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 | 79.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.79 |
Dual form | 147.6.e.g.67.1 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.176777 | − | 0.306186i | −0.763998 | − | 0.645219i | \(-0.776766\pi\) |
0.940775 | + | 0.339032i | \(0.110100\pi\) | |||||||
\(3\) | −4.50000 | − | 7.79423i | −0.288675 | − | 0.500000i | ||||
\(4\) | 14.0000 | + | 24.2487i | 0.437500 | + | 0.757772i | ||||
\(5\) | 5.50000 | − | 9.52628i | 0.0983870 | − | 0.170411i | −0.812630 | − | 0.582780i | \(-0.801965\pi\) |
0.911017 | + | 0.412368i | \(0.135298\pi\) | |||||||
\(6\) | −18.0000 | −0.204124 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 120.000 | 0.662913 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | −11.0000 | − | 19.0526i | −0.0347851 | − | 0.0602495i | ||||
\(11\) | −134.500 | − | 232.961i | −0.335151 | − | 0.580499i | 0.648363 | − | 0.761332i | \(-0.275454\pi\) |
−0.983514 | + | 0.180833i | \(0.942121\pi\) | |||||||
\(12\) | 126.000 | − | 218.238i | 0.252591 | − | 0.437500i | ||||
\(13\) | 308.000 | 0.505466 | 0.252733 | − | 0.967536i | \(-0.418671\pi\) | ||||
0.252733 | + | 0.967536i | \(0.418671\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −99.0000 | −0.113608 | ||||||||
\(16\) | −328.000 | + | 568.113i | −0.320312 | + | 0.554798i | ||||
\(17\) | 948.000 | + | 1641.98i | 0.795584 | + | 1.37799i | 0.922468 | + | 0.386074i | \(0.126169\pi\) |
−0.126884 | + | 0.991918i | \(0.540498\pi\) | |||||||
\(18\) | 81.0000 | + | 140.296i | 0.0589256 | + | 0.102062i | ||||
\(19\) | −82.0000 | + | 142.028i | −0.0521111 | + | 0.0902590i | −0.890904 | − | 0.454191i | \(-0.849928\pi\) |
0.838793 | + | 0.544450i | \(0.183262\pi\) | |||||||
\(20\) | 308.000 | 0.172177 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −538.000 | −0.236988 | ||||||||
\(23\) | 1632.00 | − | 2826.71i | 0.643281 | − | 1.11419i | −0.341415 | − | 0.939913i | \(-0.610906\pi\) |
0.984696 | − | 0.174282i | \(-0.0557605\pi\) | |||||||
\(24\) | −540.000 | − | 935.307i | −0.191366 | − | 0.331456i | ||||
\(25\) | 1502.00 | + | 2601.54i | 0.480640 | + | 0.832493i | ||||
\(26\) | 308.000 | − | 533.472i | 0.0893547 | − | 0.154767i | ||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2417.00 | 0.533681 | 0.266840 | − | 0.963741i | \(-0.414020\pi\) | ||||
0.266840 | + | 0.963741i | \(0.414020\pi\) | |||||||
\(30\) | −99.0000 | + | 171.473i | −0.0200832 | + | 0.0347851i | ||||
\(31\) | 1420.50 | + | 2460.38i | 0.265483 | + | 0.459830i | 0.967690 | − | 0.252143i | \(-0.0811352\pi\) |
−0.702207 | + | 0.711973i | \(0.747802\pi\) | |||||||
\(32\) | 2576.00 | + | 4461.76i | 0.444704 | + | 0.770250i | ||||
\(33\) | −1210.50 | + | 2096.65i | −0.193500 | + | 0.335151i | ||||
\(34\) | 3792.00 | 0.562563 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2268.00 | −0.291667 | ||||||||
\(37\) | 5664.00 | − | 9810.34i | 0.680172 | − | 1.17809i | −0.294756 | − | 0.955573i | \(-0.595238\pi\) |
0.974928 | − | 0.222520i | \(-0.0714284\pi\) | |||||||
\(38\) | 164.000 | + | 284.056i | 0.0184240 | + | 0.0319114i | ||||
\(39\) | −1386.00 | − | 2400.62i | −0.145916 | − | 0.252733i | ||||
\(40\) | 660.000 | − | 1143.15i | 0.0652220 | − | 0.112968i | ||||
\(41\) | 16856.0 | 1.56601 | 0.783006 | − | 0.622015i | \(-0.213686\pi\) | ||||
0.783006 | + | 0.622015i | \(0.213686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7894.00 | −0.651067 | −0.325534 | − | 0.945530i | \(-0.605544\pi\) | ||||
−0.325534 | + | 0.945530i | \(0.605544\pi\) | |||||||
\(44\) | 3766.00 | − | 6522.90i | 0.293257 | − | 0.507936i | ||||
\(45\) | 445.500 | + | 771.629i | 0.0327957 | + | 0.0568038i | ||||
\(46\) | −3264.00 | − | 5653.41i | −0.227434 | − | 0.393927i | ||||
\(47\) | 10551.0 | − | 18274.9i | 0.696705 | − | 1.20673i | −0.272897 | − | 0.962043i | \(-0.587982\pi\) |
0.969603 | − | 0.244685i | \(-0.0786847\pi\) | |||||||
\(48\) | 5904.00 | 0.369865 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6008.00 | 0.339864 | ||||||||
\(51\) | 8532.00 | − | 14777.9i | 0.459331 | − | 0.795584i | ||||
\(52\) | 4312.00 | + | 7468.60i | 0.221142 | + | 0.383028i | ||||
\(53\) | 14845.5 | + | 25713.2i | 0.725947 | + | 1.25738i | 0.958583 | + | 0.284814i | \(0.0919318\pi\) |
−0.232635 | + | 0.972564i | \(0.574735\pi\) | |||||||
\(54\) | 729.000 | − | 1262.67i | 0.0340207 | − | 0.0589256i | ||||
\(55\) | −2959.00 | −0.131898 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1476.00 | 0.0601727 | ||||||||
\(58\) | 2417.00 | − | 4186.37i | 0.0943423 | − | 0.163406i | ||||
\(59\) | −4081.50 | − | 7069.37i | −0.152648 | − | 0.264393i | 0.779552 | − | 0.626337i | \(-0.215447\pi\) |
−0.932200 | + | 0.361944i | \(0.882113\pi\) | |||||||
\(60\) | −1386.00 | − | 2400.62i | −0.0497033 | − | 0.0860886i | ||||
\(61\) | 7583.00 | − | 13134.1i | 0.260925 | − | 0.451936i | −0.705563 | − | 0.708648i | \(-0.749306\pi\) |
0.966488 | + | 0.256711i | \(0.0826390\pi\) | |||||||
\(62\) | 5682.00 | 0.187725 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10688.0 | −0.326172 | ||||||||
\(65\) | 1694.00 | − | 2934.09i | 0.0497313 | − | 0.0861372i | ||||
\(66\) | 2421.00 | + | 4193.30i | 0.0684124 | + | 0.118494i | ||||
\(67\) | 16039.0 | + | 27780.4i | 0.436506 | + | 0.756051i | 0.997417 | − | 0.0718253i | \(-0.0228824\pi\) |
−0.560911 | + | 0.827876i | \(0.689549\pi\) | |||||||
\(68\) | −26544.0 | + | 45975.6i | −0.696136 | + | 1.20574i | ||||
\(69\) | −29376.0 | −0.742797 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −38274.0 | −0.901069 | −0.450534 | − | 0.892759i | \(-0.648767\pi\) | ||||
−0.450534 | + | 0.892759i | \(0.648767\pi\) | |||||||
\(72\) | −4860.00 | + | 8417.77i | −0.110485 | + | 0.191366i | ||||
\(73\) | 17433.0 | + | 30194.8i | 0.382882 | + | 0.663171i | 0.991473 | − | 0.130313i | \(-0.0415982\pi\) |
−0.608591 | + | 0.793484i | \(0.708265\pi\) | |||||||
\(74\) | −11328.0 | − | 19620.7i | −0.240477 | − | 0.416519i | ||||
\(75\) | 13518.0 | − | 23413.9i | 0.277498 | − | 0.480640i | ||||
\(76\) | −4592.00 | −0.0911943 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5544.00 | −0.103178 | ||||||||
\(79\) | −6764.50 | + | 11716.5i | −0.121946 | + | 0.211217i | −0.920535 | − | 0.390660i | \(-0.872247\pi\) |
0.798589 | + | 0.601877i | \(0.205580\pi\) | |||||||
\(80\) | 3608.00 | + | 6249.24i | 0.0630292 | + | 0.109170i | ||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 16856.0 | − | 29195.4i | 0.276834 | − | 0.479491i | ||||
\(83\) | 68103.0 | 1.08510 | 0.542552 | − | 0.840023i | \(-0.317458\pi\) | ||||
0.542552 | + | 0.840023i | \(0.317458\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20856.0 | 0.313100 | ||||||||
\(86\) | −7894.00 | + | 13672.8i | −0.115094 | + | 0.199348i | ||||
\(87\) | −10876.5 | − | 18838.7i | −0.154060 | − | 0.266840i | ||||
\(88\) | −16140.0 | − | 27955.3i | −0.222176 | − | 0.384820i | ||||
\(89\) | −57461.0 | + | 99525.4i | −0.768950 | + | 1.33186i | 0.169183 | + | 0.985585i | \(0.445887\pi\) |
−0.938133 | + | 0.346276i | \(0.887446\pi\) | |||||||
\(90\) | 1782.00 | 0.0231900 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 91392.0 | 1.12574 | ||||||||
\(93\) | 12784.5 | − | 22143.4i | 0.153277 | − | 0.265483i | ||||
\(94\) | −21102.0 | − | 36549.7i | −0.246322 | − | 0.426643i | ||||
\(95\) | 902.000 | + | 1562.31i | 0.0102541 | + | 0.0177606i | ||||
\(96\) | 23184.0 | − | 40155.9i | 0.256750 | − | 0.444704i | ||||
\(97\) | −154959. | −1.67220 | −0.836099 | − | 0.548579i | \(-0.815169\pi\) | ||||
−0.836099 | + | 0.548579i | \(0.815169\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 21789.0 | 0.223434 | ||||||||
\(100\) | −42056.0 | + | 72843.1i | −0.420560 | + | 0.728431i | ||||
\(101\) | −53785.0 | − | 93158.4i | −0.524636 | − | 0.908695i | −0.999589 | − | 0.0286843i | \(-0.990868\pi\) |
0.474953 | − | 0.880011i | \(-0.342465\pi\) | |||||||
\(102\) | −17064.0 | − | 29555.7i | −0.162398 | − | 0.281281i | ||||
\(103\) | 4468.00 | − | 7738.80i | 0.0414973 | − | 0.0718755i | −0.844531 | − | 0.535507i | \(-0.820121\pi\) |
0.886028 | + | 0.463632i | \(0.153454\pi\) | |||||||
\(104\) | 36960.0 | 0.335080 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 59382.0 | 0.513322 | ||||||||
\(107\) | −96833.5 | + | 167721.i | −0.817648 | + | 1.41621i | 0.0897634 | + | 0.995963i | \(0.471389\pi\) |
−0.907411 | + | 0.420244i | \(0.861944\pi\) | |||||||
\(108\) | 10206.0 | + | 17677.3i | 0.0841969 | + | 0.145833i | ||||
\(109\) | −102555. | − | 177630.i | −0.826781 | − | 1.43203i | −0.900550 | − | 0.434752i | \(-0.856836\pi\) |
0.0737692 | − | 0.997275i | \(-0.476497\pi\) | |||||||
\(110\) | −2959.00 | + | 5125.14i | −0.0233165 | + | 0.0403854i | ||||
\(111\) | −101952. | −0.785395 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 46664.0 | 0.343784 | 0.171892 | − | 0.985116i | \(-0.445012\pi\) | ||||
0.171892 | + | 0.985116i | \(0.445012\pi\) | |||||||
\(114\) | 1476.00 | − | 2556.51i | 0.0106371 | − | 0.0184240i | ||||
\(115\) | −17952.0 | − | 31093.8i | −0.126581 | − | 0.219245i | ||||
\(116\) | 33838.0 | + | 58609.1i | 0.233485 | + | 0.404409i | ||||
\(117\) | −12474.0 | + | 21605.6i | −0.0842444 | + | 0.145916i | ||||
\(118\) | −16326.0 | −0.107938 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −11880.0 | −0.0753119 | ||||||||
\(121\) | 44345.0 | − | 76807.8i | 0.275348 | − | 0.476916i | ||||
\(122\) | −15166.0 | − | 26268.3i | −0.0922511 | − | 0.159784i | ||||
\(123\) | −75852.0 | − | 131380.i | −0.452069 | − | 0.783006i | ||||
\(124\) | −39774.0 | + | 68890.6i | −0.232298 | + | 0.402352i | ||||
\(125\) | 67419.0 | 0.385929 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −304365. | −1.67450 | −0.837250 | − | 0.546820i | \(-0.815838\pi\) | ||||
−0.837250 | + | 0.546820i | \(0.815838\pi\) | |||||||
\(128\) | −93120.0 | + | 161289.i | −0.502363 | + | 0.870119i | ||||
\(129\) | 35523.0 | + | 61527.6i | 0.187947 | + | 0.325534i | ||||
\(130\) | −3388.00 | − | 5868.19i | −0.0175827 | − | 0.0304541i | ||||
\(131\) | −6651.50 | + | 11520.7i | −0.0338642 | + | 0.0586546i | −0.882461 | − | 0.470386i | \(-0.844115\pi\) |
0.848597 | + | 0.529041i | \(0.177448\pi\) | |||||||
\(132\) | −67788.0 | −0.338624 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 64156.0 | 0.308656 | ||||||||
\(135\) | 4009.50 | − | 6944.66i | 0.0189346 | − | 0.0327957i | ||||
\(136\) | 113760. | + | 197038.i | 0.527403 | + | 0.913488i | ||||
\(137\) | 199131. | + | 344905.i | 0.906437 | + | 1.56999i | 0.818977 | + | 0.573826i | \(0.194542\pi\) |
0.0874596 | + | 0.996168i | \(0.472125\pi\) | |||||||
\(138\) | −29376.0 | + | 50880.7i | −0.131309 | + | 0.227434i | ||||
\(139\) | −230286. | −1.01095 | −0.505476 | − | 0.862841i | \(-0.668683\pi\) | ||||
−0.505476 | + | 0.862841i | \(0.668683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −189918. | −0.804486 | ||||||||
\(142\) | −38274.0 | + | 66292.5i | −0.159288 | + | 0.275895i | ||||
\(143\) | −41426.0 | − | 71751.9i | −0.169408 | − | 0.293423i | ||||
\(144\) | −26568.0 | − | 46017.1i | −0.106771 | − | 0.184933i | ||||
\(145\) | 13293.5 | − | 23025.0i | 0.0525073 | − | 0.0909452i | ||||
\(146\) | 69732.0 | 0.270738 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 317184. | 1.19030 | ||||||||
\(149\) | 48567.0 | − | 84120.5i | 0.179216 | − | 0.310410i | −0.762397 | − | 0.647110i | \(-0.775977\pi\) |
0.941612 | + | 0.336700i | \(0.109311\pi\) | |||||||
\(150\) | −27036.0 | − | 46827.7i | −0.0981102 | − | 0.169932i | ||||
\(151\) | 14523.5 | + | 25155.4i | 0.0518357 | + | 0.0897821i | 0.890779 | − | 0.454437i | \(-0.150159\pi\) |
−0.838943 | + | 0.544219i | \(0.816826\pi\) | |||||||
\(152\) | −9840.00 | + | 17043.4i | −0.0345451 | + | 0.0598338i | ||||
\(153\) | −153576. | −0.530389 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 31251.0 | 0.104480 | ||||||||
\(156\) | 38808.0 | − | 67217.4i | 0.127676 | − | 0.221142i | ||||
\(157\) | −288250. | − | 499264.i | −0.933298 | − | 1.61652i | −0.777642 | − | 0.628708i | \(-0.783584\pi\) |
−0.155656 | − | 0.987811i | \(-0.549749\pi\) | |||||||
\(158\) | 13529.0 | + | 23432.9i | 0.0431145 | + | 0.0746764i | ||||
\(159\) | 133610. | − | 231418.i | 0.419126 | − | 0.725947i | ||||
\(160\) | 56672.0 | 0.175012 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −13122.0 | −0.0392837 | ||||||||
\(163\) | 132616. | − | 229698.i | 0.390955 | − | 0.677154i | −0.601621 | − | 0.798782i | \(-0.705478\pi\) |
0.992576 | + | 0.121628i | \(0.0388114\pi\) | |||||||
\(164\) | 235984. | + | 408736.i | 0.685130 | + | 1.18668i | ||||
\(165\) | 13315.5 | + | 23063.1i | 0.0380757 | + | 0.0659490i | ||||
\(166\) | 68103.0 | − | 117958.i | 0.191821 | − | 0.332244i | ||||
\(167\) | 363790. | 1.00939 | 0.504696 | − | 0.863297i | \(-0.331605\pi\) | ||||
0.504696 | + | 0.863297i | \(0.331605\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −276429. | −0.744504 | ||||||||
\(170\) | 20856.0 | − | 36123.7i | 0.0553489 | − | 0.0958670i | ||||
\(171\) | −6642.00 | − | 11504.3i | −0.0173704 | − | 0.0300863i | ||||
\(172\) | −110516. | − | 191419.i | −0.284842 | − | 0.493361i | ||||
\(173\) | −82423.0 | + | 142761.i | −0.209379 | + | 0.362655i | −0.951519 | − | 0.307590i | \(-0.900478\pi\) |
0.742140 | + | 0.670245i | \(0.233811\pi\) | |||||||
\(174\) | −43506.0 | −0.108937 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 176464. | 0.429412 | ||||||||
\(177\) | −36733.5 | + | 63624.3i | −0.0881311 | + | 0.152648i | ||||
\(178\) | 114922. | + | 199051.i | 0.271865 | + | 0.470884i | ||||
\(179\) | −15314.0 | − | 26524.6i | −0.0357237 | − | 0.0618752i | 0.847611 | − | 0.530618i | \(-0.178040\pi\) |
−0.883334 | + | 0.468743i | \(0.844707\pi\) | |||||||
\(180\) | −12474.0 | + | 21605.6i | −0.0286962 | + | 0.0497033i | ||||
\(181\) | 651392. | 1.47790 | 0.738952 | − | 0.673759i | \(-0.235321\pi\) | ||||
0.738952 | + | 0.673759i | \(0.235321\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −136494. | −0.301291 | ||||||||
\(184\) | 195840. | − | 339205.i | 0.426439 | − | 0.738614i | ||||
\(185\) | −62304.0 | − | 107914.i | −0.133840 | − | 0.231818i | ||||
\(186\) | −25569.0 | − | 44286.8i | −0.0541915 | − | 0.0938625i | ||||
\(187\) | 255012. | − | 441694.i | 0.533282 | − | 0.923671i | ||||
\(188\) | 590856. | 1.21923 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3608.00 | 0.00725074 | ||||||||
\(191\) | 378680. | − | 655893.i | 0.751085 | − | 1.30092i | −0.196213 | − | 0.980561i | \(-0.562864\pi\) |
0.947297 | − | 0.320356i | \(-0.103802\pi\) | |||||||
\(192\) | 48096.0 | + | 83304.7i | 0.0941577 | + | 0.163086i | ||||
\(193\) | 80169.5 | + | 138858.i | 0.154923 | + | 0.268335i | 0.933031 | − | 0.359796i | \(-0.117154\pi\) |
−0.778108 | + | 0.628131i | \(0.783820\pi\) | |||||||
\(194\) | −154959. | + | 268397.i | −0.295605 | + | 0.512004i | ||||
\(195\) | −30492.0 | −0.0574248 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −61738.0 | −0.113341 | −0.0566705 | − | 0.998393i | \(-0.518048\pi\) | ||||
−0.0566705 | + | 0.998393i | \(0.518048\pi\) | |||||||
\(198\) | 21789.0 | − | 37739.7i | 0.0394979 | − | 0.0684124i | ||||
\(199\) | 185454. | + | 321216.i | 0.331974 | + | 0.574995i | 0.982899 | − | 0.184147i | \(-0.0589522\pi\) |
−0.650925 | + | 0.759142i | \(0.725619\pi\) | |||||||
\(200\) | 180240. | + | 312185.i | 0.318622 | + | 0.551870i | ||||
\(201\) | 144351. | − | 250023.i | 0.252017 | − | 0.436506i | ||||
\(202\) | −215140. | −0.370973 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 477792. | 0.803829 | ||||||||
\(205\) | 92708.0 | − | 160575.i | 0.154075 | − | 0.266866i | ||||
\(206\) | −8936.00 | − | 15477.6i | −0.0146715 | − | 0.0254118i | ||||
\(207\) | 132192. | + | 228963.i | 0.214427 | + | 0.371398i | ||||
\(208\) | −101024. | + | 174979.i | −0.161907 | + | 0.280432i | ||||
\(209\) | 44116.0 | 0.0698603 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 217450. | 0.336243 | 0.168122 | − | 0.985766i | \(-0.446230\pi\) | ||||
0.168122 | + | 0.985766i | \(0.446230\pi\) | |||||||
\(212\) | −415674. | + | 719968.i | −0.635204 | + | 1.10021i | ||||
\(213\) | 172233. | + | 298316.i | 0.260116 | + | 0.450534i | ||||
\(214\) | 193667. | + | 335441.i | 0.289082 | + | 0.500705i | ||||
\(215\) | −43417.0 | + | 75200.4i | −0.0640566 | + | 0.110949i | ||||
\(216\) | 87480.0 | 0.127578 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −410220. | −0.584623 | ||||||||
\(219\) | 156897. | − | 271754.i | 0.221057 | − | 0.382882i | ||||
\(220\) | −41426.0 | − | 71751.9i | −0.0577054 | − | 0.0999486i | ||||
\(221\) | 291984. | + | 505731.i | 0.402141 | + | 0.696529i | ||||
\(222\) | −101952. | + | 176586.i | −0.138840 | + | 0.240477i | ||||
\(223\) | −589771. | −0.794184 | −0.397092 | − | 0.917779i | \(-0.629981\pi\) | ||||
−0.397092 | + | 0.917779i | \(0.629981\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −243324. | −0.320427 | ||||||||
\(226\) | 46664.0 | − | 80824.4i | 0.0607730 | − | 0.105262i | ||||
\(227\) | −193522. | − | 335191.i | −0.249268 | − | 0.431745i | 0.714055 | − | 0.700090i | \(-0.246857\pi\) |
−0.963323 | + | 0.268345i | \(0.913523\pi\) | |||||||
\(228\) | 20664.0 | + | 35791.1i | 0.0263255 | + | 0.0455972i | ||||
\(229\) | −116366. | + | 201552.i | −0.146635 | + | 0.253979i | −0.929982 | − | 0.367606i | \(-0.880178\pi\) |
0.783347 | + | 0.621585i | \(0.213511\pi\) | |||||||
\(230\) | −71808.0 | −0.0895062 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 290040. | 0.353784 | ||||||||
\(233\) | −21048.0 | + | 36456.2i | −0.0253993 | + | 0.0439928i | −0.878446 | − | 0.477842i | \(-0.841419\pi\) |
0.853046 | + | 0.521835i | \(0.174752\pi\) | |||||||
\(234\) | 24948.0 | + | 43211.2i | 0.0297849 | + | 0.0515890i | ||||
\(235\) | −116061. | − | 201024.i | −0.137093 | − | 0.237453i | ||||
\(236\) | 114282. | − | 197942.i | 0.133567 | − | 0.231344i | ||||
\(237\) | 121761. | 0.140811 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −313416. | −0.354917 | −0.177458 | − | 0.984128i | \(-0.556788\pi\) | ||||
−0.177458 | + | 0.984128i | \(0.556788\pi\) | |||||||
\(240\) | 32472.0 | − | 56243.2i | 0.0363899 | − | 0.0630292i | ||||
\(241\) | 428904. | + | 742883.i | 0.475682 | + | 0.823906i | 0.999612 | − | 0.0278556i | \(-0.00886787\pi\) |
−0.523930 | + | 0.851762i | \(0.675535\pi\) | |||||||
\(242\) | −88690.0 | − | 153616.i | −0.0973501 | − | 0.168615i | ||||
\(243\) | −29524.5 | + | 51137.9i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 424648. | 0.456620 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −303408. | −0.319661 | ||||||||
\(247\) | −25256.0 | + | 43744.7i | −0.0263404 | + | 0.0456229i | ||||
\(248\) | 170460. | + | 295245.i | 0.175992 | + | 0.304827i | ||||
\(249\) | −306464. | − | 530810.i | −0.313242 | − | 0.542552i | ||||
\(250\) | 67419.0 | − | 116773.i | 0.0682232 | − | 0.118166i | ||||
\(251\) | −454517. | −0.455371 | −0.227686 | − | 0.973735i | \(-0.573116\pi\) | ||||
−0.227686 | + | 0.973735i | \(0.573116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −878016. | −0.862385 | ||||||||
\(254\) | −304365. | + | 527176.i | −0.296013 | + | 0.512709i | ||||
\(255\) | −93852.0 | − | 162556.i | −0.0903843 | − | 0.156550i | ||||
\(256\) | 15232.0 | + | 26382.6i | 0.0145264 | + | 0.0251604i | ||||
\(257\) | 439091. | − | 760528.i | 0.414688 | − | 0.718261i | −0.580707 | − | 0.814112i | \(-0.697224\pi\) |
0.995396 | + | 0.0958512i | \(0.0305573\pi\) | |||||||
\(258\) | 142092. | 0.132899 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 94864.0 | 0.0870298 | ||||||||
\(261\) | −97888.5 | + | 169548.i | −0.0889468 | + | 0.154060i | ||||
\(262\) | 13303.0 | + | 23041.5i | 0.0119728 | + | 0.0207375i | ||||
\(263\) | −980467. | − | 1.69822e6i | −0.874065 | − | 1.51392i | −0.857756 | − | 0.514058i | \(-0.828142\pi\) |
−0.0163091 | − | 0.999867i | \(-0.505192\pi\) | |||||||
\(264\) | −145260. | + | 251598.i | −0.128273 | + | 0.222176i | ||||
\(265\) | 326601. | 0.285695 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.03430e6 | 0.887907 | ||||||||
\(268\) | −449092. | + | 777850.i | −0.381943 | + | 0.661544i | ||||
\(269\) | −526898. | − | 912613.i | −0.443962 | − | 0.768964i | 0.554018 | − | 0.832505i | \(-0.313094\pi\) |
−0.997979 | + | 0.0635408i | \(0.979761\pi\) | |||||||
\(270\) | −8019.00 | − | 13889.3i | −0.00669439 | − | 0.0115950i | ||||
\(271\) | −52529.5 | + | 90983.8i | −0.0434490 | + | 0.0752559i | −0.886932 | − | 0.461900i | \(-0.847168\pi\) |
0.843483 | + | 0.537156i | \(0.180501\pi\) | |||||||
\(272\) | −1.24378e6 | −1.01934 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 796524. | 0.640948 | ||||||||
\(275\) | 404038. | − | 699814.i | 0.322174 | − | 0.558022i | ||||
\(276\) | −411264. | − | 712330.i | −0.324974 | − | 0.562871i | ||||
\(277\) | 213796. | + | 370306.i | 0.167417 | + | 0.289975i | 0.937511 | − | 0.347955i | \(-0.113124\pi\) |
−0.770094 | + | 0.637931i | \(0.779791\pi\) | |||||||
\(278\) | −230286. | + | 398867.i | −0.178713 | + | 0.309540i | ||||
\(279\) | −230121. | −0.176989 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 638878. | 0.482672 | 0.241336 | − | 0.970442i | \(-0.422414\pi\) | ||||
0.241336 | + | 0.970442i | \(0.422414\pi\) | |||||||
\(282\) | −189918. | + | 328948.i | −0.142214 | + | 0.246322i | ||||
\(283\) | −1.22571e6 | − | 2.12299e6i | −0.909750 | − | 1.57573i | −0.814411 | − | 0.580288i | \(-0.802940\pi\) |
−0.0953386 | − | 0.995445i | \(-0.530393\pi\) | |||||||
\(284\) | −535836. | − | 928095.i | −0.394218 | − | 0.682805i | ||||
\(285\) | 8118.00 | − | 14060.8i | 0.00592021 | − | 0.0102541i | ||||
\(286\) | −165704. | −0.119789 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −417312. | −0.296469 | ||||||||
\(289\) | −1.08748e6 | + | 1.88357e6i | −0.765908 | + | 1.32659i | ||||
\(290\) | −26587.0 | − | 46050.0i | −0.0185641 | − | 0.0321540i | ||||
\(291\) | 697316. | + | 1.20779e6i | 0.482722 | + | 0.836099i | ||||
\(292\) | −488124. | + | 845456.i | −0.335022 | + | 0.580275i | ||||
\(293\) | −1.71617e6 | −1.16786 | −0.583930 | − | 0.811804i | \(-0.698486\pi\) | ||||
−0.583930 | + | 0.811804i | \(0.698486\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −89793.0 | −0.0600741 | ||||||||
\(296\) | 679680. | − | 1.17724e6i | 0.450895 | − | 0.780973i | ||||
\(297\) | −98050.5 | − | 169828.i | −0.0644998 | − | 0.111717i | ||||
\(298\) | −97134.0 | − | 168241.i | −0.0633623 | − | 0.109747i | ||||
\(299\) | 502656. | − | 870626.i | 0.325157 | − | 0.563188i | ||||
\(300\) | 757008. | 0.485621 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 58094.0 | 0.0366534 | ||||||||
\(303\) | −484065. | + | 838425.i | −0.302898 | + | 0.524636i | ||||
\(304\) | −53792.0 | − | 93170.5i | −0.0333836 | − | 0.0578222i | ||||
\(305\) | −83413.0 | − | 144476.i | −0.0513433 | − | 0.0889293i | ||||
\(306\) | −153576. | + | 266001.i | −0.0937605 | + | 0.162398i | ||||
\(307\) | −1.80897e6 | −1.09543 | −0.547715 | − | 0.836665i | \(-0.684502\pi\) | ||||
−0.547715 | + | 0.836665i | \(0.684502\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −80424.0 | −0.0479170 | ||||||||
\(310\) | 31251.0 | − | 54128.3i | 0.0184697 | − | 0.0319904i | ||||
\(311\) | 760728. | + | 1.31762e6i | 0.445993 | + | 0.772483i | 0.998121 | − | 0.0612765i | \(-0.0195171\pi\) |
−0.552127 | + | 0.833760i | \(0.686184\pi\) | |||||||
\(312\) | −166320. | − | 288075.i | −0.0967293 | − | 0.167540i | ||||
\(313\) | −674200. | + | 1.16775e6i | −0.388980 | + | 0.673734i | −0.992313 | − | 0.123756i | \(-0.960506\pi\) |
0.603332 | + | 0.797490i | \(0.293839\pi\) | |||||||
\(314\) | −1.15300e6 | −0.659941 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −378812. | −0.213406 | ||||||||
\(317\) | 24847.5 | − | 43037.1i | 0.0138878 | − | 0.0240544i | −0.858998 | − | 0.511979i | \(-0.828913\pi\) |
0.872886 | + | 0.487925i | \(0.162246\pi\) | |||||||
\(318\) | −267219. | − | 462837.i | −0.148183 | − | 0.256661i | ||||
\(319\) | −325086. | − | 563066.i | −0.178864 | − | 0.309801i | ||||
\(320\) | −58784.0 | + | 101817.i | −0.0320911 | + | 0.0555834i | ||||
\(321\) | 1.74300e6 | 0.944138 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −310944. | −0.165835 | ||||||||
\(324\) | 91854.0 | − | 159096.i | 0.0486111 | − | 0.0841969i | ||||
\(325\) | 462616. | + | 801274.i | 0.242947 | + | 0.420797i | ||||
\(326\) | −265232. | − | 459395.i | −0.138224 | − | 0.239410i | ||||
\(327\) | −922995. | + | 1.59867e6i | −0.477342 | + | 0.826781i | ||||
\(328\) | 2.02272e6 | 1.03813 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 53262.0 | 0.0269236 | ||||||||
\(331\) | −793918. | + | 1.37511e6i | −0.398296 | + | 0.689868i | −0.993516 | − | 0.113694i | \(-0.963732\pi\) |
0.595220 | + | 0.803563i | \(0.297065\pi\) | |||||||
\(332\) | 953442. | + | 1.65141e6i | 0.474733 | + | 0.822261i | ||||
\(333\) | 458784. | + | 794637.i | 0.226724 | + | 0.392698i | ||||
\(334\) | 363790. | − | 630103.i | 0.178437 | − | 0.309062i | ||||
\(335\) | 352858. | 0.171786 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 214825. | 0.103041 | 0.0515205 | − | 0.998672i | \(-0.483593\pi\) | ||||
0.0515205 | + | 0.998672i | \(0.483593\pi\) | |||||||
\(338\) | −276429. | + | 478789.i | −0.131611 | + | 0.227957i | ||||
\(339\) | −209988. | − | 363710.i | −0.0992419 | − | 0.171892i | ||||
\(340\) | 291984. | + | 505731.i | 0.136981 | + | 0.237259i | ||||
\(341\) | 382114. | − | 661842.i | 0.177954 | − | 0.308225i | ||||
\(342\) | −26568.0 | −0.0122827 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −947280. | −0.431601 | ||||||||
\(345\) | −161568. | + | 279844.i | −0.0730815 | + | 0.126581i | ||||
\(346\) | 164846. | + | 285522.i | 0.0740267 | + | 0.128218i | ||||
\(347\) | −1.29430e6 | − | 2.24179e6i | −0.577046 | − | 0.999473i | −0.995816 | − | 0.0913809i | \(-0.970872\pi\) |
0.418770 | − | 0.908092i | \(-0.362461\pi\) | |||||||
\(348\) | 304542. | − | 527482.i | 0.134803 | − | 0.233485i | ||||
\(349\) | 24878.0 | 0.0109333 | 0.00546666 | − | 0.999985i | \(-0.498260\pi\) | ||||
0.00546666 | + | 0.999985i | \(0.498260\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 224532. | 0.0972771 | ||||||||
\(352\) | 692944. | − | 1.20021e6i | 0.298086 | − | 0.516300i | ||||
\(353\) | −868004. | − | 1.50343e6i | −0.370753 | − | 0.642163i | 0.618928 | − | 0.785447i | \(-0.287567\pi\) |
−0.989682 | + | 0.143284i | \(0.954234\pi\) | |||||||
\(354\) | 73467.0 | + | 127249.i | 0.0311590 | + | 0.0539691i | ||||
\(355\) | −210507. | + | 364609.i | −0.0886535 | + | 0.153552i | ||||
\(356\) | −3.21782e6 | −1.34566 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −61256.0 | −0.0252604 | ||||||||
\(359\) | −431213. | + | 746883.i | −0.176586 | + | 0.305856i | −0.940709 | − | 0.339215i | \(-0.889839\pi\) |
0.764123 | + | 0.645070i | \(0.223172\pi\) | |||||||
\(360\) | 53460.0 | + | 92595.4i | 0.0217407 | + | 0.0376559i | ||||
\(361\) | 1.22460e6 | + | 2.12107e6i | 0.494569 | + | 0.856618i | ||||
\(362\) | 651392. | − | 1.12824e6i | 0.261259 | − | 0.452514i | ||||
\(363\) | −798210. | −0.317944 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 383526. | 0.150682 | ||||||||
\(366\) | −136494. | + | 236415.i | −0.0532612 | + | 0.0922511i | ||||
\(367\) | 1.55771e6 | + | 2.69803e6i | 0.603700 | + | 1.04564i | 0.992255 | + | 0.124214i | \(0.0396409\pi\) |
−0.388555 | + | 0.921425i | \(0.627026\pi\) | |||||||
\(368\) | 1.07059e6 | + | 1.85432e6i | 0.412102 | + | 0.713781i | ||||
\(369\) | −682668. | + | 1.18242e6i | −0.261002 | + | 0.452069i | ||||
\(370\) | −249216. | −0.0946393 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 715932. | 0.268234 | ||||||||
\(373\) | 898472. | − | 1.55620e6i | 0.334374 | − | 0.579153i | −0.648990 | − | 0.760797i | \(-0.724808\pi\) |
0.983364 | + | 0.181644i | \(0.0581418\pi\) | |||||||
\(374\) | −510024. | − | 883387.i | −0.188544 | − | 0.326567i | ||||
\(375\) | −303386. | − | 525479.i | −0.111408 | − | 0.192964i | ||||
\(376\) | 1.26612e6 | − | 2.19298e6i | 0.461855 | − | 0.799956i | ||||
\(377\) | 744436. | 0.269758 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.45466e6 | 1.23540 | 0.617699 | − | 0.786415i | \(-0.288065\pi\) | ||||
0.617699 | + | 0.786415i | \(0.288065\pi\) | |||||||
\(380\) | −25256.0 | + | 43744.7i | −0.00897234 | + | 0.0155405i | ||||
\(381\) | 1.36964e6 | + | 2.37229e6i | 0.483387 | + | 0.837250i | ||||
\(382\) | −757360. | − | 1.31179e6i | −0.265549 | − | 0.459944i | ||||
\(383\) | 1.07752e6 | − | 1.86632e6i | 0.375343 | − | 0.650113i | −0.615036 | − | 0.788499i | \(-0.710858\pi\) |
0.990378 | + | 0.138387i | \(0.0441917\pi\) | |||||||
\(384\) | 1.67616e6 | 0.580079 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 320678. | 0.109547 | ||||||||
\(387\) | 319707. | − | 553749.i | 0.108511 | − | 0.187947i | ||||
\(388\) | −2.16943e6 | − | 3.75756e6i | −0.731586 | − | 1.26714i | ||||
\(389\) | 231387. | + | 400774.i | 0.0775291 | + | 0.134284i | 0.902183 | − | 0.431353i | \(-0.141964\pi\) |
−0.824654 | + | 0.565637i | \(0.808630\pi\) | |||||||
\(390\) | −30492.0 | + | 52813.7i | −0.0101514 | + | 0.0175827i | ||||
\(391\) | 6.18854e6 | 2.04714 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 119727. | 0.0391031 | ||||||||
\(394\) | −61738.0 | + | 106933.i | −0.0200360 | + | 0.0347034i | ||||
\(395\) | 74409.5 | + | 128881.i | 0.0239958 | + | 0.0415620i | ||||
\(396\) | 305046. | + | 528355.i | 0.0977524 | + | 0.169312i | ||||
\(397\) | −2.03311e6 | + | 3.52144e6i | −0.647416 | + | 1.12136i | 0.336321 | + | 0.941747i | \(0.390817\pi\) |
−0.983738 | + | 0.179611i | \(0.942516\pi\) | |||||||
\(398\) | 741816. | 0.234741 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.97062e6 | −0.615820 | ||||||||
\(401\) | 2.53432e6 | − | 4.38956e6i | 0.787045 | − | 1.36320i | −0.140724 | − | 0.990049i | \(-0.544943\pi\) |
0.927769 | − | 0.373154i | \(-0.121724\pi\) | |||||||
\(402\) | −288702. | − | 500047.i | −0.0891014 | − | 0.154328i | ||||
\(403\) | 437514. | + | 757796.i | 0.134193 | + | 0.232429i | ||||
\(404\) | 1.50598e6 | − | 2.60843e6i | 0.459056 | − | 0.795109i | ||||
\(405\) | −72171.0 | −0.0218638 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.04723e6 | −0.911842 | ||||||||
\(408\) | 1.02384e6 | − | 1.77334e6i | 0.304496 | − | 0.527403i | ||||
\(409\) | 1.43867e6 | + | 2.49185e6i | 0.425258 | + | 0.736568i | 0.996444 | − | 0.0842522i | \(-0.0268501\pi\) |
−0.571187 | + | 0.820820i | \(0.693517\pi\) | |||||||
\(410\) | −185416. | − | 321150.i | −0.0544738 | − | 0.0943514i | ||||
\(411\) | 1.79218e6 | − | 3.10415e6i | 0.523331 | − | 0.906437i | ||||
\(412\) | 250208. | 0.0726203 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 528768. | 0.151623 | ||||||||
\(415\) | 374567. | − | 648768.i | 0.106760 | − | 0.184914i | ||||
\(416\) | 793408. | + | 1.37422e6i | 0.224783 | + | 0.389335i | ||||
\(417\) | 1.03629e6 | + | 1.79490e6i | 0.291837 | + | 0.505476i | ||||
\(418\) | 44116.0 | − | 76411.2i | 0.0123497 | − | 0.0213903i | ||||
\(419\) | 3.41342e6 | 0.949850 | 0.474925 | − | 0.880026i | \(-0.342475\pi\) | ||||
0.474925 | + | 0.880026i | \(0.342475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.30737e6 | −0.359496 | −0.179748 | − | 0.983713i | \(-0.557528\pi\) | ||||
−0.179748 | + | 0.983713i | \(0.557528\pi\) | |||||||
\(422\) | 217450. | − | 376634.i | 0.0594399 | − | 0.102953i | ||||
\(423\) | 854631. | + | 1.48026e6i | 0.232235 | + | 0.402243i | ||||
\(424\) | 1.78146e6 | + | 3.08558e6i | 0.481240 | + | 0.833532i | ||||
\(425\) | −2.84779e6 | + | 4.93252e6i | −0.764779 | + | 1.32464i | ||||
\(426\) | 688932. | 0.183930 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.42268e6 | −1.43088 | ||||||||
\(429\) | −372834. | + | 645767.i | −0.0978075 | + | 0.169408i | ||||
\(430\) | 86834.0 | + | 150401.i | 0.0226474 | + | 0.0392265i | ||||
\(431\) | −967734. | − | 1.67616e6i | −0.250936 | − | 0.434634i | 0.712848 | − | 0.701319i | \(-0.247405\pi\) |
−0.963784 | + | 0.266685i | \(0.914072\pi\) | |||||||
\(432\) | −239112. | + | 414154.i | −0.0616442 | + | 0.106771i | ||||
\(433\) | −516670. | −0.132432 | −0.0662161 | − | 0.997805i | \(-0.521093\pi\) | ||||
−0.0662161 | + | 0.997805i | \(0.521093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −239283. | −0.0606302 | ||||||||
\(436\) | 2.87154e6 | − | 4.97365e6i | 0.723434 | − | 1.25302i | ||||
\(437\) | 267648. | + | 463580.i | 0.0670441 | + | 0.116124i | ||||
\(438\) | −313794. | − | 543507.i | −0.0781555 | − | 0.135369i | ||||
\(439\) | 1.45765e6 | − | 2.52472e6i | 0.360987 | − | 0.625249i | −0.627136 | − | 0.778910i | \(-0.715773\pi\) |
0.988124 | + | 0.153661i | \(0.0491064\pi\) | |||||||
\(440\) | −355080. | −0.0874369 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.16794e6 | 0.284357 | ||||||||
\(443\) | 891896. | − | 1.54481e6i | 0.215926 | − | 0.373995i | −0.737633 | − | 0.675202i | \(-0.764056\pi\) |
0.953559 | + | 0.301208i | \(0.0973897\pi\) | |||||||
\(444\) | −1.42733e6 | − | 2.47220e6i | −0.343610 | − | 0.595151i | ||||
\(445\) | 632071. | + | 1.09478e6i | 0.151309 | + | 0.262076i | ||||
\(446\) | −589771. | + | 1.02151e6i | −0.140393 | + | 0.243168i | ||||
\(447\) | −874206. | −0.206940 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.00158e6 | 0.936733 | 0.468366 | − | 0.883534i | \(-0.344843\pi\) | ||||
0.468366 | + | 0.883534i | \(0.344843\pi\) | |||||||
\(450\) | −243324. | + | 421450.i | −0.0566440 | + | 0.0981102i | ||||
\(451\) | −2.26713e6 | − | 3.92679e6i | −0.524850 | − | 0.909067i | ||||
\(452\) | 653296. | + | 1.13154e6i | 0.150406 | + | 0.260510i | ||||
\(453\) | 130712. | − | 226399.i | 0.0299274 | − | 0.0518357i | ||||
\(454\) | −774090. | −0.176259 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 177120. | 0.0398892 | ||||||||
\(457\) | 583832. | − | 1.01123e6i | 0.130767 | − | 0.226495i | −0.793206 | − | 0.608954i | \(-0.791589\pi\) |
0.923972 | + | 0.382459i | \(0.124923\pi\) | |||||||
\(458\) | 232732. | + | 403104.i | 0.0518433 | + | 0.0897952i | ||||
\(459\) | 691092. | + | 1.19701e6i | 0.153110 | + | 0.265195i | ||||
\(460\) | 502656. | − | 870626.i | 0.110758 | − | 0.191839i | ||||
\(461\) | −3.61358e6 | −0.791928 | −0.395964 | − | 0.918266i | \(-0.629589\pi\) | ||||
−0.395964 | + | 0.918266i | \(0.629589\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.80111e6 | −0.390471 | −0.195235 | − | 0.980756i | \(-0.562547\pi\) | ||||
−0.195235 | + | 0.980756i | \(0.562547\pi\) | |||||||
\(464\) | −792776. | + | 1.37313e6i | −0.170945 | + | 0.296085i | ||||
\(465\) | −140630. | − | 243577.i | −0.0301609 | − | 0.0522402i | ||||
\(466\) | 42096.0 | + | 72912.4i | 0.00897999 | + | 0.0155538i | ||||
\(467\) | −1.18487e6 | + | 2.05226e6i | −0.251409 | + | 0.435452i | −0.963914 | − | 0.266214i | \(-0.914227\pi\) |
0.712505 | + | 0.701667i | \(0.247560\pi\) | |||||||
\(468\) | −698544. | −0.147428 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −464244. | −0.0969397 | ||||||||
\(471\) | −2.59425e6 | + | 4.49337e6i | −0.538840 | + | 0.933298i | ||||
\(472\) | −489780. | − | 848324.i | −0.101192 | − | 0.175270i | ||||
\(473\) | 1.06174e6 | + | 1.83899e6i | 0.218206 | + | 0.377944i | ||||
\(474\) | 121761. | − | 210896.i | 0.0248921 | − | 0.0431145i | ||||
\(475\) | −492656. | −0.100187 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.40497e6 | −0.483965 | ||||||||
\(478\) | −313416. | + | 542852.i | −0.0627410 | + | 0.108671i | ||||
\(479\) | 259073. | + | 448728.i | 0.0515921 | + | 0.0893602i | 0.890668 | − | 0.454654i | \(-0.150237\pi\) |
−0.839076 | + | 0.544014i | \(0.816904\pi\) | |||||||
\(480\) | −255024. | − | 441715.i | −0.0505217 | − | 0.0875062i | ||||
\(481\) | 1.74451e6 | − | 3.02158e6i | 0.343804 | − | 0.595486i | ||||
\(482\) | 1.71561e6 | 0.336358 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.48332e6 | 0.481858 | ||||||||
\(485\) | −852274. | + | 1.47618e6i | −0.164522 | + | 0.284961i | ||||
\(486\) | 59049.0 | + | 102276.i | 0.0113402 | + | 0.0196419i | ||||
\(487\) | −1.41306e6 | − | 2.44750e6i | −0.269985 | − | 0.467627i | 0.698873 | − | 0.715246i | \(-0.253685\pi\) |
−0.968858 | + | 0.247619i | \(0.920352\pi\) | |||||||
\(488\) | 909960. | − | 1.57610e6i | 0.172971 | − | 0.299594i | ||||
\(489\) | −2.38709e6 | −0.451436 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.34747e6 | 1.74981 | 0.874904 | − | 0.484296i | \(-0.160924\pi\) | ||||
0.874904 | + | 0.484296i | \(0.160924\pi\) | |||||||
\(492\) | 2.12386e6 | − | 3.67863e6i | 0.395560 | − | 0.685130i | ||||
\(493\) | 2.29132e6 | + | 3.96868e6i | 0.424588 | + | 0.735408i | ||||
\(494\) | 50512.0 | + | 87489.4i | 0.00931273 | + | 0.0161301i | ||||
\(495\) | 119840. | − | 207568.i | 0.0219830 | − | 0.0380757i | ||||
\(496\) | −1.86370e6 | −0.340150 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.22585e6 | −0.221496 | ||||||||
\(499\) | −4.08593e6 | + | 7.07703e6i | −0.734580 | + | 1.27233i | 0.220327 | + | 0.975426i | \(0.429288\pi\) |
−0.954907 | + | 0.296904i | \(0.904046\pi\) | |||||||
\(500\) | 943866. | + | 1.63482e6i | 0.168844 | + | 0.292446i | ||||
\(501\) | −1.63706e6 | − | 2.83546e6i | −0.291386 | − | 0.504696i | ||||
\(502\) | −454517. | + | 787247.i | −0.0804991 | + | 0.139428i | ||||
\(503\) | 7.37713e6 | 1.30007 | 0.650036 | − | 0.759903i | \(-0.274754\pi\) | ||||
0.650036 | + | 0.759903i | \(0.274754\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.18327e6 | −0.206469 | ||||||||
\(506\) | −878016. | + | 1.52077e6i | −0.152450 | + | 0.264050i | ||||
\(507\) | 1.24393e6 | + | 2.15455e6i | 0.214920 | + | 0.372252i | ||||
\(508\) | −4.26111e6 | − | 7.38046e6i | −0.732594 | − | 1.26889i | ||||
\(509\) | −163158. | + | 282597.i | −0.0279134 | + | 0.0483474i | −0.879645 | − | 0.475631i | \(-0.842220\pi\) |
0.851731 | + | 0.523979i | \(0.175553\pi\) | |||||||
\(510\) | −375408. | −0.0639114 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.89875e6 | −0.994455 | ||||||||
\(513\) | −59778.0 | + | 103539.i | −0.0100288 | + | 0.0173704i | ||||
\(514\) | −878182. | − | 1.52106e6i | −0.146614 | − | 0.253944i | ||||
\(515\) | −49148.0 | − | 85126.8i | −0.00816559 | − | 0.0141432i | ||||
\(516\) | −994644. | + | 1.72277e6i | −0.164454 | + | 0.284842i | ||||
\(517\) | −5.67644e6 | −0.934006 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.48361e6 | 0.241770 | ||||||||
\(520\) | 203280. | − | 352091.i | 0.0329675 | − | 0.0571014i | ||||
\(521\) | −1.08351e6 | − | 1.87670e6i | −0.174880 | − | 0.302901i | 0.765240 | − | 0.643745i | \(-0.222620\pi\) |
−0.940120 | + | 0.340844i | \(0.889287\pi\) | |||||||
\(522\) | 195777. | + | 339096.i | 0.0314474 | + | 0.0544686i | ||||
\(523\) | −361702. | + | 626486.i | −0.0578225 | + | 0.100151i | −0.893488 | − | 0.449088i | \(-0.851749\pi\) |
0.835665 | + | 0.549239i | \(0.185082\pi\) | |||||||
\(524\) | −372484. | −0.0592624 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.92187e6 | −0.618057 | ||||||||
\(527\) | −2.69327e6 | + | 4.66488e6i | −0.422428 | + | 0.731667i | ||||
\(528\) | −794088. | − | 1.37540e6i | −0.123961 | − | 0.214706i | ||||
\(529\) | −2.10868e6 | − | 3.65233e6i | −0.327620 | − | 0.567455i | ||||
\(530\) | 326601. | − | 565690.i | 0.0505042 | − | 0.0874759i | ||||
\(531\) | 661203. | 0.101765 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.19165e6 | 0.791566 | ||||||||
\(534\) | 1.03430e6 | − | 1.79146e6i | 0.156961 | − | 0.271865i | ||||
\(535\) | 1.06517e6 | + | 1.84493e6i | 0.160892 | + | 0.278673i | ||||
\(536\) | 1.92468e6 | + | 3.33364e6i | 0.289365 | + | 0.501196i | ||||
\(537\) | −137826. | + | 238722.i | −0.0206251 | + | 0.0357237i | ||||
\(538\) | −2.10759e6 | −0.313928 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 224532. | 0.0331355 | ||||||||
\(541\) | −2.99982e6 | + | 5.19584e6i | −0.440659 | + | 0.763243i | −0.997738 | − | 0.0672159i | \(-0.978588\pi\) |
0.557080 | + | 0.830459i | \(0.311922\pi\) | |||||||
\(542\) | 105059. | + | 181968.i | 0.0153616 | + | 0.0266070i | ||||
\(543\) | −2.93126e6 | − | 5.07710e6i | −0.426634 | − | 0.738952i | ||||
\(544\) | −4.88410e6 | + | 8.45950e6i | −0.707599 | + | 1.22560i | ||||
\(545\) | −2.25621e6 | −0.325378 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.01570e6 | 1.00254 | 0.501271 | − | 0.865290i | \(-0.332866\pi\) | ||||
0.501271 | + | 0.865290i | \(0.332866\pi\) | |||||||
\(548\) | −5.57567e6 | + | 9.65734e6i | −0.793132 | + | 1.37375i | ||||
\(549\) | 614223. | + | 1.06387e6i | 0.0869752 | + | 0.150645i | ||||
\(550\) | −808076. | − | 1.39963e6i | −0.113906 | − | 0.197290i | ||||
\(551\) | −198194. | + | 343282.i | −0.0278107 | + | 0.0481695i | ||||
\(552\) | −3.52512e6 | −0.492409 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 855184. | 0.118382 | ||||||||
\(555\) | −560736. | + | 971223.i | −0.0772727 | + | 0.133840i | ||||
\(556\) | −3.22400e6 | − | 5.58414e6i | −0.442291 | − | 0.766071i | ||||
\(557\) | 4.45936e6 | + | 7.72384e6i | 0.609025 | + | 1.05486i | 0.991402 | + | 0.130855i | \(0.0417722\pi\) |
−0.382377 | + | 0.924006i | \(0.624894\pi\) | |||||||
\(558\) | −230121. | + | 398581.i | −0.0312875 | + | 0.0541915i | ||||
\(559\) | −2.43135e6 | −0.329093 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.59022e6 | −0.615781 | ||||||||
\(562\) | 638878. | − | 1.10657e6i | 0.0853252 | − | 0.147788i | ||||
\(563\) | −6.67412e6 | − | 1.15599e7i | −0.887407 | − | 1.53703i | −0.842930 | − | 0.538023i | \(-0.819171\pi\) |
−0.0444767 | − | 0.999010i | \(-0.514162\pi\) | |||||||
\(564\) | −2.65885e6 | − | 4.60527e6i | −0.351963 | − | 0.609617i | ||||
\(565\) | 256652. | − | 444534.i | 0.0338239 | − | 0.0585847i | ||||
\(566\) | −4.90284e6 | −0.643290 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.59288e6 | −0.597330 | ||||||||
\(569\) | −551074. | + | 954488.i | −0.0713558 | + | 0.123592i | −0.899496 | − | 0.436930i | \(-0.856066\pi\) |
0.828140 | + | 0.560521i | \(0.189399\pi\) | |||||||
\(570\) | −16236.0 | − | 28121.6i | −0.00209311 | − | 0.00362537i | ||||
\(571\) | −946741. | − | 1.63980e6i | −0.121518 | − | 0.210475i | 0.798848 | − | 0.601532i | \(-0.205443\pi\) |
−0.920367 | + | 0.391057i | \(0.872110\pi\) | |||||||
\(572\) | 1.15993e6 | − | 2.00905e6i | 0.148232 | − | 0.256745i | ||||
\(573\) | −6.81624e6 | −0.867278 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.80506e6 | 1.23675 | ||||||||
\(576\) | 432864. | − | 749742.i | 0.0543620 | − | 0.0941577i | ||||
\(577\) | 1.41476e6 | + | 2.45043e6i | 0.176906 | + | 0.306410i | 0.940819 | − | 0.338909i | \(-0.110058\pi\) |
−0.763913 | + | 0.645319i | \(0.776725\pi\) | |||||||
\(578\) | 2.17496e6 | + | 3.76714e6i | 0.270789 | + | 0.469021i | ||||
\(579\) | 721526. | − | 1.24972e6i | 0.0894448 | − | 0.154923i | ||||
\(580\) | 744436. | 0.0918877 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.78926e6 | 0.341336 | ||||||||
\(583\) | 3.99344e6 | − | 6.91684e6i | 0.486604 | − | 0.842823i | ||||
\(584\) | 2.09196e6 | + | 3.62338e6i | 0.253817 | + | 0.439624i | ||||
\(585\) | 137214. | + | 237662.i | 0.0165771 | + | 0.0287124i | ||||
\(586\) | −1.71617e6 | + | 2.97249e6i | −0.206451 | + | 0.357583i | ||||
\(587\) | 1.06799e7 | 1.27930 | 0.639649 | − | 0.768667i | \(-0.279080\pi\) | ||||
0.639649 | + | 0.768667i | \(0.279080\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −465924. | −0.0553384 | ||||||||
\(590\) | −89793.0 | + | 155526.i | −0.0106197 | + | 0.0183939i | ||||
\(591\) | 277821. | + | 481200.i | 0.0327187 | + | 0.0566705i | ||||
\(592\) | 3.71558e6 | + | 6.43558e6i | 0.435735 | + | 0.754716i | ||||
\(593\) | −7.34984e6 | + | 1.27303e7i | −0.858304 | + | 1.48663i | 0.0152406 | + | 0.999884i | \(0.495149\pi\) |
−0.873545 | + | 0.486743i | \(0.838185\pi\) | |||||||
\(594\) | −392202. | −0.0456083 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.71975e6 | 0.313627 | ||||||||
\(597\) | 1.66909e6 | − | 2.89094e6i | 0.191665 | − | 0.331974i | ||||
\(598\) | −1.00531e6 | − | 1.74125e6i | −0.114960 | − | 0.199117i | ||||
\(599\) | −4.24581e6 | − | 7.35396e6i | −0.483497 | − | 0.837441i | 0.516323 | − | 0.856394i | \(-0.327300\pi\) |
−0.999820 | + | 0.0189523i | \(0.993967\pi\) | |||||||
\(600\) | 1.62216e6 | − | 2.80966e6i | 0.183957 | − | 0.318622i | ||||
\(601\) | −8.62947e6 | −0.974536 | −0.487268 | − | 0.873253i | \(-0.662006\pi\) | ||||
−0.487268 | + | 0.873253i | \(0.662006\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.59832e6 | −0.291004 | ||||||||
\(604\) | −406658. | + | 704352.i | −0.0453562 | + | 0.0785593i | ||||
\(605\) | −487795. | − | 844886.i | −0.0541812 | − | 0.0938447i | ||||
\(606\) | 968130. | + | 1.67685e6i | 0.107091 | + | 0.185487i | ||||
\(607\) | 5.29037e6 | − | 9.16319e6i | 0.582793 | − | 1.00943i | −0.412354 | − | 0.911024i | \(-0.635293\pi\) |
0.995147 | − | 0.0984029i | \(-0.0313734\pi\) | |||||||
\(608\) | −844928. | −0.0926959 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −333652. | −0.0363052 | ||||||||
\(611\) | 3.24971e6 | − | 5.62866e6i | 0.352161 | − | 0.609961i | ||||
\(612\) | −2.15006e6 | − | 3.72402e6i | −0.232045 | − | 0.401914i | ||||
\(613\) | −1.92392e6 | − | 3.33233e6i | −0.206793 | − | 0.358176i | 0.743910 | − | 0.668280i | \(-0.232969\pi\) |
−0.950703 | + | 0.310104i | \(0.899636\pi\) | |||||||
\(614\) | −1.80897e6 | + | 3.13322e6i | −0.193647 | + | 0.335406i | ||||
\(615\) | −1.66874e6 | −0.177911 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.51001e7 | −1.59686 | −0.798428 | − | 0.602090i | \(-0.794335\pi\) | ||||
−0.798428 | + | 0.602090i | \(0.794335\pi\) | |||||||
\(618\) | −80424.0 | + | 139298.i | −0.00847061 | + | 0.0146715i | ||||
\(619\) | 4.96551e6 | + | 8.60051e6i | 0.520879 | + | 0.902190i | 0.999705 | + | 0.0242796i | \(0.00772920\pi\) |
−0.478826 | + | 0.877910i | \(0.658937\pi\) | |||||||
\(620\) | 437514. | + | 757796.i | 0.0457102 | + | 0.0791723i | ||||
\(621\) | 1.18973e6 | − | 2.06067e6i | 0.123799 | − | 0.214427i | ||||
\(622\) | 3.04291e6 | 0.315365 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.81843e6 | 0.186954 | ||||||||
\(625\) | −4.32295e6 | + | 7.48756e6i | −0.442670 | + | 0.766726i | ||||
\(626\) | 1.34840e6 | + | 2.33550e6i | 0.137525 | + | 0.238201i | ||||
\(627\) | −198522. | − | 343850.i | −0.0201669 | − | 0.0349301i | ||||
\(628\) | 8.07100e6 | − | 1.39794e7i | 0.816635 | − | 1.41445i | ||||
\(629\) | 2.14779e7 | 2.16454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.25224e6 | −0.925068 | −0.462534 | − | 0.886602i | \(-0.653060\pi\) | ||||
−0.462534 | + | 0.886602i | \(0.653060\pi\) | |||||||
\(632\) | −811740. | + | 1.40597e6i | −0.0808396 | + | 0.140018i | ||||
\(633\) | −978525. | − | 1.69486e6i | −0.0970650 | − | 0.168122i | ||||
\(634\) | −49695.0 | − | 86074.3i | −0.00491009 | − | 0.00850453i | ||||
\(635\) | −1.67401e6 | + | 2.89947e6i | −0.164749 | + | 0.285354i | ||||
\(636\) | 7.48213e6 | 0.733470 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.30035e6 | −0.126476 | ||||||||
\(639\) | 1.55010e6 | − | 2.68485e6i | 0.150178 | − | 0.260116i | ||||
\(640\) | 1.02432e6 | + | 1.77417e6i | 0.0988521 | + | 0.171217i | ||||
\(641\) | −2.50214e6 | − | 4.33384e6i | −0.240529 | − | 0.416608i | 0.720336 | − | 0.693625i | \(-0.243987\pi\) |
−0.960865 | + | 0.277017i | \(0.910654\pi\) | |||||||
\(642\) | 1.74300e6 | − | 3.01897e6i | 0.166902 | − | 0.289082i | ||||
\(643\) | −1.26137e7 | −1.20314 | −0.601569 | − | 0.798821i | \(-0.705457\pi\) | ||||
−0.601569 | + | 0.798821i | \(0.705457\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 781506. | 0.0739662 | ||||||||
\(646\) | −310944. | + | 538571.i | −0.0293157 | + | 0.0507764i | ||||
\(647\) | −6.26916e6 | − | 1.08585e7i | −0.588774 | − | 1.01979i | −0.994393 | − | 0.105744i | \(-0.966278\pi\) |
0.405620 | − | 0.914042i | \(-0.367056\pi\) | |||||||
\(648\) | −393660. | − | 681839.i | −0.0368285 | − | 0.0637888i | ||||
\(649\) | −1.09792e6 | + | 1.90166e6i | −0.102320 | + | 0.177223i | ||||
\(650\) | 1.85046e6 | 0.171790 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.42650e6 | 0.684171 | ||||||||
\(653\) | 4.33033e6 | − | 7.50035e6i | 0.397409 | − | 0.688333i | −0.595996 | − | 0.802987i | \(-0.703243\pi\) |
0.993405 | + | 0.114654i | \(0.0365760\pi\) | |||||||
\(654\) | 1.84599e6 | + | 3.19735e6i | 0.168766 | + | 0.292311i | ||||
\(655\) | 73166.5 | + | 126728.i | 0.00666360 | + | 0.0115417i | ||||
\(656\) | −5.52877e6 | + | 9.57611e6i | −0.501613 | + | 0.868819i | ||||
\(657\) | −2.82415e6 | −0.255255 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.94177e6 | 0.712367 | 0.356183 | − | 0.934416i | \(-0.384078\pi\) | ||||
0.356183 | + | 0.934416i | \(0.384078\pi\) | |||||||
\(660\) | −372834. | + | 645767.i | −0.0333162 | + | 0.0577054i | ||||
\(661\) | −1.05708e6 | − | 1.83092e6i | −0.0941032 | − | 0.162992i | 0.815131 | − | 0.579277i | \(-0.196665\pi\) |
−0.909234 | + | 0.416285i | \(0.863332\pi\) | |||||||
\(662\) | 1.58784e6 | + | 2.75021e6i | 0.140819 | + | 0.243905i | ||||
\(663\) | 2.62786e6 | − | 4.55158e6i | 0.232176 | − | 0.402141i | ||||
\(664\) | 8.17236e6 | 0.719329 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.83514e6 | 0.160318 | ||||||||
\(667\) | 3.94454e6 | − | 6.83215e6i | 0.343307 | − | 0.594625i | ||||
\(668\) | 5.09306e6 | + | 8.82144e6i | 0.441609 | + | 0.764889i | ||||
\(669\) | 2.65397e6 | + | 4.59681e6i | 0.229261 | + | 0.397092i | ||||
\(670\) | 352858. | − | 611168.i | 0.0303678 | − | 0.0525985i | ||||
\(671\) | −4.07965e6 | −0.349798 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −442307. | −0.0376432 | −0.0188216 | − | 0.999823i | \(-0.505991\pi\) | ||||
−0.0188216 | + | 0.999823i | \(0.505991\pi\) | |||||||
\(674\) | 214825. | − | 372088.i | 0.0182152 | − | 0.0315497i | ||||
\(675\) | 1.09496e6 | + | 1.89652e6i | 0.0924992 | + | 0.160213i | ||||
\(676\) | −3.87001e6 | − | 6.70305e6i | −0.325720 | − | 0.564164i | ||||
\(677\) | 5.37804e6 | − | 9.31503e6i | 0.450975 | − | 0.781111i | −0.547472 | − | 0.836824i | \(-0.684410\pi\) |
0.998447 | + | 0.0557130i | \(0.0177432\pi\) | |||||||
\(678\) | −839952. | −0.0701746 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.50272e6 | 0.207558 | ||||||||
\(681\) | −1.74170e6 | + | 3.01672e6i | −0.143915 | + | 0.249268i | ||||
\(682\) | −764229. | − | 1.32368e6i | −0.0629162 | − | 0.108974i | ||||
\(683\) | 5.74430e6 | + | 9.94941e6i | 0.471178 | + | 0.816104i | 0.999456 | − | 0.0329669i | \(-0.0104956\pi\) |
−0.528278 | + | 0.849071i | \(0.677162\pi\) | |||||||
\(684\) | 185976. | − | 322120.i | 0.0151991 | − | 0.0263255i | ||||
\(685\) | 4.38088e6 | 0.356726 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.09459e6 | 0.169319 | ||||||||
\(688\) | 2.58923e6 | − | 4.48468e6i | 0.208545 | − | 0.361211i | ||||
\(689\) | 4.57241e6 | + | 7.91965e6i | 0.366942 | + | 0.635562i | ||||
\(690\) | 323136. | + | 559688.i | 0.0258382 | + | 0.0447531i | ||||
\(691\) | 5.06942e6 | − | 8.78049e6i | 0.403890 | − | 0.699558i | −0.590302 | − | 0.807183i | \(-0.700991\pi\) |
0.994192 | + | 0.107625i | \(0.0343246\pi\) | |||||||
\(692\) | −4.61569e6 | −0.366413 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.17719e6 | −0.408033 | ||||||||
\(695\) | −1.26657e6 | + | 2.19377e6i | −0.0994645 | + | 0.172278i | ||||
\(696\) | −1.30518e6 | − | 2.26064e6i | −0.102129 | − | 0.176892i | ||||
\(697\) | 1.59795e7 | + | 2.76773e7i | 1.24589 | + | 2.15795i | ||||
\(698\) | 24878.0 | − | 43090.0i | 0.00193276 | − | 0.00334763i | ||||
\(699\) | 378864. | 0.0293285 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.96839e7 | −1.51292 | −0.756459 | − | 0.654041i | \(-0.773073\pi\) | ||||
−0.756459 | + | 0.654041i | \(0.773073\pi\) | |||||||
\(702\) | 224532. | − | 388901.i | 0.0171963 | − | 0.0297849i | ||||
\(703\) | 928896. | + | 1.60890e6i | 0.0708890 | + | 0.122783i | ||||
\(704\) | 1.43754e6 | + | 2.48989e6i | 0.109317 | + | 0.189342i | ||||
\(705\) | −1.04455e6 | + | 1.80921e6i | −0.0791509 | + | 0.137093i | ||||
\(706\) | −3.47202e6 | −0.262162 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.05708e6 | −0.154229 | ||||||||
\(709\) | 1.00859e7 | − | 1.74692e7i | 0.753524 | − | 1.30514i | −0.192581 | − | 0.981281i | \(-0.561686\pi\) |
0.946105 | − | 0.323861i | \(-0.104981\pi\) | |||||||
\(710\) | 421014. | + | 729218.i | 0.0313437 | + | 0.0542889i | ||||
\(711\) | −547924. | − | 949033.i | −0.0406487 | − | 0.0704056i | ||||
\(712\) | −6.89532e6 | + | 1.19430e7i | −0.509747 | + | 0.882907i | ||||
\(713\) | 9.27302e6 | 0.683121 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −911372. | −0.0666700 | ||||||||
\(716\) | 428792. | − | 742690.i | 0.0312582 | − | 0.0541408i | ||||
\(717\) | 1.41037e6 | + | 2.44284e6i | 0.102456 | + | 0.177458i | ||||
\(718\) | 862426. | + | 1.49377e6i | 0.0624325 | + | 0.108136i | ||||
\(719\) | 2.07867e6 | − | 3.60037e6i | 0.149956 | − | 0.259731i | −0.781255 | − | 0.624212i | \(-0.785420\pi\) |
0.931211 | + | 0.364481i | \(0.118753\pi\) | |||||||
\(720\) | −584496. | −0.0420194 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.89841e6 | 0.349713 | ||||||||
\(723\) | 3.86013e6 | − | 6.68594e6i | 0.274635 | − | 0.475682i | ||||
\(724\) | 9.11949e6 | + | 1.57954e7i | 0.646583 | + | 1.11991i | ||||
\(725\) | 3.63033e6 | + | 6.28792e6i | 0.256508 | + | 0.444286i | ||||
\(726\) | −798210. | + | 1.38254e6i | −0.0562051 | + | 0.0973501i | ||||
\(727\) | 1.54433e7 | 1.08369 | 0.541845 | − | 0.840479i | \(-0.317726\pi\) | ||||
0.541845 | + | 0.840479i | \(0.317726\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 383526. | − | 664287.i | 0.0266371 | − | 0.0461369i | ||||
\(731\) | −7.48351e6 | − | 1.29618e7i | −0.517979 | − | 0.897166i | ||||
\(732\) | −1.91092e6 | − | 3.30980e6i | −0.131815 | − | 0.228310i | ||||
\(733\) | −3.10207e6 | + | 5.37294e6i | −0.213251 | + | 0.369362i | −0.952730 | − | 0.303818i | \(-0.901739\pi\) |
0.739479 | + | 0.673180i | \(0.235072\pi\) | |||||||
\(734\) | 6.23084e6 | 0.426880 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.68161e7 | 1.14428 | ||||||||
\(737\) | 4.31449e6 | − | 7.47292e6i | 0.292591 | − | 0.506782i | ||||
\(738\) | 1.36534e6 | + | 2.36483e6i | 0.0922781 | + | 0.159830i | ||||
\(739\) | −1.09492e7 | − | 1.89646e7i | −0.737517 | − | 1.27742i | −0.953610 | − | 0.301045i | \(-0.902665\pi\) |
0.216093 | − | 0.976373i | \(-0.430669\pi\) | |||||||
\(740\) | 1.74451e6 | − | 3.02158e6i | 0.117110 | − | 0.202841i | ||||
\(741\) | 454608. | 0.0304153 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.75483e6 | −0.183073 | −0.0915363 | − | 0.995802i | \(-0.529178\pi\) | ||||
−0.0915363 | + | 0.995802i | \(0.529178\pi\) | |||||||
\(744\) | 1.53414e6 | − | 2.65721e6i | 0.101609 | − | 0.175992i | ||||
\(745\) | −534237. | − | 925326.i | −0.0352650 | − | 0.0610807i | ||||
\(746\) | −1.79694e6 | − | 3.11240e6i | −0.118219 | − | 0.204761i | ||||
\(747\) | −2.75817e6 | + | 4.77729e6i | −0.180851 | + | 0.313242i | ||||
\(748\) | 1.42807e7 | 0.933243 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.21354e6 | −0.0787774 | ||||||||
\(751\) | −6.45604e6 | + | 1.11822e7i | −0.417702 | + | 0.723481i | −0.995708 | − | 0.0925517i | \(-0.970498\pi\) |
0.578006 | + | 0.816032i | \(0.303831\pi\) | |||||||
\(752\) | 6.92146e6 | + | 1.19883e7i | 0.446327 | + | 0.773061i | ||||
\(753\) | 2.04533e6 | + | 3.54261e6i | 0.131454 | + | 0.227686i | ||||
\(754\) | 744436. | − | 1.28940e6i | 0.0476869 | − | 0.0825961i | ||||
\(755\) | 319517. | 0.0203998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.64315e7 | −1.67642 | −0.838209 | − | 0.545349i | \(-0.816397\pi\) | ||||
−0.838209 | + | 0.545349i | \(0.816397\pi\) | |||||||
\(758\) | 3.45466e6 | − | 5.98364e6i | 0.218390 | − | 0.378262i | ||||
\(759\) | 3.95107e6 | + | 6.84346e6i | 0.248949 | + | 0.431192i | ||||
\(760\) | 108240. | + | 187477.i | 0.00679757 | + | 0.0117737i | ||||
\(761\) | 6.11069e6 | − | 1.05840e7i | 0.382498 | − | 0.662506i | −0.608921 | − | 0.793231i | \(-0.708397\pi\) |
0.991419 | + | 0.130725i | \(0.0417306\pi\) | |||||||
\(762\) | 5.47857e6 | 0.341806 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.12061e7 | 1.31440 | ||||||||
\(765\) | −844668. | + | 1.46301e6i | −0.0521834 | + | 0.0903843i | ||||
\(766\) | −2.15504e6 | − | 3.73264e6i | −0.132704 | − | 0.229850i | ||||
\(767\) | −1.25710e6 | − | 2.17736e6i | −0.0771582 | − | 0.133642i | ||||
\(768\) | 137088. | − | 237443.i | 0.00838680 | − | 0.0145264i | ||||
\(769\) | −6.10654e6 | −0.372374 | −0.186187 | − | 0.982514i | \(-0.559613\pi\) | ||||
−0.186187 | + | 0.982514i | \(0.559613\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.90364e6 | −0.478841 | ||||||||
\(772\) | −2.24475e6 | + | 3.88801e6i | −0.135558 | + | 0.234793i | ||||
\(773\) | −1.51110e6 | − | 2.61730e6i | −0.0909588 | − | 0.157545i | 0.816956 | − | 0.576700i | \(-0.195660\pi\) |
−0.907915 | + | 0.419155i | \(0.862326\pi\) | |||||||
\(774\) | −639414. | − | 1.10750e6i | −0.0383645 | − | 0.0664493i | ||||
\(775\) | −4.26718e6 | + | 7.39098e6i | −0.255204 | + | 0.442026i | ||||
\(776\) | −1.85951e7 | −1.10852 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 925548. | 0.0548214 | ||||||||
\(779\) | −1.38219e6 | + | 2.39403e6i | −0.0816065 | + | 0.141347i | ||||
\(780\) | −426888. | − | 739392.i | −0.0251233 | − | 0.0435149i | ||||
\(781\) | 5.14785e6 | + | 8.91634e6i | 0.301994 | + | 0.523069i | ||||
\(782\) | 6.18854e6 | − | 1.07189e7i | 0.361886 | − | 0.626805i | ||||
\(783\) | 1.76199e6 | 0.102707 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.34150e6 | −0.367297 | ||||||||
\(786\) | 119727. | − | 207373.i | 0.00691251 | − | 0.0119728i | ||||
\(787\) | −1.04143e7 | − | 1.80380e7i | −0.599365 | − | 1.03813i | −0.992915 | − | 0.118828i | \(-0.962086\pi\) |
0.393550 | − | 0.919303i | \(-0.371247\pi\) | |||||||
\(788\) | −864332. | − | 1.49707e6i | −0.0495867 | − | 0.0858867i | ||||
\(789\) | −8.82420e6 | + | 1.52840e7i | −0.504642 | + | 0.874065i | ||||
\(790\) | 297638. | 0.0169676 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.61468e6 | 0.148117 | ||||||||
\(793\) | 2.33556e6 | − | 4.04532e6i | 0.131889 | − | 0.228439i | ||||
\(794\) | 4.06621e6 | + | 7.04289e6i | 0.228896 | + | 0.396460i | ||||
\(795\) | −1.46970e6 | − | 2.54560e6i | −0.0824731 | − | 0.142848i | ||||
\(796\) | −5.19271e6 | + | 8.99404e6i | −0.290477 | + | 0.503121i | ||||
\(797\) | −2.32328e7 | −1.29556 | −0.647778 | − | 0.761829i | \(-0.724302\pi\) | ||||
−0.647778 | + | 0.761829i | \(0.724302\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00094e7 | 2.21715 | ||||||||
\(800\) | −7.73830e6 | + | 1.34031e7i | −0.427485 | + | 0.740426i | ||||
\(801\) | −4.65434e6 | − | 8.06156e6i | −0.256317 | − | 0.443954i | ||||
\(802\) | −5.06863e6 | − | 8.77913e6i | −0.278263 | − | 0.481965i | ||||
\(803\) | 4.68948e6 | − | 8.12241e6i | 0.256647 | − | 0.444525i | ||||
\(804\) | 8.08366e6 | 0.441030 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.75006e6 | 0.0948887 | ||||||||
\(807\) | −4.74208e6 | + | 8.21352e6i | −0.256321 | + | 0.443962i | ||||
\(808\) | −6.45420e6 | − | 1.11790e7i | −0.347788 | − | 0.602386i | ||||
\(809\) | −5.43338e6 | − | 9.41090e6i | −0.291876 | − | 0.505545i | 0.682377 | − | 0.731000i | \(-0.260946\pi\) |
−0.974253 | + | 0.225456i | \(0.927613\pi\) | |||||||
\(810\) | −72171.0 | + | 125004.i | −0.00386501 | + | 0.00669439i | ||||
\(811\) | 2.22632e7 | 1.18860 | 0.594299 | − | 0.804244i | \(-0.297430\pi\) | ||||
0.594299 | + | 0.804244i | \(0.297430\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 945531. | 0.0501706 | ||||||||
\(814\) | −3.04723e6 | + | 5.27796e6i | −0.161192 | + | 0.279193i | ||||
\(815\) | −1.45878e6 | − | 2.52667e6i | −0.0769298 | − | 0.133246i | ||||
\(816\) | 5.59699e6 | + | 9.69427e6i | 0.294259 | + | 0.509671i | ||||
\(817\) | 647308. | − | 1.12117e6i | 0.0339278 | − | 0.0587647i | ||||
\(818\) | 5.75467e6 | 0.300703 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.19165e6 | 0.269631 | ||||||||
\(821\) | 6.19405e6 | − | 1.07284e7i | 0.320713 | − | 0.555491i | −0.659922 | − | 0.751334i | \(-0.729411\pi\) |
0.980635 | + | 0.195843i | \(0.0627442\pi\) | |||||||
\(822\) | −3.58436e6 | − | 6.20829e6i | −0.185026 | − | 0.320474i | ||||
\(823\) | −847404. | − | 1.46775e6i | −0.0436105 | − | 0.0755356i | 0.843396 | − | 0.537292i | \(-0.180553\pi\) |
−0.887007 | + | 0.461757i | \(0.847219\pi\) | |||||||
\(824\) | 536160. | − | 928656.i | 0.0275091 | − | 0.0476472i | ||||
\(825\) | −7.27268e6 | −0.372014 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −378495. | −0.0192440 | −0.00962202 | − | 0.999954i | \(-0.503063\pi\) | ||||
−0.00962202 | + | 0.999954i | \(0.503063\pi\) | |||||||
\(828\) | −3.70138e6 | + | 6.41097e6i | −0.187624 | + | 0.324974i | ||||
\(829\) | −5.21437e6 | − | 9.03156e6i | −0.263521 | − | 0.456432i | 0.703654 | − | 0.710543i | \(-0.251551\pi\) |
−0.967175 | + | 0.254111i | \(0.918217\pi\) | |||||||
\(830\) | −749133. | − | 1.29754e6i | −0.0377454 | − | 0.0653769i | ||||
\(831\) | 1.92416e6 | − | 3.33275e6i | 0.0966584 | − | 0.167417i | ||||
\(832\) | −3.29190e6 | −0.164869 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.14515e6 | 0.206360 | ||||||||
\(835\) | 2.00084e6 | − | 3.46557e6i | 0.0993110 | − | 0.172012i | ||||
\(836\) | 617624. | + | 1.06976e6i | 0.0305639 | + | 0.0529382i | ||||
\(837\) | 1.03554e6 | + | 1.79362e6i | 0.0510923 | + | 0.0884944i | ||||
\(838\) | 3.41342e6 | − | 5.91222e6i | 0.167911 | − | 0.290831i | ||||
\(839\) | −3.04082e7 | −1.49137 | −0.745686 | − | 0.666297i | \(-0.767878\pi\) | ||||
−0.745686 | + | 0.666297i | \(0.767878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.46693e7 | −0.715185 | ||||||||
\(842\) | −1.30737e6 | + | 2.26444e6i | −0.0635506 | + | 0.110073i | ||||
\(843\) | −2.87495e6 | − | 4.97956e6i | −0.139335 | − | 0.241336i | ||||
\(844\) | 3.04430e6 | + | 5.27288e6i | 0.147106 | + | 0.254796i | ||||
\(845\) | −1.52036e6 | + | 2.63334e6i | −0.0732495 | + | 0.126872i | ||||
\(846\) | 3.41852e6 | 0.164215 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.94773e7 | −0.930120 | ||||||||
\(849\) | −1.10314e7 | + | 1.91069e7i | −0.525244 | + | 0.909750i | ||||
\(850\) | 5.69558e6 | + | 9.86504e6i | 0.270390 | + | 0.468330i | ||||
\(851\) | −1.84873e7 | − | 3.20209e7i | −0.875083 | − | 1.51569i | ||||
\(852\) | −4.82252e6 | + | 8.35286e6i | −0.227602 | + | 0.394218i | ||||
\(853\) | −2.80315e7 | −1.31909 | −0.659544 | − | 0.751666i | \(-0.729250\pi\) | ||||
−0.659544 | + | 0.751666i | \(0.729250\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −146124. | −0.00683607 | ||||||||
\(856\) | −1.16200e7 | + | 2.01265e7i | −0.542029 | + | 0.938822i | ||||
\(857\) | 9.40148e6 | + | 1.62838e7i | 0.437264 | + | 0.757364i | 0.997477 | − | 0.0709844i | \(-0.0226141\pi\) |
−0.560213 | + | 0.828349i | \(0.689281\pi\) | |||||||
\(858\) | 745668. | + | 1.29153e6i | 0.0345802 | + | 0.0598946i | ||||
\(859\) | 3.93162e6 | − | 6.80976e6i | 0.181798 | − | 0.314883i | −0.760695 | − | 0.649109i | \(-0.775142\pi\) |
0.942493 | + | 0.334227i | \(0.108475\pi\) | |||||||
\(860\) | −2.43135e6 | −0.112099 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.87094e6 | −0.177438 | ||||||||
\(863\) | 5.64288e6 | − | 9.77376e6i | 0.257913 | − | 0.446719i | −0.707769 | − | 0.706444i | \(-0.750298\pi\) |
0.965683 | + | 0.259724i | \(0.0836317\pi\) | |||||||
\(864\) | 1.87790e6 | + | 3.25263e6i | 0.0855833 | + | 0.148235i | ||||
\(865\) | 906653. | + | 1.57037e6i | 0.0412003 | + | 0.0713611i | ||||
\(866\) | −516670. | + | 894899.i | −0.0234109 | + | 0.0405489i | ||||
\(867\) | 1.95746e7 | 0.884394 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.63930e6 | 0.163481 | ||||||||
\(870\) | −239283. | + | 414450.i | −0.0107180 | + | 0.0185641i | ||||
\(871\) | 4.94001e6 | + | 8.55635e6i | 0.220639 | + | 0.382158i | ||||
\(872\) | −1.23066e7 | − | 2.13157e7i | −0.548084 | − | 0.949309i | ||||
\(873\) | 6.27584e6 | − | 1.08701e7i | 0.278700 | − | 0.482722i | ||||
\(874\) | 1.07059e6 | 0.0474073 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.78623e6 | 0.386850 | ||||||||
\(877\) | −6.70750e6 | + | 1.16177e7i | −0.294484 | + | 0.510062i | −0.974865 | − | 0.222797i | \(-0.928481\pi\) |
0.680381 | + | 0.732859i | \(0.261814\pi\) | |||||||
\(878\) | −2.91530e6 | − | 5.04945e6i | −0.127628 | − | 0.221059i | ||||
\(879\) | 7.72276e6 | + | 1.33762e7i | 0.337132 | + | 0.583930i | ||||
\(880\) | 970552. | − | 1.68105e6i | 0.0422486 | − | 0.0731767i | ||||
\(881\) | −3.18547e7 | −1.38272 | −0.691359 | − | 0.722511i | \(-0.742988\pi\) | ||||
−0.691359 | + | 0.722511i | \(0.742988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.05922e7 | −1.32041 | −0.660205 | − | 0.751086i | \(-0.729530\pi\) | ||||
−0.660205 | + | 0.751086i | \(0.729530\pi\) | |||||||
\(884\) | −8.17555e6 | + | 1.41605e7i | −0.351873 | + | 0.609463i | ||||
\(885\) | 404068. | + | 699867.i | 0.0173419 | + | 0.0300371i | ||||
\(886\) | −1.78379e6 | − | 3.08962e6i | −0.0763413 | − | 0.132227i | ||||
\(887\) | −2.31886e6 | + | 4.01638e6i | −0.0989613 | + | 0.171406i | −0.911255 | − | 0.411843i | \(-0.864885\pi\) |
0.812294 | + | 0.583249i | \(0.198219\pi\) | |||||||
\(888\) | −1.22342e7 | −0.520648 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.52828e6 | 0.106992 | ||||||||
\(891\) | −882454. | + | 1.52846e6i | −0.0372390 | + | 0.0644998i | ||||
\(892\) | −8.25679e6 | − | 1.43012e7i | −0.347456 | − | 0.601811i | ||||
\(893\) | 1.73036e6 | + | 2.99708e6i | 0.0726121 | + | 0.125768i | ||||
\(894\) | −874206. | + | 1.51417e6i | −0.0365822 | + | 0.0633623i | ||||
\(895\) | −336908. | −0.0140590 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.04781e6 | −0.375459 | ||||||||
\(898\) | 4.00158e6 | − | 6.93094e6i | 0.165592 | − | 0.286815i | ||||
\(899\) | 3.43335e6 | + | 5.94673e6i | 0.141683 | + | 0.245403i | ||||
\(900\) | −3.40654e6 | − | 5.90029e6i | −0.140187 | − | 0.242810i | ||||
\(901\) | −2.81471e7 | + | 4.87522e7i | −1.15510 | + | 2.00070i | ||||
\(902\) | −9.06853e6 | −0.371125 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.59968e6 | 0.227899 | ||||||||
\(905\) | 3.58266e6 | − | 6.20534e6i | 0.145406 | − | 0.251851i | ||||
\(906\) | −261423. | − | 452798.i | −0.0105809 | − | 0.0183267i | ||||
\(907\) | −302188. | − | 523405.i | −0.0121972 | − | 0.0211261i | 0.859862 | − | 0.510526i | \(-0.170549\pi\) |
−0.872060 | + | 0.489400i | \(0.837216\pi\) | |||||||
\(908\) | 5.41863e6 | − | 9.38534e6i | 0.218110 | − | 0.377777i | ||||
\(909\) | 8.71317e6 | 0.349757 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.44059e7 | −0.974315 | −0.487157 | − | 0.873314i | \(-0.661966\pi\) | ||||
−0.487157 | + | 0.873314i | \(0.661966\pi\) | |||||||
\(912\) | −484128. | + | 838534.i | −0.0192741 | + | 0.0333836i | ||||
\(913\) | −9.15985e6 | − | 1.58653e7i | −0.363673 | − | 0.629901i | ||||
\(914\) | −1.16766e6 | − | 2.02246e6i | −0.0462331 | − | 0.0800780i | ||||
\(915\) | −750717. | + | 1.30028e6i | −0.0296431 | + | 0.0513433i | ||||
\(916\) | −6.51650e6 | −0.256611 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.76437e6 | 0.108265 | ||||||||
\(919\) | −1.83547e7 | + | 3.17914e7i | −0.716902 | + | 1.24171i | 0.245320 | + | 0.969442i | \(0.421107\pi\) |
−0.962221 | + | 0.272268i | \(0.912226\pi\) | |||||||
\(920\) | −2.15424e6 | − | 3.73125e6i | −0.0839121 | − | 0.145340i | ||||
\(921\) | 8.14036e6 | + | 1.40995e7i | 0.316224 | + | 0.547715i | ||||
\(922\) | −3.61358e6 | + | 6.25891e6i | −0.139994 | + | 0.242477i | ||||
\(923\) | −1.17884e7 | −0.455460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.40293e7 | 1.30767 | ||||||||
\(926\) | −1.80111e6 | + | 3.11962e6i | −0.0690261 | + | 0.119557i | ||||
\(927\) | 361908. | + | 626843.i | 0.0138324 | + | 0.0239585i | ||||
\(928\) | 6.22619e6 | + | 1.07841e7i | 0.237330 | + | 0.411068i | ||||
\(929\) | −1.14544e7 | + | 1.98396e7i | −0.435446 | + | 0.754214i | −0.997332 | − | 0.0730004i | \(-0.976743\pi\) |
0.561886 | + | 0.827215i | \(0.310076\pi\) | |||||||
\(930\) | −562518. | −0.0213270 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.17869e6 | −0.0444487 | ||||||||
\(933\) | 6.84655e6 | − | 1.18586e7i | 0.257494 | − | 0.445993i | ||||
\(934\) | 2.36975e6 | + | 4.10452e6i | 0.0888863 | + | 0.153956i | ||||
\(935\) | −2.80513e6 | − | 4.85863e6i | −0.104936 | − | 0.181754i | ||||
\(936\) | −1.49688e6 | + | 2.59267e6i | −0.0558467 | + | 0.0967293i | ||||
\(937\) | 5.99611e6 | 0.223111 | 0.111555 | − | 0.993758i | \(-0.464417\pi\) | ||||
0.111555 | + | 0.993758i | \(0.464417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.21356e7 | 0.449156 | ||||||||
\(940\) | 3.24971e6 | − | 5.62866e6i | 0.119957 | − | 0.207771i | ||||
\(941\) | −5.82579e6 | − | 1.00906e7i | −0.214477 | − | 0.371485i | 0.738634 | − | 0.674107i | \(-0.235471\pi\) |
−0.953111 | + | 0.302622i | \(0.902138\pi\) | |||||||
\(942\) | 5.18850e6 | + | 8.98675e6i | 0.190509 | + | 0.329971i | ||||
\(943\) | 2.75090e7 | − | 4.76470e7i | 1.00738 | − | 1.74484i | ||||
\(944\) | 5.35493e6 | 0.195580 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.24697e6 | 0.154295 | ||||||||
\(947\) | 554632. | − | 960651.i | 0.0200969 | − | 0.0348089i | −0.855802 | − | 0.517303i | \(-0.826936\pi\) |
0.875899 | + | 0.482495i | \(0.160269\pi\) | |||||||
\(948\) | 1.70465e6 | + | 2.95255e6i | 0.0616049 | + | 0.106703i | ||||
\(949\) | 5.36936e6 | + | 9.30001e6i | 0.193534 | + | 0.335211i | ||||
\(950\) | −492656. | + | 853305.i | −0.0177107 | + | 0.0306758i | ||||
\(951\) | −447255. | −0.0160363 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.05743e7 | 0.377155 | 0.188578 | − | 0.982058i | \(-0.439612\pi\) | ||||
0.188578 | + | 0.982058i | \(0.439612\pi\) | |||||||
\(954\) | −2.40497e6 | + | 4.16553e6i | −0.0855537 | + | 0.148183i | ||||
\(955\) | −4.16548e6 | − | 7.21482e6i | −0.147794 | − | 0.255987i | ||||
\(956\) | −4.38782e6 | − | 7.59993e6i | −0.155276 | − | 0.268946i | ||||
\(957\) | −2.92578e6 | + | 5.06760e6i | −0.103267 | + | 0.178864i | ||||
\(958\) | 1.03629e6 | 0.0364811 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.05811e6 | 0.0370556 | ||||||||
\(961\) | 1.02789e7 | − | 1.78036e7i | 0.359037 | − | 0.621871i | ||||
\(962\) | −3.48902e6 | − | 6.04317e6i | −0.121553 | − | 0.210536i | ||||
\(963\) | −7.84351e6 | − | 1.35854e7i | −0.272549 | − | 0.472069i | ||||
\(964\) | −1.20093e7 | + | 2.08007e7i | −0.416222 | + | 0.720918i | ||||
\(965\) | 1.76373e6 | 0.0609696 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.32666e6 | 0.217575 | 0.108787 | − | 0.994065i | \(-0.465303\pi\) | ||||
0.108787 | + | 0.994065i | \(0.465303\pi\) | |||||||
\(968\) | 5.32140e6 | − | 9.21694e6i | 0.182531 | − | 0.316154i | ||||
\(969\) | 1.39925e6 | + | 2.42357e6i | 0.0478724 | + | 0.0829174i | ||||
\(970\) | 1.70455e6 | + | 2.95237e6i | 0.0581675 | + | 0.100749i | ||||
\(971\) | 1.96197e7 | − | 3.39824e7i | 0.667798 | − | 1.15666i | −0.310721 | − | 0.950501i | \(-0.600570\pi\) |
0.978519 | − | 0.206158i | \(-0.0660962\pi\) | |||||||
\(972\) | −1.65337e6 | −0.0561313 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.65225e6 | −0.190908 | ||||||||
\(975\) | 4.16354e6 | − | 7.21147e6i | 0.140266 | − | 0.242947i | ||||
\(976\) | 4.97445e6 | + | 8.61600e6i | 0.167155 | + | 0.289522i | ||||
\(977\) | 775371. | + | 1.34298e6i | 0.0259880 | + | 0.0450126i | 0.878727 | − | 0.477325i | \(-0.158393\pi\) |
−0.852739 | + | 0.522337i | \(0.825060\pi\) | |||||||
\(978\) | −2.38709e6 | + | 4.13456e6i | −0.0798034 | + | 0.138224i | ||||
\(979\) | 3.09140e7 | 1.03086 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.66139e7 | 0.551187 | ||||||||
\(982\) | 9.34747e6 | − | 1.61903e7i | 0.309325 | − | 0.535767i | ||||
\(983\) | −2.43742e7 | − | 4.22174e7i | −0.804538 | − | 1.39350i | −0.916602 | − | 0.399801i | \(-0.869079\pi\) |
0.112064 | − | 0.993701i | \(-0.464254\pi\) | |||||||
\(984\) | −9.10224e6 | − | 1.57655e7i | −0.299682 | − | 0.519064i | ||||
\(985\) | −339559. | + | 588133.i | −0.0111513 | + | 0.0193146i | ||||
\(986\) | 9.16526e6 | 0.300229 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.41434e6 | −0.0460957 | ||||||||
\(989\) | −1.28830e7 | + | 2.23140e7i | −0.418819 | + | 0.725416i | ||||
\(990\) | −239679. | − | 415136.i | −0.00777216 | − | 0.0134618i | ||||
\(991\) | 962758. | + | 1.66754e6i | 0.0311410 | + | 0.0539378i | 0.881176 | − | 0.472789i | \(-0.156753\pi\) |
−0.850035 | + | 0.526726i | \(0.823419\pi\) | |||||||
\(992\) | −7.31842e6 | + | 1.26759e7i | −0.236123 | + | 0.408977i | ||||
\(993\) | 1.42905e7 | 0.459912 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.07999e6 | 0.130648 | ||||||||
\(996\) | 8.58098e6 | − | 1.48627e7i | 0.274087 | − | 0.474733i | ||||
\(997\) | 2.71282e7 | + | 4.69874e7i | 0.864337 | + | 1.49708i | 0.867704 | + | 0.497081i | \(0.165595\pi\) |
−0.00336739 | + | 0.999994i | \(0.501072\pi\) | |||||||
\(998\) | 8.17185e6 | + | 1.41541e7i | 0.259713 | + | 0.449837i | ||||
\(999\) | 4.12906e6 | − | 7.15173e6i | 0.130899 | − | 0.226724i |
(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.g.79.1 | 2 | ||
7.2 | even | 3 | 147.6.a.d.1.1 | 1 | |||
7.3 | odd | 6 | 21.6.e.a.4.1 | ✓ | 2 | ||
7.4 | even | 3 | inner | 147.6.e.g.67.1 | 2 | ||
7.5 | odd | 6 | 147.6.a.c.1.1 | 1 | |||
7.6 | odd | 2 | 21.6.e.a.16.1 | yes | 2 | ||
21.2 | odd | 6 | 441.6.a.h.1.1 | 1 | |||
21.5 | even | 6 | 441.6.a.g.1.1 | 1 | |||
21.17 | even | 6 | 63.6.e.a.46.1 | 2 | |||
21.20 | even | 2 | 63.6.e.a.37.1 | 2 | |||
28.3 | even | 6 | 336.6.q.b.193.1 | 2 | |||
28.27 | even | 2 | 336.6.q.b.289.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.a.4.1 | ✓ | 2 | 7.3 | odd | 6 | ||
21.6.e.a.16.1 | yes | 2 | 7.6 | odd | 2 | ||
63.6.e.a.37.1 | 2 | 21.20 | even | 2 | |||
63.6.e.a.46.1 | 2 | 21.17 | even | 6 | |||
147.6.a.c.1.1 | 1 | 7.5 | odd | 6 | |||
147.6.a.d.1.1 | 1 | 7.2 | even | 3 | |||
147.6.e.g.67.1 | 2 | 7.4 | even | 3 | inner | ||
147.6.e.g.79.1 | 2 | 1.1 | even | 1 | trivial | ||
336.6.q.b.193.1 | 2 | 28.3 | even | 6 | |||
336.6.q.b.289.1 | 2 | 28.27 | even | 2 | |||
441.6.a.g.1.1 | 1 | 21.5 | even | 6 | |||
441.6.a.h.1.1 | 1 | 21.2 | odd | 6 |