Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,6,Mod(2,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.2");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.d (of order \(8\), degree \(4\), 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: | \(2.72652493682\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 9.3 | ||
Character | \(\chi\) | \(=\) | 17.9 |
Dual form | 17.6.d.a.2.3 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.63520 | + | 1.63520i | −0.289066 | + | 0.289066i | −0.836711 | − | 0.547645i | \(-0.815524\pi\) |
0.547645 | + | 0.836711i | \(0.315524\pi\) | |||||||
\(3\) | 3.76372 | + | 1.55898i | 0.241443 | + | 0.100009i | 0.500124 | − | 0.865954i | \(-0.333288\pi\) |
−0.258681 | + | 0.965963i | \(0.583288\pi\) | |||||||
\(4\) | 26.6522i | 0.832882i | ||||||||
\(5\) | −7.23148 | + | 17.4583i | −0.129361 | + | 0.312304i | −0.975268 | − | 0.221026i | \(-0.929060\pi\) |
0.845907 | + | 0.533330i | \(0.179060\pi\) | |||||||
\(6\) | −8.70370 | + | 3.60519i | −0.0987020 | + | 0.0408837i | ||||
\(7\) | 93.1665 | + | 224.924i | 0.718646 | + | 1.73496i | 0.677172 | + | 0.735825i | \(0.263205\pi\) |
0.0414740 | + | 0.999140i | \(0.486795\pi\) | |||||||
\(8\) | −95.9083 | − | 95.9083i | −0.529823 | − | 0.529823i | ||||
\(9\) | −160.092 | − | 160.092i | −0.658814 | − | 0.658814i | ||||
\(10\) | −16.7230 | − | 40.3729i | −0.0528827 | − | 0.127670i | ||||
\(11\) | 522.229 | − | 216.314i | 1.30130 | − | 0.539018i | 0.378969 | − | 0.925409i | \(-0.376279\pi\) |
0.922335 | + | 0.386391i | \(0.126279\pi\) | |||||||
\(12\) | −41.5504 | + | 100.312i | −0.0832956 | + | 0.201093i | ||||
\(13\) | − | 679.500i | − | 1.11515i | −0.830128 | − | 0.557573i | \(-0.811733\pi\) | ||
0.830128 | − | 0.557573i | \(-0.188267\pi\) | |||||||
\(14\) | −520.143 | − | 215.450i | −0.709255 | − | 0.293783i | ||||
\(15\) | −54.4345 | + | 54.4345i | −0.0624664 | + | 0.0624664i | ||||
\(16\) | −539.212 | −0.526574 | ||||||||
\(17\) | 755.598 | + | 921.373i | 0.634116 | + | 0.773238i | ||||
\(18\) | 523.565 | 0.380881 | ||||||||
\(19\) | −185.984 | + | 185.984i | −0.118193 | + | 0.118193i | −0.763730 | − | 0.645536i | \(-0.776634\pi\) |
0.645536 | + | 0.763730i | \(0.276634\pi\) | |||||||
\(20\) | −465.303 | − | 192.735i | −0.260112 | − | 0.107742i | ||||
\(21\) | 991.796i | 0.490766i | ||||||||
\(22\) | −500.232 | + | 1207.67i | −0.220351 | + | 0.531974i | ||||
\(23\) | 831.458 | − | 344.401i | 0.327733 | − | 0.135752i | −0.212749 | − | 0.977107i | \(-0.568242\pi\) |
0.540483 | + | 0.841355i | \(0.318242\pi\) | |||||||
\(24\) | −211.453 | − | 510.492i | −0.0749350 | − | 0.180909i | ||||
\(25\) | 1957.21 | + | 1957.21i | 0.626307 | + | 0.626307i | ||||
\(26\) | 1111.12 | + | 1111.12i | 0.322350 | + | 0.322350i | ||||
\(27\) | −731.794 | − | 1766.71i | −0.193188 | − | 0.466396i | ||||
\(28\) | −5994.72 | + | 2483.10i | −1.44502 | + | 0.598547i | ||||
\(29\) | 1807.49 | − | 4363.67i | 0.399100 | − | 0.963512i | −0.588780 | − | 0.808293i | \(-0.700392\pi\) |
0.987880 | − | 0.155219i | \(-0.0496084\pi\) | |||||||
\(30\) | − | 178.023i | − | 0.0361138i | ||||||
\(31\) | 429.659 | + | 177.971i | 0.0803008 | + | 0.0332617i | 0.422472 | − | 0.906376i | \(-0.361162\pi\) |
−0.342171 | + | 0.939638i | \(0.611162\pi\) | |||||||
\(32\) | 3950.79 | − | 3950.79i | 0.682038 | − | 0.682038i | ||||
\(33\) | 2302.75 | 0.368097 | ||||||||
\(34\) | −2742.19 | − | 271.076i | −0.406818 | − | 0.0402155i | ||||
\(35\) | −4600.53 | −0.634801 | ||||||||
\(36\) | 4266.80 | − | 4266.80i | 0.548714 | − | 0.548714i | ||||
\(37\) | −8362.22 | − | 3463.74i | −1.00419 | − | 0.415950i | −0.180860 | − | 0.983509i | \(-0.557888\pi\) |
−0.823333 | + | 0.567558i | \(0.807888\pi\) | |||||||
\(38\) | − | 608.245i | − | 0.0683313i | ||||||
\(39\) | 1059.33 | − | 2557.45i | 0.111524 | − | 0.269244i | ||||
\(40\) | 2367.96 | − | 980.840i | 0.234004 | − | 0.0969278i | ||||
\(41\) | 3414.99 | + | 8244.51i | 0.317271 | + | 0.765959i | 0.999397 | + | 0.0347245i | \(0.0110554\pi\) |
−0.682126 | + | 0.731234i | \(0.738945\pi\) | |||||||
\(42\) | −1621.79 | − | 1621.79i | −0.141864 | − | 0.141864i | ||||
\(43\) | 6161.24 | + | 6161.24i | 0.508156 | + | 0.508156i | 0.913960 | − | 0.405804i | \(-0.133008\pi\) |
−0.405804 | + | 0.913960i | \(0.633008\pi\) | |||||||
\(44\) | 5765.25 | + | 13918.6i | 0.448938 | + | 1.08383i | ||||
\(45\) | 3952.64 | − | 1637.24i | 0.290975 | − | 0.120526i | ||||
\(46\) | −796.437 | + | 1922.77i | −0.0554954 | + | 0.133978i | ||||
\(47\) | − | 16695.6i | − | 1.10245i | −0.834358 | − | 0.551223i | \(-0.814161\pi\) | ||
0.834358 | − | 0.551223i | \(-0.185839\pi\) | |||||||
\(48\) | −2029.44 | − | 840.623i | −0.127138 | − | 0.0526621i | ||||
\(49\) | −30026.4 | + | 30026.4i | −1.78654 | + | 1.78654i | ||||
\(50\) | −6400.87 | −0.362088 | ||||||||
\(51\) | 1407.45 | + | 4645.76i | 0.0757720 | + | 0.250110i | ||||
\(52\) | 18110.2 | 0.928784 | ||||||||
\(53\) | 273.629 | − | 273.629i | 0.0133805 | − | 0.0133805i | −0.700385 | − | 0.713765i | \(-0.746988\pi\) |
0.713765 | + | 0.700385i | \(0.246988\pi\) | |||||||
\(54\) | 4085.55 | + | 1692.29i | 0.190663 | + | 0.0789752i | ||||
\(55\) | 10681.5i | 0.476130i | ||||||||
\(56\) | 12636.6 | − | 30507.5i | 0.538469 | − | 1.29998i | ||||
\(57\) | −989.941 | + | 410.047i | −0.0403573 | + | 0.0167165i | ||||
\(58\) | 4179.88 | + | 10091.1i | 0.163152 | + | 0.393885i | ||||
\(59\) | −17360.6 | − | 17360.6i | −0.649283 | − | 0.649283i | 0.303537 | − | 0.952820i | \(-0.401832\pi\) |
−0.952820 | + | 0.303537i | \(0.901832\pi\) | |||||||
\(60\) | −1450.80 | − | 1450.80i | −0.0520271 | − | 0.0520271i | ||||
\(61\) | −3933.89 | − | 9497.25i | −0.135362 | − | 0.326794i | 0.841634 | − | 0.540048i | \(-0.181594\pi\) |
−0.976997 | + | 0.213254i | \(0.931594\pi\) | |||||||
\(62\) | −993.598 | + | 411.562i | −0.0328270 | + | 0.0135974i | ||||
\(63\) | 21093.3 | − | 50923.7i | 0.669565 | − | 1.61647i | ||||
\(64\) | − | 4334.11i | − | 0.132267i | ||||||
\(65\) | 11862.9 | + | 4913.79i | 0.348264 | + | 0.144256i | ||||
\(66\) | −3765.47 | + | 3765.47i | −0.106404 | + | 0.106404i | ||||
\(67\) | −3468.50 | −0.0943962 | −0.0471981 | − | 0.998886i | \(-0.515029\pi\) | ||||
−0.0471981 | + | 0.998886i | \(0.515029\pi\) | |||||||
\(68\) | −24556.6 | + | 20138.4i | −0.644016 | + | 0.528144i | ||||
\(69\) | 3666.29 | 0.0927053 | ||||||||
\(70\) | 7522.80 | − | 7522.80i | 0.183499 | − | 0.183499i | ||||
\(71\) | −54753.6 | − | 22679.7i | −1.28904 | − | 0.533938i | −0.370341 | − | 0.928896i | \(-0.620759\pi\) |
−0.918699 | + | 0.394958i | \(0.870759\pi\) | |||||||
\(72\) | 30708.3i | 0.698110i | ||||||||
\(73\) | 7341.72 | − | 17724.5i | 0.161247 | − | 0.389284i | −0.822520 | − | 0.568736i | \(-0.807433\pi\) |
0.983767 | + | 0.179452i | \(0.0574326\pi\) | |||||||
\(74\) | 19337.9 | − | 8010.00i | 0.410515 | − | 0.170041i | ||||
\(75\) | 4315.13 | + | 10417.7i | 0.0885811 | + | 0.213854i | ||||
\(76\) | −4956.90 | − | 4956.90i | −0.0984410 | − | 0.0984410i | ||||
\(77\) | 97308.5 | + | 97308.5i | 1.87035 | + | 1.87035i | ||||
\(78\) | 2449.73 | + | 5914.17i | 0.0455913 | + | 0.110067i | ||||
\(79\) | −56793.4 | + | 23524.6i | −1.02384 | + | 0.424087i | −0.830484 | − | 0.557043i | \(-0.811936\pi\) |
−0.193352 | + | 0.981129i | \(0.561936\pi\) | |||||||
\(80\) | 3899.30 | − | 9413.74i | 0.0681180 | − | 0.164451i | ||||
\(81\) | 47225.9i | 0.799775i | ||||||||
\(82\) | −19065.7 | − | 7897.25i | −0.313125 | − | 0.129700i | ||||
\(83\) | 28179.1 | − | 28179.1i | 0.448985 | − | 0.448985i | −0.446032 | − | 0.895017i | \(-0.647163\pi\) |
0.895017 | + | 0.446032i | \(0.147163\pi\) | |||||||
\(84\) | −26433.6 | −0.408750 | ||||||||
\(85\) | −21549.7 | + | 6528.59i | −0.323515 | + | 0.0980104i | ||||
\(86\) | −20149.8 | −0.293781 | ||||||||
\(87\) | 13605.8 | − | 13605.8i | 0.192720 | − | 0.192720i | ||||
\(88\) | −70832.4 | − | 29339.7i | −0.975046 | − | 0.403877i | ||||
\(89\) | 38305.9i | 0.512614i | 0.966595 | + | 0.256307i | \(0.0825058\pi\) | ||||
−0.966595 | + | 0.256307i | \(0.917494\pi\) | |||||||
\(90\) | −3786.15 | + | 9140.57i | −0.0492710 | + | 0.118951i | ||||
\(91\) | 152836. | − | 63306.7i | 1.93474 | − | 0.801394i | ||||
\(92\) | 9179.06 | + | 22160.2i | 0.113065 | + | 0.272963i | ||||
\(93\) | 1339.66 | + | 1339.66i | 0.0160616 | + | 0.0160616i | ||||
\(94\) | 27300.7 | + | 27300.7i | 0.318679 | + | 0.318679i | ||||
\(95\) | −1902.04 | − | 4591.92i | −0.0216227 | − | 0.0522018i | ||||
\(96\) | 21028.9 | − | 8710.45i | 0.232883 | − | 0.0964633i | ||||
\(97\) | 26282.0 | − | 63450.5i | 0.283615 | − | 0.684708i | −0.716299 | − | 0.697794i | \(-0.754165\pi\) |
0.999914 | + | 0.0130854i | \(0.00416532\pi\) | |||||||
\(98\) | − | 98198.6i | − | 1.03286i | ||||||
\(99\) | −118235. | − | 48974.4i | −1.21243 | − | 0.502205i | ||||
\(100\) | −52164.0 | + | 52164.0i | −0.521640 | + | 0.521640i | ||||
\(101\) | −148424. | −1.44777 | −0.723886 | − | 0.689919i | \(-0.757646\pi\) | ||||
−0.723886 | + | 0.689919i | \(0.757646\pi\) | |||||||
\(102\) | −9898.23 | − | 5295.28i | −0.0942014 | − | 0.0503951i | ||||
\(103\) | 168356. | 1.56363 | 0.781817 | − | 0.623508i | \(-0.214293\pi\) | ||||
0.781817 | + | 0.623508i | \(0.214293\pi\) | |||||||
\(104\) | −65169.7 | + | 65169.7i | −0.590830 | + | 0.590830i | ||||
\(105\) | −17315.1 | − | 7172.15i | −0.153268 | − | 0.0634858i | ||||
\(106\) | 894.877i | 0.00773568i | ||||||||
\(107\) | 45720.7 | − | 110380.i | 0.386059 | − | 0.932028i | −0.604708 | − | 0.796448i | \(-0.706710\pi\) |
0.990766 | − | 0.135581i | \(-0.0432900\pi\) | |||||||
\(108\) | 47086.6 | − | 19503.9i | 0.388453 | − | 0.160902i | ||||
\(109\) | 46496.7 | + | 112253.i | 0.374849 | + | 0.904965i | 0.992914 | + | 0.118838i | \(0.0379168\pi\) |
−0.618065 | + | 0.786127i | \(0.712083\pi\) | |||||||
\(110\) | −17466.4 | − | 17466.4i | −0.137633 | − | 0.137633i | ||||
\(111\) | −26073.1 | − | 26073.1i | −0.200857 | − | 0.200857i | ||||
\(112\) | −50236.5 | − | 121282.i | −0.378420 | − | 0.913588i | ||||
\(113\) | 80565.3 | − | 33371.2i | 0.593542 | − | 0.245853i | −0.0656314 | − | 0.997844i | \(-0.520906\pi\) |
0.659174 | + | 0.751991i | \(0.270906\pi\) | |||||||
\(114\) | 948.244 | − | 2289.26i | 0.00683373 | − | 0.0164981i | ||||
\(115\) | 17006.4i | 0.119913i | ||||||||
\(116\) | 116302. | + | 48173.7i | 0.802492 | + | 0.332403i | ||||
\(117\) | −108782. | + | 108782.i | −0.734673 | + | 0.734673i | ||||
\(118\) | 56776.1 | 0.375371 | ||||||||
\(119\) | −136842. | + | 255793.i | −0.885836 | + | 1.65585i | ||||
\(120\) | 10441.4 | 0.0661923 | ||||||||
\(121\) | 112051. | − | 112051.i | 0.695746 | − | 0.695746i | ||||
\(122\) | 21962.6 | + | 9097.23i | 0.133593 | + | 0.0553362i | ||||
\(123\) | 36354.0i | 0.216665i | ||||||||
\(124\) | −4743.31 | + | 11451.4i | −0.0277031 | + | 0.0668811i | ||||
\(125\) | −102880. | + | 42614.5i | −0.588922 | + | 0.243939i | ||||
\(126\) | 48778.8 | + | 117762.i | 0.273719 | + | 0.660815i | ||||
\(127\) | −138220. | − | 138220.i | −0.760434 | − | 0.760434i | 0.215967 | − | 0.976401i | \(-0.430710\pi\) |
−0.976401 | + | 0.215967i | \(0.930710\pi\) | |||||||
\(128\) | 133512. | + | 133512.i | 0.720272 | + | 0.720272i | ||||
\(129\) | 13583.9 | + | 32794.5i | 0.0718705 | + | 0.173511i | ||||
\(130\) | −27433.4 | + | 11363.3i | −0.142371 | + | 0.0589719i | ||||
\(131\) | −22432.9 | + | 54157.7i | −0.114211 | + | 0.275729i | −0.970641 | − | 0.240534i | \(-0.922677\pi\) |
0.856430 | + | 0.516263i | \(0.172677\pi\) | |||||||
\(132\) | 61373.5i | 0.306582i | ||||||||
\(133\) | −59159.9 | − | 24504.8i | −0.290000 | − | 0.120122i | ||||
\(134\) | 5671.70 | − | 5671.70i | 0.0272867 | − | 0.0272867i | ||||
\(135\) | 36135.7 | 0.170648 | ||||||||
\(136\) | 15899.2 | − | 160835.i | 0.0737102 | − | 0.745649i | ||||
\(137\) | −101634. | −0.462636 | −0.231318 | − | 0.972878i | \(-0.574304\pi\) | ||||
−0.231318 | + | 0.972878i | \(0.574304\pi\) | |||||||
\(138\) | −5995.13 | + | 5995.13i | −0.0267979 | + | 0.0267979i | ||||
\(139\) | 60555.6 | + | 25083.0i | 0.265838 | + | 0.110114i | 0.511621 | − | 0.859211i | \(-0.329045\pi\) |
−0.245783 | + | 0.969325i | \(0.579045\pi\) | |||||||
\(140\) | − | 122614.i | − | 0.528714i | ||||||
\(141\) | 26028.2 | − | 62837.6i | 0.110254 | − | 0.266178i | ||||
\(142\) | 126619. | − | 52447.3i | 0.526961 | − | 0.218274i | ||||
\(143\) | −146986. | − | 354855.i | −0.601083 | − | 1.45114i | ||||
\(144\) | 86323.4 | + | 86323.4i | 0.346914 | + | 0.346914i | ||||
\(145\) | 63111.6 | + | 63111.6i | 0.249281 | + | 0.249281i | ||||
\(146\) | 16977.9 | + | 40988.3i | 0.0659177 | + | 0.159139i | ||||
\(147\) | −159822. | + | 66200.4i | −0.610018 | + | 0.252678i | ||||
\(148\) | 92316.5 | − | 222872.i | 0.346438 | − | 0.836374i | ||||
\(149\) | − | 4198.73i | − | 0.0154936i | −0.999970 | − | 0.00774679i | \(-0.997534\pi\) | ||
0.999970 | − | 0.00774679i | \(-0.00246591\pi\) | |||||||
\(150\) | −24091.1 | − | 9978.86i | −0.0874235 | − | 0.0362120i | ||||
\(151\) | 31506.0 | − | 31506.0i | 0.112448 | − | 0.112448i | −0.648644 | − | 0.761092i | \(-0.724664\pi\) |
0.761092 | + | 0.648644i | \(0.224664\pi\) | |||||||
\(152\) | 35674.9 | 0.125243 | ||||||||
\(153\) | 26539.2 | − | 268469.i | 0.0916557 | − | 0.927184i | ||||
\(154\) | −318238. | −1.08131 | ||||||||
\(155\) | −6214.14 | + | 6214.14i | −0.0207755 | + | 0.0207755i | ||||
\(156\) | 68161.7 | + | 28233.5i | 0.224248 | + | 0.0928867i | ||||
\(157\) | 12962.5i | 0.0419701i | 0.999780 | + | 0.0209851i | \(0.00668024\pi\) | ||||
−0.999780 | + | 0.0209851i | \(0.993320\pi\) | |||||||
\(158\) | 54401.3 | − | 131336.i | 0.173367 | − | 0.418545i | ||||
\(159\) | 1456.45 | − | 603.279i | 0.00456879 | − | 0.00189246i | ||||
\(160\) | 40404.1 | + | 97544.2i | 0.124774 | + | 0.301232i | ||||
\(161\) | 154928. | + | 154928.i | 0.471049 | + | 0.471049i | ||||
\(162\) | −77224.0 | − | 77224.0i | −0.231188 | − | 0.231188i | ||||
\(163\) | 137817. | + | 332720.i | 0.406288 | + | 0.980865i | 0.986106 | + | 0.166119i | \(0.0531237\pi\) |
−0.579818 | + | 0.814746i | \(0.696876\pi\) | |||||||
\(164\) | −219735. | + | 91017.1i | −0.637953 | + | 0.264249i | ||||
\(165\) | −16652.3 | + | 40202.2i | −0.0476173 | + | 0.114958i | ||||
\(166\) | 92157.1i | 0.259573i | ||||||||
\(167\) | 290558. | + | 120353.i | 0.806197 | + | 0.333938i | 0.747436 | − | 0.664334i | \(-0.231285\pi\) |
0.0587616 | + | 0.998272i | \(0.481285\pi\) | |||||||
\(168\) | 95121.5 | − | 95121.5i | 0.260019 | − | 0.260019i | ||||
\(169\) | −90427.8 | −0.243548 | ||||||||
\(170\) | 24562.6 | − | 45913.8i | 0.0651857 | − | 0.121849i | ||||
\(171\) | 59549.2 | 0.155735 | ||||||||
\(172\) | −164211. | + | 164211.i | −0.423234 | + | 0.423234i | ||||
\(173\) | −21768.4 | − | 9016.75i | −0.0552981 | − | 0.0229052i | 0.354863 | − | 0.934918i | \(-0.384528\pi\) |
−0.410161 | + | 0.912013i | \(0.634528\pi\) | |||||||
\(174\) | 44496.5i | 0.111417i | ||||||||
\(175\) | −257877. | + | 622570.i | −0.636528 | + | 1.53671i | ||||
\(176\) | −281592. | + | 116639.i | −0.685234 | + | 0.283833i | ||||
\(177\) | −38275.5 | − | 92405.2i | −0.0918306 | − | 0.221699i | ||||
\(178\) | −62637.9 | − | 62637.9i | −0.148179 | − | 0.148179i | ||||
\(179\) | −238431. | − | 238431.i | −0.556198 | − | 0.556198i | 0.372025 | − | 0.928223i | \(-0.378664\pi\) |
−0.928223 | + | 0.372025i | \(0.878664\pi\) | |||||||
\(180\) | 43636.0 | + | 105347.i | 0.100384 | + | 0.242348i | ||||
\(181\) | 560632. | − | 232222.i | 1.27198 | − | 0.526873i | 0.358417 | − | 0.933561i | \(-0.383317\pi\) |
0.913567 | + | 0.406688i | \(0.133317\pi\) | |||||||
\(182\) | −146398. | + | 353437.i | −0.327611 | + | 0.790922i | ||||
\(183\) | − | 41877.9i | − | 0.0924394i | ||||||
\(184\) | −112775. | − | 46712.8i | −0.245565 | − | 0.101716i | ||||
\(185\) | 120942. | − | 120942.i | 0.259806 | − | 0.259806i | ||||
\(186\) | −4381.25 | −0.00928571 | ||||||||
\(187\) | 593901. | + | 317721.i | 1.24197 | + | 0.664418i | ||||
\(188\) | 444975. | 0.918207 | ||||||||
\(189\) | 329196. | − | 329196.i | 0.670347 | − | 0.670347i | ||||
\(190\) | 10618.9 | + | 4398.51i | 0.0213401 | + | 0.00883937i | ||||
\(191\) | − | 192675.i | − | 0.382158i | −0.981575 | − | 0.191079i | \(-0.938801\pi\) | ||
0.981575 | − | 0.191079i | \(-0.0611986\pi\) | |||||||
\(192\) | 6756.82 | − | 16312.4i | 0.0132278 | − | 0.0319348i | ||||
\(193\) | −786968. | + | 325973.i | −1.52077 | + | 0.629924i | −0.977746 | − | 0.209793i | \(-0.932721\pi\) |
−0.543024 | + | 0.839717i | \(0.682721\pi\) | |||||||
\(194\) | 60777.9 | + | 146731.i | 0.115942 | + | 0.279909i | ||||
\(195\) | 36988.3 | + | 36988.3i | 0.0696591 | + | 0.0696591i | ||||
\(196\) | −800271. | − | 800271.i | −1.48798 | − | 1.48798i | ||||
\(197\) | −356519. | − | 860713.i | −0.654512 | − | 1.58013i | −0.806161 | − | 0.591696i | \(-0.798458\pi\) |
0.151649 | − | 0.988434i | \(-0.451542\pi\) | |||||||
\(198\) | 273421. | − | 113255.i | 0.495642 | − | 0.205302i | ||||
\(199\) | −144810. | + | 349602.i | −0.259219 | + | 0.625809i | −0.998887 | − | 0.0471622i | \(-0.984982\pi\) |
0.739669 | + | 0.672971i | \(0.234982\pi\) | |||||||
\(200\) | − | 375425.i | − | 0.663664i | ||||||
\(201\) | −13054.5 | − | 5407.33i | −0.0227913 | − | 0.00944046i | ||||
\(202\) | 242703. | − | 242703.i | 0.418501 | − | 0.418501i | ||||
\(203\) | 1.14989e6 | 1.95847 | ||||||||
\(204\) | −123820. | + | 37511.8i | −0.208312 | + | 0.0631092i | ||||
\(205\) | −168631. | −0.280254 | ||||||||
\(206\) | −275296. | + | 275296.i | −0.451993 | + | 0.451993i | ||||
\(207\) | −188245. | − | 77973.8i | −0.305350 | − | 0.126480i | ||||
\(208\) | 366395.i | 0.587207i | ||||||||
\(209\) | −56895.3 | + | 137357.i | −0.0900971 | + | 0.217514i | ||||
\(210\) | 40041.6 | − | 16585.8i | 0.0626561 | − | 0.0259530i | ||||
\(211\) | −207050. | − | 499863.i | −0.320161 | − | 0.772938i | −0.999244 | − | 0.0388759i | \(-0.987622\pi\) |
0.679083 | − | 0.734062i | \(-0.262378\pi\) | |||||||
\(212\) | 7292.81 | + | 7292.81i | 0.0111444 | + | 0.0111444i | ||||
\(213\) | −170720. | − | 170720.i | −0.257831 | − | 0.257831i | ||||
\(214\) | 105730. | + | 255256.i | 0.157821 | + | 0.381014i | ||||
\(215\) | −152120. | + | 63010.1i | −0.224435 | + | 0.0929639i | ||||
\(216\) | −99256.7 | + | 239627.i | −0.144752 | + | 0.349463i | ||||
\(217\) | 113222.i | 0.163222i | ||||||||
\(218\) | −259588. | − | 107525.i | −0.369950 | − | 0.153238i | ||||
\(219\) | 55264.4 | − | 55264.4i | 0.0778637 | − | 0.0778637i | ||||
\(220\) | −284686. | −0.396560 | ||||||||
\(221\) | 626073. | − | 513429.i | 0.862273 | − | 0.707131i | ||||
\(222\) | 85269.8 | 0.116121 | ||||||||
\(223\) | −600257. | + | 600257.i | −0.808305 | + | 0.808305i | −0.984377 | − | 0.176072i | \(-0.943661\pi\) |
0.176072 | + | 0.984377i | \(0.443661\pi\) | |||||||
\(224\) | 1.25671e6 | + | 520545.i | 1.67346 | + | 0.693168i | ||||
\(225\) | − | 626666.i | − | 0.825240i | ||||||
\(226\) | −77171.8 | + | 186309.i | −0.100505 | + | 0.242641i | ||||
\(227\) | −15428.9 | + | 6390.85i | −0.0198733 | + | 0.00823179i | −0.392598 | − | 0.919710i | \(-0.628424\pi\) |
0.372725 | + | 0.927942i | \(0.378424\pi\) | |||||||
\(228\) | −10928.7 | − | 26384.1i | −0.0139229 | − | 0.0336129i | ||||
\(229\) | 969150. | + | 969150.i | 1.22124 | + | 1.22124i | 0.967190 | + | 0.254053i | \(0.0817637\pi\) |
0.254053 | + | 0.967190i | \(0.418236\pi\) | |||||||
\(230\) | −27808.9 | − | 27808.9i | −0.0346629 | − | 0.0346629i | ||||
\(231\) | 214540. | + | 517944.i | 0.264532 | + | 0.638636i | ||||
\(232\) | −591866. | + | 245159.i | −0.721944 | + | 0.299039i | ||||
\(233\) | −295154. | + | 712564.i | −0.356171 | + | 0.859873i | 0.639660 | + | 0.768658i | \(0.279075\pi\) |
−0.995831 | + | 0.0912150i | \(0.970925\pi\) | |||||||
\(234\) | − | 355763.i | − | 0.424738i | ||||||
\(235\) | 291477. | + | 120734.i | 0.344298 | + | 0.142613i | ||||
\(236\) | 462698. | − | 462698.i | 0.540776 | − | 0.540776i | ||||
\(237\) | −250429. | −0.289610 | ||||||||
\(238\) | −194509. | − | 642039.i | −0.222586 | − | 0.734715i | ||||
\(239\) | −1.38078e6 | −1.56361 | −0.781807 | − | 0.623520i | \(-0.785702\pi\) | ||||
−0.781807 | + | 0.623520i | \(0.785702\pi\) | |||||||
\(240\) | 29351.8 | − | 29351.8i | 0.0328932 | − | 0.0328932i | ||||
\(241\) | −279297. | − | 115688.i | −0.309758 | − | 0.128306i | 0.222389 | − | 0.974958i | \(-0.428615\pi\) |
−0.532147 | + | 0.846652i | \(0.678615\pi\) | |||||||
\(242\) | 366451.i | 0.402233i | ||||||||
\(243\) | −251450. | + | 607055.i | −0.273172 | + | 0.659496i | ||||
\(244\) | 253123. | − | 104847.i | 0.272180 | − | 0.112741i | ||||
\(245\) | −307076. | − | 741347.i | −0.326837 | − | 0.789053i | ||||
\(246\) | −59446.1 | − | 59446.1i | −0.0626305 | − | 0.0626305i | ||||
\(247\) | 126377. | + | 126377.i | 0.131803 | + | 0.131803i | ||||
\(248\) | −24139.0 | − | 58276.7i | −0.0249224 | − | 0.0601681i | ||||
\(249\) | 149989. | − | 62127.5i | 0.153307 | − | 0.0635018i | ||||
\(250\) | 98547.1 | − | 237914.i | 0.0997226 | − | 0.240752i | ||||
\(251\) | 1.92044e6i | 1.92405i | 0.272967 | + | 0.962024i | \(0.411995\pi\) | ||||
−0.272967 | + | 0.962024i | \(0.588005\pi\) | |||||||
\(252\) | 1.35723e6 | + | 562183.i | 1.34633 | + | 0.557669i | ||||
\(253\) | 359712. | − | 359712.i | 0.353308 | − | 0.353308i | ||||
\(254\) | 452035. | 0.439631 | ||||||||
\(255\) | −91285.2 | − | 9023.88i | −0.0879123 | − | 0.00869047i | ||||
\(256\) | −297948. | −0.284145 | ||||||||
\(257\) | 894019. | − | 894019.i | 0.844333 | − | 0.844333i | −0.145086 | − | 0.989419i | \(-0.546346\pi\) |
0.989419 | + | 0.145086i | \(0.0463458\pi\) | |||||||
\(258\) | −75838.1 | − | 31413.2i | −0.0709313 | − | 0.0293807i | ||||
\(259\) | − | 2.20357e6i | − | 2.04116i | ||||||
\(260\) | −130963. | + | 316174.i | −0.120148 | + | 0.290063i | ||||
\(261\) | −987953. | + | 409224.i | −0.897708 | + | 0.371843i | ||||
\(262\) | −51876.6 | − | 125241.i | −0.0466894 | − | 0.112718i | ||||
\(263\) | −996801. | − | 996801.i | −0.888626 | − | 0.888626i | 0.105765 | − | 0.994391i | \(-0.466271\pi\) |
−0.994391 | + | 0.105765i | \(0.966271\pi\) | |||||||
\(264\) | −220853. | − | 220853.i | −0.195027 | − | 0.195027i | ||||
\(265\) | 2798.36 | + | 6755.84i | 0.00244787 | + | 0.00590969i | ||||
\(266\) | 136809. | − | 56668.1i | 0.118552 | − | 0.0491060i | ||||
\(267\) | −59718.3 | + | 144173.i | −0.0512660 | + | 0.123767i | ||||
\(268\) | − | 92443.2i | − | 0.0786209i | ||||||
\(269\) | −1.60063e6 | − | 663004.i | −1.34869 | − | 0.558644i | −0.412760 | − | 0.910840i | \(-0.635435\pi\) |
−0.935927 | + | 0.352195i | \(0.885435\pi\) | |||||||
\(270\) | −59089.2 | + | 59089.2i | −0.0493286 | + | 0.0493286i | ||||
\(271\) | 220184. | 0.182122 | 0.0910609 | − | 0.995845i | \(-0.470974\pi\) | ||||
0.0910609 | + | 0.995845i | \(0.470974\pi\) | |||||||
\(272\) | −407428. | − | 496816.i | −0.333909 | − | 0.407167i | ||||
\(273\) | 673926. | 0.547275 | ||||||||
\(274\) | 166193. | − | 166193.i | 0.133732 | − | 0.133732i | ||||
\(275\) | 1.44548e6 | + | 598739.i | 1.15261 | + | 0.477425i | ||||
\(276\) | 97714.9i | 0.0772126i | ||||||||
\(277\) | 113571. | − | 274185.i | 0.0889343 | − | 0.214706i | −0.873154 | − | 0.487444i | \(-0.837929\pi\) |
0.962088 | + | 0.272738i | \(0.0879292\pi\) | |||||||
\(278\) | −140036. | + | 58005.0i | −0.108675 | + | 0.0450146i | ||||
\(279\) | −40293.3 | − | 97276.6i | −0.0309900 | − | 0.0748165i | ||||
\(280\) | 441229. | + | 441229.i | 0.336332 | + | 0.336332i | ||||
\(281\) | −433271. | − | 433271.i | −0.327336 | − | 0.327336i | 0.524237 | − | 0.851573i | \(-0.324351\pi\) |
−0.851573 | + | 0.524237i | \(0.824351\pi\) | |||||||
\(282\) | 60190.8 | + | 145314.i | 0.0450721 | + | 0.108814i | ||||
\(283\) | 1.55254e6 | − | 643084.i | 1.15233 | − | 0.477311i | 0.277016 | − | 0.960865i | \(-0.410654\pi\) |
0.875314 | + | 0.483554i | \(0.160654\pi\) | |||||||
\(284\) | 604464. | − | 1.45930e6i | 0.444707 | − | 1.07362i | ||||
\(285\) | − | 20248.0i | − | 0.0147662i | ||||||
\(286\) | 820610. | + | 339908.i | 0.593228 | + | 0.245723i | ||||
\(287\) | −1.53623e6 | + | 1.53623e6i | −1.10091 | + | 1.10091i | ||||
\(288\) | −1.26498e6 | −0.898672 | ||||||||
\(289\) | −278000. | + | 1.39238e6i | −0.195794 | + | 0.980645i | ||||
\(290\) | −206401. | −0.144117 | ||||||||
\(291\) | 197837. | − | 197837.i | 0.136954 | − | 0.136954i | ||||
\(292\) | 472397. | + | 195673.i | 0.324227 | + | 0.134299i | ||||
\(293\) | 1.96047e6i | 1.33411i | 0.745010 | + | 0.667053i | \(0.232445\pi\) | ||||
−0.745010 | + | 0.667053i | \(0.767555\pi\) | |||||||
\(294\) | 153090. | − | 369592.i | 0.103295 | − | 0.249376i | ||||
\(295\) | 428629. | − | 177544.i | 0.286765 | − | 0.118782i | ||||
\(296\) | 469804. | + | 1.13421e6i | 0.311665 | + | 0.752425i | ||||
\(297\) | −764327. | − | 764327.i | −0.502792 | − | 0.502792i | ||||
\(298\) | 6865.77 | + | 6865.77i | 0.00447867 | + | 0.00447867i | ||||
\(299\) | −234021. | − | 564976.i | −0.151383 | − | 0.365470i | ||||
\(300\) | −277654. | + | 115008.i | −0.178115 | + | 0.0737776i | ||||
\(301\) | −811789. | + | 1.95983e6i | −0.516449 | + | 1.24682i | ||||
\(302\) | 103037.i | 0.0650096i | ||||||||
\(303\) | −558626. | − | 231391.i | −0.349554 | − | 0.144790i | ||||
\(304\) | 100285. | − | 100285.i | 0.0622375 | − | 0.0622375i | ||||
\(305\) | 194254. | 0.119570 | ||||||||
\(306\) | 395605. | + | 482399.i | 0.241523 | + | 0.294512i | ||||
\(307\) | 2.05597e6 | 1.24500 | 0.622501 | − | 0.782619i | \(-0.286116\pi\) | ||||
0.622501 | + | 0.782619i | \(0.286116\pi\) | |||||||
\(308\) | −2.59349e6 | + | 2.59349e6i | −1.55778 | + | 1.55778i | ||||
\(309\) | 633644. | + | 262464.i | 0.377528 | + | 0.156377i | ||||
\(310\) | − | 20322.8i | − | 0.0120110i | ||||||
\(311\) | 345978. | − | 835266.i | 0.202837 | − | 0.489693i | −0.789426 | − | 0.613846i | \(-0.789622\pi\) |
0.992263 | + | 0.124153i | \(0.0396215\pi\) | |||||||
\(312\) | −346879. | + | 143682.i | −0.201740 | + | 0.0835634i | ||||
\(313\) | 42712.7 | + | 103117.i | 0.0246431 | + | 0.0594938i | 0.935722 | − | 0.352738i | \(-0.114749\pi\) |
−0.911079 | + | 0.412232i | \(0.864749\pi\) | |||||||
\(314\) | −21196.3 | − | 21196.3i | −0.0121321 | − | 0.0121321i | ||||
\(315\) | 736507. | + | 736507.i | 0.418216 | + | 0.418216i | ||||
\(316\) | −626983. | − | 1.51367e6i | −0.353214 | − | 0.852735i | ||||
\(317\) | −155657. | + | 64475.3i | −0.0870004 | + | 0.0360367i | −0.425759 | − | 0.904837i | \(-0.639993\pi\) |
0.338759 | + | 0.940873i | \(0.389993\pi\) | |||||||
\(318\) | −1395.10 | + | 3368.07i | −0.000773637 | + | 0.00186773i | ||||
\(319\) | − | 2.66982e6i | − | 1.46895i | ||||||
\(320\) | 75666.4 | + | 31342.0i | 0.0413074 | + | 0.0171101i | ||||
\(321\) | 344160. | − | 344160.i | 0.186422 | − | 0.186422i | ||||
\(322\) | −506678. | −0.272328 | ||||||||
\(323\) | −311891. | − | 30831.6i | −0.166340 | − | 0.0164433i | ||||
\(324\) | −1.25868e6 | −0.666118 | ||||||||
\(325\) | 1.32992e6 | − | 1.32992e6i | 0.698423 | − | 0.698423i | ||||
\(326\) | −769423. | − | 318705.i | −0.400978 | − | 0.166091i | ||||
\(327\) | 494977.i | 0.255985i | ||||||||
\(328\) | 463191. | − | 1.11824e6i | 0.237726 | − | 0.573920i | ||||
\(329\) | 3.75524e6 | − | 1.55547e6i | 1.91270 | − | 0.792268i | ||||
\(330\) | −38508.9 | − | 92968.7i | −0.0194660 | − | 0.0469950i | ||||
\(331\) | −25528.7 | − | 25528.7i | −0.0128073 | − | 0.0128073i | 0.700674 | − | 0.713481i | \(-0.252883\pi\) |
−0.713481 | + | 0.700674i | \(0.752883\pi\) | |||||||
\(332\) | 751036. | + | 751036.i | 0.373952 | + | 0.373952i | ||||
\(333\) | 784206. | + | 1.89324e6i | 0.387542 | + | 0.935610i | ||||
\(334\) | −671922. | + | 278319.i | −0.329574 | + | 0.136514i | ||||
\(335\) | 25082.4 | − | 60554.2i | 0.0122111 | − | 0.0294803i | ||||
\(336\) | − | 534789.i | − | 0.258425i | ||||||
\(337\) | −1.58897e6 | − | 658174.i | −0.762152 | − | 0.315694i | −0.0324631 | − | 0.999473i | \(-0.510335\pi\) |
−0.729689 | + | 0.683779i | \(0.760335\pi\) | |||||||
\(338\) | 147868. | − | 147868.i | 0.0704015 | − | 0.0704015i | ||||
\(339\) | 355250. | 0.167894 | ||||||||
\(340\) | −174002. | − | 574348.i | −0.0816311 | − | 0.269450i | ||||
\(341\) | 262878. | 0.122424 | ||||||||
\(342\) | −97375.0 | + | 97375.0i | −0.0450176 | + | 0.0450176i | ||||
\(343\) | −5.77083e6 | − | 2.39035e6i | −2.64852 | − | 1.09705i | ||||
\(344\) | − | 1.18183e6i | − | 0.538466i | ||||||
\(345\) | −26512.7 | + | 64007.4i | −0.0119924 | + | 0.0289522i | ||||
\(346\) | 50339.9 | − | 20851.5i | 0.0226059 | − | 0.00936368i | ||||
\(347\) | −206624. | − | 498835.i | −0.0921207 | − | 0.222399i | 0.871103 | − | 0.491101i | \(-0.163405\pi\) |
−0.963223 | + | 0.268702i | \(0.913405\pi\) | |||||||
\(348\) | 362625. | + | 362625.i | 0.160513 | + | 0.160513i | ||||
\(349\) | 2.15125e6 | + | 2.15125e6i | 0.945423 | + | 0.945423i | 0.998586 | − | 0.0531625i | \(-0.0169301\pi\) |
−0.0531625 | + | 0.998586i | \(0.516930\pi\) | |||||||
\(350\) | −596347. | − | 1.43971e6i | −0.260213 | − | 0.628210i | ||||
\(351\) | −1.20048e6 | + | 497254.i | −0.520099 | + | 0.215432i | ||||
\(352\) | 1.20860e6 | − | 2.91782e6i | 0.519908 | − | 1.25517i | ||||
\(353\) | 3.85998e6i | 1.64873i | 0.566061 | + | 0.824363i | \(0.308467\pi\) | ||||
−0.566061 | + | 0.824363i | \(0.691533\pi\) | |||||||
\(354\) | 213689. | + | 88513.0i | 0.0906306 | + | 0.0375404i | ||||
\(355\) | 791898. | − | 791898.i | 0.333502 | − | 0.333502i | ||||
\(356\) | −1.02094e6 | −0.426947 | ||||||||
\(357\) | −913815. | + | 749400.i | −0.379479 | + | 0.311202i | ||||
\(358\) | 779765. | 0.321556 | ||||||||
\(359\) | 2.57202e6 | − | 2.57202e6i | 1.05326 | − | 1.05326i | 0.0547655 | − | 0.998499i | \(-0.482559\pi\) |
0.998499 | − | 0.0547655i | \(-0.0174411\pi\) | |||||||
\(360\) | −536115. | − | 222066.i | −0.218023 | − | 0.0903080i | ||||
\(361\) | 2.40692e6i | 0.972061i | ||||||||
\(362\) | −537018. | + | 1.29648e6i | −0.215386 | + | 0.519988i | ||||
\(363\) | 596412. | − | 247042.i | 0.237564 | − | 0.0984021i | ||||
\(364\) | 1.68726e6 | + | 4.07342e6i | 0.667467 | + | 1.61141i | ||||
\(365\) | 256348. | + | 256348.i | 0.100716 | + | 0.100716i | ||||
\(366\) | 68478.9 | + | 68478.9i | 0.0267211 | + | 0.0267211i | ||||
\(367\) | 75604.9 | + | 182526.i | 0.0293012 | + | 0.0707393i | 0.937853 | − | 0.347033i | \(-0.112811\pi\) |
−0.908552 | + | 0.417773i | \(0.862811\pi\) | |||||||
\(368\) | −448332. | + | 185705.i | −0.172576 | + | 0.0714833i | ||||
\(369\) | 773167. | − | 1.86659e6i | 0.295602 | − | 0.713647i | ||||
\(370\) | 395531.i | 0.150202i | ||||||||
\(371\) | 87038.7 | + | 36052.6i | 0.0328305 | + | 0.0135988i | ||||
\(372\) | −35705.0 | + | 35705.0i | −0.0133774 | + | 0.0133774i | ||||
\(373\) | 456411. | 0.169857 | 0.0849286 | − | 0.996387i | \(-0.472934\pi\) | ||||
0.0849286 | + | 0.996387i | \(0.472934\pi\) | |||||||
\(374\) | −1.49069e6 | + | 451611.i | −0.551071 | + | 0.166950i | ||||
\(375\) | −453649. | −0.166587 | ||||||||
\(376\) | −1.60125e6 | + | 1.60125e6i | −0.584102 | + | 0.584102i | ||||
\(377\) | −2.96512e6 | − | 1.22819e6i | −1.07446 | − | 0.445054i | ||||
\(378\) | 1.07660e6i | 0.387549i | ||||||||
\(379\) | −333763. | + | 805776.i | −0.119355 | + | 0.288148i | −0.972254 | − | 0.233927i | \(-0.924842\pi\) |
0.852899 | + | 0.522076i | \(0.174842\pi\) | |||||||
\(380\) | 122385. | − | 50693.5i | 0.0434779 | − | 0.0180092i | ||||
\(381\) | −304739. | − | 735704.i | −0.107551 | − | 0.259651i | ||||
\(382\) | 315063. | + | 315063.i | 0.110469 | + | 0.110469i | ||||
\(383\) | 2.45820e6 | + | 2.45820e6i | 0.856290 | + | 0.856290i | 0.990899 | − | 0.134608i | \(-0.0429777\pi\) |
−0.134608 | + | 0.990899i | \(0.542978\pi\) | |||||||
\(384\) | 294360. | + | 710647.i | 0.101871 | + | 0.245938i | ||||
\(385\) | −2.40253e6 | + | 995160.i | −0.826069 | + | 0.342169i | ||||
\(386\) | 753820. | − | 1.81988e6i | 0.257513 | − | 0.621692i | ||||
\(387\) | − | 1.97273e6i | − | 0.669561i | ||||||
\(388\) | 1.69110e6 | + | 700475.i | 0.570281 | + | 0.236218i | ||||
\(389\) | −2.62779e6 | + | 2.62779e6i | −0.880474 | + | 0.880474i | −0.993583 | − | 0.113109i | \(-0.963919\pi\) |
0.113109 | + | 0.993583i | \(0.463919\pi\) | |||||||
\(390\) | −120967. | −0.0402721 | ||||||||
\(391\) | 945570. | + | 505854.i | 0.312789 | + | 0.167334i | ||||
\(392\) | 5.75957e6 | 1.89310 | ||||||||
\(393\) | −168862. | + | 168862.i | −0.0551507 | + | 0.0551507i | ||||
\(394\) | 1.99042e6 | + | 824460.i | 0.645959 | + | 0.267565i | ||||
\(395\) | − | 1.16164e6i | − | 0.374608i | ||||||
\(396\) | 1.30528e6 | − | 3.15122e6i | 0.418277 | − | 1.00981i | ||||
\(397\) | −99333.6 | + | 41145.3i | −0.0316315 | + | 0.0131022i | −0.398443 | − | 0.917193i | \(-0.630449\pi\) |
0.366812 | + | 0.930295i | \(0.380449\pi\) | |||||||
\(398\) | −334877. | − | 808465.i | −0.105969 | − | 0.255831i | ||||
\(399\) | −184459. | − | 184459.i | −0.0580052 | − | 0.0580052i | ||||
\(400\) | −1.05535e6 | − | 1.05535e6i | −0.329797 | − | 0.329797i | ||||
\(401\) | 746631. | + | 1.80253e6i | 0.231870 | + | 0.559784i | 0.996397 | − | 0.0848072i | \(-0.0270274\pi\) |
−0.764527 | + | 0.644592i | \(0.777027\pi\) | |||||||
\(402\) | 30188.8 | − | 12504.6i | 0.00931709 | − | 0.00385927i | ||||
\(403\) | 120931. | − | 291954.i | 0.0370916 | − | 0.0895470i | ||||
\(404\) | − | 3.95583e6i | − | 1.20582i | ||||||
\(405\) | −824486. | − | 341513.i | −0.249773 | − | 0.103459i | ||||
\(406\) | −1.88031e6 | + | 1.88031e6i | −0.566127 | + | 0.566127i | ||||
\(407\) | −5.11625e6 | −1.53097 | ||||||||
\(408\) | 310580. | − | 580553.i | 0.0923684 | − | 0.172660i | ||||
\(409\) | −3.85305e6 | −1.13893 | −0.569464 | − | 0.822016i | \(-0.692849\pi\) | ||||
−0.569464 | + | 0.822016i | \(0.692849\pi\) | |||||||
\(410\) | 275746. | − | 275746.i | 0.0810120 | − | 0.0810120i | ||||
\(411\) | −382523. | − | 158446.i | −0.111700 | − | 0.0462677i | ||||
\(412\) | 4.48705e6i | 1.30232i | ||||||||
\(413\) | 2.28738e6 | − | 5.52223e6i | 0.659878 | − | 1.59309i | ||||
\(414\) | 435322. | − | 180316.i | 0.124827 | − | 0.0517052i | ||||
\(415\) | 288184. | + | 695737.i | 0.0821389 | + | 0.198301i | ||||
\(416\) | −2.68456e6 | − | 2.68456e6i | −0.760571 | − | 0.760571i | ||||
\(417\) | 188811. | + | 188811.i | 0.0531724 | + | 0.0531724i | ||||
\(418\) | −131572. | − | 317643.i | −0.0368318 | − | 0.0889198i | ||||
\(419\) | 5.26680e6 | − | 2.18158e6i | 1.46559 | − | 0.607066i | 0.499740 | − | 0.866175i | \(-0.333429\pi\) |
0.965848 | + | 0.259109i | \(0.0834289\pi\) | |||||||
\(420\) | 191154. | − | 461486.i | 0.0528761 | − | 0.127654i | ||||
\(421\) | − | 3.58043e6i | − | 0.984533i | −0.870444 | − | 0.492267i | \(-0.836168\pi\) | ||
0.870444 | − | 0.492267i | \(-0.163832\pi\) | |||||||
\(422\) | 1.15595e6 | + | 478808.i | 0.315977 | + | 0.130882i | ||||
\(423\) | −2.67283e6 | + | 2.67283e6i | −0.726307 | + | 0.726307i | ||||
\(424\) | −52486.5 | −0.0141786 | ||||||||
\(425\) | −324456. | + | 3.28218e6i | −0.0871333 | + | 0.881436i | ||||
\(426\) | 558323. | 0.149060 | ||||||||
\(427\) | 1.76965e6 | − | 1.76965e6i | 0.469698 | − | 0.469698i | ||||
\(428\) | 2.94186e6 | + | 1.21856e6i | 0.776269 | + | 0.321541i | ||||
\(429\) | − | 1.56472e6i | − | 0.410482i | ||||||
\(430\) | 145713. | − | 351781.i | 0.0380037 | − | 0.0917490i | ||||
\(431\) | −1.42179e6 | + | 588924.i | −0.368674 | + | 0.152710i | −0.559326 | − | 0.828948i | \(-0.688940\pi\) |
0.190652 | + | 0.981658i | \(0.438940\pi\) | |||||||
\(432\) | 394592. | + | 952629.i | 0.101728 | + | 0.245592i | ||||
\(433\) | −3.05688e6 | − | 3.05688e6i | −0.783534 | − | 0.783534i | 0.196891 | − | 0.980425i | \(-0.436916\pi\) |
−0.980425 | + | 0.196891i | \(0.936916\pi\) | |||||||
\(434\) | −185140. | − | 185140.i | −0.0471820 | − | 0.0471820i | ||||
\(435\) | 139145. | + | 335925.i | 0.0352568 | + | 0.0851175i | ||||
\(436\) | −2.99179e6 | + | 1.23924e6i | −0.753729 | + | 0.312205i | ||||
\(437\) | −90585.0 | + | 218692.i | −0.0226910 | + | 0.0547808i | ||||
\(438\) | 180737.i | 0.0450154i | ||||||||
\(439\) | −4.58716e6 | − | 1.90006e6i | −1.13601 | − | 0.470551i | −0.266191 | − | 0.963920i | \(-0.585765\pi\) |
−0.869820 | + | 0.493369i | \(0.835765\pi\) | |||||||
\(440\) | 1.02445e6 | − | 1.02445e6i | 0.252265 | − | 0.252265i | ||||
\(441\) | 9.61397e6 | 2.35400 | ||||||||
\(442\) | −184196. | + | 1.86332e6i | −0.0448461 | + | 0.453661i | ||||
\(443\) | −3.05735e6 | −0.740177 | −0.370088 | − | 0.928997i | \(-0.620673\pi\) | ||||
−0.370088 | + | 0.928997i | \(0.620673\pi\) | |||||||
\(444\) | 694907. | − | 694907.i | 0.167290 | − | 0.167290i | ||||
\(445\) | −668757. | − | 277008.i | −0.160092 | − | 0.0663121i | ||||
\(446\) | − | 1.96308e6i | − | 0.467307i | ||||||
\(447\) | 6545.75 | − | 15802.8i | 0.00154950 | − | 0.00374082i | ||||
\(448\) | 974846. | − | 403794.i | 0.229478 | − | 0.0950529i | ||||
\(449\) | 1.26412e6 | + | 3.05185e6i | 0.295918 | + | 0.714410i | 0.999991 | + | 0.00428193i | \(0.00136299\pi\) |
−0.704073 | + | 0.710128i | \(0.748637\pi\) | |||||||
\(450\) | 1.02473e6 | + | 1.02473e6i | 0.238549 | + | 0.238549i | ||||
\(451\) | 3.56681e6 | + | 3.56681e6i | 0.825731 | + | 0.825731i | ||||
\(452\) | 889417. | + | 2.14724e6i | 0.204767 | + | 0.494351i | ||||
\(453\) | 167697. | − | 69462.5i | 0.0383955 | − | 0.0159039i | ||||
\(454\) | 14779.0 | − | 35679.7i | 0.00336516 | − | 0.00812422i | ||||
\(455\) | 3.12606e6i | 0.707895i | ||||||||
\(456\) | 134270. | + | 55616.6i | 0.0302391 | + | 0.0125254i | ||||
\(457\) | −939980. | + | 939980.i | −0.210537 | + | 0.210537i | −0.804496 | − | 0.593959i | \(-0.797564\pi\) |
0.593959 | + | 0.804496i | \(0.297564\pi\) | |||||||
\(458\) | −3.16951e6 | −0.706039 | ||||||||
\(459\) | 1.07485e6 | − | 2.00917e6i | 0.238132 | − | 0.445129i | ||||
\(460\) | −453258. | −0.0998737 | ||||||||
\(461\) | −2.21800e6 | + | 2.21800e6i | −0.486082 | + | 0.486082i | −0.907067 | − | 0.420986i | \(-0.861684\pi\) |
0.420986 | + | 0.907067i | \(0.361684\pi\) | |||||||
\(462\) | −1.19776e6 | − | 496128.i | −0.261075 | − | 0.108141i | ||||
\(463\) | 3.38473e6i | 0.733790i | 0.930262 | + | 0.366895i | \(0.119579\pi\) | ||||
−0.930262 | + | 0.366895i | \(0.880421\pi\) | |||||||
\(464\) | −974622. | + | 2.35295e6i | −0.210156 | + | 0.507361i | ||||
\(465\) | −33076.1 | + | 13700.6i | −0.00709384 | + | 0.00293836i | ||||
\(466\) | −682551. | − | 1.64782e6i | −0.145603 | − | 0.351517i | ||||
\(467\) | 1.54486e6 | + | 1.54486e6i | 0.327790 | + | 0.327790i | 0.851746 | − | 0.523955i | \(-0.175544\pi\) |
−0.523955 | + | 0.851746i | \(0.675544\pi\) | |||||||
\(468\) | −2.89929e6 | − | 2.89929e6i | −0.611896 | − | 0.611896i | ||||
\(469\) | −323148. | − | 780148.i | −0.0678374 | − | 0.163774i | ||||
\(470\) | −674049. | + | 279200.i | −0.140749 | + | 0.0583003i | ||||
\(471\) | −20208.4 | + | 48787.3i | −0.00419739 | + | 0.0101334i | ||||
\(472\) | 3.33004e6i | 0.688010i | ||||||||
\(473\) | 4.55034e6 | + | 1.88481e6i | 0.935171 | + | 0.387361i | ||||
\(474\) | 409503. | − | 409503.i | 0.0837164 | − | 0.0837164i | ||||
\(475\) | −728021. | −0.148051 | ||||||||
\(476\) | −6.81746e6 | − | 3.64715e6i | −1.37913 | − | 0.737797i | ||||
\(477\) | −87611.4 | −0.0176305 | ||||||||
\(478\) | 2.25786e6 | − | 2.25786e6i | 0.451988 | − | 0.451988i | ||||
\(479\) | 573168. | + | 237414.i | 0.114141 | + | 0.0472789i | 0.439023 | − | 0.898476i | \(-0.355325\pi\) |
−0.324882 | + | 0.945755i | \(0.605325\pi\) | |||||||
\(480\) | 430119.i | 0.0852089i | ||||||||
\(481\) | −2.35362e6 | + | 5.68213e6i | −0.463845 | + | 1.11982i | ||||
\(482\) | 645880. | − | 267532.i | 0.126629 | − | 0.0524516i | ||||
\(483\) | 341576. | + | 824637.i | 0.0666223 | + | 0.160840i | ||||
\(484\) | 2.98640e6 | + | 2.98640e6i | 0.579474 | + | 0.579474i | ||||
\(485\) | 917681. | + | 917681.i | 0.177149 | + | 0.177149i | ||||
\(486\) | −581485. | − | 1.40383e6i | −0.111673 | − | 0.269602i | ||||
\(487\) | −1.48483e6 | + | 615036.i | −0.283697 | + | 0.117511i | −0.519994 | − | 0.854170i | \(-0.674066\pi\) |
0.236298 | + | 0.971681i | \(0.424066\pi\) | |||||||
\(488\) | −533573. | + | 1.28816e6i | −0.101425 | + | 0.244861i | ||||
\(489\) | 1.46712e6i | 0.277455i | ||||||||
\(490\) | 1.71438e6 | + | 710121.i | 0.322566 | + | 0.133611i | ||||
\(491\) | 5.85324e6 | − | 5.85324e6i | 1.09570 | − | 1.09570i | 0.100795 | − | 0.994907i | \(-0.467861\pi\) |
0.994907 | − | 0.100795i | \(-0.0321386\pi\) | |||||||
\(492\) | −968914. | −0.180457 | ||||||||
\(493\) | 5.38631e6 | − | 1.63181e6i | 0.998100 | − | 0.302379i | ||||
\(494\) | −413303. | −0.0761993 | ||||||||
\(495\) | 1.71002e6 | − | 1.71002e6i | 0.313681 | − | 0.313681i | ||||
\(496\) | −231677. | − | 95963.9i | −0.0422843 | − | 0.0175147i | ||||
\(497\) | − | 1.44284e7i | − | 2.62015i | ||||||
\(498\) | −143672. | + | 346854.i | −0.0259596 | + | 0.0626719i | ||||
\(499\) | −1.25730e6 | + | 520790.i | −0.226041 | + | 0.0936291i | −0.492830 | − | 0.870126i | \(-0.664037\pi\) |
0.266789 | + | 0.963755i | \(0.414037\pi\) | |||||||
\(500\) | −1.13577e6 | − | 2.74199e6i | −0.203173 | − | 0.490502i | ||||
\(501\) | 905950. | + | 905950.i | 0.161254 | + | 0.161254i | ||||
\(502\) | −3.14030e6 | − | 3.14030e6i | −0.556176 | − | 0.556176i | ||||
\(503\) | −1.27375e6 | − | 3.07509e6i | −0.224472 | − | 0.541924i | 0.771015 | − | 0.636817i | \(-0.219749\pi\) |
−0.995488 | + | 0.0948926i | \(0.969749\pi\) | |||||||
\(504\) | −6.90702e6 | + | 2.86098e6i | −1.21120 | + | 0.501694i | ||||
\(505\) | 1.07332e6 | − | 2.59123e6i | 0.187285 | − | 0.452145i | ||||
\(506\) | 1.17641e6i | 0.204259i | ||||||||
\(507\) | −340345. | − | 140976.i | −0.0588030 | − | 0.0243570i | ||||
\(508\) | 3.68387e6 | − | 3.68387e6i | 0.633352 | − | 0.633352i | ||||
\(509\) | −6.13264e6 | −1.04919 | −0.524594 | − | 0.851353i | \(-0.675783\pi\) | ||||
−0.524594 | + | 0.851353i | \(0.675783\pi\) | |||||||
\(510\) | 164026. | − | 134514.i | 0.0279246 | − | 0.0229003i | ||||
\(511\) | 4.67066e6 | 0.791273 | ||||||||
\(512\) | −3.78519e6 | + | 3.78519e6i | −0.638135 | + | 0.638135i | ||||
\(513\) | 464682. | + | 192478.i | 0.0779583 | + | 0.0322914i | ||||
\(514\) | 2.92380e6i | 0.488136i | ||||||||
\(515\) | −1.21746e6 | + | 2.93921e6i | −0.202273 | + | 0.488329i | ||||
\(516\) | −874046. | + | 362042.i | −0.144514 | + | 0.0598597i | ||||
\(517\) | −3.61149e6 | − | 8.71892e6i | −0.594238 | − | 1.43462i | ||||
\(518\) | 3.60328e6 | + | 3.60328e6i | 0.590030 | + | 0.590030i | ||||
\(519\) | −67873.1 | − | 67873.1i | −0.0110606 | − | 0.0110606i | ||||
\(520\) | −666481. | − | 1.60903e6i | −0.108089 | − | 0.260949i | ||||
\(521\) | 9.07444e6 | − | 3.75876e6i | 1.46462 | − | 0.606666i | 0.498996 | − | 0.866604i | \(-0.333702\pi\) |
0.965625 | + | 0.259938i | \(0.0837021\pi\) | |||||||
\(522\) | 946340. | − | 2.28467e6i | 0.152010 | − | 0.366984i | ||||
\(523\) | − | 3.39357e6i | − | 0.542504i | −0.962508 | − | 0.271252i | \(-0.912562\pi\) | ||
0.962508 | − | 0.271252i | \(-0.0874377\pi\) | |||||||
\(524\) | −1.44342e6 | − | 597886.i | −0.229650 | − | 0.0951240i | ||||
\(525\) | −1.94115e6 | + | 1.94115e6i | −0.307370 | + | 0.307370i | ||||
\(526\) | 3.25994e6 | 0.513743 | ||||||||
\(527\) | 160672. | + | 530351.i | 0.0252008 | + | 0.0831834i | ||||
\(528\) | −1.24167e6 | −0.193831 | ||||||||
\(529\) | −3.97847e6 | + | 3.97847e6i | −0.618126 | + | 0.618126i | ||||
\(530\) | −15623.1 | − | 6471.28i | −0.00241589 | − | 0.00100069i | ||||
\(531\) | 5.55857e6i | 0.855513i | ||||||||
\(532\) | 653108. | − | 1.57674e6i | 0.100047 | − | 0.241536i | ||||
\(533\) | 5.60215e6 | − | 2.32049e6i | 0.854155 | − | 0.353803i | ||||
\(534\) | −138100. | − | 333403.i | −0.0209576 | − | 0.0505961i | ||||
\(535\) | 1.59641e6 | + | 1.59641e6i | 0.241135 | + | 0.241135i | ||||
\(536\) | 332658. | + | 332658.i | 0.0500133 | + | 0.0500133i | ||||
\(537\) | −525677. | − | 1.26910e6i | −0.0786653 | − | 0.189915i | ||||
\(538\) | 3.70151e6 | − | 1.53321e6i | 0.551344 | − | 0.228374i | ||||
\(539\) | −9.18552e6 | + | 2.21758e7i | −1.36186 | + | 3.28782i | ||||
\(540\) | 963096.i | 0.142130i | ||||||||
\(541\) | −6.67174e6 | − | 2.76352e6i | −0.980044 | − | 0.405948i | −0.165602 | − | 0.986193i | \(-0.552957\pi\) |
−0.814442 | + | 0.580245i | \(0.802957\pi\) | |||||||
\(542\) | −360045. | + | 360045.i | −0.0526452 | + | 0.0526452i | ||||
\(543\) | 2.47209e6 | 0.359804 | ||||||||
\(544\) | 6.62536e6 | + | 654941.i | 0.959869 | + | 0.0948867i | ||||
\(545\) | −2.29599e6 | −0.331115 | ||||||||
\(546\) | −1.10201e6 | + | 1.10201e6i | −0.158198 | + | 0.158198i | ||||
\(547\) | 7.55886e6 | + | 3.13098e6i | 1.08016 | + | 0.447417i | 0.850565 | − | 0.525870i | \(-0.176260\pi\) |
0.229594 | + | 0.973286i | \(0.426260\pi\) | |||||||
\(548\) | − | 2.70878e6i | − | 0.385321i | ||||||
\(549\) | −890649. | + | 2.15022e6i | −0.126118 | + | 0.304475i | ||||
\(550\) | −3.34272e6 | + | 1.38460e6i | −0.471187 | + | 0.195172i | ||||
\(551\) | 475410. | + | 1.14774e6i | 0.0667098 | + | 0.161052i | ||||
\(552\) | −351628. | − | 351628.i | −0.0491174 | − | 0.0491174i | ||||
\(553\) | −1.05825e7 | − | 1.05825e7i | −1.47155 | − | 1.47155i | ||||
\(554\) | 262637. | + | 634061.i | 0.0363564 | + | 0.0877721i | ||||
\(555\) | 643741. | − | 266646.i | 0.0887112 | − | 0.0367454i | ||||
\(556\) | −668516. | + | 1.61394e6i | −0.0917118 | + | 0.221412i | ||||
\(557\) | 9.96469e6i | 1.36090i | 0.732795 | + | 0.680449i | \(0.238215\pi\) | ||||
−0.732795 | + | 0.680449i | \(0.761785\pi\) | |||||||
\(558\) | 224955. | + | 93179.2i | 0.0305851 | + | 0.0126687i | ||||
\(559\) | 4.18657e6 | − | 4.18657e6i | 0.566668 | − | 0.566668i | ||||
\(560\) | 2.48066e6 | 0.334270 | ||||||||
\(561\) | 1.73996e6 | + | 2.12170e6i | 0.233416 | + | 0.284627i | ||||
\(562\) | 1.41697e6 | 0.189243 | ||||||||
\(563\) | 1.64332e6 | − | 1.64332e6i | 0.218500 | − | 0.218500i | −0.589366 | − | 0.807866i | \(-0.700622\pi\) |
0.807866 | + | 0.589366i | \(0.200622\pi\) | |||||||
\(564\) | 1.67476e6 | + | 693709.i | 0.221695 | + | 0.0918289i | ||||
\(565\) | 1.64786e6i | 0.217169i | ||||||||
\(566\) | −1.48715e6 | + | 3.59029e6i | −0.195125 | + | 0.471074i | ||||
\(567\) | −1.06222e7 | + | 4.39988e6i | −1.38758 | + | 0.574755i | ||||
\(568\) | 3.07615e6 | + | 7.42649e6i | 0.400071 | + | 0.965857i | ||||
\(569\) | −8.78037e6 | − | 8.78037e6i | −1.13693 | − | 1.13693i | −0.988998 | − | 0.147927i | \(-0.952740\pi\) |
−0.147927 | − | 0.988998i | \(-0.547260\pi\) | |||||||
\(570\) | 33109.5 | + | 33109.5i | 0.00426841 | + | 0.00426841i | ||||
\(571\) | 570215. | + | 1.37662e6i | 0.0731894 | + | 0.176695i | 0.956240 | − | 0.292582i | \(-0.0945145\pi\) |
−0.883051 | + | 0.469277i | \(0.844515\pi\) | |||||||
\(572\) | 9.45766e6 | − | 3.91749e6i | 1.20863 | − | 0.500631i | ||||
\(573\) | 300378. | − | 725176.i | 0.0382192 | − | 0.0922692i | ||||
\(574\) | − | 5.02408e6i | − | 0.636469i | ||||||
\(575\) | 2.30140e6 | + | 953272.i | 0.290284 | + | 0.120240i | ||||
\(576\) | −693856. | + | 693856.i | −0.0871391 | + | 0.0871391i | ||||
\(577\) | 1.05335e7 | 1.31714 | 0.658570 | − | 0.752520i | \(-0.271162\pi\) | ||||
0.658570 | + | 0.752520i | \(0.271162\pi\) | |||||||
\(578\) | −1.82223e6 | − | 2.73140e6i | −0.226873 | − | 0.340068i | ||||
\(579\) | −3.47011e6 | −0.430177 | ||||||||
\(580\) | −1.68207e6 | + | 1.68207e6i | −0.207622 | + | 0.207622i | ||||
\(581\) | 8.96351e6 | + | 3.71281e6i | 1.10163 | + | 0.456312i | ||||
\(582\) | 647006.i | 0.0791773i | ||||||||
\(583\) | 83707.0 | − | 202086.i | 0.0101998 | − | 0.0246244i | ||||
\(584\) | −2.40406e6 | + | 995792.i | −0.291684 | + | 0.120819i | ||||
\(585\) | −1.11250e6 | − | 2.68582e6i | −0.134404 | − | 0.324479i | ||||
\(586\) | −3.20576e6 | − | 3.20576e6i | −0.385645 | − | 0.385645i | ||||
\(587\) | −7.10249e6 | − | 7.10249e6i | −0.850777 | − | 0.850777i | 0.139452 | − | 0.990229i | \(-0.455466\pi\) |
−0.990229 | + | 0.139452i | \(0.955466\pi\) | |||||||
\(588\) | −1.76439e6 | − | 4.25961e6i | −0.210451 | − | 0.508073i | ||||
\(589\) | −113010. | + | 46810.2i | −0.0134223 | + | 0.00555971i | ||||
\(590\) | −410575. | + | 991216.i | −0.0485582 | + | 0.117230i | ||||
\(591\) | − | 3.79529e6i | − | 0.446968i | ||||||
\(592\) | 4.50901e6 | + | 1.86769e6i | 0.528782 | + | 0.219029i | ||||
\(593\) | 5.67225e6 | − | 5.67225e6i | 0.662398 | − | 0.662398i | −0.293547 | − | 0.955945i | \(-0.594836\pi\) |
0.955945 | + | 0.293547i | \(0.0948357\pi\) | |||||||
\(594\) | 2.49966e6 | 0.290680 | ||||||||
\(595\) | −3.47615e6 | − | 4.23880e6i | −0.402537 | − | 0.490852i | ||||
\(596\) | 111905. | 0.0129043 | ||||||||
\(597\) | −1.09005e6 | + | 1.09005e6i | −0.125173 | + | 0.125173i | ||||
\(598\) | 1.30652e6 | + | 541179.i | 0.149405 | + | 0.0618854i | ||||
\(599\) | 4.56054e6i | 0.519337i | 0.965698 | + | 0.259668i | \(0.0836133\pi\) | ||||
−0.965698 | + | 0.259668i | \(0.916387\pi\) | |||||||
\(600\) | 585282. | − | 1.41300e6i | 0.0663723 | − | 0.160237i | ||||
\(601\) | −3.60542e6 | + | 1.49341e6i | −0.407164 | + | 0.168653i | −0.576859 | − | 0.816844i | \(-0.695722\pi\) |
0.169695 | + | 0.985497i | \(0.445722\pi\) | |||||||
\(602\) | −1.87728e6 | − | 4.53216e6i | −0.211125 | − | 0.509700i | ||||
\(603\) | 555278. | + | 555278.i | 0.0621895 | + | 0.0621895i | ||||
\(604\) | 839705. | + | 839705.i | 0.0936558 | + | 0.0936558i | ||||
\(605\) | 1.14593e6 | + | 2.76651e6i | 0.127282 | + | 0.307287i | ||||
\(606\) | 1.29184e6 | − | 535097.i | 0.142898 | − | 0.0591903i | ||||
\(607\) | 1.26095e6 | − | 3.04421e6i | 0.138908 | − | 0.335354i | −0.839082 | − | 0.544005i | \(-0.816907\pi\) |
0.977990 | + | 0.208651i | \(0.0669073\pi\) | |||||||
\(608\) | 1.46957e6i | 0.161225i | ||||||||
\(609\) | 4.32788e6 | + | 1.79267e6i | 0.472859 | + | 0.195865i | ||||
\(610\) | −317645. | + | 317645.i | −0.0345635 | + | 0.0345635i | ||||
\(611\) | −1.13447e7 | −1.22939 | ||||||||
\(612\) | 7.15530e6 | + | 707329.i | 0.772235 | + | 0.0763384i | ||||
\(613\) | −5.23221e6 | −0.562385 | −0.281193 | − | 0.959651i | \(-0.590730\pi\) | ||||
−0.281193 | + | 0.959651i | \(0.590730\pi\) | |||||||
\(614\) | −3.36192e6 | + | 3.36192e6i | −0.359888 | + | 0.359888i | ||||
\(615\) | −634680. | − | 262893.i | −0.0676654 | − | 0.0280279i | ||||
\(616\) | − | 1.86654e7i | − | 1.98191i | ||||||
\(617\) | −1.34135e6 | + | 3.23829e6i | −0.141849 | + | 0.342455i | −0.978798 | − | 0.204826i | \(-0.934337\pi\) |
0.836949 | + | 0.547281i | \(0.184337\pi\) | |||||||
\(618\) | −1.46532e6 | + | 606955.i | −0.154334 | + | 0.0639271i | ||||
\(619\) | −4.66260e6 | − | 1.12565e7i | −0.489105 | − | 1.18080i | −0.955171 | − | 0.296053i | \(-0.904329\pi\) |
0.466067 | − | 0.884750i | \(-0.345671\pi\) | |||||||
\(620\) | −165621. | − | 165621.i | −0.0173036 | − | 0.0173036i | ||||
\(621\) | −1.21691e6 | − | 1.21691e6i | −0.126628 | − | 0.126628i | ||||
\(622\) | 800084. | + | 1.93157e6i | 0.0829201 | + | 0.200187i | ||||
\(623\) | −8.61591e6 | + | 3.56883e6i | −0.889367 | + | 0.368388i | ||||
\(624\) | −571204. | + | 1.37901e6i | −0.0587259 | + | 0.141777i | ||||
\(625\) | 6.54544e6i | 0.670253i | ||||||||
\(626\) | −238462. | − | 98774.1i | −0.0243211 | − | 0.0100741i | ||||
\(627\) | −428276. | + | 428276.i | −0.0435066 | + | 0.0435066i | ||||
\(628\) | −345480. | −0.0349562 | ||||||||
\(629\) | −3.12708e6 | − | 1.03219e7i | −0.315146 | − | 1.04024i | ||||
\(630\) | −2.40868e6 | −0.241784 | ||||||||
\(631\) | 5.51204e6 | − | 5.51204e6i | 0.551111 | − | 0.551111i | −0.375650 | − | 0.926761i | \(-0.622581\pi\) |
0.926761 | + | 0.375650i | \(0.122581\pi\) | |||||||
\(632\) | 7.70317e6 | + | 3.19076e6i | 0.767143 | + | 0.317761i | ||||
\(633\) | − | 2.20413e6i | − | 0.218639i | ||||||
\(634\) | 149101. | − | 359961.i | 0.0147318 | − | 0.0355658i | ||||
\(635\) | 3.41262e6 | − | 1.41356e6i | 0.335857 | − | 0.139116i | ||||
\(636\) | 16078.7 | + | 38817.5i | 0.00157619 | + | 0.00380526i | ||||
\(637\) | 2.04030e7 | + | 2.04030e7i | 1.99225 | + | 1.99225i | ||||
\(638\) | 4.36570e6 | + | 4.36570e6i | 0.424622 | + | 0.424622i | ||||
\(639\) | 5.13477e6 | + | 1.23964e7i | 0.497472 | + | 1.20100i | ||||
\(640\) | −3.29639e6 | + | 1.36541e6i | −0.318119 | + | 0.131769i | ||||
\(641\) | 3.19076e6 | − | 7.70317e6i | 0.306725 | − | 0.740498i | −0.693083 | − | 0.720858i | \(-0.743748\pi\) |
0.999807 | − | 0.0196403i | \(-0.00625211\pi\) | |||||||
\(642\) | 1.12554e6i | 0.107777i | ||||||||
\(643\) | 9.23161e6 | + | 3.82386e6i | 0.880542 | + | 0.364732i | 0.776707 | − | 0.629862i | \(-0.216889\pi\) |
0.103835 | + | 0.994595i | \(0.466889\pi\) | |||||||
\(644\) | −4.12918e6 | + | 4.12918e6i | −0.392328 | + | 0.392328i | ||||
\(645\) | −670769. | −0.0634854 | ||||||||
\(646\) | 560420. | − | 459589.i | 0.0528363 | − | 0.0433299i | ||||
\(647\) | 4.18614e6 | 0.393145 | 0.196573 | − | 0.980489i | \(-0.437019\pi\) | ||||
0.196573 | + | 0.980489i | \(0.437019\pi\) | |||||||
\(648\) | 4.52936e6 | − | 4.52936e6i | 0.423740 | − | 0.423740i | ||||
\(649\) | −1.28215e7 | − | 5.31085e6i | −1.19489 | − | 0.494939i | ||||
\(650\) | 4.34939e6i | 0.403780i | ||||||||
\(651\) | −176511. | + | 426134.i | −0.0163237 | + | 0.0394089i | ||||
\(652\) | −8.86772e6 | + | 3.67313e6i | −0.816945 | + | 0.338390i | ||||
\(653\) | −2.03381e6 | − | 4.91005e6i | −0.186650 | − | 0.450612i | 0.802661 | − | 0.596435i | \(-0.203417\pi\) |
−0.989311 | + | 0.145824i | \(0.953417\pi\) | |||||||
\(654\) | −809387. | − | 809387.i | −0.0739966 | − | 0.0739966i | ||||
\(655\) | −783281. | − | 783281.i | −0.0713369 | − | 0.0713369i | ||||
\(656\) | −1.84140e6 | − | 4.44554e6i | −0.167067 | − | 0.403334i | ||||
\(657\) | −4.01289e6 | + | 1.66219e6i | −0.362697 | + | 0.150234i | ||||
\(658\) | −3.59707e6 | + | 8.68409e6i | −0.323880 | + | 0.781915i | ||||
\(659\) | 1.61568e7i | 1.44925i | 0.689145 | + | 0.724624i | \(0.257986\pi\) | ||||
−0.689145 | + | 0.724624i | \(0.742014\pi\) | |||||||
\(660\) | −1.07148e6 | − | 443821.i | −0.0957467 | − | 0.0396596i | ||||
\(661\) | −2.55203e6 | + | 2.55203e6i | −0.227186 | + | 0.227186i | −0.811516 | − | 0.584330i | \(-0.801357\pi\) |
0.584330 | + | 0.811516i | \(0.301357\pi\) | |||||||
\(662\) | 83489.3 | 0.00740433 | ||||||||
\(663\) | 3.15679e6 | − | 956366.i | 0.278909 | − | 0.0844968i | ||||
\(664\) | −5.40522e6 | −0.475766 | ||||||||
\(665\) | 855627. | − | 855627.i | 0.0750292 | − | 0.0750292i | ||||
\(666\) | −4.37817e6 | − | 1.81350e6i | −0.382478 | − | 0.158428i | ||||
\(667\) | − | 4.25072e6i | − | 0.369954i | ||||||
\(668\) | −3.20767e6 | + | 7.74401e6i | −0.278131 | + | 0.671467i | ||||
\(669\) | −3.19499e6 | + | 1.32341e6i | −0.275997 | + | 0.114322i | ||||
\(670\) | 58003.6 | + | 140033.i | 0.00499193 | + | 0.0120516i | ||||
\(671\) | −4.10878e6 | − | 4.10878e6i | −0.352295 | − | 0.352295i | ||||
\(672\) | 3.91838e6 | + | 3.91838e6i | 0.334721 | + | 0.334721i | ||||
\(673\) | 4.08567e6 | + | 9.86367e6i | 0.347716 | + | 0.839462i | 0.996889 | + | 0.0788205i | \(0.0251154\pi\) |
−0.649172 | + | 0.760641i | \(0.724885\pi\) | |||||||
\(674\) | 3.67454e6 | − | 1.52204e6i | 0.311568 | − | 0.129056i | ||||
\(675\) | 2.02554e6 | − | 4.89009e6i | 0.171112 | − | 0.413102i | ||||
\(676\) | − | 2.41010e6i | − | 0.202847i | ||||||
\(677\) | −1.31455e7 | − | 5.44504e6i | −1.10231 | − | 0.456593i | −0.244029 | − | 0.969768i | \(-0.578469\pi\) |
−0.858284 | + | 0.513175i | \(0.828469\pi\) | |||||||
\(678\) | −580907. | + | 580907.i | −0.0485324 | + | 0.0485324i | ||||
\(679\) | 1.67201e7 | 1.39176 | ||||||||
\(680\) | 2.69294e6 | + | 1.44065e6i | 0.223334 | + | 0.119478i | ||||
\(681\) | −68033.3 | −0.00562152 | ||||||||
\(682\) | −429859. | + | 429859.i | −0.0353887 | + | 0.0353887i | ||||
\(683\) | 1.77009e7 | + | 7.33197e6i | 1.45193 | + | 0.601407i | 0.962657 | − | 0.270725i | \(-0.0872635\pi\) |
0.489269 | + | 0.872133i | \(0.337264\pi\) | |||||||
\(684\) | 1.58712e6i | 0.129709i | ||||||||
\(685\) | 734966. | − | 1.77437e6i | 0.0598468 | − | 0.144483i | ||||
\(686\) | 1.33452e7 | − | 5.52776e6i | 1.08272 | − | 0.448475i | ||||
\(687\) | 2.13672e6 | + | 5.15850e6i | 0.172725 | + | 0.416996i | ||||
\(688\) | −3.32222e6 | − | 3.32222e6i | −0.267582 | − | 0.267582i | ||||
\(689\) | −185931. | − | 185931.i | −0.0149212 | − | 0.0149212i | ||||
\(690\) | −61311.4 | − | 148019.i | −0.00490251 | − | 0.0118357i | ||||
\(691\) | −1.10545e7 | + | 4.57891e6i | −0.880729 | + | 0.364810i | −0.776780 | − | 0.629773i | \(-0.783148\pi\) |
−0.103950 | + | 0.994583i | \(0.533148\pi\) | |||||||
\(692\) | 240316. | − | 580175.i | 0.0190774 | − | 0.0460568i | ||||
\(693\) | − | 3.11566e7i | − | 2.46443i | ||||||
\(694\) | 1.15357e6 | + | 477824.i | 0.0909169 | + | 0.0376590i | ||||
\(695\) | −875813. | + | 875813.i | −0.0687780 | + | 0.0687780i | ||||
\(696\) | −2.60982e6 | −0.204215 | ||||||||
\(697\) | −5.01591e6 | + | 9.37602e6i | −0.391082 | + | 0.731032i | ||||
\(698\) | −7.03544e6 | −0.546579 | ||||||||
\(699\) | −2.22175e6 | + | 2.22175e6i | −0.171990 | + | 0.171990i | ||||
\(700\) | −1.65929e7 | − | 6.87299e6i | −1.27990 | − | 0.530152i | ||||
\(701\) | 6.33880e6i | 0.487205i | 0.969875 | + | 0.243602i | \(0.0783292\pi\) | ||||
−0.969875 | + | 0.243602i | \(0.921671\pi\) | |||||||
\(702\) | 1.14991e6 | − | 2.77614e6i | 0.0880688 | − | 0.212617i | ||||
\(703\) | 2.19945e6 | − | 911040.i | 0.167851 | − | 0.0695263i | ||||
\(704\) | −937530. | − | 2.26340e6i | −0.0712941 | − | 0.172119i | ||||
\(705\) | 908817. | + | 908817.i | 0.0688658 | + | 0.0688658i | ||||
\(706\) | −6.31186e6 | − | 6.31186e6i | −0.476590 | − | 0.476590i | ||||
\(707\) | −1.38281e7 | − | 3.33841e7i | −1.04044 | − | 2.51183i | ||||
\(708\) | 2.46280e6 | − | 1.02013e6i | 0.184649 | − | 0.0764841i | ||||
\(709\) | −15020.1 | + | 36261.8i | −0.00112217 | + | 0.00270915i | −0.924440 | − | 0.381328i | \(-0.875467\pi\) |
0.923317 | + | 0.384038i | \(0.125467\pi\) | |||||||
\(710\) | 2.58983e6i | 0.192808i | ||||||||
\(711\) | 1.28583e7 | + | 5.32607e6i | 0.953912 | + | 0.395123i | ||||
\(712\) | 3.67385e6 | − | 3.67385e6i | 0.271595 | − | 0.271595i | ||||
\(713\) | 418537. | 0.0308326 | ||||||||
\(714\) | 268852. | − | 2.71969e6i | 0.0197364 | − | 0.199652i | ||||
\(715\) | 7.25809e6 | 0.530955 | ||||||||
\(716\) | 6.35471e6 | − | 6.35471e6i | 0.463248 | − | 0.463248i | ||||
\(717\) | −5.19687e6 | − | 2.15261e6i | −0.377524 | − | 0.156375i | ||||
\(718\) | 8.41154e6i | 0.608926i | ||||||||
\(719\) | 4.78689e6 | − | 1.15566e7i | 0.345328 | − | 0.833695i | −0.651831 | − | 0.758364i | \(-0.725999\pi\) |
0.997159 | − | 0.0753307i | \(-0.0240013\pi\) | |||||||
\(720\) | −2.13131e6 | + | 882817.i | −0.153220 | + | 0.0634658i | ||||
\(721\) | 1.56851e7 | + | 3.78672e7i | 1.12370 | + | 2.71285i | ||||
\(722\) | −3.93580e6 | − | 3.93580e6i | −0.280989 | − | 0.280989i | ||||
\(723\) | −870838. | − | 870838.i | −0.0619572 | − | 0.0619572i | ||||
\(724\) | 6.18922e6 | + | 1.49421e7i | 0.438823 | + | 1.05941i | ||||
\(725\) | 1.20783e7 | − | 5.00298e6i | 0.853414 | − | 0.353496i | ||||
\(726\) | −571291. | + | 1.37922e6i | −0.0402269 | + | 0.0971162i | ||||
\(727\) | − | 2.65391e7i | − | 1.86230i | −0.364633 | − | 0.931151i | \(-0.618806\pi\) | ||
0.364633 | − | 0.931151i | \(-0.381194\pi\) | |||||||
\(728\) | −2.07299e7 | − | 8.58659e6i | −1.44967 | − | 0.600472i | ||||
\(729\) | 6.22191e6 | − | 6.22191e6i | 0.433615 | − | 0.433615i | ||||
\(730\) | −838363. | −0.0582271 | ||||||||
\(731\) | −1.02138e6 | + | 1.03322e7i | −0.0706958 | + | 0.715155i | ||||
\(732\) | 1.11614e6 | 0.0769911 | ||||||||
\(733\) | −7.66147e6 | + | 7.66147e6i | −0.526687 | + | 0.526687i | −0.919583 | − | 0.392896i | \(-0.871473\pi\) |
0.392896 | + | 0.919583i | \(0.371473\pi\) | |||||||
\(734\) | −422097. | − | 174838.i | −0.0289183 | − | 0.0119783i | ||||
\(735\) | − | 3.26895e6i | − | 0.223198i | ||||||
\(736\) | 1.92426e6 | − | 4.64557e6i | 0.130939 | − | 0.316114i | ||||
\(737\) | −1.81135e6 | + | 750285.i | −0.122838 | + | 0.0508812i | ||||
\(738\) | 1.78797e6 | + | 4.31654e6i | 0.120842 | + | 0.291739i | ||||
\(739\) | −1.54357e7 | − | 1.54357e7i | −1.03972 | − | 1.03972i | −0.999178 | − | 0.0405371i | \(-0.987093\pi\) |
−0.0405371 | − | 0.999178i | \(-0.512907\pi\) | |||||||
\(740\) | 3.22338e6 | + | 3.22338e6i | 0.216388 | + | 0.216388i | ||||
\(741\) | 278627. | + | 672665.i | 0.0186414 | + | 0.0450042i | ||||
\(742\) | −201279. | + | 83372.6i | −0.0134211 | + | 0.00555922i | ||||
\(743\) | 3.71426e6 | − | 8.96701e6i | 0.246831 | − | 0.595903i | −0.751100 | − | 0.660188i | \(-0.770477\pi\) |
0.997932 | + | 0.0642848i | \(0.0204766\pi\) | |||||||
\(744\) | − | 256970.i | − | 0.0170196i | ||||||
\(745\) | 73302.8 | + | 30363.0i | 0.00483871 | + | 0.00200426i | ||||
\(746\) | −746325. | + | 746325.i | −0.0490999 | + | 0.0490999i | ||||
\(747\) | −9.02249e6 | −0.591595 | ||||||||
\(748\) | −8.46797e6 | + | 1.58288e7i | −0.553382 | + | 1.03441i | ||||
\(749\) | 2.90866e7 | 1.89448 | ||||||||
\(750\) | 741807. | − | 741807.i | 0.0481546 | − | 0.0481546i | ||||
\(751\) | −8.63673e6 | − | 3.57745e6i | −0.558791 | − | 0.231459i | 0.0853692 | − | 0.996349i | \(-0.472793\pi\) |
−0.644160 | + | 0.764891i | \(0.722793\pi\) | |||||||
\(752\) | 9.00247e6i | 0.580520i | ||||||||
\(753\) | −2.99393e6 | + | 7.22799e6i | −0.192422 | + | 0.464547i | ||||
\(754\) | 6.85691e6 | − | 2.84023e6i | 0.439238 | − | 0.181939i | ||||
\(755\) | 322207. | + | 777878.i | 0.0205716 | + | 0.0496642i | ||||
\(756\) | 8.77380e6 | + | 8.77380e6i | 0.558320 | + | 0.558320i | ||||
\(757\) | 7.68810e6 | + | 7.68810e6i | 0.487617 | + | 0.487617i | 0.907554 | − | 0.419936i | \(-0.137948\pi\) |
−0.419936 | + | 0.907554i | \(0.637948\pi\) | |||||||
\(758\) | −771836. | − | 1.86338e6i | −0.0487924 | − | 0.117795i | ||||
\(759\) | 1.91464e6 | − | 793071.i | 0.120638 | − | 0.0499698i | ||||
\(760\) | −257982. | + | 622824.i | −0.0162015 | + | 0.0391139i | ||||
\(761\) | 2.06830e7i | 1.29465i | 0.762214 | + | 0.647325i | \(0.224112\pi\) | ||||
−0.762214 | + | 0.647325i | \(0.775888\pi\) | |||||||
\(762\) | 1.70133e6 | + | 704716.i | 0.106146 | + | 0.0439670i | ||||
\(763\) | −2.09164e7 | + | 2.09164e7i | −1.30070 | + | 1.30070i | ||||
\(764\) | 5.13522e6 | 0.318292 | ||||||||
\(765\) | 4.49511e6 | + | 2.40476e6i | 0.277707 | + | 0.148566i | ||||
\(766\) | −8.03933e6 | −0.495048 | ||||||||
\(767\) | −1.17965e7 | + | 1.17965e7i | −0.724044 | + | 0.724044i | ||||
\(768\) | −1.12139e6 | − | 464496.i | −0.0686048 | − | 0.0284171i | ||||
\(769\) | 1.79392e7i | 1.09393i | 0.837157 | + | 0.546963i | \(0.184216\pi\) | ||||
−0.837157 | + | 0.546963i | \(0.815784\pi\) | |||||||
\(770\) | 2.30133e6 | − | 5.55591e6i | 0.139879 | − | 0.337698i | ||||
\(771\) | 4.75860e6 | − | 1.97108e6i | 0.288299 | − | 0.119417i | ||||
\(772\) | −8.68790e6 | − | 2.09744e7i | −0.524652 | − | 1.26662i | ||||
\(773\) | 1.16639e7 | + | 1.16639e7i | 0.702093 | + | 0.702093i | 0.964859 | − | 0.262766i | \(-0.0846348\pi\) |
−0.262766 | + | 0.964859i | \(0.584635\pi\) | |||||||
\(774\) | 3.22581e6 | + | 3.22581e6i | 0.193547 | + | 0.193547i | ||||
\(775\) | 492607. | + | 1.18926e6i | 0.0294609 | + | 0.0711250i | ||||
\(776\) | −8.60609e6 | + | 3.56476e6i | −0.513041 | + | 0.212508i | ||||
\(777\) | 3.43533e6 | − | 8.29362e6i | 0.204134 | − | 0.492824i | ||||
\(778\) | − | 8.59393e6i | − | 0.509030i | ||||||
\(779\) | −2.16849e6 | − | 898217.i | −0.128030 | − | 0.0530319i | ||||
\(780\) | −985820. | + | 985820.i | −0.0580178 | + | 0.0580178i | ||||
\(781\) | −3.34998e7 | −1.96524 | ||||||||
\(782\) | −2.37337e6 | + | 719025.i | −0.138787 | + | 0.0420462i | ||||
\(783\) | −9.03204e6 | −0.526480 | ||||||||
\(784\) | 1.61906e7 | − | 1.61906e7i | 0.940748 | − | 0.940748i | ||||
\(785\) | −226304. | − | 93738.2i | −0.0131074 | − | 0.00542928i | ||||
\(786\) | − | 552248.i | − | 0.0318843i | ||||||
\(787\) | −339379. | + | 819332.i | −0.0195320 | + | 0.0471545i | −0.933345 | − | 0.358982i | \(-0.883124\pi\) |
0.913813 | + | 0.406136i | \(0.133124\pi\) | |||||||
\(788\) | 2.29399e7 | − | 9.50203e6i | 1.31606 | − | 0.545131i | ||||
\(789\) | −2.19768e6 | − | 5.30568e6i | −0.125682 | − | 0.303423i | ||||
\(790\) | 1.89951e6 | + | 1.89951e6i | 0.108286 | + | 0.108286i | ||||
\(791\) | 1.50120e7 | + | 1.50120e7i | 0.853094 | + | 0.853094i | ||||
\(792\) | 6.64263e6 | + | 1.60367e7i | 0.376294 | + | 0.908454i | ||||
\(793\) | −6.45339e6 | + | 2.67308e6i | −0.364422 | + | 0.150949i | ||||
\(794\) | 95149.6 | − | 229711.i | 0.00535619 | − | 0.0129310i | ||||
\(795\) | 29789.7i | 0.00167166i | ||||||||
\(796\) | −9.31768e6 | − | 3.85951e6i | −0.521225 | − | 0.215898i | ||||
\(797\) | −5.80074e6 | + | 5.80074e6i | −0.323473 | + | 0.323473i | −0.850098 | − | 0.526625i | \(-0.823457\pi\) |
0.526625 | + | 0.850098i | \(0.323457\pi\) | |||||||
\(798\) | 603255. | 0.0335346 | ||||||||
\(799\) | 1.53829e7 | − | 1.26152e7i | 0.852453 | − | 0.699078i | ||||
\(800\) | 1.54650e7 | 0.854330 | ||||||||
\(801\) | 6.13246e6 | − | 6.13246e6i | 0.337717 | − | 0.337717i | ||||
\(802\) | −4.16839e6 | − | 1.72660e6i | −0.228840 | − | 0.0947887i | ||||
\(803\) | − | 1.08443e7i | − | 0.593491i | ||||||
\(804\) | 144117. | − | 347930.i | 0.00786279 | − | 0.0189824i | ||||
\(805\) | −3.82515e6 | + | 1.58443e6i | −0.208046 | + | 0.0861753i | ||||
\(806\) | 279656. | + | 675150.i | 0.0151631 | + | 0.0366069i | ||||
\(807\) | −4.99073e6 | − | 4.99073e6i | −0.269761 | − | 0.269761i | ||||
\(808\) | 1.42351e7 | + | 1.42351e7i | 0.767064 | + | 0.767064i | ||||
\(809\) | −9.56254e6 | − | 2.30860e7i | −0.513691 | − | 1.24016i | −0.941721 | − | 0.336395i | \(-0.890792\pi\) |
0.428030 | − | 0.903764i | \(-0.359208\pi\) | |||||||
\(810\) | 1.90664e6 | − | 789758.i | 0.102107 | − | 0.0422943i | ||||
\(811\) | 1.31069e7 | − | 3.16428e7i | 0.699758 | − | 1.68936i | −0.0243744 | − | 0.999703i | \(-0.507759\pi\) |
0.724132 | − | 0.689661i | \(-0.242241\pi\) | |||||||
\(812\) | 3.06472e7i | 1.63118i | ||||||||
\(813\) | 828710. | + | 343263.i | 0.0439720 | + | 0.0182138i | ||||
\(814\) | 8.36610e6 | − | 8.36610e6i | 0.442550 | − | 0.442550i | ||||
\(815\) | −6.80535e6 | −0.358886 | ||||||||
\(816\) | −758917. | − | 2.50505e6i | −0.0398996 | − | 0.131702i | ||||
\(817\) | −2.29179e6 | −0.120121 | ||||||||
\(818\) | 6.30052e6 | − | 6.30052e6i | 0.329225 | − | 0.329225i | ||||
\(819\) | −3.46027e7 | − | 1.43329e7i | −1.80260 | − | 0.746662i | ||||
\(820\) | − | 4.49439e6i | − | 0.233419i | ||||||
\(821\) | 1.03736e7 | − | 2.50442e7i | 0.537123 | − | 1.29673i | −0.389600 | − | 0.920984i | \(-0.627387\pi\) |
0.926723 | − | 0.375745i | \(-0.122613\pi\) | |||||||
\(822\) | 884595. | − | 366411.i | 0.0456631 | − | 0.0189143i | ||||
\(823\) | 3.00045e6 | + | 7.24373e6i | 0.154414 | + | 0.372788i | 0.982089 | − | 0.188420i | \(-0.0603366\pi\) |
−0.827675 | + | 0.561208i | \(0.810337\pi\) | |||||||
\(824\) | −1.61467e7 | − | 1.61467e7i | −0.828450 | − | 0.828450i | ||||
\(825\) | 4.50697e6 | + | 4.50697e6i | 0.230542 | + | 0.230542i | ||||
\(826\) | 5.28963e6 | + | 1.27703e7i | 0.269759 | + | 0.651255i | ||||
\(827\) | −1.97709e7 | + | 8.18937e6i | −1.00522 | + | 0.416377i | −0.823710 | − | 0.567011i | \(-0.808100\pi\) |
−0.181513 | + | 0.983388i | \(0.558100\pi\) | |||||||
\(828\) | 2.07818e6 | − | 5.01716e6i | 0.105343 | − | 0.254321i | ||||
\(829\) | 4.48825e6i | 0.226825i | 0.993548 | + | 0.113412i | \(0.0361781\pi\) | ||||
−0.993548 | + | 0.113412i | \(0.963822\pi\) | |||||||
\(830\) | −1.60891e6 | − | 666432.i | −0.0810656 | − | 0.0335785i | ||||
\(831\) | 854901. | − | 854901.i | 0.0429451 | − | 0.0429451i | ||||
\(832\) | −2.94503e6 | −0.147496 | ||||||||
\(833\) | −5.03535e7 | − | 4.97763e6i | −2.51430 | − | 0.248548i | ||||
\(834\) | −617487. | −0.0307406 | ||||||||
\(835\) | −4.20232e6 | + | 4.20232e6i | −0.208580 | + | 0.208580i | ||||
\(836\) | −3.66088e6 | − | 1.51639e6i | −0.181163 | − | 0.0750403i | ||||
\(837\) | − | 889319.i | − | 0.0438777i | ||||||
\(838\) | −5.04496e6 | + | 1.21796e7i | −0.248169 | + | 0.599133i | ||||
\(839\) | 3.15217e7 | − | 1.30567e7i | 1.54598 | − | 0.640367i | 0.563398 | − | 0.826186i | \(-0.309494\pi\) |
0.982584 | + | 0.185819i | \(0.0594938\pi\) | |||||||
\(840\) | 972794. | + | 2.34853e6i | 0.0475688 | + | 0.114841i | ||||
\(841\) | −1.27105e6 | − | 1.27105e6i | −0.0619687 | − | 0.0619687i | ||||
\(842\) | 5.85474e6 | + | 5.85474e6i | 0.284595 | + | 0.284595i | ||||
\(843\) | −955248. | − | 2.30617e6i | −0.0462964 | − | 0.111769i | ||||
\(844\) | 1.33224e7 | − | 5.51834e6i | 0.643766 | − | 0.266657i | ||||
\(845\) | 653927. | − | 1.57872e6i | 0.0315056 | − | 0.0760612i | ||||
\(846\) | − | 8.74123e6i | − | 0.419901i | ||||||
\(847\) | 3.56422e7 | + | 1.47635e7i | 1.70709 | + | 0.707100i | ||||
\(848\) | −147544. | + | 147544.i | −0.00704582 | + | 0.00704582i | ||||
\(849\) | 6.84589e6 | 0.325957 | ||||||||
\(850\) | −4.83649e6 | − | 5.89759e6i | −0.229606 | − | 0.279980i | ||||
\(851\) | −8.14575e6 | −0.385574 | ||||||||
\(852\) | 4.55007e6 | − | 4.55007e6i | 0.214743 | − | 0.214743i | ||||
\(853\) | 2.03619e7 | + | 8.43418e6i | 0.958178 | + | 0.396890i | 0.806298 | − | 0.591509i | \(-0.201468\pi\) |
0.151879 | + | 0.988399i | \(0.451468\pi\) | |||||||
\(854\) | 5.78748e6i | 0.271547i | ||||||||
\(855\) | −430629. | + | 1.03963e6i | −0.0201459 | + | 0.0486366i | ||||
\(856\) | −1.49713e7 | + | 6.20132e6i | −0.698353 | + | 0.289267i | ||||
\(857\) | 4.12513e6 | + | 9.95894e6i | 0.191860 | + | 0.463192i | 0.990311 | − | 0.138868i | \(-0.0443465\pi\) |
−0.798450 | + | 0.602061i | \(0.794347\pi\) | |||||||
\(858\) | 2.55864e6 | + | 2.55864e6i | 0.118656 | + | 0.118656i | ||||
\(859\) | 9.15991e6 | + | 9.15991e6i | 0.423553 | + | 0.423553i | 0.886425 | − | 0.462872i | \(-0.153181\pi\) |
−0.462872 | + | 0.886425i | \(0.653181\pi\) | |||||||
\(860\) | −1.67936e6 | − | 4.05433e6i | −0.0774279 | − | 0.186928i | ||||
\(861\) | −8.17688e6 | + | 3.38697e6i | −0.375906 | + | 0.155706i | ||||
\(862\) | 1.36190e6 | − | 3.28792e6i | 0.0624278 | − | 0.150714i | ||||
\(863\) | 5.30802e6i | 0.242608i | 0.992615 | + | 0.121304i | \(0.0387077\pi\) | ||||
−0.992615 | + | 0.121304i | \(0.961292\pi\) | |||||||
\(864\) | −9.87104e6 | − | 4.08872e6i | −0.449861 | − | 0.186339i | ||||
\(865\) | 314835. | − | 314835.i | 0.0143068 | − | 0.0143068i | ||||
\(866\) | 9.99723e6 | 0.452986 | ||||||||
\(867\) | −3.21701e6 | + | 4.80712e6i | −0.145346 | + | 0.217189i | ||||
\(868\) | −3.01761e6 | −0.135945 | ||||||||
\(869\) | −2.45704e7 | + | 2.45704e7i | −1.10373 | + | 1.10373i | ||||
\(870\) | −776835. | − | 321775.i | −0.0347961 | − | 0.0144130i | ||||
\(871\) | 2.35685e6i | 0.105265i | ||||||||
\(872\) | 6.30657e6 | − | 1.52254e7i | 0.280868 | − | 0.678075i | ||||
\(873\) | −1.43654e7 | + | 5.95036e6i | −0.637945 | + | 0.264245i | ||||
\(874\) | −209480. | − | 505730.i | −0.00927608 | − | 0.0223944i | ||||
\(875\) | −1.91700e7 | − | 1.91700e7i | −0.846453 | − | 0.846453i | ||||
\(876\) | 1.47292e6 | + | 1.47292e6i | 0.0648512 | + | 0.0648512i | ||||
\(877\) | 7.02220e6 | + | 1.69531e7i | 0.308300 | + | 0.744303i | 0.999760 | + | 0.0218883i | \(0.00696781\pi\) |
−0.691460 | + | 0.722415i | \(0.743032\pi\) | |||||||
\(878\) | 1.06079e7 | − | 4.39395e6i | 0.464402 | − | 0.192362i | ||||
\(879\) | −3.05634e6 | + | 7.37865e6i | −0.133423 | + | 0.322111i | ||||
\(880\) | − | 5.75960e6i | − | 0.250718i | ||||||
\(881\) | −5.05399e6 | − | 2.09343e6i | −0.219379 | − | 0.0908696i | 0.270287 | − | 0.962780i | \(-0.412881\pi\) |
−0.489666 | + | 0.871910i | \(0.662881\pi\) | |||||||
\(882\) | −1.57208e7 | + | 1.57208e7i | −0.680461 | + | 0.680461i | ||||
\(883\) | −2.26631e6 | −0.0978176 | −0.0489088 | − | 0.998803i | \(-0.515574\pi\) | ||||
−0.0489088 | + | 0.998803i | \(0.515574\pi\) | |||||||
\(884\) | 1.36840e7 | + | 1.66862e7i | 0.588957 | + | 0.718171i | ||||
\(885\) | 1.89003e6 | 0.0811167 | ||||||||
\(886\) | 4.99938e6 | − | 4.99938e6i | 0.213960 | − | 0.213960i | ||||
\(887\) | 2.25063e7 | + | 9.32243e6i | 0.960496 | + | 0.397851i | 0.807166 | − | 0.590324i | \(-0.201000\pi\) |
0.153330 | + | 0.988175i | \(0.451000\pi\) | |||||||
\(888\) | 5.00126e6i | 0.212837i | ||||||||
\(889\) | 1.82115e7 | − | 4.39664e7i | 0.772843 | − | 1.86581i | ||||
\(890\) | 1.54652e6 | − | 640589.i | 0.0654455 | − | 0.0271084i | ||||
\(891\) | 1.02156e7 | + | 2.46627e7i | 0.431093 | + | 1.04075i | ||||
\(892\) | −1.59982e7 | − | 1.59982e7i | −0.673223 | − | 0.673223i | ||||
\(893\) | 3.10512e6 | + | 3.10512e6i | 0.130302 | + | 0.130302i | ||||
\(894\) | 15137.2 | + | 36544.5i | 0.000633435 | + | 0.00152925i | ||||
\(895\) | 5.88681e6 | − | 2.43840e6i | 0.245653 | − | 0.101753i | ||||
\(896\) | −1.75912e7 | + | 4.24690e7i | −0.732026 | + | 1.76727i | ||||
\(897\) | − | 2.49125e6i | − | 0.103380i | ||||||
\(898\) | −7.05749e6 | − | 2.92331e6i | −0.292051 | − | 0.120972i | ||||
\(899\) | 1.55321e6 | − | 1.55321e6i | 0.0640961 | − | 0.0640961i | ||||
\(900\) | 1.67021e7 | 0.687327 | ||||||||
\(901\) | 458867. | + | 45360.8i | 0.0188311 | + | 0.00186152i | ||||
\(902\) | −1.16649e7 | −0.477381 | ||||||||
\(903\) | −6.11070e6 | + | 6.11070e6i | −0.249386 | + | 0.249386i | ||||
\(904\) | −1.09275e7 | − | 4.52630e6i | −0.444732 | − | 0.184214i | ||||
\(905\) | 1.14670e7i | 0.465403i | ||||||||
\(906\) | −160634. | + | 387804.i | −0.00650154 | + | 0.0156961i | ||||
\(907\) | 2.22738e7 | − | 9.22612e6i | 0.899035 | − | 0.372392i | 0.115186 | − | 0.993344i | \(-0.463254\pi\) |
0.783849 | + | 0.620952i | \(0.213254\pi\) | |||||||
\(908\) | −170330. | − | 411214.i | −0.00685611 | − | 0.0165521i | ||||
\(909\) | 2.37614e7 | + | 2.37614e7i | 0.953813 | + | 0.953813i | ||||
\(910\) | −5.11174e6 | − | 5.11174e6i | −0.204628 | − | 0.204628i | ||||
\(911\) | −5.71190e6 | − | 1.37897e7i | −0.228026 | − | 0.550504i | 0.767911 | − | 0.640557i | \(-0.221296\pi\) |
−0.995937 | + | 0.0900530i | \(0.971296\pi\) | |||||||
\(912\) | 533788. | − | 221102.i | 0.0212511 | − | 0.00880250i | ||||
\(913\) | 8.62040e6 | − | 2.08115e7i | 0.342255 | − | 0.826278i | ||||
\(914\) | − | 3.07412e6i | − | 0.121718i | ||||||
\(915\) | 731118. | + | 302839.i | 0.0288692 | + | 0.0119580i | ||||
\(916\) | −2.58300e7 | + | 2.58300e7i | −1.01715 | + | 1.01715i | ||||
\(917\) | −1.42714e7 | −0.560457 | ||||||||
\(918\) | 1.52780e6 | + | 5.04301e6i | 0.0598358 | + | 0.197507i | ||||
\(919\) | 2.97269e7 | 1.16108 | 0.580538 | − | 0.814233i | \(-0.302842\pi\) | ||||
0.580538 | + | 0.814233i | \(0.302842\pi\) | |||||||
\(920\) | 1.63105e6 | − | 1.63105e6i | 0.0635329 | − | 0.0635329i | ||||
\(921\) | 7.73809e6 | + | 3.20522e6i | 0.300597 | + | 0.124511i | ||||
\(922\) | − | 7.25376e6i | − | 0.281019i | ||||||
\(923\) | −1.54108e7 | + | 3.72051e7i | −0.595418 | + | 1.43747i | ||||
\(924\) | −1.38044e7 | + | 5.71796e6i | −0.531908 | + | 0.220324i | ||||
\(925\) | −9.58734e6 | − | 2.31459e7i | −0.368421 | − | 0.889446i | ||||
\(926\) | −5.53473e6 | − | 5.53473e6i | −0.212114 | − | 0.212114i | ||||
\(927\) | −2.69524e7 | − | 2.69524e7i | −1.03014 | − | 1.03014i | ||||
\(928\) | −1.00989e7 | − | 2.43810e7i | −0.384951 | − | 0.929353i | ||||
\(929\) | 3.51738e7 | − | 1.45695e7i | 1.33715 | − | 0.553866i | 0.404464 | − | 0.914554i | \(-0.367458\pi\) |
0.932687 | + | 0.360688i | \(0.117458\pi\) | |||||||
\(930\) | 31682.9 | − | 76489.2i | 0.00120121 | − | 0.00289997i | ||||
\(931\) | − | 1.11689e7i | − | 0.422315i | ||||||
\(932\) | −1.89914e7 | − | 7.86650e6i | −0.716172 | − | 0.296648i | ||||
\(933\) | 2.60433e6 | − | 2.60433e6i | 0.0979473 | − | 0.0979473i | ||||
\(934\) | −5.05231e6 | −0.189506 | ||||||||
\(935\) | −9.84166e6 | + | 8.07093e6i | −0.368162 | + | 0.301922i | ||||
\(936\) | 2.08663e7 | 0.778494 | ||||||||
\(937\) | 2.58983e7 | − | 2.58983e7i | 0.963658 | − | 0.963658i | −0.0357043 | − | 0.999362i | \(-0.511367\pi\) |
0.999362 | + | 0.0357043i | \(0.0113675\pi\) | |||||||
\(938\) | 1.80411e6 | + | 747288.i | 0.0669509 | + | 0.0277320i | ||||
\(939\) | 454694.i | 0.0168289i | ||||||||
\(940\) | −3.21782e6 | + | 7.76852e6i | −0.118780 | + | 0.286760i | ||||
\(941\) | −2.19997e6 | + | 911256.i | −0.0809920 | + | 0.0335480i | −0.422812 | − | 0.906218i | \(-0.638957\pi\) |
0.341820 | + | 0.939766i | \(0.388957\pi\) | |||||||
\(942\) | −46732.4 | − | 112822.i | −0.00171589 | − | 0.00414254i | ||||
\(943\) | 5.67884e6 | + | 5.67884e6i | 0.207960 | + | 0.207960i | ||||
\(944\) | 9.36103e6 | + | 9.36103e6i | 0.341896 | + | 0.341896i | ||||
\(945\) | 3.36664e6 | + | 8.12778e6i | 0.122636 | + | 0.296069i | ||||
\(946\) | −1.05228e7 | + | 4.35868e6i | −0.382299 | + | 0.158353i | ||||
\(947\) | −1.04798e7 | + | 2.53005e7i | −0.379733 | + | 0.916758i | 0.612282 | + | 0.790640i | \(0.290252\pi\) |
−0.992015 | + | 0.126118i | \(0.959748\pi\) | |||||||
\(948\) | − | 6.67450e6i | − | 0.241211i | ||||||
\(949\) | −1.20438e7 | − | 4.98870e6i | −0.434108 | − | 0.179813i | ||||
\(950\) | 1.19046e6 | − | 1.19046e6i | 0.0427963 | − | 0.0427963i | ||||
\(951\) | −686366. | −0.0246096 | ||||||||
\(952\) | 3.76570e7 | − | 1.14084e7i | 1.34665 | − | 0.407973i | ||||
\(953\) | −4.24164e6 | −0.151287 | −0.0756436 | − | 0.997135i | \(-0.524101\pi\) | ||||
−0.0756436 | + | 0.997135i | \(0.524101\pi\) | |||||||
\(954\) | 143262. | − | 143262.i | 0.00509637 | − | 0.00509637i | ||||
\(955\) | 3.36379e6 | + | 1.39333e6i | 0.119349 | + | 0.0494362i | ||||
\(956\) | − | 3.68009e7i | − | 1.30231i | ||||||
\(957\) | 4.16221e6 | − | 1.00485e7i | 0.146908 | − | 0.354666i | ||||
\(958\) | −1.32547e6 | + | 549026.i | −0.0466611 | + | 0.0193277i | ||||
\(959\) | −9.46892e6 | − | 2.28600e7i | −0.332471 | − | 0.802656i | ||||
\(960\) | 235925. | + | 235925.i | 0.00826222 | + | 0.00826222i | ||||
\(961\) | −2.00909e7 | − | 2.00909e7i | −0.701765 | − | 0.701765i | ||||
\(962\) | −5.44280e6 | − | 1.31401e7i | −0.189620 | − | 0.457784i | ||||
\(963\) | −2.49904e7 | + | 1.03513e7i | −0.868374 | + | 0.359692i | ||||
\(964\) | 3.08335e6 | − | 7.44387e6i | 0.106864 | − | 0.257992i | ||||
\(965\) | − | 1.60964e7i | − | 0.556430i | ||||||
\(966\) | −1.90699e6 | − | 789903.i | −0.0657517 | − | 0.0272352i | ||||
\(967\) | 1.06619e7 | − | 1.06619e7i | 0.366664 | − | 0.366664i | −0.499595 | − | 0.866259i | \(-0.666518\pi\) |
0.866259 | + | 0.499595i | \(0.166518\pi\) | |||||||
\(968\) | −2.14932e7 | −0.737245 | ||||||||
\(969\) | −1.12580e6 | − | 602274.i | −0.0385171 | − | 0.0206056i | ||||
\(970\) | −3.00119e6 | −0.102415 | ||||||||
\(971\) | −1.63855e7 | + | 1.63855e7i | −0.557714 | + | 0.557714i | −0.928656 | − | 0.370942i | \(-0.879035\pi\) |
0.370942 | + | 0.928656i | \(0.379035\pi\) | |||||||
\(972\) | −1.61794e7 | − | 6.70171e6i | −0.549282 | − | 0.227520i | ||||
\(973\) | 1.59573e7i | 0.540353i | ||||||||
\(974\) | 1.42229e6 | − | 3.43371e6i | 0.0480386 | − | 0.115975i | ||||
\(975\) | 7.07880e6 | − | 2.93213e6i | 0.238478 | − | 0.0987808i | ||||
\(976\) | 2.12120e6 | + | 5.12103e6i | 0.0712783 | + | 0.172081i | ||||
\(977\) | 1.63754e7 | + | 1.63754e7i | 0.548854 | + | 0.548854i | 0.926109 | − | 0.377255i | \(-0.123132\pi\) |
−0.377255 | + | 0.926109i | \(0.623132\pi\) | |||||||
\(978\) | −2.39904e6 | − | 2.39904e6i | −0.0802028 | − | 0.0802028i | ||||
\(979\) | 8.28611e6 | + | 2.00044e7i | 0.276308 | + | 0.667067i | ||||
\(980\) | 1.97585e7 | − | 8.18426e6i | 0.657188 | − | 0.272216i | ||||
\(981\) | 1.05270e7 | − | 2.54145e7i | 0.349248 | − | 0.843159i | ||||
\(982\) | 1.91425e7i | 0.633460i | ||||||||
\(983\) | 3.64475e7 | + | 1.50970e7i | 1.20305 | + | 0.498320i | 0.891983 | − | 0.452068i | \(-0.149314\pi\) |
0.311067 | + | 0.950388i | \(0.399314\pi\) | |||||||
\(984\) | 3.48665e6 | − | 3.48665e6i | 0.114794 | − | 0.114794i | ||||
\(985\) | 1.76048e7 | 0.578149 | ||||||||
\(986\) | −6.13937e6 | + | 1.14760e7i | −0.201109 | + | 0.375924i | ||||
\(987\) | 1.65586e7 | 0.541043 | ||||||||
\(988\) | −3.36822e6 | + | 3.36822e6i | −0.109776 | + | 0.109776i | ||||
\(989\) | 7.24475e6 | + | 3.00088e6i | 0.235523 | + | 0.0975567i | ||||
\(990\) | 5.59247e6i | 0.181349i | ||||||||
\(991\) | −1.97919e7 | + | 4.77818e7i | −0.640181 | + | 1.54553i | 0.186254 | + | 0.982502i | \(0.440365\pi\) |
−0.826435 | + | 0.563032i | \(0.809635\pi\) | |||||||
\(992\) | 2.40062e6 | − | 994368.i | 0.0774539 | − | 0.0320825i | ||||
\(993\) | −56284.1 | − | 135882.i | −0.00181139 | − | 0.00437309i | ||||
\(994\) | 2.35933e7 | + | 2.35933e7i | 0.757396 | + | 0.757396i | ||||
\(995\) | −5.05629e6 | − | 5.05629e6i | −0.161910 | − | 0.161910i | ||||
\(996\) | 1.65584e6 | + | 3.99754e6i | 0.0528895 | + | 0.127686i | ||||
\(997\) | −3.04073e7 | + | 1.25951e7i | −0.968812 | + | 0.401295i | −0.810270 | − | 0.586057i | \(-0.800679\pi\) |
−0.158542 | + | 0.987352i | \(0.550679\pi\) | |||||||
\(998\) | 1.20434e6 | − | 2.90753e6i | 0.0382757 | − | 0.0924056i | ||||
\(999\) | 1.73083e7i | 0.548708i |
(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 | 17.6.d.a.9.3 | yes | 28 | |
17.2 | even | 8 | inner | 17.6.d.a.2.3 | ✓ | 28 | |
17.6 | odd | 16 | 289.6.a.j.1.12 | 28 | |||
17.11 | odd | 16 | 289.6.a.j.1.11 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.6.d.a.2.3 | ✓ | 28 | 17.2 | even | 8 | inner | |
17.6.d.a.9.3 | yes | 28 | 1.1 | even | 1 | trivial | |
289.6.a.j.1.11 | 28 | 17.11 | odd | 16 | |||
289.6.a.j.1.12 | 28 | 17.6 | odd | 16 |