Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(419,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.b (of order \(2\), degree \(1\), 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: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.18 | ||
Character | \(\chi\) | \(=\) | 1045.419 |
Dual form | 1045.2.b.d.419.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.84475i | 1.30444i | 0.758031 | + | 0.652219i | \(0.226162\pi\) | ||||
−0.758031 | + | 0.652219i | \(0.773838\pi\) | |||||||
\(3\) | − | 3.33093i | − | 1.92312i | −0.274602 | − | 0.961558i | \(-0.588546\pi\) | ||
0.274602 | − | 0.961558i | \(-0.411454\pi\) | |||||||
\(4\) | −1.40312 | −0.701558 | ||||||||
\(5\) | −2.19819 | − | 0.409812i | −0.983062 | − | 0.183273i | ||||
\(6\) | 6.14475 | 2.50859 | ||||||||
\(7\) | − | 3.04962i | − | 1.15265i | −0.817222 | − | 0.576323i | \(-0.804487\pi\) | ||
0.817222 | − | 0.576323i | \(-0.195513\pi\) | |||||||
\(8\) | 1.10110i | 0.389299i | ||||||||
\(9\) | −8.09513 | −2.69838 | ||||||||
\(10\) | 0.756002 | − | 4.05513i | 0.239069 | − | 1.28234i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 4.67369i | 1.34918i | ||||||||
\(13\) | − | 2.03040i | − | 0.563130i | −0.959542 | − | 0.281565i | \(-0.909146\pi\) | ||
0.959542 | − | 0.281565i | \(-0.0908536\pi\) | |||||||
\(14\) | 5.62579 | 1.50356 | ||||||||
\(15\) | −1.36506 | + | 7.32204i | −0.352456 | + | 1.89054i | ||||
\(16\) | −4.83750 | −1.20937 | ||||||||
\(17\) | 6.84485i | 1.66012i | 0.557674 | + | 0.830060i | \(0.311694\pi\) | ||||
−0.557674 | + | 0.830060i | \(0.688306\pi\) | |||||||
\(18\) | − | 14.9335i | − | 3.51986i | ||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 3.08432 | + | 0.575014i | 0.689675 | + | 0.128577i | ||||
\(21\) | −10.1581 | −2.21667 | ||||||||
\(22\) | − | 1.84475i | − | 0.393303i | ||||||
\(23\) | − | 5.01139i | − | 1.04495i | −0.852655 | − | 0.522474i | \(-0.825009\pi\) | ||
0.852655 | − | 0.522474i | \(-0.174991\pi\) | |||||||
\(24\) | 3.66770 | 0.748667 | ||||||||
\(25\) | 4.66411 | + | 1.80169i | 0.932822 | + | 0.360338i | ||||
\(26\) | 3.74558 | 0.734569 | ||||||||
\(27\) | 16.9715i | 3.26617i | ||||||||
\(28\) | 4.27897i | 0.808649i | ||||||||
\(29\) | −7.08382 | −1.31543 | −0.657716 | − | 0.753266i | \(-0.728477\pi\) | ||||
−0.657716 | + | 0.753266i | \(0.728477\pi\) | |||||||
\(30\) | −13.5074 | − | 2.51819i | −2.46609 | − | 0.459757i | ||||
\(31\) | 5.61832 | 1.00908 | 0.504540 | − | 0.863388i | \(-0.331662\pi\) | ||||
0.504540 | + | 0.863388i | \(0.331662\pi\) | |||||||
\(32\) | − | 6.72178i | − | 1.18825i | ||||||
\(33\) | 3.33093i | 0.579841i | ||||||||
\(34\) | −12.6271 | −2.16552 | ||||||||
\(35\) | −1.24977 | + | 6.70365i | −0.211249 | + | 1.13312i | ||||
\(36\) | 11.3584 | 1.89307 | ||||||||
\(37\) | 6.54847i | 1.07656i | 0.842766 | + | 0.538281i | \(0.180926\pi\) | ||||
−0.842766 | + | 0.538281i | \(0.819074\pi\) | |||||||
\(38\) | 1.84475i | 0.299259i | ||||||||
\(39\) | −6.76312 | −1.08297 | ||||||||
\(40\) | 0.451245 | − | 2.42044i | 0.0713481 | − | 0.382705i | ||||
\(41\) | −8.63500 | −1.34856 | −0.674280 | − | 0.738476i | \(-0.735546\pi\) | ||||
−0.674280 | + | 0.738476i | \(0.735546\pi\) | |||||||
\(42\) | − | 18.7391i | − | 2.89151i | ||||||
\(43\) | − | 2.80385i | − | 0.427584i | −0.976879 | − | 0.213792i | \(-0.931419\pi\) | ||
0.976879 | − | 0.213792i | \(-0.0685814\pi\) | |||||||
\(44\) | 1.40312 | 0.211528 | ||||||||
\(45\) | 17.7947 | + | 3.31748i | 2.65267 | + | 0.494541i | ||||
\(46\) | 9.24479 | 1.36307 | ||||||||
\(47\) | 6.56671i | 0.957853i | 0.877855 | + | 0.478927i | \(0.158974\pi\) | ||||
−0.877855 | + | 0.478927i | \(0.841026\pi\) | |||||||
\(48\) | 16.1134i | 2.32577i | ||||||||
\(49\) | −2.30016 | −0.328594 | ||||||||
\(50\) | −3.32368 | + | 8.60413i | −0.470039 | + | 1.21681i | ||||
\(51\) | 22.7998 | 3.19260 | ||||||||
\(52\) | 2.84888i | 0.395069i | ||||||||
\(53\) | 11.3475i | 1.55870i | 0.626587 | + | 0.779352i | \(0.284451\pi\) | ||||
−0.626587 | + | 0.779352i | \(0.715549\pi\) | |||||||
\(54\) | −31.3083 | −4.26052 | ||||||||
\(55\) | 2.19819 | + | 0.409812i | 0.296404 | + | 0.0552590i | ||||
\(56\) | 3.35794 | 0.448724 | ||||||||
\(57\) | − | 3.33093i | − | 0.441193i | ||||||
\(58\) | − | 13.0679i | − | 1.71590i | ||||||
\(59\) | 5.84803 | 0.761349 | 0.380674 | − | 0.924709i | \(-0.375692\pi\) | ||||
0.380674 | + | 0.924709i | \(0.375692\pi\) | |||||||
\(60\) | 1.91533 | − | 10.2737i | 0.247268 | − | 1.32633i | ||||
\(61\) | −9.59640 | −1.22869 | −0.614346 | − | 0.789036i | \(-0.710580\pi\) | ||||
−0.614346 | + | 0.789036i | \(0.710580\pi\) | |||||||
\(62\) | 10.3644i | 1.31628i | ||||||||
\(63\) | 24.6870i | 3.11027i | ||||||||
\(64\) | 2.72504 | 0.340630 | ||||||||
\(65\) | −0.832080 | + | 4.46320i | −0.103207 | + | 0.553592i | ||||
\(66\) | −6.14475 | −0.756367 | ||||||||
\(67\) | − | 9.59976i | − | 1.17280i | −0.810023 | − | 0.586398i | \(-0.800545\pi\) | ||
0.810023 | − | 0.586398i | \(-0.199455\pi\) | |||||||
\(68\) | − | 9.60413i | − | 1.16467i | ||||||
\(69\) | −16.6926 | −2.00956 | ||||||||
\(70\) | −12.3666 | − | 2.30552i | −1.47809 | − | 0.275562i | ||||
\(71\) | −3.93583 | −0.467098 | −0.233549 | − | 0.972345i | \(-0.575034\pi\) | ||||
−0.233549 | + | 0.972345i | \(0.575034\pi\) | |||||||
\(72\) | − | 8.91357i | − | 1.05047i | ||||||
\(73\) | 0.181013i | 0.0211860i | 0.999944 | + | 0.0105930i | \(0.00337192\pi\) | ||||
−0.999944 | + | 0.0105930i | \(0.996628\pi\) | |||||||
\(74\) | −12.0803 | −1.40431 | ||||||||
\(75\) | 6.00132 | − | 15.5358i | 0.692972 | − | 1.79392i | ||||
\(76\) | −1.40312 | −0.160948 | ||||||||
\(77\) | 3.04962i | 0.347536i | ||||||||
\(78\) | − | 12.4763i | − | 1.41266i | ||||||
\(79\) | −14.8138 | −1.66668 | −0.833339 | − | 0.552762i | \(-0.813574\pi\) | ||||
−0.833339 | + | 0.552762i | \(0.813574\pi\) | |||||||
\(80\) | 10.6338 | + | 1.98246i | 1.18889 | + | 0.221646i | ||||
\(81\) | 32.2457 | 3.58285 | ||||||||
\(82\) | − | 15.9294i | − | 1.75911i | ||||||
\(83\) | − | 3.70100i | − | 0.406237i | −0.979154 | − | 0.203119i | \(-0.934892\pi\) | ||
0.979154 | − | 0.203119i | \(-0.0651077\pi\) | |||||||
\(84\) | 14.2530 | 1.55513 | ||||||||
\(85\) | 2.80510 | − | 15.0463i | 0.304256 | − | 1.63200i | ||||
\(86\) | 5.17242 | 0.557756 | ||||||||
\(87\) | 23.5957i | 2.52973i | ||||||||
\(88\) | − | 1.10110i | − | 0.117378i | ||||||
\(89\) | −10.3263 | −1.09458 | −0.547292 | − | 0.836942i | \(-0.684341\pi\) | ||||
−0.547292 | + | 0.836942i | \(0.684341\pi\) | |||||||
\(90\) | −6.11993 | + | 32.8268i | −0.645097 | + | 3.46024i | ||||
\(91\) | −6.19193 | −0.649090 | ||||||||
\(92\) | 7.03157i | 0.733092i | ||||||||
\(93\) | − | 18.7143i | − | 1.94058i | ||||||
\(94\) | −12.1140 | −1.24946 | ||||||||
\(95\) | −2.19819 | − | 0.409812i | −0.225530 | − | 0.0420458i | ||||
\(96\) | −22.3898 | −2.28515 | ||||||||
\(97\) | − | 5.12653i | − | 0.520520i | −0.965539 | − | 0.260260i | \(-0.916192\pi\) | ||
0.965539 | − | 0.260260i | \(-0.0838084\pi\) | |||||||
\(98\) | − | 4.24323i | − | 0.428631i | ||||||
\(99\) | 8.09513 | 0.813591 | ||||||||
\(100\) | −6.54429 | − | 2.52798i | −0.654429 | − | 0.252798i | ||||
\(101\) | −11.6087 | −1.15511 | −0.577556 | − | 0.816351i | \(-0.695993\pi\) | ||||
−0.577556 | + | 0.816351i | \(0.695993\pi\) | |||||||
\(102\) | 42.0599i | 4.16455i | ||||||||
\(103\) | − | 1.06418i | − | 0.104857i | −0.998625 | − | 0.0524284i | \(-0.983304\pi\) | ||
0.998625 | − | 0.0524284i | \(-0.0166961\pi\) | |||||||
\(104\) | 2.23568 | 0.219226 | ||||||||
\(105\) | 22.3294 | + | 4.16290i | 2.17913 | + | 0.406257i | ||||
\(106\) | −20.9334 | −2.03323 | ||||||||
\(107\) | − | 8.72445i | − | 0.843425i | −0.906730 | − | 0.421712i | \(-0.861429\pi\) | ||
0.906730 | − | 0.421712i | \(-0.138571\pi\) | |||||||
\(108\) | − | 23.8130i | − | 2.29141i | ||||||
\(109\) | −0.307944 | −0.0294956 | −0.0147478 | − | 0.999891i | \(-0.504695\pi\) | ||||
−0.0147478 | + | 0.999891i | \(0.504695\pi\) | |||||||
\(110\) | −0.756002 | + | 4.05513i | −0.0720820 | + | 0.386641i | ||||
\(111\) | 21.8125 | 2.07035 | ||||||||
\(112\) | 14.7525i | 1.39398i | ||||||||
\(113\) | − | 6.74368i | − | 0.634392i | −0.948360 | − | 0.317196i | \(-0.897259\pi\) | ||
0.948360 | − | 0.317196i | \(-0.102741\pi\) | |||||||
\(114\) | 6.14475 | 0.575509 | ||||||||
\(115\) | −2.05373 | + | 11.0160i | −0.191511 | + | 1.02725i | ||||
\(116\) | 9.93943 | 0.922853 | ||||||||
\(117\) | 16.4363i | 1.51954i | ||||||||
\(118\) | 10.7882i | 0.993132i | ||||||||
\(119\) | 20.8742 | 1.91353 | ||||||||
\(120\) | −8.06232 | − | 1.50307i | −0.735986 | − | 0.137211i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 17.7030i | − | 1.60275i | ||||||
\(123\) | 28.7626i | 2.59344i | ||||||||
\(124\) | −7.88316 | −0.707928 | ||||||||
\(125\) | −9.51426 | − | 5.87187i | −0.850981 | − | 0.525196i | ||||
\(126\) | −45.5415 | −4.05716 | ||||||||
\(127\) | − | 5.71138i | − | 0.506803i | −0.967361 | − | 0.253401i | \(-0.918451\pi\) | ||
0.967361 | − | 0.253401i | \(-0.0815493\pi\) | |||||||
\(128\) | − | 8.41654i | − | 0.743924i | ||||||
\(129\) | −9.33945 | −0.822293 | ||||||||
\(130\) | −8.23351 | − | 1.53498i | −0.722127 | − | 0.134627i | ||||
\(131\) | −13.1950 | −1.15285 | −0.576425 | − | 0.817150i | \(-0.695553\pi\) | ||||
−0.576425 | + | 0.817150i | \(0.695553\pi\) | |||||||
\(132\) | − | 4.67369i | − | 0.406792i | ||||||
\(133\) | − | 3.04962i | − | 0.264435i | ||||||
\(134\) | 17.7092 | 1.52984 | ||||||||
\(135\) | 6.95514 | − | 37.3067i | 0.598603 | − | 3.21085i | ||||
\(136\) | −7.53689 | −0.646283 | ||||||||
\(137\) | 5.25354i | 0.448841i | 0.974492 | + | 0.224420i | \(0.0720488\pi\) | ||||
−0.974492 | + | 0.224420i | \(0.927951\pi\) | |||||||
\(138\) | − | 30.7938i | − | 2.62134i | ||||||
\(139\) | 10.2849 | 0.872350 | 0.436175 | − | 0.899862i | \(-0.356333\pi\) | ||||
0.436175 | + | 0.899862i | \(0.356333\pi\) | |||||||
\(140\) | 1.75357 | − | 9.40600i | 0.148204 | − | 0.794952i | ||||
\(141\) | 21.8733 | 1.84206 | ||||||||
\(142\) | − | 7.26064i | − | 0.609300i | ||||||
\(143\) | 2.03040i | 0.169790i | ||||||||
\(144\) | 39.1601 | 3.26335 | ||||||||
\(145\) | 15.5716 | + | 2.90303i | 1.29315 | + | 0.241084i | ||||
\(146\) | −0.333925 | −0.0276358 | ||||||||
\(147\) | 7.66168i | 0.631924i | ||||||||
\(148\) | − | 9.18826i | − | 0.755270i | ||||||
\(149\) | 6.30197 | 0.516278 | 0.258139 | − | 0.966108i | \(-0.416891\pi\) | ||||
0.258139 | + | 0.966108i | \(0.416891\pi\) | |||||||
\(150\) | 28.6598 | + | 11.0710i | 2.34006 | + | 0.903939i | ||||
\(151\) | 3.24012 | 0.263677 | 0.131838 | − | 0.991271i | \(-0.457912\pi\) | ||||
0.131838 | + | 0.991271i | \(0.457912\pi\) | |||||||
\(152\) | 1.10110i | 0.0893113i | ||||||||
\(153\) | − | 55.4099i | − | 4.47963i | ||||||
\(154\) | −5.62579 | −0.453339 | ||||||||
\(155\) | −12.3502 | − | 2.30245i | −0.991988 | − | 0.184938i | ||||
\(156\) | 9.48944 | 0.759763 | ||||||||
\(157\) | − | 1.72729i | − | 0.137853i | −0.997622 | − | 0.0689263i | \(-0.978043\pi\) | ||
0.997622 | − | 0.0689263i | \(-0.0219573\pi\) | |||||||
\(158\) | − | 27.3277i | − | 2.17408i | ||||||
\(159\) | 37.7979 | 2.99757 | ||||||||
\(160\) | −2.75467 | + | 14.7758i | −0.217776 | + | 1.16813i | ||||
\(161\) | −15.2828 | −1.20446 | ||||||||
\(162\) | 59.4853i | 4.67361i | ||||||||
\(163\) | − | 9.06614i | − | 0.710115i | −0.934845 | − | 0.355057i | \(-0.884461\pi\) | ||
0.934845 | − | 0.355057i | \(-0.115539\pi\) | |||||||
\(164\) | 12.1159 | 0.946093 | ||||||||
\(165\) | 1.36506 | − | 7.32204i | 0.106270 | − | 0.570020i | ||||
\(166\) | 6.82743 | 0.529912 | ||||||||
\(167\) | − | 9.85267i | − | 0.762423i | −0.924488 | − | 0.381211i | \(-0.875507\pi\) | ||
0.924488 | − | 0.381211i | \(-0.124493\pi\) | |||||||
\(168\) | − | 11.1851i | − | 0.862948i | ||||||
\(169\) | 8.87749 | 0.682884 | ||||||||
\(170\) | 27.7567 | + | 5.17472i | 2.12884 | + | 0.396883i | ||||
\(171\) | −8.09513 | −0.619050 | ||||||||
\(172\) | 3.93413i | 0.299975i | ||||||||
\(173\) | − | 13.6308i | − | 1.03633i | −0.855281 | − | 0.518165i | \(-0.826615\pi\) | ||
0.855281 | − | 0.518165i | \(-0.173385\pi\) | |||||||
\(174\) | −43.5283 | −3.29988 | ||||||||
\(175\) | 5.49447 | − | 14.2237i | 0.415343 | − | 1.07521i | ||||
\(176\) | 4.83750 | 0.364640 | ||||||||
\(177\) | − | 19.4794i | − | 1.46416i | ||||||
\(178\) | − | 19.0495i | − | 1.42782i | ||||||
\(179\) | 1.25492 | 0.0937970 | 0.0468985 | − | 0.998900i | \(-0.485066\pi\) | ||||
0.0468985 | + | 0.998900i | \(0.485066\pi\) | |||||||
\(180\) | −24.9680 | − | 4.65481i | −1.86100 | − | 0.346949i | ||||
\(181\) | −20.8319 | −1.54842 | −0.774210 | − | 0.632929i | \(-0.781852\pi\) | ||||
−0.774210 | + | 0.632929i | \(0.781852\pi\) | |||||||
\(182\) | − | 11.4226i | − | 0.846698i | ||||||
\(183\) | 31.9650i | 2.36292i | ||||||||
\(184\) | 5.51806 | 0.406797 | ||||||||
\(185\) | 2.68364 | − | 14.3948i | 0.197305 | − | 1.05833i | ||||
\(186\) | 34.5232 | 2.53136 | ||||||||
\(187\) | − | 6.84485i | − | 0.500545i | ||||||
\(188\) | − | 9.21386i | − | 0.671990i | ||||||
\(189\) | 51.7567 | 3.76474 | ||||||||
\(190\) | 0.756002 | − | 4.05513i | 0.0548461 | − | 0.294190i | ||||
\(191\) | 20.6801 | 1.49636 | 0.748181 | − | 0.663494i | \(-0.230927\pi\) | ||||
0.748181 | + | 0.663494i | \(0.230927\pi\) | |||||||
\(192\) | − | 9.07694i | − | 0.655072i | ||||||
\(193\) | 16.6325i | 1.19723i | 0.801037 | + | 0.598615i | \(0.204282\pi\) | ||||
−0.801037 | + | 0.598615i | \(0.795718\pi\) | |||||||
\(194\) | 9.45719 | 0.678987 | ||||||||
\(195\) | 14.8666 | + | 2.77161i | 1.06462 | + | 0.198479i | ||||
\(196\) | 3.22739 | 0.230528 | ||||||||
\(197\) | − | 18.4260i | − | 1.31280i | −0.754414 | − | 0.656399i | \(-0.772079\pi\) | ||
0.754414 | − | 0.656399i | \(-0.227921\pi\) | |||||||
\(198\) | 14.9335i | 1.06128i | ||||||||
\(199\) | −16.4923 | −1.16911 | −0.584555 | − | 0.811354i | \(-0.698731\pi\) | ||||
−0.584555 | + | 0.811354i | \(0.698731\pi\) | |||||||
\(200\) | −1.98385 | + | 5.13566i | −0.140279 | + | 0.363146i | ||||
\(201\) | −31.9762 | −2.25542 | ||||||||
\(202\) | − | 21.4152i | − | 1.50677i | ||||||
\(203\) | 21.6029i | 1.51623i | ||||||||
\(204\) | −31.9907 | −2.23980 | ||||||||
\(205\) | 18.9814 | + | 3.53872i | 1.32572 | + | 0.247155i | ||||
\(206\) | 1.96315 | 0.136779 | ||||||||
\(207\) | 40.5679i | 2.81966i | ||||||||
\(208\) | 9.82203i | 0.681035i | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | −7.67952 | + | 41.1923i | −0.529937 | + | 2.84254i | ||||
\(211\) | −6.01612 | −0.414167 | −0.207083 | − | 0.978323i | \(-0.566397\pi\) | ||||
−0.207083 | + | 0.978323i | \(0.566397\pi\) | |||||||
\(212\) | − | 15.9219i | − | 1.09352i | ||||||
\(213\) | 13.1100i | 0.898283i | ||||||||
\(214\) | 16.0945 | 1.10019 | ||||||||
\(215\) | −1.14905 | + | 6.16341i | −0.0783647 | + | 0.420341i | ||||
\(216\) | −18.6874 | −1.27152 | ||||||||
\(217\) | − | 17.1337i | − | 1.16311i | ||||||
\(218\) | − | 0.568080i | − | 0.0384752i | ||||||
\(219\) | 0.602944 | 0.0407432 | ||||||||
\(220\) | −3.08432 | − | 0.575014i | −0.207945 | − | 0.0387674i | ||||
\(221\) | 13.8978 | 0.934865 | ||||||||
\(222\) | 40.2387i | 2.70065i | ||||||||
\(223\) | 20.7672i | 1.39068i | 0.718683 | + | 0.695338i | \(0.244745\pi\) | ||||
−0.718683 | + | 0.695338i | \(0.755255\pi\) | |||||||
\(224\) | −20.4989 | −1.36964 | ||||||||
\(225\) | −37.7565 | − | 14.5849i | −2.51710 | − | 0.972328i | ||||
\(226\) | 12.4404 | 0.827525 | ||||||||
\(227\) | 8.74910i | 0.580698i | 0.956921 | + | 0.290349i | \(0.0937714\pi\) | ||||
−0.956921 | + | 0.290349i | \(0.906229\pi\) | |||||||
\(228\) | 4.67369i | 0.309523i | ||||||||
\(229\) | −19.4394 | −1.28459 | −0.642297 | − | 0.766456i | \(-0.722018\pi\) | ||||
−0.642297 | + | 0.766456i | \(0.722018\pi\) | |||||||
\(230\) | −20.3218 | − | 3.78862i | −1.33998 | − | 0.249814i | ||||
\(231\) | 10.1581 | 0.668352 | ||||||||
\(232\) | − | 7.80002i | − | 0.512096i | ||||||
\(233\) | 3.01048i | 0.197223i | 0.995126 | + | 0.0986114i | \(0.0314401\pi\) | ||||
−0.995126 | + | 0.0986114i | \(0.968560\pi\) | |||||||
\(234\) | −30.3209 | −1.98214 | ||||||||
\(235\) | 2.69112 | − | 14.4349i | 0.175549 | − | 0.941629i | ||||
\(236\) | −8.20547 | −0.534130 | ||||||||
\(237\) | 49.3437i | 3.20522i | ||||||||
\(238\) | 38.5077i | 2.49608i | ||||||||
\(239\) | −9.72562 | −0.629098 | −0.314549 | − | 0.949241i | \(-0.601853\pi\) | ||||
−0.314549 | + | 0.949241i | \(0.601853\pi\) | |||||||
\(240\) | 6.60346 | − | 35.4203i | 0.426251 | − | 2.28637i | ||||
\(241\) | 6.21619 | 0.400420 | 0.200210 | − | 0.979753i | \(-0.435838\pi\) | ||||
0.200210 | + | 0.979753i | \(0.435838\pi\) | |||||||
\(242\) | 1.84475i | 0.118585i | ||||||||
\(243\) | − | 56.4937i | − | 3.62407i | ||||||
\(244\) | 13.4649 | 0.861999 | ||||||||
\(245\) | 5.05619 | + | 0.942632i | 0.323028 | + | 0.0602226i | ||||
\(246\) | −53.0599 | −3.38298 | ||||||||
\(247\) | − | 2.03040i | − | 0.129191i | ||||||
\(248\) | 6.18635i | 0.392834i | ||||||||
\(249\) | −12.3278 | −0.781242 | ||||||||
\(250\) | 10.8322 | − | 17.5515i | 0.685086 | − | 1.11005i | ||||
\(251\) | −2.92900 | −0.184877 | −0.0924385 | − | 0.995718i | \(-0.529466\pi\) | ||||
−0.0924385 | + | 0.995718i | \(0.529466\pi\) | |||||||
\(252\) | − | 34.6388i | − | 2.18204i | ||||||
\(253\) | 5.01139i | 0.315064i | ||||||||
\(254\) | 10.5361 | 0.661093 | ||||||||
\(255\) | −50.1183 | − | 9.34361i | −3.13853 | − | 0.585120i | ||||
\(256\) | 20.9765 | 1.31103 | ||||||||
\(257\) | 13.7445i | 0.857361i | 0.903456 | + | 0.428681i | \(0.141021\pi\) | ||||
−0.903456 | + | 0.428681i | \(0.858979\pi\) | |||||||
\(258\) | − | 17.2290i | − | 1.07263i | ||||||
\(259\) | 19.9703 | 1.24089 | ||||||||
\(260\) | 1.16751 | − | 6.26239i | 0.0724056 | − | 0.388377i | ||||
\(261\) | 57.3444 | 3.54953 | ||||||||
\(262\) | − | 24.3415i | − | 1.50382i | ||||||
\(263\) | − | 10.7626i | − | 0.663653i | −0.943340 | − | 0.331826i | \(-0.892335\pi\) | ||
0.943340 | − | 0.331826i | \(-0.107665\pi\) | |||||||
\(264\) | −3.66770 | −0.225732 | ||||||||
\(265\) | 4.65035 | − | 24.9441i | 0.285669 | − | 1.53230i | ||||
\(266\) | 5.62579 | 0.344939 | ||||||||
\(267\) | 34.3962i | 2.10501i | ||||||||
\(268\) | 13.4696i | 0.822785i | ||||||||
\(269\) | 19.0096 | 1.15903 | 0.579517 | − | 0.814960i | \(-0.303241\pi\) | ||||
0.579517 | + | 0.814960i | \(0.303241\pi\) | |||||||
\(270\) | 68.8217 | + | 12.8305i | 4.18835 | + | 0.780840i | ||||
\(271\) | −16.9828 | −1.03163 | −0.515816 | − | 0.856699i | \(-0.672511\pi\) | ||||
−0.515816 | + | 0.856699i | \(0.672511\pi\) | |||||||
\(272\) | − | 33.1120i | − | 2.00771i | ||||||
\(273\) | 20.6249i | 1.24828i | ||||||||
\(274\) | −9.69149 | −0.585485 | ||||||||
\(275\) | −4.66411 | − | 1.80169i | −0.281256 | − | 0.108646i | ||||
\(276\) | 23.4217 | 1.40982 | ||||||||
\(277\) | − | 13.0510i | − | 0.784158i | −0.919932 | − | 0.392079i | \(-0.871756\pi\) | ||
0.919932 | − | 0.392079i | \(-0.128244\pi\) | |||||||
\(278\) | 18.9730i | 1.13793i | ||||||||
\(279\) | −45.4810 | −2.72288 | ||||||||
\(280\) | −7.38141 | − | 1.37612i | −0.441123 | − | 0.0822392i | ||||
\(281\) | −4.68913 | −0.279730 | −0.139865 | − | 0.990171i | \(-0.544667\pi\) | ||||
−0.139865 | + | 0.990171i | \(0.544667\pi\) | |||||||
\(282\) | 40.3508i | 2.40286i | ||||||||
\(283\) | 31.8679i | 1.89435i | 0.320715 | + | 0.947176i | \(0.396077\pi\) | ||||
−0.320715 | + | 0.947176i | \(0.603923\pi\) | |||||||
\(284\) | 5.52243 | 0.327696 | ||||||||
\(285\) | −1.36506 | + | 7.32204i | −0.0808590 | + | 0.433720i | ||||
\(286\) | −3.74558 | −0.221481 | ||||||||
\(287\) | 26.3334i | 1.55441i | ||||||||
\(288\) | 54.4137i | 3.20636i | ||||||||
\(289\) | −29.8520 | −1.75600 | ||||||||
\(290\) | −5.35538 | + | 28.7258i | −0.314479 | + | 1.68684i | ||||
\(291\) | −17.0761 | −1.00102 | ||||||||
\(292\) | − | 0.253983i | − | 0.0148632i | ||||||
\(293\) | 4.17199i | 0.243730i | 0.992547 | + | 0.121865i | \(0.0388875\pi\) | ||||
−0.992547 | + | 0.121865i | \(0.961112\pi\) | |||||||
\(294\) | −14.1339 | −0.824306 | ||||||||
\(295\) | −12.8551 | − | 2.39659i | −0.748453 | − | 0.139535i | ||||
\(296\) | −7.21054 | −0.419104 | ||||||||
\(297\) | − | 16.9715i | − | 0.984788i | ||||||
\(298\) | 11.6256i | 0.673452i | ||||||||
\(299\) | −10.1751 | −0.588442 | ||||||||
\(300\) | −8.42055 | + | 21.7986i | −0.486160 | + | 1.25854i | ||||
\(301\) | −8.55068 | −0.492853 | ||||||||
\(302\) | 5.97722i | 0.343950i | ||||||||
\(303\) | 38.6679i | 2.22141i | ||||||||
\(304\) | −4.83750 | −0.277449 | ||||||||
\(305\) | 21.0947 | + | 3.93272i | 1.20788 | + | 0.225187i | ||||
\(306\) | 102.218 | 5.84340 | ||||||||
\(307\) | − | 16.6706i | − | 0.951441i | −0.879596 | − | 0.475721i | \(-0.842187\pi\) | ||
0.879596 | − | 0.475721i | \(-0.157813\pi\) | |||||||
\(308\) | − | 4.27897i | − | 0.243817i | ||||||
\(309\) | −3.54472 | −0.201652 | ||||||||
\(310\) | 4.24746 | − | 22.7830i | 0.241240 | − | 1.29399i | ||||
\(311\) | 14.0897 | 0.798955 | 0.399478 | − | 0.916743i | \(-0.369192\pi\) | ||||
0.399478 | + | 0.916743i | \(0.369192\pi\) | |||||||
\(312\) | − | 7.44689i | − | 0.421597i | ||||||
\(313\) | 11.3840i | 0.643462i | 0.946831 | + | 0.321731i | \(0.104265\pi\) | ||||
−0.946831 | + | 0.321731i | \(0.895735\pi\) | |||||||
\(314\) | 3.18642 | 0.179820 | ||||||||
\(315\) | 10.1170 | − | 54.2669i | 0.570030 | − | 3.05759i | ||||
\(316\) | 20.7854 | 1.16927 | ||||||||
\(317\) | 21.4233i | 1.20325i | 0.798777 | + | 0.601627i | \(0.205481\pi\) | ||||
−0.798777 | + | 0.601627i | \(0.794519\pi\) | |||||||
\(318\) | 69.7278i | 3.91014i | ||||||||
\(319\) | 7.08382 | 0.396618 | ||||||||
\(320\) | −5.99017 | − | 1.11676i | −0.334861 | − | 0.0624285i | ||||
\(321\) | −29.0606 | −1.62200 | ||||||||
\(322\) | − | 28.1931i | − | 1.57114i | ||||||
\(323\) | 6.84485i | 0.380858i | ||||||||
\(324\) | −45.2445 | −2.51358 | ||||||||
\(325\) | 3.65815 | − | 9.46999i | 0.202917 | − | 0.525300i | ||||
\(326\) | 16.7248 | 0.926300 | ||||||||
\(327\) | 1.02574i | 0.0567236i | ||||||||
\(328\) | − | 9.50802i | − | 0.524993i | ||||||
\(329\) | 20.0259 | 1.10407 | ||||||||
\(330\) | 13.5074 | + | 2.51819i | 0.743556 | + | 0.138622i | ||||
\(331\) | −24.0940 | −1.32433 | −0.662164 | − | 0.749359i | \(-0.730362\pi\) | ||||
−0.662164 | + | 0.749359i | \(0.730362\pi\) | |||||||
\(332\) | 5.19293i | 0.284999i | ||||||||
\(333\) | − | 53.0107i | − | 2.90497i | ||||||
\(334\) | 18.1758 | 0.994533 | ||||||||
\(335\) | −3.93409 | + | 21.1021i | −0.214942 | + | 1.15293i | ||||
\(336\) | 49.1396 | 2.68079 | ||||||||
\(337\) | − | 3.10795i | − | 0.169301i | −0.996411 | − | 0.0846505i | \(-0.973023\pi\) | ||
0.996411 | − | 0.0846505i | \(-0.0269774\pi\) | |||||||
\(338\) | 16.3768i | 0.890780i | ||||||||
\(339\) | −22.4628 | −1.22001 | ||||||||
\(340\) | −3.93588 | + | 21.1117i | −0.213453 | + | 1.14494i | ||||
\(341\) | −5.61832 | −0.304249 | ||||||||
\(342\) | − | 14.9335i | − | 0.807512i | ||||||
\(343\) | − | 14.3327i | − | 0.773894i | ||||||
\(344\) | 3.08733 | 0.166458 | ||||||||
\(345\) | 36.6936 | + | 6.84084i | 1.97552 | + | 0.368298i | ||||
\(346\) | 25.1455 | 1.35183 | ||||||||
\(347\) | − | 24.4357i | − | 1.31178i | −0.754858 | − | 0.655889i | \(-0.772294\pi\) | ||
0.754858 | − | 0.655889i | \(-0.227706\pi\) | |||||||
\(348\) | − | 33.1076i | − | 1.77475i | ||||||
\(349\) | 17.6089 | 0.942582 | 0.471291 | − | 0.881978i | \(-0.343788\pi\) | ||||
0.471291 | + | 0.881978i | \(0.343788\pi\) | |||||||
\(350\) | 26.2393 | + | 10.1359i | 1.40255 | + | 0.541789i | ||||
\(351\) | 34.4589 | 1.83928 | ||||||||
\(352\) | 6.72178i | 0.358272i | ||||||||
\(353\) | − | 1.98528i | − | 0.105666i | −0.998603 | − | 0.0528329i | \(-0.983175\pi\) | ||
0.998603 | − | 0.0528329i | \(-0.0168251\pi\) | |||||||
\(354\) | 35.9347 | 1.90991 | ||||||||
\(355\) | 8.65172 | + | 1.61295i | 0.459186 | + | 0.0856066i | ||||
\(356\) | 14.4890 | 0.767915 | ||||||||
\(357\) | − | 69.5305i | − | 3.67994i | ||||||
\(358\) | 2.31501i | 0.122352i | ||||||||
\(359\) | −20.2134 | −1.06682 | −0.533410 | − | 0.845857i | \(-0.679090\pi\) | ||||
−0.533410 | + | 0.845857i | \(0.679090\pi\) | |||||||
\(360\) | −3.65289 | + | 19.5937i | −0.192524 | + | 1.03268i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − | 38.4296i | − | 2.01982i | ||||||
\(363\) | − | 3.33093i | − | 0.174829i | ||||||
\(364\) | 8.68800 | 0.455375 | ||||||||
\(365\) | 0.0741814 | − | 0.397902i | 0.00388283 | − | 0.0208272i | ||||
\(366\) | −58.9675 | −3.08228 | ||||||||
\(367\) | 11.7258i | 0.612081i | 0.952018 | + | 0.306041i | \(0.0990044\pi\) | ||||
−0.952018 | + | 0.306041i | \(0.900996\pi\) | |||||||
\(368\) | 24.2426i | 1.26373i | ||||||||
\(369\) | 69.9014 | 3.63892 | ||||||||
\(370\) | 26.5548 | + | 4.95065i | 1.38052 | + | 0.257372i | ||||
\(371\) | 34.6056 | 1.79663 | ||||||||
\(372\) | 26.2583i | 1.36143i | ||||||||
\(373\) | − | 5.98352i | − | 0.309815i | −0.987929 | − | 0.154908i | \(-0.950492\pi\) | ||
0.987929 | − | 0.154908i | \(-0.0495080\pi\) | |||||||
\(374\) | 12.6271 | 0.652930 | ||||||||
\(375\) | −19.5588 | + | 31.6914i | −1.01001 | + | 1.63654i | ||||
\(376\) | −7.23063 | −0.372891 | ||||||||
\(377\) | 14.3830i | 0.740760i | ||||||||
\(378\) | 95.4783i | 4.91087i | ||||||||
\(379\) | 24.5366 | 1.26036 | 0.630181 | − | 0.776448i | \(-0.282981\pi\) | ||||
0.630181 | + | 0.776448i | \(0.282981\pi\) | |||||||
\(380\) | 3.08432 | + | 0.575014i | 0.158222 | + | 0.0294976i | ||||
\(381\) | −19.0242 | −0.974641 | ||||||||
\(382\) | 38.1498i | 1.95191i | ||||||||
\(383\) | − | 31.5965i | − | 1.61450i | −0.590207 | − | 0.807252i | \(-0.700954\pi\) | ||
0.590207 | − | 0.807252i | \(-0.299046\pi\) | |||||||
\(384\) | −28.0349 | −1.43065 | ||||||||
\(385\) | 1.24977 | − | 6.70365i | 0.0636941 | − | 0.341649i | ||||
\(386\) | −30.6828 | −1.56171 | ||||||||
\(387\) | 22.6975i | 1.15378i | ||||||||
\(388\) | 7.19312i | 0.365175i | ||||||||
\(389\) | −3.90790 | −0.198139 | −0.0990693 | − | 0.995081i | \(-0.531587\pi\) | ||||
−0.0990693 | + | 0.995081i | \(0.531587\pi\) | |||||||
\(390\) | −5.11293 | + | 27.4253i | −0.258903 | + | 1.38873i | ||||
\(391\) | 34.3023 | 1.73474 | ||||||||
\(392\) | − | 2.53271i | − | 0.127921i | ||||||
\(393\) | 43.9516i | 2.21706i | ||||||||
\(394\) | 33.9914 | 1.71246 | ||||||||
\(395\) | 32.5635 | + | 6.07085i | 1.63845 | + | 0.305458i | ||||
\(396\) | −11.3584 | −0.570781 | ||||||||
\(397\) | − | 29.3623i | − | 1.47365i | −0.676082 | − | 0.736826i | \(-0.736324\pi\) | ||
0.676082 | − | 0.736826i | \(-0.263676\pi\) | |||||||
\(398\) | − | 30.4243i | − | 1.52503i | ||||||
\(399\) | −10.1581 | −0.508540 | ||||||||
\(400\) | −22.5626 | − | 8.71568i | −1.12813 | − | 0.435784i | ||||
\(401\) | −14.6124 | −0.729711 | −0.364855 | − | 0.931064i | \(-0.618882\pi\) | ||||
−0.364855 | + | 0.931064i | \(0.618882\pi\) | |||||||
\(402\) | − | 58.9881i | − | 2.94206i | ||||||
\(403\) | − | 11.4074i | − | 0.568244i | ||||||
\(404\) | 16.2884 | 0.810378 | ||||||||
\(405\) | −70.8823 | − | 13.2147i | −3.52217 | − | 0.656642i | ||||
\(406\) | −39.8521 | −1.97783 | ||||||||
\(407\) | − | 6.54847i | − | 0.324595i | ||||||
\(408\) | 25.1049i | 1.24288i | ||||||||
\(409\) | 2.46414 | 0.121844 | 0.0609219 | − | 0.998143i | \(-0.480596\pi\) | ||||
0.0609219 | + | 0.998143i | \(0.480596\pi\) | |||||||
\(410\) | −6.52807 | + | 35.0160i | −0.322399 | + | 1.72932i | ||||
\(411\) | 17.4992 | 0.863172 | ||||||||
\(412\) | 1.49317i | 0.0735632i | ||||||||
\(413\) | − | 17.8342i | − | 0.877566i | ||||||
\(414\) | −74.8377 | −3.67807 | ||||||||
\(415\) | −1.51671 | + | 8.13551i | −0.0744525 | + | 0.399357i | ||||
\(416\) | −13.6479 | −0.669143 | ||||||||
\(417\) | − | 34.2582i | − | 1.67763i | ||||||
\(418\) | − | 1.84475i | − | 0.0902299i | ||||||
\(419\) | −14.9423 | −0.729980 | −0.364990 | − | 0.931011i | \(-0.618928\pi\) | ||||
−0.364990 | + | 0.931011i | \(0.618928\pi\) | |||||||
\(420\) | −31.3308 | − | 5.84103i | −1.52878 | − | 0.285013i | ||||
\(421\) | −4.00737 | −0.195307 | −0.0976536 | − | 0.995220i | \(-0.531134\pi\) | ||||
−0.0976536 | + | 0.995220i | \(0.531134\pi\) | |||||||
\(422\) | − | 11.0983i | − | 0.540255i | ||||||
\(423\) | − | 53.1584i | − | 2.58465i | ||||||
\(424\) | −12.4948 | −0.606801 | ||||||||
\(425\) | −12.3323 | + | 31.9251i | −0.598205 | + | 1.54860i | ||||
\(426\) | −24.1847 | −1.17175 | ||||||||
\(427\) | 29.2653i | 1.41625i | ||||||||
\(428\) | 12.2414i | 0.591711i | ||||||||
\(429\) | 6.76312 | 0.326526 | ||||||||
\(430\) | −11.3700 | − | 2.11972i | −0.548309 | − | 0.102222i | ||||
\(431\) | 14.0623 | 0.677358 | 0.338679 | − | 0.940902i | \(-0.390020\pi\) | ||||
0.338679 | + | 0.940902i | \(0.390020\pi\) | |||||||
\(432\) | − | 82.0997i | − | 3.95003i | ||||||
\(433\) | 17.6798i | 0.849636i | 0.905279 | + | 0.424818i | \(0.139662\pi\) | ||||
−0.905279 | + | 0.424818i | \(0.860338\pi\) | |||||||
\(434\) | 31.6075 | 1.51721 | ||||||||
\(435\) | 9.66982 | − | 51.8680i | 0.463632 | − | 2.48688i | ||||
\(436\) | 0.432081 | 0.0206929 | ||||||||
\(437\) | − | 5.01139i | − | 0.239727i | ||||||
\(438\) | 1.11228i | 0.0531469i | ||||||||
\(439\) | −21.4590 | −1.02418 | −0.512090 | − | 0.858932i | \(-0.671129\pi\) | ||||
−0.512090 | + | 0.858932i | \(0.671129\pi\) | |||||||
\(440\) | −0.451245 | + | 2.42044i | −0.0215123 | + | 0.115390i | ||||
\(441\) | 18.6201 | 0.886670 | ||||||||
\(442\) | 25.6379i | 1.21947i | ||||||||
\(443\) | 0.0673464i | 0.00319972i | 0.999999 | + | 0.00159986i | \(0.000509252\pi\) | ||||
−0.999999 | + | 0.00159986i | \(0.999491\pi\) | |||||||
\(444\) | −30.6055 | −1.45247 | ||||||||
\(445\) | 22.6992 | + | 4.23184i | 1.07604 | + | 0.200608i | ||||
\(446\) | −38.3104 | −1.81405 | ||||||||
\(447\) | − | 20.9915i | − | 0.992862i | ||||||
\(448\) | − | 8.31034i | − | 0.392626i | ||||||
\(449\) | 33.4714 | 1.57961 | 0.789806 | − | 0.613357i | \(-0.210181\pi\) | ||||
0.789806 | + | 0.613357i | \(0.210181\pi\) | |||||||
\(450\) | 26.9056 | − | 69.6515i | 1.26834 | − | 3.28340i | ||||
\(451\) | 8.63500 | 0.406606 | ||||||||
\(452\) | 9.46217i | 0.445063i | ||||||||
\(453\) | − | 10.7926i | − | 0.507081i | ||||||
\(454\) | −16.1399 | −0.757484 | ||||||||
\(455\) | 13.6111 | + | 2.53753i | 0.638096 | + | 0.118961i | ||||
\(456\) | 3.66770 | 0.171756 | ||||||||
\(457\) | 19.1342i | 0.895059i | 0.894269 | + | 0.447529i | \(0.147696\pi\) | ||||
−0.894269 | + | 0.447529i | \(0.852304\pi\) | |||||||
\(458\) | − | 35.8610i | − | 1.67567i | ||||||
\(459\) | −116.168 | −5.42224 | ||||||||
\(460\) | 2.88162 | − | 15.4567i | 0.134356 | − | 0.720675i | ||||
\(461\) | −32.2664 | −1.50280 | −0.751398 | − | 0.659849i | \(-0.770620\pi\) | ||||
−0.751398 | + | 0.659849i | \(0.770620\pi\) | |||||||
\(462\) | 18.7391i | 0.871824i | ||||||||
\(463\) | 15.8834i | 0.738163i | 0.929397 | + | 0.369082i | \(0.120328\pi\) | ||||
−0.929397 | + | 0.369082i | \(0.879672\pi\) | |||||||
\(464\) | 34.2680 | 1.59085 | ||||||||
\(465\) | −7.66932 | + | 41.1375i | −0.355656 | + | 1.90771i | ||||
\(466\) | −5.55359 | −0.257265 | ||||||||
\(467\) | − | 20.0295i | − | 0.926853i | −0.886135 | − | 0.463427i | \(-0.846620\pi\) | ||
0.886135 | − | 0.463427i | \(-0.153380\pi\) | |||||||
\(468\) | − | 23.0621i | − | 1.06604i | ||||||
\(469\) | −29.2756 | −1.35182 | ||||||||
\(470\) | 26.6288 | + | 4.96445i | 1.22830 | + | 0.228993i | ||||
\(471\) | −5.75348 | −0.265106 | ||||||||
\(472\) | 6.43928i | 0.296392i | ||||||||
\(473\) | 2.80385i | 0.128921i | ||||||||
\(474\) | −91.0269 | −4.18100 | ||||||||
\(475\) | 4.66411 | + | 1.80169i | 0.214004 | + | 0.0826673i | ||||
\(476\) | −29.2889 | −1.34245 | ||||||||
\(477\) | − | 91.8597i | − | 4.20597i | ||||||
\(478\) | − | 17.9414i | − | 0.820619i | ||||||
\(479\) | −7.84252 | −0.358334 | −0.179167 | − | 0.983819i | \(-0.557340\pi\) | ||||
−0.179167 | + | 0.983819i | \(0.557340\pi\) | |||||||
\(480\) | 49.2172 | + | 9.17562i | 2.24645 | + | 0.418808i | ||||
\(481\) | 13.2960 | 0.606244 | ||||||||
\(482\) | 11.4673i | 0.522323i | ||||||||
\(483\) | 50.9061i | 2.31631i | ||||||||
\(484\) | −1.40312 | −0.0637780 | ||||||||
\(485\) | −2.10091 | + | 11.2691i | −0.0953976 | + | 0.511704i | ||||
\(486\) | 104.217 | 4.72738 | ||||||||
\(487\) | − | 11.8634i | − | 0.537584i | −0.963198 | − | 0.268792i | \(-0.913376\pi\) | ||
0.963198 | − | 0.268792i | \(-0.0866244\pi\) | |||||||
\(488\) | − | 10.5666i | − | 0.478329i | ||||||
\(489\) | −30.1987 | −1.36563 | ||||||||
\(490\) | −1.73892 | + | 9.32743i | −0.0785566 | + | 0.421370i | ||||
\(491\) | −0.188713 | −0.00851649 | −0.00425825 | − | 0.999991i | \(-0.501355\pi\) | ||||
−0.00425825 | + | 0.999991i | \(0.501355\pi\) | |||||||
\(492\) | − | 40.3573i | − | 1.81945i | ||||||
\(493\) | − | 48.4877i | − | 2.18378i | ||||||
\(494\) | 3.74558 | 0.168522 | ||||||||
\(495\) | −17.7947 | − | 3.31748i | −0.799810 | − | 0.149110i | ||||
\(496\) | −27.1786 | −1.22036 | ||||||||
\(497\) | 12.0028i | 0.538398i | ||||||||
\(498\) | − | 22.7417i | − | 1.01908i | ||||||
\(499\) | −38.9424 | −1.74330 | −0.871650 | − | 0.490130i | \(-0.836949\pi\) | ||||
−0.871650 | + | 0.490130i | \(0.836949\pi\) | |||||||
\(500\) | 13.3496 | + | 8.23892i | 0.597013 | + | 0.368456i | ||||
\(501\) | −32.8186 | −1.46623 | ||||||||
\(502\) | − | 5.40329i | − | 0.241161i | ||||||
\(503\) | 2.24218i | 0.0999739i | 0.998750 | + | 0.0499869i | \(0.0159180\pi\) | ||||
−0.998750 | + | 0.0499869i | \(0.984082\pi\) | |||||||
\(504\) | −27.1830 | −1.21083 | ||||||||
\(505\) | 25.5182 | + | 4.75739i | 1.13555 | + | 0.211701i | ||||
\(506\) | −9.24479 | −0.410981 | ||||||||
\(507\) | − | 29.5703i | − | 1.31327i | ||||||
\(508\) | 8.01373i | 0.355552i | ||||||||
\(509\) | 17.6190 | 0.780948 | 0.390474 | − | 0.920614i | \(-0.372311\pi\) | ||||
0.390474 | + | 0.920614i | \(0.372311\pi\) | |||||||
\(510\) | 17.2367 | − | 92.4559i | 0.763252 | − | 4.09402i | ||||
\(511\) | 0.552021 | 0.0244200 | ||||||||
\(512\) | 21.8634i | 0.966237i | ||||||||
\(513\) | 16.9715i | 0.749311i | ||||||||
\(514\) | −25.3553 | −1.11837 | ||||||||
\(515\) | −0.436114 | + | 2.33928i | −0.0192175 | + | 0.103081i | ||||
\(516\) | 13.1043 | 0.576886 | ||||||||
\(517\) | − | 6.56671i | − | 0.288804i | ||||||
\(518\) | 36.8403i | 1.61867i | ||||||||
\(519\) | −45.4033 | −1.99298 | ||||||||
\(520\) | −4.91445 | − | 0.916206i | −0.215513 | − | 0.0401783i | ||||
\(521\) | 27.3830 | 1.19967 | 0.599836 | − | 0.800123i | \(-0.295233\pi\) | ||||
0.599836 | + | 0.800123i | \(0.295233\pi\) | |||||||
\(522\) | 105.786i | 4.63014i | ||||||||
\(523\) | − | 29.1248i | − | 1.27354i | −0.771054 | − | 0.636770i | \(-0.780270\pi\) | ||
0.771054 | − | 0.636770i | \(-0.219730\pi\) | |||||||
\(524\) | 18.5141 | 0.808791 | ||||||||
\(525\) | −47.3783 | − | 18.3017i | −2.06776 | − | 0.798752i | ||||
\(526\) | 19.8544 | 0.865694 | ||||||||
\(527\) | 38.4566i | 1.67519i | ||||||||
\(528\) | − | 16.1134i | − | 0.701245i | ||||||
\(529\) | −2.11407 | −0.0919159 | ||||||||
\(530\) | 46.0157 | + | 8.57876i | 1.99879 | + | 0.372637i | ||||
\(531\) | −47.3405 | −2.05440 | ||||||||
\(532\) | 4.27897i | 0.185517i | ||||||||
\(533\) | 17.5325i | 0.759415i | ||||||||
\(534\) | −63.4525 | −2.74586 | ||||||||
\(535\) | −3.57538 | + | 19.1780i | −0.154577 | + | 0.829139i | ||||
\(536\) | 10.5703 | 0.456568 | ||||||||
\(537\) | − | 4.18005i | − | 0.180382i | ||||||
\(538\) | 35.0680i | 1.51189i | ||||||||
\(539\) | 2.30016 | 0.0990748 | ||||||||
\(540\) | −9.75886 | + | 52.3457i | −0.419955 | + | 2.25260i | ||||
\(541\) | −24.2865 | −1.04416 | −0.522079 | − | 0.852897i | \(-0.674843\pi\) | ||||
−0.522079 | + | 0.852897i | \(0.674843\pi\) | |||||||
\(542\) | − | 31.3291i | − | 1.34570i | ||||||
\(543\) | 69.3896i | 2.97779i | ||||||||
\(544\) | 46.0096 | 1.97265 | ||||||||
\(545\) | 0.676920 | + | 0.126199i | 0.0289960 | + | 0.00540577i | ||||
\(546\) | −38.0479 | −1.62830 | ||||||||
\(547\) | 0.567397i | 0.0242601i | 0.999926 | + | 0.0121301i | \(0.00386122\pi\) | ||||
−0.999926 | + | 0.0121301i | \(0.996139\pi\) | |||||||
\(548\) | − | 7.37133i | − | 0.314888i | ||||||
\(549\) | 77.6840 | 3.31547 | ||||||||
\(550\) | 3.32368 | − | 8.60413i | 0.141722 | − | 0.366881i | ||||
\(551\) | −7.08382 | −0.301781 | ||||||||
\(552\) | − | 18.3803i | − | 0.782318i | ||||||
\(553\) | 45.1763i | 1.92109i | ||||||||
\(554\) | 24.0759 | 1.02289 | ||||||||
\(555\) | −47.9481 | − | 8.93903i | −2.03528 | − | 0.379440i | ||||
\(556\) | −14.4308 | −0.612004 | ||||||||
\(557\) | − | 26.4054i | − | 1.11883i | −0.828887 | − | 0.559415i | \(-0.811026\pi\) | ||
0.828887 | − | 0.559415i | \(-0.188974\pi\) | |||||||
\(558\) | − | 83.9012i | − | 3.55182i | ||||||
\(559\) | −5.69293 | −0.240785 | ||||||||
\(560\) | 6.04575 | − | 32.4289i | 0.255480 | − | 1.37037i | ||||
\(561\) | −22.7998 | −0.962607 | ||||||||
\(562\) | − | 8.65029i | − | 0.364891i | ||||||
\(563\) | 30.1196i | 1.26939i | 0.772762 | + | 0.634695i | \(0.218874\pi\) | ||||
−0.772762 | + | 0.634695i | \(0.781126\pi\) | |||||||
\(564\) | −30.6908 | −1.29231 | ||||||||
\(565\) | −2.76364 | + | 14.8239i | −0.116267 | + | 0.623647i | ||||
\(566\) | −58.7885 | −2.47106 | ||||||||
\(567\) | − | 98.3370i | − | 4.12976i | ||||||
\(568\) | − | 4.33376i | − | 0.181840i | ||||||
\(569\) | 28.0302 | 1.17509 | 0.587543 | − | 0.809193i | \(-0.300095\pi\) | ||||
0.587543 | + | 0.809193i | \(0.300095\pi\) | |||||||
\(570\) | −13.5074 | − | 2.51819i | −0.565761 | − | 0.105476i | ||||
\(571\) | 15.1718 | 0.634918 | 0.317459 | − | 0.948272i | \(-0.397170\pi\) | ||||
0.317459 | + | 0.948272i | \(0.397170\pi\) | |||||||
\(572\) | − | 2.84888i | − | 0.119118i | ||||||
\(573\) | − | 68.8842i | − | 2.87768i | ||||||
\(574\) | −48.5787 | −2.02764 | ||||||||
\(575\) | 9.02899 | − | 23.3737i | 0.376535 | − | 0.974750i | ||||
\(576\) | −22.0596 | −0.919149 | ||||||||
\(577\) | 29.2142i | 1.21620i | 0.793859 | + | 0.608102i | \(0.208069\pi\) | ||||
−0.793859 | + | 0.608102i | \(0.791931\pi\) | |||||||
\(578\) | − | 55.0696i | − | 2.29059i | ||||||
\(579\) | 55.4016 | 2.30241 | ||||||||
\(580\) | −21.8488 | − | 4.07330i | −0.907221 | − | 0.169134i | ||||
\(581\) | −11.2866 | −0.468248 | ||||||||
\(582\) | − | 31.5013i | − | 1.30577i | ||||||
\(583\) | − | 11.3475i | − | 0.469967i | ||||||
\(584\) | −0.199314 | −0.00824769 | ||||||||
\(585\) | 6.73579 | − | 36.1302i | 0.278491 | − | 1.49380i | ||||
\(586\) | −7.69629 | −0.317931 | ||||||||
\(587\) | 3.60875i | 0.148949i | 0.997223 | + | 0.0744746i | \(0.0237280\pi\) | ||||
−0.997223 | + | 0.0744746i | \(0.976272\pi\) | |||||||
\(588\) | − | 10.7502i | − | 0.443332i | ||||||
\(589\) | 5.61832 | 0.231499 | ||||||||
\(590\) | 4.42112 | − | 23.7145i | 0.182015 | − | 0.976310i | ||||
\(591\) | −61.3757 | −2.52466 | ||||||||
\(592\) | − | 31.6782i | − | 1.30197i | ||||||
\(593\) | 32.6741i | 1.34177i | 0.741564 | + | 0.670883i | \(0.234085\pi\) | ||||
−0.741564 | + | 0.670883i | \(0.765915\pi\) | |||||||
\(594\) | 31.3083 | 1.28459 | ||||||||
\(595\) | −45.8855 | − | 8.55448i | −1.88112 | − | 0.350700i | ||||
\(596\) | −8.84240 | −0.362199 | ||||||||
\(597\) | 54.9349i | 2.24833i | ||||||||
\(598\) | − | 18.7706i | − | 0.767586i | ||||||
\(599\) | −10.1407 | −0.414336 | −0.207168 | − | 0.978305i | \(-0.566425\pi\) | ||||
−0.207168 | + | 0.978305i | \(0.566425\pi\) | |||||||
\(600\) | 17.1066 | + | 6.60807i | 0.698373 | + | 0.269773i | ||||
\(601\) | 41.2285 | 1.68174 | 0.840872 | − | 0.541234i | \(-0.182043\pi\) | ||||
0.840872 | + | 0.541234i | \(0.182043\pi\) | |||||||
\(602\) | − | 15.7739i | − | 0.642896i | ||||||
\(603\) | 77.7112i | 3.16465i | ||||||||
\(604\) | −4.54626 | −0.184985 | ||||||||
\(605\) | −2.19819 | − | 0.409812i | −0.0893693 | − | 0.0166612i | ||||
\(606\) | −71.3328 | −2.89770 | ||||||||
\(607\) | − | 2.27253i | − | 0.0922392i | −0.998936 | − | 0.0461196i | \(-0.985314\pi\) | ||
0.998936 | − | 0.0461196i | \(-0.0146855\pi\) | |||||||
\(608\) | − | 6.72178i | − | 0.272604i | ||||||
\(609\) | 71.9580 | 2.91588 | ||||||||
\(610\) | −7.25489 | + | 38.9146i | −0.293742 | + | 1.57561i | ||||
\(611\) | 13.3330 | 0.539396 | ||||||||
\(612\) | 77.7466i | 3.14272i | ||||||||
\(613\) | − | 19.8710i | − | 0.802584i | −0.915950 | − | 0.401292i | \(-0.868561\pi\) | ||
0.915950 | − | 0.401292i | \(-0.131439\pi\) | |||||||
\(614\) | 30.7532 | 1.24110 | ||||||||
\(615\) | 11.7873 | − | 63.2258i | 0.475308 | − | 2.54951i | ||||
\(616\) | −3.35794 | −0.135295 | ||||||||
\(617\) | − | 1.86490i | − | 0.0750781i | −0.999295 | − | 0.0375390i | \(-0.988048\pi\) | ||
0.999295 | − | 0.0375390i | \(-0.0119519\pi\) | |||||||
\(618\) | − | 6.53913i | − | 0.263042i | ||||||
\(619\) | −7.82377 | −0.314464 | −0.157232 | − | 0.987562i | \(-0.550257\pi\) | ||||
−0.157232 | + | 0.987562i | \(0.550257\pi\) | |||||||
\(620\) | 17.3287 | + | 3.23061i | 0.695937 | + | 0.129744i | ||||
\(621\) | 85.0510 | 3.41298 | ||||||||
\(622\) | 25.9921i | 1.04219i | ||||||||
\(623\) | 31.4912i | 1.26167i | ||||||||
\(624\) | 32.7166 | 1.30971 | ||||||||
\(625\) | 18.5078 | + | 16.8066i | 0.740313 | + | 0.672263i | ||||
\(626\) | −21.0007 | −0.839356 | ||||||||
\(627\) | 3.33093i | 0.133025i | ||||||||
\(628\) | 2.42358i | 0.0967116i | ||||||||
\(629\) | −44.8233 | −1.78722 | ||||||||
\(630\) | 100.109 | + | 18.6634i | 3.98844 | + | 0.743569i | ||||
\(631\) | −38.8465 | −1.54645 | −0.773227 | − | 0.634130i | \(-0.781358\pi\) | ||||
−0.773227 | + | 0.634130i | \(0.781358\pi\) | |||||||
\(632\) | − | 16.3115i | − | 0.648836i | ||||||
\(633\) | 20.0393i | 0.796491i | ||||||||
\(634\) | −39.5208 | −1.56957 | ||||||||
\(635\) | −2.34059 | + | 12.5547i | −0.0928835 | + | 0.498219i | ||||
\(636\) | −53.0348 | −2.10297 | ||||||||
\(637\) | 4.67023i | 0.185041i | ||||||||
\(638\) | 13.0679i | 0.517363i | ||||||||
\(639\) | 31.8611 | 1.26040 | ||||||||
\(640\) | −3.44920 | + | 18.5012i | −0.136341 | + | 0.731323i | ||||
\(641\) | 19.4192 | 0.767013 | 0.383507 | − | 0.923538i | \(-0.374716\pi\) | ||||
0.383507 | + | 0.923538i | \(0.374716\pi\) | |||||||
\(642\) | − | 53.6096i | − | 2.11580i | ||||||
\(643\) | − | 42.2251i | − | 1.66520i | −0.553877 | − | 0.832598i | \(-0.686852\pi\) | ||
0.553877 | − | 0.832598i | \(-0.313148\pi\) | |||||||
\(644\) | 21.4436 | 0.844996 | ||||||||
\(645\) | 20.5299 | + | 3.82742i | 0.808365 | + | 0.150704i | ||||
\(646\) | −12.6271 | −0.496805 | ||||||||
\(647\) | − | 1.82103i | − | 0.0715920i | −0.999359 | − | 0.0357960i | \(-0.988603\pi\) | ||
0.999359 | − | 0.0357960i | \(-0.0113967\pi\) | |||||||
\(648\) | 35.5058i | 1.39480i | ||||||||
\(649\) | −5.84803 | −0.229555 | ||||||||
\(650\) | 17.4698 | + | 6.74838i | 0.685222 | + | 0.264693i | ||||
\(651\) | −57.0713 | −2.23680 | ||||||||
\(652\) | 12.7208i | 0.498187i | ||||||||
\(653\) | − | 23.1753i | − | 0.906920i | −0.891277 | − | 0.453460i | \(-0.850190\pi\) | ||
0.891277 | − | 0.453460i | \(-0.149810\pi\) | |||||||
\(654\) | −1.89224 | −0.0739924 | ||||||||
\(655\) | 29.0051 | + | 5.40745i | 1.13332 | + | 0.211287i | ||||
\(656\) | 41.7718 | 1.63091 | ||||||||
\(657\) | − | 1.46533i | − | 0.0571678i | ||||||
\(658\) | 36.9429i | 1.44019i | ||||||||
\(659\) | −19.7606 | −0.769762 | −0.384881 | − | 0.922966i | \(-0.625758\pi\) | ||||
−0.384881 | + | 0.922966i | \(0.625758\pi\) | |||||||
\(660\) | −1.91533 | + | 10.2737i | −0.0745542 | + | 0.399902i | ||||
\(661\) | 48.4365 | 1.88396 | 0.941980 | − | 0.335669i | \(-0.108962\pi\) | ||||
0.941980 | + | 0.335669i | \(0.108962\pi\) | |||||||
\(662\) | − | 44.4475i | − | 1.72750i | ||||||
\(663\) | − | 46.2925i | − | 1.79785i | ||||||
\(664\) | 4.07518 | 0.158148 | ||||||||
\(665\) | −1.24977 | + | 6.70365i | −0.0484640 | + | 0.259956i | ||||
\(666\) | 97.7916 | 3.78935 | ||||||||
\(667\) | 35.4998i | 1.37456i | ||||||||
\(668\) | 13.8244i | 0.534884i | ||||||||
\(669\) | 69.1743 | 2.67443 | ||||||||
\(670\) | −38.9282 | − | 7.25743i | −1.50393 | − | 0.280379i | ||||
\(671\) | 9.59640 | 0.370465 | ||||||||
\(672\) | 68.2804i | 2.63397i | ||||||||
\(673\) | 29.8527i | 1.15074i | 0.817895 | + | 0.575368i | \(0.195141\pi\) | ||||
−0.817895 | + | 0.575368i | \(0.804859\pi\) | |||||||
\(674\) | 5.73341 | 0.220843 | ||||||||
\(675\) | −30.5775 | + | 79.1571i | −1.17693 | + | 3.04676i | ||||
\(676\) | −12.4562 | −0.479083 | ||||||||
\(677\) | 20.9974i | 0.806997i | 0.914980 | + | 0.403498i | \(0.132206\pi\) | ||||
−0.914980 | + | 0.403498i | \(0.867794\pi\) | |||||||
\(678\) | − | 41.4383i | − | 1.59143i | ||||||
\(679\) | −15.6340 | −0.599976 | ||||||||
\(680\) | 16.5675 | + | 3.08871i | 0.635336 | + | 0.118446i | ||||
\(681\) | 29.1427 | 1.11675 | ||||||||
\(682\) | − | 10.3644i | − | 0.396874i | ||||||
\(683\) | − | 10.2432i | − | 0.391944i | −0.980609 | − | 0.195972i | \(-0.937214\pi\) | ||
0.980609 | − | 0.195972i | \(-0.0627863\pi\) | |||||||
\(684\) | 11.3584 | 0.434299 | ||||||||
\(685\) | 2.15296 | − | 11.5483i | 0.0822605 | − | 0.441238i | ||||
\(686\) | 26.4403 | 1.00950 | ||||||||
\(687\) | 64.7515i | 2.47042i | ||||||||
\(688\) | 13.5636i | 0.517109i | ||||||||
\(689\) | 23.0400 | 0.877753 | ||||||||
\(690\) | −12.6197 | + | 67.6907i | −0.480422 | + | 2.57694i | ||||
\(691\) | −11.0857 | −0.421720 | −0.210860 | − | 0.977516i | \(-0.567626\pi\) | ||||
−0.210860 | + | 0.977516i | \(0.567626\pi\) | |||||||
\(692\) | 19.1256i | 0.727046i | ||||||||
\(693\) | − | 24.6870i | − | 0.937783i | ||||||
\(694\) | 45.0779 | 1.71113 | ||||||||
\(695\) | −22.6081 | − | 4.21485i | −0.857574 | − | 0.159879i | ||||
\(696\) | −25.9814 | −0.984821 | ||||||||
\(697\) | − | 59.1053i | − | 2.23877i | ||||||
\(698\) | 32.4841i | 1.22954i | ||||||||
\(699\) | 10.0277 | 0.379282 | ||||||||
\(700\) | −7.70938 | + | 19.9576i | −0.291387 | + | 0.754325i | ||||
\(701\) | −8.41247 | −0.317735 | −0.158867 | − | 0.987300i | \(-0.550784\pi\) | ||||
−0.158867 | + | 0.987300i | \(0.550784\pi\) | |||||||
\(702\) | 63.5682i | 2.39923i | ||||||||
\(703\) | 6.54847i | 0.246980i | ||||||||
\(704\) | −2.72504 | −0.102704 | ||||||||
\(705\) | −48.0817 | − | 8.96393i | −1.81086 | − | 0.337601i | ||||
\(706\) | 3.66235 | 0.137834 | ||||||||
\(707\) | 35.4022i | 1.33144i | ||||||||
\(708\) | 27.3319i | 1.02719i | ||||||||
\(709\) | 26.1580 | 0.982383 | 0.491191 | − | 0.871052i | \(-0.336562\pi\) | ||||
0.491191 | + | 0.871052i | \(0.336562\pi\) | |||||||
\(710\) | −2.97550 | + | 15.9603i | −0.111668 | + | 0.598979i | ||||
\(711\) | 119.919 | 4.49732 | ||||||||
\(712\) | − | 11.3703i | − | 0.426120i | ||||||
\(713\) | − | 28.1556i | − | 1.05444i | ||||||
\(714\) | 128.267 | 4.80026 | ||||||||
\(715\) | 0.832080 | − | 4.46320i | 0.0311180 | − | 0.166914i | ||||
\(716\) | −1.76080 | −0.0658040 | ||||||||
\(717\) | 32.3954i | 1.20983i | ||||||||
\(718\) | − | 37.2887i | − | 1.39160i | ||||||
\(719\) | 2.98827 | 0.111444 | 0.0557218 | − | 0.998446i | \(-0.482254\pi\) | ||||
0.0557218 | + | 0.998446i | \(0.482254\pi\) | |||||||
\(720\) | −86.0816 | − | 16.0483i | −3.20807 | − | 0.598085i | ||||
\(721\) | −3.24534 | −0.120863 | ||||||||
\(722\) | 1.84475i | 0.0686546i | ||||||||
\(723\) | − | 20.7057i | − | 0.770054i | ||||||
\(724\) | 29.2295 | 1.08631 | ||||||||
\(725\) | −33.0397 | − | 12.7629i | −1.22706 | − | 0.474001i | ||||
\(726\) | 6.14475 | 0.228053 | ||||||||
\(727\) | − | 28.0389i | − | 1.03990i | −0.854196 | − | 0.519952i | \(-0.825950\pi\) | ||
0.854196 | − | 0.519952i | \(-0.174050\pi\) | |||||||
\(728\) | − | 6.81795i | − | 0.252690i | ||||||
\(729\) | −91.4397 | −3.38666 | ||||||||
\(730\) | 0.734032 | + | 0.136847i | 0.0271677 | + | 0.00506492i | ||||
\(731\) | 19.1920 | 0.709840 | ||||||||
\(732\) | − | 44.8506i | − | 1.65772i | ||||||
\(733\) | 15.1597i | 0.559935i | 0.960009 | + | 0.279968i | \(0.0903237\pi\) | ||||
−0.960009 | + | 0.279968i | \(0.909676\pi\) | |||||||
\(734\) | −21.6312 | −0.798422 | ||||||||
\(735\) | 3.13985 | − | 16.8418i | 0.115815 | − | 0.621221i | ||||
\(736\) | −33.6855 | −1.24166 | ||||||||
\(737\) | 9.59976i | 0.353612i | ||||||||
\(738\) | 128.951i | 4.74675i | ||||||||
\(739\) | −37.6776 | −1.38599 | −0.692996 | − | 0.720942i | \(-0.743709\pi\) | ||||
−0.692996 | + | 0.720942i | \(0.743709\pi\) | |||||||
\(740\) | −3.76546 | + | 20.1976i | −0.138421 | + | 0.742477i | ||||
\(741\) | −6.76312 | −0.248449 | ||||||||
\(742\) | 63.8388i | 2.34360i | ||||||||
\(743\) | − | 19.3117i | − | 0.708476i | −0.935155 | − | 0.354238i | \(-0.884740\pi\) | ||
0.935155 | − | 0.354238i | \(-0.115260\pi\) | |||||||
\(744\) | 20.6063 | 0.755464 | ||||||||
\(745\) | −13.8530 | − | 2.58262i | −0.507533 | − | 0.0946200i | ||||
\(746\) | 11.0381 | 0.404134 | ||||||||
\(747\) | 29.9601i | 1.09618i | ||||||||
\(748\) | 9.60413i | 0.351162i | ||||||||
\(749\) | −26.6062 | −0.972170 | ||||||||
\(750\) | −58.4628 | − | 36.0812i | −2.13476 | − | 1.31750i | ||||
\(751\) | 39.8039 | 1.45246 | 0.726232 | − | 0.687450i | \(-0.241270\pi\) | ||||
0.726232 | + | 0.687450i | \(0.241270\pi\) | |||||||
\(752\) | − | 31.7664i | − | 1.15840i | ||||||
\(753\) | 9.75632i | 0.355540i | ||||||||
\(754\) | −26.5330 | −0.966276 | ||||||||
\(755\) | −7.12240 | − | 1.32784i | −0.259211 | − | 0.0483250i | ||||
\(756\) | −72.6206 | −2.64119 | ||||||||
\(757\) | 3.30928i | 0.120278i | 0.998190 | + | 0.0601389i | \(0.0191543\pi\) | ||||
−0.998190 | + | 0.0601389i | \(0.980846\pi\) | |||||||
\(758\) | 45.2641i | 1.64406i | ||||||||
\(759\) | 16.6926 | 0.605904 | ||||||||
\(760\) | 0.451245 | − | 2.42044i | 0.0163684 | − | 0.0877985i | ||||
\(761\) | −35.0055 | −1.26895 | −0.634475 | − | 0.772944i | \(-0.718783\pi\) | ||||
−0.634475 | + | 0.772944i | \(0.718783\pi\) | |||||||
\(762\) | − | 35.0950i | − | 1.27136i | ||||||
\(763\) | 0.939110i | 0.0339981i | ||||||||
\(764\) | −29.0166 | −1.04979 | ||||||||
\(765\) | −22.7077 | + | 121.802i | −0.820997 | + | 4.40375i | ||||
\(766\) | 58.2877 | 2.10602 | ||||||||
\(767\) | − | 11.8738i | − | 0.428739i | ||||||
\(768\) | − | 69.8714i | − | 2.52127i | ||||||
\(769\) | −36.8582 | −1.32914 | −0.664570 | − | 0.747226i | \(-0.731385\pi\) | ||||
−0.664570 | + | 0.747226i | \(0.731385\pi\) | |||||||
\(770\) | 12.3666 | + | 2.30552i | 0.445660 | + | 0.0830850i | ||||
\(771\) | 45.7822 | 1.64880 | ||||||||
\(772\) | − | 23.3373i | − | 0.839927i | ||||||
\(773\) | − | 11.3631i | − | 0.408704i | −0.978898 | − | 0.204352i | \(-0.934491\pi\) | ||
0.978898 | − | 0.204352i | \(-0.0655087\pi\) | |||||||
\(774\) | −41.8714 | −1.50504 | ||||||||
\(775\) | 26.2044 | + | 10.1225i | 0.941292 | + | 0.363610i | ||||
\(776\) | 5.64484 | 0.202638 | ||||||||
\(777\) | − | 66.5198i | − | 2.38638i | ||||||
\(778\) | − | 7.20912i | − | 0.258460i | ||||||
\(779\) | −8.63500 | −0.309381 | ||||||||
\(780\) | −20.8596 | − | 3.88888i | −0.746894 | − | 0.139244i | ||||
\(781\) | 3.93583 | 0.140835 | ||||||||
\(782\) | 63.2792i | 2.26286i | ||||||||
\(783\) | − | 120.223i | − | 4.29643i | ||||||
\(784\) | 11.1270 | 0.397393 | ||||||||
\(785\) | −0.707863 | + | 3.79691i | −0.0252647 | + | 0.135518i | ||||
\(786\) | −81.0798 | −2.89202 | ||||||||
\(787\) | − | 31.4505i | − | 1.12109i | −0.828124 | − | 0.560545i | \(-0.810592\pi\) | ||
0.828124 | − | 0.560545i | \(-0.189408\pi\) | |||||||
\(788\) | 25.8538i | 0.921004i | ||||||||
\(789\) | −35.8497 | −1.27628 | ||||||||
\(790\) | −11.1992 | + | 60.0716i | −0.398451 | + | 2.13725i | ||||
\(791\) | −20.5656 | −0.731230 | ||||||||
\(792\) | 8.91357i | 0.316730i | ||||||||
\(793\) | 19.4845i | 0.691914i | ||||||||
\(794\) | 54.1662 | 1.92229 | ||||||||
\(795\) | −83.0871 | − | 15.4900i | −2.94679 | − | 0.549375i | ||||
\(796\) | 23.1407 | 0.820199 | ||||||||
\(797\) | 24.2997i | 0.860739i | 0.902653 | + | 0.430370i | \(0.141617\pi\) | ||||
−0.902653 | + | 0.430370i | \(0.858383\pi\) | |||||||
\(798\) | − | 18.7391i | − | 0.663358i | ||||||
\(799\) | −44.9482 | −1.59015 | ||||||||
\(800\) | 12.1106 | − | 31.3511i | 0.428174 | − | 1.10843i | ||||
\(801\) | 83.5926 | 2.95360 | ||||||||
\(802\) | − | 26.9564i | − | 0.951862i | ||||||
\(803\) | − | 0.181013i | − | 0.00638782i | ||||||
\(804\) | 44.8663 | 1.58231 | ||||||||
\(805\) | 33.5946 | + | 6.26308i | 1.18405 | + | 0.220745i | ||||
\(806\) | 21.0439 | 0.741238 | ||||||||
\(807\) | − | 63.3197i | − | 2.22896i | ||||||
\(808\) | − | 12.7824i | − | 0.449684i | ||||||
\(809\) | −7.43324 | −0.261339 | −0.130669 | − | 0.991426i | \(-0.541713\pi\) | ||||
−0.130669 | + | 0.991426i | \(0.541713\pi\) | |||||||
\(810\) | 24.3778 | − | 130.760i | 0.856549 | − | 4.59445i | ||||
\(811\) | 37.0856 | 1.30225 | 0.651126 | − | 0.758969i | \(-0.274297\pi\) | ||||
0.651126 | + | 0.758969i | \(0.274297\pi\) | |||||||
\(812\) | − | 30.3114i | − | 1.06372i | ||||||
\(813\) | 56.5686i | 1.98395i | ||||||||
\(814\) | 12.0803 | 0.423415 | ||||||||
\(815\) | −3.71541 | + | 19.9291i | −0.130145 | + | 0.698087i | ||||
\(816\) | −110.294 | −3.86105 | ||||||||
\(817\) | − | 2.80385i | − | 0.0980944i | ||||||
\(818\) | 4.54573i | 0.158938i | ||||||||
\(819\) | 50.1244 | 1.75149 | ||||||||
\(820\) | −26.6331 | − | 4.96524i | −0.930068 | − | 0.173394i | ||||
\(821\) | −33.4666 | −1.16799 | −0.583997 | − | 0.811756i | \(-0.698512\pi\) | ||||
−0.583997 | + | 0.811756i | \(0.698512\pi\) | |||||||
\(822\) | 32.2817i | 1.12595i | ||||||||
\(823\) | − | 15.7212i | − | 0.548005i | −0.961729 | − | 0.274002i | \(-0.911652\pi\) | ||
0.961729 | − | 0.274002i | \(-0.0883476\pi\) | |||||||
\(824\) | 1.17177 | 0.0408207 | ||||||||
\(825\) | −6.00132 | + | 15.5358i | −0.208939 | + | 0.540889i | ||||
\(826\) | 32.8998 | 1.14473 | ||||||||
\(827\) | − | 1.26766i | − | 0.0440808i | −0.999757 | − | 0.0220404i | \(-0.992984\pi\) | ||
0.999757 | − | 0.0220404i | \(-0.00701624\pi\) | |||||||
\(828\) | − | 56.9214i | − | 1.97816i | ||||||
\(829\) | −36.9425 | −1.28307 | −0.641534 | − | 0.767095i | \(-0.721702\pi\) | ||||
−0.641534 | + | 0.767095i | \(0.721702\pi\) | |||||||
\(830\) | −15.0080 | − | 2.79796i | −0.520936 | − | 0.0971187i | ||||
\(831\) | −43.4720 | −1.50803 | ||||||||
\(832\) | − | 5.53292i | − | 0.191819i | ||||||
\(833\) | − | 15.7442i | − | 0.545506i | ||||||
\(834\) | 63.1979 | 2.18836 | ||||||||
\(835\) | −4.03774 | + | 21.6581i | −0.139732 | + | 0.749509i | ||||
\(836\) | 1.40312 | 0.0485278 | ||||||||
\(837\) | 95.3515i | 3.29583i | ||||||||
\(838\) | − | 27.5649i | − | 0.952214i | ||||||
\(839\) | −36.7122 | −1.26745 | −0.633723 | − | 0.773560i | \(-0.718474\pi\) | ||||
−0.633723 | + | 0.773560i | \(0.718474\pi\) | |||||||
\(840\) | −4.58378 | + | 24.5870i | −0.158155 | + | 0.848331i | ||||
\(841\) | 21.1805 | 0.730363 | ||||||||
\(842\) | − | 7.39261i | − | 0.254766i | ||||||
\(843\) | 15.6192i | 0.537953i | ||||||||
\(844\) | 8.44132 | 0.290562 | ||||||||
\(845\) | −19.5144 | − | 3.63810i | −0.671317 | − | 0.125155i | ||||
\(846\) | 98.0641 | 3.37151 | ||||||||
\(847\) | − | 3.04962i | − | 0.104786i | ||||||
\(848\) | − | 54.8937i | − | 1.88506i | ||||||
\(849\) | 106.150 | 3.64306 | ||||||||
\(850\) | −58.8940 | − | 22.7501i | −2.02005 | − | 0.780321i | ||||
\(851\) | 32.8169 | 1.12495 | ||||||||
\(852\) | − | 18.3949i | − | 0.630198i | ||||||
\(853\) | 49.3564i | 1.68993i | 0.534820 | + | 0.844966i | \(0.320379\pi\) | ||||
−0.534820 | + | 0.844966i | \(0.679621\pi\) | |||||||
\(854\) | −53.9873 | −1.84741 | ||||||||
\(855\) | 17.7947 | + | 3.31748i | 0.608564 | + | 0.113455i | ||||
\(856\) | 9.60652 | 0.328344 | ||||||||
\(857\) | 20.5776i | 0.702916i | 0.936204 | + | 0.351458i | \(0.114314\pi\) | ||||
−0.936204 | + | 0.351458i | \(0.885686\pi\) | |||||||
\(858\) | 12.4763i | 0.425933i | ||||||||
\(859\) | 38.0186 | 1.29718 | 0.648589 | − | 0.761138i | \(-0.275359\pi\) | ||||
0.648589 | + | 0.761138i | \(0.275359\pi\) | |||||||
\(860\) | 1.61225 | − | 8.64798i | 0.0549774 | − | 0.294894i | ||||
\(861\) | 87.7149 | 2.98932 | ||||||||
\(862\) | 25.9415i | 0.883571i | ||||||||
\(863\) | 5.66508i | 0.192841i | 0.995341 | + | 0.0964207i | \(0.0307394\pi\) | ||||
−0.995341 | + | 0.0964207i | \(0.969261\pi\) | |||||||
\(864\) | 114.079 | 3.88105 | ||||||||
\(865\) | −5.58606 | + | 29.9631i | −0.189932 | + | 1.01878i | ||||
\(866\) | −32.6148 | −1.10830 | ||||||||
\(867\) | 99.4351i | 3.37699i | ||||||||
\(868\) | 24.0406i | 0.815991i | ||||||||
\(869\) | 14.8138 | 0.502522 | ||||||||
\(870\) | 95.6837 | + | 17.8384i | 3.24398 | + | 0.604779i | ||||
\(871\) | −19.4913 | −0.660438 | ||||||||
\(872\) | − | 0.339078i | − | 0.0114826i | ||||||
\(873\) | 41.4999i | 1.40456i | ||||||||
\(874\) | 9.24479 | 0.312710 | ||||||||
\(875\) | −17.9070 | + | 29.0148i | −0.605366 | + | 0.980880i | ||||
\(876\) | −0.846000 | −0.0285837 | ||||||||
\(877\) | 34.0684i | 1.15041i | 0.818010 | + | 0.575204i | \(0.195077\pi\) | ||||
−0.818010 | + | 0.575204i | \(0.804923\pi\) | |||||||
\(878\) | − | 39.5865i | − | 1.33598i | ||||||
\(879\) | 13.8966 | 0.468721 | ||||||||
\(880\) | −10.6338 | − | 1.98246i | −0.358464 | − | 0.0668288i | ||||
\(881\) | −2.23009 | −0.0751338 | −0.0375669 | − | 0.999294i | \(-0.511961\pi\) | ||||
−0.0375669 | + | 0.999294i | \(0.511961\pi\) | |||||||
\(882\) | 34.3494i | 1.15661i | ||||||||
\(883\) | 15.3195i | 0.515541i | 0.966206 | + | 0.257770i | \(0.0829878\pi\) | ||||
−0.966206 | + | 0.257770i | \(0.917012\pi\) | |||||||
\(884\) | −19.5002 | −0.655862 | ||||||||
\(885\) | −7.98289 | + | 42.8195i | −0.268342 | + | 1.43936i | ||||
\(886\) | −0.124238 | −0.00417384 | ||||||||
\(887\) | 26.1458i | 0.877891i | 0.898514 | + | 0.438946i | \(0.144648\pi\) | ||||
−0.898514 | + | 0.438946i | \(0.855352\pi\) | |||||||
\(888\) | 24.0178i | 0.805985i | ||||||||
\(889\) | −17.4175 | −0.584164 | ||||||||
\(890\) | −7.80669 | + | 41.8744i | −0.261681 | + | 1.40363i | ||||
\(891\) | −32.2457 | −1.08027 | ||||||||
\(892\) | − | 29.1388i | − | 0.975640i | ||||||
\(893\) | 6.56671i | 0.219747i | ||||||||
\(894\) | 38.7241 | 1.29513 | ||||||||
\(895\) | −2.75855 | − | 0.514280i | −0.0922082 | − | 0.0171905i | ||||
\(896\) | −25.6672 | −0.857481 | ||||||||
\(897\) | 33.8926i | 1.13164i | ||||||||
\(898\) | 61.7464i | 2.06050i | ||||||||
\(899\) | −39.7992 | −1.32738 | ||||||||
\(900\) | 52.9768 | + | 20.4643i | 1.76589 | + | 0.682145i | ||||
\(901\) | −77.6722 | −2.58764 | ||||||||
\(902\) | 15.9294i | 0.530392i | ||||||||
\(903\) | 28.4817i | 0.947813i | ||||||||
\(904\) | 7.42549 | 0.246968 | ||||||||
\(905\) | 45.7924 | + | 8.53714i | 1.52219 | + | 0.283784i | ||||
\(906\) | 19.9097 | 0.661456 | ||||||||
\(907\) | − | 22.8895i | − | 0.760033i | −0.924980 | − | 0.380016i | \(-0.875918\pi\) | ||
0.924980 | − | 0.380016i | \(-0.124082\pi\) | |||||||
\(908\) | − | 12.2760i | − | 0.407393i | ||||||
\(909\) | 93.9741 | 3.11692 | ||||||||
\(910\) | −4.68111 | + | 25.1090i | −0.155177 | + | 0.832357i | ||||
\(911\) | 27.2999 | 0.904486 | 0.452243 | − | 0.891895i | \(-0.350624\pi\) | ||||
0.452243 | + | 0.891895i | \(0.350624\pi\) | |||||||
\(912\) | 16.1134i | 0.533568i | ||||||||
\(913\) | 3.70100i | 0.122485i | ||||||||
\(914\) | −35.2978 | −1.16755 | ||||||||
\(915\) | 13.0996 | − | 70.2652i | 0.433060 | − | 2.32290i | ||||
\(916\) | 27.2758 | 0.901217 | ||||||||
\(917\) | 40.2396i | 1.32883i | ||||||||
\(918\) | − | 214.301i | − | 7.07298i | ||||||
\(919\) | −15.2724 | −0.503791 | −0.251895 | − | 0.967754i | \(-0.581054\pi\) | ||||
−0.251895 | + | 0.967754i | \(0.581054\pi\) | |||||||
\(920\) | −12.1298 | − | 2.26137i | −0.399907 | − | 0.0745551i | ||||
\(921\) | −55.5287 | −1.82973 | ||||||||
\(922\) | − | 59.5236i | − | 1.96030i | ||||||
\(923\) | 7.99130i | 0.263037i | ||||||||
\(924\) | −14.2530 | −0.468888 | ||||||||
\(925\) | −11.7983 | + | 30.5428i | −0.387926 | + | 1.00424i | ||||
\(926\) | −29.3009 | −0.962888 | ||||||||
\(927\) | 8.61468i | 0.282943i | ||||||||
\(928\) | 47.6159i | 1.56307i | ||||||||
\(929\) | −33.8533 | −1.11069 | −0.555346 | − | 0.831619i | \(-0.687414\pi\) | ||||
−0.555346 | + | 0.831619i | \(0.687414\pi\) | |||||||
\(930\) | −75.8886 | − | 14.1480i | −2.48849 | − | 0.463932i | ||||
\(931\) | −2.30016 | −0.0753846 | ||||||||
\(932\) | − | 4.22405i | − | 0.138363i | ||||||
\(933\) | − | 46.9320i | − | 1.53648i | ||||||
\(934\) | 36.9494 | 1.20902 | ||||||||
\(935\) | −2.80510 | + | 15.0463i | −0.0917366 | + | 0.492067i | ||||
\(936\) | −18.0981 | −0.591554 | ||||||||
\(937\) | − | 18.7055i | − | 0.611082i | −0.952179 | − | 0.305541i | \(-0.901163\pi\) | ||
0.952179 | − | 0.305541i | \(-0.0988373\pi\) | |||||||
\(938\) | − | 54.0062i | − | 1.76337i | ||||||
\(939\) | 37.9194 | 1.23745 | ||||||||
\(940\) | −3.77595 | + | 20.2538i | −0.123158 | + | 0.660608i | ||||
\(941\) | −2.89106 | −0.0942457 | −0.0471229 | − | 0.998889i | \(-0.515005\pi\) | ||||
−0.0471229 | + | 0.998889i | \(0.515005\pi\) | |||||||
\(942\) | − | 10.6138i | − | 0.345815i | ||||||
\(943\) | 43.2734i | 1.40917i | ||||||||
\(944\) | −28.2898 | −0.920755 | ||||||||
\(945\) | −113.771 | − | 21.2105i | −3.70098 | − | 0.689977i | ||||
\(946\) | −5.17242 | −0.168170 | ||||||||
\(947\) | − | 47.2698i | − | 1.53606i | −0.640412 | − | 0.768031i | \(-0.721236\pi\) | ||
0.640412 | − | 0.768031i | \(-0.278764\pi\) | |||||||
\(948\) | − | 69.2349i | − | 2.24865i | ||||||
\(949\) | 0.367529 | 0.0119305 | ||||||||
\(950\) | −3.32368 | + | 8.60413i | −0.107834 | + | 0.279155i | ||||
\(951\) | 71.3597 | 2.31400 | ||||||||
\(952\) | 22.9846i | 0.744936i | ||||||||
\(953\) | 26.8871i | 0.870958i | 0.900199 | + | 0.435479i | \(0.143421\pi\) | ||||
−0.900199 | + | 0.435479i | \(0.856579\pi\) | |||||||
\(954\) | 169.459 | 5.48642 | ||||||||
\(955\) | −45.4590 | − | 8.47497i | −1.47102 | − | 0.274244i | ||||
\(956\) | 13.6462 | 0.441349 | ||||||||
\(957\) | − | 23.5957i | − | 0.762742i | ||||||
\(958\) | − | 14.4675i | − | 0.467424i | ||||||
\(959\) | 16.0213 | 0.517354 | ||||||||
\(960\) | −3.71984 | + | 19.9529i | −0.120057 | + | 0.643976i | ||||
\(961\) | 0.565505 | 0.0182421 | ||||||||
\(962\) | 24.5278i | 0.790808i | ||||||||
\(963\) | 70.6255i | 2.27588i | ||||||||
\(964\) | −8.72204 | −0.280918 | ||||||||
\(965\) | 6.81618 | − | 36.5614i | 0.219421 | − | 1.17695i | ||||
\(966\) | −93.9092 | −3.02148 | ||||||||
\(967\) | 37.8313i | 1.21657i | 0.793718 | + | 0.608286i | \(0.208143\pi\) | ||||
−0.793718 | + | 0.608286i | \(0.791857\pi\) | |||||||
\(968\) | 1.10110i | 0.0353908i | ||||||||
\(969\) | 22.7998 | 0.732434 | ||||||||
\(970\) | −20.7887 | − | 3.87567i | −0.667486 | − | 0.124440i | ||||
\(971\) | 24.5393 | 0.787504 | 0.393752 | − | 0.919217i | \(-0.371177\pi\) | ||||
0.393752 | + | 0.919217i | \(0.371177\pi\) | |||||||
\(972\) | 79.2672i | 2.54250i | ||||||||
\(973\) | − | 31.3648i | − | 1.00551i | ||||||
\(974\) | 21.8851 | 0.701244 | ||||||||
\(975\) | −31.5439 | − | 12.1850i | −1.01021 | − | 0.390234i | ||||
\(976\) | 46.4225 | 1.48595 | ||||||||
\(977\) | 5.57772i | 0.178447i | 0.996012 | + | 0.0892236i | \(0.0284386\pi\) | ||||
−0.996012 | + | 0.0892236i | \(0.971561\pi\) | |||||||
\(978\) | − | 55.7092i | − | 1.78138i | ||||||
\(979\) | 10.3263 | 0.330030 | ||||||||
\(980\) | −7.09443 | − | 1.32262i | −0.226623 | − | 0.0422496i | ||||
\(981\) | 2.49284 | 0.0795903 | ||||||||
\(982\) | − | 0.348129i | − | 0.0111092i | ||||||
\(983\) | 38.4618i | 1.22674i | 0.789795 | + | 0.613371i | \(0.210187\pi\) | ||||
−0.789795 | + | 0.613371i | \(0.789813\pi\) | |||||||
\(984\) | −31.6706 | −1.00962 | ||||||||
\(985\) | −7.55119 | + | 40.5039i | −0.240601 | + | 1.29056i | ||||
\(986\) | 89.4479 | 2.84860 | ||||||||
\(987\) | − | 66.7051i | − | 2.12325i | ||||||
\(988\) | 2.84888i | 0.0906350i | ||||||||
\(989\) | −14.0512 | −0.446803 | ||||||||
\(990\) | 6.11993 | − | 32.8268i | 0.194504 | − | 1.04330i | ||||
\(991\) | 35.2554 | 1.11992 | 0.559962 | − | 0.828518i | \(-0.310816\pi\) | ||||
0.559962 | + | 0.828518i | \(0.310816\pi\) | |||||||
\(992\) | − | 37.7651i | − | 1.19904i | ||||||
\(993\) | 80.2556i | 2.54683i | ||||||||
\(994\) | −22.1422 | −0.702307 | ||||||||
\(995\) | 36.2533 | + | 6.75875i | 1.14931 | + | 0.214267i | ||||
\(996\) | 17.2973 | 0.548087 | ||||||||
\(997\) | − | 50.5160i | − | 1.59986i | −0.600094 | − | 0.799930i | \(-0.704870\pi\) | ||
0.600094 | − | 0.799930i | \(-0.295130\pi\) | |||||||
\(998\) | − | 71.8391i | − | 2.27403i | ||||||
\(999\) | −111.137 | −3.51623 |
(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 | 1045.2.b.d.419.18 | yes | 22 | |
5.2 | odd | 4 | 5225.2.a.bb.1.5 | 22 | |||
5.3 | odd | 4 | 5225.2.a.bb.1.18 | 22 | |||
5.4 | even | 2 | inner | 1045.2.b.d.419.5 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.b.d.419.5 | ✓ | 22 | 5.4 | even | 2 | inner | |
1045.2.b.d.419.18 | yes | 22 | 1.1 | even | 1 | trivial | |
5225.2.a.bb.1.5 | 22 | 5.2 | odd | 4 | |||
5225.2.a.bb.1.18 | 22 | 5.3 | odd | 4 |