Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3630,2,Mod(1,3630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3630.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.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: | \(28.9856959337\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3630.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.267949 | −0.101275 | −0.0506376 | − | 0.998717i | \(-0.516125\pi\) | ||||
−0.0506376 | + | 0.998717i | \(0.516125\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −4.46410 | −1.23812 | −0.619060 | − | 0.785344i | \(-0.712486\pi\) | ||||
−0.619060 | + | 0.785344i | \(0.712486\pi\) | |||||||
\(14\) | −0.267949 | −0.0716124 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.73205 | −0.420084 | −0.210042 | − | 0.977692i | \(-0.567360\pi\) | ||||
−0.210042 | + | 0.977692i | \(0.567360\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −7.00000 | −1.60591 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −0.267949 | −0.0584713 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.73205 | −1.40373 | −0.701865 | − | 0.712310i | \(-0.747649\pi\) | ||||
−0.701865 | + | 0.712310i | \(0.747649\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.46410 | −0.875482 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.267949 | −0.0506376 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 6.19615 | 1.11286 | 0.556431 | − | 0.830894i | \(-0.312170\pi\) | ||||
0.556431 | + | 0.830894i | \(0.312170\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.73205 | −0.297044 | ||||||||
\(35\) | 0.267949 | 0.0452917 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.19615 | −1.18304 | −0.591520 | − | 0.806290i | \(-0.701472\pi\) | ||||
−0.591520 | + | 0.806290i | \(0.701472\pi\) | |||||||
\(38\) | −7.00000 | −1.13555 | ||||||||
\(39\) | −4.46410 | −0.714828 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 4.19615 | 0.655329 | 0.327664 | − | 0.944794i | \(-0.393738\pi\) | ||||
0.327664 | + | 0.944794i | \(0.393738\pi\) | |||||||
\(42\) | −0.267949 | −0.0413455 | ||||||||
\(43\) | 2.19615 | 0.334910 | 0.167455 | − | 0.985880i | \(-0.446445\pi\) | ||||
0.167455 | + | 0.985880i | \(0.446445\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −6.73205 | −0.992587 | ||||||||
\(47\) | 4.92820 | 0.718852 | 0.359426 | − | 0.933174i | \(-0.382972\pi\) | ||||
0.359426 | + | 0.933174i | \(0.382972\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.92820 | −0.989743 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −1.73205 | −0.242536 | ||||||||
\(52\) | −4.46410 | −0.619060 | ||||||||
\(53\) | 0.732051 | 0.100555 | 0.0502775 | − | 0.998735i | \(-0.483989\pi\) | ||||
0.0502775 | + | 0.998735i | \(0.483989\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.267949 | −0.0358062 | ||||||||
\(57\) | −7.00000 | −0.927173 | ||||||||
\(58\) | −5.00000 | −0.656532 | ||||||||
\(59\) | −11.6603 | −1.51804 | −0.759018 | − | 0.651070i | \(-0.774321\pi\) | ||||
−0.759018 | + | 0.651070i | \(0.774321\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −15.1244 | −1.93648 | −0.968238 | − | 0.250032i | \(-0.919559\pi\) | ||||
−0.968238 | + | 0.250032i | \(0.919559\pi\) | |||||||
\(62\) | 6.19615 | 0.786912 | ||||||||
\(63\) | −0.267949 | −0.0337584 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.46410 | 0.553704 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.53590 | 0.554148 | 0.277074 | − | 0.960849i | \(-0.410635\pi\) | ||||
0.277074 | + | 0.960849i | \(0.410635\pi\) | |||||||
\(68\) | −1.73205 | −0.210042 | ||||||||
\(69\) | −6.73205 | −0.810444 | ||||||||
\(70\) | 0.267949 | 0.0320261 | ||||||||
\(71\) | −2.46410 | −0.292435 | −0.146218 | − | 0.989252i | \(-0.546710\pi\) | ||||
−0.146218 | + | 0.989252i | \(0.546710\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 9.66025 | 1.13065 | 0.565324 | − | 0.824869i | \(-0.308751\pi\) | ||||
0.565324 | + | 0.824869i | \(0.308751\pi\) | |||||||
\(74\) | −7.19615 | −0.836536 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −7.00000 | −0.802955 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.46410 | −0.505460 | ||||||||
\(79\) | 10.3923 | 1.16923 | 0.584613 | − | 0.811312i | \(-0.301246\pi\) | ||||
0.584613 | + | 0.811312i | \(0.301246\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.19615 | 0.463388 | ||||||||
\(83\) | −9.53590 | −1.04670 | −0.523350 | − | 0.852118i | \(-0.675318\pi\) | ||||
−0.523350 | + | 0.852118i | \(0.675318\pi\) | |||||||
\(84\) | −0.267949 | −0.0292357 | ||||||||
\(85\) | 1.73205 | 0.187867 | ||||||||
\(86\) | 2.19615 | 0.236817 | ||||||||
\(87\) | −5.00000 | −0.536056 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.46410 | 1.00319 | 0.501596 | − | 0.865102i | \(-0.332746\pi\) | ||||
0.501596 | + | 0.865102i | \(0.332746\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 1.19615 | 0.125391 | ||||||||
\(92\) | −6.73205 | −0.701865 | ||||||||
\(93\) | 6.19615 | 0.642511 | ||||||||
\(94\) | 4.92820 | 0.508305 | ||||||||
\(95\) | 7.00000 | 0.718185 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 8.73205 | 0.886605 | 0.443303 | − | 0.896372i | \(-0.353807\pi\) | ||||
0.443303 | + | 0.896372i | \(0.353807\pi\) | |||||||
\(98\) | −6.92820 | −0.699854 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 1.53590 | 0.152828 | 0.0764138 | − | 0.997076i | \(-0.475653\pi\) | ||||
0.0764138 | + | 0.997076i | \(0.475653\pi\) | |||||||
\(102\) | −1.73205 | −0.171499 | ||||||||
\(103\) | 3.39230 | 0.334254 | 0.167127 | − | 0.985935i | \(-0.446551\pi\) | ||||
0.167127 | + | 0.985935i | \(0.446551\pi\) | |||||||
\(104\) | −4.46410 | −0.437741 | ||||||||
\(105\) | 0.267949 | 0.0261492 | ||||||||
\(106\) | 0.732051 | 0.0711031 | ||||||||
\(107\) | −6.39230 | −0.617967 | −0.308984 | − | 0.951067i | \(-0.599989\pi\) | ||||
−0.308984 | + | 0.951067i | \(0.599989\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −8.39230 | −0.803837 | −0.401919 | − | 0.915675i | \(-0.631656\pi\) | ||||
−0.401919 | + | 0.915675i | \(0.631656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.19615 | −0.683029 | ||||||||
\(112\) | −0.267949 | −0.0253188 | ||||||||
\(113\) | 13.8564 | 1.30350 | 0.651751 | − | 0.758433i | \(-0.274035\pi\) | ||||
0.651751 | + | 0.758433i | \(0.274035\pi\) | |||||||
\(114\) | −7.00000 | −0.655610 | ||||||||
\(115\) | 6.73205 | 0.627767 | ||||||||
\(116\) | −5.00000 | −0.464238 | ||||||||
\(117\) | −4.46410 | −0.412706 | ||||||||
\(118\) | −11.6603 | −1.07341 | ||||||||
\(119\) | 0.464102 | 0.0425441 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −15.1244 | −1.36929 | ||||||||
\(123\) | 4.19615 | 0.378354 | ||||||||
\(124\) | 6.19615 | 0.556431 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.267949 | −0.0238708 | ||||||||
\(127\) | −6.53590 | −0.579967 | −0.289984 | − | 0.957032i | \(-0.593650\pi\) | ||||
−0.289984 | + | 0.957032i | \(0.593650\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.19615 | 0.193360 | ||||||||
\(130\) | 4.46410 | 0.391528 | ||||||||
\(131\) | 3.12436 | 0.272976 | 0.136488 | − | 0.990642i | \(-0.456418\pi\) | ||||
0.136488 | + | 0.990642i | \(0.456418\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.87564 | 0.162639 | ||||||||
\(134\) | 4.53590 | 0.391842 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −1.73205 | −0.148522 | ||||||||
\(137\) | 3.53590 | 0.302092 | 0.151046 | − | 0.988527i | \(-0.451736\pi\) | ||||
0.151046 | + | 0.988527i | \(0.451736\pi\) | |||||||
\(138\) | −6.73205 | −0.573070 | ||||||||
\(139\) | −7.00000 | −0.593732 | −0.296866 | − | 0.954919i | \(-0.595942\pi\) | ||||
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | 0.267949 | 0.0226458 | ||||||||
\(141\) | 4.92820 | 0.415030 | ||||||||
\(142\) | −2.46410 | −0.206783 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.00000 | 0.415227 | ||||||||
\(146\) | 9.66025 | 0.799488 | ||||||||
\(147\) | −6.92820 | −0.571429 | ||||||||
\(148\) | −7.19615 | −0.591520 | ||||||||
\(149\) | −12.3923 | −1.01522 | −0.507609 | − | 0.861588i | \(-0.669470\pi\) | ||||
−0.507609 | + | 0.861588i | \(0.669470\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −9.80385 | −0.797826 | −0.398913 | − | 0.916989i | \(-0.630612\pi\) | ||||
−0.398913 | + | 0.916989i | \(0.630612\pi\) | |||||||
\(152\) | −7.00000 | −0.567775 | ||||||||
\(153\) | −1.73205 | −0.140028 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.19615 | −0.497687 | ||||||||
\(156\) | −4.46410 | −0.357414 | ||||||||
\(157\) | 2.66025 | 0.212311 | 0.106156 | − | 0.994350i | \(-0.466146\pi\) | ||||
0.106156 | + | 0.994350i | \(0.466146\pi\) | |||||||
\(158\) | 10.3923 | 0.826767 | ||||||||
\(159\) | 0.732051 | 0.0580554 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.80385 | 0.142163 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −2.19615 | −0.172016 | −0.0860080 | − | 0.996294i | \(-0.527411\pi\) | ||||
−0.0860080 | + | 0.996294i | \(0.527411\pi\) | |||||||
\(164\) | 4.19615 | 0.327664 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.53590 | −0.740129 | ||||||||
\(167\) | 13.4641 | 1.04188 | 0.520942 | − | 0.853592i | \(-0.325581\pi\) | ||||
0.520942 | + | 0.853592i | \(0.325581\pi\) | |||||||
\(168\) | −0.267949 | −0.0206727 | ||||||||
\(169\) | 6.92820 | 0.532939 | ||||||||
\(170\) | 1.73205 | 0.132842 | ||||||||
\(171\) | −7.00000 | −0.535303 | ||||||||
\(172\) | 2.19615 | 0.167455 | ||||||||
\(173\) | −6.33975 | −0.482002 | −0.241001 | − | 0.970525i | \(-0.577476\pi\) | ||||
−0.241001 | + | 0.970525i | \(0.577476\pi\) | |||||||
\(174\) | −5.00000 | −0.379049 | ||||||||
\(175\) | −0.267949 | −0.0202551 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.6603 | −0.876438 | ||||||||
\(178\) | 9.46410 | 0.709364 | ||||||||
\(179\) | 18.5885 | 1.38937 | 0.694683 | − | 0.719316i | \(-0.255545\pi\) | ||||
0.694683 | + | 0.719316i | \(0.255545\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | −9.80385 | −0.728714 | −0.364357 | − | 0.931259i | \(-0.618711\pi\) | ||||
−0.364357 | + | 0.931259i | \(0.618711\pi\) | |||||||
\(182\) | 1.19615 | 0.0886647 | ||||||||
\(183\) | −15.1244 | −1.11802 | ||||||||
\(184\) | −6.73205 | −0.496293 | ||||||||
\(185\) | 7.19615 | 0.529072 | ||||||||
\(186\) | 6.19615 | 0.454324 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.92820 | 0.359426 | ||||||||
\(189\) | −0.267949 | −0.0194904 | ||||||||
\(190\) | 7.00000 | 0.507833 | ||||||||
\(191\) | 13.9282 | 1.00781 | 0.503905 | − | 0.863759i | \(-0.331896\pi\) | ||||
0.503905 | + | 0.863759i | \(0.331896\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −23.3205 | −1.67865 | −0.839323 | − | 0.543632i | \(-0.817049\pi\) | ||||
−0.839323 | + | 0.543632i | \(0.817049\pi\) | |||||||
\(194\) | 8.73205 | 0.626925 | ||||||||
\(195\) | 4.46410 | 0.319681 | ||||||||
\(196\) | −6.92820 | −0.494872 | ||||||||
\(197\) | −2.53590 | −0.180675 | −0.0903376 | − | 0.995911i | \(-0.528795\pi\) | ||||
−0.0903376 | + | 0.995911i | \(0.528795\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.3205 | −1.08604 | −0.543021 | − | 0.839719i | \(-0.682720\pi\) | ||||
−0.543021 | + | 0.839719i | \(0.682720\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 4.53590 | 0.319938 | ||||||||
\(202\) | 1.53590 | 0.108065 | ||||||||
\(203\) | 1.33975 | 0.0940317 | ||||||||
\(204\) | −1.73205 | −0.121268 | ||||||||
\(205\) | −4.19615 | −0.293072 | ||||||||
\(206\) | 3.39230 | 0.236353 | ||||||||
\(207\) | −6.73205 | −0.467910 | ||||||||
\(208\) | −4.46410 | −0.309530 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.267949 | 0.0184903 | ||||||||
\(211\) | −27.3923 | −1.88576 | −0.942882 | − | 0.333127i | \(-0.891896\pi\) | ||||
−0.942882 | + | 0.333127i | \(0.891896\pi\) | |||||||
\(212\) | 0.732051 | 0.0502775 | ||||||||
\(213\) | −2.46410 | −0.168837 | ||||||||
\(214\) | −6.39230 | −0.436969 | ||||||||
\(215\) | −2.19615 | −0.149776 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.66025 | −0.112705 | ||||||||
\(218\) | −8.39230 | −0.568399 | ||||||||
\(219\) | 9.66025 | 0.652779 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.73205 | 0.520114 | ||||||||
\(222\) | −7.19615 | −0.482974 | ||||||||
\(223\) | −19.2487 | −1.28899 | −0.644495 | − | 0.764609i | \(-0.722932\pi\) | ||||
−0.644495 | + | 0.764609i | \(0.722932\pi\) | |||||||
\(224\) | −0.267949 | −0.0179031 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 13.8564 | 0.921714 | ||||||||
\(227\) | 20.5359 | 1.36302 | 0.681508 | − | 0.731811i | \(-0.261325\pi\) | ||||
0.681508 | + | 0.731811i | \(0.261325\pi\) | |||||||
\(228\) | −7.00000 | −0.463586 | ||||||||
\(229\) | 21.8564 | 1.44431 | 0.722156 | − | 0.691730i | \(-0.243151\pi\) | ||||
0.722156 | + | 0.691730i | \(0.243151\pi\) | |||||||
\(230\) | 6.73205 | 0.443898 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.00000 | −0.328266 | ||||||||
\(233\) | 22.9282 | 1.50208 | 0.751038 | − | 0.660259i | \(-0.229553\pi\) | ||||
0.751038 | + | 0.660259i | \(0.229553\pi\) | |||||||
\(234\) | −4.46410 | −0.291827 | ||||||||
\(235\) | −4.92820 | −0.321481 | ||||||||
\(236\) | −11.6603 | −0.759018 | ||||||||
\(237\) | 10.3923 | 0.675053 | ||||||||
\(238\) | 0.464102 | 0.0300832 | ||||||||
\(239\) | 7.19615 | 0.465480 | 0.232740 | − | 0.972539i | \(-0.425231\pi\) | ||||
0.232740 | + | 0.972539i | \(0.425231\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −11.1962 | −0.721208 | −0.360604 | − | 0.932719i | \(-0.617429\pi\) | ||||
−0.360604 | + | 0.932719i | \(0.617429\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −15.1244 | −0.968238 | ||||||||
\(245\) | 6.92820 | 0.442627 | ||||||||
\(246\) | 4.19615 | 0.267537 | ||||||||
\(247\) | 31.2487 | 1.98831 | ||||||||
\(248\) | 6.19615 | 0.393456 | ||||||||
\(249\) | −9.53590 | −0.604313 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −3.32051 | −0.209589 | −0.104794 | − | 0.994494i | \(-0.533418\pi\) | ||||
−0.104794 | + | 0.994494i | \(0.533418\pi\) | |||||||
\(252\) | −0.267949 | −0.0168792 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.53590 | −0.410099 | ||||||||
\(255\) | 1.73205 | 0.108465 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.7846 | −1.35889 | −0.679443 | − | 0.733728i | \(-0.737779\pi\) | ||||
−0.679443 | + | 0.733728i | \(0.737779\pi\) | |||||||
\(258\) | 2.19615 | 0.136726 | ||||||||
\(259\) | 1.92820 | 0.119813 | ||||||||
\(260\) | 4.46410 | 0.276852 | ||||||||
\(261\) | −5.00000 | −0.309492 | ||||||||
\(262\) | 3.12436 | 0.193023 | ||||||||
\(263\) | 6.73205 | 0.415116 | 0.207558 | − | 0.978223i | \(-0.433448\pi\) | ||||
0.207558 | + | 0.978223i | \(0.433448\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.732051 | −0.0449695 | ||||||||
\(266\) | 1.87564 | 0.115003 | ||||||||
\(267\) | 9.46410 | 0.579194 | ||||||||
\(268\) | 4.53590 | 0.277074 | ||||||||
\(269\) | −29.9808 | −1.82796 | −0.913980 | − | 0.405760i | \(-0.867007\pi\) | ||||
−0.913980 | + | 0.405760i | \(0.867007\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 3.85641 | 0.234260 | 0.117130 | − | 0.993117i | \(-0.462631\pi\) | ||||
0.117130 | + | 0.993117i | \(0.462631\pi\) | |||||||
\(272\) | −1.73205 | −0.105021 | ||||||||
\(273\) | 1.19615 | 0.0723944 | ||||||||
\(274\) | 3.53590 | 0.213611 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.73205 | −0.405222 | ||||||||
\(277\) | 29.8564 | 1.79390 | 0.896949 | − | 0.442134i | \(-0.145779\pi\) | ||||
0.896949 | + | 0.442134i | \(0.145779\pi\) | |||||||
\(278\) | −7.00000 | −0.419832 | ||||||||
\(279\) | 6.19615 | 0.370954 | ||||||||
\(280\) | 0.267949 | 0.0160130 | ||||||||
\(281\) | −21.1244 | −1.26017 | −0.630087 | − | 0.776525i | \(-0.716981\pi\) | ||||
−0.630087 | + | 0.776525i | \(0.716981\pi\) | |||||||
\(282\) | 4.92820 | 0.293470 | ||||||||
\(283\) | −12.3923 | −0.736646 | −0.368323 | − | 0.929698i | \(-0.620068\pi\) | ||||
−0.368323 | + | 0.929698i | \(0.620068\pi\) | |||||||
\(284\) | −2.46410 | −0.146218 | ||||||||
\(285\) | 7.00000 | 0.414644 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.12436 | −0.0663686 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | 5.00000 | 0.293610 | ||||||||
\(291\) | 8.73205 | 0.511882 | ||||||||
\(292\) | 9.66025 | 0.565324 | ||||||||
\(293\) | 1.07180 | 0.0626150 | 0.0313075 | − | 0.999510i | \(-0.490033\pi\) | ||||
0.0313075 | + | 0.999510i | \(0.490033\pi\) | |||||||
\(294\) | −6.92820 | −0.404061 | ||||||||
\(295\) | 11.6603 | 0.678886 | ||||||||
\(296\) | −7.19615 | −0.418268 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.3923 | −0.717867 | ||||||||
\(299\) | 30.0526 | 1.73798 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −0.588457 | −0.0339181 | ||||||||
\(302\) | −9.80385 | −0.564148 | ||||||||
\(303\) | 1.53590 | 0.0882351 | ||||||||
\(304\) | −7.00000 | −0.401478 | ||||||||
\(305\) | 15.1244 | 0.866018 | ||||||||
\(306\) | −1.73205 | −0.0990148 | ||||||||
\(307\) | −14.5885 | −0.832607 | −0.416304 | − | 0.909226i | \(-0.636675\pi\) | ||||
−0.416304 | + | 0.909226i | \(0.636675\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.39230 | 0.192981 | ||||||||
\(310\) | −6.19615 | −0.351918 | ||||||||
\(311\) | 26.9282 | 1.52696 | 0.763479 | − | 0.645832i | \(-0.223490\pi\) | ||||
0.763479 | + | 0.645832i | \(0.223490\pi\) | |||||||
\(312\) | −4.46410 | −0.252730 | ||||||||
\(313\) | 22.1962 | 1.25460 | 0.627300 | − | 0.778777i | \(-0.284160\pi\) | ||||
0.627300 | + | 0.778777i | \(0.284160\pi\) | |||||||
\(314\) | 2.66025 | 0.150127 | ||||||||
\(315\) | 0.267949 | 0.0150972 | ||||||||
\(316\) | 10.3923 | 0.584613 | ||||||||
\(317\) | −2.19615 | −0.123348 | −0.0616741 | − | 0.998096i | \(-0.519644\pi\) | ||||
−0.0616741 | + | 0.998096i | \(0.519644\pi\) | |||||||
\(318\) | 0.732051 | 0.0410514 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −6.39230 | −0.356784 | ||||||||
\(322\) | 1.80385 | 0.100524 | ||||||||
\(323\) | 12.1244 | 0.674617 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.46410 | −0.247624 | ||||||||
\(326\) | −2.19615 | −0.121634 | ||||||||
\(327\) | −8.39230 | −0.464096 | ||||||||
\(328\) | 4.19615 | 0.231694 | ||||||||
\(329\) | −1.32051 | −0.0728020 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.1244 | 1.65578 | 0.827892 | − | 0.560887i | \(-0.189540\pi\) | ||||
0.827892 | + | 0.560887i | \(0.189540\pi\) | |||||||
\(332\) | −9.53590 | −0.523350 | ||||||||
\(333\) | −7.19615 | −0.394347 | ||||||||
\(334\) | 13.4641 | 0.736723 | ||||||||
\(335\) | −4.53590 | −0.247823 | ||||||||
\(336\) | −0.267949 | −0.0146178 | ||||||||
\(337\) | 19.8038 | 1.07878 | 0.539392 | − | 0.842055i | \(-0.318654\pi\) | ||||
0.539392 | + | 0.842055i | \(0.318654\pi\) | |||||||
\(338\) | 6.92820 | 0.376845 | ||||||||
\(339\) | 13.8564 | 0.752577 | ||||||||
\(340\) | 1.73205 | 0.0939336 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −7.00000 | −0.378517 | ||||||||
\(343\) | 3.73205 | 0.201512 | ||||||||
\(344\) | 2.19615 | 0.118409 | ||||||||
\(345\) | 6.73205 | 0.362441 | ||||||||
\(346\) | −6.33975 | −0.340827 | ||||||||
\(347\) | 7.53590 | 0.404548 | 0.202274 | − | 0.979329i | \(-0.435167\pi\) | ||||
0.202274 | + | 0.979329i | \(0.435167\pi\) | |||||||
\(348\) | −5.00000 | −0.268028 | ||||||||
\(349\) | −34.0000 | −1.81998 | −0.909989 | − | 0.414632i | \(-0.863910\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | −0.267949 | −0.0143225 | ||||||||
\(351\) | −4.46410 | −0.238276 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.8564 | −1.37620 | −0.688099 | − | 0.725617i | \(-0.741554\pi\) | ||||
−0.688099 | + | 0.725617i | \(0.741554\pi\) | |||||||
\(354\) | −11.6603 | −0.619736 | ||||||||
\(355\) | 2.46410 | 0.130781 | ||||||||
\(356\) | 9.46410 | 0.501596 | ||||||||
\(357\) | 0.464102 | 0.0245629 | ||||||||
\(358\) | 18.5885 | 0.982430 | ||||||||
\(359\) | −31.1769 | −1.64545 | −0.822727 | − | 0.568436i | \(-0.807549\pi\) | ||||
−0.822727 | + | 0.568436i | \(0.807549\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | −9.80385 | −0.515279 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.19615 | 0.0626954 | ||||||||
\(365\) | −9.66025 | −0.505641 | ||||||||
\(366\) | −15.1244 | −0.790563 | ||||||||
\(367\) | −17.0000 | −0.887393 | −0.443696 | − | 0.896177i | \(-0.646333\pi\) | ||||
−0.443696 | + | 0.896177i | \(0.646333\pi\) | |||||||
\(368\) | −6.73205 | −0.350932 | ||||||||
\(369\) | 4.19615 | 0.218443 | ||||||||
\(370\) | 7.19615 | 0.374110 | ||||||||
\(371\) | −0.196152 | −0.0101837 | ||||||||
\(372\) | 6.19615 | 0.321256 | ||||||||
\(373\) | 3.39230 | 0.175647 | 0.0878234 | − | 0.996136i | \(-0.472009\pi\) | ||||
0.0878234 | + | 0.996136i | \(0.472009\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 4.92820 | 0.254153 | ||||||||
\(377\) | 22.3205 | 1.14956 | ||||||||
\(378\) | −0.267949 | −0.0137818 | ||||||||
\(379\) | −18.1244 | −0.930986 | −0.465493 | − | 0.885052i | \(-0.654123\pi\) | ||||
−0.465493 | + | 0.885052i | \(0.654123\pi\) | |||||||
\(380\) | 7.00000 | 0.359092 | ||||||||
\(381\) | −6.53590 | −0.334844 | ||||||||
\(382\) | 13.9282 | 0.712629 | ||||||||
\(383\) | −31.8564 | −1.62779 | −0.813893 | − | 0.581015i | \(-0.802656\pi\) | ||||
−0.813893 | + | 0.581015i | \(0.802656\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.3205 | −1.18698 | ||||||||
\(387\) | 2.19615 | 0.111637 | ||||||||
\(388\) | 8.73205 | 0.443303 | ||||||||
\(389\) | 35.7128 | 1.81071 | 0.905356 | − | 0.424654i | \(-0.139604\pi\) | ||||
0.905356 | + | 0.424654i | \(0.139604\pi\) | |||||||
\(390\) | 4.46410 | 0.226049 | ||||||||
\(391\) | 11.6603 | 0.589684 | ||||||||
\(392\) | −6.92820 | −0.349927 | ||||||||
\(393\) | 3.12436 | 0.157603 | ||||||||
\(394\) | −2.53590 | −0.127757 | ||||||||
\(395\) | −10.3923 | −0.522894 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.9808 | −1.20356 | −0.601780 | − | 0.798662i | \(-0.705542\pi\) | ||||
−0.601780 | + | 0.798662i | \(0.705542\pi\) | |||||||
\(398\) | −15.3205 | −0.767948 | ||||||||
\(399\) | 1.87564 | 0.0938997 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 31.2679 | 1.56145 | 0.780723 | − | 0.624877i | \(-0.214851\pi\) | ||||
0.780723 | + | 0.624877i | \(0.214851\pi\) | |||||||
\(402\) | 4.53590 | 0.226230 | ||||||||
\(403\) | −27.6603 | −1.37786 | ||||||||
\(404\) | 1.53590 | 0.0764138 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 1.33975 | 0.0664905 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.73205 | −0.0857493 | ||||||||
\(409\) | 0.928203 | 0.0458967 | 0.0229483 | − | 0.999737i | \(-0.492695\pi\) | ||||
0.0229483 | + | 0.999737i | \(0.492695\pi\) | |||||||
\(410\) | −4.19615 | −0.207233 | ||||||||
\(411\) | 3.53590 | 0.174413 | ||||||||
\(412\) | 3.39230 | 0.167127 | ||||||||
\(413\) | 3.12436 | 0.153739 | ||||||||
\(414\) | −6.73205 | −0.330862 | ||||||||
\(415\) | 9.53590 | 0.468099 | ||||||||
\(416\) | −4.46410 | −0.218871 | ||||||||
\(417\) | −7.00000 | −0.342791 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.2487 | 1.38004 | 0.690020 | − | 0.723790i | \(-0.257602\pi\) | ||||
0.690020 | + | 0.723790i | \(0.257602\pi\) | |||||||
\(420\) | 0.267949 | 0.0130746 | ||||||||
\(421\) | 1.66025 | 0.0809158 | 0.0404579 | − | 0.999181i | \(-0.487118\pi\) | ||||
0.0404579 | + | 0.999181i | \(0.487118\pi\) | |||||||
\(422\) | −27.3923 | −1.33344 | ||||||||
\(423\) | 4.92820 | 0.239617 | ||||||||
\(424\) | 0.732051 | 0.0355515 | ||||||||
\(425\) | −1.73205 | −0.0840168 | ||||||||
\(426\) | −2.46410 | −0.119386 | ||||||||
\(427\) | 4.05256 | 0.196117 | ||||||||
\(428\) | −6.39230 | −0.308984 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.19615 | −0.105908 | ||||||||
\(431\) | 37.4449 | 1.80366 | 0.901828 | − | 0.432096i | \(-0.142226\pi\) | ||||
0.901828 | + | 0.432096i | \(0.142226\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 4.00000 | 0.192228 | 0.0961139 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961139 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(434\) | −1.66025 | −0.0796947 | ||||||||
\(435\) | 5.00000 | 0.239732 | ||||||||
\(436\) | −8.39230 | −0.401919 | ||||||||
\(437\) | 47.1244 | 2.25426 | ||||||||
\(438\) | 9.66025 | 0.461585 | ||||||||
\(439\) | 14.0000 | 0.668184 | 0.334092 | − | 0.942541i | \(-0.391570\pi\) | ||||
0.334092 | + | 0.942541i | \(0.391570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.92820 | −0.329914 | ||||||||
\(442\) | 7.73205 | 0.367776 | ||||||||
\(443\) | 21.1962 | 1.00706 | 0.503530 | − | 0.863978i | \(-0.332034\pi\) | ||||
0.503530 | + | 0.863978i | \(0.332034\pi\) | |||||||
\(444\) | −7.19615 | −0.341514 | ||||||||
\(445\) | −9.46410 | −0.448641 | ||||||||
\(446\) | −19.2487 | −0.911453 | ||||||||
\(447\) | −12.3923 | −0.586136 | ||||||||
\(448\) | −0.267949 | −0.0126594 | ||||||||
\(449\) | −29.3205 | −1.38372 | −0.691860 | − | 0.722032i | \(-0.743209\pi\) | ||||
−0.691860 | + | 0.722032i | \(0.743209\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 13.8564 | 0.651751 | ||||||||
\(453\) | −9.80385 | −0.460625 | ||||||||
\(454\) | 20.5359 | 0.963797 | ||||||||
\(455\) | −1.19615 | −0.0560765 | ||||||||
\(456\) | −7.00000 | −0.327805 | ||||||||
\(457\) | 24.7321 | 1.15692 | 0.578458 | − | 0.815712i | \(-0.303655\pi\) | ||||
0.578458 | + | 0.815712i | \(0.303655\pi\) | |||||||
\(458\) | 21.8564 | 1.02128 | ||||||||
\(459\) | −1.73205 | −0.0808452 | ||||||||
\(460\) | 6.73205 | 0.313883 | ||||||||
\(461\) | 15.3923 | 0.716891 | 0.358446 | − | 0.933551i | \(-0.383307\pi\) | ||||
0.358446 | + | 0.933551i | \(0.383307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2487 | 1.12693 | 0.563467 | − | 0.826139i | \(-0.309467\pi\) | ||||
0.563467 | + | 0.826139i | \(0.309467\pi\) | |||||||
\(464\) | −5.00000 | −0.232119 | ||||||||
\(465\) | −6.19615 | −0.287340 | ||||||||
\(466\) | 22.9282 | 1.06213 | ||||||||
\(467\) | 39.1962 | 1.81378 | 0.906891 | − | 0.421366i | \(-0.138449\pi\) | ||||
0.906891 | + | 0.421366i | \(0.138449\pi\) | |||||||
\(468\) | −4.46410 | −0.206353 | ||||||||
\(469\) | −1.21539 | −0.0561215 | ||||||||
\(470\) | −4.92820 | −0.227321 | ||||||||
\(471\) | 2.66025 | 0.122578 | ||||||||
\(472\) | −11.6603 | −0.536707 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 10.3923 | 0.477334 | ||||||||
\(475\) | −7.00000 | −0.321182 | ||||||||
\(476\) | 0.464102 | 0.0212721 | ||||||||
\(477\) | 0.732051 | 0.0335183 | ||||||||
\(478\) | 7.19615 | 0.329144 | ||||||||
\(479\) | 25.9808 | 1.18709 | 0.593546 | − | 0.804800i | \(-0.297728\pi\) | ||||
0.593546 | + | 0.804800i | \(0.297728\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 32.1244 | 1.46474 | ||||||||
\(482\) | −11.1962 | −0.509971 | ||||||||
\(483\) | 1.80385 | 0.0820779 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.73205 | −0.396502 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −40.3205 | −1.82710 | −0.913548 | − | 0.406730i | \(-0.866669\pi\) | ||||
−0.913548 | + | 0.406730i | \(0.866669\pi\) | |||||||
\(488\) | −15.1244 | −0.684647 | ||||||||
\(489\) | −2.19615 | −0.0993134 | ||||||||
\(490\) | 6.92820 | 0.312984 | ||||||||
\(491\) | 4.73205 | 0.213554 | 0.106777 | − | 0.994283i | \(-0.465947\pi\) | ||||
0.106777 | + | 0.994283i | \(0.465947\pi\) | |||||||
\(492\) | 4.19615 | 0.189177 | ||||||||
\(493\) | 8.66025 | 0.390038 | ||||||||
\(494\) | 31.2487 | 1.40595 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.19615 | 0.278215 | ||||||||
\(497\) | 0.660254 | 0.0296164 | ||||||||
\(498\) | −9.53590 | −0.427314 | ||||||||
\(499\) | −16.8038 | −0.752244 | −0.376122 | − | 0.926570i | \(-0.622743\pi\) | ||||
−0.376122 | + | 0.926570i | \(0.622743\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 13.4641 | 0.601532 | ||||||||
\(502\) | −3.32051 | −0.148202 | ||||||||
\(503\) | −41.9090 | −1.86863 | −0.934314 | − | 0.356451i | \(-0.883987\pi\) | ||||
−0.934314 | + | 0.356451i | \(0.883987\pi\) | |||||||
\(504\) | −0.267949 | −0.0119354 | ||||||||
\(505\) | −1.53590 | −0.0683466 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.92820 | 0.307692 | ||||||||
\(508\) | −6.53590 | −0.289984 | ||||||||
\(509\) | −15.8564 | −0.702823 | −0.351411 | − | 0.936221i | \(-0.614298\pi\) | ||||
−0.351411 | + | 0.936221i | \(0.614298\pi\) | |||||||
\(510\) | 1.73205 | 0.0766965 | ||||||||
\(511\) | −2.58846 | −0.114507 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −7.00000 | −0.309058 | ||||||||
\(514\) | −21.7846 | −0.960878 | ||||||||
\(515\) | −3.39230 | −0.149483 | ||||||||
\(516\) | 2.19615 | 0.0966802 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.92820 | 0.0847204 | ||||||||
\(519\) | −6.33975 | −0.278284 | ||||||||
\(520\) | 4.46410 | 0.195764 | ||||||||
\(521\) | 12.5885 | 0.551510 | 0.275755 | − | 0.961228i | \(-0.411072\pi\) | ||||
0.275755 | + | 0.961228i | \(0.411072\pi\) | |||||||
\(522\) | −5.00000 | −0.218844 | ||||||||
\(523\) | 27.1244 | 1.18607 | 0.593033 | − | 0.805178i | \(-0.297931\pi\) | ||||
0.593033 | + | 0.805178i | \(0.297931\pi\) | |||||||
\(524\) | 3.12436 | 0.136488 | ||||||||
\(525\) | −0.267949 | −0.0116943 | ||||||||
\(526\) | 6.73205 | 0.293531 | ||||||||
\(527\) | −10.7321 | −0.467495 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3205 | 0.970457 | ||||||||
\(530\) | −0.732051 | −0.0317983 | ||||||||
\(531\) | −11.6603 | −0.506012 | ||||||||
\(532\) | 1.87564 | 0.0813195 | ||||||||
\(533\) | −18.7321 | −0.811375 | ||||||||
\(534\) | 9.46410 | 0.409552 | ||||||||
\(535\) | 6.39230 | 0.276363 | ||||||||
\(536\) | 4.53590 | 0.195921 | ||||||||
\(537\) | 18.5885 | 0.802151 | ||||||||
\(538\) | −29.9808 | −1.29256 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −27.2679 | −1.17234 | −0.586170 | − | 0.810188i | \(-0.699365\pi\) | ||||
−0.586170 | + | 0.810188i | \(0.699365\pi\) | |||||||
\(542\) | 3.85641 | 0.165647 | ||||||||
\(543\) | −9.80385 | −0.420723 | ||||||||
\(544\) | −1.73205 | −0.0742611 | ||||||||
\(545\) | 8.39230 | 0.359487 | ||||||||
\(546\) | 1.19615 | 0.0511906 | ||||||||
\(547\) | −3.85641 | −0.164888 | −0.0824440 | − | 0.996596i | \(-0.526273\pi\) | ||||
−0.0824440 | + | 0.996596i | \(0.526273\pi\) | |||||||
\(548\) | 3.53590 | 0.151046 | ||||||||
\(549\) | −15.1244 | −0.645492 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.0000 | 1.49105 | ||||||||
\(552\) | −6.73205 | −0.286535 | ||||||||
\(553\) | −2.78461 | −0.118414 | ||||||||
\(554\) | 29.8564 | 1.26848 | ||||||||
\(555\) | 7.19615 | 0.305460 | ||||||||
\(556\) | −7.00000 | −0.296866 | ||||||||
\(557\) | 2.67949 | 0.113534 | 0.0567669 | − | 0.998387i | \(-0.481921\pi\) | ||||
0.0567669 | + | 0.998387i | \(0.481921\pi\) | |||||||
\(558\) | 6.19615 | 0.262304 | ||||||||
\(559\) | −9.80385 | −0.414659 | ||||||||
\(560\) | 0.267949 | 0.0113229 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −21.1244 | −0.891077 | ||||||||
\(563\) | −12.4641 | −0.525299 | −0.262650 | − | 0.964891i | \(-0.584596\pi\) | ||||
−0.262650 | + | 0.964891i | \(0.584596\pi\) | |||||||
\(564\) | 4.92820 | 0.207515 | ||||||||
\(565\) | −13.8564 | −0.582943 | ||||||||
\(566\) | −12.3923 | −0.520887 | ||||||||
\(567\) | −0.267949 | −0.0112528 | ||||||||
\(568\) | −2.46410 | −0.103391 | ||||||||
\(569\) | −6.33975 | −0.265776 | −0.132888 | − | 0.991131i | \(-0.542425\pi\) | ||||
−0.132888 | + | 0.991131i | \(0.542425\pi\) | |||||||
\(570\) | 7.00000 | 0.293198 | ||||||||
\(571\) | −11.4641 | −0.479758 | −0.239879 | − | 0.970803i | \(-0.577108\pi\) | ||||
−0.239879 | + | 0.970803i | \(0.577108\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.9282 | 0.581859 | ||||||||
\(574\) | −1.12436 | −0.0469297 | ||||||||
\(575\) | −6.73205 | −0.280746 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 45.0333 | 1.87476 | 0.937381 | − | 0.348306i | \(-0.113243\pi\) | ||||
0.937381 | + | 0.348306i | \(0.113243\pi\) | |||||||
\(578\) | −14.0000 | −0.582323 | ||||||||
\(579\) | −23.3205 | −0.969167 | ||||||||
\(580\) | 5.00000 | 0.207614 | ||||||||
\(581\) | 2.55514 | 0.106005 | ||||||||
\(582\) | 8.73205 | 0.361955 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 9.66025 | 0.399744 | ||||||||
\(585\) | 4.46410 | 0.184568 | ||||||||
\(586\) | 1.07180 | 0.0442755 | ||||||||
\(587\) | −26.1244 | −1.07827 | −0.539134 | − | 0.842220i | \(-0.681248\pi\) | ||||
−0.539134 | + | 0.842220i | \(0.681248\pi\) | |||||||
\(588\) | −6.92820 | −0.285714 | ||||||||
\(589\) | −43.3731 | −1.78716 | ||||||||
\(590\) | 11.6603 | 0.480045 | ||||||||
\(591\) | −2.53590 | −0.104313 | ||||||||
\(592\) | −7.19615 | −0.295760 | ||||||||
\(593\) | 6.78461 | 0.278611 | 0.139305 | − | 0.990249i | \(-0.455513\pi\) | ||||
0.139305 | + | 0.990249i | \(0.455513\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.464102 | −0.0190263 | ||||||||
\(596\) | −12.3923 | −0.507609 | ||||||||
\(597\) | −15.3205 | −0.627027 | ||||||||
\(598\) | 30.0526 | 1.22894 | ||||||||
\(599\) | −8.24871 | −0.337033 | −0.168517 | − | 0.985699i | \(-0.553898\pi\) | ||||
−0.168517 | + | 0.985699i | \(0.553898\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | −0.588457 | −0.0239837 | ||||||||
\(603\) | 4.53590 | 0.184716 | ||||||||
\(604\) | −9.80385 | −0.398913 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.53590 | 0.0623916 | ||||||||
\(607\) | −3.87564 | −0.157308 | −0.0786538 | − | 0.996902i | \(-0.525062\pi\) | ||||
−0.0786538 | + | 0.996902i | \(0.525062\pi\) | |||||||
\(608\) | −7.00000 | −0.283887 | ||||||||
\(609\) | 1.33975 | 0.0542892 | ||||||||
\(610\) | 15.1244 | 0.612367 | ||||||||
\(611\) | −22.0000 | −0.890025 | ||||||||
\(612\) | −1.73205 | −0.0700140 | ||||||||
\(613\) | 22.4641 | 0.907317 | 0.453658 | − | 0.891176i | \(-0.350119\pi\) | ||||
0.453658 | + | 0.891176i | \(0.350119\pi\) | |||||||
\(614\) | −14.5885 | −0.588742 | ||||||||
\(615\) | −4.19615 | −0.169205 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.1051 | 1.41328 | 0.706639 | − | 0.707574i | \(-0.250210\pi\) | ||||
0.706639 | + | 0.707574i | \(0.250210\pi\) | |||||||
\(618\) | 3.39230 | 0.136459 | ||||||||
\(619\) | −36.1244 | −1.45196 | −0.725980 | − | 0.687716i | \(-0.758614\pi\) | ||||
−0.725980 | + | 0.687716i | \(0.758614\pi\) | |||||||
\(620\) | −6.19615 | −0.248843 | ||||||||
\(621\) | −6.73205 | −0.270148 | ||||||||
\(622\) | 26.9282 | 1.07972 | ||||||||
\(623\) | −2.53590 | −0.101599 | ||||||||
\(624\) | −4.46410 | −0.178707 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 22.1962 | 0.887137 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.66025 | 0.106156 | ||||||||
\(629\) | 12.4641 | 0.496976 | ||||||||
\(630\) | 0.267949 | 0.0106754 | ||||||||
\(631\) | −24.9808 | −0.994468 | −0.497234 | − | 0.867616i | \(-0.665651\pi\) | ||||
−0.497234 | + | 0.867616i | \(0.665651\pi\) | |||||||
\(632\) | 10.3923 | 0.413384 | ||||||||
\(633\) | −27.3923 | −1.08875 | ||||||||
\(634\) | −2.19615 | −0.0872204 | ||||||||
\(635\) | 6.53590 | 0.259369 | ||||||||
\(636\) | 0.732051 | 0.0290277 | ||||||||
\(637\) | 30.9282 | 1.22542 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.46410 | −0.0974784 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 4.14359 | 0.163662 | 0.0818311 | − | 0.996646i | \(-0.473923\pi\) | ||||
0.0818311 | + | 0.996646i | \(0.473923\pi\) | |||||||
\(642\) | −6.39230 | −0.252284 | ||||||||
\(643\) | 3.21539 | 0.126803 | 0.0634013 | − | 0.997988i | \(-0.479805\pi\) | ||||
0.0634013 | + | 0.997988i | \(0.479805\pi\) | |||||||
\(644\) | 1.80385 | 0.0710816 | ||||||||
\(645\) | −2.19615 | −0.0864734 | ||||||||
\(646\) | 12.1244 | 0.477026 | ||||||||
\(647\) | −33.4641 | −1.31561 | −0.657805 | − | 0.753188i | \(-0.728515\pi\) | ||||
−0.657805 | + | 0.753188i | \(0.728515\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.46410 | −0.175096 | ||||||||
\(651\) | −1.66025 | −0.0650705 | ||||||||
\(652\) | −2.19615 | −0.0860080 | ||||||||
\(653\) | 39.5167 | 1.54641 | 0.773203 | − | 0.634158i | \(-0.218653\pi\) | ||||
0.773203 | + | 0.634158i | \(0.218653\pi\) | |||||||
\(654\) | −8.39230 | −0.328165 | ||||||||
\(655\) | −3.12436 | −0.122079 | ||||||||
\(656\) | 4.19615 | 0.163832 | ||||||||
\(657\) | 9.66025 | 0.376882 | ||||||||
\(658\) | −1.32051 | −0.0514788 | ||||||||
\(659\) | −32.2487 | −1.25623 | −0.628116 | − | 0.778120i | \(-0.716174\pi\) | ||||
−0.628116 | + | 0.778120i | \(0.716174\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.4449 | 0.717422 | 0.358711 | − | 0.933449i | \(-0.383216\pi\) | ||||
0.358711 | + | 0.933449i | \(0.383216\pi\) | |||||||
\(662\) | 30.1244 | 1.17082 | ||||||||
\(663\) | 7.73205 | 0.300288 | ||||||||
\(664\) | −9.53590 | −0.370065 | ||||||||
\(665\) | −1.87564 | −0.0727344 | ||||||||
\(666\) | −7.19615 | −0.278845 | ||||||||
\(667\) | 33.6603 | 1.30333 | ||||||||
\(668\) | 13.4641 | 0.520942 | ||||||||
\(669\) | −19.2487 | −0.744198 | ||||||||
\(670\) | −4.53590 | −0.175237 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.267949 | −0.0103364 | ||||||||
\(673\) | −30.9282 | −1.19219 | −0.596097 | − | 0.802912i | \(-0.703283\pi\) | ||||
−0.596097 | + | 0.802912i | \(0.703283\pi\) | |||||||
\(674\) | 19.8038 | 0.762816 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 6.92820 | 0.266469 | ||||||||
\(677\) | 2.87564 | 0.110520 | 0.0552600 | − | 0.998472i | \(-0.482401\pi\) | ||||
0.0552600 | + | 0.998472i | \(0.482401\pi\) | |||||||
\(678\) | 13.8564 | 0.532152 | ||||||||
\(679\) | −2.33975 | −0.0897912 | ||||||||
\(680\) | 1.73205 | 0.0664211 | ||||||||
\(681\) | 20.5359 | 0.786937 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.3731 | 1.16219 | 0.581097 | − | 0.813835i | \(-0.302624\pi\) | ||||
0.581097 | + | 0.813835i | \(0.302624\pi\) | |||||||
\(684\) | −7.00000 | −0.267652 | ||||||||
\(685\) | −3.53590 | −0.135100 | ||||||||
\(686\) | 3.73205 | 0.142490 | ||||||||
\(687\) | 21.8564 | 0.833874 | ||||||||
\(688\) | 2.19615 | 0.0837275 | ||||||||
\(689\) | −3.26795 | −0.124499 | ||||||||
\(690\) | 6.73205 | 0.256285 | ||||||||
\(691\) | −32.5167 | −1.23699 | −0.618496 | − | 0.785788i | \(-0.712258\pi\) | ||||
−0.618496 | + | 0.785788i | \(0.712258\pi\) | |||||||
\(692\) | −6.33975 | −0.241001 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.53590 | 0.286059 | ||||||||
\(695\) | 7.00000 | 0.265525 | ||||||||
\(696\) | −5.00000 | −0.189525 | ||||||||
\(697\) | −7.26795 | −0.275293 | ||||||||
\(698\) | −34.0000 | −1.28692 | ||||||||
\(699\) | 22.9282 | 0.867224 | ||||||||
\(700\) | −0.267949 | −0.0101275 | ||||||||
\(701\) | 45.2487 | 1.70902 | 0.854510 | − | 0.519435i | \(-0.173857\pi\) | ||||
0.854510 | + | 0.519435i | \(0.173857\pi\) | |||||||
\(702\) | −4.46410 | −0.168487 | ||||||||
\(703\) | 50.3731 | 1.89986 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.92820 | −0.185607 | ||||||||
\(706\) | −25.8564 | −0.973119 | ||||||||
\(707\) | −0.411543 | −0.0154777 | ||||||||
\(708\) | −11.6603 | −0.438219 | ||||||||
\(709\) | −21.2679 | −0.798735 | −0.399367 | − | 0.916791i | \(-0.630770\pi\) | ||||
−0.399367 | + | 0.916791i | \(0.630770\pi\) | |||||||
\(710\) | 2.46410 | 0.0924761 | ||||||||
\(711\) | 10.3923 | 0.389742 | ||||||||
\(712\) | 9.46410 | 0.354682 | ||||||||
\(713\) | −41.7128 | −1.56216 | ||||||||
\(714\) | 0.464102 | 0.0173686 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.5885 | 0.694683 | ||||||||
\(717\) | 7.19615 | 0.268745 | ||||||||
\(718\) | −31.1769 | −1.16351 | ||||||||
\(719\) | −25.6077 | −0.955006 | −0.477503 | − | 0.878630i | \(-0.658458\pi\) | ||||
−0.477503 | + | 0.878630i | \(0.658458\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −0.908965 | −0.0338516 | ||||||||
\(722\) | 30.0000 | 1.11648 | ||||||||
\(723\) | −11.1962 | −0.416389 | ||||||||
\(724\) | −9.80385 | −0.364357 | ||||||||
\(725\) | −5.00000 | −0.185695 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.8564 | −1.81198 | −0.905992 | − | 0.423295i | \(-0.860873\pi\) | ||||
−0.905992 | + | 0.423295i | \(0.860873\pi\) | |||||||
\(728\) | 1.19615 | 0.0443324 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −9.66025 | −0.357542 | ||||||||
\(731\) | −3.80385 | −0.140690 | ||||||||
\(732\) | −15.1244 | −0.559012 | ||||||||
\(733\) | −36.7846 | −1.35867 | −0.679335 | − | 0.733828i | \(-0.737732\pi\) | ||||
−0.679335 | + | 0.733828i | \(0.737732\pi\) | |||||||
\(734\) | −17.0000 | −0.627481 | ||||||||
\(735\) | 6.92820 | 0.255551 | ||||||||
\(736\) | −6.73205 | −0.248147 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 4.19615 | 0.154463 | ||||||||
\(739\) | 19.0000 | 0.698926 | 0.349463 | − | 0.936950i | \(-0.386364\pi\) | ||||
0.349463 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(740\) | 7.19615 | 0.264536 | ||||||||
\(741\) | 31.2487 | 1.14795 | ||||||||
\(742\) | −0.196152 | −0.00720098 | ||||||||
\(743\) | 8.73205 | 0.320348 | 0.160174 | − | 0.987089i | \(-0.448794\pi\) | ||||
0.160174 | + | 0.987089i | \(0.448794\pi\) | |||||||
\(744\) | 6.19615 | 0.227162 | ||||||||
\(745\) | 12.3923 | 0.454019 | ||||||||
\(746\) | 3.39230 | 0.124201 | ||||||||
\(747\) | −9.53590 | −0.348900 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.71281 | 0.0625848 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 15.6603 | 0.571451 | 0.285725 | − | 0.958312i | \(-0.407765\pi\) | ||||
0.285725 | + | 0.958312i | \(0.407765\pi\) | |||||||
\(752\) | 4.92820 | 0.179713 | ||||||||
\(753\) | −3.32051 | −0.121006 | ||||||||
\(754\) | 22.3205 | 0.812865 | ||||||||
\(755\) | 9.80385 | 0.356799 | ||||||||
\(756\) | −0.267949 | −0.00974522 | ||||||||
\(757\) | 15.4641 | 0.562052 | 0.281026 | − | 0.959700i | \(-0.409325\pi\) | ||||
0.281026 | + | 0.959700i | \(0.409325\pi\) | |||||||
\(758\) | −18.1244 | −0.658306 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.00000 | 0.253917 | ||||||||
\(761\) | −2.24871 | −0.0815157 | −0.0407579 | − | 0.999169i | \(-0.512977\pi\) | ||||
−0.0407579 | + | 0.999169i | \(0.512977\pi\) | |||||||
\(762\) | −6.53590 | −0.236771 | ||||||||
\(763\) | 2.24871 | 0.0814088 | ||||||||
\(764\) | 13.9282 | 0.503905 | ||||||||
\(765\) | 1.73205 | 0.0626224 | ||||||||
\(766\) | −31.8564 | −1.15102 | ||||||||
\(767\) | 52.0526 | 1.87951 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 31.8372 | 1.14808 | 0.574039 | − | 0.818828i | \(-0.305376\pi\) | ||||
0.574039 | + | 0.818828i | \(0.305376\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.7846 | −0.784554 | ||||||||
\(772\) | −23.3205 | −0.839323 | ||||||||
\(773\) | −12.3397 | −0.443830 | −0.221915 | − | 0.975066i | \(-0.571231\pi\) | ||||
−0.221915 | + | 0.975066i | \(0.571231\pi\) | |||||||
\(774\) | 2.19615 | 0.0789391 | ||||||||
\(775\) | 6.19615 | 0.222572 | ||||||||
\(776\) | 8.73205 | 0.313462 | ||||||||
\(777\) | 1.92820 | 0.0691739 | ||||||||
\(778\) | 35.7128 | 1.28037 | ||||||||
\(779\) | −29.3731 | −1.05240 | ||||||||
\(780\) | 4.46410 | 0.159840 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 11.6603 | 0.416970 | ||||||||
\(783\) | −5.00000 | −0.178685 | ||||||||
\(784\) | −6.92820 | −0.247436 | ||||||||
\(785\) | −2.66025 | −0.0949485 | ||||||||
\(786\) | 3.12436 | 0.111442 | ||||||||
\(787\) | 27.8038 | 0.991100 | 0.495550 | − | 0.868579i | \(-0.334967\pi\) | ||||
0.495550 | + | 0.868579i | \(0.334967\pi\) | |||||||
\(788\) | −2.53590 | −0.0903376 | ||||||||
\(789\) | 6.73205 | 0.239667 | ||||||||
\(790\) | −10.3923 | −0.369742 | ||||||||
\(791\) | −3.71281 | −0.132012 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 67.5167 | 2.39759 | ||||||||
\(794\) | −23.9808 | −0.851045 | ||||||||
\(795\) | −0.732051 | −0.0259632 | ||||||||
\(796\) | −15.3205 | −0.543021 | ||||||||
\(797\) | −26.8756 | −0.951984 | −0.475992 | − | 0.879450i | \(-0.657911\pi\) | ||||
−0.475992 | + | 0.879450i | \(0.657911\pi\) | |||||||
\(798\) | 1.87564 | 0.0663971 | ||||||||
\(799\) | −8.53590 | −0.301978 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 9.46410 | 0.334398 | ||||||||
\(802\) | 31.2679 | 1.10411 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4.53590 | 0.159969 | ||||||||
\(805\) | −1.80385 | −0.0635773 | ||||||||
\(806\) | −27.6603 | −0.974291 | ||||||||
\(807\) | −29.9808 | −1.05537 | ||||||||
\(808\) | 1.53590 | 0.0540327 | ||||||||
\(809\) | 8.19615 | 0.288161 | 0.144081 | − | 0.989566i | \(-0.453978\pi\) | ||||
0.144081 | + | 0.989566i | \(0.453978\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −18.1769 | −0.638278 | −0.319139 | − | 0.947708i | \(-0.603394\pi\) | ||||
−0.319139 | + | 0.947708i | \(0.603394\pi\) | |||||||
\(812\) | 1.33975 | 0.0470159 | ||||||||
\(813\) | 3.85641 | 0.135250 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.19615 | 0.0769279 | ||||||||
\(816\) | −1.73205 | −0.0606339 | ||||||||
\(817\) | −15.3731 | −0.537836 | ||||||||
\(818\) | 0.928203 | 0.0324539 | ||||||||
\(819\) | 1.19615 | 0.0417969 | ||||||||
\(820\) | −4.19615 | −0.146536 | ||||||||
\(821\) | 44.3923 | 1.54930 | 0.774651 | − | 0.632389i | \(-0.217926\pi\) | ||||
0.774651 | + | 0.632389i | \(0.217926\pi\) | |||||||
\(822\) | 3.53590 | 0.123329 | ||||||||
\(823\) | −36.3205 | −1.26605 | −0.633027 | − | 0.774130i | \(-0.718188\pi\) | ||||
−0.633027 | + | 0.774130i | \(0.718188\pi\) | |||||||
\(824\) | 3.39230 | 0.118177 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.12436 | 0.108710 | ||||||||
\(827\) | 21.0000 | 0.730242 | 0.365121 | − | 0.930960i | \(-0.381028\pi\) | ||||
0.365121 | + | 0.930960i | \(0.381028\pi\) | |||||||
\(828\) | −6.73205 | −0.233955 | ||||||||
\(829\) | 10.5885 | 0.367752 | 0.183876 | − | 0.982949i | \(-0.441135\pi\) | ||||
0.183876 | + | 0.982949i | \(0.441135\pi\) | |||||||
\(830\) | 9.53590 | 0.330996 | ||||||||
\(831\) | 29.8564 | 1.03571 | ||||||||
\(832\) | −4.46410 | −0.154765 | ||||||||
\(833\) | 12.0000 | 0.415775 | ||||||||
\(834\) | −7.00000 | −0.242390 | ||||||||
\(835\) | −13.4641 | −0.465944 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.19615 | 0.214170 | ||||||||
\(838\) | 28.2487 | 0.975836 | ||||||||
\(839\) | −22.4641 | −0.775547 | −0.387773 | − | 0.921755i | \(-0.626756\pi\) | ||||
−0.387773 | + | 0.921755i | \(0.626756\pi\) | |||||||
\(840\) | 0.267949 | 0.00924513 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 1.66025 | 0.0572161 | ||||||||
\(843\) | −21.1244 | −0.727561 | ||||||||
\(844\) | −27.3923 | −0.942882 | ||||||||
\(845\) | −6.92820 | −0.238337 | ||||||||
\(846\) | 4.92820 | 0.169435 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.732051 | 0.0251387 | ||||||||
\(849\) | −12.3923 | −0.425303 | ||||||||
\(850\) | −1.73205 | −0.0594089 | ||||||||
\(851\) | 48.4449 | 1.66067 | ||||||||
\(852\) | −2.46410 | −0.0844187 | ||||||||
\(853\) | −28.7128 | −0.983108 | −0.491554 | − | 0.870847i | \(-0.663571\pi\) | ||||
−0.491554 | + | 0.870847i | \(0.663571\pi\) | |||||||
\(854\) | 4.05256 | 0.138676 | ||||||||
\(855\) | 7.00000 | 0.239395 | ||||||||
\(856\) | −6.39230 | −0.218484 | ||||||||
\(857\) | −36.5167 | −1.24739 | −0.623693 | − | 0.781670i | \(-0.714368\pi\) | ||||
−0.623693 | + | 0.781670i | \(0.714368\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.67949 | −0.0914231 | −0.0457115 | − | 0.998955i | \(-0.514556\pi\) | ||||
−0.0457115 | + | 0.998955i | \(0.514556\pi\) | |||||||
\(860\) | −2.19615 | −0.0748882 | ||||||||
\(861\) | −1.12436 | −0.0383179 | ||||||||
\(862\) | 37.4449 | 1.27538 | ||||||||
\(863\) | −11.4641 | −0.390243 | −0.195121 | − | 0.980779i | \(-0.562510\pi\) | ||||
−0.195121 | + | 0.980779i | \(0.562510\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 6.33975 | 0.215558 | ||||||||
\(866\) | 4.00000 | 0.135926 | ||||||||
\(867\) | −14.0000 | −0.475465 | ||||||||
\(868\) | −1.66025 | −0.0563527 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 5.00000 | 0.169516 | ||||||||
\(871\) | −20.2487 | −0.686101 | ||||||||
\(872\) | −8.39230 | −0.284199 | ||||||||
\(873\) | 8.73205 | 0.295535 | ||||||||
\(874\) | 47.1244 | 1.59401 | ||||||||
\(875\) | 0.267949 | 0.00905834 | ||||||||
\(876\) | 9.66025 | 0.326390 | ||||||||
\(877\) | 22.4641 | 0.758559 | 0.379279 | − | 0.925282i | \(-0.376172\pi\) | ||||
0.379279 | + | 0.925282i | \(0.376172\pi\) | |||||||
\(878\) | 14.0000 | 0.472477 | ||||||||
\(879\) | 1.07180 | 0.0361508 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.5885 | −0.895788 | −0.447894 | − | 0.894087i | \(-0.647826\pi\) | ||||
−0.447894 | + | 0.894087i | \(0.647826\pi\) | |||||||
\(882\) | −6.92820 | −0.233285 | ||||||||
\(883\) | 26.0526 | 0.876738 | 0.438369 | − | 0.898795i | \(-0.355556\pi\) | ||||
0.438369 | + | 0.898795i | \(0.355556\pi\) | |||||||
\(884\) | 7.73205 | 0.260057 | ||||||||
\(885\) | 11.6603 | 0.391955 | ||||||||
\(886\) | 21.1962 | 0.712099 | ||||||||
\(887\) | 36.7846 | 1.23511 | 0.617553 | − | 0.786529i | \(-0.288124\pi\) | ||||
0.617553 | + | 0.786529i | \(0.288124\pi\) | |||||||
\(888\) | −7.19615 | −0.241487 | ||||||||
\(889\) | 1.75129 | 0.0587363 | ||||||||
\(890\) | −9.46410 | −0.317237 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.2487 | −0.644495 | ||||||||
\(893\) | −34.4974 | −1.15441 | ||||||||
\(894\) | −12.3923 | −0.414461 | ||||||||
\(895\) | −18.5885 | −0.621344 | ||||||||
\(896\) | −0.267949 | −0.00895155 | ||||||||
\(897\) | 30.0526 | 1.00343 | ||||||||
\(898\) | −29.3205 | −0.978438 | ||||||||
\(899\) | −30.9808 | −1.03327 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −1.26795 | −0.0422415 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.588457 | −0.0195826 | ||||||||
\(904\) | 13.8564 | 0.460857 | ||||||||
\(905\) | 9.80385 | 0.325891 | ||||||||
\(906\) | −9.80385 | −0.325711 | ||||||||
\(907\) | −48.9282 | −1.62463 | −0.812317 | − | 0.583216i | \(-0.801794\pi\) | ||||
−0.812317 | + | 0.583216i | \(0.801794\pi\) | |||||||
\(908\) | 20.5359 | 0.681508 | ||||||||
\(909\) | 1.53590 | 0.0509425 | ||||||||
\(910\) | −1.19615 | −0.0396521 | ||||||||
\(911\) | 45.1051 | 1.49440 | 0.747200 | − | 0.664600i | \(-0.231398\pi\) | ||||
0.747200 | + | 0.664600i | \(0.231398\pi\) | |||||||
\(912\) | −7.00000 | −0.231793 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 24.7321 | 0.818064 | ||||||||
\(915\) | 15.1244 | 0.499996 | ||||||||
\(916\) | 21.8564 | 0.722156 | ||||||||
\(917\) | −0.837169 | −0.0276457 | ||||||||
\(918\) | −1.73205 | −0.0571662 | ||||||||
\(919\) | −36.0526 | −1.18926 | −0.594632 | − | 0.803998i | \(-0.702702\pi\) | ||||
−0.594632 | + | 0.803998i | \(0.702702\pi\) | |||||||
\(920\) | 6.73205 | 0.221949 | ||||||||
\(921\) | −14.5885 | −0.480706 | ||||||||
\(922\) | 15.3923 | 0.506919 | ||||||||
\(923\) | 11.0000 | 0.362069 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.19615 | −0.236608 | ||||||||
\(926\) | 24.2487 | 0.796862 | ||||||||
\(927\) | 3.39230 | 0.111418 | ||||||||
\(928\) | −5.00000 | −0.164133 | ||||||||
\(929\) | −31.1244 | −1.02116 | −0.510578 | − | 0.859831i | \(-0.670569\pi\) | ||||
−0.510578 | + | 0.859831i | \(0.670569\pi\) | |||||||
\(930\) | −6.19615 | −0.203180 | ||||||||
\(931\) | 48.4974 | 1.58944 | ||||||||
\(932\) | 22.9282 | 0.751038 | ||||||||
\(933\) | 26.9282 | 0.881590 | ||||||||
\(934\) | 39.1962 | 1.28254 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.46410 | −0.145914 | ||||||||
\(937\) | −8.92820 | −0.291672 | −0.145836 | − | 0.989309i | \(-0.546587\pi\) | ||||
−0.145836 | + | 0.989309i | \(0.546587\pi\) | |||||||
\(938\) | −1.21539 | −0.0396839 | ||||||||
\(939\) | 22.1962 | 0.724344 | ||||||||
\(940\) | −4.92820 | −0.160740 | ||||||||
\(941\) | 19.9282 | 0.649641 | 0.324820 | − | 0.945776i | \(-0.394696\pi\) | ||||
0.324820 | + | 0.945776i | \(0.394696\pi\) | |||||||
\(942\) | 2.66025 | 0.0866758 | ||||||||
\(943\) | −28.2487 | −0.919905 | ||||||||
\(944\) | −11.6603 | −0.379509 | ||||||||
\(945\) | 0.267949 | 0.00871639 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.3731 | −0.922001 | −0.461000 | − | 0.887400i | \(-0.652509\pi\) | ||||
−0.461000 | + | 0.887400i | \(0.652509\pi\) | |||||||
\(948\) | 10.3923 | 0.337526 | ||||||||
\(949\) | −43.1244 | −1.39988 | ||||||||
\(950\) | −7.00000 | −0.227110 | ||||||||
\(951\) | −2.19615 | −0.0712151 | ||||||||
\(952\) | 0.464102 | 0.0150416 | ||||||||
\(953\) | 30.7846 | 0.997211 | 0.498606 | − | 0.866829i | \(-0.333846\pi\) | ||||
0.498606 | + | 0.866829i | \(0.333846\pi\) | |||||||
\(954\) | 0.732051 | 0.0237010 | ||||||||
\(955\) | −13.9282 | −0.450706 | ||||||||
\(956\) | 7.19615 | 0.232740 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.9808 | 0.839400 | ||||||||
\(959\) | −0.947441 | −0.0305945 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 7.39230 | 0.238461 | ||||||||
\(962\) | 32.1244 | 1.03573 | ||||||||
\(963\) | −6.39230 | −0.205989 | ||||||||
\(964\) | −11.1962 | −0.360604 | ||||||||
\(965\) | 23.3205 | 0.750714 | ||||||||
\(966\) | 1.80385 | 0.0580378 | ||||||||
\(967\) | 15.1769 | 0.488057 | 0.244028 | − | 0.969768i | \(-0.421531\pi\) | ||||
0.244028 | + | 0.969768i | \(0.421531\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.1244 | 0.389490 | ||||||||
\(970\) | −8.73205 | −0.280369 | ||||||||
\(971\) | −60.3923 | −1.93808 | −0.969041 | − | 0.246901i | \(-0.920588\pi\) | ||||
−0.969041 | + | 0.246901i | \(0.920588\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 1.87564 | 0.0601304 | ||||||||
\(974\) | −40.3205 | −1.29195 | ||||||||
\(975\) | −4.46410 | −0.142966 | ||||||||
\(976\) | −15.1244 | −0.484119 | ||||||||
\(977\) | 55.8564 | 1.78700 | 0.893502 | − | 0.449058i | \(-0.148241\pi\) | ||||
0.893502 | + | 0.449058i | \(0.148241\pi\) | |||||||
\(978\) | −2.19615 | −0.0702252 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.92820 | 0.221313 | ||||||||
\(981\) | −8.39230 | −0.267946 | ||||||||
\(982\) | 4.73205 | 0.151006 | ||||||||
\(983\) | −41.9090 | −1.33669 | −0.668344 | − | 0.743852i | \(-0.732997\pi\) | ||||
−0.668344 | + | 0.743852i | \(0.732997\pi\) | |||||||
\(984\) | 4.19615 | 0.133768 | ||||||||
\(985\) | 2.53590 | 0.0808004 | ||||||||
\(986\) | 8.66025 | 0.275799 | ||||||||
\(987\) | −1.32051 | −0.0420322 | ||||||||
\(988\) | 31.2487 | 0.994154 | ||||||||
\(989\) | −14.7846 | −0.470123 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.21539 | −0.0386081 | −0.0193041 | − | 0.999814i | \(-0.506145\pi\) | ||||
−0.0193041 | + | 0.999814i | \(0.506145\pi\) | |||||||
\(992\) | 6.19615 | 0.196728 | ||||||||
\(993\) | 30.1244 | 0.955968 | ||||||||
\(994\) | 0.660254 | 0.0209420 | ||||||||
\(995\) | 15.3205 | 0.485693 | ||||||||
\(996\) | −9.53590 | −0.302157 | ||||||||
\(997\) | 48.7128 | 1.54275 | 0.771375 | − | 0.636381i | \(-0.219569\pi\) | ||||
0.771375 | + | 0.636381i | \(0.219569\pi\) | |||||||
\(998\) | −16.8038 | −0.531917 | ||||||||
\(999\) | −7.19615 | −0.227676 |
(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 | 3630.2.a.bo.1.2 | yes | 2 | |
11.10 | odd | 2 | 3630.2.a.bg.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3630.2.a.bg.1.1 | ✓ | 2 | 11.10 | odd | 2 | ||
3630.2.a.bo.1.2 | yes | 2 | 1.1 | even | 1 | trivial |