Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.10 | ||
Character | \(\chi\) | \(=\) | 1008.193 |
Dual form | 1008.2.t.k.961.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.40598 | + | 1.01154i | 0.811742 | + | 0.584016i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.84095 | 1.71773 | 0.858863 | − | 0.512205i | \(-0.171171\pi\) | ||||
0.858863 | + | 0.512205i | \(0.171171\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.676469 | + | 2.55781i | −0.255681 | + | 0.966761i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.953553 | + | 2.84442i | 0.317851 | + | 0.948141i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.80663 | −0.544720 | −0.272360 | − | 0.962195i | \(-0.587804\pi\) | ||||
−0.272360 | + | 0.962195i | \(0.587804\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.692713 | + | 1.19981i | −0.192124 | + | 0.332769i | −0.945954 | − | 0.324301i | \(-0.894871\pi\) |
0.753830 | + | 0.657070i | \(0.228204\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.40030 | + | 3.88530i | 1.39435 | + | 1.00318i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.833405 | + | 1.44350i | −0.202130 | + | 0.350100i | −0.949215 | − | 0.314629i | \(-0.898120\pi\) |
0.747084 | + | 0.664729i | \(0.231453\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0802084 | + | 0.138925i | 0.0184011 | + | 0.0318716i | 0.875079 | − | 0.483980i | \(-0.160809\pi\) |
−0.856678 | + | 0.515851i | \(0.827476\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.53844 | + | 2.91195i | −0.772151 | + | 0.635439i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.20038 | −0.667326 | −0.333663 | − | 0.942692i | \(-0.608285\pi\) | ||||
−0.333663 | + | 0.942692i | \(0.608285\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.75291 | 1.95058 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.53658 | + | 4.96376i | −0.295716 | + | 0.955276i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.78000 | − | 6.54716i | −0.701929 | − | 1.21578i | −0.967788 | − | 0.251765i | \(-0.918989\pi\) |
0.265859 | − | 0.964012i | \(-0.414344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.61011 | + | 2.78879i | 0.289184 | + | 0.500881i | 0.973615 | − | 0.228196i | \(-0.0732828\pi\) |
−0.684431 | + | 0.729077i | \(0.739949\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.54009 | − | 1.82749i | −0.442172 | − | 0.318125i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.59829 | + | 9.82442i | −0.439190 | + | 1.66063i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.58395 | + | 2.74348i | 0.260399 | + | 0.451025i | 0.966348 | − | 0.257238i | \(-0.0828124\pi\) |
−0.705949 | + | 0.708263i | \(0.749479\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.18761 | + | 0.986203i | −0.350297 | + | 0.157919i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00329 | − | 10.3980i | 0.937556 | − | 1.62389i | 0.167545 | − | 0.985864i | \(-0.446416\pi\) |
0.770011 | − | 0.638030i | \(-0.220250\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.45480 | − | 5.98389i | −0.526852 | − | 0.912535i | −0.999510 | − | 0.0312891i | \(-0.990039\pi\) |
0.472658 | − | 0.881246i | \(-0.343295\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.66255 | + | 10.9253i | 0.545981 | + | 1.62865i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.71921 | − | 9.90595i | 0.834232 | − | 1.44493i | −0.0604225 | − | 0.998173i | \(-0.519245\pi\) |
0.894654 | − | 0.446759i | \(-0.147422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.08478 | − | 3.46056i | −0.869254 | − | 0.494366i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.63191 | + | 1.18650i | −0.368542 | + | 0.166144i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.37450 | − | 2.38071i | 0.188802 | − | 0.327015i | −0.756049 | − | 0.654515i | \(-0.772873\pi\) |
0.944851 | + | 0.327500i | \(0.106206\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.93918 | −0.935679 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0277576 | + | 0.276460i | −0.00367658 | + | 0.0366180i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.53527 | + | 13.0515i | 0.981009 | + | 1.69916i | 0.658482 | + | 0.752597i | \(0.271199\pi\) |
0.322527 | + | 0.946560i | \(0.395468\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.60143 | − | 7.96990i | 0.589152 | − | 1.02044i | −0.405192 | − | 0.914232i | \(-0.632795\pi\) |
0.994344 | − | 0.106210i | \(-0.0338715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.92054 | + | 0.514844i | −0.997894 | + | 0.0648643i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.66068 | + | 4.60843i | −0.330016 | + | 0.571605i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.16830 | − | 10.6838i | −0.753578 | − | 1.30523i | −0.946078 | − | 0.323938i | \(-0.894993\pi\) |
0.192501 | − | 0.981297i | \(-0.438340\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.49967 | − | 3.23733i | −0.541697 | − | 0.389729i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.93289 | 0.822783 | 0.411391 | − | 0.911459i | \(-0.365043\pi\) | ||||
0.411391 | + | 0.911459i | \(0.365043\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.22457 | + | 10.7813i | −0.728531 | + | 1.26185i | 0.228973 | + | 0.973433i | \(0.426463\pi\) |
−0.957504 | + | 0.288420i | \(0.906870\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.7124 | + | 9.86551i | 1.58337 | + | 1.13917i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.22213 | − | 4.62102i | 0.139275 | − | 0.526614i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.03716 | − | 13.9208i | 0.904251 | − | 1.56621i | 0.0823313 | − | 0.996605i | \(-0.473763\pi\) |
0.821920 | − | 0.569604i | \(-0.192903\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.18147 | + | 5.42462i | −0.797941 | + | 0.602735i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.45280 | + | 2.51633i | 0.159466 | + | 0.276203i | 0.934676 | − | 0.355500i | \(-0.115689\pi\) |
−0.775210 | + | 0.631703i | \(0.782356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.20107 | + | 5.54441i | −0.347205 | + | 0.601376i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.30814 | − | 13.0288i | 0.140247 | − | 1.39684i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.04034 | + | 8.73012i | 0.534275 | + | 0.925391i | 0.999198 | + | 0.0400399i | \(0.0127485\pi\) |
−0.464923 | + | 0.885351i | \(0.653918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.60030 | − | 2.58347i | −0.272585 | − | 0.270821i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.557207 | + | 5.54967i | −0.0577797 | + | 0.575474i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.308077 | + | 0.533604i | 0.0316080 | + | 0.0547466i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.18830 | + | 7.25435i | 0.425257 | + | 0.736567i | 0.996444 | − | 0.0842527i | \(-0.0268503\pi\) |
−0.571187 | + | 0.820820i | \(0.693517\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.72272 | − | 5.13882i | −0.173140 | − | 0.516471i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.11500 | 0.807473 | 0.403736 | − | 0.914875i | \(-0.367711\pi\) | ||||
0.403736 | + | 0.914875i | \(0.367711\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.53782 | 0.742723 | 0.371362 | − | 0.928488i | \(-0.378891\pi\) | ||||
0.371362 | + | 0.928488i | \(0.378891\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.5910 | + | 11.1846i | −1.32634 | + | 1.09151i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.95731 | + | 5.12221i | 0.285894 | + | 0.495183i | 0.972826 | − | 0.231539i | \(-0.0743762\pi\) |
−0.686932 | + | 0.726722i | \(0.741043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.48409 | + | 7.76668i | −0.429498 | + | 0.743913i | −0.996829 | − | 0.0795776i | \(-0.974643\pi\) |
0.567331 | + | 0.823490i | \(0.307976\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.548154 | + | 5.45951i | −0.0520285 | + | 0.518193i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.98131 | + | 13.8240i | −0.750819 | + | 1.30046i | 0.196608 | + | 0.980482i | \(0.437007\pi\) |
−0.947426 | + | 0.319974i | \(0.896326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.2925 | −1.14628 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.07332 | − | 0.826281i | −0.376578 | − | 0.0763897i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.12842 | − | 3.10817i | −0.286782 | − | 0.284926i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.73608 | −0.703280 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.9585 | − | 8.54677i | 1.70943 | − | 0.770636i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 18.2557 | 1.63284 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.60913 | −0.763937 | −0.381968 | − | 0.924175i | \(-0.624754\pi\) | ||||
−0.381968 | + | 0.924175i | \(0.624754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.19560 | − | 11.9079i | 0.105267 | − | 1.04843i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.92966 | 0.168595 | 0.0842976 | − | 0.996441i | \(-0.473135\pi\) | ||||
0.0842976 | + | 0.996441i | \(0.473135\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.409602 | + | 0.111179i | −0.0355170 | + | 0.00964047i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.90195 | + | 19.0656i | −0.507959 | + | 1.64090i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.70885 | −0.316868 | −0.158434 | − | 0.987370i | \(-0.550645\pi\) | ||||
−0.158434 | + | 0.987370i | \(0.550645\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.134568 | + | 0.233079i | −0.0114139 | + | 0.0197695i | −0.871676 | − | 0.490083i | \(-0.836967\pi\) |
0.860262 | + | 0.509852i | \(0.170300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.0614 | − | 8.14233i | 1.52104 | − | 0.685708i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.25148 | − | 2.16762i | 0.104654 | − | 0.181266i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.5188 | − | 25.1473i | −1.20572 | − | 2.08837i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.05456 | − | 11.0205i | −0.416893 | − | 0.908956i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.31760 | 0.681404 | 0.340702 | − | 0.940171i | \(-0.389335\pi\) | ||||
0.340702 | + | 0.940171i | \(0.389335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.74138 | −0.792742 | −0.396371 | − | 0.918090i | \(-0.629731\pi\) | ||||
−0.396371 | + | 0.918090i | \(0.629731\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.90062 | − | 0.994101i | −0.396192 | − | 0.0803683i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.18434 | + | 10.7116i | 0.496738 | + | 0.860376i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1290 | − | 21.0081i | −0.968001 | − | 1.67663i | −0.701327 | − | 0.712840i | \(-0.747409\pi\) |
−0.266674 | − | 0.963787i | \(-0.585925\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.34072 | − | 1.95685i | 0.344241 | − | 0.155189i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.16496 | − | 8.18597i | 0.170623 | − | 0.645145i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.91401 | − | 6.77927i | −0.306569 | − | 0.530993i | 0.671040 | − | 0.741421i | \(-0.265848\pi\) |
−0.977609 | + | 0.210428i | \(0.932514\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.75635 | − | 7.01930i | −0.759531 | − | 0.546451i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.15395 | − | 3.73076i | 0.166678 | − | 0.288695i | −0.770572 | − | 0.637353i | \(-0.780029\pi\) |
0.937250 | + | 0.348658i | \(0.113363\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.54030 | + | 9.59608i | 0.426177 | + | 0.738160i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.318678 | + | 0.360619i | −0.0243699 | + | 0.0275772i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.66797 | − | 15.0134i | 0.659014 | − | 1.14144i | −0.321858 | − | 0.946788i | \(-0.604307\pi\) |
0.980871 | − | 0.194657i | \(-0.0623594\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.59754 | + | 24.9461i | −0.498728 | + | 1.88575i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.60772 | + | 25.9724i | −0.196008 | + | 1.95220i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.68644 | − | 16.7774i | 0.723998 | − | 1.25400i | −0.235387 | − | 0.971902i | \(-0.575636\pi\) |
0.959385 | − | 0.282100i | \(-0.0910310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.89036 | 0.214839 | 0.107420 | − | 0.994214i | \(-0.465741\pi\) | ||||
0.107420 | + | 0.994214i | \(0.465741\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.5314 | − | 6.55097i | 1.07419 | − | 0.484261i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.08387 | + | 10.5376i | 0.447295 | + | 0.774737i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.50566 | − | 2.60787i | 0.110104 | − | 0.190706i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.6569 | − | 7.28812i | −0.847915 | − | 0.530133i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.85022 | − | 3.20468i | 0.133877 | − | 0.231882i | −0.791291 | − | 0.611440i | \(-0.790591\pi\) |
0.925168 | + | 0.379558i | \(0.123924\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.38351 | + | 11.0566i | 0.459495 | + | 0.795869i | 0.998934 | − | 0.0461554i | \(-0.0146970\pi\) |
−0.539439 | + | 0.842025i | \(0.681364\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.40249 | + | 3.78796i | −0.601715 | + | 0.271261i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.44715 | 0.174352 | 0.0871762 | − | 0.996193i | \(-0.472216\pi\) | ||||
0.0871762 | + | 0.996193i | \(0.472216\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.24829 | + | 3.89415i | −0.159377 | + | 0.276049i | −0.934644 | − | 0.355584i | \(-0.884282\pi\) |
0.775267 | + | 0.631633i | \(0.217615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.13465 | − | 21.2607i | 0.150567 | − | 1.49962i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.3034 | − | 5.23958i | 1.35484 | − | 0.367746i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.0583 | − | 39.9382i | 1.61046 | − | 2.78941i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.05174 | − | 9.10324i | −0.212110 | − | 0.632719i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.144907 | − | 0.250986i | −0.0100234 | − | 0.0173611i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.09087 | + | 1.88945i | −0.0750987 | + | 0.130075i | −0.901129 | − | 0.433551i | \(-0.857261\pi\) |
0.826030 | + | 0.563625i | \(0.190594\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.74750 | + | 7.01293i | 0.667888 | + | 0.480518i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.2697 | − | 22.9838i | −0.904988 | − | 1.56749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.22237 | + | 2.23182i | −0.558171 | + | 0.151506i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.6574 | + | 8.86181i | −1.32832 | + | 0.598826i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.15462 | − | 1.99986i | −0.0776682 | − | 0.134525i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.87967 | + | 4.98773i | 0.192837 | + | 0.334003i | 0.946189 | − | 0.323614i | \(-0.104898\pi\) |
−0.753352 | + | 0.657617i | \(0.771564\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.29992 | + | 27.7414i | 0.619995 | + | 1.84943i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.5827 | −1.10063 | −0.550316 | − | 0.834956i | \(-0.685493\pi\) | ||||
−0.550316 | + | 0.834956i | \(0.685493\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5938 | −0.964382 | −0.482191 | − | 0.876066i | \(-0.660159\pi\) | ||||
−0.482191 | + | 0.876066i | \(0.660159\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.39266 | − | 5.26081i | 0.420606 | − | 0.346136i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.949438 | + | 1.64448i | 0.0621998 | + | 0.107733i | 0.895448 | − | 0.445165i | \(-0.146855\pi\) |
−0.833249 | + | 0.552898i | \(0.813522\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.9672 | − | 38.0483i | 1.43298 | − | 2.48200i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.3816 | − | 11.4424i | 1.64871 | − | 0.743261i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.46351 | − | 7.73103i | 0.288721 | − | 0.500079i | −0.684784 | − | 0.728746i | \(-0.740103\pi\) |
0.973505 | + | 0.228667i | \(0.0734368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.2929 | −1.56485 | −0.782423 | − | 0.622748i | \(-0.786016\pi\) | ||||
−0.782423 | + | 0.622748i | \(0.786016\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5842 | + | 0.362515i | −0.999730 | + | 0.0232554i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −23.3713 | − | 13.2918i | −1.49314 | − | 0.849185i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.222246 | −0.0141411 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.502769 | + | 5.00748i | −0.0318617 | + | 0.317336i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.64873 | 0.356545 | 0.178272 | − | 0.983981i | \(-0.442949\pi\) | ||||
0.178272 | + | 0.983981i | \(0.442949\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.78191 | 0.363506 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.1091 | + | 4.55730i | −0.633054 | + | 0.285389i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.5711 | −1.47033 | −0.735163 | − | 0.677891i | \(-0.762894\pi\) | ||||
−0.735163 | + | 0.677891i | \(0.762894\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.08879 | + | 2.19556i | −0.502613 | + | 0.136425i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.0184 | − | 16.9950i | 0.929618 | − | 1.05196i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.6405 | −1.58106 | −0.790531 | − | 0.612422i | \(-0.790195\pi\) | ||||
−0.790531 | + | 0.612422i | \(0.790195\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.27940 | − | 9.14419i | 0.324311 | − | 0.561723i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.74430 | + | 17.3729i | −0.106749 | + | 1.06320i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.27239 | + | 14.3282i | −0.504376 | + | 0.873606i | 0.495611 | + | 0.868545i | \(0.334944\pi\) |
−0.999987 | + | 0.00506090i | \(0.998389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.90748 | − | 15.4282i | −0.541091 | − | 0.937197i | −0.998842 | − | 0.0481166i | \(-0.984678\pi\) |
0.457751 | − | 0.889081i | \(-0.348655\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.04267 | − | 6.26262i | −0.0631053 | − | 0.379031i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.6199 | −1.06252 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.84382 | −0.351121 | −0.175560 | − | 0.984469i | \(-0.556174\pi\) | ||||
−0.175560 | + | 0.984469i | \(0.556174\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.39716 | + | 7.23908i | −0.382988 | + | 0.433392i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.5591 | − | 18.2889i | −0.629905 | − | 1.09103i | −0.987570 | − | 0.157177i | \(-0.949761\pi\) |
0.357666 | − | 0.933850i | \(-0.383573\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.38811 | − | 11.0645i | −0.379734 | − | 0.657718i | 0.611289 | − | 0.791407i | \(-0.290651\pi\) |
−0.991023 | + | 0.133689i | \(0.957318\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.106616 | + | 1.06187i | −0.00631536 | + | 0.0628997i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.5351 | + | 22.3892i | 1.33020 | + | 1.32159i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.11087 | + | 12.3164i | 0.418287 | + | 0.724494i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.44944 | + | 14.4361i | −0.0849675 | + | 0.846260i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.93828 | − | 10.2854i | 0.346918 | − | 0.600880i | −0.638782 | − | 0.769388i | \(-0.720561\pi\) |
0.985700 | + | 0.168508i | \(0.0538948\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.9426 | + | 50.1301i | 1.68510 | + | 2.91869i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.77604 | − | 8.96768i | 0.161082 | − | 0.520358i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.21695 | − | 3.83986i | 0.128209 | − | 0.222065i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.6427 | − | 4.78881i | 1.01691 | − | 0.276022i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.4095 | + | 8.20869i | 0.655460 | + | 0.471577i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.6739 | − | 30.6120i | 1.01200 | − | 1.75284i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.93298 | 0.224467 | 0.112234 | − | 0.993682i | \(-0.464200\pi\) | ||||
0.112234 | + | 0.993682i | \(0.464200\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.5980 | + | 7.62484i | 0.602900 | + | 0.433762i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.991107 | + | 1.71665i | 0.0562005 | + | 0.0973422i | 0.892757 | − | 0.450539i | \(-0.148768\pi\) |
−0.836556 | + | 0.547881i | \(0.815435\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.2497 | + | 17.7530i | −0.579349 | + | 1.00346i | 0.416205 | + | 0.909271i | \(0.363360\pi\) |
−0.995554 | + | 0.0941908i | \(0.969974\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −30.4224 | + | 1.97749i | −1.71411 | + | 0.111419i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.75708 | + | 8.23951i | −0.267184 | + | 0.462777i | −0.968134 | − | 0.250434i | \(-0.919427\pi\) |
0.700949 | + | 0.713211i | \(0.252760\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.82907 | + | 11.8283i | 0.382355 | + | 0.662258i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.02343 | + | 10.1932i | −0.0571224 | + | 0.568927i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.267384 | −0.0148777 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.75597 | + | 11.7017i | −0.374754 | + | 0.649093i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.1609 | + | 6.38392i | −0.783099 | + | 0.353032i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.4687 | + | 21.3297i | 1.18361 | + | 1.17595i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.764929 | − | 1.32490i | 0.0420443 | − | 0.0728228i | −0.844237 | − | 0.535969i | \(-0.819946\pi\) |
0.886282 | + | 0.463146i | \(0.153280\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.29323 | + | 7.12147i | −0.344867 | + | 0.390254i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.6921 | − | 41.0360i | −1.29444 | − | 2.24204i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6972 | − | 18.5281i | 0.582714 | − | 1.00929i | −0.412442 | − | 0.910984i | \(-0.635324\pi\) |
0.995156 | − | 0.0983063i | \(-0.0313425\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.2052 | + | 11.3629i | −1.36896 | + | 0.617145i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.90887 | − | 5.03831i | −0.157524 | − | 0.272840i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.9676 | − | 13.2227i | 0.700185 | − | 0.713961i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.2830 | − | 12.4344i | −0.930487 | − | 0.669447i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.57191 | + | 4.45467i | 0.138067 | + | 0.239139i | 0.926765 | − | 0.375642i | \(-0.122578\pi\) |
−0.788698 | + | 0.614781i | \(0.789244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.207526 | + | 0.359446i | 0.0111086 | + | 0.0192407i | 0.871526 | − | 0.490349i | \(-0.163131\pi\) |
−0.860418 | + | 0.509590i | \(0.829797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.89118 | − | 5.28208i | −0.261072 | − | 0.281936i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0824 | −0.643083 | −0.321542 | − | 0.946895i | \(-0.604201\pi\) | ||||
−0.321542 | + | 0.946895i | \(0.604201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.6289 | 1.41332 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.25444 | − | 7.53457i | −0.0663920 | − | 0.398772i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.14926 | + | 14.1149i | 0.430102 | + | 0.744958i | 0.996882 | − | 0.0789113i | \(-0.0251444\pi\) |
−0.566780 | + | 0.823869i | \(0.691811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.48713 | − | 16.4322i | 0.499323 | − | 0.864852i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.8768 | − | 7.82540i | −0.570882 | − | 0.410727i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.9083 | + | 41.4104i | −1.25142 | + | 2.16752i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.7000 | −1.81133 | −0.905664 | − | 0.423996i | \(-0.860627\pi\) | ||||
−0.905664 | + | 0.423996i | \(0.860627\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 35.3008 | + | 7.16083i | 1.83768 | + | 0.372778i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.15959 | + | 5.12619i | 0.267873 | + | 0.266139i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.5066 | −0.802900 | −0.401450 | − | 0.915881i | \(-0.631494\pi\) | ||||
−0.401450 | + | 0.915881i | \(0.631494\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.6671 | + | 18.4665i | 1.32545 | + | 0.953604i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.4738 | 0.539430 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1820 | 0.831214 | 0.415607 | − | 0.909544i | \(-0.363569\pi\) | ||||
0.415607 | + | 0.909544i | \(0.363569\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.1043 | − | 8.70852i | −0.620120 | − | 0.446151i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.34054 | −0.221791 | −0.110896 | − | 0.993832i | \(-0.535372\pi\) | ||||
−0.110896 | + | 0.993832i | \(0.535372\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.69414 | − | 17.7491i | 0.239236 | − | 0.904578i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.7264 | − | 15.5329i | 0.697751 | − | 0.789580i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.5463 | 1.29525 | 0.647624 | − | 0.761960i | \(-0.275763\pi\) | ||||
0.647624 | + | 0.761960i | \(0.275763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.66722 | − | 4.61975i | 0.134887 | − | 0.233631i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.71306 | + | 1.95194i | 0.136856 | + | 0.0984623i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.8703 | − | 53.4690i | 1.55326 | − | 2.69032i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.28225 | + | 3.95297i | 0.114543 | + | 0.198394i | 0.917597 | − | 0.397512i | \(-0.130126\pi\) |
−0.803054 | + | 0.595906i | \(0.796793\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.688355 | − | 0.258015i | −0.0344608 | − | 0.0129169i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.33626 | 0.0667294 | 0.0333647 | − | 0.999443i | \(-0.489378\pi\) | ||||
0.0333647 | + | 0.999443i | \(0.489378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.46137 | −0.222237 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −27.5837 | + | 20.8357i | −1.37064 | + | 1.03533i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.86161 | − | 4.95645i | −0.141845 | − | 0.245682i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.3332 | − | 17.8976i | −0.510944 | − | 0.884981i | −0.999920 | − | 0.0126832i | \(-0.995963\pi\) |
0.488976 | − | 0.872297i | \(-0.337371\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.21456 | − | 3.75166i | −0.257215 | − | 0.185056i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −38.4806 | + | 10.4449i | −1.89350 | + | 0.513958i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.58015 | + | 9.66510i | 0.273919 | + | 0.474441i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.424970 | + | 0.191583i | −0.0208109 | + | 0.00938184i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5227 | + | 18.2259i | −0.514069 | + | 0.890394i | 0.485797 | + | 0.874071i | \(0.338529\pi\) |
−0.999867 | + | 0.0163228i | \(0.994804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.51630 | − | 14.7507i | −0.415059 | − | 0.718903i | 0.580376 | − | 0.814349i | \(-0.302906\pi\) |
−0.995435 | + | 0.0954456i | \(0.969572\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 33.6303 | + | 6.82198i | 1.63516 | + | 0.331696i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.12813 | + | 14.0783i | −0.394272 | + | 0.682899i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.2728 | + | 17.1610i | 0.835888 | + | 0.830477i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.95220 | − | 1.78171i | 0.190814 | − | 0.0860215i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.2925 | + | 31.6836i | −0.881121 | + | 1.52615i | −0.0310244 | + | 0.999519i | \(0.509877\pi\) |
−0.850096 | + | 0.526627i | \(0.823456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.6571 | −1.13689 | −0.568444 | − | 0.822722i | \(-0.692454\pi\) | ||||
−0.568444 | + | 0.822722i | \(0.692454\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.02450 | − | 50.0430i | 0.240906 | − | 2.39938i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.256698 | − | 0.444613i | −0.0122795 | − | 0.0212687i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.3932 | − | 18.0016i | 0.496041 | − | 0.859168i | −0.503949 | − | 0.863734i | \(-0.668120\pi\) |
0.999990 | + | 0.00456551i | \(0.00145325\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.04113 | − | 20.6075i | 0.192435 | − | 0.981310i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.71404 | − | 6.43290i | 0.176459 | − | 0.305636i | −0.764206 | − | 0.644972i | \(-0.776869\pi\) |
0.940665 | + | 0.339336i | \(0.110202\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.3597 | + | 33.5320i | 0.917737 | + | 1.58957i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.6944 | + | 8.41363i | 0.553125 | + | 0.397951i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.15800 | −0.385000 | −0.192500 | − | 0.981297i | \(-0.561660\pi\) | ||||
−0.192500 | + | 0.981297i | \(0.561660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8457 | + | 18.7854i | −0.510705 | + | 0.884568i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.6962 | − | 9.85384i | −0.643502 | − | 0.462974i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.98762 | − | 9.92297i | −0.468227 | − | 0.465196i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.15292 | + | 12.3892i | −0.334600 | + | 0.579544i | −0.983408 | − | 0.181408i | \(-0.941934\pi\) |
0.648808 | + | 0.760952i | \(0.275268\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.88459 | − | 6.35488i | −0.274669 | − | 0.296620i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.71961 | + | 13.3708i | 0.359538 | + | 0.622738i | 0.987884 | − | 0.155196i | \(-0.0496009\pi\) |
−0.628346 | + | 0.777934i | \(0.716268\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.5531 | + | 18.2785i | −0.490444 | + | 0.849474i | −0.999940 | − | 0.0109995i | \(-0.996499\pi\) |
0.509496 | + | 0.860473i | \(0.329832\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.14021 | + | 21.3160i | −0.0992497 | + | 0.988507i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.49896 | − | 6.06037i | −0.161912 | − | 0.280440i | 0.773642 | − | 0.633623i | \(-0.218433\pi\) |
−0.935555 | + | 0.353182i | \(0.885100\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.4998 | − | 8.55007i | 1.45453 | − | 0.394805i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.19747 | − | 41.8059i | 0.193409 | − | 1.92632i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.24155 | + | 10.8107i | 0.286987 | + | 0.497076i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.782265 | + | 1.35492i | 0.0358928 | + | 0.0621681i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.08240 | + | 1.63953i | 0.370068 | + | 0.0750691i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.08813 | −0.141100 | −0.0705500 | − | 0.997508i | \(-0.522475\pi\) | ||||
−0.0705500 | + | 0.997508i | \(0.522475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.38888 | −0.200116 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.3244 | − | 9.31935i | 0.515276 | − | 0.424045i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.0871 | + | 27.8636i | 0.730475 | + | 1.26522i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.90011 | + | 8.48725i | −0.222045 | + | 0.384594i | −0.955429 | − | 0.295221i | \(-0.904607\pi\) |
0.733384 | + | 0.679815i | \(0.237940\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.35452 | − | 13.4907i | 0.0612533 | − | 0.610071i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.98641 | + | 17.2970i | −0.450680 | + | 0.780601i | −0.998428 | − | 0.0560419i | \(-0.982152\pi\) |
0.547748 | + | 0.836643i | \(0.315485\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.6011 | 0.567525 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.61688 | − | 19.7380i | −0.297407 | − | 0.887156i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.68989 | + | 17.7330i | −0.210370 | + | 0.795435i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.3299 | 0.910092 | 0.455046 | − | 0.890468i | \(-0.349623\pi\) | ||||
0.455046 | + | 0.890468i | \(0.349623\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.80224 | − | 3.06655i | 0.303902 | − | 0.137003i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.9595 | 1.06830 | 0.534151 | − | 0.845389i | \(-0.320631\pi\) | ||||
0.534151 | + | 0.845389i | \(0.320631\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.1693 | 1.38702 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.91732 | + | 19.0961i | −0.0851512 | + | 0.848089i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.0609 | 0.445943 | 0.222971 | − | 0.974825i | \(-0.428424\pi\) | ||||
0.222971 | + | 0.974825i | \(0.428424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.3657 | − | 23.2145i | −1.03364 | − | 1.02695i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.812837 | + | 0.184665i | −0.0358876 | + | 0.00815316i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.9524 | 1.27580 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.3325 | + | 17.8964i | −0.454423 | + | 0.787083i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.3737 | − | 12.3404i | 1.20157 | − | 0.541685i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.99821 | − | 13.8533i | 0.350408 | − | 0.606924i | −0.635913 | − | 0.771761i | \(-0.719376\pi\) |
0.986321 | + | 0.164836i | \(0.0527096\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.7103 | + | 32.4072i | 0.818146 | + | 1.41707i | 0.907047 | + | 0.421029i | \(0.138331\pi\) |
−0.0889016 | + | 0.996040i | \(0.528336\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −34.5101 | + | 28.4000i | −1.50614 | + | 1.23948i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.36748 | −0.233811 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.7575 | −0.554676 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.9386 | + | 33.8788i | −1.29922 | + | 1.47021i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.31711 | + | 14.4057i | 0.360254 | + | 0.623978i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.3589 | + | 19.6742i | 0.491087 | + | 0.850588i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.5900 | − | 13.7904i | 1.32006 | − | 0.595100i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.9930 | + | 6.25195i | 0.473500 | + | 0.269291i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.229159 | + | 0.396916i | 0.00985233 | + | 0.0170647i | 0.870910 | − | 0.491443i | \(-0.163531\pi\) |
−0.861057 | + | 0.508508i | \(0.830197\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.06379 | + | 2.92373i | 0.174394 | + | 0.125469i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.2232 | + | 29.8314i | −0.737760 | + | 1.27784i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2013 | + | 19.4011i | 0.478931 | + | 0.829533i | 0.999708 | − | 0.0241596i | \(-0.00769098\pi\) |
−0.520777 | + | 0.853693i | \(0.674358\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.0575 | + | 5.48867i | 1.15478 | + | 0.234251i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.606376 | − | 1.05027i | 0.0258325 | − | 0.0447432i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.1698 | + | 29.9745i | 1.28295 | + | 1.27464i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.10543 | + | 20.9697i | −0.0893707 | + | 0.890114i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.4155 | − | 18.0401i | 0.441317 | − | 0.764383i | −0.556471 | − | 0.830867i | \(-0.687845\pi\) |
0.997787 | + | 0.0664841i | \(0.0211782\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.57275 | 0.404884 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.75490 | − | 2.14357i | 0.200752 | − | 0.0905018i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.40302 | + | 7.62626i | 0.185565 | + | 0.321409i | 0.943767 | − | 0.330612i | \(-0.107255\pi\) |
−0.758202 | + | 0.652020i | \(0.773922\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.6558 | + | 53.0975i | −1.28970 | + | 2.23383i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.01709 | − | 22.0384i | −0.378682 | − | 0.925527i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.49287 | + | 16.4421i | −0.397962 | + | 0.689290i | −0.993474 | − | 0.114056i | \(-0.963616\pi\) |
0.595513 | + | 0.803346i | \(0.296949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.87986 | − | 13.6483i | −0.329762 | − | 0.571164i | 0.652703 | − | 0.757614i | \(-0.273635\pi\) |
−0.982464 | + | 0.186450i | \(0.940302\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.84305 | − | 2.63413i | 0.244097 | − | 0.110042i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.2131 | −1.30167 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.9306 | + | 27.5927i | −0.663201 | + | 1.14870i | 0.316569 | + | 0.948570i | \(0.397469\pi\) |
−0.979770 | + | 0.200128i | \(0.935864\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.20913 | + | 22.0025i | −0.0918084 | + | 0.914393i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.41907 | + | 2.01377i | −0.307795 | + | 0.0835454i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.48322 | + | 4.30106i | −0.102844 | + | 0.178132i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.6454 | − | 3.17371i | −0.646858 | − | 0.131217i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.3597 | + | 35.2640i | 0.840333 | + | 1.45550i | 0.889613 | + | 0.456715i | \(0.150974\pi\) |
−0.0492799 | + | 0.998785i | \(0.515693\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.258288 | + | 0.447368i | −0.0106426 | + | 0.0184335i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.44065 | + | 2.47541i | 0.141529 | + | 0.101825i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.0693 | − | 24.3688i | −0.577759 | − | 1.00071i | −0.995736 | − | 0.0922500i | \(-0.970594\pi\) |
0.417977 | − | 0.908458i | \(-0.362739\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0161 | − | 11.9383i | −0.492613 | − | 0.489425i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.10015 | + | 3.20085i | −0.290590 | + | 0.131002i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.4963 | + | 28.5724i | 0.674020 | + | 1.16744i | 0.976754 | + | 0.214361i | \(0.0687670\pi\) |
−0.302735 | + | 0.953075i | \(0.597900\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.98103 | − | 3.43124i | −0.0808079 | − | 0.139963i | 0.822789 | − | 0.568347i | \(-0.192417\pi\) |
−0.903597 | + | 0.428383i | \(0.859083\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.5075 | − | 27.7328i | 0.998021 | − | 1.12937i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −29.7139 | −1.20804 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.0263 | −1.38109 | −0.690543 | − | 0.723292i | \(-0.742628\pi\) | ||||
−0.690543 | + | 0.723292i | \(0.742628\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 32.4403 | + | 12.1596i | 1.31455 | + | 0.492730i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.92354 | + | 13.7240i | 0.320552 | + | 0.555212i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.2967 | + | 26.4946i | −0.617827 | + | 1.07011i | 0.372054 | + | 0.928211i | \(0.378654\pi\) |
−0.989881 | + | 0.141897i | \(0.954680\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 72.8188 | − | 32.8277i | 2.93634 | − | 1.32374i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.7646 | − | 32.5013i | 0.755435 | − | 1.30845i | −0.189723 | − | 0.981838i | \(-0.560759\pi\) |
0.945158 | − | 0.326614i | \(-0.105908\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.84604 | 0.234972 | 0.117486 | − | 0.993075i | \(-0.462516\pi\) | ||||
0.117486 | + | 0.993075i | \(0.462516\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.91766 | − | 15.8859i | 0.197339 | − | 0.637480i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.7396 | + | 6.98656i | −1.03124 | + | 0.279911i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.3547 | 0.854189 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0501477 | − | 0.499461i | 0.00200271 | − | 0.0199466i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.28028 | −0.210539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.6347 | −1.02050 | −0.510251 | − | 0.860025i | \(-0.670448\pi\) | ||||
−0.510251 | + | 0.860025i | \(0.670448\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.44500 | + | 1.55305i | −0.136927 | + | 0.0617284i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.0673 | −1.31223 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.36703 | − | 4.90343i | 0.331514 | − | 0.194281i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.61088 | + | 19.7201i | 0.261523 | + | 0.780114i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.9647 | 1.02554 | 0.512772 | − | 0.858525i | \(-0.328619\pi\) | ||||
0.512772 | + | 0.858525i | \(0.328619\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.5634 | − | 39.0809i | 0.889812 | − | 1.54120i | 0.0497151 | − | 0.998763i | \(-0.484169\pi\) |
0.840097 | − | 0.542436i | \(-0.182498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.59223 | − | 45.7377i | 0.180819 | − | 1.80092i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.70324 | + | 4.68215i | −0.106275 | + | 0.184074i | −0.914259 | − | 0.405131i | \(-0.867226\pi\) |
0.807983 | + | 0.589206i | \(0.200559\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.6135 | − | 23.5792i | −0.534375 | − | 0.925564i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.8181 | − | 5.17941i | −0.541573 | − | 0.202997i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.9030 | −1.24846 | −0.624231 | − | 0.781240i | \(-0.714588\pi\) | ||||
−0.624231 | + | 0.781240i | \(0.714588\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.41174 | 0.289600 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.6020 | − | 7.42479i | −1.42798 | − | 0.289669i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.50215 | − | 4.33385i | −0.0974699 | − | 0.168823i | 0.813167 | − | 0.582031i | \(-0.197742\pi\) |
−0.910637 | + | 0.413208i | \(0.864408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.81703 | − | 8.34334i | −0.187361 | − | 0.324518i | 0.757009 | − | 0.653405i | \(-0.226660\pi\) |
−0.944369 | + | 0.328887i | \(0.893327\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.399578 | − | 3.97972i | 0.0155183 | − | 0.154559i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.57326 | + | 0.427034i | −0.0610085 | + | 0.0165597i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0975 | + | 20.9534i | 0.468415 | + | 0.811319i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.996563 | + | 9.92556i | −0.0385293 | + | 0.383744i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.31308 | + | 14.3987i | −0.320923 | + | 0.555855i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.5885 | + | 23.5359i | 0.523797 | + | 0.907243i | 0.999616 | + | 0.0276998i | \(0.00881825\pi\) |
−0.475819 | + | 0.879543i | \(0.657848\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.9862 | + | 48.4111i | −0.576818 | + | 1.86334i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.0251 | − | 32.9525i | 0.731194 | − | 1.26647i | −0.225179 | − | 0.974318i | \(-0.572297\pi\) |
0.956373 | − | 0.292148i | \(-0.0943701\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.3885 | + | 5.80553i | −0.820815 | + | 0.222796i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.3149 | − | 16.7741i | −0.893430 | − | 0.642786i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.0571 | + | 26.0797i | −0.576146 | + | 0.997913i | 0.419771 | + | 0.907630i | \(0.362111\pi\) |
−0.995916 | + | 0.0902831i | \(0.971223\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.2455 | −0.544293 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.5185 | − | 14.7622i | −0.782830 | − | 0.563215i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.90427 | + | 3.29830i | 0.0725470 | + | 0.125655i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.19510 | − | 12.4623i | 0.273714 | − | 0.474087i | −0.696096 | − | 0.717949i | \(-0.745081\pi\) |
0.969810 | + | 0.243862i | \(0.0784143\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.3095 | − | 0.930134i | 0.543573 | − | 0.0353329i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.516871 | + | 0.895246i | −0.0196060 | + | 0.0339586i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.0063 | + | 17.3315i | 0.379017 | + | 0.656477i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.328571 | + | 3.27250i | −0.0124277 | + | 0.123777i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.4170 | 0.544521 | 0.272261 | − | 0.962224i | \(-0.412229\pi\) | ||||
0.272261 | + | 0.962224i | \(0.412229\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.254092 | + | 0.440100i | −0.00958325 | + | 0.0165987i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 69.3730 | − | 31.2743i | 2.61274 | − | 1.17786i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.48955 | + | 20.7566i | −0.206456 | + | 0.780633i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.74410 | + | 9.94907i | −0.215724 | + | 0.373645i | −0.953496 | − | 0.301405i | \(-0.902545\pi\) |
0.737772 | + | 0.675050i | \(0.235878\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 47.2604 | + | 9.58687i | 1.77240 | + | 0.359536i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.15296 | − | 8.92519i | −0.192980 | − | 0.334251i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.80686 | − | 8.32573i | 0.179766 | − | 0.311365i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.0959 | − | 6.35462i | 0.526421 | − | 0.237318i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.9451 | − | 31.0818i | −0.669240 | − | 1.15916i | −0.978117 | − | 0.208055i | \(-0.933287\pi\) |
0.308877 | − | 0.951102i | \(-0.400047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.09910 | + | 19.2803i | −0.189901 | + | 0.718036i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −34.1554 | − | 24.5734i | −1.27025 | − | 0.913894i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −36.8660 | − | 63.8539i | −1.36917 | − | 2.37147i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.03060 | + | 8.71326i | 0.186575 | + | 0.323157i | 0.944106 | − | 0.329642i | \(-0.106928\pi\) |
−0.757531 | + | 0.652799i | \(0.773595\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.2778 | − | 15.2545i | −0.825104 | − | 0.564980i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.5170 | 0.425972 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.1381 | 1.22398 | 0.611992 | − | 0.790864i | \(-0.290369\pi\) | ||||
0.611992 | + | 0.790864i | \(0.290369\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.4143 | − | 42.3292i | −0.716108 | − | 1.56134i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.1438 | + | 19.3017i | 0.410489 | + | 0.710987i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.9237 | + | 37.9729i | −0.806475 | + | 1.39686i | 0.108816 | + | 0.994062i | \(0.465294\pi\) |
−0.915291 | + | 0.402793i | \(0.868039\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.312473 | − | 0.224811i | −0.0114790 | − | 0.00825865i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.50115 | + | 7.79622i | −0.165131 | + | 0.286016i | −0.936702 | − | 0.350128i | \(-0.886138\pi\) |
0.771571 | + | 0.636144i | \(0.219471\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.9475 | 1.17047 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.77217 | + | 6.53184i | −0.211193 | + | 0.238987i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.1022 | + | 4.09922i | −0.551821 | + | 0.149782i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.1828 | −0.408067 | −0.204033 | − | 0.978964i | \(-0.565405\pi\) | ||||
−0.204033 | + | 0.978964i | \(0.565405\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.94200 | + | 5.71395i | 0.289423 | + | 0.208228i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.4162 | −1.36171 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.1431 | 1.53172 | 0.765859 | − | 0.643009i | \(-0.222314\pi\) | ||||
0.765859 | + | 0.643009i | \(0.222314\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.12925 | + | 5.84866i | 0.295073 | + | 0.212293i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.28309 | 0.0827620 | 0.0413810 | − | 0.999143i | \(-0.486824\pi\) | ||||
0.0413810 | + | 0.999143i | \(0.486824\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.8323 | − | 16.7234i | −0.609371 | − | 0.605427i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.8230 | − | 3.81829i | −0.680548 | − | 0.138051i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.8791 | −0.753901 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.96676 | − | 15.5309i | 0.323350 | − | 0.560058i | −0.657827 | − | 0.753169i | \(-0.728524\pi\) |
0.981177 | + | 0.193111i | \(0.0618577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.1405 | − | 23.8432i | −1.19353 | − | 0.858693i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.4807 | − | 30.2775i | 0.628737 | − | 1.08901i | −0.359068 | − | 0.933311i | \(-0.616905\pi\) |
0.987805 | − | 0.155694i | \(-0.0497613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.7032 | + | 27.1988i | 0.564077 | + | 0.977009i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.5936 | − | 5.09526i | −0.487667 | − | 0.182792i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.92606 | 0.0690081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.5252 | −0.448186 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 38.3068 | − | 8.70277i | 1.36897 | − | 0.311011i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −46.5870 | − | 80.6910i | −1.66276 | − | 2.87998i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.1782 | − | 24.5573i | −0.505397 | − | 0.875374i | −0.999981 | − | 0.00624370i | \(-0.998013\pi\) |
0.494583 | − | 0.869130i | \(-0.335321\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −36.0500 | − | 25.9365i | −1.28341 | − | 0.923365i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.9601 | − | 29.7662i | −1.06526 | − | 1.05836i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.37494 | + | 11.0417i | 0.226381 | + | 0.392103i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.6725 | − | 7.51619i | 0.591312 | − | 0.266572i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.51922 | + | 16.4878i | −0.337188 | + | 0.584027i | −0.983903 | − | 0.178705i | \(-0.942809\pi\) |
0.646715 | + | 0.762732i | \(0.276143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.53283 | + | 16.5113i | 0.337247 | + | 0.584129i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.0259 | + | 22.6615i | −0.707581 | + | 0.800704i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.2455 | − | 19.4778i | 0.396845 | − | 0.687356i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.31551 | − | 31.4419i | 0.293083 | − | 1.10818i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.1244 | + | 11.7773i | −0.919623 | + | 0.414579i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.4529 | + | 18.1050i | −0.367505 | + | 0.636538i | −0.989175 | − | 0.146742i | \(-0.953121\pi\) |
0.621670 | + | 0.783280i | \(0.286455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.5392 | −0.615884 | −0.307942 | − | 0.951405i | \(-0.599640\pi\) | ||||
−0.307942 | + | 0.951405i | \(0.599640\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.08260 | − | 30.7021i | 0.108111 | − | 1.07677i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.0335 | − | 26.0388i | −0.526601 | − | 0.912101i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.554208 | − | 0.959917i | 0.0193893 | − | 0.0335832i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.86894 | − | 9.85981i | 0.170135 | − | 0.344530i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.4881 | − | 30.2903i | 0.610339 | − | 1.05714i | −0.380844 | − | 0.924639i | \(-0.624366\pi\) |
0.991183 | − | 0.132499i | \(-0.0423002\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.2118 | − | 26.3475i | −0.530249 | − | 0.918418i | −0.999377 | − | 0.0352878i | \(-0.988765\pi\) |
0.469128 | − | 0.883130i | \(-0.344568\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.7732 | − | 17.8233i | −0.862493 | − | 0.620529i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.6276 | 0.891158 | 0.445579 | − | 0.895243i | \(-0.352998\pi\) | ||||
0.445579 | + | 0.895243i | \(0.352998\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.9403 | − | 41.4658i | 0.831481 | − | 1.44017i | −0.0653833 | − | 0.997860i | \(-0.520827\pi\) |
0.896864 | − | 0.442307i | \(-0.145840\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.21628 | − | 5.91128i | −0.285020 | − | 0.205060i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.0664 | − | 5.89933i | 0.348780 | − | 0.204400i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.27323 | − | 14.3297i | 0.286307 | − | 0.495898i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.3169 | + | 3.70698i | −0.563996 | + | 0.128132i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.8466 | + | 37.8394i | 0.754227 | + | 1.30636i | 0.945758 | + | 0.324873i | \(0.105322\pi\) |
−0.191530 | + | 0.981487i | \(0.561345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0769 | + | 24.3818i | −0.485409 | + | 0.840753i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.65418 | − | 36.3949i | 0.125857 | − | 1.25351i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.2800 | + | 36.8581i | 0.732055 | + | 1.26796i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.23322 | − | 19.7874i | 0.179816 | − | 0.679904i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.21072 | − | 22.0184i | 0.0758719 | − | 0.755668i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.06924 | − | 8.78018i | −0.173771 | − | 0.300981i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.33994 | + | 14.4452i | 0.285554 | + | 0.494594i | 0.972743 | − | 0.231884i | \(-0.0744890\pi\) |
−0.687189 | + | 0.726478i | \(0.741156\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.22403 | + | 1.38512i | −0.0418609 | + | 0.0473701i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.4290 | 0.492887 | 0.246443 | − | 0.969157i | \(-0.420738\pi\) | ||||
0.246443 | + | 0.969157i | \(0.420738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.7733 | −0.777016 | −0.388508 | − | 0.921445i | \(-0.627009\pi\) | ||||
−0.388508 | + | 0.921445i | \(0.627009\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.03615 | + | 54.2740i | 0.307951 | + | 1.84965i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.97266 | + | 10.3450i | 0.203312 | + | 0.352146i | 0.949594 | − | 0.313484i | \(-0.101496\pi\) |
−0.746282 | + | 0.665630i | \(0.768163\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.2933 | − | 57.6656i | 1.13200 | − | 1.96069i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.46085 | + | 24.5096i | −0.0835748 | + | 0.832388i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.5202 | + | 25.1497i | −0.492563 | + | 0.853145i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.0914 | 0.579122 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.6407 | + | 18.8307i | −0.563201 | + | 0.637322i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.3494 | + | 46.6946i | −0.417487 | + | 1.57857i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −56.6198 | −1.91191 | −0.955957 | − | 0.293507i | \(-0.905178\pi\) | ||||
−0.955957 | + | 0.293507i | \(0.905178\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.7533 | − | 8.45423i | 0.632532 | − | 0.285154i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.41130 | −0.216002 | −0.108001 | − | 0.994151i | \(-0.534445\pi\) | ||||
−0.108001 | + | 0.994151i | \(0.534445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.7180 | 0.865481 | 0.432741 | − | 0.901518i | \(-0.357547\pi\) | ||||
0.432741 | + | 0.901518i | \(0.357547\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.0161 | + | 99.7586i | −0.336688 | + | 3.35335i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.9894 | −0.671180 | −0.335590 | − | 0.942008i | \(-0.608936\pi\) | ||||
−0.335590 | + | 0.942008i | \(0.608936\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.82381 | − | 22.0205i | 0.195324 | − | 0.738545i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.9743 | − | 9.80028i | 0.434654 | − | 0.328322i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.83491 | 0.0614030 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.2051 | − | 64.4412i | 1.24363 | − | 2.15403i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.00118 | − | 3.15623i | 0.233762 | − | 0.105383i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.1724 | − | 21.0832i | 0.405973 | − | 0.703166i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.29104 | + | 3.96819i | 0.0763254 | + | 0.132200i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29.6494 | + | 11.1134i | 0.986670 | + | 0.369832i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.1017 | 0.369035 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.3034 | −0.806981 | −0.403491 | − | 0.914984i | \(-0.632203\pi\) | ||||
−0.403491 | + | 0.914984i | \(0.632203\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.73809 | + | 23.0825i | 0.256656 | + | 0.765598i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.7871 | − | 34.2723i | −0.655577 | − | 1.13549i | −0.981749 | − | 0.190183i | \(-0.939092\pi\) |
0.326171 | − | 0.945311i | \(-0.394241\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.62468 | − | 4.54608i | −0.0868642 | − | 0.150453i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 55.8145 | − | 25.1619i | 1.84517 | − | 0.831828i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.30536 | + | 4.93571i | −0.0431067 | + | 0.162991i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.9220 | + | 22.3815i | 0.426257 | + | 0.738298i | 0.996537 | − | 0.0831519i | \(-0.0264987\pi\) |
−0.570280 | + | 0.821450i | \(0.693165\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.52969 | + | 3.97839i | 0.182209 | + | 0.131092i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.80251 | + | 8.31818i | −0.158076 | + | 0.273796i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.4481 | + | 26.7569i | 0.507930 | + | 0.879761i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.18771 | + | 21.4407i | 0.236075 | + | 0.704206i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.4253 | + | 44.0379i | −0.834178 | + | 1.44484i | 0.0605205 | + | 0.998167i | \(0.480724\pi\) |
−0.894698 | + | 0.446671i | \(0.852609\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.00729213 | − | 1.12289i | −0.000238990 | − | 0.0368014i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.342991 | + | 3.41612i | −0.0112290 | + | 0.111839i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.78315 | − | 10.0167i | 0.189129 | − | 0.327581i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.7623 | 1.07030 | 0.535149 | − | 0.844758i | \(-0.320256\pi\) | ||||
0.535149 | + | 0.844758i | \(0.320256\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.3689 | + | 14.5923i | −1.05632 | + | 0.476203i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.3396 | − | 43.8895i | −0.826048 | − | 1.43076i | −0.901115 | − | 0.433579i | \(-0.857250\pi\) |
0.0750670 | − | 0.997178i | \(-0.476083\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.2128 | + | 33.2776i | −0.625655 | + | 1.08367i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −44.7736 | − | 27.9933i | −1.45648 | − | 0.910623i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.76277 | + | 9.98140i | −0.187265 | + | 0.324352i | −0.944337 | − | 0.328979i | \(-0.893296\pi\) |
0.757073 | + | 0.653331i | \(0.226629\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.62369 | − | 14.9367i | −0.279937 | − | 0.484865i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.0230 | + | 6.77257i | −0.487154 | + | 0.219616i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.7747 | −1.48279 | −0.741395 | − | 0.671069i | \(-0.765835\pi\) | ||||
−0.741395 | + | 0.671069i | \(0.765835\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.10661 | − | 12.3090i | 0.229965 | − | 0.398310i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.36333 | + | 23.5383i | −0.0763955 | + | 0.760884i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.50892 | − | 9.48652i | 0.0810173 | − | 0.306336i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.3151 | − | 17.8663i | 0.332746 | − | 0.576332i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.7498 | + | 13.2961i | −0.378631 | + | 0.428462i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.5188 | + | 42.4678i | 0.789287 | + | 1.36709i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.07666 | − | 7.06098i | 0.131097 | − | 0.227066i | −0.793003 | − | 0.609218i | \(-0.791484\pi\) |
0.924100 | + | 0.382152i | \(0.124817\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.375937 | − | 0.270471i | −0.0120768 | − | 0.00868879i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.1137 | − | 24.4457i | −0.452932 | − | 0.784501i | 0.545635 | − | 0.838023i | \(-0.316288\pi\) |
−0.998567 | + | 0.0535223i | \(0.982955\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.505141 | − | 0.501871i | −0.0161941 | − | 0.0160893i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21.3355 | + | 9.61835i | −0.683284 | + | 0.308034i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.82510 | + | 13.5535i | 0.250347 | + | 0.433614i | 0.963621 | − | 0.267271i | \(-0.0861219\pi\) |
−0.713274 | + | 0.700885i | \(0.752789\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.10603 | − | 15.7721i | −0.291030 | − | 0.504079i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.3675 | − | 5.34871i | −0.841850 | − | 0.170771i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.95162 | −0.0941419 | −0.0470710 | − | 0.998892i | \(-0.514989\pi\) | ||||
−0.0470710 | + | 0.998892i | \(0.514989\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.39940 | 0.299490 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.60855 | + | 51.7057i | 0.274013 | + | 1.64581i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0567 | + | 19.1507i | 0.351582 | + | 0.608958i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.8182 | + | 27.3979i | −0.502482 | + | 0.870324i | 0.497514 | + | 0.867456i | \(0.334246\pi\) |
−0.999996 | + | 0.00286819i | \(0.999087\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.41567 | − | 1.08902i | 0.0766588 | − | 0.0345589i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.63557 | + | 14.9572i | −0.273766 | + | 0.474176i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.58522 | −0.0502043 | −0.0251021 | − | 0.999685i | \(-0.507991\pi\) | ||||
−0.0251021 | + | 0.999685i | \(0.507991\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.0518 | + | 3.64675i | −0.507858 | + | 0.115378i |
(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 | 1008.2.t.k.193.10 | 22 | ||
3.2 | odd | 2 | 3024.2.t.l.1873.1 | 22 | |||
4.3 | odd | 2 | 504.2.t.d.193.2 | yes | 22 | ||
7.2 | even | 3 | 1008.2.q.k.625.2 | 22 | |||
9.2 | odd | 6 | 3024.2.q.k.2881.11 | 22 | |||
9.7 | even | 3 | 1008.2.q.k.529.2 | 22 | |||
12.11 | even | 2 | 1512.2.t.d.361.1 | 22 | |||
21.2 | odd | 6 | 3024.2.q.k.2305.11 | 22 | |||
28.23 | odd | 6 | 504.2.q.d.121.10 | yes | 22 | ||
36.7 | odd | 6 | 504.2.q.d.25.10 | ✓ | 22 | ||
36.11 | even | 6 | 1512.2.q.c.1369.11 | 22 | |||
63.2 | odd | 6 | 3024.2.t.l.289.1 | 22 | |||
63.16 | even | 3 | inner | 1008.2.t.k.961.10 | 22 | ||
84.23 | even | 6 | 1512.2.q.c.793.11 | 22 | |||
252.79 | odd | 6 | 504.2.t.d.457.2 | yes | 22 | ||
252.191 | even | 6 | 1512.2.t.d.289.1 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.10 | ✓ | 22 | 36.7 | odd | 6 | ||
504.2.q.d.121.10 | yes | 22 | 28.23 | odd | 6 | ||
504.2.t.d.193.2 | yes | 22 | 4.3 | odd | 2 | ||
504.2.t.d.457.2 | yes | 22 | 252.79 | odd | 6 | ||
1008.2.q.k.529.2 | 22 | 9.7 | even | 3 | |||
1008.2.q.k.625.2 | 22 | 7.2 | even | 3 | |||
1008.2.t.k.193.10 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.t.k.961.10 | 22 | 63.16 | even | 3 | inner | ||
1512.2.q.c.793.11 | 22 | 84.23 | even | 6 | |||
1512.2.q.c.1369.11 | 22 | 36.11 | even | 6 | |||
1512.2.t.d.289.1 | 22 | 252.191 | even | 6 | |||
1512.2.t.d.361.1 | 22 | 12.11 | even | 2 | |||
3024.2.q.k.2305.11 | 22 | 21.2 | odd | 6 | |||
3024.2.q.k.2881.11 | 22 | 9.2 | odd | 6 | |||
3024.2.t.l.289.1 | 22 | 63.2 | odd | 6 | |||
3024.2.t.l.1873.1 | 22 | 3.2 | odd | 2 |