Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(109,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.o (of order \(10\), degree \(4\), 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: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 229.5 | ||
Character | \(\chi\) | \(=\) | 300.229 |
Dual form | 300.2.o.a.169.5 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) |
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 | ||||||||
\(3\) | 0.587785 | − | 0.809017i | 0.339358 | − | 0.467086i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.892889 | + | 2.05006i | 0.399312 | + | 0.916815i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.13266i | 1.56200i | 0.624532 | + | 0.780999i | \(0.285290\pi\) | ||||
−0.624532 | + | 0.780999i | \(0.714710\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.16386 | + | 3.58198i | −0.350916 | + | 1.08001i | 0.607424 | + | 0.794378i | \(0.292203\pi\) |
−0.958340 | + | 0.285630i | \(0.907797\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.664470 | − | 0.215899i | 0.184291 | − | 0.0598797i | −0.215418 | − | 0.976522i | \(-0.569111\pi\) |
0.399709 | + | 0.916642i | \(0.369111\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.18336 | + | 0.482633i | 0.563741 | + | 0.124615i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.11086 | − | 4.28173i | −0.754494 | − | 1.03847i | −0.997652 | − | 0.0684847i | \(-0.978184\pi\) |
0.243159 | − | 0.969987i | \(-0.421816\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.63966 | − | 3.37091i | 1.06441 | − | 0.773340i | 0.0895120 | − | 0.995986i | \(-0.471469\pi\) |
0.974899 | + | 0.222646i | \(0.0714692\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.34339 | + | 2.42912i | 0.729588 | + | 0.530077i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.19894 | + | 1.68924i | 1.08405 | + | 0.352231i | 0.795946 | − | 0.605367i | \(-0.206974\pi\) |
0.288108 | + | 0.957598i | \(0.406974\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.40550 | + | 3.66095i | −0.681100 | + | 0.732191i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.951057 | − | 0.309017i | −0.183031 | − | 0.0594703i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.68284 | − | 4.12883i | −1.05528 | − | 0.766704i | −0.0820685 | − | 0.996627i | \(-0.526153\pi\) |
−0.973209 | + | 0.229923i | \(0.926153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.16460 | − | 5.93193i | 1.46641 | − | 1.06541i | 0.484769 | − | 0.874642i | \(-0.338904\pi\) |
0.981636 | − | 0.190764i | \(-0.0610964\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.21379 | + | 3.04701i | 0.385371 | + | 0.530417i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.47220 | + | 3.69001i | −1.43206 | + | 0.623725i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.50175 | − | 1.78763i | 0.904482 | − | 0.293884i | 0.180396 | − | 0.983594i | \(-0.442262\pi\) |
0.724086 | + | 0.689710i | \(0.242262\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.215899 | − | 0.664470i | 0.0345716 | − | 0.106400i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.03813 | − | 6.27271i | −0.318302 | − | 0.979633i | −0.974374 | − | 0.224935i | \(-0.927783\pi\) |
0.656072 | − | 0.754698i | \(-0.272217\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.79668i | 0.731488i | 0.930716 | + | 0.365744i | \(0.119185\pi\) | ||||
−0.930716 | + | 0.365744i | \(0.880815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.67381 | − | 1.48269i | 0.249516 | − | 0.221027i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.68611 | + | 7.82626i | −0.829405 | + | 1.14158i | 0.158629 | + | 0.987338i | \(0.449293\pi\) |
−0.988033 | + | 0.154239i | \(0.950707\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.0789 | −1.43984 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.29251 | −0.741099 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.99634 | + | 2.74773i | −0.274219 | + | 0.377429i | −0.923808 | − | 0.382856i | \(-0.874941\pi\) |
0.649590 | + | 0.760285i | \(0.274941\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.38247 | + | 0.812336i | −1.13029 | + | 0.109535i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.73494i | − | 0.759611i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.230309 | − | 0.708820i | −0.0299837 | − | 0.0922804i | 0.934945 | − | 0.354793i | \(-0.115449\pi\) |
−0.964928 | + | 0.262513i | \(0.915449\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.64886 | − | 11.2300i | 0.467188 | − | 1.43786i | −0.389021 | − | 0.921229i | \(-0.627187\pi\) |
0.856210 | − | 0.516629i | \(-0.172813\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.93039 | − | 1.27706i | 0.495183 | − | 0.160895i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.03591 | + | 1.16943i | 0.128488 | + | 0.145050i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.81995 | − | 3.88133i | −0.344512 | − | 0.474180i | 0.601241 | − | 0.799068i | \(-0.294673\pi\) |
−0.945752 | + | 0.324888i | \(0.894673\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.42248 | − | 3.21312i | 0.532405 | − | 0.386815i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.54239 | + | 1.84715i | 0.301726 | + | 0.219217i | 0.728338 | − | 0.685218i | \(-0.240293\pi\) |
−0.426612 | + | 0.904435i | \(0.640293\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2213 | + | 3.32110i | 1.19631 | + | 0.388706i | 0.838403 | − | 0.545051i | \(-0.183490\pi\) |
0.357910 | + | 0.933756i | \(0.383490\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.960072 | + | 4.90696i | 0.110860 | + | 0.566607i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.8031 | − | 4.80982i | −1.68697 | − | 0.548130i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.38222 | − | 5.36349i | −0.830564 | − | 0.603440i | 0.0891546 | − | 0.996018i | \(-0.471583\pi\) |
−0.919719 | + | 0.392578i | \(0.871583\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.96148 | − | 6.82889i | −0.544593 | − | 0.749569i | 0.444673 | − | 0.895693i | \(-0.353320\pi\) |
−0.989266 | + | 0.146125i | \(0.953320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00015 | − | 10.2006i | 0.650808 | − | 1.10641i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.68058 | + | 2.17065i | −0.716234 | + | 0.232718i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.04690 | − | 3.22202i | 0.110971 | − | 0.341533i | −0.880114 | − | 0.474761i | \(-0.842534\pi\) |
0.991085 | + | 0.133228i | \(0.0425343\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.892239 | + | 2.74603i | 0.0935321 | + | 0.287862i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 10.0920i | − | 1.04649i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.0533 | + | 6.50174i | 1.13404 | + | 0.667064i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.13358 | + | 8.44215i | −0.622771 | + | 0.857170i | −0.997551 | − | 0.0699435i | \(-0.977718\pi\) |
0.374780 | + | 0.927114i | \(0.377718\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.76632 | 0.378529 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.10799 | 0.707272 | 0.353636 | − | 0.935383i | \(-0.384945\pi\) | ||||
0.353636 | + | 0.935383i | \(0.384945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.17630 | + | 9.87733i | −0.707102 | + | 0.973243i | 0.292752 | + | 0.956188i | \(0.405429\pi\) |
−0.999855 | + | 0.0170543i | \(0.994571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.99456 | + | 9.02309i | −0.194649 | + | 0.880563i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 4.04303i | − | 0.390855i | −0.980718 | − | 0.195427i | \(-0.937391\pi\) | ||
0.980718 | − | 0.195427i | \(-0.0626094\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.239122 | + | 0.735942i | 0.0229037 | + | 0.0704904i | 0.961855 | − | 0.273560i | \(-0.0882010\pi\) |
−0.938951 | + | 0.344050i | \(0.888201\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.78763 | − | 5.50175i | 0.169674 | − | 0.522203i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.08366 | + | 0.352104i | −0.101943 | + | 0.0331231i | −0.359544 | − | 0.933128i | \(-0.617068\pi\) |
0.257602 | + | 0.966251i | \(0.417068\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.17904 | + | 12.1665i | 0.109946 | + | 1.13453i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.410665 | − | 0.565232i | −0.0379660 | − | 0.0522557i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.6949 | − | 12.8561i | 1.62209 | − | 1.17852i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.57684 | − | 1.87218i | −0.234258 | − | 0.170198i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.27271 | − | 2.03813i | −0.565591 | − | 0.183772i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.5459 | − | 3.71265i | −0.943255 | − | 0.332070i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.511543 | + | 0.166210i | 0.0453921 | + | 0.0147488i | 0.331625 | − | 0.943411i | \(-0.392403\pi\) |
−0.286233 | + | 0.958160i | \(0.592403\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.88060 | + | 2.81942i | 0.341668 | + | 0.248236i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.43855 | − | 3.95134i | 0.475169 | − | 0.345230i | −0.324284 | − | 0.945960i | \(-0.605123\pi\) |
0.799452 | + | 0.600730i | \(0.205123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.9308 | + | 19.1741i | 1.20796 | + | 1.66261i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.215684 | − | 2.22564i | −0.0185632 | − | 0.191553i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.174404 | + | 0.0566672i | −0.0149003 | + | 0.00484140i | −0.316458 | − | 0.948607i | \(-0.602494\pi\) |
0.301557 | + | 0.953448i | \(0.402494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.54014 | + | 7.81775i | −0.215452 | + | 0.663093i | 0.783669 | + | 0.621178i | \(0.213346\pi\) |
−0.999121 | + | 0.0419144i | \(0.986654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.98937 | + | 9.20032i | 0.251750 | + | 0.774807i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.63140i | 0.220048i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.39020 | − | 15.3368i | 0.281541 | − | 1.27365i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.92421 | + | 8.15398i | −0.488621 | + | 0.672529i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.53790 | −0.453682 | −0.226841 | − | 0.973932i | \(-0.572840\pi\) | ||||
−0.226841 | + | 0.973932i | \(0.572840\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8736 | 1.04764 | 0.523821 | − | 0.851828i | \(-0.324506\pi\) | ||||
0.523821 | + | 0.851828i | \(0.324506\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.11086 | + | 4.28173i | −0.251498 | + | 0.346157i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.4509 | + | 11.4414i | 1.56233 | + | 0.918993i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.6395i | − | 1.16836i | −0.811625 | − | 0.584179i | \(-0.801417\pi\) | ||
0.811625 | − | 0.584179i | \(-0.198583\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.04954 | + | 3.23015i | 0.0832338 | + | 0.256167i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.98105 | + | 21.4855i | −0.550184 | + | 1.69329i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.22672 | + | 1.37334i | −0.331062 | + | 0.107569i | −0.469832 | − | 0.882756i | \(-0.655685\pi\) |
0.138769 | + | 0.990325i | \(0.455685\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.26990 | + | 7.25904i | −0.332411 | + | 0.565116i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.9690 | + | 19.2267i | 1.08095 | + | 1.48780i | 0.858467 | + | 0.512869i | \(0.171417\pi\) |
0.222487 | + | 0.974936i | \(0.428583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1223 | + | 7.35429i | −0.778639 | + | 0.565715i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.63966 | − | 3.37091i | −0.354804 | − | 0.257780i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.3484 | + | 4.66207i | 1.09089 | + | 0.354451i | 0.798589 | − | 0.601877i | \(-0.205580\pi\) |
0.292298 | + | 0.956327i | \(0.405580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.1295 | − | 14.0738i | −1.14368 | − | 1.06388i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.708820 | − | 0.230309i | −0.0532781 | − | 0.0173111i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.5238 | + | 9.82561i | 1.01082 | + | 0.734401i | 0.964380 | − | 0.264521i | \(-0.0852138\pi\) |
0.0464356 | + | 0.998921i | \(0.485214\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.40755 | + | 6.10844i | −0.624928 | + | 0.454037i | −0.854639 | − | 0.519222i | \(-0.826222\pi\) |
0.229711 | + | 0.973259i | \(0.426222\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.94054 | − | 9.55283i | −0.513059 | − | 0.706166i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.57720 | + | 9.68277i | 0.630608 | + | 0.711892i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.9576 | − | 6.15971i | 1.38632 | − | 0.450443i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.27706 | − | 3.93039i | 0.0928926 | − | 0.285894i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.10485 | − | 18.7888i | −0.441732 | − | 1.35951i | −0.886029 | − | 0.463631i | \(-0.846546\pi\) |
0.444297 | − | 0.895880i | \(-0.353454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.23549i | 0.160914i | 0.996758 | + | 0.0804571i | \(0.0256380\pi\) | ||||
−0.996758 | + | 0.0804571i | \(0.974362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.55498 | − | 0.150691i | 0.111354 | − | 0.0107912i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.3761 | − | 18.4106i | 0.953008 | − | 1.31170i | 0.00282909 | − | 0.999996i | \(-0.499099\pi\) |
0.950178 | − | 0.311706i | \(-0.100901\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.8171 | −1.61746 | −0.808731 | − | 0.588179i | \(-0.799845\pi\) | ||||
−0.808731 | + | 0.588179i | \(0.799845\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.79759 | −0.338396 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.0630 | − | 23.4853i | 1.19759 | − | 1.64834i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0396 | − | 9.77912i | 0.771040 | − | 0.683003i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.46649i | − | 0.379947i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.67464 | + | 20.5424i | 0.461695 | + | 1.42095i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.21019 | − | 19.1130i | 0.427527 | − | 1.31579i | −0.473027 | − | 0.881048i | \(-0.656839\pi\) |
0.900554 | − | 0.434745i | \(-0.143161\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.98875 | − | 0.971105i | 0.204786 | − | 0.0665390i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.83349 | + | 4.28291i | −0.670639 | + | 0.292092i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.5146 | + | 33.7415i | 1.66416 | + | 2.29052i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.69476 | − | 6.31711i | 0.587537 | − | 0.426871i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.99149 | − | 2.17345i | −0.201230 | − | 0.146202i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.7621 | − | 4.14665i | −0.854612 | − | 0.277680i | −0.151236 | − | 0.988498i | \(-0.548325\pi\) |
−0.703377 | + | 0.710817i | \(0.748325\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.53413 | + | 2.10752i | 0.302275 | + | 0.140502i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.5862 | − | 5.71411i | −1.16724 | − | 0.379259i | −0.339628 | − | 0.940560i | \(-0.610301\pi\) |
−0.827612 | + | 0.561301i | \(0.810301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.7050 | − | 11.4104i | −1.03782 | − | 0.754017i | −0.0679579 | − | 0.997688i | \(-0.521648\pi\) |
−0.969858 | + | 0.243671i | \(0.921648\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.5923 | + | 9.14882i | −0.828511 | + | 0.601948i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.16114 | − | 9.85646i | −0.469142 | − | 0.645718i | 0.507231 | − | 0.861810i | \(-0.330669\pi\) |
−0.976373 | + | 0.216092i | \(0.930669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.1214 | − | 4.66889i | −1.37781 | − | 0.304565i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.67832 | + | 2.81976i | −0.563717 | + | 0.183163i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.39823 | + | 4.30330i | −0.0904438 | + | 0.278357i | −0.986040 | − | 0.166512i | \(-0.946750\pi\) |
0.895596 | + | 0.444869i | \(0.146750\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.78479 | + | 8.57071i | 0.179384 | + | 0.552088i | 0.999807 | − | 0.0196702i | \(-0.00626163\pi\) |
−0.820422 | + | 0.571758i | \(0.806262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.99932 | − | 20.6623i | −0.574945 | − | 1.32007i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.35514 | − | 3.24157i | 0.149854 | − | 0.206256i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.44098 | −0.534925 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.16965 | 0.200066 | 0.100033 | − | 0.994984i | \(-0.468105\pi\) | ||||
0.100033 | + | 0.994984i | \(0.468105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.1016 | + | 16.6565i | −0.760824 | + | 1.04718i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.72562 | − | 10.8500i | −0.295930 | − | 0.679451i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.25241i | 0.202880i | 0.994842 | + | 0.101440i | \(0.0323450\pi\) | ||||
−0.994842 | + | 0.101440i | \(0.967655\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.38766 | + | 22.7369i | 0.459047 | + | 1.41280i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.17065 | + | 6.68058i | −0.134360 | + | 0.413518i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5187 | + | 3.41774i | −0.648612 | + | 0.210747i | −0.614802 | − | 0.788682i | \(-0.710764\pi\) |
−0.0338097 | + | 0.999428i | \(0.510764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.41552 | − | 1.63920i | −0.455532 | − | 0.100696i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.99132 | − | 2.74081i | −0.121867 | − | 0.167735i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.0279 | − | 14.5511i | 1.22112 | − | 0.887197i | 0.224929 | − | 0.974375i | \(-0.427785\pi\) |
0.996193 | + | 0.0871780i | \(0.0277849\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.202420 | − | 0.147067i | −0.0122962 | − | 0.00893369i | 0.581620 | − | 0.813460i | \(-0.302419\pi\) |
−0.593916 | + | 0.804527i | \(0.702419\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.74603 | + | 0.892239i | 0.166197 | + | 0.0540008i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.14996 | − | 16.4593i | −0.551763 | − | 0.992530i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.43658 | + | 2.74121i | 0.506905 | + | 0.164703i | 0.551294 | − | 0.834311i | \(-0.314134\pi\) |
−0.0443894 | + | 0.999014i | \(0.514134\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.16460 | − | 5.93193i | −0.488802 | − | 0.355135i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.9683 | + | 11.6016i | −0.952588 | + | 0.692096i | −0.951418 | − | 0.307904i | \(-0.900373\pi\) |
−0.00117050 | + | 0.999999i | \(0.500373\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.5421 | − | 21.3919i | −0.923882 | − | 1.27162i | −0.962198 | − | 0.272349i | \(-0.912199\pi\) |
0.0383159 | − | 0.999266i | \(-0.487801\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.7570 | − | 5.12066i | 0.696423 | − | 0.303322i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.9230 | − | 8.42289i | 1.53019 | − | 0.497187i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.40247 | + | 10.4717i | −0.200145 | + | 0.615983i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.22461 | + | 9.92434i | 0.189030 | + | 0.581775i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 19.1882i | − | 1.12099i | −0.828158 | − | 0.560494i | \(-0.810611\pi\) | ||
0.828158 | − | 0.560494i | \(-0.189389\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.24748 | − | 1.10505i | 0.0726312 | − | 0.0643382i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.21379 | − | 3.04701i | 0.128457 | − | 0.176806i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.81925 | 0.220873 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.8231 | −1.14258 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.17797 | − | 5.75049i | 0.240018 | − | 0.330357i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.2803 | − | 2.54679i | 1.50480 | − | 0.145829i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.26979i | − | 0.529055i | −0.964378 | − | 0.264527i | \(-0.914784\pi\) | ||
0.964378 | − | 0.264527i | \(-0.0852160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.77281 | + | 11.6115i | 0.214627 | + | 0.660555i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.69255 | + | 23.6752i | −0.436204 | + | 1.34250i | 0.455643 | + | 0.890163i | \(0.349409\pi\) |
−0.891847 | + | 0.452336i | \(0.850591\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.75115 | − | 1.86866i | 0.325074 | − | 0.105623i | −0.141934 | − | 0.989876i | \(-0.545332\pi\) |
0.467008 | + | 0.884253i | \(0.345332\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.12746 | + | 6.91727i | 0.345243 | + | 0.389744i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.45614 | − | 11.6389i | −0.474944 | − | 0.653705i | 0.502579 | − | 0.864531i | \(-0.332384\pi\) |
−0.977523 | + | 0.210827i | \(0.932384\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.4034 | − | 15.5505i | 1.19836 | − | 0.870659i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.27088 | − | 2.37644i | −0.182563 | − | 0.132640i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.8666 | − | 9.37934i | −1.60618 | − | 0.521881i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.47245 | + | 3.16784i | −0.0816771 | + | 0.175720i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.735942 | + | 0.239122i | 0.0406977 | + | 0.0132235i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −32.3433 | − | 23.4988i | −1.78314 | − | 1.29553i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.863126 | + | 0.627098i | −0.0474417 | + | 0.0344684i | −0.611253 | − | 0.791435i | \(-0.709334\pi\) |
0.563812 | + | 0.825903i | \(0.309334\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.40027 | − | 4.68007i | −0.186334 | − | 0.256466i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.43906 | − | 9.24667i | 0.297168 | − | 0.505200i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.8873 | + | 4.51226i | −0.756490 | + | 0.245799i | −0.661772 | − | 0.749705i | \(-0.730195\pi\) |
−0.0947186 | + | 0.995504i | \(0.530195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.352104 | + | 1.08366i | −0.0191236 | + | 0.0588565i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7456 | + | 36.1493i | 0.636062 | + | 1.95760i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 12.7239i | − | 0.687029i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.5359 | + | 6.19740i | 0.567233 | + | 0.333657i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.48995 | + | 13.0618i | −0.509447 | + | 0.701194i | −0.983826 | − | 0.179127i | \(-0.942673\pi\) |
0.474379 | + | 0.880321i | \(0.342673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.2622 | 1.19167 | 0.595834 | − | 0.803108i | \(-0.296822\pi\) | ||||
0.595834 | + | 0.803108i | \(0.296822\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.698665 | −0.0372920 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.60158 | + | 7.70991i | −0.298142 | + | 0.410357i | −0.931637 | − | 0.363389i | \(-0.881619\pi\) |
0.633496 | + | 0.773746i | \(0.281619\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.51670 | + | 6.86135i | −0.0804983 | + | 0.364162i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 21.8721i | − | 1.15760i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.18753 | + | 15.9656i | 0.273788 | + | 0.842632i | 0.989538 | + | 0.144275i | \(0.0460850\pi\) |
−0.715750 | + | 0.698357i | \(0.753915\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.29210 | − | 13.2097i | 0.225900 | − | 0.695248i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.02925 | + | 0.984264i | −0.158995 | + | 0.0516604i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.31803 | + | 23.9197i | 0.121331 | + | 1.25201i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.0893 | + | 26.2741i | 0.996452 | + | 1.37150i | 0.927477 | + | 0.373880i | \(0.121973\pi\) |
0.0689751 | + | 0.997618i | \(0.478027\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.33589 | + | 3.87675i | −0.277775 | + | 0.201815i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3554 | − | 8.25020i | −0.589544 | − | 0.428329i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.5918 | − | 4.41623i | −0.703755 | − | 0.228664i | −0.0647890 | − | 0.997899i | \(-0.520637\pi\) |
−0.638966 | + | 0.769235i | \(0.720637\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.20233 | + | 6.34958i | −0.475206 | + | 0.327891i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.66749 | − | 1.51656i | −0.240388 | − | 0.0781068i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.60155 | − | 1.89014i | −0.133633 | − | 0.0970897i | 0.518961 | − | 0.854798i | \(-0.326319\pi\) |
−0.652593 | + | 0.757708i | \(0.726319\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.435145 | − | 0.316151i | 0.0222931 | − | 0.0161969i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.26491 | + | 9.99929i | 0.371220 | + | 0.510940i | 0.953232 | − | 0.302240i | \(-0.0977344\pi\) |
−0.582012 | + | 0.813180i | \(0.697734\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.35711 | − | 34.6419i | −0.171094 | − | 1.76551i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.56192 | − | 1.48226i | 0.231895 | − | 0.0753474i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.14594 | + | 21.9930i | −0.362314 | + | 1.11509i | 0.589332 | + | 0.807891i | \(0.299391\pi\) |
−0.951646 | + | 0.307196i | \(0.900609\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.94031 | − | 27.5154i | −0.452131 | − | 1.39152i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.72242i | − | 0.339101i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.40399 | − | 19.9230i | 0.221589 | − | 1.00243i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.25095 | + | 1.72179i | −0.0627834 | + | 0.0864140i | −0.839254 | − | 0.543739i | \(-0.817008\pi\) |
0.776471 | + | 0.630153i | \(0.217008\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.7005 | 1.18651 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.8250 | −1.68914 | −0.844569 | − | 0.535447i | \(-0.820143\pi\) | ||||
−0.844569 | + | 0.535447i | \(0.820143\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.14443 | − | 5.70432i | 0.206449 | − | 0.284153i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.92736 | − | 1.13371i | −0.0957712 | − | 0.0563344i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.7877i | 1.07998i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.7434 | + | 33.0647i | 0.531226 | + | 1.63495i | 0.751665 | + | 0.659545i | \(0.229251\pi\) |
−0.220439 | + | 0.975401i | \(0.570749\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0566672 | + | 0.174404i | −0.00279518 | + | 0.00860269i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.92931 | − | 0.951790i | 0.144142 | − | 0.0468345i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.56960 | − | 16.2688i | 0.469753 | − | 0.798603i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.83163 | + | 6.65017i | 0.236606 | + | 0.325660i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.49925 | + | 3.99544i | −0.268656 | + | 0.195190i | −0.713954 | − | 0.700192i | \(-0.753098\pi\) |
0.445298 | + | 0.895382i | \(0.353098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.75730 | + | 6.36255i | 0.426805 | + | 0.310092i | 0.780370 | − | 0.625318i | \(-0.215031\pi\) |
−0.353565 | + | 0.935410i | \(0.615031\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.20032 | + | 2.98937i | 0.447335 | + | 0.145348i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.2692 | + | 3.19271i | 1.27424 | + | 0.154869i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 46.4099 | + | 15.0795i | 2.24593 | + | 0.729747i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.12884 | + | 1.54670i | 0.102782 | + | 0.0746752i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.40317 | − | 6.10526i | 0.404767 | − | 0.294080i | −0.366713 | − | 0.930334i | \(-0.619517\pi\) |
0.771480 | + | 0.636254i | \(0.219517\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.20630 | + | 12.6714i | 0.442427 | + | 0.608948i | 0.970749 | − | 0.240096i | \(-0.0771789\pi\) |
−0.528323 | + | 0.849044i | \(0.677179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.4150 | − | 11.7574i | −0.499361 | − | 0.563726i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 29.8156 | − | 9.68768i | 1.42627 | − | 0.463425i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.80071 | + | 20.9304i | −0.324580 | + | 0.998955i | 0.647050 | + | 0.762448i | \(0.276003\pi\) |
−0.971630 | + | 0.236507i | \(0.923997\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.11454 | + | 9.58558i | 0.148312 | + | 0.456456i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.4447i | 1.39896i | 0.714652 | + | 0.699480i | \(0.246585\pi\) | ||||
−0.714652 | + | 0.699480i | \(0.753415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.54010 | − | 0.730702i | 0.357435 | − | 0.0346386i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.25509 | + | 4.48025i | −0.153961 | + | 0.211909i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.3445 | −1.29047 | −0.645234 | − | 0.763985i | \(-0.723240\pi\) | ||||
−0.645234 | + | 0.763985i | \(0.723240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.8408 | 1.16971 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.56693 | − | 10.4150i | 0.355526 | − | 0.489339i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.83286 | + | 4.28104i | −0.226568 | + | 0.200698i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 33.6394i | − | 1.57359i | −0.617217 | − | 0.786793i | \(-0.711740\pi\) | ||
0.617217 | − | 0.786793i | \(-0.288260\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.63547 | + | 5.03347i | 0.0763374 | + | 0.234942i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.86199 | − | 24.1967i | 0.366169 | − | 1.12695i | −0.583076 | − | 0.812417i | \(-0.698151\pi\) |
0.949246 | − | 0.314536i | \(-0.101849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.45749 | + | 2.42308i | −0.346579 | + | 0.112610i | −0.477134 | − | 0.878831i | \(-0.658324\pi\) |
0.130555 | + | 0.991441i | \(0.458324\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.6892 | − | 9.01104i | 0.959439 | − | 0.417877i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.34847 | − | 8.73792i | −0.293772 | − | 0.404343i | 0.636463 | − | 0.771307i | \(-0.280397\pi\) |
−0.930235 | + | 0.366965i | \(0.880397\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0402 | − | 11.6539i | 0.740668 | − | 0.538127i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.8436 | − | 8.60487i | −0.545724 | − | 0.396491i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.1816 | − | 5.58265i | −0.790012 | − | 0.256691i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.45961 | + | 28.4652i | −0.158738 | + | 1.30607i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.23015 | + | 1.04954i | 0.147898 | + | 0.0480551i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.3447 | + | 13.3282i | 0.838191 | + | 0.608981i | 0.921865 | − | 0.387512i | \(-0.126665\pi\) |
−0.0836740 | + | 0.996493i | \(0.526665\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.26980 | − | 2.37565i | 0.149090 | − | 0.108320i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.2787 | + | 18.2766i | 0.604204 | + | 0.831615i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.7835 | − | 5.03631i | −1.03455 | − | 0.228687i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.74184 | − | 1.54072i | 0.214873 | − | 0.0698166i | −0.199602 | − | 0.979877i | \(-0.563965\pi\) |
0.414476 | + | 0.910060i | \(0.363965\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.37334 | + | 4.22672i | −0.0621048 | + | 0.191139i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.17443 | − | 25.1583i | −0.368907 | − | 1.13538i | −0.947498 | − | 0.319761i | \(-0.896397\pi\) |
0.578592 | − | 0.815617i | \(-0.303603\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.1766i | 1.67435i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.36290 | + | 7.72118i | 0.151151 | + | 0.347041i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.63365 | + | 10.5068i | −0.342416 | + | 0.471295i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.0875 | −1.70503 | −0.852516 | − | 0.522702i | \(-0.824924\pi\) | ||||
−0.852516 | + | 0.522702i | \(0.824924\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.7655 | 1.06176 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.38481 | + | 1.90603i | −0.0617456 | + | 0.0849856i | −0.838773 | − | 0.544481i | \(-0.816727\pi\) |
0.777027 | + | 0.629467i | \(0.216727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.34665 | + | 14.5718i | 0.282422 | + | 0.648438i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.5119i | 0.555672i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.02282 | + | 27.7694i | 0.399929 | + | 1.23086i | 0.925056 | + | 0.379832i | \(0.124018\pi\) |
−0.525126 | + | 0.851024i | \(0.675982\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.7250 | + | 42.2412i | −0.607158 | + | 1.86864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.45425 | + | 1.77219i | −0.240811 | + | 0.0782442i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.6568 | − | 5.89249i | −1.17464 | − | 0.259654i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.4157 | − | 29.4762i | −0.941862 | − | 1.29636i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.2055 | − | 8.86778i | 0.535760 | − | 0.389252i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4787 | + | 25.0503i | 1.51054 | + | 1.09747i | 0.965937 | + | 0.258779i | \(0.0833200\pi\) |
0.544604 | + | 0.838693i | \(0.316680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.6631 | + | 6.38893i | 0.859808 | + | 0.279368i | 0.705548 | − | 0.708662i | \(-0.250701\pi\) |
0.154259 | + | 0.988030i | \(0.450701\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −20.2788 | + | 3.96765i | −0.885039 | + | 0.173163i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −50.7978 | − | 16.5052i | −2.21279 | − | 0.718978i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.56809 | + | 4.04545i | 0.242091 | + | 0.175889i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.602958 | + | 0.438075i | −0.0261661 | + | 0.0190108i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.70855 | − | 3.72800i | −0.117320 | − | 0.161478i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.28846 | − | 3.60998i | 0.358342 | − | 0.156073i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.8982 | − | 5.16563i | 0.686057 | − | 0.222913i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.7304 | − | 36.1023i | 0.505262 | − | 1.55504i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.69426 | + | 11.3698i | 0.158829 | + | 0.488824i | 0.998529 | − | 0.0542264i | \(-0.0172693\pi\) |
−0.839700 | + | 0.543050i | \(0.817269\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3923i | 0.445976i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.29522 | + | 1.14733i | −0.0554810 | + | 0.0491462i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.6366 | + | 21.5220i | −0.668575 | + | 0.920214i | −0.999727 | − | 0.0233630i | \(-0.992563\pi\) |
0.331152 | + | 0.943577i | \(0.392563\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.8079 | −0.503951 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.2844 | −1.71617 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.1655 | − | 30.5082i | 0.942573 | − | 1.29734i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.8751 | − | 1.24771i | 0.546517 | − | 0.0529623i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.3420i | 1.20089i | 0.799667 | + | 0.600444i | \(0.205010\pi\) | ||||
−0.799667 | + | 0.600444i | \(0.794990\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.03560 | + | 3.18725i | 0.0438013 | + | 0.134806i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.15971 | − | 18.9576i | 0.260063 | − | 0.800393i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.85764 | + | 1.25342i | −0.162580 | + | 0.0528255i | −0.389176 | − | 0.921163i | \(-0.627240\pi\) |
0.226596 | + | 0.973989i | \(0.427240\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.68943 | − | 1.90719i | −0.0710747 | − | 0.0802360i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.42912 | − | 3.34339i | −0.102013 | − | 0.140409i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.59124 | − | 1.15610i | 0.0667081 | − | 0.0484663i | −0.553931 | − | 0.832562i | \(-0.686873\pi\) |
0.620640 | + | 0.784096i | \(0.286873\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.17273 | − | 3.03167i | −0.174623 | − | 0.126871i | 0.497040 | − | 0.867727i | \(-0.334420\pi\) |
−0.671664 | + | 0.740856i | \(0.734420\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.7888 | − | 6.10485i | −0.784914 | − | 0.255034i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.8892 | + | 13.2804i | −0.996249 | + | 0.553831i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.7286 | − | 11.9338i | −1.52903 | − | 0.496812i | −0.580706 | − | 0.814113i | \(-0.697224\pi\) |
−0.948325 | + | 0.317301i | \(0.897224\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.80855 | + | 1.31399i | 0.0751608 | + | 0.0546075i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.2215 | − | 20.5041i | 1.17083 | − | 0.850654i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.51885 | − | 10.3488i | −0.311399 | − | 0.428604i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.792082 | − | 1.34658i | 0.0327486 | − | 0.0556742i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.8420 | − | 8.39659i | 1.06662 | − | 0.346564i | 0.277447 | − | 0.960741i | \(-0.410512\pi\) |
0.789168 | + | 0.614177i | \(0.210512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8850 | − | 55.0443i | 0.736937 | − | 2.26806i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.03223 | − | 21.6430i | −0.289267 | − | 0.890273i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 30.3486i | − | 1.24627i | −0.782114 | − | 0.623135i | \(-0.785859\pi\) | ||
0.782114 | − | 0.623135i | \(-0.214141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 42.1554 | + | 24.7966i | 1.72820 | + | 1.01656i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.4116 | + | 18.4594i | −0.548899 | + | 0.755494i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.9205 | 1.09994 | 0.549971 | − | 0.835184i | \(-0.314639\pi\) | ||||
0.549971 | + | 0.835184i | \(0.314639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.9133 | −0.689910 | −0.344955 | − | 0.938619i | \(-0.612106\pi\) | ||||
−0.344955 | + | 0.938619i | \(0.612106\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.81995 | + | 3.88133i | −0.114837 | + | 0.158060i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.53726 | − | 6.95432i | 0.0624983 | − | 0.282733i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18.9715i | − | 0.770028i | −0.922911 | − | 0.385014i | \(-0.874197\pi\) | ||
0.922911 | − | 0.385014i | \(-0.125803\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.97057 | − | 27.6086i | −0.363506 | − | 1.11876i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.08857 | + | 6.42795i | −0.0844944 | + | 0.260047i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.19102 | + | 1.68666i | −0.209663 | + | 0.0681237i | −0.411966 | − | 0.911199i | \(-0.635158\pi\) |
0.202302 | + | 0.979323i | \(0.435158\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.42255 | − | 14.6793i | −0.0573628 | − | 0.591925i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.99287 | + | 9.62485i | 0.281522 | + | 0.387482i | 0.926237 | − | 0.376941i | \(-0.123024\pi\) |
−0.644715 | + | 0.764423i | \(0.723024\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.6888 | + | 7.76586i | −0.429619 | + | 0.312136i | −0.781496 | − | 0.623910i | \(-0.785543\pi\) |
0.351878 | + | 0.936046i | \(0.385543\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.42248 | − | 3.21312i | −0.177468 | − | 0.128938i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.3155 | + | 4.32647i | 0.533475 | + | 0.173336i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.80517 | − | 24.9347i | −0.0722066 | − | 0.997390i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.5424 | + | 6.67464i | 0.820386 | + | 0.266560i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.7693 | − | 17.9959i | −0.987616 | − | 0.717545i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.39932 | − | 6.82900i | 0.374181 | − | 0.271858i | −0.384762 | − | 0.923016i | \(-0.625716\pi\) |
0.758943 | + | 0.651158i | \(0.225716\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.8125 | − | 16.2585i | −0.469504 | − | 0.646217i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.116010 | + | 1.19710i | 0.00460371 | + | 0.0475055i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.69711 | + | 2.17602i | −0.265349 | + | 0.0862172i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.971105 | − | 2.98875i | 0.0384163 | − | 0.118233i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.7784 | − | 33.1725i | −0.425721 | − | 1.31023i | −0.902303 | − | 0.431103i | \(-0.858124\pi\) |
0.476582 | − | 0.879130i | \(-0.341876\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.90629i | − | 0.114613i | −0.998357 | − | 0.0573065i | \(-0.981749\pi\) | ||
0.998357 | − | 0.0573065i | \(-0.0182512\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.31504 | + | 10.4729i | −0.0911545 | + | 0.412370i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.13583 | − | 9.82163i | 0.280538 | − | 0.386128i | −0.645374 | − | 0.763867i | \(-0.723298\pi\) |
0.925912 | + | 0.377739i | \(0.123298\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.80702 | 0.110185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 41.7068 | 1.63462 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.3404 | + | 21.1143i | −0.600318 | + | 0.826266i | −0.995737 | − | 0.0922343i | \(-0.970599\pi\) |
0.395420 | + | 0.918500i | \(0.370599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.9565 | + | 7.62126i | 0.506253 | + | 0.297787i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 10.7473i | − | 0.419293i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.59035 | − | 20.2830i | −0.256724 | − | 0.790114i | −0.993485 | − | 0.113962i | \(-0.963646\pi\) |
0.736761 | − | 0.676153i | \(-0.236354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.79161 | + | 30.1355i | −0.380850 | + | 1.17213i | 0.558597 | + | 0.829439i | \(0.311340\pi\) |
−0.939447 | + | 0.342695i | \(0.888660\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.51671 | + | 1.14265i | −0.136578 | + | 0.0443768i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26.8695 | + | 45.6794i | −1.04195 | + | 1.77137i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.5702 | − | 31.0652i | −0.873922 | − | 1.20285i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.8561 | + | 7.88740i | −0.419720 | + | 0.304945i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.9790 | + | 26.1403i | 1.38895 | + | 1.00913i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.88857 | − | 0.613635i | −0.0727992 | − | 0.0236539i | 0.272391 | − | 0.962187i | \(-0.412186\pi\) |
−0.345190 | + | 0.938533i | \(0.612186\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.37012 | − | 2.42942i | 0.168206 | − | 0.0935083i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.5057 | − | 12.1864i | −1.44146 | − | 0.468360i | −0.519110 | − | 0.854708i | \(-0.673736\pi\) |
−0.922353 | + | 0.386348i | \(0.873736\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.8885 | − | 25.3480i | −1.33890 | − | 0.972767i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.9597 | + | 10.8689i | −0.573259 | + | 0.416497i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.22768 | + | 9.94805i | 0.276559 | + | 0.380651i | 0.924590 | − | 0.380962i | \(-0.124407\pi\) |
−0.648031 | + | 0.761614i | \(0.724407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.271894 | − | 0.306940i | −0.0103885 | − | 0.0117276i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.4623 | + | 5.99878i | −0.704382 | + | 0.228868i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.733276 | + | 2.25679i | −0.0279356 | + | 0.0859769i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.85334 | + | 14.9371i | 0.184630 | + | 0.568232i | 0.999942 | − | 0.0107896i | \(-0.00343451\pi\) |
−0.815312 | + | 0.579022i | \(0.803435\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.5649i | 0.591262i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.2949 | + | 1.77294i | −0.693966 | + | 0.0672514i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.5177 | + | 28.2402i | −0.777164 | + | 1.06967i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.1833 | −0.460813 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.4222 | −0.997953 | −0.498976 | − | 0.866616i | \(-0.666291\pi\) | ||||
−0.498976 | + | 0.866616i | \(0.666291\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.5003 | − | 26.8399i | 0.735469 | − | 1.01229i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.1921 | + | 14.3433i | −0.609828 | + | 0.540198i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.3749i | 1.10476i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.0638 | − | 46.3616i | −0.565733 | − | 1.74115i | −0.665763 | − | 0.746163i | \(-0.731894\pi\) |
0.100030 | − | 0.994984i | \(-0.468106\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.81976 | + | 8.67832i | −0.105749 | + | 0.325462i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.4677 | − | 17.0478i | 1.96493 | − | 0.638445i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.39452 | + | 2.34954i | −0.201744 | + | 0.0878680i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.65959 | + | 3.66061i | 0.0993241 | + | 0.136708i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.7117 | + | 20.1337i | −1.03347 | + | 0.750861i | −0.969001 | − | 0.247058i | \(-0.920536\pi\) |
−0.0644713 | + | 0.997920i | \(0.520536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.8197 | − | 29.6572i | −1.52020 | − | 1.10449i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.57071 | + | 2.78479i | 0.318748 | + | 0.103568i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.4684 | − | 6.74391i | 1.28012 | − | 0.250463i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.3168 | − | 6.60134i | −0.753510 | − | 0.244830i | −0.0930190 | − | 0.995664i | \(-0.529652\pi\) |
−0.660491 | + | 0.750834i | \(0.729652\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.5381 | − | 14.9218i | 0.759629 | − | 0.551903i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.3875 | + | 25.3083i | 0.679159 | + | 0.934782i | 0.999923 | − | 0.0123772i | \(-0.00393990\pi\) |
−0.320765 | + | 0.947159i | \(0.603940\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −22.0058 | − | 4.86440i | −0.811697 | − | 0.179426i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.1849 | − | 5.58370i | 0.633013 | − | 0.205678i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.406330 | + | 1.25056i | −0.0149471 | + | 0.0460025i | −0.958252 | − | 0.285925i | \(-0.907699\pi\) |
0.943305 | + | 0.331928i | \(0.107699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.23817 | − | 3.81070i | −0.0454853 | − | 0.139989i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.76431i | − | 0.321531i | −0.986993 | − | 0.160766i | \(-0.948604\pi\) | ||
0.986993 | − | 0.160766i | \(-0.0513963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.94473 | − | 11.3530i | −0.181161 | − | 0.415943i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.96148 | + | 6.82889i | −0.181531 | + | 0.249856i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.7085 | 0.610515 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.6570 | 1.62956 | 0.814779 | − | 0.579772i | \(-0.196858\pi\) | ||||
0.814779 | + | 0.579772i | \(0.196858\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.86307 | − | 2.56430i | 0.0678941 | − | 0.0934482i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.4947 | + | 26.3917i | 0.418336 | + | 0.960494i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.70729i | 0.280126i | 0.990143 | + | 0.140063i | \(0.0447305\pi\) | ||||
−0.990143 | + | 0.140063i | \(0.955269\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.36221 | + | 19.5809i | 0.230934 | + | 0.710740i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2344 | − | 37.6537i | 0.443498 | − | 1.36495i | −0.440625 | − | 0.897691i | \(-0.645243\pi\) |
0.884123 | − | 0.467254i | \(-0.154757\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.04140 | + | 0.988210i | −0.110106 | + | 0.0357756i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.5554 | − | 2.55434i | −0.417788 | − | 0.0923523i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.306068 | − | 0.421266i | −0.0110515 | − | 0.0152110i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.7336 | − | 17.2435i | 0.855855 | − | 0.621815i | −0.0708991 | − | 0.997483i | \(-0.522587\pi\) |
0.926754 | + | 0.375668i | \(0.122587\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.63126 | + | 1.91172i | 0.0947624 | + | 0.0688489i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.3762 | + | 3.37142i | 0.373205 | + | 0.121262i | 0.489613 | − | 0.871940i | \(-0.337138\pi\) |
−0.116408 | + | 0.993201i | \(0.537138\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.08801 | + | 50.0914i | −0.218688 | + | 1.79934i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.7369 | + | 7.38766i | 0.815681 | + | 0.265031i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.6010 | − | 22.2329i | −1.09639 | − | 0.796577i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.57543 | + | 6.95696i | −0.342636 | + | 0.248940i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.12883 | + | 5.68284i | 0.147552 | + | 0.203088i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.0118 | − | 13.0714i | 1.07117 | − | 0.466539i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.8619 | + | 11.6522i | −1.27834 | + | 0.415358i | −0.867995 | − | 0.496573i | \(-0.834591\pi\) |
−0.410344 | + | 0.911931i | \(0.634591\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.41774 | + | 10.5187i | −0.121675 | + | 0.374476i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.45512 | − | 4.47841i | −0.0517383 | − | 0.159234i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 8.24980i | − | 0.292959i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.68488 | + | 5.03578i | −0.201622 | + | 0.178601i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.9432 | − | 39.8369i | 1.02522 | − | 1.41110i | 0.116745 | − | 0.993162i | \(-0.462754\pi\) |
0.908477 | − | 0.417935i | \(-0.137246\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.1986 | 1.81128 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.38783 | −0.119703 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.7922 | + | 32.7472i | −0.839610 | + | 1.15562i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −50.2798 | + | 4.87256i | −1.77213 | + | 0.171735i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 24.7558i | − | 0.871447i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.33675 | − | 25.6579i | −0.293105 | − | 0.902083i | −0.983852 | − | 0.178987i | \(-0.942718\pi\) |
0.690747 | − | 0.723097i | \(-0.257282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.52546 | − | 7.77257i | 0.0886809 | − | 0.272932i | −0.896875 | − | 0.442285i | \(-0.854168\pi\) |
0.985555 | + | 0.169353i | \(0.0541679\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.237960 | + | 0.0773177i | −0.00834561 | + | 0.00271165i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.58943 | − | 7.43879i | −0.230818 | − | 0.260569i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.1692 | + | 22.2550i | 0.565689 | + | 0.778604i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.33591 | − | 1.69714i | 0.0816234 | − | 0.0593029i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.4256 | + | 25.7382i | 1.23636 | + | 0.898269i | 0.997350 | − | 0.0727478i | \(-0.0231768\pi\) |
0.239011 | + | 0.971017i | \(0.423177\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.6512 | + | 5.08540i | 0.545568 | + | 0.177266i | 0.568817 | − | 0.822464i | \(-0.307401\pi\) |
−0.0232493 | + | 0.999730i | \(0.507401\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.6940 | − | 2.27204i | −0.650842 | − | 0.0791021i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.82167 | + | 1.24174i | 0.132893 | + | 0.0431794i | 0.374708 | − | 0.927143i | \(-0.377743\pi\) |
−0.241816 | + | 0.970322i | \(0.577743\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.3103 | + | 22.0217i | 1.05272 | + | 0.764847i | 0.972728 | − | 0.231948i | \(-0.0745101\pi\) |
0.0799935 | + | 0.996795i | \(0.474510\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.17658 | − | 5.21409i | 0.248953 | − | 0.180875i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.3539 | + | 43.1550i | 1.08635 | + | 1.49523i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.9431 | + | 45.8046i | −0.932404 | + | 1.58513i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.59806 | + | 3.11860i | −0.331758 | + | 0.107795i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.58335 | − | 11.0284i | 0.123711 | − | 0.380743i | −0.869953 | − | 0.493135i | \(-0.835851\pi\) |
0.993664 | + | 0.112391i | \(0.0358510\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.28600 | + | 19.3463i | 0.216759 | + | 0.667114i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.7379i | 0.679809i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.1148 | − | 14.1848i | −0.829576 | − | 0.487972i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.73709 | − | 10.6492i | 0.265849 | − | 0.365910i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.4418 | −0.907481 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.6230 | 1.08402 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.777036 | − | 1.06950i | 0.0266052 | − | 0.0366189i | −0.795507 | − | 0.605944i | \(-0.792795\pi\) |
0.822112 | + | 0.569325i | \(0.192795\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.76787 | − | 12.5214i | 0.0946592 | − | 0.428224i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.5623i | 0.531598i | 0.964028 | + | 0.265799i | \(0.0856358\pi\) | ||||
−0.964028 | + | 0.265799i | \(0.914364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.46169 | + | 26.0424i | 0.288709 | + | 0.888556i | 0.985262 | + | 0.171050i | \(0.0547161\pi\) |
−0.696553 | + | 0.717505i | \(0.745284\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.42289 | − | 25.9230i | 0.287051 | − | 0.883453i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.4617 | − | 9.89760i | 1.03693 | − | 0.336918i | 0.259402 | − | 0.965769i | \(-0.416475\pi\) |
0.777526 | + | 0.628851i | \(0.216475\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.25398 | + | 33.5777i | 0.110639 | + | 1.14168i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.47188 | + | 8.90777i | 0.219796 | + | 0.302524i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.8038 | − | 20.2006i | 0.943178 | − | 0.685259i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.71175 | − | 1.97020i | −0.0918842 | − | 0.0667578i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.92434 | + | 3.22461i | 0.335888 | + | 0.109137i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.3431 | − | 43.5827i | 0.518692 | − | 1.47336i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.08119 | − | 1.32606i | −0.137812 | − | 0.0447778i | 0.239299 | − | 0.970946i | \(-0.423082\pi\) |
−0.377111 | + | 0.926168i | \(0.623082\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.5236 | − | 11.2786i | −0.523598 | − | 0.380416i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.7520 | − | 31.7877i | 1.47404 | − | 1.07095i | 0.494625 | − | 0.869106i | \(-0.335305\pi\) |
0.979417 | − | 0.201848i | \(-0.0646947\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.6340 | − | 25.6474i | −0.627083 | − | 0.863105i | 0.370762 | − | 0.928728i | \(-0.379097\pi\) |
−0.997845 | + | 0.0656228i | \(0.979097\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.160749 | − | 1.65876i | −0.00540352 | − | 0.0557587i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.11670 | − | 1.66252i | 0.171802 | − | 0.0558218i | −0.221853 | − | 0.975080i | \(-0.571211\pi\) |
0.393655 | + | 0.919258i | \(0.371211\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.686891 | + | 2.11403i | −0.0230376 | + | 0.0709024i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.16386 | − | 3.58198i | −0.0389906 | − | 0.120001i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 55.4786i | 1.85652i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.06785 | + | 36.4978i | −0.269678 | + | 1.21999i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.24490 | − | 3.08984i | 0.0749550 | − | 0.103167i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −70.8900 | −2.36432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.9753 | 0.598846 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.6517 | + | 16.0372i | −0.387744 | + | 0.533684i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.0297 | − | 11.7818i | −0.665809 | − | 0.391641i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 45.7593i | − | 1.51941i | −0.650266 | − | 0.759706i | \(-0.725343\pi\) | ||
0.650266 | − | 0.759706i | \(-0.274657\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.19649 | − | 6.76010i | −0.0728530 | − | 0.224219i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.669870 | − | 2.06165i | 0.0221938 | − | 0.0683054i | −0.939346 | − | 0.342970i | \(-0.888567\pi\) |
0.961540 | + | 0.274665i | \(0.0885669\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.2354 | − | 9.82408i | 1.00065 | − | 0.325130i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.3868 | − | 22.7581i | 0.442552 | − | 0.752361i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.3295 | + | 22.4757i | 0.539249 | + | 0.742213i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.9053 | + | 11.5559i | −0.524666 | + | 0.381192i | −0.818359 | − | 0.574708i | \(-0.805116\pi\) |
0.293693 | + | 0.955900i | \(0.405116\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.49942 | − | 5.44865i | −0.247114 | − | 0.179539i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.08814 | + | 0.678477i | 0.0687319 | + | 0.0223324i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.1918 | + | 26.2294i | −0.400863 | + | 0.862418i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.6115 | + | 3.77281i | 0.381372 | + | 0.123915i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.2728 | + | 25.6272i | 1.15726 | + | 0.840800i | 0.989429 | − | 0.145016i | \(-0.0463233\pi\) |
0.167832 | + | 0.985816i | \(0.446323\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46.7626 | + | 33.9750i | −1.53258 | + | 1.11349i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.6321 | + | 20.1393i | 0.479033 | + | 0.659333i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.5549 | + | 33.3644i | 0.966547 | + | 1.09113i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.0143 | + | 13.0014i | −1.30721 | + | 0.424738i | −0.878084 | − | 0.478506i | \(-0.841178\pi\) |
−0.429126 | + | 0.903245i | \(0.641178\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.86866 | − | 5.75115i | 0.0609815 | − | 0.187682i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.1162 | + | 46.5228i | 0.492773 | + | 1.51660i | 0.820399 | + | 0.571792i | \(0.193752\pi\) |
−0.327625 | + | 0.944808i | \(0.606248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 36.0544i | − | 1.17409i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.19782 | − | 0.891350i | 0.299205 | − | 0.0289956i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.18115 | + | 5.75486i | −0.135869 | + | 0.187008i | −0.871530 | − | 0.490342i | \(-0.836872\pi\) |
0.735661 | + | 0.677350i | \(0.236872\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.50878 | 0.243745 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.3864 | −0.466512 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.0707 | − | 17.9903i | 0.423402 | − | 0.582762i | −0.543021 | − | 0.839719i | \(-0.682720\pi\) |
0.966423 | + | 0.256957i | \(0.0827197\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.0672 | − | 29.2916i | 1.07003 | − | 0.947855i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 26.4560i | − | 0.855202i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.234186 | − | 0.720751i | −0.00756226 | − | 0.0232743i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.8934 | − | 67.3809i | 0.706238 | − | 2.17358i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.84515 | + | 1.24937i | −0.123908 | + | 0.0402603i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.58290 | + | 1.99605i | −0.147529 | + | 0.0642550i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.17914 | − | 11.2576i | −0.263023 | − | 0.362021i | 0.656996 | − | 0.753894i | \(-0.271827\pi\) |
−0.920019 | + | 0.391874i | \(0.871827\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.5554 | + | 17.8406i | −0.788834 | + | 0.573122i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.6548 | − | 14.2801i | −0.630754 | − | 0.458270i | 0.225907 | − | 0.974149i | \(-0.427465\pi\) |
−0.856661 | + | 0.515879i | \(0.827465\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.3081 | − | 10.4975i | −1.03575 | − | 0.336535i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.69735 | + | 3.05325i | 0.0543587 | + | 0.0977823i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.0637 | + | 14.3172i | 1.40972 | + | 0.458047i | 0.912322 | − | 0.409473i | \(-0.134287\pi\) |
0.497402 | + | 0.867520i | \(0.334287\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3228 | + | 7.49993i | 0.329917 | + | 0.239699i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.626030 | − | 0.454837i | 0.0199876 | − | 0.0145218i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.1334 | + | 33.2168i | 0.769736 | + | 1.05945i | 0.996341 | + | 0.0854644i | \(0.0272374\pi\) |
−0.226605 | + | 0.973987i | \(0.572763\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.6863 | + | 10.9832i | 1.58314 | + | 0.349953i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −38.0218 | + | 12.3540i | −1.21025 | + | 0.393233i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.10275 | + | 24.9377i | −0.257652 | + | 0.792972i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.26579 | + | 19.2841i | 0.199039 | + | 0.612580i | 0.999906 | + | 0.0137370i | \(0.00437276\pi\) |
−0.800866 | + | 0.598843i | \(0.795627\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.06688i | 0.0338565i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.3731 | − | 46.7765i | −0.645872 | − | 1.48291i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.3204 | + | 19.7104i | −0.453533 | + | 0.624234i | −0.973152 | − | 0.230164i | \(-0.926074\pi\) |
0.519619 | + | 0.854398i | \(0.326074\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.78488 | −0.183026 |
(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 | 300.2.o.a.229.5 | yes | 24 | |
3.2 | odd | 2 | 900.2.w.c.829.3 | 24 | |||
5.2 | odd | 4 | 1500.2.m.c.601.1 | 24 | |||
5.3 | odd | 4 | 1500.2.m.d.601.6 | 24 | |||
5.4 | even | 2 | 1500.2.o.c.649.2 | 24 | |||
25.6 | even | 5 | 1500.2.o.c.349.2 | 24 | |||
25.8 | odd | 20 | 1500.2.m.d.901.6 | 24 | |||
25.9 | even | 10 | 7500.2.d.g.1249.1 | 24 | |||
25.12 | odd | 20 | 7500.2.a.n.1.1 | 12 | |||
25.13 | odd | 20 | 7500.2.a.m.1.12 | 12 | |||
25.16 | even | 5 | 7500.2.d.g.1249.24 | 24 | |||
25.17 | odd | 20 | 1500.2.m.c.901.1 | 24 | |||
25.19 | even | 10 | inner | 300.2.o.a.169.5 | ✓ | 24 | |
75.44 | odd | 10 | 900.2.w.c.469.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.169.5 | ✓ | 24 | 25.19 | even | 10 | inner | |
300.2.o.a.229.5 | yes | 24 | 1.1 | even | 1 | trivial | |
900.2.w.c.469.3 | 24 | 75.44 | odd | 10 | |||
900.2.w.c.829.3 | 24 | 3.2 | odd | 2 | |||
1500.2.m.c.601.1 | 24 | 5.2 | odd | 4 | |||
1500.2.m.c.901.1 | 24 | 25.17 | odd | 20 | |||
1500.2.m.d.601.6 | 24 | 5.3 | odd | 4 | |||
1500.2.m.d.901.6 | 24 | 25.8 | odd | 20 | |||
1500.2.o.c.349.2 | 24 | 25.6 | even | 5 | |||
1500.2.o.c.649.2 | 24 | 5.4 | even | 2 | |||
7500.2.a.m.1.12 | 12 | 25.13 | odd | 20 | |||
7500.2.a.n.1.1 | 12 | 25.12 | odd | 20 | |||
7500.2.d.g.1249.1 | 24 | 25.9 | even | 10 | |||
7500.2.d.g.1249.24 | 24 | 25.16 | even | 5 |