Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,6,Mod(45,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.45");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.e (of order \(3\), 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: | \(12.1891703058\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} - 1275481376 x^{11} + 361098181456 x^{10} + \cdots + 80\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{3}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 49.5 | ||
Root | \(2.80322 + 4.85531i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.49 |
Dual form | 76.6.e.a.45.5 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.30322 | + | 5.72134i | −0.211901 | + | 0.367024i | −0.952310 | − | 0.305133i | \(-0.901299\pi\) |
0.740408 | + | 0.672158i | \(0.234632\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.6095 | − | 21.8402i | 0.225565 | − | 0.390690i | −0.730924 | − | 0.682459i | \(-0.760911\pi\) |
0.956489 | + | 0.291769i | \(0.0942439\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −40.7176 | −0.314078 | −0.157039 | − | 0.987592i | \(-0.550195\pi\) | ||||
−0.157039 | + | 0.987592i | \(0.550195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 99.6775 | + | 172.647i | 0.410196 | + | 0.710479i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 324.832 | 0.809426 | 0.404713 | − | 0.914444i | \(-0.367371\pi\) | ||||
0.404713 | + | 0.914444i | \(0.367371\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −48.8600 | − | 84.6280i | −0.0801854 | − | 0.138885i | 0.823144 | − | 0.567833i | \(-0.192218\pi\) |
−0.903329 | + | 0.428947i | \(0.858885\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 83.3036 | + | 144.286i | 0.0955951 | + | 0.165575i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1057.36 | + | 1831.41i | −0.887365 | + | 1.53696i | −0.0443869 | + | 0.999014i | \(0.514133\pi\) |
−0.842978 | + | 0.537947i | \(0.819200\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 806.259 | + | 1351.31i | 0.512378 | + | 0.858760i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 134.499 | − | 232.959i | 0.0665536 | − | 0.115274i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1506.33 | + | 2609.05i | 0.593748 | + | 1.02840i | 0.993722 | + | 0.111875i | \(0.0356856\pi\) |
−0.399975 | + | 0.916526i | \(0.630981\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1244.50 | + | 2155.54i | 0.398241 | + | 0.689774i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2922.39 | −0.771487 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −527.733 | − | 914.060i | −0.116525 | − | 0.201827i | 0.801863 | − | 0.597507i | \(-0.203842\pi\) |
−0.918388 | + | 0.395680i | \(0.870509\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7602.00 | 1.42077 | 0.710385 | − | 0.703813i | \(-0.248521\pi\) | ||||
0.710385 | + | 0.703813i | \(0.248521\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1072.99 | + | 1858.48i | −0.171519 | + | 0.297079i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −513.427 | + | 889.282i | −0.0708449 | + | 0.122707i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2057.16 | −0.247037 | −0.123519 | − | 0.992342i | \(-0.539418\pi\) | ||||
−0.123519 | + | 0.992342i | \(0.539418\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 645.581 | 0.0679656 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 230.415 | − | 399.091i | 0.0214068 | − | 0.0370777i | −0.855124 | − | 0.518424i | \(-0.826519\pi\) |
0.876530 | + | 0.481347i | \(0.159852\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −188.582 | + | 326.633i | −0.0155535 | + | 0.0269395i | −0.873697 | − | 0.486470i | \(-0.838284\pi\) |
0.858144 | + | 0.513409i | \(0.171618\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5027.52 | 0.370103 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8354.76 | − | 14470.9i | −0.551682 | − | 0.955542i | −0.998153 | − | 0.0607440i | \(-0.980653\pi\) |
0.446471 | − | 0.894798i | \(-0.352681\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15149.1 | −0.901355 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6985.41 | − | 12099.1i | −0.376068 | − | 0.651369i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5234.06 | + | 9065.67i | 0.255947 | + | 0.443313i | 0.965152 | − | 0.261689i | \(-0.0842795\pi\) |
−0.709206 | + | 0.705002i | \(0.750946\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4095.96 | − | 7094.41i | 0.182578 | − | 0.316235i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10394.6 | + | 149.205i | −0.423759 | + | 0.00608268i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 23733.3 | − | 41107.2i | 0.887621 | − | 1.53740i | 0.0449408 | − | 0.998990i | \(-0.485690\pi\) |
0.842680 | − | 0.538415i | \(-0.180977\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13715.7 | − | 23756.3i | −0.471948 | − | 0.817438i | 0.527537 | − | 0.849532i | \(-0.323116\pi\) |
−0.999485 | + | 0.0320943i | \(0.989782\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4058.63 | − | 7029.76i | −0.128833 | − | 0.223146i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2464.39 | −0.0723480 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 17228.2 | + | 29840.0i | 0.468869 | + | 0.812105i | 0.999367 | − | 0.0355811i | \(-0.0113282\pi\) |
−0.530498 | + | 0.847686i | \(0.677995\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −19903.0 | −0.503264 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1879.84 | − | 3255.97i | 0.0442562 | − | 0.0766541i | −0.843049 | − | 0.537837i | \(-0.819242\pi\) |
0.887305 | + | 0.461183i | \(0.152575\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6145.42 | − | 10644.2i | 0.134972 | − | 0.233779i | −0.790615 | − | 0.612314i | \(-0.790239\pi\) |
0.925587 | + | 0.378535i | \(0.123572\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16443.5 | −0.337551 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13226.4 | −0.254223 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26717.1 | − | 46275.4i | 0.481639 | − | 0.834223i | −0.518139 | − | 0.855297i | \(-0.673375\pi\) |
0.999778 | + | 0.0210731i | \(0.00670827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −14568.3 | + | 25233.1i | −0.246716 | + | 0.427325i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1317.09 | −0.0209856 | −0.0104928 | − | 0.999945i | \(-0.503340\pi\) | ||||
−0.0104928 | + | 0.999945i | \(0.503340\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26665.6 | + | 46186.2i | 0.400317 | + | 0.693369i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6972.87 | 0.0987673 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 51736.4 | + | 89610.0i | 0.692342 | + | 1.19917i | 0.971068 | + | 0.238801i | \(0.0767545\pi\) |
−0.278726 | + | 0.960371i | \(0.589912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1989.46 | + | 3445.85i | 0.0251845 | + | 0.0436208i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −25111.1 | + | 43493.7i | −0.301063 | + | 0.521457i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 39679.5 | − | 569.563i | 0.451083 | − | 0.00647489i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52995.4 | + | 91790.7i | −0.571885 | + | 0.990533i | 0.424488 | + | 0.905434i | \(0.360454\pi\) |
−0.996372 | + | 0.0850998i | \(0.972879\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 32378.5 | + | 56081.1i | 0.332023 | + | 0.575081i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −34282.4 | − | 59378.8i | −0.334401 | − | 0.579200i | 0.648969 | − | 0.760815i | \(-0.275201\pi\) |
−0.983370 | + | 0.181616i | \(0.941867\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −35253.0 | −0.327419 | −0.163709 | − | 0.986509i | \(-0.552346\pi\) | ||||
−0.163709 | + | 0.986509i | \(0.552346\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3391.92 | − | 5874.98i | −0.0300243 | − | 0.0520036i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 126916. | 1.07166 | 0.535832 | − | 0.844325i | \(-0.319998\pi\) | ||||
0.535832 | + | 0.844325i | \(0.319998\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −107794. | + | 186705.i | −0.869019 | + | 1.50519i | −0.00601921 | + | 0.999982i | \(0.501916\pi\) |
−0.863000 | + | 0.505204i | \(0.831417\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6795.23 | − | 11769.7i | 0.0523476 | − | 0.0906687i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 25767.6 | 0.189835 | 0.0949177 | − | 0.995485i | \(-0.469741\pi\) | ||||
0.0949177 | + | 0.995485i | \(0.469741\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 75976.3 | 0.535714 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9740.49 | − | 16871.0i | 0.0657834 | − | 0.113940i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 43053.4 | − | 74570.6i | 0.278702 | − | 0.482726i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −55535.1 | −0.344829 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1522.22 | + | 2636.57i | 0.00907226 | + | 0.0157136i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 141579. | 0.810446 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −59314.9 | − | 102736.i | −0.326328 | − | 0.565216i | 0.655452 | − | 0.755237i | \(-0.272478\pi\) |
−0.981780 | + | 0.190020i | \(0.939145\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1245.85 | − | 2157.88i | −0.00659163 | − | 0.0114170i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −27739.5 | + | 48046.2i | −0.141228 | + | 0.244614i | −0.927959 | − | 0.372682i | \(-0.878438\pi\) |
0.786731 | + | 0.617295i | \(0.211772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −32829.0 | − | 55022.2i | −0.160927 | − | 0.269717i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −36849.7 | + | 63825.6i | −0.174020 | + | 0.301412i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −159895. | − | 276946.i | −0.727835 | − | 1.26065i | −0.957797 | − | 0.287447i | \(-0.907193\pi\) |
0.229962 | − | 0.973200i | \(-0.426140\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −105811. | − | 183269.i | −0.464506 | − | 0.804549i | 0.534673 | − | 0.845059i | \(-0.320435\pi\) |
−0.999179 | + | 0.0405104i | \(0.987102\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 110390. | 0.467609 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15871.3 | − | 27489.9i | −0.0649041 | − | 0.112417i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26617.7 | −0.105136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 50040.7 | − | 86673.0i | 0.190998 | − | 0.330819i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 36052.9 | − | 62445.4i | 0.133037 | − | 0.230428i | −0.791809 | − | 0.610769i | \(-0.790860\pi\) |
0.924846 | + | 0.380342i | \(0.124194\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 265545. | 0.947753 | 0.473877 | − | 0.880591i | \(-0.342854\pi\) | ||||
0.473877 | + | 0.880591i | \(0.342854\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −421582. | −1.45597 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 95857.2 | − | 166029.i | 0.320476 | − | 0.555080i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −159838. | + | 276848.i | −0.517526 | + | 0.896381i | 0.482267 | + | 0.876024i | \(0.339814\pi\) |
−0.999793 | + | 0.0203568i | \(0.993520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −69157.0 | −0.216942 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −61334.4 | − | 106234.i | −0.186483 | − | 0.322998i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −202591. | −0.597244 | −0.298622 | − | 0.954371i | \(-0.596527\pi\) | ||||
−0.298622 | + | 0.954371i | \(0.596527\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 27059.7 | + | 46868.7i | 0.0773771 | + | 0.134021i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −151820. | − | 262959.i | −0.421247 | − | 0.729621i | 0.574815 | − | 0.818284i | \(-0.305074\pi\) |
−0.996062 | + | 0.0886623i | \(0.971741\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 180872. | − | 313279.i | 0.487141 | − | 0.843752i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −152933. | + | 273893.i | −0.399956 | + | 0.716294i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 328662. | − | 569260.i | 0.834900 | − | 1.44609i | −0.0592118 | − | 0.998245i | \(-0.518859\pi\) |
0.894112 | − | 0.447844i | \(-0.147808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −50673.2 | − | 87768.6i | −0.125079 | − | 0.216643i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 156792. | + | 271572.i | 0.376176 | + | 0.651557i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 265873. | 0.620215 | 0.310108 | − | 0.950701i | \(-0.399635\pi\) | ||||
0.310108 | + | 0.950701i | \(0.399635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 75575.2 | + | 130900.i | 0.171468 | + | 0.296991i | 0.938933 | − | 0.344099i | \(-0.111816\pi\) |
−0.767465 | + | 0.641090i | \(0.778482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 181224. | 0.400026 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −25939.6 | + | 44928.7i | −0.0557230 | + | 0.0965150i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −343466. | + | 594901.i | −0.718257 | + | 1.24406i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 118993. | 0.242307 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −120491. | −0.238986 | −0.119493 | − | 0.992835i | \(-0.538127\pi\) | ||||
−0.119493 | + | 0.992835i | \(0.538127\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 38385.0 | − | 66484.8i | 0.0741769 | − | 0.128478i | −0.826551 | − | 0.562862i | \(-0.809700\pi\) |
0.900728 | + | 0.434384i | \(0.143034\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8140.43 | − | 14099.6i | 0.0153307 | − | 0.0265535i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 581905. | 1.06828 | 0.534141 | − | 0.845395i | \(-0.320635\pi\) | ||||
0.534141 | + | 0.845395i | \(0.320635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 83536.9 | + | 144690.i | 0.149536 | + | 0.259004i | 0.931056 | − | 0.364876i | \(-0.118889\pi\) |
−0.781520 | + | 0.623880i | \(0.785555\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −227633. | −0.397416 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21488.0 | + | 37218.4i | 0.0365979 | + | 0.0633895i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5810.82 | − | 10064.6i | −0.00965724 | − | 0.0167268i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −300295. | + | 520127.i | −0.487105 | + | 0.843691i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 261899. | + | 438950.i | 0.414732 | + | 0.695103i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −360222. | + | 623923.i | −0.557011 | + | 0.964772i | 0.440733 | + | 0.897638i | \(0.354719\pi\) |
−0.997744 | + | 0.0671336i | \(0.978615\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12419.0 | + | 21510.4i | 0.0187559 | + | 0.0324862i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4755.83 | + | 8237.33i | 0.00701665 | + | 0.0121532i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −309536. | −0.446233 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 40599.3 | + | 70320.1i | 0.0572016 | + | 0.0990761i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 206651. | 0.284615 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −676428. | + | 1.17161e6i | −0.910876 | + | 1.57768i | −0.0980458 | + | 0.995182i | \(0.531259\pi\) |
−0.812830 | + | 0.582501i | \(0.802074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −248098. | + | 429718.i | −0.326713 | + | 0.565884i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 944144. | 1.21611 | 0.608056 | − | 0.793894i | \(-0.291950\pi\) | ||||
0.608056 | + | 0.793894i | \(0.291950\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.23700e6 | 1.55877 | 0.779383 | − | 0.626547i | \(-0.215532\pi\) | ||||
0.779383 | + | 0.626547i | \(0.215532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 43689.6 | − | 75672.7i | 0.0538702 | − | 0.0933059i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 495767. | − | 858694.i | 0.598258 | − | 1.03621i | −0.394821 | − | 0.918758i | \(-0.629193\pi\) |
0.993078 | − | 0.117454i | \(-0.0374733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −421396. | −0.497761 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 176505. | + | 305715.i | 0.204120 | + | 0.353546i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −256516. | −0.290482 | −0.145241 | − | 0.989396i | \(-0.546396\pi\) | ||||
−0.145241 | + | 0.989396i | \(0.546396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −398215. | − | 689728.i | −0.441646 | − | 0.764954i | 0.556166 | − | 0.831072i | \(-0.312272\pi\) |
−0.997812 | + | 0.0661177i | \(0.978939\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −451315. | − | 781701.i | −0.490303 | − | 0.849229i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −191022. | + | 330859.i | −0.203314 | + | 0.352150i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 74965.1 | − | 134257.i | 0.0781838 | − | 0.140022i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4350.64 | − | 7535.53i | 0.00444687 | − | 0.00770221i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −292660. | − | 506902.i | −0.293210 | − | 0.507855i | 0.681357 | − | 0.731951i | \(-0.261390\pi\) |
−0.974567 | + | 0.224097i | \(0.928057\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 489306. | + | 847503.i | 0.480595 | + | 0.832415i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −352329. | −0.339311 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −436841. | − | 756630.i | −0.412563 | − | 0.714580i | 0.582606 | − | 0.812754i | \(-0.302033\pi\) |
−0.995169 | + | 0.0981747i | \(0.968700\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 83762.5 | 0.0775890 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 105206. | − | 182222.i | 0.0955961 | − | 0.165577i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 146951. | − | 254527.i | 0.131004 | − | 0.226905i | −0.793060 | − | 0.609144i | \(-0.791513\pi\) |
0.924064 | + | 0.382238i | \(0.124847\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 263995. | 0.230930 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −683586. | −0.586833 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.16327e6 | − | 2.01484e6i | 0.980163 | − | 1.69769i | 0.318440 | − | 0.947943i | \(-0.396841\pi\) |
0.661722 | − | 0.749749i | \(-0.269826\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 130705. | − | 226387.i | 0.108111 | − | 0.187253i | −0.806894 | − | 0.590696i | \(-0.798853\pi\) |
0.915005 | + | 0.403443i | \(0.132187\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26286.5 | −0.0213465 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 404255. | + | 700189.i | 0.322347 | + | 0.558321i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.76335e6 | −1.38083 | −0.690415 | − | 0.723414i | \(-0.742572\pi\) | ||||
−0.690415 | + | 0.723414i | \(0.742572\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 757749. | + | 1.31246e6i | 0.582794 | + | 1.00943i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −477850. | − | 827661.i | −0.361016 | − | 0.625297i | 0.627113 | − | 0.778929i | \(-0.284237\pi\) |
−0.988128 | + | 0.153631i | \(0.950903\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 172840. | − | 299368.i | 0.128286 | − | 0.222197i | −0.794727 | − | 0.606967i | \(-0.792386\pi\) |
0.923013 | + | 0.384770i | \(0.125719\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −127811. | + | 228901.i | −0.0932088 | + | 0.166930i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9381.96 | + | 16250.0i | −0.00672340 | + | 0.0116453i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.52611e6 | − | 2.64330e6i | −1.07483 | − | 1.86167i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −350110. | − | 606409.i | −0.242366 | − | 0.419791i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.17269e6 | 0.798023 | 0.399011 | − | 0.916946i | \(-0.369353\pi\) | ||||
0.399011 | + | 0.916946i | \(0.369353\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −598527. | − | 1.03668e6i | −0.400432 | − | 0.693569i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −949286. | −0.624462 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 147199. | − | 254956.i | 0.0952198 | − | 0.164925i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7678.60 | − | 13299.7i | 0.00488501 | − | 0.00846109i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 452969. | 0.283440 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −691791. | −0.425819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −160062. | + | 277235.i | −0.0969264 | + | 0.167881i | −0.910411 | − | 0.413705i | \(-0.864234\pi\) |
0.813485 | + | 0.581586i | \(0.197568\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 116448. | − | 201695.i | 0.0693805 | − | 0.120171i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.45223e6 | 0.851400 | 0.425700 | − | 0.904864i | \(-0.360028\pi\) | ||||
0.425700 | + | 0.904864i | \(0.360028\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 965219. | + | 1.67181e6i | 0.556884 | + | 0.964552i | 0.997754 | + | 0.0669807i | \(0.0213366\pi\) |
−0.440870 | + | 0.897571i | \(0.645330\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −204709. | −0.116241 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 757768. | + | 1.31249e6i | 0.423534 | + | 0.733582i | 0.996282 | − | 0.0861494i | \(-0.0274562\pi\) |
−0.572749 | + | 0.819731i | \(0.694123\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −171425. | − | 296916.i | −0.0943184 | − | 0.163364i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −419233. | + | 726132.i | −0.227087 | + | 0.393326i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.32732e6 | + | 47760.6i | −1.77455 | + | 0.0254720i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 121613. | − | 210640.i | 0.0638662 | − | 0.110620i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −712136. | − | 1.23346e6i | −0.368293 | − | 0.637902i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 340186. | + | 589219.i | 0.173271 | + | 0.300115i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.41462e6 | 1.71306 | 0.856531 | − | 0.516096i | \(-0.172615\pi\) | ||||
0.856531 | + | 0.516096i | \(0.172615\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −205052. | − | 355161.i | −0.101334 | − | 0.175515i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 868951. | 0.423042 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.59676e6 | + | 2.76567e6i | −0.765888 | + | 1.32656i | 0.173889 | + | 0.984765i | \(0.444367\pi\) |
−0.939776 | + | 0.341791i | \(0.888967\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −85115.9 | + | 147425.i | −0.0402264 | + | 0.0696742i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.46938e6 | 1.15001 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.30118e6 | 0.597174 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −250966. | + | 434686.i | −0.113519 | + | 0.196620i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 405681. | − | 702659.i | 0.180868 | − | 0.313272i | −0.761309 | − | 0.648390i | \(-0.775443\pi\) |
0.942176 | + | 0.335118i | \(0.108776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −491593. | −0.216044 | −0.108022 | − | 0.994148i | \(-0.534452\pi\) | ||||
−0.108022 | + | 0.994148i | \(0.534452\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 142788. | + | 247316.i | 0.0618620 | + | 0.107148i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.82830e6 | −0.780929 | −0.390465 | − | 0.920618i | \(-0.627686\pi\) | ||||
−0.390465 | + | 0.920618i | \(0.627686\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −47407.5 | − | 82112.2i | −0.0199653 | − | 0.0345809i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 284429. | + | 492646.i | 0.118115 | + | 0.204581i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.35760e6 | + | 2.35143e6i | −0.555950 | + | 0.962934i | 0.441879 | + | 0.897075i | \(0.354312\pi\) |
−0.997829 | + | 0.0658593i | \(0.979021\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.17599e6 | + | 2.17902e6i | −0.474937 | + | 0.880020i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 183444. | − | 317735.i | 0.0730698 | − | 0.126561i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −154981. | − | 268435.i | −0.0608900 | − | 0.105465i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.32754e6 | + | 2.29937e6i | 0.514498 | + | 0.891136i | 0.999858 | + | 0.0168222i | \(0.00535492\pi\) |
−0.485361 | + | 0.874314i | \(0.661312\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 91868.9 | 0.0351239 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −213119. | − | 369132.i | −0.0803872 | − | 0.139235i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.33938e6 | 1.61494 | 0.807468 | − | 0.589911i | \(-0.200837\pi\) | ||||
0.807468 | + | 0.589911i | \(0.200837\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −467667. | + | 810023.i | −0.171735 | + | 0.297453i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −51570.1 | + | 89322.0i | −0.0186872 | + | 0.0323672i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.27824e6 | 1.17231 | 0.586155 | − | 0.810199i | \(-0.300641\pi\) | ||||
0.586155 | + | 0.810199i | \(0.300641\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 783719. | 0.276597 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.41742e6 | − | 2.45505e6i | 0.493745 | − | 0.855191i | −0.506229 | − | 0.862399i | \(-0.668961\pi\) |
0.999974 | + | 0.00720770i | \(0.00229430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −166778. | + | 288867.i | −0.0573437 | + | 0.0993223i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −75189.4 | −0.0255199 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.39366e6 | + | 2.41389e6i | 0.466963 | + | 0.808804i | 0.999288 | − | 0.0377363i | \(-0.0120147\pi\) |
−0.532324 | + | 0.846540i | \(0.678681\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.37098e6 | −2.10748 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −183259. | − | 317414.i | −0.0598528 | − | 0.103668i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −673777. | − | 1.16702e6i | −0.217282 | − | 0.376343i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.84860e6 | + | 3.20187e6i | −0.588663 | + | 1.01959i | 0.405745 | + | 0.913986i | \(0.367012\pi\) |
−0.994408 | + | 0.105607i | \(0.966321\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 423242. | − | 6075.26i | 0.133093 | − | 0.00191044i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.13618e6 | + | 3.69998e6i | −0.663404 | + | 1.14905i | 0.316312 | + | 0.948655i | \(0.397555\pi\) |
−0.979715 | + | 0.200394i | \(0.935778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −371434. | − | 643343.i | −0.113925 | − | 0.197324i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 367398. | + | 636352.i | 0.111301 | + | 0.192779i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −668230. | −0.199959 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.89320e6 | − | 5.01117e6i | −0.855205 | − | 1.48126i | −0.876454 | − | 0.481485i | \(-0.840098\pi\) |
0.0212492 | − | 0.999774i | \(-0.493236\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.11267e6 | 0.616917 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −966362. | + | 1.67379e6i | −0.278782 | + | 0.482865i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16607.8 | + | 28765.6i | −0.00473361 | + | 0.00819885i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.39806e6 | 0.393718 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.36575e6 | 0.936585 | 0.468293 | − | 0.883573i | \(-0.344869\pi\) | ||||
0.468293 | + | 0.883573i | \(0.344869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.36298e6 | − | 4.09279e6i | 0.649761 | − | 1.12542i | −0.333418 | − | 0.942779i | \(-0.608202\pi\) |
0.983180 | − | 0.182641i | \(-0.0584646\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.66556e6 | − | 2.88484e6i | 0.452595 | − | 0.783918i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.26357e6 | −1.41354 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 558472. | + | 967301.i | 0.148228 | + | 0.256739i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 209705. | 0.0550131 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 212460. | + | 367991.i | 0.0550914 | + | 0.0954211i | 0.892256 | − | 0.451530i | \(-0.149122\pi\) |
−0.837164 | + | 0.546951i | \(0.815788\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.10444e6 | − | 5.37705e6i | −0.795726 | − | 1.37824i | −0.922377 | − | 0.386291i | \(-0.873756\pi\) |
0.126651 | − | 0.991947i | \(-0.459577\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 87924.1 | − | 152289.i | 0.0222784 | − | 0.0385874i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.31114e6 | + | 4.13910e6i | −0.578926 | + | 1.03682i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.48593e6 | − | 6.03781e6i | 0.863291 | − | 1.49526i | −0.00544290 | − | 0.999985i | \(-0.501733\pi\) |
0.868734 | − | 0.495279i | \(-0.164934\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.51002e6 | − | 2.61543e6i | −0.369732 | − | 0.640394i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.32950e6 | − | 2.30277e6i | −0.321870 | − | 0.557495i | 0.659004 | − | 0.752139i | \(-0.270978\pi\) |
−0.980874 | + | 0.194645i | \(0.937645\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.60947e6 | 0.624672 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 238181. | + | 412541.i | 0.0563817 | + | 0.0976559i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −636809. | −0.149071 | −0.0745355 | − | 0.997218i | \(-0.523747\pi\) | ||||
−0.0745355 | + | 0.997218i | \(0.523747\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 74846.3 | − | 129638.i | 0.0173272 | − | 0.0300116i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −877152. | + | 1.51927e6i | −0.200830 | + | 0.347848i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 100344. | 0.0227229 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.62218e6 | −0.363337 | −0.181668 | − | 0.983360i | \(-0.558150\pi\) | ||||
−0.181668 | + | 0.983360i | \(0.558150\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.09003e6 | − | 5.35209e6i | 0.684591 | − | 1.18575i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.88236e6 | − | 3.26034e6i | 0.412525 | − | 0.714514i | −0.582640 | − | 0.812730i | \(-0.697980\pi\) |
0.995165 | + | 0.0982159i | \(0.0313136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.56420e6 | 1.85667 | 0.928334 | − | 0.371748i | \(-0.121241\pi\) | ||||
0.928334 | + | 0.371748i | \(0.121241\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 633274. | + | 1.09686e6i | 0.135819 | + | 0.235245i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.68072e6 | −1.84189 | −0.920944 | − | 0.389694i | \(-0.872581\pi\) | ||||
−0.920944 | + | 0.389694i | \(0.872581\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −701489. | − | 1.21502e6i | −0.147261 | − | 0.255064i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.05596e6 | − | 1.82898e6i | −0.219329 | − | 0.379889i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −61257.4 | + | 106101.i | −0.0125894 | + | 0.0218055i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.90942e6 | + | 3.41964e6i | −0.388300 | + | 0.695418i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.04344e6 | + | 1.80729e6i | −0.209976 | + | 0.363690i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.82656e6 | − | 8.35985e6i | −0.961167 | − | 1.66479i | −0.719578 | − | 0.694412i | \(-0.755665\pi\) |
−0.241589 | − | 0.970379i | \(-0.577669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 100513. | + | 174093.i | 0.0198088 | + | 0.0343098i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 810403. | 0.158064 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.33649e6 | + | 2.31486e6i | 0.257994 | + | 0.446859i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.07551e6 | −0.587617 | −0.293809 | − | 0.955864i | \(-0.594923\pi\) | ||||
−0.293809 | + | 0.955864i | \(0.594923\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 669203. | − | 1.15909e6i | 0.126557 | − | 0.219203i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.46681e6 | + | 6.00470e6i | −0.648973 | + | 1.12405i | 0.334395 | + | 0.942433i | \(0.391468\pi\) |
−0.983368 | + | 0.181622i | \(0.941865\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.23202e6 | 0.413601 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.63310e6 | 0.299571 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −76542.5 | + | 132576.i | −0.0138999 | + | 0.0240753i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 272382. | − | 471779.i | 0.0489696 | − | 0.0848178i | −0.840502 | − | 0.541809i | \(-0.817740\pi\) |
0.889471 | + | 0.456991i | \(0.151073\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.00597e6 | 0.357052 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.01810e6 | + | 5.22751e6i | 0.531880 | + | 0.921244i | 0.999307 | + | 0.0372121i | \(0.0118477\pi\) |
−0.467427 | + | 0.884032i | \(0.654819\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.72913e6 | −0.301716 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.19492e6 | + | 2.06966e6i | 0.206452 | + | 0.357585i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 292272. | + | 506231.i | 0.0500027 | + | 0.0866072i | 0.889943 | − | 0.456071i | \(-0.150744\pi\) |
−0.839941 | + | 0.542678i | \(0.817410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −250227. | + | 433406.i | −0.0423918 | + | 0.0734247i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.35620e6 | − | 3.94906e6i | −0.395293 | − | 0.662522i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −444522. | + | 769934.i | −0.0738542 | + | 0.127919i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.71389e6 | − | 4.70060e6i | −0.446546 | − | 0.773441i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.17129e6 | + | 3.76078e6i | 0.353833 | + | 0.612857i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.06982e6 | 0.818272 | 0.409136 | − | 0.912473i | \(-0.365830\pi\) | ||||
0.409136 | + | 0.912473i | \(0.365830\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.09028e6 | + | 3.62047e6i | 0.334157 | + | 0.578777i | 0.983323 | − | 0.181870i | \(-0.0582151\pi\) |
−0.649166 | + | 0.760647i | \(0.724882\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 669539. | 0.106017 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.03809e6 | + | 1.39224e7i | −1.26074 | + | 2.18367i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.31992e6 | + | 2.28617e6i | −0.205073 | + | 0.355196i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.46269e6 | 1.45639 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −45032.4 | −0.00686605 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.60035e6 | − | 2.77188e6i | 0.241730 | − | 0.418688i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −878238. | + | 1.52115e6i | −0.131425 | + | 0.227634i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.92091e6 | −0.729580 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.36120e6 | + | 4.08971e6i | 0.346848 | + | 0.600758i | 0.985688 | − | 0.168582i | \(-0.0539187\pi\) |
−0.638840 | + | 0.769340i | \(0.720585\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −998565. | −0.145337 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.71845e6 | + | 4.70850e6i | 0.392040 | + | 0.679034i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.59488e6 | − | 4.49447e6i | −0.370808 | − | 0.642259i | 0.618882 | − | 0.785484i | \(-0.287586\pi\) |
−0.989690 | + | 0.143225i | \(0.954253\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.73430e6 | − | 4.73594e6i | 0.387182 | − | 0.670619i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 809691. | − | 1.45010e6i | 0.113616 | − | 0.203479i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.08786e6 | + | 1.88422e6i | −0.151272 | + | 0.262011i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −171368. | − | 296819.i | −0.0236156 | − | 0.0409033i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.55878e6 | + | 6.16399e6i | 0.486030 | + | 0.841829i | 0.999871 | − | 0.0160563i | \(-0.00511109\pi\) |
−0.513841 | + | 0.857886i | \(0.671778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36856.4 | 0.00498866 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.26909e6 | − | 3.93017e6i | −0.304399 | − | 0.527235i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.55995e6 | 0.872227 | 0.436114 | − | 0.899892i | \(-0.356355\pi\) | ||||
0.436114 | + | 0.899892i | \(0.356355\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 324915. | − | 562769.i | 0.0428202 | − | 0.0741668i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 593188. | − | 1.02743e6i | 0.0774881 | − | 0.134213i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.10777e7 | 1.43440 | 0.717200 | − | 0.696868i | \(-0.245424\pi\) | ||||
0.717200 | + | 0.696868i | \(0.245424\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.64684e6 | −0.724795 | −0.362398 | − | 0.932024i | \(-0.618042\pi\) | ||||
−0.362398 | + | 0.932024i | \(0.618042\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 398009. | − | 689372.i | 0.0506415 | − | 0.0877136i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.74928e6 | + | 6.49394e6i | −0.472909 | + | 0.819103i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.99850e6 | 0.374942 | 0.187471 | − | 0.982270i | \(-0.439971\pi\) | ||||
0.187471 | + | 0.982270i | \(0.439971\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 253588. | + | 439227.i | 0.0314364 | + | 0.0544494i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 53628.9 | 0.00659110 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.70019e6 | + | 2.94482e6i | 0.207170 | + | 0.358829i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −245645. | − | 425469.i | −0.0296768 | − | 0.0514018i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.21676e6 | + | 1.24998e7i | −0.864465 | + | 1.49730i | 0.00311341 | + | 0.999995i | \(0.499009\pi\) |
−0.867578 | + | 0.497301i | \(0.834324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.12919e6 | + | 1.02727e7i | 0.727972 | + | 1.22010i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.92216e6 | + | 3.32927e6i | −0.226371 | + | 0.392086i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.75784e6 | − | 6.50878e6i | −0.438836 | − | 0.760086i | 0.558764 | − | 0.829327i | \(-0.311276\pi\) |
−0.997600 | + | 0.0692407i | \(0.977942\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.08576e6 | − | 1.88059e6i | −0.125731 | − | 0.217772i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.10376e6 | −0.126748 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.09527e6 | − | 1.40214e7i | −0.921858 | − | 1.59671i | −0.796538 | − | 0.604589i | \(-0.793337\pi\) |
−0.125321 | − | 0.992116i | \(-0.539996\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.99094e6 | 0.224839 | 0.112419 | − | 0.993661i | \(-0.464140\pi\) | ||||
0.112419 | + | 0.993661i | \(0.464140\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.43452e6 | + | 5.94876e6i | −0.384656 | + | 0.666244i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −700267. | + | 1.21290e6i | −0.0777814 | + | 0.134721i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.47599e6 | 0.162596 | 0.0812982 | − | 0.996690i | \(-0.474093\pi\) | ||||
0.0812982 | + | 0.996690i | \(0.474093\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −283919. | −0.0310206 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −816427. | + | 1.41409e6i | −0.0884737 | + | 0.153241i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.12920e6 | − | 1.06161e7i | 0.658798 | − | 1.14107i | −0.322129 | − | 0.946696i | \(-0.604398\pi\) |
0.980927 | − | 0.194376i | \(-0.0622683\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 76777.6 | 0.00818553 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.89936e6 | − | 6.75389e6i | −0.412364 | − | 0.714235i | 0.582784 | − | 0.812627i | \(-0.301963\pi\) |
−0.995148 | + | 0.0983924i | \(0.968630\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.39100e6 | 0.880212 | 0.440106 | − | 0.897946i | \(-0.354941\pi\) | ||||
0.440106 | + | 0.897946i | \(0.354941\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.40210e6 | − | 7.62466e6i | −0.458069 | − | 0.793398i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.10658e6 | − | 3.64871e6i | −0.217449 | − | 0.376633i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.10384e6 | + | 3.64395e6i | −0.215433 | + | 0.373141i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.37649e6 | + | 48466.5i | −0.343002 | + | 0.00492348i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.17516e6 | − | 3.76749e6i | 0.219212 | − | 0.379687i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 725688. | + | 1.25693e6i | 0.0725565 | + | 0.125672i | 0.900021 | − | 0.435846i | \(-0.143551\pi\) |
−0.827465 | + | 0.561518i | \(0.810218\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.37978e6 | − | 4.12191e6i | −0.236063 | − | 0.408873i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.99171e6 | −0.294432 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 740184. | + | 1.28204e6i | 0.0722755 | + | 0.125185i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 749510. | 0.0726148 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.20230e6 | + | 7.27859e6i | −0.403963 | + | 0.699684i | −0.994200 | − | 0.107545i | \(-0.965701\pi\) |
0.590237 | + | 0.807230i | \(0.299034\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.07760e6 | − | 3.59850e6i | 0.198168 | − | 0.343237i | −0.749766 | − | 0.661703i | \(-0.769834\pi\) |
0.947934 | + | 0.318465i | \(0.103167\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −62838.1 | −0.00594736 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.48842e6 | −0.515450 | −0.257725 | − | 0.966218i | \(-0.582973\pi\) | ||||
−0.257725 | + | 0.966218i | \(0.582973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.70933e6 | − | 1.33529e7i | 0.718464 | − | 1.24442i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.02246e6 | − | 1.77096e6i | 0.0945573 | − | 0.163778i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.39658e6 | 0.587036 | 0.293518 | − | 0.955954i | \(-0.405174\pi\) | ||||
0.293518 | + | 0.955954i | \(0.405174\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 699560. | + | 1.21167e6i | 0.0637120 | + | 0.110353i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.45024e6 | 0.221460 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 891088. | + | 1.54341e6i | 0.0799295 | + | 0.138442i | 0.903219 | − | 0.429179i | \(-0.141197\pi\) |
−0.823290 | + | 0.567621i | \(0.807864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.15028e6 | − | 1.41167e7i | −0.725553 | − | 1.25669i | −0.958746 | − | 0.284264i | \(-0.908251\pi\) |
0.233193 | − | 0.972430i | \(-0.425083\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −682614. | + | 1.18232e6i | −0.0603103 | + | 0.104461i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.61565e6 | + | 23191.2i | −0.141675 | + | 0.00203362i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.58988e6 | − | 2.75376e6i | 0.138373 | − | 0.239669i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.46877e6 | − | 7.74014e6i | −0.386032 | − | 0.668627i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.45531e6 | − | 7.71682e6i | −0.382007 | − | 0.661656i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.81795e6 | 0.324932 | 0.162466 | − | 0.986714i | \(-0.448055\pi\) | ||||
0.162466 | + | 0.986714i | \(0.448055\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.63692e6 | − | 6.29934e6i | −0.307238 | − | 0.532152i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.93449e6 | 0.162216 | 0.0811081 | − | 0.996705i | \(-0.474154\pi\) | ||||
0.0811081 | + | 0.996705i | \(0.474154\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.15785e6 | − | 3.73750e6i | 0.179616 | − | 0.311105i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.11871e6 | + | 5.40177e6i | −0.257696 | + | 0.446342i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 732465. | 0.0600808 | 0.0300404 | − | 0.999549i | \(-0.490436\pi\) | ||||
0.0300404 | + | 0.999549i | \(0.490436\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.06474e6 | −0.656696 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.08608e6 | + | 7.07730e6i | −0.330305 | + | 0.572105i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 511473. | − | 885897.i | 0.0410464 | − | 0.0710944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.91673e6 | −0.471397 | −0.235698 | − | 0.971826i | \(-0.575738\pi\) | ||||
−0.235698 | + | 0.971826i | \(0.575738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.31837e6 | − | 2.28349e6i | −0.104281 | − | 0.180620i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.33685e6 | −0.419105 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 487266. | + | 843969.i | 0.0379913 | + | 0.0658028i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.27525e6 | + | 5.67291e6i | 0.253543 | + | 0.439150i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.07558e6 | − | 1.39873e7i | 0.620696 | − | 1.07508i | −0.368661 | − | 0.929564i | \(-0.620184\pi\) |
0.989356 | − | 0.145513i | \(-0.0464831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.65860e6 | − | 2.77986e6i | −0.126577 | − | 0.212146i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.39196e6 | − | 2.41095e6i | 0.105476 | − | 0.182690i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.39590e6 | + | 2.41777e6i | 0.105028 | + | 0.181914i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.50009e6 | + | 6.06234e6i | 0.261495 | + | 0.452923i | 0.966640 | − | 0.256141i | \(-0.0824510\pi\) |
−0.705144 | + | 0.709064i | \(0.749118\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.06524e7 | 0.790265 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.14512e7 | + | 1.98340e7i | 0.843579 | + | 1.46112i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −800514. | −0.0585604 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 847328. | − | 1.46762e6i | 0.0615536 | − | 0.106614i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.55155e6 | − | 1.13476e7i | 0.472630 | − | 0.818620i | −0.526879 | − | 0.849940i | \(-0.676638\pi\) |
0.999509 | + | 0.0313203i | \(0.00997121\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.43542e6 | 0.102835 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.26156e6 | 0.374342 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.31353e6 | − | 2.27510e6i | 0.0928101 | − | 0.160752i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.15352e6 | + | 1.23903e7i | −0.501977 | + | 0.869449i | 0.498021 | + | 0.867165i | \(0.334060\pi\) |
−0.999997 | + | 0.00228403i | \(0.999273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.11705e6 | −0.0778490 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −398799. | − | 690741.i | −0.0276033 | − | 0.0478103i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.46017e7 | −1.69124 | −0.845620 | − | 0.533785i | \(-0.820769\pi\) | ||||
−0.845620 | + | 0.533785i | \(0.820769\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.26197e6 | − | 2.18580e6i | −0.0861651 | − | 0.149242i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.59626e6 | + | 9.69300e6i | 0.379515 | + | 0.657339i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.19096e6 | − | 5.52691e6i | 0.214937 | − | 0.372281i | −0.738316 | − | 0.674455i | \(-0.764379\pi\) |
0.953253 | + | 0.302173i | \(0.0977122\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 520506. | + | 872382.i | 0.0348241 | + | 0.0583661i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −401987. | + | 696262.i | −0.0267141 | + | 0.0462701i | −0.879073 | − | 0.476686i | \(-0.841838\pi\) |
0.852359 | + | 0.522957i | \(0.175171\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −909214. | − | 1.57480e6i | −0.0600172 | − | 0.103953i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −131284. | − | 227391.i | −0.00860819 | − | 0.0149098i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.16774e6 | −0.336586 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.22115e7 | + | 2.11510e7i | 0.790078 | + | 1.36846i | 0.925918 | + | 0.377725i | \(0.123294\pi\) |
−0.135839 | + | 0.990731i | \(0.543373\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.86688e6 | 0.248527 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.34837e6 | − | 5.79956e6i | 0.213780 | − | 0.370277i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.52156e7 | + | 2.63542e7i | −0.965050 | + | 1.67152i | −0.255570 | + | 0.966790i | \(0.582263\pi\) |
−0.709480 | + | 0.704726i | \(0.751070\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.46514e6 | −0.407355 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.72001e6 | 0.420638 | 0.210319 | − | 0.977633i | \(-0.432550\pi\) | ||||
0.210319 | + | 0.977633i | \(0.432550\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.38913e6 | − | 7.60219e6i | 0.272940 | − | 0.472745i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.31592e6 | + | 9.20744e6i | −0.328416 | + | 0.568834i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.63843e6 | −0.284697 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.61439e6 | + | 7.99236e6i | 0.281384 | + | 0.487371i | 0.971726 | − | 0.236112i | \(-0.0758734\pi\) |
−0.690342 | + | 0.723483i | \(0.742540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.77192e6 | 0.349691 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2207.17 | − | 3822.92i | −0.000132858 | − | 0.000230116i | 0.865959 | − | 0.500115i | \(-0.166709\pi\) |
−0.866092 | + | 0.499885i | \(0.833376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.46072e6 | + | 1.63864e7i | 0.565809 | + | 0.980010i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −276686. | + | 479234.i | −0.0164412 | + | 0.0284770i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 725071. | − | 10407.7i | 0.0428092 | − | 0.000614487i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 610632. | − | 1.05765e6i | 0.0358222 | − | 0.0620458i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.54224e6 | + | 2.67124e6i | 0.0898975 | + | 0.155707i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.03095e6 | + | 6.98181e6i | 0.233471 | + | 0.404384i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.44974e7 | −0.834360 | −0.417180 | − | 0.908824i | \(-0.636982\pi\) | ||||
−0.417180 | + | 0.908824i | \(0.636982\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 970823. | + | 1.68152e6i | 0.0555198 | + | 0.0961631i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.04919e6 | −0.0596231 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.34030e6 | + | 2.32147e6i | −0.0756867 | + | 0.131093i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −872032. | + | 1.51040e6i | −0.0489345 | + | 0.0847570i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.24082e7 | −0.691929 | −0.345964 | − | 0.938248i | \(-0.612448\pi\) | ||||
−0.345964 | + | 0.938248i | \(0.612448\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.53361e7 | 1.95818 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.03139e7 | + | 1.78642e7i | −0.567991 | + | 0.983790i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.99623e6 | − | 3.45757e6i | 0.109250 | − | 0.189227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.09357e6 | −0.168256 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.68504e6 | + | 1.33109e7i | 0.415396 | + | 0.719487i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.16700e7 | 1.16409 | 0.582047 | − | 0.813155i | \(-0.302252\pi\) | ||||
0.582047 | + | 0.813155i | \(0.302252\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.06018e6 | + | 3.56833e6i | 0.109990 | + | 0.190508i | 0.915766 | − | 0.401712i | \(-0.131585\pi\) |
−0.805776 | + | 0.592220i | \(0.798252\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 863493. | + | 1.49561e6i | 0.0458176 | + | 0.0793584i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.55457e6 | + | 4.42464e6i | −0.134717 | + | 0.233337i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −593429. | + | 8518.14i | −0.0311038 | + | 0.000446467i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −396610. | + | 686948.i | −0.0206611 | + | 0.0357861i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.20488e7 | + | 2.08691e7i | 0.623858 | + | 1.08055i | 0.988760 | + | 0.149509i | \(0.0477692\pi\) |
−0.364902 | + | 0.931046i | \(0.618898\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.56576e7 | − | 2.71197e7i | −0.805796 | − | 1.39568i | −0.915753 | − | 0.401743i | \(-0.868405\pi\) |
0.109957 | − | 0.993936i | \(-0.464929\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.34136e6 | −0.273223 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.78298e6 | − | 1.17485e7i | −0.344871 | − | 0.597334i | 0.640459 | − | 0.767992i | \(-0.278744\pi\) |
−0.985330 | + | 0.170658i | \(0.945411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.34177e7 | −1.18347 | −0.591737 | − | 0.806131i | \(-0.701557\pi\) | ||||
−0.591737 | + | 0.806131i | \(0.701557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.82474e6 | − | 1.00887e7i | 0.292600 | − | 0.506798i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.60181e7 | − | 2.77442e7i | 0.799831 | − | 1.38535i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.65746e6 | −0.380074 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.22160e7 | −1.09611 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.43756e7 | − | 2.48992e7i | 0.705051 | − | 1.22118i | −0.261622 | − | 0.965170i | \(-0.584257\pi\) |
0.966673 | − | 0.256014i | \(-0.0824093\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.69857e6 | − | 1.67984e7i | 0.472844 | − | 0.818990i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.31377e6 | 0.305999 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.56139e6 | − | 7.90056e6i | −0.219764 | − | 0.380642i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.26126e6 | 0.108303 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.14186e6 | + | 1.97775e6i | 0.0543679 | + | 0.0941679i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.09876e6 | − | 5.36722e6i | −0.146678 | − | 0.254054i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.39592e6 | + | 1.45422e7i | −0.395090 | + | 0.684315i | −0.993113 | − | 0.117164i | \(-0.962620\pi\) |
0.598023 | + | 0.801479i | \(0.295953\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.05348e6 | + | 6.79375e6i | 0.189633 | + | 0.317829i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.57351e6 | + | 9.65361e6i | −0.259225 | + | 0.448991i | −0.966035 | − | 0.258413i | \(-0.916800\pi\) |
0.706810 | + | 0.707404i | \(0.250134\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.21896e7 | + | 2.11131e7i | 0.563648 | + | 0.976266i | 0.997174 | + | 0.0751256i | \(0.0239358\pi\) |
−0.433526 | + | 0.901141i | \(0.642731\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −61981.3 | − | 107355.i | −0.00284940 | − | 0.00493530i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.13867e7 | 0.520440 | 0.260220 | − | 0.965549i | \(-0.416205\pi\) | ||||
0.260220 | + | 0.965549i | \(0.416205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.28850e6 | − | 1.43561e7i | −0.376648 | − | 0.652374i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.01643e7 | 0.911036 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.67858e6 | − | 1.50317e7i | 0.389851 | − | 0.675242i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.68354e6 | − | 2.91597e6i | 0.0751929 | − | 0.130238i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.11298e7 | −0.938338 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.76477e6 | −0.254543 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.95522e7 | + | 3.38654e7i | −0.858414 | + | 1.48682i | 0.0150273 | + | 0.999887i | \(0.495216\pi\) |
−0.873441 | + | 0.486930i | \(0.838117\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.87366e6 | + | 6.70938e6i | −0.169102 | + | 0.292894i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.09362e7 | 0.474708 | 0.237354 | − | 0.971423i | \(-0.423720\pi\) | ||||
0.237354 | + | 0.971423i | \(0.423720\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.14771e7 | − | 3.71994e7i | −0.926986 | − | 1.60559i | −0.788335 | − | 0.615246i | \(-0.789057\pi\) |
−0.138651 | − | 0.990341i | \(-0.544277\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.90826e6 | 0.339409 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.08256e7 | − | 1.87505e7i | −0.462001 | − | 0.800209i | 0.537060 | − | 0.843544i | \(-0.319535\pi\) |
−0.999061 | + | 0.0433353i | \(0.986202\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.41516e6 | + | 4.18318e6i | 0.102492 | + | 0.177522i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.73227e6 | + | 8.19653e6i | −0.199699 | + | 0.345888i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.28186e7 | − | 2.29572e7i | 0.537911 | − | 0.963362i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.35252e6 | − | 5.80673e6i | 0.139899 | − | 0.242312i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 972461. | + | 1.68435e6i | 0.0403544 | + | 0.0698959i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.01183e6 | − | 6.94869e6i | −0.165555 | − | 0.286750i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.21373e7 | −0.908473 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 50728.2 | + | 87863.8i | 0.00207028 | + | 0.00358584i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.81185e6 | 0.154708 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.14753e6 | − | 1.23799e7i | 0.288495 | − | 0.499687i | −0.684956 | − | 0.728584i | \(-0.740179\pi\) |
0.973451 | + | 0.228897i | \(0.0735119\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.83437e6 | − | 1.18375e7i | 0.274340 | − | 0.475170i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.67784e7 | −0.669816 | −0.334908 | − | 0.942251i | \(-0.608705\pi\) | ||||
−0.334908 | + | 0.942251i | \(0.608705\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −427834. | −0.0169863 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.28514e6 | − | 3.95797e6i | 0.0902318 | − | 0.156286i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.12949e6 | − | 1.95633e6i | 0.0443565 | − | 0.0768278i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.40604e7 | −1.33034 | −0.665168 | − | 0.746694i | \(-0.731640\pi\) | ||||
−0.665168 | + | 0.746694i | \(0.731640\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.05744e6 | − | 1.83154e6i | −0.0410777 | − | 0.0711486i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −367396. | −0.0141948 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.56014e6 | − | 4.43429e6i | −0.0983804 | − | 0.170400i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.51394e6 | − | 6.08632e6i | −0.134306 | − | 0.232624i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.16519e7 | − | 2.01817e7i | 0.442953 | − | 0.767216i | −0.554955 | − | 0.831881i | \(-0.687264\pi\) |
0.997907 | + | 0.0646644i | \(0.0205977\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.22141e7 | − | 2.04711e7i | −0.461835 | − | 0.774048i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.79703e6 | + | 8.30869e6i | −0.180413 | + | 0.312485i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.66184e6 | + | 1.50027e7i | 0.324027 | + | 0.561231i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.82963e7 | + | 3.16902e7i | 0.680794 | + | 1.17917i | 0.974739 | + | 0.223347i | \(0.0716982\pi\) |
−0.293946 | + | 0.955822i | \(0.594968\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.27533e7 | −0.472018 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.27910e7 | − | 2.21547e7i | −0.470902 | − | 0.815626i | 0.528544 | − | 0.848906i | \(-0.322738\pi\) |
−0.999446 | + | 0.0332800i | \(0.989405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.38833e6 | 0.0508409 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.50043e6 | − | 2.59883e6i | 0.0546560 | − | 0.0946669i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.62172e7 | − | 2.80890e7i | 0.587627 | − | 1.01780i | −0.406916 | − | 0.913466i | \(-0.633396\pi\) |
0.994542 | − | 0.104333i | \(-0.0332709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.20106e6 | −0.0432912 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.00123e7 | −0.358990 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.43185e7 | + | 4.21208e7i | −0.867369 | + | 1.50233i | −0.00269410 | + | 0.999996i | \(0.500858\pi\) |
−0.864675 | + | 0.502331i | \(0.832476\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.51933e6 | + | 2.63156e6i | −0.0539068 | + | 0.0933694i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.26501e6 | 0.0799448 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.51053e6 | + | 1.12766e7i | 0.228597 | + | 0.395941i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.91613e7 | 1.01859 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.26507e7 | + | 2.19117e7i | 0.439592 | + | 0.761395i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −968028. | − | 1.67667e6i | −0.0334634 | − | 0.0579603i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.29008e7 | − | 3.96653e7i | 0.787561 | − | 1.36410i | −0.139895 | − | 0.990166i | \(-0.544677\pi\) |
0.927457 | − | 0.373930i | \(-0.121990\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.07176e7 | − | 1.91945e7i | 0.366680 | − | 0.656699i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.65694e7 | − | 2.86990e7i | 0.563973 | − | 0.976830i | −0.433172 | − | 0.901311i | \(-0.642606\pi\) |
0.997144 | − | 0.0755181i | \(-0.0240611\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.30835e6 | + | 7.46229e6i | 0.145891 | + | 0.252691i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 803428. | + | 1.39158e6i | 0.0270667 | + | 0.0468809i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.87294e7 | 0.962920 | 0.481460 | − | 0.876468i | \(-0.340107\pi\) | ||||
0.481460 | + | 0.876468i | \(0.340107\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.68056e7 | + | 2.91082e7i | 0.560400 | + | 0.970641i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.29787e7 | −1.42587 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.41284e7 | − | 2.44712e7i | 0.466348 | − | 0.807739i | −0.532913 | − | 0.846170i | \(-0.678903\pi\) |
0.999261 | + | 0.0384309i | \(0.0122359\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.33750e6 | − | 1.27089e7i | 0.240967 | − | 0.417367i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.49483e6 | −0.146866 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.13627e6 | −0.0369395 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.23566e7 | + | 3.87228e7i | −0.723140 | + | 1.25251i | 0.236595 | + | 0.971608i | \(0.423968\pi\) |
−0.959735 | + | 0.280907i | \(0.909365\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.12792e7 | + | 1.95362e7i | −0.363000 | + | 0.628735i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.21342e6 | 0.134920 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.35342e7 | − | 4.07625e7i | −0.749828 | − | 1.29874i | −0.947905 | − | 0.318554i | \(-0.896803\pi\) |
0.198077 | − | 0.980187i | \(-0.436531\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.01181e6 | 0.190586 |
(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 | 76.6.e.a.49.5 | yes | 18 | |
3.2 | odd | 2 | 684.6.k.f.505.4 | 18 | |||
4.3 | odd | 2 | 304.6.i.d.49.5 | 18 | |||
19.7 | even | 3 | inner | 76.6.e.a.45.5 | ✓ | 18 | |
57.26 | odd | 6 | 684.6.k.f.577.4 | 18 | |||
76.7 | odd | 6 | 304.6.i.d.273.5 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.e.a.45.5 | ✓ | 18 | 19.7 | even | 3 | inner | |
76.6.e.a.49.5 | yes | 18 | 1.1 | even | 1 | trivial | |
304.6.i.d.49.5 | 18 | 4.3 | odd | 2 | |||
304.6.i.d.273.5 | 18 | 76.7 | odd | 6 | |||
684.6.k.f.505.4 | 18 | 3.2 | odd | 2 | |||
684.6.k.f.577.4 | 18 | 57.26 | odd | 6 |