Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(65,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.h (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 631 x^{10} - 3100 x^{9} + 142264 x^{8} - 550522 x^{7} + 14083117 x^{6} - 40335478 x^{5} + 638031136 x^{4} - 1209472584 x^{3} + \cdots + 90728724573 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 69.6 | ||
Root | \(0.500000 + 15.2283i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.69 |
Dual form | 76.5.h.a.65.6 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 12.4381 | − | 7.18116i | 1.38202 | − | 0.797907i | 0.389617 | − | 0.920977i | \(-0.372607\pi\) |
0.992398 | + | 0.123070i | \(0.0392740\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.11411 | − | 5.39380i | −0.124564 | − | 0.215752i | 0.796998 | − | 0.603982i | \(-0.206420\pi\) |
−0.921563 | + | 0.388230i | \(0.873087\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.9415 | 1.01921 | 0.509607 | − | 0.860407i | \(-0.329791\pi\) | ||||
0.509607 | + | 0.860407i | \(0.329791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 62.6382 | − | 108.493i | 0.773311 | − | 1.33941i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.88575 | 0.0155847 | 0.00779237 | − | 0.999970i | \(-0.497520\pi\) | ||||
0.00779237 | + | 0.999970i | \(0.497520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −69.0003 | − | 39.8373i | −0.408286 | − | 0.235724i | 0.281767 | − | 0.959483i | \(-0.409079\pi\) |
−0.690053 | + | 0.723759i | \(0.742413\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −77.4675 | − | 44.7259i | −0.344300 | − | 0.198782i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −119.788 | − | 207.478i | −0.414490 | − | 0.717918i | 0.580885 | − | 0.813986i | \(-0.302707\pi\) |
−0.995375 | + | 0.0960680i | \(0.969373\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 72.4707 | + | 353.651i | 0.200750 | + | 0.979643i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 621.179 | − | 358.638i | 1.40857 | − | 0.813238i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 109.429 | − | 189.537i | 0.206861 | − | 0.358294i | −0.743863 | − | 0.668332i | \(-0.767009\pi\) |
0.950724 | + | 0.310038i | \(0.100342\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 293.105 | − | 507.672i | 0.468967 | − | 0.812275i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 635.911i | − | 0.872306i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 340.159 | + | 196.391i | 0.404470 | + | 0.233521i | 0.688411 | − | 0.725321i | \(-0.258309\pi\) |
−0.283941 | + | 0.958842i | \(0.591642\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 580.549i | 0.604109i | 0.953291 | + | 0.302055i | \(0.0976725\pi\) | ||||
−0.953291 | + | 0.302055i | \(0.902327\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 23.4553 | − | 13.5419i | 0.0215383 | − | 0.0124352i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −155.523 | − | 269.374i | −0.126958 | − | 0.219898i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2478.77i | 1.81064i | 0.424727 | + | 0.905321i | \(0.360370\pi\) | ||||
−0.424727 | + | 0.905321i | \(0.639630\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1144.31 | −0.752343 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2840.91 | + | 1640.20i | −1.69001 | + | 0.975729i | −0.735516 | + | 0.677507i | \(0.763060\pi\) |
−0.954497 | + | 0.298222i | \(0.903606\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −162.917 | − | 282.181i | −0.0881111 | − | 0.152613i | 0.818602 | − | 0.574362i | \(-0.194750\pi\) |
−0.906713 | + | 0.421749i | \(0.861416\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −780.249 | −0.385308 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −969.593 | + | 1679.39i | −0.438929 | + | 0.760247i | −0.997607 | − | 0.0691376i | \(-0.977975\pi\) |
0.558678 | + | 0.829384i | \(0.311309\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 93.1537 | 0.0387979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2979.87 | − | 1720.43i | −1.14566 | − | 0.661449i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2087.49 | + | 1205.21i | 0.743142 | + | 0.429053i | 0.823211 | − | 0.567736i | \(-0.192181\pi\) |
−0.0800686 | + | 0.996789i | \(0.525514\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.87245 | − | 10.1714i | −0.00194130 | − | 0.00336244i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3441.03 | + | 3878.34i | 1.05910 | + | 1.19370i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3046.44 | − | 1758.86i | 0.875163 | − | 0.505275i | 0.00610218 | − | 0.999981i | \(-0.498058\pi\) |
0.869060 | + | 0.494706i | \(0.164724\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1039.02 | + | 1799.64i | −0.279232 | + | 0.483644i | −0.971194 | − | 0.238290i | \(-0.923413\pi\) |
0.691962 | + | 0.721934i | \(0.256747\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3128.24 | − | 5418.28i | 0.788170 | − | 1.36515i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 496.232i | 0.117451i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4389.01 | − | 2533.99i | −0.977725 | − | 0.564490i | −0.0761425 | − | 0.997097i | \(-0.524260\pi\) |
−0.901583 | + | 0.432607i | \(0.857594\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 3143.32i | − | 0.660223i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2994.82 | − | 1729.06i | 0.594092 | − | 0.342999i | −0.172622 | − | 0.984988i | \(-0.555224\pi\) |
0.766714 | + | 0.641989i | \(0.221891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4356.65 | + | 7545.94i | 0.817536 | + | 1.41601i | 0.907492 | + | 0.420069i | \(0.137994\pi\) |
−0.0899558 | + | 0.995946i | \(0.528673\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8419.33i | − | 1.49677i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 94.1773 | 0.0158842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3640.40 | − | 2101.79i | 0.583304 | − | 0.336771i | −0.179141 | − | 0.983823i | \(-0.557332\pi\) |
0.762445 | + | 0.647053i | \(0.223999\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 507.109 | + | 878.339i | 0.0772915 | + | 0.133873i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11775.2 | −1.70927 | −0.854635 | − | 0.519229i | \(-0.826219\pi\) | ||||
−0.854635 | + | 0.519229i | \(0.826219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −746.064 | + | 1292.22i | −0.103261 | + | 0.178854i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5641.26 | 0.745311 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8212.16 | − | 4741.29i | −1.03676 | − | 0.598573i | −0.117845 | − | 0.993032i | \(-0.537599\pi\) |
−0.918913 | + | 0.394460i | \(0.870932\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3445.98 | − | 1989.54i | −0.416131 | − | 0.240253i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4169.02 | + | 7220.95i | 0.482023 | + | 0.834888i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1681.84 | − | 1492.20i | 0.186354 | − | 0.165341i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5045.74 | − | 2913.16i | 0.536267 | − | 0.309614i | −0.207297 | − | 0.978278i | \(-0.566467\pi\) |
0.743565 | + | 0.668664i | \(0.233133\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 118.120 | − | 204.590i | 0.0120518 | − | 0.0208744i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9167.14 | − | 15878.0i | 0.898651 | − | 1.55651i | 0.0694313 | − | 0.997587i | \(-0.477882\pi\) |
0.829220 | − | 0.558923i | \(-0.188785\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15685.2i | 1.47848i | 0.673443 | + | 0.739239i | \(0.264815\pi\) | ||||
−0.673443 | + | 0.739239i | \(0.735185\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3868.84 | − | 2233.68i | −0.350916 | − | 0.202601i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15464.3i | − | 1.35071i | −0.737494 | − | 0.675354i | \(-0.763991\pi\) | ||
0.737494 | − | 0.675354i | \(-0.236009\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15286.3 | − | 8825.56i | 1.28662 | − | 0.742830i | 0.308569 | − | 0.951202i | \(-0.400150\pi\) |
0.978050 | + | 0.208372i | \(0.0668166\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17800.4 | + | 30831.3i | 1.44472 | + | 2.50234i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5351.37i | − | 0.419090i | −0.977799 | − | 0.209545i | \(-0.932802\pi\) | ||
0.977799 | − | 0.209545i | \(-0.0671984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1363.10 | −0.103070 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8644.10 | + | 4990.68i | −0.631464 | + | 0.364576i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5982.37 | − | 10361.8i | −0.422454 | − | 0.731712i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14637.4 | −0.999757 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23557.1 | + | 40802.1i | −1.55708 | + | 2.69695i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7543.68 | −0.482796 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5218.76 | − | 3013.05i | −0.323564 | − | 0.186810i | 0.329416 | − | 0.944185i | \(-0.393148\pi\) |
−0.652980 | + | 0.757375i | \(0.726481\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4052.78 | − | 2339.87i | −0.243542 | − | 0.140609i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5324.73 | − | 9222.71i | −0.310281 | − | 0.537423i | 0.668142 | − | 0.744034i | \(-0.267090\pi\) |
−0.978423 | + | 0.206611i | \(0.933757\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3619.30 | + | 17661.9i | 0.204607 | + | 0.998466i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3429.98 | + | 1980.30i | −0.188202 | + | 0.108658i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4402.76 | + | 7625.80i | −0.234576 | + | 0.406298i | −0.959149 | − | 0.282900i | \(-0.908704\pi\) |
0.724573 | + | 0.689198i | \(0.242037\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3584.83 | − | 6209.10i | 0.185540 | − | 0.321366i | −0.758218 | − | 0.652001i | \(-0.773930\pi\) |
0.943759 | + | 0.330636i | \(0.107263\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27851.2i | 1.40090i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −130.117 | − | 75.1234i | −0.00636302 | − | 0.00367369i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2446.33i | − | 0.116354i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1158.66 | − | 668.952i | 0.0536192 | − | 0.0309571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8324.08 | − | 14417.7i | −0.374941 | − | 0.649418i | 0.615377 | − | 0.788233i | \(-0.289004\pi\) |
−0.990318 | + | 0.138815i | \(0.955671\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1780.79i | 0.0781013i | 0.999237 | + | 0.0390506i | \(0.0124334\pi\) | ||||
−0.999237 | + | 0.0390506i | \(0.987567\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −30013.1 | −1.28212 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3131.37 | − | 1807.89i | 0.130338 | − | 0.0752506i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4609.89 | + | 7984.57i | 0.187022 | + | 0.323931i | 0.944256 | − | 0.329212i | \(-0.106783\pi\) |
−0.757234 | + | 0.653143i | \(0.773450\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 34619.2 | 1.36938 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5465.07 | − | 9465.78i | 0.210836 | − | 0.365178i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 29276.2 | 1.10189 | 0.550947 | − | 0.834540i | \(-0.314267\pi\) | ||||
0.550947 | + | 0.834540i | \(0.314267\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −146.085 | − | 84.3420i | −0.00536582 | − | 0.00309796i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −37315.4 | − | 21544.1i | −1.33800 | − | 0.772493i | −0.351487 | − | 0.936193i | \(-0.614324\pi\) |
−0.986510 | + | 0.163700i | \(0.947657\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11106.5 | − | 19237.0i | −0.388869 | − | 0.673540i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 42907.9 | + | 14289.5i | 1.46739 | + | 0.488681i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 38605.2 | − | 22288.7i | 1.28989 | − | 0.744721i | 0.311259 | − | 0.950325i | \(-0.399249\pi\) |
0.978635 | + | 0.205605i | \(0.0659161\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14638.1 | − | 25353.9i | 0.477978 | − | 0.827883i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25261.4 | − | 43754.0i | 0.806325 | − | 1.39660i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 18503.2i | − | 0.577486i | −0.957407 | − | 0.288743i | \(-0.906763\pi\) | ||
0.957407 | − | 0.288743i | \(-0.0932373\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 27630.5 | + | 15952.4i | 0.843395 | + | 0.486934i | 0.858417 | − | 0.512953i | \(-0.171448\pi\) |
−0.0150220 | + | 0.999887i | \(0.504782\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29845.6i | 0.891205i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13370.0 | − | 7719.17i | 0.390650 | − | 0.225542i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −225.890 | − | 391.253i | −0.00645972 | − | 0.0111886i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 31758.4i | − | 0.889067i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −28246.4 | −0.774276 | −0.387138 | − | 0.922022i | \(-0.626536\pi\) | ||||
−0.387138 | + | 0.922022i | \(0.626536\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −35466.8 | + | 20476.8i | −0.952154 | + | 0.549727i | −0.893750 | − | 0.448566i | \(-0.851935\pi\) |
−0.0584049 | + | 0.998293i | \(0.518601\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3563.52 | + | 6172.20i | 0.0937152 | + | 0.162319i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22359.6 | −0.576144 | −0.288072 | − | 0.957609i | \(-0.593014\pi\) | ||||
−0.288072 | + | 0.957609i | \(0.593014\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2166.66 | + | 3752.77i | −0.0547123 | + | 0.0947645i | −0.892084 | − | 0.451869i | \(-0.850757\pi\) |
0.837372 | + | 0.546633i | \(0.184091\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −72788.1 | −1.80164 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16988.1 | + | 9808.06i | 0.412241 | + | 0.238008i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17693.8 | + | 10215.5i | 0.421031 | + | 0.243082i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13708.9 | − | 23744.5i | −0.319936 | − | 0.554145i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 136.662 | + | 666.898i | 0.00312863 | + | 0.0152675i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −48243.9 | + | 27853.6i | −1.08362 | + | 0.625629i | −0.931871 | − | 0.362790i | \(-0.881824\pi\) |
−0.151750 | + | 0.988419i | \(0.548491\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24833.3 | − | 43012.6i | 0.547363 | − | 0.948060i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1014.69 | + | 1757.49i | −0.0219510 | + | 0.0380203i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28993.5i | 0.615717i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 108377. | + | 62571.6i | 2.25970 | + | 1.30464i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19088.1i | 0.390821i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23671.3 | + | 13666.6i | −0.476005 | + | 0.274822i | −0.718750 | − | 0.695268i | \(-0.755285\pi\) |
0.242745 | + | 0.970090i | \(0.421952\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −36719.1 | − | 63599.3i | −0.725315 | − | 1.25628i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 42099.3i | − | 0.817003i | −0.912758 | − | 0.408501i | \(-0.866051\pi\) | ||
0.912758 | − | 0.408501i | \(-0.133949\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12163.3 | 0.231942 | 0.115971 | − | 0.993253i | \(-0.463002\pi\) | ||||
0.115971 | + | 0.993253i | \(0.463002\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1171.39 | − | 676.303i | 0.0219522 | − | 0.0126741i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12709.0 | + | 22012.6i | 0.234098 | + | 0.405470i | 0.959010 | − | 0.283372i | \(-0.0914529\pi\) |
−0.724912 | + | 0.688841i | \(0.758120\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12077.7 | 0.218700 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 30186.5 | − | 52284.6i | 0.537424 | − | 0.930845i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −86525.4 | −1.51477 | −0.757387 | − | 0.652967i | \(-0.773524\pi\) | ||||
−0.757387 | + | 0.652967i | \(0.773524\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 45400.9 | + | 26212.2i | 0.781682 | + | 0.451305i | 0.837026 | − | 0.547163i | \(-0.184292\pi\) |
−0.0553438 | + | 0.998467i | \(0.517625\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 57222.9 | + | 33037.7i | 0.969076 | + | 0.559496i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −290.091 | − | 502.452i | −0.00483284 | − | 0.00837072i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9088.01 | − | 27289.1i | 0.148962 | − | 0.447296i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −146461. | + | 84559.4i | −2.36224 | + | 1.36384i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19639.4 | + | 34016.4i | −0.311732 | + | 0.539935i | −0.978737 | − | 0.205118i | \(-0.934242\pi\) |
0.667006 | + | 0.745053i | \(0.267576\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 206.357 | − | 357.420i | 0.00322387 | − | 0.00558391i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21430.4i | 0.329572i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 64968.9 | + | 37509.8i | 0.983646 | + | 0.567908i | 0.903369 | − | 0.428864i | \(-0.141086\pi\) |
0.0802773 | + | 0.996773i | \(0.474419\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 123793.i | 1.84543i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 42613.9 | − | 24603.1i | 0.625562 | − | 0.361168i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14757.8 | − | 25561.3i | −0.213359 | − | 0.369548i | 0.739405 | − | 0.673261i | \(-0.235107\pi\) |
−0.952764 | + | 0.303713i | \(0.901774\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15012.6i | − | 0.213779i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −136192. | −1.91042 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 87976.7 | − | 50793.4i | 1.21580 | − | 0.701944i | 0.251785 | − | 0.967783i | \(-0.418982\pi\) |
0.964017 | + | 0.265839i | \(0.0856490\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11915.4 | + | 20638.0i | 0.162244 | + | 0.281015i | 0.935673 | − | 0.352868i | \(-0.114793\pi\) |
−0.773429 | + | 0.633883i | \(0.781460\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −57148.7 | −0.766799 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 552.723 | − | 957.344i | 0.00730873 | − | 0.0126591i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −109790. | −1.43088 | −0.715438 | − | 0.698677i | \(-0.753773\pi\) | ||||
−0.715438 | + | 0.698677i | \(0.753773\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 62985.2 | + | 36364.5i | 0.809152 | + | 0.467164i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −52508.2 | − | 30315.6i | −0.664989 | − | 0.383932i | 0.129186 | − | 0.991620i | \(-0.458764\pi\) |
−0.794175 | + | 0.607689i | \(0.792097\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8384.27 | − | 14522.0i | −0.104687 | − | 0.181323i | 0.808923 | − | 0.587914i | \(-0.200051\pi\) |
−0.913610 | + | 0.406591i | \(0.866717\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10203.2 | − | 30637.8i | 0.125617 | − | 0.377196i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −141879. | + | 81914.1i | −1.72249 | + | 0.994477i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13062.3 | − | 22624.6i | 0.156396 | − | 0.270886i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 41839.7 | − | 72468.6i | 0.494087 | − | 0.855783i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 127491.i | 1.48506i | 0.669813 | + | 0.742530i | \(0.266374\pi\) | ||||
−0.669813 | + | 0.742530i | \(0.733626\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18973.9 | − | 10954.6i | −0.218028 | − | 0.125879i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1199.17i | − | 0.0135947i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15101.3 | + | 8718.75i | −0.168917 | + | 0.0975241i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8136.34 | − | 14092.6i | −0.0898041 | − | 0.155545i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 263323.i | − | 2.86816i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12942.5 | 0.139130 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 94867.2 | − | 54771.6i | 1.00656 | − | 0.581137i | 0.0963769 | − | 0.995345i | \(-0.469275\pi\) |
0.910182 | + | 0.414208i | \(0.135941\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 112638. | + | 195094.i | 1.17969 | + | 2.04328i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 150216. | 1.55309 | 0.776544 | − | 0.630063i | \(-0.216971\pi\) | ||||
0.776544 | + | 0.630063i | \(0.216971\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20012.3 | − | 34662.3i | 0.204272 | − | 0.353809i | −0.745629 | − | 0.666362i | \(-0.767851\pi\) |
0.949900 | + | 0.312553i | \(0.101184\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −38966.8 | −0.392712 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 143247. | + | 82703.8i | 1.42550 | + | 0.823013i | 0.996761 | − | 0.0804148i | \(-0.0256245\pi\) |
0.428739 | + | 0.903428i | \(0.358958\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 641.456 | + | 370.345i | 0.00630356 | + | 0.00363936i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −111051. | − | 192347.i | −1.07774 | − | 1.86670i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 64693.8 | − | 57399.1i | 0.620094 | − | 0.550174i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −40448.6 | + | 23353.0i | −0.382945 | + | 0.221094i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 126756. | − | 219547.i | 1.18542 | − | 2.05320i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −48423.0 | + | 83871.0i | −0.447362 | + | 0.774854i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 188621.i | − | 1.72161i | −0.508935 | − | 0.860805i | \(-0.669961\pi\) | ||
0.508935 | − | 0.860805i | \(-0.330039\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 268928. | + | 155266.i | 2.42520 | + | 1.40019i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 31564.6i | 0.281262i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31324.9 | − | 18085.5i | 0.275823 | − | 0.159246i | −0.355708 | − | 0.934597i | \(-0.615760\pi\) |
0.631531 | + | 0.775351i | \(0.282427\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −38429.0 | − | 66561.0i | −0.334395 | − | 0.579189i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1094.77i | 0.00941488i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −115257. | −0.979671 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16954.4 | + | 9788.65i | −0.142444 | + | 0.0822403i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −90478.1 | − | 156713.i | −0.751423 | − | 1.30150i | −0.947133 | − | 0.320841i | \(-0.896035\pi\) |
0.195710 | − | 0.980662i | \(-0.437299\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 128784. | 1.05733 | 0.528666 | − | 0.848830i | \(-0.322692\pi\) | ||||
0.528666 | + | 0.848830i | \(0.322692\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25333.0 | + | 43878.1i | −0.205623 | + | 0.356150i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 71514.4 | 0.573910 | 0.286955 | − | 0.957944i | \(-0.407357\pi\) | ||||
0.286955 | + | 0.957944i | \(0.407357\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18652.4 | − | 10769.0i | −0.148006 | − | 0.0854510i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −148819. | − | 85920.8i | −1.16768 | − | 0.674158i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 45696.9 | + | 79149.3i | 0.354566 | + | 0.614127i | 0.987044 | − | 0.160452i | \(-0.0512951\pi\) |
−0.632477 | + | 0.774579i | \(0.717962\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −119817. | + | 51258.7i | −0.919399 | + | 0.393326i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −182063. | + | 105114.i | −1.38168 | + | 0.797713i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27134.2 | − | 46997.8i | 0.203672 | − | 0.352770i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 103142. | − | 178648.i | 0.765781 | − | 1.32637i | −0.174052 | − | 0.984736i | \(-0.555686\pi\) |
0.939833 | − | 0.341634i | \(-0.110980\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 410957.i | 3.01817i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 104252. | + | 60190.0i | 0.757421 | + | 0.437297i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 63012.8i | − | 0.452909i | −0.974022 | − | 0.226454i | \(-0.927287\pi\) | ||
0.974022 | − | 0.226454i | \(-0.0727134\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −93829.4 | + | 54172.4i | −0.667231 | + | 0.385226i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15647.4 | − | 27102.1i | −0.110093 | − | 0.190686i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 74224.9i | 0.516739i | 0.966046 | + | 0.258370i | \(0.0831852\pi\) | ||||
−0.966046 | + | 0.258370i | \(0.916815\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −86548.9 | −0.596227 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −191250. | + | 110418.i | −1.30378 | + | 0.752738i | −0.981050 | − | 0.193753i | \(-0.937934\pi\) |
−0.322731 | + | 0.946491i | \(0.604601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −293.279 | − | 507.974i | −0.00197861 | − | 0.00342704i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −40819.4 | −0.272549 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −119430. | + | 206858.i | −0.789248 | + | 1.36702i | 0.137181 | + | 0.990546i | \(0.456196\pi\) |
−0.926428 | + | 0.376471i | \(0.877137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −52433.2 | −0.342967 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −132460. | − | 76475.6i | −0.857627 | − | 0.495151i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −22673.2 | − | 13090.4i | −0.145318 | − | 0.0838994i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −121860. | − | 211069.i | −0.773182 | − | 1.33919i | −0.935810 | − | 0.352504i | \(-0.885330\pi\) |
0.162628 | − | 0.986687i | \(-0.448003\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 171850. | + | 193690.i | 1.07945 | + | 1.21664i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 181404. | − | 104733.i | 1.12812 | − | 0.651323i | 0.184662 | − | 0.982802i | \(-0.440881\pi\) |
0.943463 | + | 0.331479i | \(0.107548\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23127.5 | − | 40058.1i | 0.142403 | − | 0.246649i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3158.39 | − | 5470.49i | 0.0192555 | − | 0.0333516i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4674.35i | 0.0282184i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 102139. | + | 58969.8i | 0.610581 | + | 0.352519i | 0.773193 | − | 0.634171i | \(-0.218658\pi\) |
−0.162612 | + | 0.986690i | \(0.551992\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 126468.i | 0.748679i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 152144. | − | 87840.3i | 0.891978 | − | 0.514984i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36669.2 | + | 63512.9i | 0.212914 | + | 0.368779i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 102973.i | − | 0.592176i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −59069.1 | −0.336459 | −0.168230 | − | 0.985748i | \(-0.553805\pi\) | ||||
−0.168230 | + | 0.985748i | \(0.553805\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 45326.1 | − | 26169.0i | 0.255731 | − | 0.147647i | −0.366654 | − | 0.930357i | \(-0.619497\pi\) |
0.622386 | + | 0.782711i | \(0.286164\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 121467. | + | 210387.i | 0.678857 | + | 1.17581i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −140441. | −0.777529 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −51890.4 | + | 89876.8i | −0.284597 | + | 0.492937i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2157.89 | −0.0117251 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 203718. | + | 117616.i | 1.09667 | + | 0.633160i | 0.935343 | − | 0.353742i | \(-0.115091\pi\) |
0.161322 | + | 0.986902i | \(0.448424\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −127748. | − | 73755.1i | −0.681360 | − | 0.393384i | 0.119007 | − | 0.992893i | \(-0.462029\pi\) |
−0.800367 | + | 0.599510i | \(0.795362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17567.5 | − | 30427.8i | −0.0928393 | − | 0.160802i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 74960.5 | + | 24963.9i | 0.392527 | + | 0.130722i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7033.58 | + | 4060.84i | −0.0364962 | + | 0.0210711i | −0.518137 | − | 0.855298i | \(-0.673374\pi\) |
0.481641 | + | 0.876369i | \(0.340041\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5834.98 | − | 10106.5i | 0.0300028 | − | 0.0519664i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 102446. | − | 177441.i | 0.522018 | − | 0.904162i | −0.477654 | − | 0.878548i | \(-0.658513\pi\) |
0.999672 | − | 0.0256140i | \(-0.00815408\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 59059.7i | 0.298244i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −207072. | − | 119553.i | −1.03635 | − | 0.598337i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 114834.i | 0.569611i | 0.958585 | + | 0.284806i | \(0.0919291\pi\) | ||||
−0.958585 | + | 0.284806i | \(0.908071\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5357.26 | + | 3093.01i | −0.0263384 | + | 0.0152065i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12788.1 | + | 22149.7i | 0.0623175 | + | 0.107937i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24782.6i | 0.119708i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −230282. | −1.10262 | −0.551312 | − | 0.834299i | \(-0.685873\pi\) | ||||
−0.551312 | + | 0.834299i | \(0.685873\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −131938. | + | 76174.3i | −0.626244 | + | 0.361562i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −52622.7 | − | 91145.2i | −0.247612 | − | 0.428876i | 0.715251 | − | 0.698868i | \(-0.246312\pi\) |
−0.962863 | + | 0.269992i | \(0.912979\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 103267. | 0.481724 | 0.240862 | − | 0.970559i | \(-0.422570\pi\) | ||||
0.240862 | + | 0.970559i | \(0.422570\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25965.6 | − | 44973.7i | 0.120086 | − | 0.207995i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −203377. | −0.932542 | −0.466271 | − | 0.884642i | \(-0.654403\pi\) | ||||
−0.466271 | + | 0.884642i | \(0.654403\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −219194. | − | 126552.i | −0.996511 | − | 0.575336i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 114677. | + | 66208.8i | 0.516933 | + | 0.298452i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −307.222 | − | 532.124i | −0.00137319 | − | 0.00237843i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 200780. | + | 66865.4i | 0.889885 | + | 0.296356i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 261513. | − | 150984.i | 1.14936 | − | 0.663583i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −221111. | + | 382976.i | −0.963697 | + | 1.66917i | −0.250619 | + | 0.968086i | \(0.580634\pi\) |
−0.713077 | + | 0.701086i | \(0.752699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 98747.6 | − | 171036.i | 0.426812 | − | 0.739260i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 156982.i | − | 0.672909i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31426.0 | − | 18143.8i | −0.133600 | − | 0.0771339i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 212627.i | − | 0.896519i | −0.893903 | − | 0.448260i | \(-0.852044\pi\) | ||
0.893903 | − | 0.448260i | \(-0.147956\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 364141. | − | 210237.i | 1.52283 | − | 0.879208i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 216804. | + | 375515.i | 0.899298 | + | 1.55763i | 0.828393 | + | 0.560147i | \(0.189255\pi\) |
0.0709052 | + | 0.997483i | \(0.477411\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 94100.8i | − | 0.387168i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1471.36 | −0.00600493 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 149566. | − | 86351.8i | 0.605507 | − | 0.349590i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −80809.6 | − | 139966.i | −0.324535 | − | 0.562111i | 0.656883 | − | 0.753992i | \(-0.271875\pi\) |
−0.981418 | + | 0.191881i | \(0.938541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −618846. | −2.46551 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27970.9 | − | 48446.9i | 0.110553 | − | 0.191483i | −0.805440 | − | 0.592677i | \(-0.798071\pi\) |
0.915993 | + | 0.401194i | \(0.131405\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −114190. | −0.447760 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −276288. | − | 159515.i | −1.07484 | − | 0.620562i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 180101. | + | 103981.i | 0.695152 | + | 0.401346i | 0.805539 | − | 0.592542i | \(-0.201876\pi\) |
−0.110387 | + | 0.993889i | \(0.535209\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 217578. | + | 376856.i | 0.833245 | + | 1.44322i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 224891. | − | 46085.0i | 0.854549 | − | 0.175115i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 84602.7 | − | 48845.4i | 0.318985 | − | 0.184166i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1828.41 | + | 3166.91i | −0.00684059 | + | 0.0118482i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 320118. | − | 554461.i | 1.18844 | − | 2.05843i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 207601.i | 0.764810i | 0.923995 | + | 0.382405i | \(0.124904\pi\) | ||||
−0.923995 | + | 0.382405i | \(0.875096\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35996.4 | − | 20782.5i | −0.131600 | − | 0.0759792i | 0.432755 | − | 0.901512i | \(-0.357542\pi\) |
−0.564355 | + | 0.825532i | \(0.690875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 420474.i | − | 1.52553i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 120451. | − | 69542.6i | 0.433701 | − | 0.250397i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 115971. | + | 200868.i | 0.414417 | + | 0.717792i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 440688.i | − | 1.56294i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 261365. | 0.920011 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −83411.1 | + | 48157.4i | −0.291418 | + | 0.168250i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −132875. | − | 230146.i | −0.460780 | − | 0.798094i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 175.665 | 0.000604654 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −51917.0 | + | 89922.8i | −0.177384 | + | 0.307238i | −0.940984 | − | 0.338452i | \(-0.890097\pi\) |
0.763600 | + | 0.645690i | \(0.223430\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 458229. | 1.55411 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −95206.6 | − | 54967.6i | −0.320534 | − | 0.185060i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 142979. | + | 82548.7i | 0.477855 | + | 0.275890i | 0.719522 | − | 0.694469i | \(-0.244361\pi\) |
−0.241667 | + | 0.970359i | \(0.577694\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 130165. | + | 225452.i | 0.431867 | + | 0.748015i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −44802.3 | + | 134530.i | −0.147570 | + | 0.443115i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 181807. | − | 104966.i | 0.594512 | − | 0.343242i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 110865. | − | 192024.i | 0.359923 | − | 0.623404i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30248.0 | + | 52391.2i | −0.0974960 | + | 0.168868i | −0.910648 | − | 0.413184i | \(-0.864417\pi\) |
0.813152 | + | 0.582052i | \(0.197750\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25960.8i | 0.0830796i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5619.30 | − | 3244.30i | −0.0178549 | − | 0.0103085i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 248939.i | 0.785374i | 0.919672 | + | 0.392687i | \(0.128454\pi\) | ||||
−0.919672 | + | 0.392687i | \(0.871546\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28864.2 | + | 16664.8i | −0.0904196 | + | 0.0522038i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25325.8 | + | 43865.6i | 0.0787766 | + | 0.136445i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 87739.1i | 0.270999i | 0.990777 | + | 0.135500i | \(0.0432640\pi\) | ||||
−0.990777 | + | 0.135500i | \(0.956736\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 130764. | 0.401067 | 0.200533 | − | 0.979687i | \(-0.435732\pi\) | ||||
0.200533 | + | 0.979687i | \(0.435732\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −351332. | + | 202842.i | −1.07006 | + | 0.617800i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −64148.5 | − | 111108.i | −0.194022 | − | 0.336056i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −572106. | −1.71840 | −0.859201 | − | 0.511639i | \(-0.829039\pi\) | ||||
−0.859201 | + | 0.511639i | \(0.829039\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −294094. | + | 509386.i | −0.877261 | + | 1.51946i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −588069. | −1.74211 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3936.48 | + | 2272.73i | 0.0115817 | + | 0.00668668i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 53837.4 | + | 31083.0i | 0.157316 | + | 0.0908264i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17337.7 | − | 30029.7i | −0.0503169 | − | 0.0871515i | 0.839770 | − | 0.542942i | \(-0.182690\pi\) |
−0.890087 | + | 0.455791i | \(0.849356\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −205312. | + | 42072.8i | −0.591811 | + | 0.121275i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −278112. | + | 160568.i | −0.796240 | + | 0.459710i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −200472. | + | 347228.i | −0.570092 | + | 0.987429i | 0.426463 | + | 0.904505i | \(0.359759\pi\) |
−0.996556 | + | 0.0829242i | \(0.973574\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −37259.6 | + | 64535.5i | −0.105246 | + | 0.182291i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 62236.6i | 0.174621i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −461443. | − | 266414.i | −1.28607 | − | 0.742512i | −0.308118 | − | 0.951348i | \(-0.599699\pi\) |
−0.977951 | + | 0.208836i | \(0.933032\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 169049.i | 0.468019i | 0.972234 | + | 0.234009i | \(0.0751846\pi\) | ||||
−0.972234 | + | 0.234009i | \(0.924815\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −549839. | + | 317450.i | −1.51217 | + | 0.873052i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 45582.6 | + | 78951.4i | 0.124534 | + | 0.215700i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 527599.i | 1.43195i | 0.698127 | + | 0.715974i | \(0.254017\pi\) | ||||
−0.698127 | + | 0.715974i | \(0.745983\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 281733. | 0.759632 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 133804. | − | 77252.0i | 0.358417 | − | 0.206932i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 144166. | + | 249704.i | 0.383657 | + | 0.664513i | 0.991582 | − | 0.129481i | \(-0.0413312\pi\) |
−0.607925 | + | 0.793995i | \(0.707998\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 293438. | 0.775829 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 215208. | − | 372751.i | 0.565311 | − | 0.979147i | −0.431710 | − | 0.902013i | \(-0.642090\pi\) |
0.997021 | − | 0.0771347i | \(-0.0245772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 490418. | 1.27993 | 0.639963 | − | 0.768405i | \(-0.278950\pi\) | ||||
0.639963 | + | 0.768405i | \(0.278950\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −120529. | − | 69587.4i | −0.312542 | − | 0.180446i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −410128. | − | 236787.i | −1.05668 | − | 0.610074i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −159699. | − | 276606.i | −0.408828 | − | 0.708111i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6488.92 | + | 7313.58i | 0.0165058 | + | 0.0186035i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 514291. | − | 296926.i | 1.29989 | − | 0.750493i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 65005.3 | − | 112593.i | 0.163264 | − | 0.282781i | −0.772774 | − | 0.634682i | \(-0.781131\pi\) |
0.936037 | + | 0.351901i | \(0.114464\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −400043. | + | 692894.i | −0.998387 | + | 1.72926i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37531.9i | 0.0930794i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6427.63 | − | 3710.99i | −0.0158406 | − | 0.00914558i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 433220.i | − | 1.06098i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 395283. | − | 228217.i | 0.962037 | − | 0.555432i | 0.0652376 | − | 0.997870i | \(-0.479219\pi\) |
0.896799 | + | 0.442437i | \(0.145886\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 194677. | + | 337190.i | 0.470860 | + | 0.815554i | 0.999445 | − | 0.0333268i | \(-0.0106102\pi\) |
−0.528584 | + | 0.848881i | \(0.677277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29146.5i | 0.0700595i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −656698. | −1.56876 | −0.784381 | − | 0.620279i | \(-0.787019\pi\) | ||||
−0.784381 | + | 0.620279i | \(0.787019\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5744.83 | − | 3316.78i | 0.0136392 | − | 0.00787458i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 208207. | + | 360625.i | 0.491285 | + | 0.850930i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 280986. | 0.658959 | 0.329480 | − | 0.944163i | \(-0.393127\pi\) | ||||
0.329480 | + | 0.944163i | \(0.393127\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33163.6 | + | 57441.1i | −0.0773000 | + | 0.133888i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.09157e6 | 2.52884 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −331713. | − | 191514.i | −0.763820 | − | 0.440992i | 0.0668456 | − | 0.997763i | \(-0.478707\pi\) |
−0.830666 | + | 0.556772i | \(0.812040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −314250. | − | 181433.i | −0.719239 | − | 0.415253i | 0.0952338 | − | 0.995455i | \(-0.469640\pi\) |
−0.814472 | + | 0.580202i | \(0.802973\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 137075. | + | 237420.i | 0.311839 | + | 0.540120i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 83993.6 | − | 74522.8i | 0.189934 | − | 0.168518i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 74446.8 | − | 42981.9i | 0.167338 | − | 0.0966126i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −196284. | + | 339974.i | −0.438564 | + | 0.759616i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1959.34 | + | 3393.68i | −0.00435176 | + | 0.00753747i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 191020.i | − | 0.421744i | −0.977514 | − | 0.210872i | \(-0.932370\pi\) | ||
0.977514 | − | 0.210872i | \(-0.0676304\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −322834. | − | 186389.i | −0.708553 | − | 0.409083i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 336677.i | − | 0.734575i | −0.930107 | − | 0.367287i | \(-0.880287\pi\) | ||
0.930107 | − | 0.367287i | \(-0.119713\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 251992. | − | 145488.i | 0.546571 | − | 0.315563i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −302322. | − | 523637.i | −0.651892 | − | 1.12911i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 313252.i | 0.671509i | 0.941950 | + | 0.335755i | \(0.108991\pi\) | ||||
−0.941950 | + | 0.335755i | \(0.891009\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 54842.7 | 0.116879 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 151288. | − | 87346.4i | 0.320547 | − | 0.185068i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −96024.8 | − | 166320.i | −0.202276 | − | 0.350353i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 803808. | 1.68344 | 0.841718 | − | 0.539918i | \(-0.181545\pi\) | ||||
0.841718 | + | 0.539918i | \(0.181545\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5899.10 | − | 10217.5i | 0.0122834 | − | 0.0212755i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −44654.2 | −0.0924470 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 680612. | + | 392952.i | 1.40099 | + | 0.808860i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 316152. | + | 182530.i | 0.647055 | + | 0.373577i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −247655. | − | 428950.i | −0.503977 | − | 0.872913i | −0.999989 | − | 0.00459793i | \(-0.998536\pi\) |
0.496013 | − | 0.868315i | \(-0.334797\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −876619. | + | 179638.i | −1.77378 | + | 0.363486i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 150224. | − | 86731.9i | 0.302246 | − | 0.174502i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 457821. | − | 792969.i | 0.915918 | − | 1.58642i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7754.66 | + | 13431.5i | −0.0154266 | + | 0.0267197i | −0.873636 | − | 0.486581i | \(-0.838244\pi\) |
0.858209 | + | 0.513300i | \(0.171577\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 526608.i | − | 1.04171i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 110036. | + | 63529.1i | 0.216448 | + | 0.124967i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 935.770i | 0.00183045i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.07621e6 | + | 621353.i | −2.09344 | + | 1.20865i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −377951. | − | 654630.i | −0.731102 | − | 1.26631i | −0.956413 | − | 0.292018i | \(-0.905673\pi\) |
0.225311 | − | 0.974287i | \(-0.427660\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 783342.i | 1.50689i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 752937. | 1.44040 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 199404. | − | 115126.i | 0.379366 | − | 0.219027i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −326273. | − | 565122.i | −0.617323 | − | 1.06923i | −0.989972 | − | 0.141262i | \(-0.954884\pi\) |
0.372649 | − | 0.927972i | \(-0.378449\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 866844. | 1.63112 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39031.0 | + | 67603.7i | −0.0730424 | + | 0.126513i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −811947. | −1.51119 | −0.755597 | − | 0.655037i | \(-0.772653\pi\) | ||||
−0.755597 | + | 0.655037i | \(0.772653\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7216.38 | − | 4166.38i | −0.0133581 | − | 0.00771230i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8276.58 | − | 4778.49i | −0.0152376 | − | 0.00879742i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −389853. | − | 675246.i | −0.713859 | − | 1.23644i | −0.963398 | − | 0.268075i | \(-0.913612\pi\) |
0.249539 | − | 0.968365i | \(-0.419721\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −82929.2 | − | 404688.i | −0.151033 | − | 0.737027i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −497760. | + | 287382.i | −0.901660 | + | 0.520574i | −0.877738 | − | 0.479140i | \(-0.840948\pi\) |
−0.0239215 | + | 0.999714i | \(0.507615\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −51844.2 | + | 89796.8i | −0.0934088 | + | 0.161789i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −737575. | + | 1.27752e6i | −1.32180 | + | 2.28942i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 772308.i | − | 1.37666i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 168301. | + | 97168.5i | 0.298405 | + | 0.172284i | 0.641726 | − | 0.766934i | \(-0.278219\pi\) |
−0.343321 | + | 0.939218i | \(0.611552\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 564135.i | 0.994931i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9605.21 | − | 5545.57i | 0.0168505 | − | 0.00972864i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −144106. | − | 249600.i | −0.251473 | − | 0.435564i | 0.712458 | − | 0.701714i | \(-0.247582\pi\) |
−0.963932 | + | 0.266150i | \(0.914248\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5927.53i | − | 0.0102894i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 660814. | 1.14106 | 0.570532 | − | 0.821275i | \(-0.306737\pi\) | ||||
0.570532 | + | 0.821275i | \(0.306737\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 763422. | − | 440762.i | 1.31134 | − | 0.757103i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 93464.2 | + | 161885.i | 0.159706 | + | 0.276620i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −280274. | −0.476422 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 367592. | − | 636688.i | 0.621603 | − | 1.07665i | −0.367584 | − | 0.929990i | \(-0.619815\pi\) |
0.989187 | − | 0.146658i | \(-0.0468516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.07746e6 | 1.81255 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 503015. | + | 290416.i | 0.841824 | + | 0.486028i | 0.857884 | − | 0.513843i | \(-0.171779\pi\) |
−0.0160595 | + | 0.999871i | \(0.505112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 294729. | + | 170162.i | 0.490703 | + | 0.283308i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 888981. | + | 1.53976e6i | 1.47248 | + | 2.55042i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −785942. | − | 885824.i | −1.29514 | − | 1.45973i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5647.49 | − | 3260.58i | 0.00925877 | − | 0.00534555i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 124887. | − | 216311.i | 0.203702 | − | 0.352822i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28711.5 | − | 49729.7i | 0.0465925 | − | 0.0807006i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 209530.i | − | 0.338296i | −0.985591 | − | 0.169148i | \(-0.945898\pi\) | ||
0.985591 | − | 0.169148i | \(-0.0541015\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −367119. | − | 211956.i | −0.589730 | − | 0.340481i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 267255.i | − | 0.427143i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 143386. | − | 82783.8i | 0.228013 | − | 0.131643i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −107808. | − | 186729.i | −0.170576 | − | 0.295446i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 384377.i | 0.605118i | 0.953131 | + | 0.302559i | \(0.0978410\pi\) | ||||
−0.953131 | + | 0.302559i | \(0.902159\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 464581. | 0.727726 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.02879e6 | + | 593972.i | −1.60347 | + | 0.925765i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8215.57 | + | 14229.8i | 0.0127411 | + | 0.0220682i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −68075.3 | −0.105050 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 729511. | − | 1.26355e6i | 1.12017 | − | 1.94019i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −133009. | −0.203228 | −0.101614 | − | 0.994824i | \(-0.532401\pi\) | ||||
−0.101614 | + | 0.994824i | \(0.532401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −71351.1 | − | 41194.6i | −0.108482 | − | 0.0626323i | 0.444777 | − | 0.895641i | \(-0.353283\pi\) |
−0.553259 | + | 0.833009i | \(0.686616\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 296410. | + | 171132.i | 0.448448 | + | 0.258911i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −91169.4 | − | 157910.i | −0.137257 | − | 0.237736i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 87986.9 | − | 78065.8i | 0.131818 | − | 0.116954i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −431700. | + | 249242.i | −0.643597 | + | 0.371581i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −268164. | + | 464473.i | −0.397845 | + | 0.689087i | −0.993460 | − | 0.114183i | \(-0.963575\pi\) |
0.595615 | + | 0.803270i | \(0.296908\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −236126. | + | 408982.i | −0.348613 | + | 0.603816i | −0.986003 | − | 0.166725i | \(-0.946681\pi\) |
0.637390 | + | 0.770541i | \(0.280014\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 15876.8i | − | 0.0233268i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −189650. | − | 109494.i | −0.277294 | − | 0.160096i | 0.354903 | − | 0.934903i | \(-0.384514\pi\) |
−0.632198 | + | 0.774807i | \(0.717847\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.15812e6i | 1.68517i | 0.538561 | + | 0.842586i | \(0.318968\pi\) | ||||
−0.538561 | + | 0.842586i | \(0.681032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.36558e6 | + | 788417.i | −1.97749 | + | 1.14171i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11158.7 | − | 19327.4i | −0.0160813 | − | 0.0278537i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 268362.i | 0.384901i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 369178. | 0.526969 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 576430. | − | 332802.i | 0.818885 | − | 0.472783i | −0.0311469 | − | 0.999515i | \(-0.509916\pi\) |
0.850032 | + | 0.526731i | \(0.176583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −276502. | − | 478915.i | −0.390936 | − | 0.677121i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −870806. | −1.22537 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −69173.6 | + | 119812.i | −0.0968784 | + | 0.167798i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −731016. | −1.01897 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −208569. | − | 120418.i | −0.289358 | − | 0.167061i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 469819. | + | 271250.i | 0.648742 | + | 0.374551i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 441621. | + | 764910.i | 0.606949 | + | 1.05127i | 0.991740 | + | 0.128262i | \(0.0409399\pi\) |
−0.384792 | + | 0.923003i | \(0.625727\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −56545.2 | − | 275936.i | −0.0773506 | − | 0.377464i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −680285. | + | 392763.i | −0.926252 | + | 0.534772i | −0.885624 | − | 0.464403i | \(-0.846269\pi\) |
−0.0406278 | + | 0.999174i | \(0.512936\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −727091. | + | 1.25936e6i | −0.985377 | + | 1.70672i | −0.345128 | + | 0.938556i | \(0.612164\pi\) |
−0.640249 | + | 0.768167i | \(0.721169\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.17648e6 | + | 2.03772e6i | −1.58700 | + | 2.74877i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 899567.i | − | 1.20785i | −0.797042 | − | 0.603924i | \(-0.793603\pi\) | ||
0.797042 | − | 0.603924i | \(-0.206397\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −240442. | − | 138819.i | −0.321350 | − | 0.185531i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 375211.i | − | 0.499158i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6864.90 | − | 3963.45i | 0.00909064 | − | 0.00524848i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 201895. | + | 349693.i | 0.266127 | + | 0.460946i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 729900.i | − | 0.957712i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −376743. | −0.492072 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 279525. | − | 161384.i | 0.363431 | − | 0.209827i | −0.307154 | − | 0.951660i | \(-0.599377\pi\) |
0.670585 | + | 0.741833i | \(0.266043\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 915533. | + | 1.58575e6i | 1.18494 | + | 2.05238i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 547085. | 0.704860 | 0.352430 | − | 0.935838i | \(-0.385355\pi\) | ||||
0.352430 | + | 0.935838i | \(0.385355\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 524253. | − | 908034.i | 0.672388 | − | 1.16461i | −0.304837 | − | 0.952404i | \(-0.598602\pi\) |
0.977225 | − | 0.212205i | \(-0.0680646\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −314667. | −0.401758 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 318039. | + | 183620.i | 0.404234 | + | 0.233385i | 0.688309 | − | 0.725417i | \(-0.258353\pi\) |
−0.284075 | + | 0.958802i | \(0.591687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −260633. | − | 150476.i | −0.329781 | − | 0.190399i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 956.283 | + | 1656.33i | 0.00120457 | + | 0.00208637i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −664183. | − | 221191.i | −0.832885 | − | 0.277374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −99802.7 | + | 57621.1i | −0.124594 | + | 0.0719342i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −125222. | + | 216890.i | −0.155630 | + | 0.269560i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −114015. | + | 197479.i | −0.141072 | + | 0.244344i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 577477.i | − | 0.711353i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −202402. | − | 116857.i | −0.248221 | − | 0.143311i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 198711.i | − | 0.242619i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 132002. | − | 76211.4i | 0.160460 | − | 0.0926415i | −0.417620 | − | 0.908622i | \(-0.637136\pi\) |
0.578080 | + | 0.815980i | \(0.303802\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.14843e6 | − | 1.98913e6i | −1.38987 | − | 2.40733i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 826053.i | 0.995339i | 0.867367 | + | 0.497669i | \(0.165811\pi\) | ||||
−0.867367 | + | 0.497669i | \(0.834189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22205.0 | −0.0266385 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 160981. | − | 92942.5i | 0.192279 | − | 0.111013i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −265925. | − | 460596.i | −0.316243 | − | 0.547749i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −139504. | −0.165180 | −0.0825898 | − | 0.996584i | \(-0.526319\pi\) | ||||
−0.0825898 | + | 0.996584i | \(0.526319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 786648. | − | 1.36251e6i | 0.927387 | − | 1.60628i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −275524. | −0.323412 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.25840e6 | + | 726539.i | 1.47074 | + | 0.849132i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.70172e6 | + | 982491.i | 1.98029 | + | 1.14332i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 193588. | + | 335304.i | 0.224309 | + | 0.388515i | 0.956112 | − | 0.293002i | \(-0.0946541\pi\) |
−0.731803 | + | 0.681516i | \(0.761321\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6750.91 | + | 32943.9i | 0.00778867 | + | 0.0380080i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.86841e6 | − | 1.07873e6i | 2.14639 | − | 1.23922i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1406.89 | + | 2436.81i | −0.00160930 | + | 0.00278739i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31843.4 | − | 55154.4i | 0.0362694 | − | 0.0628205i | −0.847321 | − | 0.531081i | \(-0.821786\pi\) |
0.883590 | + | 0.468261i | \(0.155119\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 574846.i | − | 0.651959i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −783860. | − | 452562.i | −0.885237 | − | 0.511092i | −0.0128552 | − | 0.999917i | \(-0.504092\pi\) |
−0.872381 | + | 0.488826i | \(0.837425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 717945.i | 0.807361i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −171298. | + | 98899.1i | −0.191818 | + | 0.110746i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 86501.2 | + | 149824.i | 0.0964544 | + | 0.167064i | 0.910215 | − | 0.414137i | \(-0.135916\pi\) |
−0.813760 | + | 0.581201i | \(0.802583\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 694230.i | − | 0.770851i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.37564e6 | 2.62675 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 796366. | − | 459782.i | 0.876853 | − | 0.506251i | 0.00723358 | − | 0.999974i | \(-0.497697\pi\) |
0.869620 | + | 0.493722i | \(0.164364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 87962.4 | + | 152355.i | 0.0964473 | + | 0.167052i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10638.0 | 0.0116155 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −219880. | + | 380844.i | −0.239083 | + | 0.414104i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 586484. | 0.635052 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.67776e6 | − | 968653.i | −1.80916 | − | 1.04452i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 220895. | + | 127534.i | 0.237209 | + | 0.136953i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51509.8 | − | 89217.7i | −0.0550855 | − | 0.0954109i | 0.837168 | − | 0.546946i | \(-0.184210\pi\) |
−0.892253 | + | 0.451535i | \(0.850876\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 392478. | − | 1.17851e6i | 0.417992 | − | 1.25513i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −157988. | + | 91214.6i | −0.167566 | + | 0.0967445i | −0.581438 | − | 0.813591i | \(-0.697510\pi\) |
0.413871 | + | 0.910335i | \(0.364176\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 179032. | − | 310092.i | 0.189105 | − | 0.327540i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −335404. | + | 580936.i | −0.352824 | + | 0.611110i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 436847.i | 0.457657i | 0.973467 | + | 0.228828i | \(0.0734895\pi\) | ||||
−0.973467 | + | 0.228828i | \(0.926511\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15486.1 | − | 8940.91i | −0.0161576 | − | 0.00932859i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2.21127e6i | − | 2.29775i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 577269. | − | 333286.i | 0.597408 | − | 0.344914i | −0.170613 | − | 0.985338i | \(-0.554575\pi\) |
0.768021 | + | 0.640424i | \(0.221241\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 69630.3 | + | 120603.i | 0.0717671 | + | 0.124304i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.39093e6i | 1.42781i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −71311.8 | −0.0729070 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −706100. | + | 407667.i | −0.718984 | + | 0.415105i | −0.814378 | − | 0.580334i | \(-0.802922\pi\) |
0.0953949 | + | 0.995440i | \(0.469589\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.35452e6 | − | 2.34610e6i | −1.37368 | − | 2.37929i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26988.9 | 0.0272608 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −720639. | + | 1.24818e6i | −0.724983 | + | 1.25571i | 0.233999 | + | 0.972237i | \(0.424819\pi\) |
−0.958981 | + | 0.283470i | \(0.908514\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.57628e6 | 1.57944 |
(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 | 76.5.h.a.69.6 | yes | 12 | |
3.2 | odd | 2 | 684.5.y.c.145.4 | 12 | |||
4.3 | odd | 2 | 304.5.r.b.145.1 | 12 | |||
19.8 | odd | 6 | inner | 76.5.h.a.65.6 | ✓ | 12 | |
57.8 | even | 6 | 684.5.y.c.217.4 | 12 | |||
76.27 | even | 6 | 304.5.r.b.65.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.h.a.65.6 | ✓ | 12 | 19.8 | odd | 6 | inner | |
76.5.h.a.69.6 | yes | 12 | 1.1 | even | 1 | trivial | |
304.5.r.b.65.1 | 12 | 76.27 | even | 6 | |||
304.5.r.b.145.1 | 12 | 4.3 | odd | 2 | |||
684.5.y.c.145.4 | 12 | 3.2 | odd | 2 | |||
684.5.y.c.217.4 | 12 | 57.8 | even | 6 |