Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,5,Mod(31,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.d (of order \(4\), degree \(2\), 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: | \(7.64937726820\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 727 x^{12} + 207381 x^{10} + 29788577 x^{8} + 2302194203 x^{6} + 92916575085 x^{4} + \cdots + 6531254919424 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.5 | ||
Root | \(6.93683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.31 |
Dual form | 74.5.d.b.43.3 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | + | 2.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 5.93683i | 0.659648i | 0.944043 | + | 0.329824i | \(0.106989\pi\) | ||||
−0.944043 | + | 0.329824i | \(0.893011\pi\) | |||||||
\(4\) | 8.00000i | 0.500000i | ||||||||
\(5\) | 34.8311 | − | 34.8311i | 1.39324 | − | 1.39324i | 0.575306 | − | 0.817938i | \(-0.304883\pi\) |
0.817938 | − | 0.575306i | \(-0.195117\pi\) | |||||||
\(6\) | −11.8737 | + | 11.8737i | −0.329824 | + | 0.329824i | ||||
\(7\) | 33.1642 | 0.676821 | 0.338410 | − | 0.940999i | \(-0.390111\pi\) | ||||
0.338410 | + | 0.940999i | \(0.390111\pi\) | |||||||
\(8\) | −16.0000 | + | 16.0000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 45.7541 | 0.564865 | ||||||||
\(10\) | 139.324 | 1.39324 | ||||||||
\(11\) | 4.42515i | 0.0365715i | 0.999833 | + | 0.0182858i | \(0.00582086\pi\) | ||||
−0.999833 | + | 0.0182858i | \(0.994179\pi\) | |||||||
\(12\) | −47.4946 | −0.329824 | ||||||||
\(13\) | −155.523 | + | 155.523i | −0.920256 | + | 0.920256i | −0.997047 | − | 0.0767912i | \(-0.975533\pi\) |
0.0767912 | + | 0.997047i | \(0.475533\pi\) | |||||||
\(14\) | 66.3284 | + | 66.3284i | 0.338410 | + | 0.338410i | ||||
\(15\) | 206.786 | + | 206.786i | 0.919050 | + | 0.919050i | ||||
\(16\) | −64.0000 | −0.250000 | ||||||||
\(17\) | 29.7847 | − | 29.7847i | 0.103061 | − | 0.103061i | −0.653696 | − | 0.756757i | \(-0.726782\pi\) |
0.756757 | + | 0.653696i | \(0.226782\pi\) | |||||||
\(18\) | 91.5081 | + | 91.5081i | 0.282432 | + | 0.282432i | ||||
\(19\) | −367.142 | + | 367.142i | −1.01701 | + | 1.01701i | −0.0171600 | + | 0.999853i | \(0.505462\pi\) |
−0.999853 | + | 0.0171600i | \(0.994538\pi\) | |||||||
\(20\) | 278.649 | + | 278.649i | 0.696622 | + | 0.696622i | ||||
\(21\) | 196.890i | 0.446463i | ||||||||
\(22\) | −8.85031 | + | 8.85031i | −0.0182858 | + | 0.0182858i | ||||
\(23\) | 647.183 | − | 647.183i | 1.22341 | − | 1.22341i | 0.256995 | − | 0.966413i | \(-0.417268\pi\) |
0.966413 | − | 0.256995i | \(-0.0827323\pi\) | |||||||
\(24\) | −94.9893 | − | 94.9893i | −0.164912 | − | 0.164912i | ||||
\(25\) | − | 1801.41i | − | 2.88226i | ||||||
\(26\) | −622.093 | −0.920256 | ||||||||
\(27\) | 752.517i | 1.03226i | ||||||||
\(28\) | 265.314i | 0.338410i | ||||||||
\(29\) | −558.837 | − | 558.837i | −0.664492 | − | 0.664492i | 0.291944 | − | 0.956435i | \(-0.405698\pi\) |
−0.956435 | + | 0.291944i | \(0.905698\pi\) | |||||||
\(30\) | 827.145i | 0.919050i | ||||||||
\(31\) | 928.228 | + | 928.228i | 0.965898 | + | 0.965898i | 0.999437 | − | 0.0335395i | \(-0.0106780\pi\) |
−0.0335395 | + | 0.999437i | \(0.510678\pi\) | |||||||
\(32\) | −128.000 | − | 128.000i | −0.125000 | − | 0.125000i | ||||
\(33\) | −26.2714 | −0.0241243 | ||||||||
\(34\) | 119.139 | 0.103061 | ||||||||
\(35\) | 1155.15 | − | 1155.15i | 0.942976 | − | 0.942976i | ||||
\(36\) | 366.033i | 0.282432i | ||||||||
\(37\) | −1012.61 | + | 921.290i | −0.739673 | + | 0.672966i | ||||
\(38\) | −1468.57 | −1.01701 | ||||||||
\(39\) | −923.315 | − | 923.315i | −0.607045 | − | 0.607045i | ||||
\(40\) | 1114.60i | 0.696622i | ||||||||
\(41\) | − | 1994.29i | − | 1.18637i | −0.805066 | − | 0.593186i | \(-0.797870\pi\) | ||
0.805066 | − | 0.593186i | \(-0.202130\pi\) | |||||||
\(42\) | −393.780 | + | 393.780i | −0.223232 | + | 0.223232i | ||||
\(43\) | −223.022 | + | 223.022i | −0.120618 | + | 0.120618i | −0.764839 | − | 0.644221i | \(-0.777182\pi\) |
0.644221 | + | 0.764839i | \(0.277182\pi\) | |||||||
\(44\) | −35.4012 | −0.0182858 | ||||||||
\(45\) | 1593.66 | − | 1593.66i | 0.786995 | − | 0.786995i | ||||
\(46\) | 2588.73 | 1.22341 | ||||||||
\(47\) | −3142.01 | −1.42237 | −0.711183 | − | 0.703007i | \(-0.751840\pi\) | ||||
−0.711183 | + | 0.703007i | \(0.751840\pi\) | |||||||
\(48\) | − | 379.957i | − | 0.164912i | ||||||
\(49\) | −1301.14 | −0.541914 | ||||||||
\(50\) | 3602.82 | − | 3602.82i | 1.44113 | − | 1.44113i | ||||
\(51\) | 176.827 | + | 176.827i | 0.0679842 | + | 0.0679842i | ||||
\(52\) | −1244.19 | − | 1244.19i | −0.460128 | − | 0.460128i | ||||
\(53\) | −1011.94 | −0.360248 | −0.180124 | − | 0.983644i | \(-0.557650\pi\) | ||||
−0.180124 | + | 0.983644i | \(0.557650\pi\) | |||||||
\(54\) | −1505.03 | + | 1505.03i | −0.516130 | + | 0.516130i | ||||
\(55\) | 154.133 | + | 154.133i | 0.0509531 | + | 0.0509531i | ||||
\(56\) | −530.627 | + | 530.627i | −0.169205 | + | 0.169205i | ||||
\(57\) | −2179.66 | − | 2179.66i | −0.670870 | − | 0.670870i | ||||
\(58\) | − | 2235.35i | − | 0.664492i | ||||||
\(59\) | 550.662 | − | 550.662i | 0.158191 | − | 0.158191i | −0.623574 | − | 0.781765i | \(-0.714320\pi\) |
0.781765 | + | 0.623574i | \(0.214320\pi\) | |||||||
\(60\) | −1654.29 | + | 1654.29i | −0.459525 | + | 0.459525i | ||||
\(61\) | −1174.38 | − | 1174.38i | −0.315608 | − | 0.315608i | 0.531469 | − | 0.847078i | \(-0.321640\pi\) |
−0.847078 | + | 0.531469i | \(0.821640\pi\) | |||||||
\(62\) | 3712.91i | 0.965898i | ||||||||
\(63\) | 1517.40 | 0.382312 | ||||||||
\(64\) | − | 512.000i | − | 0.125000i | ||||||
\(65\) | 10834.1i | 2.56428i | ||||||||
\(66\) | −52.5428 | − | 52.5428i | −0.0120622 | − | 0.0120622i | ||||
\(67\) | − | 2319.11i | − | 0.516620i | −0.966062 | − | 0.258310i | \(-0.916834\pi\) | ||
0.966062 | − | 0.258310i | \(-0.0831657\pi\) | |||||||
\(68\) | 238.278 | + | 238.278i | 0.0515307 | + | 0.0515307i | ||||
\(69\) | 3842.21 | + | 3842.21i | 0.807018 | + | 0.807018i | ||||
\(70\) | 4620.58 | 0.942976 | ||||||||
\(71\) | −3068.87 | −0.608782 | −0.304391 | − | 0.952547i | \(-0.598453\pi\) | ||||
−0.304391 | + | 0.952547i | \(0.598453\pi\) | |||||||
\(72\) | −732.065 | + | 732.065i | −0.141216 | + | 0.141216i | ||||
\(73\) | − | 11.2597i | − | 0.00211290i | −0.999999 | − | 0.00105645i | \(-0.999664\pi\) | ||
0.999999 | − | 0.00105645i | \(-0.000336279\pi\) | |||||||
\(74\) | −3867.81 | − | 182.645i | −0.706320 | − | 0.0333537i | ||||
\(75\) | 10694.7 | 1.90128 | ||||||||
\(76\) | −2937.13 | − | 2937.13i | −0.508506 | − | 0.508506i | ||||
\(77\) | 146.757i | 0.0247524i | ||||||||
\(78\) | − | 3693.26i | − | 0.607045i | ||||||
\(79\) | −2103.45 | + | 2103.45i | −0.337038 | + | 0.337038i | −0.855251 | − | 0.518214i | \(-0.826597\pi\) |
0.518214 | + | 0.855251i | \(0.326597\pi\) | |||||||
\(80\) | −2229.19 | + | 2229.19i | −0.348311 | + | 0.348311i | ||||
\(81\) | −761.486 | −0.116063 | ||||||||
\(82\) | 3988.58 | − | 3988.58i | 0.593186 | − | 0.593186i | ||||
\(83\) | 9140.45 | 1.32682 | 0.663409 | − | 0.748257i | \(-0.269109\pi\) | ||||
0.663409 | + | 0.748257i | \(0.269109\pi\) | |||||||
\(84\) | −1575.12 | −0.223232 | ||||||||
\(85\) | − | 2074.87i | − | 0.287179i | ||||||
\(86\) | −892.087 | −0.120618 | ||||||||
\(87\) | 3317.72 | − | 3317.72i | 0.438330 | − | 0.438330i | ||||
\(88\) | −70.8025 | − | 70.8025i | −0.00914288 | − | 0.00914288i | ||||
\(89\) | 2126.17 | + | 2126.17i | 0.268422 | + | 0.268422i | 0.828464 | − | 0.560042i | \(-0.189215\pi\) |
−0.560042 | + | 0.828464i | \(0.689215\pi\) | |||||||
\(90\) | 6374.66 | 0.786995 | ||||||||
\(91\) | −5157.81 | + | 5157.81i | −0.622848 | + | 0.622848i | ||||
\(92\) | 5177.46 | + | 5177.46i | 0.611704 | + | 0.611704i | ||||
\(93\) | −5510.73 | + | 5510.73i | −0.637152 | + | 0.637152i | ||||
\(94\) | −6284.02 | − | 6284.02i | −0.711183 | − | 0.711183i | ||||
\(95\) | 25575.9i | 2.83389i | ||||||||
\(96\) | 759.914 | − | 759.914i | 0.0824560 | − | 0.0824560i | ||||
\(97\) | 6567.54 | − | 6567.54i | 0.698006 | − | 0.698006i | −0.265974 | − | 0.963980i | \(-0.585693\pi\) |
0.963980 | + | 0.265974i | \(0.0856935\pi\) | |||||||
\(98\) | −2602.27 | − | 2602.27i | −0.270957 | − | 0.270957i | ||||
\(99\) | 202.469i | 0.0206580i | ||||||||
\(100\) | 14411.3 | 1.44113 | ||||||||
\(101\) | 6127.82i | 0.600708i | 0.953828 | + | 0.300354i | \(0.0971048\pi\) | ||||
−0.953828 | + | 0.300354i | \(0.902895\pi\) | |||||||
\(102\) | 707.307i | 0.0679842i | ||||||||
\(103\) | −4941.22 | − | 4941.22i | −0.465758 | − | 0.465758i | 0.434779 | − | 0.900537i | \(-0.356826\pi\) |
−0.900537 | + | 0.434779i | \(0.856826\pi\) | |||||||
\(104\) | − | 4976.74i | − | 0.460128i | ||||||
\(105\) | 6857.90 | + | 6857.90i | 0.622032 | + | 0.622032i | ||||
\(106\) | −2023.87 | − | 2023.87i | −0.180124 | − | 0.180124i | ||||
\(107\) | 4211.19 | 0.367822 | 0.183911 | − | 0.982943i | \(-0.441124\pi\) | ||||
0.183911 | + | 0.982943i | \(0.441124\pi\) | |||||||
\(108\) | −6020.14 | −0.516130 | ||||||||
\(109\) | −12057.3 | + | 12057.3i | −1.01484 | + | 1.01484i | −0.0149486 | + | 0.999888i | \(0.504758\pi\) |
−0.999888 | + | 0.0149486i | \(0.995242\pi\) | |||||||
\(110\) | 616.532i | 0.0509531i | ||||||||
\(111\) | −5469.54 | − | 6011.71i | −0.443920 | − | 0.487924i | ||||
\(112\) | −2122.51 | −0.169205 | ||||||||
\(113\) | −13317.2 | − | 13317.2i | −1.04293 | − | 1.04293i | −0.999036 | − | 0.0438926i | \(-0.986024\pi\) |
−0.0438926 | − | 0.999036i | \(-0.513976\pi\) | |||||||
\(114\) | − | 8718.63i | − | 0.670870i | ||||||
\(115\) | − | 45084.2i | − | 3.40901i | ||||||
\(116\) | 4470.70 | − | 4470.70i | 0.332246 | − | 0.332246i | ||||
\(117\) | −7115.82 | + | 7115.82i | −0.519820 | + | 0.519820i | ||||
\(118\) | 2202.65 | 0.158191 | ||||||||
\(119\) | 987.787 | − | 987.787i | 0.0697541 | − | 0.0697541i | ||||
\(120\) | −6617.16 | −0.459525 | ||||||||
\(121\) | 14621.4 | 0.998663 | ||||||||
\(122\) | − | 4697.52i | − | 0.315608i | ||||||
\(123\) | 11839.8 | 0.782587 | ||||||||
\(124\) | −7425.82 | + | 7425.82i | −0.482949 | + | 0.482949i | ||||
\(125\) | −40975.7 | − | 40975.7i | −2.62245 | − | 2.62245i | ||||
\(126\) | 3034.79 | + | 3034.79i | 0.191156 | + | 0.191156i | ||||
\(127\) | −4034.55 | −0.250143 | −0.125071 | − | 0.992148i | \(-0.539916\pi\) | ||||
−0.125071 | + | 0.992148i | \(0.539916\pi\) | |||||||
\(128\) | 1024.00 | − | 1024.00i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −1324.04 | − | 1324.04i | −0.0795651 | − | 0.0795651i | ||||
\(130\) | −21668.2 | + | 21668.2i | −1.28214 | + | 1.28214i | ||||
\(131\) | 15101.0 | + | 15101.0i | 0.879963 | + | 0.879963i | 0.993530 | − | 0.113568i | \(-0.0362279\pi\) |
−0.113568 | + | 0.993530i | \(0.536228\pi\) | |||||||
\(132\) | − | 210.171i | − | 0.0120622i | ||||||
\(133\) | −12176.0 | + | 12176.0i | −0.688335 | + | 0.688335i | ||||
\(134\) | 4638.22 | − | 4638.22i | 0.258310 | − | 0.258310i | ||||
\(135\) | 26211.0 | + | 26211.0i | 1.43819 | + | 1.43819i | ||||
\(136\) | 953.112i | 0.0515307i | ||||||||
\(137\) | −13171.6 | −0.701772 | −0.350886 | − | 0.936418i | \(-0.614120\pi\) | ||||
−0.350886 | + | 0.936418i | \(0.614120\pi\) | |||||||
\(138\) | 15368.8i | 0.807018i | ||||||||
\(139\) | 941.634i | 0.0487363i | 0.999703 | + | 0.0243681i | \(0.00775739\pi\) | ||||
−0.999703 | + | 0.0243681i | \(0.992243\pi\) | |||||||
\(140\) | 9241.17 | + | 9241.17i | 0.471488 | + | 0.471488i | ||||
\(141\) | − | 18653.6i | − | 0.938261i | ||||||
\(142\) | −6137.74 | − | 6137.74i | −0.304391 | − | 0.304391i | ||||
\(143\) | −688.214 | − | 688.214i | −0.0336552 | − | 0.0336552i | ||||
\(144\) | −2928.26 | −0.141216 | ||||||||
\(145\) | −38929.9 | −1.85160 | ||||||||
\(146\) | 22.5193 | − | 22.5193i | 0.00105645 | − | 0.00105645i | ||||
\(147\) | − | 7724.62i | − | 0.357472i | ||||||
\(148\) | −7370.32 | − | 8100.90i | −0.336483 | − | 0.369837i | ||||
\(149\) | −3780.31 | −0.170277 | −0.0851383 | − | 0.996369i | \(-0.527133\pi\) | ||||
−0.0851383 | + | 0.996369i | \(0.527133\pi\) | |||||||
\(150\) | 21389.4 | + | 21389.4i | 0.950638 | + | 0.950638i | ||||
\(151\) | 5043.24i | 0.221185i | 0.993866 | + | 0.110593i | \(0.0352749\pi\) | ||||
−0.993866 | + | 0.110593i | \(0.964725\pi\) | |||||||
\(152\) | − | 11748.5i | − | 0.508506i | ||||||
\(153\) | 1362.77 | − | 1362.77i | 0.0582158 | − | 0.0582158i | ||||
\(154\) | −293.513 | + | 293.513i | −0.0123762 | + | 0.0123762i | ||||
\(155\) | 64662.4 | 2.69146 | ||||||||
\(156\) | 7386.52 | − | 7386.52i | 0.303522 | − | 0.303522i | ||||
\(157\) | 16703.7 | 0.677661 | 0.338830 | − | 0.940847i | \(-0.389969\pi\) | ||||
0.338830 | + | 0.940847i | \(0.389969\pi\) | |||||||
\(158\) | −8413.81 | −0.337038 | ||||||||
\(159\) | − | 6007.69i | − | 0.237637i | ||||||
\(160\) | −8916.76 | −0.348311 | ||||||||
\(161\) | 21463.3 | − | 21463.3i | 0.828027 | − | 0.828027i | ||||
\(162\) | −1522.97 | − | 1522.97i | −0.0580313 | − | 0.0580313i | ||||
\(163\) | −14378.1 | − | 14378.1i | −0.541160 | − | 0.541160i | 0.382709 | − | 0.923869i | \(-0.374991\pi\) |
−0.923869 | + | 0.382709i | \(0.874991\pi\) | |||||||
\(164\) | 15954.3 | 0.593186 | ||||||||
\(165\) | −915.061 | + | 915.061i | −0.0336111 | + | 0.0336111i | ||||
\(166\) | 18280.9 | + | 18280.9i | 0.663409 | + | 0.663409i | ||||
\(167\) | −8767.98 | + | 8767.98i | −0.314389 | + | 0.314389i | −0.846607 | − | 0.532218i | \(-0.821358\pi\) |
0.532218 | + | 0.846607i | \(0.321358\pi\) | |||||||
\(168\) | −3150.24 | − | 3150.24i | −0.111616 | − | 0.111616i | ||||
\(169\) | − | 19814.0i | − | 0.693742i | ||||||
\(170\) | 4149.74 | − | 4149.74i | 0.143590 | − | 0.143590i | ||||
\(171\) | −16798.2 | + | 16798.2i | −0.574475 | + | 0.574475i | ||||
\(172\) | −1784.17 | − | 1784.17i | −0.0603088 | − | 0.0603088i | ||||
\(173\) | 24278.1i | 0.811188i | 0.914053 | + | 0.405594i | \(0.132935\pi\) | ||||
−0.914053 | + | 0.405594i | \(0.867065\pi\) | |||||||
\(174\) | 13270.9 | 0.438330 | ||||||||
\(175\) | − | 59742.4i | − | 1.95077i | ||||||
\(176\) | − | 283.210i | − | 0.00914288i | ||||||
\(177\) | 3269.19 | + | 3269.19i | 0.104350 | + | 0.104350i | ||||
\(178\) | 8504.67i | 0.268422i | ||||||||
\(179\) | 42787.2 | + | 42787.2i | 1.33539 | + | 1.33539i | 0.900468 | + | 0.434922i | \(0.143224\pi\) |
0.434922 | + | 0.900468i | \(0.356776\pi\) | |||||||
\(180\) | 12749.3 | + | 12749.3i | 0.393497 | + | 0.393497i | ||||
\(181\) | 62865.8 | 1.91892 | 0.959461 | − | 0.281841i | \(-0.0909450\pi\) | ||||
0.959461 | + | 0.281841i | \(0.0909450\pi\) | |||||||
\(182\) | −20631.2 | −0.622848 | ||||||||
\(183\) | 6972.09 | − | 6972.09i | 0.208190 | − | 0.208190i | ||||
\(184\) | 20709.8i | 0.611704i | ||||||||
\(185\) | −3180.86 | + | 67360.0i | −0.0929397 | + | 1.96815i | ||||
\(186\) | −22042.9 | −0.637152 | ||||||||
\(187\) | 131.802 | + | 131.802i | 0.00376911 | + | 0.00376911i | ||||
\(188\) | − | 25136.1i | − | 0.711183i | ||||||
\(189\) | 24956.6i | 0.698654i | ||||||||
\(190\) | −51151.8 | + | 51151.8i | −1.41695 | + | 1.41695i | ||||
\(191\) | −12310.7 | + | 12310.7i | −0.337456 | + | 0.337456i | −0.855409 | − | 0.517953i | \(-0.826694\pi\) |
0.517953 | + | 0.855409i | \(0.326694\pi\) | |||||||
\(192\) | 3039.66 | 0.0824560 | ||||||||
\(193\) | −18731.8 | + | 18731.8i | −0.502879 | + | 0.502879i | −0.912332 | − | 0.409452i | \(-0.865720\pi\) |
0.409452 | + | 0.912332i | \(0.365720\pi\) | |||||||
\(194\) | 26270.2 | 0.698006 | ||||||||
\(195\) | −64320.2 | −1.69152 | ||||||||
\(196\) | − | 10409.1i | − | 0.270957i | ||||||
\(197\) | 21741.1 | 0.560209 | 0.280104 | − | 0.959970i | \(-0.409631\pi\) | ||||
0.280104 | + | 0.959970i | \(0.409631\pi\) | |||||||
\(198\) | −404.938 | + | 404.938i | −0.0103290 | + | 0.0103290i | ||||
\(199\) | −12770.0 | − | 12770.0i | −0.322467 | − | 0.322467i | 0.527246 | − | 0.849713i | \(-0.323225\pi\) |
−0.849713 | + | 0.527246i | \(0.823225\pi\) | |||||||
\(200\) | 28822.6 | + | 28822.6i | 0.720565 | + | 0.720565i | ||||
\(201\) | 13768.2 | 0.340787 | ||||||||
\(202\) | −12255.6 | + | 12255.6i | −0.300354 | + | 0.300354i | ||||
\(203\) | −18533.4 | − | 18533.4i | −0.449742 | − | 0.449742i | ||||
\(204\) | −1414.61 | + | 1414.61i | −0.0339921 | + | 0.0339921i | ||||
\(205\) | −69463.4 | − | 69463.4i | −1.65291 | − | 1.65291i | ||||
\(206\) | − | 19764.9i | − | 0.465758i | ||||||
\(207\) | 29611.2 | − | 29611.2i | 0.691060 | − | 0.691060i | ||||
\(208\) | 9953.49 | − | 9953.49i | 0.230064 | − | 0.230064i | ||||
\(209\) | −1624.66 | − | 1624.66i | −0.0371937 | − | 0.0371937i | ||||
\(210\) | 27431.6i | 0.622032i | ||||||||
\(211\) | −14514.0 | −0.326004 | −0.163002 | − | 0.986626i | \(-0.552118\pi\) | ||||
−0.163002 | + | 0.986626i | \(0.552118\pi\) | |||||||
\(212\) | − | 8095.49i | − | 0.180124i | ||||||
\(213\) | − | 18219.4i | − | 0.401582i | ||||||
\(214\) | 8422.38 | + | 8422.38i | 0.183911 | + | 0.183911i | ||||
\(215\) | 15536.2i | 0.336099i | ||||||||
\(216\) | −12040.3 | − | 12040.3i | −0.258065 | − | 0.258065i | ||||
\(217\) | 30783.9 | + | 30783.9i | 0.653740 | + | 0.653740i | ||||
\(218\) | −48229.1 | −1.01484 | ||||||||
\(219\) | 66.8466 | 0.00139377 | ||||||||
\(220\) | −1233.06 | + | 1233.06i | −0.0254765 | + | 0.0254765i | ||||
\(221\) | 9264.44i | 0.189686i | ||||||||
\(222\) | 1084.33 | − | 22962.5i | 0.0220017 | − | 0.465922i | ||||
\(223\) | 38969.2 | 0.783631 | 0.391815 | − | 0.920044i | \(-0.371847\pi\) | ||||
0.391815 | + | 0.920044i | \(0.371847\pi\) | |||||||
\(224\) | −4245.02 | − | 4245.02i | −0.0846026 | − | 0.0846026i | ||||
\(225\) | − | 82421.9i | − | 1.62809i | ||||||
\(226\) | − | 53268.6i | − | 1.04293i | ||||||
\(227\) | −1533.11 | + | 1533.11i | −0.0297523 | + | 0.0297523i | −0.721826 | − | 0.692074i | \(-0.756697\pi\) |
0.692074 | + | 0.721826i | \(0.256697\pi\) | |||||||
\(228\) | 17437.3 | − | 17437.3i | 0.335435 | − | 0.335435i | ||||
\(229\) | −18827.0 | −0.359013 | −0.179507 | − | 0.983757i | \(-0.557450\pi\) | ||||
−0.179507 | + | 0.983757i | \(0.557450\pi\) | |||||||
\(230\) | 90168.3 | − | 90168.3i | 1.70451 | − | 1.70451i | ||||
\(231\) | −871.270 | −0.0163278 | ||||||||
\(232\) | 17882.8 | 0.332246 | ||||||||
\(233\) | 92498.5i | 1.70382i | 0.523691 | + | 0.851909i | \(0.324555\pi\) | ||||
−0.523691 | + | 0.851909i | \(0.675445\pi\) | |||||||
\(234\) | −28463.3 | −0.519820 | ||||||||
\(235\) | −109440. | + | 109440.i | −1.98170 | + | 1.98170i | ||||
\(236\) | 4405.30 | + | 4405.30i | 0.0790954 | + | 0.0790954i | ||||
\(237\) | −12487.8 | − | 12487.8i | −0.222326 | − | 0.222326i | ||||
\(238\) | 3951.15 | 0.0697541 | ||||||||
\(239\) | 6432.82 | − | 6432.82i | 0.112617 | − | 0.112617i | −0.648553 | − | 0.761170i | \(-0.724625\pi\) |
0.761170 | + | 0.648553i | \(0.224625\pi\) | |||||||
\(240\) | −13234.3 | − | 13234.3i | −0.229763 | − | 0.229763i | ||||
\(241\) | 80856.3 | − | 80856.3i | 1.39213 | − | 1.39213i | 0.571594 | − | 0.820537i | \(-0.306325\pi\) |
0.820537 | − | 0.571594i | \(-0.193675\pi\) | |||||||
\(242\) | 29242.8 | + | 29242.8i | 0.499331 | + | 0.499331i | ||||
\(243\) | 56433.1i | 0.955699i | ||||||||
\(244\) | 9395.03 | − | 9395.03i | 0.157804 | − | 0.157804i | ||||
\(245\) | −45320.0 | + | 45320.0i | −0.755019 | + | 0.755019i | ||||
\(246\) | 23679.5 | + | 23679.5i | 0.391294 | + | 0.391294i | ||||
\(247\) | − | 114198.i | − | 1.87182i | ||||||
\(248\) | −29703.3 | −0.482949 | ||||||||
\(249\) | 54265.3i | 0.875233i | ||||||||
\(250\) | − | 163903.i | − | 2.62245i | ||||||
\(251\) | 2524.56 | + | 2524.56i | 0.0400718 | + | 0.0400718i | 0.726859 | − | 0.686787i | \(-0.240979\pi\) |
−0.686787 | + | 0.726859i | \(0.740979\pi\) | |||||||
\(252\) | 12139.2i | 0.191156i | ||||||||
\(253\) | 2863.88 | + | 2863.88i | 0.0447419 | + | 0.0447419i | ||||
\(254\) | −8069.10 | − | 8069.10i | −0.125071 | − | 0.125071i | ||||
\(255\) | 12318.2 | 0.189437 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 26770.5 | − | 26770.5i | 0.405312 | − | 0.405312i | −0.474788 | − | 0.880100i | \(-0.657475\pi\) |
0.880100 | + | 0.474788i | \(0.157475\pi\) | |||||||
\(258\) | − | 5296.17i | − | 0.0795651i | ||||||
\(259\) | −33582.5 | + | 30553.9i | −0.500626 | + | 0.455477i | ||||
\(260\) | −86672.8 | −1.28214 | ||||||||
\(261\) | −25569.1 | − | 25569.1i | −0.375348 | − | 0.375348i | ||||
\(262\) | 60404.2i | 0.879963i | ||||||||
\(263\) | 259.616i | 0.00375336i | 0.999998 | + | 0.00187668i | \(0.000597367\pi\) | ||||
−0.999998 | + | 0.00187668i | \(0.999403\pi\) | |||||||
\(264\) | 420.342 | − | 420.342i | 0.00603108 | − | 0.00603108i | ||||
\(265\) | −35246.9 | + | 35246.9i | −0.501913 | + | 0.501913i | ||||
\(266\) | −48703.8 | −0.688335 | ||||||||
\(267\) | −12622.7 | + | 12622.7i | −0.177064 | + | 0.177064i | ||||
\(268\) | 18552.9 | 0.258310 | ||||||||
\(269\) | 55811.7 | 0.771295 | 0.385647 | − | 0.922646i | \(-0.373978\pi\) | ||||
0.385647 | + | 0.922646i | \(0.373978\pi\) | |||||||
\(270\) | 104844.i | 1.43819i | ||||||||
\(271\) | 115383. | 1.57110 | 0.785552 | − | 0.618796i | \(-0.212379\pi\) | ||||
0.785552 | + | 0.618796i | \(0.212379\pi\) | |||||||
\(272\) | −1906.22 | + | 1906.22i | −0.0257653 | + | 0.0257653i | ||||
\(273\) | −30621.0 | − | 30621.0i | −0.410860 | − | 0.410860i | ||||
\(274\) | −26343.1 | − | 26343.1i | −0.350886 | − | 0.350886i | ||||
\(275\) | 7971.53 | 0.105409 | ||||||||
\(276\) | −30737.7 | + | 30737.7i | −0.403509 | + | 0.403509i | ||||
\(277\) | −51689.2 | − | 51689.2i | −0.673659 | − | 0.673659i | 0.284898 | − | 0.958558i | \(-0.408040\pi\) |
−0.958558 | + | 0.284898i | \(0.908040\pi\) | |||||||
\(278\) | −1883.27 | + | 1883.27i | −0.0243681 | + | 0.0243681i | ||||
\(279\) | 42470.2 | + | 42470.2i | 0.545602 | + | 0.545602i | ||||
\(280\) | 36964.7i | 0.471488i | ||||||||
\(281\) | 80464.7 | − | 80464.7i | 1.01904 | − | 1.01904i | 0.0192283 | − | 0.999815i | \(-0.493879\pi\) |
0.999815 | − | 0.0192283i | \(-0.00612092\pi\) | |||||||
\(282\) | 37307.1 | − | 37307.1i | 0.469130 | − | 0.469130i | ||||
\(283\) | −48024.8 | − | 48024.8i | −0.599643 | − | 0.599643i | 0.340574 | − | 0.940218i | \(-0.389378\pi\) |
−0.940218 | + | 0.340574i | \(0.889378\pi\) | |||||||
\(284\) | − | 24551.0i | − | 0.304391i | ||||||
\(285\) | −151840. | −1.86937 | ||||||||
\(286\) | − | 2752.86i | − | 0.0336552i | ||||||
\(287\) | − | 66139.1i | − | 0.802961i | ||||||
\(288\) | −5856.52 | − | 5856.52i | −0.0706081 | − | 0.0706081i | ||||
\(289\) | 81746.7i | 0.978757i | ||||||||
\(290\) | −77859.7 | − | 77859.7i | −0.925799 | − | 0.925799i | ||||
\(291\) | 38990.4 | + | 38990.4i | 0.460438 | + | 0.460438i | ||||
\(292\) | 90.0772 | 0.00105645 | ||||||||
\(293\) | 105263. | 1.22615 | 0.613073 | − | 0.790026i | \(-0.289933\pi\) | ||||
0.613073 | + | 0.790026i | \(0.289933\pi\) | |||||||
\(294\) | 15449.2 | − | 15449.2i | 0.178736 | − | 0.178736i | ||||
\(295\) | − | 38360.3i | − | 0.440797i | ||||||
\(296\) | 1461.16 | − | 30942.5i | 0.0166769 | − | 0.353160i | ||||
\(297\) | −3330.00 | −0.0377513 | ||||||||
\(298\) | −7560.62 | − | 7560.62i | −0.0851383 | − | 0.0851383i | ||||
\(299\) | 201304.i | 2.25170i | ||||||||
\(300\) | 85557.4i | 0.950638i | ||||||||
\(301\) | −7396.34 | + | 7396.34i | −0.0816364 | + | 0.0816364i | ||||
\(302\) | −10086.5 | + | 10086.5i | −0.110593 | + | 0.110593i | ||||
\(303\) | −36379.8 | −0.396256 | ||||||||
\(304\) | 23497.1 | − | 23497.1i | 0.254253 | − | 0.254253i | ||||
\(305\) | −81809.8 | −0.879439 | ||||||||
\(306\) | 5451.09 | 0.0582158 | ||||||||
\(307\) | 175738.i | 1.86462i | 0.361665 | + | 0.932308i | \(0.382208\pi\) | ||||
−0.361665 | + | 0.932308i | \(0.617792\pi\) | |||||||
\(308\) | −1174.05 | −0.0123762 | ||||||||
\(309\) | 29335.2 | − | 29335.2i | 0.307236 | − | 0.307236i | ||||
\(310\) | 129325. | + | 129325.i | 1.34573 | + | 1.34573i | ||||
\(311\) | −22500.1 | − | 22500.1i | −0.232628 | − | 0.232628i | 0.581161 | − | 0.813789i | \(-0.302599\pi\) |
−0.813789 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(312\) | 29546.1 | 0.303522 | ||||||||
\(313\) | 27113.8 | − | 27113.8i | 0.276759 | − | 0.276759i | −0.555055 | − | 0.831814i | \(-0.687303\pi\) |
0.831814 | + | 0.555055i | \(0.187303\pi\) | |||||||
\(314\) | 33407.3 | + | 33407.3i | 0.338830 | + | 0.338830i | ||||
\(315\) | 52852.6 | − | 52852.6i | 0.532654 | − | 0.532654i | ||||
\(316\) | −16827.6 | − | 16827.6i | −0.168519 | − | 0.168519i | ||||
\(317\) | − | 82559.3i | − | 0.821575i | −0.911731 | − | 0.410788i | \(-0.865254\pi\) | ||
0.911731 | − | 0.410788i | \(-0.134746\pi\) | |||||||
\(318\) | 12015.4 | − | 12015.4i | 0.118818 | − | 0.118818i | ||||
\(319\) | 2472.94 | − | 2472.94i | 0.0243015 | − | 0.0243015i | ||||
\(320\) | −17833.5 | − | 17833.5i | −0.174156 | − | 0.174156i | ||||
\(321\) | 25001.1i | 0.242633i | ||||||||
\(322\) | 85853.2 | 0.828027 | ||||||||
\(323\) | 21870.4i | 0.209629i | ||||||||
\(324\) | − | 6091.89i | − | 0.0580313i | ||||||
\(325\) | 280162. | + | 280162.i | 2.65242 | + | 2.65242i | ||||
\(326\) | − | 57512.4i | − | 0.541160i | ||||||
\(327\) | −71582.0 | − | 71582.0i | −0.669435 | − | 0.669435i | ||||
\(328\) | 31908.7 | + | 31908.7i | 0.296593 | + | 0.296593i | ||||
\(329\) | −104202. | −0.962687 | ||||||||
\(330\) | −3660.25 | −0.0336111 | ||||||||
\(331\) | 96948.7 | − | 96948.7i | 0.884883 | − | 0.884883i | −0.109143 | − | 0.994026i | \(-0.534811\pi\) |
0.994026 | + | 0.109143i | \(0.0348105\pi\) | |||||||
\(332\) | 73123.6i | 0.663409i | ||||||||
\(333\) | −46331.2 | + | 42152.8i | −0.417816 | + | 0.380135i | ||||
\(334\) | −35071.9 | −0.314389 | ||||||||
\(335\) | −80777.1 | − | 80777.1i | −0.719779 | − | 0.719779i | ||||
\(336\) | − | 12601.0i | − | 0.111616i | ||||||
\(337\) | 93100.9i | 0.819774i | 0.912136 | + | 0.409887i | \(0.134432\pi\) | ||||
−0.912136 | + | 0.409887i | \(0.865568\pi\) | |||||||
\(338\) | 39628.0 | − | 39628.0i | 0.346871 | − | 0.346871i | ||||
\(339\) | 79061.7 | − | 79061.7i | 0.687966 | − | 0.687966i | ||||
\(340\) | 16599.0 | 0.143590 | ||||||||
\(341\) | −4107.55 | + | 4107.55i | −0.0353244 | + | 0.0353244i | ||||
\(342\) | −67192.9 | −0.574475 | ||||||||
\(343\) | −122778. | −1.04360 | ||||||||
\(344\) | − | 7136.70i | − | 0.0603088i | ||||||
\(345\) | 267657. | 2.24875 | ||||||||
\(346\) | −48556.1 | + | 48556.1i | −0.405594 | + | 0.405594i | ||||
\(347\) | −141764. | − | 141764.i | −1.17735 | − | 1.17735i | −0.980416 | − | 0.196937i | \(-0.936901\pi\) |
−0.196937 | − | 0.980416i | \(-0.563099\pi\) | |||||||
\(348\) | 26541.8 | + | 26541.8i | 0.219165 | + | 0.219165i | ||||
\(349\) | 145687. | 1.19611 | 0.598054 | − | 0.801456i | \(-0.295941\pi\) | ||||
0.598054 | + | 0.801456i | \(0.295941\pi\) | |||||||
\(350\) | 119485. | − | 119485.i | 0.975386 | − | 0.975386i | ||||
\(351\) | −117034. | − | 117034.i | −0.949943 | − | 0.949943i | ||||
\(352\) | 566.420 | − | 566.420i | 0.00457144 | − | 0.00457144i | ||||
\(353\) | −76108.8 | − | 76108.8i | −0.610781 | − | 0.610781i | 0.332368 | − | 0.943150i | \(-0.392152\pi\) |
−0.943150 | + | 0.332368i | \(0.892152\pi\) | |||||||
\(354\) | 13076.7i | 0.104350i | ||||||||
\(355\) | −106892. | + | 106892.i | −0.848182 | + | 0.848182i | ||||
\(356\) | −17009.3 | + | 17009.3i | −0.134211 | + | 0.134211i | ||||
\(357\) | 5864.32 | + | 5864.32i | 0.0460131 | + | 0.0460131i | ||||
\(358\) | 171149.i | 1.33539i | ||||||||
\(359\) | −137351. | −1.06572 | −0.532859 | − | 0.846204i | \(-0.678882\pi\) | ||||
−0.532859 | + | 0.846204i | \(0.678882\pi\) | |||||||
\(360\) | 50997.3i | 0.393497i | ||||||||
\(361\) | − | 139265.i | − | 1.06863i | ||||||
\(362\) | 125732. | + | 125732.i | 0.959461 | + | 0.959461i | ||||
\(363\) | 86804.9i | 0.658765i | ||||||||
\(364\) | −41262.4 | − | 41262.4i | −0.311424 | − | 0.311424i | ||||
\(365\) | −392.186 | − | 392.186i | −0.00294379 | − | 0.00294379i | ||||
\(366\) | 27888.3 | 0.208190 | ||||||||
\(367\) | 141257. | 1.04876 | 0.524381 | − | 0.851484i | \(-0.324297\pi\) | ||||
0.524381 | + | 0.851484i | \(0.324297\pi\) | |||||||
\(368\) | −41419.7 | + | 41419.7i | −0.305852 | + | 0.305852i | ||||
\(369\) | − | 91246.9i | − | 0.670140i | ||||||
\(370\) | −141082. | + | 128358.i | −1.03055 | + | 0.937606i | ||||
\(371\) | −33560.1 | −0.243823 | ||||||||
\(372\) | −44085.8 | − | 44085.8i | −0.318576 | − | 0.318576i | ||||
\(373\) | 135481.i | 0.973778i | 0.873464 | + | 0.486889i | \(0.161868\pi\) | ||||
−0.873464 | + | 0.486889i | \(0.838132\pi\) | |||||||
\(374\) | 527.208i | 0.00376911i | ||||||||
\(375\) | 243266. | − | 243266.i | 1.72989 | − | 1.72989i | ||||
\(376\) | 50272.1 | − | 50272.1i | 0.355592 | − | 0.355592i | ||||
\(377\) | 173824. | 1.22300 | ||||||||
\(378\) | −49913.3 | + | 49913.3i | −0.349327 | + | 0.349327i | ||||
\(379\) | −93988.6 | −0.654330 | −0.327165 | − | 0.944967i | \(-0.606093\pi\) | ||||
−0.327165 | + | 0.944967i | \(0.606093\pi\) | |||||||
\(380\) | −204607. | −1.41695 | ||||||||
\(381\) | − | 23952.4i | − | 0.165006i | ||||||
\(382\) | −49242.9 | −0.337456 | ||||||||
\(383\) | −119229. | + | 119229.i | −0.812800 | + | 0.812800i | −0.985053 | − | 0.172253i | \(-0.944895\pi\) |
0.172253 | + | 0.985053i | \(0.444895\pi\) | |||||||
\(384\) | 6079.31 | + | 6079.31i | 0.0412280 | + | 0.0412280i | ||||
\(385\) | 5111.70 | + | 5111.70i | 0.0344861 | + | 0.0344861i | ||||
\(386\) | −74927.0 | −0.502879 | ||||||||
\(387\) | −10204.2 | + | 10204.2i | −0.0681326 | + | 0.0681326i | ||||
\(388\) | 52540.3 | + | 52540.3i | 0.349003 | + | 0.349003i | ||||
\(389\) | 125692. | − | 125692.i | 0.830632 | − | 0.830632i | −0.156971 | − | 0.987603i | \(-0.550173\pi\) |
0.987603 | + | 0.156971i | \(0.0501730\pi\) | |||||||
\(390\) | −128640. | − | 128640.i | −0.845762 | − | 0.845762i | ||||
\(391\) | − | 38552.3i | − | 0.252172i | ||||||
\(392\) | 20818.2 | − | 20818.2i | 0.135478 | − | 0.135478i | ||||
\(393\) | −89652.3 | + | 89652.3i | −0.580465 | + | 0.580465i | ||||
\(394\) | 43482.3 | + | 43482.3i | 0.280104 | + | 0.280104i | ||||
\(395\) | 146531.i | 0.939152i | ||||||||
\(396\) | −1619.75 | −0.0103290 | ||||||||
\(397\) | − | 273617.i | − | 1.73605i | −0.496522 | − | 0.868024i | \(-0.665390\pi\) | ||
0.496522 | − | 0.868024i | \(-0.334610\pi\) | |||||||
\(398\) | − | 51080.1i | − | 0.322467i | ||||||
\(399\) | −72286.6 | − | 72286.6i | −0.454059 | − | 0.454059i | ||||
\(400\) | 115290.i | 0.720565i | ||||||||
\(401\) | −42057.3 | − | 42057.3i | −0.261548 | − | 0.261548i | 0.564134 | − | 0.825683i | \(-0.309210\pi\) |
−0.825683 | + | 0.564134i | \(0.809210\pi\) | |||||||
\(402\) | 27536.3 | + | 27536.3i | 0.170394 | + | 0.170394i | ||||
\(403\) | −288722. | −1.77775 | ||||||||
\(404\) | −49022.6 | −0.300354 | ||||||||
\(405\) | −26523.4 | + | 26523.4i | −0.161703 | + | 0.161703i | ||||
\(406\) | − | 74133.6i | − | 0.449742i | ||||||
\(407\) | −4076.85 | − | 4480.97i | −0.0246114 | − | 0.0270510i | ||||
\(408\) | −5658.46 | −0.0339921 | ||||||||
\(409\) | 48879.1 | + | 48879.1i | 0.292197 | + | 0.292197i | 0.837948 | − | 0.545750i | \(-0.183755\pi\) |
−0.545750 | + | 0.837948i | \(0.683755\pi\) | |||||||
\(410\) | − | 277853.i | − | 1.65291i | ||||||
\(411\) | − | 78197.3i | − | 0.462922i | ||||||
\(412\) | 39529.8 | − | 39529.8i | 0.232879 | − | 0.232879i | ||||
\(413\) | 18262.3 | − | 18262.3i | 0.107067 | − | 0.107067i | ||||
\(414\) | 118445. | 0.691060 | ||||||||
\(415\) | 318372. | − | 318372.i | 1.84858 | − | 1.84858i | ||||
\(416\) | 39814.0 | 0.230064 | ||||||||
\(417\) | −5590.32 | −0.0321488 | ||||||||
\(418\) | − | 6498.63i | − | 0.0371937i | ||||||
\(419\) | −330719. | −1.88378 | −0.941892 | − | 0.335916i | \(-0.890954\pi\) | ||||
−0.941892 | + | 0.335916i | \(0.890954\pi\) | |||||||
\(420\) | −54863.2 | + | 54863.2i | −0.311016 | + | 0.311016i | ||||
\(421\) | 70515.5 | + | 70515.5i | 0.397851 | + | 0.397851i | 0.877474 | − | 0.479624i | \(-0.159227\pi\) |
−0.479624 | + | 0.877474i | \(0.659227\pi\) | |||||||
\(422\) | −29028.1 | − | 29028.1i | −0.163002 | − | 0.163002i | ||||
\(423\) | −143760. | −0.803445 | ||||||||
\(424\) | 16191.0 | − | 16191.0i | 0.0900620 | − | 0.0900620i | ||||
\(425\) | −53654.6 | − | 53654.6i | −0.297050 | − | 0.297050i | ||||
\(426\) | 36438.7 | − | 36438.7i | 0.200791 | − | 0.200791i | ||||
\(427\) | −38947.4 | − | 38947.4i | −0.213610 | − | 0.213610i | ||||
\(428\) | 33689.5i | 0.183911i | ||||||||
\(429\) | 4085.81 | − | 4085.81i | 0.0222005 | − | 0.0222005i | ||||
\(430\) | −31072.4 | + | 31072.4i | −0.168050 | + | 0.168050i | ||||
\(431\) | 95292.9 | + | 95292.9i | 0.512986 | + | 0.512986i | 0.915440 | − | 0.402454i | \(-0.131843\pi\) |
−0.402454 | + | 0.915440i | \(0.631843\pi\) | |||||||
\(432\) | − | 48161.1i | − | 0.258065i | ||||||
\(433\) | −142331. | −0.759142 | −0.379571 | − | 0.925163i | \(-0.623928\pi\) | ||||
−0.379571 | + | 0.925163i | \(0.623928\pi\) | |||||||
\(434\) | 123136.i | 0.653740i | ||||||||
\(435\) | − | 231120.i | − | 1.22140i | ||||||
\(436\) | −96458.2 | − | 96458.2i | −0.507418 | − | 0.507418i | ||||
\(437\) | 475215.i | 2.48844i | ||||||||
\(438\) | 133.693 | + | 133.693i | 0.000696885 | + | 0.000696885i | ||||
\(439\) | −145482. | − | 145482.i | −0.754886 | − | 0.754886i | 0.220501 | − | 0.975387i | \(-0.429231\pi\) |
−0.975387 | + | 0.220501i | \(0.929231\pi\) | |||||||
\(440\) | −4932.26 | −0.0254765 | ||||||||
\(441\) | −59532.2 | −0.306108 | ||||||||
\(442\) | −18528.9 | + | 18528.9i | −0.0948428 | + | 0.0948428i | ||||
\(443\) | 224281.i | 1.14284i | 0.820658 | + | 0.571420i | \(0.193607\pi\) | ||||
−0.820658 | + | 0.571420i | \(0.806393\pi\) | |||||||
\(444\) | 48093.7 | − | 43756.3i | 0.243962 | − | 0.221960i | ||||
\(445\) | 148114. | 0.747954 | ||||||||
\(446\) | 77938.3 | + | 77938.3i | 0.391815 | + | 0.391815i | ||||
\(447\) | − | 22443.0i | − | 0.112322i | ||||||
\(448\) | − | 16980.1i | − | 0.0846026i | ||||||
\(449\) | −16003.6 | + | 16003.6i | −0.0793823 | + | 0.0793823i | −0.745683 | − | 0.666301i | \(-0.767877\pi\) |
0.666301 | + | 0.745683i | \(0.267877\pi\) | |||||||
\(450\) | 164844. | − | 164844.i | 0.814044 | − | 0.814044i | ||||
\(451\) | 8825.04 | 0.0433874 | ||||||||
\(452\) | 106537. | − | 106537.i | 0.521464 | − | 0.521464i | ||||
\(453\) | −29940.9 | −0.145904 | ||||||||
\(454\) | −6132.43 | −0.0297523 | ||||||||
\(455\) | 359304.i | 1.73556i | ||||||||
\(456\) | 69749.0 | 0.335435 | ||||||||
\(457\) | −45786.0 | + | 45786.0i | −0.219230 | + | 0.219230i | −0.808174 | − | 0.588944i | \(-0.799544\pi\) |
0.588944 | + | 0.808174i | \(0.299544\pi\) | |||||||
\(458\) | −37654.0 | − | 37654.0i | −0.179507 | − | 0.179507i | ||||
\(459\) | 22413.5 | + | 22413.5i | 0.106386 | + | 0.106386i | ||||
\(460\) | 360673. | 1.70451 | ||||||||
\(461\) | −57659.4 | + | 57659.4i | −0.271312 | + | 0.271312i | −0.829628 | − | 0.558316i | \(-0.811447\pi\) |
0.558316 | + | 0.829628i | \(0.311447\pi\) | |||||||
\(462\) | −1742.54 | − | 1742.54i | −0.00816392 | − | 0.00816392i | ||||
\(463\) | −53466.5 | + | 53466.5i | −0.249413 | + | 0.249413i | −0.820730 | − | 0.571316i | \(-0.806433\pi\) |
0.571316 | + | 0.820730i | \(0.306433\pi\) | |||||||
\(464\) | 35765.6 | + | 35765.6i | 0.166123 | + | 0.166123i | ||||
\(465\) | 383890.i | 1.77542i | ||||||||
\(466\) | −184997. | + | 184997.i | −0.851909 | + | 0.851909i | ||||
\(467\) | 208667. | − | 208667.i | 0.956795 | − | 0.956795i | −0.0423091 | − | 0.999105i | \(-0.513471\pi\) |
0.999105 | + | 0.0423091i | \(0.0134714\pi\) | |||||||
\(468\) | −56926.6 | − | 56926.6i | −0.259910 | − | 0.259910i | ||||
\(469\) | − | 76911.4i | − | 0.349659i | ||||||
\(470\) | −437759. | −1.98170 | ||||||||
\(471\) | 99166.8i | 0.447017i | ||||||||
\(472\) | 17621.2i | 0.0790954i | ||||||||
\(473\) | −986.906 | − | 986.906i | −0.00441117 | − | 0.00441117i | ||||
\(474\) | − | 49951.3i | − | 0.222326i | ||||||
\(475\) | 661373. | + | 661373.i | 2.93129 | + | 2.93129i | ||||
\(476\) | 7902.30 | + | 7902.30i | 0.0348770 | + | 0.0348770i | ||||
\(477\) | −46300.2 | −0.203491 | ||||||||
\(478\) | 25731.3 | 0.112617 | ||||||||
\(479\) | 138990. | − | 138990.i | 0.605775 | − | 0.605775i | −0.336064 | − | 0.941839i | \(-0.609096\pi\) |
0.941839 | + | 0.336064i | \(0.109096\pi\) | |||||||
\(480\) | − | 52937.3i | − | 0.229763i | ||||||
\(481\) | 14202.8 | − | 300767.i | 0.0613879 | − | 1.29999i | ||||
\(482\) | 323425. | 1.39213 | ||||||||
\(483\) | 127424. | + | 127424.i | 0.546206 | + | 0.546206i | ||||
\(484\) | 116971.i | 0.499331i | ||||||||
\(485\) | − | 457510.i | − | 1.94499i | ||||||
\(486\) | −112866. | + | 112866.i | −0.477850 | + | 0.477850i | ||||
\(487\) | −268161. | + | 268161.i | −1.13068 | + | 1.13068i | −0.140610 | + | 0.990065i | \(0.544906\pi\) |
−0.990065 | + | 0.140610i | \(0.955094\pi\) | |||||||
\(488\) | 37580.1 | 0.157804 | ||||||||
\(489\) | 85360.3 | − | 85360.3i | 0.356975 | − | 0.356975i | ||||
\(490\) | −181280. | −0.755019 | ||||||||
\(491\) | 317255. | 1.31597 | 0.657984 | − | 0.753032i | \(-0.271410\pi\) | ||||
0.657984 | + | 0.753032i | \(0.271410\pi\) | |||||||
\(492\) | 94718.1i | 0.391294i | ||||||||
\(493\) | −33289.6 | −0.136967 | ||||||||
\(494\) | 228396. | − | 228396.i | 0.935912 | − | 0.935912i | ||||
\(495\) | 7052.21 | + | 7052.21i | 0.0287816 | + | 0.0287816i | ||||
\(496\) | −59406.6 | − | 59406.6i | −0.241474 | − | 0.241474i | ||||
\(497\) | −101777. | −0.412036 | ||||||||
\(498\) | −108531. | + | 108531.i | −0.437616 | + | 0.437616i | ||||
\(499\) | 258204. | + | 258204.i | 1.03696 | + | 1.03696i | 0.999290 | + | 0.0376701i | \(0.0119936\pi\) |
0.0376701 | + | 0.999290i | \(0.488006\pi\) | |||||||
\(500\) | 327806. | − | 327806.i | 1.31122 | − | 1.31122i | ||||
\(501\) | −52054.0 | − | 52054.0i | −0.207386 | − | 0.207386i | ||||
\(502\) | 10098.3i | 0.0400718i | ||||||||
\(503\) | −248652. | + | 248652.i | −0.982781 | + | 0.982781i | −0.999854 | − | 0.0170737i | \(-0.994565\pi\) |
0.0170737 | + | 0.999854i | \(0.494565\pi\) | |||||||
\(504\) | −24278.4 | + | 24278.4i | −0.0955781 | + | 0.0955781i | ||||
\(505\) | 213439. | + | 213439.i | 0.836933 | + | 0.836933i | ||||
\(506\) | 11455.5i | 0.0447419i | ||||||||
\(507\) | 117632. | 0.457626 | ||||||||
\(508\) | − | 32276.4i | − | 0.125071i | ||||||
\(509\) | − | 192284.i | − | 0.742177i | −0.928598 | − | 0.371088i | \(-0.878985\pi\) | ||
0.928598 | − | 0.371088i | \(-0.121015\pi\) | |||||||
\(510\) | 24636.3 | + | 24636.3i | 0.0947186 | + | 0.0947186i | ||||
\(511\) | − | 373.417i | − | 0.00143006i | ||||||
\(512\) | 8192.00 | + | 8192.00i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −276280. | − | 276280.i | −1.04982 | − | 1.04982i | ||||
\(514\) | 107082. | 0.405312 | ||||||||
\(515\) | −344217. | −1.29783 | ||||||||
\(516\) | 10592.3 | − | 10592.3i | 0.0397825 | − | 0.0397825i | ||||
\(517\) | − | 13903.9i | − | 0.0520181i | ||||||
\(518\) | −128273. | − | 6057.27i | −0.478052 | − | 0.0225745i | ||||
\(519\) | −144135. | −0.535098 | ||||||||
\(520\) | −173346. | − | 173346.i | −0.641071 | − | 0.641071i | ||||
\(521\) | − | 231118.i | − | 0.851448i | −0.904853 | − | 0.425724i | \(-0.860019\pi\) | ||
0.904853 | − | 0.425724i | \(-0.139981\pi\) | |||||||
\(522\) | − | 102276.i | − | 0.375348i | ||||||
\(523\) | 85348.4 | − | 85348.4i | 0.312027 | − | 0.312027i | −0.533667 | − | 0.845694i | \(-0.679187\pi\) |
0.845694 | + | 0.533667i | \(0.179187\pi\) | |||||||
\(524\) | −120808. | + | 120808.i | −0.439981 | + | 0.439981i | ||||
\(525\) | 354680. | 1.28682 | ||||||||
\(526\) | −519.233 | + | 519.233i | −0.00187668 | + | 0.00187668i | ||||
\(527\) | 55294.0 | 0.199094 | ||||||||
\(528\) | 1681.37 | 0.00603108 | ||||||||
\(529\) | − | 557850.i | − | 1.99345i | ||||||
\(530\) | −140987. | −0.501913 | ||||||||
\(531\) | 25195.0 | − | 25195.0i | 0.0893564 | − | 0.0893564i | ||||
\(532\) | −97407.7 | − | 97407.7i | −0.344168 | − | 0.344168i | ||||
\(533\) | 310159. | + | 310159.i | 1.09177 | + | 1.09177i | ||||
\(534\) | −50490.8 | −0.177064 | ||||||||
\(535\) | 146680. | − | 146680.i | 0.512465 | − | 0.512465i | ||||
\(536\) | 37105.7 | + | 37105.7i | 0.129155 | + | 0.129155i | ||||
\(537\) | −254021. | + | 254021.i | −0.880887 | + | 0.880887i | ||||
\(538\) | 111623. | + | 111623.i | 0.385647 | + | 0.385647i | ||||
\(539\) | − | 5757.72i | − | 0.0198186i | ||||||
\(540\) | −209688. | + | 209688.i | −0.719095 | + | 0.719095i | ||||
\(541\) | −234565. | + | 234565.i | −0.801436 | + | 0.801436i | −0.983320 | − | 0.181884i | \(-0.941780\pi\) |
0.181884 | + | 0.983320i | \(0.441780\pi\) | |||||||
\(542\) | 230767. | + | 230767.i | 0.785552 | + | 0.785552i | ||||
\(543\) | 373224.i | 1.26581i | ||||||||
\(544\) | −7624.89 | −0.0257653 | ||||||||
\(545\) | 839937.i | 2.82783i | ||||||||
\(546\) | − | 122484.i | − | 0.410860i | ||||||
\(547\) | 157826. | + | 157826.i | 0.527476 | + | 0.527476i | 0.919819 | − | 0.392343i | \(-0.128335\pi\) |
−0.392343 | + | 0.919819i | \(0.628335\pi\) | |||||||
\(548\) | − | 105372.i | − | 0.350886i | ||||||
\(549\) | −53732.6 | − | 53732.6i | −0.178276 | − | 0.178276i | ||||
\(550\) | 15943.1 | + | 15943.1i | 0.0527043 | + | 0.0527043i | ||||
\(551\) | 410345. | 1.35159 | ||||||||
\(552\) | −122951. | −0.403509 | ||||||||
\(553\) | −69759.3 | + | 69759.3i | −0.228114 | + | 0.228114i | ||||
\(554\) | − | 206757.i | − | 0.673659i | ||||||
\(555\) | −399905. | − | 18884.2i | −1.29829 | − | 0.0613075i | ||||
\(556\) | −7533.07 | −0.0243681 | ||||||||
\(557\) | −196118. | − | 196118.i | −0.632132 | − | 0.632132i | 0.316470 | − | 0.948602i | \(-0.397502\pi\) |
−0.948602 | + | 0.316470i | \(0.897502\pi\) | |||||||
\(558\) | 169881.i | 0.545602i | ||||||||
\(559\) | − | 69370.2i | − | 0.221998i | ||||||
\(560\) | −73929.4 | + | 73929.4i | −0.235744 | + | 0.235744i | ||||
\(561\) | −782.486 | + | 782.486i | −0.00248628 | + | 0.00248628i | ||||
\(562\) | 321859. | 1.01904 | ||||||||
\(563\) | 12439.6 | − | 12439.6i | 0.0392454 | − | 0.0392454i | −0.687212 | − | 0.726457i | \(-0.741166\pi\) |
0.726457 | + | 0.687212i | \(0.241166\pi\) | |||||||
\(564\) | 149229. | 0.469130 | ||||||||
\(565\) | −927703. | −2.90611 | ||||||||
\(566\) | − | 192099.i | − | 0.599643i | ||||||
\(567\) | −25254.1 | −0.0785535 | ||||||||
\(568\) | 49101.9 | − | 49101.9i | 0.152195 | − | 0.152195i | ||||
\(569\) | −100481. | − | 100481.i | −0.310357 | − | 0.310357i | 0.534691 | − | 0.845048i | \(-0.320428\pi\) |
−0.845048 | + | 0.534691i | \(0.820428\pi\) | |||||||
\(570\) | −303679. | − | 303679.i | −0.934686 | − | 0.934686i | ||||
\(571\) | 460437. | 1.41221 | 0.706103 | − | 0.708109i | \(-0.250451\pi\) | ||||
0.706103 | + | 0.708109i | \(0.250451\pi\) | |||||||
\(572\) | 5505.72 | − | 5505.72i | 0.0168276 | − | 0.0168276i | ||||
\(573\) | −73086.7 | − | 73086.7i | −0.222602 | − | 0.222602i | ||||
\(574\) | 132278. | − | 132278.i | 0.401480 | − | 0.401480i | ||||
\(575\) | −1.16584e6 | − | 1.16584e6i | −3.52618 | − | 3.52618i | ||||
\(576\) | − | 23426.1i | − | 0.0706081i | ||||||
\(577\) | 244370. | − | 244370.i | 0.734001 | − | 0.734001i | −0.237409 | − | 0.971410i | \(-0.576298\pi\) |
0.971410 | + | 0.237409i | \(0.0762980\pi\) | |||||||
\(578\) | −163493. | + | 163493.i | −0.489378 | + | 0.489378i | ||||
\(579\) | −111207. | − | 111207.i | −0.331723 | − | 0.331723i | ||||
\(580\) | − | 311439.i | − | 0.925799i | ||||||
\(581\) | 303136. | 0.898018 | ||||||||
\(582\) | 155962.i | 0.460438i | ||||||||
\(583\) | − | 4477.97i | − | 0.0131748i | ||||||
\(584\) | 180.154 | + | 180.154i | 0.000528225 | + | 0.000528225i | ||||
\(585\) | 495704.i | 1.44847i | ||||||||
\(586\) | 210527. | + | 210527.i | 0.613073 | + | 0.613073i | ||||
\(587\) | −107059. | − | 107059.i | −0.310703 | − | 0.310703i | 0.534479 | − | 0.845182i | \(-0.320508\pi\) |
−0.845182 | + | 0.534479i | \(0.820508\pi\) | |||||||
\(588\) | 61796.9 | 0.178736 | ||||||||
\(589\) | −681582. | −1.96466 | ||||||||
\(590\) | 76720.7 | − | 76720.7i | 0.220398 | − | 0.220398i | ||||
\(591\) | 129073.i | 0.369540i | ||||||||
\(592\) | 64807.2 | − | 58962.6i | 0.184918 | − | 0.168242i | ||||
\(593\) | 311613. | 0.886149 | 0.443074 | − | 0.896485i | \(-0.353888\pi\) | ||||
0.443074 | + | 0.896485i | \(0.353888\pi\) | |||||||
\(594\) | −6660.01 | − | 6660.01i | −0.0188756 | − | 0.0188756i | ||||
\(595\) | − | 68811.4i | − | 0.194369i | ||||||
\(596\) | − | 30242.5i | − | 0.0851383i | ||||||
\(597\) | 75813.5 | − | 75813.5i | 0.212715 | − | 0.212715i | ||||
\(598\) | −402608. | + | 402608.i | −1.12585 | + | 1.12585i | ||||
\(599\) | 616554. | 1.71837 | 0.859187 | − | 0.511662i | \(-0.170970\pi\) | ||||
0.859187 | + | 0.511662i | \(0.170970\pi\) | |||||||
\(600\) | −171115. | + | 171115.i | −0.475319 | + | 0.475319i | ||||
\(601\) | 446062. | 1.23494 | 0.617471 | − | 0.786594i | \(-0.288157\pi\) | ||||
0.617471 | + | 0.786594i | \(0.288157\pi\) | |||||||
\(602\) | −29585.4 | −0.0816364 | ||||||||
\(603\) | − | 106109.i | − | 0.291821i | ||||||
\(604\) | −40345.9 | −0.110593 | ||||||||
\(605\) | 509280. | − | 509280.i | 1.39138 | − | 1.39138i | ||||
\(606\) | −72759.7 | − | 72759.7i | −0.198128 | − | 0.198128i | ||||
\(607\) | −259551. | − | 259551.i | −0.704443 | − | 0.704443i | 0.260918 | − | 0.965361i | \(-0.415975\pi\) |
−0.965361 | + | 0.260918i | \(0.915975\pi\) | |||||||
\(608\) | 93988.2 | 0.254253 | ||||||||
\(609\) | 110030. | − | 110030.i | 0.296671 | − | 0.296671i | ||||
\(610\) | −163620. | − | 163620.i | −0.439720 | − | 0.439720i | ||||
\(611\) | 488655. | − | 488655.i | 1.30894 | − | 1.30894i | ||||
\(612\) | 10902.2 | + | 10902.2i | 0.0291079 | + | 0.0291079i | ||||
\(613\) | − | 325514.i | − | 0.866261i | −0.901331 | − | 0.433130i | \(-0.857409\pi\) | ||
0.901331 | − | 0.433130i | \(-0.142591\pi\) | |||||||
\(614\) | −351476. | + | 351476.i | −0.932308 | + | 0.932308i | ||||
\(615\) | 412392. | − | 412392.i | 1.09034 | − | 1.09034i | ||||
\(616\) | −2348.11 | − | 2348.11i | −0.00618809 | − | 0.00618809i | ||||
\(617\) | − | 88330.8i | − | 0.232029i | −0.993248 | − | 0.116014i | \(-0.962988\pi\) | ||
0.993248 | − | 0.116014i | \(-0.0370119\pi\) | |||||||
\(618\) | 117341. | 0.307236 | ||||||||
\(619\) | 601121.i | 1.56885i | 0.620226 | + | 0.784423i | \(0.287041\pi\) | ||||
−0.620226 | + | 0.784423i | \(0.712959\pi\) | |||||||
\(620\) | 517299.i | 1.34573i | ||||||||
\(621\) | 487016. | + | 487016.i | 1.26287 | + | 1.26287i | ||||
\(622\) | − | 90000.2i | − | 0.232628i | ||||||
\(623\) | 70512.7 | + | 70512.7i | 0.181673 | + | 0.181673i | ||||
\(624\) | 59092.2 | + | 59092.2i | 0.151761 | + | 0.151761i | ||||
\(625\) | −1.72858e6 | −4.42516 | ||||||||
\(626\) | 108455. | 0.276759 | ||||||||
\(627\) | 9645.32 | − | 9645.32i | 0.0245347 | − | 0.0245347i | ||||
\(628\) | 133629.i | 0.338830i | ||||||||
\(629\) | −2720.01 | + | 57600.8i | −0.00687496 | + | 0.145589i | ||||
\(630\) | 211411. | 0.532654 | ||||||||
\(631\) | −167496. | − | 167496.i | −0.420673 | − | 0.420673i | 0.464762 | − | 0.885436i | \(-0.346140\pi\) |
−0.885436 | + | 0.464762i | \(0.846140\pi\) | |||||||
\(632\) | − | 67310.5i | − | 0.168519i | ||||||
\(633\) | − | 86167.4i | − | 0.215048i | ||||||
\(634\) | 165119. | − | 165119.i | 0.410788 | − | 0.410788i | ||||
\(635\) | −140528. | + | 140528.i | −0.348510 | + | 0.348510i | ||||
\(636\) | 48061.5 | 0.118818 | ||||||||
\(637\) | 202357. | − | 202357.i | 0.498700 | − | 0.498700i | ||||
\(638\) | 9891.77 | 0.0243015 | ||||||||
\(639\) | −140413. | −0.343880 | ||||||||
\(640\) | − | 71334.1i | − | 0.174156i | ||||||
\(641\) | 119109. | 0.289887 | 0.144943 | − | 0.989440i | \(-0.453700\pi\) | ||||
0.144943 | + | 0.989440i | \(0.453700\pi\) | |||||||
\(642\) | −50002.2 | + | 50002.2i | −0.121316 | + | 0.121316i | ||||
\(643\) | −122318. | − | 122318.i | −0.295847 | − | 0.295847i | 0.543538 | − | 0.839385i | \(-0.317084\pi\) |
−0.839385 | + | 0.543538i | \(0.817084\pi\) | |||||||
\(644\) | 171706. | + | 171706.i | 0.414014 | + | 0.414014i | ||||
\(645\) | −92235.7 | −0.221707 | ||||||||
\(646\) | −43740.9 | + | 43740.9i | −0.104815 | + | 0.104815i | ||||
\(647\) | −51581.0 | − | 51581.0i | −0.123220 | − | 0.123220i | 0.642808 | − | 0.766028i | \(-0.277769\pi\) |
−0.766028 | + | 0.642808i | \(0.777769\pi\) | |||||||
\(648\) | 12183.8 | − | 12183.8i | 0.0290156 | − | 0.0290156i | ||||
\(649\) | 2436.76 | + | 2436.76i | 0.00578528 | + | 0.00578528i | ||||
\(650\) | 1.12065e6i | 2.65242i | ||||||||
\(651\) | −182759. | + | 182759.i | −0.431238 | + | 0.431238i | ||||
\(652\) | 115025. | − | 115025.i | 0.270580 | − | 0.270580i | ||||
\(653\) | −54714.1 | − | 54714.1i | −0.128314 | − | 0.128314i | 0.640033 | − | 0.768347i | \(-0.278921\pi\) |
−0.768347 | + | 0.640033i | \(0.778921\pi\) | |||||||
\(654\) | − | 286328.i | − | 0.669435i | ||||||
\(655\) | 1.05197e6 | 2.45201 | ||||||||
\(656\) | 127635.i | 0.296593i | ||||||||
\(657\) | − | 515.175i | − | 0.00119350i | ||||||
\(658\) | −208404. | − | 208404.i | −0.481344 | − | 0.481344i | ||||
\(659\) | − | 650669.i | − | 1.49827i | −0.662418 | − | 0.749134i | \(-0.730470\pi\) | ||
0.662418 | − | 0.749134i | \(-0.269530\pi\) | |||||||
\(660\) | −7320.49 | − | 7320.49i | −0.0168055 | − | 0.0168055i | ||||
\(661\) | 45310.1 | + | 45310.1i | 0.103703 | + | 0.103703i | 0.757055 | − | 0.653352i | \(-0.226638\pi\) |
−0.653352 | + | 0.757055i | \(0.726638\pi\) | |||||||
\(662\) | 387795. | 0.884883 | ||||||||
\(663\) | −55001.4 | −0.125126 | ||||||||
\(664\) | −146247. | + | 146247.i | −0.331705 | + | 0.331705i | ||||
\(665\) | 848204.i | 1.91804i | ||||||||
\(666\) | −176968. | − | 8356.75i | −0.398975 | − | 0.0188403i | ||||
\(667\) | −723340. | −1.62589 | ||||||||
\(668\) | −70143.9 | − | 70143.9i | −0.157194 | − | 0.157194i | ||||
\(669\) | 231353.i | 0.516920i | ||||||||
\(670\) | − | 323109.i | − | 0.719779i | ||||||
\(671\) | 5196.81 | − | 5196.81i | 0.0115423 | − | 0.0115423i | ||||
\(672\) | 25201.9 | − | 25201.9i | 0.0558079 | − | 0.0558079i | ||||
\(673\) | −145711. | −0.321708 | −0.160854 | − | 0.986978i | \(-0.551425\pi\) | ||||
−0.160854 | + | 0.986978i | \(0.551425\pi\) | |||||||
\(674\) | −186202. | + | 186202.i | −0.409887 | + | 0.409887i | ||||
\(675\) | 1.35559e6 | 2.97524 | ||||||||
\(676\) | 158512. | 0.346871 | ||||||||
\(677\) | 94182.3i | 0.205491i | 0.994708 | + | 0.102745i | \(0.0327627\pi\) | ||||
−0.994708 | + | 0.102745i | \(0.967237\pi\) | |||||||
\(678\) | 316247. | 0.687966 | ||||||||
\(679\) | 217807. | − | 217807.i | 0.472425 | − | 0.472425i | ||||
\(680\) | 33197.9 | + | 33197.9i | 0.0717948 | + | 0.0717948i | ||||
\(681\) | −9101.80 | − | 9101.80i | −0.0196261 | − | 0.0196261i | ||||
\(682\) | −16430.2 | −0.0353244 | ||||||||
\(683\) | −377950. | + | 377950.i | −0.810201 | + | 0.810201i | −0.984664 | − | 0.174463i | \(-0.944181\pi\) |
0.174463 | + | 0.984664i | \(0.444181\pi\) | |||||||
\(684\) | −134386. | − | 134386.i | −0.287237 | − | 0.287237i | ||||
\(685\) | −458780. | + | 458780.i | −0.977740 | + | 0.977740i | ||||
\(686\) | −245557. | − | 245557.i | −0.521800 | − | 0.521800i | ||||
\(687\) | − | 111773.i | − | 0.236822i | ||||||
\(688\) | 14273.4 | − | 14273.4i | 0.0301544 | − | 0.0301544i | ||||
\(689\) | 157380. | − | 157380.i | 0.331520 | − | 0.331520i | ||||
\(690\) | 535314. | + | 535314.i | 1.12437 | + | 1.12437i | ||||
\(691\) | 572040.i | 1.19804i | 0.800735 | + | 0.599019i | \(0.204443\pi\) | ||||
−0.800735 | + | 0.599019i | \(0.795557\pi\) | |||||||
\(692\) | −194224. | −0.405594 | ||||||||
\(693\) | 6714.72i | 0.0139817i | ||||||||
\(694\) | − | 567056.i | − | 1.17735i | ||||||
\(695\) | 32798.2 | + | 32798.2i | 0.0679016 | + | 0.0679016i | ||||
\(696\) | 106167.i | 0.219165i | ||||||||
\(697\) | −59399.4 | − | 59399.4i | −0.122269 | − | 0.122269i | ||||
\(698\) | 291374. | + | 291374.i | 0.598054 | + | 0.598054i | ||||
\(699\) | −549148. | −1.12392 | ||||||||
\(700\) | 477939. | 0.975386 | ||||||||
\(701\) | 135953. | − | 135953.i | 0.276664 | − | 0.276664i | −0.555112 | − | 0.831776i | \(-0.687324\pi\) |
0.831776 | + | 0.555112i | \(0.187324\pi\) | |||||||
\(702\) | − | 468136.i | − | 0.949943i | ||||||
\(703\) | 33528.3 | − | 710016.i | 0.0678423 | − | 1.43667i | ||||
\(704\) | 2265.68 | 0.00457144 | ||||||||
\(705\) | −649724. | − | 649724.i | −1.30723 | − | 1.30723i | ||||
\(706\) | − | 304435.i | − | 0.610781i | ||||||
\(707\) | 203224.i | 0.406572i | ||||||||
\(708\) | −26153.5 | + | 26153.5i | −0.0521751 | + | 0.0521751i | ||||
\(709\) | 152643. | − | 152643.i | 0.303658 | − | 0.303658i | −0.538785 | − | 0.842443i | \(-0.681117\pi\) |
0.842443 | + | 0.538785i | \(0.181117\pi\) | |||||||
\(710\) | −427569. | −0.848182 | ||||||||
\(711\) | −96241.5 | + | 96241.5i | −0.190381 | + | 0.190381i | ||||
\(712\) | −68037.4 | −0.134211 | ||||||||
\(713\) | 1.20147e6 | 2.36337 | ||||||||
\(714\) | 23457.3i | 0.0460131i | ||||||||
\(715\) | −47942.5 | −0.0937797 | ||||||||
\(716\) | −342298. | + | 342298.i | −0.667695 | + | 0.667695i | ||||
\(717\) | 38190.5 | + | 38190.5i | 0.0742878 | + | 0.0742878i | ||||
\(718\) | −274702. | − | 274702.i | −0.532859 | − | 0.532859i | ||||
\(719\) | 46120.6 | 0.0892149 | 0.0446075 | − | 0.999005i | \(-0.485796\pi\) | ||||
0.0446075 | + | 0.999005i | \(0.485796\pi\) | |||||||
\(720\) | −101995. | + | 101995.i | −0.196749 | + | 0.196749i | ||||
\(721\) | −163872. | − | 163872.i | −0.315234 | − | 0.315234i | ||||
\(722\) | 278530. | − | 278530.i | 0.534315 | − | 0.534315i | ||||
\(723\) | 480030. | + | 480030.i | 0.918316 | + | 0.918316i | ||||
\(724\) | 502927.i | 0.959461i | ||||||||
\(725\) | −1.00670e6 | + | 1.00670e6i | −1.91524 | + | 1.91524i | ||||
\(726\) | −173610. | + | 173610.i | −0.329383 | + | 0.329383i | ||||
\(727\) | 504839. | + | 504839.i | 0.955178 | + | 0.955178i | 0.999038 | − | 0.0438596i | \(-0.0139654\pi\) |
−0.0438596 | + | 0.999038i | \(0.513965\pi\) | |||||||
\(728\) | − | 165050.i | − | 0.311424i | ||||||
\(729\) | −396714. | −0.746487 | ||||||||
\(730\) | − | 1568.74i | − | 0.00294379i | ||||||
\(731\) | 13285.3i | 0.0248620i | ||||||||
\(732\) | 55776.7 | + | 55776.7i | 0.104095 | + | 0.104095i | ||||
\(733\) | 524436.i | 0.976079i | 0.872822 | + | 0.488039i | \(0.162288\pi\) | ||||
−0.872822 | + | 0.488039i | \(0.837712\pi\) | |||||||
\(734\) | 282513. | + | 282513.i | 0.524381 | + | 0.524381i | ||||
\(735\) | −269057. | − | 269057.i | −0.498046 | − | 0.498046i | ||||
\(736\) | −165679. | −0.305852 | ||||||||
\(737\) | 10262.4 | 0.0188936 | ||||||||
\(738\) | 182494. | − | 182494.i | 0.335070 | − | 0.335070i | ||||
\(739\) | 523967.i | 0.959435i | 0.877423 | + | 0.479717i | \(0.159261\pi\) | ||||
−0.877423 | + | 0.479717i | \(0.840739\pi\) | |||||||
\(740\) | −538880. | − | 25446.9i | −0.984076 | − | 0.0464699i | ||||
\(741\) | 677975. | 1.23474 | ||||||||
\(742\) | −67120.1 | − | 67120.1i | −0.121912 | − | 0.121912i | ||||
\(743\) | − | 91675.0i | − | 0.166063i | −0.996547 | − | 0.0830316i | \(-0.973540\pi\) | ||
0.996547 | − | 0.0830316i | \(-0.0264602\pi\) | |||||||
\(744\) | − | 176343.i | − | 0.318576i | ||||||
\(745\) | −131672. | + | 131672.i | −0.237237 | + | 0.237237i | ||||
\(746\) | −270962. | + | 270962.i | −0.486889 | + | 0.486889i | ||||
\(747\) | 418213. | 0.749473 | ||||||||
\(748\) | −1054.42 | + | 1054.42i | −0.00188456 | + | 0.00188456i | ||||
\(749\) | 139661. | 0.248949 | ||||||||
\(750\) | 973064. | 1.72989 | ||||||||
\(751\) | 483848.i | 0.857885i | 0.903332 | + | 0.428943i | \(0.141114\pi\) | ||||
−0.903332 | + | 0.428943i | \(0.858886\pi\) | |||||||
\(752\) | 201089. | 0.355592 | ||||||||
\(753\) | −14987.9 | + | 14987.9i | −0.0264333 | + | 0.0264333i | ||||
\(754\) | 347649. | + | 347649.i | 0.611502 | + | 0.611502i | ||||
\(755\) | 175662. | + | 175662.i | 0.308165 | + | 0.308165i | ||||
\(756\) | −199653. | −0.349327 | ||||||||
\(757\) | 151529. | − | 151529.i | 0.264426 | − | 0.264426i | −0.562423 | − | 0.826849i | \(-0.690131\pi\) |
0.826849 | + | 0.562423i | \(0.190131\pi\) | |||||||
\(758\) | −187977. | − | 187977.i | −0.327165 | − | 0.327165i | ||||
\(759\) | −17002.4 | + | 17002.4i | −0.0295139 | + | 0.0295139i | ||||
\(760\) | −409214. | − | 409214.i | −0.708474 | − | 0.708474i | ||||
\(761\) | − | 191135.i | − | 0.330044i | −0.986290 | − | 0.165022i | \(-0.947230\pi\) | ||
0.986290 | − | 0.165022i | \(-0.0527695\pi\) | |||||||
\(762\) | 47904.9 | − | 47904.9i | 0.0825030 | − | 0.0825030i | ||||
\(763\) | −399870. | + | 399870.i | −0.686862 | + | 0.686862i | ||||
\(764\) | −98485.8 | − | 98485.8i | −0.168728 | − | 0.168728i | ||||
\(765\) | − | 94933.8i | − | 0.162218i | ||||||
\(766\) | −476915. | −0.812800 | ||||||||
\(767\) | 171282.i | 0.291152i | ||||||||
\(768\) | 24317.3i | 0.0412280i | ||||||||
\(769\) | −95194.7 | − | 95194.7i | −0.160976 | − | 0.160976i | 0.622023 | − | 0.782999i | \(-0.286311\pi\) |
−0.782999 | + | 0.622023i | \(0.786311\pi\) | |||||||
\(770\) | 20446.8i | 0.0344861i | ||||||||
\(771\) | 158932. | + | 158932.i | 0.267363 | + | 0.267363i | ||||
\(772\) | −149854. | − | 149854.i | −0.251440 | − | 0.251440i | ||||
\(773\) | −153875. | −0.257519 | −0.128760 | − | 0.991676i | \(-0.541100\pi\) | ||||
−0.128760 | + | 0.991676i | \(0.541100\pi\) | |||||||
\(774\) | −40816.6 | −0.0681326 | ||||||||
\(775\) | 1.67212e6 | − | 1.67212e6i | 2.78397 | − | 2.78397i | ||||
\(776\) | 210161.i | 0.349003i | ||||||||
\(777\) | −181393. | − | 199374.i | −0.300454 | − | 0.330237i | ||||
\(778\) | 502768. | 0.830632 | ||||||||
\(779\) | 732187. | + | 732187.i | 1.20656 | + | 1.20656i | ||||
\(780\) | − | 514561.i | − | 0.845762i | ||||||
\(781\) | − | 13580.2i | − | 0.0222641i | ||||||
\(782\) | 77104.6 | − | 77104.6i | 0.126086 | − | 0.126086i | ||||
\(783\) | 420535. | − | 420535.i | 0.685928 | − | 0.685928i | ||||
\(784\) | 83272.7 | 0.135478 | ||||||||
\(785\) | 581807. | − | 581807.i | 0.944147 | − | 0.944147i | ||||
\(786\) | −358609. | −0.580465 | ||||||||
\(787\) | −1.15334e6 | −1.86212 | −0.931060 | − | 0.364866i | \(-0.881115\pi\) | ||||
−0.931060 | + | 0.364866i | \(0.881115\pi\) | |||||||
\(788\) | 173929.i | 0.280104i | ||||||||
\(789\) | −1541.30 | −0.00247590 | ||||||||
\(790\) | −293062. | + | 293062.i | −0.469576 | + | 0.469576i | ||||
\(791\) | −441653. | − | 441653.i | −0.705876 | − | 0.705876i | ||||
\(792\) | −3239.50 | − | 3239.50i | −0.00516449 | − | 0.00516449i | ||||
\(793\) | 365287. | 0.580881 | ||||||||
\(794\) | 547234. | − | 547234.i | 0.868024 | − | 0.868024i | ||||
\(795\) | −209255. | − | 209255.i | −0.331086 | − | 0.331086i | ||||
\(796\) | 102160. | − | 102160.i | 0.161234 | − | 0.161234i | ||||
\(797\) | −582265. | − | 582265.i | −0.916651 | − | 0.916651i | 0.0801335 | − | 0.996784i | \(-0.474465\pi\) |
−0.996784 | + | 0.0801335i | \(0.974465\pi\) | |||||||
\(798\) | − | 289146.i | − | 0.454059i | ||||||
\(799\) | −93583.9 | + | 93583.9i | −0.146591 | + | 0.146591i | ||||
\(800\) | −230581. | + | 230581.i | −0.360282 | + | 0.360282i | ||||
\(801\) | 97280.8 | + | 97280.8i | 0.151622 | + | 0.151622i | ||||
\(802\) | − | 168229.i | − | 0.261548i | ||||||
\(803\) | 49.8257 | 7.72720e−5 | ||||||||
\(804\) | 110145.i | 0.170394i | ||||||||
\(805\) | − | 1.49518e6i | − | 2.30729i | ||||||
\(806\) | −577444. | − | 577444.i | −0.888873 | − | 0.888873i | ||||
\(807\) | 331344.i | 0.508783i | ||||||||
\(808\) | −98045.2 | − | 98045.2i | −0.150177 | − | 0.150177i | ||||
\(809\) | 398584. | + | 398584.i | 0.609008 | + | 0.609008i | 0.942687 | − | 0.333679i | \(-0.108290\pi\) |
−0.333679 | + | 0.942687i | \(0.608290\pi\) | |||||||
\(810\) | −106094. | −0.161703 | ||||||||
\(811\) | −369426. | −0.561675 | −0.280838 | − | 0.959755i | \(-0.590612\pi\) | ||||
−0.280838 | + | 0.959755i | \(0.590612\pi\) | |||||||
\(812\) | 148267. | − | 148267.i | 0.224871 | − | 0.224871i | ||||
\(813\) | 685011.i | 1.03637i | ||||||||
\(814\) | 808.232 | − | 17115.6i | 0.00121980 | − | 0.0258312i | ||||
\(815\) | −1.00161e6 | −1.50794 | ||||||||
\(816\) | −11316.9 | − | 11316.9i | −0.0169960 | − | 0.0169960i | ||||
\(817\) | − | 163761.i | − | 0.245339i | ||||||
\(818\) | 195516.i | 0.292197i | ||||||||
\(819\) | −235991. | + | 235991.i | −0.351825 | + | 0.351825i | ||||
\(820\) | 555707. | − | 555707.i | 0.826453 | − | 0.826453i | ||||
\(821\) | −912349. | −1.35355 | −0.676775 | − | 0.736190i | \(-0.736623\pi\) | ||||
−0.676775 | + | 0.736190i | \(0.736623\pi\) | |||||||
\(822\) | 156395. | − | 156395.i | 0.231461 | − | 0.231461i | ||||
\(823\) | −479257. | −0.707569 | −0.353785 | − | 0.935327i | \(-0.615105\pi\) | ||||
−0.353785 | + | 0.935327i | \(0.615105\pi\) | |||||||
\(824\) | 158119. | 0.232879 | ||||||||
\(825\) | 47325.6i | 0.0695325i | ||||||||
\(826\) | 73049.1 | 0.107067 | ||||||||
\(827\) | −228320. | + | 228320.i | −0.333836 | + | 0.333836i | −0.854041 | − | 0.520206i | \(-0.825855\pi\) |
0.520206 | + | 0.854041i | \(0.325855\pi\) | |||||||
\(828\) | 236890. | + | 236890.i | 0.345530 | + | 0.345530i | ||||
\(829\) | −604556. | − | 604556.i | −0.879685 | − | 0.879685i | 0.113817 | − | 0.993502i | \(-0.463692\pi\) |
−0.993502 | + | 0.113817i | \(0.963692\pi\) | |||||||
\(830\) | 1.27349e6 | 1.84858 | ||||||||
\(831\) | 306870. | − | 306870.i | 0.444378 | − | 0.444378i | ||||
\(832\) | 79627.9 | + | 79627.9i | 0.115032 | + | 0.115032i | ||||
\(833\) | −38754.0 | + | 38754.0i | −0.0558504 | + | 0.0558504i | ||||
\(834\) | −11180.6 | − | 11180.6i | −0.0160744 | − | 0.0160744i | ||||
\(835\) | 610797.i | 0.876040i | ||||||||
\(836\) | 12997.3 | − | 12997.3i | 0.0185969 | − | 0.0185969i | ||||
\(837\) | −698507. | + | 698507.i | −0.997057 | + | 0.997057i | ||||
\(838\) | −661438. | − | 661438.i | −0.941892 | − | 0.941892i | ||||
\(839\) | 26038.6i | 0.0369909i | 0.999829 | + | 0.0184954i | \(0.00588761\pi\) | ||||
−0.999829 | + | 0.0184954i | \(0.994112\pi\) | |||||||
\(840\) | −219453. | −0.311016 | ||||||||
\(841\) | − | 82682.5i | − | 0.116902i | ||||||
\(842\) | 282062.i | 0.397851i | ||||||||
\(843\) | 477705. | + | 477705.i | 0.672210 | + | 0.672210i | ||||
\(844\) | − | 116112.i | − | 0.163002i | ||||||
\(845\) | −690143. | − | 690143.i | −0.966553 | − | 0.966553i | ||||
\(846\) | −287519. | − | 287519.i | −0.401723 | − | 0.401723i | ||||
\(847\) | 484908. | 0.675915 | ||||||||
\(848\) | 64763.9 | 0.0900620 | ||||||||
\(849\) | 285115. | − | 285115.i | 0.395553 | − | 0.395553i | ||||
\(850\) | − | 214618.i | − | 0.297050i | ||||||
\(851\) | −59102.3 | + | 1.25159e6i | −0.0816103 | + | 1.72823i | ||||
\(852\) | 145755. | 0.200791 | ||||||||
\(853\) | 32147.4 | + | 32147.4i | 0.0441822 | + | 0.0441822i | 0.728853 | − | 0.684671i | \(-0.240054\pi\) |
−0.684671 | + | 0.728853i | \(0.740054\pi\) | |||||||
\(854\) | − | 155789.i | − | 0.213610i | ||||||
\(855\) | 1.17020e6i | 1.60077i | ||||||||
\(856\) | −67379.0 | + | 67379.0i | −0.0919554 | + | 0.0919554i | ||||
\(857\) | −810803. | + | 810803.i | −1.10396 | + | 1.10396i | −0.110033 | + | 0.993928i | \(0.535096\pi\) |
−0.993928 | + | 0.110033i | \(0.964904\pi\) | |||||||
\(858\) | 16343.2 | 0.0222005 | ||||||||
\(859\) | −543016. | + | 543016.i | −0.735913 | + | 0.735913i | −0.971784 | − | 0.235871i | \(-0.924206\pi\) |
0.235871 | + | 0.971784i | \(0.424206\pi\) | |||||||
\(860\) | −124290. | −0.168050 | ||||||||
\(861\) | 392656. | 0.529671 | ||||||||
\(862\) | 381171.i | 0.512986i | ||||||||
\(863\) | −827038. | −1.11046 | −0.555231 | − | 0.831696i | \(-0.687370\pi\) | ||||
−0.555231 | + | 0.831696i | \(0.687370\pi\) | |||||||
\(864\) | 96322.2 | − | 96322.2i | 0.129032 | − | 0.129032i | ||||
\(865\) | 845631. | + | 845631.i | 1.13018 | + | 1.13018i | ||||
\(866\) | −284661. | − | 284661.i | −0.379571 | − | 0.379571i | ||||
\(867\) | −485316. | −0.645635 | ||||||||
\(868\) | −246272. | + | 246272.i | −0.326870 | + | 0.326870i | ||||
\(869\) | −9308.10 | − | 9308.10i | −0.0123260 | − | 0.0123260i | ||||
\(870\) | 462240. | − | 462240.i | 0.610701 | − | 0.610701i | ||||
\(871\) | 360675. | + | 360675.i | 0.475423 | + | 0.475423i | ||||
\(872\) | − | 385833.i | − | 0.507418i | ||||||
\(873\) | 300492. | − | 300492.i | 0.394279 | − | 0.394279i | ||||
\(874\) | −950431. | + | 950431.i | −1.24422 | + | 1.24422i | ||||
\(875\) | −1.35893e6 | − | 1.35893e6i | −1.77493 | − | 1.77493i | ||||
\(876\) | 534.773i | 0.000696885i | ||||||||
\(877\) | −692104. | −0.899855 | −0.449927 | − | 0.893065i | \(-0.648550\pi\) | ||||
−0.449927 | + | 0.893065i | \(0.648550\pi\) | |||||||
\(878\) | − | 581930.i | − | 0.754886i | ||||||
\(879\) | 624931.i | 0.808824i | ||||||||
\(880\) | −9864.51 | − | 9864.51i | −0.0127383 | − | 0.0127383i | ||||
\(881\) | 441890.i | 0.569327i | 0.958627 | + | 0.284664i | \(0.0918819\pi\) | ||||
−0.958627 | + | 0.284664i | \(0.908118\pi\) | |||||||
\(882\) | −119064. | − | 119064.i | −0.153054 | − | 0.153054i | ||||
\(883\) | −978493. | − | 978493.i | −1.25498 | − | 1.25498i | −0.953461 | − | 0.301517i | \(-0.902507\pi\) |
−0.301517 | − | 0.953461i | \(-0.597493\pi\) | |||||||
\(884\) | −74115.5 | −0.0948428 | ||||||||
\(885\) | 227739. | 0.290771 | ||||||||
\(886\) | −448562. | + | 448562.i | −0.571420 | + | 0.571420i | ||||
\(887\) | 154949.i | 0.196943i | 0.995140 | + | 0.0984717i | \(0.0313954\pi\) | ||||
−0.995140 | + | 0.0984717i | \(0.968605\pi\) | |||||||
\(888\) | 183700. | + | 8674.65i | 0.232961 | + | 0.0110008i | ||||
\(889\) | −133803. | −0.169302 | ||||||||
\(890\) | 296227. | + | 296227.i | 0.373977 | + | 0.373977i | ||||
\(891\) | − | 3369.69i | − | 0.00424458i | ||||||
\(892\) | 311753.i | 0.391815i | ||||||||
\(893\) | 1.15356e6 | − | 1.15356e6i | 1.44657 | − | 1.44657i | ||||
\(894\) | 44886.1 | − | 44886.1i | 0.0561612 | − | 0.0561612i | ||||
\(895\) | 2.98065e6 | 3.72105 | ||||||||
\(896\) | 33960.1 | − | 33960.1i | 0.0423013 | − | 0.0423013i | ||||
\(897\) | −1.19511e6 | −1.48533 | ||||||||
\(898\) | −64014.2 | −0.0793823 | ||||||||
\(899\) | − | 1.03746e6i | − | 1.28366i | ||||||
\(900\) | 659375. | 0.814044 | ||||||||
\(901\) | −30140.3 | + | 30140.3i | −0.0371276 | + | 0.0371276i | ||||
\(902\) | 17650.1 | + | 17650.1i | 0.0216937 | + | 0.0216937i | ||||
\(903\) | −43910.8 | − | 43910.8i | −0.0538513 | − | 0.0538513i | ||||
\(904\) | 426149. | 0.521464 | ||||||||
\(905\) | 2.18969e6 | − | 2.18969e6i | 2.67353 | − | 2.67353i | ||||
\(906\) | −59881.7 | − | 59881.7i | −0.0729521 | − | 0.0729521i | ||||
\(907\) | 72503.8 | − | 72503.8i | 0.0881345 | − | 0.0881345i | −0.661665 | − | 0.749800i | \(-0.730150\pi\) |
0.749800 | + | 0.661665i | \(0.230150\pi\) | |||||||
\(908\) | −12264.9 | − | 12264.9i | −0.0148762 | − | 0.0148762i | ||||
\(909\) | 280373.i | 0.339319i | ||||||||
\(910\) | −718608. | + | 718608.i | −0.867780 | + | 0.867780i | ||||
\(911\) | 385446. | − | 385446.i | 0.464437 | − | 0.464437i | −0.435670 | − | 0.900107i | \(-0.643488\pi\) |
0.900107 | + | 0.435670i | \(0.143488\pi\) | |||||||
\(912\) | 139498. | + | 139498.i | 0.167718 | + | 0.167718i | ||||
\(913\) | 40447.9i | 0.0485238i | ||||||||
\(914\) | −183144. | −0.219230 | ||||||||
\(915\) | − | 485691.i | − | 0.580120i | ||||||
\(916\) | − | 150616.i | − | 0.179507i | ||||||
\(917\) | 500814. | + | 500814.i | 0.595577 | + | 0.595577i | ||||
\(918\) | 89654.1i | 0.106386i | ||||||||
\(919\) | −875288. | − | 875288.i | −1.03638 | − | 1.03638i | −0.999313 | − | 0.0370691i | \(-0.988198\pi\) |
−0.0370691 | − | 0.999313i | \(-0.511802\pi\) | |||||||
\(920\) | 721347. | + | 721347.i | 0.852253 | + | 0.852253i | ||||
\(921\) | −1.04333e6 | −1.22999 | ||||||||
\(922\) | −230638. | −0.271312 | ||||||||
\(923\) | 477281. | − | 477281.i | 0.560235 | − | 0.560235i | ||||
\(924\) | − | 6970.16i | − | 0.00816392i | ||||||
\(925\) | 1.65962e6 | + | 1.82413e6i | 1.93966 | + | 2.13193i | ||||
\(926\) | −213866. | −0.249413 | ||||||||
\(927\) | −226081. | − | 226081.i | −0.263090 | − | 0.263090i | ||||
\(928\) | 143062.i | 0.166123i | ||||||||
\(929\) | 808864.i | 0.937225i | 0.883404 | + | 0.468613i | \(0.155246\pi\) | ||||
−0.883404 | + | 0.468613i | \(0.844754\pi\) | |||||||
\(930\) | −767779. | + | 767779.i | −0.887709 | + | 0.887709i | ||||
\(931\) | 477701. | − | 477701.i | 0.551133 | − | 0.551133i | ||||
\(932\) | −739988. | −0.851909 | ||||||||
\(933\) | 133579. | − | 133579.i | 0.153453 | − | 0.153453i | ||||
\(934\) | 834666. | 0.956795 | ||||||||
\(935\) | 9181.62 | 0.0105026 | ||||||||
\(936\) | − | 227706.i | − | 0.259910i | ||||||
\(937\) | 1.37134e6 | 1.56195 | 0.780973 | − | 0.624564i | \(-0.214723\pi\) | ||||
0.780973 | + | 0.624564i | \(0.214723\pi\) | |||||||
\(938\) | 153823. | − | 153823.i | 0.174830 | − | 0.174830i | ||||
\(939\) | 160970. | + | 160970.i | 0.182563 | + | 0.182563i | ||||
\(940\) | −875517. | − | 875517.i | −0.990852 | − | 0.990852i | ||||
\(941\) | 843723. | 0.952841 | 0.476421 | − | 0.879218i | \(-0.341934\pi\) | ||||
0.476421 | + | 0.879218i | \(0.341934\pi\) | |||||||
\(942\) | −198334. | + | 198334.i | −0.223509 | + | 0.223509i | ||||
\(943\) | −1.29067e6 | − | 1.29067e6i | −1.45142 | − | 1.45142i | ||||
\(944\) | −35242.4 | + | 35242.4i | −0.0395477 | + | 0.0395477i | ||||
\(945\) | 869267. | + | 869267.i | 0.973396 | + | 0.973396i | ||||
\(946\) | − | 3947.62i | − | 0.00441117i | ||||||
\(947\) | 255718. | − | 255718.i | 0.285142 | − | 0.285142i | −0.550014 | − | 0.835156i | \(-0.685377\pi\) |
0.835156 | + | 0.550014i | \(0.185377\pi\) | |||||||
\(948\) | 99902.7 | − | 99902.7i | 0.111163 | − | 0.111163i | ||||
\(949\) | 1751.14 | + | 1751.14i | 0.00194441 | + | 0.00194441i | ||||
\(950\) | 2.64549e6i | 2.93129i | ||||||||
\(951\) | 490140. | 0.541950 | ||||||||
\(952\) | 31609.2i | 0.0348770i | ||||||||
\(953\) | − | 1.56696e6i | − | 1.72533i | −0.505772 | − | 0.862667i | \(-0.668792\pi\) | ||
0.505772 | − | 0.862667i | \(-0.331208\pi\) | |||||||
\(954\) | −92600.4 | − | 92600.4i | −0.101746 | − | 0.101746i | ||||
\(955\) | 857592.i | 0.940317i | ||||||||
\(956\) | 51462.6 | + | 51462.6i | 0.0563087 | + | 0.0563087i | ||||
\(957\) | 14681.4 | + | 14681.4i | 0.0160304 | + | 0.0160304i | ||||
\(958\) | 555959. | 0.605775 | ||||||||
\(959\) | −436824. | −0.474974 | ||||||||
\(960\) | 105875. | − | 105875.i | 0.114881 | − | 0.114881i | ||||
\(961\) | 799693.i | 0.865917i | ||||||||
\(962\) | 629939. | − | 573128.i | 0.680689 | − | 0.619301i | ||||
\(963\) | 192679. | 0.207770 | ||||||||
\(964\) | 646851. | + | 646851.i | 0.696065 | + | 0.696065i | ||||
\(965\) | 1.30490e6i | 1.40127i | ||||||||
\(966\) | 509696.i | 0.546206i | ||||||||
\(967\) | −427189. | + | 427189.i | −0.456843 | + | 0.456843i | −0.897618 | − | 0.440775i | \(-0.854704\pi\) |
0.440775 | + | 0.897618i | \(0.354704\pi\) | |||||||
\(968\) | −233943. | + | 233943.i | −0.249666 | + | 0.249666i | ||||
\(969\) | −129841. | −0.138282 | ||||||||
\(970\) | 915019. | − | 915019.i | 0.972494 | − | 0.972494i | ||||
\(971\) | 397728. | 0.421840 | 0.210920 | − | 0.977503i | \(-0.432354\pi\) | ||||
0.210920 | + | 0.977503i | \(0.432354\pi\) | |||||||
\(972\) | −451465. | −0.477850 | ||||||||
\(973\) | 31228.5i | 0.0329857i | ||||||||
\(974\) | −1.07264e6 | −1.13068 | ||||||||
\(975\) | −1.66327e6 | + | 1.66327e6i | −1.74966 | + | 1.74966i | ||||
\(976\) | 75160.3 | + | 75160.3i | 0.0789021 | + | 0.0789021i | ||||
\(977\) | 1.15077e6 | + | 1.15077e6i | 1.20559 | + | 1.20559i | 0.972441 | + | 0.233151i | \(0.0749035\pi\) |
0.233151 | + | 0.972441i | \(0.425097\pi\) | |||||||
\(978\) | 341441. | 0.356975 | ||||||||
\(979\) | −9408.62 | + | 9408.62i | −0.00981659 | + | 0.00981659i | ||||
\(980\) | −362560. | − | 362560.i | −0.377509 | − | 0.377509i | ||||
\(981\) | −551669. | + | 551669.i | −0.573246 | + | 0.573246i | ||||
\(982\) | 634510. | + | 634510.i | 0.657984 | + | 0.657984i | ||||
\(983\) | 305549.i | 0.316209i | 0.987422 | + | 0.158104i | \(0.0505383\pi\) | ||||
−0.987422 | + | 0.158104i | \(0.949462\pi\) | |||||||
\(984\) | −189436. | + | 189436.i | −0.195647 | + | 0.195647i | ||||
\(985\) | 757268. | − | 757268.i | 0.780508 | − | 0.780508i | ||||
\(986\) | −66579.3 | − | 66579.3i | −0.0684834 | − | 0.0684834i | ||||
\(987\) | − | 618631.i | − | 0.635034i | ||||||
\(988\) | 913585. | 0.935912 | ||||||||
\(989\) | 288672.i | 0.295129i | ||||||||
\(990\) | 28208.8i | 0.0287816i | ||||||||
\(991\) | 393816. | + | 393816.i | 0.401002 | + | 0.401002i | 0.878586 | − | 0.477584i | \(-0.158487\pi\) |
−0.477584 | + | 0.878586i | \(0.658487\pi\) | |||||||
\(992\) | − | 237626.i | − | 0.241474i | ||||||
\(993\) | 575568. | + | 575568.i | 0.583711 | + | 0.583711i | ||||
\(994\) | −203553. | − | 203553.i | −0.206018 | − | 0.206018i | ||||
\(995\) | −889589. | −0.898552 | ||||||||
\(996\) | −434122. | −0.437616 | ||||||||
\(997\) | −345716. | + | 345716.i | −0.347800 | + | 0.347800i | −0.859289 | − | 0.511490i | \(-0.829094\pi\) |
0.511490 | + | 0.859289i | \(0.329094\pi\) | |||||||
\(998\) | 1.03282e6i | 1.03696i | ||||||||
\(999\) | −693287. | − | 762009.i | −0.694676 | − | 0.763535i |
(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 | 74.5.d.b.31.5 | ✓ | 14 | |
37.6 | odd | 4 | inner | 74.5.d.b.43.3 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.5.d.b.31.5 | ✓ | 14 | 1.1 | even | 1 | trivial | |
74.5.d.b.43.3 | yes | 14 | 37.6 | odd | 4 | inner |