Properties

Label 4140.2.a.r.1.1
Level $4140$
Weight $2$
Character 4140.1
Self dual yes
Analytic conductor $33.058$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4140,2,Mod(1,4140)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4140.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4140.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: \(33.0580664368\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{6}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 6 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1380)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.44949\) of defining polynomial
Character \(\chi\) \(=\) 4140.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +1.00000 q^{7} -0.449490 q^{11} -2.44949 q^{13} -1.44949 q^{17} -7.34847 q^{19} -1.00000 q^{23} +1.00000 q^{25} +4.55051 q^{29} +7.89898 q^{31} +1.00000 q^{35} -0.101021 q^{37} +5.44949 q^{41} +11.7980 q^{43} +7.34847 q^{47} -6.00000 q^{49} +10.3485 q^{53} -0.449490 q^{55} +11.4495 q^{59} -4.44949 q^{61} -2.44949 q^{65} -10.7980 q^{67} +12.3485 q^{71} +7.34847 q^{73} -0.449490 q^{77} +5.79796 q^{79} +10.5505 q^{83} -1.44949 q^{85} +12.8990 q^{89} -2.44949 q^{91} -7.34847 q^{95} -4.89898 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{5} + 2 q^{7} + 4 q^{11} + 2 q^{17} - 2 q^{23} + 2 q^{25} + 14 q^{29} + 6 q^{31} + 2 q^{35} - 10 q^{37} + 6 q^{41} + 4 q^{43} - 12 q^{49} + 6 q^{53} + 4 q^{55} + 18 q^{59} - 4 q^{61} - 2 q^{67} + 10 q^{71} + 4 q^{77} - 8 q^{79} + 26 q^{83} + 2 q^{85} + 16 q^{89}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.449490 −0.135526 −0.0677631 0.997701i \(-0.521586\pi\)
−0.0677631 + 0.997701i \(0.521586\pi\)
\(12\) 0 0
\(13\) −2.44949 −0.679366 −0.339683 0.940540i \(-0.610320\pi\)
−0.339683 + 0.940540i \(0.610320\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.44949 −0.351553 −0.175776 0.984430i \(-0.556244\pi\)
−0.175776 + 0.984430i \(0.556244\pi\)
\(18\) 0 0
\(19\) −7.34847 −1.68585 −0.842927 0.538028i \(-0.819170\pi\)
−0.842927 + 0.538028i \(0.819170\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.55051 0.845009 0.422504 0.906361i \(-0.361151\pi\)
0.422504 + 0.906361i \(0.361151\pi\)
\(30\) 0 0
\(31\) 7.89898 1.41870 0.709349 0.704857i \(-0.248989\pi\)
0.709349 + 0.704857i \(0.248989\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −0.101021 −0.0166077 −0.00830384 0.999966i \(-0.502643\pi\)
−0.00830384 + 0.999966i \(0.502643\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.44949 0.851067 0.425534 0.904943i \(-0.360086\pi\)
0.425534 + 0.904943i \(0.360086\pi\)
\(42\) 0 0
\(43\) 11.7980 1.79917 0.899586 0.436744i \(-0.143868\pi\)
0.899586 + 0.436744i \(0.143868\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.34847 1.07188 0.535942 0.844255i \(-0.319956\pi\)
0.535942 + 0.844255i \(0.319956\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.3485 1.42147 0.710736 0.703459i \(-0.248362\pi\)
0.710736 + 0.703459i \(0.248362\pi\)
\(54\) 0 0
\(55\) −0.449490 −0.0606092
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 11.4495 1.49060 0.745298 0.666731i \(-0.232307\pi\)
0.745298 + 0.666731i \(0.232307\pi\)
\(60\) 0 0
\(61\) −4.44949 −0.569699 −0.284849 0.958572i \(-0.591944\pi\)
−0.284849 + 0.958572i \(0.591944\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.44949 −0.303822
\(66\) 0 0
\(67\) −10.7980 −1.31918 −0.659590 0.751625i \(-0.729270\pi\)
−0.659590 + 0.751625i \(0.729270\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.3485 1.46549 0.732747 0.680501i \(-0.238238\pi\)
0.732747 + 0.680501i \(0.238238\pi\)
\(72\) 0 0
\(73\) 7.34847 0.860073 0.430037 0.902811i \(-0.358501\pi\)
0.430037 + 0.902811i \(0.358501\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.449490 −0.0512241
\(78\) 0 0
\(79\) 5.79796 0.652321 0.326161 0.945314i \(-0.394245\pi\)
0.326161 + 0.945314i \(0.394245\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 10.5505 1.15807 0.579034 0.815303i \(-0.303430\pi\)
0.579034 + 0.815303i \(0.303430\pi\)
\(84\) 0 0
\(85\) −1.44949 −0.157219
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 12.8990 1.36729 0.683645 0.729815i \(-0.260394\pi\)
0.683645 + 0.729815i \(0.260394\pi\)
\(90\) 0 0
\(91\) −2.44949 −0.256776
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −7.34847 −0.753937
\(96\) 0 0
\(97\) −4.89898 −0.497416 −0.248708 0.968579i \(-0.580006\pi\)
−0.248708 + 0.968579i \(0.580006\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.65153 0.164333 0.0821667 0.996619i \(-0.473816\pi\)
0.0821667 + 0.996619i \(0.473816\pi\)
\(102\) 0 0
\(103\) −6.89898 −0.679777 −0.339888 0.940466i \(-0.610389\pi\)
−0.339888 + 0.940466i \(0.610389\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.3485 −1.58047 −0.790233 0.612806i \(-0.790041\pi\)
−0.790233 + 0.612806i \(0.790041\pi\)
\(108\) 0 0
\(109\) −13.5505 −1.29790 −0.648952 0.760830i \(-0.724792\pi\)
−0.648952 + 0.760830i \(0.724792\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.24745 −0.869927 −0.434963 0.900448i \(-0.643239\pi\)
−0.434963 + 0.900448i \(0.643239\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.44949 −0.132875
\(120\) 0 0
\(121\) −10.7980 −0.981633
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 18.2474 1.61920 0.809600 0.586983i \(-0.199684\pi\)
0.809600 + 0.586983i \(0.199684\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −7.34847 −0.637193
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.6969 0.913901 0.456951 0.889492i \(-0.348942\pi\)
0.456951 + 0.889492i \(0.348942\pi\)
\(138\) 0 0
\(139\) 8.79796 0.746233 0.373117 0.927784i \(-0.378289\pi\)
0.373117 + 0.927784i \(0.378289\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.10102 0.0920720
\(144\) 0 0
\(145\) 4.55051 0.377899
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.4495 0.856056 0.428028 0.903766i \(-0.359209\pi\)
0.428028 + 0.903766i \(0.359209\pi\)
\(150\) 0 0
\(151\) 15.7980 1.28562 0.642810 0.766026i \(-0.277769\pi\)
0.642810 + 0.766026i \(0.277769\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 7.89898 0.634461
\(156\) 0 0
\(157\) 11.0000 0.877896 0.438948 0.898513i \(-0.355351\pi\)
0.438948 + 0.898513i \(0.355351\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) −17.5959 −1.37822 −0.689109 0.724657i \(-0.741998\pi\)
−0.689109 + 0.724657i \(0.741998\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9.55051 −0.739041 −0.369520 0.929223i \(-0.620478\pi\)
−0.369520 + 0.929223i \(0.620478\pi\)
\(168\) 0 0
\(169\) −7.00000 −0.538462
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 9.79796 0.744925 0.372463 0.928047i \(-0.378514\pi\)
0.372463 + 0.928047i \(0.378514\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) 0 0
\(181\) 4.89898 0.364138 0.182069 0.983286i \(-0.441721\pi\)
0.182069 + 0.983286i \(0.441721\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.101021 −0.00742718
\(186\) 0 0
\(187\) 0.651531 0.0476446
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −17.1464 −1.24067 −0.620336 0.784336i \(-0.713004\pi\)
−0.620336 + 0.784336i \(0.713004\pi\)
\(192\) 0 0
\(193\) 8.89898 0.640563 0.320281 0.947322i \(-0.396223\pi\)
0.320281 + 0.947322i \(0.396223\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.10102 0.0784445 0.0392222 0.999231i \(-0.487512\pi\)
0.0392222 + 0.999231i \(0.487512\pi\)
\(198\) 0 0
\(199\) −4.69694 −0.332957 −0.166479 0.986045i \(-0.553240\pi\)
−0.166479 + 0.986045i \(0.553240\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.55051 0.319383
\(204\) 0 0
\(205\) 5.44949 0.380609
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.30306 0.228478
\(210\) 0 0
\(211\) 25.0000 1.72107 0.860535 0.509390i \(-0.170129\pi\)
0.860535 + 0.509390i \(0.170129\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 11.7980 0.804614
\(216\) 0 0
\(217\) 7.89898 0.536218
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.55051 0.238833
\(222\) 0 0
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −21.7980 −1.44678 −0.723391 0.690439i \(-0.757417\pi\)
−0.723391 + 0.690439i \(0.757417\pi\)
\(228\) 0 0
\(229\) 6.69694 0.442546 0.221273 0.975212i \(-0.428979\pi\)
0.221273 + 0.975212i \(0.428979\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 15.5959 1.02172 0.510861 0.859663i \(-0.329327\pi\)
0.510861 + 0.859663i \(0.329327\pi\)
\(234\) 0 0
\(235\) 7.34847 0.479361
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 21.0454 1.36131 0.680657 0.732602i \(-0.261694\pi\)
0.680657 + 0.732602i \(0.261694\pi\)
\(240\) 0 0
\(241\) −30.0454 −1.93539 −0.967697 0.252114i \(-0.918874\pi\)
−0.967697 + 0.252114i \(0.918874\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.00000 −0.383326
\(246\) 0 0
\(247\) 18.0000 1.14531
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) 0 0
\(253\) 0.449490 0.0282592
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.24745 0.264949 0.132474 0.991186i \(-0.457708\pi\)
0.132474 + 0.991186i \(0.457708\pi\)
\(258\) 0 0
\(259\) −0.101021 −0.00627711
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.348469 0.0214875 0.0107438 0.999942i \(-0.496580\pi\)
0.0107438 + 0.999942i \(0.496580\pi\)
\(264\) 0 0
\(265\) 10.3485 0.635701
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −15.2474 −0.929653 −0.464827 0.885402i \(-0.653883\pi\)
−0.464827 + 0.885402i \(0.653883\pi\)
\(270\) 0 0
\(271\) 6.10102 0.370611 0.185305 0.982681i \(-0.440673\pi\)
0.185305 + 0.982681i \(0.440673\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.449490 −0.0271053
\(276\) 0 0
\(277\) −0.202041 −0.0121395 −0.00606973 0.999982i \(-0.501932\pi\)
−0.00606973 + 0.999982i \(0.501932\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2.65153 0.158177 0.0790885 0.996868i \(-0.474799\pi\)
0.0790885 + 0.996868i \(0.474799\pi\)
\(282\) 0 0
\(283\) 3.89898 0.231770 0.115885 0.993263i \(-0.463030\pi\)
0.115885 + 0.993263i \(0.463030\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.44949 0.321673
\(288\) 0 0
\(289\) −14.8990 −0.876411
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −27.0454 −1.58001 −0.790005 0.613101i \(-0.789922\pi\)
−0.790005 + 0.613101i \(0.789922\pi\)
\(294\) 0 0
\(295\) 11.4495 0.666615
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.44949 0.141658
\(300\) 0 0
\(301\) 11.7980 0.680023
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.44949 −0.254777
\(306\) 0 0
\(307\) −20.2474 −1.15558 −0.577791 0.816184i \(-0.696085\pi\)
−0.577791 + 0.816184i \(0.696085\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 15.5959 0.884363 0.442182 0.896926i \(-0.354205\pi\)
0.442182 + 0.896926i \(0.354205\pi\)
\(312\) 0 0
\(313\) −4.30306 −0.243223 −0.121612 0.992578i \(-0.538806\pi\)
−0.121612 + 0.992578i \(0.538806\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −27.3485 −1.53604 −0.768022 0.640424i \(-0.778759\pi\)
−0.768022 + 0.640424i \(0.778759\pi\)
\(318\) 0 0
\(319\) −2.04541 −0.114521
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 10.6515 0.592667
\(324\) 0 0
\(325\) −2.44949 −0.135873
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7.34847 0.405134
\(330\) 0 0
\(331\) 20.7980 1.14316 0.571580 0.820547i \(-0.306331\pi\)
0.571580 + 0.820547i \(0.306331\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −10.7980 −0.589956
\(336\) 0 0
\(337\) 23.7980 1.29636 0.648179 0.761488i \(-0.275531\pi\)
0.648179 + 0.761488i \(0.275531\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.55051 −0.192271
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −28.4949 −1.52969 −0.764843 0.644217i \(-0.777184\pi\)
−0.764843 + 0.644217i \(0.777184\pi\)
\(348\) 0 0
\(349\) −33.4949 −1.79294 −0.896470 0.443104i \(-0.853877\pi\)
−0.896470 + 0.443104i \(0.853877\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5.55051 −0.295424 −0.147712 0.989030i \(-0.547191\pi\)
−0.147712 + 0.989030i \(0.547191\pi\)
\(354\) 0 0
\(355\) 12.3485 0.655389
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.55051 0.504057 0.252028 0.967720i \(-0.418902\pi\)
0.252028 + 0.967720i \(0.418902\pi\)
\(360\) 0 0
\(361\) 35.0000 1.84211
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7.34847 0.384636
\(366\) 0 0
\(367\) 29.8990 1.56071 0.780357 0.625334i \(-0.215037\pi\)
0.780357 + 0.625334i \(0.215037\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 10.3485 0.537266
\(372\) 0 0
\(373\) 10.2020 0.528242 0.264121 0.964490i \(-0.414918\pi\)
0.264121 + 0.964490i \(0.414918\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −11.1464 −0.574070
\(378\) 0 0
\(379\) 13.7980 0.708754 0.354377 0.935103i \(-0.384693\pi\)
0.354377 + 0.935103i \(0.384693\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −21.2474 −1.08569 −0.542847 0.839832i \(-0.682654\pi\)
−0.542847 + 0.839832i \(0.682654\pi\)
\(384\) 0 0
\(385\) −0.449490 −0.0229081
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 14.4949 0.734920 0.367460 0.930039i \(-0.380227\pi\)
0.367460 + 0.930039i \(0.380227\pi\)
\(390\) 0 0
\(391\) 1.44949 0.0733038
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 5.79796 0.291727
\(396\) 0 0
\(397\) −37.7980 −1.89703 −0.948513 0.316739i \(-0.897412\pi\)
−0.948513 + 0.316739i \(0.897412\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.1010 −0.654234 −0.327117 0.944984i \(-0.606077\pi\)
−0.327117 + 0.944984i \(0.606077\pi\)
\(402\) 0 0
\(403\) −19.3485 −0.963816
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.0454077 0.00225078
\(408\) 0 0
\(409\) 19.6969 0.973951 0.486975 0.873416i \(-0.338100\pi\)
0.486975 + 0.873416i \(0.338100\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 11.4495 0.563393
\(414\) 0 0
\(415\) 10.5505 0.517904
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 18.6515 0.911187 0.455593 0.890188i \(-0.349427\pi\)
0.455593 + 0.890188i \(0.349427\pi\)
\(420\) 0 0
\(421\) −7.34847 −0.358142 −0.179071 0.983836i \(-0.557309\pi\)
−0.179071 + 0.983836i \(0.557309\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.44949 −0.0703106
\(426\) 0 0
\(427\) −4.44949 −0.215326
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 36.4949 1.75790 0.878949 0.476916i \(-0.158246\pi\)
0.878949 + 0.476916i \(0.158246\pi\)
\(432\) 0 0
\(433\) −5.20204 −0.249994 −0.124997 0.992157i \(-0.539892\pi\)
−0.124997 + 0.992157i \(0.539892\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.34847 0.351525
\(438\) 0 0
\(439\) 4.69694 0.224173 0.112086 0.993698i \(-0.464247\pi\)
0.112086 + 0.993698i \(0.464247\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 22.4495 1.06661 0.533304 0.845924i \(-0.320950\pi\)
0.533304 + 0.845924i \(0.320950\pi\)
\(444\) 0 0
\(445\) 12.8990 0.611470
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −24.8434 −1.17243 −0.586215 0.810155i \(-0.699383\pi\)
−0.586215 + 0.810155i \(0.699383\pi\)
\(450\) 0 0
\(451\) −2.44949 −0.115342
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.44949 −0.114834
\(456\) 0 0
\(457\) −27.4949 −1.28616 −0.643079 0.765800i \(-0.722343\pi\)
−0.643079 + 0.765800i \(0.722343\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12.6969 0.591355 0.295678 0.955288i \(-0.404455\pi\)
0.295678 + 0.955288i \(0.404455\pi\)
\(462\) 0 0
\(463\) −7.34847 −0.341512 −0.170756 0.985313i \(-0.554621\pi\)
−0.170756 + 0.985313i \(0.554621\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.14643 −0.0993249 −0.0496624 0.998766i \(-0.515815\pi\)
−0.0496624 + 0.998766i \(0.515815\pi\)
\(468\) 0 0
\(469\) −10.7980 −0.498603
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.30306 −0.243835
\(474\) 0 0
\(475\) −7.34847 −0.337171
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −22.9444 −1.04836 −0.524178 0.851609i \(-0.675627\pi\)
−0.524178 + 0.851609i \(0.675627\pi\)
\(480\) 0 0
\(481\) 0.247449 0.0112827
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.89898 −0.222451
\(486\) 0 0
\(487\) 25.8434 1.17107 0.585537 0.810645i \(-0.300884\pi\)
0.585537 + 0.810645i \(0.300884\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 21.2474 0.958884 0.479442 0.877574i \(-0.340839\pi\)
0.479442 + 0.877574i \(0.340839\pi\)
\(492\) 0 0
\(493\) −6.59592 −0.297065
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.3485 0.553905
\(498\) 0 0
\(499\) 26.7980 1.19964 0.599821 0.800134i \(-0.295239\pi\)
0.599821 + 0.800134i \(0.295239\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 16.1464 0.719934 0.359967 0.932965i \(-0.382788\pi\)
0.359967 + 0.932965i \(0.382788\pi\)
\(504\) 0 0
\(505\) 1.65153 0.0734922
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −30.6969 −1.36062 −0.680309 0.732925i \(-0.738154\pi\)
−0.680309 + 0.732925i \(0.738154\pi\)
\(510\) 0 0
\(511\) 7.34847 0.325077
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.89898 −0.304005
\(516\) 0 0
\(517\) −3.30306 −0.145268
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −14.2474 −0.624192 −0.312096 0.950051i \(-0.601031\pi\)
−0.312096 + 0.950051i \(0.601031\pi\)
\(522\) 0 0
\(523\) −10.2020 −0.446104 −0.223052 0.974807i \(-0.571602\pi\)
−0.223052 + 0.974807i \(0.571602\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11.4495 −0.498748
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −13.3485 −0.578186
\(534\) 0 0
\(535\) −16.3485 −0.706806
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.69694 0.116165
\(540\) 0 0
\(541\) 32.4949 1.39706 0.698532 0.715578i \(-0.253837\pi\)
0.698532 + 0.715578i \(0.253837\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −13.5505 −0.580440
\(546\) 0 0
\(547\) −21.7980 −0.932013 −0.466007 0.884781i \(-0.654308\pi\)
−0.466007 + 0.884781i \(0.654308\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −33.4393 −1.42456
\(552\) 0 0
\(553\) 5.79796 0.246554
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −21.6515 −0.917405 −0.458702 0.888590i \(-0.651686\pi\)
−0.458702 + 0.888590i \(0.651686\pi\)
\(558\) 0 0
\(559\) −28.8990 −1.22230
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 32.3485 1.36333 0.681663 0.731667i \(-0.261257\pi\)
0.681663 + 0.731667i \(0.261257\pi\)
\(564\) 0 0
\(565\) −9.24745 −0.389043
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 20.6969 0.867661 0.433830 0.900995i \(-0.357162\pi\)
0.433830 + 0.900995i \(0.357162\pi\)
\(570\) 0 0
\(571\) −8.44949 −0.353600 −0.176800 0.984247i \(-0.556575\pi\)
−0.176800 + 0.984247i \(0.556575\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −13.7980 −0.574417 −0.287208 0.957868i \(-0.592727\pi\)
−0.287208 + 0.957868i \(0.592727\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 10.5505 0.437709
\(582\) 0 0
\(583\) −4.65153 −0.192647
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 39.3939 1.62596 0.812980 0.582292i \(-0.197844\pi\)
0.812980 + 0.582292i \(0.197844\pi\)
\(588\) 0 0
\(589\) −58.0454 −2.39172
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.247449 −0.0101615 −0.00508075 0.999987i \(-0.501617\pi\)
−0.00508075 + 0.999987i \(0.501617\pi\)
\(594\) 0 0
\(595\) −1.44949 −0.0594233
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −24.4949 −1.00083 −0.500417 0.865784i \(-0.666820\pi\)
−0.500417 + 0.865784i \(0.666820\pi\)
\(600\) 0 0
\(601\) 22.3939 0.913465 0.456733 0.889604i \(-0.349020\pi\)
0.456733 + 0.889604i \(0.349020\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −10.7980 −0.438999
\(606\) 0 0
\(607\) −12.0454 −0.488908 −0.244454 0.969661i \(-0.578609\pi\)
−0.244454 + 0.969661i \(0.578609\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −18.0000 −0.728202
\(612\) 0 0
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.85357 −0.316173 −0.158086 0.987425i \(-0.550532\pi\)
−0.158086 + 0.987425i \(0.550532\pi\)
\(618\) 0 0
\(619\) −45.7980 −1.84078 −0.920388 0.391007i \(-0.872127\pi\)
−0.920388 + 0.391007i \(0.872127\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12.8990 0.516787
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.146428 0.00583847
\(630\) 0 0
\(631\) −8.04541 −0.320283 −0.160141 0.987094i \(-0.551195\pi\)
−0.160141 + 0.987094i \(0.551195\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 18.2474 0.724128
\(636\) 0 0
\(637\) 14.6969 0.582314
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.449490 −0.0177538 −0.00887689 0.999961i \(-0.502826\pi\)
−0.00887689 + 0.999961i \(0.502826\pi\)
\(642\) 0 0
\(643\) −25.4949 −1.00542 −0.502710 0.864455i \(-0.667664\pi\)
−0.502710 + 0.864455i \(0.667664\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −25.3485 −0.996551 −0.498276 0.867019i \(-0.666033\pi\)
−0.498276 + 0.867019i \(0.666033\pi\)
\(648\) 0 0
\(649\) −5.14643 −0.202015
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5.34847 −0.209302 −0.104651 0.994509i \(-0.533373\pi\)
−0.104651 + 0.994509i \(0.533373\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 32.9444 1.28333 0.641666 0.766985i \(-0.278244\pi\)
0.641666 + 0.766985i \(0.278244\pi\)
\(660\) 0 0
\(661\) 15.3031 0.595220 0.297610 0.954688i \(-0.403810\pi\)
0.297610 + 0.954688i \(0.403810\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7.34847 −0.284961
\(666\) 0 0
\(667\) −4.55051 −0.176196
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.00000 0.0772091
\(672\) 0 0
\(673\) −32.4495 −1.25084 −0.625418 0.780290i \(-0.715072\pi\)
−0.625418 + 0.780290i \(0.715072\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.34847 −0.243991 −0.121996 0.992531i \(-0.538929\pi\)
−0.121996 + 0.992531i \(0.538929\pi\)
\(678\) 0 0
\(679\) −4.89898 −0.188006
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −46.0454 −1.76188 −0.880939 0.473229i \(-0.843088\pi\)
−0.880939 + 0.473229i \(0.843088\pi\)
\(684\) 0 0
\(685\) 10.6969 0.408709
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −25.3485 −0.965700
\(690\) 0 0
\(691\) −9.59592 −0.365046 −0.182523 0.983202i \(-0.558426\pi\)
−0.182523 + 0.983202i \(0.558426\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8.79796 0.333726
\(696\) 0 0
\(697\) −7.89898 −0.299195
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 31.3485 1.18402 0.592008 0.805932i \(-0.298336\pi\)
0.592008 + 0.805932i \(0.298336\pi\)
\(702\) 0 0
\(703\) 0.742346 0.0279981
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.65153 0.0621122
\(708\) 0 0
\(709\) −18.6515 −0.700473 −0.350236 0.936661i \(-0.613899\pi\)
−0.350236 + 0.936661i \(0.613899\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.89898 −0.295819
\(714\) 0 0
\(715\) 1.10102 0.0411758
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4.34847 0.162171 0.0810853 0.996707i \(-0.474161\pi\)
0.0810853 + 0.996707i \(0.474161\pi\)
\(720\) 0 0
\(721\) −6.89898 −0.256931
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4.55051 0.169002
\(726\) 0 0
\(727\) −17.8990 −0.663836 −0.331918 0.943308i \(-0.607696\pi\)
−0.331918 + 0.943308i \(0.607696\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −17.1010 −0.632504
\(732\) 0 0
\(733\) 32.3939 1.19650 0.598248 0.801311i \(-0.295864\pi\)
0.598248 + 0.801311i \(0.295864\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.85357 0.178784
\(738\) 0 0
\(739\) 46.5959 1.71406 0.857029 0.515268i \(-0.172308\pi\)
0.857029 + 0.515268i \(0.172308\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 53.7980 1.97366 0.986828 0.161774i \(-0.0517215\pi\)
0.986828 + 0.161774i \(0.0517215\pi\)
\(744\) 0 0
\(745\) 10.4495 0.382840
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −16.3485 −0.597360
\(750\) 0 0
\(751\) 10.8536 0.396052 0.198026 0.980197i \(-0.436547\pi\)
0.198026 + 0.980197i \(0.436547\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 15.7980 0.574947
\(756\) 0 0
\(757\) 9.69694 0.352441 0.176221 0.984351i \(-0.443613\pi\)
0.176221 + 0.984351i \(0.443613\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 42.1464 1.52781 0.763903 0.645331i \(-0.223280\pi\)
0.763903 + 0.645331i \(0.223280\pi\)
\(762\) 0 0
\(763\) −13.5505 −0.490561
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −28.0454 −1.01266
\(768\) 0 0
\(769\) −0.853572 −0.0307806 −0.0153903 0.999882i \(-0.504899\pi\)
−0.0153903 + 0.999882i \(0.504899\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.10102 −0.0396010 −0.0198005 0.999804i \(-0.506303\pi\)
−0.0198005 + 0.999804i \(0.506303\pi\)
\(774\) 0 0
\(775\) 7.89898 0.283740
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −40.0454 −1.43478
\(780\) 0 0
\(781\) −5.55051 −0.198613
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 11.0000 0.392607
\(786\) 0 0
\(787\) 21.2929 0.759008 0.379504 0.925190i \(-0.376095\pi\)
0.379504 + 0.925190i \(0.376095\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9.24745 −0.328801
\(792\) 0 0
\(793\) 10.8990 0.387034
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −32.5505 −1.15300 −0.576499 0.817098i \(-0.695582\pi\)
−0.576499 + 0.817098i \(0.695582\pi\)
\(798\) 0 0
\(799\) −10.6515 −0.376824
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −3.30306 −0.116563
\(804\) 0 0
\(805\) −1.00000 −0.0352454
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −41.4495 −1.45729 −0.728643 0.684893i \(-0.759849\pi\)
−0.728643 + 0.684893i \(0.759849\pi\)
\(810\) 0 0
\(811\) −13.2020 −0.463586 −0.231793 0.972765i \(-0.574459\pi\)
−0.231793 + 0.972765i \(0.574459\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −17.5959 −0.616358
\(816\) 0 0
\(817\) −86.6969 −3.03314
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 4.49490 0.156873 0.0784365 0.996919i \(-0.475007\pi\)
0.0784365 + 0.996919i \(0.475007\pi\)
\(822\) 0 0
\(823\) −1.79796 −0.0626729 −0.0313365 0.999509i \(-0.509976\pi\)
−0.0313365 + 0.999509i \(0.509976\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 52.4393 1.82349 0.911746 0.410754i \(-0.134734\pi\)
0.911746 + 0.410754i \(0.134734\pi\)
\(828\) 0 0
\(829\) −31.6969 −1.10088 −0.550440 0.834875i \(-0.685540\pi\)
−0.550440 + 0.834875i \(0.685540\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 8.69694 0.301331
\(834\) 0 0
\(835\) −9.55051 −0.330509
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.00000 0.0690477 0.0345238 0.999404i \(-0.489009\pi\)
0.0345238 + 0.999404i \(0.489009\pi\)
\(840\) 0 0
\(841\) −8.29286 −0.285961
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −7.00000 −0.240807
\(846\) 0 0
\(847\) −10.7980 −0.371022
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0.101021 0.00346294
\(852\) 0 0
\(853\) −14.8990 −0.510131 −0.255066 0.966924i \(-0.582097\pi\)
−0.255066 + 0.966924i \(0.582097\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −25.5959 −0.874340 −0.437170 0.899379i \(-0.644019\pi\)
−0.437170 + 0.899379i \(0.644019\pi\)
\(858\) 0 0
\(859\) 16.5959 0.566245 0.283123 0.959084i \(-0.408630\pi\)
0.283123 + 0.959084i \(0.408630\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −40.2929 −1.37158 −0.685792 0.727797i \(-0.740544\pi\)
−0.685792 + 0.727797i \(0.740544\pi\)
\(864\) 0 0
\(865\) 9.79796 0.333141
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.60612 −0.0884067
\(870\) 0 0
\(871\) 26.4495 0.896207
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) −4.69694 −0.158604 −0.0793022 0.996851i \(-0.525269\pi\)
−0.0793022 + 0.996851i \(0.525269\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 44.2474 1.49073 0.745367 0.666654i \(-0.232274\pi\)
0.745367 + 0.666654i \(0.232274\pi\)
\(882\) 0 0
\(883\) −17.7526 −0.597421 −0.298710 0.954344i \(-0.596556\pi\)
−0.298710 + 0.954344i \(0.596556\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −3.30306 −0.110906 −0.0554530 0.998461i \(-0.517660\pi\)
−0.0554530 + 0.998461i \(0.517660\pi\)
\(888\) 0 0
\(889\) 18.2474 0.612000
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −54.0000 −1.80704
\(894\) 0 0
\(895\) −10.0000 −0.334263
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 35.9444 1.19881
\(900\) 0 0
\(901\) −15.0000 −0.499722
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 4.89898 0.162848
\(906\) 0 0
\(907\) −45.0000 −1.49420 −0.747100 0.664711i \(-0.768555\pi\)
−0.747100 + 0.664711i \(0.768555\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −43.5959 −1.44440 −0.722199 0.691686i \(-0.756868\pi\)
−0.722199 + 0.691686i \(0.756868\pi\)
\(912\) 0 0
\(913\) −4.74235 −0.156949
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 6.20204 0.204586 0.102293 0.994754i \(-0.467382\pi\)
0.102293 + 0.994754i \(0.467382\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −30.2474 −0.995607
\(924\) 0 0
\(925\) −0.101021 −0.00332153
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 34.8434 1.14317 0.571587 0.820542i \(-0.306328\pi\)
0.571587 + 0.820542i \(0.306328\pi\)
\(930\) 0 0
\(931\) 44.0908 1.44502
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0.651531 0.0213073
\(936\) 0 0
\(937\) −36.4949 −1.19224 −0.596118 0.802897i \(-0.703291\pi\)
−0.596118 + 0.802897i \(0.703291\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 25.5505 0.832923 0.416461 0.909153i \(-0.363270\pi\)
0.416461 + 0.909153i \(0.363270\pi\)
\(942\) 0 0
\(943\) −5.44949 −0.177460
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 13.3031 0.432291 0.216146 0.976361i \(-0.430651\pi\)
0.216146 + 0.976361i \(0.430651\pi\)
\(948\) 0 0
\(949\) −18.0000 −0.584305
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −33.5959 −1.08828 −0.544139 0.838995i \(-0.683144\pi\)
−0.544139 + 0.838995i \(0.683144\pi\)
\(954\) 0 0
\(955\) −17.1464 −0.554845
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 10.6969 0.345422
\(960\) 0 0
\(961\) 31.3939 1.01271
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 8.89898 0.286468
\(966\) 0 0
\(967\) −21.3485 −0.686520 −0.343260 0.939240i \(-0.611531\pi\)
−0.343260 + 0.939240i \(0.611531\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 35.1010 1.12645 0.563223 0.826305i \(-0.309561\pi\)
0.563223 + 0.826305i \(0.309561\pi\)
\(972\) 0 0
\(973\) 8.79796 0.282050
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 7.65153 0.244794 0.122397 0.992481i \(-0.460942\pi\)
0.122397 + 0.992481i \(0.460942\pi\)
\(978\) 0 0
\(979\) −5.79796 −0.185304
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 26.1464 0.833942 0.416971 0.908920i \(-0.363092\pi\)
0.416971 + 0.908920i \(0.363092\pi\)
\(984\) 0 0
\(985\) 1.10102 0.0350814
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −11.7980 −0.375153
\(990\) 0 0
\(991\) 20.5959 0.654251 0.327125 0.944981i \(-0.393920\pi\)
0.327125 + 0.944981i \(0.393920\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −4.69694 −0.148903
\(996\) 0 0
\(997\) −27.1010 −0.858298 −0.429149 0.903234i \(-0.641186\pi\)
−0.429149 + 0.903234i \(0.641186\pi\)
\(998\) 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 4140.2.a.r.1.1 2
3.2 odd 2 1380.2.a.f.1.2 2
12.11 even 2 5520.2.a.bl.1.1 2
15.2 even 4 6900.2.f.h.6349.4 4
15.8 even 4 6900.2.f.h.6349.2 4
15.14 odd 2 6900.2.a.r.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1380.2.a.f.1.2 2 3.2 odd 2
4140.2.a.r.1.1 2 1.1 even 1 trivial
5520.2.a.bl.1.1 2 12.11 even 2
6900.2.a.r.1.2 2 15.14 odd 2
6900.2.f.h.6349.2 4 15.8 even 4
6900.2.f.h.6349.4 4 15.2 even 4