Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,6,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, 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("230.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(36.8882785570\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 1156x^{4} + 593x^{3} + 338133x^{2} + 408388x - 13033476 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(5.93160\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 7.93160 | 0.508812 | 0.254406 | − | 0.967097i | \(-0.418120\pi\) | ||||
0.254406 | + | 0.967097i | \(0.418120\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 31.7264 | 0.359785 | ||||||||
\(7\) | 221.199 | 1.70623 | 0.853115 | − | 0.521722i | \(-0.174710\pi\) | ||||
0.853115 | + | 0.521722i | \(0.174710\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | −180.090 | −0.741110 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 508.302 | 1.26660 | 0.633301 | − | 0.773906i | \(-0.281700\pi\) | ||||
0.633301 | + | 0.773906i | \(0.281700\pi\) | |||||||
\(12\) | 126.906 | 0.254406 | ||||||||
\(13\) | 148.017 | 0.242915 | 0.121458 | − | 0.992597i | \(-0.461243\pi\) | ||||
0.121458 | + | 0.992597i | \(0.461243\pi\) | |||||||
\(14\) | 884.795 | 1.20649 | ||||||||
\(15\) | −198.290 | −0.227548 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1625.64 | −1.36427 | −0.682136 | − | 0.731225i | \(-0.738949\pi\) | ||||
−0.682136 | + | 0.731225i | \(0.738949\pi\) | |||||||
\(18\) | −720.359 | −0.524044 | ||||||||
\(19\) | 1657.06 | 1.05306 | 0.526531 | − | 0.850156i | \(-0.323492\pi\) | ||||
0.526531 | + | 0.850156i | \(0.323492\pi\) | |||||||
\(20\) | −400.000 | −0.223607 | ||||||||
\(21\) | 1754.46 | 0.868151 | ||||||||
\(22\) | 2033.21 | 0.895622 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | 507.622 | 0.179892 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 592.070 | 0.171767 | ||||||||
\(27\) | −3355.78 | −0.885898 | ||||||||
\(28\) | 3539.18 | 0.853115 | ||||||||
\(29\) | 6957.76 | 1.53629 | 0.768147 | − | 0.640273i | \(-0.221179\pi\) | ||||
0.768147 | + | 0.640273i | \(0.221179\pi\) | |||||||
\(30\) | −793.160 | −0.160901 | ||||||||
\(31\) | −813.687 | −0.152073 | −0.0760367 | − | 0.997105i | \(-0.524227\pi\) | ||||
−0.0760367 | + | 0.997105i | \(0.524227\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 4031.65 | 0.644462 | ||||||||
\(34\) | −6502.54 | −0.964686 | ||||||||
\(35\) | −5529.97 | −0.763049 | ||||||||
\(36\) | −2881.44 | −0.370555 | ||||||||
\(37\) | 13541.4 | 1.62615 | 0.813074 | − | 0.582161i | \(-0.197793\pi\) | ||||
0.813074 | + | 0.582161i | \(0.197793\pi\) | |||||||
\(38\) | 6628.24 | 0.744628 | ||||||||
\(39\) | 1174.01 | 0.123598 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | −7502.30 | −0.697003 | −0.348502 | − | 0.937308i | \(-0.613309\pi\) | ||||
−0.348502 | + | 0.937308i | \(0.613309\pi\) | |||||||
\(42\) | 7017.84 | 0.613875 | ||||||||
\(43\) | 8204.16 | 0.676649 | 0.338324 | − | 0.941030i | \(-0.390140\pi\) | ||||
0.338324 | + | 0.941030i | \(0.390140\pi\) | |||||||
\(44\) | 8132.83 | 0.633301 | ||||||||
\(45\) | 4502.24 | 0.331435 | ||||||||
\(46\) | −2116.00 | −0.147442 | ||||||||
\(47\) | 4348.32 | 0.287129 | 0.143564 | − | 0.989641i | \(-0.454144\pi\) | ||||
0.143564 | + | 0.989641i | \(0.454144\pi\) | |||||||
\(48\) | 2030.49 | 0.127203 | ||||||||
\(49\) | 32121.9 | 1.91122 | ||||||||
\(50\) | 2500.00 | 0.141421 | ||||||||
\(51\) | −12893.9 | −0.694158 | ||||||||
\(52\) | 2368.28 | 0.121458 | ||||||||
\(53\) | 37777.3 | 1.84731 | 0.923657 | − | 0.383219i | \(-0.125185\pi\) | ||||
0.923657 | + | 0.383219i | \(0.125185\pi\) | |||||||
\(54\) | −13423.1 | −0.626424 | ||||||||
\(55\) | −12707.5 | −0.566441 | ||||||||
\(56\) | 14156.7 | 0.603244 | ||||||||
\(57\) | 13143.1 | 0.535811 | ||||||||
\(58\) | 27831.0 | 1.08632 | ||||||||
\(59\) | −33536.0 | −1.25424 | −0.627122 | − | 0.778921i | \(-0.715767\pi\) | ||||
−0.627122 | + | 0.778921i | \(0.715767\pi\) | |||||||
\(60\) | −3172.64 | −0.113774 | ||||||||
\(61\) | −26658.3 | −0.917292 | −0.458646 | − | 0.888619i | \(-0.651665\pi\) | ||||
−0.458646 | + | 0.888619i | \(0.651665\pi\) | |||||||
\(62\) | −3254.75 | −0.107532 | ||||||||
\(63\) | −39835.6 | −1.26450 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −3700.44 | −0.108635 | ||||||||
\(66\) | 16126.6 | 0.455704 | ||||||||
\(67\) | −1721.91 | −0.0468623 | −0.0234311 | − | 0.999725i | \(-0.507459\pi\) | ||||
−0.0234311 | + | 0.999725i | \(0.507459\pi\) | |||||||
\(68\) | −26010.2 | −0.682136 | ||||||||
\(69\) | −4195.81 | −0.106095 | ||||||||
\(70\) | −22119.9 | −0.539557 | ||||||||
\(71\) | −39497.2 | −0.929867 | −0.464934 | − | 0.885346i | \(-0.653922\pi\) | ||||
−0.464934 | + | 0.885346i | \(0.653922\pi\) | |||||||
\(72\) | −11525.7 | −0.262022 | ||||||||
\(73\) | −51003.5 | −1.12019 | −0.560096 | − | 0.828428i | \(-0.689236\pi\) | ||||
−0.560096 | + | 0.828428i | \(0.689236\pi\) | |||||||
\(74\) | 54165.7 | 1.14986 | ||||||||
\(75\) | 4957.25 | 0.101762 | ||||||||
\(76\) | 26513.0 | 0.526531 | ||||||||
\(77\) | 112436. | 2.16111 | ||||||||
\(78\) | 4696.06 | 0.0873971 | ||||||||
\(79\) | 60468.8 | 1.09009 | 0.545046 | − | 0.838406i | \(-0.316512\pi\) | ||||
0.545046 | + | 0.838406i | \(0.316512\pi\) | |||||||
\(80\) | −6400.00 | −0.111803 | ||||||||
\(81\) | 17145.1 | 0.290355 | ||||||||
\(82\) | −30009.2 | −0.492856 | ||||||||
\(83\) | 42121.0 | 0.671126 | 0.335563 | − | 0.942018i | \(-0.391073\pi\) | ||||
0.335563 | + | 0.942018i | \(0.391073\pi\) | |||||||
\(84\) | 28071.4 | 0.434075 | ||||||||
\(85\) | 40640.9 | 0.610121 | ||||||||
\(86\) | 32816.7 | 0.478463 | ||||||||
\(87\) | 55186.1 | 0.781685 | ||||||||
\(88\) | 32531.3 | 0.447811 | ||||||||
\(89\) | −86689.6 | −1.16009 | −0.580045 | − | 0.814584i | \(-0.696965\pi\) | ||||
−0.580045 | + | 0.814584i | \(0.696965\pi\) | |||||||
\(90\) | 18009.0 | 0.234360 | ||||||||
\(91\) | 32741.3 | 0.414469 | ||||||||
\(92\) | −8464.00 | −0.104257 | ||||||||
\(93\) | −6453.84 | −0.0773768 | ||||||||
\(94\) | 17393.3 | 0.203031 | ||||||||
\(95\) | −41426.5 | −0.470944 | ||||||||
\(96\) | 8121.95 | 0.0899461 | ||||||||
\(97\) | 19131.8 | 0.206456 | 0.103228 | − | 0.994658i | \(-0.467083\pi\) | ||||
0.103228 | + | 0.994658i | \(0.467083\pi\) | |||||||
\(98\) | 128488. | 1.35144 | ||||||||
\(99\) | −91540.0 | −0.938691 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 67653.5 | 0.659914 | 0.329957 | − | 0.943996i | \(-0.392966\pi\) | ||||
0.329957 | + | 0.943996i | \(0.392966\pi\) | |||||||
\(102\) | −51575.6 | −0.490844 | ||||||||
\(103\) | −84138.0 | −0.781446 | −0.390723 | − | 0.920508i | \(-0.627775\pi\) | ||||
−0.390723 | + | 0.920508i | \(0.627775\pi\) | |||||||
\(104\) | 9473.12 | 0.0858835 | ||||||||
\(105\) | −43861.5 | −0.388249 | ||||||||
\(106\) | 151109. | 1.30625 | ||||||||
\(107\) | 1260.97 | 0.0106475 | 0.00532373 | − | 0.999986i | \(-0.498305\pi\) | ||||
0.00532373 | + | 0.999986i | \(0.498305\pi\) | |||||||
\(108\) | −53692.4 | −0.442949 | ||||||||
\(109\) | 114660. | 0.924368 | 0.462184 | − | 0.886784i | \(-0.347066\pi\) | ||||
0.462184 | + | 0.886784i | \(0.347066\pi\) | |||||||
\(110\) | −50830.2 | −0.400535 | ||||||||
\(111\) | 107405. | 0.827403 | ||||||||
\(112\) | 56626.9 | 0.426558 | ||||||||
\(113\) | −177717. | −1.30928 | −0.654640 | − | 0.755941i | \(-0.727180\pi\) | ||||
−0.654640 | + | 0.755941i | \(0.727180\pi\) | |||||||
\(114\) | 52572.5 | 0.378876 | ||||||||
\(115\) | 13225.0 | 0.0932505 | ||||||||
\(116\) | 111324. | 0.768147 | ||||||||
\(117\) | −26656.4 | −0.180027 | ||||||||
\(118\) | −134144. | −0.886884 | ||||||||
\(119\) | −359589. | −2.32776 | ||||||||
\(120\) | −12690.6 | −0.0804503 | ||||||||
\(121\) | 97319.8 | 0.604279 | ||||||||
\(122\) | −106633. | −0.648623 | ||||||||
\(123\) | −59505.2 | −0.354644 | ||||||||
\(124\) | −13019.0 | −0.0760367 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −159343. | −0.894140 | ||||||||
\(127\) | −195975. | −1.07818 | −0.539089 | − | 0.842249i | \(-0.681231\pi\) | ||||
−0.539089 | + | 0.842249i | \(0.681231\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 65072.1 | 0.344287 | ||||||||
\(130\) | −14801.7 | −0.0768165 | ||||||||
\(131\) | −327925. | −1.66954 | −0.834769 | − | 0.550600i | \(-0.814399\pi\) | ||||
−0.834769 | + | 0.550600i | \(0.814399\pi\) | |||||||
\(132\) | 64506.3 | 0.322231 | ||||||||
\(133\) | 366540. | 1.79677 | ||||||||
\(134\) | −6887.64 | −0.0331366 | ||||||||
\(135\) | 83894.4 | 0.396186 | ||||||||
\(136\) | −104041. | −0.482343 | ||||||||
\(137\) | −97406.4 | −0.443390 | −0.221695 | − | 0.975116i | \(-0.571159\pi\) | ||||
−0.221695 | + | 0.975116i | \(0.571159\pi\) | |||||||
\(138\) | −16783.3 | −0.0750203 | ||||||||
\(139\) | 420401. | 1.84555 | 0.922776 | − | 0.385337i | \(-0.125915\pi\) | ||||
0.922776 | + | 0.385337i | \(0.125915\pi\) | |||||||
\(140\) | −88479.5 | −0.381525 | ||||||||
\(141\) | 34489.1 | 0.146095 | ||||||||
\(142\) | −157989. | −0.657515 | ||||||||
\(143\) | 75237.6 | 0.307677 | ||||||||
\(144\) | −46103.0 | −0.185278 | ||||||||
\(145\) | −173944. | −0.687052 | ||||||||
\(146\) | −204014. | −0.792095 | ||||||||
\(147\) | 254778. | 0.972453 | ||||||||
\(148\) | 216663. | 0.813074 | ||||||||
\(149\) | −474317. | −1.75026 | −0.875131 | − | 0.483887i | \(-0.839225\pi\) | ||||
−0.875131 | + | 0.483887i | \(0.839225\pi\) | |||||||
\(150\) | 19829.0 | 0.0719569 | ||||||||
\(151\) | −198394. | −0.708085 | −0.354043 | − | 0.935229i | \(-0.615193\pi\) | ||||
−0.354043 | + | 0.935229i | \(0.615193\pi\) | |||||||
\(152\) | 106052. | 0.372314 | ||||||||
\(153\) | 292760. | 1.01108 | ||||||||
\(154\) | 449743. | 1.52814 | ||||||||
\(155\) | 20342.2 | 0.0680093 | ||||||||
\(156\) | 18784.2 | 0.0617991 | ||||||||
\(157\) | 35380.4 | 0.114555 | 0.0572774 | − | 0.998358i | \(-0.481758\pi\) | ||||
0.0572774 | + | 0.998358i | \(0.481758\pi\) | |||||||
\(158\) | 241875. | 0.770812 | ||||||||
\(159\) | 299634. | 0.939936 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | −117014. | −0.355774 | ||||||||
\(162\) | 68580.6 | 0.205312 | ||||||||
\(163\) | 109172. | 0.321840 | 0.160920 | − | 0.986967i | \(-0.448554\pi\) | ||||
0.160920 | + | 0.986967i | \(0.448554\pi\) | |||||||
\(164\) | −120037. | −0.348502 | ||||||||
\(165\) | −100791. | −0.288212 | ||||||||
\(166\) | 168484. | 0.474558 | ||||||||
\(167\) | −348050. | −0.965717 | −0.482859 | − | 0.875698i | \(-0.660402\pi\) | ||||
−0.482859 | + | 0.875698i | \(0.660402\pi\) | |||||||
\(168\) | 112285. | 0.306938 | ||||||||
\(169\) | −349384. | −0.940992 | ||||||||
\(170\) | 162564. | 0.431421 | ||||||||
\(171\) | −298420. | −0.780436 | ||||||||
\(172\) | 131267. | 0.338324 | ||||||||
\(173\) | −312017. | −0.792617 | −0.396308 | − | 0.918117i | \(-0.629709\pi\) | ||||
−0.396308 | + | 0.918117i | \(0.629709\pi\) | |||||||
\(174\) | 220745. | 0.552735 | ||||||||
\(175\) | 138249. | 0.341246 | ||||||||
\(176\) | 130125. | 0.316650 | ||||||||
\(177\) | −265994. | −0.638174 | ||||||||
\(178\) | −346758. | −0.820308 | ||||||||
\(179\) | 379189. | 0.884552 | 0.442276 | − | 0.896879i | \(-0.354171\pi\) | ||||
0.442276 | + | 0.896879i | \(0.354171\pi\) | |||||||
\(180\) | 72035.9 | 0.165717 | ||||||||
\(181\) | −372084. | −0.844199 | −0.422099 | − | 0.906550i | \(-0.638707\pi\) | ||||
−0.422099 | + | 0.906550i | \(0.638707\pi\) | |||||||
\(182\) | 130965. | 0.293074 | ||||||||
\(183\) | −211443. | −0.466729 | ||||||||
\(184\) | −33856.0 | −0.0737210 | ||||||||
\(185\) | −338535. | −0.727235 | ||||||||
\(186\) | −25815.4 | −0.0547137 | ||||||||
\(187\) | −826314. | −1.72799 | ||||||||
\(188\) | 69573.1 | 0.143564 | ||||||||
\(189\) | −742294. | −1.51155 | ||||||||
\(190\) | −165706. | −0.333008 | ||||||||
\(191\) | −260701. | −0.517082 | −0.258541 | − | 0.966000i | \(-0.583242\pi\) | ||||
−0.258541 | + | 0.966000i | \(0.583242\pi\) | |||||||
\(192\) | 32487.8 | 0.0636015 | ||||||||
\(193\) | −681976. | −1.31788 | −0.658940 | − | 0.752195i | \(-0.728995\pi\) | ||||
−0.658940 | + | 0.752195i | \(0.728995\pi\) | |||||||
\(194\) | 76527.4 | 0.145986 | ||||||||
\(195\) | −29350.4 | −0.0552748 | ||||||||
\(196\) | 513951. | 0.955611 | ||||||||
\(197\) | 20599.0 | 0.0378165 | 0.0189083 | − | 0.999821i | \(-0.493981\pi\) | ||||
0.0189083 | + | 0.999821i | \(0.493981\pi\) | |||||||
\(198\) | −366160. | −0.663755 | ||||||||
\(199\) | −592413. | −1.06045 | −0.530227 | − | 0.847856i | \(-0.677893\pi\) | ||||
−0.530227 | + | 0.847856i | \(0.677893\pi\) | |||||||
\(200\) | 40000.0 | 0.0707107 | ||||||||
\(201\) | −13657.5 | −0.0238441 | ||||||||
\(202\) | 270614. | 0.466629 | ||||||||
\(203\) | 1.53905e6 | 2.62127 | ||||||||
\(204\) | −206302. | −0.347079 | ||||||||
\(205\) | 187558. | 0.311709 | ||||||||
\(206\) | −336552. | −0.552566 | ||||||||
\(207\) | 95267.5 | 0.154532 | ||||||||
\(208\) | 37892.5 | 0.0607288 | ||||||||
\(209\) | 842287. | 1.33381 | ||||||||
\(210\) | −175446. | −0.274533 | ||||||||
\(211\) | −1.16771e6 | −1.80563 | −0.902817 | − | 0.430025i | \(-0.858505\pi\) | ||||
−0.902817 | + | 0.430025i | \(0.858505\pi\) | |||||||
\(212\) | 604436. | 0.923657 | ||||||||
\(213\) | −313276. | −0.473128 | ||||||||
\(214\) | 5043.89 | 0.00752889 | ||||||||
\(215\) | −205104. | −0.302606 | ||||||||
\(216\) | −214770. | −0.313212 | ||||||||
\(217\) | −179987. | −0.259472 | ||||||||
\(218\) | 458639. | 0.653627 | ||||||||
\(219\) | −404539. | −0.569967 | ||||||||
\(220\) | −203321. | −0.283221 | ||||||||
\(221\) | −240623. | −0.331402 | ||||||||
\(222\) | 429620. | 0.585063 | ||||||||
\(223\) | 222295. | 0.299342 | 0.149671 | − | 0.988736i | \(-0.452179\pi\) | ||||
0.149671 | + | 0.988736i | \(0.452179\pi\) | |||||||
\(224\) | 226508. | 0.301622 | ||||||||
\(225\) | −112556. | −0.148222 | ||||||||
\(226\) | −710868. | −0.925801 | ||||||||
\(227\) | −1.06302e6 | −1.36923 | −0.684613 | − | 0.728907i | \(-0.740029\pi\) | ||||
−0.684613 | + | 0.728907i | \(0.740029\pi\) | |||||||
\(228\) | 210290. | 0.267906 | ||||||||
\(229\) | 1.29480e6 | 1.63160 | 0.815799 | − | 0.578336i | \(-0.196298\pi\) | ||||
0.815799 | + | 0.578336i | \(0.196298\pi\) | |||||||
\(230\) | 52900.0 | 0.0659380 | ||||||||
\(231\) | 891795. | 1.09960 | ||||||||
\(232\) | 445297. | 0.543162 | ||||||||
\(233\) | −48701.5 | −0.0587696 | −0.0293848 | − | 0.999568i | \(-0.509355\pi\) | ||||
−0.0293848 | + | 0.999568i | \(0.509355\pi\) | |||||||
\(234\) | −106626. | −0.127298 | ||||||||
\(235\) | −108708. | −0.128408 | ||||||||
\(236\) | −536577. | −0.627122 | ||||||||
\(237\) | 479614. | 0.554652 | ||||||||
\(238\) | −1.43835e6 | −1.64598 | ||||||||
\(239\) | 1.20769e6 | 1.36761 | 0.683803 | − | 0.729667i | \(-0.260325\pi\) | ||||
0.683803 | + | 0.729667i | \(0.260325\pi\) | |||||||
\(240\) | −50762.2 | −0.0568869 | ||||||||
\(241\) | −709454. | −0.786831 | −0.393415 | − | 0.919361i | \(-0.628707\pi\) | ||||
−0.393415 | + | 0.919361i | \(0.628707\pi\) | |||||||
\(242\) | 389279. | 0.427290 | ||||||||
\(243\) | 951442. | 1.03363 | ||||||||
\(244\) | −426532. | −0.458646 | ||||||||
\(245\) | −803048. | −0.854725 | ||||||||
\(246\) | −238021. | −0.250771 | ||||||||
\(247\) | 245274. | 0.255805 | ||||||||
\(248\) | −52076.0 | −0.0537661 | ||||||||
\(249\) | 334087. | 0.341477 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | −772995. | −0.774448 | −0.387224 | − | 0.921986i | \(-0.626566\pi\) | ||||
−0.387224 | + | 0.921986i | \(0.626566\pi\) | |||||||
\(252\) | −637370. | −0.632252 | ||||||||
\(253\) | −268892. | −0.264105 | ||||||||
\(254\) | −783898. | −0.762387 | ||||||||
\(255\) | 322347. | 0.310437 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −35070.4 | −0.0331213 | −0.0165607 | − | 0.999863i | \(-0.505272\pi\) | ||||
−0.0165607 | + | 0.999863i | \(0.505272\pi\) | |||||||
\(258\) | 260288. | 0.243448 | ||||||||
\(259\) | 2.99535e6 | 2.77458 | ||||||||
\(260\) | −59207.0 | −0.0543175 | ||||||||
\(261\) | −1.25302e6 | −1.13856 | ||||||||
\(262\) | −1.31170e6 | −1.18054 | ||||||||
\(263\) | 318972. | 0.284357 | 0.142178 | − | 0.989841i | \(-0.454589\pi\) | ||||
0.142178 | + | 0.989841i | \(0.454589\pi\) | |||||||
\(264\) | 258025. | 0.227852 | ||||||||
\(265\) | −944432. | −0.826144 | ||||||||
\(266\) | 1.46616e6 | 1.27051 | ||||||||
\(267\) | −687587. | −0.590268 | ||||||||
\(268\) | −27550.6 | −0.0234311 | ||||||||
\(269\) | 2.19198e6 | 1.84695 | 0.923477 | − | 0.383654i | \(-0.125334\pi\) | ||||
0.923477 | + | 0.383654i | \(0.125334\pi\) | |||||||
\(270\) | 335578. | 0.280146 | ||||||||
\(271\) | −94605.3 | −0.0782515 | −0.0391257 | − | 0.999234i | \(-0.512457\pi\) | ||||
−0.0391257 | + | 0.999234i | \(0.512457\pi\) | |||||||
\(272\) | −416163. | −0.341068 | ||||||||
\(273\) | 259691. | 0.210887 | ||||||||
\(274\) | −389626. | −0.313524 | ||||||||
\(275\) | 317689. | 0.253320 | ||||||||
\(276\) | −67133.0 | −0.0530473 | ||||||||
\(277\) | 2.20154e6 | 1.72396 | 0.861980 | − | 0.506942i | \(-0.169224\pi\) | ||||
0.861980 | + | 0.506942i | \(0.169224\pi\) | |||||||
\(278\) | 1.68160e6 | 1.30500 | ||||||||
\(279\) | 146537. | 0.112703 | ||||||||
\(280\) | −353918. | −0.269779 | ||||||||
\(281\) | 2.32212e6 | 1.75436 | 0.877178 | − | 0.480165i | \(-0.159423\pi\) | ||||
0.877178 | + | 0.480165i | \(0.159423\pi\) | |||||||
\(282\) | 137956. | 0.103304 | ||||||||
\(283\) | −1.14696e6 | −0.851297 | −0.425649 | − | 0.904889i | \(-0.639954\pi\) | ||||
−0.425649 | + | 0.904889i | \(0.639954\pi\) | |||||||
\(284\) | −631956. | −0.464934 | ||||||||
\(285\) | −328578. | −0.239622 | ||||||||
\(286\) | 300950. | 0.217560 | ||||||||
\(287\) | −1.65950e6 | −1.18925 | ||||||||
\(288\) | −184412. | −0.131011 | ||||||||
\(289\) | 1.22284e6 | 0.861238 | ||||||||
\(290\) | −695776. | −0.485819 | ||||||||
\(291\) | 151746. | 0.105047 | ||||||||
\(292\) | −816055. | −0.560096 | ||||||||
\(293\) | 869490. | 0.591692 | 0.295846 | − | 0.955236i | \(-0.404398\pi\) | ||||
0.295846 | + | 0.955236i | \(0.404398\pi\) | |||||||
\(294\) | 1.01911e6 | 0.687628 | ||||||||
\(295\) | 838401. | 0.560915 | ||||||||
\(296\) | 866651. | 0.574930 | ||||||||
\(297\) | −1.70575e6 | −1.12208 | ||||||||
\(298\) | −1.89727e6 | −1.23762 | ||||||||
\(299\) | −78301.2 | −0.0506513 | ||||||||
\(300\) | 79316.0 | 0.0508812 | ||||||||
\(301\) | 1.81475e6 | 1.15452 | ||||||||
\(302\) | −793575. | −0.500692 | ||||||||
\(303\) | 536601. | 0.335772 | ||||||||
\(304\) | 424207. | 0.263266 | ||||||||
\(305\) | 666457. | 0.410225 | ||||||||
\(306\) | 1.17104e6 | 0.714939 | ||||||||
\(307\) | −1.63549e6 | −0.990380 | −0.495190 | − | 0.868785i | \(-0.664902\pi\) | ||||
−0.495190 | + | 0.868785i | \(0.664902\pi\) | |||||||
\(308\) | 1.79897e6 | 1.08056 | ||||||||
\(309\) | −667349. | −0.397609 | ||||||||
\(310\) | 81368.7 | 0.0480898 | ||||||||
\(311\) | 677317. | 0.397092 | 0.198546 | − | 0.980092i | \(-0.436378\pi\) | ||||
0.198546 | + | 0.980092i | \(0.436378\pi\) | |||||||
\(312\) | 75137.0 | 0.0436986 | ||||||||
\(313\) | 1.76300e6 | 1.01716 | 0.508581 | − | 0.861014i | \(-0.330170\pi\) | ||||
0.508581 | + | 0.861014i | \(0.330170\pi\) | |||||||
\(314\) | 141521. | 0.0810025 | ||||||||
\(315\) | 995891. | 0.565504 | ||||||||
\(316\) | 967500. | 0.545046 | ||||||||
\(317\) | −2.33802e6 | −1.30678 | −0.653388 | − | 0.757023i | \(-0.726653\pi\) | ||||
−0.653388 | + | 0.757023i | \(0.726653\pi\) | |||||||
\(318\) | 1.19854e6 | 0.664635 | ||||||||
\(319\) | 3.53664e6 | 1.94587 | ||||||||
\(320\) | −102400. | −0.0559017 | ||||||||
\(321\) | 10001.5 | 0.00541756 | ||||||||
\(322\) | −468057. | −0.251570 | ||||||||
\(323\) | −2.69378e6 | −1.43666 | ||||||||
\(324\) | 274322. | 0.145177 | ||||||||
\(325\) | 92510.9 | 0.0485830 | ||||||||
\(326\) | 436686. | 0.227576 | ||||||||
\(327\) | 909436. | 0.470330 | ||||||||
\(328\) | −480147. | −0.246428 | ||||||||
\(329\) | 961843. | 0.489908 | ||||||||
\(330\) | −403165. | −0.203797 | ||||||||
\(331\) | 1.71176e6 | 0.858763 | 0.429382 | − | 0.903123i | \(-0.358732\pi\) | ||||
0.429382 | + | 0.903123i | \(0.358732\pi\) | |||||||
\(332\) | 673937. | 0.335563 | ||||||||
\(333\) | −2.43867e6 | −1.20515 | ||||||||
\(334\) | −1.39220e6 | −0.682865 | ||||||||
\(335\) | 43047.8 | 0.0209575 | ||||||||
\(336\) | 449142. | 0.217038 | ||||||||
\(337\) | −1.87213e6 | −0.897969 | −0.448984 | − | 0.893540i | \(-0.648214\pi\) | ||||
−0.448984 | + | 0.893540i | \(0.648214\pi\) | |||||||
\(338\) | −1.39754e6 | −0.665382 | ||||||||
\(339\) | −1.40958e6 | −0.666178 | ||||||||
\(340\) | 650254. | 0.305061 | ||||||||
\(341\) | −413599. | −0.192616 | ||||||||
\(342\) | −1.19368e6 | −0.551851 | ||||||||
\(343\) | 3.38764e6 | 1.55476 | ||||||||
\(344\) | 525066. | 0.239231 | ||||||||
\(345\) | 104895. | 0.0474470 | ||||||||
\(346\) | −1.24807e6 | −0.560465 | ||||||||
\(347\) | −720471. | −0.321213 | −0.160606 | − | 0.987019i | \(-0.551345\pi\) | ||||
−0.160606 | + | 0.987019i | \(0.551345\pi\) | |||||||
\(348\) | 882978. | 0.390843 | ||||||||
\(349\) | 2.15337e6 | 0.946356 | 0.473178 | − | 0.880967i | \(-0.343107\pi\) | ||||
0.473178 | + | 0.880967i | \(0.343107\pi\) | |||||||
\(350\) | 552997. | 0.241297 | ||||||||
\(351\) | −496714. | −0.215198 | ||||||||
\(352\) | 520501. | 0.223906 | ||||||||
\(353\) | 4.07233e6 | 1.73943 | 0.869713 | − | 0.493559i | \(-0.164304\pi\) | ||||
0.869713 | + | 0.493559i | \(0.164304\pi\) | |||||||
\(354\) | −1.06398e6 | −0.451257 | ||||||||
\(355\) | 987431. | 0.415849 | ||||||||
\(356\) | −1.38703e6 | −0.580045 | ||||||||
\(357\) | −2.85211e6 | −1.18439 | ||||||||
\(358\) | 1.51676e6 | 0.625473 | ||||||||
\(359\) | 1.89142e6 | 0.774555 | 0.387277 | − | 0.921963i | \(-0.373416\pi\) | ||||
0.387277 | + | 0.921963i | \(0.373416\pi\) | |||||||
\(360\) | 288144. | 0.117180 | ||||||||
\(361\) | 269749. | 0.108941 | ||||||||
\(362\) | −1.48834e6 | −0.596939 | ||||||||
\(363\) | 771901. | 0.307465 | ||||||||
\(364\) | 523861. | 0.207235 | ||||||||
\(365\) | 1.27509e6 | 0.500965 | ||||||||
\(366\) | −845771. | −0.330027 | ||||||||
\(367\) | 660710. | 0.256062 | 0.128031 | − | 0.991770i | \(-0.459134\pi\) | ||||
0.128031 | + | 0.991770i | \(0.459134\pi\) | |||||||
\(368\) | −135424. | −0.0521286 | ||||||||
\(369\) | 1.35109e6 | 0.516556 | ||||||||
\(370\) | −1.35414e6 | −0.514233 | ||||||||
\(371\) | 8.35629e6 | 3.15194 | ||||||||
\(372\) | −103261. | −0.0386884 | ||||||||
\(373\) | 228810. | 0.0851535 | 0.0425767 | − | 0.999093i | \(-0.486443\pi\) | ||||
0.0425767 | + | 0.999093i | \(0.486443\pi\) | |||||||
\(374\) | −3.30526e6 | −1.22187 | ||||||||
\(375\) | −123931. | −0.0455095 | ||||||||
\(376\) | 278292. | 0.101515 | ||||||||
\(377\) | 1.02987e6 | 0.373189 | ||||||||
\(378\) | −2.96918e6 | −1.06882 | ||||||||
\(379\) | −879111. | −0.314373 | −0.157187 | − | 0.987569i | \(-0.550242\pi\) | ||||
−0.157187 | + | 0.987569i | \(0.550242\pi\) | |||||||
\(380\) | −662824. | −0.235472 | ||||||||
\(381\) | −1.55439e6 | −0.548590 | ||||||||
\(382\) | −1.04280e6 | −0.365632 | ||||||||
\(383\) | 1.46746e6 | 0.511175 | 0.255588 | − | 0.966786i | \(-0.417731\pi\) | ||||
0.255588 | + | 0.966786i | \(0.417731\pi\) | |||||||
\(384\) | 129951. | 0.0449731 | ||||||||
\(385\) | −2.81089e6 | −0.966480 | ||||||||
\(386\) | −2.72791e6 | −0.931882 | ||||||||
\(387\) | −1.47749e6 | −0.501471 | ||||||||
\(388\) | 306110. | 0.103228 | ||||||||
\(389\) | −4.15891e6 | −1.39349 | −0.696747 | − | 0.717317i | \(-0.745370\pi\) | ||||
−0.696747 | + | 0.717317i | \(0.745370\pi\) | |||||||
\(390\) | −117401. | −0.0390852 | ||||||||
\(391\) | 859961. | 0.284470 | ||||||||
\(392\) | 2.05580e6 | 0.675719 | ||||||||
\(393\) | −2.60097e6 | −0.849481 | ||||||||
\(394\) | 82396.2 | 0.0267403 | ||||||||
\(395\) | −1.51172e6 | −0.487504 | ||||||||
\(396\) | −1.46464e6 | −0.469346 | ||||||||
\(397\) | 382116. | 0.121680 | 0.0608399 | − | 0.998148i | \(-0.480622\pi\) | ||||
0.0608399 | + | 0.998148i | \(0.480622\pi\) | |||||||
\(398\) | −2.36965e6 | −0.749854 | ||||||||
\(399\) | 2.90725e6 | 0.914217 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −1.62999e6 | −0.506202 | −0.253101 | − | 0.967440i | \(-0.581451\pi\) | ||||
−0.253101 | + | 0.967440i | \(0.581451\pi\) | |||||||
\(402\) | −54630.0 | −0.0168603 | ||||||||
\(403\) | −120440. | −0.0369409 | ||||||||
\(404\) | 1.08246e6 | 0.329957 | ||||||||
\(405\) | −428629. | −0.129851 | ||||||||
\(406\) | 6.15619e6 | 1.85352 | ||||||||
\(407\) | 6.88313e6 | 2.05968 | ||||||||
\(408\) | −825209. | −0.245422 | ||||||||
\(409\) | 2.54388e6 | 0.751949 | 0.375975 | − | 0.926630i | \(-0.377308\pi\) | ||||
0.375975 | + | 0.926630i | \(0.377308\pi\) | |||||||
\(410\) | 750230. | 0.220412 | ||||||||
\(411\) | −772588. | −0.225602 | ||||||||
\(412\) | −1.34621e6 | −0.390723 | ||||||||
\(413\) | −7.41813e6 | −2.14003 | ||||||||
\(414\) | 381070. | 0.109271 | ||||||||
\(415\) | −1.05303e6 | −0.300137 | ||||||||
\(416\) | 151570. | 0.0429417 | ||||||||
\(417\) | 3.33445e6 | 0.939039 | ||||||||
\(418\) | 3.36915e6 | 0.943147 | ||||||||
\(419\) | −5.19902e6 | −1.44673 | −0.723363 | − | 0.690468i | \(-0.757405\pi\) | ||||
−0.723363 | + | 0.690468i | \(0.757405\pi\) | |||||||
\(420\) | −701784. | −0.194124 | ||||||||
\(421\) | 1.48220e6 | 0.407569 | 0.203784 | − | 0.979016i | \(-0.434676\pi\) | ||||
0.203784 | + | 0.979016i | \(0.434676\pi\) | |||||||
\(422\) | −4.67085e6 | −1.27678 | ||||||||
\(423\) | −783087. | −0.212794 | ||||||||
\(424\) | 2.41775e6 | 0.653124 | ||||||||
\(425\) | −1.01602e6 | −0.272854 | ||||||||
\(426\) | −1.25310e6 | −0.334552 | ||||||||
\(427\) | −5.89678e6 | −1.56511 | ||||||||
\(428\) | 20175.6 | 0.00532373 | ||||||||
\(429\) | 596754. | 0.156550 | ||||||||
\(430\) | −820416. | −0.213975 | ||||||||
\(431\) | −1.88531e6 | −0.488865 | −0.244432 | − | 0.969666i | \(-0.578602\pi\) | ||||
−0.244432 | + | 0.969666i | \(0.578602\pi\) | |||||||
\(432\) | −859079. | −0.221475 | ||||||||
\(433\) | −4.29778e6 | −1.10160 | −0.550800 | − | 0.834637i | \(-0.685677\pi\) | ||||
−0.550800 | + | 0.834637i | \(0.685677\pi\) | |||||||
\(434\) | −719947. | −0.183475 | ||||||||
\(435\) | −1.37965e6 | −0.349580 | ||||||||
\(436\) | 1.83456e6 | 0.462184 | ||||||||
\(437\) | −876585. | −0.219579 | ||||||||
\(438\) | −1.61816e6 | −0.403028 | ||||||||
\(439\) | −3.24244e6 | −0.802991 | −0.401496 | − | 0.915861i | \(-0.631510\pi\) | ||||
−0.401496 | + | 0.915861i | \(0.631510\pi\) | |||||||
\(440\) | −813283. | −0.200267 | ||||||||
\(441\) | −5.78483e6 | −1.41643 | ||||||||
\(442\) | −962490. | −0.234337 | ||||||||
\(443\) | 5.95768e6 | 1.44234 | 0.721170 | − | 0.692758i | \(-0.243605\pi\) | ||||
0.721170 | + | 0.692758i | \(0.243605\pi\) | |||||||
\(444\) | 1.71848e6 | 0.413702 | ||||||||
\(445\) | 2.16724e6 | 0.518808 | ||||||||
\(446\) | 889180. | 0.211667 | ||||||||
\(447\) | −3.76209e6 | −0.890554 | ||||||||
\(448\) | 906030. | 0.213279 | ||||||||
\(449\) | −5.17530e6 | −1.21149 | −0.605745 | − | 0.795659i | \(-0.707125\pi\) | ||||
−0.605745 | + | 0.795659i | \(0.707125\pi\) | |||||||
\(450\) | −450224. | −0.104809 | ||||||||
\(451\) | −3.81343e6 | −0.882826 | ||||||||
\(452\) | −2.84347e6 | −0.654640 | ||||||||
\(453\) | −1.57358e6 | −0.360282 | ||||||||
\(454\) | −4.25206e6 | −0.968189 | ||||||||
\(455\) | −818532. | −0.185356 | ||||||||
\(456\) | 841160. | 0.189438 | ||||||||
\(457\) | −207637. | −0.0465067 | −0.0232533 | − | 0.999730i | \(-0.507402\pi\) | ||||
−0.0232533 | + | 0.999730i | \(0.507402\pi\) | |||||||
\(458\) | 5.17919e6 | 1.15371 | ||||||||
\(459\) | 5.45527e6 | 1.20861 | ||||||||
\(460\) | 211600. | 0.0466252 | ||||||||
\(461\) | 5.35749e6 | 1.17411 | 0.587056 | − | 0.809547i | \(-0.300287\pi\) | ||||
0.587056 | + | 0.809547i | \(0.300287\pi\) | |||||||
\(462\) | 3.56718e6 | 0.777535 | ||||||||
\(463\) | 497554. | 0.107867 | 0.0539334 | − | 0.998545i | \(-0.482824\pi\) | ||||
0.0539334 | + | 0.998545i | \(0.482824\pi\) | |||||||
\(464\) | 1.78119e6 | 0.384074 | ||||||||
\(465\) | 161346. | 0.0346040 | ||||||||
\(466\) | −194806. | −0.0415564 | ||||||||
\(467\) | −2.16518e6 | −0.459412 | −0.229706 | − | 0.973260i | \(-0.573776\pi\) | ||||
−0.229706 | + | 0.973260i | \(0.573776\pi\) | |||||||
\(468\) | −426503. | −0.0900135 | ||||||||
\(469\) | −380885. | −0.0799579 | ||||||||
\(470\) | −434832. | −0.0907981 | ||||||||
\(471\) | 280623. | 0.0582869 | ||||||||
\(472\) | −2.14631e6 | −0.443442 | ||||||||
\(473\) | 4.17019e6 | 0.857044 | ||||||||
\(474\) | 1.91846e6 | 0.392198 | ||||||||
\(475\) | 1.03566e6 | 0.210613 | ||||||||
\(476\) | −5.75342e6 | −1.16388 | ||||||||
\(477\) | −6.80330e6 | −1.36906 | ||||||||
\(478\) | 4.83076e6 | 0.967043 | ||||||||
\(479\) | −2.48498e6 | −0.494863 | −0.247431 | − | 0.968905i | \(-0.579586\pi\) | ||||
−0.247431 | + | 0.968905i | \(0.579586\pi\) | |||||||
\(480\) | −203049. | −0.0402251 | ||||||||
\(481\) | 2.00437e6 | 0.395016 | ||||||||
\(482\) | −2.83781e6 | −0.556374 | ||||||||
\(483\) | −928109. | −0.181022 | ||||||||
\(484\) | 1.55712e6 | 0.302140 | ||||||||
\(485\) | −478296. | −0.0923299 | ||||||||
\(486\) | 3.80577e6 | 0.730890 | ||||||||
\(487\) | 3.99273e6 | 0.762864 | 0.381432 | − | 0.924397i | \(-0.375431\pi\) | ||||
0.381432 | + | 0.924397i | \(0.375431\pi\) | |||||||
\(488\) | −1.70613e6 | −0.324312 | ||||||||
\(489\) | 865905. | 0.163756 | ||||||||
\(490\) | −3.21219e6 | −0.604382 | ||||||||
\(491\) | −3.97858e6 | −0.744773 | −0.372387 | − | 0.928078i | \(-0.621460\pi\) | ||||
−0.372387 | + | 0.928078i | \(0.621460\pi\) | |||||||
\(492\) | −952084. | −0.177322 | ||||||||
\(493\) | −1.13108e7 | −2.09592 | ||||||||
\(494\) | 981096. | 0.180881 | ||||||||
\(495\) | 2.28850e6 | 0.419795 | ||||||||
\(496\) | −208304. | −0.0380184 | ||||||||
\(497\) | −8.73674e6 | −1.58657 | ||||||||
\(498\) | 1.33635e6 | 0.241461 | ||||||||
\(499\) | 7.33673e6 | 1.31902 | 0.659509 | − | 0.751696i | \(-0.270764\pi\) | ||||
0.659509 | + | 0.751696i | \(0.270764\pi\) | |||||||
\(500\) | −250000. | −0.0447214 | ||||||||
\(501\) | −2.76059e6 | −0.491369 | ||||||||
\(502\) | −3.09198e6 | −0.547617 | ||||||||
\(503\) | 1.23312e6 | 0.217312 | 0.108656 | − | 0.994079i | \(-0.465345\pi\) | ||||
0.108656 | + | 0.994079i | \(0.465345\pi\) | |||||||
\(504\) | −2.54948e6 | −0.447070 | ||||||||
\(505\) | −1.69134e6 | −0.295122 | ||||||||
\(506\) | −1.07557e6 | −0.186750 | ||||||||
\(507\) | −2.77117e6 | −0.478788 | ||||||||
\(508\) | −3.13559e6 | −0.539089 | ||||||||
\(509\) | −3.69590e6 | −0.632304 | −0.316152 | − | 0.948709i | \(-0.602391\pi\) | ||||
−0.316152 | + | 0.948709i | \(0.602391\pi\) | |||||||
\(510\) | 1.28939e6 | 0.219512 | ||||||||
\(511\) | −1.12819e7 | −1.91131 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −5.56072e6 | −0.932906 | ||||||||
\(514\) | −140282. | −0.0234203 | ||||||||
\(515\) | 2.10345e6 | 0.349473 | ||||||||
\(516\) | 1.04115e6 | 0.172144 | ||||||||
\(517\) | 2.21026e6 | 0.363678 | ||||||||
\(518\) | 1.19814e7 | 1.96193 | ||||||||
\(519\) | −2.47479e6 | −0.403293 | ||||||||
\(520\) | −236828. | −0.0384083 | ||||||||
\(521\) | −1.80338e6 | −0.291067 | −0.145533 | − | 0.989353i | \(-0.546490\pi\) | ||||
−0.145533 | + | 0.989353i | \(0.546490\pi\) | |||||||
\(522\) | −5.01209e6 | −0.805086 | ||||||||
\(523\) | 455239. | 0.0727755 | 0.0363878 | − | 0.999338i | \(-0.488415\pi\) | ||||
0.0363878 | + | 0.999338i | \(0.488415\pi\) | |||||||
\(524\) | −5.24680e6 | −0.834769 | ||||||||
\(525\) | 1.09654e6 | 0.173630 | ||||||||
\(526\) | 1.27589e6 | 0.201070 | ||||||||
\(527\) | 1.32276e6 | 0.207470 | ||||||||
\(528\) | 1.03210e6 | 0.161116 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −3.77773e6 | −0.584172 | ||||||||
\(531\) | 6.03950e6 | 0.929532 | ||||||||
\(532\) | 5.86464e6 | 0.898384 | ||||||||
\(533\) | −1.11047e6 | −0.169313 | ||||||||
\(534\) | −2.75035e6 | −0.417383 | ||||||||
\(535\) | −31524.3 | −0.00476169 | ||||||||
\(536\) | −110202. | −0.0165683 | ||||||||
\(537\) | 3.00758e6 | 0.450071 | ||||||||
\(538\) | 8.76792e6 | 1.30599 | ||||||||
\(539\) | 1.63276e7 | 2.42076 | ||||||||
\(540\) | 1.34231e6 | 0.198093 | ||||||||
\(541\) | 1.32966e7 | 1.95321 | 0.976603 | − | 0.215048i | \(-0.0689909\pi\) | ||||
0.976603 | + | 0.215048i | \(0.0689909\pi\) | |||||||
\(542\) | −378421. | −0.0553321 | ||||||||
\(543\) | −2.95122e6 | −0.429539 | ||||||||
\(544\) | −1.66465e6 | −0.241172 | ||||||||
\(545\) | −2.86650e6 | −0.413390 | ||||||||
\(546\) | 1.03876e6 | 0.149120 | ||||||||
\(547\) | 4.51679e6 | 0.645449 | 0.322724 | − | 0.946493i | \(-0.395401\pi\) | ||||
0.322724 | + | 0.946493i | \(0.395401\pi\) | |||||||
\(548\) | −1.55850e6 | −0.221695 | ||||||||
\(549\) | 4.80088e6 | 0.679814 | ||||||||
\(550\) | 1.27075e6 | 0.179124 | ||||||||
\(551\) | 1.15294e7 | 1.61781 | ||||||||
\(552\) | −268532. | −0.0375101 | ||||||||
\(553\) | 1.33756e7 | 1.85995 | ||||||||
\(554\) | 8.80616e6 | 1.21902 | ||||||||
\(555\) | −2.68513e6 | −0.370026 | ||||||||
\(556\) | 6.72641e6 | 0.922776 | ||||||||
\(557\) | −1.43003e7 | −1.95303 | −0.976514 | − | 0.215456i | \(-0.930876\pi\) | ||||
−0.976514 | + | 0.215456i | \(0.930876\pi\) | |||||||
\(558\) | 586147. | 0.0796932 | ||||||||
\(559\) | 1.21436e6 | 0.164368 | ||||||||
\(560\) | −1.41567e6 | −0.190762 | ||||||||
\(561\) | −6.55399e6 | −0.879222 | ||||||||
\(562\) | 9.28846e6 | 1.24052 | ||||||||
\(563\) | −362252. | −0.0481659 | −0.0240830 | − | 0.999710i | \(-0.507667\pi\) | ||||
−0.0240830 | + | 0.999710i | \(0.507667\pi\) | |||||||
\(564\) | 551826. | 0.0730473 | ||||||||
\(565\) | 4.44292e6 | 0.585528 | ||||||||
\(566\) | −4.58783e6 | −0.601958 | ||||||||
\(567\) | 3.79249e6 | 0.495412 | ||||||||
\(568\) | −2.52782e6 | −0.328758 | ||||||||
\(569\) | 1.12892e7 | 1.46178 | 0.730889 | − | 0.682497i | \(-0.239106\pi\) | ||||
0.730889 | + | 0.682497i | \(0.239106\pi\) | |||||||
\(570\) | −1.31431e6 | −0.169438 | ||||||||
\(571\) | −7.90939e6 | −1.01520 | −0.507602 | − | 0.861592i | \(-0.669468\pi\) | ||||
−0.507602 | + | 0.861592i | \(0.669468\pi\) | |||||||
\(572\) | 1.20380e6 | 0.153838 | ||||||||
\(573\) | −2.06778e6 | −0.263098 | ||||||||
\(574\) | −6.63800e6 | −0.840926 | ||||||||
\(575\) | −330625. | −0.0417029 | ||||||||
\(576\) | −737648. | −0.0926388 | ||||||||
\(577\) | −1.20265e7 | −1.50384 | −0.751919 | − | 0.659256i | \(-0.770871\pi\) | ||||
−0.751919 | + | 0.659256i | \(0.770871\pi\) | |||||||
\(578\) | 4.89134e6 | 0.608987 | ||||||||
\(579\) | −5.40916e6 | −0.670554 | ||||||||
\(580\) | −2.78310e6 | −0.343526 | ||||||||
\(581\) | 9.31713e6 | 1.14510 | ||||||||
\(582\) | 606984. | 0.0742797 | ||||||||
\(583\) | 1.92023e7 | 2.33981 | ||||||||
\(584\) | −3.26422e6 | −0.396048 | ||||||||
\(585\) | 666411. | 0.0805105 | ||||||||
\(586\) | 3.47796e6 | 0.418389 | ||||||||
\(587\) | 1.73287e6 | 0.207573 | 0.103787 | − | 0.994600i | \(-0.466904\pi\) | ||||
0.103787 | + | 0.994600i | \(0.466904\pi\) | |||||||
\(588\) | 4.07645e6 | 0.486227 | ||||||||
\(589\) | −1.34833e6 | −0.160143 | ||||||||
\(590\) | 3.35360e6 | 0.396627 | ||||||||
\(591\) | 163383. | 0.0192415 | ||||||||
\(592\) | 3.46660e6 | 0.406537 | ||||||||
\(593\) | −511607. | −0.0597448 | −0.0298724 | − | 0.999554i | \(-0.509510\pi\) | ||||
−0.0298724 | + | 0.999554i | \(0.509510\pi\) | |||||||
\(594\) | −6.82299e6 | −0.793430 | ||||||||
\(595\) | 8.98972e6 | 1.04101 | ||||||||
\(596\) | −7.58907e6 | −0.875131 | ||||||||
\(597\) | −4.69878e6 | −0.539572 | ||||||||
\(598\) | −313205. | −0.0358159 | ||||||||
\(599\) | −1.10348e7 | −1.25660 | −0.628299 | − | 0.777972i | \(-0.716249\pi\) | ||||
−0.628299 | + | 0.777972i | \(0.716249\pi\) | |||||||
\(600\) | 317264. | 0.0359785 | ||||||||
\(601\) | 5.47736e6 | 0.618564 | 0.309282 | − | 0.950970i | \(-0.399911\pi\) | ||||
0.309282 | + | 0.950970i | \(0.399911\pi\) | |||||||
\(602\) | 7.25901e6 | 0.816368 | ||||||||
\(603\) | 310098. | 0.0347301 | ||||||||
\(604\) | −3.17430e6 | −0.354043 | ||||||||
\(605\) | −2.43299e6 | −0.270242 | ||||||||
\(606\) | 2.14640e6 | 0.237427 | ||||||||
\(607\) | 1.50745e7 | 1.66063 | 0.830313 | − | 0.557297i | \(-0.188162\pi\) | ||||
0.830313 | + | 0.557297i | \(0.188162\pi\) | |||||||
\(608\) | 1.69683e6 | 0.186157 | ||||||||
\(609\) | 1.22071e7 | 1.33374 | ||||||||
\(610\) | 2.66583e6 | 0.290073 | ||||||||
\(611\) | 643627. | 0.0697479 | ||||||||
\(612\) | 4.68417e6 | 0.505538 | ||||||||
\(613\) | −1.60324e7 | −1.72325 | −0.861624 | − | 0.507548i | \(-0.830552\pi\) | ||||
−0.861624 | + | 0.507548i | \(0.830552\pi\) | |||||||
\(614\) | −6.54196e6 | −0.700304 | ||||||||
\(615\) | 1.48763e6 | 0.158602 | ||||||||
\(616\) | 7.19589e6 | 0.764069 | ||||||||
\(617\) | −1.81041e7 | −1.91454 | −0.957269 | − | 0.289199i | \(-0.906611\pi\) | ||||
−0.957269 | + | 0.289199i | \(0.906611\pi\) | |||||||
\(618\) | −2.66939e6 | −0.281152 | ||||||||
\(619\) | 1.07745e7 | 1.13024 | 0.565118 | − | 0.825010i | \(-0.308831\pi\) | ||||
0.565118 | + | 0.825010i | \(0.308831\pi\) | |||||||
\(620\) | 325475. | 0.0340046 | ||||||||
\(621\) | 1.77521e6 | 0.184723 | ||||||||
\(622\) | 2.70927e6 | 0.280786 | ||||||||
\(623\) | −1.91756e7 | −1.97938 | ||||||||
\(624\) | 300548. | 0.0308995 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 7.05198e6 | 0.719243 | ||||||||
\(627\) | 6.68068e6 | 0.678659 | ||||||||
\(628\) | 566086. | 0.0572774 | ||||||||
\(629\) | −2.20134e7 | −2.21851 | ||||||||
\(630\) | 3.98356e6 | 0.399872 | ||||||||
\(631\) | −4926.90 | −0.000492607 0 | −0.000246304 | − | 1.00000i | \(-0.500078\pi\) | ||||
−0.000246304 | 1.00000i | \(0.500078\pi\) | ||||||||
\(632\) | 3.87000e6 | 0.385406 | ||||||||
\(633\) | −9.26182e6 | −0.918728 | ||||||||
\(634\) | −9.35210e6 | −0.924030 | ||||||||
\(635\) | 4.89936e6 | 0.482176 | ||||||||
\(636\) | 4.79415e6 | 0.469968 | ||||||||
\(637\) | 4.75461e6 | 0.464265 | ||||||||
\(638\) | 1.41466e7 | 1.37594 | ||||||||
\(639\) | 7.11305e6 | 0.689134 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | 1.18363e7 | 1.13781 | 0.568906 | − | 0.822403i | \(-0.307367\pi\) | ||||
0.568906 | + | 0.822403i | \(0.307367\pi\) | |||||||
\(642\) | 40006.1 | 0.00383079 | ||||||||
\(643\) | 1.28400e6 | 0.122472 | 0.0612362 | − | 0.998123i | \(-0.480496\pi\) | ||||
0.0612362 | + | 0.998123i | \(0.480496\pi\) | |||||||
\(644\) | −1.87223e6 | −0.177887 | ||||||||
\(645\) | −1.62680e6 | −0.153970 | ||||||||
\(646\) | −1.07751e7 | −1.01587 | ||||||||
\(647\) | −9.98021e6 | −0.937301 | −0.468650 | − | 0.883384i | \(-0.655260\pi\) | ||||
−0.468650 | + | 0.883384i | \(0.655260\pi\) | |||||||
\(648\) | 1.09729e6 | 0.102656 | ||||||||
\(649\) | −1.70464e7 | −1.58863 | ||||||||
\(650\) | 370044. | 0.0343534 | ||||||||
\(651\) | −1.42758e6 | −0.132023 | ||||||||
\(652\) | 1.74675e6 | 0.160920 | ||||||||
\(653\) | 1.09561e7 | 1.00548 | 0.502740 | − | 0.864438i | \(-0.332325\pi\) | ||||
0.502740 | + | 0.864438i | \(0.332325\pi\) | |||||||
\(654\) | 3.63774e6 | 0.332573 | ||||||||
\(655\) | 8.19813e6 | 0.746640 | ||||||||
\(656\) | −1.92059e6 | −0.174251 | ||||||||
\(657\) | 9.18520e6 | 0.830186 | ||||||||
\(658\) | 3.84737e6 | 0.346417 | ||||||||
\(659\) | 1.98759e7 | 1.78284 | 0.891420 | − | 0.453177i | \(-0.149710\pi\) | ||||
0.891420 | + | 0.453177i | \(0.149710\pi\) | |||||||
\(660\) | −1.61266e6 | −0.144106 | ||||||||
\(661\) | −1.50432e7 | −1.33917 | −0.669585 | − | 0.742736i | \(-0.733528\pi\) | ||||
−0.669585 | + | 0.742736i | \(0.733528\pi\) | |||||||
\(662\) | 6.84705e6 | 0.607237 | ||||||||
\(663\) | −1.90852e6 | −0.168622 | ||||||||
\(664\) | 2.69575e6 | 0.237279 | ||||||||
\(665\) | −9.16349e6 | −0.803539 | ||||||||
\(666\) | −9.75468e6 | −0.852173 | ||||||||
\(667\) | −3.68066e6 | −0.320340 | ||||||||
\(668\) | −5.56879e6 | −0.482859 | ||||||||
\(669\) | 1.76315e6 | 0.152309 | ||||||||
\(670\) | 172191. | 0.0148192 | ||||||||
\(671\) | −1.35504e7 | −1.16184 | ||||||||
\(672\) | 1.79657e6 | 0.153469 | ||||||||
\(673\) | −1.72807e6 | −0.147070 | −0.0735351 | − | 0.997293i | \(-0.523428\pi\) | ||||
−0.0735351 | + | 0.997293i | \(0.523428\pi\) | |||||||
\(674\) | −7.48852e6 | −0.634960 | ||||||||
\(675\) | −2.09736e6 | −0.177180 | ||||||||
\(676\) | −5.59014e6 | −0.470496 | ||||||||
\(677\) | −3.83766e6 | −0.321807 | −0.160903 | − | 0.986970i | \(-0.551441\pi\) | ||||
−0.160903 | + | 0.986970i | \(0.551441\pi\) | |||||||
\(678\) | −5.63832e6 | −0.471059 | ||||||||
\(679\) | 4.23194e6 | 0.352262 | ||||||||
\(680\) | 2.60102e6 | 0.215710 | ||||||||
\(681\) | −8.43141e6 | −0.696678 | ||||||||
\(682\) | −1.65440e6 | −0.136200 | ||||||||
\(683\) | −1.96704e7 | −1.61347 | −0.806737 | − | 0.590910i | \(-0.798769\pi\) | ||||
−0.806737 | + | 0.590910i | \(0.798769\pi\) | |||||||
\(684\) | −4.77471e6 | −0.390218 | ||||||||
\(685\) | 2.43516e6 | 0.198290 | ||||||||
\(686\) | 1.35506e7 | 1.09938 | ||||||||
\(687\) | 1.02698e7 | 0.830177 | ||||||||
\(688\) | 2.10027e6 | 0.169162 | ||||||||
\(689\) | 5.59170e6 | 0.448741 | ||||||||
\(690\) | 419581. | 0.0335501 | ||||||||
\(691\) | −2.06835e6 | −0.164790 | −0.0823948 | − | 0.996600i | \(-0.526257\pi\) | ||||
−0.0823948 | + | 0.996600i | \(0.526257\pi\) | |||||||
\(692\) | −4.99228e6 | −0.396308 | ||||||||
\(693\) | −2.02485e7 | −1.60162 | ||||||||
\(694\) | −2.88189e6 | −0.227132 | ||||||||
\(695\) | −1.05100e7 | −0.825356 | ||||||||
\(696\) | 3.53191e6 | 0.276367 | ||||||||
\(697\) | 1.21960e7 | 0.950902 | ||||||||
\(698\) | 8.61347e6 | 0.669174 | ||||||||
\(699\) | −386281. | −0.0299027 | ||||||||
\(700\) | 2.21199e6 | 0.170623 | ||||||||
\(701\) | −2.26675e6 | −0.174225 | −0.0871123 | − | 0.996198i | \(-0.527764\pi\) | ||||
−0.0871123 | + | 0.996198i | \(0.527764\pi\) | |||||||
\(702\) | −1.98685e6 | −0.152168 | ||||||||
\(703\) | 2.24389e7 | 1.71244 | ||||||||
\(704\) | 2.08200e6 | 0.158325 | ||||||||
\(705\) | −862227. | −0.0653355 | ||||||||
\(706\) | 1.62893e7 | 1.22996 | ||||||||
\(707\) | 1.49649e7 | 1.12596 | ||||||||
\(708\) | −4.25591e6 | −0.319087 | ||||||||
\(709\) | 4.88196e6 | 0.364736 | 0.182368 | − | 0.983230i | \(-0.441624\pi\) | ||||
0.182368 | + | 0.983230i | \(0.441624\pi\) | |||||||
\(710\) | 3.94972e6 | 0.294050 | ||||||||
\(711\) | −1.08898e7 | −0.807879 | ||||||||
\(712\) | −5.54813e6 | −0.410154 | ||||||||
\(713\) | 430441. | 0.0317095 | ||||||||
\(714\) | −1.14085e7 | −0.837493 | ||||||||
\(715\) | −1.88094e6 | −0.137597 | ||||||||
\(716\) | 6.06703e6 | 0.442276 | ||||||||
\(717\) | 9.57891e6 | 0.695854 | ||||||||
\(718\) | 7.56568e6 | 0.547693 | ||||||||
\(719\) | −9.79754e6 | −0.706797 | −0.353399 | − | 0.935473i | \(-0.614974\pi\) | ||||
−0.353399 | + | 0.935473i | \(0.614974\pi\) | |||||||
\(720\) | 1.15257e6 | 0.0828586 | ||||||||
\(721\) | −1.86112e7 | −1.33333 | ||||||||
\(722\) | 1.07900e6 | 0.0770331 | ||||||||
\(723\) | −5.62710e6 | −0.400349 | ||||||||
\(724\) | −5.95335e6 | −0.422099 | ||||||||
\(725\) | 4.34860e6 | 0.307259 | ||||||||
\(726\) | 3.08760e6 | 0.217410 | ||||||||
\(727\) | −1.45372e6 | −0.102010 | −0.0510052 | − | 0.998698i | \(-0.516243\pi\) | ||||
−0.0510052 | + | 0.998698i | \(0.516243\pi\) | |||||||
\(728\) | 2.09544e6 | 0.146537 | ||||||||
\(729\) | 3.38019e6 | 0.235571 | ||||||||
\(730\) | 5.10035e6 | 0.354236 | ||||||||
\(731\) | −1.33370e7 | −0.923133 | ||||||||
\(732\) | −3.38308e6 | −0.233365 | ||||||||
\(733\) | 1.90099e7 | 1.30683 | 0.653417 | − | 0.756999i | \(-0.273335\pi\) | ||||
0.653417 | + | 0.756999i | \(0.273335\pi\) | |||||||
\(734\) | 2.64284e6 | 0.181063 | ||||||||
\(735\) | −6.36945e6 | −0.434894 | ||||||||
\(736\) | −541696. | −0.0368605 | ||||||||
\(737\) | −875250. | −0.0593558 | ||||||||
\(738\) | 5.40435e6 | 0.365261 | ||||||||
\(739\) | 1.67293e7 | 1.12685 | 0.563425 | − | 0.826167i | \(-0.309483\pi\) | ||||
0.563425 | + | 0.826167i | \(0.309483\pi\) | |||||||
\(740\) | −5.41657e6 | −0.363618 | ||||||||
\(741\) | 1.94541e6 | 0.130157 | ||||||||
\(742\) | 3.34252e7 | 2.22876 | ||||||||
\(743\) | −3.02797e6 | −0.201224 | −0.100612 | − | 0.994926i | \(-0.532080\pi\) | ||||
−0.100612 | + | 0.994926i | \(0.532080\pi\) | |||||||
\(744\) | −413046. | −0.0273568 | ||||||||
\(745\) | 1.18579e7 | 0.782741 | ||||||||
\(746\) | 915239. | 0.0602126 | ||||||||
\(747\) | −7.58557e6 | −0.497378 | ||||||||
\(748\) | −1.32210e7 | −0.863994 | ||||||||
\(749\) | 278926. | 0.0181670 | ||||||||
\(750\) | −495725. | −0.0321801 | ||||||||
\(751\) | −3.45504e6 | −0.223539 | −0.111770 | − | 0.993734i | \(-0.535652\pi\) | ||||
−0.111770 | + | 0.993734i | \(0.535652\pi\) | |||||||
\(752\) | 1.11317e6 | 0.0717822 | ||||||||
\(753\) | −6.13108e6 | −0.394049 | ||||||||
\(754\) | 4.11948e6 | 0.263885 | ||||||||
\(755\) | 4.95984e6 | 0.316665 | ||||||||
\(756\) | −1.18767e7 | −0.755773 | ||||||||
\(757\) | 1.99821e7 | 1.26736 | 0.633681 | − | 0.773594i | \(-0.281543\pi\) | ||||
0.633681 | + | 0.773594i | \(0.281543\pi\) | |||||||
\(758\) | −3.51644e6 | −0.222295 | ||||||||
\(759\) | −2.13274e6 | −0.134380 | ||||||||
\(760\) | −2.65130e6 | −0.166504 | ||||||||
\(761\) | 1.21696e7 | 0.761755 | 0.380877 | − | 0.924626i | \(-0.375622\pi\) | ||||
0.380877 | + | 0.924626i | \(0.375622\pi\) | |||||||
\(762\) | −6.21756e6 | −0.387912 | ||||||||
\(763\) | 2.53626e7 | 1.57719 | ||||||||
\(764\) | −4.17122e6 | −0.258541 | ||||||||
\(765\) | −7.31901e6 | −0.452167 | ||||||||
\(766\) | 5.86985e6 | 0.361455 | ||||||||
\(767\) | −4.96392e6 | −0.304675 | ||||||||
\(768\) | 519805. | 0.0318008 | ||||||||
\(769\) | 3.01762e7 | 1.84013 | 0.920066 | − | 0.391764i | \(-0.128135\pi\) | ||||
0.920066 | + | 0.391764i | \(0.128135\pi\) | |||||||
\(770\) | −1.12436e7 | −0.683404 | ||||||||
\(771\) | −278164. | −0.0168525 | ||||||||
\(772\) | −1.09116e7 | −0.658940 | ||||||||
\(773\) | 1.85630e6 | 0.111737 | 0.0558687 | − | 0.998438i | \(-0.482207\pi\) | ||||
0.0558687 | + | 0.998438i | \(0.482207\pi\) | |||||||
\(774\) | −5.90994e6 | −0.354594 | ||||||||
\(775\) | −508555. | −0.0304147 | ||||||||
\(776\) | 1.22444e6 | 0.0729932 | ||||||||
\(777\) | 2.37579e7 | 1.41174 | ||||||||
\(778\) | −1.66356e7 | −0.985350 | ||||||||
\(779\) | −1.24318e7 | −0.733988 | ||||||||
\(780\) | −469606. | −0.0276374 | ||||||||
\(781\) | −2.00765e7 | −1.17777 | ||||||||
\(782\) | 3.43985e6 | 0.201151 | ||||||||
\(783\) | −2.33487e7 | −1.36100 | ||||||||
\(784\) | 8.22321e6 | 0.477806 | ||||||||
\(785\) | −884509. | −0.0512305 | ||||||||
\(786\) | −1.04039e7 | −0.600674 | ||||||||
\(787\) | 9.60964e6 | 0.553058 | 0.276529 | − | 0.961006i | \(-0.410816\pi\) | ||||
0.276529 | + | 0.961006i | \(0.410816\pi\) | |||||||
\(788\) | 329585. | 0.0189083 | ||||||||
\(789\) | 2.52996e6 | 0.144684 | ||||||||
\(790\) | −6.04688e6 | −0.344718 | ||||||||
\(791\) | −3.93108e7 | −2.23393 | ||||||||
\(792\) | −5.85856e6 | −0.331877 | ||||||||
\(793\) | −3.94589e6 | −0.222824 | ||||||||
\(794\) | 1.52846e6 | 0.0860406 | ||||||||
\(795\) | −7.49085e6 | −0.420352 | ||||||||
\(796\) | −9.47861e6 | −0.530227 | ||||||||
\(797\) | −2.16173e7 | −1.20547 | −0.602734 | − | 0.797942i | \(-0.705922\pi\) | ||||
−0.602734 | + | 0.797942i | \(0.705922\pi\) | |||||||
\(798\) | 1.16290e7 | 0.646449 | ||||||||
\(799\) | −7.06878e6 | −0.391722 | ||||||||
\(800\) | 640000. | 0.0353553 | ||||||||
\(801\) | 1.56119e7 | 0.859755 | ||||||||
\(802\) | −6.51996e6 | −0.357939 | ||||||||
\(803\) | −2.59252e7 | −1.41884 | ||||||||
\(804\) | −218520. | −0.0119221 | ||||||||
\(805\) | 2.92535e6 | 0.159107 | ||||||||
\(806\) | −481760. | −0.0261212 | ||||||||
\(807\) | 1.73859e7 | 0.939753 | ||||||||
\(808\) | 4.32983e6 | 0.233315 | ||||||||
\(809\) | 7.92785e6 | 0.425877 | 0.212938 | − | 0.977066i | \(-0.431697\pi\) | ||||
0.212938 | + | 0.977066i | \(0.431697\pi\) | |||||||
\(810\) | −1.71451e6 | −0.0918182 | ||||||||
\(811\) | 3.63619e7 | 1.94131 | 0.970654 | − | 0.240480i | \(-0.0773047\pi\) | ||||
0.970654 | + | 0.240480i | \(0.0773047\pi\) | |||||||
\(812\) | 2.46248e7 | 1.31064 | ||||||||
\(813\) | −750371. | −0.0398153 | ||||||||
\(814\) | 2.75325e7 | 1.45641 | ||||||||
\(815\) | −2.72929e6 | −0.143931 | ||||||||
\(816\) | −3.30084e6 | −0.173540 | ||||||||
\(817\) | 1.35948e7 | 0.712553 | ||||||||
\(818\) | 1.01755e7 | 0.531708 | ||||||||
\(819\) | −5.89637e6 | −0.307167 | ||||||||
\(820\) | 3.00092e6 | 0.155855 | ||||||||
\(821\) | −3.29493e7 | −1.70604 | −0.853018 | − | 0.521881i | \(-0.825230\pi\) | ||||
−0.853018 | + | 0.521881i | \(0.825230\pi\) | |||||||
\(822\) | −3.09035e6 | −0.159525 | ||||||||
\(823\) | −3.14482e7 | −1.61844 | −0.809218 | − | 0.587508i | \(-0.800109\pi\) | ||||
−0.809218 | + | 0.587508i | \(0.800109\pi\) | |||||||
\(824\) | −5.38483e6 | −0.276283 | ||||||||
\(825\) | 2.51978e6 | 0.128892 | ||||||||
\(826\) | −2.96725e7 | −1.51323 | ||||||||
\(827\) | 3.47551e7 | 1.76707 | 0.883537 | − | 0.468361i | \(-0.155155\pi\) | ||||
0.883537 | + | 0.468361i | \(0.155155\pi\) | |||||||
\(828\) | 1.52428e6 | 0.0772661 | ||||||||
\(829\) | −2.66691e6 | −0.134779 | −0.0673895 | − | 0.997727i | \(-0.521467\pi\) | ||||
−0.0673895 | + | 0.997727i | \(0.521467\pi\) | |||||||
\(830\) | −4.21210e6 | −0.212229 | ||||||||
\(831\) | 1.74617e7 | 0.877172 | ||||||||
\(832\) | 606280. | 0.0303644 | ||||||||
\(833\) | −5.22185e7 | −2.60743 | ||||||||
\(834\) | 1.33378e7 | 0.664001 | ||||||||
\(835\) | 8.70124e6 | 0.431882 | ||||||||
\(836\) | 1.34766e7 | 0.666905 | ||||||||
\(837\) | 2.73055e6 | 0.134722 | ||||||||
\(838\) | −2.07961e7 | −1.02299 | ||||||||
\(839\) | −2.87306e7 | −1.40909 | −0.704546 | − | 0.709658i | \(-0.748849\pi\) | ||||
−0.704546 | + | 0.709658i | \(0.748849\pi\) | |||||||
\(840\) | −2.80714e6 | −0.137267 | ||||||||
\(841\) | 2.78993e7 | 1.36020 | ||||||||
\(842\) | 5.92879e6 | 0.288195 | ||||||||
\(843\) | 1.84181e7 | 0.892638 | ||||||||
\(844\) | −1.86834e7 | −0.902817 | ||||||||
\(845\) | 8.73460e6 | 0.420825 | ||||||||
\(846\) | −3.13235e6 | −0.150468 | ||||||||
\(847\) | 2.15270e7 | 1.03104 | ||||||||
\(848\) | 9.67098e6 | 0.461829 | ||||||||
\(849\) | −9.09720e6 | −0.433150 | ||||||||
\(850\) | −4.06409e6 | −0.192937 | ||||||||
\(851\) | −7.16341e6 | −0.339075 | ||||||||
\(852\) | −5.01242e6 | −0.236564 | ||||||||
\(853\) | −1.79041e7 | −0.842521 | −0.421260 | − | 0.906940i | \(-0.638412\pi\) | ||||
−0.421260 | + | 0.906940i | \(0.638412\pi\) | |||||||
\(854\) | −2.35871e7 | −1.10670 | ||||||||
\(855\) | 7.46049e6 | 0.349021 | ||||||||
\(856\) | 80702.2 | 0.00376445 | ||||||||
\(857\) | 1.08685e7 | 0.505494 | 0.252747 | − | 0.967532i | \(-0.418666\pi\) | ||||
0.252747 | + | 0.967532i | \(0.418666\pi\) | |||||||
\(858\) | 2.38702e6 | 0.110697 | ||||||||
\(859\) | 2.96355e6 | 0.137034 | 0.0685172 | − | 0.997650i | \(-0.478173\pi\) | ||||
0.0685172 | + | 0.997650i | \(0.478173\pi\) | |||||||
\(860\) | −3.28167e6 | −0.151303 | ||||||||
\(861\) | −1.31625e7 | −0.605104 | ||||||||
\(862\) | −7.54122e6 | −0.345680 | ||||||||
\(863\) | −3.16541e7 | −1.44678 | −0.723391 | − | 0.690438i | \(-0.757418\pi\) | ||||
−0.723391 | + | 0.690438i | \(0.757418\pi\) | |||||||
\(864\) | −3.43632e6 | −0.156606 | ||||||||
\(865\) | 7.80043e6 | 0.354469 | ||||||||
\(866\) | −1.71911e7 | −0.778949 | ||||||||
\(867\) | 9.69903e6 | 0.438208 | ||||||||
\(868\) | −2.87979e6 | −0.129736 | ||||||||
\(869\) | 3.07364e7 | 1.38071 | ||||||||
\(870\) | −5.51861e6 | −0.247191 | ||||||||
\(871\) | −254873. | −0.0113836 | ||||||||
\(872\) | 7.33823e6 | 0.326814 | ||||||||
\(873\) | −3.44545e6 | −0.153007 | ||||||||
\(874\) | −3.50634e6 | −0.155266 | ||||||||
\(875\) | −3.45623e6 | −0.152610 | ||||||||
\(876\) | −6.47262e6 | −0.284984 | ||||||||
\(877\) | 3.92674e7 | 1.72398 | 0.861992 | − | 0.506921i | \(-0.169217\pi\) | ||||
0.861992 | + | 0.506921i | \(0.169217\pi\) | |||||||
\(878\) | −1.29698e7 | −0.567801 | ||||||||
\(879\) | 6.89645e6 | 0.301060 | ||||||||
\(880\) | −3.25313e6 | −0.141610 | ||||||||
\(881\) | 1.81431e6 | 0.0787540 | 0.0393770 | − | 0.999224i | \(-0.487463\pi\) | ||||
0.0393770 | + | 0.999224i | \(0.487463\pi\) | |||||||
\(882\) | −2.31393e7 | −1.00156 | ||||||||
\(883\) | 1.44217e7 | 0.622465 | 0.311233 | − | 0.950334i | \(-0.399258\pi\) | ||||
0.311233 | + | 0.950334i | \(0.399258\pi\) | |||||||
\(884\) | −3.84996e6 | −0.165701 | ||||||||
\(885\) | 6.64986e6 | 0.285400 | ||||||||
\(886\) | 2.38307e7 | 1.01989 | ||||||||
\(887\) | 1.99385e7 | 0.850910 | 0.425455 | − | 0.904980i | \(-0.360114\pi\) | ||||
0.425455 | + | 0.904980i | \(0.360114\pi\) | |||||||
\(888\) | 6.87392e6 | 0.292531 | ||||||||
\(889\) | −4.33493e7 | −1.83962 | ||||||||
\(890\) | 8.66896e6 | 0.366853 | ||||||||
\(891\) | 8.71491e6 | 0.367763 | ||||||||
\(892\) | 3.55672e6 | 0.149671 | ||||||||
\(893\) | 7.20542e6 | 0.302365 | ||||||||
\(894\) | −1.50484e7 | −0.629717 | ||||||||
\(895\) | −9.47973e6 | −0.395584 | ||||||||
\(896\) | 3.62412e6 | 0.150811 | ||||||||
\(897\) | −621054. | −0.0257720 | ||||||||
\(898\) | −2.07012e7 | −0.856652 | ||||||||
\(899\) | −5.66144e6 | −0.233630 | ||||||||
\(900\) | −1.80090e6 | −0.0741110 | ||||||||
\(901\) | −6.14121e7 | −2.52024 | ||||||||
\(902\) | −1.52537e7 | −0.624252 | ||||||||
\(903\) | 1.43939e7 | 0.587433 | ||||||||
\(904\) | −1.13739e7 | −0.462901 | ||||||||
\(905\) | 9.30210e6 | 0.377537 | ||||||||
\(906\) | −6.29431e6 | −0.254758 | ||||||||
\(907\) | 1.79214e7 | 0.723361 | 0.361680 | − | 0.932302i | \(-0.382203\pi\) | ||||
0.361680 | + | 0.932302i | \(0.382203\pi\) | |||||||
\(908\) | −1.70082e7 | −0.684613 | ||||||||
\(909\) | −1.21837e7 | −0.489069 | ||||||||
\(910\) | −3.27413e6 | −0.131067 | ||||||||
\(911\) | 3.84312e6 | 0.153422 | 0.0767111 | − | 0.997053i | \(-0.475558\pi\) | ||||
0.0767111 | + | 0.997053i | \(0.475558\pi\) | |||||||
\(912\) | 3.36464e6 | 0.133953 | ||||||||
\(913\) | 2.14102e7 | 0.850049 | ||||||||
\(914\) | −830550. | −0.0328852 | ||||||||
\(915\) | 5.28607e6 | 0.208728 | ||||||||
\(916\) | 2.07168e7 | 0.815799 | ||||||||
\(917\) | −7.25367e7 | −2.84862 | ||||||||
\(918\) | 2.18211e7 | 0.854613 | ||||||||
\(919\) | −1.88160e7 | −0.734917 | −0.367459 | − | 0.930040i | \(-0.619772\pi\) | ||||
−0.367459 | + | 0.930040i | \(0.619772\pi\) | |||||||
\(920\) | 846400. | 0.0329690 | ||||||||
\(921\) | −1.29720e7 | −0.503917 | ||||||||
\(922\) | 2.14300e7 | 0.830222 | ||||||||
\(923\) | −5.84628e6 | −0.225879 | ||||||||
\(924\) | 1.42687e7 | 0.549801 | ||||||||
\(925\) | 8.46339e6 | 0.325229 | ||||||||
\(926\) | 1.99022e6 | 0.0762734 | ||||||||
\(927\) | 1.51524e7 | 0.579138 | ||||||||
\(928\) | 7.12475e6 | 0.271581 | ||||||||
\(929\) | 2.15714e7 | 0.820048 | 0.410024 | − | 0.912075i | \(-0.365520\pi\) | ||||
0.410024 | + | 0.912075i | \(0.365520\pi\) | |||||||
\(930\) | 645384. | 0.0244687 | ||||||||
\(931\) | 5.32280e7 | 2.01264 | ||||||||
\(932\) | −779224. | −0.0293848 | ||||||||
\(933\) | 5.37221e6 | 0.202045 | ||||||||
\(934\) | −8.66073e6 | −0.324853 | ||||||||
\(935\) | 2.06578e7 | 0.772780 | ||||||||
\(936\) | −1.70601e6 | −0.0636491 | ||||||||
\(937\) | −5.12515e7 | −1.90703 | −0.953515 | − | 0.301344i | \(-0.902565\pi\) | ||||
−0.953515 | + | 0.301344i | \(0.902565\pi\) | |||||||
\(938\) | −1.52354e6 | −0.0565387 | ||||||||
\(939\) | 1.39834e7 | 0.517545 | ||||||||
\(940\) | −1.73933e6 | −0.0642039 | ||||||||
\(941\) | 3.93093e7 | 1.44717 | 0.723587 | − | 0.690233i | \(-0.242492\pi\) | ||||
0.723587 | + | 0.690233i | \(0.242492\pi\) | |||||||
\(942\) | 1.12249e6 | 0.0412150 | ||||||||
\(943\) | 3.96872e6 | 0.145335 | ||||||||
\(944\) | −8.58523e6 | −0.313561 | ||||||||
\(945\) | 1.85573e7 | 0.675984 | ||||||||
\(946\) | 1.66808e7 | 0.606022 | ||||||||
\(947\) | −4.72717e7 | −1.71288 | −0.856439 | − | 0.516249i | \(-0.827328\pi\) | ||||
−0.856439 | + | 0.516249i | \(0.827328\pi\) | |||||||
\(948\) | 7.67382e6 | 0.277326 | ||||||||
\(949\) | −7.54940e6 | −0.272112 | ||||||||
\(950\) | 4.14265e6 | 0.148926 | ||||||||
\(951\) | −1.85443e7 | −0.664903 | ||||||||
\(952\) | −2.30137e7 | −0.822988 | ||||||||
\(953\) | −5.19223e7 | −1.85192 | −0.925960 | − | 0.377623i | \(-0.876742\pi\) | ||||
−0.925960 | + | 0.377623i | \(0.876742\pi\) | |||||||
\(954\) | −2.72132e7 | −0.968074 | ||||||||
\(955\) | 6.51753e6 | 0.231246 | ||||||||
\(956\) | 1.93230e7 | 0.683803 | ||||||||
\(957\) | 2.80512e7 | 0.990084 | ||||||||
\(958\) | −9.93993e6 | −0.349921 | ||||||||
\(959\) | −2.15462e7 | −0.756526 | ||||||||
\(960\) | −812195. | −0.0284435 | ||||||||
\(961\) | −2.79671e7 | −0.976874 | ||||||||
\(962\) | 8.01747e6 | 0.279318 | ||||||||
\(963\) | −227088. | −0.00789094 | ||||||||
\(964\) | −1.13513e7 | −0.393415 | ||||||||
\(965\) | 1.70494e7 | 0.589374 | ||||||||
\(966\) | −3.71244e6 | −0.128002 | ||||||||
\(967\) | −3.73911e7 | −1.28588 | −0.642942 | − | 0.765915i | \(-0.722287\pi\) | ||||
−0.642942 | + | 0.765915i | \(0.722287\pi\) | |||||||
\(968\) | 6.22847e6 | 0.213645 | ||||||||
\(969\) | −2.13659e7 | −0.730992 | ||||||||
\(970\) | −1.91318e6 | −0.0652871 | ||||||||
\(971\) | −2.44905e7 | −0.833585 | −0.416793 | − | 0.909002i | \(-0.636846\pi\) | ||||
−0.416793 | + | 0.909002i | \(0.636846\pi\) | |||||||
\(972\) | 1.52231e7 | 0.516817 | ||||||||
\(973\) | 9.29921e7 | 3.14894 | ||||||||
\(974\) | 1.59709e7 | 0.539426 | ||||||||
\(975\) | 733759. | 0.0247196 | ||||||||
\(976\) | −6.82452e6 | −0.229323 | ||||||||
\(977\) | −6.82012e6 | −0.228589 | −0.114295 | − | 0.993447i | \(-0.536461\pi\) | ||||
−0.114295 | + | 0.993447i | \(0.536461\pi\) | |||||||
\(978\) | 3.46362e6 | 0.115793 | ||||||||
\(979\) | −4.40645e7 | −1.46937 | ||||||||
\(980\) | −1.28488e7 | −0.427362 | ||||||||
\(981\) | −2.06491e7 | −0.685059 | ||||||||
\(982\) | −1.59143e7 | −0.526634 | ||||||||
\(983\) | 1.76180e7 | 0.581532 | 0.290766 | − | 0.956794i | \(-0.406090\pi\) | ||||
0.290766 | + | 0.956794i | \(0.406090\pi\) | |||||||
\(984\) | −3.80833e6 | −0.125386 | ||||||||
\(985\) | −514976. | −0.0169121 | ||||||||
\(986\) | −4.52431e7 | −1.48204 | ||||||||
\(987\) | 7.62895e6 | 0.249271 | ||||||||
\(988\) | 3.92438e6 | 0.127902 | ||||||||
\(989\) | −4.34000e6 | −0.141091 | ||||||||
\(990\) | 9.15400e6 | 0.296840 | ||||||||
\(991\) | 1.22781e7 | 0.397144 | 0.198572 | − | 0.980086i | \(-0.436370\pi\) | ||||
0.198572 | + | 0.980086i | \(0.436370\pi\) | |||||||
\(992\) | −833216. | −0.0268830 | ||||||||
\(993\) | 1.35770e7 | 0.436949 | ||||||||
\(994\) | −3.49470e7 | −1.12187 | ||||||||
\(995\) | 1.48103e7 | 0.474249 | ||||||||
\(996\) | 5.34539e6 | 0.170738 | ||||||||
\(997\) | −4.31192e7 | −1.37383 | −0.686914 | − | 0.726738i | \(-0.741035\pi\) | ||||
−0.686914 | + | 0.726738i | \(0.741035\pi\) | |||||||
\(998\) | 2.93469e7 | 0.932687 | ||||||||
\(999\) | −4.54420e7 | −1.44060 |
(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 | 230.6.a.i.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.6.a.i.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial |