Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(241,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.241");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.c (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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 241.3 | ||
Root | \(0.988132 - 0.846795i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.241 |
Dual form | 363.3.c.e.241.14 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.53176i | − 1.26588i | −0.774201 | − | 0.632940i | \(-0.781848\pi\) | ||||
0.774201 | − | 0.632940i | \(-0.218152\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −2.40981 | −0.602454 | ||||||||
\(5\) | −8.44690 | −1.68938 | −0.844690 | − | 0.535255i | \(-0.820215\pi\) | ||||
−0.844690 | + | 0.535255i | \(0.820215\pi\) | |||||||
\(6\) | 4.38514i | 0.730856i | ||||||||
\(7\) | 2.44043i | 0.348633i | 0.984690 | + | 0.174316i | \(0.0557715\pi\) | ||||
−0.984690 | + | 0.174316i | \(0.944228\pi\) | |||||||
\(8\) | − 4.02597i | − 0.503246i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 21.3855i | 2.13855i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 4.17392 | 0.347827 | ||||||||
\(13\) | 11.7756i | 0.905819i | 0.891556 | + | 0.452910i | \(0.149614\pi\) | ||||
−0.891556 | + | 0.452910i | \(0.850386\pi\) | |||||||
\(14\) | 6.17858 | 0.441327 | ||||||||
\(15\) | 14.6305 | 0.975365 | ||||||||
\(16\) | −19.8321 | −1.23950 | ||||||||
\(17\) | 2.02988i | 0.119405i | 0.998216 | + | 0.0597024i | \(0.0190152\pi\) | ||||
−0.998216 | + | 0.0597024i | \(0.980985\pi\) | |||||||
\(18\) | − 7.59528i | − 0.421960i | ||||||||
\(19\) | 8.47011i | 0.445795i | 0.974842 | + | 0.222898i | \(0.0715516\pi\) | ||||
−0.974842 | + | 0.222898i | \(0.928448\pi\) | |||||||
\(20\) | 20.3555 | 1.01777 | ||||||||
\(21\) | − 4.22695i | − 0.201283i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 41.9571 | 1.82422 | 0.912110 | − | 0.409946i | \(-0.134452\pi\) | ||||
0.912110 | + | 0.409946i | \(0.134452\pi\) | |||||||
\(24\) | 6.97318i | 0.290549i | ||||||||
\(25\) | 46.3502 | 1.85401 | ||||||||
\(26\) | 29.8131 | 1.14666 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | − 5.88098i | − 0.210035i | ||||||||
\(29\) | − 24.6142i | − 0.848767i | −0.905483 | − | 0.424383i | \(-0.860491\pi\) | ||||
0.905483 | − | 0.424383i | \(-0.139509\pi\) | |||||||
\(30\) | − 37.0409i | − 1.23470i | ||||||||
\(31\) | 21.8135 | 0.703661 | 0.351831 | − | 0.936064i | \(-0.385559\pi\) | ||||
0.351831 | + | 0.936064i | \(0.385559\pi\) | |||||||
\(32\) | 34.1061i | 1.06582i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.13918 | 0.151152 | ||||||||
\(35\) | − 20.6141i | − 0.588973i | ||||||||
\(36\) | −7.22944 | −0.200818 | ||||||||
\(37\) | −16.0044 | −0.432551 | −0.216276 | − | 0.976332i | \(-0.569391\pi\) | ||||
−0.216276 | + | 0.976332i | \(0.569391\pi\) | |||||||
\(38\) | 21.4443 | 0.564324 | ||||||||
\(39\) | − 20.3960i | − 0.522975i | ||||||||
\(40\) | 34.0070i | 0.850174i | ||||||||
\(41\) | 52.6166i | 1.28333i | 0.766985 | + | 0.641665i | \(0.221756\pi\) | ||||
−0.766985 | + | 0.641665i | \(0.778244\pi\) | |||||||
\(42\) | −10.7016 | −0.254800 | ||||||||
\(43\) | 42.3507i | 0.984900i | 0.870341 | + | 0.492450i | \(0.163899\pi\) | ||||
−0.870341 | + | 0.492450i | \(0.836101\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −25.3407 | −0.563127 | ||||||||
\(46\) | − 106.225i | − 2.30924i | ||||||||
\(47\) | −16.1814 | −0.344284 | −0.172142 | − | 0.985072i | \(-0.555069\pi\) | ||||
−0.172142 | + | 0.985072i | \(0.555069\pi\) | |||||||
\(48\) | 34.3501 | 0.715628 | ||||||||
\(49\) | 43.0443 | 0.878455 | ||||||||
\(50\) | − 117.348i | − 2.34695i | ||||||||
\(51\) | − 3.51586i | − 0.0689384i | ||||||||
\(52\) | − 28.3771i | − 0.545714i | ||||||||
\(53\) | −49.5329 | −0.934582 | −0.467291 | − | 0.884104i | \(-0.654770\pi\) | ||||
−0.467291 | + | 0.884104i | \(0.654770\pi\) | |||||||
\(54\) | 13.1554i | 0.243619i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.82509 | 0.175448 | ||||||||
\(57\) | − 14.6707i | − 0.257380i | ||||||||
\(58\) | −62.3174 | −1.07444 | ||||||||
\(59\) | 19.9324 | 0.337838 | 0.168919 | − | 0.985630i | \(-0.445972\pi\) | ||||
0.168919 | + | 0.985630i | \(0.445972\pi\) | |||||||
\(60\) | −35.2567 | −0.587612 | ||||||||
\(61\) | 118.906i | 1.94928i | 0.223784 | + | 0.974639i | \(0.428159\pi\) | ||||
−0.223784 | + | 0.974639i | \(0.571841\pi\) | |||||||
\(62\) | − 55.2266i | − 0.890751i | ||||||||
\(63\) | 7.32129i | 0.116211i | ||||||||
\(64\) | 7.02040 | 0.109694 | ||||||||
\(65\) | − 99.4678i | − 1.53027i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.41442 | −0.0658869 | −0.0329434 | − | 0.999457i | \(-0.510488\pi\) | ||||
−0.0329434 | + | 0.999457i | \(0.510488\pi\) | |||||||
\(68\) | − 4.89164i | − 0.0719359i | ||||||||
\(69\) | −72.6718 | −1.05321 | ||||||||
\(70\) | −52.1899 | −0.745570 | ||||||||
\(71\) | 6.03591 | 0.0850128 | 0.0425064 | − | 0.999096i | \(-0.486466\pi\) | ||||
0.0425064 | + | 0.999096i | \(0.486466\pi\) | |||||||
\(72\) | − 12.0779i | − 0.167749i | ||||||||
\(73\) | − 6.08043i | − 0.0832936i | −0.999132 | − | 0.0416468i | \(-0.986740\pi\) | ||||
0.999132 | − | 0.0416468i | \(-0.0132604\pi\) | |||||||
\(74\) | 40.5193i | 0.547558i | ||||||||
\(75\) | −80.2809 | −1.07041 | ||||||||
\(76\) | − 20.4114i | − 0.268571i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −51.6379 | −0.662024 | ||||||||
\(79\) | 103.463i | 1.30965i | 0.755779 | + | 0.654827i | \(0.227258\pi\) | ||||
−0.755779 | + | 0.654827i | \(0.772742\pi\) | |||||||
\(80\) | 167.519 | 2.09399 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 133.213 | 1.62454 | ||||||||
\(83\) | − 30.1663i | − 0.363449i | −0.983349 | − | 0.181724i | \(-0.941832\pi\) | ||||
0.983349 | − | 0.181724i | \(-0.0581679\pi\) | |||||||
\(84\) | 10.1862i | 0.121264i | ||||||||
\(85\) | − 17.1462i | − 0.201720i | ||||||||
\(86\) | 107.222 | 1.24677 | ||||||||
\(87\) | 42.6331i | 0.490036i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −60.4650 | −0.679382 | −0.339691 | − | 0.940537i | \(-0.610323\pi\) | ||||
−0.339691 | + | 0.940537i | \(0.610323\pi\) | |||||||
\(90\) | 64.1566i | 0.712851i | ||||||||
\(91\) | −28.7376 | −0.315798 | ||||||||
\(92\) | −101.109 | −1.09901 | ||||||||
\(93\) | −37.7821 | −0.406259 | ||||||||
\(94\) | 40.9674i | 0.435823i | ||||||||
\(95\) | − 71.5462i | − 0.753118i | ||||||||
\(96\) | − 59.0736i | − 0.615350i | ||||||||
\(97\) | 36.6892 | 0.378239 | 0.189120 | − | 0.981954i | \(-0.439437\pi\) | ||||
0.189120 | + | 0.981954i | \(0.439437\pi\) | |||||||
\(98\) | − 108.978i | − 1.11202i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −111.695 | −1.11695 | ||||||||
\(101\) | 141.754i | 1.40350i | 0.712422 | + | 0.701752i | \(0.247598\pi\) | ||||
−0.712422 | + | 0.701752i | \(0.752402\pi\) | |||||||
\(102\) | −8.90131 | −0.0872678 | ||||||||
\(103\) | 39.0213 | 0.378847 | 0.189424 | − | 0.981895i | \(-0.439338\pi\) | ||||
0.189424 | + | 0.981895i | \(0.439338\pi\) | |||||||
\(104\) | 47.4084 | 0.455850 | ||||||||
\(105\) | 35.7046i | 0.340044i | ||||||||
\(106\) | 125.405i | 1.18307i | ||||||||
\(107\) | 116.623i | 1.08994i | 0.838456 | + | 0.544969i | \(0.183459\pi\) | ||||
−0.838456 | + | 0.544969i | \(0.816541\pi\) | |||||||
\(108\) | 12.5218 | 0.115942 | ||||||||
\(109\) | − 81.2670i | − 0.745569i | −0.927918 | − | 0.372784i | \(-0.878403\pi\) | ||||
0.927918 | − | 0.372784i | \(-0.121597\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 27.7204 | 0.249733 | ||||||||
\(112\) | − 48.3987i | − 0.432131i | ||||||||
\(113\) | −76.4454 | −0.676508 | −0.338254 | − | 0.941055i | \(-0.609836\pi\) | ||||
−0.338254 | + | 0.941055i | \(0.609836\pi\) | |||||||
\(114\) | −37.1426 | −0.325812 | ||||||||
\(115\) | −354.407 | −3.08180 | ||||||||
\(116\) | 59.3157i | 0.511343i | ||||||||
\(117\) | 35.3269i | 0.301940i | ||||||||
\(118\) | − 50.4642i | − 0.427663i | ||||||||
\(119\) | −4.95378 | −0.0416284 | ||||||||
\(120\) | − 58.9018i | − 0.490848i | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 301.041 | 2.46755 | ||||||||
\(123\) | − 91.1345i | − 0.740931i | ||||||||
\(124\) | −52.5665 | −0.423923 | ||||||||
\(125\) | −180.343 | −1.44274 | ||||||||
\(126\) | 18.5357 | 0.147109 | ||||||||
\(127\) | 21.0623i | 0.165845i | 0.996556 | + | 0.0829224i | \(0.0264254\pi\) | ||||
−0.996556 | + | 0.0829224i | \(0.973575\pi\) | |||||||
\(128\) | 118.651i | 0.926958i | ||||||||
\(129\) | − 73.3536i | − 0.568632i | ||||||||
\(130\) | −251.829 | −1.93714 | ||||||||
\(131\) | 106.847i | 0.815628i | 0.913065 | + | 0.407814i | \(0.133709\pi\) | ||||
−0.913065 | + | 0.407814i | \(0.866291\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.6707 | −0.155419 | ||||||||
\(134\) | 11.1763i | 0.0834049i | ||||||||
\(135\) | 43.8914 | 0.325122 | ||||||||
\(136\) | 8.17224 | 0.0600900 | ||||||||
\(137\) | 119.183 | 0.869946 | 0.434973 | − | 0.900443i | \(-0.356758\pi\) | ||||
0.434973 | + | 0.900443i | \(0.356758\pi\) | |||||||
\(138\) | 183.988i | 1.33324i | ||||||||
\(139\) | − 7.42431i | − 0.0534123i | −0.999643 | − | 0.0267061i | \(-0.991498\pi\) | ||||
0.999643 | − | 0.0267061i | \(-0.00850184\pi\) | |||||||
\(140\) | 49.6761i | 0.354829i | ||||||||
\(141\) | 28.0270 | 0.198773 | ||||||||
\(142\) | − 15.2815i | − 0.107616i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −59.4962 | −0.413168 | ||||||||
\(145\) | 207.914i | 1.43389i | ||||||||
\(146\) | −15.3942 | −0.105440 | ||||||||
\(147\) | −74.5549 | −0.507176 | ||||||||
\(148\) | 38.5676 | 0.260592 | ||||||||
\(149\) | 141.263i | 0.948075i | 0.880505 | + | 0.474038i | \(0.157204\pi\) | ||||
−0.880505 | + | 0.474038i | \(0.842796\pi\) | |||||||
\(150\) | 203.252i | 1.35501i | ||||||||
\(151\) | − 63.7331i | − 0.422074i | −0.977478 | − | 0.211037i | \(-0.932316\pi\) | ||||
0.977478 | − | 0.211037i | \(-0.0676840\pi\) | |||||||
\(152\) | 34.1004 | 0.224345 | ||||||||
\(153\) | 6.08965i | 0.0398016i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −184.257 | −1.18875 | ||||||||
\(156\) | 49.1506i | 0.315068i | ||||||||
\(157\) | 36.8901 | 0.234969 | 0.117485 | − | 0.993075i | \(-0.462517\pi\) | ||||
0.117485 | + | 0.993075i | \(0.462517\pi\) | |||||||
\(158\) | 261.943 | 1.65787 | ||||||||
\(159\) | 85.7934 | 0.539581 | ||||||||
\(160\) | − 288.091i | − 1.80057i | ||||||||
\(161\) | 102.393i | 0.635983i | ||||||||
\(162\) | − 22.7859i | − 0.140653i | ||||||||
\(163\) | −53.6360 | −0.329055 | −0.164528 | − | 0.986372i | \(-0.552610\pi\) | ||||
−0.164528 | + | 0.986372i | \(0.552610\pi\) | |||||||
\(164\) | − 126.796i | − 0.773147i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −76.3738 | −0.460083 | ||||||||
\(167\) | − 131.995i | − 0.790387i | −0.918598 | − | 0.395194i | \(-0.870677\pi\) | ||||
0.918598 | − | 0.395194i | \(-0.129323\pi\) | |||||||
\(168\) | −17.0176 | −0.101295 | ||||||||
\(169\) | 30.3341 | 0.179492 | ||||||||
\(170\) | −43.4101 | −0.255354 | ||||||||
\(171\) | 25.4103i | 0.148598i | ||||||||
\(172\) | − 102.057i | − 0.593357i | ||||||||
\(173\) | 66.5688i | 0.384791i | 0.981317 | + | 0.192395i | \(0.0616256\pi\) | ||||
−0.981317 | + | 0.192395i | \(0.938374\pi\) | |||||||
\(174\) | 107.937 | 0.620327 | ||||||||
\(175\) | 113.114i | 0.646368i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −34.5240 | −0.195051 | ||||||||
\(178\) | 153.083i | 0.860017i | ||||||||
\(179\) | 178.511 | 0.997268 | 0.498634 | − | 0.866813i | \(-0.333835\pi\) | ||||
0.498634 | + | 0.866813i | \(0.333835\pi\) | |||||||
\(180\) | 61.0664 | 0.339258 | ||||||||
\(181\) | −52.1144 | −0.287925 | −0.143962 | − | 0.989583i | \(-0.545984\pi\) | ||||
−0.143962 | + | 0.989583i | \(0.545984\pi\) | |||||||
\(182\) | 72.7568i | 0.399763i | ||||||||
\(183\) | − 205.951i | − 1.12542i | ||||||||
\(184\) | − 168.918i | − 0.918032i | ||||||||
\(185\) | 135.188 | 0.730744 | ||||||||
\(186\) | 95.6553i | 0.514276i | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 38.9941 | 0.207415 | ||||||||
\(189\) | − 12.6808i | − 0.0670944i | ||||||||
\(190\) | −181.138 | −0.953358 | ||||||||
\(191\) | −358.333 | −1.87609 | −0.938046 | − | 0.346512i | \(-0.887366\pi\) | ||||
−0.938046 | + | 0.346512i | \(0.887366\pi\) | |||||||
\(192\) | −12.1597 | −0.0633317 | ||||||||
\(193\) | − 213.899i | − 1.10829i | −0.832422 | − | 0.554143i | \(-0.813046\pi\) | ||||
0.832422 | − | 0.554143i | \(-0.186954\pi\) | |||||||
\(194\) | − 92.8883i | − 0.478806i | ||||||||
\(195\) | 172.283i | 0.883504i | ||||||||
\(196\) | −103.729 | −0.529229 | ||||||||
\(197\) | − 276.568i | − 1.40390i | −0.712227 | − | 0.701949i | \(-0.752313\pi\) | ||||
0.712227 | − | 0.701949i | \(-0.247687\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 78.8085 | 0.396022 | 0.198011 | − | 0.980200i | \(-0.436552\pi\) | ||||
0.198011 | + | 0.980200i | \(0.436552\pi\) | |||||||
\(200\) | − 186.604i | − 0.933022i | ||||||||
\(201\) | 7.64600 | 0.0380398 | ||||||||
\(202\) | 358.887 | 1.77667 | ||||||||
\(203\) | 60.0693 | 0.295908 | ||||||||
\(204\) | 8.47257i | 0.0415322i | ||||||||
\(205\) | − 444.447i | − 2.16803i | ||||||||
\(206\) | − 98.7926i | − 0.479576i | ||||||||
\(207\) | 125.871 | 0.608073 | ||||||||
\(208\) | − 233.535i | − 1.12277i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 90.3955 | 0.430455 | ||||||||
\(211\) | − 218.966i | − 1.03776i | −0.854849 | − | 0.518878i | \(-0.826350\pi\) | ||||
0.854849 | − | 0.518878i | \(-0.173650\pi\) | |||||||
\(212\) | 119.365 | 0.563042 | ||||||||
\(213\) | −10.4545 | −0.0490821 | ||||||||
\(214\) | 295.263 | 1.37973 | ||||||||
\(215\) | − 357.732i | − 1.66387i | ||||||||
\(216\) | 20.9196i | 0.0968498i | ||||||||
\(217\) | 53.2343i | 0.245319i | ||||||||
\(218\) | −205.749 | −0.943801 | ||||||||
\(219\) | 10.5316i | 0.0480896i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.9032 | −0.108159 | ||||||||
\(222\) | − 70.1815i | − 0.316133i | ||||||||
\(223\) | −209.548 | −0.939679 | −0.469839 | − | 0.882752i | \(-0.655688\pi\) | ||||
−0.469839 | + | 0.882752i | \(0.655688\pi\) | |||||||
\(224\) | −83.2336 | −0.371579 | ||||||||
\(225\) | 139.051 | 0.618003 | ||||||||
\(226\) | 193.542i | 0.856379i | ||||||||
\(227\) | − 83.3414i | − 0.367143i | −0.983006 | − | 0.183571i | \(-0.941234\pi\) | ||||
0.983006 | − | 0.183571i | \(-0.0587658\pi\) | |||||||
\(228\) | 35.3536i | 0.155060i | ||||||||
\(229\) | 330.662 | 1.44394 | 0.721969 | − | 0.691925i | \(-0.243237\pi\) | ||||
0.721969 | + | 0.691925i | \(0.243237\pi\) | |||||||
\(230\) | 897.274i | 3.90119i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −99.0962 | −0.427139 | ||||||||
\(233\) | − 165.410i | − 0.709915i | −0.934882 | − | 0.354958i | \(-0.884495\pi\) | ||||
0.934882 | − | 0.354958i | \(-0.115505\pi\) | |||||||
\(234\) | 89.4394 | 0.382220 | ||||||||
\(235\) | 136.682 | 0.581628 | ||||||||
\(236\) | −48.0335 | −0.203532 | ||||||||
\(237\) | − 179.203i | − 0.756129i | ||||||||
\(238\) | 12.5418i | 0.0526966i | ||||||||
\(239\) | 179.946i | 0.752911i | 0.926435 | + | 0.376455i | \(0.122857\pi\) | ||||
−0.926435 | + | 0.376455i | \(0.877143\pi\) | |||||||
\(240\) | −290.152 | −1.20897 | ||||||||
\(241\) | 226.632i | 0.940380i | 0.882565 | + | 0.470190i | \(0.155815\pi\) | ||||
−0.882565 | + | 0.470190i | \(0.844185\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − 286.541i | − 1.17435i | ||||||||
\(245\) | −363.591 | −1.48405 | ||||||||
\(246\) | −230.731 | −0.937930 | ||||||||
\(247\) | −99.7410 | −0.403810 | ||||||||
\(248\) | − 87.8205i | − 0.354115i | ||||||||
\(249\) | 52.2495i | 0.209837i | ||||||||
\(250\) | 456.586i | 1.82634i | ||||||||
\(251\) | −79.1282 | −0.315252 | −0.157626 | − | 0.987499i | \(-0.550384\pi\) | ||||
−0.157626 | + | 0.987499i | \(0.550384\pi\) | |||||||
\(252\) | − 17.6429i | − 0.0700117i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 53.3247 | 0.209940 | ||||||||
\(255\) | 29.6981i | 0.116463i | ||||||||
\(256\) | 328.477 | 1.28311 | ||||||||
\(257\) | 298.533 | 1.16161 | 0.580803 | − | 0.814044i | \(-0.302739\pi\) | ||||
0.580803 | + | 0.814044i | \(0.302739\pi\) | |||||||
\(258\) | −185.714 | −0.719821 | ||||||||
\(259\) | − 39.0576i | − 0.150801i | ||||||||
\(260\) | 239.699i | 0.921919i | ||||||||
\(261\) | − 73.8427i | − 0.282922i | ||||||||
\(262\) | 270.512 | 1.03249 | ||||||||
\(263\) | − 60.3285i | − 0.229386i | −0.993401 | − | 0.114693i | \(-0.963412\pi\) | ||||
0.993401 | − | 0.114693i | \(-0.0365884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 418.399 | 1.57887 | ||||||||
\(266\) | 52.3333i | 0.196742i | ||||||||
\(267\) | 104.728 | 0.392242 | ||||||||
\(268\) | 10.6379 | 0.0396938 | ||||||||
\(269\) | −195.972 | −0.728522 | −0.364261 | − | 0.931297i | \(-0.618678\pi\) | ||||
−0.364261 | + | 0.931297i | \(0.618678\pi\) | |||||||
\(270\) | − 111.123i | − 0.411565i | ||||||||
\(271\) | 340.500i | 1.25646i | 0.778029 | + | 0.628229i | \(0.216220\pi\) | ||||
−0.778029 | + | 0.628229i | \(0.783780\pi\) | |||||||
\(272\) | − 40.2567i | − 0.148003i | ||||||||
\(273\) | 49.7750 | 0.182326 | ||||||||
\(274\) | − 301.742i | − 1.10125i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 175.125 | 0.634513 | ||||||||
\(277\) | − 350.746i | − 1.26623i | −0.774057 | − | 0.633116i | \(-0.781776\pi\) | ||||
0.774057 | − | 0.633116i | \(-0.218224\pi\) | |||||||
\(278\) | −18.7966 | −0.0676136 | ||||||||
\(279\) | 65.4405 | 0.234554 | ||||||||
\(280\) | −82.9916 | −0.296399 | ||||||||
\(281\) | 408.440i | 1.45352i | 0.686890 | + | 0.726762i | \(0.258976\pi\) | ||||
−0.686890 | + | 0.726762i | \(0.741024\pi\) | |||||||
\(282\) | − 70.9576i | − 0.251623i | ||||||||
\(283\) | − 321.158i | − 1.13483i | −0.823431 | − | 0.567417i | \(-0.807943\pi\) | ||||
0.823431 | − | 0.567417i | \(-0.192057\pi\) | |||||||
\(284\) | −14.5454 | −0.0512163 | ||||||||
\(285\) | 123.922i | 0.434813i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −128.407 | −0.447411 | ||||||||
\(288\) | 102.318i | 0.355272i | ||||||||
\(289\) | 284.880 | 0.985742 | ||||||||
\(290\) | 526.389 | 1.81513 | ||||||||
\(291\) | −63.5475 | −0.218376 | ||||||||
\(292\) | 14.6527i | 0.0501805i | ||||||||
\(293\) | − 377.069i | − 1.28692i | −0.765478 | − | 0.643462i | \(-0.777497\pi\) | ||||
0.765478 | − | 0.643462i | \(-0.222503\pi\) | |||||||
\(294\) | 188.755i | 0.642025i | ||||||||
\(295\) | −168.367 | −0.570737 | ||||||||
\(296\) | 64.4332i | 0.217680i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 357.645 | 1.20015 | ||||||||
\(299\) | 494.072i | 1.65241i | ||||||||
\(300\) | 193.462 | 0.644874 | ||||||||
\(301\) | −103.354 | −0.343368 | ||||||||
\(302\) | −161.357 | −0.534295 | ||||||||
\(303\) | − 245.525i | − 0.810313i | ||||||||
\(304\) | − 167.980i | − 0.552565i | ||||||||
\(305\) | − 1004.39i | − 3.29307i | ||||||||
\(306\) | 15.4175 | 0.0503841 | ||||||||
\(307\) | 505.973i | 1.64812i | 0.566502 | + | 0.824060i | \(0.308296\pi\) | ||||
−0.566502 | + | 0.824060i | \(0.691704\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −67.5869 | −0.218728 | ||||||||
\(310\) | 466.494i | 1.50482i | ||||||||
\(311\) | −166.073 | −0.533997 | −0.266998 | − | 0.963697i | \(-0.586032\pi\) | ||||
−0.266998 | + | 0.963697i | \(0.586032\pi\) | |||||||
\(312\) | −82.1138 | −0.263185 | ||||||||
\(313\) | 93.6449 | 0.299185 | 0.149593 | − | 0.988748i | \(-0.452204\pi\) | ||||
0.149593 | + | 0.988748i | \(0.452204\pi\) | |||||||
\(314\) | − 93.3970i | − 0.297443i | ||||||||
\(315\) | − 61.8422i | − 0.196324i | ||||||||
\(316\) | − 249.326i | − 0.789006i | ||||||||
\(317\) | 149.549 | 0.471764 | 0.235882 | − | 0.971782i | \(-0.424202\pi\) | ||||
0.235882 | + | 0.971782i | \(0.424202\pi\) | |||||||
\(318\) | − 217.208i | − 0.683045i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −59.3006 | −0.185314 | ||||||||
\(321\) | − 201.998i | − 0.629276i | ||||||||
\(322\) | 259.235 | 0.805078 | ||||||||
\(323\) | −17.1933 | −0.0532301 | ||||||||
\(324\) | −21.6883 | −0.0669393 | ||||||||
\(325\) | 545.804i | 1.67940i | ||||||||
\(326\) | 135.794i | 0.416545i | ||||||||
\(327\) | 140.759i | 0.430454i | ||||||||
\(328\) | 211.833 | 0.645831 | ||||||||
\(329\) | − 39.4895i | − 0.120029i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −271.711 | −0.820880 | −0.410440 | − | 0.911888i | \(-0.634625\pi\) | ||||
−0.410440 | + | 0.911888i | \(0.634625\pi\) | |||||||
\(332\) | 72.6951i | 0.218961i | ||||||||
\(333\) | −48.0132 | −0.144184 | ||||||||
\(334\) | −334.179 | −1.00054 | ||||||||
\(335\) | 37.2882 | 0.111308 | ||||||||
\(336\) | 83.8290i | 0.249491i | ||||||||
\(337\) | 500.414i | 1.48491i | 0.669898 | + | 0.742454i | \(0.266338\pi\) | ||||
−0.669898 | + | 0.742454i | \(0.733662\pi\) | |||||||
\(338\) | − 76.7987i | − 0.227215i | ||||||||
\(339\) | 132.407 | 0.390582 | ||||||||
\(340\) | 41.3192i | 0.121527i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 64.3329 | 0.188108 | ||||||||
\(343\) | 224.628i | 0.654891i | ||||||||
\(344\) | 170.503 | 0.495647 | ||||||||
\(345\) | 613.851 | 1.77928 | ||||||||
\(346\) | 168.536 | 0.487099 | ||||||||
\(347\) | 242.729i | 0.699509i | 0.936841 | + | 0.349754i | \(0.113735\pi\) | ||||
−0.936841 | + | 0.349754i | \(0.886265\pi\) | |||||||
\(348\) | − 102.738i | − 0.295224i | ||||||||
\(349\) | 447.324i | 1.28173i | 0.767653 | + | 0.640866i | \(0.221424\pi\) | ||||
−0.767653 | + | 0.640866i | \(0.778576\pi\) | |||||||
\(350\) | 286.378 | 0.818224 | ||||||||
\(351\) | − 61.1881i | − 0.174325i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −226.910 | −0.642805 | −0.321403 | − | 0.946943i | \(-0.604154\pi\) | ||||
−0.321403 | + | 0.946943i | \(0.604154\pi\) | |||||||
\(354\) | 87.4066i | 0.246911i | ||||||||
\(355\) | −50.9847 | −0.143619 | ||||||||
\(356\) | 145.710 | 0.409296 | ||||||||
\(357\) | 8.58020 | 0.0240342 | ||||||||
\(358\) | − 451.947i | − 1.26242i | ||||||||
\(359\) | 642.653i | 1.79012i | 0.445947 | + | 0.895059i | \(0.352867\pi\) | ||||
−0.445947 | + | 0.895059i | \(0.647133\pi\) | |||||||
\(360\) | 102.021i | 0.283391i | ||||||||
\(361\) | 289.257 | 0.801267 | ||||||||
\(362\) | 131.941i | 0.364478i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 69.2524 | 0.190254 | ||||||||
\(365\) | 51.3608i | 0.140715i | ||||||||
\(366\) | −521.419 | −1.42464 | ||||||||
\(367\) | −717.882 | −1.95608 | −0.978041 | − | 0.208415i | \(-0.933170\pi\) | ||||
−0.978041 | + | 0.208415i | \(0.933170\pi\) | |||||||
\(368\) | −832.094 | −2.26113 | ||||||||
\(369\) | 157.850i | 0.427777i | ||||||||
\(370\) | − 342.263i | − 0.925034i | ||||||||
\(371\) | − 120.881i | − 0.325826i | ||||||||
\(372\) | 91.0479 | 0.244752 | ||||||||
\(373\) | 18.1857i | 0.0487552i | 0.999703 | + | 0.0243776i | \(0.00776040\pi\) | ||||
−0.999703 | + | 0.0243776i | \(0.992240\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 312.363 | 0.832969 | ||||||||
\(376\) | 65.1457i | 0.173260i | ||||||||
\(377\) | 289.849 | 0.768829 | ||||||||
\(378\) | −32.1049 | −0.0849335 | ||||||||
\(379\) | −155.717 | −0.410864 | −0.205432 | − | 0.978671i | \(-0.565860\pi\) | ||||
−0.205432 | + | 0.978671i | \(0.565860\pi\) | |||||||
\(380\) | 172.413i | 0.453719i | ||||||||
\(381\) | − 36.4810i | − 0.0957505i | ||||||||
\(382\) | 907.215i | 2.37491i | ||||||||
\(383\) | −720.395 | −1.88093 | −0.940464 | − | 0.339894i | \(-0.889609\pi\) | ||||
−0.940464 | + | 0.339894i | \(0.889609\pi\) | |||||||
\(384\) | − 205.509i | − 0.535179i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −541.542 | −1.40296 | ||||||||
\(387\) | 127.052i | 0.328300i | ||||||||
\(388\) | −88.4142 | −0.227872 | ||||||||
\(389\) | 8.88848 | 0.0228496 | 0.0114248 | − | 0.999935i | \(-0.496363\pi\) | ||||
0.0114248 | + | 0.999935i | \(0.496363\pi\) | |||||||
\(390\) | 436.180 | 1.11841 | ||||||||
\(391\) | 85.1679i | 0.217821i | ||||||||
\(392\) | − 173.295i | − 0.442079i | ||||||||
\(393\) | − 185.065i | − 0.470903i | ||||||||
\(394\) | −700.204 | −1.77717 | ||||||||
\(395\) | − 873.939i | − 2.21250i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 513.254 | 1.29283 | 0.646416 | − | 0.762985i | \(-0.276267\pi\) | ||||
0.646416 | + | 0.762985i | \(0.276267\pi\) | |||||||
\(398\) | − 199.524i | − 0.501317i | ||||||||
\(399\) | 35.8027 | 0.0897311 | ||||||||
\(400\) | −919.219 | −2.29805 | ||||||||
\(401\) | 548.823 | 1.36863 | 0.684317 | − | 0.729184i | \(-0.260100\pi\) | ||||
0.684317 | + | 0.729184i | \(0.260100\pi\) | |||||||
\(402\) | − 19.3578i | − 0.0481539i | ||||||||
\(403\) | 256.868i | 0.637390i | ||||||||
\(404\) | − 341.600i | − 0.845546i | ||||||||
\(405\) | −76.0221 | −0.187709 | ||||||||
\(406\) | − 152.081i | − 0.374584i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −14.1547 | −0.0346930 | ||||||||
\(409\) | − 506.077i | − 1.23735i | −0.785646 | − | 0.618676i | \(-0.787669\pi\) | ||||
0.785646 | − | 0.618676i | \(-0.212331\pi\) | |||||||
\(410\) | −1125.23 | −2.74447 | ||||||||
\(411\) | −206.430 | −0.502264 | ||||||||
\(412\) | −94.0341 | −0.228238 | ||||||||
\(413\) | 48.6437i | 0.117781i | ||||||||
\(414\) | − 318.676i | − 0.769748i | ||||||||
\(415\) | 254.812i | 0.614004i | ||||||||
\(416\) | −401.622 | −0.965437 | ||||||||
\(417\) | 12.8593i | 0.0308376i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −111.580 | −0.266300 | −0.133150 | − | 0.991096i | \(-0.542509\pi\) | ||||
−0.133150 | + | 0.991096i | \(0.542509\pi\) | |||||||
\(420\) | − 86.0415i | − 0.204861i | ||||||||
\(421\) | 373.299 | 0.886696 | 0.443348 | − | 0.896350i | \(-0.353791\pi\) | ||||
0.443348 | + | 0.896350i | \(0.353791\pi\) | |||||||
\(422\) | −554.370 | −1.31367 | ||||||||
\(423\) | −48.5441 | −0.114761 | ||||||||
\(424\) | 199.418i | 0.470325i | ||||||||
\(425\) | 94.0854i | 0.221377i | ||||||||
\(426\) | 26.4683i | 0.0621321i | ||||||||
\(427\) | −290.181 | −0.679582 | ||||||||
\(428\) | − 281.041i | − 0.656637i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −905.693 | −2.10626 | ||||||||
\(431\) | − 78.0726i | − 0.181143i | −0.995890 | − | 0.0905714i | \(-0.971131\pi\) | ||||
0.995890 | − | 0.0905714i | \(-0.0288693\pi\) | |||||||
\(432\) | 103.050 | 0.238543 | ||||||||
\(433\) | 711.481 | 1.64314 | 0.821572 | − | 0.570105i | \(-0.193097\pi\) | ||||
0.821572 | + | 0.570105i | \(0.193097\pi\) | |||||||
\(434\) | 134.777 | 0.310545 | ||||||||
\(435\) | − 360.118i | − 0.827857i | ||||||||
\(436\) | 195.838i | 0.449170i | ||||||||
\(437\) | 355.381i | 0.813229i | ||||||||
\(438\) | 26.6635 | 0.0608757 | ||||||||
\(439\) | − 262.674i | − 0.598347i | −0.954199 | − | 0.299173i | \(-0.903289\pi\) | ||||
0.954199 | − | 0.299173i | \(-0.0967109\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 129.133 | 0.292818 | ||||||||
\(442\) | 60.5171i | 0.136917i | ||||||||
\(443\) | −528.705 | −1.19346 | −0.596732 | − | 0.802441i | \(-0.703534\pi\) | ||||
−0.596732 | + | 0.802441i | \(0.703534\pi\) | |||||||
\(444\) | −66.8011 | −0.150453 | ||||||||
\(445\) | 510.742 | 1.14774 | ||||||||
\(446\) | 530.526i | 1.18952i | ||||||||
\(447\) | − 244.675i | − 0.547371i | ||||||||
\(448\) | 17.1328i | 0.0382428i | ||||||||
\(449\) | −287.807 | −0.640995 | −0.320498 | − | 0.947249i | \(-0.603850\pi\) | ||||
−0.320498 | + | 0.947249i | \(0.603850\pi\) | |||||||
\(450\) | − 352.043i | − 0.782318i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 184.219 | 0.407565 | ||||||||
\(453\) | 110.389i | 0.243684i | ||||||||
\(454\) | −211.000 | −0.464759 | ||||||||
\(455\) | 242.744 | 0.533503 | ||||||||
\(456\) | −59.0636 | −0.129526 | ||||||||
\(457\) | − 826.946i | − 1.80951i | −0.425932 | − | 0.904755i | \(-0.640054\pi\) | ||||
0.425932 | − | 0.904755i | \(-0.359946\pi\) | |||||||
\(458\) | − 837.157i | − 1.82785i | ||||||||
\(459\) | − 10.5476i | − 0.0229795i | ||||||||
\(460\) | 854.056 | 1.85664 | ||||||||
\(461\) | 325.354i | 0.705756i | 0.935669 | + | 0.352878i | \(0.114797\pi\) | ||||
−0.935669 | + | 0.352878i | \(0.885203\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −711.656 | −1.53705 | −0.768527 | − | 0.639818i | \(-0.779010\pi\) | ||||
−0.768527 | + | 0.639818i | \(0.779010\pi\) | |||||||
\(464\) | 488.151i | 1.05205i | ||||||||
\(465\) | 319.142 | 0.686326 | ||||||||
\(466\) | −418.779 | −0.898668 | ||||||||
\(467\) | 458.119 | 0.980982 | 0.490491 | − | 0.871446i | \(-0.336817\pi\) | ||||
0.490491 | + | 0.871446i | \(0.336817\pi\) | |||||||
\(468\) | − 85.1314i | − 0.181905i | ||||||||
\(469\) | − 10.7731i | − 0.0229703i | ||||||||
\(470\) | − 346.047i | − 0.736271i | ||||||||
\(471\) | −63.8956 | −0.135659 | ||||||||
\(472\) | − 80.2474i | − 0.170016i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −453.698 | −0.957169 | ||||||||
\(475\) | 392.591i | 0.826508i | ||||||||
\(476\) | 11.9377 | 0.0250792 | ||||||||
\(477\) | −148.599 | −0.311527 | ||||||||
\(478\) | 455.579 | 0.953095 | ||||||||
\(479\) | − 592.433i | − 1.23681i | −0.785859 | − | 0.618406i | \(-0.787779\pi\) | ||||
0.785859 | − | 0.618406i | \(-0.212221\pi\) | |||||||
\(480\) | 498.989i | 1.03956i | ||||||||
\(481\) | − 188.462i | − 0.391813i | ||||||||
\(482\) | 573.777 | 1.19041 | ||||||||
\(483\) | − 177.350i | − 0.367185i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −309.910 | −0.638990 | ||||||||
\(486\) | 39.4663i | 0.0812063i | ||||||||
\(487\) | 437.813 | 0.899001 | 0.449500 | − | 0.893280i | \(-0.351602\pi\) | ||||
0.449500 | + | 0.893280i | \(0.351602\pi\) | |||||||
\(488\) | 478.712 | 0.980967 | ||||||||
\(489\) | 92.9003 | 0.189980 | ||||||||
\(490\) | 920.526i | 1.87862i | ||||||||
\(491\) | 774.734i | 1.57787i | 0.614477 | + | 0.788935i | \(0.289367\pi\) | ||||
−0.614477 | + | 0.788935i | \(0.710633\pi\) | |||||||
\(492\) | 219.617i | 0.446377i | ||||||||
\(493\) | 49.9640 | 0.101347 | ||||||||
\(494\) | 252.521i | 0.511175i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −432.607 | −0.872191 | ||||||||
\(497\) | 14.7302i | 0.0296382i | ||||||||
\(498\) | 132.283 | 0.265629 | ||||||||
\(499\) | 262.110 | 0.525271 | 0.262636 | − | 0.964895i | \(-0.415408\pi\) | ||||
0.262636 | + | 0.964895i | \(0.415408\pi\) | |||||||
\(500\) | 434.593 | 0.869187 | ||||||||
\(501\) | 228.622i | 0.456330i | ||||||||
\(502\) | 200.334i | 0.399071i | ||||||||
\(503\) | 153.502i | 0.305174i | 0.988290 | + | 0.152587i | \(0.0487604\pi\) | ||||
−0.988290 | + | 0.152587i | \(0.951240\pi\) | |||||||
\(504\) | 29.4753 | 0.0584827 | ||||||||
\(505\) | − 1197.38i | − 2.37105i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −52.5402 | −0.103630 | ||||||||
\(508\) | − 50.7562i | − 0.0999138i | ||||||||
\(509\) | −782.781 | −1.53788 | −0.768940 | − | 0.639321i | \(-0.779215\pi\) | ||||
−0.768940 | + | 0.639321i | \(0.779215\pi\) | |||||||
\(510\) | 75.1886 | 0.147429 | ||||||||
\(511\) | 14.8389 | 0.0290389 | ||||||||
\(512\) | − 357.022i | − 0.697308i | ||||||||
\(513\) | − 44.0120i | − 0.0857933i | ||||||||
\(514\) | − 755.813i | − 1.47045i | ||||||||
\(515\) | −329.609 | −0.640018 | ||||||||
\(516\) | 176.769i | 0.342575i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −98.8844 | −0.190897 | ||||||||
\(519\) | − 115.301i | − 0.222159i | ||||||||
\(520\) | −400.454 | −0.770104 | ||||||||
\(521\) | −180.526 | −0.346498 | −0.173249 | − | 0.984878i | \(-0.555427\pi\) | ||||
−0.173249 | + | 0.984878i | \(0.555427\pi\) | |||||||
\(522\) | −186.952 | −0.358146 | ||||||||
\(523\) | − 151.833i | − 0.290311i | −0.989409 | − | 0.145156i | \(-0.953632\pi\) | ||||
0.989409 | − | 0.145156i | \(-0.0463683\pi\) | |||||||
\(524\) | − 257.482i | − 0.491378i | ||||||||
\(525\) | − 195.920i | − 0.373181i | ||||||||
\(526\) | −152.737 | −0.290375 | ||||||||
\(527\) | 44.2788i | 0.0840206i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1231.39 | 2.32778 | ||||||||
\(530\) | − 1059.29i | − 1.99865i | ||||||||
\(531\) | 59.7973 | 0.112613 | ||||||||
\(532\) | 49.8126 | 0.0936326 | ||||||||
\(533\) | −619.594 | −1.16247 | ||||||||
\(534\) | − 265.148i | − 0.496531i | ||||||||
\(535\) | − 985.107i | − 1.84132i | ||||||||
\(536\) | 17.7723i | 0.0331573i | ||||||||
\(537\) | −309.190 | −0.575773 | ||||||||
\(538\) | 496.155i | 0.922222i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −105.770 | −0.195871 | ||||||||
\(541\) | − 287.853i | − 0.532075i | −0.963963 | − | 0.266038i | \(-0.914285\pi\) | ||||
0.963963 | − | 0.266038i | \(-0.0857146\pi\) | |||||||
\(542\) | 862.065 | 1.59052 | ||||||||
\(543\) | 90.2647 | 0.166233 | ||||||||
\(544\) | −69.2314 | −0.127264 | ||||||||
\(545\) | 686.454i | 1.25955i | ||||||||
\(546\) | − 126.018i | − 0.230803i | ||||||||
\(547\) | − 122.440i | − 0.223839i | −0.993717 | − | 0.111920i | \(-0.964300\pi\) | ||||
0.993717 | − | 0.111920i | \(-0.0356999\pi\) | |||||||
\(548\) | −287.208 | −0.524102 | ||||||||
\(549\) | 356.718i | 0.649759i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 208.485 | 0.378376 | ||||||||
\(552\) | 292.574i | 0.530026i | ||||||||
\(553\) | −252.493 | −0.456588 | ||||||||
\(554\) | −888.005 | −1.60290 | ||||||||
\(555\) | −234.152 | −0.421895 | ||||||||
\(556\) | 17.8912i | 0.0321784i | ||||||||
\(557\) | 560.374i | 1.00606i | 0.864270 | + | 0.503028i | \(0.167781\pi\) | ||||
−0.864270 | + | 0.503028i | \(0.832219\pi\) | |||||||
\(558\) | − 165.680i | − 0.296917i | ||||||||
\(559\) | −498.707 | −0.892141 | ||||||||
\(560\) | 408.819i | 0.730034i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1034.07 | 1.83999 | ||||||||
\(563\) | 461.422i | 0.819577i | 0.912181 | + | 0.409788i | \(0.134397\pi\) | ||||
−0.912181 | + | 0.409788i | \(0.865603\pi\) | |||||||
\(564\) | −67.5398 | −0.119751 | ||||||||
\(565\) | 645.727 | 1.14288 | ||||||||
\(566\) | −813.095 | −1.43656 | ||||||||
\(567\) | 21.9639i | 0.0387370i | ||||||||
\(568\) | − 24.3004i | − 0.0427824i | ||||||||
\(569\) | 850.975i | 1.49556i | 0.663945 | + | 0.747781i | \(0.268881\pi\) | ||||
−0.663945 | + | 0.747781i | \(0.731119\pi\) | |||||||
\(570\) | 313.740 | 0.550421 | ||||||||
\(571\) | 558.153i | 0.977500i | 0.872424 | + | 0.488750i | \(0.162547\pi\) | ||||
−0.872424 | + | 0.488750i | \(0.837453\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 620.652 | 1.08316 | ||||||||
\(574\) | 325.096i | 0.566369i | ||||||||
\(575\) | 1944.72 | 3.38212 | ||||||||
\(576\) | 21.0612 | 0.0365646 | ||||||||
\(577\) | 1063.74 | 1.84358 | 0.921789 | − | 0.387692i | \(-0.126728\pi\) | ||||
0.921789 | + | 0.387692i | \(0.126728\pi\) | |||||||
\(578\) | − 721.247i | − 1.24783i | ||||||||
\(579\) | 370.484i | 0.639869i | ||||||||
\(580\) | − 501.034i | − 0.863852i | ||||||||
\(581\) | 73.6186 | 0.126710 | ||||||||
\(582\) | 160.887i | 0.276439i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −24.4796 | −0.0419172 | ||||||||
\(585\) | − 298.403i | − 0.510091i | ||||||||
\(586\) | −954.648 | −1.62909 | ||||||||
\(587\) | −137.730 | −0.234633 | −0.117317 | − | 0.993095i | \(-0.537429\pi\) | ||||
−0.117317 | + | 0.993095i | \(0.537429\pi\) | |||||||
\(588\) | 179.664 | 0.305550 | ||||||||
\(589\) | 184.763i | 0.313689i | ||||||||
\(590\) | 426.266i | 0.722485i | ||||||||
\(591\) | 479.030i | 0.810541i | ||||||||
\(592\) | 317.400 | 0.536148 | ||||||||
\(593\) | 42.1576i | 0.0710921i | 0.999368 | + | 0.0355461i | \(0.0113170\pi\) | ||||
−0.999368 | + | 0.0355461i | \(0.988683\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 41.8441 | 0.0703263 | ||||||||
\(596\) | − 340.418i | − 0.571171i | ||||||||
\(597\) | −136.500 | −0.228644 | ||||||||
\(598\) | 1250.87 | 2.09176 | ||||||||
\(599\) | −323.005 | −0.539240 | −0.269620 | − | 0.962967i | \(-0.586898\pi\) | ||||
−0.269620 | + | 0.962967i | \(0.586898\pi\) | |||||||
\(600\) | 323.208i | 0.538681i | ||||||||
\(601\) | 682.717i | 1.13597i | 0.823039 | + | 0.567985i | \(0.192277\pi\) | ||||
−0.823039 | + | 0.567985i | \(0.807723\pi\) | |||||||
\(602\) | 261.667i | 0.434663i | ||||||||
\(603\) | −13.2433 | −0.0219623 | ||||||||
\(604\) | 153.585i | 0.254280i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −621.610 | −1.02576 | ||||||||
\(607\) | 219.873i | 0.362229i | 0.983462 | + | 0.181114i | \(0.0579705\pi\) | ||||
−0.983462 | + | 0.181114i | \(0.942030\pi\) | |||||||
\(608\) | −288.883 | −0.475136 | ||||||||
\(609\) | −104.043 | −0.170842 | ||||||||
\(610\) | −2542.87 | −4.16864 | ||||||||
\(611\) | − 190.546i | − 0.311859i | ||||||||
\(612\) | − 14.6749i | − 0.0239786i | ||||||||
\(613\) | − 198.057i | − 0.323094i | −0.986865 | − | 0.161547i | \(-0.948352\pi\) | ||||
0.986865 | − | 0.161547i | \(-0.0516483\pi\) | |||||||
\(614\) | 1281.00 | 2.08632 | ||||||||
\(615\) | 769.805i | 1.25172i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 666.299 | 1.07990 | 0.539951 | − | 0.841697i | \(-0.318443\pi\) | ||||
0.539951 | + | 0.841697i | \(0.318443\pi\) | |||||||
\(618\) | 171.114i | 0.276883i | ||||||||
\(619\) | 506.706 | 0.818589 | 0.409294 | − | 0.912402i | \(-0.365775\pi\) | ||||
0.409294 | + | 0.912402i | \(0.365775\pi\) | |||||||
\(620\) | 444.024 | 0.716168 | ||||||||
\(621\) | −218.015 | −0.351071 | ||||||||
\(622\) | 420.457i | 0.675976i | ||||||||
\(623\) | − 147.561i | − 0.236855i | ||||||||
\(624\) | 404.495i | 0.648229i | ||||||||
\(625\) | 364.586 | 0.583337 | ||||||||
\(626\) | − 237.087i | − 0.378733i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −88.8984 | −0.141558 | ||||||||
\(629\) | − 32.4870i | − 0.0516487i | ||||||||
\(630\) | −156.570 | −0.248523 | ||||||||
\(631\) | 761.035 | 1.20608 | 0.603039 | − | 0.797712i | \(-0.293956\pi\) | ||||
0.603039 | + | 0.797712i | \(0.293956\pi\) | |||||||
\(632\) | 416.537 | 0.659078 | ||||||||
\(633\) | 379.261i | 0.599148i | ||||||||
\(634\) | − 378.623i | − 0.597197i | ||||||||
\(635\) | − 177.911i | − 0.280175i | ||||||||
\(636\) | −206.746 | −0.325073 | ||||||||
\(637\) | 506.875i | 0.795722i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.1077 | 0.0283376 | ||||||||
\(640\) | − 1002.23i | − 1.56598i | ||||||||
\(641\) | 203.013 | 0.316714 | 0.158357 | − | 0.987382i | \(-0.449380\pi\) | ||||
0.158357 | + | 0.987382i | \(0.449380\pi\) | |||||||
\(642\) | −511.410 | −0.796589 | ||||||||
\(643\) | −455.154 | −0.707860 | −0.353930 | − | 0.935272i | \(-0.615155\pi\) | ||||
−0.353930 | + | 0.935272i | \(0.615155\pi\) | |||||||
\(644\) | − 246.749i | − 0.383150i | ||||||||
\(645\) | 619.611i | 0.960637i | ||||||||
\(646\) | 43.5294i | 0.0673830i | ||||||||
\(647\) | 535.496 | 0.827659 | 0.413830 | − | 0.910354i | \(-0.364191\pi\) | ||||
0.413830 | + | 0.910354i | \(0.364191\pi\) | |||||||
\(648\) | − 36.2337i | − 0.0559162i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1381.84 | 2.12591 | ||||||||
\(651\) | − 92.2045i | − 0.141635i | ||||||||
\(652\) | 129.253 | 0.198241 | ||||||||
\(653\) | −829.067 | −1.26963 | −0.634814 | − | 0.772665i | \(-0.718923\pi\) | ||||
−0.634814 | + | 0.772665i | \(0.718923\pi\) | |||||||
\(654\) | 356.367 | 0.544904 | ||||||||
\(655\) | − 902.529i | − 1.37791i | ||||||||
\(656\) | − 1043.49i | − 1.59069i | ||||||||
\(657\) | − 18.2413i | − 0.0277645i | ||||||||
\(658\) | −99.9779 | −0.151942 | ||||||||
\(659\) | 1089.67i | 1.65353i | 0.562551 | + | 0.826763i | \(0.309820\pi\) | ||||
−0.562551 | + | 0.826763i | \(0.690180\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −920.151 | −1.39206 | −0.696029 | − | 0.718013i | \(-0.745052\pi\) | ||||
−0.696029 | + | 0.718013i | \(0.745052\pi\) | |||||||
\(662\) | 687.908i | 1.03914i | ||||||||
\(663\) | 41.4015 | 0.0624457 | ||||||||
\(664\) | −121.448 | −0.182904 | ||||||||
\(665\) | 174.603 | 0.262562 | ||||||||
\(666\) | 121.558i | 0.182519i | ||||||||
\(667\) | − 1032.74i | − 1.54834i | ||||||||
\(668\) | 318.083i | 0.476172i | ||||||||
\(669\) | 362.948 | 0.542524 | ||||||||
\(670\) | − 94.4048i | − 0.140903i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 144.165 | 0.214531 | ||||||||
\(673\) | 645.812i | 0.959602i | 0.877377 | + | 0.479801i | \(0.159291\pi\) | ||||
−0.877377 | + | 0.479801i | \(0.840709\pi\) | |||||||
\(674\) | 1266.93 | 1.87972 | ||||||||
\(675\) | −240.843 | −0.356804 | ||||||||
\(676\) | −73.0996 | −0.108135 | ||||||||
\(677\) | 737.620i | 1.08954i | 0.838585 | + | 0.544771i | \(0.183383\pi\) | ||||
−0.838585 | + | 0.544771i | \(0.816617\pi\) | |||||||
\(678\) | − 335.224i | − 0.494430i | ||||||||
\(679\) | 89.5373i | 0.131866i | ||||||||
\(680\) | −69.0302 | −0.101515 | ||||||||
\(681\) | 144.352i | 0.211970i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 527.576 | 0.772440 | 0.386220 | − | 0.922407i | \(-0.373781\pi\) | ||||
0.386220 | + | 0.922407i | \(0.373781\pi\) | |||||||
\(684\) | − 61.2342i | − 0.0895237i | ||||||||
\(685\) | −1006.72 | −1.46967 | ||||||||
\(686\) | 568.703 | 0.829014 | ||||||||
\(687\) | −572.723 | −0.833658 | ||||||||
\(688\) | − 839.901i | − 1.22079i | ||||||||
\(689\) | − 583.281i | − 0.846562i | ||||||||
\(690\) | − 1554.13i | − 2.25236i | ||||||||
\(691\) | −516.694 | −0.747748 | −0.373874 | − | 0.927479i | \(-0.621971\pi\) | ||||
−0.373874 | + | 0.927479i | \(0.621971\pi\) | |||||||
\(692\) | − 160.419i | − 0.231819i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 614.533 | 0.885494 | ||||||||
\(695\) | 62.7124i | 0.0902337i | ||||||||
\(696\) | 171.640 | 0.246609 | ||||||||
\(697\) | −106.805 | −0.153236 | ||||||||
\(698\) | 1132.52 | 1.62252 | ||||||||
\(699\) | 286.499i | 0.409870i | ||||||||
\(700\) | − 272.585i | − 0.389407i | ||||||||
\(701\) | − 699.987i | − 0.998555i | −0.866442 | − | 0.499278i | \(-0.833599\pi\) | ||||
0.866442 | − | 0.499278i | \(-0.166401\pi\) | |||||||
\(702\) | −154.914 | −0.220675 | ||||||||
\(703\) | − 135.559i | − 0.192829i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −236.741 | −0.335803 | ||||||||
\(706\) | 574.482i | 0.813714i | ||||||||
\(707\) | −345.940 | −0.489307 | ||||||||
\(708\) | 83.1965 | 0.117509 | ||||||||
\(709\) | −649.664 | −0.916310 | −0.458155 | − | 0.888872i | \(-0.651490\pi\) | ||||
−0.458155 | + | 0.888872i | \(0.651490\pi\) | |||||||
\(710\) | 129.081i | 0.181804i | ||||||||
\(711\) | 310.388i | 0.436551i | ||||||||
\(712\) | 243.430i | 0.341897i | ||||||||
\(713\) | 915.230 | 1.28363 | ||||||||
\(714\) | − 21.7230i | − 0.0304244i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −430.178 | −0.600808 | ||||||||
\(717\) | − 311.675i | − 0.434693i | ||||||||
\(718\) | 1627.04 | 2.26608 | ||||||||
\(719\) | 694.522 | 0.965955 | 0.482978 | − | 0.875633i | \(-0.339555\pi\) | ||||
0.482978 | + | 0.875633i | \(0.339555\pi\) | |||||||
\(720\) | 502.558 | 0.697998 | ||||||||
\(721\) | 95.2287i | 0.132079i | ||||||||
\(722\) | − 732.330i | − 1.01431i | ||||||||
\(723\) | − 392.537i | − 0.542929i | ||||||||
\(724\) | 125.586 | 0.173461 | ||||||||
\(725\) | − 1140.87i | − 1.57362i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −970.108 | −1.33440 | −0.667200 | − | 0.744879i | \(-0.732507\pi\) | ||||
−0.667200 | + | 0.744879i | \(0.732507\pi\) | |||||||
\(728\) | 115.697i | 0.158924i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 130.033 | 0.178128 | ||||||||
\(731\) | −85.9669 | −0.117602 | ||||||||
\(732\) | 496.304i | 0.678011i | ||||||||
\(733\) | − 157.602i | − 0.215009i | −0.994205 | − | 0.107504i | \(-0.965714\pi\) | ||||
0.994205 | − | 0.107504i | \(-0.0342860\pi\) | |||||||
\(734\) | 1817.51i | 2.47616i | ||||||||
\(735\) | 629.758 | 0.856814 | ||||||||
\(736\) | 1430.99i | 1.94428i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 399.638 | 0.541514 | ||||||||
\(739\) | − 685.531i | − 0.927647i | −0.885928 | − | 0.463823i | \(-0.846477\pi\) | ||||
0.885928 | − | 0.463823i | \(-0.153523\pi\) | |||||||
\(740\) | −325.777 | −0.440239 | ||||||||
\(741\) | 172.757 | 0.233140 | ||||||||
\(742\) | −306.043 | −0.412457 | ||||||||
\(743\) | − 516.079i | − 0.694588i | −0.937756 | − | 0.347294i | \(-0.887101\pi\) | ||||
0.937756 | − | 0.347294i | \(-0.112899\pi\) | |||||||
\(744\) | 152.110i | 0.204448i | ||||||||
\(745\) | − 1193.24i | − 1.60166i | ||||||||
\(746\) | 46.0418 | 0.0617183 | ||||||||
\(747\) | − 90.4988i | − 0.121150i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −284.611 | −0.379988 | ||||||||
\(750\) | − 790.829i | − 1.05444i | ||||||||
\(751\) | −853.690 | −1.13674 | −0.568369 | − | 0.822774i | \(-0.692425\pi\) | ||||
−0.568369 | + | 0.822774i | \(0.692425\pi\) | |||||||
\(752\) | 320.910 | 0.426742 | ||||||||
\(753\) | 137.054 | 0.182011 | ||||||||
\(754\) | − 733.827i | − 0.973246i | ||||||||
\(755\) | 538.347i | 0.713043i | ||||||||
\(756\) | 30.5585i | 0.0404213i | ||||||||
\(757\) | −496.049 | −0.655282 | −0.327641 | − | 0.944802i | \(-0.606254\pi\) | ||||
−0.327641 | + | 0.944802i | \(0.606254\pi\) | |||||||
\(758\) | 394.239i | 0.520104i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −288.043 | −0.379004 | ||||||||
\(761\) | − 1.29340i | − 0.00169961i | −1.00000 | 0.000849804i | \(-0.999729\pi\) | |||||
1.00000 | 0.000849804i | \(-0.000270501\pi\) | ||||||||
\(762\) | −92.3611 | −0.121209 | ||||||||
\(763\) | 198.326 | 0.259930 | ||||||||
\(764\) | 863.517 | 1.13026 | ||||||||
\(765\) | − 51.4387i | − 0.0672401i | ||||||||
\(766\) | 1823.87i | 2.38103i | ||||||||
\(767\) | 234.717i | 0.306020i | ||||||||
\(768\) | −568.938 | −0.740805 | ||||||||
\(769\) | − 398.342i | − 0.518000i | −0.965877 | − | 0.259000i | \(-0.916607\pi\) | ||||
0.965877 | − | 0.259000i | \(-0.0833929\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −517.073 | −0.670653 | ||||||||
\(772\) | 515.457i | 0.667691i | ||||||||
\(773\) | −637.493 | −0.824700 | −0.412350 | − | 0.911025i | \(-0.635292\pi\) | ||||
−0.412350 | + | 0.911025i | \(0.635292\pi\) | |||||||
\(774\) | 321.666 | 0.415589 | ||||||||
\(775\) | 1011.06 | 1.30459 | ||||||||
\(776\) | − 147.710i | − 0.190347i | ||||||||
\(777\) | 67.6497i | 0.0870652i | ||||||||
\(778\) | − 22.5035i | − 0.0289248i | ||||||||
\(779\) | −445.668 | −0.572103 | ||||||||
\(780\) | − 415.171i | − 0.532270i | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 215.625 | 0.275735 | ||||||||
\(783\) | 127.899i | 0.163345i | ||||||||
\(784\) | −853.657 | −1.08885 | ||||||||
\(785\) | −311.608 | −0.396952 | ||||||||
\(786\) | −468.540 | −0.596107 | ||||||||
\(787\) | − 1070.60i | − 1.36036i | −0.733045 | − | 0.680180i | \(-0.761901\pi\) | ||||
0.733045 | − | 0.680180i | \(-0.238099\pi\) | |||||||
\(788\) | 666.477i | 0.845783i | ||||||||
\(789\) | 104.492i | 0.132436i | ||||||||
\(790\) | −2212.60 | −2.80077 | ||||||||
\(791\) | − 186.560i | − 0.235853i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1400.19 | −1.76569 | ||||||||
\(794\) | − 1299.44i | − 1.63657i | ||||||||
\(795\) | −724.689 | −0.911558 | ||||||||
\(796\) | −189.914 | −0.238585 | ||||||||
\(797\) | 365.858 | 0.459044 | 0.229522 | − | 0.973303i | \(-0.426284\pi\) | ||||
0.229522 | + | 0.973303i | \(0.426284\pi\) | |||||||
\(798\) | − 90.6439i | − 0.113589i | ||||||||
\(799\) | − 32.8463i | − 0.0411092i | ||||||||
\(800\) | 1580.83i | 1.97603i | ||||||||
\(801\) | −181.395 | −0.226461 | ||||||||
\(802\) | − 1389.49i | − 1.73253i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −18.4254 | −0.0229172 | ||||||||
\(805\) | − 864.906i | − 1.07442i | ||||||||
\(806\) | 650.329 | 0.806860 | ||||||||
\(807\) | 339.434 | 0.420612 | ||||||||
\(808\) | 570.697 | 0.706308 | ||||||||
\(809\) | − 176.666i | − 0.218375i | −0.994021 | − | 0.109188i | \(-0.965175\pi\) | ||||
0.994021 | − | 0.109188i | \(-0.0348249\pi\) | |||||||
\(810\) | 192.470i | 0.237617i | ||||||||
\(811\) | − 256.402i | − 0.316156i | −0.987427 | − | 0.158078i | \(-0.949470\pi\) | ||||
0.987427 | − | 0.158078i | \(-0.0505297\pi\) | |||||||
\(812\) | −144.756 | −0.178271 | ||||||||
\(813\) | − 589.763i | − 0.725416i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 453.058 | 0.555900 | ||||||||
\(816\) | 69.7267i | 0.0854494i | ||||||||
\(817\) | −358.715 | −0.439064 | ||||||||
\(818\) | −1281.27 | −1.56634 | ||||||||
\(819\) | −86.2129 | −0.105266 | ||||||||
\(820\) | 1071.03i | 1.30614i | ||||||||
\(821\) | − 938.646i | − 1.14330i | −0.820499 | − | 0.571648i | \(-0.806304\pi\) | ||||
0.820499 | − | 0.571648i | \(-0.193696\pi\) | |||||||
\(822\) | 522.632i | 0.635806i | ||||||||
\(823\) | 558.391 | 0.678483 | 0.339241 | − | 0.940699i | \(-0.389830\pi\) | ||||
0.339241 | + | 0.940699i | \(0.389830\pi\) | |||||||
\(824\) | − 157.099i | − 0.190654i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 123.154 | 0.149097 | ||||||||
\(827\) | − 1326.63i | − 1.60414i | −0.597228 | − | 0.802072i | \(-0.703731\pi\) | ||||
0.597228 | − | 0.802072i | \(-0.296269\pi\) | |||||||
\(828\) | −303.326 | −0.366336 | ||||||||
\(829\) | −899.388 | −1.08491 | −0.542454 | − | 0.840086i | \(-0.682505\pi\) | ||||
−0.542454 | + | 0.840086i | \(0.682505\pi\) | |||||||
\(830\) | 645.122 | 0.777255 | ||||||||
\(831\) | 607.510i | 0.731059i | ||||||||
\(832\) | 82.6697i | 0.0993626i | ||||||||
\(833\) | 87.3749i | 0.104892i | ||||||||
\(834\) | 32.5566 | 0.0390367 | ||||||||
\(835\) | 1114.95i | 1.33527i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −113.346 | −0.135420 | ||||||||
\(838\) | 282.494i | 0.337104i | ||||||||
\(839\) | 283.608 | 0.338032 | 0.169016 | − | 0.985613i | \(-0.445941\pi\) | ||||
0.169016 | + | 0.985613i | \(0.445941\pi\) | |||||||
\(840\) | 143.746 | 0.171126 | ||||||||
\(841\) | 235.139 | 0.279595 | ||||||||
\(842\) | − 945.104i | − 1.12245i | ||||||||
\(843\) | − 707.439i | − 0.839192i | ||||||||
\(844\) | 527.668i | 0.625199i | ||||||||
\(845\) | −256.229 | −0.303230 | ||||||||
\(846\) | 122.902i | 0.145274i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 982.338 | 1.15842 | ||||||||
\(849\) | 556.262i | 0.655197i | ||||||||
\(850\) | 238.202 | 0.280237 | ||||||||
\(851\) | −671.497 | −0.789068 | ||||||||
\(852\) | 25.1934 | 0.0295697 | ||||||||
\(853\) | 440.959i | 0.516951i | 0.966018 | + | 0.258476i | \(0.0832202\pi\) | ||||
−0.966018 | + | 0.258476i | \(0.916780\pi\) | |||||||
\(854\) | 734.670i | 0.860269i | ||||||||
\(855\) | − 214.639i | − 0.251039i | ||||||||
\(856\) | 469.522 | 0.548507 | ||||||||
\(857\) | − 1378.52i | − 1.60854i | −0.594264 | − | 0.804270i | \(-0.702557\pi\) | ||||
0.594264 | − | 0.804270i | \(-0.297443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1387.60 | 1.61537 | 0.807685 | − | 0.589614i | \(-0.200720\pi\) | ||||
0.807685 | + | 0.589614i | \(0.200720\pi\) | |||||||
\(860\) | 862.069i | 1.00241i | ||||||||
\(861\) | 222.407 | 0.258313 | ||||||||
\(862\) | −197.661 | −0.229305 | ||||||||
\(863\) | −514.959 | −0.596708 | −0.298354 | − | 0.954455i | \(-0.596438\pi\) | ||||
−0.298354 | + | 0.954455i | \(0.596438\pi\) | |||||||
\(864\) | − 177.221i | − 0.205117i | ||||||||
\(865\) | − 562.301i | − 0.650058i | ||||||||
\(866\) | − 1801.30i | − 2.08002i | ||||||||
\(867\) | −493.426 | −0.569119 | ||||||||
\(868\) | − 128.285i | − 0.147794i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −911.732 | −1.04797 | ||||||||
\(871\) | − 51.9827i | − 0.0596816i | ||||||||
\(872\) | −327.178 | −0.375205 | ||||||||
\(873\) | 110.068 | 0.126080 | ||||||||
\(874\) | 899.740 | 1.02945 | ||||||||
\(875\) | − 440.114i | − 0.502988i | ||||||||
\(876\) | − 25.3793i | − 0.0289717i | ||||||||
\(877\) | 742.107i | 0.846188i | 0.906086 | + | 0.423094i | \(0.139056\pi\) | ||||
−0.906086 | + | 0.423094i | \(0.860944\pi\) | |||||||
\(878\) | −665.028 | −0.757435 | ||||||||
\(879\) | 653.102i | 0.743006i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −620.478 | −0.704288 | −0.352144 | − | 0.935946i | \(-0.614547\pi\) | ||||
−0.352144 | + | 0.935946i | \(0.614547\pi\) | |||||||
\(882\) | − 326.934i | − 0.370673i | ||||||||
\(883\) | 674.168 | 0.763498 | 0.381749 | − | 0.924266i | \(-0.375322\pi\) | ||||
0.381749 | + | 0.924266i | \(0.375322\pi\) | |||||||
\(884\) | 57.6022 | 0.0651609 | ||||||||
\(885\) | 291.621 | 0.329515 | ||||||||
\(886\) | 1338.55i | 1.51078i | ||||||||
\(887\) | − 1098.43i | − 1.23837i | −0.785245 | − | 0.619185i | \(-0.787463\pi\) | ||||
0.785245 | − | 0.619185i | \(-0.212537\pi\) | |||||||
\(888\) | − 111.602i | − 0.125677i | ||||||||
\(889\) | −51.4010 | −0.0578189 | ||||||||
\(890\) | − 1293.08i | − 1.45290i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 504.973 | 0.566113 | ||||||||
\(893\) | − 137.058i | − 0.153480i | ||||||||
\(894\) | −619.459 | −0.692907 | ||||||||
\(895\) | −1507.86 | −1.68477 | ||||||||
\(896\) | −289.558 | −0.323168 | ||||||||
\(897\) | − 855.757i | − 0.954021i | ||||||||
\(898\) | 728.658i | 0.811424i | ||||||||
\(899\) | − 536.923i | − 0.597244i | ||||||||
\(900\) | −335.086 | −0.372318 | ||||||||
\(901\) | − 100.546i | − 0.111594i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 179.014 | 0.198244 | ||||||||
\(904\) | 307.767i | 0.340450i | ||||||||
\(905\) | 440.205 | 0.486415 | ||||||||
\(906\) | 279.479 | 0.308475 | ||||||||
\(907\) | 247.155 | 0.272498 | 0.136249 | − | 0.990675i | \(-0.456495\pi\) | ||||
0.136249 | + | 0.990675i | \(0.456495\pi\) | |||||||
\(908\) | 200.837i | 0.221186i | ||||||||
\(909\) | 425.262i | 0.467834i | ||||||||
\(910\) | − 614.570i | − 0.675351i | ||||||||
\(911\) | 686.752 | 0.753844 | 0.376922 | − | 0.926245i | \(-0.376982\pi\) | ||||
0.376922 | + | 0.926245i | \(0.376982\pi\) | |||||||
\(912\) | 290.949i | 0.319023i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2093.63 | −2.29062 | ||||||||
\(915\) | 1739.65i | 1.90126i | ||||||||
\(916\) | −796.834 | −0.869906 | ||||||||
\(917\) | −260.753 | −0.284355 | ||||||||
\(918\) | −26.7039 | −0.0290893 | ||||||||
\(919\) | 1485.25i | 1.61615i | 0.589077 | + | 0.808077i | \(0.299491\pi\) | ||||
−0.589077 | + | 0.808077i | \(0.700509\pi\) | |||||||
\(920\) | 1426.83i | 1.55091i | ||||||||
\(921\) | − 876.371i | − 0.951543i | ||||||||
\(922\) | 823.718 | 0.893403 | ||||||||
\(923\) | 71.0767i | 0.0770062i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −741.807 | −0.801953 | ||||||||
\(926\) | 1801.74i | 1.94573i | ||||||||
\(927\) | 117.064 | 0.126282 | ||||||||
\(928\) | 839.497 | 0.904630 | ||||||||
\(929\) | −681.402 | −0.733479 | −0.366740 | − | 0.930324i | \(-0.619526\pi\) | ||||
−0.366740 | + | 0.930324i | \(0.619526\pi\) | |||||||
\(930\) | − 807.991i | − 0.868807i | ||||||||
\(931\) | 364.590i | 0.391611i | ||||||||
\(932\) | 398.608i | 0.427691i | ||||||||
\(933\) | 287.647 | 0.308303 | ||||||||
\(934\) | − 1159.85i | − 1.24181i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 142.225 | 0.151950 | ||||||||
\(937\) | 88.5349i | 0.0944876i | 0.998883 | + | 0.0472438i | \(0.0150438\pi\) | ||||
−0.998883 | + | 0.0472438i | \(0.984956\pi\) | |||||||
\(938\) | −27.2749 | −0.0290777 | ||||||||
\(939\) | −162.198 | −0.172735 | ||||||||
\(940\) | −329.379 | −0.350404 | ||||||||
\(941\) | 582.065i | 0.618560i | 0.950971 | + | 0.309280i | \(0.100088\pi\) | ||||
−0.950971 | + | 0.309280i | \(0.899912\pi\) | |||||||
\(942\) | 161.768i | 0.171729i | ||||||||
\(943\) | 2207.64i | 2.34108i | ||||||||
\(944\) | −395.301 | −0.418751 | ||||||||
\(945\) | 107.114i | 0.113348i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −912.836 | −0.963924 | −0.481962 | − | 0.876192i | \(-0.660076\pi\) | ||||
−0.481962 | + | 0.876192i | \(0.660076\pi\) | |||||||
\(948\) | 431.845i | 0.455533i | ||||||||
\(949\) | 71.6011 | 0.0754489 | ||||||||
\(950\) | 993.947 | 1.04626 | ||||||||
\(951\) | −259.027 | −0.272373 | ||||||||
\(952\) | 19.9438i | 0.0209493i | ||||||||
\(953\) | − 554.670i | − 0.582026i | −0.956719 | − | 0.291013i | \(-0.906008\pi\) | ||||
0.956719 | − | 0.291013i | \(-0.0939922\pi\) | |||||||
\(954\) | 376.216i | 0.394356i | ||||||||
\(955\) | 3026.81 | 3.16943 | ||||||||
\(956\) | − 433.636i | − 0.453594i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1499.90 | −1.56566 | ||||||||
\(959\) | 290.857i | 0.303292i | ||||||||
\(960\) | 102.712 | 0.106991 | ||||||||
\(961\) | −485.171 | −0.504861 | ||||||||
\(962\) | −477.141 | −0.495989 | ||||||||
\(963\) | 349.870i | 0.363313i | ||||||||
\(964\) | − 546.140i | − 0.566535i | ||||||||
\(965\) | 1806.79i | 1.87232i | ||||||||
\(966\) | −449.008 | −0.464812 | ||||||||
\(967\) | − 1781.13i | − 1.84191i | −0.389667 | − | 0.920956i | \(-0.627410\pi\) | ||||
0.389667 | − | 0.920956i | \(-0.372590\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.7797 | 0.0307324 | ||||||||
\(970\) | 784.618i | 0.808885i | ||||||||
\(971\) | −990.964 | −1.02056 | −0.510280 | − | 0.860008i | \(-0.670458\pi\) | ||||
−0.510280 | + | 0.860008i | \(0.670458\pi\) | |||||||
\(972\) | 37.5653 | 0.0386474 | ||||||||
\(973\) | 18.1185 | 0.0186213 | ||||||||
\(974\) | − 1108.44i | − 1.13803i | ||||||||
\(975\) | − 945.360i | − 0.969600i | ||||||||
\(976\) | − 2358.15i | − 2.41614i | ||||||||
\(977\) | 754.917 | 0.772689 | 0.386344 | − | 0.922355i | \(-0.373738\pi\) | ||||
0.386344 | + | 0.922355i | \(0.373738\pi\) | |||||||
\(978\) | − 235.201i | − 0.240492i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 876.187 | 0.894069 | ||||||||
\(981\) | − 243.801i | − 0.248523i | ||||||||
\(982\) | 1961.44 | 1.99740 | ||||||||
\(983\) | −206.512 | −0.210084 | −0.105042 | − | 0.994468i | \(-0.533498\pi\) | ||||
−0.105042 | + | 0.994468i | \(0.533498\pi\) | |||||||
\(984\) | −366.905 | −0.372871 | ||||||||
\(985\) | 2336.14i | 2.37172i | ||||||||
\(986\) | − 126.497i | − 0.128293i | ||||||||
\(987\) | 68.3978i | 0.0692987i | ||||||||
\(988\) | 240.357 | 0.243277 | ||||||||
\(989\) | 1776.91i | 1.79667i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 852.133 | 0.859872 | 0.429936 | − | 0.902859i | \(-0.358536\pi\) | ||||
0.429936 | + | 0.902859i | \(0.358536\pi\) | |||||||
\(992\) | 743.975i | 0.749974i | ||||||||
\(993\) | 470.618 | 0.473935 | ||||||||
\(994\) | 37.2933 | 0.0375185 | ||||||||
\(995\) | −665.687 | −0.669033 | ||||||||
\(996\) | − 125.912i | − 0.126417i | ||||||||
\(997\) | 1168.11i | 1.17162i | 0.810448 | + | 0.585810i | \(0.199224\pi\) | ||||
−0.810448 | + | 0.585810i | \(0.800776\pi\) | |||||||
\(998\) | − 663.601i | − 0.664931i | ||||||||
\(999\) | 83.1613 | 0.0832445 |
(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 | 363.3.c.e.241.3 | 16 | ||
3.2 | odd | 2 | 1089.3.c.m.604.14 | 16 | |||
11.2 | odd | 10 | 363.3.g.g.40.3 | 16 | |||
11.3 | even | 5 | 33.3.g.a.13.2 | ✓ | 16 | ||
11.4 | even | 5 | 363.3.g.f.94.3 | 16 | |||
11.5 | even | 5 | 363.3.g.g.118.3 | 16 | |||
11.6 | odd | 10 | 363.3.g.a.118.2 | 16 | |||
11.7 | odd | 10 | 33.3.g.a.28.2 | yes | 16 | ||
11.8 | odd | 10 | 363.3.g.f.112.3 | 16 | |||
11.9 | even | 5 | 363.3.g.a.40.2 | 16 | |||
11.10 | odd | 2 | inner | 363.3.c.e.241.14 | 16 | ||
33.14 | odd | 10 | 99.3.k.c.46.3 | 16 | |||
33.29 | even | 10 | 99.3.k.c.28.3 | 16 | |||
33.32 | even | 2 | 1089.3.c.m.604.3 | 16 | |||
44.3 | odd | 10 | 528.3.bf.b.145.1 | 16 | |||
44.7 | even | 10 | 528.3.bf.b.193.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.13.2 | ✓ | 16 | 11.3 | even | 5 | ||
33.3.g.a.28.2 | yes | 16 | 11.7 | odd | 10 | ||
99.3.k.c.28.3 | 16 | 33.29 | even | 10 | |||
99.3.k.c.46.3 | 16 | 33.14 | odd | 10 | |||
363.3.c.e.241.3 | 16 | 1.1 | even | 1 | trivial | ||
363.3.c.e.241.14 | 16 | 11.10 | odd | 2 | inner | ||
363.3.g.a.40.2 | 16 | 11.9 | even | 5 | |||
363.3.g.a.118.2 | 16 | 11.6 | odd | 10 | |||
363.3.g.f.94.3 | 16 | 11.4 | even | 5 | |||
363.3.g.f.112.3 | 16 | 11.8 | odd | 10 | |||
363.3.g.g.40.3 | 16 | 11.2 | odd | 10 | |||
363.3.g.g.118.3 | 16 | 11.5 | even | 5 | |||
528.3.bf.b.145.1 | 16 | 44.3 | odd | 10 | |||
528.3.bf.b.193.1 | 16 | 44.7 | even | 10 | |||
1089.3.c.m.604.3 | 16 | 33.32 | even | 2 | |||
1089.3.c.m.604.14 | 16 | 3.2 | odd | 2 |