Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,3,Mod(379,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.379");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.g (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: | \(13.7330053238\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.5 | ||
Character | \(\chi\) | \(=\) | 504.379 |
Dual form | 504.3.g.d.379.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.81394 | − | 0.842398i | −0.906968 | − | 0.421199i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.58073 | + | 3.05611i | 0.645183 | + | 0.764028i | ||||
\(5\) | 5.94177i | 1.18835i | 0.804334 | + | 0.594177i | \(0.202522\pi\) | ||||
−0.804334 | + | 0.594177i | \(0.797478\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | −2.10682 | − | 7.71760i | −0.263353 | − | 0.964700i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.00533 | − | 10.7780i | 0.500533 | − | 1.07780i | ||||
\(11\) | −15.0849 | −1.37136 | −0.685678 | − | 0.727905i | \(-0.740494\pi\) | ||||
−0.685678 | + | 0.727905i | \(0.740494\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.2148i | 0.862677i | 0.902190 | + | 0.431338i | \(0.141958\pi\) | ||||
−0.902190 | + | 0.431338i | \(0.858042\pi\) | |||||||
\(14\) | −2.22877 | + | 4.79923i | −0.159198 | + | 0.342802i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.67964 | + | 15.7740i | −0.167477 | + | 0.985876i | ||||
\(17\) | 22.8244 | 1.34261 | 0.671307 | − | 0.741180i | \(-0.265733\pi\) | ||||
0.671307 | + | 0.741180i | \(0.265733\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −33.0704 | −1.74055 | −0.870274 | − | 0.492567i | \(-0.836059\pi\) | ||||
−0.870274 | + | 0.492567i | \(0.836059\pi\) | |||||||
\(20\) | −18.1587 | + | 15.3341i | −0.907935 | + | 0.766706i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 27.3631 | + | 12.7075i | 1.24378 | + | 0.577613i | ||||
\(23\) | 1.69029i | 0.0734908i | 0.999325 | + | 0.0367454i | \(0.0116991\pi\) | ||||
−0.999325 | + | 0.0367454i | \(0.988301\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.3046 | −0.412185 | ||||||||
\(26\) | 9.44732 | − | 20.3429i | 0.363358 | − | 0.782420i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.08571 | − | 6.82798i | 0.288775 | − | 0.243856i | ||||
\(29\) | − | 28.9719i | − | 0.999030i | −0.866305 | − | 0.499515i | \(-0.833512\pi\) | ||
0.866305 | − | 0.499515i | \(-0.166488\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 24.7233i | − | 0.797527i | −0.917054 | − | 0.398764i | \(-0.869439\pi\) | ||
0.917054 | − | 0.398764i | \(-0.130561\pi\) | |||||||
\(32\) | 18.1487 | − | 26.3557i | 0.567146 | − | 0.823617i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −41.4021 | − | 19.2272i | −1.21771 | − | 0.565507i | ||||
\(35\) | 15.7204 | 0.449156 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 53.7870i | − | 1.45370i | −0.686795 | − | 0.726851i | \(-0.740983\pi\) | ||
0.686795 | − | 0.726851i | \(-0.259017\pi\) | |||||||
\(38\) | 59.9877 | + | 27.8584i | 1.57862 | + | 0.733117i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 45.8562 | − | 12.5183i | 1.14640 | − | 0.312957i | ||||
\(41\) | −30.8925 | −0.753476 | −0.376738 | − | 0.926320i | \(-0.622954\pi\) | ||||
−0.376738 | + | 0.926320i | \(0.622954\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −44.2731 | −1.02961 | −0.514803 | − | 0.857308i | \(-0.672135\pi\) | ||||
−0.514803 | + | 0.857308i | \(0.672135\pi\) | |||||||
\(44\) | −38.9301 | − | 46.1012i | −0.884775 | − | 1.04775i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.42389 | − | 3.06608i | 0.0309542 | − | 0.0666538i | ||||
\(47\) | 37.2829i | 0.793253i | 0.917980 | + | 0.396627i | \(0.129819\pi\) | ||||
−0.917980 | + | 0.396627i | \(0.870181\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 18.6919 | + | 8.68058i | 0.373838 | + | 0.173612i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −34.2737 | + | 28.9424i | −0.659109 | + | 0.556584i | ||||
\(53\) | − | 72.2354i | − | 1.36293i | −0.731850 | − | 0.681466i | \(-0.761343\pi\) | ||
0.731850 | − | 0.681466i | \(-0.238657\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 89.6310i | − | 1.62966i | ||||||
\(56\) | −20.4188 | + | 5.57413i | −0.364622 | + | 0.0995381i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −24.4058 | + | 52.5532i | −0.420790 | + | 0.906089i | ||||
\(59\) | −33.2212 | −0.563072 | −0.281536 | − | 0.959551i | \(-0.590844\pi\) | ||||
−0.281536 | + | 0.959551i | \(0.590844\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 96.8692i | 1.58802i | 0.607905 | + | 0.794010i | \(0.292010\pi\) | ||||
−0.607905 | + | 0.794010i | \(0.707990\pi\) | |||||||
\(62\) | −20.8269 | + | 44.8466i | −0.335917 | + | 0.723332i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −55.1226 | + | 32.5192i | −0.861290 | + | 0.508113i | ||||
\(65\) | −66.6357 | −1.02517 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −86.0604 | −1.28448 | −0.642242 | − | 0.766502i | \(-0.721995\pi\) | ||||
−0.642242 | + | 0.766502i | \(0.721995\pi\) | |||||||
\(68\) | 58.9038 | + | 69.7540i | 0.866232 | + | 1.02579i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −28.5159 | − | 13.2429i | −0.407370 | − | 0.189184i | ||||
\(71\) | 40.4798i | 0.570137i | 0.958507 | + | 0.285069i | \(0.0920164\pi\) | ||||
−0.958507 | + | 0.285069i | \(0.907984\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28.5905 | 0.391651 | 0.195826 | − | 0.980639i | \(-0.437261\pi\) | ||||
0.195826 | + | 0.980639i | \(0.437261\pi\) | |||||||
\(74\) | −45.3100 | + | 97.5662i | −0.612297 | + | 1.31846i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −85.3459 | − | 101.067i | −1.12297 | − | 1.32983i | ||||
\(77\) | 39.9109i | 0.518324i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 80.5457i | − | 1.01957i | −0.860303 | − | 0.509783i | \(-0.829726\pi\) | ||
0.860303 | − | 0.509783i | \(-0.170274\pi\) | |||||||
\(80\) | −93.7255 | − | 15.9218i | −1.17157 | − | 0.199022i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 56.0370 | + | 26.0238i | 0.683378 | + | 0.317363i | ||||
\(83\) | −36.2653 | −0.436931 | −0.218466 | − | 0.975845i | \(-0.570105\pi\) | ||||
−0.218466 | + | 0.975845i | \(0.570105\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 135.618i | 1.59550i | ||||||||
\(86\) | 80.3086 | + | 37.2955i | 0.933821 | + | 0.433669i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 31.7813 | + | 116.419i | 0.361151 | + | 1.32295i | ||||
\(89\) | −13.9430 | −0.156663 | −0.0783313 | − | 0.996927i | \(-0.524959\pi\) | ||||
−0.0783313 | + | 0.996927i | \(0.524959\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 29.6716 | 0.326061 | ||||||||
\(92\) | −5.16571 | + | 4.36218i | −0.0561490 | + | 0.0474150i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 31.4070 | − | 67.6288i | 0.334117 | − | 0.719456i | ||||
\(95\) | − | 196.497i | − | 2.06839i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −66.0297 | −0.680718 | −0.340359 | − | 0.940295i | \(-0.610549\pi\) | ||||
−0.340359 | + | 0.940295i | \(0.610549\pi\) | |||||||
\(98\) | 12.6976 | + | 5.89678i | 0.129567 | + | 0.0601713i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −26.5935 | − | 31.4921i | −0.265935 | − | 0.314921i | ||||
\(101\) | − | 158.436i | − | 1.56867i | −0.620336 | − | 0.784336i | \(-0.713004\pi\) | ||
0.620336 | − | 0.784336i | \(-0.286996\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 136.221i | − | 1.32253i | −0.750151 | − | 0.661266i | \(-0.770019\pi\) | ||
0.750151 | − | 0.661266i | \(-0.229981\pi\) | |||||||
\(104\) | 86.5513 | − | 23.6276i | 0.832224 | − | 0.227189i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −60.8509 | + | 131.030i | −0.574065 | + | 1.23614i | ||||
\(107\) | −164.556 | −1.53790 | −0.768951 | − | 0.639307i | \(-0.779221\pi\) | ||||
−0.768951 | + | 0.639307i | \(0.779221\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 18.6167i | − | 0.170796i | −0.996347 | − | 0.0853978i | \(-0.972784\pi\) | ||
0.996347 | − | 0.0853978i | \(-0.0272161\pi\) | |||||||
\(110\) | −75.5050 | + | 162.585i | −0.686409 | + | 1.47805i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 41.7341 | + | 7.08965i | 0.372626 | + | 0.0633005i | ||||
\(113\) | −140.406 | −1.24253 | −0.621267 | − | 0.783599i | \(-0.713382\pi\) | ||||
−0.621267 | + | 0.783599i | \(0.713382\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.0433 | −0.0873331 | ||||||||
\(116\) | 88.5413 | − | 74.7687i | 0.763287 | − | 0.644558i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 60.2612 | + | 27.9855i | 0.510688 | + | 0.237165i | ||||
\(119\) | − | 60.3878i | − | 0.507460i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 106.554 | 0.880615 | ||||||||
\(122\) | 81.6024 | − | 175.715i | 0.668872 | − | 1.44028i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 75.5573 | − | 63.8043i | 0.609333 | − | 0.514551i | ||||
\(125\) | 87.3166i | 0.698533i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 191.983i | 1.51168i | 0.654756 | + | 0.755840i | \(0.272771\pi\) | ||||
−0.654756 | + | 0.755840i | \(0.727229\pi\) | |||||||
\(128\) | 127.383 | − | 12.5527i | 0.995180 | − | 0.0980682i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 120.873 | + | 56.1338i | 0.929792 | + | 0.431798i | ||||
\(131\) | −13.5685 | −0.103576 | −0.0517881 | − | 0.998658i | \(-0.516492\pi\) | ||||
−0.0517881 | + | 0.998658i | \(0.516492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 87.4961i | 0.657866i | ||||||||
\(134\) | 156.108 | + | 72.4971i | 1.16499 | + | 0.541023i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −48.0871 | − | 176.150i | −0.353581 | − | 1.29522i | ||||
\(137\) | −75.2780 | −0.549475 | −0.274737 | − | 0.961519i | \(-0.588591\pi\) | ||||
−0.274737 | + | 0.961519i | \(0.588591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 222.721 | 1.60231 | 0.801153 | − | 0.598460i | \(-0.204220\pi\) | ||||
0.801153 | + | 0.598460i | \(0.204220\pi\) | |||||||
\(140\) | 40.5703 | + | 48.0434i | 0.289788 | + | 0.343167i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 34.1000 | − | 73.4277i | 0.240141 | − | 0.517097i | ||||
\(143\) | − | 169.174i | − | 1.18304i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 172.144 | 1.18720 | ||||||||
\(146\) | −51.8614 | − | 24.0846i | −0.355215 | − | 0.164963i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 164.379 | − | 138.810i | 1.11067 | − | 0.937904i | ||||
\(149\) | 173.387i | 1.16367i | 0.813307 | + | 0.581835i | \(0.197665\pi\) | ||||
−0.813307 | + | 0.581835i | \(0.802335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 84.9375i | − | 0.562500i | −0.959635 | − | 0.281250i | \(-0.909251\pi\) | ||
0.959635 | − | 0.281250i | \(-0.0907490\pi\) | |||||||
\(152\) | 69.6736 | + | 255.224i | 0.458379 | + | 1.67911i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 33.6209 | − | 72.3959i | 0.218317 | − | 0.470103i | ||||
\(155\) | 146.900 | 0.947744 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 57.6685i | 0.367316i | 0.982990 | + | 0.183658i | \(0.0587938\pi\) | ||||
−0.982990 | + | 0.183658i | \(0.941206\pi\) | |||||||
\(158\) | −67.8515 | + | 146.105i | −0.429440 | + | 0.924714i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 156.600 | + | 107.835i | 0.978748 | + | 0.673971i | ||||
\(161\) | 4.47208 | 0.0277769 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.8347 | 0.0664708 | 0.0332354 | − | 0.999448i | \(-0.489419\pi\) | ||||
0.0332354 | + | 0.999448i | \(0.489419\pi\) | |||||||
\(164\) | −79.7253 | − | 94.4109i | −0.486130 | − | 0.575676i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 65.7829 | + | 30.5498i | 0.396283 | + | 0.184035i | ||||
\(167\) | 57.5843i | 0.344816i | 0.985026 | + | 0.172408i | \(0.0551548\pi\) | ||||
−0.985026 | + | 0.172408i | \(0.944845\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 43.2283 | 0.255789 | ||||||||
\(170\) | 114.244 | − | 246.002i | 0.672023 | − | 1.44707i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −114.257 | − | 135.304i | −0.664285 | − | 0.786648i | ||||
\(173\) | 209.285i | 1.20974i | 0.796323 | + | 0.604871i | \(0.206775\pi\) | ||||
−0.796323 | + | 0.604871i | \(0.793225\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 27.2635i | 0.155791i | ||||||||
\(176\) | 40.4221 | − | 237.950i | 0.229671 | − | 1.35199i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 25.2917 | + | 11.7455i | 0.142088 | + | 0.0659861i | ||||
\(179\) | 228.951 | 1.27905 | 0.639527 | − | 0.768768i | \(-0.279130\pi\) | ||||
0.639527 | + | 0.768768i | \(0.279130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 130.515i | 0.721076i | 0.932744 | + | 0.360538i | \(0.117407\pi\) | ||||
−0.932744 | + | 0.360538i | \(0.882593\pi\) | |||||||
\(182\) | −53.8223 | − | 24.9953i | −0.295727 | − | 0.137337i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.0450 | − | 3.56114i | 0.0708965 | − | 0.0193540i | ||||
\(185\) | 319.590 | 1.72751 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −344.304 | −1.84120 | ||||||||
\(188\) | −113.941 | + | 96.2172i | −0.606068 | + | 0.511794i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −165.528 | + | 356.433i | −0.871202 | + | 1.87596i | ||||
\(191\) | − | 91.3000i | − | 0.478010i | −0.971018 | − | 0.239005i | \(-0.923179\pi\) | ||
0.971018 | − | 0.239005i | \(-0.0768213\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −125.665 | −0.651115 | −0.325557 | − | 0.945522i | \(-0.605552\pi\) | ||||
−0.325557 | + | 0.945522i | \(0.605552\pi\) | |||||||
\(194\) | 119.774 | + | 55.6232i | 0.617390 | + | 0.286718i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18.0651 | − | 21.3928i | −0.0921690 | − | 0.109147i | ||||
\(197\) | 74.5133i | 0.378240i | 0.981954 | + | 0.189120i | \(0.0605635\pi\) | ||||
−0.981954 | + | 0.189120i | \(0.939436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 77.2741i | − | 0.388312i | −0.980971 | − | 0.194156i | \(-0.937803\pi\) | ||
0.980971 | − | 0.194156i | \(-0.0621968\pi\) | |||||||
\(200\) | 21.7100 | + | 79.5269i | 0.108550 | + | 0.397634i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −133.466 | + | 287.393i | −0.660723 | + | 1.42274i | ||||
\(203\) | −76.6524 | −0.377598 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 183.556i | − | 0.895395i | ||||||
\(206\) | −114.752 | + | 247.096i | −0.557049 | + | 1.19950i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −176.902 | − | 30.0516i | −0.850492 | − | 0.144479i | ||||
\(209\) | 498.864 | 2.38691 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 283.994 | 1.34594 | 0.672971 | − | 0.739669i | \(-0.265018\pi\) | ||||
0.672971 | + | 0.739669i | \(0.265018\pi\) | |||||||
\(212\) | 220.759 | − | 186.420i | 1.04132 | − | 0.879341i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 298.493 | + | 138.621i | 1.39483 | + | 0.647763i | ||||
\(215\) | − | 263.060i | − | 1.22354i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −65.4118 | −0.301437 | ||||||||
\(218\) | −15.6827 | + | 33.7696i | −0.0719389 | + | 0.154906i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 273.922 | − | 231.314i | 1.24510 | − | 1.05143i | ||||
\(221\) | 255.971i | 1.15824i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 115.772i | − | 0.519155i | −0.965722 | − | 0.259577i | \(-0.916417\pi\) | ||
0.965722 | − | 0.259577i | \(-0.0835833\pi\) | |||||||
\(224\) | −69.7307 | − | 48.0169i | −0.311298 | − | 0.214361i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 254.688 | + | 118.278i | 1.12694 | + | 0.523354i | ||||
\(227\) | −6.83029 | −0.0300894 | −0.0150447 | − | 0.999887i | \(-0.504789\pi\) | ||||
−0.0150447 | + | 0.999887i | \(0.504789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 217.138i | − | 0.948203i | −0.880470 | − | 0.474101i | \(-0.842773\pi\) | ||
0.880470 | − | 0.474101i | \(-0.157227\pi\) | |||||||
\(230\) | 18.2179 | + | 8.46045i | 0.0792083 | + | 0.0367846i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −223.593 | + | 61.0387i | −0.963764 | + | 0.263098i | ||||
\(233\) | −134.382 | −0.576746 | −0.288373 | − | 0.957518i | \(-0.593114\pi\) | ||||
−0.288373 | + | 0.957518i | \(0.593114\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −221.526 | −0.942665 | ||||||||
\(236\) | −85.7352 | − | 101.528i | −0.363285 | − | 0.430203i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −50.8705 | + | 109.540i | −0.213742 | + | 0.460250i | ||||
\(239\) | 408.424i | 1.70889i | 0.519545 | + | 0.854443i | \(0.326101\pi\) | ||||
−0.519545 | + | 0.854443i | \(0.673899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −237.295 | −0.984629 | −0.492314 | − | 0.870418i | \(-0.663849\pi\) | ||||
−0.492314 | + | 0.870418i | \(0.663849\pi\) | |||||||
\(242\) | −193.283 | − | 89.7612i | −0.798690 | − | 0.370914i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −296.043 | + | 249.993i | −1.21329 | + | 1.02456i | ||||
\(245\) | − | 41.5924i | − | 0.169765i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 370.878i | − | 1.50153i | ||||||
\(248\) | −190.805 | + | 52.0877i | −0.769374 | + | 0.210031i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 73.5553 | − | 158.387i | 0.294221 | − | 0.633547i | ||||
\(251\) | −305.519 | −1.21721 | −0.608604 | − | 0.793474i | \(-0.708270\pi\) | ||||
−0.608604 | + | 0.793474i | \(0.708270\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 25.4978i | − | 0.100782i | ||||||
\(254\) | 161.726 | − | 348.246i | 0.636718 | − | 1.37105i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −241.639 | − | 84.5373i | −0.943903 | − | 0.330224i | ||||
\(257\) | 212.323 | 0.826158 | 0.413079 | − | 0.910695i | \(-0.364453\pi\) | ||||
0.413079 | + | 0.910695i | \(0.364453\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −142.307 | −0.549448 | ||||||||
\(260\) | −171.969 | − | 203.646i | −0.661419 | − | 0.783255i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 24.6124 | + | 11.4301i | 0.0939403 | + | 0.0436262i | ||||
\(263\) | 55.8138i | 0.212220i | 0.994354 | + | 0.106110i | \(0.0338396\pi\) | ||||
−0.994354 | + | 0.106110i | \(0.966160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 429.206 | 1.61965 | ||||||||
\(266\) | 73.7065 | − | 158.712i | 0.277092 | − | 0.596663i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −222.099 | − | 263.010i | −0.828727 | − | 0.981381i | ||||
\(269\) | − | 392.637i | − | 1.45962i | −0.683651 | − | 0.729809i | \(-0.739609\pi\) | ||
0.683651 | − | 0.729809i | \(-0.260391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 505.999i | 1.86715i | 0.358377 | + | 0.933577i | \(0.383330\pi\) | ||||
−0.358377 | + | 0.933577i | \(0.616670\pi\) | |||||||
\(272\) | −61.1612 | + | 360.033i | −0.224857 | + | 1.32365i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 136.550 | + | 63.4140i | 0.498356 | + | 0.231438i | ||||
\(275\) | 155.444 | 0.565252 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 234.703i | 0.847304i | 0.905825 | + | 0.423652i | \(0.139252\pi\) | ||||
−0.905825 | + | 0.423652i | \(0.860748\pi\) | |||||||
\(278\) | −404.001 | − | 187.619i | −1.45324 | − | 0.674889i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −33.1202 | − | 121.324i | −0.118286 | − | 0.433300i | ||||
\(281\) | 260.538 | 0.927182 | 0.463591 | − | 0.886049i | \(-0.346561\pi\) | ||||
0.463591 | + | 0.886049i | \(0.346561\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 314.398 | 1.11095 | 0.555474 | − | 0.831534i | \(-0.312537\pi\) | ||||
0.555474 | + | 0.831534i | \(0.312537\pi\) | |||||||
\(284\) | −123.711 | + | 104.467i | −0.435601 | + | 0.367843i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −142.512 | + | 306.871i | −0.498293 | + | 1.07298i | ||||
\(287\) | 81.7339i | 0.284787i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 231.955 | 0.802612 | ||||||||
\(290\) | −312.259 | − | 145.014i | −1.07675 | − | 0.500048i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 73.7846 | + | 87.3759i | 0.252687 | + | 0.299233i | ||||
\(293\) | 54.0484i | 0.184465i | 0.995737 | + | 0.0922327i | \(0.0294004\pi\) | ||||
−0.995737 | + | 0.0922327i | \(0.970600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 197.393i | − | 0.669129i | ||||||
\(296\) | −415.106 | + | 113.320i | −1.40239 | + | 0.382837i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 146.061 | − | 314.513i | 0.490136 | − | 1.05541i | ||||
\(299\) | −18.9562 | −0.0633988 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 117.136i | 0.389155i | ||||||||
\(302\) | −71.5511 | + | 154.071i | −0.236924 | + | 0.510169i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 88.6168 | − | 521.653i | 0.291502 | − | 1.71597i | ||||
\(305\) | −575.574 | −1.88713 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −82.1306 | −0.267526 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(308\) | −121.972 | + | 102.999i | −0.396014 | + | 0.334414i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −266.468 | − | 123.749i | −0.859574 | − | 0.399189i | ||||
\(311\) | 83.2457i | 0.267671i | 0.991004 | + | 0.133835i | \(0.0427294\pi\) | ||||
−0.991004 | + | 0.133835i | \(0.957271\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 49.4110 | 0.157863 | 0.0789314 | − | 0.996880i | \(-0.474849\pi\) | ||||
0.0789314 | + | 0.996880i | \(0.474849\pi\) | |||||||
\(314\) | 48.5798 | − | 104.607i | 0.154713 | − | 0.333144i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 246.157 | − | 207.867i | 0.778977 | − | 0.657807i | ||||
\(317\) | 449.103i | 1.41673i | 0.705847 | + | 0.708364i | \(0.250566\pi\) | ||||
−0.705847 | + | 0.708364i | \(0.749434\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 437.038i | 1.37003i | ||||||||
\(320\) | −193.222 | − | 327.526i | −0.603818 | − | 1.02352i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.11207 | − | 3.76727i | −0.0251928 | − | 0.0116996i | ||||
\(323\) | −754.814 | −2.33688 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 115.564i | − | 0.355582i | ||||||
\(326\) | −19.6535 | − | 9.12716i | −0.0602869 | − | 0.0279974i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 65.0851 | + | 238.416i | 0.198430 | + | 0.726877i | ||||
\(329\) | 98.6413 | 0.299822 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −107.798 | −0.325674 | −0.162837 | − | 0.986653i | \(-0.552064\pi\) | ||||
−0.162837 | + | 0.986653i | \(0.552064\pi\) | |||||||
\(332\) | −93.5910 | − | 110.831i | −0.281901 | − | 0.333828i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 48.5089 | − | 104.454i | 0.145236 | − | 0.312737i | ||||
\(335\) | − | 511.351i | − | 1.52642i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −565.146 | −1.67699 | −0.838495 | − | 0.544909i | \(-0.816564\pi\) | ||||
−0.838495 | + | 0.544909i | \(0.816564\pi\) | |||||||
\(338\) | −78.4135 | − | 36.4154i | −0.231993 | − | 0.107738i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −414.462 | + | 349.993i | −1.21901 | + | 1.02939i | ||||
\(341\) | 372.949i | 1.09369i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 93.2756 | + | 341.682i | 0.271150 | + | 0.993261i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 176.302 | − | 379.630i | 0.509542 | − | 1.09720i | ||||
\(347\) | 617.119 | 1.77844 | 0.889221 | − | 0.457478i | \(-0.151247\pi\) | ||||
0.889221 | + | 0.457478i | \(0.151247\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 208.548i | 0.597557i | 0.954322 | + | 0.298779i | \(0.0965792\pi\) | ||||
−0.954322 | + | 0.298779i | \(0.903421\pi\) | |||||||
\(350\) | 22.9667 | − | 49.4542i | 0.0656190 | − | 0.141298i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −273.771 | + | 397.574i | −0.777759 | + | 1.12947i | ||||
\(353\) | −93.3007 | −0.264308 | −0.132154 | − | 0.991229i | \(-0.542189\pi\) | ||||
−0.132154 | + | 0.991229i | \(0.542189\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −240.521 | −0.677525 | ||||||||
\(356\) | −35.9831 | − | 42.6113i | −0.101076 | − | 0.119695i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −415.302 | − | 192.868i | −1.16006 | − | 0.538736i | ||||
\(359\) | 319.598i | 0.890246i | 0.895469 | + | 0.445123i | \(0.146840\pi\) | ||||
−0.895469 | + | 0.445123i | \(0.853160\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 732.653 | 2.02951 | ||||||||
\(362\) | 109.945 | − | 236.746i | 0.303716 | − | 0.653993i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 76.5744 | + | 90.6796i | 0.210369 | + | 0.249120i | ||||
\(365\) | 169.878i | 0.465420i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 489.607i | − | 1.33408i | −0.745022 | − | 0.667040i | \(-0.767561\pi\) | ||
0.745022 | − | 0.667040i | \(-0.232439\pi\) | |||||||
\(368\) | −26.6626 | − | 4.52936i | −0.0724528 | − | 0.0123080i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −579.716 | − | 269.222i | −1.56680 | − | 0.727626i | ||||
\(371\) | −191.117 | −0.515140 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 427.590i | 1.14635i | 0.819432 | + | 0.573177i | \(0.194289\pi\) | ||||
−0.819432 | + | 0.573177i | \(0.805711\pi\) | |||||||
\(374\) | 624.547 | + | 290.041i | 1.66991 | + | 0.775511i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 287.734 | − | 78.5485i | 0.765251 | − | 0.208906i | ||||
\(377\) | 324.914 | 0.861840 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −441.475 | −1.16484 | −0.582421 | − | 0.812887i | \(-0.697894\pi\) | ||||
−0.582421 | + | 0.812887i | \(0.697894\pi\) | |||||||
\(380\) | 600.516 | − | 507.106i | 1.58031 | − | 1.33449i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −76.9109 | + | 165.612i | −0.201337 | + | 0.433540i | ||||
\(383\) | − | 392.842i | − | 1.02570i | −0.858479 | − | 0.512849i | \(-0.828590\pi\) | ||
0.858479 | − | 0.512849i | \(-0.171410\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −237.141 | −0.615952 | ||||||||
\(386\) | 227.949 | + | 105.860i | 0.590540 | + | 0.274249i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −170.405 | − | 201.794i | −0.439188 | − | 0.520088i | ||||
\(389\) | − | 539.166i | − | 1.38603i | −0.720923 | − | 0.693015i | \(-0.756282\pi\) | ||
0.720923 | − | 0.693015i | \(-0.243718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.5799i | 0.0986698i | ||||||||
\(392\) | 14.7478 | + | 54.0232i | 0.0376219 | + | 0.137814i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 62.7698 | − | 135.162i | 0.159314 | − | 0.343052i | ||||
\(395\) | 478.584 | 1.21161 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 439.822i | 1.10786i | 0.832562 | + | 0.553932i | \(0.186873\pi\) | ||||
−0.832562 | + | 0.553932i | \(0.813127\pi\) | |||||||
\(398\) | −65.0955 | + | 140.170i | −0.163557 | + | 0.352187i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 27.6126 | − | 162.545i | 0.0690316 | − | 0.406363i | ||||
\(401\) | −256.316 | −0.639191 | −0.319596 | − | 0.947554i | \(-0.603547\pi\) | ||||
−0.319596 | + | 0.947554i | \(0.603547\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 277.267 | 0.688008 | ||||||||
\(404\) | 484.198 | − | 408.881i | 1.19851 | − | 1.01208i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 139.043 | + | 64.5718i | 0.342469 | + | 0.159044i | ||||
\(407\) | 811.371i | 1.99354i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −401.361 | −0.981322 | −0.490661 | − | 0.871351i | \(-0.663245\pi\) | ||||
−0.490661 | + | 0.871351i | \(0.663245\pi\) | |||||||
\(410\) | −154.627 | + | 332.959i | −0.377139 | + | 0.812095i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 416.306 | − | 351.550i | 1.01045 | − | 0.853276i | ||||
\(413\) | 87.8951i | 0.212821i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 215.480i | − | 0.519229i | ||||||
\(416\) | 295.574 | + | 203.534i | 0.710515 | + | 0.489264i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −904.908 | − | 420.242i | −2.16485 | − | 1.00536i | ||||
\(419\) | 185.720 | 0.443247 | 0.221623 | − | 0.975132i | \(-0.428864\pi\) | ||||
0.221623 | + | 0.975132i | \(0.428864\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 361.664i | − | 0.859060i | −0.903053 | − | 0.429530i | \(-0.858679\pi\) | ||
0.903053 | − | 0.429530i | \(-0.141321\pi\) | |||||||
\(422\) | −515.147 | − | 239.236i | −1.22073 | − | 0.566909i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −557.484 | + | 152.187i | −1.31482 | + | 0.358932i | ||||
\(425\) | −235.197 | −0.553405 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 256.292 | 0.600215 | ||||||||
\(428\) | −424.674 | − | 502.900i | −0.992229 | − | 1.17500i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −221.601 | + | 477.175i | −0.515352 | + | 1.10971i | ||||
\(431\) | − | 130.748i | − | 0.303359i | −0.988430 | − | 0.151679i | \(-0.951532\pi\) | ||
0.988430 | − | 0.151679i | \(-0.0484681\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −450.084 | −1.03945 | −0.519727 | − | 0.854332i | \(-0.673966\pi\) | ||||
−0.519727 | + | 0.854332i | \(0.673966\pi\) | |||||||
\(434\) | 118.653 | + | 55.1028i | 0.273394 | + | 0.126965i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 56.8948 | − | 48.0448i | 0.130493 | − | 0.110194i | ||||
\(437\) | − | 55.8986i | − | 0.127914i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 107.851i | 0.245674i | 0.992427 | + | 0.122837i | \(0.0391992\pi\) | ||||
−0.992427 | + | 0.122837i | \(0.960801\pi\) | |||||||
\(440\) | −691.736 | + | 188.837i | −1.57213 | + | 0.429175i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 215.630 | − | 464.316i | 0.487850 | − | 1.05049i | ||||
\(443\) | 79.9983 | 0.180583 | 0.0902915 | − | 0.995915i | \(-0.471220\pi\) | ||||
0.0902915 | + | 0.995915i | \(0.471220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 82.8459i | − | 0.186171i | ||||||
\(446\) | −97.5256 | + | 210.002i | −0.218667 | + | 0.470857i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 86.0378 | + | 145.841i | 0.192049 | + | 0.325537i | ||||
\(449\) | −498.405 | −1.11003 | −0.555017 | − | 0.831839i | \(-0.687288\pi\) | ||||
−0.555017 | + | 0.831839i | \(0.687288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 466.010 | 1.03328 | ||||||||
\(452\) | −362.352 | − | 429.098i | −0.801663 | − | 0.949331i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.3897 | + | 5.75382i | 0.0272901 | + | 0.0126736i | ||||
\(455\) | 176.302i | 0.387476i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −469.124 | −1.02653 | −0.513264 | − | 0.858231i | \(-0.671564\pi\) | ||||
−0.513264 | + | 0.858231i | \(0.671564\pi\) | |||||||
\(458\) | −182.917 | + | 393.875i | −0.399382 | + | 0.859990i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −25.9191 | − | 30.6935i | −0.0563458 | − | 0.0667249i | ||||
\(461\) | − | 729.055i | − | 1.58146i | −0.612162 | − | 0.790732i | \(-0.709700\pi\) | ||
0.612162 | − | 0.790732i | \(-0.290300\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 602.290i | 1.30084i | 0.759574 | + | 0.650421i | \(0.225407\pi\) | ||||
−0.759574 | + | 0.650421i | \(0.774593\pi\) | |||||||
\(464\) | 457.003 | + | 77.6341i | 0.984920 | + | 0.167315i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 243.760 | + | 113.203i | 0.523090 | + | 0.242925i | ||||
\(467\) | 356.045 | 0.762409 | 0.381204 | − | 0.924491i | \(-0.375509\pi\) | ||||
0.381204 | + | 0.924491i | \(0.375509\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 227.694i | 0.485489i | ||||||||
\(470\) | 401.835 | + | 186.613i | 0.854968 | + | 0.397050i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 69.9913 | + | 256.388i | 0.148287 | + | 0.543195i | ||||
\(473\) | 667.855 | 1.41196 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 340.778 | 0.717427 | ||||||||
\(476\) | 184.552 | − | 155.845i | 0.387714 | − | 0.327405i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 344.055 | − | 740.855i | 0.719781 | − | 1.54991i | ||||
\(479\) | 201.862i | 0.421424i | 0.977548 | + | 0.210712i | \(0.0675782\pi\) | ||||
−0.977548 | + | 0.210712i | \(0.932422\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 603.210 | 1.25407 | ||||||||
\(482\) | 430.439 | + | 199.897i | 0.893027 | + | 0.414724i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 274.988 | + | 325.642i | 0.568158 | + | 0.672815i | ||||
\(485\) | − | 392.333i | − | 0.808934i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 343.994i | 0.706353i | 0.935557 | + | 0.353177i | \(0.114898\pi\) | ||||
−0.935557 | + | 0.353177i | \(0.885102\pi\) | |||||||
\(488\) | 747.597 | − | 204.086i | 1.53196 | − | 0.418210i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −35.0373 | + | 75.4459i | −0.0715047 | + | 0.153971i | ||||
\(491\) | −178.510 | −0.363564 | −0.181782 | − | 0.983339i | \(-0.558187\pi\) | ||||
−0.181782 | + | 0.983339i | \(0.558187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 661.267i | − | 1.34131i | ||||||
\(494\) | −312.427 | + | 672.749i | −0.632443 | + | 1.36184i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 389.986 | + | 66.2496i | 0.786263 | + | 0.133568i | ||||
\(497\) | 107.099 | 0.215492 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 548.499 | 1.09920 | 0.549598 | − | 0.835429i | \(-0.314781\pi\) | ||||
0.549598 | + | 0.835429i | \(0.314781\pi\) | |||||||
\(500\) | −266.849 | + | 225.341i | −0.533698 | + | 0.450681i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 554.193 | + | 257.369i | 1.10397 | + | 0.512687i | ||||
\(503\) | 394.287i | 0.783872i | 0.919993 | + | 0.391936i | \(0.128194\pi\) | ||||
−0.919993 | + | 0.391936i | \(0.871806\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 941.389 | 1.86414 | ||||||||
\(506\) | −21.4793 | + | 46.2515i | −0.0424492 | + | 0.0914061i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −586.723 | + | 495.458i | −1.15497 | + | 0.975310i | ||||
\(509\) | − | 863.631i | − | 1.69672i | −0.529419 | − | 0.848360i | \(-0.677590\pi\) | ||
0.529419 | − | 0.848360i | \(-0.322410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 75.6435i | − | 0.148030i | ||||||
\(512\) | 367.104 | + | 356.901i | 0.717000 | + | 0.697073i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −385.140 | − | 178.860i | −0.749299 | − | 0.347977i | ||||
\(515\) | 809.393 | 1.57164 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 562.409i | − | 1.08783i | ||||||
\(518\) | 258.136 | + | 119.879i | 0.498332 | + | 0.231427i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 140.390 | + | 514.268i | 0.269980 | + | 0.988976i | ||||
\(521\) | −499.986 | −0.959666 | −0.479833 | − | 0.877360i | \(-0.659303\pi\) | ||||
−0.479833 | + | 0.877360i | \(0.659303\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −80.9144 | −0.154712 | −0.0773561 | − | 0.997004i | \(-0.524648\pi\) | ||||
−0.0773561 | + | 0.997004i | \(0.524648\pi\) | |||||||
\(524\) | −35.0166 | − | 41.4668i | −0.0668256 | − | 0.0791351i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 47.0174 | − | 101.243i | 0.0893868 | − | 0.192477i | ||||
\(527\) | − | 564.296i | − | 1.07077i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 526.143 | 0.994599 | ||||||||
\(530\) | −778.552 | − | 361.562i | −1.46897 | − | 0.682193i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −267.398 | + | 225.804i | −0.502628 | + | 0.424444i | ||||
\(533\) | − | 346.453i | − | 0.650006i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 977.751i | − | 1.82757i | ||||||
\(536\) | 181.314 | + | 664.179i | 0.338273 | + | 1.23914i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −330.757 | + | 712.219i | −0.614789 | + | 1.32383i | ||||
\(539\) | 105.594 | 0.195908 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 552.750i | 1.02172i | 0.859664 | + | 0.510860i | \(0.170673\pi\) | ||||
−0.859664 | + | 0.510860i | \(0.829327\pi\) | |||||||
\(542\) | 426.252 | − | 917.850i | 0.786443 | − | 1.69345i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 414.233 | − | 601.555i | 0.761459 | − | 1.10580i | ||||
\(545\) | 110.616 | 0.202966 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −570.865 | −1.04363 | −0.521814 | − | 0.853059i | \(-0.674745\pi\) | ||||
−0.521814 | + | 0.853059i | \(0.674745\pi\) | |||||||
\(548\) | −194.272 | − | 230.058i | −0.354512 | − | 0.419814i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −281.966 | − | 130.946i | −0.512665 | − | 0.238083i | ||||
\(551\) | 958.112i | 1.73886i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −213.104 | −0.385360 | ||||||||
\(554\) | 197.713 | − | 425.737i | 0.356883 | − | 0.768478i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 574.782 | + | 680.659i | 1.03378 | + | 1.22421i | ||||
\(557\) | 1107.30i | 1.98797i | 0.109496 | + | 0.993987i | \(0.465076\pi\) | ||||
−0.109496 | + | 0.993987i | \(0.534924\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 496.514i | − | 0.888218i | ||||||
\(560\) | −42.1251 | + | 247.974i | −0.0752234 | + | 0.442812i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −472.600 | − | 219.477i | −0.840924 | − | 0.390528i | ||||
\(563\) | −32.2930 | −0.0573587 | −0.0286794 | − | 0.999589i | \(-0.509130\pi\) | ||||
−0.0286794 | + | 0.999589i | \(0.509130\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 834.263i | − | 1.47657i | ||||||
\(566\) | −570.298 | − | 264.848i | −1.00759 | − | 0.467930i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 312.406 | − | 85.2837i | 0.550011 | − | 0.150147i | ||||
\(569\) | −838.069 | −1.47288 | −0.736440 | − | 0.676503i | \(-0.763495\pi\) | ||||
−0.736440 | + | 0.676503i | \(0.763495\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −590.149 | −1.03354 | −0.516768 | − | 0.856126i | \(-0.672865\pi\) | ||||
−0.516768 | + | 0.856126i | \(0.672865\pi\) | |||||||
\(572\) | 517.015 | − | 436.593i | 0.903873 | − | 0.763275i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 68.8524 | − | 148.260i | 0.119952 | − | 0.258293i | ||||
\(575\) | − | 17.4178i | − | 0.0302918i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 376.385 | 0.652314 | 0.326157 | − | 0.945316i | \(-0.394246\pi\) | ||||
0.326157 | + | 0.945316i | \(0.394246\pi\) | |||||||
\(578\) | −420.751 | − | 195.398i | −0.727943 | − | 0.338059i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 444.258 | + | 526.092i | 0.765962 | + | 0.907055i | ||||
\(581\) | 95.9489i | 0.165144i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1089.66i | 1.86906i | ||||||||
\(584\) | −60.2353 | − | 220.650i | −0.103143 | − | 0.377826i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 45.5302 | − | 98.0404i | 0.0776966 | − | 0.167304i | ||||
\(587\) | 489.154 | 0.833311 | 0.416656 | − | 0.909064i | \(-0.363202\pi\) | ||||
0.416656 | + | 0.909064i | \(0.363202\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 817.611i | 1.38813i | ||||||||
\(590\) | −166.283 | + | 358.058i | −0.281836 | + | 0.606879i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 848.436 | + | 144.130i | 1.43317 | + | 0.243462i | ||||
\(593\) | −180.522 | −0.304421 | −0.152211 | − | 0.988348i | \(-0.548639\pi\) | ||||
−0.152211 | + | 0.988348i | \(0.548639\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 358.810 | 0.603042 | ||||||||
\(596\) | −529.889 | + | 447.465i | −0.889076 | + | 0.750780i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34.3854 | + | 15.9687i | 0.0575007 | + | 0.0267035i | ||||
\(599\) | 16.6365i | 0.0277738i | 0.999904 | + | 0.0138869i | \(0.00442048\pi\) | ||||
−0.999904 | + | 0.0138869i | \(0.995580\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −763.074 | −1.26967 | −0.634837 | − | 0.772646i | \(-0.718933\pi\) | ||||
−0.634837 | + | 0.772646i | \(0.718933\pi\) | |||||||
\(602\) | 98.6747 | − | 212.477i | 0.163912 | − | 0.352951i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 259.578 | − | 219.201i | 0.429765 | − | 0.362915i | ||||
\(605\) | 633.122i | 1.04648i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 82.3314i | − | 0.135637i | −0.997698 | − | 0.0678183i | \(-0.978396\pi\) | ||
0.997698 | − | 0.0678183i | \(-0.0216038\pi\) | |||||||
\(608\) | −600.185 | + | 871.596i | −0.987146 | + | 1.43355i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1044.06 | + | 484.862i | 1.71157 | + | 0.794856i | ||||
\(611\) | −418.120 | −0.684321 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 522.712i | − | 0.852712i | −0.904556 | − | 0.426356i | \(-0.859797\pi\) | ||
0.904556 | − | 0.426356i | \(-0.140203\pi\) | |||||||
\(614\) | 148.980 | + | 69.1866i | 0.242638 | + | 0.112682i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 308.016 | − | 84.0853i | 0.500026 | − | 0.136502i | ||||
\(617\) | 1005.31 | 1.62935 | 0.814674 | − | 0.579920i | \(-0.196916\pi\) | ||||
0.814674 | + | 0.579920i | \(0.196916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 519.176 | 0.838734 | 0.419367 | − | 0.907817i | \(-0.362252\pi\) | ||||
0.419367 | + | 0.907817i | \(0.362252\pi\) | |||||||
\(620\) | 379.111 | + | 448.944i | 0.611469 | + | 0.724103i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 70.1259 | − | 151.002i | 0.112743 | − | 0.242769i | ||||
\(623\) | 36.8896i | 0.0592129i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −776.430 | −1.24229 | ||||||||
\(626\) | −89.6285 | − | 41.6237i | −0.143177 | − | 0.0664916i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −176.241 | + | 148.827i | −0.280639 | + | 0.236986i | ||||
\(629\) | − | 1227.66i | − | 1.95176i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 62.6700i | − | 0.0993185i | −0.998766 | − | 0.0496592i | \(-0.984186\pi\) | ||
0.998766 | − | 0.0496592i | \(-0.0158135\pi\) | |||||||
\(632\) | −621.619 | + | 169.696i | −0.983575 | + | 0.268506i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 378.323 | − | 814.644i | 0.596724 | − | 1.28493i | ||||
\(635\) | −1140.72 | −1.79641 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 78.5036i | − | 0.123240i | ||||||
\(638\) | 368.160 | − | 792.759i | 0.577053 | − | 1.24257i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 74.5854 | + | 756.880i | 0.116540 | + | 1.18263i | ||||
\(641\) | −800.473 | −1.24879 | −0.624394 | − | 0.781110i | \(-0.714654\pi\) | ||||
−0.624394 | + | 0.781110i | \(0.714654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −818.686 | −1.27323 | −0.636614 | − | 0.771183i | \(-0.719666\pi\) | ||||
−0.636614 | + | 0.771183i | \(0.719666\pi\) | |||||||
\(644\) | 11.5412 | + | 13.6672i | 0.0179212 | + | 0.0212223i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1369.18 | + | 635.853i | 2.11948 | + | 0.984293i | ||||
\(647\) | − | 509.102i | − | 0.786866i | −0.919353 | − | 0.393433i | \(-0.871287\pi\) | ||
0.919353 | − | 0.393433i | \(-0.128713\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 501.139 | 0.772172 | ||||||||
\(650\) | −97.3510 | + | 209.626i | −0.149771 | + | 0.322502i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 27.9616 | + | 33.1122i | 0.0428859 | + | 0.0507856i | ||||
\(653\) | 997.554i | 1.52765i | 0.645424 | + | 0.763824i | \(0.276681\pi\) | ||||
−0.645424 | + | 0.763824i | \(0.723319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 80.6208i | − | 0.123085i | ||||||
\(656\) | 82.7807 | − | 487.299i | 0.126190 | − | 0.742833i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −178.929 | − | 83.0952i | −0.271929 | − | 0.126284i | ||||
\(659\) | −179.635 | −0.272588 | −0.136294 | − | 0.990668i | \(-0.543519\pi\) | ||||
−0.136294 | + | 0.990668i | \(0.543519\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 155.299i | − | 0.234946i | −0.993076 | − | 0.117473i | \(-0.962521\pi\) | ||
0.993076 | − | 0.117473i | \(-0.0374793\pi\) | |||||||
\(662\) | 195.539 | + | 90.8088i | 0.295376 | + | 0.137173i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 76.4046 | + | 279.881i | 0.115067 | + | 0.421507i | ||||
\(665\) | −519.882 | −0.781777 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.9708 | 0.0734195 | ||||||||
\(668\) | −175.984 | + | 148.610i | −0.263449 | + | 0.222470i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −430.761 | + | 927.558i | −0.642927 | + | 1.38442i | ||||
\(671\) | − | 1461.26i | − | 2.17774i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1066.49 | −1.58469 | −0.792343 | − | 0.610076i | \(-0.791139\pi\) | ||||
−0.792343 | + | 0.610076i | \(0.791139\pi\) | |||||||
\(674\) | 1025.14 | + | 476.077i | 1.52098 | + | 0.706346i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 111.561 | + | 132.111i | 0.165031 | + | 0.195430i | ||||
\(677\) | − | 248.880i | − | 0.367622i | −0.982962 | − | 0.183811i | \(-0.941157\pi\) | ||
0.982962 | − | 0.183811i | \(-0.0588434\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 174.698i | 0.257287i | ||||||||
\(680\) | 1046.64 | − | 285.722i | 1.53918 | − | 0.420180i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 314.172 | − | 676.506i | 0.460662 | − | 0.991945i | ||||
\(683\) | −465.842 | −0.682053 | −0.341026 | − | 0.940054i | \(-0.610775\pi\) | ||||
−0.341026 | + | 0.940054i | \(0.610775\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 447.285i | − | 0.652970i | ||||||
\(686\) | 15.6014 | − | 33.5946i | 0.0227426 | − | 0.0489717i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 118.636 | − | 698.364i | 0.172436 | − | 1.01506i | ||||
\(689\) | 810.105 | 1.17577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −854.073 | −1.23600 | −0.617998 | − | 0.786180i | \(-0.712056\pi\) | ||||
−0.617998 | + | 0.786180i | \(0.712056\pi\) | |||||||
\(692\) | −639.600 | + | 540.110i | −0.924277 | + | 0.780505i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1119.42 | − | 519.860i | −1.61299 | − | 0.749077i | ||||
\(695\) | 1323.35i | 1.90411i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −705.104 | −1.01163 | ||||||||
\(698\) | 175.680 | − | 378.292i | 0.251690 | − | 0.541966i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −83.3202 | + | 70.3597i | −0.119029 | + | 0.100514i | ||||
\(701\) | − | 746.975i | − | 1.06559i | −0.846246 | − | 0.532793i | \(-0.821143\pi\) | ||
0.846246 | − | 0.532793i | \(-0.178857\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1778.76i | 2.53024i | ||||||||
\(704\) | 831.519 | − | 490.550i | 1.18113 | − | 0.696804i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 169.241 | + | 78.5962i | 0.239719 | + | 0.111326i | ||||
\(707\) | −419.182 | −0.592902 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 939.270i | − | 1.32478i | −0.749158 | − | 0.662391i | \(-0.769542\pi\) | ||
0.749158 | − | 0.662391i | \(-0.230458\pi\) | |||||||
\(710\) | 436.290 | + | 202.615i | 0.614494 | + | 0.285373i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 29.3754 | + | 107.606i | 0.0412576 | + | 0.151132i | ||||
\(713\) | 41.7896 | 0.0586109 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1005.19 | 1.40587 | ||||||||
\(716\) | 590.861 | + | 699.699i | 0.825224 | + | 0.977233i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 269.229 | − | 579.731i | 0.374971 | − | 0.807425i | ||||
\(719\) | 683.284i | 0.950325i | 0.879898 | + | 0.475163i | \(0.157611\pi\) | ||||
−0.879898 | + | 0.475163i | \(0.842389\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −360.407 | −0.499870 | ||||||||
\(722\) | −1328.99 | − | 617.185i | −1.84070 | − | 0.854827i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −398.868 | + | 336.824i | −0.550922 | + | 0.465226i | ||||
\(725\) | 298.544i | 0.411785i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 77.6493i | 0.106808i | 0.998573 | + | 0.0534039i | \(0.0170071\pi\) | ||||
−0.998573 | + | 0.0534039i | \(0.982993\pi\) | |||||||
\(728\) | −62.5128 | − | 228.993i | −0.0858692 | − | 0.314551i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 143.105 | − | 308.149i | 0.196034 | − | 0.422121i | ||||
\(731\) | −1010.51 | −1.38236 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 829.362i | − | 1.13146i | −0.824590 | − | 0.565731i | \(-0.808594\pi\) | ||
0.824590 | − | 0.565731i | \(-0.191406\pi\) | |||||||
\(734\) | −412.444 | + | 888.116i | −0.561913 | + | 1.20997i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 44.5488 | + | 30.6765i | 0.0605283 | + | 0.0416800i | ||||
\(737\) | 1298.21 | 1.76148 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 961.998 | 1.30176 | 0.650878 | − | 0.759182i | \(-0.274401\pi\) | ||||
0.650878 | + | 0.759182i | \(0.274401\pi\) | |||||||
\(740\) | 824.776 | + | 976.702i | 1.11456 | + | 1.31987i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 346.674 | + | 160.996i | 0.467216 | + | 0.216976i | ||||
\(743\) | − | 1037.64i | − | 1.39656i | −0.715826 | − | 0.698279i | \(-0.753949\pi\) | ||
0.715826 | − | 0.698279i | \(-0.246051\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1030.22 | −1.38285 | ||||||||
\(746\) | 360.201 | − | 775.621i | 0.482843 | − | 1.03971i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −888.558 | − | 1052.23i | −1.18791 | − | 1.40673i | ||||
\(749\) | 435.373i | 0.581273i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 988.651i | 1.31645i | 0.752823 | + | 0.658223i | \(0.228692\pi\) | ||||
−0.752823 | + | 0.658223i | \(0.771308\pi\) | |||||||
\(752\) | −588.101 | − | 99.9047i | −0.782049 | − | 0.132852i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −589.373 | − | 273.707i | −0.781662 | − | 0.363006i | ||||
\(755\) | 504.679 | 0.668449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 398.170i | − | 0.525984i | −0.964798 | − | 0.262992i | \(-0.915291\pi\) | ||
0.964798 | − | 0.262992i | \(-0.0847093\pi\) | |||||||
\(758\) | 800.808 | + | 371.898i | 1.05647 | + | 0.490630i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1516.48 | + | 413.984i | −1.99537 | + | 0.544716i | ||||
\(761\) | −573.007 | −0.752966 | −0.376483 | − | 0.926424i | \(-0.622867\pi\) | ||||
−0.376483 | + | 0.926424i | \(0.622867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −49.2552 | −0.0645547 | ||||||||
\(764\) | 279.023 | − | 235.621i | 0.365213 | − | 0.308404i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −330.929 | + | 712.591i | −0.432023 | + | 0.930275i | ||||
\(767\) | − | 372.569i | − | 0.485749i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1317.67 | 1.71349 | 0.856743 | − | 0.515743i | \(-0.172484\pi\) | ||||
0.856743 | + | 0.515743i | \(0.172484\pi\) | |||||||
\(770\) | 430.160 | + | 199.767i | 0.558649 | + | 0.259438i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −324.308 | − | 384.047i | −0.420088 | − | 0.497470i | ||||
\(773\) | − | 753.284i | − | 0.974495i | −0.873264 | − | 0.487247i | \(-0.838001\pi\) | ||
0.873264 | − | 0.487247i | \(-0.161999\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 254.765i | 0.328728i | ||||||||
\(776\) | 139.113 | + | 509.590i | 0.179269 | + | 0.656689i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −454.192 | + | 978.013i | −0.583794 | + | 1.25709i | ||||
\(779\) | 1021.63 | 1.31146 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 610.633i | − | 0.781861i | ||||||
\(782\) | 32.4996 | − | 69.9814i | 0.0415596 | − | 0.0894903i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.7575 | − | 110.418i | 0.0239253 | − | 0.140839i | ||||
\(785\) | −342.653 | −0.436501 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −77.2279 | −0.0981295 | −0.0490648 | − | 0.998796i | \(-0.515624\pi\) | ||||
−0.0490648 | + | 0.998796i | \(0.515624\pi\) | |||||||
\(788\) | −227.721 | + | 192.299i | −0.288986 | + | 0.244034i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −868.121 | − | 403.158i | −1.09889 | − | 0.510327i | ||||
\(791\) | 371.481i | 0.469634i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1086.37 | −1.36995 | ||||||||
\(794\) | 370.505 | − | 797.809i | 0.466631 | − | 1.00480i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 236.158 | − | 199.424i | 0.296681 | − | 0.250532i | ||||
\(797\) | − | 509.008i | − | 0.638655i | −0.947644 | − | 0.319327i | \(-0.896543\pi\) | ||
0.947644 | − | 0.319327i | \(-0.103457\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 850.961i | 1.06503i | ||||||||
\(800\) | −187.015 | + | 271.586i | −0.233769 | + | 0.339482i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 464.940 | + | 215.920i | 0.579726 | + | 0.269227i | ||||
\(803\) | −431.286 | −0.537093 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.5721i | 0.0330088i | ||||||||
\(806\) | −502.945 | − | 233.569i | −0.624002 | − | 0.289788i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1222.74 | + | 333.797i | −1.51330 | + | 0.413115i | ||||
\(809\) | −692.461 | −0.855946 | −0.427973 | − | 0.903791i | \(-0.640772\pi\) | ||||
−0.427973 | + | 0.903791i | \(0.640772\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1496.99 | 1.84585 | 0.922926 | − | 0.384978i | \(-0.125791\pi\) | ||||
0.922926 | + | 0.384978i | \(0.125791\pi\) | |||||||
\(812\) | −197.819 | − | 234.258i | −0.243620 | − | 0.288495i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 683.497 | − | 1471.78i | 0.839677 | − | 1.80808i | ||||
\(815\) | 64.3775i | 0.0789909i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1464.13 | 1.79208 | ||||||||
\(818\) | 728.043 | + | 338.105i | 0.890028 | + | 0.413332i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 560.968 | − | 473.709i | 0.684107 | − | 0.577694i | ||||
\(821\) | − | 1081.65i | − | 1.31748i | −0.752371 | − | 0.658740i | \(-0.771090\pi\) | ||
0.752371 | − | 0.658740i | \(-0.228910\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 684.571i | − | 0.831799i | −0.909410 | − | 0.415900i | \(-0.863467\pi\) | ||
0.909410 | − | 0.415900i | \(-0.136533\pi\) | |||||||
\(824\) | −1051.30 | + | 286.993i | −1.27585 | + | 0.348293i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 74.0427 | − | 159.436i | 0.0896400 | − | 0.193022i | ||||
\(827\) | −526.172 | −0.636242 | −0.318121 | − | 0.948050i | \(-0.603052\pi\) | ||||
−0.318121 | + | 0.948050i | \(0.603052\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1255.76i | 1.51479i | 0.652959 | + | 0.757393i | \(0.273527\pi\) | ||||
−0.652959 | + | 0.757393i | \(0.726473\pi\) | |||||||
\(830\) | −181.520 | + | 390.867i | −0.218699 | + | 0.470924i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −364.697 | − | 618.189i | −0.438337 | − | 0.743015i | ||||
\(833\) | −159.771 | −0.191802 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −342.153 | −0.409764 | ||||||||
\(836\) | 1287.44 | + | 1524.59i | 1.53999 | + | 1.82367i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −336.885 | − | 156.450i | −0.402011 | − | 0.186695i | ||||
\(839\) | − | 93.1019i | − | 0.110968i | −0.998460 | − | 0.0554839i | \(-0.982330\pi\) | ||
0.998460 | − | 0.0554839i | \(-0.0176701\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.63019 | 0.00193840 | ||||||||
\(842\) | −304.665 | + | 656.036i | −0.361835 | + | 0.779141i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 732.912 | + | 867.917i | 0.868379 | + | 1.02834i | ||||
\(845\) | 256.853i | 0.303968i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 281.917i | − | 0.332841i | ||||||
\(848\) | 1139.44 | + | 193.565i | 1.34368 | + | 0.228260i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 426.633 | + | 198.129i | 0.501921 | + | 0.233093i | ||||
\(851\) | 90.9155 | 0.106834 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1226.85i | − | 1.43828i | −0.694867 | − | 0.719138i | \(-0.744537\pi\) | ||
0.694867 | − | 0.719138i | \(-0.255463\pi\) | |||||||
\(854\) | −464.897 | − | 215.900i | −0.544376 | − | 0.252810i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 346.690 | + | 1269.97i | 0.405011 | + | 1.48361i | ||||
\(857\) | −201.847 | −0.235528 | −0.117764 | − | 0.993042i | \(-0.537573\pi\) | ||||
−0.117764 | + | 0.993042i | \(0.537573\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1493.93 | −1.73915 | −0.869574 | − | 0.493802i | \(-0.835607\pi\) | ||||
−0.869574 | + | 0.493802i | \(0.835607\pi\) | |||||||
\(860\) | 803.942 | − | 678.889i | 0.934816 | − | 0.789405i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −110.141 | + | 237.168i | −0.127774 | + | 0.275137i | ||||
\(863\) | − | 453.506i | − | 0.525499i | −0.964864 | − | 0.262750i | \(-0.915371\pi\) | ||
0.964864 | − | 0.262750i | \(-0.0846294\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1243.53 | −1.43760 | ||||||||
\(866\) | 816.424 | + | 379.150i | 0.942753 | + | 0.437817i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −168.810 | − | 199.906i | −0.194482 | − | 0.230306i | ||||
\(869\) | 1215.02i | 1.39819i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 965.150i | − | 1.10809i | ||||||
\(872\) | −143.676 | + | 39.2222i | −0.164766 | + | 0.0449796i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −47.0888 | + | 101.396i | −0.0538774 | + | 0.116014i | ||||
\(875\) | 231.018 | 0.264020 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 75.4930i | − | 0.0860809i | −0.999073 | − | 0.0430405i | \(-0.986296\pi\) | ||
0.999073 | − | 0.0430405i | \(-0.0137044\pi\) | |||||||
\(878\) | 90.8533 | − | 195.635i | 0.103478 | − | 0.222819i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1413.84 | + | 240.179i | 1.60664 | + | 0.272930i | ||||
\(881\) | 1065.89 | 1.20986 | 0.604931 | − | 0.796278i | \(-0.293201\pi\) | ||||
0.604931 | + | 0.796278i | \(0.293201\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −956.369 | −1.08309 | −0.541545 | − | 0.840672i | \(-0.682161\pi\) | ||||
−0.541545 | + | 0.840672i | \(0.682161\pi\) | |||||||
\(884\) | −782.277 | + | 660.594i | −0.884929 | + | 0.747278i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −145.112 | − | 67.3904i | −0.163783 | − | 0.0760614i | ||||
\(887\) | − | 158.851i | − | 0.179088i | −0.995983 | − | 0.0895440i | \(-0.971459\pi\) | ||
0.995983 | − | 0.0895440i | \(-0.0285410\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 507.940 | 0.571361 | ||||||||
\(890\) | −69.7892 | + | 150.277i | −0.0784148 | + | 0.168851i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 353.811 | − | 298.775i | 0.396649 | − | 0.334950i | ||||
\(893\) | − | 1232.96i | − | 1.38070i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1360.37i | 1.51997i | ||||||||
\(896\) | −33.2114 | − | 337.024i | −0.0370663 | − | 0.376143i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 904.075 | + | 419.855i | 1.00676 | + | 0.467545i | ||||
\(899\) | −716.282 | −0.796754 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1648.73i | − | 1.82989i | ||||||
\(902\) | −845.313 | − | 392.566i | −0.937155 | − | 0.435217i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 295.812 | + | 1083.60i | 0.327225 | + | 1.19867i | ||||
\(905\) | −775.489 | −0.856894 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1106.62 | 1.22008 | 0.610042 | − | 0.792369i | \(-0.291152\pi\) | ||||
0.610042 | + | 0.792369i | \(0.291152\pi\) | |||||||
\(908\) | −17.6271 | − | 20.8741i | −0.0194132 | − | 0.0229891i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 148.516 | − | 319.800i | 0.163204 | − | 0.351428i | ||||
\(911\) | − | 950.439i | − | 1.04329i | −0.853162 | − | 0.521646i | \(-0.825318\pi\) | ||
0.853162 | − | 0.521646i | \(-0.174682\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 547.059 | 0.599188 | ||||||||
\(914\) | 850.961 | + | 395.189i | 0.931029 | + | 0.432373i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 663.599 | − | 560.376i | 0.724453 | − | 0.611764i | ||||
\(917\) | 35.8988i | 0.0391481i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 609.662i | 0.663397i | 0.943385 | + | 0.331698i | \(0.107622\pi\) | ||||
−0.943385 | + | 0.331698i | \(0.892378\pi\) | |||||||
\(920\) | 21.1595 | + | 77.5101i | 0.0229994 | + | 0.0842502i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −614.154 | + | 1322.46i | −0.666111 | + | 1.43434i | ||||
\(923\) | −453.972 | −0.491844 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 554.254i | 0.599194i | ||||||||
\(926\) | 507.367 | − | 1092.52i | 0.547913 | − | 1.17982i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −763.575 | − | 525.801i | −0.822818 | − | 0.566596i | ||||
\(929\) | 306.485 | 0.329909 | 0.164954 | − | 0.986301i | \(-0.447252\pi\) | ||||
0.164954 | + | 0.986301i | \(0.447252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 231.493 | 0.248650 | ||||||||
\(932\) | −346.804 | − | 410.686i | −0.372107 | − | 0.440650i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −645.843 | − | 299.931i | −0.691481 | − | 0.321126i | ||||
\(935\) | − | 2045.78i | − | 2.18800i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 885.867 | 0.945429 | 0.472715 | − | 0.881216i | \(-0.343274\pi\) | ||||
0.472715 | + | 0.881216i | \(0.343274\pi\) | |||||||
\(938\) | 191.809 | − | 413.023i | 0.204487 | − | 0.440323i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −571.700 | − | 677.009i | −0.608192 | − | 0.720223i | ||||
\(941\) | 1527.11i | 1.62285i | 0.584454 | + | 0.811427i | \(0.301309\pi\) | ||||
−0.584454 | + | 0.811427i | \(0.698691\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 52.2172i | − | 0.0553735i | ||||||
\(944\) | 89.0209 | − | 524.032i | 0.0943018 | − | 0.555119i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1211.45 | − | 562.600i | −1.28060 | − | 0.594714i | ||||
\(947\) | 43.0382 | 0.0454468 | 0.0227234 | − | 0.999742i | \(-0.492766\pi\) | ||||
0.0227234 | + | 0.999742i | \(0.492766\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 320.637i | 0.337868i | ||||||||
\(950\) | −618.150 | − | 287.071i | −0.650684 | − | 0.302180i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −466.048 | + | 127.226i | −0.489547 | + | 0.133641i | ||||
\(953\) | −701.454 | −0.736048 | −0.368024 | − | 0.929816i | \(-0.619966\pi\) | ||||
−0.368024 | + | 0.929816i | \(0.619966\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 542.483 | 0.568045 | ||||||||
\(956\) | −1248.19 | + | 1054.03i | −1.30564 | + | 1.10254i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 170.048 | − | 366.165i | 0.177503 | − | 0.382218i | ||||
\(959\) | 199.167i | 0.207682i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 349.756 | 0.363950 | ||||||||
\(962\) | −1094.18 | − | 508.143i | −1.13741 | − | 0.528215i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −612.396 | − | 725.202i | −0.635266 | − | 0.752284i | ||||
\(965\) | − | 746.673i | − | 0.773755i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1078.20i | − | 1.11500i | −0.830178 | − | 0.557499i | \(-0.811761\pi\) | ||
0.830178 | − | 0.557499i | \(-0.188239\pi\) | |||||||
\(968\) | −224.491 | − | 822.344i | −0.231913 | − | 0.849529i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −330.500 | + | 711.668i | −0.340722 | + | 0.733678i | ||||
\(971\) | −68.6986 | −0.0707504 | −0.0353752 | − | 0.999374i | \(-0.511263\pi\) | ||||
−0.0353752 | + | 0.999374i | \(0.511263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 589.263i | − | 0.605615i | ||||||
\(974\) | 289.780 | − | 623.983i | 0.297515 | − | 0.640640i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1528.02 | − | 259.574i | −1.56559 | − | 0.265957i | ||||
\(977\) | −785.845 | −0.804345 | −0.402172 | − | 0.915564i | \(-0.631745\pi\) | ||||
−0.402172 | + | 0.915564i | \(0.631745\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 210.328 | 0.214840 | ||||||||
\(980\) | 127.111 | − | 107.339i | 0.129705 | − | 0.109529i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 323.806 | + | 150.376i | 0.329741 | + | 0.153133i | ||||
\(983\) | 14.8697i | 0.0151269i | 0.999971 | + | 0.00756345i | \(0.00240754\pi\) | ||||
−0.999971 | + | 0.00756345i | \(0.997592\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −442.741 | −0.449483 | ||||||||
\(986\) | −557.049 | + | 1199.50i | −0.564959 | + | 1.21653i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1133.44 | − | 957.137i | 1.14721 | − | 0.968762i | ||||
\(989\) | − | 74.8343i | − | 0.0756666i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1163.67i | − | 1.17424i | −0.809499 | − | 0.587121i | \(-0.800261\pi\) | ||
0.809499 | − | 0.587121i | \(-0.199739\pi\) | |||||||
\(992\) | −651.602 | − | 448.696i | −0.656857 | − | 0.452315i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −194.271 | − | 90.2202i | −0.195444 | − | 0.0907648i | ||||
\(995\) | 459.145 | 0.461452 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1235.53i | 1.23925i | 0.784898 | + | 0.619625i | \(0.212715\pi\) | ||||
−0.784898 | + | 0.619625i | \(0.787285\pi\) | |||||||
\(998\) | −994.942 | − | 462.054i | −0.996936 | − | 0.462980i | ||||
\(999\) | 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 | 504.3.g.d.379.5 | 24 | ||
3.2 | odd | 2 | 168.3.g.a.43.20 | yes | 24 | ||
4.3 | odd | 2 | 2016.3.g.d.1135.20 | 24 | |||
8.3 | odd | 2 | inner | 504.3.g.d.379.6 | 24 | ||
8.5 | even | 2 | 2016.3.g.d.1135.5 | 24 | |||
12.11 | even | 2 | 672.3.g.a.463.4 | 24 | |||
24.5 | odd | 2 | 672.3.g.a.463.9 | 24 | |||
24.11 | even | 2 | 168.3.g.a.43.19 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.3.g.a.43.19 | ✓ | 24 | 24.11 | even | 2 | ||
168.3.g.a.43.20 | yes | 24 | 3.2 | odd | 2 | ||
504.3.g.d.379.5 | 24 | 1.1 | even | 1 | trivial | ||
504.3.g.d.379.6 | 24 | 8.3 | odd | 2 | inner | ||
672.3.g.a.463.4 | 24 | 12.11 | even | 2 | |||
672.3.g.a.463.9 | 24 | 24.5 | odd | 2 | |||
2016.3.g.d.1135.5 | 24 | 8.5 | even | 2 | |||
2016.3.g.d.1135.20 | 24 | 4.3 | odd | 2 |