\(673\) | 12.5020 | 0.481918 | 0.240959 | − | 0.970535i | \(-0.422538\pi\) | ||||
0.240959 | + | 0.970535i | \(0.422538\pi\) | |||||||
\(674\) | −7.17003 | −0.276179 | ||||||||
\(675\) | −1.67455 | −0.0644534 | ||||||||
\(676\) | −12.6950 | −0.488271 | ||||||||
\(677\) | 12.4610 | 0.478917 | 0.239459 | − | 0.970907i | \(-0.423030\pi\) | ||||
0.239459 | + | 0.970907i | \(0.423030\pi\) | |||||||
\(678\) | −9.06380 | −0.348093 | ||||||||
\(679\) | −34.6910 | −1.33132 | ||||||||
\(680\) | −4.93884 | −0.189396 | ||||||||
\(681\) | 15.8080 | 0.605762 | ||||||||
\(682\) | 1.57148 | 0.0601751 | ||||||||
\(683\) | −24.5625 | −0.939859 | −0.469930 | − | 0.882704i | \(-0.655721\pi\) | ||||
−0.469930 | + | 0.882704i | \(0.655721\pi\) | |||||||
\(684\) | 5.81279 | 0.222258 | ||||||||
\(685\) | 11.3924 | 0.435282 | ||||||||
\(686\) | 18.0510 | 0.689189 | ||||||||
\(687\) | −16.4454 | −0.627432 | ||||||||
\(688\) | 11.6613 | 0.444581 | ||||||||
\(689\) | 5.35922 | 0.204170 | ||||||||
\(690\) | 1.82358 | 0.0694226 | ||||||||
\(691\) | 42.5671 | 1.61933 | 0.809664 | − | 0.586894i | \(-0.199649\pi\) | ||||
0.809664 | + | 0.586894i | \(0.199649\pi\) | |||||||
\(692\) | −17.5964 | −0.668913 | ||||||||
\(693\) | −13.2294 | −0.502545 | ||||||||
\(694\) | −1.74790 | −0.0663493 | ||||||||
\(695\) | 8.80905 | 0.334146 | ||||||||
\(696\) | 1.00000 | 0.0379049 | ||||||||
\(697\) | 4.25226 | 0.161066 | ||||||||
\(698\) | 13.8899 | 0.525740 | ||||||||
\(699\) | −0.276491 | −0.0104579 | ||||||||
\(700\) | −4.53521 | −0.171415 | ||||||||
\(701\) | 26.6542 | 1.00672 | 0.503358 | − | 0.864078i | \(-0.332098\pi\) | ||||
0.503358 | + | 0.864078i | \(0.332098\pi\) | |||||||
\(702\) | 0.552237 | 0.0208428 | ||||||||
\(703\) | −43.7597 | −1.65043 | ||||||||
\(704\) | −4.88474 | −0.184100 | ||||||||
\(705\) | −17.4741 | −0.658111 | ||||||||
\(706\) | −5.81279 | −0.218767 | ||||||||
\(707\) | −20.1125 | −0.756408 | ||||||||
\(708\) | −7.21724 | −0.271240 | ||||||||
\(709\) | 50.7966 | 1.90771 | 0.953853 | − | 0.300275i | \(-0.0970783\pi\) | ||||
0.953853 | + | 0.300275i | \(0.0970783\pi\) | |||||||
\(710\) | −7.43491 | −0.279027 | ||||||||
\(711\) | −1.16937 | −0.0438548 | ||||||||
\(712\) | 16.8091 | 0.629946 | ||||||||
\(713\) | 0.321712 | 0.0120482 | ||||||||
\(714\) | 7.33500 | 0.274505 | ||||||||
\(715\) | −4.91917 | −0.183967 | ||||||||
\(716\) | 4.29059 | 0.160347 | ||||||||
\(717\) | 14.9002 | 0.556460 | ||||||||
\(718\) | 17.0894 | 0.637769 | ||||||||
\(719\) | 13.5804 | 0.506462 | 0.253231 | − | 0.967406i | \(-0.418507\pi\) | ||||
0.253231 | + | 0.967406i | \(0.418507\pi\) | |||||||
\(720\) | −1.82358 | −0.0679609 | ||||||||
\(721\) | −36.3073 | −1.35216 | ||||||||
\(722\) | −14.7886 | −0.550373 | ||||||||
\(723\) | −21.3111 | −0.792567 | ||||||||
\(724\) | 15.7019 | 0.583558 | ||||||||
\(725\) | 1.67455 | 0.0621911 | ||||||||
\(726\) | −12.8607 | −0.477304 | ||||||||
\(727\) | −21.3685 | −0.792513 | −0.396257 | − | 0.918140i | \(-0.629691\pi\) | ||||
−0.396257 | + | 0.918140i | \(0.629691\pi\) | |||||||
\(728\) | 1.49563 | 0.0554319 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.0101 | −0.444515 | ||||||||
\(731\) | −31.5824 | −1.16812 | ||||||||
\(732\) | −1.11526 | −0.0412213 | ||||||||
\(733\) | 12.0898 | 0.446546 | 0.223273 | − | 0.974756i | \(-0.428326\pi\) | ||||
0.223273 | + | 0.974756i | \(0.428326\pi\) | |||||||
\(734\) | 1.62559 | 0.0600015 | ||||||||
\(735\) | −0.610896 | −0.0225332 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 44.8061 | 1.65045 | ||||||||
\(738\) | 1.57007 | 0.0577952 | ||||||||
\(739\) | 17.7767 | 0.653926 | 0.326963 | − | 0.945037i | \(-0.393975\pi\) | ||||
0.326963 | + | 0.945037i | \(0.393975\pi\) | |||||||
\(740\) | 13.7282 | 0.504660 | ||||||||
\(741\) | −3.21004 | −0.117924 | ||||||||
\(742\) | 26.2831 | 0.964883 | ||||||||
\(743\) | 20.9015 | 0.766801 | 0.383401 | − | 0.923582i | \(-0.374753\pi\) | ||||
0.383401 | + | 0.923582i | \(0.374753\pi\) | |||||||
\(744\) | −0.321712 | −0.0117945 | ||||||||
\(745\) | 16.2021 | 0.593597 | ||||||||
\(746\) | −14.4562 | −0.529280 | ||||||||
\(747\) | 10.0601 | 0.368079 | ||||||||
\(748\) | 13.2294 | 0.483716 | ||||||||
\(749\) | 22.9021 | 0.836826 | ||||||||
\(750\) | −12.1716 | −0.444444 | ||||||||
\(751\) | 33.8003 | 1.23339 | 0.616696 | − | 0.787202i | \(-0.288471\pi\) | ||||
0.616696 | + | 0.787202i | \(0.288471\pi\) | |||||||
\(752\) | 9.58227 | 0.349429 | ||||||||
\(753\) | −4.05411 | −0.147740 | ||||||||
\(754\) | −0.552237 | −0.0201113 | ||||||||
\(755\) | 10.5605 | 0.384335 | ||||||||
\(756\) | 2.70832 | 0.0985006 | ||||||||
\(757\) | 43.7565 | 1.59036 | 0.795179 | − | 0.606375i | \(-0.207377\pi\) | ||||
0.795179 | + | 0.606375i | \(0.207377\pi\) | |||||||
\(758\) | 11.2970 | 0.410325 | ||||||||
\(759\) | −4.88474 | −0.177305 | ||||||||
\(760\) | 10.6001 | 0.384506 | ||||||||
\(761\) | −1.33500 | −0.0483936 | −0.0241968 | − | 0.999707i | \(-0.507703\pi\) | ||||
−0.0241968 | + | 0.999707i | \(0.507703\pi\) | |||||||
\(762\) | 13.4262 | 0.486379 | ||||||||
\(763\) | 35.6538 | 1.29075 | ||||||||
\(764\) | 9.36253 | 0.338725 | ||||||||
\(765\) | 4.93884 | 0.178564 | ||||||||
\(766\) | 5.02548 | 0.181578 | ||||||||
\(767\) | 3.98562 | 0.143913 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 18.8799 | 0.680827 | 0.340413 | − | 0.940276i | \(-0.389433\pi\) | ||||
0.340413 | + | 0.940276i | \(0.389433\pi\) | |||||||
\(770\) | −24.1250 | −0.869403 | ||||||||
\(771\) | −14.8091 | −0.533335 | ||||||||
\(772\) | −11.3376 | −0.408051 | ||||||||
\(773\) | 17.3328 | 0.623418 | 0.311709 | − | 0.950178i | \(-0.399099\pi\) | ||||
0.311709 | + | 0.950178i | \(0.399099\pi\) | |||||||
\(774\) | −11.6613 | −0.419155 | ||||||||
\(775\) | −0.538723 | −0.0193515 | ||||||||
\(776\) | 12.8091 | 0.459818 | ||||||||
\(777\) | −20.3887 | −0.731440 | ||||||||
\(778\) | −29.6742 | −1.06387 | ||||||||
\(779\) | −9.12652 | −0.326991 | ||||||||
\(780\) | 1.00705 | 0.0360581 | ||||||||
\(781\) | 19.9155 | 0.712633 | ||||||||
\(782\) | 2.70832 | 0.0968493 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0.334998 | 0.0119642 | ||||||||
\(785\) | −16.7468 | −0.597719 | ||||||||
\(786\) | 1.64452 | 0.0586579 | ||||||||
\(787\) | 23.0963 | 0.823295 | 0.411648 | − | 0.911343i | \(-0.364953\pi\) | ||||
0.411648 | + | 0.911343i | \(0.364953\pi\) | |||||||
\(788\) | −10.5070 | −0.374297 | ||||||||
\(789\) | −2.43183 | −0.0865754 | ||||||||
\(790\) | −2.13244 | −0.0758688 | ||||||||
\(791\) | 24.5477 | 0.872815 | ||||||||
\(792\) | 4.88474 | 0.173572 | ||||||||
\(793\) | 0.615889 | 0.0218708 | ||||||||
\(794\) | 8.87395 | 0.314925 | ||||||||
\(795\) | 17.6971 | 0.627651 | ||||||||
\(796\) | −5.78026 | −0.204876 | ||||||||
\(797\) | −36.2791 | −1.28507 | −0.642537 | − | 0.766255i | \(-0.722118\pi\) | ||||
−0.642537 | + | 0.766255i | \(0.722118\pi\) | |||||||
\(798\) | −15.7429 | −0.557293 | ||||||||
\(799\) | −25.9519 | −0.918111 | ||||||||
\(800\) | 1.67455 | 0.0592042 | ||||||||
\(801\) | −16.8091 | −0.593919 | ||||||||
\(802\) | 16.2073 | 0.572298 | ||||||||
\(803\) | 32.1709 | 1.13529 | ||||||||
\(804\) | −9.17268 | −0.323495 | ||||||||
\(805\) | −4.93884 | −0.174071 | ||||||||
\(806\) | 0.177661 | 0.00625785 | ||||||||
\(807\) | −16.9678 | −0.597294 | ||||||||
\(808\) | 7.42619 | 0.261252 | ||||||||
\(809\) | 23.4620 | 0.824881 | 0.412440 | − | 0.910985i | \(-0.364677\pi\) | ||||
0.412440 | + | 0.910985i | \(0.364677\pi\) | |||||||
\(810\) | 1.82358 | 0.0640741 | ||||||||
\(811\) | −11.6395 | −0.408719 | −0.204359 | − | 0.978896i | \(-0.565511\pi\) | ||||
−0.204359 | + | 0.978896i | \(0.565511\pi\) | |||||||
\(812\) | −2.70832 | −0.0950434 | ||||||||
\(813\) | 19.5078 | 0.684169 | ||||||||
\(814\) | −36.7731 | −1.28890 | ||||||||
\(815\) | 33.0746 | 1.15855 | ||||||||
\(816\) | −2.70832 | −0.0948102 | ||||||||
\(817\) | 67.7845 | 2.37148 | ||||||||
\(818\) | −23.1428 | −0.809169 | ||||||||
\(819\) | −1.49563 | −0.0522617 | ||||||||
\(820\) | 2.86316 | 0.0999859 | ||||||||
\(821\) | −1.96416 | −0.0685497 | −0.0342749 | − | 0.999412i | \(-0.510912\pi\) | ||||
−0.0342749 | + | 0.999412i | \(0.510912\pi\) | |||||||
\(822\) | 6.24727 | 0.217899 | ||||||||
\(823\) | −34.3932 | −1.19887 | −0.599436 | − | 0.800423i | \(-0.704609\pi\) | ||||
−0.599436 | + | 0.800423i | \(0.704609\pi\) | |||||||
\(824\) | 13.4059 | 0.467015 | ||||||||
\(825\) | 8.17973 | 0.284782 | ||||||||
\(826\) | 19.5466 | 0.680113 | ||||||||
\(827\) | 26.3857 | 0.917520 | 0.458760 | − | 0.888560i | \(-0.348294\pi\) | ||||
0.458760 | + | 0.888560i | \(0.348294\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 16.1731 | 0.561715 | 0.280858 | − | 0.959749i | \(-0.409381\pi\) | ||||
0.280858 | + | 0.959749i | \(0.409381\pi\) | |||||||
\(830\) | 18.3454 | 0.636777 | ||||||||
\(831\) | −22.1728 | −0.769167 | ||||||||
\(832\) | −0.552237 | −0.0191454 | ||||||||
\(833\) | −0.907281 | −0.0314354 | ||||||||
\(834\) | 4.83063 | 0.167271 | ||||||||
\(835\) | −35.8762 | −1.24155 | ||||||||
\(836\) | −28.3940 | −0.982026 | ||||||||
\(837\) | 0.321712 | 0.0111200 | ||||||||
\(838\) | 25.8843 | 0.894159 | ||||||||
\(839\) | −3.90522 | −0.134823 | −0.0674117 | − | 0.997725i | \(-0.521474\pi\) | ||||
−0.0674117 | + | 0.997725i | \(0.521474\pi\) | |||||||
\(840\) | 4.93884 | 0.170406 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −4.11417 | −0.141784 | ||||||||
\(843\) | −8.04332 | −0.277027 | ||||||||
\(844\) | 17.6708 | 0.608254 | ||||||||
\(845\) | 23.1504 | 0.796399 | ||||||||
\(846\) | −9.58227 | −0.329445 | ||||||||
\(847\) | 34.8308 | 1.19680 | ||||||||
\(848\) | −9.70458 | −0.333257 | ||||||||
\(849\) | 13.1612 | 0.451692 | ||||||||
\(850\) | −4.53521 | −0.155556 | ||||||||
\(851\) | −7.52816 | −0.258062 | ||||||||
\(852\) | −4.07709 | −0.139679 | ||||||||
\(853\) | −43.7431 | −1.49773 | −0.748867 | − | 0.662720i | \(-0.769402\pi\) | ||||
−0.748867 | + | 0.662720i | \(0.769402\pi\) | |||||||
\(854\) | 3.02049 | 0.103359 | ||||||||
\(855\) | −10.6001 | −0.362516 | ||||||||
\(856\) | −8.45622 | −0.289028 | ||||||||
\(857\) | 8.81551 | 0.301132 | 0.150566 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150566 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(858\) | −2.69753 | −0.0920922 | ||||||||
\(859\) | −14.2831 | −0.487333 | −0.243667 | − | 0.969859i | \(-0.578350\pi\) | ||||
−0.243667 | + | 0.969859i | \(0.578350\pi\) | |||||||
\(860\) | −21.2653 | −0.725140 | ||||||||
\(861\) | −4.25226 | −0.144917 | ||||||||
\(862\) | −13.4281 | −0.457363 | ||||||||
\(863\) | −31.2535 | −1.06388 | −0.531942 | − | 0.846781i | \(-0.678537\pi\) | ||||
−0.531942 | + | 0.846781i | \(0.678537\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 32.0884 | 1.09104 | ||||||||
\(866\) | −8.56162 | −0.290936 | ||||||||
\(867\) | −9.66500 | −0.328241 | ||||||||
\(868\) | 0.871300 | 0.0295738 | ||||||||
\(869\) | 5.71206 | 0.193768 | ||||||||
\(870\) | −1.82358 | −0.0618252 | ||||||||
\(871\) | 5.06549 | 0.171638 | ||||||||
\(872\) | −13.1645 | −0.445808 | ||||||||
\(873\) | −12.8091 | −0.433521 | ||||||||
\(874\) | −5.81279 | −0.196621 | ||||||||
\(875\) | 32.9646 | 1.11441 | ||||||||
\(876\) | −6.58601 | −0.222521 | ||||||||
\(877\) | 25.3863 | 0.857233 | 0.428617 | − | 0.903486i | \(-0.359001\pi\) | ||||
0.428617 | + | 0.903486i | \(0.359001\pi\) | |||||||
\(878\) | −8.42700 | −0.284397 | ||||||||
\(879\) | 14.4129 | 0.486135 | ||||||||
\(880\) | 8.90772 | 0.300279 | ||||||||
\(881\) | 54.3583 | 1.83138 | 0.915689 | − | 0.401888i | \(-0.131646\pi\) | ||||
0.915689 | + | 0.401888i | \(0.131646\pi\) | |||||||
\(882\) | −0.334998 | −0.0112800 | ||||||||
\(883\) | 24.6076 | 0.828111 | 0.414056 | − | 0.910252i | \(-0.364112\pi\) | ||||
0.414056 | + | 0.910252i | \(0.364112\pi\) | |||||||
\(884\) | 1.49563 | 0.0503036 | ||||||||
\(885\) | 13.1612 | 0.442410 | ||||||||
\(886\) | 9.49563 | 0.319012 | ||||||||
\(887\) | 11.9875 | 0.402502 | 0.201251 | − | 0.979540i | \(-0.435499\pi\) | ||||
0.201251 | + | 0.979540i | \(0.435499\pi\) | |||||||
\(888\) | 7.52816 | 0.252629 | ||||||||
\(889\) | −36.3624 | −1.21956 | ||||||||
\(890\) | −30.6527 | −1.02748 | ||||||||
\(891\) | −4.88474 | −0.163645 | ||||||||
\(892\) | −25.0996 | −0.840398 | ||||||||
\(893\) | 55.6997 | 1.86392 | ||||||||
\(894\) | 8.88474 | 0.297150 | ||||||||
\(895\) | −7.82424 | −0.261536 | ||||||||
\(896\) | −2.70832 | −0.0904786 | ||||||||
\(897\) | −0.552237 | −0.0184386 | ||||||||
\(898\) | 11.1165 | 0.370963 | ||||||||
\(899\) | −0.321712 | −0.0107297 | ||||||||
\(900\) | −1.67455 | −0.0558183 | ||||||||
\(901\) | 26.2831 | 0.875617 | ||||||||
\(902\) | −7.66940 | −0.255363 | ||||||||
\(903\) | 31.5824 | 1.05100 | ||||||||
\(904\) | −9.06380 | −0.301458 | ||||||||
\(905\) | −28.6338 | −0.951818 | ||||||||
\(906\) | 5.79105 | 0.192395 | ||||||||
\(907\) | 46.0795 | 1.53004 | 0.765022 | − | 0.644005i | \(-0.222728\pi\) | ||||
0.765022 | + | 0.644005i | \(0.222728\pi\) | |||||||
\(908\) | 15.8080 | 0.524606 | ||||||||
\(909\) | −7.42619 | −0.246311 | ||||||||
\(910\) | −2.72741 | −0.0904128 | ||||||||
\(911\) | 27.6380 | 0.915688 | 0.457844 | − | 0.889033i | \(-0.348622\pi\) | ||||
0.457844 | + | 0.889033i | \(0.348622\pi\) | |||||||
\(912\) | 5.81279 | 0.192481 | ||||||||
\(913\) | −49.1408 | −1.62632 | ||||||||
\(914\) | 23.7977 | 0.787157 | ||||||||
\(915\) | 2.03377 | 0.0672344 | ||||||||
\(916\) | −16.4454 | −0.543372 | ||||||||
\(917\) | −4.45387 | −0.147080 | ||||||||
\(918\) | 2.70832 | 0.0893879 | ||||||||
\(919\) | 0.836122 | 0.0275811 | 0.0137906 | − | 0.999905i | \(-0.495610\pi\) | ||||
0.0137906 | + | 0.999905i | \(0.495610\pi\) | |||||||
\(920\) | 1.82358 | 0.0601217 | ||||||||
\(921\) | 23.2632 | 0.766549 | ||||||||
\(922\) | 39.2849 | 1.29378 | ||||||||
\(923\) | 2.25152 | 0.0741096 | ||||||||
\(924\) | −13.2294 | −0.435216 | ||||||||
\(925\) | 12.6063 | 0.414492 | ||||||||
\(926\) | −22.5163 | −0.739931 | ||||||||
\(927\) | −13.4059 | −0.440306 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −41.4694 | −1.36057 | −0.680283 | − | 0.732949i | \(-0.738143\pi\) | ||||
−0.680283 | + | 0.732949i | \(0.738143\pi\) | |||||||
\(930\) | 0.586669 | 0.0192376 | ||||||||
\(931\) | 1.94727 | 0.0638193 | ||||||||
\(932\) | −0.276491 | −0.00905677 | ||||||||
\(933\) | −29.7024 | −0.972413 | ||||||||
\(934\) | 22.2582 | 0.728311 | ||||||||
\(935\) | −24.1250 | −0.788971 | ||||||||
\(936\) | 0.552237 | 0.0180504 | ||||||||
\(937\) | −21.9085 | −0.715721 | −0.357860 | − | 0.933775i | \(-0.616494\pi\) | ||||
−0.357860 | + | 0.933775i | \(0.616494\pi\) | |||||||
\(938\) | 24.8425 | 0.811138 | ||||||||
\(939\) | −24.2473 | −0.791280 | ||||||||
\(940\) | −17.4741 | −0.569941 | ||||||||
\(941\) | 32.2202 | 1.05035 | 0.525174 | − | 0.850995i | \(-0.324000\pi\) | ||||
0.525174 | + | 0.850995i | \(0.324000\pi\) | |||||||
\(942\) | −9.18347 | −0.299214 | ||||||||
\(943\) | −1.57007 | −0.0511287 | ||||||||
\(944\) | −7.21724 | −0.234901 | ||||||||
\(945\) | −4.93884 | −0.160661 | ||||||||
\(946\) | 56.9622 | 1.85200 | ||||||||
\(947\) | −13.0996 | −0.425681 | −0.212841 | − | 0.977087i | \(-0.568272\pi\) | ||||
−0.212841 | + | 0.977087i | \(0.568272\pi\) | |||||||
\(948\) | −1.16937 | −0.0379793 | ||||||||
\(949\) | 3.63704 | 0.118063 | ||||||||
\(950\) | 9.73380 | 0.315806 | ||||||||
\(951\) | 18.4543 | 0.598422 | ||||||||
\(952\) | 7.33500 | 0.237729 | ||||||||
\(953\) | −23.2563 | −0.753346 | −0.376673 | − | 0.926346i | \(-0.622932\pi\) | ||||
−0.376673 | + | 0.926346i | \(0.622932\pi\) | |||||||
\(954\) | 9.70458 | 0.314197 | ||||||||
\(955\) | −17.0734 | −0.552481 | ||||||||
\(956\) | 14.9002 | 0.481908 | ||||||||
\(957\) | 4.88474 | 0.157901 | ||||||||
\(958\) | 12.4859 | 0.403402 | ||||||||
\(959\) | −16.9196 | −0.546363 | ||||||||
\(960\) | −1.82358 | −0.0588559 | ||||||||
\(961\) | −30.8965 | −0.996661 | ||||||||
\(962\) | −4.15733 | −0.134038 | ||||||||
\(963\) | 8.45622 | 0.272498 | ||||||||
\(964\) | −21.3111 | −0.686384 | ||||||||
\(965\) | 20.6751 | 0.665556 | ||||||||
\(966\) | −2.70832 | −0.0871388 | ||||||||
\(967\) | 37.7354 | 1.21349 | 0.606745 | − | 0.794897i | \(-0.292475\pi\) | ||||
0.606745 | + | 0.794897i | \(0.292475\pi\) | |||||||
\(968\) | −12.8607 | −0.413357 | ||||||||
\(969\) | −15.7429 | −0.505735 | ||||||||
\(970\) | −23.3584 | −0.749992 | ||||||||
\(971\) | 12.3447 | 0.396160 | 0.198080 | − | 0.980186i | \(-0.436529\pi\) | ||||
0.198080 | + | 0.980186i | \(0.436529\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −13.0829 | −0.419418 | ||||||||
\(974\) | 16.6942 | 0.534917 | ||||||||
\(975\) | 0.924747 | 0.0296156 | ||||||||
\(976\) | −1.11526 | −0.0356987 | ||||||||
\(977\) | −18.9184 | −0.605253 | −0.302627 | − | 0.953109i | \(-0.597863\pi\) | ||||
−0.302627 | + | 0.953109i | \(0.597863\pi\) | |||||||
\(978\) | 18.1372 | 0.579962 | ||||||||
\(979\) | 82.1078 | 2.62418 | ||||||||
\(980\) | −0.610896 | −0.0195143 | ||||||||
\(981\) | 13.1645 | 0.420311 | ||||||||
\(982\) | −5.82689 | −0.185944 | ||||||||
\(983\) | 44.2215 | 1.41045 | 0.705224 | − | 0.708985i | \(-0.250847\pi\) | ||||
0.705224 | + | 0.708985i | \(0.250847\pi\) | |||||||
\(984\) | 1.57007 | 0.0500521 | ||||||||
\(985\) | 19.1604 | 0.610501 | ||||||||
\(986\) | −2.70832 | −0.0862505 | ||||||||
\(987\) | 25.9519 | 0.826057 | ||||||||
\(988\) | −3.21004 | −0.102125 | ||||||||
\(989\) | 11.6613 | 0.370807 | ||||||||
\(990\) | −8.90772 | −0.283106 | ||||||||
\(991\) | −57.0882 | −1.81347 | −0.906733 | − | 0.421705i | \(-0.861432\pi\) | ||||
−0.906733 | + | 0.421705i | \(0.861432\pi\) | |||||||
\(992\) | −0.321712 | −0.0102144 | ||||||||
\(993\) | 25.7072 | 0.815794 | ||||||||
\(994\) | 11.0421 | 0.350233 | ||||||||
\(995\) | 10.5408 | 0.334165 | ||||||||
\(996\) | 10.0601 | 0.318765 | ||||||||
\(997\) | −30.0627 | −0.952096 | −0.476048 | − | 0.879419i | \(-0.657931\pi\) | ||||
−0.476048 | + | 0.879419i | \(0.657931\pi\) | |||||||
\(998\) | −22.6359 | −0.716528 | ||||||||
\(999\) | −7.52816 | −0.238181 |
(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 | 4002.2.a.bb.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4002.2.a.bb.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial |