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Properties

Label 2325.2.a.f.1.1
Level $2325$
Weight $2$
Character 2325.1
Self dual yes
Analytic conductor $18.565$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2325,2,Mod(1,2325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2325.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2325, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 2325 = 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2325.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-1,-2,0,0,0,0,1,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(18.5652184699\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2325.1

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{9} -3.00000 q^{11} +2.00000 q^{12} +4.00000 q^{13} +4.00000 q^{16} -7.00000 q^{17} +3.00000 q^{19} +5.00000 q^{23} -1.00000 q^{27} +1.00000 q^{29} +1.00000 q^{31} +3.00000 q^{33} -2.00000 q^{36} -4.00000 q^{39} -8.00000 q^{41} +10.0000 q^{43} +6.00000 q^{44} -2.00000 q^{47} -4.00000 q^{48} -7.00000 q^{49} +7.00000 q^{51} -8.00000 q^{52} +9.00000 q^{53} -3.00000 q^{57} -12.0000 q^{59} -2.00000 q^{61} -8.00000 q^{64} +11.0000 q^{67} +14.0000 q^{68} -5.00000 q^{69} -2.00000 q^{71} -10.0000 q^{73} -6.00000 q^{76} -10.0000 q^{79} +1.00000 q^{81} -3.00000 q^{83} -1.00000 q^{87} +7.00000 q^{89} -10.0000 q^{92} -1.00000 q^{93} -1.00000 q^{97} -3.00000 q^{99} +O(q^{100})\)

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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) −1.00000 −0.577350
\(4\) −2.00000 −1.00000
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 − 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 2.00000 0.577350
\(13\) 4.00000 1.10940 0.554700 − 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) −7.00000 −1.69775 −0.848875 − 0.528594i \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) 0 0
\(19\) 3.00000 0.688247 0.344124 − 0.938924i \(-0.388176\pi\)
0.344124 + 0.938924i \(0.388176\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.00000 1.04257 0.521286 − 0.853382i \(-0.325452\pi\)
0.521286 + 0.853382i \(0.325452\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695 0.0928477 − 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 0 0
\(31\) 1.00000 0.179605
\(32\) 0 0
\(33\) 3.00000 0.522233
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 − 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 − 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 6.00000 0.904534
\(45\) 0 0
\(46\) 0 0
\(47\) −2.00000 −0.291730 −0.145865 − 0.989305i \(-0.546597\pi\)
−0.145865 + 0.989305i \(0.546597\pi\)
\(48\) −4.00000 −0.577350
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 7.00000 0.980196
\(52\) −8.00000 −1.10940
\(53\) 9.00000 1.23625 0.618123 − 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.00000 −0.397360
\(58\) 0 0
\(59\) −12.0000 −1.56227 −0.781133 − 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 − 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 11.0000 1.34386 0.671932 − 0.740613i \(-0.265465\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) 14.0000 1.69775
\(69\) −5.00000 −0.601929
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 − 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 − 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) 0 0
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 − 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −3.00000 −0.329293 −0.164646 − 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 7.00000 0.741999 0.370999 − 0.928633i \(-0.379015\pi\)
0.370999 + 0.928633i \(0.379015\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −10.0000 −1.04257
\(93\) −1.00000 −0.103695
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.00000 −0.101535 −0.0507673 − 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) 0 0
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) −10.0000 −0.995037 −0.497519 − 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) −11.0000 −1.08386 −0.541931 − 0.840423i \(-0.682307\pi\)
−0.541931 + 0.840423i \(0.682307\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.00000 −0.580042 −0.290021 − 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 2.00000 0.192450
\(109\) 2.00000 0.191565 0.0957826 − 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 − 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.00000 −0.185695
\(117\) 4.00000 0.369800
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 8.00000 0.721336
\(124\) −2.00000 −0.179605
\(125\) 0 0
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 − 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) −10.0000 −0.880451
\(130\) 0 0
\(131\) −6.00000 −0.524222 −0.262111 − 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) −6.00000 −0.522233
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 17.0000 1.45241 0.726204 − 0.687479i \(-0.241283\pi\)
0.726204 + 0.687479i \(0.241283\pi\)
\(138\) 0 0
\(139\) −20.0000 −1.69638 −0.848189 − 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 2.00000 0.168430
\(142\) 0 0
\(143\) −12.0000 −1.00349
\(144\) 4.00000 0.333333
\(145\) 0 0
\(146\) 0 0
\(147\) 7.00000 0.577350
\(148\) 0 0
\(149\) 4.00000 0.327693 0.163846 − 0.986486i \(-0.447610\pi\)
0.163846 + 0.986486i \(0.447610\pi\)
\(150\) 0 0
\(151\) −24.0000 −1.95309 −0.976546 − 0.215308i \(-0.930924\pi\)
−0.976546 + 0.215308i \(0.930924\pi\)
\(152\) 0 0
\(153\) −7.00000 −0.565916
\(154\) 0 0
\(155\) 0 0
\(156\) 8.00000 0.640513
\(157\) 7.00000 0.558661 0.279330 − 0.960195i \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(158\) 0 0
\(159\) −9.00000 −0.713746
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 11.0000 0.861586 0.430793 − 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) 16.0000 1.24939
\(165\) 0 0
\(166\) 0 0
\(167\) −16.0000 −1.23812 −0.619059 − 0.785345i \(-0.712486\pi\)
−0.619059 + 0.785345i \(0.712486\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 3.00000 0.229416
\(172\) −20.0000 −1.52499
\(173\) −16.0000 −1.21646 −0.608229 − 0.793762i \(-0.708120\pi\)
−0.608229 + 0.793762i \(0.708120\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −12.0000 −0.904534
\(177\) 12.0000 0.901975
\(178\) 0 0
\(179\) −20.0000 −1.49487 −0.747435 − 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 − 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 21.0000 1.53567
\(188\) 4.00000 0.291730
\(189\) 0 0
\(190\) 0 0
\(191\) 10.0000 0.723575 0.361787 − 0.932261i \(-0.382167\pi\)
0.361787 + 0.932261i \(0.382167\pi\)
\(192\) 8.00000 0.577350
\(193\) 21.0000 1.51161 0.755807 − 0.654795i \(-0.227245\pi\)
0.755807 + 0.654795i \(0.227245\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 14.0000 1.00000
\(197\) −6.00000 −0.427482 −0.213741 − 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) −20.0000 −1.41776 −0.708881 − 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) 0 0
\(201\) −11.0000 −0.775880
\(202\) 0 0
\(203\) 0 0
\(204\) −14.0000 −0.980196
\(205\) 0 0
\(206\) 0 0
\(207\) 5.00000 0.347524
\(208\) 16.0000 1.10940
\(209\) −9.00000 −0.622543
\(210\) 0 0
\(211\) 11.0000 0.757271 0.378636 − 0.925546i \(-0.376393\pi\)
0.378636 + 0.925546i \(0.376393\pi\)
\(212\) −18.0000 −1.23625
\(213\) 2.00000 0.137038
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 10.0000 0.675737
\(220\) 0 0
\(221\) −28.0000 −1.88348
\(222\) 0 0
\(223\) −6.00000 −0.401790 −0.200895 − 0.979613i \(-0.564385\pi\)
−0.200895 + 0.979613i \(0.564385\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −12.0000 −0.796468 −0.398234 − 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) 6.00000 0.397360
\(229\) 4.00000 0.264327 0.132164 − 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 24.0000 1.57229 0.786146 − 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 24.0000 1.56227
\(237\) 10.0000 0.649570
\(238\) 0 0
\(239\) −15.0000 −0.970269 −0.485135 − 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) 0 0
\(241\) 18.0000 1.15948 0.579741 − 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 4.00000 0.256074
\(245\) 0 0
\(246\) 0 0
\(247\) 12.0000 0.763542
\(248\) 0 0
\(249\) 3.00000 0.190117
\(250\) 0 0
\(251\) −21.0000 −1.32551 −0.662754 − 0.748837i \(-0.730613\pi\)
−0.662754 + 0.748837i \(0.730613\pi\)
\(252\) 0 0
\(253\) −15.0000 −0.943042
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −26.0000 −1.62184 −0.810918 − 0.585160i \(-0.801032\pi\)
−0.810918 + 0.585160i \(0.801032\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) −24.0000 −1.47990 −0.739952 − 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −7.00000 −0.428393
\(268\) −22.0000 −1.34386
\(269\) 26.0000 1.58525 0.792624 − 0.609711i \(-0.208714\pi\)
0.792624 + 0.609711i \(0.208714\pi\)
\(270\) 0 0
\(271\) 10.0000 0.607457 0.303728 − 0.952759i \(-0.401768\pi\)
0.303728 + 0.952759i \(0.401768\pi\)
\(272\) −28.0000 −1.69775
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 10.0000 0.601929
\(277\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) −2.00000 −0.119310 −0.0596550 − 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 0 0
\(283\) 15.0000 0.891657 0.445829 − 0.895118i \(-0.352909\pi\)
0.445829 + 0.895118i \(0.352909\pi\)
\(284\) 4.00000 0.237356
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 0 0
\(291\) 1.00000 0.0586210
\(292\) 20.0000 1.17041
\(293\) −24.0000 −1.40209 −0.701047 − 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.00000 0.174078
\(298\) 0 0
\(299\) 20.0000 1.15663
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 10.0000 0.574485
\(304\) 12.0000 0.688247
\(305\) 0 0
\(306\) 0 0
\(307\) −8.00000 −0.456584 −0.228292 − 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) 11.0000 0.625768
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 − 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 18.0000 1.01742 0.508710 − 0.860938i \(-0.330123\pi\)
0.508710 + 0.860938i \(0.330123\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 20.0000 1.12509
\(317\) −8.00000 −0.449325 −0.224662 − 0.974437i \(-0.572128\pi\)
−0.224662 + 0.974437i \(0.572128\pi\)
\(318\) 0 0
\(319\) −3.00000 −0.167968
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) −21.0000 −1.16847
\(324\) −2.00000 −0.111111
\(325\) 0 0
\(326\) 0 0
\(327\) −2.00000 −0.110600
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −24.0000 −1.31916 −0.659580 − 0.751635i \(-0.729266\pi\)
−0.659580 + 0.751635i \(0.729266\pi\)
\(332\) 6.00000 0.329293
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 28.0000 1.52526 0.762629 − 0.646837i \(-0.223908\pi\)
0.762629 + 0.646837i \(0.223908\pi\)
\(338\) 0 0
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) −3.00000 −0.162459
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.00000 0.214731 0.107366 − 0.994220i \(-0.465758\pi\)
0.107366 + 0.994220i \(0.465758\pi\)
\(348\) 2.00000 0.107211
\(349\) 9.00000 0.481759 0.240879 − 0.970555i \(-0.422564\pi\)
0.240879 + 0.970555i \(0.422564\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) −3.00000 −0.159674 −0.0798369 − 0.996808i \(-0.525440\pi\)
−0.0798369 + 0.996808i \(0.525440\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) 0 0
\(359\) 30.0000 1.58334 0.791670 − 0.610949i \(-0.209212\pi\)
0.791670 + 0.610949i \(0.209212\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) 0 0
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 − 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 20.0000 1.04257
\(369\) −8.00000 −0.416463
\(370\) 0 0
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) 3.00000 0.155334 0.0776671 − 0.996979i \(-0.475253\pi\)
0.0776671 + 0.996979i \(0.475253\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 − 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 0 0
\(381\) 16.0000 0.819705
\(382\) 0 0
\(383\) 3.00000 0.153293 0.0766464 − 0.997058i \(-0.475579\pi\)
0.0766464 + 0.997058i \(0.475579\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 10.0000 0.508329
\(388\) 2.00000 0.101535
\(389\) −14.0000 −0.709828 −0.354914 − 0.934899i \(-0.615490\pi\)
−0.354914 + 0.934899i \(0.615490\pi\)
\(390\) 0 0
\(391\) −35.0000 −1.77003
\(392\) 0 0
\(393\) 6.00000 0.302660
\(394\) 0 0
\(395\) 0 0
\(396\) 6.00000 0.301511
\(397\) 29.0000 1.45547 0.727734 − 0.685859i \(-0.240573\pi\)
0.727734 + 0.685859i \(0.240573\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 31.0000 1.54807 0.774033 − 0.633145i \(-0.218236\pi\)
0.774033 + 0.633145i \(0.218236\pi\)
\(402\) 0 0
\(403\) 4.00000 0.199254
\(404\) 20.0000 0.995037
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 20.0000 0.988936 0.494468 − 0.869196i \(-0.335363\pi\)
0.494468 + 0.869196i \(0.335363\pi\)
\(410\) 0 0
\(411\) −17.0000 −0.838548
\(412\) 22.0000 1.08386
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 20.0000 0.979404
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 − 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 − 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 0 0
\(423\) −2.00000 −0.0972433
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 12.0000 0.579365
\(430\) 0 0
\(431\) 16.0000 0.770693 0.385346 − 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) −4.00000 −0.192450
\(433\) 2.00000 0.0961139 0.0480569 − 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.00000 −0.191565
\(437\) 15.0000 0.717547
\(438\) 0 0
\(439\) −36.0000 −1.71819 −0.859093 − 0.511819i \(-0.828972\pi\)
−0.859093 + 0.511819i \(0.828972\pi\)
\(440\) 0 0
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) −6.00000 −0.285069 −0.142534 − 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −4.00000 −0.189194
\(448\) 0 0
\(449\) −25.0000 −1.17982 −0.589911 − 0.807468i \(-0.700837\pi\)
−0.589911 + 0.807468i \(0.700837\pi\)
\(450\) 0 0
\(451\) 24.0000 1.13012
\(452\) 12.0000 0.564433
\(453\) 24.0000 1.12762
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −8.00000 −0.374224 −0.187112 − 0.982339i \(-0.559913\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) 0 0
\(459\) 7.00000 0.326732
\(460\) 0 0
\(461\) −27.0000 −1.25752 −0.628758 − 0.777601i \(-0.716436\pi\)
−0.628758 + 0.777601i \(0.716436\pi\)
\(462\) 0 0
\(463\) −14.0000 −0.650635 −0.325318 − 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) 4.00000 0.185695
\(465\) 0 0
\(466\) 0 0
\(467\) −6.00000 −0.277647 −0.138823 − 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) −8.00000 −0.369800
\(469\) 0 0
\(470\) 0 0
\(471\) −7.00000 −0.322543
\(472\) 0 0
\(473\) −30.0000 −1.37940
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 9.00000 0.412082
\(478\) 0 0
\(479\) 6.00000 0.274147 0.137073 − 0.990561i \(-0.456230\pi\)
0.137073 + 0.990561i \(0.456230\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 4.00000 0.181818
\(485\) 0 0
\(486\) 0 0
\(487\) −28.0000 −1.26880 −0.634401 − 0.773004i \(-0.718753\pi\)
−0.634401 + 0.773004i \(0.718753\pi\)
\(488\) 0 0
\(489\) −11.0000 −0.497437
\(490\) 0 0
\(491\) −1.00000 −0.0451294 −0.0225647 − 0.999745i \(-0.507183\pi\)
−0.0225647 + 0.999745i \(0.507183\pi\)
\(492\) −16.0000 −0.721336
\(493\) −7.00000 −0.315264
\(494\) 0 0
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 10.0000 0.447661 0.223831 − 0.974628i \(-0.428144\pi\)
0.223831 + 0.974628i \(0.428144\pi\)
\(500\) 0 0
\(501\) 16.0000 0.714827
\(502\) 0 0
\(503\) −28.0000 −1.24846 −0.624229 − 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −3.00000 −0.133235
\(508\) 32.0000 1.41977
\(509\) 15.0000 0.664863 0.332432 − 0.943127i \(-0.392131\pi\)
0.332432 + 0.943127i \(0.392131\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −3.00000 −0.132453
\(514\) 0 0
\(515\) 0 0
\(516\) 20.0000 0.880451
\(517\) 6.00000 0.263880
\(518\) 0 0
\(519\) 16.0000 0.702322
\(520\) 0 0
\(521\) −12.0000 −0.525730 −0.262865 − 0.964833i \(-0.584667\pi\)
−0.262865 + 0.964833i \(0.584667\pi\)
\(522\) 0 0
\(523\) −28.0000 −1.22435 −0.612177 − 0.790721i \(-0.709706\pi\)
−0.612177 + 0.790721i \(0.709706\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 0 0
\(527\) −7.00000 −0.304925
\(528\) 12.0000 0.522233
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) −32.0000 −1.38607
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 20.0000 0.863064
\(538\) 0 0
\(539\) 21.0000 0.904534
\(540\) 0 0
\(541\) −35.0000 −1.50477 −0.752384 − 0.658725i \(-0.771096\pi\)
−0.752384 + 0.658725i \(0.771096\pi\)
\(542\) 0 0
\(543\) −8.00000 −0.343313
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 19.0000 0.812381 0.406191 − 0.913788i \(-0.366857\pi\)
0.406191 + 0.913788i \(0.366857\pi\)
\(548\) −34.0000 −1.45241
\(549\) −2.00000 −0.0853579
\(550\) 0 0
\(551\) 3.00000 0.127804
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 40.0000 1.69638
\(557\) −25.0000 −1.05928 −0.529642 − 0.848221i \(-0.677674\pi\)
−0.529642 + 0.848221i \(0.677674\pi\)
\(558\) 0 0
\(559\) 40.0000 1.69182
\(560\) 0 0
\(561\) −21.0000 −0.886621
\(562\) 0 0
\(563\) −34.0000 −1.43293 −0.716465 − 0.697623i \(-0.754241\pi\)
−0.716465 + 0.697623i \(0.754241\pi\)
\(564\) −4.00000 −0.168430
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17.0000 −0.712677 −0.356339 − 0.934357i \(-0.615975\pi\)
−0.356339 + 0.934357i \(0.615975\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 − 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 24.0000 1.00349
\(573\) −10.0000 −0.417756
\(574\) 0 0
\(575\) 0 0
\(576\) −8.00000 −0.333333
\(577\) −2.00000 −0.0832611 −0.0416305 − 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 0 0
\(579\) −21.0000 −0.872730
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −27.0000 −1.11823
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5.00000 0.206372 0.103186 − 0.994662i \(-0.467096\pi\)
0.103186 + 0.994662i \(0.467096\pi\)
\(588\) −14.0000 −0.577350
\(589\) 3.00000 0.123613
\(590\) 0 0
\(591\) 6.00000 0.246807
\(592\) 0 0
\(593\) 4.00000 0.164260 0.0821302 − 0.996622i \(-0.473828\pi\)
0.0821302 + 0.996622i \(0.473828\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −8.00000 −0.327693
\(597\) 20.0000 0.818546
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 − 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) 42.0000 1.71322 0.856608 − 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) 0 0
\(603\) 11.0000 0.447955
\(604\) 48.0000 1.95309
\(605\) 0 0
\(606\) 0 0
\(607\) 29.0000 1.17707 0.588537 − 0.808470i \(-0.299704\pi\)
0.588537 + 0.808470i \(0.299704\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −8.00000 −0.323645
\(612\) 14.0000 0.565916
\(613\) −10.0000 −0.403896 −0.201948 − 0.979396i \(-0.564727\pi\)
−0.201948 + 0.979396i \(0.564727\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000 0.483102 0.241551 − 0.970388i \(-0.422344\pi\)
0.241551 + 0.970388i \(0.422344\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 − 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 0 0
\(621\) −5.00000 −0.200643
\(622\) 0 0
\(623\) 0 0
\(624\) −16.0000 −0.640513
\(625\) 0 0
\(626\) 0 0
\(627\) 9.00000 0.359425
\(628\) −14.0000 −0.558661
\(629\) 0 0
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 − 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 0 0
\(633\) −11.0000 −0.437211
\(634\) 0 0
\(635\) 0 0
\(636\) 18.0000 0.713746
\(637\) −28.0000 −1.10940
\(638\) 0 0
\(639\) −2.00000 −0.0791188
\(640\) 0 0
\(641\) 41.0000 1.61940 0.809701 − 0.586842i \(-0.199629\pi\)
0.809701 + 0.586842i \(0.199629\pi\)
\(642\) 0 0
\(643\) 34.0000 1.34083 0.670415 − 0.741987i \(-0.266116\pi\)
0.670415 + 0.741987i \(0.266116\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.00000 0.117942 0.0589711 − 0.998260i \(-0.481218\pi\)
0.0589711 + 0.998260i \(0.481218\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) 0 0
\(652\) −22.0000 −0.861586
\(653\) 10.0000 0.391330 0.195665 − 0.980671i \(-0.437313\pi\)
0.195665 + 0.980671i \(0.437313\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −32.0000 −1.24939
\(657\) −10.0000 −0.390137
\(658\) 0 0
\(659\) −10.0000 −0.389545 −0.194772 − 0.980848i \(-0.562397\pi\)
−0.194772 + 0.980848i \(0.562397\pi\)
\(660\) 0 0
\(661\) 19.0000 0.739014 0.369507 − 0.929228i \(-0.379527\pi\)
0.369507 + 0.929228i \(0.379527\pi\)
\(662\) 0 0
\(663\) 28.0000 1.08743
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 5.00000 0.193601
\(668\) 32.0000 1.23812
\(669\) 6.00000 0.231973
\(670\) 0 0
\(671\) 6.00000 0.231627
\(672\) 0 0
\(673\) −22.0000 −0.848038 −0.424019 − 0.905653i \(-0.639381\pi\)
−0.424019 + 0.905653i \(0.639381\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −6.00000 −0.230769
\(677\) 18.0000 0.691796 0.345898 − 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) 14.0000 0.535695 0.267848 − 0.963461i \(-0.413688\pi\)
0.267848 + 0.963461i \(0.413688\pi\)
\(684\) −6.00000 −0.229416
\(685\) 0 0
\(686\) 0 0
\(687\) −4.00000 −0.152610
\(688\) 40.0000 1.52499
\(689\) 36.0000 1.37149
\(690\) 0 0
\(691\) 23.0000 0.874961 0.437481 − 0.899228i \(-0.355871\pi\)
0.437481 + 0.899228i \(0.355871\pi\)
\(692\) 32.0000 1.21646
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 56.0000 2.12115
\(698\) 0 0
\(699\) −24.0000 −0.907763
\(700\) 0 0
\(701\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 24.0000 0.904534
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) −24.0000 −0.901975
\(709\) −40.0000 −1.50223 −0.751116 − 0.660171i \(-0.770484\pi\)
−0.751116 + 0.660171i \(0.770484\pi\)
\(710\) 0 0
\(711\) −10.0000 −0.375029
\(712\) 0 0
\(713\) 5.00000 0.187251
\(714\) 0 0
\(715\) 0 0
\(716\) 40.0000 1.49487
\(717\) 15.0000 0.560185
\(718\) 0 0
\(719\) −28.0000 −1.04422 −0.522112 − 0.852877i \(-0.674856\pi\)
−0.522112 + 0.852877i \(0.674856\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −18.0000 −0.669427
\(724\) −16.0000 −0.594635
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −70.0000 −2.58904
\(732\) −4.00000 −0.147844
\(733\) −45.0000 −1.66211 −0.831056 − 0.556188i \(-0.812263\pi\)
−0.831056 + 0.556188i \(0.812263\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −33.0000 −1.21557
\(738\) 0 0
\(739\) −38.0000 −1.39785 −0.698926 − 0.715194i \(-0.746338\pi\)
−0.698926 + 0.715194i \(0.746338\pi\)
\(740\) 0 0
\(741\) −12.0000 −0.440831
\(742\) 0 0
\(743\) 29.0000 1.06391 0.531953 − 0.846774i \(-0.321458\pi\)
0.531953 + 0.846774i \(0.321458\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −3.00000 −0.109764
\(748\) −42.0000 −1.53567
\(749\) 0 0
\(750\) 0 0
\(751\) 49.0000 1.78804 0.894018 − 0.448032i \(-0.147875\pi\)
0.894018 + 0.448032i \(0.147875\pi\)
\(752\) −8.00000 −0.291730
\(753\) 21.0000 0.765283
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −34.0000 −1.23575 −0.617876 − 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 0 0
\(759\) 15.0000 0.544466
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 − 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −20.0000 −0.723575
\(765\) 0 0
\(766\) 0 0
\(767\) −48.0000 −1.73318
\(768\) −16.0000 −0.577350
\(769\) 21.0000 0.757279 0.378640 − 0.925544i \(-0.376392\pi\)
0.378640 + 0.925544i \(0.376392\pi\)
\(770\) 0 0
\(771\) 26.0000 0.936367
\(772\) −42.0000 −1.51161
\(773\) −37.0000 −1.33080 −0.665399 − 0.746488i \(-0.731738\pi\)
−0.665399 + 0.746488i \(0.731738\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) −28.0000 −1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) −8.00000 −0.285169 −0.142585 − 0.989783i \(-0.545541\pi\)
−0.142585 + 0.989783i \(0.545541\pi\)
\(788\) 12.0000 0.427482
\(789\) 24.0000 0.854423
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −8.00000 −0.284088
\(794\) 0 0
\(795\) 0 0
\(796\) 40.0000 1.41776
\(797\) 26.0000 0.920967 0.460484 − 0.887668i \(-0.347676\pi\)
0.460484 + 0.887668i \(0.347676\pi\)
\(798\) 0 0
\(799\) 14.0000 0.495284
\(800\) 0 0
\(801\) 7.00000 0.247333
\(802\) 0 0
\(803\) 30.0000 1.05868
\(804\) 22.0000 0.775880
\(805\) 0 0
\(806\) 0 0
\(807\) −26.0000 −0.915243
\(808\) 0 0
\(809\) −19.0000 −0.668004 −0.334002 − 0.942572i \(-0.608399\pi\)
−0.334002 + 0.942572i \(0.608399\pi\)
\(810\) 0 0
\(811\) −36.0000 −1.26413 −0.632065 − 0.774915i \(-0.717793\pi\)
−0.632065 + 0.774915i \(0.717793\pi\)
\(812\) 0 0
\(813\) −10.0000 −0.350715
\(814\) 0 0
\(815\) 0 0
\(816\) 28.0000 0.980196
\(817\) 30.0000 1.04957
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −23.0000 −0.802706 −0.401353 − 0.915924i \(-0.631460\pi\)
−0.401353 + 0.915924i \(0.631460\pi\)
\(822\) 0 0
\(823\) 12.0000 0.418294 0.209147 − 0.977884i \(-0.432931\pi\)
0.209147 + 0.977884i \(0.432931\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 23.0000 0.799788 0.399894 − 0.916561i \(-0.369047\pi\)
0.399894 + 0.916561i \(0.369047\pi\)
\(828\) −10.0000 −0.347524
\(829\) 10.0000 0.347314 0.173657 − 0.984806i \(-0.444442\pi\)
0.173657 + 0.984806i \(0.444442\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −32.0000 −1.10940
\(833\) 49.0000 1.69775
\(834\) 0 0
\(835\) 0 0
\(836\) 18.0000 0.622543
\(837\) −1.00000 −0.0345651
\(838\) 0 0
\(839\) −48.0000 −1.65714 −0.828572 − 0.559883i \(-0.810846\pi\)
−0.828572 + 0.559883i \(0.810846\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) 0 0
\(843\) 2.00000 0.0688837
\(844\) −22.0000 −0.757271
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 36.0000 1.23625
\(849\) −15.0000 −0.514799
\(850\) 0 0
\(851\) 0 0
\(852\) −4.00000 −0.137038
\(853\) 10.0000 0.342393 0.171197 − 0.985237i \(-0.445237\pi\)
0.171197 + 0.985237i \(0.445237\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −54.0000 −1.84460 −0.922302 − 0.386469i \(-0.873695\pi\)
−0.922302 + 0.386469i \(0.873695\pi\)
\(858\) 0 0
\(859\) 44.0000 1.50126 0.750630 − 0.660722i \(-0.229750\pi\)
0.750630 + 0.660722i \(0.229750\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 4.00000 0.136162 0.0680808 − 0.997680i \(-0.478312\pi\)
0.0680808 + 0.997680i \(0.478312\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −32.0000 −1.08678
\(868\) 0 0
\(869\) 30.0000 1.01768
\(870\) 0 0
\(871\) 44.0000 1.49088
\(872\) 0 0
\(873\) −1.00000 −0.0338449
\(874\) 0 0
\(875\) 0 0
\(876\) −20.0000 −0.675737
\(877\) 22.0000 0.742887 0.371444 − 0.928456i \(-0.378863\pi\)
0.371444 + 0.928456i \(0.378863\pi\)
\(878\) 0 0
\(879\) 24.0000 0.809500
\(880\) 0 0
\(881\) −10.0000 −0.336909 −0.168454 − 0.985709i \(-0.553878\pi\)
−0.168454 + 0.985709i \(0.553878\pi\)
\(882\) 0 0
\(883\) 2.00000 0.0673054 0.0336527 − 0.999434i \(-0.489286\pi\)
0.0336527 + 0.999434i \(0.489286\pi\)
\(884\) 56.0000 1.88348
\(885\) 0 0
\(886\) 0 0
\(887\) 8.00000 0.268614 0.134307 − 0.990940i \(-0.457119\pi\)
0.134307 + 0.990940i \(0.457119\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −3.00000 −0.100504
\(892\) 12.0000 0.401790
\(893\) −6.00000 −0.200782
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −20.0000 −0.667781
\(898\) 0 0
\(899\) 1.00000 0.0333519
\(900\) 0 0
\(901\) −63.0000 −2.09883
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 23.0000 0.763702 0.381851 − 0.924224i \(-0.375287\pi\)
0.381851 + 0.924224i \(0.375287\pi\)
\(908\) 24.0000 0.796468
\(909\) −10.0000 −0.331679
\(910\) 0 0
\(911\) 29.0000 0.960813 0.480406 − 0.877046i \(-0.340489\pi\)
0.480406 + 0.877046i \(0.340489\pi\)
\(912\) −12.0000 −0.397360
\(913\) 9.00000 0.297857
\(914\) 0 0
\(915\) 0 0
\(916\) −8.00000 −0.264327
\(917\) 0 0
\(918\) 0 0
\(919\) −11.0000 −0.362857 −0.181428 − 0.983404i \(-0.558072\pi\)
−0.181428 + 0.983404i \(0.558072\pi\)
\(920\) 0 0
\(921\) 8.00000 0.263609
\(922\) 0 0
\(923\) −8.00000 −0.263323
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −11.0000 −0.361287
\(928\) 0 0
\(929\) −23.0000 −0.754606 −0.377303 − 0.926090i \(-0.623148\pi\)
−0.377303 + 0.926090i \(0.623148\pi\)
\(930\) 0 0
\(931\) −21.0000 −0.688247
\(932\) −48.0000 −1.57229
\(933\) −24.0000 −0.785725
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −7.00000 −0.228680 −0.114340 − 0.993442i \(-0.536475\pi\)
−0.114340 + 0.993442i \(0.536475\pi\)
\(938\) 0 0
\(939\) −18.0000 −0.587408
\(940\) 0 0
\(941\) 19.0000 0.619382 0.309691 − 0.950837i \(-0.399774\pi\)
0.309691 + 0.950837i \(0.399774\pi\)
\(942\) 0 0
\(943\) −40.0000 −1.30258
\(944\) −48.0000 −1.56227
\(945\) 0 0
\(946\) 0 0
\(947\) 51.0000 1.65728 0.828639 − 0.559784i \(-0.189116\pi\)
0.828639 + 0.559784i \(0.189116\pi\)
\(948\) −20.0000 −0.649570
\(949\) −40.0000 −1.29845
\(950\) 0 0
\(951\) 8.00000 0.259418
\(952\) 0 0
\(953\) −22.0000 −0.712650 −0.356325 − 0.934362i \(-0.615970\pi\)
−0.356325 + 0.934362i \(0.615970\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 30.0000 0.970269
\(957\) 3.00000 0.0969762
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 0.0322581
\(962\) 0 0
\(963\) −6.00000 −0.193347
\(964\) −36.0000 −1.15948
\(965\) 0 0
\(966\) 0 0
\(967\) −42.0000 −1.35063 −0.675314 − 0.737530i \(-0.735992\pi\)
−0.675314 + 0.737530i \(0.735992\pi\)
\(968\) 0 0
\(969\) 21.0000 0.674617
\(970\) 0 0
\(971\) 36.0000 1.15529 0.577647 − 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 2.00000 0.0641500
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −8.00000 −0.256074
\(977\) 38.0000 1.21573 0.607864 − 0.794041i \(-0.292027\pi\)
0.607864 + 0.794041i \(0.292027\pi\)
\(978\) 0 0
\(979\) −21.0000 −0.671163
\(980\) 0 0
\(981\) 2.00000 0.0638551
\(982\) 0 0
\(983\) 25.0000 0.797376 0.398688 − 0.917087i \(-0.369466\pi\)
0.398688 + 0.917087i \(0.369466\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −24.0000 −0.763542
\(989\) 50.0000 1.58991
\(990\) 0 0
\(991\) 2.00000 0.0635321 0.0317660 − 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) 0 0
\(993\) 24.0000 0.761617
\(994\) 0 0
\(995\) 0 0
\(996\) −6.00000 −0.190117
\(997\) −57.0000 −1.80521 −0.902604 − 0.430472i \(-0.858347\pi\)
−0.902604 + 0.430472i \(0.858347\pi\)
\(998\) 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 2325.2.a.f.1.1 ✓ 1
3.2 odd 2 6975.2.a.k.1.1 1
5.2 odd 4 2325.2.c.g.1024.2 2
5.3 odd 4 2325.2.c.g.1024.1 2
5.4 even 2 2325.2.a.g.1.1 yes 1
15.14 odd 2 6975.2.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2325.2.a.f.1.1 ✓ 1 1.1 even 1 trivial
2325.2.a.g.1.1 yes 1 5.4 even 2
2325.2.c.g.1024.1 2 5.3 odd 4
2325.2.c.g.1024.2 2 5.2 odd 4
6975.2.a.j.1.1 1 15.14 odd 2
6975.2.a.k.1.1 1 3.2 odd 2