Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.a (trivial) |
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: | yes |
Analytic conductor: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2636.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 14x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.58966\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.03251 | −1.77926 | −0.889630 | − | 0.456681i | \(-0.849038\pi\) | ||||
−0.889630 | + | 0.456681i | \(0.849038\pi\) | |||||||
\(3\) | −8.47535 | −1.63108 | −0.815541 | − | 0.578699i | \(-0.803561\pi\) | ||||
−0.815541 | + | 0.578699i | \(0.803561\pi\) | |||||||
\(4\) | 17.3261 | 2.16577 | ||||||||
\(5\) | −0.885690 | −0.0792185 | −0.0396092 | − | 0.999215i | \(-0.512611\pi\) | ||||
−0.0396092 | + | 0.999215i | \(0.512611\pi\) | |||||||
\(6\) | 42.6523 | 2.90212 | ||||||||
\(7\) | −3.81828 | −0.206168 | −0.103084 | − | 0.994673i | \(-0.532871\pi\) | ||||
−0.103084 | + | 0.994673i | \(0.532871\pi\) | |||||||
\(8\) | −46.9339 | −2.07421 | ||||||||
\(9\) | 44.8316 | 1.66043 | ||||||||
\(10\) | 4.45724 | 0.140950 | ||||||||
\(11\) | 52.3720 | 1.43552 | 0.717761 | − | 0.696289i | \(-0.245167\pi\) | ||||
0.717761 | + | 0.696289i | \(0.245167\pi\) | |||||||
\(12\) | −146.845 | −3.53255 | ||||||||
\(13\) | −8.06025 | −0.171962 | −0.0859811 | − | 0.996297i | \(-0.527402\pi\) | ||||
−0.0859811 | + | 0.996297i | \(0.527402\pi\) | |||||||
\(14\) | 19.2156 | 0.366827 | ||||||||
\(15\) | 7.50653 | 0.129212 | ||||||||
\(16\) | 97.5862 | 1.52478 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −225.616 | −2.95434 | ||||||||
\(19\) | −66.5154 | −0.803141 | −0.401570 | − | 0.915828i | \(-0.631535\pi\) | ||||
−0.401570 | + | 0.915828i | \(0.631535\pi\) | |||||||
\(20\) | −15.3456 | −0.171569 | ||||||||
\(21\) | 32.3613 | 0.336277 | ||||||||
\(22\) | −263.563 | −2.55417 | ||||||||
\(23\) | −180.226 | −1.63390 | −0.816948 | − | 0.576711i | \(-0.804336\pi\) | ||||
−0.816948 | + | 0.576711i | \(0.804336\pi\) | |||||||
\(24\) | 397.782 | 3.38320 | ||||||||
\(25\) | −124.216 | −0.993724 | ||||||||
\(26\) | 40.5633 | 0.305966 | ||||||||
\(27\) | −151.129 | −1.07722 | ||||||||
\(28\) | −66.1562 | −0.446512 | ||||||||
\(29\) | 41.2800 | 0.264328 | 0.132164 | − | 0.991228i | \(-0.457807\pi\) | ||||
0.132164 | + | 0.991228i | \(0.457807\pi\) | |||||||
\(30\) | −37.7767 | −0.229902 | ||||||||
\(31\) | 34.9114 | 0.202267 | 0.101133 | − | 0.994873i | \(-0.467753\pi\) | ||||
0.101133 | + | 0.994873i | \(0.467753\pi\) | |||||||
\(32\) | −115.632 | −0.638783 | ||||||||
\(33\) | −443.871 | −2.34146 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.38182 | 0.0163323 | ||||||||
\(36\) | 776.759 | 3.59611 | ||||||||
\(37\) | −130.368 | −0.579255 | −0.289627 | − | 0.957139i | \(-0.593531\pi\) | ||||
−0.289627 | + | 0.957139i | \(0.593531\pi\) | |||||||
\(38\) | 334.739 | 1.42900 | ||||||||
\(39\) | 68.3134 | 0.280485 | ||||||||
\(40\) | 41.5689 | 0.164315 | ||||||||
\(41\) | 17.9081 | 0.0682142 | 0.0341071 | − | 0.999418i | \(-0.489141\pi\) | ||||
0.0341071 | + | 0.999418i | \(0.489141\pi\) | |||||||
\(42\) | −162.859 | −0.598325 | ||||||||
\(43\) | 277.620 | 0.984573 | 0.492287 | − | 0.870433i | \(-0.336161\pi\) | ||||
0.492287 | + | 0.870433i | \(0.336161\pi\) | |||||||
\(44\) | 907.405 | 3.10901 | ||||||||
\(45\) | −39.7069 | −0.131537 | ||||||||
\(46\) | 906.987 | 2.90713 | ||||||||
\(47\) | 463.789 | 1.43937 | 0.719687 | − | 0.694299i | \(-0.244285\pi\) | ||||
0.719687 | + | 0.694299i | \(0.244285\pi\) | |||||||
\(48\) | −827.078 | −2.48705 | ||||||||
\(49\) | −328.421 | −0.957495 | ||||||||
\(50\) | 625.116 | 1.76809 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −139.653 | −0.372431 | ||||||||
\(53\) | −329.944 | −0.855118 | −0.427559 | − | 0.903987i | \(-0.640626\pi\) | ||||
−0.427559 | + | 0.903987i | \(0.640626\pi\) | |||||||
\(54\) | 760.560 | 1.91665 | ||||||||
\(55\) | −46.3853 | −0.113720 | ||||||||
\(56\) | 179.207 | 0.427635 | ||||||||
\(57\) | 563.741 | 1.30999 | ||||||||
\(58\) | −207.742 | −0.470308 | ||||||||
\(59\) | 678.656 | 1.49752 | 0.748759 | − | 0.662843i | \(-0.230650\pi\) | ||||
0.748759 | + | 0.662843i | \(0.230650\pi\) | |||||||
\(60\) | 130.059 | 0.279843 | ||||||||
\(61\) | −340.280 | −0.714237 | −0.357118 | − | 0.934059i | \(-0.616241\pi\) | ||||
−0.357118 | + | 0.934059i | \(0.616241\pi\) | |||||||
\(62\) | −175.692 | −0.359885 | ||||||||
\(63\) | −171.180 | −0.342328 | ||||||||
\(64\) | −198.770 | −0.388223 | ||||||||
\(65\) | 7.13888 | 0.0136226 | ||||||||
\(66\) | 2233.79 | 4.16606 | ||||||||
\(67\) | 15.3925 | 0.0280671 | 0.0140336 | − | 0.999902i | \(-0.495533\pi\) | ||||
0.0140336 | + | 0.999902i | \(0.495533\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1527.48 | 2.66502 | ||||||||
\(70\) | −17.0190 | −0.0290595 | ||||||||
\(71\) | 670.203 | 1.12026 | 0.560130 | − | 0.828405i | \(-0.310751\pi\) | ||||
0.560130 | + | 0.828405i | \(0.310751\pi\) | |||||||
\(72\) | −2104.12 | −3.44408 | ||||||||
\(73\) | −193.480 | −0.310207 | −0.155103 | − | 0.987898i | \(-0.549571\pi\) | ||||
−0.155103 | + | 0.987898i | \(0.549571\pi\) | |||||||
\(74\) | 656.080 | 1.03065 | ||||||||
\(75\) | 1052.77 | 1.62085 | ||||||||
\(76\) | −1152.46 | −1.73942 | ||||||||
\(77\) | −199.971 | −0.295959 | ||||||||
\(78\) | −343.788 | −0.499055 | ||||||||
\(79\) | −1080.15 | −1.53831 | −0.769156 | − | 0.639061i | \(-0.779323\pi\) | ||||
−0.769156 | + | 0.639061i | \(0.779323\pi\) | |||||||
\(80\) | −86.4311 | −0.120791 | ||||||||
\(81\) | 70.4207 | 0.0965990 | ||||||||
\(82\) | −90.1229 | −0.121371 | ||||||||
\(83\) | −865.668 | −1.14481 | −0.572406 | − | 0.819970i | \(-0.693990\pi\) | ||||
−0.572406 | + | 0.819970i | \(0.693990\pi\) | |||||||
\(84\) | 560.697 | 0.728298 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1397.13 | −1.75181 | ||||||||
\(87\) | −349.863 | −0.431141 | ||||||||
\(88\) | −2458.02 | −2.97757 | ||||||||
\(89\) | 1129.46 | 1.34520 | 0.672599 | − | 0.740008i | \(-0.265178\pi\) | ||||
0.672599 | + | 0.740008i | \(0.265178\pi\) | |||||||
\(90\) | 199.825 | 0.234038 | ||||||||
\(91\) | 30.7763 | 0.0354531 | ||||||||
\(92\) | −3122.61 | −3.53864 | ||||||||
\(93\) | −295.886 | −0.329914 | ||||||||
\(94\) | −2334.02 | −2.56102 | ||||||||
\(95\) | 58.9120 | 0.0636236 | ||||||||
\(96\) | 980.023 | 1.04191 | ||||||||
\(97\) | 379.412 | 0.397149 | 0.198574 | − | 0.980086i | \(-0.436369\pi\) | ||||
0.198574 | + | 0.980086i | \(0.436369\pi\) | |||||||
\(98\) | 1652.78 | 1.70363 | ||||||||
\(99\) | 2347.92 | 2.38359 | ||||||||
\(100\) | −2152.18 | −2.15218 | ||||||||
\(101\) | 131.732 | 0.129780 | 0.0648902 | − | 0.997892i | \(-0.479330\pi\) | ||||
0.0648902 | + | 0.997892i | \(0.479330\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 195.988 | 0.187488 | 0.0937442 | − | 0.995596i | \(-0.470116\pi\) | ||||
0.0937442 | + | 0.995596i | \(0.470116\pi\) | |||||||
\(104\) | 378.299 | 0.356685 | ||||||||
\(105\) | −28.6621 | −0.0266394 | ||||||||
\(106\) | 1660.45 | 1.52148 | ||||||||
\(107\) | 485.147 | 0.438326 | 0.219163 | − | 0.975688i | \(-0.429667\pi\) | ||||
0.219163 | + | 0.975688i | \(0.429667\pi\) | |||||||
\(108\) | −2618.49 | −2.33300 | ||||||||
\(109\) | 1255.12 | 1.10292 | 0.551460 | − | 0.834201i | \(-0.314071\pi\) | ||||
0.551460 | + | 0.834201i | \(0.314071\pi\) | |||||||
\(110\) | 233.435 | 0.202337 | ||||||||
\(111\) | 1104.92 | 0.944812 | ||||||||
\(112\) | −372.612 | −0.314362 | ||||||||
\(113\) | 1013.35 | 0.843612 | 0.421806 | − | 0.906686i | \(-0.361396\pi\) | ||||
0.421806 | + | 0.906686i | \(0.361396\pi\) | |||||||
\(114\) | −2837.03 | −2.33081 | ||||||||
\(115\) | 159.624 | 0.129435 | ||||||||
\(116\) | 715.224 | 0.572473 | ||||||||
\(117\) | −361.354 | −0.285531 | ||||||||
\(118\) | −3415.34 | −2.66447 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −352.311 | −0.268012 | ||||||||
\(121\) | 1411.83 | 1.06073 | ||||||||
\(122\) | 1712.46 | 1.27081 | ||||||||
\(123\) | −151.778 | −0.111263 | ||||||||
\(124\) | 604.880 | 0.438063 | ||||||||
\(125\) | 220.728 | 0.157940 | ||||||||
\(126\) | 861.464 | 0.609090 | ||||||||
\(127\) | 1927.72 | 1.34691 | 0.673456 | − | 0.739227i | \(-0.264809\pi\) | ||||
0.673456 | + | 0.739227i | \(0.264809\pi\) | |||||||
\(128\) | 1925.37 | 1.32953 | ||||||||
\(129\) | −2352.93 | −1.60592 | ||||||||
\(130\) | −35.9265 | −0.0242381 | ||||||||
\(131\) | 406.738 | 0.271274 | 0.135637 | − | 0.990759i | \(-0.456692\pi\) | ||||
0.135637 | + | 0.990759i | \(0.456692\pi\) | |||||||
\(132\) | −7690.58 | −5.07105 | ||||||||
\(133\) | 253.975 | 0.165582 | ||||||||
\(134\) | −77.4631 | −0.0499387 | ||||||||
\(135\) | 133.854 | 0.0853355 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −130.552 | −0.0814149 | −0.0407074 | − | 0.999171i | \(-0.512961\pi\) | ||||
−0.0407074 | + | 0.999171i | \(0.512961\pi\) | |||||||
\(138\) | −7687.03 | −4.74177 | ||||||||
\(139\) | −2073.54 | −1.26529 | −0.632644 | − | 0.774443i | \(-0.718030\pi\) | ||||
−0.632644 | + | 0.774443i | \(0.718030\pi\) | |||||||
\(140\) | 58.5938 | 0.0353720 | ||||||||
\(141\) | −3930.78 | −2.34774 | ||||||||
\(142\) | −3372.80 | −1.99323 | ||||||||
\(143\) | −422.131 | −0.246856 | ||||||||
\(144\) | 4374.95 | 2.53180 | ||||||||
\(145\) | −36.5613 | −0.0209397 | ||||||||
\(146\) | 973.689 | 0.551939 | ||||||||
\(147\) | 2783.48 | 1.56175 | ||||||||
\(148\) | −2258.78 | −1.25453 | ||||||||
\(149\) | −1852.73 | −1.01867 | −0.509334 | − | 0.860569i | \(-0.670108\pi\) | ||||
−0.509334 | + | 0.860569i | \(0.670108\pi\) | |||||||
\(150\) | −5298.08 | −2.88391 | ||||||||
\(151\) | 2050.86 | 1.10527 | 0.552637 | − | 0.833422i | \(-0.313622\pi\) | ||||
0.552637 | + | 0.833422i | \(0.313622\pi\) | |||||||
\(152\) | 3121.83 | 1.66588 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1006.36 | 0.526588 | ||||||||
\(155\) | −30.9207 | −0.0160233 | ||||||||
\(156\) | 1183.61 | 0.607465 | ||||||||
\(157\) | −262.991 | −0.133688 | −0.0668438 | − | 0.997763i | \(-0.521293\pi\) | ||||
−0.0668438 | + | 0.997763i | \(0.521293\pi\) | |||||||
\(158\) | 5435.88 | 2.73706 | ||||||||
\(159\) | 2796.39 | 1.39477 | ||||||||
\(160\) | 102.414 | 0.0506035 | ||||||||
\(161\) | 688.152 | 0.336857 | ||||||||
\(162\) | −354.393 | −0.171875 | ||||||||
\(163\) | 1444.98 | 0.694354 | 0.347177 | − | 0.937800i | \(-0.387140\pi\) | ||||
0.347177 | + | 0.937800i | \(0.387140\pi\) | |||||||
\(164\) | 310.279 | 0.147736 | ||||||||
\(165\) | 393.132 | 0.185487 | ||||||||
\(166\) | 4356.48 | 2.03692 | ||||||||
\(167\) | 501.565 | 0.232409 | 0.116204 | − | 0.993225i | \(-0.462927\pi\) | ||||
0.116204 | + | 0.993225i | \(0.462927\pi\) | |||||||
\(168\) | −1518.84 | −0.697508 | ||||||||
\(169\) | −2132.03 | −0.970429 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2981.99 | −1.33356 | ||||||||
\(172\) | 4810.08 | 2.13236 | ||||||||
\(173\) | 2590.14 | 1.13829 | 0.569146 | − | 0.822237i | \(-0.307274\pi\) | ||||
0.569146 | + | 0.822237i | \(0.307274\pi\) | |||||||
\(174\) | 1760.69 | 0.767112 | ||||||||
\(175\) | 474.290 | 0.204874 | ||||||||
\(176\) | 5110.79 | 2.18886 | ||||||||
\(177\) | −5751.85 | −2.44257 | ||||||||
\(178\) | −5684.02 | −2.39346 | ||||||||
\(179\) | 2165.65 | 0.904294 | 0.452147 | − | 0.891943i | \(-0.350658\pi\) | ||||
0.452147 | + | 0.891943i | \(0.350658\pi\) | |||||||
\(180\) | −687.968 | −0.284878 | ||||||||
\(181\) | 1925.56 | 0.790750 | 0.395375 | − | 0.918520i | \(-0.370615\pi\) | ||||
0.395375 | + | 0.918520i | \(0.370615\pi\) | |||||||
\(182\) | −154.882 | −0.0630803 | ||||||||
\(183\) | 2884.00 | 1.16498 | ||||||||
\(184\) | 8458.69 | 3.38904 | ||||||||
\(185\) | 115.466 | 0.0458877 | ||||||||
\(186\) | 1489.05 | 0.587003 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8035.68 | 3.11735 | ||||||||
\(189\) | 577.055 | 0.222088 | ||||||||
\(190\) | −296.475 | −0.113203 | ||||||||
\(191\) | −2783.52 | −1.05449 | −0.527247 | − | 0.849712i | \(-0.676776\pi\) | ||||
−0.527247 | + | 0.849712i | \(0.676776\pi\) | |||||||
\(192\) | 1684.65 | 0.633223 | ||||||||
\(193\) | −2258.27 | −0.842246 | −0.421123 | − | 0.907004i | \(-0.638364\pi\) | ||||
−0.421123 | + | 0.907004i | \(0.638364\pi\) | |||||||
\(194\) | −1909.39 | −0.706631 | ||||||||
\(195\) | −60.5045 | −0.0222196 | ||||||||
\(196\) | −5690.27 | −2.07371 | ||||||||
\(197\) | 1270.70 | 0.459560 | 0.229780 | − | 0.973243i | \(-0.426199\pi\) | ||||
0.229780 | + | 0.973243i | \(0.426199\pi\) | |||||||
\(198\) | −11815.9 | −4.24102 | ||||||||
\(199\) | 4794.36 | 1.70786 | 0.853928 | − | 0.520392i | \(-0.174214\pi\) | ||||
0.853928 | + | 0.520392i | \(0.174214\pi\) | |||||||
\(200\) | 5829.92 | 2.06119 | ||||||||
\(201\) | −130.457 | −0.0457798 | ||||||||
\(202\) | −662.942 | −0.230913 | ||||||||
\(203\) | −157.619 | −0.0544960 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.8611 | −0.00540383 | ||||||||
\(206\) | −986.313 | −0.333591 | ||||||||
\(207\) | −8079.80 | −2.71297 | ||||||||
\(208\) | −786.569 | −0.262205 | ||||||||
\(209\) | −3483.54 | −1.15293 | ||||||||
\(210\) | 144.242 | 0.0473984 | ||||||||
\(211\) | 2807.00 | 0.915837 | 0.457918 | − | 0.888994i | \(-0.348595\pi\) | ||||
0.457918 | + | 0.888994i | \(0.348595\pi\) | |||||||
\(212\) | −5716.66 | −1.85199 | ||||||||
\(213\) | −5680.21 | −1.82724 | ||||||||
\(214\) | −2441.50 | −0.779896 | ||||||||
\(215\) | −245.885 | −0.0779964 | ||||||||
\(216\) | 7093.09 | 2.23437 | ||||||||
\(217\) | −133.302 | −0.0417009 | ||||||||
\(218\) | −6316.38 | −1.96238 | ||||||||
\(219\) | 1639.81 | 0.505973 | ||||||||
\(220\) | −803.679 | −0.246291 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5560.51 | −1.68107 | ||||||||
\(223\) | 4684.30 | 1.40665 | 0.703327 | − | 0.710866i | \(-0.251697\pi\) | ||||
0.703327 | + | 0.710866i | \(0.251697\pi\) | |||||||
\(224\) | 441.516 | 0.131697 | ||||||||
\(225\) | −5568.79 | −1.65001 | ||||||||
\(226\) | −5099.70 | −1.50101 | ||||||||
\(227\) | 1395.72 | 0.408095 | 0.204047 | − | 0.978961i | \(-0.434590\pi\) | ||||
0.204047 | + | 0.978961i | \(0.434590\pi\) | |||||||
\(228\) | 9767.47 | 2.83713 | ||||||||
\(229\) | 894.638 | 0.258163 | 0.129082 | − | 0.991634i | \(-0.458797\pi\) | ||||
0.129082 | + | 0.991634i | \(0.458797\pi\) | |||||||
\(230\) | −803.309 | −0.230298 | ||||||||
\(231\) | 1694.83 | 0.482733 | ||||||||
\(232\) | −1937.43 | −0.548270 | ||||||||
\(233\) | −1196.13 | −0.336313 | −0.168156 | − | 0.985760i | \(-0.553781\pi\) | ||||
−0.168156 | + | 0.985760i | \(0.553781\pi\) | |||||||
\(234\) | 1818.52 | 0.508035 | ||||||||
\(235\) | −410.773 | −0.114025 | ||||||||
\(236\) | 11758.5 | 3.24328 | ||||||||
\(237\) | 9154.67 | 2.50911 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4948.82 | 1.33938 | 0.669691 | − | 0.742639i | \(-0.266426\pi\) | ||||
0.669691 | + | 0.742639i | \(0.266426\pi\) | |||||||
\(240\) | 732.534 | 0.197020 | ||||||||
\(241\) | 6702.73 | 1.79154 | 0.895770 | − | 0.444518i | \(-0.146625\pi\) | ||||
0.895770 | + | 0.444518i | \(0.146625\pi\) | |||||||
\(242\) | −7105.03 | −1.88731 | ||||||||
\(243\) | 3483.65 | 0.919656 | ||||||||
\(244\) | −5895.75 | −1.54687 | ||||||||
\(245\) | 290.879 | 0.0758513 | ||||||||
\(246\) | 763.824 | 0.197966 | ||||||||
\(247\) | 536.130 | 0.138110 | ||||||||
\(248\) | −1638.53 | −0.419543 | ||||||||
\(249\) | 7336.85 | 1.86728 | ||||||||
\(250\) | −1110.81 | −0.281016 | ||||||||
\(251\) | −4756.08 | −1.19602 | −0.598010 | − | 0.801489i | \(-0.704042\pi\) | ||||
−0.598010 | + | 0.801489i | \(0.704042\pi\) | |||||||
\(252\) | −2965.89 | −0.741402 | ||||||||
\(253\) | −9438.77 | −2.34550 | ||||||||
\(254\) | −9701.29 | −2.39651 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8099.28 | −1.97736 | ||||||||
\(257\) | 2892.84 | 0.702143 | 0.351071 | − | 0.936349i | \(-0.385817\pi\) | ||||
0.351071 | + | 0.936349i | \(0.385817\pi\) | |||||||
\(258\) | 11841.1 | 2.85735 | ||||||||
\(259\) | 497.784 | 0.119424 | ||||||||
\(260\) | 123.689 | 0.0295034 | ||||||||
\(261\) | 1850.65 | 0.438898 | ||||||||
\(262\) | −2046.92 | −0.482667 | ||||||||
\(263\) | 5415.48 | 1.26971 | 0.634853 | − | 0.772633i | \(-0.281061\pi\) | ||||
0.634853 | + | 0.772633i | \(0.281061\pi\) | |||||||
\(264\) | 20832.6 | 4.85666 | ||||||||
\(265\) | 292.228 | 0.0677412 | ||||||||
\(266\) | −1278.13 | −0.294613 | ||||||||
\(267\) | −9572.58 | −2.19413 | ||||||||
\(268\) | 266.693 | 0.0607869 | ||||||||
\(269\) | −5787.00 | −1.31167 | −0.655835 | − | 0.754904i | \(-0.727683\pi\) | ||||
−0.655835 | + | 0.754904i | \(0.727683\pi\) | |||||||
\(270\) | −673.620 | −0.151834 | ||||||||
\(271\) | 5465.13 | 1.22503 | 0.612515 | − | 0.790459i | \(-0.290158\pi\) | ||||
0.612515 | + | 0.790459i | \(0.290158\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −260.840 | −0.0578270 | ||||||||
\(274\) | 657.006 | 0.144858 | ||||||||
\(275\) | −6505.42 | −1.42651 | ||||||||
\(276\) | 26465.3 | 5.77182 | ||||||||
\(277\) | 1207.65 | 0.261952 | 0.130976 | − | 0.991386i | \(-0.458189\pi\) | ||||
0.130976 | + | 0.991386i | \(0.458189\pi\) | |||||||
\(278\) | 10435.1 | 2.25128 | ||||||||
\(279\) | 1565.13 | 0.335850 | ||||||||
\(280\) | −158.722 | −0.0338766 | ||||||||
\(281\) | −1197.18 | −0.254155 | −0.127077 | − | 0.991893i | \(-0.540560\pi\) | ||||
−0.127077 | + | 0.991893i | \(0.540560\pi\) | |||||||
\(282\) | 19781.7 | 4.17724 | ||||||||
\(283\) | −3164.73 | −0.664748 | −0.332374 | − | 0.943148i | \(-0.607850\pi\) | ||||
−0.332374 | + | 0.943148i | \(0.607850\pi\) | |||||||
\(284\) | 11612.0 | 2.42622 | ||||||||
\(285\) | −499.300 | −0.103775 | ||||||||
\(286\) | 2124.38 | 0.439221 | ||||||||
\(287\) | −68.3784 | −0.0140636 | ||||||||
\(288\) | −5183.98 | −1.06066 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 183.995 | 0.0372571 | ||||||||
\(291\) | −3215.65 | −0.647782 | ||||||||
\(292\) | −3352.26 | −0.671836 | ||||||||
\(293\) | 7456.21 | 1.48668 | 0.743339 | − | 0.668915i | \(-0.233241\pi\) | ||||
0.743339 | + | 0.668915i | \(0.233241\pi\) | |||||||
\(294\) | −14007.9 | −2.77877 | ||||||||
\(295\) | −601.079 | −0.118631 | ||||||||
\(296\) | 6118.70 | 1.20149 | ||||||||
\(297\) | −7914.94 | −1.54637 | ||||||||
\(298\) | 9323.89 | 1.81248 | ||||||||
\(299\) | 1452.66 | 0.280969 | ||||||||
\(300\) | 18240.5 | 3.51038 | ||||||||
\(301\) | −1060.03 | −0.202988 | ||||||||
\(302\) | −10321.0 | −1.96657 | ||||||||
\(303\) | −1116.47 | −0.211683 | ||||||||
\(304\) | −6490.98 | −1.22462 | ||||||||
\(305\) | 301.383 | 0.0565808 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6535.48 | −1.21498 | −0.607491 | − | 0.794327i | \(-0.707824\pi\) | ||||
−0.607491 | + | 0.794327i | \(0.707824\pi\) | |||||||
\(308\) | −3464.73 | −0.640978 | ||||||||
\(309\) | −1661.07 | −0.305809 | ||||||||
\(310\) | 155.608 | 0.0285096 | ||||||||
\(311\) | 8935.89 | 1.62928 | 0.814642 | − | 0.579963i | \(-0.196933\pi\) | ||||
0.814642 | + | 0.579963i | \(0.196933\pi\) | |||||||
\(312\) | −3206.22 | −0.581783 | ||||||||
\(313\) | 2628.71 | 0.474707 | 0.237353 | − | 0.971423i | \(-0.423720\pi\) | ||||
0.237353 | + | 0.971423i | \(0.423720\pi\) | |||||||
\(314\) | 1323.50 | 0.237865 | ||||||||
\(315\) | 151.612 | 0.0271187 | ||||||||
\(316\) | −18714.9 | −3.33163 | ||||||||
\(317\) | −4268.54 | −0.756293 | −0.378147 | − | 0.925746i | \(-0.623438\pi\) | ||||
−0.378147 | + | 0.925746i | \(0.623438\pi\) | |||||||
\(318\) | −14072.9 | −2.48166 | ||||||||
\(319\) | 2161.92 | 0.379449 | ||||||||
\(320\) | 176.048 | 0.0307544 | ||||||||
\(321\) | −4111.79 | −0.714946 | ||||||||
\(322\) | −3463.13 | −0.599357 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1220.12 | 0.209211 | ||||||||
\(325\) | 1001.21 | 0.170883 | ||||||||
\(326\) | −7271.89 | −1.23544 | ||||||||
\(327\) | −10637.5 | −1.79895 | ||||||||
\(328\) | −840.500 | −0.141490 | ||||||||
\(329\) | −1770.88 | −0.296753 | ||||||||
\(330\) | −1978.44 | −0.330029 | ||||||||
\(331\) | 992.298 | 0.164778 | 0.0823892 | − | 0.996600i | \(-0.473745\pi\) | ||||
0.0823892 | + | 0.996600i | \(0.473745\pi\) | |||||||
\(332\) | −14998.7 | −2.47940 | ||||||||
\(333\) | −5844.63 | −0.961812 | ||||||||
\(334\) | −2524.13 | −0.413516 | ||||||||
\(335\) | −13.6330 | −0.00222344 | ||||||||
\(336\) | 3158.02 | 0.512750 | ||||||||
\(337\) | −8042.26 | −1.29997 | −0.649985 | − | 0.759947i | \(-0.725225\pi\) | ||||
−0.649985 | + | 0.759947i | \(0.725225\pi\) | |||||||
\(338\) | 10729.5 | 1.72665 | ||||||||
\(339\) | −8588.52 | −1.37600 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1828.38 | 0.290359 | ||||||||
\(342\) | 15006.9 | 2.37275 | ||||||||
\(343\) | 2563.68 | 0.403573 | ||||||||
\(344\) | −13029.8 | −2.04221 | ||||||||
\(345\) | −1352.87 | −0.211119 | ||||||||
\(346\) | −13034.9 | −2.02532 | ||||||||
\(347\) | 7414.16 | 1.14701 | 0.573506 | − | 0.819202i | \(-0.305583\pi\) | ||||
0.573506 | + | 0.819202i | \(0.305583\pi\) | |||||||
\(348\) | −6061.78 | −0.933751 | ||||||||
\(349\) | −859.194 | −0.131781 | −0.0658905 | − | 0.997827i | \(-0.520989\pi\) | ||||
−0.0658905 | + | 0.997827i | \(0.520989\pi\) | |||||||
\(350\) | −2386.87 | −0.364525 | ||||||||
\(351\) | 1218.14 | 0.185241 | ||||||||
\(352\) | −6055.89 | −0.916988 | ||||||||
\(353\) | 569.084 | 0.0858053 | 0.0429027 | − | 0.999079i | \(-0.486339\pi\) | ||||
0.0429027 | + | 0.999079i | \(0.486339\pi\) | |||||||
\(354\) | 28946.3 | 4.34598 | ||||||||
\(355\) | −593.592 | −0.0887453 | ||||||||
\(356\) | 19569.2 | 2.91339 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10898.7 | −1.60897 | ||||||||
\(359\) | −5005.21 | −0.735835 | −0.367918 | − | 0.929858i | \(-0.619929\pi\) | ||||
−0.367918 | + | 0.929858i | \(0.619929\pi\) | |||||||
\(360\) | 1863.60 | 0.272834 | ||||||||
\(361\) | −2434.71 | −0.354965 | ||||||||
\(362\) | −9690.40 | −1.40695 | ||||||||
\(363\) | −11965.7 | −1.73013 | ||||||||
\(364\) | 533.235 | 0.0767833 | ||||||||
\(365\) | 171.363 | 0.0245741 | ||||||||
\(366\) | −14513.7 | −2.07280 | ||||||||
\(367\) | 10975.3 | 1.56105 | 0.780523 | − | 0.625127i | \(-0.214953\pi\) | ||||
0.780523 | + | 0.625127i | \(0.214953\pi\) | |||||||
\(368\) | −17587.5 | −2.49134 | ||||||||
\(369\) | 802.851 | 0.113265 | ||||||||
\(370\) | −581.083 | −0.0816462 | ||||||||
\(371\) | 1259.82 | 0.176298 | ||||||||
\(372\) | −5126.57 | −0.714517 | ||||||||
\(373\) | −3211.72 | −0.445835 | −0.222918 | − | 0.974837i | \(-0.571558\pi\) | ||||
−0.222918 | + | 0.974837i | \(0.571558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1870.74 | −0.257613 | ||||||||
\(376\) | −21767.4 | −2.98556 | ||||||||
\(377\) | −332.727 | −0.0454544 | ||||||||
\(378\) | −2904.03 | −0.395152 | ||||||||
\(379\) | −8051.48 | −1.09123 | −0.545616 | − | 0.838035i | \(-0.683704\pi\) | ||||
−0.545616 | + | 0.838035i | \(0.683704\pi\) | |||||||
\(380\) | 1020.72 | 0.137794 | ||||||||
\(381\) | −16338.1 | −2.19692 | ||||||||
\(382\) | 14008.1 | 1.87622 | ||||||||
\(383\) | −2584.16 | −0.344763 | −0.172382 | − | 0.985030i | \(-0.555146\pi\) | ||||
−0.172382 | + | 0.985030i | \(0.555146\pi\) | |||||||
\(384\) | −16318.2 | −2.16858 | ||||||||
\(385\) | 177.112 | 0.0234454 | ||||||||
\(386\) | 11364.7 | 1.49858 | ||||||||
\(387\) | 12446.2 | 1.63482 | ||||||||
\(388\) | 6573.74 | 0.860132 | ||||||||
\(389\) | −5174.31 | −0.674417 | −0.337208 | − | 0.941430i | \(-0.609483\pi\) | ||||
−0.337208 | + | 0.941430i | \(0.609483\pi\) | |||||||
\(390\) | 304.489 | 0.0395344 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 15414.1 | 1.98604 | ||||||||
\(393\) | −3447.25 | −0.442470 | ||||||||
\(394\) | −6394.79 | −0.817677 | ||||||||
\(395\) | 956.680 | 0.121863 | ||||||||
\(396\) | 40680.4 | 5.16230 | ||||||||
\(397\) | 5149.36 | 0.650980 | 0.325490 | − | 0.945545i | \(-0.394471\pi\) | ||||
0.325490 | + | 0.945545i | \(0.394471\pi\) | |||||||
\(398\) | −24127.7 | −3.03872 | ||||||||
\(399\) | −2152.53 | −0.270078 | ||||||||
\(400\) | −12121.7 | −1.51522 | ||||||||
\(401\) | −8700.49 | −1.08350 | −0.541748 | − | 0.840541i | \(-0.682237\pi\) | ||||
−0.541748 | + | 0.840541i | \(0.682237\pi\) | |||||||
\(402\) | 656.527 | 0.0814542 | ||||||||
\(403\) | −281.394 | −0.0347823 | ||||||||
\(404\) | 2282.41 | 0.281074 | ||||||||
\(405\) | −62.3709 | −0.00765243 | ||||||||
\(406\) | 793.219 | 0.0969625 | ||||||||
\(407\) | −6827.65 | −0.831533 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12346.0 | 1.49260 | 0.746299 | − | 0.665611i | \(-0.231829\pi\) | ||||
0.746299 | + | 0.665611i | \(0.231829\pi\) | |||||||
\(410\) | 79.8209 | 0.00961482 | ||||||||
\(411\) | 1106.48 | 0.132794 | ||||||||
\(412\) | 3395.72 | 0.406056 | ||||||||
\(413\) | −2591.30 | −0.308740 | ||||||||
\(414\) | 40661.7 | 4.82708 | ||||||||
\(415\) | 766.713 | 0.0906903 | ||||||||
\(416\) | 932.023 | 0.109847 | ||||||||
\(417\) | 17574.0 | 2.06379 | ||||||||
\(418\) | 17531.0 | 2.05136 | ||||||||
\(419\) | 5763.33 | 0.671974 | 0.335987 | − | 0.941867i | \(-0.390930\pi\) | ||||
0.335987 | + | 0.941867i | \(0.390930\pi\) | |||||||
\(420\) | −496.604 | −0.0576947 | ||||||||
\(421\) | −1876.12 | −0.217188 | −0.108594 | − | 0.994086i | \(-0.534635\pi\) | ||||
−0.108594 | + | 0.994086i | \(0.534635\pi\) | |||||||
\(422\) | −14126.2 | −1.62951 | ||||||||
\(423\) | 20792.4 | 2.38998 | ||||||||
\(424\) | 15485.6 | 1.77369 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 28585.7 | 3.25113 | ||||||||
\(427\) | 1299.29 | 0.147253 | ||||||||
\(428\) | 8405.72 | 0.949313 | ||||||||
\(429\) | 3577.71 | 0.402642 | ||||||||
\(430\) | 1237.42 | 0.138776 | ||||||||
\(431\) | −83.9299 | −0.00937996 | −0.00468998 | − | 0.999989i | \(-0.501493\pi\) | ||||
−0.00468998 | + | 0.999989i | \(0.501493\pi\) | |||||||
\(432\) | −14748.1 | −1.64252 | ||||||||
\(433\) | −15345.0 | −1.70308 | −0.851539 | − | 0.524291i | \(-0.824331\pi\) | ||||
−0.851539 | + | 0.524291i | \(0.824331\pi\) | |||||||
\(434\) | 670.842 | 0.0741968 | ||||||||
\(435\) | 309.870 | 0.0341543 | ||||||||
\(436\) | 21746.3 | 2.38867 | ||||||||
\(437\) | 11987.8 | 1.31225 | ||||||||
\(438\) | −8252.36 | −0.900258 | ||||||||
\(439\) | −3064.74 | −0.333194 | −0.166597 | − | 0.986025i | \(-0.553278\pi\) | ||||
−0.166597 | + | 0.986025i | \(0.553278\pi\) | |||||||
\(440\) | 2177.05 | 0.235879 | ||||||||
\(441\) | −14723.6 | −1.58985 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1792.97 | −0.192295 | −0.0961474 | − | 0.995367i | \(-0.530652\pi\) | ||||
−0.0961474 | + | 0.995367i | \(0.530652\pi\) | |||||||
\(444\) | 19144.0 | 2.04624 | ||||||||
\(445\) | −1000.35 | −0.106564 | ||||||||
\(446\) | −23573.8 | −2.50281 | ||||||||
\(447\) | 15702.6 | 1.66153 | ||||||||
\(448\) | 758.960 | 0.0800391 | ||||||||
\(449\) | −2499.19 | −0.262681 | −0.131341 | − | 0.991337i | \(-0.541928\pi\) | ||||
−0.131341 | + | 0.991337i | \(0.541928\pi\) | |||||||
\(450\) | 28025.0 | 2.93580 | ||||||||
\(451\) | 937.885 | 0.0979231 | ||||||||
\(452\) | 17557.5 | 1.82707 | ||||||||
\(453\) | −17381.7 | −1.80279 | ||||||||
\(454\) | −7024.00 | −0.726107 | ||||||||
\(455\) | −27.2583 | −0.00280854 | ||||||||
\(456\) | −26458.6 | −2.71719 | ||||||||
\(457\) | 14784.4 | 1.51331 | 0.756656 | − | 0.653813i | \(-0.226832\pi\) | ||||
0.756656 | + | 0.653813i | \(0.226832\pi\) | |||||||
\(458\) | −4502.28 | −0.459340 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2765.67 | 0.280326 | ||||||||
\(461\) | −17746.9 | −1.79297 | −0.896483 | − | 0.443078i | \(-0.853887\pi\) | ||||
−0.896483 | + | 0.443078i | \(0.853887\pi\) | |||||||
\(462\) | −8529.23 | −0.858909 | ||||||||
\(463\) | 18486.4 | 1.85559 | 0.927793 | − | 0.373096i | \(-0.121704\pi\) | ||||
0.927793 | + | 0.373096i | \(0.121704\pi\) | |||||||
\(464\) | 4028.36 | 0.403043 | ||||||||
\(465\) | 262.064 | 0.0261353 | ||||||||
\(466\) | 6019.52 | 0.598388 | ||||||||
\(467\) | 7406.57 | 0.733908 | 0.366954 | − | 0.930239i | \(-0.380401\pi\) | ||||
0.366954 | + | 0.930239i | \(0.380401\pi\) | |||||||
\(468\) | −6260.87 | −0.618395 | ||||||||
\(469\) | −58.7731 | −0.00578655 | ||||||||
\(470\) | 2067.22 | 0.202880 | ||||||||
\(471\) | 2228.94 | 0.218055 | ||||||||
\(472\) | −31852.0 | −3.10616 | ||||||||
\(473\) | 14539.5 | 1.41338 | ||||||||
\(474\) | −46071.0 | −4.46437 | ||||||||
\(475\) | 8262.24 | 0.798101 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14791.9 | −1.41986 | ||||||||
\(478\) | −24905.0 | −2.38311 | ||||||||
\(479\) | 18550.9 | 1.76955 | 0.884775 | − | 0.466019i | \(-0.154312\pi\) | ||||
0.884775 | + | 0.466019i | \(0.154312\pi\) | |||||||
\(480\) | −867.997 | −0.0825384 | ||||||||
\(481\) | 1050.80 | 0.0996100 | ||||||||
\(482\) | −33731.6 | −3.18762 | ||||||||
\(483\) | −5832.34 | −0.549442 | ||||||||
\(484\) | 24461.5 | 2.29729 | ||||||||
\(485\) | −336.041 | −0.0314615 | ||||||||
\(486\) | −17531.5 | −1.63631 | ||||||||
\(487\) | −10203.4 | −0.949406 | −0.474703 | − | 0.880146i | \(-0.657444\pi\) | ||||
−0.474703 | + | 0.880146i | \(0.657444\pi\) | |||||||
\(488\) | 15970.7 | 1.48147 | ||||||||
\(489\) | −12246.7 | −1.13255 | ||||||||
\(490\) | −1463.85 | −0.134959 | ||||||||
\(491\) | −1247.46 | −0.114658 | −0.0573290 | − | 0.998355i | \(-0.518258\pi\) | ||||
−0.0573290 | + | 0.998355i | \(0.518258\pi\) | |||||||
\(492\) | −2629.73 | −0.240970 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2698.08 | −0.245734 | ||||||||
\(495\) | −2079.53 | −0.188824 | ||||||||
\(496\) | 3406.87 | 0.308413 | ||||||||
\(497\) | −2559.03 | −0.230962 | ||||||||
\(498\) | −36922.7 | −3.32238 | ||||||||
\(499\) | −70.0303 | −0.00628254 | −0.00314127 | − | 0.999995i | \(-0.501000\pi\) | ||||
−0.00314127 | + | 0.999995i | \(0.501000\pi\) | |||||||
\(500\) | 3824.36 | 0.342061 | ||||||||
\(501\) | −4250.94 | −0.379078 | ||||||||
\(502\) | 23935.0 | 2.12803 | ||||||||
\(503\) | −1444.29 | −0.128028 | −0.0640138 | − | 0.997949i | \(-0.520390\pi\) | ||||
−0.0640138 | + | 0.997949i | \(0.520390\pi\) | |||||||
\(504\) | 8034.15 | 0.710058 | ||||||||
\(505\) | −116.674 | −0.0102810 | ||||||||
\(506\) | 47500.7 | 4.17325 | ||||||||
\(507\) | 18069.7 | 1.58285 | ||||||||
\(508\) | 33400.0 | 2.91710 | ||||||||
\(509\) | 14272.8 | 1.24289 | 0.621445 | − | 0.783458i | \(-0.286546\pi\) | ||||
0.621445 | + | 0.783458i | \(0.286546\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 738.761 | 0.0639547 | ||||||||
\(512\) | 25356.7 | 2.18871 | ||||||||
\(513\) | 10052.4 | 0.865157 | ||||||||
\(514\) | −14558.3 | −1.24929 | ||||||||
\(515\) | −173.585 | −0.0148525 | ||||||||
\(516\) | −40767.2 | −3.47805 | ||||||||
\(517\) | 24289.6 | 2.06625 | ||||||||
\(518\) | −2505.10 | −0.212486 | ||||||||
\(519\) | −21952.3 | −1.85665 | ||||||||
\(520\) | −335.055 | −0.0282561 | ||||||||
\(521\) | −14874.0 | −1.25075 | −0.625376 | − | 0.780324i | \(-0.715054\pi\) | ||||
−0.625376 | + | 0.780324i | \(0.715054\pi\) | |||||||
\(522\) | −9313.42 | −0.780914 | ||||||||
\(523\) | −8142.90 | −0.680811 | −0.340406 | − | 0.940279i | \(-0.610564\pi\) | ||||
−0.340406 | + | 0.940279i | \(0.610564\pi\) | |||||||
\(524\) | 7047.21 | 0.587517 | ||||||||
\(525\) | −4019.78 | −0.334167 | ||||||||
\(526\) | −27253.4 | −2.25914 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −43315.7 | −3.57022 | ||||||||
\(529\) | 20314.2 | 1.66962 | ||||||||
\(530\) | −1470.64 | −0.120529 | ||||||||
\(531\) | 30425.3 | 2.48652 | ||||||||
\(532\) | 4400.40 | 0.358612 | ||||||||
\(533\) | −144.344 | −0.0117303 | ||||||||
\(534\) | 48174.1 | 3.90393 | ||||||||
\(535\) | −429.689 | −0.0347235 | ||||||||
\(536\) | −722.432 | −0.0582170 | ||||||||
\(537\) | −18354.7 | −1.47498 | ||||||||
\(538\) | 29123.1 | 2.33380 | ||||||||
\(539\) | −17200.0 | −1.37451 | ||||||||
\(540\) | 2319.17 | 0.184817 | ||||||||
\(541\) | −3179.67 | −0.252689 | −0.126344 | − | 0.991986i | \(-0.540324\pi\) | ||||
−0.126344 | + | 0.991986i | \(0.540324\pi\) | |||||||
\(542\) | −27503.3 | −2.17965 | ||||||||
\(543\) | −16319.8 | −1.28978 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1111.64 | −0.0873716 | ||||||||
\(546\) | 1312.68 | 0.102889 | ||||||||
\(547\) | −2107.07 | −0.164702 | −0.0823509 | − | 0.996603i | \(-0.526243\pi\) | ||||
−0.0823509 | + | 0.996603i | \(0.526243\pi\) | |||||||
\(548\) | −2261.97 | −0.176326 | ||||||||
\(549\) | −15255.3 | −1.18594 | ||||||||
\(550\) | 32738.6 | 2.53814 | ||||||||
\(551\) | −2745.76 | −0.212292 | ||||||||
\(552\) | −71690.4 | −5.52780 | ||||||||
\(553\) | 4124.33 | 0.317151 | ||||||||
\(554\) | −6077.51 | −0.466081 | ||||||||
\(555\) | −978.614 | −0.0748466 | ||||||||
\(556\) | −35926.4 | −2.74032 | ||||||||
\(557\) | 467.382 | 0.0355540 | 0.0177770 | − | 0.999842i | \(-0.494341\pi\) | ||||
0.0177770 | + | 0.999842i | \(0.494341\pi\) | |||||||
\(558\) | −7876.55 | −0.597565 | ||||||||
\(559\) | −2237.69 | −0.169309 | ||||||||
\(560\) | 330.019 | 0.0249033 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6024.80 | 0.452208 | ||||||||
\(563\) | 14612.6 | 1.09387 | 0.546935 | − | 0.837175i | \(-0.315794\pi\) | ||||
0.546935 | + | 0.837175i | \(0.315794\pi\) | |||||||
\(564\) | −68105.2 | −5.08466 | ||||||||
\(565\) | −897.515 | −0.0668297 | ||||||||
\(566\) | 15926.5 | 1.18276 | ||||||||
\(567\) | −268.886 | −0.0199156 | ||||||||
\(568\) | −31455.3 | −2.32365 | ||||||||
\(569\) | 11602.3 | 0.854821 | 0.427410 | − | 0.904058i | \(-0.359426\pi\) | ||||
0.427410 | + | 0.904058i | \(0.359426\pi\) | |||||||
\(570\) | 2512.73 | 0.184643 | ||||||||
\(571\) | 10534.9 | 0.772104 | 0.386052 | − | 0.922477i | \(-0.373839\pi\) | ||||
0.386052 | + | 0.922477i | \(0.373839\pi\) | |||||||
\(572\) | −7313.91 | −0.534633 | ||||||||
\(573\) | 23591.3 | 1.71997 | ||||||||
\(574\) | 344.115 | 0.0250228 | ||||||||
\(575\) | 22386.8 | 1.62364 | ||||||||
\(576\) | −8911.18 | −0.644617 | ||||||||
\(577\) | 14404.7 | 1.03930 | 0.519650 | − | 0.854379i | \(-0.326062\pi\) | ||||
0.519650 | + | 0.854379i | \(0.326062\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19139.6 | 1.37377 | ||||||||
\(580\) | −633.466 | −0.0453504 | ||||||||
\(581\) | 3305.37 | 0.236024 | ||||||||
\(582\) | 16182.8 | 1.15257 | ||||||||
\(583\) | −17279.8 | −1.22754 | ||||||||
\(584\) | 9080.77 | 0.643433 | ||||||||
\(585\) | 320.047 | 0.0226194 | ||||||||
\(586\) | −37523.5 | −2.64519 | ||||||||
\(587\) | −11004.9 | −0.773799 | −0.386900 | − | 0.922122i | \(-0.626454\pi\) | ||||
−0.386900 | + | 0.922122i | \(0.626454\pi\) | |||||||
\(588\) | 48227.0 | 3.38240 | ||||||||
\(589\) | −2322.14 | −0.162449 | ||||||||
\(590\) | 3024.94 | 0.211076 | ||||||||
\(591\) | −10769.6 | −0.749581 | ||||||||
\(592\) | −12722.2 | −0.883239 | ||||||||
\(593\) | 1853.59 | 0.128361 | 0.0641804 | − | 0.997938i | \(-0.479557\pi\) | ||||
0.0641804 | + | 0.997938i | \(0.479557\pi\) | |||||||
\(594\) | 39832.0 | 2.75139 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −32100.7 | −2.20620 | ||||||||
\(597\) | −40633.9 | −2.78565 | ||||||||
\(598\) | −7310.53 | −0.499916 | ||||||||
\(599\) | 19074.7 | 1.30112 | 0.650559 | − | 0.759456i | \(-0.274535\pi\) | ||||
0.650559 | + | 0.759456i | \(0.274535\pi\) | |||||||
\(600\) | −49410.7 | −3.36197 | ||||||||
\(601\) | 27776.0 | 1.88520 | 0.942600 | − | 0.333923i | \(-0.108373\pi\) | ||||
0.942600 | + | 0.333923i | \(0.108373\pi\) | |||||||
\(602\) | 5334.62 | 0.361168 | ||||||||
\(603\) | 690.073 | 0.0466035 | ||||||||
\(604\) | 35533.4 | 2.39377 | ||||||||
\(605\) | −1250.44 | −0.0840291 | ||||||||
\(606\) | 5618.67 | 0.376638 | ||||||||
\(607\) | −18728.3 | −1.25232 | −0.626159 | − | 0.779695i | \(-0.715374\pi\) | ||||
−0.626159 | + | 0.779695i | \(0.715374\pi\) | |||||||
\(608\) | 7691.32 | 0.513033 | ||||||||
\(609\) | 1335.88 | 0.0888874 | ||||||||
\(610\) | −1516.71 | −0.100672 | ||||||||
\(611\) | −3738.25 | −0.247518 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24405.3 | −1.60802 | −0.804012 | − | 0.594613i | \(-0.797305\pi\) | ||||
−0.804012 | + | 0.594613i | \(0.797305\pi\) | |||||||
\(614\) | 32889.8 | 2.16177 | ||||||||
\(615\) | 134.428 | 0.00881409 | ||||||||
\(616\) | 9385.43 | 0.613880 | ||||||||
\(617\) | 22516.4 | 1.46917 | 0.734584 | − | 0.678518i | \(-0.237377\pi\) | ||||
0.734584 | + | 0.678518i | \(0.237377\pi\) | |||||||
\(618\) | 8359.35 | 0.544114 | ||||||||
\(619\) | 5146.53 | 0.334179 | 0.167089 | − | 0.985942i | \(-0.446563\pi\) | ||||
0.167089 | + | 0.985942i | \(0.446563\pi\) | |||||||
\(620\) | −535.736 | −0.0347027 | ||||||||
\(621\) | 27237.4 | 1.76006 | ||||||||
\(622\) | −44969.9 | −2.89892 | ||||||||
\(623\) | −4312.60 | −0.277337 | ||||||||
\(624\) | 6666.45 | 0.427679 | ||||||||
\(625\) | 15331.4 | 0.981213 | ||||||||
\(626\) | −13229.0 | −0.844627 | ||||||||
\(627\) | 29524.3 | 1.88052 | ||||||||
\(628\) | −4556.62 | −0.289536 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −762.990 | −0.0482512 | ||||||||
\(631\) | −3858.77 | −0.243447 | −0.121724 | − | 0.992564i | \(-0.538842\pi\) | ||||
−0.121724 | + | 0.992564i | \(0.538842\pi\) | |||||||
\(632\) | 50695.8 | 3.19078 | ||||||||
\(633\) | −23790.3 | −1.49381 | ||||||||
\(634\) | 21481.5 | 1.34564 | ||||||||
\(635\) | −1707.36 | −0.106700 | ||||||||
\(636\) | 48450.7 | 3.02075 | ||||||||
\(637\) | 2647.15 | 0.164653 | ||||||||
\(638\) | −10879.9 | −0.675138 | ||||||||
\(639\) | 30046.3 | 1.86011 | ||||||||
\(640\) | −1705.28 | −0.105324 | ||||||||
\(641\) | −18689.3 | −1.15161 | −0.575805 | − | 0.817587i | \(-0.695311\pi\) | ||||
−0.575805 | + | 0.817587i | \(0.695311\pi\) | |||||||
\(642\) | 20692.6 | 1.27208 | ||||||||
\(643\) | −26473.5 | −1.62366 | −0.811831 | − | 0.583893i | \(-0.801529\pi\) | ||||
−0.811831 | + | 0.583893i | \(0.801529\pi\) | |||||||
\(644\) | 11923.0 | 0.729555 | ||||||||
\(645\) | 2083.96 | 0.127219 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14397.7 | 0.874855 | 0.437427 | − | 0.899254i | \(-0.355890\pi\) | ||||
0.437427 | + | 0.899254i | \(0.355890\pi\) | |||||||
\(648\) | −3305.12 | −0.200366 | ||||||||
\(649\) | 35542.6 | 2.14972 | ||||||||
\(650\) | −5038.59 | −0.304046 | ||||||||
\(651\) | 1129.78 | 0.0680177 | ||||||||
\(652\) | 25036.0 | 1.50381 | ||||||||
\(653\) | −20939.5 | −1.25486 | −0.627431 | − | 0.778672i | \(-0.715893\pi\) | ||||
−0.627431 | + | 0.778672i | \(0.715893\pi\) | |||||||
\(654\) | 53533.6 | 3.20081 | ||||||||
\(655\) | −360.244 | −0.0214899 | ||||||||
\(656\) | 1747.59 | 0.104012 | ||||||||
\(657\) | −8674.02 | −0.515077 | ||||||||
\(658\) | 8911.96 | 0.528001 | ||||||||
\(659\) | 4031.76 | 0.238323 | 0.119162 | − | 0.992875i | \(-0.461979\pi\) | ||||
0.119162 | + | 0.992875i | \(0.461979\pi\) | |||||||
\(660\) | 6811.47 | 0.401721 | ||||||||
\(661\) | 6691.52 | 0.393752 | 0.196876 | − | 0.980428i | \(-0.436920\pi\) | ||||
0.196876 | + | 0.980428i | \(0.436920\pi\) | |||||||
\(662\) | −4993.75 | −0.293184 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 40629.2 | 2.37458 | ||||||||
\(665\) | −224.943 | −0.0131171 | ||||||||
\(666\) | 29413.1 | 1.71131 | ||||||||
\(667\) | −7439.71 | −0.431884 | ||||||||
\(668\) | 8690.19 | 0.503344 | ||||||||
\(669\) | −39701.1 | −2.29437 | ||||||||
\(670\) | 68.6083 | 0.00395607 | ||||||||
\(671\) | −17821.2 | −1.02530 | ||||||||
\(672\) | −3742.01 | −0.214808 | ||||||||
\(673\) | −10319.2 | −0.591048 | −0.295524 | − | 0.955335i | \(-0.595494\pi\) | ||||
−0.295524 | + | 0.955335i | \(0.595494\pi\) | |||||||
\(674\) | 40472.7 | 2.31298 | ||||||||
\(675\) | 18772.6 | 1.07046 | ||||||||
\(676\) | −36939.9 | −2.10172 | ||||||||
\(677\) | 19813.3 | 1.12480 | 0.562398 | − | 0.826866i | \(-0.309879\pi\) | ||||
0.562398 | + | 0.826866i | \(0.309879\pi\) | |||||||
\(678\) | 43221.8 | 2.44826 | ||||||||
\(679\) | −1448.70 | −0.0818793 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11829.3 | −0.665636 | ||||||||
\(682\) | −9201.33 | −0.516624 | ||||||||
\(683\) | −5924.61 | −0.331916 | −0.165958 | − | 0.986133i | \(-0.553072\pi\) | ||||
−0.165958 | + | 0.986133i | \(0.553072\pi\) | |||||||
\(684\) | −51666.4 | −2.88818 | ||||||||
\(685\) | 115.629 | 0.00644957 | ||||||||
\(686\) | −12901.7 | −0.718061 | ||||||||
\(687\) | −7582.38 | −0.421085 | ||||||||
\(688\) | 27091.9 | 1.50126 | ||||||||
\(689\) | 2659.43 | 0.147048 | ||||||||
\(690\) | 6808.33 | 0.375636 | ||||||||
\(691\) | −1973.16 | −0.108629 | −0.0543143 | − | 0.998524i | \(-0.517297\pi\) | ||||
−0.0543143 | + | 0.998524i | \(0.517297\pi\) | |||||||
\(692\) | 44877.1 | 2.46528 | ||||||||
\(693\) | −8965.03 | −0.491419 | ||||||||
\(694\) | −37311.8 | −2.04083 | ||||||||
\(695\) | 1836.51 | 0.100234 | ||||||||
\(696\) | 16420.4 | 0.894274 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 4323.90 | 0.234473 | ||||||||
\(699\) | 10137.6 | 0.548554 | ||||||||
\(700\) | 8217.63 | 0.443710 | ||||||||
\(701\) | −12840.1 | −0.691815 | −0.345907 | − | 0.938269i | \(-0.612429\pi\) | ||||
−0.345907 | + | 0.938269i | \(0.612429\pi\) | |||||||
\(702\) | −6130.30 | −0.329591 | ||||||||
\(703\) | 8671.50 | 0.465223 | ||||||||
\(704\) | −10410.0 | −0.557302 | ||||||||
\(705\) | 3481.45 | 0.185984 | ||||||||
\(706\) | −2863.92 | −0.152670 | ||||||||
\(707\) | −502.990 | −0.0267566 | ||||||||
\(708\) | −99657.5 | −5.29005 | ||||||||
\(709\) | 27749.7 | 1.46990 | 0.734952 | − | 0.678119i | \(-0.237204\pi\) | ||||
0.734952 | + | 0.678119i | \(0.237204\pi\) | |||||||
\(710\) | 2987.26 | 0.157901 | ||||||||
\(711\) | −48425.0 | −2.55426 | ||||||||
\(712\) | −53010.0 | −2.79022 | ||||||||
\(713\) | −6291.92 | −0.330483 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 373.877 | 0.0195555 | ||||||||
\(716\) | 37522.4 | 1.95849 | ||||||||
\(717\) | −41943.0 | −2.18464 | ||||||||
\(718\) | 25188.8 | 1.30924 | ||||||||
\(719\) | −16888.3 | −0.875979 | −0.437989 | − | 0.898980i | \(-0.644309\pi\) | ||||
−0.437989 | + | 0.898980i | \(0.644309\pi\) | |||||||
\(720\) | −3874.85 | −0.200565 | ||||||||
\(721\) | −748.339 | −0.0386541 | ||||||||
\(722\) | 12252.7 | 0.631575 | ||||||||
\(723\) | −56808.0 | −2.92215 | ||||||||
\(724\) | 33362.6 | 1.71258 | ||||||||
\(725\) | −5127.62 | −0.262669 | ||||||||
\(726\) | 60217.6 | 3.07835 | ||||||||
\(727\) | 2135.25 | 0.108930 | 0.0544649 | − | 0.998516i | \(-0.482655\pi\) | ||||
0.0544649 | + | 0.998516i | \(0.482655\pi\) | |||||||
\(728\) | −1444.45 | −0.0735371 | ||||||||
\(729\) | −31426.5 | −1.59663 | ||||||||
\(730\) | −862.386 | −0.0437238 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 49968.6 | 2.52308 | ||||||||
\(733\) | 4795.27 | 0.241633 | 0.120817 | − | 0.992675i | \(-0.461449\pi\) | ||||
0.120817 | + | 0.992675i | \(0.461449\pi\) | |||||||
\(734\) | −55233.1 | −2.77751 | ||||||||
\(735\) | −2465.30 | −0.123720 | ||||||||
\(736\) | 20839.9 | 1.04371 | ||||||||
\(737\) | 806.138 | 0.0402910 | ||||||||
\(738\) | −4040.36 | −0.201528 | ||||||||
\(739\) | −32747.6 | −1.63010 | −0.815048 | − | 0.579393i | \(-0.803290\pi\) | ||||
−0.815048 | + | 0.579393i | \(0.803290\pi\) | |||||||
\(740\) | 2000.58 | 0.0993821 | ||||||||
\(741\) | −4543.89 | −0.225269 | ||||||||
\(742\) | −6340.05 | −0.313680 | ||||||||
\(743\) | −12299.4 | −0.607298 | −0.303649 | − | 0.952784i | \(-0.598205\pi\) | ||||
−0.303649 | + | 0.952784i | \(0.598205\pi\) | |||||||
\(744\) | 13887.1 | 0.684309 | ||||||||
\(745\) | 1640.94 | 0.0806974 | ||||||||
\(746\) | 16163.0 | 0.793257 | ||||||||
\(747\) | −38809.3 | −1.90088 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1852.43 | −0.0903688 | ||||||||
\(750\) | 9414.54 | 0.458361 | ||||||||
\(751\) | −30102.6 | −1.46266 | −0.731332 | − | 0.682021i | \(-0.761101\pi\) | ||||
−0.731332 | + | 0.682021i | \(0.761101\pi\) | |||||||
\(752\) | 45259.4 | 2.19474 | ||||||||
\(753\) | 40309.4 | 1.95081 | ||||||||
\(754\) | 1674.45 | 0.0808753 | ||||||||
\(755\) | −1816.42 | −0.0875581 | ||||||||
\(756\) | 9998.14 | 0.480990 | ||||||||
\(757\) | 38826.3 | 1.86416 | 0.932078 | − | 0.362257i | \(-0.117994\pi\) | ||||
0.932078 | + | 0.362257i | \(0.117994\pi\) | |||||||
\(758\) | 40519.2 | 1.94159 | ||||||||
\(759\) | 79996.9 | 3.82570 | ||||||||
\(760\) | −2764.97 | −0.131968 | ||||||||
\(761\) | 19981.6 | 0.951815 | 0.475907 | − | 0.879495i | \(-0.342120\pi\) | ||||
0.475907 | + | 0.879495i | \(0.342120\pi\) | |||||||
\(762\) | 82221.8 | 3.90890 | ||||||||
\(763\) | −4792.39 | −0.227387 | ||||||||
\(764\) | −48227.7 | −2.28379 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13004.8 | 0.613424 | ||||||||
\(767\) | −5470.14 | −0.257517 | ||||||||
\(768\) | 68644.2 | 3.22524 | ||||||||
\(769\) | −22407.7 | −1.05077 | −0.525384 | − | 0.850865i | \(-0.676078\pi\) | ||||
−0.525384 | + | 0.850865i | \(0.676078\pi\) | |||||||
\(770\) | −891.320 | −0.0417155 | ||||||||
\(771\) | −24517.9 | −1.14525 | ||||||||
\(772\) | −39127.0 | −1.82411 | ||||||||
\(773\) | −6902.77 | −0.321184 | −0.160592 | − | 0.987021i | \(-0.551340\pi\) | ||||
−0.160592 | + | 0.987021i | \(0.551340\pi\) | |||||||
\(774\) | −62635.4 | −2.90876 | ||||||||
\(775\) | −4336.54 | −0.200997 | ||||||||
\(776\) | −17807.3 | −0.823768 | ||||||||
\(777\) | −4218.89 | −0.194790 | ||||||||
\(778\) | 26039.8 | 1.19996 | ||||||||
\(779\) | −1191.17 | −0.0547856 | ||||||||
\(780\) | −1048.31 | −0.0481225 | ||||||||
\(781\) | 35099.9 | 1.60816 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6238.62 | −0.284738 | ||||||||
\(784\) | −32049.3 | −1.45997 | ||||||||
\(785\) | 232.928 | 0.0105905 | ||||||||
\(786\) | 17348.3 | 0.787270 | ||||||||
\(787\) | 22185.9 | 1.00488 | 0.502442 | − | 0.864611i | \(-0.332435\pi\) | ||||
0.502442 | + | 0.864611i | \(0.332435\pi\) | |||||||
\(788\) | 22016.3 | 0.995301 | ||||||||
\(789\) | −45898.1 | −2.07099 | ||||||||
\(790\) | −4814.50 | −0.216826 | ||||||||
\(791\) | −3869.27 | −0.173926 | ||||||||
\(792\) | −110197. | −4.94405 | ||||||||
\(793\) | 2742.74 | 0.122822 | ||||||||
\(794\) | −25914.2 | −1.15826 | ||||||||
\(795\) | −2476.73 | −0.110491 | ||||||||
\(796\) | 83067.8 | 3.69882 | ||||||||
\(797\) | −16291.1 | −0.724040 | −0.362020 | − | 0.932170i | \(-0.617913\pi\) | ||||
−0.362020 | + | 0.932170i | \(0.617913\pi\) | |||||||
\(798\) | 10832.6 | 0.480539 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 14363.3 | 0.634775 | ||||||||
\(801\) | 50635.5 | 2.23361 | ||||||||
\(802\) | 43785.3 | 1.92782 | ||||||||
\(803\) | −10132.9 | −0.445309 | ||||||||
\(804\) | −2260.32 | −0.0991485 | ||||||||
\(805\) | −609.489 | −0.0266853 | ||||||||
\(806\) | 1416.12 | 0.0618867 | ||||||||
\(807\) | 49046.8 | 2.13944 | ||||||||
\(808\) | −6182.70 | −0.269191 | ||||||||
\(809\) | −17696.8 | −0.769082 | −0.384541 | − | 0.923108i | \(-0.625640\pi\) | ||||
−0.384541 | + | 0.923108i | \(0.625640\pi\) | |||||||
\(810\) | 313.882 | 0.0136157 | ||||||||
\(811\) | 3095.34 | 0.134022 | 0.0670111 | − | 0.997752i | \(-0.478654\pi\) | ||||
0.0670111 | + | 0.997752i | \(0.478654\pi\) | |||||||
\(812\) | −2730.93 | −0.118026 | ||||||||
\(813\) | −46318.9 | −1.99812 | ||||||||
\(814\) | 34360.2 | 1.47951 | ||||||||
\(815\) | −1279.81 | −0.0550057 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18466.0 | −0.790751 | ||||||||
\(818\) | −62131.5 | −2.65572 | ||||||||
\(819\) | 1379.75 | 0.0588674 | ||||||||
\(820\) | −274.811 | −0.0117034 | ||||||||
\(821\) | −12323.5 | −0.523864 | −0.261932 | − | 0.965086i | \(-0.584360\pi\) | ||||
−0.261932 | + | 0.965086i | \(0.584360\pi\) | |||||||
\(822\) | −5568.36 | −0.236276 | ||||||||
\(823\) | 34436.5 | 1.45854 | 0.729271 | − | 0.684225i | \(-0.239860\pi\) | ||||
0.729271 | + | 0.684225i | \(0.239860\pi\) | |||||||
\(824\) | −9198.50 | −0.388889 | ||||||||
\(825\) | 55135.7 | 2.32676 | ||||||||
\(826\) | 13040.8 | 0.549329 | ||||||||
\(827\) | −18761.6 | −0.788880 | −0.394440 | − | 0.918922i | \(-0.629061\pi\) | ||||
−0.394440 | + | 0.918922i | \(0.629061\pi\) | |||||||
\(828\) | −139992. | −5.87567 | ||||||||
\(829\) | 22423.8 | 0.939457 | 0.469728 | − | 0.882811i | \(-0.344352\pi\) | ||||
0.469728 | + | 0.882811i | \(0.344352\pi\) | |||||||
\(830\) | −3858.49 | −0.161362 | ||||||||
\(831\) | −10235.3 | −0.427265 | ||||||||
\(832\) | 1602.13 | 0.0667596 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −88441.1 | −3.67202 | ||||||||
\(835\) | −444.231 | −0.0184111 | ||||||||
\(836\) | −60356.4 | −2.49697 | ||||||||
\(837\) | −5276.13 | −0.217885 | ||||||||
\(838\) | −29004.0 | −1.19562 | ||||||||
\(839\) | −9128.63 | −0.375632 | −0.187816 | − | 0.982204i | \(-0.560141\pi\) | ||||
−0.187816 | + | 0.982204i | \(0.560141\pi\) | |||||||
\(840\) | 1345.22 | 0.0552555 | ||||||||
\(841\) | −22685.0 | −0.930131 | ||||||||
\(842\) | 9441.58 | 0.386435 | ||||||||
\(843\) | 10146.5 | 0.414547 | ||||||||
\(844\) | 48634.4 | 1.98349 | ||||||||
\(845\) | 1888.32 | 0.0768759 | ||||||||
\(846\) | −104638. | −4.25240 | ||||||||
\(847\) | −5390.75 | −0.218688 | ||||||||
\(848\) | −32198.0 | −1.30387 | ||||||||
\(849\) | 26822.2 | 1.08426 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23495.7 | 0.946442 | ||||||||
\(852\) | −98416.1 | −3.95737 | ||||||||
\(853\) | −27204.8 | −1.09200 | −0.545999 | − | 0.837786i | \(-0.683850\pi\) | ||||
−0.545999 | + | 0.837786i | \(0.683850\pi\) | |||||||
\(854\) | −6538.68 | −0.262001 | ||||||||
\(855\) | 2641.12 | 0.105643 | ||||||||
\(856\) | −22769.8 | −0.909179 | ||||||||
\(857\) | 38060.0 | 1.51704 | 0.758520 | − | 0.651649i | \(-0.225923\pi\) | ||||
0.758520 | + | 0.651649i | \(0.225923\pi\) | |||||||
\(858\) | −18004.9 | −0.716405 | ||||||||
\(859\) | −33326.2 | −1.32372 | −0.661860 | − | 0.749627i | \(-0.730233\pi\) | ||||
−0.661860 | + | 0.749627i | \(0.730233\pi\) | |||||||
\(860\) | −4260.24 | −0.168922 | ||||||||
\(861\) | 579.531 | 0.0229389 | ||||||||
\(862\) | 422.378 | 0.0166894 | ||||||||
\(863\) | −41724.2 | −1.64578 | −0.822890 | − | 0.568201i | \(-0.807640\pi\) | ||||
−0.822890 | + | 0.568201i | \(0.807640\pi\) | |||||||
\(864\) | 17475.4 | 0.688108 | ||||||||
\(865\) | −2294.06 | −0.0901737 | ||||||||
\(866\) | 77223.8 | 3.03022 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2309.60 | −0.0903146 | ||||||||
\(869\) | −56569.7 | −2.20828 | ||||||||
\(870\) | −1559.42 | −0.0607694 | ||||||||
\(871\) | −124.068 | −0.00482649 | ||||||||
\(872\) | −58907.5 | −2.28768 | ||||||||
\(873\) | 17009.6 | 0.659438 | ||||||||
\(874\) | −60328.6 | −2.33483 | ||||||||
\(875\) | −842.801 | −0.0325621 | ||||||||
\(876\) | 28411.6 | 1.09582 | ||||||||
\(877\) | 49337.3 | 1.89966 | 0.949830 | − | 0.312767i | \(-0.101256\pi\) | ||||
0.949830 | + | 0.312767i | \(0.101256\pi\) | |||||||
\(878\) | 15423.3 | 0.592838 | ||||||||
\(879\) | −63194.0 | −2.42489 | ||||||||
\(880\) | −4526.57 | −0.173398 | ||||||||
\(881\) | −8845.46 | −0.338265 | −0.169132 | − | 0.985593i | \(-0.554097\pi\) | ||||
−0.169132 | + | 0.985593i | \(0.554097\pi\) | |||||||
\(882\) | 74096.8 | 2.82876 | ||||||||
\(883\) | 14724.2 | 0.561165 | 0.280582 | − | 0.959830i | \(-0.409472\pi\) | ||||
0.280582 | + | 0.959830i | \(0.409472\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5094.36 | 0.193497 | ||||||||
\(886\) | 9023.14 | 0.342143 | ||||||||
\(887\) | −3864.38 | −0.146283 | −0.0731415 | − | 0.997322i | \(-0.523302\pi\) | ||||
−0.0731415 | + | 0.997322i | \(0.523302\pi\) | |||||||
\(888\) | −51858.1 | −1.95974 | ||||||||
\(889\) | −7360.60 | −0.277690 | ||||||||
\(890\) | 5034.28 | 0.189606 | ||||||||
\(891\) | 3688.07 | 0.138670 | ||||||||
\(892\) | 81160.9 | 3.04649 | ||||||||
\(893\) | −30849.1 | −1.15602 | ||||||||
\(894\) | −79023.2 | −2.95630 | ||||||||
\(895\) | −1918.10 | −0.0716368 | ||||||||
\(896\) | −7351.61 | −0.274107 | ||||||||
\(897\) | −12311.8 | −0.458283 | ||||||||
\(898\) | 12577.2 | 0.467379 | ||||||||
\(899\) | 1441.14 | 0.0534648 | ||||||||
\(900\) | −96485.6 | −3.57354 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −4719.92 | −0.174231 | ||||||||
\(903\) | 8984.15 | 0.331089 | ||||||||
\(904\) | −47560.6 | −1.74982 | ||||||||
\(905\) | −1705.45 | −0.0626421 | ||||||||
\(906\) | 87473.7 | 3.20764 | ||||||||
\(907\) | 743.409 | 0.0272155 | 0.0136078 | − | 0.999907i | \(-0.495668\pi\) | ||||
0.0136078 | + | 0.999907i | \(0.495668\pi\) | |||||||
\(908\) | 24182.5 | 0.883839 | ||||||||
\(909\) | 5905.76 | 0.215491 | ||||||||
\(910\) | 137.177 | 0.00499713 | ||||||||
\(911\) | −16291.0 | −0.592475 | −0.296238 | − | 0.955114i | \(-0.595732\pi\) | ||||
−0.296238 | + | 0.955114i | \(0.595732\pi\) | |||||||
\(912\) | 55013.4 | 1.99745 | ||||||||
\(913\) | −45336.8 | −1.64340 | ||||||||
\(914\) | −74402.5 | −2.69258 | ||||||||
\(915\) | −2554.33 | −0.0922879 | ||||||||
\(916\) | 15500.6 | 0.559122 | ||||||||
\(917\) | −1553.04 | −0.0559280 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6188.99 | −0.222150 | −0.111075 | − | 0.993812i | \(-0.535429\pi\) | ||||
−0.111075 | + | 0.993812i | \(0.535429\pi\) | |||||||
\(920\) | −7491.78 | −0.268474 | ||||||||
\(921\) | 55390.5 | 1.98174 | ||||||||
\(922\) | 89311.6 | 3.19015 | ||||||||
\(923\) | −5402.00 | −0.192643 | ||||||||
\(924\) | 29364.8 | 1.04549 | ||||||||
\(925\) | 16193.8 | 0.575620 | ||||||||
\(926\) | −93033.0 | −3.30157 | ||||||||
\(927\) | 8786.47 | 0.311311 | ||||||||
\(928\) | −4773.30 | −0.168848 | ||||||||
\(929\) | 31661.7 | 1.11818 | 0.559089 | − | 0.829108i | \(-0.311151\pi\) | ||||
0.559089 | + | 0.829108i | \(0.311151\pi\) | |||||||
\(930\) | −1318.84 | −0.0465015 | ||||||||
\(931\) | 21845.0 | 0.769003 | ||||||||
\(932\) | −20724.3 | −0.728376 | ||||||||
\(933\) | −75734.8 | −2.65750 | ||||||||
\(934\) | −37273.6 | −1.30581 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 16959.8 | 0.592251 | ||||||||
\(937\) | 35010.5 | 1.22064 | 0.610322 | − | 0.792153i | \(-0.291040\pi\) | ||||
0.610322 | + | 0.792153i | \(0.291040\pi\) | |||||||
\(938\) | 295.776 | 0.0102958 | ||||||||
\(939\) | −22279.2 | −0.774286 | ||||||||
\(940\) | −7117.12 | −0.246952 | ||||||||
\(941\) | 45625.8 | 1.58061 | 0.790307 | − | 0.612711i | \(-0.209921\pi\) | ||||
0.790307 | + | 0.612711i | \(0.209921\pi\) | |||||||
\(942\) | −11217.2 | −0.387977 | ||||||||
\(943\) | −3227.51 | −0.111455 | ||||||||
\(944\) | 66227.5 | 2.28339 | ||||||||
\(945\) | −511.092 | −0.0175934 | ||||||||
\(946\) | −73170.2 | −2.51477 | ||||||||
\(947\) | 21508.4 | 0.738044 | 0.369022 | − | 0.929421i | \(-0.379693\pi\) | ||||
0.369022 | + | 0.929421i | \(0.379693\pi\) | |||||||
\(948\) | 158615. | 5.43416 | ||||||||
\(949\) | 1559.50 | 0.0533439 | ||||||||
\(950\) | −41579.8 | −1.42003 | ||||||||
\(951\) | 36177.4 | 1.23358 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35686.7 | 1.21302 | 0.606509 | − | 0.795076i | \(-0.292569\pi\) | ||||
0.606509 | + | 0.795076i | \(0.292569\pi\) | |||||||
\(954\) | 74440.5 | 2.52631 | ||||||||
\(955\) | 2465.34 | 0.0835355 | ||||||||
\(956\) | 85744.0 | 2.90079 | ||||||||
\(957\) | −18323.0 | −0.618912 | ||||||||
\(958\) | −93357.8 | −3.14849 | ||||||||
\(959\) | 498.486 | 0.0167851 | ||||||||
\(960\) | −1492.07 | −0.0501630 | ||||||||
\(961\) | −28572.2 | −0.959088 | ||||||||
\(962\) | −5288.17 | −0.177232 | ||||||||
\(963\) | 21749.9 | 0.727810 | ||||||||
\(964\) | 116133. | 3.88006 | ||||||||
\(965\) | 2000.12 | 0.0667215 | ||||||||
\(966\) | 29351.3 | 0.977600 | ||||||||
\(967\) | −3731.33 | −0.124086 | −0.0620432 | − | 0.998073i | \(-0.519762\pi\) | ||||
−0.0620432 | + | 0.998073i | \(0.519762\pi\) | |||||||
\(968\) | −66262.5 | −2.20016 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1691.13 | 0.0559782 | ||||||||
\(971\) | 17645.1 | 0.583171 | 0.291585 | − | 0.956545i | \(-0.405817\pi\) | ||||
0.291585 | + | 0.956545i | \(0.405817\pi\) | |||||||
\(972\) | 60358.3 | 1.99176 | ||||||||
\(973\) | 7917.35 | 0.260862 | ||||||||
\(974\) | 51348.7 | 1.68924 | ||||||||
\(975\) | −8485.59 | −0.278725 | ||||||||
\(976\) | −33206.7 | −1.08906 | ||||||||
\(977\) | 24941.2 | 0.816723 | 0.408362 | − | 0.912820i | \(-0.366100\pi\) | ||||
0.408362 | + | 0.912820i | \(0.366100\pi\) | |||||||
\(978\) | 61631.8 | 2.01510 | ||||||||
\(979\) | 59152.1 | 1.93106 | ||||||||
\(980\) | 5039.81 | 0.164276 | ||||||||
\(981\) | 56268.9 | 1.83132 | ||||||||
\(982\) | 6277.85 | 0.204006 | ||||||||
\(983\) | 22506.2 | 0.730252 | 0.365126 | − | 0.930958i | \(-0.381026\pi\) | ||||
0.365126 | + | 0.930958i | \(0.381026\pi\) | |||||||
\(984\) | 7123.53 | 0.230782 | ||||||||
\(985\) | −1125.44 | −0.0364057 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15008.8 | 0.484029 | ||||||||
\(988\) | 9289.07 | 0.299114 | ||||||||
\(989\) | −50034.2 | −1.60869 | ||||||||
\(990\) | 10465.3 | 0.335967 | ||||||||
\(991\) | −32694.1 | −1.04799 | −0.523997 | − | 0.851720i | \(-0.675560\pi\) | ||||
−0.523997 | + | 0.851720i | \(0.675560\pi\) | |||||||
\(992\) | −4036.88 | −0.129205 | ||||||||
\(993\) | −8410.08 | −0.268767 | ||||||||
\(994\) | 12878.3 | 0.410941 | ||||||||
\(995\) | −4246.32 | −0.135294 | ||||||||
\(996\) | 127119. | 4.04410 | ||||||||
\(997\) | −18248.8 | −0.579686 | −0.289843 | − | 0.957074i | \(-0.593603\pi\) | ||||
−0.289843 | + | 0.957074i | \(0.593603\pi\) | |||||||
\(998\) | 352.428 | 0.0111783 | ||||||||
\(999\) | 19702.5 | 0.623983 |
(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 | 289.4.a.b.1.1 | 3 | ||
17.4 | even | 4 | 289.4.b.b.288.6 | 6 | |||
17.13 | even | 4 | 289.4.b.b.288.5 | 6 | |||
17.16 | even | 2 | 17.4.a.b.1.1 | ✓ | 3 | ||
51.50 | odd | 2 | 153.4.a.g.1.3 | 3 | |||
68.67 | odd | 2 | 272.4.a.h.1.1 | 3 | |||
85.33 | odd | 4 | 425.4.b.f.324.6 | 6 | |||
85.67 | odd | 4 | 425.4.b.f.324.1 | 6 | |||
85.84 | even | 2 | 425.4.a.g.1.3 | 3 | |||
119.118 | odd | 2 | 833.4.a.d.1.1 | 3 | |||
136.67 | odd | 2 | 1088.4.a.x.1.3 | 3 | |||
136.101 | even | 2 | 1088.4.a.v.1.1 | 3 | |||
187.186 | odd | 2 | 2057.4.a.e.1.3 | 3 | |||
204.203 | even | 2 | 2448.4.a.bi.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.a.b.1.1 | ✓ | 3 | 17.16 | even | 2 | ||
153.4.a.g.1.3 | 3 | 51.50 | odd | 2 | |||
272.4.a.h.1.1 | 3 | 68.67 | odd | 2 | |||
289.4.a.b.1.1 | 3 | 1.1 | even | 1 | trivial | ||
289.4.b.b.288.5 | 6 | 17.13 | even | 4 | |||
289.4.b.b.288.6 | 6 | 17.4 | even | 4 | |||
425.4.a.g.1.3 | 3 | 85.84 | even | 2 | |||
425.4.b.f.324.1 | 6 | 85.67 | odd | 4 | |||
425.4.b.f.324.6 | 6 | 85.33 | odd | 4 | |||
833.4.a.d.1.1 | 3 | 119.118 | odd | 2 | |||
1088.4.a.v.1.1 | 3 | 136.101 | even | 2 | |||
1088.4.a.x.1.3 | 3 | 136.67 | odd | 2 | |||
2057.4.a.e.1.3 | 3 | 187.186 | odd | 2 | |||
2448.4.a.bi.1.2 | 3 | 204.203 | even | 2 |