Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(217,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.217");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.i (of order \(3\), degree \(2\), not 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: | \(38.2332376837\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 433.1 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.433 |
Dual form | 648.4.i.s.217.1 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.61684 | + | 11.4607i | −0.591829 | + | 1.02508i | 0.402158 | + | 0.915570i | \(0.368260\pi\) |
−0.993986 | + | 0.109507i | \(0.965073\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.61684 | + | 4.53251i | 0.141296 | + | 0.244732i | 0.927985 | − | 0.372617i | \(-0.121540\pi\) |
−0.786689 | + | 0.617350i | \(0.788206\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.0137051 | + | 0.0237379i | 0.872797 | − | 0.488084i | \(-0.162304\pi\) |
−0.859092 | + | 0.511822i | \(0.828971\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −42.4674 | + | 73.5557i | −0.906025 | + | 1.56928i | −0.0864907 | + | 0.996253i | \(0.527565\pi\) |
−0.819535 | + | 0.573029i | \(0.805768\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −40.9348 | −0.584008 | −0.292004 | − | 0.956417i | \(-0.594322\pi\) | ||||
−0.292004 | + | 0.956417i | \(0.594322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 57.5326 | 0.694678 | 0.347339 | − | 0.937740i | \(-0.387085\pi\) | ||||
0.347339 | + | 0.937740i | \(0.387085\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 57.4674 | − | 99.5364i | 0.520990 | − | 0.902382i | −0.478712 | − | 0.877972i | \(-0.658896\pi\) |
0.999702 | − | 0.0244095i | \(-0.00777056\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −25.0652 | − | 43.4143i | −0.200522 | − | 0.347314i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −101.234 | − | 175.342i | −0.648228 | − | 1.12276i | −0.983546 | − | 0.180659i | \(-0.942177\pi\) |
0.335317 | − | 0.942105i | \(-0.391156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −137.084 | + | 237.437i | −0.794228 | + | 1.37564i | 0.129101 | + | 0.991631i | \(0.458791\pi\) |
−0.923329 | + | 0.384011i | \(0.874542\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −69.2610 | −0.334493 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 242.935 | 1.07941 | 0.539706 | − | 0.841854i | \(-0.318535\pi\) | ||||
0.539706 | + | 0.841854i | \(0.318535\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −164.168 | + | 284.348i | −0.625337 | + | 1.08311i | 0.363139 | + | 0.931735i | \(0.381705\pi\) |
−0.988476 | + | 0.151380i | \(0.951628\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −140.636 | − | 243.588i | −0.498762 | − | 0.863881i | 0.501237 | − | 0.865310i | \(-0.332878\pi\) |
−0.999999 | + | 0.00142907i | \(0.999545\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.9348 | + | 20.6716i | 0.0370396 | + | 0.0641545i | 0.883951 | − | 0.467580i | \(-0.154874\pi\) |
−0.846911 | + | 0.531734i | \(0.821541\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 157.804 | − | 273.325i | 0.460071 | − | 0.796866i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −300.038 | −0.777611 | −0.388805 | − | 0.921320i | \(-0.627112\pi\) | ||||
−0.388805 | + | 0.921320i | \(0.627112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.2337 | −0.0324442 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 376.804 | − | 652.644i | 0.831453 | − | 1.44012i | −0.0654327 | − | 0.997857i | \(-0.520843\pi\) |
0.896886 | − | 0.442262i | \(-0.145824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −247.739 | − | 429.097i | −0.519996 | − | 0.900659i | −0.999730 | − | 0.0232449i | \(-0.992600\pi\) |
0.479734 | − | 0.877414i | \(-0.340733\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −562.000 | − | 973.413i | −1.07242 | − | 1.85749i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 204.973 | − | 355.023i | 0.373752 | − | 0.647358i | −0.616387 | − | 0.787443i | \(-0.711404\pi\) |
0.990139 | + | 0.140085i | \(0.0447377\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1114.80 | −1.86342 | −0.931711 | − | 0.363201i | \(-0.881684\pi\) | ||||
−0.931711 | + | 0.363201i | \(0.881684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −287.000 | −0.460148 | −0.230074 | − | 0.973173i | \(-0.573897\pi\) | ||||
−0.230074 | + | 0.973173i | \(0.573897\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.61684 | + | 4.53251i | −0.00387295 | + | 0.00670814i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 615.739 | + | 1066.49i | 0.876912 | + | 1.51886i | 0.854712 | + | 0.519103i | \(0.173734\pi\) |
0.0222001 | + | 0.999754i | \(0.492933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −471.239 | − | 816.210i | −0.623195 | − | 1.07941i | −0.988887 | − | 0.148670i | \(-0.952501\pi\) |
0.365692 | − | 0.930736i | \(-0.380832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 270.859 | − | 469.141i | 0.345633 | − | 0.598653i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 190.206 | 0.226537 | 0.113269 | − | 0.993564i | \(-0.463868\pi\) | ||||
0.113269 | + | 0.993564i | \(0.463868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −444.522 | −0.512072 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −380.684 | + | 659.365i | −0.411130 | + | 0.712099i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 153.435 | + | 265.757i | 0.160608 | + | 0.278181i | 0.935087 | − | 0.354419i | \(-0.115321\pi\) |
−0.774479 | + | 0.632599i | \(0.781988\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −336.448 | − | 582.746i | −0.331464 | − | 0.574113i | 0.651335 | − | 0.758790i | \(-0.274209\pi\) |
−0.982799 | + | 0.184678i | \(0.940876\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −420.076 | + | 727.593i | −0.401857 | + | 0.696037i | −0.993950 | − | 0.109832i | \(-0.964969\pi\) |
0.592093 | + | 0.805870i | \(0.298302\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1658.09 | −1.49807 | −0.749034 | − | 0.662532i | \(-0.769482\pi\) | ||||
−0.749034 | + | 0.662532i | \(0.769482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1263.76 | −1.11052 | −0.555258 | − | 0.831678i | \(-0.687381\pi\) | ||||
−0.555258 | + | 0.831678i | \(0.687381\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 237.179 | − | 410.806i | 0.197451 | − | 0.341995i | −0.750250 | − | 0.661154i | \(-0.770067\pi\) |
0.947701 | + | 0.319159i | \(0.103400\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 760.505 | + | 1317.23i | 0.616674 | + | 1.06811i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −107.120 | − | 185.537i | −0.0825182 | − | 0.142926i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 665.000 | − | 1151.81i | 0.499624 | − | 0.865375i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −990.800 | −0.708959 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −560.375 | −0.391537 | −0.195769 | − | 0.980650i | \(-0.562720\pi\) | ||||
−0.195769 | + | 0.980650i | \(0.562720\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 394.652 | − | 683.557i | 0.263213 | − | 0.455898i | −0.703881 | − | 0.710318i | \(-0.748551\pi\) |
0.967094 | + | 0.254420i | \(0.0818845\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 150.554 | + | 260.767i | 0.0981555 | + | 0.170010i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −665.234 | − | 1152.22i | −0.414852 | − | 0.718545i | 0.580561 | − | 0.814217i | \(-0.302833\pi\) |
−0.995413 | + | 0.0956719i | \(0.969500\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1569.68 | + | 2718.77i | −0.957834 | + | 1.65902i | −0.230088 | + | 0.973170i | \(0.573901\pi\) |
−0.727746 | + | 0.685847i | \(0.759432\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −84.9348 | −0.0496685 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2679.39 | 1.53456 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1333.12 | − | 2309.04i | 0.732977 | − | 1.26955i | −0.222628 | − | 0.974904i | \(-0.571463\pi\) |
0.955605 | − | 0.294650i | \(-0.0952032\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −239.703 | − | 415.178i | −0.129184 | − | 0.223753i | 0.794177 | − | 0.607687i | \(-0.207902\pi\) |
−0.923361 | + | 0.383934i | \(0.874569\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1814.13 | − | 3142.16i | −0.940093 | − | 1.62829i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1002.41 | − | 1736.23i | 0.509562 | − | 0.882587i | −0.490377 | − | 0.871511i | \(-0.663141\pi\) |
0.999939 | − | 0.0110768i | \(-0.00352592\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 601.533 | 0.294456 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −832.043 | −0.399820 | −0.199910 | − | 0.979814i | \(-0.564065\pi\) | ||||
−0.199910 | + | 0.979814i | \(0.564065\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1435.83 | + | 2486.92i | −0.665314 | + | 1.15236i | 0.313885 | + | 0.949461i | \(0.398369\pi\) |
−0.979200 | + | 0.202898i | \(0.934964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2508.46 | − | 4344.77i | −1.14176 | − | 1.97759i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1789.72 | + | 3099.89i | 0.786531 | + | 1.36231i | 0.928080 | + | 0.372381i | \(0.121458\pi\) |
−0.141549 | + | 0.989931i | \(0.545208\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 131.184 | − | 227.217i | 0.0566660 | − | 0.0981484i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2162.09 | 0.902804 | 0.451402 | − | 0.892321i | \(-0.350924\pi\) | ||||
0.451402 | + | 0.892321i | \(0.350924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1740.26 | 0.714655 | 0.357328 | − | 0.933979i | \(-0.383688\pi\) | ||||
0.357328 | + | 0.933979i | \(0.383688\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1607.46 | + | 2784.20i | −0.638827 | + | 1.10648i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.4674 | − | 35.4505i | −0.00800387 | − | 0.0138631i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1268.90 | + | 2197.80i | 0.480704 | + | 0.832604i | 0.999755 | − | 0.0221395i | \(-0.00704779\pi\) |
−0.519051 | + | 0.854743i | \(0.673714\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −95.1738 | + | 164.846i | −0.0354962 | + | 0.0614811i | −0.883228 | − | 0.468944i | \(-0.844634\pi\) |
0.847732 | + | 0.530425i | \(0.177968\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5314.25 | −1.92195 | −0.960977 | − | 0.276629i | \(-0.910783\pi\) | ||||
−0.960977 | + | 0.276629i | \(0.910783\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3787.15 | 1.34906 | 0.674532 | − | 0.738246i | \(-0.264346\pi\) | ||||
0.674532 | + | 0.738246i | \(0.264346\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 529.826 | − | 917.685i | 0.183185 | − | 0.317285i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2172.55 | − | 3762.97i | −0.740184 | − | 1.28204i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.7663 | + | 49.8247i | 0.00952061 | + | 0.0164902i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1221.03 | + | 2114.88i | −0.398384 | + | 0.690021i | −0.993527 | − | 0.113599i | \(-0.963762\pi\) |
0.595143 | + | 0.803620i | \(0.297095\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3722.26 | 1.18073 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1434.91 | −0.448886 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1738.39 | − | 3010.98i | 0.529126 | − | 0.916473i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1164.93 | + | 2017.73i | 0.349820 | + | 0.605906i | 0.986217 | − | 0.165456i | \(-0.0529095\pi\) |
−0.636397 | + | 0.771361i | \(0.719576\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 663.196 | + | 1148.69i | 0.193911 | + | 0.335864i | 0.946543 | − | 0.322577i | \(-0.104549\pi\) |
−0.752632 | + | 0.658442i | \(0.771216\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 772.065 | − | 1337.26i | 0.222793 | − | 0.385888i | −0.732862 | − | 0.680377i | \(-0.761816\pi\) |
0.955655 | + | 0.294489i | \(0.0951494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2266.32 | 0.637216 | 0.318608 | − | 0.947887i | \(-0.396785\pi\) | ||||
0.318608 | + | 0.947887i | \(0.396785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −315.882 | −0.0876844 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.8376 | + | 44.7520i | −0.00699286 | + | 0.0121120i | −0.869501 | − | 0.493932i | \(-0.835559\pi\) |
0.862508 | + | 0.506044i | \(0.168893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1161.98 | + | 2012.60i | 0.310579 | + | 0.537939i | 0.978488 | − | 0.206304i | \(-0.0661437\pi\) |
−0.667909 | + | 0.744243i | \(0.732810\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2088.33 | + | 3617.10i | 0.544566 | + | 0.943216i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2443.26 | + | 4231.85i | −0.629396 | + | 1.09015i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6958.52 | 1.74987 | 0.874936 | − | 0.484239i | \(-0.160903\pi\) | ||||
0.874936 | + | 0.484239i | \(0.160903\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 114.935 | 0.0285608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1487.46 | + | 2576.35i | −0.361031 | + | 0.625324i | −0.988131 | − | 0.153615i | \(-0.950909\pi\) |
0.627100 | + | 0.778939i | \(0.284242\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 635.722 | + | 1101.10i | 0.152517 | + | 0.264167i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −58.4234 | − | 101.192i | −0.0136979 | − | 0.0237254i | 0.859095 | − | 0.511816i | \(-0.171027\pi\) |
−0.872793 | + | 0.488090i | \(0.837694\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1985.30 | − | 3438.65i | 0.460212 | − | 0.797111i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3334.81 | 0.755863 | 0.377932 | − | 0.925834i | \(-0.376635\pi\) | ||||
0.377932 | + | 0.925834i | \(0.376635\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3120.23 | −0.699412 | −0.349706 | − | 0.936860i | \(-0.613718\pi\) | ||||
−0.349706 | + | 0.936860i | \(0.613718\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.0652 | − | 43.4143i | 0.00549633 | − | 0.00951993i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1297.20 | + | 2246.81i | 0.281375 | + | 0.487356i | 0.971724 | − | 0.236121i | \(-0.0758761\pi\) |
−0.690348 | + | 0.723477i | \(0.742543\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1141.55 | + | 1977.23i | 0.242347 | + | 0.419757i | 0.961382 | − | 0.275217i | \(-0.0887496\pi\) |
−0.719036 | + | 0.694973i | \(0.755416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −823.798 | + | 1426.86i | −0.173038 | + | 0.299710i | −0.939480 | − | 0.342602i | \(-0.888692\pi\) |
0.766443 | + | 0.642313i | \(0.222025\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1718.41 | −0.353431 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3237.35 | −0.658935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1466.66 | + | 2540.32i | −0.292434 | + | 0.506510i | −0.974385 | − | 0.224888i | \(-0.927798\pi\) |
0.681951 | + | 0.731398i | \(0.261132\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4986.51 | + | 8636.89i | 0.984155 | + | 1.70461i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4880.98 | + | 8454.10i | 0.944061 | + | 1.63516i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 736.044 | − | 1274.87i | 0.140946 | − | 0.244126i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6557.00 | 1.23099 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8216.93 | −1.52757 | −0.763787 | − | 0.645468i | \(-0.776662\pi\) | ||||
−0.763787 | + | 0.645468i | \(0.776662\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −168.815 | + | 292.396i | −0.0307801 | + | 0.0533127i | −0.881005 | − | 0.473107i | \(-0.843132\pi\) |
0.850225 | + | 0.526419i | \(0.176466\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 386.283 | + | 669.062i | 0.0697572 | + | 0.120823i | 0.898794 | − | 0.438370i | \(-0.144444\pi\) |
−0.829037 | + | 0.559194i | \(0.811111\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3886.96 | + | 6732.42i | 0.688686 | + | 1.19284i | 0.972263 | + | 0.233890i | \(0.0751456\pi\) |
−0.283577 | + | 0.958950i | \(0.591521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 101.234 | − | 175.342i | 0.0177680 | − | 0.0307751i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2355.08 | −0.405698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4257.82 | 0.726712 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −62.4628 | + | 108.189i | −0.0104671 | + | 0.0181296i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2130.66 | − | 3690.41i | −0.353811 | − | 0.612819i | 0.633103 | − | 0.774068i | \(-0.281781\pi\) |
−0.986914 | + | 0.161249i | \(0.948448\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2712.54 | + | 4698.27i | 0.442394 | + | 0.766250i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2364.46 | − | 4095.36i | 0.382196 | − | 0.661983i | −0.609180 | − | 0.793032i | \(-0.708501\pi\) |
0.991376 | + | 0.131049i | \(0.0418345\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −274.168 | −0.0435397 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3446.95 | 0.542618 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1292.02 | + | 2237.85i | −0.199883 | + | 0.346207i | −0.948490 | − | 0.316806i | \(-0.897389\pi\) |
0.748608 | + | 0.663013i | \(0.230723\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2061.23 | − | 3570.15i | −0.316146 | − | 0.547581i | 0.663534 | − | 0.748146i | \(-0.269056\pi\) |
−0.979680 | + | 0.200565i | \(0.935722\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4762.46 | − | 8248.82i | −0.718074 | − | 1.24374i | −0.961762 | − | 0.273887i | \(-0.911691\pi\) |
0.243688 | − | 0.969854i | \(-0.421643\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7376.49 | − | 12776.4i | 1.10283 | − | 1.91015i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3048.39 | 0.448156 | 0.224078 | − | 0.974571i | \(-0.428063\pi\) | ||||
0.224078 | + | 0.974571i | \(0.428063\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3549.00 | −0.517422 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1899.03 | − | 3289.22i | 0.272329 | − | 0.471687i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2618.95 | + | 4536.15i | 0.372501 | + | 0.645191i | 0.989950 | − | 0.141420i | \(-0.0451668\pi\) |
−0.617448 | + | 0.786612i | \(0.711833\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −785.152 | − | 1359.92i | −0.109874 | − | 0.190307i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1435.75 | + | 2486.79i | −0.199304 | + | 0.345205i | −0.948303 | − | 0.317367i | \(-0.897201\pi\) |
0.748999 | + | 0.662571i | \(0.230535\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17196.5 | 2.34925 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1649.20 | 0.223518 | 0.111759 | − | 0.993735i | \(-0.464351\pi\) | ||||
0.111759 | + | 0.993735i | \(0.464351\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4091.38 | − | 7086.48i | 0.545848 | − | 0.945437i | −0.452705 | − | 0.891660i | \(-0.649541\pi\) |
0.998553 | − | 0.0537762i | \(-0.0171257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −34.6305 | − | 59.9818i | −0.00458424 | − | 0.00794014i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −690.289 | − | 1195.62i | −0.0899719 | − | 0.155836i | 0.817527 | − | 0.575890i | \(-0.195344\pi\) |
−0.907499 | + | 0.420054i | \(0.862011\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2352.41 | + | 4074.50i | −0.304262 | + | 0.526998i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16297.0 | −2.07593 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5772.41 | −0.729746 | −0.364873 | − | 0.931057i | \(-0.618888\pi\) | ||||
−0.364873 | + | 0.931057i | \(0.618888\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4689.42 | + | 8122.32i | −0.583987 | + | 1.01149i | 0.411014 | + | 0.911629i | \(0.365175\pi\) |
−0.995001 | + | 0.0998656i | \(0.968159\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11643.2 | − | 20166.6i | −1.43918 | − | 2.49273i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 121.467 | + | 210.388i | 0.0147934 | + | 0.0256229i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3536.54 | + | 6125.47i | −0.427557 | + | 0.740551i | −0.996655 | − | 0.0817189i | \(-0.973959\pi\) |
0.569098 | + | 0.822269i | \(0.307292\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3944.15 | 0.469925 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12472.5 | 1.47530 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4717.82 | + | 8171.51i | −0.550073 | + | 0.952755i | 0.448195 | + | 0.893936i | \(0.352067\pi\) |
−0.998269 | + | 0.0588195i | \(0.981266\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1310.06 | + | 2269.10i | 0.151659 | + | 0.262682i | 0.931838 | − | 0.362876i | \(-0.118205\pi\) |
−0.780178 | + | 0.625557i | \(0.784872\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1026.04 | + | 1777.15i | 0.117106 | + | 0.202834i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1296.59 | − | 2245.76i | 0.146947 | − | 0.254519i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3485.65 | −0.389555 | −0.194777 | − | 0.980847i | \(-0.562398\pi\) | ||||
−0.194777 | + | 0.980847i | \(0.562398\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9818.69 | 1.08974 | 0.544869 | − | 0.838521i | \(-0.316579\pi\) | ||||
0.544869 | + | 0.838521i | \(0.316579\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3306.25 | − | 5726.59i | 0.361921 | − | 0.626865i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 617.502 | + | 1069.54i | 0.0671338 | + | 0.116279i | 0.897639 | − | 0.440732i | \(-0.145281\pi\) |
−0.830505 | + | 0.557012i | \(0.811948\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5372.17 | + | 9304.88i | 0.576162 | + | 0.997941i | 0.995914 | + | 0.0903028i | \(0.0287835\pi\) |
−0.419753 | + | 0.907639i | \(0.637883\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1258.57 | + | 2179.90i | −0.134071 | + | 0.232218i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16166.3 | −1.69919 | −0.849595 | − | 0.527435i | \(-0.823154\pi\) | ||||
−0.849595 | + | 0.527435i | \(0.823154\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −328.337 | −0.0342811 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2941.33 | − | 5094.54i | 0.303059 | − | 0.524913i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1061.13 | + | 1837.93i | 0.108616 | + | 0.188129i | 0.915210 | − | 0.402977i | \(-0.132025\pi\) |
−0.806594 | + | 0.591106i | \(0.798691\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1736.70 | − | 3008.06i | −0.175459 | − | 0.303903i | 0.764861 | − | 0.644195i | \(-0.222807\pi\) |
−0.940320 | + | 0.340292i | \(0.889474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1787.85 | + | 3096.65i | −0.179457 | + | 0.310828i | −0.941695 | − | 0.336469i | \(-0.890767\pi\) |
0.762238 | + | 0.647297i | \(0.224101\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9406.95 | 0.932124 | 0.466062 | − | 0.884752i | \(-0.345672\pi\) | ||||
0.466062 | + | 0.884752i | \(0.345672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2145.53 | 0.211239 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 140.636 | − | 243.588i | 0.0136711 | − | 0.0236791i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1442.07 | − | 2497.74i | −0.139298 | − | 0.241272i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9262.02 | − | 16042.3i | −0.883492 | − | 1.53025i | −0.847433 | − | 0.530903i | \(-0.821853\pi\) |
−0.0360589 | − | 0.999350i | \(-0.511480\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10316.8 | + | 17869.2i | −0.977974 | + | 1.69390i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4061.02 | −0.380209 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −825.955 | −0.0768533 | −0.0384267 | − | 0.999261i | \(-0.512235\pi\) | ||||
−0.0384267 | + | 0.999261i | \(0.512235\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4459.18 | − | 7723.52i | 0.409857 | − | 0.709893i | −0.585016 | − | 0.811021i | \(-0.698912\pi\) |
0.994873 | + | 0.101128i | \(0.0322453\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4143.98 | + | 7177.58i | 0.378571 | + | 0.655703i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2917.27 | − | 5052.86i | −0.263295 | − | 0.456040i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9107.20 | + | 15774.1i | −0.817022 | + | 1.41512i | 0.0908443 | + | 0.995865i | \(0.471043\pi\) |
−0.907867 | + | 0.419259i | \(0.862290\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2264.42 | −0.200726 | −0.100363 | − | 0.994951i | \(-0.532000\pi\) | ||||
−0.100363 | + | 0.994951i | \(0.532000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8904.91 | 0.784679 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7117.59 | + | 12328.0i | −0.619806 | + | 1.07354i | 0.369714 | + | 0.929145i | \(0.379456\pi\) |
−0.989521 | + | 0.144391i | \(0.953878\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −751.034 | − | 1300.83i | −0.0650172 | − | 0.112613i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5559.15 | − | 9628.74i | −0.475661 | − | 0.823870i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.9348 | + | 20.6716i | −0.00101526 | + | 0.00175848i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11343.3 | −0.953856 | −0.476928 | − | 0.878942i | \(-0.658250\pi\) | ||||
−0.476928 | + | 0.878942i | \(0.658250\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20464.1 | −1.71096 | −0.855482 | − | 0.517832i | \(-0.826739\pi\) | ||||
−0.855482 | + | 0.517832i | \(0.826739\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5611.51 | − | 9719.42i | 0.463835 | − | 0.803386i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −521.499 | − | 903.262i | −0.0428617 | − | 0.0742387i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13943.6 | − | 24151.0i | −1.13314 | − | 1.96266i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10971.3 | − | 19002.8i | 0.886599 | − | 1.53564i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 315.609 | 0.0252212 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1993.69 | −0.158439 | −0.0792196 | − | 0.996857i | \(-0.525243\pi\) | ||||
−0.0792196 | + | 0.996857i | \(0.525243\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8362.10 | − | 14483.6i | 0.657235 | − | 1.13836i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1362.01 | + | 2359.07i | 0.106463 | + | 0.184399i | 0.914335 | − | 0.404959i | \(-0.132714\pi\) |
−0.807872 | + | 0.589358i | \(0.799381\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5824.24 | − | 10087.9i | −0.450310 | − | 0.779960i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3222.59 | + | 5581.68i | −0.247809 | + | 0.429218i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15046.5 | −1.14460 | −0.572299 | − | 0.820045i | \(-0.693948\pi\) | ||||
−0.572299 | + | 0.820045i | \(0.693948\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23889.7 | 1.80756 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9804.28 | + | 16981.5i | −0.733928 | + | 1.27120i | 0.221265 | + | 0.975214i | \(0.428982\pi\) |
−0.955192 | + | 0.295986i | \(0.904352\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3138.75 | + | 5436.48i | 0.233714 | + | 0.404804i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6984.27 | + | 12097.1i | 0.514580 | + | 0.891278i | 0.999857 | + | 0.0169178i | \(0.00538536\pi\) |
−0.485277 | + | 0.874360i | \(0.661281\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11807.0 | − | 20450.4i | 0.865339 | − | 1.49881i | −0.00137176 | − | 0.999999i | \(-0.500437\pi\) |
0.866710 | − | 0.498812i | \(-0.166230\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5761.74 | −0.417880 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23002.4 | −1.65962 | −0.829811 | − | 0.558044i | \(-0.811552\pi\) | ||||
−0.829811 | + | 0.558044i | \(0.811552\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2466.32 | − | 4271.79i | 0.176110 | − | 0.305032i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −150.019 | − | 259.840i | −0.0106572 | − | 0.0184588i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4050.22 | − | 7015.19i | −0.284788 | − | 0.493267i | 0.687770 | − | 0.725929i | \(-0.258590\pi\) |
−0.972558 | + | 0.232662i | \(0.925256\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7886.81 | + | 13660.4i | −0.551733 | + | 0.955629i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22256.2 | −1.54124 | −0.770618 | − | 0.637298i | \(-0.780052\pi\) | ||||
−0.770618 | + | 0.637298i | \(0.780052\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2835.18 | 0.195346 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4193.15 | + | 7262.75i | −0.286023 | + | 0.495406i | −0.972857 | − | 0.231409i | \(-0.925667\pi\) |
0.686834 | + | 0.726814i | \(0.259000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4907.11 | + | 8499.36i | 0.333053 | + | 0.576865i | 0.983109 | − | 0.183021i | \(-0.0585877\pi\) |
−0.650056 | + | 0.759887i | \(0.725254\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8800.40 | + | 15242.7i | 0.591384 | + | 1.02431i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12038.8 | − | 20851.9i | 0.805011 | − | 1.39432i | −0.111273 | − | 0.993790i | \(-0.535493\pi\) |
0.916284 | − | 0.400530i | \(-0.131174\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2027.35 | −0.134235 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18679.6 | −1.23077 | −0.615386 | − | 0.788226i | \(-0.711000\pi\) | ||||
−0.615386 | + | 0.788226i | \(0.711000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −825.440 | + | 1429.70i | −0.0538589 | + | 0.0932864i | −0.891698 | − | 0.452631i | \(-0.850485\pi\) |
0.837839 | + | 0.545917i | \(0.183819\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12516.4 | − | 21679.1i | −0.812727 | − | 1.40768i | −0.910949 | − | 0.412520i | \(-0.864649\pi\) |
0.0982217 | − | 0.995165i | \(-0.468685\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 497.740 | + | 862.112i | 0.0320089 | + | 0.0554411i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9689.12 | − | 16782.1i | 0.620104 | − | 1.07405i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9944.47 | −0.630385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1666.38 | 0.105131 | 0.0525653 | − | 0.998617i | \(-0.483260\pi\) | ||||
0.0525653 | + | 0.998617i | \(0.483260\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3707.91 | − | 6422.29i | 0.231723 | − | 0.401356i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13403.1 | + | 23214.8i | 0.833672 | + | 1.44396i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12013.3 | − | 20807.6i | −0.740243 | − | 1.28214i | −0.952385 | − | 0.304900i | \(-0.901377\pi\) |
0.212142 | − | 0.977239i | \(-0.431956\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6386.25 | − | 11061.3i | 0.391678 | − | 0.678407i | −0.600993 | − | 0.799254i | \(-0.705228\pi\) |
0.992671 | + | 0.120848i | \(0.0385613\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19420.6 | 1.18007 | 0.590034 | − | 0.807378i | \(-0.299114\pi\) | ||||
0.590034 | + | 0.807378i | \(0.299114\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 753.609 | 0.0455805 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 405.872 | − | 702.991i | 0.0243231 | − | 0.0421289i | −0.853608 | − | 0.520917i | \(-0.825590\pi\) |
0.877931 | + | 0.478788i | \(0.158924\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5222.70 | + | 9045.98i | 0.311554 | + | 0.539627i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6082.89 | − | 10535.9i | −0.359569 | − | 0.622791i | 0.628320 | − | 0.777955i | \(-0.283743\pi\) |
−0.987889 | + | 0.155164i | \(0.950410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1502.17 | − | 2601.83i | 0.0883925 | − | 0.153100i | −0.818439 | − | 0.574593i | \(-0.805160\pi\) |
0.906832 | + | 0.421493i | \(0.138494\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3984.77 | −0.232365 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23270.5 | −1.35088 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 247.739 | − | 429.097i | 0.0142531 | − | 0.0246872i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 636.413 | + | 1102.30i | 0.0364516 | + | 0.0631360i | 0.883676 | − | 0.468100i | \(-0.155061\pi\) |
−0.847224 | + | 0.531236i | \(0.821728\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5519.94 | − | 9560.81i | −0.313366 | − | 0.542765i | 0.665723 | − | 0.746199i | \(-0.268123\pi\) |
−0.979089 | + | 0.203434i | \(0.934790\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −803.030 | + | 1390.89i | −0.0453865 | + | 0.0786118i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6103.65 | −0.341947 | −0.170974 | − | 0.985276i | \(-0.554691\pi\) | ||||
−0.170974 | + | 0.985276i | \(0.554691\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17607.0 | 0.982085 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12741.8 | − | 22069.5i | 0.704535 | − | 1.22029i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15379.6 | − | 26638.3i | −0.846698 | − | 1.46652i | −0.884139 | − | 0.467225i | \(-0.845254\pi\) |
0.0374409 | − | 0.999299i | \(-0.488079\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20772.7 | − | 35979.4i | −1.13375 | − | 1.96371i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6720.19 | − | 11639.7i | 0.365202 | − | 0.632548i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30619.5 | 1.64976 | 0.824880 | − | 0.565308i | \(-0.191243\pi\) | ||||
0.824880 | + | 0.565308i | \(0.191243\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13976.7 | 0.749844 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1760.87 | − | 3049.91i | 0.0936693 | − | 0.162240i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14325.5 | − | 24812.5i | −0.758822 | − | 1.31432i | −0.943452 | − | 0.331510i | \(-0.892442\pi\) |
0.184630 | − | 0.982808i | \(-0.440891\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15755.7 | + | 27289.7i | 0.827570 | + | 1.43339i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 562.000 | − | 973.413i | 0.0293953 | − | 0.0509141i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24899.6 | −1.29151 | −0.645756 | − | 0.763544i | \(-0.723458\pi\) | ||||
−0.645756 | + | 0.763544i | \(0.723458\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4397.09 | −0.227124 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5074.90 | + | 8789.98i | −0.259968 | + | 0.450278i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17159.0 | + | 29720.3i | 0.875369 | + | 1.51618i | 0.856370 | + | 0.516363i | \(0.172715\pi\) |
0.0189990 | + | 0.999820i | \(0.493952\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5756.89 | + | 9971.23i | 0.291281 | + | 0.504513i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13876.0 | + | 24033.9i | −0.699209 | + | 1.21107i | 0.269532 | + | 0.962992i | \(0.413131\pi\) |
−0.968741 | + | 0.248074i | \(0.920202\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 409.945 | 0.0204892 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24701.0 | −1.22955 | −0.614777 | − | 0.788701i | \(-0.710754\pi\) | ||||
−0.614777 | + | 0.788701i | \(0.710754\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11593.4 | + | 20080.4i | −0.572438 | + | 0.991491i | 0.423877 | + | 0.905720i | \(0.360669\pi\) |
−0.996315 | + | 0.0857715i | \(0.972664\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17642.1 | + | 30557.1i | 0.867594 | + | 1.50272i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4338.95 | − | 7515.29i | −0.211671 | − | 0.366626i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12455.0 | + | 21572.6i | −0.605177 | + | 1.04820i | 0.386846 | + | 0.922144i | \(0.373564\pi\) |
−0.992023 | + | 0.126053i | \(0.959769\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6344.32 | 0.305819 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2659.35 | 0.127682 | 0.0638412 | − | 0.997960i | \(-0.479665\pi\) | ||||
0.0638412 | + | 0.997960i | \(0.479665\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12707.6 | − | 22010.3i | 0.605324 | − | 1.04845i | −0.386677 | − | 0.922215i | \(-0.626377\pi\) |
0.992000 | − | 0.126236i | \(-0.0402896\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3307.06 | − | 5728.00i | −0.156912 | − | 0.271779i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32003.8 | + | 55432.2i | 1.50664 | + | 2.60957i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15026.6 | + | 26026.8i | −0.704645 | + | 1.22048i | 0.262175 | + | 0.965020i | \(0.415560\pi\) |
−0.966820 | + | 0.255460i | \(0.917773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6066.30 | 0.282263 | 0.141132 | − | 0.989991i | \(-0.454926\pi\) | ||||
0.141132 | + | 0.989991i | \(0.454926\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13744.2 | 0.637040 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9445.04 | + | 16359.3i | −0.434408 | + | 0.752416i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −557.402 | − | 965.449i | −0.0255383 | − | 0.0442336i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13265.6 | + | 22976.7i | 0.603147 | + | 1.04468i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2748.09 | − | 4759.83i | 0.124471 | − | 0.215590i | −0.797055 | − | 0.603907i | \(-0.793610\pi\) |
0.921526 | + | 0.388316i | \(0.126943\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2482.64 | 0.111596 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42083.3 | 1.88452 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13904.0 | + | 24082.5i | −0.617949 | + | 1.07032i | 0.371910 | + | 0.928269i | \(0.378703\pi\) |
−0.989859 | + | 0.142051i | \(0.954630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −488.546 | − | 846.187i | −0.0216314 | − | 0.0374667i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −143.500 | − | 248.549i | −0.00630636 | − | 0.0109229i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3980.25 | + | 6893.99i | −0.174267 | + | 0.301840i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6720.58 | 0.292068 | 0.146034 | − | 0.989280i | \(-0.453349\pi\) | ||||
0.146034 | + | 0.989280i | \(0.453349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9923.66 | 0.429675 | 0.214838 | − | 0.976650i | \(-0.431078\pi\) | ||||
0.214838 | + | 0.976650i | \(0.431078\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5505.50 | − | 9535.80i | 0.236625 | − | 0.409846i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8091.15 | − | 14014.3i | −0.346479 | − | 0.600119i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9559.38 | − | 16557.3i | −0.406364 | − | 0.703843i | 0.588115 | − | 0.808777i | \(-0.299870\pi\) |
−0.994479 | + | 0.104934i | \(0.966537\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14171.6 | + | 24546.0i | −0.600234 | + | 1.03963i | 0.392552 | + | 0.919730i | \(0.371592\pi\) |
−0.992785 | + | 0.119905i | \(0.961741\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25909.2 | −1.08942 | −0.544711 | − | 0.838624i | \(-0.683361\pi\) | ||||
−0.544711 | + | 0.838624i | \(0.683361\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3137.00 | −0.131426 | −0.0657132 | − | 0.997839i | \(-0.520932\pi\) | ||||
−0.0657132 | + | 0.997839i | \(0.520932\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6459.68 | + | 11188.5i | −0.268685 | + | 0.465376i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19001.3 | − | 32911.2i | −0.787504 | − | 1.36400i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4055.31 | + | 7024.01i | 0.166871 | + | 0.289030i | 0.937318 | − | 0.348475i | \(-0.113300\pi\) |
−0.770447 | + | 0.637504i | \(0.779967\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8302.02 | + | 14379.5i | −0.340400 | + | 0.589590i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 66392.2 | 2.70291 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6960.80 | 0.282380 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13960.8 | − | 24180.9i | 0.562363 | − | 0.974041i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10158.7 | − | 17595.3i | −0.407768 | − | 0.706275i | 0.586871 | − | 0.809680i | \(-0.300360\pi\) |
−0.994639 | + | 0.103405i | \(0.967026\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1469.32 | + | 2544.93i | 0.0585658 | + | 0.101439i | 0.893822 | − | 0.448422i | \(-0.148014\pi\) |
−0.835256 | + | 0.549861i | \(0.814681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5355.13 | − | 9275.35i | 0.212706 | − | 0.368418i | −0.739854 | − | 0.672767i | \(-0.765106\pi\) |
0.952561 | + | 0.304349i | \(0.0984390\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12400.3 | 0.489122 | 0.244561 | − | 0.969634i | \(-0.421356\pi\) | ||||
0.244561 | + | 0.969634i | \(0.421356\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −47369.2 | −1.86197 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −615.739 | + | 1066.49i | −0.0240363 | + | 0.0416320i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17409.3 | + | 30153.8i | 0.677258 | + | 1.17305i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2592.77 | − | 4490.81i | −0.100173 | − | 0.173505i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15395.1 | − | 26665.1i | 0.592765 | − | 1.02670i | −0.401093 | − | 0.916037i | \(-0.631370\pi\) |
0.993858 | − | 0.110662i | \(-0.0352970\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20320.3 | −0.777082 | −0.388541 | − | 0.921431i | \(-0.627021\pi\) | ||||
−0.388541 | + | 0.921431i | \(0.627021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27680.1 | 1.05494 | 0.527468 | − | 0.849575i | \(-0.323141\pi\) | ||||
0.527468 | + | 0.849575i | \(0.323141\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20562.4 | + | 35615.1i | −0.778374 | + | 1.34818i | 0.154504 | + | 0.987992i | \(0.450622\pi\) |
−0.932878 | + | 0.360191i | \(0.882711\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1466.41 | − | 2539.90i | −0.0553228 | − | 0.0958218i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 686.638 | + | 1189.29i | 0.0257306 | + | 0.0445668i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14306.2 | + | 24779.0i | −0.534305 | + | 0.925444i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 55510.2 | 2.05936 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12282.0 | 0.454131 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11515.0 | + | 19944.6i | −0.422953 | + | 0.732577i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13485.7 | − | 23357.9i | −0.493698 | − | 0.855111i | 0.506275 | − | 0.862372i | \(-0.331022\pi\) |
−0.999974 | + | 0.00726135i | \(0.997689\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23141.0 | + | 40081.4i | 0.841597 | + | 1.45769i | 0.888544 | + | 0.458792i | \(0.151718\pi\) |
−0.0469462 | + | 0.998897i | \(0.514949\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 471.239 | − | 816.210i | 0.0170819 | − | 0.0295866i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4130.97 | 0.148764 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36864.3 | 1.32322 | 0.661611 | − | 0.749847i | \(-0.269873\pi\) | ||||
0.661611 | + | 0.749847i | \(0.269873\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 47342.8 | − | 82000.2i | 1.68831 | − | 2.92423i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6089.22 | − | 10546.8i | −0.216446 | − | 0.374895i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17139.3 | + | 29686.2i | 0.605299 | + | 1.04841i | 0.992004 | + | 0.126205i | \(0.0402798\pi\) |
−0.386705 | + | 0.922203i | \(0.626387\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9078.89 | − | 15725.1i | 0.319601 | − | 0.553565i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 541.718 | 0.0189477 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 450.515 | 0.0157072 | 0.00785362 | − | 0.999969i | \(-0.497500\pi\) | ||||
0.00785362 | + | 0.999969i | \(0.497500\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3549.44 | + | 6147.80i | −0.122963 | + | 0.212978i | −0.920935 | − | 0.389716i | \(-0.872573\pi\) |
0.797972 | + | 0.602695i | \(0.205906\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18868.7 | + | 32681.5i | 0.651589 | + | 1.12858i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4916.68 | + | 8515.93i | 0.168712 | + | 0.292218i | 0.937967 | − | 0.346724i | \(-0.112706\pi\) |
−0.769255 | + | 0.638942i | \(0.779372\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12188.1 | − | 21110.5i | 0.416906 | − | 0.722102i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41260.1 | 1.40246 | 0.701231 | − | 0.712934i | \(-0.252634\pi\) | ||||
0.701231 | + | 0.712934i | \(0.252634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33584.5 | −1.13798 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3481.63 | − | 6030.35i | 0.117234 | − | 0.203056i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22688.7 | − | 39297.9i | −0.761595 | − | 1.31912i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1259.50 | − | 2181.52i | −0.0420153 | − | 0.0727726i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11321.4 | − | 19609.2i | 0.376496 | − | 0.652110i | −0.614054 | − | 0.789264i | \(-0.710462\pi\) |
0.990550 | + | 0.137154i | \(0.0437955\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3166.82 | 0.104663 | 0.0523316 | − | 0.998630i | \(-0.483335\pi\) | ||||
0.0523316 | + | 0.998630i | \(0.483335\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16430.5 | −0.541353 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10321.5 | + | 17877.4i | −0.337988 | + | 0.585413i | −0.984054 | − | 0.177869i | \(-0.943080\pi\) |
0.646066 | + | 0.763282i | \(0.276413\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 95.1032 | + | 164.724i | 0.00310471 | + | 0.00537752i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29644.7 | + | 51346.2i | 0.961872 | + | 1.66601i | 0.717793 | + | 0.696257i | \(0.245153\pi\) |
0.244080 | + | 0.969755i | \(0.421514\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35163.6 | − | 60905.1i | 1.13747 | − | 1.97015i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32327.9 | −1.03940 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14404.0 | −0.461712 | −0.230856 | − | 0.972988i | \(-0.574153\pi\) | ||||
−0.230856 | + | 0.972988i | \(0.574153\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25059.0 | + | 43403.4i | −0.798414 | + | 1.38289i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24447.4 | + | 42344.2i | 0.776588 | + | 1.34509i | 0.933898 | + | 0.357541i | \(0.116385\pi\) |
−0.157309 | + | 0.987549i | \(0.550282\pi\) | |||||||
\(998\) | 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 | 648.4.i.s.433.1 | 4 | ||
3.2 | odd | 2 | 648.4.i.m.433.2 | 4 | |||
9.2 | odd | 6 | 648.4.i.m.217.2 | 4 | |||
9.4 | even | 3 | 216.4.a.e.1.2 | ✓ | 2 | ||
9.5 | odd | 6 | 216.4.a.h.1.1 | yes | 2 | ||
9.7 | even | 3 | inner | 648.4.i.s.217.1 | 4 | ||
36.23 | even | 6 | 432.4.a.s.1.1 | 2 | |||
36.31 | odd | 6 | 432.4.a.o.1.2 | 2 | |||
72.5 | odd | 6 | 1728.4.a.bh.1.2 | 2 | |||
72.13 | even | 6 | 1728.4.a.bt.1.1 | 2 | |||
72.59 | even | 6 | 1728.4.a.bg.1.2 | 2 | |||
72.67 | odd | 6 | 1728.4.a.bs.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.4.a.e.1.2 | ✓ | 2 | 9.4 | even | 3 | ||
216.4.a.h.1.1 | yes | 2 | 9.5 | odd | 6 | ||
432.4.a.o.1.2 | 2 | 36.31 | odd | 6 | |||
432.4.a.s.1.1 | 2 | 36.23 | even | 6 | |||
648.4.i.m.217.2 | 4 | 9.2 | odd | 6 | |||
648.4.i.m.433.2 | 4 | 3.2 | odd | 2 | |||
648.4.i.s.217.1 | 4 | 9.7 | even | 3 | inner | ||
648.4.i.s.433.1 | 4 | 1.1 | even | 1 | trivial | ||
1728.4.a.bg.1.2 | 2 | 72.59 | even | 6 | |||
1728.4.a.bh.1.2 | 2 | 72.5 | odd | 6 | |||
1728.4.a.bs.1.1 | 2 | 72.67 | odd | 6 | |||
1728.4.a.bt.1.1 | 2 | 72.13 | even | 6 |