Properties

Label 4650.2.a.bi.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: no (minimal twist has level 930)
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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -5.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -5.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} +1.00000 q^{12} -5.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +3.00000 q^{19} -5.00000 q^{21} -1.00000 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{27} -5.00000 q^{28} +6.00000 q^{29} -1.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} +4.00000 q^{34} +1.00000 q^{36} +4.00000 q^{37} +3.00000 q^{38} +2.00000 q^{41} -5.00000 q^{42} +1.00000 q^{43} -1.00000 q^{44} +1.00000 q^{46} -4.00000 q^{47} +1.00000 q^{48} +18.0000 q^{49} +4.00000 q^{51} -3.00000 q^{53} +1.00000 q^{54} -5.00000 q^{56} +3.00000 q^{57} +6.00000 q^{58} -14.0000 q^{59} +14.0000 q^{61} -1.00000 q^{62} -5.00000 q^{63} +1.00000 q^{64} -1.00000 q^{66} -10.0000 q^{67} +4.00000 q^{68} +1.00000 q^{69} +9.00000 q^{71} +1.00000 q^{72} +7.00000 q^{73} +4.00000 q^{74} +3.00000 q^{76} +5.00000 q^{77} +15.0000 q^{79} +1.00000 q^{81} +2.00000 q^{82} +10.0000 q^{83} -5.00000 q^{84} +1.00000 q^{86} +6.00000 q^{87} -1.00000 q^{88} -1.00000 q^{89} +1.00000 q^{92} -1.00000 q^{93} -4.00000 q^{94} +1.00000 q^{96} -10.0000 q^{97} +18.0000 q^{98} -1.00000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) −5.00000 −1.88982 −0.944911 0.327327i \(-0.893852\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −5.00000 −1.33631
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 1.00000 0.235702
\(19\) 3.00000 0.688247 0.344124 0.938924i \(-0.388176\pi\)
0.344124 + 0.938924i \(0.388176\pi\)
\(20\) 0 0
\(21\) −5.00000 −1.09109
\(22\) −1.00000 −0.213201
\(23\) 1.00000 0.208514 0.104257 0.994550i \(-0.466753\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(24\) 1.00000 0.204124
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −5.00000 −0.944911
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) −1.00000 −0.174078
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 3.00000 0.486664
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) −5.00000 −0.771517
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) 1.00000 0.144338
\(49\) 18.0000 2.57143
\(50\) 0 0
\(51\) 4.00000 0.560112
\(52\) 0 0
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −5.00000 −0.668153
\(57\) 3.00000 0.397360
\(58\) 6.00000 0.787839
\(59\) −14.0000 −1.82264 −0.911322 0.411693i \(-0.864937\pi\)
−0.911322 + 0.411693i \(0.864937\pi\)
\(60\) 0 0
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) −1.00000 −0.127000
\(63\) −5.00000 −0.629941
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −1.00000 −0.123091
\(67\) −10.0000 −1.22169 −0.610847 0.791748i \(-0.709171\pi\)
−0.610847 + 0.791748i \(0.709171\pi\)
\(68\) 4.00000 0.485071
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) 1.00000 0.117851
\(73\) 7.00000 0.819288 0.409644 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) 3.00000 0.344124
\(77\) 5.00000 0.569803
\(78\) 0 0
\(79\) 15.0000 1.68763 0.843816 0.536633i \(-0.180304\pi\)
0.843816 + 0.536633i \(0.180304\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 2.00000 0.220863
\(83\) 10.0000 1.09764 0.548821 0.835940i \(-0.315077\pi\)
0.548821 + 0.835940i \(0.315077\pi\)
\(84\) −5.00000 −0.545545
\(85\) 0 0
\(86\) 1.00000 0.107833
\(87\) 6.00000 0.643268
\(88\) −1.00000 −0.106600
\(89\) −1.00000 −0.106000 −0.0529999 0.998595i \(-0.516878\pi\)
−0.0529999 + 0.998595i \(0.516878\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.00000 0.104257
\(93\) −1.00000 −0.103695
\(94\) −4.00000 −0.412568
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 18.0000 1.81827
\(99\) −1.00000 −0.100504
\(100\) 0 0
\(101\) 7.00000 0.696526 0.348263 0.937397i \(-0.386772\pi\)
0.348263 + 0.937397i \(0.386772\pi\)
\(102\) 4.00000 0.396059
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −3.00000 −0.291386
\(107\) −9.00000 −0.870063 −0.435031 0.900415i \(-0.643263\pi\)
−0.435031 + 0.900415i \(0.643263\pi\)
\(108\) 1.00000 0.0962250
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) −5.00000 −0.472456
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 3.00000 0.280976
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) −14.0000 −1.28880
\(119\) −20.0000 −1.83340
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 14.0000 1.26750
\(123\) 2.00000 0.180334
\(124\) −1.00000 −0.0898027
\(125\) 0 0
\(126\) −5.00000 −0.445435
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.00000 0.0880451
\(130\) 0 0
\(131\) 18.0000 1.57267 0.786334 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −15.0000 −1.30066
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 4.00000 0.342997
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 1.00000 0.0851257
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −4.00000 −0.336861
\(142\) 9.00000 0.755263
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 7.00000 0.579324
\(147\) 18.0000 1.48461
\(148\) 4.00000 0.328798
\(149\) 1.00000 0.0819232 0.0409616 0.999161i \(-0.486958\pi\)
0.0409616 + 0.999161i \(0.486958\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 3.00000 0.243332
\(153\) 4.00000 0.323381
\(154\) 5.00000 0.402911
\(155\) 0 0
\(156\) 0 0
\(157\) −1.00000 −0.0798087 −0.0399043 0.999204i \(-0.512705\pi\)
−0.0399043 + 0.999204i \(0.512705\pi\)
\(158\) 15.0000 1.19334
\(159\) −3.00000 −0.237915
\(160\) 0 0
\(161\) −5.00000 −0.394055
\(162\) 1.00000 0.0785674
\(163\) 8.00000 0.626608 0.313304 0.949653i \(-0.398564\pi\)
0.313304 + 0.949653i \(0.398564\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) 10.0000 0.776151
\(167\) 9.00000 0.696441 0.348220 0.937413i \(-0.386786\pi\)
0.348220 + 0.937413i \(0.386786\pi\)
\(168\) −5.00000 −0.385758
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 3.00000 0.229416
\(172\) 1.00000 0.0762493
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 6.00000 0.454859
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) −14.0000 −1.05230
\(178\) −1.00000 −0.0749532
\(179\) −8.00000 −0.597948 −0.298974 0.954261i \(-0.596644\pi\)
−0.298974 + 0.954261i \(0.596644\pi\)
\(180\) 0 0
\(181\) 11.0000 0.817624 0.408812 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) 1.00000 0.0737210
\(185\) 0 0
\(186\) −1.00000 −0.0733236
\(187\) −4.00000 −0.292509
\(188\) −4.00000 −0.291730
\(189\) −5.00000 −0.363696
\(190\) 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
\(193\) 10.0000 0.719816 0.359908 0.932988i \(-0.382808\pi\)
0.359908 + 0.932988i \(0.382808\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) 18.0000 1.28571
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) −1.00000 −0.0710669
\(199\) −9.00000 −0.637993 −0.318997 0.947756i \(-0.603346\pi\)
−0.318997 + 0.947756i \(0.603346\pi\)
\(200\) 0 0
\(201\) −10.0000 −0.705346
\(202\) 7.00000 0.492518
\(203\) −30.0000 −2.10559
\(204\) 4.00000 0.280056
\(205\) 0 0
\(206\) 8.00000 0.557386
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) −21.0000 −1.44570 −0.722850 0.691005i \(-0.757168\pi\)
−0.722850 + 0.691005i \(0.757168\pi\)
\(212\) −3.00000 −0.206041
\(213\) 9.00000 0.616670
\(214\) −9.00000 −0.615227
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 5.00000 0.339422
\(218\) 10.0000 0.677285
\(219\) 7.00000 0.473016
\(220\) 0 0
\(221\) 0 0
\(222\) 4.00000 0.268462
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) −5.00000 −0.334077
\(225\) 0 0
\(226\) 9.00000 0.598671
\(227\) −29.0000 −1.92480 −0.962399 0.271640i \(-0.912434\pi\)
−0.962399 + 0.271640i \(0.912434\pi\)
\(228\) 3.00000 0.198680
\(229\) 23.0000 1.51988 0.759941 0.649992i \(-0.225228\pi\)
0.759941 + 0.649992i \(0.225228\pi\)
\(230\) 0 0
\(231\) 5.00000 0.328976
\(232\) 6.00000 0.393919
\(233\) −13.0000 −0.851658 −0.425829 0.904804i \(-0.640018\pi\)
−0.425829 + 0.904804i \(0.640018\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −14.0000 −0.911322
\(237\) 15.0000 0.974355
\(238\) −20.0000 −1.29641
\(239\) −22.0000 −1.42306 −0.711531 0.702655i \(-0.751998\pi\)
−0.711531 + 0.702655i \(0.751998\pi\)
\(240\) 0 0
\(241\) 4.00000 0.257663 0.128831 0.991667i \(-0.458877\pi\)
0.128831 + 0.991667i \(0.458877\pi\)
\(242\) −10.0000 −0.642824
\(243\) 1.00000 0.0641500
\(244\) 14.0000 0.896258
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) 0 0
\(248\) −1.00000 −0.0635001
\(249\) 10.0000 0.633724
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) −5.00000 −0.314970
\(253\) −1.00000 −0.0628695
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −3.00000 −0.187135 −0.0935674 0.995613i \(-0.529827\pi\)
−0.0935674 + 0.995613i \(0.529827\pi\)
\(258\) 1.00000 0.0622573
\(259\) −20.0000 −1.24274
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 18.0000 1.11204
\(263\) −8.00000 −0.493301 −0.246651 0.969104i \(-0.579330\pi\)
−0.246651 + 0.969104i \(0.579330\pi\)
\(264\) −1.00000 −0.0615457
\(265\) 0 0
\(266\) −15.0000 −0.919709
\(267\) −1.00000 −0.0611990
\(268\) −10.0000 −0.610847
\(269\) 30.0000 1.82913 0.914566 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(270\) 0 0
\(271\) 13.0000 0.789694 0.394847 0.918747i \(-0.370798\pi\)
0.394847 + 0.918747i \(0.370798\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 0 0
\(276\) 1.00000 0.0601929
\(277\) −26.0000 −1.56219 −0.781094 0.624413i \(-0.785338\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) 4.00000 0.239904
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) −4.00000 −0.238197
\(283\) −22.0000 −1.30776 −0.653882 0.756596i \(-0.726861\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) 9.00000 0.534052
\(285\) 0 0
\(286\) 0 0
\(287\) −10.0000 −0.590281
\(288\) 1.00000 0.0589256
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) −10.0000 −0.586210
\(292\) 7.00000 0.409644
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 18.0000 1.04978
\(295\) 0 0
\(296\) 4.00000 0.232495
\(297\) −1.00000 −0.0580259
\(298\) 1.00000 0.0579284
\(299\) 0 0
\(300\) 0 0
\(301\) −5.00000 −0.288195
\(302\) −8.00000 −0.460348
\(303\) 7.00000 0.402139
\(304\) 3.00000 0.172062
\(305\) 0 0
\(306\) 4.00000 0.228665
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 5.00000 0.284901
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −26.0000 −1.46961 −0.734803 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) −1.00000 −0.0564333
\(315\) 0 0
\(316\) 15.0000 0.843816
\(317\) 22.0000 1.23564 0.617822 0.786318i \(-0.288015\pi\)
0.617822 + 0.786318i \(0.288015\pi\)
\(318\) −3.00000 −0.168232
\(319\) −6.00000 −0.335936
\(320\) 0 0
\(321\) −9.00000 −0.502331
\(322\) −5.00000 −0.278639
\(323\) 12.0000 0.667698
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 8.00000 0.443079
\(327\) 10.0000 0.553001
\(328\) 2.00000 0.110432
\(329\) 20.0000 1.10264
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 10.0000 0.548821
\(333\) 4.00000 0.219199
\(334\) 9.00000 0.492458
\(335\) 0 0
\(336\) −5.00000 −0.272772
\(337\) 10.0000 0.544735 0.272367 0.962193i \(-0.412193\pi\)
0.272367 + 0.962193i \(0.412193\pi\)
\(338\) −13.0000 −0.707107
\(339\) 9.00000 0.488813
\(340\) 0 0
\(341\) 1.00000 0.0541530
\(342\) 3.00000 0.162221
\(343\) −55.0000 −2.96972
\(344\) 1.00000 0.0539164
\(345\) 0 0
\(346\) 2.00000 0.107521
\(347\) −30.0000 −1.61048 −0.805242 0.592946i \(-0.797965\pi\)
−0.805242 + 0.592946i \(0.797965\pi\)
\(348\) 6.00000 0.321634
\(349\) −32.0000 −1.71292 −0.856460 0.516213i \(-0.827341\pi\)
−0.856460 + 0.516213i \(0.827341\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.00000 −0.0533002
\(353\) 8.00000 0.425797 0.212899 0.977074i \(-0.431710\pi\)
0.212899 + 0.977074i \(0.431710\pi\)
\(354\) −14.0000 −0.744092
\(355\) 0 0
\(356\) −1.00000 −0.0529999
\(357\) −20.0000 −1.05851
\(358\) −8.00000 −0.422813
\(359\) −15.0000 −0.791670 −0.395835 0.918322i \(-0.629545\pi\)
−0.395835 + 0.918322i \(0.629545\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) 11.0000 0.578147
\(363\) −10.0000 −0.524864
\(364\) 0 0
\(365\) 0 0
\(366\) 14.0000 0.731792
\(367\) −26.0000 −1.35719 −0.678594 0.734513i \(-0.737411\pi\)
−0.678594 + 0.734513i \(0.737411\pi\)
\(368\) 1.00000 0.0521286
\(369\) 2.00000 0.104116
\(370\) 0 0
\(371\) 15.0000 0.778761
\(372\) −1.00000 −0.0518476
\(373\) 3.00000 0.155334 0.0776671 0.996979i \(-0.475253\pi\)
0.0776671 + 0.996979i \(0.475253\pi\)
\(374\) −4.00000 −0.206835
\(375\) 0 0
\(376\) −4.00000 −0.206284
\(377\) 0 0
\(378\) −5.00000 −0.257172
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) 0 0
\(381\) 16.0000 0.819705
\(382\) 24.0000 1.22795
\(383\) 20.0000 1.02195 0.510976 0.859595i \(-0.329284\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) 1.00000 0.0508329
\(388\) −10.0000 −0.507673
\(389\) −16.0000 −0.811232 −0.405616 0.914044i \(-0.632943\pi\)
−0.405616 + 0.914044i \(0.632943\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 18.0000 0.909137
\(393\) 18.0000 0.907980
\(394\) 2.00000 0.100759
\(395\) 0 0
\(396\) −1.00000 −0.0502519
\(397\) −17.0000 −0.853206 −0.426603 0.904439i \(-0.640290\pi\)
−0.426603 + 0.904439i \(0.640290\pi\)
\(398\) −9.00000 −0.451129
\(399\) −15.0000 −0.750939
\(400\) 0 0
\(401\) −29.0000 −1.44819 −0.724095 0.689700i \(-0.757743\pi\)
−0.724095 + 0.689700i \(0.757743\pi\)
\(402\) −10.0000 −0.498755
\(403\) 0 0
\(404\) 7.00000 0.348263
\(405\) 0 0
\(406\) −30.0000 −1.48888
\(407\) −4.00000 −0.198273
\(408\) 4.00000 0.198030
\(409\) −16.0000 −0.791149 −0.395575 0.918434i \(-0.629455\pi\)
−0.395575 + 0.918434i \(0.629455\pi\)
\(410\) 0 0
\(411\) 6.00000 0.295958
\(412\) 8.00000 0.394132
\(413\) 70.0000 3.44447
\(414\) 1.00000 0.0491473
\(415\) 0 0
\(416\) 0 0
\(417\) 4.00000 0.195881
\(418\) −3.00000 −0.146735
\(419\) 26.0000 1.27018 0.635092 0.772437i \(-0.280962\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −21.0000 −1.02226
\(423\) −4.00000 −0.194487
\(424\) −3.00000 −0.145693
\(425\) 0 0
\(426\) 9.00000 0.436051
\(427\) −70.0000 −3.38754
\(428\) −9.00000 −0.435031
\(429\) 0 0
\(430\) 0 0
\(431\) 8.00000 0.385346 0.192673 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) 1.00000 0.0481125
\(433\) −11.0000 −0.528626 −0.264313 0.964437i \(-0.585145\pi\)
−0.264313 + 0.964437i \(0.585145\pi\)
\(434\) 5.00000 0.240008
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) 3.00000 0.143509
\(438\) 7.00000 0.334473
\(439\) 36.0000 1.71819 0.859093 0.511819i \(-0.171028\pi\)
0.859093 + 0.511819i \(0.171028\pi\)
\(440\) 0 0
\(441\) 18.0000 0.857143
\(442\) 0 0
\(443\) −15.0000 −0.712672 −0.356336 0.934358i \(-0.615974\pi\)
−0.356336 + 0.934358i \(0.615974\pi\)
\(444\) 4.00000 0.189832
\(445\) 0 0
\(446\) −8.00000 −0.378811
\(447\) 1.00000 0.0472984
\(448\) −5.00000 −0.236228
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) −2.00000 −0.0941763
\(452\) 9.00000 0.423324
\(453\) −8.00000 −0.375873
\(454\) −29.0000 −1.36104
\(455\) 0 0
\(456\) 3.00000 0.140488
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 23.0000 1.07472
\(459\) 4.00000 0.186704
\(460\) 0 0
\(461\) 24.0000 1.11779 0.558896 0.829238i \(-0.311225\pi\)
0.558896 + 0.829238i \(0.311225\pi\)
\(462\) 5.00000 0.232621
\(463\) 6.00000 0.278844 0.139422 0.990233i \(-0.455476\pi\)
0.139422 + 0.990233i \(0.455476\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −13.0000 −0.602213
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) 50.0000 2.30879
\(470\) 0 0
\(471\) −1.00000 −0.0460776
\(472\) −14.0000 −0.644402
\(473\) −1.00000 −0.0459800
\(474\) 15.0000 0.688973
\(475\) 0 0
\(476\) −20.0000 −0.916698
\(477\) −3.00000 −0.137361
\(478\) −22.0000 −1.00626
\(479\) 29.0000 1.32504 0.662522 0.749043i \(-0.269486\pi\)
0.662522 + 0.749043i \(0.269486\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 4.00000 0.182195
\(483\) −5.00000 −0.227508
\(484\) −10.0000 −0.454545
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −36.0000 −1.63132 −0.815658 0.578535i \(-0.803625\pi\)
−0.815658 + 0.578535i \(0.803625\pi\)
\(488\) 14.0000 0.633750
\(489\) 8.00000 0.361773
\(490\) 0 0
\(491\) 27.0000 1.21849 0.609246 0.792981i \(-0.291472\pi\)
0.609246 + 0.792981i \(0.291472\pi\)
\(492\) 2.00000 0.0901670
\(493\) 24.0000 1.08091
\(494\) 0 0
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) −45.0000 −2.01853
\(498\) 10.0000 0.448111
\(499\) −42.0000 −1.88018 −0.940089 0.340929i \(-0.889258\pi\)
−0.940089 + 0.340929i \(0.889258\pi\)
\(500\) 0 0
\(501\) 9.00000 0.402090
\(502\) −12.0000 −0.535586
\(503\) −42.0000 −1.87269 −0.936344 0.351085i \(-0.885813\pi\)
−0.936344 + 0.351085i \(0.885813\pi\)
\(504\) −5.00000 −0.222718
\(505\) 0 0
\(506\) −1.00000 −0.0444554
\(507\) −13.0000 −0.577350
\(508\) 16.0000 0.709885
\(509\) −36.0000 −1.59567 −0.797836 0.602875i \(-0.794022\pi\)
−0.797836 + 0.602875i \(0.794022\pi\)
\(510\) 0 0
\(511\) −35.0000 −1.54831
\(512\) 1.00000 0.0441942
\(513\) 3.00000 0.132453
\(514\) −3.00000 −0.132324
\(515\) 0 0
\(516\) 1.00000 0.0440225
\(517\) 4.00000 0.175920
\(518\) −20.0000 −0.878750
\(519\) 2.00000 0.0877903
\(520\) 0 0
\(521\) −20.0000 −0.876216 −0.438108 0.898922i \(-0.644351\pi\)
−0.438108 + 0.898922i \(0.644351\pi\)
\(522\) 6.00000 0.262613
\(523\) 41.0000 1.79280 0.896402 0.443241i \(-0.146171\pi\)
0.896402 + 0.443241i \(0.146171\pi\)
\(524\) 18.0000 0.786334
\(525\) 0 0
\(526\) −8.00000 −0.348817
\(527\) −4.00000 −0.174243
\(528\) −1.00000 −0.0435194
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) −14.0000 −0.607548
\(532\) −15.0000 −0.650332
\(533\) 0 0
\(534\) −1.00000 −0.0432742
\(535\) 0 0
\(536\) −10.0000 −0.431934
\(537\) −8.00000 −0.345225
\(538\) 30.0000 1.29339
\(539\) −18.0000 −0.775315
\(540\) 0 0
\(541\) 4.00000 0.171973 0.0859867 0.996296i \(-0.472596\pi\)
0.0859867 + 0.996296i \(0.472596\pi\)
\(542\) 13.0000 0.558398
\(543\) 11.0000 0.472055
\(544\) 4.00000 0.171499
\(545\) 0 0
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 6.00000 0.256307
\(549\) 14.0000 0.597505
\(550\) 0 0
\(551\) 18.0000 0.766826
\(552\) 1.00000 0.0425628
\(553\) −75.0000 −3.18932
\(554\) −26.0000 −1.10463
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) 33.0000 1.39825 0.699127 0.714997i \(-0.253572\pi\)
0.699127 + 0.714997i \(0.253572\pi\)
\(558\) −1.00000 −0.0423334
\(559\) 0 0
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) 0 0
\(563\) −4.00000 −0.168580 −0.0842900 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) −4.00000 −0.168430
\(565\) 0 0
\(566\) −22.0000 −0.924729
\(567\) −5.00000 −0.209980
\(568\) 9.00000 0.377632
\(569\) −1.00000 −0.0419222 −0.0209611 0.999780i \(-0.506673\pi\)
−0.0209611 + 0.999780i \(0.506673\pi\)
\(570\) 0 0
\(571\) 34.0000 1.42286 0.711428 0.702759i \(-0.248049\pi\)
0.711428 + 0.702759i \(0.248049\pi\)
\(572\) 0 0
\(573\) 24.0000 1.00261
\(574\) −10.0000 −0.417392
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 10.0000 0.416305 0.208153 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 10.0000 0.415586
\(580\) 0 0
\(581\) −50.0000 −2.07435
\(582\) −10.0000 −0.414513
\(583\) 3.00000 0.124247
\(584\) 7.00000 0.289662
\(585\) 0 0
\(586\) −30.0000 −1.23929
\(587\) 30.0000 1.23823 0.619116 0.785299i \(-0.287491\pi\)
0.619116 + 0.785299i \(0.287491\pi\)
\(588\) 18.0000 0.742307
\(589\) −3.00000 −0.123613
\(590\) 0 0
\(591\) 2.00000 0.0822690
\(592\) 4.00000 0.164399
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) 1.00000 0.0409616
\(597\) −9.00000 −0.368345
\(598\) 0 0
\(599\) 15.0000 0.612883 0.306442 0.951889i \(-0.400862\pi\)
0.306442 + 0.951889i \(0.400862\pi\)
\(600\) 0 0
\(601\) −28.0000 −1.14214 −0.571072 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) −5.00000 −0.203785
\(603\) −10.0000 −0.407231
\(604\) −8.00000 −0.325515
\(605\) 0 0
\(606\) 7.00000 0.284356
\(607\) 23.0000 0.933541 0.466771 0.884378i \(-0.345417\pi\)
0.466771 + 0.884378i \(0.345417\pi\)
\(608\) 3.00000 0.121666
\(609\) −30.0000 −1.21566
\(610\) 0 0
\(611\) 0 0
\(612\) 4.00000 0.161690
\(613\) 16.0000 0.646234 0.323117 0.946359i \(-0.395269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(614\) −12.0000 −0.484281
\(615\) 0 0
\(616\) 5.00000 0.201456
\(617\) 13.0000 0.523360 0.261680 0.965155i \(-0.415723\pi\)
0.261680 + 0.965155i \(0.415723\pi\)
\(618\) 8.00000 0.321807
\(619\) −28.0000 −1.12542 −0.562708 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 5.00000 0.200321
\(624\) 0 0
\(625\) 0 0
\(626\) −26.0000 −1.03917
\(627\) −3.00000 −0.119808
\(628\) −1.00000 −0.0399043
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) 29.0000 1.15447 0.577236 0.816577i \(-0.304131\pi\)
0.577236 + 0.816577i \(0.304131\pi\)
\(632\) 15.0000 0.596668
\(633\) −21.0000 −0.834675
\(634\) 22.0000 0.873732
\(635\) 0 0
\(636\) −3.00000 −0.118958
\(637\) 0 0
\(638\) −6.00000 −0.237542
\(639\) 9.00000 0.356034
\(640\) 0 0
\(641\) 38.0000 1.50091 0.750455 0.660922i \(-0.229834\pi\)
0.750455 + 0.660922i \(0.229834\pi\)
\(642\) −9.00000 −0.355202
\(643\) 3.00000 0.118308 0.0591542 0.998249i \(-0.481160\pi\)
0.0591542 + 0.998249i \(0.481160\pi\)
\(644\) −5.00000 −0.197028
\(645\) 0 0
\(646\) 12.0000 0.472134
\(647\) 27.0000 1.06148 0.530740 0.847535i \(-0.321914\pi\)
0.530740 + 0.847535i \(0.321914\pi\)
\(648\) 1.00000 0.0392837
\(649\) 14.0000 0.549548
\(650\) 0 0
\(651\) 5.00000 0.195965
\(652\) 8.00000 0.313304
\(653\) −2.00000 −0.0782660 −0.0391330 0.999234i \(-0.512460\pi\)
−0.0391330 + 0.999234i \(0.512460\pi\)
\(654\) 10.0000 0.391031
\(655\) 0 0
\(656\) 2.00000 0.0780869
\(657\) 7.00000 0.273096
\(658\) 20.0000 0.779681
\(659\) 10.0000 0.389545 0.194772 0.980848i \(-0.437603\pi\)
0.194772 + 0.980848i \(0.437603\pi\)
\(660\) 0 0
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) 28.0000 1.08825
\(663\) 0 0
\(664\) 10.0000 0.388075
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 6.00000 0.232321
\(668\) 9.00000 0.348220
\(669\) −8.00000 −0.309298
\(670\) 0 0
\(671\) −14.0000 −0.540464
\(672\) −5.00000 −0.192879
\(673\) 6.00000 0.231283 0.115642 0.993291i \(-0.463108\pi\)
0.115642 + 0.993291i \(0.463108\pi\)
\(674\) 10.0000 0.385186
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) −11.0000 −0.422764 −0.211382 0.977403i \(-0.567796\pi\)
−0.211382 + 0.977403i \(0.567796\pi\)
\(678\) 9.00000 0.345643
\(679\) 50.0000 1.91882
\(680\) 0 0
\(681\) −29.0000 −1.11128
\(682\) 1.00000 0.0382920
\(683\) 31.0000 1.18618 0.593091 0.805135i \(-0.297907\pi\)
0.593091 + 0.805135i \(0.297907\pi\)
\(684\) 3.00000 0.114708
\(685\) 0 0
\(686\) −55.0000 −2.09991
\(687\) 23.0000 0.877505
\(688\) 1.00000 0.0381246
\(689\) 0 0
\(690\) 0 0
\(691\) −5.00000 −0.190209 −0.0951045 0.995467i \(-0.530319\pi\)
−0.0951045 + 0.995467i \(0.530319\pi\)
\(692\) 2.00000 0.0760286
\(693\) 5.00000 0.189934
\(694\) −30.0000 −1.13878
\(695\) 0 0
\(696\) 6.00000 0.227429
\(697\) 8.00000 0.303022
\(698\) −32.0000 −1.21122
\(699\) −13.0000 −0.491705
\(700\) 0 0
\(701\) 35.0000 1.32193 0.660966 0.750416i \(-0.270147\pi\)
0.660966 + 0.750416i \(0.270147\pi\)
\(702\) 0 0
\(703\) 12.0000 0.452589
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 8.00000 0.301084
\(707\) −35.0000 −1.31631
\(708\) −14.0000 −0.526152
\(709\) 21.0000 0.788672 0.394336 0.918966i \(-0.370975\pi\)
0.394336 + 0.918966i \(0.370975\pi\)
\(710\) 0 0
\(711\) 15.0000 0.562544
\(712\) −1.00000 −0.0374766
\(713\) −1.00000 −0.0374503
\(714\) −20.0000 −0.748481
\(715\) 0 0
\(716\) −8.00000 −0.298974
\(717\) −22.0000 −0.821605
\(718\) −15.0000 −0.559795
\(719\) 50.0000 1.86469 0.932343 0.361576i \(-0.117761\pi\)
0.932343 + 0.361576i \(0.117761\pi\)
\(720\) 0 0
\(721\) −40.0000 −1.48968
\(722\) −10.0000 −0.372161
\(723\) 4.00000 0.148762
\(724\) 11.0000 0.408812
\(725\) 0 0
\(726\) −10.0000 −0.371135
\(727\) 27.0000 1.00137 0.500687 0.865628i \(-0.333081\pi\)
0.500687 + 0.865628i \(0.333081\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 4.00000 0.147945
\(732\) 14.0000 0.517455
\(733\) −34.0000 −1.25582 −0.627909 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) −26.0000 −0.959678
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) 10.0000 0.368355
\(738\) 2.00000 0.0736210
\(739\) 46.0000 1.69214 0.846069 0.533074i \(-0.178963\pi\)
0.846069 + 0.533074i \(0.178963\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 15.0000 0.550667
\(743\) −21.0000 −0.770415 −0.385208 0.922830i \(-0.625870\pi\)
−0.385208 + 0.922830i \(0.625870\pi\)
\(744\) −1.00000 −0.0366618
\(745\) 0 0
\(746\) 3.00000 0.109838
\(747\) 10.0000 0.365881
\(748\) −4.00000 −0.146254
\(749\) 45.0000 1.64426
\(750\) 0 0
\(751\) 2.00000 0.0729810 0.0364905 0.999334i \(-0.488382\pi\)
0.0364905 + 0.999334i \(0.488382\pi\)
\(752\) −4.00000 −0.145865
\(753\) −12.0000 −0.437304
\(754\) 0 0
\(755\) 0 0
\(756\) −5.00000 −0.181848
\(757\) 4.00000 0.145382 0.0726912 0.997354i \(-0.476841\pi\)
0.0726912 + 0.997354i \(0.476841\pi\)
\(758\) −19.0000 −0.690111
\(759\) −1.00000 −0.0362977
\(760\) 0 0
\(761\) −21.0000 −0.761249 −0.380625 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) 16.0000 0.579619
\(763\) −50.0000 −1.81012
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) 20.0000 0.722629
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −27.0000 −0.973645 −0.486822 0.873501i \(-0.661844\pi\)
−0.486822 + 0.873501i \(0.661844\pi\)
\(770\) 0 0
\(771\) −3.00000 −0.108042
\(772\) 10.0000 0.359908
\(773\) 51.0000 1.83434 0.917171 0.398493i \(-0.130467\pi\)
0.917171 + 0.398493i \(0.130467\pi\)
\(774\) 1.00000 0.0359443
\(775\) 0 0
\(776\) −10.0000 −0.358979
\(777\) −20.0000 −0.717496
\(778\) −16.0000 −0.573628
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) −9.00000 −0.322045
\(782\) 4.00000 0.143040
\(783\) 6.00000 0.214423
\(784\) 18.0000 0.642857
\(785\) 0 0
\(786\) 18.0000 0.642039
\(787\) 25.0000 0.891154 0.445577 0.895244i \(-0.352999\pi\)
0.445577 + 0.895244i \(0.352999\pi\)
\(788\) 2.00000 0.0712470
\(789\) −8.00000 −0.284808
\(790\) 0 0
\(791\) −45.0000 −1.60002
\(792\) −1.00000 −0.0355335
\(793\) 0 0
\(794\) −17.0000 −0.603307
\(795\) 0 0
\(796\) −9.00000 −0.318997
\(797\) 34.0000 1.20434 0.602171 0.798367i \(-0.294303\pi\)
0.602171 + 0.798367i \(0.294303\pi\)
\(798\) −15.0000 −0.530994
\(799\) −16.0000 −0.566039
\(800\) 0 0
\(801\) −1.00000 −0.0353333
\(802\) −29.0000 −1.02403
\(803\) −7.00000 −0.247025
\(804\) −10.0000 −0.352673
\(805\) 0 0
\(806\) 0 0
\(807\) 30.0000 1.05605
\(808\) 7.00000 0.246259
\(809\) 15.0000 0.527372 0.263686 0.964609i \(-0.415062\pi\)
0.263686 + 0.964609i \(0.415062\pi\)
\(810\) 0 0
\(811\) −17.0000 −0.596951 −0.298475 0.954417i \(-0.596478\pi\)
−0.298475 + 0.954417i \(0.596478\pi\)
\(812\) −30.0000 −1.05279
\(813\) 13.0000 0.455930
\(814\) −4.00000 −0.140200
\(815\) 0 0
\(816\) 4.00000 0.140028
\(817\) 3.00000 0.104957
\(818\) −16.0000 −0.559427
\(819\) 0 0
\(820\) 0 0
\(821\) 10.0000 0.349002 0.174501 0.984657i \(-0.444169\pi\)
0.174501 + 0.984657i \(0.444169\pi\)
\(822\) 6.00000 0.209274
\(823\) −18.0000 −0.627441 −0.313720 0.949515i \(-0.601575\pi\)
−0.313720 + 0.949515i \(0.601575\pi\)
\(824\) 8.00000 0.278693
\(825\) 0 0
\(826\) 70.0000 2.43561
\(827\) 34.0000 1.18230 0.591148 0.806563i \(-0.298675\pi\)
0.591148 + 0.806563i \(0.298675\pi\)
\(828\) 1.00000 0.0347524
\(829\) 39.0000 1.35453 0.677263 0.735741i \(-0.263166\pi\)
0.677263 + 0.735741i \(0.263166\pi\)
\(830\) 0 0
\(831\) −26.0000 −0.901930
\(832\) 0 0
\(833\) 72.0000 2.49465
\(834\) 4.00000 0.138509
\(835\) 0 0
\(836\) −3.00000 −0.103757
\(837\) −1.00000 −0.0345651
\(838\) 26.0000 0.898155
\(839\) −35.0000 −1.20833 −0.604167 0.796858i \(-0.706494\pi\)
−0.604167 + 0.796858i \(0.706494\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 22.0000 0.758170
\(843\) 0 0
\(844\) −21.0000 −0.722850
\(845\) 0 0
\(846\) −4.00000 −0.137523
\(847\) 50.0000 1.71802
\(848\) −3.00000 −0.103020
\(849\) −22.0000 −0.755038
\(850\) 0 0
\(851\) 4.00000 0.137118
\(852\) 9.00000 0.308335
\(853\) −49.0000 −1.67773 −0.838864 0.544341i \(-0.816780\pi\)
−0.838864 + 0.544341i \(0.816780\pi\)
\(854\) −70.0000 −2.39535
\(855\) 0 0
\(856\) −9.00000 −0.307614
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) −40.0000 −1.36478 −0.682391 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(860\) 0 0
\(861\) −10.0000 −0.340799
\(862\) 8.00000 0.272481
\(863\) −57.0000 −1.94030 −0.970151 0.242500i \(-0.922032\pi\)
−0.970151 + 0.242500i \(0.922032\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) −11.0000 −0.373795
\(867\) −1.00000 −0.0339618
\(868\) 5.00000 0.169711
\(869\) −15.0000 −0.508840
\(870\) 0 0
\(871\) 0 0
\(872\) 10.0000 0.338643
\(873\) −10.0000 −0.338449
\(874\) 3.00000 0.101477
\(875\) 0 0
\(876\) 7.00000 0.236508
\(877\) −34.0000 −1.14810 −0.574049 0.818821i \(-0.694628\pi\)
−0.574049 + 0.818821i \(0.694628\pi\)
\(878\) 36.0000 1.21494
\(879\) −30.0000 −1.01187
\(880\) 0 0
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) 18.0000 0.606092
\(883\) 39.0000 1.31245 0.656227 0.754563i \(-0.272151\pi\)
0.656227 + 0.754563i \(0.272151\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −15.0000 −0.503935
\(887\) −48.0000 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) 4.00000 0.134231
\(889\) −80.0000 −2.68311
\(890\) 0 0
\(891\) −1.00000 −0.0335013
\(892\) −8.00000 −0.267860
\(893\) −12.0000 −0.401565
\(894\) 1.00000 0.0334450
\(895\) 0 0
\(896\) −5.00000 −0.167038
\(897\) 0 0
\(898\) 6.00000 0.200223
\(899\) −6.00000 −0.200111
\(900\) 0 0
\(901\) −12.0000 −0.399778
\(902\) −2.00000 −0.0665927
\(903\) −5.00000 −0.166390
\(904\) 9.00000 0.299336
\(905\) 0 0
\(906\) −8.00000 −0.265782
\(907\) −24.0000 −0.796907 −0.398453 0.917189i \(-0.630453\pi\)
−0.398453 + 0.917189i \(0.630453\pi\)
\(908\) −29.0000 −0.962399
\(909\) 7.00000 0.232175
\(910\) 0 0
\(911\) 18.0000 0.596367 0.298183 0.954509i \(-0.403619\pi\)
0.298183 + 0.954509i \(0.403619\pi\)
\(912\) 3.00000 0.0993399
\(913\) −10.0000 −0.330952
\(914\) 10.0000 0.330771
\(915\) 0 0
\(916\) 23.0000 0.759941
\(917\) −90.0000 −2.97206
\(918\) 4.00000 0.132020
\(919\) 24.0000 0.791687 0.395843 0.918318i \(-0.370452\pi\)
0.395843 + 0.918318i \(0.370452\pi\)
\(920\) 0 0
\(921\) −12.0000 −0.395413
\(922\) 24.0000 0.790398
\(923\) 0 0
\(924\) 5.00000 0.164488
\(925\) 0 0
\(926\) 6.00000 0.197172
\(927\) 8.00000 0.262754
\(928\) 6.00000 0.196960
\(929\) 33.0000 1.08269 0.541347 0.840799i \(-0.317914\pi\)
0.541347 + 0.840799i \(0.317914\pi\)
\(930\) 0 0
\(931\) 54.0000 1.76978
\(932\) −13.0000 −0.425829
\(933\) 0 0
\(934\) 12.0000 0.392652
\(935\) 0 0
\(936\) 0 0
\(937\) 38.0000 1.24141 0.620703 0.784046i \(-0.286847\pi\)
0.620703 + 0.784046i \(0.286847\pi\)
\(938\) 50.0000 1.63256
\(939\) −26.0000 −0.848478
\(940\) 0 0
\(941\) −52.0000 −1.69515 −0.847576 0.530674i \(-0.821939\pi\)
−0.847576 + 0.530674i \(0.821939\pi\)
\(942\) −1.00000 −0.0325818
\(943\) 2.00000 0.0651290
\(944\) −14.0000 −0.455661
\(945\) 0 0
\(946\) −1.00000 −0.0325128
\(947\) −18.0000 −0.584921 −0.292461 0.956278i \(-0.594474\pi\)
−0.292461 + 0.956278i \(0.594474\pi\)
\(948\) 15.0000 0.487177
\(949\) 0 0
\(950\) 0 0
\(951\) 22.0000 0.713399
\(952\) −20.0000 −0.648204
\(953\) −4.00000 −0.129573 −0.0647864 0.997899i \(-0.520637\pi\)
−0.0647864 + 0.997899i \(0.520637\pi\)
\(954\) −3.00000 −0.0971286
\(955\) 0 0
\(956\) −22.0000 −0.711531
\(957\) −6.00000 −0.193952
\(958\) 29.0000 0.936947
\(959\) −30.0000 −0.968751
\(960\) 0 0
\(961\) 1.00000 0.0322581
\(962\) 0 0
\(963\) −9.00000 −0.290021
\(964\) 4.00000 0.128831
\(965\) 0 0
\(966\) −5.00000 −0.160872
\(967\) −28.0000 −0.900419 −0.450210 0.892923i \(-0.648651\pi\)
−0.450210 + 0.892923i \(0.648651\pi\)
\(968\) −10.0000 −0.321412
\(969\) 12.0000 0.385496
\(970\) 0 0
\(971\) −6.00000 −0.192549 −0.0962746 0.995355i \(-0.530693\pi\)
−0.0962746 + 0.995355i \(0.530693\pi\)
\(972\) 1.00000 0.0320750
\(973\) −20.0000 −0.641171
\(974\) −36.0000 −1.15351
\(975\) 0 0
\(976\) 14.0000 0.448129
\(977\) 30.0000 0.959785 0.479893 0.877327i \(-0.340676\pi\)
0.479893 + 0.877327i \(0.340676\pi\)
\(978\) 8.00000 0.255812
\(979\) 1.00000 0.0319601
\(980\) 0 0
\(981\) 10.0000 0.319275
\(982\) 27.0000 0.861605
\(983\) −28.0000 −0.893061 −0.446531 0.894768i \(-0.647341\pi\)
−0.446531 + 0.894768i \(0.647341\pi\)
\(984\) 2.00000 0.0637577
\(985\) 0 0
\(986\) 24.0000 0.764316
\(987\) 20.0000 0.636607
\(988\) 0 0
\(989\) 1.00000 0.0317982
\(990\) 0 0
\(991\) −17.0000 −0.540023 −0.270011 0.962857i \(-0.587027\pi\)
−0.270011 + 0.962857i \(0.587027\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 28.0000 0.888553
\(994\) −45.0000 −1.42731
\(995\) 0 0
\(996\) 10.0000 0.316862
\(997\) −6.00000 −0.190022 −0.0950110 0.995476i \(-0.530289\pi\)
−0.0950110 + 0.995476i \(0.530289\pi\)
\(998\) −42.0000 −1.32949
\(999\) 4.00000 0.126554
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.bi.1.1 1
5.2 odd 4 930.2.d.c.559.2 yes 2
5.3 odd 4 930.2.d.c.559.1 2
5.4 even 2 4650.2.a.m.1.1 1
15.2 even 4 2790.2.d.e.559.1 2
15.8 even 4 2790.2.d.e.559.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.d.c.559.1 2 5.3 odd 4
930.2.d.c.559.2 yes 2 5.2 odd 4
2790.2.d.e.559.1 2 15.2 even 4
2790.2.d.e.559.2 2 15.8 even 4
4650.2.a.m.1.1 1 5.4 even 2
4650.2.a.bi.1.1 1 1.1 even 1 trivial