Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(149,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.u (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.11 | ||
Character | \(\chi\) | \(=\) | 900.149 |
Dual form | 900.3.u.d.749.11 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.28947 | + | 2.70874i | 0.429825 | + | 0.902912i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.36178 | − | 5.40503i | 1.33740 | − | 0.772147i | 0.350977 | − | 0.936384i | \(-0.385850\pi\) |
0.986421 | + | 0.164237i | \(0.0525162\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.67451 | + | 6.98569i | −0.630501 | + | 0.776188i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.78876 | − | 4.49684i | 0.708069 | − | 0.408804i | −0.102277 | − | 0.994756i | \(-0.532613\pi\) |
0.810346 | + | 0.585952i | \(0.199279\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.96157 | + | 2.28721i | 0.304736 | + | 0.175939i | 0.644568 | − | 0.764547i | \(-0.277037\pi\) |
−0.339833 | + | 0.940486i | \(0.610370\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.55187 | 0.444227 | 0.222114 | − | 0.975021i | \(-0.428704\pi\) | ||||
0.222114 | + | 0.975021i | \(0.428704\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.73166 | −0.459561 | −0.229780 | − | 0.973242i | \(-0.573801\pi\) | ||||
−0.229780 | + | 0.973242i | \(0.573801\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 26.7126 | + | 18.3890i | 1.27203 | + | 0.875665i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.02351 | − | 6.96892i | 0.174935 | − | 0.302997i | −0.765204 | − | 0.643788i | \(-0.777362\pi\) |
0.940139 | + | 0.340792i | \(0.110695\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −26.2395 | − | 6.36289i | −0.971835 | − | 0.235663i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 38.2046 | − | 22.0575i | 1.31740 | − | 0.760602i | 0.334092 | − | 0.942541i | \(-0.391571\pi\) |
0.983310 | + | 0.181939i | \(0.0582372\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.53586 | − | 7.85634i | 0.146318 | − | 0.253430i | −0.783546 | − | 0.621334i | \(-0.786591\pi\) |
0.929864 | + | 0.367904i | \(0.119924\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 22.2242 | + | 15.2991i | 0.673459 | + | 0.463610i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 56.1237i | − | 1.51686i | −0.651756 | − | 0.758428i | \(-0.725968\pi\) | ||
0.651756 | − | 0.758428i | \(-0.274032\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.08712 | + | 13.6801i | −0.0278748 | + | 0.350773i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 53.9651 | + | 31.1568i | 1.31622 | + | 0.759921i | 0.983119 | − | 0.182969i | \(-0.0585709\pi\) |
0.333103 | + | 0.942890i | \(0.391904\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −34.7294 | + | 20.0510i | −0.807660 | + | 0.466303i | −0.846143 | − | 0.532957i | \(-0.821081\pi\) |
0.0384827 | + | 0.999259i | \(0.487748\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.10452 | + | 15.7695i | 0.193713 | + | 0.335521i | 0.946478 | − | 0.322769i | \(-0.104614\pi\) |
−0.752765 | + | 0.658290i | \(0.771280\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 33.9287 | − | 58.7662i | 0.692422 | − | 1.19931i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.73794 | + | 20.4560i | 0.190940 | + | 0.401098i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −23.7994 | −0.449045 | −0.224522 | − | 0.974469i | \(-0.572082\pi\) | ||||
−0.224522 | + | 0.974469i | \(0.572082\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.2592 | − | 23.6518i | −0.197531 | − | 0.414943i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 59.3003 | + | 34.2370i | 1.00509 | + | 0.580289i | 0.909750 | − | 0.415156i | \(-0.136273\pi\) |
0.0953396 | + | 0.995445i | \(0.469606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16.3946 | + | 28.3963i | 0.268765 | + | 0.465514i | 0.968543 | − | 0.248846i | \(-0.0800513\pi\) |
−0.699779 | + | 0.714360i | \(0.746718\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.3657 | + | 96.0695i | −0.243900 | + | 1.52491i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.20078 | − | 4.15737i | −0.107474 | − | 0.0620503i | 0.445299 | − | 0.895382i | \(-0.353097\pi\) |
−0.552774 | + | 0.833331i | \(0.686431\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 24.0652 | + | 1.91238i | 0.348771 | + | 0.0277157i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 115.480i | − | 1.62648i | −0.581930 | − | 0.813239i | \(-0.697702\pi\) | ||
0.581930 | − | 0.813239i | \(-0.302298\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 125.300i | 1.71643i | 0.513287 | + | 0.858217i | \(0.328428\pi\) | ||||
−0.513287 | + | 0.858217i | \(0.671572\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 48.6111 | − | 84.1969i | 0.631313 | − | 1.09347i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.5289 | − | 26.8968i | −0.196568 | − | 0.340466i | 0.750845 | − | 0.660478i | \(-0.229646\pi\) |
−0.947413 | + | 0.320012i | \(0.896313\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −16.5998 | − | 79.2808i | −0.204936 | − | 0.978775i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 77.0272 | + | 133.415i | 0.928038 | + | 1.60741i | 0.786601 | + | 0.617462i | \(0.211839\pi\) |
0.141438 | + | 0.989947i | \(0.454827\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 109.012 | + | 75.0438i | 1.25301 | + | 0.862572i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 131.044i | 1.47241i | 0.676760 | + | 0.736204i | \(0.263384\pi\) | ||||
−0.676760 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49.4498 | 0.543404 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 27.1296 | + | 2.15590i | 0.291716 | + | 0.0231818i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −143.990 | + | 83.1329i | −1.48444 | + | 0.857040i | −0.999843 | − | 0.0176993i | \(-0.994366\pi\) |
−0.484594 | + | 0.874739i | \(0.661033\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.7839 | + | 79.9272i | −0.129130 | + | 0.807346i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −140.647 | + | 81.2027i | −1.39255 | + | 0.803987i | −0.993597 | − | 0.112985i | \(-0.963959\pi\) |
−0.398950 | + | 0.916973i | \(0.630625\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −56.8073 | − | 32.7977i | −0.551527 | − | 0.318424i | 0.198211 | − | 0.980159i | \(-0.436487\pi\) |
−0.749738 | + | 0.661735i | \(0.769820\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.4315 | −0.106837 | −0.0534184 | − | 0.998572i | \(-0.517012\pi\) | ||||
−0.0534184 | + | 0.998572i | \(0.517012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 157.169 | 1.44191 | 0.720957 | − | 0.692980i | \(-0.243703\pi\) | ||||
0.720957 | + | 0.692980i | \(0.243703\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 152.024 | − | 72.3701i | 1.36959 | − | 0.651983i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.4504 | − | 19.8326i | 0.101331 | − | 0.175510i | −0.810903 | − | 0.585181i | \(-0.801023\pi\) |
0.912233 | + | 0.409672i | \(0.134357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −38.4577 | + | 14.6955i | −0.328698 | + | 0.125602i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 70.6990 | − | 40.8181i | 0.594109 | − | 0.343009i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −20.0568 | + | 34.7395i | −0.165759 | + | 0.287103i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.8089 | + | 186.353i | −0.120397 | + | 1.51507i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 99.3417i | 0.782218i | 0.920344 | + | 0.391109i | \(0.127908\pi\) | ||||
−0.920344 | + | 0.391109i | \(0.872092\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −99.0956 | − | 68.2175i | −0.768183 | − | 0.528818i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.22017 | + | 3.59122i | 0.0474822 | + | 0.0274139i | 0.523553 | − | 0.851993i | \(-0.324606\pi\) |
−0.476071 | + | 0.879407i | \(0.657939\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −81.7439 | + | 47.1949i | −0.614616 | + | 0.354849i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −125.761 | − | 217.824i | −0.917962 | − | 1.58996i | −0.802506 | − | 0.596644i | \(-0.796501\pi\) |
−0.115455 | − | 0.993313i | \(-0.536833\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 82.6116 | − | 143.087i | 0.594328 | − | 1.02941i | −0.399313 | − | 0.916815i | \(-0.630751\pi\) |
0.993641 | − | 0.112592i | \(-0.0359152\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30.9753 | + | 44.9961i | −0.219683 | + | 0.319121i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 41.1409 | 0.287699 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 202.932 | + | 16.1264i | 1.38049 | + | 0.109703i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 197.430 | + | 113.986i | 1.32503 | + | 0.765008i | 0.984527 | − | 0.175234i | \(-0.0560683\pi\) |
0.340506 | + | 0.940242i | \(0.389402\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 86.0019 | + | 148.960i | 0.569549 | + | 0.986488i | 0.996610 | + | 0.0822653i | \(0.0262155\pi\) |
−0.427061 | + | 0.904223i | \(0.640451\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −42.8532 | + | 52.7550i | −0.280086 | + | 0.344804i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −211.376 | − | 122.038i | −1.34634 | − | 0.777313i | −0.358615 | − | 0.933485i | \(-0.616751\pi\) |
−0.987730 | + | 0.156173i | \(0.950084\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −30.6887 | − | 64.4662i | −0.193010 | − | 0.405448i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 86.9887i | − | 0.540303i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 192.188i | − | 1.17907i | −0.807744 | − | 0.589534i | \(-0.799311\pi\) | ||
0.807744 | − | 0.589534i | \(-0.200689\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 105.498 | − | 182.728i | 0.631726 | − | 1.09418i | −0.355472 | − | 0.934687i | \(-0.615680\pi\) |
0.987199 | − | 0.159495i | \(-0.0509867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −74.0373 | − | 128.236i | −0.438091 | − | 0.758795i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 49.5479 | − | 60.9967i | 0.289754 | − | 0.356706i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −74.8995 | − | 129.730i | −0.432945 | − | 0.749882i | 0.564181 | − | 0.825651i | \(-0.309192\pi\) |
−0.997125 | + | 0.0757690i | \(0.975859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.2729 | + | 204.777i | −0.0919376 | + | 1.15693i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 58.2813i | − | 0.325594i | −0.986660 | − | 0.162797i | \(-0.947948\pi\) | ||
0.986660 | − | 0.162797i | \(-0.0520516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.7702 | −0.147902 | −0.0739508 | − | 0.997262i | \(-0.523561\pi\) | ||||
−0.0739508 | + | 0.997262i | \(0.523561\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −55.7778 | + | 81.0251i | −0.304797 | + | 0.442760i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 58.8197 | − | 33.9595i | 0.314544 | − | 0.181602i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −280.041 | + | 82.2574i | −1.48170 | + | 0.435225i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −72.3294 | + | 41.7594i | −0.378688 | + | 0.218636i | −0.677247 | − | 0.735755i | \(-0.736827\pi\) |
0.298559 | + | 0.954391i | \(0.403494\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −72.0695 | − | 41.6094i | −0.373417 | − | 0.215593i | 0.301533 | − | 0.953456i | \(-0.402502\pi\) |
−0.674950 | + | 0.737863i | \(0.735835\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 171.229 | 0.869183 | 0.434592 | − | 0.900628i | \(-0.356893\pi\) | ||||
0.434592 | + | 0.900628i | \(0.356893\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −151.309 | −0.760348 | −0.380174 | − | 0.924915i | \(-0.624136\pi\) | ||||
−0.380174 | + | 0.924915i | \(0.624136\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.97601 | − | 24.8658i | 0.00983089 | − | 0.123711i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 238.442 | − | 412.994i | 1.17459 | − | 2.03445i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.8513 | + | 67.6522i | 0.124886 | + | 0.326822i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −68.0088 | + | 39.2649i | −0.325401 | + | 0.187870i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −44.8904 | + | 77.7525i | −0.212751 | + | 0.368495i | −0.952574 | − | 0.304306i | \(-0.901576\pi\) |
0.739824 | + | 0.672801i | \(0.234909\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 312.805 | − | 148.908i | 1.46857 | − | 0.699100i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 98.0658i | − | 0.451916i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −339.404 | + | 161.571i | −1.54979 | + | 0.737766i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.9172 | + | 17.2727i | 0.135372 | + | 0.0781571i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −80.4290 | + | 46.4357i | −0.360668 | + | 0.208232i | −0.669374 | − | 0.742926i | \(-0.733438\pi\) |
0.308706 | + | 0.951158i | \(0.400104\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 111.320 | + | 192.811i | 0.490395 | + | 0.849389i | 0.999939 | − | 0.0110555i | \(-0.00351915\pi\) |
−0.509544 | + | 0.860445i | \(0.670186\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 92.0380 | − | 159.414i | 0.401913 | − | 0.696133i | −0.592044 | − | 0.805906i | \(-0.701679\pi\) |
0.993957 | + | 0.109772i | \(0.0350122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 290.750 | + | 23.1050i | 1.25866 | + | 0.100022i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 56.6725 | 0.243230 | 0.121615 | − | 0.992577i | \(-0.461193\pi\) | ||||
0.121615 | + | 0.992577i | \(0.461193\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 52.8323 | − | 76.7464i | 0.222921 | − | 0.323824i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 358.499 | + | 206.980i | 1.50000 | + | 0.866024i | 1.00000 | 2.96133e-6i | \(-9.42621e-7\pi\) | |
0.499997 | + | 0.866027i | \(0.333334\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −58.6707 | − | 101.621i | −0.243447 | − | 0.421663i | 0.718247 | − | 0.695788i | \(-0.244945\pi\) |
−0.961694 | + | 0.274126i | \(0.911612\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 193.346 | − | 147.195i | 0.795662 | − | 0.605741i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −34.5910 | − | 19.9711i | −0.140045 | − | 0.0808548i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −262.062 | + | 380.682i | −1.05246 | + | 1.52884i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 122.169i | − | 0.486729i | −0.969935 | − | 0.243364i | \(-0.921749\pi\) | ||
0.969935 | − | 0.243364i | \(-0.0782511\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 72.3723i | − | 0.286057i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −144.758 | + | 250.728i | −0.563260 | + | 0.975596i | 0.433949 | + | 0.900938i | \(0.357120\pi\) |
−0.997209 | + | 0.0746580i | \(0.976213\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −303.350 | − | 525.418i | −1.17124 | − | 2.02864i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −62.7061 | + | 392.051i | −0.240253 | + | 1.50211i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −98.2473 | − | 170.169i | −0.373564 | − | 0.647032i | 0.616547 | − | 0.787318i | \(-0.288531\pi\) |
−0.990111 | + | 0.140286i | \(0.955198\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −354.964 | + | 168.978i | −1.32946 | + | 0.632877i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 254.946i | 0.947756i | 0.880591 | + | 0.473878i | \(0.157146\pi\) | ||||
−0.880591 | + | 0.473878i | \(0.842854\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −139.138 | −0.513425 | −0.256713 | − | 0.966488i | \(-0.582639\pi\) | ||||
−0.256713 | + | 0.966488i | \(0.582639\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 63.7642 | + | 133.946i | 0.233568 | + | 0.490646i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −75.5437 | + | 43.6152i | −0.272721 | + | 0.157456i | −0.630124 | − | 0.776495i | \(-0.716996\pi\) |
0.357403 | + | 0.933950i | \(0.383662\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 29.1432 | + | 76.2670i | 0.104456 | + | 0.273358i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.2605 | − | 18.6256i | 0.114806 | − | 0.0662833i | −0.441497 | − | 0.897263i | \(-0.645553\pi\) |
0.556303 | + | 0.830979i | \(0.312219\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −396.990 | − | 229.202i | −1.40279 | − | 0.809902i | −0.408113 | − | 0.912931i | \(-0.633813\pi\) |
−0.994678 | + | 0.103029i | \(0.967146\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 673.613 | 2.34708 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −231.969 | −0.802662 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −410.857 | − | 282.834i | −1.41188 | − | 0.971939i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 193.893 | − | 335.832i | 0.661750 | − | 1.14618i | −0.318406 | − | 0.947954i | \(-0.603147\pi\) |
0.980156 | − | 0.198230i | \(-0.0635192\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −232.986 | + | 68.4360i | −0.784466 | + | 0.230424i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31.8788 | − | 18.4052i | 0.106618 | − | 0.0615560i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −216.753 | + | 375.427i | −0.720108 | + | 1.24726i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −401.318 | − | 276.268i | −1.32448 | − | 0.911774i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.0128i | 0.110791i | 0.998464 | + | 0.0553955i | \(0.0176420\pi\) | ||||
−0.998464 | + | 0.0553955i | \(0.982358\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.5888 | − | 196.168i | 0.0504492 | − | 0.634847i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −465.755 | − | 268.904i | −1.49760 | − | 0.864642i | −0.497607 | − | 0.867402i | \(-0.665788\pi\) |
−0.999996 | + | 0.00276044i | \(0.999121\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −141.592 | + | 81.7480i | −0.452370 | + | 0.261176i | −0.708830 | − | 0.705379i | \(-0.750777\pi\) |
0.256461 | + | 0.966555i | \(0.417444\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −270.355 | − | 468.269i | −0.852856 | − | 1.47719i | −0.878620 | − | 0.477522i | \(-0.841535\pi\) |
0.0257634 | − | 0.999668i | \(-0.491798\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 198.378 | − | 343.600i | 0.621874 | − | 1.07712i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.7407 | − | 30.9650i | −0.0459211 | − | 0.0964642i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −65.9403 | −0.204150 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 202.665 | + | 425.728i | 0.619770 | + | 1.30192i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 170.469 | + | 98.4203i | 0.518143 | + | 0.299150i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −121.090 | − | 209.734i | −0.365831 | − | 0.633638i | 0.623078 | − | 0.782160i | \(-0.285882\pi\) |
−0.988909 | + | 0.148522i | \(0.952549\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 392.063 | + | 318.475i | 1.17737 | + | 0.956380i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −286.441 | − | 165.377i | −0.849973 | − | 0.490732i | 0.0106686 | − | 0.999943i | \(-0.496604\pi\) |
−0.860642 | + | 0.509211i | \(0.829937\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 68.4862 | + | 5.44238i | 0.202024 | + | 0.0160542i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 81.5882i | − | 0.239261i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 203.849i | − | 0.594312i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −249.485 | + | 432.122i | −0.718978 | + | 1.24531i | 0.242427 | + | 0.970170i | \(0.422057\pi\) |
−0.961405 | + | 0.275137i | \(0.911277\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −144.309 | − | 249.950i | −0.413492 | − | 0.716190i | 0.581777 | − | 0.813349i | \(-0.302358\pi\) |
−0.995269 | + | 0.0971589i | \(0.969024\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −89.3964 | − | 85.2224i | −0.254691 | − | 0.242799i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −173.782 | − | 300.999i | −0.492299 | − | 0.852687i | 0.507661 | − | 0.861557i | \(-0.330510\pi\) |
−0.999961 | + | 0.00886928i | \(0.997177\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 201.730 | + | 138.871i | 0.565070 | + | 0.388994i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 408.046i | − | 1.13662i | −0.822815 | − | 0.568310i | \(-0.807597\pi\) | ||
0.822815 | − | 0.568310i | \(-0.192403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −284.758 | −0.788804 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −119.963 | − | 9.53306i | −0.330476 | − | 0.0262619i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −239.351 | + | 138.189i | −0.652183 | + | 0.376538i | −0.789292 | − | 0.614018i | \(-0.789552\pi\) |
0.137109 | + | 0.990556i | \(0.456219\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −523.877 | + | 200.184i | −1.41972 | + | 0.542504i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −222.804 | + | 128.636i | −0.600551 | + | 0.346728i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −129.870 | − | 74.9808i | −0.348178 | − | 0.201021i | 0.315704 | − | 0.948858i | \(-0.397759\pi\) |
−0.663883 | + | 0.747837i | \(0.731093\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 201.800 | 0.535279 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 385.068 | 1.01601 | 0.508005 | − | 0.861354i | \(-0.330383\pi\) | ||||
0.508005 | + | 0.861354i | \(0.330383\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −269.091 | + | 128.099i | −0.706274 | + | 0.336217i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −66.9947 | + | 116.038i | −0.174921 | + | 0.302972i | −0.940134 | − | 0.340805i | \(-0.889300\pi\) |
0.765213 | + | 0.643777i | \(0.222634\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 57.0021 | − | 356.388i | 0.147292 | − | 0.920901i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −360.786 | + | 208.300i | −0.927470 | + | 0.535475i | −0.886011 | − | 0.463665i | \(-0.846534\pi\) |
−0.0414597 | + | 0.999140i | \(0.513201\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.3850 | − | 52.6284i | 0.0777110 | − | 0.134599i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.70691 | + | 21.4796i | −0.00434329 | + | 0.0546554i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 414.289i | 1.04355i | 0.853083 | + | 0.521775i | \(0.174730\pi\) | ||||
−0.853083 | + | 0.521775i | \(0.825270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −233.245 | − | 160.566i | −0.584574 | − | 0.402421i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −210.716 | − | 121.657i | −0.525476 | − | 0.303384i | 0.213696 | − | 0.976900i | \(-0.431450\pi\) |
−0.739172 | + | 0.673516i | \(0.764783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.9382 | − | 20.7489i | 0.0891767 | − | 0.0514862i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −252.379 | − | 437.134i | −0.620097 | − | 1.07404i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −308.993 | + | 535.191i | −0.755483 | + | 1.30854i | 0.189650 | + | 0.981852i | \(0.439265\pi\) |
−0.945134 | + | 0.326684i | \(0.894069\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 427.863 | − | 621.531i | 1.04103 | − | 1.51224i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 740.209 | 1.79227 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 494.112 | + | 39.2655i | 1.18492 | + | 0.0941618i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 601.137 | + | 347.066i | 1.43469 | + | 0.828321i | 0.997474 | − | 0.0710339i | \(-0.0226299\pi\) |
0.437220 | + | 0.899355i | \(0.355963\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 56.2394 | + | 97.4094i | 0.133585 | + | 0.231376i | 0.925056 | − | 0.379831i | \(-0.124018\pi\) |
−0.791471 | + | 0.611207i | \(0.790684\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −161.824 | − | 25.8828i | −0.382564 | − | 0.0611886i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 306.966 | + | 177.227i | 0.718890 | + | 0.415051i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 53.0501 | + | 111.440i | 0.123660 | + | 0.259767i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 419.462i | 0.973229i | 0.873617 | + | 0.486615i | \(0.161768\pi\) | ||||
−0.873617 | + | 0.486615i | \(0.838232\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 21.7422i | − | 0.0502129i | −0.999685 | − | 0.0251065i | \(-0.992008\pi\) | ||
0.999685 | − | 0.0251065i | \(-0.00799248\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −35.1319 | + | 60.8502i | −0.0803934 | + | 0.139245i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 348.778 | + | 604.101i | 0.794483 | + | 1.37608i | 0.923167 | + | 0.384399i | \(0.125591\pi\) |
−0.128684 | + | 0.991686i | \(0.541075\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 217.994 | + | 570.485i | 0.494317 | + | 1.29362i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 111.780 | + | 193.609i | 0.252325 | + | 0.437040i | 0.964166 | − | 0.265301i | \(-0.0854714\pi\) |
−0.711840 | + | 0.702341i | \(0.752138\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −54.1779 | + | 681.768i | −0.121203 | + | 1.52521i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 104.042i | 0.231719i | 0.993266 | + | 0.115860i | \(0.0369623\pi\) | ||||
−0.993266 | + | 0.115860i | \(0.963038\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 560.428 | 1.24263 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −292.595 | + | 425.036i | −0.645906 | + | 0.938270i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −579.342 | + | 334.483i | −1.26771 | + | 0.731910i | −0.974553 | − | 0.224155i | \(-0.928038\pi\) |
−0.293153 | + | 0.956066i | \(0.594704\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −198.158 | − | 48.0517i | −0.431716 | − | 0.104688i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.222592 | − | 0.128513i | 0.000482846 | − | 0.000278771i | −0.499759 | − | 0.866165i | \(-0.666578\pi\) |
0.500241 | + | 0.865886i | \(0.333245\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 481.854 | + | 278.199i | 1.04072 | + | 0.600861i | 0.920038 | − | 0.391830i | \(-0.128158\pi\) |
0.120684 | + | 0.992691i | \(0.461491\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 357.378 | 0.765262 | 0.382631 | − | 0.923901i | \(-0.375018\pi\) | ||||
0.382631 | + | 0.923901i | \(0.375018\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −89.8828 | −0.191648 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 58.0050 | − | 729.927i | 0.123153 | − | 1.54974i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −180.332 | + | 312.345i | −0.381253 | + | 0.660349i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 135.050 | − | 166.255i | 0.283123 | − | 0.348543i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −350.791 | + | 202.529i | −0.732341 | + | 0.422817i | −0.819278 | − | 0.573397i | \(-0.805625\pi\) |
0.0869370 | + | 0.996214i | \(0.472292\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 128.367 | − | 222.338i | 0.266875 | − | 0.462241i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 235.630 | − | 112.170i | 0.487846 | − | 0.232235i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 586.853i | − | 1.20504i | −0.798105 | − | 0.602518i | \(-0.794164\pi\) | ||
0.798105 | − | 0.602518i | \(-0.205836\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 520.587 | − | 247.822i | 1.06459 | − | 0.506792i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 304.133 | + | 175.591i | 0.619415 | + | 0.357619i | 0.776641 | − | 0.629943i | \(-0.216922\pi\) |
−0.157226 | + | 0.987563i | \(0.550255\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 288.516 | − | 166.575i | 0.585226 | − | 0.337880i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −624.172 | − | 1081.10i | −1.25588 | − | 2.17525i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 481.765 | − | 834.442i | 0.965461 | − | 1.67223i | 0.257091 | − | 0.966387i | \(-0.417236\pi\) |
0.708370 | − | 0.705841i | \(-0.249431\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 631.001 | + | 50.1436i | 1.25948 | + | 0.100087i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −858.481 | −1.70672 | −0.853361 | − | 0.521321i | \(-0.825439\pi\) | ||||
−0.853361 | + | 0.521321i | \(0.825439\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 251.890 | − | 365.905i | 0.496824 | − | 0.721707i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −437.729 | − | 252.723i | −0.859978 | − | 0.496508i | 0.00402718 | − | 0.999992i | \(-0.498718\pi\) |
−0.864005 | + | 0.503484i | \(0.832051\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 677.249 | + | 1173.03i | 1.32534 | + | 2.29556i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 229.115 | + | 55.5586i | 0.446617 | + | 0.108301i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 141.826 | + | 81.8831i | 0.274324 | + | 0.158381i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 254.823 | − | 370.166i | 0.490988 | − | 0.713229i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 640.397i | − | 1.22917i | −0.788851 | − | 0.614585i | \(-0.789324\pi\) | ||
0.788851 | − | 0.614585i | \(-0.210676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 91.8967i | 0.175711i | 0.996133 | + | 0.0878553i | \(0.0280013\pi\) | ||||
−0.996133 | + | 0.0878553i | \(0.971999\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34.2542 | − | 59.3300i | 0.0649985 | − | 0.112581i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 232.123 | + | 402.048i | 0.438795 | + | 0.760016i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −575.670 | + | 219.975i | −1.08412 | + | 0.414266i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 142.524 | + | 246.859i | 0.267400 | + | 0.463150i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 157.869 | − | 75.1523i | 0.293983 | − | 0.139948i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 610.287i | − | 1.13226i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −391.152 | −0.723017 | −0.361509 | − | 0.932369i | \(-0.617738\pi\) | ||||
−0.361509 | + | 0.932369i | \(0.617738\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −34.5195 | − | 72.5134i | −0.0635718 | − | 0.133542i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 712.576 | − | 411.406i | 1.30270 | − | 0.752113i | 0.321832 | − | 0.946797i | \(-0.395701\pi\) |
0.980866 | + | 0.194683i | \(0.0623679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −291.400 | − | 46.6075i | −0.530783 | − | 0.0848953i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −333.590 | + | 192.598i | −0.605426 | + | 0.349543i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −290.756 | − | 167.868i | −0.525779 | − | 0.303559i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 111.213 | 0.199665 | 0.0998323 | − | 0.995004i | \(-0.468169\pi\) | ||||
0.0998323 | + | 0.995004i | \(0.468169\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −183.444 | −0.328164 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 167.834 | + | 115.537i | 0.299169 | + | 0.205948i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 108.786 | − | 188.423i | 0.193226 | − | 0.334677i | −0.753092 | − | 0.657916i | \(-0.771438\pi\) |
0.946317 | + | 0.323239i | \(0.104772\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −583.919 | − | 652.487i | −1.02984 | − | 1.15077i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 141.705 | − | 81.8136i | 0.249043 | − | 0.143785i | −0.370283 | − | 0.928919i | \(-0.620739\pi\) |
0.619326 | + | 0.785134i | \(0.287406\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 380.199 | − | 658.524i | 0.665848 | − | 1.15328i | −0.313207 | − | 0.949685i | \(-0.601403\pi\) |
0.979055 | − | 0.203598i | \(-0.0652635\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −206.382 | − | 142.074i | −0.360178 | − | 0.247947i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.9318i | 0.0466756i | 0.999728 | + | 0.0233378i | \(0.00742932\pi\) | ||||
−0.999728 | + | 0.0233378i | \(0.992571\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.7770 | − | 248.872i | 0.0341572 | − | 0.429830i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1442.22 | + | 832.668i | 2.48231 | + | 1.43316i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −185.367 | + | 107.022i | −0.317954 | + | 0.183571i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 247.572 | + | 428.807i | 0.421758 | + | 0.730506i | 0.996112 | − | 0.0881015i | \(-0.0280800\pi\) |
−0.574354 | + | 0.818607i | \(0.694747\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −39.6056 | + | 68.5989i | −0.0672420 | + | 0.116467i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 220.796 | + | 463.815i | 0.373597 | + | 0.784796i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −102.991 | −0.173678 | −0.0868392 | − | 0.996222i | \(-0.527677\pi\) | ||||
−0.0868392 | + | 0.996222i | \(0.527677\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −195.109 | − | 409.857i | −0.326817 | − | 0.686528i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 492.666 | + | 284.441i | 0.822481 | + | 0.474860i | 0.851271 | − | 0.524726i | \(-0.175832\pi\) |
−0.0287900 | + | 0.999585i | \(0.509165\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −445.951 | − | 772.410i | −0.742016 | − | 1.28521i | −0.951576 | − | 0.307413i | \(-0.900537\pi\) |
0.209561 | − | 0.977796i | \(-0.432797\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 69.9030 | − | 26.7114i | 0.115925 | − | 0.0442975i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −356.909 | − | 206.061i | −0.587988 | − | 0.339475i | 0.176314 | − | 0.984334i | \(-0.443583\pi\) |
−0.764301 | + | 0.644859i | \(0.776916\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1426.16 | + | 113.332i | 2.34180 | + | 0.186096i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 83.2958i | 0.136327i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 994.307i | 1.62203i | 0.585023 | + | 0.811017i | \(0.301086\pi\) | ||||
−0.585023 | + | 0.811017i | \(0.698914\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −340.183 | + | 589.215i | −0.551351 | + | 0.954967i | 0.446827 | + | 0.894620i | \(0.352554\pi\) |
−0.998177 | + | 0.0603468i | \(0.980779\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −371.748 | − | 643.887i | −0.600563 | − | 1.04021i | −0.992736 | − | 0.120314i | \(-0.961610\pi\) |
0.392173 | − | 0.919891i | \(-0.371723\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −149.918 | + | 157.260i | −0.241413 | + | 0.253237i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 708.298 | + | 1226.81i | 1.13692 | + | 1.96919i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −194.054 | − | 133.587i | −0.309496 | − | 0.213057i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 423.839i | − | 0.673829i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 894.208 | 1.41713 | 0.708564 | − | 0.705646i | \(-0.249343\pi\) | ||||
0.708564 | + | 0.705646i | \(0.249343\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −268.496 | − | 21.3365i | −0.424165 | − | 0.0337070i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 268.821 | − | 155.204i | 0.422011 | − | 0.243648i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 806.707 | + | 655.292i | 1.26245 | + | 1.02550i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 446.198 | − | 257.613i | 0.696097 | − | 0.401892i | −0.109795 | − | 0.993954i | \(-0.535019\pi\) |
0.805892 | + | 0.592062i | \(0.201686\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 591.217 | + | 341.339i | 0.919466 | + | 0.530854i | 0.883465 | − | 0.468498i | \(-0.155205\pi\) |
0.0360013 | + | 0.999352i | \(0.488538\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 740.660 | 1.14476 | 0.572380 | − | 0.819988i | \(-0.306020\pi\) | ||||
0.572380 | + | 0.819988i | \(0.306020\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 615.834 | 0.948897 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 265.634 | − | 126.453i | 0.408041 | − | 0.194245i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −155.252 | + | 268.904i | −0.237751 | + | 0.411797i | −0.960069 | − | 0.279764i | \(-0.909744\pi\) |
0.722317 | + | 0.691562i | \(0.243077\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −875.305 | − | 711.015i | −1.33228 | − | 1.08221i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −218.218 | + | 125.988i | −0.331135 | + | 0.191181i | −0.656345 | − | 0.754461i | \(-0.727898\pi\) |
0.325210 | + | 0.945642i | \(0.394565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −154.032 | + | 266.791i | −0.233029 | + | 0.403618i | −0.958698 | − | 0.284426i | \(-0.908197\pi\) |
0.725669 | + | 0.688044i | \(0.241530\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.20976 | + | 103.311i | −0.0123827 | + | 0.155823i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 354.994i | − | 0.532224i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −229.493 | − | 157.983i | −0.343039 | − | 0.236148i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 255.388 | + | 147.448i | 0.380608 | + | 0.219744i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −610.473 | + | 352.456i | −0.907091 | + | 0.523709i | −0.879494 | − | 0.475910i | \(-0.842119\pi\) |
−0.0275972 | + | 0.999619i | \(0.508786\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 123.043 | + | 213.117i | 0.181748 | + | 0.314797i | 0.942476 | − | 0.334274i | \(-0.108491\pi\) |
−0.760728 | + | 0.649071i | \(0.775158\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −898.671 | + | 1556.54i | −1.32352 | + | 2.29241i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −378.731 | + | 550.161i | −0.556140 | + | 0.807872i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −430.637 | −0.630507 | −0.315254 | − | 0.949007i | \(-0.602090\pi\) | ||||
−0.315254 | + | 0.949007i | \(0.602090\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 550.493 | + | 43.7459i | 0.801299 | + | 0.0636767i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −94.2827 | − | 54.4342i | −0.136840 | − | 0.0790046i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −244.885 | − | 424.153i | −0.354392 | − | 0.613825i | 0.632622 | − | 0.774461i | \(-0.281979\pi\) |
−0.987014 | + | 0.160636i | \(0.948645\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 312.329 | + | 817.359i | 0.450692 | + | 1.17945i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 407.537 | + | 235.292i | 0.584702 | + | 0.337578i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 73.0777 | + | 153.511i | 0.104546 | + | 0.219615i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1398.45i | − | 1.99494i | −0.0711109 | − | 0.997468i | \(-0.522654\pi\) | ||
0.0711109 | − | 0.997468i | \(-0.477346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 490.053i | 0.697088i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −877.806 | + | 1520.40i | −1.24159 | + | 2.15050i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 615.327 | + | 1065.78i | 0.867880 | + | 1.50321i | 0.864158 | + | 0.503220i | \(0.167851\pi\) |
0.00372210 | + | 0.999993i | \(0.498815\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 276.012 | + | 44.1463i | 0.388202 | + | 0.0620904i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.5001 | − | 63.2201i | −0.0511924 | − | 0.0886678i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −98.3779 | + | 1237.98i | −0.137208 | + | 1.72660i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 205.324i | − | 0.285569i | −0.989754 | − | 0.142785i | \(-0.954394\pi\) | ||
0.989754 | − | 0.142785i | \(-0.0456056\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −709.090 | −0.983481 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 199.609 | − | 289.961i | 0.276085 | − | 0.401052i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 801.453 | − | 462.719i | 1.10241 | − | 0.636477i | 0.165558 | − | 0.986200i | \(-0.447058\pi\) |
0.936853 | + | 0.349723i | \(0.113724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 648.027 | + | 333.919i | 0.888926 | + | 0.458050i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −262.272 | + | 151.423i | −0.358785 | + | 0.207144i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 541.875 | + | 312.852i | 0.739257 | + | 0.426810i | 0.821799 | − | 0.569777i | \(-0.192971\pi\) |
−0.0825420 | + | 0.996588i | \(0.526304\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −74.7801 | −0.101466 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −487.290 | −0.659392 | −0.329696 | − | 0.944087i | \(-0.606946\pi\) | ||||
−0.329696 | + | 0.944087i | \(0.606946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.49233 | − | 119.450i | 0.0128102 | − | 0.161201i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −303.238 | + | 525.224i | −0.408127 | + | 0.706897i | −0.994680 | − | 0.103014i | \(-0.967151\pi\) |
0.586553 | + | 0.809911i | \(0.300485\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1369.09 | − | 218.977i | −1.83278 | − | 0.293142i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −107.020 | + | 61.7877i | −0.142883 | + | 0.0824937i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −174.790 | + | 302.746i | −0.232744 | + | 0.403124i | −0.958615 | − | 0.284707i | \(-0.908104\pi\) |
0.725871 | + | 0.687831i | \(0.241437\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 330.923 | − | 157.534i | 0.439473 | − | 0.209208i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 242.544i | − | 0.320402i | −0.987084 | − | 0.160201i | \(-0.948786\pi\) | ||
0.987084 | − | 0.160201i | \(-0.0512142\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 196.038 | − | 93.3223i | 0.258284 | − | 0.122954i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1023.42 | + | 590.870i | 1.34483 | + | 0.776439i | 0.987512 | − | 0.157543i | \(-0.0503574\pi\) |
0.357319 | + | 0.933982i | \(0.383691\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1471.38 | − | 849.500i | 1.92841 | − | 1.11337i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 156.615 | + | 271.265i | 0.204191 | + | 0.353670i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 219.654 | − | 380.451i | 0.285635 | − | 0.494735i | −0.687128 | − | 0.726537i | \(-0.741129\pi\) |
0.972763 | + | 0.231802i | \(0.0744620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −865.818 | − | 68.8038i | −1.12298 | − | 0.0892397i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1157.27 | −1.49711 | −0.748556 | − | 0.663072i | \(-0.769252\pi\) | ||||
−0.748556 | + | 0.663072i | \(0.769252\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1032.06 | − | 1499.21i | 1.32826 | − | 1.92948i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −471.205 | − | 272.050i | −0.604884 | − | 0.349230i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −519.295 | − | 899.445i | −0.664910 | − | 1.15166i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1142.82 | + | 335.686i | −1.45954 | + | 0.428717i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1018.63 | + | 588.108i | 1.29432 | + | 0.747279i | 0.979418 | − | 0.201844i | \(-0.0646933\pi\) |
0.314907 | + | 0.949122i | \(0.398027\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 334.257 | − | 485.555i | 0.423646 | − | 0.615406i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 247.558i | − | 0.312968i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 149.992i | 0.189145i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.9607 | + | 18.9845i | −0.0137525 | + | 0.0238200i | −0.872820 | − | 0.488043i | \(-0.837711\pi\) |
0.859067 | + | 0.511863i | \(0.171044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 68.7561 | + | 119.089i | 0.0860527 | + | 0.149048i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −915.435 | − | 743.612i | −1.14287 | − | 0.928355i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 563.453 | + | 975.929i | 0.701685 | + | 1.21535i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −690.583 | + | 328.747i | −0.855741 | + | 0.407369i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1548.54i | − | 1.91414i | −0.289857 | − | 0.957070i | \(-0.593608\pi\) | ||
0.289857 | − | 0.957070i | \(-0.406392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 235.109 | 0.289900 | 0.144950 | − | 0.989439i | \(-0.453698\pi\) | ||||
0.144950 | + | 0.989439i | \(0.453698\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −179.415 | − | 376.889i | −0.220683 | − | 0.463578i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 303.245 | − | 175.079i | 0.371169 | − | 0.214294i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −280.603 | + | 345.441i | −0.342617 | + | 0.421784i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −814.987 | + | 470.533i | −0.992676 | + | 0.573122i | −0.906073 | − | 0.423121i | \(-0.860935\pi\) |
−0.0866031 | + | 0.996243i | \(0.527601\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −250.019 | − | 144.349i | −0.303790 | − | 0.175393i | 0.340354 | − | 0.940297i | \(-0.389453\pi\) |
−0.644144 | + | 0.764904i | \(0.722786\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −853.621 | −1.03219 | −0.516095 | − | 0.856531i | \(-0.672615\pi\) | ||||
−0.516095 | + | 0.856531i | \(0.672615\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.6812 | 0.0165033 | 0.00825164 | − | 0.999966i | \(-0.497373\pi\) | ||||
0.00825164 | + | 0.999966i | \(0.497373\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −215.554 | − | 148.387i | −0.259391 | − | 0.178565i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 256.225 | − | 443.794i | 0.307593 | − | 0.532766i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −169.008 | + | 177.286i | −0.201921 | + | 0.211811i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −102.968 | + | 59.4488i | −0.122727 | + | 0.0708567i | −0.560107 | − | 0.828420i | \(-0.689240\pi\) |
0.437380 | + | 0.899277i | \(0.355907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 552.563 | − | 957.067i | 0.657031 | − | 1.13801i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 92.0509 | + | 63.3679i | 0.109194 | + | 0.0751696i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 433.631i | 0.511961i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 108.940 | − | 1370.89i | 0.128316 | − | 1.61471i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −391.122 | − | 225.814i | −0.459603 | − | 0.265352i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −577.231 | + | 333.265i | −0.676707 | + | 0.390697i | −0.798613 | − | 0.601845i | \(-0.794433\pi\) |
0.121906 | + | 0.992542i | \(0.461099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −306.171 | − | 530.304i | −0.357259 | − | 0.618791i | 0.630243 | − | 0.776398i | \(-0.282955\pi\) |
−0.987502 | + | 0.157607i | \(0.949622\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −665.233 | + | 1152.22i | −0.774427 | + | 1.34135i | 0.160689 | + | 0.987005i | \(0.448628\pi\) |
−0.935116 | + | 0.354342i | \(0.884705\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 868.606 | + | 1824.64i | 1.00883 | + | 2.11921i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1042.02 | −1.20744 | −0.603719 | − | 0.797197i | \(-0.706315\pi\) | ||||
−0.603719 | + | 0.797197i | \(0.706315\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −299.118 | − | 628.344i | −0.345004 | − | 0.724733i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −241.901 | − | 139.662i | −0.278367 | − | 0.160716i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.0176 | − | 32.9394i | −0.0218342 | − | 0.0378179i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 236.334 | − | 1477.61i | 0.270715 | − | 1.69257i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −193.736 | − | 111.854i | −0.220908 | − | 0.127541i | 0.385463 | − | 0.922723i | \(-0.374042\pi\) |
−0.606371 | + | 0.795182i | \(0.707375\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1159.70 | + | 92.1576i | 1.31934 | + | 0.104844i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 447.183i | 0.507586i | 0.967259 | + | 0.253793i | \(0.0816782\pi\) | ||||
−0.967259 | + | 0.253793i | \(0.918322\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1028.50i | − | 1.16478i | −0.812910 | − | 0.582389i | \(-0.802118\pi\) | ||
0.812910 | − | 0.582389i | \(-0.197882\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −228.301 | + | 395.428i | −0.257385 | + | 0.445804i | −0.965541 | − | 0.260252i | \(-0.916194\pi\) |
0.708155 | + | 0.706057i | \(0.249528\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 536.945 | + | 930.016i | 0.603987 | + | 1.04614i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −485.805 | − | 542.852i | −0.545236 | − | 0.609262i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −79.4975 | − | 137.694i | −0.0890230 | − | 0.154192i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 90.9618 | + | 62.6182i | 0.101407 | + | 0.0698085i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 400.198i | − | 0.445159i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −179.730 | −0.199478 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1296.43 | − | 103.023i | −1.43569 | − | 0.114090i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −331.435 | + | 191.354i | −0.365419 | + | 0.210975i | −0.671455 | − | 0.741045i | \(-0.734330\pi\) |
0.306036 | + | 0.952020i | \(0.400997\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 230.847 | − | 1443.30i | 0.253957 | − | 1.58779i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1556.93 | + | 898.893i | −1.70903 | + | 0.986710i | −0.773272 | + | 0.634075i | \(0.781381\pi\) |
−0.935761 | + | 0.352636i | \(0.885286\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1199.89 | + | 692.758i | 1.31423 | + | 0.758771i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 77.6425 | 0.0846702 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 888.894 | 0.967240 | 0.483620 | − | 0.875278i | \(-0.339322\pi\) | ||||
0.483620 | + | 0.875278i | \(0.339322\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −92.1318 | + | 43.8587i | −0.100035 | + | 0.0476207i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 264.127 | − | 457.481i | 0.286161 | − | 0.495646i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 551.468 | − | 210.727i | 0.594895 | − | 0.227322i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1525.09 | + | 880.512i | −1.64165 | + | 0.947807i | −0.661402 | + | 0.750032i | \(0.730038\pi\) |
−0.980247 | + | 0.197775i | \(0.936628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −296.254 | + | 513.126i | −0.318210 | + | 0.551156i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 127.811 | − | 1608.35i | 0.136989 | − | 1.72385i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1536.39i | 1.63969i | 0.572588 | + | 0.819843i | \(0.305940\pi\) | ||||
−0.572588 | + | 0.819843i | \(0.694060\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −404.013 | − | 278.123i | −0.430258 | − | 0.296190i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1324.15 | + | 764.496i | 1.40717 | + | 0.812429i | 0.995114 | − | 0.0987296i | \(-0.0314779\pi\) |
0.412055 | + | 0.911159i | \(0.364811\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 434.258 | − | 250.719i | 0.460507 | − | 0.265874i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −498.186 | − | 862.884i | −0.526068 | − | 0.911176i | −0.999539 | − | 0.0303669i | \(-0.990332\pi\) |
0.473471 | − | 0.880809i | \(-0.343001\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −286.587 | + | 496.383i | −0.301988 | + | 0.523059i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 919.802 | − | 1336.14i | 0.967195 | − | 1.40499i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1005.97 | −1.05559 | −0.527794 | − | 0.849373i | \(-0.676981\pi\) | ||||
−0.527794 | + | 0.849373i | \(0.676981\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1186.53 | + | 94.2894i | 1.23984 | + | 0.0985260i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2354.69 | − | 1359.48i | −2.45536 | − | 1.41760i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 439.352 | + | 760.980i | 0.457182 | + | 0.791863i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 64.8684 | − | 79.8572i | 0.0673607 | − | 0.0829254i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −558.267 | − | 322.316i | −0.577319 | − | 0.333315i | 0.182748 | − | 0.983160i | \(-0.441501\pi\) |
−0.760067 | + | 0.649844i | \(0.774834\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −85.0283 | − | 178.615i | −0.0877485 | − | 0.184329i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 215.087i | − | 0.221511i | −0.993848 | − | 0.110756i | \(-0.964673\pi\) | ||
0.993848 | − | 0.110756i | \(-0.0353271\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1786.07i | − | 1.83563i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.6583 | + | 53.1017i | −0.0313800 | + | 0.0543518i | −0.881289 | − | 0.472578i | \(-0.843324\pi\) |
0.849909 | + | 0.526930i | \(0.176657\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 589.285 | + | 1020.67i | 0.601926 | + | 1.04257i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −891.855 | + | 1097.93i | −0.909128 | + | 1.11920i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 580.428 | + | 1005.33i | 0.590466 | + | 1.02272i | 0.994170 | + | 0.107827i | \(0.0343893\pi\) |
−0.403704 | + | 0.914890i | \(0.632277\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −46.7794 | + | 588.666i | −0.0473956 | + | 0.596420i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 322.702i | 0.326291i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 763.478 | 0.770412 | 0.385206 | − | 0.922831i | \(-0.374130\pi\) | ||||
0.385206 | + | 0.922831i | \(0.374130\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 411.972 | − | 598.448i | 0.414876 | − | 0.602667i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −89.2750 | + | 51.5429i | −0.0895436 | + | 0.0516980i | −0.544103 | − | 0.839018i | \(-0.683130\pi\) |
0.454560 | + | 0.890716i | \(0.349797\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −357.109 | + | 1472.66i | −0.357467 | + | 1.47413i |
(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 | 900.3.u.d.149.11 | 32 | ||
3.2 | odd | 2 | 2700.3.u.d.449.16 | 32 | |||
5.2 | odd | 4 | 900.3.p.d.401.7 | yes | 16 | ||
5.3 | odd | 4 | 900.3.p.e.401.2 | yes | 16 | ||
5.4 | even | 2 | inner | 900.3.u.d.149.6 | 32 | ||
9.2 | odd | 6 | inner | 900.3.u.d.749.6 | 32 | ||
9.7 | even | 3 | 2700.3.u.d.2249.1 | 32 | |||
15.2 | even | 4 | 2700.3.p.e.2501.8 | 16 | |||
15.8 | even | 4 | 2700.3.p.d.2501.1 | 16 | |||
15.14 | odd | 2 | 2700.3.u.d.449.1 | 32 | |||
45.2 | even | 12 | 900.3.p.d.101.7 | ✓ | 16 | ||
45.7 | odd | 12 | 2700.3.p.e.1601.8 | 16 | |||
45.29 | odd | 6 | inner | 900.3.u.d.749.11 | 32 | ||
45.34 | even | 6 | 2700.3.u.d.2249.16 | 32 | |||
45.38 | even | 12 | 900.3.p.e.101.2 | yes | 16 | ||
45.43 | odd | 12 | 2700.3.p.d.1601.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.p.d.101.7 | ✓ | 16 | 45.2 | even | 12 | ||
900.3.p.d.401.7 | yes | 16 | 5.2 | odd | 4 | ||
900.3.p.e.101.2 | yes | 16 | 45.38 | even | 12 | ||
900.3.p.e.401.2 | yes | 16 | 5.3 | odd | 4 | ||
900.3.u.d.149.6 | 32 | 5.4 | even | 2 | inner | ||
900.3.u.d.149.11 | 32 | 1.1 | even | 1 | trivial | ||
900.3.u.d.749.6 | 32 | 9.2 | odd | 6 | inner | ||
900.3.u.d.749.11 | 32 | 45.29 | odd | 6 | inner | ||
2700.3.p.d.1601.1 | 16 | 45.43 | odd | 12 | |||
2700.3.p.d.2501.1 | 16 | 15.8 | even | 4 | |||
2700.3.p.e.1601.8 | 16 | 45.7 | odd | 12 | |||
2700.3.p.e.2501.8 | 16 | 15.2 | even | 4 | |||
2700.3.u.d.449.1 | 32 | 15.14 | odd | 2 | |||
2700.3.u.d.449.16 | 32 | 3.2 | odd | 2 | |||
2700.3.u.d.2249.1 | 32 | 9.7 | even | 3 | |||
2700.3.u.d.2249.16 | 32 | 45.34 | even | 6 |