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 | 109.1 | ||
Character | \(\chi\) | \(=\) | 300.109 |
Dual form | 300.2.o.a.289.1 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
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 | ||||||||
\(3\) | −0.951057 | + | 0.309017i | −0.549093 | + | 0.178411i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.10592 | + | 0.751722i | −0.941798 | + | 0.336180i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.595901i | 0.225229i | 0.993639 | + | 0.112615i | \(0.0359225\pi\) | ||||
−0.993639 | + | 0.112615i | \(0.964077\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.809017 | − | 0.587785i | 0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.71474 | − | 1.97238i | −0.818526 | − | 0.594694i | 0.0977636 | − | 0.995210i | \(-0.468831\pi\) |
−0.916290 | + | 0.400515i | \(0.868831\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.80319 | − | 3.85825i | −0.777464 | − | 1.07009i | −0.995557 | − | 0.0941591i | \(-0.969984\pi\) |
0.218094 | − | 0.975928i | \(-0.430016\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.77056 | − | 1.36570i | 0.457156 | − | 0.352621i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.11384 | − | 2.31143i | −1.72536 | − | 0.560603i | −0.732593 | − | 0.680667i | \(-0.761690\pi\) |
−0.992766 | + | 0.120064i | \(0.961690\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.91242 | + | 5.88583i | −0.438740 | + | 1.35030i | 0.450466 | + | 0.892794i | \(0.351258\pi\) |
−0.889205 | + | 0.457508i | \(0.848742\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.184143 | − | 0.566735i | −0.0401834 | − | 0.123672i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.59154 | + | 3.56694i | −0.540373 | + | 0.743759i | −0.988667 | − | 0.150127i | \(-0.952032\pi\) |
0.448294 | + | 0.893886i | \(0.352032\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.86983 | − | 3.16614i | 0.773966 | − | 0.633228i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.587785 | + | 0.809017i | −0.113119 | + | 0.155695i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.853035 | + | 2.62537i | 0.158405 | + | 0.487519i | 0.998490 | − | 0.0549349i | \(-0.0174951\pi\) |
−0.840085 | + | 0.542454i | \(0.817495\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.38708 | − | 4.26899i | 0.249127 | − | 0.766734i | −0.745803 | − | 0.666166i | \(-0.767934\pi\) |
0.994930 | − | 0.100567i | \(-0.0320658\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.19137 | + | 1.03694i | 0.555547 | + | 0.180508i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.447952 | − | 1.25492i | −0.0757176 | − | 0.212120i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.764512 | − | 1.05226i | −0.125685 | − | 0.172991i | 0.741537 | − | 0.670912i | \(-0.234097\pi\) |
−0.867222 | + | 0.497921i | \(0.834097\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.85825 | + | 2.80319i | 0.617815 | + | 0.448869i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.61184 | − | 5.53032i | 1.18877 | − | 0.863691i | 0.195636 | − | 0.980677i | \(-0.437323\pi\) |
0.993134 | + | 0.116985i | \(0.0373230\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.59854i | 1.15877i | 0.815055 | + | 0.579383i | \(0.196706\pi\) | ||||
−0.815055 | + | 0.579383i | \(0.803294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.26188 | + | 1.84599i | −0.188109 | + | 0.275183i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.18645 | + | 1.36026i | −0.610656 | + | 0.198414i | −0.597987 | − | 0.801506i | \(-0.704033\pi\) |
−0.0126688 | + | 0.999920i | \(0.504033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.64490 | 0.949272 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.47993 | 1.04740 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.80561 | + | 2.53620i | −1.07218 | + | 0.348373i | −0.791338 | − | 0.611379i | \(-0.790615\pi\) |
−0.280846 | + | 0.959753i | \(0.590615\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.19972 | + | 2.11294i | 0.970811 | + | 0.284909i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.18873i | − | 0.819717i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.80309 | + | 1.31002i | −0.234743 | + | 0.170550i | −0.698938 | − | 0.715182i | \(-0.746344\pi\) |
0.464195 | + | 0.885733i | \(0.346344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.2014 | − | 7.41175i | −1.30615 | − | 0.948977i | −0.306159 | − | 0.951980i | \(-0.599044\pi\) |
−0.999995 | + | 0.00300353i | \(0.999044\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.350262 | + | 0.482094i | 0.0441288 | + | 0.0607381i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.80363 | + | 6.01797i | 1.09196 | + | 0.746437i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.94930 | + | 2.58288i | 0.971161 | + | 0.315549i | 0.751285 | − | 0.659978i | \(-0.229435\pi\) |
0.219877 | + | 0.975528i | \(0.429435\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.36245 | − | 4.19319i | 0.164020 | − | 0.504801i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.09986 | + | 6.46271i | 0.249208 | + | 0.766983i | 0.994916 | + | 0.100710i | \(0.0321114\pi\) |
−0.745708 | + | 0.666273i | \(0.767889\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.29801 | − | 5.91570i | 0.503044 | − | 0.692381i | −0.479683 | − | 0.877442i | \(-0.659248\pi\) |
0.982727 | + | 0.185061i | \(0.0592483\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.70203 | + | 4.20702i | −0.312004 | + | 0.485785i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.17534 | − | 1.61772i | 0.133943 | − | 0.184356i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.26546 | + | 10.0500i | 0.367393 | + | 1.13072i | 0.948469 | + | 0.316870i | \(0.102632\pi\) |
−0.581076 | + | 0.813849i | \(0.697368\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.97694 | − | 1.29219i | −0.436526 | − | 0.141836i | 0.0825062 | − | 0.996591i | \(-0.473708\pi\) |
−0.519032 | + | 0.854755i | \(0.673708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.7188 | − | 0.479942i | 1.81340 | − | 0.0520571i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.62257 | − | 2.23328i | −0.173958 | − | 0.239432i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.43862 | + | 2.49830i | 0.364493 | + | 0.264819i | 0.754924 | − | 0.655813i | \(-0.227674\pi\) |
−0.390431 | + | 0.920632i | \(0.627674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.29914 | − | 1.67042i | 0.241015 | − | 0.175108i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.48868i | 0.465455i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.397094 | − | 13.8327i | −0.0407409 | − | 1.41921i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.6744 | + | 3.79326i | −1.18536 | + | 0.385147i | −0.834355 | − | 0.551227i | \(-0.814160\pi\) |
−0.351004 | + | 0.936374i | \(0.614160\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.35561 | −0.337251 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.00835 | −0.796860 | −0.398430 | − | 0.917199i | \(-0.630445\pi\) | ||||
−0.398430 | + | 0.917199i | \(0.630445\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.34989 | + | 1.73829i | −0.527141 | + | 0.171278i | −0.560484 | − | 0.828166i | \(-0.689385\pi\) |
0.0333428 | + | 0.999444i | \(0.489385\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.813819 | + | 1.05508i | 0.0794206 | + | 0.102965i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13.7701i | − | 1.33120i | −0.746308 | − | 0.665601i | \(-0.768175\pi\) | ||
0.746308 | − | 0.665601i | \(-0.231825\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.3566 | + | 7.52450i | −0.991981 | + | 0.720716i | −0.960354 | − | 0.278784i | \(-0.910069\pi\) |
−0.0316266 | + | 0.999500i | \(0.510069\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.05226 | + | 0.764512i | 0.0998761 | + | 0.0725643i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.84147 | + | 9.41647i | 0.643591 | + | 0.885827i | 0.998801 | − | 0.0489597i | \(-0.0155906\pi\) |
−0.355210 | + | 0.934787i | \(0.615591\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.77623 | − | 9.45983i | 0.258885 | − | 0.882133i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.53565 | − | 1.47372i | −0.419321 | − | 0.136246i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.37738 | − | 4.23914i | 0.126264 | − | 0.388601i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0803793 | + | 0.247382i | 0.00730721 | + | 0.0224893i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.53032 | + | 7.61184i | −0.498652 | + | 0.686336i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.76951 | + | 9.57668i | −0.516040 | + | 0.856564i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.56452 | − | 2.15338i | 0.138829 | − | 0.191081i | −0.733941 | − | 0.679213i | \(-0.762321\pi\) |
0.872770 | + | 0.488132i | \(0.162321\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.34808 | − | 7.22664i | −0.206737 | − | 0.636270i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00070 | − | 9.23520i | 0.262172 | − | 0.806883i | −0.730159 | − | 0.683277i | \(-0.760554\pi\) |
0.992331 | − | 0.123606i | \(-0.0394458\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.50737 | − | 1.13961i | −0.304128 | − | 0.0988170i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.629675 | − | 2.14558i | 0.0541938 | − | 0.184662i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.25823 | − | 3.10819i | −0.192934 | − | 0.265551i | 0.701580 | − | 0.712591i | \(-0.252478\pi\) |
−0.894514 | + | 0.447040i | \(0.852478\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.98655 | − | 2.89640i | −0.338135 | − | 0.245670i | 0.405740 | − | 0.913989i | \(-0.367014\pi\) |
−0.743875 | + | 0.668319i | \(0.767014\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.56121 | − | 2.58737i | 0.299908 | − | 0.217896i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.0031i | 1.33825i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.76998 | − | 4.88759i | −0.313080 | − | 0.405892i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.31968 | + | 2.05339i | −0.521238 | + | 0.169361i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.59040 | 0.539907 | 0.269953 | − | 0.962873i | \(-0.412992\pi\) | ||||
0.269953 | + | 0.962873i | \(0.412992\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5433 | −1.59041 | −0.795207 | − | 0.606338i | \(-0.792638\pi\) | ||||
−0.795207 | + | 0.606338i | \(0.792638\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.11384 | + | 2.31143i | −0.575120 | + | 0.186868i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.288012 | + | 10.0329i | 0.0231337 | + | 0.805859i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 0.341995i | − | 0.0272942i | −0.999907 | − | 0.0136471i | \(-0.995656\pi\) | ||
0.999907 | − | 0.0136471i | \(-0.00434414\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.63985 | − | 4.82413i | 0.526574 | − | 0.382579i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.12554 | − | 1.54430i | −0.167516 | − | 0.121708i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.2347 | − | 18.2161i | −1.03663 | − | 1.42679i | −0.899855 | − | 0.436190i | \(-0.856328\pi\) |
−0.136770 | − | 0.990603i | \(-0.543672\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.50028 | + | 0.215309i | −0.583896 | + | 0.0167618i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.10375 | + | 1.33339i | 0.317557 | + | 0.103181i | 0.463459 | − | 0.886118i | \(-0.346608\pi\) |
−0.145901 | + | 0.989299i | \(0.546608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.01105 | + | 9.26706i | −0.231619 | + | 0.712851i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.91242 | + | 5.88583i | 0.146247 | + | 0.450101i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0916 | − | 13.8898i | 0.767247 | − | 1.05602i | −0.229330 | − | 0.973349i | \(-0.573653\pi\) |
0.996577 | − | 0.0826755i | \(-0.0263465\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.88670 | + | 2.30603i | 0.142621 | + | 0.174320i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.31002 | − | 1.80309i | 0.0984674 | − | 0.135529i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.328670 | − | 1.01154i | −0.0245659 | − | 0.0756062i | 0.938022 | − | 0.346576i | \(-0.112656\pi\) |
−0.962588 | + | 0.270970i | \(0.912656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.71645 | + | 11.4380i | −0.276241 | + | 0.850183i | 0.712647 | + | 0.701523i | \(0.247496\pi\) |
−0.988888 | + | 0.148660i | \(0.952504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.9925 | + | 3.89659i | 0.886508 | + | 0.288044i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.40101 | + | 1.64128i | 0.176526 | + | 0.120669i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.7533 | + | 20.3061i | 1.07886 | + | 1.48493i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.482094 | − | 0.350262i | −0.0350672 | − | 0.0254778i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.7737 | − | 12.9134i | 1.28606 | − | 0.934379i | 0.286344 | − | 0.958127i | \(-0.407560\pi\) |
0.999718 | + | 0.0237480i | \(0.00755992\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 20.4002i | − | 1.46844i | −0.678912 | − | 0.734220i | \(-0.737548\pi\) | ||
0.678912 | − | 0.734220i | \(-0.262452\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.2324 | − | 3.00296i | −0.732758 | − | 0.215046i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.90410 | + | 1.26852i | −0.278155 | + | 0.0903781i | −0.444773 | − | 0.895644i | \(-0.646716\pi\) |
0.166617 | + | 0.986022i | \(0.446716\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.5940 | −1.81431 | −0.907156 | − | 0.420795i | \(-0.861751\pi\) | ||||
−0.907156 | + | 0.420795i | \(0.861751\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.35839 | −0.589555 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.56446 | + | 0.508324i | −0.109804 | + | 0.0356774i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.8727 | + | 17.3684i | −0.829224 | + | 1.21306i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.40898i | 0.306446i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.8008 | − | 12.2065i | 1.16214 | − | 0.844342i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.7826 | − | 11.4667i | −1.08652 | − | 0.789402i | −0.107710 | − | 0.994182i | \(-0.534352\pi\) |
−0.978808 | + | 0.204781i | \(0.934352\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.99418 | − | 5.49751i | −0.273676 | − | 0.376683i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.71199 | − | 16.0019i | −0.389554 | − | 1.09132i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.54389 | + | 0.826561i | 0.172691 | + | 0.0561106i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.25960 | + | 6.95433i | −0.152689 | + | 0.469930i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.0233 | + | 33.9263i | 0.741510 | + | 2.28213i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.30975 | − | 1.80271i | 0.0877071 | − | 0.120718i | −0.762909 | − | 0.646506i | \(-0.776229\pi\) |
0.850616 | + | 0.525788i | \(0.176229\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.26975 | − | 4.83609i | 0.0846498 | − | 0.322406i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.67322 | + | 3.67938i | −0.177428 | + | 0.244209i | −0.888463 | − | 0.458947i | \(-0.848227\pi\) |
0.711035 | + | 0.703156i | \(0.248227\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.05533 | − | 3.24796i | −0.0697380 | − | 0.214631i | 0.910113 | − | 0.414359i | \(-0.135994\pi\) |
−0.979851 | + | 0.199728i | \(0.935994\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.617913 | + | 1.90174i | −0.0406557 | + | 0.125125i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.9202 | + | 5.17279i | 1.04297 | + | 0.338881i | 0.779905 | − | 0.625898i | \(-0.215267\pi\) |
0.263063 | + | 0.964779i | \(0.415267\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.79380 | − | 6.01165i | 0.508412 | − | 0.392157i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.21127 | − | 8.54908i | −0.403465 | − | 0.555323i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.0931 | − | 13.1454i | −1.17035 | − | 0.850306i | −0.179295 | − | 0.983795i | \(-0.557382\pi\) |
−0.991050 | + | 0.133490i | \(0.957382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.214678 | + | 0.155973i | −0.0138286 | + | 0.0100471i | −0.594678 | − | 0.803964i | \(-0.702720\pi\) |
0.580849 | + | 0.814011i | \(0.302720\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.9937 | + | 4.99512i | −0.894022 | + | 0.319126i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.0699 | − | 9.12046i | 1.78604 | − | 0.580321i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.18160 | 0.264998 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.0694 | 1.83484 | 0.917422 | − | 0.397915i | \(-0.130266\pi\) | ||||
0.917422 | + | 0.397915i | \(0.130266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.0707 | − | 4.57185i | 0.884619 | − | 0.287430i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.7522 | + | 5.62283i | −0.986439 | + | 0.352115i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.05952i | 0.440361i | 0.975459 | + | 0.220180i | \(0.0706646\pi\) | ||||
−0.975459 | + | 0.220180i | \(0.929335\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.627043 | − | 0.455573i | 0.0389625 | − | 0.0283079i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.23328 | + | 1.62257i | 0.138236 | + | 0.100435i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.814961 | − | 1.12170i | −0.0502527 | − | 0.0691669i | 0.783151 | − | 0.621831i | \(-0.213611\pi\) |
−0.833404 | + | 0.552665i | \(0.813611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.5315 | − | 11.2087i | 0.892663 | − | 0.688544i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.04234 | − | 1.31343i | −0.247387 | − | 0.0803809i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.38039 | − | 13.4815i | 0.267077 | − | 0.821979i | −0.724130 | − | 0.689663i | \(-0.757759\pi\) |
0.991208 | − | 0.132316i | \(-0.0422414\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.64795 | + | 14.3049i | 0.282343 | + | 0.868963i | 0.987182 | + | 0.159596i | \(0.0510191\pi\) |
−0.704839 | + | 0.709367i | \(0.748981\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.67042 | + | 2.29914i | −0.101098 | + | 0.139150i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.7504 | + | 0.962496i | −1.01009 | + | 0.0580407i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.51973 | + | 10.3500i | −0.451817 | + | 0.621873i | −0.972787 | − | 0.231703i | \(-0.925570\pi\) |
0.520970 | + | 0.853575i | \(0.325570\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.38708 | − | 4.26899i | −0.0830423 | − | 0.255578i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.72976 | + | 14.5567i | −0.282154 | + | 0.868380i | 0.705084 | + | 0.709124i | \(0.250909\pi\) |
−0.987237 | + | 0.159256i | \(0.949091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.2073 | + | 7.21559i | 1.32009 | + | 0.428923i | 0.882525 | − | 0.470265i | \(-0.155842\pi\) |
0.437563 | + | 0.899188i | \(0.355842\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.65220 | + | 13.0330i | 0.275573 | + | 0.772008i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.29552 | + | 4.53590i | 0.194529 | + | 0.267746i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.5107 | + | 22.8939i | 1.85357 | + | 1.34670i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.93087 | − | 7.21520i | 0.582158 | − | 0.422963i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.36651i | 0.371936i | 0.982556 | + | 0.185968i | \(0.0595420\pi\) | ||||
−0.982556 | + | 0.185968i | \(0.940458\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.81240 | − | 4.11423i | 0.163744 | − | 0.239540i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.19137 | − | 1.03694i | 0.185182 | − | 0.0601694i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.0267 | 1.21601 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.52797 | −0.260988 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.61639 | − | 2.47472i | 0.437550 | − | 0.142169i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.0549 | + | 7.93996i | 1.54916 | + | 0.454641i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.2317i | 1.55419i | 0.629382 | + | 0.777096i | \(0.283308\pi\) | ||||
−0.629382 | + | 0.777096i | \(0.716692\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.55089 | − | 3.30642i | 0.258891 | − | 0.188095i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.8814 | − | 10.0854i | −0.787142 | − | 0.571892i | 0.119972 | − | 0.992777i | \(-0.461719\pi\) |
−0.907114 | + | 0.420885i | \(0.861719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.9120 | − | 16.3955i | −0.673307 | − | 0.926728i | 0.326523 | − | 0.945189i | \(-0.394123\pi\) |
−0.999830 | + | 0.0184618i | \(0.994123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.10002 | − | 0.751953i | −0.0619794 | − | 0.0423678i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.9868 | + | 6.49409i | 1.12257 | + | 0.364745i | 0.810747 | − | 0.585396i | \(-0.199061\pi\) |
0.311821 | + | 0.950141i | \(0.399061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.86245 | − | 8.80972i | 0.160267 | − | 0.493250i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.25518 | + | 13.0961i | 0.237501 | + | 0.730953i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.2093 | − | 37.4504i | 1.51397 | − | 2.08380i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.0636 | − | 6.05550i | −1.27934 | − | 0.335899i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.52450 | − | 10.3566i | 0.416106 | − | 0.572720i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.810579 | − | 2.49471i | −0.0446887 | − | 0.137538i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.93765 | + | 12.1188i | −0.216433 | + | 0.666111i | 0.782616 | + | 0.622505i | \(0.213885\pi\) |
−0.999049 | + | 0.0436066i | \(0.986115\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.23701 | − | 0.401928i | −0.0677875 | − | 0.0220255i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.6822 | + | 0.536308i | −1.02072 | + | 0.0293016i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.25720 | + | 9.98868i | 0.395325 | + | 0.544118i | 0.959563 | − | 0.281494i | \(-0.0908300\pi\) |
−0.564238 | + | 0.825612i | \(0.690830\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.41647 | − | 6.84147i | −0.511432 | − | 0.371577i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.1856 | + | 8.85338i | −0.659889 | + | 0.479437i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.13100i | 0.439033i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.282898 | + | 9.85473i | 0.0152307 | + | 0.530561i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.5175 | − | 4.06718i | 0.671974 | − | 0.218337i | 0.0468956 | − | 0.998900i | \(-0.485067\pi\) |
0.625078 | + | 0.780562i | \(0.285067\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.8060 | −1.11372 | −0.556861 | − | 0.830606i | \(-0.687994\pi\) | ||||
−0.556861 | + | 0.830606i | \(0.687994\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.76906 | 0.254554 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.3852 | + | 8.89800i | −1.45757 | + | 0.473593i | −0.927326 | − | 0.374254i | \(-0.877899\pi\) |
−0.530242 | + | 0.847846i | \(0.677899\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.28031 | − | 12.0315i | −0.492548 | − | 0.638564i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.45730i | 0.235905i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.9627 | + | 19.5896i | −1.42304 | + | 1.03390i | −0.431779 | + | 0.901979i | \(0.642114\pi\) |
−0.991260 | + | 0.131919i | \(0.957886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6143 | − | 11.3445i | −0.821806 | − | 0.597077i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.152891 | − | 0.210436i | −0.00802468 | − | 0.0110450i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.60432 | + | 15.6889i | −0.241001 | + | 0.821196i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.80441 | + | 0.586288i | 0.0941894 | + | 0.0306040i | 0.355733 | − | 0.934588i | \(-0.384231\pi\) |
−0.261543 | + | 0.965192i | \(0.584231\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.90746 | − | 8.94825i | 0.151356 | − | 0.465827i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.51132 | − | 4.65137i | −0.0784639 | − | 0.241487i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.1572 | − | 24.9912i | 0.940143 | − | 1.29400i | −0.0156262 | − | 0.999878i | \(-0.504974\pi\) |
0.955769 | − | 0.294118i | \(-0.0950258\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.52777 | − | 10.8908i | 0.130533 | − | 0.562401i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.73814 | − | 10.6506i | 0.398534 | − | 0.548535i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.96979 | − | 21.4508i | −0.358014 | − | 1.10185i | −0.954241 | − | 0.299038i | \(-0.903334\pi\) |
0.596227 | − | 0.802816i | \(-0.296666\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.822516 | + | 2.53145i | −0.0421388 | + | 0.129690i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.13113 | − | 1.34229i | −0.211091 | − | 0.0685877i | 0.201563 | − | 0.979476i | \(-0.435398\pi\) |
−0.412654 | + | 0.910888i | \(0.635398\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.25910 | + | 4.29032i | −0.0641699 | + | 0.218655i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.46631 | + | 6.14735i | 0.227035 | + | 0.312487i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0039 | − | 10.9010i | −0.760729 | − | 0.552702i | 0.138405 | − | 0.990376i | \(-0.455802\pi\) |
−0.899134 | + | 0.437674i | \(0.855802\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.6805 | − | 19.3845i | 1.34929 | − | 0.980317i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.71046i | 0.489828i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.4317 | − | 18.7099i | −0.726135 | − | 0.941398i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.672391 | − | 0.218473i | 0.0337463 | − | 0.0109648i | −0.292095 | − | 0.956389i | \(-0.594352\pi\) |
0.325842 | + | 0.945424i | \(0.394352\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.68787 | 0.184624 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.8304 | −1.23997 | −0.619986 | − | 0.784613i | \(-0.712862\pi\) | ||||
−0.619986 | + | 0.784613i | \(0.712862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.3591 | + | 6.61507i | −1.01416 | + | 0.329520i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.0641640 | + | 2.23515i | 0.00318833 | + | 0.111065i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.36453i | 0.216341i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.590588 | + | 0.429087i | −0.0292027 | + | 0.0212170i | −0.602291 | − | 0.798277i | \(-0.705745\pi\) |
0.573088 | + | 0.819494i | \(0.305745\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.10819 | + | 2.25823i | 0.153316 | + | 0.111390i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.780643 | − | 1.07446i | −0.0384130 | − | 0.0528709i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.34650 | − | 0.268308i | 0.458802 | − | 0.0131707i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.68647 | + | 1.52273i | 0.229498 | + | 0.0745683i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.98923 | − | 12.2776i | 0.194887 | − | 0.599799i | −0.805091 | − | 0.593151i | \(-0.797884\pi\) |
0.999978 | − | 0.00664830i | \(-0.00211623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.7828 | + | 36.2639i | 0.574261 | + | 1.76739i | 0.638683 | + | 0.769470i | \(0.279480\pi\) |
−0.0644219 | + | 0.997923i | \(0.520520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.58737 | + | 3.56121i | −0.125802 | + | 0.173152i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.8476 | + | 13.5786i | −1.69036 | + | 0.658658i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.41666 | − | 6.07902i | 0.213737 | − | 0.294184i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.94523 | − | 15.2199i | −0.238758 | − | 0.734822i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.1829 | + | 34.4175i | −0.538663 | + | 1.65783i | 0.196936 | + | 0.980416i | \(0.436901\pi\) |
−0.735599 | + | 0.677418i | \(0.763099\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.6842 | + | 6.72071i | 0.994021 | + | 0.322977i | 0.760474 | − | 0.649369i | \(-0.224967\pi\) |
0.233547 | + | 0.972346i | \(0.424967\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.09581 | + | 3.48339i | 0.244325 | + | 0.167016i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0383 | − | 22.0748i | −0.767217 | − | 1.05598i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.8418 | − | 23.1344i | −1.51973 | − | 1.10415i | −0.961623 | − | 0.274374i | \(-0.911529\pi\) |
−0.558103 | − | 0.829772i | \(-0.688471\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.37584 | − | 3.90578i | 0.255992 | − | 0.185989i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.4919i | 1.30618i | 0.757281 | + | 0.653089i | \(0.226527\pi\) | ||||
−0.757281 | + | 0.653089i | \(0.773473\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.11949 | − | 2.67635i | −0.432305 | − | 0.126871i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.26784 | + | 2.03655i | −0.296459 | + | 0.0963253i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.51087 | −0.165688 | −0.0828441 | − | 0.996563i | \(-0.526400\pi\) | ||||
−0.0828441 | + | 0.996563i | \(0.526400\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.5721 | −1.48667 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.5868 | − | 6.03923i | 0.873285 | − | 0.283748i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.58611 | + | 5.24609i | −0.168120 | + | 0.245940i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.1677i | − | 0.475624i | −0.971311 | − | 0.237812i | \(-0.923570\pi\) | ||
0.971311 | − | 0.237812i | \(-0.0764302\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.05139 | − | 4.39659i | 0.282455 | − | 0.205215i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.755758 | − | 0.549090i | −0.0351992 | − | 0.0255737i | 0.570047 | − | 0.821612i | \(-0.306925\pi\) |
−0.605246 | + | 0.796039i | \(0.706925\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.87183 | + | 3.95274i | 0.133465 | + | 0.183699i | 0.870519 | − | 0.492135i | \(-0.163783\pi\) |
−0.737053 | + | 0.675835i | \(0.763783\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.37424 | − | 9.45282i | −0.156477 | − | 0.438364i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.5416 | − | 7.97406i | −1.13565 | − | 0.368996i | −0.319931 | − | 0.947441i | \(-0.603660\pi\) |
−0.815721 | + | 0.578445i | \(0.803660\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.53914 | + | 4.73699i | −0.0710710 | + | 0.218734i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.105682 | + | 0.325257i | 0.00486958 | + | 0.0149870i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.9872 | − | 20.6281i | 0.689111 | − | 0.948480i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.2346 | + | 28.8321i | 0.515479 | + | 1.32291i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.82413 | + | 6.63985i | −0.220882 | + | 0.304018i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.22721 | + | 16.0877i | 0.238837 | + | 0.735065i | 0.996589 | + | 0.0825225i | \(0.0262976\pi\) |
−0.757752 | + | 0.652543i | \(0.773702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.91682 | + | 5.89936i | −0.0873994 | + | 0.268988i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.49873 | + | 0.811885i | 0.113696 | + | 0.0369421i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.7340 | − | 16.7642i | 0.986890 | − | 0.761225i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.63237 | − | 13.2578i | −0.436484 | − | 0.600769i | 0.532942 | − | 0.846152i | \(-0.321086\pi\) |
−0.969426 | + | 0.245383i | \(0.921086\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.2161 | + | 13.2347i | 0.823759 | + | 0.598496i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.30972 | − | 6.03737i | 0.375013 | − | 0.272463i | −0.384274 | − | 0.923219i | \(-0.625548\pi\) |
0.759286 | + | 0.650757i | \(0.225548\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 20.6482i | − | 0.929948i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.06666 | − | 2.52249i | 0.317623 | − | 0.113377i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.85113 | + | 1.25131i | −0.172747 | + | 0.0561289i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5015 | 0.738707 | 0.369354 | − | 0.929289i | \(-0.379579\pi\) | ||||
0.369354 | + | 0.929289i | \(0.379579\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.31493 | −0.192777 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.22834 | + | 2.34863i | −0.322296 | + | 0.104720i | −0.465697 | − | 0.884944i | \(-0.654196\pi\) |
0.143401 | + | 0.989665i | \(0.454196\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.8650 | − | 6.02005i | 0.750481 | − | 0.267889i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 9.74397i | − | 0.432745i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.7590 | + | 12.9027i | −0.787154 | + | 0.571901i | −0.907118 | − | 0.420877i | \(-0.861722\pi\) |
0.119963 | + | 0.992778i | \(0.461722\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.52517 | + | 2.56119i | 0.155944 | + | 0.113300i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.63764 | − | 5.00679i | −0.160606 | − | 0.221055i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.95976 | − | 7.68233i | 0.438879 | − | 0.338524i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.0481 | + | 4.56450i | 0.617834 | + | 0.200746i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.30544 | + | 16.3285i | −0.232883 | + | 0.716741i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.3835 | − | 35.0349i | −0.498722 | − | 1.53491i | −0.811075 | − | 0.584942i | \(-0.801117\pi\) |
0.312353 | − | 0.949966i | \(-0.398883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.4517 | + | 33.6548i | −1.06920 | + | 1.47162i | −0.198310 | + | 0.980139i | \(0.563545\pi\) |
−0.870887 | + | 0.491484i | \(0.836455\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.50696 | − | 1.61014i | −0.109413 | − | 0.0702724i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.7349 | + | 27.1628i | −0.859667 | + | 1.18323i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.10036 | + | 3.38657i | 0.0478419 | + | 0.147242i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.688720 | + | 2.11966i | −0.0298879 | + | 0.0919855i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −42.6748 | − | 13.8659i | −1.84845 | − | 0.600598i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.3513 | + | 28.9987i | 0.447524 | + | 1.25372i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.625167 | + | 0.860469i | 0.0269779 | + | 0.0371320i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.0392 | − | 13.1063i | −0.777004 | − | 0.564526i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5570 | − | 9.12319i | 0.539867 | − | 0.392237i | −0.284168 | − | 0.958774i | \(-0.591717\pi\) |
0.824036 | + | 0.566538i | \(0.191717\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 12.0267i | − | 0.516114i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.1538 | − | 23.6313i | 0.691954 | − | 1.01225i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.1633 | − | 7.20130i | 0.947636 | − | 0.307906i | 0.205881 | − | 0.978577i | \(-0.433994\pi\) |
0.741755 | + | 0.670671i | \(0.233994\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.6096 | −0.538165 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.0839 | −0.727797 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.98883 | + | 1.94589i | −0.254671 | + | 0.0827476i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.79068 | − | 0.818996i | −0.118458 | − | 0.0347645i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.0914i | 0.469959i | 0.972000 | + | 0.234979i | \(0.0755023\pi\) | ||||
−0.972000 | + | 0.234979i | \(0.924498\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.3171 | − | 21.3001i | 1.23998 | − | 0.900898i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.3061 | − | 14.7533i | −0.857325 | − | 0.622883i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.40836 | + | 11.5731i | 0.354370 | + | 0.487749i | 0.948569 | − | 0.316569i | \(-0.102531\pi\) |
−0.594199 | + | 0.804318i | \(0.702531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.4862 | − | 14.6875i | −0.903930 | − | 0.617907i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.566735 | + | 0.184143i | 0.0238006 | + | 0.00773330i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.89176 | − | 27.3660i | 0.372762 | − | 1.14724i | −0.572214 | − | 0.820104i | \(-0.693915\pi\) |
0.944976 | − | 0.327139i | \(-0.106085\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.02941 | − | 12.4012i | −0.168625 | − | 0.518976i | 0.830660 | − | 0.556780i | \(-0.187963\pi\) |
−0.999285 | + | 0.0378048i | \(0.987963\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.9134 | + | 17.7737i | −0.539464 | + | 0.742508i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.26464 | + | 22.0086i | 0.0527390 | + | 0.917823i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.05786 | − | 1.45601i | 0.0440391 | − | 0.0606147i | −0.786430 | − | 0.617680i | \(-0.788073\pi\) |
0.830469 | + | 0.557065i | \(0.188073\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.30401 | + | 19.4018i | 0.261986 | + | 0.806309i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.770015 | − | 2.36986i | 0.0319456 | − | 0.0983184i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.1926 | + | 8.51049i | 1.08479 | + | 0.352468i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.6596 | − | 0.306002i | 0.440719 | − | 0.0126516i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.8620 | + | 32.8432i | 0.984889 | + | 1.35558i | 0.934153 | + | 0.356872i | \(0.116157\pi\) |
0.0507360 | + | 0.998712i | \(0.483843\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.4739 | + | 16.3282i | 0.926020 | + | 0.672793i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.32102 | − | 2.41286i | 0.136609 | − | 0.0992519i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.4991i | 1.21138i | 0.795700 | + | 0.605690i | \(0.207103\pi\) | ||||
−0.795700 | + | 0.605690i | \(0.792897\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.285998 | + | 9.96271i | 0.0117248 | + | 0.408431i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.3413 | − | 7.90898i | 0.996225 | − | 0.323693i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.91418 | 0.364224 | 0.182112 | − | 0.983278i | \(-0.441707\pi\) | ||||
0.182112 | + | 0.983278i | \(0.441707\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.6757 | 0.680217 | 0.340109 | − | 0.940386i | \(-0.389536\pi\) | ||||
0.340109 | + | 0.940386i | \(0.389536\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.94930 | − | 2.58288i | 0.323720 | − | 0.105183i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.355235 | − | 0.460545i | −0.0144424 | − | 0.0187238i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26.9626i | − | 1.09438i | −0.837008 | − | 0.547190i | \(-0.815698\pi\) | ||
0.837008 | − | 0.547190i | \(-0.184302\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.33081 | − | 0.966890i | 0.0539271 | − | 0.0391804i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.9836 | + | 12.3393i | 0.687083 | + | 0.499195i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.71195 | − | 13.3673i | −0.392262 | − | 0.539902i | 0.566519 | − | 0.824049i | \(-0.308290\pi\) |
−0.958781 | + | 0.284147i | \(0.908290\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.92445 | − | 20.1872i | 0.238897 | − | 0.814027i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.8628 | − | 7.10364i | −0.880161 | − | 0.285982i | −0.166137 | − | 0.986103i | \(-0.553129\pi\) |
−0.714024 | + | 0.700121i | \(0.753129\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.2396 | + | 46.9028i | −0.612533 | + | 1.88518i | −0.179658 | + | 0.983729i | \(0.557499\pi\) |
−0.432875 | + | 0.901454i | \(0.642501\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.36245 | − | 4.19319i | −0.0546733 | − | 0.168267i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.48874 | + | 2.04907i | −0.0596451 | + | 0.0820944i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.95114 | − | 24.5048i | 0.198045 | − | 0.980193i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.2065 | + | 16.8008i | −0.487481 | + | 0.670960i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.00639 | + | 9.25273i | 0.119873 | + | 0.368930i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.47148 | − | 22.9948i | 0.297435 | − | 0.915410i | −0.684958 | − | 0.728583i | \(-0.740179\pi\) |
0.982393 | − | 0.186828i | \(-0.0598206\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.5535 | + | 6.02841i | 0.737437 | + | 0.239608i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.67602 | + | 5.71093i | −0.0665107 | + | 0.226631i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.6269 | − | 25.6377i | −0.738024 | − | 1.01580i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.49751 | + | 3.99418i | 0.217478 | + | 0.158007i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.9382 | − | 29.0168i | 1.57746 | − | 1.14610i | 0.657935 | − | 0.753075i | \(-0.271430\pi\) |
0.919530 | − | 0.393020i | \(-0.128570\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.97743i | 0.156854i | 0.996920 | + | 0.0784272i | \(0.0249898\pi\) | ||||
−0.996920 | + | 0.0784272i | \(0.975010\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.3773 | + | 13.4536i | 0.408606 | + | 0.529737i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.964765 | − | 0.313471i | 0.0379288 | − | 0.0123238i | −0.289991 | − | 0.957029i | \(-0.593652\pi\) |
0.327920 | + | 0.944706i | \(0.393652\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.47879 | 0.293568 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.67481 | −0.104834 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.77161 | − | 2.52515i | 0.304127 | − | 0.0988167i | −0.152978 | − | 0.988230i | \(-0.548886\pi\) |
0.457105 | + | 0.889413i | \(0.348886\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.623062 | + | 21.7043i | 0.0243450 | + | 0.848057i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 7.31221i | − | 0.285277i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.22020 | − | 4.51924i | 0.242305 | − | 0.176045i | −0.460005 | − | 0.887916i | \(-0.652152\pi\) |
0.702309 | + | 0.711872i | \(0.252152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.2864 | + | 21.2778i | 1.13911 | + | 0.827611i | 0.986995 | − | 0.160752i | \(-0.0513919\pi\) |
0.152114 | + | 0.988363i | \(0.451392\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.9676 | − | 28.8595i | −0.814316 | − | 1.12081i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.24292 | − | 0.236628i | 0.319647 | − | 0.00917605i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.5752 | − | 3.76102i | −0.448195 | − | 0.145627i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.688574 | + | 2.11921i | −0.0266218 | + | 0.0819335i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.0754 | + | 40.2420i | 0.504771 | + | 1.55353i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.7405 | + | 24.4177i | −0.683845 | + | 0.941233i | −0.999972 | − | 0.00748451i | \(-0.997618\pi\) |
0.316127 | + | 0.948717i | \(0.397618\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.286832 | + | 4.99177i | 0.0110402 | + | 0.192133i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.6349 | − | 38.0362i | 1.06210 | − | 1.46185i | 0.184268 | − | 0.982876i | \(-0.441009\pi\) |
0.877829 | − | 0.478975i | \(-0.158991\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.26040 | − | 6.95680i | −0.0867463 | − | 0.266978i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.40540 | − | 4.32537i | 0.0538549 | − | 0.165748i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.08476 | + | 0.677379i | 0.0797710 | + | 0.0259192i | 0.348631 | − | 0.937260i | \(-0.386647\pi\) |
−0.268860 | + | 0.963179i | \(0.586647\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.09217 | + | 4.84805i | 0.270978 | + | 0.185235i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00735 | + | 2.76288i | 0.0765852 | + | 0.105411i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 31.6659 | + | 23.0066i | 1.20637 | + | 0.876482i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.44427 | + | 1.04932i | −0.0549425 | + | 0.0399181i | −0.614918 | − | 0.788591i | \(-0.710811\pi\) |
0.559975 | + | 0.828509i | \(0.310811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1.99961i | − | 0.0759589i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.5727 | + | 3.10282i | 0.401044 | + | 0.117697i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −66.9323 | + | 21.7476i | −2.53524 | + | 0.823750i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.7395 | −0.633146 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.0728 | −0.418215 | −0.209107 | − | 0.977893i | \(-0.567056\pi\) | ||||
−0.209107 | + | 0.977893i | \(0.567056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.65550 | − | 2.48742i | 0.288733 | − | 0.0938149i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.55464 | + | 8.12583i | −0.209200 | + | 0.306037i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.77218i | − | 0.179476i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.1099 | − | 11.7045i | 0.605020 | − | 0.439573i | −0.242637 | − | 0.970117i | \(-0.578012\pi\) |
0.847657 | + | 0.530544i | \(0.178012\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.54908 | + | 6.21127i | 0.320616 | + | 0.232941i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.6326 | + | 16.0109i | 0.435644 | + | 0.599612i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0299 | − | 33.7013i | −0.449892 | − | 1.26036i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.2697 | + | 6.91095i | 0.794332 | + | 0.258094i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.7477 | + | 33.0782i | −0.400823 | + | 1.23361i | 0.523509 | + | 0.852020i | \(0.324623\pi\) |
−0.924333 | + | 0.381587i | \(0.875377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.03585 | − | 3.18801i | −0.0385769 | − | 0.118728i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.155973 | − | 0.214678i | 0.00580068 | − | 0.00798395i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.6134 | + | 7.45891i | 0.431311 | + | 0.277017i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.38558 | + | 12.9181i | −0.348092 | + | 0.479107i | −0.946783 | − | 0.321873i | \(-0.895688\pi\) |
0.598691 | + | 0.800980i | \(0.295688\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.309017 | − | 0.951057i | −0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.5635 | − | 54.0548i | 0.649608 | − | 1.99929i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.64606 | + | 3.13420i | 0.356286 | + | 0.115764i | 0.481690 | − | 0.876341i | \(-0.340023\pi\) |
−0.125405 | + | 0.992106i | \(0.540023\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.7652 | − | 9.07492i | 0.433965 | − | 0.334733i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.4859 | − | 22.6909i | −0.607266 | − | 0.835830i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.65234 | + | 1.92704i | 0.0975681 | + | 0.0708873i | 0.635500 | − | 0.772101i | \(-0.280794\pi\) |
−0.537932 | + | 0.842988i | \(0.680794\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.8777 | + | 17.3482i | −0.877169 | + | 0.637300i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 38.7278i | − | 1.42078i | −0.703806 | − | 0.710392i | \(-0.748518\pi\) | ||
0.703806 | − | 0.710392i | \(-0.251482\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.8789 | + | 4.95415i | −0.508483 | + | 0.181506i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.97694 | + | 1.29219i | −0.145509 | + | 0.0472786i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.20559 | 0.299826 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0211 | 0.475146 | 0.237573 | − | 0.971370i | \(-0.423648\pi\) | ||||
0.237573 | + | 0.971370i | \(0.423648\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.6466 | + | 8.98294i | −1.00750 | + | 0.327357i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.1568 | − | 14.6912i | 1.49785 | − | 0.534666i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.4057i | 1.21415i | 0.794645 | + | 0.607075i | \(0.207657\pi\) | ||||
−0.794645 | + | 0.607075i | \(0.792343\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.9693 | + | 8.69618i | −0.434457 | + | 0.315651i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.0536 | − | 17.4760i | −0.871943 | − | 0.633504i | 0.0591647 | − | 0.998248i | \(-0.481156\pi\) |
−0.931108 | + | 0.364745i | \(0.881156\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.48385 | − | 6.17149i | −0.162326 | − | 0.223423i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.2437 | − | 10.2153i | 0.478825 | − | 0.369336i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.1088 | + | 3.28455i | 0.365008 | + | 0.118598i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.68546 | − | 5.18732i | 0.0607794 | − | 0.187060i | −0.916057 | − | 0.401049i | \(-0.868646\pi\) |
0.976836 | + | 0.213989i | \(0.0686458\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.18151 | − | 6.71400i | −0.0785652 | − | 0.241799i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.0953 | − | 23.5297i | 0.614875 | − | 0.846303i | −0.382092 | − | 0.924124i | \(-0.624796\pi\) |
0.996967 | + | 0.0778211i | \(0.0247963\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.14846 | − | 20.9119i | −0.292701 | − | 0.751179i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.455573 | + | 0.627043i | −0.0163436 | + | 0.0224950i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.9935 | + | 55.3783i | 0.644684 | + | 1.98413i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.04632 | − | 21.6863i | 0.252137 | − | 0.775998i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.62537 | − | 0.853035i | −0.0938232 | − | 0.0304850i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.257085 | + | 0.720216i | 0.00917577 | + | 0.0257056i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0518 | − | 27.5989i | −0.714768 | − | 0.983794i | −0.999681 | − | 0.0252406i | \(-0.991965\pi\) |
0.284913 | − | 0.958553i | \(-0.408035\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.12170 | + | 0.814961i | 0.0399335 | + | 0.0290134i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.61128 | + | 4.07683i | −0.199514 | + | 0.144955i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 60.1361i | 2.13549i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.3566 | + | 15.1506i | −0.367311 | + | 0.537336i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.2590 | − | 7.55732i | 0.823877 | − | 0.267694i | 0.133413 | − | 0.991061i | \(-0.457406\pi\) |
0.690464 | + | 0.723367i | \(0.257406\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.9259 | 1.16483 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.25036 | 0.150179 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.3360 | + | 7.58233i | −0.823510 | + | 0.267574i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.63712 | + | 1.65436i | 0.198682 | + | 0.0583084i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.1752i | 0.498992i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.2701 | + | 30.7110i | −1.48614 | + | 1.07974i | −0.510623 | + | 0.859805i | \(0.670585\pi\) |
−0.975514 | + | 0.219937i | \(0.929415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.2781 | − | 10.3736i | −0.501371 | − | 0.364267i | 0.308170 | − | 0.951331i | \(-0.400284\pi\) |
−0.809540 | + | 0.587064i | \(0.800284\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.84093 | − | 12.1685i | −0.310065 | − | 0.426768i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41.5648 | + | 28.4128i | 1.45595 | + | 0.995257i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −44.7237 | − | 14.5316i | −1.56468 | − | 0.508397i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.878192 | − | 2.70280i | 0.0306865 | − | 0.0944433i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.5469 | − | 32.4602i | −0.368091 | − | 1.13287i | −0.948023 | − | 0.318202i | \(-0.896921\pi\) |
0.579932 | − | 0.814665i | \(-0.303079\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.7608 | + | 36.8331i | −0.932823 | + | 1.28392i | 0.0259255 | + | 0.999664i | \(0.491747\pi\) |
−0.958748 | + | 0.284257i | \(0.908253\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.6332 | − | 6.09155i | 0.544277 | − | 0.212081i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.2248 | + | 15.4496i | −0.390323 | + | 0.537234i | −0.958282 | − | 0.285823i | \(-0.907733\pi\) |
0.567959 | + | 0.823057i | \(0.307733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.51719 | − | 10.8248i | −0.122157 | − | 0.375961i | 0.871215 | − | 0.490901i | \(-0.163332\pi\) |
−0.993372 | + | 0.114940i | \(0.963332\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.95336 | − | 12.1672i | 0.137140 | − | 0.422075i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −47.2708 | − | 15.3592i | −1.63783 | − | 0.532165i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.64451 | + | 0.276863i | −0.333762 | + | 0.00958125i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.63838 | + | 3.63142i | 0.0911958 | + | 0.125520i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.8665 | + | 15.1604i | 0.720391 | + | 0.523395i | 0.886509 | − | 0.462711i | \(-0.153123\pi\) |
−0.166118 | + | 0.986106i | \(0.553123\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.2966 | − | 12.5667i | 0.596434 | − | 0.433335i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 15.3058i | − | 0.527160i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.625212 | − | 21.7792i | −0.0215079 | − | 0.749227i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.147415 | + | 0.0478981i | −0.00506525 | + | 0.00164580i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.3502 | −0.801375 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.73461 | 0.196580 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.9706 | + | 4.86423i | −0.512582 | + | 0.166548i | −0.553876 | − | 0.832599i | \(-0.686852\pi\) |
0.0412941 | + | 0.999147i | \(0.486852\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.45192 | − | 10.9575i | −0.289050 | − | 0.374739i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.4948i | 1.58823i | 0.607767 | + | 0.794116i | \(0.292066\pi\) | ||||
−0.607767 | + | 0.794116i | \(0.707934\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.86663 | − | 7.16852i | 0.336645 | − | 0.244587i | −0.406600 | − | 0.913606i | \(-0.633286\pi\) |
0.743245 | + | 0.669019i | \(0.233286\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.53590 | − | 3.29552i | −0.154583 | − | 0.112311i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.6811 | + | 36.7234i | 0.908235 | + | 1.25008i | 0.967766 | + | 0.251852i | \(0.0810396\pi\) |
−0.0595307 | + | 0.998226i | \(0.518960\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.8107 | + | 36.8370i | −0.367576 | + | 1.25249i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37.0431 | − | 12.0360i | −1.25805 | − | 0.408765i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.9576 | − | 33.7240i | 0.371711 | − | 1.14401i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.3179 | − | 37.9107i | −0.417377 | − | 1.28456i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.21520 | + | 9.93087i | −0.244198 | + | 0.336109i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.70675 | − | 3.43805i | −0.192923 | − | 0.116227i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.1859 | − | 15.3960i | 0.377720 | − | 0.519887i | −0.577259 | − | 0.816561i | \(-0.695878\pi\) |
0.954979 | + | 0.296675i | \(0.0958777\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.96736 | − | 6.05491i | −0.0663574 | − | 0.204227i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.70004 | + | 14.4652i | −0.158348 | + | 0.487346i | −0.998485 | − | 0.0550289i | \(-0.982475\pi\) |
0.840136 | + | 0.542375i | \(0.182475\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.9532 | − | 14.9311i | −1.54645 | − | 0.502472i | −0.593303 | − | 0.804979i | \(-0.702176\pi\) |
−0.953147 | + | 0.302507i | \(0.902176\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.40338 | + | 4.78195i | −0.0471742 | + | 0.160743i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.0449 | − | 26.2130i | −0.639464 | − | 0.880146i | 0.359123 | − | 0.933290i | \(-0.383076\pi\) |
−0.998587 | + | 0.0531439i | \(0.983076\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.28320 | + | 0.932298i | 0.0430371 | + | 0.0312683i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.71474 | + | 1.97238i | −0.0909474 | + | 0.0660771i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 27.2421i | − | 0.911622i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.45255 | + | 1.88316i | 0.0485534 | + | 0.0629471i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.9976 | + | 6.49762i | −0.667701 | + | 0.216949i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.3909 | 0.413260 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 61.3901 | 2.04520 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.30636 | − | 1.39922i | 0.143307 | − | 0.0465631i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.771680 | − | 26.8814i | −0.0256515 | − | 0.893568i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 30.8525i | − | 1.02444i | −0.858854 | − | 0.512220i | \(-0.828823\pi\) | ||
0.858854 | − | 0.512220i | \(-0.171177\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.47889 | + | 4.70719i | −0.214891 | + | 0.156128i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.3011 | − | 21.2885i | −0.970787 | − | 0.705318i | −0.0151564 | − | 0.999885i | \(-0.504825\pi\) |
−0.955631 | + | 0.294567i | \(0.904825\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.24770 | + | 11.3520i | 0.272959 | + | 0.375696i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28.1843 | + | 0.809083i | −0.931746 | + | 0.0267475i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.50326 | + | 1.78812i | 0.181734 | + | 0.0590488i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.7420 | − | 36.1380i | 0.387331 | − | 1.19208i | −0.547444 | − | 0.836842i | \(-0.684399\pi\) |
0.934775 | − | 0.355240i | \(-0.115601\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.41505 | − | 25.8988i | −0.277285 | − | 0.853396i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.0485 | − | 26.2180i | 0.626988 | − | 0.862975i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.29013 | − | 1.65152i | −0.206818 | − | 0.0543015i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.30642 | + | 4.55089i | −0.108597 | + | 0.149471i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.23230 | + | 9.94801i | 0.106048 | + | 0.326384i | 0.989975 | − | 0.141242i | \(-0.0451096\pi\) |
−0.883927 | + | 0.467626i | \(0.845110\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.7079 | + | 39.1108i | −0.416483 | + | 1.28180i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.3186 | + | 5.30222i | 0.534246 | + | 0.173587i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −46.3338 | − | 31.6728i | −1.51528 | − | 1.03581i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.8458 | − | 27.3155i | −0.648335 | − | 0.892357i | 0.350690 | − | 0.936492i | \(-0.385947\pi\) |
−0.999026 | + | 0.0441344i | \(0.985947\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.3955 | + | 11.9120i | 0.535046 | + | 0.388734i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.80449 | + | 1.31104i | −0.0588247 | + | 0.0427386i | −0.616809 | − | 0.787113i | \(-0.711575\pi\) |
0.557984 | + | 0.829851i | \(0.311575\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.4830i | 1.35087i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.27855 | + | 0.375224i | 0.0415913 | + | 0.0122060i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.27701 | + | 2.36444i | −0.236471 | + | 0.0768341i | −0.424855 | − | 0.905261i | \(-0.639675\pi\) |
0.188384 | + | 0.982095i | \(0.439675\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.8724 | −1.13201 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.0153 | −0.681469 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.0823 | + | 3.60086i | −0.358991 | + | 0.116643i | −0.482959 | − | 0.875643i | \(-0.660438\pi\) |
0.123968 | + | 0.992286i | \(0.460438\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.7229 | + | 40.5555i | −0.897091 | + | 1.31234i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.26309i | 0.299433i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.85217 | − | 1.34568i | 0.0598098 | − | 0.0434544i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.77922 | + | 6.37848i | 0.283201 | + | 0.205757i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.09384 | − | 11.1402i | −0.260820 | − | 0.358988i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.3353 | + | 42.9613i | 0.493660 | + | 1.38297i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.1250 | − | 10.4380i | −1.03307 | − | 0.335665i | −0.257067 | − | 0.966394i | \(-0.582756\pi\) |
−0.776004 | + | 0.630729i | \(0.782756\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.3048 | + | 44.0256i | −0.459536 | + | 1.41431i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.4403 | + | 32.1319i | 0.335045 | + | 1.03116i | 0.966700 | + | 0.255913i | \(0.0823760\pi\) |
−0.631655 | + | 0.775250i | \(0.717624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.72597 | − | 2.37559i | 0.0553320 | − | 0.0761579i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.8060 | − | 1.36792i | 0.762404 | − | 0.0438085i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.21653 | + | 3.05079i | −0.0709131 | + | 0.0976035i | −0.843000 | − | 0.537913i | \(-0.819213\pi\) |
0.772087 | + | 0.635517i | \(0.219213\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.40737 | − | 13.5645i | −0.140860 | − | 0.433523i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.95586 | + | 12.1749i | −0.126301 | + | 0.388714i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.2335 | − | 13.0727i | −1.28325 | − | 0.416953i | −0.413526 | − | 0.910492i | \(-0.635703\pi\) |
−0.869723 | + | 0.493539i | \(0.835703\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.26815 | − | 5.60620i | 0.231583 | − | 0.178628i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.54181 | + | 2.12212i | 0.0490765 | + | 0.0675480i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.1036 | − | 19.6919i | −0.861843 | − | 0.626165i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.8789 | + | 18.8021i | −0.822071 | + | 0.597269i | −0.917305 | − | 0.398186i | \(-0.869640\pi\) |
0.0952341 | + | 0.995455i | \(0.469640\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 12.7425i | − | 0.404371i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 53.8990 | − | 19.2396i | 1.70871 | − | 0.609936i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.8900 | − | 5.16296i | 0.503240 | − | 0.163513i | −0.0463858 | − | 0.998924i | \(-0.514770\pi\) |
0.549626 | + | 0.835411i | \(0.314770\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.30067 | 0.0411512 |
(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.109.1 | ✓ | 24 | |
3.2 | odd | 2 | 900.2.w.c.109.6 | 24 | |||
5.2 | odd | 4 | 1500.2.m.c.1201.3 | 24 | |||
5.3 | odd | 4 | 1500.2.m.d.1201.4 | 24 | |||
5.4 | even | 2 | 1500.2.o.c.49.5 | 24 | |||
25.2 | odd | 20 | 1500.2.m.c.301.3 | 24 | |||
25.6 | even | 5 | 7500.2.d.g.1249.19 | 24 | |||
25.8 | odd | 20 | 7500.2.a.m.1.7 | 12 | |||
25.11 | even | 5 | 1500.2.o.c.949.5 | 24 | |||
25.14 | even | 10 | inner | 300.2.o.a.289.1 | yes | 24 | |
25.17 | odd | 20 | 7500.2.a.n.1.6 | 12 | |||
25.19 | even | 10 | 7500.2.d.g.1249.6 | 24 | |||
25.23 | odd | 20 | 1500.2.m.d.301.4 | 24 | |||
75.14 | odd | 10 | 900.2.w.c.289.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
300.2.o.a.289.1 | yes | 24 | 25.14 | even | 10 | inner | |
900.2.w.c.109.6 | 24 | 3.2 | odd | 2 | |||
900.2.w.c.289.6 | 24 | 75.14 | odd | 10 | |||
1500.2.m.c.301.3 | 24 | 25.2 | odd | 20 | |||
1500.2.m.c.1201.3 | 24 | 5.2 | odd | 4 | |||
1500.2.m.d.301.4 | 24 | 25.23 | odd | 20 | |||
1500.2.m.d.1201.4 | 24 | 5.3 | odd | 4 | |||
1500.2.o.c.49.5 | 24 | 5.4 | even | 2 | |||
1500.2.o.c.949.5 | 24 | 25.11 | even | 5 | |||
7500.2.a.m.1.7 | 12 | 25.8 | odd | 20 | |||
7500.2.a.n.1.6 | 12 | 25.17 | odd | 20 | |||
7500.2.d.g.1249.6 | 24 | 25.19 | even | 10 | |||
7500.2.d.g.1249.19 | 24 | 25.6 | even | 5 |