Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,6,Mod(11,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.11");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.92460583776\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 7x^{6} + 6x^{5} - 11x^{4} - 73x^{3} + 223x^{2} - 768x + 912 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.7 | ||
Root | \(0.410606 - 2.17330i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.11 |
Dual form | 12.6.b.a.11.8 |
$q$-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 \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.41443 | − | 1.63829i | 0.957144 | − | 0.289612i | ||||
\(3\) | −4.17995 | − | 15.0176i | −0.268144 | − | 0.963379i | ||||
\(4\) | 26.6320 | − | 17.7408i | 0.832250 | − | 0.554400i | ||||
\(5\) | 73.1202i | 1.30801i | 0.756489 | + | 0.654007i | \(0.226913\pi\) | ||||
−0.756489 | + | 0.654007i | \(0.773087\pi\) | |||||||
\(6\) | −47.2352 | − | 74.4637i | −0.535658 | − | 0.844435i | ||||
\(7\) | 51.8209i | 0.399723i | 0.979824 | + | 0.199862i | \(0.0640493\pi\) | ||||
−0.979824 | + | 0.199862i | \(0.935951\pi\) | |||||||
\(8\) | 115.132 | − | 139.687i | 0.636023 | − | 0.771670i | ||||
\(9\) | −208.056 | + | 125.545i | −0.856198 | + | 0.516648i | ||||
\(10\) | 119.792 | + | 395.904i | 0.378816 | + | 1.25196i | ||||
\(11\) | −371.603 | −0.925971 | −0.462986 | − | 0.886366i | \(-0.653222\pi\) | ||||
−0.462986 | + | 0.886366i | \(0.653222\pi\) | |||||||
\(12\) | −377.744 | − | 325.793i | −0.757260 | − | 0.653114i | ||||
\(13\) | 424.112 | 0.696021 | 0.348011 | − | 0.937491i | \(-0.386857\pi\) | ||||
0.348011 | + | 0.937491i | \(0.386857\pi\) | |||||||
\(14\) | 84.8976 | + | 280.580i | 0.115764 | + | 0.382593i | ||||
\(15\) | 1098.09 | − | 305.638i | 1.26011 | − | 0.350736i | ||||
\(16\) | 394.528 | − | 944.946i | 0.385281 | − | 0.922799i | ||||
\(17\) | − | 1401.69i | − | 1.17634i | −0.808739 | − | 0.588168i | \(-0.799849\pi\) | ||
0.808739 | − | 0.588168i | \(-0.200151\pi\) | |||||||
\(18\) | −920.824 | + | 1020.61i | −0.669878 | + | 0.742471i | ||||
\(19\) | 319.814i | 0.203242i | 0.994823 | + | 0.101621i | \(0.0324029\pi\) | ||||
−0.994823 | + | 0.101621i | \(0.967597\pi\) | |||||||
\(20\) | 1297.21 | + | 1947.34i | 0.725163 | + | 1.08859i | ||||
\(21\) | 778.224 | − | 216.608i | 0.385085 | − | 0.107183i | ||||
\(22\) | −2012.02 | + | 608.793i | −0.886288 | + | 0.268172i | ||||
\(23\) | −2421.07 | −0.954306 | −0.477153 | − | 0.878820i | \(-0.658331\pi\) | ||||
−0.477153 | + | 0.878820i | \(0.658331\pi\) | |||||||
\(24\) | −2579.01 | − | 1145.13i | −0.913956 | − | 0.405813i | ||||
\(25\) | −2221.56 | −0.710899 | ||||||||
\(26\) | 2296.32 | − | 694.819i | 0.666193 | − | 0.201576i | ||||
\(27\) | 2755.05 | + | 2599.73i | 0.727312 | + | 0.686307i | ||||
\(28\) | 919.343 | + | 1380.09i | 0.221607 | + | 0.332670i | ||||
\(29\) | 3392.51i | 0.749076i | 0.927212 | + | 0.374538i | \(0.122199\pi\) | ||||
−0.927212 | + | 0.374538i | \(0.877801\pi\) | |||||||
\(30\) | 5444.80 | − | 3453.85i | 1.10453 | − | 0.700648i | ||||
\(31\) | − | 4656.09i | − | 0.870197i | −0.900383 | − | 0.435098i | \(-0.856714\pi\) | ||
0.900383 | − | 0.435098i | \(-0.143286\pi\) | |||||||
\(32\) | 588.047 | − | 5762.69i | 0.101517 | − | 0.994834i | ||||
\(33\) | 1553.28 | + | 5580.58i | 0.248293 | + | 0.892061i | ||||
\(34\) | −2296.38 | − | 7589.37i | −0.340680 | − | 1.12592i | ||||
\(35\) | −3789.15 | −0.522843 | ||||||||
\(36\) | −3313.68 | + | 7034.61i | −0.426141 | + | 0.904657i | ||||
\(37\) | 395.888 | 0.0475409 | 0.0237705 | − | 0.999717i | \(-0.492433\pi\) | ||||
0.0237705 | + | 0.999717i | \(0.492433\pi\) | |||||||
\(38\) | 523.948 | + | 1731.61i | 0.0588612 | + | 0.194532i | ||||
\(39\) | −1772.77 | − | 6369.14i | −0.186634 | − | 0.670532i | ||||
\(40\) | 10214.0 | + | 8418.51i | 1.00935 | + | 0.831927i | ||||
\(41\) | − | 5780.65i | − | 0.537053i | −0.963272 | − | 0.268526i | \(-0.913463\pi\) | ||
0.963272 | − | 0.268526i | \(-0.0865367\pi\) | |||||||
\(42\) | 3858.77 | − | 2447.77i | 0.337540 | − | 0.214115i | ||||
\(43\) | 16385.7i | 1.35143i | 0.737164 | + | 0.675714i | \(0.236165\pi\) | ||||
−0.737164 | + | 0.675714i | \(0.763835\pi\) | |||||||
\(44\) | −9896.53 | + | 6592.53i | −0.770640 | + | 0.513358i | ||||
\(45\) | −9179.91 | − | 15213.1i | −0.675783 | − | 1.11992i | ||||
\(46\) | −13108.7 | + | 3966.42i | −0.913409 | + | 0.276378i | ||||
\(47\) | 23646.2 | 1.56141 | 0.780706 | − | 0.624899i | \(-0.214860\pi\) | ||||
0.780706 | + | 0.624899i | \(0.214860\pi\) | |||||||
\(48\) | −15839.9 | − | 1975.04i | −0.992316 | − | 0.123729i | ||||
\(49\) | 14121.6 | 0.840221 | ||||||||
\(50\) | −12028.5 | + | 3639.56i | −0.680433 | + | 0.205885i | ||||
\(51\) | −21050.1 | + | 5859.01i | −1.13326 | + | 0.315427i | ||||
\(52\) | 11295.0 | − | 7524.09i | 0.579264 | − | 0.385874i | ||||
\(53\) | 1965.93i | 0.0961345i | 0.998844 | + | 0.0480673i | \(0.0153062\pi\) | ||||
−0.998844 | + | 0.0480673i | \(0.984694\pi\) | |||||||
\(54\) | 19176.1 | + | 9562.46i | 0.894905 | + | 0.446257i | ||||
\(55\) | − | 27171.7i | − | 1.21118i | ||||||
\(56\) | 7238.71 | + | 5966.26i | 0.308454 | + | 0.254233i | ||||
\(57\) | 4802.83 | − | 1336.80i | 0.195799 | − | 0.0544980i | ||||
\(58\) | 5557.91 | + | 18368.5i | 0.216941 | + | 0.716974i | ||||
\(59\) | 7861.94 | 0.294035 | 0.147018 | − | 0.989134i | \(-0.453033\pi\) | ||||
0.147018 | + | 0.989134i | \(0.453033\pi\) | |||||||
\(60\) | 23822.0 | − | 27620.7i | 0.854281 | − | 0.990506i | ||||
\(61\) | −9360.60 | −0.322091 | −0.161046 | − | 0.986947i | \(-0.551487\pi\) | ||||
−0.161046 | + | 0.986947i | \(0.551487\pi\) | |||||||
\(62\) | −7628.03 | − | 25210.1i | −0.252019 | − | 0.832904i | ||||
\(63\) | −6505.87 | − | 10781.6i | −0.206516 | − | 0.342242i | ||||
\(64\) | −6257.03 | − | 32165.1i | −0.190949 | − | 0.981600i | ||||
\(65\) | 31011.2i | 0.910405i | ||||||||
\(66\) | 17552.7 | + | 27670.9i | 0.496004 | + | 0.781922i | ||||
\(67\) | 37881.9i | 1.03097i | 0.856899 | + | 0.515484i | \(0.172388\pi\) | ||||
−0.856899 | + | 0.515484i | \(0.827612\pi\) | |||||||
\(68\) | −24867.2 | − | 37330.0i | −0.652160 | − | 0.979006i | ||||
\(69\) | 10119.9 | + | 36358.6i | 0.255891 | + | 0.919359i | ||||
\(70\) | −20516.1 | + | 6207.73i | −0.500437 | + | 0.151421i | ||||
\(71\) | −20357.6 | −0.479271 | −0.239635 | − | 0.970863i | \(-0.577028\pi\) | ||||
−0.239635 | + | 0.970863i | \(0.577028\pi\) | |||||||
\(72\) | −6416.92 | + | 43517.1i | −0.145880 | + | 0.989302i | ||||
\(73\) | −62082.6 | −1.36352 | −0.681762 | − | 0.731574i | \(-0.738786\pi\) | ||||
−0.681762 | + | 0.731574i | \(0.738786\pi\) | |||||||
\(74\) | 2143.51 | − | 648.579i | 0.0455035 | − | 0.0137684i | ||||
\(75\) | 9286.01 | + | 33362.5i | 0.190623 | + | 0.684866i | ||||
\(76\) | 5673.75 | + | 8517.28i | 0.112677 | + | 0.169148i | ||||
\(77\) | − | 19256.8i | − | 0.370132i | ||||||
\(78\) | −20033.0 | − | 31580.9i | −0.372829 | − | 0.587745i | ||||
\(79\) | − | 64254.3i | − | 1.15834i | −0.815209 | − | 0.579168i | \(-0.803378\pi\) | ||
0.815209 | − | 0.579168i | \(-0.196622\pi\) | |||||||
\(80\) | 69094.6 | + | 28848.0i | 1.20703 | + | 0.503953i | ||||
\(81\) | 27525.7 | − | 52241.0i | 0.466150 | − | 0.884706i | ||||
\(82\) | −9470.38 | − | 31298.9i | −0.155537 | − | 0.514037i | ||||
\(83\) | −10042.5 | −0.160009 | −0.0800046 | − | 0.996794i | \(-0.525494\pi\) | ||||
−0.0800046 | + | 0.996794i | \(0.525494\pi\) | |||||||
\(84\) | 16882.9 | − | 19575.0i | 0.261065 | − | 0.302694i | ||||
\(85\) | 102492. | 1.53866 | ||||||||
\(86\) | 26844.5 | + | 88719.0i | 0.391389 | + | 1.29351i | ||||
\(87\) | 50947.3 | − | 14180.5i | 0.721644 | − | 0.200860i | ||||
\(88\) | −42783.6 | + | 51908.2i | −0.588939 | + | 0.714544i | ||||
\(89\) | − | 56638.8i | − | 0.757947i | −0.925407 | − | 0.378974i | \(-0.876277\pi\) | ||
0.925407 | − | 0.378974i | \(-0.123723\pi\) | |||||||
\(90\) | −74627.4 | − | 67330.8i | −0.971163 | − | 0.876209i | ||||
\(91\) | 21977.9i | 0.278216i | ||||||||
\(92\) | −64478.0 | + | 42951.7i | −0.794222 | + | 0.529067i | ||||
\(93\) | −69923.3 | + | 19462.2i | −0.838329 | + | 0.233338i | ||||
\(94\) | 128031. | − | 38739.4i | 1.49450 | − | 0.452203i | ||||
\(95\) | −23384.8 | −0.265843 | ||||||||
\(96\) | −88999.8 | + | 15256.7i | −0.985623 | + | 0.168960i | ||||
\(97\) | −22348.7 | −0.241170 | −0.120585 | − | 0.992703i | \(-0.538477\pi\) | ||||
−0.120585 | + | 0.992703i | \(0.538477\pi\) | |||||||
\(98\) | 76460.4 | − | 23135.3i | 0.804213 | − | 0.243338i | ||||
\(99\) | 77314.3 | − | 46653.1i | 0.792814 | − | 0.478401i | ||||
\(100\) | −59164.6 | + | 39412.3i | −0.591646 | + | 0.394123i | ||||
\(101\) | − | 48423.5i | − | 0.472338i | −0.971712 | − | 0.236169i | \(-0.924108\pi\) | ||
0.971712 | − | 0.236169i | \(-0.0758919\pi\) | |||||||
\(102\) | −104375. | + | 66209.3i | −0.993339 | + | 0.630113i | ||||
\(103\) | 152205.i | 1.41363i | 0.707400 | + | 0.706813i | \(0.249868\pi\) | ||||
−0.707400 | + | 0.706813i | \(0.750132\pi\) | |||||||
\(104\) | 48829.1 | − | 59243.0i | 0.442685 | − | 0.537099i | ||||
\(105\) | 15838.4 | + | 56903.9i | 0.140197 | + | 0.503696i | ||||
\(106\) | 3220.77 | + | 10644.4i | 0.0278417 | + | 0.0920146i | ||||
\(107\) | −161378. | −1.36265 | −0.681325 | − | 0.731981i | \(-0.738596\pi\) | ||||
−0.681325 | + | 0.731981i | \(0.738596\pi\) | |||||||
\(108\) | 119494. | + | 20359.1i | 0.985794 | + | 0.167958i | ||||
\(109\) | 1239.70 | 0.00999422 | 0.00499711 | − | 0.999988i | \(-0.498409\pi\) | ||||
0.00499711 | + | 0.999988i | \(0.498409\pi\) | |||||||
\(110\) | −44515.1 | − | 147119.i | −0.350772 | − | 1.15928i | ||||
\(111\) | −1654.79 | − | 5945.28i | −0.0127478 | − | 0.0457999i | ||||
\(112\) | 48967.9 | + | 20444.8i | 0.368864 | + | 0.154006i | ||||
\(113\) | 156709.i | 1.15451i | 0.816565 | + | 0.577254i | \(0.195876\pi\) | ||||
−0.816565 | + | 0.577254i | \(0.804124\pi\) | |||||||
\(114\) | 23814.5 | − | 15106.5i | 0.171625 | − | 0.108868i | ||||
\(115\) | − | 177029.i | − | 1.24825i | ||||||
\(116\) | 60185.8 | + | 90349.3i | 0.415288 | + | 0.623419i | ||||
\(117\) | −88239.1 | + | 53245.4i | −0.595932 | + | 0.359598i | ||||
\(118\) | 42567.9 | − | 12880.1i | 0.281434 | − | 0.0851560i | ||||
\(119\) | 72637.0 | 0.470209 | ||||||||
\(120\) | 83731.9 | − | 188578.i | 0.530809 | − | 1.19547i | ||||
\(121\) | −22962.3 | −0.142578 | ||||||||
\(122\) | −50682.3 | + | 15335.4i | −0.308288 | + | 0.0932814i | ||||
\(123\) | −86811.4 | + | 24162.8i | −0.517385 | + | 0.144007i | ||||
\(124\) | −82602.8 | − | 124001.i | −0.482437 | − | 0.724221i | ||||
\(125\) | 66059.6i | 0.378147i | ||||||||
\(126\) | −52889.0 | − | 47717.9i | −0.296783 | − | 0.267766i | ||||
\(127\) | − | 23830.0i | − | 0.131104i | −0.997849 | − | 0.0655519i | \(-0.979119\pi\) | ||
0.997849 | − | 0.0655519i | \(-0.0208808\pi\) | |||||||
\(128\) | −86573.9 | − | 163905.i | −0.467049 | − | 0.884232i | ||||
\(129\) | 246073. | − | 68491.2i | 1.30194 | − | 0.362377i | ||||
\(130\) | 50805.3 | + | 167908.i | 0.263664 | + | 0.871389i | ||||
\(131\) | 346584. | 1.76454 | 0.882269 | − | 0.470746i | \(-0.156015\pi\) | ||||
0.882269 | + | 0.470746i | \(0.156015\pi\) | |||||||
\(132\) | 140371. | + | 121066.i | 0.701201 | + | 0.604764i | ||||
\(133\) | −16573.0 | −0.0812405 | ||||||||
\(134\) | 62061.6 | + | 205109.i | 0.298580 | + | 0.986785i | ||||
\(135\) | −190093. | + | 201450.i | −0.897699 | + | 0.951334i | ||||
\(136\) | −195799. | − | 161381.i | −0.907743 | − | 0.748177i | ||||
\(137\) | − | 182307.i | − | 0.829856i | −0.909854 | − | 0.414928i | \(-0.863807\pi\) | ||
0.909854 | − | 0.414928i | \(-0.136193\pi\) | |||||||
\(138\) | 114360. | + | 180282.i | 0.511182 | + | 0.805850i | ||||
\(139\) | − | 64467.5i | − | 0.283011i | −0.989937 | − | 0.141506i | \(-0.954806\pi\) | ||
0.989937 | − | 0.141506i | \(-0.0451944\pi\) | |||||||
\(140\) | −100913. | + | 67222.6i | −0.435137 | + | 0.289864i | ||||
\(141\) | −98840.0 | − | 355110.i | −0.418683 | − | 1.50423i | ||||
\(142\) | −110225. | + | 33351.7i | −0.458731 | + | 0.138802i | ||||
\(143\) | −157601. | −0.644495 | ||||||||
\(144\) | 36549.8 | + | 246133.i | 0.146885 | + | 0.989154i | ||||
\(145\) | −248061. | −0.979801 | ||||||||
\(146\) | −336141. | + | 101709.i | −1.30509 | + | 0.394892i | ||||
\(147\) | −59027.5 | − | 212072.i | −0.225300 | − | 0.809451i | ||||
\(148\) | 10543.3 | − | 7023.37i | 0.0395660 | − | 0.0263567i | ||||
\(149\) | − | 25638.2i | − | 0.0946067i | −0.998881 | − | 0.0473033i | \(-0.984937\pi\) | ||
0.998881 | − | 0.0473033i | \(-0.0150627\pi\) | |||||||
\(150\) | 104936. | + | 165426.i | 0.380799 | + | 0.600308i | ||||
\(151\) | 393481.i | 1.40437i | 0.711995 | + | 0.702185i | \(0.247792\pi\) | ||||
−0.711995 | + | 0.702185i | \(0.752208\pi\) | |||||||
\(152\) | 44673.9 | + | 36820.9i | 0.156836 | + | 0.129266i | ||||
\(153\) | 175976. | + | 291631.i | 0.607751 | + | 1.00718i | ||||
\(154\) | −31548.2 | − | 104264.i | −0.107195 | − | 0.354270i | ||||
\(155\) | 340454. | 1.13823 | ||||||||
\(156\) | −160206. | − | 138173.i | −0.527069 | − | 0.454581i | ||||
\(157\) | 463686. | 1.50133 | 0.750663 | − | 0.660686i | \(-0.229734\pi\) | ||||
0.750663 | + | 0.660686i | \(0.229734\pi\) | |||||||
\(158\) | −105267. | − | 347900.i | −0.335467 | − | 1.10869i | ||||
\(159\) | 29523.6 | − | 8217.50i | 0.0926140 | − | 0.0257779i | ||||
\(160\) | 421369. | + | 42998.1i | 1.30126 | + | 0.132785i | ||||
\(161\) | − | 125462.i | − | 0.381458i | ||||||
\(162\) | 63449.8 | − | 327950.i | 0.189952 | − | 0.981793i | ||||
\(163\) | − | 369066.i | − | 1.08801i | −0.839081 | − | 0.544007i | \(-0.816906\pi\) | ||
0.839081 | − | 0.544007i | \(-0.183094\pi\) | |||||||
\(164\) | −102553. | − | 153950.i | −0.297742 | − | 0.446962i | ||||
\(165\) | −408053. | + | 113576.i | −1.16683 | + | 0.324771i | ||||
\(166\) | −54374.2 | + | 16452.5i | −0.153152 | + | 0.0463405i | ||||
\(167\) | −17762.9 | −0.0492858 | −0.0246429 | − | 0.999696i | \(-0.507845\pi\) | ||||
−0.0246429 | + | 0.999696i | \(0.507845\pi\) | |||||||
\(168\) | 59341.5 | − | 133647.i | 0.162213 | − | 0.365330i | ||||
\(169\) | −191422. | −0.515555 | ||||||||
\(170\) | 554936. | − | 167912.i | 1.47272 | − | 0.445614i | ||||
\(171\) | −40151.2 | − | 66539.2i | −0.105004 | − | 0.174015i | ||||
\(172\) | 290695. | + | 436383.i | 0.749232 | + | 1.12473i | ||||
\(173\) | 720659.i | 1.83069i | 0.402672 | + | 0.915344i | \(0.368081\pi\) | ||||
−0.402672 | + | 0.915344i | \(0.631919\pi\) | |||||||
\(174\) | 252618. | − | 160246.i | 0.632546 | − | 0.401248i | ||||
\(175\) | − | 115123.i | − | 0.284163i | ||||||
\(176\) | −146608. | + | 351145.i | −0.356759 | + | 0.854485i | ||||
\(177\) | −32862.5 | − | 118067.i | −0.0788437 | − | 0.283267i | ||||
\(178\) | −92790.8 | − | 306666.i | −0.219510 | − | 0.725465i | ||||
\(179\) | −817432. | −1.90686 | −0.953431 | − | 0.301613i | \(-0.902475\pi\) | ||||
−0.953431 | + | 0.301613i | \(0.902475\pi\) | |||||||
\(180\) | −514372. | − | 242297.i | −1.18330 | − | 0.557399i | ||||
\(181\) | 389376. | 0.883431 | 0.441716 | − | 0.897155i | \(-0.354370\pi\) | ||||
0.441716 | + | 0.897155i | \(0.354370\pi\) | |||||||
\(182\) | 36006.1 | + | 118997.i | 0.0805745 | + | 0.266293i | ||||
\(183\) | 39126.8 | + | 140574.i | 0.0863668 | + | 0.310296i | ||||
\(184\) | −278744. | + | 338193.i | −0.606961 | + | 0.736410i | ||||
\(185\) | 28947.4i | 0.0621842i | ||||||||
\(186\) | −346710. | + | 219931.i | −0.734825 | + | 0.466128i | ||||
\(187\) | 520874.i | 1.08925i | ||||||||
\(188\) | 629747. | − | 419503.i | 1.29949 | − | 0.865647i | ||||
\(189\) | −134720. | + | 142769.i | −0.274333 | + | 0.290723i | ||||
\(190\) | −126615. | + | 38311.1i | −0.254450 | + | 0.0769912i | ||||
\(191\) | 477051. | 0.946197 | 0.473099 | − | 0.881009i | \(-0.343135\pi\) | ||||
0.473099 | + | 0.881009i | \(0.343135\pi\) | |||||||
\(192\) | −456888. | + | 228414.i | −0.894451 | + | 0.447166i | ||||
\(193\) | −757371. | −1.46358 | −0.731788 | − | 0.681533i | \(-0.761314\pi\) | ||||
−0.731788 | + | 0.681533i | \(0.761314\pi\) | |||||||
\(194\) | −121005. | + | 36613.7i | −0.230834 | + | 0.0698456i | ||||
\(195\) | 465713. | − | 129625.i | 0.877065 | − | 0.244119i | ||||
\(196\) | 376087. | − | 250528.i | 0.699274 | − | 0.465819i | ||||
\(197\) | − | 948808.i | − | 1.74186i | −0.491409 | − | 0.870929i | \(-0.663518\pi\) | ||
0.491409 | − | 0.870929i | \(-0.336482\pi\) | |||||||
\(198\) | 342181. | − | 379263.i | 0.620287 | − | 0.687507i | ||||
\(199\) | 221239.i | 0.396030i | 0.980199 | + | 0.198015i | \(0.0634495\pi\) | ||||
−0.980199 | + | 0.198015i | \(0.936551\pi\) | |||||||
\(200\) | −255774. | + | 310324.i | −0.452148 | + | 0.548580i | ||||
\(201\) | 568895. | − | 158344.i | 0.993212 | − | 0.276447i | ||||
\(202\) | −79331.8 | − | 262186.i | −0.136795 | − | 0.452096i | ||||
\(203\) | −175803. | −0.299423 | ||||||||
\(204\) | −456663. | + | 529483.i | −0.768281 | + | 0.890792i | ||||
\(205\) | 422682. | 0.702472 | ||||||||
\(206\) | 249355. | + | 824100.i | 0.409403 | + | 1.35304i | ||||
\(207\) | 503718. | − | 303954.i | 0.817075 | − | 0.493040i | ||||
\(208\) | 167324. | − | 400763.i | 0.268164 | − | 0.642288i | ||||
\(209\) | − | 118844.i | − | 0.188196i | ||||||
\(210\) | 178981. | + | 282154.i | 0.280065 | + | 0.441507i | ||||
\(211\) | − | 670682.i | − | 1.03708i | −0.855055 | − | 0.518538i | \(-0.826476\pi\) | ||
0.855055 | − | 0.518538i | \(-0.173524\pi\) | |||||||
\(212\) | 34877.3 | + | 52356.8i | 0.0532970 | + | 0.0800080i | ||||
\(213\) | 85093.8 | + | 305722.i | 0.128513 | + | 0.461720i | ||||
\(214\) | −873768. | + | 264384.i | −1.30425 | + | 0.394639i | ||||
\(215\) | −1.19812e6 | −1.76769 | ||||||||
\(216\) | 680345. | − | 85532.7i | 0.992190 | − | 0.124738i | ||||
\(217\) | 241283. | 0.347838 | ||||||||
\(218\) | 6712.24 | − | 2030.98i | 0.00956591 | − | 0.00289444i | ||||
\(219\) | 259502. | + | 932331.i | 0.365620 | + | 1.31359i | ||||
\(220\) | −482047. | − | 723636.i | −0.671480 | − | 1.00801i | ||||
\(221\) | − | 594476.i | − | 0.818754i | ||||||
\(222\) | −18699.8 | − | 29479.3i | −0.0254657 | − | 0.0401452i | ||||
\(223\) | − | 1.21387e6i | − | 1.63459i | −0.576216 | − | 0.817297i | \(-0.695471\pi\) | ||
0.576216 | − | 0.817297i | \(-0.304529\pi\) | |||||||
\(224\) | 298628. | + | 30473.1i | 0.397658 | + | 0.0405785i | ||||
\(225\) | 462209. | − | 278907.i | 0.608671 | − | 0.367285i | ||||
\(226\) | 256734. | + | 848488.i | 0.334359 | + | 1.10503i | ||||
\(227\) | 800234. | 1.03075 | 0.515374 | − | 0.856965i | \(-0.327653\pi\) | ||||
0.515374 | + | 0.856965i | \(0.327653\pi\) | |||||||
\(228\) | 104193. | − | 120808.i | 0.132740 | − | 0.153907i | ||||
\(229\) | −937980. | −1.18197 | −0.590983 | − | 0.806684i | \(-0.701260\pi\) | ||||
−0.590983 | + | 0.806684i | \(0.701260\pi\) | |||||||
\(230\) | −290025. | − | 958511.i | −0.361506 | − | 1.19475i | ||||
\(231\) | −289190. | + | 80492.3i | −0.356578 | + | 0.0992486i | ||||
\(232\) | 473890. | + | 390588.i | 0.578039 | + | 0.476429i | ||||
\(233\) | 925881.i | 1.11729i | 0.829407 | + | 0.558645i | \(0.188678\pi\) | ||||
−0.829407 | + | 0.558645i | \(0.811322\pi\) | |||||||
\(234\) | −390533. | + | 432854.i | −0.466249 | + | 0.516776i | ||||
\(235\) | 1.72902e6i | 2.04235i | ||||||||
\(236\) | 209379. | − | 139477.i | 0.244711 | − | 0.163013i | ||||
\(237\) | −964944. | + | 268579.i | −1.11592 | + | 0.310600i | ||||
\(238\) | 393288. | − | 119001.i | 0.450058 | − | 0.136178i | ||||
\(239\) | 619662. | 0.701714 | 0.350857 | − | 0.936429i | \(-0.385890\pi\) | ||||
0.350857 | + | 0.936429i | \(0.385890\pi\) | |||||||
\(240\) | 144415. | − | 1.15822e6i | 0.161839 | − | 1.29796i | ||||
\(241\) | 39339.5 | 0.0436301 | 0.0218151 | − | 0.999762i | \(-0.493055\pi\) | ||||
0.0218151 | + | 0.999762i | \(0.493055\pi\) | |||||||
\(242\) | −124327. | + | 37618.9i | −0.136467 | + | 0.0412921i | ||||
\(243\) | −899590. | − | 195005.i | −0.977302 | − | 0.211850i | ||||
\(244\) | −249292. | + | 166065.i | −0.268061 | + | 0.178567i | ||||
\(245\) | 1.03257e6i | 1.09902i | ||||||||
\(246\) | −430448. | + | 273050.i | −0.453506 | + | 0.287677i | ||||
\(247\) | 135637.i | 0.141461i | ||||||||
\(248\) | −650397. | − | 536067.i | −0.671505 | − | 0.553465i | ||||
\(249\) | 41977.0 | + | 150814.i | 0.0429055 | + | 0.154150i | ||||
\(250\) | 108225. | + | 357675.i | 0.109516 | + | 0.361942i | ||||
\(251\) | −699759. | −0.701074 | −0.350537 | − | 0.936549i | \(-0.614001\pi\) | ||||
−0.350537 | + | 0.936549i | \(0.614001\pi\) | |||||||
\(252\) | −364539. | − | 171717.i | −0.361612 | − | 0.170339i | ||||
\(253\) | 899677. | 0.883660 | ||||||||
\(254\) | −39040.5 | − | 129026.i | −0.0379692 | − | 0.125485i | ||||
\(255\) | −428412. | − | 1.53919e6i | −0.412583 | − | 1.48232i | ||||
\(256\) | −737271. | − | 745616.i | −0.703117 | − | 0.711075i | ||||
\(257\) | 762091.i | 0.719738i | 0.933003 | + | 0.359869i | \(0.117179\pi\) | ||||
−0.933003 | + | 0.359869i | \(0.882821\pi\) | |||||||
\(258\) | 1.22014e6 | − | 773980.i | 1.14119 | − | 0.723903i | ||||
\(259\) | 20515.2i | 0.0190032i | ||||||||
\(260\) | 550163. | + | 825890.i | 0.504729 | + | 0.757685i | ||||
\(261\) | −425914. | − | 705832.i | −0.387008 | − | 0.641357i | ||||
\(262\) | 1.87656e6 | − | 567806.i | 1.68892 | − | 0.511030i | ||||
\(263\) | 1.39808e6 | 1.24636 | 0.623180 | − | 0.782079i | \(-0.285841\pi\) | ||||
0.623180 | + | 0.782079i | \(0.285841\pi\) | |||||||
\(264\) | 958369. | + | 425533.i | 0.846297 | + | 0.375771i | ||||
\(265\) | −143749. | −0.125745 | ||||||||
\(266\) | −89733.4 | + | 27151.4i | −0.0777589 | + | 0.0235282i | ||||
\(267\) | −850578. | + | 236747.i | −0.730190 | + | 0.203239i | ||||
\(268\) | 672055. | + | 1.00887e6i | 0.571568 | + | 0.858023i | ||||
\(269\) | − | 1.01587e6i | − | 0.855966i | −0.903787 | − | 0.427983i | \(-0.859224\pi\) | ||
0.903787 | − | 0.427983i | \(-0.140776\pi\) | |||||||
\(270\) | −699209. | + | 1.40216e6i | −0.583710 | + | 1.17055i | ||||
\(271\) | − | 1.06520e6i | − | 0.881068i | −0.897736 | − | 0.440534i | \(-0.854789\pi\) | ||
0.897736 | − | 0.440534i | \(-0.145211\pi\) | |||||||
\(272\) | −1.32453e6 | − | 553008.i | −1.08552 | − | 0.453220i | ||||
\(273\) | 330054. | − | 91866.3i | 0.268027 | − | 0.0746018i | ||||
\(274\) | −298672. | − | 987090.i | −0.240336 | − | 0.794292i | ||||
\(275\) | 825539. | 0.658272 | ||||||||
\(276\) | 914546. | + | 788768.i | 0.722658 | + | 0.623270i | ||||
\(277\) | 1.09974e6 | 0.861172 | 0.430586 | − | 0.902550i | \(-0.358307\pi\) | ||||
0.430586 | + | 0.902550i | \(0.358307\pi\) | |||||||
\(278\) | −105617. | − | 349055.i | −0.0819634 | − | 0.270883i | ||||
\(279\) | 584551. | + | 968728.i | 0.449585 | + | 0.745060i | ||||
\(280\) | −436254. | + | 529296.i | −0.332540 | + | 0.403463i | ||||
\(281\) | − | 1.73035e6i | − | 1.30728i | −0.756807 | − | 0.653639i | \(-0.773242\pi\) | ||
0.756807 | − | 0.653639i | \(-0.226758\pi\) | |||||||
\(282\) | −1.11693e6 | − | 1.76079e6i | −0.836383 | − | 1.31851i | ||||
\(283\) | 787037.i | 0.584156i | 0.956394 | + | 0.292078i | \(0.0943468\pi\) | ||||
−0.956394 | + | 0.292078i | \(0.905653\pi\) | |||||||
\(284\) | −542164. | + | 361160.i | −0.398873 | + | 0.265708i | ||||
\(285\) | 97747.4 | + | 351184.i | 0.0712841 | + | 0.256108i | ||||
\(286\) | −853321. | + | 258197.i | −0.616875 | + | 0.186653i | ||||
\(287\) | 299558. | 0.214673 | ||||||||
\(288\) | 601133. | + | 1.27279e6i | 0.427061 | + | 0.904223i | ||||
\(289\) | −544892. | −0.383765 | ||||||||
\(290\) | −1.34311e6 | + | 406395.i | −0.937811 | + | 0.283762i | ||||
\(291\) | 93416.4 | + | 335624.i | 0.0646682 | + | 0.232338i | ||||
\(292\) | −1.65338e6 | + | 1.10139e6i | −1.13479 | + | 0.755937i | ||||
\(293\) | 618982.i | 0.421220i | 0.977570 | + | 0.210610i | \(0.0675450\pi\) | ||||
−0.977570 | + | 0.210610i | \(0.932455\pi\) | |||||||
\(294\) | −667036. | − | 1.05155e6i | −0.450071 | − | 0.709512i | ||||
\(295\) | 574866.i | 0.384602i | ||||||||
\(296\) | 45579.5 | − | 55300.5i | 0.0302371 | − | 0.0366859i | ||||
\(297\) | −1.02379e6 | − | 966067.i | −0.673470 | − | 0.635501i | ||||
\(298\) | −42002.8 | − | 138816.i | −0.0273992 | − | 0.0905523i | ||||
\(299\) | −1.02681e6 | −0.664217 | ||||||||
\(300\) | 839182. | + | 723769.i | 0.538336 | + | 0.464298i | ||||
\(301\) | −849120. | −0.540198 | ||||||||
\(302\) | 644636. | + | 2.13047e6i | 0.406721 | + | 1.34418i | ||||
\(303\) | −727205. | + | 202408.i | −0.455041 | + | 0.126654i | ||||
\(304\) | 302207. | + | 126175.i | 0.187551 | + | 0.0783053i | ||||
\(305\) | − | 684449.i | − | 0.421300i | ||||||
\(306\) | 1.43059e6 | + | 1.29071e6i | 0.873396 | + | 0.788001i | ||||
\(307\) | − | 744212.i | − | 0.450662i | −0.974282 | − | 0.225331i | \(-0.927654\pi\) | ||
0.974282 | − | 0.225331i | \(-0.0723463\pi\) | |||||||
\(308\) | −341631. | − | 512847.i | −0.205201 | − | 0.308043i | ||||
\(309\) | 2.28575e6 | − | 636207.i | 1.36186 | − | 0.379055i | ||||
\(310\) | 1.84336e6 | − | 557763.i | 1.08945 | − | 0.329644i | ||||
\(311\) | −170581. | −0.100007 | −0.0500035 | − | 0.998749i | \(-0.515923\pi\) | ||||
−0.0500035 | + | 0.998749i | \(0.515923\pi\) | |||||||
\(312\) | −1.09379e6 | − | 485662.i | −0.636133 | − | 0.282454i | ||||
\(313\) | −772718. | −0.445821 | −0.222910 | − | 0.974839i | \(-0.571556\pi\) | ||||
−0.222910 | + | 0.974839i | \(0.571556\pi\) | |||||||
\(314\) | 2.51059e6 | − | 759652.i | 1.43699 | − | 0.434801i | ||||
\(315\) | 788356. | − | 475711.i | 0.447657 | − | 0.270126i | ||||
\(316\) | −1.13992e6 | − | 1.71122e6i | −0.642181 | − | 0.964025i | ||||
\(317\) | 1.69947e6i | 0.949874i | 0.880020 | + | 0.474937i | \(0.157529\pi\) | ||||
−0.880020 | + | 0.474937i | \(0.842471\pi\) | |||||||
\(318\) | 146391. | − | 92861.3i | 0.0811794 | − | 0.0514952i | ||||
\(319\) | − | 1.26067e6i | − | 0.693622i | ||||||
\(320\) | 2.35192e6 | − | 457515.i | 1.28395 | − | 0.249764i | ||||
\(321\) | 674550. | + | 2.42351e6i | 0.365386 | + | 1.31275i | ||||
\(322\) | −205543. | − | 679304.i | −0.110475 | − | 0.365111i | ||||
\(323\) | 448281. | 0.239081 | ||||||||
\(324\) | −193733. | − | 1.87961e6i | −0.102528 | − | 0.994730i | ||||
\(325\) | −942191. | −0.494801 | ||||||||
\(326\) | −604636. | − | 1.99828e6i | −0.315101 | − | 1.04139i | ||||
\(327\) | −5181.86 | − | 18617.2i | −0.00267989 | − | 0.00962822i | ||||
\(328\) | −807483. | − | 665540.i | −0.414428 | − | 0.341578i | ||||
\(329\) | 1.22537e6i | 0.624133i | ||||||||
\(330\) | −2.02330e6 | + | 1.28346e6i | −1.02277 | + | 0.648780i | ||||
\(331\) | − | 23171.2i | − | 0.0116246i | −0.999983 | − | 0.00581231i | \(-0.998150\pi\) | ||
0.999983 | − | 0.00581231i | \(-0.00185013\pi\) | |||||||
\(332\) | −267451. | + | 178161.i | −0.133168 | + | 0.0887091i | ||||
\(333\) | −82366.9 | + | 49701.9i | −0.0407045 | + | 0.0245619i | ||||
\(334\) | −96175.6 | + | 29100.7i | −0.0471736 | + | 0.0142737i | ||||
\(335\) | −2.76993e6 | −1.34852 | ||||||||
\(336\) | 102348. | − | 820838.i | 0.0494574 | − | 0.396652i | ||||
\(337\) | 1.55319e6 | 0.744991 | 0.372495 | − | 0.928034i | \(-0.378502\pi\) | ||||
0.372495 | + | 0.928034i | \(0.378502\pi\) | |||||||
\(338\) | −1.03644e6 | + | 313605.i | −0.493460 | + | 0.149311i | ||||
\(339\) | 2.35339e6 | − | 655034.i | 1.11223 | − | 0.309574i | ||||
\(340\) | 2.72957e6 | − | 1.81829e6i | 1.28055 | − | 0.853035i | ||||
\(341\) | 1.73022e6i | 0.805777i | ||||||||
\(342\) | −326406. | − | 294492.i | −0.150901 | − | 0.136147i | ||||
\(343\) | 1.60275e6i | 0.735579i | ||||||||
\(344\) | 2.28887e6 | + | 1.88652e6i | 1.04286 | + | 0.859540i | ||||
\(345\) | −2.65855e6 | + | 739972.i | −1.20253 | + | 0.334709i | ||||
\(346\) | 1.18065e6 | + | 3.90195e6i | 0.530188 | + | 1.75223i | ||||
\(347\) | −976969. | −0.435569 | −0.217784 | − | 0.975997i | \(-0.569883\pi\) | ||||
−0.217784 | + | 0.975997i | \(0.569883\pi\) | |||||||
\(348\) | 1.10526e6 | − | 1.28150e6i | 0.489232 | − | 0.567245i | ||||
\(349\) | −1.06380e6 | −0.467515 | −0.233758 | − | 0.972295i | \(-0.575102\pi\) | ||||
−0.233758 | + | 0.972295i | \(0.575102\pi\) | |||||||
\(350\) | −188605. | − | 623326.i | −0.0822969 | − | 0.271985i | ||||
\(351\) | 1.16845e6 | + | 1.10258e6i | 0.506224 | + | 0.477684i | ||||
\(352\) | −218520. | + | 2.14143e6i | −0.0940014 | + | 0.921187i | ||||
\(353\) | − | 3.56017e6i | − | 1.52067i | −0.649532 | − | 0.760334i | \(-0.725035\pi\) | ||
0.649532 | − | 0.760334i | \(-0.274965\pi\) | |||||||
\(354\) | −371360. | − | 585429.i | −0.157502 | − | 0.248294i | ||||
\(355\) | − | 1.48855e6i | − | 0.626893i | ||||||
\(356\) | −1.00482e6 | − | 1.50840e6i | −0.420206 | − | 0.630802i | ||||
\(357\) | −303619. | − | 1.09083e6i | −0.126084 | − | 0.452989i | ||||
\(358\) | −4.42592e6 | + | 1.33919e6i | −1.82514 | + | 0.552249i | ||||
\(359\) | −1.37771e6 | −0.564184 | −0.282092 | − | 0.959387i | \(-0.591028\pi\) | ||||
−0.282092 | + | 0.959387i | \(0.591028\pi\) | |||||||
\(360\) | −3.18198e6 | − | 469206.i | −1.29402 | − | 0.190813i | ||||
\(361\) | 2.37382e6 | 0.958693 | ||||||||
\(362\) | 2.10825e6 | − | 637911.i | 0.845571 | − | 0.255852i | ||||
\(363\) | 95981.0 | + | 344838.i | 0.0382313 | + | 0.137356i | ||||
\(364\) | 389905. | + | 585314.i | 0.154243 | + | 0.231545i | ||||
\(365\) | − | 4.53949e6i | − | 1.78351i | ||||||
\(366\) | 442150. | + | 697025.i | 0.172531 | + | 0.271985i | ||||
\(367\) | 3.26242e6i | 1.26437i | 0.774817 | + | 0.632186i | \(0.217842\pi\) | ||||
−0.774817 | + | 0.632186i | \(0.782158\pi\) | |||||||
\(368\) | −955180. | + | 2.28778e6i | −0.367676 | + | 0.880633i | ||||
\(369\) | 725734. | + | 1.20270e6i | 0.277467 | + | 0.459823i | ||||
\(370\) | 47424.2 | + | 156733.i | 0.0180093 | + | 0.0595193i | ||||
\(371\) | −101876. | −0.0384272 | ||||||||
\(372\) | −1.51692e6 | + | 1.75881e6i | −0.568337 | + | 0.658965i | ||||
\(373\) | 464538. | 0.172882 | 0.0864409 | − | 0.996257i | \(-0.472451\pi\) | ||||
0.0864409 | + | 0.996257i | \(0.472451\pi\) | |||||||
\(374\) | 853343. | + | 2.82023e6i | 0.315460 | + | 1.04257i | ||||
\(375\) | 992057. | − | 276126.i | 0.364299 | − | 0.101398i | ||||
\(376\) | 2.72245e6 | − | 3.30308e6i | 0.993094 | − | 1.20489i | ||||
\(377\) | 1.43880e6i | 0.521372i | ||||||||
\(378\) | −495535. | + | 993724.i | −0.178379 | + | 0.357714i | ||||
\(379\) | − | 2.81783e6i | − | 1.00767i | −0.863801 | − | 0.503834i | \(-0.831922\pi\) | ||
0.863801 | − | 0.503834i | \(-0.168078\pi\) | |||||||
\(380\) | −622785. | + | 414866.i | −0.221248 | + | 0.147383i | ||||
\(381\) | −357870. | + | 99608.3i | −0.126303 | + | 0.0351547i | ||||
\(382\) | 2.58296e6 | − | 781549.i | 0.905647 | − | 0.274030i | ||||
\(383\) | 1.82945e6 | 0.637270 | 0.318635 | − | 0.947878i | \(-0.396776\pi\) | ||||
0.318635 | + | 0.947878i | \(0.396776\pi\) | |||||||
\(384\) | −2.09958e6 | + | 1.98524e6i | −0.726614 | + | 0.687046i | ||||
\(385\) | 1.40806e6 | 0.484138 | ||||||||
\(386\) | −4.10073e6 | + | 1.24079e6i | −1.40085 | + | 0.423868i | ||||
\(387\) | −2.05715e6 | − | 3.40914e6i | −0.698213 | − | 1.15709i | ||||
\(388\) | −595191. | + | 396484.i | −0.200714 | + | 0.133705i | ||||
\(389\) | 4035.50i | 0.00135215i | 1.00000 | 0.000676073i | \(0.000215201\pi\) | |||||
−1.00000 | 0.000676073i | \(0.999785\pi\) | ||||||||
\(390\) | 2.30920e6 | − | 1.46482e6i | 0.768778 | − | 0.487666i | ||||
\(391\) | 3.39360e6i | 1.12258i | ||||||||
\(392\) | 1.62585e6 | − | 1.97261e6i | 0.534400 | − | 0.648374i | ||||
\(393\) | −1.44870e6 | − | 5.20486e6i | −0.473150 | − | 1.69992i | ||||
\(394\) | −1.55442e6 | − | 5.13725e6i | −0.504462 | − | 1.66721i | ||||
\(395\) | 4.69828e6 | 1.51512 | ||||||||
\(396\) | 1.23137e6 | − | 2.61408e6i | 0.394595 | − | 0.837686i | ||||
\(397\) | −2.37250e6 | −0.755493 | −0.377746 | − | 0.925909i | \(-0.623301\pi\) | ||||
−0.377746 | + | 0.925909i | \(0.623301\pi\) | |||||||
\(398\) | 362453. | + | 1.19788e6i | 0.114695 | + | 0.379058i | ||||
\(399\) | 69274.3 | + | 248887.i | 0.0217841 | + | 0.0782654i | ||||
\(400\) | −876468. | + | 2.09926e6i | −0.273896 | + | 0.656017i | ||||
\(401\) | 4.05826e6i | 1.26031i | 0.776468 | + | 0.630157i | \(0.217009\pi\) | ||||
−0.776468 | + | 0.630157i | \(0.782991\pi\) | |||||||
\(402\) | 2.82083e6 | − | 1.78936e6i | 0.870585 | − | 0.552246i | ||||
\(403\) | − | 1.97471e6i | − | 0.605675i | ||||||
\(404\) | −859072. | − | 1.28962e6i | −0.261864 | − | 0.393104i | ||||
\(405\) | 3.81987e6 | + | 2.01268e6i | 1.15721 | + | 0.609730i | ||||
\(406\) | −951870. | + | 288016.i | −0.286591 | + | 0.0867163i | ||||
\(407\) | −147113. | −0.0440215 | ||||||||
\(408\) | −1.60512e6 | + | 3.61499e6i | −0.477372 | + | 1.07512i | ||||
\(409\) | 3.68529e6 | 1.08934 | 0.544670 | − | 0.838650i | \(-0.316655\pi\) | ||||
0.544670 | + | 0.838650i | \(0.316655\pi\) | |||||||
\(410\) | 2.28858e6 | − | 692476.i | 0.672367 | − | 0.203444i | ||||
\(411\) | −2.73782e6 | + | 762035.i | −0.799466 | + | 0.222521i | ||||
\(412\) | 2.70023e6 | + | 4.05351e6i | 0.783715 | + | 1.17649i | ||||
\(413\) | 407412.i | 0.117533i | ||||||||
\(414\) | 2.22938e6 | − | 2.47098e6i | 0.639269 | − | 0.708545i | ||||
\(415\) | − | 734307.i | − | 0.209294i | ||||||
\(416\) | 249398. | − | 2.44403e6i | 0.0706576 | − | 0.692425i | ||||
\(417\) | −968147. | + | 269471.i | −0.272647 | + | 0.0758877i | ||||
\(418\) | −194700. | − | 643470.i | −0.0545037 | − | 0.180131i | ||||
\(419\) | −3.99766e6 | −1.11242 | −0.556212 | − | 0.831040i | \(-0.687746\pi\) | ||||
−0.556212 | + | 0.831040i | \(0.687746\pi\) | |||||||
\(420\) | 1.43133e6 | + | 1.23448e6i | 0.395928 | + | 0.341476i | ||||
\(421\) | −6.97378e6 | −1.91762 | −0.958811 | − | 0.284044i | \(-0.908324\pi\) | ||||
−0.958811 | + | 0.284044i | \(0.908324\pi\) | |||||||
\(422\) | −1.09877e6 | − | 3.63136e6i | −0.300349 | − | 0.992632i | ||||
\(423\) | −4.91974e6 | + | 2.96868e6i | −1.33688 | + | 0.806700i | ||||
\(424\) | 274616. | + | 226343.i | 0.0741841 | + | 0.0611438i | ||||
\(425\) | 3.11395e6i | 0.836256i | ||||||||
\(426\) | 961596. | + | 1.51590e6i | 0.256725 | + | 0.404713i | ||||
\(427\) | − | 485074.i | − | 0.128747i | ||||||
\(428\) | −4.29781e6 | + | 2.86297e6i | −1.13407 | + | 0.755453i | ||||
\(429\) | 658765. | + | 2.36679e6i | 0.172817 | + | 0.620893i | ||||
\(430\) | −6.48715e6 | + | 1.96287e6i | −1.69193 | + | 0.511943i | ||||
\(431\) | 3.92239e6 | 1.01709 | 0.508543 | − | 0.861037i | \(-0.330184\pi\) | ||||
0.508543 | + | 0.861037i | \(0.330184\pi\) | |||||||
\(432\) | 3.54355e6 | − | 1.57771e6i | 0.913543 | − | 0.406742i | ||||
\(433\) | −4.53851e6 | −1.16331 | −0.581653 | − | 0.813437i | \(-0.697594\pi\) | ||||
−0.581653 | + | 0.813437i | \(0.697594\pi\) | |||||||
\(434\) | 1.30641e6 | − | 395291.i | 0.332931 | − | 0.100738i | ||||
\(435\) | 1.03688e6 | + | 3.72527e6i | 0.262728 | + | 0.943920i | ||||
\(436\) | 33015.6 | − | 21993.2i | 0.00831769 | − | 0.00554079i | ||||
\(437\) | − | 774292.i | − | 0.193955i | ||||||
\(438\) | 2.93248e6 | + | 4.62290e6i | 0.730382 | + | 1.15141i | ||||
\(439\) | − | 4.33755e6i | − | 1.07419i | −0.843520 | − | 0.537097i | \(-0.819521\pi\) | ||
0.843520 | − | 0.537097i | \(-0.180479\pi\) | |||||||
\(440\) | −3.79554e6 | − | 3.12834e6i | −0.934633 | − | 0.770340i | ||||
\(441\) | −2.93808e6 | + | 1.77290e6i | −0.719396 | + | 0.434099i | ||||
\(442\) | −973924. | − | 3.21875e6i | −0.237121 | − | 0.783666i | ||||
\(443\) | 2.55182e6 | 0.617791 | 0.308895 | − | 0.951096i | \(-0.400041\pi\) | ||||
0.308895 | + | 0.951096i | \(0.400041\pi\) | |||||||
\(444\) | −149544. | − | 128978.i | −0.0360009 | − | 0.0310496i | ||||
\(445\) | 4.14144e6 | 0.991405 | ||||||||
\(446\) | −1.98867e6 | − | 6.57241e6i | −0.473397 | − | 1.56454i | ||||
\(447\) | −385024. | + | 107166.i | −0.0911421 | + | 0.0253682i | ||||
\(448\) | 1.66682e6 | − | 324245.i | 0.392368 | − | 0.0763269i | ||||
\(449\) | − | 1.60272e6i | − | 0.375182i | −0.982247 | − | 0.187591i | \(-0.939932\pi\) | ||
0.982247 | − | 0.187591i | \(-0.0600680\pi\) | |||||||
\(450\) | 2.04567e6 | − | 2.26735e6i | 0.476216 | − | 0.527823i | ||||
\(451\) | 2.14811e6i | 0.497295i | ||||||||
\(452\) | 2.78014e6 | + | 4.17347e6i | 0.640059 | + | 0.960840i | ||||
\(453\) | 5.90913e6 | − | 1.64473e6i | 1.35294 | − | 0.376573i | ||||
\(454\) | 4.33281e6 | − | 1.31102e6i | 0.986574 | − | 0.298516i | ||||
\(455\) | −1.60702e6 | −0.363910 | ||||||||
\(456\) | 366227. | − | 824804.i | 0.0824781 | − | 0.185754i | ||||
\(457\) | 4.62120e6 | 1.03506 | 0.517528 | − | 0.855666i | \(-0.326852\pi\) | ||||
0.517528 | + | 0.855666i | \(0.326852\pi\) | |||||||
\(458\) | −5.07862e6 | + | 1.53668e6i | −1.13131 | + | 0.342311i | ||||
\(459\) | 3.64403e6 | − | 3.86175e6i | 0.807327 | − | 0.855563i | ||||
\(460\) | −3.14064e6 | − | 4.71464e6i | −0.692027 | − | 1.03885i | ||||
\(461\) | 1.81893e6i | 0.398625i | 0.979936 | + | 0.199313i | \(0.0638709\pi\) | ||||
−0.979936 | + | 0.199313i | \(0.936129\pi\) | |||||||
\(462\) | −1.43393e6 | + | 909598.i | −0.312553 | + | 0.198264i | ||||
\(463\) | 4.06917e6i | 0.882171i | 0.897465 | + | 0.441086i | \(0.145406\pi\) | ||||
−0.897465 | + | 0.441086i | \(0.854594\pi\) | |||||||
\(464\) | 3.20574e6 | + | 1.33844e6i | 0.691246 | + | 0.288605i | ||||
\(465\) | −1.42308e6 | − | 5.11280e6i | −0.305209 | − | 1.09655i | ||||
\(466\) | 1.51686e6 | + | 5.01312e6i | 0.323580 | + | 1.06941i | ||||
\(467\) | 4.47865e6 | 0.950287 | 0.475143 | − | 0.879908i | \(-0.342396\pi\) | ||||
0.475143 | + | 0.879908i | \(0.342396\pi\) | |||||||
\(468\) | −1.40537e6 | + | 2.98346e6i | −0.296603 | + | 0.629660i | ||||
\(469\) | −1.96307e6 | −0.412102 | ||||||||
\(470\) | 2.83263e6 | + | 9.36164e6i | 0.591487 | + | 1.95482i | ||||
\(471\) | −1.93818e6 | − | 6.96345e6i | −0.402571 | − | 1.44635i | ||||
\(472\) | 905164. | − | 1.09821e6i | 0.187013 | − | 0.226898i | ||||
\(473\) | − | 6.08896e6i | − | 1.25138i | ||||||
\(474\) | −4.78461e6 | + | 3.03506e6i | −0.978139 | + | 0.620471i | ||||
\(475\) | − | 710486.i | − | 0.144485i | ||||||
\(476\) | 1.93447e6 | − | 1.28864e6i | 0.391331 | − | 0.260684i | ||||
\(477\) | −246814. | − | 409025.i | −0.0496677 | − | 0.0823102i | ||||
\(478\) | 3.35512e6 | − | 1.01519e6i | 0.671642 | − | 0.203225i | ||||
\(479\) | −4.95004e6 | −0.985757 | −0.492879 | − | 0.870098i | \(-0.664055\pi\) | ||||
−0.492879 | + | 0.870098i | \(0.664055\pi\) | |||||||
\(480\) | −1.11557e6 | − | 6.50768e6i | −0.221001 | − | 1.28921i | ||||
\(481\) | 167901. | 0.0330895 | ||||||||
\(482\) | 213001. | − | 64449.6i | 0.0417603 | − | 0.0126358i | ||||
\(483\) | −1.88414e6 | + | 524424.i | −0.367489 | + | 0.102286i | ||||
\(484\) | −611531. | + | 407369.i | −0.118660 | + | 0.0790450i | ||||
\(485\) | − | 1.63414e6i | − | 0.315453i | ||||||
\(486\) | −5.19024e6 | + | 417950.i | −0.996773 | + | 0.0802665i | ||||
\(487\) | − | 3.60548e6i | − | 0.688875i | −0.938809 | − | 0.344438i | \(-0.888070\pi\) | ||
0.938809 | − | 0.344438i | \(-0.111930\pi\) | |||||||
\(488\) | −1.07771e6 | + | 1.30756e6i | −0.204858 | + | 0.248548i | ||||
\(489\) | −5.54248e6 | + | 1.54267e6i | −1.04817 | + | 0.291744i | ||||
\(490\) | 1.69166e6 | + | 5.59079e6i | 0.318289 | + | 1.05192i | ||||
\(491\) | −2.76149e6 | −0.516939 | −0.258469 | − | 0.966019i | \(-0.583218\pi\) | ||||
−0.258469 | + | 0.966019i | \(0.583218\pi\) | |||||||
\(492\) | −1.88330e6 | + | 2.18361e6i | −0.350756 | + | 0.406689i | ||||
\(493\) | 4.75526e6 | 0.881164 | ||||||||
\(494\) | 222213. | + | 734396.i | 0.0409686 | + | 0.135398i | ||||
\(495\) | 3.41128e6 | + | 5.65323e6i | 0.625755 | + | 1.03701i | ||||
\(496\) | −4.39976e6 | − | 1.83696e6i | −0.803017 | − | 0.335270i | ||||
\(497\) | − | 1.05495e6i | − | 0.191576i | ||||||
\(498\) | 474358. | + | 747799.i | 0.0857102 | + | 0.135117i | ||||
\(499\) | 1.08070e7i | 1.94292i | 0.237211 | + | 0.971458i | \(0.423767\pi\) | ||||
−0.237211 | + | 0.971458i | \(0.576233\pi\) | |||||||
\(500\) | 1.17195e6 | + | 1.75930e6i | 0.209645 | + | 0.314713i | ||||
\(501\) | 74247.8 | + | 266755.i | 0.0132157 | + | 0.0474809i | ||||
\(502\) | −3.78879e6 | + | 1.14641e6i | −0.671029 | + | 0.203039i | ||||
\(503\) | 8.16383e6 | 1.43871 | 0.719356 | − | 0.694641i | \(-0.244437\pi\) | ||||
0.719356 | + | 0.694641i | \(0.244437\pi\) | |||||||
\(504\) | −2.25509e6 | − | 332530.i | −0.395447 | − | 0.0583116i | ||||
\(505\) | 3.54074e6 | 0.617825 | ||||||||
\(506\) | 4.87123e6 | − | 1.47393e6i | 0.845790 | − | 0.255918i | ||||
\(507\) | 800133. | + | 2.87470e6i | 0.138243 | + | 0.496675i | ||||
\(508\) | −422764. | − | 634642.i | −0.0726840 | − | 0.109111i | ||||
\(509\) | 2.33136e6i | 0.398855i | 0.979913 | + | 0.199428i | \(0.0639083\pi\) | ||||
−0.979913 | + | 0.199428i | \(0.936092\pi\) | |||||||
\(510\) | −4.84124e6 | − | 7.63194e6i | −0.824197 | − | 1.29930i | ||||
\(511\) | − | 3.21717e6i | − | 0.545032i | ||||||
\(512\) | −5.21344e6 | − | 2.82922e6i | −0.878919 | − | 0.476970i | ||||
\(513\) | −831429. | + | 881104.i | −0.139486 | + | 0.147820i | ||||
\(514\) | 1.24853e6 | + | 4.12629e6i | 0.208444 | + | 0.688893i | ||||
\(515\) | −1.11292e7 | −1.84904 | ||||||||
\(516\) | 5.33834e6 | − | 6.18960e6i | 0.882636 | − | 1.02338i | ||||
\(517\) | −8.78701e6 | −1.44582 | ||||||||
\(518\) | 33609.9 | + | 111078.i | 0.00550355 | + | 0.0181888i | ||||
\(519\) | 1.08226e7 | − | 3.01232e6i | 1.76365 | − | 0.490888i | ||||
\(520\) | 4.33186e6 | + | 3.57039e6i | 0.702532 | + | 0.579039i | ||||
\(521\) | 6.09574e6i | 0.983857i | 0.870636 | + | 0.491928i | \(0.163708\pi\) | ||||
−0.870636 | + | 0.491928i | \(0.836292\pi\) | |||||||
\(522\) | −3.46244e6 | − | 3.12390e6i | −0.556167 | − | 0.501789i | ||||
\(523\) | − | 1.98277e6i | − | 0.316970i | −0.987361 | − | 0.158485i | \(-0.949339\pi\) | ||
0.987361 | − | 0.158485i | \(-0.0506610\pi\) | |||||||
\(524\) | 9.23024e6 | − | 6.14868e6i | 1.46854 | − | 0.978259i | ||||
\(525\) | −1.72887e6 | + | 481209.i | −0.273757 | + | 0.0761965i | ||||
\(526\) | 7.56981e6 | − | 2.29046e6i | 1.19295 | − | 0.360960i | ||||
\(527\) | −6.52642e6 | −1.02364 | ||||||||
\(528\) | 5.88616e6 | + | 733929.i | 0.918856 | + | 0.114570i | ||||
\(529\) | −574761. | −0.0892993 | ||||||||
\(530\) | −778321. | + | 235503.i | −0.120356 | + | 0.0364173i | ||||
\(531\) | −1.63572e6 | + | 987031.i | −0.251752 | + | 0.151913i | ||||
\(532\) | −441373. | + | 294019.i | −0.0676124 | + | 0.0450397i | ||||
\(533\) | − | 2.45164e6i | − | 0.373800i | ||||||
\(534\) | −4.21753e6 | + | 2.67534e6i | −0.640037 | + | 0.406000i | ||||
\(535\) | − | 1.18000e7i | − | 1.78236i | ||||||
\(536\) | 5.29162e6 | + | 4.36144e6i | 0.795567 | + | 0.655719i | ||||
\(537\) | 3.41682e6 | + | 1.22759e7i | 0.511313 | + | 1.83703i | ||||
\(538\) | −1.66429e6 | − | 5.50034e6i | −0.247897 | − | 0.819283i | ||||
\(539\) | −5.24763e6 | −0.778021 | ||||||||
\(540\) | −1.48866e6 | + | 8.73741e6i | −0.219691 | + | 1.28943i | ||||
\(541\) | 3.04420e6 | 0.447178 | 0.223589 | − | 0.974684i | \(-0.428223\pi\) | ||||
0.223589 | + | 0.974684i | \(0.428223\pi\) | |||||||
\(542\) | −1.74511e6 | − | 5.76747e6i | −0.255168 | − | 0.843310i | ||||
\(543\) | −1.62757e6 | − | 5.84749e6i | −0.236887 | − | 0.851079i | ||||
\(544\) | −8.07754e6 | − | 824262.i | −1.17026 | − | 0.119417i | ||||
\(545\) | 90646.8i | 0.0130726i | ||||||||
\(546\) | 1.63655e6 | − | 1.03813e6i | 0.234935 | − | 0.149028i | ||||
\(547\) | 6.16452e6i | 0.880909i | 0.897775 | + | 0.440454i | \(0.145183\pi\) | ||||
−0.897775 | + | 0.440454i | \(0.854817\pi\) | |||||||
\(548\) | −3.23428e6 | − | 4.85521e6i | −0.460072 | − | 0.690648i | ||||
\(549\) | 1.94753e6 | − | 1.17518e6i | 0.275774 | − | 0.166408i | ||||
\(550\) | 4.46982e6 | − | 1.35247e6i | 0.630062 | − | 0.190643i | ||||
\(551\) | −1.08497e6 | −0.152244 | ||||||||
\(552\) | 6.24397e6 | + | 2.77243e6i | 0.872194 | + | 0.387270i | ||||
\(553\) | 3.32971e6 | 0.463013 | ||||||||
\(554\) | 5.95445e6 | − | 1.80169e6i | 0.824266 | − | 0.249405i | ||||
\(555\) | 434720. | − | 120999.i | 0.0599070 | − | 0.0166743i | ||||
\(556\) | −1.14371e6 | − | 1.71690e6i | −0.156902 | − | 0.235536i | ||||
\(557\) | 4.80670e6i | 0.656461i | 0.944598 | + | 0.328230i | \(0.106452\pi\) | ||||
−0.944598 | + | 0.328230i | \(0.893548\pi\) | |||||||
\(558\) | 4.75207e6 | + | 4.28744e6i | 0.646096 | + | 0.582925i | ||||
\(559\) | 6.94936e6i | 0.940623i | ||||||||
\(560\) | −1.49493e6 | + | 3.58054e6i | −0.201442 | + | 0.482480i | ||||
\(561\) | 7.82227e6 | − | 2.17723e6i | 1.04936 | − | 0.292076i | ||||
\(562\) | −2.83481e6 | − | 9.36884e6i | −0.378603 | − | 1.25125i | ||||
\(563\) | 8.63483e6 | 1.14811 | 0.574054 | − | 0.818818i | \(-0.305370\pi\) | ||||
0.574054 | + | 0.818818i | \(0.305370\pi\) | |||||||
\(564\) | −8.93224e6 | − | 7.70378e6i | −1.18239 | − | 1.01978i | ||||
\(565\) | −1.14586e7 | −1.51011 | ||||||||
\(566\) | 1.28940e6 | + | 4.26135e6i | 0.169178 | + | 0.559122i | ||||
\(567\) | 2.70717e6 | + | 1.42640e6i | 0.353638 | + | 0.186331i | ||||
\(568\) | −2.34382e6 | + | 2.84370e6i | −0.304827 | + | 0.369839i | ||||
\(569\) | − | 1.07164e7i | − | 1.38761i | −0.720161 | − | 0.693807i | \(-0.755932\pi\) | ||
0.720161 | − | 0.693807i | \(-0.244068\pi\) | |||||||
\(570\) | 1.10459e6 | + | 1.74132e6i | 0.142401 | + | 0.224487i | ||||
\(571\) | − | 5.59442e6i | − | 0.718066i | −0.933325 | − | 0.359033i | \(-0.883107\pi\) | ||
0.933325 | − | 0.359033i | \(-0.116893\pi\) | |||||||
\(572\) | −4.19724e6 | + | 2.79597e6i | −0.536381 | + | 0.357308i | ||||
\(573\) | −1.99405e6 | − | 7.16416e6i | −0.253717 | − | 0.911547i | ||||
\(574\) | 1.62194e6 | − | 490763.i | 0.205473 | − | 0.0621716i | ||||
\(575\) | 5.37856e6 | 0.678416 | ||||||||
\(576\) | 5.33999e6 | + | 5.90660e6i | 0.670632 | + | 0.741790i | ||||
\(577\) | −5.26236e6 | −0.658023 | −0.329012 | − | 0.944326i | \(-0.606716\pi\) | ||||
−0.329012 | + | 0.944326i | \(0.606716\pi\) | |||||||
\(578\) | −2.95028e6 | + | 892691.i | −0.367319 | + | 0.111143i | ||||
\(579\) | 3.16577e6 | + | 1.13739e7i | 0.392449 | + | 1.40998i | ||||
\(580\) | −6.60636e6 | + | 4.40080e6i | −0.815440 | + | 0.543202i | ||||
\(581\) | − | 520409.i | − | 0.0639594i | ||||||
\(582\) | 1.05565e6 | + | 1.66417e6i | 0.129185 | + | 0.203652i | ||||
\(583\) | − | 730547.i | − | 0.0890178i | ||||||
\(584\) | −7.14772e6 | + | 8.67214e6i | −0.867232 | + | 1.05219i | ||||
\(585\) | −3.89331e6 | − | 6.45206e6i | −0.470359 | − | 0.779487i | ||||
\(586\) | 1.01407e6 | + | 3.35143e6i | 0.121990 | + | 0.403168i | ||||
\(587\) | 1.09294e6 | 0.130919 | 0.0654594 | − | 0.997855i | \(-0.479149\pi\) | ||||
0.0654594 | + | 0.997855i | \(0.479149\pi\) | |||||||
\(588\) | −5.33436e6 | − | 4.60072e6i | −0.636266 | − | 0.548760i | ||||
\(589\) | 1.48908e6 | 0.176860 | ||||||||
\(590\) | 941798. | + | 3.11257e6i | 0.111385 | + | 0.368120i | ||||
\(591\) | −1.42488e7 | + | 3.96597e6i | −1.67807 | + | 0.467068i | ||||
\(592\) | 156189. | − | 374093.i | 0.0183166 | − | 0.0438707i | ||||
\(593\) | 2.21385e6i | 0.258530i | 0.991610 | + | 0.129265i | \(0.0412618\pi\) | ||||
−0.991610 | + | 0.129265i | \(0.958738\pi\) | |||||||
\(594\) | −7.12591e6 | − | 3.55344e6i | −0.828656 | − | 0.413221i | ||||
\(595\) | 5.31123e6i | 0.615039i | ||||||||
\(596\) | −454842. | − | 682797.i | −0.0524500 | − | 0.0787365i | ||||
\(597\) | 3.32247e6 | − | 924766.i | 0.381527 | − | 0.106193i | ||||
\(598\) | −5.55956e6 | + | 1.68221e6i | −0.635752 | + | 0.192365i | ||||
\(599\) | −674331. | −0.0767902 | −0.0383951 | − | 0.999263i | \(-0.512225\pi\) | ||||
−0.0383951 | + | 0.999263i | \(0.512225\pi\) | |||||||
\(600\) | 5.72943e6 | + | 2.54397e6i | 0.649731 | + | 0.288492i | ||||
\(601\) | 9.18665e6 | 1.03746 | 0.518730 | − | 0.854938i | \(-0.326405\pi\) | ||||
0.518730 | + | 0.854938i | \(0.326405\pi\) | |||||||
\(602\) | −4.59749e6 | + | 1.39110e6i | −0.517047 | + | 0.156447i | ||||
\(603\) | −4.75590e6 | − | 7.88156e6i | −0.532647 | − | 0.882712i | ||||
\(604\) | 6.98067e6 | + | 1.04792e7i | 0.778582 | + | 1.16879i | ||||
\(605\) | − | 1.67901e6i | − | 0.186493i | ||||||
\(606\) | −3.60579e6 | + | 2.28729e6i | −0.398859 | + | 0.253012i | ||||
\(607\) | − | 7.32920e6i | − | 0.807393i | −0.914893 | − | 0.403696i | \(-0.867725\pi\) | ||
0.914893 | − | 0.403696i | \(-0.132275\pi\) | |||||||
\(608\) | 1.84299e6 | + | 188065.i | 0.202192 | + | 0.0206324i | ||||
\(609\) | 734845. | + | 2.64013e6i | 0.0802884 | + | 0.288458i | ||||
\(610\) | −1.12133e6 | − | 3.70590e6i | −0.122013 | − | 0.403245i | ||||
\(611\) | 1.00287e7 | 1.08678 | ||||||||
\(612\) | 9.86038e6 | + | 4.64476e6i | 1.06418 | + | 0.501285i | ||||
\(613\) | 1.45783e7 | 1.56696 | 0.783478 | − | 0.621420i | \(-0.213444\pi\) | ||||
0.783478 | + | 0.621420i | \(0.213444\pi\) | |||||||
\(614\) | −1.21923e6 | − | 4.02948e6i | −0.130517 | − | 0.431348i | ||||
\(615\) | −1.76679e6 | − | 6.34767e6i | −0.188364 | − | 0.676747i | ||||
\(616\) | −2.68993e6 | − | 2.21708e6i | −0.285620 | − | 0.235413i | ||||
\(617\) | − | 475062.i | − | 0.0502386i | −0.999684 | − | 0.0251193i | \(-0.992003\pi\) | ||
0.999684 | − | 0.0251193i | \(-0.00799656\pi\) | |||||||
\(618\) | 1.13337e7 | − | 7.18941e6i | 1.19372 | − | 0.757220i | ||||
\(619\) | 737236.i | 0.0773357i | 0.999252 | + | 0.0386678i | \(0.0123114\pi\) | ||||
−0.999252 | + | 0.0386678i | \(0.987689\pi\) | |||||||
\(620\) | 9.06698e6 | − | 6.03993e6i | 0.947291 | − | 0.631034i | ||||
\(621\) | −6.67018e6 | − | 6.29412e6i | −0.694078 | − | 0.654947i | ||||
\(622\) | −923601. | + | 279462.i | −0.0957212 | + | 0.0289632i | ||||
\(623\) | 2.93507e6 | 0.302969 | ||||||||
\(624\) | −6.71790e6 | − | 837637.i | −0.690673 | − | 0.0861180i | ||||
\(625\) | −1.17727e7 | −1.20552 | ||||||||
\(626\) | −4.18383e6 | + | 1.26594e6i | −0.426715 | + | 0.129115i | ||||
\(627\) | −1.78475e6 | + | 496760.i | −0.181304 | + | 0.0504636i | ||||
\(628\) | 1.23489e7 | − | 8.22616e6i | 1.24948 | − | 0.832335i | ||||
\(629\) | − | 554914.i | − | 0.0559241i | ||||||
\(630\) | 3.48914e6 | − | 3.86726e6i | 0.350241 | − | 0.388196i | ||||
\(631\) | − | 153956.i | − | 0.0153930i | −0.999970 | − | 0.00769648i | \(-0.997550\pi\) | ||
0.999970 | − | 0.00769648i | \(-0.00244989\pi\) | |||||||
\(632\) | −8.97550e6 | − | 7.39775e6i | −0.893852 | − | 0.736728i | ||||
\(633\) | −1.00720e7 | + | 2.80342e6i | −0.999097 | + | 0.278085i | ||||
\(634\) | 2.78423e6 | + | 9.20167e6i | 0.275094 | + | 0.909166i | ||||
\(635\) | 1.74246e6 | 0.171486 | ||||||||
\(636\) | 640488. | − | 742621.i | 0.0627868 | − | 0.0727988i | ||||
\(637\) | 5.98914e6 | 0.584812 | ||||||||
\(638\) | −2.06534e6 | − | 6.82578e6i | −0.200881 | − | 0.663897i | ||||
\(639\) | 4.23553e6 | − | 2.55581e6i | 0.410351 | − | 0.247614i | ||||
\(640\) | 1.19847e7 | − | 6.33030e6i | 1.15659 | − | 0.610906i | ||||
\(641\) | 1.07313e7i | 1.03159i | 0.856713 | + | 0.515794i | \(0.172503\pi\) | ||||
−0.856713 | + | 0.515794i | \(0.827497\pi\) | |||||||
\(642\) | 7.62271e6 | + | 1.20168e7i | 0.729914 | + | 1.15067i | ||||
\(643\) | − | 2.61064e6i | − | 0.249011i | −0.992219 | − | 0.124506i | \(-0.960266\pi\) | ||
0.992219 | − | 0.124506i | \(-0.0397345\pi\) | |||||||
\(644\) | −2.22579e6 | − | 3.34130e6i | −0.211481 | − | 0.317469i | ||||
\(645\) | 5.00809e6 | + | 1.79929e7i | 0.473994 | + | 1.70295i | ||||
\(646\) | 2.42719e6 | − | 734415.i | 0.228835 | − | 0.0692405i | ||||
\(647\) | 2.10997e6 | 0.198160 | 0.0990800 | − | 0.995079i | \(-0.468410\pi\) | ||||
0.0990800 | + | 0.995079i | \(0.468410\pi\) | |||||||
\(648\) | −4.12830e6 | − | 9.85962e6i | −0.386219 | − | 0.922407i | ||||
\(649\) | −2.92152e6 | −0.272268 | ||||||||
\(650\) | −5.10142e6 | + | 1.54358e6i | −0.473596 | + | 0.143300i | ||||
\(651\) | −1.00855e6 | − | 3.62348e6i | −0.0932705 | − | 0.335100i | ||||
\(652\) | −6.54752e6 | − | 9.82896e6i | −0.603195 | − | 0.905500i | ||||
\(653\) | 1.32077e7i | 1.21211i | 0.795421 | + | 0.606057i | \(0.207250\pi\) | ||||
−0.795421 | + | 0.606057i | \(0.792750\pi\) | |||||||
\(654\) | −58557.2 | − | 92312.3i | −0.00535348 | − | 0.00843947i | ||||
\(655\) | 2.53423e7i | 2.30804i | ||||||||
\(656\) | −5.46240e6 | − | 2.28063e6i | −0.495592 | − | 0.206916i | ||||
\(657\) | 1.29167e7 | − | 7.79418e6i | 1.16745 | − | 0.704461i | ||||
\(658\) | 2.00751e6 | + | 6.63467e6i | 0.180756 | + | 0.597385i | ||||
\(659\) | −1.28753e7 | −1.15490 | −0.577449 | − | 0.816427i | \(-0.695952\pi\) | ||||
−0.577449 | + | 0.816427i | \(0.695952\pi\) | |||||||
\(660\) | −8.85234e6 | + | 1.02639e7i | −0.791040 | + | 0.917180i | ||||
\(661\) | −3.96909e6 | −0.353335 | −0.176668 | − | 0.984271i | \(-0.556532\pi\) | ||||
−0.176668 | + | 0.984271i | \(0.556532\pi\) | |||||||
\(662\) | −37961.2 | − | 125459.i | −0.00336663 | − | 0.0111264i | ||||
\(663\) | −8.92760e6 | + | 2.48488e6i | −0.788771 | + | 0.219544i | ||||
\(664\) | −1.15621e6 | + | 1.40280e6i | −0.101770 | + | 0.123474i | ||||
\(665\) | − | 1.21182e6i | − | 0.106264i | ||||||
\(666\) | −364543. | + | 404048.i | −0.0318466 | + | 0.0352978i | ||||
\(667\) | − | 8.21350e6i | − | 0.714848i | ||||||
\(668\) | −473060. | + | 315127.i | −0.0410181 | + | 0.0273240i | ||||
\(669\) | −1.82294e7 | + | 5.07391e6i | −1.57473 | + | 0.438306i | ||||
\(670\) | −1.49976e7 | + | 4.53795e6i | −1.29073 | + | 0.390547i | ||||
\(671\) | 3.47843e6 | 0.298247 | ||||||||
\(672\) | −790616. | − | 4.61204e6i | −0.0675371 | − | 0.393976i | ||||
\(673\) | −8.93046e6 | −0.760040 | −0.380020 | − | 0.924978i | \(-0.624083\pi\) | ||||
−0.380020 | + | 0.924978i | \(0.624083\pi\) | |||||||
\(674\) | 8.40965e6 | − | 2.54458e6i | 0.713064 | − | 0.215758i | ||||
\(675\) | −6.12052e6 | − | 5.77545e6i | −0.517046 | − | 0.487895i | ||||
\(676\) | −5.09795e6 | + | 3.39598e6i | −0.429071 | + | 0.285824i | ||||
\(677\) | − | 9.17967e6i | − | 0.769760i | −0.922967 | − | 0.384880i | \(-0.874243\pi\) | ||
0.922967 | − | 0.384880i | \(-0.125757\pi\) | |||||||
\(678\) | 1.16691e7 | − | 7.40216e6i | 0.974907 | − | 0.618421i | ||||
\(679\) | − | 1.15813e6i | − | 0.0964012i | ||||||
\(680\) | 1.18002e7 | − | 1.43168e7i | 0.978625 | − | 1.18734i | ||||
\(681\) | −3.34494e6 | − | 1.20176e7i | −0.276389 | − | 0.993001i | ||||
\(682\) | 2.83460e6 | + | 9.36813e6i | 0.233362 | + | 0.771245i | ||||
\(683\) | −498838. | −0.0409173 | −0.0204587 | − | 0.999791i | \(-0.506513\pi\) | ||||
−0.0204587 | + | 0.999791i | \(0.506513\pi\) | |||||||
\(684\) | −2.24976e6 | − | 1.05976e6i | −0.183864 | − | 0.0866097i | ||||
\(685\) | 1.33304e7 | 1.08546 | ||||||||
\(686\) | 2.62576e6 | + | 8.67795e6i | 0.213032 | + | 0.704056i | ||||
\(687\) | 3.92071e6 | + | 1.40862e7i | 0.316937 | + | 1.13868i | ||||
\(688\) | 1.54836e7 | + | 6.46461e6i | 1.24710 | + | 0.520680i | ||||
\(689\) | 833777.i | 0.0669117i | ||||||||
\(690\) | −1.31822e7 | + | 8.36200e6i | −1.05406 | + | 0.668633i | ||||
\(691\) | − | 1.14456e7i | − | 0.911894i | −0.890007 | − | 0.455947i | \(-0.849301\pi\) | ||
0.890007 | − | 0.455947i | \(-0.150699\pi\) | |||||||
\(692\) | 1.27851e7 | + | 1.91926e7i | 1.01493 | + | 1.52359i | ||||
\(693\) | 2.41760e6 | + | 4.00649e6i | 0.191228 | + | 0.316906i | ||||
\(694\) | −5.28972e6 | + | 1.60056e6i | −0.416902 | + | 0.126146i | ||||
\(695\) | 4.71388e6 | 0.370183 | ||||||||
\(696\) | 3.88485e6 | − | 8.74932e6i | 0.303984 | − | 0.684622i | ||||
\(697\) | −8.10271e6 | −0.631754 | ||||||||
\(698\) | −5.75986e6 | + | 1.74281e6i | −0.447480 | + | 0.135398i | ||||
\(699\) | 1.39045e7 | − | 3.87014e6i | 1.07637 | − | 0.299594i | ||||
\(700\) | −2.04238e6 | − | 3.06596e6i | −0.157540 | − | 0.236495i | ||||
\(701\) | − | 1.50903e7i | − | 1.15985i | −0.814670 | − | 0.579925i | \(-0.803082\pi\) | ||
0.814670 | − | 0.579925i | \(-0.196918\pi\) | |||||||
\(702\) | 8.13284e6 | + | 4.05555e6i | 0.622873 | + | 0.310604i | ||||
\(703\) | 126610.i | 0.00966231i | ||||||||
\(704\) | 2.32513e6 | + | 1.19526e7i | 0.176814 | + | 0.908933i | ||||
\(705\) | 2.59657e7 | − | 7.22720e6i | 1.96755 | − | 0.547643i | ||||
\(706\) | −5.83260e6 | − | 1.92763e7i | −0.440403 | − | 1.45550i | ||||
\(707\) | 2.50935e6 | 0.188805 | ||||||||
\(708\) | −2.96980e6 | − | 2.56136e6i | −0.222661 | − | 0.192038i | ||||
\(709\) | 9.48825e6 | 0.708876 | 0.354438 | − | 0.935080i | \(-0.384672\pi\) | ||||
0.354438 | + | 0.935080i | \(0.384672\pi\) | |||||||
\(710\) | −2.43868e6 | − | 8.05966e6i | −0.181555 | − | 0.600027i | ||||
\(711\) | 8.06683e6 | + | 1.33685e7i | 0.598451 | + | 0.991764i | ||||
\(712\) | −7.91171e6 | − | 6.52096e6i | −0.584885 | − | 0.482072i | ||||
\(713\) | 1.12727e7i | 0.830434i | ||||||||
\(714\) | −3.43102e6 | − | 5.40882e6i | −0.251871 | − | 0.397061i | ||||
\(715\) | − | 1.15238e7i | − | 0.843009i | ||||||
\(716\) | −2.17699e7 | + | 1.45019e7i | −1.58699 | + | 1.05716i | ||||
\(717\) | −2.59016e6 | − | 9.30583e6i | −0.188160 | − | 0.676017i | ||||
\(718\) | −7.45950e6 | + | 2.25708e6i | −0.540006 | + | 0.163394i | ||||
\(719\) | −2.38849e7 | −1.72306 | −0.861532 | − | 0.507703i | \(-0.830495\pi\) | ||||
−0.861532 | + | 0.507703i | \(0.830495\pi\) | |||||||
\(720\) | −1.79973e7 | + | 2.67253e6i | −1.29383 | + | 0.192128i | ||||
\(721\) | −7.88737e6 | −0.565059 | ||||||||
\(722\) | 1.28529e7 | − | 3.88900e6i | 0.917607 | − | 0.277648i | ||||
\(723\) | −164437. | − | 590785.i | −0.0116991 | − | 0.0420323i | ||||
\(724\) | 1.03699e7 | − | 6.90784e6i | 0.735236 | − | 0.489774i | ||||
\(725\) | − | 7.53666e6i | − | 0.532518i | ||||||
\(726\) | 1.08463e6 | + | 1.70985e6i | 0.0763728 | + | 0.120398i | ||||
\(727\) | − | 8.95331e6i | − | 0.628272i | −0.949378 | − | 0.314136i | \(-0.898285\pi\) | ||
0.949378 | − | 0.314136i | \(-0.101715\pi\) | |||||||
\(728\) | 3.07002e6 | + | 2.53036e6i | 0.214691 | + | 0.176952i | ||||
\(729\) | 831736. | + | 1.43248e7i | 0.0579651 | + | 0.998319i | ||||
\(730\) | −7.43700e6 | − | 2.45787e7i | −0.516524 | − | 1.70707i | ||||
\(731\) | 2.29677e7 | 1.58973 | ||||||||
\(732\) | 3.53591e6 | + | 3.04962e6i | 0.243907 | + | 0.210362i | ||||
\(733\) | −5.08443e6 | −0.349529 | −0.174764 | − | 0.984610i | \(-0.555916\pi\) | ||||
−0.174764 | + | 0.984610i | \(0.555916\pi\) | |||||||
\(734\) | 5.34479e6 | + | 1.76641e7i | 0.366177 | + | 1.21019i | ||||
\(735\) | 1.55068e7 | − | 4.31610e6i | 1.05877 | − | 0.294696i | ||||
\(736\) | −1.42370e6 | + | 1.39519e7i | −0.0968779 | + | 0.949376i | ||||
\(737\) | − | 1.40770e7i | − | 0.954646i | ||||||
\(738\) | 5.89980e6 | + | 5.32296e6i | 0.398746 | + | 0.359760i | ||||
\(739\) | 5.96874e6i | 0.402042i | 0.979587 | + | 0.201021i | \(0.0644260\pi\) | ||||
−0.979587 | + | 0.201021i | \(0.935574\pi\) | |||||||
\(740\) | 513550. | + | 770927.i | 0.0344749 | + | 0.0517528i | ||||
\(741\) | 2.03694e6 | − | 566955.i | 0.136280 | − | 0.0379318i | ||||
\(742\) | −551602. | + | 166903.i | −0.0367804 | + | 0.0111290i | ||||
\(743\) | −1.80015e7 | −1.19629 | −0.598145 | − | 0.801388i | \(-0.704095\pi\) | ||||
−0.598145 | + | 0.801388i | \(0.704095\pi\) | |||||||
\(744\) | −5.33182e6 | + | 1.20081e7i | −0.353137 | + | 0.795322i | ||||
\(745\) | 1.87467e6 | 0.123747 | ||||||||
\(746\) | 2.51521e6 | − | 761048.i | 0.165473 | − | 0.0500686i | ||||
\(747\) | 2.08940e6 | − | 1.26079e6i | 0.137000 | − | 0.0826684i | ||||
\(748\) | 9.24072e6 | + | 1.38719e7i | 0.603882 | + | 0.906531i | ||||
\(749\) | − | 8.36273e6i | − | 0.544683i | ||||||
\(750\) | 4.91904e6 | − | 3.12034e6i | 0.319321 | − | 0.202558i | ||||
\(751\) | 2.58444e7i | 1.67212i | 0.548640 | + | 0.836059i | \(0.315146\pi\) | ||||
−0.548640 | + | 0.836059i | \(0.684854\pi\) | |||||||
\(752\) | 9.32911e6 | − | 2.23444e7i | 0.601583 | − | 1.44087i | ||||
\(753\) | 2.92496e6 | + | 1.05087e7i | 0.187989 | + | 0.675400i | ||||
\(754\) | 2.35718e6 | + | 7.79029e6i | 0.150995 | + | 0.499029i | ||||
\(755\) | −2.87714e7 | −1.83693 | ||||||||
\(756\) | −1.05503e6 | + | 6.19227e6i | −0.0671366 | + | 0.394045i | ||||
\(757\) | −1.03124e7 | −0.654064 | −0.327032 | − | 0.945013i | \(-0.606049\pi\) | ||||
−0.327032 | + | 0.945013i | \(0.606049\pi\) | |||||||
\(758\) | −4.61643e6 | − | 1.52569e7i | −0.291832 | − | 0.964483i | ||||
\(759\) | −3.76060e6 | − | 1.35110e7i | −0.236948 | − | 0.851300i | ||||
\(760\) | −2.69235e6 | + | 3.26656e6i | −0.169082 | + | 0.205143i | ||||
\(761\) | − | 1.62986e7i | − | 1.02021i | −0.860112 | − | 0.510104i | \(-0.829607\pi\) | ||
0.860112 | − | 0.510104i | \(-0.170393\pi\) | |||||||
\(762\) | −1.77447e6 | + | 1.12562e6i | −0.110709 | + | 0.0702268i | ||||
\(763\) | 64242.1i | 0.00399492i | ||||||||
\(764\) | 1.27048e7 | − | 8.46327e6i | 0.787473 | − | 0.524572i | ||||
\(765\) | −2.13241e7 | + | 1.28674e7i | −1.31740 | + | 0.794947i | ||||
\(766\) | 9.90541e6 | − | 2.99717e6i | 0.609959 | − | 0.184561i | ||||
\(767\) | 3.33434e6 | 0.204655 | ||||||||
\(768\) | −8.11560e6 | + | 1.41887e7i | −0.496498 | + | 0.868038i | ||||
\(769\) | 7.98701e6 | 0.487044 | 0.243522 | − | 0.969895i | \(-0.421697\pi\) | ||||
0.243522 | + | 0.969895i | \(0.421697\pi\) | |||||||
\(770\) | 7.62383e6 | − | 2.30681e6i | 0.463390 | − | 0.140212i | ||||
\(771\) | 1.14448e7 | − | 3.18550e6i | 0.693380 | − | 0.192993i | ||||
\(772\) | −2.01703e7 | + | 1.34364e7i | −1.21806 | + | 0.811406i | ||||
\(773\) | 3.08377e7i | 1.85624i | 0.372283 | + | 0.928119i | \(0.378575\pi\) | ||||
−0.372283 | + | 0.928119i | \(0.621425\pi\) | |||||||
\(774\) | −1.67234e7 | − | 1.50883e7i | −1.00340 | − | 0.905292i | ||||
\(775\) | 1.03438e7i | 0.618622i | ||||||||
\(776\) | −2.57306e6 | + | 3.12183e6i | −0.153390 | + | 0.186104i | ||||
\(777\) | 308090. | − | 85752.6i | 0.0183073 | − | 0.00509559i | ||||
\(778\) | 6611.33 | + | 21849.9i | 0.000391597 | + | 0.00129420i | ||||
\(779\) | 1.84873e6 | 0.109152 | ||||||||
\(780\) | 1.01032e7 | − | 1.17143e7i | 0.594598 | − | 0.689413i | ||||
\(781\) | 7.56495e6 | 0.443791 | ||||||||
\(782\) | 5.55970e6 | + | 1.83744e7i | 0.325113 | + | 1.07448i | ||||
\(783\) | −8.81959e6 | + | 9.34654e6i | −0.514096 | + | 0.544812i | ||||
\(784\) | 5.57137e6 | − | 1.33442e7i | 0.323722 | − | 0.775356i | ||||
\(785\) | 3.39048e7i | 1.96375i | ||||||||
\(786\) | −1.63710e7 | − | 2.58079e7i | −0.945188 | − | 1.49004i | ||||
\(787\) | − | 2.96941e6i | − | 0.170897i | −0.996343 | − | 0.0854483i | \(-0.972768\pi\) | ||
0.996343 | − | 0.0854483i | \(-0.0272322\pi\) | |||||||
\(788\) | −1.68326e7 | − | 2.52687e7i | −0.965686 | − | 1.44966i | ||||
\(789\) | −5.84391e6 | − | 2.09958e7i | −0.334203 | − | 1.20072i | ||||
\(790\) | 2.54385e7 | − | 7.69715e6i | 1.45019 | − | 0.438796i | ||||
\(791\) | −8.12078e6 | −0.461484 | ||||||||
\(792\) | 2.38455e6 | − | 1.61711e7i | 0.135080 | − | 0.916065i | ||||
\(793\) | −3.96994e6 | −0.224182 | ||||||||
\(794\) | −1.28457e7 | + | 3.88685e6i | −0.723115 | + | 0.218799i | ||||
\(795\) | 600865. | + | 2.15877e6i | 0.0337178 | + | 0.121140i | ||||
\(796\) | 3.92495e6 | + | 5.89203e6i | 0.219559 | + | 0.329596i | ||||
\(797\) | 6.95811e6i | 0.388012i | 0.981000 | + | 0.194006i | \(0.0621482\pi\) | ||||
−0.981000 | + | 0.194006i | \(0.937852\pi\) | |||||||
\(798\) | 782830. | + | 1.23409e6i | 0.0435171 | + | 0.0686023i | ||||
\(799\) | − | 3.31448e7i | − | 1.83674i | ||||||
\(800\) | −1.30638e6 | + | 1.28022e7i | −0.0721680 | + | 0.707227i | ||||
\(801\) | 7.11074e6 | + | 1.17840e7i | 0.391592 | + | 0.648953i | ||||
\(802\) | 6.64860e6 | + | 2.19731e7i | 0.365001 | + | 1.20630i | ||||
\(803\) | 2.30701e7 | 1.26258 | ||||||||
\(804\) | 1.23417e7 | − | 1.43097e7i | 0.673339 | − | 0.780710i | ||||
\(805\) | 9.17380e6 | 0.498953 | ||||||||
\(806\) | −3.23514e6 | − | 1.06919e7i | −0.175410 | − | 0.579718i | ||||
\(807\) | −1.52559e7 | + | 4.24627e6i | −0.824619 | + | 0.229522i | ||||
\(808\) | −6.76415e6 | − | 5.57512e6i | −0.364489 | − | 0.300418i | ||||
\(809\) | − | 6.18442e6i | − | 0.332221i | −0.986107 | − | 0.166111i | \(-0.946879\pi\) | ||
0.986107 | − | 0.166111i | \(-0.0531209\pi\) | |||||||
\(810\) | 2.39798e7 | + | 4.63946e6i | 1.28420 | + | 0.248459i | ||||
\(811\) | − | 381738.i | − | 0.0203804i | −0.999948 | − | 0.0101902i | \(-0.996756\pi\) | ||
0.999948 | − | 0.0101902i | \(-0.00324370\pi\) | |||||||
\(812\) | −4.68198e6 | + | 3.11888e6i | −0.249195 | + | 0.166000i | ||||
\(813\) | −1.59968e7 | + | 4.45250e6i | −0.848803 | + | 0.236253i | ||||
\(814\) | −796533. | + | 241014.i | −0.0421350 | + | 0.0127491i | ||||
\(815\) | 2.69861e7 | 1.42314 | ||||||||
\(816\) | −2.76840e6 | + | 2.22027e7i | −0.145547 | + | 1.16730i | ||||
\(817\) | −5.24036e6 | −0.274667 | ||||||||
\(818\) | 1.99537e7 | − | 6.03758e6i | 1.04266 | − | 0.315486i | ||||
\(819\) | −2.75922e6 | − | 4.57263e6i | −0.143740 | − | 0.238208i | ||||
\(820\) | 1.12569e7 | − | 7.49872e6i | 0.584633 | − | 0.389451i | ||||
\(821\) | − | 7.63930e6i | − | 0.395545i | −0.980248 | − | 0.197772i | \(-0.936629\pi\) | ||
0.980248 | − | 0.197772i | \(-0.0633707\pi\) | |||||||
\(822\) | −1.35753e7 | + | 8.61133e6i | −0.700760 | + | 0.444519i | ||||
\(823\) | 1.36924e7i | 0.704661i | 0.935876 | + | 0.352330i | \(0.114611\pi\) | ||||
−0.935876 | + | 0.352330i | \(0.885389\pi\) | |||||||
\(824\) | 2.12610e7 | + | 1.75237e7i | 1.09085 | + | 0.899099i | ||||
\(825\) | −3.45071e6 | − | 1.23976e7i | −0.176512 | − | 0.634166i | ||||
\(826\) | 667460. | + | 2.20590e6i | 0.0340388 | + | 0.112496i | ||||
\(827\) | −1.85056e7 | −0.940891 | −0.470445 | − | 0.882429i | \(-0.655907\pi\) | ||||
−0.470445 | + | 0.882429i | \(0.655907\pi\) | |||||||
\(828\) | 8.02264e6 | − | 1.70313e7i | 0.406669 | − | 0.863320i | ||||
\(829\) | 3.00466e7 | 1.51848 | 0.759241 | − | 0.650810i | \(-0.225571\pi\) | ||||
0.759241 | + | 0.650810i | \(0.225571\pi\) | |||||||
\(830\) | −1.20301e6 | − | 3.97585e6i | −0.0606140 | − | 0.200325i | ||||
\(831\) | −4.59685e6 | − | 1.65154e7i | −0.230918 | − | 0.829635i | ||||
\(832\) | −2.65368e6 | − | 1.36416e7i | −0.132905 | − | 0.683214i | ||||
\(833\) | − | 1.97942e7i | − | 0.988382i | ||||||
\(834\) | −4.80049e6 | + | 3.04514e6i | −0.238985 | + | 0.151597i | ||||
\(835\) | − | 1.29882e6i | − | 0.0644664i | ||||||
\(836\) | −2.10838e6 | − | 3.16505e6i | −0.104336 | − | 0.156626i | ||||
\(837\) | 1.21046e7 | − | 1.28278e7i | 0.597222 | − | 0.632904i | ||||
\(838\) | −2.16450e7 | + | 6.54933e6i | −1.06475 | + | 0.322171i | ||||
\(839\) | 2.67597e7 | 1.31243 | 0.656215 | − | 0.754574i | \(-0.272157\pi\) | ||||
0.656215 | + | 0.754574i | \(0.272157\pi\) | |||||||
\(840\) | 9.77227e6 | + | 4.33906e6i | 0.477856 | + | 0.212177i | ||||
\(841\) | 9.00205e6 | 0.438886 | ||||||||
\(842\) | −3.77590e7 | + | 1.14251e7i | −1.83544 | + | 0.555366i | ||||
\(843\) | −2.59857e7 | + | 7.23276e6i | −1.25940 | + | 0.350538i | ||||
\(844\) | −1.18984e7 | − | 1.78616e7i | −0.574955 | − | 0.863107i | ||||
\(845\) | − | 1.39968e7i | − | 0.674353i | ||||||
\(846\) | −2.17740e7 | + | 2.41337e7i | −1.04596 | + | 1.15930i | ||||
\(847\) | − | 1.18992e6i | − | 0.0569916i | ||||||
\(848\) | 1.85770e6 | + | 775616.i | 0.0887129 | + | 0.0370388i | ||||
\(849\) | 1.18194e7 | − | 3.28977e6i | 0.562764 | − | 0.156638i | ||||
\(850\) | 5.10155e6 | + | 1.68603e7i | 0.242189 | + | 0.800418i | ||||
\(851\) | −958472. | −0.0453686 | ||||||||
\(852\) | 7.68998e6 | + | 6.63237e6i | 0.362933 | + | 0.313018i | ||||
\(853\) | −2.58364e7 | −1.21579 | −0.607896 | − | 0.794016i | \(-0.707986\pi\) | ||||
−0.607896 | + | 0.794016i | \(0.707986\pi\) | |||||||
\(854\) | −794692. | − | 2.62640e6i | −0.0372867 | − | 0.123230i | ||||
\(855\) | 4.86536e6 | − | 2.93586e6i | 0.227614 | − | 0.137347i | ||||
\(856\) | −1.85798e7 | + | 2.25424e7i | −0.866677 | + | 1.05152i | ||||
\(857\) | 3.41755e6i | 0.158951i | 0.996837 | + | 0.0794755i | \(0.0253245\pi\) | ||||
−0.996837 | + | 0.0794755i | \(0.974675\pi\) | |||||||
\(858\) | 7.44433e6 | + | 1.17356e7i | 0.345229 | + | 0.544234i | ||||
\(859\) | 3.12572e7i | 1.44533i | 0.691199 | + | 0.722664i | \(0.257083\pi\) | ||||
−0.691199 | + | 0.722664i | \(0.742917\pi\) | |||||||
\(860\) | −3.19084e7 | + | 2.12557e7i | −1.47116 | + | 0.980006i | ||||
\(861\) | −1.25214e6 | − | 4.49864e6i | −0.0575631 | − | 0.206811i | ||||
\(862\) | 2.12375e7 | − | 6.42601e6i | 0.973498 | − | 0.294560i | ||||
\(863\) | −613502. | −0.0280407 | −0.0140204 | − | 0.999902i | \(-0.504463\pi\) | ||||
−0.0140204 | + | 0.999902i | \(0.504463\pi\) | |||||||
\(864\) | 1.66015e7 | − | 1.43478e7i | 0.756596 | − | 0.653883i | ||||
\(865\) | −5.26947e7 | −2.39457 | ||||||||
\(866\) | −2.45735e7 | + | 7.43540e6i | −1.11345 | + | 0.336907i | ||||
\(867\) | 2.27762e6 | + | 8.18296e6i | 0.102904 | + | 0.369711i | ||||
\(868\) | 6.42584e6 | − | 4.28055e6i | 0.289488 | − | 0.192841i | ||||
\(869\) | 2.38771e7i | 1.07258i | ||||||||
\(870\) | 1.17172e7 | + | 1.84715e7i | 0.524838 | + | 0.827379i | ||||
\(871\) | 1.60662e7i | 0.717575i | ||||||||
\(872\) | 142729. | − | 173170.i | 0.00635655 | − | 0.00771224i | ||||
\(873\) | 4.64978e6 | − | 2.80578e6i | 0.206489 | − | 0.124600i | ||||
\(874\) | −1.26851e6 | − | 4.19234e6i | −0.0561716 | − | 0.185643i | ||||
\(875\) | −3.42327e6 | −0.151154 | ||||||||
\(876\) | 2.34513e7 | + | 2.02261e7i | 1.03254 | + | 0.890535i | ||||
\(877\) | 2.66479e7 | 1.16994 | 0.584971 | − | 0.811054i | \(-0.301106\pi\) | ||||
0.584971 | + | 0.811054i | \(0.301106\pi\) | |||||||
\(878\) | −7.10616e6 | − | 2.34853e7i | −0.311099 | − | 1.02816i | ||||
\(879\) | 9.29561e6 | − | 2.58731e6i | 0.405794 | − | 0.112947i | ||||
\(880\) | −2.56758e7 | − | 1.07200e7i | −1.11768 | − | 0.466646i | ||||
\(881\) | − | 4.32956e7i | − | 1.87933i | −0.342092 | − | 0.939667i | \(-0.611135\pi\) | ||
0.342092 | − | 0.939667i | \(-0.388865\pi\) | |||||||
\(882\) | −1.30035e7 | + | 1.44127e7i | −0.562846 | + | 0.623840i | ||||
\(883\) | − | 1.40501e7i | − | 0.606424i | −0.952923 | − | 0.303212i | \(-0.901941\pi\) | ||
0.952923 | − | 0.303212i | \(-0.0980590\pi\) | |||||||
\(884\) | −1.05465e7 | − | 1.58321e7i | −0.453917 | − | 0.681409i | ||||
\(885\) | 8.63311e6 | − | 2.40291e6i | 0.370518 | − | 0.103129i | ||||
\(886\) | 1.38167e7 | − | 4.18063e6i | 0.591315 | − | 0.178919i | ||||
\(887\) | 2.40151e7 | 1.02489 | 0.512444 | − | 0.858721i | \(-0.328740\pi\) | ||||
0.512444 | + | 0.858721i | \(0.328740\pi\) | |||||||
\(888\) | −1.02100e6 | − | 453342.i | −0.0434503 | − | 0.0192927i | ||||
\(889\) | 1.23489e6 | 0.0524053 | ||||||||
\(890\) | 2.24235e7 | − | 6.78488e6i | 0.948918 | − | 0.287122i | ||||
\(891\) | −1.02286e7 | + | 1.94129e7i | −0.431641 | + | 0.819212i | ||||
\(892\) | −2.15350e7 | − | 3.23278e7i | −0.906219 | − | 1.36039i | ||||
\(893\) | 7.56239e6i | 0.317344i | ||||||||
\(894\) | −1.90911e6 | + | 1.21103e6i | −0.0798892 | + | 0.0506768i | ||||
\(895\) | − | 5.97708e7i | − | 2.49420i | ||||||
\(896\) | 8.49367e6 | − | 4.48633e6i | 0.353448 | − | 0.186690i | ||||
\(897\) | 4.29199e6 | + | 1.54201e7i | 0.178106 | + | 0.639893i | ||||
\(898\) | −2.62572e6 | − | 8.67782e6i | −0.108657 | − | 0.359104i | ||||
\(899\) | 1.57958e7 | 0.651843 | ||||||||
\(900\) | 7.36153e6 | − | 1.56278e7i | 0.302944 | − | 0.643120i | ||||
\(901\) | 2.75564e6 | 0.113086 | ||||||||
\(902\) | 3.51922e6 | + | 1.16308e7i | 0.144022 | + | 0.475983i | ||||
\(903\) | 3.54927e6 | + | 1.27517e7i | 0.144851 | + | 0.520415i | ||||
\(904\) | 2.18902e7 | + | 1.80423e7i | 0.890899 | + | 0.734294i | ||||
\(905\) | 2.84712e7i | 1.15554i | ||||||||
\(906\) | 2.93000e7 | − | 1.85861e7i | 1.18590 | − | 0.752261i | ||||
\(907\) | 1.74069e7i | 0.702592i | 0.936264 | + | 0.351296i | \(0.114259\pi\) | ||||
−0.936264 | + | 0.351296i | \(0.885741\pi\) | |||||||
\(908\) | 2.13118e7 | − | 1.41968e7i | 0.857840 | − | 0.571447i | ||||
\(909\) | 6.07935e6 | + | 1.00748e7i | 0.244033 | + | 0.404415i | ||||
\(910\) | −8.70112e6 | + | 2.63277e6i | −0.348314 | + | 0.105393i | ||||
\(911\) | −2.35129e7 | −0.938666 | −0.469333 | − | 0.883021i | \(-0.655506\pi\) | ||||
−0.469333 | + | 0.883021i | \(0.655506\pi\) | |||||||
\(912\) | 631643. | − | 5.06583e6i | 0.0251469 | − | 0.201680i | ||||
\(913\) | 3.73181e6 | 0.148164 | ||||||||
\(914\) | 2.50211e7 | − | 7.57086e6i | 0.990698 | − | 0.299764i | ||||
\(915\) | −1.02788e7 | + | 2.86096e6i | −0.405871 | + | 0.112969i | ||||
\(916\) | −2.49803e7 | + | 1.66405e7i | −0.983691 | + | 0.655282i | ||||
\(917\) | 1.79603e7i | 0.705327i | ||||||||
\(918\) | 1.34036e7 | − | 2.68791e7i | 0.524948 | − | 1.05271i | ||||
\(919\) | − | 3.60463e7i | − | 1.40790i | −0.710249 | − | 0.703951i | \(-0.751418\pi\) | ||
0.710249 | − | 0.703951i | \(-0.248582\pi\) | |||||||
\(920\) | −2.47287e7 | − | 2.03818e7i | −0.963234 | − | 0.793913i | ||||
\(921\) | −1.11763e7 | + | 3.11077e6i | −0.434158 | + | 0.120842i | ||||
\(922\) | 2.97994e6 | + | 9.84848e6i | 0.115446 | + | 0.381542i | ||||
\(923\) | −8.63391e6 | −0.333583 | ||||||||
\(924\) | −6.27373e6 | + | 7.27414e6i | −0.241738 | + | 0.280286i | ||||
\(925\) | −879489. | −0.0337968 | ||||||||
\(926\) | 6.66647e6 | + | 2.20322e7i | 0.255487 | + | 0.844365i | ||||
\(927\) | −1.91086e7 | − | 3.16671e7i | −0.730347 | − | 1.21034i | ||||
\(928\) | 1.95500e7 | + | 1.99495e6i | 0.745206 | + | 0.0760436i | ||||
\(929\) | 5.62572e6i | 0.213865i | 0.994266 | + | 0.106932i | \(0.0341028\pi\) | ||||
−0.994266 | + | 0.106932i | \(0.965897\pi\) | |||||||
\(930\) | −1.60814e7 | − | 2.53515e7i | −0.609701 | − | 0.961160i | ||||
\(931\) | 4.51628e6i | 0.170768i | ||||||||
\(932\) | 1.64259e7 | + | 2.46581e7i | 0.619425 | + | 0.929864i | ||||
\(933\) | 713021. | + | 2.56172e6i | 0.0268163 | + | 0.0963447i | ||||
\(934\) | 2.42493e7 | − | 7.33732e6i | 0.909562 | − | 0.275214i | ||||
\(935\) | −3.80864e7 | −1.42476 | ||||||||
\(936\) | −2.72149e6 | + | 1.84561e7i | −0.101535 | + | 0.688575i | ||||
\(937\) | 3.98187e6 | 0.148162 | 0.0740812 | − | 0.997252i | \(-0.476398\pi\) | ||||
0.0740812 | + | 0.997252i | \(0.476398\pi\) | |||||||
\(938\) | −1.06289e7 | + | 3.21608e6i | −0.394441 | + | 0.119349i | ||||
\(939\) | 3.22992e6 | + | 1.16044e7i | 0.119544 | + | 0.429494i | ||||
\(940\) | 3.06742e7 | + | 4.60472e7i | 1.13228 | + | 1.69974i | ||||
\(941\) | 1.59581e7i | 0.587499i | 0.955882 | + | 0.293750i | \(0.0949032\pi\) | ||||
−0.955882 | + | 0.293750i | \(0.905097\pi\) | |||||||
\(942\) | −2.19023e7 | − | 3.45278e7i | −0.804197 | − | 1.26777i | ||||
\(943\) | 1.39954e7i | 0.512513i | ||||||||
\(944\) | 3.10176e6 | − | 7.42911e6i | 0.113286 | − | 0.271336i | ||||
\(945\) | −1.04393e7 | − | 9.85076e6i | −0.380270 | − | 0.358831i | ||||
\(946\) | −9.97549e6 | − | 3.29682e7i | −0.362415 | − | 1.19775i | ||||
\(947\) | 2.11747e7 | 0.767259 | 0.383629 | − | 0.923487i | \(-0.374674\pi\) | ||||
0.383629 | + | 0.923487i | \(0.374674\pi\) | |||||||
\(948\) | −2.09336e7 | + | 2.42717e7i | −0.756524 | + | 0.877161i | ||||
\(949\) | −2.63300e7 | −0.949041 | ||||||||
\(950\) | −1.16398e6 | − | 3.84687e6i | −0.0418444 | − | 0.138293i | ||||
\(951\) | 2.55220e7 | − | 7.10370e6i | 0.915088 | − | 0.254703i | ||||
\(952\) | 8.36288e6 | − | 1.01465e7i | 0.299064 | − | 0.362846i | ||||
\(953\) | 3.38151e7i | 1.20609i | 0.797708 | + | 0.603044i | \(0.206046\pi\) | ||||
−0.797708 | + | 0.603044i | \(0.793954\pi\) | |||||||
\(954\) | −2.00646e6 | − | 1.81028e6i | −0.0713771 | − | 0.0643984i | ||||
\(955\) | 3.48821e7i | 1.23764i | ||||||||
\(956\) | 1.65029e7 | − | 1.09933e7i | 0.584002 | − | 0.389030i | ||||
\(957\) | −1.89322e7 | + | 5.26951e6i | −0.668221 | + | 0.185990i | ||||
\(958\) | −2.68016e7 | + | 8.10960e6i | −0.943512 | + | 0.285487i | ||||
\(959\) | 9.44733e6 | 0.331713 | ||||||||
\(960\) | −1.67017e7 | − | 3.34077e7i | −0.584900 | − | 1.16995i | ||||
\(961\) | 6.94995e6 | 0.242758 | ||||||||
\(962\) | 909087. | − | 275070.i | 0.0316714 | − | 0.00958310i | ||||
\(963\) | 3.35756e7 | − | 2.02602e7i | 1.16670 | − | 0.704010i | ||||
\(964\) | 1.04769e6 | − | 697915.i | 0.0363112 | − | 0.0241885i | ||||
\(965\) | − | 5.53791e7i | − | 1.91438i | ||||||
\(966\) | −9.34236e6 | + | 5.92622e6i | −0.322117 | + | 0.204331i | ||||
\(967\) | 4.65695e7i | 1.60153i | 0.598977 | + | 0.800766i | \(0.295574\pi\) | ||||
−0.598977 | + | 0.800766i | \(0.704426\pi\) | |||||||
\(968\) | −2.64370e6 | + | 3.20753e6i | −0.0906826 | + | 0.110023i | ||||
\(969\) | −1.87379e6 | − | 6.73211e6i | −0.0641080 | − | 0.230325i | ||||
\(970\) | −2.67720e6 | − | 8.84794e6i | −0.0913590 | − | 0.301935i | ||||
\(971\) | −2.54579e7 | −0.866512 | −0.433256 | − | 0.901271i | \(-0.642635\pi\) | ||||
−0.433256 | + | 0.901271i | \(0.642635\pi\) | |||||||
\(972\) | −2.74174e7 | + | 1.07661e7i | −0.930810 | + | 0.365504i | ||||
\(973\) | 3.34076e6 | 0.113126 | ||||||||
\(974\) | −5.90682e6 | − | 1.95216e7i | −0.199506 | − | 0.659353i | ||||
\(975\) | 3.93831e6 | + | 1.41494e7i | 0.132678 | + | 0.476681i | ||||
\(976\) | −3.69302e6 | + | 8.84526e6i | −0.124096 | + | 0.297226i | ||||
\(977\) | − | 1.14688e7i | − | 0.384399i | −0.981356 | − | 0.192200i | \(-0.938438\pi\) | ||
0.981356 | − | 0.192200i | \(-0.0615621\pi\) | |||||||
\(978\) | −2.74820e7 | + | 1.74329e7i | −0.918757 | + | 0.582803i | ||||
\(979\) | 2.10471e7i | 0.701837i | ||||||||
\(980\) | 1.83187e7 | + | 2.74995e7i | 0.609297 | + | 0.914660i | ||||
\(981\) | −257926. | + | 155638.i | −0.00855703 | + | 0.00516349i | ||||
\(982\) | −1.49519e7 | + | 4.52411e6i | −0.494785 | + | 0.149711i | ||||
\(983\) | −1.13955e7 | −0.376139 | −0.188070 | − | 0.982156i | \(-0.560223\pi\) | ||||
−0.188070 | + | 0.982156i | \(0.560223\pi\) | |||||||
\(984\) | −6.61958e6 | + | 1.49084e7i | −0.217943 | + | 0.490843i | ||||
\(985\) | 6.93770e7 | 2.27837 | ||||||||
\(986\) | 2.57470e7 | − | 7.79049e6i | 0.843401 | − | 0.255195i | ||||
\(987\) | 1.84021e7 | − | 5.12197e6i | 0.601276 | − | 0.167357i | ||||
\(988\) | 2.40631e6 | + | 3.61228e6i | 0.0784257 | + | 0.117731i | ||||
\(989\) | − | 3.96709e7i | − | 1.28968i | ||||||
\(990\) | 2.77318e7 | + | 2.50203e7i | 0.899269 | + | 0.811344i | ||||
\(991\) | − | 4.64763e7i | − | 1.50331i | −0.659558 | − | 0.751653i | \(-0.729257\pi\) | ||
0.659558 | − | 0.751653i | \(-0.270743\pi\) | |||||||
\(992\) | −2.68316e7 | − | 2.73800e6i | −0.865701 | − | 0.0883393i | ||||
\(993\) | −347976. | + | 96854.5i | −0.0111989 | + | 0.00311707i | ||||
\(994\) | −1.72831e6 | − | 5.71194e6i | −0.0554825 | − | 0.183366i | ||||
\(995\) | −1.61770e7 | −0.518013 | ||||||||
\(996\) | 3.79349e6 | + | 3.27176e6i | 0.121169 | + | 0.104504i | ||||
\(997\) | −2.78641e7 | −0.887782 | −0.443891 | − | 0.896081i | \(-0.646402\pi\) | ||||
−0.443891 | + | 0.896081i | \(0.646402\pi\) | |||||||
\(998\) | 1.77050e7 | + | 5.85137e7i | 0.562691 | + | 1.85965i | ||||
\(999\) | 1.09069e6 | + | 1.02920e6i | 0.0345771 | + | 0.0326277i |
(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 | 12.6.b.a.11.7 | yes | 8 | |
3.2 | odd | 2 | inner | 12.6.b.a.11.2 | yes | 8 | |
4.3 | odd | 2 | inner | 12.6.b.a.11.1 | ✓ | 8 | |
8.3 | odd | 2 | 192.6.c.e.191.3 | 8 | |||
8.5 | even | 2 | 192.6.c.e.191.6 | 8 | |||
12.11 | even | 2 | inner | 12.6.b.a.11.8 | yes | 8 | |
24.5 | odd | 2 | 192.6.c.e.191.4 | 8 | |||
24.11 | even | 2 | 192.6.c.e.191.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.6.b.a.11.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
12.6.b.a.11.2 | yes | 8 | 3.2 | odd | 2 | inner | |
12.6.b.a.11.7 | yes | 8 | 1.1 | even | 1 | trivial | |
12.6.b.a.11.8 | yes | 8 | 12.11 | even | 2 | inner | |
192.6.c.e.191.3 | 8 | 8.3 | odd | 2 | |||
192.6.c.e.191.4 | 8 | 24.5 | odd | 2 | |||
192.6.c.e.191.5 | 8 | 24.11 | even | 2 | |||
192.6.c.e.191.6 | 8 | 8.5 | even | 2 |