Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.30 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45635i | 1.73690i | 0.495778 | + | 0.868449i | \(0.334883\pi\) | ||||
−0.495778 | + | 0.868449i | \(0.665117\pi\) | |||||||
\(3\) | 2.80039 | 1.61680 | 0.808402 | − | 0.588631i | \(-0.200333\pi\) | ||||
0.808402 | + | 0.588631i | \(0.200333\pi\) | |||||||
\(4\) | −4.03363 | −2.01682 | ||||||||
\(5\) | − | 3.48535i | − | 1.55870i | −0.626591 | − | 0.779348i | \(-0.715550\pi\) | ||
0.626591 | − | 0.779348i | \(-0.284450\pi\) | |||||||
\(6\) | 6.87871i | 2.80822i | ||||||||
\(7\) | 3.54003i | 1.33801i | 0.743259 | + | 0.669004i | \(0.233279\pi\) | ||||
−0.743259 | + | 0.669004i | \(0.766721\pi\) | |||||||
\(8\) | − | 4.99531i | − | 1.76611i | ||||||
\(9\) | 4.84216 | 1.61405 | ||||||||
\(10\) | 8.56123 | 2.70730 | ||||||||
\(11\) | 5.60543i | 1.69010i | 0.534686 | + | 0.845051i | \(0.320430\pi\) | ||||
−0.534686 | + | 0.845051i | \(0.679570\pi\) | |||||||
\(12\) | −11.2957 | −3.26080 | ||||||||
\(13\) | 3.17012 | − | 1.71765i | 0.879233 | − | 0.476392i | ||||
\(14\) | −8.69555 | −2.32398 | ||||||||
\(15\) | − | 9.76032i | − | 2.52010i | ||||||
\(16\) | 4.20294 | 1.05073 | ||||||||
\(17\) | 2.47924 | 0.601305 | 0.300652 | − | 0.953734i | \(-0.402796\pi\) | ||||
0.300652 | + | 0.953734i | \(0.402796\pi\) | |||||||
\(18\) | 11.8940i | 2.80345i | ||||||||
\(19\) | − | 2.94408i | − | 0.675418i | −0.941251 | − | 0.337709i | \(-0.890348\pi\) | ||
0.941251 | − | 0.337709i | \(-0.109652\pi\) | |||||||
\(20\) | 14.0586i | 3.14360i | ||||||||
\(21\) | 9.91346i | 2.16329i | ||||||||
\(22\) | −13.7689 | −2.93553 | ||||||||
\(23\) | −1.33162 | −0.277663 | −0.138831 | − | 0.990316i | \(-0.544335\pi\) | ||||
−0.138831 | + | 0.990316i | \(0.544335\pi\) | |||||||
\(24\) | − | 13.9888i | − | 2.85545i | ||||||
\(25\) | −7.14767 | −1.42953 | ||||||||
\(26\) | 4.21915 | + | 7.78691i | 0.827444 | + | 1.52714i | ||||
\(27\) | 5.15875 | 0.992802 | ||||||||
\(28\) | − | 14.2792i | − | 2.69852i | ||||||
\(29\) | −6.22251 | −1.15549 | −0.577746 | − | 0.816217i | \(-0.696067\pi\) | ||||
−0.577746 | + | 0.816217i | \(0.696067\pi\) | |||||||
\(30\) | 23.9747 | 4.37717 | ||||||||
\(31\) | 1.00000i | 0.179605i | ||||||||
\(32\) | 0.333245i | 0.0589100i | ||||||||
\(33\) | 15.6974i | 2.73256i | ||||||||
\(34\) | 6.08988i | 1.04441i | ||||||||
\(35\) | 12.3383 | 2.08555 | ||||||||
\(36\) | −19.5315 | −3.25525 | ||||||||
\(37\) | − | 7.14956i | − | 1.17538i | −0.809086 | − | 0.587691i | \(-0.800037\pi\) | ||
0.809086 | − | 0.587691i | \(-0.199963\pi\) | |||||||
\(38\) | 7.23168 | 1.17313 | ||||||||
\(39\) | 8.87756 | − | 4.81009i | 1.42155 | − | 0.770232i | ||||
\(40\) | −17.4104 | −2.75283 | ||||||||
\(41\) | − | 4.88228i | − | 0.762484i | −0.924475 | − | 0.381242i | \(-0.875496\pi\) | ||
0.924475 | − | 0.381242i | \(-0.124504\pi\) | |||||||
\(42\) | −24.3509 | −3.75742 | ||||||||
\(43\) | 0.926054 | 0.141222 | 0.0706110 | − | 0.997504i | \(-0.477505\pi\) | ||||
0.0706110 | + | 0.997504i | \(0.477505\pi\) | |||||||
\(44\) | − | 22.6103i | − | 3.40862i | ||||||
\(45\) | − | 16.8766i | − | 2.51582i | ||||||
\(46\) | − | 3.27093i | − | 0.482272i | ||||||
\(47\) | − | 11.4047i | − | 1.66355i | −0.555116 | − | 0.831773i | \(-0.687326\pi\) | ||
0.555116 | − | 0.831773i | \(-0.312674\pi\) | |||||||
\(48\) | 11.7698 | 1.69883 | ||||||||
\(49\) | −5.53184 | −0.790263 | ||||||||
\(50\) | − | 17.5571i | − | 2.48296i | ||||||
\(51\) | 6.94284 | 0.972191 | ||||||||
\(52\) | −12.7871 | + | 6.92839i | −1.77325 | + | 0.960795i | ||||
\(53\) | −9.27473 | −1.27398 | −0.636991 | − | 0.770871i | \(-0.719821\pi\) | ||||
−0.636991 | + | 0.770871i | \(0.719821\pi\) | |||||||
\(54\) | 12.6717i | 1.72440i | ||||||||
\(55\) | 19.5369 | 2.63435 | ||||||||
\(56\) | 17.6836 | 2.36307 | ||||||||
\(57\) | − | 8.24456i | − | 1.09202i | ||||||
\(58\) | − | 15.2846i | − | 2.00697i | ||||||
\(59\) | 6.89104i | 0.897137i | 0.893749 | + | 0.448568i | \(0.148066\pi\) | ||||
−0.893749 | + | 0.448568i | \(0.851934\pi\) | |||||||
\(60\) | 39.3696i | 5.08259i | ||||||||
\(61\) | 5.72757 | 0.733340 | 0.366670 | − | 0.930351i | \(-0.380498\pi\) | ||||
0.366670 | + | 0.930351i | \(0.380498\pi\) | |||||||
\(62\) | −2.45635 | −0.311956 | ||||||||
\(63\) | 17.1414i | 2.15961i | ||||||||
\(64\) | 7.58730 | 0.948413 | ||||||||
\(65\) | −5.98663 | − | 11.0490i | −0.742550 | − | 1.37046i | ||||
\(66\) | −38.5582 | −4.74618 | ||||||||
\(67\) | 9.27764i | 1.13344i | 0.823909 | + | 0.566722i | \(0.191789\pi\) | ||||
−0.823909 | + | 0.566722i | \(0.808211\pi\) | |||||||
\(68\) | −10.0004 | −1.21272 | ||||||||
\(69\) | −3.72906 | −0.448926 | ||||||||
\(70\) | 30.3070i | 3.62238i | ||||||||
\(71\) | − | 0.850046i | − | 0.100882i | −0.998727 | − | 0.0504410i | \(-0.983937\pi\) | ||
0.998727 | − | 0.0504410i | \(-0.0160627\pi\) | |||||||
\(72\) | − | 24.1881i | − | 2.85059i | ||||||
\(73\) | − | 8.68621i | − | 1.01664i | −0.861167 | − | 0.508322i | \(-0.830266\pi\) | ||
0.861167 | − | 0.508322i | \(-0.169734\pi\) | |||||||
\(74\) | 17.5618 | 2.04152 | ||||||||
\(75\) | −20.0162 | −2.31127 | ||||||||
\(76\) | 11.8753i | 1.36219i | ||||||||
\(77\) | −19.8434 | −2.26137 | ||||||||
\(78\) | 11.8153 | + | 21.8064i | 1.33781 | + | 2.46908i | ||||
\(79\) | −5.69838 | −0.641117 | −0.320559 | − | 0.947229i | \(-0.603871\pi\) | ||||
−0.320559 | + | 0.947229i | \(0.603871\pi\) | |||||||
\(80\) | − | 14.6487i | − | 1.63777i | ||||||
\(81\) | −0.0799826 | −0.00888695 | ||||||||
\(82\) | 11.9926 | 1.32436 | ||||||||
\(83\) | − | 10.1834i | − | 1.11778i | −0.829243 | − | 0.558888i | \(-0.811228\pi\) | ||
0.829243 | − | 0.558888i | \(-0.188772\pi\) | |||||||
\(84\) | − | 39.9873i | − | 4.36297i | ||||||
\(85\) | − | 8.64103i | − | 0.937251i | ||||||
\(86\) | 2.27471i | 0.245288i | ||||||||
\(87\) | −17.4254 | −1.86820 | ||||||||
\(88\) | 28.0009 | 2.98490 | ||||||||
\(89\) | 3.72778i | 0.395144i | 0.980288 | + | 0.197572i | \(0.0633056\pi\) | ||||
−0.980288 | + | 0.197572i | \(0.936694\pi\) | |||||||
\(90\) | 41.4548 | 4.36972 | ||||||||
\(91\) | 6.08056 | + | 11.2223i | 0.637415 | + | 1.17642i | ||||
\(92\) | 5.37128 | 0.559995 | ||||||||
\(93\) | 2.80039i | 0.290386i | ||||||||
\(94\) | 28.0139 | 2.88941 | ||||||||
\(95\) | −10.2611 | −1.05277 | ||||||||
\(96\) | 0.933216i | 0.0952459i | ||||||||
\(97\) | 11.4074i | 1.15824i | 0.815241 | + | 0.579122i | \(0.196604\pi\) | ||||
−0.815241 | + | 0.579122i | \(0.803396\pi\) | |||||||
\(98\) | − | 13.5881i | − | 1.37261i | ||||||
\(99\) | 27.1424i | 2.72791i | ||||||||
\(100\) | 28.8311 | 2.88311 | ||||||||
\(101\) | 6.14390 | 0.611341 | 0.305671 | − | 0.952137i | \(-0.401119\pi\) | ||||
0.305671 | + | 0.952137i | \(0.401119\pi\) | |||||||
\(102\) | 17.0540i | 1.68860i | ||||||||
\(103\) | 9.77159 | 0.962823 | 0.481412 | − | 0.876495i | \(-0.340124\pi\) | ||||
0.481412 | + | 0.876495i | \(0.340124\pi\) | |||||||
\(104\) | −8.58021 | − | 15.8357i | −0.841359 | − | 1.55282i | ||||
\(105\) | 34.5519 | 3.37192 | ||||||||
\(106\) | − | 22.7819i | − | 2.21278i | ||||||
\(107\) | −0.0150159 | −0.00145164 | −0.000725821 | − | 1.00000i | \(-0.500231\pi\) | ||||
−0.000725821 | 1.00000i | \(0.500231\pi\) | ||||||||
\(108\) | −20.8085 | −2.00230 | ||||||||
\(109\) | 0.921927i | 0.0883046i | 0.999025 | + | 0.0441523i | \(0.0140587\pi\) | ||||
−0.999025 | + | 0.0441523i | \(0.985941\pi\) | |||||||
\(110\) | 47.9894i | 4.57561i | ||||||||
\(111\) | − | 20.0215i | − | 1.90036i | ||||||
\(112\) | 14.8785i | 1.40589i | ||||||||
\(113\) | −5.96949 | −0.561562 | −0.280781 | − | 0.959772i | \(-0.590594\pi\) | ||||
−0.280781 | + | 0.959772i | \(0.590594\pi\) | |||||||
\(114\) | 20.2515 | 1.89673 | ||||||||
\(115\) | 4.64118i | 0.432792i | ||||||||
\(116\) | 25.0993 | 2.33041 | ||||||||
\(117\) | 15.3502 | − | 8.31715i | 1.41913 | − | 0.768921i | ||||
\(118\) | −16.9268 | −1.55824 | ||||||||
\(119\) | 8.77660i | 0.804550i | ||||||||
\(120\) | −48.7558 | −4.45078 | ||||||||
\(121\) | −20.4209 | −1.85644 | ||||||||
\(122\) | 14.0689i | 1.27374i | ||||||||
\(123\) | − | 13.6723i | − | 1.23279i | ||||||
\(124\) | − | 4.03363i | − | 0.362231i | ||||||
\(125\) | 7.48538i | 0.669512i | ||||||||
\(126\) | −42.1052 | −3.75103 | ||||||||
\(127\) | −4.63997 | −0.411731 | −0.205865 | − | 0.978580i | \(-0.566001\pi\) | ||||
−0.205865 | + | 0.978580i | \(0.566001\pi\) | |||||||
\(128\) | 19.3035i | 1.70621i | ||||||||
\(129\) | 2.59331 | 0.228328 | ||||||||
\(130\) | 27.1401 | − | 14.7052i | 2.38035 | − | 1.28973i | ||||
\(131\) | −12.9817 | −1.13421 | −0.567107 | − | 0.823644i | \(-0.691938\pi\) | ||||
−0.567107 | + | 0.823644i | \(0.691938\pi\) | |||||||
\(132\) | − | 63.3174i | − | 5.51108i | ||||||
\(133\) | 10.4221 | 0.903714 | ||||||||
\(134\) | −22.7891 | −1.96868 | ||||||||
\(135\) | − | 17.9801i | − | 1.54748i | ||||||
\(136\) | − | 12.3846i | − | 1.06197i | ||||||
\(137\) | 4.66000i | 0.398131i | 0.979986 | + | 0.199065i | \(0.0637906\pi\) | ||||
−0.979986 | + | 0.199065i | \(0.936209\pi\) | |||||||
\(138\) | − | 9.15986i | − | 0.779739i | ||||||
\(139\) | 14.8173 | 1.25679 | 0.628393 | − | 0.777896i | \(-0.283713\pi\) | ||||
0.628393 | + | 0.777896i | \(0.283713\pi\) | |||||||
\(140\) | −49.7680 | −4.20617 | ||||||||
\(141\) | − | 31.9375i | − | 2.68963i | ||||||
\(142\) | 2.08801 | 0.175222 | ||||||||
\(143\) | 9.62820 | + | 17.7699i | 0.805150 | + | 1.48599i | ||||
\(144\) | 20.3513 | 1.69594 | ||||||||
\(145\) | 21.6876i | 1.80106i | ||||||||
\(146\) | 21.3363 | 1.76581 | ||||||||
\(147\) | −15.4913 | −1.27770 | ||||||||
\(148\) | 28.8387i | 2.37053i | ||||||||
\(149\) | 2.85800i | 0.234137i | 0.993124 | + | 0.117068i | \(0.0373496\pi\) | ||||
−0.993124 | + | 0.117068i | \(0.962650\pi\) | |||||||
\(150\) | − | 49.1668i | − | 4.01445i | ||||||
\(151\) | 0.429054i | 0.0349159i | 0.999848 | + | 0.0174580i | \(0.00555732\pi\) | ||||
−0.999848 | + | 0.0174580i | \(0.994443\pi\) | |||||||
\(152\) | −14.7066 | −1.19286 | ||||||||
\(153\) | 12.0049 | 0.970537 | ||||||||
\(154\) | − | 48.7423i | − | 3.92777i | ||||||
\(155\) | 3.48535 | 0.279950 | ||||||||
\(156\) | −35.8088 | + | 19.4022i | −2.86700 | + | 1.55342i | ||||
\(157\) | −4.78512 | −0.381894 | −0.190947 | − | 0.981600i | \(-0.561156\pi\) | ||||
−0.190947 | + | 0.981600i | \(0.561156\pi\) | |||||||
\(158\) | − | 13.9972i | − | 1.11356i | ||||||
\(159\) | −25.9728 | −2.05978 | ||||||||
\(160\) | 1.16148 | 0.0918228 | ||||||||
\(161\) | − | 4.71399i | − | 0.371515i | ||||||
\(162\) | − | 0.196465i | − | 0.0154357i | ||||||
\(163\) | 21.8453i | 1.71105i | 0.517758 | + | 0.855527i | \(0.326767\pi\) | ||||
−0.517758 | + | 0.855527i | \(0.673233\pi\) | |||||||
\(164\) | 19.6933i | 1.53779i | ||||||||
\(165\) | 54.7108 | 4.25923 | ||||||||
\(166\) | 25.0140 | 1.94146 | ||||||||
\(167\) | 3.37083i | 0.260843i | 0.991459 | + | 0.130421i | \(0.0416330\pi\) | ||||
−0.991459 | + | 0.130421i | \(0.958367\pi\) | |||||||
\(168\) | 49.5208 | 3.82061 | ||||||||
\(169\) | 7.09933 | − | 10.8903i | 0.546102 | − | 0.837719i | ||||
\(170\) | 21.2254 | 1.62791 | ||||||||
\(171\) | − | 14.2557i | − | 1.09016i | ||||||
\(172\) | −3.73536 | −0.284819 | ||||||||
\(173\) | −14.7745 | −1.12329 | −0.561643 | − | 0.827379i | \(-0.689831\pi\) | ||||
−0.561643 | + | 0.827379i | \(0.689831\pi\) | |||||||
\(174\) | − | 42.8029i | − | 3.24488i | ||||||
\(175\) | − | 25.3030i | − | 1.91273i | ||||||
\(176\) | 23.5593i | 1.77585i | ||||||||
\(177\) | 19.2976i | 1.45049i | ||||||||
\(178\) | −9.15671 | −0.686325 | ||||||||
\(179\) | −24.6355 | −1.84134 | −0.920672 | − | 0.390337i | \(-0.872359\pi\) | ||||
−0.920672 | + | 0.390337i | \(0.872359\pi\) | |||||||
\(180\) | 68.0741i | 5.07394i | ||||||||
\(181\) | 5.26608 | 0.391425 | 0.195712 | − | 0.980661i | \(-0.437298\pi\) | ||||
0.195712 | + | 0.980661i | \(0.437298\pi\) | |||||||
\(182\) | −27.5659 | + | 14.9359i | −2.04332 | + | 1.10713i | ||||
\(183\) | 16.0394 | 1.18567 | ||||||||
\(184\) | 6.65187i | 0.490383i | ||||||||
\(185\) | −24.9187 | −1.83206 | ||||||||
\(186\) | −6.87871 | −0.504372 | ||||||||
\(187\) | 13.8972i | 1.01627i | ||||||||
\(188\) | 46.0024i | 3.35507i | ||||||||
\(189\) | 18.2622i | 1.32838i | ||||||||
\(190\) | − | 25.2049i | − | 1.82856i | ||||||
\(191\) | −4.61535 | −0.333955 | −0.166978 | − | 0.985961i | \(-0.553401\pi\) | ||||
−0.166978 | + | 0.985961i | \(0.553401\pi\) | |||||||
\(192\) | 21.2474 | 1.53340 | ||||||||
\(193\) | − | 1.61977i | − | 0.116594i | −0.998299 | − | 0.0582969i | \(-0.981433\pi\) | ||
0.998299 | − | 0.0582969i | \(-0.0185670\pi\) | |||||||
\(194\) | −28.0205 | −2.01175 | ||||||||
\(195\) | −16.7649 | − | 30.9414i | −1.20056 | − | 2.21576i | ||||
\(196\) | 22.3134 | 1.59382 | ||||||||
\(197\) | 8.32063i | 0.592820i | 0.955061 | + | 0.296410i | \(0.0957896\pi\) | ||||
−0.955061 | + | 0.296410i | \(0.904210\pi\) | |||||||
\(198\) | −66.6711 | −4.73811 | ||||||||
\(199\) | 23.6343 | 1.67539 | 0.837694 | − | 0.546140i | \(-0.183903\pi\) | ||||
0.837694 | + | 0.546140i | \(0.183903\pi\) | |||||||
\(200\) | 35.7048i | 2.52471i | ||||||||
\(201\) | 25.9810i | 1.83256i | ||||||||
\(202\) | 15.0916i | 1.06184i | ||||||||
\(203\) | − | 22.0279i | − | 1.54606i | ||||||
\(204\) | −28.0049 | −1.96073 | ||||||||
\(205\) | −17.0165 | −1.18848 | ||||||||
\(206\) | 24.0024i | 1.67233i | ||||||||
\(207\) | −6.44793 | −0.448162 | ||||||||
\(208\) | 13.3238 | − | 7.21919i | 0.923840 | − | 0.500561i | ||||
\(209\) | 16.5028 | 1.14153 | ||||||||
\(210\) | 84.8714i | 5.85668i | ||||||||
\(211\) | 22.5919 | 1.55529 | 0.777647 | − | 0.628701i | \(-0.216413\pi\) | ||||
0.777647 | + | 0.628701i | \(0.216413\pi\) | |||||||
\(212\) | 37.4109 | 2.56939 | ||||||||
\(213\) | − | 2.38046i | − | 0.163106i | ||||||
\(214\) | − | 0.0368842i | − | 0.00252135i | ||||||
\(215\) | − | 3.22762i | − | 0.220122i | ||||||
\(216\) | − | 25.7696i | − | 1.75340i | ||||||
\(217\) | −3.54003 | −0.240313 | ||||||||
\(218\) | −2.26457 | −0.153376 | ||||||||
\(219\) | − | 24.3247i | − | 1.64371i | ||||||
\(220\) | −78.8047 | −5.31301 | ||||||||
\(221\) | 7.85950 | − | 4.25848i | 0.528687 | − | 0.286457i | ||||
\(222\) | 49.1798 | 3.30073 | ||||||||
\(223\) | 24.0641i | 1.61145i | 0.592288 | + | 0.805726i | \(0.298225\pi\) | ||||
−0.592288 | + | 0.805726i | \(0.701775\pi\) | |||||||
\(224\) | −1.17970 | −0.0788220 | ||||||||
\(225\) | −34.6101 | −2.30734 | ||||||||
\(226\) | − | 14.6631i | − | 0.975377i | ||||||
\(227\) | − | 8.15313i | − | 0.541142i | −0.962700 | − | 0.270571i | \(-0.912787\pi\) | ||
0.962700 | − | 0.270571i | \(-0.0872125\pi\) | |||||||
\(228\) | 33.2555i | 2.20240i | ||||||||
\(229\) | − | 5.28147i | − | 0.349010i | −0.984656 | − | 0.174505i | \(-0.944168\pi\) | ||
0.984656 | − | 0.174505i | \(-0.0558324\pi\) | |||||||
\(230\) | −11.4003 | −0.751716 | ||||||||
\(231\) | −55.5692 | −3.65619 | ||||||||
\(232\) | 31.0834i | 2.04072i | ||||||||
\(233\) | 10.6469 | 0.697501 | 0.348750 | − | 0.937216i | \(-0.386606\pi\) | ||||
0.348750 | + | 0.937216i | \(0.386606\pi\) | |||||||
\(234\) | 20.4298 | + | 37.7055i | 1.33554 | + | 2.46488i | ||||
\(235\) | −39.7494 | −2.59296 | ||||||||
\(236\) | − | 27.7959i | − | 1.80936i | ||||||
\(237\) | −15.9576 | −1.03656 | ||||||||
\(238\) | −21.5584 | −1.39742 | ||||||||
\(239\) | − | 6.31548i | − | 0.408514i | −0.978917 | − | 0.204257i | \(-0.934522\pi\) | ||
0.978917 | − | 0.204257i | \(-0.0654779\pi\) | |||||||
\(240\) | − | 41.0220i | − | 2.64796i | ||||||
\(241\) | 14.7695i | 0.951389i | 0.879610 | + | 0.475695i | \(0.157803\pi\) | ||||
−0.879610 | + | 0.475695i | \(0.842197\pi\) | |||||||
\(242\) | − | 50.1607i | − | 3.22445i | ||||||
\(243\) | −15.7002 | −1.00717 | ||||||||
\(244\) | −23.1029 | −1.47901 | ||||||||
\(245\) | 19.2804i | 1.23178i | ||||||||
\(246\) | 33.5838 | 2.14123 | ||||||||
\(247\) | −5.05691 | − | 9.33309i | −0.321764 | − | 0.593850i | ||||
\(248\) | 4.99531 | 0.317202 | ||||||||
\(249\) | − | 28.5175i | − | 1.80723i | ||||||
\(250\) | −18.3867 | −1.16288 | ||||||||
\(251\) | −12.3317 | −0.778372 | −0.389186 | − | 0.921159i | \(-0.627244\pi\) | ||||
−0.389186 | + | 0.921159i | \(0.627244\pi\) | |||||||
\(252\) | − | 69.1421i | − | 4.35555i | ||||||
\(253\) | − | 7.46433i | − | 0.469278i | ||||||
\(254\) | − | 11.3974i | − | 0.715135i | ||||||
\(255\) | − | 24.1982i | − | 1.51535i | ||||||
\(256\) | −32.2415 | −2.01510 | ||||||||
\(257\) | 27.5568 | 1.71895 | 0.859474 | − | 0.511180i | \(-0.170791\pi\) | ||||
0.859474 | + | 0.511180i | \(0.170791\pi\) | |||||||
\(258\) | 6.37006i | 0.396583i | ||||||||
\(259\) | 25.3097 | 1.57267 | ||||||||
\(260\) | 24.1479 | + | 44.5675i | 1.49759 | + | 2.76396i | ||||
\(261\) | −30.1304 | −1.86502 | ||||||||
\(262\) | − | 31.8875i | − | 1.97002i | ||||||
\(263\) | 26.3404 | 1.62422 | 0.812111 | − | 0.583503i | \(-0.198319\pi\) | ||||
0.812111 | + | 0.583503i | \(0.198319\pi\) | |||||||
\(264\) | 78.4132 | 4.82600 | ||||||||
\(265\) | 32.3257i | 1.98575i | ||||||||
\(266\) | 25.6004i | 1.56966i | ||||||||
\(267\) | 10.4392i | 0.638870i | ||||||||
\(268\) | − | 37.4226i | − | 2.28595i | ||||||
\(269\) | −18.9927 | −1.15801 | −0.579004 | − | 0.815325i | \(-0.696558\pi\) | ||||
−0.579004 | + | 0.815325i | \(0.696558\pi\) | |||||||
\(270\) | 44.1652 | 2.68781 | ||||||||
\(271\) | − | 8.87920i | − | 0.539373i | −0.962948 | − | 0.269686i | \(-0.913080\pi\) | ||
0.962948 | − | 0.269686i | \(-0.0869200\pi\) | |||||||
\(272\) | 10.4201 | 0.631811 | ||||||||
\(273\) | 17.0279 | + | 31.4269i | 1.03058 | + | 1.90204i | ||||
\(274\) | −11.4466 | −0.691513 | ||||||||
\(275\) | − | 40.0658i | − | 2.41606i | ||||||
\(276\) | 15.0417 | 0.905402 | ||||||||
\(277\) | 0.263699 | 0.0158442 | 0.00792208 | − | 0.999969i | \(-0.497478\pi\) | ||||
0.00792208 | + | 0.999969i | \(0.497478\pi\) | |||||||
\(278\) | 36.3964i | 2.18291i | ||||||||
\(279\) | 4.84216i | 0.289892i | ||||||||
\(280\) | − | 61.6334i | − | 3.68330i | ||||||
\(281\) | 6.28589i | 0.374985i | 0.982266 | + | 0.187492i | \(0.0600360\pi\) | ||||
−0.982266 | + | 0.187492i | \(0.939964\pi\) | |||||||
\(282\) | 78.4497 | 4.67161 | ||||||||
\(283\) | 11.3137 | 0.672527 | 0.336264 | − | 0.941768i | \(-0.390837\pi\) | ||||
0.336264 | + | 0.941768i | \(0.390837\pi\) | |||||||
\(284\) | 3.42878i | 0.203460i | ||||||||
\(285\) | −28.7352 | −1.70212 | ||||||||
\(286\) | −43.6490 | + | 23.6502i | −2.58102 | + | 1.39846i | ||||
\(287\) | 17.2834 | 1.02021 | ||||||||
\(288\) | 1.61363i | 0.0950839i | ||||||||
\(289\) | −10.8534 | −0.638433 | ||||||||
\(290\) | −53.2723 | −3.12826 | ||||||||
\(291\) | 31.9450i | 1.87265i | ||||||||
\(292\) | 35.0370i | 2.05038i | ||||||||
\(293\) | − | 19.5031i | − | 1.13938i | −0.821858 | − | 0.569692i | \(-0.807062\pi\) | ||
0.821858 | − | 0.569692i | \(-0.192938\pi\) | |||||||
\(294\) | − | 38.0520i | − | 2.21924i | ||||||
\(295\) | 24.0177 | 1.39836 | ||||||||
\(296\) | −35.7143 | −2.07585 | ||||||||
\(297\) | 28.9170i | 1.67794i | ||||||||
\(298\) | −7.02024 | −0.406672 | ||||||||
\(299\) | −4.22141 | + | 2.28727i | −0.244130 | + | 0.132276i | ||||
\(300\) | 80.7381 | 4.66142 | ||||||||
\(301\) | 3.27826i | 0.188956i | ||||||||
\(302\) | −1.05390 | −0.0606454 | ||||||||
\(303\) | 17.2053 | 0.988419 | ||||||||
\(304\) | − | 12.3738i | − | 0.709685i | ||||||
\(305\) | − | 19.9626i | − | 1.14305i | ||||||
\(306\) | 29.4881i | 1.68573i | ||||||||
\(307\) | 31.6864i | 1.80844i | 0.427069 | + | 0.904219i | \(0.359546\pi\) | ||||
−0.427069 | + | 0.904219i | \(0.640454\pi\) | |||||||
\(308\) | 80.0411 | 4.56076 | ||||||||
\(309\) | 27.3642 | 1.55670 | ||||||||
\(310\) | 8.56123i | 0.486245i | ||||||||
\(311\) | −1.23362 | −0.0699522 | −0.0349761 | − | 0.999388i | \(-0.511136\pi\) | ||||
−0.0349761 | + | 0.999388i | \(0.511136\pi\) | |||||||
\(312\) | −24.0279 | − | 44.3461i | −1.36031 | − | 2.51061i | ||||
\(313\) | −19.5774 | −1.10658 | −0.553291 | − | 0.832988i | \(-0.686628\pi\) | ||||
−0.553291 | + | 0.832988i | \(0.686628\pi\) | |||||||
\(314\) | − | 11.7539i | − | 0.663312i | ||||||
\(315\) | 59.7438 | 3.36618 | ||||||||
\(316\) | 22.9852 | 1.29302 | ||||||||
\(317\) | − | 2.05349i | − | 0.115336i | −0.998336 | − | 0.0576678i | \(-0.981634\pi\) | ||
0.998336 | − | 0.0576678i | \(-0.0183664\pi\) | |||||||
\(318\) | − | 63.7982i | − | 3.57762i | ||||||
\(319\) | − | 34.8799i | − | 1.95290i | ||||||
\(320\) | − | 26.4444i | − | 1.47829i | ||||||
\(321\) | −0.0420503 | −0.00234702 | ||||||||
\(322\) | 11.5792 | 0.645284 | ||||||||
\(323\) | − | 7.29909i | − | 0.406132i | ||||||
\(324\) | 0.322620 | 0.0179234 | ||||||||
\(325\) | −22.6590 | + | 12.2772i | −1.25689 | + | 0.681018i | ||||
\(326\) | −53.6595 | −2.97193 | ||||||||
\(327\) | 2.58175i | 0.142771i | ||||||||
\(328\) | −24.3885 | −1.34663 | ||||||||
\(329\) | 40.3730 | 2.22584 | ||||||||
\(330\) | 134.389i | 7.39785i | ||||||||
\(331\) | − | 13.2618i | − | 0.728933i | −0.931216 | − | 0.364467i | \(-0.881251\pi\) | ||
0.931216 | − | 0.364467i | \(-0.118749\pi\) | |||||||
\(332\) | 41.0762i | 2.25435i | ||||||||
\(333\) | − | 34.6193i | − | 1.89713i | ||||||
\(334\) | −8.27993 | −0.453057 | ||||||||
\(335\) | 32.3358 | 1.76670 | ||||||||
\(336\) | 41.6656i | 2.27305i | ||||||||
\(337\) | 35.1836 | 1.91657 | 0.958287 | − | 0.285806i | \(-0.0922613\pi\) | ||||
0.958287 | + | 0.285806i | \(0.0922613\pi\) | |||||||
\(338\) | 26.7504 | + | 17.4384i | 1.45503 | + | 0.948524i | ||||
\(339\) | −16.7169 | −0.907936 | ||||||||
\(340\) | 34.8548i | 1.89026i | ||||||||
\(341\) | −5.60543 | −0.303551 | ||||||||
\(342\) | 35.0169 | 1.89350 | ||||||||
\(343\) | 5.19733i | 0.280629i | ||||||||
\(344\) | − | 4.62593i | − | 0.249413i | ||||||
\(345\) | 12.9971i | 0.699739i | ||||||||
\(346\) | − | 36.2913i | − | 1.95104i | ||||||
\(347\) | −12.0992 | −0.649519 | −0.324759 | − | 0.945797i | \(-0.605283\pi\) | ||||
−0.324759 | + | 0.945797i | \(0.605283\pi\) | |||||||
\(348\) | 70.2878 | 3.76782 | ||||||||
\(349\) | − | 28.7745i | − | 1.54026i | −0.637886 | − | 0.770131i | \(-0.720191\pi\) | ||
0.637886 | − | 0.770131i | \(-0.279809\pi\) | |||||||
\(350\) | 62.1529 | 3.32221 | ||||||||
\(351\) | 16.3539 | − | 8.86095i | 0.872905 | − | 0.472963i | ||||
\(352\) | −1.86798 | −0.0995639 | ||||||||
\(353\) | − | 15.0930i | − | 0.803321i | −0.915789 | − | 0.401660i | \(-0.868433\pi\) | ||
0.915789 | − | 0.401660i | \(-0.131567\pi\) | |||||||
\(354\) | −47.4015 | −2.51936 | ||||||||
\(355\) | −2.96271 | −0.157244 | ||||||||
\(356\) | − | 15.0365i | − | 0.796933i | ||||||
\(357\) | 24.5779i | 1.30080i | ||||||||
\(358\) | − | 60.5133i | − | 3.19823i | ||||||
\(359\) | − | 2.92054i | − | 0.154140i | −0.997026 | − | 0.0770701i | \(-0.975443\pi\) | ||
0.997026 | − | 0.0770701i | \(-0.0245565\pi\) | |||||||
\(360\) | −84.3039 | −4.44321 | ||||||||
\(361\) | 10.3324 | 0.543810 | ||||||||
\(362\) | 12.9353i | 0.679865i | ||||||||
\(363\) | −57.1863 | −3.00150 | ||||||||
\(364\) | −24.5267 | − | 45.2668i | −1.28555 | − | 2.37262i | ||||
\(365\) | −30.2745 | −1.58464 | ||||||||
\(366\) | 39.3983i | 2.05938i | ||||||||
\(367\) | 7.03364 | 0.367153 | 0.183576 | − | 0.983005i | \(-0.441233\pi\) | ||||
0.183576 | + | 0.983005i | \(0.441233\pi\) | |||||||
\(368\) | −5.59673 | −0.291750 | ||||||||
\(369\) | − | 23.6408i | − | 1.23069i | ||||||
\(370\) | − | 61.2090i | − | 3.18211i | ||||||
\(371\) | − | 32.8328i | − | 1.70460i | ||||||
\(372\) | − | 11.2957i | − | 0.585656i | ||||||
\(373\) | −9.23107 | −0.477967 | −0.238983 | − | 0.971024i | \(-0.576814\pi\) | ||||
−0.238983 | + | 0.971024i | \(0.576814\pi\) | |||||||
\(374\) | −34.1364 | −1.76515 | ||||||||
\(375\) | 20.9619i | 1.08247i | ||||||||
\(376\) | −56.9700 | −2.93800 | ||||||||
\(377\) | −19.7261 | + | 10.6881i | −1.01595 | + | 0.550466i | ||||
\(378\) | −44.8582 | −2.30726 | ||||||||
\(379\) | 14.1434i | 0.726499i | 0.931692 | + | 0.363249i | \(0.118333\pi\) | ||||
−0.931692 | + | 0.363249i | \(0.881667\pi\) | |||||||
\(380\) | 41.3897 | 2.12325 | ||||||||
\(381\) | −12.9937 | −0.665688 | ||||||||
\(382\) | − | 11.3369i | − | 0.580046i | ||||||
\(383\) | − | 9.51959i | − | 0.486428i | −0.969973 | − | 0.243214i | \(-0.921798\pi\) | ||
0.969973 | − | 0.243214i | \(-0.0782018\pi\) | |||||||
\(384\) | 54.0573i | 2.75860i | ||||||||
\(385\) | 69.1613i | 3.52478i | ||||||||
\(386\) | 3.97872 | 0.202512 | ||||||||
\(387\) | 4.48410 | 0.227940 | ||||||||
\(388\) | − | 46.0132i | − | 2.33596i | ||||||
\(389\) | 9.65776 | 0.489668 | 0.244834 | − | 0.969565i | \(-0.421267\pi\) | ||||
0.244834 | + | 0.969565i | \(0.421267\pi\) | |||||||
\(390\) | 76.0028 | − | 41.1803i | 3.84855 | − | 2.08525i | ||||
\(391\) | −3.30142 | −0.166960 | ||||||||
\(392\) | 27.6333i | 1.39569i | ||||||||
\(393\) | −36.3537 | −1.83380 | ||||||||
\(394\) | −20.4383 | −1.02967 | ||||||||
\(395\) | 19.8608i | 0.999307i | ||||||||
\(396\) | − | 109.482i | − | 5.50170i | ||||||
\(397\) | − | 13.1443i | − | 0.659692i | −0.944035 | − | 0.329846i | \(-0.893003\pi\) | ||
0.944035 | − | 0.329846i | \(-0.106997\pi\) | |||||||
\(398\) | 58.0539i | 2.90998i | ||||||||
\(399\) | 29.1860 | 1.46113 | ||||||||
\(400\) | −30.0412 | −1.50206 | ||||||||
\(401\) | 22.7879i | 1.13798i | 0.822346 | + | 0.568988i | \(0.192665\pi\) | ||||
−0.822346 | + | 0.568988i | \(0.807335\pi\) | |||||||
\(402\) | −63.8182 | −3.18296 | ||||||||
\(403\) | 1.71765 | + | 3.17012i | 0.0855625 | + | 0.157915i | ||||
\(404\) | −24.7823 | −1.23296 | ||||||||
\(405\) | 0.278767i | 0.0138521i | ||||||||
\(406\) | 54.1081 | 2.68534 | ||||||||
\(407\) | 40.0764 | 1.98651 | ||||||||
\(408\) | − | 34.6816i | − | 1.71700i | ||||||
\(409\) | 20.1639i | 0.997043i | 0.866877 | + | 0.498521i | \(0.166123\pi\) | ||||
−0.866877 | + | 0.498521i | \(0.833877\pi\) | |||||||
\(410\) | − | 41.7983i | − | 2.06427i | ||||||
\(411\) | 13.0498i | 0.643699i | ||||||||
\(412\) | −39.4150 | −1.94184 | ||||||||
\(413\) | −24.3945 | −1.20038 | ||||||||
\(414\) | − | 15.8384i | − | 0.778413i | ||||||
\(415\) | −35.4928 | −1.74227 | ||||||||
\(416\) | 0.572401 | + | 1.05643i | 0.0280642 | + | 0.0517957i | ||||
\(417\) | 41.4941 | 2.03198 | ||||||||
\(418\) | 40.5367i | 1.98271i | ||||||||
\(419\) | 2.09350 | 0.102274 | 0.0511371 | − | 0.998692i | \(-0.483715\pi\) | ||||
0.0511371 | + | 0.998692i | \(0.483715\pi\) | |||||||
\(420\) | −139.370 | −6.80054 | ||||||||
\(421\) | 15.1244i | 0.737120i | 0.929604 | + | 0.368560i | \(0.120149\pi\) | ||||
−0.929604 | + | 0.368560i | \(0.879851\pi\) | |||||||
\(422\) | 55.4936i | 2.70139i | ||||||||
\(423\) | − | 55.2233i | − | 2.68505i | ||||||
\(424\) | 46.3301i | 2.24999i | ||||||||
\(425\) | −17.7208 | −0.859585 | ||||||||
\(426\) | 5.84723 | 0.283299 | ||||||||
\(427\) | 20.2758i | 0.981214i | ||||||||
\(428\) | 0.0605686 | 0.00292770 | ||||||||
\(429\) | 26.9627 | + | 49.7625i | 1.30177 | + | 2.40256i | ||||
\(430\) | 7.92816 | 0.382330 | ||||||||
\(431\) | − | 12.5939i | − | 0.606628i | −0.952891 | − | 0.303314i | \(-0.901907\pi\) | ||
0.952891 | − | 0.303314i | \(-0.0980930\pi\) | |||||||
\(432\) | 21.6819 | 1.04317 | ||||||||
\(433\) | −6.05166 | −0.290824 | −0.145412 | − | 0.989371i | \(-0.546451\pi\) | ||||
−0.145412 | + | 0.989371i | \(0.546451\pi\) | |||||||
\(434\) | − | 8.69555i | − | 0.417400i | ||||||
\(435\) | 60.7337i | 2.91196i | ||||||||
\(436\) | − | 3.71872i | − | 0.178094i | ||||||
\(437\) | 3.92041i | 0.187539i | ||||||||
\(438\) | 59.7499 | 2.85496 | ||||||||
\(439\) | 2.35627 | 0.112458 | 0.0562292 | − | 0.998418i | \(-0.482092\pi\) | ||||
0.0562292 | + | 0.998418i | \(0.482092\pi\) | |||||||
\(440\) | − | 97.5928i | − | 4.65255i | ||||||
\(441\) | −26.7861 | −1.27553 | ||||||||
\(442\) | 10.4603 | + | 19.3056i | 0.497546 | + | 0.918276i | ||||
\(443\) | 7.64035 | 0.363004 | 0.181502 | − | 0.983391i | \(-0.441904\pi\) | ||||
0.181502 | + | 0.983391i | \(0.441904\pi\) | |||||||
\(444\) | 80.7595i | 3.83268i | ||||||||
\(445\) | 12.9926 | 0.615909 | ||||||||
\(446\) | −59.1098 | −2.79893 | ||||||||
\(447\) | 8.00351i | 0.378553i | ||||||||
\(448\) | 26.8593i | 1.26898i | ||||||||
\(449\) | 31.4131i | 1.48247i | 0.671243 | + | 0.741237i | \(0.265761\pi\) | ||||
−0.671243 | + | 0.741237i | \(0.734239\pi\) | |||||||
\(450\) | − | 85.0145i | − | 4.00762i | ||||||
\(451\) | 27.3673 | 1.28868 | ||||||||
\(452\) | 24.0787 | 1.13257 | ||||||||
\(453\) | 1.20152i | 0.0564522i | ||||||||
\(454\) | 20.0269 | 0.939909 | ||||||||
\(455\) | 39.1138 | − | 21.1929i | 1.83368 | − | 0.993537i | ||||
\(456\) | −41.1841 | −1.92862 | ||||||||
\(457\) | 14.1833i | 0.663466i | 0.943373 | + | 0.331733i | \(0.107633\pi\) | ||||
−0.943373 | + | 0.331733i | \(0.892367\pi\) | |||||||
\(458\) | 12.9731 | 0.606194 | ||||||||
\(459\) | 12.7898 | 0.596977 | ||||||||
\(460\) | − | 18.7208i | − | 0.872862i | ||||||
\(461\) | − | 0.852165i | − | 0.0396893i | −0.999803 | − | 0.0198446i | \(-0.993683\pi\) | ||
0.999803 | − | 0.0198446i | \(-0.00631716\pi\) | |||||||
\(462\) | − | 136.497i | − | 6.35043i | ||||||
\(463\) | 26.5817i | 1.23535i | 0.786432 | + | 0.617677i | \(0.211926\pi\) | ||||
−0.786432 | + | 0.617677i | \(0.788074\pi\) | |||||||
\(464\) | −26.1528 | −1.21411 | ||||||||
\(465\) | 9.76032 | 0.452624 | ||||||||
\(466\) | 26.1524i | 1.21149i | ||||||||
\(467\) | −26.5943 | −1.23064 | −0.615320 | − | 0.788278i | \(-0.710973\pi\) | ||||
−0.615320 | + | 0.788278i | \(0.710973\pi\) | |||||||
\(468\) | −61.9172 | + | 33.5484i | −2.86212 | + | 1.55077i | ||||
\(469\) | −32.8432 | −1.51656 | ||||||||
\(470\) | − | 97.6382i | − | 4.50371i | ||||||
\(471\) | −13.4002 | −0.617448 | ||||||||
\(472\) | 34.4228 | 1.58444 | ||||||||
\(473\) | 5.19093i | 0.238679i | ||||||||
\(474\) | − | 39.1975i | − | 1.80040i | ||||||
\(475\) | 21.0433i | 0.965533i | ||||||||
\(476\) | − | 35.4016i | − | 1.62263i | ||||||
\(477\) | −44.9097 | −2.05627 | ||||||||
\(478\) | 15.5130 | 0.709548 | ||||||||
\(479\) | 28.3556i | 1.29560i | 0.761809 | + | 0.647801i | \(0.224311\pi\) | ||||
−0.761809 | + | 0.647801i | \(0.775689\pi\) | |||||||
\(480\) | 3.25258 | 0.148459 | ||||||||
\(481\) | −12.2805 | − | 22.6650i | −0.559942 | − | 1.03343i | ||||
\(482\) | −36.2791 | −1.65247 | ||||||||
\(483\) | − | 13.2010i | − | 0.600666i | ||||||
\(484\) | 82.3703 | 3.74410 | ||||||||
\(485\) | 39.7587 | 1.80535 | ||||||||
\(486\) | − | 38.5652i | − | 1.74935i | ||||||
\(487\) | − | 30.9730i | − | 1.40352i | −0.712414 | − | 0.701760i | \(-0.752398\pi\) | ||
0.712414 | − | 0.701760i | \(-0.247602\pi\) | |||||||
\(488\) | − | 28.6110i | − | 1.29516i | ||||||
\(489\) | 61.1752i | 2.76644i | ||||||||
\(490\) | −47.3593 | −2.13948 | ||||||||
\(491\) | −2.33609 | −0.105426 | −0.0527131 | − | 0.998610i | \(-0.516787\pi\) | ||||
−0.0527131 | + | 0.998610i | \(0.516787\pi\) | |||||||
\(492\) | 55.1489i | 2.48631i | ||||||||
\(493\) | −15.4271 | −0.694802 | ||||||||
\(494\) | 22.9253 | − | 12.4215i | 1.03146 | − | 0.558871i | ||||
\(495\) | 94.6007 | 4.25199 | ||||||||
\(496\) | 4.20294i | 0.188717i | ||||||||
\(497\) | 3.00919 | 0.134981 | ||||||||
\(498\) | 70.0489 | 3.13897 | ||||||||
\(499\) | − | 19.4432i | − | 0.870396i | −0.900335 | − | 0.435198i | \(-0.856678\pi\) | ||
0.900335 | − | 0.435198i | \(-0.143322\pi\) | |||||||
\(500\) | − | 30.1933i | − | 1.35028i | ||||||
\(501\) | 9.43963i | 0.421731i | ||||||||
\(502\) | − | 30.2910i | − | 1.35195i | ||||||
\(503\) | 10.6345 | 0.474170 | 0.237085 | − | 0.971489i | \(-0.423808\pi\) | ||||
0.237085 | + | 0.971489i | \(0.423808\pi\) | |||||||
\(504\) | 85.6266 | 3.81411 | ||||||||
\(505\) | − | 21.4137i | − | 0.952895i | ||||||
\(506\) | 18.3350 | 0.815089 | ||||||||
\(507\) | 19.8808 | − | 30.4972i | 0.882939 | − | 1.35443i | ||||
\(508\) | 18.7159 | 0.830386 | ||||||||
\(509\) | 43.8547i | 1.94383i | 0.235338 | + | 0.971913i | \(0.424380\pi\) | ||||
−0.235338 | + | 0.971913i | \(0.575620\pi\) | |||||||
\(510\) | 59.4392 | 2.63201 | ||||||||
\(511\) | 30.7495 | 1.36028 | ||||||||
\(512\) | − | 40.5893i | − | 1.79381i | ||||||
\(513\) | − | 15.1878i | − | 0.670557i | ||||||
\(514\) | 67.6891i | 2.98564i | ||||||||
\(515\) | − | 34.0574i | − | 1.50075i | ||||||
\(516\) | −10.4605 | −0.460496 | ||||||||
\(517\) | 63.9283 | 2.81156 | ||||||||
\(518\) | 62.1694i | 2.73157i | ||||||||
\(519\) | −41.3744 | −1.81613 | ||||||||
\(520\) | −55.1931 | + | 29.9051i | −2.42038 | + | 1.31142i | ||||
\(521\) | 34.6533 | 1.51819 | 0.759095 | − | 0.650980i | \(-0.225642\pi\) | ||||
0.759095 | + | 0.650980i | \(0.225642\pi\) | |||||||
\(522\) | − | 74.0106i | − | 3.23936i | ||||||
\(523\) | −13.5927 | −0.594369 | −0.297184 | − | 0.954820i | \(-0.596048\pi\) | ||||
−0.297184 | + | 0.954820i | \(0.596048\pi\) | |||||||
\(524\) | 52.3634 | 2.28750 | ||||||||
\(525\) | − | 70.8581i | − | 3.09250i | ||||||
\(526\) | 64.7012i | 2.82111i | ||||||||
\(527\) | 2.47924i | 0.107998i | ||||||||
\(528\) | 65.9750i | 2.87119i | ||||||||
\(529\) | −21.2268 | −0.922903 | ||||||||
\(530\) | −79.4030 | −3.44905 | ||||||||
\(531\) | 33.3675i | 1.44803i | ||||||||
\(532\) | −42.0391 | −1.82263 | ||||||||
\(533\) | −8.38607 | − | 15.4774i | −0.363241 | − | 0.670401i | ||||
\(534\) | −25.6423 | −1.10965 | ||||||||
\(535\) | 0.0523357i | 0.00226267i | ||||||||
\(536\) | 46.3447 | 2.00179 | ||||||||
\(537\) | −68.9889 | −2.97709 | ||||||||
\(538\) | − | 46.6527i | − | 2.01134i | ||||||
\(539\) | − | 31.0084i | − | 1.33562i | ||||||
\(540\) | 72.5250i | 3.12098i | ||||||||
\(541\) | 13.9830i | 0.601178i | 0.953754 | + | 0.300589i | \(0.0971832\pi\) | ||||
−0.953754 | + | 0.300589i | \(0.902817\pi\) | |||||||
\(542\) | 21.8104 | 0.936836 | ||||||||
\(543\) | 14.7471 | 0.632857 | ||||||||
\(544\) | 0.826196i | 0.0354229i | ||||||||
\(545\) | 3.21324 | 0.137640 | ||||||||
\(546\) | −77.1952 | + | 41.8264i | −3.30365 | + | 1.79000i | ||||
\(547\) | −39.4448 | −1.68654 | −0.843269 | − | 0.537492i | \(-0.819372\pi\) | ||||
−0.843269 | + | 0.537492i | \(0.819372\pi\) | |||||||
\(548\) | − | 18.7967i | − | 0.802957i | ||||||
\(549\) | 27.7338 | 1.18365 | ||||||||
\(550\) | 98.4154 | 4.19645 | ||||||||
\(551\) | 18.3196i | 0.780440i | ||||||||
\(552\) | 18.6278i | 0.792852i | ||||||||
\(553\) | − | 20.1724i | − | 0.857820i | ||||||
\(554\) | 0.647737i | 0.0275197i | ||||||||
\(555\) | −69.7821 | −2.96208 | ||||||||
\(556\) | −59.7676 | −2.53471 | ||||||||
\(557\) | 27.8887i | 1.18168i | 0.806788 | + | 0.590841i | \(0.201204\pi\) | ||||
−0.806788 | + | 0.590841i | \(0.798796\pi\) | |||||||
\(558\) | −11.8940 | −0.503514 | ||||||||
\(559\) | 2.93570 | − | 1.59064i | 0.124167 | − | 0.0672769i | ||||
\(560\) | 51.8569 | 2.19135 | ||||||||
\(561\) | 38.9176i | 1.64310i | ||||||||
\(562\) | −15.4403 | −0.651310 | ||||||||
\(563\) | −23.7172 | −0.999559 | −0.499780 | − | 0.866153i | \(-0.666586\pi\) | ||||
−0.499780 | + | 0.866153i | \(0.666586\pi\) | |||||||
\(564\) | 128.824i | 5.42449i | ||||||||
\(565\) | 20.8058i | 0.875305i | ||||||||
\(566\) | 27.7903i | 1.16811i | ||||||||
\(567\) | − | 0.283141i | − | 0.0118908i | ||||||
\(568\) | −4.24624 | −0.178168 | ||||||||
\(569\) | −15.1352 | −0.634501 | −0.317251 | − | 0.948342i | \(-0.602760\pi\) | ||||
−0.317251 | + | 0.948342i | \(0.602760\pi\) | |||||||
\(570\) | − | 70.5835i | − | 2.95642i | ||||||
\(571\) | −33.0021 | −1.38109 | −0.690547 | − | 0.723288i | \(-0.742630\pi\) | ||||
−0.690547 | + | 0.723288i | \(0.742630\pi\) | |||||||
\(572\) | −38.8366 | − | 71.6772i | −1.62384 | − | 2.99698i | ||||
\(573\) | −12.9248 | −0.539940 | ||||||||
\(574\) | 42.4541i | 1.77200i | ||||||||
\(575\) | 9.51801 | 0.396928 | ||||||||
\(576\) | 36.7389 | 1.53079 | ||||||||
\(577\) | − | 15.1583i | − | 0.631049i | −0.948917 | − | 0.315525i | \(-0.897819\pi\) | ||
0.948917 | − | 0.315525i | \(-0.102181\pi\) | |||||||
\(578\) | − | 26.6596i | − | 1.10889i | ||||||
\(579\) | − | 4.53599i | − | 0.188509i | ||||||
\(580\) | − | 87.4800i | − | 3.63241i | ||||||
\(581\) | 36.0497 | 1.49559 | ||||||||
\(582\) | −78.4681 | −3.25261 | ||||||||
\(583\) | − | 51.9888i | − | 2.15316i | ||||||
\(584\) | −43.3903 | −1.79550 | ||||||||
\(585\) | −28.9882 | − | 53.5009i | −1.19851 | − | 2.21199i | ||||
\(586\) | 47.9064 | 1.97899 | ||||||||
\(587\) | 7.05245i | 0.291086i | 0.989352 | + | 0.145543i | \(0.0464929\pi\) | ||||
−0.989352 | + | 0.145543i | \(0.953507\pi\) | |||||||
\(588\) | 62.4862 | 2.57689 | ||||||||
\(589\) | 2.94408 | 0.121309 | ||||||||
\(590\) | 58.9957i | 2.42882i | ||||||||
\(591\) | 23.3010i | 0.958474i | ||||||||
\(592\) | − | 30.0492i | − | 1.23501i | ||||||
\(593\) | 21.3706i | 0.877584i | 0.898589 | + | 0.438792i | \(0.144593\pi\) | ||||
−0.898589 | + | 0.438792i | \(0.855407\pi\) | |||||||
\(594\) | −71.0302 | −2.91440 | ||||||||
\(595\) | 30.5895 | 1.25405 | ||||||||
\(596\) | − | 11.5281i | − | 0.472211i | ||||||
\(597\) | 66.1850 | 2.70877 | ||||||||
\(598\) | −5.61833 | − | 10.3692i | −0.229750 | − | 0.424030i | ||||
\(599\) | 21.7134 | 0.887184 | 0.443592 | − | 0.896229i | \(-0.353704\pi\) | ||||
0.443592 | + | 0.896229i | \(0.353704\pi\) | |||||||
\(600\) | 99.9872i | 4.08196i | ||||||||
\(601\) | 6.23220 | 0.254217 | 0.127108 | − | 0.991889i | \(-0.459430\pi\) | ||||
0.127108 | + | 0.991889i | \(0.459430\pi\) | |||||||
\(602\) | −8.05255 | −0.328197 | ||||||||
\(603\) | 44.9238i | 1.82944i | ||||||||
\(604\) | − | 1.73065i | − | 0.0704190i | ||||||
\(605\) | 71.1739i | 2.89363i | ||||||||
\(606\) | 42.2622i | 1.71678i | ||||||||
\(607\) | −6.62821 | −0.269031 | −0.134515 | − | 0.990912i | \(-0.542948\pi\) | ||||
−0.134515 | + | 0.990912i | \(0.542948\pi\) | |||||||
\(608\) | 0.981101 | 0.0397889 | ||||||||
\(609\) | − | 61.6866i | − | 2.49967i | ||||||
\(610\) | 49.0350 | 1.98537 | ||||||||
\(611\) | −19.5893 | − | 36.1543i | −0.792500 | − | 1.46265i | ||||
\(612\) | −48.4233 | −1.95740 | ||||||||
\(613\) | − | 15.3431i | − | 0.619700i | −0.950785 | − | 0.309850i | \(-0.899721\pi\) | ||
0.950785 | − | 0.309850i | \(-0.100279\pi\) | |||||||
\(614\) | −77.8327 | −3.14107 | ||||||||
\(615\) | −47.6526 | −1.92154 | ||||||||
\(616\) | 99.1240i | 3.99382i | ||||||||
\(617\) | − | 10.2734i | − | 0.413592i | −0.978384 | − | 0.206796i | \(-0.933696\pi\) | ||
0.978384 | − | 0.206796i | \(-0.0663037\pi\) | |||||||
\(618\) | 67.2160i | 2.70382i | ||||||||
\(619\) | − | 39.0227i | − | 1.56845i | −0.620474 | − | 0.784227i | \(-0.713060\pi\) | ||
0.620474 | − | 0.784227i | \(-0.286940\pi\) | |||||||
\(620\) | −14.0586 | −0.564608 | ||||||||
\(621\) | −6.86952 | −0.275664 | ||||||||
\(622\) | − | 3.03020i | − | 0.121500i | ||||||
\(623\) | −13.1965 | −0.528705 | ||||||||
\(624\) | 37.3118 | − | 20.2165i | 1.49367 | − | 0.809308i | ||||
\(625\) | −9.64918 | −0.385967 | ||||||||
\(626\) | − | 48.0889i | − | 1.92202i | ||||||
\(627\) | 46.2143 | 1.84562 | ||||||||
\(628\) | 19.3014 | 0.770211 | ||||||||
\(629\) | − | 17.7255i | − | 0.706762i | ||||||
\(630\) | 146.751i | 5.84672i | ||||||||
\(631\) | − | 0.624321i | − | 0.0248538i | −0.999923 | − | 0.0124269i | \(-0.996044\pi\) | ||
0.999923 | − | 0.0124269i | \(-0.00395571\pi\) | |||||||
\(632\) | 28.4651i | 1.13228i | ||||||||
\(633\) | 63.2662 | 2.51460 | ||||||||
\(634\) | 5.04409 | 0.200326 | ||||||||
\(635\) | 16.1719i | 0.641763i | ||||||||
\(636\) | 104.765 | 4.15419 | ||||||||
\(637\) | −17.5366 | + | 9.50179i | −0.694826 | + | 0.376475i | ||||
\(638\) | 85.6770 | 3.39198 | ||||||||
\(639\) | − | 4.11606i | − | 0.162829i | ||||||
\(640\) | 67.2796 | 2.65946 | ||||||||
\(641\) | −15.3676 | −0.606983 | −0.303492 | − | 0.952834i | \(-0.598152\pi\) | ||||
−0.303492 | + | 0.952834i | \(0.598152\pi\) | |||||||
\(642\) | − | 0.103290i | − | 0.00407653i | ||||||
\(643\) | − | 37.6317i | − | 1.48405i | −0.670372 | − | 0.742025i | \(-0.733865\pi\) | ||
0.670372 | − | 0.742025i | \(-0.266135\pi\) | |||||||
\(644\) | 19.0145i | 0.749277i | ||||||||
\(645\) | − | 9.03859i | − | 0.355894i | ||||||
\(646\) | 17.9291 | 0.705410 | ||||||||
\(647\) | −31.8747 | −1.25312 | −0.626562 | − | 0.779372i | \(-0.715538\pi\) | ||||
−0.626562 | + | 0.779372i | \(0.715538\pi\) | |||||||
\(648\) | 0.399538i | 0.0156953i | ||||||||
\(649\) | −38.6272 | −1.51625 | ||||||||
\(650\) | −30.1571 | − | 55.6583i | −1.18286 | − | 2.18310i | ||||
\(651\) | −9.91346 | −0.388539 | ||||||||
\(652\) | − | 88.1158i | − | 3.45088i | ||||||
\(653\) | 37.9437 | 1.48485 | 0.742426 | − | 0.669928i | \(-0.233675\pi\) | ||||
0.742426 | + | 0.669928i | \(0.233675\pi\) | |||||||
\(654\) | −6.34167 | −0.247979 | ||||||||
\(655\) | 45.2457i | 1.76790i | ||||||||
\(656\) | − | 20.5199i | − | 0.801168i | ||||||
\(657\) | − | 42.0600i | − | 1.64092i | ||||||
\(658\) | 99.1701i | 3.86605i | ||||||||
\(659\) | 34.4697 | 1.34275 | 0.671374 | − | 0.741119i | \(-0.265705\pi\) | ||||
0.671374 | + | 0.741119i | \(0.265705\pi\) | |||||||
\(660\) | −220.683 | −8.59009 | ||||||||
\(661\) | − | 26.3201i | − | 1.02373i | −0.859065 | − | 0.511867i | \(-0.828954\pi\) | ||
0.859065 | − | 0.511867i | \(-0.171046\pi\) | |||||||
\(662\) | 32.5755 | 1.26608 | ||||||||
\(663\) | 22.0096 | − | 11.9254i | 0.854783 | − | 0.463144i | ||||
\(664\) | −50.8694 | −1.97411 | ||||||||
\(665\) | − | 36.3248i | − | 1.40862i | ||||||
\(666\) | 85.0370 | 3.29512 | ||||||||
\(667\) | 8.28605 | 0.320837 | ||||||||
\(668\) | − | 13.5967i | − | 0.526072i | ||||||
\(669\) | 67.3888i | 2.60540i | ||||||||
\(670\) | 79.4280i | 3.06857i | ||||||||
\(671\) | 32.1055i | 1.23942i | ||||||||
\(672\) | −3.30362 | −0.127440 | ||||||||
\(673\) | 22.6031 | 0.871284 | 0.435642 | − | 0.900120i | \(-0.356521\pi\) | ||||
0.435642 | + | 0.900120i | \(0.356521\pi\) | |||||||
\(674\) | 86.4232i | 3.32890i | ||||||||
\(675\) | −36.8730 | −1.41924 | ||||||||
\(676\) | −28.6361 | + | 43.9277i | −1.10139 | + | 1.68953i | ||||
\(677\) | 22.8439 | 0.877962 | 0.438981 | − | 0.898496i | \(-0.355339\pi\) | ||||
0.438981 | + | 0.898496i | \(0.355339\pi\) | |||||||
\(678\) | − | 41.0624i | − | 1.57699i | ||||||
\(679\) | −40.3825 | −1.54974 | ||||||||
\(680\) | −43.1646 | −1.65529 | ||||||||
\(681\) | − | 22.8319i | − | 0.874921i | ||||||
\(682\) | − | 13.7689i | − | 0.527238i | ||||||
\(683\) | − | 19.3530i | − | 0.740523i | −0.928927 | − | 0.370262i | \(-0.879268\pi\) | ||
0.928927 | − | 0.370262i | \(-0.120732\pi\) | |||||||
\(684\) | 57.5023i | 2.19865i | ||||||||
\(685\) | 16.2417 | 0.620565 | ||||||||
\(686\) | −12.7664 | −0.487425 | ||||||||
\(687\) | − | 14.7902i | − | 0.564280i | ||||||
\(688\) | 3.89215 | 0.148387 | ||||||||
\(689\) | −29.4020 | + | 15.9308i | −1.12013 | + | 0.606914i | ||||
\(690\) | −31.9253 | −1.21538 | ||||||||
\(691\) | 33.9864i | 1.29290i | 0.762955 | + | 0.646452i | \(0.223748\pi\) | ||||
−0.762955 | + | 0.646452i | \(0.776252\pi\) | |||||||
\(692\) | 59.5950 | 2.26546 | ||||||||
\(693\) | −96.0850 | −3.64997 | ||||||||
\(694\) | − | 29.7198i | − | 1.12815i | ||||||
\(695\) | − | 51.6435i | − | 1.95895i | ||||||
\(696\) | 87.0454i | 3.29945i | ||||||||
\(697\) | − | 12.1044i | − | 0.458485i | ||||||
\(698\) | 70.6800 | 2.67528 | ||||||||
\(699\) | 29.8154 | 1.12772 | ||||||||
\(700\) | 102.063i | 3.85762i | ||||||||
\(701\) | −14.0298 | −0.529898 | −0.264949 | − | 0.964262i | \(-0.585355\pi\) | ||||
−0.264949 | + | 0.964262i | \(0.585355\pi\) | |||||||
\(702\) | 21.7656 | + | 40.1707i | 0.821488 | + | 1.51615i | ||||
\(703\) | −21.0489 | −0.793874 | ||||||||
\(704\) | 42.5301i | 1.60291i | ||||||||
\(705\) | −111.314 | −4.19231 | ||||||||
\(706\) | 37.0737 | 1.39529 | ||||||||
\(707\) | 21.7496i | 0.817979i | ||||||||
\(708\) | − | 77.8393i | − | 2.92538i | ||||||
\(709\) | 6.14179i | 0.230660i | 0.993327 | + | 0.115330i | \(0.0367925\pi\) | ||||
−0.993327 | + | 0.115330i | \(0.963207\pi\) | |||||||
\(710\) | − | 7.27744i | − | 0.273117i | ||||||
\(711\) | −27.5924 | −1.03480 | ||||||||
\(712\) | 18.6214 | 0.697867 | ||||||||
\(713\) | − | 1.33162i | − | 0.0498697i | ||||||
\(714\) | −60.3718 | −2.25936 | ||||||||
\(715\) | 61.9343 | − | 33.5576i | 2.31621 | − | 1.25498i | ||||
\(716\) | 99.3706 | 3.71365 | ||||||||
\(717\) | − | 17.6858i | − | 0.660487i | ||||||
\(718\) | 7.17386 | 0.267726 | ||||||||
\(719\) | −8.98548 | −0.335102 | −0.167551 | − | 0.985863i | \(-0.553586\pi\) | ||||
−0.167551 | + | 0.985863i | \(0.553586\pi\) | |||||||
\(720\) | − | 70.9313i | − | 2.64345i | ||||||
\(721\) | 34.5918i | 1.28826i | ||||||||
\(722\) | 25.3799i | 0.944543i | ||||||||
\(723\) | 41.3604i | 1.53821i | ||||||||
\(724\) | −21.2414 | −0.789432 | ||||||||
\(725\) | 44.4764 | 1.65181 | ||||||||
\(726\) | − | 140.469i | − | 5.21330i | ||||||
\(727\) | 30.2413 | 1.12159 | 0.560795 | − | 0.827955i | \(-0.310496\pi\) | ||||
0.560795 | + | 0.827955i | \(0.310496\pi\) | |||||||
\(728\) | 56.0590 | − | 30.3742i | 2.07769 | − | 1.12574i | ||||
\(729\) | −43.7268 | −1.61951 | ||||||||
\(730\) | − | 74.3646i | − | 2.75236i | ||||||
\(731\) | 2.29591 | 0.0849174 | ||||||||
\(732\) | −64.6971 | −2.39127 | ||||||||
\(733\) | − | 51.5640i | − | 1.90456i | −0.305227 | − | 0.952280i | \(-0.598732\pi\) | ||
0.305227 | − | 0.952280i | \(-0.401268\pi\) | |||||||
\(734\) | 17.2770i | 0.637707i | ||||||||
\(735\) | 53.9926i | 1.99155i | ||||||||
\(736\) | − | 0.443758i | − | 0.0163571i | ||||||
\(737\) | −52.0052 | −1.91564 | ||||||||
\(738\) | 58.0699 | 2.13758 | ||||||||
\(739\) | 10.0098i | 0.368216i | 0.982906 | + | 0.184108i | \(0.0589397\pi\) | ||||
−0.982906 | + | 0.184108i | \(0.941060\pi\) | |||||||
\(740\) | 100.513 | 3.69493 | ||||||||
\(741\) | −14.1613 | − | 26.1362i | −0.520228 | − | 0.960139i | ||||
\(742\) | 80.6488 | 2.96071 | ||||||||
\(743\) | − | 16.9940i | − | 0.623449i | −0.950173 | − | 0.311724i | \(-0.899093\pi\) | ||
0.950173 | − | 0.311724i | \(-0.100907\pi\) | |||||||
\(744\) | 13.9888 | 0.512854 | ||||||||
\(745\) | 9.96114 | 0.364948 | ||||||||
\(746\) | − | 22.6747i | − | 0.830179i | ||||||
\(747\) | − | 49.3098i | − | 1.80415i | ||||||
\(748\) | − | 56.0563i | − | 2.04962i | ||||||
\(749\) | − | 0.0531568i | − | 0.00194231i | ||||||
\(750\) | −51.4898 | −1.88014 | ||||||||
\(751\) | −37.7192 | −1.37639 | −0.688196 | − | 0.725524i | \(-0.741597\pi\) | ||||
−0.688196 | + | 0.725524i | \(0.741597\pi\) | |||||||
\(752\) | − | 47.9332i | − | 1.74794i | ||||||
\(753\) | −34.5336 | −1.25847 | ||||||||
\(754\) | −26.2537 | − | 48.4541i | −0.956104 | − | 1.76460i | ||||
\(755\) | 1.49540 | 0.0544233 | ||||||||
\(756\) | − | 73.6628i | − | 2.67909i | ||||||
\(757\) | −5.31555 | −0.193197 | −0.0965984 | − | 0.995323i | \(-0.530796\pi\) | ||||
−0.0965984 | + | 0.995323i | \(0.530796\pi\) | |||||||
\(758\) | −34.7411 | −1.26186 | ||||||||
\(759\) | − | 20.9030i | − | 0.758731i | ||||||
\(760\) | 51.2576i | 1.85931i | ||||||||
\(761\) | − | 29.2832i | − | 1.06152i | −0.847524 | − | 0.530758i | \(-0.821907\pi\) | ||
0.847524 | − | 0.530758i | \(-0.178093\pi\) | |||||||
\(762\) | − | 31.9170i | − | 1.15623i | ||||||
\(763\) | −3.26365 | −0.118152 | ||||||||
\(764\) | 18.6166 | 0.673527 | ||||||||
\(765\) | − | 41.8412i | − | 1.51277i | ||||||
\(766\) | 23.3834 | 0.844877 | ||||||||
\(767\) | 11.8364 | + | 21.8454i | 0.427388 | + | 0.788792i | ||||
\(768\) | −90.2887 | −3.25801 | ||||||||
\(769\) | − | 29.7376i | − | 1.07237i | −0.844102 | − | 0.536183i | \(-0.819866\pi\) | ||
0.844102 | − | 0.536183i | \(-0.180134\pi\) | |||||||
\(770\) | −169.884 | −6.12219 | ||||||||
\(771\) | 77.1697 | 2.77920 | ||||||||
\(772\) | 6.53357i | 0.235148i | ||||||||
\(773\) | 1.75024i | 0.0629517i | 0.999505 | + | 0.0314758i | \(0.0100207\pi\) | ||||
−0.999505 | + | 0.0314758i | \(0.989979\pi\) | |||||||
\(774\) | 11.0145i | 0.395908i | ||||||||
\(775\) | − | 7.14767i | − | 0.256752i | ||||||
\(776\) | 56.9833 | 2.04558 | ||||||||
\(777\) | 70.8769 | 2.54270 | ||||||||
\(778\) | 23.7228i | 0.850503i | ||||||||
\(779\) | −14.3738 | −0.514996 | ||||||||
\(780\) | 67.6233 | + | 124.806i | 2.42130 | + | 4.46878i | ||||
\(781\) | 4.76488 | 0.170501 | ||||||||
\(782\) | − | 8.10943i | − | 0.289993i | ||||||
\(783\) | −32.1004 | −1.14717 | ||||||||
\(784\) | −23.2500 | −0.830356 | ||||||||
\(785\) | 16.6778i | 0.595257i | ||||||||
\(786\) | − | 89.2973i | − | 3.18513i | ||||||
\(787\) | 1.92314i | 0.0685524i | 0.999412 | + | 0.0342762i | \(0.0109126\pi\) | ||||
−0.999412 | + | 0.0342762i | \(0.989087\pi\) | |||||||
\(788\) | − | 33.5624i | − | 1.19561i | ||||||
\(789\) | 73.7634 | 2.62605 | ||||||||
\(790\) | −48.7851 | −1.73570 | ||||||||
\(791\) | − | 21.1322i | − | 0.751375i | ||||||
\(792\) | 135.585 | 4.81779 | ||||||||
\(793\) | 18.1571 | − | 9.83799i | 0.644777 | − | 0.349357i | ||||
\(794\) | 32.2869 | 1.14582 | ||||||||
\(795\) | 90.5243i | 3.21057i | ||||||||
\(796\) | −95.3320 | −3.37895 | ||||||||
\(797\) | −5.24943 | −0.185944 | −0.0929721 | − | 0.995669i | \(-0.529637\pi\) | ||||
−0.0929721 | + | 0.995669i | \(0.529637\pi\) | |||||||
\(798\) | 71.6909i | 2.53783i | ||||||||
\(799\) | − | 28.2750i | − | 1.00030i | ||||||
\(800\) | − | 2.38193i | − | 0.0842139i | ||||||
\(801\) | 18.0505i | 0.637783i | ||||||||
\(802\) | −55.9750 | −1.97655 | ||||||||
\(803\) | 48.6899 | 1.71823 | ||||||||
\(804\) | − | 104.798i | − | 3.69593i | ||||||
\(805\) | −16.4299 | −0.579079 | ||||||||
\(806\) | −7.78691 | + | 4.21915i | −0.274282 | + | 0.148613i | ||||
\(807\) | −53.1870 | −1.87227 | ||||||||
\(808\) | − | 30.6907i | − | 1.07969i | ||||||
\(809\) | −34.3076 | −1.20619 | −0.603095 | − | 0.797670i | \(-0.706066\pi\) | ||||
−0.603095 | + | 0.797670i | \(0.706066\pi\) | |||||||
\(810\) | −0.684749 | −0.0240596 | ||||||||
\(811\) | − | 21.9495i | − | 0.770751i | −0.922760 | − | 0.385375i | \(-0.874072\pi\) | ||
0.922760 | − | 0.385375i | \(-0.125928\pi\) | |||||||
\(812\) | 88.8525i | 3.11811i | ||||||||
\(813\) | − | 24.8652i | − | 0.872060i | ||||||
\(814\) | 98.4415i | 3.45037i | ||||||||
\(815\) | 76.1384 | 2.66701 | ||||||||
\(816\) | 29.1803 | 1.02151 | ||||||||
\(817\) | − | 2.72638i | − | 0.0953839i | ||||||
\(818\) | −49.5296 | −1.73176 | ||||||||
\(819\) | 29.4430 | + | 54.3403i | 1.02882 | + | 1.89880i | ||||
\(820\) | 68.6382 | 2.39695 | ||||||||
\(821\) | − | 7.27538i | − | 0.253912i | −0.991908 | − | 0.126956i | \(-0.959479\pi\) | ||
0.991908 | − | 0.126956i | \(-0.0405208\pi\) | |||||||
\(822\) | −32.0548 | −1.11804 | ||||||||
\(823\) | −42.3561 | −1.47644 | −0.738221 | − | 0.674559i | \(-0.764334\pi\) | ||||
−0.738221 | + | 0.674559i | \(0.764334\pi\) | |||||||
\(824\) | − | 48.8121i | − | 1.70045i | ||||||
\(825\) | − | 112.200i | − | 3.90629i | ||||||
\(826\) | − | 59.9213i | − | 2.08493i | ||||||
\(827\) | 48.1056i | 1.67279i | 0.548124 | + | 0.836397i | \(0.315342\pi\) | ||||
−0.548124 | + | 0.836397i | \(0.684658\pi\) | |||||||
\(828\) | 26.0086 | 0.903862 | ||||||||
\(829\) | −27.6670 | −0.960915 | −0.480458 | − | 0.877018i | \(-0.659529\pi\) | ||||
−0.480458 | + | 0.877018i | \(0.659529\pi\) | |||||||
\(830\) | − | 87.1826i | − | 3.02615i | ||||||
\(831\) | 0.738460 | 0.0256169 | ||||||||
\(832\) | 24.0527 | − | 13.0324i | 0.833876 | − | 0.451816i | ||||
\(833\) | −13.7148 | −0.475189 | ||||||||
\(834\) | 101.924i | 3.52934i | ||||||||
\(835\) | 11.7485 | 0.406575 | ||||||||
\(836\) | −66.5664 | −2.30225 | ||||||||
\(837\) | 5.15875i | 0.178313i | ||||||||
\(838\) | 5.14237i | 0.177640i | ||||||||
\(839\) | − | 32.7819i | − | 1.13176i | −0.824489 | − | 0.565878i | \(-0.808537\pi\) | ||
0.824489 | − | 0.565878i | \(-0.191463\pi\) | |||||||
\(840\) | − | 172.597i | − | 5.95517i | ||||||
\(841\) | 9.71964 | 0.335160 | ||||||||
\(842\) | −37.1508 | −1.28030 | ||||||||
\(843\) | 17.6029i | 0.606276i | ||||||||
\(844\) | −91.1277 | −3.13674 | ||||||||
\(845\) | −37.9567 | − | 24.7436i | −1.30575 | − | 0.851207i | ||||
\(846\) | 135.648 | 4.66366 | ||||||||
\(847\) | − | 72.2906i | − | 2.48393i | ||||||
\(848\) | −38.9811 | −1.33862 | ||||||||
\(849\) | 31.6826 | 1.08734 | ||||||||
\(850\) | − | 43.5284i | − | 1.49301i | ||||||
\(851\) | 9.52053i | 0.326360i | ||||||||
\(852\) | 9.60189i | 0.328955i | ||||||||
\(853\) | 5.61212i | 0.192155i | 0.995374 | + | 0.0960777i | \(0.0306297\pi\) | ||||
−0.995374 | + | 0.0960777i | \(0.969370\pi\) | |||||||
\(854\) | −49.8044 | −1.70427 | ||||||||
\(855\) | −49.6861 | −1.69923 | ||||||||
\(856\) | 0.0750090i | 0.00256376i | ||||||||
\(857\) | 31.9107 | 1.09005 | 0.545024 | − | 0.838420i | \(-0.316520\pi\) | ||||
0.545024 | + | 0.838420i | \(0.316520\pi\) | |||||||
\(858\) | −122.234 | + | 66.2296i | −4.17300 | + | 2.26104i | ||||
\(859\) | 57.3951 | 1.95829 | 0.979147 | − | 0.203153i | \(-0.0651189\pi\) | ||||
0.979147 | + | 0.203153i | \(0.0651189\pi\) | |||||||
\(860\) | 13.0191i | 0.443946i | ||||||||
\(861\) | 48.4003 | 1.64948 | ||||||||
\(862\) | 30.9350 | 1.05365 | ||||||||
\(863\) | − | 31.8387i | − | 1.08380i | −0.840442 | − | 0.541901i | \(-0.817705\pi\) | ||
0.840442 | − | 0.541901i | \(-0.182295\pi\) | |||||||
\(864\) | 1.71913i | 0.0584860i | ||||||||
\(865\) | 51.4944i | 1.75086i | ||||||||
\(866\) | − | 14.8650i | − | 0.505133i | ||||||
\(867\) | −30.3936 | −1.03222 | ||||||||
\(868\) | 14.2792 | 0.484668 | ||||||||
\(869\) | − | 31.9419i | − | 1.08355i | ||||||
\(870\) | −149.183 | −5.05778 | ||||||||
\(871\) | 15.9358 | + | 29.4112i | 0.539963 | + | 0.996562i | ||||
\(872\) | 4.60531 | 0.155955 | ||||||||
\(873\) | 55.2363i | 1.86947i | ||||||||
\(874\) | −9.62988 | −0.325735 | ||||||||
\(875\) | −26.4985 | −0.895812 | ||||||||
\(876\) | 98.1171i | 3.31507i | ||||||||
\(877\) | 11.7085i | 0.395370i | 0.980266 | + | 0.197685i | \(0.0633422\pi\) | ||||
−0.980266 | + | 0.197685i | \(0.936658\pi\) | |||||||
\(878\) | 5.78780i | 0.195329i | ||||||||
\(879\) | − | 54.6162i | − | 1.84216i | ||||||
\(880\) | 82.1123 | 2.76801 | ||||||||
\(881\) | 34.9127 | 1.17624 | 0.588120 | − | 0.808774i | \(-0.299868\pi\) | ||||
0.588120 | + | 0.808774i | \(0.299868\pi\) | |||||||
\(882\) | − | 65.7958i | − | 2.21546i | ||||||
\(883\) | −30.8289 | −1.03748 | −0.518738 | − | 0.854933i | \(-0.673598\pi\) | ||||
−0.518738 | + | 0.854933i | \(0.673598\pi\) | |||||||
\(884\) | −31.7023 | + | 17.1772i | −1.06627 | + | 0.577730i | ||||
\(885\) | 67.2587 | 2.26088 | ||||||||
\(886\) | 18.7674i | 0.630501i | ||||||||
\(887\) | −30.6338 | −1.02858 | −0.514292 | − | 0.857615i | \(-0.671945\pi\) | ||||
−0.514292 | + | 0.857615i | \(0.671945\pi\) | |||||||
\(888\) | −100.014 | −3.35624 | ||||||||
\(889\) | − | 16.4257i | − | 0.550899i | ||||||
\(890\) | 31.9144i | 1.06977i | ||||||||
\(891\) | − | 0.448337i | − | 0.0150199i | ||||||
\(892\) | − | 97.0658i | − | 3.25000i | ||||||
\(893\) | −33.5763 | −1.12359 | ||||||||
\(894\) | −19.6594 | −0.657508 | ||||||||
\(895\) | 85.8634i | 2.87010i | ||||||||
\(896\) | −68.3352 | −2.28292 | ||||||||
\(897\) | −11.8216 | + | 6.40524i | −0.394711 | + | 0.213865i | ||||
\(898\) | −77.1614 | −2.57491 | ||||||||
\(899\) | − | 6.22251i | − | 0.207532i | ||||||
\(900\) | 139.605 | 4.65349 | ||||||||
\(901\) | −22.9943 | −0.766051 | ||||||||
\(902\) | 67.2235i | 2.23830i | ||||||||
\(903\) | 9.18040i | 0.305505i | ||||||||
\(904\) | 29.8194i | 0.991780i | ||||||||
\(905\) | − | 18.3541i | − | 0.610112i | ||||||
\(906\) | −2.95134 | −0.0980517 | ||||||||
\(907\) | 24.1238 | 0.801019 | 0.400510 | − | 0.916293i | \(-0.368833\pi\) | ||||
0.400510 | + | 0.916293i | \(0.368833\pi\) | |||||||
\(908\) | 32.8867i | 1.09139i | ||||||||
\(909\) | 29.7498 | 0.986737 | ||||||||
\(910\) | 52.0570 | + | 96.0769i | 1.72567 | + | 3.18492i | ||||
\(911\) | −18.7893 | −0.622518 | −0.311259 | − | 0.950325i | \(-0.600751\pi\) | ||||
−0.311259 | + | 0.950325i | \(0.600751\pi\) | |||||||
\(912\) | − | 34.6513i | − | 1.14742i | ||||||
\(913\) | 57.0825 | 1.88916 | ||||||||
\(914\) | −34.8391 | −1.15237 | ||||||||
\(915\) | − | 55.9029i | − | 1.84809i | ||||||
\(916\) | 21.3035i | 0.703888i | ||||||||
\(917\) | − | 45.9556i | − | 1.51759i | ||||||
\(918\) | 31.4162i | 1.03689i | ||||||||
\(919\) | 43.9357 | 1.44930 | 0.724652 | − | 0.689115i | \(-0.242001\pi\) | ||||
0.724652 | + | 0.689115i | \(0.242001\pi\) | |||||||
\(920\) | 23.1841 | 0.764357 | ||||||||
\(921\) | 88.7341i | 2.92389i | ||||||||
\(922\) | 2.09321 | 0.0689362 | ||||||||
\(923\) | −1.46009 | − | 2.69475i | −0.0480593 | − | 0.0886988i | ||||
\(924\) | 224.146 | 7.37386 | ||||||||
\(925\) | 51.1027i | 1.68025i | ||||||||
\(926\) | −65.2937 | −2.14569 | ||||||||
\(927\) | 47.3156 | 1.55405 | ||||||||
\(928\) | − | 2.07362i | − | 0.0680700i | ||||||
\(929\) | 2.75930i | 0.0905299i | 0.998975 | + | 0.0452649i | \(0.0144132\pi\) | ||||
−0.998975 | + | 0.0452649i | \(0.985587\pi\) | |||||||
\(930\) | 23.9747i | 0.786162i | ||||||||
\(931\) | 16.2862i | 0.533758i | ||||||||
\(932\) | −42.9456 | −1.40673 | ||||||||
\(933\) | −3.45461 | −0.113099 | ||||||||
\(934\) | − | 65.3249i | − | 2.13750i | ||||||
\(935\) | 48.4367 | 1.58405 | ||||||||
\(936\) | −41.5467 | − | 76.6791i | −1.35800 | − | 2.50633i | ||||
\(937\) | 38.8818 | 1.27021 | 0.635107 | − | 0.772424i | \(-0.280956\pi\) | ||||
0.635107 | + | 0.772424i | \(0.280956\pi\) | |||||||
\(938\) | − | 80.6742i | − | 2.63411i | ||||||
\(939\) | −54.8243 | −1.78912 | ||||||||
\(940\) | 160.334 | 5.22953 | ||||||||
\(941\) | − | 36.4643i | − | 1.18870i | −0.804206 | − | 0.594350i | \(-0.797409\pi\) | ||
0.804206 | − | 0.594350i | \(-0.202591\pi\) | |||||||
\(942\) | − | 32.9155i | − | 1.07244i | ||||||
\(943\) | 6.50136i | 0.211713i | ||||||||
\(944\) | 28.9626i | 0.942652i | ||||||||
\(945\) | 63.6500 | 2.07053 | ||||||||
\(946\) | −12.7507 | −0.414562 | ||||||||
\(947\) | 46.9659i | 1.52619i | 0.646289 | + | 0.763093i | \(0.276320\pi\) | ||||
−0.646289 | + | 0.763093i | \(0.723680\pi\) | |||||||
\(948\) | 64.3673 | 2.09055 | ||||||||
\(949\) | −14.9199 | − | 27.5363i | −0.484321 | − | 0.893867i | ||||
\(950\) | −51.6896 | −1.67703 | ||||||||
\(951\) | − | 5.75057i | − | 0.186475i | ||||||
\(952\) | 43.8418 | 1.42092 | ||||||||
\(953\) | 29.9638 | 0.970624 | 0.485312 | − | 0.874341i | \(-0.338706\pi\) | ||||
0.485312 | + | 0.874341i | \(0.338706\pi\) | |||||||
\(954\) | − | 110.314i | − | 3.57154i | ||||||
\(955\) | 16.0861i | 0.520535i | ||||||||
\(956\) | 25.4743i | 0.823899i | ||||||||
\(957\) | − | 97.6770i | − | 3.15745i | ||||||
\(958\) | −69.6513 | −2.25033 | ||||||||
\(959\) | −16.4966 | −0.532702 | ||||||||
\(960\) | − | 74.0545i | − | 2.39010i | ||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 55.6730 | − | 30.1651i | 1.79497 | − | 0.972562i | ||||
\(963\) | −0.0727093 | −0.00234303 | ||||||||
\(964\) | − | 59.5749i | − | 1.91878i | ||||||
\(965\) | −5.64548 | −0.181734 | ||||||||
\(966\) | 32.4262 | 1.04330 | ||||||||
\(967\) | 45.1554i | 1.45210i | 0.687641 | + | 0.726050i | \(0.258646\pi\) | ||||
−0.687641 | + | 0.726050i | \(0.741354\pi\) | |||||||
\(968\) | 102.009i | 3.27868i | ||||||||
\(969\) | − | 20.4403i | − | 0.656636i | ||||||
\(970\) | 97.6611i | 3.13571i | ||||||||
\(971\) | −44.4756 | −1.42729 | −0.713645 | − | 0.700508i | \(-0.752957\pi\) | ||||
−0.713645 | + | 0.700508i | \(0.752957\pi\) | |||||||
\(972\) | 63.3290 | 2.03128 | ||||||||
\(973\) | 52.4537i | 1.68159i | ||||||||
\(974\) | 76.0803 | 2.43777 | ||||||||
\(975\) | −63.4538 | + | 34.3810i | −2.03215 | + | 1.10107i | ||||
\(976\) | 24.0726 | 0.770545 | ||||||||
\(977\) | 16.3554i | 0.523255i | 0.965169 | + | 0.261628i | \(0.0842592\pi\) | ||||
−0.965169 | + | 0.261628i | \(0.915741\pi\) | |||||||
\(978\) | −150.267 | −4.80502 | ||||||||
\(979\) | −20.8958 | −0.667833 | ||||||||
\(980\) | − | 77.7701i | − | 2.48428i | ||||||
\(981\) | 4.46412i | 0.142528i | ||||||||
\(982\) | − | 5.73824i | − | 0.183115i | ||||||
\(983\) | 54.2695i | 1.73093i | 0.500971 | + | 0.865464i | \(0.332976\pi\) | ||||
−0.500971 | + | 0.865464i | \(0.667024\pi\) | |||||||
\(984\) | −68.2972 | −2.17723 | ||||||||
\(985\) | 29.0003 | 0.924027 | ||||||||
\(986\) | − | 37.8943i | − | 1.20680i | ||||||
\(987\) | 113.060 | 3.59874 | ||||||||
\(988\) | 20.3977 | + | 37.6463i | 0.648938 | + | 1.19769i | ||||
\(989\) | −1.23316 | −0.0392121 | ||||||||
\(990\) | 232.372i | 7.38527i | ||||||||
\(991\) | −41.4631 | −1.31712 | −0.658560 | − | 0.752528i | \(-0.728834\pi\) | ||||
−0.658560 | + | 0.752528i | \(0.728834\pi\) | |||||||
\(992\) | −0.333245 | −0.0105806 | ||||||||
\(993\) | − | 37.1381i | − | 1.17854i | ||||||
\(994\) | 7.39162i | 0.234448i | ||||||||
\(995\) | − | 82.3737i | − | 2.61142i | ||||||
\(996\) | 115.029i | 3.64484i | ||||||||
\(997\) | 39.9735 | 1.26597 | 0.632986 | − | 0.774163i | \(-0.281829\pi\) | ||||
0.632986 | + | 0.774163i | \(0.281829\pi\) | |||||||
\(998\) | 47.7592 | 1.51179 | ||||||||
\(999\) | − | 36.8828i | − | 1.16692i |
(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 | 403.2.c.b.311.30 | yes | 32 | |
13.5 | odd | 4 | 5239.2.a.k.1.16 | 16 | |||
13.8 | odd | 4 | 5239.2.a.l.1.1 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.3 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.3 | ✓ | 32 | 13.12 | even | 2 | inner | |
403.2.c.b.311.30 | yes | 32 | 1.1 | even | 1 | trivial | |
5239.2.a.k.1.16 | 16 | 13.5 | odd | 4 | |||
5239.2.a.l.1.1 | 16 | 13.8 | odd | 4 |