Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,6,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(3.36806021607\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 484x^{10} + 194194x^{8} - 39867800x^{6} + 5398720873x^{4} - 310089434788x^{2} + 9371104623076 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.7 | ||
Root | \(6.98672 - 2.99433i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.6.c.a.20.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.99433i | 0.529327i | 0.964341 | + | 0.264664i | \(0.0852609\pi\) | ||||
−0.964341 | + | 0.264664i | \(0.914739\pi\) | |||||||
\(3\) | −9.94100 | − | 12.0074i | −0.637716 | − | 0.770272i | ||||
\(4\) | 23.0340 | 0.719813 | ||||||||
\(5\) | 61.8023 | 1.10555 | 0.552777 | − | 0.833329i | \(-0.313568\pi\) | ||||
0.552777 | + | 0.833329i | \(0.313568\pi\) | |||||||
\(6\) | 35.9539 | − | 29.7666i | 0.407726 | − | 0.337560i | ||||
\(7\) | 92.4210 | − | 90.9140i | 0.712895 | − | 0.701271i | ||||
\(8\) | 164.790i | 0.910344i | ||||||||
\(9\) | −45.3530 | + | 238.730i | −0.186638 | + | 0.982429i | ||||
\(10\) | 185.056i | 0.585200i | ||||||||
\(11\) | − | 615.301i | − | 1.53323i | −0.642110 | − | 0.766613i | \(-0.721941\pi\) | ||
0.642110 | − | 0.766613i | \(-0.278059\pi\) | |||||||
\(12\) | −228.981 | − | 276.577i | −0.459036 | − | 0.554452i | ||||
\(13\) | 322.895i | 0.529911i | 0.964261 | + | 0.264955i | \(0.0853572\pi\) | ||||
−0.964261 | + | 0.264955i | \(0.914643\pi\) | |||||||
\(14\) | 272.226 | + | 276.739i | 0.371202 | + | 0.377355i | ||||
\(15\) | −614.377 | − | 742.083i | −0.705029 | − | 0.851577i | ||||
\(16\) | 243.654 | 0.237943 | ||||||||
\(17\) | −1537.42 | −1.29024 | −0.645120 | − | 0.764081i | \(-0.723193\pi\) | ||||
−0.645120 | + | 0.764081i | \(0.723193\pi\) | |||||||
\(18\) | −714.836 | − | 135.802i | −0.520026 | − | 0.0987925i | ||||
\(19\) | 2171.63i | 1.38007i | 0.723775 | + | 0.690036i | \(0.242405\pi\) | ||||
−0.723775 | + | 0.690036i | \(0.757595\pi\) | |||||||
\(20\) | 1423.56 | 0.795792 | ||||||||
\(21\) | −2010.39 | − | 205.956i | −0.994793 | − | 0.101912i | ||||
\(22\) | 1842.41 | 0.811578 | ||||||||
\(23\) | 793.329i | 0.312704i | 0.987701 | + | 0.156352i | \(0.0499735\pi\) | ||||
−0.987701 | + | 0.156352i | \(0.950027\pi\) | |||||||
\(24\) | 1978.69 | − | 1638.18i | 0.701212 | − | 0.580540i | ||||
\(25\) | 694.530 | 0.222250 | ||||||||
\(26\) | −966.853 | −0.280496 | ||||||||
\(27\) | 3317.37 | − | 1828.65i | 0.875759 | − | 0.482748i | ||||
\(28\) | 2128.83 | − | 2094.11i | 0.513151 | − | 0.504784i | ||||
\(29\) | − | 513.596i | − | 0.113404i | −0.998391 | − | 0.0567018i | \(-0.981942\pi\) | ||
0.998391 | − | 0.0567018i | \(-0.0180584\pi\) | |||||||
\(30\) | 2222.04 | − | 1839.65i | 0.450763 | − | 0.373191i | ||||
\(31\) | 161.215i | 0.0301302i | 0.999887 | + | 0.0150651i | \(0.00479555\pi\) | ||||
−0.999887 | + | 0.0150651i | \(0.995204\pi\) | |||||||
\(32\) | 6002.85i | 1.03629i | ||||||||
\(33\) | −7388.14 | + | 6116.71i | −1.18100 | + | 0.977762i | ||||
\(34\) | − | 4603.54i | − | 0.682959i | ||||||
\(35\) | 5711.84 | − | 5618.70i | 0.788144 | − | 0.775293i | ||||
\(36\) | −1044.66 | + | 5498.91i | −0.134344 | + | 0.707165i | ||||
\(37\) | −8593.37 | −1.03195 | −0.515976 | − | 0.856603i | \(-0.672571\pi\) | ||||
−0.515976 | + | 0.856603i | \(0.672571\pi\) | |||||||
\(38\) | −6502.57 | −0.730510 | ||||||||
\(39\) | 3877.11 | − | 3209.90i | 0.408175 | − | 0.337932i | ||||
\(40\) | 10184.4i | 1.00643i | ||||||||
\(41\) | 7004.53 | 0.650758 | 0.325379 | − | 0.945584i | \(-0.394508\pi\) | ||||
0.325379 | + | 0.945584i | \(0.394508\pi\) | |||||||
\(42\) | 616.698 | − | 6019.78i | 0.0539448 | − | 0.526571i | ||||
\(43\) | −7726.50 | −0.637253 | −0.318627 | − | 0.947880i | \(-0.603222\pi\) | ||||
−0.318627 | + | 0.947880i | \(0.603222\pi\) | |||||||
\(44\) | − | 14172.9i | − | 1.10364i | ||||||
\(45\) | −2802.92 | + | 14754.1i | −0.206338 | + | 1.08613i | ||||
\(46\) | −2375.49 | −0.165523 | ||||||||
\(47\) | −17604.2 | −1.16244 | −0.581221 | − | 0.813745i | \(-0.697425\pi\) | ||||
−0.581221 | + | 0.813745i | \(0.697425\pi\) | |||||||
\(48\) | −2422.16 | − | 2925.64i | −0.151740 | − | 0.183281i | ||||
\(49\) | 276.290 | − | 16804.7i | 0.0164390 | − | 0.999865i | ||||
\(50\) | 2079.65i | 0.117643i | ||||||||
\(51\) | 15283.5 | + | 18460.3i | 0.822806 | + | 0.993835i | ||||
\(52\) | 7437.56i | 0.381437i | ||||||||
\(53\) | 7345.26i | 0.359184i | 0.983741 | + | 0.179592i | \(0.0574778\pi\) | ||||
−0.983741 | + | 0.179592i | \(0.942522\pi\) | |||||||
\(54\) | 5475.57 | + | 9933.29i | 0.255532 | + | 0.463563i | ||||
\(55\) | − | 38027.1i | − | 1.69506i | ||||||
\(56\) | 14981.7 | + | 15230.0i | 0.638397 | + | 0.648979i | ||||
\(57\) | 26075.5 | − | 21588.2i | 1.06303 | − | 0.880093i | ||||
\(58\) | 1537.87 | 0.0600276 | ||||||||
\(59\) | 23416.6 | 0.875779 | 0.437889 | − | 0.899029i | \(-0.355726\pi\) | ||||
0.437889 | + | 0.899029i | \(0.355726\pi\) | |||||||
\(60\) | −14151.6 | − | 17093.1i | −0.507489 | − | 0.612976i | ||||
\(61\) | 13344.8i | 0.459186i | 0.973287 | + | 0.229593i | \(0.0737395\pi\) | ||||
−0.973287 | + | 0.229593i | \(0.926260\pi\) | |||||||
\(62\) | −482.731 | −0.0159487 | ||||||||
\(63\) | 17512.3 | + | 26186.9i | 0.555895 | + | 0.831252i | ||||
\(64\) | −10177.6 | −0.310595 | ||||||||
\(65\) | 19955.7i | 0.585845i | ||||||||
\(66\) | −18315.4 | − | 22122.5i | −0.517556 | − | 0.625136i | ||||
\(67\) | 14471.1 | 0.393835 | 0.196918 | − | 0.980420i | \(-0.436907\pi\) | ||||
0.196918 | + | 0.980420i | \(0.436907\pi\) | |||||||
\(68\) | −35413.0 | −0.928731 | ||||||||
\(69\) | 9525.78 | − | 7886.48i | 0.240867 | − | 0.199416i | ||||
\(70\) | 16824.2 | + | 17103.1i | 0.410383 | + | 0.417186i | ||||
\(71\) | 7370.42i | 0.173519i | 0.996229 | + | 0.0867593i | \(0.0276511\pi\) | ||||
−0.996229 | + | 0.0867593i | \(0.972349\pi\) | |||||||
\(72\) | −39340.3 | − | 7473.71i | −0.894348 | − | 0.169905i | ||||
\(73\) | 9422.68i | 0.206951i | 0.994632 | + | 0.103475i | \(0.0329963\pi\) | ||||
−0.994632 | + | 0.103475i | \(0.967004\pi\) | |||||||
\(74\) | − | 25731.4i | − | 0.546240i | ||||||
\(75\) | −6904.32 | − | 8339.47i | −0.141732 | − | 0.171193i | ||||
\(76\) | 50021.3i | 0.993394i | ||||||||
\(77\) | −55939.5 | − | 56866.8i | −1.07521 | − | 1.09303i | ||||
\(78\) | 9611.48 | + | 11609.3i | 0.178877 | + | 0.216058i | ||||
\(79\) | 27229.8 | 0.490882 | 0.245441 | − | 0.969412i | \(-0.421067\pi\) | ||||
0.245441 | + | 0.969412i | \(0.421067\pi\) | |||||||
\(80\) | 15058.4 | 0.263059 | ||||||||
\(81\) | −54935.2 | − | 21654.3i | −0.930333 | − | 0.366717i | ||||
\(82\) | 20973.8i | 0.344464i | ||||||||
\(83\) | 15577.0 | 0.248192 | 0.124096 | − | 0.992270i | \(-0.460397\pi\) | ||||
0.124096 | + | 0.992270i | \(0.460397\pi\) | |||||||
\(84\) | −46307.4 | − | 4743.98i | −0.716065 | − | 0.0733576i | ||||
\(85\) | −95016.2 | −1.42643 | ||||||||
\(86\) | − | 23135.7i | − | 0.337315i | ||||||
\(87\) | −6166.93 | + | 5105.66i | −0.0873516 | + | 0.0723192i | ||||
\(88\) | 101395. | 1.39576 | ||||||||
\(89\) | 90024.7 | 1.20472 | 0.602361 | − | 0.798224i | \(-0.294227\pi\) | ||||
0.602361 | + | 0.798224i | \(0.294227\pi\) | |||||||
\(90\) | −44178.5 | − | 8392.86i | −0.574917 | − | 0.109220i | ||||
\(91\) | 29355.7 | + | 29842.3i | 0.371611 | + | 0.377771i | ||||
\(92\) | 18273.5i | 0.225089i | ||||||||
\(93\) | 1935.77 | − | 1602.64i | 0.0232085 | − | 0.0192145i | ||||
\(94\) | − | 52712.7i | − | 0.615313i | ||||||
\(95\) | 134212.i | 1.52574i | ||||||||
\(96\) | 72078.4 | − | 59674.4i | 0.798228 | − | 0.660860i | ||||
\(97\) | 84850.1i | 0.915637i | 0.889046 | + | 0.457818i | \(0.151369\pi\) | ||||
−0.889046 | + | 0.457818i | \(0.848631\pi\) | |||||||
\(98\) | 50318.8 | + | 827.302i | 0.529256 | + | 0.00870160i | ||||
\(99\) | 146891. | + | 27905.8i | 1.50628 | + | 0.286158i | ||||
\(100\) | 15997.8 | 0.159978 | ||||||||
\(101\) | −80893.8 | −0.789063 | −0.394532 | − | 0.918882i | \(-0.629093\pi\) | ||||
−0.394532 | + | 0.918882i | \(0.629093\pi\) | |||||||
\(102\) | −55276.3 | + | 45763.8i | −0.526064 | + | 0.435533i | ||||
\(103\) | − | 214822.i | − | 1.99520i | −0.0692543 | − | 0.997599i | \(-0.522062\pi\) | ||
0.0692543 | − | 0.997599i | \(-0.477938\pi\) | |||||||
\(104\) | −53209.8 | −0.482401 | ||||||||
\(105\) | −124247. | − | 12728.5i | −1.09980 | − | 0.112669i | ||||
\(106\) | −21994.1 | −0.190126 | ||||||||
\(107\) | − | 120007.i | − | 1.01332i | −0.862146 | − | 0.506660i | \(-0.830880\pi\) | ||
0.862146 | − | 0.506660i | \(-0.169120\pi\) | |||||||
\(108\) | 76412.4 | − | 42121.1i | 0.630383 | − | 0.347488i | ||||
\(109\) | 29204.1 | 0.235439 | 0.117719 | − | 0.993047i | \(-0.462442\pi\) | ||||
0.117719 | + | 0.993047i | \(0.462442\pi\) | |||||||
\(110\) | 113865. | 0.897243 | ||||||||
\(111\) | 85426.7 | + | 103184.i | 0.658091 | + | 0.794883i | ||||
\(112\) | 22518.7 | − | 22151.6i | 0.169629 | − | 0.166863i | ||||
\(113\) | − | 64313.7i | − | 0.473813i | −0.971532 | − | 0.236907i | \(-0.923866\pi\) | ||
0.971532 | − | 0.236907i | \(-0.0761335\pi\) | |||||||
\(114\) | 64642.0 | + | 78078.6i | 0.465857 | + | 0.562691i | ||||
\(115\) | 49029.6i | 0.345711i | ||||||||
\(116\) | − | 11830.2i | − | 0.0816293i | ||||||
\(117\) | −77084.8 | − | 14644.3i | −0.520600 | − | 0.0989014i | ||||
\(118\) | 70117.0i | 0.463573i | ||||||||
\(119\) | −142090. | + | 139773.i | −0.919805 | + | 0.904807i | ||||
\(120\) | 122288. | − | 101243.i | 0.775228 | − | 0.641819i | ||||
\(121\) | −217545. | −1.35078 | ||||||||
\(122\) | −39958.8 | −0.243060 | ||||||||
\(123\) | −69632.0 | − | 84105.8i | −0.414998 | − | 0.501260i | ||||
\(124\) | 3713.44i | 0.0216881i | ||||||||
\(125\) | −150209. | −0.859845 | ||||||||
\(126\) | −78412.2 | + | 52437.7i | −0.440004 | + | 0.294250i | ||||
\(127\) | −293422. | −1.61430 | −0.807149 | − | 0.590348i | \(-0.798990\pi\) | ||||
−0.807149 | + | 0.590348i | \(0.798990\pi\) | |||||||
\(128\) | 161616.i | 0.871887i | ||||||||
\(129\) | 76809.2 | + | 92774.9i | 0.406386 | + | 0.490858i | ||||
\(130\) | −59753.8 | −0.310104 | ||||||||
\(131\) | 159323. | 0.811147 | 0.405573 | − | 0.914063i | \(-0.367072\pi\) | ||||
0.405573 | + | 0.914063i | \(0.367072\pi\) | |||||||
\(132\) | −170178. | + | 140892.i | −0.850099 | + | 0.703805i | ||||
\(133\) | 197432. | + | 200704.i | 0.967804 | + | 0.983847i | ||||
\(134\) | 43331.2i | 0.208468i | ||||||||
\(135\) | 205021. | − | 113015.i | 0.968199 | − | 0.533704i | ||||
\(136\) | − | 253351.i | − | 1.17456i | ||||||
\(137\) | − | 387950.i | − | 1.76593i | −0.469436 | − | 0.882967i | \(-0.655543\pi\) | ||
0.469436 | − | 0.882967i | \(-0.344457\pi\) | |||||||
\(138\) | 23614.7 | + | 28523.3i | 0.105556 | + | 0.127498i | ||||
\(139\) | − | 324317.i | − | 1.42375i | −0.702308 | − | 0.711874i | \(-0.747847\pi\) | ||
0.702308 | − | 0.711874i | \(-0.252153\pi\) | |||||||
\(140\) | 131566. | − | 129421.i | 0.567316 | − | 0.558066i | ||||
\(141\) | 175003. | + | 211380.i | 0.741308 | + | 0.895397i | ||||
\(142\) | −22069.4 | −0.0918481 | ||||||||
\(143\) | 198678. | 0.812473 | ||||||||
\(144\) | −11050.4 | + | 58167.6i | −0.0444092 | + | 0.233762i | ||||
\(145\) | − | 31741.4i | − | 0.125374i | ||||||
\(146\) | −28214.6 | −0.109545 | ||||||||
\(147\) | −204527. | + | 163738.i | −0.780651 | + | 0.624967i | ||||
\(148\) | −197940. | −0.742812 | ||||||||
\(149\) | 318945.i | 1.17693i | 0.808523 | + | 0.588464i | \(0.200267\pi\) | ||||
−0.808523 | + | 0.588464i | \(0.799733\pi\) | |||||||
\(150\) | 24971.1 | − | 20673.8i | 0.0906169 | − | 0.0750226i | ||||
\(151\) | 479410. | 1.71106 | 0.855529 | − | 0.517754i | \(-0.173232\pi\) | ||||
0.855529 | + | 0.517754i | \(0.173232\pi\) | |||||||
\(152\) | −357862. | −1.25634 | ||||||||
\(153\) | 69726.6 | − | 367029.i | 0.240808 | − | 1.26757i | ||||
\(154\) | 170278. | − | 167501.i | 0.578570 | − | 0.569136i | ||||
\(155\) | 9963.49i | 0.0333106i | ||||||||
\(156\) | 89305.4 | − | 73936.8i | 0.293810 | − | 0.243248i | ||||
\(157\) | 323801.i | 1.04840i | 0.851594 | + | 0.524202i | \(0.175636\pi\) | ||||
−0.851594 | + | 0.524202i | \(0.824364\pi\) | |||||||
\(158\) | 81535.0i | 0.259837i | ||||||||
\(159\) | 88197.1 | − | 73019.2i | 0.276670 | − | 0.229057i | ||||
\(160\) | 370990.i | 1.14568i | ||||||||
\(161\) | 72124.7 | + | 73320.3i | 0.219290 | + | 0.222925i | ||||
\(162\) | 64839.9 | − | 164494.i | 0.194113 | − | 0.492450i | ||||
\(163\) | −21423.8 | −0.0631579 | −0.0315789 | − | 0.999501i | \(-0.510054\pi\) | ||||
−0.0315789 | + | 0.999501i | \(0.510054\pi\) | |||||||
\(164\) | 161342. | 0.468424 | ||||||||
\(165\) | −456604. | + | 378027.i | −1.30566 | + | 1.08097i | ||||
\(166\) | 46642.6i | 0.131375i | ||||||||
\(167\) | 436305. | 1.21059 | 0.605297 | − | 0.796000i | \(-0.293054\pi\) | ||||
0.605297 | + | 0.796000i | \(0.293054\pi\) | |||||||
\(168\) | 33939.4 | − | 331292.i | 0.0927749 | − | 0.905604i | ||||
\(169\) | 267032. | 0.719195 | ||||||||
\(170\) | − | 284509.i | − | 0.755048i | ||||||
\(171\) | −518434. | − | 98489.9i | −1.35582 | − | 0.257574i | ||||
\(172\) | −177972. | −0.458703 | ||||||||
\(173\) | −185581. | −0.471431 | −0.235715 | − | 0.971822i | \(-0.575743\pi\) | ||||
−0.235715 | + | 0.971822i | \(0.575743\pi\) | |||||||
\(174\) | −15288.0 | − | 18465.8i | −0.0382805 | − | 0.0462376i | ||||
\(175\) | 64189.2 | − | 63142.5i | 0.158441 | − | 0.155857i | ||||
\(176\) | − | 149921.i | − | 0.364821i | ||||||
\(177\) | −232785. | − | 281172.i | −0.558498 | − | 0.674588i | ||||
\(178\) | 269563.i | 0.637692i | ||||||||
\(179\) | 170761.i | 0.398341i | 0.979965 | + | 0.199171i | \(0.0638248\pi\) | ||||
−0.979965 | + | 0.199171i | \(0.936175\pi\) | |||||||
\(180\) | −64562.5 | + | 339846.i | −0.148525 | + | 0.781809i | ||||
\(181\) | − | 326285.i | − | 0.740289i | −0.928974 | − | 0.370144i | \(-0.879308\pi\) | ||
0.928974 | − | 0.370144i | \(-0.120692\pi\) | |||||||
\(182\) | −89357.5 | + | 87900.4i | −0.199964 | + | 0.196704i | ||||
\(183\) | 160236. | − | 132661.i | 0.353698 | − | 0.292830i | ||||
\(184\) | −130733. | −0.284668 | ||||||||
\(185\) | −531090. | −1.14088 | ||||||||
\(186\) | 4798.83 | + | 5796.33i | 0.0101708 | + | 0.0122849i | ||||
\(187\) | 945977.i | 1.97823i | ||||||||
\(188\) | −405495. | −0.836741 | ||||||||
\(189\) | 140345. | − | 470601.i | 0.285787 | − | 0.958293i | ||||
\(190\) | −401874. | −0.807618 | ||||||||
\(191\) | − | 296995.i | − | 0.589069i | −0.955641 | − | 0.294534i | \(-0.904835\pi\) | ||
0.955641 | − | 0.294534i | \(-0.0951646\pi\) | |||||||
\(192\) | 101175. | + | 122206.i | 0.198071 | + | 0.239243i | ||||
\(193\) | 414092. | 0.800208 | 0.400104 | − | 0.916470i | \(-0.368974\pi\) | ||||
0.400104 | + | 0.916470i | \(0.368974\pi\) | |||||||
\(194\) | −254069. | −0.484671 | ||||||||
\(195\) | 239615. | − | 198379.i | 0.451260 | − | 0.373602i | ||||
\(196\) | 6364.07 | − | 387080.i | 0.0118330 | − | 0.719716i | ||||
\(197\) | 216937.i | 0.398262i | 0.979973 | + | 0.199131i | \(0.0638119\pi\) | ||||
−0.979973 | + | 0.199131i | \(0.936188\pi\) | |||||||
\(198\) | −83558.9 | + | 439840.i | −0.151471 | + | 0.797317i | ||||
\(199\) | − | 36716.3i | − | 0.0657244i | −0.999460 | − | 0.0328622i | \(-0.989538\pi\) | ||
0.999460 | − | 0.0328622i | \(-0.0104623\pi\) | |||||||
\(200\) | 114451.i | 0.202323i | ||||||||
\(201\) | −143857. | − | 173760.i | −0.251155 | − | 0.303360i | ||||
\(202\) | − | 242222.i | − | 0.417672i | ||||||
\(203\) | −46693.1 | − | 47467.1i | −0.0795266 | − | 0.0808448i | ||||
\(204\) | 352040. | + | 425216.i | 0.592266 | + | 0.715375i | ||||
\(205\) | 432896. | 0.719448 | ||||||||
\(206\) | 643248. | 1.05611 | ||||||||
\(207\) | −189392. | − | 35979.8i | −0.307210 | − | 0.0583624i | ||||
\(208\) | 78674.6i | 0.126089i | ||||||||
\(209\) | 1.33621e6 | 2.11596 | ||||||||
\(210\) | 38113.4 | − | 372036.i | 0.0596389 | − | 0.582153i | ||||
\(211\) | −587416. | −0.908321 | −0.454161 | − | 0.890920i | \(-0.650061\pi\) | ||||
−0.454161 | + | 0.890920i | \(0.650061\pi\) | |||||||
\(212\) | 169191.i | 0.258545i | ||||||||
\(213\) | 88499.2 | − | 73269.3i | 0.133657 | − | 0.110656i | ||||
\(214\) | 359340. | 0.536378 | ||||||||
\(215\) | −477516. | −0.704518 | ||||||||
\(216\) | 301342. | + | 546669.i | 0.439467 | + | 0.797242i | ||||
\(217\) | 14656.7 | + | 14899.7i | 0.0211294 | + | 0.0214797i | ||||
\(218\) | 87446.7i | 0.124624i | ||||||||
\(219\) | 113141. | − | 93670.8i | 0.159408 | − | 0.131976i | ||||
\(220\) | − | 875916.i | − | 1.22013i | ||||||
\(221\) | − | 496425.i | − | 0.683712i | ||||||
\(222\) | −308965. | + | 255795.i | −0.420753 | + | 0.348346i | ||||
\(223\) | − | 349812.i | − | 0.471056i | −0.971868 | − | 0.235528i | \(-0.924318\pi\) | ||
0.971868 | − | 0.235528i | \(-0.0756819\pi\) | |||||||
\(224\) | 545743. | + | 554790.i | 0.726722 | + | 0.738769i | ||||
\(225\) | −31499.0 | + | 165805.i | −0.0414802 | + | 0.218344i | ||||
\(226\) | 192576. | 0.250802 | ||||||||
\(227\) | −925060. | −1.19153 | −0.595766 | − | 0.803158i | \(-0.703151\pi\) | ||||
−0.595766 | + | 0.803158i | \(0.703151\pi\) | |||||||
\(228\) | 600624. | − | 497262.i | 0.765183 | − | 0.633502i | ||||
\(229\) | − | 136041.i | − | 0.171428i | −0.996320 | − | 0.0857142i | \(-0.972683\pi\) | ||
0.996320 | − | 0.0857142i | \(-0.0273172\pi\) | |||||||
\(230\) | −146811. | −0.182994 | ||||||||
\(231\) | −126725. | + | 1.23700e6i | −0.156254 | + | 1.52524i | ||||
\(232\) | 84635.4 | 0.103236 | ||||||||
\(233\) | 1.13764e6i | 1.37283i | 0.727212 | + | 0.686413i | \(0.240816\pi\) | ||||
−0.727212 | + | 0.686413i | \(0.759184\pi\) | |||||||
\(234\) | 43849.7 | − | 230817.i | 0.0523512 | − | 0.275567i | ||||
\(235\) | −1.08798e6 | −1.28514 | ||||||||
\(236\) | 539379. | 0.630397 | ||||||||
\(237\) | −270692. | − | 326958.i | −0.313043 | − | 0.378113i | ||||
\(238\) | −418526. | − | 425464.i | −0.478939 | − | 0.486878i | ||||
\(239\) | − | 1.04427e6i | − | 1.18254i | −0.806473 | − | 0.591271i | \(-0.798626\pi\) | ||
0.806473 | − | 0.591271i | \(-0.201374\pi\) | |||||||
\(240\) | −149695. | − | 180811.i | −0.167757 | − | 0.202627i | ||||
\(241\) | 503492.i | 0.558406i | 0.960232 | + | 0.279203i | \(0.0900702\pi\) | ||||
−0.960232 | + | 0.279203i | \(0.909930\pi\) | |||||||
\(242\) | − | 651400.i | − | 0.715005i | ||||||
\(243\) | 286101. | + | 874891.i | 0.310816 | + | 0.950470i | ||||
\(244\) | 307385.i | 0.330528i | ||||||||
\(245\) | 17075.4 | − | 1.03857e6i | 0.0181742 | − | 1.10540i | ||||
\(246\) | 251840. | − | 208501.i | 0.265331 | − | 0.219670i | ||||
\(247\) | −701208. | −0.731315 | ||||||||
\(248\) | −26566.6 | −0.0274288 | ||||||||
\(249\) | −154851. | − | 187038.i | −0.158276 | − | 0.191175i | ||||
\(250\) | − | 449774.i | − | 0.455139i | ||||||
\(251\) | −1.68197e6 | −1.68514 | −0.842568 | − | 0.538590i | \(-0.818957\pi\) | ||||
−0.842568 | + | 0.538590i | \(0.818957\pi\) | |||||||
\(252\) | 403380. | + | 603190.i | 0.400141 | + | 0.598346i | ||||
\(253\) | 488136. | 0.479446 | ||||||||
\(254\) | − | 878601.i | − | 0.854491i | ||||||
\(255\) | 944556. | + | 1.14089e6i | 0.909656 | + | 1.09874i | ||||
\(256\) | −809614. | −0.772108 | ||||||||
\(257\) | 953741. | 0.900736 | 0.450368 | − | 0.892843i | \(-0.351293\pi\) | ||||
0.450368 | + | 0.892843i | \(0.351293\pi\) | |||||||
\(258\) | −277798. | + | 229992.i | −0.259825 | + | 0.215111i | ||||
\(259\) | −794208. | + | 781258.i | −0.735673 | + | 0.723677i | ||||
\(260\) | 459659.i | 0.421699i | ||||||||
\(261\) | 122611. | + | 23293.1i | 0.111411 | + | 0.0211654i | ||||
\(262\) | 477064.i | 0.429362i | ||||||||
\(263\) | 1.64469e6i | 1.46621i | 0.680117 | + | 0.733104i | \(0.261929\pi\) | ||||
−0.680117 | + | 0.733104i | \(0.738071\pi\) | |||||||
\(264\) | −1.00797e6 | − | 1.21749e6i | −0.890099 | − | 1.07512i | ||||
\(265\) | 453954.i | 0.397098i | ||||||||
\(266\) | −600974. | + | 591174.i | −0.520777 | + | 0.512285i | ||||
\(267\) | −894935. | − | 1.08096e6i | −0.768269 | − | 0.927963i | ||||
\(268\) | 333328. | 0.283488 | ||||||||
\(269\) | 76973.2 | 0.0648573 | 0.0324286 | − | 0.999474i | \(-0.489676\pi\) | ||||
0.0324286 | + | 0.999474i | \(0.489676\pi\) | |||||||
\(270\) | 338403. | + | 613901.i | 0.282504 | + | 0.512494i | ||||
\(271\) | − | 1.79795e6i | − | 1.48715i | −0.668652 | − | 0.743576i | \(-0.733128\pi\) | ||
0.668652 | − | 0.743576i | \(-0.266872\pi\) | |||||||
\(272\) | −374599. | −0.307004 | ||||||||
\(273\) | 66502.0 | − | 649146.i | 0.0540043 | − | 0.527152i | ||||
\(274\) | 1.16165e6 | 0.934756 | ||||||||
\(275\) | − | 427345.i | − | 0.340759i | ||||||
\(276\) | 219417. | − | 181657.i | 0.173379 | − | 0.143542i | ||||
\(277\) | 1.16102e6 | 0.909160 | 0.454580 | − | 0.890706i | \(-0.349789\pi\) | ||||
0.454580 | + | 0.890706i | \(0.349789\pi\) | |||||||
\(278\) | 971111. | 0.753628 | ||||||||
\(279\) | −38487.0 | − | 7311.60i | −0.0296008 | − | 0.00562344i | ||||
\(280\) | 925904. | + | 941252.i | 0.705783 | + | 0.717482i | ||||
\(281\) | 1.50031e6i | 1.13348i | 0.823896 | + | 0.566741i | \(0.191796\pi\) | ||||
−0.823896 | + | 0.566741i | \(0.808204\pi\) | |||||||
\(282\) | −632940. | + | 524017.i | −0.473958 | + | 0.392394i | ||||
\(283\) | − | 775321.i | − | 0.575460i | −0.957712 | − | 0.287730i | \(-0.907099\pi\) | ||
0.957712 | − | 0.287730i | \(-0.0929006\pi\) | |||||||
\(284\) | 169770.i | 0.124901i | ||||||||
\(285\) | 1.61153e6 | − | 1.33420e6i | 1.17524 | − | 0.972991i | ||||
\(286\) | 594906.i | 0.430064i | ||||||||
\(287\) | 647366. | − | 636810.i | 0.463922 | − | 0.456357i | ||||
\(288\) | −1.43306e6 | − | 272247.i | −1.01808 | − | 0.193412i | ||||
\(289\) | 943804. | 0.664718 | ||||||||
\(290\) | 95044.2 | 0.0663637 | ||||||||
\(291\) | 1.01883e6 | − | 843495.i | 0.705289 | − | 0.583916i | ||||
\(292\) | 217042.i | 0.148966i | ||||||||
\(293\) | 194034. | 0.132041 | 0.0660206 | − | 0.997818i | \(-0.478970\pi\) | ||||
0.0660206 | + | 0.997818i | \(0.478970\pi\) | |||||||
\(294\) | −490286. | − | 612420.i | −0.330812 | − | 0.413220i | ||||
\(295\) | 1.44720e6 | 0.968221 | ||||||||
\(296\) | − | 1.41610e6i | − | 0.939430i | ||||||
\(297\) | −1.12517e6 | − | 2.04118e6i | −0.740162 | − | 1.34274i | ||||
\(298\) | −955026. | −0.622980 | ||||||||
\(299\) | −256162. | −0.165705 | ||||||||
\(300\) | −159034. | − | 192091.i | −0.102021 | − | 0.123227i | ||||
\(301\) | −714091. | + | 702447.i | −0.454295 | + | 0.446887i | ||||
\(302\) | 1.43551e6i | 0.905710i | ||||||||
\(303\) | 804165. | + | 971320.i | 0.503198 | + | 0.607793i | ||||
\(304\) | 529126.i | 0.328379i | ||||||||
\(305\) | 824742.i | 0.507655i | ||||||||
\(306\) | 1.09900e6 | + | 208784.i | 0.670958 | + | 0.127466i | ||||
\(307\) | 394659.i | 0.238988i | 0.992835 | + | 0.119494i | \(0.0381273\pi\) | ||||
−0.992835 | + | 0.119494i | \(0.961873\pi\) | |||||||
\(308\) | −1.28851e6 | − | 1.30987e6i | −0.773947 | − | 0.786776i | ||||
\(309\) | −2.57945e6 | + | 2.13555e6i | −1.53685 | + | 1.27237i | ||||
\(310\) | −29833.9 | −0.0176322 | ||||||||
\(311\) | 2.29757e6 | 1.34700 | 0.673501 | − | 0.739186i | \(-0.264790\pi\) | ||||
0.673501 | + | 0.739186i | \(0.264790\pi\) | |||||||
\(312\) | 528958. | + | 638908.i | 0.307635 | + | 0.371580i | ||||
\(313\) | − | 634859.i | − | 0.366283i | −0.983087 | − | 0.183141i | \(-0.941373\pi\) | ||
0.983087 | − | 0.183141i | \(-0.0586266\pi\) | |||||||
\(314\) | −969566. | −0.554949 | ||||||||
\(315\) | 1.08230e6 | + | 1.61841e6i | 0.614572 | + | 0.918994i | ||||
\(316\) | 627212. | 0.353343 | ||||||||
\(317\) | − | 192873.i | − | 0.107801i | −0.998546 | − | 0.0539005i | \(-0.982835\pi\) | ||
0.998546 | − | 0.0539005i | \(-0.0171654\pi\) | |||||||
\(318\) | 218643. | + | 264091.i | 0.121246 | + | 0.146449i | ||||
\(319\) | −316016. | −0.173873 | ||||||||
\(320\) | −628998. | −0.343379 | ||||||||
\(321\) | −1.44096e6 | + | 1.19299e6i | −0.780532 | + | 0.646210i | ||||
\(322\) | −219545. | + | 215965.i | −0.118000 | + | 0.116076i | ||||
\(323\) | − | 3.33871e6i | − | 1.78062i | ||||||
\(324\) | −1.26538e6 | − | 498784.i | −0.669665 | − | 0.263967i | ||||
\(325\) | 224260.i | 0.117772i | ||||||||
\(326\) | − | 64149.9i | − | 0.0334312i | ||||||
\(327\) | −290318. | − | 350664.i | −0.150143 | − | 0.181352i | ||||
\(328\) | 1.15427e6i | 0.592413i | ||||||||
\(329\) | −1.62700e6 | + | 1.60047e6i | −0.828700 | + | 0.815187i | ||||
\(330\) | −1.13194e6 | − | 1.36722e6i | −0.572186 | − | 0.691121i | ||||
\(331\) | −2.85474e6 | −1.43218 | −0.716088 | − | 0.698010i | \(-0.754069\pi\) | ||||
−0.716088 | + | 0.698010i | \(0.754069\pi\) | |||||||
\(332\) | 358800. | 0.178652 | ||||||||
\(333\) | 389735. | − | 2.05150e6i | 0.192601 | − | 1.01382i | ||||
\(334\) | 1.30644e6i | 0.640800i | ||||||||
\(335\) | 894348. | 0.435406 | ||||||||
\(336\) | −489840. | − | 50181.9i | −0.236704 | − | 0.0242493i | ||||
\(337\) | 3.37722e6 | 1.61989 | 0.809944 | − | 0.586507i | \(-0.199497\pi\) | ||||
0.809944 | + | 0.586507i | \(0.199497\pi\) | |||||||
\(338\) | 799581.i | 0.380689i | ||||||||
\(339\) | −772237. | + | 639342.i | −0.364965 | + | 0.302158i | ||||
\(340\) | −2.18860e6 | −1.02676 | ||||||||
\(341\) | 99196.0 | 0.0461964 | ||||||||
\(342\) | 294911. | − | 1.55236e6i | 0.136341 | − | 0.717674i | ||||
\(343\) | −1.50225e6 | − | 1.57823e6i | −0.689457 | − | 0.724327i | ||||
\(344\) | − | 1.27325e6i | − | 0.580119i | ||||||
\(345\) | 588716. | − | 487403.i | 0.266292 | − | 0.220466i | ||||
\(346\) | − | 555690.i | − | 0.249541i | ||||||
\(347\) | − | 547961.i | − | 0.244301i | −0.992512 | − | 0.122151i | \(-0.961021\pi\) | ||
0.992512 | − | 0.122151i | \(-0.0389791\pi\) | |||||||
\(348\) | −142049. | + | 117604.i | −0.0628768 | + | 0.0520563i | ||||
\(349\) | 1206.49i | 0.000530223i | 1.00000 | 0.000265112i | \(8.43876e-5\pi\) | |||||
−1.00000 | 0.000265112i | \(0.999916\pi\) | ||||||||
\(350\) | 189069. | + | 192203.i | 0.0824994 | + | 0.0838669i | ||||
\(351\) | 590461. | + | 1.07116e6i | 0.255813 | + | 0.464074i | ||||
\(352\) | 3.69356e6 | 1.58887 | ||||||||
\(353\) | −1.15208e6 | −0.492090 | −0.246045 | − | 0.969258i | \(-0.579131\pi\) | ||||
−0.246045 | + | 0.969258i | \(0.579131\pi\) | |||||||
\(354\) | 841920. | − | 697033.i | 0.357078 | − | 0.295628i | ||||
\(355\) | 455509.i | 0.191834i | ||||||||
\(356\) | 2.07363e6 | 0.867174 | ||||||||
\(357\) | 3.09082e6 | + | 316640.i | 1.28352 | + | 0.131491i | ||||
\(358\) | −511313. | −0.210853 | ||||||||
\(359\) | 2.10870e6i | 0.863531i | 0.901986 | + | 0.431766i | \(0.142109\pi\) | ||||
−0.901986 | + | 0.431766i | \(0.857891\pi\) | |||||||
\(360\) | −2.43132e6 | − | 461893.i | −0.988750 | − | 0.187839i | ||||
\(361\) | −2.23988e6 | −0.904599 | ||||||||
\(362\) | 977005. | 0.391855 | ||||||||
\(363\) | 2.16261e6 | + | 2.61213e6i | 0.861414 | + | 1.04047i | ||||
\(364\) | 676179. | + | 687387.i | 0.267490 | + | 0.271924i | ||||
\(365\) | 582344.i | 0.228795i | ||||||||
\(366\) | 397230. | + | 479799.i | 0.155003 | + | 0.187222i | ||||
\(367\) | − | 3.37130e6i | − | 1.30657i | −0.757113 | − | 0.653284i | \(-0.773391\pi\) | ||
0.757113 | − | 0.653284i | \(-0.226609\pi\) | |||||||
\(368\) | 193298.i | 0.0744059i | ||||||||
\(369\) | −317676. | + | 1.67219e6i | −0.121456 | + | 0.639323i | ||||
\(370\) | − | 1.59026e6i | − | 0.603898i | ||||||
\(371\) | 667787. | + | 678856.i | 0.251885 | + | 0.256061i | ||||
\(372\) | 44588.5 | − | 36915.3i | 0.0167057 | − | 0.0138308i | ||||
\(373\) | −65054.8 | −0.0242107 | −0.0121054 | − | 0.999927i | \(-0.503853\pi\) | ||||
−0.0121054 | + | 0.999927i | \(0.503853\pi\) | |||||||
\(374\) | −2.83256e6 | −1.04713 | ||||||||
\(375\) | 1.49323e6 | + | 1.80361e6i | 0.548337 | + | 0.662315i | ||||
\(376\) | − | 2.90099e6i | − | 1.05822i | ||||||
\(377\) | 165838. | 0.0600938 | ||||||||
\(378\) | 1.40913e6 | + | 420239.i | 0.507250 | + | 0.151275i | ||||
\(379\) | −690875. | −0.247059 | −0.123530 | − | 0.992341i | \(-0.539421\pi\) | ||||
−0.123530 | + | 0.992341i | \(0.539421\pi\) | |||||||
\(380\) | 3.09144e6i | 1.09825i | ||||||||
\(381\) | 2.91691e6 | + | 3.52322e6i | 1.02946 | + | 1.24345i | ||||
\(382\) | 889301. | 0.311810 | ||||||||
\(383\) | −2.44872e6 | −0.852986 | −0.426493 | − | 0.904491i | \(-0.640251\pi\) | ||||
−0.426493 | + | 0.904491i | \(0.640251\pi\) | |||||||
\(384\) | 1.94058e6 | − | 1.60663e6i | 0.671590 | − | 0.556016i | ||||
\(385\) | −3.45719e6 | − | 3.51450e6i | −1.18870 | − | 1.20840i | ||||
\(386\) | 1.23993e6i | 0.423572i | ||||||||
\(387\) | 350420. | − | 1.84455e6i | 0.118936 | − | 0.626056i | ||||
\(388\) | 1.95444e6i | 0.659087i | ||||||||
\(389\) | − | 3.72849e6i | − | 1.24928i | −0.780913 | − | 0.624640i | \(-0.785246\pi\) | ||
0.780913 | − | 0.624640i | \(-0.214754\pi\) | |||||||
\(390\) | 594012. | + | 717484.i | 0.197758 | + | 0.238864i | ||||
\(391\) | − | 1.21968e6i | − | 0.403463i | ||||||
\(392\) | 2.76925e6 | + | 45529.8i | 0.910221 | + | 0.0149651i | ||||
\(393\) | −1.58383e6 | − | 1.91304e6i | −0.517281 | − | 0.624803i | ||||
\(394\) | −649581. | −0.210811 | ||||||||
\(395\) | 1.68287e6 | 0.542697 | ||||||||
\(396\) | 3.38349e6 | + | 642781.i | 1.08424 | + | 0.205980i | ||||
\(397\) | 3.19740e6i | 1.01817i | 0.860716 | + | 0.509086i | \(0.170016\pi\) | ||||
−0.860716 | + | 0.509086i | \(0.829984\pi\) | |||||||
\(398\) | 109941. | 0.0347897 | ||||||||
\(399\) | 447259. | − | 4.36583e6i | 0.140646 | − | 1.37289i | ||||
\(400\) | 169225. | 0.0528828 | ||||||||
\(401\) | − | 6.01416e6i | − | 1.86773i | −0.357627 | − | 0.933865i | \(-0.616414\pi\) | ||
0.357627 | − | 0.933865i | \(-0.383586\pi\) | |||||||
\(402\) | 520293. | − | 430756.i | 0.160577 | − | 0.132943i | ||||
\(403\) | −52055.6 | −0.0159663 | ||||||||
\(404\) | −1.86331e6 | −0.567978 | ||||||||
\(405\) | −3.39512e6 | − | 1.33828e6i | −1.02853 | − | 0.405425i | ||||
\(406\) | 142132. | − | 139814.i | 0.0427934 | − | 0.0420956i | ||||
\(407\) | 5.28751e6i | 1.58221i | ||||||||
\(408\) | −3.04208e6 | + | 2.51856e6i | −0.904732 | + | 0.749036i | ||||
\(409\) | 5.69952e6i | 1.68473i | 0.538909 | + | 0.842364i | \(0.318837\pi\) | ||||
−0.538909 | + | 0.842364i | \(0.681163\pi\) | |||||||
\(410\) | 1.29623e6i | 0.380823i | ||||||||
\(411\) | −4.65825e6 | + | 3.85661e6i | −1.36025 | + | 1.12616i | ||||
\(412\) | − | 4.94822e6i | − | 1.43617i | ||||||
\(413\) | 2.16419e6 | − | 2.12890e6i | 0.624338 | − | 0.614158i | ||||
\(414\) | 107735. | − | 567100.i | 0.0308928 | − | 0.162614i | ||||
\(415\) | 962694. | 0.274390 | ||||||||
\(416\) | −1.93829e6 | −0.549143 | ||||||||
\(417\) | −3.89419e6 | + | 3.22404e6i | −1.09667 | + | 0.907946i | ||||
\(418\) | 4.00104e6i | 1.12004i | ||||||||
\(419\) | −2.40292e6 | −0.668658 | −0.334329 | − | 0.942456i | \(-0.608510\pi\) | ||||
−0.334329 | + | 0.942456i | \(0.608510\pi\) | |||||||
\(420\) | −2.86191e6 | − | 293189.i | −0.791649 | − | 0.0811007i | ||||
\(421\) | −1.84926e6 | −0.508501 | −0.254251 | − | 0.967138i | \(-0.581829\pi\) | ||||
−0.254251 | + | 0.967138i | \(0.581829\pi\) | |||||||
\(422\) | − | 1.75891e6i | − | 0.480799i | ||||||
\(423\) | 798403. | − | 4.20265e6i | 0.216956 | − | 1.14202i | ||||
\(424\) | −1.21042e6 | −0.326981 | ||||||||
\(425\) | −1.06778e6 | −0.286755 | ||||||||
\(426\) | 219392. | + | 264995.i | 0.0585730 | + | 0.0707481i | ||||
\(427\) | 1.21323e6 | + | 1.23334e6i | 0.322014 | + | 0.327351i | ||||
\(428\) | − | 2.76424e6i | − | 0.729401i | ||||||
\(429\) | −1.97505e6 | − | 2.38559e6i | −0.518127 | − | 0.625825i | ||||
\(430\) | − | 1.42984e6i | − | 0.372920i | ||||||
\(431\) | 670021.i | 0.173738i | 0.996220 | + | 0.0868691i | \(0.0276862\pi\) | ||||
−0.996220 | + | 0.0868691i | \(0.972314\pi\) | |||||||
\(432\) | 808291. | − | 445557.i | 0.208381 | − | 0.114867i | ||||
\(433\) | 3.18314e6i | 0.815898i | 0.913005 | + | 0.407949i | \(0.133756\pi\) | ||||
−0.913005 | + | 0.407949i | \(0.866244\pi\) | |||||||
\(434\) | −44614.5 | + | 43887.0i | −0.0113698 | + | 0.0111844i | ||||
\(435\) | −381131. | + | 315542.i | −0.0965719 | + | 0.0799528i | ||||
\(436\) | 672688. | 0.169472 | ||||||||
\(437\) | −1.72282e6 | −0.431554 | ||||||||
\(438\) | 280481. | + | 338782.i | 0.0698583 | + | 0.0843792i | ||||
\(439\) | 3.04218e6i | 0.753396i | 0.926336 | + | 0.376698i | \(0.122941\pi\) | ||||
−0.926336 | + | 0.376698i | \(0.877059\pi\) | |||||||
\(440\) | 6.26647e6 | 1.54309 | ||||||||
\(441\) | 3.99927e6 | + | 828104.i | 0.979228 | + | 0.202763i | ||||
\(442\) | 1.48646e6 | 0.361907 | ||||||||
\(443\) | 4.06656e6i | 0.984505i | 0.870452 | + | 0.492253i | \(0.163826\pi\) | ||||
−0.870452 | + | 0.492253i | \(0.836174\pi\) | |||||||
\(444\) | 1.96772e6 | + | 2.37673e6i | 0.473703 | + | 0.572167i | ||||
\(445\) | 5.56374e6 | 1.33188 | ||||||||
\(446\) | 1.04745e6 | 0.249343 | ||||||||
\(447\) | 3.82969e6 | − | 3.17063e6i | 0.906555 | − | 0.750546i | ||||
\(448\) | −940622. | + | 925284.i | −0.221422 | + | 0.217811i | ||||
\(449\) | − | 3.30712e6i | − | 0.774166i | −0.922045 | − | 0.387083i | \(-0.873483\pi\) | ||
0.922045 | − | 0.387083i | \(-0.126517\pi\) | |||||||
\(450\) | −496475. | − | 94318.3i | −0.115576 | − | 0.0219566i | ||||
\(451\) | − | 4.30990e6i | − | 0.997758i | ||||||
\(452\) | − | 1.48140e6i | − | 0.341057i | ||||||
\(453\) | −4.76582e6 | − | 5.75645e6i | −1.09117 | − | 1.31798i | ||||
\(454\) | − | 2.76993e6i | − | 0.630710i | ||||||
\(455\) | 1.81425e6 | + | 1.84432e6i | 0.410836 | + | 0.417646i | ||||
\(456\) | 3.55751e6 | + | 4.29698e6i | 0.801187 | + | 0.967723i | ||||
\(457\) | 797135. | 0.178542 | 0.0892712 | − | 0.996007i | \(-0.471546\pi\) | ||||
0.0892712 | + | 0.996007i | \(0.471546\pi\) | |||||||
\(458\) | 407352. | 0.0907416 | ||||||||
\(459\) | −5.10019e6 | + | 2.81140e6i | −1.12994 | + | 0.622861i | ||||
\(460\) | 1.12935e6i | 0.248847i | ||||||||
\(461\) | −4.32869e6 | −0.948646 | −0.474323 | − | 0.880351i | \(-0.657307\pi\) | ||||
−0.474323 | + | 0.880351i | \(0.657307\pi\) | |||||||
\(462\) | −3.70398e6 | − | 379455.i | −0.807352 | − | 0.0827095i | ||||
\(463\) | 5.38489e6 | 1.16741 | 0.583706 | − | 0.811965i | \(-0.301602\pi\) | ||||
0.583706 | + | 0.811965i | \(0.301602\pi\) | |||||||
\(464\) | − | 125140.i | − | 0.0269836i | ||||||
\(465\) | 119635. | − | 99047.1i | 0.0256582 | − | 0.0212427i | ||||
\(466\) | −3.40647e6 | −0.726674 | ||||||||
\(467\) | 677568. | 0.143767 | 0.0718837 | − | 0.997413i | \(-0.477099\pi\) | ||||
0.0718837 | + | 0.997413i | \(0.477099\pi\) | |||||||
\(468\) | −1.77557e6 | − | 337316.i | −0.374734 | − | 0.0711905i | ||||
\(469\) | 1.33743e6 | − | 1.31563e6i | 0.280763 | − | 0.276185i | ||||
\(470\) | − | 3.25777e6i | − | 0.680261i | ||||||
\(471\) | 3.88799e6 | − | 3.21891e6i | 0.807557 | − | 0.668584i | ||||
\(472\) | 3.85882e6i | 0.797259i | ||||||||
\(473\) | 4.75413e6i | 0.977053i | ||||||||
\(474\) | 979019. | − | 810539.i | 0.200145 | − | 0.165702i | ||||
\(475\) | 1.50826e6i | 0.306720i | ||||||||
\(476\) | −3.27290e6 | + | 3.21953e6i | −0.662088 | + | 0.651292i | ||||
\(477\) | −1.75353e6 | − | 333130.i | −0.352873 | − | 0.0670374i | ||||
\(478\) | 3.12687e6 | 0.625951 | ||||||||
\(479\) | 7.87592e6 | 1.56842 | 0.784210 | − | 0.620495i | \(-0.213068\pi\) | ||||
0.784210 | + | 0.620495i | \(0.213068\pi\) | |||||||
\(480\) | 4.45461e6 | − | 3.68802e6i | 0.882484 | − | 0.730617i | ||||
\(481\) | − | 2.77476e6i | − | 0.546842i | ||||||
\(482\) | −1.50762e6 | −0.295579 | ||||||||
\(483\) | 163391. | − | 1.59490e6i | 0.0318683 | − | 0.311076i | ||||
\(484\) | −5.01092e6 | −0.972309 | ||||||||
\(485\) | 5.24394e6i | 1.01229i | ||||||||
\(486\) | −2.61971e6 | + | 856679.i | −0.503110 | + | 0.164523i | ||||
\(487\) | 6.38336e6 | 1.21963 | 0.609813 | − | 0.792545i | \(-0.291244\pi\) | ||||
0.609813 | + | 0.792545i | \(0.291244\pi\) | |||||||
\(488\) | −2.19909e6 | −0.418017 | ||||||||
\(489\) | 212974. | + | 257243.i | 0.0402768 | + | 0.0486488i | ||||
\(490\) | 3.10982e6 | + | 51129.2i | 0.585121 | + | 0.00962009i | ||||
\(491\) | − | 837734.i | − | 0.156820i | −0.996921 | − | 0.0784102i | \(-0.975016\pi\) | ||
0.996921 | − | 0.0784102i | \(-0.0249844\pi\) | |||||||
\(492\) | −1.60390e6 | − | 1.93729e6i | −0.298721 | − | 0.360814i | ||||
\(493\) | 789613.i | 0.146318i | ||||||||
\(494\) | − | 2.09965e6i | − | 0.387105i | ||||||
\(495\) | 9.07821e6 | + | 1.72464e6i | 1.66528 | + | 0.316363i | ||||
\(496\) | 39280.8i | 0.00716928i | ||||||||
\(497\) | 670074. | + | 681182.i | 0.121684 | + | 0.123701i | ||||
\(498\) | 560054. | − | 463674.i | 0.101194 | − | 0.0837798i | ||||
\(499\) | −4.80919e6 | −0.864611 | −0.432306 | − | 0.901727i | \(-0.642300\pi\) | ||||
−0.432306 | + | 0.901727i | \(0.642300\pi\) | |||||||
\(500\) | −3.45991e6 | −0.618927 | ||||||||
\(501\) | −4.33731e6 | − | 5.23886e6i | −0.772015 | − | 0.932487i | ||||
\(502\) | − | 5.03638e6i | − | 0.891988i | ||||||
\(503\) | −2.58231e6 | −0.455081 | −0.227540 | − | 0.973769i | \(-0.573068\pi\) | ||||
−0.227540 | + | 0.973769i | \(0.573068\pi\) | |||||||
\(504\) | −4.31534e6 | + | 2.88586e6i | −0.756725 | + | 0.506056i | ||||
\(505\) | −4.99943e6 | −0.872352 | ||||||||
\(506\) | 1.46164e6i | 0.253784i | ||||||||
\(507\) | −2.65456e6 | − | 3.20635e6i | −0.458642 | − | 0.553975i | ||||
\(508\) | −6.75869e6 | −1.16199 | ||||||||
\(509\) | 5.81775e6 | 0.995315 | 0.497658 | − | 0.867374i | \(-0.334194\pi\) | ||||
0.497658 | + | 0.867374i | \(0.334194\pi\) | |||||||
\(510\) | −3.41621e6 | + | 2.82831e6i | −0.581592 | + | 0.481506i | ||||
\(511\) | 856653. | + | 870853.i | 0.145129 | + | 0.147534i | ||||
\(512\) | 2.74747e6i | 0.463189i | ||||||||
\(513\) | 3.97115e6 | + | 7.20410e6i | 0.666227 | + | 1.20861i | ||||
\(514\) | 2.85581e6i | 0.476784i | ||||||||
\(515\) | − | 1.32765e7i | − | 2.20580i | ||||||
\(516\) | 1.76922e6 | + | 2.13698e6i | 0.292522 | + | 0.353326i | ||||
\(517\) | 1.08319e7i | 1.78229i | ||||||||
\(518\) | −2.33934e6 | − | 2.37812e6i | −0.383062 | − | 0.389412i | ||||
\(519\) | 1.84486e6 | + | 2.22833e6i | 0.300639 | + | 0.363130i | ||||
\(520\) | −3.28849e6 | −0.533320 | ||||||||
\(521\) | −7.44578e6 | −1.20175 | −0.600877 | − | 0.799341i | \(-0.705182\pi\) | ||||
−0.600877 | + | 0.799341i | \(0.705182\pi\) | |||||||
\(522\) | −69747.2 | + | 367137.i | −0.0112034 | + | 0.0589728i | ||||
\(523\) | − | 2.68003e6i | − | 0.428435i | −0.976786 | − | 0.214218i | \(-0.931280\pi\) | ||
0.976786 | − | 0.214218i | \(-0.0687202\pi\) | |||||||
\(524\) | 3.66984e6 | 0.583874 | ||||||||
\(525\) | −1.39628e6 | − | 143042.i | −0.221092 | − | 0.0226499i | ||||
\(526\) | −4.92475e6 | −0.776103 | ||||||||
\(527\) | − | 247856.i | − | 0.0388752i | ||||||
\(528\) | −1.80015e6 | + | 1.49036e6i | −0.281011 | + | 0.232652i | ||||
\(529\) | 5.80697e6 | 0.902216 | ||||||||
\(530\) | −1.35929e6 | −0.210195 | ||||||||
\(531\) | −1.06201e6 | + | 5.59026e6i | −0.163453 | + | 0.860390i | ||||
\(532\) | 4.54764e6 | + | 4.62302e6i | 0.696638 | + | 0.708185i | ||||
\(533\) | 2.26173e6i | 0.344844i | ||||||||
\(534\) | 3.23674e6 | − | 2.67973e6i | 0.491196 | − | 0.406666i | ||||
\(535\) | − | 7.41670e6i | − | 1.12028i | ||||||
\(536\) | 2.38469e6i | 0.358525i | ||||||||
\(537\) | 2.05038e6 | − | 1.69753e6i | 0.306831 | − | 0.254028i | ||||
\(538\) | 230483.i | 0.0343307i | ||||||||
\(539\) | −1.03400e7 | − | 170002.i | −1.53302 | − | 0.0252047i | ||||
\(540\) | 4.72246e6 | − | 2.60318e6i | 0.696922 | − | 0.384167i | ||||
\(541\) | −7.33897e6 | −1.07806 | −0.539029 | − | 0.842288i | \(-0.681209\pi\) | ||||
−0.539029 | + | 0.842288i | \(0.681209\pi\) | |||||||
\(542\) | 5.38366e6 | 0.787190 | ||||||||
\(543\) | −3.91782e6 | + | 3.24360e6i | −0.570224 | + | 0.472094i | ||||
\(544\) | − | 9.22891e6i | − | 1.33707i | ||||||
\(545\) | 1.80488e6 | 0.260290 | ||||||||
\(546\) | 1.94375e6 | + | 199129.i | 0.279036 | + | 0.0285859i | ||||
\(547\) | −3.63983e6 | −0.520131 | −0.260066 | − | 0.965591i | \(-0.583744\pi\) | ||||
−0.260066 | + | 0.965591i | \(0.583744\pi\) | |||||||
\(548\) | − | 8.93604e6i | − | 1.27114i | ||||||
\(549\) | −3.18582e6 | − | 605228.i | −0.451118 | − | 0.0857015i | ||||
\(550\) | 1.27961e6 | 0.180373 | ||||||||
\(551\) | 1.11534e6 | 0.156505 | ||||||||
\(552\) | 1.29961e6 | + | 1.56975e6i | 0.181537 | + | 0.219272i | ||||
\(553\) | 2.51661e6 | − | 2.47557e6i | 0.349947 | − | 0.344241i | ||||
\(554\) | 3.47647e6i | 0.481243i | ||||||||
\(555\) | 5.27957e6 | + | 6.37699e6i | 0.727556 | + | 0.878786i | ||||
\(556\) | − | 7.47032e6i | − | 1.02483i | ||||||
\(557\) | 1.12162e7i | 1.53183i | 0.642944 | + | 0.765913i | \(0.277713\pi\) | ||||
−0.642944 | + | 0.765913i | \(0.722287\pi\) | |||||||
\(558\) | 21893.3 | − | 115243.i | 0.00297664 | − | 0.0156685i | ||||
\(559\) | − | 2.49485e6i | − | 0.337687i | ||||||
\(560\) | 1.39171e6 | − | 1.36902e6i | 0.187534 | − | 0.184476i | ||||
\(561\) | 1.13587e7 | − | 9.40395e6i | 1.52377 | − | 1.26155i | ||||
\(562\) | −4.49241e6 | −0.599983 | ||||||||
\(563\) | 1.46722e7 | 1.95085 | 0.975426 | − | 0.220326i | \(-0.0707120\pi\) | ||||
0.975426 | + | 0.220326i | \(0.0707120\pi\) | |||||||
\(564\) | 4.03103e6 | + | 4.86892e6i | 0.533603 | + | 0.644518i | ||||
\(565\) | − | 3.97474e6i | − | 0.523826i | ||||||
\(566\) | 2.32156e6 | 0.304607 | ||||||||
\(567\) | −7.04584e6 | + | 2.99307e6i | −0.920397 | + | 0.390984i | ||||
\(568\) | −1.21457e6 | −0.157962 | ||||||||
\(569\) | − | 5.12118e6i | − | 0.663116i | −0.943435 | − | 0.331558i | \(-0.892426\pi\) | ||
0.943435 | − | 0.331558i | \(-0.107574\pi\) | |||||||
\(570\) | 3.99503e6 | + | 4.82544e6i | 0.515030 | + | 0.622085i | ||||
\(571\) | 4.08710e6 | 0.524596 | 0.262298 | − | 0.964987i | \(-0.415520\pi\) | ||||
0.262298 | + | 0.964987i | \(0.415520\pi\) | |||||||
\(572\) | 4.57634e6 | 0.584828 | ||||||||
\(573\) | −3.56613e6 | + | 2.95243e6i | −0.453743 | + | 0.375658i | ||||
\(574\) | 1.90682e6 | + | 1.93842e6i | 0.241562 | + | 0.245566i | ||||
\(575\) | 550991.i | 0.0694984i | ||||||||
\(576\) | 461583. | − | 2.42969e6i | 0.0579688 | − | 0.305137i | ||||
\(577\) | − | 2.58345e6i | − | 0.323043i | −0.986869 | − | 0.161521i | \(-0.948360\pi\) | ||
0.986869 | − | 0.161521i | \(-0.0516401\pi\) | |||||||
\(578\) | 2.82606e6i | 0.351853i | ||||||||
\(579\) | −4.11648e6 | − | 4.97214e6i | −0.510305 | − | 0.616378i | ||||
\(580\) | − | 731133.i | − | 0.0902456i | ||||||
\(581\) | 1.43964e6 | − | 1.41617e6i | 0.176935 | − | 0.174050i | ||||
\(582\) | 2.52570e6 | + | 3.05070e6i | 0.309082 | + | 0.373329i | ||||
\(583\) | 4.51955e6 | 0.550711 | ||||||||
\(584\) | −1.55276e6 | −0.188396 | ||||||||
\(585\) | −4.76402e6 | − | 905049.i | −0.575551 | − | 0.109341i | ||||
\(586\) | 581002.i | 0.0698929i | ||||||||
\(587\) | −9.72773e6 | −1.16524 | −0.582621 | − | 0.812744i | \(-0.697973\pi\) | ||||
−0.582621 | + | 0.812744i | \(0.697973\pi\) | |||||||
\(588\) | −4.71107e6 | + | 3.77155e6i | −0.561923 | + | 0.449859i | ||||
\(589\) | −350100. | −0.0415819 | ||||||||
\(590\) | 4.33340e6i | 0.512505i | ||||||||
\(591\) | 2.60484e6 | − | 2.15657e6i | 0.306770 | − | 0.253978i | ||||
\(592\) | −2.09381e6 | −0.245546 | ||||||||
\(593\) | 9.57397e6 | 1.11803 | 0.559017 | − | 0.829156i | \(-0.311179\pi\) | ||||
0.559017 | + | 0.829156i | \(0.311179\pi\) | |||||||
\(594\) | 6.11197e6 | − | 3.36912e6i | 0.710747 | − | 0.391788i | ||||
\(595\) | −8.78149e6 | + | 8.63830e6i | −1.01689 | + | 1.00031i | ||||
\(596\) | 7.34658e6i | 0.847169i | ||||||||
\(597\) | −440866. | + | 364997.i | −0.0506257 | + | 0.0419135i | ||||
\(598\) | − | 767032.i | − | 0.0877123i | ||||||
\(599\) | 5.71115e6i | 0.650364i | 0.945651 | + | 0.325182i | \(0.105426\pi\) | ||||
−0.945651 | + | 0.325182i | \(0.894574\pi\) | |||||||
\(600\) | 1.37426e6 | − | 1.13776e6i | 0.155844 | − | 0.129025i | ||||
\(601\) | − | 1.49010e6i | − | 0.168279i | −0.996454 | − | 0.0841395i | \(-0.973186\pi\) | ||
0.996454 | − | 0.0841395i | \(-0.0268141\pi\) | |||||||
\(602\) | −2.10336e6 | − | 2.13822e6i | −0.236549 | − | 0.240470i | ||||
\(603\) | −656308. | + | 3.45469e6i | −0.0735046 | + | 0.386915i | ||||
\(604\) | 1.10427e7 | 1.23164 | ||||||||
\(605\) | −1.34448e7 | −1.49336 | ||||||||
\(606\) | −2.90845e6 | + | 2.40793e6i | −0.321721 | + | 0.266356i | ||||
\(607\) | 1.13768e7i | 1.25328i | 0.779308 | + | 0.626641i | \(0.215571\pi\) | ||||
−0.779308 | + | 0.626641i | \(0.784429\pi\) | |||||||
\(608\) | −1.30360e7 | −1.43016 | ||||||||
\(609\) | −105778. | + | 1.03253e6i | −0.0115572 | + | 0.112813i | ||||
\(610\) | −2.46955e6 | −0.268716 | ||||||||
\(611\) | − | 5.68431e6i | − | 0.615991i | ||||||
\(612\) | 1.60608e6 | − | 8.45414e6i | 0.173336 | − | 0.912412i | ||||
\(613\) | 8.50093e6 | 0.913724 | 0.456862 | − | 0.889537i | \(-0.348973\pi\) | ||||
0.456862 | + | 0.889537i | \(0.348973\pi\) | |||||||
\(614\) | −1.18174e6 | −0.126503 | ||||||||
\(615\) | −4.30342e6 | − | 5.19794e6i | −0.458803 | − | 0.554170i | ||||
\(616\) | 9.37106e6 | − | 9.21826e6i | 0.995032 | − | 0.978807i | ||||
\(617\) | − | 1.82563e7i | − | 1.93064i | −0.261073 | − | 0.965319i | \(-0.584076\pi\) | ||
0.261073 | − | 0.965319i | \(-0.415924\pi\) | |||||||
\(618\) | −6.39453e6 | − | 7.72370e6i | −0.673499 | − | 0.813494i | ||||
\(619\) | 1.24791e7i | 1.30905i | 0.756041 | + | 0.654524i | \(0.227131\pi\) | ||||
−0.756041 | + | 0.654524i | \(0.772869\pi\) | |||||||
\(620\) | 229499.i | 0.0239774i | ||||||||
\(621\) | 1.45072e6 | + | 2.63177e6i | 0.150957 | + | 0.273854i | ||||
\(622\) | 6.87968e6i | 0.713005i | ||||||||
\(623\) | 8.32017e6 | − | 8.18450e6i | 0.858840 | − | 0.844836i | ||||
\(624\) | 944674. | − | 782104.i | 0.0971226 | − | 0.0804087i | ||||
\(625\) | −1.14537e7 | −1.17285 | ||||||||
\(626\) | 1.90098e6 | 0.193883 | ||||||||
\(627\) | −1.32832e7 | − | 1.60443e7i | −1.34938 | − | 1.62987i | ||||
\(628\) | 7.45843e6i | 0.754655i | ||||||||
\(629\) | 1.32116e7 | 1.33146 | ||||||||
\(630\) | −4.84606e6 | + | 3.24077e6i | −0.486449 | + | 0.325310i | ||||
\(631\) | −1.52412e7 | −1.52387 | −0.761933 | − | 0.647656i | \(-0.775749\pi\) | ||||
−0.761933 | + | 0.647656i | \(0.775749\pi\) | |||||||
\(632\) | 4.48720e6i | 0.446871i | ||||||||
\(633\) | 5.83950e6 | + | 7.05331e6i | 0.579250 | + | 0.699654i | ||||
\(634\) | 577525. | 0.0570620 | ||||||||
\(635\) | −1.81342e7 | −1.78469 | ||||||||
\(636\) | 2.03153e6 | − | 1.68193e6i | 0.199150 | − | 0.164878i | ||||
\(637\) | 5.42616e6 | + | 89212.6i | 0.529839 | + | 0.00871119i | ||||
\(638\) | − | 946256.i | − | 0.0920358i | ||||||
\(639\) | −1.75954e6 | − | 334271.i | −0.170470 | − | 0.0323852i | ||||
\(640\) | 9.98827e6i | 0.963918i | ||||||||
\(641\) | 3.06269e6i | 0.294414i | 0.989106 | + | 0.147207i | \(0.0470283\pi\) | ||||
−0.989106 | + | 0.147207i | \(0.952972\pi\) | |||||||
\(642\) | −3.57220e6 | − | 4.31472e6i | −0.342056 | − | 0.413157i | ||||
\(643\) | − | 4.16015e6i | − | 0.396809i | −0.980120 | − | 0.198404i | \(-0.936424\pi\) | ||
0.980120 | − | 0.198404i | \(-0.0635760\pi\) | |||||||
\(644\) | 1.66132e6 | + | 1.68886e6i | 0.157848 | + | 0.160465i | ||||
\(645\) | 4.74699e6 | + | 5.73370e6i | 0.449282 | + | 0.542670i | ||||
\(646\) | 9.99718e6 | 0.942532 | ||||||||
\(647\) | −1.44997e7 | −1.36175 | −0.680877 | − | 0.732398i | \(-0.738401\pi\) | ||||
−0.680877 | + | 0.732398i | \(0.738401\pi\) | |||||||
\(648\) | 3.56840e6 | − | 9.05276e6i | 0.333838 | − | 0.846922i | ||||
\(649\) | − | 1.44083e7i | − | 1.34277i | ||||||
\(650\) | −671508. | −0.0623402 | ||||||||
\(651\) | 33203.2 | − | 324106.i | 0.00307063 | − | 0.0299733i | ||||
\(652\) | −493476. | −0.0454619 | ||||||||
\(653\) | 5.47090e6i | 0.502084i | 0.967976 | + | 0.251042i | \(0.0807732\pi\) | ||||
−0.967976 | + | 0.251042i | \(0.919227\pi\) | |||||||
\(654\) | 1.05000e6 | − | 869308.i | 0.0959945 | − | 0.0794747i | ||||
\(655\) | 9.84652e6 | 0.896766 | ||||||||
\(656\) | 1.70668e6 | 0.154843 | ||||||||
\(657\) | −2.24948e6 | − | 427347.i | −0.203314 | − | 0.0386249i | ||||
\(658\) | −4.79232e6 | − | 4.87176e6i | −0.431501 | − | 0.438653i | ||||
\(659\) | 1.88834e7i | 1.69381i | 0.531741 | + | 0.846907i | \(0.321538\pi\) | ||||
−0.531741 | + | 0.846907i | \(0.678462\pi\) | |||||||
\(660\) | −1.05174e7 | + | 8.70748e6i | −0.939831 | + | 0.778095i | ||||
\(661\) | 4.64223e6i | 0.413260i | 0.978419 | + | 0.206630i | \(0.0662496\pi\) | ||||
−0.978419 | + | 0.206630i | \(0.933750\pi\) | |||||||
\(662\) | − | 8.54802e6i | − | 0.758089i | ||||||
\(663\) | −5.96075e6 | + | 4.93496e6i | −0.526644 | + | 0.436014i | ||||
\(664\) | 2.56693e6i | 0.225940i | ||||||||
\(665\) | 1.22017e7 | + | 1.24040e7i | 1.06996 | + | 1.08770i | ||||
\(666\) | 6.14285e6 | + | 1.16699e6i | 0.536642 | + | 0.101949i | ||||
\(667\) | 407451. | 0.0354618 | ||||||||
\(668\) | 1.00498e7 | 0.871401 | ||||||||
\(669\) | −4.20031e6 | + | 3.47748e6i | −0.362841 | + | 0.300400i | ||||
\(670\) | 2.67797e6i | 0.230472i | ||||||||
\(671\) | 8.21109e6 | 0.704036 | ||||||||
\(672\) | 1.23632e6 | − | 1.20681e7i | 0.105611 | − | 1.03090i | ||||
\(673\) | 629529. | 0.0535770 | 0.0267885 | − | 0.999641i | \(-0.491472\pi\) | ||||
0.0267885 | + | 0.999641i | \(0.491472\pi\) | |||||||
\(674\) | 1.01125e7i | 0.857451i | ||||||||
\(675\) | 2.30401e6 | − | 1.27005e6i | 0.194637 | − | 0.107291i | ||||
\(676\) | 6.15082e6 | 0.517685 | ||||||||
\(677\) | 6.49528e6 | 0.544661 | 0.272331 | − | 0.962204i | \(-0.412206\pi\) | ||||
0.272331 | + | 0.962204i | \(0.412206\pi\) | |||||||
\(678\) | −1.91440e6 | − | 2.31233e6i | −0.159940 | − | 0.193186i | ||||
\(679\) | 7.71406e6 | + | 7.84193e6i | 0.642109 | + | 0.652753i | ||||
\(680\) | − | 1.56577e7i | − | 1.29854i | ||||||
\(681\) | 9.19603e6 | + | 1.11075e7i | 0.759858 | + | 0.917803i | ||||
\(682\) | 297025.i | 0.0244530i | ||||||||
\(683\) | − | 8.25581e6i | − | 0.677186i | −0.940933 | − | 0.338593i | \(-0.890049\pi\) | ||
0.940933 | − | 0.338593i | \(-0.109951\pi\) | |||||||
\(684\) | −1.19416e7 | − | 2.26862e6i | −0.975938 | − | 0.185405i | ||||
\(685\) | − | 2.39762e7i | − | 1.95233i | ||||||
\(686\) | 4.72573e6 | − | 4.49823e6i | 0.383406 | − | 0.364948i | ||||
\(687\) | −1.63350e6 | + | 1.35239e6i | −0.132046 | + | 0.109322i | ||||
\(688\) | −1.88259e6 | −0.151630 | ||||||||
\(689\) | −2.37175e6 | −0.190336 | ||||||||
\(690\) | 1.45944e6 | + | 1.76281e6i | 0.116698 | + | 0.140955i | ||||
\(691\) | 2.21202e7i | 1.76235i | 0.472787 | + | 0.881177i | \(0.343248\pi\) | ||||
−0.472787 | + | 0.881177i | \(0.656752\pi\) | |||||||
\(692\) | −4.27467e6 | −0.339342 | ||||||||
\(693\) | 1.61128e7 | − | 1.07754e7i | 1.27450 | − | 0.852313i | ||||
\(694\) | 1.64077e6 | 0.129315 | ||||||||
\(695\) | − | 2.00436e7i | − | 1.57403i | ||||||
\(696\) | −841360. | − | 1.01625e6i | −0.0658353 | − | 0.0795199i | ||||
\(697\) | −1.07689e7 | −0.839633 | ||||||||
\(698\) | −3612.61 | −0.000280661 | ||||||||
\(699\) | 1.36600e7 | − | 1.13093e7i | 1.05745 | − | 0.875472i | ||||
\(700\) | 1.47853e6 | − | 1.45442e6i | 0.114048 | − | 0.112188i | ||||
\(701\) | 4.20151e6i | 0.322932i | 0.986878 | + | 0.161466i | \(0.0516222\pi\) | ||||
−0.986878 | + | 0.161466i | \(0.948378\pi\) | |||||||
\(702\) | −3.20741e6 | + | 1.76803e6i | −0.245647 | + | 0.135409i | ||||
\(703\) | − | 1.86616e7i | − | 1.42417i | ||||||
\(704\) | 6.26227e6i | 0.476212i | ||||||||
\(705\) | 1.08156e7 | + | 1.30638e7i | 0.819556 | + | 0.989910i | ||||
\(706\) | − | 3.44969e6i | − | 0.260476i | ||||||
\(707\) | −7.47629e6 | + | 7.35438e6i | −0.562519 | + | 0.553347i | ||||
\(708\) | −5.36197e6 | − | 6.47651e6i | −0.402014 | − | 0.485577i | ||||
\(709\) | 1.27013e7 | 0.948928 | 0.474464 | − | 0.880275i | \(-0.342642\pi\) | ||||
0.474464 | + | 0.880275i | \(0.342642\pi\) | |||||||
\(710\) | −1.36394e6 | −0.101543 | ||||||||
\(711\) | −1.23495e6 | + | 6.50058e6i | −0.0916172 | + | 0.482257i | ||||
\(712\) | 1.48351e7i | 1.09671i | ||||||||
\(713\) | −127897. | −0.00942185 | ||||||||
\(714\) | −948124. | + | 9.25492e6i | −0.0696017 | + | 0.679403i | ||||
\(715\) | 1.22787e7 | 0.898233 | ||||||||
\(716\) | 3.93330e6i | 0.286731i | ||||||||
\(717\) | −1.25389e7 | + | 1.03810e7i | −0.910879 | + | 0.754125i | ||||
\(718\) | −6.31413e6 | −0.457091 | ||||||||
\(719\) | −1.21200e7 | −0.874337 | −0.437169 | − | 0.899380i | \(-0.644019\pi\) | ||||
−0.437169 | + | 0.899380i | \(0.644019\pi\) | |||||||
\(720\) | −682943. | + | 3.59489e6i | −0.0490968 | + | 0.258437i | ||||
\(721\) | −1.95303e7 | − | 1.98541e7i | −1.39917 | − | 1.42237i | ||||
\(722\) | − | 6.70692e6i | − | 0.478829i | ||||||
\(723\) | 6.04560e6 | − | 5.00521e6i | 0.430124 | − | 0.356104i | ||||
\(724\) | − | 7.51566e6i | − | 0.532869i | ||||||
\(725\) | − | 356708.i | − | 0.0252039i | ||||||
\(726\) | −7.82158e6 | + | 6.47556e6i | −0.550748 | + | 0.455970i | ||||
\(727\) | 3.77140e6i | 0.264647i | 0.991207 | + | 0.132323i | \(0.0422437\pi\) | ||||
−0.991207 | + | 0.132323i | \(0.957756\pi\) | |||||||
\(728\) | −4.91770e6 | + | 4.83751e6i | −0.343901 | + | 0.338294i | ||||
\(729\) | 7.66100e6 | − | 1.21326e7i | 0.533908 | − | 0.845542i | ||||
\(730\) | −1.74373e6 | −0.121108 | ||||||||
\(731\) | 1.18789e7 | 0.822209 | ||||||||
\(732\) | 3.69088e6 | − | 3.05572e6i | 0.254596 | − | 0.210783i | ||||
\(733\) | − | 1.16976e7i | − | 0.804148i | −0.915607 | − | 0.402074i | \(-0.868289\pi\) | ||
0.915607 | − | 0.402074i | \(-0.131711\pi\) | |||||||
\(734\) | 1.00948e7 | 0.691601 | ||||||||
\(735\) | −1.26402e7 | + | 1.01194e7i | −0.863052 | + | 0.690935i | ||||
\(736\) | −4.76224e6 | −0.324053 | ||||||||
\(737\) | − | 8.90409e6i | − | 0.603838i | ||||||
\(738\) | −5.00709e6 | − | 951227.i | −0.338411 | − | 0.0642900i | ||||
\(739\) | −1.02243e6 | −0.0688689 | −0.0344344 | − | 0.999407i | \(-0.510963\pi\) | ||||
−0.0344344 | + | 0.999407i | \(0.510963\pi\) | |||||||
\(740\) | −1.22331e7 | −0.821219 | ||||||||
\(741\) | 6.97071e6 | + | 8.41965e6i | 0.466371 | + | 0.563312i | ||||
\(742\) | −2.03272e6 | + | 1.99957e6i | −0.135540 | + | 0.133330i | ||||
\(743\) | 1.29463e7i | 0.860345i | 0.902747 | + | 0.430173i | \(0.141547\pi\) | ||||
−0.902747 | + | 0.430173i | \(0.858453\pi\) | |||||||
\(744\) | 264099. | + | 318995.i | 0.0174918 | + | 0.0211277i | ||||
\(745\) | 1.97116e7i | 1.30116i | ||||||||
\(746\) | − | 194795.i | − | 0.0128154i | ||||||
\(747\) | −706463. | + | 3.71870e6i | −0.0463221 | + | 0.243831i | ||||
\(748\) | 2.17896e7i | 1.42395i | ||||||||
\(749\) | −1.09103e7 | − | 1.10912e7i | −0.710612 | − | 0.722391i | ||||
\(750\) | −5.40059e6 | + | 4.47120e6i | −0.350581 | + | 0.290249i | ||||
\(751\) | −2.90253e7 | −1.87792 | −0.938959 | − | 0.344028i | \(-0.888208\pi\) | ||||
−0.938959 | + | 0.344028i | \(0.888208\pi\) | |||||||
\(752\) | −4.28933e6 | −0.276596 | ||||||||
\(753\) | 1.67205e7 | + | 2.01960e7i | 1.07464 | + | 1.29801i | ||||
\(754\) | 496572.i | 0.0318093i | ||||||||
\(755\) | 2.96287e7 | 1.89167 | ||||||||
\(756\) | 3.23271e6 | − | 1.08398e7i | 0.205713 | − | 0.689792i | ||||
\(757\) | −1.29941e7 | −0.824148 | −0.412074 | − | 0.911150i | \(-0.635195\pi\) | ||||
−0.412074 | + | 0.911150i | \(0.635195\pi\) | |||||||
\(758\) | − | 2.06870e6i | − | 0.130775i | ||||||
\(759\) | −4.85256e6 | − | 5.86122e6i | −0.305750 | − | 0.369304i | ||||
\(760\) | −2.21167e7 | −1.38895 | ||||||||
\(761\) | −1.68382e7 | −1.05398 | −0.526991 | − | 0.849871i | \(-0.676680\pi\) | ||||
−0.526991 | + | 0.849871i | \(0.676680\pi\) | |||||||
\(762\) | −1.05497e7 | + | 8.73418e6i | −0.658191 | + | 0.544922i | ||||
\(763\) | 2.69908e6 | − | 2.65506e6i | 0.167843 | − | 0.165106i | ||||
\(764\) | − | 6.84099e6i | − | 0.424019i | ||||||
\(765\) | 4.30927e6 | − | 2.26832e7i | 0.266226 | − | 1.40137i | ||||
\(766\) | − | 7.33226e6i | − | 0.451509i | ||||||
\(767\) | 7.56111e6i | 0.464085i | ||||||||
\(768\) | 8.04838e6 | + | 9.72132e6i | 0.492385 | + | 0.594733i | ||||
\(769\) | − | 2.53765e7i | − | 1.54745i | −0.633525 | − | 0.773723i | \(-0.718392\pi\) | ||
0.633525 | − | 0.773723i | \(-0.281608\pi\) | |||||||
\(770\) | 1.05236e7 | − | 1.03520e7i | 0.639640 | − | 0.629210i | ||||
\(771\) | −9.48114e6 | − | 1.14519e7i | −0.574413 | − | 0.693812i | ||||
\(772\) | 9.53819e6 | 0.576000 | ||||||||
\(773\) | 3.00362e6 | 0.180799 | 0.0903996 | − | 0.995906i | \(-0.471186\pi\) | ||||
0.0903996 | + | 0.995906i | \(0.471186\pi\) | |||||||
\(774\) | 5.52318e6 | + | 1.04927e6i | 0.331388 | + | 0.0629558i | ||||
\(775\) | 111969.i | 0.00669643i | ||||||||
\(776\) | −1.39824e7 | −0.833544 | ||||||||
\(777\) | 1.72761e7 | + | 1.76985e6i | 1.02658 | + | 0.105168i | ||||
\(778\) | 1.11643e7 | 0.661277 | ||||||||
\(779\) | 1.52112e7i | 0.898093i | ||||||||
\(780\) | 5.51929e6 | − | 4.56947e6i | 0.324823 | − | 0.268924i | ||||
\(781\) | 4.53503e6 | 0.266043 | ||||||||
\(782\) | 3.65212e6 | 0.213564 | ||||||||
\(783\) | −939186. | − | 1.70379e6i | −0.0547454 | − | 0.0993142i | ||||
\(784\) | 67319.1 | − | 4.09454e6i | 0.00391155 | − | 0.237911i | ||||
\(785\) | 2.00117e7i | 1.15907i | ||||||||
\(786\) | 5.72828e6 | − | 4.74249e6i | 0.330725 | − | 0.273811i | ||||
\(787\) | − | 9.42926e6i | − | 0.542676i | −0.962484 | − | 0.271338i | \(-0.912534\pi\) | ||
0.962484 | − | 0.271338i | \(-0.0874662\pi\) | |||||||
\(788\) | 4.99694e6i | 0.286674i | ||||||||
\(789\) | 1.97484e7 | − | 1.63499e7i | 1.12938 | − | 0.935023i | ||||
\(790\) | 5.03905e6i | 0.287264i | ||||||||
\(791\) | −5.84701e6 | − | 5.94393e6i | −0.332271 | − | 0.337779i | ||||
\(792\) | −4.59858e6 | + | 2.42061e7i | −0.260502 | + | 1.37124i | ||||
\(793\) | −4.30898e6 | −0.243328 | ||||||||
\(794\) | −9.57407e6 | −0.538946 | ||||||||
\(795\) | 5.45079e6 | − | 4.51276e6i | 0.305873 | − | 0.253235i | ||||
\(796\) | − | 845725.i | − | 0.0473093i | ||||||
\(797\) | −6.70033e6 | −0.373637 | −0.186819 | − | 0.982394i | \(-0.559818\pi\) | ||||
−0.186819 | + | 0.982394i | \(0.559818\pi\) | |||||||
\(798\) | 1.30727e7 | + | 1.33924e6i | 0.726706 | + | 0.0744477i | ||||
\(799\) | 2.70651e7 | 1.49983 | ||||||||
\(800\) | 4.16916e6i | 0.230316i | ||||||||
\(801\) | −4.08289e6 | + | 2.14916e7i | −0.224847 | + | 1.18355i | ||||
\(802\) | 1.80084e7 | 0.988640 | ||||||||
\(803\) | 5.79778e6 | 0.317302 | ||||||||
\(804\) | −3.31361e6 | − | 4.00238e6i | −0.180784 | − | 0.218363i | ||||
\(805\) | 4.45748e6 | + | 4.53137e6i | 0.242437 | + | 0.246456i | ||||
\(806\) | − | 155872.i | − | 0.00845141i | ||||||
\(807\) | −765190. | − | 924244.i | −0.0413605 | − | 0.0499577i | ||||
\(808\) | − | 1.33305e7i | − | 0.718318i | ||||||
\(809\) | − | 2.51823e7i | − | 1.35277i | −0.736547 | − | 0.676386i | \(-0.763545\pi\) | ||
0.736547 | − | 0.676386i | \(-0.236455\pi\) | |||||||
\(810\) | 4.00726e6 | − | 1.01661e7i | 0.214603 | − | 0.544430i | ||||
\(811\) | 2.59174e6i | 0.138369i | 0.997604 | + | 0.0691846i | \(0.0220397\pi\) | ||||
−0.997604 | + | 0.0691846i | \(0.977960\pi\) | |||||||
\(812\) | −1.07553e6 | − | 1.09336e6i | −0.0572442 | − | 0.0581931i | ||||
\(813\) | −2.15887e7 | + | 1.78735e7i | −1.14551 | + | 0.948380i | ||||
\(814\) | −1.58325e7 | −0.837509 | ||||||||
\(815\) | −1.32404e6 | −0.0698245 | ||||||||
\(816\) | 3.72388e6 | + | 4.49794e6i | 0.195781 | + | 0.236476i | ||||
\(817\) | − | 1.67791e7i | − | 0.879455i | ||||||
\(818\) | −1.70662e7 | −0.891772 | ||||||||
\(819\) | −8.45562e6 | + | 5.65465e6i | −0.440490 | + | 0.294575i | ||||
\(820\) | 9.97134e6 | 0.517868 | ||||||||
\(821\) | 2.39963e7i | 1.24247i | 0.783623 | + | 0.621237i | \(0.213370\pi\) | ||||
−0.783623 | + | 0.621237i | \(0.786630\pi\) | |||||||
\(822\) | −1.15480e7 | − | 1.39483e7i | −0.596109 | − | 0.720017i | ||||
\(823\) | −1.47240e7 | −0.757748 | −0.378874 | − | 0.925448i | \(-0.623689\pi\) | ||||
−0.378874 | + | 0.925448i | \(0.623689\pi\) | |||||||
\(824\) | 3.54005e7 | 1.81632 | ||||||||
\(825\) | −5.13128e6 | + | 4.24824e6i | −0.262477 | + | 0.217307i | ||||
\(826\) | 6.37462e6 | + | 6.48029e6i | 0.325090 | + | 0.330479i | ||||
\(827\) | − | 2.95165e7i | − | 1.50072i | −0.661028 | − | 0.750361i | \(-0.729879\pi\) | ||
0.661028 | − | 0.750361i | \(-0.270121\pi\) | |||||||
\(828\) | −4.36245e6 | − | 828760.i | −0.221133 | − | 0.0420100i | ||||
\(829\) | 3.36080e7i | 1.69846i | 0.528019 | + | 0.849232i | \(0.322935\pi\) | ||||
−0.528019 | + | 0.849232i | \(0.677065\pi\) | |||||||
\(830\) | 2.88262e6i | 0.145242i | ||||||||
\(831\) | −1.15417e7 | − | 1.39408e7i | −0.579785 | − | 0.700300i | ||||
\(832\) | − | 3.28629e6i | − | 0.164588i | ||||||
\(833\) | −424774. | + | 2.58359e7i | −0.0212102 | + | 1.29007i | ||||
\(834\) | −9.65382e6 | − | 1.16605e7i | −0.480600 | − | 0.580498i | ||||
\(835\) | 2.69647e7 | 1.33838 | ||||||||
\(836\) | 3.07782e7 | 1.52310 | ||||||||
\(837\) | 294806. | + | 534811.i | 0.0145453 | + | 0.0263868i | ||||
\(838\) | − | 7.19513e6i | − | 0.353939i | ||||||
\(839\) | 6.45947e6 | 0.316805 | 0.158402 | − | 0.987375i | \(-0.449366\pi\) | ||||
0.158402 | + | 0.987375i | \(0.449366\pi\) | |||||||
\(840\) | 2.09753e6 | − | 2.04746e7i | 0.102568 | − | 1.00119i | ||||
\(841\) | 2.02474e7 | 0.987140 | ||||||||
\(842\) | − | 5.53728e6i | − | 0.269164i | ||||||
\(843\) | 1.80147e7 | − | 1.49146e7i | 0.873089 | − | 0.722839i | ||||
\(844\) | −1.35305e7 | −0.653821 | ||||||||
\(845\) | 1.65032e7 | 0.795108 | ||||||||
\(846\) | 1.25841e7 | + | 2.39068e6i | 0.604501 | + | 0.114841i | ||||
\(847\) | −2.01057e7 | + | 1.97779e7i | −0.962965 | + | 0.947263i | ||||
\(848\) | 1.78970e6i | 0.0854655i | ||||||||
\(849\) | −9.30955e6 | + | 7.70746e6i | −0.443261 | + | 0.366980i | ||||
\(850\) | − | 3.19730e6i | − | 0.151787i | ||||||
\(851\) | − | 6.81737e6i | − | 0.322696i | ||||||
\(852\) | 2.03849e6 | − | 1.68769e6i | 0.0962077 | − | 0.0796513i | ||||
\(853\) | 4.03008e7i | 1.89645i | 0.317602 | + | 0.948224i | \(0.397123\pi\) | ||||
−0.317602 | + | 0.948224i | \(0.602877\pi\) | |||||||
\(854\) | −3.69303e6 | + | 3.63281e6i | −0.173276 | + | 0.170451i | ||||
\(855\) | −3.20404e7 | − | 6.08691e6i | −1.49893 | − | 0.284762i | ||||
\(856\) | 1.97759e7 | 0.922469 | ||||||||
\(857\) | −9.87862e6 | −0.459456 | −0.229728 | − | 0.973255i | \(-0.573784\pi\) | ||||
−0.229728 | + | 0.973255i | \(0.573784\pi\) | |||||||
\(858\) | 7.14324e6 | − | 5.91396e6i | 0.331266 | − | 0.274258i | ||||
\(859\) | − | 4.71083e6i | − | 0.217829i | −0.994051 | − | 0.108914i | \(-0.965263\pi\) | ||
0.994051 | − | 0.108914i | \(-0.0347374\pi\) | |||||||
\(860\) | −1.09991e7 | −0.507121 | ||||||||
\(861\) | −1.40819e7 | − | 1.44262e6i | −0.647369 | − | 0.0663200i | ||||
\(862\) | −2.00626e6 | −0.0919643 | ||||||||
\(863\) | − | 8.17467e6i | − | 0.373632i | −0.982395 | − | 0.186816i | \(-0.940183\pi\) | ||
0.982395 | − | 0.186816i | \(-0.0598167\pi\) | |||||||
\(864\) | 1.09771e7 | + | 1.99137e7i | 0.500269 | + | 0.907543i | ||||
\(865\) | −1.14693e7 | −0.521192 | ||||||||
\(866\) | −9.53136e6 | −0.431877 | ||||||||
\(867\) | −9.38236e6 | − | 1.13326e7i | −0.423901 | − | 0.512014i | ||||
\(868\) | 337603. | + | 343200.i | 0.0152092 | + | 0.0154614i | ||||
\(869\) | − | 1.67545e7i | − | 0.752633i | ||||||
\(870\) | −944835. | − | 1.14123e6i | −0.0423212 | − | 0.0511181i | ||||
\(871\) | 4.67264e6i | 0.208698i | ||||||||
\(872\) | 4.81254e6i | 0.214330i | ||||||||
\(873\) | −2.02563e7 | − | 3.84821e6i | −0.899548 | − | 0.170892i | ||||
\(874\) | − | 5.15868e6i | − | 0.228433i | ||||||
\(875\) | −1.38824e7 | + | 1.36561e7i | −0.612979 | + | 0.602984i | ||||
\(876\) | 2.60610e6 | − | 2.15762e6i | 0.114744 | − | 0.0949978i | ||||
\(877\) | −1.16202e7 | −0.510169 | −0.255084 | − | 0.966919i | \(-0.582103\pi\) | ||||
−0.255084 | + | 0.966919i | \(0.582103\pi\) | |||||||
\(878\) | −9.10927e6 | −0.398793 | ||||||||
\(879\) | −1.92889e6 | − | 2.32984e6i | −0.0842047 | − | 0.101708i | ||||
\(880\) | − | 9.26544e6i | − | 0.403329i | ||||||
\(881\) | −4.28179e7 | −1.85860 | −0.929300 | − | 0.369327i | \(-0.879588\pi\) | ||||
−0.929300 | + | 0.369327i | \(0.879588\pi\) | |||||||
\(882\) | −2.47961e6 | + | 1.19751e7i | −0.107328 | + | 0.518332i | ||||
\(883\) | 2.20297e7 | 0.950839 | 0.475420 | − | 0.879759i | \(-0.342296\pi\) | ||||
0.475420 | + | 0.879759i | \(0.342296\pi\) | |||||||
\(884\) | − | 1.14347e7i | − | 0.492145i | ||||||
\(885\) | −1.43866e7 | − | 1.73771e7i | −0.617449 | − | 0.745793i | ||||
\(886\) | −1.21766e7 | −0.521125 | ||||||||
\(887\) | 1.86327e7 | 0.795181 | 0.397590 | − | 0.917563i | \(-0.369847\pi\) | ||||
0.397590 | + | 0.917563i | \(0.369847\pi\) | |||||||
\(888\) | −1.70036e7 | + | 1.40774e7i | −0.723617 | + | 0.599089i | ||||
\(889\) | −2.71184e7 | + | 2.66762e7i | −1.15082 | + | 1.13206i | ||||
\(890\) | 1.66596e7i | 0.705003i | ||||||||
\(891\) | −1.33239e7 | + | 3.38017e7i | −0.562260 | + | 1.42641i | ||||
\(892\) | − | 8.05757e6i | − | 0.339072i | ||||||
\(893\) | − | 3.82298e7i | − | 1.60426i | ||||||
\(894\) | 9.49391e6 | + | 1.14673e7i | 0.397284 | + | 0.479864i | ||||
\(895\) | 1.05534e7i | 0.440388i | ||||||||
\(896\) | 1.46932e7 | + | 1.49367e7i | 0.611429 | + | 0.621564i | ||||
\(897\) | 2.54651e6 | + | 3.07583e6i | 0.105673 | + | 0.127638i | ||||
\(898\) | 9.90260e6 | 0.409787 | ||||||||
\(899\) | 82799.6 | 0.00341687 | ||||||||
\(900\) | −725549. | + | 3.81916e6i | −0.0298580 | + | 0.157167i | ||||
\(901\) | − | 1.12927e7i | − | 0.463434i | ||||||
\(902\) | 1.29052e7 | 0.528141 | ||||||||
\(903\) | 1.55333e7 | + | 1.59132e6i | 0.633935 | + | 0.0649437i | ||||
\(904\) | 1.05982e7 | 0.431333 | ||||||||
\(905\) | − | 2.01652e7i | − | 0.818429i | ||||||
\(906\) | 1.72367e7 | − | 1.42704e7i | 0.697643 | − | 0.577585i | ||||
\(907\) | 5.81361e6 | 0.234654 | 0.117327 | − | 0.993093i | \(-0.462567\pi\) | ||||
0.117327 | + | 0.993093i | \(0.462567\pi\) | |||||||
\(908\) | −2.13078e7 | −0.857679 | ||||||||
\(909\) | 3.66878e6 | − | 1.93118e7i | 0.147269 | − | 0.775198i | ||||
\(910\) | −5.52250e6 | + | 5.43245e6i | −0.221071 | + | 0.217467i | ||||
\(911\) | − | 2.69096e7i | − | 1.07426i | −0.843498 | − | 0.537132i | \(-0.819508\pi\) | ||
0.843498 | − | 0.537132i | \(-0.180492\pi\) | |||||||
\(912\) | 6.35340e6 | − | 5.26004e6i | 0.252941 | − | 0.209412i | ||||
\(913\) | − | 9.58454e6i | − | 0.380535i | ||||||
\(914\) | 2.38688e6i | 0.0945073i | ||||||||
\(915\) | 9.90297e6 | − | 8.19876e6i | 0.391032 | − | 0.323739i | ||||
\(916\) | − | 3.13358e6i | − | 0.123396i | ||||||
\(917\) | 1.47248e7 | − | 1.44847e7i | 0.578262 | − | 0.568833i | ||||
\(918\) | −8.41825e6 | − | 1.52716e7i | −0.329697 | − | 0.598107i | ||||
\(919\) | 1.86255e7 | 0.727476 | 0.363738 | − | 0.931501i | \(-0.381500\pi\) | ||||
0.363738 | + | 0.931501i | \(0.381500\pi\) | |||||||
\(920\) | −8.07958e6 | −0.314716 | ||||||||
\(921\) | 4.73881e6 | − | 3.92331e6i | 0.184086 | − | 0.152406i | ||||
\(922\) | − | 1.29615e7i | − | 0.502144i | ||||||
\(923\) | −2.37987e6 | −0.0919494 | ||||||||
\(924\) | −2.91898e6 | + | 2.84930e7i | −0.112474 | + | 1.09789i | ||||
\(925\) | −5.96835e6 | −0.229351 | ||||||||
\(926\) | 1.61241e7i | 0.617943i | ||||||||
\(927\) | 5.12845e7 | + | 9.74283e6i | 1.96014 | + | 0.372380i | ||||
\(928\) | 3.08304e6 | 0.117519 | ||||||||
\(929\) | 2.43516e7 | 0.925740 | 0.462870 | − | 0.886426i | \(-0.346820\pi\) | ||||
0.462870 | + | 0.886426i | \(0.346820\pi\) | |||||||
\(930\) | 296579. | + | 358227.i | 0.0112443 | + | 0.0135816i | ||||
\(931\) | 3.64936e7 | + | 600000.i | 1.37989 | + | 0.0226870i | ||||
\(932\) | 2.62044e7i | 0.988177i | ||||||||
\(933\) | −2.28402e7 | − | 2.75878e7i | −0.859004 | − | 1.03756i | ||||
\(934\) | 2.02886e6i | 0.0761000i | ||||||||
\(935\) | 5.84636e7i | 2.18704i | ||||||||
\(936\) | 2.41322e6 | − | 1.27028e7i | 0.0900343 | − | 0.473924i | ||||
\(937\) | − | 6.06143e6i | − | 0.225541i | −0.993621 | − | 0.112771i | \(-0.964027\pi\) | ||
0.993621 | − | 0.112771i | \(-0.0359725\pi\) | |||||||
\(938\) | 3.93941e6 | + | 4.00471e6i | 0.146192 | + | 0.148616i | ||||
\(939\) | −7.62298e6 | + | 6.31114e6i | −0.282137 | + | 0.233584i | ||||
\(940\) | −2.50606e7 | −0.925063 | ||||||||
\(941\) | −1.76788e6 | −0.0650847 | −0.0325424 | − | 0.999470i | \(-0.510360\pi\) | ||||
−0.0325424 | + | 0.999470i | \(0.510360\pi\) | |||||||
\(942\) | 9.63845e6 | + | 1.16419e7i | 0.353900 | + | 0.427462i | ||||
\(943\) | 5.55690e6i | 0.203495i | ||||||||
\(944\) | 5.70555e6 | 0.208386 | ||||||||
\(945\) | 8.67366e6 | − | 2.90842e7i | 0.315953 | − | 1.05944i | ||||
\(946\) | −1.42354e7 | −0.517180 | ||||||||
\(947\) | 4.74165e7i | 1.71812i | 0.511872 | + | 0.859061i | \(0.328952\pi\) | ||||
−0.511872 | + | 0.859061i | \(0.671048\pi\) | |||||||
\(948\) | −6.23512e6 | − | 7.53116e6i | −0.225332 | − | 0.272170i | ||||
\(949\) | −3.04253e6 | −0.109665 | ||||||||
\(950\) | −4.51623e6 | −0.162355 | ||||||||
\(951\) | −2.31589e6 | + | 1.91735e6i | −0.0830362 | + | 0.0687464i | ||||
\(952\) | −2.30332e7 | − | 2.34150e7i | −0.823685 | − | 0.837339i | ||||
\(953\) | 3.22073e7i | 1.14874i | 0.818596 | + | 0.574370i | \(0.194753\pi\) | ||||
−0.818596 | + | 0.574370i | \(0.805247\pi\) | |||||||
\(954\) | 997498. | − | 5.25066e6i | 0.0354847 | − | 0.186785i | ||||
\(955\) | − | 1.83550e7i | − | 0.651247i | ||||||
\(956\) | − | 2.40536e7i | − | 0.851209i | ||||||
\(957\) | 3.14152e6 | + | 3.79452e6i | 0.110882 | + | 0.133930i | ||||
\(958\) | 2.35831e7i | 0.830207i | ||||||||
\(959\) | −3.52701e7 | − | 3.58547e7i | −1.23840 | − | 1.25893i | ||||
\(960\) | 6.25287e6 | + | 7.55260e6i | 0.218978 | + | 0.264496i | ||||
\(961\) | 2.86032e7 | 0.999092 | ||||||||
\(962\) | 8.30852e6 | 0.289458 | ||||||||
\(963\) | 2.86493e7 | + | 5.44267e6i | 0.995515 | + | 0.189124i | ||||
\(964\) | 1.15974e7i | 0.401948i | ||||||||
\(965\) | 2.55918e7 | 0.884674 | ||||||||
\(966\) | 4.77566e6 | + | 489245.i | 0.164661 | + | 0.0168688i | ||||
\(967\) | 2.97124e7 | 1.02181 | 0.510906 | − | 0.859637i | \(-0.329310\pi\) | ||||
0.510906 | + | 0.859637i | \(0.329310\pi\) | |||||||
\(968\) | − | 3.58491e7i | − | 1.22967i | ||||||
\(969\) | −4.00890e7 | + | 3.31901e7i | −1.37156 | + | 1.13553i | ||||
\(970\) | −1.57021e7 | −0.535830 | ||||||||
\(971\) | 1.54497e7 | 0.525861 | 0.262931 | − | 0.964815i | \(-0.415311\pi\) | ||||
0.262931 | + | 0.964815i | \(0.415311\pi\) | |||||||
\(972\) | 6.59005e6 | + | 2.01523e7i | 0.223729 | + | 0.684161i | ||||
\(973\) | −2.94850e7 | − | 2.99737e7i | −0.998432 | − | 1.01498i | ||||
\(974\) | 1.91139e7i | 0.645581i | ||||||||
\(975\) | 2.69277e6 | − | 2.22937e6i | 0.0907168 | − | 0.0751053i | ||||
\(976\) | 3.25152e6i | 0.109260i | ||||||||
\(977\) | 2.78966e7i | 0.935008i | 0.883991 | + | 0.467504i | \(0.154847\pi\) | ||||
−0.883991 | + | 0.467504i | \(0.845153\pi\) | |||||||
\(978\) | −770270. | + | 637714.i | −0.0257511 | + | 0.0213196i | ||||
\(979\) | − | 5.53923e7i | − | 1.84711i | ||||||
\(980\) | 393314. | − | 2.39225e7i | 0.0130820 | − | 0.795684i | ||||
\(981\) | −1.32449e6 | + | 6.97191e6i | −0.0439418 | + | 0.231302i | ||||
\(982\) | 2.50845e6 | 0.0830093 | ||||||||
\(983\) | 3.66294e6 | 0.120905 | 0.0604527 | − | 0.998171i | \(-0.480746\pi\) | ||||
0.0604527 | + | 0.998171i | \(0.480746\pi\) | |||||||
\(984\) | 1.38598e7 | − | 1.14746e7i | 0.456319 | − | 0.377791i | ||||
\(985\) | 1.34072e7i | 0.440300i | ||||||||
\(986\) | −2.36436e6 | −0.0774499 | ||||||||
\(987\) | 3.53914e7 | + | 3.62568e6i | 1.15639 | + | 0.118467i | ||||
\(988\) | −1.61516e7 | −0.526410 | ||||||||
\(989\) | − | 6.12966e6i | − | 0.199272i | ||||||
\(990\) | −5.16414e6 | + | 2.71831e7i | −0.167460 | + | 0.881478i | ||||
\(991\) | 5.89627e6 | 0.190719 | 0.0953594 | − | 0.995443i | \(-0.469600\pi\) | ||||
0.0953594 | + | 0.995443i | \(0.469600\pi\) | |||||||
\(992\) | −967752. | −0.0312237 | ||||||||
\(993\) | 2.83789e7 | + | 3.42778e7i | 0.913320 | + | 1.10316i | ||||
\(994\) | −2.03968e6 | + | 2.00642e6i | −0.0654781 | + | 0.0644104i | ||||
\(995\) | − | 2.26916e6i | − | 0.0726619i | ||||||
\(996\) | −3.56684e6 | − | 4.30824e6i | −0.113929 | − | 0.137611i | ||||
\(997\) | − | 1.33192e7i | − | 0.424366i | −0.977230 | − | 0.212183i | \(-0.931943\pi\) | ||
0.977230 | − | 0.212183i | \(-0.0680572\pi\) | |||||||
\(998\) | − | 1.44003e7i | − | 0.457662i | ||||||
\(999\) | −2.85074e7 | + | 1.57142e7i | −0.903741 | + | 0.498173i |
(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 | 21.6.c.a.20.7 | yes | 12 | |
3.2 | odd | 2 | inner | 21.6.c.a.20.6 | yes | 12 | |
4.3 | odd | 2 | 336.6.k.d.209.10 | 12 | |||
7.6 | odd | 2 | inner | 21.6.c.a.20.8 | yes | 12 | |
12.11 | even | 2 | 336.6.k.d.209.4 | 12 | |||
21.20 | even | 2 | inner | 21.6.c.a.20.5 | ✓ | 12 | |
28.27 | even | 2 | 336.6.k.d.209.3 | 12 | |||
84.83 | odd | 2 | 336.6.k.d.209.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.c.a.20.5 | ✓ | 12 | 21.20 | even | 2 | inner | |
21.6.c.a.20.6 | yes | 12 | 3.2 | odd | 2 | inner | |
21.6.c.a.20.7 | yes | 12 | 1.1 | even | 1 | trivial | |
21.6.c.a.20.8 | yes | 12 | 7.6 | odd | 2 | inner | |
336.6.k.d.209.3 | 12 | 28.27 | even | 2 | |||
336.6.k.d.209.4 | 12 | 12.11 | even | 2 | |||
336.6.k.d.209.9 | 12 | 84.83 | odd | 2 | |||
336.6.k.d.209.10 | 12 | 4.3 | odd | 2 |