Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,6,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, 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("531.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(85.1638083207\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 269 x^{10} + 143 x^{9} + 25384 x^{8} + 8539 x^{7} - 1009736 x^{6} - 720516 x^{5} + \cdots + 49172480 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.38446\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.615542 | −0.108813 | −0.0544067 | − | 0.998519i | \(-0.517327\pi\) | ||||
−0.0544067 | + | 0.998519i | \(0.517327\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −31.6211 | −0.988160 | ||||||||
\(5\) | −61.9372 | −1.10797 | −0.553984 | − | 0.832528i | \(-0.686893\pi\) | ||||
−0.553984 | + | 0.832528i | \(0.686893\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −209.534 | −1.61625 | −0.808125 | − | 0.589011i | \(-0.799518\pi\) | ||||
−0.808125 | + | 0.589011i | \(0.799518\pi\) | |||||||
\(8\) | 39.1615 | 0.216339 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 38.1250 | 0.120562 | ||||||||
\(11\) | −1.45515 | −0.00362599 | −0.00181299 | − | 0.999998i | \(-0.500577\pi\) | ||||
−0.00181299 | + | 0.999998i | \(0.500577\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 351.120 | 0.576231 | 0.288116 | − | 0.957596i | \(-0.406971\pi\) | ||||
0.288116 | + | 0.957596i | \(0.406971\pi\) | |||||||
\(14\) | 128.977 | 0.175870 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 987.770 | 0.964619 | ||||||||
\(17\) | −689.107 | −0.578315 | −0.289157 | − | 0.957282i | \(-0.593375\pi\) | ||||
−0.289157 | + | 0.957282i | \(0.593375\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2735.73 | 1.73856 | 0.869278 | − | 0.494323i | \(-0.164584\pi\) | ||||
0.869278 | + | 0.494323i | \(0.164584\pi\) | |||||||
\(20\) | 1958.52 | 1.09485 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.895706 | 0.000394556 0 | ||||||||
\(23\) | 1310.96 | 0.516737 | 0.258369 | − | 0.966046i | \(-0.416815\pi\) | ||||
0.258369 | + | 0.966046i | \(0.416815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 711.222 | 0.227591 | ||||||||
\(26\) | −216.129 | −0.0627017 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6625.69 | 1.59711 | ||||||||
\(29\) | −508.995 | −0.112388 | −0.0561938 | − | 0.998420i | \(-0.517896\pi\) | ||||
−0.0561938 | + | 0.998420i | \(0.517896\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4218.33 | 0.788381 | 0.394191 | − | 0.919029i | \(-0.371025\pi\) | ||||
0.394191 | + | 0.919029i | \(0.371025\pi\) | |||||||
\(32\) | −1861.18 | −0.321302 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 424.174 | 0.0629285 | ||||||||
\(35\) | 12977.9 | 1.79075 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4022.89 | 0.483096 | 0.241548 | − | 0.970389i | \(-0.422345\pi\) | ||||
0.241548 | + | 0.970389i | \(0.422345\pi\) | |||||||
\(38\) | −1683.95 | −0.189178 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2425.55 | −0.239696 | ||||||||
\(41\) | −7333.96 | −0.681364 | −0.340682 | − | 0.940179i | \(-0.610658\pi\) | ||||
−0.340682 | + | 0.940179i | \(0.610658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5250.80 | 0.433066 | 0.216533 | − | 0.976275i | \(-0.430525\pi\) | ||||
0.216533 | + | 0.976275i | \(0.430525\pi\) | |||||||
\(44\) | 46.0135 | 0.00358305 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −806.951 | −0.0562280 | ||||||||
\(47\) | −25394.3 | −1.67684 | −0.838420 | − | 0.545024i | \(-0.816521\pi\) | ||||
−0.838420 | + | 0.545024i | \(0.816521\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 27097.3 | 1.61227 | ||||||||
\(50\) | −437.787 | −0.0247650 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −11102.8 | −0.569408 | ||||||||
\(53\) | 16562.5 | 0.809911 | 0.404956 | − | 0.914336i | \(-0.367287\pi\) | ||||
0.404956 | + | 0.914336i | \(0.367287\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 90.1280 | 0.00401747 | ||||||||
\(56\) | −8205.64 | −0.349657 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 313.308 | 0.0122293 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4267.66 | −0.146847 | −0.0734235 | − | 0.997301i | \(-0.523392\pi\) | ||||
−0.0734235 | + | 0.997301i | \(0.523392\pi\) | |||||||
\(62\) | −2596.56 | −0.0857865 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −30463.0 | −0.929657 | ||||||||
\(65\) | −21747.4 | −0.638445 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13390.6 | 0.364429 | 0.182215 | − | 0.983259i | \(-0.441673\pi\) | ||||
0.182215 | + | 0.983259i | \(0.441673\pi\) | |||||||
\(68\) | 21790.3 | 0.571467 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7988.46 | −0.194858 | ||||||||
\(71\) | −54112.6 | −1.27395 | −0.636976 | − | 0.770884i | \(-0.719815\pi\) | ||||
−0.636976 | + | 0.770884i | \(0.719815\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −32575.3 | −0.715453 | −0.357726 | − | 0.933826i | \(-0.616448\pi\) | ||||
−0.357726 | + | 0.933826i | \(0.616448\pi\) | |||||||
\(74\) | −2476.26 | −0.0525674 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −86506.7 | −1.71797 | ||||||||
\(77\) | 304.903 | 0.00586050 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 59592.4 | 1.07429 | 0.537147 | − | 0.843489i | \(-0.319502\pi\) | ||||
0.537147 | + | 0.843489i | \(0.319502\pi\) | |||||||
\(80\) | −61179.7 | −1.06877 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4514.36 | 0.0741415 | ||||||||
\(83\) | −94095.2 | −1.49924 | −0.749622 | − | 0.661867i | \(-0.769764\pi\) | ||||
−0.749622 | + | 0.661867i | \(0.769764\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 42681.4 | 0.640754 | ||||||||
\(86\) | −3232.09 | −0.0471235 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −56.9858 | −0.000784441 0 | ||||||||
\(89\) | 136311. | 1.82414 | 0.912068 | − | 0.410040i | \(-0.134485\pi\) | ||||
0.912068 | + | 0.410040i | \(0.134485\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −73571.4 | −0.931334 | ||||||||
\(92\) | −41454.0 | −0.510619 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15631.3 | 0.182463 | ||||||||
\(95\) | −169443. | −1.92626 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 135175. | 1.45870 | 0.729350 | − | 0.684141i | \(-0.239823\pi\) | ||||
0.729350 | + | 0.684141i | \(0.239823\pi\) | |||||||
\(98\) | −16679.6 | −0.175436 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −22489.6 | −0.224896 | ||||||||
\(101\) | 25496.8 | 0.248704 | 0.124352 | − | 0.992238i | \(-0.460315\pi\) | ||||
0.124352 | + | 0.992238i | \(0.460315\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 62339.3 | 0.578987 | 0.289493 | − | 0.957180i | \(-0.406513\pi\) | ||||
0.289493 | + | 0.957180i | \(0.406513\pi\) | |||||||
\(104\) | 13750.4 | 0.124661 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10194.9 | −0.0881293 | ||||||||
\(107\) | 16258.7 | 0.137286 | 0.0686429 | − | 0.997641i | \(-0.478133\pi\) | ||||
0.0686429 | + | 0.997641i | \(0.478133\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −209396. | −1.68812 | −0.844059 | − | 0.536250i | \(-0.819840\pi\) | ||||
−0.844059 | + | 0.536250i | \(0.819840\pi\) | |||||||
\(110\) | −55.4776 | −0.000437155 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −206971. | −1.55907 | ||||||||
\(113\) | 143342. | 1.05603 | 0.528017 | − | 0.849234i | \(-0.322936\pi\) | ||||
0.528017 | + | 0.849234i | \(0.322936\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −81197.2 | −0.572528 | ||||||||
\(116\) | 16095.0 | 0.111057 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2142.70 | −0.0141663 | ||||||||
\(119\) | 144391. | 0.934702 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −161049. | −0.999987 | ||||||||
\(122\) | 2626.92 | 0.0159789 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −133388. | −0.779046 | ||||||||
\(125\) | 149503. | 0.855804 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 79745.4 | 0.438729 | 0.219365 | − | 0.975643i | \(-0.429602\pi\) | ||||
0.219365 | + | 0.975643i | \(0.429602\pi\) | |||||||
\(128\) | 78309.0 | 0.422461 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13386.4 | 0.0694714 | ||||||||
\(131\) | 5118.41 | 0.0260589 | 0.0130295 | − | 0.999915i | \(-0.495852\pi\) | ||||
0.0130295 | + | 0.999915i | \(0.495852\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −573227. | −2.80994 | ||||||||
\(134\) | −8242.49 | −0.0396548 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −26986.4 | −0.125112 | ||||||||
\(137\) | 237403. | 1.08065 | 0.540324 | − | 0.841457i | \(-0.318302\pi\) | ||||
0.540324 | + | 0.841457i | \(0.318302\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −60191.4 | −0.264239 | −0.132120 | − | 0.991234i | \(-0.542178\pi\) | ||||
−0.132120 | + | 0.991234i | \(0.542178\pi\) | |||||||
\(140\) | −410377. | −1.76955 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 33308.6 | 0.138623 | ||||||||
\(143\) | −510.932 | −0.00208941 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 31525.7 | 0.124522 | ||||||||
\(146\) | 20051.4 | 0.0778509 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −127208. | −0.477376 | ||||||||
\(149\) | 226647. | 0.836343 | 0.418171 | − | 0.908368i | \(-0.362671\pi\) | ||||
0.418171 | + | 0.908368i | \(0.362671\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −294492. | −1.05107 | −0.525534 | − | 0.850773i | \(-0.676134\pi\) | ||||
−0.525534 | + | 0.850773i | \(0.676134\pi\) | |||||||
\(152\) | 107135. | 0.376117 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −187.681 | −0.000637702 0 | ||||||||
\(155\) | −261272. | −0.873500 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 527580. | 1.70820 | 0.854101 | − | 0.520108i | \(-0.174108\pi\) | ||||
0.854101 | + | 0.520108i | \(0.174108\pi\) | |||||||
\(158\) | −36681.6 | −0.116898 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 115276. | 0.355992 | ||||||||
\(161\) | −274690. | −0.835177 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 138581. | 0.408540 | 0.204270 | − | 0.978915i | \(-0.434518\pi\) | ||||
0.204270 | + | 0.978915i | \(0.434518\pi\) | |||||||
\(164\) | 231908. | 0.673296 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 57919.5 | 0.163138 | ||||||||
\(167\) | −201512. | −0.559126 | −0.279563 | − | 0.960127i | \(-0.590190\pi\) | ||||
−0.279563 | + | 0.960127i | \(0.590190\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −248008. | −0.667958 | ||||||||
\(170\) | −26272.2 | −0.0697227 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −166036. | −0.427939 | ||||||||
\(173\) | −463291. | −1.17690 | −0.588449 | − | 0.808535i | \(-0.700261\pi\) | ||||
−0.588449 | + | 0.808535i | \(0.700261\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −149025. | −0.367844 | ||||||||
\(176\) | −1437.35 | −0.00349770 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −83905.4 | −0.198490 | ||||||||
\(179\) | 235004. | 0.548205 | 0.274103 | − | 0.961700i | \(-0.411619\pi\) | ||||
0.274103 | + | 0.961700i | \(0.411619\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 345261. | 0.783341 | 0.391670 | − | 0.920106i | \(-0.371897\pi\) | ||||
0.391670 | + | 0.920106i | \(0.371897\pi\) | |||||||
\(182\) | 45286.3 | 0.101342 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 51339.1 | 0.111790 | ||||||||
\(185\) | −249167. | −0.535255 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1002.75 | 0.00209696 | ||||||||
\(188\) | 802996. | 1.65699 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 104300. | 0.209603 | ||||||||
\(191\) | −973228. | −1.93033 | −0.965164 | − | 0.261646i | \(-0.915735\pi\) | ||||
−0.965164 | + | 0.261646i | \(0.915735\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −493451. | −0.953567 | −0.476783 | − | 0.879021i | \(-0.658197\pi\) | ||||
−0.476783 | + | 0.879021i | \(0.658197\pi\) | |||||||
\(194\) | −83205.7 | −0.158726 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −856848. | −1.59318 | ||||||||
\(197\) | −339146. | −0.622616 | −0.311308 | − | 0.950309i | \(-0.600767\pi\) | ||||
−0.311308 | + | 0.950309i | \(0.600767\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −589702. | −1.05560 | −0.527801 | − | 0.849368i | \(-0.676983\pi\) | ||||
−0.527801 | + | 0.849368i | \(0.676983\pi\) | |||||||
\(200\) | 27852.5 | 0.0492368 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15694.4 | −0.0270623 | ||||||||
\(203\) | 106652. | 0.181646 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 454245. | 0.754929 | ||||||||
\(206\) | −38372.4 | −0.0630015 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 346825. | 0.555844 | ||||||||
\(209\) | −3980.89 | −0.00630398 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 779769. | 1.20576 | 0.602879 | − | 0.797833i | \(-0.294020\pi\) | ||||
0.602879 | + | 0.797833i | \(0.294020\pi\) | |||||||
\(212\) | −523726. | −0.800322 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10007.9 | −0.0149385 | ||||||||
\(215\) | −325220. | −0.479823 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −883882. | −1.27422 | ||||||||
\(218\) | 128892. | 0.183690 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2849.95 | −0.00396991 | ||||||||
\(221\) | −241959. | −0.333243 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 148653. | 0.200176 | 0.100088 | − | 0.994979i | \(-0.468088\pi\) | ||||
0.100088 | + | 0.994979i | \(0.468088\pi\) | |||||||
\(224\) | 389980. | 0.519305 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −88233.2 | −0.114911 | ||||||||
\(227\) | 705507. | 0.908733 | 0.454367 | − | 0.890815i | \(-0.349866\pi\) | ||||
0.454367 | + | 0.890815i | \(0.349866\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 221449. | 0.279052 | 0.139526 | − | 0.990218i | \(-0.455442\pi\) | ||||
0.139526 | + | 0.990218i | \(0.455442\pi\) | |||||||
\(230\) | 49980.3 | 0.0622987 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19933.0 | −0.0243138 | ||||||||
\(233\) | 303806. | 0.366612 | 0.183306 | − | 0.983056i | \(-0.441320\pi\) | ||||
0.183306 | + | 0.983056i | \(0.441320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.57285e6 | 1.85788 | ||||||||
\(236\) | −110073. | −0.128647 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −88878.8 | −0.101708 | ||||||||
\(239\) | −1.12989e6 | −1.27950 | −0.639751 | − | 0.768583i | \(-0.720962\pi\) | ||||
−0.639751 | + | 0.768583i | \(0.720962\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.30930e6 | −1.45210 | −0.726049 | − | 0.687643i | \(-0.758645\pi\) | ||||
−0.726049 | + | 0.687643i | \(0.758645\pi\) | |||||||
\(242\) | 99132.3 | 0.108812 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 134948. | 0.145108 | ||||||||
\(245\) | −1.67834e6 | −1.78634 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 960568. | 1.00181 | ||||||||
\(248\) | 165196. | 0.170557 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −92025.2 | −0.0931230 | ||||||||
\(251\) | 948490. | 0.950273 | 0.475136 | − | 0.879912i | \(-0.342399\pi\) | ||||
0.475136 | + | 0.879912i | \(0.342399\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1907.64 | −0.00187368 | ||||||||
\(254\) | −49086.7 | −0.0477396 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 926614. | 0.883688 | ||||||||
\(257\) | −1.82976e6 | −1.72807 | −0.864036 | − | 0.503431i | \(-0.832071\pi\) | ||||
−0.864036 | + | 0.503431i | \(0.832071\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −842930. | −0.780804 | ||||||||
\(260\) | 687676. | 0.630886 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3150.60 | −0.00283556 | ||||||||
\(263\) | −1.23847e6 | −1.10407 | −0.552033 | − | 0.833822i | \(-0.686148\pi\) | ||||
−0.552033 | + | 0.833822i | \(0.686148\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.02584e6 | −0.897355 | ||||||||
\(266\) | 352845. | 0.305760 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −423426. | −0.360115 | ||||||||
\(269\) | −1.19822e6 | −1.00962 | −0.504808 | − | 0.863232i | \(-0.668437\pi\) | ||||
−0.504808 | + | 0.863232i | \(0.668437\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −907388. | −0.750533 | −0.375267 | − | 0.926917i | \(-0.622449\pi\) | ||||
−0.375267 | + | 0.926917i | \(0.622449\pi\) | |||||||
\(272\) | −680679. | −0.557854 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −146131. | −0.117589 | ||||||||
\(275\) | −1034.94 | −0.000825243 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 196862. | 0.154157 | 0.0770783 | − | 0.997025i | \(-0.475441\pi\) | ||||
0.0770783 | + | 0.997025i | \(0.475441\pi\) | |||||||
\(278\) | 37050.3 | 0.0287528 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 508235. | 0.387409 | ||||||||
\(281\) | −2.31407e6 | −1.74828 | −0.874140 | − | 0.485674i | \(-0.838574\pi\) | ||||
−0.874140 | + | 0.485674i | \(0.838574\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 42804.6 | 0.0317705 | 0.0158852 | − | 0.999874i | \(-0.494943\pi\) | ||||
0.0158852 | + | 0.999874i | \(0.494943\pi\) | |||||||
\(284\) | 1.71110e6 | 1.25887 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 314.500 | 0.000227356 0 | ||||||||
\(287\) | 1.53671e6 | 1.10125 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −944988. | −0.665552 | ||||||||
\(290\) | −19405.4 | −0.0135496 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.03007e6 | 0.706981 | ||||||||
\(293\) | 943192. | 0.641846 | 0.320923 | − | 0.947105i | \(-0.396007\pi\) | ||||
0.320923 | + | 0.947105i | \(0.396007\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −215604. | −0.144245 | ||||||||
\(296\) | 157542. | 0.104512 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −139511. | −0.0910054 | ||||||||
\(299\) | 460304. | 0.297760 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.10022e6 | −0.699944 | ||||||||
\(302\) | 181272. | 0.114370 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.70227e6 | 1.67704 | ||||||||
\(305\) | 264327. | 0.162702 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.05157e6 | −0.636784 | −0.318392 | − | 0.947959i | \(-0.603143\pi\) | ||||
−0.318392 | + | 0.947959i | \(0.603143\pi\) | |||||||
\(308\) | −9641.37 | −0.00579111 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 160824. | 0.0950486 | ||||||||
\(311\) | 616781. | 0.361601 | 0.180801 | − | 0.983520i | \(-0.442131\pi\) | ||||
0.180801 | + | 0.983520i | \(0.442131\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.22803e6 | 0.708516 | 0.354258 | − | 0.935148i | \(-0.384733\pi\) | ||||
0.354258 | + | 0.935148i | \(0.384733\pi\) | |||||||
\(314\) | −324747. | −0.185875 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.88438e6 | −1.06157 | ||||||||
\(317\) | 2.46036e6 | 1.37515 | 0.687577 | − | 0.726112i | \(-0.258675\pi\) | ||||
0.687577 | + | 0.726112i | \(0.258675\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 740.664 | 0.000407516 0 | ||||||||
\(320\) | 1.88679e6 | 1.03003 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 169083. | 0.0908785 | ||||||||
\(323\) | −1.88521e6 | −1.00543 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 249724. | 0.131145 | ||||||||
\(326\) | −85302.3 | −0.0444546 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −287209. | −0.147405 | ||||||||
\(329\) | 5.32096e6 | 2.71019 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 58317.0 | 0.0292567 | 0.0146283 | − | 0.999893i | \(-0.495343\pi\) | ||||
0.0146283 | + | 0.999893i | \(0.495343\pi\) | |||||||
\(332\) | 2.97539e6 | 1.48149 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 124039. | 0.0608405 | ||||||||
\(335\) | −829378. | −0.403776 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.05912e6 | 0.987658 | 0.493829 | − | 0.869559i | \(-0.335597\pi\) | ||||
0.493829 | + | 0.869559i | \(0.335597\pi\) | |||||||
\(338\) | 152659. | 0.0726828 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.34963e6 | −0.633167 | ||||||||
\(341\) | −6138.30 | −0.00285866 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.15617e6 | −0.989574 | ||||||||
\(344\) | 205629. | 0.0936890 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 285175. | 0.128062 | ||||||||
\(347\) | 3.05058e6 | 1.36006 | 0.680030 | − | 0.733184i | \(-0.261967\pi\) | ||||
0.680030 | + | 0.733184i | \(0.261967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.54878e6 | −1.12013 | −0.560065 | − | 0.828449i | \(-0.689224\pi\) | ||||
−0.560065 | + | 0.828449i | \(0.689224\pi\) | |||||||
\(350\) | 91731.2 | 0.0400264 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2708.30 | 0.00116504 | ||||||||
\(353\) | 139978. | 0.0597891 | 0.0298945 | − | 0.999553i | \(-0.490483\pi\) | ||||
0.0298945 | + | 0.999553i | \(0.490483\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.35159e6 | 1.41150 | ||||||||
\(356\) | −4.31032e6 | −1.80254 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −144655. | −0.0596521 | ||||||||
\(359\) | 587724. | 0.240679 | 0.120339 | − | 0.992733i | \(-0.461602\pi\) | ||||
0.120339 | + | 0.992733i | \(0.461602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00810e6 | 2.02258 | ||||||||
\(362\) | −212522. | −0.0852380 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.32641e6 | 0.920307 | ||||||||
\(365\) | 2.01762e6 | 0.792698 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 360316. | 0.139643 | 0.0698214 | − | 0.997560i | \(-0.477757\pi\) | ||||
0.0698214 | + | 0.997560i | \(0.477757\pi\) | |||||||
\(368\) | 1.29493e6 | 0.498455 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 153372. | 0.0582429 | ||||||||
\(371\) | −3.47041e6 | −1.30902 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.26924e6 | 1.96099 | 0.980497 | − | 0.196535i | \(-0.0629690\pi\) | ||||
0.980497 | + | 0.196535i | \(0.0629690\pi\) | |||||||
\(374\) | −617.237 | −0.000228178 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −994478. | −0.362765 | ||||||||
\(377\) | −178718. | −0.0647612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.43445e6 | 1.22817 | 0.614086 | − | 0.789239i | \(-0.289525\pi\) | ||||
0.614086 | + | 0.789239i | \(0.289525\pi\) | |||||||
\(380\) | 5.35799e6 | 1.90346 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 599062. | 0.210046 | ||||||||
\(383\) | 3.55421e6 | 1.23807 | 0.619036 | − | 0.785363i | \(-0.287524\pi\) | ||||
0.619036 | + | 0.785363i | \(0.287524\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18884.8 | −0.00649324 | ||||||||
\(386\) | 303740. | 0.103761 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.27437e6 | −1.44143 | ||||||||
\(389\) | −4.52272e6 | −1.51539 | −0.757697 | − | 0.652606i | \(-0.773676\pi\) | ||||
−0.757697 | + | 0.652606i | \(0.773676\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −903392. | −0.298837 | ||||||||
\(392\) | 1.06117e6 | 0.348795 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 208758. | 0.0677491 | ||||||||
\(395\) | −3.69099e6 | −1.19028 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 407622. | 0.129802 | 0.0649011 | − | 0.997892i | \(-0.479327\pi\) | ||||
0.0649011 | + | 0.997892i | \(0.479327\pi\) | |||||||
\(398\) | 362987. | 0.114864 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 702524. | 0.219539 | ||||||||
\(401\) | −3.00347e6 | −0.932743 | −0.466372 | − | 0.884589i | \(-0.654439\pi\) | ||||
−0.466372 | + | 0.884589i | \(0.654439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.48114e6 | 0.454290 | ||||||||
\(404\) | −806237. | −0.245759 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −65648.5 | −0.0197656 | ||||||||
\(407\) | −5853.91 | −0.00175170 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.77645e6 | −1.41188 | −0.705938 | − | 0.708274i | \(-0.749474\pi\) | ||||
−0.705938 | + | 0.708274i | \(0.749474\pi\) | |||||||
\(410\) | −279607. | −0.0821464 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.97124e6 | −0.572131 | ||||||||
\(413\) | −729387. | −0.210418 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.82799e6 | 1.66111 | ||||||||
\(416\) | −653497. | −0.185144 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2450.41 | 0.000685958 0 | ||||||||
\(419\) | 2.95949e6 | 0.823535 | 0.411768 | − | 0.911289i | \(-0.364912\pi\) | ||||
0.411768 | + | 0.911289i | \(0.364912\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.17118e6 | 0.322047 | 0.161024 | − | 0.986951i | \(-0.448520\pi\) | ||||
0.161024 | + | 0.986951i | \(0.448520\pi\) | |||||||
\(422\) | −479981. | −0.131203 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 648614. | 0.175215 | ||||||||
\(425\) | −490108. | −0.131619 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 894218. | 0.237342 | ||||||||
\(428\) | −514117. | −0.135660 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 200187. | 0.0522112 | ||||||||
\(431\) | 2.43477e6 | 0.631341 | 0.315671 | − | 0.948869i | \(-0.397771\pi\) | ||||
0.315671 | + | 0.948869i | \(0.397771\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −229760. | −0.0588917 | −0.0294459 | − | 0.999566i | \(-0.509374\pi\) | ||||
−0.0294459 | + | 0.999566i | \(0.509374\pi\) | |||||||
\(434\) | 544066. | 0.138652 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.62134e6 | 1.66813 | ||||||||
\(437\) | 3.58643e6 | 0.898377 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.63343e6 | −0.652168 | −0.326084 | − | 0.945341i | \(-0.605729\pi\) | ||||
−0.326084 | + | 0.945341i | \(0.605729\pi\) | |||||||
\(440\) | 3529.54 | 0.000869134 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 148936. | 0.0362613 | ||||||||
\(443\) | 5.30123e6 | 1.28342 | 0.641708 | − | 0.766949i | \(-0.278226\pi\) | ||||
0.641708 | + | 0.766949i | \(0.278226\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.44275e6 | −2.02108 | ||||||||
\(446\) | −91502.4 | −0.0217819 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.38302e6 | 1.50256 | ||||||||
\(449\) | −2.32172e6 | −0.543494 | −0.271747 | − | 0.962369i | \(-0.587601\pi\) | ||||
−0.271747 | + | 0.962369i | \(0.587601\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10672.0 | 0.00247062 | ||||||||
\(452\) | −4.53264e6 | −1.04353 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −434269. | −0.0988824 | ||||||||
\(455\) | 4.55681e6 | 1.03189 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.05394e6 | −0.684022 | −0.342011 | − | 0.939696i | \(-0.611108\pi\) | ||||
−0.342011 | + | 0.939696i | \(0.611108\pi\) | |||||||
\(458\) | −136311. | −0.0303647 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.56755e6 | 0.565749 | ||||||||
\(461\) | −4.33222e6 | −0.949419 | −0.474710 | − | 0.880143i | \(-0.657447\pi\) | ||||
−0.474710 | + | 0.880143i | \(0.657447\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.38768e6 | −1.38481 | −0.692406 | − | 0.721508i | \(-0.743449\pi\) | ||||
−0.692406 | + | 0.721508i | \(0.743449\pi\) | |||||||
\(464\) | −502770. | −0.108411 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −187006. | −0.0398924 | ||||||||
\(467\) | −595087. | −0.126266 | −0.0631332 | − | 0.998005i | \(-0.520109\pi\) | ||||
−0.0631332 | + | 0.998005i | \(0.520109\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.80578e6 | −0.589009 | ||||||||
\(470\) | −968158. | −0.202163 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 136321. | 0.0281649 | ||||||||
\(473\) | −7640.71 | −0.00157029 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.94571e6 | 0.395680 | ||||||||
\(476\) | −4.56581e6 | −0.923635 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 695494. | 0.139227 | ||||||||
\(479\) | −854216. | −0.170110 | −0.0850548 | − | 0.996376i | \(-0.527107\pi\) | ||||
−0.0850548 | + | 0.996376i | \(0.527107\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.41251e6 | 0.278375 | ||||||||
\(482\) | 805928. | 0.158008 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.09254e6 | 0.988147 | ||||||||
\(485\) | −8.37235e6 | −1.61619 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.99300e6 | −1.33611 | −0.668054 | − | 0.744113i | \(-0.732872\pi\) | ||||
−0.668054 | + | 0.744113i | \(0.732872\pi\) | |||||||
\(488\) | −167128. | −0.0317687 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.03309e6 | 0.194378 | ||||||||
\(491\) | −6.08880e6 | −1.13980 | −0.569899 | − | 0.821715i | \(-0.693018\pi\) | ||||
−0.569899 | + | 0.821715i | \(0.693018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 350752. | 0.0649954 | ||||||||
\(494\) | −591270. | −0.109010 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.16674e6 | 0.760487 | ||||||||
\(497\) | 1.13384e7 | 2.05902 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.04489e7 | 1.87853 | 0.939264 | − | 0.343196i | \(-0.111510\pi\) | ||||
0.939264 | + | 0.343196i | \(0.111510\pi\) | |||||||
\(500\) | −4.72744e6 | −0.845671 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −583835. | −0.103403 | ||||||||
\(503\) | −3.92622e6 | −0.691918 | −0.345959 | − | 0.938250i | \(-0.612446\pi\) | ||||
−0.345959 | + | 0.938250i | \(0.612446\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.57920e6 | −0.275556 | ||||||||
\(506\) | 1174.23 | 0.000203882 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.52164e6 | −0.433534 | ||||||||
\(509\) | 5.65513e6 | 0.967493 | 0.483746 | − | 0.875208i | \(-0.339276\pi\) | ||||
0.483746 | + | 0.875208i | \(0.339276\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.82561e6 | 1.15635 | ||||||||
\(512\) | −3.07626e6 | −0.518618 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.12629e6 | 0.188037 | ||||||||
\(515\) | −3.86112e6 | −0.641498 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36952.5 | 0.00608020 | ||||||||
\(518\) | 518859. | 0.0849620 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −851659. | −0.138120 | ||||||||
\(521\) | 1.00145e7 | 1.61634 | 0.808172 | − | 0.588947i | \(-0.200457\pi\) | ||||
0.808172 | + | 0.588947i | \(0.200457\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.06776e6 | −1.44959 | −0.724796 | − | 0.688964i | \(-0.758066\pi\) | ||||
−0.724796 | + | 0.688964i | \(0.758066\pi\) | |||||||
\(524\) | −161850. | −0.0257504 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 762328. | 0.120137 | ||||||||
\(527\) | −2.90688e6 | −0.455933 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.71773e6 | −0.732983 | ||||||||
\(530\) | 631447. | 0.0976443 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.81261e7 | 2.77667 | ||||||||
\(533\) | −2.57510e6 | −0.392623 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.00702e6 | −0.152108 | ||||||||
\(536\) | 524396. | 0.0788402 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 737555. | 0.109860 | ||||||||
\(539\) | −39430.7 | −0.00584605 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.13999e7 | 1.67459 | 0.837296 | − | 0.546750i | \(-0.184135\pi\) | ||||
0.837296 | + | 0.546750i | \(0.184135\pi\) | |||||||
\(542\) | 558536. | 0.0816681 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.28255e6 | 0.185814 | ||||||||
\(545\) | 1.29694e7 | 1.87038 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.29969e6 | 1.32892 | 0.664462 | − | 0.747322i | \(-0.268661\pi\) | ||||
0.664462 | + | 0.747322i | \(0.268661\pi\) | |||||||
\(548\) | −7.50694e6 | −1.06785 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 637.046 | 8.97975e−5 0 | ||||||||
\(551\) | −1.39247e6 | −0.195392 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.24866e7 | −1.73633 | ||||||||
\(554\) | −121177. | −0.0167743 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.90332e6 | 0.261110 | ||||||||
\(557\) | 5.55080e6 | 0.758084 | 0.379042 | − | 0.925379i | \(-0.376254\pi\) | ||||
0.379042 | + | 0.925379i | \(0.376254\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.84366e6 | 0.249546 | ||||||||
\(560\) | 1.28192e7 | 1.72739 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.42441e6 | 0.190236 | ||||||||
\(563\) | −361373. | −0.0480490 | −0.0240245 | − | 0.999711i | \(-0.507648\pi\) | ||||
−0.0240245 | + | 0.999711i | \(0.507648\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.87823e6 | −1.17005 | ||||||||
\(566\) | −26348.0 | −0.00345706 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.11913e6 | −0.275605 | ||||||||
\(569\) | −6.95770e6 | −0.900917 | −0.450459 | − | 0.892797i | \(-0.648739\pi\) | ||||
−0.450459 | + | 0.892797i | \(0.648739\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.46705e7 | −1.88302 | −0.941511 | − | 0.336982i | \(-0.890594\pi\) | ||||
−0.941511 | + | 0.336982i | \(0.890594\pi\) | |||||||
\(572\) | 16156.2 | 0.00206467 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −945911. | −0.119831 | ||||||||
\(575\) | 932384. | 0.117605 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.16193e7 | −1.45291 | −0.726457 | − | 0.687212i | \(-0.758834\pi\) | ||||
−0.726457 | + | 0.687212i | \(0.758834\pi\) | |||||||
\(578\) | 581680. | 0.0724210 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −996879. | −0.123047 | ||||||||
\(581\) | 1.97161e7 | 2.42315 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24101.0 | −0.00293673 | ||||||||
\(584\) | −1.27570e6 | −0.154780 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −580574. | −0.0698415 | ||||||||
\(587\) | −1.26219e7 | −1.51192 | −0.755959 | − | 0.654619i | \(-0.772829\pi\) | ||||
−0.755959 | + | 0.654619i | \(0.772829\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.15402e7 | 1.37064 | ||||||||
\(590\) | 132713. | 0.0156958 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.97369e6 | 0.466004 | ||||||||
\(593\) | −8.70200e6 | −1.01621 | −0.508103 | − | 0.861296i | \(-0.669653\pi\) | ||||
−0.508103 | + | 0.861296i | \(0.669653\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.94319e6 | −1.03562 | ||||||||
\(596\) | −7.16683e6 | −0.826440 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −283336. | −0.0324003 | ||||||||
\(599\) | −314477. | −0.0358115 | −0.0179057 | − | 0.999840i | \(-0.505700\pi\) | ||||
−0.0179057 | + | 0.999840i | \(0.505700\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.33321e7 | −1.50561 | −0.752803 | − | 0.658246i | \(-0.771299\pi\) | ||||
−0.752803 | + | 0.658246i | \(0.771299\pi\) | |||||||
\(602\) | 677231. | 0.0761633 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.31216e6 | 1.03862 | ||||||||
\(605\) | 9.97492e6 | 1.10795 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.65927e6 | 0.513270 | 0.256635 | − | 0.966508i | \(-0.417386\pi\) | ||||
0.256635 | + | 0.966508i | \(0.417386\pi\) | |||||||
\(608\) | −5.09168e6 | −0.558602 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −162704. | −0.0177041 | ||||||||
\(611\) | −8.91644e6 | −0.966248 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.95032e6 | 0.424601 | 0.212301 | − | 0.977204i | \(-0.431904\pi\) | ||||
0.212301 | + | 0.977204i | \(0.431904\pi\) | |||||||
\(614\) | 647286. | 0.0692907 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11940.4 | 0.00126785 | ||||||||
\(617\) | −9.77175e6 | −1.03338 | −0.516689 | − | 0.856173i | \(-0.672836\pi\) | ||||
−0.516689 | + | 0.856173i | \(0.672836\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.29372e7 | 1.35710 | 0.678552 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678552 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(620\) | 8.26170e6 | 0.863158 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −379655. | −0.0393471 | ||||||||
\(623\) | −2.85618e7 | −2.94826 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.14824e7 | −1.17579 | ||||||||
\(626\) | −755907. | −0.0770961 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.66827e7 | −1.68798 | ||||||||
\(629\) | −2.77220e6 | −0.279382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.78566e7 | −1.78536 | −0.892680 | − | 0.450690i | \(-0.851178\pi\) | ||||
−0.892680 | + | 0.450690i | \(0.851178\pi\) | |||||||
\(632\) | 2.33373e6 | 0.232411 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.51446e6 | −0.149635 | ||||||||
\(635\) | −4.93921e6 | −0.486097 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.51441e6 | 0.929038 | ||||||||
\(638\) | −455.910 | −4.43432e−5 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.85025e6 | −0.468073 | ||||||||
\(641\) | 1.43521e7 | 1.37966 | 0.689828 | − | 0.723973i | \(-0.257686\pi\) | ||||
0.689828 | + | 0.723973i | \(0.257686\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.09103e6 | −0.104066 | −0.0520329 | − | 0.998645i | \(-0.516570\pi\) | ||||
−0.0520329 | + | 0.998645i | \(0.516570\pi\) | |||||||
\(644\) | 8.68601e6 | 0.825288 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.16043e6 | 0.109405 | ||||||||
\(647\) | 6.11094e6 | 0.573914 | 0.286957 | − | 0.957943i | \(-0.407356\pi\) | ||||
0.286957 | + | 0.957943i | \(0.407356\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5065.38 | −0.000472063 0 | ||||||||
\(650\) | −153716. | −0.0142704 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.38208e6 | −0.403702 | ||||||||
\(653\) | −9.26459e6 | −0.850243 | −0.425122 | − | 0.905136i | \(-0.639769\pi\) | ||||
−0.425122 | + | 0.905136i | \(0.639769\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −317020. | −0.0288724 | ||||||||
\(656\) | −7.24427e6 | −0.657256 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.27528e6 | −0.294906 | ||||||||
\(659\) | −1.26244e7 | −1.13239 | −0.566196 | − | 0.824271i | \(-0.691585\pi\) | ||||
−0.566196 | + | 0.824271i | \(0.691585\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.62521e6 | 0.589788 | 0.294894 | − | 0.955530i | \(-0.404716\pi\) | ||||
0.294894 | + | 0.955530i | \(0.404716\pi\) | |||||||
\(662\) | −35896.5 | −0.00318352 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.68490e6 | −0.324344 | ||||||||
\(665\) | 3.55041e7 | 3.11332 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −667272. | −0.0580748 | ||||||||
\(668\) | 6.37203e6 | 0.552506 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 510517. | 0.0439363 | ||||||||
\(671\) | 6210.08 | 0.000532465 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.38372e6 | −0.373083 | −0.186541 | − | 0.982447i | \(-0.559728\pi\) | ||||
−0.186541 | + | 0.982447i | \(0.559728\pi\) | |||||||
\(674\) | −1.26747e6 | −0.107470 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.84229e6 | 0.660049 | ||||||||
\(677\) | −1.24543e7 | −1.04435 | −0.522177 | − | 0.852837i | \(-0.674880\pi\) | ||||
−0.522177 | + | 0.852837i | \(0.674880\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.83236e7 | −2.35762 | ||||||||
\(680\) | 1.67147e6 | 0.138620 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3778.38 | 0.000311061 0 | ||||||||
\(683\) | 5.99410e6 | 0.491668 | 0.245834 | − | 0.969312i | \(-0.420938\pi\) | ||||
0.245834 | + | 0.969312i | \(0.420938\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.47041e7 | −1.19732 | ||||||||
\(686\) | 1.32722e6 | 0.107679 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.18658e6 | 0.417744 | ||||||||
\(689\) | 5.81544e6 | 0.466696 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.41412e7 | −1.12666 | −0.563329 | − | 0.826232i | \(-0.690480\pi\) | ||||
−0.563329 | + | 0.826232i | \(0.690480\pi\) | |||||||
\(692\) | 1.46498e7 | 1.16296 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.87776e6 | −0.147993 | ||||||||
\(695\) | 3.72809e6 | 0.292768 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.05388e6 | 0.394043 | ||||||||
\(698\) | 1.56888e6 | 0.121885 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.71234e6 | 0.363489 | ||||||||
\(701\) | −1.48140e7 | −1.13861 | −0.569307 | − | 0.822125i | \(-0.692788\pi\) | ||||
−0.569307 | + | 0.822125i | \(0.692788\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.10055e7 | 0.839890 | ||||||||
\(704\) | 44328.3 | 0.00337092 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −86162.1 | −0.00650586 | ||||||||
\(707\) | −5.34244e6 | −0.401968 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.25689e6 | −0.542170 | −0.271085 | − | 0.962555i | \(-0.587382\pi\) | ||||
−0.271085 | + | 0.962555i | \(0.587382\pi\) | |||||||
\(710\) | −2.06304e6 | −0.153590 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.33815e6 | 0.394631 | ||||||||
\(713\) | 5.53006e6 | 0.407386 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31645.7 | 0.00231499 | ||||||||
\(716\) | −7.43109e6 | −0.541714 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −361769. | −0.0261891 | ||||||||
\(719\) | 4.63110e6 | 0.334089 | 0.167044 | − | 0.985949i | \(-0.446578\pi\) | ||||
0.167044 | + | 0.985949i | \(0.446578\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.30622e7 | −0.935787 | ||||||||
\(722\) | −3.08270e6 | −0.220084 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.09175e7 | −0.774066 | ||||||||
\(725\) | −362009. | −0.0255784 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.27291e7 | −0.893224 | −0.446612 | − | 0.894728i | \(-0.647369\pi\) | ||||
−0.446612 | + | 0.894728i | \(0.647369\pi\) | |||||||
\(728\) | −2.88116e6 | −0.201483 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.24193e6 | −0.0862562 | ||||||||
\(731\) | −3.61836e6 | −0.250449 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.43767e6 | −0.511302 | −0.255651 | − | 0.966769i | \(-0.582290\pi\) | ||||
−0.255651 | + | 0.966769i | \(0.582290\pi\) | |||||||
\(734\) | −221790. | −0.0151950 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.43993e6 | −0.166029 | ||||||||
\(737\) | −19485.4 | −0.00132142 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.96771e6 | 0.132541 | 0.0662705 | − | 0.997802i | \(-0.478890\pi\) | ||||
0.0662705 | + | 0.997802i | \(0.478890\pi\) | |||||||
\(740\) | 7.87892e6 | 0.528917 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.13618e6 | 0.142439 | ||||||||
\(743\) | −1.30961e7 | −0.870300 | −0.435150 | − | 0.900358i | \(-0.643305\pi\) | ||||
−0.435150 | + | 0.900358i | \(0.643305\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.40379e7 | −0.926640 | ||||||||
\(746\) | −3.24344e6 | −0.213383 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −31708.2 | −0.00207213 | ||||||||
\(749\) | −3.40674e6 | −0.221888 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.49792e7 | −1.61614 | −0.808068 | − | 0.589089i | \(-0.799487\pi\) | ||||
−0.808068 | + | 0.589089i | \(0.799487\pi\) | |||||||
\(752\) | −2.50837e7 | −1.61751 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 110008. | 0.00704689 | ||||||||
\(755\) | 1.82400e7 | 1.16455 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −553214. | −0.0350876 | −0.0175438 | − | 0.999846i | \(-0.505585\pi\) | ||||
−0.0175438 | + | 0.999846i | \(0.505585\pi\) | |||||||
\(758\) | −2.11405e6 | −0.133642 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.63565e6 | −0.416725 | ||||||||
\(761\) | 6.91848e6 | 0.433061 | 0.216530 | − | 0.976276i | \(-0.430526\pi\) | ||||
0.216530 | + | 0.976276i | \(0.430526\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.38756e7 | 2.72842 | ||||||||
\(764\) | 3.07745e7 | 1.90747 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.18776e6 | −0.134719 | ||||||||
\(767\) | 1.22225e6 | 0.0750189 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.29851e7 | −0.791825 | −0.395912 | − | 0.918288i | \(-0.629572\pi\) | ||||
−0.395912 | + | 0.918288i | \(0.629572\pi\) | |||||||
\(770\) | 11624.4 | 0.000706552 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.56035e7 | 0.942276 | ||||||||
\(773\) | 5.40829e6 | 0.325545 | 0.162773 | − | 0.986664i | \(-0.447956\pi\) | ||||
0.162773 | + | 0.986664i | \(0.447956\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.00017e6 | 0.179429 | ||||||||
\(776\) | 5.29364e6 | 0.315573 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.78392e6 | 0.164895 | ||||||||
\(779\) | −2.00637e7 | −1.18459 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 78742.0 | 0.00461933 | ||||||||
\(782\) | 556075. | 0.0325175 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.67659e7 | 1.55522 | ||||||||
\(785\) | −3.26768e7 | −1.89263 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.47738e6 | 0.257684 | 0.128842 | − | 0.991665i | \(-0.458874\pi\) | ||||
0.128842 | + | 0.991665i | \(0.458874\pi\) | |||||||
\(788\) | 1.07242e7 | 0.615244 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.27196e6 | 0.129519 | ||||||||
\(791\) | −3.00350e7 | −1.70682 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.49846e6 | −0.0846178 | ||||||||
\(794\) | −250909. | −0.0141242 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.86470e7 | 1.04310 | ||||||||
\(797\) | 2.50186e7 | 1.39514 | 0.697570 | − | 0.716516i | \(-0.254264\pi\) | ||||
0.697570 | + | 0.716516i | \(0.254264\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.74994e7 | 0.969742 | ||||||||
\(800\) | −1.32371e6 | −0.0731255 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.84876e6 | 0.101495 | ||||||||
\(803\) | 47401.9 | 0.00259422 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.70136e7 | 0.925348 | ||||||||
\(806\) | −911703. | −0.0494328 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 998492. | 0.0538042 | ||||||||
\(809\) | 3.51699e7 | 1.88929 | 0.944646 | − | 0.328090i | \(-0.106405\pi\) | ||||
0.944646 | + | 0.328090i | \(0.106405\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.65046e6 | −0.141504 | −0.0707521 | − | 0.997494i | \(-0.522540\pi\) | ||||
−0.0707521 | + | 0.997494i | \(0.522540\pi\) | |||||||
\(812\) | −3.37244e6 | −0.179496 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3603.32 | 0.000190609 0 | ||||||||
\(815\) | −8.58332e6 | −0.452649 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.43648e7 | 0.752910 | ||||||||
\(818\) | 2.94010e6 | 0.153631 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.43637e7 | −0.745990 | ||||||||
\(821\) | −9.39154e6 | −0.486272 | −0.243136 | − | 0.969992i | \(-0.578176\pi\) | ||||
−0.243136 | + | 0.969992i | \(0.578176\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.99606e6 | −0.102725 | −0.0513623 | − | 0.998680i | \(-0.516356\pi\) | ||||
−0.0513623 | + | 0.998680i | \(0.516356\pi\) | |||||||
\(824\) | 2.44130e6 | 0.125257 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 448968. | 0.0228963 | ||||||||
\(827\) | −6.93283e6 | −0.352490 | −0.176245 | − | 0.984346i | \(-0.556395\pi\) | ||||
−0.176245 | + | 0.984346i | \(0.556395\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.01802e7 | −1.52523 | −0.762616 | − | 0.646851i | \(-0.776085\pi\) | ||||
−0.762616 | + | 0.646851i | \(0.776085\pi\) | |||||||
\(830\) | −3.58738e6 | −0.180751 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.06962e7 | −0.535697 | ||||||||
\(833\) | −1.86730e7 | −0.932397 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.24811e7 | 0.619493 | ||||||||
\(836\) | 125880. | 0.00622934 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.82169e6 | −0.0896117 | ||||||||
\(839\) | 1.09044e7 | 0.534809 | 0.267404 | − | 0.963584i | \(-0.413834\pi\) | ||||
0.267404 | + | 0.963584i | \(0.413834\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.02521e7 | −0.987369 | ||||||||
\(842\) | −720913. | −0.0350431 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.46572e7 | −1.19148 | ||||||||
\(845\) | 1.53609e7 | 0.740075 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.37452e7 | 1.61623 | ||||||||
\(848\) | 1.63600e7 | 0.781256 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 301682. | 0.0143220 | ||||||||
\(851\) | 5.27384e6 | 0.249634 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.47613e6 | 0.398864 | 0.199432 | − | 0.979912i | \(-0.436090\pi\) | ||||
0.199432 | + | 0.979912i | \(0.436090\pi\) | |||||||
\(854\) | −550429. | −0.0258260 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 636713. | 0.0297002 | ||||||||
\(857\) | −2.96420e7 | −1.37865 | −0.689327 | − | 0.724450i | \(-0.742094\pi\) | ||||
−0.689327 | + | 0.724450i | \(0.742094\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −58116.2 | −0.00268729 | −0.00134364 | − | 0.999999i | \(-0.500428\pi\) | ||||
−0.00134364 | + | 0.999999i | \(0.500428\pi\) | |||||||
\(860\) | 1.02838e7 | 0.474142 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.49870e6 | −0.0686984 | ||||||||
\(863\) | −6.44367e6 | −0.294514 | −0.147257 | − | 0.989098i | \(-0.547044\pi\) | ||||
−0.147257 | + | 0.989098i | \(0.547044\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.86950e7 | 1.30396 | ||||||||
\(866\) | 141427. | 0.00640821 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.79493e7 | 1.25913 | ||||||||
\(869\) | −86715.9 | −0.00389538 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.70171e6 | 0.209996 | ||||||||
\(872\) | −8.20027e6 | −0.365205 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.20760e6 | −0.0977555 | ||||||||
\(875\) | −3.13259e7 | −1.38319 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.86307e7 | −0.817957 | −0.408979 | − | 0.912544i | \(-0.634115\pi\) | ||||
−0.408979 | + | 0.912544i | \(0.634115\pi\) | |||||||
\(878\) | 1.62098e6 | 0.0709647 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 89025.7 | 0.00387533 | ||||||||
\(881\) | −6.95060e6 | −0.301705 | −0.150853 | − | 0.988556i | \(-0.548202\pi\) | ||||
−0.150853 | + | 0.988556i | \(0.548202\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.75323e7 | −0.756722 | −0.378361 | − | 0.925658i | \(-0.623512\pi\) | ||||
−0.378361 | + | 0.925658i | \(0.623512\pi\) | |||||||
\(884\) | 7.65101e6 | 0.329297 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.26313e6 | −0.139653 | ||||||||
\(887\) | −4.14544e6 | −0.176914 | −0.0884568 | − | 0.996080i | \(-0.528194\pi\) | ||||
−0.0884568 | + | 0.996080i | \(0.528194\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.67093e7 | −0.709096 | ||||||||
\(890\) | 5.19687e6 | 0.219921 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.70058e6 | −0.197806 | ||||||||
\(893\) | −6.94719e7 | −2.91528 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.45555e7 | −0.607393 | ||||||||
\(896\) | −1.64084e7 | −0.682803 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.42912e6 | 0.0591395 | ||||||||
\(899\) | −2.14711e6 | −0.0886042 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.14134e7 | −0.468384 | ||||||||
\(902\) | −6569.07 | −0.000268836 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.61349e6 | 0.228461 | ||||||||
\(905\) | −2.13845e7 | −0.867916 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.52626e6 | 0.263418 | 0.131709 | − | 0.991288i | \(-0.457953\pi\) | ||||
0.131709 | + | 0.991288i | \(0.457953\pi\) | |||||||
\(908\) | −2.23089e7 | −0.897974 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.80491e6 | −0.112283 | ||||||||
\(911\) | −4.12964e6 | −0.164860 | −0.0824302 | − | 0.996597i | \(-0.526268\pi\) | ||||
−0.0824302 | + | 0.996597i | \(0.526268\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 136923. | 0.00543623 | ||||||||
\(914\) | 1.87983e6 | 0.0744308 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.00248e6 | −0.275748 | ||||||||
\(917\) | −1.07248e6 | −0.0421178 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.37200e7 | −1.31704 | −0.658520 | − | 0.752563i | \(-0.728817\pi\) | ||||
−0.658520 | + | 0.752563i | \(0.728817\pi\) | |||||||
\(920\) | −3.17980e6 | −0.123860 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.66666e6 | 0.103310 | ||||||||
\(923\) | −1.90000e7 | −0.734090 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.86117e6 | 0.109948 | ||||||||
\(926\) | 3.93188e6 | 0.150686 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 947331. | 0.0361104 | ||||||||
\(929\) | 2.85561e7 | 1.08557 | 0.542787 | − | 0.839870i | \(-0.317369\pi\) | ||||
0.542787 | + | 0.839870i | \(0.317369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.41309e7 | 2.80301 | ||||||||
\(932\) | −9.60669e6 | −0.362272 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 366301. | 0.0137395 | ||||||||
\(935\) | −62107.9 | −0.00232337 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.16758e7 | 0.434446 | 0.217223 | − | 0.976122i | \(-0.430300\pi\) | ||||
0.217223 | + | 0.976122i | \(0.430300\pi\) | |||||||
\(938\) | 1.72708e6 | 0.0640922 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.97354e7 | −1.83589 | ||||||||
\(941\) | 1.56740e7 | 0.577040 | 0.288520 | − | 0.957474i | \(-0.406837\pi\) | ||||
0.288520 | + | 0.957474i | \(0.406837\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.61453e6 | −0.352086 | ||||||||
\(944\) | 3.43843e6 | 0.125583 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4703.18 | 0.000170869 0 | ||||||||
\(947\) | 2.91932e7 | 1.05781 | 0.528904 | − | 0.848681i | \(-0.322603\pi\) | ||||
0.528904 | + | 0.848681i | \(0.322603\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.14378e7 | −0.412266 | ||||||||
\(950\) | −1.19767e6 | −0.0430553 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.65457e6 | 0.202212 | ||||||||
\(953\) | 4.07979e7 | 1.45514 | 0.727571 | − | 0.686032i | \(-0.240649\pi\) | ||||
0.727571 | + | 0.686032i | \(0.240649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.02790e7 | 2.13874 | ||||||||
\(956\) | 3.57283e7 | 1.26435 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 525806. | 0.0185102 | ||||||||
\(959\) | −4.97439e7 | −1.74660 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.08349e7 | −0.378455 | ||||||||
\(962\) | −869462. | −0.0302910 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.14015e7 | 1.43490 | ||||||||
\(965\) | 3.05630e7 | 1.05652 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.00499e7 | −0.689519 | −0.344760 | − | 0.938691i | \(-0.612040\pi\) | ||||
−0.344760 | + | 0.938691i | \(0.612040\pi\) | |||||||
\(968\) | −6.30691e6 | −0.216336 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.15353e6 | 0.175863 | ||||||||
\(971\) | 5.07323e7 | 1.72678 | 0.863388 | − | 0.504540i | \(-0.168338\pi\) | ||||
0.863388 | + | 0.504540i | \(0.168338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.26121e7 | 0.427077 | ||||||||
\(974\) | 4.30449e6 | 0.145386 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.21546e6 | −0.141651 | ||||||||
\(977\) | −4.01142e7 | −1.34450 | −0.672252 | − | 0.740322i | \(-0.734673\pi\) | ||||
−0.672252 | + | 0.740322i | \(0.734673\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −198354. | −0.00661429 | ||||||||
\(980\) | 5.30708e7 | 1.76519 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.74791e6 | 0.124025 | ||||||||
\(983\) | 5.36333e7 | 1.77032 | 0.885159 | − | 0.465289i | \(-0.154050\pi\) | ||||
0.885159 | + | 0.465289i | \(0.154050\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.10057e7 | 0.689839 | ||||||||
\(986\) | −215903. | −0.00707238 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.03742e7 | −0.989949 | ||||||||
\(989\) | 6.88359e6 | 0.223782 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.34550e7 | 1.40558 | 0.702790 | − | 0.711397i | \(-0.251937\pi\) | ||||
0.702790 | + | 0.711397i | \(0.251937\pi\) | |||||||
\(992\) | −7.85107e6 | −0.253308 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.97927e6 | −0.224050 | ||||||||
\(995\) | 3.65245e7 | 1.16957 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.48232e7 | 1.10951 | 0.554754 | − | 0.832015i | \(-0.312812\pi\) | ||||
0.554754 | + | 0.832015i | \(0.312812\pi\) | |||||||
\(998\) | −6.43171e6 | −0.204409 | ||||||||
\(999\) | 0 | 0 |
(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 | 531.6.a.c.1.7 | 12 | ||
3.2 | odd | 2 | 177.6.a.c.1.6 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.c.1.6 | ✓ | 12 | 3.2 | odd | 2 | ||
531.6.a.c.1.7 | 12 | 1.1 | even | 1 | trivial |