Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4225,2,Mod(1,4225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.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: | \(33.7367948540\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 17x^{7} - 9x^{6} + 59x^{5} + 32x^{4} - 44x^{3} - 23x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 845) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.421015\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0240266 | −0.0169894 | −0.00849470 | − | 0.999964i | \(-0.502704\pi\) | ||||
−0.00849470 | + | 0.999964i | \(0.502704\pi\) | |||||||
\(3\) | −2.93017 | −1.69173 | −0.845867 | − | 0.533394i | \(-0.820916\pi\) | ||||
−0.845867 | + | 0.533394i | \(0.820916\pi\) | |||||||
\(4\) | −1.99942 | −0.999711 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0704021 | 0.0287415 | ||||||||
\(7\) | 1.66541 | 0.629467 | 0.314734 | − | 0.949180i | \(-0.398085\pi\) | ||||
0.314734 | + | 0.949180i | \(0.398085\pi\) | |||||||
\(8\) | 0.0960927 | 0.0339739 | ||||||||
\(9\) | 5.58589 | 1.86196 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.33397 | 1.00523 | 0.502615 | − | 0.864510i | \(-0.332371\pi\) | ||||
0.502615 | + | 0.864510i | \(0.332371\pi\) | |||||||
\(12\) | 5.85865 | 1.69125 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.0400143 | −0.0106943 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.99654 | 0.999134 | ||||||||
\(17\) | −7.07621 | −1.71623 | −0.858116 | − | 0.513455i | \(-0.828365\pi\) | ||||
−0.858116 | + | 0.513455i | \(0.828365\pi\) | |||||||
\(18\) | −0.134210 | −0.0316337 | ||||||||
\(19\) | −6.68286 | −1.53315 | −0.766577 | − | 0.642153i | \(-0.778042\pi\) | ||||
−0.766577 | + | 0.642153i | \(0.778042\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.87994 | −1.06489 | ||||||||
\(22\) | −0.0801041 | −0.0170783 | ||||||||
\(23\) | −4.02860 | −0.840021 | −0.420011 | − | 0.907519i | \(-0.637974\pi\) | ||||
−0.420011 | + | 0.907519i | \(0.637974\pi\) | |||||||
\(24\) | −0.281568 | −0.0574748 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.57710 | −1.45821 | ||||||||
\(28\) | −3.32987 | −0.629286 | ||||||||
\(29\) | −0.000401110 0 | −7.44842e−5 0 | −3.72421e−5 | − | 1.00000i | \(-0.500012\pi\) | ||||
−3.72421e−5 | 1.00000i | \(0.500012\pi\) | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.14759 | 0.744929 | 0.372464 | − | 0.928046i | \(-0.378513\pi\) | ||||
0.372464 | + | 0.928046i | \(0.378513\pi\) | |||||||
\(32\) | −0.288209 | −0.0509486 | ||||||||
\(33\) | −9.76910 | −1.70058 | ||||||||
\(34\) | 0.170018 | 0.0291578 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11.1686 | −1.86143 | ||||||||
\(37\) | 8.96459 | 1.47377 | 0.736885 | − | 0.676018i | \(-0.236296\pi\) | ||||
0.736885 | + | 0.676018i | \(0.236296\pi\) | |||||||
\(38\) | 0.160567 | 0.0260474 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.60848 | 1.50059 | 0.750296 | − | 0.661102i | \(-0.229911\pi\) | ||||
0.750296 | + | 0.661102i | \(0.229911\pi\) | |||||||
\(42\) | 0.117249 | 0.0180919 | ||||||||
\(43\) | −2.78606 | −0.424870 | −0.212435 | − | 0.977175i | \(-0.568139\pi\) | ||||
−0.212435 | + | 0.977175i | \(0.568139\pi\) | |||||||
\(44\) | −6.66601 | −1.00494 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0967937 | 0.0142715 | ||||||||
\(47\) | −0.958374 | −0.139793 | −0.0698966 | − | 0.997554i | \(-0.522267\pi\) | ||||
−0.0698966 | + | 0.997554i | \(0.522267\pi\) | |||||||
\(48\) | −11.7105 | −1.69027 | ||||||||
\(49\) | −4.22640 | −0.603771 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.7345 | 2.90341 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.68268 | 0.505855 | 0.252928 | − | 0.967485i | \(-0.418607\pi\) | ||||
0.252928 | + | 0.967485i | \(0.418607\pi\) | |||||||
\(54\) | 0.182052 | 0.0247742 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.160034 | 0.0213855 | ||||||||
\(57\) | 19.5819 | 2.59369 | ||||||||
\(58\) | 9.63732e−6 0 | 1.26544e−6 0 | ||||||||
\(59\) | 7.99148 | 1.04040 | 0.520201 | − | 0.854044i | \(-0.325857\pi\) | ||||
0.520201 | + | 0.854044i | \(0.325857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.14117 | −1.17041 | −0.585203 | − | 0.810886i | \(-0.698985\pi\) | ||||
−0.585203 | + | 0.810886i | \(0.698985\pi\) | |||||||
\(62\) | −0.0996526 | −0.0126559 | ||||||||
\(63\) | 9.30282 | 1.17205 | ||||||||
\(64\) | −7.98615 | −0.998269 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.234719 | 0.0288919 | ||||||||
\(67\) | 6.72871 | 0.822042 | 0.411021 | − | 0.911626i | \(-0.365172\pi\) | ||||
0.411021 | + | 0.911626i | \(0.365172\pi\) | |||||||
\(68\) | 14.1483 | 1.71574 | ||||||||
\(69\) | 11.8045 | 1.42109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.38321 | −0.520191 | −0.260096 | − | 0.965583i | \(-0.583754\pi\) | ||||
−0.260096 | + | 0.965583i | \(0.583754\pi\) | |||||||
\(72\) | 0.536763 | 0.0632582 | ||||||||
\(73\) | 1.97245 | 0.230858 | 0.115429 | − | 0.993316i | \(-0.463176\pi\) | ||||
0.115429 | + | 0.993316i | \(0.463176\pi\) | |||||||
\(74\) | −0.215389 | −0.0250385 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.3619 | 1.53271 | ||||||||
\(77\) | 5.55244 | 0.632759 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.77988 | −0.425269 | −0.212635 | − | 0.977132i | \(-0.568204\pi\) | ||||
−0.212635 | + | 0.977132i | \(0.568204\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.44451 | 0.604945 | ||||||||
\(82\) | −0.230860 | −0.0254942 | ||||||||
\(83\) | −3.64818 | −0.400440 | −0.200220 | − | 0.979751i | \(-0.564166\pi\) | ||||
−0.200220 | + | 0.979751i | \(0.564166\pi\) | |||||||
\(84\) | 9.75707 | 1.06458 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.0669397 | 0.00721830 | ||||||||
\(87\) | 0.00117532 | 0.000126007 0 | ||||||||
\(88\) | 0.320370 | 0.0341516 | ||||||||
\(89\) | −0.989573 | −0.104895 | −0.0524473 | − | 0.998624i | \(-0.516702\pi\) | ||||
−0.0524473 | + | 0.998624i | \(0.516702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.05487 | 0.839779 | ||||||||
\(93\) | −12.1531 | −1.26022 | ||||||||
\(94\) | 0.0230265 | 0.00237500 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.844500 | 0.0861915 | ||||||||
\(97\) | 18.4460 | 1.87291 | 0.936454 | − | 0.350790i | \(-0.114087\pi\) | ||||
0.936454 | + | 0.350790i | \(0.114087\pi\) | |||||||
\(98\) | 0.101546 | 0.0102577 | ||||||||
\(99\) | 18.6232 | 1.87170 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.86892 | −0.981994 | −0.490997 | − | 0.871161i | \(-0.663367\pi\) | ||||
−0.490997 | + | 0.871161i | \(0.663367\pi\) | |||||||
\(102\) | −0.498180 | −0.0493272 | ||||||||
\(103\) | 15.1288 | 1.49069 | 0.745344 | − | 0.666680i | \(-0.232285\pi\) | ||||
0.745344 | + | 0.666680i | \(0.232285\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.0884825 | −0.00859418 | ||||||||
\(107\) | −2.99312 | −0.289356 | −0.144678 | − | 0.989479i | \(-0.546215\pi\) | ||||
−0.144678 | + | 0.989479i | \(0.546215\pi\) | |||||||
\(108\) | 15.1498 | 1.45779 | ||||||||
\(109\) | 13.4179 | 1.28520 | 0.642602 | − | 0.766200i | \(-0.277855\pi\) | ||||
0.642602 | + | 0.766200i | \(0.277855\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.2678 | −2.49323 | ||||||||
\(112\) | 6.65589 | 0.628922 | ||||||||
\(113\) | 3.38444 | 0.318382 | 0.159191 | − | 0.987248i | \(-0.449111\pi\) | ||||
0.159191 | + | 0.987248i | \(0.449111\pi\) | |||||||
\(114\) | −0.470488 | −0.0440652 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.000801988 0 | 7.44627e−5 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.192009 | −0.0176758 | ||||||||
\(119\) | −11.7848 | −1.08031 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.115354 | 0.0104868 | ||||||||
\(122\) | 0.219632 | 0.0198845 | ||||||||
\(123\) | −28.1545 | −2.53860 | ||||||||
\(124\) | −8.29278 | −0.744714 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.223516 | −0.0199124 | ||||||||
\(127\) | −8.29226 | −0.735819 | −0.367910 | − | 0.929862i | \(-0.619926\pi\) | ||||
−0.367910 | + | 0.929862i | \(0.619926\pi\) | |||||||
\(128\) | 0.768298 | 0.0679086 | ||||||||
\(129\) | 8.16363 | 0.718768 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.86438 | 0.425003 | 0.212501 | − | 0.977161i | \(-0.431839\pi\) | ||||
0.212501 | + | 0.977161i | \(0.431839\pi\) | |||||||
\(132\) | 19.5326 | 1.70009 | ||||||||
\(133\) | −11.1297 | −0.965070 | ||||||||
\(134\) | −0.161668 | −0.0139660 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.679972 | −0.0583071 | ||||||||
\(137\) | 4.43432 | 0.378850 | 0.189425 | − | 0.981895i | \(-0.439338\pi\) | ||||
0.189425 | + | 0.981895i | \(0.439338\pi\) | |||||||
\(138\) | −0.283622 | −0.0241435 | ||||||||
\(139\) | 6.07076 | 0.514915 | 0.257457 | − | 0.966290i | \(-0.417115\pi\) | ||||
0.257457 | + | 0.966290i | \(0.417115\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.80820 | 0.236493 | ||||||||
\(142\) | 0.105314 | 0.00883773 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 22.3242 | 1.86035 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.0473914 | −0.00392214 | ||||||||
\(147\) | 12.3841 | 1.02142 | ||||||||
\(148\) | −17.9240 | −1.47334 | ||||||||
\(149\) | −12.0203 | −0.984741 | −0.492370 | − | 0.870386i | \(-0.663869\pi\) | ||||
−0.492370 | + | 0.870386i | \(0.663869\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.64251 | 0.540560 | 0.270280 | − | 0.962782i | \(-0.412884\pi\) | ||||
0.270280 | + | 0.962782i | \(0.412884\pi\) | |||||||
\(152\) | −0.642174 | −0.0520872 | ||||||||
\(153\) | −39.5269 | −3.19556 | ||||||||
\(154\) | −0.133406 | −0.0107502 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.94035 | −0.713517 | −0.356759 | − | 0.934197i | \(-0.616118\pi\) | ||||
−0.356759 | + | 0.934197i | \(0.616118\pi\) | |||||||
\(158\) | 0.0908177 | 0.00722507 | ||||||||
\(159\) | −10.7909 | −0.855773 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.70929 | −0.528766 | ||||||||
\(162\) | −0.130813 | −0.0102777 | ||||||||
\(163\) | 4.49497 | 0.352073 | 0.176037 | − | 0.984384i | \(-0.443672\pi\) | ||||
0.176037 | + | 0.984384i | \(0.443672\pi\) | |||||||
\(164\) | −19.2114 | −1.50016 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0876536 | 0.00680324 | ||||||||
\(167\) | −18.1721 | −1.40620 | −0.703098 | − | 0.711093i | \(-0.748201\pi\) | ||||
−0.703098 | + | 0.711093i | \(0.748201\pi\) | |||||||
\(168\) | −0.468927 | −0.0361785 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −37.3297 | −2.85468 | ||||||||
\(172\) | 5.57052 | 0.424748 | ||||||||
\(173\) | −0.0851909 | −0.00647694 | −0.00323847 | − | 0.999995i | \(-0.501031\pi\) | ||||
−0.00323847 | + | 0.999995i | \(0.501031\pi\) | |||||||
\(174\) | −2.82390e−5 0 | −2.14079e−6 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.3243 | 1.00436 | ||||||||
\(177\) | −23.4164 | −1.76008 | ||||||||
\(178\) | 0.0237761 | 0.00178210 | ||||||||
\(179\) | 9.57903 | 0.715970 | 0.357985 | − | 0.933727i | \(-0.383464\pi\) | ||||
0.357985 | + | 0.933727i | \(0.383464\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0716 | −0.822946 | −0.411473 | − | 0.911422i | \(-0.634986\pi\) | ||||
−0.411473 | + | 0.911422i | \(0.634986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.7852 | 1.98002 | ||||||||
\(184\) | −0.387119 | −0.0285388 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.291999 | 0.0214104 | ||||||||
\(187\) | −23.5919 | −1.72521 | ||||||||
\(188\) | 1.91619 | 0.139753 | ||||||||
\(189\) | −12.6190 | −0.917898 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.6800 | −1.42399 | −0.711996 | − | 0.702183i | \(-0.752209\pi\) | ||||
−0.711996 | + | 0.702183i | \(0.752209\pi\) | |||||||
\(192\) | 23.4008 | 1.68880 | ||||||||
\(193\) | 2.22851 | 0.160412 | 0.0802060 | − | 0.996778i | \(-0.474442\pi\) | ||||
0.0802060 | + | 0.996778i | \(0.474442\pi\) | |||||||
\(194\) | −0.443196 | −0.0318196 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.45035 | 0.603597 | ||||||||
\(197\) | −9.53209 | −0.679134 | −0.339567 | − | 0.940582i | \(-0.610280\pi\) | ||||
−0.339567 | + | 0.940582i | \(0.610280\pi\) | |||||||
\(198\) | −0.447453 | −0.0317991 | ||||||||
\(199\) | −20.4192 | −1.44748 | −0.723741 | − | 0.690072i | \(-0.757579\pi\) | ||||
−0.723741 | + | 0.690072i | \(0.757579\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.7162 | −1.39068 | ||||||||
\(202\) | 0.237117 | 0.0166835 | ||||||||
\(203\) | −0.000668014 0 | −4.68854e−5 0 | ||||||||
\(204\) | −41.4570 | −2.90257 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.363495 | −0.0253259 | ||||||||
\(207\) | −22.5033 | −1.56409 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.2805 | −1.54117 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.41514 | −0.441637 | −0.220818 | − | 0.975315i | \(-0.570873\pi\) | ||||
−0.220818 | + | 0.975315i | \(0.570873\pi\) | |||||||
\(212\) | −7.36324 | −0.505709 | ||||||||
\(213\) | 12.8435 | 0.880025 | ||||||||
\(214\) | 0.0719146 | 0.00491598 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.728104 | −0.0495412 | ||||||||
\(217\) | 6.90745 | 0.468908 | ||||||||
\(218\) | −0.322388 | −0.0218349 | ||||||||
\(219\) | −5.77962 | −0.390550 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.631127 | 0.0423584 | ||||||||
\(223\) | −2.85750 | −0.191353 | −0.0956763 | − | 0.995412i | \(-0.530501\pi\) | ||||
−0.0956763 | + | 0.995412i | \(0.530501\pi\) | |||||||
\(224\) | −0.479987 | −0.0320705 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.0813168 | −0.00540911 | ||||||||
\(227\) | −22.2069 | −1.47393 | −0.736963 | − | 0.675933i | \(-0.763741\pi\) | ||||
−0.736963 | + | 0.675933i | \(0.763741\pi\) | |||||||
\(228\) | −39.1525 | −2.59294 | ||||||||
\(229\) | −20.0068 | −1.32209 | −0.661045 | − | 0.750347i | \(-0.729887\pi\) | ||||
−0.661045 | + | 0.750347i | \(0.729887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.2696 | −1.07046 | ||||||||
\(232\) | −3.85437e−5 0 | −2.53052e−6 0 | ||||||||
\(233\) | −2.11070 | −0.138276 | −0.0691381 | − | 0.997607i | \(-0.522025\pi\) | ||||
−0.0691381 | + | 0.997607i | \(0.522025\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.9784 | −1.04010 | ||||||||
\(237\) | 11.0757 | 0.719442 | ||||||||
\(238\) | 0.283150 | 0.0183539 | ||||||||
\(239\) | −18.8655 | −1.22031 | −0.610154 | − | 0.792283i | \(-0.708892\pi\) | ||||
−0.610154 | + | 0.792283i | \(0.708892\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0649 | −0.841584 | −0.420792 | − | 0.907157i | \(-0.638248\pi\) | ||||
−0.420792 | + | 0.907157i | \(0.638248\pi\) | |||||||
\(242\) | −0.00277158 | −0.000178164 0 | ||||||||
\(243\) | 6.77797 | 0.434807 | ||||||||
\(244\) | 18.2771 | 1.17007 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.676458 | 0.0431294 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.398553 | 0.0253081 | ||||||||
\(249\) | 10.6898 | 0.677438 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.9931 | 0.757001 | 0.378500 | − | 0.925601i | \(-0.376440\pi\) | ||||
0.378500 | + | 0.925601i | \(0.376440\pi\) | |||||||
\(252\) | −18.6003 | −1.17171 | ||||||||
\(253\) | −13.4312 | −0.844414 | ||||||||
\(254\) | 0.199235 | 0.0125011 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.9538 | 0.997115 | ||||||||
\(257\) | 26.6130 | 1.66007 | 0.830036 | − | 0.557709i | \(-0.188320\pi\) | ||||
0.830036 | + | 0.557709i | \(0.188320\pi\) | |||||||
\(258\) | −0.196145 | −0.0122114 | ||||||||
\(259\) | 14.9298 | 0.927690 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.00224056 | −0.000138687 0 | ||||||||
\(262\) | −0.116875 | −0.00722055 | ||||||||
\(263\) | 17.0235 | 1.04971 | 0.524856 | − | 0.851191i | \(-0.324119\pi\) | ||||
0.524856 | + | 0.851191i | \(0.324119\pi\) | |||||||
\(264\) | −0.938739 | −0.0577754 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.267410 | 0.0163960 | ||||||||
\(267\) | 2.89962 | 0.177454 | ||||||||
\(268\) | −13.4535 | −0.821805 | ||||||||
\(269\) | 5.98522 | 0.364925 | 0.182463 | − | 0.983213i | \(-0.441593\pi\) | ||||
0.182463 | + | 0.983213i | \(0.441593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.11684 | −0.432317 | −0.216159 | − | 0.976358i | \(-0.569353\pi\) | ||||
−0.216159 | + | 0.976358i | \(0.569353\pi\) | |||||||
\(272\) | −28.2803 | −1.71475 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.106542 | −0.00643643 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −23.6021 | −1.42068 | ||||||||
\(277\) | −7.48738 | −0.449873 | −0.224936 | − | 0.974373i | \(-0.572217\pi\) | ||||
−0.224936 | + | 0.974373i | \(0.572217\pi\) | |||||||
\(278\) | −0.145860 | −0.00874810 | ||||||||
\(279\) | 23.1680 | 1.38703 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.8752 | 1.48393 | 0.741964 | − | 0.670440i | \(-0.233895\pi\) | ||||
0.741964 | + | 0.670440i | \(0.233895\pi\) | |||||||
\(282\) | −0.0674716 | −0.00401787 | ||||||||
\(283\) | −12.7413 | −0.757390 | −0.378695 | − | 0.925522i | \(-0.623627\pi\) | ||||
−0.378695 | + | 0.925522i | \(0.623627\pi\) | |||||||
\(284\) | 8.76388 | 0.520041 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.0021 | 0.944574 | ||||||||
\(288\) | −1.60990 | −0.0948644 | ||||||||
\(289\) | 33.0727 | 1.94545 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −54.0499 | −3.16846 | ||||||||
\(292\) | −3.94377 | −0.230791 | ||||||||
\(293\) | 17.5748 | 1.02673 | 0.513365 | − | 0.858171i | \(-0.328399\pi\) | ||||
0.513365 | + | 0.858171i | \(0.328399\pi\) | |||||||
\(294\) | −0.297547 | −0.0173533 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.861432 | 0.0500697 | ||||||||
\(297\) | −25.2618 | −1.46584 | ||||||||
\(298\) | 0.288807 | 0.0167302 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.63995 | −0.267442 | ||||||||
\(302\) | −0.159597 | −0.00918379 | ||||||||
\(303\) | 28.9176 | 1.66127 | ||||||||
\(304\) | −26.7083 | −1.53183 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.949700 | 0.0542907 | ||||||||
\(307\) | −0.592094 | −0.0337926 | −0.0168963 | − | 0.999857i | \(-0.505379\pi\) | ||||
−0.0168963 | + | 0.999857i | \(0.505379\pi\) | |||||||
\(308\) | −11.1017 | −0.632577 | ||||||||
\(309\) | −44.3300 | −2.52185 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.6771 | −1.34260 | −0.671301 | − | 0.741185i | \(-0.734264\pi\) | ||||
−0.671301 | + | 0.741185i | \(0.734264\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.09689 | −0.514187 | −0.257093 | − | 0.966387i | \(-0.582765\pi\) | ||||
−0.257093 | + | 0.966387i | \(0.582765\pi\) | |||||||
\(314\) | 0.214807 | 0.0121222 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.55757 | 0.425146 | ||||||||
\(317\) | −4.34397 | −0.243982 | −0.121991 | − | 0.992531i | \(-0.538928\pi\) | ||||
−0.121991 | + | 0.992531i | \(0.538928\pi\) | |||||||
\(318\) | 0.259269 | 0.0145391 | ||||||||
\(319\) | −0.00133729 | −7.48737e−5 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.77034 | 0.489513 | ||||||||
\(322\) | 0.161202 | 0.00898342 | ||||||||
\(323\) | 47.2893 | 2.63125 | ||||||||
\(324\) | −10.8859 | −0.604771 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.107999 | −0.00598152 | ||||||||
\(327\) | −39.3168 | −2.17422 | ||||||||
\(328\) | 0.923305 | 0.0509810 | ||||||||
\(329\) | −1.59609 | −0.0879953 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.3221 | −1.06204 | −0.531019 | − | 0.847360i | \(-0.678191\pi\) | ||||
−0.531019 | + | 0.847360i | \(0.678191\pi\) | |||||||
\(332\) | 7.29426 | 0.400324 | ||||||||
\(333\) | 50.0752 | 2.74411 | ||||||||
\(334\) | 0.436614 | 0.0238904 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −19.5029 | −1.06397 | ||||||||
\(337\) | 5.22779 | 0.284776 | 0.142388 | − | 0.989811i | \(-0.454522\pi\) | ||||
0.142388 | + | 0.989811i | \(0.454522\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.91699 | −0.538617 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.8279 | 0.748825 | ||||||||
\(342\) | 0.896908 | 0.0484992 | ||||||||
\(343\) | −18.6966 | −1.00952 | ||||||||
\(344\) | −0.267720 | −0.0144345 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.00204685 | 0.000110039 0 | ||||||||
\(347\) | 18.8624 | 1.01259 | 0.506293 | − | 0.862361i | \(-0.331015\pi\) | ||||
0.506293 | + | 0.862361i | \(0.331015\pi\) | |||||||
\(348\) | −0.00234996 | −0.000125971 0 | ||||||||
\(349\) | 27.8225 | 1.48930 | 0.744652 | − | 0.667453i | \(-0.232616\pi\) | ||||
0.744652 | + | 0.667453i | \(0.232616\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.960879 | −0.0512150 | ||||||||
\(353\) | −34.6884 | −1.84627 | −0.923137 | − | 0.384470i | \(-0.874384\pi\) | ||||
−0.923137 | + | 0.384470i | \(0.874384\pi\) | |||||||
\(354\) | 0.562617 | 0.0299028 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.97858 | 0.104864 | ||||||||
\(357\) | 34.5315 | 1.82760 | ||||||||
\(358\) | −0.230152 | −0.0121639 | ||||||||
\(359\) | 27.1511 | 1.43298 | 0.716490 | − | 0.697597i | \(-0.245747\pi\) | ||||
0.716490 | + | 0.697597i | \(0.245747\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.6606 | 1.35056 | ||||||||
\(362\) | 0.266014 | 0.0139814 | ||||||||
\(363\) | −0.338008 | −0.0177408 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.643558 | −0.0336393 | ||||||||
\(367\) | −25.2613 | −1.31863 | −0.659315 | − | 0.751867i | \(-0.729153\pi\) | ||||
−0.659315 | + | 0.751867i | \(0.729153\pi\) | |||||||
\(368\) | −16.1004 | −0.839294 | ||||||||
\(369\) | 53.6719 | 2.79405 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.13319 | 0.318419 | ||||||||
\(372\) | 24.2993 | 1.25986 | ||||||||
\(373\) | −4.53353 | −0.234737 | −0.117369 | − | 0.993088i | \(-0.537446\pi\) | ||||
−0.117369 | + | 0.993088i | \(0.537446\pi\) | |||||||
\(374\) | 0.566833 | 0.0293103 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.0920928 | −0.00474932 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.303192 | 0.0155945 | ||||||||
\(379\) | −5.35880 | −0.275263 | −0.137632 | − | 0.990483i | \(-0.543949\pi\) | ||||
−0.137632 | + | 0.990483i | \(0.543949\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.2977 | 1.24481 | ||||||||
\(382\) | 0.472843 | 0.0241928 | ||||||||
\(383\) | −5.61342 | −0.286832 | −0.143416 | − | 0.989662i | \(-0.545809\pi\) | ||||
−0.143416 | + | 0.989662i | \(0.545809\pi\) | |||||||
\(384\) | −2.25124 | −0.114883 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.0535437 | −0.00272530 | ||||||||
\(387\) | −15.5626 | −0.791093 | ||||||||
\(388\) | −36.8814 | −1.87237 | ||||||||
\(389\) | 2.71877 | 0.137847 | 0.0689236 | − | 0.997622i | \(-0.478044\pi\) | ||||
0.0689236 | + | 0.997622i | \(0.478044\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.5072 | 1.44167 | ||||||||
\(392\) | −0.406126 | −0.0205125 | ||||||||
\(393\) | −14.2535 | −0.718992 | ||||||||
\(394\) | 0.229024 | 0.0115381 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −37.2356 | −1.87116 | ||||||||
\(397\) | −5.01013 | −0.251451 | −0.125726 | − | 0.992065i | \(-0.540126\pi\) | ||||
−0.125726 | + | 0.992065i | \(0.540126\pi\) | |||||||
\(398\) | 0.490606 | 0.0245919 | ||||||||
\(399\) | 32.6120 | 1.63264 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.0325 | −0.950435 | −0.475218 | − | 0.879868i | \(-0.657631\pi\) | ||||
−0.475218 | + | 0.879868i | \(0.657631\pi\) | |||||||
\(402\) | 0.473715 | 0.0236268 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 19.7321 | 0.981711 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.60501e−5 0 | 7.96555e−7 0 | ||||||||
\(407\) | 29.8877 | 1.48148 | ||||||||
\(408\) | 1.99243 | 0.0986401 | ||||||||
\(409\) | −11.9424 | −0.590513 | −0.295256 | − | 0.955418i | \(-0.595405\pi\) | ||||
−0.295256 | + | 0.955418i | \(0.595405\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.9933 | −0.640913 | ||||||||
\(412\) | −30.2489 | −1.49026 | ||||||||
\(413\) | 13.3091 | 0.654899 | ||||||||
\(414\) | 0.540679 | 0.0265729 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.7883 | −0.871099 | ||||||||
\(418\) | 0.535325 | 0.0261836 | ||||||||
\(419\) | −2.49593 | −0.121934 | −0.0609671 | − | 0.998140i | \(-0.519418\pi\) | ||||
−0.0609671 | + | 0.998140i | \(0.519418\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.2220 | 1.13177 | 0.565885 | − | 0.824484i | \(-0.308535\pi\) | ||||
0.565885 | + | 0.824484i | \(0.308535\pi\) | |||||||
\(422\) | 0.154134 | 0.00750314 | ||||||||
\(423\) | −5.35337 | −0.260290 | ||||||||
\(424\) | 0.353879 | 0.0171859 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.308587 | −0.0149511 | ||||||||
\(427\) | −15.2238 | −0.736733 | ||||||||
\(428\) | 5.98451 | 0.289272 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.6779 | −0.899682 | −0.449841 | − | 0.893109i | \(-0.648519\pi\) | ||||
−0.449841 | + | 0.893109i | \(0.648519\pi\) | |||||||
\(432\) | −30.2822 | −1.45695 | ||||||||
\(433\) | −26.2912 | −1.26348 | −0.631738 | − | 0.775182i | \(-0.717658\pi\) | ||||
−0.631738 | + | 0.775182i | \(0.717658\pi\) | |||||||
\(434\) | −0.165963 | −0.00796647 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −26.8281 | −1.28483 | ||||||||
\(437\) | 26.9226 | 1.28788 | ||||||||
\(438\) | 0.138865 | 0.00663522 | ||||||||
\(439\) | 7.98298 | 0.381007 | 0.190503 | − | 0.981687i | \(-0.438988\pi\) | ||||
0.190503 | + | 0.981687i | \(0.438988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −23.6082 | −1.12420 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −40.4743 | −1.92299 | −0.961495 | − | 0.274823i | \(-0.911381\pi\) | ||||
−0.961495 | + | 0.274823i | \(0.911381\pi\) | |||||||
\(444\) | 52.5204 | 2.49251 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.0686562 | 0.00325097 | ||||||||
\(447\) | 35.2215 | 1.66592 | ||||||||
\(448\) | −13.3002 | −0.628377 | ||||||||
\(449\) | 15.7278 | 0.742241 | 0.371121 | − | 0.928585i | \(-0.378974\pi\) | ||||
0.371121 | + | 0.928585i | \(0.378974\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.0344 | 1.50844 | ||||||||
\(452\) | −6.76693 | −0.318290 | ||||||||
\(453\) | −19.4637 | −0.914483 | ||||||||
\(454\) | 0.533558 | 0.0250411 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.88168 | 0.0881177 | ||||||||
\(457\) | 21.2829 | 0.995573 | 0.497786 | − | 0.867300i | \(-0.334146\pi\) | ||||
0.497786 | + | 0.867300i | \(0.334146\pi\) | |||||||
\(458\) | 0.480697 | 0.0224615 | ||||||||
\(459\) | 53.6171 | 2.50263 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.2892 | 1.78331 | 0.891653 | − | 0.452720i | \(-0.149546\pi\) | ||||
0.891653 | + | 0.452720i | \(0.149546\pi\) | |||||||
\(462\) | 0.390904 | 0.0181865 | ||||||||
\(463\) | −12.1131 | −0.562944 | −0.281472 | − | 0.959569i | \(-0.590823\pi\) | ||||
−0.281472 | + | 0.959569i | \(0.590823\pi\) | |||||||
\(464\) | −0.00160305 | −7.44197e−5 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.0507129 | 0.00234923 | ||||||||
\(467\) | −23.2313 | −1.07502 | −0.537509 | − | 0.843258i | \(-0.680635\pi\) | ||||
−0.537509 | + | 0.843258i | \(0.680635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2061 | 0.517449 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 26.1967 | 1.20708 | ||||||||
\(472\) | 0.767923 | 0.0353465 | ||||||||
\(473\) | −9.28865 | −0.427092 | ||||||||
\(474\) | −0.266111 | −0.0122229 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 23.5628 | 1.08000 | ||||||||
\(477\) | 20.5711 | 0.941884 | ||||||||
\(478\) | 0.453275 | 0.0207323 | ||||||||
\(479\) | −37.9716 | −1.73497 | −0.867483 | − | 0.497466i | \(-0.834264\pi\) | ||||
−0.867483 | + | 0.497466i | \(0.834264\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.313906 | 0.0142980 | ||||||||
\(483\) | 19.6593 | 0.894531 | ||||||||
\(484\) | −0.230642 | −0.0104837 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.162852 | −0.00738711 | ||||||||
\(487\) | −22.1216 | −1.00242 | −0.501212 | − | 0.865324i | \(-0.667112\pi\) | ||||
−0.501212 | + | 0.865324i | \(0.667112\pi\) | |||||||
\(488\) | −0.878400 | −0.0397633 | ||||||||
\(489\) | −13.1710 | −0.595615 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.1440 | −1.17986 | −0.589931 | − | 0.807453i | \(-0.700845\pi\) | ||||
−0.589931 | + | 0.807453i | \(0.700845\pi\) | |||||||
\(492\) | 56.2927 | 2.53787 | ||||||||
\(493\) | 0.00283834 | 0.000127832 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.5760 | 0.744284 | ||||||||
\(497\) | −7.29986 | −0.327443 | ||||||||
\(498\) | −0.256840 | −0.0115093 | ||||||||
\(499\) | 22.5180 | 1.00805 | 0.504023 | − | 0.863690i | \(-0.331853\pi\) | ||||
0.504023 | + | 0.863690i | \(0.331853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 53.2472 | 2.37891 | ||||||||
\(502\) | −0.288155 | −0.0128610 | ||||||||
\(503\) | −20.4701 | −0.912716 | −0.456358 | − | 0.889796i | \(-0.650846\pi\) | ||||
−0.456358 | + | 0.889796i | \(0.650846\pi\) | |||||||
\(504\) | 0.893933 | 0.0398190 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.322707 | 0.0143461 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.5797 | 0.735607 | ||||||||
\(509\) | −20.2724 | −0.898557 | −0.449278 | − | 0.893392i | \(-0.648319\pi\) | ||||
−0.449278 | + | 0.893392i | \(0.648319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.28495 | 0.145318 | ||||||||
\(512\) | −1.91991 | −0.0848490 | ||||||||
\(513\) | 50.6367 | 2.23567 | ||||||||
\(514\) | −0.639421 | −0.0282036 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −16.3226 | −0.718560 | ||||||||
\(517\) | −3.19519 | −0.140524 | ||||||||
\(518\) | −0.358712 | −0.0157609 | ||||||||
\(519\) | 0.249624 | 0.0109573 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.1602 | −1.32134 | −0.660670 | − | 0.750676i | \(-0.729728\pi\) | ||||
−0.660670 | + | 0.750676i | \(0.729728\pi\) | |||||||
\(522\) | 5.38330e−5 0 | 2.35621e−6 0 | ||||||||
\(523\) | −14.1082 | −0.616910 | −0.308455 | − | 0.951239i | \(-0.599812\pi\) | ||||
−0.308455 | + | 0.951239i | \(0.599812\pi\) | |||||||
\(524\) | −9.72595 | −0.424880 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.409017 | −0.0178340 | ||||||||
\(527\) | −29.3492 | −1.27847 | ||||||||
\(528\) | −39.0425 | −1.69911 | ||||||||
\(529\) | −6.77038 | −0.294364 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 44.6396 | 1.93719 | ||||||||
\(532\) | 22.2530 | 0.964792 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.0696681 | −0.00301483 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.646580 | 0.0279280 | ||||||||
\(537\) | −28.0682 | −1.21123 | ||||||||
\(538\) | −0.143805 | −0.00619986 | ||||||||
\(539\) | −14.0907 | −0.606928 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.5648 | −1.44306 | −0.721532 | − | 0.692381i | \(-0.756562\pi\) | ||||
−0.721532 | + | 0.692381i | \(0.756562\pi\) | |||||||
\(542\) | 0.170994 | 0.00734481 | ||||||||
\(543\) | 32.4417 | 1.39221 | ||||||||
\(544\) | 2.03943 | 0.0874396 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.8045 | −1.48813 | −0.744067 | − | 0.668106i | \(-0.767105\pi\) | ||||
−0.744067 | + | 0.668106i | \(0.767105\pi\) | |||||||
\(548\) | −8.86609 | −0.378740 | ||||||||
\(549\) | −51.0616 | −2.17926 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.00268056 | 0.000114196 0 | ||||||||
\(552\) | 1.13432 | 0.0482801 | ||||||||
\(553\) | −6.29506 | −0.267693 | ||||||||
\(554\) | 0.179897 | 0.00764307 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.1380 | −0.514766 | ||||||||
\(557\) | −18.3989 | −0.779587 | −0.389794 | − | 0.920902i | \(-0.627454\pi\) | ||||
−0.389794 | + | 0.920902i | \(0.627454\pi\) | |||||||
\(558\) | −0.556649 | −0.0235648 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 69.1282 | 2.91859 | ||||||||
\(562\) | −0.597667 | −0.0252110 | ||||||||
\(563\) | −18.6109 | −0.784357 | −0.392178 | − | 0.919889i | \(-0.628278\pi\) | ||||
−0.392178 | + | 0.919889i | \(0.628278\pi\) | |||||||
\(564\) | −5.61477 | −0.236425 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.306130 | 0.0128676 | ||||||||
\(567\) | 9.06736 | 0.380793 | ||||||||
\(568\) | −0.421194 | −0.0176729 | ||||||||
\(569\) | −10.8666 | −0.455550 | −0.227775 | − | 0.973714i | \(-0.573145\pi\) | ||||
−0.227775 | + | 0.973714i | \(0.573145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.9376 | 1.62949 | 0.814743 | − | 0.579822i | \(-0.196878\pi\) | ||||
0.814743 | + | 0.579822i | \(0.196878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 57.6656 | 2.40902 | ||||||||
\(574\) | −0.384477 | −0.0160477 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −44.6098 | −1.85874 | ||||||||
\(577\) | 33.9986 | 1.41538 | 0.707691 | − | 0.706522i | \(-0.249737\pi\) | ||||
0.707691 | + | 0.706522i | \(0.249737\pi\) | |||||||
\(578\) | −0.794627 | −0.0330521 | ||||||||
\(579\) | −6.52992 | −0.271374 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.07573 | −0.252064 | ||||||||
\(582\) | 1.29864 | 0.0538303 | ||||||||
\(583\) | 12.2780 | 0.508501 | ||||||||
\(584\) | 0.189538 | 0.00784315 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.422263 | −0.0174435 | ||||||||
\(587\) | −17.9777 | −0.742018 | −0.371009 | − | 0.928629i | \(-0.620988\pi\) | ||||
−0.371009 | + | 0.928629i | \(0.620988\pi\) | |||||||
\(588\) | −24.7610 | −1.02112 | ||||||||
\(589\) | −27.7178 | −1.14209 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.9306 | 1.14891 | ||||||||
\(592\) | 35.8273 | 1.47249 | ||||||||
\(593\) | −26.9189 | −1.10542 | −0.552712 | − | 0.833372i | \(-0.686407\pi\) | ||||
−0.552712 | + | 0.833372i | \(0.686407\pi\) | |||||||
\(594\) | 0.606957 | 0.0249037 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.0336 | 0.984457 | ||||||||
\(597\) | 59.8318 | 2.44875 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.68542 | −0.354877 | −0.177438 | − | 0.984132i | \(-0.556781\pi\) | ||||
−0.177438 | + | 0.984132i | \(0.556781\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.3757 | −1.27984 | −0.639921 | − | 0.768440i | \(-0.721033\pi\) | ||||
−0.639921 | + | 0.768440i | \(0.721033\pi\) | |||||||
\(602\) | 0.111482 | 0.00454368 | ||||||||
\(603\) | 37.5858 | 1.53061 | ||||||||
\(604\) | −13.2812 | −0.540404 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.694793 | −0.0282240 | ||||||||
\(607\) | −3.77489 | −0.153218 | −0.0766091 | − | 0.997061i | \(-0.524409\pi\) | ||||
−0.0766091 | + | 0.997061i | \(0.524409\pi\) | |||||||
\(608\) | 1.92606 | 0.0781120 | ||||||||
\(609\) | 0.00195739 | 7.93176e−5 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 79.0310 | 3.19464 | ||||||||
\(613\) | 28.6074 | 1.15544 | 0.577722 | − | 0.816234i | \(-0.303942\pi\) | ||||
0.577722 | + | 0.816234i | \(0.303942\pi\) | |||||||
\(614\) | 0.0142260 | 0.000574116 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.533549 | 0.0214973 | ||||||||
\(617\) | −12.6947 | −0.511071 | −0.255535 | − | 0.966800i | \(-0.582252\pi\) | ||||
−0.255535 | + | 0.966800i | \(0.582252\pi\) | |||||||
\(618\) | 1.06510 | 0.0428447 | ||||||||
\(619\) | −24.5421 | −0.986430 | −0.493215 | − | 0.869907i | \(-0.664178\pi\) | ||||
−0.493215 | + | 0.869907i | \(0.664178\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.5251 | 1.22493 | ||||||||
\(622\) | 0.568880 | 0.0228100 | ||||||||
\(623\) | −1.64805 | −0.0660277 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.218568 | 0.00873573 | ||||||||
\(627\) | 65.2855 | 2.60725 | ||||||||
\(628\) | 17.8755 | 0.713311 | ||||||||
\(629\) | −63.4353 | −2.52933 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.66905 | −0.305300 | −0.152650 | − | 0.988280i | \(-0.548781\pi\) | ||||
−0.152650 | + | 0.988280i | \(0.548781\pi\) | |||||||
\(632\) | −0.363218 | −0.0144481 | ||||||||
\(633\) | 18.7974 | 0.747132 | ||||||||
\(634\) | 0.104371 | 0.00414510 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 21.5755 | 0.855526 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.21305e−5 0 | 1.27206e−6 0 | ||||||||
\(639\) | −24.4841 | −0.968577 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.98009 | −0.354692 | −0.177346 | − | 0.984149i | \(-0.556751\pi\) | ||||
−0.177346 | + | 0.984149i | \(0.556751\pi\) | |||||||
\(642\) | −0.210722 | −0.00831653 | ||||||||
\(643\) | −14.1503 | −0.558032 | −0.279016 | − | 0.960287i | \(-0.590008\pi\) | ||||
−0.279016 | + | 0.960287i | \(0.590008\pi\) | |||||||
\(644\) | 13.4147 | 0.528613 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.13620 | −0.0447033 | ||||||||
\(647\) | −21.8757 | −0.860024 | −0.430012 | − | 0.902823i | \(-0.641491\pi\) | ||||
−0.430012 | + | 0.902823i | \(0.641491\pi\) | |||||||
\(648\) | 0.523177 | 0.0205524 | ||||||||
\(649\) | 26.6434 | 1.04584 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.2400 | −0.793268 | ||||||||
\(652\) | −8.98735 | −0.351972 | ||||||||
\(653\) | 45.1455 | 1.76668 | 0.883340 | − | 0.468733i | \(-0.155289\pi\) | ||||
0.883340 | + | 0.468733i | \(0.155289\pi\) | |||||||
\(654\) | 0.944651 | 0.0369388 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 38.4006 | 1.49929 | ||||||||
\(657\) | 11.0179 | 0.429849 | ||||||||
\(658\) | 0.0383487 | 0.00149499 | ||||||||
\(659\) | 32.9439 | 1.28331 | 0.641656 | − | 0.766993i | \(-0.278248\pi\) | ||||
0.641656 | + | 0.766993i | \(0.278248\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.7714 | −1.15798 | −0.578988 | − | 0.815336i | \(-0.696552\pi\) | ||||
−0.578988 | + | 0.815336i | \(0.696552\pi\) | |||||||
\(662\) | 0.464245 | 0.0180434 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.350564 | −0.0136045 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.20314 | −0.0466207 | ||||||||
\(667\) | 0.00161591 | 6.25683e−5 0 | ||||||||
\(668\) | 36.3336 | 1.40579 | ||||||||
\(669\) | 8.37297 | 0.323718 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.4764 | −1.17653 | ||||||||
\(672\) | 1.40644 | 0.0542547 | ||||||||
\(673\) | 24.7144 | 0.952671 | 0.476336 | − | 0.879264i | \(-0.341965\pi\) | ||||
0.476336 | + | 0.879264i | \(0.341965\pi\) | |||||||
\(674\) | −0.125606 | −0.00483817 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −47.2303 | −1.81521 | −0.907605 | − | 0.419826i | \(-0.862091\pi\) | ||||
−0.907605 | + | 0.419826i | \(0.862091\pi\) | |||||||
\(678\) | 0.238272 | 0.00915078 | ||||||||
\(679\) | 30.7202 | 1.17893 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 65.0700 | 2.49349 | ||||||||
\(682\) | −0.332239 | −0.0127221 | ||||||||
\(683\) | 32.6572 | 1.24959 | 0.624797 | − | 0.780787i | \(-0.285182\pi\) | ||||
0.624797 | + | 0.780787i | \(0.285182\pi\) | |||||||
\(684\) | 74.6379 | 2.85385 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.449216 | 0.0171512 | ||||||||
\(687\) | 58.6234 | 2.23662 | ||||||||
\(688\) | −11.1346 | −0.424503 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.93042 | −0.111479 | −0.0557393 | − | 0.998445i | \(-0.517752\pi\) | ||||
−0.0557393 | + | 0.998445i | \(0.517752\pi\) | |||||||
\(692\) | 0.170333 | 0.00647507 | ||||||||
\(693\) | 31.0153 | 1.17817 | ||||||||
\(694\) | −0.453200 | −0.0172032 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.000112940 0 | 4.28097e−6 0 | ||||||||
\(697\) | −67.9916 | −2.57537 | ||||||||
\(698\) | −0.668481 | −0.0253024 | ||||||||
\(699\) | 6.18469 | 0.233927 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.4881 | 0.547210 | 0.273605 | − | 0.961842i | \(-0.411784\pi\) | ||||
0.273605 | + | 0.961842i | \(0.411784\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −59.9091 | −2.25952 | ||||||||
\(704\) | −26.6256 | −1.00349 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.833445 | 0.0313671 | ||||||||
\(707\) | −16.4358 | −0.618133 | ||||||||
\(708\) | 46.8193 | 1.75958 | ||||||||
\(709\) | 49.2943 | 1.85129 | 0.925643 | − | 0.378397i | \(-0.123525\pi\) | ||||
0.925643 | + | 0.378397i | \(0.123525\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.1140 | −0.791836 | ||||||||
\(712\) | −0.0950908 | −0.00356368 | ||||||||
\(713\) | −16.7090 | −0.625756 | ||||||||
\(714\) | −0.829676 | −0.0310499 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.1525 | −0.715764 | ||||||||
\(717\) | 55.2791 | 2.06444 | ||||||||
\(718\) | −0.652350 | −0.0243455 | ||||||||
\(719\) | −26.0709 | −0.972282 | −0.486141 | − | 0.873880i | \(-0.661596\pi\) | ||||
−0.486141 | + | 0.873880i | \(0.661596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.1958 | 0.938339 | ||||||||
\(722\) | −0.616539 | −0.0229452 | ||||||||
\(723\) | 38.2823 | 1.42374 | ||||||||
\(724\) | 22.1368 | 0.822709 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.00812119 | 0.000301405 0 | ||||||||
\(727\) | 53.8109 | 1.99574 | 0.997868 | − | 0.0652593i | \(-0.0207875\pi\) | ||||
0.997868 | + | 0.0652593i | \(0.0207875\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −36.1941 | −1.34052 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.7148 | 0.729177 | ||||||||
\(732\) | −53.5549 | −1.97945 | ||||||||
\(733\) | −16.4544 | −0.607758 | −0.303879 | − | 0.952711i | \(-0.598282\pi\) | ||||
−0.303879 | + | 0.952711i | \(0.598282\pi\) | |||||||
\(734\) | 0.606944 | 0.0224027 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.16108 | 0.0427979 | ||||||||
\(737\) | 22.4333 | 0.826341 | ||||||||
\(738\) | −1.28956 | −0.0474692 | ||||||||
\(739\) | −8.56267 | −0.314983 | −0.157491 | − | 0.987520i | \(-0.550341\pi\) | ||||
−0.157491 | + | 0.987520i | \(0.550341\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.147360 | −0.00540976 | ||||||||
\(743\) | 36.8946 | 1.35353 | 0.676766 | − | 0.736199i | \(-0.263381\pi\) | ||||
0.676766 | + | 0.736199i | \(0.263381\pi\) | |||||||
\(744\) | −1.16783 | −0.0428146 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.108926 | 0.00398805 | ||||||||
\(747\) | −20.3783 | −0.745605 | ||||||||
\(748\) | 47.1701 | 1.72471 | ||||||||
\(749\) | −4.98478 | −0.182140 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.2206 | −0.701369 | −0.350685 | − | 0.936494i | \(-0.614051\pi\) | ||||
−0.350685 | + | 0.936494i | \(0.614051\pi\) | |||||||
\(752\) | −3.83018 | −0.139672 | ||||||||
\(753\) | −35.1420 | −1.28064 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 25.2307 | 0.917633 | ||||||||
\(757\) | 36.7110 | 1.33428 | 0.667142 | − | 0.744931i | \(-0.267518\pi\) | ||||
0.667142 | + | 0.744931i | \(0.267518\pi\) | |||||||
\(758\) | 0.128754 | 0.00467656 | ||||||||
\(759\) | 39.3558 | 1.42852 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.8270 | −0.464979 | −0.232489 | − | 0.972599i | \(-0.574687\pi\) | ||||
−0.232489 | + | 0.972599i | \(0.574687\pi\) | |||||||
\(762\) | −0.583793 | −0.0211486 | ||||||||
\(763\) | 22.3464 | 0.808994 | ||||||||
\(764\) | 39.3486 | 1.42358 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.134872 | 0.00487311 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −46.7474 | −1.68685 | ||||||||
\(769\) | −34.6300 | −1.24879 | −0.624396 | − | 0.781108i | \(-0.714655\pi\) | ||||
−0.624396 | + | 0.781108i | \(0.714655\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −77.9806 | −2.80840 | ||||||||
\(772\) | −4.45574 | −0.160366 | ||||||||
\(773\) | 21.1483 | 0.760653 | 0.380326 | − | 0.924852i | \(-0.375812\pi\) | ||||
0.380326 | + | 0.924852i | \(0.375812\pi\) | |||||||
\(774\) | 0.373918 | 0.0134402 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.77253 | 0.0636300 | ||||||||
\(777\) | −43.7467 | −1.56941 | ||||||||
\(778\) | −0.0653229 | −0.00234194 | ||||||||
\(779\) | −64.2122 | −2.30064 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.6135 | −0.522911 | ||||||||
\(782\) | −0.684933 | −0.0244931 | ||||||||
\(783\) | 0.00303925 | 0.000108614 0 | ||||||||
\(784\) | −16.8909 | −0.603248 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.342463 | 0.0122152 | ||||||||
\(787\) | −20.7662 | −0.740235 | −0.370117 | − | 0.928985i | \(-0.620683\pi\) | ||||
−0.370117 | + | 0.928985i | \(0.620683\pi\) | |||||||
\(788\) | 19.0587 | 0.678938 | ||||||||
\(789\) | −49.8816 | −1.77583 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.63650 | 0.200411 | ||||||||
\(792\) | 1.78955 | 0.0635890 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.120377 | 0.00427200 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 40.8267 | 1.44706 | ||||||||
\(797\) | 15.7183 | 0.556770 | 0.278385 | − | 0.960470i | \(-0.410201\pi\) | ||||
0.278385 | + | 0.960470i | \(0.410201\pi\) | |||||||
\(798\) | −0.783557 | −0.0277376 | ||||||||
\(799\) | 6.78165 | 0.239918 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.52765 | −0.195310 | ||||||||
\(802\) | 0.457286 | 0.0161473 | ||||||||
\(803\) | 6.57610 | 0.232065 | ||||||||
\(804\) | 39.4211 | 1.39028 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.5377 | −0.617356 | ||||||||
\(808\) | −0.948331 | −0.0333622 | ||||||||
\(809\) | −5.08807 | −0.178887 | −0.0894435 | − | 0.995992i | \(-0.528509\pi\) | ||||
−0.0894435 | + | 0.995992i | \(0.528509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.0950 | 1.23235 | 0.616176 | − | 0.787608i | \(-0.288681\pi\) | ||||
0.616176 | + | 0.787608i | \(0.288681\pi\) | |||||||
\(812\) | 0.00133564 | 4.68718e−5 0 | ||||||||
\(813\) | 20.8536 | 0.731366 | ||||||||
\(814\) | −0.718101 | −0.0251694 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 82.8661 | 2.90090 | ||||||||
\(817\) | 18.6189 | 0.651392 | ||||||||
\(818\) | 0.286935 | 0.0100325 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.4352 | 0.922596 | 0.461298 | − | 0.887245i | \(-0.347384\pi\) | ||||
0.461298 | + | 0.887245i | \(0.347384\pi\) | |||||||
\(822\) | 0.312186 | 0.0108887 | ||||||||
\(823\) | −45.9498 | −1.60171 | −0.800854 | − | 0.598859i | \(-0.795621\pi\) | ||||
−0.800854 | + | 0.598859i | \(0.795621\pi\) | |||||||
\(824\) | 1.45377 | 0.0506445 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.319774 | −0.0111263 | ||||||||
\(827\) | −25.1837 | −0.875723 | −0.437861 | − | 0.899042i | \(-0.644264\pi\) | ||||
−0.437861 | + | 0.899042i | \(0.644264\pi\) | |||||||
\(828\) | 44.9937 | 1.56364 | ||||||||
\(829\) | 19.5773 | 0.679947 | 0.339973 | − | 0.940435i | \(-0.389582\pi\) | ||||
0.339973 | + | 0.940435i | \(0.389582\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.9393 | 0.761065 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.9069 | 1.03621 | ||||||||
\(834\) | 0.427394 | 0.0147995 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 44.5481 | 1.54073 | ||||||||
\(837\) | −31.4267 | −1.08627 | ||||||||
\(838\) | 0.0599689 | 0.00207159 | ||||||||
\(839\) | −14.1467 | −0.488398 | −0.244199 | − | 0.969725i | \(-0.578525\pi\) | ||||
−0.244199 | + | 0.969725i | \(0.578525\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | −0.557946 | −0.0192281 | ||||||||
\(843\) | −72.8884 | −2.51041 | ||||||||
\(844\) | 12.8266 | 0.441509 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.128624 | 0.00442217 | ||||||||
\(847\) | 0.192113 | 0.00660107 | ||||||||
\(848\) | 14.7180 | 0.505417 | ||||||||
\(849\) | 37.3341 | 1.28130 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.1148 | −1.23800 | ||||||||
\(852\) | −25.6797 | −0.879771 | ||||||||
\(853\) | 2.86179 | 0.0979860 | 0.0489930 | − | 0.998799i | \(-0.484399\pi\) | ||||
0.0489930 | + | 0.998799i | \(0.484399\pi\) | |||||||
\(854\) | 0.365778 | 0.0125167 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.287617 | −0.00983054 | ||||||||
\(857\) | −28.2816 | −0.966082 | −0.483041 | − | 0.875598i | \(-0.660468\pi\) | ||||
−0.483041 | + | 0.875598i | \(0.660468\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.52025 | −0.290707 | −0.145354 | − | 0.989380i | \(-0.546432\pi\) | ||||
−0.145354 | + | 0.989380i | \(0.546432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −46.8889 | −1.59797 | ||||||||
\(862\) | 0.448767 | 0.0152851 | ||||||||
\(863\) | −36.8913 | −1.25579 | −0.627897 | − | 0.778297i | \(-0.716084\pi\) | ||||
−0.627897 | + | 0.778297i | \(0.716084\pi\) | |||||||
\(864\) | 2.18379 | 0.0742939 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.631690 | 0.0214657 | ||||||||
\(867\) | −96.9087 | −3.29119 | ||||||||
\(868\) | −13.8109 | −0.468773 | ||||||||
\(869\) | −12.6020 | −0.427493 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.28936 | 0.0436634 | ||||||||
\(873\) | 103.037 | 3.48729 | ||||||||
\(874\) | −0.646859 | −0.0218803 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.5559 | 0.390438 | ||||||||
\(877\) | 37.6091 | 1.26997 | 0.634984 | − | 0.772525i | \(-0.281006\pi\) | ||||
0.634984 | + | 0.772525i | \(0.281006\pi\) | |||||||
\(878\) | −0.191804 | −0.00647308 | ||||||||
\(879\) | −51.4971 | −1.73695 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.3542 | 1.32588 | 0.662938 | − | 0.748675i | \(-0.269309\pi\) | ||||
0.662938 | + | 0.748675i | \(0.269309\pi\) | |||||||
\(882\) | 0.567226 | 0.0190995 | ||||||||
\(883\) | 9.17085 | 0.308624 | 0.154312 | − | 0.988022i | \(-0.450684\pi\) | ||||
0.154312 | + | 0.988022i | \(0.450684\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.972460 | 0.0326704 | ||||||||
\(887\) | −35.6093 | −1.19564 | −0.597822 | − | 0.801629i | \(-0.703967\pi\) | ||||
−0.597822 | + | 0.801629i | \(0.703967\pi\) | |||||||
\(888\) | −2.52414 | −0.0847047 | ||||||||
\(889\) | −13.8100 | −0.463174 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.1518 | 0.608109 | ||||||||
\(892\) | 5.71336 | 0.191297 | ||||||||
\(893\) | 6.40468 | 0.214324 | ||||||||
\(894\) | −0.846254 | −0.0283030 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.27953 | 0.0427462 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.377886 | −0.0126102 | ||||||||
\(899\) | −0.00166364 | −5.54855e−5 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.0594 | −0.868165 | ||||||||
\(902\) | −0.769679 | −0.0256275 | ||||||||
\(903\) | 13.5958 | 0.452441 | ||||||||
\(904\) | 0.325220 | 0.0108167 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.467647 | 0.0155365 | ||||||||
\(907\) | −32.1739 | −1.06832 | −0.534158 | − | 0.845385i | \(-0.679371\pi\) | ||||
−0.534158 | + | 0.845385i | \(0.679371\pi\) | |||||||
\(908\) | 44.4010 | 1.47350 | ||||||||
\(909\) | −55.1267 | −1.82844 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.5764 | 1.37749 | 0.688743 | − | 0.725005i | \(-0.258163\pi\) | ||||
0.688743 | + | 0.725005i | \(0.258163\pi\) | |||||||
\(912\) | 78.2598 | 2.59144 | ||||||||
\(913\) | −12.1629 | −0.402534 | ||||||||
\(914\) | −0.511357 | −0.0169142 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 40.0021 | 1.32171 | ||||||||
\(917\) | 8.10121 | 0.267525 | ||||||||
\(918\) | −1.28824 | −0.0425182 | ||||||||
\(919\) | −29.1810 | −0.962592 | −0.481296 | − | 0.876558i | \(-0.659834\pi\) | ||||
−0.481296 | + | 0.876558i | \(0.659834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.73493 | 0.0571680 | ||||||||
\(922\) | −0.919961 | −0.0302973 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 32.5298 | 1.07015 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.291037 | 0.00956408 | ||||||||
\(927\) | 84.5080 | 2.77561 | ||||||||
\(928\) | 0.000115603 0 | 3.79487e−6 0 | ||||||||
\(929\) | 0.0200966 | 0.000659349 0 | 0.000329675 | − | 1.00000i | \(-0.499895\pi\) | ||||
0.000329675 | 1.00000i | \(0.499895\pi\) | ||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.2444 | 0.925674 | ||||||||
\(932\) | 4.22017 | 0.138236 | ||||||||
\(933\) | 69.3778 | 2.27133 | ||||||||
\(934\) | 0.558171 | 0.0182639 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.2388 | 1.67390 | 0.836949 | − | 0.547281i | \(-0.184337\pi\) | ||||
0.836949 | + | 0.547281i | \(0.184337\pi\) | |||||||
\(938\) | −0.269245 | −0.00879114 | ||||||||
\(939\) | 26.6554 | 0.869867 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.4122 | 1.05661 | 0.528304 | − | 0.849055i | \(-0.322828\pi\) | ||||
0.528304 | + | 0.849055i | \(0.322828\pi\) | |||||||
\(942\) | −0.629419 | −0.0205076 | ||||||||
\(943\) | −38.7087 | −1.26053 | ||||||||
\(944\) | 31.9383 | 1.03950 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.223175 | 0.00725605 | ||||||||
\(947\) | −29.2152 | −0.949365 | −0.474683 | − | 0.880157i | \(-0.657437\pi\) | ||||
−0.474683 | + | 0.880157i | \(0.657437\pi\) | |||||||
\(948\) | −22.1450 | −0.719235 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.7286 | 0.412752 | ||||||||
\(952\) | −1.13243 | −0.0367024 | ||||||||
\(953\) | 13.0955 | 0.424204 | 0.212102 | − | 0.977248i | \(-0.431969\pi\) | ||||
0.212102 | + | 0.977248i | \(0.431969\pi\) | |||||||
\(954\) | −0.494254 | −0.0160021 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 37.7201 | 1.21996 | ||||||||
\(957\) | 0.00391848 | 0.000126666 0 | ||||||||
\(958\) | 0.912330 | 0.0294761 | ||||||||
\(959\) | 7.38498 | 0.238474 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7975 | −0.445081 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.7192 | −0.538770 | ||||||||
\(964\) | 26.1222 | 0.841341 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.472348 | −0.0151976 | ||||||||
\(967\) | 28.4227 | 0.914012 | 0.457006 | − | 0.889464i | \(-0.348922\pi\) | ||||
0.457006 | + | 0.889464i | \(0.348922\pi\) | |||||||
\(968\) | 0.0110847 | 0.000356276 0 | ||||||||
\(969\) | −138.566 | −4.45137 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.1760 | 1.25722 | 0.628608 | − | 0.777722i | \(-0.283625\pi\) | ||||
0.628608 | + | 0.777722i | \(0.283625\pi\) | |||||||
\(972\) | −13.5520 | −0.434681 | ||||||||
\(973\) | 10.1103 | 0.324122 | ||||||||
\(974\) | 0.531507 | 0.0170306 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −36.5330 | −1.16939 | ||||||||
\(977\) | −51.4703 | −1.64668 | −0.823340 | − | 0.567549i | \(-0.807892\pi\) | ||||
−0.823340 | + | 0.567549i | \(0.807892\pi\) | |||||||
\(978\) | 0.316456 | 0.0101191 | ||||||||
\(979\) | −3.29921 | −0.105443 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 74.9511 | 2.39300 | ||||||||
\(982\) | 0.628153 | 0.0200452 | ||||||||
\(983\) | −62.1330 | −1.98173 | −0.990867 | − | 0.134841i | \(-0.956948\pi\) | ||||
−0.990867 | + | 0.134841i | \(0.956948\pi\) | |||||||
\(984\) | −2.70544 | −0.0862463 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.81957e−5 0 | −2.17179e−6 0 | ||||||||
\(987\) | 4.67681 | 0.148865 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.2239 | 0.356900 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.63773 | 0.274387 | 0.137193 | − | 0.990544i | \(-0.456192\pi\) | ||||
0.137193 | + | 0.990544i | \(0.456192\pi\) | |||||||
\(992\) | −1.19537 | −0.0379531 | ||||||||
\(993\) | 56.6170 | 1.79669 | ||||||||
\(994\) | 0.175391 | 0.00556307 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.3734 | −0.677242 | ||||||||
\(997\) | −5.36590 | −0.169940 | −0.0849698 | − | 0.996384i | \(-0.527079\pi\) | ||||
−0.0849698 | + | 0.996384i | \(0.527079\pi\) | |||||||
\(998\) | −0.541033 | −0.0171261 | ||||||||
\(999\) | −67.9256 | −2.14907 |
(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 | 4225.2.a.bs.1.5 | 9 | ||
5.4 | even | 2 | 845.2.a.o.1.5 | yes | 9 | ||
13.12 | even | 2 | 4225.2.a.bt.1.5 | 9 | |||
15.14 | odd | 2 | 7605.2.a.cp.1.5 | 9 | |||
65.4 | even | 6 | 845.2.e.p.146.5 | 18 | |||
65.9 | even | 6 | 845.2.e.o.146.5 | 18 | |||
65.19 | odd | 12 | 845.2.m.j.361.9 | 36 | |||
65.24 | odd | 12 | 845.2.m.j.316.9 | 36 | |||
65.29 | even | 6 | 845.2.e.o.191.5 | 18 | |||
65.34 | odd | 4 | 845.2.c.h.506.10 | 18 | |||
65.44 | odd | 4 | 845.2.c.h.506.9 | 18 | |||
65.49 | even | 6 | 845.2.e.p.191.5 | 18 | |||
65.54 | odd | 12 | 845.2.m.j.316.10 | 36 | |||
65.59 | odd | 12 | 845.2.m.j.361.10 | 36 | |||
65.64 | even | 2 | 845.2.a.n.1.5 | ✓ | 9 | ||
195.194 | odd | 2 | 7605.2.a.cs.1.5 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
845.2.a.n.1.5 | ✓ | 9 | 65.64 | even | 2 | ||
845.2.a.o.1.5 | yes | 9 | 5.4 | even | 2 | ||
845.2.c.h.506.9 | 18 | 65.44 | odd | 4 | |||
845.2.c.h.506.10 | 18 | 65.34 | odd | 4 | |||
845.2.e.o.146.5 | 18 | 65.9 | even | 6 | |||
845.2.e.o.191.5 | 18 | 65.29 | even | 6 | |||
845.2.e.p.146.5 | 18 | 65.4 | even | 6 | |||
845.2.e.p.191.5 | 18 | 65.49 | even | 6 | |||
845.2.m.j.316.9 | 36 | 65.24 | odd | 12 | |||
845.2.m.j.316.10 | 36 | 65.54 | odd | 12 | |||
845.2.m.j.361.9 | 36 | 65.19 | odd | 12 | |||
845.2.m.j.361.10 | 36 | 65.59 | odd | 12 | |||
4225.2.a.bs.1.5 | 9 | 1.1 | even | 1 | trivial | ||
4225.2.a.bt.1.5 | 9 | 13.12 | even | 2 | |||
7605.2.a.cp.1.5 | 9 | 15.14 | odd | 2 | |||
7605.2.a.cs.1.5 | 9 | 195.194 | odd | 2 |