Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,5,Mod(2,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.f (of order \(12\), degree \(4\), 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: | \(1.34380952009\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + 100636992 x^{2} + 3779136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2}\cdot 13^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 6.4 | ||
Root | \(-0.200628i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 13.6 |
Dual form | 13.5.f.a.11.4 |
$q$-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 \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.59772 | + | 5.96275i | 0.399429 | + | 1.49069i | 0.814104 | + | 0.580719i | \(0.197229\pi\) |
−0.414675 | + | 0.909969i | \(0.636105\pi\) | |||||||
\(3\) | 2.76012 | − | 4.78067i | 0.306680 | − | 0.531186i | −0.670954 | − | 0.741499i | \(-0.734115\pi\) |
0.977634 | + | 0.210314i | \(0.0674485\pi\) | |||||||
\(4\) | −19.1453 | + | 11.0536i | −1.19658 | + | 0.690848i | ||||
\(5\) | −5.37551 | + | 5.37551i | −0.215021 | + | 0.215021i | −0.806396 | − | 0.591376i | \(-0.798585\pi\) |
0.591376 | + | 0.806396i | \(0.298585\pi\) | |||||||
\(6\) | 32.9158 | + | 8.81977i | 0.914329 | + | 0.244994i | ||||
\(7\) | 23.3974 | − | 87.3205i | 0.477499 | − | 1.78205i | −0.134194 | − | 0.990955i | \(-0.542845\pi\) |
0.611693 | − | 0.791095i | \(-0.290489\pi\) | |||||||
\(8\) | −26.6579 | − | 26.6579i | −0.416529 | − | 0.416529i | ||||
\(9\) | 25.2635 | + | 43.7576i | 0.311895 | + | 0.540217i | ||||
\(10\) | −40.6414 | − | 23.4643i | −0.406414 | − | 0.234643i | ||||
\(11\) | −131.169 | + | 35.1465i | −1.08404 | + | 0.290467i | −0.756249 | − | 0.654284i | \(-0.772970\pi\) |
−0.327789 | + | 0.944751i | \(0.606304\pi\) | |||||||
\(12\) | 122.037i | 0.847477i | ||||||||
\(13\) | −164.495 | − | 38.7617i | −0.973342 | − | 0.229359i | ||||
\(14\) | 558.053 | 2.84721 | ||||||||
\(15\) | 10.8615 | + | 40.5356i | 0.0482733 | + | 0.180158i | ||||
\(16\) | −60.4944 | + | 104.779i | −0.236306 | + | 0.409295i | ||||
\(17\) | 97.4284 | − | 56.2503i | 0.337122 | − | 0.194638i | −0.321876 | − | 0.946782i | \(-0.604314\pi\) |
0.658999 | + | 0.752144i | \(0.270980\pi\) | |||||||
\(18\) | −220.552 | + | 220.552i | −0.680716 | + | 0.680716i | ||||
\(19\) | −27.6068 | − | 7.39723i | −0.0764732 | − | 0.0204909i | 0.220380 | − | 0.975414i | \(-0.429270\pi\) |
−0.296853 | + | 0.954923i | \(0.595937\pi\) | |||||||
\(20\) | 43.4974 | − | 162.335i | 0.108744 | − | 0.405837i | ||||
\(21\) | −352.871 | − | 352.871i | −0.800160 | − | 0.800160i | ||||
\(22\) | −419.140 | − | 725.972i | −0.865992 | − | 1.49994i | ||||
\(23\) | 382.304 | + | 220.723i | 0.722691 | + | 0.417246i | 0.815742 | − | 0.578415i | \(-0.196329\pi\) |
−0.0930512 | + | 0.995661i | \(0.529662\pi\) | |||||||
\(24\) | −201.021 | + | 53.8635i | −0.348995 | + | 0.0935131i | ||||
\(25\) | 567.208i | 0.907532i | ||||||||
\(26\) | −31.6895 | − | 1042.77i | −0.0468779 | − | 1.54256i | ||||
\(27\) | 726.060 | 0.995968 | ||||||||
\(28\) | 517.250 | + | 1930.41i | 0.659758 | + | 2.46225i | ||||
\(29\) | 141.434 | − | 244.970i | 0.168173 | − | 0.291284i | −0.769604 | − | 0.638521i | \(-0.779547\pi\) |
0.937778 | + | 0.347237i | \(0.112880\pi\) | |||||||
\(30\) | −224.350 | + | 129.529i | −0.249278 | + | 0.143921i | ||||
\(31\) | 596.807 | − | 596.807i | 0.621027 | − | 0.621027i | −0.324767 | − | 0.945794i | \(-0.605286\pi\) |
0.945794 | + | 0.324767i | \(0.105286\pi\) | |||||||
\(32\) | −1304.07 | − | 349.425i | −1.27351 | − | 0.341235i | ||||
\(33\) | −194.017 | + | 724.082i | −0.178161 | + | 0.664906i | ||||
\(34\) | 491.070 | + | 491.070i | 0.424801 | + | 0.424801i | ||||
\(35\) | 343.619 | + | 595.166i | 0.280505 | + | 0.485850i | ||||
\(36\) | −967.355 | − | 558.503i | −0.746416 | − | 0.430943i | ||||
\(37\) | −358.208 | + | 95.9816i | −0.261657 | + | 0.0701107i | −0.387262 | − | 0.921970i | \(-0.626579\pi\) |
0.125606 | + | 0.992080i | \(0.459913\pi\) | |||||||
\(38\) | − | 176.431i | − | 0.122182i | ||||||
\(39\) | −639.332 | + | 679.408i | −0.420337 | + | 0.446685i | ||||
\(40\) | 286.599 | 0.179125 | ||||||||
\(41\) | −339.191 | − | 1265.88i | −0.201780 | − | 0.753051i | −0.990407 | − | 0.138180i | \(-0.955875\pi\) |
0.788628 | − | 0.614871i | \(-0.210792\pi\) | |||||||
\(42\) | 1540.29 | − | 2667.87i | 0.873182 | − | 1.51240i | ||||
\(43\) | −37.5303 | + | 21.6682i | −0.0202976 | + | 0.0117189i | −0.510114 | − | 0.860107i | \(-0.670397\pi\) |
0.489817 | + | 0.871825i | \(0.337064\pi\) | |||||||
\(44\) | 2122.77 | − | 2122.77i | 1.09647 | − | 1.09647i | ||||
\(45\) | −371.024 | − | 99.4155i | −0.183222 | − | 0.0490941i | ||||
\(46\) | −705.305 | + | 2632.24i | −0.333320 | + | 1.24397i | ||||
\(47\) | 2361.67 | + | 2361.67i | 1.06911 | + | 1.06911i | 0.997427 | + | 0.0716878i | \(0.0228385\pi\) |
0.0716878 | + | 0.997427i | \(0.477161\pi\) | |||||||
\(48\) | 333.944 | + | 578.408i | 0.144941 | + | 0.251045i | ||||
\(49\) | −4998.10 | − | 2885.65i | −2.08167 | − | 1.20185i | ||||
\(50\) | −3382.12 | + | 906.236i | −1.35285 | + | 0.362495i | ||||
\(51\) | − | 621.031i | − | 0.238766i | ||||||
\(52\) | 3577.76 | − | 1076.15i | 1.32314 | − | 0.397984i | ||||
\(53\) | −150.315 | −0.0535120 | −0.0267560 | − | 0.999642i | \(-0.508518\pi\) | ||||
−0.0267560 | + | 0.999642i | \(0.508518\pi\) | |||||||
\(54\) | 1160.04 | + | 4329.32i | 0.397818 | + | 1.48468i | ||||
\(55\) | 516.168 | − | 894.029i | 0.170634 | − | 0.295547i | ||||
\(56\) | −2951.50 | + | 1704.05i | −0.941168 | + | 0.543384i | ||||
\(57\) | −111.562 | + | 111.562i | −0.0343373 | + | 0.0343373i | ||||
\(58\) | 1686.67 | + | 451.941i | 0.501387 | + | 0.134346i | ||||
\(59\) | −447.938 | + | 1671.73i | −0.128681 | + | 0.480244i | −0.999944 | − | 0.0105725i | \(-0.996635\pi\) |
0.871263 | + | 0.490816i | \(0.163301\pi\) | |||||||
\(60\) | −656.010 | − | 656.010i | −0.182225 | − | 0.182225i | ||||
\(61\) | 1068.49 | + | 1850.67i | 0.287150 | + | 0.497358i | 0.973128 | − | 0.230264i | \(-0.0739588\pi\) |
−0.685978 | + | 0.727622i | \(0.740626\pi\) | |||||||
\(62\) | 4512.14 | + | 2605.09i | 1.17381 | + | 0.677702i | ||||
\(63\) | 4412.04 | − | 1182.20i | 1.11162 | − | 0.297859i | ||||
\(64\) | − | 6398.32i | − | 1.56209i | ||||||
\(65\) | 1092.61 | − | 675.880i | 0.258605 | − | 0.159972i | ||||
\(66\) | −4627.51 | −1.06233 | ||||||||
\(67\) | −1444.15 | − | 5389.66i | −0.321710 | − | 1.20064i | −0.917578 | − | 0.397555i | \(-0.869859\pi\) |
0.595869 | − | 0.803082i | \(-0.296808\pi\) | |||||||
\(68\) | −1243.53 | + | 2153.86i | −0.268930 | + | 0.465801i | ||||
\(69\) | 2110.41 | − | 1218.45i | 0.443270 | − | 0.255922i | ||||
\(70\) | −2999.82 | + | 2999.82i | −0.612208 | + | 0.612208i | ||||
\(71\) | −6954.13 | − | 1863.35i | −1.37951 | − | 0.369640i | −0.508570 | − | 0.861021i | \(-0.669826\pi\) |
−0.870945 | + | 0.491381i | \(0.836492\pi\) | |||||||
\(72\) | 493.014 | − | 1839.95i | 0.0951031 | − | 0.354930i | ||||
\(73\) | −3856.78 | − | 3856.78i | −0.723734 | − | 0.723734i | 0.245630 | − | 0.969364i | \(-0.421005\pi\) |
−0.969364 | + | 0.245630i | \(0.921005\pi\) | |||||||
\(74\) | −1144.63 | − | 1982.56i | −0.209026 | − | 0.362045i | ||||
\(75\) | 2711.63 | + | 1565.56i | 0.482068 | + | 0.278322i | ||||
\(76\) | 610.308 | − | 163.531i | 0.105663 | − | 0.0283122i | ||||
\(77\) | 12276.0i | 2.07051i | ||||||||
\(78\) | −5072.62 | − | 2726.68i | −0.833763 | − | 0.448172i | ||||
\(79\) | 9010.15 | 1.44370 | 0.721851 | − | 0.692048i | \(-0.243291\pi\) | ||||
0.721851 | + | 0.692048i | \(0.243291\pi\) | |||||||
\(80\) | −238.055 | − | 888.432i | −0.0371960 | − | 0.138817i | ||||
\(81\) | −42.3260 | + | 73.3108i | −0.00645116 | + | 0.0111737i | ||||
\(82\) | 7006.20 | − | 4045.03i | 1.04197 | − | 0.601581i | ||||
\(83\) | −2184.19 | + | 2184.19i | −0.317055 | + | 0.317055i | −0.847635 | − | 0.530580i | \(-0.821974\pi\) |
0.530580 | + | 0.847635i | \(0.321974\pi\) | |||||||
\(84\) | 10656.3 | + | 2855.35i | 1.51025 | + | 0.404669i | ||||
\(85\) | −221.353 | + | 826.102i | −0.0306371 | + | 0.114339i | ||||
\(86\) | −189.165 | − | 189.165i | −0.0255766 | − | 0.0255766i | ||||
\(87\) | −780.747 | − | 1352.29i | −0.103151 | − | 0.178662i | ||||
\(88\) | 4433.61 | + | 2559.74i | 0.572522 | + | 0.330545i | ||||
\(89\) | 1348.94 | − | 361.446i | 0.170299 | − | 0.0456314i | −0.172662 | − | 0.984981i | \(-0.555237\pi\) |
0.342961 | + | 0.939350i | \(0.388570\pi\) | |||||||
\(90\) | − | 2371.16i | − | 0.292736i | ||||||
\(91\) | −7233.45 | + | 13456.8i | −0.873499 | + | 1.62503i | ||||
\(92\) | −9759.11 | −1.15301 | ||||||||
\(93\) | −1205.88 | − | 4500.40i | −0.139424 | − | 0.520338i | ||||
\(94\) | −10308.8 | + | 17855.4i | −1.16668 | + | 2.02075i | ||||
\(95\) | 188.165 | − | 108.637i | 0.0208493 | − | 0.0120373i | ||||
\(96\) | −5269.88 | + | 5269.88i | −0.571819 | + | 0.571819i | ||||
\(97\) | 6839.94 | + | 1832.76i | 0.726957 | + | 0.194788i | 0.603274 | − | 0.797534i | \(-0.293863\pi\) |
0.123683 | + | 0.992322i | \(0.460529\pi\) | |||||||
\(98\) | 9220.90 | − | 34412.9i | 0.960110 | − | 3.58318i | ||||
\(99\) | −4851.70 | − | 4851.70i | −0.495021 | − | 0.495021i | ||||
\(100\) | −6269.67 | − | 10859.4i | −0.626967 | − | 1.08594i | ||||
\(101\) | 3354.45 | + | 1936.69i | 0.328835 | + | 0.189853i | 0.655324 | − | 0.755348i | \(-0.272532\pi\) |
−0.326489 | + | 0.945201i | \(0.605865\pi\) | |||||||
\(102\) | 3703.05 | − | 992.230i | 0.355926 | − | 0.0953700i | ||||
\(103\) | − | 3372.99i | − | 0.317937i | −0.987284 | − | 0.158968i | \(-0.949183\pi\) | ||
0.987284 | − | 0.158968i | \(-0.0508168\pi\) | |||||||
\(104\) | 3351.78 | + | 5418.38i | 0.309891 | + | 0.500960i | ||||
\(105\) | 3793.72 | 0.344102 | ||||||||
\(106\) | −240.161 | − | 896.292i | −0.0213742 | − | 0.0797697i | ||||
\(107\) | 1930.57 | − | 3343.84i | 0.168623 | − | 0.292064i | −0.769313 | − | 0.638872i | \(-0.779401\pi\) |
0.937936 | + | 0.346808i | \(0.112735\pi\) | |||||||
\(108\) | −13900.7 | + | 8025.56i | −1.19176 | + | 0.688062i | ||||
\(109\) | 8275.58 | − | 8275.58i | 0.696539 | − | 0.696539i | −0.267123 | − | 0.963662i | \(-0.586073\pi\) |
0.963662 | + | 0.267123i | \(0.0860731\pi\) | |||||||
\(110\) | 6155.57 | + | 1649.38i | 0.508724 | + | 0.136312i | ||||
\(111\) | −529.842 | + | 1977.40i | −0.0430031 | + | 0.160490i | ||||
\(112\) | 7733.97 | + | 7733.97i | 0.616548 | + | 0.616548i | ||||
\(113\) | 4225.16 | + | 7318.19i | 0.330892 | + | 0.573121i | 0.982687 | − | 0.185274i | \(-0.0593171\pi\) |
−0.651795 | + | 0.758395i | \(0.725984\pi\) | |||||||
\(114\) | −843.460 | − | 486.972i | −0.0649015 | − | 0.0374709i | ||||
\(115\) | −3241.58 | + | 868.578i | −0.245110 | + | 0.0656770i | ||||
\(116\) | 6253.38i | 0.464728i | ||||||||
\(117\) | −2459.59 | − | 8177.15i | −0.179676 | − | 0.597352i | ||||
\(118\) | −10683.8 | −0.767292 | ||||||||
\(119\) | −2632.23 | − | 9823.60i | −0.185879 | − | 0.693708i | ||||
\(120\) | 791.049 | − | 1370.14i | 0.0549340 | − | 0.0951484i | ||||
\(121\) | 3290.45 | − | 1899.74i | 0.224742 | − | 0.129755i | ||||
\(122\) | −9327.96 | + | 9327.96i | −0.626711 | + | 0.626711i | ||||
\(123\) | −6987.96 | − | 1872.42i | −0.461892 | − | 0.123764i | ||||
\(124\) | −4829.23 | + | 18022.9i | −0.314076 | + | 1.17215i | ||||
\(125\) | −6408.73 | − | 6408.73i | −0.410159 | − | 0.410159i | ||||
\(126\) | 14098.4 | + | 24419.1i | 0.888029 | + | 1.53811i | ||||
\(127\) | 3336.63 | + | 1926.41i | 0.206872 | + | 0.119437i | 0.599857 | − | 0.800107i | \(-0.295224\pi\) |
−0.392985 | + | 0.919545i | \(0.628558\pi\) | |||||||
\(128\) | 17286.5 | − | 4631.89i | 1.05508 | − | 0.282708i | ||||
\(129\) | 239.227i | 0.0143758i | ||||||||
\(130\) | 5775.78 | + | 5435.09i | 0.341762 | + | 0.321603i | ||||
\(131\) | −18579.1 | −1.08264 | −0.541318 | − | 0.840818i | \(-0.682074\pi\) | ||||
−0.541318 | + | 0.840818i | \(0.682074\pi\) | |||||||
\(132\) | −4289.17 | − | 16007.4i | −0.246164 | − | 0.918698i | ||||
\(133\) | −1291.86 | + | 2237.56i | −0.0730318 | + | 0.126495i | ||||
\(134\) | 29829.9 | − | 17222.3i | 1.66128 | − | 0.959138i | ||||
\(135\) | −3902.95 | + | 3902.95i | −0.214154 | + | 0.214154i | ||||
\(136\) | −4096.75 | − | 1097.72i | −0.221494 | − | 0.0593490i | ||||
\(137\) | −7754.09 | + | 28938.6i | −0.413133 | + | 1.54183i | 0.375414 | + | 0.926857i | \(0.377500\pi\) |
−0.788547 | + | 0.614975i | \(0.789166\pi\) | |||||||
\(138\) | 10637.1 | + | 10637.1i | 0.558555 | + | 0.558555i | ||||
\(139\) | −7596.66 | − | 13157.8i | −0.393182 | − | 0.681011i | 0.599686 | − | 0.800236i | \(-0.295292\pi\) |
−0.992867 | + | 0.119225i | \(0.961959\pi\) | |||||||
\(140\) | −13157.4 | − | 7596.43i | −0.671296 | − | 0.387573i | ||||
\(141\) | 17808.9 | − | 4771.88i | 0.895775 | − | 0.240022i | ||||
\(142\) | − | 44442.9i | − | 2.20407i | ||||||
\(143\) | 22938.9 | − | 697.105i | 1.12176 | − | 0.0340899i | ||||
\(144\) | −6113.19 | −0.294811 | ||||||||
\(145\) | 556.562 | + | 2077.12i | 0.0264714 | + | 0.0987928i | ||||
\(146\) | 16835.0 | − | 29159.1i | 0.789782 | − | 1.36794i | ||||
\(147\) | −27590.7 | + | 15929.5i | −1.27682 | + | 0.737170i | ||||
\(148\) | 5797.08 | − | 5797.08i | 0.264658 | − | 0.264658i | ||||
\(149\) | −21511.3 | − | 5763.93i | −0.968933 | − | 0.259625i | −0.260555 | − | 0.965459i | \(-0.583906\pi\) |
−0.708377 | + | 0.705834i | \(0.750572\pi\) | |||||||
\(150\) | −5002.64 | + | 18670.1i | −0.222340 | + | 0.829783i | ||||
\(151\) | −10348.1 | − | 10348.1i | −0.453845 | − | 0.453845i | 0.442783 | − | 0.896629i | \(-0.353991\pi\) |
−0.896629 | + | 0.442783i | \(0.853991\pi\) | |||||||
\(152\) | 538.745 | + | 933.133i | 0.0233182 | + | 0.0403884i | ||||
\(153\) | 4922.76 | + | 2842.15i | 0.210293 | + | 0.121413i | ||||
\(154\) | −73199.0 | + | 19613.6i | −3.08648 | + | 0.827021i | ||||
\(155\) | 6416.29i | 0.267067i | ||||||||
\(156\) | 4730.35 | − | 20074.4i | 0.194377 | − | 0.824885i | ||||
\(157\) | 22244.0 | 0.902431 | 0.451215 | − | 0.892415i | \(-0.350991\pi\) | ||||
0.451215 | + | 0.892415i | \(0.350991\pi\) | |||||||
\(158\) | 14395.6 | + | 53725.3i | 0.576656 | + | 2.15211i | ||||
\(159\) | −414.888 | + | 718.607i | −0.0164111 | + | 0.0284248i | ||||
\(160\) | 8888.40 | − | 5131.72i | 0.347203 | − | 0.200458i | ||||
\(161\) | 28218.6 | − | 28218.6i | 1.08864 | − | 1.08864i | ||||
\(162\) | −504.759 | − | 135.250i | −0.0192333 | − | 0.00515355i | ||||
\(163\) | −1844.86 | + | 6885.11i | −0.0694365 | + | 0.259141i | −0.991914 | − | 0.126910i | \(-0.959494\pi\) |
0.922478 | + | 0.386050i | \(0.126161\pi\) | |||||||
\(164\) | 20486.4 | + | 20486.4i | 0.761690 | + | 0.761690i | ||||
\(165\) | −2849.37 | − | 4935.26i | −0.104660 | − | 0.181277i | ||||
\(166\) | −16513.5 | − | 9534.08i | −0.599271 | − | 0.345989i | ||||
\(167\) | 29795.5 | − | 7983.69i | 1.06836 | − | 0.286267i | 0.318542 | − | 0.947909i | \(-0.396807\pi\) |
0.749820 | + | 0.661642i | \(0.230140\pi\) | |||||||
\(168\) | 18813.6i | 0.666580i | ||||||||
\(169\) | 25556.1 | + | 12752.2i | 0.894789 | + | 0.446489i | ||||
\(170\) | −5279.50 | −0.182682 | ||||||||
\(171\) | −373.759 | − | 1394.89i | −0.0127820 | − | 0.0477032i | ||||
\(172\) | 479.021 | − | 829.688i | 0.0161919 | − | 0.0280452i | ||||
\(173\) | −47178.7 | + | 27238.7i | −1.57636 | + | 0.910109i | −0.580994 | + | 0.813908i | \(0.697336\pi\) |
−0.995362 | + | 0.0962012i | \(0.969331\pi\) | |||||||
\(174\) | 6815.99 | − | 6815.99i | 0.225128 | − | 0.225128i | ||||
\(175\) | 49528.8 | + | 13271.2i | 1.61727 | + | 0.433346i | ||||
\(176\) | 4252.34 | − | 15869.9i | 0.137278 | − | 0.512330i | ||||
\(177\) | 6755.62 | + | 6755.62i | 0.215635 | + | 0.215635i | ||||
\(178\) | 4310.43 | + | 7465.88i | 0.136044 | + | 0.235636i | ||||
\(179\) | −12658.7 | − | 7308.50i | −0.395078 | − | 0.228099i | 0.289280 | − | 0.957245i | \(-0.406584\pi\) |
−0.684358 | + | 0.729146i | \(0.739917\pi\) | |||||||
\(180\) | 8202.27 | − | 2197.79i | 0.253156 | − | 0.0678331i | ||||
\(181\) | 15636.6i | 0.477292i | 0.971107 | + | 0.238646i | \(0.0767036\pi\) | ||||
−0.971107 | + | 0.238646i | \(0.923296\pi\) | |||||||
\(182\) | −91796.8 | − | 21631.1i | −2.77131 | − | 0.653033i | ||||
\(183\) | 11796.6 | 0.352253 | ||||||||
\(184\) | −4307.39 | − | 16075.4i | −0.127227 | − | 0.474817i | ||||
\(185\) | 1409.60 | − | 2441.50i | 0.0411863 | − | 0.0713368i | ||||
\(186\) | 24908.1 | − | 14380.7i | 0.719971 | − | 0.415676i | ||||
\(187\) | −10802.5 | + | 10802.5i | −0.308918 | + | 0.308918i | ||||
\(188\) | −71320.0 | − | 19110.1i | −2.01788 | − | 0.540690i | ||||
\(189\) | 16988.0 | − | 63399.9i | 0.475574 | − | 1.77486i | ||||
\(190\) | 948.409 | + | 948.409i | 0.0262717 | + | 0.0262717i | ||||
\(191\) | −10415.6 | − | 18040.4i | −0.285508 | − | 0.494514i | 0.687224 | − | 0.726445i | \(-0.258829\pi\) |
−0.972732 | + | 0.231931i | \(0.925496\pi\) | |||||||
\(192\) | −30588.3 | − | 17660.1i | −0.829760 | − | 0.479062i | ||||
\(193\) | −47365.6 | + | 12691.6i | −1.27159 | + | 0.340722i | −0.830641 | − | 0.556808i | \(-0.812026\pi\) |
−0.440952 | + | 0.897530i | \(0.645359\pi\) | |||||||
\(194\) | 43713.1i | 1.16147i | ||||||||
\(195\) | −215.429 | − | 7088.91i | −0.00566547 | − | 0.186428i | ||||
\(196\) | 127587. | 3.32119 | ||||||||
\(197\) | 16495.3 | + | 61561.3i | 0.425038 | + | 1.58626i | 0.763841 | + | 0.645405i | \(0.223311\pi\) |
−0.338803 | + | 0.940857i | \(0.610022\pi\) | |||||||
\(198\) | 21177.9 | − | 36681.1i | 0.540197 | − | 0.935648i | ||||
\(199\) | 21392.2 | − | 12350.8i | 0.540193 | − | 0.311881i | −0.204964 | − | 0.978770i | \(-0.565708\pi\) |
0.745157 | + | 0.666889i | \(0.232374\pi\) | |||||||
\(200\) | 15120.5 | − | 15120.5i | 0.378014 | − | 0.378014i | ||||
\(201\) | −29752.2 | − | 7972.08i | −0.736423 | − | 0.197324i | ||||
\(202\) | −6188.56 | + | 23096.0i | −0.151666 | + | 0.566024i | ||||
\(203\) | −18081.7 | − | 18081.7i | −0.438781 | − | 0.438781i | ||||
\(204\) | 6864.60 | + | 11889.8i | 0.164951 | + | 0.285704i | ||||
\(205\) | 8628.08 | + | 4981.42i | 0.205308 | + | 0.118535i | ||||
\(206\) | 20112.3 | − | 5389.08i | 0.473945 | − | 0.126993i | ||||
\(207\) | 22304.9i | 0.520547i | ||||||||
\(208\) | 14012.4 | − | 14890.8i | 0.323882 | − | 0.344185i | ||||
\(209\) | 3881.14 | 0.0888518 | ||||||||
\(210\) | 6061.28 | + | 22621.0i | 0.137444 | + | 0.512948i | ||||
\(211\) | −7684.22 | + | 13309.5i | −0.172598 | + | 0.298948i | −0.939327 | − | 0.343022i | \(-0.888549\pi\) |
0.766730 | + | 0.641970i | \(0.221883\pi\) | |||||||
\(212\) | 2877.83 | − | 1661.52i | 0.0640315 | − | 0.0369686i | ||||
\(213\) | −28102.3 | + | 28102.3i | −0.619417 | + | 0.619417i | ||||
\(214\) | 23023.0 | + | 6168.99i | 0.502729 | + | 0.134706i | ||||
\(215\) | 85.2674 | − | 318.222i | 0.00184462 | − | 0.00688420i | ||||
\(216\) | −19355.2 | − | 19355.2i | −0.414850 | − | 0.414850i | ||||
\(217\) | −38149.7 | − | 66077.3i | −0.810162 | − | 1.40324i | ||||
\(218\) | 62567.3 | + | 36123.2i | 1.31654 | + | 0.760105i | ||||
\(219\) | −29083.2 | + | 7792.81i | −0.606392 | + | 0.162482i | ||||
\(220\) | 22822.0i | 0.471529i | ||||||||
\(221\) | −18206.8 | + | 5476.39i | −0.372777 | + | 0.112127i | ||||
\(222\) | −12637.3 | −0.256417 | ||||||||
\(223\) | −360.162 | − | 1344.14i | −0.00724250 | − | 0.0270294i | 0.962210 | − | 0.272308i | \(-0.0877871\pi\) |
−0.969453 | + | 0.245279i | \(0.921120\pi\) | |||||||
\(224\) | −61023.9 | + | 105697.i | −1.21620 | + | 2.10652i | ||||
\(225\) | −24819.7 | + | 14329.6i | −0.490265 | + | 0.283054i | ||||
\(226\) | −36886.0 | + | 36886.0i | −0.722178 | + | 0.722178i | ||||
\(227\) | 76619.8 | + | 20530.2i | 1.48693 | + | 0.398420i | 0.908698 | − | 0.417455i | \(-0.137078\pi\) |
0.578228 | + | 0.815876i | \(0.303745\pi\) | |||||||
\(228\) | 902.733 | − | 3369.05i | 0.0173656 | − | 0.0648093i | ||||
\(229\) | −49114.8 | − | 49114.8i | −0.936573 | − | 0.936573i | 0.0615317 | − | 0.998105i | \(-0.480401\pi\) |
−0.998105 | + | 0.0615317i | \(0.980401\pi\) | |||||||
\(230\) | −10358.2 | − | 17941.0i | −0.195808 | − | 0.339149i | ||||
\(231\) | 58687.7 | + | 33883.4i | 1.09982 | + | 0.634984i | ||||
\(232\) | −10300.7 | + | 2760.06i | −0.191377 | + | 0.0512794i | ||||
\(233\) | − | 90643.7i | − | 1.66965i | −0.550515 | − | 0.834826i | \(-0.685568\pi\) | ||
0.550515 | − | 0.834826i | \(-0.314432\pi\) | |||||||
\(234\) | 44828.6 | − | 27730.7i | 0.818698 | − | 0.506441i | ||||
\(235\) | −25390.4 | −0.459763 | ||||||||
\(236\) | −9902.63 | − | 36957.1i | −0.177798 | − | 0.663551i | ||||
\(237\) | 24869.1 | − | 43074.5i | 0.442755 | − | 0.766874i | ||||
\(238\) | 54370.2 | − | 31390.6i | 0.959858 | − | 0.554174i | ||||
\(239\) | 53610.9 | − | 53610.9i | 0.938549 | − | 0.938549i | −0.0596691 | − | 0.998218i | \(-0.519005\pi\) |
0.998218 | + | 0.0596691i | \(0.0190045\pi\) | |||||||
\(240\) | −4904.36 | − | 1314.12i | −0.0851451 | − | 0.0228146i | ||||
\(241\) | −6713.31 | + | 25054.4i | −0.115585 | + | 0.431370i | −0.999330 | − | 0.0365992i | \(-0.988348\pi\) |
0.883745 | + | 0.467969i | \(0.155014\pi\) | |||||||
\(242\) | 16584.9 | + | 16584.9i | 0.283193 | + | 0.283193i | ||||
\(243\) | 29639.1 | + | 51336.4i | 0.501941 | + | 0.869387i | ||||
\(244\) | −40913.0 | − | 23621.1i | −0.687198 | − | 0.396754i | ||||
\(245\) | 42379.2 | − | 11355.5i | 0.706026 | − | 0.189179i | ||||
\(246\) | − | 44659.1i | − | 0.737972i | ||||||
\(247\) | 4254.45 | + | 2286.89i | 0.0697348 | + | 0.0374845i | ||||
\(248\) | −31819.2 | −0.517352 | ||||||||
\(249\) | 4413.26 | + | 16470.5i | 0.0711805 | + | 0.265649i | ||||
\(250\) | 27974.4 | − | 48453.0i | 0.447590 | − | 0.775248i | ||||
\(251\) | −57981.5 | + | 33475.7i | −0.920327 | + | 0.531351i | −0.883739 | − | 0.467979i | \(-0.844982\pi\) |
−0.0365878 | + | 0.999330i | \(0.511649\pi\) | |||||||
\(252\) | −71402.4 | + | 71402.4i | −1.12438 | + | 1.12438i | ||||
\(253\) | −57903.9 | − | 15515.3i | −0.904621 | − | 0.242392i | ||||
\(254\) | −6155.70 | + | 22973.4i | −0.0954135 | + | 0.356088i | ||||
\(255\) | 3338.36 | + | 3338.36i | 0.0513396 | + | 0.0513396i | ||||
\(256\) | 4051.12 | + | 7016.75i | 0.0618152 | + | 0.107067i | ||||
\(257\) | −32203.7 | − | 18592.8i | −0.487573 | − | 0.281500i | 0.235994 | − | 0.971754i | \(-0.424165\pi\) |
−0.723567 | + | 0.690254i | \(0.757499\pi\) | |||||||
\(258\) | −1426.45 | + | 382.216i | −0.0214298 | + | 0.00574209i | ||||
\(259\) | 33524.6i | 0.499763i | ||||||||
\(260\) | −13447.5 | + | 25017.2i | −0.198927 | + | 0.370076i | ||||
\(261\) | 14292.4 | 0.209809 | ||||||||
\(262\) | −29684.1 | − | 110783.i | −0.432436 | − | 1.61387i | ||||
\(263\) | 10900.9 | − | 18881.0i | 0.157598 | − | 0.272969i | −0.776404 | − | 0.630236i | \(-0.782958\pi\) |
0.934002 | + | 0.357267i | \(0.116291\pi\) | |||||||
\(264\) | 24474.6 | − | 14130.4i | 0.351162 | − | 0.202743i | ||||
\(265\) | 808.021 | − | 808.021i | 0.0115062 | − | 0.0115062i | ||||
\(266\) | −15406.1 | − | 4128.04i | −0.217735 | − | 0.0583420i | ||||
\(267\) | 1995.27 | − | 7446.45i | 0.0279885 | − | 0.104454i | ||||
\(268\) | 87223.8 | + | 87223.8i | 1.21441 | + | 1.21441i | ||||
\(269\) | 53948.9 | + | 93442.2i | 0.745552 | + | 1.29133i | 0.949936 | + | 0.312444i | \(0.101148\pi\) |
−0.204384 | + | 0.978891i | \(0.565519\pi\) | |||||||
\(270\) | −29508.1 | − | 17036.5i | −0.404775 | − | 0.233697i | ||||
\(271\) | 42444.4 | − | 11372.9i | 0.577939 | − | 0.154858i | 0.0420036 | − | 0.999117i | \(-0.486626\pi\) |
0.535935 | + | 0.844259i | \(0.319959\pi\) | |||||||
\(272\) | 13611.3i | 0.183976i | ||||||||
\(273\) | 44367.5 | + | 71723.2i | 0.595305 | + | 0.962353i | ||||
\(274\) | −184943. | −2.46341 | ||||||||
\(275\) | −19935.4 | − | 74399.8i | −0.263608 | − | 0.983800i | ||||
\(276\) | −26936.3 | + | 46655.1i | −0.353606 | + | 0.612464i | ||||
\(277\) | −1084.76 | + | 626.285i | −0.0141375 | + | 0.00816230i | −0.507052 | − | 0.861915i | \(-0.669265\pi\) |
0.492915 | + | 0.870078i | \(0.335932\pi\) | |||||||
\(278\) | 66319.5 | − | 66319.5i | 0.858127 | − | 0.858127i | ||||
\(279\) | 41192.3 | + | 11037.4i | 0.529185 | + | 0.141795i | ||||
\(280\) | 6705.70 | − | 25026.0i | 0.0855318 | − | 0.319209i | ||||
\(281\) | 74905.1 | + | 74905.1i | 0.948634 | + | 0.948634i | 0.998744 | − | 0.0501093i | \(-0.0159570\pi\) |
−0.0501093 | + | 0.998744i | \(0.515957\pi\) | |||||||
\(282\) | 56907.1 | + | 98566.0i | 0.715596 | + | 1.23945i | ||||
\(283\) | −37049.3 | − | 21390.4i | −0.462601 | − | 0.267083i | 0.250536 | − | 0.968107i | \(-0.419393\pi\) |
−0.713137 | + | 0.701024i | \(0.752726\pi\) | |||||||
\(284\) | 153736. | − | 41193.4i | 1.90607 | − | 0.510730i | ||||
\(285\) | − | 1199.40i | − | 0.0147664i | ||||||
\(286\) | 40806.5 | + | 135665.i | 0.498881 | + | 1.65858i | ||||
\(287\) | −118473. | −1.43833 | ||||||||
\(288\) | −17655.4 | − | 65890.8i | −0.212859 | − | 0.794400i | ||||
\(289\) | −35432.3 | + | 61370.6i | −0.424232 | + | 0.734792i | ||||
\(290\) | −11496.1 | + | 6637.29i | −0.136696 | + | 0.0789213i | ||||
\(291\) | 27640.9 | − | 27640.9i | 0.326412 | − | 0.326412i | ||||
\(292\) | 116471. | + | 31208.2i | 1.36600 | + | 0.366018i | ||||
\(293\) | 8238.85 | − | 30747.8i | 0.0959691 | − | 0.358162i | −0.901195 | − | 0.433413i | \(-0.857309\pi\) |
0.997165 | + | 0.0752512i | \(0.0239759\pi\) | |||||||
\(294\) | −139066. | − | 139066.i | −1.60889 | − | 1.60889i | ||||
\(295\) | −6578.50 | − | 11394.3i | −0.0755932 | − | 0.130931i | ||||
\(296\) | 12107.7 | + | 6990.40i | 0.138191 | + | 0.0797845i | ||||
\(297\) | −95236.3 | + | 25518.5i | −1.07967 | + | 0.289296i | ||||
\(298\) | − | 137476.i | − | 1.54808i | ||||||
\(299\) | −54331.4 | − | 51126.5i | −0.607727 | − | 0.571879i | ||||
\(300\) | −69220.2 | −0.769113 | ||||||||
\(301\) | 1013.96 | + | 3784.15i | 0.0111915 | + | 0.0417672i | ||||
\(302\) | 45170.0 | − | 78236.7i | 0.495263 | − | 0.857821i | ||||
\(303\) | 18517.4 | − | 10691.0i | 0.201694 | − | 0.116448i | ||||
\(304\) | 2445.14 | − | 2445.14i | 0.0264579 | − | 0.0264579i | ||||
\(305\) | −15692.0 | − | 4204.65i | −0.168685 | − | 0.0451991i | ||||
\(306\) | −9081.91 | + | 33894.1i | −0.0969916 | + | 0.361978i | ||||
\(307\) | 84129.7 | + | 84129.7i | 0.892632 | + | 0.892632i | 0.994770 | − | 0.102138i | \(-0.0325683\pi\) |
−0.102138 | + | 0.994770i | \(0.532568\pi\) | |||||||
\(308\) | −135694. | − | 235029.i | −1.43041 | − | 2.47754i | ||||
\(309\) | −16125.2 | − | 9309.86i | −0.168883 | − | 0.0975048i | ||||
\(310\) | −38258.8 | + | 10251.4i | −0.398114 | + | 0.106674i | ||||
\(311\) | − | 13886.4i | − | 0.143572i | −0.997420 | − | 0.0717860i | \(-0.977130\pi\) | ||
0.997420 | − | 0.0717860i | \(-0.0228699\pi\) | |||||||
\(312\) | 35154.8 | − | 1068.34i | 0.361140 | − | 0.0109749i | ||||
\(313\) | 63260.4 | 0.645718 | 0.322859 | − | 0.946447i | \(-0.395356\pi\) | ||||
0.322859 | + | 0.946447i | \(0.395356\pi\) | |||||||
\(314\) | 35539.6 | + | 132636.i | 0.360457 | + | 1.34524i | ||||
\(315\) | −17362.0 | + | 30071.9i | −0.174976 | + | 0.303068i | ||||
\(316\) | −172502. | + | 99594.3i | −1.72751 | + | 0.997379i | ||||
\(317\) | −10553.4 | + | 10553.4i | −0.105020 | + | 0.105020i | −0.757664 | − | 0.652644i | \(-0.773660\pi\) |
0.652644 | + | 0.757664i | \(0.273660\pi\) | |||||||
\(318\) | −4947.75 | − | 1325.75i | −0.0489275 | − | 0.0131101i | ||||
\(319\) | −9941.79 | + | 37103.3i | −0.0976975 | + | 0.364612i | ||||
\(320\) | 34394.3 | + | 34394.3i | 0.335881 | + | 0.335881i | ||||
\(321\) | −10657.2 | − | 18458.8i | −0.103427 | − | 0.179140i | ||||
\(322\) | 213346. | + | 123175.i | 2.05765 | + | 1.18799i | ||||
\(323\) | −3105.78 | + | 832.192i | −0.0297691 | + | 0.00797662i | ||||
\(324\) | − | 1871.41i | − | 0.0178271i | ||||||
\(325\) | 21985.9 | − | 93302.7i | 0.208151 | − | 0.883339i | ||||
\(326\) | −44001.8 | −0.414033 | ||||||||
\(327\) | −16721.2 | − | 62404.4i | −0.156377 | − | 0.583606i | ||||
\(328\) | −24703.5 | + | 42787.8i | −0.229621 | + | 0.397715i | ||||
\(329\) | 261480. | − | 150965.i | 2.41572 | − | 1.39472i | ||||
\(330\) | 24875.2 | − | 24875.2i | 0.228423 | − | 0.228423i | ||||
\(331\) | −45405.1 | − | 12166.3i | −0.414428 | − | 0.111046i | 0.0455795 | − | 0.998961i | \(-0.485487\pi\) |
−0.460007 | + | 0.887915i | \(0.652153\pi\) | |||||||
\(332\) | 17674.0 | − | 65960.2i | 0.160346 | − | 0.598419i | ||||
\(333\) | −13249.5 | − | 13249.5i | −0.119484 | − | 0.119484i | ||||
\(334\) | 95209.6 | + | 164908.i | 0.853469 | + | 1.47825i | ||||
\(335\) | 36735.3 | + | 21209.1i | 0.327336 | + | 0.188987i | ||||
\(336\) | 58320.3 | − | 15626.9i | 0.516584 | − | 0.138418i | ||||
\(337\) | 8592.02i | 0.0756546i | 0.999284 | + | 0.0378273i | \(0.0120437\pi\) | ||||
−0.999284 | + | 0.0378273i | \(0.987956\pi\) | |||||||
\(338\) | −35206.8 | + | 172759.i | −0.308172 | + | 1.51219i | ||||
\(339\) | 46647.8 | 0.405912 | ||||||||
\(340\) | −4893.49 | − | 18262.7i | −0.0423312 | − | 0.157982i | ||||
\(341\) | −57306.7 | + | 99258.1i | −0.492829 | + | 0.853605i | ||||
\(342\) | 7720.21 | − | 4457.27i | 0.0660051 | − | 0.0381080i | ||||
\(343\) | −215440. | + | 215440.i | −1.83121 | + | 1.83121i | ||||
\(344\) | 1578.11 | + | 422.852i | 0.0133358 | + | 0.00357332i | ||||
\(345\) | −4794.76 | + | 17894.3i | −0.0402837 | + | 0.150341i | ||||
\(346\) | −237796. | − | 237796.i | −1.98633 | − | 1.98633i | ||||
\(347\) | −86232.5 | − | 149359.i | −0.716163 | − | 1.24043i | −0.962509 | − | 0.271249i | \(-0.912563\pi\) |
0.246346 | − | 0.969182i | \(-0.420770\pi\) | |||||||
\(348\) | 29895.3 | + | 17260.1i | 0.246857 | + | 0.142523i | ||||
\(349\) | 126776. | − | 33969.6i | 1.04085 | − | 0.278894i | 0.302383 | − | 0.953186i | \(-0.402218\pi\) |
0.738465 | + | 0.674292i | \(0.235551\pi\) | |||||||
\(350\) | 316532.i | 2.58393i | ||||||||
\(351\) | −119433. | − | 28143.3i | −0.969417 | − | 0.228434i | ||||
\(352\) | 183334. | 1.47965 | ||||||||
\(353\) | −11384.2 | − | 42486.4i | −0.0913593 | − | 0.340958i | 0.905083 | − | 0.425235i | \(-0.139809\pi\) |
−0.996442 | + | 0.0842773i | \(0.973142\pi\) | |||||||
\(354\) | −29488.5 | + | 51075.6i | −0.235313 | + | 0.407575i | ||||
\(355\) | 47398.5 | − | 27365.6i | 0.376104 | − | 0.217144i | ||||
\(356\) | −21830.6 | + | 21830.6i | −0.172252 | + | 0.172252i | ||||
\(357\) | −54228.7 | − | 14530.5i | −0.425493 | − | 0.114011i | ||||
\(358\) | 23353.8 | − | 87157.6i | 0.182218 | − | 0.680048i | ||||
\(359\) | −15691.6 | − | 15691.6i | −0.121753 | − | 0.121753i | 0.643605 | − | 0.765358i | \(-0.277438\pi\) |
−0.765358 | + | 0.643605i | \(0.777438\pi\) | |||||||
\(360\) | 7240.50 | + | 12540.9i | 0.0558680 | + | 0.0967662i | ||||
\(361\) | −112154. | − | 64752.1i | −0.860597 | − | 0.496866i | ||||
\(362\) | −93237.1 | + | 24982.8i | −0.711494 | + | 0.190644i | ||||
\(363\) | − | 20974.1i | − | 0.159173i | ||||||
\(364\) | −10259.3 | − | 337591.i | −0.0774308 | − | 2.54793i | ||||
\(365\) | 41464.3 | 0.311235 | ||||||||
\(366\) | 18847.6 | + | 70340.2i | 0.140700 | + | 0.525099i | ||||
\(367\) | 100985. | − | 174910.i | 0.749761 | − | 1.29862i | −0.198175 | − | 0.980167i | \(-0.563502\pi\) |
0.947937 | − | 0.318458i | \(-0.103165\pi\) | |||||||
\(368\) | −46254.5 | + | 26705.0i | −0.341553 | + | 0.197196i | ||||
\(369\) | 46822.7 | − | 46822.7i | 0.343878 | − | 0.343878i | ||||
\(370\) | 16810.2 | + | 4504.29i | 0.122792 | + | 0.0329020i | ||||
\(371\) | −3516.99 | + | 13125.6i | −0.0255519 | + | 0.0953610i | ||||
\(372\) | 72832.4 | + | 72832.4i | 0.526307 | + | 0.526307i | ||||
\(373\) | 124830. | + | 216212.i | 0.897226 | + | 1.55404i | 0.831025 | + | 0.556235i | \(0.187755\pi\) |
0.0662014 | + | 0.997806i | \(0.478912\pi\) | |||||||
\(374\) | −81672.3 | − | 47153.5i | −0.583891 | − | 0.337109i | ||||
\(375\) | −48326.9 | + | 12949.1i | −0.343658 | + | 0.0920828i | ||||
\(376\) | − | 125914.i | − | 0.890635i | ||||||
\(377\) | −32760.5 | + | 34814.1i | −0.230499 | + | 0.244947i | ||||
\(378\) | 405180. | 2.83573 | ||||||||
\(379\) | 19032.3 | + | 71029.7i | 0.132499 | + | 0.494494i | 0.999996 | − | 0.00294932i | \(-0.000938800\pi\) |
−0.867496 | + | 0.497444i | \(0.834272\pi\) | |||||||
\(380\) | −2401.65 | + | 4159.78i | −0.0166319 | + | 0.0288074i | ||||
\(381\) | 18419.0 | − | 10634.2i | 0.126887 | − | 0.0732582i | ||||
\(382\) | 90929.1 | − | 90929.1i | 0.623127 | − | 0.623127i | ||||
\(383\) | −97227.9 | − | 26052.1i | −0.662817 | − | 0.177601i | −0.0882998 | − | 0.996094i | \(-0.528143\pi\) |
−0.574517 | + | 0.818493i | \(0.694810\pi\) | |||||||
\(384\) | 25569.2 | − | 95425.4i | 0.173402 | − | 0.647145i | ||||
\(385\) | −65990.0 | − | 65990.0i | −0.445202 | − | 0.445202i | ||||
\(386\) | −151353. | − | 262152.i | −1.01582 | − | 1.75946i | ||||
\(387\) | −1896.29 | − | 1094.83i | −0.0126615 | − | 0.00731009i | ||||
\(388\) | −151211. | + | 40517.0i | −1.00443 | + | 0.269137i | ||||
\(389\) | 214008.i | 1.41426i | 0.707082 | + | 0.707131i | \(0.250011\pi\) | ||||
−0.707082 | + | 0.707131i | \(0.749989\pi\) | |||||||
\(390\) | 41925.2 | − | 12610.6i | 0.275642 | − | 0.0829100i | ||||
\(391\) | 49663.0 | 0.324847 | ||||||||
\(392\) | 56313.3 | + | 210164.i | 0.366470 | + | 1.36768i | ||||
\(393\) | −51280.6 | + | 88820.6i | −0.332023 | + | 0.575080i | ||||
\(394\) | −340720. | + | 196715.i | −2.19485 | + | 1.26720i | ||||
\(395\) | −48434.2 | + | 48434.2i | −0.310426 | + | 0.310426i | ||||
\(396\) | 146516. | + | 39258.9i | 0.934318 | + | 0.250350i | ||||
\(397\) | 35355.3 | − | 131948.i | 0.224323 | − | 0.837184i | −0.758352 | − | 0.651845i | \(-0.773995\pi\) |
0.982675 | − | 0.185339i | \(-0.0593382\pi\) | |||||||
\(398\) | 107823. | + | 107823.i | 0.680686 | + | 0.680686i | ||||
\(399\) | 7131.37 | + | 12351.9i | 0.0447948 | + | 0.0775868i | ||||
\(400\) | −59431.7 | − | 34312.9i | −0.371448 | − | 0.214456i | ||||
\(401\) | −197833. | + | 53009.2i | −1.23030 | + | 0.329657i | −0.814695 | − | 0.579890i | \(-0.803096\pi\) |
−0.415602 | + | 0.909547i | \(0.636429\pi\) | |||||||
\(402\) | − | 190142.i | − | 1.17659i | ||||||
\(403\) | −121305. | + | 75038.4i | −0.746910 | + | 0.462034i | ||||
\(404\) | −85629.4 | −0.524638 | ||||||||
\(405\) | −166.559 | − | 621.608i | −0.00101545 | − | 0.00378971i | ||||
\(406\) | 78927.4 | − | 136706.i | 0.478824 | − | 0.829347i | ||||
\(407\) | 43612.2 | − | 25179.5i | 0.263281 | − | 0.152005i | ||||
\(408\) | −16555.3 | + | 16555.3i | −0.0994530 | + | 0.0994530i | ||||
\(409\) | 152546. | + | 40874.6i | 0.911916 | + | 0.244347i | 0.684126 | − | 0.729363i | \(-0.260184\pi\) |
0.227789 | + | 0.973710i | \(0.426850\pi\) | |||||||
\(410\) | −15917.8 | + | 59406.0i | −0.0946924 | + | 0.353397i | ||||
\(411\) | 116944. | + | 116944.i | 0.692299 | + | 0.692299i | ||||
\(412\) | 37283.6 | + | 64577.0i | 0.219646 | + | 0.380438i | ||||
\(413\) | 135495. | + | 78228.3i | 0.794373 | + | 0.458632i | ||||
\(414\) | −132999. | + | 35636.9i | −0.775974 | + | 0.207922i | ||||
\(415\) | − | 23482.3i | − | 0.136347i | ||||||
\(416\) | 200969. | + | 108027.i | 1.16129 | + | 0.624229i | ||||
\(417\) | −83870.9 | −0.482324 | ||||||||
\(418\) | 6200.95 | + | 23142.3i | 0.0354900 | + | 0.132450i | ||||
\(419\) | 98539.2 | − | 170675.i | 0.561282 | − | 0.972168i | −0.436103 | − | 0.899897i | \(-0.643642\pi\) |
0.997385 | − | 0.0722718i | \(-0.0230249\pi\) | |||||||
\(420\) | −72632.1 | + | 41934.1i | −0.411746 | + | 0.237722i | ||||
\(421\) | 107929. | − | 107929.i | 0.608939 | − | 0.608939i | −0.333729 | − | 0.942669i | \(-0.608307\pi\) |
0.942669 | + | 0.333729i | \(0.108307\pi\) | |||||||
\(422\) | −91638.2 | − | 24554.4i | −0.514579 | − | 0.137881i | ||||
\(423\) | −43677.1 | + | 163005.i | −0.244103 | + | 0.911006i | ||||
\(424\) | 4007.08 | + | 4007.08i | 0.0222893 | + | 0.0222893i | ||||
\(425\) | 31905.6 | + | 55262.1i | 0.176640 | + | 0.305949i | ||||
\(426\) | −212467. | − | 122668.i | −1.17077 | − | 0.675945i | ||||
\(427\) | 186601. | − | 49999.7i | 1.02343 | − | 0.274228i | ||||
\(428\) | 85358.6i | 0.465972i | ||||||||
\(429\) | 59981.5 | − | 111587.i | 0.325914 | − | 0.606318i | ||||
\(430\) | 2033.71 | 0.0109990 | ||||||||
\(431\) | 32479.2 | + | 121214.i | 0.174844 | + | 0.652528i | 0.996578 | + | 0.0826563i | \(0.0263404\pi\) |
−0.821734 | + | 0.569871i | \(0.806993\pi\) | |||||||
\(432\) | −43922.6 | + | 76076.2i | −0.235353 | + | 0.407644i | ||||
\(433\) | 228921. | − | 132167.i | 1.22098 | − | 0.704934i | 0.255855 | − | 0.966715i | \(-0.417643\pi\) |
0.965127 | + | 0.261781i | \(0.0843097\pi\) | |||||||
\(434\) | 333050. | − | 333050.i | 1.76819 | − | 1.76819i | ||||
\(435\) | 11466.2 | + | 3072.36i | 0.0605955 | + | 0.0162365i | ||||
\(436\) | −66964.1 | + | 249913.i | −0.352265 | + | 1.31467i | ||||
\(437\) | −8921.45 | − | 8921.45i | −0.0467168 | − | 0.0467168i | ||||
\(438\) | −92933.2 | − | 160965.i | −0.484421 | − | 0.839042i | ||||
\(439\) | −207852. | − | 120004.i | −1.07851 | − | 0.622680i | −0.148019 | − | 0.988985i | \(-0.547290\pi\) |
−0.930495 | + | 0.366304i | \(0.880623\pi\) | |||||||
\(440\) | −37592.9 | + | 10073.0i | −0.194178 | + | 0.0520298i | ||||
\(441\) | − | 291606.i | − | 1.49941i | ||||||
\(442\) | −61743.7 | − | 99813.0i | −0.316044 | − | 0.510908i | ||||
\(443\) | 56485.3 | 0.287825 | 0.143912 | − | 0.989590i | \(-0.454032\pi\) | ||||
0.143912 | + | 0.989590i | \(0.454032\pi\) | |||||||
\(444\) | −11713.3 | − | 43714.5i | −0.0594172 | − | 0.221748i | ||||
\(445\) | −5308.26 | + | 9194.18i | −0.0268060 | + | 0.0464294i | ||||
\(446\) | 7439.36 | − | 4295.12i | 0.0373995 | − | 0.0215926i | ||||
\(447\) | −86929.1 | + | 86929.1i | −0.435061 | + | 0.435061i | ||||
\(448\) | −558704. | − | 149704.i | −2.78372 | − | 0.745896i | ||||
\(449\) | −34627.1 | + | 129230.i | −0.171761 | + | 0.641020i | 0.825320 | + | 0.564665i | \(0.190995\pi\) |
−0.997081 | + | 0.0763545i | \(0.975672\pi\) | |||||||
\(450\) | −125099. | − | 125099.i | −0.617772 | − | 0.617772i | ||||
\(451\) | 88982.5 | + | 154122.i | 0.437473 | + | 0.757726i | ||||
\(452\) | −161784. | − | 93406.1i | −0.791879 | − | 0.457192i | ||||
\(453\) | −78033.0 | + | 20908.9i | −0.380261 | + | 0.101891i | ||||
\(454\) | 489666.i | 2.37568i | ||||||||
\(455\) | −33453.9 | − | 111221.i | −0.161594 | − | 0.537234i | ||||
\(456\) | 5948.00 | 0.0286050 | ||||||||
\(457\) | 46049.5 | + | 171859.i | 0.220492 | + | 0.822886i | 0.984161 | + | 0.177278i | \(0.0567293\pi\) |
−0.763669 | + | 0.645608i | \(0.776604\pi\) | |||||||
\(458\) | 214388. | − | 371331.i | 1.02204 | − | 1.77023i | ||||
\(459\) | 70738.9 | − | 40841.1i | 0.335763 | − | 0.193853i | ||||
\(460\) | 52460.2 | − | 52460.2i | 0.247922 | − | 0.247922i | ||||
\(461\) | −303818. | − | 81407.7i | −1.42959 | − | 0.383057i | −0.540714 | − | 0.841207i | \(-0.681846\pi\) |
−0.888875 | + | 0.458149i | \(0.848512\pi\) | |||||||
\(462\) | −108272. | + | 404076.i | −0.507262 | + | 1.89313i | ||||
\(463\) | 238507. | + | 238507.i | 1.11260 | + | 1.11260i | 0.992797 | + | 0.119805i | \(0.0382269\pi\) |
0.119805 | + | 0.992797i | \(0.461773\pi\) | |||||||
\(464\) | 17111.9 | + | 29638.6i | 0.0794807 | + | 0.137665i | ||||
\(465\) | 30674.2 | + | 17709.7i | 0.141862 | + | 0.0819042i | ||||
\(466\) | 540486. | − | 144823.i | 2.48893 | − | 0.666907i | ||||
\(467\) | − | 300948.i | − | 1.37993i | −0.723842 | − | 0.689965i | \(-0.757626\pi\) | ||
0.723842 | − | 0.689965i | \(-0.242374\pi\) | |||||||
\(468\) | 137476. | + | 129367.i | 0.627677 | + | 0.590653i | ||||
\(469\) | −504417. | −2.29321 | ||||||||
\(470\) | −40566.7 | − | 151397.i | −0.183643 | − | 0.685364i | ||||
\(471\) | 61396.2 | − | 106341.i | 0.276758 | − | 0.479358i | ||||
\(472\) | 56505.8 | − | 32623.6i | 0.253635 | − | 0.146436i | ||||
\(473\) | 4161.24 | − | 4161.24i | 0.0185995 | − | 0.0185995i | ||||
\(474\) | 296577. | + | 79467.5i | 1.32002 | + | 0.353698i | ||||
\(475\) | 4195.76 | − | 15658.8i | 0.0185962 | − | 0.0694019i | ||||
\(476\) | 158981. | + | 158981.i | 0.701666 | + | 0.701666i | ||||
\(477\) | −3797.48 | − | 6577.43i | −0.0166901 | − | 0.0289081i | ||||
\(478\) | 405323. | + | 234014.i | 1.77397 | + | 1.02420i | ||||
\(479\) | −206969. | + | 55457.3i | −0.902059 | + | 0.241706i | −0.679900 | − | 0.733304i | \(-0.737977\pi\) |
−0.222159 | + | 0.975010i | \(0.571310\pi\) | |||||||
\(480\) | − | 56656.6i | − | 0.245906i | ||||||
\(481\) | 62643.8 | − | 1903.72i | 0.270762 | − | 0.00822836i | ||||
\(482\) | −160119. | −0.689206 | ||||||||
\(483\) | −57017.0 | − | 212790.i | −0.244405 | − | 0.912132i | ||||
\(484\) | −41997.8 | + | 72742.4i | −0.179282 | + | 0.310525i | ||||
\(485\) | −46620.2 | + | 26916.2i | −0.198194 | + | 0.114427i | ||||
\(486\) | −258752. | + | 258752.i | −1.09550 | + | 1.09550i | ||||
\(487\) | 55699.6 | + | 14924.7i | 0.234852 | + | 0.0629283i | 0.374325 | − | 0.927297i | \(-0.377874\pi\) |
−0.139474 | + | 0.990226i | \(0.544541\pi\) | |||||||
\(488\) | 20851.4 | − | 77818.5i | 0.0875579 | − | 0.326771i | ||||
\(489\) | 27823.4 | + | 27823.4i | 0.116357 | + | 0.116357i | ||||
\(490\) | 135420. | + | 234554.i | 0.564014 | + | 0.976901i | ||||
\(491\) | 339332. | + | 195914.i | 1.40754 | + | 0.812646i | 0.995151 | − | 0.0983596i | \(-0.0313595\pi\) |
0.412394 | + | 0.911006i | \(0.364693\pi\) | |||||||
\(492\) | 154484. | − | 41393.8i | 0.638194 | − | 0.171004i | ||||
\(493\) | − | 31822.7i | − | 0.130931i | ||||||
\(494\) | −6838.78 | + | 29022.0i | −0.0280236 | + | 0.118925i | ||||
\(495\) | 52160.8 | 0.212879 | ||||||||
\(496\) | 26429.6 | + | 98636.6i | 0.107430 | + | 0.400936i | ||||
\(497\) | −325418. | + | 563640.i | −1.31743 | + | 2.28186i | ||||
\(498\) | −91158.5 | + | 52630.4i | −0.367569 | + | 0.212216i | ||||
\(499\) | −49256.6 | + | 49256.6i | −0.197817 | + | 0.197817i | −0.799063 | − | 0.601247i | \(-0.794671\pi\) |
0.601247 | + | 0.799063i | \(0.294671\pi\) | |||||||
\(500\) | 193537. | + | 51858.0i | 0.774146 | + | 0.207432i | ||||
\(501\) | 44071.9 | − | 164479.i | 0.175585 | − | 0.655290i | ||||
\(502\) | −292245. | − | 292245.i | −1.15968 | − | 1.15968i | ||||
\(503\) | −207038. | − | 358600.i | −0.818302 | − | 1.41734i | −0.906932 | − | 0.421276i | \(-0.861582\pi\) |
0.0886300 | − | 0.996065i | \(-0.471751\pi\) | |||||||
\(504\) | −149130. | − | 86100.5i | −0.587091 | − | 0.338957i | ||||
\(505\) | −28442.6 | + | 7621.17i | −0.111529 | + | 0.0298840i | ||||
\(506\) | − | 370056.i | − | 1.44533i | ||||||
\(507\) | 131502. | − | 86977.5i | 0.511583 | − | 0.338369i | ||||
\(508\) | −85174.6 | −0.330052 | ||||||||
\(509\) | −32960.3 | − | 123010.i | −0.127220 | − | 0.474792i | 0.872689 | − | 0.488277i | \(-0.162374\pi\) |
−0.999909 | + | 0.0134846i | \(0.995708\pi\) | |||||||
\(510\) | −14572.1 | + | 25239.6i | −0.0560248 | + | 0.0970379i | ||||
\(511\) | −427015. | + | 246537.i | −1.63531 | + | 0.944149i | ||||
\(512\) | 167106. | − | 167106.i | 0.637461 | − | 0.637461i | ||||
\(513\) | −20044.2 | − | 5370.83i | −0.0761648 | − | 0.0204083i | ||||
\(514\) | 59412.0 | − | 221729.i | 0.224879 | − | 0.839258i | ||||
\(515\) | 18131.6 | + | 18131.6i | 0.0683629 | + | 0.0683629i | ||||
\(516\) | −2644.31 | − | 4580.08i | −0.00993146 | − | 0.0172018i | ||||
\(517\) | −392782. | − | 226773.i | −1.46950 | − | 0.848419i | ||||
\(518\) | −199899. | + | 53562.8i | −0.744991 | + | 0.199620i | ||||
\(519\) | 300728.i | 1.11645i | ||||||||
\(520\) | −47144.1 | − | 11109.1i | −0.174350 | − | 0.0410839i | ||||
\(521\) | 288110. | 1.06141 | 0.530705 | − | 0.847557i | \(-0.321927\pi\) | ||||
0.530705 | + | 0.847557i | \(0.321927\pi\) | |||||||
\(522\) | 22835.2 | + | 85222.1i | 0.0838038 | + | 0.312760i | ||||
\(523\) | 170871. | − | 295958.i | 0.624692 | − | 1.08200i | −0.363909 | − | 0.931435i | \(-0.618558\pi\) |
0.988600 | − | 0.150563i | \(-0.0481087\pi\) | |||||||
\(524\) | 355703. | − | 205365.i | 1.29546 | − | 0.747937i | ||||
\(525\) | 200151. | − | 200151.i | 0.726171 | − | 0.726171i | ||||
\(526\) | 129999. | + | 34833.2i | 0.469861 | + | 0.125899i | ||||
\(527\) | 24575.4 | − | 91716.6i | 0.0884869 | − | 0.330238i | ||||
\(528\) | −64132.0 | − | 64132.0i | −0.230042 | − | 0.230042i | ||||
\(529\) | −42483.1 | − | 73582.9i | −0.151812 | − | 0.262945i | ||||
\(530\) | 6109.02 | + | 3527.04i | 0.0217480 | + | 0.0125562i | ||||
\(531\) | −84467.3 | + | 22632.9i | −0.299571 | + | 0.0802698i | ||||
\(532\) | − | 57118.6i | − | 0.201815i | ||||||
\(533\) | 6727.60 | + | 221378.i | 0.0236813 | + | 0.779256i | ||||
\(534\) | 47589.2 | 0.166888 | ||||||||
\(535\) | 7597.07 | + | 28352.7i | 0.0265423 | + | 0.0990572i | ||||
\(536\) | −105179. | + | 182175.i | −0.366099 | + | 0.634102i | ||||
\(537\) | −69879.1 | + | 40344.7i | −0.242325 | + | 0.139907i | ||||
\(538\) | −470978. | + | 470978.i | −1.62718 | + | 1.62718i | ||||
\(539\) | 757014. | + | 202841.i | 2.60571 | + | 0.698198i | ||||
\(540\) | 31581.8 | − | 117865.i | 0.108305 | − | 0.404200i | ||||
\(541\) | −195832. | − | 195832.i | −0.669096 | − | 0.669096i | 0.288411 | − | 0.957507i | \(-0.406873\pi\) |
−0.957507 | + | 0.288411i | \(0.906873\pi\) | |||||||
\(542\) | 135628. | + | 234915.i | 0.461691 | + | 0.799672i | ||||
\(543\) | 74753.3 | + | 43158.8i | 0.253531 | + | 0.146376i | ||||
\(544\) | −146709. | + | 39310.5i | −0.495745 | + | 0.132835i | ||||
\(545\) | 88971.0i | 0.299540i | ||||||||
\(546\) | −356781. | + | 379146.i | −1.19679 | + | 1.27181i | ||||
\(547\) | 232302. | 0.776387 | 0.388194 | − | 0.921578i | \(-0.373099\pi\) | ||||
0.388194 | + | 0.921578i | \(0.373099\pi\) | |||||||
\(548\) | −171421. | − | 639750.i | −0.570824 | − | 2.13034i | ||||
\(549\) | −53987.3 | + | 93508.7i | −0.179121 | + | 0.310247i | ||||
\(550\) | 411777. | − | 237740.i | 1.36125 | − | 0.785916i | ||||
\(551\) | −5716.63 | + | 5716.63i | −0.0188294 | + | 0.0188294i | ||||
\(552\) | −88740.1 | − | 23777.8i | −0.291234 | − | 0.0780359i | ||||
\(553\) | 210814. | − | 786770.i | 0.689366 | − | 2.57275i | ||||
\(554\) | −5467.52 | − | 5467.52i | −0.0178144 | − | 0.0178144i | ||||
\(555\) | −7781.35 | − | 13477.7i | −0.0252621 | − | 0.0437552i | ||||
\(556\) | 290881. | + | 167940.i | 0.940950 | + | 0.543258i | ||||
\(557\) | 379764. | − | 101757.i | 1.22406 | − | 0.327986i | 0.411797 | − | 0.911276i | \(-0.364901\pi\) |
0.812264 | + | 0.583290i | \(0.198235\pi\) | |||||||
\(558\) | 263254.i | 0.845487i | ||||||||
\(559\) | 7013.44 | − | 2109.56i | 0.0224444 | − | 0.00675100i | ||||
\(560\) | −83148.1 | −0.265141 | ||||||||
\(561\) | 21827.1 | + | 81459.7i | 0.0693537 | + | 0.258831i | ||||
\(562\) | −326964. | + | 566318.i | −1.03521 | + | 1.79303i | ||||
\(563\) | −270897. | + | 156402.i | −0.854648 | + | 0.493431i | −0.862216 | − | 0.506540i | \(-0.830924\pi\) |
0.00756835 | + | 0.999971i | \(0.497591\pi\) | |||||||
\(564\) | −288211. | + | 288211.i | −0.906050 | + | 0.906050i | ||||
\(565\) | −62051.4 | − | 16626.6i | −0.194381 | − | 0.0520843i | ||||
\(566\) | 68351.5 | − | 255091.i | 0.213361 | − | 0.796275i | ||||
\(567\) | 5411.22 | + | 5411.22i | 0.0168317 | + | 0.0168317i | ||||
\(568\) | 135709. | + | 235055.i | 0.420642 | + | 0.728574i | ||||
\(569\) | 121130. | + | 69934.3i | 0.374133 | + | 0.216006i | 0.675263 | − | 0.737577i | \(-0.264030\pi\) |
−0.301129 | + | 0.953583i | \(0.597364\pi\) | |||||||
\(570\) | 7151.76 | − | 1916.31i | 0.0220122 | − | 0.00589814i | ||||
\(571\) | 53058.0i | 0.162734i | 0.996684 | + | 0.0813671i | \(0.0259286\pi\) | ||||
−0.996684 | + | 0.0813671i | \(0.974071\pi\) | |||||||
\(572\) | −431467. | + | 266903.i | −1.31873 | + | 0.815758i | ||||
\(573\) | −114993. | −0.350238 | ||||||||
\(574\) | −189287. | − | 706428.i | −0.574508 | − | 2.14409i | ||||
\(575\) | −125196. | + | 216846.i | −0.378664 | + | 0.655866i | ||||
\(576\) | 279975. | − | 161644.i | 0.843868 | − | 0.487207i | ||||
\(577\) | −321525. | + | 321525.i | −0.965748 | + | 0.965748i | −0.999433 | − | 0.0336847i | \(-0.989276\pi\) |
0.0336847 | + | 0.999433i | \(0.489276\pi\) | |||||||
\(578\) | −422548. | − | 113221.i | −1.26480 | − | 0.338901i | ||||
\(579\) | −70060.5 | + | 261470.i | −0.208986 | + | 0.779945i | ||||
\(580\) | −33615.1 | − | 33615.1i | −0.0999261 | − | 0.0999261i | ||||
\(581\) | 139620. | + | 241829.i | 0.413614 | + | 0.716401i | ||||
\(582\) | 208978. | + | 120653.i | 0.616956 | + | 0.356200i | ||||
\(583\) | 19716.6 | − | 5283.05i | 0.0580090 | − | 0.0155435i | ||||
\(584\) | 205627.i | 0.602913i | ||||||||
\(585\) | 57178.0 | + | 30734.8i | 0.167077 | + | 0.0898088i | ||||
\(586\) | 196505. | 0.572240 | ||||||||
\(587\) | 105377. | + | 393271.i | 0.305822 | + | 1.14134i | 0.932236 | + | 0.361852i | \(0.117855\pi\) |
−0.626414 | + | 0.779491i | \(0.715478\pi\) | |||||||
\(588\) | 352156. | − | 609951.i | 1.01854 | − | 1.76417i | ||||
\(589\) | −20890.7 | + | 12061.2i | −0.0602174 | + | 0.0347665i | ||||
\(590\) | 57430.8 | − | 57430.8i | 0.164984 | − | 0.164984i | ||||
\(591\) | 339833. | + | 91058.0i | 0.972950 | + | 0.260701i | ||||
\(592\) | 11612.7 | − | 43339.2i | 0.0331352 | − | 0.123662i | ||||
\(593\) | −65134.9 | − | 65134.9i | −0.185227 | − | 0.185227i | 0.608402 | − | 0.793629i | \(-0.291811\pi\) |
−0.793629 | + | 0.608402i | \(0.791811\pi\) | |||||||
\(594\) | −304321. | − | 527100.i | −0.862500 | − | 1.49389i | ||||
\(595\) | 66956.5 | + | 38657.3i | 0.189129 | + | 0.109194i | ||||
\(596\) | 475552. | − | 127424.i | 1.33877 | − | 0.358722i | ||||
\(597\) | − | 136359.i | − | 0.382591i | ||||||
\(598\) | 218049. | − | 405650.i | 0.609750 | − | 1.13436i | ||||
\(599\) | −267881. | −0.746600 | −0.373300 | − | 0.927711i | \(-0.621774\pi\) | ||||
−0.373300 | + | 0.927711i | \(0.621774\pi\) | |||||||
\(600\) | −30551.8 | − | 114021.i | −0.0848661 | − | 0.316725i | ||||
\(601\) | 92557.9 | − | 160315.i | 0.256250 | − | 0.443839i | −0.708984 | − | 0.705225i | \(-0.750846\pi\) |
0.965234 | + | 0.261386i | \(0.0841795\pi\) | |||||||
\(602\) | −20943.9 | + | 12092.0i | −0.0577916 | + | 0.0333660i | ||||
\(603\) | 199354. | − | 199354.i | 0.548265 | − | 0.548265i | ||||
\(604\) | 312502. | + | 83734.7i | 0.856602 | + | 0.229526i | ||||
\(605\) | −7475.76 | + | 27899.9i | −0.0204242 | + | 0.0762241i | ||||
\(606\) | 93333.3 | + | 93333.3i | 0.254151 | + | 0.254151i | ||||
\(607\) | −159586. | − | 276411.i | −0.433129 | − | 0.750201i | 0.564012 | − | 0.825766i | \(-0.309257\pi\) |
−0.997141 | + | 0.0755656i | \(0.975924\pi\) | |||||||
\(608\) | 33416.5 | + | 19293.0i | 0.0903970 | + | 0.0521907i | ||||
\(609\) | −136350. | + | 36535.0i | −0.367639 | + | 0.0985087i | ||||
\(610\) | − | 100285.i | − | 0.269511i | ||||||
\(611\) | −296941. | − | 480026.i | −0.795403 | − | 1.28583i | ||||
\(612\) | −125664. | −0.335511 | ||||||||
\(613\) | 152708. | + | 569912.i | 0.406387 | + | 1.51666i | 0.801484 | + | 0.598017i | \(0.204044\pi\) |
−0.395097 | + | 0.918640i | \(0.629289\pi\) | |||||||
\(614\) | −367229. | + | 636060.i | −0.974094 | + | 1.68718i | ||||
\(615\) | 47629.1 | − | 27498.7i | 0.125928 | − | 0.0727045i | ||||
\(616\) | 327253. | − | 327253.i | 0.862427 | − | 0.862427i | ||||
\(617\) | −473767. | − | 126946.i | −1.24450 | − | 0.333463i | −0.424290 | − | 0.905526i | \(-0.639476\pi\) |
−0.820209 | + | 0.572063i | \(0.806143\pi\) | |||||||
\(618\) | 29749.0 | − | 111025.i | 0.0778925 | − | 0.290699i | ||||
\(619\) | −241958. | − | 241958.i | −0.631478 | − | 0.631478i | 0.316961 | − | 0.948439i | \(-0.397338\pi\) |
−0.948439 | + | 0.316961i | \(0.897338\pi\) | |||||||
\(620\) | −70922.9 | − | 122842.i | −0.184503 | − | 0.319568i | ||||
\(621\) | 277576. | + | 160258.i | 0.719777 | + | 0.415564i | ||||
\(622\) | 82801.4 | − | 22186.6i | 0.214021 | − | 0.0573468i | ||||
\(623\) | − | 126247.i | − | 0.325270i | ||||||
\(624\) | −32512.0 | − | 108089.i | −0.0834976 | − | 0.277596i | ||||
\(625\) | −285604. | −0.731147 | ||||||||
\(626\) | 101072. | + | 377206.i | 0.257918 | + | 0.962565i | ||||
\(627\) | 10712.4 | − | 18554.4i | 0.0272491 | − | 0.0471968i | ||||
\(628\) | −425869. | + | 245876.i | −1.07983 | + | 0.623442i | ||||
\(629\) | −29500.6 | + | 29500.6i | −0.0745642 | + | 0.0745642i | ||||
\(630\) | −207051. | − | 55479.1i | −0.521670 | − | 0.139781i | ||||
\(631\) | −79353.2 | + | 296150.i | −0.199299 | + | 0.743795i | 0.791813 | + | 0.610764i | \(0.209138\pi\) |
−0.991112 | + | 0.133031i | \(0.957529\pi\) | |||||||
\(632\) | −240191. | − | 240191.i | −0.601344 | − | 0.601344i | ||||
\(633\) | 42418.8 | + | 73471.4i | 0.105865 | + | 0.183363i | ||||
\(634\) | −79788.5 | − | 46065.9i | −0.198501 | − | 0.114604i | ||||
\(635\) | −28291.5 | + | 7580.70i | −0.0701632 | + | 0.0188002i | ||||
\(636\) | − | 18344.0i | − | 0.0453502i | ||||||
\(637\) | 710308. | + | 668409.i | 1.75052 | + | 1.64727i | ||||
\(638\) | −237122. | −0.582546 | ||||||||
\(639\) | −94149.6 | − | 351371.i | −0.230577 | − | 0.860526i | ||||
\(640\) | −68024.8 | + | 117822.i | −0.166076 | + | 0.287652i | ||||
\(641\) | 98429.5 | − | 56828.3i | 0.239557 | − | 0.138308i | −0.375416 | − | 0.926856i | \(-0.622500\pi\) |
0.614973 | + | 0.788548i | \(0.289167\pi\) | |||||||
\(642\) | 93038.2 | − | 93038.2i | 0.225731 | − | 0.225731i | ||||
\(643\) | −14225.1 | − | 3811.61i | −0.0344060 | − | 0.00921906i | 0.241575 | − | 0.970382i | \(-0.422336\pi\) |
−0.275981 | + | 0.961163i | \(0.589003\pi\) | |||||||
\(644\) | −228338. | + | 852170.i | −0.550563 | + | 2.05473i | ||||
\(645\) | −1285.97 | − | 1285.97i | −0.00309108 | − | 0.00309108i | ||||
\(646\) | −9924.32 | − | 17189.4i | −0.0237813 | − | 0.0411904i | ||||
\(647\) | −213468. | − | 123246.i | −0.509946 | − | 0.294417i | 0.222866 | − | 0.974849i | \(-0.428459\pi\) |
−0.732811 | + | 0.680432i | \(0.761792\pi\) | |||||||
\(648\) | 3082.63 | − | 825.989i | 0.00734128 | − | 0.00196709i | ||||
\(649\) | − | 235022.i | − | 0.557980i | ||||||
\(650\) | 591468. | − | 17974.5i | 1.39993 | − | 0.0425432i | ||||
\(651\) | −421191. | −0.993843 | ||||||||
\(652\) | −40784.5 | − | 152210.i | −0.0959401 | − | 0.358053i | ||||
\(653\) | 114446. | − | 198226.i | 0.268394 | − | 0.464872i | −0.700053 | − | 0.714091i | \(-0.746840\pi\) |
0.968447 | + | 0.249219i | \(0.0801738\pi\) | |||||||
\(654\) | 345386. | − | 199409.i | 0.807513 | − | 0.466218i | ||||
\(655\) | 99872.3 | − | 99872.3i | 0.232789 | − | 0.232789i | ||||
\(656\) | 153157. | + | 41038.4i | 0.355902 | + | 0.0953636i | ||||
\(657\) | 71327.8 | − | 266199.i | 0.165245 | − | 0.616703i | ||||
\(658\) | 1.31794e6 | + | 1.31794e6i | 3.04399 | + | 3.04399i | ||||
\(659\) | −139582. | − | 241763.i | −0.321409 | − | 0.556697i | 0.659370 | − | 0.751819i | \(-0.270823\pi\) |
−0.980779 | + | 0.195122i | \(0.937490\pi\) | |||||||
\(660\) | 109104. | + | 62991.4i | 0.250469 | + | 0.144608i | ||||
\(661\) | 85509.9 | − | 22912.3i | 0.195710 | − | 0.0524404i | −0.159632 | − | 0.987177i | \(-0.551031\pi\) |
0.355343 | + | 0.934736i | \(0.384364\pi\) | |||||||
\(662\) | − | 290178.i | − | 0.662138i | ||||||
\(663\) | −24072.2 | + | 102156.i | −0.0547631 | + | 0.232401i | ||||
\(664\) | 116452. | 0.264125 | ||||||||
\(665\) | −5083.66 | − | 18972.5i | −0.0114956 | − | 0.0429023i | ||||
\(666\) | 57834.6 | − | 100172.i | 0.130388 | − | 0.225839i | ||||
\(667\) | 108141. | − | 62435.3i | 0.243074 | − | 0.140339i | ||||
\(668\) | −482197. | + | 482197.i | −1.08062 | + | 1.08062i | ||||
\(669\) | −7420.00 | − | 1988.18i | −0.0165787 | − | 0.00444226i | ||||
\(670\) | −67772.2 | + | 252929.i | −0.150974 | + | 0.563443i | ||||
\(671\) | −205196. | − | 205196.i | −0.455748 | − | 0.455748i | ||||
\(672\) | 336867. | + | 583470.i | 0.745967 | + | 1.29205i | ||||
\(673\) | 130883. | + | 75565.6i | 0.288971 | + | 0.166838i | 0.637478 | − | 0.770469i | \(-0.279978\pi\) |
−0.348507 | + | 0.937306i | \(0.613311\pi\) | |||||||
\(674\) | −51232.1 | + | 13727.6i | −0.112777 | + | 0.0302186i | ||||
\(675\) | 411827.i | 0.903873i | ||||||||
\(676\) | −630237. | + | 38340.7i | −1.37915 | + | 0.0839010i | ||||
\(677\) | 752917. | 1.64274 | 0.821372 | − | 0.570393i | \(-0.193209\pi\) | ||||
0.821372 | + | 0.570393i | \(0.193209\pi\) | |||||||
\(678\) | 74529.9 | + | 278149.i | 0.162133 | + | 0.605088i | ||||
\(679\) | 320074. | − | 554385.i | 0.694243 | − | 1.20246i | ||||
\(680\) | 27922.9 | − | 16121.3i | 0.0603869 | − | 0.0348644i | ||||
\(681\) | 309628. | − | 309628.i | 0.667645 | − | 0.667645i | ||||
\(682\) | −683411. | − | 183120.i | −1.46931 | − | 0.393700i | ||||
\(683\) | −145592. | + | 543357.i | −0.312102 | + | 1.16478i | 0.614555 | + | 0.788874i | \(0.289335\pi\) |
−0.926657 | + | 0.375907i | \(0.877331\pi\) | |||||||
\(684\) | 22574.2 | + | 22574.2i | 0.0482504 | + | 0.0482504i | ||||
\(685\) | −113878. | − | 197242.i | −0.242694 | − | 0.420358i | ||||
\(686\) | −1.62883e6 | − | 940404.i | −3.46120 | − | 1.99833i | ||||
\(687\) | −370365. | + | 99238.9i | −0.784723 | + | 0.210266i | ||||
\(688\) | − | 5243.21i | − | 0.0110770i | ||||||
\(689\) | 24726.1 | + | 5826.47i | 0.0520854 | + | 0.0122735i | ||||
\(690\) | −114360. | −0.240202 | ||||||||
\(691\) | −103894. | − | 387737.i | −0.217588 | − | 0.812048i | −0.985240 | − | 0.171181i | \(-0.945242\pi\) |
0.767652 | − | 0.640867i | \(-0.221425\pi\) | |||||||
\(692\) | 602169. | − | 1.04299e6i | 1.25749 | − | 2.17804i | ||||
\(693\) | −537170. | + | 310135.i | −1.11852 | + | 0.645780i | ||||
\(694\) | 752816. | − | 752816.i | 1.56304 | − | 1.56304i | ||||
\(695\) | 111566. | + | 29894.0i | 0.230973 | + | 0.0618892i | ||||
\(696\) | −15236.2 | + | 56862.3i | −0.0314528 | + | 0.117383i | ||||
\(697\) | −104253. | − | 104253.i | −0.214597 | − | 0.214597i | ||||
\(698\) | 405105. | + | 701662.i | 0.831489 | + | 1.44018i | ||||
\(699\) | −433338. | − | 250188.i | −0.886894 | − | 0.512049i | ||||
\(700\) | −1.09494e6 | + | 293388.i | −2.23457 | + | 0.598752i | ||||
\(701\) | − | 465668.i | − | 0.947634i | −0.880623 | − | 0.473817i | \(-0.842876\pi\) | ||
0.880623 | − | 0.473817i | \(-0.157124\pi\) | |||||||
\(702\) | −23008.5 | − | 757116.i | −0.0466889 | − | 1.53634i | ||||
\(703\) | 10599.0 | 0.0214464 | ||||||||
\(704\) | 224879. | + | 839259.i | 0.453736 | + | 1.69336i | ||||
\(705\) | −70080.7 | + | 121383.i | −0.141000 | + | 0.244220i | ||||
\(706\) | 235147. | − | 135762.i | 0.471770 | − | 0.272377i | ||||
\(707\) | 247598. | − | 247598.i | 0.495346 | − | 0.495346i | ||||
\(708\) | −204012. | − | 54664.9i | −0.406995 | − | 0.109054i | ||||
\(709\) | −198348. | + | 740245.i | −0.394581 | + | 1.47259i | 0.427913 | + | 0.903820i | \(0.359249\pi\) |
−0.822493 | + | 0.568775i | \(0.807418\pi\) | |||||||
\(710\) | 238903. | + | 238903.i | 0.473921 | + | 0.473921i | ||||
\(711\) | 227628. | + | 394262.i | 0.450283 | + | 0.779913i | ||||
\(712\) | −45595.1 | − | 26324.4i | −0.0899412 | − | 0.0519276i | ||||
\(713\) | 359891. | − | 96432.5i | 0.707932 | − | 0.189690i | ||||
\(714\) | − | 346568.i | − | 0.679817i | ||||||
\(715\) | −119561. | + | 127056.i | −0.233872 | + | 0.248532i | ||||
\(716\) | 323140. | 0.630326 | ||||||||
\(717\) | −108323. | − | 404268.i | −0.210709 | − | 0.786378i | ||||
\(718\) | 68494.5 | − | 118636.i | 0.132864 | − | 0.230127i | ||||
\(719\) | −579881. | + | 334794.i | −1.12171 | + | 0.647620i | −0.941837 | − | 0.336070i | \(-0.890902\pi\) |
−0.179874 | + | 0.983690i | \(0.557569\pi\) | |||||||
\(720\) | 32861.6 | − | 32861.6i | 0.0633904 | − | 0.0633904i | ||||
\(721\) | −294531. | − | 78919.4i | −0.566579 | − | 0.151814i | ||||
\(722\) | 206911. | − | 772201.i | 0.396925 | − | 1.48134i | ||||
\(723\) | 101247. | + | 101247.i | 0.193690 | + | 0.193690i | ||||
\(724\) | −172840. | − | 299368.i | −0.329736 | − | 0.571120i | ||||
\(725\) | 138949. | + | 80222.2i | 0.264350 | + | 0.152622i | ||||
\(726\) | 125063. | − | 33510.6i | 0.237277 | − | 0.0635783i | ||||
\(727\) | 852719.i | 1.61338i | 0.590974 | + | 0.806690i | \(0.298743\pi\) | ||||
−0.590974 | + | 0.806690i | \(0.701257\pi\) | |||||||
\(728\) | 551559. | − | 165902.i | 1.04071 | − | 0.313033i | ||||
\(729\) | 320373. | 0.602839 | ||||||||
\(730\) | 66248.2 | + | 247242.i | 0.124316 | + | 0.463955i | ||||
\(731\) | −2437.68 | + | 4222.19i | −0.00456186 | + | 0.00790137i | ||||
\(732\) | −225850. | + | 130394.i | −0.421500 | + | 0.243353i | ||||
\(733\) | 195353. | − | 195353.i | 0.363590 | − | 0.363590i | −0.501543 | − | 0.865133i | \(-0.667234\pi\) |
0.865133 | + | 0.501543i | \(0.167234\pi\) | |||||||
\(734\) | 1.20429e6 | + | 322689.i | 2.23532 | + | 0.598953i | ||||
\(735\) | 62684.9 | − | 233943.i | 0.116035 | − | 0.433048i | ||||
\(736\) | −421425. | − | 421425.i | −0.777974 | − | 0.777974i | ||||
\(737\) | 378855. | + | 656197.i | 0.697491 | + | 1.20809i | ||||
\(738\) | 354002. | + | 204383.i | 0.649969 | + | 0.375260i | ||||
\(739\) | 341809. | − | 91587.4i | 0.625885 | − | 0.167705i | 0.0680832 | − | 0.997680i | \(-0.478312\pi\) |
0.557802 | + | 0.829974i | \(0.311645\pi\) | |||||||
\(740\) | 62324.5i | 0.113814i | ||||||||
\(741\) | 22675.7 | − | 14027.0i | 0.0412975 | − | 0.0255464i | ||||
\(742\) | −83883.8 | −0.152360 | ||||||||
\(743\) | −107468. | − | 401075.i | −0.194671 | − | 0.726520i | −0.992352 | − | 0.123441i | \(-0.960607\pi\) |
0.797681 | − | 0.603079i | \(-0.206060\pi\) | |||||||
\(744\) | −87824.9 | + | 152117.i | −0.158662 | + | 0.274810i | ||||
\(745\) | 146618. | − | 84650.1i | 0.264165 | − | 0.152516i | ||||
\(746\) | −1.08978e6 | + | 1.08978e6i | −1.95821 | + | 1.95821i | ||||
\(747\) | −150755. | − | 40394.7i | −0.270166 | − | 0.0723908i | ||||
\(748\) | 87411.7 | − | 326225.i | 0.156231 | − | 0.583061i | ||||
\(749\) | −246815. | − | 246815.i | −0.439955 | − | 0.439955i | ||||
\(750\) | −154425. | − | 267472.i | −0.274534 | − | 0.475506i | ||||
\(751\) | 163029. | + | 94124.8i | 0.289058 | + | 0.166888i | 0.637517 | − | 0.770436i | \(-0.279962\pi\) |
−0.348459 | + | 0.937324i | \(0.613295\pi\) | |||||||
\(752\) | −390323. | + | 104587.i | −0.690222 | + | 0.184944i | ||||
\(753\) | 369587.i | 0.651819i | ||||||||
\(754\) | −259930. | − | 139720.i | −0.457208 | − | 0.245763i | ||||
\(755\) | 111253. | 0.195172 | ||||||||
\(756\) | 375555. | + | 1.40159e6i | 0.657098 | + | 2.45232i | ||||
\(757\) | −399242. | + | 691507.i | −0.696698 | + | 1.20672i | 0.272908 | + | 0.962040i | \(0.412015\pi\) |
−0.969605 | + | 0.244675i | \(0.921319\pi\) | |||||||
\(758\) | −393124. | + | 226970.i | −0.684213 | + | 0.395031i | ||||
\(759\) | −233995. | + | 233995.i | −0.406185 | + | 0.406185i | ||||
\(760\) | −7912.10 | − | 2120.04i | −0.0136982 | − | 0.00367043i | ||||
\(761\) | 24628.2 | − | 91913.9i | 0.0425269 | − | 0.158713i | −0.941397 | − | 0.337300i | \(-0.890486\pi\) |
0.983924 | + | 0.178588i | \(0.0571528\pi\) | |||||||
\(762\) | 92837.7 | + | 92837.7i | 0.159887 | + | 0.159887i | ||||
\(763\) | −529000. | − | 916255.i | −0.908671 | − | 1.57386i | ||||
\(764\) | 398821. | + | 230259.i | 0.683268 | + | 0.394485i | ||||
\(765\) | −41740.4 | + | 11184.3i | −0.0713237 | + | 0.0191111i | ||||
\(766\) | − | 621370.i | − | 1.05899i | ||||||
\(767\) | 138482. | − | 257628.i | 0.235399 | − | 0.437927i | ||||
\(768\) | 44726.3 | 0.0758300 | ||||||||
\(769\) | 110548. | + | 412572.i | 0.186939 | + | 0.697666i | 0.994207 | + | 0.107481i | \(0.0342784\pi\) |
−0.807268 | + | 0.590185i | \(0.799055\pi\) | |||||||
\(770\) | 288049. | − | 498916.i | 0.485831 | − | 0.841484i | ||||
\(771\) | −177772. | + | 102637.i | −0.299058 | + | 0.172661i | ||||
\(772\) | 766543. | − | 766543.i | 1.28618 | − | 1.28618i | ||||
\(773\) | −931158. | − | 249503.i | −1.55835 | − | 0.417558i | −0.626208 | − | 0.779656i | \(-0.715394\pi\) |
−0.932140 | + | 0.362097i | \(0.882061\pi\) | |||||||
\(774\) | 3498.44 | − | 13056.3i | 0.00583972 | − | 0.0217941i | ||||
\(775\) | 338514. | + | 338514.i | 0.563602 | + | 0.563602i | ||||
\(776\) | −133481. | − | 231196.i | −0.221664 | − | 0.383934i | ||||
\(777\) | 160270. | + | 92532.0i | 0.265467 | + | 0.153267i | ||||
\(778\) | −1.27607e6 | + | 341923.i | −2.10822 | + | 0.564897i | ||||
\(779\) | 37456.0i | 0.0617229i | ||||||||
\(780\) | 82482.2 | + | 133338.i | 0.135572 | + | 0.219162i | ||||
\(781\) | 977654. | 1.60281 | ||||||||
\(782\) | 79347.3 | + | 296128.i | 0.129753 | + | 0.484246i | ||||
\(783\) | 102689. | − | 177863.i | 0.167495 | − | 0.290110i | ||||
\(784\) | 604714. | − | 349132.i | 0.983825 | − | 0.568012i | ||||
\(785\) | −119573. | + | 119573.i | −0.194041 | + | 0.194041i | ||||
\(786\) | −611547. | − | 163864.i | −0.989885 | − | 0.265239i | ||||
\(787\) | −179306. | + | 669180.i | −0.289498 | + | 1.08042i | 0.655991 | + | 0.754769i | \(0.272251\pi\) |
−0.945489 | + | 0.325653i | \(0.894416\pi\) | |||||||
\(788\) | −996279. | − | 996279.i | −1.60446 | − | 1.60446i | ||||
\(789\) | −60175.8 | − | 104227.i | −0.0966646 | − | 0.167428i | ||||
\(790\) | −366185. | − | 211417.i | −0.586741 | − | 0.338755i | ||||
\(791\) | 737885. | − | 197716.i | 1.17933 | − | 0.316001i | ||||
\(792\) | 258672.i | 0.412381i | ||||||||
\(793\) | −104025. | − | 345842.i | −0.165422 | − | 0.549960i | ||||
\(794\) | 843260. | 1.33758 | ||||||||
\(795\) | −1632.65 | − | 6093.12i | −0.00258320 | − | 0.00964063i | ||||
\(796\) | −273041. | + | 472920.i | −0.430924 | + | 0.746383i | ||||
\(797\) | 806320. | − | 465529.i | 1.26938 | − | 0.732875i | 0.294507 | − | 0.955649i | \(-0.404845\pi\) |
0.974870 | + | 0.222774i | \(0.0715112\pi\) | |||||||
\(798\) | −62257.4 | + | 62257.4i | −0.0977655 | + | 0.0977655i | ||||
\(799\) | 362939. | + | 97249.2i | 0.568513 | + | 0.152333i | ||||
\(800\) | 198197. | − | 739680.i | 0.309682 | − | 1.15575i | ||||
\(801\) | 49894.8 | + | 49894.8i | 0.0777661 | + | 0.0777661i | ||||
\(802\) | −632161. | − | 1.09494e6i | −0.982832 | − | 1.70231i | ||||
\(803\) | 641441. | + | 370336.i | 0.994777 | + | 0.574334i | ||||
\(804\) | 657736. | − | 176240.i | 1.01751 | − | 0.272642i | ||||
\(805\) | 303379.i | 0.468159i | ||||||||
\(806\) | −641247. | − | 603422.i | −0.987086 | − | 0.928861i | ||||
\(807\) | 595622. | 0.914584 | ||||||||
\(808\) | −37794.4 | − | 141051.i | −0.0578901 | − | 0.216049i | ||||
\(809\) | 26946.9 | − | 46673.5i | 0.0411730 | − | 0.0713137i | −0.844705 | − | 0.535233i | \(-0.820224\pi\) |
0.885878 | + | 0.463919i | \(0.153557\pi\) | |||||||
\(810\) | 3440.38 | − | 1986.30i | 0.00524368 | − | 0.00302744i | ||||
\(811\) | −867670. | + | 867670.i | −1.31921 | + | 1.31921i | −0.404803 | + | 0.914404i | \(0.632660\pi\) |
−0.914404 | + | 0.404803i | \(0.867340\pi\) | |||||||
\(812\) | 546048. | + | 146313.i | 0.828169 | + | 0.221907i | ||||
\(813\) | 62781.4 | − | 234303.i | 0.0949838 | − | 0.354485i | ||||
\(814\) | 219819. | + | 219819.i | 0.331755 | + | 0.331755i | ||||
\(815\) | −27093.9 | − | 46928.0i | −0.0407903 | − | 0.0706508i | ||||
\(816\) | 65071.2 | + | 37568.9i | 0.0977257 | + | 0.0564219i | ||||
\(817\) | 1196.38 | − | 320.569i | 0.00179236 | − | 0.000480260i | ||||
\(818\) | 974901.i | 1.45698i | ||||||||
\(819\) | −771581. | + | 23448.1i | −1.15031 | + | 0.0349574i | ||||
\(820\) | −220250. | −0.327558 | ||||||||
\(821\) | −277240. | − | 1.03468e6i | −0.411311 | − | 1.53503i | −0.792112 | − | 0.610376i | \(-0.791018\pi\) |
0.380801 | − | 0.924657i | \(-0.375648\pi\) | |||||||
\(822\) | −510465. | + | 884151.i | −0.755478 | + | 1.30853i | ||||
\(823\) | 948821. | − | 547802.i | 1.40083 | − | 0.808768i | 0.406350 | − | 0.913718i | \(-0.366801\pi\) |
0.994478 | + | 0.104950i | \(0.0334682\pi\) | |||||||
\(824\) | −89916.7 | + | 89916.7i | −0.132430 | + | 0.132430i | ||||
\(825\) | −410705. | − | 110048.i | −0.603424 | − | 0.161687i | ||||
\(826\) | −249973. | + | 932913.i | −0.366381 | + | 1.36735i | ||||
\(827\) | −118484. | − | 118484.i | −0.173240 | − | 0.173240i | 0.615161 | − | 0.788401i | \(-0.289091\pi\) |
−0.788401 | + | 0.615161i | \(0.789091\pi\) | |||||||
\(828\) | −246549. | − | 427035.i | −0.359619 | − | 0.622878i | ||||
\(829\) | −598258. | − | 345405.i | −0.870522 | − | 0.502596i | −0.00300029 | − | 0.999995i | \(-0.500955\pi\) |
−0.867522 | + | 0.497399i | \(0.834288\pi\) | |||||||
\(830\) | 140019. | − | 37518.0i | 0.203250 | − | 0.0544608i | ||||
\(831\) | 6914.49i | 0.0100129i | ||||||||
\(832\) | −248010. | + | 1.05249e6i | −0.358279 | + | 1.52045i | ||||
\(833\) | −649275. | −0.935705 | ||||||||
\(834\) | −134002. | − | 500101.i | −0.192654 | − | 0.718995i | ||||
\(835\) | −117250. | + | 203083.i | −0.168166 | + | 0.291273i | ||||
\(836\) | −74305.7 | + | 42900.4i | −0.106319 | + | 0.0613831i | ||||
\(837\) | 433318. | − | 433318.i | 0.618523 | − | 0.618523i | ||||
\(838\) | 1.17513e6 | + | 314875.i | 1.67339 | + | 0.448384i | ||||
\(839\) | 43984.2 | − | 164151.i | 0.0624845 | − | 0.233195i | −0.927620 | − | 0.373524i | \(-0.878149\pi\) |
0.990105 | + | 0.140329i | \(0.0448160\pi\) | |||||||
\(840\) | −101132. | − | 101132.i | −0.143328 | − | 0.143328i | ||||
\(841\) | 313634. | + | 543229.i | 0.443436 | + | 0.768053i | ||||
\(842\) | 815994. | + | 471114.i | 1.15097 | + | 0.664511i | ||||
\(843\) | 564844. | − | 151349.i | 0.794828 | − | 0.212974i | ||||
\(844\) | − | 339752.i | − | 0.476955i | ||||||
\(845\) | −205927. | + | 68827.4i | −0.288402 | + | 0.0963936i | ||||
\(846\) | −1.04174e6 | −1.45553 | ||||||||
\(847\) | −88898.2 | − | 331773.i | −0.123916 | − | 0.462459i | ||||
\(848\) | 9093.23 | − | 15749.9i | 0.0126452 | − | 0.0219022i | ||||
\(849\) | −204521. | + | 118080.i | −0.283741 | + | 0.163818i | ||||
\(850\) | −278538. | + | 278538.i | −0.385520 | + | 0.385520i | ||||
\(851\) | −158130. | − | 42370.7i | −0.218350 | − | 0.0585068i | ||||
\(852\) | 227398. | − | 848660.i | 0.313261 | − | 1.16911i | ||||
\(853\) | −621614. | − | 621614.i | −0.854324 | − | 0.854324i | 0.136338 | − | 0.990662i | \(-0.456467\pi\) |
−0.990662 | + | 0.136338i | \(0.956467\pi\) | |||||||
\(854\) | 596271. | + | 1.03277e6i | 0.817576 | + | 1.41608i | ||||
\(855\) | 9507.39 | + | 5489.09i | 0.0130056 | + | 0.00750876i | ||||
\(856\) | −140604. | + | 37674.9i | −0.191890 | + | 0.0514167i | ||||
\(857\) | 433050.i | 0.589626i | 0.955555 | + | 0.294813i | \(0.0952574\pi\) | ||||
−0.955555 | + | 0.294813i | \(0.904743\pi\) | |||||||
\(858\) | 761201. | + | 179370.i | 1.03401 | + | 0.243655i | ||||
\(859\) | 264929. | 0.359040 | 0.179520 | − | 0.983754i | \(-0.442546\pi\) | ||||
0.179520 | + | 0.983754i | \(0.442546\pi\) | |||||||
\(860\) | 1885.02 | + | 7034.98i | 0.00254870 | + | 0.00951188i | ||||
\(861\) | −327001. | + | 566382.i | −0.441106 | + | 0.764017i | ||||
\(862\) | −670878. | + | 387332.i | −0.902878 | + | 0.521277i | ||||
\(863\) | 344574. | − | 344574.i | 0.462659 | − | 0.462659i | −0.436867 | − | 0.899526i | \(-0.643912\pi\) |
0.899526 | + | 0.436867i | \(0.143912\pi\) | |||||||
\(864\) | −946835. | − | 253704.i | −1.26837 | − | 0.339859i | ||||
\(865\) | 107188. | − | 400032.i | 0.143257 | − | 0.534641i | ||||
\(866\) | 1.15383e6 | + | 1.15383e6i | 1.53853 | + | 1.53853i | ||||
\(867\) | 195595. | + | 338780.i | 0.260207 | + | 0.450692i | ||||
\(868\) | 1.46078e6 | + | 843381.i | 1.93885 | + | 1.11940i | ||||
\(869\) | −1.18185e6 | + | 316675.i | −1.56503 | + | 0.419348i | ||||
\(870\) | 73278.8i | 0.0968144i | ||||||||
\(871\) | 28643.7 | + | 942548.i | 0.0377566 | + | 1.24242i | ||||
\(872\) | −441219. | −0.580258 | ||||||||
\(873\) | 92603.6 | + | 345601.i | 0.121506 | + | 0.453468i | ||||
\(874\) | 38942.5 | − | 67450.4i | 0.0509801 | − | 0.0883002i | ||||
\(875\) | −709561. | + | 409665.i | −0.926774 | + | 0.535073i | ||||
\(876\) | 470669. | − | 470669.i | 0.613348 | − | 0.613348i | ||||
\(877\) | 910707. | + | 244023.i | 1.18408 | + | 0.317272i | 0.796542 | − | 0.604583i | \(-0.206660\pi\) |
0.387534 | + | 0.921855i | \(0.373327\pi\) | |||||||
\(878\) | 383463. | − | 1.43110e6i | 0.497433 | − | 1.85644i | ||||
\(879\) | −124255. | − | 124255.i | −0.160818 | − | 0.160818i | ||||
\(880\) | 62450.6 | + | 108168.i | 0.0806438 | + | 0.139679i | ||||
\(881\) | −896268. | − | 517461.i | −1.15475 | − | 0.666692i | −0.204706 | − | 0.978823i | \(-0.565624\pi\) |
−0.950039 | + | 0.312131i | \(0.898957\pi\) | |||||||
\(882\) | 1.73878e6 | − | 465904.i | 2.23515 | − | 0.598907i | ||||
\(883\) | − | 200330.i | − | 0.256936i | −0.991714 | − | 0.128468i | \(-0.958994\pi\) | ||
0.991714 | − | 0.128468i | \(-0.0410059\pi\) | |||||||
\(884\) | 288042. | − | 306098.i | 0.368596 | − | 0.391702i | ||||
\(885\) | −72629.8 | −0.0927317 | ||||||||
\(886\) | 90247.5 | + | 336808.i | 0.114966 | + | 0.429057i | ||||
\(887\) | 661285. | − | 1.14538e6i | 0.840507 | − | 1.45580i | −0.0489590 | − | 0.998801i | \(-0.515590\pi\) |
0.889466 | − | 0.457001i | \(-0.151076\pi\) | |||||||
\(888\) | 66837.6 | − | 38588.7i | 0.0847608 | − | 0.0489366i | ||||
\(889\) | 246283. | − | 246283.i | 0.311625 | − | 0.311625i | ||||
\(890\) | −63303.7 | − | 16962.2i | −0.0799189 | − | 0.0214142i | ||||
\(891\) | 2975.23 | − | 11103.7i | 0.00374770 | − | 0.0139866i | ||||
\(892\) | 21753.0 | + | 21753.0i | 0.0273394 | + | 0.0273394i | ||||
\(893\) | −47728.5 | − | 82668.2i | −0.0598515 | − | 0.103666i | ||||
\(894\) | −657225. | − | 379449.i | −0.822317 | − | 0.474765i | ||||
\(895\) | 107334. | − | 28760.1i | 0.133996 | − | 0.0359041i | ||||
\(896\) | − | 1.61784e6i | − | 2.01520i | ||||||
\(897\) | −394380. | + | 118625.i | −0.490151 | + | 0.147432i | ||||
\(898\) | −825892. | −1.02417 | ||||||||
\(899\) | −61791.4 | − | 230609.i | −0.0764554 | − | 0.285336i | ||||
\(900\) | 316787. | − | 548691.i | 0.391095 | − | 0.677397i | ||||
\(901\) | −14645.0 | + | 8455.27i | −0.0180401 | + | 0.0104154i | ||||
\(902\) | −776824. | + | 776824.i | −0.954794 | + | 0.954794i | ||||
\(903\) | 20889.4 | + | 5597.30i | 0.0256183 | + | 0.00686441i | ||||
\(904\) | 82453.6 | − | 307721.i | 0.100896 | − | 0.376548i | ||||
\(905\) | −84054.6 | − | 84054.6i | −0.102628 | − | 0.102628i | ||||
\(906\) | −249349. | − | 431885.i | −0.303775 | − | 0.526153i | ||||
\(907\) | −1.13720e6 | − | 656563.i | −1.38236 | − | 0.798108i | −0.389925 | − | 0.920847i | \(-0.627499\pi\) |
−0.992439 | + | 0.122738i | \(0.960832\pi\) | |||||||
\(908\) | −1.69384e6 | + | 453864.i | −2.05448 | + | 0.550496i | ||||
\(909\) | 195710.i | 0.236857i | ||||||||
\(910\) | 609733. | − | 377177.i | 0.736304 | − | 0.455473i | ||||
\(911\) | −773793. | −0.932370 | −0.466185 | − | 0.884687i | \(-0.654372\pi\) | ||||
−0.466185 | + | 0.884687i | \(0.654372\pi\) | |||||||
\(912\) | −4940.52 | − | 18438.3i | −0.00593995 | − | 0.0221682i | ||||
\(913\) | 209731. | − | 363264.i | 0.251605 | − | 0.435793i | ||||
\(914\) | −951179. | + | 549164.i | −1.13860 | + | 0.657369i | ||||
\(915\) | −63412.8 | + | 63412.8i | −0.0757416 | + | 0.0757416i | ||||
\(916\) | 1.48321e6 | + | 397426.i | 1.76772 | + | 0.473659i | ||||
\(917\) | −434704. | + | 1.62234e6i | −0.516957 | + | 1.92931i | ||||
\(918\) | 356546. | + | 356546.i | 0.423088 | + | 0.423088i | ||||
\(919\) | 6404.07 | + | 11092.2i | 0.00758272 | + | 0.0131337i | 0.869792 | − | 0.493419i | \(-0.164253\pi\) |
−0.862209 | + | 0.506552i | \(0.830920\pi\) | |||||||
\(920\) | 109568. | + | 63259.1i | 0.129452 | + | 0.0747390i | ||||
\(921\) | 634404. | − | 169988.i | 0.747906 | − | 0.200401i | ||||
\(922\) | − | 1.94166e6i | − | 2.28408i | ||||||
\(923\) | 1.07169e6 | + | 576066.i | 1.25796 | + | 0.676190i | ||||
\(924\) | −1.49813e6 | −1.75471 | ||||||||
\(925\) | −54441.5 | − | 203178.i | −0.0636277 | − | 0.237462i | ||||
\(926\) | −1.04109e6 | + | 1.80323e6i | −1.21414 | + | 2.10295i | ||||
\(927\) | 147594. | − | 85213.4i | 0.171755 | − | 0.0991627i | ||||
\(928\) | −270038. | + | 270038.i | −0.313566 | + | 0.313566i | ||||
\(929\) | −552161. | − | 147951.i | −0.639786 | − | 0.171430i | −0.0756793 | − | 0.997132i | \(-0.524113\pi\) |
−0.564106 | + | 0.825702i | \(0.690779\pi\) | |||||||
\(930\) | −56590.2 | + | 211198.i | −0.0654298 | + | 0.244187i | ||||
\(931\) | 116636. | + | 116636.i | 0.134565 | + | 0.134565i | ||||
\(932\) | 1.00194e6 | + | 1.73540e6i | 1.15347 | + | 1.99788i | ||||
\(933\) | −66386.4 | − | 38328.2i | −0.0762634 | − | 0.0440307i | ||||
\(934\) | 1.79448e6 | − | 480829.i | 2.05705 | − | 0.551184i | ||||
\(935\) | − | 116138.i | − | 0.132847i | ||||||
\(936\) | −152418. | + | 283553.i | −0.173974 | + | 0.323655i | ||||
\(937\) | −763773. | −0.869931 | −0.434966 | − | 0.900447i | \(-0.643239\pi\) | ||||
−0.434966 | + | 0.900447i | \(0.643239\pi\) | |||||||
\(938\) | −805915. | − | 3.00771e6i | −0.915975 | − | 3.41846i | ||||
\(939\) | 174606. | − | 302427.i | 0.198029 | − | 0.342996i | ||||
\(940\) | 486108. | − | 280655.i | 0.550145 | − | 0.317627i | ||||
\(941\) | 408742. | − | 408742.i | 0.461604 | − | 0.461604i | −0.437577 | − | 0.899181i | \(-0.644163\pi\) |
0.899181 | + | 0.437577i | \(0.144163\pi\) | |||||||
\(942\) | 732181. | + | 196187.i | 0.825119 | + | 0.221090i | ||||
\(943\) | 149735. | − | 558818.i | 0.168383 | − | 0.628415i | ||||
\(944\) | −148065. | − | 148065.i | −0.166153 | − | 0.166153i | ||||
\(945\) | 249488. | + | 432126.i | 0.279374 | + | 0.483890i | ||||
\(946\) | 31460.9 | + | 18164.0i | 0.0351552 | + | 0.0202969i | ||||
\(947\) | 70724.2 | − | 18950.5i | 0.0788620 | − | 0.0211310i | −0.219172 | − | 0.975686i | \(-0.570336\pi\) |
0.298034 | + | 0.954555i | \(0.403669\pi\) | |||||||
\(948\) | 1.09957e6i | 1.22350i | ||||||||
\(949\) | 484925. | + | 783915.i | 0.538446 | + | 0.870436i | ||||
\(950\) | 100073. | 0.110884 | ||||||||
\(951\) | 21323.6 | + | 79580.8i | 0.0235776 | + | 0.0879928i | ||||
\(952\) | −191707. | + | 332046.i | −0.211526 | + | 0.366374i | ||||
\(953\) | 896707. | − | 517714.i | 0.987335 | − | 0.570038i | 0.0828585 | − | 0.996561i | \(-0.473595\pi\) |
0.904477 | + | 0.426523i | \(0.140262\pi\) | |||||||
\(954\) | 33152.3 | − | 33152.3i | 0.0364265 | − | 0.0364265i | ||||
\(955\) | 152966. | + | 40987.0i | 0.167721 | + | 0.0449406i | ||||
\(956\) | −433807. | + | 1.61899e6i | −0.474658 | + | 1.77145i | ||||
\(957\) | 149938. | + | 149938.i | 0.163715 | + | 0.163715i | ||||
\(958\) | −661356. | − | 1.14550e6i | −0.720617 | − | 1.24815i | ||||
\(959\) | 2.34551e6 | + | 1.35418e6i | 2.55035 | + | 1.47245i | ||||
\(960\) | 259360. | − | 69495.3i | 0.281424 | − | 0.0754072i | ||||
\(961\) | 211163.i | 0.228650i | ||||||||
\(962\) | 111438. | + | 370488.i | 0.120416 | + | 0.400335i | ||||
\(963\) | 195091. | 0.210371 | ||||||||
\(964\) | −148412. | − | 553881.i | −0.159704 | − | 0.596022i | ||||
\(965\) | 186391. | − | 322838.i | 0.200156 | − | 0.346681i | ||||
\(966\) | 1.17772e6 | − | 679957.i | 1.26208 | − | 0.728664i | ||||
\(967\) | −191562. | + | 191562.i | −0.204860 | + | 0.204860i | −0.802078 | − | 0.597219i | \(-0.796272\pi\) |
0.597219 | + | 0.802078i | \(0.296272\pi\) | |||||||
\(968\) | −138359. | − | 37073.3i | −0.147658 | − | 0.0395649i | ||||
\(969\) | −4593.90 | + | 17144.7i | −0.00489254 | + | 0.0182592i | ||||
\(970\) | −234980. | − | 234980.i | −0.249740 | − | 0.249740i | ||||
\(971\) | 544139. | + | 942477.i | 0.577127 | + | 0.999614i | 0.995807 | + | 0.0914796i | \(0.0291596\pi\) |
−0.418680 | + | 0.908134i | \(0.637507\pi\) | |||||||
\(972\) | −1.13490e6 | − | 655235.i | −1.20123 | − | 0.693529i | ||||
\(973\) | −1.32669e6 | + | 355485.i | −1.40134 | + | 0.375488i | ||||
\(974\) | 355968.i | 0.375226i | ||||||||
\(975\) | −385366. | − | 362634.i | −0.405381 | − | 0.381469i | ||||
\(976\) | −258550. | −0.271421 | ||||||||
\(977\) | −1357.53 | − | 5066.37i | −0.00142220 | − | 0.00530771i | 0.965211 | − | 0.261472i | \(-0.0842079\pi\) |
−0.966633 | + | 0.256164i | \(0.917541\pi\) | |||||||
\(978\) | −121450. | + | 210358.i | −0.126976 | + | 0.219928i | ||||
\(979\) | −164234. | + | 94820.8i | −0.171356 | + | 0.0989323i | ||||
\(980\) | −685846. | + | 685846.i | −0.714125 | + | 0.714125i | ||||
\(981\) | 571189. | + | 153050.i | 0.593529 | + | 0.159036i | ||||
\(982\) | −626028. | + | 2.33637e6i | −0.649189 | + | 2.42280i | ||||
\(983\) | 779317. | + | 779317.i | 0.806505 | + | 0.806505i | 0.984103 | − | 0.177598i | \(-0.0568326\pi\) |
−0.177598 | + | 0.984103i | \(0.556833\pi\) | |||||||
\(984\) | 136369. | + | 236199.i | 0.140840 | + | 0.243943i | ||||
\(985\) | −419594. | − | 242253.i | −0.432471 | − | 0.249687i | ||||
\(986\) | 189751. | − | 50843.6i | 0.195178 | − | 0.0522977i | ||||
\(987\) | − | 1.66673e6i | − | 1.71093i | ||||||
\(988\) | −106731. | + | 3243.52i | −0.109340 | + | 0.00332279i | ||||
\(989\) | −19130.7 | −0.0195586 | ||||||||
\(990\) | 83338.1 | + | 311022.i | 0.0850302 | + | 0.317337i | ||||
\(991\) | −67246.2 | + | 116474.i | −0.0684732 | + | 0.118599i | −0.898229 | − | 0.439527i | \(-0.855146\pi\) |
0.829756 | + | 0.558126i | \(0.188479\pi\) | |||||||
\(992\) | −986819. | + | 569740.i | −1.00280 | + | 0.578967i | ||||
\(993\) | −183487. | + | 183487.i | −0.186083 | + | 0.186083i | ||||
\(994\) | −3.88077e6 | − | 1.03985e6i | −3.92777 | − | 1.05244i | ||||
\(995\) | −48602.2 | + | 181386.i | −0.0490919 | + | 0.183213i | ||||
\(996\) | −266551. | − | 266551.i | −0.268697 | − | 0.268697i | ||||
\(997\) | −949605. | − | 1.64476e6i | −0.955329 | − | 1.65468i | −0.733614 | − | 0.679567i | \(-0.762168\pi\) |
−0.221715 | − | 0.975112i | \(-0.571165\pi\) | |||||||
\(998\) | −372403. | − | 215007.i | −0.373897 | − | 0.215870i | ||||
\(999\) | −260081. | + | 69688.4i | −0.260602 | + | 0.0698280i |
(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 | 13.5.f.a.6.4 | ✓ | 16 | |
3.2 | odd | 2 | 117.5.bd.c.19.1 | 16 | |||
13.4 | even | 6 | 169.5.d.c.70.2 | 16 | |||
13.6 | odd | 12 | 169.5.d.c.99.2 | 16 | |||
13.7 | odd | 12 | 169.5.d.d.99.7 | 16 | |||
13.9 | even | 3 | 169.5.d.d.70.7 | 16 | |||
13.11 | odd | 12 | inner | 13.5.f.a.11.4 | yes | 16 | |
39.11 | even | 12 | 117.5.bd.c.37.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.5.f.a.6.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
13.5.f.a.11.4 | yes | 16 | 13.11 | odd | 12 | inner | |
117.5.bd.c.19.1 | 16 | 3.2 | odd | 2 | |||
117.5.bd.c.37.1 | 16 | 39.11 | even | 12 | |||
169.5.d.c.70.2 | 16 | 13.4 | even | 6 | |||
169.5.d.c.99.2 | 16 | 13.6 | odd | 12 | |||
169.5.d.d.70.7 | 16 | 13.9 | even | 3 | |||
169.5.d.d.99.7 | 16 | 13.7 | odd | 12 |