Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(101,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bi (of order \(6\), degree \(2\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 9 x^{14} - 18 x^{13} + 32 x^{12} - 36 x^{11} + 51 x^{9} - 167 x^{8} + 153 x^{7} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.8 | ||
Root | \(-1.66463 + 0.478563i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1601 |
Dual form | 2100.2.bi.l.101.8 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.66463 | + | 0.478563i | 0.961072 | + | 0.276298i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.25338 | − | 2.33003i | −0.473732 | − | 0.880669i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.54196 | + | 1.59326i | 0.847318 | + | 0.531085i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.63831 | + | 2.67793i | −1.39850 | + | 0.807426i | −0.994236 | − | 0.107214i | \(-0.965807\pi\) |
−0.404268 | + | 0.914641i | \(0.632474\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.13670i | 1.14732i | 0.819095 | + | 0.573658i | \(0.194476\pi\) | ||||
−0.819095 | + | 0.573658i | \(0.805524\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0773793 | + | 0.134025i | 0.0187672 | + | 0.0325058i | 0.875257 | − | 0.483659i | \(-0.160693\pi\) |
−0.856489 | + | 0.516165i | \(0.827359\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.40485 | − | 1.96579i | −0.781126 | − | 0.450983i | 0.0557031 | − | 0.998447i | \(-0.482260\pi\) |
−0.836829 | + | 0.547464i | \(0.815593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.971337 | − | 4.47845i | −0.211963 | − | 0.977278i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.19273 | + | 2.99803i | 1.08276 | + | 0.625132i | 0.931640 | − | 0.363384i | \(-0.118379\pi\) |
0.151120 | + | 0.988515i | \(0.451712\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.46893 | + | 3.86866i | 0.667596 | + | 0.744524i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.3150i | 1.91544i | 0.287703 | + | 0.957720i | \(0.407108\pi\) | ||||
−0.287703 | + | 0.957720i | \(0.592892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.70071 | − | 3.86866i | 1.20348 | − | 0.694832i | 0.242156 | − | 0.970237i | \(-0.422146\pi\) |
0.961328 | + | 0.275406i | \(0.0888122\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.00261 | + | 2.23803i | −1.56715 | + | 0.389591i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.24072 | + | 9.07719i | −0.861569 | + | 1.49228i | 0.00884571 | + | 0.999961i | \(0.497184\pi\) |
−0.870414 | + | 0.492320i | \(0.836149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.97967 | + | 6.88606i | −0.317001 | + | 1.10265i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.33876 | 0.365253 | 0.182627 | − | 0.983182i | \(-0.441540\pi\) | ||||
0.182627 | + | 0.983182i | \(0.441540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.78236 | 0.271807 | 0.135903 | − | 0.990722i | \(-0.456606\pi\) | ||||
0.135903 | + | 0.990722i | \(0.456606\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.80118 | + | 3.11974i | −0.262729 | + | 0.455061i | −0.966966 | − | 0.254905i | \(-0.917956\pi\) |
0.704237 | + | 0.709965i | \(0.251289\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.85809 | + | 5.84082i | −0.551156 | + | 0.834402i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0646682 | + | 0.260132i | 0.00905537 | + | 0.0364258i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.29470 | + | 2.47955i | −0.589923 | + | 0.340592i | −0.765067 | − | 0.643951i | \(-0.777294\pi\) |
0.175144 | + | 0.984543i | \(0.443961\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.72705 | − | 4.90174i | −0.626112 | − | 0.649251i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.27011 | + | 9.12810i | 0.686110 | + | 1.18838i | 0.973087 | + | 0.230440i | \(0.0740165\pi\) |
−0.286976 | + | 0.957938i | \(0.592650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.25602 | − | 1.87987i | −0.416891 | − | 0.240692i | 0.276855 | − | 0.960912i | \(-0.410708\pi\) |
−0.693746 | + | 0.720219i | \(0.744041\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.526307 | − | 7.91979i | 0.0663085 | − | 0.997799i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.444690 | + | 0.770225i | 0.0543275 | + | 0.0940980i | 0.891910 | − | 0.452213i | \(-0.149365\pi\) |
−0.837583 | + | 0.546311i | \(0.816032\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.20921 | + | 7.47564i | 0.867887 | + | 0.899961i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.6200i | − | 1.37904i | −0.724269 | − | 0.689518i | \(-0.757822\pi\) | ||
0.724269 | − | 0.689518i | \(-0.242178\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.6097 | + | 6.12550i | −1.24177 | + | 0.716935i | −0.969454 | − | 0.245273i | \(-0.921122\pi\) |
−0.272314 | + | 0.962208i | \(0.587789\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0532 | + | 7.45095i | 1.37359 | + | 0.849115i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.61147 | − | 6.25525i | 0.406322 | − | 0.703770i | −0.588152 | − | 0.808750i | \(-0.700144\pi\) |
0.994474 | + | 0.104980i | \(0.0334778\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.92307 | + | 8.09997i | 0.435897 | + | 0.899997i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.14180 | 0.564386 | 0.282193 | − | 0.959358i | \(-0.408938\pi\) | ||||
0.282193 | + | 0.959358i | \(0.408938\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.93635 | + | 17.1705i | −0.529233 | + | 1.84087i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.58428 | − | 14.8684i | 0.909932 | − | 1.57605i | 0.0957761 | − | 0.995403i | \(-0.469467\pi\) |
0.814156 | − | 0.580646i | \(-0.197200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.63865 | − | 5.18485i | 1.01041 | − | 0.543520i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.0056 | − | 3.23316i | 1.34862 | − | 0.335263i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.28309i | − | 0.434882i | −0.976073 | − | 0.217441i | \(-0.930229\pi\) | ||
0.976073 | − | 0.217441i | \(-0.0697710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.0570 | − | 0.582836i | −1.61379 | − | 0.0585772i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.04794 | − | 5.27919i | −0.303282 | − | 0.525299i | 0.673596 | − | 0.739100i | \(-0.264749\pi\) |
−0.976877 | + | 0.213801i | \(0.931416\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.73132 | + | 2.15428i | 0.367658 | + | 0.212267i | 0.672435 | − | 0.740157i | \(-0.265249\pi\) |
−0.304777 | + | 0.952424i | \(0.598582\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.3579 | + | 8.28953i | 1.38803 | + | 0.801379i | 0.993093 | − | 0.117330i | \(-0.0374334\pi\) |
0.394936 | + | 0.918709i | \(0.370767\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.92426 | − | 3.33292i | −0.184311 | − | 0.319236i | 0.759033 | − | 0.651052i | \(-0.225672\pi\) |
−0.943344 | + | 0.331816i | \(0.892339\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.0678 | + | 12.6021i | −1.24034 | + | 1.19614i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.94281i | 0.935341i | 0.883903 | + | 0.467671i | \(0.154907\pi\) | ||||
−0.883903 | + | 0.467671i | \(0.845093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.59083 | + | 10.5153i | −0.609322 | + | 0.972141i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.215297 | − | 0.348280i | 0.0197362 | − | 0.0319268i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.84262 | − | 15.3159i | 0.803875 | − | 1.39235i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.89316 | + | 1.11924i | 0.351035 | + | 0.100919i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.64472 | −0.412152 | −0.206076 | − | 0.978536i | \(-0.566069\pi\) | ||||
−0.206076 | + | 0.978536i | \(0.566069\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.96695 | + | 0.852969i | 0.261226 | + | 0.0750997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.31417 | + | 5.74031i | −0.289561 | + | 0.501534i | −0.973705 | − | 0.227813i | \(-0.926842\pi\) |
0.684144 | + | 0.729347i | \(0.260176\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.312794 | + | 10.3973i | −0.0271227 | + | 0.901559i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.08389 | − | 2.35783i | 0.348910 | − | 0.201443i | −0.315295 | − | 0.948994i | \(-0.602103\pi\) |
0.664205 | + | 0.747550i | \(0.268770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.56273i | 0.811100i | 0.914073 | + | 0.405550i | \(0.132920\pi\) | ||||
−0.914073 | + | 0.405550i | \(0.867080\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.49128 | + | 4.33122i | −0.378234 | + | 0.364754i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.0778 | − | 19.1873i | −0.926373 | − | 1.60452i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.21748 | + | 7.87643i | −0.760245 | + | 0.649637i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.6339 | − | 10.1809i | −1.44462 | − | 0.834054i | −0.446471 | − | 0.894798i | \(-0.647319\pi\) |
−0.998153 | + | 0.0607437i | \(0.980653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.69396 | − | 9.86223i | −0.463368 | − | 0.802577i | 0.535758 | − | 0.844371i | \(-0.320026\pi\) |
−0.999126 | + | 0.0417947i | \(0.986692\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0168412 | + | 0.463970i | −0.00136153 | + | 0.0375098i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.89957 | − | 3.40612i | 0.470837 | − | 0.271838i | −0.245753 | − | 0.969332i | \(-0.579035\pi\) |
0.716590 | + | 0.697495i | \(0.245702\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.33569 | + | 2.07223i | −0.661063 | + | 0.164339i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.477042 | − | 15.8569i | 0.0375962 | − | 1.24970i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.95589 | + | 6.85180i | −0.309849 | + | 0.536674i | −0.978329 | − | 0.207056i | \(-0.933612\pi\) |
0.668480 | + | 0.743730i | \(0.266945\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.2507 | −1.48966 | −0.744832 | − | 0.667252i | \(-0.767470\pi\) | ||||
−0.744832 | + | 0.667252i | \(0.767470\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.11232 | −0.316332 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.52297 | − | 10.4217i | −0.422352 | − | 0.796971i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.07129 | + | 12.2478i | −0.537621 | + | 0.931186i | 0.461411 | + | 0.887186i | \(0.347343\pi\) |
−0.999032 | + | 0.0439995i | \(0.985990\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.40439 | + | 17.7169i | 0.331054 | + | 1.33169i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.79606 | − | 1.03696i | 0.134244 | − | 0.0775058i | −0.431374 | − | 0.902173i | \(-0.641971\pi\) |
0.565618 | + | 0.824667i | \(0.308638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.7401i | − | 1.61593i | −0.589231 | − | 0.807965i | \(-0.700569\pi\) | ||
0.589231 | − | 0.807965i | \(-0.299431\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.52043 | − | 4.68749i | −0.334160 | − | 0.346509i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.717819 | − | 0.414433i | −0.0524921 | − | 0.0303063i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.66622 | − | 12.9316i | 0.339417 | − | 0.940636i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.00687 | + | 1.15867i | 0.145212 | + | 0.0838383i | 0.570846 | − | 0.821057i | \(-0.306615\pi\) |
−0.425634 | + | 0.904896i | \(0.639949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.93203 | − | 15.4707i | −0.642942 | − | 1.11361i | −0.984773 | − | 0.173846i | \(-0.944380\pi\) |
0.341831 | − | 0.939761i | \(-0.388953\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.3849i | 1.30987i | 0.755685 | + | 0.654936i | \(0.227304\pi\) | ||||
−0.755685 | + | 0.654936i | \(0.772696\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.70763 | + | 0.985902i | −0.121051 | + | 0.0698887i | −0.559303 | − | 0.828963i | \(-0.688931\pi\) |
0.438252 | + | 0.898852i | \(0.355598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.371641 | + | 1.49495i | 0.0262135 | + | 0.105446i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.0342 | − | 12.9285i | 1.68687 | − | 0.907405i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.42307 | + | 15.8942i | 0.585444 | + | 1.10472i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.0570 | 1.45654 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.07968 | 0.0743282 | 0.0371641 | − | 0.999309i | \(-0.488168\pi\) | ||||
0.0371641 | + | 0.999309i | \(0.488168\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.56088 | − | 19.3429i | 0.381025 | − | 1.32535i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.4126 | − | 10.7640i | −1.18205 | − | 0.730707i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.5926 | + | 5.11926i | −1.39152 | + | 0.345928i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.554421 | + | 0.320095i | −0.0372944 | + | 0.0215319i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.3841i | 1.03020i | 0.857131 | + | 0.515099i | \(0.172245\pi\) | ||||
−0.857131 | + | 0.515099i | \(0.827755\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.975410 | − | 1.68946i | −0.0647402 | − | 0.112133i | 0.831838 | − | 0.555018i | \(-0.187289\pi\) |
−0.896579 | + | 0.442884i | \(0.853955\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.44750 | + | 1.41307i | 0.161735 | + | 0.0933780i | 0.578683 | − | 0.815553i | \(-0.303567\pi\) |
−0.416948 | + | 0.908930i | \(0.636900\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.4983 | + | 18.1713i | 1.08551 | + | 1.19558i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.80293 | + | 2.19563i | 0.249139 | + | 0.143840i | 0.619370 | − | 0.785099i | \(-0.287388\pi\) |
−0.370231 | + | 0.928940i | \(0.620722\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.00527 | − | 8.68433i | 0.584955 | − | 0.564108i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.6724i | 1.14313i | 0.820556 | + | 0.571566i | \(0.193664\pi\) | ||||
−0.820556 | + | 0.571566i | \(0.806336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.69148 | + | 2.13128i | −0.237789 | + | 0.137288i | −0.614160 | − | 0.789181i | \(-0.710505\pi\) |
0.376371 | + | 0.926469i | \(0.377172\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.65410 | + | 15.3609i | 0.170261 | + | 0.985399i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.13190 | − | 14.0849i | 0.517420 | − | 0.896198i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.55917 | + | 2.46067i | 0.542415 | + | 0.155939i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.87820 | 0.244790 | 0.122395 | − | 0.992481i | \(-0.460943\pi\) | ||||
0.122395 | + | 0.992481i | \(0.460943\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.1140 | −2.01899 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.85563 | − | 15.3384i | 0.552399 | − | 0.956784i | −0.445702 | − | 0.895182i | \(-0.647046\pi\) |
0.998101 | − | 0.0616020i | \(-0.0196209\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.7187 | + | 0.833896i | 1.72236 | + | 0.0518158i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.4344 | + | 26.2202i | −1.01726 | + | 1.62299i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.84912 | − | 2.79964i | 0.299010 | − | 0.172633i | −0.342988 | − | 0.939340i | \(-0.611439\pi\) |
0.641998 | + | 0.766706i | \(0.278106\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.4051 | − | 20.6422i | 1.30997 | − | 1.26328i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.53335 | − | 14.7802i | −0.520288 | − | 0.901165i | −0.999722 | − | 0.0235867i | \(-0.992491\pi\) |
0.479434 | − | 0.877578i | \(-0.340842\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.7661 | + | 8.52521i | 0.896977 | + | 0.517870i | 0.876218 | − | 0.481915i | \(-0.160059\pi\) |
0.0207586 | + | 0.999785i | \(0.493392\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.5260 | − | 4.01813i | 1.12125 | − | 0.243188i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.26868 | − | 9.12563i | −0.316565 | − | 0.548306i | 0.663204 | − | 0.748438i | \(-0.269196\pi\) |
−0.979769 | + | 0.200133i | \(0.935863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.1967 | + | 0.841992i | 1.38875 | + | 0.0504087i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.2208i | 1.14662i | 0.819339 | + | 0.573309i | \(0.194340\pi\) | ||||
−0.819339 | + | 0.573309i | \(0.805660\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5733 | − | 8.99126i | 0.925738 | − | 0.534475i | 0.0402770 | − | 0.999189i | \(-0.487176\pi\) |
0.885461 | + | 0.464713i | \(0.153843\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.93135 | − | 5.44939i | −0.173032 | − | 0.321667i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.48802 | − | 14.7017i | 0.499296 | − | 0.864805i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.04973 | − | 7.12974i | 0.120157 | − | 0.417953i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.2153 | −1.47309 | −0.736546 | − | 0.676388i | \(-0.763544\pi\) | ||||
−0.736546 | + | 0.676388i | \(0.763544\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26.4500 | − | 8.65449i | −1.53478 | − | 0.502184i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.4019 | + | 21.4808i | −0.717223 | + | 1.24227i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.23396 | − | 4.15294i | −0.128764 | − | 0.239372i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.54726 | − | 10.2465i | −0.146336 | − | 0.588646i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.28693i | − | 0.472960i | −0.971636 | − | 0.236480i | \(-0.924006\pi\) | ||
0.971636 | − | 0.236480i | \(-0.0759938\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.18029 | + | 5.37173i | 0.294696 | + | 0.305587i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.28958 | − | 7.42977i | −0.243240 | − | 0.421304i | 0.718395 | − | 0.695635i | \(-0.244877\pi\) |
−0.961635 | + | 0.274331i | \(0.911544\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.807839 | + | 0.466406i | 0.0456617 | + | 0.0263628i | 0.522657 | − | 0.852543i | \(-0.324941\pi\) |
−0.476995 | + | 0.878906i | \(0.658274\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.58262 | − | 1.49108i | −0.145054 | − | 0.0837472i | 0.425716 | − | 0.904857i | \(-0.360022\pi\) |
−0.570771 | + | 0.821109i | \(0.693355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.6227 | − | 47.8440i | −1.54658 | − | 2.67875i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.9334 | + | 20.6701i | 1.11258 | + | 1.15369i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.608446i | − | 0.0338549i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.60817 | − | 6.46895i | −0.0889317 | − | 0.357734i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.52665 | + | 0.286602i | 0.525221 | + | 0.0158009i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9541 | − | 18.9730i | 0.602091 | − | 1.04285i | −0.390413 | − | 0.920640i | \(-0.627668\pi\) |
0.992504 | − | 0.122213i | \(-0.0389990\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27.7840 | + | 14.7240i | −1.52255 | + | 0.806871i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 36.4696 | 1.98663 | 0.993314 | − | 0.115448i | \(-0.0368304\pi\) | ||||
0.993314 | + | 0.115448i | \(0.0368304\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.75826 | + | 16.5511i | −0.258433 | + | 0.898930i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.7200 | + | 35.8881i | −1.12205 | + | 1.94345i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4449 | + | 1.66873i | 0.995932 | + | 0.0901031i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.62881 | − | 2.09509i | 0.194805 | − | 0.112471i | −0.399425 | − | 0.916766i | \(-0.630790\pi\) |
0.594230 | + | 0.804295i | \(0.297457\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.2897i | 1.19314i | 0.802560 | + | 0.596571i | \(0.203470\pi\) | ||||
−0.802560 | + | 0.596571i | \(0.796530\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.0035 | + | 14.3499i | −0.854203 | + | 0.765943i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.72220 | + | 15.1073i | 0.464236 | + | 0.804080i | 0.999167 | − | 0.0408157i | \(-0.0129956\pi\) |
−0.534931 | + | 0.844896i | \(0.679662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.525062 | − | 0.476723i | 0.0277892 | − | 0.0252308i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.2564 | − | 14.5818i | −1.33298 | − | 0.769599i | −0.347228 | − | 0.937781i | \(-0.612877\pi\) |
−0.985756 | + | 0.168182i | \(0.946210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.77133 | − | 3.06803i | −0.0932279 | − | 0.161476i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.0493 | − | 21.2634i | 1.15729 | − | 1.11604i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.1633 | − | 13.3734i | 1.20912 | − | 0.698084i | 0.246550 | − | 0.969130i | \(-0.420703\pi\) |
0.962566 | + | 0.271046i | \(0.0873696\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.94503 | + | 3.72625i | 0.309486 | + | 0.193981i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.1603 | + | 6.89898i | 0.579414 | + | 0.358177i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.56718 | − | 4.44649i | 0.132924 | − | 0.230231i | −0.791879 | − | 0.610678i | \(-0.790897\pi\) |
0.924802 | + | 0.380448i | \(0.124230\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −42.6699 | −2.19761 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3320 | −0.890284 | −0.445142 | − | 0.895460i | \(-0.646847\pi\) | ||||
−0.445142 | + | 0.895460i | \(0.646847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.73172 | − | 2.22279i | −0.396108 | − | 0.113877i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.8457 | + | 18.7852i | −0.554188 | + | 0.959881i | 0.443779 | + | 0.896136i | \(0.353638\pi\) |
−0.997966 | + | 0.0637447i | \(0.979696\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.53067 | + | 2.83975i | 0.230307 | + | 0.144353i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.6759 | + | 6.74110i | −0.591993 | + | 0.341787i | −0.765885 | − | 0.642977i | \(-0.777699\pi\) |
0.173892 | + | 0.984765i | \(0.444366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.927941i | 0.0469280i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.26396 | + | 7.96943i | −0.416861 | + | 0.402005i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.8800 | + | 6.85891i | 0.596240 | + | 0.344239i | 0.767561 | − | 0.640976i | \(-0.221470\pi\) |
−0.171321 | + | 0.985215i | \(0.554804\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.49644 | + | 17.1579i | −0.275166 | + | 0.858969i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.4976 | + | 9.52487i | 0.823849 | + | 0.475649i | 0.851742 | − | 0.523962i | \(-0.175547\pi\) |
−0.0278932 | + | 0.999611i | \(0.508880\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.0035 | + | 27.7189i | 0.797191 | + | 1.38078i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 56.1371i | − | 2.78261i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.1428 | − | 17.4030i | 1.49047 | − | 0.860521i | 0.490526 | − | 0.871427i | \(-0.336805\pi\) |
0.999941 | + | 0.0109054i | \(0.00347135\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.92652 | − | 1.97051i | 0.390986 | − | 0.0971983i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.6633 | − | 23.7205i | 0.721535 | − | 1.16721i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.57637 | + | 15.9184i | −0.224106 | + | 0.779526i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.7934 | 0.966971 | 0.483486 | − | 0.875352i | \(-0.339371\pi\) | ||||
0.483486 | + | 0.875352i | \(0.339371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2279 | −0.595951 | −0.297975 | − | 0.954574i | \(-0.596311\pi\) | ||||
−0.297975 | + | 0.954574i | \(0.596311\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.54906 | + | 5.06049i | −0.464291 | + | 0.246050i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.299122 | + | 9.94282i | −0.0144755 | + | 0.481167i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.25806 | − | 37.2411i | −0.446983 | − | 1.79802i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.22781 | − | 5.32768i | 0.444488 | − | 0.256625i | −0.261012 | − | 0.965336i | \(-0.584056\pi\) |
0.705499 | + | 0.708711i | \(0.250723\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.5027i | 1.22558i | 0.790245 | + | 0.612791i | \(0.209953\pi\) | ||||
−0.790245 | + | 0.612791i | \(0.790047\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.7870 | − | 20.4157i | −0.563848 | − | 0.976613i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.8206 | + | 13.7528i | 1.13689 | + | 0.656386i | 0.945660 | − | 0.325158i | \(-0.105418\pi\) |
0.191234 | + | 0.981544i | \(0.438751\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.1130 | + | 8.70016i | −0.910143 | + | 0.414294i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.7785 | − | 9.68708i | −0.797171 | − | 0.460247i | 0.0453099 | − | 0.998973i | \(-0.485572\pi\) |
−0.842481 | + | 0.538726i | \(0.818906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.4816 | − | 25.3864i | −1.15794 | − | 1.20073i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.9504i | 1.27187i | 0.771744 | + | 0.635934i | \(0.219385\pi\) | ||||
−0.771744 | + | 0.635934i | \(0.780615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8479 | + | 6.26304i | −0.510808 | + | 0.294915i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.75861 | − | 19.1418i | −0.223579 | − | 0.899362i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.18704 | − | 15.9124i | 0.429752 | − | 0.744352i | −0.567099 | − | 0.823649i | \(-0.691934\pi\) |
0.996851 | + | 0.0792977i | \(0.0252678\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.250073 | + | 0.764277i | −0.0116724 | + | 0.0356734i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.2344 | 0.569814 | 0.284907 | − | 0.958555i | \(-0.408037\pi\) | ||||
0.284907 | + | 0.958555i | \(0.408037\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4136 | 0.530433 | 0.265217 | − | 0.964189i | \(-0.414556\pi\) | ||||
0.265217 | + | 0.964189i | \(0.414556\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.665893 | + | 1.15336i | −0.0308138 | + | 0.0533711i | −0.881021 | − | 0.473077i | \(-0.843143\pi\) |
0.850207 | + | 0.526448i | \(0.176477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.23728 | − | 2.00152i | 0.0571325 | − | 0.0924218i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.4506 | − | 2.84659i | 0.527616 | − | 0.131164i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.26712 | + | 4.77302i | −0.380123 | + | 0.219464i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.8675 | − | 0.539659i | −0.680736 | − | 0.0247093i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.7342 | − | 18.5922i | −0.490458 | − | 0.849498i | 0.509482 | − | 0.860481i | \(-0.329837\pi\) |
−0.999940 | + | 0.0109835i | \(0.996504\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.5496 | − | 21.6793i | −1.71212 | − | 0.988491i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.38261 | − | 26.1675i | 0.381422 | − | 1.19066i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.8630 | − | 24.0115i | −0.628195 | − | 1.08807i | −0.987914 | − | 0.155004i | \(-0.950461\pi\) |
0.359719 | − | 0.933061i | \(-0.382873\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.86409 | + | 9.51254i | −0.446070 | + | 0.430172i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.536100i | 0.0241938i | 0.999927 | + | 0.0120969i | \(0.00385066\pi\) | ||||
−0.999927 | + | 0.0120969i | \(0.996149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.38246 | + | 0.798164i | −0.0622629 | + | 0.0359475i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.0749 | + | 14.5642i | −1.21447 | + | 0.653293i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.1191 | − | 26.1870i | 0.676823 | − | 1.17229i | −0.299110 | − | 0.954219i | \(-0.596690\pi\) |
0.975933 | − | 0.218072i | \(-0.0699769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.0452 | − | 9.21267i | −1.43167 | − | 0.411592i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.5176 | 1.44989 | 0.724945 | − | 0.688807i | \(-0.241865\pi\) | ||||
0.724945 | + | 0.688807i | \(0.241865\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.84547 | − | 1.96800i | −0.304018 | − | 0.0874021i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.1885 | − | 22.8432i | 0.584570 | − | 1.01251i | −0.410359 | − | 0.911924i | \(-0.634597\pi\) |
0.994929 | − | 0.100581i | \(-0.0320702\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.5705 | + | 17.0433i | 1.21965 | + | 0.753952i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.20621 | − | 19.9914i | −0.185709 | − | 0.882642i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 19.2938i | − | 0.848538i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.6324 | + | 17.0040i | −0.773977 | + | 0.746393i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.39842 | + | 9.35035i | 0.236509 | + | 0.409646i | 0.959710 | − | 0.280992i | \(-0.0906633\pi\) |
−0.723201 | + | 0.690638i | \(0.757330\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.206455 | + | 0.119197i | 0.00902764 | + | 0.00521211i | 0.504507 | − | 0.863408i | \(-0.331674\pi\) |
−0.495479 | + | 0.868620i | \(0.665008\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.03699 | + | 0.598708i | 0.0451721 | + | 0.0260801i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.47632 | + | 11.2173i | 0.281579 | + | 0.487709i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.14701 | + | 31.5999i | −0.0497760 | + | 1.37132i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.67476i | 0.419061i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.48602 | − | 0.866616i | 0.150433 | − | 0.0373972i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.25374 | − | 37.4232i | 0.0970753 | − | 1.61193i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.28056 | + | 2.21799i | −0.0550555 | + | 0.0953588i | −0.892240 | − | 0.451562i | \(-0.850867\pi\) |
0.837184 | + | 0.546921i | \(0.184200\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.4040 | − | 36.1891i | 0.446479 | − | 1.55302i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.1549 | 1.16106 | 0.580529 | − | 0.814239i | \(-0.302846\pi\) | ||||
0.580529 | + | 0.814239i | \(0.302846\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.28156 | − | 9.96621i | −0.225411 | − | 0.425348i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.2770 | − | 35.1209i | 0.863831 | − | 1.49620i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.1015 | − | 0.574652i | −0.812277 | − | 0.0244367i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.7984 | − | 12.0080i | 0.881257 | − | 0.508794i | 0.0101846 | − | 0.999948i | \(-0.496758\pi\) |
0.871073 | + | 0.491154i | \(0.163425\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.37308i | 0.311848i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.996567 | − | 1.03340i | −0.0420751 | − | 0.0436300i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.1487 | − | 34.8986i | −0.849168 | − | 1.47080i | −0.881952 | − | 0.471340i | \(-0.843771\pi\) |
0.0327839 | − | 0.999462i | \(-0.489563\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.9561 | − | 19.2932i | 0.586101 | − | 0.810238i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.46883 | + | 2.58008i | 0.187343 | + | 0.108163i | 0.590738 | − | 0.806863i | \(-0.298837\pi\) |
−0.403395 | + | 0.915026i | \(0.632170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.841937 | + | 1.45828i | 0.0352340 | + | 0.0610270i | 0.883105 | − | 0.469176i | \(-0.155449\pi\) |
−0.847871 | + | 0.530203i | \(0.822116\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.78620 | + | 2.88916i | 0.116395 | + | 0.120697i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.5104 | − | 14.7284i | 1.06201 | − | 0.613153i | 0.136024 | − | 0.990706i | \(-0.456568\pi\) |
0.925988 | + | 0.377552i | \(0.123234\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.46477 | − | 30.0275i | −0.310225 | − | 1.24790i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.44461 | − | 11.9806i | −0.267368 | − | 0.497037i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.2801 | − | 23.0018i | 0.550006 | − | 0.952638i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.9862 | 1.89805 | 0.949027 | − | 0.315195i | \(-0.102070\pi\) | ||||
0.949027 | + | 0.315195i | \(0.102070\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.4199 | −1.25343 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.79834 | + | 30.6040i | −0.361915 | + | 1.25888i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.954084 | − | 1.65252i | 0.0391795 | − | 0.0678610i | −0.845771 | − | 0.533547i | \(-0.820859\pi\) |
0.884950 | + | 0.465686i | \(0.154192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.31438 | + | 0.823948i | −0.135649 | + | 0.0337219i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.2188 | + | 10.5186i | −0.744401 | + | 0.429780i | −0.823667 | − | 0.567073i | \(-0.808076\pi\) |
0.0792661 | + | 0.996853i | \(0.474742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.3573i | 1.23830i | 0.785273 | + | 0.619150i | \(0.212523\pi\) | ||||
−0.785273 | + | 0.619150i | \(0.787477\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0967842 | + | 2.66638i | −0.00394136 | + | 0.108583i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.4049 | + | 8.89399i | 0.625264 | + | 0.360996i | 0.778915 | − | 0.627129i | \(-0.215770\pi\) |
−0.153652 | + | 0.988125i | \(0.549103\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 46.1950 | − | 10.0193i | 1.87192 | − | 0.406002i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.9054 | − | 7.45095i | −0.522098 | − | 0.301433i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.5074 | − | 25.1276i | −0.585950 | − | 1.01490i | −0.994756 | − | 0.102274i | \(-0.967388\pi\) |
0.408806 | − | 0.912621i | \(-0.365945\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.32967i | 0.134047i | 0.997751 | + | 0.0670237i | \(0.0213503\pi\) | ||||
−0.997751 | + | 0.0670237i | \(0.978650\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.6135 | − | 24.0256i | 1.67259 | − | 0.965669i | 0.706406 | − | 0.707806i | \(-0.250315\pi\) |
0.966182 | − | 0.257863i | \(-0.0830182\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.41489 | + | 30.4889i | 0.257421 | + | 1.22348i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.4032 | − | 1.36592i | −1.81904 | − | 0.0547244i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 35.0520 | + | 10.0771i | 1.39984 | + | 0.402441i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.62209 | −0.0646771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.8726 | 0.631878 | 0.315939 | − | 0.948779i | \(-0.397680\pi\) | ||||
0.315939 | + | 0.948779i | \(0.397680\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.79726 | + | 0.516694i | 0.0714347 | + | 0.0205368i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.1617 | − | 15.9598i | −0.957322 | − | 0.632350i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.5136 | − | 29.5374i | 0.732385 | − | 1.16848i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.34785 | + | 1.93288i | −0.132232 | + | 0.0763443i | −0.564657 | − | 0.825326i | \(-0.690991\pi\) |
0.432425 | + | 0.901670i | \(0.357658\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.7423i | 1.48841i | 0.667950 | + | 0.744206i | \(0.267172\pi\) | ||||
−0.667950 | + | 0.744206i | \(0.732828\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.9230 | + | 18.9193i | 0.429429 | + | 0.743793i | 0.996823 | − | 0.0796536i | \(-0.0253814\pi\) |
−0.567393 | + | 0.823447i | \(0.692048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.8888 | − | 28.2260i | −1.91905 | − | 1.10797i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.8342 | − | 26.2510i | −0.934138 | − | 1.02886i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.14321 | − | 1.81473i | −0.123003 | − | 0.0710159i | 0.437236 | − | 0.899347i | \(-0.355957\pi\) |
−0.560239 | + | 0.828331i | \(0.689291\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.7288 | − | 1.33318i | −1.43293 | − | 0.0520123i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22.4040i | − | 0.872737i | −0.899768 | − | 0.436369i | \(-0.856264\pi\) | ||
0.899768 | − | 0.436369i | \(-0.143736\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6525 | − | 7.88230i | 0.531023 | − | 0.306586i | −0.210410 | − | 0.977613i | \(-0.567480\pi\) |
0.741433 | + | 0.671027i | \(0.234147\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.07609 | + | 0.267513i | −0.0417919 | + | 0.0103894i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.9245 | + | 53.5628i | −1.19740 | + | 2.07396i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.36227 | + | 25.6088i | −0.284642 | + | 0.990094i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.1366 | 0.777365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.84031 | 0.340769 | 0.170385 | − | 0.985378i | \(-0.445499\pi\) | ||||
0.170385 | + | 0.985378i | \(0.445499\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.82417 | + | 13.5519i | −0.300707 | + | 0.520840i | −0.976296 | − | 0.216438i | \(-0.930556\pi\) |
0.675589 | + | 0.737278i | \(0.263889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.97974 | + | 5.36833i | −0.382987 | + | 0.206018i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.815180 | − | 3.27911i | −0.0312378 | − | 0.125656i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.7691 | + | 18.9193i | −1.25388 | + | 0.723926i | −0.971877 | − | 0.235489i | \(-0.924331\pi\) |
−0.281999 | + | 0.959415i | \(0.590998\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.39793 | + | 3.52351i | 0.129639 | + | 0.134430i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.2572 | − | 17.7659i | −0.390766 | − | 0.676827i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5792 | − | 8.41732i | −0.554620 | − | 0.320210i | 0.196363 | − | 0.980531i | \(-0.437087\pi\) |
−0.750983 | + | 0.660321i | \(0.770420\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.7675 | + | 38.1438i | 0.712917 | + | 1.44896i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.180972 | + | 0.313452i | 0.00685480 | + | 0.0118729i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.27972 | + | 5.47484i | 0.199697 | + | 0.207077i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.2554i | 1.06719i | 0.845740 | + | 0.533596i | \(0.179160\pi\) | ||||
−0.845740 | + | 0.533596i | \(0.820840\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.6877 | − | 20.6043i | 1.34599 | − | 0.777106i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.48046 | + | 13.7186i | −0.318940 | + | 0.515942i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.40632 | + | 12.8281i | −0.278150 | + | 0.481770i | −0.970925 | − | 0.239384i | \(-0.923055\pi\) |
0.692775 | + | 0.721154i | \(0.256388\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.1464 | − | 10.1466i | 0.718046 | − | 0.380526i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 46.3934 | 1.73744 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.45734 | + | 29.4179i | −0.315845 | + | 1.09863i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.1406 | + | 17.5640i | −0.378179 | + | 0.655025i | −0.990797 | − | 0.135353i | \(-0.956783\pi\) |
0.612618 | + | 0.790379i | \(0.290116\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.342786 | − | 11.3942i | 0.0127660 | − | 0.424342i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.16488 | + | 1.78117i | −0.266465 | + | 0.0662425i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.81854i | − | 0.104534i | −0.998633 | − | 0.0522670i | \(-0.983355\pi\) | ||
0.998633 | − | 0.0522670i | \(-0.0166447\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.93304 | + | 26.8402i | −0.108631 | + | 0.994082i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.137917 | + | 0.238880i | 0.00510106 | + | 0.00883530i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.2169 | − | 17.4457i | −1.11609 | − | 0.644372i | −0.175687 | − | 0.984446i | \(-0.556215\pi\) |
−0.940399 | + | 0.340074i | \(0.889548\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.12522 | − | 2.38170i | −0.151954 | − | 0.0877309i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.4220 | + | 23.2476i | 0.493737 | + | 0.855177i | 0.999974 | − | 0.00721695i | \(-0.00229725\pi\) |
−0.506237 | + | 0.862394i | \(0.668964\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.2770 | − | 19.5544i | 0.744896 | − | 0.718348i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.24499i | 0.0823607i | 0.999152 | + | 0.0411804i | \(0.0131118\pi\) | ||||
−0.999152 | + | 0.0411804i | \(0.986888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.0702 | + | 8.19220i | 0.478215 | + | 0.299737i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.31902 | − | 43.8442i | 0.0481959 | − | 1.60203i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.56634 | + | 2.71297i | −0.0571564 | + | 0.0989978i | −0.893188 | − | 0.449684i | \(-0.851537\pi\) |
0.836031 | + | 0.548682i | \(0.184870\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.45575 | + | 1.85596i | 0.235261 | + | 0.0676350i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.5473 | 0.928532 | 0.464266 | − | 0.885696i | \(-0.346318\pi\) | ||||
0.464266 | + | 0.885696i | \(0.346318\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −53.4578 | − | 15.3686i | −1.94040 | − | 0.557844i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.16163 | − | 3.74406i | 0.0783591 | − | 0.135722i | −0.824183 | − | 0.566324i | \(-0.808365\pi\) |
0.902542 | + | 0.430602i | \(0.141699\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.35399 | + | 8.66100i | −0.193827 | + | 0.313549i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.7603 | + | 21.8009i | −1.36344 | + | 0.787185i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.4529i | 1.24240i | 0.783650 | + | 0.621202i | \(0.213355\pi\) | ||||
−0.783650 | + | 0.621202i | \(0.786645\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.0817 | − | 21.2947i | 0.795253 | − | 0.766911i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.19273 | + | 8.99408i | 0.186770 | + | 0.323494i | 0.944171 | − | 0.329455i | \(-0.106865\pi\) |
−0.757402 | + | 0.652949i | \(0.773532\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 45.7422 | + | 14.6533i | 1.64099 | + | 0.525683i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.96313 | − | 4.59752i | −0.285309 | − | 0.164723i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.1174 | + | 53.8970i | 1.11347 | + | 1.92859i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −39.9050 | + | 35.7819i | −1.42609 | + | 1.27874i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.1681 | + | 21.4590i | −1.32490 | + | 0.764931i | −0.984506 | − | 0.175352i | \(-0.943894\pi\) |
−0.340394 | + | 0.940283i | \(0.610560\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.41178 | − | 2.33975i | 0.335068 | − | 0.0832972i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.1671 | − | 12.4621i | 0.823726 | − | 0.443101i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.77645 | − | 13.4692i | 0.276150 | − | 0.478306i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.3628 | −0.685866 | −0.342933 | − | 0.939360i | \(-0.611420\pi\) | ||||
−0.342933 | + | 0.939360i | \(0.611420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.557497 | −0.0197228 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 45.5101 | − | 24.1179i | 1.60802 | − | 0.852164i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.8073 | − | 56.8239i | 1.15774 | − | 2.00527i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.13158 | − | 28.6872i | −0.251043 | − | 1.00984i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.120667 | − | 0.0696669i | 0.00424241 | − | 0.00244936i | −0.497877 | − | 0.867247i | \(-0.665887\pi\) |
0.502120 | + | 0.864798i | \(0.332554\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 43.5559i | − | 1.52945i | −0.644354 | − | 0.764727i | \(-0.722874\pi\) | ||
0.644354 | − | 0.764727i | \(-0.277126\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.5002 | + | 21.2578i | 0.718973 | + | 0.745543i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.06865 | − | 3.50374i | −0.212315 | − | 0.122580i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 32.7618 | + | 2.17718i | 1.14479 | + | 0.0760767i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.9212 | − | 23.0485i | −1.39326 | − | 0.804400i | −0.399586 | − | 0.916696i | \(-0.630846\pi\) |
−0.993675 | + | 0.112296i | \(0.964180\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2425 | − | 19.4726i | −0.391889 | − | 0.678772i | 0.600809 | − | 0.799392i | \(-0.294845\pi\) |
−0.992699 | + | 0.120620i | \(0.961512\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 52.2536i | − | 1.81704i | −0.417846 | − | 0.908518i | \(-0.637215\pi\) | ||
0.417846 | − | 0.908518i | \(-0.362785\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.26705 | − | 1.88623i | 0.113469 | − | 0.0655115i | −0.442191 | − | 0.896921i | \(-0.645799\pi\) |
0.555661 | + | 0.831409i | \(0.312465\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.40320 | − | 17.7121i | −0.152745 | − | 0.614428i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.08135 | − | 0.0651222i | −0.0374666 | − | 0.00225635i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.2108 | + | 12.5027i | 1.32076 | + | 0.432155i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.7191 | 1.40578 | 0.702890 | − | 0.711299i | \(-0.251893\pi\) | ||||
0.702890 | + | 0.711299i | \(0.251893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −77.3983 | −2.66891 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.19837 | + | 31.9955i | −0.316809 | + | 1.10198i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −46.7696 | − | 1.40703i | −1.60702 | − | 0.0483460i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.2266 | − | 7.51427i | 1.03738 | − | 0.257889i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −54.4273 | + | 31.4236i | −1.86574 | + | 1.07719i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.21298i | − | 0.110010i | −0.998486 | − | 0.0550051i | \(-0.982482\pi\) | ||
0.998486 | − | 0.0550051i | \(-0.0175175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0555 | + | 41.6653i | 0.821720 | + | 1.42326i | 0.904400 | + | 0.426685i | \(0.140319\pi\) |
−0.0826803 | + | 0.996576i | \(0.526348\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.4266 | + | 6.01978i | 0.355750 | + | 0.205392i | 0.667215 | − | 0.744865i | \(-0.267486\pi\) |
−0.311465 | + | 0.950258i | \(0.600820\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.27173 | − | 10.4740i | −0.0774202 | − | 0.356954i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.51239 | − | 3.75993i | −0.221684 | − | 0.127989i | 0.385046 | − | 0.922898i | \(-0.374186\pi\) |
−0.606730 | + | 0.794908i | \(0.707519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.1651 | − | 20.4108i | 0.718803 | − | 0.693186i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 38.6851i | 1.31230i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.18619 | + | 1.83955i | −0.107960 | + | 0.0623308i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.82406 | − | 10.8874i | 0.230959 | − | 0.368484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.6367 | + | 28.8156i | −0.561781 | + | 0.973033i | 0.435560 | + | 0.900160i | \(0.356550\pi\) |
−0.997341 | + | 0.0728736i | \(0.976783\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.9740 | − | 12.0671i | −1.41575 | − | 0.407013i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.9614 | −0.672515 | −0.336258 | − | 0.941770i | \(-0.609161\pi\) | ||||
−0.336258 | + | 0.941770i | \(0.609161\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.3120 | −1.72679 | −0.863393 | − | 0.504533i | \(-0.831665\pi\) | ||||
−0.863393 | + | 0.504533i | \(0.831665\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.94659 | + | 17.2280i | −0.333974 | + | 0.578460i | −0.983287 | − | 0.182061i | \(-0.941723\pi\) |
0.649313 | + | 0.760521i | \(0.275056\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.82158 | + | 10.8223i | 0.195250 | + | 0.362970i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −39.8876 | − | 27.0645i | −1.33628 | − | 0.906694i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.2655 | − | 7.08149i | 0.410450 | − | 0.236973i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.9245 | + | 29.8224i | −1.03254 | + | 0.995740i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.9050 | + | 69.1176i | 1.33091 | + | 2.30520i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.664642 | − | 0.383731i | −0.0221424 | − | 0.0127839i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.73127 | − | 7.98219i | −0.0576130 | − | 0.265631i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.4200 | − | 37.1005i | −0.711239 | − | 1.23190i | −0.964392 | − | 0.264476i | \(-0.914801\pi\) |
0.253153 | − | 0.967426i | \(-0.418532\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.663367 | − | 18.2756i | 0.0220025 | − | 0.606164i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.5359i | 0.945437i | 0.881213 | + | 0.472719i | \(0.156727\pi\) | ||||
−0.881213 | + | 0.472719i | \(0.843273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.8493 | + | 13.7694i | −0.789296 | + | 0.455700i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.5290 | + | 0.527347i | 0.578859 | + | 0.0174145i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.41160 | − | 7.64112i | 0.145525 | − | 0.252057i | −0.784043 | − | 0.620706i | \(-0.786846\pi\) |
0.929569 | + | 0.368649i | \(0.120179\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.96582 | − | 13.7946i | 0.130678 | − | 0.454549i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.0683 | 1.58219 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.05253 | + | 11.4210i | 0.198791 | + | 0.375115i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.1691 | + | 47.0583i | −0.891389 | + | 1.54393i | −0.0531782 | + | 0.998585i | \(0.516935\pi\) |
−0.838211 | + | 0.545346i | \(0.816398\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.6180 | − | 12.3029i | 0.806824 | − | 0.403211i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.58493 | − | 14.4206i | −0.117365 | − | 0.472110i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.3198i | 0.533144i | 0.963815 | + | 0.266572i | \(0.0858911\pi\) | ||||
−0.963815 | + | 0.266572i | \(0.914109\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.12154 | + | 1.16299i | 0.0366002 | + | 0.0379528i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.80594 | − | 6.59208i | −0.124070 | − | 0.214896i | 0.797299 | − | 0.603585i | \(-0.206261\pi\) |
−0.921369 | + | 0.388689i | \(0.872928\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.1446 | + | 7.01167i | 0.395481 | + | 0.228331i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.9034 | + | 11.4912i | 0.646774 | + | 0.373415i | 0.787219 | − | 0.616673i | \(-0.211520\pi\) |
−0.140445 | + | 0.990088i | \(0.544853\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.3394 | − | 43.8891i | −0.822551 | − | 1.42470i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.58552 | − | 3.71803i | −0.116269 | − | 0.120565i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.5633i | 1.31397i | 0.753902 | + | 0.656986i | \(0.228169\pi\) | ||||
−0.753902 | + | 0.656986i | \(0.771831\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.0852 | − | 92.8615i | −0.746237 | − | 3.00179i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.6125 | − | 6.56034i | −0.342695 | − | 0.211844i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.4330 | − | 24.9988i | 0.465582 | − | 0.806412i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 23.2898 | + | 43.9474i | 0.750502 | + | 1.41618i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.10140 | −0.0997343 | −0.0498672 | − | 0.998756i | \(-0.515880\pi\) | ||||
−0.0498672 | + | 0.998756i | \(0.515880\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.291180 | − | 1.01284i | 0.00935404 | − | 0.0325370i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.5212 | − | 39.0078i | 0.722739 | − | 1.25182i | −0.237159 | − | 0.971471i | \(-0.576216\pi\) |
0.959898 | − | 0.280350i | \(-0.0904505\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.2815 | − | 11.9857i | 0.714311 | − | 0.384244i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.8598 | − | 12.6207i | 0.699356 | − | 0.403773i | −0.107751 | − | 0.994178i | \(-0.534365\pi\) |
0.807108 | + | 0.590404i | \(0.201032\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 91.9525i | 2.93881i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.418805 | − | 11.5380i | 0.0133714 | − | 0.368379i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.1759 | + | 52.2661i | 0.962461 | + | 1.66703i | 0.716288 | + | 0.697805i | \(0.245840\pi\) |
0.246173 | + | 0.969226i | \(0.420827\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.7211 | + | 5.03618i | 0.500409 | + | 0.160303i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.25530 | + | 5.34355i | 0.294301 | + | 0.169915i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.93445 | + | 8.54672i | 0.156748 | + | 0.271495i | 0.933694 | − | 0.358072i | \(-0.116566\pi\) |
−0.776946 | + | 0.629567i | \(0.783232\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.3142 | − | 26.3408i | 0.866792 | − | 0.835900i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.3385 | − | 13.4745i | 0.739138 | − | 0.426742i | −0.0826177 | − | 0.996581i | \(-0.526328\pi\) |
0.821756 | + | 0.569840i | \(0.192995\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −53.2962 | + | 11.2136i | −1.68622 | + | 0.354782i |
(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 | 2100.2.bi.l.1601.8 | yes | 16 | |
3.2 | odd | 2 | inner | 2100.2.bi.l.1601.6 | yes | 16 | |
5.2 | odd | 4 | 2100.2.bo.i.1349.10 | 32 | |||
5.3 | odd | 4 | 2100.2.bo.i.1349.7 | 32 | |||
5.4 | even | 2 | 2100.2.bi.m.1601.1 | yes | 16 | ||
7.3 | odd | 6 | inner | 2100.2.bi.l.101.6 | ✓ | 16 | |
15.2 | even | 4 | 2100.2.bo.i.1349.2 | 32 | |||
15.8 | even | 4 | 2100.2.bo.i.1349.15 | 32 | |||
15.14 | odd | 2 | 2100.2.bi.m.1601.3 | yes | 16 | ||
21.17 | even | 6 | inner | 2100.2.bi.l.101.8 | yes | 16 | |
35.3 | even | 12 | 2100.2.bo.i.1949.2 | 32 | |||
35.17 | even | 12 | 2100.2.bo.i.1949.15 | 32 | |||
35.24 | odd | 6 | 2100.2.bi.m.101.3 | yes | 16 | ||
105.17 | odd | 12 | 2100.2.bo.i.1949.7 | 32 | |||
105.38 | odd | 12 | 2100.2.bo.i.1949.10 | 32 | |||
105.59 | even | 6 | 2100.2.bi.m.101.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.bi.l.101.6 | ✓ | 16 | 7.3 | odd | 6 | inner | |
2100.2.bi.l.101.8 | yes | 16 | 21.17 | even | 6 | inner | |
2100.2.bi.l.1601.6 | yes | 16 | 3.2 | odd | 2 | inner | |
2100.2.bi.l.1601.8 | yes | 16 | 1.1 | even | 1 | trivial | |
2100.2.bi.m.101.1 | yes | 16 | 105.59 | even | 6 | ||
2100.2.bi.m.101.3 | yes | 16 | 35.24 | odd | 6 | ||
2100.2.bi.m.1601.1 | yes | 16 | 5.4 | even | 2 | ||
2100.2.bi.m.1601.3 | yes | 16 | 15.14 | odd | 2 | ||
2100.2.bo.i.1349.2 | 32 | 15.2 | even | 4 | |||
2100.2.bo.i.1349.7 | 32 | 5.3 | odd | 4 | |||
2100.2.bo.i.1349.10 | 32 | 5.2 | odd | 4 | |||
2100.2.bo.i.1349.15 | 32 | 15.8 | even | 4 | |||
2100.2.bo.i.1949.2 | 32 | 35.3 | even | 12 | |||
2100.2.bo.i.1949.7 | 32 | 105.17 | odd | 12 | |||
2100.2.bo.i.1949.10 | 32 | 105.38 | odd | 12 | |||
2100.2.bo.i.1949.15 | 32 | 35.17 | even | 12 |