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Properties

Label 9200.2.a.bl.1.1
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9200,2,Mod(1,9200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9200, 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("9200.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.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: \(73.4623698596\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1150)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} +4.00000 q^{7} +6.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} +4.00000 q^{7} +6.00000 q^{9} -3.00000 q^{11} +6.00000 q^{13} -5.00000 q^{17} +1.00000 q^{19} +12.0000 q^{21} +1.00000 q^{23} +9.00000 q^{27} -8.00000 q^{29} +8.00000 q^{31} -9.00000 q^{33} -2.00000 q^{37} +18.0000 q^{39} -7.00000 q^{41} +4.00000 q^{43} +10.0000 q^{47} +9.00000 q^{49} -15.0000 q^{51} +12.0000 q^{53} +3.00000 q^{57} -4.00000 q^{59} -8.00000 q^{61} +24.0000 q^{63} +3.00000 q^{67} +3.00000 q^{69} -4.00000 q^{71} +7.00000 q^{73} -12.0000 q^{77} +6.00000 q^{79} +9.00000 q^{81} +11.0000 q^{83} -24.0000 q^{87} -3.00000 q^{89} +24.0000 q^{91} +24.0000 q^{93} +14.0000 q^{97} -18.0000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(3\) 3.00000 1.73205 0.866025 − 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.00000 1.51186 0.755929 − 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 0 0
\(9\) 6.00000 2.00000
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 − 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 − 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.00000 −1.21268 −0.606339 − 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 − 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 12.0000 2.61861
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 9.00000 1.73205
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 − 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 − 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0 0
\(33\) −9.00000 −1.56670
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 18.0000 2.88231
\(40\) 0 0
\(41\) −7.00000 −1.09322 −0.546608 − 0.837389i \(-0.684081\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 − 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.0000 1.45865 0.729325 − 0.684167i \(-0.239834\pi\)
0.729325 + 0.684167i \(0.239834\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) −15.0000 −2.10042
\(52\) 0 0
\(53\) 12.0000 1.64833 0.824163 − 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 − 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 − 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 0 0
\(63\) 24.0000 3.02372
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 3.00000 0.366508 0.183254 − 0.983066i \(-0.441337\pi\)
0.183254 + 0.983066i \(0.441337\pi\)
\(68\) 0 0
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 − 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) 7.00000 0.819288 0.409644 − 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −12.0000 −1.36753
\(78\) 0 0
\(79\) 6.00000 0.675053 0.337526 − 0.941316i \(-0.390410\pi\)
0.337526 + 0.941316i \(0.390410\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 11.0000 1.20741 0.603703 − 0.797209i \(-0.293691\pi\)
0.603703 + 0.797209i \(0.293691\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −24.0000 −2.57307
\(88\) 0 0
\(89\) −3.00000 −0.317999 −0.159000 − 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) 24.0000 2.51588
\(92\) 0 0
\(93\) 24.0000 2.48868
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 14.0000 1.42148 0.710742 − 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) −18.0000 −1.80907
\(100\) 0 0
\(101\) 4.00000 0.398015 0.199007 − 0.979998i \(-0.436228\pi\)
0.199007 + 0.979998i \(0.436228\pi\)
\(102\) 0 0
\(103\) 10.0000 0.985329 0.492665 − 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.00000 0.483368 0.241684 − 0.970355i \(-0.422300\pi\)
0.241684 + 0.970355i \(0.422300\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 − 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) −6.00000 −0.569495
\(112\) 0 0
\(113\) −15.0000 −1.41108 −0.705541 − 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 36.0000 3.32820
\(118\) 0 0
\(119\) −20.0000 −1.83340
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) −21.0000 −1.89351
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 − 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 12.0000 1.05654
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 − 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.00000 0.256307 0.128154 − 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 0 0
\(139\) 19.0000 1.61156 0.805779 − 0.592216i \(-0.201747\pi\)
0.805779 + 0.592216i \(0.201747\pi\)
\(140\) 0 0
\(141\) 30.0000 2.52646
\(142\) 0 0
\(143\) −18.0000 −1.50524
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 27.0000 2.22692
\(148\) 0 0
\(149\) 6.00000 0.491539 0.245770 − 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) −20.0000 −1.62758 −0.813788 − 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 0 0
\(153\) −30.0000 −2.42536
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −14.0000 −1.11732 −0.558661 − 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 0 0
\(159\) 36.0000 2.85499
\(160\) 0 0
\(161\) 4.00000 0.315244
\(162\) 0 0
\(163\) 5.00000 0.391630 0.195815 − 0.980641i \(-0.437265\pi\)
0.195815 + 0.980641i \(0.437265\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 22.0000 1.70241 0.851206 − 0.524832i \(-0.175872\pi\)
0.851206 + 0.524832i \(0.175872\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) 6.00000 0.458831
\(172\) 0 0
\(173\) −4.00000 −0.304114 −0.152057 − 0.988372i \(-0.548590\pi\)
−0.152057 + 0.988372i \(0.548590\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −12.0000 −0.901975
\(178\) 0 0
\(179\) 3.00000 0.224231 0.112115 − 0.993695i \(-0.464237\pi\)
0.112115 + 0.993695i \(0.464237\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 − 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) −24.0000 −1.77413
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 15.0000 1.09691
\(188\) 0 0
\(189\) 36.0000 2.61861
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 − 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) 9.00000 0.647834 0.323917 − 0.946085i \(-0.395000\pi\)
0.323917 + 0.946085i \(0.395000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.00000 0.569976 0.284988 − 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 0 0
\(199\) −18.0000 −1.27599 −0.637993 − 0.770042i \(-0.720235\pi\)
−0.637993 + 0.770042i \(0.720235\pi\)
\(200\) 0 0
\(201\) 9.00000 0.634811
\(202\) 0 0
\(203\) −32.0000 −2.24596
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.00000 0.417029
\(208\) 0 0
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) 1.00000 0.0688428 0.0344214 − 0.999407i \(-0.489041\pi\)
0.0344214 + 0.999407i \(0.489041\pi\)
\(212\) 0 0
\(213\) −12.0000 −0.822226
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 32.0000 2.17230
\(218\) 0 0
\(219\) 21.0000 1.41905
\(220\) 0 0
\(221\) −30.0000 −2.01802
\(222\) 0 0
\(223\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.00000 −0.530979 −0.265489 − 0.964114i \(-0.585534\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(228\) 0 0
\(229\) −30.0000 −1.98246 −0.991228 − 0.132164i \(-0.957808\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) 0 0
\(231\) −36.0000 −2.36863
\(232\) 0 0
\(233\) 14.0000 0.917170 0.458585 − 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 18.0000 1.16923
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 − 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) 23.0000 1.48156 0.740780 − 0.671748i \(-0.234456\pi\)
0.740780 + 0.671748i \(0.234456\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.00000 0.381771
\(248\) 0 0
\(249\) 33.0000 2.09129
\(250\) 0 0
\(251\) 7.00000 0.441836 0.220918 − 0.975292i \(-0.429095\pi\)
0.220918 + 0.975292i \(0.429095\pi\)
\(252\) 0 0
\(253\) −3.00000 −0.188608
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.00000 −0.124757 −0.0623783 − 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 0 0
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) −48.0000 −2.97113
\(262\) 0 0
\(263\) −4.00000 −0.246651 −0.123325 − 0.992366i \(-0.539356\pi\)
−0.123325 + 0.992366i \(0.539356\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −9.00000 −0.550791
\(268\) 0 0
\(269\) −6.00000 −0.365826 −0.182913 − 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) −10.0000 −0.607457 −0.303728 − 0.952759i \(-0.598232\pi\)
−0.303728 + 0.952759i \(0.598232\pi\)
\(272\) 0 0
\(273\) 72.0000 4.35764
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 28.0000 1.68236 0.841178 − 0.540758i \(-0.181862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 0 0
\(279\) 48.0000 2.87368
\(280\) 0 0
\(281\) −30.0000 −1.78965 −0.894825 − 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) 0 0
\(283\) −33.0000 −1.96165 −0.980823 − 0.194900i \(-0.937562\pi\)
−0.980823 + 0.194900i \(0.937562\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −28.0000 −1.65279
\(288\) 0 0
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) 42.0000 2.46208
\(292\) 0 0
\(293\) −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
\(297\) −27.0000 −1.56670
\(298\) 0 0
\(299\) 6.00000 0.346989
\(300\) 0 0
\(301\) 16.0000 0.922225
\(302\) 0 0
\(303\) 12.0000 0.689382
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −9.00000 −0.513657 −0.256829 − 0.966457i \(-0.582678\pi\)
−0.256829 + 0.966457i \(0.582678\pi\)
\(308\) 0 0
\(309\) 30.0000 1.70664
\(310\) 0 0
\(311\) −2.00000 −0.113410 −0.0567048 − 0.998391i \(-0.518059\pi\)
−0.0567048 + 0.998391i \(0.518059\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 − 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.0000 −0.673987 −0.336994 − 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 0 0
\(319\) 24.0000 1.34374
\(320\) 0 0
\(321\) 15.0000 0.837218
\(322\) 0 0
\(323\) −5.00000 −0.278207
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −30.0000 −1.65900
\(328\) 0 0
\(329\) 40.0000 2.20527
\(330\) 0 0
\(331\) −25.0000 −1.37412 −0.687062 − 0.726599i \(-0.741100\pi\)
−0.687062 + 0.726599i \(0.741100\pi\)
\(332\) 0 0
\(333\) −12.0000 −0.657596
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −3.00000 −0.163420 −0.0817102 − 0.996656i \(-0.526038\pi\)
−0.0817102 + 0.996656i \(0.526038\pi\)
\(338\) 0 0
\(339\) −45.0000 −2.44406
\(340\) 0 0
\(341\) −24.0000 −1.29967
\(342\) 0 0
\(343\) 8.00000 0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.00000 0.375780 0.187890 − 0.982190i \(-0.439835\pi\)
0.187890 + 0.982190i \(0.439835\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 − 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) 54.0000 2.88231
\(352\) 0 0
\(353\) −18.0000 −0.958043 −0.479022 − 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −60.0000 −3.17554
\(358\) 0 0
\(359\) 20.0000 1.05556 0.527780 − 0.849381i \(-0.323025\pi\)
0.527780 + 0.849381i \(0.323025\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) −6.00000 −0.314918
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 2.00000 0.104399 0.0521996 − 0.998637i \(-0.483377\pi\)
0.0521996 + 0.998637i \(0.483377\pi\)
\(368\) 0 0
\(369\) −42.0000 −2.18643
\(370\) 0 0
\(371\) 48.0000 2.49204
\(372\) 0 0
\(373\) 12.0000 0.621336 0.310668 − 0.950518i \(-0.399447\pi\)
0.310668 + 0.950518i \(0.399447\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −48.0000 −2.47213
\(378\) 0 0
\(379\) −5.00000 −0.256833 −0.128416 − 0.991720i \(-0.540989\pi\)
−0.128416 + 0.991720i \(0.540989\pi\)
\(380\) 0 0
\(381\) −24.0000 −1.22956
\(382\) 0 0
\(383\) −6.00000 −0.306586 −0.153293 − 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 24.0000 1.21999
\(388\) 0 0
\(389\) −36.0000 −1.82527 −0.912636 − 0.408773i \(-0.865957\pi\)
−0.912636 + 0.408773i \(0.865957\pi\)
\(390\) 0 0
\(391\) −5.00000 −0.252861
\(392\) 0 0
\(393\) −36.0000 −1.81596
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 12.0000 0.602263 0.301131 − 0.953583i \(-0.402636\pi\)
0.301131 + 0.953583i \(0.402636\pi\)
\(398\) 0 0
\(399\) 12.0000 0.600751
\(400\) 0 0
\(401\) −5.00000 −0.249688 −0.124844 − 0.992176i \(-0.539843\pi\)
−0.124844 + 0.992176i \(0.539843\pi\)
\(402\) 0 0
\(403\) 48.0000 2.39105
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) 21.0000 1.03838 0.519192 − 0.854658i \(-0.326233\pi\)
0.519192 + 0.854658i \(0.326233\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) 0 0
\(413\) −16.0000 −0.787309
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 57.0000 2.79130
\(418\) 0 0
\(419\) −3.00000 −0.146560 −0.0732798 − 0.997311i \(-0.523347\pi\)
−0.0732798 + 0.997311i \(0.523347\pi\)
\(420\) 0 0
\(421\) −14.0000 −0.682318 −0.341159 − 0.940006i \(-0.610819\pi\)
−0.341159 + 0.940006i \(0.610819\pi\)
\(422\) 0 0
\(423\) 60.0000 2.91730
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −32.0000 −1.54859
\(428\) 0 0
\(429\) −54.0000 −2.60714
\(430\) 0 0
\(431\) 4.00000 0.192673 0.0963366 − 0.995349i \(-0.469287\pi\)
0.0963366 + 0.995349i \(0.469287\pi\)
\(432\) 0 0
\(433\) −29.0000 −1.39365 −0.696826 − 0.717241i \(-0.745405\pi\)
−0.696826 + 0.717241i \(0.745405\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.00000 0.0478365
\(438\) 0 0
\(439\) 6.00000 0.286364 0.143182 − 0.989696i \(-0.454267\pi\)
0.143182 + 0.989696i \(0.454267\pi\)
\(440\) 0 0
\(441\) 54.0000 2.57143
\(442\) 0 0
\(443\) −39.0000 −1.85295 −0.926473 − 0.376361i \(-0.877175\pi\)
−0.926473 + 0.376361i \(0.877175\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 18.0000 0.851371
\(448\) 0 0
\(449\) 5.00000 0.235965 0.117982 − 0.993016i \(-0.462357\pi\)
0.117982 + 0.993016i \(0.462357\pi\)
\(450\) 0 0
\(451\) 21.0000 0.988851
\(452\) 0 0
\(453\) −60.0000 −2.81905
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7.00000 0.327446 0.163723 − 0.986506i \(-0.447650\pi\)
0.163723 + 0.986506i \(0.447650\pi\)
\(458\) 0 0
\(459\) −45.0000 −2.10042
\(460\) 0 0
\(461\) −24.0000 −1.11779 −0.558896 − 0.829238i \(-0.688775\pi\)
−0.558896 + 0.829238i \(0.688775\pi\)
\(462\) 0 0
\(463\) 26.0000 1.20832 0.604161 − 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 28.0000 1.29569 0.647843 − 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) 0 0
\(469\) 12.0000 0.554109
\(470\) 0 0
\(471\) −42.0000 −1.93526
\(472\) 0 0
\(473\) −12.0000 −0.551761
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 72.0000 3.29665
\(478\) 0 0
\(479\) 4.00000 0.182765 0.0913823 − 0.995816i \(-0.470871\pi\)
0.0913823 + 0.995816i \(0.470871\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) 0 0
\(483\) 12.0000 0.546019
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −30.0000 −1.35943 −0.679715 − 0.733476i \(-0.737896\pi\)
−0.679715 + 0.733476i \(0.737896\pi\)
\(488\) 0 0
\(489\) 15.0000 0.678323
\(490\) 0 0
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 40.0000 1.80151
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.0000 −0.717698
\(498\) 0 0
\(499\) 12.0000 0.537194 0.268597 − 0.963253i \(-0.413440\pi\)
0.268597 + 0.963253i \(0.413440\pi\)
\(500\) 0 0
\(501\) 66.0000 2.94866
\(502\) 0 0
\(503\) −24.0000 −1.07011 −0.535054 − 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 69.0000 3.06440
\(508\) 0 0
\(509\) 36.0000 1.59567 0.797836 − 0.602875i \(-0.205978\pi\)
0.797836 + 0.602875i \(0.205978\pi\)
\(510\) 0 0
\(511\) 28.0000 1.23865
\(512\) 0 0
\(513\) 9.00000 0.397360
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −30.0000 −1.31940
\(518\) 0 0
\(519\) −12.0000 −0.526742
\(520\) 0 0
\(521\) 31.0000 1.35813 0.679067 − 0.734076i \(-0.262384\pi\)
0.679067 + 0.734076i \(0.262384\pi\)
\(522\) 0 0
\(523\) 37.0000 1.61790 0.808949 − 0.587879i \(-0.200037\pi\)
0.808949 + 0.587879i \(0.200037\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −40.0000 −1.74243
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −24.0000 −1.04151
\(532\) 0 0
\(533\) −42.0000 −1.81922
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 9.00000 0.388379
\(538\) 0 0
\(539\) −27.0000 −1.16297
\(540\) 0 0
\(541\) 16.0000 0.687894 0.343947 − 0.938989i \(-0.388236\pi\)
0.343947 + 0.938989i \(0.388236\pi\)
\(542\) 0 0
\(543\) −66.0000 −2.83233
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −17.0000 −0.726868 −0.363434 − 0.931620i \(-0.618396\pi\)
−0.363434 + 0.931620i \(0.618396\pi\)
\(548\) 0 0
\(549\) −48.0000 −2.04859
\(550\) 0 0
\(551\) −8.00000 −0.340811
\(552\) 0 0
\(553\) 24.0000 1.02058
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 30.0000 1.27114 0.635570 − 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 0 0
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 45.0000 1.89990
\(562\) 0 0
\(563\) −4.00000 −0.168580 −0.0842900 − 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 36.0000 1.51186
\(568\) 0 0
\(569\) −9.00000 −0.377300 −0.188650 − 0.982044i \(-0.560411\pi\)
−0.188650 + 0.982044i \(0.560411\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 − 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) −36.0000 −1.50392
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −17.0000 −0.707719 −0.353860 − 0.935299i \(-0.615131\pi\)
−0.353860 + 0.935299i \(0.615131\pi\)
\(578\) 0 0
\(579\) 27.0000 1.12208
\(580\) 0 0
\(581\) 44.0000 1.82543
\(582\) 0 0
\(583\) −36.0000 −1.49097
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 17.0000 0.701665 0.350833 − 0.936438i \(-0.385899\pi\)
0.350833 + 0.936438i \(0.385899\pi\)
\(588\) 0 0
\(589\) 8.00000 0.329634
\(590\) 0 0
\(591\) 24.0000 0.987228
\(592\) 0 0
\(593\) 35.0000 1.43728 0.718639 − 0.695383i \(-0.244765\pi\)
0.718639 + 0.695383i \(0.244765\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −54.0000 −2.21007
\(598\) 0 0
\(599\) 20.0000 0.817178 0.408589 − 0.912719i \(-0.366021\pi\)
0.408589 + 0.912719i \(0.366021\pi\)
\(600\) 0 0
\(601\) 31.0000 1.26452 0.632258 − 0.774758i \(-0.282128\pi\)
0.632258 + 0.774758i \(0.282128\pi\)
\(602\) 0 0
\(603\) 18.0000 0.733017
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 10.0000 0.405887 0.202944 − 0.979190i \(-0.434949\pi\)
0.202944 + 0.979190i \(0.434949\pi\)
\(608\) 0 0
\(609\) −96.0000 −3.89012
\(610\) 0 0
\(611\) 60.0000 2.42734
\(612\) 0 0
\(613\) 8.00000 0.323117 0.161558 − 0.986863i \(-0.448348\pi\)
0.161558 + 0.986863i \(0.448348\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 − 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) −28.0000 −1.12542 −0.562708 − 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(620\) 0 0
\(621\) 9.00000 0.361158
\(622\) 0 0
\(623\) −12.0000 −0.480770
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −9.00000 −0.359425
\(628\) 0 0
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) −30.0000 −1.19428 −0.597141 − 0.802137i \(-0.703697\pi\)
−0.597141 + 0.802137i \(0.703697\pi\)
\(632\) 0 0
\(633\) 3.00000 0.119239
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 54.0000 2.13956
\(638\) 0 0
\(639\) −24.0000 −0.949425
\(640\) 0 0
\(641\) 30.0000 1.18493 0.592464 − 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 0 0
\(643\) 32.0000 1.26196 0.630978 − 0.775800i \(-0.282654\pi\)
0.630978 + 0.775800i \(0.282654\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 28.0000 1.10079 0.550397 − 0.834903i \(-0.314476\pi\)
0.550397 + 0.834903i \(0.314476\pi\)
\(648\) 0 0
\(649\) 12.0000 0.471041
\(650\) 0 0
\(651\) 96.0000 3.76254
\(652\) 0 0
\(653\) −14.0000 −0.547862 −0.273931 − 0.961749i \(-0.588324\pi\)
−0.273931 + 0.961749i \(0.588324\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 42.0000 1.63858
\(658\) 0 0
\(659\) −5.00000 −0.194772 −0.0973862 − 0.995247i \(-0.531048\pi\)
−0.0973862 + 0.995247i \(0.531048\pi\)
\(660\) 0 0
\(661\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) −90.0000 −3.49531
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −8.00000 −0.309761
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 24.0000 0.926510
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 − 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −42.0000 −1.61419 −0.807096 − 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 0 0
\(679\) 56.0000 2.14908
\(680\) 0 0
\(681\) −24.0000 −0.919682
\(682\) 0 0
\(683\) 35.0000 1.33924 0.669619 − 0.742705i \(-0.266457\pi\)
0.669619 + 0.742705i \(0.266457\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −90.0000 −3.43371
\(688\) 0 0
\(689\) 72.0000 2.74298
\(690\) 0 0
\(691\) −29.0000 −1.10321 −0.551606 − 0.834105i \(-0.685985\pi\)
−0.551606 + 0.834105i \(0.685985\pi\)
\(692\) 0 0
\(693\) −72.0000 −2.73505
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 35.0000 1.32572
\(698\) 0 0
\(699\) 42.0000 1.58859
\(700\) 0 0
\(701\) −8.00000 −0.302156 −0.151078 − 0.988522i \(-0.548274\pi\)
−0.151078 + 0.988522i \(0.548274\pi\)
\(702\) 0 0
\(703\) −2.00000 −0.0754314
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 16.0000 0.601742
\(708\) 0 0
\(709\) 16.0000 0.600893 0.300446 − 0.953799i \(-0.402864\pi\)
0.300446 + 0.953799i \(0.402864\pi\)
\(710\) 0 0
\(711\) 36.0000 1.35011
\(712\) 0 0
\(713\) 8.00000 0.299602
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 18.0000 0.672222
\(718\) 0 0
\(719\) −8.00000 −0.298350 −0.149175 − 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) 0 0
\(721\) 40.0000 1.48968
\(722\) 0 0
\(723\) 69.0000 2.56614
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −28.0000 −1.03846 −0.519231 − 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −20.0000 −0.739727
\(732\) 0 0
\(733\) −38.0000 −1.40356 −0.701781 − 0.712393i \(-0.747612\pi\)
−0.701781 + 0.712393i \(0.747612\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9.00000 −0.331519
\(738\) 0 0
\(739\) 4.00000 0.147142 0.0735712 − 0.997290i \(-0.476560\pi\)
0.0735712 + 0.997290i \(0.476560\pi\)
\(740\) 0 0
\(741\) 18.0000 0.661247
\(742\) 0 0
\(743\) 26.0000 0.953847 0.476924 − 0.878945i \(-0.341752\pi\)
0.476924 + 0.878945i \(0.341752\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 66.0000 2.41481
\(748\) 0 0
\(749\) 20.0000 0.730784
\(750\) 0 0
\(751\) −24.0000 −0.875772 −0.437886 − 0.899030i \(-0.644273\pi\)
−0.437886 + 0.899030i \(0.644273\pi\)
\(752\) 0 0
\(753\) 21.0000 0.765283
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −16.0000 −0.581530 −0.290765 − 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) 0 0
\(759\) −9.00000 −0.326679
\(760\) 0 0
\(761\) −15.0000 −0.543750 −0.271875 − 0.962333i \(-0.587644\pi\)
−0.271875 + 0.962333i \(0.587644\pi\)
\(762\) 0 0
\(763\) −40.0000 −1.44810
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −24.0000 −0.866590
\(768\) 0 0
\(769\) −21.0000 −0.757279 −0.378640 − 0.925544i \(-0.623608\pi\)
−0.378640 + 0.925544i \(0.623608\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 0 0
\(773\) −4.00000 −0.143870 −0.0719350 − 0.997409i \(-0.522917\pi\)
−0.0719350 + 0.997409i \(0.522917\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −24.0000 −0.860995
\(778\) 0 0
\(779\) −7.00000 −0.250801
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) 0 0
\(783\) −72.0000 −2.57307
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −52.0000 −1.85360 −0.926800 − 0.375555i \(-0.877452\pi\)
−0.926800 + 0.375555i \(0.877452\pi\)
\(788\) 0 0
\(789\) −12.0000 −0.427211
\(790\) 0 0
\(791\) −60.0000 −2.13335
\(792\) 0 0
\(793\) −48.0000 −1.70453
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 18.0000 0.637593 0.318796 − 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) −50.0000 −1.76887
\(800\) 0 0
\(801\) −18.0000 −0.635999
\(802\) 0 0
\(803\) −21.0000 −0.741074
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −18.0000 −0.633630
\(808\) 0 0
\(809\) 10.0000 0.351581 0.175791 − 0.984428i \(-0.443752\pi\)
0.175791 + 0.984428i \(0.443752\pi\)
\(810\) 0 0
\(811\) −4.00000 −0.140459 −0.0702295 − 0.997531i \(-0.522373\pi\)
−0.0702295 + 0.997531i \(0.522373\pi\)
\(812\) 0 0
\(813\) −30.0000 −1.05215
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 4.00000 0.139942
\(818\) 0 0
\(819\) 144.000 5.03177
\(820\) 0 0
\(821\) 16.0000 0.558404 0.279202 − 0.960232i \(-0.409930\pi\)
0.279202 + 0.960232i \(0.409930\pi\)
\(822\) 0 0
\(823\) −26.0000 −0.906303 −0.453152 − 0.891434i \(-0.649700\pi\)
−0.453152 + 0.891434i \(0.649700\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −17.0000 −0.591148 −0.295574 − 0.955320i \(-0.595511\pi\)
−0.295574 + 0.955320i \(0.595511\pi\)
\(828\) 0 0
\(829\) 24.0000 0.833554 0.416777 − 0.909009i \(-0.363160\pi\)
0.416777 + 0.909009i \(0.363160\pi\)
\(830\) 0 0
\(831\) 84.0000 2.91393
\(832\) 0 0
\(833\) −45.0000 −1.55916
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 72.0000 2.48868
\(838\) 0 0
\(839\) −26.0000 −0.897620 −0.448810 − 0.893627i \(-0.648152\pi\)
−0.448810 + 0.893627i \(0.648152\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) 0 0
\(843\) −90.0000 −3.09976
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −8.00000 −0.274883
\(848\) 0 0
\(849\) −99.0000 −3.39767
\(850\) 0 0
\(851\) −2.00000 −0.0685591
\(852\) 0 0
\(853\) −12.0000 −0.410872 −0.205436 − 0.978671i \(-0.565861\pi\)
−0.205436 + 0.978671i \(0.565861\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 21.0000 0.717346 0.358673 − 0.933463i \(-0.383229\pi\)
0.358673 + 0.933463i \(0.383229\pi\)
\(858\) 0 0
\(859\) 11.0000 0.375315 0.187658 − 0.982235i \(-0.439910\pi\)
0.187658 + 0.982235i \(0.439910\pi\)
\(860\) 0 0
\(861\) −84.0000 −2.86271
\(862\) 0 0
\(863\) 24.0000 0.816970 0.408485 − 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 24.0000 0.815083
\(868\) 0 0
\(869\) −18.0000 −0.610608
\(870\) 0 0
\(871\) 18.0000 0.609907
\(872\) 0 0
\(873\) 84.0000 2.84297
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −38.0000 −1.28317 −0.641584 − 0.767052i \(-0.721723\pi\)
−0.641584 + 0.767052i \(0.721723\pi\)
\(878\) 0 0
\(879\) −72.0000 −2.42850
\(880\) 0 0
\(881\) −30.0000 −1.01073 −0.505363 − 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) 0 0
\(883\) −37.0000 −1.24515 −0.622575 − 0.782560i \(-0.713913\pi\)
−0.622575 + 0.782560i \(0.713913\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 12.0000 0.402921 0.201460 − 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) 0 0
\(889\) −32.0000 −1.07325
\(890\) 0 0
\(891\) −27.0000 −0.904534
\(892\) 0 0
\(893\) 10.0000 0.334637
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 18.0000 0.601003
\(898\) 0 0
\(899\) −64.0000 −2.13452
\(900\) 0 0
\(901\) −60.0000 −1.99889
\(902\) 0 0
\(903\) 48.0000 1.59734
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −28.0000 −0.929725 −0.464862 − 0.885383i \(-0.653896\pi\)
−0.464862 + 0.885383i \(0.653896\pi\)
\(908\) 0 0
\(909\) 24.0000 0.796030
\(910\) 0 0
\(911\) 10.0000 0.331315 0.165657 − 0.986183i \(-0.447025\pi\)
0.165657 + 0.986183i \(0.447025\pi\)
\(912\) 0 0
\(913\) −33.0000 −1.09214
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −48.0000 −1.58510
\(918\) 0 0
\(919\) −52.0000 −1.71532 −0.857661 − 0.514216i \(-0.828083\pi\)
−0.857661 + 0.514216i \(0.828083\pi\)
\(920\) 0 0
\(921\) −27.0000 −0.889680
\(922\) 0 0
\(923\) −24.0000 −0.789970
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 60.0000 1.97066
\(928\) 0 0
\(929\) −22.0000 −0.721797 −0.360898 − 0.932605i \(-0.617530\pi\)
−0.360898 + 0.932605i \(0.617530\pi\)
\(930\) 0 0
\(931\) 9.00000 0.294963
\(932\) 0 0
\(933\) −6.00000 −0.196431
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 9.00000 0.294017 0.147009 − 0.989135i \(-0.453036\pi\)
0.147009 + 0.989135i \(0.453036\pi\)
\(938\) 0 0
\(939\) 30.0000 0.979013
\(940\) 0 0
\(941\) 4.00000 0.130396 0.0651981 − 0.997872i \(-0.479232\pi\)
0.0651981 + 0.997872i \(0.479232\pi\)
\(942\) 0 0
\(943\) −7.00000 −0.227951
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 12.0000 0.389948 0.194974 − 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 0 0
\(949\) 42.0000 1.36338
\(950\) 0 0
\(951\) −36.0000 −1.16738
\(952\) 0 0
\(953\) 27.0000 0.874616 0.437308 − 0.899312i \(-0.355932\pi\)
0.437308 + 0.899312i \(0.355932\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 72.0000 2.32743
\(958\) 0 0
\(959\) 12.0000 0.387500
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 0 0
\(963\) 30.0000 0.966736
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −28.0000 −0.900419 −0.450210 − 0.892923i \(-0.648651\pi\)
−0.450210 + 0.892923i \(0.648651\pi\)
\(968\) 0 0
\(969\) −15.0000 −0.481869
\(970\) 0 0
\(971\) −15.0000 −0.481373 −0.240686 − 0.970603i \(-0.577373\pi\)
−0.240686 + 0.970603i \(0.577373\pi\)
\(972\) 0 0
\(973\) 76.0000 2.43645
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −17.0000 −0.543878 −0.271939 − 0.962314i \(-0.587665\pi\)
−0.271939 + 0.962314i \(0.587665\pi\)
\(978\) 0 0
\(979\) 9.00000 0.287641
\(980\) 0 0
\(981\) −60.0000 −1.91565
\(982\) 0 0
\(983\) 42.0000 1.33959 0.669796 − 0.742545i \(-0.266382\pi\)
0.669796 + 0.742545i \(0.266382\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 120.000 3.81964
\(988\) 0 0
\(989\) 4.00000 0.127193
\(990\) 0 0
\(991\) −2.00000 −0.0635321 −0.0317660 − 0.999495i \(-0.510113\pi\)
−0.0317660 + 0.999495i \(0.510113\pi\)
\(992\) 0 0
\(993\) −75.0000 −2.38005
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −22.0000 −0.696747 −0.348373 − 0.937356i \(-0.613266\pi\)
−0.348373 + 0.937356i \(0.613266\pi\)
\(998\) 0 0
\(999\) −18.0000 −0.569495
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 9200.2.a.bl.1.1 1
4.3 odd 2 1150.2.a.e.1.1 yes 1
5.4 even 2 9200.2.a.a.1.1 1
20.3 even 4 1150.2.b.a.599.1 2
20.7 even 4 1150.2.b.a.599.2 2
20.19 odd 2 1150.2.a.d.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1150.2.a.d.1.1 ✓ 1 20.19 odd 2
1150.2.a.e.1.1 yes 1 4.3 odd 2
1150.2.b.a.599.1 2 20.3 even 4
1150.2.b.a.599.2 2 20.7 even 4
9200.2.a.a.1.1 1 5.4 even 2
9200.2.a.bl.1.1 1 1.1 even 1 trivial