Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(223,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.223");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.p (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.17 | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.d.223.18 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.64166 | −0.146834 | −0.0734171 | − | 0.997301i | \(-0.523390\pi\) | ||||
−0.0734171 | + | 0.997301i | \(0.523390\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.2747 | − | 10.4729i | 0.824758 | − | 0.565486i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.3470 | 0.557714 | 0.278857 | − | 0.960333i | \(-0.410044\pi\) | ||||
0.278857 | + | 0.960333i | \(0.410044\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0999 | −0.279482 | −0.139741 | − | 0.990188i | \(-0.544627\pi\) | ||||
−0.139741 | + | 0.990188i | \(0.544627\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.92497i | 0.0847748i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.9396i | 0.341542i | 0.985311 | + | 0.170771i | \(0.0546258\pi\) | ||||
−0.985311 | + | 0.170771i | \(0.945374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 87.7589i | − | 1.05965i | −0.848108 | − | 0.529823i | \(-0.822258\pi\) | ||
0.848108 | − | 0.529823i | \(-0.177742\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −31.4188 | − | 45.8242i | −0.326483 | − | 0.476174i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 73.6175i | − | 0.667405i | −0.942678 | − | 0.333703i | \(-0.891702\pi\) | ||
0.942678 | − | 0.333703i | \(-0.108298\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −122.305 | −0.978440 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 58.9537i | 0.377498i | 0.982025 | + | 0.188749i | \(0.0604432\pi\) | ||||
−0.982025 | + | 0.188749i | \(0.939557\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −124.909 | −0.723686 | −0.361843 | − | 0.932239i | \(-0.617852\pi\) | ||||
−0.361843 | + | 0.932239i | \(0.617852\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 61.0410i | − | 0.321996i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −25.0759 | + | 17.1930i | −0.121103 | + | 0.0830327i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 56.5972i | − | 0.251474i | −0.992064 | − | 0.125737i | \(-0.959871\pi\) | ||
0.992064 | − | 0.125737i | \(-0.0401295\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.2998i | 0.161359i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 135.651i | 0.516711i | 0.966050 | + | 0.258356i | \(0.0831806\pi\) | ||||
−0.966050 | + | 0.258356i | \(0.916819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 259.929 | 0.921833 | 0.460917 | − | 0.887443i | \(-0.347521\pi\) | ||||
0.460917 | + | 0.887443i | \(0.347521\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.7749 | 0.0489448 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 217.682 | 0.675580 | 0.337790 | − | 0.941222i | \(-0.390321\pi\) | ||||
0.337790 | + | 0.941222i | \(0.390321\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 123.635 | − | 319.943i | 0.360452 | − | 0.932778i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 71.8188 | 0.197189 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 529.342i | − | 1.37190i | −0.727649 | − | 0.685950i | \(-0.759387\pi\) | ||
0.727649 | − | 0.685950i | \(-0.240613\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −33.4028 | −0.0818916 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −263.277 | −0.611787 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 685.329i | − | 1.51224i | −0.654433 | − | 0.756120i | \(-0.727092\pi\) | ||
0.654433 | − | 0.756120i | \(-0.272908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −149.916 | −0.314668 | −0.157334 | − | 0.987545i | \(-0.550290\pi\) | ||||
−0.157334 | + | 0.987545i | \(0.550290\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −137.473 | + | 94.2565i | −0.274919 | + | 0.188495i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 21.5056 | 0.0410376 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −409.156 | −0.746066 | −0.373033 | − | 0.927818i | \(-0.621682\pi\) | ||||
−0.373033 | + | 0.927818i | \(0.621682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −220.853 | −0.385326 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 885.869i | 1.48075i | 0.672194 | + | 0.740375i | \(0.265352\pi\) | ||||
−0.672194 | + | 0.740375i | \(0.734648\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 269.426i | − | 0.431971i | −0.976397 | − | 0.215986i | \(-0.930704\pi\) | ||
0.976397 | − | 0.215986i | \(-0.0692964\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 366.915i | 0.564902i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 310.795 | − | 213.093i | 0.459979 | − | 0.315379i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 902.587i | 1.28543i | 0.766105 | + | 0.642715i | \(0.222192\pi\) | ||||
−0.766105 | + | 0.642715i | \(0.777808\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 623.963i | − | 0.825166i | −0.910920 | − | 0.412583i | \(-0.864627\pi\) | ||
0.910920 | − | 0.412583i | \(-0.135373\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 39.3006i | − | 0.0501500i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 176.861 | 0.217948 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 986.131i | − | 1.17449i | −0.809409 | − | 0.587245i | \(-0.800212\pi\) | ||
0.809409 | − | 0.587245i | \(-0.199788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −200.098 | + | 137.195i | −0.230505 | + | 0.158043i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 374.726i | 0.417821i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 144.070i | 0.155592i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 179.437i | − | 0.187825i | −0.995580 | − | 0.0939127i | \(-0.970063\pi\) | ||
0.995580 | − | 0.0939127i | \(-0.0299375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −183.123 | −0.185905 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 266.959 | 0.263004 | 0.131502 | − | 0.991316i | \(-0.458020\pi\) | ||||
0.131502 | + | 0.991316i | \(0.458020\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −988.258 | −0.945398 | −0.472699 | − | 0.881224i | \(-0.656720\pi\) | ||||
−0.472699 | + | 0.881224i | \(0.656720\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 51.5789 | + | 75.2276i | 0.0479389 | + | 0.0699187i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1115.52 | −1.00787 | −0.503934 | − | 0.863742i | \(-0.668114\pi\) | ||||
−0.503934 | + | 0.863742i | \(0.668114\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 286.196i | 0.251492i | 0.992062 | + | 0.125746i | \(0.0401324\pi\) | ||||
−0.992062 | + | 0.125746i | \(0.959868\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −169.792 | −0.145188 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −728.322 | −0.606326 | −0.303163 | − | 0.952939i | \(-0.598043\pi\) | ||||
−0.303163 | + | 0.952939i | \(0.598043\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 120.855i | 0.0979979i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 117.899 | 0.0931607 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 250.718 | + | 365.671i | 0.193137 | + | 0.281689i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −916.999 | −0.688955 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 406.953 | 0.298323 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 405.990 | 0.290503 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 159.234i | − | 0.111258i | −0.998452 | − | 0.0556288i | \(-0.982284\pi\) | ||
0.998452 | − | 0.0556288i | \(-0.0177163\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 779.787i | − | 0.532221i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 748.323i | − | 0.499094i | −0.968363 | − | 0.249547i | \(-0.919718\pi\) | ||
0.968363 | − | 0.249547i | \(-0.0802817\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −919.093 | − | 1340.49i | −0.599214 | − | 0.873951i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 44.3247i | − | 0.0282583i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1189.48 | −0.741780 | −0.370890 | − | 0.928677i | \(-0.620947\pi\) | ||||
−0.370890 | + | 0.928677i | \(0.620947\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 546.158i | − | 0.333270i | −0.986019 | − | 0.166635i | \(-0.946710\pi\) | ||
0.986019 | − | 0.166635i | \(-0.0532901\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 653.047i | − | 0.390046i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −266.545 | −0.155871 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 96.7818i | − | 0.0554296i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −959.828 | − | 370.905i | −0.538539 | − | 0.208107i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2169.41i | − | 1.19279i | −0.802693 | − | 0.596393i | \(-0.796600\pi\) | ||
0.802693 | − | 0.596393i | \(-0.203400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1873.28i | 1.00957i | 0.863244 | + | 0.504786i | \(0.168429\pi\) | ||||
−0.863244 | + | 0.504786i | \(0.831571\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 215.457i | − | 0.113847i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 205.057 | 0.106262 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2457.07 | 1.24902 | 0.624508 | − | 0.781018i | \(-0.285299\pi\) | ||||
0.624508 | + | 0.781018i | \(0.285299\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1588.02 | −0.792066 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −770.992 | − | 1124.49i | −0.377408 | − | 0.550448i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1184.76 | −0.569308 | −0.284654 | − | 0.958630i | \(-0.591879\pi\) | ||||
−0.284654 | + | 0.958630i | \(0.591879\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 100.208i | 0.0472801i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2493.54 | −1.15543 | −0.577713 | − | 0.816240i | \(-0.696055\pi\) | ||||
−0.577713 | + | 0.816240i | \(0.696055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2025.39 | −0.921890 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 789.830i | 0.353215i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −336.961 | −0.148085 | −0.0740424 | − | 0.997255i | \(-0.523590\pi\) | ||||
−0.0740424 | + | 0.997255i | \(0.523590\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1868.18 | + | 1280.89i | −0.806976 | + | 0.553294i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2055.99 | −0.873092 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 403.536 | 0.168501 | 0.0842506 | − | 0.996445i | \(-0.473150\pi\) | ||||
0.0842506 | + | 0.996445i | \(0.473150\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 626.262 | 0.257180 | 0.128590 | − | 0.991698i | \(-0.458955\pi\) | ||||
0.128590 | + | 0.991698i | \(0.458955\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 449.747i | 0.181674i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 92.9132i | 0.0369249i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 487.100i | 0.190483i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 282.769 | + | 412.418i | 0.108828 | + | 0.158725i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 696.358i | 0.263805i | 0.991263 | + | 0.131902i | \(0.0421085\pi\) | ||||
−0.991263 | + | 0.131902i | \(0.957891\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3330.70 | −1.24222 | −0.621111 | − | 0.783723i | \(-0.713318\pi\) | ||||
−0.621111 | + | 0.783723i | \(0.713318\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 64.5168i | − | 0.0236930i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 841.118i | − | 0.304199i | −0.988365 | − | 0.152099i | \(-0.951397\pi\) | ||
0.988365 | − | 0.152099i | \(-0.0486034\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 719.574 | 0.256328 | 0.128164 | − | 0.991753i | \(-0.459092\pi\) | ||||
0.128164 | + | 0.991753i | \(0.459092\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1227.47i | 0.430741i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 617.419 | + | 900.503i | 0.213470 | + | 0.311344i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 222.693i | − | 0.0758709i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 662.558i | 0.222468i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1785.63i | − | 0.590979i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4957.51 | −1.61748 | −0.808742 | − | 0.588163i | \(-0.799851\pi\) | ||||
−0.808742 | + | 0.588163i | \(0.799851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2657.61 | 0.854912 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −426.715 | −0.135357 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1907.95 | + | 1308.16i | −0.596866 | + | 0.409234i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −808.277 | −0.249399 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 313.607i | − | 0.0954548i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3947.42 | −1.18538 | −0.592688 | − | 0.805432i | \(-0.701933\pi\) | ||||
−0.592688 | + | 0.805432i | \(0.701933\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1100.74 | 0.326147 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2044.37i | − | 0.597751i | −0.954292 | − | 0.298876i | \(-0.903388\pi\) | ||
0.954292 | − | 0.298876i | \(-0.0966115\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4391.90 | 1.26736 | 0.633679 | − | 0.773596i | \(-0.281544\pi\) | ||||
0.633679 | + | 0.773596i | \(0.281544\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −639.279 | − | 932.386i | −0.182084 | − | 0.265569i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1970.16 | −0.553946 | −0.276973 | − | 0.960878i | \(-0.589331\pi\) | ||||
−0.276973 | + | 0.960878i | \(0.589331\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −357.360 | −0.0991983 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2707.76 | 0.742144 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2964.89i | 0.802437i | 0.915982 | + | 0.401219i | \(0.131413\pi\) | ||||
−0.915982 | + | 0.401219i | \(0.868587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3658.31i | − | 0.977810i | −0.872337 | − | 0.488905i | \(-0.837396\pi\) | ||
0.872337 | − | 0.488905i | \(-0.162604\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −202.966 | + | 525.236i | −0.0529267 | + | 0.136964i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1149.64i | 0.296152i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1871.89 | −0.476410 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2719.35i | − | 0.683840i | −0.939729 | − | 0.341920i | \(-0.888923\pi\) | ||
0.939729 | − | 0.341920i | \(-0.111077\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1497.90i | − | 0.372221i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −117.902 | −0.0289541 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6798.11i | − | 1.65002i | −0.565120 | − | 0.825009i | \(-0.691170\pi\) | ||
0.565120 | − | 0.825009i | \(-0.308830\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −592.739 | − | 864.507i | −0.142205 | − | 0.207405i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 530.584i | − | 0.125833i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7965.94i | 1.86768i | 0.357686 | + | 0.933842i | \(0.383566\pi\) | ||||
−0.357686 | + | 0.933842i | \(0.616434\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 868.997i | 0.201442i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2958.39 | −0.678092 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5718.64 | −1.29618 | −0.648089 | − | 0.761565i | \(-0.724431\pi\) | ||||
−0.648089 | + | 0.761565i | \(0.724431\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1289.85 | 0.289124 | 0.144562 | − | 0.989496i | \(-0.453823\pi\) | ||||
0.144562 | + | 0.989496i | \(0.453823\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 411.584 | + | 600.294i | 0.0912462 | + | 0.133082i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2488.54 | −0.545690 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4121.16i | 0.893922i | 0.894553 | + | 0.446961i | \(0.147494\pi\) | ||||
−0.894553 | + | 0.446961i | \(0.852506\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1124.18 | 0.241229 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2432.92 | −0.516497 | −0.258248 | − | 0.966079i | \(-0.583145\pi\) | ||||
−0.258248 | + | 0.966079i | \(0.583145\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.386542i | 8.11927e-5i | 1.00000 | 4.05963e-5i | \(1.29222e-5\pi\) | |||||
−1.00000 | 4.05963e-5i | \(0.999987\pi\) | ||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 432.210 | 0.0898312 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1420.67 | + | 2072.04i | 0.292193 | + | 0.426162i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4339.89 | 0.883349 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −538.311 | −0.108441 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3394.41 | −0.676805 | −0.338402 | − | 0.941002i | \(-0.609886\pi\) | ||||
−0.338402 | + | 0.941002i | \(0.609886\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1125.07i | 0.222049i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 549.369i | 0.107332i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 964.385i | 0.186528i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3970.35 | − | 2722.22i | 0.760289 | − | 0.521283i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 800.877i | − | 0.151845i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 246.110 | 0.0462040 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1720.47i | 0.319844i | 0.987130 | + | 0.159922i | \(0.0511243\pi\) | ||||
−0.987130 | + | 0.159922i | \(0.948876\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2964.77i | 0.545826i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4721.33 | −0.860843 | −0.430422 | − | 0.902628i | \(-0.641635\pi\) | ||||
−0.430422 | + | 0.902628i | \(0.641635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 483.679i | − | 0.0873455i | −0.999046 | − | 0.0436728i | \(-0.986094\pi\) | ||
0.999046 | − | 0.0436728i | \(-0.0139059\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 225.683 | − | 154.737i | 0.0403676 | − | 0.0276776i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 6443.81i | − | 1.14170i | −0.821053 | − | 0.570852i | \(-0.806613\pi\) | ||
0.821053 | − | 0.570852i | \(-0.193387\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1199.53i | 0.210536i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3346.57i | 0.581893i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2100.91 | 0.361913 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1602.19 | 0.273456 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 858.588 | 0.145199 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3325.04 | − | 2279.78i | 0.557190 | − | 0.382031i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2784.85 | −0.462444 | −0.231222 | − | 0.972901i | \(-0.574272\pi\) | ||||
−0.231222 | + | 0.972901i | \(0.574272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 509.375i | 0.0838245i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 671.694 | 0.109548 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4181.48 | −0.675904 | −0.337952 | − | 0.941163i | \(-0.609734\pi\) | ||||
−0.337952 | + | 0.941163i | \(0.609734\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2184.97i | 0.350062i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2541.52 | −0.403610 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1462.25 | − | 6181.86i | −0.230187 | − | 0.973146i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 362.564 | 0.0565791 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9524.25 | 1.47345 | 0.736727 | − | 0.676190i | \(-0.236370\pi\) | ||||
0.736727 | + | 0.676190i | \(0.236370\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1248.33 | −0.191465 | −0.0957327 | − | 0.995407i | \(-0.530519\pi\) | ||||
−0.0957327 | + | 0.995407i | \(0.530519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 353.698i | − | 0.0537864i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 605.680i | − | 0.0913233i | −0.998957 | − | 0.0456616i | \(-0.985460\pi\) | ||
0.998957 | − | 0.0456616i | \(-0.0145396\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1454.29i | − | 0.217425i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1097.01 | − | 752.154i | 0.162633 | − | 0.111508i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 83.1817i | − | 0.0122289i | −0.999981 | − | 0.00611443i | \(-0.998054\pi\) | ||
0.999981 | − | 0.00611443i | \(-0.00194630\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −842.618 | −0.122849 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2751.00i | 0.397768i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 442.305i | 0.0634282i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4636.32 | −0.659439 | −0.329719 | − | 0.944079i | \(-0.606954\pi\) | ||||
−0.329719 | + | 0.944079i | \(0.606954\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1220.86i | − | 0.172237i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5543.76 | − | 8085.55i | −0.775789 | − | 1.13148i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2555.59i | − | 0.354754i | −0.984143 | − | 0.177377i | \(-0.943239\pi\) | ||
0.984143 | − | 0.177377i | \(-0.0567612\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1217.97i | − | 0.167722i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 772.290i | − | 0.105504i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8981.28 | 1.21725 | 0.608624 | − | 0.793459i | \(-0.291722\pi\) | ||||
0.608624 | + | 0.793459i | \(0.291722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −477.701 | −0.0642346 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12164.5 | 1.62291 | 0.811456 | − | 0.584413i | \(-0.198675\pi\) | ||||
0.811456 | + | 0.584413i | \(0.198675\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −510.219 | + | 349.826i | −0.0675407 | + | 0.0463085i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2339.36 | −0.307278 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3569.55i | − | 0.465252i | −0.972566 | − | 0.232626i | \(-0.925268\pi\) | ||
0.972566 | − | 0.232626i | \(-0.0747319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1762.38 | 0.227947 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2244.97 | −0.288152 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1481.74i | − | 0.188745i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 984.957 | 0.124518 | 0.0622589 | − | 0.998060i | \(-0.480170\pi\) | ||||
0.0622589 | + | 0.998060i | \(0.480170\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4021.48 | + | 2757.28i | −0.504576 | + | 0.345957i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1700.17 | 0.211727 | 0.105863 | − | 0.994381i | \(-0.466239\pi\) | ||||
0.105863 | + | 0.994381i | \(0.466239\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1636.30 | 0.202257 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −132.974 | −0.0163149 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1151.58i | − | 0.140250i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2739.61i | 0.331210i | 0.986192 | + | 0.165605i | \(0.0529577\pi\) | ||||
−0.986192 | + | 0.165605i | \(0.947042\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3568.43i | 0.428267i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7177.41 | − | 10468.2i | −0.855150 | − | 1.24723i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1024.33i | 0.121163i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1638.47 | −0.192413 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 13461.7i | − | 1.56957i | −0.619770 | − | 0.784783i | \(-0.712774\pi\) | ||
0.619770 | − | 0.784783i | \(-0.287226\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5618.17i | 0.650387i | 0.945647 | + | 0.325194i | \(0.105429\pi\) | ||||
−0.945647 | + | 0.325194i | \(0.894571\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1959.14 | −0.225193 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2927.93i | − | 0.334178i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2289.92 | + | 1570.06i | −0.259525 | + | 0.177940i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 799.634i | 0.0899923i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 7137.27i | − | 0.797657i | −0.917026 | − | 0.398828i | \(-0.869417\pi\) | ||
0.917026 | − | 0.398828i | \(-0.130583\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1458.21i | 0.161841i | 0.996721 | + | 0.0809203i | \(0.0257859\pi\) | ||||
−0.996721 | + | 0.0809203i | \(0.974214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −290.346 | −0.0320023 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6460.59 | −0.707213 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3231.27 | 0.351299 | 0.175650 | − | 0.984453i | \(-0.443797\pi\) | ||||
0.175650 | + | 0.984453i | \(0.443797\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1112.72 | + | 2879.48i | −0.120151 | + | 0.310926i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17504.9 | 1.87739 | 0.938694 | − | 0.344751i | \(-0.112037\pi\) | ||||
0.938694 | + | 0.344751i | \(0.112037\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1618.89i | 0.172455i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6508.23 | −0.688655 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9069.04 | 0.953217 | 0.476608 | − | 0.879116i | \(-0.341866\pi\) | ||||
0.476608 | + | 0.879116i | \(0.341866\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2760.10i | 0.288177i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5619.84 | 0.582877 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 328.492 | − | 225.227i | 0.0338461 | − | 0.0232062i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1722.16 | −0.176279 | −0.0881394 | − | 0.996108i | \(-0.528092\pi\) | ||||
−0.0881394 | + | 0.996108i | \(0.528092\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −646.370 | −0.0657297 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14064.0 | −1.42088 | −0.710442 | − | 0.703755i | \(-0.751505\pi\) | ||||
−0.710442 | + | 0.703755i | \(0.751505\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7092.58i | − | 0.711923i | −0.934501 | − | 0.355961i | \(-0.884153\pi\) | ||
0.934501 | − | 0.355961i | \(-0.115847\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 615.172i | − | 0.0613504i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 8397.55i | − | 0.832103i | −0.909341 | − | 0.416052i | \(-0.863414\pi\) | ||
0.909341 | − | 0.416052i | \(-0.136586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6249.76 | + | 4285.07i | −0.615324 | + | 0.421889i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7371.21i | − | 0.721120i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5288.78 | 0.514119 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10733.3i | 1.03680i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4764.07i | 0.457300i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20229.8 | 1.92970 | 0.964849 | − | 0.262807i | \(-0.0846482\pi\) | ||||
0.964849 | + | 0.262807i | \(0.0846482\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 741.419i | 0.0702824i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3373.46 | + | 2312.98i | −0.317801 | + | 0.217897i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 294.574i | 0.0275792i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1879.06i | − | 0.174843i | −0.996171 | − | 0.0874213i | \(-0.972137\pi\) | ||
0.996171 | − | 0.0874213i | \(-0.0278626\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3554.27i | 0.328690i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9249.10 | 0.850114 | 0.425057 | − | 0.905167i | \(-0.360254\pi\) | ||||
0.425057 | + | 0.905167i | \(0.360254\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1411.33 | −0.128931 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 300.625 | 0.0272972 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9277.65 | + | 13531.4i | 0.837343 | + | 1.22126i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18142.9 | −1.62763 | −0.813813 | − | 0.581126i | \(-0.802612\pi\) | ||||
−0.813813 | + | 0.581126i | \(0.802612\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7480.63i | 0.667086i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7981.16 | 0.707480 | 0.353740 | − | 0.935344i | \(-0.384910\pi\) | ||||
0.353740 | + | 0.935344i | \(0.384910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −438.255 | −0.0386180 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6076.18i | 0.532253i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9093.08 | 0.791834 | 0.395917 | − | 0.918286i | \(-0.370427\pi\) | ||||
0.395917 | + | 0.918286i | \(0.370427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2821.68 | − | 4115.41i | −0.244274 | − | 0.356272i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2369.49 | 0.203929 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1622.38 | 0.138817 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4429.19 | 0.376780 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1010.88i | 0.0854968i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 10886.0i | − | 0.915399i | −0.889107 | − | 0.457699i | \(-0.848674\pi\) | ||
0.889107 | − | 0.457699i | \(-0.151326\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16709.0i | 1.39701i | 0.715607 | + | 0.698503i | \(0.246150\pi\) | ||||
−0.715607 | + | 0.698503i | \(0.753850\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3842.68 | + | 5604.53i | 0.319444 | + | 0.465908i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2990.27i | − | 0.247169i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6747.46 | 0.554570 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6167.96i | 0.504080i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1777.02i | − | 0.144411i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1831.31 | 0.147990 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1210.61i | − | 0.0972842i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2515.60 | − | 6509.88i | 0.201029 | − | 0.520223i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9846.26i | 0.782484i | 0.920288 | + | 0.391242i | \(0.127954\pi\) | ||||
−0.920288 | + | 0.391242i | \(0.872046\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1878.78i | − | 0.148483i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 469.836i | − | 0.0369276i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3956.47 | −0.309262 | −0.154631 | − | 0.987972i | \(-0.549419\pi\) | ||||
−0.154631 | + | 0.987972i | \(0.549419\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1349.24 | 0.104889 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5173.71 | 0.400014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9452.74 | + | 13786.8i | 0.726892 | + | 1.06017i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 278.740 | 0.0213186 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10754.5i | 0.818106i | 0.912511 | + | 0.409053i | \(0.134141\pi\) | ||||
−0.912511 | + | 0.409053i | \(0.865859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3405.05 | −0.257636 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1461.30 | 0.109975 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 9499.10i | − | 0.711082i | −0.934661 | − | 0.355541i | \(-0.884297\pi\) | ||
0.934661 | − | 0.355541i | \(-0.115703\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1195.66 | 0.0890294 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1237.25 | − | 848.308i | 0.0916398 | − | 0.0628317i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21157.1 | 1.55879 | 0.779395 | − | 0.626533i | \(-0.215526\pi\) | ||||
0.779395 | + | 0.626533i | \(0.215526\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21995.3 | 1.61204 | 0.806021 | − | 0.591887i | \(-0.201617\pi\) | ||||
0.806021 | + | 0.591887i | \(0.201617\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2089.07 | 0.152308 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9003.79i | 0.653016i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7582.38i | 0.547068i | 0.961862 | + | 0.273534i | \(0.0881927\pi\) | ||||
−0.961862 | + | 0.273534i | \(0.911807\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9992.09i | 0.717197i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6534.72 | − | 9530.86i | −0.466620 | − | 0.680563i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 10770.5i | − | 0.765128i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −193.550 | −0.0136792 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 2177.57i | − | 0.153114i | −0.997065 | − | 0.0765569i | \(-0.975607\pi\) | ||
0.997065 | − | 0.0765569i | \(-0.0243927\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10961.9i | 0.766851i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2523.35 | −0.175629 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 181.962i | 0.0126008i | 0.999980 | + | 0.00630042i | \(0.00200550\pi\) | ||||
−0.999980 | + | 0.00630042i | \(0.997995\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −411.593 | − | 600.307i | −0.0283591 | − | 0.0413616i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 2158.72i | − | 0.147991i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 255.073i | − | 0.0173990i | −0.999962 | − | 0.00869949i | \(-0.997231\pi\) | ||
0.999962 | − | 0.00869949i | \(-0.00276917\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21122.3i | 1.43361i | 0.697275 | + | 0.716804i | \(0.254396\pi\) | ||||
−0.697275 | + | 0.716804i | \(0.745604\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3682.41 | 0.248689 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1505.40 | 0.101162 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20997.8 | 1.40408 | 0.702038 | − | 0.712139i | \(-0.252273\pi\) | ||||
0.702038 | + | 0.712139i | \(0.252273\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2701.51 | − | 1852.26i | 0.179755 | − | 0.123247i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2851.63 | −0.188813 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13781.4i | 0.908032i | 0.890993 | + | 0.454016i | \(0.150009\pi\) | ||||
−0.890993 | + | 0.454016i | \(0.849991\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −668.078 | −0.0438041 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15885.1 | 1.03648 | 0.518242 | − | 0.855234i | \(-0.326586\pi\) | ||||
0.518242 | + | 0.855234i | \(0.326586\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26764.3i | 1.73788i | 0.494917 | + | 0.868940i | \(0.335198\pi\) | ||||
−0.494917 | + | 0.868940i | \(0.664802\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1987.67 | 0.128442 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10327.7 | − | 15062.9i | −0.664157 | − | 0.968671i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14621.6 | 0.935784 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5356.89 | −0.341202 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1354.91 | 0.0858887 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12538.1i | − | 0.791022i | −0.918461 | − | 0.395511i | \(-0.870568\pi\) | ||
0.918461 | − | 0.395511i | \(-0.129432\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14872.5i | 0.933855i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 261.407i | 0.0163364i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1619.61 | + | 4191.23i | −0.100740 | + | 0.260695i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 7972.82i | − | 0.493584i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10139.1 | −0.624761 | −0.312380 | − | 0.949957i | \(-0.601126\pi\) | ||||
−0.312380 | + | 0.949957i | \(0.601126\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 14901.0i | − | 0.913902i | −0.889492 | − | 0.456951i | \(-0.848941\pi\) | ||
0.889492 | − | 0.456951i | \(-0.151059\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1280.14i | 0.0781482i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23608.6 | 1.43454 | 0.717271 | − | 0.696794i | \(-0.245391\pi\) | ||||
0.717271 | + | 0.696794i | \(0.245391\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 13944.4i | − | 0.843398i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3924.49 | + | 5723.85i | 0.236272 | + | 0.344601i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1066.91i | − | 0.0639380i | −0.999489 | − | 0.0319690i | \(-0.989822\pi\) | ||
0.999489 | − | 0.0319690i | \(-0.0101778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1228.49i | 0.0732841i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2424.83i | 0.143990i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1256.55 | 0.0742766 | 0.0371383 | − | 0.999310i | \(-0.488176\pi\) | ||||
0.0371383 | + | 0.999310i | \(0.488176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11557.5 | 0.680080 | 0.340040 | − | 0.940411i | \(-0.389559\pi\) | ||||
0.340040 | + | 0.940411i | \(0.389559\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −940.822 | −0.0551109 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1508.84 | + | 2200.63i | 0.0879852 | + | 0.128326i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4340.03 | 0.251944 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11842.3i | 0.684377i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3050.34 | −0.175495 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4626.18 | 0.264972 | 0.132486 | − | 0.991185i | \(-0.457704\pi\) | ||||
0.132486 | + | 0.991185i | \(0.457704\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 3302.23i | − | 0.188301i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33749.5 | −1.91595 | −0.957975 | − | 0.286850i | \(-0.907392\pi\) | ||||
−0.957975 | + | 0.286850i | \(0.907392\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1879.23 | − | 2740.85i | −0.106213 | − | 0.154911i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6133.11 | −0.345112 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22799.7 | 1.27732 | 0.638658 | − | 0.769491i | \(-0.279490\pi\) | ||||
0.638658 | + | 0.769491i | \(0.279490\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1952.71 | 0.108919 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 13175.7i | − | 0.731709i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6934.34i | 0.383421i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22334.8i | 1.22960i | 0.788682 | + | 0.614802i | \(0.210764\pi\) | ||||
−0.788682 | + | 0.614802i | \(0.789236\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2797.16 | + | 1917.84i | −0.153326 | + | 0.105126i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 896.603i | 0.0489354i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3247.44 | −0.176478 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5910.48i | 0.319821i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8429.88i | − | 0.454197i | −0.973872 | − | 0.227099i | \(-0.927076\pi\) | ||
0.973872 | − | 0.227099i | \(-0.0729240\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4966.91 | −0.266473 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1072.08i | 0.0572722i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4077.73 | − | 2795.85i | 0.216915 | − | 0.148725i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6186.00i | 0.327673i | 0.986488 | + | 0.163837i | \(0.0523870\pi\) | ||||
−0.986488 | + | 0.163837i | \(0.947613\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8123.29i | − | 0.428477i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9195.48i | 0.482992i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 437.575 | 0.0228872 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8894.66 | 0.463287 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17866.0 | 0.926688 | 0.463344 | − | 0.886178i | \(-0.346649\pi\) | ||||
0.463344 | + | 0.886178i | \(0.346649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15095.4 | + | 10350.0i | −0.779725 | + | 0.534609i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10974.9 | −0.564539 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 7210.34i | − | 0.369359i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27651.7 | −1.41065 | −0.705326 | − | 0.708883i | \(-0.749199\pi\) | ||||
−0.705326 | + | 0.708883i | \(0.749199\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6222.60i | 0.314844i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26895.7 | 1.35527 | 0.677636 | − | 0.735397i | \(-0.263004\pi\) | ||||
0.677636 | + | 0.735397i | \(0.263004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1575.71 | + | 608.899i | 0.0790761 | + | 0.0305573i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8325.11 | −0.416091 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22507.8 | −1.12038 | −0.560191 | − | 0.828364i | \(-0.689272\pi\) | ||||
−0.560191 | + | 0.828364i | \(0.689272\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3448.91 | 0.170983 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 19387.3i | − | 0.957268i | −0.878014 | − | 0.478634i | \(-0.841132\pi\) | ||
0.878014 | − | 0.478634i | \(-0.158868\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3561.43i | 0.175142i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5615.66i | 0.275055i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17039.3 | + | 11682.8i | −0.831247 | + | 0.569935i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 34865.6i | − | 1.69409i | −0.531518 | − | 0.847047i | \(-0.678378\pi\) | ||
0.531518 | − | 0.847047i | \(-0.321622\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8158.04 | −0.394815 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3075.29i | − | 0.148240i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 19477.5i | − | 0.935165i | −0.883949 | − | 0.467583i | \(-0.845125\pi\) | ||
0.883949 | − | 0.467583i | \(-0.154875\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4493.69 | −0.214902 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 33587.3i | − | 1.59992i | −0.600053 | − | 0.799960i | \(-0.704854\pi\) | ||
0.600053 | − | 0.799960i | \(-0.295146\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2997.31 | + | 4371.57i | 0.142215 | + | 0.207420i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 353.706i | 0.0167167i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8977.76i | 0.422644i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30658.2i | 1.43766i | 0.695185 | + | 0.718831i | \(0.255323\pi\) | ||||
−0.695185 | + | 0.718831i | \(0.744677\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20394.3 | −0.952638 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12029.2 | −0.559714 | −0.279857 | − | 0.960042i | \(-0.590287\pi\) | ||||
−0.279857 | + | 0.960042i | \(0.590287\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15277.0 | 0.708084 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2593.52 | + | 1778.22i | −0.119745 | + | 0.0821019i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11904.6 | 0.547530 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18024.8i | 0.825836i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1591.75 | −0.0726495 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4033.67 | −0.183398 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 33352.6i | − | 1.51066i | −0.655342 | − | 0.755332i | \(-0.727476\pi\) | ||
0.655342 | − | 0.755332i | \(-0.272524\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23897.8 | 1.07831 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11124.9 | + | 7627.68i | −0.500072 | + | 0.342868i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1963.89 | 0.0879440 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2606.99 | 0.116302 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44570.0 | −1.98087 | −0.990434 | − | 0.137989i | \(-0.955936\pi\) | ||||
−0.990434 | + | 0.137989i | \(0.955936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5211.23i | 0.230739i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8875.18i | 0.391497i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 5482.01i | − | 0.240916i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1265.70 | + | 1846.02i | 0.0554164 | + | 0.0808246i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17155.9i | 0.748349i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33277.9 | 1.44621 | 0.723107 | − | 0.690736i | \(-0.242713\pi\) | ||||
0.723107 | + | 0.690736i | \(0.242713\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5936.77i | − | 0.257051i | −0.991706 | − | 0.128525i | \(-0.958976\pi\) | ||
0.991706 | − | 0.128525i | \(-0.0410244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 3869.54i | − | 0.166926i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1944.96 | 0.0835939 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 22811.1i | − | 0.976816i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1800.88 | − | 1234.75i | 0.0768351 | − | 0.0526810i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 12777.3i | − | 0.543154i | −0.962417 | − | 0.271577i | \(-0.912455\pi\) | ||
0.962417 | − | 0.271577i | \(-0.0875452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 10978.0i | − | 0.464968i | −0.972600 | − | 0.232484i | \(-0.925315\pi\) | ||
0.972600 | − | 0.232484i | \(-0.0746854\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7465.62i | 0.315054i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40213.5 | 1.69088 | 0.845442 | − | 0.534067i | \(-0.179337\pi\) | ||||
0.845442 | + | 0.534067i | \(0.179337\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1332.10 | 0.0558090 | 0.0279045 | − | 0.999611i | \(-0.491117\pi\) | ||||
0.0279045 | + | 0.999611i | \(0.491117\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12363.5 | 0.516106 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7659.31 | + | 2959.78i | 0.318583 | + | 0.123109i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4093.55 | 0.169656 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 3372.54i | − | 0.139274i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −728.570 | −0.0299798 | −0.0149899 | − | 0.999888i | \(-0.504772\pi\) | ||||
−0.0149899 | + | 0.999888i | \(0.504772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20913.5 | 0.857495 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7298.75i | 0.298200i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3325.00 | 0.135365 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14006.9 | + | 9603.68i | −0.568221 | + | 0.389594i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.15963 | 4.68766e−5 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4166.55 | −0.167835 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22239.8 | −0.892703 | −0.446352 | − | 0.894858i | \(-0.647277\pi\) | ||||
−0.446352 | + | 0.894858i | \(0.647277\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1296.63i | − | 0.0518641i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 40668.9i | − | 1.62103i | −0.585716 | − | 0.810516i | \(-0.699187\pi\) | ||
0.585716 | − | 0.810516i | \(-0.300813\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31416.1i | 1.24785i | 0.781485 | + | 0.623925i | \(0.214463\pi\) | ||||
−0.781485 | + | 0.623925i | \(0.785537\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6216.11 | − | 4262.00i | 0.246045 | − | 0.168698i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 7916.87i | − | 0.312275i | −0.987735 | − | 0.156138i | \(-0.950096\pi\) | ||
0.987735 | − | 0.156138i | \(-0.0499043\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 553.175 | 0.0217439 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 13019.7i | − | 0.510002i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18365.0i | 0.716903i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5359.92 | 0.208512 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1614.93i | 0.0626085i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6201.39 | − | 4251.91i | 0.239595 | − | 0.164275i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 13698.3i | − | 0.527432i | −0.964600 | − | 0.263716i | \(-0.915052\pi\) | ||
0.964600 | − | 0.263716i | \(-0.0849483\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10183.2i | 0.390753i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28771.4i | 1.10026i | 0.835078 | + | 0.550132i | \(0.185423\pi\) | ||||
−0.835078 | + | 0.550132i | \(0.814577\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12122.7 | −0.462019 | −0.231009 | − | 0.972952i | \(-0.574203\pi\) | ||||
−0.231009 | + | 0.972952i | \(0.574203\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3375.22 | 0.128200 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40858.2 | 1.54666 | 0.773328 | − | 0.634006i | \(-0.218591\pi\) | ||||
0.773328 | + | 0.634006i | \(0.218591\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1667.65 | − | 2432.25i | −0.0629146 | − | 0.0917606i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1648.11 | 0.0619682 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 19103.6i | − | 0.715875i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −662.468 | −0.0247418 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2893.15 | 0.107692 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 7363.84i | − | 0.273190i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12672.2 | 0.468561 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8166.67 | − | 11911.0i | −0.300963 | − | 0.438953i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1028.11 | −0.0377629 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12054.9 | 0.441318 | 0.220659 | − | 0.975351i | \(-0.429179\pi\) | ||||
0.220659 | + | 0.975351i | \(0.429179\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2402.63 | −0.0876680 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41363.5i | 1.50432i | 0.658981 | + | 0.752160i | \(0.270988\pi\) | ||||
−0.658981 | + | 0.752160i | \(0.729012\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12695.8i | − | 0.460207i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 738.331i | − | 0.0266759i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7837.15 | − | 11430.4i | −0.282230 | − | 0.411632i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43591.9i | 1.56470i | 0.622836 | + | 0.782352i | \(0.285980\pi\) | ||||
−0.622836 | + | 0.782352i | \(0.714020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5161.40 | 0.184662 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 11604.8i | − | 0.413843i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6922.12i | 0.246052i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8894.32 | 0.315133 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 23421.9i | − | 0.827179i | −0.910464 | − | 0.413589i | \(-0.864275\pi\) | ||
0.910464 | − | 0.413589i | \(-0.135725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28077.8 | − | 10850.1i | −0.988414 | − | 0.381951i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14164.0i | 0.497008i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 799.651i | − | 0.0279694i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 12461.9i | − | 0.434486i | −0.976118 | − | 0.217243i | \(-0.930294\pi\) | ||
0.976118 | − | 0.217243i | \(-0.0697064\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1451.04 | −0.0504290 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4981.43 | 0.172572 | 0.0862858 | − | 0.996270i | \(-0.472500\pi\) | ||||
0.0862858 | + | 0.996270i | \(0.472500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9986.30 | 0.344856 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −464.210 | − | 677.049i | −0.0159796 | − | 0.0233062i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9015.91 | −0.309374 | −0.154687 | − | 0.987963i | \(-0.549437\pi\) | ||||
−0.154687 | + | 0.987963i | \(0.549437\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3529.46i | 0.120728i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19331.4 | −0.659163 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25785.1 | −0.876455 | −0.438227 | − | 0.898864i | \(-0.644394\pi\) | ||||
−0.438227 | + | 0.898864i | \(0.644394\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1143.18i | − | 0.0387356i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3598.60 | 0.121553 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18168.9 | + | 12457.3i | −0.611789 | + | 0.419466i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14188.8 | −0.476278 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10039.7 | 0.335956 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5467.86 | 0.182401 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11328.2i | 0.376721i | 0.982100 | + | 0.188361i | \(0.0603174\pi\) | ||||
−0.982100 | + | 0.188361i | \(0.939683\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 6302.74i | − | 0.208951i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21613.7i | 0.714331i | 0.934041 | + | 0.357166i | \(0.116257\pi\) | ||||
−0.934041 | + | 0.357166i | \(0.883743\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5719.88 | − | 8342.41i | −0.188459 | − | 0.274867i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 4806.56i | − | 0.157880i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −289.064 | −0.00946570 | −0.00473285 | − | 0.999989i | \(-0.501507\pi\) | ||||
−0.00473285 | + | 0.999989i | \(0.501507\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 20064.8i | − | 0.655030i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2575.76i | − | 0.0838306i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6611.03 | 0.214506 | 0.107253 | − | 0.994232i | \(-0.465795\pi\) | ||||
0.107253 | + | 0.994232i | \(0.465795\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1380.83i | 0.0446668i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6839.33 | − | 9975.13i | −0.220566 | − | 0.321694i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 19135.3i | − | 0.615236i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6406.80i | 0.205367i | 0.994714 | + | 0.102684i | \(0.0327429\pi\) | ||||
−0.994714 | + | 0.102684i | \(0.967257\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8354.54i | 0.266992i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1181.29 | −0.0376377 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21635.3 | 0.687257 | 0.343629 | − | 0.939106i | \(-0.388344\pi\) | ||||
0.343629 | + | 0.939106i | \(0.388344\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1528.12 | 0.0483961 |
(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 | 1344.4.p.d.223.17 | yes | 32 | |
4.3 | odd | 2 | inner | 1344.4.p.d.223.20 | yes | 32 | |
7.6 | odd | 2 | 1344.4.p.c.223.24 | yes | 32 | ||
8.3 | odd | 2 | 1344.4.p.c.223.23 | yes | 32 | ||
8.5 | even | 2 | 1344.4.p.c.223.16 | yes | 32 | ||
28.27 | even | 2 | 1344.4.p.c.223.15 | ✓ | 32 | ||
56.13 | odd | 2 | inner | 1344.4.p.d.223.19 | yes | 32 | |
56.27 | even | 2 | inner | 1344.4.p.d.223.18 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.c.223.15 | ✓ | 32 | 28.27 | even | 2 | ||
1344.4.p.c.223.16 | yes | 32 | 8.5 | even | 2 | ||
1344.4.p.c.223.23 | yes | 32 | 8.3 | odd | 2 | ||
1344.4.p.c.223.24 | yes | 32 | 7.6 | odd | 2 | ||
1344.4.p.d.223.17 | yes | 32 | 1.1 | even | 1 | trivial | |
1344.4.p.d.223.18 | yes | 32 | 56.27 | even | 2 | inner | |
1344.4.p.d.223.19 | yes | 32 | 56.13 | odd | 2 | inner | |
1344.4.p.d.223.20 | yes | 32 | 4.3 | odd | 2 | inner |