Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(604,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, 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("1089.604");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.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: | \(29.6731007888\) |
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 | 604.3 | ||
Root | \(0.988132 - 0.846795i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.m.604.14 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | \(-0.218152\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.40981 | −0.602454 | ||||||||
\(5\) | 8.44690 | 1.68938 | 0.844690 | − | 0.535255i | \(-0.179785\pi\) | ||||
0.844690 | + | 0.535255i | \(0.179785\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.44043i | − 0.348633i | −0.984690 | − | 0.174316i | \(-0.944228\pi\) | ||||
0.984690 | − | 0.174316i | \(-0.0557715\pi\) | |||||||
\(8\) | − 4.02597i | − 0.503246i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 21.3855i | − 2.13855i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 11.7756i | − 0.905819i | −0.891556 | − | 0.452910i | \(-0.850386\pi\) | ||||
0.891556 | − | 0.452910i | \(-0.149614\pi\) | |||||||
\(14\) | −6.17858 | −0.441327 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.8321 | −1.23950 | ||||||||
\(17\) | 2.02988i | 0.119405i | 0.998216 | + | 0.0597024i | \(0.0190152\pi\) | ||||
−0.998216 | + | 0.0597024i | \(0.980985\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 8.47011i | − 0.445795i | −0.974842 | − | 0.222898i | \(-0.928448\pi\) | ||||
0.974842 | − | 0.222898i | \(-0.0715516\pi\) | |||||||
\(20\) | −20.3555 | −1.01777 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −41.9571 | −1.82422 | −0.912110 | − | 0.409946i | \(-0.865548\pi\) | ||||
−0.912110 | + | 0.409946i | \(0.865548\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 46.3502 | 1.85401 | ||||||||
\(26\) | −29.8131 | −1.14666 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.88098i | 0.210035i | ||||||||
\(29\) | − 24.6142i | − 0.848767i | −0.905483 | − | 0.424383i | \(-0.860491\pi\) | ||||
0.905483 | − | 0.424383i | \(-0.139509\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 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 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −16.0044 | −0.432551 | −0.216276 | − | 0.976332i | \(-0.569391\pi\) | ||||
−0.216276 | + | 0.976332i | \(0.569391\pi\) | |||||||
\(38\) | −21.4443 | −0.564324 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 34.0070i | − 0.850174i | ||||||||
\(41\) | 52.6166i | 1.28333i | 0.766985 | + | 0.641665i | \(0.221756\pi\) | ||||
−0.766985 | + | 0.641665i | \(0.778244\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 42.3507i | − 0.984900i | −0.870341 | − | 0.492450i | \(-0.836101\pi\) | ||||
0.870341 | − | 0.492450i | \(-0.163899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 106.225i | 2.30924i | ||||||||
\(47\) | 16.1814 | 0.344284 | 0.172142 | − | 0.985072i | \(-0.444931\pi\) | ||||
0.172142 | + | 0.985072i | \(0.444931\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 43.0443 | 0.878455 | ||||||||
\(50\) | − 117.348i | − 2.34695i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 28.3771i | 0.545714i | ||||||||
\(53\) | 49.5329 | 0.934582 | 0.467291 | − | 0.884104i | \(-0.345230\pi\) | ||||
0.467291 | + | 0.884104i | \(0.345230\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.82509 | −0.175448 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −62.3174 | −1.07444 | ||||||||
\(59\) | −19.9324 | −0.337838 | −0.168919 | − | 0.985630i | \(-0.554028\pi\) | ||||
−0.168919 | + | 0.985630i | \(0.554028\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 118.906i | − 1.94928i | −0.223784 | − | 0.974639i | \(-0.571841\pi\) | ||||
0.223784 | − | 0.974639i | \(-0.428159\pi\) | |||||||
\(62\) | − 55.2266i | − 0.890751i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −52.1899 | −0.745570 | ||||||||
\(71\) | −6.03591 | −0.0850128 | −0.0425064 | − | 0.999096i | \(-0.513534\pi\) | ||||
−0.0425064 | + | 0.999096i | \(0.513534\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.08043i | 0.0832936i | 0.999132 | + | 0.0416468i | \(0.0132604\pi\) | ||||
−0.999132 | + | 0.0416468i | \(0.986740\pi\) | |||||||
\(74\) | 40.5193i | 0.547558i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.4114i | 0.268571i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 103.463i | − 1.30965i | −0.755779 | − | 0.654827i | \(-0.772742\pi\) | ||||
0.755779 | − | 0.654827i | \(-0.227258\pi\) | |||||||
\(80\) | −167.519 | −2.09399 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 133.213 | 1.62454 | ||||||||
\(83\) | − 30.1663i | − 0.363449i | −0.983349 | − | 0.181724i | \(-0.941832\pi\) | ||||
0.983349 | − | 0.181724i | \(-0.0581679\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.1462i | 0.201720i | ||||||||
\(86\) | −107.222 | −1.24677 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 60.4650 | 0.679382 | 0.339691 | − | 0.940537i | \(-0.389677\pi\) | ||||
0.339691 | + | 0.940537i | \(0.389677\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −28.7376 | −0.315798 | ||||||||
\(92\) | 101.109 | 1.09901 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 40.9674i | − 0.435823i | ||||||||
\(95\) | − 71.5462i | − 0.753118i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 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 | \(0.752402\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 39.0213 | 0.378847 | 0.189424 | − | 0.981895i | \(-0.439338\pi\) | ||||
0.189424 | + | 0.981895i | \(0.439338\pi\) | |||||||
\(104\) | −47.4084 | −0.455850 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 125.405i | − 1.18307i | ||||||||
\(107\) | 116.623i | 1.08994i | 0.838456 | + | 0.544969i | \(0.183459\pi\) | ||||
−0.838456 | + | 0.544969i | \(0.816541\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 81.2670i | 0.745569i | 0.927918 | + | 0.372784i | \(0.121597\pi\) | ||||
−0.927918 | + | 0.372784i | \(0.878403\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 48.3987i | 0.432131i | ||||||||
\(113\) | 76.4454 | 0.676508 | 0.338254 | − | 0.941055i | \(-0.390164\pi\) | ||||
0.338254 | + | 0.941055i | \(0.390164\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −354.407 | −3.08180 | ||||||||
\(116\) | 59.3157i | 0.511343i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 50.4642i | 0.427663i | ||||||||
\(119\) | 4.95378 | 0.0416284 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −301.041 | −2.46755 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −52.5665 | −0.423923 | ||||||||
\(125\) | 180.343 | 1.44274 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 21.0623i | − 0.165845i | −0.996556 | − | 0.0829224i | \(-0.973575\pi\) | ||||
0.996556 | − | 0.0829224i | \(-0.0264254\pi\) | |||||||
\(128\) | 118.651i | 0.926958i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −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 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.17224 | 0.0600900 | ||||||||
\(137\) | −119.183 | −0.869946 | −0.434973 | − | 0.900443i | \(-0.643242\pi\) | ||||
−0.434973 | + | 0.900443i | \(0.643242\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.42431i | 0.0534123i | 0.999643 | + | 0.0267061i | \(0.00850184\pi\) | ||||
−0.999643 | + | 0.0267061i | \(0.991498\pi\) | |||||||
\(140\) | 49.6761i | 0.354829i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.2815i | 0.107616i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 207.914i | − 1.43389i | ||||||||
\(146\) | 15.3942 | 0.105440 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 38.5676 | 0.260592 | ||||||||
\(149\) | 141.263i | 0.948075i | 0.880505 | + | 0.474038i | \(0.157204\pi\) | ||||
−0.880505 | + | 0.474038i | \(0.842796\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 63.7331i | 0.422074i | 0.977478 | + | 0.211037i | \(0.0676840\pi\) | ||||
−0.977478 | + | 0.211037i | \(0.932316\pi\) | |||||||
\(152\) | −34.1004 | −0.224345 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 184.257 | 1.18875 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.8901 | 0.234969 | 0.117485 | − | 0.993075i | \(-0.462517\pi\) | ||||
0.117485 | + | 0.993075i | \(0.462517\pi\) | |||||||
\(158\) | −261.943 | −1.65787 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 288.091i | 1.80057i | ||||||||
\(161\) | 102.393i | 0.635983i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −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 | \(-0.129323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.3341 | 0.179492 | ||||||||
\(170\) | 43.4101 | 0.255354 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 102.057i | 0.593357i | ||||||||
\(173\) | 66.5688i | 0.384791i | 0.981317 | + | 0.192395i | \(0.0616256\pi\) | ||||
−0.981317 | + | 0.192395i | \(0.938374\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 113.114i | − 0.646368i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 153.083i | − 0.860017i | ||||||||
\(179\) | −178.511 | −0.997268 | −0.498634 | − | 0.866813i | \(-0.666165\pi\) | ||||
−0.498634 | + | 0.866813i | \(0.666165\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −52.1144 | −0.287925 | −0.143962 | − | 0.989583i | \(-0.545984\pi\) | ||||
−0.143962 | + | 0.989583i | \(0.545984\pi\) | |||||||
\(182\) | 72.7568i | 0.399763i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 168.918i | 0.918032i | ||||||||
\(185\) | −135.188 | −0.730744 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −38.9941 | −0.207415 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −181.138 | −0.953358 | ||||||||
\(191\) | 358.333 | 1.87609 | 0.938046 | − | 0.346512i | \(-0.112634\pi\) | ||||
0.938046 | + | 0.346512i | \(0.112634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 213.899i | 1.10829i | 0.832422 | + | 0.554143i | \(0.186954\pi\) | ||||
−0.832422 | + | 0.554143i | \(0.813046\pi\) | |||||||
\(194\) | − 92.8883i | − 0.478806i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −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 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 358.887 | 1.77667 | ||||||||
\(203\) | −60.0693 | −0.295908 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 444.447i | 2.16803i | ||||||||
\(206\) | − 98.7926i | − 0.479576i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 233.535i | 1.12277i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 218.966i | 1.03776i | 0.854849 | + | 0.518878i | \(0.173650\pi\) | ||||
−0.854849 | + | 0.518878i | \(0.826350\pi\) | |||||||
\(212\) | −119.365 | −0.563042 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 295.263 | 1.37973 | ||||||||
\(215\) | − 357.732i | − 1.66387i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 53.2343i | − 0.245319i | ||||||||
\(218\) | 205.749 | 0.943801 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.9032 | 0.108159 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −209.548 | −0.939679 | −0.469839 | − | 0.882752i | \(-0.655688\pi\) | ||||
−0.469839 | + | 0.882752i | \(0.655688\pi\) | |||||||
\(224\) | 83.2336 | 0.371579 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 193.542i | − 0.856379i | ||||||||
\(227\) | − 83.3414i | − 0.367143i | −0.983006 | − | 0.183571i | \(-0.941234\pi\) | ||||
0.983006 | − | 0.183571i | \(-0.0587658\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 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 | \(-0.115505\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 136.682 | 0.581628 | ||||||||
\(236\) | 48.0335 | 0.203532 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 12.5418i | − 0.0526966i | ||||||||
\(239\) | 179.946i | 0.752911i | 0.926435 | + | 0.376455i | \(0.122857\pi\) | ||||
−0.926435 | + | 0.376455i | \(0.877143\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 226.632i | − 0.940380i | −0.882565 | − | 0.470190i | \(-0.844185\pi\) | ||||
0.882565 | − | 0.470190i | \(-0.155815\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 286.541i | 1.17435i | ||||||||
\(245\) | 363.591 | 1.48405 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −99.7410 | −0.403810 | ||||||||
\(248\) | − 87.8205i | − 0.354115i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 456.586i | − 1.82634i | ||||||||
\(251\) | 79.1282 | 0.315252 | 0.157626 | − | 0.987499i | \(-0.449616\pi\) | ||||
0.157626 | + | 0.987499i | \(0.449616\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −53.3247 | −0.209940 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 328.477 | 1.28311 | ||||||||
\(257\) | −298.533 | −1.16161 | −0.580803 | − | 0.814044i | \(-0.697261\pi\) | ||||
−0.580803 | + | 0.814044i | \(0.697261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 39.0576i | 0.150801i | ||||||||
\(260\) | 239.699i | 0.921919i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.6379 | 0.0396938 | ||||||||
\(269\) | 195.972 | 0.728522 | 0.364261 | − | 0.931297i | \(-0.381322\pi\) | ||||
0.364261 | + | 0.931297i | \(0.381322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 340.500i | − 1.25646i | −0.778029 | − | 0.628229i | \(-0.783780\pi\) | ||||
0.778029 | − | 0.628229i | \(-0.216220\pi\) | |||||||
\(272\) | − 40.2567i | − 0.148003i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 301.742i | 1.10125i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 350.746i | 1.26623i | 0.774057 | + | 0.633116i | \(0.218224\pi\) | ||||
−0.774057 | + | 0.633116i | \(0.781776\pi\) | |||||||
\(278\) | 18.7966 | 0.0676136 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −82.9916 | −0.296399 | ||||||||
\(281\) | 408.440i | 1.45352i | 0.686890 | + | 0.726762i | \(0.258976\pi\) | ||||
−0.686890 | + | 0.726762i | \(0.741024\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 321.158i | 1.13483i | 0.823431 | + | 0.567417i | \(0.192057\pi\) | ||||
−0.823431 | + | 0.567417i | \(0.807943\pi\) | |||||||
\(284\) | 14.5454 | 0.0512163 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 128.407 | 0.447411 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 284.880 | 0.985742 | ||||||||
\(290\) | −526.389 | −1.81513 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 14.6527i | − 0.0501805i | ||||||||
\(293\) | − 377.069i | − 1.28692i | −0.765478 | − | 0.643462i | \(-0.777497\pi\) | ||||
0.765478 | − | 0.643462i | \(-0.222503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −168.367 | −0.570737 | ||||||||
\(296\) | 64.4332i | 0.217680i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 357.645 | 1.20015 | ||||||||
\(299\) | 494.072i | 1.65241i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −103.354 | −0.343368 | ||||||||
\(302\) | 161.357 | 0.534295 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 167.980i | 0.552565i | ||||||||
\(305\) | − 1004.39i | − 3.29307i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 505.973i | − 1.64812i | −0.566502 | − | 0.824060i | \(-0.691704\pi\) | ||||
0.566502 | − | 0.824060i | \(-0.308296\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 466.494i | − 1.50482i | ||||||||
\(311\) | 166.073 | 0.533997 | 0.266998 | − | 0.963697i | \(-0.413968\pi\) | ||||
0.266998 | + | 0.963697i | \(0.413968\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 93.6449 | 0.299185 | 0.149593 | − | 0.988748i | \(-0.452204\pi\) | ||||
0.149593 | + | 0.988748i | \(0.452204\pi\) | |||||||
\(314\) | − 93.3970i | − 0.297443i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 249.326i | 0.789006i | ||||||||
\(317\) | −149.549 | −0.471764 | −0.235882 | − | 0.971782i | \(-0.575798\pi\) | ||||
−0.235882 | + | 0.971782i | \(0.575798\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 59.3006 | 0.185314 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 259.235 | 0.805078 | ||||||||
\(323\) | 17.1933 | 0.0532301 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 545.804i | − 1.67940i | ||||||||
\(326\) | 135.794i | 0.416545i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −334.179 | −1.00054 | ||||||||
\(335\) | −37.2882 | −0.111308 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 500.414i | − 1.48491i | −0.669898 | − | 0.742454i | \(-0.733662\pi\) | ||||
0.669898 | − | 0.742454i | \(-0.266338\pi\) | |||||||
\(338\) | − 76.7987i | − 0.227215i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 41.3192i | − 0.121527i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 224.628i | − 0.654891i | ||||||||
\(344\) | −170.503 | −0.495647 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 168.536 | 0.487099 | ||||||||
\(347\) | 242.729i | 0.699509i | 0.936841 | + | 0.349754i | \(0.113735\pi\) | ||||
−0.936841 | + | 0.349754i | \(0.886265\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 447.324i | − 1.28173i | −0.767653 | − | 0.640866i | \(-0.778576\pi\) | ||||
0.767653 | − | 0.640866i | \(-0.221424\pi\) | |||||||
\(350\) | −286.378 | −0.818224 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 226.910 | 0.642805 | 0.321403 | − | 0.946943i | \(-0.395846\pi\) | ||||
0.321403 | + | 0.946943i | \(0.395846\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −50.9847 | −0.143619 | ||||||||
\(356\) | −145.710 | −0.409296 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 451.947i | 1.26242i | ||||||||
\(359\) | 642.653i | 1.79012i | 0.445947 | + | 0.895059i | \(0.352867\pi\) | ||||
−0.445947 | + | 0.895059i | \(0.647133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 289.257 | 0.801267 | ||||||||
\(362\) | 131.941i | 0.364478i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 69.2524 | 0.190254 | ||||||||
\(365\) | 51.3608i | 0.140715i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −717.882 | −1.95608 | −0.978041 | − | 0.208415i | \(-0.933170\pi\) | ||||
−0.978041 | + | 0.208415i | \(0.933170\pi\) | |||||||
\(368\) | 832.094 | 2.26113 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 342.263i | 0.925034i | ||||||||
\(371\) | − 120.881i | − 0.325826i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 18.1857i | − 0.0487552i | −0.999703 | − | 0.0243776i | \(-0.992240\pi\) | ||||
0.999703 | − | 0.0243776i | \(-0.00776040\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 65.1457i | − 0.173260i | ||||||||
\(377\) | −289.849 | −0.768829 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −155.717 | −0.410864 | −0.205432 | − | 0.978671i | \(-0.565860\pi\) | ||||
−0.205432 | + | 0.978671i | \(0.565860\pi\) | |||||||
\(380\) | 172.413i | 0.453719i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 907.215i | − 2.37491i | ||||||||
\(383\) | 720.395 | 1.88093 | 0.940464 | − | 0.339894i | \(-0.110391\pi\) | ||||
0.940464 | + | 0.339894i | \(0.110391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 541.542 | 1.40296 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −88.4142 | −0.227872 | ||||||||
\(389\) | −8.88848 | −0.0228496 | −0.0114248 | − | 0.999935i | \(-0.503637\pi\) | ||||
−0.0114248 | + | 0.999935i | \(0.503637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 85.1679i | − 0.217821i | ||||||||
\(392\) | − 173.295i | − 0.442079i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −919.219 | −2.29805 | ||||||||
\(401\) | −548.823 | −1.36863 | −0.684317 | − | 0.729184i | \(-0.739900\pi\) | ||||
−0.684317 | + | 0.729184i | \(0.739900\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 256.868i | − 0.637390i | ||||||||
\(404\) | − 341.600i | − 0.845546i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 152.081i | 0.374584i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 506.077i | 1.23735i | 0.785646 | + | 0.618676i | \(0.212331\pi\) | ||||
−0.785646 | + | 0.618676i | \(0.787669\pi\) | |||||||
\(410\) | 1125.23 | 2.74447 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −94.0341 | −0.228238 | ||||||||
\(413\) | 48.6437i | 0.117781i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 254.812i | − 0.614004i | ||||||||
\(416\) | 401.622 | 0.965437 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 111.580 | 0.266300 | 0.133150 | − | 0.991096i | \(-0.457491\pi\) | ||||
0.133150 | + | 0.991096i | \(0.457491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 373.299 | 0.886696 | 0.443348 | − | 0.896350i | \(-0.353791\pi\) | ||||
0.443348 | + | 0.896350i | \(0.353791\pi\) | |||||||
\(422\) | 554.370 | 1.31367 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − 199.418i | − 0.470325i | ||||||||
\(425\) | 94.0854i | 0.221377i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −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 | \(-0.0288693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 711.481 | 1.64314 | 0.821572 | − | 0.570105i | \(-0.193097\pi\) | ||||
0.821572 | + | 0.570105i | \(0.193097\pi\) | |||||||
\(434\) | −134.777 | −0.310545 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 195.838i | − 0.449170i | ||||||||
\(437\) | 355.381i | 0.813229i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 262.674i | 0.598347i | 0.954199 | + | 0.299173i | \(0.0967109\pi\) | ||||
−0.954199 | + | 0.299173i | \(0.903289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 60.5171i | − 0.136917i | ||||||||
\(443\) | 528.705 | 1.19346 | 0.596732 | − | 0.802441i | \(-0.296466\pi\) | ||||
0.596732 | + | 0.802441i | \(0.296466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 510.742 | 1.14774 | ||||||||
\(446\) | 530.526i | 1.18952i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 17.1328i | − 0.0382428i | ||||||||
\(449\) | 287.807 | 0.640995 | 0.320498 | − | 0.947249i | \(-0.396150\pi\) | ||||
0.320498 | + | 0.947249i | \(0.396150\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −184.219 | −0.407565 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −211.000 | −0.464759 | ||||||||
\(455\) | −242.744 | −0.533503 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 826.946i | 1.80951i | 0.425932 | + | 0.904755i | \(0.359946\pi\) | ||||
−0.425932 | + | 0.904755i | \(0.640054\pi\) | |||||||
\(458\) | − 837.157i | − 1.82785i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 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 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −418.779 | −0.898668 | ||||||||
\(467\) | −458.119 | −0.980982 | −0.490491 | − | 0.871446i | \(-0.663183\pi\) | ||||
−0.490491 | + | 0.871446i | \(0.663183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.7731i | 0.0229703i | ||||||||
\(470\) | − 346.047i | − 0.736271i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 80.2474i | 0.170016i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 392.591i | − 0.826508i | ||||||||
\(476\) | −11.9377 | −0.0250792 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 455.579 | 0.953095 | ||||||||
\(479\) | − 592.433i | − 1.23681i | −0.785859 | − | 0.618406i | \(-0.787779\pi\) | ||||
0.785859 | − | 0.618406i | \(-0.212221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 188.462i | 0.391813i | ||||||||
\(482\) | −573.777 | −1.19041 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 309.910 | 0.638990 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 437.813 | 0.899001 | 0.449500 | − | 0.893280i | \(-0.351602\pi\) | ||||
0.449500 | + | 0.893280i | \(0.351602\pi\) | |||||||
\(488\) | −478.712 | −0.980967 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − 920.526i | − 1.87862i | ||||||||
\(491\) | 774.734i | 1.57787i | 0.614477 | + | 0.788935i | \(0.289367\pi\) | ||||
−0.614477 | + | 0.788935i | \(0.710633\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 49.9640 | 0.101347 | ||||||||
\(494\) | 252.521i | 0.511175i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −432.607 | −0.872191 | ||||||||
\(497\) | 14.7302i | 0.0296382i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 262.110 | 0.525271 | 0.262636 | − | 0.964895i | \(-0.415408\pi\) | ||||
0.262636 | + | 0.964895i | \(0.415408\pi\) | |||||||
\(500\) | −434.593 | −0.869187 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 200.334i | − 0.399071i | ||||||||
\(503\) | 153.502i | 0.305174i | 0.988290 | + | 0.152587i | \(0.0487604\pi\) | ||||
−0.988290 | + | 0.152587i | \(0.951240\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1197.38i | 2.37105i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 50.7562i | 0.0999138i | ||||||||
\(509\) | 782.781 | 1.53788 | 0.768940 | − | 0.639321i | \(-0.220785\pi\) | ||||
0.768940 | + | 0.639321i | \(0.220785\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.8389 | 0.0290389 | ||||||||
\(512\) | − 357.022i | − 0.697308i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 755.813i | 1.47045i | ||||||||
\(515\) | 329.609 | 0.640018 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 98.8844 | 0.190897 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −400.454 | −0.770104 | ||||||||
\(521\) | 180.526 | 0.346498 | 0.173249 | − | 0.984878i | \(-0.444573\pi\) | ||||
0.173249 | + | 0.984878i | \(0.444573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 151.833i | 0.290311i | 0.989409 | + | 0.145156i | \(0.0463683\pi\) | ||||
−0.989409 | + | 0.145156i | \(0.953632\pi\) | |||||||
\(524\) | − 257.482i | − 0.491378i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −152.737 | −0.290375 | ||||||||
\(527\) | 44.2788i | 0.0840206i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1231.39 | 2.32778 | ||||||||
\(530\) | − 1059.29i | − 1.99865i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 49.8126 | 0.0936326 | ||||||||
\(533\) | 619.594 | 1.16247 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 985.107i | 1.84132i | ||||||||
\(536\) | 17.7723i | 0.0331573i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 496.155i | − 0.922222i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 287.853i | 0.532075i | 0.963963 | + | 0.266038i | \(0.0857146\pi\) | ||||
−0.963963 | + | 0.266038i | \(0.914285\pi\) | |||||||
\(542\) | −862.065 | −1.59052 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −69.2314 | −0.127264 | ||||||||
\(545\) | 686.454i | 1.25955i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 122.440i | 0.223839i | 0.993717 | + | 0.111920i | \(0.0356999\pi\) | ||||
−0.993717 | + | 0.111920i | \(0.964300\pi\) | |||||||
\(548\) | 287.208 | 0.524102 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −208.485 | −0.378376 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −252.493 | −0.456588 | ||||||||
\(554\) | 888.005 | 1.60290 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 17.8912i | − 0.0321784i | ||||||||
\(557\) | 560.374i | 1.00606i | 0.864270 | + | 0.503028i | \(0.167781\pi\) | ||||
−0.864270 | + | 0.503028i | \(0.832219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −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 | \(0.865603\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 645.727 | 1.14288 | ||||||||
\(566\) | 813.095 | 1.43656 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.3004i | 0.0427824i | ||||||||
\(569\) | 850.975i | 1.49556i | 0.663945 | + | 0.747781i | \(0.268881\pi\) | ||||
−0.663945 | + | 0.747781i | \(0.731119\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 558.153i | − 0.977500i | −0.872424 | − | 0.488750i | \(-0.837453\pi\) | ||||
0.872424 | − | 0.488750i | \(-0.162547\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − 325.096i | − 0.566369i | ||||||||
\(575\) | −1944.72 | −3.38212 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1063.74 | 1.84358 | 0.921789 | − | 0.387692i | \(-0.126728\pi\) | ||||
0.921789 | + | 0.387692i | \(0.126728\pi\) | |||||||
\(578\) | − 721.247i | − 1.24783i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 501.034i | 0.863852i | ||||||||
\(581\) | −73.6186 | −0.126710 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 24.4796 | 0.0419172 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −954.648 | −1.62909 | ||||||||
\(587\) | 137.730 | 0.234633 | 0.117317 | − | 0.993095i | \(-0.462571\pi\) | ||||
0.117317 | + | 0.993095i | \(0.462571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 184.763i | − 0.313689i | ||||||||
\(590\) | 426.266i | 0.722485i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 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 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1250.87 | 2.09176 | ||||||||
\(599\) | 323.005 | 0.539240 | 0.269620 | − | 0.962967i | \(-0.413102\pi\) | ||||
0.269620 | + | 0.962967i | \(0.413102\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 682.717i | − 1.13597i | −0.823039 | − | 0.567985i | \(-0.807723\pi\) | ||||
0.823039 | − | 0.567985i | \(-0.192277\pi\) | |||||||
\(602\) | 261.667i | 0.434663i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 153.585i | − 0.254280i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 219.873i | − 0.362229i | −0.983462 | − | 0.181114i | \(-0.942030\pi\) | ||||
0.983462 | − | 0.181114i | \(-0.0579705\pi\) | |||||||
\(608\) | 288.883 | 0.475136 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2542.87 | −4.16864 | ||||||||
\(611\) | − 190.546i | − 0.311859i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 198.057i | 0.323094i | 0.986865 | + | 0.161547i | \(0.0516483\pi\) | ||||
−0.986865 | + | 0.161547i | \(0.948352\pi\) | |||||||
\(614\) | −1281.00 | −2.08632 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −666.299 | −1.07990 | −0.539951 | − | 0.841697i | \(-0.681557\pi\) | ||||
−0.539951 | + | 0.841697i | \(0.681557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 506.706 | 0.818589 | 0.409294 | − | 0.912402i | \(-0.365775\pi\) | ||||
0.409294 | + | 0.912402i | \(0.365775\pi\) | |||||||
\(620\) | −444.024 | −0.716168 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 420.457i | − 0.675976i | ||||||||
\(623\) | − 147.561i | − 0.236855i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 364.586 | 0.583337 | ||||||||
\(626\) | − 237.087i | − 0.378733i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −88.8984 | −0.141558 | ||||||||
\(629\) | − 32.4870i | − 0.0516487i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 761.035 | 1.20608 | 0.603039 | − | 0.797712i | \(-0.293956\pi\) | ||||
0.603039 | + | 0.797712i | \(0.293956\pi\) | |||||||
\(632\) | −416.537 | −0.659078 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 378.623i | 0.597197i | ||||||||
\(635\) | − 177.911i | − 0.280175i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 506.875i | − 0.795722i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1002.23i | 1.56598i | ||||||||
\(641\) | −203.013 | −0.316714 | −0.158357 | − | 0.987382i | \(-0.550620\pi\) | ||||
−0.158357 | + | 0.987382i | \(0.550620\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −455.154 | −0.707860 | −0.353930 | − | 0.935272i | \(-0.615155\pi\) | ||||
−0.353930 | + | 0.935272i | \(0.615155\pi\) | |||||||
\(644\) | − 246.749i | − 0.383150i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − 43.5294i | − 0.0673830i | ||||||||
\(647\) | −535.496 | −0.827659 | −0.413830 | − | 0.910354i | \(-0.635809\pi\) | ||||
−0.413830 | + | 0.910354i | \(0.635809\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1381.84 | −2.12591 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 129.253 | 0.198241 | ||||||||
\(653\) | 829.067 | 1.26963 | 0.634814 | − | 0.772665i | \(-0.281077\pi\) | ||||
0.634814 | + | 0.772665i | \(0.281077\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 902.529i | 1.37791i | ||||||||
\(656\) | − 1043.49i | − 1.59069i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −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 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −121.448 | −0.182904 | ||||||||
\(665\) | −174.603 | −0.262562 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1032.74i | 1.54834i | ||||||||
\(668\) | 318.083i | 0.476172i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 94.4048i | 0.140903i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 645.812i | − 0.959602i | −0.877377 | − | 0.479801i | \(-0.840709\pi\) | ||||
0.877377 | − | 0.479801i | \(-0.159291\pi\) | |||||||
\(674\) | −1266.93 | −1.87972 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −73.0996 | −0.108135 | ||||||||
\(677\) | 737.620i | 1.08954i | 0.838585 | + | 0.544771i | \(0.183383\pi\) | ||||
−0.838585 | + | 0.544771i | \(0.816617\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 89.5373i | − 0.131866i | ||||||||
\(680\) | 69.0302 | 0.101515 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −527.576 | −0.772440 | −0.386220 | − | 0.922407i | \(-0.626219\pi\) | ||||
−0.386220 | + | 0.922407i | \(0.626219\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1006.72 | −1.46967 | ||||||||
\(686\) | −568.703 | −0.829014 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 839.901i | 1.22079i | ||||||||
\(689\) | − 583.281i | − 0.846562i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −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 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −106.805 | −0.153236 | ||||||||
\(698\) | −1132.52 | −1.62252 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 272.585i | 0.389407i | ||||||||
\(701\) | − 699.987i | − 0.998555i | −0.866442 | − | 0.499278i | \(-0.833599\pi\) | ||||
0.866442 | − | 0.499278i | \(-0.166401\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 135.559i | 0.192829i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 574.482i | − 0.813714i | ||||||||
\(707\) | 345.940 | 0.489307 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −649.664 | −0.916310 | −0.458155 | − | 0.888872i | \(-0.651490\pi\) | ||||
−0.458155 | + | 0.888872i | \(0.651490\pi\) | |||||||
\(710\) | 129.081i | 0.181804i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 243.430i | − 0.341897i | ||||||||
\(713\) | −915.230 | −1.28363 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 430.178 | 0.600808 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1627.04 | 2.26608 | ||||||||
\(719\) | −694.522 | −0.965955 | −0.482978 | − | 0.875633i | \(-0.660445\pi\) | ||||
−0.482978 | + | 0.875633i | \(0.660445\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 95.2287i | − 0.132079i | ||||||||
\(722\) | − 732.330i | − 1.01431i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 130.033 | 0.178128 | ||||||||
\(731\) | 85.9669 | 0.117602 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 157.602i | 0.215009i | 0.994205 | + | 0.107504i | \(0.0342860\pi\) | ||||
−0.994205 | + | 0.107504i | \(0.965714\pi\) | |||||||
\(734\) | 1817.51i | 2.47616i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 1430.99i | − 1.94428i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 685.531i | 0.927647i | 0.885928 | + | 0.463823i | \(0.153523\pi\) | ||||
−0.885928 | + | 0.463823i | \(0.846477\pi\) | |||||||
\(740\) | 325.777 | 0.440239 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −306.043 | −0.412457 | ||||||||
\(743\) | − 516.079i | − 0.694588i | −0.937756 | − | 0.347294i | \(-0.887101\pi\) | ||||
0.937756 | − | 0.347294i | \(-0.112899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1193.24i | 1.60166i | ||||||||
\(746\) | −46.0418 | −0.0617183 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 284.611 | 0.379988 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −853.690 | −1.13674 | −0.568369 | − | 0.822774i | \(-0.692425\pi\) | ||||
−0.568369 | + | 0.822774i | \(0.692425\pi\) | |||||||
\(752\) | −320.910 | −0.426742 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 733.827i | 0.973246i | ||||||||
\(755\) | 538.347i | 0.713043i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −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 | \(-0.000270501\pi\) | ||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 198.326 | 0.259930 | ||||||||
\(764\) | −863.517 | −1.13026 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 1823.87i | − 2.38103i | ||||||||
\(767\) | 234.717i | 0.306020i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 398.342i | 0.518000i | 0.965877 | + | 0.259000i | \(0.0833929\pi\) | ||||
−0.965877 | + | 0.259000i | \(0.916607\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 515.457i | − 0.667691i | ||||||||
\(773\) | 637.493 | 0.824700 | 0.412350 | − | 0.911025i | \(-0.364708\pi\) | ||||
0.412350 | + | 0.911025i | \(0.364708\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1011.06 | 1.30459 | ||||||||
\(776\) | − 147.710i | − 0.190347i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.5035i | 0.0289248i | ||||||||
\(779\) | 445.668 | 0.572103 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −215.625 | −0.275735 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −853.657 | −1.08885 | ||||||||
\(785\) | 311.608 | 0.396952 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1070.60i | 1.36036i | 0.733045 | + | 0.680180i | \(0.238099\pi\) | ||||
−0.733045 | + | 0.680180i | \(0.761901\pi\) | |||||||
\(788\) | 666.477i | 0.845783i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2212.60 | −2.80077 | ||||||||
\(791\) | − 186.560i | − 0.235853i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1400.19 | −1.76569 | ||||||||
\(794\) | − 1299.44i | − 1.63657i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −189.914 | −0.238585 | ||||||||
\(797\) | −365.858 | −0.459044 | −0.229522 | − | 0.973303i | \(-0.573716\pi\) | ||||
−0.229522 | + | 0.973303i | \(0.573716\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.8463i | 0.0411092i | ||||||||
\(800\) | 1580.83i | 1.97603i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1389.49i | 1.73253i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 864.906i | 1.07442i | ||||||||
\(806\) | −650.329 | −0.806860 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 570.697 | 0.706308 | ||||||||
\(809\) | − 176.666i | − 0.218375i | −0.994021 | − | 0.109188i | \(-0.965175\pi\) | ||||
0.994021 | − | 0.109188i | \(-0.0348249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 256.402i | 0.316156i | 0.987427 | + | 0.158078i | \(0.0505297\pi\) | ||||
−0.987427 | + | 0.158078i | \(0.949470\pi\) | |||||||
\(812\) | 144.756 | 0.178271 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −453.058 | −0.555900 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −358.715 | −0.439064 | ||||||||
\(818\) | 1281.27 | 1.56634 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − 1071.03i | − 1.30614i | ||||||||
\(821\) | − 938.646i | − 1.14330i | −0.820499 | − | 0.571648i | \(-0.806304\pi\) | ||||
0.820499 | − | 0.571648i | \(-0.193696\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 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 | \(-0.296269\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −899.388 | −1.08491 | −0.542454 | − | 0.840086i | \(-0.682505\pi\) | ||||
−0.542454 | + | 0.840086i | \(0.682505\pi\) | |||||||
\(830\) | −645.122 | −0.777255 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 82.6697i | − 0.0993626i | ||||||||
\(833\) | 87.3749i | 0.104892i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1114.95i | − 1.33527i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 282.494i | − 0.337104i | ||||||||
\(839\) | −283.608 | −0.338032 | −0.169016 | − | 0.985613i | \(-0.554059\pi\) | ||||
−0.169016 | + | 0.985613i | \(0.554059\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 235.139 | 0.279595 | ||||||||
\(842\) | − 945.104i | − 1.12245i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − 527.668i | − 0.625199i | ||||||||
\(845\) | 256.229 | 0.303230 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −982.338 | −1.15842 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 238.202 | 0.280237 | ||||||||
\(851\) | 671.497 | 0.789068 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 440.959i | − 0.516951i | −0.966018 | − | 0.258476i | \(-0.916780\pi\) | ||||
0.966018 | − | 0.258476i | \(-0.0832202\pi\) | |||||||
\(854\) | 734.670i | 0.860269i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −197.661 | −0.229305 | ||||||||
\(863\) | 514.959 | 0.596708 | 0.298354 | − | 0.954455i | \(-0.403562\pi\) | ||||
0.298354 | + | 0.954455i | \(0.403562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 562.301i | 0.650058i | ||||||||
\(866\) | − 1801.30i | − 2.08002i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 128.285i | 0.147794i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 51.9827i | 0.0596816i | ||||||||
\(872\) | 327.178 | 0.375205 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 899.740 | 1.02945 | ||||||||
\(875\) | − 440.114i | − 0.502988i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 742.107i | − 0.846188i | −0.906086 | − | 0.423094i | \(-0.860944\pi\) | ||||
0.906086 | − | 0.423094i | \(-0.139056\pi\) | |||||||
\(878\) | 665.028 | 0.757435 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 620.478 | 0.704288 | 0.352144 | − | 0.935946i | \(-0.385453\pi\) | ||||
0.352144 | + | 0.935946i | \(0.385453\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 674.168 | 0.763498 | 0.381749 | − | 0.924266i | \(-0.375322\pi\) | ||||
0.381749 | + | 0.924266i | \(0.375322\pi\) | |||||||
\(884\) | −57.6022 | −0.0651609 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 1338.55i | − 1.51078i | ||||||||
\(887\) | − 1098.43i | − 1.23837i | −0.785245 | − | 0.619185i | \(-0.787463\pi\) | ||||
0.785245 | − | 0.619185i | \(-0.212537\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −51.4010 | −0.0578189 | ||||||||
\(890\) | − 1293.08i | − 1.45290i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 504.973 | 0.566113 | ||||||||
\(893\) | − 137.058i | − 0.153480i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1507.86 | −1.68477 | ||||||||
\(896\) | 289.558 | 0.323168 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 728.658i | − 0.811424i | ||||||||
\(899\) | − 536.923i | − 0.597244i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 100.546i | 0.111594i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 307.767i | − 0.340450i | ||||||||
\(905\) | −440.205 | −0.486415 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 247.155 | 0.272498 | 0.136249 | − | 0.990675i | \(-0.456495\pi\) | ||||
0.136249 | + | 0.990675i | \(0.456495\pi\) | |||||||
\(908\) | 200.837i | 0.221186i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 614.570i | 0.675351i | ||||||||
\(911\) | −686.752 | −0.753844 | −0.376922 | − | 0.926245i | \(-0.623018\pi\) | ||||
−0.376922 | + | 0.926245i | \(0.623018\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 2093.63 | 2.29062 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −796.834 | −0.869906 | ||||||||
\(917\) | 260.753 | 0.284355 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1485.25i | − 1.61615i | −0.589077 | − | 0.808077i | \(-0.700509\pi\) | ||||
0.589077 | − | 0.808077i | \(-0.299491\pi\) | |||||||
\(920\) | 1426.83i | 1.55091i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 823.718 | 0.893403 | ||||||||
\(923\) | 71.0767i | 0.0770062i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −741.807 | −0.801953 | ||||||||
\(926\) | 1801.74i | 1.94573i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 839.497 | 0.904630 | ||||||||
\(929\) | 681.402 | 0.733479 | 0.366740 | − | 0.930324i | \(-0.380474\pi\) | ||||
0.366740 | + | 0.930324i | \(0.380474\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 364.590i | − 0.391611i | ||||||||
\(932\) | 398.608i | 0.427691i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1159.85i | 1.24181i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 88.5349i | − 0.0944876i | −0.998883 | − | 0.0472438i | \(-0.984956\pi\) | ||||
0.998883 | − | 0.0472438i | \(-0.0150438\pi\) | |||||||
\(938\) | 27.2749 | 0.0290777 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −329.379 | −0.350404 | ||||||||
\(941\) | 582.065i | 0.618560i | 0.950971 | + | 0.309280i | \(0.100088\pi\) | ||||
−0.950971 | + | 0.309280i | \(0.899912\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2207.64i | − 2.34108i | ||||||||
\(944\) | 395.301 | 0.418751 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 912.836 | 0.963924 | 0.481962 | − | 0.876192i | \(-0.339924\pi\) | ||||
0.481962 | + | 0.876192i | \(0.339924\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 71.6011 | 0.0754489 | ||||||||
\(950\) | −993.947 | −1.04626 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 19.9438i | − 0.0209493i | ||||||||
\(953\) | − 554.670i | − 0.582026i | −0.956719 | − | 0.291013i | \(-0.906008\pi\) | ||||
0.956719 | − | 0.291013i | \(-0.0939922\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3026.81 | 3.16943 | ||||||||
\(956\) | − 433.636i | − 0.453594i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1499.90 | −1.56566 | ||||||||
\(959\) | 290.857i | 0.303292i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −485.171 | −0.504861 | ||||||||
\(962\) | 477.141 | 0.495989 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 546.140i | 0.566535i | ||||||||
\(965\) | 1806.79i | 1.87232i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1781.13i | 1.84191i | 0.389667 | + | 0.920956i | \(0.372590\pi\) | ||||
−0.389667 | + | 0.920956i | \(0.627410\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − 784.618i | − 0.808885i | ||||||||
\(971\) | 990.964 | 1.02056 | 0.510280 | − | 0.860008i | \(-0.329542\pi\) | ||||
0.510280 | + | 0.860008i | \(0.329542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.1185 | 0.0186213 | ||||||||
\(974\) | − 1108.44i | − 1.13803i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2358.15i | 2.41614i | ||||||||
\(977\) | −754.917 | −0.772689 | −0.386344 | − | 0.922355i | \(-0.626262\pi\) | ||||
−0.386344 | + | 0.922355i | \(0.626262\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −876.187 | −0.894069 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1961.44 | 1.99740 | ||||||||
\(983\) | 206.512 | 0.210084 | 0.105042 | − | 0.994468i | \(-0.466502\pi\) | ||||
0.105042 | + | 0.994468i | \(0.466502\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 2336.14i | − 2.37172i | ||||||||
\(986\) | − 126.497i | − 0.128293i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 37.2933 | 0.0375185 | ||||||||
\(995\) | 665.687 | 0.669033 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1168.11i | − 1.17162i | −0.810448 | − | 0.585810i | \(-0.800776\pi\) | ||||
0.810448 | − | 0.585810i | \(-0.199224\pi\) | |||||||
\(998\) | − 663.601i | − 0.664931i | ||||||||
\(999\) | 0 | 0 |
(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 | 1089.3.c.m.604.3 | 16 | ||
3.2 | odd | 2 | 363.3.c.e.241.14 | 16 | |||
11.4 | even | 5 | 99.3.k.c.28.3 | 16 | |||
11.8 | odd | 10 | 99.3.k.c.46.3 | 16 | |||
11.10 | odd | 2 | inner | 1089.3.c.m.604.14 | 16 | ||
33.2 | even | 10 | 363.3.g.a.40.2 | 16 | |||
33.5 | odd | 10 | 363.3.g.a.118.2 | 16 | |||
33.8 | even | 10 | 33.3.g.a.13.2 | ✓ | 16 | ||
33.14 | odd | 10 | 363.3.g.f.112.3 | 16 | |||
33.17 | even | 10 | 363.3.g.g.118.3 | 16 | |||
33.20 | odd | 10 | 363.3.g.g.40.3 | 16 | |||
33.26 | odd | 10 | 33.3.g.a.28.2 | yes | 16 | ||
33.29 | even | 10 | 363.3.g.f.94.3 | 16 | |||
33.32 | even | 2 | 363.3.c.e.241.3 | 16 | |||
132.59 | even | 10 | 528.3.bf.b.193.1 | 16 | |||
132.107 | odd | 10 | 528.3.bf.b.145.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.13.2 | ✓ | 16 | 33.8 | even | 10 | ||
33.3.g.a.28.2 | yes | 16 | 33.26 | odd | 10 | ||
99.3.k.c.28.3 | 16 | 11.4 | even | 5 | |||
99.3.k.c.46.3 | 16 | 11.8 | odd | 10 | |||
363.3.c.e.241.3 | 16 | 33.32 | even | 2 | |||
363.3.c.e.241.14 | 16 | 3.2 | odd | 2 | |||
363.3.g.a.40.2 | 16 | 33.2 | even | 10 | |||
363.3.g.a.118.2 | 16 | 33.5 | odd | 10 | |||
363.3.g.f.94.3 | 16 | 33.29 | even | 10 | |||
363.3.g.f.112.3 | 16 | 33.14 | odd | 10 | |||
363.3.g.g.40.3 | 16 | 33.20 | odd | 10 | |||
363.3.g.g.118.3 | 16 | 33.17 | even | 10 | |||
528.3.bf.b.145.1 | 16 | 132.107 | odd | 10 | |||
528.3.bf.b.193.1 | 16 | 132.59 | even | 10 | |||
1089.3.c.m.604.3 | 16 | 1.1 | even | 1 | trivial | ||
1089.3.c.m.604.14 | 16 | 11.10 | odd | 2 | inner |