Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(28.3879361069\) |
Analytic rank: | \(0\) |
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: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(12.3715\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.3715 | −1.83343 | −0.916715 | − | 0.399541i | \(-0.869170\pi\) | ||||
−0.916715 | + | 0.399541i | \(0.869170\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 75.5670 | 2.36147 | ||||||||
\(5\) | 33.2592 | 0.594958 | 0.297479 | − | 0.954728i | \(-0.403854\pi\) | ||||
0.297479 | + | 0.954728i | \(0.403854\pi\) | |||||||
\(6\) | −93.3431 | −1.05853 | ||||||||
\(7\) | −56.9512 | −0.439297 | −0.219648 | − | 0.975579i | \(-0.570491\pi\) | ||||
−0.219648 | + | 0.975579i | \(0.570491\pi\) | |||||||
\(8\) | −451.853 | −2.49616 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −344.946 | −1.09081 | ||||||||
\(11\) | 432.466 | 1.07763 | 0.538816 | − | 0.842423i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842423i | \(0.318872\pi\) | |||||||
\(12\) | 680.103 | 1.36339 | ||||||||
\(13\) | 178.063 | 0.292224 | 0.146112 | − | 0.989268i | \(-0.453324\pi\) | ||||
0.146112 | + | 0.989268i | \(0.453324\pi\) | |||||||
\(14\) | 590.667 | 0.805420 | ||||||||
\(15\) | 299.333 | 0.343499 | ||||||||
\(16\) | 2268.23 | 2.21507 | ||||||||
\(17\) | 1658.66 | 1.39199 | 0.695993 | − | 0.718048i | \(-0.254964\pi\) | ||||
0.695993 | + | 0.718048i | \(0.254964\pi\) | |||||||
\(18\) | −840.088 | −0.611144 | ||||||||
\(19\) | −168.835 | −0.107295 | −0.0536473 | − | 0.998560i | \(-0.517085\pi\) | ||||
−0.0536473 | + | 0.998560i | \(0.517085\pi\) | |||||||
\(20\) | 2513.30 | 1.40498 | ||||||||
\(21\) | −512.561 | −0.253628 | ||||||||
\(22\) | −4485.30 | −1.97576 | ||||||||
\(23\) | 143.318 | 0.0564914 | 0.0282457 | − | 0.999601i | \(-0.491008\pi\) | ||||
0.0282457 | + | 0.999601i | \(0.491008\pi\) | |||||||
\(24\) | −4066.68 | −1.44116 | ||||||||
\(25\) | −2018.83 | −0.646025 | ||||||||
\(26\) | −1846.77 | −0.535772 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −4303.63 | −1.03739 | ||||||||
\(29\) | 275.265 | 0.0607794 | 0.0303897 | − | 0.999538i | \(-0.490325\pi\) | ||||
0.0303897 | + | 0.999538i | \(0.490325\pi\) | |||||||
\(30\) | −3104.51 | −0.629782 | ||||||||
\(31\) | −2273.75 | −0.424950 | −0.212475 | − | 0.977166i | \(-0.568152\pi\) | ||||
−0.212475 | + | 0.977166i | \(0.568152\pi\) | |||||||
\(32\) | −9065.52 | −1.56501 | ||||||||
\(33\) | 3892.20 | 0.622171 | ||||||||
\(34\) | −17202.7 | −2.55211 | ||||||||
\(35\) | −1894.15 | −0.261363 | ||||||||
\(36\) | 6120.93 | 0.787156 | ||||||||
\(37\) | −1120.19 | −0.134520 | −0.0672601 | − | 0.997735i | \(-0.521426\pi\) | ||||
−0.0672601 | + | 0.997735i | \(0.521426\pi\) | |||||||
\(38\) | 1751.06 | 0.196717 | ||||||||
\(39\) | 1602.57 | 0.168715 | ||||||||
\(40\) | −15028.3 | −1.48511 | ||||||||
\(41\) | −2114.42 | −0.196441 | −0.0982203 | − | 0.995165i | \(-0.531315\pi\) | ||||
−0.0982203 | + | 0.995165i | \(0.531315\pi\) | |||||||
\(42\) | 5316.00 | 0.465009 | ||||||||
\(43\) | 3840.06 | 0.316714 | 0.158357 | − | 0.987382i | \(-0.449380\pi\) | ||||
0.158357 | + | 0.987382i | \(0.449380\pi\) | |||||||
\(44\) | 32680.2 | 2.54479 | ||||||||
\(45\) | 2693.99 | 0.198319 | ||||||||
\(46\) | −1486.42 | −0.103573 | ||||||||
\(47\) | 14809.7 | 0.977917 | 0.488959 | − | 0.872307i | \(-0.337377\pi\) | ||||
0.488959 | + | 0.872307i | \(0.337377\pi\) | |||||||
\(48\) | 20414.1 | 1.27887 | ||||||||
\(49\) | −13563.6 | −0.807019 | ||||||||
\(50\) | 20938.2 | 1.18444 | ||||||||
\(51\) | 14927.9 | 0.803664 | ||||||||
\(52\) | 13455.7 | 0.690077 | ||||||||
\(53\) | 9651.99 | 0.471984 | 0.235992 | − | 0.971755i | \(-0.424166\pi\) | ||||
0.235992 | + | 0.971755i | \(0.424166\pi\) | |||||||
\(54\) | −7560.79 | −0.352844 | ||||||||
\(55\) | 14383.5 | 0.641146 | ||||||||
\(56\) | 25733.6 | 1.09655 | ||||||||
\(57\) | −1519.51 | −0.0619466 | ||||||||
\(58\) | −2854.90 | −0.111435 | ||||||||
\(59\) | −3481.00 | −0.130189 | ||||||||
\(60\) | 22619.7 | 0.811163 | ||||||||
\(61\) | 29254.1 | 1.00661 | 0.503307 | − | 0.864108i | \(-0.332117\pi\) | ||||
0.503307 | + | 0.864108i | \(0.332117\pi\) | |||||||
\(62\) | 23582.1 | 0.779117 | ||||||||
\(63\) | −4613.05 | −0.146432 | ||||||||
\(64\) | 21439.3 | 0.654275 | ||||||||
\(65\) | 5922.23 | 0.173861 | ||||||||
\(66\) | −40367.7 | −1.14071 | ||||||||
\(67\) | 15092.5 | 0.410747 | 0.205374 | − | 0.978684i | \(-0.434159\pi\) | ||||
0.205374 | + | 0.978684i | \(0.434159\pi\) | |||||||
\(68\) | 125340. | 3.28713 | ||||||||
\(69\) | 1289.86 | 0.0326153 | ||||||||
\(70\) | 19645.1 | 0.479191 | ||||||||
\(71\) | 13271.8 | 0.312453 | 0.156226 | − | 0.987721i | \(-0.450067\pi\) | ||||
0.156226 | + | 0.987721i | \(0.450067\pi\) | |||||||
\(72\) | −36600.1 | −0.832053 | ||||||||
\(73\) | 42497.1 | 0.933366 | 0.466683 | − | 0.884425i | \(-0.345449\pi\) | ||||
0.466683 | + | 0.884425i | \(0.345449\pi\) | |||||||
\(74\) | 11618.0 | 0.246634 | ||||||||
\(75\) | −18169.4 | −0.372983 | ||||||||
\(76\) | −12758.3 | −0.253373 | ||||||||
\(77\) | −24629.5 | −0.473400 | ||||||||
\(78\) | −16620.9 | −0.309328 | ||||||||
\(79\) | −55585.7 | −1.00206 | −0.501032 | − | 0.865429i | \(-0.667046\pi\) | ||||
−0.501032 | + | 0.865429i | \(0.667046\pi\) | |||||||
\(80\) | 75439.4 | 1.31787 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 21929.6 | 0.360160 | ||||||||
\(83\) | 81043.5 | 1.29129 | 0.645643 | − | 0.763639i | \(-0.276589\pi\) | ||||
0.645643 | + | 0.763639i | \(0.276589\pi\) | |||||||
\(84\) | −38732.7 | −0.598935 | ||||||||
\(85\) | 55165.7 | 0.828174 | ||||||||
\(86\) | −39827.0 | −0.580673 | ||||||||
\(87\) | 2477.39 | 0.0350910 | ||||||||
\(88\) | −195411. | −2.68994 | ||||||||
\(89\) | 107408. | 1.43734 | 0.718672 | − | 0.695349i | \(-0.244750\pi\) | ||||
0.718672 | + | 0.695349i | \(0.244750\pi\) | |||||||
\(90\) | −27940.6 | −0.363605 | ||||||||
\(91\) | −10140.9 | −0.128373 | ||||||||
\(92\) | 10830.1 | 0.133403 | ||||||||
\(93\) | −20463.7 | −0.245345 | ||||||||
\(94\) | −153598. | −1.79294 | ||||||||
\(95\) | −5615.31 | −0.0638358 | ||||||||
\(96\) | −81589.7 | −0.903560 | ||||||||
\(97\) | −92436.4 | −0.997502 | −0.498751 | − | 0.866745i | \(-0.666208\pi\) | ||||
−0.498751 | + | 0.866745i | \(0.666208\pi\) | |||||||
\(98\) | 140674. | 1.47961 | ||||||||
\(99\) | 35029.8 | 0.359211 | ||||||||
\(100\) | −152557. | −1.52557 | ||||||||
\(101\) | −134769. | −1.31458 | −0.657291 | − | 0.753637i | \(-0.728298\pi\) | ||||
−0.657291 | + | 0.753637i | \(0.728298\pi\) | |||||||
\(102\) | −154824. | −1.47346 | ||||||||
\(103\) | 166146. | 1.54311 | 0.771553 | − | 0.636165i | \(-0.219480\pi\) | ||||
0.771553 | + | 0.636165i | \(0.219480\pi\) | |||||||
\(104\) | −80458.3 | −0.729437 | ||||||||
\(105\) | −17047.3 | −0.150898 | ||||||||
\(106\) | −100105. | −0.865350 | ||||||||
\(107\) | 120010. | 1.01335 | 0.506674 | − | 0.862138i | \(-0.330875\pi\) | ||||
0.506674 | + | 0.862138i | \(0.330875\pi\) | |||||||
\(108\) | 55088.3 | 0.454465 | ||||||||
\(109\) | 188031. | 1.51587 | 0.757937 | − | 0.652328i | \(-0.226207\pi\) | ||||
0.757937 | + | 0.652328i | \(0.226207\pi\) | |||||||
\(110\) | −149177. | −1.17550 | ||||||||
\(111\) | −10081.7 | −0.0776653 | ||||||||
\(112\) | −129178. | −0.973071 | ||||||||
\(113\) | 114073. | 0.840401 | 0.420201 | − | 0.907431i | \(-0.361960\pi\) | ||||
0.420201 | + | 0.907431i | \(0.361960\pi\) | |||||||
\(114\) | 15759.6 | 0.113575 | ||||||||
\(115\) | 4766.65 | 0.0336100 | ||||||||
\(116\) | 20801.0 | 0.143529 | ||||||||
\(117\) | 14423.1 | 0.0974079 | ||||||||
\(118\) | 36103.0 | 0.238692 | ||||||||
\(119\) | −94462.7 | −0.611495 | ||||||||
\(120\) | −135254. | −0.857429 | ||||||||
\(121\) | 25976.1 | 0.161291 | ||||||||
\(122\) | −303408. | −1.84556 | ||||||||
\(123\) | −19029.8 | −0.113415 | ||||||||
\(124\) | −171820. | −1.00351 | ||||||||
\(125\) | −171079. | −0.979316 | ||||||||
\(126\) | 47844.0 | 0.268473 | ||||||||
\(127\) | 305300. | 1.67964 | 0.839822 | − | 0.542861i | \(-0.182659\pi\) | ||||
0.839822 | + | 0.542861i | \(0.182659\pi\) | |||||||
\(128\) | 67740.1 | 0.365444 | ||||||||
\(129\) | 34560.6 | 0.182855 | ||||||||
\(130\) | −61422.1 | −0.318762 | ||||||||
\(131\) | −152752. | −0.777695 | −0.388848 | − | 0.921302i | \(-0.627127\pi\) | ||||
−0.388848 | + | 0.921302i | \(0.627127\pi\) | |||||||
\(132\) | 294122. | 1.46924 | ||||||||
\(133\) | 9615.35 | 0.0471342 | ||||||||
\(134\) | −156531. | −0.753077 | ||||||||
\(135\) | 24245.9 | 0.114500 | ||||||||
\(136\) | −749471. | −3.47462 | ||||||||
\(137\) | −128339. | −0.584196 | −0.292098 | − | 0.956388i | \(-0.594353\pi\) | ||||
−0.292098 | + | 0.956388i | \(0.594353\pi\) | |||||||
\(138\) | −13377.8 | −0.0597979 | ||||||||
\(139\) | 155483. | 0.682566 | 0.341283 | − | 0.939961i | \(-0.389139\pi\) | ||||
0.341283 | + | 0.939961i | \(0.389139\pi\) | |||||||
\(140\) | −143135. | −0.617201 | ||||||||
\(141\) | 133287. | 0.564601 | ||||||||
\(142\) | −137648. | −0.572860 | ||||||||
\(143\) | 77006.3 | 0.314910 | ||||||||
\(144\) | 183726. | 0.738355 | ||||||||
\(145\) | 9155.09 | 0.0361612 | ||||||||
\(146\) | −440756. | −1.71126 | ||||||||
\(147\) | −122072. | −0.465932 | ||||||||
\(148\) | −84649.5 | −0.317665 | ||||||||
\(149\) | 444140. | 1.63891 | 0.819454 | − | 0.573146i | \(-0.194277\pi\) | ||||
0.819454 | + | 0.573146i | \(0.194277\pi\) | |||||||
\(150\) | 188444. | 0.683838 | ||||||||
\(151\) | −68940.1 | −0.246054 | −0.123027 | − | 0.992403i | \(-0.539260\pi\) | ||||
−0.123027 | + | 0.992403i | \(0.539260\pi\) | |||||||
\(152\) | 76288.6 | 0.267825 | ||||||||
\(153\) | 134351. | 0.463996 | ||||||||
\(154\) | 255443. | 0.867946 | ||||||||
\(155\) | −75623.0 | −0.252828 | ||||||||
\(156\) | 121101. | 0.398416 | ||||||||
\(157\) | −69283.9 | −0.224328 | −0.112164 | − | 0.993690i | \(-0.535778\pi\) | ||||
−0.112164 | + | 0.993690i | \(0.535778\pi\) | |||||||
\(158\) | 576504. | 1.83721 | ||||||||
\(159\) | 86868.0 | 0.272500 | ||||||||
\(160\) | −301512. | −0.931117 | ||||||||
\(161\) | −8162.15 | −0.0248165 | ||||||||
\(162\) | −68047.1 | −0.203715 | ||||||||
\(163\) | −267280. | −0.787946 | −0.393973 | − | 0.919122i | \(-0.628900\pi\) | ||||
−0.393973 | + | 0.919122i | \(0.628900\pi\) | |||||||
\(164\) | −159780. | −0.463888 | ||||||||
\(165\) | 129451. | 0.370166 | ||||||||
\(166\) | −840538. | −2.36749 | ||||||||
\(167\) | 387809. | 1.07604 | 0.538018 | − | 0.842934i | \(-0.319173\pi\) | ||||
0.538018 | + | 0.842934i | \(0.319173\pi\) | |||||||
\(168\) | 231602. | 0.633096 | ||||||||
\(169\) | −339587. | −0.914605 | ||||||||
\(170\) | −572148. | −1.51840 | ||||||||
\(171\) | −13675.6 | −0.0357649 | ||||||||
\(172\) | 290182. | 0.747910 | ||||||||
\(173\) | −190512. | −0.483958 | −0.241979 | − | 0.970281i | \(-0.577797\pi\) | ||||
−0.241979 | + | 0.970281i | \(0.577797\pi\) | |||||||
\(174\) | −25694.1 | −0.0643369 | ||||||||
\(175\) | 114975. | 0.283796 | ||||||||
\(176\) | 980932. | 2.38703 | ||||||||
\(177\) | −31329.0 | −0.0751646 | ||||||||
\(178\) | −1.11397e6 | −2.63527 | ||||||||
\(179\) | −173534. | −0.404811 | −0.202406 | − | 0.979302i | \(-0.564876\pi\) | ||||
−0.202406 | + | 0.979302i | \(0.564876\pi\) | |||||||
\(180\) | 203577. | 0.468325 | ||||||||
\(181\) | 717762. | 1.62849 | 0.814243 | − | 0.580524i | \(-0.197152\pi\) | ||||
0.814243 | + | 0.580524i | \(0.197152\pi\) | |||||||
\(182\) | 105176. | 0.235363 | ||||||||
\(183\) | 263287. | 0.581168 | ||||||||
\(184\) | −64758.8 | −0.141011 | ||||||||
\(185\) | −37256.6 | −0.0800339 | ||||||||
\(186\) | 212239. | 0.449824 | ||||||||
\(187\) | 717315. | 1.50005 | ||||||||
\(188\) | 1.11913e6 | 2.30932 | ||||||||
\(189\) | −41517.4 | −0.0845427 | ||||||||
\(190\) | 58238.9 | 0.117039 | ||||||||
\(191\) | 336630. | 0.667681 | 0.333841 | − | 0.942630i | \(-0.391655\pi\) | ||||
0.333841 | + | 0.942630i | \(0.391655\pi\) | |||||||
\(192\) | 192954. | 0.377746 | ||||||||
\(193\) | 293107. | 0.566413 | 0.283206 | − | 0.959059i | \(-0.408602\pi\) | ||||
0.283206 | + | 0.959059i | \(0.408602\pi\) | |||||||
\(194\) | 958699. | 1.82885 | ||||||||
\(195\) | 53300.1 | 0.100379 | ||||||||
\(196\) | −1.02496e6 | −1.90575 | ||||||||
\(197\) | −254135. | −0.466551 | −0.233276 | − | 0.972411i | \(-0.574944\pi\) | ||||
−0.233276 | + | 0.972411i | \(0.574944\pi\) | |||||||
\(198\) | −363310. | −0.658588 | ||||||||
\(199\) | 65290.6 | 0.116874 | 0.0584370 | − | 0.998291i | \(-0.481388\pi\) | ||||
0.0584370 | + | 0.998291i | \(0.481388\pi\) | |||||||
\(200\) | 912213. | 1.61258 | ||||||||
\(201\) | 135833. | 0.237145 | ||||||||
\(202\) | 1.39775e6 | 2.41020 | ||||||||
\(203\) | −15676.7 | −0.0267002 | ||||||||
\(204\) | 1.12806e6 | 1.89783 | ||||||||
\(205\) | −70323.8 | −0.116874 | ||||||||
\(206\) | −1.72317e6 | −2.82918 | ||||||||
\(207\) | 11608.8 | 0.0188305 | ||||||||
\(208\) | 403888. | 0.647295 | ||||||||
\(209\) | −73015.4 | −0.115624 | ||||||||
\(210\) | 176806. | 0.276661 | ||||||||
\(211\) | 93142.8 | 0.144027 | 0.0720134 | − | 0.997404i | \(-0.477058\pi\) | ||||
0.0720134 | + | 0.997404i | \(0.477058\pi\) | |||||||
\(212\) | 729372. | 1.11458 | ||||||||
\(213\) | 119446. | 0.180395 | ||||||||
\(214\) | −1.24468e6 | −1.85790 | ||||||||
\(215\) | 127717. | 0.188432 | ||||||||
\(216\) | −329401. | −0.480386 | ||||||||
\(217\) | 129493. | 0.186679 | ||||||||
\(218\) | −1.95015e6 | −2.77925 | ||||||||
\(219\) | 382474. | 0.538879 | ||||||||
\(220\) | 1.08692e6 | 1.51405 | ||||||||
\(221\) | 295346. | 0.406772 | ||||||||
\(222\) | 104562. | 0.142394 | ||||||||
\(223\) | 30528.4 | 0.0411095 | 0.0205548 | − | 0.999789i | \(-0.493457\pi\) | ||||
0.0205548 | + | 0.999789i | \(0.493457\pi\) | |||||||
\(224\) | 516292. | 0.687504 | ||||||||
\(225\) | −163525. | −0.215342 | ||||||||
\(226\) | −1.18310e6 | −1.54082 | ||||||||
\(227\) | −777882. | −1.00196 | −0.500979 | − | 0.865460i | \(-0.667027\pi\) | ||||
−0.500979 | + | 0.865460i | \(0.667027\pi\) | |||||||
\(228\) | −114825. | −0.146285 | ||||||||
\(229\) | −763186. | −0.961705 | −0.480852 | − | 0.876802i | \(-0.659673\pi\) | ||||
−0.480852 | + | 0.876802i | \(0.659673\pi\) | |||||||
\(230\) | −49437.1 | −0.0616216 | ||||||||
\(231\) | −221665. | −0.273318 | ||||||||
\(232\) | −124379. | −0.151715 | ||||||||
\(233\) | −1.27683e6 | −1.54079 | −0.770393 | − | 0.637570i | \(-0.779940\pi\) | ||||
−0.770393 | + | 0.637570i | \(0.779940\pi\) | |||||||
\(234\) | −149589. | −0.178591 | ||||||||
\(235\) | 492559. | 0.581820 | ||||||||
\(236\) | −263049. | −0.307437 | ||||||||
\(237\) | −500271. | −0.578542 | ||||||||
\(238\) | 979715. | 1.12113 | ||||||||
\(239\) | 71356.0 | 0.0808045 | 0.0404023 | − | 0.999183i | \(-0.487136\pi\) | ||||
0.0404023 | + | 0.999183i | \(0.487136\pi\) | |||||||
\(240\) | 678954. | 0.760874 | ||||||||
\(241\) | −1.25147e6 | −1.38797 | −0.693984 | − | 0.719991i | \(-0.744146\pi\) | ||||
−0.693984 | + | 0.719991i | \(0.744146\pi\) | |||||||
\(242\) | −269410. | −0.295716 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 2.21065e6 | 2.37709 | ||||||||
\(245\) | −451113. | −0.480142 | ||||||||
\(246\) | 197366. | 0.207939 | ||||||||
\(247\) | −30063.3 | −0.0313540 | ||||||||
\(248\) | 1.02740e6 | 1.06074 | ||||||||
\(249\) | 729391. | 0.745525 | ||||||||
\(250\) | 1.77434e6 | 1.79551 | ||||||||
\(251\) | −1.22669e6 | −1.22900 | −0.614501 | − | 0.788916i | \(-0.710642\pi\) | ||||
−0.614501 | + | 0.788916i | \(0.710642\pi\) | |||||||
\(252\) | −348594. | −0.345795 | ||||||||
\(253\) | 61980.3 | 0.0608769 | ||||||||
\(254\) | −3.16640e6 | −3.07951 | ||||||||
\(255\) | 496491. | 0.478146 | ||||||||
\(256\) | −1.38862e6 | −1.32429 | ||||||||
\(257\) | −1.22989e6 | −1.16154 | −0.580770 | − | 0.814068i | \(-0.697248\pi\) | ||||
−0.580770 | + | 0.814068i | \(0.697248\pi\) | |||||||
\(258\) | −358443. | −0.335252 | ||||||||
\(259\) | 63796.2 | 0.0590943 | ||||||||
\(260\) | 447525. | 0.410567 | ||||||||
\(261\) | 22296.5 | 0.0202598 | ||||||||
\(262\) | 1.58426e6 | 1.42585 | ||||||||
\(263\) | −1.03240e6 | −0.920364 | −0.460182 | − | 0.887825i | \(-0.652216\pi\) | ||||
−0.460182 | + | 0.887825i | \(0.652216\pi\) | |||||||
\(264\) | −1.75870e6 | −1.55304 | ||||||||
\(265\) | 321017. | 0.280811 | ||||||||
\(266\) | −99725.1 | −0.0864173 | ||||||||
\(267\) | 966670. | 0.829851 | ||||||||
\(268\) | 1.14050e6 | 0.969967 | ||||||||
\(269\) | −565251. | −0.476278 | −0.238139 | − | 0.971231i | \(-0.576537\pi\) | ||||
−0.238139 | + | 0.971231i | \(0.576537\pi\) | |||||||
\(270\) | −251466. | −0.209927 | ||||||||
\(271\) | −1.35862e6 | −1.12376 | −0.561880 | − | 0.827219i | \(-0.689922\pi\) | ||||
−0.561880 | + | 0.827219i | \(0.689922\pi\) | |||||||
\(272\) | 3.76222e6 | 3.08334 | ||||||||
\(273\) | −91268.1 | −0.0741161 | ||||||||
\(274\) | 1.33107e6 | 1.07108 | ||||||||
\(275\) | −873075. | −0.696177 | ||||||||
\(276\) | 97471.2 | 0.0770200 | ||||||||
\(277\) | 219170. | 0.171625 | 0.0858127 | − | 0.996311i | \(-0.472651\pi\) | ||||
0.0858127 | + | 0.996311i | \(0.472651\pi\) | |||||||
\(278\) | −1.61258e6 | −1.25144 | ||||||||
\(279\) | −184174. | −0.141650 | ||||||||
\(280\) | 855877. | 0.652404 | ||||||||
\(281\) | 1.54978e6 | 1.17086 | 0.585431 | − | 0.810722i | \(-0.300925\pi\) | ||||
0.585431 | + | 0.810722i | \(0.300925\pi\) | |||||||
\(282\) | −1.38238e6 | −1.03516 | ||||||||
\(283\) | −1.39782e6 | −1.03749 | −0.518746 | − | 0.854928i | \(-0.673601\pi\) | ||||
−0.518746 | + | 0.854928i | \(0.673601\pi\) | |||||||
\(284\) | 1.00291e6 | 0.737847 | ||||||||
\(285\) | −50537.8 | −0.0368556 | ||||||||
\(286\) | −798667. | −0.577365 | ||||||||
\(287\) | 120419. | 0.0862957 | ||||||||
\(288\) | −734307. | −0.521671 | ||||||||
\(289\) | 1.33130e6 | 0.937628 | ||||||||
\(290\) | −94951.6 | −0.0662990 | ||||||||
\(291\) | −831927. | −0.575908 | ||||||||
\(292\) | 3.21138e6 | 2.20411 | ||||||||
\(293\) | 2.33918e6 | 1.59182 | 0.795910 | − | 0.605415i | \(-0.206993\pi\) | ||||
0.795910 | + | 0.605415i | \(0.206993\pi\) | |||||||
\(294\) | 1.26606e6 | 0.854255 | ||||||||
\(295\) | −115775. | −0.0774569 | ||||||||
\(296\) | 506162. | 0.335784 | ||||||||
\(297\) | 315268. | 0.207390 | ||||||||
\(298\) | −4.60638e6 | −3.00482 | ||||||||
\(299\) | 25519.7 | 0.0165081 | ||||||||
\(300\) | −1.37301e6 | −0.880787 | ||||||||
\(301\) | −218696. | −0.139131 | ||||||||
\(302\) | 715009. | 0.451122 | ||||||||
\(303\) | −1.21292e6 | −0.758975 | ||||||||
\(304\) | −382956. | −0.237665 | ||||||||
\(305\) | 972968. | 0.598893 | ||||||||
\(306\) | −1.39342e6 | −0.850704 | ||||||||
\(307\) | 1.73450e6 | 1.05034 | 0.525170 | − | 0.850998i | \(-0.324002\pi\) | ||||
0.525170 | + | 0.850998i | \(0.324002\pi\) | |||||||
\(308\) | −1.86118e6 | −1.11792 | ||||||||
\(309\) | 1.49531e6 | 0.890913 | ||||||||
\(310\) | 784320. | 0.463542 | ||||||||
\(311\) | −1.36982e6 | −0.803086 | −0.401543 | − | 0.915840i | \(-0.631526\pi\) | ||||
−0.401543 | + | 0.915840i | \(0.631526\pi\) | |||||||
\(312\) | −724125. | −0.421140 | ||||||||
\(313\) | −2.30372e6 | −1.32914 | −0.664569 | − | 0.747227i | \(-0.731385\pi\) | ||||
−0.664569 | + | 0.747227i | \(0.731385\pi\) | |||||||
\(314\) | 718575. | 0.411290 | ||||||||
\(315\) | −153426. | −0.0871210 | ||||||||
\(316\) | −4.20045e6 | −2.36634 | ||||||||
\(317\) | 2.31279e6 | 1.29267 | 0.646337 | − | 0.763052i | \(-0.276300\pi\) | ||||
0.646337 | + | 0.763052i | \(0.276300\pi\) | |||||||
\(318\) | −900947. | −0.499610 | ||||||||
\(319\) | 119043. | 0.0654978 | ||||||||
\(320\) | 713053. | 0.389266 | ||||||||
\(321\) | 1.08009e6 | 0.585056 | ||||||||
\(322\) | 84653.3 | 0.0454993 | ||||||||
\(323\) | −280040. | −0.149353 | ||||||||
\(324\) | 495795. | 0.262385 | ||||||||
\(325\) | −359479. | −0.188784 | ||||||||
\(326\) | 2.77208e6 | 1.44465 | ||||||||
\(327\) | 1.69228e6 | 0.875190 | ||||||||
\(328\) | 955406. | 0.490347 | ||||||||
\(329\) | −843431. | −0.429596 | ||||||||
\(330\) | −1.34260e6 | −0.678673 | ||||||||
\(331\) | 1.01902e6 | 0.511224 | 0.255612 | − | 0.966779i | \(-0.417723\pi\) | ||||
0.255612 | + | 0.966779i | \(0.417723\pi\) | |||||||
\(332\) | 6.12421e6 | 3.04933 | ||||||||
\(333\) | −90735.5 | −0.0448401 | ||||||||
\(334\) | −4.02214e6 | −1.97284 | ||||||||
\(335\) | 501965. | 0.244377 | ||||||||
\(336\) | −1.16260e6 | −0.561803 | ||||||||
\(337\) | 1.96163e6 | 0.940899 | 0.470450 | − | 0.882427i | \(-0.344092\pi\) | ||||
0.470450 | + | 0.882427i | \(0.344092\pi\) | |||||||
\(338\) | 3.52201e6 | 1.67687 | ||||||||
\(339\) | 1.02666e6 | 0.485206 | ||||||||
\(340\) | 4.16870e6 | 1.95571 | ||||||||
\(341\) | −983320. | −0.457940 | ||||||||
\(342\) | 141836. | 0.0655725 | ||||||||
\(343\) | 1.72964e6 | 0.793817 | ||||||||
\(344\) | −1.73514e6 | −0.790569 | ||||||||
\(345\) | 42899.8 | 0.0194047 | ||||||||
\(346\) | 1.97589e6 | 0.887304 | ||||||||
\(347\) | 567054. | 0.252814 | 0.126407 | − | 0.991978i | \(-0.459656\pi\) | ||||
0.126407 | + | 0.991978i | \(0.459656\pi\) | |||||||
\(348\) | 187209. | 0.0828663 | ||||||||
\(349\) | 2.79317e6 | 1.22753 | 0.613767 | − | 0.789487i | \(-0.289653\pi\) | ||||
0.613767 | + | 0.789487i | \(0.289653\pi\) | |||||||
\(350\) | −1.19245e6 | −0.520321 | ||||||||
\(351\) | 129808. | 0.0562385 | ||||||||
\(352\) | −3.92053e6 | −1.68651 | ||||||||
\(353\) | 2.82854e6 | 1.20816 | 0.604081 | − | 0.796923i | \(-0.293540\pi\) | ||||
0.604081 | + | 0.796923i | \(0.293540\pi\) | |||||||
\(354\) | 324927. | 0.137809 | ||||||||
\(355\) | 441409. | 0.185896 | ||||||||
\(356\) | 8.11648e6 | 3.39424 | ||||||||
\(357\) | −850164. | −0.353047 | ||||||||
\(358\) | 1.79980e6 | 0.742194 | ||||||||
\(359\) | −200396. | −0.0820641 | −0.0410321 | − | 0.999158i | \(-0.513065\pi\) | ||||
−0.0410321 | + | 0.999158i | \(0.513065\pi\) | |||||||
\(360\) | −1.21729e6 | −0.495037 | ||||||||
\(361\) | −2.44759e6 | −0.988488 | ||||||||
\(362\) | −7.44424e6 | −2.98572 | ||||||||
\(363\) | 233785. | 0.0931214 | ||||||||
\(364\) | −766318. | −0.303148 | ||||||||
\(365\) | 1.41342e6 | 0.555313 | ||||||||
\(366\) | −2.73067e6 | −1.06553 | ||||||||
\(367\) | −1.05311e6 | −0.408140 | −0.204070 | − | 0.978956i | \(-0.565417\pi\) | ||||
−0.204070 | + | 0.978956i | \(0.565417\pi\) | |||||||
\(368\) | 325079. | 0.125132 | ||||||||
\(369\) | −171268. | −0.0654802 | ||||||||
\(370\) | 386405. | 0.146737 | ||||||||
\(371\) | −549693. | −0.207341 | ||||||||
\(372\) | −1.54638e6 | −0.579375 | ||||||||
\(373\) | −1.20089e6 | −0.446922 | −0.223461 | − | 0.974713i | \(-0.571735\pi\) | ||||
−0.223461 | + | 0.974713i | \(0.571735\pi\) | |||||||
\(374\) | −7.43959e6 | −2.75024 | ||||||||
\(375\) | −1.53971e6 | −0.565408 | ||||||||
\(376\) | −6.69182e6 | −2.44104 | ||||||||
\(377\) | 49014.5 | 0.0177612 | ||||||||
\(378\) | 430596. | 0.155003 | ||||||||
\(379\) | −3.95845e6 | −1.41556 | −0.707778 | − | 0.706435i | \(-0.750302\pi\) | ||||
−0.707778 | + | 0.706435i | \(0.750302\pi\) | |||||||
\(380\) | −424332. | −0.150746 | ||||||||
\(381\) | 2.74770e6 | 0.969743 | ||||||||
\(382\) | −3.49134e6 | −1.22415 | ||||||||
\(383\) | −3.58271e6 | −1.24800 | −0.624000 | − | 0.781424i | \(-0.714494\pi\) | ||||
−0.624000 | + | 0.781424i | \(0.714494\pi\) | |||||||
\(384\) | 609661. | 0.210989 | ||||||||
\(385\) | −819156. | −0.281653 | ||||||||
\(386\) | −3.03994e6 | −1.03848 | ||||||||
\(387\) | 311045. | 0.105571 | ||||||||
\(388\) | −6.98514e6 | −2.35557 | ||||||||
\(389\) | −2.75954e6 | −0.924619 | −0.462309 | − | 0.886719i | \(-0.652979\pi\) | ||||
−0.462309 | + | 0.886719i | \(0.652979\pi\) | |||||||
\(390\) | −552799. | −0.184037 | ||||||||
\(391\) | 237716. | 0.0786352 | ||||||||
\(392\) | 6.12874e6 | 2.01445 | ||||||||
\(393\) | −1.37477e6 | −0.449003 | ||||||||
\(394\) | 2.63575e6 | 0.855390 | ||||||||
\(395\) | −1.84873e6 | −0.596186 | ||||||||
\(396\) | 2.64709e6 | 0.848265 | ||||||||
\(397\) | 4.77985e6 | 1.52208 | 0.761041 | − | 0.648704i | \(-0.224689\pi\) | ||||
0.761041 | + | 0.648704i | \(0.224689\pi\) | |||||||
\(398\) | −677158. | −0.214280 | ||||||||
\(399\) | 86538.2 | 0.0272129 | ||||||||
\(400\) | −4.57916e6 | −1.43099 | ||||||||
\(401\) | −4.79242e6 | −1.48831 | −0.744156 | − | 0.668005i | \(-0.767148\pi\) | ||||
−0.744156 | + | 0.668005i | \(0.767148\pi\) | |||||||
\(402\) | −1.40878e6 | −0.434789 | ||||||||
\(403\) | −404871. | −0.124181 | ||||||||
\(404\) | −1.01841e7 | −3.10435 | ||||||||
\(405\) | 218213. | 0.0661065 | ||||||||
\(406\) | 162590. | 0.0489529 | ||||||||
\(407\) | −484445. | −0.144963 | ||||||||
\(408\) | −6.74524e6 | −2.00607 | ||||||||
\(409\) | 804704. | 0.237864 | 0.118932 | − | 0.992902i | \(-0.462053\pi\) | ||||
0.118932 | + | 0.992902i | \(0.462053\pi\) | |||||||
\(410\) | 729360. | 0.214280 | ||||||||
\(411\) | −1.15505e6 | −0.337286 | ||||||||
\(412\) | 1.25551e7 | 3.64400 | ||||||||
\(413\) | 198247. | 0.0571915 | ||||||||
\(414\) | −120400. | −0.0345243 | ||||||||
\(415\) | 2.69544e6 | 0.768262 | ||||||||
\(416\) | −1.61423e6 | −0.457334 | ||||||||
\(417\) | 1.39934e6 | 0.394080 | ||||||||
\(418\) | 757276. | 0.211989 | ||||||||
\(419\) | 5.46503e6 | 1.52075 | 0.760374 | − | 0.649486i | \(-0.225016\pi\) | ||||
0.760374 | + | 0.649486i | \(0.225016\pi\) | |||||||
\(420\) | −1.28822e6 | −0.356341 | ||||||||
\(421\) | −1.96598e6 | −0.540597 | −0.270298 | − | 0.962777i | \(-0.587122\pi\) | ||||
−0.270298 | + | 0.962777i | \(0.587122\pi\) | |||||||
\(422\) | −966026. | −0.264063 | ||||||||
\(423\) | 1.19959e6 | 0.325972 | ||||||||
\(424\) | −4.36128e6 | −1.17815 | ||||||||
\(425\) | −3.34855e6 | −0.899258 | ||||||||
\(426\) | −1.23883e6 | −0.330741 | ||||||||
\(427\) | −1.66606e6 | −0.442202 | ||||||||
\(428\) | 9.06880e6 | 2.39299 | ||||||||
\(429\) | 693056. | 0.181813 | ||||||||
\(430\) | −1.32461e6 | −0.345476 | ||||||||
\(431\) | 6.18098e6 | 1.60274 | 0.801372 | − | 0.598167i | \(-0.204104\pi\) | ||||
0.801372 | + | 0.598167i | \(0.204104\pi\) | |||||||
\(432\) | 1.65354e6 | 0.426290 | ||||||||
\(433\) | −6.81186e6 | −1.74601 | −0.873003 | − | 0.487715i | \(-0.837831\pi\) | ||||
−0.873003 | + | 0.487715i | \(0.837831\pi\) | |||||||
\(434\) | −1.34303e6 | −0.342264 | ||||||||
\(435\) | 82395.8 | 0.0208777 | ||||||||
\(436\) | 1.42089e7 | 3.57969 | ||||||||
\(437\) | −24197.1 | −0.00606122 | ||||||||
\(438\) | −3.96681e6 | −0.987997 | ||||||||
\(439\) | 5.97720e6 | 1.48026 | 0.740128 | − | 0.672466i | \(-0.234765\pi\) | ||||
0.740128 | + | 0.672466i | \(0.234765\pi\) | |||||||
\(440\) | −6.49921e6 | −1.60040 | ||||||||
\(441\) | −1.09865e6 | −0.269006 | ||||||||
\(442\) | −3.06317e6 | −0.745787 | ||||||||
\(443\) | −490983. | −0.118866 | −0.0594330 | − | 0.998232i | \(-0.518929\pi\) | ||||
−0.0594330 | + | 0.998232i | \(0.518929\pi\) | |||||||
\(444\) | −761845. | −0.183404 | ||||||||
\(445\) | 3.57229e6 | 0.855159 | ||||||||
\(446\) | −316624. | −0.0753715 | ||||||||
\(447\) | 3.99726e6 | 0.946223 | ||||||||
\(448\) | −1.22099e6 | −0.287421 | ||||||||
\(449\) | 7.25924e6 | 1.69932 | 0.849660 | − | 0.527331i | \(-0.176807\pi\) | ||||
0.849660 | + | 0.527331i | \(0.176807\pi\) | |||||||
\(450\) | 1.69599e6 | 0.394814 | ||||||||
\(451\) | −914415. | −0.211691 | ||||||||
\(452\) | 8.62015e6 | 1.98458 | ||||||||
\(453\) | −620461. | −0.142059 | ||||||||
\(454\) | 8.06777e6 | 1.83702 | ||||||||
\(455\) | −337278. | −0.0763765 | ||||||||
\(456\) | 686597. | 0.154629 | ||||||||
\(457\) | −2.78034e6 | −0.622740 | −0.311370 | − | 0.950289i | \(-0.600788\pi\) | ||||
−0.311370 | + | 0.950289i | \(0.600788\pi\) | |||||||
\(458\) | 7.91535e6 | 1.76322 | ||||||||
\(459\) | 1.20916e6 | 0.267888 | ||||||||
\(460\) | 360201. | 0.0793690 | ||||||||
\(461\) | −6.01371e6 | −1.31792 | −0.658962 | − | 0.752176i | \(-0.729004\pi\) | ||||
−0.658962 | + | 0.752176i | \(0.729004\pi\) | |||||||
\(462\) | 2.29899e6 | 0.501109 | ||||||||
\(463\) | −7.10787e6 | −1.54094 | −0.770472 | − | 0.637474i | \(-0.779979\pi\) | ||||
−0.770472 | + | 0.637474i | \(0.779979\pi\) | |||||||
\(464\) | 624364. | 0.134630 | ||||||||
\(465\) | −680607. | −0.145970 | ||||||||
\(466\) | 1.32425e7 | 2.82492 | ||||||||
\(467\) | 5.51961e6 | 1.17116 | 0.585579 | − | 0.810615i | \(-0.300867\pi\) | ||||
0.585579 | + | 0.810615i | \(0.300867\pi\) | |||||||
\(468\) | 1.08991e6 | 0.230026 | ||||||||
\(469\) | −859537. | −0.180440 | ||||||||
\(470\) | −5.10855e6 | −1.06673 | ||||||||
\(471\) | −623555. | −0.129516 | ||||||||
\(472\) | 1.57290e6 | 0.324972 | ||||||||
\(473\) | 1.66070e6 | 0.341301 | ||||||||
\(474\) | 5.18854e6 | 1.06072 | ||||||||
\(475\) | 340849. | 0.0693150 | ||||||||
\(476\) | −7.13826e6 | −1.44403 | ||||||||
\(477\) | 781812. | 0.157328 | ||||||||
\(478\) | −740065. | −0.148150 | ||||||||
\(479\) | −3.18017e6 | −0.633304 | −0.316652 | − | 0.948542i | \(-0.602559\pi\) | ||||
−0.316652 | + | 0.948542i | \(0.602559\pi\) | |||||||
\(480\) | −2.71360e6 | −0.537580 | ||||||||
\(481\) | −199465. | −0.0393100 | ||||||||
\(482\) | 1.29796e7 | 2.54474 | ||||||||
\(483\) | −73459.3 | −0.0143278 | ||||||||
\(484\) | 1.96293e6 | 0.380884 | ||||||||
\(485\) | −3.07436e6 | −0.593472 | ||||||||
\(486\) | −612424. | −0.117615 | ||||||||
\(487\) | −4.01718e6 | −0.767537 | −0.383768 | − | 0.923429i | \(-0.625374\pi\) | ||||
−0.383768 | + | 0.923429i | \(0.625374\pi\) | |||||||
\(488\) | −1.32186e7 | −2.51267 | ||||||||
\(489\) | −2.40552e6 | −0.454921 | ||||||||
\(490\) | 4.67869e6 | 0.880308 | ||||||||
\(491\) | 2.25211e6 | 0.421585 | 0.210793 | − | 0.977531i | \(-0.432396\pi\) | ||||
0.210793 | + | 0.977531i | \(0.432396\pi\) | |||||||
\(492\) | −1.43802e6 | −0.267826 | ||||||||
\(493\) | 456571. | 0.0846041 | ||||||||
\(494\) | 311800. | 0.0574855 | ||||||||
\(495\) | 1.16506e6 | 0.213715 | ||||||||
\(496\) | −5.15738e6 | −0.941293 | ||||||||
\(497\) | −755845. | −0.137259 | ||||||||
\(498\) | −7.56484e6 | −1.36687 | ||||||||
\(499\) | 4.87566e6 | 0.876561 | 0.438281 | − | 0.898838i | \(-0.355588\pi\) | ||||
0.438281 | + | 0.898838i | \(0.355588\pi\) | |||||||
\(500\) | −1.29280e7 | −2.31262 | ||||||||
\(501\) | 3.49028e6 | 0.621249 | ||||||||
\(502\) | 1.27226e7 | 2.25329 | ||||||||
\(503\) | −3.03011e6 | −0.533996 | −0.266998 | − | 0.963697i | \(-0.586032\pi\) | ||||
−0.266998 | + | 0.963697i | \(0.586032\pi\) | |||||||
\(504\) | 2.08442e6 | 0.365518 | ||||||||
\(505\) | −4.48232e6 | −0.782122 | ||||||||
\(506\) | −642826. | −0.111614 | ||||||||
\(507\) | −3.05628e6 | −0.528048 | ||||||||
\(508\) | 2.30706e7 | 3.96643 | ||||||||
\(509\) | −6.31223e6 | −1.07991 | −0.539956 | − | 0.841693i | \(-0.681559\pi\) | ||||
−0.539956 | + | 0.841693i | \(0.681559\pi\) | |||||||
\(510\) | −5.14933e6 | −0.876648 | ||||||||
\(511\) | −2.42026e6 | −0.410024 | ||||||||
\(512\) | 1.22343e7 | 2.06255 | ||||||||
\(513\) | −123081. | −0.0206489 | ||||||||
\(514\) | 1.27558e7 | 2.12960 | ||||||||
\(515\) | 5.52586e6 | 0.918083 | ||||||||
\(516\) | 2.61164e6 | 0.431806 | ||||||||
\(517\) | 6.40470e6 | 1.05384 | ||||||||
\(518\) | −661659. | −0.108345 | ||||||||
\(519\) | −1.71461e6 | −0.279414 | ||||||||
\(520\) | −2.67598e6 | −0.433984 | ||||||||
\(521\) | −1.00384e7 | −1.62021 | −0.810106 | − | 0.586283i | \(-0.800591\pi\) | ||||
−0.810106 | + | 0.586283i | \(0.800591\pi\) | |||||||
\(522\) | −231247. | −0.0371449 | ||||||||
\(523\) | 4.29564e6 | 0.686710 | 0.343355 | − | 0.939206i | \(-0.388437\pi\) | ||||
0.343355 | + | 0.939206i | \(0.388437\pi\) | |||||||
\(524\) | −1.15430e7 | −1.83650 | ||||||||
\(525\) | 1.03477e6 | 0.163850 | ||||||||
\(526\) | 1.07075e7 | 1.68742 | ||||||||
\(527\) | −3.77138e6 | −0.591525 | ||||||||
\(528\) | 8.82839e6 | 1.37815 | ||||||||
\(529\) | −6.41580e6 | −0.996809 | ||||||||
\(530\) | −3.32942e6 | −0.514847 | ||||||||
\(531\) | −281961. | −0.0433963 | ||||||||
\(532\) | 726603. | 0.111306 | ||||||||
\(533\) | −376500. | −0.0574046 | ||||||||
\(534\) | −1.00258e7 | −1.52147 | ||||||||
\(535\) | 3.99144e6 | 0.602899 | ||||||||
\(536\) | −6.81960e6 | −1.02529 | ||||||||
\(537\) | −1.56181e6 | −0.233718 | ||||||||
\(538\) | 5.86247e6 | 0.873223 | ||||||||
\(539\) | −5.86578e6 | −0.869669 | ||||||||
\(540\) | 1.83219e6 | 0.270388 | ||||||||
\(541\) | −6.40724e6 | −0.941190 | −0.470595 | − | 0.882349i | \(-0.655961\pi\) | ||||
−0.470595 | + | 0.882349i | \(0.655961\pi\) | |||||||
\(542\) | 1.40908e7 | 2.06033 | ||||||||
\(543\) | 6.45986e6 | 0.940207 | ||||||||
\(544\) | −1.50366e7 | −2.17848 | ||||||||
\(545\) | 6.25375e6 | 0.901882 | ||||||||
\(546\) | 946583. | 0.135887 | ||||||||
\(547\) | 2.87214e6 | 0.410429 | 0.205214 | − | 0.978717i | \(-0.434211\pi\) | ||||
0.205214 | + | 0.978717i | \(0.434211\pi\) | |||||||
\(548\) | −9.69822e6 | −1.37956 | ||||||||
\(549\) | 2.36958e6 | 0.335538 | ||||||||
\(550\) | 9.05505e6 | 1.27639 | ||||||||
\(551\) | −46474.4 | −0.00652130 | ||||||||
\(552\) | −582829. | −0.0814130 | ||||||||
\(553\) | 3.16567e6 | 0.440203 | ||||||||
\(554\) | −2.27311e6 | −0.314663 | ||||||||
\(555\) | −335310. | −0.0462076 | ||||||||
\(556\) | 1.17494e7 | 1.61186 | ||||||||
\(557\) | −1.93992e6 | −0.264939 | −0.132470 | − | 0.991187i | \(-0.542291\pi\) | ||||
−0.132470 | + | 0.991187i | \(0.542291\pi\) | |||||||
\(558\) | 1.91015e6 | 0.259706 | ||||||||
\(559\) | 683774. | 0.0925514 | ||||||||
\(560\) | −4.29636e6 | −0.578937 | ||||||||
\(561\) | 6.45583e6 | 0.866054 | ||||||||
\(562\) | −1.60735e7 | −2.14669 | ||||||||
\(563\) | 2.17438e6 | 0.289110 | 0.144555 | − | 0.989497i | \(-0.453825\pi\) | ||||
0.144555 | + | 0.989497i | \(0.453825\pi\) | |||||||
\(564\) | 1.00721e7 | 1.33329 | ||||||||
\(565\) | 3.79397e6 | 0.500004 | ||||||||
\(566\) | 1.44974e7 | 1.90217 | ||||||||
\(567\) | −373657. | −0.0488107 | ||||||||
\(568\) | −5.99690e6 | −0.779931 | ||||||||
\(569\) | −4.07789e6 | −0.528025 | −0.264012 | − | 0.964519i | \(-0.585046\pi\) | ||||
−0.264012 | + | 0.964519i | \(0.585046\pi\) | |||||||
\(570\) | 524150. | 0.0675723 | ||||||||
\(571\) | 7.41602e6 | 0.951876 | 0.475938 | − | 0.879479i | \(-0.342109\pi\) | ||||
0.475938 | + | 0.879479i | \(0.342109\pi\) | |||||||
\(572\) | 5.81913e6 | 0.743649 | ||||||||
\(573\) | 3.02967e6 | 0.385486 | ||||||||
\(574\) | −1.24892e6 | −0.158217 | ||||||||
\(575\) | −289335. | −0.0364948 | ||||||||
\(576\) | 1.73658e6 | 0.218092 | ||||||||
\(577\) | 1.29497e6 | 0.161927 | 0.0809636 | − | 0.996717i | \(-0.474200\pi\) | ||||
0.0809636 | + | 0.996717i | \(0.474200\pi\) | |||||||
\(578\) | −1.38075e7 | −1.71908 | ||||||||
\(579\) | 2.63796e6 | 0.327018 | ||||||||
\(580\) | 691823. | 0.0853935 | ||||||||
\(581\) | −4.61552e6 | −0.567258 | ||||||||
\(582\) | 8.62829e6 | 1.05589 | ||||||||
\(583\) | 4.17416e6 | 0.508625 | ||||||||
\(584\) | −1.92024e7 | −2.32983 | ||||||||
\(585\) | 479701. | 0.0579536 | ||||||||
\(586\) | −2.42607e7 | −2.91849 | ||||||||
\(587\) | 9.79730e6 | 1.17358 | 0.586788 | − | 0.809741i | \(-0.300392\pi\) | ||||
0.586788 | + | 0.809741i | \(0.300392\pi\) | |||||||
\(588\) | −9.22462e6 | −1.10028 | ||||||||
\(589\) | 383888. | 0.0455949 | ||||||||
\(590\) | 1.20076e6 | 0.142012 | ||||||||
\(591\) | −2.28722e6 | −0.269364 | ||||||||
\(592\) | −2.54085e6 | −0.297971 | ||||||||
\(593\) | 2.89314e6 | 0.337857 | 0.168929 | − | 0.985628i | \(-0.445969\pi\) | ||||
0.168929 | + | 0.985628i | \(0.445969\pi\) | |||||||
\(594\) | −3.26979e6 | −0.380236 | ||||||||
\(595\) | −3.14175e6 | −0.363814 | ||||||||
\(596\) | 3.35623e7 | 3.87023 | ||||||||
\(597\) | 587615. | 0.0674772 | ||||||||
\(598\) | −264676. | −0.0302665 | ||||||||
\(599\) | 1.07146e6 | 0.122013 | 0.0610066 | − | 0.998137i | \(-0.480569\pi\) | ||||
0.0610066 | + | 0.998137i | \(0.480569\pi\) | |||||||
\(600\) | 8.20992e6 | 0.931024 | ||||||||
\(601\) | −8.77640e6 | −0.991129 | −0.495564 | − | 0.868571i | \(-0.665039\pi\) | ||||
−0.495564 | + | 0.868571i | \(0.665039\pi\) | |||||||
\(602\) | 2.26820e6 | 0.255088 | ||||||||
\(603\) | 1.22249e6 | 0.136916 | ||||||||
\(604\) | −5.20960e6 | −0.581048 | ||||||||
\(605\) | 863943. | 0.0959614 | ||||||||
\(606\) | 1.25798e7 | 1.39153 | ||||||||
\(607\) | −1.38832e7 | −1.52939 | −0.764696 | − | 0.644391i | \(-0.777111\pi\) | ||||
−0.764696 | + | 0.644391i | \(0.777111\pi\) | |||||||
\(608\) | 1.53058e6 | 0.167917 | ||||||||
\(609\) | −141090. | −0.0154153 | ||||||||
\(610\) | −1.00911e7 | −1.09803 | ||||||||
\(611\) | 2.63706e6 | 0.285771 | ||||||||
\(612\) | 1.01525e7 | 1.09571 | ||||||||
\(613\) | −2.96162e6 | −0.318330 | −0.159165 | − | 0.987252i | \(-0.550880\pi\) | ||||
−0.159165 | + | 0.987252i | \(0.550880\pi\) | |||||||
\(614\) | −1.79893e7 | −1.92572 | ||||||||
\(615\) | −632914. | −0.0674772 | ||||||||
\(616\) | 1.11289e7 | 1.18168 | ||||||||
\(617\) | −1.63962e7 | −1.73393 | −0.866964 | − | 0.498370i | \(-0.833932\pi\) | ||||
−0.866964 | + | 0.498370i | \(0.833932\pi\) | |||||||
\(618\) | −1.55085e7 | −1.63343 | ||||||||
\(619\) | −1.35257e7 | −1.41884 | −0.709418 | − | 0.704788i | \(-0.751042\pi\) | ||||
−0.709418 | + | 0.704788i | \(0.751042\pi\) | |||||||
\(620\) | −5.71460e6 | −0.597045 | ||||||||
\(621\) | 104479. | 0.0108718 | ||||||||
\(622\) | 1.42070e7 | 1.47240 | ||||||||
\(623\) | −6.11700e6 | −0.631420 | ||||||||
\(624\) | 3.63499e6 | 0.373716 | ||||||||
\(625\) | 618876. | 0.0633729 | ||||||||
\(626\) | 2.38930e7 | 2.43688 | ||||||||
\(627\) | −657139. | −0.0667557 | ||||||||
\(628\) | −5.23558e6 | −0.529743 | ||||||||
\(629\) | −1.85802e6 | −0.187250 | ||||||||
\(630\) | 1.59125e6 | 0.159730 | ||||||||
\(631\) | −1.19825e7 | −1.19805 | −0.599025 | − | 0.800731i | \(-0.704445\pi\) | ||||
−0.599025 | + | 0.800731i | \(0.704445\pi\) | |||||||
\(632\) | 2.51166e7 | 2.50131 | ||||||||
\(633\) | 838285. | 0.0831539 | ||||||||
\(634\) | −2.39870e7 | −2.37003 | ||||||||
\(635\) | 1.01540e7 | 0.999318 | ||||||||
\(636\) | 6.56435e6 | 0.643501 | ||||||||
\(637\) | −2.41517e6 | −0.235830 | ||||||||
\(638\) | −1.23465e6 | −0.120086 | ||||||||
\(639\) | 1.07502e6 | 0.104151 | ||||||||
\(640\) | 2.25298e6 | 0.217424 | ||||||||
\(641\) | −7.00957e6 | −0.673823 | −0.336912 | − | 0.941536i | \(-0.609382\pi\) | ||||
−0.336912 | + | 0.941536i | \(0.609382\pi\) | |||||||
\(642\) | −1.12021e7 | −1.07266 | ||||||||
\(643\) | 605033. | 0.0577101 | 0.0288550 | − | 0.999584i | \(-0.490814\pi\) | ||||
0.0288550 | + | 0.999584i | \(0.490814\pi\) | |||||||
\(644\) | −616789. | −0.0586033 | ||||||||
\(645\) | 1.14946e6 | 0.108791 | ||||||||
\(646\) | 2.90442e6 | 0.273828 | ||||||||
\(647\) | 1.46414e7 | 1.37506 | 0.687531 | − | 0.726155i | \(-0.258695\pi\) | ||||
0.687531 | + | 0.726155i | \(0.258695\pi\) | |||||||
\(648\) | −2.96461e6 | −0.277351 | ||||||||
\(649\) | −1.50542e6 | −0.140296 | ||||||||
\(650\) | 3.72831e6 | 0.346122 | ||||||||
\(651\) | 1.16543e6 | 0.107779 | ||||||||
\(652\) | −2.01975e7 | −1.86071 | ||||||||
\(653\) | 3.99497e6 | 0.366632 | 0.183316 | − | 0.983054i | \(-0.441317\pi\) | ||||
0.183316 | + | 0.983054i | \(0.441317\pi\) | |||||||
\(654\) | −1.75514e7 | −1.60460 | ||||||||
\(655\) | −5.08041e6 | −0.462696 | ||||||||
\(656\) | −4.79598e6 | −0.435129 | ||||||||
\(657\) | 3.44226e6 | 0.311122 | ||||||||
\(658\) | 8.74761e6 | 0.787634 | ||||||||
\(659\) | 274018. | 0.0245791 | 0.0122895 | − | 0.999924i | \(-0.496088\pi\) | ||||
0.0122895 | + | 0.999924i | \(0.496088\pi\) | |||||||
\(660\) | 9.78224e6 | 0.874135 | ||||||||
\(661\) | −1.92782e7 | −1.71618 | −0.858091 | − | 0.513497i | \(-0.828350\pi\) | ||||
−0.858091 | + | 0.513497i | \(0.828350\pi\) | |||||||
\(662\) | −1.05687e7 | −0.937294 | ||||||||
\(663\) | 2.65811e6 | 0.234850 | ||||||||
\(664\) | −3.66197e7 | −3.22326 | ||||||||
\(665\) | 319799. | 0.0280429 | ||||||||
\(666\) | 941058. | 0.0822112 | ||||||||
\(667\) | 39450.5 | 0.00343351 | ||||||||
\(668\) | 2.93056e7 | 2.54102 | ||||||||
\(669\) | 274756. | 0.0237346 | ||||||||
\(670\) | −5.20610e6 | −0.448049 | ||||||||
\(671\) | 1.26514e7 | 1.08476 | ||||||||
\(672\) | 4.64663e6 | 0.396931 | ||||||||
\(673\) | −1.19222e7 | −1.01466 | −0.507329 | − | 0.861753i | \(-0.669367\pi\) | ||||
−0.507329 | + | 0.861753i | \(0.669367\pi\) | |||||||
\(674\) | −2.03450e7 | −1.72507 | ||||||||
\(675\) | −1.47173e6 | −0.124328 | ||||||||
\(676\) | −2.56615e7 | −2.15981 | ||||||||
\(677\) | −3.81809e6 | −0.320166 | −0.160083 | − | 0.987104i | \(-0.551176\pi\) | ||||
−0.160083 | + | 0.987104i | \(0.551176\pi\) | |||||||
\(678\) | −1.06479e7 | −0.889591 | ||||||||
\(679\) | 5.26436e6 | 0.438199 | ||||||||
\(680\) | −2.49268e7 | −2.06725 | ||||||||
\(681\) | −7.00094e6 | −0.578480 | ||||||||
\(682\) | 1.01985e7 | 0.839602 | ||||||||
\(683\) | 1.71086e7 | 1.40334 | 0.701672 | − | 0.712500i | \(-0.252437\pi\) | ||||
0.701672 | + | 0.712500i | \(0.252437\pi\) | |||||||
\(684\) | −1.03343e6 | −0.0844577 | ||||||||
\(685\) | −4.26846e6 | −0.347572 | ||||||||
\(686\) | −1.79389e7 | −1.45541 | ||||||||
\(687\) | −6.86867e6 | −0.555240 | ||||||||
\(688\) | 8.71014e6 | 0.701543 | ||||||||
\(689\) | 1.71866e6 | 0.137925 | ||||||||
\(690\) | −444933. | −0.0355772 | ||||||||
\(691\) | 1.16432e6 | 0.0927639 | 0.0463820 | − | 0.998924i | \(-0.485231\pi\) | ||||
0.0463820 | + | 0.998924i | \(0.485231\pi\) | |||||||
\(692\) | −1.43965e7 | −1.14285 | ||||||||
\(693\) | −1.99499e6 | −0.157800 | ||||||||
\(694\) | −5.88117e6 | −0.463516 | ||||||||
\(695\) | 5.17122e6 | 0.406098 | ||||||||
\(696\) | −1.11941e6 | −0.0875927 | ||||||||
\(697\) | −3.50710e6 | −0.273443 | ||||||||
\(698\) | −2.89692e7 | −2.25060 | ||||||||
\(699\) | −1.14914e7 | −0.889573 | ||||||||
\(700\) | 8.68829e6 | 0.670177 | ||||||||
\(701\) | −2.35243e6 | −0.180810 | −0.0904050 | − | 0.995905i | \(-0.528816\pi\) | ||||
−0.0904050 | + | 0.995905i | \(0.528816\pi\) | |||||||
\(702\) | −1.34630e6 | −0.103109 | ||||||||
\(703\) | 189127. | 0.0144333 | ||||||||
\(704\) | 9.27177e6 | 0.705068 | ||||||||
\(705\) | 4.43303e6 | 0.335914 | ||||||||
\(706\) | −2.93360e7 | −2.21508 | ||||||||
\(707\) | 7.67528e6 | 0.577492 | ||||||||
\(708\) | −2.36744e6 | −0.177499 | ||||||||
\(709\) | −2.37540e7 | −1.77468 | −0.887342 | − | 0.461112i | \(-0.847451\pi\) | ||||
−0.887342 | + | 0.461112i | \(0.847451\pi\) | |||||||
\(710\) | −4.57805e6 | −0.340828 | ||||||||
\(711\) | −4.50244e6 | −0.334021 | ||||||||
\(712\) | −4.85325e7 | −3.58784 | ||||||||
\(713\) | −325870. | −0.0240060 | ||||||||
\(714\) | 8.81744e6 | 0.647287 | ||||||||
\(715\) | 2.56116e6 | 0.187358 | ||||||||
\(716\) | −1.31135e7 | −0.955949 | ||||||||
\(717\) | 642204. | 0.0466525 | ||||||||
\(718\) | 2.07840e6 | 0.150459 | ||||||||
\(719\) | 7.28156e6 | 0.525294 | 0.262647 | − | 0.964892i | \(-0.415405\pi\) | ||||
0.262647 | + | 0.964892i | \(0.415405\pi\) | |||||||
\(720\) | 6.11059e6 | 0.439291 | ||||||||
\(721\) | −9.46219e6 | −0.677881 | ||||||||
\(722\) | 2.53851e7 | 1.81232 | ||||||||
\(723\) | −1.12633e7 | −0.801344 | ||||||||
\(724\) | 5.42392e7 | 3.84562 | ||||||||
\(725\) | −555713. | −0.0392650 | ||||||||
\(726\) | −2.42469e6 | −0.170732 | ||||||||
\(727\) | 400663. | 0.0281153 | 0.0140577 | − | 0.999901i | \(-0.495525\pi\) | ||||
0.0140577 | + | 0.999901i | \(0.495525\pi\) | |||||||
\(728\) | 4.58220e6 | 0.320439 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.46592e7 | −1.01813 | ||||||||
\(731\) | 6.36936e6 | 0.440862 | ||||||||
\(732\) | 1.98958e7 | 1.37241 | ||||||||
\(733\) | 2.06252e7 | 1.41787 | 0.708937 | − | 0.705272i | \(-0.249175\pi\) | ||||
0.708937 | + | 0.705272i | \(0.249175\pi\) | |||||||
\(734\) | 1.09223e7 | 0.748297 | ||||||||
\(735\) | −4.06001e6 | −0.277210 | ||||||||
\(736\) | −1.29925e6 | −0.0884097 | ||||||||
\(737\) | 6.52701e6 | 0.442634 | ||||||||
\(738\) | 1.77630e6 | 0.120053 | ||||||||
\(739\) | −1.36694e7 | −0.920744 | −0.460372 | − | 0.887726i | \(-0.652284\pi\) | ||||
−0.460372 | + | 0.887726i | \(0.652284\pi\) | |||||||
\(740\) | −2.81537e6 | −0.188998 | ||||||||
\(741\) | −270569. | −0.0181023 | ||||||||
\(742\) | 5.70111e6 | 0.380145 | ||||||||
\(743\) | 1.13736e7 | 0.755833 | 0.377917 | − | 0.925840i | \(-0.376641\pi\) | ||||
0.377917 | + | 0.925840i | \(0.376641\pi\) | |||||||
\(744\) | 9.24660e6 | 0.612421 | ||||||||
\(745\) | 1.47717e7 | 0.975081 | ||||||||
\(746\) | 1.24550e7 | 0.819400 | ||||||||
\(747\) | 6.56452e6 | 0.430429 | ||||||||
\(748\) | 5.42053e7 | 3.54232 | ||||||||
\(749\) | −6.83472e6 | −0.445160 | ||||||||
\(750\) | 1.59691e7 | 1.03664 | ||||||||
\(751\) | −1.25684e6 | −0.0813171 | −0.0406585 | − | 0.999173i | \(-0.512946\pi\) | ||||
−0.0406585 | + | 0.999173i | \(0.512946\pi\) | |||||||
\(752\) | 3.35918e7 | 2.16615 | ||||||||
\(753\) | −1.10403e7 | −0.709564 | ||||||||
\(754\) | −508352. | −0.0325639 | ||||||||
\(755\) | −2.29289e6 | −0.146392 | ||||||||
\(756\) | −3.13735e6 | −0.199645 | ||||||||
\(757\) | −1.34819e7 | −0.855087 | −0.427544 | − | 0.903995i | \(-0.640621\pi\) | ||||
−0.427544 | + | 0.903995i | \(0.640621\pi\) | |||||||
\(758\) | 4.10549e7 | 2.59533 | ||||||||
\(759\) | 557823. | 0.0351473 | ||||||||
\(760\) | 2.53729e6 | 0.159344 | ||||||||
\(761\) | −865364. | −0.0541673 | −0.0270837 | − | 0.999633i | \(-0.508622\pi\) | ||||
−0.0270837 | + | 0.999633i | \(0.508622\pi\) | |||||||
\(762\) | −2.84976e7 | −1.77796 | ||||||||
\(763\) | −1.07086e7 | −0.665918 | ||||||||
\(764\) | 2.54381e7 | 1.57671 | ||||||||
\(765\) | 4.46842e6 | 0.276058 | ||||||||
\(766\) | 3.71579e7 | 2.28812 | ||||||||
\(767\) | −619837. | −0.0380443 | ||||||||
\(768\) | −1.24976e7 | −0.764580 | ||||||||
\(769\) | −2.08760e7 | −1.27301 | −0.636503 | − | 0.771274i | \(-0.719620\pi\) | ||||
−0.636503 | + | 0.771274i | \(0.719620\pi\) | |||||||
\(770\) | 8.49584e6 | 0.516392 | ||||||||
\(771\) | −1.10690e7 | −0.670615 | ||||||||
\(772\) | 2.21492e7 | 1.33757 | ||||||||
\(773\) | 2.75458e7 | 1.65809 | 0.829043 | − | 0.559185i | \(-0.188886\pi\) | ||||
0.829043 | + | 0.559185i | \(0.188886\pi\) | |||||||
\(774\) | −3.22599e6 | −0.193558 | ||||||||
\(775\) | 4.59031e6 | 0.274529 | ||||||||
\(776\) | 4.17677e7 | 2.48992 | ||||||||
\(777\) | 574166. | 0.0341181 | ||||||||
\(778\) | 2.86204e7 | 1.69522 | ||||||||
\(779\) | 356988. | 0.0210770 | ||||||||
\(780\) | 4.02773e6 | 0.237041 | ||||||||
\(781\) | 5.73961e6 | 0.336709 | ||||||||
\(782\) | −2.46546e6 | −0.144172 | ||||||||
\(783\) | 200668. | 0.0116970 | ||||||||
\(784\) | −3.07652e7 | −1.78760 | ||||||||
\(785\) | −2.30433e6 | −0.133466 | ||||||||
\(786\) | 1.42584e7 | 0.823215 | ||||||||
\(787\) | 1.86224e7 | 1.07176 | 0.535881 | − | 0.844293i | \(-0.319979\pi\) | ||||
0.535881 | + | 0.844293i | \(0.319979\pi\) | |||||||
\(788\) | −1.92042e7 | −1.10175 | ||||||||
\(789\) | −9.29162e6 | −0.531373 | ||||||||
\(790\) | 1.91741e7 | 1.09307 | ||||||||
\(791\) | −6.49659e6 | −0.369185 | ||||||||
\(792\) | −1.58283e7 | −0.896647 | ||||||||
\(793\) | 5.20908e6 | 0.294156 | ||||||||
\(794\) | −4.95740e7 | −2.79063 | ||||||||
\(795\) | 2.88916e6 | 0.162126 | ||||||||
\(796\) | 4.93381e6 | 0.275994 | ||||||||
\(797\) | −1.01313e7 | −0.564965 | −0.282482 | − | 0.959272i | \(-0.591158\pi\) | ||||
−0.282482 | + | 0.959272i | \(0.591158\pi\) | |||||||
\(798\) | −897526. | −0.0498930 | ||||||||
\(799\) | 2.45643e7 | 1.36125 | ||||||||
\(800\) | 1.83017e7 | 1.01104 | ||||||||
\(801\) | 8.70003e6 | 0.479115 | ||||||||
\(802\) | 4.97044e7 | 2.72872 | ||||||||
\(803\) | 1.83785e7 | 1.00582 | ||||||||
\(804\) | 1.02645e7 | 0.560011 | ||||||||
\(805\) | −271466. | −0.0147648 | ||||||||
\(806\) | 4.19910e6 | 0.227677 | ||||||||
\(807\) | −5.08726e6 | −0.274979 | ||||||||
\(808\) | 6.08960e7 | 3.28141 | ||||||||
\(809\) | 1.76196e7 | 0.946507 | 0.473254 | − | 0.880926i | \(-0.343079\pi\) | ||||
0.473254 | + | 0.880926i | \(0.343079\pi\) | |||||||
\(810\) | −2.26319e6 | −0.121202 | ||||||||
\(811\) | −1.37418e6 | −0.0733654 | −0.0366827 | − | 0.999327i | \(-0.511679\pi\) | ||||
−0.0366827 | + | 0.999327i | \(0.511679\pi\) | |||||||
\(812\) | −1.18464e6 | −0.0630516 | ||||||||
\(813\) | −1.22275e7 | −0.648803 | ||||||||
\(814\) | 5.02440e6 | 0.265780 | ||||||||
\(815\) | −8.88950e6 | −0.468795 | ||||||||
\(816\) | 3.38600e7 | 1.78017 | ||||||||
\(817\) | −648337. | −0.0339817 | ||||||||
\(818\) | −8.34595e6 | −0.436107 | ||||||||
\(819\) | −821413. | −0.0427909 | ||||||||
\(820\) | −5.31416e6 | −0.275994 | ||||||||
\(821\) | −1.13057e7 | −0.585382 | −0.292691 | − | 0.956207i | \(-0.594551\pi\) | ||||
−0.292691 | + | 0.956207i | \(0.594551\pi\) | |||||||
\(822\) | 1.19796e7 | 0.618390 | ||||||||
\(823\) | 2.63250e7 | 1.35478 | 0.677389 | − | 0.735625i | \(-0.263111\pi\) | ||||
0.677389 | + | 0.735625i | \(0.263111\pi\) | |||||||
\(824\) | −7.50734e7 | −3.85184 | ||||||||
\(825\) | −7.85767e6 | −0.401938 | ||||||||
\(826\) | −2.05611e6 | −0.104857 | ||||||||
\(827\) | 2.02274e6 | 0.102843 | 0.0514217 | − | 0.998677i | \(-0.483625\pi\) | ||||
0.0514217 | + | 0.998677i | \(0.483625\pi\) | |||||||
\(828\) | 877241. | 0.0444675 | ||||||||
\(829\) | −1.96942e7 | −0.995297 | −0.497649 | − | 0.867379i | \(-0.665803\pi\) | ||||
−0.497649 | + | 0.867379i | \(0.665803\pi\) | |||||||
\(830\) | −2.79556e7 | −1.40855 | ||||||||
\(831\) | 1.97253e6 | 0.0990880 | ||||||||
\(832\) | 3.81754e6 | 0.191195 | ||||||||
\(833\) | −2.24973e7 | −1.12336 | ||||||||
\(834\) | −1.45132e7 | −0.722518 | ||||||||
\(835\) | 1.28982e7 | 0.640196 | ||||||||
\(836\) | −5.51756e6 | −0.273043 | ||||||||
\(837\) | −1.65756e6 | −0.0817818 | ||||||||
\(838\) | −5.66803e7 | −2.78819 | ||||||||
\(839\) | −3.39690e6 | −0.166601 | −0.0833006 | − | 0.996524i | \(-0.526546\pi\) | ||||
−0.0833006 | + | 0.996524i | \(0.526546\pi\) | |||||||
\(840\) | 7.70290e6 | 0.376665 | ||||||||
\(841\) | −2.04354e7 | −0.996306 | ||||||||
\(842\) | 2.03900e7 | 0.991147 | ||||||||
\(843\) | 1.39481e7 | 0.675997 | ||||||||
\(844\) | 7.03852e6 | 0.340115 | ||||||||
\(845\) | −1.12944e7 | −0.544152 | ||||||||
\(846\) | −1.24415e7 | −0.597648 | ||||||||
\(847\) | −1.47937e6 | −0.0708546 | ||||||||
\(848\) | 2.18929e7 | 1.04548 | ||||||||
\(849\) | −1.25804e7 | −0.598997 | ||||||||
\(850\) | 3.47293e7 | 1.64873 | ||||||||
\(851\) | −160544. | −0.00759923 | ||||||||
\(852\) | 9.02619e6 | 0.425996 | ||||||||
\(853\) | −8.12673e6 | −0.382422 | −0.191211 | − | 0.981549i | \(-0.561242\pi\) | ||||
−0.191211 | + | 0.981549i | \(0.561242\pi\) | |||||||
\(854\) | 1.72794e7 | 0.810746 | ||||||||
\(855\) | −454840. | −0.0212786 | ||||||||
\(856\) | −5.42269e7 | −2.52948 | ||||||||
\(857\) | 2.17376e7 | 1.01102 | 0.505509 | − | 0.862821i | \(-0.331305\pi\) | ||||
0.505509 | + | 0.862821i | \(0.331305\pi\) | |||||||
\(858\) | −7.18800e6 | −0.333342 | ||||||||
\(859\) | 180961. | 0.00836764 | 0.00418382 | − | 0.999991i | \(-0.498668\pi\) | ||||
0.00418382 | + | 0.999991i | \(0.498668\pi\) | |||||||
\(860\) | 9.65122e6 | 0.444975 | ||||||||
\(861\) | 1.08377e6 | 0.0498228 | ||||||||
\(862\) | −6.41057e7 | −2.93852 | ||||||||
\(863\) | 3.07976e7 | 1.40764 | 0.703818 | − | 0.710381i | \(-0.251477\pi\) | ||||
0.703818 | + | 0.710381i | \(0.251477\pi\) | |||||||
\(864\) | −6.60876e6 | −0.301187 | ||||||||
\(865\) | −6.33629e6 | −0.287935 | ||||||||
\(866\) | 7.06488e7 | 3.20118 | ||||||||
\(867\) | 1.19817e7 | 0.541340 | ||||||||
\(868\) | 9.78538e6 | 0.440837 | ||||||||
\(869\) | −2.40389e7 | −1.07986 | ||||||||
\(870\) | −854564. | −0.0382778 | ||||||||
\(871\) | 2.68742e6 | 0.120030 | ||||||||
\(872\) | −8.49624e7 | −3.78386 | ||||||||
\(873\) | −7.48735e6 | −0.332501 | ||||||||
\(874\) | 250959. | 0.0111128 | ||||||||
\(875\) | 9.74318e6 | 0.430210 | ||||||||
\(876\) | 2.89024e7 | 1.27255 | ||||||||
\(877\) | 1.10924e7 | 0.486998 | 0.243499 | − | 0.969901i | \(-0.421705\pi\) | ||||
0.243499 | + | 0.969901i | \(0.421705\pi\) | |||||||
\(878\) | −6.19923e7 | −2.71395 | ||||||||
\(879\) | 2.10526e7 | 0.919038 | ||||||||
\(880\) | 3.26250e7 | 1.42018 | ||||||||
\(881\) | 3.34548e7 | 1.45217 | 0.726086 | − | 0.687603i | \(-0.241337\pi\) | ||||
0.726086 | + | 0.687603i | \(0.241337\pi\) | |||||||
\(882\) | 1.13946e7 | 0.493204 | ||||||||
\(883\) | −2.73782e7 | −1.18169 | −0.590844 | − | 0.806786i | \(-0.701205\pi\) | ||||
−0.590844 | + | 0.806786i | \(0.701205\pi\) | |||||||
\(884\) | 2.23184e7 | 0.960578 | ||||||||
\(885\) | −1.04198e6 | −0.0447198 | ||||||||
\(886\) | 5.09221e6 | 0.217932 | ||||||||
\(887\) | −2.42168e7 | −1.03350 | −0.516748 | − | 0.856138i | \(-0.672857\pi\) | ||||
−0.516748 | + | 0.856138i | \(0.672857\pi\) | |||||||
\(888\) | 4.55546e6 | 0.193865 | ||||||||
\(889\) | −1.73872e7 | −0.737862 | ||||||||
\(890\) | −3.70499e7 | −1.56788 | ||||||||
\(891\) | 2.83741e6 | 0.119737 | ||||||||
\(892\) | 2.30694e6 | 0.0970788 | ||||||||
\(893\) | −2.50040e6 | −0.104925 | ||||||||
\(894\) | −4.14574e7 | −1.73484 | ||||||||
\(895\) | −5.77161e6 | −0.240846 | ||||||||
\(896\) | −3.85788e6 | −0.160538 | ||||||||
\(897\) | 229677. | 0.00953096 | ||||||||
\(898\) | −7.52888e7 | −3.11559 | ||||||||
\(899\) | −625884. | −0.0258282 | ||||||||
\(900\) | −1.23571e7 | −0.508523 | ||||||||
\(901\) | 1.60094e7 | 0.656996 | ||||||||
\(902\) | 9.48381e6 | 0.388120 | ||||||||
\(903\) | −1.96827e6 | −0.0803276 | ||||||||
\(904\) | −5.15442e7 | −2.09778 | ||||||||
\(905\) | 2.38722e7 | 0.968881 | ||||||||
\(906\) | 6.43508e6 | 0.260455 | ||||||||
\(907\) | −2.31796e7 | −0.935595 | −0.467797 | − | 0.883836i | \(-0.654952\pi\) | ||||
−0.467797 | + | 0.883836i | \(0.654952\pi\) | |||||||
\(908\) | −5.87822e7 | −2.36609 | ||||||||
\(909\) | −1.09163e7 | −0.438194 | ||||||||
\(910\) | 3.49806e6 | 0.140031 | ||||||||
\(911\) | 1.41080e7 | 0.563209 | 0.281605 | − | 0.959531i | \(-0.409133\pi\) | ||||
0.281605 | + | 0.959531i | \(0.409133\pi\) | |||||||
\(912\) | −3.44660e6 | −0.137216 | ||||||||
\(913\) | 3.50486e7 | 1.39153 | ||||||||
\(914\) | 2.88361e7 | 1.14175 | ||||||||
\(915\) | 8.75671e6 | 0.345771 | ||||||||
\(916\) | −5.76717e7 | −2.27104 | ||||||||
\(917\) | 8.69943e6 | 0.341639 | ||||||||
\(918\) | −1.25408e7 | −0.491154 | ||||||||
\(919\) | 3.48252e7 | 1.36020 | 0.680102 | − | 0.733117i | \(-0.261935\pi\) | ||||
0.680102 | + | 0.733117i | \(0.261935\pi\) | |||||||
\(920\) | −2.15382e6 | −0.0838959 | ||||||||
\(921\) | 1.56105e7 | 0.606414 | ||||||||
\(922\) | 6.23709e7 | 2.41632 | ||||||||
\(923\) | 2.36322e6 | 0.0913060 | ||||||||
\(924\) | −1.67506e7 | −0.645431 | ||||||||
\(925\) | 2.26147e6 | 0.0869034 | ||||||||
\(926\) | 7.37189e7 | 2.82521 | ||||||||
\(927\) | 1.34578e7 | 0.514369 | ||||||||
\(928\) | −2.49542e6 | −0.0951204 | ||||||||
\(929\) | 8.18223e6 | 0.311052 | 0.155526 | − | 0.987832i | \(-0.450293\pi\) | ||||
0.155526 | + | 0.987832i | \(0.450293\pi\) | |||||||
\(930\) | 7.05888e6 | 0.267626 | ||||||||
\(931\) | 2.29000e6 | 0.0865888 | ||||||||
\(932\) | −9.64860e7 | −3.63852 | ||||||||
\(933\) | −1.23284e7 | −0.463662 | ||||||||
\(934\) | −5.72463e7 | −2.14724 | ||||||||
\(935\) | 2.38573e7 | 0.892467 | ||||||||
\(936\) | −6.51712e6 | −0.243146 | ||||||||
\(937\) | −3.29144e7 | −1.22472 | −0.612361 | − | 0.790578i | \(-0.709780\pi\) | ||||
−0.612361 | + | 0.790578i | \(0.709780\pi\) | |||||||
\(938\) | 8.91465e6 | 0.330824 | ||||||||
\(939\) | −2.07335e7 | −0.767378 | ||||||||
\(940\) | 3.72212e7 | 1.37395 | ||||||||
\(941\) | 2.12414e7 | 0.782004 | 0.391002 | − | 0.920390i | \(-0.372128\pi\) | ||||
0.391002 | + | 0.920390i | \(0.372128\pi\) | |||||||
\(942\) | 6.46717e6 | 0.237458 | ||||||||
\(943\) | −303035. | −0.0110972 | ||||||||
\(944\) | −7.89570e6 | −0.288377 | ||||||||
\(945\) | −1.38084e6 | −0.0502993 | ||||||||
\(946\) | −1.72239e7 | −0.625752 | ||||||||
\(947\) | 4.07231e7 | 1.47559 | 0.737795 | − | 0.675025i | \(-0.235867\pi\) | ||||
0.737795 | + | 0.675025i | \(0.235867\pi\) | |||||||
\(948\) | −3.78040e7 | −1.36621 | ||||||||
\(949\) | 7.56716e6 | 0.272752 | ||||||||
\(950\) | −3.53509e6 | −0.127084 | ||||||||
\(951\) | 2.08151e7 | 0.746325 | ||||||||
\(952\) | 4.26833e7 | 1.52639 | ||||||||
\(953\) | −3.41302e7 | −1.21733 | −0.608663 | − | 0.793429i | \(-0.708294\pi\) | ||||
−0.608663 | + | 0.793429i | \(0.708294\pi\) | |||||||
\(954\) | −8.10852e6 | −0.288450 | ||||||||
\(955\) | 1.11960e7 | 0.397242 | ||||||||
\(956\) | 5.39216e6 | 0.190817 | ||||||||
\(957\) | 1.07139e6 | 0.0378152 | ||||||||
\(958\) | 3.29830e7 | 1.16112 | ||||||||
\(959\) | 7.30908e6 | 0.256635 | ||||||||
\(960\) | 6.41748e6 | 0.224743 | ||||||||
\(961\) | −2.34592e7 | −0.819417 | ||||||||
\(962\) | 2.06874e6 | 0.0720722 | ||||||||
\(963\) | 9.72082e6 | 0.337782 | ||||||||
\(964\) | −9.45702e7 | −3.27764 | ||||||||
\(965\) | 9.74849e6 | 0.336992 | ||||||||
\(966\) | 761880. | 0.0262690 | ||||||||
\(967\) | 5.84049e6 | 0.200855 | 0.100428 | − | 0.994944i | \(-0.467979\pi\) | ||||
0.100428 | + | 0.994944i | \(0.467979\pi\) | |||||||
\(968\) | −1.17374e7 | −0.402608 | ||||||||
\(969\) | −2.52036e6 | −0.0862289 | ||||||||
\(970\) | 3.18855e7 | 1.08809 | ||||||||
\(971\) | −3.95959e7 | −1.34773 | −0.673864 | − | 0.738856i | \(-0.735367\pi\) | ||||
−0.673864 | + | 0.738856i | \(0.735367\pi\) | |||||||
\(972\) | 4.46216e6 | 0.151488 | ||||||||
\(973\) | −8.85492e6 | −0.299849 | ||||||||
\(974\) | 4.16640e7 | 1.40723 | ||||||||
\(975\) | −3.23531e6 | −0.108994 | ||||||||
\(976\) | 6.63550e7 | 2.22971 | ||||||||
\(977\) | 2.78950e7 | 0.934955 | 0.467477 | − | 0.884005i | \(-0.345163\pi\) | ||||
0.467477 | + | 0.884005i | \(0.345163\pi\) | |||||||
\(978\) | 2.49487e7 | 0.834066 | ||||||||
\(979\) | 4.64502e7 | 1.54893 | ||||||||
\(980\) | −3.40892e7 | −1.13384 | ||||||||
\(981\) | 1.52305e7 | 0.505291 | ||||||||
\(982\) | −2.33576e7 | −0.772948 | ||||||||
\(983\) | −2.02573e7 | −0.668650 | −0.334325 | − | 0.942458i | \(-0.608508\pi\) | ||||
−0.334325 | + | 0.942458i | \(0.608508\pi\) | |||||||
\(984\) | 8.59866e6 | 0.283102 | ||||||||
\(985\) | −8.45233e6 | −0.277579 | ||||||||
\(986\) | −4.73531e6 | −0.155116 | ||||||||
\(987\) | −7.59088e6 | −0.248027 | ||||||||
\(988\) | −2.27179e6 | −0.0740416 | ||||||||
\(989\) | 550352. | 0.0178916 | ||||||||
\(990\) | −1.20834e7 | −0.391832 | ||||||||
\(991\) | 4.46979e6 | 0.144578 | 0.0722891 | − | 0.997384i | \(-0.476970\pi\) | ||||
0.0722891 | + | 0.997384i | \(0.476970\pi\) | |||||||
\(992\) | 2.06127e7 | 0.665053 | ||||||||
\(993\) | 9.17115e6 | 0.295155 | ||||||||
\(994\) | 7.83921e6 | 0.251655 | ||||||||
\(995\) | 2.17151e6 | 0.0695351 | ||||||||
\(996\) | 5.51179e7 | 1.76053 | ||||||||
\(997\) | −482842. | −0.0153839 | −0.00769196 | − | 0.999970i | \(-0.502448\pi\) | ||||
−0.00769196 | + | 0.999970i | \(0.502448\pi\) | |||||||
\(998\) | −5.05677e7 | −1.60711 | ||||||||
\(999\) | −816619. | −0.0258884 |
(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 | 177.6.a.c.1.1 | ✓ | 12 | |
3.2 | odd | 2 | 531.6.a.c.1.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.c.1.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
531.6.a.c.1.12 | 12 | 3.2 | odd | 2 |