Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(113\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30912 | −1.63280 | −0.816398 | − | 0.577489i | \(-0.804033\pi\) | ||||
−0.816398 | + | 0.577489i | \(0.804033\pi\) | |||||||
\(3\) | −2.56184 | −1.47908 | −0.739539 | − | 0.673114i | \(-0.764956\pi\) | ||||
−0.739539 | + | 0.673114i | \(0.764956\pi\) | |||||||
\(4\) | 3.33205 | 1.66602 | ||||||||
\(5\) | −3.64906 | −1.63191 | −0.815955 | − | 0.578115i | \(-0.803789\pi\) | ||||
−0.815955 | + | 0.578115i | \(0.803789\pi\) | |||||||
\(6\) | 5.91560 | 2.41503 | ||||||||
\(7\) | −1.49745 | −0.565982 | −0.282991 | − | 0.959123i | \(-0.591327\pi\) | ||||
−0.282991 | + | 0.959123i | \(0.591327\pi\) | |||||||
\(8\) | −3.07586 | −1.08748 | ||||||||
\(9\) | 3.56301 | 1.18767 | ||||||||
\(10\) | 8.42614 | 2.66458 | ||||||||
\(11\) | −3.48349 | −1.05031 | −0.525156 | − | 0.851006i | \(-0.675993\pi\) | ||||
−0.525156 | + | 0.851006i | \(0.675993\pi\) | |||||||
\(12\) | −8.53617 | −2.46418 | ||||||||
\(13\) | −6.84422 | −1.89824 | −0.949122 | − | 0.314908i | \(-0.898026\pi\) | ||||
−0.949122 | + | 0.314908i | \(0.898026\pi\) | |||||||
\(14\) | 3.45779 | 0.924134 | ||||||||
\(15\) | 9.34831 | 2.41372 | ||||||||
\(16\) | 0.438451 | 0.109613 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −8.22743 | −1.93922 | ||||||||
\(19\) | −4.85370 | −1.11352 | −0.556758 | − | 0.830675i | \(-0.687955\pi\) | ||||
−0.556758 | + | 0.830675i | \(0.687955\pi\) | |||||||
\(20\) | −12.1589 | −2.71880 | ||||||||
\(21\) | 3.83622 | 0.837132 | ||||||||
\(22\) | 8.04381 | 1.71495 | ||||||||
\(23\) | −3.52454 | −0.734918 | −0.367459 | − | 0.930040i | \(-0.619772\pi\) | ||||
−0.367459 | + | 0.930040i | \(0.619772\pi\) | |||||||
\(24\) | 7.87986 | 1.60847 | ||||||||
\(25\) | 8.31567 | 1.66313 | ||||||||
\(26\) | 15.8041 | 3.09945 | ||||||||
\(27\) | −1.44234 | −0.277578 | ||||||||
\(28\) | −4.98957 | −0.942940 | ||||||||
\(29\) | 0.257619 | 0.0478386 | 0.0239193 | − | 0.999714i | \(-0.492386\pi\) | ||||
0.0239193 | + | 0.999714i | \(0.492386\pi\) | |||||||
\(30\) | −21.5864 | −3.94112 | ||||||||
\(31\) | −10.5212 | −1.88966 | −0.944830 | − | 0.327561i | \(-0.893773\pi\) | ||||
−0.944830 | + | 0.327561i | \(0.893773\pi\) | |||||||
\(32\) | 5.13929 | 0.908507 | ||||||||
\(33\) | 8.92414 | 1.55349 | ||||||||
\(34\) | 2.30912 | 0.396011 | ||||||||
\(35\) | 5.46429 | 0.923633 | ||||||||
\(36\) | 11.8721 | 1.97869 | ||||||||
\(37\) | 9.05762 | 1.48906 | 0.744532 | − | 0.667587i | \(-0.232673\pi\) | ||||
0.744532 | + | 0.667587i | \(0.232673\pi\) | |||||||
\(38\) | 11.2078 | 1.81814 | ||||||||
\(39\) | 17.5338 | 2.80765 | ||||||||
\(40\) | 11.2240 | 1.77467 | ||||||||
\(41\) | −8.20246 | −1.28101 | −0.640505 | − | 0.767954i | \(-0.721275\pi\) | ||||
−0.640505 | + | 0.767954i | \(0.721275\pi\) | |||||||
\(42\) | −8.85830 | −1.36687 | ||||||||
\(43\) | 2.07454 | 0.316365 | 0.158183 | − | 0.987410i | \(-0.449437\pi\) | ||||
0.158183 | + | 0.987410i | \(0.449437\pi\) | |||||||
\(44\) | −11.6072 | −1.74985 | ||||||||
\(45\) | −13.0016 | −1.93817 | ||||||||
\(46\) | 8.13860 | 1.19997 | ||||||||
\(47\) | −9.47289 | −1.38176 | −0.690882 | − | 0.722968i | \(-0.742777\pi\) | ||||
−0.690882 | + | 0.722968i | \(0.742777\pi\) | |||||||
\(48\) | −1.12324 | −0.162126 | ||||||||
\(49\) | −4.75765 | −0.679664 | ||||||||
\(50\) | −19.2019 | −2.71556 | ||||||||
\(51\) | 2.56184 | 0.358729 | ||||||||
\(52\) | −22.8053 | −3.16252 | ||||||||
\(53\) | 1.76880 | 0.242963 | 0.121481 | − | 0.992594i | \(-0.461236\pi\) | ||||
0.121481 | + | 0.992594i | \(0.461236\pi\) | |||||||
\(54\) | 3.33053 | 0.453228 | ||||||||
\(55\) | 12.7115 | 1.71402 | ||||||||
\(56\) | 4.60595 | 0.615496 | ||||||||
\(57\) | 12.4344 | 1.64698 | ||||||||
\(58\) | −0.594873 | −0.0781106 | ||||||||
\(59\) | −4.14338 | −0.539422 | −0.269711 | − | 0.962941i | \(-0.586928\pi\) | ||||
−0.269711 | + | 0.962941i | \(0.586928\pi\) | |||||||
\(60\) | 31.1490 | 4.02132 | ||||||||
\(61\) | 8.79865 | 1.12655 | 0.563276 | − | 0.826269i | \(-0.309541\pi\) | ||||
0.563276 | + | 0.826269i | \(0.309541\pi\) | |||||||
\(62\) | 24.2947 | 3.08543 | ||||||||
\(63\) | −5.33542 | −0.672200 | ||||||||
\(64\) | −12.7442 | −1.59302 | ||||||||
\(65\) | 24.9750 | 3.09777 | ||||||||
\(66\) | −20.6069 | −2.53654 | ||||||||
\(67\) | 0.775554 | 0.0947491 | 0.0473745 | − | 0.998877i | \(-0.484915\pi\) | ||||
0.0473745 | + | 0.998877i | \(0.484915\pi\) | |||||||
\(68\) | −3.33205 | −0.404070 | ||||||||
\(69\) | 9.02931 | 1.08700 | ||||||||
\(70\) | −12.6177 | −1.50810 | ||||||||
\(71\) | −15.9272 | −1.89021 | −0.945107 | − | 0.326762i | \(-0.894042\pi\) | ||||
−0.945107 | + | 0.326762i | \(0.894042\pi\) | |||||||
\(72\) | −10.9593 | −1.29157 | ||||||||
\(73\) | 12.4024 | 1.45159 | 0.725793 | − | 0.687913i | \(-0.241473\pi\) | ||||
0.725793 | + | 0.687913i | \(0.241473\pi\) | |||||||
\(74\) | −20.9152 | −2.43134 | ||||||||
\(75\) | −21.3034 | −2.45990 | ||||||||
\(76\) | −16.1728 | −1.85514 | ||||||||
\(77\) | 5.21635 | 0.594458 | ||||||||
\(78\) | −40.4876 | −4.58432 | ||||||||
\(79\) | 1.78756 | 0.201116 | 0.100558 | − | 0.994931i | \(-0.467937\pi\) | ||||
0.100558 | + | 0.994931i | \(0.467937\pi\) | |||||||
\(80\) | −1.59994 | −0.178878 | ||||||||
\(81\) | −6.99399 | −0.777110 | ||||||||
\(82\) | 18.9405 | 2.09163 | ||||||||
\(83\) | −14.5821 | −1.60059 | −0.800294 | − | 0.599607i | \(-0.795323\pi\) | ||||
−0.800294 | + | 0.599607i | \(0.795323\pi\) | |||||||
\(84\) | 12.7825 | 1.39468 | ||||||||
\(85\) | 3.64906 | 0.395797 | ||||||||
\(86\) | −4.79038 | −0.516560 | ||||||||
\(87\) | −0.659977 | −0.0707569 | ||||||||
\(88\) | 10.7148 | 1.14220 | ||||||||
\(89\) | −10.9734 | −1.16318 | −0.581590 | − | 0.813482i | \(-0.697569\pi\) | ||||
−0.581590 | + | 0.813482i | \(0.697569\pi\) | |||||||
\(90\) | 30.0224 | 3.16464 | ||||||||
\(91\) | 10.2489 | 1.07437 | ||||||||
\(92\) | −11.7440 | −1.22439 | ||||||||
\(93\) | 26.9535 | 2.79495 | ||||||||
\(94\) | 21.8741 | 2.25614 | ||||||||
\(95\) | 17.7115 | 1.81716 | ||||||||
\(96\) | −13.1660 | −1.34375 | ||||||||
\(97\) | 10.9242 | 1.10919 | 0.554594 | − | 0.832121i | \(-0.312874\pi\) | ||||
0.554594 | + | 0.832121i | \(0.312874\pi\) | |||||||
\(98\) | 10.9860 | 1.10975 | ||||||||
\(99\) | −12.4117 | −1.24742 | ||||||||
\(100\) | 27.7082 | 2.77082 | ||||||||
\(101\) | 3.79515 | 0.377631 | 0.188816 | − | 0.982013i | \(-0.439535\pi\) | ||||
0.188816 | + | 0.982013i | \(0.439535\pi\) | |||||||
\(102\) | −5.91560 | −0.585731 | ||||||||
\(103\) | 0.673794 | 0.0663909 | 0.0331955 | − | 0.999449i | \(-0.489432\pi\) | ||||
0.0331955 | + | 0.999449i | \(0.489432\pi\) | |||||||
\(104\) | 21.0519 | 2.06431 | ||||||||
\(105\) | −13.9986 | −1.36612 | ||||||||
\(106\) | −4.08437 | −0.396709 | ||||||||
\(107\) | 4.69255 | 0.453646 | 0.226823 | − | 0.973936i | \(-0.427166\pi\) | ||||
0.226823 | + | 0.973936i | \(0.427166\pi\) | |||||||
\(108\) | −4.80594 | −0.462452 | ||||||||
\(109\) | −16.7869 | −1.60789 | −0.803945 | − | 0.594704i | \(-0.797269\pi\) | ||||
−0.803945 | + | 0.594704i | \(0.797269\pi\) | |||||||
\(110\) | −29.3524 | −2.79864 | ||||||||
\(111\) | −23.2042 | −2.20244 | ||||||||
\(112\) | −0.656558 | −0.0620389 | ||||||||
\(113\) | 5.49015 | 0.516470 | 0.258235 | − | 0.966082i | \(-0.416859\pi\) | ||||
0.258235 | + | 0.966082i | \(0.416859\pi\) | |||||||
\(114\) | −28.7125 | −2.68918 | ||||||||
\(115\) | 12.8613 | 1.19932 | ||||||||
\(116\) | 0.858398 | 0.0797002 | ||||||||
\(117\) | −24.3860 | −2.25449 | ||||||||
\(118\) | 9.56757 | 0.880766 | ||||||||
\(119\) | 1.49745 | 0.137271 | ||||||||
\(120\) | −28.7541 | −2.62488 | ||||||||
\(121\) | 1.13472 | 0.103157 | ||||||||
\(122\) | −20.3172 | −1.83943 | ||||||||
\(123\) | 21.0134 | 1.89471 | ||||||||
\(124\) | −35.0571 | −3.14822 | ||||||||
\(125\) | −12.0991 | −1.08217 | ||||||||
\(126\) | 12.3201 | 1.09757 | ||||||||
\(127\) | −18.8335 | −1.67121 | −0.835604 | − | 0.549333i | \(-0.814882\pi\) | ||||
−0.835604 | + | 0.549333i | \(0.814882\pi\) | |||||||
\(128\) | 19.1492 | 1.69257 | ||||||||
\(129\) | −5.31465 | −0.467928 | ||||||||
\(130\) | −57.6703 | −5.05802 | ||||||||
\(131\) | 20.4316 | 1.78511 | 0.892557 | − | 0.450935i | \(-0.148909\pi\) | ||||
0.892557 | + | 0.450935i | \(0.148909\pi\) | |||||||
\(132\) | 29.7357 | 2.58816 | ||||||||
\(133\) | 7.26817 | 0.630230 | ||||||||
\(134\) | −1.79085 | −0.154706 | ||||||||
\(135\) | 5.26318 | 0.452982 | ||||||||
\(136\) | 3.07586 | 0.263753 | ||||||||
\(137\) | 3.94979 | 0.337453 | 0.168727 | − | 0.985663i | \(-0.446035\pi\) | ||||
0.168727 | + | 0.985663i | \(0.446035\pi\) | |||||||
\(138\) | −20.8498 | −1.77485 | ||||||||
\(139\) | 23.2945 | 1.97582 | 0.987909 | − | 0.155037i | \(-0.0495496\pi\) | ||||
0.987909 | + | 0.155037i | \(0.0495496\pi\) | |||||||
\(140\) | 18.2073 | 1.53879 | ||||||||
\(141\) | 24.2680 | 2.04373 | ||||||||
\(142\) | 36.7779 | 3.08633 | ||||||||
\(143\) | 23.8418 | 1.99375 | ||||||||
\(144\) | 1.56220 | 0.130184 | ||||||||
\(145\) | −0.940066 | −0.0780683 | ||||||||
\(146\) | −28.6386 | −2.37014 | ||||||||
\(147\) | 12.1883 | 1.00528 | ||||||||
\(148\) | 30.1804 | 2.48082 | ||||||||
\(149\) | −7.77384 | −0.636858 | −0.318429 | − | 0.947947i | \(-0.603155\pi\) | ||||
−0.318429 | + | 0.947947i | \(0.603155\pi\) | |||||||
\(150\) | 49.1921 | 4.01652 | ||||||||
\(151\) | 8.41967 | 0.685183 | 0.342592 | − | 0.939484i | \(-0.388695\pi\) | ||||
0.342592 | + | 0.939484i | \(0.388695\pi\) | |||||||
\(152\) | 14.9293 | 1.21093 | ||||||||
\(153\) | −3.56301 | −0.288052 | ||||||||
\(154\) | −12.0452 | −0.970630 | ||||||||
\(155\) | 38.3925 | 3.08376 | ||||||||
\(156\) | 58.4234 | 4.67761 | ||||||||
\(157\) | 9.78727 | 0.781109 | 0.390555 | − | 0.920580i | \(-0.372283\pi\) | ||||
0.390555 | + | 0.920580i | \(0.372283\pi\) | |||||||
\(158\) | −4.12770 | −0.328382 | ||||||||
\(159\) | −4.53137 | −0.359361 | ||||||||
\(160\) | −18.7536 | −1.48260 | ||||||||
\(161\) | 5.27782 | 0.415951 | ||||||||
\(162\) | 16.1500 | 1.26886 | ||||||||
\(163\) | 21.0012 | 1.64494 | 0.822471 | − | 0.568807i | \(-0.192595\pi\) | ||||
0.822471 | + | 0.568807i | \(0.192595\pi\) | |||||||
\(164\) | −27.3310 | −2.13419 | ||||||||
\(165\) | −32.5648 | −2.53516 | ||||||||
\(166\) | 33.6718 | 2.61344 | ||||||||
\(167\) | 0.574794 | 0.0444789 | 0.0222395 | − | 0.999753i | \(-0.492920\pi\) | ||||
0.0222395 | + | 0.999753i | \(0.492920\pi\) | |||||||
\(168\) | −11.7997 | −0.910366 | ||||||||
\(169\) | 33.8433 | 2.60333 | ||||||||
\(170\) | −8.42614 | −0.646255 | ||||||||
\(171\) | −17.2938 | −1.32249 | ||||||||
\(172\) | 6.91248 | 0.527072 | ||||||||
\(173\) | 6.68565 | 0.508301 | 0.254150 | − | 0.967165i | \(-0.418204\pi\) | ||||
0.254150 | + | 0.967165i | \(0.418204\pi\) | |||||||
\(174\) | 1.52397 | 0.115532 | ||||||||
\(175\) | −12.4523 | −0.941304 | ||||||||
\(176\) | −1.52734 | −0.115128 | ||||||||
\(177\) | 10.6147 | 0.797847 | ||||||||
\(178\) | 25.3390 | 1.89924 | ||||||||
\(179\) | 8.59297 | 0.642269 | 0.321134 | − | 0.947034i | \(-0.395936\pi\) | ||||
0.321134 | + | 0.947034i | \(0.395936\pi\) | |||||||
\(180\) | −43.3221 | −3.22904 | ||||||||
\(181\) | 8.97075 | 0.666791 | 0.333395 | − | 0.942787i | \(-0.391806\pi\) | ||||
0.333395 | + | 0.942787i | \(0.391806\pi\) | |||||||
\(182\) | −23.6659 | −1.75423 | ||||||||
\(183\) | −22.5407 | −1.66626 | ||||||||
\(184\) | 10.8410 | 0.799210 | ||||||||
\(185\) | −33.0518 | −2.43002 | ||||||||
\(186\) | −62.2391 | −4.56359 | ||||||||
\(187\) | 3.48349 | 0.254738 | ||||||||
\(188\) | −31.5641 | −2.30205 | ||||||||
\(189\) | 2.15983 | 0.157104 | ||||||||
\(190\) | −40.8980 | −2.96705 | ||||||||
\(191\) | 22.8167 | 1.65096 | 0.825478 | − | 0.564435i | \(-0.190906\pi\) | ||||
0.825478 | + | 0.564435i | \(0.190906\pi\) | |||||||
\(192\) | 32.6485 | 2.35620 | ||||||||
\(193\) | −4.58486 | −0.330026 | −0.165013 | − | 0.986291i | \(-0.552767\pi\) | ||||
−0.165013 | + | 0.986291i | \(0.552767\pi\) | |||||||
\(194\) | −25.2254 | −1.81108 | ||||||||
\(195\) | −63.9818 | −4.58183 | ||||||||
\(196\) | −15.8527 | −1.13234 | ||||||||
\(197\) | 14.0861 | 1.00359 | 0.501795 | − | 0.864986i | \(-0.332673\pi\) | ||||
0.501795 | + | 0.864986i | \(0.332673\pi\) | |||||||
\(198\) | 28.6602 | 2.03679 | ||||||||
\(199\) | −22.9916 | −1.62983 | −0.814914 | − | 0.579582i | \(-0.803216\pi\) | ||||
−0.814914 | + | 0.579582i | \(0.803216\pi\) | |||||||
\(200\) | −25.5779 | −1.80863 | ||||||||
\(201\) | −1.98684 | −0.140141 | ||||||||
\(202\) | −8.76346 | −0.616595 | ||||||||
\(203\) | −0.385771 | −0.0270758 | ||||||||
\(204\) | 8.53617 | 0.597651 | ||||||||
\(205\) | 29.9313 | 2.09049 | ||||||||
\(206\) | −1.55587 | −0.108403 | ||||||||
\(207\) | −12.5580 | −0.872840 | ||||||||
\(208\) | −3.00085 | −0.208072 | ||||||||
\(209\) | 16.9078 | 1.16954 | ||||||||
\(210\) | 32.3245 | 2.23060 | ||||||||
\(211\) | 14.3859 | 0.990368 | 0.495184 | − | 0.868788i | \(-0.335101\pi\) | ||||
0.495184 | + | 0.868788i | \(0.335101\pi\) | |||||||
\(212\) | 5.89371 | 0.404782 | ||||||||
\(213\) | 40.8029 | 2.79577 | ||||||||
\(214\) | −10.8357 | −0.740711 | ||||||||
\(215\) | −7.57015 | −0.516280 | ||||||||
\(216\) | 4.43643 | 0.301861 | ||||||||
\(217\) | 15.7549 | 1.06951 | ||||||||
\(218\) | 38.7629 | 2.62536 | ||||||||
\(219\) | −31.7728 | −2.14701 | ||||||||
\(220\) | 42.3553 | 2.85559 | ||||||||
\(221\) | 6.84422 | 0.460392 | ||||||||
\(222\) | 53.5812 | 3.59614 | ||||||||
\(223\) | −7.62441 | −0.510568 | −0.255284 | − | 0.966866i | \(-0.582169\pi\) | ||||
−0.255284 | + | 0.966866i | \(0.582169\pi\) | |||||||
\(224\) | −7.69582 | −0.514199 | ||||||||
\(225\) | 29.6288 | 1.97525 | ||||||||
\(226\) | −12.6774 | −0.843291 | ||||||||
\(227\) | −16.8693 | −1.11966 | −0.559828 | − | 0.828609i | \(-0.689133\pi\) | ||||
−0.559828 | + | 0.828609i | \(0.689133\pi\) | |||||||
\(228\) | 41.4320 | 2.74390 | ||||||||
\(229\) | −12.5587 | −0.829900 | −0.414950 | − | 0.909844i | \(-0.636201\pi\) | ||||
−0.414950 | + | 0.909844i | \(0.636201\pi\) | |||||||
\(230\) | −29.6983 | −1.95825 | ||||||||
\(231\) | −13.3634 | −0.879250 | ||||||||
\(232\) | −0.792400 | −0.0520236 | ||||||||
\(233\) | −9.14685 | −0.599230 | −0.299615 | − | 0.954060i | \(-0.596858\pi\) | ||||
−0.299615 | + | 0.954060i | \(0.596858\pi\) | |||||||
\(234\) | 56.3103 | 3.68112 | ||||||||
\(235\) | 34.5672 | 2.25491 | ||||||||
\(236\) | −13.8059 | −0.898690 | ||||||||
\(237\) | −4.57944 | −0.297467 | ||||||||
\(238\) | −3.45779 | −0.224135 | ||||||||
\(239\) | −24.0337 | −1.55461 | −0.777304 | − | 0.629125i | \(-0.783413\pi\) | ||||
−0.777304 | + | 0.629125i | \(0.783413\pi\) | |||||||
\(240\) | 4.09877 | 0.264575 | ||||||||
\(241\) | −5.94699 | −0.383079 | −0.191540 | − | 0.981485i | \(-0.561348\pi\) | ||||
−0.191540 | + | 0.981485i | \(0.561348\pi\) | |||||||
\(242\) | −2.62021 | −0.168434 | ||||||||
\(243\) | 22.2445 | 1.42698 | ||||||||
\(244\) | 29.3175 | 1.87686 | ||||||||
\(245\) | 17.3610 | 1.10915 | ||||||||
\(246\) | −48.5225 | −3.09368 | ||||||||
\(247\) | 33.2198 | 2.11372 | ||||||||
\(248\) | 32.3617 | 2.05497 | ||||||||
\(249\) | 37.3569 | 2.36739 | ||||||||
\(250\) | 27.9383 | 1.76697 | ||||||||
\(251\) | 9.11959 | 0.575623 | 0.287812 | − | 0.957687i | \(-0.407072\pi\) | ||||
0.287812 | + | 0.957687i | \(0.407072\pi\) | |||||||
\(252\) | −17.7779 | −1.11990 | ||||||||
\(253\) | 12.2777 | 0.771894 | ||||||||
\(254\) | 43.4890 | 2.72874 | ||||||||
\(255\) | −9.34831 | −0.585414 | ||||||||
\(256\) | −18.7296 | −1.17060 | ||||||||
\(257\) | −6.90176 | −0.430520 | −0.215260 | − | 0.976557i | \(-0.569060\pi\) | ||||
−0.215260 | + | 0.976557i | \(0.569060\pi\) | |||||||
\(258\) | 12.2722 | 0.764032 | ||||||||
\(259\) | −13.5633 | −0.842784 | ||||||||
\(260\) | 83.2179 | 5.16095 | ||||||||
\(261\) | 0.917897 | 0.0568164 | ||||||||
\(262\) | −47.1790 | −2.91473 | ||||||||
\(263\) | −2.12604 | −0.131097 | −0.0655487 | − | 0.997849i | \(-0.520880\pi\) | ||||
−0.0655487 | + | 0.997849i | \(0.520880\pi\) | |||||||
\(264\) | −27.4494 | −1.68940 | ||||||||
\(265\) | −6.45445 | −0.396494 | ||||||||
\(266\) | −16.7831 | −1.02904 | ||||||||
\(267\) | 28.1121 | 1.72043 | ||||||||
\(268\) | 2.58419 | 0.157854 | ||||||||
\(269\) | −13.8243 | −0.842881 | −0.421440 | − | 0.906856i | \(-0.638475\pi\) | ||||
−0.421440 | + | 0.906856i | \(0.638475\pi\) | |||||||
\(270\) | −12.1533 | −0.739628 | ||||||||
\(271\) | 24.0480 | 1.46081 | 0.730407 | − | 0.683012i | \(-0.239331\pi\) | ||||
0.730407 | + | 0.683012i | \(0.239331\pi\) | |||||||
\(272\) | −0.438451 | −0.0265850 | ||||||||
\(273\) | −26.2559 | −1.58908 | ||||||||
\(274\) | −9.12055 | −0.550992 | ||||||||
\(275\) | −28.9676 | −1.74681 | ||||||||
\(276\) | 30.0861 | 1.81097 | ||||||||
\(277\) | −5.63419 | −0.338526 | −0.169263 | − | 0.985571i | \(-0.554139\pi\) | ||||
−0.169263 | + | 0.985571i | \(0.554139\pi\) | |||||||
\(278\) | −53.7900 | −3.22611 | ||||||||
\(279\) | −37.4871 | −2.24429 | ||||||||
\(280\) | −16.8074 | −1.00443 | ||||||||
\(281\) | −23.3461 | −1.39271 | −0.696356 | − | 0.717697i | \(-0.745196\pi\) | ||||
−0.696356 | + | 0.717697i | \(0.745196\pi\) | |||||||
\(282\) | −56.0378 | −3.33700 | ||||||||
\(283\) | −23.8214 | −1.41603 | −0.708017 | − | 0.706195i | \(-0.750410\pi\) | ||||
−0.708017 | + | 0.706195i | \(0.750410\pi\) | |||||||
\(284\) | −53.0703 | −3.14914 | ||||||||
\(285\) | −45.3739 | −2.68772 | ||||||||
\(286\) | −55.0536 | −3.25539 | ||||||||
\(287\) | 12.2828 | 0.725029 | ||||||||
\(288\) | 18.3113 | 1.07901 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 2.17073 | 0.127470 | ||||||||
\(291\) | −27.9861 | −1.64057 | ||||||||
\(292\) | 41.3253 | 2.41838 | ||||||||
\(293\) | −3.67793 | −0.214867 | −0.107434 | − | 0.994212i | \(-0.534263\pi\) | ||||
−0.107434 | + | 0.994212i | \(0.534263\pi\) | |||||||
\(294\) | −28.1443 | −1.64141 | ||||||||
\(295\) | 15.1195 | 0.880289 | ||||||||
\(296\) | −27.8600 | −1.61933 | ||||||||
\(297\) | 5.02437 | 0.291544 | ||||||||
\(298\) | 17.9507 | 1.03986 | ||||||||
\(299\) | 24.1227 | 1.39505 | ||||||||
\(300\) | −70.9839 | −4.09826 | ||||||||
\(301\) | −3.10652 | −0.179057 | ||||||||
\(302\) | −19.4421 | −1.11876 | ||||||||
\(303\) | −9.72255 | −0.558546 | ||||||||
\(304\) | −2.12811 | −0.122055 | ||||||||
\(305\) | −32.1069 | −1.83843 | ||||||||
\(306\) | 8.22743 | 0.470331 | ||||||||
\(307\) | 21.0777 | 1.20297 | 0.601485 | − | 0.798884i | \(-0.294576\pi\) | ||||
0.601485 | + | 0.798884i | \(0.294576\pi\) | |||||||
\(308\) | 17.3811 | 0.990382 | ||||||||
\(309\) | −1.72615 | −0.0981973 | ||||||||
\(310\) | −88.6529 | −5.03515 | ||||||||
\(311\) | −14.6991 | −0.833509 | −0.416755 | − | 0.909019i | \(-0.636833\pi\) | ||||
−0.416755 | + | 0.909019i | \(0.636833\pi\) | |||||||
\(312\) | −53.9315 | −3.05327 | ||||||||
\(313\) | 29.5056 | 1.66776 | 0.833878 | − | 0.551948i | \(-0.186115\pi\) | ||||
0.833878 | + | 0.551948i | \(0.186115\pi\) | |||||||
\(314\) | −22.6000 | −1.27539 | ||||||||
\(315\) | 19.4693 | 1.09697 | ||||||||
\(316\) | 5.95624 | 0.335065 | ||||||||
\(317\) | −3.51756 | −0.197566 | −0.0987828 | − | 0.995109i | \(-0.531495\pi\) | ||||
−0.0987828 | + | 0.995109i | \(0.531495\pi\) | |||||||
\(318\) | 10.4635 | 0.586763 | ||||||||
\(319\) | −0.897412 | −0.0502454 | ||||||||
\(320\) | 46.5042 | 2.59967 | ||||||||
\(321\) | −12.0215 | −0.670977 | ||||||||
\(322\) | −12.1871 | −0.679163 | ||||||||
\(323\) | 4.85370 | 0.270067 | ||||||||
\(324\) | −23.3043 | −1.29468 | ||||||||
\(325\) | −56.9142 | −3.15703 | ||||||||
\(326\) | −48.4944 | −2.68586 | ||||||||
\(327\) | 43.0052 | 2.37819 | ||||||||
\(328\) | 25.2297 | 1.39307 | ||||||||
\(329\) | 14.1852 | 0.782054 | ||||||||
\(330\) | 75.1960 | 4.13941 | ||||||||
\(331\) | 9.14988 | 0.502923 | 0.251462 | − | 0.967867i | \(-0.419089\pi\) | ||||
0.251462 | + | 0.967867i | \(0.419089\pi\) | |||||||
\(332\) | −48.5881 | −2.66662 | ||||||||
\(333\) | 32.2724 | 1.76852 | ||||||||
\(334\) | −1.32727 | −0.0726250 | ||||||||
\(335\) | −2.83005 | −0.154622 | ||||||||
\(336\) | 1.68199 | 0.0917603 | ||||||||
\(337\) | 31.1959 | 1.69935 | 0.849674 | − | 0.527308i | \(-0.176799\pi\) | ||||
0.849674 | + | 0.527308i | \(0.176799\pi\) | |||||||
\(338\) | −78.1483 | −4.25071 | ||||||||
\(339\) | −14.0649 | −0.763899 | ||||||||
\(340\) | 12.1589 | 0.659407 | ||||||||
\(341\) | 36.6505 | 1.98473 | ||||||||
\(342\) | 39.9335 | 2.15936 | ||||||||
\(343\) | 17.6065 | 0.950660 | ||||||||
\(344\) | −6.38102 | −0.344041 | ||||||||
\(345\) | −32.9485 | −1.77389 | ||||||||
\(346\) | −15.4380 | −0.829952 | ||||||||
\(347\) | 25.8642 | 1.38846 | 0.694232 | − | 0.719752i | \(-0.255744\pi\) | ||||
0.694232 | + | 0.719752i | \(0.255744\pi\) | |||||||
\(348\) | −2.19907 | −0.117883 | ||||||||
\(349\) | −24.2935 | −1.30040 | −0.650202 | − | 0.759762i | \(-0.725316\pi\) | ||||
−0.650202 | + | 0.759762i | \(0.725316\pi\) | |||||||
\(350\) | 28.7538 | 1.53696 | ||||||||
\(351\) | 9.87167 | 0.526911 | ||||||||
\(352\) | −17.9027 | −0.954216 | ||||||||
\(353\) | −1.00000 | −0.0532246 | ||||||||
\(354\) | −24.5106 | −1.30272 | ||||||||
\(355\) | 58.1194 | 3.08466 | ||||||||
\(356\) | −36.5640 | −1.93789 | ||||||||
\(357\) | −3.83622 | −0.203034 | ||||||||
\(358\) | −19.8422 | −1.04869 | ||||||||
\(359\) | −9.11539 | −0.481092 | −0.240546 | − | 0.970638i | \(-0.577326\pi\) | ||||
−0.240546 | + | 0.970638i | \(0.577326\pi\) | |||||||
\(360\) | 39.9913 | 2.10773 | ||||||||
\(361\) | 4.55843 | 0.239918 | ||||||||
\(362\) | −20.7146 | −1.08873 | ||||||||
\(363\) | −2.90697 | −0.152576 | ||||||||
\(364\) | 34.1497 | 1.78993 | ||||||||
\(365\) | −45.2570 | −2.36886 | ||||||||
\(366\) | 52.0493 | 2.72066 | ||||||||
\(367\) | 13.5739 | 0.708553 | 0.354276 | − | 0.935141i | \(-0.384727\pi\) | ||||
0.354276 | + | 0.935141i | \(0.384727\pi\) | |||||||
\(368\) | −1.54534 | −0.0805564 | ||||||||
\(369\) | −29.2254 | −1.52142 | ||||||||
\(370\) | 76.3208 | 3.96773 | ||||||||
\(371\) | −2.64868 | −0.137513 | ||||||||
\(372\) | 89.8105 | 4.65646 | ||||||||
\(373\) | −3.63303 | −0.188111 | −0.0940555 | − | 0.995567i | \(-0.529983\pi\) | ||||
−0.0940555 | + | 0.995567i | \(0.529983\pi\) | |||||||
\(374\) | −8.04381 | −0.415936 | ||||||||
\(375\) | 30.9959 | 1.60062 | ||||||||
\(376\) | 29.1373 | 1.50264 | ||||||||
\(377\) | −1.76320 | −0.0908093 | ||||||||
\(378\) | −4.98730 | −0.256519 | ||||||||
\(379\) | 27.2845 | 1.40151 | 0.700755 | − | 0.713402i | \(-0.252847\pi\) | ||||
0.700755 | + | 0.713402i | \(0.252847\pi\) | |||||||
\(380\) | 59.0155 | 3.02743 | ||||||||
\(381\) | 48.2485 | 2.47184 | ||||||||
\(382\) | −52.6865 | −2.69567 | ||||||||
\(383\) | 0.767520 | 0.0392184 | 0.0196092 | − | 0.999808i | \(-0.493758\pi\) | ||||
0.0196092 | + | 0.999808i | \(0.493758\pi\) | |||||||
\(384\) | −49.0572 | −2.50344 | ||||||||
\(385\) | −19.0348 | −0.970103 | ||||||||
\(386\) | 10.5870 | 0.538865 | ||||||||
\(387\) | 7.39162 | 0.375737 | ||||||||
\(388\) | 36.4001 | 1.84793 | ||||||||
\(389\) | 13.4355 | 0.681205 | 0.340602 | − | 0.940207i | \(-0.389369\pi\) | ||||
0.340602 | + | 0.940207i | \(0.389369\pi\) | |||||||
\(390\) | 147.742 | 7.48120 | ||||||||
\(391\) | 3.52454 | 0.178244 | ||||||||
\(392\) | 14.6339 | 0.739122 | ||||||||
\(393\) | −52.3423 | −2.64032 | ||||||||
\(394\) | −32.5265 | −1.63866 | ||||||||
\(395\) | −6.52293 | −0.328204 | ||||||||
\(396\) | −41.3564 | −2.07824 | ||||||||
\(397\) | −16.4452 | −0.825362 | −0.412681 | − | 0.910876i | \(-0.635407\pi\) | ||||
−0.412681 | + | 0.910876i | \(0.635407\pi\) | |||||||
\(398\) | 53.0903 | 2.66118 | ||||||||
\(399\) | −18.6199 | −0.932159 | ||||||||
\(400\) | 3.64601 | 0.182301 | ||||||||
\(401\) | 19.7553 | 0.986534 | 0.493267 | − | 0.869878i | \(-0.335803\pi\) | ||||
0.493267 | + | 0.869878i | \(0.335803\pi\) | |||||||
\(402\) | 4.58787 | 0.228822 | ||||||||
\(403\) | 72.0092 | 3.58704 | ||||||||
\(404\) | 12.6456 | 0.629143 | ||||||||
\(405\) | 25.5215 | 1.26818 | ||||||||
\(406\) | 0.890792 | 0.0442092 | ||||||||
\(407\) | −31.5522 | −1.56398 | ||||||||
\(408\) | −7.87986 | −0.390111 | ||||||||
\(409\) | −20.8827 | −1.03258 | −0.516291 | − | 0.856413i | \(-0.672688\pi\) | ||||
−0.516291 | + | 0.856413i | \(0.672688\pi\) | |||||||
\(410\) | −69.1151 | −3.41335 | ||||||||
\(411\) | −10.1187 | −0.499119 | ||||||||
\(412\) | 2.24512 | 0.110609 | ||||||||
\(413\) | 6.20450 | 0.305303 | ||||||||
\(414\) | 28.9979 | 1.42517 | ||||||||
\(415\) | 53.2109 | 2.61202 | ||||||||
\(416\) | −35.1744 | −1.72457 | ||||||||
\(417\) | −59.6768 | −2.92239 | ||||||||
\(418\) | −39.0423 | −1.90962 | ||||||||
\(419\) | −31.1082 | −1.51973 | −0.759867 | − | 0.650079i | \(-0.774736\pi\) | ||||
−0.759867 | + | 0.650079i | \(0.774736\pi\) | |||||||
\(420\) | −46.6440 | −2.27600 | ||||||||
\(421\) | 32.1011 | 1.56451 | 0.782257 | − | 0.622956i | \(-0.214069\pi\) | ||||
0.782257 | + | 0.622956i | \(0.214069\pi\) | |||||||
\(422\) | −33.2189 | −1.61707 | ||||||||
\(423\) | −33.7520 | −1.64108 | ||||||||
\(424\) | −5.44057 | −0.264218 | ||||||||
\(425\) | −8.31567 | −0.403369 | ||||||||
\(426\) | −94.2190 | −4.56493 | ||||||||
\(427\) | −13.1755 | −0.637609 | ||||||||
\(428\) | 15.6358 | 0.755785 | ||||||||
\(429\) | −61.0788 | −2.94891 | ||||||||
\(430\) | 17.4804 | 0.842980 | ||||||||
\(431\) | 5.58008 | 0.268783 | 0.134391 | − | 0.990928i | \(-0.457092\pi\) | ||||
0.134391 | + | 0.990928i | \(0.457092\pi\) | |||||||
\(432\) | −0.632394 | −0.0304261 | ||||||||
\(433\) | 5.82127 | 0.279753 | 0.139876 | − | 0.990169i | \(-0.455330\pi\) | ||||
0.139876 | + | 0.990169i | \(0.455330\pi\) | |||||||
\(434\) | −36.3801 | −1.74630 | ||||||||
\(435\) | 2.40830 | 0.115469 | ||||||||
\(436\) | −55.9346 | −2.67878 | ||||||||
\(437\) | 17.1071 | 0.818343 | ||||||||
\(438\) | 73.3673 | 3.50563 | ||||||||
\(439\) | −8.56672 | −0.408867 | −0.204434 | − | 0.978880i | \(-0.565535\pi\) | ||||
−0.204434 | + | 0.978880i | \(0.565535\pi\) | |||||||
\(440\) | −39.0988 | −1.86396 | ||||||||
\(441\) | −16.9515 | −0.807216 | ||||||||
\(442\) | −15.8041 | −0.751726 | ||||||||
\(443\) | −39.6410 | −1.88340 | −0.941700 | − | 0.336454i | \(-0.890772\pi\) | ||||
−0.941700 | + | 0.336454i | \(0.890772\pi\) | |||||||
\(444\) | −77.3174 | −3.66932 | ||||||||
\(445\) | 40.0427 | 1.89821 | ||||||||
\(446\) | 17.6057 | 0.833654 | ||||||||
\(447\) | 19.9153 | 0.941962 | ||||||||
\(448\) | 19.0837 | 0.901621 | ||||||||
\(449\) | 20.6015 | 0.972243 | 0.486122 | − | 0.873891i | \(-0.338411\pi\) | ||||
0.486122 | + | 0.873891i | \(0.338411\pi\) | |||||||
\(450\) | −68.4165 | −3.22519 | ||||||||
\(451\) | 28.5732 | 1.34546 | ||||||||
\(452\) | 18.2935 | 0.860452 | ||||||||
\(453\) | −21.5698 | −1.01344 | ||||||||
\(454\) | 38.9533 | 1.82817 | ||||||||
\(455\) | −37.3988 | −1.75328 | ||||||||
\(456\) | −38.2465 | −1.79106 | ||||||||
\(457\) | −4.01128 | −0.187640 | −0.0938199 | − | 0.995589i | \(-0.529908\pi\) | ||||
−0.0938199 | + | 0.995589i | \(0.529908\pi\) | |||||||
\(458\) | 28.9995 | 1.35506 | ||||||||
\(459\) | 1.44234 | 0.0673225 | ||||||||
\(460\) | 42.8544 | 1.99810 | ||||||||
\(461\) | 24.2369 | 1.12883 | 0.564413 | − | 0.825493i | \(-0.309103\pi\) | ||||
0.564413 | + | 0.825493i | \(0.309103\pi\) | |||||||
\(462\) | 30.8578 | 1.43564 | ||||||||
\(463\) | 24.7970 | 1.15241 | 0.576207 | − | 0.817304i | \(-0.304532\pi\) | ||||
0.576207 | + | 0.817304i | \(0.304532\pi\) | |||||||
\(464\) | 0.112953 | 0.00524372 | ||||||||
\(465\) | −98.3552 | −4.56111 | ||||||||
\(466\) | 21.1212 | 0.978421 | ||||||||
\(467\) | 28.4656 | 1.31723 | 0.658615 | − | 0.752480i | \(-0.271143\pi\) | ||||
0.658615 | + | 0.752480i | \(0.271143\pi\) | |||||||
\(468\) | −81.2554 | −3.75603 | ||||||||
\(469\) | −1.16135 | −0.0536263 | ||||||||
\(470\) | −79.8199 | −3.68182 | ||||||||
\(471\) | −25.0734 | −1.15532 | ||||||||
\(472\) | 12.7445 | 0.586612 | ||||||||
\(473\) | −7.22666 | −0.332282 | ||||||||
\(474\) | 10.5745 | 0.485703 | ||||||||
\(475\) | −40.3618 | −1.85193 | ||||||||
\(476\) | 4.98957 | 0.228697 | ||||||||
\(477\) | 6.30223 | 0.288559 | ||||||||
\(478\) | 55.4967 | 2.53836 | ||||||||
\(479\) | 12.1444 | 0.554893 | 0.277447 | − | 0.960741i | \(-0.410512\pi\) | ||||
0.277447 | + | 0.960741i | \(0.410512\pi\) | |||||||
\(480\) | 48.0437 | 2.19288 | ||||||||
\(481\) | −61.9923 | −2.82661 | ||||||||
\(482\) | 13.7323 | 0.625491 | ||||||||
\(483\) | −13.5209 | −0.615223 | ||||||||
\(484\) | 3.78095 | 0.171861 | ||||||||
\(485\) | −39.8632 | −1.81009 | ||||||||
\(486\) | −51.3652 | −2.32998 | ||||||||
\(487\) | −1.20765 | −0.0547237 | −0.0273619 | − | 0.999626i | \(-0.508711\pi\) | ||||
−0.0273619 | + | 0.999626i | \(0.508711\pi\) | |||||||
\(488\) | −27.0635 | −1.22511 | ||||||||
\(489\) | −53.8017 | −2.43300 | ||||||||
\(490\) | −40.0886 | −1.81102 | ||||||||
\(491\) | −38.1387 | −1.72117 | −0.860587 | − | 0.509304i | \(-0.829903\pi\) | ||||
−0.860587 | + | 0.509304i | \(0.829903\pi\) | |||||||
\(492\) | 70.0176 | 3.15664 | ||||||||
\(493\) | −0.257619 | −0.0116026 | ||||||||
\(494\) | −76.7086 | −3.45128 | ||||||||
\(495\) | 45.2911 | 2.03569 | ||||||||
\(496\) | −4.61302 | −0.207131 | ||||||||
\(497\) | 23.8502 | 1.06983 | ||||||||
\(498\) | −86.2616 | −3.86547 | ||||||||
\(499\) | −31.6833 | −1.41834 | −0.709171 | − | 0.705037i | \(-0.750930\pi\) | ||||
−0.709171 | + | 0.705037i | \(0.750930\pi\) | |||||||
\(500\) | −40.3147 | −1.80293 | ||||||||
\(501\) | −1.47253 | −0.0657878 | ||||||||
\(502\) | −21.0583 | −0.939876 | ||||||||
\(503\) | −40.8882 | −1.82311 | −0.911556 | − | 0.411175i | \(-0.865119\pi\) | ||||
−0.911556 | + | 0.411175i | \(0.865119\pi\) | |||||||
\(504\) | 16.4110 | 0.731006 | ||||||||
\(505\) | −13.8487 | −0.616261 | ||||||||
\(506\) | −28.3508 | −1.26035 | ||||||||
\(507\) | −86.7010 | −3.85053 | ||||||||
\(508\) | −62.7543 | −2.78427 | ||||||||
\(509\) | −35.5649 | −1.57638 | −0.788192 | − | 0.615429i | \(-0.788983\pi\) | ||||
−0.788192 | + | 0.615429i | \(0.788983\pi\) | |||||||
\(510\) | 21.5864 | 0.955861 | ||||||||
\(511\) | −18.5719 | −0.821572 | ||||||||
\(512\) | 4.95056 | 0.218786 | ||||||||
\(513\) | 7.00068 | 0.309087 | ||||||||
\(514\) | 15.9370 | 0.702952 | ||||||||
\(515\) | −2.45872 | −0.108344 | ||||||||
\(516\) | −17.7087 | −0.779580 | ||||||||
\(517\) | 32.9988 | 1.45128 | ||||||||
\(518\) | 31.3194 | 1.37609 | ||||||||
\(519\) | −17.1276 | −0.751816 | ||||||||
\(520\) | −76.8196 | −3.36876 | ||||||||
\(521\) | 34.2199 | 1.49920 | 0.749601 | − | 0.661890i | \(-0.230245\pi\) | ||||
0.749601 | + | 0.661890i | \(0.230245\pi\) | |||||||
\(522\) | −2.11954 | −0.0927696 | ||||||||
\(523\) | −7.24758 | −0.316915 | −0.158457 | − | 0.987366i | \(-0.550652\pi\) | ||||
−0.158457 | + | 0.987366i | \(0.550652\pi\) | |||||||
\(524\) | 68.0789 | 2.97404 | ||||||||
\(525\) | 31.9007 | 1.39226 | ||||||||
\(526\) | 4.90930 | 0.214056 | ||||||||
\(527\) | 10.5212 | 0.458310 | ||||||||
\(528\) | 3.91280 | 0.170283 | ||||||||
\(529\) | −10.5776 | −0.459895 | ||||||||
\(530\) | 14.9041 | 0.647393 | ||||||||
\(531\) | −14.7629 | −0.640655 | ||||||||
\(532\) | 24.2179 | 1.04998 | ||||||||
\(533\) | 56.1394 | 2.43167 | ||||||||
\(534\) | −64.9143 | −2.80912 | ||||||||
\(535\) | −17.1234 | −0.740310 | ||||||||
\(536\) | −2.38550 | −0.103038 | ||||||||
\(537\) | −22.0138 | −0.949965 | ||||||||
\(538\) | 31.9219 | 1.37625 | ||||||||
\(539\) | 16.5732 | 0.713860 | ||||||||
\(540\) | 17.5372 | 0.754680 | ||||||||
\(541\) | −19.6874 | −0.846427 | −0.423214 | − | 0.906030i | \(-0.639098\pi\) | ||||
−0.423214 | + | 0.906030i | \(0.639098\pi\) | |||||||
\(542\) | −55.5298 | −2.38521 | ||||||||
\(543\) | −22.9816 | −0.986235 | ||||||||
\(544\) | −5.13929 | −0.220345 | ||||||||
\(545\) | 61.2563 | 2.62393 | ||||||||
\(546\) | 60.6281 | 2.59464 | ||||||||
\(547\) | −14.6812 | −0.627724 | −0.313862 | − | 0.949469i | \(-0.601623\pi\) | ||||
−0.313862 | + | 0.949469i | \(0.601623\pi\) | |||||||
\(548\) | 13.1609 | 0.562205 | ||||||||
\(549\) | 31.3497 | 1.33797 | ||||||||
\(550\) | 66.8897 | 2.85218 | ||||||||
\(551\) | −1.25040 | −0.0532690 | ||||||||
\(552\) | −27.7729 | −1.18209 | ||||||||
\(553\) | −2.67678 | −0.113828 | ||||||||
\(554\) | 13.0100 | 0.552743 | ||||||||
\(555\) | 84.6734 | 3.59419 | ||||||||
\(556\) | 77.6186 | 3.29176 | ||||||||
\(557\) | −26.3781 | −1.11767 | −0.558837 | − | 0.829277i | \(-0.688752\pi\) | ||||
−0.558837 | + | 0.829277i | \(0.688752\pi\) | |||||||
\(558\) | 86.5622 | 3.66447 | ||||||||
\(559\) | −14.1986 | −0.600538 | ||||||||
\(560\) | 2.39582 | 0.101242 | ||||||||
\(561\) | −8.92414 | −0.376778 | ||||||||
\(562\) | 53.9090 | 2.27401 | ||||||||
\(563\) | −44.7185 | −1.88466 | −0.942330 | − | 0.334684i | \(-0.891370\pi\) | ||||
−0.942330 | + | 0.334684i | \(0.891370\pi\) | |||||||
\(564\) | 80.8622 | 3.40491 | ||||||||
\(565\) | −20.0339 | −0.842833 | ||||||||
\(566\) | 55.0065 | 2.31210 | ||||||||
\(567\) | 10.4731 | 0.439831 | ||||||||
\(568\) | 48.9900 | 2.05557 | ||||||||
\(569\) | −3.69040 | −0.154710 | −0.0773548 | − | 0.997004i | \(-0.524647\pi\) | ||||
−0.0773548 | + | 0.997004i | \(0.524647\pi\) | |||||||
\(570\) | 104.774 | 4.38850 | ||||||||
\(571\) | −31.8871 | −1.33443 | −0.667216 | − | 0.744864i | \(-0.732514\pi\) | ||||
−0.667216 | + | 0.744864i | \(0.732514\pi\) | |||||||
\(572\) | 79.4420 | 3.32164 | ||||||||
\(573\) | −58.4526 | −2.44189 | ||||||||
\(574\) | −28.3624 | −1.18382 | ||||||||
\(575\) | −29.3089 | −1.22227 | ||||||||
\(576\) | −45.4075 | −1.89198 | ||||||||
\(577\) | −22.5777 | −0.939923 | −0.469961 | − | 0.882687i | \(-0.655732\pi\) | ||||
−0.469961 | + | 0.882687i | \(0.655732\pi\) | |||||||
\(578\) | −2.30912 | −0.0960469 | ||||||||
\(579\) | 11.7457 | 0.488133 | ||||||||
\(580\) | −3.13235 | −0.130064 | ||||||||
\(581\) | 21.8359 | 0.905905 | ||||||||
\(582\) | 64.6233 | 2.67872 | ||||||||
\(583\) | −6.16159 | −0.255187 | ||||||||
\(584\) | −38.1480 | −1.57857 | ||||||||
\(585\) | 88.9861 | 3.67912 | ||||||||
\(586\) | 8.49280 | 0.350834 | ||||||||
\(587\) | −12.6124 | −0.520569 | −0.260285 | − | 0.965532i | \(-0.583816\pi\) | ||||
−0.260285 | + | 0.965532i | \(0.583816\pi\) | |||||||
\(588\) | 40.6121 | 1.67481 | ||||||||
\(589\) | 51.0667 | 2.10417 | ||||||||
\(590\) | −34.9127 | −1.43733 | ||||||||
\(591\) | −36.0862 | −1.48439 | ||||||||
\(592\) | 3.97132 | 0.163220 | ||||||||
\(593\) | 8.35891 | 0.343259 | 0.171630 | − | 0.985162i | \(-0.445097\pi\) | ||||
0.171630 | + | 0.985162i | \(0.445097\pi\) | |||||||
\(594\) | −11.6019 | −0.476031 | ||||||||
\(595\) | −5.46429 | −0.224014 | ||||||||
\(596\) | −25.9028 | −1.06102 | ||||||||
\(597\) | 58.9006 | 2.41064 | ||||||||
\(598\) | −55.7024 | −2.27784 | ||||||||
\(599\) | −39.2464 | −1.60356 | −0.801781 | − | 0.597617i | \(-0.796114\pi\) | ||||
−0.801781 | + | 0.597617i | \(0.796114\pi\) | |||||||
\(600\) | 65.5263 | 2.67510 | ||||||||
\(601\) | −33.8652 | −1.38139 | −0.690695 | − | 0.723146i | \(-0.742695\pi\) | ||||
−0.690695 | + | 0.723146i | \(0.742695\pi\) | |||||||
\(602\) | 7.17335 | 0.292364 | ||||||||
\(603\) | 2.76331 | 0.112531 | ||||||||
\(604\) | 28.0548 | 1.14153 | ||||||||
\(605\) | −4.14067 | −0.168342 | ||||||||
\(606\) | 22.4506 | 0.911992 | ||||||||
\(607\) | 43.3780 | 1.76066 | 0.880329 | − | 0.474363i | \(-0.157322\pi\) | ||||
0.880329 | + | 0.474363i | \(0.157322\pi\) | |||||||
\(608\) | −24.9446 | −1.01164 | ||||||||
\(609\) | 0.988281 | 0.0400472 | ||||||||
\(610\) | 74.1387 | 3.00179 | ||||||||
\(611\) | 64.8345 | 2.62292 | ||||||||
\(612\) | −11.8721 | −0.479902 | ||||||||
\(613\) | 12.4888 | 0.504420 | 0.252210 | − | 0.967673i | \(-0.418843\pi\) | ||||
0.252210 | + | 0.967673i | \(0.418843\pi\) | |||||||
\(614\) | −48.6710 | −1.96420 | ||||||||
\(615\) | −76.6791 | −3.09200 | ||||||||
\(616\) | −16.0448 | −0.646463 | ||||||||
\(617\) | 12.1206 | 0.487955 | 0.243978 | − | 0.969781i | \(-0.421548\pi\) | ||||
0.243978 | + | 0.969781i | \(0.421548\pi\) | |||||||
\(618\) | 3.98590 | 0.160336 | ||||||||
\(619\) | −27.3827 | −1.10060 | −0.550301 | − | 0.834966i | \(-0.685487\pi\) | ||||
−0.550301 | + | 0.834966i | \(0.685487\pi\) | |||||||
\(620\) | 127.926 | 5.13761 | ||||||||
\(621\) | 5.08358 | 0.203997 | ||||||||
\(622\) | 33.9420 | 1.36095 | ||||||||
\(623\) | 16.4321 | 0.658339 | ||||||||
\(624\) | 7.68770 | 0.307754 | ||||||||
\(625\) | 2.57197 | 0.102879 | ||||||||
\(626\) | −68.1321 | −2.72311 | ||||||||
\(627\) | −43.3151 | −1.72984 | ||||||||
\(628\) | 32.6117 | 1.30135 | ||||||||
\(629\) | −9.05762 | −0.361151 | ||||||||
\(630\) | −44.9570 | −1.79113 | ||||||||
\(631\) | 11.4977 | 0.457717 | 0.228858 | − | 0.973460i | \(-0.426501\pi\) | ||||
0.228858 | + | 0.973460i | \(0.426501\pi\) | |||||||
\(632\) | −5.49830 | −0.218710 | ||||||||
\(633\) | −36.8544 | −1.46483 | ||||||||
\(634\) | 8.12247 | 0.322585 | ||||||||
\(635\) | 68.7248 | 2.72726 | ||||||||
\(636\) | −15.0987 | −0.598704 | ||||||||
\(637\) | 32.5624 | 1.29017 | ||||||||
\(638\) | 2.07224 | 0.0820406 | ||||||||
\(639\) | −56.7488 | −2.24495 | ||||||||
\(640\) | −69.8768 | −2.76212 | ||||||||
\(641\) | −15.5911 | −0.615812 | −0.307906 | − | 0.951417i | \(-0.599628\pi\) | ||||
−0.307906 | + | 0.951417i | \(0.599628\pi\) | |||||||
\(642\) | 27.7592 | 1.09557 | ||||||||
\(643\) | −21.9751 | −0.866615 | −0.433308 | − | 0.901246i | \(-0.642654\pi\) | ||||
−0.433308 | + | 0.901246i | \(0.642654\pi\) | |||||||
\(644\) | 17.5860 | 0.692984 | ||||||||
\(645\) | 19.3935 | 0.763617 | ||||||||
\(646\) | −11.2078 | −0.440965 | ||||||||
\(647\) | 7.53796 | 0.296348 | 0.148174 | − | 0.988961i | \(-0.452660\pi\) | ||||
0.148174 | + | 0.988961i | \(0.452660\pi\) | |||||||
\(648\) | 21.5126 | 0.845094 | ||||||||
\(649\) | 14.4334 | 0.566562 | ||||||||
\(650\) | 131.422 | 5.15479 | ||||||||
\(651\) | −40.3616 | −1.58189 | ||||||||
\(652\) | 69.9771 | 2.74051 | ||||||||
\(653\) | −9.42288 | −0.368746 | −0.184373 | − | 0.982856i | \(-0.559025\pi\) | ||||
−0.184373 | + | 0.982856i | \(0.559025\pi\) | |||||||
\(654\) | −99.3043 | −3.88311 | ||||||||
\(655\) | −74.5561 | −2.91315 | ||||||||
\(656\) | −3.59638 | −0.140415 | ||||||||
\(657\) | 44.1897 | 1.72400 | ||||||||
\(658\) | −32.7553 | −1.27693 | ||||||||
\(659\) | 24.3252 | 0.947577 | 0.473788 | − | 0.880639i | \(-0.342886\pi\) | ||||
0.473788 | + | 0.880639i | \(0.342886\pi\) | |||||||
\(660\) | −108.507 | −4.22364 | ||||||||
\(661\) | 16.9884 | 0.660773 | 0.330386 | − | 0.943846i | \(-0.392821\pi\) | ||||
0.330386 | + | 0.943846i | \(0.392821\pi\) | |||||||
\(662\) | −21.1282 | −0.821171 | ||||||||
\(663\) | −17.5338 | −0.680955 | ||||||||
\(664\) | 44.8524 | 1.74061 | ||||||||
\(665\) | −26.5220 | −1.02848 | ||||||||
\(666\) | −74.5209 | −2.88763 | ||||||||
\(667\) | −0.907988 | −0.0351574 | ||||||||
\(668\) | 1.91524 | 0.0741030 | ||||||||
\(669\) | 19.5325 | 0.755170 | ||||||||
\(670\) | 6.53493 | 0.252466 | ||||||||
\(671\) | −30.6500 | −1.18323 | ||||||||
\(672\) | 19.7154 | 0.760540 | ||||||||
\(673\) | 9.60265 | 0.370155 | 0.185078 | − | 0.982724i | \(-0.440746\pi\) | ||||
0.185078 | + | 0.982724i | \(0.440746\pi\) | |||||||
\(674\) | −72.0351 | −2.77469 | ||||||||
\(675\) | −11.9940 | −0.461649 | ||||||||
\(676\) | 112.768 | 4.33721 | ||||||||
\(677\) | 1.57534 | 0.0605453 | 0.0302726 | − | 0.999542i | \(-0.490362\pi\) | ||||
0.0302726 | + | 0.999542i | \(0.490362\pi\) | |||||||
\(678\) | 32.4775 | 1.24729 | ||||||||
\(679\) | −16.3585 | −0.627780 | ||||||||
\(680\) | −11.2240 | −0.430422 | ||||||||
\(681\) | 43.2164 | 1.65606 | ||||||||
\(682\) | −84.6304 | −3.24067 | ||||||||
\(683\) | 4.48393 | 0.171573 | 0.0857865 | − | 0.996314i | \(-0.472660\pi\) | ||||
0.0857865 | + | 0.996314i | \(0.472660\pi\) | |||||||
\(684\) | −57.6237 | −2.20330 | ||||||||
\(685\) | −14.4130 | −0.550694 | ||||||||
\(686\) | −40.6555 | −1.55223 | ||||||||
\(687\) | 32.1732 | 1.22749 | ||||||||
\(688\) | 0.909586 | 0.0346776 | ||||||||
\(689\) | −12.1060 | −0.461203 | ||||||||
\(690\) | 76.0822 | 2.89640 | ||||||||
\(691\) | 4.98889 | 0.189786 | 0.0948931 | − | 0.995487i | \(-0.469749\pi\) | ||||
0.0948931 | + | 0.995487i | \(0.469749\pi\) | |||||||
\(692\) | 22.2769 | 0.846842 | ||||||||
\(693\) | 18.5859 | 0.706020 | ||||||||
\(694\) | −59.7236 | −2.26708 | ||||||||
\(695\) | −85.0033 | −3.22436 | ||||||||
\(696\) | 2.03000 | 0.0769469 | ||||||||
\(697\) | 8.20246 | 0.310690 | ||||||||
\(698\) | 56.0968 | 2.12329 | ||||||||
\(699\) | 23.4327 | 0.886308 | ||||||||
\(700\) | −41.4916 | −1.56824 | ||||||||
\(701\) | 45.6486 | 1.72412 | 0.862062 | − | 0.506802i | \(-0.169173\pi\) | ||||
0.862062 | + | 0.506802i | \(0.169173\pi\) | |||||||
\(702\) | −22.7949 | −0.860338 | ||||||||
\(703\) | −43.9630 | −1.65810 | ||||||||
\(704\) | 44.3942 | 1.67317 | ||||||||
\(705\) | −88.5555 | −3.33519 | ||||||||
\(706\) | 2.30912 | 0.0869050 | ||||||||
\(707\) | −5.68304 | −0.213733 | ||||||||
\(708\) | 35.3686 | 1.32923 | ||||||||
\(709\) | −12.9810 | −0.487510 | −0.243755 | − | 0.969837i | \(-0.578379\pi\) | ||||
−0.243755 | + | 0.969837i | \(0.578379\pi\) | |||||||
\(710\) | −134.205 | −5.03662 | ||||||||
\(711\) | 6.36910 | 0.238860 | ||||||||
\(712\) | 33.7527 | 1.26494 | ||||||||
\(713\) | 37.0824 | 1.38875 | ||||||||
\(714\) | 8.85830 | 0.331514 | ||||||||
\(715\) | −87.0002 | −3.25362 | ||||||||
\(716\) | 28.6322 | 1.07004 | ||||||||
\(717\) | 61.5703 | 2.29939 | ||||||||
\(718\) | 21.0486 | 0.785525 | ||||||||
\(719\) | −19.9910 | −0.745538 | −0.372769 | − | 0.927924i | \(-0.621592\pi\) | ||||
−0.372769 | + | 0.927924i | \(0.621592\pi\) | |||||||
\(720\) | −5.70058 | −0.212448 | ||||||||
\(721\) | −1.00897 | −0.0375761 | ||||||||
\(722\) | −10.5260 | −0.391736 | ||||||||
\(723\) | 15.2352 | 0.566604 | ||||||||
\(724\) | 29.8910 | 1.11089 | ||||||||
\(725\) | 2.14227 | 0.0795619 | ||||||||
\(726\) | 6.71256 | 0.249126 | ||||||||
\(727\) | −16.7412 | −0.620895 | −0.310448 | − | 0.950590i | \(-0.600479\pi\) | ||||
−0.310448 | + | 0.950590i | \(0.600479\pi\) | |||||||
\(728\) | −31.5241 | −1.16836 | ||||||||
\(729\) | −36.0048 | −1.33351 | ||||||||
\(730\) | 104.504 | 3.86786 | ||||||||
\(731\) | −2.07454 | −0.0767298 | ||||||||
\(732\) | −75.1068 | −2.77603 | ||||||||
\(733\) | −18.1403 | −0.670026 | −0.335013 | − | 0.942213i | \(-0.608741\pi\) | ||||
−0.335013 | + | 0.942213i | \(0.608741\pi\) | |||||||
\(734\) | −31.3439 | −1.15692 | ||||||||
\(735\) | −44.4760 | −1.64052 | ||||||||
\(736\) | −18.1137 | −0.667678 | ||||||||
\(737\) | −2.70164 | −0.0995161 | ||||||||
\(738\) | 67.4851 | 2.48416 | ||||||||
\(739\) | 20.1204 | 0.740142 | 0.370071 | − | 0.929003i | \(-0.379333\pi\) | ||||
0.370071 | + | 0.929003i | \(0.379333\pi\) | |||||||
\(740\) | −110.130 | −4.04847 | ||||||||
\(741\) | −85.1037 | −3.12636 | ||||||||
\(742\) | 6.11613 | 0.224530 | ||||||||
\(743\) | −14.4646 | −0.530654 | −0.265327 | − | 0.964158i | \(-0.585480\pi\) | ||||
−0.265327 | + | 0.964158i | \(0.585480\pi\) | |||||||
\(744\) | −82.9055 | −3.03946 | ||||||||
\(745\) | 28.3672 | 1.03929 | ||||||||
\(746\) | 8.38911 | 0.307147 | ||||||||
\(747\) | −51.9560 | −1.90097 | ||||||||
\(748\) | 11.6072 | 0.424400 | ||||||||
\(749\) | −7.02685 | −0.256756 | ||||||||
\(750\) | −71.5733 | −2.61349 | ||||||||
\(751\) | 0.843350 | 0.0307743 | 0.0153871 | − | 0.999882i | \(-0.495102\pi\) | ||||
0.0153871 | + | 0.999882i | \(0.495102\pi\) | |||||||
\(752\) | −4.15340 | −0.151459 | ||||||||
\(753\) | −23.3629 | −0.851392 | ||||||||
\(754\) | 4.07144 | 0.148273 | ||||||||
\(755\) | −30.7239 | −1.11816 | ||||||||
\(756\) | 7.19664 | 0.261739 | ||||||||
\(757\) | −10.1330 | −0.368290 | −0.184145 | − | 0.982899i | \(-0.558952\pi\) | ||||
−0.184145 | + | 0.982899i | \(0.558952\pi\) | |||||||
\(758\) | −63.0033 | −2.28838 | ||||||||
\(759\) | −31.4535 | −1.14169 | ||||||||
\(760\) | −54.4781 | −1.97613 | ||||||||
\(761\) | 27.7194 | 1.00483 | 0.502414 | − | 0.864627i | \(-0.332445\pi\) | ||||
0.502414 | + | 0.864627i | \(0.332445\pi\) | |||||||
\(762\) | −111.412 | −4.03602 | ||||||||
\(763\) | 25.1375 | 0.910037 | ||||||||
\(764\) | 76.0262 | 2.75053 | ||||||||
\(765\) | 13.0016 | 0.470076 | ||||||||
\(766\) | −1.77230 | −0.0640357 | ||||||||
\(767\) | 28.3582 | 1.02395 | ||||||||
\(768\) | 47.9823 | 1.73141 | ||||||||
\(769\) | 1.94791 | 0.0702434 | 0.0351217 | − | 0.999383i | \(-0.488818\pi\) | ||||
0.0351217 | + | 0.999383i | \(0.488818\pi\) | |||||||
\(770\) | 43.9537 | 1.58398 | ||||||||
\(771\) | 17.6812 | 0.636772 | ||||||||
\(772\) | −15.2770 | −0.549831 | ||||||||
\(773\) | 8.47858 | 0.304953 | 0.152477 | − | 0.988307i | \(-0.451275\pi\) | ||||
0.152477 | + | 0.988307i | \(0.451275\pi\) | |||||||
\(774\) | −17.0682 | −0.613502 | ||||||||
\(775\) | −87.4906 | −3.14276 | ||||||||
\(776\) | −33.6014 | −1.20622 | ||||||||
\(777\) | 34.7470 | 1.24654 | ||||||||
\(778\) | −31.0241 | −1.11227 | ||||||||
\(779\) | 39.8123 | 1.42642 | ||||||||
\(780\) | −213.191 | −7.63345 | ||||||||
\(781\) | 55.4824 | 1.98531 | ||||||||
\(782\) | −8.13860 | −0.291036 | ||||||||
\(783\) | −0.371573 | −0.0132789 | ||||||||
\(784\) | −2.08599 | −0.0744998 | ||||||||
\(785\) | −35.7144 | −1.27470 | ||||||||
\(786\) | 120.865 | 4.31111 | ||||||||
\(787\) | −15.3984 | −0.548894 | −0.274447 | − | 0.961602i | \(-0.588495\pi\) | ||||
−0.274447 | + | 0.961602i | \(0.588495\pi\) | |||||||
\(788\) | 46.9355 | 1.67201 | ||||||||
\(789\) | 5.44658 | 0.193903 | ||||||||
\(790\) | 15.0622 | 0.535890 | ||||||||
\(791\) | −8.22122 | −0.292313 | ||||||||
\(792\) | 38.1768 | 1.35655 | ||||||||
\(793\) | −60.2199 | −2.13847 | ||||||||
\(794\) | 37.9740 | 1.34765 | ||||||||
\(795\) | 16.5352 | 0.586445 | ||||||||
\(796\) | −76.6090 | −2.71533 | ||||||||
\(797\) | −8.64188 | −0.306111 | −0.153056 | − | 0.988218i | \(-0.548911\pi\) | ||||
−0.153056 | + | 0.988218i | \(0.548911\pi\) | |||||||
\(798\) | 42.9956 | 1.52203 | ||||||||
\(799\) | 9.47289 | 0.335127 | ||||||||
\(800\) | 42.7366 | 1.51097 | ||||||||
\(801\) | −39.0984 | −1.38147 | ||||||||
\(802\) | −45.6175 | −1.61081 | ||||||||
\(803\) | −43.2035 | −1.52462 | ||||||||
\(804\) | −6.62026 | −0.233479 | ||||||||
\(805\) | −19.2591 | −0.678795 | ||||||||
\(806\) | −166.278 | −5.85690 | ||||||||
\(807\) | 35.4155 | 1.24669 | ||||||||
\(808\) | −11.6734 | −0.410667 | ||||||||
\(809\) | 38.8969 | 1.36754 | 0.683772 | − | 0.729696i | \(-0.260338\pi\) | ||||
0.683772 | + | 0.729696i | \(0.260338\pi\) | |||||||
\(810\) | −58.9324 | −2.07067 | ||||||||
\(811\) | 5.99010 | 0.210341 | 0.105170 | − | 0.994454i | \(-0.466461\pi\) | ||||
0.105170 | + | 0.994454i | \(0.466461\pi\) | |||||||
\(812\) | −1.28541 | −0.0451089 | ||||||||
\(813\) | −61.6071 | −2.16066 | ||||||||
\(814\) | 72.8578 | 2.55367 | ||||||||
\(815\) | −76.6348 | −2.68440 | ||||||||
\(816\) | 1.12324 | 0.0393213 | ||||||||
\(817\) | −10.0692 | −0.352278 | ||||||||
\(818\) | 48.2206 | 1.68600 | ||||||||
\(819\) | 36.5168 | 1.27600 | ||||||||
\(820\) | 99.7326 | 3.48281 | ||||||||
\(821\) | 2.33058 | 0.0813377 | 0.0406689 | − | 0.999173i | \(-0.487051\pi\) | ||||
0.0406689 | + | 0.999173i | \(0.487051\pi\) | |||||||
\(822\) | 23.3654 | 0.814960 | ||||||||
\(823\) | −5.46723 | −0.190576 | −0.0952878 | − | 0.995450i | \(-0.530377\pi\) | ||||
−0.0952878 | + | 0.995450i | \(0.530377\pi\) | |||||||
\(824\) | −2.07250 | −0.0721989 | ||||||||
\(825\) | 74.2102 | 2.58367 | ||||||||
\(826\) | −14.3269 | −0.498498 | ||||||||
\(827\) | −9.92201 | −0.345022 | −0.172511 | − | 0.985008i | \(-0.555188\pi\) | ||||
−0.172511 | + | 0.985008i | \(0.555188\pi\) | |||||||
\(828\) | −41.8438 | −1.45417 | ||||||||
\(829\) | 17.7453 | 0.616319 | 0.308160 | − | 0.951335i | \(-0.400287\pi\) | ||||
0.308160 | + | 0.951335i | \(0.400287\pi\) | |||||||
\(830\) | −122.870 | −4.26489 | ||||||||
\(831\) | 14.4339 | 0.500705 | ||||||||
\(832\) | 87.2238 | 3.02394 | ||||||||
\(833\) | 4.75765 | 0.164843 | ||||||||
\(834\) | 137.801 | 4.77166 | ||||||||
\(835\) | −2.09746 | −0.0725856 | ||||||||
\(836\) | 56.3377 | 1.94848 | ||||||||
\(837\) | 15.1751 | 0.524528 | ||||||||
\(838\) | 71.8326 | 2.48142 | ||||||||
\(839\) | 16.4743 | 0.568756 | 0.284378 | − | 0.958712i | \(-0.408213\pi\) | ||||
0.284378 | + | 0.958712i | \(0.408213\pi\) | |||||||
\(840\) | 43.0578 | 1.48564 | ||||||||
\(841\) | −28.9336 | −0.997711 | ||||||||
\(842\) | −74.1255 | −2.55453 | ||||||||
\(843\) | 59.8089 | 2.05993 | ||||||||
\(844\) | 47.9346 | 1.64998 | ||||||||
\(845\) | −123.496 | −4.24840 | ||||||||
\(846\) | 77.9375 | 2.67955 | ||||||||
\(847\) | −1.69919 | −0.0583848 | ||||||||
\(848\) | 0.775530 | 0.0266318 | ||||||||
\(849\) | 61.0265 | 2.09443 | ||||||||
\(850\) | 19.2019 | 0.658620 | ||||||||
\(851\) | −31.9240 | −1.09434 | ||||||||
\(852\) | 135.957 | 4.65782 | ||||||||
\(853\) | 12.4408 | 0.425963 | 0.212982 | − | 0.977056i | \(-0.431683\pi\) | ||||
0.212982 | + | 0.977056i | \(0.431683\pi\) | |||||||
\(854\) | 30.4239 | 1.04109 | ||||||||
\(855\) | 63.1061 | 2.15818 | ||||||||
\(856\) | −14.4336 | −0.493332 | ||||||||
\(857\) | −41.3994 | −1.41418 | −0.707088 | − | 0.707125i | \(-0.749992\pi\) | ||||
−0.707088 | + | 0.707125i | \(0.749992\pi\) | |||||||
\(858\) | 141.038 | 4.81497 | ||||||||
\(859\) | 31.8145 | 1.08550 | 0.542749 | − | 0.839895i | \(-0.317384\pi\) | ||||
0.542749 | + | 0.839895i | \(0.317384\pi\) | |||||||
\(860\) | −25.2241 | −0.860134 | ||||||||
\(861\) | −31.4664 | −1.07237 | ||||||||
\(862\) | −12.8851 | −0.438868 | ||||||||
\(863\) | 14.7534 | 0.502211 | 0.251106 | − | 0.967960i | \(-0.419206\pi\) | ||||
0.251106 | + | 0.967960i | \(0.419206\pi\) | |||||||
\(864\) | −7.41259 | −0.252181 | ||||||||
\(865\) | −24.3964 | −0.829502 | ||||||||
\(866\) | −13.4420 | −0.456779 | ||||||||
\(867\) | −2.56184 | −0.0870045 | ||||||||
\(868\) | 52.4962 | 1.78184 | ||||||||
\(869\) | −6.22696 | −0.211235 | ||||||||
\(870\) | −5.56105 | −0.188537 | ||||||||
\(871\) | −5.30806 | −0.179857 | ||||||||
\(872\) | 51.6341 | 1.74855 | ||||||||
\(873\) | 38.9231 | 1.31735 | ||||||||
\(874\) | −39.5024 | −1.33619 | ||||||||
\(875\) | 18.1177 | 0.612492 | ||||||||
\(876\) | −105.869 | −3.57697 | ||||||||
\(877\) | 45.8325 | 1.54765 | 0.773827 | − | 0.633398i | \(-0.218340\pi\) | ||||
0.773827 | + | 0.633398i | \(0.218340\pi\) | |||||||
\(878\) | 19.7816 | 0.667597 | ||||||||
\(879\) | 9.42226 | 0.317805 | ||||||||
\(880\) | 5.57336 | 0.187878 | ||||||||
\(881\) | 7.33502 | 0.247123 | 0.123562 | − | 0.992337i | \(-0.460568\pi\) | ||||
0.123562 | + | 0.992337i | \(0.460568\pi\) | |||||||
\(882\) | 39.1432 | 1.31802 | ||||||||
\(883\) | −13.9038 | −0.467898 | −0.233949 | − | 0.972249i | \(-0.575165\pi\) | ||||
−0.233949 | + | 0.972249i | \(0.575165\pi\) | |||||||
\(884\) | 22.8053 | 0.767024 | ||||||||
\(885\) | −38.7336 | −1.30201 | ||||||||
\(886\) | 91.5359 | 3.07521 | ||||||||
\(887\) | −48.0058 | −1.61188 | −0.805939 | − | 0.591999i | \(-0.798339\pi\) | ||||
−0.805939 | + | 0.591999i | \(0.798339\pi\) | |||||||
\(888\) | 71.3728 | 2.39512 | ||||||||
\(889\) | 28.2023 | 0.945874 | ||||||||
\(890\) | −92.4635 | −3.09938 | ||||||||
\(891\) | 24.3635 | 0.816209 | ||||||||
\(892\) | −25.4049 | −0.850619 | ||||||||
\(893\) | 45.9786 | 1.53862 | ||||||||
\(894\) | −45.9869 | −1.53803 | ||||||||
\(895\) | −31.3563 | −1.04813 | ||||||||
\(896\) | −28.6750 | −0.957965 | ||||||||
\(897\) | −61.7985 | −2.06339 | ||||||||
\(898\) | −47.5713 | −1.58748 | ||||||||
\(899\) | −2.71045 | −0.0903986 | ||||||||
\(900\) | 98.7246 | 3.29082 | ||||||||
\(901\) | −1.76880 | −0.0589271 | ||||||||
\(902\) | −65.9791 | −2.19686 | ||||||||
\(903\) | 7.95841 | 0.264839 | ||||||||
\(904\) | −16.8870 | −0.561652 | ||||||||
\(905\) | −32.7348 | −1.08814 | ||||||||
\(906\) | 49.8074 | 1.65474 | ||||||||
\(907\) | −20.8859 | −0.693505 | −0.346752 | − | 0.937957i | \(-0.612716\pi\) | ||||
−0.346752 | + | 0.937957i | \(0.612716\pi\) | |||||||
\(908\) | −56.2094 | −1.86537 | ||||||||
\(909\) | 13.5221 | 0.448501 | ||||||||
\(910\) | 86.3583 | 2.86275 | ||||||||
\(911\) | 15.5342 | 0.514670 | 0.257335 | − | 0.966322i | \(-0.417156\pi\) | ||||
0.257335 | + | 0.966322i | \(0.417156\pi\) | |||||||
\(912\) | 5.45187 | 0.180530 | ||||||||
\(913\) | 50.7965 | 1.68112 | ||||||||
\(914\) | 9.26255 | 0.306378 | ||||||||
\(915\) | 82.2525 | 2.71918 | ||||||||
\(916\) | −41.8461 | −1.38263 | ||||||||
\(917\) | −30.5952 | −1.01034 | ||||||||
\(918\) | −3.33053 | −0.109924 | ||||||||
\(919\) | −22.5667 | −0.744407 | −0.372203 | − | 0.928151i | \(-0.621398\pi\) | ||||
−0.372203 | + | 0.928151i | \(0.621398\pi\) | |||||||
\(920\) | −39.5596 | −1.30424 | ||||||||
\(921\) | −53.9977 | −1.77928 | ||||||||
\(922\) | −55.9660 | −1.84314 | ||||||||
\(923\) | 109.009 | 3.58809 | ||||||||
\(924\) | −44.5276 | −1.46485 | ||||||||
\(925\) | 75.3202 | 2.47651 | ||||||||
\(926\) | −57.2593 | −1.88166 | ||||||||
\(927\) | 2.40074 | 0.0788505 | ||||||||
\(928\) | 1.32398 | 0.0434617 | ||||||||
\(929\) | 36.8657 | 1.20952 | 0.604762 | − | 0.796406i | \(-0.293268\pi\) | ||||
0.604762 | + | 0.796406i | \(0.293268\pi\) | |||||||
\(930\) | 227.114 | 7.44737 | ||||||||
\(931\) | 23.0922 | 0.756817 | ||||||||
\(932\) | −30.4778 | −0.998332 | ||||||||
\(933\) | 37.6567 | 1.23282 | ||||||||
\(934\) | −65.7305 | −2.15077 | ||||||||
\(935\) | −12.7115 | −0.415710 | ||||||||
\(936\) | 75.0080 | 2.45171 | ||||||||
\(937\) | −51.7830 | −1.69168 | −0.845839 | − | 0.533439i | \(-0.820899\pi\) | ||||
−0.845839 | + | 0.533439i | \(0.820899\pi\) | |||||||
\(938\) | 2.68171 | 0.0875608 | ||||||||
\(939\) | −75.5886 | −2.46674 | ||||||||
\(940\) | 115.180 | 3.75674 | ||||||||
\(941\) | −6.71582 | −0.218929 | −0.109465 | − | 0.993991i | \(-0.534914\pi\) | ||||
−0.109465 | + | 0.993991i | \(0.534914\pi\) | |||||||
\(942\) | 57.8975 | 1.88640 | ||||||||
\(943\) | 28.9099 | 0.941437 | ||||||||
\(944\) | −1.81667 | −0.0591275 | ||||||||
\(945\) | −7.88134 | −0.256380 | ||||||||
\(946\) | 16.6872 | 0.542549 | ||||||||
\(947\) | 37.3223 | 1.21281 | 0.606406 | − | 0.795155i | \(-0.292611\pi\) | ||||
0.606406 | + | 0.795155i | \(0.292611\pi\) | |||||||
\(948\) | −15.2589 | −0.495587 | ||||||||
\(949\) | −84.8844 | −2.75546 | ||||||||
\(950\) | 93.2003 | 3.02382 | ||||||||
\(951\) | 9.01141 | 0.292215 | ||||||||
\(952\) | −4.60595 | −0.149280 | ||||||||
\(953\) | 19.6806 | 0.637518 | 0.318759 | − | 0.947836i | \(-0.396734\pi\) | ||||
0.318759 | + | 0.947836i | \(0.396734\pi\) | |||||||
\(954\) | −14.5526 | −0.471159 | ||||||||
\(955\) | −83.2594 | −2.69421 | ||||||||
\(956\) | −80.0813 | −2.59002 | ||||||||
\(957\) | 2.29902 | 0.0743169 | ||||||||
\(958\) | −28.0430 | −0.906027 | ||||||||
\(959\) | −5.91460 | −0.190993 | ||||||||
\(960\) | −119.136 | −3.84511 | ||||||||
\(961\) | 79.6952 | 2.57081 | ||||||||
\(962\) | 143.148 | 4.61527 | ||||||||
\(963\) | 16.7196 | 0.538781 | ||||||||
\(964\) | −19.8157 | −0.638220 | ||||||||
\(965\) | 16.7305 | 0.538572 | ||||||||
\(966\) | 31.2215 | 1.00453 | ||||||||
\(967\) | −10.9726 | −0.352856 | −0.176428 | − | 0.984314i | \(-0.556454\pi\) | ||||
−0.176428 | + | 0.984314i | \(0.556454\pi\) | |||||||
\(968\) | −3.49025 | −0.112181 | ||||||||
\(969\) | −12.4344 | −0.399450 | ||||||||
\(970\) | 92.0490 | 2.95552 | ||||||||
\(971\) | −46.5795 | −1.49481 | −0.747404 | − | 0.664369i | \(-0.768700\pi\) | ||||
−0.747404 | + | 0.664369i | \(0.768700\pi\) | |||||||
\(972\) | 74.1197 | 2.37739 | ||||||||
\(973\) | −34.8824 | −1.11828 | ||||||||
\(974\) | 2.78861 | 0.0893527 | ||||||||
\(975\) | 145.805 | 4.66950 | ||||||||
\(976\) | 3.85778 | 0.123484 | ||||||||
\(977\) | −54.0820 | −1.73024 | −0.865119 | − | 0.501567i | \(-0.832757\pi\) | ||||
−0.865119 | + | 0.501567i | \(0.832757\pi\) | |||||||
\(978\) | 124.235 | 3.97259 | ||||||||
\(979\) | 38.2258 | 1.22170 | ||||||||
\(980\) | 57.8476 | 1.84787 | ||||||||
\(981\) | −59.8117 | −1.90964 | ||||||||
\(982\) | 88.0668 | 2.81033 | ||||||||
\(983\) | −40.8441 | −1.30272 | −0.651362 | − | 0.758767i | \(-0.725802\pi\) | ||||
−0.651362 | + | 0.758767i | \(0.725802\pi\) | |||||||
\(984\) | −64.6343 | −2.06047 | ||||||||
\(985\) | −51.4010 | −1.63777 | ||||||||
\(986\) | 0.594873 | 0.0189446 | ||||||||
\(987\) | −36.3401 | −1.15672 | ||||||||
\(988\) | 110.690 | 3.52152 | ||||||||
\(989\) | −7.31182 | −0.232502 | ||||||||
\(990\) | −104.583 | −3.32386 | ||||||||
\(991\) | 13.3924 | 0.425424 | 0.212712 | − | 0.977115i | \(-0.431770\pi\) | ||||
0.212712 | + | 0.977115i | \(0.431770\pi\) | |||||||
\(992\) | −54.0714 | −1.71677 | ||||||||
\(993\) | −23.4405 | −0.743862 | ||||||||
\(994\) | −55.0730 | −1.74681 | ||||||||
\(995\) | 83.8977 | 2.65973 | ||||||||
\(996\) | 124.475 | 3.94414 | ||||||||
\(997\) | −37.5304 | −1.18860 | −0.594299 | − | 0.804244i | \(-0.702570\pi\) | ||||
−0.594299 | + | 0.804244i | \(0.702570\pi\) | |||||||
\(998\) | 73.1607 | 2.31586 | ||||||||
\(999\) | −13.0641 | −0.413331 |
(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 | 6001.2.a.a.1.13 | ✓ | 113 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.a.1.13 | ✓ | 113 | 1.1 | even | 1 | trivial |