Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,5,Mod(145,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.145");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.y (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: | \(70.7050547493\) |
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: | \( x^{12} - 6 x^{11} + 631 x^{10} - 3100 x^{9} + 142264 x^{8} - 550522 x^{7} + 14083117 x^{6} - 40335478 x^{5} + 638031136 x^{4} - 1209472584 x^{3} + \cdots + 90728724573 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.6 | ||
Root | \(0.500000 + 6.42649i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.145 |
Dual form | 684.5.y.c.217.6 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 13.2594 | + | 22.9660i | 0.530376 | + | 0.918638i | 0.999372 | + | 0.0354377i | \(0.0112825\pi\) |
−0.468996 | + | 0.883200i | \(0.655384\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −84.4930 | −1.72435 | −0.862174 | − | 0.506613i | \(-0.830897\pi\) | ||||
−0.862174 | + | 0.506613i | \(0.830897\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −33.3991 | −0.276025 | −0.138013 | − | 0.990430i | \(-0.544071\pi\) | ||||
−0.138013 | + | 0.990430i | \(0.544071\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 62.9369 | + | 109.010i | 0.217775 | + | 0.377197i | 0.954127 | − | 0.299401i | \(-0.0967869\pi\) |
−0.736353 | + | 0.676598i | \(0.763454\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −354.290 | − | 69.2806i | −0.981412 | − | 0.191913i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −199.345 | + | 345.275i | −0.376833 | + | 0.652695i | −0.990600 | − | 0.136793i | \(-0.956320\pi\) |
0.613766 | + | 0.789488i | \(0.289654\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −39.1233 | + | 67.7635i | −0.0625972 | + | 0.108422i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 480.756 | + | 277.565i | 0.571648 | + | 0.330041i | 0.757807 | − | 0.652478i | \(-0.226271\pi\) |
−0.186159 | + | 0.982520i | \(0.559604\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1323.28i | − | 1.37698i | −0.725244 | − | 0.688492i | \(-0.758273\pi\) | ||
0.725244 | − | 0.688492i | \(-0.241727\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2615.46 | + | 1510.04i | −1.55589 | + | 0.898296i | −0.558251 | + | 0.829672i | \(0.688527\pi\) |
−0.997643 | + | 0.0686238i | \(0.978139\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1710.41 | − | 2962.52i | 0.774292 | − | 1.34111i | −0.160900 | − | 0.986971i | \(-0.551440\pi\) |
0.935192 | − | 0.354142i | \(-0.115227\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4738.07 | 1.97337 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 527.826 | + | 304.741i | 0.187905 | + | 0.108487i | 0.591002 | − | 0.806670i | \(-0.298733\pi\) |
−0.403096 | + | 0.915158i | \(0.632066\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −442.852 | − | 767.041i | −0.146397 | − | 0.253567i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4229.93 | − | 2442.15i | 1.21515 | − | 0.701566i | 0.251271 | − | 0.967917i | \(-0.419151\pi\) |
0.963876 | + | 0.266351i | \(0.0858180\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −588.629 | + | 339.845i | −0.116768 | + | 0.0674162i | −0.557247 | − | 0.830347i | \(-0.688142\pi\) |
0.440478 | + | 0.897763i | \(0.354809\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3820.26 | 0.554545 | 0.277272 | − | 0.960791i | \(-0.410570\pi\) | ||||
0.277272 | + | 0.960791i | \(0.410570\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1669.01 | + | 2890.81i | −0.231005 | + | 0.400112i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12667.5 | + | 7313.61i | 1.59924 | + | 0.923319i | 0.991635 | + | 0.129077i | \(0.0412014\pi\) |
0.607601 | + | 0.794242i | \(0.292132\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2722.03 | + | 1571.56i | 0.328707 | + | 0.189779i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5659.50 | + | 9802.55i | −0.554799 | + | 0.960940i | 0.443120 | + | 0.896462i | \(0.353871\pi\) |
−0.997919 | + | 0.0644777i | \(0.979462\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6757.10i | − | 0.636922i | −0.947936 | − | 0.318461i | \(-0.896834\pi\) | ||
0.947936 | − | 0.318461i | \(-0.103166\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7055.61i | − | 0.616264i | −0.951344 | − | 0.308132i | \(-0.900296\pi\) | ||
0.951344 | − | 0.308132i | \(-0.0997039\pi\) | |||||||
\(108\) | 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 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4623.82i | − | 0.362113i | −0.983473 | − | 0.181056i | \(-0.942048\pi\) | ||
0.983473 | − | 0.181056i | \(-0.0579516\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10572.8 | −0.799454 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5317.73 | − | 9210.57i | −0.375519 | − | 0.650418i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13525.5 | −0.923810 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9571.65 | − | 16578.6i | −0.557756 | − | 0.966062i | −0.997683 | − | 0.0680283i | \(-0.978329\pi\) |
0.439927 | − | 0.898033i | \(-0.355004\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 29935.0 | + | 5853.73i | 1.69230 | + | 0.330925i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6048.91 | − | 10477.0i | 0.322282 | − | 0.558208i | −0.658677 | − | 0.752426i | \(-0.728883\pi\) |
0.980958 | + | 0.194218i | \(0.0622168\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1075.98 | + | 621.220i | 0.0526179 | + | 0.0303790i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14721.4i | 0.700184i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2080.34 | − | 3603.26i | −0.0937049 | − | 0.162302i | 0.815362 | − | 0.578951i | \(-0.196538\pi\) |
−0.909067 | + | 0.416649i | \(0.863204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 23274.8i | − | 1.02078i | −0.859943 | − | 0.510390i | \(-0.829501\pi\) | ||
0.859943 | − | 0.510390i | \(-0.170499\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16030.7 | + | 9255.32i | 0.574803 | + | 0.331863i | 0.759065 | − | 0.651014i | \(-0.225656\pi\) |
−0.184262 | + | 0.982877i | \(0.558990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13588.6 | − | 23536.1i | −0.475774 | − | 0.824065i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 30408.0 | − | 17556.0i | 1.01600 | − | 0.586590i | 0.103059 | − | 0.994675i | \(-0.467137\pi\) |
0.912944 | + | 0.408086i | \(0.133804\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3305.64 | − | 5725.54i | 0.107939 | − | 0.186956i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 20859.6i | − | 0.651028i | −0.945537 | − | 0.325514i | \(-0.894463\pi\) | ||
0.945537 | − | 0.325514i | \(-0.105537\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 52465.4 | 1.43816 | 0.719079 | − | 0.694929i | \(-0.244564\pi\) | ||||
0.719079 | + | 0.694929i | \(0.244564\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10872.8 | 0.280161 | 0.140081 | − | 0.990140i | \(-0.455264\pi\) | ||||
0.140081 | + | 0.990140i | \(0.455264\pi\) | |||||||
\(198\) | 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 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25278.9 | + | 43784.3i | −0.546865 | + | 0.947199i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 111808.i | 2.37440i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 51321.1i | 0.995966i | 0.867187 | + | 0.497983i | \(0.165926\pi\) | ||||
−0.867187 | + | 0.497983i | \(0.834074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9344.76 | 0.178196 | 0.0890978 | − | 0.996023i | \(-0.471602\pi\) | ||||
0.0890978 | + | 0.996023i | \(0.471602\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −37637.2 | − | 65189.6i | −0.693275 | − | 1.20079i | −0.970759 | − | 0.240057i | \(-0.922834\pi\) |
0.277484 | − | 0.960730i | \(-0.410500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 90716.0 | 1.64266 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −32265.1 | −0.564855 | −0.282427 | − | 0.959289i | \(-0.591140\pi\) | ||||
−0.282427 | + | 0.959289i | \(0.591140\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 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 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −58283.1 | + | 100949.i | −0.925114 | + | 1.60234i | −0.133736 | + | 0.991017i | \(0.542697\pi\) |
−0.791378 | + | 0.611327i | \(0.790636\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6657.93 | − | 11531.9i | 0.104016 | − | 0.180160i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −86480.5 | − | 49929.6i | −1.30934 | − | 0.755947i | −0.327353 | − | 0.944902i | \(-0.606157\pi\) |
−0.981986 | + | 0.188955i | \(0.939490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 53271.2i | 0.794132i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27926.3 | − | 48369.8i | −0.403740 | − | 0.699299i | 0.590434 | − | 0.807086i | \(-0.298957\pi\) |
−0.994174 | + | 0.107788i | \(0.965623\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16162.7i | 0.230156i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −82433.0 | + | 47592.7i | −1.13919 | + | 0.657712i | −0.946230 | − | 0.323495i | \(-0.895142\pi\) |
−0.192961 | + | 0.981207i | \(0.561809\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −112961. | − | 65217.8i | −1.43059 | − | 0.825950i | −0.433421 | − | 0.901191i | \(-0.642694\pi\) |
−0.997165 | + | 0.0752419i | \(0.976027\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 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 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26421.2i | 0.307763i | 0.988089 | + | 0.153882i | \(0.0491775\pi\) | ||||
−0.988089 | + | 0.153882i | \(0.950823\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 112173. | + | 64762.9i | 1.28897 | + | 0.744187i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 66871.7 | 0.691388 | 0.345694 | − | 0.938347i | \(-0.387644\pi\) | ||||
0.345694 | + | 0.938347i | \(0.387644\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 74607.7 | + | 43074.8i | 0.742447 | + | 0.428652i | 0.822958 | − | 0.568102i | \(-0.192322\pi\) |
−0.0805116 | + | 0.996754i | \(0.525655\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16056.8 | − | 9270.40i | −0.157789 | − | 0.0910998i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 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 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 44196.4i | 0.380082i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −197466. | −1.67843 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −107740. | − | 186612.i | −0.894786 | − | 1.54981i | −0.834069 | − | 0.551660i | \(-0.813995\pi\) |
−0.0607169 | − | 0.998155i | \(-0.519339\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −61536.9 | −0.505225 | −0.252612 | − | 0.967568i | \(-0.581290\pi\) | ||||
−0.252612 | + | 0.967568i | \(0.581290\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 184748. | 1.48262 | 0.741311 | − | 0.671162i | \(-0.234204\pi\) | ||||
0.741311 | + | 0.671162i | \(0.234204\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15609.7 | − | 9012.29i | −0.123862 | − | 0.0715119i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 40117.9 | + | 69486.2i | 0.311279 | + | 0.539150i | 0.978639 | − | 0.205584i | \(-0.0659095\pi\) |
−0.667361 | + | 0.744734i | \(0.732576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 120721. | + | 49090.8i | 0.926339 | + | 0.376692i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 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 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −199020. | + | 114904.i | −1.35675 | + | 0.783320i | −0.989184 | − | 0.146677i | \(-0.953142\pi\) |
−0.367566 | + | 0.929998i | \(0.619809\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 37417.9 | + | 64809.6i | 0.252440 | + | 0.437238i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −125565. | + | 217485.i | −0.829793 | + | 1.43724i | 0.0684079 | + | 0.997657i | \(0.478208\pi\) |
−0.898201 | + | 0.439586i | \(0.855125\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −50184.6 | −0.328259 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 102868. | − | 59390.9i | 0.639723 | − | 0.369344i | −0.144785 | − | 0.989463i | \(-0.546249\pi\) |
0.784508 | + | 0.620119i | \(0.212916\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24612.9 | + | 42630.8i | −0.151549 | + | 0.262491i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 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 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10223.8 | −0.0582350 | −0.0291175 | − | 0.999576i | \(-0.509270\pi\) | ||||
−0.0291175 | + | 0.999576i | \(0.509270\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9849.18 | −0.0545283 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −179158. | + | 310311.i | −0.982608 | + | 1.70193i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 75203.7 | + | 43418.8i | 0.404841 | + | 0.233735i | 0.688571 | − | 0.725169i | \(-0.258239\pi\) |
−0.283730 | + | 0.958904i | \(0.591572\pi\) | |||||||
\(432\) | 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 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −103566. | + | 179381.i | −0.527726 | + | 0.914048i | 0.471752 | + | 0.881731i | \(0.343622\pi\) |
−0.999478 | + | 0.0323166i | \(0.989712\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 387896.i | 1.95882i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 320126.i | 1.58792i | 0.607971 | + | 0.793959i | \(0.291984\pi\) | ||||
−0.607971 | + | 0.793959i | \(0.708016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 87353.8 | − | 50433.8i | 0.429466 | − | 0.247952i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8745.73 | − | 15148.0i | −0.0411523 | − | 0.0712779i | 0.844716 | − | 0.535215i | \(-0.179770\pi\) |
−0.885868 | + | 0.463938i | \(0.846436\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 168691. | 0.786920 | 0.393460 | − | 0.919342i | \(-0.371278\pi\) | ||||
0.393460 | + | 0.919342i | \(0.371278\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −183184. | −0.839950 | −0.419975 | − | 0.907536i | \(-0.637961\pi\) | ||||
−0.419975 | + | 0.907536i | \(0.637961\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 270253. | + | 156030.i | 1.22864 | + | 0.709355i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 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 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −159926. | + | 276999.i | −0.697022 | + | 1.20728i | 0.272472 | + | 0.962164i | \(0.412159\pi\) |
−0.969494 | + | 0.245114i | \(0.921174\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11726.9 | + | 20311.5i | −0.0506865 | + | 0.0877916i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 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 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −102131. | − | 176895.i | −0.423636 | − | 0.733759i | 0.572656 | − | 0.819796i | \(-0.305913\pi\) |
−0.996292 | + | 0.0860370i | \(0.972580\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 69876.2i | 0.287498i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 217012. | − | 375875.i | 0.857724 | − | 1.48562i | −0.0163716 | − | 0.999866i | \(-0.505211\pi\) |
0.874095 | − | 0.485755i | \(-0.161455\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −300166. | −1.17701 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 315207. | + | 181985.i | 1.21663 | + | 0.702424i | 0.964196 | − | 0.265189i | \(-0.0854345\pi\) |
0.252437 | + | 0.967613i | \(0.418768\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −192513. | − | 333441.i | −0.737254 | − | 1.27696i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 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 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 100484.i | − | 0.370187i | −0.982721 | − | 0.185094i | \(-0.940741\pi\) | ||
0.982721 | − | 0.185094i | \(-0.0592589\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 112346. | 0.395461 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 162039. | − | 93553.1i | 0.566124 | − | 0.326852i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −151097. | − | 131645.i | −0.497683 | − | 0.433613i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 572826. | − | 330721.i | 1.87315 | − | 1.08146i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 52344.2 | − | 90662.9i | 0.168717 | − | 0.292226i | −0.769252 | − | 0.638945i | \(-0.779371\pi\) |
0.937969 | + | 0.346719i | \(0.112704\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 70920.9i | − | 0.226961i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3123.45i | 0.00985411i | 0.999988 | + | 0.00492706i | \(0.00156834\pi\) | ||||
−0.999988 | + | 0.00492706i | \(0.998432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 106190. | − | 61309.0i | 0.332650 | − | 0.192056i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35963.3i | 0.111080i | 0.998456 | + | 0.0555399i | \(0.0176880\pi\) | ||||
−0.998456 | + | 0.0555399i | \(0.982312\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 62530.8 | 0.191788 | 0.0958941 | − | 0.995392i | \(-0.469429\pi\) | ||||
0.0958941 | + | 0.995392i | \(0.469429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −322785. | −0.956228 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17628.9 | − | 10178.0i | −0.0518666 | − | 0.0299452i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10340.3 | − | 17910.0i | −0.0300095 | − | 0.0519779i | 0.850631 | − | 0.525764i | \(-0.176220\pi\) |
−0.880640 | + | 0.473786i | \(0.842887\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −91677.8 | + | 468825.i | −0.264261 | + | 1.35139i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 73184.7 | − | 126760.i | 0.208118 | − | 0.360472i | −0.743003 | − | 0.669288i | \(-0.766599\pi\) |
0.951122 | + | 0.308816i | \(0.0999327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 141020. | − | 244253.i | 0.398333 | − | 0.689932i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28855.0 | + | 16659.4i | 0.0804206 | + | 0.0464308i | 0.539671 | − | 0.841876i | \(-0.318549\pi\) |
−0.459250 | + | 0.888307i | \(0.651882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 301579.i | − | 0.834933i | −0.908692 | − | 0.417467i | \(-0.862918\pi\) | ||
0.908692 | − | 0.417467i | \(-0.137082\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 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 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −61529.0 | + | 106571.i | −0.161625 | + | 0.279943i | −0.935452 | − | 0.353455i | \(-0.885007\pi\) |
0.773826 | + | 0.633398i | \(0.218340\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 159886. | 0.417283 | 0.208641 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208641 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 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 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 450495.i | 1.11723i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −152642. | − | 88127.7i | −0.376179 | − | 0.217187i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −142059. | + | 82017.6i | −0.345742 | + | 0.199614i | −0.662808 | − | 0.748789i | \(-0.730636\pi\) |
0.317066 | + | 0.948403i | \(0.397302\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −95116.5 | −0.227220 | −0.113610 | − | 0.993525i | \(-0.536241\pi\) | ||||
−0.113610 | + | 0.993525i | \(0.536241\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −141276. | + | 81565.6i | −0.335412 | + | 0.193650i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 586580. | 1.37563 | 0.687813 | − | 0.725888i | \(-0.258571\pi\) | ||||
0.687813 | + | 0.725888i | \(0.258571\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 253829. | − | 439644.i | 0.591641 | − | 1.02475i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 619966. | + | 357938.i | 1.42757 | + | 0.824207i | 0.996929 | − | 0.0783166i | \(-0.0249545\pi\) |
0.430640 | + | 0.902524i | \(0.358288\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 262484. | + | 765103.i | 0.593552 | + | 1.73012i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −191673. | + | 110662.i | −0.430832 | + | 0.248741i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 789698.i | − | 1.72299i | −0.507762 | − | 0.861497i | \(-0.669527\pi\) | ||
0.507762 | − | 0.861497i | \(-0.330473\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −689224. | + | 397924.i | −1.49493 | + | 0.863099i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 644105.i | − | 1.38075i | −0.723451 | − | 0.690376i | \(-0.757445\pi\) | ||
0.723451 | − | 0.690376i | \(-0.242555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 320819. | 0.683722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 778623. | 1.61197 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −329217. | − | 190074.i | −0.677668 | − | 0.391252i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 150371. | + | 260451.i | 0.306006 | + | 0.530017i | 0.977485 | − | 0.211006i | \(-0.0676741\pi\) |
−0.671479 | + | 0.741023i | \(0.734341\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43680.1 | + | 223373.i | −0.0883838 | + | 0.451980i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 456897. | + | 263789.i | 0.898750 | + | 0.518894i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32948.0i | 0.0644491i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −135419. | − | 234553.i | −0.261952 | − | 0.453715i | 0.704808 | − | 0.709398i | \(-0.251033\pi\) |
−0.966761 | + | 0.255683i | \(0.917700\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 570928.i | 1.09827i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 643576. | − | 371569.i | 1.16580 | − | 0.673072i | 0.213109 | − | 0.977028i | \(-0.431641\pi\) |
0.952686 | + | 0.303956i | \(0.0983076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55168.2 | − | 95554.1i | 0.0993977 | − | 0.172162i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 275441. | 0.475619 | 0.237809 | − | 0.971312i | \(-0.423571\pi\) | ||||
0.237809 | + | 0.971312i | \(0.423571\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −180918. | + | 104453.i | −0.310766 | + | 0.179421i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −955688. | − | 551767.i | −1.59940 | − | 0.923414i | −0.991603 | − | 0.129321i | \(-0.958720\pi\) |
−0.607797 | − | 0.794092i | \(-0.707947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 89670.1 | + | 51771.1i | 0.149295 | + | 0.0861953i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 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 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 390680.i | 0.624408i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −136621. | + | 78878.1i | −0.217255 | + | 0.125432i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22197.8i | 0.0349457i | 0.999847 | + | 0.0174728i | \(0.00556206\pi\) | ||||
−0.999847 | + | 0.0174728i | \(0.994438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 430591. | 0.674484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −76097.9 | − | 131805.i | −0.118016 | − | 0.204410i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 893326. | 1.37854 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −110260. | −0.168469 | −0.0842345 | − | 0.996446i | \(-0.526844\pi\) | ||||
−0.0842345 | + | 0.996446i | \(0.526844\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −339262. | − | 587619.i | −0.510764 | − | 0.884669i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −223337. | − | 650997.i | −0.334593 | − | 0.975292i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 423971. | − | 734339.i | 0.628999 | − | 1.08946i | −0.358754 | − | 0.933432i | \(-0.616798\pi\) |
0.987753 | − | 0.156026i | \(-0.0498683\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 615143. | + | 355153.i | 0.899425 | + | 0.519283i | 0.877014 | − | 0.480466i | \(-0.159532\pi\) |
0.0224113 | + | 0.999749i | \(0.492866\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 986161.i | 1.43496i | 0.696581 | + | 0.717479i | \(0.254704\pi\) | ||||
−0.696581 | + | 0.717479i | \(0.745296\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 298199. | + | 516496.i | 0.429751 | + | 0.744350i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 490880.i | 0.704048i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −296225. | + | 171026.i | −0.420822 | + | 0.242962i | −0.695429 | − | 0.718595i | \(-0.744786\pi\) |
0.274607 | + | 0.961557i | \(0.411452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −199556. | − | 345641.i | −0.282146 | − | 0.488690i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 360353. | − | 624150.i | 0.504678 | − | 0.874129i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.14281e6 | 1.59297 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.22953e6 | + | 709870.i | −1.67409 | + | 0.966535i | −0.708776 | + | 0.705434i | \(0.750752\pi\) |
−0.965312 | + | 0.261101i | \(0.915914\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.04519e6i | − | 1.40338i | −0.712483 | − | 0.701690i | \(-0.752429\pi\) | ||
0.712483 | − | 0.701690i | \(-0.247571\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 806382. | + | 465565.i | 1.07773 | + | 0.622226i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −517628. | −0.666908 | −0.333454 | − | 0.942766i | \(-0.608214\pi\) | ||||
−0.333454 | + | 0.942766i | \(0.608214\pi\) | |||||||
\(882\) | 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 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −902167. | − | 520867.i | −1.14667 | − | 0.662032i | −0.198599 | − | 0.980081i | \(-0.563639\pi\) |
−0.948074 | + | 0.318048i | \(0.896973\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.24305e6 | − | 717674.i | −1.57284 | − | 0.908079i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −811226. | + | 931091.i | −1.01728 | + | 1.16759i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 479061. | − | 276586.i | 0.598059 | − | 0.345290i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 367296. | − | 636176.i | 0.454461 | − | 0.787150i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 76717.7i | 0.0945030i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.38700e6i | − | 1.67125i | −0.549301 | − | 0.835625i | \(-0.685106\pi\) | ||
0.549301 | − | 0.835625i | \(-0.314894\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −127593. | −0.153068 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25284.4 | 0.0296790 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42723.5 | + | 24666.4i | 0.0499325 | + | 0.0288286i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −570771. | − | 988605.i | −0.661349 | − | 1.14549i | −0.980261 | − | 0.197706i | \(-0.936651\pi\) |
0.318912 | − | 0.947784i | \(-0.396683\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.67865e6 | − | 328257.i | −1.93669 | − | 0.378716i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 927824. | + | 535679.i | 1.04782 | + | 0.604959i | 0.922038 | − | 0.387100i | \(-0.126523\pi\) |
0.125781 | + | 0.992058i | \(0.459856\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.20407e6i | − | 1.35403i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 721456. | + | 1.24960e6i | 0.804470 | + | 1.39338i | 0.916648 | + | 0.399695i | \(0.130884\pi\) |
−0.112178 | + | 0.993688i | \(0.535783\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 169515.i | − | 0.188225i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −239343. | + | 138185.i | −0.263533 | + | 0.152151i | −0.625945 | − | 0.779867i | \(-0.715287\pi\) |
0.362412 | + | 0.932018i | \(0.381953\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 695660. | + | 1.20492e6i | 0.762764 | + | 1.32115i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −511090. | + | 885234.i | −0.555726 | + | 0.962545i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −827553. | −0.896084 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −483492. | + | 279144.i | −0.512803 | + | 0.296067i | −0.733985 | − | 0.679166i | \(-0.762342\pi\) |
0.221182 | + | 0.975233i | \(0.429008\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.24041e6 | + | 2.14845e6i | −1.31020 | + | 2.26934i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36446.8i | 0.0381830i | 0.999818 | + | 0.0190915i | \(0.00607738\pi\) | ||||
−0.999818 | + | 0.0190915i | \(0.993923\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −423084. | − | 244268.i | −0.441430 | − | 0.254859i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −819884. | + | 473360.i | −0.848487 | + | 0.489874i | −0.860140 | − | 0.510058i | \(-0.829624\pi\) |
0.0116529 | + | 0.999932i | \(0.496291\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 144167. | + | 249704.i | 0.148591 | + | 0.257367i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | 0 | 0 |
(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 | 684.5.y.c.145.6 | 12 | ||
3.2 | odd | 2 | 76.5.h.a.69.5 | yes | 12 | ||
12.11 | even | 2 | 304.5.r.b.145.2 | 12 | |||
19.8 | odd | 6 | inner | 684.5.y.c.217.6 | 12 | ||
57.8 | even | 6 | 76.5.h.a.65.5 | ✓ | 12 | ||
228.179 | odd | 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 | 57.8 | even | 6 | ||
76.5.h.a.69.5 | yes | 12 | 3.2 | odd | 2 | ||
304.5.r.b.65.2 | 12 | 228.179 | odd | 6 | |||
304.5.r.b.145.2 | 12 | 12.11 | even | 2 | |||
684.5.y.c.145.6 | 12 | 1.1 | even | 1 | trivial | ||
684.5.y.c.217.6 | 12 | 19.8 | odd | 6 | inner |