Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 | ||||||||
\(3\) | −1.80649 | −1.04298 | −0.521488 | − | 0.853258i | \(-0.674623\pi\) | ||||
−0.521488 | + | 0.853258i | \(0.674623\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.991336 | 0.443339 | 0.221670 | − | 0.975122i | \(-0.428849\pi\) | ||||
0.221670 | + | 0.975122i | \(0.428849\pi\) | |||||||
\(6\) | 1.80649 | 0.737496 | ||||||||
\(7\) | 3.46798 | 1.31077 | 0.655387 | − | 0.755293i | \(-0.272506\pi\) | ||||
0.655387 | + | 0.755293i | \(0.272506\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.263400 | 0.0878000 | ||||||||
\(10\) | −0.991336 | −0.313488 | ||||||||
\(11\) | −4.83823 | −1.45878 | −0.729390 | − | 0.684098i | \(-0.760196\pi\) | ||||
−0.729390 | + | 0.684098i | \(0.760196\pi\) | |||||||
\(12\) | −1.80649 | −0.521488 | ||||||||
\(13\) | 4.44127 | 1.23179 | 0.615894 | − | 0.787829i | \(-0.288795\pi\) | ||||
0.615894 | + | 0.787829i | \(0.288795\pi\) | |||||||
\(14\) | −3.46798 | −0.926857 | ||||||||
\(15\) | −1.79084 | −0.462392 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.57513 | 1.10963 | 0.554816 | − | 0.831973i | \(-0.312789\pi\) | ||||
0.554816 | + | 0.831973i | \(0.312789\pi\) | |||||||
\(18\) | −0.263400 | −0.0620840 | ||||||||
\(19\) | 5.87465 | 1.34774 | 0.673869 | − | 0.738851i | \(-0.264631\pi\) | ||||
0.673869 | + | 0.738851i | \(0.264631\pi\) | |||||||
\(20\) | 0.991336 | 0.221670 | ||||||||
\(21\) | −6.26487 | −1.36711 | ||||||||
\(22\) | 4.83823 | 1.03151 | ||||||||
\(23\) | 0.390058 | 0.0813328 | 0.0406664 | − | 0.999173i | \(-0.487052\pi\) | ||||
0.0406664 | + | 0.999173i | \(0.487052\pi\) | |||||||
\(24\) | 1.80649 | 0.368748 | ||||||||
\(25\) | −4.01725 | −0.803450 | ||||||||
\(26\) | −4.44127 | −0.871005 | ||||||||
\(27\) | 4.94364 | 0.951403 | ||||||||
\(28\) | 3.46798 | 0.655387 | ||||||||
\(29\) | −5.36675 | −0.996580 | −0.498290 | − | 0.867011i | \(-0.666038\pi\) | ||||
−0.498290 | + | 0.867011i | \(0.666038\pi\) | |||||||
\(30\) | 1.79084 | 0.326961 | ||||||||
\(31\) | −3.85804 | −0.692924 | −0.346462 | − | 0.938064i | \(-0.612617\pi\) | ||||
−0.346462 | + | 0.938064i | \(0.612617\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 8.74020 | 1.52147 | ||||||||
\(34\) | −4.57513 | −0.784628 | ||||||||
\(35\) | 3.43794 | 0.581117 | ||||||||
\(36\) | 0.263400 | 0.0439000 | ||||||||
\(37\) | 1.64933 | 0.271149 | 0.135574 | − | 0.990767i | \(-0.456712\pi\) | ||||
0.135574 | + | 0.990767i | \(0.456712\pi\) | |||||||
\(38\) | −5.87465 | −0.952995 | ||||||||
\(39\) | −8.02311 | −1.28473 | ||||||||
\(40\) | −0.991336 | −0.156744 | ||||||||
\(41\) | 0.615159 | 0.0960717 | 0.0480359 | − | 0.998846i | \(-0.484704\pi\) | ||||
0.0480359 | + | 0.998846i | \(0.484704\pi\) | |||||||
\(42\) | 6.26487 | 0.966690 | ||||||||
\(43\) | 3.89233 | 0.593575 | 0.296787 | − | 0.954944i | \(-0.404085\pi\) | ||||
0.296787 | + | 0.954944i | \(0.404085\pi\) | |||||||
\(44\) | −4.83823 | −0.729390 | ||||||||
\(45\) | 0.261118 | 0.0389252 | ||||||||
\(46\) | −0.390058 | −0.0575110 | ||||||||
\(47\) | 9.56451 | 1.39513 | 0.697564 | − | 0.716523i | \(-0.254268\pi\) | ||||
0.697564 | + | 0.716523i | \(0.254268\pi\) | |||||||
\(48\) | −1.80649 | −0.260744 | ||||||||
\(49\) | 5.02690 | 0.718128 | ||||||||
\(50\) | 4.01725 | 0.568125 | ||||||||
\(51\) | −8.26492 | −1.15732 | ||||||||
\(52\) | 4.44127 | 0.615894 | ||||||||
\(53\) | 5.41601 | 0.743947 | 0.371973 | − | 0.928243i | \(-0.378681\pi\) | ||||
0.371973 | + | 0.928243i | \(0.378681\pi\) | |||||||
\(54\) | −4.94364 | −0.672744 | ||||||||
\(55\) | −4.79631 | −0.646735 | ||||||||
\(56\) | −3.46798 | −0.463429 | ||||||||
\(57\) | −10.6125 | −1.40566 | ||||||||
\(58\) | 5.36675 | 0.704688 | ||||||||
\(59\) | 2.15882 | 0.281055 | 0.140527 | − | 0.990077i | \(-0.455120\pi\) | ||||
0.140527 | + | 0.990077i | \(0.455120\pi\) | |||||||
\(60\) | −1.79084 | −0.231196 | ||||||||
\(61\) | −0.659535 | −0.0844448 | −0.0422224 | − | 0.999108i | \(-0.513444\pi\) | ||||
−0.0422224 | + | 0.999108i | \(0.513444\pi\) | |||||||
\(62\) | 3.85804 | 0.489972 | ||||||||
\(63\) | 0.913467 | 0.115086 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.40280 | 0.546100 | ||||||||
\(66\) | −8.74020 | −1.07584 | ||||||||
\(67\) | −3.75828 | −0.459147 | −0.229574 | − | 0.973291i | \(-0.573733\pi\) | ||||
−0.229574 | + | 0.973291i | \(0.573733\pi\) | |||||||
\(68\) | 4.57513 | 0.554816 | ||||||||
\(69\) | −0.704636 | −0.0848282 | ||||||||
\(70\) | −3.43794 | −0.410912 | ||||||||
\(71\) | 7.60582 | 0.902644 | 0.451322 | − | 0.892361i | \(-0.350953\pi\) | ||||
0.451322 | + | 0.892361i | \(0.350953\pi\) | |||||||
\(72\) | −0.263400 | −0.0310420 | ||||||||
\(73\) | 7.96823 | 0.932610 | 0.466305 | − | 0.884624i | \(-0.345585\pi\) | ||||
0.466305 | + | 0.884624i | \(0.345585\pi\) | |||||||
\(74\) | −1.64933 | −0.191731 | ||||||||
\(75\) | 7.25712 | 0.837980 | ||||||||
\(76\) | 5.87465 | 0.673869 | ||||||||
\(77\) | −16.7789 | −1.91213 | ||||||||
\(78\) | 8.02311 | 0.908438 | ||||||||
\(79\) | 7.32579 | 0.824216 | 0.412108 | − | 0.911135i | \(-0.364793\pi\) | ||||
0.412108 | + | 0.911135i | \(0.364793\pi\) | |||||||
\(80\) | 0.991336 | 0.110835 | ||||||||
\(81\) | −9.72082 | −1.08009 | ||||||||
\(82\) | −0.615159 | −0.0679330 | ||||||||
\(83\) | −4.60880 | −0.505881 | −0.252941 | − | 0.967482i | \(-0.581398\pi\) | ||||
−0.252941 | + | 0.967482i | \(0.581398\pi\) | |||||||
\(84\) | −6.26487 | −0.683553 | ||||||||
\(85\) | 4.53549 | 0.491943 | ||||||||
\(86\) | −3.89233 | −0.419721 | ||||||||
\(87\) | 9.69496 | 1.03941 | ||||||||
\(88\) | 4.83823 | 0.515757 | ||||||||
\(89\) | −17.5829 | −1.86378 | −0.931892 | − | 0.362736i | \(-0.881843\pi\) | ||||
−0.931892 | + | 0.362736i | \(0.881843\pi\) | |||||||
\(90\) | −0.261118 | −0.0275243 | ||||||||
\(91\) | 15.4023 | 1.61459 | ||||||||
\(92\) | 0.390058 | 0.0406664 | ||||||||
\(93\) | 6.96950 | 0.722704 | ||||||||
\(94\) | −9.56451 | −0.986504 | ||||||||
\(95\) | 5.82376 | 0.597505 | ||||||||
\(96\) | 1.80649 | 0.184374 | ||||||||
\(97\) | −0.900577 | −0.0914397 | −0.0457199 | − | 0.998954i | \(-0.514558\pi\) | ||||
−0.0457199 | + | 0.998954i | \(0.514558\pi\) | |||||||
\(98\) | −5.02690 | −0.507793 | ||||||||
\(99\) | −1.27439 | −0.128081 | ||||||||
\(100\) | −4.01725 | −0.401725 | ||||||||
\(101\) | −12.6829 | −1.26200 | −0.630999 | − | 0.775784i | \(-0.717355\pi\) | ||||
−0.630999 | + | 0.775784i | \(0.717355\pi\) | |||||||
\(102\) | 8.26492 | 0.818349 | ||||||||
\(103\) | 5.27874 | 0.520130 | 0.260065 | − | 0.965591i | \(-0.416256\pi\) | ||||
0.260065 | + | 0.965591i | \(0.416256\pi\) | |||||||
\(104\) | −4.44127 | −0.435503 | ||||||||
\(105\) | −6.21059 | −0.606092 | ||||||||
\(106\) | −5.41601 | −0.526050 | ||||||||
\(107\) | 3.15234 | 0.304748 | 0.152374 | − | 0.988323i | \(-0.451308\pi\) | ||||
0.152374 | + | 0.988323i | \(0.451308\pi\) | |||||||
\(108\) | 4.94364 | 0.475702 | ||||||||
\(109\) | 2.14772 | 0.205715 | 0.102857 | − | 0.994696i | \(-0.467201\pi\) | ||||
0.102857 | + | 0.994696i | \(0.467201\pi\) | |||||||
\(110\) | 4.79631 | 0.457310 | ||||||||
\(111\) | −2.97950 | −0.282802 | ||||||||
\(112\) | 3.46798 | 0.327693 | ||||||||
\(113\) | −4.18617 | −0.393802 | −0.196901 | − | 0.980423i | \(-0.563088\pi\) | ||||
−0.196901 | + | 0.980423i | \(0.563088\pi\) | |||||||
\(114\) | 10.6125 | 0.993951 | ||||||||
\(115\) | 0.386679 | 0.0360580 | ||||||||
\(116\) | −5.36675 | −0.498290 | ||||||||
\(117\) | 1.16983 | 0.108151 | ||||||||
\(118\) | −2.15882 | −0.198736 | ||||||||
\(119\) | 15.8665 | 1.45448 | ||||||||
\(120\) | 1.79084 | 0.163480 | ||||||||
\(121\) | 12.4085 | 1.12804 | ||||||||
\(122\) | 0.659535 | 0.0597115 | ||||||||
\(123\) | −1.11128 | −0.100201 | ||||||||
\(124\) | −3.85804 | −0.346462 | ||||||||
\(125\) | −8.93913 | −0.799540 | ||||||||
\(126\) | −0.913467 | −0.0813781 | ||||||||
\(127\) | −1.41613 | −0.125661 | −0.0628306 | − | 0.998024i | \(-0.520013\pi\) | ||||
−0.0628306 | + | 0.998024i | \(0.520013\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.03145 | −0.619085 | ||||||||
\(130\) | −4.40280 | −0.386151 | ||||||||
\(131\) | −6.01277 | −0.525338 | −0.262669 | − | 0.964886i | \(-0.584603\pi\) | ||||
−0.262669 | + | 0.964886i | \(0.584603\pi\) | |||||||
\(132\) | 8.74020 | 0.760737 | ||||||||
\(133\) | 20.3732 | 1.76658 | ||||||||
\(134\) | 3.75828 | 0.324666 | ||||||||
\(135\) | 4.90081 | 0.421794 | ||||||||
\(136\) | −4.57513 | −0.392314 | ||||||||
\(137\) | −2.75774 | −0.235610 | −0.117805 | − | 0.993037i | \(-0.537586\pi\) | ||||
−0.117805 | + | 0.993037i | \(0.537586\pi\) | |||||||
\(138\) | 0.704636 | 0.0599826 | ||||||||
\(139\) | −10.1459 | −0.860564 | −0.430282 | − | 0.902695i | \(-0.641586\pi\) | ||||
−0.430282 | + | 0.902695i | \(0.641586\pi\) | |||||||
\(140\) | 3.43794 | 0.290559 | ||||||||
\(141\) | −17.2782 | −1.45508 | ||||||||
\(142\) | −7.60582 | −0.638266 | ||||||||
\(143\) | −21.4879 | −1.79691 | ||||||||
\(144\) | 0.263400 | 0.0219500 | ||||||||
\(145\) | −5.32025 | −0.441823 | ||||||||
\(146\) | −7.96823 | −0.659455 | ||||||||
\(147\) | −9.08103 | −0.748991 | ||||||||
\(148\) | 1.64933 | 0.135574 | ||||||||
\(149\) | −8.07347 | −0.661405 | −0.330702 | − | 0.943735i | \(-0.607286\pi\) | ||||
−0.330702 | + | 0.943735i | \(0.607286\pi\) | |||||||
\(150\) | −7.25712 | −0.592541 | ||||||||
\(151\) | 13.3238 | 1.08427 | 0.542136 | − | 0.840290i | \(-0.317616\pi\) | ||||
0.542136 | + | 0.840290i | \(0.317616\pi\) | |||||||
\(152\) | −5.87465 | −0.476497 | ||||||||
\(153\) | 1.20509 | 0.0974257 | ||||||||
\(154\) | 16.7789 | 1.35208 | ||||||||
\(155\) | −3.82462 | −0.307200 | ||||||||
\(156\) | −8.02311 | −0.642363 | ||||||||
\(157\) | 13.5492 | 1.08135 | 0.540673 | − | 0.841233i | \(-0.318170\pi\) | ||||
0.540673 | + | 0.841233i | \(0.318170\pi\) | |||||||
\(158\) | −7.32579 | −0.582809 | ||||||||
\(159\) | −9.78396 | −0.775919 | ||||||||
\(160\) | −0.991336 | −0.0783720 | ||||||||
\(161\) | 1.35272 | 0.106609 | ||||||||
\(162\) | 9.72082 | 0.763740 | ||||||||
\(163\) | 23.3382 | 1.82799 | 0.913996 | − | 0.405724i | \(-0.132981\pi\) | ||||
0.913996 | + | 0.405724i | \(0.132981\pi\) | |||||||
\(164\) | 0.615159 | 0.0480359 | ||||||||
\(165\) | 8.66448 | 0.674529 | ||||||||
\(166\) | 4.60880 | 0.357712 | ||||||||
\(167\) | 1.63790 | 0.126744 | 0.0633722 | − | 0.997990i | \(-0.479814\pi\) | ||||
0.0633722 | + | 0.997990i | \(0.479814\pi\) | |||||||
\(168\) | 6.26487 | 0.483345 | ||||||||
\(169\) | 6.72490 | 0.517300 | ||||||||
\(170\) | −4.53549 | −0.347856 | ||||||||
\(171\) | 1.54738 | 0.118331 | ||||||||
\(172\) | 3.89233 | 0.296787 | ||||||||
\(173\) | 16.1710 | 1.22946 | 0.614729 | − | 0.788739i | \(-0.289265\pi\) | ||||
0.614729 | + | 0.788739i | \(0.289265\pi\) | |||||||
\(174\) | −9.69496 | −0.734973 | ||||||||
\(175\) | −13.9318 | −1.05314 | ||||||||
\(176\) | −4.83823 | −0.364695 | ||||||||
\(177\) | −3.89989 | −0.293133 | ||||||||
\(178\) | 17.5829 | 1.31789 | ||||||||
\(179\) | −20.3815 | −1.52339 | −0.761694 | − | 0.647937i | \(-0.775632\pi\) | ||||
−0.761694 | + | 0.647937i | \(0.775632\pi\) | |||||||
\(180\) | 0.261118 | 0.0194626 | ||||||||
\(181\) | −9.22723 | −0.685855 | −0.342927 | − | 0.939362i | \(-0.611418\pi\) | ||||
−0.342927 | + | 0.939362i | \(0.611418\pi\) | |||||||
\(182\) | −15.4023 | −1.14169 | ||||||||
\(183\) | 1.19144 | 0.0880740 | ||||||||
\(184\) | −0.390058 | −0.0287555 | ||||||||
\(185\) | 1.63505 | 0.120211 | ||||||||
\(186\) | −6.96950 | −0.511029 | ||||||||
\(187\) | −22.1355 | −1.61871 | ||||||||
\(188\) | 9.56451 | 0.697564 | ||||||||
\(189\) | 17.1444 | 1.24707 | ||||||||
\(190\) | −5.82376 | −0.422500 | ||||||||
\(191\) | −0.252623 | −0.0182792 | −0.00913958 | − | 0.999958i | \(-0.502909\pi\) | ||||
−0.00913958 | + | 0.999958i | \(0.502909\pi\) | |||||||
\(192\) | −1.80649 | −0.130372 | ||||||||
\(193\) | −1.91294 | −0.137696 | −0.0688481 | − | 0.997627i | \(-0.521932\pi\) | ||||
−0.0688481 | + | 0.997627i | \(0.521932\pi\) | |||||||
\(194\) | 0.900577 | 0.0646576 | ||||||||
\(195\) | −7.95360 | −0.569569 | ||||||||
\(196\) | 5.02690 | 0.359064 | ||||||||
\(197\) | −4.73274 | −0.337193 | −0.168597 | − | 0.985685i | \(-0.553924\pi\) | ||||
−0.168597 | + | 0.985685i | \(0.553924\pi\) | |||||||
\(198\) | 1.27439 | 0.0905670 | ||||||||
\(199\) | −4.27859 | −0.303301 | −0.151651 | − | 0.988434i | \(-0.548459\pi\) | ||||
−0.151651 | + | 0.988434i | \(0.548459\pi\) | |||||||
\(200\) | 4.01725 | 0.284063 | ||||||||
\(201\) | 6.78930 | 0.478880 | ||||||||
\(202\) | 12.6829 | 0.892367 | ||||||||
\(203\) | −18.6118 | −1.30629 | ||||||||
\(204\) | −8.26492 | −0.578660 | ||||||||
\(205\) | 0.609830 | 0.0425924 | ||||||||
\(206\) | −5.27874 | −0.367787 | ||||||||
\(207\) | 0.102741 | 0.00714102 | ||||||||
\(208\) | 4.44127 | 0.307947 | ||||||||
\(209\) | −28.4229 | −1.96605 | ||||||||
\(210\) | 6.21059 | 0.428572 | ||||||||
\(211\) | 11.5068 | 0.792159 | 0.396079 | − | 0.918216i | \(-0.370371\pi\) | ||||
0.396079 | + | 0.918216i | \(0.370371\pi\) | |||||||
\(212\) | 5.41601 | 0.371973 | ||||||||
\(213\) | −13.7398 | −0.941437 | ||||||||
\(214\) | −3.15234 | −0.215489 | ||||||||
\(215\) | 3.85861 | 0.263155 | ||||||||
\(216\) | −4.94364 | −0.336372 | ||||||||
\(217\) | −13.3796 | −0.908267 | ||||||||
\(218\) | −2.14772 | −0.145462 | ||||||||
\(219\) | −14.3945 | −0.972691 | ||||||||
\(220\) | −4.79631 | −0.323367 | ||||||||
\(221\) | 20.3194 | 1.36683 | ||||||||
\(222\) | 2.97950 | 0.199971 | ||||||||
\(223\) | −3.74371 | −0.250697 | −0.125349 | − | 0.992113i | \(-0.540005\pi\) | ||||
−0.125349 | + | 0.992113i | \(0.540005\pi\) | |||||||
\(224\) | −3.46798 | −0.231714 | ||||||||
\(225\) | −1.05814 | −0.0705430 | ||||||||
\(226\) | 4.18617 | 0.278460 | ||||||||
\(227\) | −2.29245 | −0.152156 | −0.0760778 | − | 0.997102i | \(-0.524240\pi\) | ||||
−0.0760778 | + | 0.997102i | \(0.524240\pi\) | |||||||
\(228\) | −10.6125 | −0.702830 | ||||||||
\(229\) | −7.69231 | −0.508322 | −0.254161 | − | 0.967162i | \(-0.581799\pi\) | ||||
−0.254161 | + | 0.967162i | \(0.581799\pi\) | |||||||
\(230\) | −0.386679 | −0.0254969 | ||||||||
\(231\) | 30.3109 | 1.99431 | ||||||||
\(232\) | 5.36675 | 0.352344 | ||||||||
\(233\) | 16.1219 | 1.05618 | 0.528090 | − | 0.849188i | \(-0.322908\pi\) | ||||
0.528090 | + | 0.849188i | \(0.322908\pi\) | |||||||
\(234\) | −1.16983 | −0.0764743 | ||||||||
\(235\) | 9.48165 | 0.618514 | ||||||||
\(236\) | 2.15882 | 0.140527 | ||||||||
\(237\) | −13.2340 | −0.859638 | ||||||||
\(238\) | −15.8665 | −1.02847 | ||||||||
\(239\) | 20.9409 | 1.35456 | 0.677278 | − | 0.735727i | \(-0.263159\pi\) | ||||
0.677278 | + | 0.735727i | \(0.263159\pi\) | |||||||
\(240\) | −1.79084 | −0.115598 | ||||||||
\(241\) | 22.1655 | 1.42781 | 0.713904 | − | 0.700244i | \(-0.246925\pi\) | ||||
0.713904 | + | 0.700244i | \(0.246925\pi\) | |||||||
\(242\) | −12.4085 | −0.797646 | ||||||||
\(243\) | 2.72964 | 0.175107 | ||||||||
\(244\) | −0.659535 | −0.0422224 | ||||||||
\(245\) | 4.98335 | 0.318374 | ||||||||
\(246\) | 1.11128 | 0.0708525 | ||||||||
\(247\) | 26.0909 | 1.66013 | ||||||||
\(248\) | 3.85804 | 0.244986 | ||||||||
\(249\) | 8.32574 | 0.527622 | ||||||||
\(250\) | 8.93913 | 0.565360 | ||||||||
\(251\) | 23.1640 | 1.46210 | 0.731049 | − | 0.682324i | \(-0.239031\pi\) | ||||
0.731049 | + | 0.682324i | \(0.239031\pi\) | |||||||
\(252\) | 0.913467 | 0.0575430 | ||||||||
\(253\) | −1.88719 | −0.118647 | ||||||||
\(254\) | 1.41613 | 0.0888558 | ||||||||
\(255\) | −8.19332 | −0.513085 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.7051 | 0.667766 | 0.333883 | − | 0.942614i | \(-0.391641\pi\) | ||||
0.333883 | + | 0.942614i | \(0.391641\pi\) | |||||||
\(258\) | 7.03145 | 0.437759 | ||||||||
\(259\) | 5.71986 | 0.355415 | ||||||||
\(260\) | 4.40280 | 0.273050 | ||||||||
\(261\) | −1.41360 | −0.0874997 | ||||||||
\(262\) | 6.01277 | 0.371470 | ||||||||
\(263\) | 24.7435 | 1.52575 | 0.762875 | − | 0.646546i | \(-0.223787\pi\) | ||||
0.762875 | + | 0.646546i | \(0.223787\pi\) | |||||||
\(264\) | −8.74020 | −0.537922 | ||||||||
\(265\) | 5.36909 | 0.329821 | ||||||||
\(266\) | −20.3732 | −1.24916 | ||||||||
\(267\) | 31.7633 | 1.94388 | ||||||||
\(268\) | −3.75828 | −0.229574 | ||||||||
\(269\) | −5.46180 | −0.333012 | −0.166506 | − | 0.986040i | \(-0.553248\pi\) | ||||
−0.166506 | + | 0.986040i | \(0.553248\pi\) | |||||||
\(270\) | −4.90081 | −0.298254 | ||||||||
\(271\) | 17.0311 | 1.03457 | 0.517283 | − | 0.855814i | \(-0.326943\pi\) | ||||
0.517283 | + | 0.855814i | \(0.326943\pi\) | |||||||
\(272\) | 4.57513 | 0.277408 | ||||||||
\(273\) | −27.8240 | −1.68398 | ||||||||
\(274\) | 2.75774 | 0.166601 | ||||||||
\(275\) | 19.4364 | 1.17206 | ||||||||
\(276\) | −0.704636 | −0.0424141 | ||||||||
\(277\) | −13.9848 | −0.840267 | −0.420134 | − | 0.907462i | \(-0.638017\pi\) | ||||
−0.420134 | + | 0.907462i | \(0.638017\pi\) | |||||||
\(278\) | 10.1459 | 0.608511 | ||||||||
\(279\) | −1.01621 | −0.0608388 | ||||||||
\(280\) | −3.43794 | −0.205456 | ||||||||
\(281\) | −27.4034 | −1.63475 | −0.817375 | − | 0.576106i | \(-0.804571\pi\) | ||||
−0.817375 | + | 0.576106i | \(0.804571\pi\) | |||||||
\(282\) | 17.2782 | 1.02890 | ||||||||
\(283\) | 1.39969 | 0.0832027 | 0.0416013 | − | 0.999134i | \(-0.486754\pi\) | ||||
0.0416013 | + | 0.999134i | \(0.486754\pi\) | |||||||
\(284\) | 7.60582 | 0.451322 | ||||||||
\(285\) | −10.5206 | −0.623184 | ||||||||
\(286\) | 21.4879 | 1.27061 | ||||||||
\(287\) | 2.13336 | 0.125928 | ||||||||
\(288\) | −0.263400 | −0.0155210 | ||||||||
\(289\) | 3.93182 | 0.231284 | ||||||||
\(290\) | 5.32025 | 0.312416 | ||||||||
\(291\) | 1.62688 | 0.0953695 | ||||||||
\(292\) | 7.96823 | 0.466305 | ||||||||
\(293\) | 16.6471 | 0.972535 | 0.486267 | − | 0.873810i | \(-0.338358\pi\) | ||||
0.486267 | + | 0.873810i | \(0.338358\pi\) | |||||||
\(294\) | 9.08103 | 0.529616 | ||||||||
\(295\) | 2.14012 | 0.124603 | ||||||||
\(296\) | −1.64933 | −0.0958656 | ||||||||
\(297\) | −23.9184 | −1.38789 | ||||||||
\(298\) | 8.07347 | 0.467684 | ||||||||
\(299\) | 1.73236 | 0.100185 | ||||||||
\(300\) | 7.25712 | 0.418990 | ||||||||
\(301\) | 13.4985 | 0.778042 | ||||||||
\(302\) | −13.3238 | −0.766697 | ||||||||
\(303\) | 22.9115 | 1.31623 | ||||||||
\(304\) | 5.87465 | 0.336935 | ||||||||
\(305\) | −0.653821 | −0.0374377 | ||||||||
\(306\) | −1.20509 | −0.0688904 | ||||||||
\(307\) | 4.66626 | 0.266317 | 0.133159 | − | 0.991095i | \(-0.457488\pi\) | ||||
0.133159 | + | 0.991095i | \(0.457488\pi\) | |||||||
\(308\) | −16.7789 | −0.956066 | ||||||||
\(309\) | −9.53598 | −0.542483 | ||||||||
\(310\) | 3.82462 | 0.217224 | ||||||||
\(311\) | −7.36031 | −0.417365 | −0.208682 | − | 0.977983i | \(-0.566918\pi\) | ||||
−0.208682 | + | 0.977983i | \(0.566918\pi\) | |||||||
\(312\) | 8.02311 | 0.454219 | ||||||||
\(313\) | 17.9361 | 1.01381 | 0.506906 | − | 0.862002i | \(-0.330789\pi\) | ||||
0.506906 | + | 0.862002i | \(0.330789\pi\) | |||||||
\(314\) | −13.5492 | −0.764627 | ||||||||
\(315\) | 0.905553 | 0.0510221 | ||||||||
\(316\) | 7.32579 | 0.412108 | ||||||||
\(317\) | 22.6279 | 1.27091 | 0.635456 | − | 0.772137i | \(-0.280812\pi\) | ||||
0.635456 | + | 0.772137i | \(0.280812\pi\) | |||||||
\(318\) | 9.78396 | 0.548657 | ||||||||
\(319\) | 25.9655 | 1.45379 | ||||||||
\(320\) | 0.991336 | 0.0554174 | ||||||||
\(321\) | −5.69466 | −0.317845 | ||||||||
\(322\) | −1.35272 | −0.0753839 | ||||||||
\(323\) | 26.8773 | 1.49549 | ||||||||
\(324\) | −9.72082 | −0.540046 | ||||||||
\(325\) | −17.8417 | −0.989680 | ||||||||
\(326\) | −23.3382 | −1.29259 | ||||||||
\(327\) | −3.87984 | −0.214556 | ||||||||
\(328\) | −0.615159 | −0.0339665 | ||||||||
\(329\) | 33.1695 | 1.82870 | ||||||||
\(330\) | −8.66448 | −0.476964 | ||||||||
\(331\) | 13.1505 | 0.722815 | 0.361408 | − | 0.932408i | \(-0.382296\pi\) | ||||
0.361408 | + | 0.932408i | \(0.382296\pi\) | |||||||
\(332\) | −4.60880 | −0.252941 | ||||||||
\(333\) | 0.434435 | 0.0238069 | ||||||||
\(334\) | −1.63790 | −0.0896219 | ||||||||
\(335\) | −3.72572 | −0.203558 | ||||||||
\(336\) | −6.26487 | −0.341777 | ||||||||
\(337\) | 8.66798 | 0.472175 | 0.236088 | − | 0.971732i | \(-0.424135\pi\) | ||||
0.236088 | + | 0.971732i | \(0.424135\pi\) | |||||||
\(338\) | −6.72490 | −0.365786 | ||||||||
\(339\) | 7.56226 | 0.410726 | ||||||||
\(340\) | 4.53549 | 0.245972 | ||||||||
\(341\) | 18.6661 | 1.01082 | ||||||||
\(342\) | −1.54738 | −0.0836730 | ||||||||
\(343\) | −6.84268 | −0.369470 | ||||||||
\(344\) | −3.89233 | −0.209860 | ||||||||
\(345\) | −0.698531 | −0.0376076 | ||||||||
\(346\) | −16.1710 | −0.869358 | ||||||||
\(347\) | 30.4882 | 1.63669 | 0.818346 | − | 0.574726i | \(-0.194891\pi\) | ||||
0.818346 | + | 0.574726i | \(0.194891\pi\) | |||||||
\(348\) | 9.69496 | 0.519705 | ||||||||
\(349\) | 10.3172 | 0.552268 | 0.276134 | − | 0.961119i | \(-0.410947\pi\) | ||||
0.276134 | + | 0.961119i | \(0.410947\pi\) | |||||||
\(350\) | 13.9318 | 0.744684 | ||||||||
\(351\) | 21.9560 | 1.17193 | ||||||||
\(352\) | 4.83823 | 0.257878 | ||||||||
\(353\) | 21.7091 | 1.15546 | 0.577728 | − | 0.816229i | \(-0.303939\pi\) | ||||
0.577728 | + | 0.816229i | \(0.303939\pi\) | |||||||
\(354\) | 3.89989 | 0.207277 | ||||||||
\(355\) | 7.53992 | 0.400177 | ||||||||
\(356\) | −17.5829 | −0.931892 | ||||||||
\(357\) | −28.6626 | −1.51699 | ||||||||
\(358\) | 20.3815 | 1.07720 | ||||||||
\(359\) | 24.3223 | 1.28368 | 0.641842 | − | 0.766837i | \(-0.278171\pi\) | ||||
0.641842 | + | 0.766837i | \(0.278171\pi\) | |||||||
\(360\) | −0.261118 | −0.0137621 | ||||||||
\(361\) | 15.5116 | 0.816398 | ||||||||
\(362\) | 9.22723 | 0.484973 | ||||||||
\(363\) | −22.4157 | −1.17652 | ||||||||
\(364\) | 15.4023 | 0.807297 | ||||||||
\(365\) | 7.89919 | 0.413463 | ||||||||
\(366\) | −1.19144 | −0.0622777 | ||||||||
\(367\) | −5.77669 | −0.301541 | −0.150770 | − | 0.988569i | \(-0.548175\pi\) | ||||
−0.150770 | + | 0.988569i | \(0.548175\pi\) | |||||||
\(368\) | 0.390058 | 0.0203332 | ||||||||
\(369\) | 0.162033 | 0.00843510 | ||||||||
\(370\) | −1.63505 | −0.0850020 | ||||||||
\(371\) | 18.7826 | 0.975146 | ||||||||
\(372\) | 6.96950 | 0.361352 | ||||||||
\(373\) | 26.6727 | 1.38106 | 0.690529 | − | 0.723304i | \(-0.257378\pi\) | ||||
0.690529 | + | 0.723304i | \(0.257378\pi\) | |||||||
\(374\) | 22.1355 | 1.14460 | ||||||||
\(375\) | 16.1484 | 0.833902 | ||||||||
\(376\) | −9.56451 | −0.493252 | ||||||||
\(377\) | −23.8352 | −1.22757 | ||||||||
\(378\) | −17.1444 | −0.881815 | ||||||||
\(379\) | −7.02665 | −0.360935 | −0.180467 | − | 0.983581i | \(-0.557761\pi\) | ||||
−0.180467 | + | 0.983581i | \(0.557761\pi\) | |||||||
\(380\) | 5.82376 | 0.298753 | ||||||||
\(381\) | 2.55822 | 0.131062 | ||||||||
\(382\) | 0.252623 | 0.0129253 | ||||||||
\(383\) | −5.62613 | −0.287482 | −0.143741 | − | 0.989615i | \(-0.545913\pi\) | ||||
−0.143741 | + | 0.989615i | \(0.545913\pi\) | |||||||
\(384\) | 1.80649 | 0.0921870 | ||||||||
\(385\) | −16.6335 | −0.847723 | ||||||||
\(386\) | 1.91294 | 0.0973659 | ||||||||
\(387\) | 1.02524 | 0.0521159 | ||||||||
\(388\) | −0.900577 | −0.0457199 | ||||||||
\(389\) | −16.1901 | −0.820872 | −0.410436 | − | 0.911889i | \(-0.634624\pi\) | ||||
−0.410436 | + | 0.911889i | \(0.634624\pi\) | |||||||
\(390\) | 7.95360 | 0.402746 | ||||||||
\(391\) | 1.78457 | 0.0902495 | ||||||||
\(392\) | −5.02690 | −0.253897 | ||||||||
\(393\) | 10.8620 | 0.547916 | ||||||||
\(394\) | 4.73274 | 0.238432 | ||||||||
\(395\) | 7.26232 | 0.365407 | ||||||||
\(396\) | −1.27439 | −0.0640405 | ||||||||
\(397\) | −25.5830 | −1.28398 | −0.641988 | − | 0.766715i | \(-0.721890\pi\) | ||||
−0.641988 | + | 0.766715i | \(0.721890\pi\) | |||||||
\(398\) | 4.27859 | 0.214466 | ||||||||
\(399\) | −36.8039 | −1.84250 | ||||||||
\(400\) | −4.01725 | −0.200863 | ||||||||
\(401\) | 19.0673 | 0.952175 | 0.476088 | − | 0.879398i | \(-0.342054\pi\) | ||||
0.476088 | + | 0.879398i | \(0.342054\pi\) | |||||||
\(402\) | −6.78930 | −0.338619 | ||||||||
\(403\) | −17.1346 | −0.853536 | ||||||||
\(404\) | −12.6829 | −0.630999 | ||||||||
\(405\) | −9.63660 | −0.478847 | ||||||||
\(406\) | 18.6118 | 0.923687 | ||||||||
\(407\) | −7.97986 | −0.395547 | ||||||||
\(408\) | 8.26492 | 0.409175 | ||||||||
\(409\) | 20.2004 | 0.998844 | 0.499422 | − | 0.866359i | \(-0.333546\pi\) | ||||
0.499422 | + | 0.866359i | \(0.333546\pi\) | |||||||
\(410\) | −0.609830 | −0.0301173 | ||||||||
\(411\) | 4.98182 | 0.245735 | ||||||||
\(412\) | 5.27874 | 0.260065 | ||||||||
\(413\) | 7.48676 | 0.368399 | ||||||||
\(414\) | −0.102741 | −0.00504946 | ||||||||
\(415\) | −4.56887 | −0.224277 | ||||||||
\(416\) | −4.44127 | −0.217751 | ||||||||
\(417\) | 18.3284 | 0.897548 | ||||||||
\(418\) | 28.4229 | 1.39021 | ||||||||
\(419\) | 8.13037 | 0.397195 | 0.198597 | − | 0.980081i | \(-0.436361\pi\) | ||||
0.198597 | + | 0.980081i | \(0.436361\pi\) | |||||||
\(420\) | −6.21059 | −0.303046 | ||||||||
\(421\) | −21.7269 | −1.05891 | −0.529453 | − | 0.848339i | \(-0.677603\pi\) | ||||
−0.529453 | + | 0.848339i | \(0.677603\pi\) | |||||||
\(422\) | −11.5068 | −0.560141 | ||||||||
\(423\) | 2.51929 | 0.122492 | ||||||||
\(424\) | −5.41601 | −0.263025 | ||||||||
\(425\) | −18.3795 | −0.891534 | ||||||||
\(426\) | 13.7398 | 0.665696 | ||||||||
\(427\) | −2.28726 | −0.110688 | ||||||||
\(428\) | 3.15234 | 0.152374 | ||||||||
\(429\) | 38.8176 | 1.87413 | ||||||||
\(430\) | −3.85861 | −0.186079 | ||||||||
\(431\) | 24.8566 | 1.19730 | 0.598650 | − | 0.801011i | \(-0.295704\pi\) | ||||
0.598650 | + | 0.801011i | \(0.295704\pi\) | |||||||
\(432\) | 4.94364 | 0.237851 | ||||||||
\(433\) | 21.4707 | 1.03182 | 0.515908 | − | 0.856644i | \(-0.327455\pi\) | ||||
0.515908 | + | 0.856644i | \(0.327455\pi\) | |||||||
\(434\) | 13.3796 | 0.642242 | ||||||||
\(435\) | 9.61097 | 0.460811 | ||||||||
\(436\) | 2.14772 | 0.102857 | ||||||||
\(437\) | 2.29146 | 0.109615 | ||||||||
\(438\) | 14.3945 | 0.687796 | ||||||||
\(439\) | 20.6508 | 0.985609 | 0.492804 | − | 0.870140i | \(-0.335972\pi\) | ||||
0.492804 | + | 0.870140i | \(0.335972\pi\) | |||||||
\(440\) | 4.79631 | 0.228655 | ||||||||
\(441\) | 1.32409 | 0.0630517 | ||||||||
\(442\) | −20.3194 | −0.966495 | ||||||||
\(443\) | −13.9285 | −0.661764 | −0.330882 | − | 0.943672i | \(-0.607346\pi\) | ||||
−0.330882 | + | 0.943672i | \(0.607346\pi\) | |||||||
\(444\) | −2.97950 | −0.141401 | ||||||||
\(445\) | −17.4306 | −0.826288 | ||||||||
\(446\) | 3.74371 | 0.177270 | ||||||||
\(447\) | 14.5846 | 0.689830 | ||||||||
\(448\) | 3.46798 | 0.163847 | ||||||||
\(449\) | 3.56271 | 0.168135 | 0.0840675 | − | 0.996460i | \(-0.473209\pi\) | ||||
0.0840675 | + | 0.996460i | \(0.473209\pi\) | |||||||
\(450\) | 1.05814 | 0.0498814 | ||||||||
\(451\) | −2.97628 | −0.140148 | ||||||||
\(452\) | −4.18617 | −0.196901 | ||||||||
\(453\) | −24.0692 | −1.13087 | ||||||||
\(454\) | 2.29245 | 0.107590 | ||||||||
\(455\) | 15.2688 | 0.715813 | ||||||||
\(456\) | 10.6125 | 0.496976 | ||||||||
\(457\) | −20.6838 | −0.967549 | −0.483775 | − | 0.875193i | \(-0.660735\pi\) | ||||
−0.483775 | + | 0.875193i | \(0.660735\pi\) | |||||||
\(458\) | 7.69231 | 0.359438 | ||||||||
\(459\) | 22.6178 | 1.05571 | ||||||||
\(460\) | 0.386679 | 0.0180290 | ||||||||
\(461\) | −1.39819 | −0.0651201 | −0.0325600 | − | 0.999470i | \(-0.510366\pi\) | ||||
−0.0325600 | + | 0.999470i | \(0.510366\pi\) | |||||||
\(462\) | −30.3109 | −1.41019 | ||||||||
\(463\) | 18.4190 | 0.856003 | 0.428002 | − | 0.903778i | \(-0.359218\pi\) | ||||
0.428002 | + | 0.903778i | \(0.359218\pi\) | |||||||
\(464\) | −5.36675 | −0.249145 | ||||||||
\(465\) | 6.90912 | 0.320403 | ||||||||
\(466\) | −16.1219 | −0.746832 | ||||||||
\(467\) | 17.8825 | 0.827504 | 0.413752 | − | 0.910390i | \(-0.364218\pi\) | ||||
0.413752 | + | 0.910390i | \(0.364218\pi\) | |||||||
\(468\) | 1.16983 | 0.0540755 | ||||||||
\(469\) | −13.0337 | −0.601838 | ||||||||
\(470\) | −9.48165 | −0.437356 | ||||||||
\(471\) | −24.4765 | −1.12782 | ||||||||
\(472\) | −2.15882 | −0.0993678 | ||||||||
\(473\) | −18.8320 | −0.865896 | ||||||||
\(474\) | 13.2340 | 0.607856 | ||||||||
\(475\) | −23.6000 | −1.08284 | ||||||||
\(476\) | 15.8665 | 0.727238 | ||||||||
\(477\) | 1.42658 | 0.0653185 | ||||||||
\(478\) | −20.9409 | −0.957816 | ||||||||
\(479\) | −22.2536 | −1.01679 | −0.508396 | − | 0.861123i | \(-0.669762\pi\) | ||||
−0.508396 | + | 0.861123i | \(0.669762\pi\) | |||||||
\(480\) | 1.79084 | 0.0817402 | ||||||||
\(481\) | 7.32514 | 0.333998 | ||||||||
\(482\) | −22.1655 | −1.00961 | ||||||||
\(483\) | −2.44366 | −0.111191 | ||||||||
\(484\) | 12.4085 | 0.564021 | ||||||||
\(485\) | −0.892775 | −0.0405388 | ||||||||
\(486\) | −2.72964 | −0.123819 | ||||||||
\(487\) | 8.74071 | 0.396079 | 0.198040 | − | 0.980194i | \(-0.436543\pi\) | ||||
0.198040 | + | 0.980194i | \(0.436543\pi\) | |||||||
\(488\) | 0.659535 | 0.0298557 | ||||||||
\(489\) | −42.1602 | −1.90655 | ||||||||
\(490\) | −4.98335 | −0.225125 | ||||||||
\(491\) | −7.08110 | −0.319566 | −0.159783 | − | 0.987152i | \(-0.551079\pi\) | ||||
−0.159783 | + | 0.987152i | \(0.551079\pi\) | |||||||
\(492\) | −1.11128 | −0.0501003 | ||||||||
\(493\) | −24.5536 | −1.10584 | ||||||||
\(494\) | −26.0909 | −1.17389 | ||||||||
\(495\) | −1.26335 | −0.0567833 | ||||||||
\(496\) | −3.85804 | −0.173231 | ||||||||
\(497\) | 26.3768 | 1.18316 | ||||||||
\(498\) | −8.32574 | −0.373085 | ||||||||
\(499\) | 5.27856 | 0.236301 | 0.118150 | − | 0.992996i | \(-0.462303\pi\) | ||||
0.118150 | + | 0.992996i | \(0.462303\pi\) | |||||||
\(500\) | −8.93913 | −0.399770 | ||||||||
\(501\) | −2.95885 | −0.132192 | ||||||||
\(502\) | −23.1640 | −1.03386 | ||||||||
\(503\) | −21.5204 | −0.959546 | −0.479773 | − | 0.877393i | \(-0.659281\pi\) | ||||
−0.479773 | + | 0.877393i | \(0.659281\pi\) | |||||||
\(504\) | −0.913467 | −0.0406890 | ||||||||
\(505\) | −12.5730 | −0.559493 | ||||||||
\(506\) | 1.88719 | 0.0838959 | ||||||||
\(507\) | −12.1485 | −0.539532 | ||||||||
\(508\) | −1.41613 | −0.0628306 | ||||||||
\(509\) | 29.2034 | 1.29442 | 0.647210 | − | 0.762312i | \(-0.275936\pi\) | ||||
0.647210 | + | 0.762312i | \(0.275936\pi\) | |||||||
\(510\) | 8.19332 | 0.362806 | ||||||||
\(511\) | 27.6337 | 1.22244 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 29.0422 | 1.28224 | ||||||||
\(514\) | −10.7051 | −0.472182 | ||||||||
\(515\) | 5.23301 | 0.230594 | ||||||||
\(516\) | −7.03145 | −0.309542 | ||||||||
\(517\) | −46.2753 | −2.03518 | ||||||||
\(518\) | −5.71986 | −0.251316 | ||||||||
\(519\) | −29.2127 | −1.28230 | ||||||||
\(520\) | −4.40280 | −0.193075 | ||||||||
\(521\) | −30.3033 | −1.32761 | −0.663805 | − | 0.747905i | \(-0.731060\pi\) | ||||
−0.663805 | + | 0.747905i | \(0.731060\pi\) | |||||||
\(522\) | 1.41360 | 0.0618717 | ||||||||
\(523\) | −32.9269 | −1.43979 | −0.719896 | − | 0.694082i | \(-0.755811\pi\) | ||||
−0.719896 | + | 0.694082i | \(0.755811\pi\) | |||||||
\(524\) | −6.01277 | −0.262669 | ||||||||
\(525\) | 25.1676 | 1.09840 | ||||||||
\(526\) | −24.7435 | −1.07887 | ||||||||
\(527\) | −17.6510 | −0.768891 | ||||||||
\(528\) | 8.74020 | 0.380369 | ||||||||
\(529\) | −22.8479 | −0.993385 | ||||||||
\(530\) | −5.36909 | −0.233218 | ||||||||
\(531\) | 0.568634 | 0.0246766 | ||||||||
\(532\) | 20.3732 | 0.883290 | ||||||||
\(533\) | 2.73209 | 0.118340 | ||||||||
\(534\) | −31.7633 | −1.37453 | ||||||||
\(535\) | 3.12503 | 0.135107 | ||||||||
\(536\) | 3.75828 | 0.162333 | ||||||||
\(537\) | 36.8190 | 1.58886 | ||||||||
\(538\) | 5.46180 | 0.235475 | ||||||||
\(539\) | −24.3213 | −1.04759 | ||||||||
\(540\) | 4.90081 | 0.210897 | ||||||||
\(541\) | 6.11490 | 0.262900 | 0.131450 | − | 0.991323i | \(-0.458037\pi\) | ||||
0.131450 | + | 0.991323i | \(0.458037\pi\) | |||||||
\(542\) | −17.0311 | −0.731549 | ||||||||
\(543\) | 16.6689 | 0.715330 | ||||||||
\(544\) | −4.57513 | −0.196157 | ||||||||
\(545\) | 2.12912 | 0.0912013 | ||||||||
\(546\) | 27.8240 | 1.19076 | ||||||||
\(547\) | −46.1801 | −1.97452 | −0.987258 | − | 0.159126i | \(-0.949133\pi\) | ||||
−0.987258 | + | 0.159126i | \(0.949133\pi\) | |||||||
\(548\) | −2.75774 | −0.117805 | ||||||||
\(549\) | −0.173722 | −0.00741426 | ||||||||
\(550\) | −19.4364 | −0.828770 | ||||||||
\(551\) | −31.5278 | −1.34313 | ||||||||
\(552\) | 0.704636 | 0.0299913 | ||||||||
\(553\) | 25.4057 | 1.08036 | ||||||||
\(554\) | 13.9848 | 0.594159 | ||||||||
\(555\) | −2.95369 | −0.125377 | ||||||||
\(556\) | −10.1459 | −0.430282 | ||||||||
\(557\) | 34.3387 | 1.45498 | 0.727488 | − | 0.686120i | \(-0.240688\pi\) | ||||
0.727488 | + | 0.686120i | \(0.240688\pi\) | |||||||
\(558\) | 1.01621 | 0.0430195 | ||||||||
\(559\) | 17.2869 | 0.731158 | ||||||||
\(560\) | 3.43794 | 0.145279 | ||||||||
\(561\) | 39.9876 | 1.68828 | ||||||||
\(562\) | 27.4034 | 1.15594 | ||||||||
\(563\) | −12.7013 | −0.535296 | −0.267648 | − | 0.963517i | \(-0.586246\pi\) | ||||
−0.267648 | + | 0.963517i | \(0.586246\pi\) | |||||||
\(564\) | −17.2782 | −0.727542 | ||||||||
\(565\) | −4.14990 | −0.174588 | ||||||||
\(566\) | −1.39969 | −0.0588332 | ||||||||
\(567\) | −33.7116 | −1.41576 | ||||||||
\(568\) | −7.60582 | −0.319133 | ||||||||
\(569\) | 12.6056 | 0.528456 | 0.264228 | − | 0.964460i | \(-0.414883\pi\) | ||||
0.264228 | + | 0.964460i | \(0.414883\pi\) | |||||||
\(570\) | 10.5206 | 0.440657 | ||||||||
\(571\) | 39.7015 | 1.66146 | 0.830728 | − | 0.556679i | \(-0.187925\pi\) | ||||
0.830728 | + | 0.556679i | \(0.187925\pi\) | |||||||
\(572\) | −21.4879 | −0.898454 | ||||||||
\(573\) | 0.456361 | 0.0190647 | ||||||||
\(574\) | −2.13336 | −0.0890448 | ||||||||
\(575\) | −1.56696 | −0.0653469 | ||||||||
\(576\) | 0.263400 | 0.0109750 | ||||||||
\(577\) | 18.2349 | 0.759130 | 0.379565 | − | 0.925165i | \(-0.376074\pi\) | ||||
0.379565 | + | 0.925165i | \(0.376074\pi\) | |||||||
\(578\) | −3.93182 | −0.163542 | ||||||||
\(579\) | 3.45570 | 0.143614 | ||||||||
\(580\) | −5.32025 | −0.220911 | ||||||||
\(581\) | −15.9832 | −0.663096 | ||||||||
\(582\) | −1.62688 | −0.0674364 | ||||||||
\(583\) | −26.2039 | −1.08525 | ||||||||
\(584\) | −7.96823 | −0.329728 | ||||||||
\(585\) | 1.15970 | 0.0479476 | ||||||||
\(586\) | −16.6471 | −0.687686 | ||||||||
\(587\) | −46.2844 | −1.91036 | −0.955182 | − | 0.296020i | \(-0.904340\pi\) | ||||
−0.955182 | + | 0.296020i | \(0.904340\pi\) | |||||||
\(588\) | −9.08103 | −0.374495 | ||||||||
\(589\) | −22.6647 | −0.933881 | ||||||||
\(590\) | −2.14012 | −0.0881073 | ||||||||
\(591\) | 8.54963 | 0.351685 | ||||||||
\(592\) | 1.64933 | 0.0677872 | ||||||||
\(593\) | −39.2941 | −1.61362 | −0.806808 | − | 0.590813i | \(-0.798807\pi\) | ||||
−0.806808 | + | 0.590813i | \(0.798807\pi\) | |||||||
\(594\) | 23.9184 | 0.981386 | ||||||||
\(595\) | 15.7290 | 0.644826 | ||||||||
\(596\) | −8.07347 | −0.330702 | ||||||||
\(597\) | 7.72922 | 0.316336 | ||||||||
\(598\) | −1.73236 | −0.0708413 | ||||||||
\(599\) | 18.9396 | 0.773850 | 0.386925 | − | 0.922111i | \(-0.373537\pi\) | ||||
0.386925 | + | 0.922111i | \(0.373537\pi\) | |||||||
\(600\) | −7.25712 | −0.296271 | ||||||||
\(601\) | 1.18833 | 0.0484730 | 0.0242365 | − | 0.999706i | \(-0.492285\pi\) | ||||
0.0242365 | + | 0.999706i | \(0.492285\pi\) | |||||||
\(602\) | −13.4985 | −0.550159 | ||||||||
\(603\) | −0.989932 | −0.0403132 | ||||||||
\(604\) | 13.3238 | 0.542136 | ||||||||
\(605\) | 12.3010 | 0.500105 | ||||||||
\(606\) | −22.9115 | −0.930718 | ||||||||
\(607\) | 22.5047 | 0.913439 | 0.456719 | − | 0.889611i | \(-0.349024\pi\) | ||||
0.456719 | + | 0.889611i | \(0.349024\pi\) | |||||||
\(608\) | −5.87465 | −0.238249 | ||||||||
\(609\) | 33.6220 | 1.36243 | ||||||||
\(610\) | 0.653821 | 0.0264724 | ||||||||
\(611\) | 42.4786 | 1.71850 | ||||||||
\(612\) | 1.20509 | 0.0487129 | ||||||||
\(613\) | −35.1216 | −1.41855 | −0.709274 | − | 0.704933i | \(-0.750977\pi\) | ||||
−0.709274 | + | 0.704933i | \(0.750977\pi\) | |||||||
\(614\) | −4.66626 | −0.188315 | ||||||||
\(615\) | −1.10165 | −0.0444228 | ||||||||
\(616\) | 16.7789 | 0.676041 | ||||||||
\(617\) | −45.6860 | −1.83925 | −0.919624 | − | 0.392799i | \(-0.871507\pi\) | ||||
−0.919624 | + | 0.392799i | \(0.871507\pi\) | |||||||
\(618\) | 9.53598 | 0.383593 | ||||||||
\(619\) | −5.56332 | −0.223609 | −0.111804 | − | 0.993730i | \(-0.535663\pi\) | ||||
−0.111804 | + | 0.993730i | \(0.535663\pi\) | |||||||
\(620\) | −3.82462 | −0.153600 | ||||||||
\(621\) | 1.92831 | 0.0773803 | ||||||||
\(622\) | 7.36031 | 0.295122 | ||||||||
\(623\) | −60.9772 | −2.44300 | ||||||||
\(624\) | −8.02311 | −0.321181 | ||||||||
\(625\) | 11.2246 | 0.448983 | ||||||||
\(626\) | −17.9361 | −0.716873 | ||||||||
\(627\) | 51.3457 | 2.05055 | ||||||||
\(628\) | 13.5492 | 0.540673 | ||||||||
\(629\) | 7.54592 | 0.300876 | ||||||||
\(630\) | −0.905553 | −0.0360781 | ||||||||
\(631\) | 40.7240 | 1.62120 | 0.810598 | − | 0.585603i | \(-0.199142\pi\) | ||||
0.810598 | + | 0.585603i | \(0.199142\pi\) | |||||||
\(632\) | −7.32579 | −0.291404 | ||||||||
\(633\) | −20.7868 | −0.826203 | ||||||||
\(634\) | −22.6279 | −0.898670 | ||||||||
\(635\) | −1.40386 | −0.0557105 | ||||||||
\(636\) | −9.78396 | −0.387959 | ||||||||
\(637\) | 22.3258 | 0.884581 | ||||||||
\(638\) | −25.9655 | −1.02799 | ||||||||
\(639\) | 2.00337 | 0.0792522 | ||||||||
\(640\) | −0.991336 | −0.0391860 | ||||||||
\(641\) | 5.93815 | 0.234543 | 0.117271 | − | 0.993100i | \(-0.462585\pi\) | ||||
0.117271 | + | 0.993100i | \(0.462585\pi\) | |||||||
\(642\) | 5.69466 | 0.224750 | ||||||||
\(643\) | 22.7412 | 0.896827 | 0.448414 | − | 0.893826i | \(-0.351989\pi\) | ||||
0.448414 | + | 0.893826i | \(0.351989\pi\) | |||||||
\(644\) | 1.35272 | 0.0533044 | ||||||||
\(645\) | −6.97053 | −0.274464 | ||||||||
\(646\) | −26.8773 | −1.05747 | ||||||||
\(647\) | −37.4156 | −1.47096 | −0.735479 | − | 0.677548i | \(-0.763043\pi\) | ||||
−0.735479 | + | 0.677548i | \(0.763043\pi\) | |||||||
\(648\) | 9.72082 | 0.381870 | ||||||||
\(649\) | −10.4449 | −0.409997 | ||||||||
\(650\) | 17.8417 | 0.699810 | ||||||||
\(651\) | 24.1701 | 0.947301 | ||||||||
\(652\) | 23.3382 | 0.913996 | ||||||||
\(653\) | −44.6646 | −1.74786 | −0.873930 | − | 0.486052i | \(-0.838437\pi\) | ||||
−0.873930 | + | 0.486052i | \(0.838437\pi\) | |||||||
\(654\) | 3.87984 | 0.151714 | ||||||||
\(655\) | −5.96068 | −0.232903 | ||||||||
\(656\) | 0.615159 | 0.0240179 | ||||||||
\(657\) | 2.09883 | 0.0818832 | ||||||||
\(658\) | −33.1695 | −1.29308 | ||||||||
\(659\) | 17.9391 | 0.698809 | 0.349405 | − | 0.936972i | \(-0.386384\pi\) | ||||
0.349405 | + | 0.936972i | \(0.386384\pi\) | |||||||
\(660\) | 8.66448 | 0.337265 | ||||||||
\(661\) | 20.0545 | 0.780028 | 0.390014 | − | 0.920809i | \(-0.372470\pi\) | ||||
0.390014 | + | 0.920809i | \(0.372470\pi\) | |||||||
\(662\) | −13.1505 | −0.511108 | ||||||||
\(663\) | −36.7068 | −1.42557 | ||||||||
\(664\) | 4.60880 | 0.178856 | ||||||||
\(665\) | 20.1967 | 0.783194 | ||||||||
\(666\) | −0.434435 | −0.0168340 | ||||||||
\(667\) | −2.09334 | −0.0810546 | ||||||||
\(668\) | 1.63790 | 0.0633722 | ||||||||
\(669\) | 6.76297 | 0.261471 | ||||||||
\(670\) | 3.72572 | 0.143937 | ||||||||
\(671\) | 3.19098 | 0.123186 | ||||||||
\(672\) | 6.26487 | 0.241673 | ||||||||
\(673\) | 39.2695 | 1.51373 | 0.756863 | − | 0.653573i | \(-0.226731\pi\) | ||||
0.756863 | + | 0.653573i | \(0.226731\pi\) | |||||||
\(674\) | −8.66798 | −0.333878 | ||||||||
\(675\) | −19.8598 | −0.764405 | ||||||||
\(676\) | 6.72490 | 0.258650 | ||||||||
\(677\) | 22.2291 | 0.854333 | 0.427166 | − | 0.904173i | \(-0.359512\pi\) | ||||
0.427166 | + | 0.904173i | \(0.359512\pi\) | |||||||
\(678\) | −7.56226 | −0.290427 | ||||||||
\(679\) | −3.12318 | −0.119857 | ||||||||
\(680\) | −4.53549 | −0.173928 | ||||||||
\(681\) | 4.14129 | 0.158695 | ||||||||
\(682\) | −18.6661 | −0.714761 | ||||||||
\(683\) | 18.1134 | 0.693091 | 0.346546 | − | 0.938033i | \(-0.387355\pi\) | ||||
0.346546 | + | 0.938033i | \(0.387355\pi\) | |||||||
\(684\) | 1.54738 | 0.0591657 | ||||||||
\(685\) | −2.73385 | −0.104455 | ||||||||
\(686\) | 6.84268 | 0.261255 | ||||||||
\(687\) | 13.8961 | 0.530168 | ||||||||
\(688\) | 3.89233 | 0.148394 | ||||||||
\(689\) | 24.0540 | 0.916384 | ||||||||
\(690\) | 0.698531 | 0.0265926 | ||||||||
\(691\) | 7.91737 | 0.301191 | 0.150596 | − | 0.988595i | \(-0.451881\pi\) | ||||
0.150596 | + | 0.988595i | \(0.451881\pi\) | |||||||
\(692\) | 16.1710 | 0.614729 | ||||||||
\(693\) | −4.41956 | −0.167885 | ||||||||
\(694\) | −30.4882 | −1.15732 | ||||||||
\(695\) | −10.0580 | −0.381522 | ||||||||
\(696\) | −9.69496 | −0.367487 | ||||||||
\(697\) | 2.81443 | 0.106604 | ||||||||
\(698\) | −10.3172 | −0.390512 | ||||||||
\(699\) | −29.1240 | −1.10157 | ||||||||
\(700\) | −13.9318 | −0.526571 | ||||||||
\(701\) | 22.7900 | 0.860766 | 0.430383 | − | 0.902646i | \(-0.358379\pi\) | ||||
0.430383 | + | 0.902646i | \(0.358379\pi\) | |||||||
\(702\) | −21.9560 | −0.828677 | ||||||||
\(703\) | 9.68927 | 0.365438 | ||||||||
\(704\) | −4.83823 | −0.182348 | ||||||||
\(705\) | −17.1285 | −0.645096 | ||||||||
\(706\) | −21.7091 | −0.817031 | ||||||||
\(707\) | −43.9841 | −1.65419 | ||||||||
\(708\) | −3.89989 | −0.146567 | ||||||||
\(709\) | 11.1318 | 0.418063 | 0.209032 | − | 0.977909i | \(-0.432969\pi\) | ||||
0.209032 | + | 0.977909i | \(0.432969\pi\) | |||||||
\(710\) | −7.53992 | −0.282968 | ||||||||
\(711\) | 1.92961 | 0.0723662 | ||||||||
\(712\) | 17.5829 | 0.658947 | ||||||||
\(713\) | −1.50486 | −0.0563575 | ||||||||
\(714\) | 28.6626 | 1.07267 | ||||||||
\(715\) | −21.3017 | −0.796640 | ||||||||
\(716\) | −20.3815 | −0.761694 | ||||||||
\(717\) | −37.8296 | −1.41277 | ||||||||
\(718\) | −24.3223 | −0.907701 | ||||||||
\(719\) | −26.7265 | −0.996730 | −0.498365 | − | 0.866967i | \(-0.666066\pi\) | ||||
−0.498365 | + | 0.866967i | \(0.666066\pi\) | |||||||
\(720\) | 0.261118 | 0.00973130 | ||||||||
\(721\) | 18.3066 | 0.681772 | ||||||||
\(722\) | −15.5116 | −0.577281 | ||||||||
\(723\) | −40.0418 | −1.48917 | ||||||||
\(724\) | −9.22723 | −0.342927 | ||||||||
\(725\) | 21.5596 | 0.800702 | ||||||||
\(726\) | 22.4157 | 0.831926 | ||||||||
\(727\) | 5.91475 | 0.219366 | 0.109683 | − | 0.993967i | \(-0.465016\pi\) | ||||
0.109683 | + | 0.993967i | \(0.465016\pi\) | |||||||
\(728\) | −15.4023 | −0.570845 | ||||||||
\(729\) | 24.2314 | 0.897459 | ||||||||
\(730\) | −7.89919 | −0.292362 | ||||||||
\(731\) | 17.8079 | 0.658650 | ||||||||
\(732\) | 1.19144 | 0.0440370 | ||||||||
\(733\) | −16.1525 | −0.596606 | −0.298303 | − | 0.954471i | \(-0.596421\pi\) | ||||
−0.298303 | + | 0.954471i | \(0.596421\pi\) | |||||||
\(734\) | 5.77669 | 0.213222 | ||||||||
\(735\) | −9.00236 | −0.332057 | ||||||||
\(736\) | −0.390058 | −0.0143777 | ||||||||
\(737\) | 18.1834 | 0.669796 | ||||||||
\(738\) | −0.162033 | −0.00596452 | ||||||||
\(739\) | 4.56505 | 0.167928 | 0.0839640 | − | 0.996469i | \(-0.473242\pi\) | ||||
0.0839640 | + | 0.996469i | \(0.473242\pi\) | |||||||
\(740\) | 1.63505 | 0.0601055 | ||||||||
\(741\) | −47.1330 | −1.73147 | ||||||||
\(742\) | −18.7826 | −0.689532 | ||||||||
\(743\) | −1.10692 | −0.0406089 | −0.0203045 | − | 0.999794i | \(-0.506464\pi\) | ||||
−0.0203045 | + | 0.999794i | \(0.506464\pi\) | |||||||
\(744\) | −6.96950 | −0.255514 | ||||||||
\(745\) | −8.00353 | −0.293227 | ||||||||
\(746\) | −26.6727 | −0.976556 | ||||||||
\(747\) | −1.21396 | −0.0444164 | ||||||||
\(748\) | −22.1355 | −0.809355 | ||||||||
\(749\) | 10.9322 | 0.399456 | ||||||||
\(750\) | −16.1484 | −0.589657 | ||||||||
\(751\) | −4.06957 | −0.148501 | −0.0742504 | − | 0.997240i | \(-0.523656\pi\) | ||||
−0.0742504 | + | 0.997240i | \(0.523656\pi\) | |||||||
\(752\) | 9.56451 | 0.348782 | ||||||||
\(753\) | −41.8455 | −1.52493 | ||||||||
\(754\) | 23.8352 | 0.868026 | ||||||||
\(755\) | 13.2083 | 0.480701 | ||||||||
\(756\) | 17.1444 | 0.623537 | ||||||||
\(757\) | −31.9015 | −1.15948 | −0.579740 | − | 0.814801i | \(-0.696846\pi\) | ||||
−0.579740 | + | 0.814801i | \(0.696846\pi\) | |||||||
\(758\) | 7.02665 | 0.255219 | ||||||||
\(759\) | 3.40919 | 0.123746 | ||||||||
\(760\) | −5.82376 | −0.211250 | ||||||||
\(761\) | 41.5648 | 1.50672 | 0.753361 | − | 0.657607i | \(-0.228431\pi\) | ||||
0.753361 | + | 0.657607i | \(0.228431\pi\) | |||||||
\(762\) | −2.55822 | −0.0926745 | ||||||||
\(763\) | 7.44827 | 0.269645 | ||||||||
\(764\) | −0.252623 | −0.00913958 | ||||||||
\(765\) | 1.19465 | 0.0431926 | ||||||||
\(766\) | 5.62613 | 0.203280 | ||||||||
\(767\) | 9.58792 | 0.346200 | ||||||||
\(768\) | −1.80649 | −0.0651860 | ||||||||
\(769\) | 1.47872 | 0.0533241 | 0.0266620 | − | 0.999645i | \(-0.491512\pi\) | ||||
0.0266620 | + | 0.999645i | \(0.491512\pi\) | |||||||
\(770\) | 16.6335 | 0.599431 | ||||||||
\(771\) | −19.3387 | −0.696465 | ||||||||
\(772\) | −1.91294 | −0.0688481 | ||||||||
\(773\) | −37.2985 | −1.34154 | −0.670768 | − | 0.741668i | \(-0.734035\pi\) | ||||
−0.670768 | + | 0.741668i | \(0.734035\pi\) | |||||||
\(774\) | −1.02524 | −0.0368515 | ||||||||
\(775\) | 15.4987 | 0.556730 | ||||||||
\(776\) | 0.900577 | 0.0323288 | ||||||||
\(777\) | −10.3329 | −0.370689 | ||||||||
\(778\) | 16.1901 | 0.580444 | ||||||||
\(779\) | 3.61385 | 0.129480 | ||||||||
\(780\) | −7.95360 | −0.284784 | ||||||||
\(781\) | −36.7987 | −1.31676 | ||||||||
\(782\) | −1.78457 | −0.0638160 | ||||||||
\(783\) | −26.5312 | −0.948149 | ||||||||
\(784\) | 5.02690 | 0.179532 | ||||||||
\(785\) | 13.4318 | 0.479403 | ||||||||
\(786\) | −10.8620 | −0.387435 | ||||||||
\(787\) | 36.3902 | 1.29717 | 0.648585 | − | 0.761142i | \(-0.275361\pi\) | ||||
0.648585 | + | 0.761142i | \(0.275361\pi\) | |||||||
\(788\) | −4.73274 | −0.168597 | ||||||||
\(789\) | −44.6989 | −1.59132 | ||||||||
\(790\) | −7.26232 | −0.258382 | ||||||||
\(791\) | −14.5176 | −0.516185 | ||||||||
\(792\) | 1.27439 | 0.0452835 | ||||||||
\(793\) | −2.92917 | −0.104018 | ||||||||
\(794\) | 25.5830 | 0.907908 | ||||||||
\(795\) | −9.69920 | −0.343995 | ||||||||
\(796\) | −4.27859 | −0.151651 | ||||||||
\(797\) | −22.1309 | −0.783917 | −0.391959 | − | 0.919983i | \(-0.628202\pi\) | ||||
−0.391959 | + | 0.919983i | \(0.628202\pi\) | |||||||
\(798\) | 36.8039 | 1.30285 | ||||||||
\(799\) | 43.7589 | 1.54808 | ||||||||
\(800\) | 4.01725 | 0.142031 | ||||||||
\(801\) | −4.63134 | −0.163640 | ||||||||
\(802\) | −19.0673 | −0.673290 | ||||||||
\(803\) | −38.5521 | −1.36047 | ||||||||
\(804\) | 6.78930 | 0.239440 | ||||||||
\(805\) | 1.34100 | 0.0472639 | ||||||||
\(806\) | 17.1346 | 0.603541 | ||||||||
\(807\) | 9.86668 | 0.347323 | ||||||||
\(808\) | 12.6829 | 0.446184 | ||||||||
\(809\) | 50.9644 | 1.79181 | 0.895906 | − | 0.444243i | \(-0.146527\pi\) | ||||
0.895906 | + | 0.444243i | \(0.146527\pi\) | |||||||
\(810\) | 9.63660 | 0.338596 | ||||||||
\(811\) | 29.8202 | 1.04713 | 0.523564 | − | 0.851986i | \(-0.324602\pi\) | ||||
0.523564 | + | 0.851986i | \(0.324602\pi\) | |||||||
\(812\) | −18.6118 | −0.653145 | ||||||||
\(813\) | −30.7665 | −1.07903 | ||||||||
\(814\) | 7.97986 | 0.279694 | ||||||||
\(815\) | 23.1360 | 0.810420 | ||||||||
\(816\) | −8.26492 | −0.289330 | ||||||||
\(817\) | 22.8661 | 0.799984 | ||||||||
\(818\) | −20.2004 | −0.706289 | ||||||||
\(819\) | 4.05695 | 0.141761 | ||||||||
\(820\) | 0.609830 | 0.0212962 | ||||||||
\(821\) | −31.0815 | −1.08475 | −0.542376 | − | 0.840136i | \(-0.682475\pi\) | ||||
−0.542376 | + | 0.840136i | \(0.682475\pi\) | |||||||
\(822\) | −4.98182 | −0.173761 | ||||||||
\(823\) | 9.16996 | 0.319645 | 0.159822 | − | 0.987146i | \(-0.448908\pi\) | ||||
0.159822 | + | 0.987146i | \(0.448908\pi\) | |||||||
\(824\) | −5.27874 | −0.183894 | ||||||||
\(825\) | −35.1116 | −1.22243 | ||||||||
\(826\) | −7.48676 | −0.260498 | ||||||||
\(827\) | 2.37504 | 0.0825881 | 0.0412941 | − | 0.999147i | \(-0.486852\pi\) | ||||
0.0412941 | + | 0.999147i | \(0.486852\pi\) | |||||||
\(828\) | 0.102741 | 0.00357051 | ||||||||
\(829\) | −31.1481 | −1.08182 | −0.540909 | − | 0.841081i | \(-0.681920\pi\) | ||||
−0.540909 | + | 0.841081i | \(0.681920\pi\) | |||||||
\(830\) | 4.56887 | 0.158588 | ||||||||
\(831\) | 25.2634 | 0.876379 | ||||||||
\(832\) | 4.44127 | 0.153973 | ||||||||
\(833\) | 22.9987 | 0.796858 | ||||||||
\(834\) | −18.3284 | −0.634662 | ||||||||
\(835\) | 1.62371 | 0.0561908 | ||||||||
\(836\) | −28.4229 | −0.983027 | ||||||||
\(837\) | −19.0727 | −0.659250 | ||||||||
\(838\) | −8.13037 | −0.280859 | ||||||||
\(839\) | 29.8781 | 1.03151 | 0.515754 | − | 0.856737i | \(-0.327512\pi\) | ||||
0.515754 | + | 0.856737i | \(0.327512\pi\) | |||||||
\(840\) | 6.21059 | 0.214286 | ||||||||
\(841\) | −0.198037 | −0.00682887 | ||||||||
\(842\) | 21.7269 | 0.748760 | ||||||||
\(843\) | 49.5039 | 1.70501 | ||||||||
\(844\) | 11.5068 | 0.396079 | ||||||||
\(845\) | 6.66664 | 0.229339 | ||||||||
\(846\) | −2.51929 | −0.0866151 | ||||||||
\(847\) | 43.0323 | 1.47861 | ||||||||
\(848\) | 5.41601 | 0.185987 | ||||||||
\(849\) | −2.52852 | −0.0867785 | ||||||||
\(850\) | 18.3795 | 0.630410 | ||||||||
\(851\) | 0.643337 | 0.0220533 | ||||||||
\(852\) | −13.7398 | −0.470718 | ||||||||
\(853\) | −39.1255 | −1.33963 | −0.669816 | − | 0.742527i | \(-0.733627\pi\) | ||||
−0.669816 | + | 0.742527i | \(0.733627\pi\) | |||||||
\(854\) | 2.28726 | 0.0782683 | ||||||||
\(855\) | 1.53398 | 0.0524610 | ||||||||
\(856\) | −3.15234 | −0.107745 | ||||||||
\(857\) | −5.63162 | −0.192372 | −0.0961862 | − | 0.995363i | \(-0.530664\pi\) | ||||
−0.0961862 | + | 0.995363i | \(0.530664\pi\) | |||||||
\(858\) | −38.8176 | −1.32521 | ||||||||
\(859\) | −13.3591 | −0.455806 | −0.227903 | − | 0.973684i | \(-0.573187\pi\) | ||||
−0.227903 | + | 0.973684i | \(0.573187\pi\) | |||||||
\(860\) | 3.85861 | 0.131577 | ||||||||
\(861\) | −3.85389 | −0.131340 | ||||||||
\(862\) | −24.8566 | −0.846619 | ||||||||
\(863\) | −38.7837 | −1.32021 | −0.660106 | − | 0.751172i | \(-0.729489\pi\) | ||||
−0.660106 | + | 0.751172i | \(0.729489\pi\) | |||||||
\(864\) | −4.94364 | −0.168186 | ||||||||
\(865\) | 16.0309 | 0.545067 | ||||||||
\(866\) | −21.4707 | −0.729604 | ||||||||
\(867\) | −7.10279 | −0.241223 | ||||||||
\(868\) | −13.3796 | −0.454134 | ||||||||
\(869\) | −35.4438 | −1.20235 | ||||||||
\(870\) | −9.61097 | −0.325842 | ||||||||
\(871\) | −16.6916 | −0.565572 | ||||||||
\(872\) | −2.14772 | −0.0727311 | ||||||||
\(873\) | −0.237212 | −0.00802841 | ||||||||
\(874\) | −2.29146 | −0.0775097 | ||||||||
\(875\) | −31.0007 | −1.04802 | ||||||||
\(876\) | −14.3945 | −0.486345 | ||||||||
\(877\) | −17.6039 | −0.594441 | −0.297220 | − | 0.954809i | \(-0.596060\pi\) | ||||
−0.297220 | + | 0.954809i | \(0.596060\pi\) | |||||||
\(878\) | −20.6508 | −0.696931 | ||||||||
\(879\) | −30.0728 | −1.01433 | ||||||||
\(880\) | −4.79631 | −0.161684 | ||||||||
\(881\) | 37.3148 | 1.25717 | 0.628583 | − | 0.777742i | \(-0.283635\pi\) | ||||
0.628583 | + | 0.777742i | \(0.283635\pi\) | |||||||
\(882\) | −1.32409 | −0.0445843 | ||||||||
\(883\) | −44.9842 | −1.51384 | −0.756920 | − | 0.653508i | \(-0.773297\pi\) | ||||
−0.756920 | + | 0.653508i | \(0.773297\pi\) | |||||||
\(884\) | 20.3194 | 0.683415 | ||||||||
\(885\) | −3.86610 | −0.129958 | ||||||||
\(886\) | 13.9285 | 0.467938 | ||||||||
\(887\) | 57.1469 | 1.91881 | 0.959403 | − | 0.282040i | \(-0.0910111\pi\) | ||||
0.959403 | + | 0.282040i | \(0.0910111\pi\) | |||||||
\(888\) | 2.97950 | 0.0999856 | ||||||||
\(889\) | −4.91111 | −0.164713 | ||||||||
\(890\) | 17.4306 | 0.584274 | ||||||||
\(891\) | 47.0316 | 1.57562 | ||||||||
\(892\) | −3.74371 | −0.125349 | ||||||||
\(893\) | 56.1882 | 1.88027 | ||||||||
\(894\) | −14.5846 | −0.487783 | ||||||||
\(895\) | −20.2050 | −0.675377 | ||||||||
\(896\) | −3.46798 | −0.115857 | ||||||||
\(897\) | −3.12948 | −0.104490 | ||||||||
\(898\) | −3.56271 | −0.118889 | ||||||||
\(899\) | 20.7051 | 0.690554 | ||||||||
\(900\) | −1.05814 | −0.0352715 | ||||||||
\(901\) | 24.7790 | 0.825507 | ||||||||
\(902\) | 2.97628 | 0.0990993 | ||||||||
\(903\) | −24.3849 | −0.811480 | ||||||||
\(904\) | 4.18617 | 0.139230 | ||||||||
\(905\) | −9.14729 | −0.304066 | ||||||||
\(906\) | 24.0692 | 0.799647 | ||||||||
\(907\) | −5.87490 | −0.195073 | −0.0975364 | − | 0.995232i | \(-0.531096\pi\) | ||||
−0.0975364 | + | 0.995232i | \(0.531096\pi\) | |||||||
\(908\) | −2.29245 | −0.0760778 | ||||||||
\(909\) | −3.34068 | −0.110803 | ||||||||
\(910\) | −15.2688 | −0.506156 | ||||||||
\(911\) | −56.7383 | −1.87982 | −0.939912 | − | 0.341416i | \(-0.889093\pi\) | ||||
−0.939912 | + | 0.341416i | \(0.889093\pi\) | |||||||
\(912\) | −10.6125 | −0.351415 | ||||||||
\(913\) | 22.2984 | 0.737970 | ||||||||
\(914\) | 20.6838 | 0.684161 | ||||||||
\(915\) | 1.18112 | 0.0390466 | ||||||||
\(916\) | −7.69231 | −0.254161 | ||||||||
\(917\) | −20.8522 | −0.688600 | ||||||||
\(918\) | −22.6178 | −0.746498 | ||||||||
\(919\) | −30.4436 | −1.00424 | −0.502121 | − | 0.864797i | \(-0.667447\pi\) | ||||
−0.502121 | + | 0.864797i | \(0.667447\pi\) | |||||||
\(920\) | −0.386679 | −0.0127484 | ||||||||
\(921\) | −8.42954 | −0.277763 | ||||||||
\(922\) | 1.39819 | 0.0460469 | ||||||||
\(923\) | 33.7795 | 1.11187 | ||||||||
\(924\) | 30.3109 | 0.997154 | ||||||||
\(925\) | −6.62579 | −0.217855 | ||||||||
\(926\) | −18.4190 | −0.605286 | ||||||||
\(927\) | 1.39042 | 0.0456674 | ||||||||
\(928\) | 5.36675 | 0.176172 | ||||||||
\(929\) | 43.8675 | 1.43925 | 0.719623 | − | 0.694365i | \(-0.244315\pi\) | ||||
0.719623 | + | 0.694365i | \(0.244315\pi\) | |||||||
\(930\) | −6.90912 | −0.226559 | ||||||||
\(931\) | 29.5313 | 0.967849 | ||||||||
\(932\) | 16.1219 | 0.528090 | ||||||||
\(933\) | 13.2963 | 0.435302 | ||||||||
\(934\) | −17.8825 | −0.585134 | ||||||||
\(935\) | −21.9438 | −0.717638 | ||||||||
\(936\) | −1.16983 | −0.0382371 | ||||||||
\(937\) | 17.4667 | 0.570612 | 0.285306 | − | 0.958437i | \(-0.407905\pi\) | ||||
0.285306 | + | 0.958437i | \(0.407905\pi\) | |||||||
\(938\) | 13.0337 | 0.425564 | ||||||||
\(939\) | −32.4014 | −1.05738 | ||||||||
\(940\) | 9.48165 | 0.309257 | ||||||||
\(941\) | −15.0431 | −0.490392 | −0.245196 | − | 0.969474i | \(-0.578852\pi\) | ||||
−0.245196 | + | 0.969474i | \(0.578852\pi\) | |||||||
\(942\) | 24.4765 | 0.797488 | ||||||||
\(943\) | 0.239948 | 0.00781378 | ||||||||
\(944\) | 2.15882 | 0.0702637 | ||||||||
\(945\) | 16.9959 | 0.552877 | ||||||||
\(946\) | 18.8320 | 0.612281 | ||||||||
\(947\) | −10.9124 | −0.354604 | −0.177302 | − | 0.984156i | \(-0.556737\pi\) | ||||
−0.177302 | + | 0.984156i | \(0.556737\pi\) | |||||||
\(948\) | −13.2340 | −0.429819 | ||||||||
\(949\) | 35.3891 | 1.14878 | ||||||||
\(950\) | 23.6000 | 0.765684 | ||||||||
\(951\) | −40.8771 | −1.32553 | ||||||||
\(952\) | −15.8665 | −0.514235 | ||||||||
\(953\) | 54.7022 | 1.77198 | 0.885990 | − | 0.463705i | \(-0.153480\pi\) | ||||
0.885990 | + | 0.463705i | \(0.153480\pi\) | |||||||
\(954\) | −1.42658 | −0.0461872 | ||||||||
\(955\) | −0.250434 | −0.00810387 | ||||||||
\(956\) | 20.9409 | 0.677278 | ||||||||
\(957\) | −46.9065 | −1.51627 | ||||||||
\(958\) | 22.2536 | 0.718981 | ||||||||
\(959\) | −9.56379 | −0.308831 | ||||||||
\(960\) | −1.79084 | −0.0577990 | ||||||||
\(961\) | −16.1155 | −0.519856 | ||||||||
\(962\) | −7.32514 | −0.236172 | ||||||||
\(963\) | 0.830326 | 0.0267569 | ||||||||
\(964\) | 22.1655 | 0.713904 | ||||||||
\(965\) | −1.89636 | −0.0610461 | ||||||||
\(966\) | 2.44366 | 0.0786236 | ||||||||
\(967\) | −14.7095 | −0.473025 | −0.236513 | − | 0.971628i | \(-0.576004\pi\) | ||||
−0.236513 | + | 0.971628i | \(0.576004\pi\) | |||||||
\(968\) | −12.4085 | −0.398823 | ||||||||
\(969\) | −48.5536 | −1.55976 | ||||||||
\(970\) | 0.892775 | 0.0286653 | ||||||||
\(971\) | 32.4180 | 1.04034 | 0.520171 | − | 0.854062i | \(-0.325868\pi\) | ||||
0.520171 | + | 0.854062i | \(0.325868\pi\) | |||||||
\(972\) | 2.72964 | 0.0875533 | ||||||||
\(973\) | −35.1858 | −1.12800 | ||||||||
\(974\) | −8.74071 | −0.280070 | ||||||||
\(975\) | 32.2308 | 1.03221 | ||||||||
\(976\) | −0.659535 | −0.0211112 | ||||||||
\(977\) | −26.1555 | −0.836790 | −0.418395 | − | 0.908265i | \(-0.637407\pi\) | ||||
−0.418395 | + | 0.908265i | \(0.637407\pi\) | |||||||
\(978\) | 42.1602 | 1.34814 | ||||||||
\(979\) | 85.0701 | 2.71885 | ||||||||
\(980\) | 4.98335 | 0.159187 | ||||||||
\(981\) | 0.565711 | 0.0180618 | ||||||||
\(982\) | 7.08110 | 0.225967 | ||||||||
\(983\) | 3.91663 | 0.124921 | 0.0624605 | − | 0.998047i | \(-0.480105\pi\) | ||||
0.0624605 | + | 0.998047i | \(0.480105\pi\) | |||||||
\(984\) | 1.11128 | 0.0354262 | ||||||||
\(985\) | −4.69173 | −0.149491 | ||||||||
\(986\) | 24.5536 | 0.781945 | ||||||||
\(987\) | −59.9204 | −1.90729 | ||||||||
\(988\) | 26.0909 | 0.830064 | ||||||||
\(989\) | 1.51824 | 0.0482771 | ||||||||
\(990\) | 1.26335 | 0.0401519 | ||||||||
\(991\) | 52.1499 | 1.65660 | 0.828298 | − | 0.560288i | \(-0.189310\pi\) | ||||
0.828298 | + | 0.560288i | \(0.189310\pi\) | |||||||
\(992\) | 3.85804 | 0.122493 | ||||||||
\(993\) | −23.7562 | −0.753880 | ||||||||
\(994\) | −26.3768 | −0.836622 | ||||||||
\(995\) | −4.24152 | −0.134465 | ||||||||
\(996\) | 8.32574 | 0.263811 | ||||||||
\(997\) | −43.4143 | −1.37494 | −0.687472 | − | 0.726211i | \(-0.741279\pi\) | ||||
−0.687472 | + | 0.726211i | \(0.741279\pi\) | |||||||
\(998\) | −5.27856 | −0.167090 | ||||||||
\(999\) | 8.15371 | 0.257972 |
(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 | 4034.2.a.c.1.12 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.c.1.12 | ✓ | 49 | 1.1 | even | 1 | trivial |