Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(6.89650425196\) |
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: | \( x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + 8437093 x^{2} - 5752252 x - 22734604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(3.50018\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50018 | −0.441974 | −0.220987 | − | 0.975277i | \(-0.570928\pi\) | ||||
−0.220987 | + | 0.975277i | \(0.570928\pi\) | |||||||
\(3\) | 16.8892 | 1.08344 | 0.541720 | − | 0.840559i | \(-0.317773\pi\) | ||||
0.541720 | + | 0.840559i | \(0.317773\pi\) | |||||||
\(4\) | −25.7491 | −0.804659 | ||||||||
\(5\) | 47.4635 | 0.849053 | 0.424526 | − | 0.905416i | \(-0.360441\pi\) | ||||
0.424526 | + | 0.905416i | \(0.360441\pi\) | |||||||
\(6\) | −42.2260 | −0.478853 | ||||||||
\(7\) | 67.4603 | 0.520359 | 0.260180 | − | 0.965560i | \(-0.416218\pi\) | ||||
0.260180 | + | 0.965560i | \(0.416218\pi\) | |||||||
\(8\) | 144.383 | 0.797612 | ||||||||
\(9\) | 42.2439 | 0.173843 | ||||||||
\(10\) | −118.667 | −0.375259 | ||||||||
\(11\) | 81.3987 | 0.202832 | 0.101416 | − | 0.994844i | \(-0.467663\pi\) | ||||
0.101416 | + | 0.994844i | \(0.467663\pi\) | |||||||
\(12\) | −434.881 | −0.871800 | ||||||||
\(13\) | 1058.72 | 1.73750 | 0.868749 | − | 0.495253i | \(-0.164925\pi\) | ||||
0.868749 | + | 0.495253i | \(0.164925\pi\) | |||||||
\(14\) | −168.663 | −0.229985 | ||||||||
\(15\) | 801.619 | 0.919898 | ||||||||
\(16\) | 462.986 | 0.452135 | ||||||||
\(17\) | 251.378 | 0.210962 | 0.105481 | − | 0.994421i | \(-0.466362\pi\) | ||||
0.105481 | + | 0.994421i | \(0.466362\pi\) | |||||||
\(18\) | −105.617 | −0.0768341 | ||||||||
\(19\) | 1612.95 | 1.02503 | 0.512515 | − | 0.858679i | \(-0.328714\pi\) | ||||
0.512515 | + | 0.858679i | \(0.328714\pi\) | |||||||
\(20\) | −1222.14 | −0.683198 | ||||||||
\(21\) | 1139.35 | 0.563778 | ||||||||
\(22\) | −203.512 | −0.0896463 | ||||||||
\(23\) | −32.7403 | −0.0129052 | −0.00645258 | − | 0.999979i | \(-0.502054\pi\) | ||||
−0.00645258 | + | 0.999979i | \(0.502054\pi\) | |||||||
\(24\) | 2438.51 | 0.864165 | ||||||||
\(25\) | −872.217 | −0.279109 | ||||||||
\(26\) | −2647.00 | −0.767929 | ||||||||
\(27\) | −3390.60 | −0.895092 | ||||||||
\(28\) | −1737.04 | −0.418712 | ||||||||
\(29\) | −2583.75 | −0.570499 | −0.285249 | − | 0.958453i | \(-0.592076\pi\) | ||||
−0.285249 | + | 0.958453i | \(0.592076\pi\) | |||||||
\(30\) | −2004.19 | −0.406571 | ||||||||
\(31\) | −7206.51 | −1.34685 | −0.673427 | − | 0.739254i | \(-0.735179\pi\) | ||||
−0.673427 | + | 0.739254i | \(0.735179\pi\) | |||||||
\(32\) | −5777.81 | −0.997444 | ||||||||
\(33\) | 1374.76 | 0.219756 | ||||||||
\(34\) | −628.491 | −0.0932399 | ||||||||
\(35\) | 3201.90 | 0.441812 | ||||||||
\(36\) | −1087.74 | −0.139884 | ||||||||
\(37\) | −6174.39 | −0.741463 | −0.370731 | − | 0.928740i | \(-0.620893\pi\) | ||||
−0.370731 | + | 0.928740i | \(0.620893\pi\) | |||||||
\(38\) | −4032.66 | −0.453036 | ||||||||
\(39\) | 17881.0 | 1.88248 | ||||||||
\(40\) | 6852.93 | 0.677215 | ||||||||
\(41\) | 15514.4 | 1.44137 | 0.720685 | − | 0.693262i | \(-0.243827\pi\) | ||||
0.720685 | + | 0.693262i | \(0.243827\pi\) | |||||||
\(42\) | −2848.58 | −0.249175 | ||||||||
\(43\) | 1849.00 | 0.152499 | ||||||||
\(44\) | −2095.94 | −0.163210 | ||||||||
\(45\) | 2005.04 | 0.147602 | ||||||||
\(46\) | 81.8569 | 0.00570375 | ||||||||
\(47\) | −1692.39 | −0.111752 | −0.0558760 | − | 0.998438i | \(-0.517795\pi\) | ||||
−0.0558760 | + | 0.998438i | \(0.517795\pi\) | |||||||
\(48\) | 7819.45 | 0.489861 | ||||||||
\(49\) | −12256.1 | −0.729226 | ||||||||
\(50\) | 2180.70 | 0.123359 | ||||||||
\(51\) | 4245.56 | 0.228565 | ||||||||
\(52\) | −27261.2 | −1.39809 | ||||||||
\(53\) | −25612.3 | −1.25245 | −0.626223 | − | 0.779644i | \(-0.715400\pi\) | ||||
−0.626223 | + | 0.779644i | \(0.715400\pi\) | |||||||
\(54\) | 8477.13 | 0.395607 | ||||||||
\(55\) | 3863.47 | 0.172215 | ||||||||
\(56\) | 9740.14 | 0.415045 | ||||||||
\(57\) | 27241.3 | 1.11056 | ||||||||
\(58\) | 6459.83 | 0.252146 | ||||||||
\(59\) | 24532.0 | 0.917495 | 0.458748 | − | 0.888567i | \(-0.348298\pi\) | ||||
0.458748 | + | 0.888567i | \(0.348298\pi\) | |||||||
\(60\) | −20641.0 | −0.740204 | ||||||||
\(61\) | 8209.11 | 0.282470 | 0.141235 | − | 0.989976i | \(-0.454893\pi\) | ||||
0.141235 | + | 0.989976i | \(0.454893\pi\) | |||||||
\(62\) | 18017.6 | 0.595275 | ||||||||
\(63\) | 2849.78 | 0.0904608 | ||||||||
\(64\) | −369.967 | −0.0112905 | ||||||||
\(65\) | 50250.7 | 1.47523 | ||||||||
\(66\) | −3437.14 | −0.0971264 | ||||||||
\(67\) | −12302.3 | −0.334810 | −0.167405 | − | 0.985888i | \(-0.553539\pi\) | ||||
−0.167405 | + | 0.985888i | \(0.553539\pi\) | |||||||
\(68\) | −6472.75 | −0.169753 | ||||||||
\(69\) | −552.957 | −0.0139820 | ||||||||
\(70\) | −8005.34 | −0.195270 | ||||||||
\(71\) | 18712.0 | 0.440530 | 0.220265 | − | 0.975440i | \(-0.429308\pi\) | ||||
0.220265 | + | 0.975440i | \(0.429308\pi\) | |||||||
\(72\) | 6099.31 | 0.138659 | ||||||||
\(73\) | −12126.5 | −0.266334 | −0.133167 | − | 0.991094i | \(-0.542515\pi\) | ||||
−0.133167 | + | 0.991094i | \(0.542515\pi\) | |||||||
\(74\) | 15437.1 | 0.327707 | ||||||||
\(75\) | −14731.0 | −0.302398 | ||||||||
\(76\) | −41531.9 | −0.824799 | ||||||||
\(77\) | 5491.18 | 0.105545 | ||||||||
\(78\) | −44705.7 | −0.832005 | ||||||||
\(79\) | −52372.8 | −0.944144 | −0.472072 | − | 0.881560i | \(-0.656494\pi\) | ||||
−0.472072 | + | 0.881560i | \(0.656494\pi\) | |||||||
\(80\) | 21974.9 | 0.383886 | ||||||||
\(81\) | −67529.7 | −1.14362 | ||||||||
\(82\) | −38788.9 | −0.637048 | ||||||||
\(83\) | 28935.9 | 0.461043 | 0.230521 | − | 0.973067i | \(-0.425957\pi\) | ||||
0.230521 | + | 0.973067i | \(0.425957\pi\) | |||||||
\(84\) | −29337.2 | −0.453649 | ||||||||
\(85\) | 11931.3 | 0.179118 | ||||||||
\(86\) | −4622.84 | −0.0674004 | ||||||||
\(87\) | −43637.3 | −0.618101 | ||||||||
\(88\) | 11752.6 | 0.161781 | ||||||||
\(89\) | 117315. | 1.56992 | 0.784962 | − | 0.619544i | \(-0.212683\pi\) | ||||
0.784962 | + | 0.619544i | \(0.212683\pi\) | |||||||
\(90\) | −5012.97 | −0.0652362 | ||||||||
\(91\) | 71421.8 | 0.904123 | ||||||||
\(92\) | 843.034 | 0.0103843 | ||||||||
\(93\) | −121712. | −1.45924 | ||||||||
\(94\) | 4231.28 | 0.0493915 | ||||||||
\(95\) | 76556.1 | 0.870304 | ||||||||
\(96\) | −97582.5 | −1.08067 | ||||||||
\(97\) | −147143. | −1.58785 | −0.793925 | − | 0.608016i | \(-0.791966\pi\) | ||||
−0.793925 | + | 0.608016i | \(0.791966\pi\) | |||||||
\(98\) | 30642.5 | 0.322299 | ||||||||
\(99\) | 3438.60 | 0.0352609 | ||||||||
\(100\) | 22458.8 | 0.224588 | ||||||||
\(101\) | −118561. | −1.15648 | −0.578239 | − | 0.815867i | \(-0.696260\pi\) | ||||
−0.578239 | + | 0.815867i | \(0.696260\pi\) | |||||||
\(102\) | −10614.7 | −0.101020 | ||||||||
\(103\) | 49153.5 | 0.456522 | 0.228261 | − | 0.973600i | \(-0.426696\pi\) | ||||
0.228261 | + | 0.973600i | \(0.426696\pi\) | |||||||
\(104\) | 152862. | 1.38585 | ||||||||
\(105\) | 54077.4 | 0.478677 | ||||||||
\(106\) | 64035.4 | 0.553549 | ||||||||
\(107\) | −156632. | −1.32258 | −0.661290 | − | 0.750130i | \(-0.729991\pi\) | ||||
−0.661290 | + | 0.750130i | \(0.729991\pi\) | |||||||
\(108\) | 87304.9 | 0.720244 | ||||||||
\(109\) | 208919. | 1.68427 | 0.842135 | − | 0.539267i | \(-0.181299\pi\) | ||||
0.842135 | + | 0.539267i | \(0.181299\pi\) | |||||||
\(110\) | −9659.37 | −0.0761144 | ||||||||
\(111\) | −104280. | −0.803331 | ||||||||
\(112\) | 31233.2 | 0.235273 | ||||||||
\(113\) | 33491.2 | 0.246737 | 0.123369 | − | 0.992361i | \(-0.460630\pi\) | ||||
0.123369 | + | 0.992361i | \(0.460630\pi\) | |||||||
\(114\) | −68108.3 | −0.490838 | ||||||||
\(115\) | −1553.97 | −0.0109572 | ||||||||
\(116\) | 66529.1 | 0.459057 | ||||||||
\(117\) | 44724.6 | 0.302052 | ||||||||
\(118\) | −61334.6 | −0.405509 | ||||||||
\(119\) | 16958.0 | 0.109776 | ||||||||
\(120\) | 115740. | 0.733722 | ||||||||
\(121\) | −154425. | −0.958859 | ||||||||
\(122\) | −20524.3 | −0.124844 | ||||||||
\(123\) | 262025. | 1.56164 | ||||||||
\(124\) | 185561. | 1.08376 | ||||||||
\(125\) | −189722. | −1.08603 | ||||||||
\(126\) | −7124.98 | −0.0399813 | ||||||||
\(127\) | 72430.2 | 0.398483 | 0.199242 | − | 0.979950i | \(-0.436152\pi\) | ||||
0.199242 | + | 0.979950i | \(0.436152\pi\) | |||||||
\(128\) | 185815. | 1.00243 | ||||||||
\(129\) | 31228.1 | 0.165223 | ||||||||
\(130\) | −125636. | −0.652012 | ||||||||
\(131\) | −73042.1 | −0.371873 | −0.185937 | − | 0.982562i | \(-0.559532\pi\) | ||||
−0.185937 | + | 0.982562i | \(0.559532\pi\) | |||||||
\(132\) | −35398.7 | −0.176829 | ||||||||
\(133\) | 108810. | 0.533383 | ||||||||
\(134\) | 30757.9 | 0.147977 | ||||||||
\(135\) | −160930. | −0.759980 | ||||||||
\(136\) | 36294.8 | 0.168266 | ||||||||
\(137\) | 290889. | 1.32412 | 0.662058 | − | 0.749453i | \(-0.269683\pi\) | ||||
0.662058 | + | 0.749453i | \(0.269683\pi\) | |||||||
\(138\) | 1382.49 | 0.00617967 | ||||||||
\(139\) | −375146. | −1.64689 | −0.823443 | − | 0.567399i | \(-0.807950\pi\) | ||||
−0.823443 | + | 0.567399i | \(0.807950\pi\) | |||||||
\(140\) | −82446.0 | −0.355508 | ||||||||
\(141\) | −28583.0 | −0.121077 | ||||||||
\(142\) | −46783.5 | −0.194703 | ||||||||
\(143\) | 86178.7 | 0.352420 | ||||||||
\(144\) | 19558.3 | 0.0786005 | ||||||||
\(145\) | −122634. | −0.484384 | ||||||||
\(146\) | 30318.3 | 0.117713 | ||||||||
\(147\) | −206995. | −0.790073 | ||||||||
\(148\) | 158985. | 0.596625 | ||||||||
\(149\) | 431136. | 1.59092 | 0.795460 | − | 0.606006i | \(-0.207229\pi\) | ||||
0.795460 | + | 0.606006i | \(0.207229\pi\) | |||||||
\(150\) | 36830.2 | 0.133652 | ||||||||
\(151\) | 17252.4 | 0.0615755 | 0.0307878 | − | 0.999526i | \(-0.490198\pi\) | ||||
0.0307878 | + | 0.999526i | \(0.490198\pi\) | |||||||
\(152\) | 232883. | 0.817576 | ||||||||
\(153\) | 10619.2 | 0.0366743 | ||||||||
\(154\) | −13729.0 | −0.0466483 | ||||||||
\(155\) | −342046. | −1.14355 | ||||||||
\(156\) | −460418. | −1.51475 | ||||||||
\(157\) | −139497. | −0.451663 | −0.225832 | − | 0.974166i | \(-0.572510\pi\) | ||||
−0.225832 | + | 0.974166i | \(0.572510\pi\) | |||||||
\(158\) | 130942. | 0.417287 | ||||||||
\(159\) | −432570. | −1.35695 | ||||||||
\(160\) | −274235. | −0.846883 | ||||||||
\(161\) | −2208.67 | −0.00671532 | ||||||||
\(162\) | 168837. | 0.505451 | ||||||||
\(163\) | −556197. | −1.63968 | −0.819841 | − | 0.572591i | \(-0.805938\pi\) | ||||
−0.819841 | + | 0.572591i | \(0.805938\pi\) | |||||||
\(164\) | −399482. | −1.15981 | ||||||||
\(165\) | 65250.7 | 0.186584 | ||||||||
\(166\) | −72345.0 | −0.203769 | ||||||||
\(167\) | −239206. | −0.663713 | −0.331857 | − | 0.943330i | \(-0.607675\pi\) | ||||
−0.331857 | + | 0.943330i | \(0.607675\pi\) | |||||||
\(168\) | 164503. | 0.449676 | ||||||||
\(169\) | 749603. | 2.01890 | ||||||||
\(170\) | −29830.4 | −0.0791656 | ||||||||
\(171\) | 68137.1 | 0.178194 | ||||||||
\(172\) | −47610.1 | −0.122709 | ||||||||
\(173\) | 79563.7 | 0.202116 | 0.101058 | − | 0.994881i | \(-0.467777\pi\) | ||||
0.101058 | + | 0.994881i | \(0.467777\pi\) | |||||||
\(174\) | 109101. | 0.273185 | ||||||||
\(175\) | −58840.0 | −0.145237 | ||||||||
\(176\) | 37686.5 | 0.0917073 | ||||||||
\(177\) | 414326. | 0.994051 | ||||||||
\(178\) | −293309. | −0.693865 | ||||||||
\(179\) | −95838.9 | −0.223568 | −0.111784 | − | 0.993733i | \(-0.535656\pi\) | ||||
−0.111784 | + | 0.993733i | \(0.535656\pi\) | |||||||
\(180\) | −51628.0 | −0.118769 | ||||||||
\(181\) | −219413. | −0.497813 | −0.248906 | − | 0.968528i | \(-0.580071\pi\) | ||||
−0.248906 | + | 0.968528i | \(0.580071\pi\) | |||||||
\(182\) | −178568. | −0.399599 | ||||||||
\(183\) | 138645. | 0.306039 | ||||||||
\(184\) | −4727.16 | −0.0102933 | ||||||||
\(185\) | −293058. | −0.629541 | ||||||||
\(186\) | 304302. | 0.644945 | ||||||||
\(187\) | 20461.8 | 0.0427898 | ||||||||
\(188\) | 43577.5 | 0.0899223 | ||||||||
\(189\) | −228731. | −0.465769 | ||||||||
\(190\) | −191404. | −0.384652 | ||||||||
\(191\) | 328729. | 0.652011 | 0.326005 | − | 0.945368i | \(-0.394297\pi\) | ||||
0.326005 | + | 0.945368i | \(0.394297\pi\) | |||||||
\(192\) | −6248.43 | −0.0122326 | ||||||||
\(193\) | 575743. | 1.11259 | 0.556295 | − | 0.830985i | \(-0.312222\pi\) | ||||
0.556295 | + | 0.830985i | \(0.312222\pi\) | |||||||
\(194\) | 367884. | 0.701788 | ||||||||
\(195\) | 848693. | 1.59832 | ||||||||
\(196\) | 315584. | 0.586779 | ||||||||
\(197\) | 962886. | 1.76770 | 0.883852 | − | 0.467768i | \(-0.154942\pi\) | ||||
0.883852 | + | 0.467768i | \(0.154942\pi\) | |||||||
\(198\) | −8597.12 | −0.0155844 | ||||||||
\(199\) | −760147. | −1.36071 | −0.680354 | − | 0.732884i | \(-0.738174\pi\) | ||||
−0.680354 | + | 0.732884i | \(0.738174\pi\) | |||||||
\(200\) | −125933. | −0.222621 | ||||||||
\(201\) | −207775. | −0.362747 | ||||||||
\(202\) | 296424. | 0.511133 | ||||||||
\(203\) | −174300. | −0.296864 | ||||||||
\(204\) | −109319. | −0.183917 | ||||||||
\(205\) | 736368. | 1.22380 | ||||||||
\(206\) | −122893. | −0.201771 | ||||||||
\(207\) | −1383.08 | −0.00224347 | ||||||||
\(208\) | 490175. | 0.785584 | ||||||||
\(209\) | 131292. | 0.207908 | ||||||||
\(210\) | −135203. | −0.211563 | ||||||||
\(211\) | −979789. | −1.51505 | −0.757524 | − | 0.652807i | \(-0.773591\pi\) | ||||
−0.757524 | + | 0.652807i | \(0.773591\pi\) | |||||||
\(212\) | 659493. | 1.00779 | ||||||||
\(213\) | 316031. | 0.477288 | ||||||||
\(214\) | 391610. | 0.584546 | ||||||||
\(215\) | 87760.0 | 0.129479 | ||||||||
\(216\) | −489546. | −0.713936 | ||||||||
\(217\) | −486153. | −0.700848 | ||||||||
\(218\) | −522336. | −0.744404 | ||||||||
\(219\) | −204806. | −0.288557 | ||||||||
\(220\) | −99480.7 | −0.138574 | ||||||||
\(221\) | 266140. | 0.366547 | ||||||||
\(222\) | 260720. | 0.355051 | ||||||||
\(223\) | 668754. | 0.900542 | 0.450271 | − | 0.892892i | \(-0.351327\pi\) | ||||
0.450271 | + | 0.892892i | \(0.351327\pi\) | |||||||
\(224\) | −389773. | −0.519029 | ||||||||
\(225\) | −36845.8 | −0.0485212 | ||||||||
\(226\) | −83734.2 | −0.109052 | ||||||||
\(227\) | −1.40720e6 | −1.81256 | −0.906280 | − | 0.422677i | \(-0.861090\pi\) | ||||
−0.906280 | + | 0.422677i | \(0.861090\pi\) | |||||||
\(228\) | −701439. | −0.893620 | ||||||||
\(229\) | 706746. | 0.890583 | 0.445292 | − | 0.895386i | \(-0.353100\pi\) | ||||
0.445292 | + | 0.895386i | \(0.353100\pi\) | |||||||
\(230\) | 3885.21 | 0.00484278 | ||||||||
\(231\) | 92741.4 | 0.114352 | ||||||||
\(232\) | −373050. | −0.455037 | ||||||||
\(233\) | 810873. | 0.978505 | 0.489252 | − | 0.872142i | \(-0.337270\pi\) | ||||
0.489252 | + | 0.872142i | \(0.337270\pi\) | |||||||
\(234\) | −111820. | −0.133499 | ||||||||
\(235\) | −80326.7 | −0.0948834 | ||||||||
\(236\) | −631678. | −0.738271 | ||||||||
\(237\) | −884533. | −1.02292 | ||||||||
\(238\) | −42398.2 | −0.0485182 | ||||||||
\(239\) | 81145.7 | 0.0918905 | 0.0459453 | − | 0.998944i | \(-0.485370\pi\) | ||||
0.0459453 | + | 0.998944i | \(0.485370\pi\) | |||||||
\(240\) | 371138. | 0.415918 | ||||||||
\(241\) | 538808. | 0.597574 | 0.298787 | − | 0.954320i | \(-0.403418\pi\) | ||||
0.298787 | + | 0.954320i | \(0.403418\pi\) | |||||||
\(242\) | 386091. | 0.423791 | ||||||||
\(243\) | −316604. | −0.343954 | ||||||||
\(244\) | −211377. | −0.227292 | ||||||||
\(245\) | −581718. | −0.619152 | ||||||||
\(246\) | −655111. | −0.690204 | ||||||||
\(247\) | 1.70767e6 | 1.78099 | ||||||||
\(248\) | −1.04050e6 | −1.07427 | ||||||||
\(249\) | 488703. | 0.499512 | ||||||||
\(250\) | 474339. | 0.479998 | ||||||||
\(251\) | −228910. | −0.229340 | −0.114670 | − | 0.993404i | \(-0.536581\pi\) | ||||
−0.114670 | + | 0.993404i | \(0.536581\pi\) | |||||||
\(252\) | −73379.3 | −0.0727901 | ||||||||
\(253\) | −2665.02 | −0.00261758 | ||||||||
\(254\) | −181089. | −0.176119 | ||||||||
\(255\) | 201509. | 0.194064 | ||||||||
\(256\) | −452733. | −0.431759 | ||||||||
\(257\) | 1.42445e6 | 1.34528 | 0.672642 | − | 0.739968i | \(-0.265160\pi\) | ||||
0.672642 | + | 0.739968i | \(0.265160\pi\) | |||||||
\(258\) | −78075.9 | −0.0730243 | ||||||||
\(259\) | −416526. | −0.385827 | ||||||||
\(260\) | −1.29391e6 | −1.18705 | ||||||||
\(261\) | −109147. | −0.0991773 | ||||||||
\(262\) | 182618. | 0.164358 | ||||||||
\(263\) | 60691.4 | 0.0541050 | 0.0270525 | − | 0.999634i | \(-0.491388\pi\) | ||||
0.0270525 | + | 0.999634i | \(0.491388\pi\) | |||||||
\(264\) | 198492. | 0.175280 | ||||||||
\(265\) | −1.21565e6 | −1.06339 | ||||||||
\(266\) | −272045. | −0.235742 | ||||||||
\(267\) | 1.98135e6 | 1.70092 | ||||||||
\(268\) | 316772. | 0.269408 | ||||||||
\(269\) | −1.85520e6 | −1.56319 | −0.781594 | − | 0.623788i | \(-0.785593\pi\) | ||||
−0.781594 | + | 0.623788i | \(0.785593\pi\) | |||||||
\(270\) | 402354. | 0.335892 | ||||||||
\(271\) | −1.57226e6 | −1.30047 | −0.650236 | − | 0.759732i | \(-0.725330\pi\) | ||||
−0.650236 | + | 0.759732i | \(0.725330\pi\) | |||||||
\(272\) | 116385. | 0.0953834 | ||||||||
\(273\) | 1.20625e6 | 0.979563 | ||||||||
\(274\) | −727276. | −0.585225 | ||||||||
\(275\) | −70997.3 | −0.0566122 | ||||||||
\(276\) | 14238.1 | 0.0112507 | ||||||||
\(277\) | 321513. | 0.251767 | 0.125883 | − | 0.992045i | \(-0.459823\pi\) | ||||
0.125883 | + | 0.992045i | \(0.459823\pi\) | |||||||
\(278\) | 937934. | 0.727881 | ||||||||
\(279\) | −304431. | −0.234141 | ||||||||
\(280\) | 462301. | 0.352395 | ||||||||
\(281\) | −501565. | −0.378932 | −0.189466 | − | 0.981887i | \(-0.560676\pi\) | ||||
−0.189466 | + | 0.981887i | \(0.560676\pi\) | |||||||
\(282\) | 71462.8 | 0.0535127 | ||||||||
\(283\) | 347650. | 0.258034 | 0.129017 | − | 0.991642i | \(-0.458818\pi\) | ||||
0.129017 | + | 0.991642i | \(0.458818\pi\) | |||||||
\(284\) | −481818. | −0.354476 | ||||||||
\(285\) | 1.29297e6 | 0.942922 | ||||||||
\(286\) | −215463. | −0.155760 | ||||||||
\(287\) | 1.04661e6 | 0.750030 | ||||||||
\(288\) | −244077. | −0.173399 | ||||||||
\(289\) | −1.35667e6 | −0.955495 | ||||||||
\(290\) | 306606. | 0.214085 | ||||||||
\(291\) | −2.48512e6 | −1.72034 | ||||||||
\(292\) | 312245. | 0.214308 | ||||||||
\(293\) | −1.60874e6 | −1.09475 | −0.547376 | − | 0.836886i | \(-0.684373\pi\) | ||||
−0.547376 | + | 0.836886i | \(0.684373\pi\) | |||||||
\(294\) | 517526. | 0.349192 | ||||||||
\(295\) | 1.16438e6 | 0.779002 | ||||||||
\(296\) | −891478. | −0.591400 | ||||||||
\(297\) | −275991. | −0.181553 | ||||||||
\(298\) | −1.07792e6 | −0.703145 | ||||||||
\(299\) | −34663.0 | −0.0224227 | ||||||||
\(300\) | 379310. | 0.243328 | ||||||||
\(301\) | 124734. | 0.0793540 | ||||||||
\(302\) | −43134.2 | −0.0272148 | ||||||||
\(303\) | −2.00239e6 | −1.25298 | ||||||||
\(304\) | 746772. | 0.463451 | ||||||||
\(305\) | 389633. | 0.239832 | ||||||||
\(306\) | −26549.9 | −0.0162091 | ||||||||
\(307\) | 2.50047e6 | 1.51417 | 0.757085 | − | 0.653316i | \(-0.226623\pi\) | ||||
0.757085 | + | 0.653316i | \(0.226623\pi\) | |||||||
\(308\) | −141393. | −0.0849279 | ||||||||
\(309\) | 830162. | 0.494614 | ||||||||
\(310\) | 855178. | 0.505420 | ||||||||
\(311\) | 2.80353e6 | 1.64363 | 0.821816 | − | 0.569753i | \(-0.192961\pi\) | ||||
0.821816 | + | 0.569753i | \(0.192961\pi\) | |||||||
\(312\) | 2.58171e6 | 1.50149 | ||||||||
\(313\) | −102581. | −0.0591841 | −0.0295920 | − | 0.999562i | \(-0.509421\pi\) | ||||
−0.0295920 | + | 0.999562i | \(0.509421\pi\) | |||||||
\(314\) | 348767. | 0.199623 | ||||||||
\(315\) | 135261. | 0.0768060 | ||||||||
\(316\) | 1.34855e6 | 0.759714 | ||||||||
\(317\) | −263420. | −0.147232 | −0.0736158 | − | 0.997287i | \(-0.523454\pi\) | ||||
−0.0736158 | + | 0.997287i | \(0.523454\pi\) | |||||||
\(318\) | 1.08151e6 | 0.599737 | ||||||||
\(319\) | −210313. | −0.115715 | ||||||||
\(320\) | −17559.9 | −0.00958623 | ||||||||
\(321\) | −2.64539e6 | −1.43294 | ||||||||
\(322\) | 5522.09 | 0.00296800 | ||||||||
\(323\) | 405459. | 0.216243 | ||||||||
\(324\) | 1.73883e6 | 0.920225 | ||||||||
\(325\) | −923437. | −0.484952 | ||||||||
\(326\) | 1.39059e6 | 0.724697 | ||||||||
\(327\) | 3.52847e6 | 1.82481 | ||||||||
\(328\) | 2.24002e6 | 1.14965 | ||||||||
\(329\) | −114169. | −0.0581512 | ||||||||
\(330\) | −163139. | −0.0824655 | ||||||||
\(331\) | −2.31706e6 | −1.16243 | −0.581216 | − | 0.813749i | \(-0.697423\pi\) | ||||
−0.581216 | + | 0.813749i | \(0.697423\pi\) | |||||||
\(332\) | −745072. | −0.370982 | ||||||||
\(333\) | −260830. | −0.128898 | ||||||||
\(334\) | 598058. | 0.293344 | ||||||||
\(335\) | −583909. | −0.284271 | ||||||||
\(336\) | 527502. | 0.254904 | ||||||||
\(337\) | 1.40113e6 | 0.672055 | 0.336028 | − | 0.941852i | \(-0.390916\pi\) | ||||
0.336028 | + | 0.941852i | \(0.390916\pi\) | |||||||
\(338\) | −1.87414e6 | −0.892301 | ||||||||
\(339\) | 565639. | 0.267325 | ||||||||
\(340\) | −307219. | −0.144129 | ||||||||
\(341\) | −586600. | −0.273185 | ||||||||
\(342\) | −170355. | −0.0787572 | ||||||||
\(343\) | −1.96061e6 | −0.899819 | ||||||||
\(344\) | 266965. | 0.121635 | ||||||||
\(345\) | −26245.3 | −0.0118714 | ||||||||
\(346\) | −198924. | −0.0893298 | ||||||||
\(347\) | −3.64231e6 | −1.62388 | −0.811940 | − | 0.583741i | \(-0.801588\pi\) | ||||
−0.811940 | + | 0.583741i | \(0.801588\pi\) | |||||||
\(348\) | 1.12362e6 | 0.497361 | ||||||||
\(349\) | 2.59872e6 | 1.14208 | 0.571039 | − | 0.820923i | \(-0.306540\pi\) | ||||
0.571039 | + | 0.820923i | \(0.306540\pi\) | |||||||
\(350\) | 147111. | 0.0641910 | ||||||||
\(351\) | −3.58971e6 | −1.55522 | ||||||||
\(352\) | −470306. | −0.202313 | ||||||||
\(353\) | −4.35884e6 | −1.86180 | −0.930902 | − | 0.365269i | \(-0.880977\pi\) | ||||
−0.930902 | + | 0.365269i | \(0.880977\pi\) | |||||||
\(354\) | −1.03589e6 | −0.439345 | ||||||||
\(355\) | 888139. | 0.374033 | ||||||||
\(356\) | −3.02075e6 | −1.26325 | ||||||||
\(357\) | 286407. | 0.118936 | ||||||||
\(358\) | 239615. | 0.0988112 | ||||||||
\(359\) | 3.30615e6 | 1.35390 | 0.676949 | − | 0.736029i | \(-0.263302\pi\) | ||||
0.676949 | + | 0.736029i | \(0.263302\pi\) | |||||||
\(360\) | 289494. | 0.117729 | ||||||||
\(361\) | 125500. | 0.0506845 | ||||||||
\(362\) | 548573. | 0.220020 | ||||||||
\(363\) | −2.60811e6 | −1.03887 | ||||||||
\(364\) | −1.83905e6 | −0.727511 | ||||||||
\(365\) | −575564. | −0.226132 | ||||||||
\(366\) | −346638. | −0.135261 | ||||||||
\(367\) | −548156. | −0.212441 | −0.106221 | − | 0.994343i | \(-0.533875\pi\) | ||||
−0.106221 | + | 0.994343i | \(0.533875\pi\) | |||||||
\(368\) | −15158.3 | −0.00583488 | ||||||||
\(369\) | 655389. | 0.250572 | ||||||||
\(370\) | 732698. | 0.278241 | ||||||||
\(371\) | −1.72781e6 | −0.651722 | ||||||||
\(372\) | 3.13397e6 | 1.17419 | ||||||||
\(373\) | −549721. | −0.204583 | −0.102292 | − | 0.994754i | \(-0.532617\pi\) | ||||
−0.102292 | + | 0.994754i | \(0.532617\pi\) | |||||||
\(374\) | −51158.3 | −0.0189120 | ||||||||
\(375\) | −3.20424e6 | −1.17665 | ||||||||
\(376\) | −244353. | −0.0891348 | ||||||||
\(377\) | −2.73547e6 | −0.991240 | ||||||||
\(378\) | 571870. | 0.205858 | ||||||||
\(379\) | −2.24483e6 | −0.802760 | −0.401380 | − | 0.915912i | \(-0.631469\pi\) | ||||
−0.401380 | + | 0.915912i | \(0.631469\pi\) | |||||||
\(380\) | −1.97125e6 | −0.700298 | ||||||||
\(381\) | 1.22329e6 | 0.431733 | ||||||||
\(382\) | −821883. | −0.288172 | ||||||||
\(383\) | 5.10313e6 | 1.77762 | 0.888812 | − | 0.458272i | \(-0.151531\pi\) | ||||
0.888812 | + | 0.458272i | \(0.151531\pi\) | |||||||
\(384\) | 3.13826e6 | 1.08608 | ||||||||
\(385\) | 260631. | 0.0896135 | ||||||||
\(386\) | −1.43946e6 | −0.491736 | ||||||||
\(387\) | 78108.9 | 0.0265108 | ||||||||
\(388\) | 3.78879e6 | 1.27768 | ||||||||
\(389\) | 4.70768e6 | 1.57737 | 0.788683 | − | 0.614800i | \(-0.210763\pi\) | ||||
0.788683 | + | 0.614800i | \(0.210763\pi\) | |||||||
\(390\) | −2.12189e6 | −0.706416 | ||||||||
\(391\) | −8230.20 | −0.00272250 | ||||||||
\(392\) | −1.76958e6 | −0.581640 | ||||||||
\(393\) | −1.23362e6 | −0.402902 | ||||||||
\(394\) | −2.40739e6 | −0.781279 | ||||||||
\(395\) | −2.48580e6 | −0.801628 | ||||||||
\(396\) | −88540.7 | −0.0283730 | ||||||||
\(397\) | 3.81755e6 | 1.21565 | 0.607825 | − | 0.794071i | \(-0.292042\pi\) | ||||
0.607825 | + | 0.794071i | \(0.292042\pi\) | |||||||
\(398\) | 1.90051e6 | 0.601397 | ||||||||
\(399\) | 1.83771e6 | 0.577889 | ||||||||
\(400\) | −403824. | −0.126195 | ||||||||
\(401\) | 1.31578e6 | 0.408622 | 0.204311 | − | 0.978906i | \(-0.434505\pi\) | ||||
0.204311 | + | 0.978906i | \(0.434505\pi\) | |||||||
\(402\) | 519476. | 0.160325 | ||||||||
\(403\) | −7.62970e6 | −2.34016 | ||||||||
\(404\) | 3.05283e6 | 0.930571 | ||||||||
\(405\) | −3.20520e6 | −0.970995 | ||||||||
\(406\) | 435782. | 0.131206 | ||||||||
\(407\) | −502587. | −0.150392 | ||||||||
\(408\) | 612988. | 0.182306 | ||||||||
\(409\) | 3.92071e6 | 1.15893 | 0.579464 | − | 0.814998i | \(-0.303262\pi\) | ||||
0.579464 | + | 0.814998i | \(0.303262\pi\) | |||||||
\(410\) | −1.84105e6 | −0.540888 | ||||||||
\(411\) | 4.91287e6 | 1.43460 | ||||||||
\(412\) | −1.26566e6 | −0.367344 | ||||||||
\(413\) | 1.65494e6 | 0.477427 | ||||||||
\(414\) | 3457.95 | 0.000991557 0 | ||||||||
\(415\) | 1.37340e6 | 0.391450 | ||||||||
\(416\) | −6.11711e6 | −1.73306 | ||||||||
\(417\) | −6.33591e6 | −1.78430 | ||||||||
\(418\) | −328253. | −0.0918901 | ||||||||
\(419\) | 2.92842e6 | 0.814890 | 0.407445 | − | 0.913230i | \(-0.366420\pi\) | ||||
0.407445 | + | 0.913230i | \(0.366420\pi\) | |||||||
\(420\) | −1.39244e6 | −0.385172 | ||||||||
\(421\) | 4.43337e6 | 1.21907 | 0.609535 | − | 0.792759i | \(-0.291356\pi\) | ||||
0.609535 | + | 0.792759i | \(0.291356\pi\) | |||||||
\(422\) | 2.44965e6 | 0.669612 | ||||||||
\(423\) | −71493.0 | −0.0194273 | ||||||||
\(424\) | −3.69799e6 | −0.998966 | ||||||||
\(425\) | −219256. | −0.0588816 | ||||||||
\(426\) | −790135. | −0.210949 | ||||||||
\(427\) | 553789. | 0.146986 | ||||||||
\(428\) | 4.03314e6 | 1.06423 | ||||||||
\(429\) | 1.45549e6 | 0.381826 | ||||||||
\(430\) | −219416. | −0.0572265 | ||||||||
\(431\) | 4.27188e6 | 1.10771 | 0.553854 | − | 0.832614i | \(-0.313156\pi\) | ||||
0.553854 | + | 0.832614i | \(0.313156\pi\) | |||||||
\(432\) | −1.56980e6 | −0.404702 | ||||||||
\(433\) | −1.65833e6 | −0.425061 | −0.212531 | − | 0.977154i | \(-0.568171\pi\) | ||||
−0.212531 | + | 0.977154i | \(0.568171\pi\) | |||||||
\(434\) | 1.21547e6 | 0.309757 | ||||||||
\(435\) | −2.07118e6 | −0.524801 | ||||||||
\(436\) | −5.37947e6 | −1.35526 | ||||||||
\(437\) | −52808.5 | −0.0132282 | ||||||||
\(438\) | 512052. | 0.127535 | ||||||||
\(439\) | −1.44252e6 | −0.357240 | −0.178620 | − | 0.983918i | \(-0.557163\pi\) | ||||
−0.178620 | + | 0.983918i | \(0.557163\pi\) | |||||||
\(440\) | 557820. | 0.137361 | ||||||||
\(441\) | −517745. | −0.126771 | ||||||||
\(442\) | −665398. | −0.162004 | ||||||||
\(443\) | 5.80251e6 | 1.40477 | 0.702387 | − | 0.711795i | \(-0.252118\pi\) | ||||
0.702387 | + | 0.711795i | \(0.252118\pi\) | |||||||
\(444\) | 2.68512e6 | 0.646407 | ||||||||
\(445\) | 5.56818e6 | 1.33295 | ||||||||
\(446\) | −1.67201e6 | −0.398016 | ||||||||
\(447\) | 7.28152e6 | 1.72367 | ||||||||
\(448\) | −24958.1 | −0.00587511 | ||||||||
\(449\) | −1.86453e6 | −0.436470 | −0.218235 | − | 0.975896i | \(-0.570030\pi\) | ||||
−0.218235 | + | 0.975896i | \(0.570030\pi\) | |||||||
\(450\) | 92121.2 | 0.0214451 | ||||||||
\(451\) | 1.26285e6 | 0.292355 | ||||||||
\(452\) | −862368. | −0.198539 | ||||||||
\(453\) | 291379. | 0.0667134 | ||||||||
\(454\) | 3.51827e6 | 0.801105 | ||||||||
\(455\) | 3.38993e6 | 0.767648 | ||||||||
\(456\) | 3.93319e6 | 0.885795 | ||||||||
\(457\) | 3.61109e6 | 0.808812 | 0.404406 | − | 0.914580i | \(-0.367478\pi\) | ||||
0.404406 | + | 0.914580i | \(0.367478\pi\) | |||||||
\(458\) | −1.76699e6 | −0.393615 | ||||||||
\(459\) | −852323. | −0.188831 | ||||||||
\(460\) | 40013.3 | 0.00881679 | ||||||||
\(461\) | 5.82273e6 | 1.27607 | 0.638034 | − | 0.770008i | \(-0.279748\pi\) | ||||
0.638034 | + | 0.770008i | \(0.279748\pi\) | |||||||
\(462\) | −231871. | −0.0505406 | ||||||||
\(463\) | 759569. | 0.164670 | 0.0823351 | − | 0.996605i | \(-0.473762\pi\) | ||||
0.0823351 | + | 0.996605i | \(0.473762\pi\) | |||||||
\(464\) | −1.19624e6 | −0.257942 | ||||||||
\(465\) | −5.77687e6 | −1.23897 | ||||||||
\(466\) | −2.02733e6 | −0.432474 | ||||||||
\(467\) | 3.30533e6 | 0.701330 | 0.350665 | − | 0.936501i | \(-0.385956\pi\) | ||||
0.350665 | + | 0.936501i | \(0.385956\pi\) | |||||||
\(468\) | −1.15162e6 | −0.243049 | ||||||||
\(469\) | −829915. | −0.174221 | ||||||||
\(470\) | 200831. | 0.0419360 | ||||||||
\(471\) | −2.35598e6 | −0.489350 | ||||||||
\(472\) | 3.54202e6 | 0.731805 | ||||||||
\(473\) | 150506. | 0.0309315 | ||||||||
\(474\) | 2.21149e6 | 0.452106 | ||||||||
\(475\) | −1.40684e6 | −0.286095 | ||||||||
\(476\) | −436654. | −0.0883324 | ||||||||
\(477\) | −1.08196e6 | −0.217729 | ||||||||
\(478\) | −202879. | −0.0406132 | ||||||||
\(479\) | −7.63918e6 | −1.52128 | −0.760638 | − | 0.649176i | \(-0.775114\pi\) | ||||
−0.760638 | + | 0.649176i | \(0.775114\pi\) | |||||||
\(480\) | −4.63160e6 | −0.917547 | ||||||||
\(481\) | −6.53697e6 | −1.28829 | ||||||||
\(482\) | −1.34712e6 | −0.264112 | ||||||||
\(483\) | −37302.7 | −0.00727565 | ||||||||
\(484\) | 3.97631e6 | 0.771555 | ||||||||
\(485\) | −6.98391e6 | −1.34817 | ||||||||
\(486\) | 791567. | 0.152019 | ||||||||
\(487\) | −4.03922e6 | −0.771747 | −0.385873 | − | 0.922552i | \(-0.626100\pi\) | ||||
−0.385873 | + | 0.922552i | \(0.626100\pi\) | |||||||
\(488\) | 1.18526e6 | 0.225301 | ||||||||
\(489\) | −9.39371e6 | −1.77650 | ||||||||
\(490\) | 1.45440e6 | 0.273649 | ||||||||
\(491\) | 7.62584e6 | 1.42753 | 0.713763 | − | 0.700387i | \(-0.246989\pi\) | ||||
0.713763 | + | 0.700387i | \(0.246989\pi\) | |||||||
\(492\) | −6.74691e6 | −1.25659 | ||||||||
\(493\) | −649497. | −0.120354 | ||||||||
\(494\) | −4.26948e6 | −0.787149 | ||||||||
\(495\) | 163208. | 0.0299383 | ||||||||
\(496\) | −3.33651e6 | −0.608960 | ||||||||
\(497\) | 1.26232e6 | 0.229234 | ||||||||
\(498\) | −1.22185e6 | −0.220772 | ||||||||
\(499\) | 9.55168e6 | 1.71723 | 0.858615 | − | 0.512621i | \(-0.171325\pi\) | ||||
0.858615 | + | 0.512621i | \(0.171325\pi\) | |||||||
\(500\) | 4.88516e6 | 0.873885 | ||||||||
\(501\) | −4.03999e6 | −0.719094 | ||||||||
\(502\) | 572316. | 0.101362 | ||||||||
\(503\) | −4.69119e6 | −0.826730 | −0.413365 | − | 0.910566i | \(-0.635647\pi\) | ||||
−0.413365 | + | 0.910566i | \(0.635647\pi\) | |||||||
\(504\) | 411461. | 0.0721527 | ||||||||
\(505\) | −5.62731e6 | −0.981911 | ||||||||
\(506\) | 6663.04 | 0.00115690 | ||||||||
\(507\) | 1.26602e7 | 2.18736 | ||||||||
\(508\) | −1.86501e6 | −0.320643 | ||||||||
\(509\) | 2.37623e6 | 0.406531 | 0.203265 | − | 0.979124i | \(-0.434845\pi\) | ||||
0.203265 | + | 0.979124i | \(0.434845\pi\) | |||||||
\(510\) | −503810. | −0.0857712 | ||||||||
\(511\) | −818054. | −0.138589 | ||||||||
\(512\) | −4.81417e6 | −0.811608 | ||||||||
\(513\) | −5.46886e6 | −0.917495 | ||||||||
\(514\) | −3.56138e6 | −0.594580 | ||||||||
\(515\) | 2.33300e6 | 0.387611 | ||||||||
\(516\) | −804094. | −0.132948 | ||||||||
\(517\) | −137758. | −0.0226668 | ||||||||
\(518\) | 1.04139e6 | 0.170526 | ||||||||
\(519\) | 1.34376e6 | 0.218980 | ||||||||
\(520\) | 7.25536e6 | 1.17666 | ||||||||
\(521\) | 6.31208e6 | 1.01878 | 0.509388 | − | 0.860537i | \(-0.329872\pi\) | ||||
0.509388 | + | 0.860537i | \(0.329872\pi\) | |||||||
\(522\) | 272888. | 0.0438338 | ||||||||
\(523\) | −1.03668e7 | −1.65725 | −0.828627 | − | 0.559801i | \(-0.810878\pi\) | ||||
−0.828627 | + | 0.559801i | \(0.810878\pi\) | |||||||
\(524\) | 1.88077e6 | 0.299231 | ||||||||
\(525\) | −993758. | −0.157356 | ||||||||
\(526\) | −151739. | −0.0239130 | ||||||||
\(527\) | −1.81156e6 | −0.284136 | ||||||||
\(528\) | 636493. | 0.0993594 | ||||||||
\(529\) | −6.43527e6 | −0.999833 | ||||||||
\(530\) | 3.03935e6 | 0.469992 | ||||||||
\(531\) | 1.03633e6 | 0.159500 | ||||||||
\(532\) | −2.80176e6 | −0.429192 | ||||||||
\(533\) | 1.64255e7 | 2.50438 | ||||||||
\(534\) | −4.95374e6 | −0.751762 | ||||||||
\(535\) | −7.43432e6 | −1.12294 | ||||||||
\(536\) | −1.77624e6 | −0.267049 | ||||||||
\(537\) | −1.61864e6 | −0.242222 | ||||||||
\(538\) | 4.63835e6 | 0.690888 | ||||||||
\(539\) | −997631. | −0.147910 | ||||||||
\(540\) | 4.14380e6 | 0.611525 | ||||||||
\(541\) | −5.71736e6 | −0.839851 | −0.419926 | − | 0.907559i | \(-0.637944\pi\) | ||||
−0.419926 | + | 0.907559i | \(0.637944\pi\) | |||||||
\(542\) | 3.93093e6 | 0.574775 | ||||||||
\(543\) | −3.70570e6 | −0.539350 | ||||||||
\(544\) | −1.45242e6 | −0.210423 | ||||||||
\(545\) | 9.91603e6 | 1.43003 | ||||||||
\(546\) | −3.01586e6 | −0.432941 | ||||||||
\(547\) | 4.37335e6 | 0.624950 | 0.312475 | − | 0.949926i | \(-0.398842\pi\) | ||||
0.312475 | + | 0.949926i | \(0.398842\pi\) | |||||||
\(548\) | −7.49013e6 | −1.06546 | ||||||||
\(549\) | 346785. | 0.0491054 | ||||||||
\(550\) | 177506. | 0.0250211 | ||||||||
\(551\) | −4.16744e6 | −0.584778 | ||||||||
\(552\) | −79837.8 | −0.0111522 | ||||||||
\(553\) | −3.53309e6 | −0.491294 | ||||||||
\(554\) | −803841. | −0.111274 | ||||||||
\(555\) | −4.94950e6 | −0.682070 | ||||||||
\(556\) | 9.65967e6 | 1.32518 | ||||||||
\(557\) | −5.52441e6 | −0.754481 | −0.377240 | − | 0.926115i | \(-0.623127\pi\) | ||||
−0.377240 | + | 0.926115i | \(0.623127\pi\) | |||||||
\(558\) | 761133. | 0.103484 | ||||||||
\(559\) | 1.95758e6 | 0.264966 | ||||||||
\(560\) | 1.48244e6 | 0.199759 | ||||||||
\(561\) | 345583. | 0.0463602 | ||||||||
\(562\) | 1.25400e6 | 0.167478 | ||||||||
\(563\) | 1.38558e7 | 1.84230 | 0.921149 | − | 0.389211i | \(-0.127252\pi\) | ||||
0.921149 | + | 0.389211i | \(0.127252\pi\) | |||||||
\(564\) | 735987. | 0.0974254 | ||||||||
\(565\) | 1.58961e6 | 0.209493 | ||||||||
\(566\) | −869189. | −0.114044 | ||||||||
\(567\) | −4.55557e6 | −0.595094 | ||||||||
\(568\) | 2.70171e6 | 0.351372 | ||||||||
\(569\) | 8.96028e6 | 1.16022 | 0.580111 | − | 0.814538i | \(-0.303009\pi\) | ||||
0.580111 | + | 0.814538i | \(0.303009\pi\) | |||||||
\(570\) | −3.23266e6 | −0.416747 | ||||||||
\(571\) | 1.86281e6 | 0.239099 | 0.119550 | − | 0.992828i | \(-0.461855\pi\) | ||||
0.119550 | + | 0.992828i | \(0.461855\pi\) | |||||||
\(572\) | −2.21902e6 | −0.283578 | ||||||||
\(573\) | 5.55196e6 | 0.706415 | ||||||||
\(574\) | −2.61671e6 | −0.331494 | ||||||||
\(575\) | 28556.7 | 0.00360195 | ||||||||
\(576\) | −15628.8 | −0.00196277 | ||||||||
\(577\) | −8.48683e6 | −1.06122 | −0.530610 | − | 0.847616i | \(-0.678037\pi\) | ||||
−0.530610 | + | 0.847616i | \(0.678037\pi\) | |||||||
\(578\) | 3.39191e6 | 0.422304 | ||||||||
\(579\) | 9.72382e6 | 1.20543 | ||||||||
\(580\) | 3.15770e6 | 0.389764 | ||||||||
\(581\) | 1.95202e6 | 0.239908 | ||||||||
\(582\) | 6.21325e6 | 0.760346 | ||||||||
\(583\) | −2.08481e6 | −0.254036 | ||||||||
\(584\) | −1.75086e6 | −0.212431 | ||||||||
\(585\) | 2.12279e6 | 0.256458 | ||||||||
\(586\) | 4.02214e6 | 0.483852 | ||||||||
\(587\) | −9.06080e6 | −1.08535 | −0.542677 | − | 0.839942i | \(-0.682589\pi\) | ||||
−0.542677 | + | 0.839942i | \(0.682589\pi\) | |||||||
\(588\) | 5.32994e6 | 0.635740 | ||||||||
\(589\) | −1.16237e7 | −1.38056 | ||||||||
\(590\) | −2.91115e6 | −0.344299 | ||||||||
\(591\) | 1.62623e7 | 1.91520 | ||||||||
\(592\) | −2.85866e6 | −0.335241 | ||||||||
\(593\) | 1.56414e7 | 1.82658 | 0.913290 | − | 0.407310i | \(-0.133533\pi\) | ||||
0.913290 | + | 0.407310i | \(0.133533\pi\) | |||||||
\(594\) | 690027. | 0.0802417 | ||||||||
\(595\) | 804887. | 0.0932058 | ||||||||
\(596\) | −1.11013e7 | −1.28015 | ||||||||
\(597\) | −1.28382e7 | −1.47425 | ||||||||
\(598\) | 86663.8 | 0.00991025 | ||||||||
\(599\) | −1.40306e6 | −0.159775 | −0.0798877 | − | 0.996804i | \(-0.525456\pi\) | ||||
−0.0798877 | + | 0.996804i | \(0.525456\pi\) | |||||||
\(600\) | −2.12691e6 | −0.241197 | ||||||||
\(601\) | −1.02325e6 | −0.115557 | −0.0577786 | − | 0.998329i | \(-0.518402\pi\) | ||||
−0.0577786 | + | 0.998329i | \(0.518402\pi\) | |||||||
\(602\) | −311858. | −0.0350724 | ||||||||
\(603\) | −519696. | −0.0582044 | ||||||||
\(604\) | −444235. | −0.0495473 | ||||||||
\(605\) | −7.32956e6 | −0.814122 | ||||||||
\(606\) | 5.00635e6 | 0.553783 | ||||||||
\(607\) | 6.79951e6 | 0.749042 | 0.374521 | − | 0.927219i | \(-0.377807\pi\) | ||||
0.374521 | + | 0.927219i | \(0.377807\pi\) | |||||||
\(608\) | −9.31931e6 | −1.02241 | ||||||||
\(609\) | −2.94378e6 | −0.321635 | ||||||||
\(610\) | −974154. | −0.105999 | ||||||||
\(611\) | −1.79177e6 | −0.194169 | ||||||||
\(612\) | −273434. | −0.0295103 | ||||||||
\(613\) | 3.70194e6 | 0.397904 | 0.198952 | − | 0.980009i | \(-0.436246\pi\) | ||||
0.198952 | + | 0.980009i | \(0.436246\pi\) | |||||||
\(614\) | −6.25162e6 | −0.669224 | ||||||||
\(615\) | 1.24366e7 | 1.32591 | ||||||||
\(616\) | 792834. | 0.0841842 | ||||||||
\(617\) | 1.14193e7 | 1.20761 | 0.603806 | − | 0.797131i | \(-0.293650\pi\) | ||||
0.603806 | + | 0.797131i | \(0.293650\pi\) | |||||||
\(618\) | −2.07556e6 | −0.218607 | ||||||||
\(619\) | −8.12725e6 | −0.852545 | −0.426272 | − | 0.904595i | \(-0.640173\pi\) | ||||
−0.426272 | + | 0.904595i | \(0.640173\pi\) | |||||||
\(620\) | 8.80737e6 | 0.920168 | ||||||||
\(621\) | 111010. | 0.0115513 | ||||||||
\(622\) | −7.00934e6 | −0.726443 | ||||||||
\(623\) | 7.91410e6 | 0.816924 | ||||||||
\(624\) | 8.27864e6 | 0.851133 | ||||||||
\(625\) | −6.27919e6 | −0.642989 | ||||||||
\(626\) | 256470. | 0.0261578 | ||||||||
\(627\) | 2.21741e6 | 0.225256 | ||||||||
\(628\) | 3.59191e6 | 0.363435 | ||||||||
\(629\) | −1.55210e6 | −0.156421 | ||||||||
\(630\) | −338176. | −0.0339463 | ||||||||
\(631\) | 8.36884e6 | 0.836743 | 0.418371 | − | 0.908276i | \(-0.362601\pi\) | ||||
0.418371 | + | 0.908276i | \(0.362601\pi\) | |||||||
\(632\) | −7.56176e6 | −0.753061 | ||||||||
\(633\) | −1.65478e7 | −1.64146 | ||||||||
\(634\) | 658599. | 0.0650725 | ||||||||
\(635\) | 3.43779e6 | 0.338334 | ||||||||
\(636\) | 1.11383e7 | 1.09188 | ||||||||
\(637\) | −1.29758e7 | −1.26703 | ||||||||
\(638\) | 525822. | 0.0511431 | ||||||||
\(639\) | 790469. | 0.0765831 | ||||||||
\(640\) | 8.81943e6 | 0.851120 | ||||||||
\(641\) | −1.04858e7 | −1.00799 | −0.503996 | − | 0.863706i | \(-0.668137\pi\) | ||||
−0.503996 | + | 0.863706i | \(0.668137\pi\) | |||||||
\(642\) | 6.61396e6 | 0.633321 | ||||||||
\(643\) | 1.22946e7 | 1.17270 | 0.586349 | − | 0.810058i | \(-0.300565\pi\) | ||||
0.586349 | + | 0.810058i | \(0.300565\pi\) | |||||||
\(644\) | 56871.3 | 0.00540354 | ||||||||
\(645\) | 1.48219e6 | 0.140283 | ||||||||
\(646\) | −1.01372e6 | −0.0955736 | ||||||||
\(647\) | −1.39774e7 | −1.31270 | −0.656349 | − | 0.754457i | \(-0.727900\pi\) | ||||
−0.656349 | + | 0.754457i | \(0.727900\pi\) | |||||||
\(648\) | −9.75016e6 | −0.912167 | ||||||||
\(649\) | 1.99688e6 | 0.186097 | ||||||||
\(650\) | 2.30876e6 | 0.214336 | ||||||||
\(651\) | −8.21072e6 | −0.759327 | ||||||||
\(652\) | 1.43216e7 | 1.31939 | ||||||||
\(653\) | −5.00675e6 | −0.459487 | −0.229743 | − | 0.973251i | \(-0.573789\pi\) | ||||
−0.229743 | + | 0.973251i | \(0.573789\pi\) | |||||||
\(654\) | −8.82181e6 | −0.806517 | ||||||||
\(655\) | −3.46683e6 | −0.315740 | ||||||||
\(656\) | 7.18296e6 | 0.651694 | ||||||||
\(657\) | −512268. | −0.0463003 | ||||||||
\(658\) | 285443. | 0.0257013 | ||||||||
\(659\) | 5.50845e6 | 0.494101 | 0.247050 | − | 0.969003i | \(-0.420539\pi\) | ||||
0.247050 | + | 0.969003i | \(0.420539\pi\) | |||||||
\(660\) | −1.68015e6 | −0.150137 | ||||||||
\(661\) | −6.69305e6 | −0.595827 | −0.297914 | − | 0.954593i | \(-0.596291\pi\) | ||||
−0.297914 | + | 0.954593i | \(0.596291\pi\) | |||||||
\(662\) | 5.79308e6 | 0.513765 | ||||||||
\(663\) | 4.49488e6 | 0.397131 | ||||||||
\(664\) | 4.17786e6 | 0.367733 | ||||||||
\(665\) | 5.16450e6 | 0.452870 | ||||||||
\(666\) | 652122. | 0.0569697 | ||||||||
\(667\) | 84592.7 | 0.00736238 | ||||||||
\(668\) | 6.15933e6 | 0.534063 | ||||||||
\(669\) | 1.12947e7 | 0.975684 | ||||||||
\(670\) | 1.45988e6 | 0.125641 | ||||||||
\(671\) | 668211. | 0.0572938 | ||||||||
\(672\) | −6.58294e6 | −0.562337 | ||||||||
\(673\) | −7.54961e6 | −0.642521 | −0.321260 | − | 0.946991i | \(-0.604106\pi\) | ||||
−0.321260 | + | 0.946991i | \(0.604106\pi\) | |||||||
\(674\) | −3.50309e6 | −0.297031 | ||||||||
\(675\) | 2.95734e6 | 0.249828 | ||||||||
\(676\) | −1.93016e7 | −1.62453 | ||||||||
\(677\) | −1.51658e6 | −0.127173 | −0.0635863 | − | 0.997976i | \(-0.520254\pi\) | ||||
−0.0635863 | + | 0.997976i | \(0.520254\pi\) | |||||||
\(678\) | −1.41420e6 | −0.118151 | ||||||||
\(679\) | −9.92629e6 | −0.826252 | ||||||||
\(680\) | 1.72268e6 | 0.142867 | ||||||||
\(681\) | −2.37665e7 | −1.96380 | ||||||||
\(682\) | 1.46661e6 | 0.120741 | ||||||||
\(683\) | −2.30637e7 | −1.89181 | −0.945904 | − | 0.324448i | \(-0.894822\pi\) | ||||
−0.945904 | + | 0.324448i | \(0.894822\pi\) | |||||||
\(684\) | −1.75447e6 | −0.143386 | ||||||||
\(685\) | 1.38066e7 | 1.12424 | ||||||||
\(686\) | 4.90187e6 | 0.397696 | ||||||||
\(687\) | 1.19363e7 | 0.964894 | ||||||||
\(688\) | 856062. | 0.0689499 | ||||||||
\(689\) | −2.71164e7 | −2.17612 | ||||||||
\(690\) | 65618.0 | 0.00524687 | ||||||||
\(691\) | −1.55625e7 | −1.23990 | −0.619948 | − | 0.784643i | \(-0.712846\pi\) | ||||
−0.619948 | + | 0.784643i | \(0.712846\pi\) | |||||||
\(692\) | −2.04869e6 | −0.162634 | ||||||||
\(693\) | 231969. | 0.0183483 | ||||||||
\(694\) | 9.10645e6 | 0.717713 | ||||||||
\(695\) | −1.78058e7 | −1.39829 | ||||||||
\(696\) | −6.30050e6 | −0.493005 | ||||||||
\(697\) | 3.89998e6 | 0.304075 | ||||||||
\(698\) | −6.49727e6 | −0.504769 | ||||||||
\(699\) | 1.36950e7 | 1.06015 | ||||||||
\(700\) | 1.51508e6 | 0.116866 | ||||||||
\(701\) | 1.48227e6 | 0.113929 | 0.0569643 | − | 0.998376i | \(-0.481858\pi\) | ||||
0.0569643 | + | 0.998376i | \(0.481858\pi\) | |||||||
\(702\) | 8.97494e6 | 0.687367 | ||||||||
\(703\) | −9.95896e6 | −0.760021 | ||||||||
\(704\) | −30114.8 | −0.00229007 | ||||||||
\(705\) | −1.35665e6 | −0.102800 | ||||||||
\(706\) | 1.08979e7 | 0.822869 | ||||||||
\(707\) | −7.99814e6 | −0.601784 | ||||||||
\(708\) | −1.06685e7 | −0.799872 | ||||||||
\(709\) | 1.23095e7 | 0.919652 | 0.459826 | − | 0.888009i | \(-0.347912\pi\) | ||||
0.459826 | + | 0.888009i | \(0.347912\pi\) | |||||||
\(710\) | −2.22051e6 | −0.165313 | ||||||||
\(711\) | −2.21243e6 | −0.164133 | ||||||||
\(712\) | 1.69383e7 | 1.25219 | ||||||||
\(713\) | 235944. | 0.0173814 | ||||||||
\(714\) | −716070. | −0.0525666 | ||||||||
\(715\) | 4.09034e6 | 0.299223 | ||||||||
\(716\) | 2.46776e6 | 0.179896 | ||||||||
\(717\) | 1.37048e6 | 0.0995579 | ||||||||
\(718\) | −8.26598e6 | −0.598388 | ||||||||
\(719\) | −2.07641e7 | −1.49793 | −0.748963 | − | 0.662612i | \(-0.769448\pi\) | ||||
−0.748963 | + | 0.662612i | \(0.769448\pi\) | |||||||
\(720\) | 928307. | 0.0667360 | ||||||||
\(721\) | 3.31591e6 | 0.237555 | ||||||||
\(722\) | −313773. | −0.0224012 | ||||||||
\(723\) | 9.10002e6 | 0.647435 | ||||||||
\(724\) | 5.64968e6 | 0.400569 | ||||||||
\(725\) | 2.25359e6 | 0.159232 | ||||||||
\(726\) | 6.52076e6 | 0.459152 | ||||||||
\(727\) | −7.15312e6 | −0.501949 | −0.250974 | − | 0.967994i | \(-0.580751\pi\) | ||||
−0.250974 | + | 0.967994i | \(0.580751\pi\) | |||||||
\(728\) | 1.03121e7 | 0.721140 | ||||||||
\(729\) | 1.10625e7 | 0.770968 | ||||||||
\(730\) | 1.43901e6 | 0.0999443 | ||||||||
\(731\) | 464798. | 0.0321715 | ||||||||
\(732\) | −3.56998e6 | −0.246257 | ||||||||
\(733\) | 1.65135e7 | 1.13521 | 0.567607 | − | 0.823299i | \(-0.307869\pi\) | ||||
0.567607 | + | 0.823299i | \(0.307869\pi\) | |||||||
\(734\) | 1.37049e6 | 0.0938936 | ||||||||
\(735\) | −9.82473e6 | −0.670814 | ||||||||
\(736\) | 189168. | 0.0128722 | ||||||||
\(737\) | −1.00139e6 | −0.0679100 | ||||||||
\(738\) | −1.63859e6 | −0.110746 | ||||||||
\(739\) | −7.25575e6 | −0.488733 | −0.244366 | − | 0.969683i | \(-0.578580\pi\) | ||||
−0.244366 | + | 0.969683i | \(0.578580\pi\) | |||||||
\(740\) | 7.54597e6 | 0.506566 | ||||||||
\(741\) | 2.88410e7 | 1.92959 | ||||||||
\(742\) | 4.31985e6 | 0.288044 | ||||||||
\(743\) | −1.59618e7 | −1.06074 | −0.530372 | − | 0.847765i | \(-0.677948\pi\) | ||||
−0.530372 | + | 0.847765i | \(0.677948\pi\) | |||||||
\(744\) | −1.75732e7 | −1.16391 | ||||||||
\(745\) | 2.04632e7 | 1.35077 | ||||||||
\(746\) | 1.37440e6 | 0.0904205 | ||||||||
\(747\) | 1.22236e6 | 0.0801491 | ||||||||
\(748\) | −526874. | −0.0344312 | ||||||||
\(749\) | −1.05665e7 | −0.688217 | ||||||||
\(750\) | 8.01120e6 | 0.520049 | ||||||||
\(751\) | 2.56869e7 | 1.66192 | 0.830962 | − | 0.556329i | \(-0.187791\pi\) | ||||
0.830962 | + | 0.556329i | \(0.187791\pi\) | |||||||
\(752\) | −783553. | −0.0505270 | ||||||||
\(753\) | −3.86610e6 | −0.248476 | ||||||||
\(754\) | 6.83918e6 | 0.438102 | ||||||||
\(755\) | 818861. | 0.0522809 | ||||||||
\(756\) | 5.88962e6 | 0.374785 | ||||||||
\(757\) | 7.97201e6 | 0.505624 | 0.252812 | − | 0.967515i | \(-0.418645\pi\) | ||||
0.252812 | + | 0.967515i | \(0.418645\pi\) | |||||||
\(758\) | 5.61249e6 | 0.354799 | ||||||||
\(759\) | −45010.0 | −0.00283599 | ||||||||
\(760\) | 1.10534e7 | 0.694165 | ||||||||
\(761\) | 2.21020e7 | 1.38347 | 0.691736 | − | 0.722150i | \(-0.256846\pi\) | ||||
0.691736 | + | 0.722150i | \(0.256846\pi\) | |||||||
\(762\) | −3.05844e6 | −0.190815 | ||||||||
\(763\) | 1.40937e7 | 0.876425 | ||||||||
\(764\) | −8.46448e6 | −0.524646 | ||||||||
\(765\) | 504023. | 0.0311385 | ||||||||
\(766\) | −1.27588e7 | −0.785664 | ||||||||
\(767\) | 2.59727e7 | 1.59415 | ||||||||
\(768\) | −7.64628e6 | −0.467786 | ||||||||
\(769\) | −2.64726e7 | −1.61428 | −0.807142 | − | 0.590357i | \(-0.798987\pi\) | ||||
−0.807142 | + | 0.590357i | \(0.798987\pi\) | |||||||
\(770\) | −651624. | −0.0396068 | ||||||||
\(771\) | 2.40577e7 | 1.45753 | ||||||||
\(772\) | −1.48249e7 | −0.895256 | ||||||||
\(773\) | 2.48033e7 | 1.49301 | 0.746503 | − | 0.665382i | \(-0.231732\pi\) | ||||
0.746503 | + | 0.665382i | \(0.231732\pi\) | |||||||
\(774\) | −195287. | −0.0117171 | ||||||||
\(775\) | 6.28564e6 | 0.375920 | ||||||||
\(776\) | −2.12449e7 | −1.26649 | ||||||||
\(777\) | −7.03477e6 | −0.418021 | ||||||||
\(778\) | −1.17701e7 | −0.697155 | ||||||||
\(779\) | 2.50239e7 | 1.47745 | ||||||||
\(780\) | −2.18531e7 | −1.28610 | ||||||||
\(781\) | 1.52314e6 | 0.0893534 | ||||||||
\(782\) | 20577.0 | 0.00120328 | ||||||||
\(783\) | 8.76045e6 | 0.510649 | ||||||||
\(784\) | −5.67441e6 | −0.329709 | ||||||||
\(785\) | −6.62100e6 | −0.383486 | ||||||||
\(786\) | 3.08427e6 | 0.178072 | ||||||||
\(787\) | 8.09631e6 | 0.465962 | 0.232981 | − | 0.972481i | \(-0.425152\pi\) | ||||
0.232981 | + | 0.972481i | \(0.425152\pi\) | |||||||
\(788\) | −2.47934e7 | −1.42240 | ||||||||
\(789\) | 1.02503e6 | 0.0586196 | ||||||||
\(790\) | 6.21495e6 | 0.354299 | ||||||||
\(791\) | 2.25933e6 | 0.128392 | ||||||||
\(792\) | 496476. | 0.0281245 | ||||||||
\(793\) | 8.69118e6 | 0.490790 | ||||||||
\(794\) | −9.54457e6 | −0.537286 | ||||||||
\(795\) | −2.05313e7 | −1.15212 | ||||||||
\(796\) | 1.95731e7 | 1.09491 | ||||||||
\(797\) | 1.30377e7 | 0.727034 | 0.363517 | − | 0.931587i | \(-0.381576\pi\) | ||||
0.363517 | + | 0.931587i | \(0.381576\pi\) | |||||||
\(798\) | −4.59461e6 | −0.255412 | ||||||||
\(799\) | −425429. | −0.0235755 | ||||||||
\(800\) | 5.03951e6 | 0.278396 | ||||||||
\(801\) | 4.95584e6 | 0.272920 | ||||||||
\(802\) | −3.28968e6 | −0.180600 | ||||||||
\(803\) | −987077. | −0.0540210 | ||||||||
\(804\) | 5.35002e6 | 0.291887 | ||||||||
\(805\) | −104831. | −0.00570166 | ||||||||
\(806\) | 1.90756e7 | 1.03429 | ||||||||
\(807\) | −3.13329e7 | −1.69362 | ||||||||
\(808\) | −1.71182e7 | −0.922422 | ||||||||
\(809\) | −3.29258e6 | −0.176874 | −0.0884371 | − | 0.996082i | \(-0.528187\pi\) | ||||
−0.0884371 | + | 0.996082i | \(0.528187\pi\) | |||||||
\(810\) | 8.01358e6 | 0.429155 | ||||||||
\(811\) | 8.58147e6 | 0.458152 | 0.229076 | − | 0.973409i | \(-0.426430\pi\) | ||||
0.229076 | + | 0.973409i | \(0.426430\pi\) | |||||||
\(812\) | 4.48807e6 | 0.238874 | ||||||||
\(813\) | −2.65541e7 | −1.40898 | ||||||||
\(814\) | 1.25656e6 | 0.0664694 | ||||||||
\(815\) | −2.63991e7 | −1.39218 | ||||||||
\(816\) | 1.96564e6 | 0.103342 | ||||||||
\(817\) | 2.98234e6 | 0.156315 | ||||||||
\(818\) | −9.80249e6 | −0.512216 | ||||||||
\(819\) | 3.01713e6 | 0.157175 | ||||||||
\(820\) | −1.89608e7 | −0.984741 | ||||||||
\(821\) | −7.34065e6 | −0.380081 | −0.190041 | − | 0.981776i | \(-0.560862\pi\) | ||||
−0.190041 | + | 0.981776i | \(0.560862\pi\) | |||||||
\(822\) | −1.22831e7 | −0.634056 | ||||||||
\(823\) | 3.32707e7 | 1.71223 | 0.856116 | − | 0.516783i | \(-0.172871\pi\) | ||||
0.856116 | + | 0.516783i | \(0.172871\pi\) | |||||||
\(824\) | 7.09694e6 | 0.364127 | ||||||||
\(825\) | −1.19908e6 | −0.0613359 | ||||||||
\(826\) | −4.13765e6 | −0.211010 | ||||||||
\(827\) | −3.77399e7 | −1.91883 | −0.959417 | − | 0.281992i | \(-0.909005\pi\) | ||||
−0.959417 | + | 0.281992i | \(0.909005\pi\) | |||||||
\(828\) | 35613.0 | 0.00180523 | ||||||||
\(829\) | −2.81993e7 | −1.42512 | −0.712560 | − | 0.701611i | \(-0.752465\pi\) | ||||
−0.712560 | + | 0.701611i | \(0.752465\pi\) | |||||||
\(830\) | −3.43374e6 | −0.173011 | ||||||||
\(831\) | 5.43008e6 | 0.272775 | ||||||||
\(832\) | −391693. | −0.0196172 | ||||||||
\(833\) | −3.08092e6 | −0.153839 | ||||||||
\(834\) | 1.58409e7 | 0.788616 | ||||||||
\(835\) | −1.13535e7 | −0.563528 | ||||||||
\(836\) | −3.38064e6 | −0.167295 | ||||||||
\(837\) | 2.44344e7 | 1.20556 | ||||||||
\(838\) | −7.32159e6 | −0.360160 | ||||||||
\(839\) | −9.00386e6 | −0.441594 | −0.220797 | − | 0.975320i | \(-0.570866\pi\) | ||||
−0.220797 | + | 0.975320i | \(0.570866\pi\) | |||||||
\(840\) | 7.80788e6 | 0.381799 | ||||||||
\(841\) | −1.38354e7 | −0.674531 | ||||||||
\(842\) | −1.10842e7 | −0.538797 | ||||||||
\(843\) | −8.47102e6 | −0.410551 | ||||||||
\(844\) | 2.52287e7 | 1.21910 | ||||||||
\(845\) | 3.55788e7 | 1.71415 | ||||||||
\(846\) | 178746. | 0.00858637 | ||||||||
\(847\) | −1.04176e7 | −0.498951 | ||||||||
\(848\) | −1.18581e7 | −0.566275 | ||||||||
\(849\) | 5.87152e6 | 0.279564 | ||||||||
\(850\) | 548180. | 0.0260241 | ||||||||
\(851\) | 202152. | 0.00956870 | ||||||||
\(852\) | −8.13751e6 | −0.384054 | ||||||||
\(853\) | 2.76660e7 | 1.30189 | 0.650944 | − | 0.759126i | \(-0.274373\pi\) | ||||
0.650944 | + | 0.759126i | \(0.274373\pi\) | |||||||
\(854\) | −1.38457e6 | −0.0649638 | ||||||||
\(855\) | 3.23403e6 | 0.151296 | ||||||||
\(856\) | −2.26151e7 | −1.05491 | ||||||||
\(857\) | −3.77780e7 | −1.75706 | −0.878531 | − | 0.477686i | \(-0.841476\pi\) | ||||
−0.878531 | + | 0.477686i | \(0.841476\pi\) | |||||||
\(858\) | −3.63898e6 | −0.168757 | ||||||||
\(859\) | 2.02066e7 | 0.934352 | 0.467176 | − | 0.884164i | \(-0.345271\pi\) | ||||
0.467176 | + | 0.884164i | \(0.345271\pi\) | |||||||
\(860\) | −2.25974e6 | −0.104187 | ||||||||
\(861\) | 1.76763e7 | 0.812613 | ||||||||
\(862\) | −1.06805e7 | −0.489578 | ||||||||
\(863\) | −992399. | −0.0453586 | −0.0226793 | − | 0.999743i | \(-0.507220\pi\) | ||||
−0.0226793 | + | 0.999743i | \(0.507220\pi\) | |||||||
\(864\) | 1.95903e7 | 0.892804 | ||||||||
\(865\) | 3.77637e6 | 0.171607 | ||||||||
\(866\) | 4.14613e6 | 0.187866 | ||||||||
\(867\) | −2.29130e7 | −1.03522 | ||||||||
\(868\) | 1.25180e7 | 0.563944 | ||||||||
\(869\) | −4.26308e6 | −0.191502 | ||||||||
\(870\) | 5.17832e6 | 0.231948 | ||||||||
\(871\) | −1.30247e7 | −0.581732 | ||||||||
\(872\) | 3.01644e7 | 1.34339 | ||||||||
\(873\) | −6.21588e6 | −0.276037 | ||||||||
\(874\) | 132031. | 0.00584651 | ||||||||
\(875\) | −1.27987e7 | −0.565126 | ||||||||
\(876\) | 5.27356e6 | 0.232190 | ||||||||
\(877\) | 3.48750e7 | 1.53114 | 0.765572 | − | 0.643351i | \(-0.222456\pi\) | ||||
0.765572 | + | 0.643351i | \(0.222456\pi\) | |||||||
\(878\) | 3.60656e6 | 0.157891 | ||||||||
\(879\) | −2.71702e7 | −1.18610 | ||||||||
\(880\) | 1.78873e6 | 0.0778643 | ||||||||
\(881\) | 2.68921e7 | 1.16731 | 0.583654 | − | 0.812002i | \(-0.301622\pi\) | ||||
0.583654 | + | 0.812002i | \(0.301622\pi\) | |||||||
\(882\) | 1.29446e6 | 0.0560295 | ||||||||
\(883\) | −2.40336e6 | −0.103733 | −0.0518666 | − | 0.998654i | \(-0.516517\pi\) | ||||
−0.0518666 | + | 0.998654i | \(0.516517\pi\) | |||||||
\(884\) | −6.85286e6 | −0.294945 | ||||||||
\(885\) | 1.96653e7 | 0.844002 | ||||||||
\(886\) | −1.45073e7 | −0.620874 | ||||||||
\(887\) | −2.56525e7 | −1.09477 | −0.547383 | − | 0.836882i | \(-0.684376\pi\) | ||||
−0.547383 | + | 0.836882i | \(0.684376\pi\) | |||||||
\(888\) | −1.50563e7 | −0.640747 | ||||||||
\(889\) | 4.88616e6 | 0.207355 | ||||||||
\(890\) | −1.39215e7 | −0.589128 | ||||||||
\(891\) | −5.49683e6 | −0.231963 | ||||||||
\(892\) | −1.72198e7 | −0.724629 | ||||||||
\(893\) | −2.72973e6 | −0.114549 | ||||||||
\(894\) | −1.82051e7 | −0.761816 | ||||||||
\(895\) | −4.54885e6 | −0.189821 | ||||||||
\(896\) | 1.25351e7 | 0.521626 | ||||||||
\(897\) | −585429. | −0.0242937 | ||||||||
\(898\) | 4.66167e6 | 0.192908 | ||||||||
\(899\) | 1.86198e7 | 0.768379 | ||||||||
\(900\) | 948746. | 0.0390430 | ||||||||
\(901\) | −6.43837e6 | −0.264219 | ||||||||
\(902\) | −3.15736e6 | −0.129214 | ||||||||
\(903\) | 2.10665e6 | 0.0859753 | ||||||||
\(904\) | 4.83557e6 | 0.196801 | ||||||||
\(905\) | −1.04141e7 | −0.422669 | ||||||||
\(906\) | −728501. | −0.0294856 | ||||||||
\(907\) | −2.68686e7 | −1.08450 | −0.542248 | − | 0.840219i | \(-0.682426\pi\) | ||||
−0.542248 | + | 0.840219i | \(0.682426\pi\) | |||||||
\(908\) | 3.62342e7 | 1.45849 | ||||||||
\(909\) | −5.00847e6 | −0.201046 | ||||||||
\(910\) | −8.47544e6 | −0.339280 | ||||||||
\(911\) | 1.69356e7 | 0.676091 | 0.338045 | − | 0.941130i | \(-0.390234\pi\) | ||||
0.338045 | + | 0.941130i | \(0.390234\pi\) | |||||||
\(912\) | 1.26124e7 | 0.502122 | ||||||||
\(913\) | 2.35534e6 | 0.0935141 | ||||||||
\(914\) | −9.02838e6 | −0.357474 | ||||||||
\(915\) | 6.58058e6 | 0.259843 | ||||||||
\(916\) | −1.81981e7 | −0.716616 | ||||||||
\(917\) | −4.92744e6 | −0.193508 | ||||||||
\(918\) | 2.13096e6 | 0.0834582 | ||||||||
\(919\) | −2.20166e7 | −0.859927 | −0.429964 | − | 0.902846i | \(-0.641474\pi\) | ||||
−0.429964 | + | 0.902846i | \(0.641474\pi\) | |||||||
\(920\) | −224367. | −0.00873957 | ||||||||
\(921\) | 4.22308e7 | 1.64051 | ||||||||
\(922\) | −1.45579e7 | −0.563989 | ||||||||
\(923\) | 1.98109e7 | 0.765420 | ||||||||
\(924\) | −2.38801e6 | −0.0920144 | ||||||||
\(925\) | 5.38540e6 | 0.206949 | ||||||||
\(926\) | −1.89906e6 | −0.0727799 | ||||||||
\(927\) | 2.07643e6 | 0.0793631 | ||||||||
\(928\) | 1.49284e7 | 0.569041 | ||||||||
\(929\) | −8.11263e6 | −0.308406 | −0.154203 | − | 0.988039i | \(-0.549281\pi\) | ||||
−0.154203 | + | 0.988039i | \(0.549281\pi\) | |||||||
\(930\) | 1.44432e7 | 0.547592 | ||||||||
\(931\) | −1.97685e7 | −0.747478 | ||||||||
\(932\) | −2.08792e7 | −0.787362 | ||||||||
\(933\) | 4.73493e7 | 1.78078 | ||||||||
\(934\) | −8.26392e6 | −0.309970 | ||||||||
\(935\) | 971190. | 0.0363308 | ||||||||
\(936\) | 6.45748e6 | 0.240920 | ||||||||
\(937\) | −1.80064e7 | −0.670004 | −0.335002 | − | 0.942217i | \(-0.608737\pi\) | ||||
−0.335002 | + | 0.942217i | \(0.608737\pi\) | |||||||
\(938\) | 2.07494e6 | 0.0770013 | ||||||||
\(939\) | −1.73250e6 | −0.0641224 | ||||||||
\(940\) | 2.06834e6 | 0.0763488 | ||||||||
\(941\) | 2.90643e7 | 1.07000 | 0.535002 | − | 0.844851i | \(-0.320311\pi\) | ||||
0.535002 | + | 0.844851i | \(0.320311\pi\) | |||||||
\(942\) | 5.89039e6 | 0.216280 | ||||||||
\(943\) | −507947. | −0.0186011 | ||||||||
\(944\) | 1.13580e7 | 0.414832 | ||||||||
\(945\) | −1.08564e7 | −0.395463 | ||||||||
\(946\) | −376293. | −0.0136709 | ||||||||
\(947\) | −1.97188e7 | −0.714504 | −0.357252 | − | 0.934008i | \(-0.616286\pi\) | ||||
−0.357252 | + | 0.934008i | \(0.616286\pi\) | |||||||
\(948\) | 2.27759e7 | 0.823105 | ||||||||
\(949\) | −1.28386e7 | −0.462755 | ||||||||
\(950\) | 3.51736e6 | 0.126447 | ||||||||
\(951\) | −4.44895e6 | −0.159517 | ||||||||
\(952\) | 2.44846e6 | 0.0875588 | ||||||||
\(953\) | −5.34568e6 | −0.190665 | −0.0953325 | − | 0.995445i | \(-0.530391\pi\) | ||||
−0.0953325 | + | 0.995445i | \(0.530391\pi\) | |||||||
\(954\) | 2.70510e6 | 0.0962306 | ||||||||
\(955\) | 1.56026e7 | 0.553592 | ||||||||
\(956\) | −2.08943e6 | −0.0739405 | ||||||||
\(957\) | −3.55202e6 | −0.125370 | ||||||||
\(958\) | 1.90993e7 | 0.672364 | ||||||||
\(959\) | 1.96235e7 | 0.689016 | ||||||||
\(960\) | −296572. | −0.0103861 | ||||||||
\(961\) | 2.33046e7 | 0.814017 | ||||||||
\(962\) | 1.63436e7 | 0.569391 | ||||||||
\(963\) | −6.61676e6 | −0.229922 | ||||||||
\(964\) | −1.38738e7 | −0.480843 | ||||||||
\(965\) | 2.73268e7 | 0.944648 | ||||||||
\(966\) | 93263.4 | 0.00321565 | ||||||||
\(967\) | −605934. | −0.0208381 | −0.0104191 | − | 0.999946i | \(-0.503317\pi\) | ||||
−0.0104191 | + | 0.999946i | \(0.503317\pi\) | |||||||
\(968\) | −2.22964e7 | −0.764798 | ||||||||
\(969\) | 6.84787e6 | 0.234286 | ||||||||
\(970\) | 1.74610e7 | 0.595855 | ||||||||
\(971\) | 2.31358e7 | 0.787475 | 0.393737 | − | 0.919223i | \(-0.371182\pi\) | ||||
0.393737 | + | 0.919223i | \(0.371182\pi\) | |||||||
\(972\) | 8.15226e6 | 0.276766 | ||||||||
\(973\) | −2.53075e7 | −0.856972 | ||||||||
\(974\) | 1.00988e7 | 0.341092 | ||||||||
\(975\) | −1.55961e7 | −0.525416 | ||||||||
\(976\) | 3.80071e6 | 0.127714 | ||||||||
\(977\) | 2.22967e6 | 0.0747315 | 0.0373658 | − | 0.999302i | \(-0.488103\pi\) | ||||
0.0373658 | + | 0.999302i | \(0.488103\pi\) | |||||||
\(978\) | 2.34860e7 | 0.785166 | ||||||||
\(979\) | 9.54928e6 | 0.318430 | ||||||||
\(980\) | 1.49787e7 | 0.498206 | ||||||||
\(981\) | 8.82555e6 | 0.292799 | ||||||||
\(982\) | −1.90660e7 | −0.630929 | ||||||||
\(983\) | −2.21182e6 | −0.0730071 | −0.0365036 | − | 0.999334i | \(-0.511622\pi\) | ||||
−0.0365036 | + | 0.999334i | \(0.511622\pi\) | |||||||
\(984\) | 3.78321e7 | 1.24558 | ||||||||
\(985\) | 4.57019e7 | 1.50087 | ||||||||
\(986\) | 1.62386e6 | 0.0531932 | ||||||||
\(987\) | −1.92822e6 | −0.0630033 | ||||||||
\(988\) | −4.39708e7 | −1.43309 | ||||||||
\(989\) | −60536.9 | −0.00196802 | ||||||||
\(990\) | −408049. | −0.0132320 | ||||||||
\(991\) | −1.66837e7 | −0.539645 | −0.269823 | − | 0.962910i | \(-0.586965\pi\) | ||||
−0.269823 | + | 0.962910i | \(0.586965\pi\) | |||||||
\(992\) | 4.16379e7 | 1.34341 | ||||||||
\(993\) | −3.91332e7 | −1.25943 | ||||||||
\(994\) | −3.15603e6 | −0.101315 | ||||||||
\(995\) | −3.60792e7 | −1.15531 | ||||||||
\(996\) | −1.25836e7 | −0.401937 | ||||||||
\(997\) | 1.01549e7 | 0.323547 | 0.161774 | − | 0.986828i | \(-0.448279\pi\) | ||||
0.161774 | + | 0.986828i | \(0.448279\pi\) | |||||||
\(998\) | −2.38810e7 | −0.758971 | ||||||||
\(999\) | 2.09349e7 | 0.663677 |
(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 | 43.6.a.b.1.4 | ✓ | 10 | |
3.2 | odd | 2 | 387.6.a.e.1.7 | 10 | |||
4.3 | odd | 2 | 688.6.a.h.1.4 | 10 | |||
5.4 | even | 2 | 1075.6.a.b.1.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.b.1.4 | ✓ | 10 | 1.1 | even | 1 | trivial | |
387.6.a.e.1.7 | 10 | 3.2 | odd | 2 | |||
688.6.a.h.1.4 | 10 | 4.3 | odd | 2 | |||
1075.6.a.b.1.7 | 10 | 5.4 | even | 2 |