Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.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: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.67 |
Dual form | 147.6.e.d.79.1 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50000 | − | 4.33013i | −0.441942 | − | 0.765466i | 0.555892 | − | 0.831255i | \(-0.312377\pi\) |
−0.997834 | + | 0.0657891i | \(0.979044\pi\) | |||||||
\(3\) | 4.50000 | − | 7.79423i | 0.288675 | − | 0.500000i | ||||
\(4\) | 3.50000 | − | 6.06218i | 0.109375 | − | 0.189443i | ||||
\(5\) | 47.0000 | + | 81.4064i | 0.840762 | + | 1.45624i | 0.889252 | + | 0.457418i | \(0.151226\pi\) |
−0.0484902 | + | 0.998824i | \(0.515441\pi\) | |||||||
\(6\) | −45.0000 | −0.510310 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −195.000 | −1.07723 | ||||||||
\(9\) | −40.5000 | − | 70.1481i | −0.166667 | − | 0.288675i | ||||
\(10\) | 235.000 | − | 407.032i | 0.743135 | − | 1.28715i | ||||
\(11\) | −26.0000 | + | 45.0333i | −0.0647876 | + | 0.112215i | −0.896600 | − | 0.442842i | \(-0.853970\pi\) |
0.831812 | + | 0.555057i | \(0.187304\pi\) | |||||||
\(12\) | −31.5000 | − | 54.5596i | −0.0631477 | − | 0.109375i | ||||
\(13\) | 770.000 | 1.26367 | 0.631833 | − | 0.775104i | \(-0.282303\pi\) | ||||
0.631833 | + | 0.775104i | \(0.282303\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 846.000 | 0.970828 | ||||||||
\(16\) | 375.500 | + | 650.385i | 0.366699 | + | 0.635142i | ||||
\(17\) | −1011.00 | + | 1751.10i | −0.848455 | + | 1.46957i | 0.0341315 | + | 0.999417i | \(0.489134\pi\) |
−0.882587 | + | 0.470150i | \(0.844200\pi\) | |||||||
\(18\) | −202.500 | + | 350.740i | −0.147314 | + | 0.255155i | ||||
\(19\) | 866.000 | + | 1499.96i | 0.550344 | + | 0.953223i | 0.998250 | + | 0.0591424i | \(0.0188366\pi\) |
−0.447906 | + | 0.894081i | \(0.647830\pi\) | |||||||
\(20\) | 658.000 | 0.367833 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 260.000 | 0.114529 | ||||||||
\(23\) | 288.000 | + | 498.831i | 0.113520 | + | 0.196623i | 0.917187 | − | 0.398457i | \(-0.130454\pi\) |
−0.803667 | + | 0.595079i | \(0.797121\pi\) | |||||||
\(24\) | −877.500 | + | 1519.87i | −0.310970 | + | 0.538616i | ||||
\(25\) | −2855.50 | + | 4945.87i | −0.913760 | + | 1.58268i | ||||
\(26\) | −1925.00 | − | 3334.20i | −0.558467 | − | 0.967293i | ||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5518.00 | 1.21839 | 0.609196 | − | 0.793020i | \(-0.291492\pi\) | ||||
0.609196 | + | 0.793020i | \(0.291492\pi\) | |||||||
\(30\) | −2115.00 | − | 3663.29i | −0.429049 | − | 0.743135i | ||||
\(31\) | 3168.00 | − | 5487.14i | 0.592081 | − | 1.02551i | −0.401871 | − | 0.915696i | \(-0.631640\pi\) |
0.993952 | − | 0.109818i | \(-0.0350267\pi\) | |||||||
\(32\) | −1242.50 | + | 2152.07i | −0.214497 | + | 0.371520i | ||||
\(33\) | 234.000 | + | 405.300i | 0.0374051 | + | 0.0647876i | ||||
\(34\) | 10110.0 | 1.49987 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −567.000 | −0.0729167 | ||||||||
\(37\) | 3669.00 | + | 6354.89i | 0.440599 | + | 0.763140i | 0.997734 | − | 0.0672822i | \(-0.0214328\pi\) |
−0.557135 | + | 0.830422i | \(0.688099\pi\) | |||||||
\(38\) | 4330.00 | − | 7499.78i | 0.486440 | − | 0.842538i | ||||
\(39\) | 3465.00 | − | 6001.56i | 0.364789 | − | 0.631833i | ||||
\(40\) | −9165.00 | − | 15874.2i | −0.905696 | − | 1.56871i | ||||
\(41\) | 3262.00 | 0.303057 | 0.151528 | − | 0.988453i | \(-0.451580\pi\) | ||||
0.151528 | + | 0.988453i | \(0.451580\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5420.00 | 0.447021 | 0.223511 | − | 0.974701i | \(-0.428248\pi\) | ||||
0.223511 | + | 0.974701i | \(0.428248\pi\) | |||||||
\(44\) | 182.000 | + | 315.233i | 0.0141723 | + | 0.0245471i | ||||
\(45\) | 3807.00 | − | 6593.92i | 0.280254 | − | 0.485414i | ||||
\(46\) | 1440.00 | − | 2494.15i | 0.100339 | − | 0.173792i | ||||
\(47\) | 432.000 | + | 748.246i | 0.0285259 | + | 0.0494083i | 0.879936 | − | 0.475092i | \(-0.157585\pi\) |
−0.851410 | + | 0.524501i | \(0.824252\pi\) | |||||||
\(48\) | 6759.00 | 0.423428 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 28555.0 | 1.61531 | ||||||||
\(51\) | 9099.00 | + | 15759.9i | 0.489856 | + | 0.848455i | ||||
\(52\) | 2695.00 | − | 4667.88i | 0.138213 | − | 0.239393i | ||||
\(53\) | −2091.00 | + | 3621.72i | −0.102250 | + | 0.177103i | −0.912611 | − | 0.408828i | \(-0.865938\pi\) |
0.810361 | + | 0.585931i | \(0.199271\pi\) | |||||||
\(54\) | 1822.50 | + | 3156.66i | 0.0850517 | + | 0.147314i | ||||
\(55\) | −4888.00 | −0.217884 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15588.0 | 0.635482 | ||||||||
\(58\) | −13795.0 | − | 23893.6i | −0.538458 | − | 0.932636i | ||||
\(59\) | −5610.00 | + | 9716.81i | −0.209813 | + | 0.363407i | −0.951656 | − | 0.307167i | \(-0.900619\pi\) |
0.741842 | + | 0.670574i | \(0.233952\pi\) | |||||||
\(60\) | 2961.00 | − | 5128.60i | 0.106184 | − | 0.183917i | ||||
\(61\) | −22801.0 | − | 39492.5i | −0.784566 | − | 1.35891i | −0.929258 | − | 0.369431i | \(-0.879553\pi\) |
0.144693 | − | 0.989477i | \(-0.453781\pi\) | |||||||
\(62\) | −31680.0 | −1.04666 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 36457.0 | 1.11258 | ||||||||
\(65\) | 36190.0 | + | 62682.9i | 1.06244 | + | 1.84020i | ||||
\(66\) | 1170.00 | − | 2026.50i | 0.0330618 | − | 0.0572647i | ||||
\(67\) | −698.000 | + | 1208.97i | −0.0189963 | + | 0.0329025i | −0.875367 | − | 0.483459i | \(-0.839380\pi\) |
0.856371 | + | 0.516361i | \(0.172714\pi\) | |||||||
\(68\) | 7077.00 | + | 12257.7i | 0.185600 | + | 0.321468i | ||||
\(69\) | 5184.00 | 0.131082 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 18720.0 | 0.440717 | 0.220359 | − | 0.975419i | \(-0.429277\pi\) | ||||
0.220359 | + | 0.975419i | \(0.429277\pi\) | |||||||
\(72\) | 7897.50 | + | 13678.9i | 0.179539 | + | 0.310970i | ||||
\(73\) | 23181.0 | − | 40150.7i | 0.509126 | − | 0.881832i | −0.490818 | − | 0.871262i | \(-0.663302\pi\) |
0.999944 | − | 0.0105697i | \(-0.00336450\pi\) | |||||||
\(74\) | 18345.0 | − | 31774.5i | 0.389438 | − | 0.674527i | ||||
\(75\) | 25699.5 | + | 44512.8i | 0.527560 | + | 0.913760i | ||||
\(76\) | 12124.0 | 0.240775 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −34650.0 | −0.644862 | ||||||||
\(79\) | −48712.0 | − | 84371.7i | −0.878149 | − | 1.52100i | −0.853370 | − | 0.521306i | \(-0.825445\pi\) |
−0.0247791 | − | 0.999693i | \(-0.507888\pi\) | |||||||
\(80\) | −35297.0 | + | 61136.2i | −0.616613 | + | 1.06801i | ||||
\(81\) | −3280.50 | + | 5681.99i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −8155.00 | − | 14124.9i | −0.133934 | − | 0.231980i | ||||
\(83\) | 81228.0 | 1.29423 | 0.647114 | − | 0.762394i | \(-0.275976\pi\) | ||||
0.647114 | + | 0.762394i | \(0.275976\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −190068. | −2.85339 | ||||||||
\(86\) | −13550.0 | − | 23469.3i | −0.197557 | − | 0.342179i | ||||
\(87\) | 24831.0 | − | 43008.6i | 0.351719 | − | 0.609196i | ||||
\(88\) | 5070.00 | − | 8781.50i | 0.0697913 | − | 0.120882i | ||||
\(89\) | −1591.00 | − | 2755.69i | −0.0212910 | − | 0.0368770i | 0.855184 | − | 0.518325i | \(-0.173444\pi\) |
−0.876475 | + | 0.481448i | \(0.840111\pi\) | |||||||
\(90\) | −38070.0 | −0.495424 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4032.00 | 0.0496651 | ||||||||
\(93\) | −28512.0 | − | 49384.2i | −0.341838 | − | 0.592081i | ||||
\(94\) | 2160.00 | − | 3741.23i | 0.0252136 | − | 0.0436712i | ||||
\(95\) | −81404.0 | + | 140996.i | −0.925415 | + | 1.60287i | ||||
\(96\) | 11182.5 | + | 19368.7i | 0.123840 | + | 0.214497i | ||||
\(97\) | −4914.00 | −0.0530281 | −0.0265140 | − | 0.999648i | \(-0.508441\pi\) | ||||
−0.0265140 | + | 0.999648i | \(0.508441\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4212.00 | 0.0431917 | ||||||||
\(100\) | 19988.5 | + | 34621.1i | 0.199885 | + | 0.346211i | ||||
\(101\) | −83177.0 | + | 144067.i | −0.811334 | + | 1.40527i | 0.100596 | + | 0.994927i | \(0.467925\pi\) |
−0.911930 | + | 0.410345i | \(0.865408\pi\) | |||||||
\(102\) | 45495.0 | − | 78799.7i | 0.432975 | − | 0.749935i | ||||
\(103\) | 78580.0 | + | 136105.i | 0.729825 | + | 1.26409i | 0.956957 | + | 0.290231i | \(0.0937320\pi\) |
−0.227131 | + | 0.973864i | \(0.572935\pi\) | |||||||
\(104\) | −150150. | −1.36126 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 20910.0 | 0.180755 | ||||||||
\(107\) | 3382.00 | + | 5857.80i | 0.0285571 | + | 0.0494624i | 0.879951 | − | 0.475065i | \(-0.157575\pi\) |
−0.851394 | + | 0.524527i | \(0.824242\pi\) | |||||||
\(108\) | −2551.50 | + | 4419.33i | −0.0210492 | + | 0.0364583i | ||||
\(109\) | −89199.0 | + | 154497.i | −0.719107 | + | 1.24553i | 0.242246 | + | 0.970215i | \(0.422116\pi\) |
−0.961354 | + | 0.275316i | \(0.911218\pi\) | |||||||
\(110\) | 12220.0 | + | 21165.7i | 0.0962918 | + | 0.166782i | ||||
\(111\) | 66042.0 | 0.508760 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −45134.0 | −0.332512 | −0.166256 | − | 0.986083i | \(-0.553168\pi\) | ||||
−0.166256 | + | 0.986083i | \(0.553168\pi\) | |||||||
\(114\) | −38970.0 | − | 67498.0i | −0.280846 | − | 0.486440i | ||||
\(115\) | −27072.0 | + | 46890.1i | −0.190887 | + | 0.330626i | ||||
\(116\) | 19313.0 | − | 33451.1i | 0.133262 | − | 0.230816i | ||||
\(117\) | −31185.0 | − | 54014.0i | −0.210611 | − | 0.364789i | ||||
\(118\) | 56100.0 | 0.370901 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −164970. | −1.04581 | ||||||||
\(121\) | 79173.5 | + | 137133.i | 0.491605 | + | 0.851485i | ||||
\(122\) | −114005. | + | 197462.i | −0.693465 | + | 1.20112i | ||||
\(123\) | 14679.0 | − | 25424.8i | 0.0874850 | − | 0.151528i | ||||
\(124\) | −22176.0 | − | 38410.0i | −0.129518 | − | 0.224331i | ||||
\(125\) | −243084. | −1.39149 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −205056. | −1.12814 | −0.564070 | − | 0.825727i | \(-0.690765\pi\) | ||||
−0.564070 | + | 0.825727i | \(0.690765\pi\) | |||||||
\(128\) | −51382.5 | − | 88997.1i | −0.277198 | − | 0.480121i | ||||
\(129\) | 24390.0 | − | 42244.7i | 0.129044 | − | 0.223511i | ||||
\(130\) | 180950. | − | 313415.i | 0.939075 | − | 1.62653i | ||||
\(131\) | 36482.0 | + | 63188.7i | 0.185738 | + | 0.321707i | 0.943825 | − | 0.330446i | \(-0.107199\pi\) |
−0.758087 | + | 0.652153i | \(0.773866\pi\) | |||||||
\(132\) | 3276.00 | 0.0163647 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6980.00 | 0.0335810 | ||||||||
\(135\) | −34263.0 | − | 59345.3i | −0.161805 | − | 0.280254i | ||||
\(136\) | 197145. | − | 341465.i | 0.913984 | − | 1.58307i | ||||
\(137\) | 47091.0 | − | 81564.0i | 0.214356 | − | 0.371276i | −0.738717 | − | 0.674016i | \(-0.764568\pi\) |
0.953073 | + | 0.302740i | \(0.0979013\pi\) | |||||||
\(138\) | −12960.0 | − | 22447.4i | −0.0579305 | − | 0.100339i | ||||
\(139\) | 47796.0 | 0.209824 | 0.104912 | − | 0.994482i | \(-0.466544\pi\) | ||||
0.104912 | + | 0.994482i | \(0.466544\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7776.00 | 0.0329389 | ||||||||
\(142\) | −46800.0 | − | 81060.0i | −0.194771 | − | 0.337354i | ||||
\(143\) | −20020.0 | + | 34675.7i | −0.0818698 | + | 0.141803i | ||||
\(144\) | 30415.5 | − | 52681.2i | 0.122233 | − | 0.211714i | ||||
\(145\) | 259346. | + | 449200.i | 1.02438 | + | 1.77427i | ||||
\(146\) | −231810. | −0.900016 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 51366.0 | 0.192762 | ||||||||
\(149\) | 62133.0 | + | 107618.i | 0.229275 | + | 0.397116i | 0.957593 | − | 0.288123i | \(-0.0930312\pi\) |
−0.728318 | + | 0.685239i | \(0.759698\pi\) | |||||||
\(150\) | 128498. | − | 222564.i | 0.466301 | − | 0.807657i | ||||
\(151\) | 223148. | − | 386504.i | 0.796436 | − | 1.37947i | −0.125488 | − | 0.992095i | \(-0.540050\pi\) |
0.921924 | − | 0.387372i | \(-0.126617\pi\) | |||||||
\(152\) | −168870. | − | 292491.i | −0.592848 | − | 1.02684i | ||||
\(153\) | 163782. | 0.565637 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 595584. | 1.99119 | ||||||||
\(156\) | −24255.0 | − | 42010.9i | −0.0797976 | − | 0.138213i | ||||
\(157\) | −79873.0 | + | 138344.i | −0.258613 | + | 0.447931i | −0.965871 | − | 0.259025i | \(-0.916599\pi\) |
0.707257 | + | 0.706956i | \(0.249932\pi\) | |||||||
\(158\) | −243560. | + | 421858.i | −0.776181 | + | 1.34439i | ||||
\(159\) | 18819.0 | + | 32595.5i | 0.0590342 | + | 0.102250i | ||||
\(160\) | −233590. | −0.721364 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 32805.0 | 0.0982093 | ||||||||
\(163\) | −123626. | − | 214127.i | −0.364452 | − | 0.631250i | 0.624236 | − | 0.781236i | \(-0.285410\pi\) |
−0.988688 | + | 0.149986i | \(0.952077\pi\) | |||||||
\(164\) | 11417.0 | − | 19774.8i | 0.0331469 | − | 0.0574120i | ||||
\(165\) | −21996.0 | + | 38098.2i | −0.0628976 | + | 0.108942i | ||||
\(166\) | −203070. | − | 351728.i | −0.571973 | − | 0.990686i | ||||
\(167\) | 684488. | 1.89922 | 0.949609 | − | 0.313438i | \(-0.101481\pi\) | ||||
0.949609 | + | 0.313438i | \(0.101481\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 221607. | 0.596852 | ||||||||
\(170\) | 475170. | + | 823019.i | 1.26103 | + | 2.18417i | ||||
\(171\) | 70146.0 | − | 121496.i | 0.183448 | − | 0.317741i | ||||
\(172\) | 18970.0 | − | 32857.0i | 0.0488929 | − | 0.0846851i | ||||
\(173\) | −305237. | − | 528686.i | −0.775393 | − | 1.34302i | −0.934573 | − | 0.355771i | \(-0.884218\pi\) |
0.159180 | − | 0.987250i | \(-0.449115\pi\) | |||||||
\(174\) | −248310. | −0.621758 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −39052.0 | −0.0950302 | ||||||||
\(177\) | 50490.0 | + | 87451.2i | 0.121136 | + | 0.209813i | ||||
\(178\) | −7955.00 | + | 13778.5i | −0.0188187 | + | 0.0325950i | ||||
\(179\) | −331126. | + | 573527.i | −0.772433 | + | 1.33789i | 0.163793 | + | 0.986495i | \(0.447627\pi\) |
−0.936226 | + | 0.351398i | \(0.885706\pi\) | |||||||
\(180\) | −26649.0 | − | 46157.4i | −0.0613055 | − | 0.106184i | ||||
\(181\) | −154630. | −0.350830 | −0.175415 | − | 0.984495i | \(-0.556127\pi\) | ||||
−0.175415 | + | 0.984495i | \(0.556127\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −410418. | −0.905938 | ||||||||
\(184\) | −56160.0 | − | 97272.0i | −0.122288 | − | 0.211808i | ||||
\(185\) | −344886. | + | 597360.i | −0.740877 | + | 1.28324i | ||||
\(186\) | −142560. | + | 246921.i | −0.302145 | + | 0.523330i | ||||
\(187\) | −52572.0 | − | 91057.4i | −0.109939 | − | 0.190419i | ||||
\(188\) | 6048.00 | 0.0124801 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 814040. | 1.63592 | ||||||||
\(191\) | −243452. | − | 421671.i | −0.482870 | − | 0.836355i | 0.516937 | − | 0.856024i | \(-0.327072\pi\) |
−0.999807 | + | 0.0196687i | \(0.993739\pi\) | |||||||
\(192\) | 164056. | − | 284154.i | 0.321174 | − | 0.556290i | ||||
\(193\) | −310273. | + | 537409.i | −0.599585 | + | 1.03851i | 0.393297 | + | 0.919411i | \(0.371334\pi\) |
−0.992882 | + | 0.119100i | \(0.961999\pi\) | |||||||
\(194\) | 12285.0 | + | 21278.2i | 0.0234353 | + | 0.0405912i | ||||
\(195\) | 651420. | 1.22680 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −236570. | −0.434304 | −0.217152 | − | 0.976138i | \(-0.569677\pi\) | ||||
−0.217152 | + | 0.976138i | \(0.569677\pi\) | |||||||
\(198\) | −10530.0 | − | 18238.5i | −0.0190882 | − | 0.0330618i | ||||
\(199\) | 41052.0 | − | 71104.1i | 0.0734855 | − | 0.127281i | −0.826941 | − | 0.562288i | \(-0.809921\pi\) |
0.900427 | + | 0.435008i | \(0.143254\pi\) | |||||||
\(200\) | 556822. | − | 964445.i | 0.984332 | − | 1.70491i | ||||
\(201\) | 6282.00 | + | 10880.7i | 0.0109675 | + | 0.0189963i | ||||
\(202\) | 831770. | 1.43425 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 127386. | 0.214312 | ||||||||
\(205\) | 153314. | + | 265548.i | 0.254799 | + | 0.441324i | ||||
\(206\) | 392900. | − | 680523.i | 0.645081 | − | 1.11731i | ||||
\(207\) | 23328.0 | − | 40405.3i | 0.0378400 | − | 0.0655409i | ||||
\(208\) | 289135. | + | 500797.i | 0.463385 | + | 0.802607i | ||||
\(209\) | −90064.0 | −0.142622 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 99892.0 | 0.154463 | 0.0772315 | − | 0.997013i | \(-0.475392\pi\) | ||||
0.0772315 | + | 0.997013i | \(0.475392\pi\) | |||||||
\(212\) | 14637.0 | + | 25352.0i | 0.0223672 | + | 0.0387412i | ||||
\(213\) | 84240.0 | − | 145908.i | 0.127224 | − | 0.220359i | ||||
\(214\) | 16910.0 | − | 29289.0i | 0.0252412 | − | 0.0437190i | ||||
\(215\) | 254740. | + | 441223.i | 0.375838 | + | 0.650971i | ||||
\(216\) | 142155. | 0.207314 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 891990. | 1.27121 | ||||||||
\(219\) | −208629. | − | 361356.i | −0.293944 | − | 0.509126i | ||||
\(220\) | −17108.0 | + | 29631.9i | −0.0238310 | + | 0.0412765i | ||||
\(221\) | −778470. | + | 1.34835e6i | −1.07216 | + | 1.85704i | ||||
\(222\) | −165105. | − | 285970.i | −0.224842 | − | 0.389438i | ||||
\(223\) | 186704. | 0.251415 | 0.125708 | − | 0.992067i | \(-0.459880\pi\) | ||||
0.125708 | + | 0.992067i | \(0.459880\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 462591. | 0.609173 | ||||||||
\(226\) | 112835. | + | 195436.i | 0.146951 | + | 0.254527i | ||||
\(227\) | 168186. | − | 291307.i | 0.216633 | − | 0.375220i | −0.737143 | − | 0.675736i | \(-0.763826\pi\) |
0.953777 | + | 0.300517i | \(0.0971591\pi\) | |||||||
\(228\) | 54558.0 | − | 94497.2i | 0.0695058 | − | 0.120388i | ||||
\(229\) | −463157. | − | 802211.i | −0.583633 | − | 1.01088i | −0.995044 | − | 0.0994317i | \(-0.968298\pi\) |
0.411412 | − | 0.911450i | \(-0.365036\pi\) | |||||||
\(230\) | 270720. | 0.337443 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.07601e6 | −1.31249 | ||||||||
\(233\) | −628557. | − | 1.08869e6i | −0.758499 | − | 1.31376i | −0.943616 | − | 0.331042i | \(-0.892600\pi\) |
0.185117 | − | 0.982716i | \(-0.440733\pi\) | |||||||
\(234\) | −155925. | + | 270070.i | −0.186156 | + | 0.322431i | ||||
\(235\) | −40608.0 | + | 70335.1i | −0.0479669 | + | 0.0830812i | ||||
\(236\) | 39270.0 | + | 68017.6i | 0.0458966 | + | 0.0794953i | ||||
\(237\) | −876816. | −1.01400 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −347016. | −0.392966 | −0.196483 | − | 0.980507i | \(-0.562952\pi\) | ||||
−0.196483 | + | 0.980507i | \(0.562952\pi\) | |||||||
\(240\) | 317673. | + | 550226.i | 0.356002 | + | 0.616613i | ||||
\(241\) | 49585.0 | − | 85883.7i | 0.0549930 | − | 0.0952507i | −0.837218 | − | 0.546869i | \(-0.815820\pi\) |
0.892211 | + | 0.451618i | \(0.149153\pi\) | |||||||
\(242\) | 395868. | − | 685663.i | 0.434522 | − | 0.752614i | ||||
\(243\) | 29524.5 | + | 51137.9i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −319214. | −0.343247 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −146790. | −0.154653 | ||||||||
\(247\) | 666820. | + | 1.15497e6i | 0.695451 | + | 1.20456i | ||||
\(248\) | −617760. | + | 1.06999e6i | −0.637809 | + | 1.10472i | ||||
\(249\) | 365526. | − | 633110.i | 0.373611 | − | 0.647114i | ||||
\(250\) | 607710. | + | 1.05258e6i | 0.614959 | + | 1.06514i | ||||
\(251\) | −344428. | −0.345076 | −0.172538 | − | 0.985003i | \(-0.555197\pi\) | ||||
−0.172538 | + | 0.985003i | \(0.555197\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29952.0 | −0.0294188 | ||||||||
\(254\) | 512640. | + | 887919.i | 0.498572 | + | 0.863553i | ||||
\(255\) | −855306. | + | 1.48143e6i | −0.823704 | + | 1.42670i | ||||
\(256\) | 326400. | − | 565341.i | 0.311279 | − | 0.539151i | ||||
\(257\) | 147565. | + | 255590.i | 0.139364 | + | 0.241386i | 0.927256 | − | 0.374428i | \(-0.122161\pi\) |
−0.787892 | + | 0.615813i | \(0.788828\pi\) | |||||||
\(258\) | −243900. | −0.228120 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 506660. | 0.464818 | ||||||||
\(261\) | −223479. | − | 387077.i | −0.203065 | − | 0.351719i | ||||
\(262\) | 182410. | − | 315943.i | 0.164171 | − | 0.284352i | ||||
\(263\) | 636232. | − | 1.10199e6i | 0.567187 | − | 0.982396i | −0.429656 | − | 0.902993i | \(-0.641365\pi\) |
0.996843 | − | 0.0794036i | \(-0.0253016\pi\) | |||||||
\(264\) | −45630.0 | − | 79033.5i | −0.0402940 | − | 0.0697913i | ||||
\(265\) | −393108. | −0.343872 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28638.0 | −0.0245847 | ||||||||
\(268\) | 4886.00 | + | 8462.80i | 0.00415543 | + | 0.00719742i | ||||
\(269\) | 138387. | − | 239693.i | 0.116604 | − | 0.201965i | −0.801816 | − | 0.597572i | \(-0.796132\pi\) |
0.918420 | + | 0.395607i | \(0.129466\pi\) | |||||||
\(270\) | −171315. | + | 296726.i | −0.143016 | + | 0.247712i | ||||
\(271\) | −644968. | − | 1.11712e6i | −0.533476 | − | 0.924008i | −0.999235 | − | 0.0390962i | \(-0.987552\pi\) |
0.465759 | − | 0.884911i | \(-0.345781\pi\) | |||||||
\(272\) | −1.51852e6 | −1.24451 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −470910. | −0.378932 | ||||||||
\(275\) | −148486. | − | 257185.i | −0.118401 | − | 0.205076i | ||||
\(276\) | 18144.0 | − | 31426.3i | 0.0143371 | − | 0.0248325i | ||||
\(277\) | −858275. | + | 1.48658e6i | −0.672089 | + | 1.16409i | 0.305221 | + | 0.952281i | \(0.401270\pi\) |
−0.977311 | + | 0.211811i | \(0.932064\pi\) | |||||||
\(278\) | −119490. | − | 206963.i | −0.0927299 | − | 0.160613i | ||||
\(279\) | −513216. | −0.394720 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.47218e6 | −1.11223 | −0.556116 | − | 0.831104i | \(-0.687709\pi\) | ||||
−0.556116 | + | 0.831104i | \(0.687709\pi\) | |||||||
\(282\) | −19440.0 | − | 33671.1i | −0.0145571 | − | 0.0252136i | ||||
\(283\) | 514406. | − | 890977.i | 0.381804 | − | 0.661303i | −0.609517 | − | 0.792773i | \(-0.708636\pi\) |
0.991320 | + | 0.131470i | \(0.0419698\pi\) | |||||||
\(284\) | 65520.0 | − | 113484.i | 0.0482034 | − | 0.0834908i | ||||
\(285\) | 732636. | + | 1.26896e6i | 0.534289 | + | 0.925415i | ||||
\(286\) | 200200. | 0.144727 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 201285. | 0.142998 | ||||||||
\(289\) | −1.33431e6 | − | 2.31110e6i | −0.939752 | − | 1.62770i | ||||
\(290\) | 1.29673e6 | − | 2.24600e6i | 0.905429 | − | 1.56825i | ||||
\(291\) | −22113.0 | + | 38300.8i | −0.0153079 | + | 0.0265140i | ||||
\(292\) | −162267. | − | 281055.i | −0.111371 | − | 0.192901i | ||||
\(293\) | 1.18607e6 | 0.807123 | 0.403562 | − | 0.914952i | \(-0.367772\pi\) | ||||
0.403562 | + | 0.914952i | \(0.367772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.05468e6 | −0.705612 | ||||||||
\(296\) | −715455. | − | 1.23920e6i | −0.474628 | − | 0.822079i | ||||
\(297\) | 18954.0 | − | 32829.3i | 0.0124684 | − | 0.0215959i | ||||
\(298\) | 310665. | − | 538088.i | 0.202652 | − | 0.351004i | ||||
\(299\) | 221760. | + | 384100.i | 0.143452 | + | 0.248465i | ||||
\(300\) | 359793. | 0.230807 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.23148e6 | −1.40791 | ||||||||
\(303\) | 748593. | + | 1.29660e6i | 0.468424 | + | 0.811334i | ||||
\(304\) | −650366. | + | 1.12647e6i | −0.403621 | + | 0.699092i | ||||
\(305\) | 2.14329e6 | − | 3.71229e6i | 1.31927 | − | 2.28503i | ||||
\(306\) | −409455. | − | 709197.i | −0.249978 | − | 0.432975i | ||||
\(307\) | −1.51892e6 | −0.919788 | −0.459894 | − | 0.887974i | \(-0.652113\pi\) | ||||
−0.459894 | + | 0.887974i | \(0.652113\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.41444e6 | 0.842730 | ||||||||
\(310\) | −1.48896e6 | − | 2.57895e6i | −0.879992 | − | 1.52419i | ||||
\(311\) | 106404. | − | 184297.i | 0.0623817 | − | 0.108048i | −0.833148 | − | 0.553050i | \(-0.813464\pi\) |
0.895530 | + | 0.445002i | \(0.146797\pi\) | |||||||
\(312\) | −675675. | + | 1.17030e6i | −0.392963 | + | 0.680631i | ||||
\(313\) | −947.000 | − | 1640.25i | −0.000546373 | − | 0.000946346i | 0.865752 | − | 0.500473i | \(-0.166841\pi\) |
−0.866298 | + | 0.499527i | \(0.833507\pi\) | |||||||
\(314\) | 798730. | 0.457168 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −681968. | −0.384190 | ||||||||
\(317\) | 789489. | + | 1.36744e6i | 0.441263 | + | 0.764291i | 0.997784 | − | 0.0665435i | \(-0.0211971\pi\) |
−0.556520 | + | 0.830834i | \(0.687864\pi\) | |||||||
\(318\) | 94095.0 | − | 162977.i | 0.0521794 | − | 0.0903773i | ||||
\(319\) | −143468. | + | 248494.i | −0.0789366 | + | 0.136722i | ||||
\(320\) | 1.71348e6 | + | 2.96783e6i | 0.935414 | + | 1.62018i | ||||
\(321\) | 60876.0 | 0.0329749 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.50210e6 | −1.86777 | ||||||||
\(324\) | 22963.5 | + | 39773.9i | 0.0121528 | + | 0.0210492i | ||||
\(325\) | −2.19874e6 | + | 3.80832e6i | −1.15469 | + | 1.99998i | ||||
\(326\) | −618130. | + | 1.07063e6i | −0.322133 | + | 0.557951i | ||||
\(327\) | 802791. | + | 1.39047e6i | 0.415177 | + | 0.719107i | ||||
\(328\) | −636090. | −0.326463 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 219960. | 0.111188 | ||||||||
\(331\) | 1.69735e6 | + | 2.93990e6i | 0.851535 | + | 1.47490i | 0.879823 | + | 0.475302i | \(0.157661\pi\) |
−0.0282879 | + | 0.999600i | \(0.509006\pi\) | |||||||
\(332\) | 284298. | − | 492419.i | 0.141556 | − | 0.245182i | ||||
\(333\) | 297189. | − | 514746.i | 0.146866 | − | 0.254380i | ||||
\(334\) | −1.71122e6 | − | 2.96392e6i | −0.839343 | − | 1.45379i | ||||
\(335\) | −131224. | −0.0638853 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.02731e6 | 0.972403 | 0.486201 | − | 0.873847i | \(-0.338382\pi\) | ||||
0.486201 | + | 0.873847i | \(0.338382\pi\) | |||||||
\(338\) | −554018. | − | 959586.i | −0.263774 | − | 0.456870i | ||||
\(339\) | −203103. | + | 351785.i | −0.0959880 | + | 0.166256i | ||||
\(340\) | −665238. | + | 1.15223e6i | −0.312090 | + | 0.540556i | ||||
\(341\) | 164736. | + | 285331.i | 0.0767189 | + | 0.132881i | ||||
\(342\) | −701460. | −0.324293 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.05690e6 | −0.481546 | ||||||||
\(345\) | 243648. | + | 422011.i | 0.110209 | + | 0.190887i | ||||
\(346\) | −1.52618e6 | + | 2.64343e6i | −0.685357 | + | 1.18707i | ||||
\(347\) | −1.74443e6 | + | 3.02143e6i | −0.777730 | + | 1.34707i | 0.155517 | + | 0.987833i | \(0.450296\pi\) |
−0.933247 | + | 0.359235i | \(0.883038\pi\) | |||||||
\(348\) | −173817. | − | 301060.i | −0.0769386 | − | 0.133262i | ||||
\(349\) | −965566. | −0.424344 | −0.212172 | − | 0.977232i | \(-0.568054\pi\) | ||||
−0.212172 | + | 0.977232i | \(0.568054\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −561330. | −0.243193 | ||||||||
\(352\) | −64610.0 | − | 111908.i | −0.0277935 | − | 0.0481397i | ||||
\(353\) | 576965. | − | 999333.i | 0.246441 | − | 0.426848i | −0.716095 | − | 0.698003i | \(-0.754072\pi\) |
0.962536 | + | 0.271155i | \(0.0874056\pi\) | |||||||
\(354\) | 252450. | − | 437256.i | 0.107070 | − | 0.185450i | ||||
\(355\) | 879840. | + | 1.52393e6i | 0.370538 | + | 0.641791i | ||||
\(356\) | −22274.0 | −0.00931479 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.31126e6 | 1.36548 | ||||||||
\(359\) | −805552. | − | 1.39526e6i | −0.329881 | − | 0.571371i | 0.652607 | − | 0.757697i | \(-0.273675\pi\) |
−0.982488 | + | 0.186326i | \(0.940342\pi\) | |||||||
\(360\) | −742365. | + | 1.28581e6i | −0.301899 | + | 0.522904i | ||||
\(361\) | −261862. | + | 453559.i | −0.105756 | + | 0.183175i | ||||
\(362\) | 386575. | + | 669568.i | 0.155047 | + | 0.268549i | ||||
\(363\) | 1.42512e6 | 0.567657 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.35803e6 | 1.71221 | ||||||||
\(366\) | 1.02605e6 | + | 1.77716e6i | 0.400372 | + | 0.693465i | ||||
\(367\) | 1.83874e6 | − | 3.18478e6i | 0.712614 | − | 1.23428i | −0.251259 | − | 0.967920i | \(-0.580845\pi\) |
0.963873 | − | 0.266363i | \(-0.0858221\pi\) | |||||||
\(368\) | −216288. | + | 374622.i | −0.0832555 | + | 0.144203i | ||||
\(369\) | −132111. | − | 228823.i | −0.0505095 | − | 0.0874850i | ||||
\(370\) | 3.44886e6 | 1.30970 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −399168. | −0.149554 | ||||||||
\(373\) | −324883. | − | 562714.i | −0.120908 | − | 0.209419i | 0.799218 | − | 0.601041i | \(-0.205247\pi\) |
−0.920126 | + | 0.391622i | \(0.871914\pi\) | |||||||
\(374\) | −262860. | + | 455287.i | −0.0971730 | + | 0.168309i | ||||
\(375\) | −1.09388e6 | + | 1.89465e6i | −0.401690 | + | 0.695747i | ||||
\(376\) | −84240.0 | − | 145908.i | −0.0307290 | − | 0.0532242i | ||||
\(377\) | 4.24886e6 | 1.53964 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 320700. | 0.114683 | 0.0573417 | − | 0.998355i | \(-0.481738\pi\) | ||||
0.0573417 | + | 0.998355i | \(0.481738\pi\) | |||||||
\(380\) | 569828. | + | 986971.i | 0.202435 | + | 0.350627i | ||||
\(381\) | −922752. | + | 1.59825e6i | −0.325666 | + | 0.564070i | ||||
\(382\) | −1.21726e6 | + | 2.10836e6i | −0.426801 | + | 0.739240i | ||||
\(383\) | −1.18094e6 | − | 2.04546e6i | −0.411370 | − | 0.712513i | 0.583670 | − | 0.811991i | \(-0.301616\pi\) |
−0.995040 | + | 0.0994776i | \(0.968283\pi\) | |||||||
\(384\) | −924885. | −0.320081 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.10273e6 | 1.05993 | ||||||||
\(387\) | −219510. | − | 380202.i | −0.0745035 | − | 0.129044i | ||||
\(388\) | −17199.0 | + | 29789.5i | −0.00579995 | + | 0.0100458i | ||||
\(389\) | 1.76695e6 | − | 3.06045e6i | 0.592039 | − | 1.02544i | −0.401919 | − | 0.915675i | \(-0.631657\pi\) |
0.993957 | − | 0.109766i | \(-0.0350100\pi\) | |||||||
\(390\) | −1.62855e6 | − | 2.82073e6i | −0.542175 | − | 0.939075i | ||||
\(391\) | −1.16467e6 | −0.385267 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 656676. | 0.214472 | ||||||||
\(394\) | 591425. | + | 1.02438e6i | 0.191937 | + | 0.332445i | ||||
\(395\) | 4.57893e6 | − | 7.93094e6i | 1.47663 | − | 2.55759i | ||||
\(396\) | 14742.0 | − | 25533.9i | 0.00472409 | − | 0.00818237i | ||||
\(397\) | 2.02405e6 | + | 3.50577e6i | 0.644534 | + | 1.11637i | 0.984409 | + | 0.175895i | \(0.0562820\pi\) |
−0.339875 | + | 0.940471i | \(0.610385\pi\) | |||||||
\(398\) | −410520. | −0.129905 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.28896e6 | −1.34030 | ||||||||
\(401\) | −1.03822e6 | − | 1.79826e6i | −0.322426 | − | 0.558459i | 0.658562 | − | 0.752527i | \(-0.271165\pi\) |
−0.980988 | + | 0.194068i | \(0.937832\pi\) | |||||||
\(402\) | 31410.0 | − | 54403.7i | 0.00969400 | − | 0.0167905i | ||||
\(403\) | 2.43936e6 | − | 4.22510e6i | 0.748192 | − | 1.29591i | ||||
\(404\) | 582239. | + | 1.00847e6i | 0.177479 | + | 0.307403i | ||||
\(405\) | −616734. | −0.186836 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −381576. | −0.114181 | ||||||||
\(408\) | −1.77431e6 | − | 3.07319e6i | −0.527689 | − | 0.913984i | ||||
\(409\) | 1.28716e6 | − | 2.22942e6i | 0.380472 | − | 0.658998i | −0.610657 | − | 0.791895i | \(-0.709095\pi\) |
0.991130 | + | 0.132897i | \(0.0424280\pi\) | |||||||
\(410\) | 766570. | − | 1.32774e6i | 0.225212 | − | 0.390079i | ||||
\(411\) | −423819. | − | 734076.i | −0.123759 | − | 0.214356i | ||||
\(412\) | 1.10012e6 | 0.319299 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −233280. | −0.0668924 | ||||||||
\(415\) | 3.81772e6 | + | 6.61248e6i | 1.08814 | + | 1.88471i | ||||
\(416\) | −956725. | + | 1.65710e6i | −0.271053 | + | 0.469477i | ||||
\(417\) | 215082. | − | 372533.i | 0.0605709 | − | 0.104912i | ||||
\(418\) | 225160. | + | 389989.i | 0.0630305 | + | 0.109172i | ||||
\(419\) | −848148. | −0.236013 | −0.118007 | − | 0.993013i | \(-0.537650\pi\) | ||||
−0.118007 | + | 0.993013i | \(0.537650\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.43682e6 | 0.395092 | 0.197546 | − | 0.980294i | \(-0.436703\pi\) | ||||
0.197546 | + | 0.980294i | \(0.436703\pi\) | |||||||
\(422\) | −249730. | − | 432545.i | −0.0682637 | − | 0.118236i | ||||
\(423\) | 34992.0 | − | 60607.9i | 0.00950863 | − | 0.0164694i | ||||
\(424\) | 407745. | − | 706235.i | 0.110147 | − | 0.190781i | ||||
\(425\) | −5.77382e6 | − | 1.00006e7i | −1.55057 | − | 2.68566i | ||||
\(426\) | −842400. | −0.224903 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 47348.0 | 0.0124937 | ||||||||
\(429\) | 180180. | + | 312081.i | 0.0472676 | + | 0.0818698i | ||||
\(430\) | 1.27370e6 | − | 2.20611e6i | 0.332197 | − | 0.575382i | ||||
\(431\) | −1.17719e6 | + | 2.03895e6i | −0.305248 | + | 0.528705i | −0.977316 | − | 0.211784i | \(-0.932073\pi\) |
0.672069 | + | 0.740489i | \(0.265406\pi\) | |||||||
\(432\) | −273740. | − | 474131.i | −0.0705713 | − | 0.122233i | ||||
\(433\) | 3.78808e6 | 0.970955 | 0.485478 | − | 0.874249i | \(-0.338646\pi\) | ||||
0.485478 | + | 0.874249i | \(0.338646\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.66823e6 | 1.18285 | ||||||||
\(436\) | 624393. | + | 1.08148e6i | 0.157305 | + | 0.272460i | ||||
\(437\) | −498816. | + | 863975.i | −0.124950 | + | 0.216420i | ||||
\(438\) | −1.04314e6 | + | 1.80678e6i | −0.259812 | + | 0.450008i | ||||
\(439\) | −1.82161e6 | − | 3.15512e6i | −0.451123 | − | 0.781367i | 0.547333 | − | 0.836915i | \(-0.315643\pi\) |
−0.998456 | + | 0.0555474i | \(0.982310\pi\) | |||||||
\(440\) | 953160. | 0.234711 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.78470e6 | 1.89534 | ||||||||
\(443\) | −1.24195e6 | − | 2.15111e6i | −0.300672 | − | 0.520780i | 0.675616 | − | 0.737254i | \(-0.263878\pi\) |
−0.976288 | + | 0.216474i | \(0.930544\pi\) | |||||||
\(444\) | 231147. | − | 400358.i | 0.0556456 | − | 0.0963810i | ||||
\(445\) | 149554. | − | 259035.i | 0.0358012 | − | 0.0620096i | ||||
\(446\) | −466760. | − | 808452.i | −0.111111 | − | 0.192450i | ||||
\(447\) | 1.11839e6 | 0.264744 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.63177e6 | −0.616074 | −0.308037 | − | 0.951374i | \(-0.599672\pi\) | ||||
−0.308037 | + | 0.951374i | \(0.599672\pi\) | |||||||
\(450\) | −1.15648e6 | − | 2.00308e6i | −0.269219 | − | 0.466301i | ||||
\(451\) | −84812.0 | + | 146899.i | −0.0196343 | + | 0.0340076i | ||||
\(452\) | −157969. | + | 273610.i | −0.0363685 | + | 0.0629921i | ||||
\(453\) | −2.00833e6 | − | 3.47853e6i | −0.459822 | − | 0.796436i | ||||
\(454\) | −1.68186e6 | −0.382957 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.03966e6 | −0.684562 | ||||||||
\(457\) | 580651. | + | 1.00572e6i | 0.130054 | + | 0.225261i | 0.923697 | − | 0.383123i | \(-0.125152\pi\) |
−0.793643 | + | 0.608384i | \(0.791818\pi\) | |||||||
\(458\) | −2.31578e6 | + | 4.01106e6i | −0.515863 | + | 0.893501i | ||||
\(459\) | 737019. | − | 1.27655e6i | 0.163285 | − | 0.282818i | ||||
\(460\) | 189504. | + | 328231.i | 0.0417565 | + | 0.0723243i | ||||
\(461\) | −2.81385e6 | −0.616663 | −0.308332 | − | 0.951279i | \(-0.599771\pi\) | ||||
−0.308332 | + | 0.951279i | \(0.599771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.84299e6 | 1.48352 | 0.741760 | − | 0.670665i | \(-0.233991\pi\) | ||||
0.741760 | + | 0.670665i | \(0.233991\pi\) | |||||||
\(464\) | 2.07201e6 | + | 3.58882e6i | 0.446783 | + | 0.773851i | ||||
\(465\) | 2.68013e6 | − | 4.64212e6i | 0.574808 | − | 0.995597i | ||||
\(466\) | −3.14279e6 | + | 5.44346e6i | −0.670425 | + | 1.16121i | ||||
\(467\) | 1.67157e6 | + | 2.89524e6i | 0.354676 | + | 0.614318i | 0.987063 | − | 0.160336i | \(-0.0512577\pi\) |
−0.632386 | + | 0.774653i | \(0.717924\pi\) | |||||||
\(468\) | −436590. | −0.0921423 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 406080. | 0.0847944 | ||||||||
\(471\) | 718857. | + | 1.24510e6i | 0.149310 | + | 0.258613i | ||||
\(472\) | 1.09395e6 | − | 1.89478e6i | 0.226018 | − | 0.391474i | ||||
\(473\) | −140920. | + | 244081.i | −0.0289614 | + | 0.0501626i | ||||
\(474\) | 2.19204e6 | + | 3.79672e6i | 0.448129 | + | 0.776181i | ||||
\(475\) | −9.89145e6 | −2.01153 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 338742. | 0.0681668 | ||||||||
\(478\) | 867540. | + | 1.50262e6i | 0.173668 | + | 0.300802i | ||||
\(479\) | −2.14124e6 | + | 3.70874e6i | −0.426409 | + | 0.738562i | −0.996551 | − | 0.0829840i | \(-0.973555\pi\) |
0.570142 | + | 0.821546i | \(0.306888\pi\) | |||||||
\(480\) | −1.05116e6 | + | 1.82065e6i | −0.208240 | + | 0.360682i | ||||
\(481\) | 2.82513e6 | + | 4.89327e6i | 0.556770 | + | 0.964354i | ||||
\(482\) | −495850. | −0.0972149 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.10843e6 | 0.215077 | ||||||||
\(485\) | −230958. | − | 400031.i | −0.0445840 | − | 0.0772217i | ||||
\(486\) | 147622. | − | 255690.i | 0.0283506 | − | 0.0491046i | ||||
\(487\) | 4.46588e6 | − | 7.73512e6i | 0.853266 | − | 1.47790i | −0.0249791 | − | 0.999688i | \(-0.507952\pi\) |
0.878245 | − | 0.478211i | \(-0.158715\pi\) | |||||||
\(488\) | 4.44620e6 | + | 7.70104e6i | 0.845160 | + | 1.46386i | ||||
\(489\) | −2.22527e6 | −0.420833 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.75306e6 | 0.515361 | 0.257681 | − | 0.966230i | \(-0.417042\pi\) | ||||
0.257681 | + | 0.966230i | \(0.417042\pi\) | |||||||
\(492\) | −102753. | − | 177973.i | −0.0191373 | − | 0.0331469i | ||||
\(493\) | −5.57870e6 | + | 9.66259e6i | −1.03375 | + | 1.79051i | ||||
\(494\) | 3.33410e6 | − | 5.77483e6i | 0.614697 | − | 1.06469i | ||||
\(495\) | 197964. | + | 342884.i | 0.0363139 | + | 0.0628976i | ||||
\(496\) | 4.75834e6 | 0.868462 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.65526e6 | −0.660458 | ||||||||
\(499\) | −2.40204e6 | − | 4.16046e6i | −0.431846 | − | 0.747980i | 0.565186 | − | 0.824963i | \(-0.308804\pi\) |
−0.997032 | + | 0.0769837i | \(0.975471\pi\) | |||||||
\(500\) | −850794. | + | 1.47362e6i | −0.152195 | + | 0.263609i | ||||
\(501\) | 3.08020e6 | − | 5.33506e6i | 0.548257 | − | 0.949609i | ||||
\(502\) | 861070. | + | 1.49142e6i | 0.152503 | + | 0.264143i | ||||
\(503\) | 6.02465e6 | 1.06172 | 0.530862 | − | 0.847458i | \(-0.321868\pi\) | ||||
0.530862 | + | 0.847458i | \(0.321868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.56373e7 | −2.72855 | ||||||||
\(506\) | 74880.0 | + | 129696.i | 0.0130014 | + | 0.0225191i | ||||
\(507\) | 997232. | − | 1.72726e6i | 0.172296 | − | 0.298426i | ||||
\(508\) | −717696. | + | 1.24309e6i | −0.123390 | + | 0.213718i | ||||
\(509\) | −4.21493e6 | − | 7.30048e6i | −0.721101 | − | 1.24898i | −0.960559 | − | 0.278077i | \(-0.910303\pi\) |
0.239458 | − | 0.970907i | \(-0.423030\pi\) | |||||||
\(510\) | 8.55306e6 | 1.45612 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.55248e6 | −1.10466 | ||||||||
\(513\) | −631314. | − | 1.09347e6i | −0.105914 | − | 0.183448i | ||||
\(514\) | 737825. | − | 1.27795e6i | 0.123182 | − | 0.213357i | ||||
\(515\) | −7.38652e6 | + | 1.27938e7i | −1.22722 | + | 2.12560i | ||||
\(516\) | −170730. | − | 295713.i | −0.0282284 | − | 0.0488929i | ||||
\(517\) | −44928.0 | −0.00739249 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.49427e6 | −0.895347 | ||||||||
\(520\) | −7.05705e6 | − | 1.22232e7i | −1.14450 | − | 1.98233i | ||||
\(521\) | 4.62529e6 | − | 8.01124e6i | 0.746525 | − | 1.29302i | −0.202953 | − | 0.979188i | \(-0.565054\pi\) |
0.949479 | − | 0.313831i | \(-0.101613\pi\) | |||||||
\(522\) | −1.11740e6 | + | 1.93538e6i | −0.179486 | + | 0.310879i | ||||
\(523\) | 2.92247e6 | + | 5.06187e6i | 0.467192 | + | 0.809201i | 0.999297 | − | 0.0374773i | \(-0.0119322\pi\) |
−0.532105 | + | 0.846678i | \(0.678599\pi\) | |||||||
\(524\) | 510748. | 0.0812603 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.36232e6 | −1.00265 | ||||||||
\(527\) | 6.40570e6 | + | 1.10950e7i | 1.00471 | + | 1.74021i | ||||
\(528\) | −175734. | + | 304380.i | −0.0274329 | + | 0.0475151i | ||||
\(529\) | 3.05228e6 | − | 5.28671e6i | 0.474226 | − | 0.821384i | ||||
\(530\) | 982770. | + | 1.70221e6i | 0.151972 | + | 0.263222i | ||||
\(531\) | 908820. | 0.139875 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.51174e6 | 0.382963 | ||||||||
\(534\) | 71595.0 | + | 124006.i | 0.0108650 | + | 0.0188187i | ||||
\(535\) | −317908. | + | 550633.i | −0.0480194 | + | 0.0831721i | ||||
\(536\) | 136110. | − | 235749.i | 0.0204634 | − | 0.0354437i | ||||
\(537\) | 2.98013e6 | + | 5.16174e6i | 0.445964 | + | 0.772433i | ||||
\(538\) | −1.38387e6 | −0.206129 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −479682. | −0.0707895 | ||||||||
\(541\) | −4.61266e6 | − | 7.98937e6i | −0.677577 | − | 1.17360i | −0.975709 | − | 0.219073i | \(-0.929697\pi\) |
0.298132 | − | 0.954525i | \(-0.403637\pi\) | |||||||
\(542\) | −3.22484e6 | + | 5.58559e6i | −0.471531 | + | 0.816715i | ||||
\(543\) | −695835. | + | 1.20522e6i | −0.101276 | + | 0.175415i | ||||
\(544\) | −2.51234e6 | − | 4.35149e6i | −0.363982 | − | 0.630436i | ||||
\(545\) | −1.67694e7 | −2.41839 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.44337e6 | −0.920757 | −0.460378 | − | 0.887723i | \(-0.652286\pi\) | ||||
−0.460378 | + | 0.887723i | \(0.652286\pi\) | |||||||
\(548\) | −329637. | − | 570948.i | −0.0468905 | − | 0.0812167i | ||||
\(549\) | −1.84688e6 | + | 3.19889e6i | −0.261522 | + | 0.452969i | ||||
\(550\) | −742430. | + | 1.28593e6i | −0.104652 | + | 0.181263i | ||||
\(551\) | 4.77859e6 | + | 8.27676e6i | 0.670534 | + | 1.16140i | ||||
\(552\) | −1.01088e6 | −0.141206 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.58275e6 | 1.18810 | ||||||||
\(555\) | 3.10397e6 | + | 5.37624e6i | 0.427746 | + | 0.740877i | ||||
\(556\) | 167286. | − | 289748.i | 0.0229495 | − | 0.0397496i | ||||
\(557\) | −1.87106e6 | + | 3.24078e6i | −0.255535 | + | 0.442600i | −0.965041 | − | 0.262100i | \(-0.915585\pi\) |
0.709506 | + | 0.704700i | \(0.248918\pi\) | |||||||
\(558\) | 1.28304e6 | + | 2.22229e6i | 0.174443 | + | 0.302145i | ||||
\(559\) | 4.17340e6 | 0.564886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −946296. | −0.126946 | ||||||||
\(562\) | 3.68046e6 | + | 6.37474e6i | 0.491542 | + | 0.851376i | ||||
\(563\) | −7.31918e6 | + | 1.26772e7i | −0.973176 | + | 1.68559i | −0.287350 | + | 0.957826i | \(0.592774\pi\) |
−0.685826 | + | 0.727765i | \(0.740559\pi\) | |||||||
\(564\) | 27216.0 | − | 47139.5i | 0.00360269 | − | 0.00624004i | ||||
\(565\) | −2.12130e6 | − | 3.67420e6i | −0.279564 | − | 0.484218i | ||||
\(566\) | −5.14406e6 | −0.674940 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.65040e6 | −0.474755 | ||||||||
\(569\) | −7.09023e6 | − | 1.22806e7i | −0.918078 | − | 1.59016i | −0.802331 | − | 0.596879i | \(-0.796407\pi\) |
−0.115747 | − | 0.993279i | \(-0.536926\pi\) | |||||||
\(570\) | 3.66318e6 | − | 6.34481e6i | 0.472249 | − | 0.817959i | ||||
\(571\) | 625802. | − | 1.08392e6i | 0.0803242 | − | 0.139126i | −0.823065 | − | 0.567947i | \(-0.807738\pi\) |
0.903389 | + | 0.428822i | \(0.141071\pi\) | |||||||
\(572\) | 140140. | + | 242730.i | 0.0179090 | + | 0.0310193i | ||||
\(573\) | −4.38214e6 | −0.557570 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.28954e6 | −0.414921 | ||||||||
\(576\) | −1.47651e6 | − | 2.55739e6i | −0.185430 | − | 0.321174i | ||||
\(577\) | 2.97189e6 | − | 5.14746e6i | 0.371615 | − | 0.643656i | −0.618199 | − | 0.786021i | \(-0.712138\pi\) |
0.989814 | + | 0.142366i | \(0.0454709\pi\) | |||||||
\(578\) | −6.67157e6 | + | 1.15555e7i | −0.830631 | + | 1.43870i | ||||
\(579\) | 2.79246e6 | + | 4.83668e6i | 0.346171 | + | 0.599585i | ||||
\(580\) | 3.63084e6 | 0.448165 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 221130. | 0.0270608 | ||||||||
\(583\) | −108732. | − | 188329.i | −0.0132491 | − | 0.0229481i | ||||
\(584\) | −4.52030e6 | + | 7.82938e6i | −0.548447 | + | 0.949938i | ||||
\(585\) | 2.93139e6 | − | 5.07732e6i | 0.354147 | − | 0.613401i | ||||
\(586\) | −2.96516e6 | − | 5.13582e6i | −0.356701 | − | 0.617825i | ||||
\(587\) | 6.46192e6 | 0.774046 | 0.387023 | − | 0.922070i | \(-0.373503\pi\) | ||||
0.387023 | + | 0.922070i | \(0.373503\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.09740e7 | 1.30339 | ||||||||
\(590\) | 2.63670e6 | + | 4.56690e6i | 0.311839 | + | 0.540121i | ||||
\(591\) | −1.06456e6 | + | 1.84388e6i | −0.125373 | + | 0.217152i | ||||
\(592\) | −2.75542e6 | + | 4.77253e6i | −0.323135 | + | 0.559685i | ||||
\(593\) | −1.17303e6 | − | 2.03174e6i | −0.136984 | − | 0.237264i | 0.789369 | − | 0.613919i | \(-0.210408\pi\) |
−0.926354 | + | 0.376655i | \(0.877074\pi\) | |||||||
\(594\) | −189540. | −0.0220412 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 869862. | 0.100308 | ||||||||
\(597\) | −369468. | − | 639937.i | −0.0424269 | − | 0.0734855i | ||||
\(598\) | 1.10880e6 | − | 1.92050e6i | 0.126794 | − | 0.219614i | ||||
\(599\) | 6.74796e6 | − | 1.16878e7i | 0.768432 | − | 1.33096i | −0.169981 | − | 0.985447i | \(-0.554371\pi\) |
0.938413 | − | 0.345516i | \(-0.112296\pi\) | |||||||
\(600\) | −5.01140e6 | − | 8.68000e6i | −0.568305 | − | 0.984332i | ||||
\(601\) | −3.87849e6 | −0.438002 | −0.219001 | − | 0.975725i | \(-0.570280\pi\) | ||||
−0.219001 | + | 0.975725i | \(0.570280\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 113076. | 0.0126642 | ||||||||
\(604\) | −1.56204e6 | − | 2.70553e6i | −0.174220 | − | 0.301758i | ||||
\(605\) | −7.44231e6 | + | 1.28905e7i | −0.826645 | + | 1.43179i | ||||
\(606\) | 3.74296e6 | − | 6.48301e6i | 0.414032 | − | 0.717125i | ||||
\(607\) | −266744. | − | 462014.i | −0.0293848 | − | 0.0508960i | 0.850959 | − | 0.525232i | \(-0.176021\pi\) |
−0.880344 | + | 0.474336i | \(0.842688\pi\) | |||||||
\(608\) | −4.30402e6 | −0.472188 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.14329e7 | −2.33215 | ||||||||
\(611\) | 332640. | + | 576149.i | 0.0360472 | + | 0.0624356i | ||||
\(612\) | 573237. | − | 992876.i | 0.0618665 | − | 0.107156i | ||||
\(613\) | −2.57305e6 | + | 4.45666e6i | −0.276565 | + | 0.479025i | −0.970529 | − | 0.240985i | \(-0.922529\pi\) |
0.693964 | + | 0.720010i | \(0.255863\pi\) | |||||||
\(614\) | 3.79729e6 | + | 6.57710e6i | 0.406493 | + | 0.704066i | ||||
\(615\) | 2.75965e6 | 0.294216 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.37860e6 | −0.251541 | −0.125770 | − | 0.992059i | \(-0.540140\pi\) | ||||
−0.125770 | + | 0.992059i | \(0.540140\pi\) | |||||||
\(618\) | −3.53610e6 | − | 6.12470e6i | −0.372437 | − | 0.645081i | ||||
\(619\) | 8.00116e6 | − | 1.38584e7i | 0.839317 | − | 1.45374i | −0.0511488 | − | 0.998691i | \(-0.516288\pi\) |
0.890466 | − | 0.455049i | \(-0.150378\pi\) | |||||||
\(620\) | 2.08454e6 | − | 3.61054e6i | 0.217787 | − | 0.377218i | ||||
\(621\) | −209952. | − | 363648.i | −0.0218470 | − | 0.0378400i | ||||
\(622\) | −1.06404e6 | −0.110276 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.20443e6 | 0.535071 | ||||||||
\(625\) | −2.50151e6 | − | 4.33274e6i | −0.256155 | − | 0.443673i | ||||
\(626\) | −4735.00 | + | 8201.26i | −0.000482930 | + | 0.000836459i | ||||
\(627\) | −405288. | + | 701979.i | −0.0411713 | + | 0.0713108i | ||||
\(628\) | 559111. | + | 968409.i | 0.0565717 | + | 0.0979850i | ||||
\(629\) | −1.48374e7 | −1.49531 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.23459e7 | 1.23439 | 0.617193 | − | 0.786812i | \(-0.288270\pi\) | ||||
0.617193 | + | 0.786812i | \(0.288270\pi\) | |||||||
\(632\) | 9.49884e6 | + | 1.64525e7i | 0.945971 | + | 1.63847i | ||||
\(633\) | 449514. | − | 778581.i | 0.0445896 | − | 0.0772315i | ||||
\(634\) | 3.94744e6 | − | 6.83718e6i | 0.390025 | − | 0.675544i | ||||
\(635\) | −9.63763e6 | − | 1.66929e7i | −0.948497 | − | 1.64285i | ||||
\(636\) | 263466. | 0.0258275 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.43468e6 | 0.139541 | ||||||||
\(639\) | −758160. | − | 1.31317e6i | −0.0734529 | − | 0.127224i | ||||
\(640\) | 4.82996e6 | − | 8.36573e6i | 0.466115 | − | 0.807335i | ||||
\(641\) | 1.71878e6 | − | 2.97701e6i | 0.165224 | − | 0.286177i | −0.771511 | − | 0.636216i | \(-0.780499\pi\) |
0.936735 | + | 0.350040i | \(0.113832\pi\) | |||||||
\(642\) | −152190. | − | 263601.i | −0.0145730 | − | 0.0252412i | ||||
\(643\) | 1.62191e7 | 1.54703 | 0.773515 | − | 0.633778i | \(-0.218497\pi\) | ||||
0.773515 | + | 0.633778i | \(0.218497\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.58532e6 | 0.433981 | ||||||||
\(646\) | 8.75526e6 | + | 1.51646e7i | 0.825444 | + | 1.42971i | ||||
\(647\) | 5.99643e6 | − | 1.03861e7i | 0.563160 | − | 0.975422i | −0.434058 | − | 0.900885i | \(-0.642919\pi\) |
0.997218 | − | 0.0745371i | \(-0.0237479\pi\) | |||||||
\(648\) | 639698. | − | 1.10799e6i | 0.0598463 | − | 0.103657i | ||||
\(649\) | −291720. | − | 505274.i | −0.0271866 | − | 0.0470885i | ||||
\(650\) | 2.19873e7 | 2.04122 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.73076e6 | −0.159448 | ||||||||
\(653\) | −790047. | − | 1.36840e6i | −0.0725053 | − | 0.125583i | 0.827493 | − | 0.561475i | \(-0.189766\pi\) |
−0.899999 | + | 0.435893i | \(0.856433\pi\) | |||||||
\(654\) | 4.01396e6 | − | 6.95237e6i | 0.366968 | − | 0.635607i | ||||
\(655\) | −3.42931e6 | + | 5.93974e6i | −0.312322 | + | 0.540958i | ||||
\(656\) | 1.22488e6 | + | 2.12156e6i | 0.111131 | + | 0.192484i | ||||
\(657\) | −3.75532e6 | −0.339417 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.98358e6 | 0.626419 | 0.313209 | − | 0.949684i | \(-0.398596\pi\) | ||||
0.313209 | + | 0.949684i | \(0.398596\pi\) | |||||||
\(660\) | 153972. | + | 266687.i | 0.0137588 | + | 0.0238310i | ||||
\(661\) | 1.84801e6 | − | 3.20085e6i | 0.164513 | − | 0.284945i | −0.771969 | − | 0.635660i | \(-0.780728\pi\) |
0.936482 | + | 0.350715i | \(0.114061\pi\) | |||||||
\(662\) | 8.48677e6 | − | 1.46995e7i | 0.752658 | − | 1.30364i | ||||
\(663\) | 7.00623e6 | + | 1.21351e7i | 0.619014 | + | 1.07216i | ||||
\(664\) | −1.58395e7 | −1.39418 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.97189e6 | −0.259625 | ||||||||
\(667\) | 1.58918e6 | + | 2.75255e6i | 0.138312 | + | 0.239563i | ||||
\(668\) | 2.39571e6 | − | 4.14949e6i | 0.207727 | − | 0.359794i | ||||
\(669\) | 840168. | − | 1.45521e6i | 0.0725773 | − | 0.125708i | ||||
\(670\) | 328060. | + | 568217.i | 0.0282336 | + | 0.0489020i | ||||
\(671\) | 2.37130e6 | 0.203320 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.84688e6 | 0.157182 | 0.0785908 | − | 0.996907i | \(-0.474958\pi\) | ||||
0.0785908 | + | 0.996907i | \(0.474958\pi\) | |||||||
\(674\) | −5.06828e6 | − | 8.77853e6i | −0.429745 | − | 0.744341i | ||||
\(675\) | 2.08166e6 | − | 3.60554e6i | 0.175853 | − | 0.304587i | ||||
\(676\) | 775624. | − | 1.34342e6i | 0.0652807 | − | 0.113069i | ||||
\(677\) | −3.84250e6 | − | 6.65541e6i | −0.322213 | − | 0.558089i | 0.658732 | − | 0.752378i | \(-0.271093\pi\) |
−0.980944 | + | 0.194289i | \(0.937760\pi\) | |||||||
\(678\) | 2.03103e6 | 0.169684 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.70633e7 | 3.07377 | ||||||||
\(681\) | −1.51367e6 | − | 2.62176e6i | −0.125073 | − | 0.216633i | ||||
\(682\) | 823680. | − | 1.42666e6i | 0.0678106 | − | 0.117451i | ||||
\(683\) | −3.56090e6 | + | 6.16766e6i | −0.292084 | + | 0.505904i | −0.974302 | − | 0.225244i | \(-0.927682\pi\) |
0.682218 | + | 0.731149i | \(0.261015\pi\) | |||||||
\(684\) | −491022. | − | 850475.i | −0.0401292 | − | 0.0695058i | ||||
\(685\) | 8.85311e6 | 0.720891 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.33683e6 | −0.673921 | ||||||||
\(688\) | 2.03521e6 | + | 3.52509e6i | 0.163922 | + | 0.283922i | ||||
\(689\) | −1.61007e6 | + | 2.78872e6i | −0.129210 | + | 0.223799i | ||||
\(690\) | 1.21824e6 | − | 2.11005e6i | 0.0974115 | − | 0.168722i | ||||
\(691\) | −1.61893e6 | − | 2.80408e6i | −0.128983 | − | 0.223406i | 0.794300 | − | 0.607526i | \(-0.207838\pi\) |
−0.923283 | + | 0.384120i | \(0.874505\pi\) | |||||||
\(692\) | −4.27332e6 | −0.339234 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.74443e7 | 1.37485 | ||||||||
\(695\) | 2.24641e6 | + | 3.89090e6i | 0.176412 | + | 0.305554i | ||||
\(696\) | −4.84204e6 | + | 8.38667e6i | −0.378884 | + | 0.656246i | ||||
\(697\) | −3.29788e6 | + | 5.71210e6i | −0.257130 | + | 0.445363i | ||||
\(698\) | 2.41392e6 | + | 4.18102e6i | 0.187535 | + | 0.324821i | ||||
\(699\) | −1.13140e7 | −0.875839 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.39163e6 | −0.568127 | −0.284063 | − | 0.958805i | \(-0.591683\pi\) | ||||
−0.284063 | + | 0.958805i | \(0.591683\pi\) | |||||||
\(702\) | 1.40332e6 | + | 2.43063e6i | 0.107477 | + | 0.186156i | ||||
\(703\) | −6.35471e6 | + | 1.10067e7i | −0.484962 | + | 0.839978i | ||||
\(704\) | −947882. | + | 1.64178e6i | −0.0720813 | + | 0.124848i | ||||
\(705\) | 365472. | + | 633016.i | 0.0276937 | + | 0.0479669i | ||||
\(706\) | −5.76965e6 | −0.435650 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 706860. | 0.0529969 | ||||||||
\(709\) | 2.66680e6 | + | 4.61904e6i | 0.199240 | + | 0.345093i | 0.948282 | − | 0.317429i | \(-0.102819\pi\) |
−0.749042 | + | 0.662522i | \(0.769486\pi\) | |||||||
\(710\) | 4.39920e6 | − | 7.61964e6i | 0.327512 | − | 0.567268i | ||||
\(711\) | −3.94567e6 | + | 6.83410e6i | −0.292716 | + | 0.507000i | ||||
\(712\) | 310245. | + | 537360.i | 0.0229353 | + | 0.0397251i | ||||
\(713\) | 3.64954e6 | 0.268852 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.76376e6 | −0.275332 | ||||||||
\(716\) | 2.31788e6 | + | 4.01469e6i | 0.168970 | + | 0.292664i | ||||
\(717\) | −1.56157e6 | + | 2.70472e6i | −0.113439 | + | 0.196483i | ||||
\(718\) | −4.02776e6 | + | 6.97628e6i | −0.291576 | + | 0.505025i | ||||
\(719\) | −5.72820e6 | − | 9.92153e6i | −0.413234 | − | 0.715742i | 0.582007 | − | 0.813184i | \(-0.302267\pi\) |
−0.995241 | + | 0.0974414i | \(0.968934\pi\) | |||||||
\(720\) | 5.71811e6 | 0.411075 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.61862e6 | 0.186952 | ||||||||
\(723\) | −446265. | − | 772954.i | −0.0317502 | − | 0.0549930i | ||||
\(724\) | −541205. | + | 937395.i | −0.0383721 | + | 0.0664624i | ||||
\(725\) | −1.57566e7 | + | 2.72913e7i | −1.11332 | + | 1.92832i | ||||
\(726\) | −3.56281e6 | − | 6.17096e6i | −0.250871 | − | 0.434522i | ||||
\(727\) | 2.49540e7 | 1.75107 | 0.875536 | − | 0.483153i | \(-0.160508\pi\) | ||||
0.875536 | + | 0.483153i | \(0.160508\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.08951e7 | − | 1.88708e7i | −0.756699 | − | 1.31064i | ||||
\(731\) | −5.47962e6 | + | 9.49098e6i | −0.379277 | + | 0.656928i | ||||
\(732\) | −1.43646e6 | + | 2.48803e6i | −0.0990870 | + | 0.171624i | ||||
\(733\) | −7.16991e6 | − | 1.24187e7i | −0.492894 | − | 0.853718i | 0.507072 | − | 0.861904i | \(-0.330728\pi\) |
−0.999966 | + | 0.00818541i | \(0.997394\pi\) | |||||||
\(734\) | −1.83874e7 | −1.25974 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.43136e6 | −0.0973990 | ||||||||
\(737\) | −36296.0 | − | 62866.5i | −0.00246144 | − | 0.00426335i | ||||
\(738\) | −660555. | + | 1.14411e6i | −0.0446445 | + | 0.0773266i | ||||
\(739\) | −461466. | + | 799283.i | −0.0310834 | + | 0.0538380i | −0.881149 | − | 0.472839i | \(-0.843229\pi\) |
0.850065 | + | 0.526677i | \(0.176562\pi\) | |||||||
\(740\) | 2.41420e6 | + | 4.18152e6i | 0.162067 | + | 0.280708i | ||||
\(741\) | 1.20028e7 | 0.803037 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.38995e6 | −0.624010 | −0.312005 | − | 0.950081i | \(-0.601001\pi\) | ||||
−0.312005 | + | 0.950081i | \(0.601001\pi\) | |||||||
\(744\) | 5.55984e6 | + | 9.62993e6i | 0.368239 | + | 0.637809i | ||||
\(745\) | −5.84050e6 | + | 1.01160e7i | −0.385531 | + | 0.667760i | ||||
\(746\) | −1.62442e6 | + | 2.81357e6i | −0.106869 | + | 0.185102i | ||||
\(747\) | −3.28973e6 | − | 5.69799e6i | −0.215705 | − | 0.373611i | ||||
\(748\) | −736008. | −0.0480982 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.09388e7 | 0.710094 | ||||||||
\(751\) | 204016. | + | 353366.i | 0.0131997 | + | 0.0228626i | 0.872550 | − | 0.488525i | \(-0.162465\pi\) |
−0.859350 | + | 0.511388i | \(0.829132\pi\) | |||||||
\(752\) | −324432. | + | 561933.i | −0.0209208 | + | 0.0362360i | ||||
\(753\) | −1.54993e6 | + | 2.68455e6i | −0.0996147 | + | 0.172538i | ||||
\(754\) | −1.06222e7 | − | 1.83981e7i | −0.680431 | − | 1.17854i | ||||
\(755\) | 4.19518e7 | 2.67845 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.59605e7 | 1.64654 | 0.823271 | − | 0.567649i | \(-0.192147\pi\) | ||||
0.823271 | + | 0.567649i | \(0.192147\pi\) | |||||||
\(758\) | −801750. | − | 1.38867e6i | −0.0506834 | − | 0.0877863i | ||||
\(759\) | −134784. | + | 233453.i | −0.00849247 | + | 0.0147094i | ||||
\(760\) | 1.58738e7 | − | 2.74942e7i | 0.996888 | − | 1.72666i | ||||
\(761\) | 9.17770e6 | + | 1.58963e7i | 0.574477 | + | 0.995023i | 0.996098 | + | 0.0882510i | \(0.0281278\pi\) |
−0.421622 | + | 0.906772i | \(0.638539\pi\) | |||||||
\(762\) | 9.22752e6 | 0.575702 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.40833e6 | −0.211255 | ||||||||
\(765\) | 7.69775e6 | + | 1.33329e7i | 0.475566 | + | 0.823704i | ||||
\(766\) | −5.90472e6 | + | 1.02273e7i | −0.363603 | + | 0.629779i | ||||
\(767\) | −4.31970e6 | + | 7.48194e6i | −0.265134 | + | 0.459225i | ||||
\(768\) | −2.93760e6 | − | 5.08806e6i | −0.179717 | − | 0.311279i | ||||
\(769\) | 747166. | 0.0455618 | 0.0227809 | − | 0.999740i | \(-0.492748\pi\) | ||||
0.0227809 | + | 0.999740i | \(0.492748\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.65617e6 | 0.160924 | ||||||||
\(772\) | 2.17191e6 | + | 3.76186e6i | 0.131159 | + | 0.227174i | ||||
\(773\) | 1.01346e7 | − | 1.75536e7i | 0.610038 | − | 1.05662i | −0.381195 | − | 0.924495i | \(-0.624487\pi\) |
0.991233 | − | 0.132123i | \(-0.0421793\pi\) | |||||||
\(774\) | −1.09755e6 | + | 1.90101e6i | −0.0658524 | + | 0.114060i | ||||
\(775\) | 1.80924e7 | + | 3.13370e7i | 1.08204 | + | 1.87415i | ||||
\(776\) | 958230. | 0.0571236 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.76695e7 | −1.04659 | ||||||||
\(779\) | 2.82489e6 | + | 4.89286e6i | 0.166785 | + | 0.288881i | ||||
\(780\) | 2.27997e6 | − | 3.94902e6i | 0.134181 | − | 0.232409i | ||||
\(781\) | −486720. | + | 843024.i | −0.0285530 | + | 0.0494552i | ||||
\(782\) | 2.91168e6 | + | 5.04318e6i | 0.170266 | + | 0.294909i | ||||
\(783\) | −4.02262e6 | −0.234479 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.50161e7 | −0.869729 | ||||||||
\(786\) | −1.64169e6 | − | 2.84349e6i | −0.0947839 | − | 0.164171i | ||||
\(787\) | −2.34991e6 | + | 4.07016e6i | −0.135243 | + | 0.234248i | −0.925690 | − | 0.378282i | \(-0.876515\pi\) |
0.790447 | + | 0.612530i | \(0.209848\pi\) | |||||||
\(788\) | −827995. | + | 1.43413e6i | −0.0475020 | + | 0.0822759i | ||||
\(789\) | −5.72609e6 | − | 9.91788e6i | −0.327465 | − | 0.567187i | ||||
\(790\) | −4.57893e7 | −2.61033 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −821340. | −0.0465275 | ||||||||
\(793\) | −1.75568e7 | − | 3.04092e7i | −0.991429 | − | 1.71721i | ||||
\(794\) | 1.01203e7 | − | 1.75288e7i | 0.569693 | − | 0.986738i | ||||
\(795\) | −1.76899e6 | + | 3.06397e6i | −0.0992674 | + | 0.171936i | ||||
\(796\) | −287364. | − | 497729.i | −0.0160750 | − | 0.0278426i | ||||
\(797\) | −584710. | −0.0326058 | −0.0163029 | − | 0.999867i | \(-0.505190\pi\) | ||||
−0.0163029 | + | 0.999867i | \(0.505190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.74701e6 | −0.0968117 | ||||||||
\(800\) | −7.09592e6 | − | 1.22905e7i | −0.391998 | − | 0.678960i | ||||
\(801\) | −128871. | + | 223211.i | −0.00709699 | + | 0.0122923i | ||||
\(802\) | −5.19112e6 | + | 8.99129e6i | −0.284987 | + | 0.493613i | ||||
\(803\) | 1.20541e6 | + | 2.08783e6i | 0.0659700 | + | 0.114263i | ||||
\(804\) | 87948.0 | 0.00479828 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.43936e7 | −1.32263 | ||||||||
\(807\) | −1.24548e6 | − | 2.15724e6i | −0.0673215 | − | 0.116604i | ||||
\(808\) | 1.62195e7 | − | 2.80930e7i | 0.873996 | − | 1.51381i | ||||
\(809\) | 8.20063e6 | − | 1.42039e7i | 0.440531 | − | 0.763022i | −0.557198 | − | 0.830380i | \(-0.688124\pi\) |
0.997729 | + | 0.0673580i | \(0.0214570\pi\) | |||||||
\(810\) | 1.54183e6 | + | 2.67054e6i | 0.0825706 | + | 0.143016i | ||||
\(811\) | 304948. | 0.0162807 | 0.00814036 | − | 0.999967i | \(-0.497409\pi\) | ||||
0.00814036 | + | 0.999967i | \(0.497409\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.16094e7 | −0.616005 | ||||||||
\(814\) | 953940. | + | 1.65227e6i | 0.0504615 | + | 0.0874019i | ||||
\(815\) | 1.16208e7 | − | 2.01279e7i | 0.612835 | − | 1.06146i | ||||
\(816\) | −6.83335e6 | + | 1.18357e7i | −0.359259 | + | 0.622256i | ||||
\(817\) | 4.69372e6 | + | 8.12976e6i | 0.246015 | + | 0.426111i | ||||
\(818\) | −1.28716e7 | −0.672587 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.14640e6 | 0.111474 | ||||||||
\(821\) | −1.71714e7 | − | 2.97418e7i | −0.889095 | − | 1.53996i | −0.840947 | − | 0.541118i | \(-0.818001\pi\) |
−0.0481486 | − | 0.998840i | \(-0.515332\pi\) | |||||||
\(822\) | −2.11910e6 | + | 3.67038e6i | −0.109388 | + | 0.189466i | ||||
\(823\) | −7.83419e6 | + | 1.35692e7i | −0.403176 | + | 0.698321i | −0.994107 | − | 0.108401i | \(-0.965427\pi\) |
0.590932 | + | 0.806722i | \(0.298760\pi\) | |||||||
\(824\) | −1.53231e7 | − | 2.65404e7i | −0.786192 | − | 1.36172i | ||||
\(825\) | −2.67275e6 | −0.136717 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.96886e7 | −1.50948 | −0.754738 | − | 0.656026i | \(-0.772236\pi\) | ||||
−0.754738 | + | 0.656026i | \(0.772236\pi\) | |||||||
\(828\) | −163296. | − | 282837.i | −0.00827751 | − | 0.0143371i | ||||
\(829\) | −1.15354e7 | + | 1.99799e7i | −0.582970 | + | 1.00973i | 0.412155 | + | 0.911114i | \(0.364776\pi\) |
−0.995125 | + | 0.0986203i | \(0.968557\pi\) | |||||||
\(830\) | 1.90886e7 | − | 3.30624e7i | 0.961786 | − | 1.66586i | ||||
\(831\) | 7.72448e6 | + | 1.33792e7i | 0.388031 | + | 0.672089i | ||||
\(832\) | 2.80719e7 | 1.40593 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.15082e6 | −0.107075 | ||||||||
\(835\) | 3.21709e7 | + | 5.57217e7i | 1.59679 | + | 2.76572i | ||||
\(836\) | −315224. | + | 545984.i | −0.0155992 | + | 0.0270187i | ||||
\(837\) | −2.30947e6 | + | 4.00012e6i | −0.113946 | + | 0.197360i | ||||
\(838\) | 2.12037e6 | + | 3.67259e6i | 0.104304 | + | 0.180660i | ||||
\(839\) | −2.32642e7 | −1.14100 | −0.570498 | − | 0.821299i | \(-0.693250\pi\) | ||||
−0.570498 | + | 0.821299i | \(0.693250\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.93718e6 | 0.484477 | ||||||||
\(842\) | −3.59206e6 | − | 6.22162e6i | −0.174607 | − | 0.302429i | ||||
\(843\) | −6.62482e6 | + | 1.14745e7i | −0.321074 | + | 0.556116i | ||||
\(844\) | 349622. | − | 605563.i | 0.0168944 | − | 0.0292619i | ||||
\(845\) | 1.04155e7 | + | 1.80402e7i | 0.501810 | + | 0.869161i | ||||
\(846\) | −349920. | −0.0168090 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.14068e6 | −0.149980 | ||||||||
\(849\) | −4.62965e6 | − | 8.01880e6i | −0.220434 | − | 0.381804i | ||||
\(850\) | −2.88691e7 | + | 5.00028e7i | −1.37052 | + | 2.37381i | ||||
\(851\) | −2.11334e6 | + | 3.66042e6i | −0.100034 | + | 0.173263i | ||||
\(852\) | −589680. | − | 1.02136e6i | −0.0278303 | − | 0.0482034i | ||||
\(853\) | −1.91515e7 | −0.901219 | −0.450610 | − | 0.892721i | \(-0.648793\pi\) | ||||
−0.450610 | + | 0.892721i | \(0.648793\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.31874e7 | 0.616944 | ||||||||
\(856\) | −659490. | − | 1.14227e6i | −0.0307627 | − | 0.0532825i | ||||
\(857\) | −2.67342e6 | + | 4.63049e6i | −0.124341 | + | 0.215365i | −0.921475 | − | 0.388437i | \(-0.873015\pi\) |
0.797134 | + | 0.603802i | \(0.206348\pi\) | |||||||
\(858\) | 900900. | − | 1.56040e6i | 0.0417790 | − | 0.0723634i | ||||
\(859\) | 1.97929e7 | + | 3.42823e7i | 0.915223 | + | 1.58521i | 0.806574 | + | 0.591132i | \(0.201319\pi\) |
0.108648 | + | 0.994080i | \(0.465348\pi\) | |||||||
\(860\) | 3.56636e6 | 0.164429 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.17719e7 | 0.539607 | ||||||||
\(863\) | 1.25142e7 | + | 2.16752e7i | 0.571973 | + | 0.990687i | 0.996363 | + | 0.0852072i | \(0.0271552\pi\) |
−0.424390 | + | 0.905479i | \(0.639511\pi\) | |||||||
\(864\) | 905782. | − | 1.56886e6i | 0.0412800 | − | 0.0714990i | ||||
\(865\) | 2.86923e7 | − | 4.96965e7i | 1.30384 | − | 2.25832i | ||||
\(866\) | −9.47020e6 | − | 1.64029e7i | −0.429106 | − | 0.743233i | ||||
\(867\) | −2.40176e7 | −1.08513 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.06605e6 | 0.227573 | ||||||||
\(870\) | −1.16706e7 | − | 2.02140e7i | −0.522750 | − | 0.905429i | ||||
\(871\) | −537460. | + | 930908.i | −0.0240049 | + | 0.0415778i | ||||
\(872\) | 1.73938e7 | − | 3.01270e7i | 0.774646 | − | 1.34173i | ||||
\(873\) | 199017. | + | 344708.i | 0.00883801 | + | 0.0153079i | ||||
\(874\) | 4.98816e6 | 0.220883 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.92081e6 | −0.128600 | ||||||||
\(877\) | 2.51294e6 | + | 4.35255e6i | 0.110328 | + | 0.191093i | 0.915902 | − | 0.401401i | \(-0.131477\pi\) |
−0.805575 | + | 0.592494i | \(0.798143\pi\) | |||||||
\(878\) | −9.10806e6 | + | 1.57756e7i | −0.398740 | + | 0.690638i | ||||
\(879\) | 5.33730e6 | − | 9.24447e6i | 0.232996 | − | 0.403562i | ||||
\(880\) | −1.83544e6 | − | 3.17908e6i | −0.0798977 | − | 0.138387i | ||||
\(881\) | 2.60490e7 | 1.13071 | 0.565356 | − | 0.824847i | \(-0.308739\pi\) | ||||
0.565356 | + | 0.824847i | \(0.308739\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.82462e6 | −0.294562 | −0.147281 | − | 0.989095i | \(-0.547052\pi\) | ||||
−0.147281 | + | 0.989095i | \(0.547052\pi\) | |||||||
\(884\) | 5.44929e6 | + | 9.43845e6i | 0.234536 | + | 0.406228i | ||||
\(885\) | −4.74606e6 | + | 8.22042e6i | −0.203693 | + | 0.352806i | ||||
\(886\) | −6.20973e6 | + | 1.07556e7i | −0.265759 | + | 0.460309i | ||||
\(887\) | 1.16917e7 | + | 2.02507e7i | 0.498965 | + | 0.864233i | 0.999999 | − | 0.00119429i | \(-0.000380154\pi\) |
−0.501034 | + | 0.865428i | \(0.667047\pi\) | |||||||
\(888\) | −1.28782e7 | −0.548053 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.49554e6 | −0.0632882 | ||||||||
\(891\) | −170586. | − | 295464.i | −0.00719862 | − | 0.0124684i | ||||
\(892\) | 653464. | − | 1.13183e6i | 0.0274985 | − | 0.0476289i | ||||
\(893\) | −748224. | + | 1.29596e6i | −0.0313981 | + | 0.0543831i | ||||
\(894\) | −2.79598e6 | − | 4.84279e6i | −0.117001 | − | 0.202652i | ||||
\(895\) | −6.22517e7 | −2.59773 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.99168e6 | 0.165644 | ||||||||
\(898\) | 6.57944e6 | + | 1.13959e7i | 0.272269 | + | 0.471583i | ||||
\(899\) | 1.74810e7 | − | 3.02780e7i | 0.721386 | − | 1.24948i | ||||
\(900\) | 1.61907e6 | − | 2.80431e6i | 0.0666283 | − | 0.115404i | ||||
\(901\) | −4.22800e6 | − | 7.32311e6i | −0.173509 | − | 0.300527i | ||||
\(902\) | 848120. | 0.0347089 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.80113e6 | 0.358193 | ||||||||
\(905\) | −7.26761e6 | − | 1.25879e7i | −0.294965 | − | 0.510894i | ||||
\(906\) | −1.00417e7 | + | 1.73927e7i | −0.406429 | + | 0.703956i | ||||
\(907\) | −1.97980e7 | + | 3.42911e7i | −0.799102 | + | 1.38409i | 0.121100 | + | 0.992640i | \(0.461358\pi\) |
−0.920202 | + | 0.391445i | \(0.871975\pi\) | |||||||
\(908\) | −1.17730e6 | − | 2.03915e6i | −0.0473885 | − | 0.0820793i | ||||
\(909\) | 1.34747e7 | 0.540890 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.67570e6 | −0.186660 | −0.0933300 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933300 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(912\) | 5.85329e6 | + | 1.01382e7i | 0.233031 | + | 0.403621i | ||||
\(913\) | −2.11193e6 | + | 3.65797e6i | −0.0838498 | + | 0.145232i | ||||
\(914\) | 2.90326e6 | − | 5.02859e6i | 0.114953 | − | 0.199104i | ||||
\(915\) | −1.92896e7 | − | 3.34106e7i | −0.761678 | − | 1.31927i | ||||
\(916\) | −6.48420e6 | −0.255339 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.37019e6 | −0.288650 | ||||||||
\(919\) | 2.46297e6 | + | 4.26599e6i | 0.0961990 | + | 0.166622i | 0.910108 | − | 0.414370i | \(-0.135998\pi\) |
−0.813909 | + | 0.580992i | \(0.802665\pi\) | |||||||
\(920\) | 5.27904e6 | − | 9.14357e6i | 0.205629 | − | 0.356161i | ||||
\(921\) | −6.83512e6 | + | 1.18388e7i | −0.265520 | + | 0.459894i | ||||
\(922\) | 7.03462e6 | + | 1.21843e7i | 0.272529 | + | 0.472034i | ||||
\(923\) | 1.44144e7 | 0.556919 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.19073e7 | −1.61041 | ||||||||
\(926\) | −1.71075e7 | − | 2.96310e7i | −0.655630 | − | 1.13558i | ||||
\(927\) | 6.36498e6 | − | 1.10245e7i | 0.243275 | − | 0.421365i | ||||
\(928\) | −6.85612e6 | + | 1.18751e7i | −0.261341 | + | 0.452657i | ||||
\(929\) | −1.61844e7 | − | 2.80322e7i | −0.615258 | − | 1.06566i | −0.990339 | − | 0.138666i | \(-0.955719\pi\) |
0.375082 | − | 0.926992i | \(-0.377615\pi\) | |||||||
\(930\) | −2.68013e7 | −1.01613 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.79980e6 | −0.331843 | ||||||||
\(933\) | −957636. | − | 1.65867e6i | −0.0360161 | − | 0.0623817i | ||||
\(934\) | 8.35785e6 | − | 1.44762e7i | 0.313493 | − | 0.542985i | ||||
\(935\) | 4.94177e6 | − | 8.55939e6i | 0.184864 | − | 0.320195i | ||||
\(936\) | 6.08108e6 | + | 1.05327e7i | 0.226877 | + | 0.392963i | ||||
\(937\) | 3.32337e7 | 1.23660 | 0.618301 | − | 0.785941i | \(-0.287821\pi\) | ||||
0.618301 | + | 0.785941i | \(0.287821\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17046.0 | −0.000630897 | ||||||||
\(940\) | 284256. | + | 492346.i | 0.0104928 | + | 0.0181740i | ||||
\(941\) | −1.33213e7 | + | 2.30732e7i | −0.490426 | + | 0.849443i | −0.999939 | − | 0.0110202i | \(-0.996492\pi\) |
0.509513 | + | 0.860463i | \(0.329825\pi\) | |||||||
\(942\) | 3.59428e6 | − | 6.22548e6i | 0.131973 | − | 0.228584i | ||||
\(943\) | 939456. | + | 1.62719e6i | 0.0344031 | + | 0.0595879i | ||||
\(944\) | −8.42622e6 | −0.307753 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.40920e6 | 0.0511970 | ||||||||
\(947\) | −1.57332e7 | − | 2.72506e7i | −0.570086 | − | 0.987419i | −0.996556 | − | 0.0829170i | \(-0.973576\pi\) |
0.426470 | − | 0.904502i | \(-0.359757\pi\) | |||||||
\(948\) | −3.06886e6 | + | 5.31541e6i | −0.110906 | + | 0.192095i | ||||
\(949\) | 1.78494e7 | − | 3.09160e7i | 0.643365 | − | 1.11434i | ||||
\(950\) | 2.47286e7 | + | 4.28312e7i | 0.888978 | + | 1.53976i | ||||
\(951\) | 1.42108e7 | 0.509527 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.34516e7 | −0.479779 | −0.239890 | − | 0.970800i | \(-0.577111\pi\) | ||||
−0.239890 | + | 0.970800i | \(0.577111\pi\) | |||||||
\(954\) | −846855. | − | 1.46680e6i | −0.0301258 | − | 0.0521794i | ||||
\(955\) | 2.28845e7 | − | 3.96371e7i | 0.811957 | − | 1.40635i | ||||
\(956\) | −1.21456e6 | + | 2.10367e6i | −0.0429806 | + | 0.0744446i | ||||
\(957\) | 1.29121e6 | + | 2.23644e6i | 0.0455741 | + | 0.0789366i | ||||
\(958\) | 2.14124e7 | 0.753792 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.08426e7 | 1.08012 | ||||||||
\(961\) | −5.75787e6 | − | 9.97293e6i | −0.201119 | − | 0.348349i | ||||
\(962\) | 1.41256e7 | − | 2.44663e7i | 0.492120 | − | 0.852376i | ||||
\(963\) | 273942. | − | 474481.i | 0.00951903 | − | 0.0164875i | ||||
\(964\) | −347095. | − | 601186.i | −0.0120297 | − | 0.0208361i | ||||
\(965\) | −5.83313e7 | −2.01643 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.84963e7 | −0.979992 | −0.489996 | − | 0.871725i | \(-0.663002\pi\) | ||||
−0.489996 | + | 0.871725i | \(0.663002\pi\) | |||||||
\(968\) | −1.54388e7 | − | 2.67408e7i | −0.529573 | − | 0.917248i | ||||
\(969\) | −1.57595e7 | + | 2.72962e7i | −0.539178 | + | 0.933884i | ||||
\(970\) | −1.15479e6 | + | 2.00015e6i | −0.0394070 | + | 0.0682550i | ||||
\(971\) | 9.09289e6 | + | 1.57493e7i | 0.309495 | + | 0.536061i | 0.978252 | − | 0.207420i | \(-0.0665067\pi\) |
−0.668757 | + | 0.743481i | \(0.733173\pi\) | |||||||
\(972\) | 413343. | 0.0140328 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.46588e7 | −1.50837 | ||||||||
\(975\) | 1.97886e7 | + | 3.42749e7i | 0.666659 | + | 1.15469i | ||||
\(976\) | 1.71236e7 | − | 2.96589e7i | 0.575399 | − | 0.996621i | ||||
\(977\) | −1.60471e7 | + | 2.77943e7i | −0.537847 | + | 0.931579i | 0.461172 | + | 0.887311i | \(0.347429\pi\) |
−0.999020 | + | 0.0442683i | \(0.985904\pi\) | |||||||
\(978\) | 5.56317e6 | + | 9.63569e6i | 0.185984 | + | 0.322133i | ||||
\(979\) | 165464. | 0.00551756 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.44502e7 | 0.479405 | ||||||||
\(982\) | −6.88265e6 | − | 1.19211e7i | −0.227760 | − | 0.394491i | ||||
\(983\) | 7.80769e6 | − | 1.35233e7i | 0.257715 | − | 0.446375i | −0.707915 | − | 0.706298i | \(-0.750364\pi\) |
0.965629 | + | 0.259923i | \(0.0836973\pi\) | |||||||
\(984\) | −2.86240e6 | + | 4.95783e6i | −0.0942417 | + | 0.163231i | ||||
\(985\) | −1.11188e7 | − | 1.92583e7i | −0.365146 | − | 0.632452i | ||||
\(986\) | 5.57870e7 | 1.82743 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.33548e6 | 0.304260 | ||||||||
\(989\) | 1.56096e6 | + | 2.70366e6i | 0.0507459 | + | 0.0878945i | ||||
\(990\) | 989820. | − | 1.71442e6i | 0.0320973 | − | 0.0555941i | ||||
\(991\) | −2.42250e7 | + | 4.19589e7i | −0.783572 | + | 1.35719i | 0.146276 | + | 0.989244i | \(0.453271\pi\) |
−0.929848 | + | 0.367943i | \(0.880062\pi\) | |||||||
\(992\) | 7.87248e6 | + | 1.36355e7i | 0.253999 | + | 0.439940i | ||||
\(993\) | 3.05524e7 | 0.983268 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.71778e6 | 0.247135 | ||||||||
\(996\) | −2.55868e6 | − | 4.43177e6i | −0.0817275 | − | 0.141556i | ||||
\(997\) | −2.27168e7 | + | 3.93466e7i | −0.723784 | + | 1.25363i | 0.235689 | + | 0.971829i | \(0.424265\pi\) |
−0.959473 | + | 0.281802i | \(0.909068\pi\) | |||||||
\(998\) | −1.20102e7 | + | 2.08023e7i | −0.381702 | + | 0.661127i | ||||
\(999\) | −2.67470e6 | − | 4.63272e6i | −0.0847933 | − | 0.146866i |
(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 | 147.6.e.d.67.1 | 2 | ||
7.2 | even | 3 | inner | 147.6.e.d.79.1 | 2 | ||
7.3 | odd | 6 | 21.6.a.c.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 147.6.a.f.1.1 | 1 | |||
7.5 | odd | 6 | 147.6.e.c.79.1 | 2 | |||
7.6 | odd | 2 | 147.6.e.c.67.1 | 2 | |||
21.11 | odd | 6 | 441.6.a.c.1.1 | 1 | |||
21.17 | even | 6 | 63.6.a.b.1.1 | 1 | |||
28.3 | even | 6 | 336.6.a.i.1.1 | 1 | |||
35.3 | even | 12 | 525.6.d.c.274.1 | 2 | |||
35.17 | even | 12 | 525.6.d.c.274.2 | 2 | |||
35.24 | odd | 6 | 525.6.a.b.1.1 | 1 | |||
84.59 | odd | 6 | 1008.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.a.c.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
63.6.a.b.1.1 | 1 | 21.17 | even | 6 | |||
147.6.a.f.1.1 | 1 | 7.4 | even | 3 | |||
147.6.e.c.67.1 | 2 | 7.6 | odd | 2 | |||
147.6.e.c.79.1 | 2 | 7.5 | odd | 6 | |||
147.6.e.d.67.1 | 2 | 1.1 | even | 1 | trivial | ||
147.6.e.d.79.1 | 2 | 7.2 | even | 3 | inner | ||
336.6.a.i.1.1 | 1 | 28.3 | even | 6 | |||
441.6.a.c.1.1 | 1 | 21.11 | odd | 6 | |||
525.6.a.b.1.1 | 1 | 35.24 | odd | 6 | |||
525.6.d.c.274.1 | 2 | 35.3 | even | 12 | |||
525.6.d.c.274.2 | 2 | 35.17 | even | 12 | |||
1008.6.a.a.1.1 | 1 | 84.59 | odd | 6 |