Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.a (trivial) |
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: | yes |
Analytic conductor: | \(39.2940358542\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 246 x^{8} - 192 x^{7} + 20336 x^{6} + 25380 x^{5} - 639206 x^{4} - 722920 x^{3} + 7583055 x^{2} + 5935300 x - 22888100 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 7^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.72637\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.72637 | −0.658735 | −0.329368 | − | 0.944202i | \(-0.606836\pi\) | ||||
−0.329368 | + | 0.944202i | \(0.606836\pi\) | |||||||
\(3\) | −21.0476 | −1.35020 | −0.675101 | − | 0.737725i | \(-0.735900\pi\) | ||||
−0.675101 | + | 0.737725i | \(0.735900\pi\) | |||||||
\(4\) | −18.1142 | −0.566068 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 78.4311 | 0.889426 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 186.744 | 1.03162 | ||||||||
\(9\) | 200.001 | 0.823048 | ||||||||
\(10\) | −93.1592 | −0.294595 | ||||||||
\(11\) | −164.736 | −0.410494 | −0.205247 | − | 0.978710i | \(-0.565800\pi\) | ||||
−0.205247 | + | 0.978710i | \(0.565800\pi\) | |||||||
\(12\) | 381.259 | 0.764306 | ||||||||
\(13\) | 250.121 | 0.410479 | 0.205240 | − | 0.978712i | \(-0.434203\pi\) | ||||
0.205240 | + | 0.978712i | \(0.434203\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −526.190 | −0.603829 | ||||||||
\(16\) | −116.224 | −0.113500 | ||||||||
\(17\) | −2178.31 | −1.82809 | −0.914046 | − | 0.405611i | \(-0.867059\pi\) | ||||
−0.914046 | + | 0.405611i | \(0.867059\pi\) | |||||||
\(18\) | −745.276 | −0.542171 | ||||||||
\(19\) | −18.8660 | −0.0119893 | −0.00599467 | − | 0.999982i | \(-0.501908\pi\) | ||||
−0.00599467 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(20\) | −452.854 | −0.253153 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 613.867 | 0.270407 | ||||||||
\(23\) | −2625.76 | −1.03499 | −0.517495 | − | 0.855686i | \(-0.673135\pi\) | ||||
−0.517495 | + | 0.855686i | \(0.673135\pi\) | |||||||
\(24\) | −3930.51 | −1.39290 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −932.042 | −0.270397 | ||||||||
\(27\) | 905.032 | 0.238921 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7253.02 | −1.60149 | −0.800745 | − | 0.599006i | \(-0.795563\pi\) | ||||
−0.800745 | + | 0.599006i | \(0.795563\pi\) | |||||||
\(30\) | 1960.78 | 0.397764 | ||||||||
\(31\) | −1686.54 | −0.315205 | −0.157603 | − | 0.987503i | \(-0.550377\pi\) | ||||
−0.157603 | + | 0.987503i | \(0.550377\pi\) | |||||||
\(32\) | −5542.71 | −0.956858 | ||||||||
\(33\) | 3467.29 | 0.554250 | ||||||||
\(34\) | 8117.20 | 1.20423 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3622.85 | −0.465901 | ||||||||
\(37\) | 738.487 | 0.0886827 | 0.0443413 | − | 0.999016i | \(-0.485881\pi\) | ||||
0.0443413 | + | 0.999016i | \(0.485881\pi\) | |||||||
\(38\) | 70.3016 | 0.00789780 | ||||||||
\(39\) | −5264.44 | −0.554230 | ||||||||
\(40\) | 4668.60 | 0.461356 | ||||||||
\(41\) | −3352.52 | −0.311467 | −0.155733 | − | 0.987799i | \(-0.549774\pi\) | ||||
−0.155733 | + | 0.987799i | \(0.549774\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −15658.3 | −1.29144 | −0.645720 | − | 0.763574i | \(-0.723443\pi\) | ||||
−0.645720 | + | 0.763574i | \(0.723443\pi\) | |||||||
\(44\) | 2984.06 | 0.232367 | ||||||||
\(45\) | 5000.02 | 0.368078 | ||||||||
\(46\) | 9784.56 | 0.681784 | ||||||||
\(47\) | 18604.8 | 1.22851 | 0.614257 | − | 0.789106i | \(-0.289456\pi\) | ||||
0.614257 | + | 0.789106i | \(0.289456\pi\) | |||||||
\(48\) | 2446.23 | 0.153247 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2328.98 | −0.131747 | ||||||||
\(51\) | 45848.2 | 2.46829 | ||||||||
\(52\) | −4530.73 | −0.232359 | ||||||||
\(53\) | 24842.7 | 1.21481 | 0.607405 | − | 0.794392i | \(-0.292211\pi\) | ||||
0.607405 | + | 0.794392i | \(0.292211\pi\) | |||||||
\(54\) | −3372.49 | −0.157386 | ||||||||
\(55\) | −4118.40 | −0.183579 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 397.083 | 0.0161880 | ||||||||
\(58\) | 27027.4 | 1.05496 | ||||||||
\(59\) | 32607.2 | 1.21950 | 0.609752 | − | 0.792592i | \(-0.291269\pi\) | ||||
0.609752 | + | 0.792592i | \(0.291269\pi\) | |||||||
\(60\) | 9531.48 | 0.341808 | ||||||||
\(61\) | −32034.5 | −1.10228 | −0.551141 | − | 0.834412i | \(-0.685808\pi\) | ||||
−0.551141 | + | 0.834412i | \(0.685808\pi\) | |||||||
\(62\) | 6284.69 | 0.207637 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 24373.4 | 0.743816 | ||||||||
\(65\) | 6253.02 | 0.183572 | ||||||||
\(66\) | −12920.4 | −0.365104 | ||||||||
\(67\) | −47369.8 | −1.28918 | −0.644592 | − | 0.764527i | \(-0.722973\pi\) | ||||
−0.644592 | + | 0.764527i | \(0.722973\pi\) | |||||||
\(68\) | 39458.3 | 1.03482 | ||||||||
\(69\) | 55266.0 | 1.39745 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −46886.4 | −1.10383 | −0.551913 | − | 0.833902i | \(-0.686102\pi\) | ||||
−0.551913 | + | 0.833902i | \(0.686102\pi\) | |||||||
\(72\) | 37348.9 | 0.849076 | ||||||||
\(73\) | 42017.5 | 0.922833 | 0.461417 | − | 0.887184i | \(-0.347341\pi\) | ||||
0.461417 | + | 0.887184i | \(0.347341\pi\) | |||||||
\(74\) | −2751.88 | −0.0584184 | ||||||||
\(75\) | −13154.7 | −0.270041 | ||||||||
\(76\) | 341.741 | 0.00678678 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 19617.2 | 0.365091 | ||||||||
\(79\) | 14811.9 | 0.267020 | 0.133510 | − | 0.991047i | \(-0.457375\pi\) | ||||
0.133510 | + | 0.991047i | \(0.457375\pi\) | |||||||
\(80\) | −2905.59 | −0.0507586 | ||||||||
\(81\) | −67648.9 | −1.14564 | ||||||||
\(82\) | 12492.7 | 0.205174 | ||||||||
\(83\) | 109539. | 1.74531 | 0.872657 | − | 0.488334i | \(-0.162395\pi\) | ||||
0.872657 | + | 0.488334i | \(0.162395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −54457.8 | −0.817547 | ||||||||
\(86\) | 58348.7 | 0.850717 | ||||||||
\(87\) | 152659. | 2.16234 | ||||||||
\(88\) | −30763.4 | −0.423476 | ||||||||
\(89\) | −13073.0 | −0.174944 | −0.0874720 | − | 0.996167i | \(-0.527879\pi\) | ||||
−0.0874720 | + | 0.996167i | \(0.527879\pi\) | |||||||
\(90\) | −18631.9 | −0.242466 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 47563.5 | 0.585874 | ||||||||
\(93\) | 35497.7 | 0.425591 | ||||||||
\(94\) | −69328.4 | −0.809266 | ||||||||
\(95\) | −471.649 | −0.00536180 | ||||||||
\(96\) | 116661. | 1.29195 | ||||||||
\(97\) | 113426. | 1.22400 | 0.612002 | − | 0.790856i | \(-0.290364\pi\) | ||||
0.612002 | + | 0.790856i | \(0.290364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −32947.3 | −0.337856 | ||||||||
\(100\) | −11321.4 | −0.113214 | ||||||||
\(101\) | −200104. | −1.95188 | −0.975939 | − | 0.218044i | \(-0.930032\pi\) | ||||
−0.975939 | + | 0.218044i | \(0.930032\pi\) | |||||||
\(102\) | −170847. | −1.62595 | ||||||||
\(103\) | 90658.9 | 0.842010 | 0.421005 | − | 0.907058i | \(-0.361677\pi\) | ||||
0.421005 | + | 0.907058i | \(0.361677\pi\) | |||||||
\(104\) | 46708.5 | 0.423460 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −92572.9 | −0.800238 | ||||||||
\(107\) | −172387. | −1.45561 | −0.727805 | − | 0.685784i | \(-0.759459\pi\) | ||||
−0.727805 | + | 0.685784i | \(0.759459\pi\) | |||||||
\(108\) | −16393.9 | −0.135246 | ||||||||
\(109\) | −29409.0 | −0.237090 | −0.118545 | − | 0.992949i | \(-0.537823\pi\) | ||||
−0.118545 | + | 0.992949i | \(0.537823\pi\) | |||||||
\(110\) | 15346.7 | 0.120930 | ||||||||
\(111\) | −15543.4 | −0.119740 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 167768. | 1.23598 | 0.617991 | − | 0.786185i | \(-0.287947\pi\) | ||||
0.617991 | + | 0.786185i | \(0.287947\pi\) | |||||||
\(114\) | −1479.68 | −0.0106636 | ||||||||
\(115\) | −65644.1 | −0.462861 | ||||||||
\(116\) | 131382. | 0.906551 | ||||||||
\(117\) | 50024.3 | 0.337844 | ||||||||
\(118\) | −121506. | −0.803330 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −98262.7 | −0.622925 | ||||||||
\(121\) | −133913. | −0.831495 | ||||||||
\(122\) | 119372. | 0.726113 | ||||||||
\(123\) | 70562.4 | 0.420543 | ||||||||
\(124\) | 30550.3 | 0.178428 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 109259. | 0.601101 | 0.300551 | − | 0.953766i | \(-0.402830\pi\) | ||||
0.300551 | + | 0.953766i | \(0.402830\pi\) | |||||||
\(128\) | 86542.7 | 0.466880 | ||||||||
\(129\) | 329570. | 1.74371 | ||||||||
\(130\) | −23301.1 | −0.120925 | ||||||||
\(131\) | 125858. | 0.640770 | 0.320385 | − | 0.947287i | \(-0.396188\pi\) | ||||
0.320385 | + | 0.947287i | \(0.396188\pi\) | |||||||
\(132\) | −62807.2 | −0.313743 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 176517. | 0.849231 | ||||||||
\(135\) | 22625.8 | 0.106849 | ||||||||
\(136\) | −406787. | −1.88590 | ||||||||
\(137\) | 40244.5 | 0.183191 | 0.0915957 | − | 0.995796i | \(-0.470803\pi\) | ||||
0.0915957 | + | 0.995796i | \(0.470803\pi\) | |||||||
\(138\) | −205941. | −0.920547 | ||||||||
\(139\) | 397049. | 1.74304 | 0.871519 | − | 0.490362i | \(-0.163135\pi\) | ||||
0.871519 | + | 0.490362i | \(0.163135\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −391586. | −1.65874 | ||||||||
\(142\) | 174716. | 0.727129 | ||||||||
\(143\) | −41203.9 | −0.168499 | ||||||||
\(144\) | −23244.8 | −0.0934156 | ||||||||
\(145\) | −181326. | −0.716208 | ||||||||
\(146\) | −156573. | −0.607903 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13377.1 | −0.0502004 | ||||||||
\(149\) | −243879. | −0.899928 | −0.449964 | − | 0.893047i | \(-0.648563\pi\) | ||||
−0.449964 | + | 0.893047i | \(0.648563\pi\) | |||||||
\(150\) | 49019.4 | 0.177885 | ||||||||
\(151\) | 487037. | 1.73828 | 0.869139 | − | 0.494567i | \(-0.164674\pi\) | ||||
0.869139 | + | 0.494567i | \(0.164674\pi\) | |||||||
\(152\) | −3523.11 | −0.0123685 | ||||||||
\(153\) | −435664. | −1.50461 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −42163.6 | −0.140964 | ||||||||
\(156\) | 95360.9 | 0.313732 | ||||||||
\(157\) | 138655. | 0.448939 | 0.224470 | − | 0.974481i | \(-0.427935\pi\) | ||||
0.224470 | + | 0.974481i | \(0.427935\pi\) | |||||||
\(158\) | −55194.8 | −0.175896 | ||||||||
\(159\) | −522878. | −1.64024 | ||||||||
\(160\) | −138568. | −0.427920 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 252085. | 0.754674 | ||||||||
\(163\) | 329961. | 0.972732 | 0.486366 | − | 0.873755i | \(-0.338322\pi\) | ||||
0.486366 | + | 0.873755i | \(0.338322\pi\) | |||||||
\(164\) | 60728.1 | 0.176311 | ||||||||
\(165\) | 86682.4 | 0.247868 | ||||||||
\(166\) | −408183. | −1.14970 | ||||||||
\(167\) | −218143. | −0.605273 | −0.302636 | − | 0.953106i | \(-0.597867\pi\) | ||||
−0.302636 | + | 0.953106i | \(0.597867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −308733. | −0.831507 | ||||||||
\(170\) | 202930. | 0.538547 | ||||||||
\(171\) | −3773.21 | −0.00986780 | ||||||||
\(172\) | 283638. | 0.731043 | ||||||||
\(173\) | −161771. | −0.410948 | −0.205474 | − | 0.978663i | \(-0.565874\pi\) | ||||
−0.205474 | + | 0.978663i | \(0.565874\pi\) | |||||||
\(174\) | −568862. | −1.42441 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19146.2 | 0.0465909 | ||||||||
\(177\) | −686302. | −1.64658 | ||||||||
\(178\) | 48714.7 | 0.115242 | ||||||||
\(179\) | −139043. | −0.324351 | −0.162175 | − | 0.986762i | \(-0.551851\pi\) | ||||
−0.162175 | + | 0.986762i | \(0.551851\pi\) | |||||||
\(180\) | −90571.1 | −0.208357 | ||||||||
\(181\) | −625698. | −1.41961 | −0.709804 | − | 0.704399i | \(-0.751217\pi\) | ||||
−0.709804 | + | 0.704399i | \(0.751217\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 674248. | 1.48831 | ||||||||
\(184\) | −490345. | −1.06772 | ||||||||
\(185\) | 18462.2 | 0.0396601 | ||||||||
\(186\) | −132277. | −0.280352 | ||||||||
\(187\) | 358847. | 0.750421 | ||||||||
\(188\) | −337011. | −0.695423 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1757.54 | 0.00353200 | ||||||||
\(191\) | −144788. | −0.287178 | −0.143589 | − | 0.989637i | \(-0.545864\pi\) | ||||
−0.143589 | + | 0.989637i | \(0.545864\pi\) | |||||||
\(192\) | −513000. | −1.00430 | ||||||||
\(193\) | 363906. | 0.703227 | 0.351613 | − | 0.936145i | \(-0.385633\pi\) | ||||
0.351613 | + | 0.936145i | \(0.385633\pi\) | |||||||
\(194\) | −422667. | −0.806295 | ||||||||
\(195\) | −131611. | −0.247859 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 839307. | 1.54083 | 0.770416 | − | 0.637541i | \(-0.220048\pi\) | ||||
0.770416 | + | 0.637541i | \(0.220048\pi\) | |||||||
\(198\) | 122774. | 0.222558 | ||||||||
\(199\) | −214187. | −0.383408 | −0.191704 | − | 0.981453i | \(-0.561401\pi\) | ||||
−0.191704 | + | 0.981453i | \(0.561401\pi\) | |||||||
\(200\) | 116715. | 0.206325 | ||||||||
\(201\) | 997020. | 1.74066 | ||||||||
\(202\) | 745662. | 1.28577 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −830502. | −1.39722 | ||||||||
\(205\) | −83812.9 | −0.139292 | ||||||||
\(206\) | −337829. | −0.554662 | ||||||||
\(207\) | −525154. | −0.851846 | ||||||||
\(208\) | −29069.9 | −0.0465892 | ||||||||
\(209\) | 3107.91 | 0.00492155 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 771009. | 1.19221 | 0.596106 | − | 0.802906i | \(-0.296714\pi\) | ||||
0.596106 | + | 0.802906i | \(0.296714\pi\) | |||||||
\(212\) | −450004. | −0.687665 | ||||||||
\(213\) | 986844. | 1.49039 | ||||||||
\(214\) | 642378. | 0.958862 | ||||||||
\(215\) | −391458. | −0.577550 | ||||||||
\(216\) | 169009. | 0.246477 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 109589. | 0.156180 | ||||||||
\(219\) | −884367. | −1.24601 | ||||||||
\(220\) | 74601.4 | 0.103918 | ||||||||
\(221\) | −544841. | −0.750394 | ||||||||
\(222\) | 57920.4 | 0.0788767 | ||||||||
\(223\) | 217469. | 0.292843 | 0.146422 | − | 0.989222i | \(-0.453224\pi\) | ||||
0.146422 | + | 0.989222i | \(0.453224\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 125000. | 0.164610 | ||||||||
\(226\) | −625165. | −0.814186 | ||||||||
\(227\) | −1.07247e6 | −1.38140 | −0.690699 | − | 0.723143i | \(-0.742697\pi\) | ||||
−0.690699 | + | 0.723143i | \(0.742697\pi\) | |||||||
\(228\) | −7192.83 | −0.00916353 | ||||||||
\(229\) | 122096. | 0.153855 | 0.0769277 | − | 0.997037i | \(-0.475489\pi\) | ||||
0.0769277 | + | 0.997037i | \(0.475489\pi\) | |||||||
\(230\) | 244614. | 0.304903 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.35446e6 | −1.65213 | ||||||||
\(233\) | 153610. | 0.185366 | 0.0926831 | − | 0.995696i | \(-0.470456\pi\) | ||||
0.0926831 | + | 0.995696i | \(0.470456\pi\) | |||||||
\(234\) | −186409. | −0.222550 | ||||||||
\(235\) | 465120. | 0.549409 | ||||||||
\(236\) | −590652. | −0.690322 | ||||||||
\(237\) | −311756. | −0.360532 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 580774. | 0.657677 | 0.328838 | − | 0.944386i | \(-0.393343\pi\) | ||||
0.328838 | + | 0.944386i | \(0.393343\pi\) | |||||||
\(240\) | 61155.6 | 0.0685344 | ||||||||
\(241\) | 25512.4 | 0.0282949 | 0.0141475 | − | 0.999900i | \(-0.495497\pi\) | ||||
0.0141475 | + | 0.999900i | \(0.495497\pi\) | |||||||
\(242\) | 499010. | 0.547735 | ||||||||
\(243\) | 1.20392e6 | 1.30793 | ||||||||
\(244\) | 580278. | 0.623967 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −262942. | −0.277027 | ||||||||
\(247\) | −4718.77 | −0.00492138 | ||||||||
\(248\) | −314952. | −0.325173 | ||||||||
\(249\) | −2.30553e6 | −2.35653 | ||||||||
\(250\) | −58224.5 | −0.0589191 | ||||||||
\(251\) | 1.55324e6 | 1.55616 | 0.778080 | − | 0.628165i | \(-0.216194\pi\) | ||||
0.778080 | + | 0.628165i | \(0.216194\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 432558. | 0.424857 | ||||||||
\(254\) | −407139. | −0.395967 | ||||||||
\(255\) | 1.14621e6 | 1.10385 | ||||||||
\(256\) | −1.10244e6 | −1.05137 | ||||||||
\(257\) | −679193. | −0.641446 | −0.320723 | − | 0.947173i | \(-0.603926\pi\) | ||||
−0.320723 | + | 0.947173i | \(0.603926\pi\) | |||||||
\(258\) | −1.22810e6 | −1.14864 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −113268. | −0.103914 | ||||||||
\(261\) | −1.45061e6 | −1.31810 | ||||||||
\(262\) | −468993. | −0.422098 | ||||||||
\(263\) | 1.90847e6 | 1.70136 | 0.850680 | − | 0.525684i | \(-0.176191\pi\) | ||||
0.850680 | + | 0.525684i | \(0.176191\pi\) | |||||||
\(264\) | 647496. | 0.571778 | ||||||||
\(265\) | 621066. | 0.543279 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 275154. | 0.236210 | ||||||||
\(268\) | 858065. | 0.729765 | ||||||||
\(269\) | 965048. | 0.813145 | 0.406573 | − | 0.913619i | \(-0.366724\pi\) | ||||
0.406573 | + | 0.913619i | \(0.366724\pi\) | |||||||
\(270\) | −84312.1 | −0.0703851 | ||||||||
\(271\) | 1.27445e6 | 1.05414 | 0.527071 | − | 0.849822i | \(-0.323290\pi\) | ||||
0.527071 | + | 0.849822i | \(0.323290\pi\) | |||||||
\(272\) | 253171. | 0.207488 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −149966. | −0.120675 | ||||||||
\(275\) | −102960. | −0.0820988 | ||||||||
\(276\) | −1.00110e6 | −0.791049 | ||||||||
\(277\) | 187333. | 0.146695 | 0.0733474 | − | 0.997306i | \(-0.476632\pi\) | ||||
0.0733474 | + | 0.997306i | \(0.476632\pi\) | |||||||
\(278\) | −1.47955e6 | −1.14820 | ||||||||
\(279\) | −337310. | −0.259429 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.24432e6 | 1.69558 | 0.847792 | − | 0.530329i | \(-0.177931\pi\) | ||||
0.847792 | + | 0.530329i | \(0.177931\pi\) | |||||||
\(282\) | 1.45919e6 | 1.09267 | ||||||||
\(283\) | 2.40515e6 | 1.78516 | 0.892578 | − | 0.450894i | \(-0.148895\pi\) | ||||
0.892578 | + | 0.450894i | \(0.148895\pi\) | |||||||
\(284\) | 849307. | 0.624840 | ||||||||
\(285\) | 9927.08 | 0.00723951 | ||||||||
\(286\) | 153541. | 0.110996 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.10855e6 | −0.787540 | ||||||||
\(289\) | 3.32519e6 | 2.34192 | ||||||||
\(290\) | 675686. | 0.471791 | ||||||||
\(291\) | −2.38734e6 | −1.65265 | ||||||||
\(292\) | −761112. | −0.522386 | ||||||||
\(293\) | −978243. | −0.665698 | −0.332849 | − | 0.942980i | \(-0.608010\pi\) | ||||
−0.332849 | + | 0.942980i | \(0.608010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 815179. | 0.545379 | ||||||||
\(296\) | 137908. | 0.0914872 | ||||||||
\(297\) | −149091. | −0.0980757 | ||||||||
\(298\) | 908782. | 0.592815 | ||||||||
\(299\) | −656758. | −0.424842 | ||||||||
\(300\) | 238287. | 0.152861 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.81488e6 | −1.14507 | ||||||||
\(303\) | 4.21171e6 | 2.63543 | ||||||||
\(304\) | 2192.67 | 0.00136078 | ||||||||
\(305\) | −800862. | −0.492956 | ||||||||
\(306\) | 1.62344e6 | 0.991138 | ||||||||
\(307\) | 199481. | 0.120797 | 0.0603984 | − | 0.998174i | \(-0.480763\pi\) | ||||
0.0603984 | + | 0.998174i | \(0.480763\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.90815e6 | −1.13688 | ||||||||
\(310\) | 157117. | 0.0928580 | ||||||||
\(311\) | −641054. | −0.375832 | −0.187916 | − | 0.982185i | \(-0.560173\pi\) | ||||
−0.187916 | + | 0.982185i | \(0.560173\pi\) | |||||||
\(312\) | −983101. | −0.571757 | ||||||||
\(313\) | 823954. | 0.475381 | 0.237691 | − | 0.971341i | \(-0.423610\pi\) | ||||
0.237691 | + | 0.971341i | \(0.423610\pi\) | |||||||
\(314\) | −516681. | −0.295732 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −268306. | −0.151152 | ||||||||
\(317\) | 1.05147e6 | 0.587689 | 0.293845 | − | 0.955853i | \(-0.405065\pi\) | ||||
0.293845 | + | 0.955853i | \(0.405065\pi\) | |||||||
\(318\) | 1.94844e6 | 1.08048 | ||||||||
\(319\) | 1.19483e6 | 0.657402 | ||||||||
\(320\) | 609334. | 0.332645 | ||||||||
\(321\) | 3.62833e6 | 1.96537 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41096.0 | 0.0219176 | ||||||||
\(324\) | 1.22540e6 | 0.648510 | ||||||||
\(325\) | 156325. | 0.0820959 | ||||||||
\(326\) | −1.22956e6 | −0.640773 | ||||||||
\(327\) | 618988. | 0.320120 | ||||||||
\(328\) | −626062. | −0.321316 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −323011. | −0.163280 | ||||||||
\(331\) | −1.72153e6 | −0.863661 | −0.431831 | − | 0.901955i | \(-0.642132\pi\) | ||||
−0.431831 | + | 0.901955i | \(0.642132\pi\) | |||||||
\(332\) | −1.98421e6 | −0.987966 | ||||||||
\(333\) | 147698. | 0.0729901 | ||||||||
\(334\) | 812883. | 0.398714 | ||||||||
\(335\) | −1.18425e6 | −0.576540 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.89933e6 | −1.39067 | −0.695334 | − | 0.718687i | \(-0.744744\pi\) | ||||
−0.695334 | + | 0.718687i | \(0.744744\pi\) | |||||||
\(338\) | 1.15045e6 | 0.547743 | ||||||||
\(339\) | −3.53111e6 | −1.66883 | ||||||||
\(340\) | 986458. | 0.462787 | ||||||||
\(341\) | 277835. | 0.129390 | ||||||||
\(342\) | 14060.4 | 0.00650027 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.92410e6 | −1.33228 | ||||||||
\(345\) | 1.38165e6 | 0.624957 | ||||||||
\(346\) | 602820. | 0.270706 | ||||||||
\(347\) | 2.16973e6 | 0.967346 | 0.483673 | − | 0.875249i | \(-0.339302\pi\) | ||||
0.483673 | + | 0.875249i | \(0.339302\pi\) | |||||||
\(348\) | −2.76528e6 | −1.22403 | ||||||||
\(349\) | 2.32054e6 | 1.01982 | 0.509912 | − | 0.860226i | \(-0.329678\pi\) | ||||
0.509912 | + | 0.860226i | \(0.329678\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 226367. | 0.0980722 | ||||||||
\(352\) | 913085. | 0.392784 | ||||||||
\(353\) | 3.37510e6 | 1.44162 | 0.720808 | − | 0.693135i | \(-0.243771\pi\) | ||||
0.720808 | + | 0.693135i | \(0.243771\pi\) | |||||||
\(354\) | 2.55742e6 | 1.08466 | ||||||||
\(355\) | −1.17216e6 | −0.493646 | ||||||||
\(356\) | 236806. | 0.0990301 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 518124. | 0.213661 | ||||||||
\(359\) | −1.33592e6 | −0.547070 | −0.273535 | − | 0.961862i | \(-0.588193\pi\) | ||||
−0.273535 | + | 0.961862i | \(0.588193\pi\) | |||||||
\(360\) | 933723. | 0.379718 | ||||||||
\(361\) | −2.47574e6 | −0.999856 | ||||||||
\(362\) | 2.33158e6 | 0.935146 | ||||||||
\(363\) | 2.81855e6 | 1.12269 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.05044e6 | 0.412704 | ||||||||
\(366\) | −2.51250e6 | −0.980399 | ||||||||
\(367\) | −970553. | −0.376144 | −0.188072 | − | 0.982155i | \(-0.560224\pi\) | ||||
−0.188072 | + | 0.982155i | \(0.560224\pi\) | |||||||
\(368\) | 305176. | 0.117471 | ||||||||
\(369\) | −670506. | −0.256352 | ||||||||
\(370\) | −68796.9 | −0.0261255 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −643011. | −0.240913 | ||||||||
\(373\) | −985907. | −0.366914 | −0.183457 | − | 0.983028i | \(-0.558729\pi\) | ||||
−0.183457 | + | 0.983028i | \(0.558729\pi\) | |||||||
\(374\) | −1.33719e6 | −0.494329 | ||||||||
\(375\) | −328868. | −0.120766 | ||||||||
\(376\) | 3.47433e6 | 1.26737 | ||||||||
\(377\) | −1.81413e6 | −0.657378 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.30811e6 | 1.18299 | 0.591496 | − | 0.806308i | \(-0.298538\pi\) | ||||
0.591496 | + | 0.806308i | \(0.298538\pi\) | |||||||
\(380\) | 8543.54 | 0.00303514 | ||||||||
\(381\) | −2.29964e6 | −0.811609 | ||||||||
\(382\) | 539535. | 0.189174 | ||||||||
\(383\) | −4.09037e6 | −1.42484 | −0.712419 | − | 0.701754i | \(-0.752401\pi\) | ||||
−0.712419 | + | 0.701754i | \(0.752401\pi\) | |||||||
\(384\) | −1.82151e6 | −0.630383 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.35605e6 | −0.463240 | ||||||||
\(387\) | −3.13168e6 | −1.06292 | ||||||||
\(388\) | −2.05462e6 | −0.692869 | ||||||||
\(389\) | −5.11644e6 | −1.71433 | −0.857164 | − | 0.515043i | \(-0.827776\pi\) | ||||
−0.857164 | + | 0.515043i | \(0.827776\pi\) | |||||||
\(390\) | 490431. | 0.163274 | ||||||||
\(391\) | 5.71973e6 | 1.89206 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.64900e6 | −0.865169 | ||||||||
\(394\) | −3.12757e6 | −1.01500 | ||||||||
\(395\) | 370299. | 0.119415 | ||||||||
\(396\) | 596813. | 0.191250 | ||||||||
\(397\) | 5.36835e6 | 1.70948 | 0.854742 | − | 0.519054i | \(-0.173716\pi\) | ||||
0.854742 | + | 0.519054i | \(0.173716\pi\) | |||||||
\(398\) | 798140. | 0.252564 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −72639.7 | −0.0226999 | ||||||||
\(401\) | −3.83942e6 | −1.19235 | −0.596176 | − | 0.802854i | \(-0.703314\pi\) | ||||
−0.596176 | + | 0.802854i | \(0.703314\pi\) | |||||||
\(402\) | −3.71527e6 | −1.14663 | ||||||||
\(403\) | −421840. | −0.129385 | ||||||||
\(404\) | 3.62472e6 | 1.10490 | ||||||||
\(405\) | −1.69122e6 | −0.512346 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −121655. | −0.0364037 | ||||||||
\(408\) | 8.56187e6 | 2.54635 | ||||||||
\(409\) | 576841. | 0.170509 | 0.0852546 | − | 0.996359i | \(-0.472830\pi\) | ||||
0.0852546 | + | 0.996359i | \(0.472830\pi\) | |||||||
\(410\) | 312318. | 0.0917566 | ||||||||
\(411\) | −847049. | −0.247345 | ||||||||
\(412\) | −1.64221e6 | −0.476635 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.95692e6 | 0.561141 | ||||||||
\(415\) | 2.73847e6 | 0.780528 | ||||||||
\(416\) | −1.38635e6 | −0.392770 | ||||||||
\(417\) | −8.35691e6 | −2.35345 | ||||||||
\(418\) | −11581.2 | −0.00324200 | ||||||||
\(419\) | 65975.8 | 0.0183590 | 0.00917951 | − | 0.999958i | \(-0.497078\pi\) | ||||
0.00917951 | + | 0.999958i | \(0.497078\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.95046e6 | −0.811306 | −0.405653 | − | 0.914027i | \(-0.632956\pi\) | ||||
−0.405653 | + | 0.914027i | \(0.632956\pi\) | |||||||
\(422\) | −2.87307e6 | −0.785352 | ||||||||
\(423\) | 3.72097e6 | 1.01113 | ||||||||
\(424\) | 4.63921e6 | 1.25323 | ||||||||
\(425\) | −1.36145e6 | −0.365618 | ||||||||
\(426\) | −3.67735e6 | −0.981772 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.12265e6 | 0.823974 | ||||||||
\(429\) | 867242. | 0.227508 | ||||||||
\(430\) | 1.45872e6 | 0.380452 | ||||||||
\(431\) | 3.42138e6 | 0.887174 | 0.443587 | − | 0.896231i | \(-0.353706\pi\) | ||||
0.443587 | + | 0.896231i | \(0.353706\pi\) | |||||||
\(432\) | −105186. | −0.0271175 | ||||||||
\(433\) | −6.00598e6 | −1.53944 | −0.769722 | − | 0.638379i | \(-0.779605\pi\) | ||||
−0.769722 | + | 0.638379i | \(0.779605\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.81646e6 | 0.967026 | ||||||||
\(436\) | 532720. | 0.134209 | ||||||||
\(437\) | 49537.6 | 0.0124088 | ||||||||
\(438\) | 3.29548e6 | 0.820792 | ||||||||
\(439\) | 58817.4 | 0.0145661 | 0.00728307 | − | 0.999973i | \(-0.497682\pi\) | ||||
0.00728307 | + | 0.999973i | \(0.497682\pi\) | |||||||
\(440\) | −769086. | −0.189384 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.03028e6 | 0.494311 | ||||||||
\(443\) | −3.30577e6 | −0.800320 | −0.400160 | − | 0.916445i | \(-0.631046\pi\) | ||||
−0.400160 | + | 0.916445i | \(0.631046\pi\) | |||||||
\(444\) | 281555. | 0.0677807 | ||||||||
\(445\) | −326824. | −0.0782373 | ||||||||
\(446\) | −810369. | −0.192906 | ||||||||
\(447\) | 5.13305e6 | 1.21509 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.71550e6 | 1.57204 | 0.786018 | − | 0.618203i | \(-0.212139\pi\) | ||||
0.786018 | + | 0.618203i | \(0.212139\pi\) | |||||||
\(450\) | −465798. | −0.108434 | ||||||||
\(451\) | 552280. | 0.127855 | ||||||||
\(452\) | −3.03897e6 | −0.699650 | ||||||||
\(453\) | −1.02509e7 | −2.34703 | ||||||||
\(454\) | 3.99640e6 | 0.909975 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 74152.9 | 0.0167000 | ||||||||
\(457\) | −8.13981e6 | −1.82316 | −0.911578 | − | 0.411126i | \(-0.865135\pi\) | ||||
−0.911578 | + | 0.411126i | \(0.865135\pi\) | |||||||
\(458\) | −454975. | −0.101350 | ||||||||
\(459\) | −1.97144e6 | −0.436770 | ||||||||
\(460\) | 1.18909e6 | 0.262011 | ||||||||
\(461\) | −6.80207e6 | −1.49070 | −0.745348 | − | 0.666676i | \(-0.767717\pi\) | ||||
−0.745348 | + | 0.666676i | \(0.767717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.62848e6 | −0.353045 | −0.176523 | − | 0.984297i | \(-0.556485\pi\) | ||||
−0.176523 | + | 0.984297i | \(0.556485\pi\) | |||||||
\(464\) | 842972. | 0.181768 | ||||||||
\(465\) | 887442. | 0.190330 | ||||||||
\(466\) | −572409. | −0.122107 | ||||||||
\(467\) | −4.85435e6 | −1.03000 | −0.515002 | − | 0.857189i | \(-0.672209\pi\) | ||||
−0.515002 | + | 0.857189i | \(0.672209\pi\) | |||||||
\(468\) | −906149. | −0.191243 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.73321e6 | −0.361915 | ||||||||
\(471\) | −2.91836e6 | −0.606159 | ||||||||
\(472\) | 6.08919e6 | 1.25807 | ||||||||
\(473\) | 2.57949e6 | 0.530128 | ||||||||
\(474\) | 1.16172e6 | 0.237495 | ||||||||
\(475\) | −11791.2 | −0.00239787 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.96855e6 | 0.999847 | ||||||||
\(478\) | −2.16418e6 | −0.433235 | ||||||||
\(479\) | −1.79890e6 | −0.358235 | −0.179118 | − | 0.983828i | \(-0.557324\pi\) | ||||
−0.179118 | + | 0.983828i | \(0.557324\pi\) | |||||||
\(480\) | 2.91652e6 | 0.577779 | ||||||||
\(481\) | 184711. | 0.0364024 | ||||||||
\(482\) | −95068.6 | −0.0186389 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.42572e6 | 0.470682 | ||||||||
\(485\) | 2.83565e6 | 0.547391 | ||||||||
\(486\) | −4.48626e6 | −0.861577 | ||||||||
\(487\) | 5.00914e6 | 0.957063 | 0.478531 | − | 0.878070i | \(-0.341169\pi\) | ||||
0.478531 | + | 0.878070i | \(0.341169\pi\) | |||||||
\(488\) | −5.98224e6 | −1.13714 | ||||||||
\(489\) | −6.94487e6 | −1.31339 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −439989. | −0.0823641 | −0.0411820 | − | 0.999152i | \(-0.513112\pi\) | ||||
−0.0411820 | + | 0.999152i | \(0.513112\pi\) | |||||||
\(492\) | −1.27818e6 | −0.238056 | ||||||||
\(493\) | 1.57993e7 | 2.92767 | ||||||||
\(494\) | 17583.9 | 0.00324188 | ||||||||
\(495\) | −823683. | −0.151094 | ||||||||
\(496\) | 196016. | 0.0357757 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.59126e6 | 1.55233 | ||||||||
\(499\) | −178880. | −0.0321597 | −0.0160798 | − | 0.999871i | \(-0.505119\pi\) | ||||
−0.0160798 | + | 0.999871i | \(0.505119\pi\) | |||||||
\(500\) | −283034. | −0.0506306 | ||||||||
\(501\) | 4.59139e6 | 0.817241 | ||||||||
\(502\) | −5.78795e6 | −1.02510 | ||||||||
\(503\) | −447148. | −0.0788009 | −0.0394004 | − | 0.999224i | \(-0.512545\pi\) | ||||
−0.0394004 | + | 0.999224i | \(0.512545\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.00260e6 | −0.872906 | ||||||||
\(506\) | −1.61187e6 | −0.279868 | ||||||||
\(507\) | 6.49807e6 | 1.12270 | ||||||||
\(508\) | −1.97914e6 | −0.340264 | ||||||||
\(509\) | −98185.6 | −0.0167978 | −0.00839892 | − | 0.999965i | \(-0.502673\pi\) | ||||
−0.00839892 | + | 0.999965i | \(0.502673\pi\) | |||||||
\(510\) | −4.27118e6 | −0.727148 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.33872e6 | 0.225692 | ||||||||
\(513\) | −17074.3 | −0.00286451 | ||||||||
\(514\) | 2.53092e6 | 0.422543 | ||||||||
\(515\) | 2.26647e6 | 0.376558 | ||||||||
\(516\) | −5.96989e6 | −0.987056 | ||||||||
\(517\) | −3.06488e6 | −0.504298 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.40490e6 | 0.554863 | ||||||||
\(520\) | 1.16771e6 | 0.189377 | ||||||||
\(521\) | −1.02358e7 | −1.65207 | −0.826036 | − | 0.563618i | \(-0.809409\pi\) | ||||
−0.826036 | + | 0.563618i | \(0.809409\pi\) | |||||||
\(522\) | 5.40551e6 | 0.868281 | ||||||||
\(523\) | 7.82929e6 | 1.25161 | 0.625804 | − | 0.779981i | \(-0.284771\pi\) | ||||
0.625804 | + | 0.779981i | \(0.284771\pi\) | |||||||
\(524\) | −2.27981e6 | −0.362719 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.11167e6 | −1.12075 | ||||||||
\(527\) | 3.67382e6 | 0.576224 | ||||||||
\(528\) | −402981. | −0.0629072 | ||||||||
\(529\) | 458288. | 0.0712032 | ||||||||
\(530\) | −2.31432e6 | −0.357877 | ||||||||
\(531\) | 6.52146e6 | 1.00371 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −838534. | −0.127851 | ||||||||
\(534\) | −1.02533e6 | −0.155600 | ||||||||
\(535\) | −4.30967e6 | −0.650968 | ||||||||
\(536\) | −8.84603e6 | −1.32995 | ||||||||
\(537\) | 2.92651e6 | 0.437939 | ||||||||
\(538\) | −3.59612e6 | −0.535647 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −409848. | −0.0604837 | ||||||||
\(541\) | −5.83527e6 | −0.857172 | −0.428586 | − | 0.903501i | \(-0.640988\pi\) | ||||
−0.428586 | + | 0.903501i | \(0.640988\pi\) | |||||||
\(542\) | −4.74906e6 | −0.694400 | ||||||||
\(543\) | 1.31694e7 | 1.91676 | ||||||||
\(544\) | 1.20738e7 | 1.74922 | ||||||||
\(545\) | −735225. | −0.106030 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.82111e6 | 0.260237 | 0.130118 | − | 0.991498i | \(-0.458464\pi\) | ||||
0.130118 | + | 0.991498i | \(0.458464\pi\) | |||||||
\(548\) | −728995. | −0.103699 | ||||||||
\(549\) | −6.40692e6 | −0.907232 | ||||||||
\(550\) | 383667. | 0.0540814 | ||||||||
\(551\) | 136835. | 0.0192008 | ||||||||
\(552\) | 1.03206e7 | 1.44164 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −698072. | −0.0966331 | ||||||||
\(555\) | −388584. | −0.0535492 | ||||||||
\(556\) | −7.19221e6 | −0.986677 | ||||||||
\(557\) | −1.09965e7 | −1.50182 | −0.750911 | − | 0.660404i | \(-0.770385\pi\) | ||||
−0.750911 | + | 0.660404i | \(0.770385\pi\) | |||||||
\(558\) | 1.25694e6 | 0.170895 | ||||||||
\(559\) | −3.91647e6 | −0.530109 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.55285e6 | −1.01322 | ||||||||
\(562\) | −8.36317e6 | −1.11694 | ||||||||
\(563\) | 2.09557e6 | 0.278632 | 0.139316 | − | 0.990248i | \(-0.455510\pi\) | ||||
0.139316 | + | 0.990248i | \(0.455510\pi\) | |||||||
\(564\) | 7.09326e6 | 0.938962 | ||||||||
\(565\) | 4.19419e6 | 0.552748 | ||||||||
\(566\) | −8.96248e6 | −1.17594 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.75574e6 | −1.13873 | ||||||||
\(569\) | 6.24664e6 | 0.808846 | 0.404423 | − | 0.914572i | \(-0.367472\pi\) | ||||
0.404423 | + | 0.914572i | \(0.367472\pi\) | |||||||
\(570\) | −36992.0 | −0.00476892 | ||||||||
\(571\) | 8.34847e6 | 1.07156 | 0.535780 | − | 0.844358i | \(-0.320018\pi\) | ||||
0.535780 | + | 0.844358i | \(0.320018\pi\) | |||||||
\(572\) | 746374. | 0.0953820 | ||||||||
\(573\) | 3.04745e6 | 0.387748 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.64110e6 | −0.206998 | ||||||||
\(576\) | 4.87469e6 | 0.612196 | ||||||||
\(577\) | −3.77464e6 | −0.471993 | −0.235997 | − | 0.971754i | \(-0.575835\pi\) | ||||
−0.235997 | + | 0.971754i | \(0.575835\pi\) | |||||||
\(578\) | −1.23909e7 | −1.54270 | ||||||||
\(579\) | −7.65933e6 | −0.949499 | ||||||||
\(580\) | 3.28456e6 | 0.405422 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.89612e6 | 1.08866 | ||||||||
\(583\) | −4.09248e6 | −0.498672 | ||||||||
\(584\) | 7.84652e6 | 0.952017 | ||||||||
\(585\) | 1.25061e6 | 0.151088 | ||||||||
\(586\) | 3.64529e6 | 0.438519 | ||||||||
\(587\) | −1.53838e6 | −0.184275 | −0.0921377 | − | 0.995746i | \(-0.529370\pi\) | ||||
−0.0921377 | + | 0.995746i | \(0.529370\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31818.3 | 0.00377910 | ||||||||
\(590\) | −3.03766e6 | −0.359260 | ||||||||
\(591\) | −1.76654e7 | −2.08044 | ||||||||
\(592\) | −85829.6 | −0.0100654 | ||||||||
\(593\) | 2.65317e6 | 0.309834 | 0.154917 | − | 0.987928i | \(-0.450489\pi\) | ||||
0.154917 | + | 0.987928i | \(0.450489\pi\) | |||||||
\(594\) | 555570. | 0.0646060 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.41766e6 | 0.509420 | ||||||||
\(597\) | 4.50812e6 | 0.517678 | ||||||||
\(598\) | 2.44732e6 | 0.279858 | ||||||||
\(599\) | −1.43136e7 | −1.62998 | −0.814992 | − | 0.579472i | \(-0.803259\pi\) | ||||
−0.814992 | + | 0.579472i | \(0.803259\pi\) | |||||||
\(600\) | −2.45657e6 | −0.278580 | ||||||||
\(601\) | −3.27781e6 | −0.370167 | −0.185084 | − | 0.982723i | \(-0.559256\pi\) | ||||
−0.185084 | + | 0.982723i | \(0.559256\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.47399e6 | −1.06106 | ||||||||
\(604\) | −8.82226e6 | −0.983983 | ||||||||
\(605\) | −3.34783e6 | −0.371856 | ||||||||
\(606\) | −1.56944e7 | −1.73605 | ||||||||
\(607\) | 7.19646e6 | 0.792770 | 0.396385 | − | 0.918084i | \(-0.370264\pi\) | ||||
0.396385 | + | 0.918084i | \(0.370264\pi\) | |||||||
\(608\) | 104569. | 0.0114721 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.98431e6 | 0.324727 | ||||||||
\(611\) | 4.65345e6 | 0.504280 | ||||||||
\(612\) | 7.89169e6 | 0.851709 | ||||||||
\(613\) | 1.05406e7 | 1.13296 | 0.566478 | − | 0.824077i | \(-0.308306\pi\) | ||||
0.566478 | + | 0.824077i | \(0.308306\pi\) | |||||||
\(614\) | −743340. | −0.0795732 | ||||||||
\(615\) | 1.76406e6 | 0.188073 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.88228e6 | 0.199054 | 0.0995272 | − | 0.995035i | \(-0.468267\pi\) | ||||
0.0995272 | + | 0.995035i | \(0.468267\pi\) | |||||||
\(618\) | 7.11047e6 | 0.748906 | ||||||||
\(619\) | 4.38233e6 | 0.459705 | 0.229852 | − | 0.973226i | \(-0.426176\pi\) | ||||
0.229852 | + | 0.973226i | \(0.426176\pi\) | |||||||
\(620\) | 763759. | 0.0797952 | ||||||||
\(621\) | −2.37640e6 | −0.247281 | ||||||||
\(622\) | 2.38880e6 | 0.247574 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 611852. | 0.0629049 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −3.07036e6 | −0.313151 | ||||||||
\(627\) | −65413.9 | −0.00664509 | ||||||||
\(628\) | −2.51163e6 | −0.254130 | ||||||||
\(629\) | −1.60866e6 | −0.162120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.59096e7 | −1.59069 | −0.795345 | − | 0.606157i | \(-0.792710\pi\) | ||||
−0.795345 | + | 0.606157i | \(0.792710\pi\) | |||||||
\(632\) | 2.76604e6 | 0.275465 | ||||||||
\(633\) | −1.62279e7 | −1.60973 | ||||||||
\(634\) | −3.91816e6 | −0.387132 | ||||||||
\(635\) | 2.73147e6 | 0.268821 | ||||||||
\(636\) | 9.47149e6 | 0.928487 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.45239e6 | −0.433054 | ||||||||
\(639\) | −9.37730e6 | −0.908502 | ||||||||
\(640\) | 2.16357e6 | 0.208795 | ||||||||
\(641\) | 5.45547e6 | 0.524430 | 0.262215 | − | 0.965009i | \(-0.415547\pi\) | ||||
0.262215 | + | 0.965009i | \(0.415547\pi\) | |||||||
\(642\) | −1.35205e7 | −1.29466 | ||||||||
\(643\) | 45853.5 | 0.00437366 | 0.00218683 | − | 0.999998i | \(-0.499304\pi\) | ||||
0.00218683 | + | 0.999998i | \(0.499304\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.23925e6 | 0.779809 | ||||||||
\(646\) | −153139. | −0.0144379 | ||||||||
\(647\) | −1.75738e6 | −0.165046 | −0.0825230 | − | 0.996589i | \(-0.526298\pi\) | ||||
−0.0825230 | + | 0.996589i | \(0.526298\pi\) | |||||||
\(648\) | −1.26330e7 | −1.18187 | ||||||||
\(649\) | −5.37158e6 | −0.500599 | ||||||||
\(650\) | −582526. | −0.0540794 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.97696e6 | −0.550632 | ||||||||
\(653\) | 6.36106e6 | 0.583776 | 0.291888 | − | 0.956452i | \(-0.405716\pi\) | ||||
0.291888 | + | 0.956452i | \(0.405716\pi\) | |||||||
\(654\) | −2.30658e6 | −0.210875 | ||||||||
\(655\) | 3.14645e6 | 0.286561 | ||||||||
\(656\) | 389642. | 0.0353513 | ||||||||
\(657\) | 8.40353e6 | 0.759536 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.78759e6 | −0.877935 | −0.438967 | − | 0.898503i | \(-0.644656\pi\) | ||||
−0.438967 | + | 0.898503i | \(0.644656\pi\) | |||||||
\(660\) | −1.57018e6 | −0.140310 | ||||||||
\(661\) | 1.43971e7 | 1.28165 | 0.640827 | − | 0.767686i | \(-0.278592\pi\) | ||||
0.640827 | + | 0.767686i | \(0.278592\pi\) | |||||||
\(662\) | 6.41504e6 | 0.568924 | ||||||||
\(663\) | 1.14676e7 | 1.01318 | ||||||||
\(664\) | 2.04557e7 | 1.80051 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −550377. | −0.0480811 | ||||||||
\(667\) | 1.90447e7 | 1.65752 | ||||||||
\(668\) | 3.95149e6 | 0.342625 | ||||||||
\(669\) | −4.57719e6 | −0.395398 | ||||||||
\(670\) | 4.41294e6 | 0.379788 | ||||||||
\(671\) | 5.27723e6 | 0.452481 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.07466e6 | 0.602099 | 0.301050 | − | 0.953608i | \(-0.402663\pi\) | ||||
0.301050 | + | 0.953608i | \(0.402663\pi\) | |||||||
\(674\) | 1.08040e7 | 0.916082 | ||||||||
\(675\) | 565645. | 0.0477842 | ||||||||
\(676\) | 5.59243e6 | 0.470689 | ||||||||
\(677\) | 1.29681e7 | 1.08744 | 0.543720 | − | 0.839267i | \(-0.317015\pi\) | ||||
0.543720 | + | 0.839267i | \(0.317015\pi\) | |||||||
\(678\) | 1.31582e7 | 1.09932 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.01697e7 | −0.843402 | ||||||||
\(681\) | 2.25728e7 | 1.86517 | ||||||||
\(682\) | −1.03531e6 | −0.0852337 | ||||||||
\(683\) | 1.23817e6 | 0.101561 | 0.0507806 | − | 0.998710i | \(-0.483829\pi\) | ||||
0.0507806 | + | 0.998710i | \(0.483829\pi\) | |||||||
\(684\) | 68348.5 | 0.00558584 | ||||||||
\(685\) | 1.00611e6 | 0.0819256 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.56983e6 | −0.207736 | ||||||||
\(688\) | 1.81987e6 | 0.146578 | ||||||||
\(689\) | 6.21366e6 | 0.498654 | ||||||||
\(690\) | −5.14853e6 | −0.411681 | ||||||||
\(691\) | 1.48745e7 | 1.18508 | 0.592541 | − | 0.805541i | \(-0.298125\pi\) | ||||
0.592541 | + | 0.805541i | \(0.298125\pi\) | |||||||
\(692\) | 2.93036e6 | 0.232624 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.08521e6 | −0.637225 | ||||||||
\(695\) | 9.92622e6 | 0.779510 | ||||||||
\(696\) | 2.85081e7 | 2.23072 | ||||||||
\(697\) | 7.30283e6 | 0.569389 | ||||||||
\(698\) | −8.64719e6 | −0.671795 | ||||||||
\(699\) | −3.23313e6 | −0.250282 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.89434e7 | 1.45601 | 0.728004 | − | 0.685573i | \(-0.240448\pi\) | ||||
0.728004 | + | 0.685573i | \(0.240448\pi\) | |||||||
\(702\) | −843528. | −0.0646036 | ||||||||
\(703\) | −13932.3 | −0.00106325 | ||||||||
\(704\) | −4.01517e6 | −0.305332 | ||||||||
\(705\) | −9.78965e6 | −0.741813 | ||||||||
\(706\) | −1.25769e7 | −0.949643 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.24318e7 | 0.932074 | ||||||||
\(709\) | 1.10355e7 | 0.824472 | 0.412236 | − | 0.911077i | \(-0.364748\pi\) | ||||
0.412236 | + | 0.911077i | \(0.364748\pi\) | |||||||
\(710\) | 4.36790e6 | 0.325182 | ||||||||
\(711\) | 2.96240e6 | 0.219771 | ||||||||
\(712\) | −2.44130e6 | −0.180476 | ||||||||
\(713\) | 4.42846e6 | 0.326234 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.03010e6 | −0.0753552 | ||||||||
\(716\) | 2.51864e6 | 0.183605 | ||||||||
\(717\) | −1.22239e7 | −0.887997 | ||||||||
\(718\) | 4.97812e6 | 0.360375 | ||||||||
\(719\) | 4.65186e6 | 0.335587 | 0.167793 | − | 0.985822i | \(-0.446336\pi\) | ||||
0.167793 | + | 0.985822i | \(0.446336\pi\) | |||||||
\(720\) | −581120. | −0.0417767 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.22553e6 | 0.658641 | ||||||||
\(723\) | −536974. | −0.0382039 | ||||||||
\(724\) | 1.13340e7 | 0.803594 | ||||||||
\(725\) | −4.53314e6 | −0.320298 | ||||||||
\(726\) | −1.05029e7 | −0.739553 | ||||||||
\(727\) | −1.87498e7 | −1.31571 | −0.657857 | − | 0.753143i | \(-0.728537\pi\) | ||||
−0.657857 | + | 0.753143i | \(0.728537\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.90098e6 | −0.620325 | ||||||||
\(730\) | −3.91432e6 | −0.271862 | ||||||||
\(731\) | 3.41087e7 | 2.36087 | ||||||||
\(732\) | −1.22134e7 | −0.842482 | ||||||||
\(733\) | 1.08016e7 | 0.742557 | 0.371279 | − | 0.928521i | \(-0.378919\pi\) | ||||
0.371279 | + | 0.928521i | \(0.378919\pi\) | |||||||
\(734\) | 3.61664e6 | 0.247779 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.45539e7 | 0.990338 | ||||||||
\(737\) | 7.80351e6 | 0.529202 | ||||||||
\(738\) | 2.49855e6 | 0.168868 | ||||||||
\(739\) | 1.72048e7 | 1.15888 | 0.579442 | − | 0.815014i | \(-0.303271\pi\) | ||||
0.579442 | + | 0.815014i | \(0.303271\pi\) | |||||||
\(740\) | −334427. | −0.0224503 | ||||||||
\(741\) | 99318.7 | 0.00664486 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.25027e6 | 0.415362 | 0.207681 | − | 0.978197i | \(-0.433408\pi\) | ||||
0.207681 | + | 0.978197i | \(0.433408\pi\) | |||||||
\(744\) | 6.62897e6 | 0.439050 | ||||||||
\(745\) | −6.09696e6 | −0.402460 | ||||||||
\(746\) | 3.67385e6 | 0.241699 | ||||||||
\(747\) | 2.19079e7 | 1.43648 | ||||||||
\(748\) | −6.50021e6 | −0.424789 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.22549e6 | 0.0795527 | ||||||||
\(751\) | −1.71447e7 | −1.10925 | −0.554626 | − | 0.832099i | \(-0.687139\pi\) | ||||
−0.554626 | + | 0.832099i | \(0.687139\pi\) | |||||||
\(752\) | −2.16232e6 | −0.139436 | ||||||||
\(753\) | −3.26919e7 | −2.10113 | ||||||||
\(754\) | 6.76012e6 | 0.433038 | ||||||||
\(755\) | 1.21759e7 | 0.777382 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.56731e7 | −1.62831 | −0.814157 | − | 0.580645i | \(-0.802800\pi\) | ||||
−0.814157 | + | 0.580645i | \(0.802800\pi\) | |||||||
\(758\) | −1.23272e7 | −0.779279 | ||||||||
\(759\) | −9.10429e6 | −0.573643 | ||||||||
\(760\) | −88077.7 | −0.00553136 | ||||||||
\(761\) | −198469. | −0.0124231 | −0.00621156 | − | 0.999981i | \(-0.501977\pi\) | ||||
−0.00621156 | + | 0.999981i | \(0.501977\pi\) | |||||||
\(762\) | 8.56930e6 | 0.534635 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.62272e6 | 0.162562 | ||||||||
\(765\) | −1.08916e7 | −0.672881 | ||||||||
\(766\) | 1.52422e7 | 0.938591 | ||||||||
\(767\) | 8.15573e6 | 0.500581 | ||||||||
\(768\) | 2.32036e7 | 1.41956 | ||||||||
\(769\) | 3.50740e6 | 0.213880 | 0.106940 | − | 0.994265i | \(-0.465895\pi\) | ||||
0.106940 | + | 0.994265i | \(0.465895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.42954e7 | 0.866083 | ||||||||
\(772\) | −6.59185e6 | −0.398074 | ||||||||
\(773\) | −1.80013e7 | −1.08356 | −0.541782 | − | 0.840519i | \(-0.682250\pi\) | ||||
−0.541782 | + | 0.840519i | \(0.682250\pi\) | |||||||
\(774\) | 1.16698e7 | 0.700181 | ||||||||
\(775\) | −1.05409e6 | −0.0630410 | ||||||||
\(776\) | 2.11816e7 | 1.26271 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.90658e7 | 1.12929 | ||||||||
\(779\) | 63248.5 | 0.00373428 | ||||||||
\(780\) | 2.38402e6 | 0.140305 | ||||||||
\(781\) | 7.72387e6 | 0.453114 | ||||||||
\(782\) | −2.13138e7 | −1.24636 | ||||||||
\(783\) | −6.56422e6 | −0.382630 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.46639e6 | 0.200772 | ||||||||
\(786\) | 9.87116e6 | 0.569917 | ||||||||
\(787\) | 1.79041e7 | 1.03042 | 0.515211 | − | 0.857063i | \(-0.327714\pi\) | ||||
0.515211 | + | 0.857063i | \(0.327714\pi\) | |||||||
\(788\) | −1.52034e7 | −0.872216 | ||||||||
\(789\) | −4.01687e7 | −2.29718 | ||||||||
\(790\) | −1.37987e6 | −0.0786630 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.15271e6 | −0.348541 | ||||||||
\(793\) | −8.01249e6 | −0.452464 | ||||||||
\(794\) | −2.00045e7 | −1.12610 | ||||||||
\(795\) | −1.30719e7 | −0.733537 | ||||||||
\(796\) | 3.87982e6 | 0.217035 | ||||||||
\(797\) | −7.45389e6 | −0.415659 | −0.207829 | − | 0.978165i | \(-0.566640\pi\) | ||||
−0.207829 | + | 0.978165i | \(0.566640\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.05271e7 | −2.24584 | ||||||||
\(800\) | −3.46420e6 | −0.191372 | ||||||||
\(801\) | −2.61460e6 | −0.143987 | ||||||||
\(802\) | 1.43071e7 | 0.785444 | ||||||||
\(803\) | −6.92180e6 | −0.378818 | ||||||||
\(804\) | −1.80602e7 | −0.985331 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.57193e6 | 0.0852306 | ||||||||
\(807\) | −2.03119e7 | −1.09791 | ||||||||
\(808\) | −3.73682e7 | −2.01360 | ||||||||
\(809\) | −7.85717e6 | −0.422080 | −0.211040 | − | 0.977477i | \(-0.567685\pi\) | ||||
−0.211040 | + | 0.977477i | \(0.567685\pi\) | |||||||
\(810\) | 6.30212e6 | 0.337500 | ||||||||
\(811\) | −550490. | −0.0293899 | −0.0146949 | − | 0.999892i | \(-0.504678\pi\) | ||||
−0.0146949 | + | 0.999892i | \(0.504678\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.68240e7 | −1.42330 | ||||||||
\(814\) | 453333. | 0.0239804 | ||||||||
\(815\) | 8.24901e6 | 0.435019 | ||||||||
\(816\) | −5.32864e6 | −0.280150 | ||||||||
\(817\) | 295410. | 0.0154835 | ||||||||
\(818\) | −2.14952e6 | −0.112320 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.51820e6 | 0.0788487 | ||||||||
\(821\) | 2.66311e7 | 1.37890 | 0.689448 | − | 0.724335i | \(-0.257853\pi\) | ||||
0.689448 | + | 0.724335i | \(0.257853\pi\) | |||||||
\(822\) | 3.15642e6 | 0.162935 | ||||||||
\(823\) | 1.47532e7 | 0.759253 | 0.379627 | − | 0.925140i | \(-0.376052\pi\) | ||||
0.379627 | + | 0.925140i | \(0.376052\pi\) | |||||||
\(824\) | 1.69300e7 | 0.868638 | ||||||||
\(825\) | 2.16706e6 | 0.110850 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.54872e7 | −1.29586 | −0.647931 | − | 0.761699i | \(-0.724365\pi\) | ||||
−0.647931 | + | 0.761699i | \(0.724365\pi\) | |||||||
\(828\) | 9.51273e6 | 0.482202 | ||||||||
\(829\) | 941474. | 0.0475797 | 0.0237899 | − | 0.999717i | \(-0.492427\pi\) | ||||
0.0237899 | + | 0.999717i | \(0.492427\pi\) | |||||||
\(830\) | −1.02046e7 | −0.514161 | ||||||||
\(831\) | −3.94291e6 | −0.198068 | ||||||||
\(832\) | 6.09628e6 | 0.305321 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.11410e7 | 1.55030 | ||||||||
\(835\) | −5.45359e6 | −0.270686 | ||||||||
\(836\) | −56297.1 | −0.00278593 | ||||||||
\(837\) | −1.52638e6 | −0.0753092 | ||||||||
\(838\) | −245850. | −0.0120937 | ||||||||
\(839\) | 2.99251e7 | 1.46768 | 0.733839 | − | 0.679323i | \(-0.237727\pi\) | ||||
0.733839 | + | 0.679323i | \(0.237727\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.20952e7 | 1.56477 | ||||||||
\(842\) | 1.09945e7 | 0.534436 | ||||||||
\(843\) | −4.72376e7 | −2.28938 | ||||||||
\(844\) | −1.39662e7 | −0.674873 | ||||||||
\(845\) | −7.71832e6 | −0.371861 | ||||||||
\(846\) | −1.38657e7 | −0.666065 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.88730e6 | −0.137880 | ||||||||
\(849\) | −5.06226e7 | −2.41032 | ||||||||
\(850\) | 5.07325e6 | 0.240846 | ||||||||
\(851\) | −1.93909e6 | −0.0917856 | ||||||||
\(852\) | −1.78759e7 | −0.843661 | ||||||||
\(853\) | 1.25646e7 | 0.591254 | 0.295627 | − | 0.955303i | \(-0.404471\pi\) | ||||
0.295627 | + | 0.955303i | \(0.404471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −94330.2 | −0.00441301 | ||||||||
\(856\) | −3.21922e7 | −1.50164 | ||||||||
\(857\) | −2.20590e7 | −1.02597 | −0.512985 | − | 0.858398i | \(-0.671460\pi\) | ||||
−0.512985 | + | 0.858398i | \(0.671460\pi\) | |||||||
\(858\) | −3.23167e6 | −0.149868 | ||||||||
\(859\) | −1.44949e6 | −0.0670243 | −0.0335122 | − | 0.999438i | \(-0.510669\pi\) | ||||
−0.0335122 | + | 0.999438i | \(0.510669\pi\) | |||||||
\(860\) | 7.09094e6 | 0.326932 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.27493e7 | −0.584413 | ||||||||
\(863\) | −3.08530e7 | −1.41016 | −0.705082 | − | 0.709125i | \(-0.749090\pi\) | ||||
−0.705082 | + | 0.709125i | \(0.749090\pi\) | |||||||
\(864\) | −5.01634e6 | −0.228614 | ||||||||
\(865\) | −4.04429e6 | −0.183781 | ||||||||
\(866\) | 2.23805e7 | 1.01409 | ||||||||
\(867\) | −6.99872e7 | −3.16206 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.44006e6 | −0.109610 | ||||||||
\(870\) | −1.42216e7 | −0.637014 | ||||||||
\(871\) | −1.18482e7 | −0.529183 | ||||||||
\(872\) | −5.49195e6 | −0.244588 | ||||||||
\(873\) | 2.26853e7 | 1.00741 | ||||||||
\(874\) | −184595. | −0.00817414 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.60196e7 | 0.705327 | ||||||||
\(877\) | 3.59009e7 | 1.57618 | 0.788090 | − | 0.615560i | \(-0.211070\pi\) | ||||
0.788090 | + | 0.615560i | \(0.211070\pi\) | |||||||
\(878\) | −219175. | −0.00959523 | ||||||||
\(879\) | 2.05896e7 | 0.898828 | ||||||||
\(880\) | 478655. | 0.0208361 | ||||||||
\(881\) | −4.08291e6 | −0.177227 | −0.0886135 | − | 0.996066i | \(-0.528244\pi\) | ||||
−0.0886135 | + | 0.996066i | \(0.528244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.66369e6 | 0.158131 | 0.0790655 | − | 0.996869i | \(-0.474806\pi\) | ||||
0.0790655 | + | 0.996869i | \(0.474806\pi\) | |||||||
\(884\) | 9.86934e6 | 0.424774 | ||||||||
\(885\) | −1.71576e7 | −0.736372 | ||||||||
\(886\) | 1.23185e7 | 0.527199 | ||||||||
\(887\) | −2.52478e7 | −1.07749 | −0.538746 | − | 0.842468i | \(-0.681102\pi\) | ||||
−0.538746 | + | 0.842468i | \(0.681102\pi\) | |||||||
\(888\) | −2.90263e6 | −0.123526 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.21787e6 | 0.0515377 | ||||||||
\(891\) | 1.11442e7 | 0.470278 | ||||||||
\(892\) | −3.93927e6 | −0.165769 | ||||||||
\(893\) | −350998. | −0.0147291 | ||||||||
\(894\) | −1.91277e7 | −0.800420 | ||||||||
\(895\) | −3.47606e6 | −0.145054 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.38232e7 | 0.573623 | ||||||||
\(898\) | −2.50244e7 | −1.03556 | ||||||||
\(899\) | 1.22325e7 | 0.504798 | ||||||||
\(900\) | −2.26428e6 | −0.0931802 | ||||||||
\(901\) | −5.41151e7 | −2.22078 | ||||||||
\(902\) | −2.05800e6 | −0.0842227 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.13296e7 | 1.27507 | ||||||||
\(905\) | −1.56425e7 | −0.634868 | ||||||||
\(906\) | 3.81988e7 | 1.54607 | ||||||||
\(907\) | 3.59572e7 | 1.45134 | 0.725668 | − | 0.688045i | \(-0.241531\pi\) | ||||
0.725668 | + | 0.688045i | \(0.241531\pi\) | |||||||
\(908\) | 1.94268e7 | 0.781964 | ||||||||
\(909\) | −4.00210e7 | −1.60649 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.81358e6 | −0.272006 | −0.136003 | − | 0.990708i | \(-0.543426\pi\) | ||||
−0.136003 | + | 0.990708i | \(0.543426\pi\) | |||||||
\(912\) | −46150.4 | −0.00183734 | ||||||||
\(913\) | −1.80450e7 | −0.716441 | ||||||||
\(914\) | 3.03320e7 | 1.20098 | ||||||||
\(915\) | 1.68562e7 | 0.665590 | ||||||||
\(916\) | −2.21167e6 | −0.0870926 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7.34633e6 | 0.287716 | ||||||||
\(919\) | 1.37705e7 | 0.537848 | 0.268924 | − | 0.963161i | \(-0.413332\pi\) | ||||
0.268924 | + | 0.963161i | \(0.413332\pi\) | |||||||
\(920\) | −1.22586e7 | −0.477499 | ||||||||
\(921\) | −4.19859e6 | −0.163100 | ||||||||
\(922\) | 2.53470e7 | 0.981974 | ||||||||
\(923\) | −1.17272e7 | −0.453098 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 461555. | 0.0177365 | ||||||||
\(926\) | 6.06832e6 | 0.232563 | ||||||||
\(927\) | 1.81318e7 | 0.693015 | ||||||||
\(928\) | 4.02014e7 | 1.53240 | ||||||||
\(929\) | −5.04155e7 | −1.91657 | −0.958285 | − | 0.285814i | \(-0.907736\pi\) | ||||
−0.958285 | + | 0.285814i | \(0.907736\pi\) | |||||||
\(930\) | −3.30694e6 | −0.125377 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.78252e6 | −0.104930 | ||||||||
\(933\) | 1.34926e7 | 0.507449 | ||||||||
\(934\) | 1.80891e7 | 0.678500 | ||||||||
\(935\) | 8.97116e6 | 0.335598 | ||||||||
\(936\) | 9.34173e6 | 0.348528 | ||||||||
\(937\) | −7.60181e6 | −0.282858 | −0.141429 | − | 0.989948i | \(-0.545170\pi\) | ||||
−0.141429 | + | 0.989948i | \(0.545170\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.73422e7 | −0.641861 | ||||||||
\(940\) | −8.42526e6 | −0.311002 | ||||||||
\(941\) | 1.02579e6 | 0.0377647 | 0.0188824 | − | 0.999822i | \(-0.493989\pi\) | ||||
0.0188824 | + | 0.999822i | \(0.493989\pi\) | |||||||
\(942\) | 1.08749e7 | 0.399299 | ||||||||
\(943\) | 8.80292e6 | 0.322365 | ||||||||
\(944\) | −3.78972e6 | −0.138413 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.61214e6 | −0.349214 | ||||||||
\(947\) | 3.46475e6 | 0.125544 | 0.0627722 | − | 0.998028i | \(-0.480006\pi\) | ||||
0.0627722 | + | 0.998028i | \(0.480006\pi\) | |||||||
\(948\) | 5.64719e6 | 0.204085 | ||||||||
\(949\) | 1.05095e7 | 0.378804 | ||||||||
\(950\) | 43938.5 | 0.00157956 | ||||||||
\(951\) | −2.21309e7 | −0.793500 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −728447. | −0.0259816 | −0.0129908 | − | 0.999916i | \(-0.504135\pi\) | ||||
−0.0129908 | + | 0.999916i | \(0.504135\pi\) | |||||||
\(954\) | −1.85146e7 | −0.658634 | ||||||||
\(955\) | −3.61971e6 | −0.128430 | ||||||||
\(956\) | −1.05202e7 | −0.372290 | ||||||||
\(957\) | −2.51484e7 | −0.887626 | ||||||||
\(958\) | 6.70337e6 | 0.235982 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.28250e7 | −0.449138 | ||||||||
\(961\) | −2.57847e7 | −0.900646 | ||||||||
\(962\) | −688301. | −0.0239795 | ||||||||
\(963\) | −3.44775e7 | −1.19804 | ||||||||
\(964\) | −462136. | −0.0160168 | ||||||||
\(965\) | 9.09764e6 | 0.314493 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.01305e7 | 1.72399 | 0.861997 | − | 0.506913i | \(-0.169213\pi\) | ||||
0.861997 | + | 0.506913i | \(0.169213\pi\) | |||||||
\(968\) | −2.50074e7 | −0.857790 | ||||||||
\(969\) | −864971. | −0.0295932 | ||||||||
\(970\) | −1.05667e7 | −0.360586 | ||||||||
\(971\) | −2.12323e7 | −0.722684 | −0.361342 | − | 0.932433i | \(-0.617681\pi\) | ||||
−0.361342 | + | 0.932433i | \(0.617681\pi\) | |||||||
\(972\) | −2.18081e7 | −0.740374 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.86659e7 | −0.630451 | ||||||||
\(975\) | −3.29027e6 | −0.110846 | ||||||||
\(976\) | 3.72316e6 | 0.125109 | ||||||||
\(977\) | −5.47337e6 | −0.183450 | −0.0917251 | − | 0.995784i | \(-0.529238\pi\) | ||||
−0.0917251 | + | 0.995784i | \(0.529238\pi\) | |||||||
\(978\) | 2.58792e7 | 0.865173 | ||||||||
\(979\) | 2.15359e6 | 0.0718135 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.88182e6 | −0.195137 | ||||||||
\(982\) | 1.63956e6 | 0.0542561 | ||||||||
\(983\) | 1.74099e7 | 0.574663 | 0.287331 | − | 0.957831i | \(-0.407232\pi\) | ||||
0.287331 | + | 0.957831i | \(0.407232\pi\) | |||||||
\(984\) | 1.31771e7 | 0.433842 | ||||||||
\(985\) | 2.09827e7 | 0.689081 | ||||||||
\(986\) | −5.88742e7 | −1.92856 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 85476.6 | 0.00278583 | ||||||||
\(989\) | 4.11151e7 | 1.33663 | ||||||||
\(990\) | 3.06935e6 | 0.0995309 | ||||||||
\(991\) | 2.81682e7 | 0.911119 | 0.455559 | − | 0.890205i | \(-0.349439\pi\) | ||||
0.455559 | + | 0.890205i | \(0.349439\pi\) | |||||||
\(992\) | 9.34803e6 | 0.301607 | ||||||||
\(993\) | 3.62339e7 | 1.16612 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.35468e6 | −0.171465 | ||||||||
\(996\) | 4.17628e7 | 1.33395 | ||||||||
\(997\) | 2.73631e7 | 0.871822 | 0.435911 | − | 0.899990i | \(-0.356426\pi\) | ||||
0.435911 | + | 0.899990i | \(0.356426\pi\) | |||||||
\(998\) | 666575. | 0.0211847 | ||||||||
\(999\) | 668355. | 0.0211882 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 245.6.a.m.1.3 | yes | 10 | |
7.6 | odd | 2 | 245.6.a.l.1.3 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.6.a.l.1.3 | ✓ | 10 | 7.6 | odd | 2 | ||
245.6.a.m.1.3 | yes | 10 | 1.1 | even | 1 | trivial |