Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,6,Mod(1,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, 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("325.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.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: | \(52.1247414392\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 257 x^{9} + 1165 x^{8} + 22234 x^{7} - 90282 x^{6} - 751180 x^{5} + 2564400 x^{4} + \cdots + 44115200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(11.2252\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.2252 | −1.98435 | −0.992174 | − | 0.124864i | \(-0.960151\pi\) | ||||
−0.992174 | + | 0.124864i | \(0.960151\pi\) | |||||||
\(3\) | −19.1897 | −1.23102 | −0.615511 | − | 0.788129i | \(-0.711050\pi\) | ||||
−0.615511 | + | 0.788129i | \(0.711050\pi\) | |||||||
\(4\) | 94.0044 | 2.93764 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 215.408 | 2.44277 | ||||||||
\(7\) | −70.9909 | −0.547593 | −0.273796 | − | 0.961788i | \(-0.588279\pi\) | ||||
−0.273796 | + | 0.961788i | \(0.588279\pi\) | |||||||
\(8\) | −696.009 | −3.84494 | ||||||||
\(9\) | 125.246 | 0.515414 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −161.025 | −0.401246 | −0.200623 | − | 0.979669i | \(-0.564297\pi\) | ||||
−0.200623 | + | 0.979669i | \(0.564297\pi\) | |||||||
\(12\) | −1803.92 | −3.61629 | ||||||||
\(13\) | −169.000 | −0.277350 | ||||||||
\(14\) | 796.885 | 1.08661 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4804.68 | 4.69207 | ||||||||
\(17\) | 121.397 | 0.101879 | 0.0509396 | − | 0.998702i | \(-0.483778\pi\) | ||||
0.0509396 | + | 0.998702i | \(0.483778\pi\) | |||||||
\(18\) | −1405.90 | −1.02276 | ||||||||
\(19\) | −3111.76 | −1.97753 | −0.988764 | − | 0.149485i | \(-0.952238\pi\) | ||||
−0.988764 | + | 0.149485i | \(0.952238\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1362.30 | 0.674099 | ||||||||
\(22\) | 1807.53 | 0.796211 | ||||||||
\(23\) | 3100.00 | 1.22192 | 0.610959 | − | 0.791662i | \(-0.290784\pi\) | ||||
0.610959 | + | 0.791662i | \(0.290784\pi\) | |||||||
\(24\) | 13356.2 | 4.73321 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1897.05 | 0.550359 | ||||||||
\(27\) | 2259.68 | 0.596536 | ||||||||
\(28\) | −6673.46 | −1.60863 | ||||||||
\(29\) | 3172.08 | 0.700404 | 0.350202 | − | 0.936674i | \(-0.386113\pi\) | ||||
0.350202 | + | 0.936674i | \(0.386113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3515.11 | −0.656953 | −0.328476 | − | 0.944512i | \(-0.606535\pi\) | ||||
−0.328476 | + | 0.944512i | \(0.606535\pi\) | |||||||
\(32\) | −31661.0 | −5.46575 | ||||||||
\(33\) | 3090.02 | 0.493942 | ||||||||
\(34\) | −1362.70 | −0.202164 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 11773.6 | 1.51410 | ||||||||
\(37\) | −6991.30 | −0.839563 | −0.419782 | − | 0.907625i | \(-0.637893\pi\) | ||||
−0.419782 | + | 0.907625i | \(0.637893\pi\) | |||||||
\(38\) | 34930.1 | 3.92410 | ||||||||
\(39\) | 3243.06 | 0.341424 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −19551.6 | −1.81644 | −0.908222 | − | 0.418488i | \(-0.862560\pi\) | ||||
−0.908222 | + | 0.418488i | \(0.862560\pi\) | |||||||
\(42\) | −15292.0 | −1.33765 | ||||||||
\(43\) | −13398.3 | −1.10504 | −0.552522 | − | 0.833498i | \(-0.686335\pi\) | ||||
−0.552522 | + | 0.833498i | \(0.686335\pi\) | |||||||
\(44\) | −15137.0 | −1.17871 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −34798.0 | −2.42471 | ||||||||
\(47\) | −7637.52 | −0.504322 | −0.252161 | − | 0.967685i | \(-0.581141\pi\) | ||||
−0.252161 | + | 0.967685i | \(0.581141\pi\) | |||||||
\(48\) | −92200.5 | −5.77604 | ||||||||
\(49\) | −11767.3 | −0.700142 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2329.57 | −0.125415 | ||||||||
\(52\) | −15886.7 | −0.814754 | ||||||||
\(53\) | −27750.4 | −1.35700 | −0.678500 | − | 0.734600i | \(-0.737370\pi\) | ||||
−0.678500 | + | 0.734600i | \(0.737370\pi\) | |||||||
\(54\) | −25365.2 | −1.18374 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 49410.3 | 2.10546 | ||||||||
\(57\) | 59713.9 | 2.43438 | ||||||||
\(58\) | −35607.1 | −1.38985 | ||||||||
\(59\) | 33042.3 | 1.23578 | 0.617889 | − | 0.786265i | \(-0.287988\pi\) | ||||
0.617889 | + | 0.786265i | \(0.287988\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −33195.2 | −1.14222 | −0.571110 | − | 0.820873i | \(-0.693487\pi\) | ||||
−0.571110 | + | 0.820873i | \(0.693487\pi\) | |||||||
\(62\) | 39457.6 | 1.30362 | ||||||||
\(63\) | −8891.30 | −0.282237 | ||||||||
\(64\) | 201651. | 6.15389 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −34686.0 | −0.980153 | ||||||||
\(67\) | −24591.9 | −0.669275 | −0.334637 | − | 0.942347i | \(-0.608614\pi\) | ||||
−0.334637 | + | 0.942347i | \(0.608614\pi\) | |||||||
\(68\) | 11411.8 | 0.299284 | ||||||||
\(69\) | −59488.1 | −1.50421 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16641.4 | 0.391781 | 0.195891 | − | 0.980626i | \(-0.437240\pi\) | ||||
0.195891 | + | 0.980626i | \(0.437240\pi\) | |||||||
\(72\) | −87172.0 | −1.98174 | ||||||||
\(73\) | 5252.97 | 0.115371 | 0.0576856 | − | 0.998335i | \(-0.481628\pi\) | ||||
0.0576856 | + | 0.998335i | \(0.481628\pi\) | |||||||
\(74\) | 78478.5 | 1.66599 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −292519. | −5.80926 | ||||||||
\(77\) | 11431.3 | 0.219719 | ||||||||
\(78\) | −36403.9 | −0.677504 | ||||||||
\(79\) | −3121.54 | −0.0562731 | −0.0281366 | − | 0.999604i | \(-0.508957\pi\) | ||||
−0.0281366 | + | 0.999604i | \(0.508957\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73797.2 | −1.24976 | ||||||||
\(82\) | 219470. | 3.60446 | ||||||||
\(83\) | 25125.8 | 0.400336 | 0.200168 | − | 0.979762i | \(-0.435851\pi\) | ||||
0.200168 | + | 0.979762i | \(0.435851\pi\) | |||||||
\(84\) | 128062. | 1.98026 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 150399. | 2.19279 | ||||||||
\(87\) | −60871.3 | −0.862213 | ||||||||
\(88\) | 112075. | 1.54277 | ||||||||
\(89\) | 634.739 | 0.00849416 | 0.00424708 | − | 0.999991i | \(-0.498648\pi\) | ||||
0.00424708 | + | 0.999991i | \(0.498648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11997.5 | 0.151875 | ||||||||
\(92\) | 291413. | 3.58955 | ||||||||
\(93\) | 67453.9 | 0.808723 | ||||||||
\(94\) | 85732.5 | 1.00075 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 607566. | 6.72846 | ||||||||
\(97\) | −156159. | −1.68514 | −0.842572 | − | 0.538584i | \(-0.818959\pi\) | ||||
−0.842572 | + | 0.538584i | \(0.818959\pi\) | |||||||
\(98\) | 132090. | 1.38933 | ||||||||
\(99\) | −20167.6 | −0.206808 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −165081. | −1.61026 | −0.805128 | − | 0.593101i | \(-0.797903\pi\) | ||||
−0.805128 | + | 0.593101i | \(0.797903\pi\) | |||||||
\(102\) | 26149.9 | 0.248868 | ||||||||
\(103\) | −75861.6 | −0.704578 | −0.352289 | − | 0.935891i | \(-0.614597\pi\) | ||||
−0.352289 | + | 0.935891i | \(0.614597\pi\) | |||||||
\(104\) | 117626. | 1.06640 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 311503. | 2.69276 | ||||||||
\(107\) | 141728. | 1.19673 | 0.598366 | − | 0.801223i | \(-0.295817\pi\) | ||||
0.598366 | + | 0.801223i | \(0.295817\pi\) | |||||||
\(108\) | 212419. | 1.75241 | ||||||||
\(109\) | 11820.9 | 0.0952981 | 0.0476490 | − | 0.998864i | \(-0.484827\pi\) | ||||
0.0476490 | + | 0.998864i | \(0.484827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 134161. | 1.03352 | ||||||||
\(112\) | −341089. | −2.56934 | ||||||||
\(113\) | 43552.7 | 0.320862 | 0.160431 | − | 0.987047i | \(-0.448712\pi\) | ||||
0.160431 | + | 0.987047i | \(0.448712\pi\) | |||||||
\(114\) | −670298. | −4.83065 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 298189. | 2.05753 | ||||||||
\(117\) | −21166.5 | −0.142950 | ||||||||
\(118\) | −370906. | −2.45222 | ||||||||
\(119\) | −8618.08 | −0.0557883 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −135122. | −0.839002 | ||||||||
\(122\) | 372621. | 2.26656 | ||||||||
\(123\) | 375189. | 2.23608 | ||||||||
\(124\) | −330435. | −1.92989 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 99806.3 | 0.560056 | ||||||||
\(127\) | −229412. | −1.26214 | −0.631068 | − | 0.775727i | \(-0.717383\pi\) | ||||
−0.631068 | + | 0.775727i | \(0.717383\pi\) | |||||||
\(128\) | −1.25041e6 | −6.74570 | ||||||||
\(129\) | 257110. | 1.36033 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −161719. | −0.823347 | −0.411674 | − | 0.911331i | \(-0.635056\pi\) | ||||
−0.411674 | + | 0.911331i | \(0.635056\pi\) | |||||||
\(132\) | 290475. | 1.45102 | ||||||||
\(133\) | 220907. | 1.08288 | ||||||||
\(134\) | 276048. | 1.32807 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −84493.4 | −0.391720 | ||||||||
\(137\) | −233597. | −1.06332 | −0.531662 | − | 0.846956i | \(-0.678433\pi\) | ||||
−0.531662 | + | 0.846956i | \(0.678433\pi\) | |||||||
\(138\) | 667764. | 2.98487 | ||||||||
\(139\) | 97992.9 | 0.430187 | 0.215094 | − | 0.976593i | \(-0.430994\pi\) | ||||
0.215094 | + | 0.976593i | \(0.430994\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 146562. | 0.620831 | ||||||||
\(142\) | −186802. | −0.777430 | ||||||||
\(143\) | 27213.1 | 0.111286 | ||||||||
\(144\) | 601765. | 2.41836 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −58965.4 | −0.228937 | ||||||||
\(147\) | 225811. | 0.861890 | ||||||||
\(148\) | −657212. | −2.46633 | ||||||||
\(149\) | 267805. | 0.988219 | 0.494110 | − | 0.869400i | \(-0.335494\pi\) | ||||
0.494110 | + | 0.869400i | \(0.335494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −125041. | −0.446283 | −0.223141 | − | 0.974786i | \(-0.571631\pi\) | ||||
−0.223141 | + | 0.974786i | \(0.571631\pi\) | |||||||
\(152\) | 2.16582e6 | 7.60348 | ||||||||
\(153\) | 15204.4 | 0.0525099 | ||||||||
\(154\) | −128318. | −0.436000 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 304862. | 1.00298 | ||||||||
\(157\) | 323793. | 1.04838 | 0.524189 | − | 0.851602i | \(-0.324368\pi\) | ||||
0.524189 | + | 0.851602i | \(0.324368\pi\) | |||||||
\(158\) | 35039.8 | 0.111665 | ||||||||
\(159\) | 532523. | 1.67050 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −220072. | −0.669113 | ||||||||
\(162\) | 828386. | 2.47996 | ||||||||
\(163\) | 483015. | 1.42394 | 0.711970 | − | 0.702210i | \(-0.247803\pi\) | ||||
0.711970 | + | 0.702210i | \(0.247803\pi\) | |||||||
\(164\) | −1.83793e6 | −5.33605 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −282041. | −0.794406 | ||||||||
\(167\) | −272660. | −0.756538 | −0.378269 | − | 0.925696i | \(-0.623480\pi\) | ||||
−0.378269 | + | 0.925696i | \(0.623480\pi\) | |||||||
\(168\) | −948171. | −2.59187 | ||||||||
\(169\) | 28561.0 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −389734. | −1.01924 | ||||||||
\(172\) | −1.25950e6 | −3.24622 | ||||||||
\(173\) | −248584. | −0.631477 | −0.315738 | − | 0.948846i | \(-0.602252\pi\) | ||||
−0.315738 | + | 0.948846i | \(0.602252\pi\) | |||||||
\(174\) | 683290. | 1.71093 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −773671. | −1.88267 | ||||||||
\(177\) | −634073. | −1.52127 | ||||||||
\(178\) | −7125.05 | −0.0168554 | ||||||||
\(179\) | 29132.9 | 0.0679597 | 0.0339798 | − | 0.999423i | \(-0.489182\pi\) | ||||
0.0339798 | + | 0.999423i | \(0.489182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 583931. | 1.32485 | 0.662423 | − | 0.749130i | \(-0.269528\pi\) | ||||
0.662423 | + | 0.749130i | \(0.269528\pi\) | |||||||
\(182\) | −134674. | −0.301373 | ||||||||
\(183\) | 637006. | 1.40610 | ||||||||
\(184\) | −2.15763e6 | −4.69820 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −757181. | −1.60479 | ||||||||
\(187\) | −19547.9 | −0.0408786 | ||||||||
\(188\) | −717960. | −1.48151 | ||||||||
\(189\) | −160417. | −0.326659 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 708228. | 1.40472 | 0.702359 | − | 0.711822i | \(-0.252130\pi\) | ||||
0.702359 | + | 0.711822i | \(0.252130\pi\) | |||||||
\(192\) | −3.86962e6 | −7.57557 | ||||||||
\(193\) | 596277. | 1.15227 | 0.576136 | − | 0.817354i | \(-0.304560\pi\) | ||||
0.576136 | + | 0.817354i | \(0.304560\pi\) | |||||||
\(194\) | 1.75291e6 | 3.34391 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.10618e6 | −2.05676 | ||||||||
\(197\) | 23822.5 | 0.0437342 | 0.0218671 | − | 0.999761i | \(-0.493039\pi\) | ||||
0.0218671 | + | 0.999761i | \(0.493039\pi\) | |||||||
\(198\) | 226385. | 0.410378 | ||||||||
\(199\) | 470656. | 0.842503 | 0.421251 | − | 0.906944i | \(-0.361591\pi\) | ||||
0.421251 | + | 0.906944i | \(0.361591\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 471911. | 0.823892 | ||||||||
\(202\) | 1.85307e6 | 3.19531 | ||||||||
\(203\) | −225189. | −0.383536 | ||||||||
\(204\) | −218990. | −0.368425 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 851560. | 1.39813 | ||||||||
\(207\) | 388261. | 0.629793 | ||||||||
\(208\) | −811991. | −1.30135 | ||||||||
\(209\) | 501070. | 0.793475 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −619805. | −0.958405 | −0.479202 | − | 0.877704i | \(-0.659074\pi\) | ||||
−0.479202 | + | 0.877704i | \(0.659074\pi\) | |||||||
\(212\) | −2.60866e6 | −3.98637 | ||||||||
\(213\) | −319344. | −0.482291 | ||||||||
\(214\) | −1.59092e6 | −2.37473 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.57276e6 | −2.29365 | ||||||||
\(217\) | 249541. | 0.359743 | ||||||||
\(218\) | −132692. | −0.189105 | ||||||||
\(219\) | −100803. | −0.142024 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20516.1 | −0.0282562 | ||||||||
\(222\) | −1.50598e6 | −2.05086 | ||||||||
\(223\) | 310997. | 0.418787 | 0.209394 | − | 0.977831i | \(-0.432851\pi\) | ||||
0.209394 | + | 0.977831i | \(0.432851\pi\) | |||||||
\(224\) | 2.24765e6 | 2.99301 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −488886. | −0.636702 | ||||||||
\(227\) | 450336. | 0.580059 | 0.290030 | − | 0.957018i | \(-0.406335\pi\) | ||||
0.290030 | + | 0.957018i | \(0.406335\pi\) | |||||||
\(228\) | 5.61337e6 | 7.15132 | ||||||||
\(229\) | 855126. | 1.07756 | 0.538780 | − | 0.842447i | \(-0.318886\pi\) | ||||
0.538780 | + | 0.842447i | \(0.318886\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −219363. | −0.270479 | ||||||||
\(232\) | −2.20779e6 | −2.69301 | ||||||||
\(233\) | 1.09514e6 | 1.32153 | 0.660767 | − | 0.750591i | \(-0.270231\pi\) | ||||
0.660767 | + | 0.750591i | \(0.270231\pi\) | |||||||
\(234\) | 237597. | 0.283663 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.10612e6 | 3.63027 | ||||||||
\(237\) | 59901.4 | 0.0692734 | ||||||||
\(238\) | 96739.4 | 0.110703 | ||||||||
\(239\) | 917921. | 1.03947 | 0.519733 | − | 0.854329i | \(-0.326031\pi\) | ||||
0.519733 | + | 0.854329i | \(0.326031\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −642632. | −0.712721 | −0.356361 | − | 0.934349i | \(-0.615982\pi\) | ||||
−0.356361 | + | 0.934349i | \(0.615982\pi\) | |||||||
\(242\) | 1.51677e6 | 1.66487 | ||||||||
\(243\) | 867047. | 0.941948 | ||||||||
\(244\) | −3.12049e6 | −3.35543 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.21156e6 | −4.43717 | ||||||||
\(247\) | 525888. | 0.548468 | ||||||||
\(248\) | 2.44655e6 | 2.52595 | ||||||||
\(249\) | −482157. | −0.492822 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −96744.1 | −0.0969260 | −0.0484630 | − | 0.998825i | \(-0.515432\pi\) | ||||
−0.0484630 | + | 0.998825i | \(0.515432\pi\) | |||||||
\(252\) | −835821. | −0.829109 | ||||||||
\(253\) | −499176. | −0.490289 | ||||||||
\(254\) | 2.57518e6 | 2.50452 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.58322e6 | 7.23192 | ||||||||
\(257\) | −1.06681e6 | −1.00752 | −0.503759 | − | 0.863844i | \(-0.668050\pi\) | ||||
−0.503759 | + | 0.863844i | \(0.668050\pi\) | |||||||
\(258\) | −2.88611e6 | −2.69937 | ||||||||
\(259\) | 496319. | 0.459739 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 397288. | 0.360998 | ||||||||
\(262\) | 1.81532e6 | 1.63381 | ||||||||
\(263\) | −503116. | −0.448517 | −0.224258 | − | 0.974530i | \(-0.571996\pi\) | ||||
−0.224258 | + | 0.974530i | \(0.571996\pi\) | |||||||
\(264\) | −2.15068e6 | −1.89918 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.47972e6 | −2.14881 | ||||||||
\(267\) | −12180.5 | −0.0104565 | ||||||||
\(268\) | −2.31174e6 | −1.96609 | ||||||||
\(269\) | −104820. | −0.0883212 | −0.0441606 | − | 0.999024i | \(-0.514061\pi\) | ||||
−0.0441606 | + | 0.999024i | \(0.514061\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −168792. | −0.139614 | −0.0698069 | − | 0.997561i | \(-0.522238\pi\) | ||||
−0.0698069 | + | 0.997561i | \(0.522238\pi\) | |||||||
\(272\) | 583273. | 0.478024 | ||||||||
\(273\) | −230228. | −0.186961 | ||||||||
\(274\) | 2.62217e6 | 2.11001 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.59214e6 | −4.41881 | ||||||||
\(277\) | 863313. | 0.676034 | 0.338017 | − | 0.941140i | \(-0.390244\pi\) | ||||
0.338017 | + | 0.941140i | \(0.390244\pi\) | |||||||
\(278\) | −1.09999e6 | −0.853641 | ||||||||
\(279\) | −440251. | −0.338602 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.56951e6 | −1.18577 | −0.592883 | − | 0.805289i | \(-0.702010\pi\) | ||||
−0.592883 | + | 0.805289i | \(0.702010\pi\) | |||||||
\(282\) | −1.64518e6 | −1.23194 | ||||||||
\(283\) | −1.10553e6 | −0.820546 | −0.410273 | − | 0.911963i | \(-0.634567\pi\) | ||||
−0.410273 | + | 0.911963i | \(0.634567\pi\) | |||||||
\(284\) | 1.56436e6 | 1.15091 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −305472. | −0.220829 | ||||||||
\(287\) | 1.38799e6 | 0.994672 | ||||||||
\(288\) | −3.96540e6 | −2.81712 | ||||||||
\(289\) | −1.40512e6 | −0.989621 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.99664e6 | 2.07445 | ||||||||
\(292\) | 493802. | 0.338919 | ||||||||
\(293\) | 116407. | 0.0792155 | 0.0396077 | − | 0.999215i | \(-0.487389\pi\) | ||||
0.0396077 | + | 0.999215i | \(0.487389\pi\) | |||||||
\(294\) | −2.53477e6 | −1.71029 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.86601e6 | 3.22807 | ||||||||
\(297\) | −363863. | −0.239358 | ||||||||
\(298\) | −3.00616e6 | −1.96097 | ||||||||
\(299\) | −523900. | −0.338899 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 951161. | 0.605115 | ||||||||
\(302\) | 1.40361e6 | 0.885580 | ||||||||
\(303\) | 3.16787e6 | 1.98226 | ||||||||
\(304\) | −1.49510e7 | −9.27870 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −170672. | −0.104198 | ||||||||
\(307\) | 830234. | 0.502753 | 0.251376 | − | 0.967889i | \(-0.419117\pi\) | ||||
0.251376 | + | 0.967889i | \(0.419117\pi\) | |||||||
\(308\) | 1.07459e6 | 0.645455 | ||||||||
\(309\) | 1.45576e6 | 0.867351 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 204863. | 0.120105 | 0.0600526 | − | 0.998195i | \(-0.480873\pi\) | ||||
0.0600526 | + | 0.998195i | \(0.480873\pi\) | |||||||
\(312\) | −2.25720e6 | −1.31276 | ||||||||
\(313\) | 1.96760e6 | 1.13521 | 0.567604 | − | 0.823302i | \(-0.307871\pi\) | ||||
0.567604 | + | 0.823302i | \(0.307871\pi\) | |||||||
\(314\) | −3.63463e6 | −2.08035 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −293438. | −0.165310 | ||||||||
\(317\) | 2.47859e6 | 1.38534 | 0.692670 | − | 0.721255i | \(-0.256434\pi\) | ||||
0.692670 | + | 0.721255i | \(0.256434\pi\) | |||||||
\(318\) | −5.97766e6 | −3.31485 | ||||||||
\(319\) | −510782. | −0.281034 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.71973e6 | −1.47320 | ||||||||
\(322\) | 2.47034e6 | 1.32775 | ||||||||
\(323\) | −377759. | −0.201469 | ||||||||
\(324\) | −6.93726e6 | −3.67135 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.42193e6 | −2.82559 | ||||||||
\(327\) | −226840. | −0.117314 | ||||||||
\(328\) | 1.36081e7 | 6.98413 | ||||||||
\(329\) | 542195. | 0.276163 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.17720e6 | −1.59395 | −0.796974 | − | 0.604013i | \(-0.793567\pi\) | ||||
−0.796974 | + | 0.604013i | \(0.793567\pi\) | |||||||
\(332\) | 2.36193e6 | 1.17604 | ||||||||
\(333\) | −875629. | −0.432722 | ||||||||
\(334\) | 3.06066e6 | 1.50123 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.54540e6 | 3.16292 | ||||||||
\(337\) | −1.04972e6 | −0.503500 | −0.251750 | − | 0.967792i | \(-0.581006\pi\) | ||||
−0.251750 | + | 0.967792i | \(0.581006\pi\) | |||||||
\(338\) | −320602. | −0.152642 | ||||||||
\(339\) | −835764. | −0.394988 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 566018. | 0.263599 | ||||||||
\(342\) | 4.37483e6 | 2.02254 | ||||||||
\(343\) | 2.02852e6 | 0.930986 | ||||||||
\(344\) | 9.32537e6 | 4.24883 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.79039e6 | 1.25307 | ||||||||
\(347\) | −502238. | −0.223916 | −0.111958 | − | 0.993713i | \(-0.535712\pi\) | ||||
−0.111958 | + | 0.993713i | \(0.535712\pi\) | |||||||
\(348\) | −5.72217e6 | −2.53287 | ||||||||
\(349\) | −1.28824e6 | −0.566152 | −0.283076 | − | 0.959098i | \(-0.591355\pi\) | ||||
−0.283076 | + | 0.959098i | \(0.591355\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −381885. | −0.165449 | ||||||||
\(352\) | 5.09820e6 | 2.19311 | ||||||||
\(353\) | −3.80443e6 | −1.62500 | −0.812499 | − | 0.582962i | \(-0.801893\pi\) | ||||
−0.812499 | + | 0.582962i | \(0.801893\pi\) | |||||||
\(354\) | 7.11758e6 | 3.01873 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 59668.2 | 0.0249527 | ||||||||
\(357\) | 165379. | 0.0686766 | ||||||||
\(358\) | −327022. | −0.134856 | ||||||||
\(359\) | 3.18303e6 | 1.30348 | 0.651740 | − | 0.758442i | \(-0.274039\pi\) | ||||
0.651740 | + | 0.758442i | \(0.274039\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.20697e6 | 2.91062 | ||||||||
\(362\) | −6.55472e6 | −2.62895 | ||||||||
\(363\) | 2.59296e6 | 1.03283 | ||||||||
\(364\) | 1.12781e6 | 0.446153 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.15050e6 | −2.79019 | ||||||||
\(367\) | −1.51403e6 | −0.586770 | −0.293385 | − | 0.955994i | \(-0.594782\pi\) | ||||
−0.293385 | + | 0.955994i | \(0.594782\pi\) | |||||||
\(368\) | 1.48945e7 | 5.73332 | ||||||||
\(369\) | −2.44875e6 | −0.936221 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.97003e6 | 0.743084 | ||||||||
\(372\) | 6.34096e6 | 2.37573 | ||||||||
\(373\) | −1.59920e6 | −0.595156 | −0.297578 | − | 0.954698i | \(-0.596179\pi\) | ||||
−0.297578 | + | 0.954698i | \(0.596179\pi\) | |||||||
\(374\) | 219428. | 0.0811173 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.31579e6 | 1.93909 | ||||||||
\(377\) | −536081. | −0.194257 | ||||||||
\(378\) | 1.80070e6 | 0.648205 | ||||||||
\(379\) | 2.52547e6 | 0.903116 | 0.451558 | − | 0.892242i | \(-0.350868\pi\) | ||||
0.451558 | + | 0.892242i | \(0.350868\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.40235e6 | 1.55372 | ||||||||
\(382\) | −7.94997e6 | −2.78745 | ||||||||
\(383\) | 3.16883e6 | 1.10383 | 0.551915 | − | 0.833900i | \(-0.313897\pi\) | ||||
0.551915 | + | 0.833900i | \(0.313897\pi\) | |||||||
\(384\) | 2.39950e7 | 8.30410 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.69331e6 | −2.28651 | ||||||||
\(387\) | −1.67808e6 | −0.569555 | ||||||||
\(388\) | −1.46796e7 | −4.95034 | ||||||||
\(389\) | 1.03129e6 | 0.345545 | 0.172773 | − | 0.984962i | \(-0.444727\pi\) | ||||
0.172773 | + | 0.984962i | \(0.444727\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 376330. | 0.124488 | ||||||||
\(392\) | 8.19014e6 | 2.69201 | ||||||||
\(393\) | 3.10334e6 | 1.01356 | ||||||||
\(394\) | −267411. | −0.0867838 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.89584e6 | −0.607525 | ||||||||
\(397\) | −634862. | −0.202164 | −0.101082 | − | 0.994878i | \(-0.532230\pi\) | ||||
−0.101082 | + | 0.994878i | \(0.532230\pi\) | |||||||
\(398\) | −5.28320e6 | −1.67182 | ||||||||
\(399\) | −4.23915e6 | −1.33305 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.19913e6 | 0.682952 | 0.341476 | − | 0.939890i | \(-0.389073\pi\) | ||||
0.341476 | + | 0.939890i | \(0.389073\pi\) | |||||||
\(402\) | −5.29728e6 | −1.63489 | ||||||||
\(403\) | 594053. | 0.182206 | ||||||||
\(404\) | −1.55184e7 | −4.73035 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.52778e6 | 0.761070 | ||||||||
\(407\) | 1.12577e6 | 0.336871 | ||||||||
\(408\) | 1.62140e6 | 0.482215 | ||||||||
\(409\) | −4.25223e6 | −1.25692 | −0.628461 | − | 0.777841i | \(-0.716315\pi\) | ||||
−0.628461 | + | 0.777841i | \(0.716315\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.48266e6 | 1.30898 | ||||||||
\(412\) | −7.13132e6 | −2.06979 | ||||||||
\(413\) | −2.34571e6 | −0.676704 | ||||||||
\(414\) | −4.35829e6 | −1.24973 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.35071e6 | 1.51593 | ||||||||
\(417\) | −1.88046e6 | −0.529570 | ||||||||
\(418\) | −5.62460e6 | −1.57453 | ||||||||
\(419\) | 3.54751e6 | 0.987161 | 0.493581 | − | 0.869700i | \(-0.335688\pi\) | ||||
0.493581 | + | 0.869700i | \(0.335688\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.40038e6 | 0.385071 | 0.192535 | − | 0.981290i | \(-0.438329\pi\) | ||||
0.192535 | + | 0.981290i | \(0.438329\pi\) | |||||||
\(422\) | 6.95742e6 | 1.90181 | ||||||||
\(423\) | −956565. | −0.259934 | ||||||||
\(424\) | 1.93146e7 | 5.21759 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.58469e6 | 0.957033 | ||||||||
\(427\) | 2.35656e6 | 0.625472 | ||||||||
\(428\) | 1.33231e7 | 3.51556 | ||||||||
\(429\) | −522213. | −0.136995 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.41665e6 | 1.40455 | 0.702276 | − | 0.711905i | \(-0.252167\pi\) | ||||
0.702276 | + | 0.711905i | \(0.252167\pi\) | |||||||
\(432\) | 1.08570e7 | 2.79899 | ||||||||
\(433\) | −5.58069e6 | −1.43043 | −0.715217 | − | 0.698902i | \(-0.753672\pi\) | ||||
−0.715217 | + | 0.698902i | \(0.753672\pi\) | |||||||
\(434\) | −2.80113e6 | −0.713854 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.11122e6 | 0.279951 | ||||||||
\(437\) | −9.64646e6 | −2.41638 | ||||||||
\(438\) | 1.13153e6 | 0.281826 | ||||||||
\(439\) | −1.76748e6 | −0.437716 | −0.218858 | − | 0.975757i | \(-0.570233\pi\) | ||||
−0.218858 | + | 0.975757i | \(0.570233\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.47380e6 | −0.360863 | ||||||||
\(442\) | 230296. | 0.0560701 | ||||||||
\(443\) | 2.11511e6 | 0.512062 | 0.256031 | − | 0.966669i | \(-0.417585\pi\) | ||||
0.256031 | + | 0.966669i | \(0.417585\pi\) | |||||||
\(444\) | 1.26117e7 | 3.03611 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.49099e6 | −0.831019 | ||||||||
\(447\) | −5.13911e6 | −1.21652 | ||||||||
\(448\) | −1.43154e7 | −3.36982 | ||||||||
\(449\) | 2.74804e6 | 0.643290 | 0.321645 | − | 0.946860i | \(-0.395764\pi\) | ||||
0.321645 | + | 0.946860i | \(0.395764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.14828e6 | 0.728841 | ||||||||
\(452\) | 4.09414e6 | 0.942577 | ||||||||
\(453\) | 2.39950e6 | 0.549384 | ||||||||
\(454\) | −5.05510e6 | −1.15104 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.15614e7 | −9.36005 | ||||||||
\(457\) | −3.46825e6 | −0.776820 | −0.388410 | − | 0.921487i | \(-0.626976\pi\) | ||||
−0.388410 | + | 0.921487i | \(0.626976\pi\) | |||||||
\(458\) | −9.59893e6 | −2.13825 | ||||||||
\(459\) | 274318. | 0.0607746 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.16521e6 | 1.13197 | 0.565986 | − | 0.824415i | \(-0.308496\pi\) | ||||
0.565986 | + | 0.824415i | \(0.308496\pi\) | |||||||
\(462\) | 2.46239e6 | 0.536725 | ||||||||
\(463\) | −6.87934e6 | −1.49140 | −0.745700 | − | 0.666282i | \(-0.767885\pi\) | ||||
−0.745700 | + | 0.666282i | \(0.767885\pi\) | |||||||
\(464\) | 1.52408e7 | 3.28634 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.22931e7 | −2.62238 | ||||||||
\(467\) | −569700. | −0.120880 | −0.0604400 | − | 0.998172i | \(-0.519250\pi\) | ||||
−0.0604400 | + | 0.998172i | \(0.519250\pi\) | |||||||
\(468\) | −1.98974e6 | −0.419935 | ||||||||
\(469\) | 1.74580e6 | 0.366490 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.21350e6 | −1.29058 | ||||||||
\(472\) | −2.29978e7 | −4.75150 | ||||||||
\(473\) | 2.15746e6 | 0.443394 | ||||||||
\(474\) | −672404. | −0.137463 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −810137. | −0.163886 | ||||||||
\(477\) | −3.47562e6 | −0.699417 | ||||||||
\(478\) | −1.03038e7 | −2.06266 | ||||||||
\(479\) | −3.33256e6 | −0.663649 | −0.331825 | − | 0.943341i | \(-0.607664\pi\) | ||||
−0.331825 | + | 0.943341i | \(0.607664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.18153e6 | 0.232853 | ||||||||
\(482\) | 7.21365e6 | 1.41429 | ||||||||
\(483\) | 4.22312e6 | 0.823693 | ||||||||
\(484\) | −1.27021e7 | −2.46468 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.73275e6 | −1.86915 | ||||||||
\(487\) | −5.24387e6 | −1.00191 | −0.500956 | − | 0.865473i | \(-0.667018\pi\) | ||||
−0.500956 | + | 0.865473i | \(0.667018\pi\) | |||||||
\(488\) | 2.31041e7 | 4.39177 | ||||||||
\(489\) | −9.26893e6 | −1.75290 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.52706e6 | −0.847447 | −0.423724 | − | 0.905792i | \(-0.639277\pi\) | ||||
−0.423724 | + | 0.905792i | \(0.639277\pi\) | |||||||
\(492\) | 3.52694e7 | 6.56880 | ||||||||
\(493\) | 385080. | 0.0713566 | ||||||||
\(494\) | −5.90318e6 | −1.08835 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.68890e7 | −3.08247 | ||||||||
\(497\) | −1.18139e6 | −0.214537 | ||||||||
\(498\) | 5.41229e6 | 0.977930 | ||||||||
\(499\) | 8.06232e6 | 1.44947 | 0.724734 | − | 0.689029i | \(-0.241963\pi\) | ||||
0.724734 | + | 0.689029i | \(0.241963\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.23227e6 | 0.931314 | ||||||||
\(502\) | 1.08597e6 | 0.192335 | ||||||||
\(503\) | 3.91235e6 | 0.689474 | 0.344737 | − | 0.938699i | \(-0.387968\pi\) | ||||
0.344737 | + | 0.938699i | \(0.387968\pi\) | |||||||
\(504\) | 6.18842e6 | 1.08518 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.60333e6 | 0.972904 | ||||||||
\(507\) | −548078. | −0.0946940 | ||||||||
\(508\) | −2.15657e7 | −3.70770 | ||||||||
\(509\) | −1.01584e7 | −1.73792 | −0.868959 | − | 0.494884i | \(-0.835210\pi\) | ||||
−0.868959 | + | 0.494884i | \(0.835210\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −372913. | −0.0631765 | ||||||||
\(512\) | −4.51098e7 | −7.60495 | ||||||||
\(513\) | −7.03158e6 | −1.17967 | ||||||||
\(514\) | 1.19751e7 | 1.99927 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.41695e7 | 3.99616 | ||||||||
\(517\) | 1.22983e6 | 0.202357 | ||||||||
\(518\) | −5.57126e6 | −0.912282 | ||||||||
\(519\) | 4.77025e6 | 0.777361 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.44957e6 | 0.233962 | 0.116981 | − | 0.993134i | \(-0.462678\pi\) | ||||
0.116981 | + | 0.993134i | \(0.462678\pi\) | |||||||
\(522\) | −4.45963e6 | −0.716345 | ||||||||
\(523\) | 203871. | 0.0325912 | 0.0162956 | − | 0.999867i | \(-0.494813\pi\) | ||||
0.0162956 | + | 0.999867i | \(0.494813\pi\) | |||||||
\(524\) | −1.52023e7 | −2.41869 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.64756e6 | 0.890013 | ||||||||
\(527\) | −426723. | −0.0669298 | ||||||||
\(528\) | 1.48465e7 | 2.31761 | ||||||||
\(529\) | 3.17365e6 | 0.493082 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.13841e6 | 0.636937 | ||||||||
\(532\) | 2.07662e7 | 3.18111 | ||||||||
\(533\) | 3.30422e6 | 0.503791 | ||||||||
\(534\) | 136728. | 0.0207493 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.71162e7 | 2.57332 | ||||||||
\(537\) | −559052. | −0.0836598 | ||||||||
\(538\) | 1.17663e6 | 0.175260 | ||||||||
\(539\) | 1.89482e6 | 0.280929 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.28883e6 | 1.07069 | 0.535346 | − | 0.844633i | \(-0.320181\pi\) | ||||
0.535346 | + | 0.844633i | \(0.320181\pi\) | |||||||
\(542\) | 1.89472e6 | 0.277042 | ||||||||
\(543\) | −1.12055e7 | −1.63091 | ||||||||
\(544\) | −3.84355e6 | −0.556846 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.58435e6 | 0.370996 | ||||||||
\(547\) | 5.64096e6 | 0.806092 | 0.403046 | − | 0.915180i | \(-0.367951\pi\) | ||||
0.403046 | + | 0.915180i | \(0.367951\pi\) | |||||||
\(548\) | −2.19591e7 | −3.12366 | ||||||||
\(549\) | −4.15754e6 | −0.588716 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.87075e6 | −1.38507 | ||||||||
\(552\) | 4.14043e7 | 5.78359 | ||||||||
\(553\) | 221601. | 0.0308148 | ||||||||
\(554\) | −9.69083e6 | −1.34149 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.21176e6 | 1.26373 | ||||||||
\(557\) | −910831. | −0.124394 | −0.0621971 | − | 0.998064i | \(-0.519811\pi\) | ||||
−0.0621971 | + | 0.998064i | \(0.519811\pi\) | |||||||
\(558\) | 4.94189e6 | 0.671905 | ||||||||
\(559\) | 2.26432e6 | 0.306484 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 375119. | 0.0503224 | ||||||||
\(562\) | 1.76180e7 | 2.35297 | ||||||||
\(563\) | −7.96586e6 | −1.05916 | −0.529580 | − | 0.848260i | \(-0.677651\pi\) | ||||
−0.529580 | + | 0.848260i | \(0.677651\pi\) | |||||||
\(564\) | 1.37775e7 | 1.82378 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.24097e7 | 1.62825 | ||||||||
\(567\) | 5.23893e6 | 0.684361 | ||||||||
\(568\) | −1.15826e7 | −1.50638 | ||||||||
\(569\) | −3.26286e6 | −0.422492 | −0.211246 | − | 0.977433i | \(-0.567752\pi\) | ||||
−0.211246 | + | 0.977433i | \(0.567752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.89949e6 | −1.01393 | −0.506966 | − | 0.861966i | \(-0.669233\pi\) | ||||
−0.506966 | + | 0.861966i | \(0.669233\pi\) | |||||||
\(572\) | 2.55815e6 | 0.326916 | ||||||||
\(573\) | −1.35907e7 | −1.72924 | ||||||||
\(574\) | −1.55804e7 | −1.97378 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.52558e7 | 3.17180 | ||||||||
\(577\) | 1.91866e6 | 0.239916 | 0.119958 | − | 0.992779i | \(-0.461724\pi\) | ||||
0.119958 | + | 0.992779i | \(0.461724\pi\) | |||||||
\(578\) | 1.57727e7 | 1.96375 | ||||||||
\(579\) | −1.14424e7 | −1.41847 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.78370e6 | −0.219221 | ||||||||
\(582\) | −3.36378e7 | −4.11642 | ||||||||
\(583\) | 4.46850e6 | 0.544491 | ||||||||
\(584\) | −3.65611e6 | −0.443596 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.30669e6 | −0.157191 | ||||||||
\(587\) | −1.98302e6 | −0.237537 | −0.118769 | − | 0.992922i | \(-0.537895\pi\) | ||||
−0.118769 | + | 0.992922i | \(0.537895\pi\) | |||||||
\(588\) | 2.12272e7 | 2.53192 | ||||||||
\(589\) | 1.09382e7 | 1.29914 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −457146. | −0.0538377 | ||||||||
\(592\) | −3.35909e7 | −3.93929 | ||||||||
\(593\) | −9.43563e6 | −1.10188 | −0.550940 | − | 0.834545i | \(-0.685731\pi\) | ||||
−0.550940 | + | 0.834545i | \(0.685731\pi\) | |||||||
\(594\) | 4.08443e6 | 0.474969 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.51749e7 | 2.90303 | ||||||||
\(597\) | −9.03177e6 | −1.03714 | ||||||||
\(598\) | 5.88086e6 | 0.672493 | ||||||||
\(599\) | 6.57359e6 | 0.748576 | 0.374288 | − | 0.927313i | \(-0.377887\pi\) | ||||
0.374288 | + | 0.927313i | \(0.377887\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.04817e6 | 1.02182 | 0.510910 | − | 0.859634i | \(-0.329308\pi\) | ||||
0.510910 | + | 0.859634i | \(0.329308\pi\) | |||||||
\(602\) | −1.06769e7 | −1.20076 | ||||||||
\(603\) | −3.08002e6 | −0.344953 | ||||||||
\(604\) | −1.17544e7 | −1.31102 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.55598e7 | −3.93349 | ||||||||
\(607\) | −2.54414e6 | −0.280266 | −0.140133 | − | 0.990133i | \(-0.544753\pi\) | ||||
−0.140133 | + | 0.990133i | \(0.544753\pi\) | |||||||
\(608\) | 9.85216e7 | 10.8087 | ||||||||
\(609\) | 4.32131e6 | 0.472141 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.29074e6 | 0.139874 | ||||||||
\(612\) | 1.42928e6 | 0.154255 | ||||||||
\(613\) | −7.53921e6 | −0.810354 | −0.405177 | − | 0.914238i | \(-0.632790\pi\) | ||||
−0.405177 | + | 0.914238i | \(0.632790\pi\) | |||||||
\(614\) | −9.31951e6 | −0.997636 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.95628e6 | −0.844808 | ||||||||
\(617\) | −1.44546e6 | −0.152860 | −0.0764300 | − | 0.997075i | \(-0.524352\pi\) | ||||
−0.0764300 | + | 0.997075i | \(0.524352\pi\) | |||||||
\(618\) | −1.63412e7 | −1.72113 | ||||||||
\(619\) | 832032. | 0.0872797 | 0.0436399 | − | 0.999047i | \(-0.486105\pi\) | ||||
0.0436399 | + | 0.999047i | \(0.486105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.00499e6 | 0.728918 | ||||||||
\(622\) | −2.29962e6 | −0.238330 | ||||||||
\(623\) | −45060.7 | −0.00465134 | ||||||||
\(624\) | 1.55819e7 | 1.60198 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.20866e7 | −2.25265 | ||||||||
\(627\) | −9.61540e6 | −0.976784 | ||||||||
\(628\) | 3.04379e7 | 3.07975 | ||||||||
\(629\) | −848722. | −0.0855340 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.42941e6 | 0.142916 | 0.0714582 | − | 0.997444i | \(-0.477235\pi\) | ||||
0.0714582 | + | 0.997444i | \(0.477235\pi\) | |||||||
\(632\) | 2.17262e6 | 0.216367 | ||||||||
\(633\) | 1.18939e7 | 1.17982 | ||||||||
\(634\) | −2.78226e7 | −2.74900 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.00595e7 | 4.90731 | ||||||||
\(637\) | 1.98867e6 | 0.194184 | ||||||||
\(638\) | 5.73362e6 | 0.557669 | ||||||||
\(639\) | 2.08426e6 | 0.201929 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.54071e7 | −1.48107 | −0.740537 | − | 0.672015i | \(-0.765429\pi\) | ||||
−0.740537 | + | 0.672015i | \(0.765429\pi\) | |||||||
\(642\) | 3.05294e7 | 2.92335 | ||||||||
\(643\) | 3.71125e6 | 0.353992 | 0.176996 | − | 0.984212i | \(-0.443362\pi\) | ||||
0.176996 | + | 0.984212i | \(0.443362\pi\) | |||||||
\(644\) | −2.06877e7 | −1.96561 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.24040e6 | 0.399784 | ||||||||
\(647\) | 8.31438e6 | 0.780853 | 0.390426 | − | 0.920634i | \(-0.372328\pi\) | ||||
0.390426 | + | 0.920634i | \(0.372328\pi\) | |||||||
\(648\) | 5.13635e7 | 4.80527 | ||||||||
\(649\) | −5.32063e6 | −0.495851 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.78862e6 | −0.442851 | ||||||||
\(652\) | 4.54055e7 | 4.18302 | ||||||||
\(653\) | −2.58516e6 | −0.237249 | −0.118624 | − | 0.992939i | \(-0.537848\pi\) | ||||
−0.118624 | + | 0.992939i | \(0.537848\pi\) | |||||||
\(654\) | 2.54631e6 | 0.232792 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.39391e7 | −8.52289 | ||||||||
\(657\) | 657911. | 0.0594639 | ||||||||
\(658\) | −6.08623e6 | −0.548004 | ||||||||
\(659\) | 1.77052e7 | 1.58813 | 0.794065 | − | 0.607833i | \(-0.207961\pi\) | ||||
0.794065 | + | 0.607833i | \(0.207961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.01104e6 | 0.179027 | 0.0895134 | − | 0.995986i | \(-0.471469\pi\) | ||||
0.0895134 | + | 0.995986i | \(0.471469\pi\) | |||||||
\(662\) | 3.56646e7 | 3.16295 | ||||||||
\(663\) | 393698. | 0.0347840 | ||||||||
\(664\) | −1.74878e7 | −1.53927 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.82908e6 | 0.858672 | ||||||||
\(667\) | 9.83343e6 | 0.855836 | ||||||||
\(668\) | −2.56312e7 | −2.22243 | ||||||||
\(669\) | −5.96794e6 | −0.515536 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.34523e6 | 0.458311 | ||||||||
\(672\) | −4.31317e7 | −3.68446 | ||||||||
\(673\) | 5.48300e6 | 0.466639 | 0.233319 | − | 0.972400i | \(-0.425041\pi\) | ||||
0.233319 | + | 0.972400i | \(0.425041\pi\) | |||||||
\(674\) | 1.17833e7 | 0.999119 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.68486e6 | 0.225972 | ||||||||
\(677\) | 1.58127e7 | 1.32597 | 0.662987 | − | 0.748631i | \(-0.269288\pi\) | ||||
0.662987 | + | 0.748631i | \(0.269288\pi\) | |||||||
\(678\) | 9.38159e6 | 0.783794 | ||||||||
\(679\) | 1.10859e7 | 0.922772 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.64183e6 | −0.714065 | ||||||||
\(682\) | −6.35365e6 | −0.523073 | ||||||||
\(683\) | −2.24599e7 | −1.84229 | −0.921143 | − | 0.389225i | \(-0.872743\pi\) | ||||
−0.921143 | + | 0.389225i | \(0.872743\pi\) | |||||||
\(684\) | −3.66367e7 | −2.99417 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.27704e7 | −1.84740 | ||||||||
\(687\) | −1.64096e7 | −1.32650 | ||||||||
\(688\) | −6.43747e7 | −5.18495 | ||||||||
\(689\) | 4.68982e6 | 0.376364 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.90456e6 | −0.709443 | −0.354721 | − | 0.934972i | \(-0.615424\pi\) | ||||
−0.354721 | + | 0.934972i | \(0.615424\pi\) | |||||||
\(692\) | −2.33679e7 | −1.85505 | ||||||||
\(693\) | 1.43172e6 | 0.113246 | ||||||||
\(694\) | 5.63770e6 | 0.444328 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.23670e7 | 3.31516 | ||||||||
\(697\) | −2.37350e6 | −0.185058 | ||||||||
\(698\) | 1.44607e7 | 1.12344 | ||||||||
\(699\) | −2.10154e7 | −1.62684 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.83550e7 | −1.41078 | −0.705392 | − | 0.708818i | \(-0.749229\pi\) | ||||
−0.705392 | + | 0.708818i | \(0.749229\pi\) | |||||||
\(702\) | 4.28673e6 | 0.328309 | ||||||||
\(703\) | 2.17553e7 | 1.66026 | ||||||||
\(704\) | −3.24707e7 | −2.46922 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.27054e7 | 3.22456 | ||||||||
\(707\) | 1.17193e7 | 0.881765 | ||||||||
\(708\) | −5.96057e7 | −4.46894 | ||||||||
\(709\) | −2.57581e7 | −1.92441 | −0.962207 | − | 0.272318i | \(-0.912210\pi\) | ||||
−0.962207 | + | 0.272318i | \(0.912210\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −390959. | −0.0290039 | ||||||||
\(712\) | −441784. | −0.0326596 | ||||||||
\(713\) | −1.08968e7 | −0.802742 | ||||||||
\(714\) | −1.85640e6 | −0.136278 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.73862e6 | 0.199641 | ||||||||
\(717\) | −1.76146e7 | −1.27961 | ||||||||
\(718\) | −3.57300e7 | −2.58656 | ||||||||
\(719\) | 1.69710e6 | 0.122429 | 0.0612146 | − | 0.998125i | \(-0.480503\pi\) | ||||
0.0612146 | + | 0.998125i | \(0.480503\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.38549e6 | 0.385822 | ||||||||
\(722\) | −8.08995e7 | −5.77568 | ||||||||
\(723\) | 1.23319e7 | 0.877375 | ||||||||
\(724\) | 5.48921e7 | 3.89191 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.91064e7 | −2.04949 | ||||||||
\(727\) | 1.84315e7 | 1.29338 | 0.646689 | − | 0.762754i | \(-0.276153\pi\) | ||||
0.646689 | + | 0.762754i | \(0.276153\pi\) | |||||||
\(728\) | −8.35035e6 | −0.583951 | ||||||||
\(729\) | 1.29433e6 | 0.0902041 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.62652e6 | −0.112581 | ||||||||
\(732\) | 5.98813e7 | 4.13060 | ||||||||
\(733\) | 1.79395e7 | 1.23325 | 0.616624 | − | 0.787258i | \(-0.288500\pi\) | ||||
0.616624 | + | 0.787258i | \(0.288500\pi\) | |||||||
\(734\) | 1.69952e7 | 1.16436 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.81491e7 | −6.67870 | ||||||||
\(737\) | 3.95989e6 | 0.268544 | ||||||||
\(738\) | 2.74876e7 | 1.85779 | ||||||||
\(739\) | 1.84597e7 | 1.24341 | 0.621703 | − | 0.783253i | \(-0.286441\pi\) | ||||
0.621703 | + | 0.783253i | \(0.286441\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.00916e7 | −0.675175 | ||||||||
\(742\) | −2.21139e7 | −1.47454 | ||||||||
\(743\) | 3.97606e6 | 0.264229 | 0.132115 | − | 0.991234i | \(-0.457823\pi\) | ||||
0.132115 | + | 0.991234i | \(0.457823\pi\) | |||||||
\(744\) | −4.69485e7 | −3.10949 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.79513e7 | 1.18100 | ||||||||
\(747\) | 3.14689e6 | 0.206339 | ||||||||
\(748\) | −1.83759e6 | −0.120086 | ||||||||
\(749\) | −1.00614e7 | −0.655322 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.25945e7 | 1.46185 | 0.730925 | − | 0.682458i | \(-0.239089\pi\) | ||||
0.730925 | + | 0.682458i | \(0.239089\pi\) | |||||||
\(752\) | −3.66958e7 | −2.36631 | ||||||||
\(753\) | 1.85649e6 | 0.119318 | ||||||||
\(754\) | 6.01760e6 | 0.385474 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.50799e7 | −0.959605 | ||||||||
\(757\) | 1.40367e7 | 0.890279 | 0.445139 | − | 0.895461i | \(-0.353154\pi\) | ||||
0.445139 | + | 0.895461i | \(0.353154\pi\) | |||||||
\(758\) | −2.83488e7 | −1.79210 | ||||||||
\(759\) | 9.57905e6 | 0.603556 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.05735e6 | −0.379159 | −0.189579 | − | 0.981865i | \(-0.560712\pi\) | ||||
−0.189579 | + | 0.981865i | \(0.560712\pi\) | |||||||
\(762\) | −4.94171e7 | −3.08311 | ||||||||
\(763\) | −839177. | −0.0521846 | ||||||||
\(764\) | 6.65765e7 | 4.12655 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.55707e7 | −2.19038 | ||||||||
\(767\) | −5.58416e6 | −0.342743 | ||||||||
\(768\) | −1.45520e8 | −8.90265 | ||||||||
\(769\) | 1.07705e7 | 0.656778 | 0.328389 | − | 0.944543i | \(-0.393494\pi\) | ||||
0.328389 | + | 0.944543i | \(0.393494\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.04717e7 | 1.24028 | ||||||||
\(772\) | 5.60527e7 | 3.38496 | ||||||||
\(773\) | 8.92164e6 | 0.537027 | 0.268514 | − | 0.963276i | \(-0.413468\pi\) | ||||
0.268514 | + | 0.963276i | \(0.413468\pi\) | |||||||
\(774\) | 1.88367e7 | 1.13020 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.08688e8 | 6.47928 | ||||||||
\(777\) | −9.52422e6 | −0.565949 | ||||||||
\(778\) | −1.15764e7 | −0.685682 | ||||||||
\(779\) | 6.08399e7 | 3.59207 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.67967e6 | −0.157201 | ||||||||
\(782\) | −4.22437e6 | −0.247027 | ||||||||
\(783\) | 7.16787e6 | 0.417816 | ||||||||
\(784\) | −5.65380e7 | −3.28511 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.48356e7 | −2.01125 | ||||||||
\(787\) | 542225. | 0.0312063 | 0.0156032 | − | 0.999878i | \(-0.495033\pi\) | ||||
0.0156032 | + | 0.999878i | \(0.495033\pi\) | |||||||
\(788\) | 2.23941e6 | 0.128475 | ||||||||
\(789\) | 9.65466e6 | 0.552134 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.09185e6 | −0.175702 | ||||||||
\(792\) | 1.40368e7 | 0.795163 | ||||||||
\(793\) | 5.60998e6 | 0.316795 | ||||||||
\(794\) | 7.12643e6 | 0.401163 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.42437e7 | 2.47497 | ||||||||
\(797\) | −1.82250e7 | −1.01630 | −0.508149 | − | 0.861269i | \(-0.669670\pi\) | ||||
−0.508149 | + | 0.861269i | \(0.669670\pi\) | |||||||
\(798\) | 4.75851e7 | 2.64523 | ||||||||
\(799\) | −927172. | −0.0513799 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 79498.2 | 0.00437800 | ||||||||
\(802\) | −2.46856e7 | −1.35522 | ||||||||
\(803\) | −845857. | −0.0462922 | ||||||||
\(804\) | 4.43617e7 | 2.42029 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.66834e6 | −0.361560 | ||||||||
\(807\) | 2.01147e6 | 0.108725 | ||||||||
\(808\) | 1.14898e8 | 6.19134 | ||||||||
\(809\) | −3.56238e7 | −1.91368 | −0.956840 | − | 0.290615i | \(-0.906140\pi\) | ||||
−0.956840 | + | 0.290615i | \(0.906140\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.68050e6 | 0.516828 | 0.258414 | − | 0.966034i | \(-0.416800\pi\) | ||||
0.258414 | + | 0.966034i | \(0.416800\pi\) | |||||||
\(812\) | −2.11687e7 | −1.12669 | ||||||||
\(813\) | 3.23907e6 | 0.171868 | ||||||||
\(814\) | −1.26370e7 | −0.668470 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.11929e7 | −0.588458 | ||||||||
\(817\) | 4.16925e7 | 2.18526 | ||||||||
\(818\) | 4.77320e7 | 2.49417 | ||||||||
\(819\) | 1.50263e6 | 0.0782784 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.15879e7 | 1.11777 | 0.558885 | − | 0.829245i | \(-0.311229\pi\) | ||||
0.558885 | + | 0.829245i | \(0.311229\pi\) | |||||||
\(822\) | −5.03186e7 | −2.59746 | ||||||||
\(823\) | 2.95621e7 | 1.52137 | 0.760686 | − | 0.649120i | \(-0.224863\pi\) | ||||
0.760686 | + | 0.649120i | \(0.224863\pi\) | |||||||
\(824\) | 5.28004e7 | 2.70906 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.63309e7 | 1.34282 | ||||||||
\(827\) | 2.85332e7 | 1.45073 | 0.725364 | − | 0.688365i | \(-0.241671\pi\) | ||||
0.725364 | + | 0.688365i | \(0.241671\pi\) | |||||||
\(828\) | 3.64982e7 | 1.85010 | ||||||||
\(829\) | −2.02156e7 | −1.02165 | −0.510823 | − | 0.859686i | \(-0.670659\pi\) | ||||
−0.510823 | + | 0.859686i | \(0.670659\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.65667e7 | −0.832213 | ||||||||
\(832\) | −3.40789e7 | −1.70678 | ||||||||
\(833\) | −1.42851e6 | −0.0713299 | ||||||||
\(834\) | 2.11084e7 | 1.05085 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.71028e7 | 2.33094 | ||||||||
\(837\) | −7.94300e6 | −0.391896 | ||||||||
\(838\) | −3.98214e7 | −1.95887 | ||||||||
\(839\) | −6.64057e6 | −0.325687 | −0.162843 | − | 0.986652i | \(-0.552067\pi\) | ||||
−0.162843 | + | 0.986652i | \(0.552067\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.04491e7 | −0.509434 | ||||||||
\(842\) | −1.57195e7 | −0.764114 | ||||||||
\(843\) | 3.01185e7 | 1.45970 | ||||||||
\(844\) | −5.82644e7 | −2.81544 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.07376e7 | 0.515800 | ||||||||
\(847\) | 9.59244e6 | 0.459432 | ||||||||
\(848\) | −1.33332e8 | −6.36714 | ||||||||
\(849\) | 2.12148e7 | 1.01011 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.16730e7 | −1.02588 | ||||||||
\(852\) | −3.00197e7 | −1.41680 | ||||||||
\(853\) | −1.92258e7 | −0.904716 | −0.452358 | − | 0.891836i | \(-0.649417\pi\) | ||||
−0.452358 | + | 0.891836i | \(0.649417\pi\) | |||||||
\(854\) | −2.64527e7 | −1.24115 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.86442e7 | −4.60137 | ||||||||
\(857\) | −1.98896e6 | −0.0925068 | −0.0462534 | − | 0.998930i | \(-0.514728\pi\) | ||||
−0.0462534 | + | 0.998930i | \(0.514728\pi\) | |||||||
\(858\) | 5.86193e6 | 0.271845 | ||||||||
\(859\) | −7.32029e6 | −0.338490 | −0.169245 | − | 0.985574i | \(-0.554133\pi\) | ||||
−0.169245 | + | 0.985574i | \(0.554133\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.66351e7 | −1.22446 | ||||||||
\(862\) | −6.08028e7 | −2.78712 | ||||||||
\(863\) | 3.13431e7 | 1.43257 | 0.716283 | − | 0.697809i | \(-0.245842\pi\) | ||||
0.716283 | + | 0.697809i | \(0.245842\pi\) | |||||||
\(864\) | −7.15437e7 | −3.26052 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.26441e7 | 2.83848 | ||||||||
\(867\) | 2.69639e7 | 1.21824 | ||||||||
\(868\) | 2.34579e7 | 1.05679 | ||||||||
\(869\) | 502644. | 0.0225793 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.15603e6 | 0.185623 | ||||||||
\(872\) | −8.22745e6 | −0.366416 | ||||||||
\(873\) | −1.95582e7 | −0.868546 | ||||||||
\(874\) | 1.08283e8 | 4.79493 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.47592e6 | −0.417216 | ||||||||
\(877\) | −2.47672e7 | −1.08737 | −0.543686 | − | 0.839289i | \(-0.682972\pi\) | ||||
−0.543686 | + | 0.839289i | \(0.682972\pi\) | |||||||
\(878\) | 1.98402e7 | 0.868581 | ||||||||
\(879\) | −2.23382e6 | −0.0975160 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.22752e7 | 0.532831 | 0.266415 | − | 0.963858i | \(-0.414161\pi\) | ||||
0.266415 | + | 0.963858i | \(0.414161\pi\) | |||||||
\(882\) | 1.65436e7 | 0.716077 | ||||||||
\(883\) | 2.56013e7 | 1.10500 | 0.552498 | − | 0.833514i | \(-0.313675\pi\) | ||||
0.552498 | + | 0.833514i | \(0.313675\pi\) | |||||||
\(884\) | −1.92860e6 | −0.0830064 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.37424e7 | −1.01611 | ||||||||
\(887\) | −5.01026e6 | −0.213821 | −0.106911 | − | 0.994269i | \(-0.534096\pi\) | ||||
−0.106911 | + | 0.994269i | \(0.534096\pi\) | |||||||
\(888\) | −9.33773e7 | −3.97383 | ||||||||
\(889\) | 1.62862e7 | 0.691137 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.18832e7 | 0.501462 | ||||||||
\(892\) | 2.92350e7 | 1.23024 | ||||||||
\(893\) | 2.37662e7 | 0.997311 | ||||||||
\(894\) | 5.76873e7 | 2.41400 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.87676e7 | 3.69390 | ||||||||
\(897\) | 1.00535e7 | 0.417192 | ||||||||
\(898\) | −3.08472e7 | −1.27651 | ||||||||
\(899\) | −1.11502e7 | −0.460132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.36882e6 | −0.138250 | ||||||||
\(902\) | −3.53400e7 | −1.44627 | ||||||||
\(903\) | −1.82525e7 | −0.744909 | ||||||||
\(904\) | −3.03131e7 | −1.23370 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.69348e7 | −1.09017 | ||||||||
\(907\) | −4.85441e7 | −1.95938 | −0.979688 | − | 0.200527i | \(-0.935734\pi\) | ||||
−0.979688 | + | 0.200527i | \(0.935734\pi\) | |||||||
\(908\) | 4.23336e7 | 1.70400 | ||||||||
\(909\) | −2.06757e7 | −0.829948 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.03805e7 | −1.21283 | −0.606413 | − | 0.795150i | \(-0.707392\pi\) | ||||
−0.606413 | + | 0.795150i | \(0.707392\pi\) | |||||||
\(912\) | 2.86906e8 | 11.4223 | ||||||||
\(913\) | −4.04587e6 | −0.160633 | ||||||||
\(914\) | 3.89317e7 | 1.54148 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.03855e7 | 3.16548 | ||||||||
\(917\) | 1.14806e7 | 0.450859 | ||||||||
\(918\) | −3.07926e6 | −0.120598 | ||||||||
\(919\) | −3.70802e7 | −1.44828 | −0.724141 | − | 0.689652i | \(-0.757764\pi\) | ||||
−0.724141 | + | 0.689652i | \(0.757764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.59320e7 | −0.618899 | ||||||||
\(922\) | −5.79803e7 | −2.24623 | ||||||||
\(923\) | −2.81239e6 | −0.108661 | ||||||||
\(924\) | −2.06211e7 | −0.794569 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.72217e7 | 2.95946 | ||||||||
\(927\) | −9.50133e6 | −0.363149 | ||||||||
\(928\) | −1.00431e8 | −3.82824 | ||||||||
\(929\) | 2.82561e6 | 0.107417 | 0.0537084 | − | 0.998557i | \(-0.482896\pi\) | ||||
0.0537084 | + | 0.998557i | \(0.482896\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.66170e7 | 1.38455 | ||||||||
\(932\) | 1.02948e8 | 3.88219 | ||||||||
\(933\) | −3.93126e6 | −0.147852 | ||||||||
\(934\) | 6.39498e6 | 0.239868 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.47321e7 | 0.549635 | ||||||||
\(937\) | 3.19406e6 | 0.118849 | 0.0594243 | − | 0.998233i | \(-0.481074\pi\) | ||||
0.0594243 | + | 0.998233i | \(0.481074\pi\) | |||||||
\(938\) | −1.95969e7 | −0.727244 | ||||||||
\(939\) | −3.77576e7 | −1.39746 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.22120e7 | −0.817738 | −0.408869 | − | 0.912593i | \(-0.634077\pi\) | ||||
−0.408869 | + | 0.912593i | \(0.634077\pi\) | |||||||
\(942\) | 6.97475e7 | 2.56095 | ||||||||
\(943\) | −6.06099e7 | −2.21955 | ||||||||
\(944\) | 1.58758e8 | 5.79836 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.42179e7 | −0.879849 | ||||||||
\(947\) | 2.24064e7 | 0.811889 | 0.405945 | − | 0.913898i | \(-0.366943\pi\) | ||||
0.405945 | + | 0.913898i | \(0.366943\pi\) | |||||||
\(948\) | 5.63100e6 | 0.203500 | ||||||||
\(949\) | −887751. | −0.0319982 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.75634e7 | −1.70538 | ||||||||
\(952\) | 5.99826e6 | 0.214503 | ||||||||
\(953\) | 1.48416e7 | 0.529358 | 0.264679 | − | 0.964337i | \(-0.414734\pi\) | ||||
0.264679 | + | 0.964337i | \(0.414734\pi\) | |||||||
\(954\) | 3.90144e7 | 1.38789 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.62886e7 | 3.05357 | ||||||||
\(957\) | 9.80177e6 | 0.345959 | ||||||||
\(958\) | 3.74085e7 | 1.31691 | ||||||||
\(959\) | 1.65833e7 | 0.582269 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.62732e7 | −0.568413 | ||||||||
\(962\) | −1.32629e7 | −0.462061 | ||||||||
\(963\) | 1.77508e7 | 0.616812 | ||||||||
\(964\) | −6.04102e7 | −2.09371 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.74052e7 | −1.63449 | ||||||||
\(967\) | 3.06919e7 | 1.05550 | 0.527749 | − | 0.849401i | \(-0.323036\pi\) | ||||
0.527749 | + | 0.849401i | \(0.323036\pi\) | |||||||
\(968\) | 9.40462e7 | 3.22591 | ||||||||
\(969\) | 7.24908e6 | 0.248013 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.18932e7 | −1.42592 | −0.712961 | − | 0.701203i | \(-0.752646\pi\) | ||||
−0.712961 | + | 0.701203i | \(0.752646\pi\) | |||||||
\(972\) | 8.15062e7 | 2.76710 | ||||||||
\(973\) | −6.95661e6 | −0.235568 | ||||||||
\(974\) | 5.88633e7 | 1.98814 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.59492e8 | −5.35938 | ||||||||
\(977\) | −2.54822e7 | −0.854084 | −0.427042 | − | 0.904232i | \(-0.640444\pi\) | ||||
−0.427042 | + | 0.904232i | \(0.640444\pi\) | |||||||
\(978\) | 1.04045e8 | 3.47837 | ||||||||
\(979\) | −102209. | −0.00340824 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.48051e6 | 0.0491179 | ||||||||
\(982\) | 5.08170e7 | 1.68163 | ||||||||
\(983\) | −5.91830e7 | −1.95350 | −0.976749 | − | 0.214388i | \(-0.931224\pi\) | ||||
−0.976749 | + | 0.214388i | \(0.931224\pi\) | |||||||
\(984\) | −2.61135e8 | −8.59761 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.32259e6 | −0.141596 | ||||||||
\(987\) | −1.04046e7 | −0.339963 | ||||||||
\(988\) | 4.94358e7 | 1.61120 | ||||||||
\(989\) | −4.15348e7 | −1.35027 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −625464. | −0.0202310 | −0.0101155 | − | 0.999949i | \(-0.503220\pi\) | ||||
−0.0101155 | + | 0.999949i | \(0.503220\pi\) | |||||||
\(992\) | 1.11292e8 | 3.59074 | ||||||||
\(993\) | 6.09695e7 | 1.96218 | ||||||||
\(994\) | 1.32613e7 | 0.425715 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.53249e7 | −1.44773 | ||||||||
\(997\) | 5.76822e7 | 1.83783 | 0.918913 | − | 0.394461i | \(-0.129069\pi\) | ||||
0.918913 | + | 0.394461i | \(0.129069\pi\) | |||||||
\(998\) | −9.05009e7 | −2.87625 | ||||||||
\(999\) | −1.57981e7 | −0.500830 |
(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 | 325.6.a.j.1.1 | ✓ | 11 | |
5.2 | odd | 4 | 325.6.b.i.274.1 | 22 | |||
5.3 | odd | 4 | 325.6.b.i.274.22 | 22 | |||
5.4 | even | 2 | 325.6.a.k.1.11 | yes | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.6.a.j.1.1 | ✓ | 11 | 1.1 | even | 1 | trivial | |
325.6.a.k.1.11 | yes | 11 | 5.4 | even | 2 | ||
325.6.b.i.274.1 | 22 | 5.2 | odd | 4 | |||
325.6.b.i.274.22 | 22 | 5.3 | odd | 4 |