Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [704,6,Mod(1,704)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(704, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("704.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 704 = 2^{6} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 704.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: | \(112.910209148\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 1343x^{5} + 3732x^{4} + 459776x^{3} - 2085920x^{2} - 16548352x + 80811520 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | no (minimal twist has level 352) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(5.85632\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 704.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −6.85632 | −0.439833 | −0.219917 | − | 0.975519i | \(-0.570579\pi\) | ||||
−0.219917 | + | 0.975519i | \(0.570579\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −88.9891 | −1.59189 | −0.795943 | − | 0.605371i | \(-0.793025\pi\) | ||||
−0.795943 | + | 0.605371i | \(0.793025\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0104569 | 8.06600e−5 0 | 4.03300e−5 | − | 1.00000i | \(-0.499987\pi\) | ||||
4.03300e−5 | 1.00000i | \(0.499987\pi\) | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −195.991 | −0.806547 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −401.821 | −0.659439 | −0.329719 | − | 0.944079i | \(-0.606954\pi\) | ||||
−0.329719 | + | 0.944079i | \(0.606954\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 610.138 | 0.700165 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1024.26 | 0.859582 | 0.429791 | − | 0.902928i | \(-0.358587\pi\) | ||||
0.429791 | + | 0.902928i | \(0.358587\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1549.75 | 0.984864 | 0.492432 | − | 0.870351i | \(-0.336108\pi\) | ||||
0.492432 | + | 0.870351i | \(0.336108\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0716960 | −3.54770e−5 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1888.01 | 0.744191 | 0.372095 | − | 0.928194i | \(-0.378639\pi\) | ||||
0.372095 | + | 0.928194i | \(0.378639\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4794.07 | 1.53410 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3009.86 | 0.794579 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4166.32 | −0.919936 | −0.459968 | − | 0.887935i | \(-0.652139\pi\) | ||||
−0.459968 | + | 0.887935i | \(0.652139\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8188.45 | 1.53037 | 0.765187 | − | 0.643808i | \(-0.222646\pi\) | ||||
0.765187 | + | 0.643808i | \(0.222646\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 829.615 | 0.132615 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.930552 | −0.000128402 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3447.51 | −0.414000 | −0.207000 | − | 0.978341i | \(-0.566370\pi\) | ||||
−0.207000 | + | 0.978341i | \(0.566370\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2755.01 | 0.290043 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4388.74 | 0.407737 | 0.203868 | − | 0.978998i | \(-0.434649\pi\) | ||||
0.203868 | + | 0.978998i | \(0.434649\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −899.922 | −0.0742221 | −0.0371111 | − | 0.999311i | \(-0.511816\pi\) | ||||
−0.0371111 | + | 0.999311i | \(0.511816\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 17441.1 | 1.28393 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5031.99 | −0.332273 | −0.166137 | − | 0.986103i | \(-0.553129\pi\) | ||||
−0.166137 | + | 0.986103i | \(0.553129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16807.0 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7022.65 | −0.378073 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6994.19 | 0.342017 | 0.171008 | − | 0.985270i | \(-0.445297\pi\) | ||||
0.171008 | + | 0.985270i | \(0.445297\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10767.7 | 0.479972 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10625.6 | −0.433176 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 36929.5 | 1.38116 | 0.690579 | − | 0.723257i | \(-0.257356\pi\) | ||||
0.690579 | + | 0.723257i | \(0.257356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −20688.1 | −0.711863 | −0.355931 | − | 0.934512i | \(-0.615836\pi\) | ||||
−0.355931 | + | 0.934512i | \(0.615836\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.04946 | −6.50561e−5 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 35757.7 | 1.04975 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24257.0 | −0.660160 | −0.330080 | − | 0.943953i | \(-0.607076\pi\) | ||||
−0.330080 | + | 0.943953i | \(0.607076\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12944.8 | −0.327320 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12264.1 | 0.288728 | 0.144364 | − | 0.989525i | \(-0.453886\pi\) | ||||
0.144364 | + | 0.989525i | \(0.453886\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 64629.8 | 1.41947 | 0.709734 | − | 0.704470i | \(-0.248815\pi\) | ||||
0.709734 | + | 0.704470i | \(0.248815\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −32869.7 | −0.674749 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.26529 | −2.43199e−5 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −80768.6 | −1.45605 | −0.728023 | − | 0.685553i | \(-0.759560\pi\) | ||||
−0.728023 | + | 0.685553i | \(0.759560\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 26989.2 | 0.457064 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14464.4 | 0.230465 | 0.115232 | − | 0.993339i | \(-0.463239\pi\) | ||||
0.115232 | + | 0.993339i | \(0.463239\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −91147.9 | −1.36836 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 28565.6 | 0.404619 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 118460. | 1.58524 | 0.792622 | − | 0.609713i | \(-0.208715\pi\) | ||||
0.792622 | + | 0.609713i | \(0.208715\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.20181 | −5.31903e−5 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −56142.7 | −0.673110 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −137911. | −1.56779 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 125566. | 1.35501 | 0.677504 | − | 0.735519i | \(-0.263062\pi\) | ||||
0.677504 | + | 0.735519i | \(0.263062\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23714.9 | 0.243183 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16450.1 | −0.160459 | −0.0802297 | − | 0.996776i | \(-0.525565\pi\) | ||||
−0.0802297 | + | 0.996776i | \(0.525565\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −32828.2 | −0.304897 | −0.152449 | − | 0.988311i | \(-0.548716\pi\) | ||||
−0.152449 | + | 0.988311i | \(0.548716\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.38016 | 5.64753e−5 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −165956. | −1.40131 | −0.700656 | − | 0.713500i | \(-0.747109\pi\) | ||||
−0.700656 | + | 0.713500i | \(0.747109\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −133827. | −1.07889 | −0.539445 | − | 0.842021i | \(-0.681366\pi\) | ||||
−0.539445 | + | 0.842021i | \(0.681366\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23637.2 | 0.182091 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −38902.3 | −0.286602 | −0.143301 | − | 0.989679i | \(-0.545772\pi\) | ||||
−0.143301 | + | 0.989679i | \(0.545772\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −168012. | −1.18467 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 78753.2 | 0.531868 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.7106 | 6.93339e−5 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −30090.6 | −0.179336 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −148529. | −0.850229 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −314751. | −1.73164 | −0.865821 | − | 0.500354i | \(-0.833203\pi\) | ||||
−0.865821 | + | 0.500354i | \(0.833203\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6170.15 | 0.0326454 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −62894.2 | −0.320208 | −0.160104 | − | 0.987100i | \(-0.551183\pi\) | ||||
−0.160104 | + | 0.987100i | \(0.551183\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.2056 | 7.94392e−5 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −267845. | −1.26488 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −87570.6 | −0.398618 | −0.199309 | − | 0.979937i | \(-0.563870\pi\) | ||||
−0.199309 | + | 0.979937i | \(0.563870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −27685.9 | −0.121541 | −0.0607703 | − | 0.998152i | \(-0.519356\pi\) | ||||
−0.0607703 | + | 0.998152i | \(0.519356\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 34501.0 | 0.146145 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 48620.3 | 0.198828 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 370757. | 1.46443 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 115234. | 0.439833 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −93713.5 | −0.345809 | −0.172905 | − | 0.984939i | \(-0.555315\pi\) | ||||
−0.172905 | + | 0.984939i | \(0.555315\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 449253. | 1.60343 | 0.801713 | − | 0.597709i | \(-0.203922\pi\) | ||||
0.801713 | + | 0.597709i | \(0.203922\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −200745. | −0.693293 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −728683. | −2.43618 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −109665. | −0.355073 | −0.177537 | − | 0.984114i | \(-0.556813\pi\) | ||||
−0.177537 | + | 0.984114i | \(0.556813\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −47954.4 | −0.150430 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.7427 | 6.00265e−5 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 353482. | 1.04207 | 0.521036 | − | 0.853535i | \(-0.325546\pi\) | ||||
0.521036 | + | 0.853535i | \(0.325546\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −73826.7 | −0.211108 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −25150.8 | −0.0697847 | −0.0348923 | − | 0.999391i | \(-0.511109\pi\) | ||||
−0.0348923 | + | 0.999391i | \(0.511109\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −209833. | −0.565141 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −303736. | −0.794339 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 422495. | 1.07326 | 0.536632 | − | 0.843816i | \(-0.319696\pi\) | ||||
0.536632 | + | 0.843816i | \(0.319696\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 50.1312 | 0.000123741 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −253201. | −0.607479 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 592592. | 1.38237 | 0.691183 | − | 0.722680i | \(-0.257090\pi\) | ||||
0.691183 | + | 0.722680i | \(0.257090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −671765. | −1.52413 | −0.762063 | − | 0.647503i | \(-0.775813\pi\) | ||||
−0.762063 | + | 0.647503i | \(0.775813\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 141844. | 0.313101 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 306791. | 0.659041 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −123935. | −0.259174 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 31.4739 | 6.40908e−5 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.00017e6 | −1.98377 | −0.991886 | − | 0.127129i | \(-0.959424\pi\) | ||||
−0.991886 | + | 0.127129i | \(0.959424\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 451893. | 0.873258 | 0.436629 | − | 0.899642i | \(-0.356172\pi\) | ||||
0.436629 | + | 0.899642i | \(0.356172\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −245166. | −0.461715 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 404618. | 0.742814 | 0.371407 | − | 0.928470i | \(-0.378875\pi\) | ||||
0.371407 | + | 0.928470i | \(0.378875\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 424308. | 0.759536 | 0.379768 | − | 0.925082i | \(-0.376004\pi\) | ||||
0.379768 | + | 0.925082i | \(0.376004\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 166314. | 0.290360 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −43.5669 | −7.42021e−5 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −390550. | −0.649071 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −370032. | −0.600225 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −187519. | −0.296948 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −782758. | −1.21038 | −0.605190 | − | 0.796081i | \(-0.706903\pi\) | ||||
−0.605190 | + | 0.796081i | \(0.706903\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −84086.4 | −0.126992 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 80083.2 | 0.118153 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 85.6260 | 0.000123440 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −443123. | −0.624329 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −411569. | −0.566841 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.16642e6 | −1.57069 | −0.785347 | − | 0.619056i | \(-0.787515\pi\) | ||||
−0.785347 | + | 0.619056i | \(0.787515\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −939593. | −1.23732 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 575923. | 0.741822 | 0.370911 | − | 0.928668i | \(-0.379045\pi\) | ||||
0.370911 | + | 0.928668i | \(0.379045\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 631491. | 0.795753 | 0.397877 | − | 0.917439i | \(-0.369747\pi\) | ||||
0.397877 | + | 0.917439i | \(0.369747\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.67521 | 1.06967e−5 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.07545e6 | −1.29778 | −0.648889 | − | 0.760883i | \(-0.724766\pi\) | ||||
−0.648889 | + | 0.760883i | \(0.724766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 447793. | 0.528941 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 553776. | 0.640417 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 591325. | 0.669624 | 0.334812 | − | 0.942285i | \(-0.391327\pi\) | ||||
0.334812 | + | 0.942285i | \(0.391327\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 464766. | 0.515456 | 0.257728 | − | 0.966218i | \(-0.417026\pi\) | ||||
0.257728 | + | 0.966218i | \(0.417026\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −916443. | −0.995611 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.49564e6 | 1.59189 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −622721. | −0.649458 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −99172.5 | −0.101366 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 379607. | 0.380321 | 0.190160 | − | 0.981753i | \(-0.439099\pi\) | ||||
0.190160 | + | 0.981753i | \(0.439099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −228449. | −0.224382 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 624939. | 0.601849 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.98149e6 | −1.87136 | −0.935682 | − | 0.352846i | \(-0.885214\pi\) | ||||
−0.935682 | + | 0.352846i | \(0.885214\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −36.0503 | −3.33933e−5 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 816561. | 0.741971 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −342106. | −0.304980 | −0.152490 | − | 0.988305i | \(-0.548729\pi\) | ||||
−0.152490 | + | 0.988305i | \(0.548729\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −622407. | −0.544452 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −812199. | −0.697243 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 555873. | 0.468377 | 0.234188 | − | 0.972191i | \(-0.424757\pi\) | ||||
0.234188 | + | 0.972191i | \(0.424757\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.33716e6 | −1.93315 | −0.966573 | − | 0.256392i | \(-0.917466\pi\) | ||||
−0.966573 | + | 0.256392i | \(0.917466\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 28.8090 | 2.33949e−5 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −580082. | −0.462549 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.27147e6 | 0.995647 | 0.497824 | − | 0.867278i | \(-0.334133\pi\) | ||||
0.497824 | + | 0.867278i | \(0.334133\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.60486e6 | −1.23432 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 125820. | 0.0950569 | 0.0475284 | − | 0.998870i | \(-0.484866\pi\) | ||||
0.0475284 | + | 0.998870i | \(0.484866\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.59512e6 | −1.92616 | −0.963079 | − | 0.269219i | \(-0.913235\pi\) | ||||
−0.963079 | + | 0.269219i | \(0.913235\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 945559. | 0.689567 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 45.8926 | 3.28881e−5 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −370752. | −0.261119 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −860919. | −0.595978 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.32770e6 | 0.903505 | 0.451753 | − | 0.892143i | \(-0.350799\pi\) | ||||
0.451753 | + | 0.892143i | \(0.350799\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.28632e6 | −2.19865 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −364193. | −0.239575 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −758642. | −0.490748 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.41040 | −5.98676e−6 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 112787. | 0.0705754 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.84102e6 | 1.13320 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.66798e6 | −1.61561 | −0.807805 | − | 0.589450i | \(-0.799345\pi\) | ||||
−0.807805 | + | 0.589450i | \(0.799345\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 225080. | 0.134104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.09601e6 | 0.642562 | 0.321281 | − | 0.946984i | \(-0.395887\pi\) | ||||
0.321281 | + | 0.946984i | \(0.395887\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.18409e6 | −1.26011 | −0.630057 | − | 0.776549i | \(-0.716969\pi\) | ||||
−0.630057 | + | 0.776549i | \(0.716969\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 182.380 | 0.000103562 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.27349e6 | −0.711782 | −0.355891 | − | 0.934528i | \(-0.615823\pi\) | ||||
−0.355891 | + | 0.934528i | \(0.615823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 504125. | 0.277371 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.13785e6 | 0.616343 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.58734e6 | 0.846572 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.92636e6 | −1.01165 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 917560. | 0.474532 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −52.6191 | −2.68012e−5 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 598901. | 0.300459 | 0.150230 | − | 0.988651i | \(-0.451999\pi\) | ||||
0.150230 | + | 0.988651i | \(0.451999\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 675680. | 0.333911 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.15861e6 | 1.05090 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.99004e6 | 0.954526 | 0.477263 | − | 0.878761i | \(-0.341629\pi\) | ||||
0.477263 | + | 0.878761i | \(0.341629\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 266727. | 0.126057 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −990803. | −0.461425 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −351.499 | −0.000161320 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.15195e6 | 0.521056 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.28963e6 | 1.02080 | 0.510401 | − | 0.859936i | \(-0.329497\pi\) | ||||
0.510401 | + | 0.859936i | \(0.329497\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.80188e6 | 1.23136 | 0.615680 | − | 0.787996i | \(-0.288881\pi\) | ||||
0.615680 | + | 0.787996i | \(0.288881\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.20943e6 | −0.523976 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 929917. | 0.397198 | 0.198599 | − | 0.980081i | \(-0.436361\pi\) | ||||
0.198599 | + | 0.980081i | \(0.436361\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.09137e6 | −0.459622 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −73.4352 | −3.04954e−5 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.53352e6 | 0.627990 | 0.313995 | − | 0.949425i | \(-0.398332\pi\) | ||||
0.313995 | + | 0.949425i | \(0.398332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −74386.9 | −0.0300420 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −100383. | −0.0399848 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.75135e6 | −2.25963 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 815086. | 0.315892 | 0.157946 | − | 0.987448i | \(-0.449513\pi\) | ||||
0.157946 | + | 0.987448i | \(0.449513\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −860152. | −0.328859 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 73.1376 | 2.75871e−5 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −951641. | −0.354161 | −0.177081 | − | 0.984196i | \(-0.556665\pi\) | ||||
−0.177081 | + | 0.984196i | \(0.556665\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.01836e6 | 0.373959 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.67412e6 | 0.606641 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.97579e6 | 1.42176 | 0.710879 | − | 0.703315i | \(-0.248298\pi\) | ||||
0.710879 | + | 0.703315i | \(0.248298\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.15804e6 | 0.761634 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.30638e6 | 0.803404 | 0.401702 | − | 0.915771i | \(-0.368419\pi\) | ||||
0.401702 | + | 0.915771i | \(0.368419\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 112.597 | 3.87145e−5 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 176376. | 0.0598636 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.53163e6 | −1.18332 | −0.591658 | − | 0.806189i | \(-0.701527\pi\) | ||||
−0.591658 | + | 0.806189i | \(0.701527\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.93381e6 | 0.639693 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 431223. | 0.140838 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.18753e6 | 2.31786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.65786e6 | 1.48324 | 0.741618 | − | 0.670822i | \(-0.234059\pi\) | ||||
0.741618 | + | 0.670822i | \(0.234059\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −111.111 | −3.49400e−5 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.84367e6 | −0.572563 | −0.286281 | − | 0.958146i | \(-0.592419\pi\) | ||||
−0.286281 | + | 0.958146i | \(0.592419\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.29029e6 | −1.00919 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.40174e6 | −0.727594 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 417148. | 0.124826 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.37722e6 | −1.88505 | −0.942526 | − | 0.334134i | \(-0.891556\pi\) | ||||
−0.942526 | + | 0.334134i | \(0.891556\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 600412. | 0.175325 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 386.169 | 0.000111404 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.28717e6 | −0.366874 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 189823. | 0.0534576 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.80523e6 | 0.780609 | 0.390305 | − | 0.920686i | \(-0.372370\pi\) | ||||
0.390305 | + | 0.920686i | \(0.372370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.65201e6 | 1.82914 | 0.914571 | − | 0.404424i | \(-0.132528\pi\) | ||||
0.914571 | + | 0.404424i | \(0.132528\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 986225. | 0.267994 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.91036e6 | 1.31869 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −216.334 | −5.74189e−5 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −333357. | −0.0874513 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 930197. | 0.241202 | 0.120601 | − | 0.992701i | \(-0.461518\pi\) | ||||
0.120601 | + | 0.992701i | \(0.461518\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.40769e6 | −1.12977 | −0.564887 | − | 0.825168i | \(-0.691080\pi\) | ||||
−0.564887 | + | 0.825168i | \(0.691080\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.54203e6 | −0.644107 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.92593e6 | 0.732927 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.59326e6 | 1.13752 | 0.568761 | − | 0.822503i | \(-0.307423\pi\) | ||||
0.568761 | + | 0.822503i | \(0.307423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.29402e6 | 0.806547 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.66510e6 | 1.37151 | 0.685754 | − | 0.727833i | \(-0.259472\pi\) | ||||
0.685754 | + | 0.727833i | \(0.259472\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.05416e7 | −2.52353 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 642530. | 0.152098 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.39840e6 | 0.561443 | 0.280721 | − | 0.959789i | \(-0.409426\pi\) | ||||
0.280721 | + | 0.959789i | \(0.409426\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −531037. | −0.122937 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.08023e6 | −0.705240 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 373.915 | 8.46730e−5 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.58804e6 | 1.47559 | 0.737795 | − | 0.675025i | \(-0.235867\pi\) | ||||
0.737795 | + | 0.675025i | \(0.235867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.08288e6 | 0.683006 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.02859e6 | −0.444573 | −0.222286 | − | 0.974981i | \(-0.571352\pi\) | ||||
−0.222286 | + | 0.974981i | \(0.571352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.09155e6 | −1.32061 | −0.660306 | − | 0.750996i | \(-0.729574\pi\) | ||||
−0.660306 | + | 0.750996i | \(0.729574\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.99609e6 | 1.07151 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.13147e6 | −1.51317 | −0.756583 | − | 0.653897i | \(-0.773133\pi\) | ||||
−0.756583 | + | 0.653897i | \(0.773133\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −253.653 | −5.32486e−5 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 751897. | 0.156173 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 108891. | 0.0223788 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.42959e6 | 1.51088 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.37080e6 | −0.275853 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.49383e6 | 0.297482 | 0.148741 | − | 0.988876i | \(-0.452478\pi\) | ||||
0.148741 | + | 0.988876i | \(0.452478\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.38528e6 | 0.273008 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −135.363 | −2.64016e−5 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.11740e7 | −2.15702 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.29051e6 | −0.246568 | −0.123284 | − | 0.992371i | \(-0.539343\pi\) | ||||
−0.123284 | + | 0.992371i | \(0.539343\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.42358e6 | −0.458338 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.83433e6 | −0.904967 | −0.452484 | − | 0.891773i | \(-0.649462\pi\) | ||||
−0.452484 | + | 0.891773i | \(0.649462\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.26739e6 | −0.790760 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.11037e6 | −0.387120 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 128.244 | 2.32888e−5 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.59558e6 | −0.826207 | −0.413104 | − | 0.910684i | \(-0.635555\pi\) | ||||
−0.413104 | + | 0.910684i | \(0.635555\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 172442. | 0.0306936 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.34644e6 | −0.589743 | −0.294871 | − | 0.955537i | \(-0.595277\pi\) | ||||
−0.294871 | + | 0.955537i | \(0.595277\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.46388e6 | 0.255433 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.43868e6 | 0.248568 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28293.3 | 0.00484049 | 0.00242024 | − | 0.999997i | \(-0.499230\pi\) | ||||
0.00242024 | + | 0.999997i | \(0.499230\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 675.828 | 0.000114494 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.66452e6 | 0.782553 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.92135e6 | 0.485362 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 608871. | 0.100184 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.89676e6 | −0.472057 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.57403e6 | −0.576852 | −0.288426 | − | 0.957502i | \(-0.593132\pi\) | ||||
−0.288426 | + | 0.957502i | \(0.593132\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.11186e6 | 0.497469 | 0.248735 | − | 0.968572i | \(-0.419985\pi\) | ||||
0.248735 | + | 0.968572i | \(0.419985\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −343.715 | −5.44253e−5 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.38709e6 | 1.31548 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.87177e6 | −0.446180 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.23784e6 | −1.11397 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.76349e6 | −0.268877 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.47683e7 | 2.23073 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.06300e6 | −0.608011 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.03365e6 | 0.301511 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.27977e6 | −0.775571 | −0.387786 | − | 0.921750i | \(-0.626760\pi\) | ||||
−0.387786 | + | 0.921750i | \(0.626760\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.60584e6 | 0.670361 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.19091e7 | 1.71747 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.01043e7 | 1.44390 | 0.721950 | − | 0.691945i | \(-0.243246\pi\) | ||||
0.721950 | + | 0.691945i | \(0.243246\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.05468e6 | 0.574151 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.45674e6 | −0.906012 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −844.590 | −0.000117445 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.10346e6 | −0.289868 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −962698. | −0.131478 | −0.0657389 | − | 0.997837i | \(-0.520940\pi\) | ||||
−0.0657389 | + | 0.997837i | \(0.520940\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 361607. | 0.0489449 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 849740. | 0.113993 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.33941e6 | 0.975866 | 0.487933 | − | 0.872881i | \(-0.337751\pi\) | ||||
0.487933 | + | 0.872881i | \(0.337751\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.46188e6 | 0.456238 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 282.224 | 3.68668e−5 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.33115e7 | 1.72364 | 0.861819 | − | 0.507216i | \(-0.169325\pi\) | ||||
0.861819 | + | 0.507216i | \(0.169325\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −366749. | −0.0470738 | −0.0235369 | − | 0.999723i | \(-0.507493\pi\) | ||||
−0.0235369 | + | 0.999723i | \(0.507493\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.85751e6 | 0.872529 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.05124e6 | 1.14166 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.28992e7 | −1.61296 | −0.806478 | − | 0.591264i | \(-0.798629\pi\) | ||||
−0.806478 | + | 0.591264i | \(0.798629\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.09833e6 | −0.384088 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 151.253 | 1.85893e−5 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −846297. | −0.103122 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.00818e6 | −0.846673 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.09826e6 | −0.371127 | −0.185563 | − | 0.982632i | \(-0.559411\pi\) | ||||
−0.185563 | + | 0.982632i | \(0.559411\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.26900e7 | 1.50721 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.77419e6 | −0.326714 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.00158e6 | −0.350520 | −0.175260 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175260 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −953.126 | −0.000110372 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.90919e6 | −0.334069 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.38210e7 | 1.57389 | 0.786944 | − | 0.617024i | \(-0.211662\pi\) | ||||
0.786944 | + | 0.617024i | \(0.211662\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.44913e6 | −1.06710 | −0.533550 | − | 0.845768i | \(-0.679143\pi\) | ||||
−0.533550 | + | 0.845768i | \(0.679143\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.75414e6 | 0.532450 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.30289e6 | −0.144717 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.69053e7 | −1.86230 | −0.931151 | − | 0.364635i | \(-0.881194\pi\) | ||||
−0.931151 | + | 0.364635i | \(0.881194\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 298.708 | 3.26365e−5 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.02196e6 | 0.219114 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.58788e6 | 0.923070 | 0.461535 | − | 0.887122i | \(-0.347299\pi\) | ||||
0.461535 | + | 0.887122i | \(0.347299\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.67774e6 | 0.285483 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 903145. | 0.0955091 | 0.0477545 | − | 0.998859i | \(-0.484793\pi\) | ||||
0.0477545 | + | 0.998859i | \(0.484793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.38444e6 | −0.669724 | −0.334862 | − | 0.942267i | \(-0.608690\pi\) | ||||
−0.334862 | + | 0.942267i | \(0.608690\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.68265e6 | 0.591319 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1238.72 | 0.000127866 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.76400e6 | −0.180634 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.28569e6 | 0.130608 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.53114e6 | −0.355867 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.32430e7 | 1.32408 | 0.662039 | − | 0.749469i | \(-0.269691\pi\) | ||||
0.662039 | + | 0.749469i | \(0.269691\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.36684e6 | 0.532365 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.80094e7 | 2.75658 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.75341e6 | 0.659439 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.40365e6 | −0.232873 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.78618e6 | −0.267833 | −0.133916 | − | 0.990993i | \(-0.542755\pi\) | ||||
−0.133916 | + | 0.990993i | \(0.542755\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.59102e6 | 0.151757 | 0.0758783 | − | 0.997117i | \(-0.475824\pi\) | ||||
0.0758783 | + | 0.997117i | \(0.475824\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −549077. | −0.0519677 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.40368e6 | 0.413575 | 0.206788 | − | 0.978386i | \(-0.433699\pi\) | ||||
0.206788 | + | 0.978386i | \(0.433699\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.46847e6 | −0.416435 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −587.079 | −5.42930e−5 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.13978e6 | −0.288149 | −0.144074 | − | 0.989567i | \(-0.546020\pi\) | ||||
−0.144074 | + | 0.989567i | \(0.546020\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.59690e6 | 0.509735 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.26668e7 | −1.14487 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.19749e7 | −1.07413 | −0.537067 | − | 0.843540i | \(-0.680468\pi\) | ||||
−0.537067 | + | 0.843540i | \(0.680468\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.91351e6 | 0.615453 | 0.307727 | − | 0.951475i | \(-0.400432\pi\) | ||||
0.307727 | + | 0.951475i | \(0.400432\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.82185e6 | 0.249316 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1442.12 | −0.000126458 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.86605e6 | −0.684608 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.99733e6 | 0.690843 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.50326e6 | 0.214635 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.93001e6 | −0.504682 | −0.252341 | − | 0.967638i | \(-0.581200\pi\) | ||||
−0.252341 | + | 0.967638i | \(0.581200\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.44295e7 | 1.21897 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.65327e6 | 0.725619 | 0.362810 | − | 0.931863i | \(-0.381818\pi\) | ||||
0.362810 | + | 0.931863i | \(0.381818\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1313.03 | 0.000109295 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.94871e6 | −0.326278 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.45086e6 | 0.611159 | 0.305580 | − | 0.952167i | \(-0.401150\pi\) | ||||
0.305580 | + | 0.952167i | \(0.401150\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.79283e6 | 0.634555 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.32970e6 | −0.349999 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.81041e6 | −0.225539 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.05191e6 | 0.402495 | 0.201247 | − | 0.979540i | \(-0.435500\pi\) | ||||
0.201247 | + | 0.979540i | \(0.435500\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 247.985 | 1.96151e−5 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.46374e6 | 0.193479 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.49520e6 | 0.350483 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.37363e6 | 0.570806 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.21918e6 | 0.324290 | 0.162145 | − | 0.986767i | \(-0.448159\pi\) | ||||
0.162145 | + | 0.986767i | \(0.448159\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.34276e6 | −0.407734 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.07021e6 | −0.232646 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −172.017 | −1.29427e−5 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.99207e6 | −0.298251 | −0.149126 | − | 0.988818i | \(-0.547646\pi\) | ||||
−0.149126 | + | 0.988818i | \(0.547646\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.58299e7 | 1.17437 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.54599e7 | 1.13889 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.32668e6 | −0.316512 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.05431e6 | −0.294523 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.76545e7 | −1.27360 | −0.636801 | − | 0.771028i | \(-0.719743\pi\) | ||||
−0.636801 | + | 0.771028i | \(0.719743\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −343.281 | −2.45930e−5 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.18658e6 | −0.226715 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.99736e7 | −1.41128 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.39538e7 | −0.979166 | −0.489583 | − | 0.871957i | \(-0.662851\pi\) | ||||
−0.489583 | + | 0.871957i | \(0.662851\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −274941. | −0.0191611 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −921752. | −0.0638000 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.86172e6 | 0.471708 | 0.235854 | − | 0.971789i | \(-0.424211\pi\) | ||||
0.235854 | + | 0.971789i | \(0.424211\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.02546e7 | −0.700165 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.93509e6 | 0.199046 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.31502e7 | 0.885774 | 0.442887 | − | 0.896578i | \(-0.353954\pi\) | ||||
0.442887 | + | 0.896578i | \(0.353954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.26957e6 | 0.285653 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.94159e7 | 1.29028 | 0.645142 | − | 0.764063i | \(-0.276798\pi\) | ||||
0.645142 | + | 0.764063i | \(0.276798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.33948e6 | 0.550489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.83489e6 | −0.185881 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1735.39 | −0.000113030 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.23128e7 | −0.796631 | −0.398315 | − | 0.917248i | \(-0.630405\pi\) | ||||
−0.398315 | + | 0.917248i | \(0.630405\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.60271e6 | −0.167278 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.99787e7 | −2.55247 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 533087. | 0.0338110 | 0.0169055 | − | 0.999857i | \(-0.494619\pi\) | ||||
0.0169055 | + | 0.999857i | \(0.494619\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.56632e6 | 0.0986907 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.19162e7 | −1.37184 | −0.685921 | − | 0.727676i | \(-0.740600\pi\) | ||||
−0.685921 | + | 0.727676i | \(0.740600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1399.42 | −8.70233e−5 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.78642e7 | 1.10364 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.48391e7 | −0.910789 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.03975e7 | 0.634035 | 0.317018 | − | 0.948420i | \(-0.397319\pi\) | ||||
0.317018 | + | 0.948420i | \(0.397319\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.35857e7 | 0.823088 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.35084e7 | 0.813122 | 0.406561 | − | 0.913624i | \(-0.366728\pi\) | ||||
0.406561 | + | 0.913624i | \(0.366728\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.92560e7 | 2.34775 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 247.172 | 1.46875e−5 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.80143e6 | 0.401565 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.48395e6 | −0.0870547 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.25401e7 | −0.730962 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.75898e6 | 0.565237 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.74398e7 | −1.00370 | −0.501852 | − | 0.864954i | \(-0.667348\pi\) | ||||
−0.501852 | + | 0.864954i | \(0.667348\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.34559e6 | 0.134141 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −406.798 | −2.31173e−5 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.31292e6 | 0.469430 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.26742e6 | 0.239468 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.43089e7 | −1.35556 | −0.677781 | − | 0.735264i | \(-0.737058\pi\) | ||||
−0.677781 | + | 0.735264i | \(0.737058\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.15406e6 | −0.285616 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.32170e7 | −1.27857 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.82020e6 | −0.427986 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1756.89 | −9.55553e−5 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.81125e6 | −0.206008 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.53077e7 | −1.89670 | −0.948348 | − | 0.317232i | \(-0.897247\pi\) | ||||
−0.948348 | + | 0.317232i | \(0.897247\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.67923e7 | −1.43040 | −0.715200 | − | 0.698920i | \(-0.753664\pi\) | ||||
−0.715200 | + | 0.698920i | \(0.753664\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.60243e7 | 0.850262 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.14560e7 | −1.65886 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.39465e6 | −0.0730988 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 823.516 | 4.29005e−5 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.44086e7 | −1.26382 | −0.631910 | − | 0.775042i | \(-0.717729\pi\) | ||||
−0.631910 | + | 0.775042i | \(0.717729\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.11851e7 | −1.09026 | −0.545132 | − | 0.838350i | \(-0.683520\pi\) | ||||
−0.545132 | + | 0.838350i | \(0.683520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.97723e6 | 0.203444 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.13240e7 | −0.575755 | −0.287877 | − | 0.957667i | \(-0.592950\pi\) | ||||
−0.287877 | + | 0.957667i | \(0.592950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.42114e6 | −0.0718211 | −0.0359105 | − | 0.999355i | \(-0.511433\pi\) | ||||
−0.0359105 | + | 0.999355i | \(0.511433\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.71758e6 | −0.437919 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.72147e7 | −0.859582 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.23815e6 | 0.111089 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.46461e7 | 1.21600 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.08557e6 | −0.347512 | −0.173756 | − | 0.984789i | \(-0.555590\pi\) | ||||
−0.173756 | + | 0.984789i | \(0.555590\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.15292e6 | −0.153718 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −862662. | −0.0418092 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.86728e7 | 0.899640 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 153.100 | 7.33273e−6 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.77930e7 | 0.847189 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.50892e6 | −0.308095 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.19098e7 | −1.50159 | −0.750796 | − | 0.660534i | \(-0.770330\pi\) | ||||
−0.750796 | + | 0.660534i | \(0.770330\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.70292e7 | 1.26450 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.11472e6 | −0.0518460 | −0.0259230 | − | 0.999664i | \(-0.508252\pi\) | ||||
−0.0259230 | + | 0.999664i | \(0.508252\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.39926e6 | −0.342141 | −0.171070 | − | 0.985259i | \(-0.554723\pi\) | ||||
−0.171070 | + | 0.985259i | \(0.554723\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −314.655 | −1.44653e−5 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.53363e6 | −0.161508 | −0.0807540 | − | 0.996734i | \(-0.525733\pi\) | ||||
−0.0807540 | + | 0.996734i | \(0.525733\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.75975e7 | −1.70851 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.54199e6 | 0.114849 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.77300e6 | 0.439014 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.74696e6 | 0.435335 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.46097e7 | −1.09288 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1553.15 | −6.85795e−5 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.15792e7 | −1.38644 | −0.693222 | − | 0.720724i | \(-0.743810\pi\) | ||||
−0.693222 | + | 0.720724i | \(0.743810\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.10314e6 | −0.397392 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.75463e7 | 0.761634 | 0.380817 | − | 0.924650i | \(-0.375643\pi\) | ||||
0.380817 | + | 0.924650i | \(0.375643\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.57681e7 | −1.54381 | −0.771905 | − | 0.635738i | \(-0.780696\pi\) | ||||
−0.771905 | + | 0.635738i | \(0.780696\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.25321e7 | 0.967038 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.99661e6 | 0.127886 | 0.0639428 | − | 0.997954i | \(-0.479632\pi\) | ||||
0.0639428 | + | 0.997954i | \(0.479632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3291.33 | −0.000139674 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.26569e6 | −0.137810 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.79831e6 | −0.327244 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.27342e7 | −2.20057 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.20149e6 | 0.215847 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.41157e7 | −1.40785 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.16385e6 | 0.293991 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 64.5208 | 2.63318e−6 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.97798e7 | 2.42623 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.68471e7 | −1.48725 | −0.743626 | − | 0.668596i | \(-0.766896\pi\) | ||||
−0.743626 | + | 0.668596i | \(0.766896\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.22407e6 | 0.129418 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.79651e7 | −1.91483 | −0.957414 | − | 0.288720i | \(-0.906770\pi\) | ||||
−0.957414 | + | 0.288720i | \(0.906770\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.75019e6 | −0.0694878 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.26226e7 | −0.498421 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −657.679 | −2.58280e−5 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.94973e7 | −0.761528 | −0.380764 | − | 0.924672i | \(-0.624339\pi\) | ||||
−0.380764 | + | 0.924672i | \(0.624339\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.82925e7 | 0.710599 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.92796e6 | −0.190398 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.65276e7 | −0.635119 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.43402e6 | 0.245914 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.03735e7 | 1.53482 | 0.767409 | − | 0.641158i | \(-0.221546\pi\) | ||||
0.767409 | + | 0.641158i | \(0.221546\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.60466e7 | −0.984864 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.51462e6 | −0.282620 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.10289e7 | 0.412575 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.95553e7 | 1.09973 | 0.549866 | − | 0.835253i | \(-0.314679\pi\) | ||||
0.549866 | + | 0.835253i | \(0.314679\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.49748e7 | 0.554240 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.27570e7 | −1.57410 | −0.787051 | − | 0.616887i | \(-0.788393\pi\) | ||||
−0.787051 | + | 0.616887i | \(0.788393\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.28597e6 | 0.303434 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2800.83 | −0.000102025 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.20841e7 | −1.52491 | −0.762453 | − | 0.647044i | \(-0.776005\pi\) | ||||
−0.762453 | + | 0.647044i | \(0.776005\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.59696e7 | −0.936052 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.73145e6 | 0.313065 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.36894e7 | 0.844933 | 0.422467 | − | 0.906378i | \(-0.361164\pi\) | ||||
0.422467 | + | 0.906378i | \(0.361164\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.90046e7 | 3.15794 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.45644e6 | −0.121997 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −915.718 | −3.21525e−5 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.84216e7 | 1.34205 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.25259e7 | 1.13022 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.02136e7 | −1.39013 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.21518e7 | 0.761802 | 0.380901 | − | 0.924616i | \(-0.375614\pi\) | ||||
0.380901 | + | 0.924616i | \(0.375614\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.08833e7 | −0.372350 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.49276e7 | 1.86957 | 0.934787 | − | 0.355208i | \(-0.115590\pi\) | ||||
0.934787 | + | 0.355208i | \(0.115590\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −289.509 | −9.80347e−6 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.32077e7 | 0.444955 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.79300e7 | 0.600959 | 0.300480 | − | 0.953788i | \(-0.402853\pi\) | ||||
0.300480 | + | 0.953788i | \(0.402853\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.43336e7 | −0.477969 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.62288e7 | 0.870175 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.46366e7 | −1.80343 | −0.901717 | − | 0.432328i | \(-0.857692\pi\) | ||||
−0.901717 | + | 0.432328i | \(0.857692\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.60066e7 | −1.18248 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 360.774 | 1.17881e−5 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.69906e6 | −0.0552354 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.02992e7 | 0.333135 | 0.166568 | − | 0.986030i | \(-0.446732\pi\) | ||||
0.166568 | + | 0.986030i | \(0.446732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.10626e6 | −0.132152 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.77588e7 | −1.20909 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.72521e7 | −0.868284 | −0.434142 | − | 0.900845i | \(-0.642948\pi\) | ||||
−0.434142 | + | 0.900845i | \(0.642948\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.03765e7 | −0.328956 |
(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 | 704.6.a.be.1.3 | 7 | ||
4.3 | odd | 2 | 704.6.a.bf.1.5 | 7 | |||
8.3 | odd | 2 | 352.6.a.g.1.3 | ✓ | 7 | ||
8.5 | even | 2 | 352.6.a.h.1.5 | yes | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
352.6.a.g.1.3 | ✓ | 7 | 8.3 | odd | 2 | ||
352.6.a.h.1.5 | yes | 7 | 8.5 | even | 2 | ||
704.6.a.be.1.3 | 7 | 1.1 | even | 1 | trivial | ||
704.6.a.bf.1.5 | 7 | 4.3 | odd | 2 |