Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, 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("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65707 | −1.87883 | −0.939415 | − | 0.342782i | \(-0.888631\pi\) | ||||
−0.939415 | + | 0.342782i | \(0.888631\pi\) | |||||||
\(3\) | 2.92115 | 1.68653 | 0.843264 | − | 0.537499i | \(-0.180631\pi\) | ||||
0.843264 | + | 0.537499i | \(0.180631\pi\) | |||||||
\(4\) | 5.06000 | 2.53000 | ||||||||
\(5\) | 0.928477 | 0.415227 | 0.207614 | − | 0.978211i | \(-0.433430\pi\) | ||||
0.207614 | + | 0.978211i | \(0.433430\pi\) | |||||||
\(6\) | −7.76170 | −3.16870 | ||||||||
\(7\) | 3.41739 | 1.29165 | 0.645825 | − | 0.763485i | \(-0.276513\pi\) | ||||
0.645825 | + | 0.763485i | \(0.276513\pi\) | |||||||
\(8\) | −8.13063 | −2.87461 | ||||||||
\(9\) | 5.53314 | 1.84438 | ||||||||
\(10\) | −2.46702 | −0.780142 | ||||||||
\(11\) | 3.81271 | 1.14958 | 0.574788 | − | 0.818303i | \(-0.305085\pi\) | ||||
0.574788 | + | 0.818303i | \(0.305085\pi\) | |||||||
\(12\) | 14.7810 | 4.26692 | ||||||||
\(13\) | 0.216731 | 0.0601104 | 0.0300552 | − | 0.999548i | \(-0.490432\pi\) | ||||
0.0300552 | + | 0.999548i | \(0.490432\pi\) | |||||||
\(14\) | −9.08022 | −2.42679 | ||||||||
\(15\) | 2.71222 | 0.700293 | ||||||||
\(16\) | 11.4836 | 2.87091 | ||||||||
\(17\) | −1.11046 | −0.269326 | −0.134663 | − | 0.990891i | \(-0.542995\pi\) | ||||
−0.134663 | + | 0.990891i | \(0.542995\pi\) | |||||||
\(18\) | −14.7019 | −3.46528 | ||||||||
\(19\) | 2.30245 | 0.528218 | 0.264109 | − | 0.964493i | \(-0.414922\pi\) | ||||
0.264109 | + | 0.964493i | \(0.414922\pi\) | |||||||
\(20\) | 4.69809 | 1.05053 | ||||||||
\(21\) | 9.98271 | 2.17841 | ||||||||
\(22\) | −10.1306 | −2.15986 | ||||||||
\(23\) | 9.12530 | 1.90276 | 0.951378 | − | 0.308025i | \(-0.0996682\pi\) | ||||
0.951378 | + | 0.308025i | \(0.0996682\pi\) | |||||||
\(24\) | −23.7508 | −4.84812 | ||||||||
\(25\) | −4.13793 | −0.827586 | ||||||||
\(26\) | −0.575869 | −0.112937 | ||||||||
\(27\) | 7.39969 | 1.42407 | ||||||||
\(28\) | 17.2920 | 3.26788 | ||||||||
\(29\) | 0.567784 | 0.105435 | 0.0527174 | − | 0.998609i | \(-0.483212\pi\) | ||||
0.0527174 | + | 0.998609i | \(0.483212\pi\) | |||||||
\(30\) | −7.20656 | −1.31573 | ||||||||
\(31\) | −8.02797 | −1.44187 | −0.720933 | − | 0.693005i | \(-0.756286\pi\) | ||||
−0.720933 | + | 0.693005i | \(0.756286\pi\) | |||||||
\(32\) | −14.2515 | −2.51933 | ||||||||
\(33\) | 11.1375 | 1.93879 | ||||||||
\(34\) | 2.95057 | 0.506018 | ||||||||
\(35\) | 3.17296 | 0.536329 | ||||||||
\(36\) | 27.9977 | 4.66628 | ||||||||
\(37\) | −4.36760 | −0.718030 | −0.359015 | − | 0.933332i | \(-0.616887\pi\) | ||||
−0.359015 | + | 0.933332i | \(0.616887\pi\) | |||||||
\(38\) | −6.11776 | −0.992432 | ||||||||
\(39\) | 0.633105 | 0.101378 | ||||||||
\(40\) | −7.54910 | −1.19362 | ||||||||
\(41\) | 3.05078 | 0.476451 | 0.238226 | − | 0.971210i | \(-0.423434\pi\) | ||||
0.238226 | + | 0.971210i | \(0.423434\pi\) | |||||||
\(42\) | −26.5247 | −4.09285 | ||||||||
\(43\) | 7.90720 | 1.20584 | 0.602918 | − | 0.797803i | \(-0.294004\pi\) | ||||
0.602918 | + | 0.797803i | \(0.294004\pi\) | |||||||
\(44\) | 19.2923 | 2.90843 | ||||||||
\(45\) | 5.13739 | 0.765837 | ||||||||
\(46\) | −24.2465 | −3.57496 | ||||||||
\(47\) | 6.04383 | 0.881584 | 0.440792 | − | 0.897609i | \(-0.354698\pi\) | ||||
0.440792 | + | 0.897609i | \(0.354698\pi\) | |||||||
\(48\) | 33.5454 | 4.84187 | ||||||||
\(49\) | 4.67853 | 0.668361 | ||||||||
\(50\) | 10.9948 | 1.55489 | ||||||||
\(51\) | −3.24382 | −0.454226 | ||||||||
\(52\) | 1.09666 | 0.152079 | ||||||||
\(53\) | −8.67944 | −1.19221 | −0.596107 | − | 0.802905i | \(-0.703286\pi\) | ||||
−0.596107 | + | 0.802905i | \(0.703286\pi\) | |||||||
\(54\) | −19.6615 | −2.67559 | ||||||||
\(55\) | 3.54001 | 0.477335 | ||||||||
\(56\) | −27.7855 | −3.71299 | ||||||||
\(57\) | 6.72581 | 0.890855 | ||||||||
\(58\) | −1.50864 | −0.198094 | ||||||||
\(59\) | −0.276534 | −0.0360017 | −0.0180008 | − | 0.999838i | \(-0.505730\pi\) | ||||
−0.0180008 | + | 0.999838i | \(0.505730\pi\) | |||||||
\(60\) | 13.7239 | 1.77174 | ||||||||
\(61\) | 1.01388 | 0.129813 | 0.0649067 | − | 0.997891i | \(-0.479325\pi\) | ||||
0.0649067 | + | 0.997891i | \(0.479325\pi\) | |||||||
\(62\) | 21.3308 | 2.70902 | ||||||||
\(63\) | 18.9089 | 2.38229 | ||||||||
\(64\) | 14.8999 | 1.86249 | ||||||||
\(65\) | 0.201230 | 0.0249595 | ||||||||
\(66\) | −29.5931 | −3.64266 | ||||||||
\(67\) | −5.11816 | −0.625283 | −0.312641 | − | 0.949871i | \(-0.601214\pi\) | ||||
−0.312641 | + | 0.949871i | \(0.601214\pi\) | |||||||
\(68\) | −5.61893 | −0.681395 | ||||||||
\(69\) | 26.6564 | 3.20905 | ||||||||
\(70\) | −8.43077 | −1.00767 | ||||||||
\(71\) | −1.17876 | −0.139892 | −0.0699462 | − | 0.997551i | \(-0.522283\pi\) | ||||
−0.0699462 | + | 0.997551i | \(0.522283\pi\) | |||||||
\(72\) | −44.9879 | −5.30188 | ||||||||
\(73\) | −2.92582 | −0.342441 | −0.171221 | − | 0.985233i | \(-0.554771\pi\) | ||||
−0.171221 | + | 0.985233i | \(0.554771\pi\) | |||||||
\(74\) | 11.6050 | 1.34906 | ||||||||
\(75\) | −12.0875 | −1.39575 | ||||||||
\(76\) | 11.6504 | 1.33639 | ||||||||
\(77\) | 13.0295 | 1.48485 | ||||||||
\(78\) | −1.68220 | −0.190472 | ||||||||
\(79\) | 5.80150 | 0.652719 | 0.326360 | − | 0.945246i | \(-0.394178\pi\) | ||||
0.326360 | + | 0.945246i | \(0.394178\pi\) | |||||||
\(80\) | 10.6623 | 1.19208 | ||||||||
\(81\) | 5.01621 | 0.557357 | ||||||||
\(82\) | −8.10611 | −0.895170 | ||||||||
\(83\) | 6.36225 | 0.698348 | 0.349174 | − | 0.937058i | \(-0.386462\pi\) | ||||
0.349174 | + | 0.937058i | \(0.386462\pi\) | |||||||
\(84\) | 50.5125 | 5.51137 | ||||||||
\(85\) | −1.03104 | −0.111832 | ||||||||
\(86\) | −21.0100 | −2.26556 | ||||||||
\(87\) | 1.65858 | 0.177819 | ||||||||
\(88\) | −30.9997 | −3.30458 | ||||||||
\(89\) | 11.9820 | 1.27009 | 0.635047 | − | 0.772473i | \(-0.280981\pi\) | ||||
0.635047 | + | 0.772473i | \(0.280981\pi\) | |||||||
\(90\) | −13.6504 | −1.43888 | ||||||||
\(91\) | 0.740654 | 0.0776416 | ||||||||
\(92\) | 46.1740 | 4.81398 | ||||||||
\(93\) | −23.4509 | −2.43175 | ||||||||
\(94\) | −16.0589 | −1.65635 | ||||||||
\(95\) | 2.13777 | 0.219331 | ||||||||
\(96\) | −41.6308 | −4.24892 | ||||||||
\(97\) | −11.2544 | −1.14271 | −0.571357 | − | 0.820702i | \(-0.693583\pi\) | ||||
−0.571357 | + | 0.820702i | \(0.693583\pi\) | |||||||
\(98\) | −12.4312 | −1.25574 | ||||||||
\(99\) | 21.0962 | 2.12025 | ||||||||
\(100\) | −20.9379 | −2.09379 | ||||||||
\(101\) | −1.85556 | −0.184635 | −0.0923177 | − | 0.995730i | \(-0.529428\pi\) | ||||
−0.0923177 | + | 0.995730i | \(0.529428\pi\) | |||||||
\(102\) | 8.61906 | 0.853414 | ||||||||
\(103\) | −4.75261 | −0.468289 | −0.234144 | − | 0.972202i | \(-0.575229\pi\) | ||||
−0.234144 | + | 0.972202i | \(0.575229\pi\) | |||||||
\(104\) | −1.76216 | −0.172794 | ||||||||
\(105\) | 9.26871 | 0.904534 | ||||||||
\(106\) | 23.0619 | 2.23997 | ||||||||
\(107\) | −8.94794 | −0.865030 | −0.432515 | − | 0.901627i | \(-0.642374\pi\) | ||||
−0.432515 | + | 0.901627i | \(0.642374\pi\) | |||||||
\(108\) | 37.4424 | 3.60290 | ||||||||
\(109\) | −8.54537 | −0.818498 | −0.409249 | − | 0.912423i | \(-0.634209\pi\) | ||||
−0.409249 | + | 0.912423i | \(0.634209\pi\) | |||||||
\(110\) | −9.40604 | −0.896831 | ||||||||
\(111\) | −12.7584 | −1.21098 | ||||||||
\(112\) | 39.2440 | 3.70821 | ||||||||
\(113\) | 4.04230 | 0.380268 | 0.190134 | − | 0.981758i | \(-0.439108\pi\) | ||||
0.190134 | + | 0.981758i | \(0.439108\pi\) | |||||||
\(114\) | −17.8709 | −1.67377 | ||||||||
\(115\) | 8.47263 | 0.790076 | ||||||||
\(116\) | 2.87299 | 0.266750 | ||||||||
\(117\) | 1.19920 | 0.110866 | ||||||||
\(118\) | 0.734770 | 0.0676411 | ||||||||
\(119\) | −3.79487 | −0.347875 | ||||||||
\(120\) | −22.0521 | −2.01307 | ||||||||
\(121\) | 3.53675 | 0.321523 | ||||||||
\(122\) | −2.69393 | −0.243897 | ||||||||
\(123\) | 8.91178 | 0.803548 | ||||||||
\(124\) | −40.6215 | −3.64792 | ||||||||
\(125\) | −8.48436 | −0.758864 | ||||||||
\(126\) | −50.2421 | −4.47593 | ||||||||
\(127\) | −21.4121 | −1.90002 | −0.950009 | − | 0.312223i | \(-0.898926\pi\) | ||||
−0.950009 | + | 0.312223i | \(0.898926\pi\) | |||||||
\(128\) | −11.0871 | −0.979967 | ||||||||
\(129\) | 23.0982 | 2.03368 | ||||||||
\(130\) | −0.534681 | −0.0468946 | ||||||||
\(131\) | −0.256110 | −0.0223765 | −0.0111882 | − | 0.999937i | \(-0.503561\pi\) | ||||
−0.0111882 | + | 0.999937i | \(0.503561\pi\) | |||||||
\(132\) | 56.3558 | 4.90515 | ||||||||
\(133\) | 7.86836 | 0.682273 | ||||||||
\(134\) | 13.5993 | 1.17480 | ||||||||
\(135\) | 6.87044 | 0.591313 | ||||||||
\(136\) | 9.02874 | 0.774208 | ||||||||
\(137\) | 20.4368 | 1.74603 | 0.873017 | − | 0.487689i | \(-0.162160\pi\) | ||||
0.873017 | + | 0.487689i | \(0.162160\pi\) | |||||||
\(138\) | −70.8278 | −6.02926 | ||||||||
\(139\) | 10.3999 | 0.882110 | 0.441055 | − | 0.897480i | \(-0.354604\pi\) | ||||
0.441055 | + | 0.897480i | \(0.354604\pi\) | |||||||
\(140\) | 16.0552 | 1.35691 | ||||||||
\(141\) | 17.6550 | 1.48682 | ||||||||
\(142\) | 3.13203 | 0.262834 | ||||||||
\(143\) | 0.826332 | 0.0691014 | ||||||||
\(144\) | 63.5405 | 5.29504 | ||||||||
\(145\) | 0.527174 | 0.0437794 | ||||||||
\(146\) | 7.77410 | 0.643389 | ||||||||
\(147\) | 13.6667 | 1.12721 | ||||||||
\(148\) | −22.1001 | −1.81662 | ||||||||
\(149\) | −3.10424 | −0.254309 | −0.127154 | − | 0.991883i | \(-0.540584\pi\) | ||||
−0.127154 | + | 0.991883i | \(0.540584\pi\) | |||||||
\(150\) | 32.1174 | 2.62237 | ||||||||
\(151\) | −8.44808 | −0.687495 | −0.343748 | − | 0.939062i | \(-0.611696\pi\) | ||||
−0.343748 | + | 0.939062i | \(0.611696\pi\) | |||||||
\(152\) | −18.7204 | −1.51842 | ||||||||
\(153\) | −6.14433 | −0.496740 | ||||||||
\(154\) | −34.6202 | −2.78978 | ||||||||
\(155\) | −7.45378 | −0.598702 | ||||||||
\(156\) | 3.20351 | 0.256486 | ||||||||
\(157\) | −8.02902 | −0.640785 | −0.320393 | − | 0.947285i | \(-0.603815\pi\) | ||||
−0.320393 | + | 0.947285i | \(0.603815\pi\) | |||||||
\(158\) | −15.4150 | −1.22635 | ||||||||
\(159\) | −25.3540 | −2.01070 | ||||||||
\(160\) | −13.2322 | −1.04610 | ||||||||
\(161\) | 31.1847 | 2.45770 | ||||||||
\(162\) | −13.3284 | −1.04718 | ||||||||
\(163\) | 10.0422 | 0.786568 | 0.393284 | − | 0.919417i | \(-0.371339\pi\) | ||||
0.393284 | + | 0.919417i | \(0.371339\pi\) | |||||||
\(164\) | 15.4369 | 1.20542 | ||||||||
\(165\) | 10.3409 | 0.805039 | ||||||||
\(166\) | −16.9049 | −1.31208 | ||||||||
\(167\) | 4.39680 | 0.340235 | 0.170117 | − | 0.985424i | \(-0.445585\pi\) | ||||
0.170117 | + | 0.985424i | \(0.445585\pi\) | |||||||
\(168\) | −81.1657 | −6.26207 | ||||||||
\(169\) | −12.9530 | −0.996387 | ||||||||
\(170\) | 2.73953 | 0.210112 | ||||||||
\(171\) | 12.7398 | 0.974235 | ||||||||
\(172\) | 40.0105 | 3.05077 | ||||||||
\(173\) | −8.81909 | −0.670503 | −0.335251 | − | 0.942129i | \(-0.608821\pi\) | ||||
−0.335251 | + | 0.942129i | \(0.608821\pi\) | |||||||
\(174\) | −4.40697 | −0.334091 | ||||||||
\(175\) | −14.1409 | −1.06895 | ||||||||
\(176\) | 43.7837 | 3.30032 | ||||||||
\(177\) | −0.807799 | −0.0607179 | ||||||||
\(178\) | −31.8371 | −2.38629 | ||||||||
\(179\) | −14.4810 | −1.08236 | −0.541180 | − | 0.840907i | \(-0.682022\pi\) | ||||
−0.541180 | + | 0.840907i | \(0.682022\pi\) | |||||||
\(180\) | 25.9952 | 1.93757 | ||||||||
\(181\) | 14.5720 | 1.08313 | 0.541565 | − | 0.840659i | \(-0.317832\pi\) | ||||
0.541565 | + | 0.840659i | \(0.317832\pi\) | |||||||
\(182\) | −1.96797 | −0.145875 | ||||||||
\(183\) | 2.96169 | 0.218934 | ||||||||
\(184\) | −74.1944 | −5.46969 | ||||||||
\(185\) | −4.05522 | −0.298146 | ||||||||
\(186\) | 62.3107 | 4.56884 | ||||||||
\(187\) | −4.23386 | −0.309611 | ||||||||
\(188\) | 30.5818 | 2.23041 | ||||||||
\(189\) | 25.2876 | 1.83940 | ||||||||
\(190\) | −5.68020 | −0.412085 | ||||||||
\(191\) | 10.9393 | 0.791538 | 0.395769 | − | 0.918350i | \(-0.370478\pi\) | ||||
0.395769 | + | 0.918350i | \(0.370478\pi\) | |||||||
\(192\) | 43.5249 | 3.14114 | ||||||||
\(193\) | 18.1844 | 1.30894 | 0.654471 | − | 0.756087i | \(-0.272891\pi\) | ||||
0.654471 | + | 0.756087i | \(0.272891\pi\) | |||||||
\(194\) | 29.9037 | 2.14696 | ||||||||
\(195\) | 0.587823 | 0.0420949 | ||||||||
\(196\) | 23.6734 | 1.69096 | ||||||||
\(197\) | −10.0282 | −0.714481 | −0.357241 | − | 0.934012i | \(-0.616282\pi\) | ||||
−0.357241 | + | 0.934012i | \(0.616282\pi\) | |||||||
\(198\) | −56.0541 | −3.98359 | ||||||||
\(199\) | −8.42428 | −0.597181 | −0.298591 | − | 0.954381i | \(-0.596516\pi\) | ||||
−0.298591 | + | 0.954381i | \(0.596516\pi\) | |||||||
\(200\) | 33.6440 | 2.37899 | ||||||||
\(201\) | −14.9509 | −1.05456 | ||||||||
\(202\) | 4.93035 | 0.346899 | ||||||||
\(203\) | 1.94034 | 0.136185 | ||||||||
\(204\) | −16.4138 | −1.14919 | ||||||||
\(205\) | 2.83257 | 0.197835 | ||||||||
\(206\) | 12.6280 | 0.879835 | ||||||||
\(207\) | 50.4915 | 3.50940 | ||||||||
\(208\) | 2.48886 | 0.172571 | ||||||||
\(209\) | 8.77857 | 0.607226 | ||||||||
\(210\) | −24.6276 | −1.69947 | ||||||||
\(211\) | 9.58370 | 0.659769 | 0.329884 | − | 0.944021i | \(-0.392990\pi\) | ||||
0.329884 | + | 0.944021i | \(0.392990\pi\) | |||||||
\(212\) | −43.9180 | −3.01630 | ||||||||
\(213\) | −3.44332 | −0.235933 | ||||||||
\(214\) | 23.7753 | 1.62524 | ||||||||
\(215\) | 7.34165 | 0.500696 | ||||||||
\(216\) | −60.1641 | −4.09365 | ||||||||
\(217\) | −27.4347 | −1.86239 | ||||||||
\(218\) | 22.7056 | 1.53782 | ||||||||
\(219\) | −8.54677 | −0.577537 | ||||||||
\(220\) | 17.9125 | 1.20766 | ||||||||
\(221\) | −0.240671 | −0.0161893 | ||||||||
\(222\) | 33.9000 | 2.27522 | ||||||||
\(223\) | 6.19198 | 0.414645 | 0.207323 | − | 0.978273i | \(-0.433525\pi\) | ||||
0.207323 | + | 0.978273i | \(0.433525\pi\) | |||||||
\(224\) | −48.7028 | −3.25410 | ||||||||
\(225\) | −22.8957 | −1.52638 | ||||||||
\(226\) | −10.7407 | −0.714458 | ||||||||
\(227\) | −2.19145 | −0.145452 | −0.0727260 | − | 0.997352i | \(-0.523170\pi\) | ||||
−0.0727260 | + | 0.997352i | \(0.523170\pi\) | |||||||
\(228\) | 34.0326 | 2.25386 | ||||||||
\(229\) | 8.12996 | 0.537243 | 0.268621 | − | 0.963246i | \(-0.413432\pi\) | ||||
0.268621 | + | 0.963246i | \(0.413432\pi\) | |||||||
\(230\) | −22.5123 | −1.48442 | ||||||||
\(231\) | 38.0612 | 2.50424 | ||||||||
\(232\) | −4.61644 | −0.303084 | ||||||||
\(233\) | −19.6215 | −1.28545 | −0.642725 | − | 0.766097i | \(-0.722196\pi\) | ||||
−0.642725 | + | 0.766097i | \(0.722196\pi\) | |||||||
\(234\) | −3.18636 | −0.208299 | ||||||||
\(235\) | 5.61156 | 0.366058 | ||||||||
\(236\) | −1.39926 | −0.0910843 | ||||||||
\(237\) | 16.9471 | 1.10083 | ||||||||
\(238\) | 10.0832 | 0.653598 | ||||||||
\(239\) | 4.24206 | 0.274396 | 0.137198 | − | 0.990544i | \(-0.456190\pi\) | ||||
0.137198 | + | 0.990544i | \(0.456190\pi\) | |||||||
\(240\) | 31.1461 | 2.01047 | ||||||||
\(241\) | 20.0319 | 1.29037 | 0.645184 | − | 0.764028i | \(-0.276781\pi\) | ||||
0.645184 | + | 0.764028i | \(0.276781\pi\) | |||||||
\(242\) | −9.39738 | −0.604087 | ||||||||
\(243\) | −7.54594 | −0.484072 | ||||||||
\(244\) | 5.13021 | 0.328428 | ||||||||
\(245\) | 4.34391 | 0.277522 | ||||||||
\(246\) | −23.6792 | −1.50973 | ||||||||
\(247\) | 0.499012 | 0.0317514 | ||||||||
\(248\) | 65.2725 | 4.14481 | ||||||||
\(249\) | 18.5851 | 1.17778 | ||||||||
\(250\) | 22.5435 | 1.42578 | ||||||||
\(251\) | −11.7713 | −0.742996 | −0.371498 | − | 0.928434i | \(-0.621156\pi\) | ||||
−0.371498 | + | 0.928434i | \(0.621156\pi\) | |||||||
\(252\) | 95.6790 | 6.02721 | ||||||||
\(253\) | 34.7921 | 2.18736 | ||||||||
\(254\) | 56.8934 | 3.56981 | ||||||||
\(255\) | −3.01181 | −0.188607 | ||||||||
\(256\) | −0.340740 | −0.0212962 | ||||||||
\(257\) | 5.52632 | 0.344723 | 0.172361 | − | 0.985034i | \(-0.444860\pi\) | ||||
0.172361 | + | 0.985034i | \(0.444860\pi\) | |||||||
\(258\) | −61.3733 | −3.82094 | ||||||||
\(259\) | −14.9258 | −0.927443 | ||||||||
\(260\) | 1.01822 | 0.0631475 | ||||||||
\(261\) | 3.14163 | 0.194462 | ||||||||
\(262\) | 0.680502 | 0.0420416 | ||||||||
\(263\) | 16.1830 | 0.997889 | 0.498944 | − | 0.866634i | \(-0.333721\pi\) | ||||
0.498944 | + | 0.866634i | \(0.333721\pi\) | |||||||
\(264\) | −90.5550 | −5.57327 | ||||||||
\(265\) | −8.05866 | −0.495039 | ||||||||
\(266\) | −20.9068 | −1.28188 | ||||||||
\(267\) | 35.0014 | 2.14205 | ||||||||
\(268\) | −25.8979 | −1.58197 | ||||||||
\(269\) | 9.33375 | 0.569089 | 0.284544 | − | 0.958663i | \(-0.408158\pi\) | ||||
0.284544 | + | 0.958663i | \(0.408158\pi\) | |||||||
\(270\) | −18.2552 | −1.11098 | ||||||||
\(271\) | 4.16548 | 0.253035 | 0.126517 | − | 0.991964i | \(-0.459620\pi\) | ||||
0.126517 | + | 0.991964i | \(0.459620\pi\) | |||||||
\(272\) | −12.7521 | −0.773210 | ||||||||
\(273\) | 2.16356 | 0.130945 | ||||||||
\(274\) | −54.3020 | −3.28050 | ||||||||
\(275\) | −15.7767 | −0.951372 | ||||||||
\(276\) | 134.881 | 8.11891 | ||||||||
\(277\) | −12.7210 | −0.764333 | −0.382166 | − | 0.924093i | \(-0.624822\pi\) | ||||
−0.382166 | + | 0.924093i | \(0.624822\pi\) | |||||||
\(278\) | −27.6333 | −1.65733 | ||||||||
\(279\) | −44.4199 | −2.65935 | ||||||||
\(280\) | −25.7982 | −1.54174 | ||||||||
\(281\) | −0.499785 | −0.0298147 | −0.0149073 | − | 0.999889i | \(-0.504745\pi\) | ||||
−0.0149073 | + | 0.999889i | \(0.504745\pi\) | |||||||
\(282\) | −46.9104 | −2.79348 | ||||||||
\(283\) | 25.9117 | 1.54029 | 0.770147 | − | 0.637867i | \(-0.220183\pi\) | ||||
0.770147 | + | 0.637867i | \(0.220183\pi\) | |||||||
\(284\) | −5.96450 | −0.353928 | ||||||||
\(285\) | 6.24476 | 0.369907 | ||||||||
\(286\) | −2.19562 | −0.129830 | ||||||||
\(287\) | 10.4257 | 0.615408 | ||||||||
\(288\) | −78.8555 | −4.64660 | ||||||||
\(289\) | −15.7669 | −0.927463 | ||||||||
\(290\) | −1.40074 | −0.0822541 | ||||||||
\(291\) | −32.8759 | −1.92722 | ||||||||
\(292\) | −14.8047 | −0.866377 | ||||||||
\(293\) | 23.8129 | 1.39117 | 0.695583 | − | 0.718445i | \(-0.255146\pi\) | ||||
0.695583 | + | 0.718445i | \(0.255146\pi\) | |||||||
\(294\) | −36.3133 | −2.11784 | ||||||||
\(295\) | −0.256756 | −0.0149489 | ||||||||
\(296\) | 35.5114 | 2.06406 | ||||||||
\(297\) | 28.2129 | 1.63708 | ||||||||
\(298\) | 8.24816 | 0.477803 | ||||||||
\(299\) | 1.97774 | 0.114375 | ||||||||
\(300\) | −61.1630 | −3.53124 | ||||||||
\(301\) | 27.0220 | 1.55752 | ||||||||
\(302\) | 22.4471 | 1.29169 | ||||||||
\(303\) | −5.42038 | −0.311393 | ||||||||
\(304\) | 26.4405 | 1.51646 | ||||||||
\(305\) | 0.941360 | 0.0539021 | ||||||||
\(306\) | 16.3259 | 0.933289 | ||||||||
\(307\) | −26.6855 | −1.52302 | −0.761510 | − | 0.648154i | \(-0.775542\pi\) | ||||
−0.761510 | + | 0.648154i | \(0.775542\pi\) | |||||||
\(308\) | 65.9293 | 3.75667 | ||||||||
\(309\) | −13.8831 | −0.789783 | ||||||||
\(310\) | 19.8052 | 1.12486 | ||||||||
\(311\) | −28.2797 | −1.60360 | −0.801799 | − | 0.597594i | \(-0.796123\pi\) | ||||
−0.801799 | + | 0.597594i | \(0.796123\pi\) | |||||||
\(312\) | −5.14754 | −0.291422 | ||||||||
\(313\) | −0.894123 | −0.0505388 | −0.0252694 | − | 0.999681i | \(-0.508044\pi\) | ||||
−0.0252694 | + | 0.999681i | \(0.508044\pi\) | |||||||
\(314\) | 21.3336 | 1.20393 | ||||||||
\(315\) | 17.5564 | 0.989194 | ||||||||
\(316\) | 29.3556 | 1.65138 | ||||||||
\(317\) | 31.5491 | 1.77197 | 0.885986 | − | 0.463713i | \(-0.153483\pi\) | ||||
0.885986 | + | 0.463713i | \(0.153483\pi\) | |||||||
\(318\) | 67.3672 | 3.77777 | ||||||||
\(319\) | 2.16480 | 0.121205 | ||||||||
\(320\) | 13.8342 | 0.773356 | ||||||||
\(321\) | −26.1383 | −1.45890 | ||||||||
\(322\) | −82.8597 | −4.61759 | ||||||||
\(323\) | −2.55678 | −0.142263 | ||||||||
\(324\) | 25.3820 | 1.41011 | ||||||||
\(325\) | −0.896818 | −0.0497465 | ||||||||
\(326\) | −26.6829 | −1.47783 | ||||||||
\(327\) | −24.9623 | −1.38042 | ||||||||
\(328\) | −24.8047 | −1.36961 | ||||||||
\(329\) | 20.6541 | 1.13870 | ||||||||
\(330\) | −27.4765 | −1.51253 | ||||||||
\(331\) | −10.8083 | −0.594076 | −0.297038 | − | 0.954866i | \(-0.595999\pi\) | ||||
−0.297038 | + | 0.954866i | \(0.595999\pi\) | |||||||
\(332\) | 32.1930 | 1.76682 | ||||||||
\(333\) | −24.1666 | −1.32432 | ||||||||
\(334\) | −11.6826 | −0.639244 | ||||||||
\(335\) | −4.75209 | −0.259635 | ||||||||
\(336\) | 114.638 | 6.25400 | ||||||||
\(337\) | −23.0281 | −1.25442 | −0.627212 | − | 0.778849i | \(-0.715804\pi\) | ||||
−0.627212 | + | 0.778849i | \(0.715804\pi\) | |||||||
\(338\) | 34.4171 | 1.87204 | ||||||||
\(339\) | 11.8082 | 0.641333 | ||||||||
\(340\) | −5.21704 | −0.282934 | ||||||||
\(341\) | −30.6083 | −1.65753 | ||||||||
\(342\) | −33.8504 | −1.83042 | ||||||||
\(343\) | −7.93336 | −0.428361 | ||||||||
\(344\) | −64.2905 | −3.46631 | ||||||||
\(345\) | 24.7498 | 1.33249 | ||||||||
\(346\) | 23.4329 | 1.25976 | ||||||||
\(347\) | 3.71783 | 0.199584 | 0.0997918 | − | 0.995008i | \(-0.468182\pi\) | ||||
0.0997918 | + | 0.995008i | \(0.468182\pi\) | |||||||
\(348\) | 8.39244 | 0.449882 | ||||||||
\(349\) | −10.8487 | −0.580716 | −0.290358 | − | 0.956918i | \(-0.593774\pi\) | ||||
−0.290358 | + | 0.956918i | \(0.593774\pi\) | |||||||
\(350\) | 37.5733 | 2.00838 | ||||||||
\(351\) | 1.60374 | 0.0856014 | ||||||||
\(352\) | −54.3368 | −2.89616 | ||||||||
\(353\) | 13.7699 | 0.732900 | 0.366450 | − | 0.930438i | \(-0.380573\pi\) | ||||
0.366450 | + | 0.930438i | \(0.380573\pi\) | |||||||
\(354\) | 2.14638 | 0.114079 | ||||||||
\(355\) | −1.09445 | −0.0580872 | ||||||||
\(356\) | 60.6292 | 3.21334 | ||||||||
\(357\) | −11.0854 | −0.586702 | ||||||||
\(358\) | 38.4770 | 2.03357 | ||||||||
\(359\) | −18.2381 | −0.962568 | −0.481284 | − | 0.876565i | \(-0.659829\pi\) | ||||
−0.481284 | + | 0.876565i | \(0.659829\pi\) | |||||||
\(360\) | −41.7702 | −2.20148 | ||||||||
\(361\) | −13.6987 | −0.720986 | ||||||||
\(362\) | −38.7189 | −2.03502 | ||||||||
\(363\) | 10.3314 | 0.542257 | ||||||||
\(364\) | 3.74771 | 0.196433 | ||||||||
\(365\) | −2.71655 | −0.142191 | ||||||||
\(366\) | −7.86940 | −0.411340 | ||||||||
\(367\) | −23.7312 | −1.23876 | −0.619379 | − | 0.785092i | \(-0.712616\pi\) | ||||
−0.619379 | + | 0.785092i | \(0.712616\pi\) | |||||||
\(368\) | 104.791 | 5.46263 | ||||||||
\(369\) | 16.8804 | 0.878757 | ||||||||
\(370\) | 10.7750 | 0.560165 | ||||||||
\(371\) | −29.6610 | −1.53992 | ||||||||
\(372\) | −118.662 | −6.15233 | ||||||||
\(373\) | 23.7322 | 1.22880 | 0.614402 | − | 0.788993i | \(-0.289397\pi\) | ||||
0.614402 | + | 0.788993i | \(0.289397\pi\) | |||||||
\(374\) | 11.2496 | 0.581705 | ||||||||
\(375\) | −24.7841 | −1.27985 | ||||||||
\(376\) | −49.1402 | −2.53421 | ||||||||
\(377\) | 0.123056 | 0.00633773 | ||||||||
\(378\) | −67.1908 | −3.45592 | ||||||||
\(379\) | −29.5080 | −1.51573 | −0.757863 | − | 0.652414i | \(-0.773756\pi\) | ||||
−0.757863 | + | 0.652414i | \(0.773756\pi\) | |||||||
\(380\) | 10.8171 | 0.554907 | ||||||||
\(381\) | −62.5481 | −3.20443 | ||||||||
\(382\) | −29.0664 | −1.48716 | ||||||||
\(383\) | −24.2379 | −1.23850 | −0.619250 | − | 0.785194i | \(-0.712563\pi\) | ||||
−0.619250 | + | 0.785194i | \(0.712563\pi\) | |||||||
\(384\) | −32.3870 | −1.65274 | ||||||||
\(385\) | 12.0976 | 0.616550 | ||||||||
\(386\) | −48.3172 | −2.45928 | ||||||||
\(387\) | 43.7516 | 2.22402 | ||||||||
\(388\) | −56.9474 | −2.89107 | ||||||||
\(389\) | −30.8281 | −1.56305 | −0.781523 | − | 0.623877i | \(-0.785557\pi\) | ||||
−0.781523 | + | 0.623877i | \(0.785557\pi\) | |||||||
\(390\) | −1.56188 | −0.0790891 | ||||||||
\(391\) | −10.1333 | −0.512462 | ||||||||
\(392\) | −38.0394 | −1.92128 | ||||||||
\(393\) | −0.748138 | −0.0377385 | ||||||||
\(394\) | 26.6457 | 1.34239 | ||||||||
\(395\) | 5.38655 | 0.271027 | ||||||||
\(396\) | 106.747 | 5.36424 | ||||||||
\(397\) | −20.1646 | −1.01203 | −0.506015 | − | 0.862524i | \(-0.668882\pi\) | ||||
−0.506015 | + | 0.862524i | \(0.668882\pi\) | |||||||
\(398\) | 22.3839 | 1.12200 | ||||||||
\(399\) | 22.9847 | 1.15067 | ||||||||
\(400\) | −47.5184 | −2.37592 | ||||||||
\(401\) | 1.54569 | 0.0771879 | 0.0385939 | − | 0.999255i | \(-0.487712\pi\) | ||||
0.0385939 | + | 0.999255i | \(0.487712\pi\) | |||||||
\(402\) | 39.7256 | 1.98133 | ||||||||
\(403\) | −1.73991 | −0.0866711 | ||||||||
\(404\) | −9.38915 | −0.467128 | ||||||||
\(405\) | 4.65743 | 0.231430 | ||||||||
\(406\) | −5.15561 | −0.255868 | ||||||||
\(407\) | −16.6524 | −0.825429 | ||||||||
\(408\) | 26.3743 | 1.30572 | ||||||||
\(409\) | −36.7548 | −1.81741 | −0.908704 | − | 0.417442i | \(-0.862927\pi\) | ||||
−0.908704 | + | 0.417442i | \(0.862927\pi\) | |||||||
\(410\) | −7.52634 | −0.371699 | ||||||||
\(411\) | 59.6991 | 2.94474 | ||||||||
\(412\) | −24.0482 | −1.18477 | ||||||||
\(413\) | −0.945024 | −0.0465016 | ||||||||
\(414\) | −134.159 | −6.59357 | ||||||||
\(415\) | 5.90720 | 0.289973 | ||||||||
\(416\) | −3.08874 | −0.151438 | ||||||||
\(417\) | 30.3798 | 1.48770 | ||||||||
\(418\) | −23.3252 | −1.14087 | ||||||||
\(419\) | 17.1981 | 0.840182 | 0.420091 | − | 0.907482i | \(-0.361998\pi\) | ||||
0.420091 | + | 0.907482i | \(0.361998\pi\) | |||||||
\(420\) | 46.8997 | 2.28847 | ||||||||
\(421\) | 10.6017 | 0.516693 | 0.258347 | − | 0.966052i | \(-0.416822\pi\) | ||||
0.258347 | + | 0.966052i | \(0.416822\pi\) | |||||||
\(422\) | −25.4645 | −1.23959 | ||||||||
\(423\) | 33.4414 | 1.62598 | ||||||||
\(424\) | 70.5693 | 3.42715 | ||||||||
\(425\) | 4.59501 | 0.222891 | ||||||||
\(426\) | 9.14914 | 0.443277 | ||||||||
\(427\) | 3.46480 | 0.167674 | ||||||||
\(428\) | −45.2766 | −2.18853 | ||||||||
\(429\) | 2.41384 | 0.116541 | ||||||||
\(430\) | −19.5073 | −0.940723 | ||||||||
\(431\) | −11.2876 | −0.543704 | −0.271852 | − | 0.962339i | \(-0.587636\pi\) | ||||
−0.271852 | + | 0.962339i | \(0.587636\pi\) | |||||||
\(432\) | 84.9752 | 4.08837 | ||||||||
\(433\) | −6.71586 | −0.322743 | −0.161372 | − | 0.986894i | \(-0.551592\pi\) | ||||
−0.161372 | + | 0.986894i | \(0.551592\pi\) | |||||||
\(434\) | 72.8958 | 3.49911 | ||||||||
\(435\) | 1.53996 | 0.0738353 | ||||||||
\(436\) | −43.2396 | −2.07080 | ||||||||
\(437\) | 21.0105 | 1.00507 | ||||||||
\(438\) | 22.7093 | 1.08509 | ||||||||
\(439\) | 41.2325 | 1.96792 | 0.983959 | − | 0.178392i | \(-0.0570895\pi\) | ||||
0.983959 | + | 0.178392i | \(0.0570895\pi\) | |||||||
\(440\) | −28.7825 | −1.37215 | ||||||||
\(441\) | 25.8870 | 1.23271 | ||||||||
\(442\) | 0.639479 | 0.0304169 | ||||||||
\(443\) | −32.3888 | −1.53884 | −0.769418 | − | 0.638745i | \(-0.779454\pi\) | ||||
−0.769418 | + | 0.638745i | \(0.779454\pi\) | |||||||
\(444\) | −64.5577 | −3.06378 | ||||||||
\(445\) | 11.1250 | 0.527378 | ||||||||
\(446\) | −16.4525 | −0.779048 | ||||||||
\(447\) | −9.06795 | −0.428899 | ||||||||
\(448\) | 50.9187 | 2.40568 | ||||||||
\(449\) | −36.6881 | −1.73142 | −0.865710 | − | 0.500546i | \(-0.833133\pi\) | ||||
−0.865710 | + | 0.500546i | \(0.833133\pi\) | |||||||
\(450\) | 60.8355 | 2.86781 | ||||||||
\(451\) | 11.6317 | 0.547716 | ||||||||
\(452\) | 20.4541 | 0.962078 | ||||||||
\(453\) | −24.6781 | −1.15948 | ||||||||
\(454\) | 5.82284 | 0.273279 | ||||||||
\(455\) | 0.687679 | 0.0322389 | ||||||||
\(456\) | −54.6851 | −2.56086 | ||||||||
\(457\) | −35.2168 | −1.64737 | −0.823686 | − | 0.567047i | \(-0.808086\pi\) | ||||
−0.823686 | + | 0.567047i | \(0.808086\pi\) | |||||||
\(458\) | −21.6018 | −1.00939 | ||||||||
\(459\) | −8.21706 | −0.383539 | ||||||||
\(460\) | 42.8715 | 1.99889 | ||||||||
\(461\) | 16.5160 | 0.769228 | 0.384614 | − | 0.923077i | \(-0.374335\pi\) | ||||
0.384614 | + | 0.923077i | \(0.374335\pi\) | |||||||
\(462\) | −101.131 | −4.70504 | ||||||||
\(463\) | 34.2064 | 1.58971 | 0.794853 | − | 0.606802i | \(-0.207548\pi\) | ||||
0.794853 | + | 0.606802i | \(0.207548\pi\) | |||||||
\(464\) | 6.52022 | 0.302693 | ||||||||
\(465\) | −21.7736 | −1.00973 | ||||||||
\(466\) | 52.1357 | 2.41514 | ||||||||
\(467\) | −3.25276 | −0.150520 | −0.0752599 | − | 0.997164i | \(-0.523979\pi\) | ||||
−0.0752599 | + | 0.997164i | \(0.523979\pi\) | |||||||
\(468\) | 6.06797 | 0.280492 | ||||||||
\(469\) | −17.4907 | −0.807647 | ||||||||
\(470\) | −14.9103 | −0.687760 | ||||||||
\(471\) | −23.4540 | −1.08070 | ||||||||
\(472\) | 2.24840 | 0.103491 | ||||||||
\(473\) | 30.1479 | 1.38620 | ||||||||
\(474\) | −45.0295 | −2.06827 | ||||||||
\(475\) | −9.52738 | −0.437146 | ||||||||
\(476\) | −19.2021 | −0.880125 | ||||||||
\(477\) | −48.0246 | −2.19889 | ||||||||
\(478\) | −11.2714 | −0.515544 | ||||||||
\(479\) | −0.133163 | −0.00608438 | −0.00304219 | − | 0.999995i | \(-0.500968\pi\) | ||||
−0.00304219 | + | 0.999995i | \(0.500968\pi\) | |||||||
\(480\) | −38.6532 | −1.76427 | ||||||||
\(481\) | −0.946595 | −0.0431610 | ||||||||
\(482\) | −53.2261 | −2.42438 | ||||||||
\(483\) | 91.0952 | 4.14498 | ||||||||
\(484\) | 17.8960 | 0.813453 | ||||||||
\(485\) | −10.4495 | −0.474486 | ||||||||
\(486\) | 20.0501 | 0.909490 | ||||||||
\(487\) | −38.4819 | −1.74378 | −0.871892 | − | 0.489699i | \(-0.837107\pi\) | ||||
−0.871892 | + | 0.489699i | \(0.837107\pi\) | |||||||
\(488\) | −8.24345 | −0.373163 | ||||||||
\(489\) | 29.3349 | 1.32657 | ||||||||
\(490\) | −11.5420 | −0.521416 | ||||||||
\(491\) | −8.38529 | −0.378423 | −0.189211 | − | 0.981936i | \(-0.560593\pi\) | ||||
−0.189211 | + | 0.981936i | \(0.560593\pi\) | |||||||
\(492\) | 45.0936 | 2.03298 | ||||||||
\(493\) | −0.630501 | −0.0283964 | ||||||||
\(494\) | −1.32591 | −0.0596554 | ||||||||
\(495\) | 19.5874 | 0.880387 | ||||||||
\(496\) | −92.1902 | −4.13946 | ||||||||
\(497\) | −4.02826 | −0.180692 | ||||||||
\(498\) | −49.3819 | −2.21286 | ||||||||
\(499\) | −33.4695 | −1.49830 | −0.749151 | − | 0.662399i | \(-0.769538\pi\) | ||||
−0.749151 | + | 0.662399i | \(0.769538\pi\) | |||||||
\(500\) | −42.9309 | −1.91993 | ||||||||
\(501\) | 12.8437 | 0.573816 | ||||||||
\(502\) | 31.2770 | 1.39596 | ||||||||
\(503\) | 30.3689 | 1.35408 | 0.677042 | − | 0.735944i | \(-0.263262\pi\) | ||||
0.677042 | + | 0.735944i | \(0.263262\pi\) | |||||||
\(504\) | −153.741 | −6.84817 | ||||||||
\(505\) | −1.72285 | −0.0766657 | ||||||||
\(506\) | −92.4449 | −4.10968 | ||||||||
\(507\) | −37.8378 | −1.68044 | ||||||||
\(508\) | −108.345 | −4.80705 | ||||||||
\(509\) | −19.0336 | −0.843651 | −0.421826 | − | 0.906677i | \(-0.638611\pi\) | ||||
−0.421826 | + | 0.906677i | \(0.638611\pi\) | |||||||
\(510\) | 8.00259 | 0.354361 | ||||||||
\(511\) | −9.99865 | −0.442314 | ||||||||
\(512\) | 23.0795 | 1.01998 | ||||||||
\(513\) | 17.0374 | 0.752220 | ||||||||
\(514\) | −14.6838 | −0.647675 | ||||||||
\(515\) | −4.41269 | −0.194446 | ||||||||
\(516\) | 116.877 | 5.14521 | ||||||||
\(517\) | 23.0434 | 1.01345 | ||||||||
\(518\) | 39.6588 | 1.74251 | ||||||||
\(519\) | −25.7619 | −1.13082 | ||||||||
\(520\) | −1.63612 | −0.0717488 | ||||||||
\(521\) | 12.6476 | 0.554100 | 0.277050 | − | 0.960855i | \(-0.410643\pi\) | ||||
0.277050 | + | 0.960855i | \(0.410643\pi\) | |||||||
\(522\) | −8.34751 | −0.365361 | ||||||||
\(523\) | 35.7242 | 1.56211 | 0.781054 | − | 0.624463i | \(-0.214682\pi\) | ||||
0.781054 | + | 0.624463i | \(0.214682\pi\) | |||||||
\(524\) | −1.29592 | −0.0566125 | ||||||||
\(525\) | −41.3078 | −1.80282 | ||||||||
\(526\) | −42.9994 | −1.87486 | ||||||||
\(527\) | 8.91474 | 0.388332 | ||||||||
\(528\) | 127.899 | 5.56609 | ||||||||
\(529\) | 60.2711 | 2.62048 | ||||||||
\(530\) | 21.4124 | 0.930095 | ||||||||
\(531\) | −1.53010 | −0.0664008 | ||||||||
\(532\) | 39.8139 | 1.72615 | ||||||||
\(533\) | 0.661198 | 0.0286396 | ||||||||
\(534\) | −93.0010 | −4.02455 | ||||||||
\(535\) | −8.30796 | −0.359184 | ||||||||
\(536\) | 41.6139 | 1.79745 | ||||||||
\(537\) | −42.3012 | −1.82543 | ||||||||
\(538\) | −24.8004 | −1.06922 | ||||||||
\(539\) | 17.8379 | 0.768332 | ||||||||
\(540\) | 34.7644 | 1.49602 | ||||||||
\(541\) | 29.9478 | 1.28756 | 0.643779 | − | 0.765212i | \(-0.277366\pi\) | ||||
0.643779 | + | 0.765212i | \(0.277366\pi\) | |||||||
\(542\) | −11.0680 | −0.475410 | ||||||||
\(543\) | 42.5671 | 1.82673 | ||||||||
\(544\) | 15.8257 | 0.678521 | ||||||||
\(545\) | −7.93418 | −0.339863 | ||||||||
\(546\) | −5.74873 | −0.246023 | ||||||||
\(547\) | −8.30101 | −0.354925 | −0.177463 | − | 0.984128i | \(-0.556789\pi\) | ||||
−0.177463 | + | 0.984128i | \(0.556789\pi\) | |||||||
\(548\) | 103.410 | 4.41747 | ||||||||
\(549\) | 5.60991 | 0.239425 | ||||||||
\(550\) | 41.9198 | 1.78747 | ||||||||
\(551\) | 1.30729 | 0.0556926 | ||||||||
\(552\) | −216.733 | −9.22478 | ||||||||
\(553\) | 19.8260 | 0.843085 | ||||||||
\(554\) | 33.8006 | 1.43605 | ||||||||
\(555\) | −11.8459 | −0.502831 | ||||||||
\(556\) | 52.6236 | 2.23174 | ||||||||
\(557\) | 24.9047 | 1.05525 | 0.527623 | − | 0.849479i | \(-0.323083\pi\) | ||||
0.527623 | + | 0.849479i | \(0.323083\pi\) | |||||||
\(558\) | 118.027 | 4.99646 | ||||||||
\(559\) | 1.71374 | 0.0724833 | ||||||||
\(560\) | 36.4371 | 1.53975 | ||||||||
\(561\) | −12.3678 | −0.522167 | ||||||||
\(562\) | 1.32796 | 0.0560167 | ||||||||
\(563\) | 21.1368 | 0.890810 | 0.445405 | − | 0.895329i | \(-0.353060\pi\) | ||||
0.445405 | + | 0.895329i | \(0.353060\pi\) | |||||||
\(564\) | 89.3342 | 3.76165 | ||||||||
\(565\) | 3.75318 | 0.157898 | ||||||||
\(566\) | −68.8492 | −2.89395 | ||||||||
\(567\) | 17.1423 | 0.719910 | ||||||||
\(568\) | 9.58402 | 0.402137 | ||||||||
\(569\) | 14.3064 | 0.599757 | 0.299879 | − | 0.953977i | \(-0.403054\pi\) | ||||
0.299879 | + | 0.953977i | \(0.403054\pi\) | |||||||
\(570\) | −16.5927 | −0.694993 | ||||||||
\(571\) | −6.16416 | −0.257962 | −0.128981 | − | 0.991647i | \(-0.541171\pi\) | ||||
−0.128981 | + | 0.991647i | \(0.541171\pi\) | |||||||
\(572\) | 4.18124 | 0.174827 | ||||||||
\(573\) | 31.9553 | 1.33495 | ||||||||
\(574\) | −27.7017 | −1.15625 | ||||||||
\(575\) | −37.7599 | −1.57469 | ||||||||
\(576\) | 82.4432 | 3.43514 | ||||||||
\(577\) | −1.97725 | −0.0823139 | −0.0411570 | − | 0.999153i | \(-0.513104\pi\) | ||||
−0.0411570 | + | 0.999153i | \(0.513104\pi\) | |||||||
\(578\) | 41.8936 | 1.74255 | ||||||||
\(579\) | 53.1194 | 2.20757 | ||||||||
\(580\) | 2.66750 | 0.110762 | ||||||||
\(581\) | 21.7423 | 0.902022 | ||||||||
\(582\) | 87.3534 | 3.62092 | ||||||||
\(583\) | −33.0922 | −1.37054 | ||||||||
\(584\) | 23.7888 | 0.984386 | ||||||||
\(585\) | 1.11343 | 0.0460347 | ||||||||
\(586\) | −63.2726 | −2.61377 | ||||||||
\(587\) | 8.38286 | 0.345998 | 0.172999 | − | 0.984922i | \(-0.444654\pi\) | ||||
0.172999 | + | 0.984922i | \(0.444654\pi\) | |||||||
\(588\) | 69.1536 | 2.85184 | ||||||||
\(589\) | −18.4840 | −0.761620 | ||||||||
\(590\) | 0.682217 | 0.0280864 | ||||||||
\(591\) | −29.2940 | −1.20499 | ||||||||
\(592\) | −50.1559 | −2.06140 | ||||||||
\(593\) | −23.2981 | −0.956738 | −0.478369 | − | 0.878159i | \(-0.658772\pi\) | ||||
−0.478369 | + | 0.878159i | \(0.658772\pi\) | |||||||
\(594\) | −74.9634 | −3.07579 | ||||||||
\(595\) | −3.52345 | −0.144447 | ||||||||
\(596\) | −15.7074 | −0.643402 | ||||||||
\(597\) | −24.6086 | −1.00716 | ||||||||
\(598\) | −5.25497 | −0.214892 | ||||||||
\(599\) | 10.9090 | 0.445728 | 0.222864 | − | 0.974850i | \(-0.428459\pi\) | ||||
0.222864 | + | 0.974850i | \(0.428459\pi\) | |||||||
\(600\) | 98.2793 | 4.01223 | ||||||||
\(601\) | 39.1730 | 1.59790 | 0.798950 | − | 0.601398i | \(-0.205389\pi\) | ||||
0.798950 | + | 0.601398i | \(0.205389\pi\) | |||||||
\(602\) | −71.7992 | −2.92631 | ||||||||
\(603\) | −28.3195 | −1.15326 | ||||||||
\(604\) | −42.7473 | −1.73936 | ||||||||
\(605\) | 3.28379 | 0.133505 | ||||||||
\(606\) | 14.4023 | 0.585054 | ||||||||
\(607\) | −17.4809 | −0.709527 | −0.354763 | − | 0.934956i | \(-0.615439\pi\) | ||||
−0.354763 | + | 0.934956i | \(0.615439\pi\) | |||||||
\(608\) | −32.8133 | −1.33076 | ||||||||
\(609\) | 5.66802 | 0.229680 | ||||||||
\(610\) | −2.50126 | −0.101273 | ||||||||
\(611\) | 1.30989 | 0.0529923 | ||||||||
\(612\) | −31.0903 | −1.25675 | ||||||||
\(613\) | 13.5173 | 0.545957 | 0.272978 | − | 0.962020i | \(-0.411991\pi\) | ||||
0.272978 | + | 0.962020i | \(0.411991\pi\) | |||||||
\(614\) | 70.9050 | 2.86149 | ||||||||
\(615\) | 8.27438 | 0.333655 | ||||||||
\(616\) | −105.938 | −4.26837 | ||||||||
\(617\) | 42.1812 | 1.69815 | 0.849075 | − | 0.528273i | \(-0.177160\pi\) | ||||
0.849075 | + | 0.528273i | \(0.177160\pi\) | |||||||
\(618\) | 36.8884 | 1.48387 | ||||||||
\(619\) | 24.1302 | 0.969874 | 0.484937 | − | 0.874549i | \(-0.338843\pi\) | ||||
0.484937 | + | 0.874549i | \(0.338843\pi\) | |||||||
\(620\) | −37.7162 | −1.51472 | ||||||||
\(621\) | 67.5244 | 2.70966 | ||||||||
\(622\) | 75.1412 | 3.01289 | ||||||||
\(623\) | 40.9473 | 1.64052 | ||||||||
\(624\) | 7.27033 | 0.291046 | ||||||||
\(625\) | 12.8121 | 0.512485 | ||||||||
\(626\) | 2.37574 | 0.0949538 | ||||||||
\(627\) | 25.6436 | 1.02410 | ||||||||
\(628\) | −40.6269 | −1.62119 | ||||||||
\(629\) | 4.85005 | 0.193384 | ||||||||
\(630\) | −46.6486 | −1.85853 | ||||||||
\(631\) | −24.5942 | −0.979080 | −0.489540 | − | 0.871981i | \(-0.662835\pi\) | ||||
−0.489540 | + | 0.871981i | \(0.662835\pi\) | |||||||
\(632\) | −47.1698 | −1.87632 | ||||||||
\(633\) | 27.9955 | 1.11272 | ||||||||
\(634\) | −83.8279 | −3.32923 | ||||||||
\(635\) | −19.8806 | −0.788939 | ||||||||
\(636\) | −128.291 | −5.08708 | ||||||||
\(637\) | 1.01398 | 0.0401754 | ||||||||
\(638\) | −5.75200 | −0.227724 | ||||||||
\(639\) | −6.52222 | −0.258015 | ||||||||
\(640\) | −10.2941 | −0.406909 | ||||||||
\(641\) | −29.7856 | −1.17646 | −0.588231 | − | 0.808693i | \(-0.700175\pi\) | ||||
−0.588231 | + | 0.808693i | \(0.700175\pi\) | |||||||
\(642\) | 69.4513 | 2.74102 | ||||||||
\(643\) | −0.763355 | −0.0301038 | −0.0150519 | − | 0.999887i | \(-0.504791\pi\) | ||||
−0.0150519 | + | 0.999887i | \(0.504791\pi\) | |||||||
\(644\) | 157.795 | 6.21797 | ||||||||
\(645\) | 21.4461 | 0.844439 | ||||||||
\(646\) | 6.79353 | 0.267288 | ||||||||
\(647\) | 9.33095 | 0.366838 | 0.183419 | − | 0.983035i | \(-0.441284\pi\) | ||||
0.183419 | + | 0.983035i | \(0.441284\pi\) | |||||||
\(648\) | −40.7850 | −1.60218 | ||||||||
\(649\) | −1.05434 | −0.0413866 | ||||||||
\(650\) | 2.38291 | 0.0934652 | ||||||||
\(651\) | −80.1409 | −3.14097 | ||||||||
\(652\) | 50.8137 | 1.99002 | ||||||||
\(653\) | −6.28140 | −0.245810 | −0.122905 | − | 0.992418i | \(-0.539221\pi\) | ||||
−0.122905 | + | 0.992418i | \(0.539221\pi\) | |||||||
\(654\) | 66.3266 | 2.59358 | ||||||||
\(655\) | −0.237792 | −0.00929132 | ||||||||
\(656\) | 35.0339 | 1.36785 | ||||||||
\(657\) | −16.1890 | −0.631592 | ||||||||
\(658\) | −54.8794 | −2.13942 | ||||||||
\(659\) | −29.7976 | −1.16075 | −0.580375 | − | 0.814349i | \(-0.697094\pi\) | ||||
−0.580375 | + | 0.814349i | \(0.697094\pi\) | |||||||
\(660\) | 52.3251 | 2.03675 | ||||||||
\(661\) | −2.41915 | −0.0940942 | −0.0470471 | − | 0.998893i | \(-0.514981\pi\) | ||||
−0.0470471 | + | 0.998893i | \(0.514981\pi\) | |||||||
\(662\) | 28.7183 | 1.11617 | ||||||||
\(663\) | −0.703037 | −0.0273037 | ||||||||
\(664\) | −51.7291 | −2.00748 | ||||||||
\(665\) | 7.30559 | 0.283299 | ||||||||
\(666\) | 64.2122 | 2.48817 | ||||||||
\(667\) | 5.18120 | 0.200617 | ||||||||
\(668\) | 22.2478 | 0.860795 | ||||||||
\(669\) | 18.0877 | 0.699311 | ||||||||
\(670\) | 12.6266 | 0.487809 | ||||||||
\(671\) | 3.86561 | 0.149230 | ||||||||
\(672\) | −142.268 | −5.48813 | ||||||||
\(673\) | 33.6552 | 1.29731 | 0.648656 | − | 0.761081i | \(-0.275331\pi\) | ||||
0.648656 | + | 0.761081i | \(0.275331\pi\) | |||||||
\(674\) | 61.1873 | 2.35685 | ||||||||
\(675\) | −30.6194 | −1.17854 | ||||||||
\(676\) | −65.5424 | −2.52086 | ||||||||
\(677\) | 23.5998 | 0.907015 | 0.453508 | − | 0.891252i | \(-0.350172\pi\) | ||||
0.453508 | + | 0.891252i | \(0.350172\pi\) | |||||||
\(678\) | −31.3751 | −1.20495 | ||||||||
\(679\) | −38.4607 | −1.47599 | ||||||||
\(680\) | 8.38297 | 0.321472 | ||||||||
\(681\) | −6.40158 | −0.245309 | ||||||||
\(682\) | 81.3283 | 3.11422 | ||||||||
\(683\) | −13.1054 | −0.501465 | −0.250733 | − | 0.968056i | \(-0.580671\pi\) | ||||
−0.250733 | + | 0.968056i | \(0.580671\pi\) | |||||||
\(684\) | 64.4633 | 2.46482 | ||||||||
\(685\) | 18.9751 | 0.725001 | ||||||||
\(686\) | 21.0795 | 0.804818 | ||||||||
\(687\) | 23.7489 | 0.906075 | ||||||||
\(688\) | 90.8033 | 3.46184 | ||||||||
\(689\) | −1.88110 | −0.0716644 | ||||||||
\(690\) | −65.7620 | −2.50352 | ||||||||
\(691\) | −0.156446 | −0.00595149 | −0.00297575 | − | 0.999996i | \(-0.500947\pi\) | ||||
−0.00297575 | + | 0.999996i | \(0.500947\pi\) | |||||||
\(692\) | −44.6246 | −1.69637 | ||||||||
\(693\) | 72.0940 | 2.73863 | ||||||||
\(694\) | −9.87852 | −0.374984 | ||||||||
\(695\) | 9.65609 | 0.366276 | ||||||||
\(696\) | −13.4853 | −0.511160 | ||||||||
\(697\) | −3.38776 | −0.128321 | ||||||||
\(698\) | 28.8257 | 1.09107 | ||||||||
\(699\) | −57.3175 | −2.16795 | ||||||||
\(700\) | −71.5530 | −2.70445 | ||||||||
\(701\) | 18.4837 | 0.698121 | 0.349060 | − | 0.937100i | \(-0.386501\pi\) | ||||
0.349060 | + | 0.937100i | \(0.386501\pi\) | |||||||
\(702\) | −4.26125 | −0.160830 | ||||||||
\(703\) | −10.0562 | −0.379276 | ||||||||
\(704\) | 56.8090 | 2.14107 | ||||||||
\(705\) | 16.3922 | 0.617367 | ||||||||
\(706\) | −36.5877 | −1.37700 | ||||||||
\(707\) | −6.34118 | −0.238484 | ||||||||
\(708\) | −4.08747 | −0.153616 | ||||||||
\(709\) | 47.1285 | 1.76995 | 0.884973 | − | 0.465642i | \(-0.154177\pi\) | ||||
0.884973 | + | 0.465642i | \(0.154177\pi\) | |||||||
\(710\) | 2.90802 | 0.109136 | ||||||||
\(711\) | 32.1005 | 1.20386 | ||||||||
\(712\) | −97.4216 | −3.65103 | ||||||||
\(713\) | −73.2576 | −2.74352 | ||||||||
\(714\) | 29.4546 | 1.10231 | ||||||||
\(715\) | 0.767230 | 0.0286928 | ||||||||
\(716\) | −73.2738 | −2.73837 | ||||||||
\(717\) | 12.3917 | 0.462777 | ||||||||
\(718\) | 48.4598 | 1.80850 | ||||||||
\(719\) | −17.6068 | −0.656622 | −0.328311 | − | 0.944570i | \(-0.606479\pi\) | ||||
−0.328311 | + | 0.944570i | \(0.606479\pi\) | |||||||
\(720\) | 58.9958 | 2.19865 | ||||||||
\(721\) | −16.2415 | −0.604866 | ||||||||
\(722\) | 36.3984 | 1.35461 | ||||||||
\(723\) | 58.5162 | 2.17624 | ||||||||
\(724\) | 73.7345 | 2.74032 | ||||||||
\(725\) | −2.34945 | −0.0872564 | ||||||||
\(726\) | −27.4512 | −1.01881 | ||||||||
\(727\) | 35.6057 | 1.32054 | 0.660272 | − | 0.751027i | \(-0.270441\pi\) | ||||
0.660272 | + | 0.751027i | \(0.270441\pi\) | |||||||
\(728\) | −6.02198 | −0.223189 | ||||||||
\(729\) | −37.0915 | −1.37376 | ||||||||
\(730\) | 7.21807 | 0.267153 | ||||||||
\(731\) | −8.78063 | −0.324763 | ||||||||
\(732\) | 14.9861 | 0.553904 | ||||||||
\(733\) | −31.8583 | −1.17671 | −0.588356 | − | 0.808602i | \(-0.700225\pi\) | ||||
−0.588356 | + | 0.808602i | \(0.700225\pi\) | |||||||
\(734\) | 63.0554 | 2.32742 | ||||||||
\(735\) | 12.6892 | 0.468049 | ||||||||
\(736\) | −130.049 | −4.79367 | ||||||||
\(737\) | −19.5141 | −0.718810 | ||||||||
\(738\) | −44.8522 | −1.65103 | ||||||||
\(739\) | −5.59398 | −0.205778 | −0.102889 | − | 0.994693i | \(-0.532809\pi\) | ||||
−0.102889 | + | 0.994693i | \(0.532809\pi\) | |||||||
\(740\) | −20.5194 | −0.754309 | ||||||||
\(741\) | 1.45769 | 0.0535496 | ||||||||
\(742\) | 78.8113 | 2.89325 | ||||||||
\(743\) | 40.5598 | 1.48799 | 0.743997 | − | 0.668183i | \(-0.232928\pi\) | ||||
0.743997 | + | 0.668183i | \(0.232928\pi\) | |||||||
\(744\) | 190.671 | 6.99033 | ||||||||
\(745\) | −2.88221 | −0.105596 | ||||||||
\(746\) | −63.0579 | −2.30871 | ||||||||
\(747\) | 35.2032 | 1.28802 | ||||||||
\(748\) | −21.4233 | −0.783315 | ||||||||
\(749\) | −30.5786 | −1.11732 | ||||||||
\(750\) | 65.8530 | 2.40461 | ||||||||
\(751\) | −5.47987 | −0.199963 | −0.0999816 | − | 0.994989i | \(-0.531878\pi\) | ||||
−0.0999816 | + | 0.994989i | \(0.531878\pi\) | |||||||
\(752\) | 69.4051 | 2.53094 | ||||||||
\(753\) | −34.3857 | −1.25308 | ||||||||
\(754\) | −0.326969 | −0.0119075 | ||||||||
\(755\) | −7.84385 | −0.285467 | ||||||||
\(756\) | 127.955 | 4.65369 | ||||||||
\(757\) | 20.8712 | 0.758577 | 0.379289 | − | 0.925278i | \(-0.376169\pi\) | ||||
0.379289 | + | 0.925278i | \(0.376169\pi\) | |||||||
\(758\) | 78.4048 | 2.84779 | ||||||||
\(759\) | 101.633 | 3.68905 | ||||||||
\(760\) | −17.3814 | −0.630490 | ||||||||
\(761\) | 44.8125 | 1.62445 | 0.812225 | − | 0.583344i | \(-0.198256\pi\) | ||||
0.812225 | + | 0.583344i | \(0.198256\pi\) | |||||||
\(762\) | 166.194 | 6.02059 | ||||||||
\(763\) | −29.2028 | −1.05721 | ||||||||
\(764\) | 55.3527 | 2.00259 | ||||||||
\(765\) | −5.70487 | −0.206260 | ||||||||
\(766\) | 64.4018 | 2.32693 | ||||||||
\(767\) | −0.0599335 | −0.00216407 | ||||||||
\(768\) | −0.995353 | −0.0359167 | ||||||||
\(769\) | 32.3485 | 1.16652 | 0.583258 | − | 0.812287i | \(-0.301778\pi\) | ||||
0.583258 | + | 0.812287i | \(0.301778\pi\) | |||||||
\(770\) | −32.1441 | −1.15839 | ||||||||
\(771\) | 16.1432 | 0.581385 | ||||||||
\(772\) | 92.0131 | 3.31163 | ||||||||
\(773\) | −45.6741 | −1.64278 | −0.821391 | − | 0.570365i | \(-0.806802\pi\) | ||||
−0.821391 | + | 0.570365i | \(0.806802\pi\) | |||||||
\(774\) | −116.251 | −4.17856 | ||||||||
\(775\) | 33.2192 | 1.19327 | ||||||||
\(776\) | 91.5055 | 3.28486 | ||||||||
\(777\) | −43.6005 | −1.56416 | ||||||||
\(778\) | 81.9122 | 2.93670 | ||||||||
\(779\) | 7.02426 | 0.251670 | ||||||||
\(780\) | 2.97438 | 0.106500 | ||||||||
\(781\) | −4.49425 | −0.160817 | ||||||||
\(782\) | 26.9248 | 0.962829 | ||||||||
\(783\) | 4.20142 | 0.150147 | ||||||||
\(784\) | 53.7265 | 1.91880 | ||||||||
\(785\) | −7.45476 | −0.266072 | ||||||||
\(786\) | 1.98785 | 0.0709043 | ||||||||
\(787\) | −8.86566 | −0.316027 | −0.158013 | − | 0.987437i | \(-0.550509\pi\) | ||||
−0.158013 | + | 0.987437i | \(0.550509\pi\) | |||||||
\(788\) | −50.7428 | −1.80764 | ||||||||
\(789\) | 47.2731 | 1.68297 | ||||||||
\(790\) | −14.3124 | −0.509214 | ||||||||
\(791\) | 13.8141 | 0.491173 | ||||||||
\(792\) | −171.526 | −6.09490 | ||||||||
\(793\) | 0.219738 | 0.00780313 | ||||||||
\(794\) | 53.5786 | 1.90143 | ||||||||
\(795\) | −23.5406 | −0.834898 | ||||||||
\(796\) | −42.6269 | −1.51087 | ||||||||
\(797\) | −45.0509 | −1.59579 | −0.797893 | − | 0.602800i | \(-0.794052\pi\) | ||||
−0.797893 | + | 0.602800i | \(0.794052\pi\) | |||||||
\(798\) | −61.0718 | −2.16192 | ||||||||
\(799\) | −6.71143 | −0.237433 | ||||||||
\(800\) | 58.9717 | 2.08496 | ||||||||
\(801\) | 66.2983 | 2.34254 | ||||||||
\(802\) | −4.10699 | −0.145023 | ||||||||
\(803\) | −11.1553 | −0.393662 | ||||||||
\(804\) | −75.6518 | −2.66803 | ||||||||
\(805\) | 28.9542 | 1.02050 | ||||||||
\(806\) | 4.62306 | 0.162840 | ||||||||
\(807\) | 27.2653 | 0.959785 | ||||||||
\(808\) | 15.0869 | 0.530755 | ||||||||
\(809\) | −23.2365 | −0.816952 | −0.408476 | − | 0.912769i | \(-0.633940\pi\) | ||||
−0.408476 | + | 0.912769i | \(0.633940\pi\) | |||||||
\(810\) | −12.3751 | −0.434817 | ||||||||
\(811\) | 26.9919 | 0.947814 | 0.473907 | − | 0.880575i | \(-0.342843\pi\) | ||||
0.473907 | + | 0.880575i | \(0.342843\pi\) | |||||||
\(812\) | 9.81811 | 0.344548 | ||||||||
\(813\) | 12.1680 | 0.426751 | ||||||||
\(814\) | 44.2465 | 1.55084 | ||||||||
\(815\) | 9.32398 | 0.326605 | ||||||||
\(816\) | −37.2508 | −1.30404 | ||||||||
\(817\) | 18.2059 | 0.636945 | ||||||||
\(818\) | 97.6599 | 3.41460 | ||||||||
\(819\) | 4.09814 | 0.143201 | ||||||||
\(820\) | 14.3328 | 0.500524 | ||||||||
\(821\) | 9.63379 | 0.336222 | 0.168111 | − | 0.985768i | \(-0.446233\pi\) | ||||
0.168111 | + | 0.985768i | \(0.446233\pi\) | |||||||
\(822\) | −158.624 | −5.53266 | ||||||||
\(823\) | −19.4544 | −0.678138 | −0.339069 | − | 0.940762i | \(-0.610112\pi\) | ||||
−0.339069 | + | 0.940762i | \(0.610112\pi\) | |||||||
\(824\) | 38.6417 | 1.34615 | ||||||||
\(825\) | −46.0862 | −1.60452 | ||||||||
\(826\) | 2.51099 | 0.0873686 | ||||||||
\(827\) | 3.46264 | 0.120408 | 0.0602040 | − | 0.998186i | \(-0.480825\pi\) | ||||
0.0602040 | + | 0.998186i | \(0.480825\pi\) | |||||||
\(828\) | 255.487 | 8.87880 | ||||||||
\(829\) | 10.9182 | 0.379203 | 0.189602 | − | 0.981861i | \(-0.439280\pi\) | ||||
0.189602 | + | 0.981861i | \(0.439280\pi\) | |||||||
\(830\) | −15.6958 | −0.544810 | ||||||||
\(831\) | −37.1601 | −1.28907 | ||||||||
\(832\) | 3.22927 | 0.111955 | ||||||||
\(833\) | −5.19532 | −0.180007 | ||||||||
\(834\) | −80.7211 | −2.79514 | ||||||||
\(835\) | 4.08233 | 0.141275 | ||||||||
\(836\) | 44.4196 | 1.53628 | ||||||||
\(837\) | −59.4045 | −2.05332 | ||||||||
\(838\) | −45.6965 | −1.57856 | ||||||||
\(839\) | 31.3279 | 1.08156 | 0.540780 | − | 0.841164i | \(-0.318129\pi\) | ||||
0.540780 | + | 0.841164i | \(0.318129\pi\) | |||||||
\(840\) | −75.3605 | −2.60018 | ||||||||
\(841\) | −28.6776 | −0.988883 | ||||||||
\(842\) | −28.1693 | −0.970779 | ||||||||
\(843\) | −1.45995 | −0.0502833 | ||||||||
\(844\) | 48.4935 | 1.66922 | ||||||||
\(845\) | −12.0266 | −0.413727 | ||||||||
\(846\) | −88.8560 | −3.05493 | ||||||||
\(847\) | 12.0864 | 0.415295 | ||||||||
\(848\) | −99.6714 | −3.42273 | ||||||||
\(849\) | 75.6922 | 2.59775 | ||||||||
\(850\) | −12.2092 | −0.418773 | ||||||||
\(851\) | −39.8557 | −1.36624 | ||||||||
\(852\) | −17.4232 | −0.596910 | ||||||||
\(853\) | 21.5084 | 0.736433 | 0.368217 | − | 0.929740i | \(-0.379968\pi\) | ||||
0.368217 | + | 0.929740i | \(0.379968\pi\) | |||||||
\(854\) | −9.20622 | −0.315030 | ||||||||
\(855\) | 11.8286 | 0.404529 | ||||||||
\(856\) | 72.7524 | 2.48663 | ||||||||
\(857\) | 40.1034 | 1.36991 | 0.684954 | − | 0.728587i | \(-0.259822\pi\) | ||||
0.684954 | + | 0.728587i | \(0.259822\pi\) | |||||||
\(858\) | −6.41374 | −0.218962 | ||||||||
\(859\) | −5.10522 | −0.174188 | −0.0870939 | − | 0.996200i | \(-0.527758\pi\) | ||||
−0.0870939 | + | 0.996200i | \(0.527758\pi\) | |||||||
\(860\) | 37.1488 | 1.26676 | ||||||||
\(861\) | 30.4550 | 1.03790 | ||||||||
\(862\) | 29.9919 | 1.02153 | ||||||||
\(863\) | −36.0059 | −1.22566 | −0.612828 | − | 0.790216i | \(-0.709968\pi\) | ||||
−0.612828 | + | 0.790216i | \(0.709968\pi\) | |||||||
\(864\) | −105.457 | −3.58771 | ||||||||
\(865\) | −8.18831 | −0.278411 | ||||||||
\(866\) | 17.8445 | 0.606380 | ||||||||
\(867\) | −46.0575 | −1.56419 | ||||||||
\(868\) | −138.820 | −4.71184 | ||||||||
\(869\) | 22.1194 | 0.750350 | ||||||||
\(870\) | −4.09177 | −0.138724 | ||||||||
\(871\) | −1.10926 | −0.0375860 | ||||||||
\(872\) | 69.4793 | 2.35286 | ||||||||
\(873\) | −62.2723 | −2.10760 | ||||||||
\(874\) | −55.8264 | −1.88836 | ||||||||
\(875\) | −28.9943 | −0.980187 | ||||||||
\(876\) | −43.2467 | −1.46117 | ||||||||
\(877\) | 3.43723 | 0.116067 | 0.0580335 | − | 0.998315i | \(-0.481517\pi\) | ||||
0.0580335 | + | 0.998315i | \(0.481517\pi\) | |||||||
\(878\) | −109.557 | −3.69738 | ||||||||
\(879\) | 69.5613 | 2.34624 | ||||||||
\(880\) | 40.6521 | 1.37038 | ||||||||
\(881\) | 33.9638 | 1.14427 | 0.572136 | − | 0.820159i | \(-0.306115\pi\) | ||||
0.572136 | + | 0.820159i | \(0.306115\pi\) | |||||||
\(882\) | −68.7834 | −2.31606 | ||||||||
\(883\) | 29.7487 | 1.00112 | 0.500562 | − | 0.865701i | \(-0.333127\pi\) | ||||
0.500562 | + | 0.865701i | \(0.333127\pi\) | |||||||
\(884\) | −1.21780 | −0.0409589 | ||||||||
\(885\) | −0.750022 | −0.0252117 | ||||||||
\(886\) | 86.0591 | 2.89121 | ||||||||
\(887\) | 44.7362 | 1.50209 | 0.751047 | − | 0.660249i | \(-0.229549\pi\) | ||||
0.751047 | + | 0.660249i | \(0.229549\pi\) | |||||||
\(888\) | 103.734 | 3.48109 | ||||||||
\(889\) | −73.1735 | −2.45416 | ||||||||
\(890\) | −29.5600 | −0.990853 | ||||||||
\(891\) | 19.1254 | 0.640723 | ||||||||
\(892\) | 31.3314 | 1.04905 | ||||||||
\(893\) | 13.9156 | 0.465668 | ||||||||
\(894\) | 24.0941 | 0.805829 | ||||||||
\(895\) | −13.4453 | −0.449425 | ||||||||
\(896\) | −37.8888 | −1.26578 | ||||||||
\(897\) | 5.77727 | 0.192897 | ||||||||
\(898\) | 97.4828 | 3.25304 | ||||||||
\(899\) | −4.55815 | −0.152023 | ||||||||
\(900\) | −115.853 | −3.86175 | ||||||||
\(901\) | 9.63817 | 0.321094 | ||||||||
\(902\) | −30.9062 | −1.02907 | ||||||||
\(903\) | 78.9353 | 2.62680 | ||||||||
\(904\) | −32.8665 | −1.09312 | ||||||||
\(905\) | 13.5298 | 0.449745 | ||||||||
\(906\) | 65.5715 | 2.17847 | ||||||||
\(907\) | 18.4734 | 0.613400 | 0.306700 | − | 0.951806i | \(-0.400775\pi\) | ||||
0.306700 | + | 0.951806i | \(0.400775\pi\) | |||||||
\(908\) | −11.0888 | −0.367994 | ||||||||
\(909\) | −10.2671 | −0.340538 | ||||||||
\(910\) | −1.82721 | −0.0605714 | ||||||||
\(911\) | −44.2452 | −1.46591 | −0.732955 | − | 0.680277i | \(-0.761859\pi\) | ||||
−0.732955 | + | 0.680277i | \(0.761859\pi\) | |||||||
\(912\) | 77.2366 | 2.55756 | ||||||||
\(913\) | 24.2574 | 0.802804 | ||||||||
\(914\) | 93.5733 | 3.09513 | ||||||||
\(915\) | 2.74986 | 0.0909074 | ||||||||
\(916\) | 41.1376 | 1.35922 | ||||||||
\(917\) | −0.875228 | −0.0289026 | ||||||||
\(918\) | 21.8333 | 0.720605 | ||||||||
\(919\) | 8.17401 | 0.269636 | 0.134818 | − | 0.990870i | \(-0.456955\pi\) | ||||
0.134818 | + | 0.990870i | \(0.456955\pi\) | |||||||
\(920\) | −68.8878 | −2.27116 | ||||||||
\(921\) | −77.9523 | −2.56862 | ||||||||
\(922\) | −43.8842 | −1.44525 | ||||||||
\(923\) | −0.255473 | −0.00840899 | ||||||||
\(924\) | 192.590 | 6.33573 | ||||||||
\(925\) | 18.0728 | 0.594231 | ||||||||
\(926\) | −90.8887 | −2.98679 | ||||||||
\(927\) | −26.2969 | −0.863702 | ||||||||
\(928\) | −8.09177 | −0.265625 | ||||||||
\(929\) | −20.7450 | −0.680621 | −0.340310 | − | 0.940313i | \(-0.610532\pi\) | ||||
−0.340310 | + | 0.940313i | \(0.610532\pi\) | |||||||
\(930\) | 57.8540 | 1.89711 | ||||||||
\(931\) | 10.7721 | 0.353041 | ||||||||
\(932\) | −99.2851 | −3.25219 | ||||||||
\(933\) | −82.6095 | −2.70451 | ||||||||
\(934\) | 8.64281 | 0.282801 | ||||||||
\(935\) | −3.93104 | −0.128559 | ||||||||
\(936\) | −9.75028 | −0.318698 | ||||||||
\(937\) | 1.42837 | 0.0466629 | 0.0233315 | − | 0.999728i | \(-0.492573\pi\) | ||||
0.0233315 | + | 0.999728i | \(0.492573\pi\) | |||||||
\(938\) | 46.4740 | 1.51743 | ||||||||
\(939\) | −2.61187 | −0.0852351 | ||||||||
\(940\) | 28.3945 | 0.926126 | ||||||||
\(941\) | 4.63184 | 0.150994 | 0.0754968 | − | 0.997146i | \(-0.475946\pi\) | ||||
0.0754968 | + | 0.997146i | \(0.475946\pi\) | |||||||
\(942\) | 62.3188 | 2.03046 | ||||||||
\(943\) | 27.8392 | 0.906570 | ||||||||
\(944\) | −3.17561 | −0.103357 | ||||||||
\(945\) | 23.4789 | 0.763770 | ||||||||
\(946\) | −80.1049 | −2.60443 | ||||||||
\(947\) | −9.36568 | −0.304344 | −0.152172 | − | 0.988354i | \(-0.548627\pi\) | ||||
−0.152172 | + | 0.988354i | \(0.548627\pi\) | |||||||
\(948\) | 85.7522 | 2.78510 | ||||||||
\(949\) | −0.634116 | −0.0205843 | ||||||||
\(950\) | 25.3149 | 0.821323 | ||||||||
\(951\) | 92.1596 | 2.98848 | ||||||||
\(952\) | 30.8547 | 1.00001 | ||||||||
\(953\) | −21.1901 | −0.686414 | −0.343207 | − | 0.939260i | \(-0.611513\pi\) | ||||
−0.343207 | + | 0.939260i | \(0.611513\pi\) | |||||||
\(954\) | 127.604 | 4.13135 | ||||||||
\(955\) | 10.1569 | 0.328668 | ||||||||
\(956\) | 21.4648 | 0.694223 | ||||||||
\(957\) | 6.32370 | 0.204416 | ||||||||
\(958\) | 0.353823 | 0.0114315 | ||||||||
\(959\) | 69.8405 | 2.25527 | ||||||||
\(960\) | 40.4119 | 1.30429 | ||||||||
\(961\) | 33.4483 | 1.07898 | ||||||||
\(962\) | 2.51517 | 0.0810922 | ||||||||
\(963\) | −49.5102 | −1.59544 | ||||||||
\(964\) | 101.361 | 3.26463 | ||||||||
\(965\) | 16.8838 | 0.543509 | ||||||||
\(966\) | −242.046 | −7.78770 | ||||||||
\(967\) | 52.7597 | 1.69664 | 0.848319 | − | 0.529485i | \(-0.177615\pi\) | ||||
0.848319 | + | 0.529485i | \(0.177615\pi\) | |||||||
\(968\) | −28.7560 | −0.924253 | ||||||||
\(969\) | −7.46874 | −0.239931 | ||||||||
\(970\) | 27.7649 | 0.891478 | ||||||||
\(971\) | −6.43887 | −0.206633 | −0.103317 | − | 0.994649i | \(-0.532945\pi\) | ||||
−0.103317 | + | 0.994649i | \(0.532945\pi\) | |||||||
\(972\) | −38.1825 | −1.22470 | ||||||||
\(973\) | 35.5406 | 1.13938 | ||||||||
\(974\) | 102.249 | 3.27627 | ||||||||
\(975\) | −2.61974 | −0.0838989 | ||||||||
\(976\) | 11.6430 | 0.372682 | ||||||||
\(977\) | −2.35728 | −0.0754161 | −0.0377080 | − | 0.999289i | \(-0.512006\pi\) | ||||
−0.0377080 | + | 0.999289i | \(0.512006\pi\) | |||||||
\(978\) | −77.9448 | −2.49240 | ||||||||
\(979\) | 45.6840 | 1.46007 | ||||||||
\(980\) | 21.9802 | 0.702131 | ||||||||
\(981\) | −47.2827 | −1.50962 | ||||||||
\(982\) | 22.2803 | 0.710992 | ||||||||
\(983\) | 25.2175 | 0.804313 | 0.402156 | − | 0.915571i | \(-0.368261\pi\) | ||||
0.402156 | + | 0.915571i | \(0.368261\pi\) | |||||||
\(984\) | −72.4584 | −2.30989 | ||||||||
\(985\) | −9.31097 | −0.296672 | ||||||||
\(986\) | 1.67528 | 0.0533519 | ||||||||
\(987\) | 60.3338 | 1.92045 | ||||||||
\(988\) | 2.52500 | 0.0803310 | ||||||||
\(989\) | 72.1556 | 2.29441 | ||||||||
\(990\) | −52.0450 | −1.65410 | ||||||||
\(991\) | −26.8966 | −0.854399 | −0.427200 | − | 0.904157i | \(-0.640500\pi\) | ||||
−0.427200 | + | 0.904157i | \(0.640500\pi\) | |||||||
\(992\) | 114.410 | 3.63254 | ||||||||
\(993\) | −31.5726 | −1.00193 | ||||||||
\(994\) | 10.7034 | 0.339490 | ||||||||
\(995\) | −7.82174 | −0.247966 | ||||||||
\(996\) | 94.0408 | 2.97980 | ||||||||
\(997\) | −8.01923 | −0.253971 | −0.126986 | − | 0.991905i | \(-0.540530\pi\) | ||||
−0.126986 | + | 0.991905i | \(0.540530\pi\) | |||||||
\(998\) | 88.9308 | 2.81506 | ||||||||
\(999\) | −32.3189 | −1.02252 |
(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 | 6037.2.a.b.1.4 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.b.1.4 | ✓ | 259 | 1.1 | even | 1 | trivial |