Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(65,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.h (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 631 x^{10} - 3100 x^{9} + 142264 x^{8} - 550522 x^{7} + 14083117 x^{6} + \cdots + 90728724573 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 69.5 | ||
Root | \(0.500000 + 6.42649i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.69 |
Dual form | 76.5.h.a.65.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.81550 | − | 2.78023i | 0.535056 | − | 0.308914i | −0.208017 | − | 0.978125i | \(-0.566701\pi\) |
0.743073 | + | 0.669211i | \(0.233368\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −13.2594 | − | 22.9660i | −0.530376 | − | 0.918638i | −0.999372 | − | 0.0354377i | \(-0.988717\pi\) |
0.468996 | − | 0.883200i | \(-0.344616\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −84.4930 | −1.72435 | −0.862174 | − | 0.506613i | \(-0.830897\pi\) | ||||
−0.862174 | + | 0.506613i | \(0.830897\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.0406 | + | 43.3717i | −0.309144 | + | 0.535453i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 33.3991 | 0.276025 | 0.138013 | − | 0.990430i | \(-0.455929\pi\) | ||||
0.138013 | + | 0.990430i | \(0.455929\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −32.2160 | − | 18.5999i | −0.190627 | − | 0.110059i | 0.401649 | − | 0.915794i | \(-0.368437\pi\) |
−0.592276 | + | 0.805735i | \(0.701771\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −127.701 | − | 73.7284i | −0.567561 | − | 0.327682i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −62.9369 | − | 109.010i | −0.217775 | − | 0.377197i | 0.736353 | − | 0.676598i | \(-0.236546\pi\) |
−0.954127 | + | 0.299401i | \(0.903213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −354.290 | − | 69.2806i | −0.981412 | − | 0.191913i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −406.876 | + | 234.910i | −0.922622 | + | 0.532676i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 199.345 | − | 345.275i | 0.376833 | − | 0.652695i | −0.613766 | − | 0.789488i | \(-0.710346\pi\) |
0.990600 | + | 0.136793i | \(0.0436796\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −39.1233 | + | 67.7635i | −0.0625972 | + | 0.108422i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 728.872i | 0.999825i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −480.756 | − | 277.565i | −0.571648 | − | 0.330041i | 0.186159 | − | 0.982520i | \(-0.440396\pi\) |
−0.757807 | + | 0.652478i | \(0.773729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1323.28i | − | 1.37698i | −0.725244 | − | 0.688492i | \(-0.758273\pi\) | ||
0.725244 | − | 0.688492i | \(-0.241727\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 160.833 | − | 92.8571i | 0.147689 | − | 0.0852682i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1120.33 | + | 1940.46i | 0.914552 | + | 1.58405i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 630.480i | − | 0.460541i | −0.973127 | − | 0.230270i | \(-0.926039\pi\) | ||
0.973127 | − | 0.230270i | \(-0.0739610\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −206.848 | −0.135995 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2615.46 | − | 1510.04i | 1.55589 | − | 0.898296i | 0.558251 | − | 0.829672i | \(-0.311473\pi\) |
0.997643 | − | 0.0686238i | \(-0.0218608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 953.243 | + | 1651.07i | 0.515545 | + | 0.892950i | 0.999837 | + | 0.0180440i | \(0.00574389\pi\) |
−0.484292 | + | 0.874906i | \(0.660923\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1328.10 | 0.655850 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1710.41 | + | 2962.52i | −0.774292 | + | 1.34111i | 0.160900 | + | 0.986971i | \(0.448560\pi\) |
−0.935192 | + | 0.354142i | \(0.884773\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4738.07 | 1.97337 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −606.145 | − | 349.958i | −0.233043 | − | 0.134547i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −527.826 | − | 304.741i | −0.187905 | − | 0.108487i | 0.403096 | − | 0.915158i | \(-0.367934\pi\) |
−0.591002 | + | 0.806670i | \(0.701267\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −442.852 | − | 767.041i | −0.146397 | − | 0.253567i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1898.70 | + | 651.386i | −0.584395 | + | 0.200488i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4229.93 | + | 2442.15i | −1.21515 | + | 0.701566i | −0.963876 | − | 0.266351i | \(-0.914182\pi\) |
−0.251271 | + | 0.967917i | \(0.580849\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2120.39 | − | 3672.62i | 0.569844 | − | 0.986998i | −0.426737 | − | 0.904376i | \(-0.640337\pi\) |
0.996581 | − | 0.0826224i | \(-0.0263295\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2115.76 | − | 3664.60i | 0.533071 | − | 0.923306i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 986.495i | 0.233490i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3198.52 | − | 1846.67i | −0.712524 | − | 0.411376i | 0.0994711 | − | 0.995040i | \(-0.468285\pi\) |
−0.811995 | + | 0.583665i | \(0.801618\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2216.90i | − | 0.465637i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 588.629 | − | 339.845i | 0.116768 | − | 0.0674162i | −0.440478 | − | 0.897763i | \(-0.645191\pi\) |
0.557247 | + | 0.830347i | \(0.311858\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2278.44 | + | 3946.38i | 0.427555 | + | 0.740548i | 0.996655 | − | 0.0817208i | \(-0.0260416\pi\) |
−0.569100 | + | 0.822268i | \(0.692708\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 435.087i | 0.0773487i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2821.99 | −0.475964 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6779.56 | + | 3914.18i | −1.08629 | + | 0.627172i | −0.932587 | − | 0.360944i | \(-0.882455\pi\) |
−0.153707 | + | 0.988116i | \(0.549121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.85929 | − | 3.22038i | −0.000283384 | − | 0.000490836i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3820.26 | −0.554545 | −0.277272 | − | 0.960791i | \(-0.589430\pi\) | ||||
−0.277272 | + | 0.960791i | \(0.589430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1669.01 | + | 2890.81i | −0.231005 | + | 0.400112i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3086.77 | −0.407818 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12667.5 | − | 7313.61i | −1.59924 | − | 0.923319i | −0.991635 | − | 0.129077i | \(-0.958799\pi\) |
−0.607601 | − | 0.794242i | \(-0.707868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2722.03 | + | 1571.56i | 0.328707 | + | 0.189779i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3679.03 | − | 6372.26i | −0.425370 | − | 0.736763i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3106.57 | + | 9055.22i | 0.344219 | + | 1.00335i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8157.18 | − | 4709.55i | 0.866955 | − | 0.500536i | 0.000619586 | − | 1.00000i | \(-0.499803\pi\) |
0.866335 | + | 0.499463i | \(0.166469\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −836.334 | + | 1448.57i | −0.0853315 | + | 0.147799i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5659.50 | − | 9802.55i | 0.554799 | − | 0.960940i | −0.443120 | − | 0.896462i | \(-0.646129\pi\) |
0.997919 | − | 0.0644777i | \(-0.0205381\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6757.10i | − | 0.636922i | −0.947936 | − | 0.318461i | \(-0.896834\pi\) | ||
0.947936 | − | 0.318461i | \(-0.103166\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10789.9 | + | 6229.53i | 0.978673 | + | 0.565037i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7055.61i | 0.616264i | 0.951344 | + | 0.308132i | \(0.0997039\pi\) | ||||
−0.951344 | + | 0.308132i | \(0.900296\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2141.22 | − | 1236.23i | 0.180222 | − | 0.104051i | −0.407175 | − | 0.913350i | \(-0.633486\pi\) |
0.587397 | + | 0.809299i | \(0.300153\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1752.88 | − | 3036.08i | −0.142268 | − | 0.246415i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4623.82i | 0.362113i | 0.983473 | + | 0.181056i | \(0.0579516\pi\) | ||||
−0.983473 | + | 0.181056i | \(0.942048\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10572.8 | −0.799454 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1613.42 | − | 931.507i | 0.117862 | − | 0.0680479i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5317.73 | + | 9210.57i | 0.375519 | + | 0.650418i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13525.5 | −0.923810 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8396.49 | − | 14543.1i | 0.554993 | − | 0.961276i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −14499.2 | −0.927952 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14711.8 | + | 8493.88i | 0.912136 | + | 0.526622i | 0.881118 | − | 0.472897i | \(-0.156792\pi\) |
0.0310181 | + | 0.999519i | \(0.490125\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9180.68 | + | 5300.47i | 0.551691 | + | 0.318519i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9571.65 | + | 16578.6i | 0.557756 | + | 0.966062i | 0.997683 | + | 0.0680283i | \(0.0216708\pi\) |
−0.439927 | + | 0.898033i | \(0.644996\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 29935.0 | + | 5853.73i | 1.69230 | + | 0.330925i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16739.2 | − | 9664.41i | 0.918477 | − | 0.530283i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6048.91 | + | 10477.0i | −0.322282 | + | 0.558208i | −0.980958 | − | 0.194218i | \(-0.937783\pi\) |
0.658677 | + | 0.752426i | \(0.271117\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14680.6 | − | 25427.5i | 0.759826 | − | 1.31606i | −0.183114 | − | 0.983092i | \(-0.558618\pi\) |
0.942939 | − | 0.332965i | \(-0.108049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19021.3i | 0.956759i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1075.98 | − | 621.220i | −0.0526179 | − | 0.0303790i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14721.4i | 0.700184i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22816.2 | − | 13172.9i | 1.05586 | − | 0.609604i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2080.34 | + | 3603.26i | 0.0937049 | + | 0.162302i | 0.909067 | − | 0.416649i | \(-0.136796\pi\) |
−0.815362 | + | 0.578951i | \(0.803462\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 23274.8i | − | 1.02078i | −0.859943 | − | 0.510390i | \(-0.829501\pi\) | ||
0.859943 | − | 0.510390i | \(-0.170499\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6303.92 | 0.269295 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −30390.4 | + | 17545.9i | −1.26495 | + | 0.730319i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20323.4 | − | 35201.2i | −0.824513 | − | 1.42810i | −0.902291 | − | 0.431127i | \(-0.858116\pi\) |
0.0777786 | − | 0.996971i | \(-0.475217\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3388.99 | −0.134053 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16843.3 | + | 29173.4i | −0.649792 | + | 1.12547i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −25586.5 | −0.963023 | −0.481511 | − | 0.876440i | \(-0.659912\pi\) | ||||
−0.481511 | + | 0.876440i | \(0.659912\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4265.10 | − | 2462.46i | −0.156661 | − | 0.0904484i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16030.7 | − | 9255.32i | −0.574803 | − | 0.331863i | 0.184262 | − | 0.982877i | \(-0.441010\pi\) |
−0.759065 | + | 0.651014i | \(0.774344\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13588.6 | − | 23536.1i | −0.475774 | − | 0.824065i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11876.5 | − | 13631.3i | 0.406158 | − | 0.466171i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −30408.0 | + | 17556.0i | −1.01600 | + | 0.586590i | −0.912944 | − | 0.408086i | \(-0.866196\pi\) |
−0.103059 | + | 0.994675i | \(0.532863\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3305.64 | − | 5725.54i | 0.107939 | − | 0.186956i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13579.5 | + | 23520.4i | −0.433448 | + | 0.750753i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20859.6i | 0.651028i | 0.945537 | + | 0.325514i | \(0.105537\pi\) | ||||
−0.945537 | + | 0.325514i | \(0.894463\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 41594.9 | + | 24014.8i | 1.26965 | + | 0.733030i | 0.974921 | − | 0.222552i | \(-0.0714387\pi\) |
0.294725 | + | 0.955582i | \(0.404772\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 23580.7i | − | 0.704132i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14479.6 | + | 8359.79i | −0.423070 | + | 0.244260i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2102.03 | − | 3640.83i | −0.0601113 | − | 0.104116i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 61584.6i | − | 1.72405i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −52465.4 | −1.43816 | −0.719079 | − | 0.694929i | \(-0.755436\pi\) | ||||
−0.719079 | + | 0.694929i | \(0.755436\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 46145.2 | − | 26642.0i | 1.23883 | − | 0.715240i | 0.269976 | − | 0.962867i | \(-0.412984\pi\) |
0.968855 | + | 0.247627i | \(0.0796508\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2742.68 | + | 4750.46i | 0.0721284 | + | 0.124930i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10872.8 | −0.280161 | −0.140081 | − | 0.990140i | \(-0.544736\pi\) | ||||
−0.140081 | + | 0.990140i | \(0.544736\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10950.4 | + | 18966.6i | −0.276517 | + | 0.478942i | −0.970517 | − | 0.241033i | \(-0.922514\pi\) |
0.694000 | + | 0.719975i | \(0.255847\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20536.6 | −0.508320 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 40620.5 | + | 23452.3i | 0.985720 | + | 0.569106i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −69358.8 | − | 40044.3i | −1.65042 | − | 0.952869i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9983.45 | + | 17291.8i | 0.232991 | + | 0.403553i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11832.9 | − | 2313.91i | −0.270895 | − | 0.0529729i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19016.9 | + | 10979.4i | −0.427143 | + | 0.246611i | −0.698129 | − | 0.715972i | \(-0.745984\pi\) |
0.270985 | + | 0.962583i | \(0.412650\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1889.70 | − | 3273.05i | 0.0416517 | − | 0.0721429i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25278.9 | − | 43784.3i | 0.546865 | − | 0.947199i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 111808.i | 2.37440i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21943.7 | + | 12669.2i | 0.457532 | + | 0.264156i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4682.48i | 0.0958719i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 36180.1 | − | 20888.6i | 0.727545 | − | 0.420048i | −0.0899783 | − | 0.995944i | \(-0.528680\pi\) |
0.817523 | + | 0.575895i | \(0.195346\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1959.34 | − | 3393.68i | −0.0387031 | − | 0.0670357i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 51321.1i | − | 0.995966i | −0.867187 | − | 0.497983i | \(-0.834074\pi\) | ||
0.867187 | − | 0.497983i | \(-0.165926\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9344.76 | 0.178196 | 0.0890978 | − | 0.996023i | \(-0.471602\pi\) | ||||
0.0890978 | + | 0.996023i | \(0.471602\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13589.3 | + | 7845.78i | −0.254667 | + | 0.147032i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 37637.2 | + | 65189.6i | 0.693275 | + | 1.20079i | 0.970759 | + | 0.240057i | \(0.0771662\pi\) |
−0.277484 | + | 0.960730i | \(0.589500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 90716.0 | 1.64266 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21764.7 | + | 37697.5i | −0.387485 | + | 0.671144i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 32265.1 | 0.564855 | 0.282427 | − | 0.959289i | \(-0.408860\pi\) | ||||
0.282427 | + | 0.959289i | \(0.408860\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13807.1 | + | 7971.52i | 0.237721 | + | 0.137248i | 0.614129 | − | 0.789206i | \(-0.289507\pi\) |
−0.376408 | + | 0.926454i | \(0.622841\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −51146.9 | − | 29529.7i | −0.866177 | − | 0.500087i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −62824.0 | − | 108814.i | −1.04663 | − | 1.81282i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10125.2 | + | 8821.70i | 0.165962 | + | 0.144597i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18396.5 | + | 10621.2i | −0.296712 | + | 0.171307i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 58283.1 | − | 100949.i | 0.925114 | − | 1.60234i | 0.133736 | − | 0.991017i | \(-0.457303\pi\) |
0.791378 | − | 0.611327i | \(-0.209364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6657.93 | − | 11531.9i | 0.104016 | − | 0.180160i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18560.9i | 0.285443i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 86480.5 | + | 49929.6i | 1.30934 | + | 0.755947i | 0.981986 | − | 0.188955i | \(-0.0605100\pi\) |
0.327353 | + | 0.944902i | \(0.393843\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 53271.2i | 0.794132i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24076.9 | − | 13900.8i | 0.353443 | − | 0.204060i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27926.3 | + | 48369.8i | 0.403740 | + | 0.699299i | 0.994174 | − | 0.107788i | \(-0.0343766\pi\) |
−0.590434 | + | 0.807086i | \(0.701043\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16162.7i | 0.230156i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −81334.1 | −1.14091 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 82433.0 | − | 47592.7i | 1.13919 | − | 0.657712i | 0.192961 | − | 0.981207i | \(-0.438191\pi\) |
0.946230 | + | 0.323495i | \(0.104858\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19687.4 | + | 34099.6i | 0.268071 | + | 0.464313i | 0.968364 | − | 0.249543i | \(-0.0802804\pi\) |
−0.700293 | + | 0.713856i | \(0.746947\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17477.2 | 0.234502 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1306.68 | + | 2263.24i | −0.0172784 | + | 0.0299271i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −52790.5 | −0.688013 | −0.344006 | − | 0.938967i | \(-0.611784\pi\) | ||||
−0.344006 | + | 0.938967i | \(0.611784\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 57392.9 | + | 33135.8i | 0.737310 | + | 0.425686i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 112961. | + | 65217.8i | 1.43059 | + | 0.825950i | 0.997165 | − | 0.0752419i | \(-0.0239729\pi\) |
0.433421 | + | 0.901191i | \(0.357306\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −37625.8 | − | 65169.8i | −0.469800 | − | 0.813718i | 0.529604 | − | 0.848245i | \(-0.322341\pi\) |
−0.999404 | + | 0.0345275i | \(0.989007\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 40135.3 | + | 34968.4i | 0.494125 | + | 0.430513i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −220988. | + | 127587.i | −2.68290 | + | 1.54897i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33838.4 | − | 58609.8i | 0.405148 | − | 0.701738i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26187.3 | − | 45357.7i | 0.309246 | − | 0.535630i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 26421.2i | − | 0.307763i | −0.988089 | − | 0.153882i | \(-0.950823\pi\) | ||
0.988089 | − | 0.153882i | \(-0.0491775\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 112173. | + | 64762.9i | 1.28897 | + | 0.744187i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24343.7i | 0.275977i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12844.2 | + | 7415.60i | −0.143669 | + | 0.0829476i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −80542.4 | − | 139503.i | −0.888979 | − | 1.53976i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 62938.9i | − | 0.685542i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −112460. | −1.20893 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −113735. | + | 65665.0i | −1.20675 | + | 0.696718i | −0.962048 | − | 0.272880i | \(-0.912024\pi\) |
−0.244703 | + | 0.969598i | \(0.578690\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18786.3 | − | 32538.8i | −0.196754 | − | 0.340789i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −66871.7 | −0.691388 | −0.345694 | − | 0.938347i | \(-0.612356\pi\) | ||||
−0.345694 | + | 0.938347i | \(0.612356\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12163.3 | − | 21067.4i | 0.124154 | − | 0.215042i | −0.797248 | − | 0.603652i | \(-0.793712\pi\) |
0.921402 | + | 0.388611i | \(0.127045\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −112215. | −1.13091 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −74607.7 | − | 43074.8i | −0.742447 | − | 0.428652i | 0.0805116 | − | 0.996754i | \(-0.474345\pi\) |
−0.822958 | + | 0.568102i | \(0.807678\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16056.8 | − | 9270.40i | −0.157789 | − | 0.0910998i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19616.2 | + | 33976.3i | 0.190373 | + | 0.329736i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14745.6 | + | 42981.4i | 0.141338 | + | 0.411979i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2520.79 | − | 1455.38i | 0.0238655 | − | 0.0137787i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6874.03 | − | 11906.2i | 0.0642859 | − | 0.111346i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 144518. | − | 250312.i | 1.33515 | − | 2.31254i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 101411.i | − | 0.925616i | −0.886459 | − | 0.462808i | \(-0.846842\pi\) | ||
0.886459 | − | 0.462808i | \(-0.153158\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27345.0 | + | 15787.6i | 0.246598 | + | 0.142373i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 97942.7i | 0.872735i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30062.6 | + | 17356.6i | −0.264708 | + | 0.152829i | −0.626480 | − | 0.779437i | \(-0.715505\pi\) |
0.361773 | + | 0.932266i | \(0.382172\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12855.3 | + | 22266.0i | 0.111862 | + | 0.193750i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 44196.4i | − | 0.380082i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −197466. | −1.67843 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −50913.2 | + | 29394.7i | −0.427752 | + | 0.246963i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 107740. | + | 186612.i | 0.894786 | + | 1.54981i | 0.834069 | + | 0.551660i | \(0.186005\pi\) |
0.0607169 | + | 0.998155i | \(0.480661\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −61536.9 | −0.505225 | −0.252612 | − | 0.967568i | \(-0.581290\pi\) | ||||
−0.252612 | + | 0.967568i | \(0.581290\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13557.0 | − | 23481.3i | 0.110039 | − | 0.190594i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −184748. | −1.48262 | −0.741311 | − | 0.671162i | \(-0.765796\pi\) | ||||
−0.741311 | + | 0.671162i | \(0.765796\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15609.7 | − | 9012.29i | −0.123862 | − | 0.0715119i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 51215.0 | + | 29569.0i | 0.401847 | + | 0.232007i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −40117.9 | − | 69486.2i | −0.311279 | − | 0.539150i | 0.667361 | − | 0.744734i | \(-0.267424\pi\) |
−0.978639 | + | 0.205584i | \(0.934091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 120721. | + | 49090.8i | 0.926339 | + | 0.376692i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −65132.1 | + | 37604.0i | −0.494290 | + | 0.285378i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 60421.6 | − | 104653.i | 0.453530 | − | 0.785537i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10611.8 | − | 18380.2i | 0.0787877 | − | 0.136464i | −0.823939 | − | 0.566678i | \(-0.808228\pi\) |
0.902727 | + | 0.430214i | \(0.141562\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 151249.i | 1.11081i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 44597.6 | + | 25748.4i | 0.324014 | + | 0.187070i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 136406.i | 0.980428i | 0.871602 | + | 0.490214i | \(0.163081\pi\) | ||||
−0.871602 | + | 0.490214i | \(0.836919\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −69821.1 | + | 40311.2i | −0.496506 | + | 0.286658i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10325.4 | + | 17884.0i | 0.0726478 | + | 0.125830i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 120694.i | − | 0.840244i | −0.907468 | − | 0.420122i | \(-0.861987\pi\) | ||
0.907468 | − | 0.420122i | \(-0.138013\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 94459.8 | 0.650724 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 199020. | − | 114904.i | 1.35675 | − | 0.783320i | 0.367566 | − | 0.929998i | \(-0.380191\pi\) |
0.989184 | + | 0.146677i | \(0.0468579\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 37417.9 | + | 64809.6i | 0.252440 | + | 0.437238i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −95479.3 | −0.637510 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 125565. | − | 217485.i | 0.829793 | − | 1.43724i | −0.0684079 | − | 0.997657i | \(-0.521792\pi\) |
0.898201 | − | 0.439586i | \(-0.144875\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −50184.6 | −0.328259 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 92184.6 | + | 53222.8i | 0.596861 | + | 0.344598i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 179786. | + | 103799.i | 1.15229 | + | 0.665274i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37440.2 | − | 64848.4i | −0.237551 | − | 0.411451i | 0.722460 | − | 0.691413i | \(-0.243012\pi\) |
−0.960011 | + | 0.279962i | \(0.909678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 160427. | − | 55037.6i | 1.00770 | − | 0.345711i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −102868. | + | 59390.9i | −0.639723 | + | 0.369344i | −0.784508 | − | 0.620119i | \(-0.787084\pi\) |
0.144785 | + | 0.989463i | \(0.453751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24612.9 | + | 42630.8i | −0.151549 | + | 0.262491i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −49.3060 | + | 85.4005i | −0.000300601 | + | 0.000520655i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 21057.4i | − | 0.127121i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 282457. | + | 163076.i | 1.68852 | + | 0.974865i | 0.955655 | + | 0.294487i | \(0.0951488\pi\) |
0.732861 | + | 0.680378i | \(0.238185\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 67269.4i | 0.398230i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 357399. | − | 206345.i | 2.09534 | − | 1.20974i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 50654.3 | + | 87735.9i | 0.294117 | + | 0.509426i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 163262.i | − | 0.938884i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10223.8 | 0.0582350 | 0.0291175 | − | 0.999576i | \(-0.490730\pi\) | ||||
0.0291175 | + | 0.999576i | \(0.490730\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −221712. | + | 128006.i | −1.25091 | + | 0.722213i | −0.971290 | − | 0.237898i | \(-0.923541\pi\) |
−0.279619 | + | 0.960111i | \(0.590208\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −85659.5 | − | 148367.i | −0.478735 | − | 0.829193i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9849.18 | 0.0545283 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −179158. | + | 310311.i | −0.982608 | + | 1.70193i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6908.54 | −0.0375380 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −75203.7 | − | 43418.8i | −0.404841 | − | 0.233735i | 0.283730 | − | 0.958904i | \(-0.408428\pi\) |
−0.688571 | + | 0.725169i | \(0.741761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −282022. | − | 162825.i | −1.50420 | − | 0.868453i | −0.999988 | − | 0.00487606i | \(-0.998448\pi\) |
−0.504217 | − | 0.863577i | \(-0.668219\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 40928.8 | + | 70890.7i | 0.216297 | + | 0.374637i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −94546.8 | + | 108517.i | −0.495090 | + | 0.568243i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 200497. | − | 115757.i | 1.04035 | − | 0.600647i | 0.120418 | − | 0.992723i | \(-0.461576\pi\) |
0.919933 | + | 0.392076i | \(0.128243\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −118644. | + | 205498.i | −0.610056 | + | 1.05665i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 103566. | − | 179381.i | 0.527726 | − | 0.914048i | −0.471752 | − | 0.881731i | \(-0.656378\pi\) |
0.999478 | − | 0.0323166i | \(-0.0102885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 387896.i | 1.95882i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20035.8 | + | 11567.7i | 0.100275 | + | 0.0578936i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 320126.i | − | 1.58792i | −0.607971 | − | 0.793959i | \(-0.708016\pi\) | ||
0.607971 | − | 0.793959i | \(-0.291984\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 87353.8 | − | 50433.8i | 0.429466 | − | 0.247952i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −64709.4 | − | 112080.i | −0.315334 | − | 0.546174i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 83351.9i | − | 0.402618i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −186438. | −0.892695 | −0.446347 | − | 0.894860i | \(-0.647275\pi\) | ||||
−0.446347 | + | 0.894860i | \(0.647275\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 79454.3 | − | 45872.9i | 0.377131 | − | 0.217736i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8745.73 | + | 15148.0i | 0.0411523 | + | 0.0712779i | 0.885868 | − | 0.463938i | \(-0.153564\pi\) |
−0.844716 | + | 0.535215i | \(0.820230\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 168691. | 0.786920 | 0.393460 | − | 0.919342i | \(-0.371278\pi\) | ||||
0.393460 | + | 0.919342i | \(0.371278\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −97563.4 | + | 168985.i | −0.451212 | + | 0.781522i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 183184. | 0.839950 | 0.419975 | − | 0.907536i | \(-0.362039\pi\) | ||||
0.419975 | + | 0.907536i | \(0.362039\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 270253. | + | 156030.i | 1.22864 | + | 0.709355i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −195735. | − | 113008.i | −0.882320 | − | 0.509408i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31837.4 | + | 55144.0i | 0.142304 | + | 0.246477i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18555.7 | − | 21297.4i | 0.0822412 | − | 0.0943930i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26434.2 | − | 15261.8i | 0.116179 | − | 0.0670763i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 159926. | − | 276999.i | 0.697022 | − | 1.20728i | −0.272472 | − | 0.962164i | \(-0.587841\pi\) |
0.969494 | − | 0.245114i | \(-0.0788255\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11726.9 | + | 20311.5i | −0.0506865 | + | 0.0877916i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 187312.i | 0.802920i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −216318. | − | 124892.i | −0.919624 | − | 0.530945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22667.1i | − | 0.0955736i | −0.998858 | − | 0.0477868i | \(-0.984783\pi\) | ||
0.998858 | − | 0.0477868i | \(-0.0152168\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −123212. | + | 71136.5i | −0.515271 | + | 0.297492i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 102131. | + | 176895.i | 0.423636 | + | 0.733759i | 0.996292 | − | 0.0860370i | \(-0.0274203\pi\) |
−0.572656 | + | 0.819796i | \(0.694087\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 69876.2i | 0.287498i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 44357.1 | 0.181031 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −49735.1 | + | 28714.6i | −0.201349 | + | 0.116249i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −207921. | − | 360129.i | −0.835020 | − | 1.44630i | −0.894015 | − | 0.448038i | \(-0.852123\pi\) |
0.0589950 | − | 0.998258i | \(-0.481210\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −102928. | −0.410069 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −217012. | + | 375875.i | −0.857724 | + | 1.48562i | 0.0163716 | + | 0.999866i | \(0.494789\pi\) |
−0.874095 | + | 0.485755i | \(0.838545\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −300166. | −1.17701 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −130872. | − | 75558.8i | −0.509131 | − | 0.293947i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −315207. | − | 181985.i | −1.21663 | − | 0.702424i | −0.252437 | − | 0.967613i | \(-0.581232\pi\) |
−0.964196 | + | 0.265189i | \(0.914566\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −192513. | − | 333441.i | −0.737254 | − | 1.27696i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 50496.7 | − | 258232.i | 0.191880 | − | 0.981240i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −155183. | + | 89595.1i | −0.585101 | + | 0.337808i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −57126.1 | + | 98945.3i | −0.213724 | + | 0.370181i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −97619.7 | + | 169082.i | −0.362412 | + | 0.627716i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 100484.i | 0.370187i | 0.982721 | + | 0.185094i | \(0.0592589\pi\) | ||||
−0.982721 | + | 0.185094i | \(0.940741\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5151.62 | + | 2974.29i | 0.0188339 | + | 0.0108738i | 0.509387 | − | 0.860537i | \(-0.329872\pi\) |
−0.490553 | + | 0.871411i | \(0.663205\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 36761.8i | − | 0.133376i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −144251. | + | 83283.2i | −0.519394 | + | 0.299872i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 60443.7 | + | 104692.i | 0.215993 | + | 0.374111i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 244612.i | − | 0.867539i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −112346. | −0.395461 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 162039. | − | 93553.1i | 0.566124 | − | 0.326852i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 57994.5 | + | 100449.i | 0.201112 | + | 0.348336i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 158247. | 0.544701 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25692.0 | + | 44499.9i | −0.0877817 | + | 0.152042i | −0.906573 | − | 0.422049i | \(-0.861311\pi\) |
0.818791 | + | 0.574091i | \(0.194644\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 267067. | 0.905775 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −56782.5 | − | 32783.4i | −0.191171 | − | 0.110373i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −253560. | − | 146393.i | −0.847434 | − | 0.489266i | 0.0123501 | − | 0.999924i | \(-0.496069\pi\) |
−0.859784 | + | 0.510657i | \(0.829402\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 106192. | + | 183929.i | 0.352327 | + | 0.610248i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 151097. | + | 131645.i | 0.497683 | + | 0.433613i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 572826. | − | 330721.i | 1.87315 | − | 1.08146i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −46484.3 | + | 80513.1i | −0.150911 | + | 0.261385i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −52344.2 | + | 90662.9i | −0.168717 | + | 0.292226i | −0.937969 | − | 0.346719i | \(-0.887296\pi\) |
0.769252 | + | 0.638945i | \(0.220629\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 70920.9i | − | 0.226961i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20244.7 | − | 11688.3i | −0.0643258 | − | 0.0371385i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 3123.45i | − | 0.00985411i | −0.999988 | − | 0.00492706i | \(-0.998432\pi\) | ||
0.999988 | − | 0.00492706i | \(-0.00156834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 106190. | − | 61309.0i | 0.332650 | − | 0.192056i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 157.097 | + | 272.099i | 0.000488653 | + | 0.000846372i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 35963.3i | − | 0.111080i | −0.998456 | − | 0.0555399i | \(-0.982312\pi\) | ||
0.998456 | − | 0.0555399i | \(-0.0176880\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 62530.8 | 0.191788 | 0.0958941 | − | 0.995392i | \(-0.469429\pi\) | ||||
0.0958941 | + | 0.995392i | \(0.469429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −252647. | + | 145866.i | −0.769494 | + | 0.444268i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15598.0 | + | 27016.6i | 0.0471774 | + | 0.0817137i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 242182. | 0.727429 | 0.363715 | − | 0.931510i | \(-0.381508\pi\) | ||||
0.363715 | + | 0.931510i | \(0.381508\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 148142. | − | 256589.i | 0.441896 | − | 0.765386i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 322785. | 0.956228 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17628.9 | − | 10178.0i | −0.0518666 | − | 0.0299452i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −42785.9 | − | 24702.5i | −0.125023 | − | 0.0721819i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10340.3 | + | 17910.0i | 0.0300095 | + | 0.0519779i | 0.880640 | − | 0.473786i | \(-0.157113\pi\) |
−0.850631 | + | 0.525764i | \(0.823780\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −91677.8 | + | 468825.i | −0.264261 | + | 1.35139i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −52357.9 | + | 30228.8i | −0.149902 | + | 0.0865459i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −73184.7 | + | 126760.i | −0.208118 | + | 0.360472i | −0.951122 | − | 0.308816i | \(-0.900067\pi\) |
0.743003 | + | 0.669288i | \(0.233401\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 141020. | − | 244253.i | 0.398333 | − | 0.689932i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 121778.i | 0.341681i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28855.0 | − | 16659.4i | −0.0804206 | − | 0.0464308i | 0.459250 | − | 0.888307i | \(-0.348118\pi\) |
−0.539671 | + | 0.841876i | \(0.681451\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 301579.i | − | 0.834933i | −0.908692 | − | 0.417467i | \(-0.862918\pi\) | ||
0.908692 | − | 0.417467i | \(-0.137082\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 160186. | − | 92483.4i | 0.440544 | − | 0.254348i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 179340. | + | 310626.i | 0.489967 | + | 0.848647i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 671101.i | 1.82142i | 0.413045 | + | 0.910711i | \(0.364465\pi\) | ||||
−0.413045 | + | 0.910711i | \(0.635535\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 260811. | 0.703220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 110205. | − | 63627.0i | 0.295202 | − | 0.170435i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −116030. | − | 200969.i | −0.308779 | − | 0.534822i | 0.669316 | − | 0.742978i | \(-0.266587\pi\) |
−0.978096 | + | 0.208156i | \(0.933254\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −445330. | −1.17742 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 61529.0 | − | 106571.i | 0.161625 | − | 0.279943i | −0.773826 | − | 0.633398i | \(-0.781660\pi\) |
0.935452 | + | 0.353455i | \(0.114993\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 159886. | 0.417283 | 0.208641 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208641 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 251662. | + | 145297.i | 0.652580 | + | 0.376767i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.07032e6 | + | 617949.i | 2.75764 | + | 1.59212i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 216703. | + | 375341.i | 0.554760 | + | 0.960873i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −63414.7 | + | 21755.7i | −0.161308 | + | 0.0553398i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −68728.5 | + | 39680.4i | −0.173714 | + | 0.100294i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 92668.8 | − | 160507.i | 0.232742 | − | 0.403121i | −0.725872 | − | 0.687830i | \(-0.758564\pi\) |
0.958614 | + | 0.284709i | \(0.0918969\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −61050.4 | + | 105742.i | −0.152364 | + | 0.263902i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 450495.i | − | 1.11723i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −152642. | − | 88127.7i | −0.376179 | − | 0.217187i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34039.8i | 0.0833652i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 142059. | − | 82017.6i | 0.345742 | − | 0.199614i | −0.317066 | − | 0.948403i | \(-0.602698\pi\) |
0.662808 | + | 0.748789i | \(0.269364\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −252661. | − | 437622.i | −0.611106 | − | 1.05847i | −0.991054 | − | 0.133459i | \(-0.957391\pi\) |
0.379948 | − | 0.925008i | \(-0.375942\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 281124.i | − | 0.675739i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 95116.5 | 0.227220 | 0.113610 | − | 0.993525i | \(-0.463759\pi\) | ||||
0.113610 | + | 0.993525i | \(0.463759\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −141276. | + | 81565.6i | −0.335412 | + | 0.193650i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 310852. | + | 538412.i | 0.733486 | + | 1.27043i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −586580. | −1.37563 | −0.687813 | − | 0.725888i | \(-0.741429\pi\) | ||||
−0.687813 | + | 0.725888i | \(0.741429\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 253829. | − | 439644.i | 0.591641 | − | 1.02475i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −228215. | −0.528704 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −619966. | − | 357938.i | −1.42757 | − | 0.824207i | −0.430640 | − | 0.902524i | \(-0.641712\pi\) |
−0.996929 | + | 0.0783166i | \(0.975046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 316498. | + | 182730.i | 0.724383 | + | 0.418223i | 0.816364 | − | 0.577538i | \(-0.195987\pi\) |
−0.0919808 | + | 0.995761i | \(0.529320\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13018.4 | + | 22548.5i | 0.0296162 | + | 0.0512968i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −262484. | − | 765103.i | −0.593552 | − | 1.73012i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −191673. | + | 110662.i | −0.430832 | + | 0.248741i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 116150. | − | 201178.i | 0.259518 | − | 0.449498i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 70819.0 | − | 122662.i | 0.157291 | − | 0.272436i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 769776.i | − | 1.69955i | −0.527144 | − | 0.849776i | \(-0.676737\pi\) | ||
0.527144 | − | 0.849776i | \(-0.323263\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −49390.9 | − | 28515.9i | −0.108403 | − | 0.0625862i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 789698.i | 1.72299i | 0.507762 | + | 0.861497i | \(0.330473\pi\) | ||||
−0.507762 | + | 0.861497i | \(0.669527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −689224. | + | 397924.i | −1.49493 | + | 0.863099i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −142685. | − | 247137.i | −0.307668 | − | 0.532897i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 644105.i | 1.38075i | 0.723451 | + | 0.690376i | \(0.242555\pi\) | ||||
−0.723451 | + | 0.690376i | \(0.757445\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 320819. | 0.683722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 44999.7 | − | 25980.6i | 0.0953445 | − | 0.0550472i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11336.3 | + | 19635.0i | 0.0238799 | + | 0.0413612i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 338350. | 0.708616 | 0.354308 | − | 0.935129i | \(-0.384717\pi\) | ||||
0.354308 | + | 0.935129i | \(0.384717\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 70664.4 | − | 122394.i | 0.147141 | − | 0.254856i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −778623. | −1.61197 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −329217. | − | 190074.i | −0.677668 | − | 0.391252i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 362484. | + | 209280.i | 0.741881 | + | 0.428325i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −150371. | − | 260451.i | −0.306006 | − | 0.530017i | 0.671479 | − | 0.741023i | \(-0.265659\pi\) |
−0.977485 | + | 0.211006i | \(0.932326\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43680.1 | + | 223373.i | −0.0883838 | + | 0.451980i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 436843. | − | 252211.i | 0.878916 | − | 0.507442i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −478189. | + | 828247.i | −0.956666 | + | 1.65699i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −207160. | + | 358811.i | −0.412110 | + | 0.713795i | −0.995120 | − | 0.0986695i | \(-0.968541\pi\) |
0.583010 | + | 0.812465i | \(0.301875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 392055.i | − | 0.775546i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −456897. | − | 263789.i | −0.898750 | − | 0.518894i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32948.0i | 0.0644491i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 155372. | − | 89704.3i | 0.302229 | − | 0.174492i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 135419. | + | 234553.i | 0.261952 | + | 0.453715i | 0.966761 | − | 0.255683i | \(-0.0823003\pi\) |
−0.704808 | + | 0.709398i | \(0.748967\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 570928.i | 1.09827i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 88650.7 | 0.169592 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 37617.5 | − | 21718.5i | 0.0715672 | − | 0.0413193i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4386.18 | + | 7597.09i | 0.00829885 | + | 0.0143740i | 0.870145 | − | 0.492796i | \(-0.164025\pi\) |
−0.861846 | + | 0.507170i | \(0.830692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −328096. | −0.617370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 119988. | − | 207826.i | 0.224545 | − | 0.388924i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 653473. | 1.21624 | 0.608121 | − | 0.793844i | \(-0.291924\pi\) | ||||
0.608121 | + | 0.793844i | \(0.291924\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −605058. | − | 349330.i | −1.12001 | − | 0.646638i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −106828. | − | 61676.9i | −0.196675 | − | 0.113550i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 189565. | + | 328336.i | 0.347112 | + | 0.601215i | 0.985735 | − | 0.168304i | \(-0.0538292\pi\) |
−0.638623 | + | 0.769519i | \(0.720496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 73284.2 | + | 14330.6i | 0.133467 | + | 0.0260992i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −643576. | + | 371569.i | −1.16580 | + | 0.673072i | −0.952686 | − | 0.303956i | \(-0.901692\pi\) |
−0.213109 | + | 0.977028i | \(0.568359\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55168.2 | − | 95554.1i | 0.0993977 | − | 0.172162i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 95661.7 | − | 165691.i | 0.171434 | − | 0.296933i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 596150.i | − | 1.06265i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −832933. | − | 480894.i | −1.47683 | − | 0.852648i | −0.477172 | − | 0.878810i | \(-0.658338\pi\) |
−0.999658 | + | 0.0261621i | \(0.991671\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 648162.i | − | 1.14312i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −534528. | + | 308610.i | −0.937728 | + | 0.541398i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −68686.5 | − | 118968.i | −0.119861 | − | 0.207606i | 0.799851 | − | 0.600198i | \(-0.204912\pi\) |
−0.919713 | + | 0.392592i | \(0.871578\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 74042.4i | − | 0.128528i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −275441. | −0.475619 | −0.237809 | − | 0.971312i | \(-0.576429\pi\) | ||||
−0.237809 | + | 0.971312i | \(0.576429\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −180918. | + | 104453.i | −0.310766 | + | 0.179421i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −83586.2 | − | 144775.i | −0.142827 | − | 0.247384i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 181695. | 0.308854 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 303928. | − | 526419.i | 0.513947 | − | 0.890182i | −0.485922 | − | 0.874002i | \(-0.661516\pi\) |
0.999869 | − | 0.0161801i | \(-0.00515050\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 555263. | 0.934092 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 955688. | + | 551767.i | 1.59940 | + | 0.923414i | 0.991603 | + | 0.129321i | \(0.0412799\pi\) |
0.607797 | + | 0.794092i | \(0.292053\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 89670.1 | + | 51771.1i | 0.149295 | + | 0.0861953i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 148106. | + | 256527.i | 0.245319 | + | 0.424905i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.03125e6 | + | 353789.i | −1.69937 | + | 0.583002i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19659.7 | − | 11350.5i | 0.0322310 | − | 0.0186086i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 202309. | − | 350410.i | 0.329983 | − | 0.571548i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −538952. | + | 933493.i | −0.874603 | + | 1.51486i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 619317.i | − | 0.999916i | −0.866050 | − | 0.499958i | \(-0.833349\pi\) | ||
0.866050 | − | 0.499958i | \(-0.166651\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 268958. | + | 155283.i | 0.432047 | + | 0.249442i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 390680.i | − | 0.624408i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −136621. | + | 78878.1i | −0.217255 | + | 0.125432i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 44936.0 | + | 77831.5i | 0.0710985 | + | 0.123146i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 22197.8i | − | 0.0349457i | −0.999847 | − | 0.0174728i | \(-0.994438\pi\) | ||
0.999847 | − | 0.0174728i | \(-0.00556206\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 430591. | 0.674484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 634407. | − | 366275.i | 0.988787 | − | 0.570877i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 76097.9 | + | 131805.i | 0.118016 | + | 0.204410i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 893326. | 1.37854 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 264637. | − | 458365.i | 0.406353 | − | 0.703825i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 110260. | 0.168469 | 0.0842345 | − | 0.996446i | \(-0.473156\pi\) | ||||
0.0842345 | + | 0.996446i | \(0.473156\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 274722. | + | 158611.i | 0.417688 | + | 0.241152i | 0.694088 | − | 0.719890i | \(-0.255808\pi\) |
−0.276399 | + | 0.961043i | \(0.589141\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 189609. | + | 109471.i | 0.286866 | + | 0.165622i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 339262. | + | 587619.i | 0.510764 | + | 0.884669i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −223337. | − | 650997.i | −0.334593 | − | 0.975292i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −136323. | + | 78705.9i | −0.203236 | + | 0.117338i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −423971. | + | 734339.i | −0.628999 | + | 1.08946i | 0.358754 | + | 0.933432i | \(0.383202\pi\) |
−0.987753 | + | 0.156026i | \(0.950132\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −295443. | + | 511723.i | −0.436189 | + | 0.755502i | −0.997392 | − | 0.0721768i | \(-0.977005\pi\) |
0.561203 | + | 0.827678i | \(0.310339\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14531.5i | 0.0213502i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −615143. | − | 355153.i | −0.899425 | − | 0.519283i | −0.0224113 | − | 0.999749i | \(-0.507134\pi\) |
−0.877014 | + | 0.480466i | \(0.840468\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 986161.i | 1.43496i | 0.696581 | + | 0.717479i | \(0.254704\pi\) | ||||
−0.696581 | + | 0.717479i | \(0.745296\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −254213. | + | 146770.i | −0.368125 | + | 0.212537i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −298199. | − | 516496.i | −0.429751 | − | 0.744350i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 490880.i | 0.704048i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 964503. | 1.37674 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 296225. | − | 171026.i | 0.420822 | − | 0.242962i | −0.274607 | − | 0.961557i | \(-0.588548\pi\) |
0.695429 | + | 0.718595i | \(0.255214\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −199556. | − | 345641.i | −0.282146 | − | 0.488690i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 725282. | 1.02059 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −360353. | + | 624150.i | −0.504678 | + | 0.874129i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.14281e6 | 1.59297 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −362374. | − | 209217.i | −0.502738 | − | 0.290256i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −217689. | − | 125683.i | −0.300592 | − | 0.173547i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −478069. | − | 828040.i | −0.657041 | − | 1.13803i | −0.981378 | − | 0.192087i | \(-0.938474\pi\) |
0.324337 | − | 0.945942i | \(-0.394859\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −470530. | − | 92011.3i | −0.643659 | − | 0.125866i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.22953e6 | − | 709870.i | 1.67409 | − | 0.966535i | 0.708776 | − | 0.705434i | \(-0.249248\pi\) |
0.965312 | − | 0.261101i | \(-0.0840855\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 557394. | − | 965435.i | 0.755399 | − | 1.30839i | −0.189777 | − | 0.981827i | \(-0.560777\pi\) |
0.945176 | − | 0.326562i | \(-0.105890\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −709445. | + | 1.22879e6i | −0.957001 | + | 1.65757i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.04519e6i | 1.40338i | 0.712483 | + | 0.701690i | \(0.247571\pi\) | ||||
−0.712483 | + | 0.701690i | \(0.752429\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 806382. | + | 465565.i | 1.07773 | + | 0.622226i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 376314.i | − | 0.500625i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −226431. | + | 130730.i | −0.299845 | + | 0.173116i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 68695.6 | + | 118984.i | 0.0905509 | + | 0.156839i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 471720.i | 0.618951i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.22508e6 | 1.60011 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 121311. | − | 70038.7i | 0.157725 | − | 0.0910624i | −0.419060 | − | 0.907958i | \(-0.637640\pi\) |
0.576785 | + | 0.816896i | \(0.304307\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −73457.0 | − | 127231.i | −0.0950726 | − | 0.164670i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 517628. | 0.666908 | 0.333454 | − | 0.942766i | \(-0.391786\pi\) | ||||
0.333454 | + | 0.942766i | \(0.391786\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −199591. | + | 345702.i | −0.255988 | + | 0.443384i | −0.965163 | − | 0.261648i | \(-0.915734\pi\) |
0.709176 | + | 0.705032i | \(0.249067\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 720223. | 0.919561 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 902167. | + | 520867.i | 1.14667 | + | 0.662032i | 0.948074 | − | 0.318048i | \(-0.103027\pi\) |
0.198599 | + | 0.980081i | \(0.436361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.24305e6 | − | 717674.i | −1.57284 | − | 0.908079i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −62.0984 | − | 107.558i | −7.82213e−5 | − | 0.000135483i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 811226. | − | 931091.i | 1.01728 | − | 1.16759i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 479061. | − | 276586.i | 0.598059 | − | 0.345290i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −41234.1 | + | 71419.6i | −0.0512474 | + | 0.0887631i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −367296. | + | 636176.i | −0.454461 | + | 0.787150i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 76717.7i | 0.0945030i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −775704. | − | 447853.i | −0.951306 | − | 0.549237i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.27369e6i | − | 1.55513i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 694514. | − | 400978.i | 0.844241 | − | 0.487422i | −0.0144629 | − | 0.999895i | \(-0.504604\pi\) |
0.858703 | + | 0.512473i | \(0.171271\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 283435. | + | 490924.i | 0.343025 | + | 0.594137i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.38700e6i | 1.67125i | 0.549301 | + | 0.835625i | \(0.314894\pi\) | ||||
−0.549301 | + | 0.835625i | \(0.685106\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −127593. | −0.153068 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −541552. | + | 312665.i | −0.646842 | + | 0.373454i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −808738. | − | 1.40077e6i | −0.961765 | − | 1.66583i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −751701. | −0.890049 | −0.445025 | − | 0.895518i | \(-0.646805\pi\) | ||||
−0.445025 | + | 0.895518i | \(0.646805\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −365127. | + | 632419.i | −0.430453 | + | 0.745566i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25284.4 | −0.0296790 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42723.5 | + | 24666.4i | 0.0499325 | + | 0.0288286i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 293067. | + | 169202.i | 0.341041 | + | 0.196900i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 570771. | + | 988605.i | 0.661349 | + | 1.14549i | 0.980261 | + | 0.197706i | \(0.0633492\pi\) |
−0.318912 | + | 0.947784i | \(0.603317\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.67865e6 | − | 328257.i | −1.93669 | − | 0.378716i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −322021. | + | 185919.i | −0.369931 | + | 0.213580i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −55743.4 | + | 96550.4i | −0.0637632 | + | 0.110441i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −281582. | + | 487714.i | −0.320719 | + | 0.555502i | −0.980637 | − | 0.195836i | \(-0.937258\pi\) |
0.659917 | + | 0.751338i | \(0.270591\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 135267.i | − | 0.153412i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −927824. | − | 535679.i | −1.04782 | − | 0.604959i | −0.125781 | − | 0.992058i | \(-0.540144\pi\) |
−0.922038 | + | 0.387100i | \(0.873477\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.20407e6i | − | 1.35403i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.41435e6 | + | 816575.i | −1.58377 | + | 0.914392i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −721456. | − | 1.24960e6i | −0.804470 | − | 1.39338i | −0.916648 | − | 0.399695i | \(-0.869116\pi\) |
0.112178 | − | 0.993688i | \(-0.464217\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 169515.i | − | 0.188225i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −479031. | −0.529667 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 239343. | − | 138185.i | 0.263533 | − | 0.152151i | −0.362412 | − | 0.932018i | \(-0.618047\pi\) |
0.625945 | + | 0.779867i | \(0.284713\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 695660. | + | 1.20492e6i | 0.762764 | + | 1.32115i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −103095. | −0.112568 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 511090. | − | 885234.i | 0.555726 | − | 0.962545i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −827553. | −0.896084 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −306013. | − | 176677.i | −0.329980 | − | 0.190514i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.22372e6 | − | 706513.i | −1.31409 | − | 0.758692i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43685.9 | − | 75666.3i | −0.0467185 | − | 0.0809188i | 0.841721 | − | 0.539913i | \(-0.181543\pi\) |
−0.888439 | + | 0.458995i | \(0.848210\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 190506. | + | 165981.i | 0.202890 | + | 0.176771i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 483492. | − | 279144.i | 0.512803 | − | 0.296067i | −0.221182 | − | 0.975233i | \(-0.570992\pi\) |
0.733985 | + | 0.679166i | \(0.237658\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.24041e6 | + | 2.14845e6i | −1.31020 | + | 2.26934i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8092.57 | − | 14016.7i | 0.00851290 | − | 0.0147448i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 36446.8i | − | 0.0381830i | −0.999818 | − | 0.0190915i | \(-0.993923\pi\) | ||
0.999818 | − | 0.0190915i | \(-0.00607738\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −423084. | − | 244268.i | −0.441430 | − | 0.254859i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 123824.i | 0.128667i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 819884. | − | 473360.i | 0.848487 | − | 0.489874i | −0.0116529 | − | 0.999932i | \(-0.503709\pi\) |
0.860140 | + | 0.510058i | \(0.170376\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 144167. | + | 249704.i | 0.148591 | + | 0.257367i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.60717e6i | − | 1.64979i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 760097. | 0.777099 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 361483. | − | 208702.i | 0.368078 | − | 0.212510i | −0.304540 | − | 0.952499i | \(-0.598503\pi\) |
0.672619 | + | 0.739989i | \(0.265169\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −281947. | − | 488347.i | −0.285936 | − | 0.495256i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 580781. | 0.586632 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 247061. | − | 427922.i | 0.248550 | − | 0.430501i | −0.714574 | − | 0.699560i | \(-0.753379\pi\) |
0.963124 | + | 0.269059i | \(0.0867126\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 459539. | 0.460460 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 76.5.h.a.69.5 | yes | 12 | |
3.2 | odd | 2 | 684.5.y.c.145.6 | 12 | |||
4.3 | odd | 2 | 304.5.r.b.145.2 | 12 | |||
19.8 | odd | 6 | inner | 76.5.h.a.65.5 | ✓ | 12 | |
57.8 | even | 6 | 684.5.y.c.217.6 | 12 | |||
76.27 | even | 6 | 304.5.r.b.65.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.h.a.65.5 | ✓ | 12 | 19.8 | odd | 6 | inner | |
76.5.h.a.69.5 | yes | 12 | 1.1 | even | 1 | trivial | |
304.5.r.b.65.2 | 12 | 76.27 | even | 6 | |||
304.5.r.b.145.2 | 12 | 4.3 | odd | 2 | |||
684.5.y.c.145.6 | 12 | 3.2 | odd | 2 | |||
684.5.y.c.217.6 | 12 | 57.8 | even | 6 |