Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.97637 | −1.14106 | −0.570528 | − | 0.821278i | \(-0.693262\pi\) | ||||
−0.570528 | + | 0.821278i | \(0.693262\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.168031 | −0.0751460 | −0.0375730 | − | 0.999294i | \(-0.511963\pi\) | ||||
−0.0375730 | + | 0.999294i | \(0.511963\pi\) | |||||||
\(6\) | −1.97637 | −0.806849 | ||||||||
\(7\) | −1.30361 | −0.492718 | −0.246359 | − | 0.969179i | \(-0.579234\pi\) | ||||
−0.246359 | + | 0.969179i | \(0.579234\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.906032 | 0.302011 | ||||||||
\(10\) | −0.168031 | −0.0531362 | ||||||||
\(11\) | −4.48117 | −1.35113 | −0.675563 | − | 0.737303i | \(-0.736099\pi\) | ||||
−0.675563 | + | 0.737303i | \(0.736099\pi\) | |||||||
\(12\) | −1.97637 | −0.570528 | ||||||||
\(13\) | 2.33495 | 0.647599 | 0.323800 | − | 0.946126i | \(-0.395040\pi\) | ||||
0.323800 | + | 0.946126i | \(0.395040\pi\) | |||||||
\(14\) | −1.30361 | −0.348404 | ||||||||
\(15\) | 0.332092 | 0.0857458 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.76866 | 0.914033 | 0.457017 | − | 0.889458i | \(-0.348918\pi\) | ||||
0.457017 | + | 0.889458i | \(0.348918\pi\) | |||||||
\(18\) | 0.906032 | 0.213554 | ||||||||
\(19\) | 1.05517 | 0.242073 | 0.121036 | − | 0.992648i | \(-0.461378\pi\) | ||||
0.121036 | + | 0.992648i | \(0.461378\pi\) | |||||||
\(20\) | −0.168031 | −0.0375730 | ||||||||
\(21\) | 2.57641 | 0.562220 | ||||||||
\(22\) | −4.48117 | −0.955390 | ||||||||
\(23\) | 4.38036 | 0.913368 | 0.456684 | − | 0.889629i | \(-0.349037\pi\) | ||||
0.456684 | + | 0.889629i | \(0.349037\pi\) | |||||||
\(24\) | −1.97637 | −0.403425 | ||||||||
\(25\) | −4.97177 | −0.994353 | ||||||||
\(26\) | 2.33495 | 0.457922 | ||||||||
\(27\) | 4.13845 | 0.796446 | ||||||||
\(28\) | −1.30361 | −0.246359 | ||||||||
\(29\) | −6.31021 | −1.17178 | −0.585888 | − | 0.810392i | \(-0.699254\pi\) | ||||
−0.585888 | + | 0.810392i | \(0.699254\pi\) | |||||||
\(30\) | 0.332092 | 0.0606314 | ||||||||
\(31\) | 1.19262 | 0.214201 | 0.107100 | − | 0.994248i | \(-0.465843\pi\) | ||||
0.107100 | + | 0.994248i | \(0.465843\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 8.85645 | 1.54171 | ||||||||
\(34\) | 3.76866 | 0.646319 | ||||||||
\(35\) | 0.219048 | 0.0370258 | ||||||||
\(36\) | 0.906032 | 0.151005 | ||||||||
\(37\) | −5.98531 | −0.983979 | −0.491990 | − | 0.870601i | \(-0.663730\pi\) | ||||
−0.491990 | + | 0.870601i | \(0.663730\pi\) | |||||||
\(38\) | 1.05517 | 0.171171 | ||||||||
\(39\) | −4.61472 | −0.738947 | ||||||||
\(40\) | −0.168031 | −0.0265681 | ||||||||
\(41\) | 7.86206 | 1.22785 | 0.613923 | − | 0.789366i | \(-0.289590\pi\) | ||||
0.613923 | + | 0.789366i | \(0.289590\pi\) | |||||||
\(42\) | 2.57641 | 0.397549 | ||||||||
\(43\) | 2.84566 | 0.433959 | 0.216980 | − | 0.976176i | \(-0.430379\pi\) | ||||
0.216980 | + | 0.976176i | \(0.430379\pi\) | |||||||
\(44\) | −4.48117 | −0.675563 | ||||||||
\(45\) | −0.152242 | −0.0226949 | ||||||||
\(46\) | 4.38036 | 0.645849 | ||||||||
\(47\) | 6.14204 | 0.895908 | 0.447954 | − | 0.894057i | \(-0.352153\pi\) | ||||
0.447954 | + | 0.894057i | \(0.352153\pi\) | |||||||
\(48\) | −1.97637 | −0.285264 | ||||||||
\(49\) | −5.30060 | −0.757229 | ||||||||
\(50\) | −4.97177 | −0.703114 | ||||||||
\(51\) | −7.44825 | −1.04296 | ||||||||
\(52\) | 2.33495 | 0.323800 | ||||||||
\(53\) | −0.518989 | −0.0712887 | −0.0356443 | − | 0.999365i | \(-0.511348\pi\) | ||||
−0.0356443 | + | 0.999365i | \(0.511348\pi\) | |||||||
\(54\) | 4.13845 | 0.563172 | ||||||||
\(55\) | 0.752978 | 0.101532 | ||||||||
\(56\) | −1.30361 | −0.174202 | ||||||||
\(57\) | −2.08540 | −0.276219 | ||||||||
\(58\) | −6.31021 | −0.828571 | ||||||||
\(59\) | 5.21300 | 0.678674 | 0.339337 | − | 0.940665i | \(-0.389797\pi\) | ||||
0.339337 | + | 0.940665i | \(0.389797\pi\) | |||||||
\(60\) | 0.332092 | 0.0428729 | ||||||||
\(61\) | 7.76239 | 0.993873 | 0.496936 | − | 0.867787i | \(-0.334458\pi\) | ||||
0.496936 | + | 0.867787i | \(0.334458\pi\) | |||||||
\(62\) | 1.19262 | 0.151463 | ||||||||
\(63\) | −1.18111 | −0.148806 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.392345 | −0.0486645 | ||||||||
\(66\) | 8.85645 | 1.09015 | ||||||||
\(67\) | −5.81318 | −0.710193 | −0.355096 | − | 0.934830i | \(-0.615552\pi\) | ||||
−0.355096 | + | 0.934830i | \(0.615552\pi\) | |||||||
\(68\) | 3.76866 | 0.457017 | ||||||||
\(69\) | −8.65720 | −1.04220 | ||||||||
\(70\) | 0.219048 | 0.0261812 | ||||||||
\(71\) | −2.67321 | −0.317252 | −0.158626 | − | 0.987339i | \(-0.550706\pi\) | ||||
−0.158626 | + | 0.987339i | \(0.550706\pi\) | |||||||
\(72\) | 0.906032 | 0.106777 | ||||||||
\(73\) | −10.0953 | −1.18157 | −0.590785 | − | 0.806829i | \(-0.701182\pi\) | ||||
−0.590785 | + | 0.806829i | \(0.701182\pi\) | |||||||
\(74\) | −5.98531 | −0.695778 | ||||||||
\(75\) | 9.82604 | 1.13461 | ||||||||
\(76\) | 1.05517 | 0.121036 | ||||||||
\(77\) | 5.84170 | 0.665724 | ||||||||
\(78\) | −4.61472 | −0.522515 | ||||||||
\(79\) | 3.11698 | 0.350687 | 0.175344 | − | 0.984507i | \(-0.443896\pi\) | ||||
0.175344 | + | 0.984507i | \(0.443896\pi\) | |||||||
\(80\) | −0.168031 | −0.0187865 | ||||||||
\(81\) | −10.8972 | −1.21080 | ||||||||
\(82\) | 7.86206 | 0.868219 | ||||||||
\(83\) | 15.6884 | 1.72202 | 0.861011 | − | 0.508586i | \(-0.169832\pi\) | ||||
0.861011 | + | 0.508586i | \(0.169832\pi\) | |||||||
\(84\) | 2.57641 | 0.281110 | ||||||||
\(85\) | −0.633253 | −0.0686859 | ||||||||
\(86\) | 2.84566 | 0.306855 | ||||||||
\(87\) | 12.4713 | 1.33706 | ||||||||
\(88\) | −4.48117 | −0.477695 | ||||||||
\(89\) | −1.95686 | −0.207427 | −0.103713 | − | 0.994607i | \(-0.533072\pi\) | ||||
−0.103713 | + | 0.994607i | \(0.533072\pi\) | |||||||
\(90\) | −0.152242 | −0.0160477 | ||||||||
\(91\) | −3.04387 | −0.319084 | ||||||||
\(92\) | 4.38036 | 0.456684 | ||||||||
\(93\) | −2.35705 | −0.244415 | ||||||||
\(94\) | 6.14204 | 0.633503 | ||||||||
\(95\) | −0.177302 | −0.0181908 | ||||||||
\(96\) | −1.97637 | −0.201712 | ||||||||
\(97\) | 0.204240 | 0.0207374 | 0.0103687 | − | 0.999946i | \(-0.496699\pi\) | ||||
0.0103687 | + | 0.999946i | \(0.496699\pi\) | |||||||
\(98\) | −5.30060 | −0.535442 | ||||||||
\(99\) | −4.06009 | −0.408054 | ||||||||
\(100\) | −4.97177 | −0.497177 | ||||||||
\(101\) | 1.62093 | 0.161289 | 0.0806443 | − | 0.996743i | \(-0.474302\pi\) | ||||
0.0806443 | + | 0.996743i | \(0.474302\pi\) | |||||||
\(102\) | −7.44825 | −0.737487 | ||||||||
\(103\) | −19.5068 | −1.92206 | −0.961032 | − | 0.276437i | \(-0.910846\pi\) | ||||
−0.961032 | + | 0.276437i | \(0.910846\pi\) | |||||||
\(104\) | 2.33495 | 0.228961 | ||||||||
\(105\) | −0.432919 | −0.0422485 | ||||||||
\(106\) | −0.518989 | −0.0504087 | ||||||||
\(107\) | −15.1972 | −1.46917 | −0.734586 | − | 0.678515i | \(-0.762624\pi\) | ||||
−0.734586 | + | 0.678515i | \(0.762624\pi\) | |||||||
\(108\) | 4.13845 | 0.398223 | ||||||||
\(109\) | 10.6327 | 1.01843 | 0.509214 | − | 0.860640i | \(-0.329936\pi\) | ||||
0.509214 | + | 0.860640i | \(0.329936\pi\) | |||||||
\(110\) | 0.752978 | 0.0717937 | ||||||||
\(111\) | 11.8292 | 1.12278 | ||||||||
\(112\) | −1.30361 | −0.123180 | ||||||||
\(113\) | −3.37491 | −0.317485 | −0.158742 | − | 0.987320i | \(-0.550744\pi\) | ||||
−0.158742 | + | 0.987320i | \(0.550744\pi\) | |||||||
\(114\) | −2.08540 | −0.195316 | ||||||||
\(115\) | −0.736038 | −0.0686359 | ||||||||
\(116\) | −6.31021 | −0.585888 | ||||||||
\(117\) | 2.11554 | 0.195582 | ||||||||
\(118\) | 5.21300 | 0.479895 | ||||||||
\(119\) | −4.91286 | −0.450361 | ||||||||
\(120\) | 0.332092 | 0.0303157 | ||||||||
\(121\) | 9.08093 | 0.825539 | ||||||||
\(122\) | 7.76239 | 0.702774 | ||||||||
\(123\) | −15.5383 | −1.40104 | ||||||||
\(124\) | 1.19262 | 0.107100 | ||||||||
\(125\) | 1.67557 | 0.149868 | ||||||||
\(126\) | −1.18111 | −0.105222 | ||||||||
\(127\) | −8.66633 | −0.769013 | −0.384506 | − | 0.923122i | \(-0.625628\pi\) | ||||
−0.384506 | + | 0.923122i | \(0.625628\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.62407 | −0.495172 | ||||||||
\(130\) | −0.392345 | −0.0344110 | ||||||||
\(131\) | 13.8235 | 1.20777 | 0.603883 | − | 0.797073i | \(-0.293619\pi\) | ||||
0.603883 | + | 0.797073i | \(0.293619\pi\) | |||||||
\(132\) | 8.85645 | 0.770855 | ||||||||
\(133\) | −1.37553 | −0.119274 | ||||||||
\(134\) | −5.81318 | −0.502182 | ||||||||
\(135\) | −0.695390 | −0.0598497 | ||||||||
\(136\) | 3.76866 | 0.323160 | ||||||||
\(137\) | 3.07452 | 0.262674 | 0.131337 | − | 0.991338i | \(-0.458073\pi\) | ||||
0.131337 | + | 0.991338i | \(0.458073\pi\) | |||||||
\(138\) | −8.65720 | −0.736950 | ||||||||
\(139\) | −11.0174 | −0.934488 | −0.467244 | − | 0.884128i | \(-0.654753\pi\) | ||||
−0.467244 | + | 0.884128i | \(0.654753\pi\) | |||||||
\(140\) | 0.219048 | 0.0185129 | ||||||||
\(141\) | −12.1389 | −1.02228 | ||||||||
\(142\) | −2.67321 | −0.224331 | ||||||||
\(143\) | −10.4633 | −0.874987 | ||||||||
\(144\) | 0.906032 | 0.0755027 | ||||||||
\(145\) | 1.06031 | 0.0880542 | ||||||||
\(146\) | −10.0953 | −0.835496 | ||||||||
\(147\) | 10.4759 | 0.864041 | ||||||||
\(148\) | −5.98531 | −0.491990 | ||||||||
\(149\) | −13.8344 | −1.13336 | −0.566679 | − | 0.823939i | \(-0.691772\pi\) | ||||
−0.566679 | + | 0.823939i | \(0.691772\pi\) | |||||||
\(150\) | 9.82604 | 0.802293 | ||||||||
\(151\) | −2.43642 | −0.198273 | −0.0991366 | − | 0.995074i | \(-0.531608\pi\) | ||||
−0.0991366 | + | 0.995074i | \(0.531608\pi\) | |||||||
\(152\) | 1.05517 | 0.0855856 | ||||||||
\(153\) | 3.41452 | 0.276048 | ||||||||
\(154\) | 5.84170 | 0.470738 | ||||||||
\(155\) | −0.200398 | −0.0160963 | ||||||||
\(156\) | −4.61472 | −0.369474 | ||||||||
\(157\) | −18.6718 | −1.49017 | −0.745086 | − | 0.666968i | \(-0.767592\pi\) | ||||
−0.745086 | + | 0.666968i | \(0.767592\pi\) | |||||||
\(158\) | 3.11698 | 0.247973 | ||||||||
\(159\) | 1.02571 | 0.0813444 | ||||||||
\(160\) | −0.168031 | −0.0132841 | ||||||||
\(161\) | −5.71028 | −0.450033 | ||||||||
\(162\) | −10.8972 | −0.856165 | ||||||||
\(163\) | −0.807239 | −0.0632278 | −0.0316139 | − | 0.999500i | \(-0.510065\pi\) | ||||
−0.0316139 | + | 0.999500i | \(0.510065\pi\) | |||||||
\(164\) | 7.86206 | 0.613923 | ||||||||
\(165\) | −1.48816 | −0.115853 | ||||||||
\(166\) | 15.6884 | 1.21765 | ||||||||
\(167\) | 14.3175 | 1.10792 | 0.553960 | − | 0.832543i | \(-0.313116\pi\) | ||||
0.553960 | + | 0.832543i | \(0.313116\pi\) | |||||||
\(168\) | 2.57641 | 0.198775 | ||||||||
\(169\) | −7.54800 | −0.580615 | ||||||||
\(170\) | −0.633253 | −0.0485683 | ||||||||
\(171\) | 0.956017 | 0.0731085 | ||||||||
\(172\) | 2.84566 | 0.216980 | ||||||||
\(173\) | −15.2909 | −1.16254 | −0.581272 | − | 0.813709i | \(-0.697445\pi\) | ||||
−0.581272 | + | 0.813709i | \(0.697445\pi\) | |||||||
\(174\) | 12.4713 | 0.945446 | ||||||||
\(175\) | 6.48124 | 0.489936 | ||||||||
\(176\) | −4.48117 | −0.337781 | ||||||||
\(177\) | −10.3028 | −0.774406 | ||||||||
\(178\) | −1.95686 | −0.146673 | ||||||||
\(179\) | −9.35245 | −0.699035 | −0.349517 | − | 0.936930i | \(-0.613654\pi\) | ||||
−0.349517 | + | 0.936930i | \(0.613654\pi\) | |||||||
\(180\) | −0.152242 | −0.0113474 | ||||||||
\(181\) | 24.0169 | 1.78516 | 0.892580 | − | 0.450889i | \(-0.148893\pi\) | ||||
0.892580 | + | 0.450889i | \(0.148893\pi\) | |||||||
\(182\) | −3.04387 | −0.225626 | ||||||||
\(183\) | −15.3414 | −1.13407 | ||||||||
\(184\) | 4.38036 | 0.322924 | ||||||||
\(185\) | 1.00572 | 0.0739421 | ||||||||
\(186\) | −2.35705 | −0.172828 | ||||||||
\(187\) | −16.8880 | −1.23497 | ||||||||
\(188\) | 6.14204 | 0.447954 | ||||||||
\(189\) | −5.39493 | −0.392423 | ||||||||
\(190\) | −0.177302 | −0.0128628 | ||||||||
\(191\) | −16.8777 | −1.22123 | −0.610614 | − | 0.791928i | \(-0.709077\pi\) | ||||
−0.610614 | + | 0.791928i | \(0.709077\pi\) | |||||||
\(192\) | −1.97637 | −0.142632 | ||||||||
\(193\) | −24.0536 | −1.73142 | −0.865710 | − | 0.500546i | \(-0.833132\pi\) | ||||
−0.865710 | + | 0.500546i | \(0.833132\pi\) | |||||||
\(194\) | 0.204240 | 0.0146636 | ||||||||
\(195\) | 0.775419 | 0.0555289 | ||||||||
\(196\) | −5.30060 | −0.378614 | ||||||||
\(197\) | −10.6357 | −0.757764 | −0.378882 | − | 0.925445i | \(-0.623691\pi\) | ||||
−0.378882 | + | 0.925445i | \(0.623691\pi\) | |||||||
\(198\) | −4.06009 | −0.288538 | ||||||||
\(199\) | 8.49276 | 0.602036 | 0.301018 | − | 0.953618i | \(-0.402674\pi\) | ||||
0.301018 | + | 0.953618i | \(0.402674\pi\) | |||||||
\(200\) | −4.97177 | −0.351557 | ||||||||
\(201\) | 11.4890 | 0.810370 | ||||||||
\(202\) | 1.62093 | 0.114048 | ||||||||
\(203\) | 8.22605 | 0.577355 | ||||||||
\(204\) | −7.44825 | −0.521482 | ||||||||
\(205\) | −1.32107 | −0.0922677 | ||||||||
\(206\) | −19.5068 | −1.35910 | ||||||||
\(207\) | 3.96875 | 0.275847 | ||||||||
\(208\) | 2.33495 | 0.161900 | ||||||||
\(209\) | −4.72840 | −0.327070 | ||||||||
\(210\) | −0.432919 | −0.0298742 | ||||||||
\(211\) | 18.6669 | 1.28508 | 0.642540 | − | 0.766252i | \(-0.277881\pi\) | ||||
0.642540 | + | 0.766252i | \(0.277881\pi\) | |||||||
\(212\) | −0.518989 | −0.0356443 | ||||||||
\(213\) | 5.28326 | 0.362003 | ||||||||
\(214\) | −15.1972 | −1.03886 | ||||||||
\(215\) | −0.478161 | −0.0326103 | ||||||||
\(216\) | 4.13845 | 0.281586 | ||||||||
\(217\) | −1.55471 | −0.105541 | ||||||||
\(218\) | 10.6327 | 0.720137 | ||||||||
\(219\) | 19.9521 | 1.34824 | ||||||||
\(220\) | 0.752978 | 0.0507658 | ||||||||
\(221\) | 8.79963 | 0.591927 | ||||||||
\(222\) | 11.8292 | 0.793922 | ||||||||
\(223\) | 20.2007 | 1.35274 | 0.676370 | − | 0.736562i | \(-0.263552\pi\) | ||||
0.676370 | + | 0.736562i | \(0.263552\pi\) | |||||||
\(224\) | −1.30361 | −0.0871011 | ||||||||
\(225\) | −4.50458 | −0.300305 | ||||||||
\(226\) | −3.37491 | −0.224496 | ||||||||
\(227\) | 18.1102 | 1.20202 | 0.601008 | − | 0.799243i | \(-0.294766\pi\) | ||||
0.601008 | + | 0.799243i | \(0.294766\pi\) | |||||||
\(228\) | −2.08540 | −0.138109 | ||||||||
\(229\) | 2.03970 | 0.134787 | 0.0673937 | − | 0.997726i | \(-0.478532\pi\) | ||||
0.0673937 | + | 0.997726i | \(0.478532\pi\) | |||||||
\(230\) | −0.736038 | −0.0485329 | ||||||||
\(231\) | −11.5454 | −0.759629 | ||||||||
\(232\) | −6.31021 | −0.414285 | ||||||||
\(233\) | −7.97305 | −0.522332 | −0.261166 | − | 0.965294i | \(-0.584107\pi\) | ||||
−0.261166 | + | 0.965294i | \(0.584107\pi\) | |||||||
\(234\) | 2.11554 | 0.138297 | ||||||||
\(235\) | −1.03206 | −0.0673239 | ||||||||
\(236\) | 5.21300 | 0.339337 | ||||||||
\(237\) | −6.16029 | −0.400154 | ||||||||
\(238\) | −4.91286 | −0.318453 | ||||||||
\(239\) | −17.1569 | −1.10979 | −0.554894 | − | 0.831921i | \(-0.687241\pi\) | ||||
−0.554894 | + | 0.831921i | \(0.687241\pi\) | |||||||
\(240\) | 0.332092 | 0.0214365 | ||||||||
\(241\) | −22.8505 | −1.47193 | −0.735965 | − | 0.677020i | \(-0.763271\pi\) | ||||
−0.735965 | + | 0.677020i | \(0.763271\pi\) | |||||||
\(242\) | 9.08093 | 0.583744 | ||||||||
\(243\) | 9.12153 | 0.585146 | ||||||||
\(244\) | 7.76239 | 0.496936 | ||||||||
\(245\) | 0.890668 | 0.0569027 | ||||||||
\(246\) | −15.5383 | −0.990687 | ||||||||
\(247\) | 2.46377 | 0.156766 | ||||||||
\(248\) | 1.19262 | 0.0757314 | ||||||||
\(249\) | −31.0060 | −1.96493 | ||||||||
\(250\) | 1.67557 | 0.105972 | ||||||||
\(251\) | −16.0932 | −1.01579 | −0.507897 | − | 0.861418i | \(-0.669577\pi\) | ||||
−0.507897 | + | 0.861418i | \(0.669577\pi\) | |||||||
\(252\) | −1.18111 | −0.0744031 | ||||||||
\(253\) | −19.6292 | −1.23407 | ||||||||
\(254\) | −8.66633 | −0.543774 | ||||||||
\(255\) | 1.25154 | 0.0783745 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.7996 | −1.48458 | −0.742290 | − | 0.670078i | \(-0.766261\pi\) | ||||
−0.742290 | + | 0.670078i | \(0.766261\pi\) | |||||||
\(258\) | −5.62407 | −0.350140 | ||||||||
\(259\) | 7.80251 | 0.484824 | ||||||||
\(260\) | −0.392345 | −0.0243322 | ||||||||
\(261\) | −5.71725 | −0.353889 | ||||||||
\(262\) | 13.8235 | 0.854020 | ||||||||
\(263\) | 8.33080 | 0.513699 | 0.256850 | − | 0.966451i | \(-0.417315\pi\) | ||||
0.256850 | + | 0.966451i | \(0.417315\pi\) | |||||||
\(264\) | 8.85645 | 0.545077 | ||||||||
\(265\) | 0.0872065 | 0.00535706 | ||||||||
\(266\) | −1.37553 | −0.0843391 | ||||||||
\(267\) | 3.86747 | 0.236685 | ||||||||
\(268\) | −5.81318 | −0.355096 | ||||||||
\(269\) | −13.8061 | −0.841775 | −0.420887 | − | 0.907113i | \(-0.638281\pi\) | ||||
−0.420887 | + | 0.907113i | \(0.638281\pi\) | |||||||
\(270\) | −0.695390 | −0.0423201 | ||||||||
\(271\) | 5.14386 | 0.312467 | 0.156234 | − | 0.987720i | \(-0.450065\pi\) | ||||
0.156234 | + | 0.987720i | \(0.450065\pi\) | |||||||
\(272\) | 3.76866 | 0.228508 | ||||||||
\(273\) | 6.01580 | 0.364093 | ||||||||
\(274\) | 3.07452 | 0.185739 | ||||||||
\(275\) | 22.2794 | 1.34350 | ||||||||
\(276\) | −8.65720 | −0.521102 | ||||||||
\(277\) | −8.24857 | −0.495608 | −0.247804 | − | 0.968810i | \(-0.579709\pi\) | ||||
−0.247804 | + | 0.968810i | \(0.579709\pi\) | |||||||
\(278\) | −11.0174 | −0.660783 | ||||||||
\(279\) | 1.08055 | 0.0646909 | ||||||||
\(280\) | 0.219048 | 0.0130906 | ||||||||
\(281\) | 21.1214 | 1.26000 | 0.630000 | − | 0.776595i | \(-0.283055\pi\) | ||||
0.630000 | + | 0.776595i | \(0.283055\pi\) | |||||||
\(282\) | −12.1389 | −0.722863 | ||||||||
\(283\) | 8.10533 | 0.481812 | 0.240906 | − | 0.970548i | \(-0.422555\pi\) | ||||
0.240906 | + | 0.970548i | \(0.422555\pi\) | |||||||
\(284\) | −2.67321 | −0.158626 | ||||||||
\(285\) | 0.350414 | 0.0207567 | ||||||||
\(286\) | −10.4633 | −0.618709 | ||||||||
\(287\) | −10.2491 | −0.604983 | ||||||||
\(288\) | 0.906032 | 0.0533884 | ||||||||
\(289\) | −2.79724 | −0.164543 | ||||||||
\(290\) | 1.06031 | 0.0622637 | ||||||||
\(291\) | −0.403653 | −0.0236626 | ||||||||
\(292\) | −10.0953 | −0.590785 | ||||||||
\(293\) | −30.8519 | −1.80239 | −0.901194 | − | 0.433417i | \(-0.857308\pi\) | ||||
−0.901194 | + | 0.433417i | \(0.857308\pi\) | |||||||
\(294\) | 10.4759 | 0.610969 | ||||||||
\(295\) | −0.875948 | −0.0509996 | ||||||||
\(296\) | −5.98531 | −0.347889 | ||||||||
\(297\) | −18.5451 | −1.07610 | ||||||||
\(298\) | −13.8344 | −0.801404 | ||||||||
\(299\) | 10.2279 | 0.591496 | ||||||||
\(300\) | 9.82604 | 0.567307 | ||||||||
\(301\) | −3.70963 | −0.213820 | ||||||||
\(302\) | −2.43642 | −0.140200 | ||||||||
\(303\) | −3.20356 | −0.184040 | ||||||||
\(304\) | 1.05517 | 0.0605181 | ||||||||
\(305\) | −1.30433 | −0.0746855 | ||||||||
\(306\) | 3.41452 | 0.195195 | ||||||||
\(307\) | 0.307125 | 0.0175286 | 0.00876429 | − | 0.999962i | \(-0.497210\pi\) | ||||
0.00876429 | + | 0.999962i | \(0.497210\pi\) | |||||||
\(308\) | 5.84170 | 0.332862 | ||||||||
\(309\) | 38.5527 | 2.19318 | ||||||||
\(310\) | −0.200398 | −0.0113818 | ||||||||
\(311\) | −21.5954 | −1.22457 | −0.612283 | − | 0.790639i | \(-0.709749\pi\) | ||||
−0.612283 | + | 0.790639i | \(0.709749\pi\) | |||||||
\(312\) | −4.61472 | −0.261257 | ||||||||
\(313\) | −26.7242 | −1.51054 | −0.755269 | − | 0.655415i | \(-0.772494\pi\) | ||||
−0.755269 | + | 0.655415i | \(0.772494\pi\) | |||||||
\(314\) | −18.6718 | −1.05371 | ||||||||
\(315\) | 0.198464 | 0.0111822 | ||||||||
\(316\) | 3.11698 | 0.175344 | ||||||||
\(317\) | −15.0854 | −0.847279 | −0.423639 | − | 0.905831i | \(-0.639248\pi\) | ||||
−0.423639 | + | 0.905831i | \(0.639248\pi\) | |||||||
\(318\) | 1.02571 | 0.0575192 | ||||||||
\(319\) | 28.2771 | 1.58322 | ||||||||
\(320\) | −0.168031 | −0.00939325 | ||||||||
\(321\) | 30.0353 | 1.67641 | ||||||||
\(322\) | −5.71028 | −0.318221 | ||||||||
\(323\) | 3.97657 | 0.221262 | ||||||||
\(324\) | −10.8972 | −0.605400 | ||||||||
\(325\) | −11.6088 | −0.643942 | ||||||||
\(326\) | −0.807239 | −0.0447088 | ||||||||
\(327\) | −21.0141 | −1.16208 | ||||||||
\(328\) | 7.86206 | 0.434109 | ||||||||
\(329\) | −8.00682 | −0.441430 | ||||||||
\(330\) | −1.48816 | −0.0819207 | ||||||||
\(331\) | −27.7004 | −1.52255 | −0.761275 | − | 0.648429i | \(-0.775426\pi\) | ||||
−0.761275 | + | 0.648429i | \(0.775426\pi\) | |||||||
\(332\) | 15.6884 | 0.861011 | ||||||||
\(333\) | −5.42288 | −0.297172 | ||||||||
\(334\) | 14.3175 | 0.783418 | ||||||||
\(335\) | 0.976797 | 0.0533681 | ||||||||
\(336\) | 2.57641 | 0.140555 | ||||||||
\(337\) | −22.6359 | −1.23306 | −0.616528 | − | 0.787333i | \(-0.711461\pi\) | ||||
−0.616528 | + | 0.787333i | \(0.711461\pi\) | |||||||
\(338\) | −7.54800 | −0.410557 | ||||||||
\(339\) | 6.67007 | 0.362268 | ||||||||
\(340\) | −0.633253 | −0.0343430 | ||||||||
\(341\) | −5.34433 | −0.289412 | ||||||||
\(342\) | 0.956017 | 0.0516955 | ||||||||
\(343\) | 16.0352 | 0.865819 | ||||||||
\(344\) | 2.84566 | 0.153428 | ||||||||
\(345\) | 1.45468 | 0.0783175 | ||||||||
\(346\) | −15.2909 | −0.822043 | ||||||||
\(347\) | −1.80578 | −0.0969393 | −0.0484696 | − | 0.998825i | \(-0.515434\pi\) | ||||
−0.0484696 | + | 0.998825i | \(0.515434\pi\) | |||||||
\(348\) | 12.4713 | 0.668531 | ||||||||
\(349\) | 18.3573 | 0.982642 | 0.491321 | − | 0.870978i | \(-0.336514\pi\) | ||||
0.491321 | + | 0.870978i | \(0.336514\pi\) | |||||||
\(350\) | 6.48124 | 0.346437 | ||||||||
\(351\) | 9.66309 | 0.515777 | ||||||||
\(352\) | −4.48117 | −0.238847 | ||||||||
\(353\) | 22.8849 | 1.21804 | 0.609020 | − | 0.793155i | \(-0.291563\pi\) | ||||
0.609020 | + | 0.793155i | \(0.291563\pi\) | |||||||
\(354\) | −10.3028 | −0.547588 | ||||||||
\(355\) | 0.449184 | 0.0238402 | ||||||||
\(356\) | −1.95686 | −0.103713 | ||||||||
\(357\) | 9.70961 | 0.513887 | ||||||||
\(358\) | −9.35245 | −0.494292 | ||||||||
\(359\) | −30.5646 | −1.61314 | −0.806569 | − | 0.591140i | \(-0.798678\pi\) | ||||
−0.806569 | + | 0.591140i | \(0.798678\pi\) | |||||||
\(360\) | −0.152242 | −0.00802385 | ||||||||
\(361\) | −17.8866 | −0.941401 | ||||||||
\(362\) | 24.0169 | 1.26230 | ||||||||
\(363\) | −17.9473 | −0.941987 | ||||||||
\(364\) | −3.04387 | −0.159542 | ||||||||
\(365\) | 1.69633 | 0.0887902 | ||||||||
\(366\) | −15.3414 | −0.801905 | ||||||||
\(367\) | 27.3795 | 1.42920 | 0.714599 | − | 0.699534i | \(-0.246609\pi\) | ||||
0.714599 | + | 0.699534i | \(0.246609\pi\) | |||||||
\(368\) | 4.38036 | 0.228342 | ||||||||
\(369\) | 7.12327 | 0.370823 | ||||||||
\(370\) | 1.00572 | 0.0522849 | ||||||||
\(371\) | 0.676560 | 0.0351252 | ||||||||
\(372\) | −2.35705 | −0.122208 | ||||||||
\(373\) | 8.47849 | 0.438999 | 0.219500 | − | 0.975613i | \(-0.429557\pi\) | ||||
0.219500 | + | 0.975613i | \(0.429557\pi\) | |||||||
\(374\) | −16.8880 | −0.873258 | ||||||||
\(375\) | −3.31154 | −0.171007 | ||||||||
\(376\) | 6.14204 | 0.316751 | ||||||||
\(377\) | −14.7340 | −0.758841 | ||||||||
\(378\) | −5.39493 | −0.277485 | ||||||||
\(379\) | 29.1535 | 1.49752 | 0.748758 | − | 0.662843i | \(-0.230650\pi\) | ||||
0.748758 | + | 0.662843i | \(0.230650\pi\) | |||||||
\(380\) | −0.177302 | −0.00909539 | ||||||||
\(381\) | 17.1279 | 0.877487 | ||||||||
\(382\) | −16.8777 | −0.863538 | ||||||||
\(383\) | −17.6296 | −0.900829 | −0.450415 | − | 0.892820i | \(-0.648724\pi\) | ||||
−0.450415 | + | 0.892820i | \(0.648724\pi\) | |||||||
\(384\) | −1.97637 | −0.100856 | ||||||||
\(385\) | −0.981590 | −0.0500265 | ||||||||
\(386\) | −24.0536 | −1.22430 | ||||||||
\(387\) | 2.57826 | 0.131060 | ||||||||
\(388\) | 0.204240 | 0.0103687 | ||||||||
\(389\) | 11.6697 | 0.591678 | 0.295839 | − | 0.955238i | \(-0.404401\pi\) | ||||
0.295839 | + | 0.955238i | \(0.404401\pi\) | |||||||
\(390\) | 0.775419 | 0.0392649 | ||||||||
\(391\) | 16.5081 | 0.834849 | ||||||||
\(392\) | −5.30060 | −0.267721 | ||||||||
\(393\) | −27.3204 | −1.37813 | ||||||||
\(394\) | −10.6357 | −0.535820 | ||||||||
\(395\) | −0.523750 | −0.0263527 | ||||||||
\(396\) | −4.06009 | −0.204027 | ||||||||
\(397\) | −5.76210 | −0.289192 | −0.144596 | − | 0.989491i | \(-0.546188\pi\) | ||||
−0.144596 | + | 0.989491i | \(0.546188\pi\) | |||||||
\(398\) | 8.49276 | 0.425704 | ||||||||
\(399\) | 2.71855 | 0.136098 | ||||||||
\(400\) | −4.97177 | −0.248588 | ||||||||
\(401\) | 6.15823 | 0.307527 | 0.153764 | − | 0.988108i | \(-0.450861\pi\) | ||||
0.153764 | + | 0.988108i | \(0.450861\pi\) | |||||||
\(402\) | 11.4890 | 0.573018 | ||||||||
\(403\) | 2.78471 | 0.138716 | ||||||||
\(404\) | 1.62093 | 0.0806443 | ||||||||
\(405\) | 1.83107 | 0.0909868 | ||||||||
\(406\) | 8.22605 | 0.408252 | ||||||||
\(407\) | 26.8212 | 1.32948 | ||||||||
\(408\) | −7.44825 | −0.368743 | ||||||||
\(409\) | 11.7294 | 0.579981 | 0.289991 | − | 0.957029i | \(-0.406348\pi\) | ||||
0.289991 | + | 0.957029i | \(0.406348\pi\) | |||||||
\(410\) | −1.32107 | −0.0652431 | ||||||||
\(411\) | −6.07639 | −0.299726 | ||||||||
\(412\) | −19.5068 | −0.961032 | ||||||||
\(413\) | −6.79572 | −0.334395 | ||||||||
\(414\) | 3.96875 | 0.195053 | ||||||||
\(415\) | −2.63614 | −0.129403 | ||||||||
\(416\) | 2.33495 | 0.114480 | ||||||||
\(417\) | 21.7745 | 1.06630 | ||||||||
\(418\) | −4.72840 | −0.231274 | ||||||||
\(419\) | 4.04766 | 0.197741 | 0.0988705 | − | 0.995100i | \(-0.468477\pi\) | ||||
0.0988705 | + | 0.995100i | \(0.468477\pi\) | |||||||
\(420\) | −0.432919 | −0.0211243 | ||||||||
\(421\) | 10.9475 | 0.533548 | 0.266774 | − | 0.963759i | \(-0.414042\pi\) | ||||
0.266774 | + | 0.963759i | \(0.414042\pi\) | |||||||
\(422\) | 18.6669 | 0.908689 | ||||||||
\(423\) | 5.56488 | 0.270574 | ||||||||
\(424\) | −0.518989 | −0.0252043 | ||||||||
\(425\) | −18.7369 | −0.908872 | ||||||||
\(426\) | 5.28326 | 0.255975 | ||||||||
\(427\) | −10.1191 | −0.489699 | ||||||||
\(428\) | −15.1972 | −0.734586 | ||||||||
\(429\) | 20.6794 | 0.998410 | ||||||||
\(430\) | −0.478161 | −0.0230590 | ||||||||
\(431\) | −27.5446 | −1.32678 | −0.663388 | − | 0.748276i | \(-0.730882\pi\) | ||||
−0.663388 | + | 0.748276i | \(0.730882\pi\) | |||||||
\(432\) | 4.13845 | 0.199111 | ||||||||
\(433\) | −27.4780 | −1.32051 | −0.660255 | − | 0.751041i | \(-0.729552\pi\) | ||||
−0.660255 | + | 0.751041i | \(0.729552\pi\) | |||||||
\(434\) | −1.55471 | −0.0746285 | ||||||||
\(435\) | −2.09557 | −0.100475 | ||||||||
\(436\) | 10.6327 | 0.509214 | ||||||||
\(437\) | 4.62202 | 0.221101 | ||||||||
\(438\) | 19.9521 | 0.953349 | ||||||||
\(439\) | 13.5683 | 0.647578 | 0.323789 | − | 0.946129i | \(-0.395043\pi\) | ||||
0.323789 | + | 0.946129i | \(0.395043\pi\) | |||||||
\(440\) | 0.752978 | 0.0358968 | ||||||||
\(441\) | −4.80251 | −0.228691 | ||||||||
\(442\) | 8.79963 | 0.418556 | ||||||||
\(443\) | −0.790011 | −0.0375345 | −0.0187673 | − | 0.999824i | \(-0.505974\pi\) | ||||
−0.0187673 | + | 0.999824i | \(0.505974\pi\) | |||||||
\(444\) | 11.8292 | 0.561388 | ||||||||
\(445\) | 0.328814 | 0.0155873 | ||||||||
\(446\) | 20.2007 | 0.956531 | ||||||||
\(447\) | 27.3418 | 1.29322 | ||||||||
\(448\) | −1.30361 | −0.0615898 | ||||||||
\(449\) | 39.0557 | 1.84315 | 0.921576 | − | 0.388199i | \(-0.126903\pi\) | ||||
0.921576 | + | 0.388199i | \(0.126903\pi\) | |||||||
\(450\) | −4.50458 | −0.212348 | ||||||||
\(451\) | −35.2312 | −1.65897 | ||||||||
\(452\) | −3.37491 | −0.158742 | ||||||||
\(453\) | 4.81527 | 0.226241 | ||||||||
\(454\) | 18.1102 | 0.849954 | ||||||||
\(455\) | 0.511465 | 0.0239779 | ||||||||
\(456\) | −2.08540 | −0.0976580 | ||||||||
\(457\) | 3.85746 | 0.180444 | 0.0902221 | − | 0.995922i | \(-0.471242\pi\) | ||||
0.0902221 | + | 0.995922i | \(0.471242\pi\) | |||||||
\(458\) | 2.03970 | 0.0953090 | ||||||||
\(459\) | 15.5964 | 0.727978 | ||||||||
\(460\) | −0.736038 | −0.0343180 | ||||||||
\(461\) | −20.8437 | −0.970790 | −0.485395 | − | 0.874295i | \(-0.661324\pi\) | ||||
−0.485395 | + | 0.874295i | \(0.661324\pi\) | |||||||
\(462\) | −11.5454 | −0.537139 | ||||||||
\(463\) | 12.5445 | 0.582990 | 0.291495 | − | 0.956572i | \(-0.405847\pi\) | ||||
0.291495 | + | 0.956572i | \(0.405847\pi\) | |||||||
\(464\) | −6.31021 | −0.292944 | ||||||||
\(465\) | 0.396059 | 0.0183668 | ||||||||
\(466\) | −7.97305 | −0.369345 | ||||||||
\(467\) | 16.7817 | 0.776564 | 0.388282 | − | 0.921541i | \(-0.373069\pi\) | ||||
0.388282 | + | 0.921541i | \(0.373069\pi\) | |||||||
\(468\) | 2.11554 | 0.0977909 | ||||||||
\(469\) | 7.57812 | 0.349925 | ||||||||
\(470\) | −1.03206 | −0.0476052 | ||||||||
\(471\) | 36.9024 | 1.70037 | ||||||||
\(472\) | 5.21300 | 0.239948 | ||||||||
\(473\) | −12.7519 | −0.586333 | ||||||||
\(474\) | −6.16029 | −0.282952 | ||||||||
\(475\) | −5.24606 | −0.240706 | ||||||||
\(476\) | −4.91286 | −0.225180 | ||||||||
\(477\) | −0.470221 | −0.0215299 | ||||||||
\(478\) | −17.1569 | −0.784738 | ||||||||
\(479\) | −42.5719 | −1.94516 | −0.972580 | − | 0.232568i | \(-0.925287\pi\) | ||||
−0.972580 | + | 0.232568i | \(0.925287\pi\) | |||||||
\(480\) | 0.332092 | 0.0151579 | ||||||||
\(481\) | −13.9754 | −0.637224 | ||||||||
\(482\) | −22.8505 | −1.04081 | ||||||||
\(483\) | 11.2856 | 0.513513 | ||||||||
\(484\) | 9.08093 | 0.412769 | ||||||||
\(485\) | −0.0343187 | −0.00155833 | ||||||||
\(486\) | 9.12153 | 0.413761 | ||||||||
\(487\) | −17.4778 | −0.791993 | −0.395996 | − | 0.918252i | \(-0.629601\pi\) | ||||
−0.395996 | + | 0.918252i | \(0.629601\pi\) | |||||||
\(488\) | 7.76239 | 0.351387 | ||||||||
\(489\) | 1.59540 | 0.0721465 | ||||||||
\(490\) | 0.890668 | 0.0402363 | ||||||||
\(491\) | −8.76263 | −0.395452 | −0.197726 | − | 0.980257i | \(-0.563356\pi\) | ||||
−0.197726 | + | 0.980257i | \(0.563356\pi\) | |||||||
\(492\) | −15.5383 | −0.700522 | ||||||||
\(493\) | −23.7810 | −1.07104 | ||||||||
\(494\) | 2.46377 | 0.110850 | ||||||||
\(495\) | 0.682223 | 0.0306636 | ||||||||
\(496\) | 1.19262 | 0.0535502 | ||||||||
\(497\) | 3.48483 | 0.156316 | ||||||||
\(498\) | −31.0060 | −1.38941 | ||||||||
\(499\) | −13.6928 | −0.612975 | −0.306488 | − | 0.951875i | \(-0.599154\pi\) | ||||
−0.306488 | + | 0.951875i | \(0.599154\pi\) | |||||||
\(500\) | 1.67557 | 0.0749338 | ||||||||
\(501\) | −28.2966 | −1.26420 | ||||||||
\(502\) | −16.0932 | −0.718274 | ||||||||
\(503\) | −16.6337 | −0.741659 | −0.370829 | − | 0.928701i | \(-0.620927\pi\) | ||||
−0.370829 | + | 0.928701i | \(0.620927\pi\) | |||||||
\(504\) | −1.18111 | −0.0526109 | ||||||||
\(505\) | −0.272367 | −0.0121202 | ||||||||
\(506\) | −19.6292 | −0.872622 | ||||||||
\(507\) | 14.9176 | 0.662515 | ||||||||
\(508\) | −8.66633 | −0.384506 | ||||||||
\(509\) | −17.6916 | −0.784167 | −0.392084 | − | 0.919930i | \(-0.628246\pi\) | ||||
−0.392084 | + | 0.919930i | \(0.628246\pi\) | |||||||
\(510\) | 1.25154 | 0.0554192 | ||||||||
\(511\) | 13.1604 | 0.582181 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.36677 | 0.192798 | ||||||||
\(514\) | −23.7996 | −1.04976 | ||||||||
\(515\) | 3.27776 | 0.144435 | ||||||||
\(516\) | −5.62407 | −0.247586 | ||||||||
\(517\) | −27.5235 | −1.21048 | ||||||||
\(518\) | 7.80251 | 0.342823 | ||||||||
\(519\) | 30.2204 | 1.32653 | ||||||||
\(520\) | −0.392345 | −0.0172055 | ||||||||
\(521\) | 8.65584 | 0.379219 | 0.189610 | − | 0.981860i | \(-0.439278\pi\) | ||||
0.189610 | + | 0.981860i | \(0.439278\pi\) | |||||||
\(522\) | −5.71725 | −0.250237 | ||||||||
\(523\) | 7.15968 | 0.313071 | 0.156536 | − | 0.987672i | \(-0.449967\pi\) | ||||
0.156536 | + | 0.987672i | \(0.449967\pi\) | |||||||
\(524\) | 13.8235 | 0.603883 | ||||||||
\(525\) | −12.8093 | −0.559045 | ||||||||
\(526\) | 8.33080 | 0.363240 | ||||||||
\(527\) | 4.49457 | 0.195787 | ||||||||
\(528\) | 8.85645 | 0.385428 | ||||||||
\(529\) | −3.81245 | −0.165759 | ||||||||
\(530\) | 0.0872065 | 0.00378801 | ||||||||
\(531\) | 4.72314 | 0.204967 | ||||||||
\(532\) | −1.37553 | −0.0596368 | ||||||||
\(533\) | 18.3575 | 0.795153 | ||||||||
\(534\) | 3.86747 | 0.167362 | ||||||||
\(535\) | 2.55361 | 0.110402 | ||||||||
\(536\) | −5.81318 | −0.251091 | ||||||||
\(537\) | 18.4839 | 0.797639 | ||||||||
\(538\) | −13.8061 | −0.595225 | ||||||||
\(539\) | 23.7529 | 1.02311 | ||||||||
\(540\) | −0.695390 | −0.0299248 | ||||||||
\(541\) | 30.2707 | 1.30144 | 0.650719 | − | 0.759318i | \(-0.274467\pi\) | ||||
0.650719 | + | 0.759318i | \(0.274467\pi\) | |||||||
\(542\) | 5.14386 | 0.220948 | ||||||||
\(543\) | −47.4662 | −2.03697 | ||||||||
\(544\) | 3.76866 | 0.161580 | ||||||||
\(545\) | −1.78663 | −0.0765308 | ||||||||
\(546\) | 6.01580 | 0.257453 | ||||||||
\(547\) | 25.9528 | 1.10966 | 0.554830 | − | 0.831964i | \(-0.312783\pi\) | ||||
0.554830 | + | 0.831964i | \(0.312783\pi\) | |||||||
\(548\) | 3.07452 | 0.131337 | ||||||||
\(549\) | 7.03298 | 0.300160 | ||||||||
\(550\) | 22.2794 | 0.949995 | ||||||||
\(551\) | −6.65834 | −0.283655 | ||||||||
\(552\) | −8.65720 | −0.368475 | ||||||||
\(553\) | −4.06332 | −0.172790 | ||||||||
\(554\) | −8.24857 | −0.350448 | ||||||||
\(555\) | −1.98767 | −0.0843721 | ||||||||
\(556\) | −11.0174 | −0.467244 | ||||||||
\(557\) | −1.49382 | −0.0632954 | −0.0316477 | − | 0.999499i | \(-0.510075\pi\) | ||||
−0.0316477 | + | 0.999499i | \(0.510075\pi\) | |||||||
\(558\) | 1.08055 | 0.0457434 | ||||||||
\(559\) | 6.64448 | 0.281032 | ||||||||
\(560\) | 0.219048 | 0.00925645 | ||||||||
\(561\) | 33.3769 | 1.40917 | ||||||||
\(562\) | 21.1214 | 0.890954 | ||||||||
\(563\) | −6.75713 | −0.284779 | −0.142389 | − | 0.989811i | \(-0.545479\pi\) | ||||
−0.142389 | + | 0.989811i | \(0.545479\pi\) | |||||||
\(564\) | −12.1389 | −0.511141 | ||||||||
\(565\) | 0.567091 | 0.0238577 | ||||||||
\(566\) | 8.10533 | 0.340692 | ||||||||
\(567\) | 14.2057 | 0.596583 | ||||||||
\(568\) | −2.67321 | −0.112166 | ||||||||
\(569\) | 3.12500 | 0.131007 | 0.0655033 | − | 0.997852i | \(-0.479135\pi\) | ||||
0.0655033 | + | 0.997852i | \(0.479135\pi\) | |||||||
\(570\) | 0.350414 | 0.0146772 | ||||||||
\(571\) | 22.1690 | 0.927744 | 0.463872 | − | 0.885902i | \(-0.346460\pi\) | ||||
0.463872 | + | 0.885902i | \(0.346460\pi\) | |||||||
\(572\) | −10.4633 | −0.437494 | ||||||||
\(573\) | 33.3566 | 1.39349 | ||||||||
\(574\) | −10.2491 | −0.427787 | ||||||||
\(575\) | −21.7781 | −0.908210 | ||||||||
\(576\) | 0.906032 | 0.0377513 | ||||||||
\(577\) | 15.0891 | 0.628169 | 0.314084 | − | 0.949395i | \(-0.398303\pi\) | ||||
0.314084 | + | 0.949395i | \(0.398303\pi\) | |||||||
\(578\) | −2.79724 | −0.116350 | ||||||||
\(579\) | 47.5389 | 1.97565 | ||||||||
\(580\) | 1.06031 | 0.0440271 | ||||||||
\(581\) | −20.4515 | −0.848472 | ||||||||
\(582\) | −0.403653 | −0.0167320 | ||||||||
\(583\) | 2.32568 | 0.0963199 | ||||||||
\(584\) | −10.0953 | −0.417748 | ||||||||
\(585\) | −0.355477 | −0.0146972 | ||||||||
\(586\) | −30.8519 | −1.27448 | ||||||||
\(587\) | −2.04081 | −0.0842333 | −0.0421167 | − | 0.999113i | \(-0.513410\pi\) | ||||
−0.0421167 | + | 0.999113i | \(0.513410\pi\) | |||||||
\(588\) | 10.4759 | 0.432020 | ||||||||
\(589\) | 1.25842 | 0.0518521 | ||||||||
\(590\) | −0.875948 | −0.0360622 | ||||||||
\(591\) | 21.0201 | 0.864652 | ||||||||
\(592\) | −5.98531 | −0.245995 | ||||||||
\(593\) | −27.8250 | −1.14263 | −0.571317 | − | 0.820729i | \(-0.693567\pi\) | ||||
−0.571317 | + | 0.820729i | \(0.693567\pi\) | |||||||
\(594\) | −18.5451 | −0.760916 | ||||||||
\(595\) | 0.825515 | 0.0338428 | ||||||||
\(596\) | −13.8344 | −0.566679 | ||||||||
\(597\) | −16.7848 | −0.686957 | ||||||||
\(598\) | 10.2279 | 0.418251 | ||||||||
\(599\) | 16.6896 | 0.681919 | 0.340959 | − | 0.940078i | \(-0.389248\pi\) | ||||
0.340959 | + | 0.940078i | \(0.389248\pi\) | |||||||
\(600\) | 9.82604 | 0.401146 | ||||||||
\(601\) | 17.4131 | 0.710296 | 0.355148 | − | 0.934810i | \(-0.384430\pi\) | ||||
0.355148 | + | 0.934810i | \(0.384430\pi\) | |||||||
\(602\) | −3.70963 | −0.151193 | ||||||||
\(603\) | −5.26692 | −0.214486 | ||||||||
\(604\) | −2.43642 | −0.0991366 | ||||||||
\(605\) | −1.52588 | −0.0620359 | ||||||||
\(606\) | −3.20356 | −0.130136 | ||||||||
\(607\) | −32.8203 | −1.33214 | −0.666068 | − | 0.745891i | \(-0.732024\pi\) | ||||
−0.666068 | + | 0.745891i | \(0.732024\pi\) | |||||||
\(608\) | 1.05517 | 0.0427928 | ||||||||
\(609\) | −16.2577 | −0.658795 | ||||||||
\(610\) | −1.30433 | −0.0528106 | ||||||||
\(611\) | 14.3414 | 0.580189 | ||||||||
\(612\) | 3.41452 | 0.138024 | ||||||||
\(613\) | 43.2006 | 1.74486 | 0.872428 | − | 0.488742i | \(-0.162544\pi\) | ||||
0.872428 | + | 0.488742i | \(0.162544\pi\) | |||||||
\(614\) | 0.307125 | 0.0123946 | ||||||||
\(615\) | 2.61093 | 0.105283 | ||||||||
\(616\) | 5.84170 | 0.235369 | ||||||||
\(617\) | −12.7481 | −0.513221 | −0.256610 | − | 0.966515i | \(-0.582606\pi\) | ||||
−0.256610 | + | 0.966515i | \(0.582606\pi\) | |||||||
\(618\) | 38.5527 | 1.55082 | ||||||||
\(619\) | 18.0393 | 0.725061 | 0.362531 | − | 0.931972i | \(-0.381913\pi\) | ||||
0.362531 | + | 0.931972i | \(0.381913\pi\) | |||||||
\(620\) | −0.200398 | −0.00804816 | ||||||||
\(621\) | 18.1279 | 0.727448 | ||||||||
\(622\) | −21.5954 | −0.865899 | ||||||||
\(623\) | 2.55098 | 0.102203 | ||||||||
\(624\) | −4.61472 | −0.184737 | ||||||||
\(625\) | 24.5773 | 0.983091 | ||||||||
\(626\) | −26.7242 | −1.06811 | ||||||||
\(627\) | 9.34506 | 0.373206 | ||||||||
\(628\) | −18.6718 | −0.745086 | ||||||||
\(629\) | −22.5566 | −0.899389 | ||||||||
\(630\) | 0.198464 | 0.00790700 | ||||||||
\(631\) | −21.1879 | −0.843475 | −0.421738 | − | 0.906718i | \(-0.638580\pi\) | ||||
−0.421738 | + | 0.906718i | \(0.638580\pi\) | |||||||
\(632\) | 3.11698 | 0.123987 | ||||||||
\(633\) | −36.8926 | −1.46635 | ||||||||
\(634\) | −15.0854 | −0.599116 | ||||||||
\(635\) | 1.45622 | 0.0577882 | ||||||||
\(636\) | 1.02571 | 0.0406722 | ||||||||
\(637\) | −12.3766 | −0.490381 | ||||||||
\(638\) | 28.2771 | 1.11950 | ||||||||
\(639\) | −2.42202 | −0.0958135 | ||||||||
\(640\) | −0.168031 | −0.00664203 | ||||||||
\(641\) | −36.0637 | −1.42443 | −0.712216 | − | 0.701960i | \(-0.752308\pi\) | ||||
−0.712216 | + | 0.701960i | \(0.752308\pi\) | |||||||
\(642\) | 30.0353 | 1.18540 | ||||||||
\(643\) | 28.0858 | 1.10760 | 0.553798 | − | 0.832651i | \(-0.313178\pi\) | ||||
0.553798 | + | 0.832651i | \(0.313178\pi\) | |||||||
\(644\) | −5.71028 | −0.225017 | ||||||||
\(645\) | 0.945021 | 0.0372102 | ||||||||
\(646\) | 3.97657 | 0.156456 | ||||||||
\(647\) | 13.9193 | 0.547225 | 0.273613 | − | 0.961840i | \(-0.411781\pi\) | ||||
0.273613 | + | 0.961840i | \(0.411781\pi\) | |||||||
\(648\) | −10.8972 | −0.428083 | ||||||||
\(649\) | −23.3604 | −0.916974 | ||||||||
\(650\) | −11.6088 | −0.455336 | ||||||||
\(651\) | 3.07268 | 0.120428 | ||||||||
\(652\) | −0.807239 | −0.0316139 | ||||||||
\(653\) | −39.8089 | −1.55784 | −0.778921 | − | 0.627122i | \(-0.784233\pi\) | ||||
−0.778921 | + | 0.627122i | \(0.784233\pi\) | |||||||
\(654\) | −21.0141 | −0.821718 | ||||||||
\(655\) | −2.32279 | −0.0907588 | ||||||||
\(656\) | 7.86206 | 0.306962 | ||||||||
\(657\) | −9.14670 | −0.356847 | ||||||||
\(658\) | −8.00682 | −0.312138 | ||||||||
\(659\) | −46.3426 | −1.80525 | −0.902625 | − | 0.430427i | \(-0.858363\pi\) | ||||
−0.902625 | + | 0.430427i | \(0.858363\pi\) | |||||||
\(660\) | −1.48816 | −0.0579267 | ||||||||
\(661\) | −30.8679 | −1.20062 | −0.600311 | − | 0.799766i | \(-0.704957\pi\) | ||||
−0.600311 | + | 0.799766i | \(0.704957\pi\) | |||||||
\(662\) | −27.7004 | −1.07661 | ||||||||
\(663\) | −17.3913 | −0.675422 | ||||||||
\(664\) | 15.6884 | 0.608827 | ||||||||
\(665\) | 0.231132 | 0.00896293 | ||||||||
\(666\) | −5.42288 | −0.210132 | ||||||||
\(667\) | −27.6410 | −1.07026 | ||||||||
\(668\) | 14.3175 | 0.553960 | ||||||||
\(669\) | −39.9240 | −1.54355 | ||||||||
\(670\) | 0.976797 | 0.0377369 | ||||||||
\(671\) | −34.7846 | −1.34285 | ||||||||
\(672\) | 2.57641 | 0.0993873 | ||||||||
\(673\) | −15.7020 | −0.605269 | −0.302634 | − | 0.953107i | \(-0.597866\pi\) | ||||
−0.302634 | + | 0.953107i | \(0.597866\pi\) | |||||||
\(674\) | −22.6359 | −0.871903 | ||||||||
\(675\) | −20.5754 | −0.791948 | ||||||||
\(676\) | −7.54800 | −0.290308 | ||||||||
\(677\) | −43.8194 | −1.68412 | −0.842058 | − | 0.539387i | \(-0.818656\pi\) | ||||
−0.842058 | + | 0.539387i | \(0.818656\pi\) | |||||||
\(678\) | 6.67007 | 0.256162 | ||||||||
\(679\) | −0.266249 | −0.0102177 | ||||||||
\(680\) | −0.633253 | −0.0242841 | ||||||||
\(681\) | −35.7924 | −1.37157 | ||||||||
\(682\) | −5.34433 | −0.204645 | ||||||||
\(683\) | 28.4584 | 1.08893 | 0.544465 | − | 0.838784i | \(-0.316733\pi\) | ||||
0.544465 | + | 0.838784i | \(0.316733\pi\) | |||||||
\(684\) | 0.956017 | 0.0365542 | ||||||||
\(685\) | −0.516616 | −0.0197389 | ||||||||
\(686\) | 16.0352 | 0.612226 | ||||||||
\(687\) | −4.03120 | −0.153800 | ||||||||
\(688\) | 2.84566 | 0.108490 | ||||||||
\(689\) | −1.21181 | −0.0461665 | ||||||||
\(690\) | 1.45468 | 0.0553788 | ||||||||
\(691\) | −6.24695 | −0.237645 | −0.118822 | − | 0.992916i | \(-0.537912\pi\) | ||||
−0.118822 | + | 0.992916i | \(0.537912\pi\) | |||||||
\(692\) | −15.2909 | −0.581272 | ||||||||
\(693\) | 5.29277 | 0.201056 | ||||||||
\(694\) | −1.80578 | −0.0685464 | ||||||||
\(695\) | 1.85128 | 0.0702230 | ||||||||
\(696\) | 12.4713 | 0.472723 | ||||||||
\(697\) | 29.6294 | 1.12229 | ||||||||
\(698\) | 18.3573 | 0.694833 | ||||||||
\(699\) | 15.7577 | 0.596011 | ||||||||
\(700\) | 6.48124 | 0.244968 | ||||||||
\(701\) | 8.70130 | 0.328644 | 0.164322 | − | 0.986407i | \(-0.447456\pi\) | ||||
0.164322 | + | 0.986407i | \(0.447456\pi\) | |||||||
\(702\) | 9.66309 | 0.364710 | ||||||||
\(703\) | −6.31552 | −0.238194 | ||||||||
\(704\) | −4.48117 | −0.168891 | ||||||||
\(705\) | 2.03972 | 0.0768204 | ||||||||
\(706\) | 22.8849 | 0.861284 | ||||||||
\(707\) | −2.11306 | −0.0794699 | ||||||||
\(708\) | −10.3028 | −0.387203 | ||||||||
\(709\) | −51.3155 | −1.92719 | −0.963597 | − | 0.267360i | \(-0.913849\pi\) | ||||
−0.963597 | + | 0.267360i | \(0.913849\pi\) | |||||||
\(710\) | 0.449184 | 0.0168576 | ||||||||
\(711\) | 2.82408 | 0.105911 | ||||||||
\(712\) | −1.95686 | −0.0733364 | ||||||||
\(713\) | 5.22410 | 0.195644 | ||||||||
\(714\) | 9.70961 | 0.363373 | ||||||||
\(715\) | 1.75817 | 0.0657518 | ||||||||
\(716\) | −9.35245 | −0.349517 | ||||||||
\(717\) | 33.9083 | 1.26633 | ||||||||
\(718\) | −30.5646 | −1.14066 | ||||||||
\(719\) | 12.1836 | 0.454372 | 0.227186 | − | 0.973851i | \(-0.427048\pi\) | ||||
0.227186 | + | 0.973851i | \(0.427048\pi\) | |||||||
\(720\) | −0.152242 | −0.00567372 | ||||||||
\(721\) | 25.4293 | 0.947036 | ||||||||
\(722\) | −17.8866 | −0.665671 | ||||||||
\(723\) | 45.1610 | 1.67956 | ||||||||
\(724\) | 24.0169 | 0.892580 | ||||||||
\(725\) | 31.3729 | 1.16516 | ||||||||
\(726\) | −17.9473 | −0.666085 | ||||||||
\(727\) | −44.2616 | −1.64157 | −0.820786 | − | 0.571236i | \(-0.806464\pi\) | ||||
−0.820786 | + | 0.571236i | \(0.806464\pi\) | |||||||
\(728\) | −3.04387 | −0.112813 | ||||||||
\(729\) | 14.6641 | 0.543115 | ||||||||
\(730\) | 1.69633 | 0.0627842 | ||||||||
\(731\) | 10.7243 | 0.396653 | ||||||||
\(732\) | −15.3414 | −0.567033 | ||||||||
\(733\) | 26.5028 | 0.978903 | 0.489451 | − | 0.872031i | \(-0.337197\pi\) | ||||
0.489451 | + | 0.872031i | \(0.337197\pi\) | |||||||
\(734\) | 27.3795 | 1.01060 | ||||||||
\(735\) | −1.76029 | −0.0649292 | ||||||||
\(736\) | 4.38036 | 0.161462 | ||||||||
\(737\) | 26.0499 | 0.959559 | ||||||||
\(738\) | 7.12327 | 0.262211 | ||||||||
\(739\) | −41.5250 | −1.52752 | −0.763762 | − | 0.645498i | \(-0.776650\pi\) | ||||
−0.763762 | + | 0.645498i | \(0.776650\pi\) | |||||||
\(740\) | 1.00572 | 0.0369710 | ||||||||
\(741\) | −4.86932 | −0.178879 | ||||||||
\(742\) | 0.676560 | 0.0248373 | ||||||||
\(743\) | 5.76455 | 0.211481 | 0.105740 | − | 0.994394i | \(-0.466279\pi\) | ||||
0.105740 | + | 0.994394i | \(0.466279\pi\) | |||||||
\(744\) | −2.35705 | −0.0864138 | ||||||||
\(745\) | 2.32461 | 0.0851672 | ||||||||
\(746\) | 8.47849 | 0.310420 | ||||||||
\(747\) | 14.2142 | 0.520069 | ||||||||
\(748\) | −16.8880 | −0.617487 | ||||||||
\(749\) | 19.8113 | 0.723888 | ||||||||
\(750\) | −3.31154 | −0.120921 | ||||||||
\(751\) | −17.3145 | −0.631815 | −0.315907 | − | 0.948790i | \(-0.602309\pi\) | ||||
−0.315907 | + | 0.948790i | \(0.602309\pi\) | |||||||
\(752\) | 6.14204 | 0.223977 | ||||||||
\(753\) | 31.8061 | 1.15908 | ||||||||
\(754\) | −14.7340 | −0.536582 | ||||||||
\(755\) | 0.409396 | 0.0148994 | ||||||||
\(756\) | −5.39493 | −0.196212 | ||||||||
\(757\) | 17.4218 | 0.633208 | 0.316604 | − | 0.948558i | \(-0.397457\pi\) | ||||
0.316604 | + | 0.948558i | \(0.397457\pi\) | |||||||
\(758\) | 29.1535 | 1.05890 | ||||||||
\(759\) | 38.7944 | 1.40815 | ||||||||
\(760\) | −0.177302 | −0.00643141 | ||||||||
\(761\) | −46.9236 | −1.70098 | −0.850489 | − | 0.525993i | \(-0.823694\pi\) | ||||
−0.850489 | + | 0.525993i | \(0.823694\pi\) | |||||||
\(762\) | 17.1279 | 0.620477 | ||||||||
\(763\) | −13.8609 | −0.501798 | ||||||||
\(764\) | −16.8777 | −0.610614 | ||||||||
\(765\) | −0.573747 | −0.0207439 | ||||||||
\(766\) | −17.6296 | −0.636982 | ||||||||
\(767\) | 12.1721 | 0.439509 | ||||||||
\(768\) | −1.97637 | −0.0713161 | ||||||||
\(769\) | −6.81037 | −0.245588 | −0.122794 | − | 0.992432i | \(-0.539186\pi\) | ||||
−0.122794 | + | 0.992432i | \(0.539186\pi\) | |||||||
\(770\) | −0.981590 | −0.0353741 | ||||||||
\(771\) | 47.0369 | 1.69399 | ||||||||
\(772\) | −24.0536 | −0.865710 | ||||||||
\(773\) | −11.8880 | −0.427582 | −0.213791 | − | 0.976879i | \(-0.568581\pi\) | ||||
−0.213791 | + | 0.976879i | \(0.568581\pi\) | |||||||
\(774\) | 2.57826 | 0.0926736 | ||||||||
\(775\) | −5.92942 | −0.212991 | ||||||||
\(776\) | 0.204240 | 0.00733178 | ||||||||
\(777\) | −15.4206 | −0.553212 | ||||||||
\(778\) | 11.6697 | 0.418380 | ||||||||
\(779\) | 8.29580 | 0.297228 | ||||||||
\(780\) | 0.775419 | 0.0277645 | ||||||||
\(781\) | 11.9791 | 0.428647 | ||||||||
\(782\) | 16.5081 | 0.590327 | ||||||||
\(783\) | −26.1145 | −0.933255 | ||||||||
\(784\) | −5.30060 | −0.189307 | ||||||||
\(785\) | 3.13745 | 0.111980 | ||||||||
\(786\) | −27.3204 | −0.974486 | ||||||||
\(787\) | −38.9054 | −1.38683 | −0.693414 | − | 0.720540i | \(-0.743894\pi\) | ||||
−0.693414 | + | 0.720540i | \(0.743894\pi\) | |||||||
\(788\) | −10.6357 | −0.378882 | ||||||||
\(789\) | −16.4647 | −0.586160 | ||||||||
\(790\) | −0.523750 | −0.0186342 | ||||||||
\(791\) | 4.39957 | 0.156431 | ||||||||
\(792\) | −4.06009 | −0.144269 | ||||||||
\(793\) | 18.1248 | 0.643631 | ||||||||
\(794\) | −5.76210 | −0.204489 | ||||||||
\(795\) | −0.172352 | −0.00611270 | ||||||||
\(796\) | 8.49276 | 0.301018 | ||||||||
\(797\) | −10.0987 | −0.357715 | −0.178858 | − | 0.983875i | \(-0.557240\pi\) | ||||
−0.178858 | + | 0.983875i | \(0.557240\pi\) | |||||||
\(798\) | 2.71855 | 0.0962358 | ||||||||
\(799\) | 23.1472 | 0.818890 | ||||||||
\(800\) | −4.97177 | −0.175778 | ||||||||
\(801\) | −1.77298 | −0.0626450 | ||||||||
\(802\) | 6.15823 | 0.217455 | ||||||||
\(803\) | 45.2390 | 1.59645 | ||||||||
\(804\) | 11.4890 | 0.405185 | ||||||||
\(805\) | 0.959507 | 0.0338182 | ||||||||
\(806\) | 2.78471 | 0.0980871 | ||||||||
\(807\) | 27.2860 | 0.960513 | ||||||||
\(808\) | 1.62093 | 0.0570242 | ||||||||
\(809\) | −26.5634 | −0.933918 | −0.466959 | − | 0.884279i | \(-0.654650\pi\) | ||||
−0.466959 | + | 0.884279i | \(0.654650\pi\) | |||||||
\(810\) | 1.83107 | 0.0643373 | ||||||||
\(811\) | 51.4445 | 1.80646 | 0.903231 | − | 0.429156i | \(-0.141189\pi\) | ||||
0.903231 | + | 0.429156i | \(0.141189\pi\) | |||||||
\(812\) | 8.22605 | 0.288678 | ||||||||
\(813\) | −10.1662 | −0.356543 | ||||||||
\(814\) | 26.8212 | 0.940083 | ||||||||
\(815\) | 0.135641 | 0.00475131 | ||||||||
\(816\) | −7.44825 | −0.260741 | ||||||||
\(817\) | 3.00265 | 0.105050 | ||||||||
\(818\) | 11.7294 | 0.410109 | ||||||||
\(819\) | −2.75784 | −0.0963667 | ||||||||
\(820\) | −1.32107 | −0.0461339 | ||||||||
\(821\) | −43.6714 | −1.52414 | −0.762071 | − | 0.647494i | \(-0.775817\pi\) | ||||
−0.762071 | + | 0.647494i | \(0.775817\pi\) | |||||||
\(822\) | −6.07639 | −0.211938 | ||||||||
\(823\) | 46.6151 | 1.62490 | 0.812450 | − | 0.583031i | \(-0.198133\pi\) | ||||
0.812450 | + | 0.583031i | \(0.198133\pi\) | |||||||
\(824\) | −19.5068 | −0.679552 | ||||||||
\(825\) | −44.0322 | −1.53300 | ||||||||
\(826\) | −6.79572 | −0.236453 | ||||||||
\(827\) | 17.7647 | 0.617740 | 0.308870 | − | 0.951104i | \(-0.400049\pi\) | ||||
0.308870 | + | 0.951104i | \(0.400049\pi\) | |||||||
\(828\) | 3.96875 | 0.137923 | ||||||||
\(829\) | 37.4854 | 1.30192 | 0.650961 | − | 0.759111i | \(-0.274366\pi\) | ||||
0.650961 | + | 0.759111i | \(0.274366\pi\) | |||||||
\(830\) | −2.63614 | −0.0915018 | ||||||||
\(831\) | 16.3022 | 0.565517 | ||||||||
\(832\) | 2.33495 | 0.0809499 | ||||||||
\(833\) | −19.9761 | −0.692132 | ||||||||
\(834\) | 21.7745 | 0.753991 | ||||||||
\(835\) | −2.40579 | −0.0832557 | ||||||||
\(836\) | −4.72840 | −0.163535 | ||||||||
\(837\) | 4.93560 | 0.170599 | ||||||||
\(838\) | 4.04766 | 0.139824 | ||||||||
\(839\) | 30.8409 | 1.06474 | 0.532372 | − | 0.846510i | \(-0.321301\pi\) | ||||
0.532372 | + | 0.846510i | \(0.321301\pi\) | |||||||
\(840\) | −0.432919 | −0.0149371 | ||||||||
\(841\) | 10.8187 | 0.373058 | ||||||||
\(842\) | 10.9475 | 0.377276 | ||||||||
\(843\) | −41.7437 | −1.43773 | ||||||||
\(844\) | 18.6669 | 0.642540 | ||||||||
\(845\) | 1.26830 | 0.0436309 | ||||||||
\(846\) | 5.56488 | 0.191325 | ||||||||
\(847\) | −11.8380 | −0.406758 | ||||||||
\(848\) | −0.518989 | −0.0178222 | ||||||||
\(849\) | −16.0191 | −0.549775 | ||||||||
\(850\) | −18.7369 | −0.642669 | ||||||||
\(851\) | −26.2178 | −0.898735 | ||||||||
\(852\) | 5.28326 | 0.181001 | ||||||||
\(853\) | 40.1040 | 1.37314 | 0.686568 | − | 0.727066i | \(-0.259116\pi\) | ||||
0.686568 | + | 0.727066i | \(0.259116\pi\) | |||||||
\(854\) | −10.1191 | −0.346270 | ||||||||
\(855\) | −0.160641 | −0.00549381 | ||||||||
\(856\) | −15.1972 | −0.519431 | ||||||||
\(857\) | −18.9045 | −0.645766 | −0.322883 | − | 0.946439i | \(-0.604652\pi\) | ||||
−0.322883 | + | 0.946439i | \(0.604652\pi\) | |||||||
\(858\) | 20.6794 | 0.705983 | ||||||||
\(859\) | 30.8310 | 1.05194 | 0.525970 | − | 0.850503i | \(-0.323702\pi\) | ||||
0.525970 | + | 0.850503i | \(0.323702\pi\) | |||||||
\(860\) | −0.478161 | −0.0163051 | ||||||||
\(861\) | 20.2559 | 0.690320 | ||||||||
\(862\) | −27.5446 | −0.938172 | ||||||||
\(863\) | −24.3604 | −0.829238 | −0.414619 | − | 0.909995i | \(-0.636085\pi\) | ||||
−0.414619 | + | 0.909995i | \(0.636085\pi\) | |||||||
\(864\) | 4.13845 | 0.140793 | ||||||||
\(865\) | 2.56935 | 0.0873605 | ||||||||
\(866\) | −27.4780 | −0.933742 | ||||||||
\(867\) | 5.52837 | 0.187753 | ||||||||
\(868\) | −1.55471 | −0.0527703 | ||||||||
\(869\) | −13.9677 | −0.473822 | ||||||||
\(870\) | −2.09557 | −0.0710465 | ||||||||
\(871\) | −13.5735 | −0.459920 | ||||||||
\(872\) | 10.6327 | 0.360069 | ||||||||
\(873\) | 0.185048 | 0.00626292 | ||||||||
\(874\) | 4.62202 | 0.156342 | ||||||||
\(875\) | −2.18429 | −0.0738425 | ||||||||
\(876\) | 19.9521 | 0.674119 | ||||||||
\(877\) | 34.0992 | 1.15145 | 0.575725 | − | 0.817644i | \(-0.304720\pi\) | ||||
0.575725 | + | 0.817644i | \(0.304720\pi\) | |||||||
\(878\) | 13.5683 | 0.457907 | ||||||||
\(879\) | 60.9747 | 2.05663 | ||||||||
\(880\) | 0.752978 | 0.0253829 | ||||||||
\(881\) | −1.04893 | −0.0353394 | −0.0176697 | − | 0.999844i | \(-0.505625\pi\) | ||||
−0.0176697 | + | 0.999844i | \(0.505625\pi\) | |||||||
\(882\) | −4.80251 | −0.161709 | ||||||||
\(883\) | −37.6484 | −1.26697 | −0.633484 | − | 0.773755i | \(-0.718376\pi\) | ||||
−0.633484 | + | 0.773755i | \(0.718376\pi\) | |||||||
\(884\) | 8.79963 | 0.295964 | ||||||||
\(885\) | 1.73120 | 0.0581935 | ||||||||
\(886\) | −0.790011 | −0.0265409 | ||||||||
\(887\) | 27.7832 | 0.932868 | 0.466434 | − | 0.884556i | \(-0.345539\pi\) | ||||
0.466434 | + | 0.884556i | \(0.345539\pi\) | |||||||
\(888\) | 11.8292 | 0.396961 | ||||||||
\(889\) | 11.2975 | 0.378907 | ||||||||
\(890\) | 0.328814 | 0.0110219 | ||||||||
\(891\) | 48.8323 | 1.63594 | ||||||||
\(892\) | 20.2007 | 0.676370 | ||||||||
\(893\) | 6.48089 | 0.216875 | ||||||||
\(894\) | 27.3418 | 0.914448 | ||||||||
\(895\) | 1.57151 | 0.0525297 | ||||||||
\(896\) | −1.30361 | −0.0435506 | ||||||||
\(897\) | −20.2142 | −0.674931 | ||||||||
\(898\) | 39.0557 | 1.30330 | ||||||||
\(899\) | −7.52567 | −0.250995 | ||||||||
\(900\) | −4.50458 | −0.150153 | ||||||||
\(901\) | −1.95589 | −0.0651602 | ||||||||
\(902\) | −35.2312 | −1.17307 | ||||||||
\(903\) | 7.33160 | 0.243980 | ||||||||
\(904\) | −3.37491 | −0.112248 | ||||||||
\(905\) | −4.03559 | −0.134148 | ||||||||
\(906\) | 4.81527 | 0.159977 | ||||||||
\(907\) | 7.46053 | 0.247723 | 0.123861 | − | 0.992300i | \(-0.460472\pi\) | ||||
0.123861 | + | 0.992300i | \(0.460472\pi\) | |||||||
\(908\) | 18.1102 | 0.601008 | ||||||||
\(909\) | 1.46862 | 0.0487109 | ||||||||
\(910\) | 0.511465 | 0.0169549 | ||||||||
\(911\) | 7.81434 | 0.258901 | 0.129450 | − | 0.991586i | \(-0.458679\pi\) | ||||
0.129450 | + | 0.991586i | \(0.458679\pi\) | |||||||
\(912\) | −2.08540 | −0.0690546 | ||||||||
\(913\) | −70.3023 | −2.32667 | ||||||||
\(914\) | 3.85746 | 0.127593 | ||||||||
\(915\) | 2.57783 | 0.0852204 | ||||||||
\(916\) | 2.03970 | 0.0673937 | ||||||||
\(917\) | −18.0205 | −0.595089 | ||||||||
\(918\) | 15.5964 | 0.514758 | ||||||||
\(919\) | −57.4085 | −1.89373 | −0.946865 | − | 0.321631i | \(-0.895769\pi\) | ||||
−0.946865 | + | 0.321631i | \(0.895769\pi\) | |||||||
\(920\) | −0.736038 | −0.0242665 | ||||||||
\(921\) | −0.606993 | −0.0200011 | ||||||||
\(922\) | −20.8437 | −0.686452 | ||||||||
\(923\) | −6.24183 | −0.205452 | ||||||||
\(924\) | −11.5454 | −0.379814 | ||||||||
\(925\) | 29.7576 | 0.978423 | ||||||||
\(926\) | 12.5445 | 0.412236 | ||||||||
\(927\) | −17.6738 | −0.580484 | ||||||||
\(928\) | −6.31021 | −0.207143 | ||||||||
\(929\) | −37.9459 | −1.24497 | −0.622483 | − | 0.782633i | \(-0.713876\pi\) | ||||
−0.622483 | + | 0.782633i | \(0.713876\pi\) | |||||||
\(930\) | 0.396059 | 0.0129873 | ||||||||
\(931\) | −5.59303 | −0.183304 | ||||||||
\(932\) | −7.97305 | −0.261166 | ||||||||
\(933\) | 42.6806 | 1.39730 | ||||||||
\(934\) | 16.7817 | 0.549114 | ||||||||
\(935\) | 2.83772 | 0.0928032 | ||||||||
\(936\) | 2.11554 | 0.0691486 | ||||||||
\(937\) | 29.6653 | 0.969125 | 0.484562 | − | 0.874757i | \(-0.338979\pi\) | ||||
0.484562 | + | 0.874757i | \(0.338979\pi\) | |||||||
\(938\) | 7.57812 | 0.247434 | ||||||||
\(939\) | 52.8168 | 1.72361 | ||||||||
\(940\) | −1.03206 | −0.0336619 | ||||||||
\(941\) | 49.4730 | 1.61277 | 0.806387 | − | 0.591388i | \(-0.201420\pi\) | ||||
0.806387 | + | 0.591388i | \(0.201420\pi\) | |||||||
\(942\) | 36.9024 | 1.20234 | ||||||||
\(943\) | 34.4386 | 1.12148 | ||||||||
\(944\) | 5.21300 | 0.169669 | ||||||||
\(945\) | 0.906518 | 0.0294890 | ||||||||
\(946\) | −12.7519 | −0.414600 | ||||||||
\(947\) | 35.5162 | 1.15412 | 0.577061 | − | 0.816701i | \(-0.304199\pi\) | ||||
0.577061 | + | 0.816701i | \(0.304199\pi\) | |||||||
\(948\) | −6.16029 | −0.200077 | ||||||||
\(949\) | −23.5721 | −0.765184 | ||||||||
\(950\) | −5.24606 | −0.170205 | ||||||||
\(951\) | 29.8142 | 0.966793 | ||||||||
\(952\) | −4.91286 | −0.159227 | ||||||||
\(953\) | 20.5083 | 0.664329 | 0.332165 | − | 0.943221i | \(-0.392221\pi\) | ||||
0.332165 | + | 0.943221i | \(0.392221\pi\) | |||||||
\(954\) | −0.470221 | −0.0152240 | ||||||||
\(955\) | 2.83599 | 0.0917703 | ||||||||
\(956\) | −17.1569 | −0.554894 | ||||||||
\(957\) | −55.8860 | −1.80654 | ||||||||
\(958\) | −42.5719 | −1.37544 | ||||||||
\(959\) | −4.00798 | −0.129424 | ||||||||
\(960\) | 0.332092 | 0.0107182 | ||||||||
\(961\) | −29.5777 | −0.954118 | ||||||||
\(962\) | −13.9754 | −0.450585 | ||||||||
\(963\) | −13.7692 | −0.443706 | ||||||||
\(964\) | −22.8505 | −0.735965 | ||||||||
\(965\) | 4.04177 | 0.130109 | ||||||||
\(966\) | 11.2856 | 0.363109 | ||||||||
\(967\) | −10.7690 | −0.346307 | −0.173153 | − | 0.984895i | \(-0.555396\pi\) | ||||
−0.173153 | + | 0.984895i | \(0.555396\pi\) | |||||||
\(968\) | 9.08093 | 0.291872 | ||||||||
\(969\) | −7.85917 | −0.252473 | ||||||||
\(970\) | −0.0343187 | −0.00110191 | ||||||||
\(971\) | −13.1794 | −0.422947 | −0.211474 | − | 0.977384i | \(-0.567826\pi\) | ||||
−0.211474 | + | 0.977384i | \(0.567826\pi\) | |||||||
\(972\) | 9.12153 | 0.292573 | ||||||||
\(973\) | 14.3625 | 0.460439 | ||||||||
\(974\) | −17.4778 | −0.560023 | ||||||||
\(975\) | 22.9433 | 0.734775 | ||||||||
\(976\) | 7.76239 | 0.248468 | ||||||||
\(977\) | −32.7763 | −1.04861 | −0.524303 | − | 0.851532i | \(-0.675674\pi\) | ||||
−0.524303 | + | 0.851532i | \(0.675674\pi\) | |||||||
\(978\) | 1.59540 | 0.0510153 | ||||||||
\(979\) | 8.76902 | 0.280259 | ||||||||
\(980\) | 0.890668 | 0.0284513 | ||||||||
\(981\) | 9.63357 | 0.307576 | ||||||||
\(982\) | −8.76263 | −0.279627 | ||||||||
\(983\) | −36.9148 | −1.17740 | −0.588700 | − | 0.808351i | \(-0.700360\pi\) | ||||
−0.588700 | + | 0.808351i | \(0.700360\pi\) | |||||||
\(984\) | −15.5383 | −0.495344 | ||||||||
\(985\) | 1.78714 | 0.0569429 | ||||||||
\(986\) | −23.7810 | −0.757341 | ||||||||
\(987\) | 15.8244 | 0.503697 | ||||||||
\(988\) | 2.46377 | 0.0783830 | ||||||||
\(989\) | 12.4650 | 0.396364 | ||||||||
\(990\) | 0.682223 | 0.0216825 | ||||||||
\(991\) | −2.15837 | −0.0685630 | −0.0342815 | − | 0.999412i | \(-0.510914\pi\) | ||||
−0.0342815 | + | 0.999412i | \(0.510914\pi\) | |||||||
\(992\) | 1.19262 | 0.0378657 | ||||||||
\(993\) | 54.7461 | 1.73732 | ||||||||
\(994\) | 3.48483 | 0.110532 | ||||||||
\(995\) | −1.42705 | −0.0452406 | ||||||||
\(996\) | −31.0060 | −0.982463 | ||||||||
\(997\) | −5.17430 | −0.163872 | −0.0819358 | − | 0.996638i | \(-0.526110\pi\) | ||||
−0.0819358 | + | 0.996638i | \(0.526110\pi\) | |||||||
\(998\) | −13.6928 | −0.433439 | ||||||||
\(999\) | −24.7699 | −0.783686 |
(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 | 8026.2.a.a.1.16 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.a.1.16 | ✓ | 71 | 1.1 | even | 1 | trivial |