Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4007,2,Mod(1,4007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4007, 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("4007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4007.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: | \(31.9960560899\) |
Analytic rank: | \(0\) |
Dimension: | \(195\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.77052 | −1.95905 | −0.979525 | − | 0.201322i | \(-0.935476\pi\) | ||||
−0.979525 | + | 0.201322i | \(0.935476\pi\) | |||||||
\(3\) | −1.23937 | −0.715549 | −0.357774 | − | 0.933808i | \(-0.616464\pi\) | ||||
−0.357774 | + | 0.933808i | \(0.616464\pi\) | |||||||
\(4\) | 5.67576 | 2.83788 | ||||||||
\(5\) | −3.30641 | −1.47867 | −0.739336 | − | 0.673336i | \(-0.764861\pi\) | ||||
−0.739336 | + | 0.673336i | \(0.764861\pi\) | |||||||
\(6\) | 3.43369 | 1.40180 | ||||||||
\(7\) | 0.994092 | 0.375731 | 0.187866 | − | 0.982195i | \(-0.439843\pi\) | ||||
0.187866 | + | 0.982195i | \(0.439843\pi\) | |||||||
\(8\) | −10.1837 | −3.60050 | ||||||||
\(9\) | −1.46397 | −0.487990 | ||||||||
\(10\) | 9.16047 | 2.89679 | ||||||||
\(11\) | 2.91316 | 0.878351 | 0.439176 | − | 0.898401i | \(-0.355271\pi\) | ||||
0.439176 | + | 0.898401i | \(0.355271\pi\) | |||||||
\(12\) | −7.03435 | −2.03064 | ||||||||
\(13\) | 2.07626 | 0.575852 | 0.287926 | − | 0.957653i | \(-0.407034\pi\) | ||||
0.287926 | + | 0.957653i | \(0.407034\pi\) | |||||||
\(14\) | −2.75415 | −0.736076 | ||||||||
\(15\) | 4.09786 | 1.05806 | ||||||||
\(16\) | 16.8627 | 4.21567 | ||||||||
\(17\) | 4.81136 | 1.16693 | 0.583463 | − | 0.812140i | \(-0.301698\pi\) | ||||
0.583463 | + | 0.812140i | \(0.301698\pi\) | |||||||
\(18\) | 4.05595 | 0.955996 | ||||||||
\(19\) | 1.21446 | 0.278617 | 0.139309 | − | 0.990249i | \(-0.455512\pi\) | ||||
0.139309 | + | 0.990249i | \(0.455512\pi\) | |||||||
\(20\) | −18.7664 | −4.19629 | ||||||||
\(21\) | −1.23204 | −0.268854 | ||||||||
\(22\) | −8.07096 | −1.72073 | ||||||||
\(23\) | 6.65884 | 1.38846 | 0.694232 | − | 0.719752i | \(-0.255744\pi\) | ||||
0.694232 | + | 0.719752i | \(0.255744\pi\) | |||||||
\(24\) | 12.6214 | 2.57633 | ||||||||
\(25\) | 5.93236 | 1.18647 | ||||||||
\(26\) | −5.75232 | −1.12812 | ||||||||
\(27\) | 5.53250 | 1.06473 | ||||||||
\(28\) | 5.64222 | 1.06628 | ||||||||
\(29\) | −2.11829 | −0.393356 | −0.196678 | − | 0.980468i | \(-0.563015\pi\) | ||||
−0.196678 | + | 0.980468i | \(0.563015\pi\) | |||||||
\(30\) | −11.3532 | −2.07280 | ||||||||
\(31\) | 10.3256 | 1.85454 | 0.927269 | − | 0.374396i | \(-0.122150\pi\) | ||||
0.927269 | + | 0.374396i | \(0.122150\pi\) | |||||||
\(32\) | −26.3509 | −4.65822 | ||||||||
\(33\) | −3.61048 | −0.628503 | ||||||||
\(34\) | −13.3299 | −2.28606 | ||||||||
\(35\) | −3.28688 | −0.555583 | ||||||||
\(36\) | −8.30913 | −1.38486 | ||||||||
\(37\) | 5.71649 | 0.939785 | 0.469892 | − | 0.882724i | \(-0.344293\pi\) | ||||
0.469892 | + | 0.882724i | \(0.344293\pi\) | |||||||
\(38\) | −3.36469 | −0.545825 | ||||||||
\(39\) | −2.57325 | −0.412050 | ||||||||
\(40\) | 33.6716 | 5.32395 | ||||||||
\(41\) | 3.53656 | 0.552317 | 0.276159 | − | 0.961112i | \(-0.410938\pi\) | ||||
0.276159 | + | 0.961112i | \(0.410938\pi\) | |||||||
\(42\) | 3.41340 | 0.526699 | ||||||||
\(43\) | 5.71015 | 0.870790 | 0.435395 | − | 0.900239i | \(-0.356609\pi\) | ||||
0.435395 | + | 0.900239i | \(0.356609\pi\) | |||||||
\(44\) | 16.5344 | 2.49265 | ||||||||
\(45\) | 4.84048 | 0.721577 | ||||||||
\(46\) | −18.4484 | −2.72007 | ||||||||
\(47\) | 4.09201 | 0.596881 | 0.298440 | − | 0.954428i | \(-0.403534\pi\) | ||||
0.298440 | + | 0.954428i | \(0.403534\pi\) | |||||||
\(48\) | −20.8991 | −3.01652 | ||||||||
\(49\) | −6.01178 | −0.858826 | ||||||||
\(50\) | −16.4357 | −2.32436 | ||||||||
\(51\) | −5.96304 | −0.834992 | ||||||||
\(52\) | 11.7844 | 1.63420 | ||||||||
\(53\) | −3.54063 | −0.486342 | −0.243171 | − | 0.969983i | \(-0.578188\pi\) | ||||
−0.243171 | + | 0.969983i | \(0.578188\pi\) | |||||||
\(54\) | −15.3279 | −2.08586 | ||||||||
\(55\) | −9.63211 | −1.29879 | ||||||||
\(56\) | −10.1236 | −1.35282 | ||||||||
\(57\) | −1.50517 | −0.199364 | ||||||||
\(58\) | 5.86875 | 0.770605 | ||||||||
\(59\) | −9.23267 | −1.20199 | −0.600995 | − | 0.799252i | \(-0.705229\pi\) | ||||
−0.600995 | + | 0.799252i | \(0.705229\pi\) | |||||||
\(60\) | 23.2584 | 3.00265 | ||||||||
\(61\) | −14.5531 | −1.86334 | −0.931669 | − | 0.363307i | \(-0.881648\pi\) | ||||
−0.931669 | + | 0.363307i | \(0.881648\pi\) | |||||||
\(62\) | −28.6073 | −3.63313 | ||||||||
\(63\) | −1.45532 | −0.183353 | ||||||||
\(64\) | 39.2801 | 4.91002 | ||||||||
\(65\) | −6.86498 | −0.851496 | ||||||||
\(66\) | 10.0029 | 1.23127 | ||||||||
\(67\) | 8.60276 | 1.05099 | 0.525497 | − | 0.850795i | \(-0.323879\pi\) | ||||
0.525497 | + | 0.850795i | \(0.323879\pi\) | |||||||
\(68\) | 27.3081 | 3.31159 | ||||||||
\(69\) | −8.25274 | −0.993513 | ||||||||
\(70\) | 9.10634 | 1.08842 | ||||||||
\(71\) | 1.60963 | 0.191028 | 0.0955140 | − | 0.995428i | \(-0.469551\pi\) | ||||
0.0955140 | + | 0.995428i | \(0.469551\pi\) | |||||||
\(72\) | 14.9087 | 1.75700 | ||||||||
\(73\) | 5.73619 | 0.671370 | 0.335685 | − | 0.941974i | \(-0.391032\pi\) | ||||
0.335685 | + | 0.941974i | \(0.391032\pi\) | |||||||
\(74\) | −15.8376 | −1.84109 | ||||||||
\(75\) | −7.35237 | −0.848979 | ||||||||
\(76\) | 6.89300 | 0.790681 | ||||||||
\(77\) | 2.89595 | 0.330024 | ||||||||
\(78\) | 7.12924 | 0.807227 | ||||||||
\(79\) | 16.4185 | 1.84722 | 0.923611 | − | 0.383331i | \(-0.125223\pi\) | ||||
0.923611 | + | 0.383331i | \(0.125223\pi\) | |||||||
\(80\) | −55.7550 | −6.23360 | ||||||||
\(81\) | −2.46489 | −0.273876 | ||||||||
\(82\) | −9.79808 | −1.08202 | ||||||||
\(83\) | −6.24645 | −0.685637 | −0.342818 | − | 0.939402i | \(-0.611382\pi\) | ||||
−0.342818 | + | 0.939402i | \(0.611382\pi\) | |||||||
\(84\) | −6.99278 | −0.762975 | ||||||||
\(85\) | −15.9083 | −1.72550 | ||||||||
\(86\) | −15.8201 | −1.70592 | ||||||||
\(87\) | 2.62534 | 0.281466 | ||||||||
\(88\) | −29.6669 | −3.16250 | ||||||||
\(89\) | −3.62229 | −0.383962 | −0.191981 | − | 0.981399i | \(-0.561491\pi\) | ||||
−0.191981 | + | 0.981399i | \(0.561491\pi\) | |||||||
\(90\) | −13.4106 | −1.41361 | ||||||||
\(91\) | 2.06400 | 0.216366 | ||||||||
\(92\) | 37.7939 | 3.94029 | ||||||||
\(93\) | −12.7972 | −1.32701 | ||||||||
\(94\) | −11.3370 | −1.16932 | ||||||||
\(95\) | −4.01552 | −0.411984 | ||||||||
\(96\) | 32.6584 | 3.33319 | ||||||||
\(97\) | −10.3255 | −1.04840 | −0.524199 | − | 0.851596i | \(-0.675635\pi\) | ||||
−0.524199 | + | 0.851596i | \(0.675635\pi\) | |||||||
\(98\) | 16.6557 | 1.68248 | ||||||||
\(99\) | −4.26478 | −0.428626 | ||||||||
\(100\) | 33.6706 | 3.36706 | ||||||||
\(101\) | 6.07427 | 0.604413 | 0.302206 | − | 0.953243i | \(-0.402277\pi\) | ||||
0.302206 | + | 0.953243i | \(0.402277\pi\) | |||||||
\(102\) | 16.5207 | 1.63579 | ||||||||
\(103\) | 9.62892 | 0.948766 | 0.474383 | − | 0.880319i | \(-0.342671\pi\) | ||||
0.474383 | + | 0.880319i | \(0.342671\pi\) | |||||||
\(104\) | −21.1441 | −2.07335 | ||||||||
\(105\) | 4.07365 | 0.397547 | ||||||||
\(106\) | 9.80936 | 0.952769 | ||||||||
\(107\) | 13.0355 | 1.26019 | 0.630096 | − | 0.776517i | \(-0.283016\pi\) | ||||
0.630096 | + | 0.776517i | \(0.283016\pi\) | |||||||
\(108\) | 31.4011 | 3.02157 | ||||||||
\(109\) | 5.73531 | 0.549343 | 0.274672 | − | 0.961538i | \(-0.411431\pi\) | ||||
0.274672 | + | 0.961538i | \(0.411431\pi\) | |||||||
\(110\) | 26.6859 | 2.54440 | ||||||||
\(111\) | −7.08483 | −0.672462 | ||||||||
\(112\) | 16.7631 | 1.58396 | ||||||||
\(113\) | −11.8656 | −1.11622 | −0.558109 | − | 0.829768i | \(-0.688473\pi\) | ||||
−0.558109 | + | 0.829768i | \(0.688473\pi\) | |||||||
\(114\) | 4.17009 | 0.390565 | ||||||||
\(115\) | −22.0169 | −2.05308 | ||||||||
\(116\) | −12.0229 | −1.11630 | ||||||||
\(117\) | −3.03958 | −0.281010 | ||||||||
\(118\) | 25.5792 | 2.35476 | ||||||||
\(119\) | 4.78293 | 0.438450 | ||||||||
\(120\) | −41.7315 | −3.80955 | ||||||||
\(121\) | −2.51349 | −0.228499 | ||||||||
\(122\) | 40.3197 | 3.65037 | ||||||||
\(123\) | −4.38309 | −0.395210 | ||||||||
\(124\) | 58.6058 | 5.26295 | ||||||||
\(125\) | −3.08277 | −0.275731 | ||||||||
\(126\) | 4.03198 | 0.359198 | ||||||||
\(127\) | 16.5332 | 1.46708 | 0.733541 | − | 0.679645i | \(-0.237866\pi\) | ||||
0.733541 | + | 0.679645i | \(0.237866\pi\) | |||||||
\(128\) | −56.1244 | −4.96075 | ||||||||
\(129\) | −7.07698 | −0.623093 | ||||||||
\(130\) | 19.0195 | 1.66812 | ||||||||
\(131\) | 11.7205 | 1.02403 | 0.512013 | − | 0.858977i | \(-0.328900\pi\) | ||||
0.512013 | + | 0.858977i | \(0.328900\pi\) | |||||||
\(132\) | −20.4922 | −1.78362 | ||||||||
\(133\) | 1.20729 | 0.104685 | ||||||||
\(134\) | −23.8341 | −2.05895 | ||||||||
\(135\) | −18.2927 | −1.57439 | ||||||||
\(136\) | −48.9976 | −4.20151 | ||||||||
\(137\) | 1.51778 | 0.129673 | 0.0648365 | − | 0.997896i | \(-0.479347\pi\) | ||||
0.0648365 | + | 0.997896i | \(0.479347\pi\) | |||||||
\(138\) | 22.8643 | 1.94634 | ||||||||
\(139\) | −15.5439 | −1.31842 | −0.659209 | − | 0.751960i | \(-0.729109\pi\) | ||||
−0.659209 | + | 0.751960i | \(0.729109\pi\) | |||||||
\(140\) | −18.6555 | −1.57668 | ||||||||
\(141\) | −5.07150 | −0.427098 | ||||||||
\(142\) | −4.45951 | −0.374233 | ||||||||
\(143\) | 6.04849 | 0.505800 | ||||||||
\(144\) | −24.6865 | −2.05721 | ||||||||
\(145\) | 7.00394 | 0.581645 | ||||||||
\(146\) | −15.8922 | −1.31525 | ||||||||
\(147\) | 7.45081 | 0.614532 | ||||||||
\(148\) | 32.4454 | 2.66699 | ||||||||
\(149\) | 3.00769 | 0.246400 | 0.123200 | − | 0.992382i | \(-0.460684\pi\) | ||||
0.123200 | + | 0.992382i | \(0.460684\pi\) | |||||||
\(150\) | 20.3699 | 1.66319 | ||||||||
\(151\) | −5.08613 | −0.413904 | −0.206952 | − | 0.978351i | \(-0.566354\pi\) | ||||
−0.206952 | + | 0.978351i | \(0.566354\pi\) | |||||||
\(152\) | −12.3678 | −1.00316 | ||||||||
\(153\) | −7.04367 | −0.569447 | ||||||||
\(154\) | −8.02327 | −0.646534 | ||||||||
\(155\) | −34.1408 | −2.74225 | ||||||||
\(156\) | −14.6052 | −1.16935 | ||||||||
\(157\) | 9.43823 | 0.753253 | 0.376626 | − | 0.926365i | \(-0.377084\pi\) | ||||
0.376626 | + | 0.926365i | \(0.377084\pi\) | |||||||
\(158\) | −45.4876 | −3.61880 | ||||||||
\(159\) | 4.38814 | 0.348002 | ||||||||
\(160\) | 87.1269 | 6.88798 | ||||||||
\(161\) | 6.61949 | 0.521689 | ||||||||
\(162\) | 6.82901 | 0.536538 | ||||||||
\(163\) | −4.63869 | −0.363330 | −0.181665 | − | 0.983360i | \(-0.558149\pi\) | ||||
−0.181665 | + | 0.983360i | \(0.558149\pi\) | |||||||
\(164\) | 20.0726 | 1.56741 | ||||||||
\(165\) | 11.9377 | 0.929351 | ||||||||
\(166\) | 17.3059 | 1.34320 | ||||||||
\(167\) | −16.7707 | −1.29776 | −0.648879 | − | 0.760892i | \(-0.724762\pi\) | ||||
−0.648879 | + | 0.760892i | \(0.724762\pi\) | |||||||
\(168\) | 12.5468 | 0.968008 | ||||||||
\(169\) | −8.68913 | −0.668395 | ||||||||
\(170\) | 44.0743 | 3.38034 | ||||||||
\(171\) | −1.77794 | −0.135962 | ||||||||
\(172\) | 32.4094 | 2.47120 | ||||||||
\(173\) | −1.46616 | −0.111470 | −0.0557352 | − | 0.998446i | \(-0.517750\pi\) | ||||
−0.0557352 | + | 0.998446i | \(0.517750\pi\) | |||||||
\(174\) | −7.27354 | −0.551406 | ||||||||
\(175\) | 5.89731 | 0.445795 | ||||||||
\(176\) | 49.1238 | 3.70284 | ||||||||
\(177\) | 11.4427 | 0.860083 | ||||||||
\(178\) | 10.0356 | 0.752201 | ||||||||
\(179\) | −22.3085 | −1.66742 | −0.833708 | − | 0.552205i | \(-0.813786\pi\) | ||||
−0.833708 | + | 0.552205i | \(0.813786\pi\) | |||||||
\(180\) | 27.4734 | 2.04775 | ||||||||
\(181\) | −1.89933 | −0.141176 | −0.0705882 | − | 0.997506i | \(-0.522488\pi\) | ||||
−0.0705882 | + | 0.997506i | \(0.522488\pi\) | |||||||
\(182\) | −5.71833 | −0.423871 | ||||||||
\(183\) | 18.0367 | 1.33331 | ||||||||
\(184\) | −67.8118 | −4.99916 | ||||||||
\(185\) | −18.9011 | −1.38963 | ||||||||
\(186\) | 35.4550 | 2.59968 | ||||||||
\(187\) | 14.0163 | 1.02497 | ||||||||
\(188\) | 23.2252 | 1.69388 | ||||||||
\(189\) | 5.49981 | 0.400052 | ||||||||
\(190\) | 11.1251 | 0.807096 | ||||||||
\(191\) | 0.205124 | 0.0148423 | 0.00742114 | − | 0.999972i | \(-0.497638\pi\) | ||||
0.00742114 | + | 0.999972i | \(0.497638\pi\) | |||||||
\(192\) | −48.6825 | −3.51336 | ||||||||
\(193\) | 2.88113 | 0.207388 | 0.103694 | − | 0.994609i | \(-0.466934\pi\) | ||||
0.103694 | + | 0.994609i | \(0.466934\pi\) | |||||||
\(194\) | 28.6070 | 2.05387 | ||||||||
\(195\) | 8.50823 | 0.609287 | ||||||||
\(196\) | −34.1214 | −2.43724 | ||||||||
\(197\) | 3.47856 | 0.247837 | 0.123918 | − | 0.992292i | \(-0.460454\pi\) | ||||
0.123918 | + | 0.992292i | \(0.460454\pi\) | |||||||
\(198\) | 11.8156 | 0.839701 | ||||||||
\(199\) | 11.7514 | 0.833037 | 0.416519 | − | 0.909127i | \(-0.363250\pi\) | ||||
0.416519 | + | 0.909127i | \(0.363250\pi\) | |||||||
\(200\) | −60.4136 | −4.27189 | ||||||||
\(201\) | −10.6620 | −0.752038 | ||||||||
\(202\) | −16.8289 | −1.18407 | ||||||||
\(203\) | −2.10577 | −0.147796 | ||||||||
\(204\) | −33.8447 | −2.36961 | ||||||||
\(205\) | −11.6933 | −0.816696 | ||||||||
\(206\) | −26.6771 | −1.85868 | ||||||||
\(207\) | −9.74833 | −0.677556 | ||||||||
\(208\) | 35.0114 | 2.42760 | ||||||||
\(209\) | 3.53793 | 0.244724 | ||||||||
\(210\) | −11.2861 | −0.778815 | ||||||||
\(211\) | −15.1168 | −1.04068 | −0.520340 | − | 0.853959i | \(-0.674195\pi\) | ||||
−0.520340 | + | 0.853959i | \(0.674195\pi\) | |||||||
\(212\) | −20.0957 | −1.38018 | ||||||||
\(213\) | −1.99492 | −0.136690 | ||||||||
\(214\) | −36.1151 | −2.46878 | ||||||||
\(215\) | −18.8801 | −1.28761 | ||||||||
\(216\) | −56.3415 | −3.83355 | ||||||||
\(217\) | 10.2646 | 0.696808 | ||||||||
\(218\) | −15.8898 | −1.07619 | ||||||||
\(219\) | −7.10925 | −0.480398 | ||||||||
\(220\) | −54.6695 | −3.68582 | ||||||||
\(221\) | 9.98964 | 0.671976 | ||||||||
\(222\) | 19.6286 | 1.31739 | ||||||||
\(223\) | −1.10236 | −0.0738195 | −0.0369098 | − | 0.999319i | \(-0.511751\pi\) | ||||
−0.0369098 | + | 0.999319i | \(0.511751\pi\) | |||||||
\(224\) | −26.1952 | −1.75024 | ||||||||
\(225\) | −8.68479 | −0.578986 | ||||||||
\(226\) | 32.8737 | 2.18673 | ||||||||
\(227\) | 13.1157 | 0.870517 | 0.435258 | − | 0.900306i | \(-0.356657\pi\) | ||||
0.435258 | + | 0.900306i | \(0.356657\pi\) | |||||||
\(228\) | −8.54296 | −0.565771 | ||||||||
\(229\) | −12.1917 | −0.805651 | −0.402826 | − | 0.915277i | \(-0.631972\pi\) | ||||
−0.402826 | + | 0.915277i | \(0.631972\pi\) | |||||||
\(230\) | 60.9980 | 4.02209 | ||||||||
\(231\) | −3.58914 | −0.236148 | ||||||||
\(232\) | 21.5721 | 1.41628 | ||||||||
\(233\) | −20.2198 | −1.32464 | −0.662322 | − | 0.749219i | \(-0.730429\pi\) | ||||
−0.662322 | + | 0.749219i | \(0.730429\pi\) | |||||||
\(234\) | 8.42122 | 0.550512 | ||||||||
\(235\) | −13.5299 | −0.882591 | ||||||||
\(236\) | −52.4024 | −3.41110 | ||||||||
\(237\) | −20.3485 | −1.32178 | ||||||||
\(238\) | −13.2512 | −0.858946 | ||||||||
\(239\) | 7.73971 | 0.500640 | 0.250320 | − | 0.968163i | \(-0.419464\pi\) | ||||
0.250320 | + | 0.968163i | \(0.419464\pi\) | |||||||
\(240\) | 69.1009 | 4.46045 | ||||||||
\(241\) | −8.80975 | −0.567486 | −0.283743 | − | 0.958900i | \(-0.591576\pi\) | ||||
−0.283743 | + | 0.958900i | \(0.591576\pi\) | |||||||
\(242\) | 6.96366 | 0.447641 | ||||||||
\(243\) | −13.5426 | −0.868757 | ||||||||
\(244\) | −82.6001 | −5.28793 | ||||||||
\(245\) | 19.8774 | 1.26992 | ||||||||
\(246\) | 12.1434 | 0.774236 | ||||||||
\(247\) | 2.52155 | 0.160442 | ||||||||
\(248\) | −105.154 | −6.67726 | ||||||||
\(249\) | 7.74164 | 0.490607 | ||||||||
\(250\) | 8.54087 | 0.540172 | ||||||||
\(251\) | 29.6227 | 1.86977 | 0.934883 | − | 0.354956i | \(-0.115504\pi\) | ||||
0.934883 | + | 0.354956i | \(0.115504\pi\) | |||||||
\(252\) | −8.26004 | −0.520333 | ||||||||
\(253\) | 19.3983 | 1.21956 | ||||||||
\(254\) | −45.8054 | −2.87409 | ||||||||
\(255\) | 19.7163 | 1.23468 | ||||||||
\(256\) | 76.9334 | 4.80834 | ||||||||
\(257\) | 14.2007 | 0.885812 | 0.442906 | − | 0.896568i | \(-0.353947\pi\) | ||||
0.442906 | + | 0.896568i | \(0.353947\pi\) | |||||||
\(258\) | 19.6069 | 1.22067 | ||||||||
\(259\) | 5.68271 | 0.353107 | ||||||||
\(260\) | −38.9640 | −2.41644 | ||||||||
\(261\) | 3.10111 | 0.191954 | ||||||||
\(262\) | −32.4719 | −2.00612 | ||||||||
\(263\) | 31.6261 | 1.95015 | 0.975075 | − | 0.221875i | \(-0.0712178\pi\) | ||||
0.975075 | + | 0.221875i | \(0.0712178\pi\) | |||||||
\(264\) | 36.7682 | 2.26292 | ||||||||
\(265\) | 11.7068 | 0.719141 | ||||||||
\(266\) | −3.34481 | −0.205084 | ||||||||
\(267\) | 4.48935 | 0.274744 | ||||||||
\(268\) | 48.8272 | 2.98259 | ||||||||
\(269\) | −20.9269 | −1.27593 | −0.637967 | − | 0.770064i | \(-0.720224\pi\) | ||||
−0.637967 | + | 0.770064i | \(0.720224\pi\) | |||||||
\(270\) | 50.6802 | 3.08430 | ||||||||
\(271\) | −16.7834 | −1.01952 | −0.509759 | − | 0.860317i | \(-0.670266\pi\) | ||||
−0.509759 | + | 0.860317i | \(0.670266\pi\) | |||||||
\(272\) | 81.1324 | 4.91938 | ||||||||
\(273\) | −2.55805 | −0.154820 | ||||||||
\(274\) | −4.20504 | −0.254036 | ||||||||
\(275\) | 17.2819 | 1.04214 | ||||||||
\(276\) | −46.8405 | −2.81947 | ||||||||
\(277\) | −23.7231 | −1.42539 | −0.712693 | − | 0.701476i | \(-0.752525\pi\) | ||||
−0.712693 | + | 0.701476i | \(0.752525\pi\) | |||||||
\(278\) | 43.0647 | 2.58285 | ||||||||
\(279\) | −15.1164 | −0.904995 | ||||||||
\(280\) | 33.4727 | 2.00038 | ||||||||
\(281\) | 15.7495 | 0.939537 | 0.469769 | − | 0.882790i | \(-0.344337\pi\) | ||||
0.469769 | + | 0.882790i | \(0.344337\pi\) | |||||||
\(282\) | 14.0507 | 0.836706 | ||||||||
\(283\) | −22.7026 | −1.34953 | −0.674764 | − | 0.738034i | \(-0.735754\pi\) | ||||
−0.674764 | + | 0.738034i | \(0.735754\pi\) | |||||||
\(284\) | 9.13587 | 0.542114 | ||||||||
\(285\) | 4.97670 | 0.294794 | ||||||||
\(286\) | −16.7574 | −0.990888 | ||||||||
\(287\) | 3.51566 | 0.207523 | ||||||||
\(288\) | 38.5769 | 2.27316 | ||||||||
\(289\) | 6.14914 | 0.361714 | ||||||||
\(290\) | −19.4045 | −1.13947 | ||||||||
\(291\) | 12.7971 | 0.750180 | ||||||||
\(292\) | 32.5572 | 1.90527 | ||||||||
\(293\) | −15.8556 | −0.926295 | −0.463148 | − | 0.886281i | \(-0.653280\pi\) | ||||
−0.463148 | + | 0.886281i | \(0.653280\pi\) | |||||||
\(294\) | −20.6426 | −1.20390 | ||||||||
\(295\) | 30.5270 | 1.77735 | ||||||||
\(296\) | −58.2152 | −3.38369 | ||||||||
\(297\) | 16.1171 | 0.935207 | ||||||||
\(298\) | −8.33286 | −0.482709 | ||||||||
\(299\) | 13.8255 | 0.799549 | ||||||||
\(300\) | −41.7303 | −2.40930 | ||||||||
\(301\) | 5.67641 | 0.327183 | ||||||||
\(302\) | 14.0912 | 0.810858 | ||||||||
\(303\) | −7.52825 | −0.432487 | ||||||||
\(304\) | 20.4791 | 1.17456 | ||||||||
\(305\) | 48.1187 | 2.75527 | ||||||||
\(306\) | 19.5146 | 1.11558 | ||||||||
\(307\) | 26.4237 | 1.50808 | 0.754039 | − | 0.656829i | \(-0.228103\pi\) | ||||
0.754039 | + | 0.656829i | \(0.228103\pi\) | |||||||
\(308\) | 16.4367 | 0.936568 | ||||||||
\(309\) | −11.9338 | −0.678888 | ||||||||
\(310\) | 94.5876 | 5.37221 | ||||||||
\(311\) | 18.8003 | 1.06607 | 0.533034 | − | 0.846094i | \(-0.321052\pi\) | ||||
0.533034 | + | 0.846094i | \(0.321052\pi\) | |||||||
\(312\) | 26.2053 | 1.48358 | ||||||||
\(313\) | 28.1506 | 1.59117 | 0.795584 | − | 0.605843i | \(-0.207164\pi\) | ||||
0.795584 | + | 0.605843i | \(0.207164\pi\) | |||||||
\(314\) | −26.1488 | −1.47566 | ||||||||
\(315\) | 4.81188 | 0.271119 | ||||||||
\(316\) | 93.1872 | 5.24219 | ||||||||
\(317\) | 10.3844 | 0.583246 | 0.291623 | − | 0.956533i | \(-0.405805\pi\) | ||||
0.291623 | + | 0.956533i | \(0.405805\pi\) | |||||||
\(318\) | −12.1574 | −0.681753 | ||||||||
\(319\) | −6.17092 | −0.345505 | ||||||||
\(320\) | −129.876 | −7.26031 | ||||||||
\(321\) | −16.1558 | −0.901729 | ||||||||
\(322\) | −18.3394 | −1.02202 | ||||||||
\(323\) | 5.84322 | 0.325125 | ||||||||
\(324\) | −13.9901 | −0.777228 | ||||||||
\(325\) | 12.3171 | 0.683232 | ||||||||
\(326\) | 12.8516 | 0.711783 | ||||||||
\(327\) | −7.10816 | −0.393082 | ||||||||
\(328\) | −36.0154 | −1.98862 | ||||||||
\(329\) | 4.06783 | 0.224267 | ||||||||
\(330\) | −33.0737 | −1.82064 | ||||||||
\(331\) | 5.48437 | 0.301448 | 0.150724 | − | 0.988576i | \(-0.451839\pi\) | ||||
0.150724 | + | 0.988576i | \(0.451839\pi\) | |||||||
\(332\) | −35.4533 | −1.94575 | ||||||||
\(333\) | −8.36876 | −0.458605 | ||||||||
\(334\) | 46.4636 | 2.54237 | ||||||||
\(335\) | −28.4443 | −1.55408 | ||||||||
\(336\) | −20.7756 | −1.13340 | ||||||||
\(337\) | 5.96960 | 0.325185 | 0.162593 | − | 0.986693i | \(-0.448014\pi\) | ||||
0.162593 | + | 0.986693i | \(0.448014\pi\) | |||||||
\(338\) | 24.0734 | 1.30942 | ||||||||
\(339\) | 14.7058 | 0.798708 | ||||||||
\(340\) | −90.2918 | −4.89676 | ||||||||
\(341\) | 30.0802 | 1.62894 | ||||||||
\(342\) | 4.92580 | 0.266357 | ||||||||
\(343\) | −12.9349 | −0.698419 | ||||||||
\(344\) | −58.1507 | −3.13528 | ||||||||
\(345\) | 27.2870 | 1.46908 | ||||||||
\(346\) | 4.06203 | 0.218376 | ||||||||
\(347\) | 6.44036 | 0.345737 | 0.172868 | − | 0.984945i | \(-0.444696\pi\) | ||||
0.172868 | + | 0.984945i | \(0.444696\pi\) | |||||||
\(348\) | 14.9008 | 0.798766 | ||||||||
\(349\) | −27.3391 | −1.46343 | −0.731714 | − | 0.681611i | \(-0.761280\pi\) | ||||
−0.731714 | + | 0.681611i | \(0.761280\pi\) | |||||||
\(350\) | −16.3386 | −0.873334 | ||||||||
\(351\) | 11.4869 | 0.613126 | ||||||||
\(352\) | −76.7644 | −4.09155 | ||||||||
\(353\) | −8.29497 | −0.441497 | −0.220748 | − | 0.975331i | \(-0.570850\pi\) | ||||
−0.220748 | + | 0.975331i | \(0.570850\pi\) | |||||||
\(354\) | −31.7021 | −1.68495 | ||||||||
\(355\) | −5.32210 | −0.282468 | ||||||||
\(356\) | −20.5592 | −1.08964 | ||||||||
\(357\) | −5.92780 | −0.313733 | ||||||||
\(358\) | 61.8061 | 3.26655 | ||||||||
\(359\) | 1.02179 | 0.0539280 | 0.0269640 | − | 0.999636i | \(-0.491416\pi\) | ||||
0.0269640 | + | 0.999636i | \(0.491416\pi\) | |||||||
\(360\) | −49.2942 | −2.59803 | ||||||||
\(361\) | −17.5251 | −0.922372 | ||||||||
\(362\) | 5.26214 | 0.276572 | ||||||||
\(363\) | 3.11513 | 0.163502 | ||||||||
\(364\) | 11.7147 | 0.614019 | ||||||||
\(365\) | −18.9662 | −0.992737 | ||||||||
\(366\) | −49.9709 | −2.61202 | ||||||||
\(367\) | 34.3198 | 1.79148 | 0.895740 | − | 0.444579i | \(-0.146647\pi\) | ||||
0.895740 | + | 0.444579i | \(0.146647\pi\) | |||||||
\(368\) | 112.286 | 5.85331 | ||||||||
\(369\) | −5.17741 | −0.269525 | ||||||||
\(370\) | 52.3657 | 2.72236 | ||||||||
\(371\) | −3.51971 | −0.182734 | ||||||||
\(372\) | −72.6341 | −3.76590 | ||||||||
\(373\) | 16.9249 | 0.876336 | 0.438168 | − | 0.898893i | \(-0.355628\pi\) | ||||
0.438168 | + | 0.898893i | \(0.355628\pi\) | |||||||
\(374\) | −38.8323 | −2.00797 | ||||||||
\(375\) | 3.82069 | 0.197299 | ||||||||
\(376\) | −41.6720 | −2.14907 | ||||||||
\(377\) | −4.39813 | −0.226515 | ||||||||
\(378\) | −15.2373 | −0.783722 | ||||||||
\(379\) | 38.8632 | 1.99627 | 0.998134 | − | 0.0610647i | \(-0.0194496\pi\) | ||||
0.998134 | + | 0.0610647i | \(0.0194496\pi\) | |||||||
\(380\) | −22.7911 | −1.16916 | ||||||||
\(381\) | −20.4907 | −1.04977 | ||||||||
\(382\) | −0.568300 | −0.0290768 | ||||||||
\(383\) | −11.6681 | −0.596214 | −0.298107 | − | 0.954532i | \(-0.596355\pi\) | ||||
−0.298107 | + | 0.954532i | \(0.596355\pi\) | |||||||
\(384\) | 69.5588 | 3.54966 | ||||||||
\(385\) | −9.57520 | −0.487998 | ||||||||
\(386\) | −7.98221 | −0.406284 | ||||||||
\(387\) | −8.35949 | −0.424937 | ||||||||
\(388\) | −58.6052 | −2.97523 | ||||||||
\(389\) | −32.1958 | −1.63239 | −0.816196 | − | 0.577775i | \(-0.803921\pi\) | ||||
−0.816196 | + | 0.577775i | \(0.803921\pi\) | |||||||
\(390\) | −23.5722 | −1.19362 | ||||||||
\(391\) | 32.0380 | 1.62023 | ||||||||
\(392\) | 61.2224 | 3.09220 | ||||||||
\(393\) | −14.5260 | −0.732741 | ||||||||
\(394\) | −9.63739 | −0.485525 | ||||||||
\(395\) | −54.2862 | −2.73144 | ||||||||
\(396\) | −24.2058 | −1.21639 | ||||||||
\(397\) | −3.85497 | −0.193476 | −0.0967378 | − | 0.995310i | \(-0.530841\pi\) | ||||
−0.0967378 | + | 0.995310i | \(0.530841\pi\) | |||||||
\(398\) | −32.5575 | −1.63196 | ||||||||
\(399\) | −1.49627 | −0.0749074 | ||||||||
\(400\) | 100.036 | 5.00178 | ||||||||
\(401\) | 1.19710 | 0.0597804 | 0.0298902 | − | 0.999553i | \(-0.490484\pi\) | ||||
0.0298902 | + | 0.999553i | \(0.490484\pi\) | |||||||
\(402\) | 29.5392 | 1.47328 | ||||||||
\(403\) | 21.4387 | 1.06794 | ||||||||
\(404\) | 34.4761 | 1.71525 | ||||||||
\(405\) | 8.14994 | 0.404974 | ||||||||
\(406\) | 5.83408 | 0.289540 | ||||||||
\(407\) | 16.6531 | 0.825461 | ||||||||
\(408\) | 60.7260 | 3.00638 | ||||||||
\(409\) | 18.8864 | 0.933873 | 0.466937 | − | 0.884291i | \(-0.345358\pi\) | ||||
0.466937 | + | 0.884291i | \(0.345358\pi\) | |||||||
\(410\) | 32.3965 | 1.59995 | ||||||||
\(411\) | −1.88109 | −0.0927873 | ||||||||
\(412\) | 54.6514 | 2.69248 | ||||||||
\(413\) | −9.17812 | −0.451626 | ||||||||
\(414\) | 27.0079 | 1.32737 | ||||||||
\(415\) | 20.6533 | 1.01383 | ||||||||
\(416\) | −54.7114 | −2.68244 | ||||||||
\(417\) | 19.2646 | 0.943393 | ||||||||
\(418\) | −9.80189 | −0.479426 | ||||||||
\(419\) | 16.1793 | 0.790411 | 0.395205 | − | 0.918593i | \(-0.370673\pi\) | ||||
0.395205 | + | 0.918593i | \(0.370673\pi\) | |||||||
\(420\) | 23.1210 | 1.12819 | ||||||||
\(421\) | −14.7816 | −0.720409 | −0.360204 | − | 0.932873i | \(-0.617293\pi\) | ||||
−0.360204 | + | 0.932873i | \(0.617293\pi\) | |||||||
\(422\) | 41.8812 | 2.03875 | ||||||||
\(423\) | −5.99058 | −0.291272 | ||||||||
\(424\) | 36.0568 | 1.75107 | ||||||||
\(425\) | 28.5427 | 1.38452 | ||||||||
\(426\) | 5.52697 | 0.267782 | ||||||||
\(427\) | −14.4672 | −0.700115 | ||||||||
\(428\) | 73.9865 | 3.57627 | ||||||||
\(429\) | −7.49630 | −0.361925 | ||||||||
\(430\) | 52.3077 | 2.52250 | ||||||||
\(431\) | −7.87624 | −0.379385 | −0.189693 | − | 0.981844i | \(-0.560749\pi\) | ||||
−0.189693 | + | 0.981844i | \(0.560749\pi\) | |||||||
\(432\) | 93.2928 | 4.48855 | ||||||||
\(433\) | −12.1158 | −0.582248 | −0.291124 | − | 0.956685i | \(-0.594029\pi\) | ||||
−0.291124 | + | 0.956685i | \(0.594029\pi\) | |||||||
\(434\) | −28.4383 | −1.36508 | ||||||||
\(435\) | −8.68045 | −0.416196 | ||||||||
\(436\) | 32.5522 | 1.55897 | ||||||||
\(437\) | 8.08692 | 0.386850 | ||||||||
\(438\) | 19.6963 | 0.941125 | ||||||||
\(439\) | 36.1669 | 1.72615 | 0.863075 | − | 0.505075i | \(-0.168535\pi\) | ||||
0.863075 | + | 0.505075i | \(0.168535\pi\) | |||||||
\(440\) | 98.0909 | 4.67630 | ||||||||
\(441\) | 8.80106 | 0.419098 | ||||||||
\(442\) | −27.6765 | −1.31643 | ||||||||
\(443\) | 39.6356 | 1.88315 | 0.941573 | − | 0.336809i | \(-0.109348\pi\) | ||||
0.941573 | + | 0.336809i | \(0.109348\pi\) | |||||||
\(444\) | −40.2118 | −1.90837 | ||||||||
\(445\) | 11.9768 | 0.567754 | ||||||||
\(446\) | 3.05411 | 0.144616 | ||||||||
\(447\) | −3.72763 | −0.176311 | ||||||||
\(448\) | 39.0480 | 1.84485 | ||||||||
\(449\) | −20.3594 | −0.960820 | −0.480410 | − | 0.877044i | \(-0.659512\pi\) | ||||
−0.480410 | + | 0.877044i | \(0.659512\pi\) | |||||||
\(450\) | 24.0614 | 1.13426 | ||||||||
\(451\) | 10.3026 | 0.485129 | ||||||||
\(452\) | −67.3460 | −3.16769 | ||||||||
\(453\) | 6.30359 | 0.296168 | ||||||||
\(454\) | −36.3371 | −1.70539 | ||||||||
\(455\) | −6.82442 | −0.319934 | ||||||||
\(456\) | 15.3282 | 0.717810 | ||||||||
\(457\) | −1.35708 | −0.0634814 | −0.0317407 | − | 0.999496i | \(-0.510105\pi\) | ||||
−0.0317407 | + | 0.999496i | \(0.510105\pi\) | |||||||
\(458\) | 33.7773 | 1.57831 | ||||||||
\(459\) | 26.6188 | 1.24246 | ||||||||
\(460\) | −124.962 | −5.82640 | ||||||||
\(461\) | −16.5480 | −0.770716 | −0.385358 | − | 0.922767i | \(-0.625922\pi\) | ||||
−0.385358 | + | 0.922767i | \(0.625922\pi\) | |||||||
\(462\) | 9.94378 | 0.462627 | ||||||||
\(463\) | −4.37814 | −0.203469 | −0.101735 | − | 0.994812i | \(-0.532439\pi\) | ||||
−0.101735 | + | 0.994812i | \(0.532439\pi\) | |||||||
\(464\) | −35.7201 | −1.65826 | ||||||||
\(465\) | 42.3130 | 1.96222 | ||||||||
\(466\) | 56.0193 | 2.59505 | ||||||||
\(467\) | 38.6359 | 1.78785 | 0.893927 | − | 0.448212i | \(-0.147939\pi\) | ||||
0.893927 | + | 0.448212i | \(0.147939\pi\) | |||||||
\(468\) | −17.2519 | −0.797471 | ||||||||
\(469\) | 8.55193 | 0.394892 | ||||||||
\(470\) | 37.4847 | 1.72904 | ||||||||
\(471\) | −11.6974 | −0.538989 | ||||||||
\(472\) | 94.0231 | 4.32776 | ||||||||
\(473\) | 16.6346 | 0.764860 | ||||||||
\(474\) | 56.3759 | 2.58943 | ||||||||
\(475\) | 7.20464 | 0.330572 | ||||||||
\(476\) | 27.1467 | 1.24427 | ||||||||
\(477\) | 5.18337 | 0.237330 | ||||||||
\(478\) | −21.4430 | −0.980780 | ||||||||
\(479\) | −25.4982 | −1.16504 | −0.582521 | − | 0.812816i | \(-0.697934\pi\) | ||||
−0.582521 | + | 0.812816i | \(0.697934\pi\) | |||||||
\(480\) | −107.982 | −4.92869 | ||||||||
\(481\) | 11.8689 | 0.541177 | ||||||||
\(482\) | 24.4075 | 1.11173 | ||||||||
\(483\) | −8.20398 | −0.373294 | ||||||||
\(484\) | −14.2659 | −0.648452 | ||||||||
\(485\) | 34.1405 | 1.55024 | ||||||||
\(486\) | 37.5200 | 1.70194 | ||||||||
\(487\) | −29.3505 | −1.33000 | −0.664999 | − | 0.746844i | \(-0.731568\pi\) | ||||
−0.664999 | + | 0.746844i | \(0.731568\pi\) | |||||||
\(488\) | 148.205 | 6.70894 | ||||||||
\(489\) | 5.74904 | 0.259981 | ||||||||
\(490\) | −55.0707 | −2.48784 | ||||||||
\(491\) | 6.33901 | 0.286075 | 0.143038 | − | 0.989717i | \(-0.454313\pi\) | ||||
0.143038 | + | 0.989717i | \(0.454313\pi\) | |||||||
\(492\) | −24.8774 | −1.12156 | ||||||||
\(493\) | −10.1918 | −0.459017 | ||||||||
\(494\) | −6.98598 | −0.314314 | ||||||||
\(495\) | 14.1011 | 0.633798 | ||||||||
\(496\) | 174.118 | 7.81813 | ||||||||
\(497\) | 1.60012 | 0.0717752 | ||||||||
\(498\) | −21.4483 | −0.961123 | ||||||||
\(499\) | 12.2642 | 0.549019 | 0.274510 | − | 0.961584i | \(-0.411484\pi\) | ||||
0.274510 | + | 0.961584i | \(0.411484\pi\) | |||||||
\(500\) | −17.4971 | −0.782492 | ||||||||
\(501\) | 20.7851 | 0.928609 | ||||||||
\(502\) | −82.0701 | −3.66297 | ||||||||
\(503\) | 15.0338 | 0.670324 | 0.335162 | − | 0.942161i | \(-0.391209\pi\) | ||||
0.335162 | + | 0.942161i | \(0.391209\pi\) | |||||||
\(504\) | 14.8206 | 0.660162 | ||||||||
\(505\) | −20.0840 | −0.893728 | ||||||||
\(506\) | −53.7432 | −2.38918 | ||||||||
\(507\) | 10.7690 | 0.478269 | ||||||||
\(508\) | 93.8383 | 4.16340 | ||||||||
\(509\) | 5.58218 | 0.247426 | 0.123713 | − | 0.992318i | \(-0.460520\pi\) | ||||
0.123713 | + | 0.992318i | \(0.460520\pi\) | |||||||
\(510\) | −54.6242 | −2.41880 | ||||||||
\(511\) | 5.70230 | 0.252255 | ||||||||
\(512\) | −100.896 | −4.45903 | ||||||||
\(513\) | 6.71902 | 0.296652 | ||||||||
\(514\) | −39.3431 | −1.73535 | ||||||||
\(515\) | −31.8372 | −1.40291 | ||||||||
\(516\) | −40.1672 | −1.76826 | ||||||||
\(517\) | 11.9207 | 0.524271 | ||||||||
\(518\) | −15.7440 | −0.691753 | ||||||||
\(519\) | 1.81712 | 0.0797625 | ||||||||
\(520\) | 69.9112 | 3.06581 | ||||||||
\(521\) | 10.6706 | 0.467489 | 0.233745 | − | 0.972298i | \(-0.424902\pi\) | ||||
0.233745 | + | 0.972298i | \(0.424902\pi\) | |||||||
\(522\) | −8.59167 | −0.376047 | ||||||||
\(523\) | −19.5622 | −0.855396 | −0.427698 | − | 0.903922i | \(-0.640675\pi\) | ||||
−0.427698 | + | 0.903922i | \(0.640675\pi\) | |||||||
\(524\) | 66.5228 | 2.90606 | ||||||||
\(525\) | −7.30893 | −0.318988 | ||||||||
\(526\) | −87.6207 | −3.82044 | ||||||||
\(527\) | 49.6803 | 2.16411 | ||||||||
\(528\) | −60.8824 | −2.64957 | ||||||||
\(529\) | 21.3401 | 0.927830 | ||||||||
\(530\) | −32.4338 | −1.40883 | ||||||||
\(531\) | 13.5163 | 0.586559 | ||||||||
\(532\) | 6.85227 | 0.297084 | ||||||||
\(533\) | 7.34282 | 0.318053 | ||||||||
\(534\) | −12.4378 | −0.538237 | ||||||||
\(535\) | −43.1008 | −1.86341 | ||||||||
\(536\) | −87.6083 | −3.78410 | ||||||||
\(537\) | 27.6484 | 1.19312 | ||||||||
\(538\) | 57.9782 | 2.49962 | ||||||||
\(539\) | −17.5133 | −0.754351 | ||||||||
\(540\) | −103.825 | −4.46792 | ||||||||
\(541\) | −16.7851 | −0.721648 | −0.360824 | − | 0.932634i | \(-0.617505\pi\) | ||||
−0.360824 | + | 0.932634i | \(0.617505\pi\) | |||||||
\(542\) | 46.4987 | 1.99729 | ||||||||
\(543\) | 2.35397 | 0.101019 | ||||||||
\(544\) | −126.783 | −5.43579 | ||||||||
\(545\) | −18.9633 | −0.812299 | ||||||||
\(546\) | 7.08711 | 0.303300 | ||||||||
\(547\) | −8.29108 | −0.354501 | −0.177251 | − | 0.984166i | \(-0.556720\pi\) | ||||
−0.177251 | + | 0.984166i | \(0.556720\pi\) | |||||||
\(548\) | 8.61457 | 0.367996 | ||||||||
\(549\) | 21.3053 | 0.909290 | ||||||||
\(550\) | −47.8799 | −2.04160 | ||||||||
\(551\) | −2.57259 | −0.109596 | ||||||||
\(552\) | 84.0438 | 3.57714 | ||||||||
\(553\) | 16.3215 | 0.694059 | ||||||||
\(554\) | 65.7253 | 2.79240 | ||||||||
\(555\) | 23.4254 | 0.994351 | ||||||||
\(556\) | −88.2235 | −3.74151 | ||||||||
\(557\) | 2.90235 | 0.122977 | 0.0614883 | − | 0.998108i | \(-0.480415\pi\) | ||||
0.0614883 | + | 0.998108i | \(0.480415\pi\) | |||||||
\(558\) | 41.8802 | 1.77293 | ||||||||
\(559\) | 11.8558 | 0.501446 | ||||||||
\(560\) | −55.4256 | −2.34216 | ||||||||
\(561\) | −17.3713 | −0.733416 | ||||||||
\(562\) | −43.6343 | −1.84060 | ||||||||
\(563\) | 40.1832 | 1.69352 | 0.846761 | − | 0.531974i | \(-0.178550\pi\) | ||||
0.846761 | + | 0.531974i | \(0.178550\pi\) | |||||||
\(564\) | −28.7846 | −1.21205 | ||||||||
\(565\) | 39.2324 | 1.65052 | ||||||||
\(566\) | 62.8978 | 2.64379 | ||||||||
\(567\) | −2.45032 | −0.102904 | ||||||||
\(568\) | −16.3921 | −0.687795 | ||||||||
\(569\) | −0.650783 | −0.0272823 | −0.0136411 | − | 0.999907i | \(-0.504342\pi\) | ||||
−0.0136411 | + | 0.999907i | \(0.504342\pi\) | |||||||
\(570\) | −13.7880 | −0.577517 | ||||||||
\(571\) | 10.7445 | 0.449642 | 0.224821 | − | 0.974400i | \(-0.427820\pi\) | ||||
0.224821 | + | 0.974400i | \(0.427820\pi\) | |||||||
\(572\) | 34.3298 | 1.43540 | ||||||||
\(573\) | −0.254225 | −0.0106204 | ||||||||
\(574\) | −9.74019 | −0.406548 | ||||||||
\(575\) | 39.5026 | 1.64737 | ||||||||
\(576\) | −57.5049 | −2.39604 | ||||||||
\(577\) | −34.9364 | −1.45442 | −0.727210 | − | 0.686415i | \(-0.759183\pi\) | ||||
−0.727210 | + | 0.686415i | \(0.759183\pi\) | |||||||
\(578\) | −17.0363 | −0.708616 | ||||||||
\(579\) | −3.57077 | −0.148396 | ||||||||
\(580\) | 39.7526 | 1.65064 | ||||||||
\(581\) | −6.20954 | −0.257615 | ||||||||
\(582\) | −35.4546 | −1.46964 | ||||||||
\(583\) | −10.3144 | −0.427180 | ||||||||
\(584\) | −58.4159 | −2.41727 | ||||||||
\(585\) | 10.0501 | 0.415521 | ||||||||
\(586\) | 43.9283 | 1.81466 | ||||||||
\(587\) | −8.91214 | −0.367843 | −0.183922 | − | 0.982941i | \(-0.558879\pi\) | ||||
−0.183922 | + | 0.982941i | \(0.558879\pi\) | |||||||
\(588\) | 42.2890 | 1.74397 | ||||||||
\(589\) | 12.5401 | 0.516706 | ||||||||
\(590\) | −84.5755 | −3.48192 | ||||||||
\(591\) | −4.31121 | −0.177339 | ||||||||
\(592\) | 96.3954 | 3.96183 | ||||||||
\(593\) | 34.4392 | 1.41425 | 0.707124 | − | 0.707090i | \(-0.249992\pi\) | ||||
0.707124 | + | 0.707090i | \(0.249992\pi\) | |||||||
\(594\) | −44.6526 | −1.83212 | ||||||||
\(595\) | −15.8143 | −0.648324 | ||||||||
\(596\) | 17.0709 | 0.699252 | ||||||||
\(597\) | −14.5643 | −0.596079 | ||||||||
\(598\) | −38.3037 | −1.56636 | ||||||||
\(599\) | 43.1271 | 1.76213 | 0.881063 | − | 0.472999i | \(-0.156829\pi\) | ||||
0.881063 | + | 0.472999i | \(0.156829\pi\) | |||||||
\(600\) | 74.8747 | 3.05675 | ||||||||
\(601\) | 43.4254 | 1.77136 | 0.885679 | − | 0.464297i | \(-0.153693\pi\) | ||||
0.885679 | + | 0.464297i | \(0.153693\pi\) | |||||||
\(602\) | −15.7266 | −0.640968 | ||||||||
\(603\) | −12.5942 | −0.512874 | ||||||||
\(604\) | −28.8677 | −1.17461 | ||||||||
\(605\) | 8.31063 | 0.337875 | ||||||||
\(606\) | 20.8571 | 0.847263 | ||||||||
\(607\) | −26.7000 | −1.08372 | −0.541859 | − | 0.840469i | \(-0.682279\pi\) | ||||
−0.541859 | + | 0.840469i | \(0.682279\pi\) | |||||||
\(608\) | −32.0022 | −1.29786 | ||||||||
\(609\) | 2.60983 | 0.105755 | ||||||||
\(610\) | −133.314 | −5.39771 | ||||||||
\(611\) | 8.49609 | 0.343715 | ||||||||
\(612\) | −39.9782 | −1.61602 | ||||||||
\(613\) | −3.16393 | −0.127790 | −0.0638949 | − | 0.997957i | \(-0.520352\pi\) | ||||
−0.0638949 | + | 0.997957i | \(0.520352\pi\) | |||||||
\(614\) | −73.2072 | −2.95440 | ||||||||
\(615\) | 14.4923 | 0.584386 | ||||||||
\(616\) | −29.4916 | −1.18825 | ||||||||
\(617\) | −10.2086 | −0.410981 | −0.205491 | − | 0.978659i | \(-0.565879\pi\) | ||||
−0.205491 | + | 0.978659i | \(0.565879\pi\) | |||||||
\(618\) | 33.0627 | 1.32998 | ||||||||
\(619\) | −38.1505 | −1.53340 | −0.766700 | − | 0.642006i | \(-0.778103\pi\) | ||||
−0.766700 | + | 0.642006i | \(0.778103\pi\) | |||||||
\(620\) | −193.775 | −7.78218 | ||||||||
\(621\) | 36.8400 | 1.47834 | ||||||||
\(622\) | −52.0866 | −2.08848 | ||||||||
\(623\) | −3.60089 | −0.144267 | ||||||||
\(624\) | −43.3920 | −1.73707 | ||||||||
\(625\) | −19.4689 | −0.778756 | ||||||||
\(626\) | −77.9918 | −3.11718 | ||||||||
\(627\) | −4.38479 | −0.175112 | ||||||||
\(628\) | 53.5691 | 2.13764 | ||||||||
\(629\) | 27.5041 | 1.09666 | ||||||||
\(630\) | −13.3314 | −0.531136 | ||||||||
\(631\) | 34.3996 | 1.36942 | 0.684712 | − | 0.728813i | \(-0.259928\pi\) | ||||
0.684712 | + | 0.728813i | \(0.259928\pi\) | |||||||
\(632\) | −167.201 | −6.65092 | ||||||||
\(633\) | 18.7352 | 0.744658 | ||||||||
\(634\) | −28.7702 | −1.14261 | ||||||||
\(635\) | −54.6655 | −2.16933 | ||||||||
\(636\) | 24.9060 | 0.987587 | ||||||||
\(637\) | −12.4820 | −0.494556 | ||||||||
\(638\) | 17.0966 | 0.676862 | ||||||||
\(639\) | −2.35645 | −0.0932197 | ||||||||
\(640\) | 185.571 | 7.33532 | ||||||||
\(641\) | 17.8686 | 0.705769 | 0.352885 | − | 0.935667i | \(-0.385201\pi\) | ||||
0.352885 | + | 0.935667i | \(0.385201\pi\) | |||||||
\(642\) | 44.7599 | 1.76653 | ||||||||
\(643\) | −16.4515 | −0.648784 | −0.324392 | − | 0.945923i | \(-0.605160\pi\) | ||||
−0.324392 | + | 0.945923i | \(0.605160\pi\) | |||||||
\(644\) | 37.5706 | 1.48049 | ||||||||
\(645\) | 23.3994 | 0.921350 | ||||||||
\(646\) | −16.1887 | −0.636937 | ||||||||
\(647\) | 11.5109 | 0.452542 | 0.226271 | − | 0.974064i | \(-0.427347\pi\) | ||||
0.226271 | + | 0.974064i | \(0.427347\pi\) | |||||||
\(648\) | 25.1018 | 0.986091 | ||||||||
\(649\) | −26.8963 | −1.05577 | ||||||||
\(650\) | −34.1248 | −1.33849 | ||||||||
\(651\) | −12.7216 | −0.498600 | ||||||||
\(652\) | −26.3281 | −1.03109 | ||||||||
\(653\) | −13.1104 | −0.513050 | −0.256525 | − | 0.966538i | \(-0.582578\pi\) | ||||
−0.256525 | + | 0.966538i | \(0.582578\pi\) | |||||||
\(654\) | 19.6933 | 0.770068 | ||||||||
\(655\) | −38.7529 | −1.51420 | ||||||||
\(656\) | 59.6359 | 2.32839 | ||||||||
\(657\) | −8.39761 | −0.327622 | ||||||||
\(658\) | −11.2700 | −0.439350 | ||||||||
\(659\) | −16.4133 | −0.639369 | −0.319685 | − | 0.947524i | \(-0.603577\pi\) | ||||
−0.319685 | + | 0.947524i | \(0.603577\pi\) | |||||||
\(660\) | 67.7556 | 2.63738 | ||||||||
\(661\) | 1.40641 | 0.0547029 | 0.0273514 | − | 0.999626i | \(-0.491293\pi\) | ||||
0.0273514 | + | 0.999626i | \(0.491293\pi\) | |||||||
\(662\) | −15.1945 | −0.590552 | ||||||||
\(663\) | −12.3808 | −0.480832 | ||||||||
\(664\) | 63.6122 | 2.46863 | ||||||||
\(665\) | −3.99179 | −0.154795 | ||||||||
\(666\) | 23.1858 | 0.898431 | ||||||||
\(667\) | −14.1053 | −0.546161 | ||||||||
\(668\) | −95.1865 | −3.68288 | ||||||||
\(669\) | 1.36623 | 0.0528215 | ||||||||
\(670\) | 78.8053 | 3.04451 | ||||||||
\(671\) | −42.3957 | −1.63667 | ||||||||
\(672\) | 32.4655 | 1.25238 | ||||||||
\(673\) | −1.68108 | −0.0648011 | −0.0324005 | − | 0.999475i | \(-0.510315\pi\) | ||||
−0.0324005 | + | 0.999475i | \(0.510315\pi\) | |||||||
\(674\) | −16.5389 | −0.637054 | ||||||||
\(675\) | 32.8208 | 1.26327 | ||||||||
\(676\) | −49.3174 | −1.89682 | ||||||||
\(677\) | 32.6504 | 1.25486 | 0.627428 | − | 0.778674i | \(-0.284107\pi\) | ||||
0.627428 | + | 0.778674i | \(0.284107\pi\) | |||||||
\(678\) | −40.7426 | −1.56471 | ||||||||
\(679\) | −10.2645 | −0.393916 | ||||||||
\(680\) | 162.006 | 6.21265 | ||||||||
\(681\) | −16.2551 | −0.622897 | ||||||||
\(682\) | −83.3377 | −3.19117 | ||||||||
\(683\) | −30.9987 | −1.18613 | −0.593067 | − | 0.805153i | \(-0.702083\pi\) | ||||
−0.593067 | + | 0.805153i | \(0.702083\pi\) | |||||||
\(684\) | −10.0911 | −0.385844 | ||||||||
\(685\) | −5.01842 | −0.191744 | ||||||||
\(686\) | 35.8363 | 1.36824 | ||||||||
\(687\) | 15.1100 | 0.576483 | ||||||||
\(688\) | 96.2886 | 3.67097 | ||||||||
\(689\) | −7.35127 | −0.280061 | ||||||||
\(690\) | −75.5990 | −2.87800 | ||||||||
\(691\) | −29.8119 | −1.13410 | −0.567049 | − | 0.823684i | \(-0.691915\pi\) | ||||
−0.567049 | + | 0.823684i | \(0.691915\pi\) | |||||||
\(692\) | −8.32159 | −0.316339 | ||||||||
\(693\) | −4.23958 | −0.161048 | ||||||||
\(694\) | −17.8431 | −0.677316 | ||||||||
\(695\) | 51.3946 | 1.94951 | ||||||||
\(696\) | −26.7358 | −1.01342 | ||||||||
\(697\) | 17.0156 | 0.644513 | ||||||||
\(698\) | 75.7434 | 2.86693 | ||||||||
\(699\) | 25.0598 | 0.947848 | ||||||||
\(700\) | 33.4717 | 1.26511 | ||||||||
\(701\) | −21.0046 | −0.793334 | −0.396667 | − | 0.917963i | \(-0.629833\pi\) | ||||
−0.396667 | + | 0.917963i | \(0.629833\pi\) | |||||||
\(702\) | −31.8247 | −1.20115 | ||||||||
\(703\) | 6.94247 | 0.261840 | ||||||||
\(704\) | 114.429 | 4.31272 | ||||||||
\(705\) | 16.7685 | 0.631537 | ||||||||
\(706\) | 22.9814 | 0.864915 | ||||||||
\(707\) | 6.03838 | 0.227097 | ||||||||
\(708\) | 64.9458 | 2.44081 | ||||||||
\(709\) | 26.7448 | 1.00442 | 0.502210 | − | 0.864745i | \(-0.332520\pi\) | ||||
0.502210 | + | 0.864745i | \(0.332520\pi\) | |||||||
\(710\) | 14.7450 | 0.553369 | ||||||||
\(711\) | −24.0361 | −0.901425 | ||||||||
\(712\) | 36.8885 | 1.38245 | ||||||||
\(713\) | 68.7567 | 2.57496 | ||||||||
\(714\) | 16.4231 | 0.614618 | ||||||||
\(715\) | −19.9988 | −0.747913 | ||||||||
\(716\) | −126.618 | −4.73192 | ||||||||
\(717\) | −9.59235 | −0.358233 | ||||||||
\(718\) | −2.83088 | −0.105648 | ||||||||
\(719\) | −25.7531 | −0.960430 | −0.480215 | − | 0.877151i | \(-0.659441\pi\) | ||||
−0.480215 | + | 0.877151i | \(0.659441\pi\) | |||||||
\(720\) | 81.6236 | 3.04193 | ||||||||
\(721\) | 9.57203 | 0.356481 | ||||||||
\(722\) | 48.5535 | 1.80697 | ||||||||
\(723\) | 10.9185 | 0.406064 | ||||||||
\(724\) | −10.7802 | −0.400641 | ||||||||
\(725\) | −12.5665 | −0.466706 | ||||||||
\(726\) | −8.63053 | −0.320309 | ||||||||
\(727\) | −24.6883 | −0.915637 | −0.457819 | − | 0.889046i | \(-0.651369\pi\) | ||||
−0.457819 | + | 0.889046i | \(0.651369\pi\) | |||||||
\(728\) | −21.0192 | −0.779023 | ||||||||
\(729\) | 24.1789 | 0.895515 | ||||||||
\(730\) | 52.5462 | 1.94482 | ||||||||
\(731\) | 27.4736 | 1.01615 | ||||||||
\(732\) | 102.372 | 3.78377 | ||||||||
\(733\) | −43.1386 | −1.59336 | −0.796679 | − | 0.604402i | \(-0.793412\pi\) | ||||
−0.796679 | + | 0.604402i | \(0.793412\pi\) | |||||||
\(734\) | −95.0835 | −3.50960 | ||||||||
\(735\) | −24.6354 | −0.908692 | ||||||||
\(736\) | −175.466 | −6.46777 | ||||||||
\(737\) | 25.0612 | 0.923142 | ||||||||
\(738\) | 14.3441 | 0.528013 | ||||||||
\(739\) | 5.54957 | 0.204144 | 0.102072 | − | 0.994777i | \(-0.467453\pi\) | ||||
0.102072 | + | 0.994777i | \(0.467453\pi\) | |||||||
\(740\) | −107.278 | −3.94361 | ||||||||
\(741\) | −3.12512 | −0.114804 | ||||||||
\(742\) | 9.75140 | 0.357985 | ||||||||
\(743\) | 14.2930 | 0.524358 | 0.262179 | − | 0.965019i | \(-0.415559\pi\) | ||||
0.262179 | + | 0.965019i | \(0.415559\pi\) | |||||||
\(744\) | 130.324 | 4.77790 | ||||||||
\(745\) | −9.94467 | −0.364344 | ||||||||
\(746\) | −46.8906 | −1.71679 | ||||||||
\(747\) | 9.14460 | 0.334584 | ||||||||
\(748\) | 79.5529 | 2.90874 | ||||||||
\(749\) | 12.9585 | 0.473493 | ||||||||
\(750\) | −10.5853 | −0.386519 | ||||||||
\(751\) | 28.9497 | 1.05639 | 0.528195 | − | 0.849123i | \(-0.322869\pi\) | ||||
0.528195 | + | 0.849123i | \(0.322869\pi\) | |||||||
\(752\) | 69.0023 | 2.51626 | ||||||||
\(753\) | −36.7134 | −1.33791 | ||||||||
\(754\) | 12.1851 | 0.443754 | ||||||||
\(755\) | 16.8169 | 0.612028 | ||||||||
\(756\) | 31.2156 | 1.13530 | ||||||||
\(757\) | 42.5901 | 1.54796 | 0.773982 | − | 0.633207i | \(-0.218262\pi\) | ||||
0.773982 | + | 0.633207i | \(0.218262\pi\) | |||||||
\(758\) | −107.671 | −3.91079 | ||||||||
\(759\) | −24.0416 | −0.872654 | ||||||||
\(760\) | 40.8930 | 1.48334 | ||||||||
\(761\) | −20.6990 | −0.750337 | −0.375168 | − | 0.926957i | \(-0.622415\pi\) | ||||
−0.375168 | + | 0.926957i | \(0.622415\pi\) | |||||||
\(762\) | 56.7697 | 2.05655 | ||||||||
\(763\) | 5.70143 | 0.206405 | ||||||||
\(764\) | 1.16424 | 0.0421206 | ||||||||
\(765\) | 23.2893 | 0.842026 | ||||||||
\(766\) | 32.3268 | 1.16801 | ||||||||
\(767\) | −19.1694 | −0.692169 | ||||||||
\(768\) | −95.3487 | −3.44060 | ||||||||
\(769\) | 52.8861 | 1.90712 | 0.953561 | − | 0.301199i | \(-0.0973869\pi\) | ||||
0.953561 | + | 0.301199i | \(0.0973869\pi\) | |||||||
\(770\) | 26.5282 | 0.956012 | ||||||||
\(771\) | −17.5998 | −0.633842 | ||||||||
\(772\) | 16.3526 | 0.588542 | ||||||||
\(773\) | 17.4646 | 0.628156 | 0.314078 | − | 0.949397i | \(-0.398305\pi\) | ||||
0.314078 | + | 0.949397i | \(0.398305\pi\) | |||||||
\(774\) | 23.1601 | 0.832472 | ||||||||
\(775\) | 61.2554 | 2.20036 | ||||||||
\(776\) | 105.152 | 3.77475 | ||||||||
\(777\) | −7.04297 | −0.252665 | ||||||||
\(778\) | 89.1990 | 3.19794 | ||||||||
\(779\) | 4.29502 | 0.153885 | ||||||||
\(780\) | 48.2907 | 1.72908 | ||||||||
\(781\) | 4.68911 | 0.167790 | ||||||||
\(782\) | −88.7618 | −3.17412 | ||||||||
\(783\) | −11.7194 | −0.418818 | ||||||||
\(784\) | −101.375 | −3.62053 | ||||||||
\(785\) | −31.2067 | −1.11381 | ||||||||
\(786\) | 40.2446 | 1.43548 | ||||||||
\(787\) | −20.2259 | −0.720976 | −0.360488 | − | 0.932764i | \(-0.617390\pi\) | ||||
−0.360488 | + | 0.932764i | \(0.617390\pi\) | |||||||
\(788\) | 19.7434 | 0.703331 | ||||||||
\(789\) | −39.1964 | −1.39543 | ||||||||
\(790\) | 150.401 | 5.35102 | ||||||||
\(791\) | −11.7954 | −0.419398 | ||||||||
\(792\) | 43.4314 | 1.54327 | ||||||||
\(793\) | −30.2162 | −1.07301 | ||||||||
\(794\) | 10.6803 | 0.379028 | ||||||||
\(795\) | −14.5090 | −0.514581 | ||||||||
\(796\) | 66.6983 | 2.36406 | ||||||||
\(797\) | 11.5428 | 0.408868 | 0.204434 | − | 0.978880i | \(-0.434465\pi\) | ||||
0.204434 | + | 0.978880i | \(0.434465\pi\) | |||||||
\(798\) | 4.14545 | 0.146747 | ||||||||
\(799\) | 19.6881 | 0.696515 | ||||||||
\(800\) | −156.323 | −5.52685 | ||||||||
\(801\) | 5.30292 | 0.187370 | ||||||||
\(802\) | −3.31659 | −0.117113 | ||||||||
\(803\) | 16.7105 | 0.589699 | ||||||||
\(804\) | −60.5148 | −2.13419 | ||||||||
\(805\) | −21.8868 | −0.771407 | ||||||||
\(806\) | −59.3963 | −2.09215 | ||||||||
\(807\) | 25.9361 | 0.912993 | ||||||||
\(808\) | −61.8588 | −2.17618 | ||||||||
\(809\) | −50.5446 | −1.77705 | −0.888526 | − | 0.458826i | \(-0.848270\pi\) | ||||
−0.888526 | + | 0.458826i | \(0.848270\pi\) | |||||||
\(810\) | −22.5795 | −0.793364 | ||||||||
\(811\) | 4.62428 | 0.162380 | 0.0811902 | − | 0.996699i | \(-0.474128\pi\) | ||||
0.0811902 | + | 0.996699i | \(0.474128\pi\) | |||||||
\(812\) | −11.9519 | −0.419428 | ||||||||
\(813\) | 20.8008 | 0.729516 | ||||||||
\(814\) | −46.1375 | −1.61712 | ||||||||
\(815\) | 15.3374 | 0.537247 | ||||||||
\(816\) | −100.553 | −3.52005 | ||||||||
\(817\) | 6.93478 | 0.242617 | ||||||||
\(818\) | −52.3251 | −1.82950 | ||||||||
\(819\) | −3.02163 | −0.105584 | ||||||||
\(820\) | −66.3684 | −2.31768 | ||||||||
\(821\) | 8.33512 | 0.290898 | 0.145449 | − | 0.989366i | \(-0.453537\pi\) | ||||
0.145449 | + | 0.989366i | \(0.453537\pi\) | |||||||
\(822\) | 5.21159 | 0.181775 | ||||||||
\(823\) | −52.0095 | −1.81294 | −0.906469 | − | 0.422272i | \(-0.861233\pi\) | ||||
−0.906469 | + | 0.422272i | \(0.861233\pi\) | |||||||
\(824\) | −98.0584 | −3.41603 | ||||||||
\(825\) | −21.4187 | −0.745702 | ||||||||
\(826\) | 25.4281 | 0.884757 | ||||||||
\(827\) | 20.7693 | 0.722219 | 0.361110 | − | 0.932523i | \(-0.382398\pi\) | ||||
0.361110 | + | 0.932523i | \(0.382398\pi\) | |||||||
\(828\) | −55.3291 | −1.92282 | ||||||||
\(829\) | −35.7403 | −1.24131 | −0.620657 | − | 0.784082i | \(-0.713134\pi\) | ||||
−0.620657 | + | 0.784082i | \(0.713134\pi\) | |||||||
\(830\) | −57.2204 | −1.98615 | ||||||||
\(831\) | 29.4017 | 1.01993 | ||||||||
\(832\) | 81.5559 | 2.82744 | ||||||||
\(833\) | −28.9248 | −1.00219 | ||||||||
\(834\) | −53.3729 | −1.84815 | ||||||||
\(835\) | 55.4509 | 1.91896 | ||||||||
\(836\) | 20.0804 | 0.694496 | ||||||||
\(837\) | 57.1265 | 1.97458 | ||||||||
\(838\) | −44.8250 | −1.54845 | ||||||||
\(839\) | −14.6182 | −0.504675 | −0.252338 | − | 0.967639i | \(-0.581199\pi\) | ||||
−0.252338 | + | 0.967639i | \(0.581199\pi\) | |||||||
\(840\) | −41.4850 | −1.43137 | ||||||||
\(841\) | −24.5129 | −0.845271 | ||||||||
\(842\) | 40.9525 | 1.41132 | ||||||||
\(843\) | −19.5194 | −0.672285 | ||||||||
\(844\) | −85.7990 | −2.95332 | ||||||||
\(845\) | 28.7298 | 0.988337 | ||||||||
\(846\) | 16.5970 | 0.570616 | ||||||||
\(847\) | −2.49864 | −0.0858542 | ||||||||
\(848\) | −59.7045 | −2.05026 | ||||||||
\(849\) | 28.1368 | 0.965653 | ||||||||
\(850\) | −79.0780 | −2.71235 | ||||||||
\(851\) | 38.0651 | 1.30486 | ||||||||
\(852\) | −11.3227 | −0.387909 | ||||||||
\(853\) | −26.5056 | −0.907535 | −0.453768 | − | 0.891120i | \(-0.649920\pi\) | ||||
−0.453768 | + | 0.891120i | \(0.649920\pi\) | |||||||
\(854\) | 40.0815 | 1.37156 | ||||||||
\(855\) | 5.87859 | 0.201044 | ||||||||
\(856\) | −132.750 | −4.53731 | ||||||||
\(857\) | −1.52870 | −0.0522193 | −0.0261096 | − | 0.999659i | \(-0.508312\pi\) | ||||
−0.0261096 | + | 0.999659i | \(0.508312\pi\) | |||||||
\(858\) | 20.7686 | 0.709029 | ||||||||
\(859\) | 38.2527 | 1.30516 | 0.652582 | − | 0.757718i | \(-0.273686\pi\) | ||||
0.652582 | + | 0.757718i | \(0.273686\pi\) | |||||||
\(860\) | −107.159 | −3.65409 | ||||||||
\(861\) | −4.35719 | −0.148493 | ||||||||
\(862\) | 21.8212 | 0.743234 | ||||||||
\(863\) | 34.7680 | 1.18352 | 0.591758 | − | 0.806116i | \(-0.298434\pi\) | ||||
0.591758 | + | 0.806116i | \(0.298434\pi\) | |||||||
\(864\) | −145.786 | −4.95975 | ||||||||
\(865\) | 4.84774 | 0.164828 | ||||||||
\(866\) | 33.5670 | 1.14065 | ||||||||
\(867\) | −7.62104 | −0.258824 | ||||||||
\(868\) | 58.2595 | 1.97746 | ||||||||
\(869\) | 47.8297 | 1.62251 | ||||||||
\(870\) | 24.0493 | 0.815348 | ||||||||
\(871\) | 17.8616 | 0.605217 | ||||||||
\(872\) | −58.4069 | −1.97791 | ||||||||
\(873\) | 15.1163 | 0.511608 | ||||||||
\(874\) | −22.4049 | −0.757858 | ||||||||
\(875\) | −3.06456 | −0.103601 | ||||||||
\(876\) | −40.3504 | −1.36331 | ||||||||
\(877\) | −10.2852 | −0.347305 | −0.173653 | − | 0.984807i | \(-0.555557\pi\) | ||||
−0.173653 | + | 0.984807i | \(0.555557\pi\) | |||||||
\(878\) | −100.201 | −3.38162 | ||||||||
\(879\) | 19.6509 | 0.662810 | ||||||||
\(880\) | −162.423 | −5.47529 | ||||||||
\(881\) | −11.5947 | −0.390634 | −0.195317 | − | 0.980740i | \(-0.562574\pi\) | ||||
−0.195317 | + | 0.980740i | \(0.562574\pi\) | |||||||
\(882\) | −24.3835 | −0.821034 | ||||||||
\(883\) | −10.0511 | −0.338247 | −0.169124 | − | 0.985595i | \(-0.554094\pi\) | ||||
−0.169124 | + | 0.985595i | \(0.554094\pi\) | |||||||
\(884\) | 56.6988 | 1.90699 | ||||||||
\(885\) | −37.8342 | −1.27178 | ||||||||
\(886\) | −109.811 | −3.68918 | ||||||||
\(887\) | −55.7582 | −1.87218 | −0.936088 | − | 0.351766i | \(-0.885581\pi\) | ||||
−0.936088 | + | 0.351766i | \(0.885581\pi\) | |||||||
\(888\) | 72.1500 | 2.42120 | ||||||||
\(889\) | 16.4355 | 0.551229 | ||||||||
\(890\) | −33.1819 | −1.11226 | ||||||||
\(891\) | −7.18062 | −0.240560 | ||||||||
\(892\) | −6.25673 | −0.209491 | ||||||||
\(893\) | 4.96960 | 0.166301 | ||||||||
\(894\) | 10.3275 | 0.345402 | ||||||||
\(895\) | 73.7611 | 2.46556 | ||||||||
\(896\) | −55.7928 | −1.86391 | ||||||||
\(897\) | −17.1349 | −0.572116 | ||||||||
\(898\) | 56.4061 | 1.88230 | ||||||||
\(899\) | −21.8727 | −0.729494 | ||||||||
\(900\) | −49.2928 | −1.64309 | ||||||||
\(901\) | −17.0352 | −0.567525 | ||||||||
\(902\) | −28.5434 | −0.950391 | ||||||||
\(903\) | −7.03516 | −0.234116 | ||||||||
\(904\) | 120.836 | 4.01894 | ||||||||
\(905\) | 6.27998 | 0.208754 | ||||||||
\(906\) | −17.4642 | −0.580209 | ||||||||
\(907\) | −35.7345 | −1.18654 | −0.593272 | − | 0.805002i | \(-0.702164\pi\) | ||||
−0.593272 | + | 0.805002i | \(0.702164\pi\) | |||||||
\(908\) | 74.4413 | 2.47042 | ||||||||
\(909\) | −8.89255 | −0.294947 | ||||||||
\(910\) | 18.9072 | 0.626766 | ||||||||
\(911\) | 42.4552 | 1.40660 | 0.703302 | − | 0.710891i | \(-0.251708\pi\) | ||||
0.703302 | + | 0.710891i | \(0.251708\pi\) | |||||||
\(912\) | −25.3812 | −0.840454 | ||||||||
\(913\) | −18.1969 | −0.602230 | ||||||||
\(914\) | 3.75981 | 0.124363 | ||||||||
\(915\) | −59.6367 | −1.97153 | ||||||||
\(916\) | −69.1972 | −2.28634 | ||||||||
\(917\) | 11.6513 | 0.384759 | ||||||||
\(918\) | −73.7478 | −2.43404 | ||||||||
\(919\) | −52.4298 | −1.72950 | −0.864750 | − | 0.502202i | \(-0.832523\pi\) | ||||
−0.864750 | + | 0.502202i | \(0.832523\pi\) | |||||||
\(920\) | 224.214 | 7.39211 | ||||||||
\(921\) | −32.7486 | −1.07910 | ||||||||
\(922\) | 45.8464 | 1.50987 | ||||||||
\(923\) | 3.34202 | 0.110004 | ||||||||
\(924\) | −20.3711 | −0.670160 | ||||||||
\(925\) | 33.9123 | 1.11503 | ||||||||
\(926\) | 12.1297 | 0.398607 | ||||||||
\(927\) | −14.0964 | −0.462988 | ||||||||
\(928\) | 55.8188 | 1.83234 | ||||||||
\(929\) | 38.3706 | 1.25890 | 0.629449 | − | 0.777041i | \(-0.283280\pi\) | ||||
0.629449 | + | 0.777041i | \(0.283280\pi\) | |||||||
\(930\) | −117.229 | −3.84408 | ||||||||
\(931\) | −7.30109 | −0.239284 | ||||||||
\(932\) | −114.763 | −3.75918 | ||||||||
\(933\) | −23.3005 | −0.762824 | ||||||||
\(934\) | −107.041 | −3.50250 | ||||||||
\(935\) | −46.3435 | −1.51560 | ||||||||
\(936\) | 30.9543 | 1.01177 | ||||||||
\(937\) | −25.5850 | −0.835825 | −0.417913 | − | 0.908487i | \(-0.637238\pi\) | ||||
−0.417913 | + | 0.908487i | \(0.637238\pi\) | |||||||
\(938\) | −23.6933 | −0.773612 | ||||||||
\(939\) | −34.8890 | −1.13856 | ||||||||
\(940\) | −76.7922 | −2.50469 | ||||||||
\(941\) | −33.3218 | −1.08626 | −0.543131 | − | 0.839648i | \(-0.682761\pi\) | ||||
−0.543131 | + | 0.839648i | \(0.682761\pi\) | |||||||
\(942\) | 32.4079 | 1.05591 | ||||||||
\(943\) | 23.5493 | 0.766872 | ||||||||
\(944\) | −155.688 | −5.06720 | ||||||||
\(945\) | −18.1846 | −0.591546 | ||||||||
\(946\) | −46.0864 | −1.49840 | ||||||||
\(947\) | −8.75634 | −0.284543 | −0.142271 | − | 0.989828i | \(-0.545441\pi\) | ||||
−0.142271 | + | 0.989828i | \(0.545441\pi\) | |||||||
\(948\) | −115.493 | −3.75104 | ||||||||
\(949\) | 11.9098 | 0.386610 | ||||||||
\(950\) | −19.9606 | −0.647606 | ||||||||
\(951\) | −12.8701 | −0.417341 | ||||||||
\(952\) | −48.7081 | −1.57864 | ||||||||
\(953\) | 47.3454 | 1.53367 | 0.766834 | − | 0.641845i | \(-0.221831\pi\) | ||||
0.766834 | + | 0.641845i | \(0.221831\pi\) | |||||||
\(954\) | −14.3606 | −0.464942 | ||||||||
\(955\) | −0.678226 | −0.0219469 | ||||||||
\(956\) | 43.9287 | 1.42076 | ||||||||
\(957\) | 7.64803 | 0.247226 | ||||||||
\(958\) | 70.6431 | 2.28238 | ||||||||
\(959\) | 1.50882 | 0.0487222 | ||||||||
\(960\) | 160.964 | 5.19510 | ||||||||
\(961\) | 75.6186 | 2.43931 | ||||||||
\(962\) | −32.8831 | −1.06019 | ||||||||
\(963\) | −19.0836 | −0.614961 | ||||||||
\(964\) | −50.0020 | −1.61045 | ||||||||
\(965\) | −9.52619 | −0.306659 | ||||||||
\(966\) | 22.7293 | 0.731302 | ||||||||
\(967\) | −1.01063 | −0.0324996 | −0.0162498 | − | 0.999868i | \(-0.505173\pi\) | ||||
−0.0162498 | + | 0.999868i | \(0.505173\pi\) | |||||||
\(968\) | 25.5967 | 0.822709 | ||||||||
\(969\) | −7.24189 | −0.232643 | ||||||||
\(970\) | −94.5866 | −3.03699 | ||||||||
\(971\) | −6.31925 | −0.202795 | −0.101397 | − | 0.994846i | \(-0.532331\pi\) | ||||
−0.101397 | + | 0.994846i | \(0.532331\pi\) | |||||||
\(972\) | −76.8644 | −2.46543 | ||||||||
\(973\) | −15.4521 | −0.495371 | ||||||||
\(974\) | 81.3160 | 2.60553 | ||||||||
\(975\) | −15.2655 | −0.488886 | ||||||||
\(976\) | −245.405 | −7.85523 | ||||||||
\(977\) | 8.48019 | 0.271305 | 0.135653 | − | 0.990756i | \(-0.456687\pi\) | ||||
0.135653 | + | 0.990756i | \(0.456687\pi\) | |||||||
\(978\) | −15.9278 | −0.509315 | ||||||||
\(979\) | −10.5523 | −0.337254 | ||||||||
\(980\) | 112.819 | 3.60388 | ||||||||
\(981\) | −8.39632 | −0.268074 | ||||||||
\(982\) | −17.5623 | −0.560436 | ||||||||
\(983\) | −9.57551 | −0.305411 | −0.152706 | − | 0.988272i | \(-0.548799\pi\) | ||||
−0.152706 | + | 0.988272i | \(0.548799\pi\) | |||||||
\(984\) | 44.6363 | 1.42295 | ||||||||
\(985\) | −11.5015 | −0.366469 | ||||||||
\(986\) | 28.2367 | 0.899238 | ||||||||
\(987\) | −5.04154 | −0.160474 | ||||||||
\(988\) | 14.3117 | 0.455315 | ||||||||
\(989\) | 38.0230 | 1.20906 | ||||||||
\(990\) | −39.0674 | −1.24164 | ||||||||
\(991\) | −32.9046 | −1.04525 | −0.522624 | − | 0.852563i | \(-0.675047\pi\) | ||||
−0.522624 | + | 0.852563i | \(0.675047\pi\) | |||||||
\(992\) | −272.089 | −8.63885 | ||||||||
\(993\) | −6.79715 | −0.215701 | ||||||||
\(994\) | −4.43316 | −0.140611 | ||||||||
\(995\) | −38.8551 | −1.23179 | ||||||||
\(996\) | 43.9397 | 1.39228 | ||||||||
\(997\) | 6.86670 | 0.217470 | 0.108735 | − | 0.994071i | \(-0.465320\pi\) | ||||
0.108735 | + | 0.994071i | \(0.465320\pi\) | |||||||
\(998\) | −33.9781 | −1.07556 | ||||||||
\(999\) | 31.6264 | 1.00062 |
(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 | 4007.2.a.b.1.3 | ✓ | 195 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4007.2.a.b.1.3 | ✓ | 195 | 1.1 | even | 1 | trivial |