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Properties

Label 4650.2.a.q.1.1
Level $4650$
Weight $2$
Character 4650.1
Self dual yes
Analytic conductor $37.130$
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] = [4650,2,Mod(1,4650)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4650, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4650.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4650.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: \(37.1304369399\)
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 \(\chi\) \(=\) 4650.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.00000 q^{11} +1.00000 q^{12} +5.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{21} -3.00000 q^{22} +6.00000 q^{23} -1.00000 q^{24} -5.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -6.00000 q^{29} +1.00000 q^{31} -1.00000 q^{32} +3.00000 q^{33} +1.00000 q^{36} +5.00000 q^{37} +4.00000 q^{38} +5.00000 q^{39} +3.00000 q^{41} +1.00000 q^{42} -1.00000 q^{43} +3.00000 q^{44} -6.00000 q^{46} +9.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} +5.00000 q^{52} +3.00000 q^{53} -1.00000 q^{54} +1.00000 q^{56} -4.00000 q^{57} +6.00000 q^{58} +11.0000 q^{61} -1.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -3.00000 q^{66} -4.00000 q^{67} +6.00000 q^{69} -3.00000 q^{71} -1.00000 q^{72} -4.00000 q^{73} -5.00000 q^{74} -4.00000 q^{76} -3.00000 q^{77} -5.00000 q^{78} -10.0000 q^{79} +1.00000 q^{81} -3.00000 q^{82} +9.00000 q^{83} -1.00000 q^{84} +1.00000 q^{86} -6.00000 q^{87} -3.00000 q^{88} +6.00000 q^{89} -5.00000 q^{91} +6.00000 q^{92} +1.00000 q^{93} -9.00000 q^{94} -1.00000 q^{96} -10.0000 q^{97} +6.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964 −0.188982 − 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 − 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 1.00000 0.288675
\(13\) 5.00000 1.38675 0.693375 − 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.00000 −0.917663 −0.458831 − 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) −3.00000 −0.639602
\(23\) 6.00000 1.25109 0.625543 − 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) −5.00000 −0.980581
\(27\) 1.00000 0.192450
\(28\) −1.00000 −0.188982
\(29\) −6.00000 −1.11417 −0.557086 − 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 1.00000 0.179605
\(32\) −1.00000 −0.176777
\(33\) 3.00000 0.522233
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 5.00000 0.821995 0.410997 − 0.911636i \(-0.365181\pi\)
0.410997 + 0.911636i \(0.365181\pi\)
\(38\) 4.00000 0.648886
\(39\) 5.00000 0.800641
\(40\) 0 0
\(41\) 3.00000 0.468521 0.234261 − 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 1.00000 0.154303
\(43\) −1.00000 −0.152499 −0.0762493 − 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 9.00000 1.31278 0.656392 − 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 5.00000 0.693375
\(53\) 3.00000 0.412082 0.206041 − 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) −4.00000 −0.529813
\(58\) 6.00000 0.787839
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 11.0000 1.40841 0.704203 − 0.709999i \(-0.251305\pi\)
0.704203 + 0.709999i \(0.251305\pi\)
\(62\) −1.00000 −0.127000
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.00000 −0.369274
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) −3.00000 −0.356034 −0.178017 − 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) −1.00000 −0.117851
\(73\) −4.00000 −0.468165 −0.234082 − 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) −5.00000 −0.581238
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) −3.00000 −0.341882
\(78\) −5.00000 −0.566139
\(79\) −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
\(82\) −3.00000 −0.331295
\(83\) 9.00000 0.987878 0.493939 − 0.869496i \(-0.335557\pi\)
0.493939 + 0.869496i \(0.335557\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) 1.00000 0.107833
\(87\) −6.00000 −0.643268
\(88\) −3.00000 −0.319801
\(89\) 6.00000 0.635999 0.317999 − 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) −5.00000 −0.524142
\(92\) 6.00000 0.625543
\(93\) 1.00000 0.103695
\(94\) −9.00000 −0.928279
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −10.0000 −1.01535 −0.507673 − 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 6.00000 0.606092
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) −12.0000 −1.19404 −0.597022 − 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 0 0
\(103\) 11.0000 1.08386 0.541931 − 0.840423i \(-0.317693\pi\)
0.541931 + 0.840423i \(0.317693\pi\)
\(104\) −5.00000 −0.490290
\(105\) 0 0
\(106\) −3.00000 −0.291386
\(107\) −6.00000 −0.580042 −0.290021 − 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 1.00000 0.0962250
\(109\) 8.00000 0.766261 0.383131 − 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 0 0
\(111\) 5.00000 0.474579
\(112\) −1.00000 −0.0944911
\(113\) 6.00000 0.564433 0.282216 − 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 4.00000 0.374634
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 5.00000 0.462250
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −11.0000 −0.995893
\(123\) 3.00000 0.270501
\(124\) 1.00000 0.0898027
\(125\) 0 0
\(126\) 1.00000 0.0890871
\(127\) −4.00000 −0.354943 −0.177471 − 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.00000 −0.0880451
\(130\) 0 0
\(131\) 6.00000 0.524222 0.262111 − 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 3.00000 0.261116
\(133\) 4.00000 0.346844
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 0.512615 0.256307 − 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) −6.00000 −0.510754
\(139\) 5.00000 0.424094 0.212047 − 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) 0 0
\(141\) 9.00000 0.757937
\(142\) 3.00000 0.251754
\(143\) 15.0000 1.25436
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) −6.00000 −0.494872
\(148\) 5.00000 0.410997
\(149\) 6.00000 0.491539 0.245770 − 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 − 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 4.00000 0.324443
\(153\) 0 0
\(154\) 3.00000 0.241747
\(155\) 0 0
\(156\) 5.00000 0.400320
\(157\) 2.00000 0.159617 0.0798087 − 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 10.0000 0.795557
\(159\) 3.00000 0.237915
\(160\) 0 0
\(161\) −6.00000 −0.472866
\(162\) −1.00000 −0.0785674
\(163\) 2.00000 0.156652 0.0783260 − 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 3.00000 0.234261
\(165\) 0 0
\(166\) −9.00000 −0.698535
\(167\) 18.0000 1.39288 0.696441 − 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) 1.00000 0.0771517
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) −1.00000 −0.0762493
\(173\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 6.00000 0.454859
\(175\) 0 0
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) 9.00000 0.672692 0.336346 − 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) 0 0
\(181\) −25.0000 −1.85824 −0.929118 − 0.369784i \(-0.879432\pi\)
−0.929118 + 0.369784i \(0.879432\pi\)
\(182\) 5.00000 0.370625
\(183\) 11.0000 0.813143
\(184\) −6.00000 −0.442326
\(185\) 0 0
\(186\) −1.00000 −0.0733236
\(187\) 0 0
\(188\) 9.00000 0.656392
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) 24.0000 1.73658 0.868290 − 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) 1.00000 0.0721688
\(193\) 23.0000 1.65558 0.827788 − 0.561041i \(-0.189599\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) 3.00000 0.213741 0.106871 − 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) −3.00000 −0.213201
\(199\) −10.0000 −0.708881 −0.354441 − 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 12.0000 0.844317
\(203\) 6.00000 0.421117
\(204\) 0 0
\(205\) 0 0
\(206\) −11.0000 −0.766406
\(207\) 6.00000 0.417029
\(208\) 5.00000 0.346688
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 − 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 3.00000 0.206041
\(213\) −3.00000 −0.205557
\(214\) 6.00000 0.410152
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −1.00000 −0.0678844
\(218\) −8.00000 −0.541828
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) 0 0
\(222\) −5.00000 −0.335578
\(223\) 26.0000 1.74109 0.870544 − 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) −4.00000 −0.264906
\(229\) 14.0000 0.925146 0.462573 − 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) −3.00000 −0.197386
\(232\) 6.00000 0.393919
\(233\) 3.00000 0.196537 0.0982683 − 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) −5.00000 −0.326860
\(235\) 0 0
\(236\) 0 0
\(237\) −10.0000 −0.649570
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 − 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 − 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 2.00000 0.128565
\(243\) 1.00000 0.0641500
\(244\) 11.0000 0.704203
\(245\) 0 0
\(246\) −3.00000 −0.191273
\(247\) −20.0000 −1.27257
\(248\) −1.00000 −0.0635001
\(249\) 9.00000 0.570352
\(250\) 0 0
\(251\) 15.0000 0.946792 0.473396 − 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 18.0000 1.13165
\(254\) 4.00000 0.250982
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 3.00000 0.187135 0.0935674 − 0.995613i \(-0.470173\pi\)
0.0935674 + 0.995613i \(0.470173\pi\)
\(258\) 1.00000 0.0622573
\(259\) −5.00000 −0.310685
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) −6.00000 −0.370681
\(263\) −12.0000 −0.739952 −0.369976 − 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(264\) −3.00000 −0.184637
\(265\) 0 0
\(266\) −4.00000 −0.245256
\(267\) 6.00000 0.367194
\(268\) −4.00000 −0.244339
\(269\) −18.0000 −1.09748 −0.548740 − 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 0 0
\(271\) −28.0000 −1.70088 −0.850439 − 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 0 0
\(273\) −5.00000 −0.302614
\(274\) −6.00000 −0.362473
\(275\) 0 0
\(276\) 6.00000 0.361158
\(277\) 26.0000 1.56219 0.781094 − 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) −5.00000 −0.299880
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) 15.0000 0.894825 0.447412 − 0.894328i \(-0.352346\pi\)
0.447412 + 0.894328i \(0.352346\pi\)
\(282\) −9.00000 −0.535942
\(283\) −4.00000 −0.237775 −0.118888 − 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) −3.00000 −0.178017
\(285\) 0 0
\(286\) −15.0000 −0.886969
\(287\) −3.00000 −0.177084
\(288\) −1.00000 −0.0589256
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) −10.0000 −0.586210
\(292\) −4.00000 −0.234082
\(293\) −30.0000 −1.75262 −0.876309 − 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 6.00000 0.349927
\(295\) 0 0
\(296\) −5.00000 −0.290619
\(297\) 3.00000 0.174078
\(298\) −6.00000 −0.347571
\(299\) 30.0000 1.73494
\(300\) 0 0
\(301\) 1.00000 0.0576390
\(302\) 10.0000 0.575435
\(303\) −12.0000 −0.689382
\(304\) −4.00000 −0.229416
\(305\) 0 0
\(306\) 0 0
\(307\) −22.0000 −1.25561 −0.627803 − 0.778372i \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) −3.00000 −0.170941
\(309\) 11.0000 0.625768
\(310\) 0 0
\(311\) 9.00000 0.510343 0.255172 − 0.966896i \(-0.417868\pi\)
0.255172 + 0.966896i \(0.417868\pi\)
\(312\) −5.00000 −0.283069
\(313\) 14.0000 0.791327 0.395663 − 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 12.0000 0.673987 0.336994 − 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) −3.00000 −0.168232
\(319\) −18.0000 −1.00781
\(320\) 0 0
\(321\) −6.00000 −0.334887
\(322\) 6.00000 0.334367
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −2.00000 −0.110770
\(327\) 8.00000 0.442401
\(328\) −3.00000 −0.165647
\(329\) −9.00000 −0.496186
\(330\) 0 0
\(331\) −1.00000 −0.0549650 −0.0274825 − 0.999622i \(-0.508749\pi\)
−0.0274825 + 0.999622i \(0.508749\pi\)
\(332\) 9.00000 0.493939
\(333\) 5.00000 0.273998
\(334\) −18.0000 −0.984916
\(335\) 0 0
\(336\) −1.00000 −0.0545545
\(337\) −28.0000 −1.52526 −0.762629 − 0.646837i \(-0.776092\pi\)
−0.762629 + 0.646837i \(0.776092\pi\)
\(338\) −12.0000 −0.652714
\(339\) 6.00000 0.325875
\(340\) 0 0
\(341\) 3.00000 0.162459
\(342\) 4.00000 0.216295
\(343\) 13.0000 0.701934
\(344\) 1.00000 0.0539164
\(345\) 0 0
\(346\) 0 0
\(347\) 33.0000 1.77153 0.885766 − 0.464131i \(-0.153633\pi\)
0.885766 + 0.464131i \(0.153633\pi\)
\(348\) −6.00000 −0.321634
\(349\) −16.0000 −0.856460 −0.428230 − 0.903670i \(-0.640863\pi\)
−0.428230 + 0.903670i \(0.640863\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) −3.00000 −0.159901
\(353\) 30.0000 1.59674 0.798369 − 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) −9.00000 −0.475665
\(359\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 25.0000 1.31397
\(363\) −2.00000 −0.104973
\(364\) −5.00000 −0.262071
\(365\) 0 0
\(366\) −11.0000 −0.574979
\(367\) 26.0000 1.35719 0.678594 − 0.734513i \(-0.262589\pi\)
0.678594 + 0.734513i \(0.262589\pi\)
\(368\) 6.00000 0.312772
\(369\) 3.00000 0.156174
\(370\) 0 0
\(371\) −3.00000 −0.155752
\(372\) 1.00000 0.0518476
\(373\) 8.00000 0.414224 0.207112 − 0.978317i \(-0.433593\pi\)
0.207112 + 0.978317i \(0.433593\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −9.00000 −0.464140
\(377\) −30.0000 −1.54508
\(378\) 1.00000 0.0514344
\(379\) 26.0000 1.33553 0.667765 − 0.744372i \(-0.267251\pi\)
0.667765 + 0.744372i \(0.267251\pi\)
\(380\) 0 0
\(381\) −4.00000 −0.204926
\(382\) −24.0000 −1.22795
\(383\) −36.0000 −1.83951 −0.919757 − 0.392488i \(-0.871614\pi\)
−0.919757 + 0.392488i \(0.871614\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −23.0000 −1.17067
\(387\) −1.00000 −0.0508329
\(388\) −10.0000 −0.507673
\(389\) 6.00000 0.304212 0.152106 − 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 6.00000 0.303046
\(393\) 6.00000 0.302660
\(394\) −3.00000 −0.151138
\(395\) 0 0
\(396\) 3.00000 0.150756
\(397\) 2.00000 0.100377 0.0501886 − 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 10.0000 0.501255
\(399\) 4.00000 0.200250
\(400\) 0 0
\(401\) −6.00000 −0.299626 −0.149813 − 0.988714i \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) 4.00000 0.199502
\(403\) 5.00000 0.249068
\(404\) −12.0000 −0.597022
\(405\) 0 0
\(406\) −6.00000 −0.297775
\(407\) 15.0000 0.743522
\(408\) 0 0
\(409\) −4.00000 −0.197787 −0.0988936 − 0.995098i \(-0.531530\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) 0 0
\(411\) 6.00000 0.295958
\(412\) 11.0000 0.541931
\(413\) 0 0
\(414\) −6.00000 −0.294884
\(415\) 0 0
\(416\) −5.00000 −0.245145
\(417\) 5.00000 0.244851
\(418\) 12.0000 0.586939
\(419\) 18.0000 0.879358 0.439679 − 0.898155i \(-0.355092\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(420\) 0 0
\(421\) 26.0000 1.26716 0.633581 − 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) −8.00000 −0.389434
\(423\) 9.00000 0.437595
\(424\) −3.00000 −0.145693
\(425\) 0 0
\(426\) 3.00000 0.145350
\(427\) −11.0000 −0.532327
\(428\) −6.00000 −0.290021
\(429\) 15.0000 0.724207
\(430\) 0 0
\(431\) −3.00000 −0.144505 −0.0722525 − 0.997386i \(-0.523019\pi\)
−0.0722525 + 0.997386i \(0.523019\pi\)
\(432\) 1.00000 0.0481125
\(433\) 2.00000 0.0961139 0.0480569 − 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 1.00000 0.0480015
\(435\) 0 0
\(436\) 8.00000 0.383131
\(437\) −24.0000 −1.14808
\(438\) 4.00000 0.191127
\(439\) 8.00000 0.381819 0.190910 − 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) −30.0000 −1.42534 −0.712672 − 0.701498i \(-0.752515\pi\)
−0.712672 + 0.701498i \(0.752515\pi\)
\(444\) 5.00000 0.237289
\(445\) 0 0
\(446\) −26.0000 −1.23114
\(447\) 6.00000 0.283790
\(448\) −1.00000 −0.0472456
\(449\) 18.0000 0.849473 0.424736 − 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) 9.00000 0.423793
\(452\) 6.00000 0.282216
\(453\) −10.0000 −0.469841
\(454\) 0 0
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −22.0000 −1.02912 −0.514558 − 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) −14.0000 −0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) 9.00000 0.419172 0.209586 − 0.977790i \(-0.432788\pi\)
0.209586 + 0.977790i \(0.432788\pi\)
\(462\) 3.00000 0.139573
\(463\) −22.0000 −1.02243 −0.511213 − 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −3.00000 −0.138972
\(467\) 12.0000 0.555294 0.277647 − 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 5.00000 0.231125
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) 2.00000 0.0921551
\(472\) 0 0
\(473\) −3.00000 −0.137940
\(474\) 10.0000 0.459315
\(475\) 0 0
\(476\) 0 0
\(477\) 3.00000 0.137361
\(478\) −24.0000 −1.09773
\(479\) −36.0000 −1.64488 −0.822441 − 0.568850i \(-0.807388\pi\)
−0.822441 + 0.568850i \(0.807388\pi\)
\(480\) 0 0
\(481\) 25.0000 1.13990
\(482\) 22.0000 1.00207
\(483\) −6.00000 −0.273009
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −22.0000 −0.996915 −0.498458 − 0.866914i \(-0.666100\pi\)
−0.498458 + 0.866914i \(0.666100\pi\)
\(488\) −11.0000 −0.497947
\(489\) 2.00000 0.0904431
\(490\) 0 0
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 3.00000 0.135250
\(493\) 0 0
\(494\) 20.0000 0.899843
\(495\) 0 0
\(496\) 1.00000 0.0449013
\(497\) 3.00000 0.134568
\(498\) −9.00000 −0.403300
\(499\) 20.0000 0.895323 0.447661 − 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 0 0
\(501\) 18.0000 0.804181
\(502\) −15.0000 −0.669483
\(503\) 9.00000 0.401290 0.200645 − 0.979664i \(-0.435696\pi\)
0.200645 + 0.979664i \(0.435696\pi\)
\(504\) 1.00000 0.0445435
\(505\) 0 0
\(506\) −18.0000 −0.800198
\(507\) 12.0000 0.532939
\(508\) −4.00000 −0.177471
\(509\) −15.0000 −0.664863 −0.332432 − 0.943127i \(-0.607869\pi\)
−0.332432 + 0.943127i \(0.607869\pi\)
\(510\) 0 0
\(511\) 4.00000 0.176950
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 −0.176604
\(514\) −3.00000 −0.132324
\(515\) 0 0
\(516\) −1.00000 −0.0440225
\(517\) 27.0000 1.18746
\(518\) 5.00000 0.219687
\(519\) 0 0
\(520\) 0 0
\(521\) 39.0000 1.70862 0.854311 − 0.519763i \(-0.173980\pi\)
0.854311 + 0.519763i \(0.173980\pi\)
\(522\) 6.00000 0.262613
\(523\) −4.00000 −0.174908 −0.0874539 − 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) 12.0000 0.523225
\(527\) 0 0
\(528\) 3.00000 0.130558
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) 15.0000 0.649722
\(534\) −6.00000 −0.259645
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) 9.00000 0.388379
\(538\) 18.0000 0.776035
\(539\) −18.0000 −0.775315
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 − 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 28.0000 1.20270
\(543\) −25.0000 −1.07285
\(544\) 0 0
\(545\) 0 0
\(546\) 5.00000 0.213980
\(547\) −22.0000 −0.940652 −0.470326 − 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) 6.00000 0.256307
\(549\) 11.0000 0.469469
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) −6.00000 −0.255377
\(553\) 10.0000 0.425243
\(554\) −26.0000 −1.10463
\(555\) 0 0
\(556\) 5.00000 0.212047
\(557\) −18.0000 −0.762684 −0.381342 − 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) −1.00000 −0.0423334
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) 0 0
\(562\) −15.0000 −0.632737
\(563\) 24.0000 1.01148 0.505740 − 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) 9.00000 0.378968
\(565\) 0 0
\(566\) 4.00000 0.168133
\(567\) −1.00000 −0.0419961
\(568\) 3.00000 0.125877
\(569\) 18.0000 0.754599 0.377300 − 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) 0 0
\(571\) 23.0000 0.962520 0.481260 − 0.876578i \(-0.340179\pi\)
0.481260 + 0.876578i \(0.340179\pi\)
\(572\) 15.0000 0.627182
\(573\) 24.0000 1.00261
\(574\) 3.00000 0.125218
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 14.0000 0.582828 0.291414 − 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 17.0000 0.707107
\(579\) 23.0000 0.955847
\(580\) 0 0
\(581\) −9.00000 −0.373383
\(582\) 10.0000 0.414513
\(583\) 9.00000 0.372742
\(584\) 4.00000 0.165521
\(585\) 0 0
\(586\) 30.0000 1.23929
\(587\) 15.0000 0.619116 0.309558 − 0.950881i \(-0.399819\pi\)
0.309558 + 0.950881i \(0.399819\pi\)
\(588\) −6.00000 −0.247436
\(589\) −4.00000 −0.164817
\(590\) 0 0
\(591\) 3.00000 0.123404
\(592\) 5.00000 0.205499
\(593\) 33.0000 1.35515 0.677574 − 0.735455i \(-0.263031\pi\)
0.677574 + 0.735455i \(0.263031\pi\)
\(594\) −3.00000 −0.123091
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) −10.0000 −0.409273
\(598\) −30.0000 −1.22679
\(599\) 27.0000 1.10319 0.551595 − 0.834112i \(-0.314019\pi\)
0.551595 + 0.834112i \(0.314019\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 − 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) −1.00000 −0.0407570
\(603\) −4.00000 −0.162893
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 12.0000 0.487467
\(607\) 11.0000 0.446476 0.223238 − 0.974764i \(-0.428337\pi\)
0.223238 + 0.974764i \(0.428337\pi\)
\(608\) 4.00000 0.162221
\(609\) 6.00000 0.243132
\(610\) 0 0
\(611\) 45.0000 1.82051
\(612\) 0 0
\(613\) 26.0000 1.05013 0.525065 − 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 22.0000 0.887848
\(615\) 0 0
\(616\) 3.00000 0.120873
\(617\) −3.00000 −0.120775 −0.0603877 − 0.998175i \(-0.519234\pi\)
−0.0603877 + 0.998175i \(0.519234\pi\)
\(618\) −11.0000 −0.442485
\(619\) −31.0000 −1.24600 −0.622998 − 0.782224i \(-0.714085\pi\)
−0.622998 + 0.782224i \(0.714085\pi\)
\(620\) 0 0
\(621\) 6.00000 0.240772
\(622\) −9.00000 −0.360867
\(623\) −6.00000 −0.240385
\(624\) 5.00000 0.200160
\(625\) 0 0
\(626\) −14.0000 −0.559553
\(627\) −12.0000 −0.479234
\(628\) 2.00000 0.0798087
\(629\) 0 0
\(630\) 0 0
\(631\) −22.0000 −0.875806 −0.437903 − 0.899022i \(-0.644279\pi\)
−0.437903 + 0.899022i \(0.644279\pi\)
\(632\) 10.0000 0.397779
\(633\) 8.00000 0.317971
\(634\) −12.0000 −0.476581
\(635\) 0 0
\(636\) 3.00000 0.118958
\(637\) −30.0000 −1.18864
\(638\) 18.0000 0.712627
\(639\) −3.00000 −0.118678
\(640\) 0 0
\(641\) 30.0000 1.18493 0.592464 − 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 6.00000 0.236801
\(643\) −31.0000 −1.22252 −0.611260 − 0.791430i \(-0.709337\pi\)
−0.611260 + 0.791430i \(0.709337\pi\)
\(644\) −6.00000 −0.236433
\(645\) 0 0
\(646\) 0 0
\(647\) 6.00000 0.235884 0.117942 − 0.993020i \(-0.462370\pi\)
0.117942 + 0.993020i \(0.462370\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) −1.00000 −0.0391931
\(652\) 2.00000 0.0783260
\(653\) −24.0000 −0.939193 −0.469596 − 0.882881i \(-0.655601\pi\)
−0.469596 + 0.882881i \(0.655601\pi\)
\(654\) −8.00000 −0.312825
\(655\) 0 0
\(656\) 3.00000 0.117130
\(657\) −4.00000 −0.156055
\(658\) 9.00000 0.350857
\(659\) 30.0000 1.16863 0.584317 − 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) 0 0
\(661\) −16.0000 −0.622328 −0.311164 − 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) 1.00000 0.0388661
\(663\) 0 0
\(664\) −9.00000 −0.349268
\(665\) 0 0
\(666\) −5.00000 −0.193746
\(667\) −36.0000 −1.39393
\(668\) 18.0000 0.696441
\(669\) 26.0000 1.00522
\(670\) 0 0
\(671\) 33.0000 1.27395
\(672\) 1.00000 0.0385758
\(673\) −10.0000 −0.385472 −0.192736 − 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) 28.0000 1.07852
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) −9.00000 −0.345898 −0.172949 − 0.984931i \(-0.555330\pi\)
−0.172949 + 0.984931i \(0.555330\pi\)
\(678\) −6.00000 −0.230429
\(679\) 10.0000 0.383765
\(680\) 0 0
\(681\) 0 0
\(682\) −3.00000 −0.114876
\(683\) −36.0000 −1.37750 −0.688751 − 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) −4.00000 −0.152944
\(685\) 0 0
\(686\) −13.0000 −0.496342
\(687\) 14.0000 0.534133
\(688\) −1.00000 −0.0381246
\(689\) 15.0000 0.571454
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 − 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 0 0
\(693\) −3.00000 −0.113961
\(694\) −33.0000 −1.25266
\(695\) 0 0
\(696\) 6.00000 0.227429
\(697\) 0 0
\(698\) 16.0000 0.605609
\(699\) 3.00000 0.113470
\(700\) 0 0
\(701\) −12.0000 −0.453234 −0.226617 − 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) −5.00000 −0.188713
\(703\) −20.0000 −0.754314
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) −30.0000 −1.12906
\(707\) 12.0000 0.451306
\(708\) 0 0
\(709\) −46.0000 −1.72757 −0.863783 − 0.503864i \(-0.831911\pi\)
−0.863783 + 0.503864i \(0.831911\pi\)
\(710\) 0 0
\(711\) −10.0000 −0.375029
\(712\) −6.00000 −0.224860
\(713\) 6.00000 0.224702
\(714\) 0 0
\(715\) 0 0
\(716\) 9.00000 0.336346
\(717\) 24.0000 0.896296
\(718\) 0 0
\(719\) −24.0000 −0.895049 −0.447524 − 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) −11.0000 −0.409661
\(722\) 3.00000 0.111648
\(723\) −22.0000 −0.818189
\(724\) −25.0000 −0.929118
\(725\) 0 0
\(726\) 2.00000 0.0742270
\(727\) 17.0000 0.630495 0.315248 − 0.949009i \(-0.397912\pi\)
0.315248 + 0.949009i \(0.397912\pi\)
\(728\) 5.00000 0.185312
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 11.0000 0.406572
\(733\) 2.00000 0.0738717 0.0369358 − 0.999318i \(-0.488240\pi\)
0.0369358 + 0.999318i \(0.488240\pi\)
\(734\) −26.0000 −0.959678
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) −12.0000 −0.442026
\(738\) −3.00000 −0.110432
\(739\) 44.0000 1.61857 0.809283 − 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) 0 0
\(741\) −20.0000 −0.734718
\(742\) 3.00000 0.110133
\(743\) −36.0000 −1.32071 −0.660356 − 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) −1.00000 −0.0366618
\(745\) 0 0
\(746\) −8.00000 −0.292901
\(747\) 9.00000 0.329293
\(748\) 0 0
\(749\) 6.00000 0.219235
\(750\) 0 0
\(751\) 29.0000 1.05823 0.529113 − 0.848552i \(-0.322525\pi\)
0.529113 + 0.848552i \(0.322525\pi\)
\(752\) 9.00000 0.328196
\(753\) 15.0000 0.546630
\(754\) 30.0000 1.09254
\(755\) 0 0
\(756\) −1.00000 −0.0363696
\(757\) −13.0000 −0.472493 −0.236247 − 0.971693i \(-0.575917\pi\)
−0.236247 + 0.971693i \(0.575917\pi\)
\(758\) −26.0000 −0.944363
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) −48.0000 −1.74000 −0.869999 − 0.493053i \(-0.835881\pi\)
−0.869999 + 0.493053i \(0.835881\pi\)
\(762\) 4.00000 0.144905
\(763\) −8.00000 −0.289619
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) 36.0000 1.30073
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −25.0000 −0.901523 −0.450762 − 0.892644i \(-0.648848\pi\)
−0.450762 + 0.892644i \(0.648848\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) 23.0000 0.827788
\(773\) −18.0000 −0.647415 −0.323708 − 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 1.00000 0.0359443
\(775\) 0 0
\(776\) 10.0000 0.358979
\(777\) −5.00000 −0.179374
\(778\) −6.00000 −0.215110
\(779\) −12.0000 −0.429945
\(780\) 0 0
\(781\) −9.00000 −0.322045
\(782\) 0 0
\(783\) −6.00000 −0.214423
\(784\) −6.00000 −0.214286
\(785\) 0 0
\(786\) −6.00000 −0.214013
\(787\) −7.00000 −0.249523 −0.124762 − 0.992187i \(-0.539817\pi\)
−0.124762 + 0.992187i \(0.539817\pi\)
\(788\) 3.00000 0.106871
\(789\) −12.0000 −0.427211
\(790\) 0 0
\(791\) −6.00000 −0.213335
\(792\) −3.00000 −0.106600
\(793\) 55.0000 1.95311
\(794\) −2.00000 −0.0709773
\(795\) 0 0
\(796\) −10.0000 −0.354441
\(797\) −30.0000 −1.06265 −0.531327 − 0.847167i \(-0.678307\pi\)
−0.531327 + 0.847167i \(0.678307\pi\)
\(798\) −4.00000 −0.141598
\(799\) 0 0
\(800\) 0 0
\(801\) 6.00000 0.212000
\(802\) 6.00000 0.211867
\(803\) −12.0000 −0.423471
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) −5.00000 −0.176117
\(807\) −18.0000 −0.633630
\(808\) 12.0000 0.422159
\(809\) −18.0000 −0.632846 −0.316423 − 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) 0 0
\(811\) −16.0000 −0.561836 −0.280918 − 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) 6.00000 0.210559
\(813\) −28.0000 −0.982003
\(814\) −15.0000 −0.525750
\(815\) 0 0
\(816\) 0 0
\(817\) 4.00000 0.139942
\(818\) 4.00000 0.139857
\(819\) −5.00000 −0.174714
\(820\) 0 0
\(821\) −45.0000 −1.57051 −0.785255 − 0.619172i \(-0.787468\pi\)
−0.785255 + 0.619172i \(0.787468\pi\)
\(822\) −6.00000 −0.209274
\(823\) −16.0000 −0.557725 −0.278862 − 0.960331i \(-0.589957\pi\)
−0.278862 + 0.960331i \(0.589957\pi\)
\(824\) −11.0000 −0.383203
\(825\) 0 0
\(826\) 0 0
\(827\) −36.0000 −1.25184 −0.625921 − 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) 6.00000 0.208514
\(829\) −25.0000 −0.868286 −0.434143 − 0.900844i \(-0.642949\pi\)
−0.434143 + 0.900844i \(0.642949\pi\)
\(830\) 0 0
\(831\) 26.0000 0.901930
\(832\) 5.00000 0.173344
\(833\) 0 0
\(834\) −5.00000 −0.173136
\(835\) 0 0
\(836\) −12.0000 −0.415029
\(837\) 1.00000 0.0345651
\(838\) −18.0000 −0.621800
\(839\) −15.0000 −0.517858 −0.258929 − 0.965896i \(-0.583369\pi\)
−0.258929 + 0.965896i \(0.583369\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −26.0000 −0.896019
\(843\) 15.0000 0.516627
\(844\) 8.00000 0.275371
\(845\) 0 0
\(846\) −9.00000 −0.309426
\(847\) 2.00000 0.0687208
\(848\) 3.00000 0.103020
\(849\) −4.00000 −0.137280
\(850\) 0 0
\(851\) 30.0000 1.02839
\(852\) −3.00000 −0.102778
\(853\) 8.00000 0.273915 0.136957 − 0.990577i \(-0.456268\pi\)
0.136957 + 0.990577i \(0.456268\pi\)
\(854\) 11.0000 0.376412
\(855\) 0 0
\(856\) 6.00000 0.205076
\(857\) 33.0000 1.12726 0.563629 − 0.826028i \(-0.309405\pi\)
0.563629 + 0.826028i \(0.309405\pi\)
\(858\) −15.0000 −0.512092
\(859\) −7.00000 −0.238837 −0.119418 − 0.992844i \(-0.538103\pi\)
−0.119418 + 0.992844i \(0.538103\pi\)
\(860\) 0 0
\(861\) −3.00000 −0.102240
\(862\) 3.00000 0.102180
\(863\) −48.0000 −1.63394 −0.816970 − 0.576681i \(-0.804348\pi\)
−0.816970 + 0.576681i \(0.804348\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) −2.00000 −0.0679628
\(867\) −17.0000 −0.577350
\(868\) −1.00000 −0.0339422
\(869\) −30.0000 −1.01768
\(870\) 0 0
\(871\) −20.0000 −0.677674
\(872\) −8.00000 −0.270914
\(873\) −10.0000 −0.338449
\(874\) 24.0000 0.811812
\(875\) 0 0
\(876\) −4.00000 −0.135147
\(877\) −40.0000 −1.35070 −0.675352 − 0.737496i \(-0.736008\pi\)
−0.675352 + 0.737496i \(0.736008\pi\)
\(878\) −8.00000 −0.269987
\(879\) −30.0000 −1.01187
\(880\) 0 0
\(881\) 48.0000 1.61716 0.808581 − 0.588386i \(-0.200236\pi\)
0.808581 + 0.588386i \(0.200236\pi\)
\(882\) 6.00000 0.202031
\(883\) 5.00000 0.168263 0.0841317 − 0.996455i \(-0.473188\pi\)
0.0841317 + 0.996455i \(0.473188\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 30.0000 1.00787
\(887\) 9.00000 0.302190 0.151095 − 0.988519i \(-0.451720\pi\)
0.151095 + 0.988519i \(0.451720\pi\)
\(888\) −5.00000 −0.167789
\(889\) 4.00000 0.134156
\(890\) 0 0
\(891\) 3.00000 0.100504
\(892\) 26.0000 0.870544
\(893\) −36.0000 −1.20469
\(894\) −6.00000 −0.200670
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 30.0000 1.00167
\(898\) −18.0000 −0.600668
\(899\) −6.00000 −0.200111
\(900\) 0 0
\(901\) 0 0
\(902\) −9.00000 −0.299667
\(903\) 1.00000 0.0332779
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) 10.0000 0.332228
\(907\) 8.00000 0.265636 0.132818 − 0.991140i \(-0.457597\pi\)
0.132818 + 0.991140i \(0.457597\pi\)
\(908\) 0 0
\(909\) −12.0000 −0.398015
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 − 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) −4.00000 −0.132453
\(913\) 27.0000 0.893570
\(914\) 22.0000 0.727695
\(915\) 0 0
\(916\) 14.0000 0.462573
\(917\) −6.00000 −0.198137
\(918\) 0 0
\(919\) −25.0000 −0.824674 −0.412337 − 0.911031i \(-0.635287\pi\)
−0.412337 + 0.911031i \(0.635287\pi\)
\(920\) 0 0
\(921\) −22.0000 −0.724925
\(922\) −9.00000 −0.296399
\(923\) −15.0000 −0.493731
\(924\) −3.00000 −0.0986928
\(925\) 0 0
\(926\) 22.0000 0.722965
\(927\) 11.0000 0.361287
\(928\) 6.00000 0.196960
\(929\) −6.00000 −0.196854 −0.0984268 − 0.995144i \(-0.531381\pi\)
−0.0984268 + 0.995144i \(0.531381\pi\)
\(930\) 0 0
\(931\) 24.0000 0.786568
\(932\) 3.00000 0.0982683
\(933\) 9.00000 0.294647
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) −5.00000 −0.163430
\(937\) 2.00000 0.0653372 0.0326686 − 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) −4.00000 −0.130605
\(939\) 14.0000 0.456873
\(940\) 0 0
\(941\) 18.0000 0.586783 0.293392 − 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 18.0000 0.586161
\(944\) 0 0
\(945\) 0 0
\(946\) 3.00000 0.0975384
\(947\) 3.00000 0.0974869 0.0487435 − 0.998811i \(-0.484478\pi\)
0.0487435 + 0.998811i \(0.484478\pi\)
\(948\) −10.0000 −0.324785
\(949\) −20.0000 −0.649227
\(950\) 0 0
\(951\) 12.0000 0.389127
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 − 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) −3.00000 −0.0971286
\(955\) 0 0
\(956\) 24.0000 0.776215
\(957\) −18.0000 −0.581857
\(958\) 36.0000 1.16311
\(959\) −6.00000 −0.193750
\(960\) 0 0
\(961\) 1.00000 0.0322581
\(962\) −25.0000 −0.806032
\(963\) −6.00000 −0.193347
\(964\) −22.0000 −0.708572
\(965\) 0 0
\(966\) 6.00000 0.193047
\(967\) 14.0000 0.450210 0.225105 − 0.974335i \(-0.427728\pi\)
0.225105 + 0.974335i \(0.427728\pi\)
\(968\) 2.00000 0.0642824
\(969\) 0 0
\(970\) 0 0
\(971\) 12.0000 0.385098 0.192549 − 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) 1.00000 0.0320750
\(973\) −5.00000 −0.160293
\(974\) 22.0000 0.704925
\(975\) 0 0
\(976\) 11.0000 0.352101
\(977\) −57.0000 −1.82359 −0.911796 − 0.410644i \(-0.865304\pi\)
−0.911796 + 0.410644i \(0.865304\pi\)
\(978\) −2.00000 −0.0639529
\(979\) 18.0000 0.575282
\(980\) 0 0
\(981\) 8.00000 0.255420
\(982\) 0 0
\(983\) −6.00000 −0.191370 −0.0956851 − 0.995412i \(-0.530504\pi\)
−0.0956851 + 0.995412i \(0.530504\pi\)
\(984\) −3.00000 −0.0956365
\(985\) 0 0
\(986\) 0 0
\(987\) −9.00000 −0.286473
\(988\) −20.0000 −0.636285
\(989\) −6.00000 −0.190789
\(990\) 0 0
\(991\) 38.0000 1.20711 0.603555 − 0.797321i \(-0.293750\pi\)
0.603555 + 0.797321i \(0.293750\pi\)
\(992\) −1.00000 −0.0317500
\(993\) −1.00000 −0.0317340
\(994\) −3.00000 −0.0951542
\(995\) 0 0
\(996\) 9.00000 0.285176
\(997\) −28.0000 −0.886769 −0.443384 − 0.896332i \(-0.646222\pi\)
−0.443384 + 0.896332i \(0.646222\pi\)
\(998\) −20.0000 −0.633089
\(999\) 5.00000 0.158193
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 4650.2.a.q.1.1 ✓ 1
5.2 odd 4 4650.2.d.i.3349.1 2
5.3 odd 4 4650.2.d.i.3349.2 2
5.4 even 2 4650.2.a.bf.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4650.2.a.q.1.1 ✓ 1 1.1 even 1 trivial
4650.2.a.bf.1.1 yes 1 5.4 even 2
4650.2.d.i.3349.1 2 5.2 odd 4
4650.2.d.i.3349.2 2 5.3 odd 4