Properties

Label 6012.2.h.a.3005.2
Level $6012$
Weight $2$
Character 6012.3005
Analytic conductor $48.006$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6012,2,Mod(3005,6012)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6012.3005");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6012.h (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(48.0060616952\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3005.2
Character \(\chi\) \(=\) 6012.3005
Dual form 6012.2.h.a.3005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.09297 q^{5} +2.29241 q^{7} +O(q^{10})\) \(q-4.09297 q^{5} +2.29241 q^{7} -1.40323i q^{11} -5.26451i q^{13} -0.313267 q^{17} -0.473923 q^{19} +8.04034 q^{23} +11.7524 q^{25} +2.26656i q^{29} +1.40647 q^{31} -9.38276 q^{35} +3.51582i q^{37} -2.02537 q^{41} -7.09211i q^{43} +8.55435i q^{47} -1.74486 q^{49} -8.65647 q^{53} +5.74337i q^{55} +2.04140 q^{59} +11.9929 q^{61} +21.5475i q^{65} -2.40852i q^{67} -10.6701 q^{71} +5.44685i q^{73} -3.21677i q^{77} +3.13005i q^{79} -5.01486 q^{83} +1.28219 q^{85} +3.62776i q^{89} -12.0684i q^{91} +1.93975 q^{95} +13.7994 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 8 q^{19} + 64 q^{25} - 8 q^{31} + 56 q^{49} - 8 q^{61} + 32 q^{85} - 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6012\mathbb{Z}\right)^\times\).

\(n\) \(3007\) \(3341\) \(4681\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −4.09297 −1.83043 −0.915216 0.402963i \(-0.867980\pi\)
−0.915216 + 0.402963i \(0.867980\pi\)
\(6\) 0 0
\(7\) 2.29241 0.866449 0.433224 0.901286i \(-0.357376\pi\)
0.433224 + 0.901286i \(0.357376\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.40323i 0.423089i −0.977368 0.211545i \(-0.932151\pi\)
0.977368 0.211545i \(-0.0678494\pi\)
\(12\) 0 0
\(13\) 5.26451i 1.46011i −0.683387 0.730057i \(-0.739494\pi\)
0.683387 0.730057i \(-0.260506\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.313267 −0.0759783 −0.0379891 0.999278i \(-0.512095\pi\)
−0.0379891 + 0.999278i \(0.512095\pi\)
\(18\) 0 0
\(19\) −0.473923 −0.108725 −0.0543627 0.998521i \(-0.517313\pi\)
−0.0543627 + 0.998521i \(0.517313\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 8.04034 1.67653 0.838263 0.545265i \(-0.183571\pi\)
0.838263 + 0.545265i \(0.183571\pi\)
\(24\) 0 0
\(25\) 11.7524 2.35048
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.26656i 0.420889i 0.977606 + 0.210445i \(0.0674912\pi\)
−0.977606 + 0.210445i \(0.932509\pi\)
\(30\) 0 0
\(31\) 1.40647 0.252609 0.126304 0.991992i \(-0.459688\pi\)
0.126304 + 0.991992i \(0.459688\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −9.38276 −1.58598
\(36\) 0 0
\(37\) 3.51582i 0.577997i 0.957330 + 0.288998i \(0.0933222\pi\)
−0.957330 + 0.288998i \(0.906678\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.02537 −0.316310 −0.158155 0.987414i \(-0.550554\pi\)
−0.158155 + 0.987414i \(0.550554\pi\)
\(42\) 0 0
\(43\) 7.09211i 1.08154i −0.841171 0.540769i \(-0.818133\pi\)
0.841171 0.540769i \(-0.181867\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.55435i 1.24778i 0.781512 + 0.623890i \(0.214449\pi\)
−0.781512 + 0.623890i \(0.785551\pi\)
\(48\) 0 0
\(49\) −1.74486 −0.249266
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8.65647 −1.18906 −0.594529 0.804074i \(-0.702661\pi\)
−0.594529 + 0.804074i \(0.702661\pi\)
\(54\) 0 0
\(55\) 5.74337i 0.774436i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.04140 0.265767 0.132884 0.991132i \(-0.457576\pi\)
0.132884 + 0.991132i \(0.457576\pi\)
\(60\) 0 0
\(61\) 11.9929 1.53554 0.767770 0.640726i \(-0.221366\pi\)
0.767770 + 0.640726i \(0.221366\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 21.5475i 2.67264i
\(66\) 0 0
\(67\) 2.40852i 0.294247i −0.989118 0.147124i \(-0.952998\pi\)
0.989118 0.147124i \(-0.0470016\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −10.6701 −1.26631 −0.633153 0.774027i \(-0.718240\pi\)
−0.633153 + 0.774027i \(0.718240\pi\)
\(72\) 0 0
\(73\) 5.44685i 0.637505i 0.947838 + 0.318753i \(0.103264\pi\)
−0.947838 + 0.318753i \(0.896736\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.21677i 0.366585i
\(78\) 0 0
\(79\) 3.13005i 0.352158i 0.984376 + 0.176079i \(0.0563415\pi\)
−0.984376 + 0.176079i \(0.943659\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.01486 −0.550452 −0.275226 0.961380i \(-0.588753\pi\)
−0.275226 + 0.961380i \(0.588753\pi\)
\(84\) 0 0
\(85\) 1.28219 0.139073
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.62776i 0.384542i 0.981342 + 0.192271i \(0.0615853\pi\)
−0.981342 + 0.192271i \(0.938415\pi\)
\(90\) 0 0
\(91\) 12.0684i 1.26511i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.93975 0.199014
\(96\) 0 0
\(97\) 13.7994 1.40111 0.700557 0.713596i \(-0.252935\pi\)
0.700557 + 0.713596i \(0.252935\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.20749 0.418661 0.209330 0.977845i \(-0.432872\pi\)
0.209330 + 0.977845i \(0.432872\pi\)
\(102\) 0 0
\(103\) 17.4177i 1.71621i −0.513470 0.858107i \(-0.671640\pi\)
0.513470 0.858107i \(-0.328360\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.21671i 0.891013i −0.895279 0.445507i \(-0.853024\pi\)
0.895279 0.445507i \(-0.146976\pi\)
\(108\) 0 0
\(109\) 13.7151i 1.31367i −0.754036 0.656833i \(-0.771895\pi\)
0.754036 0.656833i \(-0.228105\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −11.9552 −1.12465 −0.562326 0.826916i \(-0.690093\pi\)
−0.562326 + 0.826916i \(0.690093\pi\)
\(114\) 0 0
\(115\) −32.9089 −3.06877
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.718135 −0.0658313
\(120\) 0 0
\(121\) 9.03095 0.820996
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −27.6375 −2.47197
\(126\) 0 0
\(127\) 0.269256 0.0238926 0.0119463 0.999929i \(-0.496197\pi\)
0.0119463 + 0.999929i \(0.496197\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.7781 0.941688 0.470844 0.882217i \(-0.343949\pi\)
0.470844 + 0.882217i \(0.343949\pi\)
\(132\) 0 0
\(133\) −1.08642 −0.0942049
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 13.6657i 1.16754i −0.811920 0.583768i \(-0.801578\pi\)
0.811920 0.583768i \(-0.198422\pi\)
\(138\) 0 0
\(139\) 8.54589i 0.724853i 0.932012 + 0.362426i \(0.118052\pi\)
−0.932012 + 0.362426i \(0.881948\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −7.38731 −0.617758
\(144\) 0 0
\(145\) 9.27696i 0.770409i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.13771 −0.338974 −0.169487 0.985532i \(-0.554211\pi\)
−0.169487 + 0.985532i \(0.554211\pi\)
\(150\) 0 0
\(151\) 13.7983i 1.12289i −0.827515 0.561443i \(-0.810246\pi\)
0.827515 0.561443i \(-0.189754\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5.75662 −0.462383
\(156\) 0 0
\(157\) −15.9049 −1.26935 −0.634675 0.772779i \(-0.718866\pi\)
−0.634675 + 0.772779i \(0.718866\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 18.4317 1.45263
\(162\) 0 0
\(163\) 9.80969i 0.768354i −0.923259 0.384177i \(-0.874485\pi\)
0.923259 0.384177i \(-0.125515\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 11.8941 5.05270i 0.920395 0.390990i
\(168\) 0 0
\(169\) −14.7151 −1.13193
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.08630i 0.310675i −0.987861 0.155338i \(-0.950353\pi\)
0.987861 0.155338i \(-0.0496466\pi\)
\(174\) 0 0
\(175\) 26.9413 2.03657
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 25.8548i 1.93248i −0.257650 0.966238i \(-0.582948\pi\)
0.257650 0.966238i \(-0.417052\pi\)
\(180\) 0 0
\(181\) 4.62380 0.343685 0.171842 0.985124i \(-0.445028\pi\)
0.171842 + 0.985124i \(0.445028\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 14.3901i 1.05798i
\(186\) 0 0
\(187\) 0.439584i 0.0321456i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 20.0201i 1.44861i −0.689482 0.724303i \(-0.742162\pi\)
0.689482 0.724303i \(-0.257838\pi\)
\(192\) 0 0
\(193\) 25.5047i 1.83586i 0.396737 + 0.917932i \(0.370143\pi\)
−0.396737 + 0.917932i \(0.629857\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.7184 1.33363 0.666817 0.745222i \(-0.267656\pi\)
0.666817 + 0.745222i \(0.267656\pi\)
\(198\) 0 0
\(199\) 1.99785 0.141624 0.0708120 0.997490i \(-0.477441\pi\)
0.0708120 + 0.997490i \(0.477441\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.19588i 0.364679i
\(204\) 0 0
\(205\) 8.28978 0.578983
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.665022i 0.0460005i
\(210\) 0 0
\(211\) −7.85976 −0.541088 −0.270544 0.962708i \(-0.587204\pi\)
−0.270544 + 0.962708i \(0.587204\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 29.0278i 1.97968i
\(216\) 0 0
\(217\) 3.22419 0.218873
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.64920i 0.110937i
\(222\) 0 0
\(223\) −9.96950 −0.667607 −0.333803 0.942643i \(-0.608332\pi\)
−0.333803 + 0.942643i \(0.608332\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.58319 −0.171452 −0.0857262 0.996319i \(-0.527321\pi\)
−0.0857262 + 0.996319i \(0.527321\pi\)
\(228\) 0 0
\(229\) −0.0922633 −0.00609693 −0.00304846 0.999995i \(-0.500970\pi\)
−0.00304846 + 0.999995i \(0.500970\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 22.0534i 1.44477i 0.691492 + 0.722384i \(0.256954\pi\)
−0.691492 + 0.722384i \(0.743046\pi\)
\(234\) 0 0
\(235\) 35.0127i 2.28398i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 21.9512i 1.41991i −0.704249 0.709953i \(-0.748716\pi\)
0.704249 0.709953i \(-0.251284\pi\)
\(240\) 0 0
\(241\) 20.8816i 1.34510i 0.740052 + 0.672550i \(0.234801\pi\)
−0.740052 + 0.672550i \(0.765199\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 7.14168 0.456265
\(246\) 0 0
\(247\) 2.49497i 0.158751i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 14.8849i 0.939526i −0.882793 0.469763i \(-0.844339\pi\)
0.882793 0.469763i \(-0.155661\pi\)
\(252\) 0 0
\(253\) 11.2824i 0.709320i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0.502162 0.0313240 0.0156620 0.999877i \(-0.495014\pi\)
0.0156620 + 0.999877i \(0.495014\pi\)
\(258\) 0 0
\(259\) 8.05969i 0.500804i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 17.6073i 1.08571i 0.839826 + 0.542855i \(0.182657\pi\)
−0.839826 + 0.542855i \(0.817343\pi\)
\(264\) 0 0
\(265\) 35.4307 2.17649
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.56273 0.217223 0.108612 0.994084i \(-0.465359\pi\)
0.108612 + 0.994084i \(0.465359\pi\)
\(270\) 0 0
\(271\) 16.9568i 1.03005i 0.857174 + 0.515027i \(0.172218\pi\)
−0.857174 + 0.515027i \(0.827782\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 16.4913i 0.994464i
\(276\) 0 0
\(277\) 16.7583i 1.00691i −0.864022 0.503454i \(-0.832062\pi\)
0.864022 0.503454i \(-0.167938\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.5849i 0.750752i −0.926873 0.375376i \(-0.877514\pi\)
0.926873 0.375376i \(-0.122486\pi\)
\(282\) 0 0
\(283\) 5.95647 0.354075 0.177038 0.984204i \(-0.443349\pi\)
0.177038 + 0.984204i \(0.443349\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.64297 −0.274066
\(288\) 0 0
\(289\) −16.9019 −0.994227
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 11.1176i 0.649494i 0.945801 + 0.324747i \(0.105279\pi\)
−0.945801 + 0.324747i \(0.894721\pi\)
\(294\) 0 0
\(295\) −8.35539 −0.486469
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 42.3285i 2.44792i
\(300\) 0 0
\(301\) 16.2580i 0.937097i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −49.0868 −2.81070
\(306\) 0 0
\(307\) 2.18955i 0.124964i 0.998046 + 0.0624821i \(0.0199016\pi\)
−0.998046 + 0.0624821i \(0.980098\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 23.8065i 1.34994i −0.737844 0.674971i \(-0.764156\pi\)
0.737844 0.674971i \(-0.235844\pi\)
\(312\) 0 0
\(313\) 21.6598i 1.22428i −0.790748 0.612142i \(-0.790308\pi\)
0.790748 0.612142i \(-0.209692\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 28.9496i 1.62597i −0.582282 0.812987i \(-0.697840\pi\)
0.582282 0.812987i \(-0.302160\pi\)
\(318\) 0 0
\(319\) 3.18050 0.178074
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.148464 0.00826076
\(324\) 0 0
\(325\) 61.8708i 3.43197i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 19.6101i 1.08114i
\(330\) 0 0
\(331\) 30.2737i 1.66400i −0.554779 0.831998i \(-0.687197\pi\)
0.554779 0.831998i \(-0.312803\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 9.85800i 0.538600i
\(336\) 0 0
\(337\) 1.69185 0.0921611 0.0460805 0.998938i \(-0.485327\pi\)
0.0460805 + 0.998938i \(0.485327\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.97359i 0.106876i
\(342\) 0 0
\(343\) −20.0468 −1.08243
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 18.9707 1.01840 0.509201 0.860648i \(-0.329941\pi\)
0.509201 + 0.860648i \(0.329941\pi\)
\(348\) 0 0
\(349\) 10.5336i 0.563849i −0.959437 0.281925i \(-0.909027\pi\)
0.959437 0.281925i \(-0.0909728\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9.52080i 0.506741i 0.967369 + 0.253370i \(0.0815392\pi\)
−0.967369 + 0.253370i \(0.918461\pi\)
\(354\) 0 0
\(355\) 43.6724 2.31789
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 15.5816i 0.822366i 0.911553 + 0.411183i \(0.134884\pi\)
−0.911553 + 0.411183i \(0.865116\pi\)
\(360\) 0 0
\(361\) −18.7754 −0.988179
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 22.2938i 1.16691i
\(366\) 0 0
\(367\) −31.7003 −1.65474 −0.827371 0.561655i \(-0.810165\pi\)
−0.827371 + 0.561655i \(0.810165\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −19.8442 −1.03026
\(372\) 0 0
\(373\) 18.7719i 0.971973i −0.873966 0.485986i \(-0.838460\pi\)
0.873966 0.485986i \(-0.161540\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 11.9323 0.614546
\(378\) 0 0
\(379\) 24.3145i 1.24895i 0.781045 + 0.624475i \(0.214687\pi\)
−0.781045 + 0.624475i \(0.785313\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 26.0531i 1.33125i −0.746285 0.665627i \(-0.768164\pi\)
0.746285 0.665627i \(-0.231836\pi\)
\(384\) 0 0
\(385\) 13.1662i 0.671009i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −30.3750 −1.54007 −0.770036 0.638001i \(-0.779762\pi\)
−0.770036 + 0.638001i \(0.779762\pi\)
\(390\) 0 0
\(391\) −2.51877 −0.127380
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 12.8112i 0.644602i
\(396\) 0 0
\(397\) −19.8263 −0.995053 −0.497527 0.867449i \(-0.665758\pi\)
−0.497527 + 0.867449i \(0.665758\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.0482552 −0.00240975 −0.00120487 0.999999i \(-0.500384\pi\)
−0.00120487 + 0.999999i \(0.500384\pi\)
\(402\) 0 0
\(403\) 7.40436i 0.368837i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.93349 0.244544
\(408\) 0 0
\(409\) 13.5257 0.668804 0.334402 0.942431i \(-0.391466\pi\)
0.334402 + 0.942431i \(0.391466\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4.67972 0.230274
\(414\) 0 0
\(415\) 20.5257 1.00757
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 12.3643i 0.604036i 0.953302 + 0.302018i \(0.0976603\pi\)
−0.953302 + 0.302018i \(0.902340\pi\)
\(420\) 0 0
\(421\) −33.8891 −1.65166 −0.825828 0.563923i \(-0.809292\pi\)
−0.825828 + 0.563923i \(0.809292\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.68164 −0.178586
\(426\) 0 0
\(427\) 27.4927 1.33047
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12.6335i 0.608534i −0.952587 0.304267i \(-0.901589\pi\)
0.952587 0.304267i \(-0.0984115\pi\)
\(432\) 0 0
\(433\) 8.31009 0.399357 0.199679 0.979861i \(-0.436010\pi\)
0.199679 + 0.979861i \(0.436010\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.81050 −0.182281
\(438\) 0 0
\(439\) 32.4531i 1.54890i −0.632634 0.774451i \(-0.718026\pi\)
0.632634 0.774451i \(-0.281974\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.84588 −0.325258 −0.162629 0.986687i \(-0.551997\pi\)
−0.162629 + 0.986687i \(0.551997\pi\)
\(444\) 0 0
\(445\) 14.8483i 0.703879i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 17.2495i 0.814056i −0.913416 0.407028i \(-0.866565\pi\)
0.913416 0.407028i \(-0.133435\pi\)
\(450\) 0 0
\(451\) 2.84205i 0.133827i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 49.3957i 2.31571i
\(456\) 0 0
\(457\) 23.2886i 1.08939i −0.838633 0.544697i \(-0.816645\pi\)
0.838633 0.544697i \(-0.183355\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.93021i 0.0898990i −0.998989 0.0449495i \(-0.985687\pi\)
0.998989 0.0449495i \(-0.0143127\pi\)
\(462\) 0 0
\(463\) 7.27902i 0.338285i 0.985592 + 0.169142i \(0.0540998\pi\)
−0.985592 + 0.169142i \(0.945900\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.77061i 0.220757i 0.993890 + 0.110379i \(0.0352064\pi\)
−0.993890 + 0.110379i \(0.964794\pi\)
\(468\) 0 0
\(469\) 5.52131i 0.254950i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −9.95185 −0.457587
\(474\) 0 0
\(475\) −5.56974 −0.255557
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.73270 −0.0791691 −0.0395846 0.999216i \(-0.512603\pi\)
−0.0395846 + 0.999216i \(0.512603\pi\)
\(480\) 0 0
\(481\) 18.5091 0.843940
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −56.4805 −2.56465
\(486\) 0 0
\(487\) 11.9288i 0.540544i 0.962784 + 0.270272i \(0.0871136\pi\)
−0.962784 + 0.270272i \(0.912886\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16.7052i 0.753895i −0.926235 0.376948i \(-0.876974\pi\)
0.926235 0.376948i \(-0.123026\pi\)
\(492\) 0 0
\(493\) 0.710037i 0.0319784i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −24.4602 −1.09719
\(498\) 0 0
\(499\) 13.7439i 0.615263i 0.951506 + 0.307631i \(0.0995364\pi\)
−0.951506 + 0.307631i \(0.900464\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.44347i 0.331888i −0.986135 0.165944i \(-0.946933\pi\)
0.986135 0.165944i \(-0.0530671\pi\)
\(504\) 0 0
\(505\) −17.2211 −0.766330
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 20.1790i 0.894418i 0.894429 + 0.447209i \(0.147582\pi\)
−0.894429 + 0.447209i \(0.852418\pi\)
\(510\) 0 0
\(511\) 12.4864i 0.552366i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 71.2901i 3.14142i
\(516\) 0 0
\(517\) 12.0037 0.527922
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 26.8880 1.17798 0.588991 0.808139i \(-0.299525\pi\)
0.588991 + 0.808139i \(0.299525\pi\)
\(522\) 0 0
\(523\) −20.0539 −0.876895 −0.438448 0.898757i \(-0.644472\pi\)
−0.438448 + 0.898757i \(0.644472\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.440599 −0.0191928
\(528\) 0 0
\(529\) 41.6471 1.81074
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 10.6626i 0.461848i
\(534\) 0 0
\(535\) 37.7238i 1.63094i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.44844i 0.105462i
\(540\) 0 0
\(541\) 21.8696i 0.940248i −0.882600 0.470124i \(-0.844209\pi\)
0.882600 0.470124i \(-0.155791\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 56.1355i 2.40458i
\(546\) 0 0
\(547\) 29.8845i 1.27777i 0.769303 + 0.638884i \(0.220604\pi\)
−0.769303 + 0.638884i \(0.779396\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.07417i 0.0457613i
\(552\) 0 0
\(553\) 7.17536i 0.305127i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 30.7789i 1.30414i 0.758158 + 0.652071i \(0.226100\pi\)
−0.758158 + 0.652071i \(0.773900\pi\)
\(558\) 0 0
\(559\) −37.3365 −1.57917
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 25.0579i 1.05607i 0.849224 + 0.528033i \(0.177070\pi\)
−0.849224 + 0.528033i \(0.822930\pi\)
\(564\) 0 0
\(565\) 48.9323 2.05860
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.04649 −0.211560 −0.105780 0.994390i \(-0.533734\pi\)
−0.105780 + 0.994390i \(0.533734\pi\)
\(570\) 0 0
\(571\) 5.72341i 0.239517i −0.992803 0.119759i \(-0.961788\pi\)
0.992803 0.119759i \(-0.0382120\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 94.4935 3.94065
\(576\) 0 0
\(577\) 18.9725 0.789835 0.394917 0.918717i \(-0.370773\pi\)
0.394917 + 0.918717i \(0.370773\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −11.4961 −0.476939
\(582\) 0 0
\(583\) 12.1470i 0.503077i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −30.7081 −1.26746 −0.633730 0.773554i \(-0.718477\pi\)
−0.633730 + 0.773554i \(0.718477\pi\)
\(588\) 0 0
\(589\) −0.666556 −0.0274650
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −42.8134 −1.75814 −0.879068 0.476696i \(-0.841834\pi\)
−0.879068 + 0.476696i \(0.841834\pi\)
\(594\) 0 0
\(595\) 2.93931 0.120500
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5.22309i 0.213410i 0.994291 + 0.106705i \(0.0340300\pi\)
−0.994291 + 0.106705i \(0.965970\pi\)
\(600\) 0 0
\(601\) 36.4071 1.48508 0.742538 0.669804i \(-0.233622\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −36.9634 −1.50278
\(606\) 0 0
\(607\) 16.7018i 0.677904i 0.940804 + 0.338952i \(0.110072\pi\)
−0.940804 + 0.338952i \(0.889928\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 45.0345 1.82190
\(612\) 0 0
\(613\) −17.1592 −0.693055 −0.346527 0.938040i \(-0.612639\pi\)
−0.346527 + 0.938040i \(0.612639\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 34.0578i 1.37112i −0.728017 0.685559i \(-0.759558\pi\)
0.728017 0.685559i \(-0.240442\pi\)
\(618\) 0 0
\(619\) 21.0690i 0.846833i −0.905935 0.423416i \(-0.860831\pi\)
0.905935 0.423416i \(-0.139169\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8.31632i 0.333186i
\(624\) 0 0
\(625\) 54.3573 2.17429
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.10139i 0.0439152i
\(630\) 0 0
\(631\) 16.2976 0.648797 0.324398 0.945921i \(-0.394838\pi\)
0.324398 + 0.945921i \(0.394838\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.10206 −0.0437337
\(636\) 0 0
\(637\) 9.18586i 0.363957i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −13.8706 −0.547858 −0.273929 0.961750i \(-0.588323\pi\)
−0.273929 + 0.961750i \(0.588323\pi\)
\(642\) 0 0
\(643\) 18.1271i 0.714865i 0.933939 + 0.357432i \(0.116348\pi\)
−0.933939 + 0.357432i \(0.883652\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −34.0926 −1.34032 −0.670159 0.742218i \(-0.733774\pi\)
−0.670159 + 0.742218i \(0.733774\pi\)
\(648\) 0 0
\(649\) 2.86455i 0.112443i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 28.3491i 1.10939i −0.832055 0.554693i \(-0.812836\pi\)
0.832055 0.554693i \(-0.187164\pi\)
\(654\) 0 0
\(655\) −44.1145 −1.72370
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −21.2879 −0.829260 −0.414630 0.909990i \(-0.636089\pi\)
−0.414630 + 0.909990i \(0.636089\pi\)
\(660\) 0 0
\(661\) 15.5357i 0.604267i −0.953266 0.302134i \(-0.902301\pi\)
0.953266 0.302134i \(-0.0976989\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.44671 0.172436
\(666\) 0 0
\(667\) 18.2239i 0.705632i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 16.8288i 0.649670i
\(672\) 0 0
\(673\) 28.1672i 1.08577i −0.839808 0.542883i \(-0.817333\pi\)
0.839808 0.542883i \(-0.182667\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 44.4868i 1.70977i −0.518820 0.854883i \(-0.673629\pi\)
0.518820 0.854883i \(-0.326371\pi\)
\(678\) 0 0
\(679\) 31.6338 1.21399
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.976098 −0.0373493 −0.0186747 0.999826i \(-0.505945\pi\)
−0.0186747 + 0.999826i \(0.505945\pi\)
\(684\) 0 0
\(685\) 55.9332i 2.13710i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 45.5721i 1.73616i
\(690\) 0 0
\(691\) 48.3214i 1.83823i 0.393985 + 0.919117i \(0.371096\pi\)
−0.393985 + 0.919117i \(0.628904\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 34.9781i 1.32679i
\(696\) 0 0
\(697\) 0.634480 0.0240327
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 27.1624i 1.02591i −0.858416 0.512955i \(-0.828551\pi\)
0.858416 0.512955i \(-0.171449\pi\)
\(702\) 0 0
\(703\) 1.66623i 0.0628429i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.64528 0.362748
\(708\) 0 0
\(709\) 0.178679i 0.00671042i −0.999994 0.00335521i \(-0.998932\pi\)
0.999994 0.00335521i \(-0.00106800\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 11.3085 0.423505
\(714\) 0 0
\(715\) 30.2361 1.13076
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 21.2941 0.794137 0.397068 0.917789i \(-0.370028\pi\)
0.397068 + 0.917789i \(0.370028\pi\)
\(720\) 0 0
\(721\) 39.9284i 1.48701i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 26.6375i 0.989293i
\(726\) 0 0
\(727\) 18.3771i 0.681570i 0.940141 + 0.340785i \(0.110693\pi\)
−0.940141 + 0.340785i \(0.889307\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.22172i 0.0821733i
\(732\) 0 0
\(733\) 32.1446 1.18729 0.593644 0.804727i \(-0.297689\pi\)
0.593644 + 0.804727i \(0.297689\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.37970 −0.124493
\(738\) 0 0
\(739\) 16.9885i 0.624931i −0.949929 0.312465i \(-0.898845\pi\)
0.949929 0.312465i \(-0.101155\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 18.7879i 0.689262i −0.938738 0.344631i \(-0.888004\pi\)
0.938738 0.344631i \(-0.111996\pi\)
\(744\) 0 0
\(745\) 16.9355 0.620469
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 21.1285i 0.772018i
\(750\) 0 0
\(751\) 3.66376i 0.133692i −0.997763 0.0668462i \(-0.978706\pi\)
0.997763 0.0668462i \(-0.0212937\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 56.4759i 2.05537i
\(756\) 0 0
\(757\) −54.8790 −1.99461 −0.997306 0.0733524i \(-0.976630\pi\)
−0.997306 + 0.0733524i \(0.976630\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 22.2256i 0.805678i 0.915271 + 0.402839i \(0.131976\pi\)
−0.915271 + 0.402839i \(0.868024\pi\)
\(762\) 0 0
\(763\) 31.4406i 1.13823i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 10.7470i 0.388050i
\(768\) 0 0
\(769\) 12.6337i 0.455583i 0.973710 + 0.227792i \(0.0731505\pi\)
−0.973710 + 0.227792i \(0.926849\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 28.6153 1.02922 0.514611 0.857424i \(-0.327936\pi\)
0.514611 + 0.857424i \(0.327936\pi\)
\(774\) 0 0
\(775\) 16.5294 0.593753
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.959869 0.0343909
\(780\) 0 0
\(781\) 14.9726i 0.535760i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 65.0984 2.32346
\(786\) 0 0
\(787\) 21.4638i 0.765103i 0.923934 + 0.382552i \(0.124955\pi\)
−0.923934 + 0.382552i \(0.875045\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −27.4062 −0.974453
\(792\) 0 0
\(793\) 63.1370i 2.24206i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 29.7969 1.05546 0.527730 0.849412i \(-0.323043\pi\)
0.527730 + 0.849412i \(0.323043\pi\)
\(798\) 0 0
\(799\) 2.67979i 0.0948042i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 7.64317 0.269722
\(804\) 0 0
\(805\) −75.4406 −2.65893
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 36.4507i 1.28154i −0.767733 0.640770i \(-0.778615\pi\)
0.767733 0.640770i \(-0.221385\pi\)
\(810\) 0 0
\(811\) 23.3990i 0.821649i 0.911714 + 0.410825i \(0.134759\pi\)
−0.911714 + 0.410825i \(0.865241\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 40.1508i 1.40642i
\(816\) 0 0
\(817\) 3.36111i 0.117590i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0.804310 0.0280706 0.0140353 0.999902i \(-0.495532\pi\)
0.0140353 + 0.999902i \(0.495532\pi\)
\(822\) 0 0
\(823\) 14.0945i 0.491304i −0.969358 0.245652i \(-0.920998\pi\)
0.969358 0.245652i \(-0.0790020\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 27.5615 0.958409 0.479204 0.877703i \(-0.340925\pi\)
0.479204 + 0.877703i \(0.340925\pi\)
\(828\) 0 0
\(829\) 1.36108i 0.0472721i 0.999721 + 0.0236361i \(0.00752430\pi\)
−0.999721 + 0.0236361i \(0.992476\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0.546607 0.0189388
\(834\) 0 0
\(835\) −48.6823 + 20.6806i −1.68472 + 0.715680i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 30.3893i 1.04916i 0.851362 + 0.524578i \(0.175777\pi\)
−0.851362 + 0.524578i \(0.824223\pi\)
\(840\) 0 0
\(841\) 23.8627 0.822852
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 60.2285 2.07192
\(846\) 0 0
\(847\) 20.7026 0.711351
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 28.2684i 0.969027i
\(852\) 0 0
\(853\) 6.51966 0.223229 0.111614 0.993752i \(-0.464398\pi\)
0.111614 + 0.993752i \(0.464398\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 35.2333i 1.20355i 0.798667 + 0.601773i \(0.205539\pi\)
−0.798667 + 0.601773i \(0.794461\pi\)
\(858\) 0 0
\(859\) 15.2774 0.521259 0.260629 0.965439i \(-0.416070\pi\)
0.260629 + 0.965439i \(0.416070\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 8.76077i 0.298220i 0.988821 + 0.149110i \(0.0476409\pi\)
−0.988821 + 0.149110i \(0.952359\pi\)
\(864\) 0 0
\(865\) 16.7251i 0.568670i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4.39218 0.148994
\(870\) 0 0
\(871\) −12.6797 −0.429635
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −63.3564 −2.14184
\(876\) 0 0
\(877\) −51.8404 −1.75053 −0.875263 0.483647i \(-0.839312\pi\)
−0.875263 + 0.483647i \(0.839312\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −13.6955 −0.461414 −0.230707 0.973023i \(-0.574104\pi\)
−0.230707 + 0.973023i \(0.574104\pi\)
\(882\) 0 0
\(883\) −9.19585 −0.309465 −0.154732 0.987956i \(-0.549452\pi\)
−0.154732 + 0.987956i \(0.549452\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 23.3766 0.784908 0.392454 0.919772i \(-0.371626\pi\)
0.392454 + 0.919772i \(0.371626\pi\)
\(888\) 0 0
\(889\) 0.617244 0.0207017
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4.05410i 0.135665i
\(894\) 0 0
\(895\) 105.823i 3.53727i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.18784i 0.106320i
\(900\) 0 0
\(901\) 2.71178 0.0903425
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −18.9251 −0.629092
\(906\) 0 0
\(907\) 8.41355 0.279367 0.139684 0.990196i \(-0.455391\pi\)
0.139684 + 0.990196i \(0.455391\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 4.20618i 0.139357i −0.997570 0.0696784i \(-0.977803\pi\)
0.997570 0.0696784i \(-0.0221973\pi\)
\(912\) 0 0
\(913\) 7.03699i 0.232890i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 24.7078 0.815924
\(918\) 0 0
\(919\) −47.5330 −1.56797 −0.783985 0.620780i \(-0.786816\pi\)
−0.783985 + 0.620780i \(0.786816\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 56.1728i 1.84895i
\(924\) 0 0
\(925\) 41.3193i 1.35857i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.94411i 0.162211i 0.996706 + 0.0811055i \(0.0258451\pi\)
−0.996706 + 0.0811055i \(0.974155\pi\)
\(930\) 0 0
\(931\) 0.826931 0.0271016
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.79921i 0.0588403i
\(936\) 0 0
\(937\) 9.97855i 0.325985i 0.986627 + 0.162993i \(0.0521147\pi\)
−0.986627 + 0.162993i \(0.947885\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 42.5662 1.38762 0.693810 0.720158i \(-0.255931\pi\)
0.693810 + 0.720158i \(0.255931\pi\)
\(942\) 0 0
\(943\) −16.2847 −0.530301
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 38.5239i 1.25186i 0.779879 + 0.625930i \(0.215280\pi\)
−0.779879 + 0.625930i \(0.784720\pi\)
\(948\) 0 0
\(949\) 28.6750 0.930830
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −18.3136 −0.593235 −0.296618 0.954996i \(-0.595859\pi\)
−0.296618 + 0.954996i \(0.595859\pi\)
\(954\) 0 0
\(955\) 81.9418i 2.65157i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 31.3273i 1.01161i
\(960\) 0 0
\(961\) −29.0219 −0.936189
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 104.390i 3.36043i
\(966\) 0 0
\(967\) 8.66245 0.278566 0.139283 0.990253i \(-0.455520\pi\)
0.139283 + 0.990253i \(0.455520\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −17.4415 −0.559726 −0.279863 0.960040i \(-0.590289\pi\)
−0.279863 + 0.960040i \(0.590289\pi\)
\(972\) 0 0
\(973\) 19.5907i 0.628048i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 32.5726 1.04209 0.521045 0.853530i \(-0.325543\pi\)
0.521045 + 0.853530i \(0.325543\pi\)
\(978\) 0 0
\(979\) 5.09058 0.162696
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 49.4885 1.57844 0.789219 0.614112i \(-0.210486\pi\)
0.789219 + 0.614112i \(0.210486\pi\)
\(984\) 0 0
\(985\) −76.6140 −2.44113
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 57.0230i 1.81323i
\(990\) 0 0
\(991\) 30.9501i 0.983161i −0.870832 0.491580i \(-0.836419\pi\)
0.870832 0.491580i \(-0.163581\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −8.17716 −0.259233
\(996\) 0 0
\(997\) −46.5747 −1.47504 −0.737518 0.675328i \(-0.764002\pi\)
−0.737518 + 0.675328i \(0.764002\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 6012.2.h.a.3005.2 yes 56
3.2 odd 2 inner 6012.2.h.a.3005.56 yes 56
167.166 odd 2 inner 6012.2.h.a.3005.55 yes 56
501.500 even 2 inner 6012.2.h.a.3005.1 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6012.2.h.a.3005.1 56 501.500 even 2 inner
6012.2.h.a.3005.2 yes 56 1.1 even 1 trivial
6012.2.h.a.3005.55 yes 56 167.166 odd 2 inner
6012.2.h.a.3005.56 yes 56 3.2 odd 2 inner