Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8032,2,Mod(1,8032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8032, 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("8032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8032 = 2^{5} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8032.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: | \(64.1358429035\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8032.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.692263 | 0.399678 | 0.199839 | − | 0.979829i | \(-0.435958\pi\) | ||||
0.199839 | + | 0.979829i | \(0.435958\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.18782 | 1.42564 | 0.712818 | − | 0.701349i | \(-0.247418\pi\) | ||||
0.712818 | + | 0.701349i | \(0.247418\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.79509 | −1.43441 | −0.717205 | − | 0.696862i | \(-0.754579\pi\) | ||||
−0.717205 | + | 0.696862i | \(0.754579\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.52077 | −0.840257 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.76100 | 0.832473 | 0.416236 | − | 0.909256i | \(-0.363349\pi\) | ||||
0.416236 | + | 0.909256i | \(0.363349\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.89831 | 0.803846 | 0.401923 | − | 0.915674i | \(-0.368342\pi\) | ||||
0.401923 | + | 0.915674i | \(0.368342\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.20681 | 0.569796 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.05358 | −1.71074 | −0.855372 | − | 0.518014i | \(-0.826672\pi\) | ||||
−0.855372 | + | 0.518014i | \(0.826672\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.44520 | 1.24921 | 0.624607 | − | 0.780939i | \(-0.285259\pi\) | ||||
0.624607 | + | 0.780939i | \(0.285259\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.62720 | −0.573302 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.85093 | 1.22000 | 0.610001 | − | 0.792401i | \(-0.291169\pi\) | ||||
0.610001 | + | 0.792401i | \(0.291169\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.16220 | 1.03244 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.82182 | −0.735511 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0264724 | −0.00491579 | −0.00245790 | − | 0.999997i | \(-0.500782\pi\) | ||||
−0.00245790 | + | 0.999997i | \(0.500782\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.32998 | 0.238871 | 0.119435 | − | 0.992842i | \(-0.461892\pi\) | ||||
0.119435 | + | 0.992842i | \(0.461892\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.91134 | 0.332721 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.0981 | −2.04495 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.73112 | 1.59979 | 0.799894 | − | 0.600142i | \(-0.204889\pi\) | ||||
0.799894 | + | 0.600142i | \(0.204889\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00639 | 0.321279 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.29149 | 0.201696 | 0.100848 | − | 0.994902i | \(-0.467844\pi\) | ||||
0.100848 | + | 0.994902i | \(0.467844\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.70603 | −1.32766 | −0.663829 | − | 0.747885i | \(-0.731070\pi\) | ||||
−0.663829 | + | 0.747885i | \(0.731070\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.03577 | −1.19790 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.73457 | 1.27407 | 0.637034 | − | 0.770836i | \(-0.280161\pi\) | ||||
0.637034 | + | 0.770836i | \(0.280161\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.40273 | 1.05753 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.88293 | −0.683747 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.78784 | −0.932381 | −0.466190 | − | 0.884684i | \(-0.654374\pi\) | ||||
−0.466190 | + | 0.884684i | \(0.654374\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.80157 | 1.18680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.76951 | 0.499283 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.43996 | 0.317656 | 0.158828 | − | 0.987306i | \(-0.449228\pi\) | ||||
0.158828 | + | 0.987306i | \(0.449228\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8180 | −1.38511 | −0.692553 | − | 0.721367i | \(-0.743514\pi\) | ||||
−0.692553 | + | 0.721367i | \(0.743514\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.56656 | 1.20527 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.23928 | 1.14599 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.31102 | 1.01535 | 0.507676 | − | 0.861548i | \(-0.330505\pi\) | ||||
0.507676 | + | 0.861548i | \(0.330505\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.05038 | 0.487608 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.40977 | 0.404665 | 0.202332 | − | 0.979317i | \(-0.435148\pi\) | ||||
0.202332 | + | 0.979317i | \(0.435148\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.12050 | −0.131145 | −0.0655723 | − | 0.997848i | \(-0.520887\pi\) | ||||
−0.0655723 | + | 0.997848i | \(0.520887\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.57360 | 0.412644 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.4782 | −1.19411 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.98388 | 0.223204 | 0.111602 | − | 0.993753i | \(-0.464402\pi\) | ||||
0.111602 | + | 0.993753i | \(0.464402\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.91661 | 0.546290 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.57987 | 0.831999 | 0.415999 | − | 0.909365i | \(-0.363432\pi\) | ||||
0.415999 | + | 0.909365i | \(0.363432\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.4855 | −2.43890 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0183258 | −0.00196474 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.29651 | −0.349429 | −0.174715 | − | 0.984619i | \(-0.555900\pi\) | ||||
−0.174715 | + | 0.984619i | \(0.555900\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.9993 | −1.15304 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.920692 | 0.0954714 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.3583 | 1.78092 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.3429 | 1.86244 | 0.931221 | − | 0.364454i | \(-0.118745\pi\) | ||||
0.931221 | + | 0.364454i | \(0.118745\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.95985 | −0.699491 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.41903 | −0.240702 | −0.120351 | − | 0.992731i | \(-0.538402\pi\) | ||||
−0.120351 | + | 0.992731i | \(0.538402\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.9147 | −1.27252 | −0.636261 | − | 0.771474i | \(-0.719520\pi\) | ||||
−0.636261 | + | 0.771474i | \(0.719520\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.37505 | −0.817321 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.1989 | 1.46934 | 0.734669 | − | 0.678426i | \(-0.237338\pi\) | ||||
0.734669 | + | 0.678426i | \(0.237338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.8621 | −1.13618 | −0.568090 | − | 0.822966i | \(-0.692318\pi\) | ||||
−0.568090 | + | 0.822966i | \(0.692318\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.73650 | 0.639400 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.17337 | −0.862958 | −0.431479 | − | 0.902123i | \(-0.642008\pi\) | ||||
−0.431479 | + | 0.902123i | \(0.642008\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.6517 | 1.73928 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.30597 | −0.675437 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26.7690 | 2.45391 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.37688 | −0.306989 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.894048 | 0.0806136 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.517064 | 0.0462476 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.59719 | −0.674141 | −0.337071 | − | 0.941479i | \(-0.609436\pi\) | ||||
−0.337071 | + | 0.941479i | \(0.609436\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.02686 | −0.530636 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2028 | 0.978795 | 0.489397 | − | 0.872061i | \(-0.337217\pi\) | ||||
0.489397 | + | 0.872061i | \(0.337217\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.6650 | −1.79189 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.1833 | −1.04857 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.23911 | 0.447608 | 0.223804 | − | 0.974634i | \(-0.428152\pi\) | ||||
0.223804 | + | 0.974634i | \(0.428152\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.98594 | 0.507720 | 0.253860 | − | 0.967241i | \(-0.418300\pi\) | ||||
0.253860 | + | 0.967241i | \(0.418300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.04661 | 0.509217 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00222 | 0.669179 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0843891 | −0.00700814 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.12463 | 0.422673 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.2512 | 0.839809 | 0.419905 | − | 0.907568i | \(-0.362064\pi\) | ||||
0.419905 | + | 0.907568i | \(0.362064\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7923 | 0.878268 | 0.439134 | − | 0.898422i | \(-0.355285\pi\) | ||||
0.439134 | + | 0.898422i | \(0.355285\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.7805 | 1.43747 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.23972 | 0.340543 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.40554 | −0.271792 | −0.135896 | − | 0.990723i | \(-0.543391\pi\) | ||||
−0.135896 | + | 0.990723i | \(0.543391\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.69897 | −0.372652 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.2048 | −1.74998 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.986389 | −0.0772600 | −0.0386300 | − | 0.999254i | \(-0.512299\pi\) | ||||
−0.0386300 | + | 0.999254i | \(0.512299\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.09300 | 0.474339 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.0960 | 1.16816 | 0.584081 | − | 0.811695i | \(-0.301455\pi\) | ||||
0.584081 | + | 0.811695i | \(0.301455\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.59982 | −0.353832 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.7261 | −1.04966 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.6440 | 1.18939 | 0.594694 | − | 0.803952i | \(-0.297273\pi\) | ||||
0.594694 | + | 0.803952i | \(0.297273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.5910 | −1.48094 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.68910 | 0.126960 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.3507 | 0.848393 | 0.424196 | − | 0.905570i | \(-0.360557\pi\) | ||||
0.424196 | + | 0.905570i | \(0.360557\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.10012 | 0.676407 | 0.338203 | − | 0.941073i | \(-0.390181\pi\) | ||||
0.338203 | + | 0.941073i | \(0.390181\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.48892 | −0.553597 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 31.0211 | 2.28072 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.4749 | −1.42415 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.5042 | 1.05502 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3414 | 0.748280 | 0.374140 | − | 0.927372i | \(-0.377938\pi\) | ||||
0.374140 | + | 0.927372i | \(0.377938\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.2006 | 1.52605 | 0.763026 | − | 0.646367i | \(-0.223713\pi\) | ||||
0.763026 | + | 0.646367i | \(0.223713\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.39601 | 0.458028 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.7730 | 1.62251 | 0.811254 | − | 0.584693i | \(-0.198785\pi\) | ||||
0.811254 | + | 0.584693i | \(0.198785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.6343 | 1.67539 | 0.837695 | − | 0.546138i | \(-0.183903\pi\) | ||||
0.837695 | + | 0.546138i | \(0.183903\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.75341 | 0.405814 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.100465 | 0.00705127 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.11703 | 0.287546 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.7489 | −1.02512 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.0342 | 1.03994 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0811 | 1.24476 | 0.622379 | − | 0.782716i | \(-0.286166\pi\) | ||||
0.622379 | + | 0.782716i | \(0.286166\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.36045 | 0.161736 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −27.7533 | −1.89276 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.04738 | −0.342639 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.775681 | −0.0524156 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.4434 | −1.37517 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.4484 | 0.900574 | 0.450287 | − | 0.892884i | \(-0.351322\pi\) | ||||
0.450287 | + | 0.892884i | \(0.351322\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0127 | −0.867515 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.7353 | −1.17713 | −0.588566 | − | 0.808449i | \(-0.700307\pi\) | ||||
−0.588566 | + | 0.808449i | \(0.700307\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.5514 | 1.55632 | 0.778160 | − | 0.628067i | \(-0.216153\pi\) | ||||
0.778160 | + | 0.628067i | \(0.216153\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.25370 | −0.477259 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.0903 | −1.05411 | −0.527054 | − | 0.849832i | \(-0.676703\pi\) | ||||
−0.527054 | + | 0.849832i | \(0.676703\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.8442 | 1.81636 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.37336 | 0.0892096 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.6115 | −1.46262 | −0.731309 | − | 0.682046i | \(-0.761090\pi\) | ||||
−0.731309 | + | 0.682046i | \(0.761090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3471 | 0.730934 | 0.365467 | − | 0.930824i | \(-0.380909\pi\) | ||||
0.365467 | + | 0.930824i | \(0.380909\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8691 | 0.953851 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.5986 | 1.50766 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.7818 | 1.00417 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.24726 | 0.332532 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.1544 | 1.01562 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.5659 | −0.974775 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.53878 | −0.0959864 | −0.0479932 | − | 0.998848i | \(-0.515283\pi\) | ||||
−0.0479932 | + | 0.998848i | \(0.515283\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −36.9305 | −2.29475 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0667308 | 0.00413053 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.64663 | 0.471511 | 0.235756 | − | 0.971812i | \(-0.424244\pi\) | ||||
0.235756 | + | 0.971812i | \(0.424244\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.6384 | −1.32924 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.28205 | −0.139659 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.9400 | −1.45965 | −0.729823 | − | 0.683636i | \(-0.760398\pi\) | ||||
−0.729823 | + | 0.683636i | \(0.760398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.8113 | −0.778230 | −0.389115 | − | 0.921189i | \(-0.627219\pi\) | ||||
−0.389115 | + | 0.921189i | \(0.627219\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.61443 | −0.460847 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.2528 | 0.859478 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.62818 | 0.458333 | 0.229167 | − | 0.973387i | \(-0.426400\pi\) | ||||
0.229167 | + | 0.973387i | \(0.426400\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.35257 | −0.200713 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.84530 | −0.110082 | −0.0550408 | − | 0.998484i | \(-0.517529\pi\) | ||||
−0.0550408 | + | 0.998484i | \(0.517529\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.859606 | −0.0510983 | −0.0255491 | − | 0.999674i | \(-0.508133\pi\) | ||||
−0.0255491 | + | 0.999674i | \(0.508133\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.0165 | 0.711797 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.90131 | −0.289315 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.7530 | 1.92665 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.6981 | 0.744377 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.7664 | −1.44687 | −0.723433 | − | 0.690394i | \(-0.757437\pi\) | ||||
−0.723433 | + | 0.690394i | \(0.757437\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.77816 | 0.452862 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.5521 | −0.612292 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.9578 | 0.980693 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.0402 | 1.90441 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.67460 | −0.0962035 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −34.4859 | −1.97466 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.284741 | −0.0162510 | −0.00812552 | − | 0.999967i | \(-0.502586\pi\) | ||||
−0.00812552 | + | 0.999967i | \(0.502586\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.94036 | −0.508599 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.91584 | −0.448866 | −0.224433 | − | 0.974490i | \(-0.572053\pi\) | ||||
−0.224433 | + | 0.974490i | \(0.572053\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.2409 | 1.14408 | 0.572042 | − | 0.820224i | \(-0.306151\pi\) | ||||
0.572042 | + | 0.820224i | \(0.306151\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 30.4965 | 1.71828 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.6944 | −0.937652 | −0.468826 | − | 0.883291i | \(-0.655323\pi\) | ||||
−0.468826 | + | 0.883291i | \(0.655323\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0730902 | −0.00409226 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.5217 | 0.587262 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −38.4081 | −2.13709 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.9616 | 0.829922 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.21167 | −0.454107 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −33.1485 | −1.82754 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.3193 | 1.06189 | 0.530943 | − | 0.847407i | \(-0.321838\pi\) | ||||
0.530943 | + | 0.847407i | \(0.321838\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.5299 | −1.34423 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.4940 | 1.44752 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9173 | 1.03049 | 0.515246 | − | 0.857042i | \(-0.327701\pi\) | ||||
0.515246 | + | 0.857042i | \(0.327701\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.35038 | −0.344906 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.67206 | 0.198853 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.52840 | −0.0825257 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.9119 | 0.695152 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.4847 | 1.69019 | 0.845094 | − | 0.534618i | \(-0.179544\pi\) | ||||
0.845094 | + | 0.534618i | \(0.179544\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0100 | −0.535822 | −0.267911 | − | 0.963444i | \(-0.586333\pi\) | ||||
−0.267911 | + | 0.963444i | \(0.586333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.0768 | −0.591237 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.2836 | 0.866688 | 0.433344 | − | 0.901229i | \(-0.357334\pi\) | ||||
0.433344 | + | 0.901229i | \(0.357334\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8697 | 0.576905 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.5312 | 0.980774 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.5621 | −1.87690 | −0.938449 | − | 0.345418i | \(-0.887737\pi\) | ||||
−0.938449 | + | 0.345418i | \(0.887737\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.6502 | 0.560535 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.33769 | −0.122697 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.57195 | −0.186965 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.72195 | 0.0898849 | 0.0449424 | − | 0.998990i | \(-0.485690\pi\) | ||||
0.0449424 | + | 0.998990i | \(0.485690\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.25554 | −0.169477 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.7605 | 1.33742 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.4746 | −1.52614 | −0.763068 | − | 0.646318i | \(-0.776308\pi\) | ||||
−0.763068 | + | 0.646318i | \(0.776308\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.357944 | 0.0184841 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.0767250 | −0.00395154 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.18299 | −0.368965 | −0.184483 | − | 0.982836i | \(-0.559061\pi\) | ||||
−0.184483 | + | 0.982836i | \(0.559061\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.25925 | −0.269440 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.1908 | 1.23609 | 0.618046 | − | 0.786142i | \(-0.287924\pi\) | ||||
0.618046 | + | 0.786142i | \(0.287924\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −33.4028 | −1.70236 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.9459 | 1.11557 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.43968 | −0.326505 | −0.163252 | − | 0.986584i | \(-0.552198\pi\) | ||||
−0.163252 | + | 0.986584i | \(0.552198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.2700 | −2.08711 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.75529 | 0.391203 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.32425 | 0.318207 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.39591 | 0.421379 | 0.210689 | − | 0.977553i | \(-0.432429\pi\) | ||||
0.210689 | + | 0.977553i | \(0.432429\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.3056 | −0.716177 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.8030 | 1.83786 | 0.918928 | − | 0.394425i | \(-0.129056\pi\) | ||||
0.918928 | + | 0.394425i | \(0.129056\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.85468 | 0.192015 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.6733 | 0.778811 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.8676 | 1.33178 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.3352 | −1.35164 | −0.675819 | − | 0.737068i | \(-0.736210\pi\) | ||||
−0.675819 | + | 0.737068i | \(0.736210\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.62684 | 0.178899 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.25988 | −0.455649 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.1633 | 1.18613 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.14384 | 0.202925 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.3918 | 0.654231 | 0.327116 | − | 0.944984i | \(-0.393923\pi\) | ||||
0.327116 | + | 0.944984i | \(0.393923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.9695 | −0.729569 | −0.364784 | − | 0.931092i | \(-0.618857\pi\) | ||||
−0.364784 | + | 0.931092i | \(0.618857\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.0179 | −1.07054 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −36.4120 | −1.76624 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.0554 | 1.98681 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.53964 | 0.267456 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.3376 | 1.60582 | 0.802909 | − | 0.596102i | \(-0.203285\pi\) | ||||
0.802909 | + | 0.596102i | \(0.203285\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.23369 | 0.203458 | 0.101729 | − | 0.994812i | \(-0.467563\pi\) | ||||
0.101729 | + | 0.994812i | \(0.467563\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0584195 | −0.00280100 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.8594 | 1.52404 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.7546 | −0.990564 | −0.495282 | − | 0.868732i | \(-0.664935\pi\) | ||||
−0.495282 | + | 0.868732i | \(0.664935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.6606 | −0.888600 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.1315 | −1.14652 | −0.573261 | − | 0.819373i | \(-0.694322\pi\) | ||||
−0.573261 | + | 0.819373i | \(0.694322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.5087 | −0.498159 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.09651 | 0.335653 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.4130 | −1.76563 | −0.882815 | − | 0.469720i | \(-0.844355\pi\) | ||||
−0.882815 | + | 0.469720i | \(0.844355\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.56579 | 0.167907 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.47113 | 0.351024 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −35.0639 | −1.64382 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.1698 | 0.709612 | 0.354806 | − | 0.934940i | \(-0.384547\pi\) | ||||
0.354806 | + | 0.934940i | \(0.384547\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.9575 | 1.25827 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.4457 | −1.51115 | −0.755573 | − | 0.655064i | \(-0.772642\pi\) | ||||
−0.755573 | + | 0.655064i | \(0.772642\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9901 | 0.603703 | 0.301851 | − | 0.953355i | \(-0.402395\pi\) | ||||
0.301851 | + | 0.953355i | \(0.402395\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.93500 | 0.136107 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.9067 | −0.736074 | −0.368037 | − | 0.929811i | \(-0.619970\pi\) | ||||
−0.368037 | + | 0.929811i | \(0.619970\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.5411 | −1.45643 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.35753 | −0.108629 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.0373 | −1.10524 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.1092 | 1.28974 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.1106 | 0.783440 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.78977 | 0.0817768 | 0.0408884 | − | 0.999164i | \(-0.486981\pi\) | ||||
0.0408884 | + | 0.999164i | \(0.486981\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.2038 | 1.28598 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.3716 | −0.699430 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 58.4740 | 2.65517 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.9530 | −1.53856 | −0.769279 | − | 0.638913i | \(-0.779384\pi\) | ||||
−0.769279 | + | 0.638913i | \(0.779384\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.682840 | −0.0308791 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.1809 | −1.72308 | −0.861540 | − | 0.507690i | \(-0.830500\pi\) | ||||
−0.861540 | + | 0.507690i | \(0.830500\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.186725 | 0.00840967 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.1868 | −0.997221 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.9404 | −0.580456 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.1759 | 0.947963 | 0.473982 | − | 0.880535i | \(-0.342816\pi\) | ||||
0.473982 | + | 0.880535i | \(0.342816\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.4504 | 0.466889 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.2551 | −1.75030 | −0.875149 | − | 0.483854i | \(-0.839236\pi\) | ||||
−0.875149 | + | 0.483854i | \(0.839236\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.71143 | −0.343154 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.18428 | −0.141419 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.7738 | −1.31970 | −0.659850 | − | 0.751397i | \(-0.729380\pi\) | ||||
−0.659850 | + | 0.751397i | \(0.729380\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.25240 | 0.188115 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.8106 | −0.918810 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −41.1697 | −1.81416 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.1161 | 1.06063 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.8297 | 0.475372 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.5279 | 0.943156 | 0.471578 | − | 0.881824i | \(-0.343684\pi\) | ||||
0.471578 | + | 0.881824i | \(0.343684\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.6347 | −1.03347 | −0.516737 | − | 0.856144i | \(-0.672854\pi\) | ||||
−0.516737 | + | 0.856144i | \(0.672854\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.5621 | −0.591900 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.38109 | −0.408647 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2333 | 0.488406 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.15059 | −0.266913 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.74312 | 0.162133 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 48.4515 | 2.09474 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.85768 | 0.339084 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.4389 | 0.880367 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.1463 | −0.737178 | −0.368589 | − | 0.929592i | \(-0.620159\pi\) | ||||
−0.368589 | + | 0.929592i | \(0.620159\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.29968 | 0.270345 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −37.8142 | −1.61978 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.4058 | 1.17179 | 0.585893 | − | 0.810389i | \(-0.300744\pi\) | ||||
0.585893 | + | 0.810389i | \(0.300744\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.2698 | 1.16385 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.144147 | −0.00614088 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.52900 | −0.320166 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.4747 | 0.911552 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.6536 | 1.34121 | 0.670603 | − | 0.741817i | \(-0.266035\pi\) | ||||
0.670603 | + | 0.741817i | \(0.266035\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.2327 | −1.06723 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.4818 | −0.569201 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.64185 | −0.279921 | −0.139960 | − | 0.990157i | \(-0.544697\pi\) | ||||
−0.139960 | + | 0.990157i | \(0.544697\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.2431 | −1.23027 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.6590 | −0.783604 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.8101 | 0.578948 | 0.289474 | − | 0.957186i | \(-0.406520\pi\) | ||||
0.289474 | + | 0.957186i | \(0.406520\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.9911 | 1.21324 | 0.606619 | − | 0.794992i | \(-0.292525\pi\) | ||||
0.606619 | + | 0.794992i | \(0.292525\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.15899 | 0.299071 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.2036 | 1.25958 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.0491 | 1.33422 | 0.667110 | − | 0.744959i | \(-0.267531\pi\) | ||||
0.667110 | + | 0.744959i | \(0.267531\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.6764 | 0.609930 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.7663 | −1.19343 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.7412 | −0.776182 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −23.2901 | −0.962928 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.7229 | −0.937876 | −0.468938 | − | 0.883231i | \(-0.655363\pi\) | ||||
−0.468938 | + | 0.883231i | \(0.655363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.24198 | 0.298401 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.7649 | 0.648481 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.81024 | 0.115403 | 0.0577014 | − | 0.998334i | \(-0.481623\pi\) | ||||
0.0577014 | + | 0.998334i | \(0.481623\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 85.3347 | 3.49838 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.3611 | 0.669617 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.412660 | 0.0168608 | 0.00843041 | − | 0.999964i | \(-0.497316\pi\) | ||||
0.00843041 | + | 0.999964i | \(0.497316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.3952 | −0.831938 | −0.415969 | − | 0.909379i | \(-0.636558\pi\) | ||||
−0.415969 | + | 0.909379i | \(0.636558\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20.9502 | −0.853157 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.7649 | −0.437655 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.01905 | 0.122539 | 0.0612697 | − | 0.998121i | \(-0.480485\pi\) | ||||
0.0612697 | + | 0.998121i | \(0.480485\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0695482 | 0.00281824 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.3154 | 1.02415 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.9897 | −0.968933 | −0.484467 | − | 0.874810i | \(-0.660986\pi\) | ||||
−0.484467 | + | 0.874810i | \(0.660986\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.85007 | 0.114926 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.03444 | 0.162420 | 0.0812102 | − | 0.996697i | \(-0.474121\pi\) | ||||
0.0812102 | + | 0.996697i | \(0.474121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.05253 | 0.283465 | 0.141732 | − | 0.989905i | \(-0.454733\pi\) | ||||
0.141732 | + | 0.989905i | \(0.454733\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.3612 | −0.897325 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.5106 | 0.501225 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.1627 | −0.966508 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.4076 | 0.415640 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −68.6393 | −2.73683 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.46677 | 0.0583912 | 0.0291956 | − | 0.999574i | \(-0.490705\pi\) | ||||
0.0291956 | + | 0.999574i | \(0.490705\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.5169 | 0.497502 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.2185 | −0.961081 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.4554 | 0.850093 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.59525 | −0.340023 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.390772 | 0.0154346 | 0.00771728 | − | 0.999970i | \(-0.497543\pi\) | ||||
0.00771728 | + | 0.999970i | \(0.497543\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.1837 | −0.598788 | −0.299394 | − | 0.954130i | \(-0.596785\pi\) | ||||
−0.299394 | + | 0.954130i | \(0.596785\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.2126 | −0.756494 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.8127 | 0.975486 | 0.487743 | − | 0.872987i | \(-0.337820\pi\) | ||||
0.487743 | + | 0.872987i | \(0.337820\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.73674 | 0.264440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.49411 | −0.136945 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 41.4722 | 1.62293 | 0.811465 | − | 0.584401i | \(-0.198670\pi\) | ||||
0.811465 | + | 0.584401i | \(0.198670\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35.7126 | 1.39541 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.82453 | 0.110195 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.5869 | −1.30836 | −0.654180 | − | 0.756339i | \(-0.726986\pi\) | ||||
−0.654180 | + | 0.756339i | \(0.726986\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.8961 | −1.59068 | −0.795338 | − | 0.606167i | \(-0.792706\pi\) | ||||
−0.795338 | + | 0.606167i | \(0.792706\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.1522 | −0.549627 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −65.8764 | −2.55458 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.154888 | −0.00599728 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.30985 | 0.359940 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.8686 | −1.15306 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.82118 | −0.147295 | −0.0736477 | − | 0.997284i | \(-0.523464\pi\) | ||||
−0.0736477 | + | 0.997284i | \(0.523464\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.7290 | −0.759370 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.9609 | 1.42052 | 0.710261 | − | 0.703938i | \(-0.248577\pi\) | ||||
0.710261 | + | 0.703938i | \(0.248577\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −69.6131 | −2.67151 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.2775 | −0.470474 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.8824 | −1.52606 | −0.763029 | − | 0.646364i | \(-0.776289\pi\) | ||||
−0.763029 | + | 0.646364i | \(0.776289\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.7014 | 0.638126 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.3037 | 0.622027 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.6732 | −0.749490 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.9976 | −1.17920 | −0.589602 | − | 0.807694i | \(-0.700715\pi\) | ||||
−0.589602 | + | 0.807694i | \(0.700715\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 26.4133 | 1.00336 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.0821 | 0.723825 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.10961 | −0.345051 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.1387 | −0.421304 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.5425 | −1.41796 | −0.708981 | − | 0.705228i | \(-0.750845\pi\) | ||||
−0.708981 | + | 0.705228i | \(0.750845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.9879 | 1.99848 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.2755 | 0.725958 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.18044 | 0.345266 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.66690 | −0.212825 | −0.106412 | − | 0.994322i | \(-0.533936\pi\) | ||||
−0.106412 | + | 0.994322i | \(0.533936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.00091 | −0.187549 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.78159 | 0.291423 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.5096 | 0.954007 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.6531 | −0.584576 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.62894 | 0.321805 | 0.160903 | − | 0.986970i | \(-0.448560\pi\) | ||||
0.160903 | + | 0.986970i | \(0.448560\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.0125 | 1.82532 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.85520 | 0.292138 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.136656 | −0.00507526 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.7941 | −1.14209 | −0.571046 | − | 0.820918i | \(-0.693462\pi\) | ||||
−0.571046 | + | 0.820918i | \(0.693462\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.45653 | −0.165057 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 61.4087 | 2.27128 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.6430 | −0.393107 | −0.196554 | − | 0.980493i | \(-0.562975\pi\) | ||||
−0.196554 | + | 0.980493i | \(0.562975\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.3364 | 0.602578 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.9467 | 0.845253 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.0597 | −0.701124 | −0.350562 | − | 0.936539i | \(-0.614009\pi\) | ||||
−0.350562 | + | 0.936539i | \(0.614009\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.9252 | 0.401347 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.7132 | −0.466402 | −0.233201 | − | 0.972429i | \(-0.574920\pi\) | ||||
−0.233201 | + | 0.972429i | \(0.574920\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.6789 | 1.19726 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.1071 | −0.699093 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −57.6814 | −2.10763 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.8832 | 0.980982 | 0.490491 | − | 0.871446i | \(-0.336817\pi\) | ||||
0.490491 | + | 0.871446i | \(0.336817\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.692263 | −0.0252275 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.4040 | 1.25209 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.85548 | 0.176475 | 0.0882377 | − | 0.996099i | \(-0.471876\pi\) | ||||
0.0882377 | + | 0.996099i | \(0.471876\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.1831 | 0.405920 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.4115 | 1.57366 | 0.786832 | − | 0.617167i | \(-0.211720\pi\) | ||||
0.786832 | + | 0.617167i | \(0.211720\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 45.0177 | 1.62975 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 56.6809 | 2.04930 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.07176 | 0.255346 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.8291 | −0.823239 | −0.411619 | − | 0.911356i | \(-0.635037\pi\) | ||||
−0.411619 | + | 0.911356i | \(0.635037\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.06524 | −0.0383636 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.96647 | 0.322501 | 0.161251 | − | 0.986913i | \(-0.448447\pi\) | ||||
0.161251 | + | 0.986913i | \(0.448447\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.86560 | 0.246620 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25.5656 | −0.917162 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.03240 | 0.251962 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.41437 | 0.336872 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.101173 | 0.00361562 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.8562 | −0.387476 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.6377 | −0.735655 | −0.367828 | − | 0.929894i | \(-0.619898\pi\) | ||||
−0.367828 | + | 0.929894i | \(0.619898\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.29347 | 0.188453 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.8138 | 1.23784 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.3540 | −1.11341 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.9795 | −0.531267 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.94902 | −0.352413 | −0.176206 | − | 0.984353i | \(-0.556383\pi\) | ||||
−0.176206 | + | 0.984353i | \(0.556383\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −61.6100 | −2.17960 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.30975 | 0.293611 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.09370 | −0.109174 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −70.7849 | −2.49484 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.5728 | −0.583389 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.2389 | −0.711562 | −0.355781 | − | 0.934569i | \(-0.615785\pi\) | ||||
−0.355781 | + | 0.934569i | \(0.615785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.9341 | 1.33205 | 0.666024 | − | 0.745930i | \(-0.267995\pi\) | ||||
0.666024 | + | 0.745930i | \(0.267995\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.86878 | −0.311042 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.14443 | −0.110145 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.4061 | −1.65853 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.7268 | 0.968854 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.5637 | 0.717677 | 0.358839 | − | 0.933400i | \(-0.383173\pi\) | ||||
0.358839 | + | 0.933400i | \(0.383173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −50.4042 | −1.75698 | −0.878489 | − | 0.477762i | \(-0.841448\pi\) | ||||
−0.878489 | + | 0.477762i | \(0.841448\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.86670 | 0.343515 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.89613 | −0.205028 | −0.102514 | − | 0.994732i | \(-0.532689\pi\) | ||||
−0.102514 | + | 0.994732i | \(0.532689\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.16574 | −0.0404880 | −0.0202440 | − | 0.999795i | \(-0.506444\pi\) | ||||
−0.0202440 | + | 0.999795i | \(0.506444\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.28071 | 0.183186 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −52.2157 | −1.80917 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.1233 | 1.66537 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.08293 | −0.175692 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.8260 | −1.68566 | −0.842831 | − | 0.538179i | \(-0.819112\pi\) | ||||
−0.842831 | + | 0.538179i | \(0.819112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9993 | −0.999976 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.27743 | −0.0439972 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.6634 | −0.504436 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.8156 | 0.440349 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.595073 | −0.0204229 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 56.9361 | 1.95174 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.7449 | 0.847248 | 0.423624 | − | 0.905838i | \(-0.360758\pi\) | ||||
0.423624 | + | 0.905838i | \(0.360758\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −43.7563 | −1.49644 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.8182 | 0.881932 | 0.440966 | − | 0.897524i | \(-0.354636\pi\) | ||||
0.440966 | + | 0.897524i | \(0.354636\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.9861 | 1.19371 | 0.596855 | − | 0.802349i | \(-0.296417\pi\) | ||||
0.596855 | + | 0.802349i | \(0.296417\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.39300 | −0.115633 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.1255 | 1.26377 | 0.631884 | − | 0.775063i | \(-0.282282\pi\) | ||||
0.631884 | + | 0.775063i | \(0.282282\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 49.8701 | 1.69564 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.6737 | 0.770039 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.47749 | 0.185811 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0879 | 0.816186 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −46.2384 | −1.56493 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.96231 | −0.0663380 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.08105 | 0.306645 | 0.153323 | − | 0.988176i | \(-0.451003\pi\) | ||||
0.153323 | + | 0.988176i | \(0.451003\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.1448 | −0.578281 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.1440 | −0.611286 | −0.305643 | − | 0.952146i | \(-0.598871\pi\) | ||||
−0.305643 | + | 0.952146i | \(0.598871\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 58.4498 | 1.96699 | 0.983497 | − | 0.180925i | \(-0.0579090\pi\) | ||||
0.983497 | + | 0.180925i | \(0.0579090\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.38453 | 0.180999 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.7133 | −0.863369 | −0.431685 | − | 0.902025i | \(-0.642081\pi\) | ||||
−0.431685 | + | 0.902025i | \(0.642081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.8320 | 0.966995 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.5748 | 0.454771 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 47.5614 | 1.59158 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.1841 | 1.20950 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.7392 | 0.391962 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.0352076 | −0.00117424 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.8785 | 1.59507 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.8725 | 0.761149 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.0096 | 0.964310 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.2876 | 1.66977 | 0.834887 | − | 0.550422i | \(-0.185533\pi\) | ||||
0.834887 | + | 0.550422i | \(0.185533\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.09782 | 0.202252 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.5893 | 1.84176 | 0.920878 | − | 0.389852i | \(-0.127474\pi\) | ||||
0.920878 | + | 0.389852i | \(0.127474\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.9280 | 0.692616 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.8733 | −0.789228 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −42.5157 | −1.40399 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.3486 | −0.803186 | −0.401593 | − | 0.915818i | \(-0.631543\pi\) | ||||
−0.401593 | + | 0.915818i | \(0.631543\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.197116 | −0.00649518 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.88255 | 0.325288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.2340 | 1.65168 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32.5550 | 1.06925 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.1855 | 1.44968 | 0.724839 | − | 0.688918i | \(-0.241914\pi\) | ||||
0.724839 | + | 0.688918i | \(0.241914\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.3093 | 1.32108 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.47984 | −0.179402 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −62.0826 | −2.03032 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.3389 | −1.31781 | −0.658907 | − | 0.752225i | \(-0.728981\pi\) | ||||
−0.658907 | + | 0.752225i | \(0.728981\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0120 | 0.457265 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.6135 | −1.25876 | −0.629382 | − | 0.777096i | \(-0.716692\pi\) | ||||
−0.629382 | + | 0.777096i | \(0.716692\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.55639 | 0.246070 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 46.2367 | 1.50408 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.82218 | −0.124204 | −0.0621021 | − | 0.998070i | \(-0.519780\pi\) | ||||
−0.0621021 | + | 0.998070i | \(0.519780\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.24755 | −0.105420 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.5569 | −0.374759 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.5098 | 0.696771 | 0.348385 | − | 0.937351i | \(-0.386730\pi\) | ||||
0.348385 | + | 0.937351i | \(0.386730\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.9667 | 1.06678 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0505976 | −0.00163559 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.8829 | −0.642053 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.2312 | −0.942941 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38.3131 | −1.23462 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 67.5837 | 2.17560 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.97580 | −0.224326 | −0.112163 | − | 0.993690i | \(-0.535778\pi\) | ||||
−0.112163 | + | 0.993690i | \(0.535778\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26.5885 | −0.854146 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.46260 | −0.143212 | −0.0716058 | − | 0.997433i | \(-0.522812\pi\) | ||||
−0.0716058 | + | 0.997433i | \(0.522812\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.7172 | −0.728279 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.3574 | 0.331702 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.4911 | 1.39140 | 0.695702 | − | 0.718330i | \(-0.255093\pi\) | ||||
0.695702 | + | 0.718330i | \(0.255093\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.10166 | −0.290890 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.9016 | 0.954685 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.7255 | 0.852411 | 0.426205 | − | 0.904626i | \(-0.359850\pi\) | ||||
0.426205 | + | 0.904626i | \(0.359850\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 72.5962 | 2.31311 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.9475 | −0.730426 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50.9383 | −1.61975 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.0783 | −1.30490 | −0.652448 | − | 0.757834i | \(-0.726258\pi\) | ||||
−0.652448 | + | 0.757834i | \(0.726258\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.3741 | 0.424413 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 75.3419 | 2.38850 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.2506 | −0.578001 | −0.289001 | − | 0.957329i | \(-0.593323\pi\) | ||||
−0.289001 | + | 0.957329i | \(0.593323\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37.1907 | −1.17666 |
(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 | 8032.2.a.j.1.16 | yes | 30 | |
4.3 | odd | 2 | 8032.2.a.g.1.15 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8032.2.a.g.1.15 | ✓ | 30 | 4.3 | odd | 2 | ||
8032.2.a.j.1.16 | yes | 30 | 1.1 | even | 1 | trivial |