Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 116.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.116 |
Dual form | 245.4.e.h.226.1 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70711 | − | 4.68885i | −0.957107 | − | 1.65776i | −0.729472 | − | 0.684011i | \(-0.760234\pi\) |
−0.227635 | − | 0.973746i | \(-0.573099\pi\) | |||||||
\(3\) | 2.32843 | − | 4.03295i | 0.448106 | − | 0.776142i | −0.550157 | − | 0.835061i | \(-0.685432\pi\) |
0.998263 | + | 0.0589190i | \(0.0187654\pi\) | |||||||
\(4\) | −10.6569 | + | 18.4582i | −1.33211 | + | 2.30728i | ||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | −25.2132 | −1.71554 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 72.0833 | 3.18566 | ||||||||
\(9\) | 2.65685 | + | 4.60181i | 0.0984020 | + | 0.170437i | ||||
\(10\) | 13.5355 | − | 23.4442i | 0.428031 | − | 0.741372i | ||||
\(11\) | 26.1274 | − | 45.2540i | 0.716156 | − | 1.24042i | −0.246356 | − | 0.969179i | \(-0.579233\pi\) |
0.962512 | − | 0.271239i | \(-0.0874333\pi\) | |||||||
\(12\) | 49.6274 | + | 85.9572i | 1.19385 | + | 2.06781i | ||||
\(13\) | 30.6569 | 0.654052 | 0.327026 | − | 0.945015i | \(-0.393953\pi\) | ||||
0.327026 | + | 0.945015i | \(0.393953\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 23.2843 | 0.400798 | ||||||||
\(16\) | −109.882 | − | 190.322i | −1.71691 | − | 2.97378i | ||||
\(17\) | −18.6127 | + | 32.2381i | −0.265544 | + | 0.459935i | −0.967706 | − | 0.252082i | \(-0.918885\pi\) |
0.702162 | + | 0.712017i | \(0.252218\pi\) | |||||||
\(18\) | 14.3848 | − | 24.9152i | 0.188362 | − | 0.326253i | ||||
\(19\) | −40.1127 | − | 69.4772i | −0.484341 | − | 0.838904i | 0.515497 | − | 0.856891i | \(-0.327607\pi\) |
−0.999838 | + | 0.0179877i | \(0.994274\pi\) | |||||||
\(20\) | −106.569 | −1.19147 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −282.919 | −2.74175 | ||||||||
\(23\) | −12.9167 | − | 22.3724i | −0.117101 | − | 0.202825i | 0.801517 | − | 0.597973i | \(-0.204027\pi\) |
−0.918618 | + | 0.395147i | \(0.870694\pi\) | |||||||
\(24\) | 167.841 | − | 290.708i | 1.42751 | − | 2.47253i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | −82.9914 | − | 143.745i | −0.625998 | − | 1.08426i | ||||
\(27\) | 150.480 | 1.07259 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20.9411 | 0.134092 | 0.0670460 | − | 0.997750i | \(-0.478643\pi\) | ||||
0.0670460 | + | 0.997750i | \(0.478643\pi\) | |||||||
\(30\) | −63.0330 | − | 109.176i | −0.383607 | − | 0.664426i | ||||
\(31\) | 157.279 | − | 272.416i | 0.911232 | − | 1.57830i | 0.0989050 | − | 0.995097i | \(-0.468466\pi\) |
0.812327 | − | 0.583203i | \(-0.198201\pi\) | |||||||
\(32\) | −306.593 | + | 531.035i | −1.69370 | + | 2.93358i | ||||
\(33\) | −121.672 | − | 210.741i | −0.641827 | − | 1.11168i | ||||
\(34\) | 201.546 | 1.01661 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −113.255 | −0.524328 | ||||||||
\(37\) | −98.5736 | − | 170.734i | −0.437984 | − | 0.758610i | 0.559550 | − | 0.828797i | \(-0.310974\pi\) |
−0.997534 | + | 0.0701864i | \(0.977641\pi\) | |||||||
\(38\) | −217.179 | + | 376.165i | −0.927133 | + | 1.60584i | ||||
\(39\) | 71.3823 | − | 123.638i | 0.293085 | − | 0.507638i | ||||
\(40\) | 180.208 | + | 312.130i | 0.712335 | + | 1.23380i | ||||
\(41\) | 11.3625 | 0.0432810 | 0.0216405 | − | 0.999766i | \(-0.493111\pi\) | ||||
0.0216405 | + | 0.999766i | \(0.493111\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −33.8335 | −0.119990 | −0.0599948 | − | 0.998199i | \(-0.519108\pi\) | ||||
−0.0599948 | + | 0.998199i | \(0.519108\pi\) | |||||||
\(44\) | 556.872 | + | 964.531i | 1.90799 | + | 3.30474i | ||||
\(45\) | −13.2843 | + | 23.0090i | −0.0440067 | + | 0.0762219i | ||||
\(46\) | −69.9340 | + | 121.129i | −0.224157 | + | 0.388251i | ||||
\(47\) | 180.838 | + | 313.221i | 0.561233 | + | 0.972084i | 0.997389 | + | 0.0722130i | \(0.0230061\pi\) |
−0.436156 | + | 0.899871i | \(0.643661\pi\) | |||||||
\(48\) | −1023.41 | −3.07743 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 135.355 | 0.382843 | ||||||||
\(51\) | 86.6766 | + | 150.128i | 0.237983 | + | 0.412199i | ||||
\(52\) | −326.706 | + | 565.871i | −0.871268 | + | 1.50908i | ||||
\(53\) | −76.5097 | + | 132.519i | −0.198291 | + | 0.343450i | −0.947974 | − | 0.318347i | \(-0.896872\pi\) |
0.749684 | + | 0.661796i | \(0.230206\pi\) | |||||||
\(54\) | −407.366 | − | 705.579i | −1.02658 | − | 1.77809i | ||||
\(55\) | 261.274 | 0.640549 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −373.598 | −0.868145 | ||||||||
\(58\) | −56.6899 | − | 98.1897i | −0.128340 | − | 0.222292i | ||||
\(59\) | 308.000 | − | 533.472i | 0.679630 | − | 1.17715i | −0.295462 | − | 0.955354i | \(-0.595474\pi\) |
0.975092 | − | 0.221800i | \(-0.0711931\pi\) | |||||||
\(60\) | −248.137 | + | 429.786i | −0.533906 | + | 0.924752i | ||||
\(61\) | −7.63247 | − | 13.2198i | −0.0160203 | − | 0.0277479i | 0.857904 | − | 0.513810i | \(-0.171766\pi\) |
−0.873924 | + | 0.486062i | \(0.838433\pi\) | |||||||
\(62\) | −1703.09 | −3.48858 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1561.80 | 3.05040 | ||||||||
\(65\) | 76.6421 | + | 132.748i | 0.146251 | + | 0.253313i | ||||
\(66\) | −658.756 | + | 1141.00i | −1.22859 | + | 2.12799i | ||||
\(67\) | 83.2548 | − | 144.202i | 0.151809 | − | 0.262941i | −0.780084 | − | 0.625675i | \(-0.784824\pi\) |
0.931893 | + | 0.362735i | \(0.118157\pi\) | |||||||
\(68\) | −396.706 | − | 687.114i | −0.707465 | − | 1.22537i | ||||
\(69\) | −120.303 | −0.209895 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −952.000 | −1.59129 | −0.795645 | − | 0.605763i | \(-0.792868\pi\) | ||||
−0.795645 | + | 0.605763i | \(0.792868\pi\) | |||||||
\(72\) | 191.515 | + | 331.713i | 0.313475 | + | 0.542955i | ||||
\(73\) | 74.2447 | − | 128.596i | 0.119037 | − | 0.206178i | −0.800349 | − | 0.599534i | \(-0.795353\pi\) |
0.919386 | + | 0.393356i | \(0.128686\pi\) | |||||||
\(74\) | −533.698 | + | 924.393i | −0.838394 | + | 1.45214i | ||||
\(75\) | 58.2107 | + | 100.824i | 0.0896212 | + | 0.155228i | ||||
\(76\) | 1709.90 | 2.58078 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −772.958 | −1.12205 | ||||||||
\(79\) | −428.862 | − | 742.812i | −0.610770 | − | 1.05788i | −0.991111 | − | 0.133038i | \(-0.957527\pi\) |
0.380341 | − | 0.924846i | \(-0.375807\pi\) | |||||||
\(80\) | 549.411 | − | 951.608i | 0.767826 | − | 1.32991i | ||||
\(81\) | 278.647 | − | 482.631i | 0.382232 | − | 0.662045i | ||||
\(82\) | −30.7595 | − | 53.2769i | −0.0414246 | − | 0.0717494i | ||||
\(83\) | 660.528 | 0.873523 | 0.436761 | − | 0.899577i | \(-0.356125\pi\) | ||||
0.436761 | + | 0.899577i | \(0.356125\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −186.127 | −0.237509 | ||||||||
\(86\) | 91.5908 | + | 158.640i | 0.114843 | + | 0.198914i | ||||
\(87\) | 48.7599 | − | 84.4546i | 0.0600875 | − | 0.104075i | ||||
\(88\) | 1883.35 | − | 3262.06i | 2.28143 | − | 3.95155i | ||||
\(89\) | 22.8873 | + | 39.6420i | 0.0272590 | + | 0.0472139i | 0.879333 | − | 0.476207i | \(-0.157989\pi\) |
−0.852074 | + | 0.523421i | \(0.824655\pi\) | |||||||
\(90\) | 143.848 | 0.168477 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 550.607 | 0.623965 | ||||||||
\(93\) | −732.426 | − | 1268.60i | −0.816657 | − | 1.41449i | ||||
\(94\) | 979.096 | − | 1695.84i | 1.07432 | − | 1.86078i | ||||
\(95\) | 200.563 | − | 347.386i | 0.216604 | − | 0.375169i | ||||
\(96\) | 1427.76 | + | 2472.95i | 1.51792 | + | 2.62911i | ||||
\(97\) | 1682.13 | 1.76076 | 0.880382 | − | 0.474265i | \(-0.157286\pi\) | ||||
0.880382 | + | 0.474265i | \(0.157286\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 277.667 | 0.281885 | ||||||||
\(100\) | −266.421 | − | 461.455i | −0.266421 | − | 0.461455i | ||||
\(101\) | 217.083 | − | 375.999i | 0.213867 | − | 0.370429i | −0.739054 | − | 0.673646i | \(-0.764727\pi\) |
0.952922 | + | 0.303217i | \(0.0980607\pi\) | |||||||
\(102\) | 469.286 | − | 812.827i | 0.455551 | − | 0.789038i | ||||
\(103\) | −172.788 | − | 299.278i | −0.165295 | − | 0.286299i | 0.771465 | − | 0.636272i | \(-0.219524\pi\) |
−0.936760 | + | 0.349973i | \(0.886191\pi\) | |||||||
\(104\) | 2209.85 | 2.08359 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 828.479 | 0.759142 | ||||||||
\(107\) | −108.559 | − | 188.030i | −0.0980825 | − | 0.169884i | 0.812808 | − | 0.582531i | \(-0.197938\pi\) |
−0.910891 | + | 0.412647i | \(0.864604\pi\) | |||||||
\(108\) | −1603.65 | + | 2777.60i | −1.42880 | + | 2.47476i | ||||
\(109\) | −867.205 | + | 1502.04i | −0.762047 | + | 1.31990i | 0.179746 | + | 0.983713i | \(0.442472\pi\) |
−0.941794 | + | 0.336192i | \(0.890861\pi\) | |||||||
\(110\) | −707.297 | − | 1225.07i | −0.613074 | − | 1.06188i | ||||
\(111\) | −918.086 | −0.785053 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1854.20 | −1.54362 | −0.771809 | − | 0.635855i | \(-0.780648\pi\) | ||||
−0.771809 | + | 0.635855i | \(0.780648\pi\) | |||||||
\(114\) | 1011.37 | + | 1751.74i | 0.830907 | + | 1.43917i | ||||
\(115\) | 64.5837 | − | 111.862i | 0.0523692 | − | 0.0907062i | ||||
\(116\) | −223.167 | + | 386.536i | −0.178625 | + | 0.309387i | ||||
\(117\) | 81.4508 | + | 141.077i | 0.0643601 | + | 0.111475i | ||||
\(118\) | −3335.16 | −2.60191 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1678.41 | 1.27681 | ||||||||
\(121\) | −699.784 | − | 1212.06i | −0.525758 | − | 0.910639i | ||||
\(122\) | −41.3238 | + | 71.5749i | −0.0306662 | + | 0.0531155i | ||||
\(123\) | 26.4567 | − | 45.8244i | 0.0193945 | − | 0.0335922i | ||||
\(124\) | 3352.20 | + | 5806.19i | 2.42772 | + | 4.20493i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1394.51 | 0.974352 | 0.487176 | − | 0.873304i | \(-0.338027\pi\) | ||||
0.487176 | + | 0.873304i | \(0.338027\pi\) | |||||||
\(128\) | −1775.22 | − | 3074.78i | −1.22585 | − | 2.12324i | ||||
\(129\) | −78.7788 | + | 136.449i | −0.0537681 | + | 0.0931291i | ||||
\(130\) | 414.957 | − | 718.726i | 0.279955 | − | 0.484896i | ||||
\(131\) | −881.209 | − | 1526.30i | −0.587722 | − | 1.01796i | −0.994530 | − | 0.104451i | \(-0.966691\pi\) |
0.406808 | − | 0.913514i | \(-0.366642\pi\) | |||||||
\(132\) | 5186.54 | 3.41993 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −901.519 | −0.581189 | ||||||||
\(135\) | 376.201 | + | 651.599i | 0.239838 | + | 0.415412i | ||||
\(136\) | −1341.66 | + | 2323.83i | −0.845932 | + | 1.46520i | ||||
\(137\) | 461.474 | − | 799.297i | 0.287784 | − | 0.498457i | −0.685496 | − | 0.728076i | \(-0.740415\pi\) |
0.973281 | + | 0.229619i | \(0.0737481\pi\) | |||||||
\(138\) | 325.672 | + | 564.081i | 0.200892 | + | 0.347955i | ||||
\(139\) | −196.039 | −0.119624 | −0.0598122 | − | 0.998210i | \(-0.519050\pi\) | ||||
−0.0598122 | + | 0.998210i | \(0.519050\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1684.27 | 1.00597 | ||||||||
\(142\) | 2577.17 | + | 4463.78i | 1.52303 | + | 2.63797i | ||||
\(143\) | 800.984 | − | 1387.35i | 0.468403 | − | 0.811298i | ||||
\(144\) | 583.882 | − | 1011.31i | 0.337895 | − | 0.585251i | ||||
\(145\) | 52.3528 | + | 90.6777i | 0.0299839 | + | 0.0519336i | ||||
\(146\) | −803.954 | −0.455724 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4201.94 | 2.33376 | ||||||||
\(149\) | −390.186 | − | 675.822i | −0.214532 | − | 0.371580i | 0.738596 | − | 0.674149i | \(-0.235489\pi\) |
−0.953128 | + | 0.302568i | \(0.902156\pi\) | |||||||
\(150\) | 315.165 | − | 545.882i | 0.171554 | − | 0.297140i | ||||
\(151\) | 1159.71 | − | 2008.68i | 0.625008 | − | 1.08255i | −0.363531 | − | 0.931582i | \(-0.618429\pi\) |
0.988539 | − | 0.150964i | \(-0.0482377\pi\) | |||||||
\(152\) | −2891.45 | − | 5008.15i | −1.54295 | − | 2.67246i | ||||
\(153\) | −197.805 | −0.104520 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1572.79 | 0.815030 | ||||||||
\(156\) | 1521.42 | + | 2635.18i | 0.780841 | + | 1.35246i | ||||
\(157\) | −511.451 | + | 885.859i | −0.259989 | + | 0.450314i | −0.966239 | − | 0.257649i | \(-0.917052\pi\) |
0.706250 | + | 0.707963i | \(0.250385\pi\) | |||||||
\(158\) | −2321.95 | + | 4021.74i | −1.16914 | + | 2.02502i | ||||
\(159\) | 356.294 | + | 617.120i | 0.177711 | + | 0.307804i | ||||
\(160\) | −3065.93 | −1.51489 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3017.31 | −1.46335 | ||||||||
\(163\) | 675.313 | + | 1169.68i | 0.324507 | + | 0.562062i | 0.981412 | − | 0.191911i | \(-0.0614684\pi\) |
−0.656906 | + | 0.753973i | \(0.728135\pi\) | |||||||
\(164\) | −121.088 | + | 209.731i | −0.0576549 | + | 0.0998613i | ||||
\(165\) | 608.358 | − | 1053.71i | 0.287034 | − | 0.497157i | ||||
\(166\) | −1788.12 | − | 3097.12i | −0.836054 | − | 1.44809i | ||||
\(167\) | −1230.58 | −0.570209 | −0.285105 | − | 0.958496i | \(-0.592028\pi\) | ||||
−0.285105 | + | 0.958496i | \(0.592028\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1257.16 | −0.572215 | ||||||||
\(170\) | 503.866 | + | 872.721i | 0.227322 | + | 0.393733i | ||||
\(171\) | 213.147 | − | 369.182i | 0.0953203 | − | 0.165100i | ||||
\(172\) | 360.558 | − | 624.506i | 0.159839 | − | 0.276849i | ||||
\(173\) | 1243.83 | + | 2154.37i | 0.546626 | + | 0.946785i | 0.998503 | + | 0.0547040i | \(0.0174215\pi\) |
−0.451876 | + | 0.892081i | \(0.649245\pi\) | |||||||
\(174\) | −527.993 | −0.230040 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11483.8 | −4.91830 | ||||||||
\(177\) | −1434.31 | − | 2484.30i | −0.609093 | − | 1.05498i | ||||
\(178\) | 123.917 | − | 214.630i | 0.0521795 | − | 0.0903776i | ||||
\(179\) | −810.589 | + | 1403.98i | −0.338471 | + | 0.586248i | −0.984145 | − | 0.177364i | \(-0.943243\pi\) |
0.645675 | + | 0.763613i | \(0.276576\pi\) | |||||||
\(180\) | −283.137 | − | 490.408i | −0.117243 | − | 0.203071i | ||||
\(181\) | 2593.69 | 1.06512 | 0.532561 | − | 0.846392i | \(-0.321230\pi\) | ||||
0.532561 | + | 0.846392i | \(0.321230\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −71.0866 | −0.0287151 | ||||||||
\(184\) | −931.081 | − | 1612.68i | −0.373044 | − | 0.646132i | ||||
\(185\) | 492.868 | − | 853.672i | 0.195872 | − | 0.339261i | ||||
\(186\) | −3965.51 | + | 6868.47i | −1.56326 | + | 2.70764i | ||||
\(187\) | 972.603 | + | 1684.60i | 0.380341 | + | 0.658770i | ||||
\(188\) | −7708.66 | −2.99049 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2171.79 | −0.829253 | ||||||||
\(191\) | 911.539 | + | 1578.83i | 0.345323 | + | 0.598116i | 0.985412 | − | 0.170184i | \(-0.0544362\pi\) |
−0.640090 | + | 0.768300i | \(0.721103\pi\) | |||||||
\(192\) | 3636.54 | − | 6298.68i | 1.36690 | − | 2.36754i | ||||
\(193\) | 770.514 | − | 1334.57i | 0.287372 | − | 0.497743i | −0.685810 | − | 0.727781i | \(-0.740552\pi\) |
0.973182 | + | 0.230038i | \(0.0738851\pi\) | |||||||
\(194\) | −4553.70 | − | 7887.24i | −1.68524 | − | 2.91892i | ||||
\(195\) | 713.823 | 0.262143 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 701.243 | 0.253612 | 0.126806 | − | 0.991928i | \(-0.459527\pi\) | ||||
0.126806 | + | 0.991928i | \(0.459527\pi\) | |||||||
\(198\) | −751.674 | − | 1301.94i | −0.269794 | − | 0.467296i | ||||
\(199\) | −1647.48 | + | 2853.52i | −0.586868 | + | 1.01649i | 0.407771 | + | 0.913084i | \(0.366306\pi\) |
−0.994640 | + | 0.103402i | \(0.967027\pi\) | |||||||
\(200\) | −901.041 | + | 1560.65i | −0.318566 | + | 0.551773i | ||||
\(201\) | −387.706 | − | 671.526i | −0.136053 | − | 0.235651i | ||||
\(202\) | −2350.67 | −0.818775 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3694.80 | −1.26808 | ||||||||
\(205\) | 28.4062 | + | 49.2010i | 0.00967793 | + | 0.0167627i | ||||
\(206\) | −935.514 | + | 1620.36i | −0.316409 | + | 0.548037i | ||||
\(207\) | 68.6358 | − | 118.881i | 0.0230460 | − | 0.0399168i | ||||
\(208\) | −3368.64 | − | 5834.66i | −1.12295 | − | 1.94501i | ||||
\(209\) | −4192.16 | −1.38746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4082.35 | 1.33195 | 0.665974 | − | 0.745975i | \(-0.268016\pi\) | ||||
0.665974 | + | 0.745975i | \(0.268016\pi\) | |||||||
\(212\) | −1630.70 | − | 2824.46i | −0.528289 | − | 0.915023i | ||||
\(213\) | −2216.66 | + | 3839.37i | −0.713067 | + | 1.23507i | ||||
\(214\) | −587.763 | + | 1018.04i | −0.187751 | + | 0.325194i | ||||
\(215\) | −84.5837 | − | 146.503i | −0.0268305 | − | 0.0464718i | ||||
\(216\) | 10847.1 | 3.41691 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 9390.46 | 2.91744 | ||||||||
\(219\) | −345.747 | − | 598.851i | −0.106682 | − | 0.184779i | ||||
\(220\) | −2784.36 | + | 4822.65i | −0.853280 | + | 1.47792i | ||||
\(221\) | −570.607 | + | 988.320i | −0.173679 | + | 0.300822i | ||||
\(222\) | 2485.36 | + | 4304.76i | 0.751379 | + | 1.30143i | ||||
\(223\) | 747.161 | 0.224366 | 0.112183 | − | 0.993688i | \(-0.464216\pi\) | ||||
0.112183 | + | 0.993688i | \(0.464216\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −132.843 | −0.0393608 | ||||||||
\(226\) | 5019.53 | + | 8694.08i | 1.47741 | + | 2.55894i | ||||
\(227\) | −832.837 | + | 1442.52i | −0.243513 | + | 0.421776i | −0.961712 | − | 0.274061i | \(-0.911633\pi\) |
0.718200 | + | 0.695837i | \(0.244966\pi\) | |||||||
\(228\) | 3981.38 | − | 6895.95i | 1.15646 | − | 2.00305i | ||||
\(229\) | 3314.18 | + | 5740.32i | 0.956362 | + | 1.65647i | 0.731219 | + | 0.682143i | \(0.238952\pi\) |
0.225143 | + | 0.974326i | \(0.427715\pi\) | |||||||
\(230\) | −699.340 | −0.200492 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1509.50 | 0.427172 | ||||||||
\(233\) | 216.215 | + | 374.496i | 0.0607929 | + | 0.105296i | 0.894820 | − | 0.446427i | \(-0.147304\pi\) |
−0.834027 | + | 0.551723i | \(0.813970\pi\) | |||||||
\(234\) | 440.992 | − | 763.821i | 0.123199 | − | 0.213387i | ||||
\(235\) | −904.190 | + | 1566.10i | −0.250991 | + | 0.434729i | ||||
\(236\) | 6564.62 | + | 11370.3i | 1.81068 | + | 3.13619i | ||||
\(237\) | −3994.30 | −1.09476 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5580.44 | 1.51033 | 0.755165 | − | 0.655535i | \(-0.227557\pi\) | ||||
0.755165 | + | 0.655535i | \(0.227557\pi\) | |||||||
\(240\) | −2558.53 | − | 4431.50i | −0.688135 | − | 1.19188i | ||||
\(241\) | 3148.43 | − | 5453.25i | 0.841529 | − | 1.45757i | −0.0470730 | − | 0.998891i | \(-0.514989\pi\) |
0.888602 | − | 0.458679i | \(-0.151677\pi\) | |||||||
\(242\) | −3788.78 | + | 6562.36i | −1.00641 | + | 1.74316i | ||||
\(243\) | 733.864 | + | 1271.09i | 0.193734 | + | 0.335557i | ||||
\(244\) | 325.352 | 0.0853629 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −286.485 | −0.0742504 | ||||||||
\(247\) | −1229.73 | − | 2129.95i | −0.316785 | − | 0.548687i | ||||
\(248\) | 11337.2 | − | 19636.6i | 2.90287 | − | 5.02793i | ||||
\(249\) | 1537.99 | − | 2663.88i | 0.391431 | − | 0.677978i | ||||
\(250\) | 338.388 | + | 586.106i | 0.0856062 | + | 0.148274i | ||||
\(251\) | 311.921 | 0.0784393 | 0.0392197 | − | 0.999231i | \(-0.487513\pi\) | ||||
0.0392197 | + | 0.999231i | \(0.487513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1349.92 | −0.335451 | ||||||||
\(254\) | −3775.09 | − | 6538.64i | −0.932559 | − | 1.61524i | ||||
\(255\) | −433.383 | + | 750.642i | −0.106429 | + | 0.184341i | ||||
\(256\) | −3364.23 | + | 5827.02i | −0.821346 | + | 1.42261i | ||||
\(257\) | 3930.69 | + | 6808.16i | 0.954046 | + | 1.65246i | 0.736535 | + | 0.676399i | \(0.236461\pi\) |
0.217511 | + | 0.976058i | \(0.430206\pi\) | |||||||
\(258\) | 853.050 | 0.205847 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3267.06 | −0.779285 | ||||||||
\(261\) | 55.6375 | + | 96.3670i | 0.0131949 | + | 0.0228543i | ||||
\(262\) | −4771.06 | + | 8263.71i | −1.12503 | + | 1.94860i | ||||
\(263\) | −2613.55 | + | 4526.80i | −0.612769 | + | 1.06135i | 0.378003 | + | 0.925804i | \(0.376611\pi\) |
−0.990772 | + | 0.135542i | \(0.956722\pi\) | |||||||
\(264\) | −8770.48 | − | 15190.9i | −2.04464 | − | 3.54143i | ||||
\(265\) | −765.097 | −0.177357 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 213.166 | 0.0488596 | ||||||||
\(268\) | 1774.47 | + | 3073.47i | 0.404451 | + | 0.700530i | ||||
\(269\) | −640.854 | + | 1109.99i | −0.145255 | + | 0.251589i | −0.929468 | − | 0.368903i | \(-0.879734\pi\) |
0.784213 | + | 0.620491i | \(0.213067\pi\) | |||||||
\(270\) | 2036.83 | − | 3527.89i | 0.459102 | − | 0.795188i | ||||
\(271\) | −2352.07 | − | 4073.91i | −0.527226 | − | 0.913182i | −0.999497 | − | 0.0317282i | \(-0.989899\pi\) |
0.472271 | − | 0.881453i | \(-0.343434\pi\) | |||||||
\(272\) | 8180.82 | 1.82366 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4997.04 | −1.10176 | ||||||||
\(275\) | 653.185 | + | 1131.35i | 0.143231 | + | 0.248084i | ||||
\(276\) | 1282.05 | − | 2220.57i | 0.279602 | − | 0.484286i | ||||
\(277\) | −4479.28 | + | 7758.34i | −0.971603 | + | 1.68286i | −0.280883 | + | 0.959742i | \(0.590627\pi\) |
−0.690719 | + | 0.723123i | \(0.742706\pi\) | |||||||
\(278\) | 530.698 | + | 919.195i | 0.114493 | + | 0.198308i | ||||
\(279\) | 1671.47 | 0.358668 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −370.904 | −0.0787412 | −0.0393706 | − | 0.999225i | \(-0.512535\pi\) | ||||
−0.0393706 | + | 0.999225i | \(0.512535\pi\) | |||||||
\(282\) | −4559.51 | − | 7897.30i | −0.962818 | − | 1.66765i | ||||
\(283\) | 2911.13 | − | 5042.22i | 0.611479 | − | 1.05911i | −0.379512 | − | 0.925187i | \(-0.623908\pi\) |
0.990991 | − | 0.133926i | \(-0.0427585\pi\) | |||||||
\(284\) | 10145.3 | − | 17572.2i | 2.11977 | − | 3.67155i | ||||
\(285\) | −933.995 | − | 1617.73i | −0.194123 | − | 0.336231i | ||||
\(286\) | −8673.40 | −1.79325 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3258.29 | −0.666655 | ||||||||
\(289\) | 1763.63 | + | 3054.71i | 0.358973 | + | 0.621760i | ||||
\(290\) | 283.449 | − | 490.949i | 0.0573956 | − | 0.0994121i | ||||
\(291\) | 3916.71 | − | 6783.94i | 0.789009 | − | 1.36660i | ||||
\(292\) | 1582.43 | + | 2740.85i | 0.317140 | + | 0.549302i | ||||
\(293\) | 7443.79 | 1.48420 | 0.742100 | − | 0.670289i | \(-0.233830\pi\) | ||||
0.742100 | + | 0.670289i | \(0.233830\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3080.00 | 0.607880 | ||||||||
\(296\) | −7105.51 | − | 12307.1i | −1.39527 | − | 2.41667i | ||||
\(297\) | 3931.66 | − | 6809.83i | 0.768142 | − | 1.33046i | ||||
\(298\) | −2112.55 | + | 3659.04i | −0.410660 | + | 0.711284i | ||||
\(299\) | −395.987 | − | 685.869i | −0.0765903 | − | 0.132658i | ||||
\(300\) | −2481.37 | −0.477540 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12557.9 | −2.39280 | ||||||||
\(303\) | −1010.93 | − | 1750.97i | −0.191670 | − | 0.331983i | ||||
\(304\) | −8815.35 | + | 15268.6i | −1.66314 | + | 2.88064i | ||||
\(305\) | 38.1623 | − | 66.0991i | 0.00716449 | − | 0.0124093i | ||||
\(306\) | 535.479 | + | 927.477i | 0.100037 | + | 0.173269i | ||||
\(307\) | −761.674 | −0.141600 | −0.0707998 | − | 0.997491i | \(-0.522555\pi\) | ||||
−0.0707998 | + | 0.997491i | \(0.522555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1609.30 | −0.296278 | ||||||||
\(310\) | −4257.72 | − | 7374.58i | −0.780071 | − | 1.35112i | ||||
\(311\) | −3859.35 | + | 6684.58i | −0.703677 | + | 1.21880i | 0.263490 | + | 0.964662i | \(0.415126\pi\) |
−0.967167 | + | 0.254142i | \(0.918207\pi\) | |||||||
\(312\) | 5145.47 | − | 8912.21i | 0.933669 | − | 1.61716i | ||||
\(313\) | −4278.00 | − | 7409.72i | −0.772546 | − | 1.33809i | −0.936163 | − | 0.351565i | \(-0.885650\pi\) |
0.163617 | − | 0.986524i | \(-0.447684\pi\) | |||||||
\(314\) | 5538.21 | 0.995348 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18281.3 | 3.25444 | ||||||||
\(317\) | 3890.48 | + | 6738.50i | 0.689309 | + | 1.19392i | 0.972062 | + | 0.234725i | \(0.0754189\pi\) |
−0.282753 | + | 0.959193i | \(0.591248\pi\) | |||||||
\(318\) | 1929.05 | − | 3341.22i | 0.340176 | − | 0.589202i | ||||
\(319\) | 547.138 | − | 947.670i | 0.0960308 | − | 0.166330i | ||||
\(320\) | 3904.51 | + | 6762.81i | 0.682089 | + | 1.18141i | ||||
\(321\) | −1011.09 | −0.175805 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2986.42 | 0.514455 | ||||||||
\(324\) | 5939.00 | + | 10286.7i | 1.01835 | + | 1.76383i | ||||
\(325\) | −383.211 | + | 663.740i | −0.0654052 | + | 0.113285i | ||||
\(326\) | 3656.29 | − | 6332.88i | 0.621175 | − | 1.07591i | ||||
\(327\) | 4038.45 | + | 6994.79i | 0.682956 | + | 1.18291i | ||||
\(328\) | 819.045 | 0.137879 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6587.56 | −1.09889 | ||||||||
\(331\) | 2466.06 | + | 4271.34i | 0.409507 | + | 0.709288i | 0.994835 | − | 0.101510i | \(-0.0323673\pi\) |
−0.585327 | + | 0.810797i | \(0.699034\pi\) | |||||||
\(332\) | −7039.15 | + | 12192.2i | −1.16363 | + | 2.01546i | ||||
\(333\) | 523.791 | − | 907.233i | 0.0861970 | − | 0.149298i | ||||
\(334\) | 3331.31 | + | 5769.99i | 0.545751 | + | 0.945269i | ||||
\(335\) | 832.548 | 0.135782 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7121.13 | −1.15108 | −0.575538 | − | 0.817775i | \(-0.695207\pi\) | ||||
−0.575538 | + | 0.817775i | \(0.695207\pi\) | |||||||
\(338\) | 3403.26 | + | 5894.62i | 0.547671 | + | 0.948594i | ||||
\(339\) | −4317.38 | + | 7477.92i | −0.691704 | + | 1.19807i | ||||
\(340\) | 1983.53 | − | 3435.57i | 0.316388 | − | 0.548000i | ||||
\(341\) | −8218.60 | − | 14235.0i | −1.30517 | − | 2.26062i | ||||
\(342\) | −2308.05 | −0.364927 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2438.83 | −0.382246 | ||||||||
\(345\) | −300.757 | − | 520.926i | −0.0469339 | − | 0.0812919i | ||||
\(346\) | 6734.34 | − | 11664.2i | 1.04636 | − | 1.81235i | ||||
\(347\) | −4770.29 | + | 8262.39i | −0.737991 | + | 1.27824i | 0.215408 | + | 0.976524i | \(0.430892\pi\) |
−0.953399 | + | 0.301713i | \(0.902442\pi\) | |||||||
\(348\) | 1039.25 | + | 1800.04i | 0.160086 | + | 0.277277i | ||||
\(349\) | 1281.65 | 0.196576 | 0.0982880 | − | 0.995158i | \(-0.468663\pi\) | ||||
0.0982880 | + | 0.995158i | \(0.468663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4613.25 | 0.701530 | ||||||||
\(352\) | 16021.0 | + | 27749.1i | 2.42591 | + | 4.20180i | ||||
\(353\) | −2899.03 | + | 5021.27i | −0.437110 | + | 0.757097i | −0.997465 | − | 0.0711552i | \(-0.977331\pi\) |
0.560355 | + | 0.828253i | \(0.310665\pi\) | |||||||
\(354\) | −7765.67 | + | 13450.5i | −1.16593 | + | 2.01946i | ||||
\(355\) | −2380.00 | − | 4122.28i | −0.355823 | − | 0.616304i | ||||
\(356\) | −975.627 | −0.145247 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8777.40 | 1.29581 | ||||||||
\(359\) | −1133.65 | − | 1963.53i | −0.166662 | − | 0.288666i | 0.770583 | − | 0.637340i | \(-0.219965\pi\) |
−0.937244 | + | 0.348674i | \(0.886632\pi\) | |||||||
\(360\) | −957.574 | + | 1658.57i | −0.140190 | + | 0.242817i | ||||
\(361\) | 211.443 | − | 366.230i | 0.0308271 | − | 0.0533940i | ||||
\(362\) | −7021.38 | − | 12161.4i | −1.01944 | − | 1.76571i | ||||
\(363\) | −6517.58 | −0.942381 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 742.447 | 0.106470 | ||||||||
\(366\) | 192.439 | + | 333.314i | 0.0274835 | + | 0.0476027i | ||||
\(367\) | 3686.42 | − | 6385.07i | 0.524332 | − | 0.908169i | −0.475267 | − | 0.879842i | \(-0.657649\pi\) |
0.999599 | − | 0.0283274i | \(-0.00901809\pi\) | |||||||
\(368\) | −2838.64 | + | 4916.67i | −0.402104 | + | 0.696465i | ||||
\(369\) | 30.1885 | + | 52.2879i | 0.00425894 | + | 0.00737670i | ||||
\(370\) | −5336.98 | −0.749883 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 31221.4 | 4.35150 | ||||||||
\(373\) | −3223.57 | − | 5583.39i | −0.447480 | − | 0.775059i | 0.550741 | − | 0.834676i | \(-0.314345\pi\) |
−0.998221 | + | 0.0596176i | \(0.981012\pi\) | |||||||
\(374\) | 5265.88 | − | 9120.78i | 0.728054 | − | 1.26103i | ||||
\(375\) | −291.053 | + | 504.119i | −0.0400798 | + | 0.0694203i | ||||
\(376\) | 13035.4 | + | 22578.0i | 1.78790 | + | 3.09673i | ||||
\(377\) | 641.989 | 0.0877032 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4247.57 | −0.575680 | −0.287840 | − | 0.957678i | \(-0.592937\pi\) | ||||
−0.287840 | + | 0.957678i | \(0.592937\pi\) | |||||||
\(380\) | 4274.75 | + | 7404.09i | 0.577079 | + | 0.999531i | ||||
\(381\) | 3247.01 | − | 5623.99i | 0.436613 | − | 0.756236i | ||||
\(382\) | 4935.27 | − | 8548.13i | 0.661021 | − | 1.14492i | ||||
\(383\) | 3340.93 | + | 5786.66i | 0.445727 | + | 0.772022i | 0.998103 | − | 0.0615735i | \(-0.0196119\pi\) |
−0.552375 | + | 0.833595i | \(0.686279\pi\) | |||||||
\(384\) | −16533.9 | −2.19725 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8343.45 | −1.10018 | ||||||||
\(387\) | −89.8906 | − | 155.695i | −0.0118072 | − | 0.0204507i | ||||
\(388\) | −17926.2 | + | 31049.1i | −2.34553 | + | 4.06257i | ||||
\(389\) | 3185.89 | − | 5518.12i | 0.415247 | − | 0.719229i | −0.580207 | − | 0.814469i | \(-0.697029\pi\) |
0.995454 | + | 0.0952400i | \(0.0303619\pi\) | |||||||
\(390\) | −1932.39 | − | 3347.00i | −0.250899 | − | 0.434570i | ||||
\(391\) | 961.661 | 0.124382 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8207.33 | −1.05345 | ||||||||
\(394\) | −1898.34 | − | 3288.02i | −0.242733 | − | 0.420427i | ||||
\(395\) | 2144.31 | − | 3714.06i | 0.273144 | − | 0.473100i | ||||
\(396\) | −2959.06 | + | 5125.24i | −0.375500 | + | 0.650386i | ||||
\(397\) | −2123.96 | − | 3678.81i | −0.268510 | − | 0.465074i | 0.699967 | − | 0.714175i | \(-0.253198\pi\) |
−0.968477 | + | 0.249101i | \(0.919865\pi\) | |||||||
\(398\) | 17839.6 | 2.24678 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5494.11 | 0.686764 | ||||||||
\(401\) | 4416.81 | + | 7650.14i | 0.550038 | + | 0.952693i | 0.998271 | + | 0.0587765i | \(0.0187199\pi\) |
−0.448234 | + | 0.893916i | \(0.647947\pi\) | |||||||
\(402\) | −2099.12 | + | 3635.78i | −0.260434 | + | 0.451086i | ||||
\(403\) | 4821.69 | − | 8351.41i | 0.595993 | − | 1.03229i | ||||
\(404\) | 4626.85 | + | 8013.94i | 0.569788 | + | 0.986902i | ||||
\(405\) | 2786.47 | 0.341879 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10301.9 | −1.25466 | ||||||||
\(408\) | 6247.93 | + | 10821.7i | 0.758134 | + | 1.31313i | ||||
\(409\) | 159.602 | − | 276.439i | 0.0192954 | − | 0.0334206i | −0.856216 | − | 0.516617i | \(-0.827191\pi\) |
0.875512 | + | 0.483197i | \(0.160524\pi\) | |||||||
\(410\) | 153.797 | − | 266.385i | 0.0185256 | − | 0.0320873i | ||||
\(411\) | −2149.02 | − | 3722.21i | −0.257916 | − | 0.446723i | ||||
\(412\) | 7365.53 | 0.880761 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −743.218 | −0.0882298 | ||||||||
\(415\) | 1651.32 | + | 2860.17i | 0.195326 | + | 0.338314i | ||||
\(416\) | −9399.17 | + | 16279.8i | −1.10777 | + | 1.91871i | ||||
\(417\) | −456.462 | + | 790.615i | −0.0536044 | + | 0.0928455i | ||||
\(418\) | 11348.6 | + | 19656.4i | 1.32794 | + | 2.30006i | ||||
\(419\) | −12789.2 | −1.49115 | −0.745577 | − | 0.666420i | \(-0.767826\pi\) | ||||
−0.745577 | + | 0.666420i | \(0.767826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6747.40 | −0.781112 | −0.390556 | − | 0.920579i | \(-0.627717\pi\) | ||||
−0.390556 | + | 0.920579i | \(0.627717\pi\) | |||||||
\(422\) | −11051.4 | − | 19141.5i | −1.27482 | − | 2.20805i | ||||
\(423\) | −960.921 | + | 1664.36i | −0.110453 | + | 0.191310i | ||||
\(424\) | −5515.07 | + | 9552.38i | −0.631687 | + | 1.09411i | ||||
\(425\) | −465.317 | − | 805.953i | −0.0531087 | − | 0.0919870i | ||||
\(426\) | 24003.0 | 2.72992 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4627.60 | 0.522625 | ||||||||
\(429\) | −3730.07 | − | 6460.67i | −0.419789 | − | 0.727095i | ||||
\(430\) | −457.954 | + | 793.200i | −0.0513593 | + | 0.0889570i | ||||
\(431\) | 2592.37 | − | 4490.12i | 0.289722 | − | 0.501813i | −0.684021 | − | 0.729462i | \(-0.739770\pi\) |
0.973743 | + | 0.227649i | \(0.0731038\pi\) | |||||||
\(432\) | −16535.1 | − | 28639.6i | −1.84154 | − | 3.18964i | ||||
\(433\) | −4242.03 | −0.470806 | −0.235403 | − | 0.971898i | \(-0.575641\pi\) | ||||
−0.235403 | + | 0.971898i | \(0.575641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 487.599 | 0.0537439 | ||||||||
\(436\) | −18483.3 | − | 32014.1i | −2.03026 | − | 3.51651i | ||||
\(437\) | −1036.25 | + | 1794.84i | −0.113434 | + | 0.196473i | ||||
\(438\) | −1871.95 | + | 3242.31i | −0.204213 | + | 0.353707i | ||||
\(439\) | 2717.06 | + | 4706.08i | 0.295394 | + | 0.511638i | 0.975077 | − | 0.221869i | \(-0.0712156\pi\) |
−0.679682 | + | 0.733507i | \(0.737882\pi\) | |||||||
\(440\) | 18833.5 | 2.04057 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6178.77 | 0.664919 | ||||||||
\(443\) | 5746.89 | + | 9953.91i | 0.616350 | + | 1.06755i | 0.990146 | + | 0.140039i | \(0.0447228\pi\) |
−0.373796 | + | 0.927511i | \(0.621944\pi\) | |||||||
\(444\) | 9783.91 | − | 16946.2i | 1.04577 | − | 1.81133i | ||||
\(445\) | −114.437 | + | 198.210i | −0.0121906 | + | 0.0211147i | ||||
\(446\) | −2022.65 | − | 3503.32i | −0.214742 | − | 0.371944i | ||||
\(447\) | −3634.08 | −0.384532 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16849.3 | −1.77098 | −0.885489 | − | 0.464661i | \(-0.846176\pi\) | ||||
−0.885489 | + | 0.464661i | \(0.846176\pi\) | |||||||
\(450\) | 359.619 | + | 622.879i | 0.0376725 | + | 0.0652507i | ||||
\(451\) | 296.872 | − | 514.198i | 0.0309959 | − | 0.0536865i | ||||
\(452\) | 19760.0 | − | 34225.3i | 2.05626 | − | 3.56155i | ||||
\(453\) | −5400.62 | − | 9354.15i | −0.560140 | − | 0.970191i | ||||
\(454\) | 9018.32 | 0.932270 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −26930.2 | −2.76561 | ||||||||
\(457\) | −7674.25 | − | 13292.2i | −0.785528 | − | 1.36057i | −0.928683 | − | 0.370875i | \(-0.879058\pi\) |
0.143155 | − | 0.989700i | \(-0.454275\pi\) | |||||||
\(458\) | 17943.7 | − | 31079.3i | 1.83068 | − | 3.17083i | ||||
\(459\) | −2800.84 | + | 4851.20i | −0.284820 | + | 0.493322i | ||||
\(460\) | 1376.52 | + | 2384.20i | 0.139523 | + | 0.241661i | ||||
\(461\) | 14038.4 | 1.41830 | 0.709148 | − | 0.705059i | \(-0.249080\pi\) | ||||
0.709148 | + | 0.705059i | \(0.249080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8661.23 | −0.869377 | −0.434689 | − | 0.900581i | \(-0.643142\pi\) | ||||
−0.434689 | + | 0.900581i | \(0.643142\pi\) | |||||||
\(464\) | −2301.06 | − | 3985.55i | −0.230224 | − | 0.398760i | ||||
\(465\) | 3662.13 | − | 6343.00i | 0.365220 | − | 0.632580i | ||||
\(466\) | 1170.64 | − | 2027.60i | 0.116371 | − | 0.201560i | ||||
\(467\) | −3507.35 | − | 6074.91i | −0.347539 | − | 0.601956i | 0.638272 | − | 0.769811i | \(-0.279649\pi\) |
−0.985812 | + | 0.167855i | \(0.946316\pi\) | |||||||
\(468\) | −3472.04 | −0.342938 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9790.96 | 0.960901 | ||||||||
\(471\) | 2381.75 | + | 4125.32i | 0.233005 | + | 0.403576i | ||||
\(472\) | 22201.6 | − | 38454.4i | 2.16507 | − | 3.75001i | ||||
\(473\) | −883.981 | + | 1531.10i | −0.0859313 | + | 0.148837i | ||||
\(474\) | 10813.0 | + | 18728.7i | 1.04780 | + | 1.81484i | ||||
\(475\) | 2005.63 | 0.193737 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −813.100 | −0.0780488 | ||||||||
\(478\) | −15106.9 | − | 26165.8i | −1.44555 | − | 2.50376i | ||||
\(479\) | −9067.34 | + | 15705.1i | −0.864922 | + | 1.49809i | 0.00220344 | + | 0.999998i | \(0.499299\pi\) |
−0.867125 | + | 0.498091i | \(0.834035\pi\) | |||||||
\(480\) | −7138.79 | + | 12364.8i | −0.678833 | + | 1.17577i | ||||
\(481\) | −3021.96 | − | 5234.18i | −0.286464 | − | 0.496171i | ||||
\(482\) | −34092.6 | −3.22173 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 29830.0 | 2.80146 | ||||||||
\(485\) | 4205.32 | + | 7283.82i | 0.393719 | + | 0.681941i | ||||
\(486\) | 3973.30 | − | 6881.95i | 0.370848 | − | 0.642328i | ||||
\(487\) | −8268.92 | + | 14322.2i | −0.769405 | + | 1.33265i | 0.168480 | + | 0.985705i | \(0.446114\pi\) |
−0.937886 | + | 0.346944i | \(0.887219\pi\) | |||||||
\(488\) | −550.173 | − | 952.928i | −0.0510352 | − | 0.0883955i | ||||
\(489\) | 6289.67 | 0.581654 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 220.608 | 0.0202768 | 0.0101384 | − | 0.999949i | \(-0.496773\pi\) | ||||
0.0101384 | + | 0.999949i | \(0.496773\pi\) | |||||||
\(492\) | 563.891 | + | 976.687i | 0.0516710 | + | 0.0894969i | ||||
\(493\) | −389.771 | + | 675.103i | −0.0356073 | + | 0.0616736i | ||||
\(494\) | −6658.02 | + | 11532.0i | −0.606393 | + | 1.05030i | ||||
\(495\) | 694.167 | + | 1202.33i | 0.0630313 | + | 0.109173i | ||||
\(496\) | −69128.8 | −6.25801 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16654.0 | −1.49856 | ||||||||
\(499\) | −2969.52 | − | 5143.36i | −0.266401 | − | 0.461419i | 0.701529 | − | 0.712641i | \(-0.252501\pi\) |
−0.967930 | + | 0.251222i | \(0.919168\pi\) | |||||||
\(500\) | 1332.11 | − | 2307.28i | 0.119147 | − | 0.206369i | ||||
\(501\) | −2865.31 | + | 4962.86i | −0.255514 | + | 0.442564i | ||||
\(502\) | −844.403 | − | 1462.55i | −0.0750748 | − | 0.130033i | ||||
\(503\) | −11604.8 | −1.02869 | −0.514345 | − | 0.857584i | \(-0.671965\pi\) | ||||
−0.514345 | + | 0.857584i | \(0.671965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2170.83 | 0.191289 | ||||||||
\(506\) | 3654.39 | + | 6329.59i | 0.321062 | + | 0.556096i | ||||
\(507\) | −2927.20 | + | 5070.06i | −0.256413 | + | 0.444121i | ||||
\(508\) | −14861.1 | + | 25740.2i | −1.29794 | + | 2.24810i | ||||
\(509\) | 933.836 | + | 1617.45i | 0.0813193 | + | 0.140849i | 0.903817 | − | 0.427919i | \(-0.140753\pi\) |
−0.822498 | + | 0.568769i | \(0.807420\pi\) | |||||||
\(510\) | 4692.86 | 0.407457 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8025.75 | 0.692757 | ||||||||
\(513\) | −6036.17 | − | 10454.9i | −0.519500 | − | 0.899800i | ||||
\(514\) | 21281.6 | − | 36860.8i | 1.82625 | − | 3.16316i | ||||
\(515\) | 863.942 | − | 1496.39i | 0.0739220 | − | 0.128037i | ||||
\(516\) | −1679.07 | − | 2908.23i | −0.143250 | − | 0.248116i | ||||
\(517\) | 18899.3 | 1.60772 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11584.6 | 0.979786 | ||||||||
\(520\) | 5524.62 | + | 9568.91i | 0.465905 | + | 0.806970i | ||||
\(521\) | −3058.60 | + | 5297.66i | −0.257197 | + | 0.445479i | −0.965490 | − | 0.260440i | \(-0.916132\pi\) |
0.708293 | + | 0.705919i | \(0.249466\pi\) | |||||||
\(522\) | 301.233 | − | 521.752i | 0.0252579 | − | 0.0437480i | ||||
\(523\) | 8342.80 | + | 14450.2i | 0.697524 | + | 1.20815i | 0.969322 | + | 0.245793i | \(0.0790484\pi\) |
−0.271798 | + | 0.962354i | \(0.587618\pi\) | |||||||
\(524\) | 37563.7 | 3.13164 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28300.6 | 2.34594 | ||||||||
\(527\) | 5854.78 | + | 10140.8i | 0.483944 | + | 0.838215i | ||||
\(528\) | −26739.1 | + | 46313.5i | −2.20392 | + | 3.81730i | ||||
\(529\) | 5749.82 | − | 9958.97i | 0.472575 | − | 0.818523i | ||||
\(530\) | 2071.20 | + | 3587.42i | 0.169749 | + | 0.294014i | ||||
\(531\) | 3273.24 | 0.267508 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 348.338 | 0.0283081 | ||||||||
\(534\) | −577.062 | − | 999.501i | −0.0467639 | − | 0.0809975i | ||||
\(535\) | 542.797 | − | 940.151i | 0.0438638 | − | 0.0759744i | ||||
\(536\) | 6001.28 | − | 10394.5i | 0.483612 | − | 0.837640i | ||||
\(537\) | 3774.79 | + | 6538.13i | 0.303341 | + | 0.525403i | ||||
\(538\) | 6939.44 | 0.556097 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −16036.5 | −1.27796 | ||||||||
\(541\) | −4654.51 | − | 8061.86i | −0.369895 | − | 0.640677i | 0.619654 | − | 0.784875i | \(-0.287273\pi\) |
−0.989549 | + | 0.144198i | \(0.953940\pi\) | |||||||
\(542\) | −12734.6 | + | 22057.0i | −1.00922 | + | 1.74802i | ||||
\(543\) | 6039.21 | − | 10460.2i | 0.477288 | − | 0.826686i | ||||
\(544\) | −11413.0 | − | 19768.0i | −0.899504 | − | 1.55799i | ||||
\(545\) | −8672.05 | −0.681596 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10894.7 | 0.851598 | 0.425799 | − | 0.904818i | \(-0.359993\pi\) | ||||
0.425799 | + | 0.904818i | \(0.359993\pi\) | |||||||
\(548\) | 9835.73 | + | 17036.0i | 0.766718 | + | 1.32799i | ||||
\(549\) | 40.5567 | − | 70.2463i | 0.00315286 | − | 0.00546091i | ||||
\(550\) | 3536.49 | − | 6125.37i | 0.274175 | − | 0.474885i | ||||
\(551\) | −840.005 | − | 1454.93i | −0.0649463 | − | 0.112490i | ||||
\(552\) | −8671.81 | −0.668654 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 48503.6 | 3.71971 | ||||||||
\(555\) | −2295.21 | − | 3975.43i | −0.175543 | − | 0.304050i | ||||
\(556\) | 2089.16 | − | 3618.52i | 0.159352 | − | 0.276006i | ||||
\(557\) | 3936.95 | − | 6818.99i | 0.299486 | − | 0.518725i | −0.676532 | − | 0.736413i | \(-0.736518\pi\) |
0.976019 | + | 0.217688i | \(0.0698514\pi\) | |||||||
\(558\) | −4524.85 | − | 7837.27i | −0.343284 | − | 0.594585i | ||||
\(559\) | −1037.23 | −0.0784796 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9058.55 | 0.681733 | ||||||||
\(562\) | 1004.08 | + | 1739.11i | 0.0753638 | + | 0.130534i | ||||
\(563\) | −10885.4 | + | 18854.0i | −0.814854 | + | 1.41137i | 0.0945786 | + | 0.995517i | \(0.469850\pi\) |
−0.909433 | + | 0.415851i | \(0.863484\pi\) | |||||||
\(564\) | −17949.1 | + | 31088.7i | −1.34006 | + | 2.32105i | ||||
\(565\) | −4635.51 | − | 8028.94i | −0.345163 | − | 0.597841i | ||||
\(566\) | −31522.9 | −2.34100 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −68623.3 | −5.06931 | ||||||||
\(569\) | 6190.63 | + | 10722.5i | 0.456106 | + | 0.790000i | 0.998751 | − | 0.0499628i | \(-0.0159103\pi\) |
−0.542645 | + | 0.839962i | \(0.682577\pi\) | |||||||
\(570\) | −5056.85 | + | 8758.72i | −0.371593 | + | 0.643618i | ||||
\(571\) | 2884.19 | − | 4995.56i | 0.211383 | − | 0.366126i | −0.740765 | − | 0.671764i | \(-0.765537\pi\) |
0.952148 | + | 0.305639i | \(0.0988700\pi\) | |||||||
\(572\) | 17071.9 | + | 29569.5i | 1.24793 | + | 2.16147i | ||||
\(573\) | 8489.81 | 0.618965 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 645.837 | 0.0468405 | ||||||||
\(576\) | 4149.48 | + | 7187.12i | 0.300165 | + | 0.519901i | ||||
\(577\) | −2366.69 | + | 4099.23i | −0.170757 | + | 0.295759i | −0.938685 | − | 0.344777i | \(-0.887955\pi\) |
0.767928 | + | 0.640536i | \(0.221288\pi\) | |||||||
\(578\) | 9548.70 | − | 16538.8i | 0.687151 | − | 1.19018i | ||||
\(579\) | −3588.17 | − | 6214.89i | −0.257546 | − | 0.446083i | ||||
\(580\) | −2231.67 | −0.159767 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −42411.8 | −3.02066 | ||||||||
\(583\) | 3998.00 | + | 6924.74i | 0.284014 | + | 0.491927i | ||||
\(584\) | 5351.80 | − | 9269.59i | 0.379211 | − | 0.656813i | ||||
\(585\) | −407.254 | + | 705.385i | −0.0287827 | + | 0.0498531i | ||||
\(586\) | −20151.1 | − | 34902.8i | −1.42054 | − | 2.46044i | ||||
\(587\) | −8441.67 | −0.593569 | −0.296785 | − | 0.954944i | \(-0.595914\pi\) | ||||
−0.296785 | + | 0.954944i | \(0.595914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25235.6 | −1.76539 | ||||||||
\(590\) | −8337.89 | − | 14441.6i | −0.581806 | − | 1.00772i | ||||
\(591\) | 1632.79 | − | 2828.08i | 0.113645 | − | 0.196839i | ||||
\(592\) | −21663.0 | + | 37521.4i | −1.50396 | + | 2.60493i | ||||
\(593\) | −9469.94 | − | 16402.4i | −0.655791 | − | 1.13586i | −0.981695 | − | 0.190460i | \(-0.939002\pi\) |
0.325904 | − | 0.945403i | \(-0.394331\pi\) | |||||||
\(594\) | −42573.7 | −2.94077 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16632.6 | 1.14312 | ||||||||
\(597\) | 7672.08 | + | 13288.4i | 0.525958 | + | 0.910987i | ||||
\(598\) | −2143.96 | + | 3713.44i | −0.146610 | + | 0.253936i | ||||
\(599\) | −11327.7 | + | 19620.1i | −0.772681 | + | 1.33832i | 0.163407 | + | 0.986559i | \(0.447752\pi\) |
−0.936089 | + | 0.351764i | \(0.885582\pi\) | |||||||
\(600\) | 4196.02 | + | 7267.71i | 0.285503 | + | 0.494505i | ||||
\(601\) | −15947.4 | −1.08237 | −0.541187 | − | 0.840902i | \(-0.682025\pi\) | ||||
−0.541187 | + | 0.840902i | \(0.682025\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 884.784 | 0.0597532 | ||||||||
\(604\) | 24717.8 | + | 42812.5i | 1.66516 | + | 2.88413i | ||||
\(605\) | 3498.92 | − | 6060.31i | 0.235126 | − | 0.407250i | ||||
\(606\) | −5473.36 | + | 9480.15i | −0.366898 | + | 0.635486i | ||||
\(607\) | 12996.6 | + | 22510.8i | 0.869053 | + | 1.50524i | 0.862966 | + | 0.505263i | \(0.168604\pi\) |
0.00608748 | + | 0.999981i | \(0.498062\pi\) | |||||||
\(608\) | 49193.1 | 3.28132 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −413.238 | −0.0274287 | ||||||||
\(611\) | 5543.93 | + | 9602.36i | 0.367076 | + | 0.635794i | ||||
\(612\) | 2107.98 | − | 3651.13i | 0.139232 | − | 0.241157i | ||||
\(613\) | −332.704 | + | 576.260i | −0.0219213 | + | 0.0379689i | −0.876778 | − | 0.480895i | \(-0.840312\pi\) |
0.854857 | + | 0.518864i | \(0.173645\pi\) | |||||||
\(614\) | 2061.93 | + | 3571.37i | 0.135526 | + | 0.234738i | ||||
\(615\) | 264.567 | 0.0173470 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18401.3 | 1.20066 | 0.600330 | − | 0.799752i | \(-0.295036\pi\) | ||||
0.600330 | + | 0.799752i | \(0.295036\pi\) | |||||||
\(618\) | 4356.55 | + | 7545.77i | 0.283570 | + | 0.491157i | ||||
\(619\) | 5575.30 | − | 9656.70i | 0.362020 | − | 0.627037i | −0.626273 | − | 0.779604i | \(-0.715421\pi\) |
0.988293 | + | 0.152567i | \(0.0487540\pi\) | |||||||
\(620\) | −16761.0 | + | 29030.9i | −1.08571 | + | 1.88050i | ||||
\(621\) | −1943.71 | − | 3366.61i | −0.125602 | − | 0.217548i | ||||
\(622\) | 41790.6 | 2.69397 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −31374.6 | −2.01280 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −23162.0 | + | 40117.8i | −1.47882 | + | 2.56139i | ||||
\(627\) | −9761.15 | + | 16906.8i | −0.621727 | + | 1.07686i | ||||
\(628\) | −10900.9 | − | 18880.9i | −0.692665 | − | 1.19973i | ||||
\(629\) | 7338.88 | 0.465215 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5381.79 | 0.339534 | 0.169767 | − | 0.985484i | \(-0.445699\pi\) | ||||
0.169767 | + | 0.985484i | \(0.445699\pi\) | |||||||
\(632\) | −30913.8 | − | 53544.3i | −1.94570 | − | 3.37006i | ||||
\(633\) | 9505.46 | − | 16463.9i | 0.596854 | − | 1.03378i | ||||
\(634\) | 21063.9 | − | 36483.7i | 1.31948 | − | 2.28541i | ||||
\(635\) | 3486.27 | + | 6038.40i | 0.217872 | + | 0.377365i | ||||
\(636\) | −15187.9 | −0.946918 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5924.64 | −0.367647 | ||||||||
\(639\) | −2529.33 | − | 4380.92i | −0.156586 | − | 0.271215i | ||||
\(640\) | 8876.12 | − | 15373.9i | 0.548218 | − | 0.949542i | ||||
\(641\) | 9727.53 | − | 16848.6i | 0.599398 | − | 1.03819i | −0.393512 | − | 0.919320i | \(-0.628740\pi\) |
0.992910 | − | 0.118869i | \(-0.0379267\pi\) | |||||||
\(642\) | 2737.13 | + | 4740.84i | 0.168265 | + | 0.291443i | ||||
\(643\) | −14695.8 | −0.901317 | −0.450658 | − | 0.892696i | \(-0.648811\pi\) | ||||
−0.450658 | + | 0.892696i | \(0.648811\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −787.788 | −0.0480917 | ||||||||
\(646\) | −8084.56 | − | 14002.9i | −0.492388 | − | 0.852842i | ||||
\(647\) | 6347.41 | − | 10994.0i | 0.385691 | − | 0.668037i | −0.606174 | − | 0.795332i | \(-0.707296\pi\) |
0.991865 | + | 0.127295i | \(0.0406296\pi\) | |||||||
\(648\) | 20085.8 | − | 34789.6i | 1.21766 | − | 2.10905i | ||||
\(649\) | −16094.5 | − | 27876.5i | −0.973442 | − | 1.68605i | ||||
\(650\) | 4149.57 | 0.250399 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −28786.8 | −1.72911 | ||||||||
\(653\) | 6192.82 | + | 10726.3i | 0.371124 | + | 0.642805i | 0.989739 | − | 0.142889i | \(-0.0456393\pi\) |
−0.618615 | + | 0.785694i | \(0.712306\pi\) | |||||||
\(654\) | 21865.0 | − | 37871.3i | 1.30732 | − | 2.26435i | ||||
\(655\) | 4406.05 | − | 7631.50i | 0.262837 | − | 0.455248i | ||||
\(656\) | −1248.54 | − | 2162.53i | −0.0743096 | − | 0.128708i | ||||
\(657\) | 789.030 | 0.0468539 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2072.18 | −0.122489 | −0.0612447 | − | 0.998123i | \(-0.519507\pi\) | ||||
−0.0612447 | + | 0.998123i | \(0.519507\pi\) | |||||||
\(660\) | 12966.4 | + | 22458.4i | 0.764720 | + | 1.32453i | ||||
\(661\) | −537.182 | + | 930.427i | −0.0316096 | + | 0.0547495i | −0.881397 | − | 0.472375i | \(-0.843397\pi\) |
0.849788 | + | 0.527125i | \(0.176730\pi\) | |||||||
\(662\) | 13351.8 | − | 23126.0i | 0.783885 | − | 1.35773i | ||||
\(663\) | 2657.23 | + | 4602.46i | 0.155654 | + | 0.269600i | ||||
\(664\) | 47613.0 | 2.78275 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5671.84 | −0.329999 | ||||||||
\(667\) | −270.491 | − | 468.504i | −0.0157023 | − | 0.0271972i | ||||
\(668\) | 13114.1 | − | 22714.3i | 0.759580 | − | 1.31563i | ||||
\(669\) | 1739.71 | − | 3013.27i | 0.100540 | − | 0.174140i | ||||
\(670\) | −2253.80 | − | 3903.69i | −0.129958 | − | 0.225094i | ||||
\(671\) | −797.667 | −0.0458921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26195.2 | 1.50037 | 0.750186 | − | 0.661226i | \(-0.229964\pi\) | ||||
0.750186 | + | 0.661226i | \(0.229964\pi\) | |||||||
\(674\) | 19277.7 | + | 33389.9i | 1.10170 | + | 1.90821i | ||||
\(675\) | −1881.00 | + | 3257.99i | −0.107259 | + | 0.185778i | ||||
\(676\) | 13397.3 | − | 23204.9i | 0.762252 | − | 1.32026i | ||||
\(677\) | 2114.22 | + | 3661.93i | 0.120024 | + | 0.207887i | 0.919777 | − | 0.392442i | \(-0.128370\pi\) |
−0.799753 | + | 0.600329i | \(0.795036\pi\) | |||||||
\(678\) | 46750.4 | 2.64814 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −13416.6 | −0.756624 | ||||||||
\(681\) | 3878.40 | + | 6717.59i | 0.218239 | + | 0.378001i | ||||
\(682\) | −44497.3 | + | 77071.5i | −2.49837 | + | 4.32730i | ||||
\(683\) | −13762.8 | + | 23837.8i | −0.771036 | + | 1.33547i | 0.165960 | + | 0.986133i | \(0.446928\pi\) |
−0.936996 | + | 0.349341i | \(0.886405\pi\) | |||||||
\(684\) | 4542.96 | + | 7868.63i | 0.253954 | + | 0.439861i | ||||
\(685\) | 4614.74 | 0.257402 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30867.3 | 1.71421 | ||||||||
\(688\) | 3717.70 | + | 6439.24i | 0.206012 | + | 0.356822i | ||||
\(689\) | −2345.55 | + | 4062.60i | −0.129693 | + | 0.224634i | ||||
\(690\) | −1628.36 | + | 2820.41i | −0.0898416 | + | 0.155610i | ||||
\(691\) | 16662.2 | + | 28859.8i | 0.917309 | + | 1.58883i | 0.803486 | + | 0.595324i | \(0.202976\pi\) |
0.113823 | + | 0.993501i | \(0.463690\pi\) | |||||||
\(692\) | −53021.1 | −2.91266 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 51654.8 | 2.82534 | ||||||||
\(695\) | −490.097 | − | 848.872i | −0.0267488 | − | 0.0463303i | ||||
\(696\) | 3514.77 | − | 6087.76i | 0.191418 | − | 0.331546i | ||||
\(697\) | −211.486 | + | 366.305i | −0.0114930 | + | 0.0199065i | ||||
\(698\) | −3469.56 | − | 6009.45i | −0.188144 | − | 0.325875i | ||||
\(699\) | 2013.77 | 0.108967 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33262.9 | −1.79219 | −0.896094 | − | 0.443864i | \(-0.853607\pi\) | ||||
−0.896094 | + | 0.443864i | \(0.853607\pi\) | |||||||
\(702\) | −12488.6 | − | 21630.8i | −0.671439 | − | 1.16297i | ||||
\(703\) | −7908.11 | + | 13697.2i | −0.424267 | + | 0.734852i | ||||
\(704\) | 40805.9 | − | 70677.9i | 2.18456 | − | 3.78377i | ||||
\(705\) | 4210.68 | + | 7293.12i | 0.224941 | + | 0.389609i | ||||
\(706\) | 31392.0 | 1.67345 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 61141.0 | 3.24551 | ||||||||
\(709\) | −6851.52 | − | 11867.2i | −0.362926 | − | 0.628606i | 0.625515 | − | 0.780212i | \(-0.284889\pi\) |
−0.988441 | + | 0.151606i | \(0.951555\pi\) | |||||||
\(710\) | −12885.8 | + | 22318.9i | −0.681122 | + | 1.17974i | ||||
\(711\) | 2278.85 | − | 3947.08i | 0.120202 | − | 0.208196i | ||||
\(712\) | 1649.79 | + | 2857.52i | 0.0868378 | + | 0.150408i | ||||
\(713\) | −8126.14 | −0.426825 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8009.84 | 0.418953 | ||||||||
\(716\) | −17276.7 | − | 29924.0i | −0.901758 | − | 1.56189i | ||||
\(717\) | 12993.7 | − | 22505.7i | 0.676788 | − | 1.17223i | ||||
\(718\) | −6137.80 | + | 10631.0i | −0.319026 | + | 0.552569i | ||||
\(719\) | 4037.47 | + | 6993.10i | 0.209419 | + | 0.362724i | 0.951532 | − | 0.307551i | \(-0.0995095\pi\) |
−0.742113 | + | 0.670275i | \(0.766176\pi\) | |||||||
\(720\) | 5838.82 | 0.302222 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2289.59 | −0.118019 | ||||||||
\(723\) | −14661.8 | − | 25395.0i | −0.754188 | − | 1.30629i | ||||
\(724\) | −27640.5 | + | 47874.8i | −1.41886 | + | 2.45753i | ||||
\(725\) | −261.764 | + | 453.389i | −0.0134092 | + | 0.0232254i | ||||
\(726\) | 17643.8 | + | 30559.9i | 0.901959 | + | 1.56224i | ||||
\(727\) | −3668.70 | −0.187159 | −0.0935794 | − | 0.995612i | \(-0.529831\pi\) | ||||
−0.0935794 | + | 0.995612i | \(0.529831\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21881.9 | 1.11172 | ||||||||
\(730\) | −2009.88 | − | 3481.22i | −0.101903 | − | 0.176501i | ||||
\(731\) | 629.732 | − | 1090.73i | 0.0318625 | − | 0.0551875i | ||||
\(732\) | 757.559 | − | 1312.13i | 0.0382516 | − | 0.0662538i | ||||
\(733\) | 7490.15 | + | 12973.3i | 0.377428 | + | 0.653725i | 0.990687 | − | 0.136157i | \(-0.0434751\pi\) |
−0.613259 | + | 0.789882i | \(0.710142\pi\) | |||||||
\(734\) | −39918.2 | −2.00737 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15840.7 | 0.793338 | ||||||||
\(737\) | −4350.47 | − | 7535.23i | −0.217438 | − | 0.376613i | ||||
\(738\) | 163.447 | − | 283.098i | 0.00815252 | − | 0.0141206i | ||||
\(739\) | −3265.30 | + | 5655.66i | −0.162538 | + | 0.281525i | −0.935778 | − | 0.352589i | \(-0.885301\pi\) |
0.773240 | + | 0.634114i | \(0.218635\pi\) | |||||||
\(740\) | 10504.8 | + | 18194.9i | 0.521846 | + | 0.903863i | ||||
\(741\) | −11453.3 | −0.567812 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25952.0 | 1.28141 | 0.640704 | − | 0.767788i | \(-0.278643\pi\) | ||||
0.640704 | + | 0.767788i | \(0.278643\pi\) | |||||||
\(744\) | −52795.7 | − | 91444.8i | −2.60159 | − | 4.50609i | ||||
\(745\) | 1950.93 | − | 3379.11i | 0.0959416 | − | 0.166176i | ||||
\(746\) | −17453.1 | + | 30229.7i | −0.856573 | + | 1.48363i | ||||
\(747\) | 1754.93 | + | 3039.62i | 0.0859564 | + | 0.148881i | ||||
\(748\) | −41459.6 | −2.02662 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3151.65 | 0.153443 | ||||||||
\(751\) | 7046.97 | + | 12205.7i | 0.342407 | + | 0.593066i | 0.984879 | − | 0.173243i | \(-0.0554246\pi\) |
−0.642472 | + | 0.766309i | \(0.722091\pi\) | |||||||
\(752\) | 39741.8 | − | 68834.8i | 1.92717 | − | 3.33796i | ||||
\(753\) | 726.285 | − | 1257.96i | 0.0351491 | − | 0.0608801i | ||||
\(754\) | −1737.93 | − | 3010.19i | −0.0839414 | − | 0.145391i | ||||
\(755\) | 11597.1 | 0.559024 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2554.41 | −0.122644 | −0.0613220 | − | 0.998118i | \(-0.519532\pi\) | ||||
−0.0613220 | + | 0.998118i | \(0.519532\pi\) | |||||||
\(758\) | 11498.6 | + | 19916.2i | 0.550987 | + | 0.954338i | ||||
\(759\) | −3143.20 | + | 5444.18i | −0.150317 | + | 0.260357i | ||||
\(760\) | 14457.3 | − | 25040.7i | 0.690027 | − | 1.19516i | ||||
\(761\) | −1109.54 | − | 1921.78i | −0.0528527 | − | 0.0915435i | 0.838389 | − | 0.545073i | \(-0.183498\pi\) |
−0.891241 | + | 0.453529i | \(0.850165\pi\) | |||||||
\(762\) | −35160.1 | −1.67154 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −38856.5 | −1.84003 | ||||||||
\(765\) | −494.512 | − | 856.520i | −0.0233714 | − | 0.0404805i | ||||
\(766\) | 18088.5 | − | 31330.2i | 0.853217 | − | 1.47781i | ||||
\(767\) | 9442.31 | − | 16354.6i | 0.444514 | − | 0.769921i | ||||
\(768\) | 15666.7 | + | 27135.6i | 0.736100 | + | 1.27496i | ||||
\(769\) | −22466.2 | −1.05352 | −0.526758 | − | 0.850015i | \(-0.676592\pi\) | ||||
−0.526758 | + | 0.850015i | \(0.676592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36609.3 | 1.71006 | ||||||||
\(772\) | 16422.5 | + | 28444.6i | 0.765620 | + | 1.32609i | ||||
\(773\) | −4837.39 | + | 8378.61i | −0.225083 | + | 0.389855i | −0.956344 | − | 0.292242i | \(-0.905599\pi\) |
0.731262 | + | 0.682097i | \(0.238932\pi\) | |||||||
\(774\) | −486.687 | + | 842.967i | −0.0226016 | + | 0.0391470i | ||||
\(775\) | 3931.98 | + | 6810.39i | 0.182246 | + | 0.315660i | ||||
\(776\) | 121253. | 5.60920 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34498.2 | −1.58974 | ||||||||
\(779\) | −455.780 | − | 789.434i | −0.0209628 | − | 0.0363086i | ||||
\(780\) | −7607.10 | + | 13175.9i | −0.349203 | + | 0.604836i | ||||
\(781\) | −24873.3 | + | 43081.8i | −1.13961 | + | 1.97387i | ||||
\(782\) | −2603.32 | − | 4509.08i | −0.119047 | − | 0.206195i | ||||
\(783\) | 3151.23 | 0.143826 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5114.51 | −0.232541 | ||||||||
\(786\) | 22218.1 | + | 38482.9i | 1.00826 | + | 1.74636i | ||||
\(787\) | 10471.4 | − | 18137.0i | 0.474288 | − | 0.821491i | −0.525278 | − | 0.850930i | \(-0.676039\pi\) |
0.999567 | + | 0.0294391i | \(0.00937212\pi\) | |||||||
\(788\) | −7473.04 | + | 12943.7i | −0.337838 | + | 0.585152i | ||||
\(789\) | 12170.9 | + | 21080.6i | 0.549171 | + | 0.951192i | ||||
\(790\) | −23219.5 | −1.04571 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 20015.1 | 0.897989 | ||||||||
\(793\) | −233.987 | − | 405.278i | −0.0104781 | − | 0.0181486i | ||||
\(794\) | −11499.6 | + | 19917.9i | −0.513986 | + | 0.890251i | ||||
\(795\) | −1781.47 | + | 3085.60i | −0.0794746 | + | 0.137654i | ||||
\(796\) | −35113.9 | − | 60819.1i | −1.56354 | − | 2.70813i | ||||
\(797\) | 23526.6 | 1.04561 | 0.522807 | − | 0.852451i | \(-0.324885\pi\) | ||||
0.522807 | + | 0.852451i | \(0.324885\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13463.5 | −0.596127 | ||||||||
\(800\) | −7664.82 | − | 13275.9i | −0.338741 | − | 0.586716i | ||||
\(801\) | −121.616 | + | 210.646i | −0.00536468 | + | 0.00929189i | ||||
\(802\) | 23913.6 | − | 41419.5i | 1.05289 | − | 1.82366i | ||||
\(803\) | −3879.65 | − | 6719.74i | −0.170498 | − | 0.295311i | ||||
\(804\) | 16526.9 | 0.724948 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −52211.3 | −2.28172 | ||||||||
\(807\) | 2984.36 | + | 5169.07i | 0.130179 | + | 0.225477i | ||||
\(808\) | 15648.1 | − | 27103.3i | 0.681308 | − | 1.18006i | ||||
\(809\) | 9101.12 | − | 15763.6i | 0.395523 | − | 0.685067i | −0.597644 | − | 0.801761i | \(-0.703897\pi\) |
0.993168 | + | 0.116695i | \(0.0372299\pi\) | |||||||
\(810\) | −7543.28 | − | 13065.3i | −0.327214 | − | 0.566752i | ||||
\(811\) | −2510.24 | −0.108689 | −0.0543443 | − | 0.998522i | \(-0.517307\pi\) | ||||
−0.0543443 | + | 0.998522i | \(0.517307\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21906.5 | −0.945012 | ||||||||
\(814\) | 27888.3 | + | 48304.0i | 1.20084 | + | 2.07992i | ||||
\(815\) | −3376.56 | + | 5848.38i | −0.145124 | + | 0.251362i | ||||
\(816\) | 19048.4 | − | 32992.9i | 0.817192 | − | 1.41542i | ||||
\(817\) | 1357.15 | + | 2350.66i | 0.0581160 | + | 0.100660i | ||||
\(818\) | −1728.24 | −0.0738711 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1210.88 | −0.0515681 | ||||||||
\(821\) | −8949.81 | − | 15501.5i | −0.380451 | − | 0.658961i | 0.610675 | − | 0.791881i | \(-0.290898\pi\) |
−0.991127 | + | 0.132920i | \(0.957565\pi\) | |||||||
\(822\) | −11635.2 | + | 20152.8i | −0.493705 | + | 0.855123i | ||||
\(823\) | −7019.75 | + | 12158.6i | −0.297318 | + | 0.514970i | −0.975522 | − | 0.219904i | \(-0.929426\pi\) |
0.678203 | + | 0.734874i | \(0.262759\pi\) | |||||||
\(824\) | −12455.2 | − | 21573.0i | −0.526573 | − | 0.912051i | ||||
\(825\) | 6083.58 | 0.256731 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15127.4 | 0.636073 | 0.318036 | − | 0.948079i | \(-0.396977\pi\) | ||||
0.318036 | + | 0.948079i | \(0.396977\pi\) | |||||||
\(828\) | 1462.88 | + | 2533.79i | 0.0613994 | + | 0.106347i | ||||
\(829\) | −10993.2 | + | 19040.8i | −0.460568 | + | 0.797727i | −0.998989 | − | 0.0449487i | \(-0.985688\pi\) |
0.538421 | + | 0.842676i | \(0.319021\pi\) | |||||||
\(830\) | 8940.60 | − | 15485.6i | 0.373895 | − | 0.647605i | ||||
\(831\) | 20859.4 | + | 36129.5i | 0.870762 | + | 1.50820i | ||||
\(832\) | 47880.0 | 1.99512 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4942.76 | 0.205220 | ||||||||
\(835\) | −3076.44 | − | 5328.56i | −0.127503 | − | 0.220841i | ||||
\(836\) | 44675.3 | − | 77379.9i | 1.84824 | − | 3.20124i | ||||
\(837\) | 23667.4 | − | 40993.2i | 0.977378 | − | 1.69287i | ||||
\(838\) | 34621.7 | + | 59966.6i | 1.42719 | + | 2.47197i | ||||
\(839\) | −2276.89 | −0.0936914 | −0.0468457 | − | 0.998902i | \(-0.514917\pi\) | ||||
−0.0468457 | + | 0.998902i | \(0.514917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23950.5 | −0.982019 | ||||||||
\(842\) | 18265.9 | + | 31637.5i | 0.747607 | + | 1.29489i | ||||
\(843\) | −863.623 | + | 1495.84i | −0.0352844 | + | 0.0611144i | ||||
\(844\) | −43505.1 | + | 75353.0i | −1.77430 | + | 3.07317i | ||||
\(845\) | −3142.89 | − | 5443.65i | −0.127951 | − | 0.221618i | ||||
\(846\) | 10405.3 | 0.422861 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 33628.2 | 1.36179 | ||||||||
\(849\) | −13556.7 | − | 23480.9i | −0.548015 | − | 0.949190i | ||||
\(850\) | −2519.33 | + | 4363.60i | −0.101661 | + | 0.176083i | ||||
\(851\) | −2546.50 | + | 4410.67i | −0.102577 | + | 0.177668i | ||||
\(852\) | −47245.3 | − | 81831.3i | −1.89976 | − | 3.29048i | ||||
\(853\) | 13342.6 | 0.535570 | 0.267785 | − | 0.963479i | \(-0.413708\pi\) | ||||
0.267785 | + | 0.963479i | \(0.413708\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2131.47 | 0.0852571 | ||||||||
\(856\) | −7825.31 | − | 13553.8i | −0.312457 | − | 0.541192i | ||||
\(857\) | −9345.43 | + | 16186.8i | −0.372502 | + | 0.645192i | −0.989950 | − | 0.141420i | \(-0.954833\pi\) |
0.617448 | + | 0.786612i | \(0.288167\pi\) | |||||||
\(858\) | −20195.4 | + | 34979.4i | −0.803565 | + | 1.39182i | ||||
\(859\) | −9159.45 | − | 15864.6i | −0.363814 | − | 0.630144i | 0.624771 | − | 0.780808i | \(-0.285192\pi\) |
−0.988585 | + | 0.150664i | \(0.951859\pi\) | |||||||
\(860\) | 3605.58 | 0.142964 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28071.3 | −1.10918 | ||||||||
\(863\) | −19066.6 | − | 33024.3i | −0.752067 | − | 1.30262i | −0.946819 | − | 0.321765i | \(-0.895724\pi\) |
0.194753 | − | 0.980852i | \(-0.437610\pi\) | |||||||
\(864\) | −46136.2 | + | 79910.2i | −1.81665 | + | 3.14653i | ||||
\(865\) | −6219.13 | + | 10771.9i | −0.244459 | + | 0.423415i | ||||
\(866\) | 11483.6 | + | 19890.2i | 0.450612 | + | 0.780482i | ||||
\(867\) | 16426.0 | 0.643432 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −44820.3 | −1.74962 | ||||||||
\(870\) | −1319.98 | − | 2286.28i | −0.0514386 | − | 0.0890943i | ||||
\(871\) | 2552.33 | − | 4420.77i | 0.0992910 | − | 0.171977i | ||||
\(872\) | −62510.9 | + | 108272.i | −2.42762 | + | 4.20477i | ||||
\(873\) | 4469.17 | + | 7740.82i | 0.173263 | + | 0.300100i | ||||
\(874\) | 11221.0 | 0.434273 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14738.3 | 0.568449 | ||||||||
\(877\) | 9853.73 | + | 17067.2i | 0.379404 | + | 0.657146i | 0.990976 | − | 0.134042i | \(-0.0427959\pi\) |
−0.611572 | + | 0.791189i | \(0.709463\pi\) | |||||||
\(878\) | 14710.7 | − | 25479.7i | 0.565448 | − | 0.979385i | ||||
\(879\) | 17332.3 | − | 30020.5i | 0.665079 | − | 1.15195i | ||||
\(880\) | −28709.4 | − | 49726.1i | −1.09977 | − | 1.90485i | ||||
\(881\) | −14091.5 | −0.538883 | −0.269441 | − | 0.963017i | \(-0.586839\pi\) | ||||
−0.269441 | + | 0.963017i | \(0.586839\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3115.87 | 0.118751 | 0.0593757 | − | 0.998236i | \(-0.481089\pi\) | ||||
0.0593757 | + | 0.998236i | \(0.481089\pi\) | |||||||
\(884\) | −12161.7 | − | 21064.8i | −0.462719 | − | 0.801453i | ||||
\(885\) | 7171.56 | − | 12421.5i | 0.272395 | − | 0.471801i | ||||
\(886\) | 31114.9 | − | 53892.6i | 1.17983 | − | 2.04352i | ||||
\(887\) | −19367.3 | − | 33545.1i | −0.733134 | − | 1.26983i | −0.955537 | − | 0.294871i | \(-0.904723\pi\) |
0.222403 | − | 0.974955i | \(-0.428610\pi\) | |||||||
\(888\) | −66178.6 | −2.50091 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1239.17 | 0.0466708 | ||||||||
\(891\) | −14560.7 | − | 25219.8i | −0.547475 | − | 0.948255i | ||||
\(892\) | −7962.39 | + | 13791.3i | −0.298879 | + | 0.517674i | ||||
\(893\) | 14507.8 | − | 25128.3i | 0.543657 | − | 0.941641i | ||||
\(894\) | 9837.84 | + | 17039.6i | 0.368039 | + | 0.637461i | ||||
\(895\) | −8105.89 | −0.302737 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3688.10 | −0.137282 | ||||||||
\(898\) | 45612.9 | + | 79003.9i | 1.69501 | + | 2.93585i | ||||
\(899\) | 3293.60 | − | 5704.69i | 0.122189 | − | 0.211637i | ||||
\(900\) | 1415.69 | − | 2452.04i | 0.0524328 | − | 0.0908163i | ||||
\(901\) | −2848.10 | − | 4933.06i | −0.105310 | − | 0.182402i | ||||
\(902\) | −3214.66 | −0.118666 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −133657. | −4.91744 | ||||||||
\(905\) | 6484.21 | + | 11231.0i | 0.238169 | + | 0.412520i | ||||
\(906\) | −29240.1 | + | 50645.4i | −1.07223 | + | 1.85715i | ||||
\(907\) | −9621.43 | + | 16664.8i | −0.352232 | + | 0.610083i | −0.986640 | − | 0.162915i | \(-0.947910\pi\) |
0.634408 | + | 0.772998i | \(0.281244\pi\) | |||||||
\(908\) | −17750.8 | − | 30745.4i | −0.648769 | − | 1.12370i | ||||
\(909\) | 2307.03 | 0.0841799 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34613.3 | 1.25882 | 0.629412 | − | 0.777072i | \(-0.283296\pi\) | ||||
0.629412 | + | 0.777072i | \(0.283296\pi\) | |||||||
\(912\) | 41051.8 | + | 71103.8i | 1.49053 | + | 2.58167i | ||||
\(913\) | 17257.9 | − | 29891.5i | 0.625578 | − | 1.08353i | ||||
\(914\) | −41550.0 | + | 71966.8i | −1.50367 | + | 2.60443i | ||||
\(915\) | −177.716 | − | 307.814i | −0.00642090 | − | 0.0111213i | ||||
\(916\) | −141275. | −5.09591 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 30328.7 | 1.09041 | ||||||||
\(919\) | −12913.2 | − | 22366.3i | −0.463511 | − | 0.802825i | 0.535622 | − | 0.844458i | \(-0.320077\pi\) |
−0.999133 | + | 0.0416333i | \(0.986744\pi\) | |||||||
\(920\) | 4655.40 | − | 8063.40i | 0.166831 | − | 0.288959i | ||||
\(921\) | −1773.50 | + | 3071.80i | −0.0634516 | + | 0.109901i | ||||
\(922\) | −38003.5 | − | 65824.0i | −1.35746 | − | 2.35119i | ||||
\(923\) | −29185.3 | −1.04079 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4928.68 | 0.175194 | ||||||||
\(926\) | 23446.9 | + | 40611.2i | 0.832087 | + | 1.44122i | ||||
\(927\) | 918.147 | − | 1590.28i | 0.0325307 | − | 0.0563448i | ||||
\(928\) | −6420.40 | + | 11120.5i | −0.227112 | + | 0.393370i | ||||
\(929\) | −9725.79 | − | 16845.6i | −0.343480 | − | 0.594925i | 0.641596 | − | 0.767042i | \(-0.278272\pi\) |
−0.985076 | + | 0.172118i | \(0.944939\pi\) | |||||||
\(930\) | −39655.1 | −1.39822 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9216.70 | −0.323930 | ||||||||
\(933\) | 17972.4 | + | 31129.1i | 0.630643 | + | 1.09231i | ||||
\(934\) | −18989.6 | + | 32890.9i | −0.665265 | + | 1.15227i | ||||
\(935\) | −4863.02 | + | 8422.99i | −0.170094 | + | 0.294611i | ||||
\(936\) | 5871.24 | + | 10169.3i | 0.205029 | + | 0.355121i | ||||
\(937\) | 34469.1 | 1.20177 | 0.600884 | − | 0.799336i | \(-0.294815\pi\) | ||||
0.600884 | + | 0.799336i | \(0.294815\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −39844.1 | −1.38473 | ||||||||
\(940\) | −19271.7 | − | 33379.5i | −0.668694 | − | 1.15821i | ||||
\(941\) | −7078.18 | + | 12259.8i | −0.245209 | + | 0.424715i | −0.962190 | − | 0.272378i | \(-0.912190\pi\) |
0.716981 | + | 0.697093i | \(0.245523\pi\) | |||||||
\(942\) | 12895.3 | − | 22335.3i | 0.446021 | − | 0.772531i | ||||
\(943\) | −146.766 | − | 254.207i | −0.00506826 | − | 0.00877848i | ||||
\(944\) | −135375. | −4.66746 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9572.13 | 0.328982 | ||||||||
\(947\) | 19046.2 | + | 32989.0i | 0.653557 | + | 1.13199i | 0.982253 | + | 0.187558i | \(0.0600574\pi\) |
−0.328696 | + | 0.944436i | \(0.606609\pi\) | |||||||
\(948\) | 42566.7 | − | 73727.6i | 1.45833 | − | 2.52591i | ||||
\(949\) | 2276.11 | − | 3942.34i | 0.0778563 | − | 0.134851i | ||||
\(950\) | −5429.47 | − | 9404.11i | −0.185427 | − | 0.321168i | ||||
\(951\) | 36234.8 | 1.23553 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5037.40 | 0.171225 | 0.0856126 | − | 0.996329i | \(-0.472715\pi\) | ||||
0.0856126 | + | 0.996329i | \(0.472715\pi\) | |||||||
\(954\) | 2201.15 | + | 3812.50i | 0.0747011 | + | 0.129386i | ||||
\(955\) | −4557.69 | + | 7894.16i | −0.154433 | + | 0.267486i | ||||
\(956\) | −59470.0 | + | 103005.i | −2.01192 | + | 3.48475i | ||||
\(957\) | −2547.94 | − | 4413.16i | −0.0860639 | − | 0.149067i | ||||
\(958\) | 98185.1 | 3.31129 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 36365.4 | 1.22259 | ||||||||
\(961\) | −34578.0 | − | 59890.9i | −1.16069 | − | 2.01037i | ||||
\(962\) | −16361.5 | + | 28339.0i | −0.548354 | + | 0.949777i | ||||
\(963\) | 576.853 | − | 999.138i | 0.0193030 | − | 0.0334338i | ||||
\(964\) | 67104.8 | + | 116229.i | 2.24201 | + | 3.88328i | ||||
\(965\) | 7705.14 | 0.257033 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11495.3 | 0.382278 | 0.191139 | − | 0.981563i | \(-0.438782\pi\) | ||||
0.191139 | + | 0.981563i | \(0.438782\pi\) | |||||||
\(968\) | −50442.7 | − | 87369.3i | −1.67489 | − | 2.90099i | ||||
\(969\) | 6953.67 | − | 12044.1i | 0.230530 | − | 0.399290i | ||||
\(970\) | 22768.5 | − | 39436.2i | 0.753662 | − | 1.30538i | ||||
\(971\) | −11176.4 | − | 19358.0i | −0.369379 | − | 0.639783i | 0.620090 | − | 0.784531i | \(-0.287096\pi\) |
−0.989469 | + | 0.144748i | \(0.953763\pi\) | |||||||
\(972\) | −31282.7 | −1.03230 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 89539.4 | 2.94561 | ||||||||
\(975\) | 1784.56 | + | 3090.94i | 0.0586170 | + | 0.101528i | ||||
\(976\) | −1677.35 | + | 2905.25i | −0.0550108 | + | 0.0952815i | ||||
\(977\) | −7172.86 | + | 12423.8i | −0.234882 | + | 0.406828i | −0.959238 | − | 0.282598i | \(-0.908804\pi\) |
0.724356 | + | 0.689426i | \(0.242137\pi\) | |||||||
\(978\) | −17026.8 | − | 29491.3i | −0.556705 | − | 0.964241i | ||||
\(979\) | 2391.94 | 0.0780867 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9216.15 | −0.299948 | ||||||||
\(982\) | −597.210 | − | 1034.40i | −0.0194071 | − | 0.0336140i | ||||
\(983\) | −17230.4 | + | 29844.0i | −0.559070 | + | 0.968338i | 0.438504 | + | 0.898729i | \(0.355508\pi\) |
−0.997574 | + | 0.0696087i | \(0.977825\pi\) | |||||||
\(984\) | 1907.09 | − | 3303.17i | 0.0617842 | − | 0.107013i | ||||
\(985\) | 1753.11 | + | 3036.47i | 0.0567093 | + | 0.0982234i | ||||
\(986\) | 4220.61 | 0.136320 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 52420.2 | 1.68796 | ||||||||
\(989\) | 437.018 | + | 756.938i | 0.0140509 | + | 0.0243369i | ||||
\(990\) | 3758.37 | − | 6509.69i | 0.120655 | − | 0.208981i | ||||
\(991\) | 17594.8 | − | 30475.1i | 0.563993 | − | 0.976864i | −0.433150 | − | 0.901322i | \(-0.642598\pi\) |
0.997143 | − | 0.0755420i | \(-0.0240687\pi\) | |||||||
\(992\) | 96441.4 | + | 167041.i | 3.08671 | + | 5.34634i | ||||
\(993\) | 22968.2 | 0.734011 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16474.8 | −0.524911 | ||||||||
\(996\) | 32780.3 | + | 56777.2i | 1.04286 | + | 1.80628i | ||||
\(997\) | 25365.0 | − | 43933.4i | 0.805734 | − | 1.39557i | −0.110060 | − | 0.993925i | \(-0.535104\pi\) |
0.915794 | − | 0.401648i | \(-0.131562\pi\) | |||||||
\(998\) | −16077.6 | + | 27847.2i | −0.509948 | + | 0.883255i | ||||
\(999\) | −14833.4 | − | 25692.2i | −0.469777 | − | 0.813678i |
(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 | 245.4.e.h.116.1 | 4 | ||
7.2 | even | 3 | inner | 245.4.e.h.226.1 | 4 | ||
7.3 | odd | 6 | 245.4.a.k.1.2 | 2 | |||
7.4 | even | 3 | 35.4.a.b.1.2 | ✓ | 2 | ||
7.5 | odd | 6 | 245.4.e.i.226.1 | 4 | |||
7.6 | odd | 2 | 245.4.e.i.116.1 | 4 | |||
21.11 | odd | 6 | 315.4.a.f.1.1 | 2 | |||
21.17 | even | 6 | 2205.4.a.u.1.1 | 2 | |||
28.11 | odd | 6 | 560.4.a.r.1.2 | 2 | |||
35.4 | even | 6 | 175.4.a.c.1.1 | 2 | |||
35.18 | odd | 12 | 175.4.b.c.99.1 | 4 | |||
35.24 | odd | 6 | 1225.4.a.m.1.1 | 2 | |||
35.32 | odd | 12 | 175.4.b.c.99.4 | 4 | |||
56.11 | odd | 6 | 2240.4.a.bo.1.1 | 2 | |||
56.53 | even | 6 | 2240.4.a.bn.1.2 | 2 | |||
105.74 | odd | 6 | 1575.4.a.z.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.a.b.1.2 | ✓ | 2 | 7.4 | even | 3 | ||
175.4.a.c.1.1 | 2 | 35.4 | even | 6 | |||
175.4.b.c.99.1 | 4 | 35.18 | odd | 12 | |||
175.4.b.c.99.4 | 4 | 35.32 | odd | 12 | |||
245.4.a.k.1.2 | 2 | 7.3 | odd | 6 | |||
245.4.e.h.116.1 | 4 | 1.1 | even | 1 | trivial | ||
245.4.e.h.226.1 | 4 | 7.2 | even | 3 | inner | ||
245.4.e.i.116.1 | 4 | 7.6 | odd | 2 | |||
245.4.e.i.226.1 | 4 | 7.5 | odd | 6 | |||
315.4.a.f.1.1 | 2 | 21.11 | odd | 6 | |||
560.4.a.r.1.2 | 2 | 28.11 | odd | 6 | |||
1225.4.a.m.1.1 | 2 | 35.24 | odd | 6 | |||
1575.4.a.z.1.2 | 2 | 105.74 | odd | 6 | |||
2205.4.a.u.1.1 | 2 | 21.17 | even | 6 | |||
2240.4.a.bn.1.2 | 2 | 56.53 | even | 6 | |||
2240.4.a.bo.1.1 | 2 | 56.11 | odd | 6 |