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 | 169.6 | ||
Character | \(\chi\) | \(=\) | 300.169 |
Dual form | 300.2.o.a.229.6 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) |
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 | ||||||||
\(5\) | 1.28878 | + | 1.82730i | 0.576362 | + | 0.817194i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44380i | 0.923670i | 0.886966 | + | 0.461835i | \(0.152809\pi\) | ||||
−0.886966 | + | 0.461835i | \(0.847191\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.309017 | + | 0.951057i | −0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.178298 | − | 0.548744i | −0.0537588 | − | 0.165452i | 0.920572 | − | 0.390572i | \(-0.127723\pi\) |
−0.974331 | + | 0.225120i | \(0.927723\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.13093 | − | 1.99206i | −1.70042 | − | 0.552498i | −0.711723 | − | 0.702460i | \(-0.752085\pi\) |
−0.988692 | + | 0.149962i | \(0.952085\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.720790 | + | 2.11671i | −0.186107 | + | 0.546532i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.11545 | − | 1.53529i | 0.270537 | − | 0.372362i | −0.652034 | − | 0.758190i | \(-0.726084\pi\) |
0.922571 | + | 0.385828i | \(0.126084\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.69438 | + | 4.86375i | 1.53580 | + | 1.11582i | 0.952905 | + | 0.303269i | \(0.0980782\pi\) |
0.582890 | + | 0.812551i | \(0.301922\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.97708 | + | 1.43643i | −0.431434 | + | 0.313455i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00298 | − | 1.30065i | 0.834678 | − | 0.271203i | 0.139664 | − | 0.990199i | \(-0.455398\pi\) |
0.695015 | + | 0.718996i | \(0.255398\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.67807 | + | 4.71000i | −0.335613 | + | 0.942000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.951057 | + | 0.309017i | −0.183031 | + | 0.0594703i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.28988 | − | 3.84332i | 0.982306 | − | 0.713687i | 0.0240828 | − | 0.999710i | \(-0.492333\pi\) |
0.958223 | + | 0.286023i | \(0.0923335\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.93738 | − | 2.86068i | −0.707175 | − | 0.513793i | 0.175086 | − | 0.984553i | \(-0.443980\pi\) |
−0.882261 | + | 0.470760i | \(0.843980\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.339142 | − | 0.466789i | 0.0590371 | − | 0.0812576i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.46557 | + | 3.14954i | −0.754818 | + | 0.532369i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.207335 | − | 0.0673673i | −0.0340857 | − | 0.0110751i | 0.291925 | − | 0.956441i | \(-0.405704\pi\) |
−0.326010 | + | 0.945366i | \(0.605704\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.99206 | − | 6.13093i | −0.318985 | − | 0.981735i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.99456 | − | 6.13862i | 0.311498 | − | 0.958691i | −0.665675 | − | 0.746242i | \(-0.731856\pi\) |
0.977172 | − | 0.212449i | \(-0.0681439\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.42419i | 0.522184i | 0.965314 | + | 0.261092i | \(0.0840825\pi\) | ||||
−0.965314 | + | 0.261092i | \(0.915917\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.13612 | + | 0.661040i | −0.318435 | + | 0.0985420i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.65351 | + | 7.78140i | 0.824650 | + | 1.13503i | 0.988895 | + | 0.148614i | \(0.0474811\pi\) |
−0.164245 | + | 0.986419i | \(0.552519\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.02783 | 0.146833 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.89772 | 0.265734 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.22441 | − | 11.3199i | −1.12971 | − | 1.55491i | −0.788620 | − | 0.614881i | \(-0.789204\pi\) |
−0.341090 | − | 0.940031i | \(-0.610796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.772933 | − | 1.03302i | 0.104222 | − | 0.139292i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.27470i | 1.09601i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.72459 | − | 11.4631i | 0.484901 | − | 1.49237i | −0.347224 | − | 0.937782i | \(-0.612876\pi\) |
0.832125 | − | 0.554589i | \(-0.187124\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.48657 | − | 4.57520i | −0.190336 | − | 0.585795i | 0.809663 | − | 0.586895i | \(-0.199650\pi\) |
−0.999999 | + | 0.00110016i | \(0.999650\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.32419 | − | 0.755176i | −0.292821 | − | 0.0951433i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.26136 | − | 13.7704i | −0.528556 | − | 1.70801i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.27528 | − | 3.13165i | 0.277970 | − | 0.382592i | −0.647090 | − | 0.762413i | \(-0.724014\pi\) |
0.925060 | + | 0.379821i | \(0.124014\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.40513 | + | 2.47398i | 0.409930 | + | 0.297832i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.24443 | − | 3.81030i | 0.622399 | − | 0.452200i | −0.231359 | − | 0.972868i | \(-0.574317\pi\) |
0.853759 | + | 0.520669i | \(0.174317\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.55897 | + | 3.10590i | −1.11879 | + | 0.363518i | −0.809307 | − | 0.587386i | \(-0.800157\pi\) |
−0.309486 | + | 0.950904i | \(0.600157\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.79681 | + | 1.41088i | −0.553888 | + | 0.162915i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.34102 | − | 0.435724i | 0.152824 | − | 0.0496554i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.83854 | + | 2.78887i | −0.431870 | + | 0.313772i | −0.782396 | − | 0.622781i | \(-0.786003\pi\) |
0.350526 | + | 0.936553i | \(0.386003\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.01856 | + | 2.77831i | −0.221566 | + | 0.304959i | −0.905301 | − | 0.424772i | \(-0.860354\pi\) |
0.683735 | + | 0.729730i | \(0.260354\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.24301 | + | 0.0596122i | 0.460220 | + | 0.00646585i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.21862 | + | 2.02055i | 0.666706 | + | 0.216626i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.75719 | + | 5.40807i | 0.186262 | + | 0.573254i | 0.999968 | − | 0.00802201i | \(-0.00255351\pi\) |
−0.813706 | + | 0.581276i | \(0.802554\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.86820 | − | 14.9828i | 0.510326 | − | 1.57062i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 4.86687i | − | 0.504671i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.259929 | + | 18.5010i | −0.0266682 | + | 1.89816i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.87042 | − | 5.32717i | −0.392982 | − | 0.540893i | 0.565984 | − | 0.824416i | \(-0.308497\pi\) |
−0.958965 | + | 0.283524i | \(0.908497\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.576983 | 0.0579890 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0363 | −1.19766 | −0.598828 | − | 0.800877i | \(-0.704367\pi\) | ||||
−0.598828 | + | 0.800877i | \(0.704367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.40107 | − | 4.68117i | −0.335117 | − | 0.461249i | 0.607890 | − | 0.794021i | \(-0.292016\pi\) |
−0.943007 | + | 0.332772i | \(0.892016\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.17282 | − | 1.76147i | −0.504816 | − | 0.171902i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.07081i | 0.393540i | 0.980450 | + | 0.196770i | \(0.0630453\pi\) | ||||
−0.980450 | + | 0.196770i | \(0.936955\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.450471 | − | 1.38641i | 0.0431473 | − | 0.132794i | −0.927162 | − | 0.374660i | \(-0.877759\pi\) |
0.970310 | + | 0.241866i | \(0.0777595\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0673673 | − | 0.207335i | −0.00639422 | − | 0.0196794i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.57114 | + | 1.81017i | 0.524089 | + | 0.170287i | 0.559100 | − | 0.829100i | \(-0.311147\pi\) |
−0.0350111 | + | 0.999387i | \(0.511147\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.53565 | + | 5.63839i | 0.702703 | + | 0.525783i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.78913 | − | 5.21528i | 0.350305 | − | 0.482153i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.75194 | + | 2.72595i | 0.343940 | + | 0.249887i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.62986 | − | 6.26996i | 0.784532 | − | 0.569996i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.13862 | − | 1.99456i | 0.553500 | − | 0.179843i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.7693 | + | 3.00384i | −0.963232 | + | 0.268672i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5373 | + | 4.72346i | −1.28998 | + | 0.419139i | −0.872084 | − | 0.489357i | \(-0.837232\pi\) |
−0.417894 | + | 0.908496i | \(0.637232\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.77023 | + | 2.01269i | −0.243905 | + | 0.177207i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.03698 | + | 2.20650i | 0.265343 | + | 0.192783i | 0.712499 | − | 0.701673i | \(-0.247563\pi\) |
−0.447156 | + | 0.894456i | \(0.647563\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.8860 | + | 16.3597i | −1.03065 | + | 1.41857i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.79037 | − | 1.33961i | −0.154091 | − | 0.115295i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.2599 | + | 6.25793i | 1.64549 | + | 0.534651i | 0.977755 | − | 0.209751i | \(-0.0672652\pi\) |
0.667732 | + | 0.744402i | \(0.267265\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.287036 | + | 0.883406i | 0.0243461 | + | 0.0749295i | 0.962491 | − | 0.271312i | \(-0.0874576\pi\) |
−0.938145 | + | 0.346242i | \(0.887458\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.97223 | + | 9.14758i | −0.250307 | + | 0.770365i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.71949i | 0.311040i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.8404 | + | 4.71299i | 1.14938 | + | 0.391393i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.604143 | + | 0.831532i | 0.0498289 | + | 0.0685836i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.1432 | −1.07673 | −0.538364 | − | 0.842712i | \(-0.680958\pi\) | ||||
−0.538364 | + | 0.842712i | \(0.680958\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5864 | 1.43116 | 0.715580 | − | 0.698531i | \(-0.246163\pi\) | ||||
0.715580 | + | 0.698531i | \(0.246163\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.11545 | + | 1.53529i | 0.0901790 | + | 0.124121i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.152881 | − | 10.8816i | 0.0122797 | − | 0.874030i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.68198i | 0.692897i | 0.938069 | + | 0.346449i | \(0.112613\pi\) | ||||
−0.938069 | + | 0.346449i | \(0.887387\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.32383 | − | 13.3074i | 0.342902 | − | 1.05534i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.17852 | + | 9.78248i | 0.250503 | + | 0.770968i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.33900 | + | 0.435068i | 0.104879 | + | 0.0340771i | 0.360986 | − | 0.932571i | \(-0.382440\pi\) |
−0.256108 | + | 0.966648i | \(0.582440\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.29005 | + | 0.0181245i | 0.100430 | + | 0.00141099i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.18118 | + | 7.13128i | −0.400932 | + | 0.551835i | −0.960978 | − | 0.276626i | \(-0.910784\pi\) |
0.560046 | + | 0.828462i | \(0.310784\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.1028 | + | 16.7852i | 1.77714 | + | 1.29117i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.69438 | + | 4.86375i | −0.511932 | + | 0.371940i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.51629 | + | 2.44219i | −0.571453 | + | 0.185676i | −0.580468 | − | 0.814283i | \(-0.697130\pi\) |
0.00901487 | + | 0.999959i | \(0.497130\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.5103 | − | 4.10086i | −0.870097 | − | 0.309996i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.4631 | − | 3.72459i | 0.861621 | − | 0.279958i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.29450 | + | 6.75285i | −0.694704 | + | 0.504732i | −0.878203 | − | 0.478288i | \(-0.841258\pi\) |
0.183499 | + | 0.983020i | \(0.441258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.17383 | − | 2.30592i | −0.235909 | − | 0.171398i | 0.463550 | − | 0.886071i | \(-0.346576\pi\) |
−0.699459 | + | 0.714673i | \(0.746576\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.82763 | − | 3.89190i | 0.209024 | − | 0.287698i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.144110 | − | 0.465686i | −0.0105952 | − | 0.0342379i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.04136 | − | 0.338359i | −0.0761520 | − | 0.0247433i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.755176 | − | 2.32419i | −0.0549310 | − | 0.169060i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.89402 | + | 24.2953i | −0.571191 | + | 1.75795i | 0.0776060 | + | 0.996984i | \(0.475272\pi\) |
−0.648797 | + | 0.760961i | \(0.724728\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 0.421651i | − | 0.0303511i | −0.999885 | − | 0.0151756i | \(-0.995169\pi\) | ||
0.999885 | − | 0.0151756i | \(-0.00483071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.63573 | − | 11.5416i | 0.618418 | − | 0.826508i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.24463 | − | 5.84224i | −0.302418 | − | 0.416242i | 0.630580 | − | 0.776124i | \(-0.282817\pi\) |
−0.932998 | + | 0.359882i | \(0.882817\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.93505 | −0.278949 | −0.139474 | − | 0.990226i | \(-0.544541\pi\) | ||||
−0.139474 | + | 0.990226i | \(0.544541\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.87094 | 0.273035 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.39232 | + | 12.9274i | 0.659211 | + | 0.907327i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.7877 | − | 4.26670i | 0.962972 | − | 0.297999i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.20898i | 0.292544i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.47536 | − | 4.54069i | 0.102053 | − | 0.314086i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.65156 | − | 23.5491i | −0.526755 | − | 1.62119i | −0.760819 | − | 0.648964i | \(-0.775202\pi\) |
0.234064 | − | 0.972221i | \(-0.424798\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.16520 | + | 2.00319i | 0.422432 | + | 0.137257i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.25702 | + | 4.41304i | −0.426726 | + | 0.300967i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.99093 | − | 9.62219i | 0.474575 | − | 0.653197i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.13134 | − | 5.90777i | −0.549465 | − | 0.399210i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.89715 | + | 7.19070i | −0.665755 | + | 0.483699i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7098 | − | 6.07919i | 1.25290 | − | 0.407093i | 0.393942 | − | 0.919135i | \(-0.371111\pi\) |
0.858960 | + | 0.512043i | \(0.171111\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.96092 | − | 3.05141i | −0.264062 | − | 0.203427i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.0839 | + | 8.15025i | −1.66488 | + | 0.540951i | −0.981885 | − | 0.189476i | \(-0.939321\pi\) |
−0.682991 | + | 0.730427i | \(0.739321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.9614 | + | 9.41703i | −0.856515 | + | 0.622295i | −0.926935 | − | 0.375223i | \(-0.877566\pi\) |
0.0704195 | + | 0.997517i | \(0.477566\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.14074 | + | 0.828797i | 0.0750552 | + | 0.0545308i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.2285 | − | 23.7129i | 1.12867 | − | 1.55349i | 0.338109 | − | 0.941107i | \(-0.390213\pi\) |
0.790564 | − | 0.612379i | \(-0.209787\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.93280 | + | 20.3592i | −0.452246 | + | 1.32809i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.51248 | − | 1.46619i | −0.293117 | − | 0.0952395i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.98989 | − | 24.5904i | −0.516823 | − | 1.59062i | −0.779940 | − | 0.625854i | \(-0.784750\pi\) |
0.263117 | − | 0.964764i | \(-0.415250\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.88671 | + | 8.88437i | −0.185949 | + | 0.572292i | −0.999963 | − | 0.00855232i | \(-0.997278\pi\) |
0.814014 | + | 0.580845i | \(0.197278\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.32465 | + | 1.87816i | 0.0846289 | + | 0.119991i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −31.3539 | − | 43.1549i | −1.99500 | − | 2.74588i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.43418 | −0.217632 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.5088 | −0.852666 | −0.426333 | − | 0.904566i | \(-0.640195\pi\) | ||||
−0.426333 | + | 0.904566i | \(0.640195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.42744 | − | 1.96471i | −0.0897425 | − | 0.123520i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.44575 | + | 3.46771i | 0.153159 | + | 0.217156i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.0662i | − | 0.815044i | −0.913195 | − | 0.407522i | \(-0.866393\pi\) | ||
0.913195 | − | 0.407522i | \(-0.133607\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.164632 | − | 0.506686i | 0.0102298 | − | 0.0314839i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.02055 | + | 6.21862i | 0.125069 | + | 0.384923i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.21380 | − | 1.36915i | −0.259834 | − | 0.0844251i | 0.176203 | − | 0.984354i | \(-0.443618\pi\) |
−0.436037 | + | 0.899929i | \(0.643618\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0854 | − | 29.6174i | 0.619543 | − | 1.81938i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.34237 | + | 4.60038i | −0.204550 | + | 0.281539i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.6936 | + | 16.4879i | 1.38366 | + | 1.00528i | 0.996528 | + | 0.0832584i | \(0.0265327\pi\) |
0.387127 | + | 0.922026i | \(0.373467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.84207 | + | 3.51797i | −0.294135 | + | 0.213701i | −0.725059 | − | 0.688687i | \(-0.758188\pi\) |
0.430924 | + | 0.902388i | \(0.358188\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.9828 | − | 4.86820i | 0.906800 | − | 0.294637i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.88378 | + | 0.0810472i | 0.173898 | + | 0.00488733i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.82254 | − | 1.56694i | 0.289758 | − | 0.0941481i | −0.160531 | − | 0.987031i | \(-0.551321\pi\) |
0.450290 | + | 0.892883i | \(0.351321\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.93738 | − | 2.86068i | 0.235725 | − | 0.171264i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.6885 | + | 10.6718i | 0.876239 | + | 0.636625i | 0.932254 | − | 0.361805i | \(-0.117839\pi\) |
−0.0560144 | + | 0.998430i | \(0.517839\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.76092 | + | 3.80009i | −0.164120 | + | 0.225892i | −0.883154 | − | 0.469083i | \(-0.844584\pi\) |
0.719034 | + | 0.694975i | \(0.244584\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.1204 | + | 10.6643i | −0.895654 | + | 0.631699i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.0016 | + | 4.87430i | 0.885514 | + | 0.287721i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.14041 | + | 12.7429i | 0.243554 | + | 0.749581i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.03480 | − | 6.26247i | 0.119282 | − | 0.367112i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.60771i | 0.561288i | 0.959812 | + | 0.280644i | \(0.0905481\pi\) | ||||
−0.959812 | + | 0.280644i | \(0.909452\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.7468 | − | 7.96754i | 1.49904 | − | 0.463888i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.339142 | + | 0.466789i | 0.0196790 | + | 0.0270859i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.1329 | −1.56914 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.36804 | −0.482326 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.07476 | − | 9.73757i | −0.406434 | − | 0.559409i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.44441 | − | 8.61287i | 0.369006 | − | 0.493172i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.5400i | − | 0.772771i | −0.922337 | − | 0.386386i | \(-0.873723\pi\) | ||
0.922337 | − | 0.386386i | \(-0.126277\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.78805 | − | 5.50304i | 0.101718 | − | 0.313057i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.916931 | − | 2.82202i | −0.0519944 | − | 0.160022i | 0.921688 | − | 0.387933i | \(-0.126811\pi\) |
−0.973682 | + | 0.227910i | \(0.926811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.3203 | − | 4.32802i | −0.752906 | − | 0.244634i | −0.0926747 | − | 0.995696i | \(-0.529542\pi\) |
−0.660231 | + | 0.751063i | \(0.729542\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.61545 | − | 5.22027i | −0.0910203 | − | 0.294129i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.8806 | − | 21.8577i | 0.891941 | − | 1.22765i | −0.0810273 | − | 0.996712i | \(-0.525820\pi\) |
0.972968 | − | 0.230939i | \(-0.0741799\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.05217 | − | 2.21753i | −0.170889 | − | 0.124158i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.29336 | + | 2.39276i | −0.183817 | + | 0.133551i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.9345 | − | 4.85252i | 0.830979 | − | 0.270001i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.6707 | − | 25.5339i | 1.09114 | − | 1.41636i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.38641 | − | 0.450471i | 0.0766686 | − | 0.0249111i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.0162 | + | 13.8161i | −1.04840 | + | 0.761705i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.38394 | + | 3.91166i | 0.295928 | + | 0.215004i | 0.725835 | − | 0.687869i | \(-0.241454\pi\) |
−0.429907 | + | 0.902873i | \(0.641454\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.128140 | − | 0.176370i | 0.00702204 | − | 0.00966501i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.65482 | + | 0.121596i | 0.472863 | + | 0.00664348i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.2629 | − | 5.93398i | −0.994844 | − | 0.323245i | −0.234041 | − | 0.972227i | \(-0.575195\pi\) |
−0.760804 | + | 0.648982i | \(0.775195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.81017 | + | 5.57114i | 0.0983152 | + | 0.302583i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.867752 | + | 2.67067i | −0.0469914 | + | 0.144625i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6184i | 1.05930i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.132214 | + | 9.41063i | −0.00711819 | + | 0.506651i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.85076 | − | 13.5584i | −0.528816 | − | 0.727853i | 0.458133 | − | 0.888884i | \(-0.348518\pi\) |
−0.986949 | + | 0.161030i | \(0.948518\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9371 | −1.22780 | −0.613898 | − | 0.789385i | \(-0.710399\pi\) | ||||
−0.613898 | + | 0.789385i | \(0.710399\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.44645 | 0.344086 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.12280 | + | 5.67455i | 0.219434 | + | 0.302026i | 0.904515 | − | 0.426442i | \(-0.140233\pi\) |
−0.685081 | + | 0.728467i | \(0.740233\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.7215 | + | 4.67250i | 0.728262 | + | 0.247991i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.63766i | 0.245451i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.61051 | − | 14.1897i | 0.243333 | − | 0.748903i | −0.752573 | − | 0.658509i | \(-0.771187\pi\) |
0.995906 | − | 0.0903940i | \(-0.0288126\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2873 | + | 47.0494i | 0.804594 | + | 2.47629i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.1450 | + | 3.29631i | 0.532475 | + | 0.173012i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.9949 | − | 13.4643i | −0.941894 | − | 0.704753i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.400262 | − | 0.550914i | 0.0208935 | − | 0.0287575i | −0.798442 | − | 0.602071i | \(-0.794342\pi\) |
0.819336 | + | 0.573314i | \(0.194342\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.22182 | + | 3.79387i | 0.271837 | + | 0.197501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.6637 | − | 20.0988i | 1.43623 | − | 1.04348i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.2355 | + | 8.84935i | −1.41020 | + | 0.458202i | −0.912475 | − | 0.409133i | \(-0.865831\pi\) |
−0.497725 | + | 0.867335i | \(0.665831\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.76017 | − | 6.94690i | −0.452373 | − | 0.358736i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.0880 | + | 13.0254i | −2.06464 | + | 0.670842i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.7191 | + | 12.8737i | −0.910167 | + | 0.661275i | −0.941057 | − | 0.338247i | \(-0.890166\pi\) |
0.0308898 | + | 0.999523i | \(0.490166\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.3662 | − | 8.98455i | −0.633538 | − | 0.460293i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.68378 | − | 3.69391i | 0.137135 | − | 0.188750i | −0.734926 | − | 0.678147i | \(-0.762783\pi\) |
0.872061 | + | 0.489397i | \(0.162783\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.52449 | + | 1.88890i | 0.128660 | + | 0.0962671i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.25660 | − | 1.05813i | −0.165542 | − | 0.0537879i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.71865 | − | 20.6779i | −0.340649 | − | 1.04841i | −0.963872 | − | 0.266366i | \(-0.914177\pi\) |
0.623223 | − | 0.782044i | \(-0.285823\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.46826 | − | 7.59653i | 0.124825 | − | 0.384173i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.75392i | 0.189360i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.0432 | − | 3.41993i | −0.505326 | − | 0.172075i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.18318 | + | 12.6396i | 0.460891 | + | 0.634361i | 0.974693 | − | 0.223547i | \(-0.0717636\pi\) |
−0.513803 | + | 0.857908i | \(0.671764\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.2217 | −1.01235 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.9417 | −0.995841 | −0.497920 | − | 0.867223i | \(-0.665903\pi\) | ||||
−0.497920 | + | 0.867223i | \(0.665903\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.4412 | + | 25.3821i | 0.918622 | + | 1.26437i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.0314125 | − | 2.23585i | 0.00156090 | − | 0.111100i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.125785i | 0.00623495i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.32001 | − | 16.3733i | 0.263058 | − | 0.809608i | −0.729077 | − | 0.684432i | \(-0.760050\pi\) |
0.992134 | − | 0.125176i | \(-0.0399497\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.25793 | + | 19.2599i | 0.308681 | + | 0.950022i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.0136 | + | 9.10217i | 1.37846 | + | 0.447888i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.67830 | − | 0.107876i | −0.376913 | − | 0.00529543i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.545975 | + | 0.751470i | −0.0267365 | + | 0.0367996i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.6230 | + | 7.71804i | 0.518966 | + | 0.377051i | 0.816214 | − | 0.577749i | \(-0.196069\pi\) |
−0.297248 | + | 0.954800i | \(0.596069\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7712 | + | 10.0054i | −0.671169 | + | 0.487633i | −0.870416 | − | 0.492317i | \(-0.836150\pi\) |
0.199248 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.14758 | + | 2.97223i | −0.444770 | + | 0.144515i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.35940 | + | 7.83010i | 0.259969 | + | 0.379816i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1809 | − | 3.63289i | 0.541081 | − | 0.175808i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.00913 | + | 2.18626i | −0.145282 | + | 0.105554i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.1246 | + | 7.35594i | 0.487684 | + | 0.354323i | 0.804293 | − | 0.594233i | \(-0.202544\pi\) |
−0.316609 | + | 0.948556i | \(0.602544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.1949 | − | 16.7848i | 0.586048 | − | 0.806626i | −0.408294 | − | 0.912850i | \(-0.633876\pi\) |
0.994342 | + | 0.106225i | \(0.0338763\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.32231 | + | 13.9674i | 0.207239 | + | 0.669684i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.1234 | + | 10.7625i | 1.58451 | + | 0.514838i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2225 | + | 31.4615i | 0.487891 | + | 1.50157i | 0.827749 | + | 0.561098i | \(0.189621\pi\) |
−0.339858 | + | 0.940477i | \(0.610379\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.317617 | + | 0.977524i | −0.0151246 | + | 0.0465488i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 23.4802i | − | 1.11558i | −0.829984 | − | 0.557788i | \(-0.811650\pi\) | ||
0.829984 | − | 0.557788i | \(-0.188350\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.61754 | + | 10.1808i | −0.361106 | + | 0.482614i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.72535 | − | 10.6330i | −0.365397 | − | 0.502925i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.6965 | 1.49585 | 0.747925 | − | 0.663783i | \(-0.231050\pi\) | ||||
0.747925 | + | 0.663783i | \(0.231050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.72415 | −0.175363 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.3370 | + | 14.2277i | 0.485676 | + | 0.668475i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 33.6522 | − | 10.4139i | 1.57764 | − | 0.488212i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.2267i | 1.32039i | 0.751094 | + | 0.660196i | \(0.229527\pi\) | ||||
−0.751094 | + | 0.660196i | \(0.770473\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.586428 | + | 1.80484i | −0.0273721 | + | 0.0842427i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.52737 | − | 4.70075i | −0.0711365 | − | 0.218936i | 0.909167 | − | 0.416431i | \(-0.136719\pi\) |
−0.980304 | + | 0.197495i | \(0.936719\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.5435 | + | 5.70022i | 0.815314 | + | 0.264912i | 0.686847 | − | 0.726802i | \(-0.258994\pi\) |
0.128467 | + | 0.991714i | \(0.458994\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.89325 | − | 6.27235i | 0.412415 | − | 0.290873i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.1693 | − | 13.9969i | 0.470581 | − | 0.647699i | −0.506080 | − | 0.862487i | \(-0.668906\pi\) |
0.976661 | + | 0.214788i | \(0.0689059\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.65314 | + | 5.56033i | 0.353389 | + | 0.256752i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.02387 | + | 5.10314i | −0.323643 | + | 0.235140i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.87900 | − | 0.610525i | 0.0863966 | − | 0.0280719i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.1419 | + | 23.3688i | −1.56654 | + | 1.07223i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.3074 | − | 4.32383i | 0.609303 | − | 0.197974i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.8105 | + | 20.2055i | −1.27069 | + | 0.923212i | −0.999230 | − | 0.0392366i | \(-0.987507\pi\) |
−0.271463 | + | 0.962449i | \(0.587507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.13696 | + | 0.826049i | 0.0518408 | + | 0.0376646i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.04591 | + | 8.32148i | −0.275098 | + | 0.378640i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.74622 | − | 13.9380i | 0.215515 | − | 0.632892i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.79530 | − | 1.55809i | −0.217296 | − | 0.0706037i | 0.198346 | − | 0.980132i | \(-0.436443\pi\) |
−0.415642 | + | 0.909528i | \(0.636443\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.435068 | + | 1.33900i | 0.0196744 | + | 0.0605517i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.03949 | + | 24.7430i | −0.362817 | + | 1.11664i | 0.588520 | + | 0.808483i | \(0.299711\pi\) |
−0.951337 | + | 0.308153i | \(0.900289\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.4085i | − | 0.558852i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.743607 | + | 1.05432i | 0.0334227 | + | 0.0473883i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.31162 | + | 12.8163i | 0.417683 | + | 0.574892i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.49658 | −0.111762 | −0.0558812 | − | 0.998437i | \(-0.517797\pi\) | ||||
−0.0558812 | + | 0.998437i | \(0.517797\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.81475 | −0.393814 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.38184 | + | 11.5366i | 0.373728 | + | 0.514392i | 0.953909 | − | 0.300095i | \(-0.0970184\pi\) |
−0.580181 | + | 0.814487i | \(0.697018\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.5122 | − | 21.9940i | −0.690284 | − | 0.978718i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.5567i | 1.26825i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.82569 | − | 14.8520i | 0.213895 | − | 0.658301i | −0.785335 | − | 0.619071i | \(-0.787509\pi\) |
0.999230 | − | 0.0392303i | \(-0.0124906\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.59020 | − | 23.3602i | −0.335771 | − | 1.03340i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.86971 | − | 2.55702i | −0.347456 | − | 0.112895i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.17067 | − | 12.2478i | 0.183781 | − | 0.539703i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.26198 | − | 4.48974i | 0.143462 | − | 0.197458i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.39374 | − | 4.64533i | −0.280654 | − | 0.203907i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.6277 | + | 8.44804i | −0.509420 | + | 0.370115i | −0.812604 | − | 0.582817i | \(-0.801951\pi\) |
0.303183 | + | 0.952932i | \(0.401951\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.19878 | + | 1.36427i | −0.183600 | + | 0.0596552i | −0.399374 | − | 0.916788i | \(-0.630772\pi\) |
0.215774 | + | 0.976443i | \(0.430772\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.44792 | − | 11.7225i | −0.150480 | − | 0.511610i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.78393 | + | 2.85407i | −0.382634 | + | 0.124325i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.27526 | + | 3.10615i | −0.185881 | + | 0.135050i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.75111 | + | 7.08460i | 0.423162 | + | 0.307445i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.4570 | + | 33.6622i | −1.05935 | + | 1.45807i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.43861 | + | 5.24640i | −0.321599 | + | 0.226822i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.9263 | − | 3.55018i | −0.471507 | − | 0.153202i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.183260 | − | 0.564015i | −0.00789355 | − | 0.0242939i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.1361 | − | 34.2734i | 0.478778 | − | 1.47353i | −0.362016 | − | 0.932172i | \(-0.617912\pi\) |
0.840794 | − | 0.541355i | \(-0.182088\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 3.92307i | − | 0.168355i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.11395 | − | 0.963635i | 0.133387 | − | 0.0412776i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.11410 | + | 9.79172i | 0.304177 | + | 0.418664i | 0.933554 | − | 0.358436i | \(-0.116690\pi\) |
−0.629377 | + | 0.777100i | \(0.716690\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.81065 | 0.205314 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.1054 | 2.30497 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.81544 | − | 9.38064i | −0.289822 | − | 0.398906i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.292042 | − | 0.390311i | 0.0123965 | − | 0.0165678i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 24.0437i | − | 1.01876i | −0.860541 | − | 0.509382i | \(-0.829874\pi\) | ||
0.860541 | − | 0.509382i | \(-0.170126\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.82119 | − | 20.9935i | 0.288506 | − | 0.887929i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.338359 | − | 1.04136i | −0.0142855 | − | 0.0439664i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0159 | − | 5.85371i | −0.759278 | − | 0.246704i | −0.0963092 | − | 0.995351i | \(-0.530704\pi\) |
−0.662969 | + | 0.748647i | \(0.730704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.87227 | + | 12.5131i | 0.162908 | + | 0.526430i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.43643 | − | 1.97708i | 0.0603244 | − | 0.0830295i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.2591 | − | 18.3518i | −1.05892 | − | 0.769348i | −0.0850293 | − | 0.996378i | \(-0.527098\pi\) |
−0.973888 | + | 0.227030i | \(0.927098\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0316916 | − | 0.0230253i | 0.00132625 | − | 0.000963578i | −0.587122 | − | 0.809499i | \(-0.699739\pi\) |
0.588448 | + | 0.808535i | \(0.299739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.2953 | + | 7.89402i | −1.01495 | + | 0.329777i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.591223 | + | 21.0366i | −0.0246557 | + | 0.877286i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.1443 | + | 6.22035i | −0.796986 | + | 0.258957i | −0.679076 | − | 0.734068i | \(-0.737619\pi\) |
−0.117910 | + | 0.993024i | \(0.537619\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.341123 | − | 0.247840i | 0.0141766 | − | 0.0102999i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.78964 | − | 4.93296i | −0.281682 | − | 0.204654i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.74535 | + | 6.53141i | −0.196532 | + | 0.270503i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.4133 | + | 0.202499i | 0.595915 | + | 0.00837230i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.48143 | + | 3.08070i | 0.391341 | + | 0.127154i | 0.498076 | − | 0.867133i | \(-0.334040\pi\) |
−0.106736 | + | 0.994287i | \(0.534040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.4447 | − | 38.3009i | −0.512776 | − | 1.57816i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.23154 | − | 6.86796i | 0.0917931 | − | 0.282510i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 20.3619i | − | 0.836163i | −0.908410 | − | 0.418082i | \(-0.862703\pi\) | ||
0.908410 | − | 0.418082i | \(-0.137297\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.145680 | + | 10.3691i | −0.00597231 | + | 0.425091i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.31297 | − | 3.18353i | −0.0946634 | − | 0.130293i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.1075 | 0.985007 | 0.492503 | − | 0.870311i | \(-0.336082\pi\) | ||||
0.492503 | + | 0.870311i | \(0.336082\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.2054 | 1.51764 | 0.758820 | − | 0.651300i | \(-0.225776\pi\) | ||||
0.758820 | + | 0.651300i | \(0.225776\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.27528 | + | 3.13165i | 0.0926565 | + | 0.127531i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.5791 | + | 7.68873i | 0.917973 | + | 0.312591i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.5752i | 1.64690i | 0.567392 | + | 0.823448i | \(0.307952\pi\) | ||||
−0.567392 | + | 0.823448i | \(0.692048\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.93783 | + | 15.1971i | −0.200091 | + | 0.615817i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.1603 | − | 58.9694i | −0.775143 | − | 2.38565i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.88423 | + | 1.58698i | 0.197272 | + | 0.0640977i | 0.405987 | − | 0.913879i | \(-0.366928\pi\) |
−0.208714 | + | 0.977977i | \(0.566928\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.5560 | + | 8.64655i | 0.465983 | + | 0.348663i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.62895 | − | 13.2531i | 0.387647 | − | 0.533550i | −0.569943 | − | 0.821684i | \(-0.693035\pi\) |
0.957590 | + | 0.288134i | \(0.0930348\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.9251 | + | 10.8437i | 0.599892 | + | 0.435847i | 0.845841 | − | 0.533436i | \(-0.179099\pi\) |
−0.245948 | + | 0.969283i | \(0.579099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.40513 | + | 2.47398i | −0.136643 | + | 0.0992772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.2163 | + | 4.29422i | −0.529498 | + | 0.172044i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.3682 | − | 15.8074i | −0.774727 | − | 0.632296i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.54069 | − | 1.47536i | 0.181338 | − | 0.0589202i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.334701 | + | 0.243174i | −0.0133454 | + | 0.00969600i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1970 | − | 22.6659i | −1.24193 | − | 0.902316i | −0.244206 | − | 0.969723i | \(-0.578527\pi\) |
−0.997726 | + | 0.0674068i | \(0.978527\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.5541 | − | 20.0320i | 0.578475 | − | 0.796202i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.3667 | − | 20.4765i | −1.08601 | − | 0.812587i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.30156 | − | 2.04750i | −0.249677 | − | 0.0811249i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.00319 | + | 6.16520i | 0.0792451 | + | 0.243891i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.87099 | − | 18.0690i | 0.231890 | − | 0.713684i | −0.765629 | − | 0.643283i | \(-0.777572\pi\) |
0.997519 | − | 0.0704016i | \(-0.0224281\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 37.6504i | − | 1.48479i | −0.669964 | − | 0.742393i | \(-0.733691\pi\) | ||
0.669964 | − | 0.742393i | \(-0.266309\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.24801 | − | 2.46812i | −0.285390 | − | 0.0971821i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.37070 | + | 4.63937i | 0.132516 | + | 0.182392i | 0.870118 | − | 0.492843i | \(-0.164042\pi\) |
−0.737603 | + | 0.675235i | \(0.764042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.95440 | −0.272984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.8937 | 0.466150 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.5590 | − | 32.4262i | −0.921936 | − | 1.26894i | −0.962923 | − | 0.269777i | \(-0.913050\pi\) |
0.0409866 | − | 0.999160i | \(-0.486950\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.117920 | + | 8.39319i | −0.00460751 | + | 0.327949i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 10.0509i | − | 0.392123i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.75714 | − | 30.0294i | 0.380084 | − | 1.16978i | −0.559900 | − | 0.828560i | \(-0.689160\pi\) |
0.939984 | − | 0.341218i | \(-0.110840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.68781 | + | 29.8160i | 0.376812 | + | 1.15971i | 0.942248 | + | 0.334916i | \(0.108708\pi\) |
−0.565436 | + | 0.824792i | \(0.691292\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.6348 | − | 3.78038i | −0.451858 | − | 0.146818i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −45.2127 | − | 0.635215i | −1.75327 | − | 0.0246326i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.1765 | − | 22.2650i | 0.626355 | − | 0.862103i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.9155 | + | 11.5633i | 0.615330 | + | 0.447063i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.24556 | + | 1.63150i | −0.0866889 | + | 0.0629832i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.25575 | + | 1.38278i | −0.164047 | + | 0.0533021i | −0.389889 | − | 0.920862i | \(-0.627487\pi\) |
0.225842 | + | 0.974164i | \(0.427487\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.140467 | − | 4.99803i | 0.00540658 | − | 0.192374i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.3935 | + | 4.35181i | −0.514754 | + | 0.167254i | −0.554863 | − | 0.831942i | \(-0.687229\pi\) |
0.0401092 | + | 0.999195i | \(0.487229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.0186 | − | 9.45854i | 0.499607 | − | 0.362985i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.3376 | − | 15.5027i | −0.817660 | − | 0.594065i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.95685 | + | 9.57528i | −0.266196 | + | 0.366388i | −0.921101 | − | 0.389324i | \(-0.872709\pi\) |
0.654905 | + | 0.755711i | \(0.272709\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.3868 | + | 43.2588i | 0.511482 | + | 1.65284i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.2371 | − | 4.95082i | −0.581330 | − | 0.188886i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.8733 | + | 85.7853i | 1.06189 | + | 3.26816i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.6676 | + | 35.9091i | −0.443855 | + | 1.36605i | 0.439879 | + | 0.898057i | \(0.355021\pi\) |
−0.883734 | + | 0.467989i | \(0.844979\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.41003i | 0.0535627i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.24432 | + | 1.66302i | −0.0471998 | + | 0.0630820i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.19971 | − | 9.90956i | −0.272709 | − | 0.375351i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.3108 | 1.10864 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.1678 | −1.47935 | −0.739674 | − | 0.672965i | \(-0.765020\pi\) | ||||
−0.739674 | + | 0.672965i | \(0.765020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.06032 | − | 1.45941i | −0.0399908 | − | 0.0550426i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20.5460 | + | 6.35810i | −0.773805 | + | 0.239460i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 29.4143i | − | 1.10624i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.1296 | − | 40.4089i | 0.493094 | − | 1.51759i | −0.326812 | − | 0.945089i | \(-0.605974\pi\) |
0.819906 | − | 0.572498i | \(-0.194026\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.46619 | − | 4.51248i | −0.0549866 | − | 0.169231i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.4820 | − | 6.33008i | −0.729606 | − | 0.237063i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.79664 | + | 4.79362i | −0.254180 | + | 0.179271i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.1977 | − | 20.9178i | 0.567568 | − | 0.781190i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.0261 | + | 17.4560i | 0.896022 | + | 0.650998i | 0.937441 | − | 0.348143i | \(-0.113188\pi\) |
−0.0414189 | + | 0.999142i | \(0.513188\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.4399 | − | 8.31154i | 0.426042 | − | 0.309538i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.88437 | + | 2.88671i | −0.330413 | + | 0.107358i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.22527 | + | 31.3647i | 0.342618 | + | 1.16485i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.8796 | − | 12.9577i | 1.47905 | − | 0.480573i | 0.545222 | − | 0.838292i | \(-0.316445\pi\) |
0.933829 | + | 0.357719i | \(0.116445\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.809017 | − | 0.587785i | 0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.25712 | + | 3.81952i | 0.194441 | + | 0.141270i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.1695 | − | 23.6317i | 0.634168 | − | 0.872858i | −0.364119 | − | 0.931352i | \(-0.618630\pi\) |
0.998288 | + | 0.0584945i | \(0.0186300\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.740849 | + | 2.17562i | −0.0273266 | + | 0.0802489i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.12415 | − | 0.690179i | −0.0782441 | − | 0.0254231i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.00979 | − | 24.6516i | −0.294645 | − | 0.906824i | −0.983340 | − | 0.181773i | \(-0.941816\pi\) |
0.688695 | − | 0.725051i | \(-0.258184\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.4837 | − | 50.7317i | 0.605544 | − | 1.86367i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 9.22935i | − | 0.338592i | −0.985565 | − | 0.169296i | \(-0.945851\pi\) | ||
0.985565 | − | 0.169296i | \(-0.0541494\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.9387 | − | 24.0165i | −0.620586 | − | 0.879897i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.01856 | − | 2.77831i | −0.0738552 | − | 0.101653i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.94826 | −0.363502 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.2805 | −1.36038 | −0.680192 | − | 0.733034i | \(-0.738103\pi\) | ||||
−0.680192 | + | 0.733034i | \(0.738103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.94025 | − | 10.9288i | −0.289359 | − | 0.398268i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.6651 | + | 32.1356i | 0.824866 | + | 1.16954i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6758i | 1.00589i | 0.864317 | + | 0.502947i | \(0.167751\pi\) | ||||
−0.864317 | + | 0.502947i | \(0.832249\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.750451 | − | 2.30965i | 0.0272396 | − | 0.0838350i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.21264 | − | 12.9652i | −0.152708 | − | 0.469988i | 0.845213 | − | 0.534429i | \(-0.179473\pi\) |
−0.997921 | + | 0.0644416i | \(0.979473\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.38811 | + | 1.10086i | 0.122658 | + | 0.0398539i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.36786 | + | 4.01693i | −0.0494550 | + | 0.145232i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −45.6705 | + | 62.8600i | −1.64906 | + | 2.26974i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.6838 | − | 17.9339i | −0.890122 | − | 0.646712i | 0.0457876 | − | 0.998951i | \(-0.485420\pi\) |
−0.935910 | + | 0.352239i | \(0.885420\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5707 | − | 7.68009i | 0.380696 | − | 0.276592i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.03172 | − | 2.60967i | 0.288881 | − | 0.0938631i | −0.160992 | − | 0.986956i | \(-0.551469\pi\) |
0.449873 | + | 0.893093i | \(0.351469\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.0810 | − | 13.7447i | 0.721330 | − | 0.493723i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.506686 | − | 0.164632i | 0.0181773 | − | 0.00590615i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43.2090 | − | 31.3932i | 1.54812 | − | 1.12478i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.02595 | − | 2.19848i | −0.108277 | − | 0.0786678i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.84332 | + | 5.28988i | −0.137349 | + | 0.189045i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.8646 | + | 11.1892i | −0.566232 | + | 0.399360i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.8560 | + | 12.6251i | 1.38507 | + | 0.450036i | 0.904332 | − | 0.426829i | \(-0.140369\pi\) |
0.480736 | + | 0.876865i | \(0.340369\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.36915 | − | 4.21380i | −0.0487429 | − | 0.150015i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.42371 | + | 13.6148i | −0.157289 | + | 0.484086i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.0116i | 1.10125i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 29.8891 | − | 9.24940i | 1.06006 | − | 0.328042i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.3703 | + | 23.9082i | 0.615288 | + | 0.846871i | 0.996999 | − | 0.0774107i | \(-0.0246653\pi\) |
−0.381712 | + | 0.924281i | \(0.624665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.2529 | 0.645742 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.68638 | −0.200918 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.40868 | + | 4.69165i | 0.120290 | + | 0.165565i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.7791 | + | 18.4156i | −0.485650 | + | 0.649066i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.0509i | 0.987438i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.69396 | + | 23.6796i | −0.270505 | + | 0.832529i | 0.719869 | + | 0.694110i | \(0.244202\pi\) |
−0.990374 | + | 0.138419i | \(0.955798\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.52723 | + | 23.1664i | 0.264317 | + | 0.813483i | 0.991850 | + | 0.127411i | \(0.0406667\pi\) |
−0.727533 | + | 0.686072i | \(0.759333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.69219 | − | 1.84950i | −0.199634 | − | 0.0648650i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.930684 | + | 3.00747i | 0.0326004 | + | 0.105347i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.6544 | + | 22.9228i | −0.582663 | + | 0.801967i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.7451 | + | 9.25987i | 0.445351 | + | 0.323566i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.8023 | − | 32.5508i | 1.56361 | − | 1.13603i | 0.630642 | − | 0.776074i | \(-0.282792\pi\) |
0.932969 | − | 0.359956i | \(-0.117208\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.6101 | − | 5.39695i | 0.578992 | − | 0.188126i | −0.00485678 | − | 0.999988i | \(-0.501546\pi\) |
0.583849 | + | 0.811862i | \(0.301546\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.62947 | + | 2.38066i | 0.0567310 | + | 0.0828841i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.2394 | + | 7.22601i | −0.773338 | + | 0.251273i | −0.668993 | − | 0.743268i | \(-0.733275\pi\) |
−0.104345 | + | 0.994541i | \(0.533275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.1866 | − | 21.2053i | 1.01369 | − | 0.736491i | 0.0487125 | − | 0.998813i | \(-0.484488\pi\) |
0.964980 | + | 0.262322i | \(0.0844882\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.10230 | + | 2.98049i | 0.142307 | + | 0.103392i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.14650 | − | 1.57802i | 0.0397237 | − | 0.0546750i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.7084 | − | 0.276893i | −0.682039 | − | 0.00958229i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.62867 | + | 1.50395i | 0.159990 | + | 0.0519840i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.88419 | − | 18.1097i | −0.203145 | − | 0.625215i | −0.999784 | − | 0.0207608i | \(-0.993391\pi\) |
0.796640 | − | 0.604454i | \(-0.206609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.25019 | − | 13.0808i | 0.146558 | − | 0.451060i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.1559i | 0.625323i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.897036 | + | 63.8483i | −0.0308590 | + | 2.19645i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.3225 | + | 21.0897i | 0.526489 | + | 0.724649i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.69717 | −0.161206 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.917579 | −0.0314542 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.6095 | − | 14.6027i | −0.363261 | − | 0.499986i | 0.587793 | − | 0.809012i | \(-0.299997\pi\) |
−0.951054 | + | 0.309026i | \(0.899997\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.5151 | − | 5.96432i | −0.599005 | − | 0.203976i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.4435i | 0.425061i | 0.977154 | + | 0.212531i | \(0.0681705\pi\) | ||||
−0.977154 | + | 0.212531i | \(0.931829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.2156 | + | 43.7511i | −0.485029 | + | 1.49277i | 0.346909 | + | 0.937899i | \(0.387231\pi\) |
−0.831938 | + | 0.554868i | \(0.812769\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.87430 | + | 15.0016i | 0.166116 | + | 0.511252i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.0298 | − | 14.6311i | −1.53283 | − | 0.498048i | −0.583445 | − | 0.812153i | \(-0.698296\pi\) |
−0.949388 | + | 0.314105i | \(0.898296\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.1495 | − | 10.5871i | −0.481098 | − | 0.359972i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.87553 | + | 10.8397i | −0.267467 | + | 0.368137i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.21478 | + | 1.60913i | 0.0751311 | + | 0.0545860i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.1880 | + | 14.6675i | −0.684045 | + | 0.496988i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.26247 | − | 2.03480i | 0.211952 | − | 0.0688675i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.34079 | − | 26.3179i | −0.248164 | − | 0.889709i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.3934 | − | 9.87543i | 1.02631 | − | 0.333470i | 0.252982 | − | 0.967471i | \(-0.418589\pi\) |
0.773332 | + | 0.634001i | \(0.218589\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.77280 | + | 5.64727i | −0.262170 | + | 0.190478i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.41518 | + | 4.66090i | 0.216133 | + | 0.157030i | 0.690584 | − | 0.723252i | \(-0.257353\pi\) |
−0.474451 | + | 0.880282i | \(0.657353\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.8953 | − | 30.1363i | 0.736836 | − | 1.01417i | −0.261958 | − | 0.965079i | \(-0.584368\pi\) |
0.998794 | − | 0.0490886i | \(-0.0156317\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.5795 | + | 16.1464i | 0.725385 | + | 0.542755i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.6114 | + | 5.07245i | 0.524179 | + | 0.170316i | 0.559141 | − | 0.829072i | \(-0.311131\pi\) |
−0.0349619 | + | 0.999389i | \(0.511131\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.5432 | − | 35.5263i | −0.387147 | − | 1.19151i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.178298 | + | 0.548744i | −0.00597320 | + | 0.0183836i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 79.5889i | 2.66334i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.3181 | − | 8.28089i | −0.812865 | − | 0.276800i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.9483 | − | 21.9510i | −0.532500 | − | 0.732923i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.8228 | −1.06135 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.5533 | −0.884619 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.91861 | − | 6.76988i | −0.163681 | − | 0.225288i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.123233 | − | 8.77139i | 0.00409642 | − | 0.291571i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.85782i | − | 0.0616880i | −0.999524 | − | 0.0308440i | \(-0.990181\pi\) | ||
0.999524 | − | 0.0308440i | \(-0.00981950\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.71942 | − | 11.4472i | 0.123365 | − | 0.379680i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.95487 | − | 21.4049i | −0.230425 | − | 0.709176i | −0.997695 | − | 0.0678519i | \(-0.978385\pi\) |
0.767270 | − | 0.641324i | \(-0.221615\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.88448 | + | 0.612306i | 0.0623673 | + | 0.0202644i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.7559 | + | 0.151115i | 0.355579 | + | 0.00499569i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.39225 | + | 7.42179i | −0.178068 | + | 0.245089i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.9124 | + | 12.2876i | 0.557890 | + | 0.405331i | 0.830686 | − | 0.556741i | \(-0.187948\pi\) |
−0.272796 | + | 0.962072i | \(0.587948\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.9541 | − | 7.95864i | 0.360951 | − | 0.262246i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −39.7436 | + | 12.9135i | −1.30818 | + | 0.425052i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.665222 | − | 0.863502i | 0.0218724 | − | 0.0283918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.50304 | − | 1.78805i | 0.180744 | − | 0.0587272i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.3058 | − | 8.21417i | 0.370933 | − | 0.269498i | −0.386665 | − | 0.922220i | \(-0.626373\pi\) |
0.757598 | + | 0.652722i | \(0.226373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.88068 | + | 4.99911i | 0.225505 | + | 0.163839i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.74411 | − | 2.40056i | 0.0570995 | − | 0.0785907i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.723808 | − | 2.33896i | −0.0236710 | − | 0.0764921i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.1551 | + | 10.1229i | 1.01779 | + | 0.330701i | 0.769954 | − | 0.638100i | \(-0.220279\pi\) |
0.247840 | + | 0.968801i | \(0.420279\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.32802 | − | 13.3203i | −0.141239 | − | 0.434690i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.99456 | + | 24.6047i | −0.260615 | + | 0.802091i | 0.732056 | + | 0.681244i | \(0.238561\pi\) |
−0.992671 | + | 0.120847i | \(0.961439\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 27.1669i | − | 0.884677i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.27375 | − | 4.37532i | 0.106495 | − | 0.142329i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.7818 | + | 45.1202i | 1.06526 | + | 1.46621i | 0.874780 | + | 0.484521i | \(0.161006\pi\) |
0.190485 | + | 0.981690i | \(0.438994\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 64.7925 | 2.10325 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.0176 | 0.876106 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.6533 | + | 20.1685i | 0.474666 | + | 0.653322i | 0.977469 | − | 0.211079i | \(-0.0676977\pi\) |
−0.502803 | + | 0.864401i | \(0.667698\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −54.5685 | + | 16.8866i | −1.76580 | + | 0.546439i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.77269i | − | 0.121954i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.2931 | + | 47.0675i | −0.493841 | + | 1.51989i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.26000 | − | 6.95558i | −0.0729034 | − | 0.224373i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.87157 | − | 1.25795i | −0.124760 | − | 0.0405369i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.770484 | − | 0.543417i | 0.0248028 | − | 0.0174932i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.10669 | − | 7.02876i | 0.164220 | − | 0.226030i | −0.718974 | − | 0.695037i | \(-0.755388\pi\) |
0.883194 | + | 0.469007i | \(0.155388\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.7041 | + | 9.23004i | 0.408113 | + | 0.296512i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.9663 | + | 14.5064i | −0.640750 | + | 0.465532i | −0.860108 | − | 0.510112i | \(-0.829604\pi\) |
0.219358 | + | 0.975645i | \(0.429604\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.15887 | + | 0.701459i | −0.0692102 | + | 0.0224877i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.2195 | + | 0.905513i | 1.03185 | + | 0.0289996i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.8554 | + | 11.0003i | −1.08313 | + | 0.351930i | −0.795588 | − | 0.605838i | \(-0.792838\pi\) |
−0.287542 | + | 0.957768i | \(0.592838\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.65434 | − | 1.92849i | 0.0848332 | − | 0.0616349i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.17935 | + | 0.856848i | 0.0376537 | + | 0.0273570i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.49217 | + | 4.80656i | −0.111383 | + | 0.153305i | −0.861069 | − | 0.508488i | \(-0.830205\pi\) |
0.749686 | + | 0.661794i | \(0.230205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.20511 | − | 15.2856i | 0.165849 | − | 0.487040i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.3549 | − | 7.26354i | −0.711563 | − | 0.231201i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.45365 | + | 13.7069i | 0.141618 | + | 0.435855i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.30614 | − | 4.01987i | 0.0414908 | − | 0.127695i | −0.928166 | − | 0.372168i | \(-0.878615\pi\) |
0.969656 | + | 0.244472i | \(0.0786147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.65492i | 0.211187i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.07144 | − | 7.19053i | −0.160775 | − | 0.227955i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.37405 | + | 10.1495i | 0.233538 | + | 0.321438i | 0.909661 | − | 0.415351i | \(-0.136341\pi\) |
−0.676123 | + | 0.736789i | \(0.736341\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.218005 | 0.00689738 |
(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.169.6 | ✓ | 24 | |
3.2 | odd | 2 | 900.2.w.c.469.2 | 24 | |||
5.2 | odd | 4 | 1500.2.m.d.901.3 | 24 | |||
5.3 | odd | 4 | 1500.2.m.c.901.4 | 24 | |||
5.4 | even | 2 | 1500.2.o.c.349.1 | 24 | |||
25.2 | odd | 20 | 7500.2.a.m.1.5 | 12 | |||
25.3 | odd | 20 | 1500.2.m.c.601.4 | 24 | |||
25.4 | even | 10 | inner | 300.2.o.a.229.6 | yes | 24 | |
25.11 | even | 5 | 7500.2.d.g.1249.8 | 24 | |||
25.14 | even | 10 | 7500.2.d.g.1249.17 | 24 | |||
25.21 | even | 5 | 1500.2.o.c.649.1 | 24 | |||
25.22 | odd | 20 | 1500.2.m.d.601.3 | 24 | |||
25.23 | odd | 20 | 7500.2.a.n.1.8 | 12 | |||
75.29 | odd | 10 | 900.2.w.c.829.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.169.6 | ✓ | 24 | 1.1 | even | 1 | trivial | |
300.2.o.a.229.6 | yes | 24 | 25.4 | even | 10 | inner | |
900.2.w.c.469.2 | 24 | 3.2 | odd | 2 | |||
900.2.w.c.829.2 | 24 | 75.29 | odd | 10 | |||
1500.2.m.c.601.4 | 24 | 25.3 | odd | 20 | |||
1500.2.m.c.901.4 | 24 | 5.3 | odd | 4 | |||
1500.2.m.d.601.3 | 24 | 25.22 | odd | 20 | |||
1500.2.m.d.901.3 | 24 | 5.2 | odd | 4 | |||
1500.2.o.c.349.1 | 24 | 5.4 | even | 2 | |||
1500.2.o.c.649.1 | 24 | 25.21 | even | 5 | |||
7500.2.a.m.1.5 | 12 | 25.2 | odd | 20 | |||
7500.2.a.n.1.8 | 12 | 25.23 | odd | 20 | |||
7500.2.d.g.1249.8 | 24 | 25.11 | even | 5 | |||
7500.2.d.g.1249.17 | 24 | 25.14 | even | 10 |