Properties

Label 363.2.a.c.1.1
Level $363$
Weight $2$
Character 363.1
Self dual yes
Analytic conductor $2.899$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [363,2,Mod(1,363)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(363, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("363.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.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: \(2.89856959337\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 363.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} +4.00000 q^{5} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} +4.00000 q^{5} -2.00000 q^{6} -1.00000 q^{7} +1.00000 q^{9} +8.00000 q^{10} -2.00000 q^{12} +2.00000 q^{13} -2.00000 q^{14} -4.00000 q^{15} -4.00000 q^{16} -4.00000 q^{17} +2.00000 q^{18} +3.00000 q^{19} +8.00000 q^{20} +1.00000 q^{21} +2.00000 q^{23} +11.0000 q^{25} +4.00000 q^{26} -1.00000 q^{27} -2.00000 q^{28} -6.00000 q^{29} -8.00000 q^{30} -5.00000 q^{31} -8.00000 q^{32} -8.00000 q^{34} -4.00000 q^{35} +2.00000 q^{36} +3.00000 q^{37} +6.00000 q^{38} -2.00000 q^{39} +2.00000 q^{41} +2.00000 q^{42} -12.0000 q^{43} +4.00000 q^{45} +4.00000 q^{46} +2.00000 q^{47} +4.00000 q^{48} -6.00000 q^{49} +22.0000 q^{50} +4.00000 q^{51} +4.00000 q^{52} +6.00000 q^{53} -2.00000 q^{54} -3.00000 q^{57} -12.0000 q^{58} -10.0000 q^{59} -8.00000 q^{60} -3.00000 q^{61} -10.0000 q^{62} -1.00000 q^{63} -8.00000 q^{64} +8.00000 q^{65} -1.00000 q^{67} -8.00000 q^{68} -2.00000 q^{69} -8.00000 q^{70} +11.0000 q^{73} +6.00000 q^{74} -11.0000 q^{75} +6.00000 q^{76} -4.00000 q^{78} -11.0000 q^{79} -16.0000 q^{80} +1.00000 q^{81} +4.00000 q^{82} -6.00000 q^{83} +2.00000 q^{84} -16.0000 q^{85} -24.0000 q^{86} +6.00000 q^{87} +12.0000 q^{89} +8.00000 q^{90} -2.00000 q^{91} +4.00000 q^{92} +5.00000 q^{93} +4.00000 q^{94} +12.0000 q^{95} +8.00000 q^{96} +5.00000 q^{97} -12.0000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.00000 1.00000
\(5\) 4.00000 1.78885 0.894427 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) −2.00000 −0.816497
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 8.00000 2.52982
\(11\) 0 0
\(12\) −2.00000 −0.577350
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −2.00000 −0.534522
\(15\) −4.00000 −1.03280
\(16\) −4.00000 −1.00000
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) 2.00000 0.471405
\(19\) 3.00000 0.688247 0.344124 0.938924i \(-0.388176\pi\)
0.344124 + 0.938924i \(0.388176\pi\)
\(20\) 8.00000 1.78885
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 4.00000 0.784465
\(27\) −1.00000 −0.192450
\(28\) −2.00000 −0.377964
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −8.00000 −1.46059
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) −8.00000 −1.41421
\(33\) 0 0
\(34\) −8.00000 −1.37199
\(35\) −4.00000 −0.676123
\(36\) 2.00000 0.333333
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 6.00000 0.973329
\(39\) −2.00000 −0.320256
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 2.00000 0.308607
\(43\) −12.0000 −1.82998 −0.914991 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) 0 0
\(45\) 4.00000 0.596285
\(46\) 4.00000 0.589768
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 4.00000 0.577350
\(49\) −6.00000 −0.857143
\(50\) 22.0000 3.11127
\(51\) 4.00000 0.560112
\(52\) 4.00000 0.554700
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −2.00000 −0.272166
\(55\) 0 0
\(56\) 0 0
\(57\) −3.00000 −0.397360
\(58\) −12.0000 −1.57568
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) −8.00000 −1.03280
\(61\) −3.00000 −0.384111 −0.192055 0.981384i \(-0.561515\pi\)
−0.192055 + 0.981384i \(0.561515\pi\)
\(62\) −10.0000 −1.27000
\(63\) −1.00000 −0.125988
\(64\) −8.00000 −1.00000
\(65\) 8.00000 0.992278
\(66\) 0 0
\(67\) −1.00000 −0.122169 −0.0610847 0.998133i \(-0.519456\pi\)
−0.0610847 + 0.998133i \(0.519456\pi\)
\(68\) −8.00000 −0.970143
\(69\) −2.00000 −0.240772
\(70\) −8.00000 −0.956183
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 6.00000 0.697486
\(75\) −11.0000 −1.27017
\(76\) 6.00000 0.688247
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) −16.0000 −1.78885
\(81\) 1.00000 0.111111
\(82\) 4.00000 0.441726
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 2.00000 0.218218
\(85\) −16.0000 −1.73544
\(86\) −24.0000 −2.58799
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 12.0000 1.27200 0.635999 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) 8.00000 0.843274
\(91\) −2.00000 −0.209657
\(92\) 4.00000 0.417029
\(93\) 5.00000 0.518476
\(94\) 4.00000 0.412568
\(95\) 12.0000 1.23117
\(96\) 8.00000 0.816497
\(97\) 5.00000 0.507673 0.253837 0.967247i \(-0.418307\pi\)
0.253837 + 0.967247i \(0.418307\pi\)
\(98\) −12.0000 −1.21218
\(99\) 0 0
\(100\) 22.0000 2.20000
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 8.00000 0.792118
\(103\) −7.00000 −0.689730 −0.344865 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 0 0
\(105\) 4.00000 0.390360
\(106\) 12.0000 1.16554
\(107\) 18.0000 1.74013 0.870063 0.492941i \(-0.164078\pi\)
0.870063 + 0.492941i \(0.164078\pi\)
\(108\) −2.00000 −0.192450
\(109\) −1.00000 −0.0957826 −0.0478913 0.998853i \(-0.515250\pi\)
−0.0478913 + 0.998853i \(0.515250\pi\)
\(110\) 0 0
\(111\) −3.00000 −0.284747
\(112\) 4.00000 0.377964
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) −6.00000 −0.561951
\(115\) 8.00000 0.746004
\(116\) −12.0000 −1.11417
\(117\) 2.00000 0.184900
\(118\) −20.0000 −1.84115
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) 0 0
\(122\) −6.00000 −0.543214
\(123\) −2.00000 −0.180334
\(124\) −10.0000 −0.898027
\(125\) 24.0000 2.14663
\(126\) −2.00000 −0.178174
\(127\) 13.0000 1.15356 0.576782 0.816898i \(-0.304308\pi\)
0.576782 + 0.816898i \(0.304308\pi\)
\(128\) 0 0
\(129\) 12.0000 1.05654
\(130\) 16.0000 1.40329
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) −3.00000 −0.260133
\(134\) −2.00000 −0.172774
\(135\) −4.00000 −0.344265
\(136\) 0 0
\(137\) 8.00000 0.683486 0.341743 0.939793i \(-0.388983\pi\)
0.341743 + 0.939793i \(0.388983\pi\)
\(138\) −4.00000 −0.340503
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −8.00000 −0.676123
\(141\) −2.00000 −0.168430
\(142\) 0 0
\(143\) 0 0
\(144\) −4.00000 −0.333333
\(145\) −24.0000 −1.99309
\(146\) 22.0000 1.82073
\(147\) 6.00000 0.494872
\(148\) 6.00000 0.493197
\(149\) 16.0000 1.31077 0.655386 0.755295i \(-0.272506\pi\)
0.655386 + 0.755295i \(0.272506\pi\)
\(150\) −22.0000 −1.79629
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) −20.0000 −1.60644
\(156\) −4.00000 −0.320256
\(157\) −1.00000 −0.0798087 −0.0399043 0.999204i \(-0.512705\pi\)
−0.0399043 + 0.999204i \(0.512705\pi\)
\(158\) −22.0000 −1.75023
\(159\) −6.00000 −0.475831
\(160\) −32.0000 −2.52982
\(161\) −2.00000 −0.157622
\(162\) 2.00000 0.157135
\(163\) 25.0000 1.95815 0.979076 0.203497i \(-0.0652307\pi\)
0.979076 + 0.203497i \(0.0652307\pi\)
\(164\) 4.00000 0.312348
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) 18.0000 1.39288 0.696441 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −32.0000 −2.45429
\(171\) 3.00000 0.229416
\(172\) −24.0000 −1.82998
\(173\) −24.0000 −1.82469 −0.912343 0.409426i \(-0.865729\pi\)
−0.912343 + 0.409426i \(0.865729\pi\)
\(174\) 12.0000 0.909718
\(175\) −11.0000 −0.831522
\(176\) 0 0
\(177\) 10.0000 0.751646
\(178\) 24.0000 1.79888
\(179\) 6.00000 0.448461 0.224231 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 8.00000 0.596285
\(181\) −23.0000 −1.70958 −0.854788 0.518977i \(-0.826313\pi\)
−0.854788 + 0.518977i \(0.826313\pi\)
\(182\) −4.00000 −0.296500
\(183\) 3.00000 0.221766
\(184\) 0 0
\(185\) 12.0000 0.882258
\(186\) 10.0000 0.733236
\(187\) 0 0
\(188\) 4.00000 0.291730
\(189\) 1.00000 0.0727393
\(190\) 24.0000 1.74114
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 8.00000 0.577350
\(193\) 5.00000 0.359908 0.179954 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(194\) 10.0000 0.717958
\(195\) −8.00000 −0.572892
\(196\) −12.0000 −0.857143
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 0 0
\(199\) −21.0000 −1.48865 −0.744325 0.667817i \(-0.767229\pi\)
−0.744325 + 0.667817i \(0.767229\pi\)
\(200\) 0 0
\(201\) 1.00000 0.0705346
\(202\) 20.0000 1.40720
\(203\) 6.00000 0.421117
\(204\) 8.00000 0.560112
\(205\) 8.00000 0.558744
\(206\) −14.0000 −0.975426
\(207\) 2.00000 0.139010
\(208\) −8.00000 −0.554700
\(209\) 0 0
\(210\) 8.00000 0.552052
\(211\) 21.0000 1.44570 0.722850 0.691005i \(-0.242832\pi\)
0.722850 + 0.691005i \(0.242832\pi\)
\(212\) 12.0000 0.824163
\(213\) 0 0
\(214\) 36.0000 2.46091
\(215\) −48.0000 −3.27357
\(216\) 0 0
\(217\) 5.00000 0.339422
\(218\) −2.00000 −0.135457
\(219\) −11.0000 −0.743311
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) −6.00000 −0.402694
\(223\) −17.0000 −1.13840 −0.569202 0.822198i \(-0.692748\pi\)
−0.569202 + 0.822198i \(0.692748\pi\)
\(224\) 8.00000 0.534522
\(225\) 11.0000 0.733333
\(226\) 12.0000 0.798228
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) −6.00000 −0.397360
\(229\) −18.0000 −1.18947 −0.594737 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) 16.0000 1.05501
\(231\) 0 0
\(232\) 0 0
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 4.00000 0.261488
\(235\) 8.00000 0.521862
\(236\) −20.0000 −1.30189
\(237\) 11.0000 0.714527
\(238\) 8.00000 0.518563
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 16.0000 1.03280
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) −6.00000 −0.384111
\(245\) −24.0000 −1.53330
\(246\) −4.00000 −0.255031
\(247\) 6.00000 0.381771
\(248\) 0 0
\(249\) 6.00000 0.380235
\(250\) 48.0000 3.03579
\(251\) −2.00000 −0.126239 −0.0631194 0.998006i \(-0.520105\pi\)
−0.0631194 + 0.998006i \(0.520105\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) 26.0000 1.63139
\(255\) 16.0000 1.00196
\(256\) 16.0000 1.00000
\(257\) −14.0000 −0.873296 −0.436648 0.899632i \(-0.643834\pi\)
−0.436648 + 0.899632i \(0.643834\pi\)
\(258\) 24.0000 1.49417
\(259\) −3.00000 −0.186411
\(260\) 16.0000 0.992278
\(261\) −6.00000 −0.371391
\(262\) 12.0000 0.741362
\(263\) 10.0000 0.616626 0.308313 0.951285i \(-0.400236\pi\)
0.308313 + 0.951285i \(0.400236\pi\)
\(264\) 0 0
\(265\) 24.0000 1.47431
\(266\) −6.00000 −0.367884
\(267\) −12.0000 −0.734388
\(268\) −2.00000 −0.122169
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) −8.00000 −0.486864
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 16.0000 0.970143
\(273\) 2.00000 0.121046
\(274\) 16.0000 0.966595
\(275\) 0 0
\(276\) −4.00000 −0.240772
\(277\) 11.0000 0.660926 0.330463 0.943819i \(-0.392795\pi\)
0.330463 + 0.943819i \(0.392795\pi\)
\(278\) −32.0000 −1.91923
\(279\) −5.00000 −0.299342
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) −4.00000 −0.238197
\(283\) 11.0000 0.653882 0.326941 0.945045i \(-0.393982\pi\)
0.326941 + 0.945045i \(0.393982\pi\)
\(284\) 0 0
\(285\) −12.0000 −0.710819
\(286\) 0 0
\(287\) −2.00000 −0.118056
\(288\) −8.00000 −0.471405
\(289\) −1.00000 −0.0588235
\(290\) −48.0000 −2.81866
\(291\) −5.00000 −0.293105
\(292\) 22.0000 1.28745
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) 12.0000 0.699854
\(295\) −40.0000 −2.32889
\(296\) 0 0
\(297\) 0 0
\(298\) 32.0000 1.85371
\(299\) 4.00000 0.231326
\(300\) −22.0000 −1.27017
\(301\) 12.0000 0.691669
\(302\) 32.0000 1.84139
\(303\) −10.0000 −0.574485
\(304\) −12.0000 −0.688247
\(305\) −12.0000 −0.687118
\(306\) −8.00000 −0.457330
\(307\) 19.0000 1.08439 0.542194 0.840254i \(-0.317594\pi\)
0.542194 + 0.840254i \(0.317594\pi\)
\(308\) 0 0
\(309\) 7.00000 0.398216
\(310\) −40.0000 −2.27185
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −2.00000 −0.112867
\(315\) −4.00000 −0.225374
\(316\) −22.0000 −1.23760
\(317\) −20.0000 −1.12331 −0.561656 0.827371i \(-0.689836\pi\)
−0.561656 + 0.827371i \(0.689836\pi\)
\(318\) −12.0000 −0.672927
\(319\) 0 0
\(320\) −32.0000 −1.78885
\(321\) −18.0000 −1.00466
\(322\) −4.00000 −0.222911
\(323\) −12.0000 −0.667698
\(324\) 2.00000 0.111111
\(325\) 22.0000 1.22034
\(326\) 50.0000 2.76924
\(327\) 1.00000 0.0553001
\(328\) 0 0
\(329\) −2.00000 −0.110264
\(330\) 0 0
\(331\) −11.0000 −0.604615 −0.302307 0.953211i \(-0.597757\pi\)
−0.302307 + 0.953211i \(0.597757\pi\)
\(332\) −12.0000 −0.658586
\(333\) 3.00000 0.164399
\(334\) 36.0000 1.96983
\(335\) −4.00000 −0.218543
\(336\) −4.00000 −0.218218
\(337\) −5.00000 −0.272367 −0.136184 0.990684i \(-0.543484\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) −18.0000 −0.979071
\(339\) −6.00000 −0.325875
\(340\) −32.0000 −1.73544
\(341\) 0 0
\(342\) 6.00000 0.324443
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) −8.00000 −0.430706
\(346\) −48.0000 −2.58050
\(347\) 2.00000 0.107366 0.0536828 0.998558i \(-0.482904\pi\)
0.0536828 + 0.998558i \(0.482904\pi\)
\(348\) 12.0000 0.643268
\(349\) −15.0000 −0.802932 −0.401466 0.915874i \(-0.631499\pi\)
−0.401466 + 0.915874i \(0.631499\pi\)
\(350\) −22.0000 −1.17595
\(351\) −2.00000 −0.106752
\(352\) 0 0
\(353\) −12.0000 −0.638696 −0.319348 0.947638i \(-0.603464\pi\)
−0.319348 + 0.947638i \(0.603464\pi\)
\(354\) 20.0000 1.06299
\(355\) 0 0
\(356\) 24.0000 1.27200
\(357\) −4.00000 −0.211702
\(358\) 12.0000 0.634220
\(359\) −4.00000 −0.211112 −0.105556 0.994413i \(-0.533662\pi\)
−0.105556 + 0.994413i \(0.533662\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) −46.0000 −2.41771
\(363\) 0 0
\(364\) −4.00000 −0.209657
\(365\) 44.0000 2.30307
\(366\) 6.00000 0.313625
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) −8.00000 −0.417029
\(369\) 2.00000 0.104116
\(370\) 24.0000 1.24770
\(371\) −6.00000 −0.311504
\(372\) 10.0000 0.518476
\(373\) −7.00000 −0.362446 −0.181223 0.983442i \(-0.558006\pi\)
−0.181223 + 0.983442i \(0.558006\pi\)
\(374\) 0 0
\(375\) −24.0000 −1.23935
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 2.00000 0.102869
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 24.0000 1.23117
\(381\) −13.0000 −0.666010
\(382\) 16.0000 0.818631
\(383\) 26.0000 1.32854 0.664269 0.747494i \(-0.268743\pi\)
0.664269 + 0.747494i \(0.268743\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) −12.0000 −0.609994
\(388\) 10.0000 0.507673
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) −16.0000 −0.810191
\(391\) −8.00000 −0.404577
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) 16.0000 0.806068
\(395\) −44.0000 −2.21388
\(396\) 0 0
\(397\) 31.0000 1.55585 0.777923 0.628360i \(-0.216273\pi\)
0.777923 + 0.628360i \(0.216273\pi\)
\(398\) −42.0000 −2.10527
\(399\) 3.00000 0.150188
\(400\) −44.0000 −2.20000
\(401\) −28.0000 −1.39825 −0.699127 0.714998i \(-0.746428\pi\)
−0.699127 + 0.714998i \(0.746428\pi\)
\(402\) 2.00000 0.0997509
\(403\) −10.0000 −0.498135
\(404\) 20.0000 0.995037
\(405\) 4.00000 0.198762
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 0 0
\(409\) −21.0000 −1.03838 −0.519192 0.854658i \(-0.673767\pi\)
−0.519192 + 0.854658i \(0.673767\pi\)
\(410\) 16.0000 0.790184
\(411\) −8.00000 −0.394611
\(412\) −14.0000 −0.689730
\(413\) 10.0000 0.492068
\(414\) 4.00000 0.196589
\(415\) −24.0000 −1.17811
\(416\) −16.0000 −0.784465
\(417\) 16.0000 0.783523
\(418\) 0 0
\(419\) 26.0000 1.27018 0.635092 0.772437i \(-0.280962\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(420\) 8.00000 0.390360
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 42.0000 2.04453
\(423\) 2.00000 0.0972433
\(424\) 0 0
\(425\) −44.0000 −2.13431
\(426\) 0 0
\(427\) 3.00000 0.145180
\(428\) 36.0000 1.74013
\(429\) 0 0
\(430\) −96.0000 −4.62953
\(431\) −18.0000 −0.867029 −0.433515 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) 4.00000 0.192450
\(433\) −17.0000 −0.816968 −0.408484 0.912766i \(-0.633942\pi\)
−0.408484 + 0.912766i \(0.633942\pi\)
\(434\) 10.0000 0.480015
\(435\) 24.0000 1.15071
\(436\) −2.00000 −0.0957826
\(437\) 6.00000 0.287019
\(438\) −22.0000 −1.05120
\(439\) −37.0000 −1.76591 −0.882957 0.469454i \(-0.844451\pi\)
−0.882957 + 0.469454i \(0.844451\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) −16.0000 −0.761042
\(443\) 4.00000 0.190046 0.0950229 0.995475i \(-0.469708\pi\)
0.0950229 + 0.995475i \(0.469708\pi\)
\(444\) −6.00000 −0.284747
\(445\) 48.0000 2.27542
\(446\) −34.0000 −1.60995
\(447\) −16.0000 −0.756774
\(448\) 8.00000 0.377964
\(449\) 20.0000 0.943858 0.471929 0.881636i \(-0.343558\pi\)
0.471929 + 0.881636i \(0.343558\pi\)
\(450\) 22.0000 1.03709
\(451\) 0 0
\(452\) 12.0000 0.564433
\(453\) −16.0000 −0.751746
\(454\) 0 0
\(455\) −8.00000 −0.375046
\(456\) 0 0
\(457\) −18.0000 −0.842004 −0.421002 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) −36.0000 −1.68217
\(459\) 4.00000 0.186704
\(460\) 16.0000 0.746004
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 24.0000 1.11417
\(465\) 20.0000 0.927478
\(466\) −36.0000 −1.66767
\(467\) 24.0000 1.11059 0.555294 0.831654i \(-0.312606\pi\)
0.555294 + 0.831654i \(0.312606\pi\)
\(468\) 4.00000 0.184900
\(469\) 1.00000 0.0461757
\(470\) 16.0000 0.738025
\(471\) 1.00000 0.0460776
\(472\) 0 0
\(473\) 0 0
\(474\) 22.0000 1.01049
\(475\) 33.0000 1.51414
\(476\) 8.00000 0.366679
\(477\) 6.00000 0.274721
\(478\) −12.0000 −0.548867
\(479\) 22.0000 1.00521 0.502603 0.864517i \(-0.332376\pi\)
0.502603 + 0.864517i \(0.332376\pi\)
\(480\) 32.0000 1.46059
\(481\) 6.00000 0.273576
\(482\) 28.0000 1.27537
\(483\) 2.00000 0.0910032
\(484\) 0 0
\(485\) 20.0000 0.908153
\(486\) −2.00000 −0.0907218
\(487\) −40.0000 −1.81257 −0.906287 0.422664i \(-0.861095\pi\)
−0.906287 + 0.422664i \(0.861095\pi\)
\(488\) 0 0
\(489\) −25.0000 −1.13054
\(490\) −48.0000 −2.16842
\(491\) 14.0000 0.631811 0.315906 0.948791i \(-0.397692\pi\)
0.315906 + 0.948791i \(0.397692\pi\)
\(492\) −4.00000 −0.180334
\(493\) 24.0000 1.08091
\(494\) 12.0000 0.539906
\(495\) 0 0
\(496\) 20.0000 0.898027
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) 23.0000 1.02962 0.514811 0.857304i \(-0.327862\pi\)
0.514811 + 0.857304i \(0.327862\pi\)
\(500\) 48.0000 2.14663
\(501\) −18.0000 −0.804181
\(502\) −4.00000 −0.178529
\(503\) 32.0000 1.42681 0.713405 0.700752i \(-0.247152\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(504\) 0 0
\(505\) 40.0000 1.77998
\(506\) 0 0
\(507\) 9.00000 0.399704
\(508\) 26.0000 1.15356
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 32.0000 1.41698
\(511\) −11.0000 −0.486611
\(512\) 32.0000 1.41421
\(513\) −3.00000 −0.132453
\(514\) −28.0000 −1.23503
\(515\) −28.0000 −1.23383
\(516\) 24.0000 1.05654
\(517\) 0 0
\(518\) −6.00000 −0.263625
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −12.0000 −0.525226
\(523\) −29.0000 −1.26808 −0.634041 0.773300i \(-0.718605\pi\)
−0.634041 + 0.773300i \(0.718605\pi\)
\(524\) 12.0000 0.524222
\(525\) 11.0000 0.480079
\(526\) 20.0000 0.872041
\(527\) 20.0000 0.871214
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 48.0000 2.08499
\(531\) −10.0000 −0.433963
\(532\) −6.00000 −0.260133
\(533\) 4.00000 0.173259
\(534\) −24.0000 −1.03858
\(535\) 72.0000 3.11283
\(536\) 0 0
\(537\) −6.00000 −0.258919
\(538\) −28.0000 −1.20717
\(539\) 0 0
\(540\) −8.00000 −0.344265
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) −16.0000 −0.687259
\(543\) 23.0000 0.987024
\(544\) 32.0000 1.37199
\(545\) −4.00000 −0.171341
\(546\) 4.00000 0.171184
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 16.0000 0.683486
\(549\) −3.00000 −0.128037
\(550\) 0 0
\(551\) −18.0000 −0.766826
\(552\) 0 0
\(553\) 11.0000 0.467768
\(554\) 22.0000 0.934690
\(555\) −12.0000 −0.509372
\(556\) −32.0000 −1.35710
\(557\) 8.00000 0.338971 0.169485 0.985533i \(-0.445789\pi\)
0.169485 + 0.985533i \(0.445789\pi\)
\(558\) −10.0000 −0.423334
\(559\) −24.0000 −1.01509
\(560\) 16.0000 0.676123
\(561\) 0 0
\(562\) 24.0000 1.01238
\(563\) −28.0000 −1.18006 −0.590030 0.807382i \(-0.700884\pi\)
−0.590030 + 0.807382i \(0.700884\pi\)
\(564\) −4.00000 −0.168430
\(565\) 24.0000 1.00969
\(566\) 22.0000 0.924729
\(567\) −1.00000 −0.0419961
\(568\) 0 0
\(569\) −12.0000 −0.503066 −0.251533 0.967849i \(-0.580935\pi\)
−0.251533 + 0.967849i \(0.580935\pi\)
\(570\) −24.0000 −1.00525
\(571\) 25.0000 1.04622 0.523109 0.852266i \(-0.324772\pi\)
0.523109 + 0.852266i \(0.324772\pi\)
\(572\) 0 0
\(573\) −8.00000 −0.334205
\(574\) −4.00000 −0.166957
\(575\) 22.0000 0.917463
\(576\) −8.00000 −0.333333
\(577\) 15.0000 0.624458 0.312229 0.950007i \(-0.398924\pi\)
0.312229 + 0.950007i \(0.398924\pi\)
\(578\) −2.00000 −0.0831890
\(579\) −5.00000 −0.207793
\(580\) −48.0000 −1.99309
\(581\) 6.00000 0.248922
\(582\) −10.0000 −0.414513
\(583\) 0 0
\(584\) 0 0
\(585\) 8.00000 0.330759
\(586\) −24.0000 −0.991431
\(587\) 4.00000 0.165098 0.0825488 0.996587i \(-0.473694\pi\)
0.0825488 + 0.996587i \(0.473694\pi\)
\(588\) 12.0000 0.494872
\(589\) −15.0000 −0.618064
\(590\) −80.0000 −3.29355
\(591\) −8.00000 −0.329076
\(592\) −12.0000 −0.493197
\(593\) 46.0000 1.88899 0.944497 0.328521i \(-0.106550\pi\)
0.944497 + 0.328521i \(0.106550\pi\)
\(594\) 0 0
\(595\) 16.0000 0.655936
\(596\) 32.0000 1.31077
\(597\) 21.0000 0.859473
\(598\) 8.00000 0.327144
\(599\) −8.00000 −0.326871 −0.163436 0.986554i \(-0.552258\pi\)
−0.163436 + 0.986554i \(0.552258\pi\)
\(600\) 0 0
\(601\) 1.00000 0.0407909 0.0203954 0.999792i \(-0.493507\pi\)
0.0203954 + 0.999792i \(0.493507\pi\)
\(602\) 24.0000 0.978167
\(603\) −1.00000 −0.0407231
\(604\) 32.0000 1.30206
\(605\) 0 0
\(606\) −20.0000 −0.812444
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) −24.0000 −0.973329
\(609\) −6.00000 −0.243132
\(610\) −24.0000 −0.971732
\(611\) 4.00000 0.161823
\(612\) −8.00000 −0.323381
\(613\) 13.0000 0.525065 0.262533 0.964923i \(-0.415442\pi\)
0.262533 + 0.964923i \(0.415442\pi\)
\(614\) 38.0000 1.53356
\(615\) −8.00000 −0.322591
\(616\) 0 0
\(617\) −24.0000 −0.966204 −0.483102 0.875564i \(-0.660490\pi\)
−0.483102 + 0.875564i \(0.660490\pi\)
\(618\) 14.0000 0.563163
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) −40.0000 −1.60644
\(621\) −2.00000 −0.0802572
\(622\) 48.0000 1.92462
\(623\) −12.0000 −0.480770
\(624\) 8.00000 0.320256
\(625\) 41.0000 1.64000
\(626\) −20.0000 −0.799361
\(627\) 0 0
\(628\) −2.00000 −0.0798087
\(629\) −12.0000 −0.478471
\(630\) −8.00000 −0.318728
\(631\) −32.0000 −1.27390 −0.636950 0.770905i \(-0.719804\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) 0 0
\(633\) −21.0000 −0.834675
\(634\) −40.0000 −1.58860
\(635\) 52.0000 2.06356
\(636\) −12.0000 −0.475831
\(637\) −12.0000 −0.475457
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −24.0000 −0.947943 −0.473972 0.880540i \(-0.657180\pi\)
−0.473972 + 0.880540i \(0.657180\pi\)
\(642\) −36.0000 −1.42081
\(643\) −37.0000 −1.45914 −0.729569 0.683907i \(-0.760279\pi\)
−0.729569 + 0.683907i \(0.760279\pi\)
\(644\) −4.00000 −0.157622
\(645\) 48.0000 1.89000
\(646\) −24.0000 −0.944267
\(647\) −4.00000 −0.157256 −0.0786281 0.996904i \(-0.525054\pi\)
−0.0786281 + 0.996904i \(0.525054\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 44.0000 1.72582
\(651\) −5.00000 −0.195965
\(652\) 50.0000 1.95815
\(653\) 10.0000 0.391330 0.195665 0.980671i \(-0.437313\pi\)
0.195665 + 0.980671i \(0.437313\pi\)
\(654\) 2.00000 0.0782062
\(655\) 24.0000 0.937758
\(656\) −8.00000 −0.312348
\(657\) 11.0000 0.429151
\(658\) −4.00000 −0.155936
\(659\) −46.0000 −1.79191 −0.895953 0.444149i \(-0.853506\pi\)
−0.895953 + 0.444149i \(0.853506\pi\)
\(660\) 0 0
\(661\) −5.00000 −0.194477 −0.0972387 0.995261i \(-0.531001\pi\)
−0.0972387 + 0.995261i \(0.531001\pi\)
\(662\) −22.0000 −0.855054
\(663\) 8.00000 0.310694
\(664\) 0 0
\(665\) −12.0000 −0.465340
\(666\) 6.00000 0.232495
\(667\) −12.0000 −0.464642
\(668\) 36.0000 1.39288
\(669\) 17.0000 0.657258
\(670\) −8.00000 −0.309067
\(671\) 0 0
\(672\) −8.00000 −0.308607
\(673\) 13.0000 0.501113 0.250557 0.968102i \(-0.419386\pi\)
0.250557 + 0.968102i \(0.419386\pi\)
\(674\) −10.0000 −0.385186
\(675\) −11.0000 −0.423390
\(676\) −18.0000 −0.692308
\(677\) −12.0000 −0.461197 −0.230599 0.973049i \(-0.574068\pi\)
−0.230599 + 0.973049i \(0.574068\pi\)
\(678\) −12.0000 −0.460857
\(679\) −5.00000 −0.191882
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −34.0000 −1.30097 −0.650487 0.759517i \(-0.725435\pi\)
−0.650487 + 0.759517i \(0.725435\pi\)
\(684\) 6.00000 0.229416
\(685\) 32.0000 1.22266
\(686\) 26.0000 0.992685
\(687\) 18.0000 0.686743
\(688\) 48.0000 1.82998
\(689\) 12.0000 0.457164
\(690\) −16.0000 −0.609110
\(691\) 11.0000 0.418460 0.209230 0.977866i \(-0.432904\pi\)
0.209230 + 0.977866i \(0.432904\pi\)
\(692\) −48.0000 −1.82469
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) −64.0000 −2.42766
\(696\) 0 0
\(697\) −8.00000 −0.303022
\(698\) −30.0000 −1.13552
\(699\) 18.0000 0.680823
\(700\) −22.0000 −0.831522
\(701\) −50.0000 −1.88847 −0.944237 0.329267i \(-0.893198\pi\)
−0.944237 + 0.329267i \(0.893198\pi\)
\(702\) −4.00000 −0.150970
\(703\) 9.00000 0.339441
\(704\) 0 0
\(705\) −8.00000 −0.301297
\(706\) −24.0000 −0.903252
\(707\) −10.0000 −0.376089
\(708\) 20.0000 0.751646
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 0 0
\(711\) −11.0000 −0.412532
\(712\) 0 0
\(713\) −10.0000 −0.374503
\(714\) −8.00000 −0.299392
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 6.00000 0.224074
\(718\) −8.00000 −0.298557
\(719\) −6.00000 −0.223762 −0.111881 0.993722i \(-0.535688\pi\)
−0.111881 + 0.993722i \(0.535688\pi\)
\(720\) −16.0000 −0.596285
\(721\) 7.00000 0.260694
\(722\) −20.0000 −0.744323
\(723\) −14.0000 −0.520666
\(724\) −46.0000 −1.70958
\(725\) −66.0000 −2.45118
\(726\) 0 0
\(727\) −12.0000 −0.445055 −0.222528 0.974926i \(-0.571431\pi\)
−0.222528 + 0.974926i \(0.571431\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 88.0000 3.25703
\(731\) 48.0000 1.77534
\(732\) 6.00000 0.221766
\(733\) 30.0000 1.10808 0.554038 0.832492i \(-0.313086\pi\)
0.554038 + 0.832492i \(0.313086\pi\)
\(734\) −16.0000 −0.590571
\(735\) 24.0000 0.885253
\(736\) −16.0000 −0.589768
\(737\) 0 0
\(738\) 4.00000 0.147242
\(739\) −41.0000 −1.50821 −0.754105 0.656754i \(-0.771929\pi\)
−0.754105 + 0.656754i \(0.771929\pi\)
\(740\) 24.0000 0.882258
\(741\) −6.00000 −0.220416
\(742\) −12.0000 −0.440534
\(743\) 20.0000 0.733729 0.366864 0.930274i \(-0.380431\pi\)
0.366864 + 0.930274i \(0.380431\pi\)
\(744\) 0 0
\(745\) 64.0000 2.34478
\(746\) −14.0000 −0.512576
\(747\) −6.00000 −0.219529
\(748\) 0 0
\(749\) −18.0000 −0.657706
\(750\) −48.0000 −1.75271
\(751\) 19.0000 0.693320 0.346660 0.937991i \(-0.387316\pi\)
0.346660 + 0.937991i \(0.387316\pi\)
\(752\) −8.00000 −0.291730
\(753\) 2.00000 0.0728841
\(754\) −24.0000 −0.874028
\(755\) 64.0000 2.32920
\(756\) 2.00000 0.0727393
\(757\) 5.00000 0.181728 0.0908640 0.995863i \(-0.471037\pi\)
0.0908640 + 0.995863i \(0.471037\pi\)
\(758\) 32.0000 1.16229
\(759\) 0 0
\(760\) 0 0
\(761\) 24.0000 0.869999 0.435000 0.900431i \(-0.356748\pi\)
0.435000 + 0.900431i \(0.356748\pi\)
\(762\) −26.0000 −0.941881
\(763\) 1.00000 0.0362024
\(764\) 16.0000 0.578860
\(765\) −16.0000 −0.578481
\(766\) 52.0000 1.87884
\(767\) −20.0000 −0.722158
\(768\) −16.0000 −0.577350
\(769\) −11.0000 −0.396670 −0.198335 0.980134i \(-0.563553\pi\)
−0.198335 + 0.980134i \(0.563553\pi\)
\(770\) 0 0
\(771\) 14.0000 0.504198
\(772\) 10.0000 0.359908
\(773\) 36.0000 1.29483 0.647415 0.762138i \(-0.275850\pi\)
0.647415 + 0.762138i \(0.275850\pi\)
\(774\) −24.0000 −0.862662
\(775\) −55.0000 −1.97566
\(776\) 0 0
\(777\) 3.00000 0.107624
\(778\) 36.0000 1.29066
\(779\) 6.00000 0.214972
\(780\) −16.0000 −0.572892
\(781\) 0 0
\(782\) −16.0000 −0.572159
\(783\) 6.00000 0.214423
\(784\) 24.0000 0.857143
\(785\) −4.00000 −0.142766
\(786\) −12.0000 −0.428026
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 16.0000 0.569976
\(789\) −10.0000 −0.356009
\(790\) −88.0000 −3.13090
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) −6.00000 −0.213066
\(794\) 62.0000 2.20030
\(795\) −24.0000 −0.851192
\(796\) −42.0000 −1.48865
\(797\) −10.0000 −0.354218 −0.177109 0.984191i \(-0.556675\pi\)
−0.177109 + 0.984191i \(0.556675\pi\)
\(798\) 6.00000 0.212398
\(799\) −8.00000 −0.283020
\(800\) −88.0000 −3.11127
\(801\) 12.0000 0.423999
\(802\) −56.0000 −1.97743
\(803\) 0 0
\(804\) 2.00000 0.0705346
\(805\) −8.00000 −0.281963
\(806\) −20.0000 −0.704470
\(807\) 14.0000 0.492823
\(808\) 0 0
\(809\) 48.0000 1.68759 0.843795 0.536666i \(-0.180316\pi\)
0.843795 + 0.536666i \(0.180316\pi\)
\(810\) 8.00000 0.281091
\(811\) 17.0000 0.596951 0.298475 0.954417i \(-0.403522\pi\)
0.298475 + 0.954417i \(0.403522\pi\)
\(812\) 12.0000 0.421117
\(813\) 8.00000 0.280572
\(814\) 0 0
\(815\) 100.000 3.50285
\(816\) −16.0000 −0.560112
\(817\) −36.0000 −1.25948
\(818\) −42.0000 −1.46850
\(819\) −2.00000 −0.0698857
\(820\) 16.0000 0.558744
\(821\) 38.0000 1.32621 0.663105 0.748527i \(-0.269238\pi\)
0.663105 + 0.748527i \(0.269238\pi\)
\(822\) −16.0000 −0.558064
\(823\) −27.0000 −0.941161 −0.470580 0.882357i \(-0.655955\pi\)
−0.470580 + 0.882357i \(0.655955\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 20.0000 0.695889
\(827\) 10.0000 0.347734 0.173867 0.984769i \(-0.444374\pi\)
0.173867 + 0.984769i \(0.444374\pi\)
\(828\) 4.00000 0.139010
\(829\) −11.0000 −0.382046 −0.191023 0.981586i \(-0.561180\pi\)
−0.191023 + 0.981586i \(0.561180\pi\)
\(830\) −48.0000 −1.66610
\(831\) −11.0000 −0.381586
\(832\) −16.0000 −0.554700
\(833\) 24.0000 0.831551
\(834\) 32.0000 1.10807
\(835\) 72.0000 2.49166
\(836\) 0 0
\(837\) 5.00000 0.172825
\(838\) 52.0000 1.79631
\(839\) 16.0000 0.552381 0.276191 0.961103i \(-0.410928\pi\)
0.276191 + 0.961103i \(0.410928\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −4.00000 −0.137849
\(843\) −12.0000 −0.413302
\(844\) 42.0000 1.44570
\(845\) −36.0000 −1.23844
\(846\) 4.00000 0.137523
\(847\) 0 0
\(848\) −24.0000 −0.824163
\(849\) −11.0000 −0.377519
\(850\) −88.0000 −3.01838
\(851\) 6.00000 0.205677
\(852\) 0 0
\(853\) −11.0000 −0.376633 −0.188316 0.982108i \(-0.560303\pi\)
−0.188316 + 0.982108i \(0.560303\pi\)
\(854\) 6.00000 0.205316
\(855\) 12.0000 0.410391
\(856\) 0 0
\(857\) 4.00000 0.136637 0.0683187 0.997664i \(-0.478237\pi\)
0.0683187 + 0.997664i \(0.478237\pi\)
\(858\) 0 0
\(859\) −45.0000 −1.53538 −0.767690 0.640821i \(-0.778594\pi\)
−0.767690 + 0.640821i \(0.778594\pi\)
\(860\) −96.0000 −3.27357
\(861\) 2.00000 0.0681598
\(862\) −36.0000 −1.22616
\(863\) 30.0000 1.02121 0.510606 0.859815i \(-0.329421\pi\)
0.510606 + 0.859815i \(0.329421\pi\)
\(864\) 8.00000 0.272166
\(865\) −96.0000 −3.26410
\(866\) −34.0000 −1.15537
\(867\) 1.00000 0.0339618
\(868\) 10.0000 0.339422
\(869\) 0 0
\(870\) 48.0000 1.62735
\(871\) −2.00000 −0.0677674
\(872\) 0 0
\(873\) 5.00000 0.169224
\(874\) 12.0000 0.405906
\(875\) −24.0000 −0.811348
\(876\) −22.0000 −0.743311
\(877\) 45.0000 1.51954 0.759771 0.650191i \(-0.225311\pi\)
0.759771 + 0.650191i \(0.225311\pi\)
\(878\) −74.0000 −2.49738
\(879\) 12.0000 0.404750
\(880\) 0 0
\(881\) 2.00000 0.0673817 0.0336909 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) −12.0000 −0.404061
\(883\) 49.0000 1.64898 0.824491 0.565876i \(-0.191462\pi\)
0.824491 + 0.565876i \(0.191462\pi\)
\(884\) −16.0000 −0.538138
\(885\) 40.0000 1.34459
\(886\) 8.00000 0.268765
\(887\) 22.0000 0.738688 0.369344 0.929293i \(-0.379582\pi\)
0.369344 + 0.929293i \(0.379582\pi\)
\(888\) 0 0
\(889\) −13.0000 −0.436006
\(890\) 96.0000 3.21793
\(891\) 0 0
\(892\) −34.0000 −1.13840
\(893\) 6.00000 0.200782
\(894\) −32.0000 −1.07024
\(895\) 24.0000 0.802232
\(896\) 0 0
\(897\) −4.00000 −0.133556
\(898\) 40.0000 1.33482
\(899\) 30.0000 1.00056
\(900\) 22.0000 0.733333
\(901\) −24.0000 −0.799556
\(902\) 0 0
\(903\) −12.0000 −0.399335
\(904\) 0 0
\(905\) −92.0000 −3.05818
\(906\) −32.0000 −1.06313
\(907\) 33.0000 1.09575 0.547874 0.836561i \(-0.315438\pi\)
0.547874 + 0.836561i \(0.315438\pi\)
\(908\) 0 0
\(909\) 10.0000 0.331679
\(910\) −16.0000 −0.530395
\(911\) 36.0000 1.19273 0.596367 0.802712i \(-0.296610\pi\)
0.596367 + 0.802712i \(0.296610\pi\)
\(912\) 12.0000 0.397360
\(913\) 0 0
\(914\) −36.0000 −1.19077
\(915\) 12.0000 0.396708
\(916\) −36.0000 −1.18947
\(917\) −6.00000 −0.198137
\(918\) 8.00000 0.264039
\(919\) 5.00000 0.164935 0.0824674 0.996594i \(-0.473720\pi\)
0.0824674 + 0.996594i \(0.473720\pi\)
\(920\) 0 0
\(921\) −19.0000 −0.626071
\(922\) 12.0000 0.395199
\(923\) 0 0
\(924\) 0 0
\(925\) 33.0000 1.08503
\(926\) 32.0000 1.05159
\(927\) −7.00000 −0.229910
\(928\) 48.0000 1.57568
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 40.0000 1.31165
\(931\) −18.0000 −0.589926
\(932\) −36.0000 −1.17922
\(933\) −24.0000 −0.785725
\(934\) 48.0000 1.57061
\(935\) 0 0
\(936\) 0 0
\(937\) −23.0000 −0.751377 −0.375689 0.926746i \(-0.622594\pi\)
−0.375689 + 0.926746i \(0.622594\pi\)
\(938\) 2.00000 0.0653023
\(939\) 10.0000 0.326338
\(940\) 16.0000 0.521862
\(941\) −42.0000 −1.36916 −0.684580 0.728937i \(-0.740015\pi\)
−0.684580 + 0.728937i \(0.740015\pi\)
\(942\) 2.00000 0.0651635
\(943\) 4.00000 0.130258
\(944\) 40.0000 1.30189
\(945\) 4.00000 0.130120
\(946\) 0 0
\(947\) 54.0000 1.75476 0.877382 0.479792i \(-0.159288\pi\)
0.877382 + 0.479792i \(0.159288\pi\)
\(948\) 22.0000 0.714527
\(949\) 22.0000 0.714150
\(950\) 66.0000 2.14132
\(951\) 20.0000 0.648544
\(952\) 0 0
\(953\) −34.0000 −1.10137 −0.550684 0.834714i \(-0.685633\pi\)
−0.550684 + 0.834714i \(0.685633\pi\)
\(954\) 12.0000 0.388514
\(955\) 32.0000 1.03550
\(956\) −12.0000 −0.388108
\(957\) 0 0
\(958\) 44.0000 1.42158
\(959\) −8.00000 −0.258333
\(960\) 32.0000 1.03280
\(961\) −6.00000 −0.193548
\(962\) 12.0000 0.386896
\(963\) 18.0000 0.580042
\(964\) 28.0000 0.901819
\(965\) 20.0000 0.643823
\(966\) 4.00000 0.128698
\(967\) −13.0000 −0.418052 −0.209026 0.977910i \(-0.567029\pi\)
−0.209026 + 0.977910i \(0.567029\pi\)
\(968\) 0 0
\(969\) 12.0000 0.385496
\(970\) 40.0000 1.28432
\(971\) 2.00000 0.0641831 0.0320915 0.999485i \(-0.489783\pi\)
0.0320915 + 0.999485i \(0.489783\pi\)
\(972\) −2.00000 −0.0641500
\(973\) 16.0000 0.512936
\(974\) −80.0000 −2.56337
\(975\) −22.0000 −0.704564
\(976\) 12.0000 0.384111
\(977\) −42.0000 −1.34370 −0.671850 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) −50.0000 −1.59882
\(979\) 0 0
\(980\) −48.0000 −1.53330
\(981\) −1.00000 −0.0319275
\(982\) 28.0000 0.893516
\(983\) 6.00000 0.191370 0.0956851 0.995412i \(-0.469496\pi\)
0.0956851 + 0.995412i \(0.469496\pi\)
\(984\) 0 0
\(985\) 32.0000 1.01960
\(986\) 48.0000 1.52863
\(987\) 2.00000 0.0636607
\(988\) 12.0000 0.381771
\(989\) −24.0000 −0.763156
\(990\) 0 0
\(991\) 4.00000 0.127064 0.0635321 0.997980i \(-0.479763\pi\)
0.0635321 + 0.997980i \(0.479763\pi\)
\(992\) 40.0000 1.27000
\(993\) 11.0000 0.349074
\(994\) 0 0
\(995\) −84.0000 −2.66298
\(996\) 12.0000 0.380235
\(997\) 49.0000 1.55185 0.775923 0.630828i \(-0.217285\pi\)
0.775923 + 0.630828i \(0.217285\pi\)
\(998\) 46.0000 1.45610
\(999\) −3.00000 −0.0949158
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 363.2.a.c.1.1 yes 1
3.2 odd 2 1089.2.a.a.1.1 1
4.3 odd 2 5808.2.a.bi.1.1 1
5.4 even 2 9075.2.a.b.1.1 1
11.2 odd 10 363.2.e.i.202.1 4
11.3 even 5 363.2.e.d.130.1 4
11.4 even 5 363.2.e.d.148.1 4
11.5 even 5 363.2.e.d.124.1 4
11.6 odd 10 363.2.e.i.124.1 4
11.7 odd 10 363.2.e.i.148.1 4
11.8 odd 10 363.2.e.i.130.1 4
11.9 even 5 363.2.e.d.202.1 4
11.10 odd 2 363.2.a.a.1.1 1
33.32 even 2 1089.2.a.k.1.1 1
44.43 even 2 5808.2.a.bh.1.1 1
55.54 odd 2 9075.2.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.2.a.a.1.1 1 11.10 odd 2
363.2.a.c.1.1 yes 1 1.1 even 1 trivial
363.2.e.d.124.1 4 11.5 even 5
363.2.e.d.130.1 4 11.3 even 5
363.2.e.d.148.1 4 11.4 even 5
363.2.e.d.202.1 4 11.9 even 5
363.2.e.i.124.1 4 11.6 odd 10
363.2.e.i.130.1 4 11.8 odd 10
363.2.e.i.148.1 4 11.7 odd 10
363.2.e.i.202.1 4 11.2 odd 10
1089.2.a.a.1.1 1 3.2 odd 2
1089.2.a.k.1.1 1 33.32 even 2
5808.2.a.bh.1.1 1 44.43 even 2
5808.2.a.bi.1.1 1 4.3 odd 2
9075.2.a.b.1.1 1 5.4 even 2
9075.2.a.t.1.1 1 55.54 odd 2