Properties

Label 1296.3.e.c.161.4
Level $1296$
Weight $3$
Character 1296.161
Analytic conductor $35.313$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1296,3,Mod(161,1296)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1296, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1296.161");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1296.e (of order \(2\), degree \(1\), not 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: \(35.3134422611\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 161.4
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1296.161
Dual form 1296.3.e.c.161.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+7.38891i q^{5} +6.79796 q^{7} +O(q^{10})\) \(q+7.38891i q^{5} +6.79796 q^{7} +6.11756i q^{11} +16.7980 q^{13} +25.1701i q^{17} +17.5959 q^{19} -14.3171i q^{23} -29.5959 q^{25} -18.7026i q^{29} +46.7980 q^{31} +50.2295i q^{35} -49.5959 q^{37} -39.8372i q^{41} +44.1918 q^{43} +33.2589i q^{47} -2.78775 q^{49} +10.1708i q^{53} -45.2020 q^{55} +16.5099i q^{59} +21.2020 q^{61} +124.119i q^{65} +86.9796 q^{67} +30.2555i q^{71} -48.7878 q^{73} +41.5869i q^{77} -111.586 q^{79} -98.2485i q^{83} -185.980 q^{85} +75.5103i q^{89} +114.192 q^{91} +130.015i q^{95} -140.596 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 12 q^{7} + 28 q^{13} - 8 q^{19} - 40 q^{25} + 148 q^{31} - 120 q^{37} + 20 q^{43} + 224 q^{49} - 220 q^{55} + 124 q^{61} - 44 q^{67} + 40 q^{73} - 172 q^{79} - 352 q^{85} + 300 q^{91} - 484 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(5\) 7.38891i 1.47778i 0.673826 + 0.738891i \(0.264650\pi\)
−0.673826 + 0.738891i \(0.735350\pi\)
\(6\) 0 0
\(7\) 6.79796 0.971137 0.485568 0.874199i \(-0.338613\pi\)
0.485568 + 0.874199i \(0.338613\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 6.11756i 0.556141i 0.960561 + 0.278071i \(0.0896950\pi\)
−0.960561 + 0.278071i \(0.910305\pi\)
\(12\) 0 0
\(13\) 16.7980 1.29215 0.646075 0.763274i \(-0.276409\pi\)
0.646075 + 0.763274i \(0.276409\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 25.1701i 1.48059i 0.672279 + 0.740297i \(0.265315\pi\)
−0.672279 + 0.740297i \(0.734685\pi\)
\(18\) 0 0
\(19\) 17.5959 0.926101 0.463050 0.886332i \(-0.346755\pi\)
0.463050 + 0.886332i \(0.346755\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 14.3171i − 0.622483i −0.950331 0.311241i \(-0.899255\pi\)
0.950331 0.311241i \(-0.100745\pi\)
\(24\) 0 0
\(25\) −29.5959 −1.18384
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 18.7026i − 0.644918i −0.946583 0.322459i \(-0.895491\pi\)
0.946583 0.322459i \(-0.104509\pi\)
\(30\) 0 0
\(31\) 46.7980 1.50961 0.754806 0.655948i \(-0.227731\pi\)
0.754806 + 0.655948i \(0.227731\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 50.2295i 1.43513i
\(36\) 0 0
\(37\) −49.5959 −1.34043 −0.670215 0.742167i \(-0.733798\pi\)
−0.670215 + 0.742167i \(0.733798\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 39.8372i − 0.971638i −0.874059 0.485819i \(-0.838521\pi\)
0.874059 0.485819i \(-0.161479\pi\)
\(42\) 0 0
\(43\) 44.1918 1.02772 0.513859 0.857875i \(-0.328216\pi\)
0.513859 + 0.857875i \(0.328216\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 33.2589i 0.707636i 0.935314 + 0.353818i \(0.115117\pi\)
−0.935314 + 0.353818i \(0.884883\pi\)
\(48\) 0 0
\(49\) −2.78775 −0.0568929
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.1708i 0.191902i 0.995386 + 0.0959509i \(0.0305892\pi\)
−0.995386 + 0.0959509i \(0.969411\pi\)
\(54\) 0 0
\(55\) −45.2020 −0.821855
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 16.5099i 0.279828i 0.990164 + 0.139914i \(0.0446826\pi\)
−0.990164 + 0.139914i \(0.955317\pi\)
\(60\) 0 0
\(61\) 21.2020 0.347574 0.173787 0.984783i \(-0.444400\pi\)
0.173787 + 0.984783i \(0.444400\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 124.119i 1.90952i
\(66\) 0 0
\(67\) 86.9796 1.29820 0.649101 0.760702i \(-0.275145\pi\)
0.649101 + 0.760702i \(0.275145\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 30.2555i 0.426134i 0.977038 + 0.213067i \(0.0683453\pi\)
−0.977038 + 0.213067i \(0.931655\pi\)
\(72\) 0 0
\(73\) −48.7878 −0.668325 −0.334163 0.942515i \(-0.608454\pi\)
−0.334163 + 0.942515i \(0.608454\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 41.5869i 0.540090i
\(78\) 0 0
\(79\) −111.586 −1.41248 −0.706239 0.707974i \(-0.749609\pi\)
−0.706239 + 0.707974i \(0.749609\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 98.2485i − 1.18372i −0.806042 0.591859i \(-0.798394\pi\)
0.806042 0.591859i \(-0.201606\pi\)
\(84\) 0 0
\(85\) −185.980 −2.18800
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 75.5103i 0.848431i 0.905561 + 0.424215i \(0.139450\pi\)
−0.905561 + 0.424215i \(0.860550\pi\)
\(90\) 0 0
\(91\) 114.192 1.25486
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 130.015i 1.36857i
\(96\) 0 0
\(97\) −140.596 −1.44944 −0.724721 0.689042i \(-0.758031\pi\)
−0.724721 + 0.689042i \(0.758031\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 32.5590i − 0.322367i −0.986924 0.161183i \(-0.948469\pi\)
0.986924 0.161183i \(-0.0515310\pi\)
\(102\) 0 0
\(103\) −135.586 −1.31637 −0.658183 0.752858i \(-0.728675\pi\)
−0.658183 + 0.752858i \(0.728675\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 35.3409i − 0.330289i −0.986269 0.165144i \(-0.947191\pi\)
0.986269 0.165144i \(-0.0528090\pi\)
\(108\) 0 0
\(109\) 53.5959 0.491706 0.245853 0.969307i \(-0.420932\pi\)
0.245853 + 0.969307i \(0.420932\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 165.209i 1.46203i 0.682362 + 0.731015i \(0.260953\pi\)
−0.682362 + 0.731015i \(0.739047\pi\)
\(114\) 0 0
\(115\) 105.788 0.919894
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 171.105i 1.43786i
\(120\) 0 0
\(121\) 83.5755 0.690707
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 33.9588i − 0.271670i
\(126\) 0 0
\(127\) −11.9796 −0.0943275 −0.0471637 0.998887i \(-0.515018\pi\)
−0.0471637 + 0.998887i \(0.515018\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 15.3669i 0.117305i 0.998278 + 0.0586525i \(0.0186804\pi\)
−0.998278 + 0.0586525i \(0.981320\pi\)
\(132\) 0 0
\(133\) 119.616 0.899371
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 55.0934i 0.402141i 0.979577 + 0.201071i \(0.0644421\pi\)
−0.979577 + 0.201071i \(0.935558\pi\)
\(138\) 0 0
\(139\) −100.980 −0.726472 −0.363236 0.931697i \(-0.618328\pi\)
−0.363236 + 0.931697i \(0.618328\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 102.762i 0.718619i
\(144\) 0 0
\(145\) 138.192 0.953047
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 216.378i 1.45220i 0.687589 + 0.726100i \(0.258669\pi\)
−0.687589 + 0.726100i \(0.741331\pi\)
\(150\) 0 0
\(151\) 153.586 1.01712 0.508562 0.861025i \(-0.330177\pi\)
0.508562 + 0.861025i \(0.330177\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 345.786i 2.23088i
\(156\) 0 0
\(157\) 81.9694 0.522098 0.261049 0.965326i \(-0.415932\pi\)
0.261049 + 0.965326i \(0.415932\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 97.3271i − 0.604516i
\(162\) 0 0
\(163\) −55.2122 −0.338725 −0.169363 0.985554i \(-0.554171\pi\)
−0.169363 + 0.985554i \(0.554171\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 154.502i 0.925164i 0.886576 + 0.462582i \(0.153077\pi\)
−0.886576 + 0.462582i \(0.846923\pi\)
\(168\) 0 0
\(169\) 113.171 0.669653
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 26.3307i − 0.152201i −0.997100 0.0761003i \(-0.975753\pi\)
0.997100 0.0761003i \(-0.0242469\pi\)
\(174\) 0 0
\(175\) −201.192 −1.14967
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 266.700i − 1.48995i −0.667094 0.744973i \(-0.732462\pi\)
0.667094 0.744973i \(-0.267538\pi\)
\(180\) 0 0
\(181\) −58.4041 −0.322674 −0.161337 0.986899i \(-0.551581\pi\)
−0.161337 + 0.986899i \(0.551581\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 366.460i − 1.98086i
\(186\) 0 0
\(187\) −153.980 −0.823420
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 114.962i − 0.601896i −0.953640 0.300948i \(-0.902697\pi\)
0.953640 0.300948i \(-0.0973031\pi\)
\(192\) 0 0
\(193\) 216.980 1.12425 0.562123 0.827053i \(-0.309985\pi\)
0.562123 + 0.827053i \(0.309985\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 171.105i 0.868555i 0.900779 + 0.434278i \(0.142996\pi\)
−0.900779 + 0.434278i \(0.857004\pi\)
\(198\) 0 0
\(199\) 62.0000 0.311558 0.155779 0.987792i \(-0.450211\pi\)
0.155779 + 0.987792i \(0.450211\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 127.140i − 0.626303i
\(204\) 0 0
\(205\) 294.353 1.43587
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 107.644i 0.515043i
\(210\) 0 0
\(211\) 129.404 0.613289 0.306645 0.951824i \(-0.400794\pi\)
0.306645 + 0.951824i \(0.400794\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 326.529i 1.51874i
\(216\) 0 0
\(217\) 318.131 1.46604
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 422.807i 1.91315i
\(222\) 0 0
\(223\) −98.3735 −0.441137 −0.220568 0.975372i \(-0.570791\pi\)
−0.220568 + 0.975372i \(0.570791\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 443.002i − 1.95155i −0.218775 0.975775i \(-0.570206\pi\)
0.218775 0.975775i \(-0.429794\pi\)
\(228\) 0 0
\(229\) −112.010 −0.489128 −0.244564 0.969633i \(-0.578645\pi\)
−0.244564 + 0.969633i \(0.578645\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 80.8526i 0.347007i 0.984833 + 0.173503i \(0.0555088\pi\)
−0.984833 + 0.173503i \(0.944491\pi\)
\(234\) 0 0
\(235\) −245.747 −1.04573
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) − 43.1728i − 0.180639i −0.995913 0.0903197i \(-0.971211\pi\)
0.995913 0.0903197i \(-0.0287889\pi\)
\(240\) 0 0
\(241\) −281.808 −1.16933 −0.584664 0.811275i \(-0.698774\pi\)
−0.584664 + 0.811275i \(0.698774\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 20.5984i − 0.0840753i
\(246\) 0 0
\(247\) 295.576 1.19666
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 15.5131i − 0.0618050i −0.999522 0.0309025i \(-0.990162\pi\)
0.999522 0.0309025i \(-0.00983814\pi\)
\(252\) 0 0
\(253\) 87.5857 0.346189
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 360.307i − 1.40197i −0.713175 0.700986i \(-0.752744\pi\)
0.713175 0.700986i \(-0.247256\pi\)
\(258\) 0 0
\(259\) −337.151 −1.30174
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 48.9935i − 0.186287i −0.995653 0.0931435i \(-0.970308\pi\)
0.995653 0.0931435i \(-0.0296915\pi\)
\(264\) 0 0
\(265\) −75.1510 −0.283589
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 281.700i − 1.04721i −0.851961 0.523606i \(-0.824587\pi\)
0.851961 0.523606i \(-0.175413\pi\)
\(270\) 0 0
\(271\) 89.5959 0.330612 0.165306 0.986242i \(-0.447139\pi\)
0.165306 + 0.986242i \(0.447139\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 181.055i − 0.658381i
\(276\) 0 0
\(277\) 84.3939 0.304671 0.152336 0.988329i \(-0.451321\pi\)
0.152336 + 0.988329i \(0.451321\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 26.8668i 0.0956114i 0.998857 + 0.0478057i \(0.0152228\pi\)
−0.998857 + 0.0478057i \(0.984777\pi\)
\(282\) 0 0
\(283\) −180.980 −0.639504 −0.319752 0.947501i \(-0.603600\pi\)
−0.319752 + 0.947501i \(0.603600\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 270.811i − 0.943594i
\(288\) 0 0
\(289\) −344.535 −1.19216
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 471.100i − 1.60785i −0.594730 0.803925i \(-0.702741\pi\)
0.594730 0.803925i \(-0.297259\pi\)
\(294\) 0 0
\(295\) −121.990 −0.413525
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 240.498i − 0.804342i
\(300\) 0 0
\(301\) 300.414 0.998054
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 156.660i 0.513639i
\(306\) 0 0
\(307\) −464.747 −1.51383 −0.756917 0.653511i \(-0.773295\pi\)
−0.756917 + 0.653511i \(0.773295\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 252.126i 0.810696i 0.914162 + 0.405348i \(0.132850\pi\)
−0.914162 + 0.405348i \(0.867150\pi\)
\(312\) 0 0
\(313\) 196.212 0.626876 0.313438 0.949609i \(-0.398519\pi\)
0.313438 + 0.949609i \(0.398519\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 114.298i − 0.360560i −0.983615 0.180280i \(-0.942300\pi\)
0.983615 0.180280i \(-0.0577005\pi\)
\(318\) 0 0
\(319\) 114.414 0.358665
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 442.891i 1.37118i
\(324\) 0 0
\(325\) −497.151 −1.52970
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 226.093i 0.687212i
\(330\) 0 0
\(331\) −54.5959 −0.164942 −0.0824712 0.996593i \(-0.526281\pi\)
−0.0824712 + 0.996593i \(0.526281\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 642.684i 1.91846i
\(336\) 0 0
\(337\) −237.767 −0.705541 −0.352771 0.935710i \(-0.614760\pi\)
−0.352771 + 0.935710i \(0.614760\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 286.289i 0.839558i
\(342\) 0 0
\(343\) −352.051 −1.02639
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 125.111i − 0.360549i −0.983616 0.180275i \(-0.942301\pi\)
0.983616 0.180275i \(-0.0576987\pi\)
\(348\) 0 0
\(349\) −539.969 −1.54719 −0.773595 0.633680i \(-0.781544\pi\)
−0.773595 + 0.633680i \(0.781544\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 293.860i − 0.832463i −0.909259 0.416232i \(-0.863351\pi\)
0.909259 0.416232i \(-0.136649\pi\)
\(354\) 0 0
\(355\) −223.555 −0.629733
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 422.550i 1.17702i 0.808490 + 0.588509i \(0.200285\pi\)
−0.808490 + 0.588509i \(0.799715\pi\)
\(360\) 0 0
\(361\) −51.3837 −0.142337
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 360.488i − 0.987639i
\(366\) 0 0
\(367\) 262.716 0.715848 0.357924 0.933751i \(-0.383485\pi\)
0.357924 + 0.933751i \(0.383485\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 69.1406i 0.186363i
\(372\) 0 0
\(373\) 121.969 0.326996 0.163498 0.986544i \(-0.447722\pi\)
0.163498 + 0.986544i \(0.447722\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 314.166i − 0.833331i
\(378\) 0 0
\(379\) 641.151 1.69169 0.845846 0.533428i \(-0.179096\pi\)
0.845846 + 0.533428i \(0.179096\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) − 739.794i − 1.93158i −0.259330 0.965789i \(-0.583502\pi\)
0.259330 0.965789i \(-0.416498\pi\)
\(384\) 0 0
\(385\) −307.282 −0.798134
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 87.4709i − 0.224861i −0.993660 0.112430i \(-0.964136\pi\)
0.993660 0.112430i \(-0.0358636\pi\)
\(390\) 0 0
\(391\) 360.363 0.921645
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 824.496i − 2.08733i
\(396\) 0 0
\(397\) 483.090 1.21685 0.608425 0.793611i \(-0.291801\pi\)
0.608425 + 0.793611i \(0.291801\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 366.827i 0.914781i 0.889266 + 0.457390i \(0.151216\pi\)
−0.889266 + 0.457390i \(0.848784\pi\)
\(402\) 0 0
\(403\) 786.110 1.95065
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 303.406i − 0.745469i
\(408\) 0 0
\(409\) 535.282 1.30876 0.654379 0.756167i \(-0.272930\pi\)
0.654379 + 0.756167i \(0.272930\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 112.233i 0.271751i
\(414\) 0 0
\(415\) 725.949 1.74927
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 699.310i − 1.66900i −0.551009 0.834499i \(-0.685757\pi\)
0.551009 0.834499i \(-0.314243\pi\)
\(420\) 0 0
\(421\) −361.545 −0.858776 −0.429388 0.903120i \(-0.641271\pi\)
−0.429388 + 0.903120i \(0.641271\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 744.933i − 1.75278i
\(426\) 0 0
\(427\) 144.131 0.337542
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) − 463.747i − 1.07598i −0.842952 0.537989i \(-0.819184\pi\)
0.842952 0.537989i \(-0.180816\pi\)
\(432\) 0 0
\(433\) −689.514 −1.59241 −0.796206 0.605026i \(-0.793163\pi\)
−0.796206 + 0.605026i \(0.793163\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 251.923i − 0.576482i
\(438\) 0 0
\(439\) 621.545 1.41582 0.707910 0.706303i \(-0.249638\pi\)
0.707910 + 0.706303i \(0.249638\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 806.954i − 1.82157i −0.412884 0.910784i \(-0.635479\pi\)
0.412884 0.910784i \(-0.364521\pi\)
\(444\) 0 0
\(445\) −557.939 −1.25379
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 317.554i − 0.707248i −0.935388 0.353624i \(-0.884949\pi\)
0.935388 0.353624i \(-0.115051\pi\)
\(450\) 0 0
\(451\) 243.706 0.540368
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 843.753i 1.85440i
\(456\) 0 0
\(457\) 571.686 1.25095 0.625477 0.780243i \(-0.284905\pi\)
0.625477 + 0.780243i \(0.284905\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 552.582i 1.19866i 0.800502 + 0.599330i \(0.204566\pi\)
−0.800502 + 0.599330i \(0.795434\pi\)
\(462\) 0 0
\(463\) 120.333 0.259898 0.129949 0.991521i \(-0.458519\pi\)
0.129949 + 0.991521i \(0.458519\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 880.440i − 1.88531i −0.333767 0.942656i \(-0.608320\pi\)
0.333767 0.942656i \(-0.391680\pi\)
\(468\) 0 0
\(469\) 591.284 1.26073
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 270.346i 0.571556i
\(474\) 0 0
\(475\) −520.767 −1.09635
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 685.653i 1.43143i 0.698395 + 0.715713i \(0.253898\pi\)
−0.698395 + 0.715713i \(0.746102\pi\)
\(480\) 0 0
\(481\) −833.110 −1.73204
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 1038.85i − 2.14196i
\(486\) 0 0
\(487\) −391.131 −0.803143 −0.401571 0.915828i \(-0.631536\pi\)
−0.401571 + 0.915828i \(0.631536\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 192.222i − 0.391491i −0.980655 0.195746i \(-0.937287\pi\)
0.980655 0.195746i \(-0.0627127\pi\)
\(492\) 0 0
\(493\) 470.747 0.954862
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 205.676i 0.413834i
\(498\) 0 0
\(499\) −609.384 −1.22121 −0.610605 0.791935i \(-0.709074\pi\)
−0.610605 + 0.791935i \(0.709074\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 232.130i 0.461491i 0.973014 + 0.230746i \(0.0741165\pi\)
−0.973014 + 0.230746i \(0.925883\pi\)
\(504\) 0 0
\(505\) 240.576 0.476387
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 257.655i − 0.506198i −0.967440 0.253099i \(-0.918550\pi\)
0.967440 0.253099i \(-0.0814499\pi\)
\(510\) 0 0
\(511\) −331.657 −0.649036
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 1001.83i − 1.94530i
\(516\) 0 0
\(517\) −203.463 −0.393546
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 484.088i − 0.929152i −0.885533 0.464576i \(-0.846207\pi\)
0.885533 0.464576i \(-0.153793\pi\)
\(522\) 0 0
\(523\) 644.384 1.23209 0.616046 0.787711i \(-0.288734\pi\)
0.616046 + 0.787711i \(0.288734\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1177.91i 2.23512i
\(528\) 0 0
\(529\) 324.020 0.612515
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 669.183i − 1.25550i
\(534\) 0 0
\(535\) 261.131 0.488095
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 17.0542i − 0.0316405i
\(540\) 0 0
\(541\) −332.302 −0.614237 −0.307118 0.951671i \(-0.599365\pi\)
−0.307118 + 0.951671i \(0.599365\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 396.015i 0.726633i
\(546\) 0 0
\(547\) 314.657 0.575242 0.287621 0.957744i \(-0.407136\pi\)
0.287621 + 0.957744i \(0.407136\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) − 329.090i − 0.597259i
\(552\) 0 0
\(553\) −758.555 −1.37171
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 664.080i 1.19224i 0.802894 + 0.596122i \(0.203293\pi\)
−0.802894 + 0.596122i \(0.796707\pi\)
\(558\) 0 0
\(559\) 742.333 1.32797
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 243.670i 0.432807i 0.976304 + 0.216403i \(0.0694326\pi\)
−0.976304 + 0.216403i \(0.930567\pi\)
\(564\) 0 0
\(565\) −1220.72 −2.16056
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 579.839i 1.01905i 0.860456 + 0.509524i \(0.170179\pi\)
−0.860456 + 0.509524i \(0.829821\pi\)
\(570\) 0 0
\(571\) 713.686 1.24989 0.624944 0.780670i \(-0.285122\pi\)
0.624944 + 0.780670i \(0.285122\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 423.728i 0.736918i
\(576\) 0 0
\(577\) 829.433 1.43749 0.718746 0.695273i \(-0.244717\pi\)
0.718746 + 0.695273i \(0.244717\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 667.889i − 1.14955i
\(582\) 0 0
\(583\) −62.2204 −0.106725
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 897.756i 1.52940i 0.644388 + 0.764699i \(0.277112\pi\)
−0.644388 + 0.764699i \(0.722888\pi\)
\(588\) 0 0
\(589\) 823.453 1.39805
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 378.065i 0.637547i 0.947831 + 0.318774i \(0.103271\pi\)
−0.947831 + 0.318774i \(0.896729\pi\)
\(594\) 0 0
\(595\) −1264.28 −2.12484
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) − 949.669i − 1.58542i −0.609596 0.792712i \(-0.708668\pi\)
0.609596 0.792712i \(-0.291332\pi\)
\(600\) 0 0
\(601\) 504.616 0.839628 0.419814 0.907610i \(-0.362095\pi\)
0.419814 + 0.907610i \(0.362095\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 617.531i 1.02071i
\(606\) 0 0
\(607\) −859.908 −1.41665 −0.708326 0.705885i \(-0.750549\pi\)
−0.708326 + 0.705885i \(0.750549\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 558.682i 0.914373i
\(612\) 0 0
\(613\) −655.253 −1.06893 −0.534464 0.845191i \(-0.679487\pi\)
−0.534464 + 0.845191i \(0.679487\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 170.003i − 0.275531i −0.990465 0.137765i \(-0.956008\pi\)
0.990465 0.137765i \(-0.0439920\pi\)
\(618\) 0 0
\(619\) −541.061 −0.874089 −0.437045 0.899440i \(-0.643975\pi\)
−0.437045 + 0.899440i \(0.643975\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 513.316i 0.823943i
\(624\) 0 0
\(625\) −488.980 −0.782367
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) − 1248.33i − 1.98463i
\(630\) 0 0
\(631\) −260.788 −0.413293 −0.206646 0.978416i \(-0.566255\pi\)
−0.206646 + 0.978416i \(0.566255\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 88.5161i − 0.139395i
\(636\) 0 0
\(637\) −46.8286 −0.0735142
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 675.983i − 1.05458i −0.849687 0.527288i \(-0.823209\pi\)
0.849687 0.527288i \(-0.176791\pi\)
\(642\) 0 0
\(643\) 756.637 1.17673 0.588364 0.808596i \(-0.299772\pi\)
0.588364 + 0.808596i \(0.299772\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 554.770i 0.857450i 0.903435 + 0.428725i \(0.141037\pi\)
−0.903435 + 0.428725i \(0.858963\pi\)
\(648\) 0 0
\(649\) −101.000 −0.155624
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 201.494i 0.308567i 0.988027 + 0.154283i \(0.0493069\pi\)
−0.988027 + 0.154283i \(0.950693\pi\)
\(654\) 0 0
\(655\) −113.545 −0.173351
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 103.591i − 0.157194i −0.996906 0.0785969i \(-0.974956\pi\)
0.996906 0.0785969i \(-0.0250440\pi\)
\(660\) 0 0
\(661\) 218.414 0.330430 0.165215 0.986258i \(-0.447168\pi\)
0.165215 + 0.986258i \(0.447168\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 883.834i 1.32907i
\(666\) 0 0
\(667\) −267.767 −0.401450
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 129.705i 0.193301i
\(672\) 0 0
\(673\) 788.857 1.17215 0.586075 0.810257i \(-0.300672\pi\)
0.586075 + 0.810257i \(0.300672\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 732.715i 1.08230i 0.840927 + 0.541149i \(0.182010\pi\)
−0.840927 + 0.541149i \(0.817990\pi\)
\(678\) 0 0
\(679\) −955.765 −1.40761
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 1353.33i − 1.98145i −0.135883 0.990725i \(-0.543387\pi\)
0.135883 0.990725i \(-0.456613\pi\)
\(684\) 0 0
\(685\) −407.080 −0.594277
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 170.849i 0.247966i
\(690\) 0 0
\(691\) 736.514 1.06587 0.532934 0.846157i \(-0.321090\pi\)
0.532934 + 0.846157i \(0.321090\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) − 746.129i − 1.07357i
\(696\) 0 0
\(697\) 1002.71 1.43860
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1068.34i 1.52403i 0.647561 + 0.762014i \(0.275789\pi\)
−0.647561 + 0.762014i \(0.724211\pi\)
\(702\) 0 0
\(703\) −872.686 −1.24137
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 221.335i − 0.313062i
\(708\) 0 0
\(709\) 273.888 0.386301 0.193151 0.981169i \(-0.438129\pi\)
0.193151 + 0.981169i \(0.438129\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 670.011i − 0.939707i
\(714\) 0 0
\(715\) −759.302 −1.06196
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) − 654.423i − 0.910185i −0.890444 0.455092i \(-0.849606\pi\)
0.890444 0.455092i \(-0.150394\pi\)
\(720\) 0 0
\(721\) −921.706 −1.27837
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 553.521i 0.763477i
\(726\) 0 0
\(727\) −1166.33 −1.60431 −0.802155 0.597117i \(-0.796313\pi\)
−0.802155 + 0.597117i \(0.796313\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1112.31i 1.52163i
\(732\) 0 0
\(733\) 878.292 1.19822 0.599108 0.800668i \(-0.295522\pi\)
0.599108 + 0.800668i \(0.295522\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 532.103i 0.721984i
\(738\) 0 0
\(739\) 593.151 0.802640 0.401320 0.915938i \(-0.368552\pi\)
0.401320 + 0.915938i \(0.368552\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 54.3357i 0.0731302i 0.999331 + 0.0365651i \(0.0116416\pi\)
−0.999331 + 0.0365651i \(0.988358\pi\)
\(744\) 0 0
\(745\) −1598.80 −2.14603
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 240.246i − 0.320756i
\(750\) 0 0
\(751\) −911.141 −1.21324 −0.606618 0.794993i \(-0.707474\pi\)
−0.606618 + 0.794993i \(0.707474\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1134.83i 1.50309i
\(756\) 0 0
\(757\) 1272.22 1.68061 0.840304 0.542115i \(-0.182376\pi\)
0.840304 + 0.542115i \(0.182376\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 461.279i 0.606149i 0.952967 + 0.303074i \(0.0980131\pi\)
−0.952967 + 0.303074i \(0.901987\pi\)
\(762\) 0 0
\(763\) 364.343 0.477514
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 277.332i 0.361580i
\(768\) 0 0
\(769\) 538.878 0.700751 0.350376 0.936609i \(-0.386054\pi\)
0.350376 + 0.936609i \(0.386054\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1036.29i 1.34061i 0.742087 + 0.670304i \(0.233836\pi\)
−0.742087 + 0.670304i \(0.766164\pi\)
\(774\) 0 0
\(775\) −1385.03 −1.78713
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 700.972i − 0.899835i
\(780\) 0 0
\(781\) −185.090 −0.236991
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 605.664i 0.771546i
\(786\) 0 0
\(787\) 1412.19 1.79440 0.897199 0.441626i \(-0.145598\pi\)
0.897199 + 0.441626i \(0.145598\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1123.09i 1.41983i
\(792\) 0 0
\(793\) 356.151 0.449119
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 69.8134i 0.0875953i 0.999040 + 0.0437976i \(0.0139457\pi\)
−0.999040 + 0.0437976i \(0.986054\pi\)
\(798\) 0 0
\(799\) −837.131 −1.04772
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 298.462i − 0.371683i
\(804\) 0 0
\(805\) 719.141 0.893343
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 1263.33i − 1.56160i −0.624781 0.780800i \(-0.714812\pi\)
0.624781 0.780800i \(-0.285188\pi\)
\(810\) 0 0
\(811\) 442.241 0.545303 0.272652 0.962113i \(-0.412099\pi\)
0.272652 + 0.962113i \(0.412099\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) − 407.958i − 0.500562i
\(816\) 0 0
\(817\) 777.596 0.951770
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 575.129i − 0.700523i −0.936652 0.350261i \(-0.886093\pi\)
0.936652 0.350261i \(-0.113907\pi\)
\(822\) 0 0
\(823\) 23.2429 0.0282416 0.0141208 0.999900i \(-0.495505\pi\)
0.0141208 + 0.999900i \(0.495505\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 790.958i 0.956418i 0.878246 + 0.478209i \(0.158714\pi\)
−0.878246 + 0.478209i \(0.841286\pi\)
\(828\) 0 0
\(829\) 1159.78 1.39901 0.699503 0.714630i \(-0.253405\pi\)
0.699503 + 0.714630i \(0.253405\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 70.1681i − 0.0842354i
\(834\) 0 0
\(835\) −1141.60 −1.36719
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 546.717i 0.651629i 0.945434 + 0.325814i \(0.105638\pi\)
−0.945434 + 0.325814i \(0.894362\pi\)
\(840\) 0 0
\(841\) 491.212 0.584081
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 836.213i 0.989601i
\(846\) 0 0
\(847\) 568.143 0.670771
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 710.070i 0.834395i
\(852\) 0 0
\(853\) 216.635 0.253968 0.126984 0.991905i \(-0.459470\pi\)
0.126984 + 0.991905i \(0.459470\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 565.504i − 0.659865i −0.944005 0.329932i \(-0.892974\pi\)
0.944005 0.329932i \(-0.107026\pi\)
\(858\) 0 0
\(859\) −375.767 −0.437447 −0.218724 0.975787i \(-0.570189\pi\)
−0.218724 + 0.975787i \(0.570189\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1429.35i 1.65626i 0.560534 + 0.828131i \(0.310596\pi\)
−0.560534 + 0.828131i \(0.689404\pi\)
\(864\) 0 0
\(865\) 194.555 0.224919
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 682.632i − 0.785537i
\(870\) 0 0
\(871\) 1461.08 1.67747
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) − 230.851i − 0.263829i
\(876\) 0 0
\(877\) −841.627 −0.959665 −0.479833 0.877360i \(-0.659303\pi\)
−0.479833 + 0.877360i \(0.659303\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 449.261i 0.509944i 0.966948 + 0.254972i \(0.0820663\pi\)
−0.966948 + 0.254972i \(0.917934\pi\)
\(882\) 0 0
\(883\) −122.445 −0.138669 −0.0693346 0.997593i \(-0.522088\pi\)
−0.0693346 + 0.997593i \(0.522088\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1571.66i 1.77188i 0.463800 + 0.885940i \(0.346485\pi\)
−0.463800 + 0.885940i \(0.653515\pi\)
\(888\) 0 0
\(889\) −81.4368 −0.0916049
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 585.221i 0.655343i
\(894\) 0 0
\(895\) 1970.62 2.20182
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 875.244i − 0.973575i
\(900\) 0 0
\(901\) −256.000 −0.284129
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 431.542i − 0.476842i
\(906\) 0 0
\(907\) 698.576 0.770205 0.385102 0.922874i \(-0.374166\pi\)
0.385102 + 0.922874i \(0.374166\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) − 81.3934i − 0.0893451i −0.999002 0.0446726i \(-0.985776\pi\)
0.999002 0.0446726i \(-0.0142245\pi\)
\(912\) 0 0
\(913\) 601.041 0.658314
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 104.464i 0.113919i
\(918\) 0 0
\(919\) 348.665 0.379396 0.189698 0.981842i \(-0.439249\pi\)
0.189698 + 0.981842i \(0.439249\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 508.231i 0.550629i
\(924\) 0 0
\(925\) 1467.84 1.58685
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1076.52i 1.15880i 0.815043 + 0.579400i \(0.196713\pi\)
−0.815043 + 0.579400i \(0.803287\pi\)
\(930\) 0 0
\(931\) −49.0531 −0.0526886
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) − 1137.74i − 1.21683i
\(936\) 0 0
\(937\) −1437.39 −1.53404 −0.767018 0.641626i \(-0.778260\pi\)
−0.767018 + 0.641626i \(0.778260\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 215.457i − 0.228965i −0.993425 0.114483i \(-0.963479\pi\)
0.993425 0.114483i \(-0.0365211\pi\)
\(942\) 0 0
\(943\) −570.353 −0.604828
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 470.715i − 0.497059i −0.968624 0.248529i \(-0.920053\pi\)
0.968624 0.248529i \(-0.0799473\pi\)
\(948\) 0 0
\(949\) −819.535 −0.863577
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 1192.14i − 1.25093i −0.780251 0.625466i \(-0.784909\pi\)
0.780251 0.625466i \(-0.215091\pi\)
\(954\) 0 0
\(955\) 849.445 0.889471
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 374.522i 0.390534i
\(960\) 0 0
\(961\) 1229.05 1.27893
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1603.24i 1.66139i
\(966\) 0 0
\(967\) 192.778 0.199356 0.0996782 0.995020i \(-0.468219\pi\)
0.0996782 + 0.995020i \(0.468219\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 202.388i 0.208433i 0.994555 + 0.104216i \(0.0332335\pi\)
−0.994555 + 0.104216i \(0.966767\pi\)
\(972\) 0 0
\(973\) −686.455 −0.705504
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 40.6431i 0.0415999i 0.999784 + 0.0208000i \(0.00662131\pi\)
−0.999784 + 0.0208000i \(0.993379\pi\)
\(978\) 0 0
\(979\) −461.939 −0.471848
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 728.737i 0.741340i 0.928765 + 0.370670i \(0.120872\pi\)
−0.928765 + 0.370670i \(0.879128\pi\)
\(984\) 0 0
\(985\) −1264.28 −1.28353
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 632.699i − 0.639736i
\(990\) 0 0
\(991\) −746.527 −0.753306 −0.376653 0.926354i \(-0.622925\pi\)
−0.376653 + 0.926354i \(0.622925\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 458.112i 0.460414i
\(996\) 0 0
\(997\) 238.092 0.238808 0.119404 0.992846i \(-0.461902\pi\)
0.119404 + 0.992846i \(0.461902\pi\)
\(998\) 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 1296.3.e.c.161.4 4
3.2 odd 2 inner 1296.3.e.c.161.1 4
4.3 odd 2 648.3.e.b.161.4 4
9.2 odd 6 144.3.q.d.113.2 4
9.4 even 3 144.3.q.d.65.2 4
9.5 odd 6 432.3.q.c.305.1 4
9.7 even 3 432.3.q.c.17.1 4
12.11 even 2 648.3.e.b.161.1 4
36.7 odd 6 216.3.m.a.17.1 4
36.11 even 6 72.3.m.a.41.2 4
36.23 even 6 216.3.m.a.89.1 4
36.31 odd 6 72.3.m.a.65.2 yes 4
72.5 odd 6 1728.3.q.f.1601.2 4
72.11 even 6 576.3.q.h.257.1 4
72.13 even 6 576.3.q.c.65.1 4
72.29 odd 6 576.3.q.c.257.1 4
72.43 odd 6 1728.3.q.e.449.2 4
72.59 even 6 1728.3.q.e.1601.2 4
72.61 even 6 1728.3.q.f.449.2 4
72.67 odd 6 576.3.q.h.65.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.3.m.a.41.2 4 36.11 even 6
72.3.m.a.65.2 yes 4 36.31 odd 6
144.3.q.d.65.2 4 9.4 even 3
144.3.q.d.113.2 4 9.2 odd 6
216.3.m.a.17.1 4 36.7 odd 6
216.3.m.a.89.1 4 36.23 even 6
432.3.q.c.17.1 4 9.7 even 3
432.3.q.c.305.1 4 9.5 odd 6
576.3.q.c.65.1 4 72.13 even 6
576.3.q.c.257.1 4 72.29 odd 6
576.3.q.h.65.1 4 72.67 odd 6
576.3.q.h.257.1 4 72.11 even 6
648.3.e.b.161.1 4 12.11 even 2
648.3.e.b.161.4 4 4.3 odd 2
1296.3.e.c.161.1 4 3.2 odd 2 inner
1296.3.e.c.161.4 4 1.1 even 1 trivial
1728.3.q.e.449.2 4 72.43 odd 6
1728.3.q.e.1601.2 4 72.59 even 6
1728.3.q.f.449.2 4 72.61 even 6
1728.3.q.f.1601.2 4 72.5 odd 6