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Properties

Label 930.2.a.k.1.1
Level $930$
Weight $2$
Character 930.1
Self dual yes
Analytic conductor $7.426$
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] = [930,2,Mod(1,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, 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("930.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.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: \(7.42608738798\)
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 \(\chi\) \(=\) 930.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +4.00000 q^{13} -2.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} -1.00000 q^{20} +2.00000 q^{21} -1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} -2.00000 q^{28} +8.00000 q^{29} +1.00000 q^{30} -1.00000 q^{31} +1.00000 q^{32} +6.00000 q^{34} +2.00000 q^{35} +1.00000 q^{36} +4.00000 q^{37} -4.00000 q^{39} -1.00000 q^{40} +10.0000 q^{41} +2.00000 q^{42} +8.00000 q^{43} -1.00000 q^{45} -4.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} -6.00000 q^{51} +4.00000 q^{52} -14.0000 q^{53} -1.00000 q^{54} -2.00000 q^{56} +8.00000 q^{58} +14.0000 q^{59} +1.00000 q^{60} -6.00000 q^{61} -1.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} -10.0000 q^{67} +6.00000 q^{68} +2.00000 q^{70} +6.00000 q^{71} +1.00000 q^{72} -8.00000 q^{73} +4.00000 q^{74} -1.00000 q^{75} -4.00000 q^{78} +8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} -12.0000 q^{83} +2.00000 q^{84} -6.00000 q^{85} +8.00000 q^{86} -8.00000 q^{87} +16.0000 q^{89} -1.00000 q^{90} -8.00000 q^{91} +1.00000 q^{93} -4.00000 q^{94} -1.00000 q^{96} -10.0000 q^{97} -3.00000 q^{98} +O(q^{100})\)

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
\(5\) −1.00000 −0.447214
\(6\) −1.00000 −0.408248
\(7\) −2.00000 −0.755929 −0.377964 − 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −1.00000 −0.288675
\(13\) 4.00000 1.10940 0.554700 − 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) −2.00000 −0.534522
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 6.00000 1.45521 0.727607 − 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 1.00000 0.235702
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −1.00000 −0.223607
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 4.00000 0.784465
\(27\) −1.00000 −0.192450
\(28\) −2.00000 −0.377964
\(29\) 8.00000 1.48556 0.742781 − 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 1.00000 0.182574
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 2.00000 0.338062
\(36\) 1.00000 0.166667
\(37\) 4.00000 0.657596 0.328798 − 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) −4.00000 −0.640513
\(40\) −1.00000 −0.158114
\(41\) 10.0000 1.56174 0.780869 − 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 2.00000 0.308607
\(43\) 8.00000 1.21999 0.609994 − 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) −4.00000 −0.583460 −0.291730 − 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.00000 −0.428571
\(50\) 1.00000 0.141421
\(51\) −6.00000 −0.840168
\(52\) 4.00000 0.554700
\(53\) −14.0000 −1.92305 −0.961524 − 0.274721i \(-0.911414\pi\)
−0.961524 + 0.274721i \(0.911414\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) 0 0
\(58\) 8.00000 1.05045
\(59\) 14.0000 1.82264 0.911322 − 0.411693i \(-0.135063\pi\)
0.911322 + 0.411693i \(0.135063\pi\)
\(60\) 1.00000 0.129099
\(61\) −6.00000 −0.768221 −0.384111 − 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) −1.00000 −0.127000
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) −4.00000 −0.496139
\(66\) 0 0
\(67\) −10.0000 −1.22169 −0.610847 − 0.791748i \(-0.709171\pi\)
−0.610847 + 0.791748i \(0.709171\pi\)
\(68\) 6.00000 0.727607
\(69\) 0 0
\(70\) 2.00000 0.239046
\(71\) 6.00000 0.712069 0.356034 − 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 1.00000 0.117851
\(73\) −8.00000 −0.936329 −0.468165 − 0.883641i \(-0.655085\pi\)
−0.468165 + 0.883641i \(0.655085\pi\)
\(74\) 4.00000 0.464991
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) 8.00000 0.900070 0.450035 − 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 10.0000 1.10432
\(83\) −12.0000 −1.31717 −0.658586 − 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 2.00000 0.218218
\(85\) −6.00000 −0.650791
\(86\) 8.00000 0.862662
\(87\) −8.00000 −0.857690
\(88\) 0 0
\(89\) 16.0000 1.69600 0.847998 − 0.529999i \(-0.177808\pi\)
0.847998 + 0.529999i \(0.177808\pi\)
\(90\) −1.00000 −0.105409
\(91\) −8.00000 −0.838628
\(92\) 0 0
\(93\) 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 \(0.669494\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −6.00000 −0.597022 −0.298511 − 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) −6.00000 −0.594089
\(103\) −6.00000 −0.591198 −0.295599 − 0.955312i \(-0.595519\pi\)
−0.295599 + 0.955312i \(0.595519\pi\)
\(104\) 4.00000 0.392232
\(105\) −2.00000 −0.195180
\(106\) −14.0000 −1.35980
\(107\) 8.00000 0.773389 0.386695 − 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 18.0000 1.72409 0.862044 − 0.506834i \(-0.169184\pi\)
0.862044 + 0.506834i \(0.169184\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) −2.00000 −0.188982
\(113\) 14.0000 1.31701 0.658505 − 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 8.00000 0.742781
\(117\) 4.00000 0.369800
\(118\) 14.0000 1.28880
\(119\) −12.0000 −1.10004
\(120\) 1.00000 0.0912871
\(121\) −11.0000 −1.00000
\(122\) −6.00000 −0.543214
\(123\) −10.0000 −0.901670
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) −2.00000 −0.178174
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 1.00000 0.0883883
\(129\) −8.00000 −0.704361
\(130\) −4.00000 −0.350823
\(131\) −18.0000 −1.57267 −0.786334 − 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −10.0000 −0.863868
\(135\) 1.00000 0.0860663
\(136\) 6.00000 0.514496
\(137\) −6.00000 −0.512615 −0.256307 − 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 − 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 2.00000 0.169031
\(141\) 4.00000 0.336861
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −8.00000 −0.664364
\(146\) −8.00000 −0.662085
\(147\) 3.00000 0.247436
\(148\) 4.00000 0.328798
\(149\) 18.0000 1.47462 0.737309 − 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) −1.00000 −0.0816497
\(151\) −8.00000 −0.651031 −0.325515 − 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 1.00000 0.0803219
\(156\) −4.00000 −0.320256
\(157\) −18.0000 −1.43656 −0.718278 − 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 8.00000 0.636446
\(159\) 14.0000 1.11027
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 6.00000 0.469956 0.234978 − 0.972001i \(-0.424498\pi\)
0.234978 + 0.972001i \(0.424498\pi\)
\(164\) 10.0000 0.780869
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) −8.00000 −0.619059 −0.309529 − 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 2.00000 0.154303
\(169\) 3.00000 0.230769
\(170\) −6.00000 −0.460179
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) 10.0000 0.760286 0.380143 − 0.924928i \(-0.375875\pi\)
0.380143 + 0.924928i \(0.375875\pi\)
\(174\) −8.00000 −0.606478
\(175\) −2.00000 −0.151186
\(176\) 0 0
\(177\) −14.0000 −1.05230
\(178\) 16.0000 1.19925
\(179\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −6.00000 −0.445976 −0.222988 − 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) −8.00000 −0.592999
\(183\) 6.00000 0.443533
\(184\) 0 0
\(185\) −4.00000 −0.294086
\(186\) 1.00000 0.0733236
\(187\) 0 0
\(188\) −4.00000 −0.291730
\(189\) 2.00000 0.145479
\(190\) 0 0
\(191\) −14.0000 −1.01300 −0.506502 − 0.862239i \(-0.669062\pi\)
−0.506502 + 0.862239i \(0.669062\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −2.00000 −0.143963 −0.0719816 − 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) −10.0000 −0.717958
\(195\) 4.00000 0.286446
\(196\) −3.00000 −0.214286
\(197\) −2.00000 −0.142494 −0.0712470 − 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) −24.0000 −1.70131 −0.850657 − 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 1.00000 0.0707107
\(201\) 10.0000 0.705346
\(202\) −6.00000 −0.422159
\(203\) −16.0000 −1.12298
\(204\) −6.00000 −0.420084
\(205\) −10.0000 −0.698430
\(206\) −6.00000 −0.418040
\(207\) 0 0
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) −2.00000 −0.138013
\(211\) 16.0000 1.10149 0.550743 − 0.834675i \(-0.314345\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) −14.0000 −0.961524
\(213\) −6.00000 −0.411113
\(214\) 8.00000 0.546869
\(215\) −8.00000 −0.545595
\(216\) −1.00000 −0.0680414
\(217\) 2.00000 0.135769
\(218\) 18.0000 1.21911
\(219\) 8.00000 0.540590
\(220\) 0 0
\(221\) 24.0000 1.61441
\(222\) −4.00000 −0.268462
\(223\) −20.0000 −1.33930 −0.669650 − 0.742677i \(-0.733556\pi\)
−0.669650 + 0.742677i \(0.733556\pi\)
\(224\) −2.00000 −0.133631
\(225\) 1.00000 0.0666667
\(226\) 14.0000 0.931266
\(227\) 12.0000 0.796468 0.398234 − 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 0 0
\(229\) −10.0000 −0.660819 −0.330409 − 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.00000 0.525226
\(233\) −14.0000 −0.917170 −0.458585 − 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) 4.00000 0.261488
\(235\) 4.00000 0.260931
\(236\) 14.0000 0.911322
\(237\) −8.00000 −0.519656
\(238\) −12.0000 −0.777844
\(239\) −12.0000 −0.776215 −0.388108 − 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 1.00000 0.0645497
\(241\) −14.0000 −0.901819 −0.450910 − 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) −11.0000 −0.707107
\(243\) −1.00000 −0.0641500
\(244\) −6.00000 −0.384111
\(245\) 3.00000 0.191663
\(246\) −10.0000 −0.637577
\(247\) 0 0
\(248\) −1.00000 −0.0635001
\(249\) 12.0000 0.760469
\(250\) −1.00000 −0.0632456
\(251\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) 0 0
\(255\) 6.00000 0.375735
\(256\) 1.00000 0.0625000
\(257\) 2.00000 0.124757 0.0623783 − 0.998053i \(-0.480131\pi\)
0.0623783 + 0.998053i \(0.480131\pi\)
\(258\) −8.00000 −0.498058
\(259\) −8.00000 −0.497096
\(260\) −4.00000 −0.248069
\(261\) 8.00000 0.495188
\(262\) −18.0000 −1.11204
\(263\) 16.0000 0.986602 0.493301 − 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) 14.0000 0.860013
\(266\) 0 0
\(267\) −16.0000 −0.979184
\(268\) −10.0000 −0.610847
\(269\) 24.0000 1.46331 0.731653 − 0.681677i \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) 1.00000 0.0608581
\(271\) −16.0000 −0.971931 −0.485965 − 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 6.00000 0.363803
\(273\) 8.00000 0.484182
\(274\) −6.00000 −0.362473
\(275\) 0 0
\(276\) 0 0
\(277\) 16.0000 0.961347 0.480673 − 0.876900i \(-0.340392\pi\)
0.480673 + 0.876900i \(0.340392\pi\)
\(278\) 4.00000 0.239904
\(279\) −1.00000 −0.0598684
\(280\) 2.00000 0.119523
\(281\) 30.0000 1.78965 0.894825 − 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 4.00000 0.238197
\(283\) 14.0000 0.832214 0.416107 − 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) 0 0
\(287\) −20.0000 −1.18056
\(288\) 1.00000 0.0589256
\(289\) 19.0000 1.11765
\(290\) −8.00000 −0.469776
\(291\) 10.0000 0.586210
\(292\) −8.00000 −0.468165
\(293\) 6.00000 0.350524 0.175262 − 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 3.00000 0.174964
\(295\) −14.0000 −0.815112
\(296\) 4.00000 0.232495
\(297\) 0 0
\(298\) 18.0000 1.04271
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) −16.0000 −0.922225
\(302\) −8.00000 −0.460348
\(303\) 6.00000 0.344691
\(304\) 0 0
\(305\) 6.00000 0.343559
\(306\) 6.00000 0.342997
\(307\) 10.0000 0.570730 0.285365 − 0.958419i \(-0.407885\pi\)
0.285365 + 0.958419i \(0.407885\pi\)
\(308\) 0 0
\(309\) 6.00000 0.341328
\(310\) 1.00000 0.0567962
\(311\) 18.0000 1.02069 0.510343 − 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) −4.00000 −0.226455
\(313\) −16.0000 −0.904373 −0.452187 − 0.891923i \(-0.649356\pi\)
−0.452187 + 0.891923i \(0.649356\pi\)
\(314\) −18.0000 −1.01580
\(315\) 2.00000 0.112687
\(316\) 8.00000 0.450035
\(317\) −10.0000 −0.561656 −0.280828 − 0.959758i \(-0.590609\pi\)
−0.280828 + 0.959758i \(0.590609\pi\)
\(318\) 14.0000 0.785081
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) −8.00000 −0.446516
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 4.00000 0.221880
\(326\) 6.00000 0.332309
\(327\) −18.0000 −0.995402
\(328\) 10.0000 0.552158
\(329\) 8.00000 0.441054
\(330\) 0 0
\(331\) −12.0000 −0.659580 −0.329790 − 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) −12.0000 −0.658586
\(333\) 4.00000 0.219199
\(334\) −8.00000 −0.437741
\(335\) 10.0000 0.546358
\(336\) 2.00000 0.109109
\(337\) 4.00000 0.217894 0.108947 − 0.994048i \(-0.465252\pi\)
0.108947 + 0.994048i \(0.465252\pi\)
\(338\) 3.00000 0.163178
\(339\) −14.0000 −0.760376
\(340\) −6.00000 −0.325396
\(341\) 0 0
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) 10.0000 0.537603
\(347\) 20.0000 1.07366 0.536828 − 0.843692i \(-0.319622\pi\)
0.536828 + 0.843692i \(0.319622\pi\)
\(348\) −8.00000 −0.428845
\(349\) 2.00000 0.107058 0.0535288 − 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) −2.00000 −0.106904
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) 14.0000 0.745145 0.372572 − 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) −14.0000 −0.744092
\(355\) −6.00000 −0.318447
\(356\) 16.0000 0.847998
\(357\) 12.0000 0.635107
\(358\) 0 0
\(359\) 18.0000 0.950004 0.475002 − 0.879985i \(-0.342447\pi\)
0.475002 + 0.879985i \(0.342447\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −19.0000 −1.00000
\(362\) −6.00000 −0.315353
\(363\) 11.0000 0.577350
\(364\) −8.00000 −0.419314
\(365\) 8.00000 0.418739
\(366\) 6.00000 0.313625
\(367\) −36.0000 −1.87918 −0.939592 − 0.342296i \(-0.888796\pi\)
−0.939592 + 0.342296i \(0.888796\pi\)
\(368\) 0 0
\(369\) 10.0000 0.520579
\(370\) −4.00000 −0.207950
\(371\) 28.0000 1.45369
\(372\) 1.00000 0.0518476
\(373\) 6.00000 0.310668 0.155334 − 0.987862i \(-0.450355\pi\)
0.155334 + 0.987862i \(0.450355\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) −4.00000 −0.206284
\(377\) 32.0000 1.64808
\(378\) 2.00000 0.102869
\(379\) 8.00000 0.410932 0.205466 − 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −14.0000 −0.716302
\(383\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) 8.00000 0.406663
\(388\) −10.0000 −0.507673
\(389\) −32.0000 −1.62246 −0.811232 − 0.584724i \(-0.801203\pi\)
−0.811232 + 0.584724i \(0.801203\pi\)
\(390\) 4.00000 0.202548
\(391\) 0 0
\(392\) −3.00000 −0.151523
\(393\) 18.0000 0.907980
\(394\) −2.00000 −0.100759
\(395\) −8.00000 −0.402524
\(396\) 0 0
\(397\) 18.0000 0.903394 0.451697 − 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 4.00000 0.199750 0.0998752 − 0.995000i \(-0.468156\pi\)
0.0998752 + 0.995000i \(0.468156\pi\)
\(402\) 10.0000 0.498755
\(403\) −4.00000 −0.199254
\(404\) −6.00000 −0.298511
\(405\) −1.00000 −0.0496904
\(406\) −16.0000 −0.794067
\(407\) 0 0
\(408\) −6.00000 −0.297044
\(409\) 30.0000 1.48340 0.741702 − 0.670729i \(-0.234019\pi\)
0.741702 + 0.670729i \(0.234019\pi\)
\(410\) −10.0000 −0.493865
\(411\) 6.00000 0.295958
\(412\) −6.00000 −0.295599
\(413\) −28.0000 −1.37779
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) 4.00000 0.196116
\(417\) −4.00000 −0.195881
\(418\) 0 0
\(419\) −6.00000 −0.293119 −0.146560 − 0.989202i \(-0.546820\pi\)
−0.146560 + 0.989202i \(0.546820\pi\)
\(420\) −2.00000 −0.0975900
\(421\) −6.00000 −0.292422 −0.146211 − 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) 16.0000 0.778868
\(423\) −4.00000 −0.194487
\(424\) −14.0000 −0.679900
\(425\) 6.00000 0.291043
\(426\) −6.00000 −0.290701
\(427\) 12.0000 0.580721
\(428\) 8.00000 0.386695
\(429\) 0 0
\(430\) −8.00000 −0.385794
\(431\) −6.00000 −0.289010 −0.144505 − 0.989504i \(-0.546159\pi\)
−0.144505 + 0.989504i \(0.546159\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −16.0000 −0.768911 −0.384455 − 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 2.00000 0.0960031
\(435\) 8.00000 0.383571
\(436\) 18.0000 0.862044
\(437\) 0 0
\(438\) 8.00000 0.382255
\(439\) 24.0000 1.14546 0.572729 − 0.819745i \(-0.305885\pi\)
0.572729 + 0.819745i \(0.305885\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 24.0000 1.14156
\(443\) −36.0000 −1.71041 −0.855206 − 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) −4.00000 −0.189832
\(445\) −16.0000 −0.758473
\(446\) −20.0000 −0.947027
\(447\) −18.0000 −0.851371
\(448\) −2.00000 −0.0944911
\(449\) −20.0000 −0.943858 −0.471929 − 0.881636i \(-0.656442\pi\)
−0.471929 + 0.881636i \(0.656442\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) 14.0000 0.658505
\(453\) 8.00000 0.375873
\(454\) 12.0000 0.563188
\(455\) 8.00000 0.375046
\(456\) 0 0
\(457\) 8.00000 0.374224 0.187112 − 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) −10.0000 −0.467269
\(459\) −6.00000 −0.280056
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 − 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 8.00000 0.371391
\(465\) −1.00000 −0.0463739
\(466\) −14.0000 −0.648537
\(467\) −32.0000 −1.48078 −0.740392 − 0.672176i \(-0.765360\pi\)
−0.740392 + 0.672176i \(0.765360\pi\)
\(468\) 4.00000 0.184900
\(469\) 20.0000 0.923514
\(470\) 4.00000 0.184506
\(471\) 18.0000 0.829396
\(472\) 14.0000 0.644402
\(473\) 0 0
\(474\) −8.00000 −0.367452
\(475\) 0 0
\(476\) −12.0000 −0.550019
\(477\) −14.0000 −0.641016
\(478\) −12.0000 −0.548867
\(479\) −42.0000 −1.91903 −0.959514 − 0.281659i \(-0.909115\pi\)
−0.959514 + 0.281659i \(0.909115\pi\)
\(480\) 1.00000 0.0456435
\(481\) 16.0000 0.729537
\(482\) −14.0000 −0.637683
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 10.0000 0.454077
\(486\) −1.00000 −0.0453609
\(487\) −8.00000 −0.362515 −0.181257 − 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) −6.00000 −0.271607
\(489\) −6.00000 −0.271329
\(490\) 3.00000 0.135526
\(491\) 36.0000 1.62466 0.812329 − 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) −10.0000 −0.450835
\(493\) 48.0000 2.16181
\(494\) 0 0
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) −12.0000 −0.538274
\(498\) 12.0000 0.537733
\(499\) 20.0000 0.895323 0.447661 − 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 8.00000 0.357414
\(502\) 0 0
\(503\) −20.0000 −0.891756 −0.445878 − 0.895094i \(-0.647108\pi\)
−0.445878 + 0.895094i \(0.647108\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) −3.00000 −0.133235
\(508\) 0 0
\(509\) 4.00000 0.177297 0.0886484 − 0.996063i \(-0.471745\pi\)
0.0886484 + 0.996063i \(0.471745\pi\)
\(510\) 6.00000 0.265684
\(511\) 16.0000 0.707798
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 2.00000 0.0882162
\(515\) 6.00000 0.264392
\(516\) −8.00000 −0.352180
\(517\) 0 0
\(518\) −8.00000 −0.351500
\(519\) −10.0000 −0.438951
\(520\) −4.00000 −0.175412
\(521\) −6.00000 −0.262865 −0.131432 − 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 8.00000 0.350150
\(523\) 24.0000 1.04945 0.524723 − 0.851273i \(-0.324169\pi\)
0.524723 + 0.851273i \(0.324169\pi\)
\(524\) −18.0000 −0.786334
\(525\) 2.00000 0.0872872
\(526\) 16.0000 0.697633
\(527\) −6.00000 −0.261364
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 14.0000 0.608121
\(531\) 14.0000 0.607548
\(532\) 0 0
\(533\) 40.0000 1.73259
\(534\) −16.0000 −0.692388
\(535\) −8.00000 −0.345870
\(536\) −10.0000 −0.431934
\(537\) 0 0
\(538\) 24.0000 1.03471
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) 18.0000 0.773880 0.386940 − 0.922105i \(-0.373532\pi\)
0.386940 + 0.922105i \(0.373532\pi\)
\(542\) −16.0000 −0.687259
\(543\) 6.00000 0.257485
\(544\) 6.00000 0.257248
\(545\) −18.0000 −0.771035
\(546\) 8.00000 0.342368
\(547\) 6.00000 0.256541 0.128271 − 0.991739i \(-0.459057\pi\)
0.128271 + 0.991739i \(0.459057\pi\)
\(548\) −6.00000 −0.256307
\(549\) −6.00000 −0.256074
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −16.0000 −0.680389
\(554\) 16.0000 0.679775
\(555\) 4.00000 0.169791
\(556\) 4.00000 0.169638
\(557\) −30.0000 −1.27114 −0.635570 − 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) −1.00000 −0.0423334
\(559\) 32.0000 1.35346
\(560\) 2.00000 0.0845154
\(561\) 0 0
\(562\) 30.0000 1.26547
\(563\) −32.0000 −1.34864 −0.674320 − 0.738440i \(-0.735563\pi\)
−0.674320 + 0.738440i \(0.735563\pi\)
\(564\) 4.00000 0.168430
\(565\) −14.0000 −0.588984
\(566\) 14.0000 0.588464
\(567\) −2.00000 −0.0839921
\(568\) 6.00000 0.251754
\(569\) 4.00000 0.167689 0.0838444 − 0.996479i \(-0.473280\pi\)
0.0838444 + 0.996479i \(0.473280\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 − 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 14.0000 0.584858
\(574\) −20.0000 −0.834784
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −6.00000 −0.249783 −0.124892 − 0.992170i \(-0.539858\pi\)
−0.124892 + 0.992170i \(0.539858\pi\)
\(578\) 19.0000 0.790296
\(579\) 2.00000 0.0831172
\(580\) −8.00000 −0.332182
\(581\) 24.0000 0.995688
\(582\) 10.0000 0.414513
\(583\) 0 0
\(584\) −8.00000 −0.331042
\(585\) −4.00000 −0.165380
\(586\) 6.00000 0.247858
\(587\) 12.0000 0.495293 0.247647 − 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 3.00000 0.123718
\(589\) 0 0
\(590\) −14.0000 −0.576371
\(591\) 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 \(0.460686\pi\)
\(594\) 0 0
\(595\) 12.0000 0.491952
\(596\) 18.0000 0.737309
\(597\) 24.0000 0.982255
\(598\) 0 0
\(599\) 42.0000 1.71607 0.858037 − 0.513588i \(-0.171684\pi\)
0.858037 + 0.513588i \(0.171684\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −10.0000 −0.407909 −0.203954 − 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) −16.0000 −0.652111
\(603\) −10.0000 −0.407231
\(604\) −8.00000 −0.325515
\(605\) 11.0000 0.447214
\(606\) 6.00000 0.243733
\(607\) 2.00000 0.0811775 0.0405887 − 0.999176i \(-0.487077\pi\)
0.0405887 + 0.999176i \(0.487077\pi\)
\(608\) 0 0
\(609\) 16.0000 0.648353
\(610\) 6.00000 0.242933
\(611\) −16.0000 −0.647291
\(612\) 6.00000 0.242536
\(613\) 16.0000 0.646234 0.323117 − 0.946359i \(-0.395269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(614\) 10.0000 0.403567
\(615\) 10.0000 0.403239
\(616\) 0 0
\(617\) 38.0000 1.52982 0.764911 − 0.644136i \(-0.222783\pi\)
0.764911 + 0.644136i \(0.222783\pi\)
\(618\) 6.00000 0.241355
\(619\) 4.00000 0.160774 0.0803868 − 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 1.00000 0.0401610
\(621\) 0 0
\(622\) 18.0000 0.721734
\(623\) −32.0000 −1.28205
\(624\) −4.00000 −0.160128
\(625\) 1.00000 0.0400000
\(626\) −16.0000 −0.639489
\(627\) 0 0
\(628\) −18.0000 −0.718278
\(629\) 24.0000 0.956943
\(630\) 2.00000 0.0796819
\(631\) −8.00000 −0.318475 −0.159237 − 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 8.00000 0.318223
\(633\) −16.0000 −0.635943
\(634\) −10.0000 −0.397151
\(635\) 0 0
\(636\) 14.0000 0.555136
\(637\) −12.0000 −0.475457
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) −1.00000 −0.0395285
\(641\) −44.0000 −1.73790 −0.868948 − 0.494904i \(-0.835203\pi\)
−0.868948 + 0.494904i \(0.835203\pi\)
\(642\) −8.00000 −0.315735
\(643\) −16.0000 −0.630978 −0.315489 − 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 0 0
\(647\) −16.0000 −0.629025 −0.314512 − 0.949253i \(-0.601841\pi\)
−0.314512 + 0.949253i \(0.601841\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 4.00000 0.156893
\(651\) −2.00000 −0.0783862
\(652\) 6.00000 0.234978
\(653\) −10.0000 −0.391330 −0.195665 − 0.980671i \(-0.562687\pi\)
−0.195665 + 0.980671i \(0.562687\pi\)
\(654\) −18.0000 −0.703856
\(655\) 18.0000 0.703318
\(656\) 10.0000 0.390434
\(657\) −8.00000 −0.312110
\(658\) 8.00000 0.311872
\(659\) −30.0000 −1.16863 −0.584317 − 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) −42.0000 −1.63361 −0.816805 − 0.576913i \(-0.804257\pi\)
−0.816805 + 0.576913i \(0.804257\pi\)
\(662\) −12.0000 −0.466393
\(663\) −24.0000 −0.932083
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 0 0
\(668\) −8.00000 −0.309529
\(669\) 20.0000 0.773245
\(670\) 10.0000 0.386334
\(671\) 0 0
\(672\) 2.00000 0.0771517
\(673\) −20.0000 −0.770943 −0.385472 − 0.922720i \(-0.625961\pi\)
−0.385472 + 0.922720i \(0.625961\pi\)
\(674\) 4.00000 0.154074
\(675\) −1.00000 −0.0384900
\(676\) 3.00000 0.115385
\(677\) −22.0000 −0.845529 −0.422764 − 0.906240i \(-0.638940\pi\)
−0.422764 + 0.906240i \(0.638940\pi\)
\(678\) −14.0000 −0.537667
\(679\) 20.0000 0.767530
\(680\) −6.00000 −0.230089
\(681\) −12.0000 −0.459841
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 − 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) 20.0000 0.763604
\(687\) 10.0000 0.381524
\(688\) 8.00000 0.304997
\(689\) −56.0000 −2.13343
\(690\) 0 0
\(691\) −4.00000 −0.152167 −0.0760836 − 0.997101i \(-0.524242\pi\)
−0.0760836 + 0.997101i \(0.524242\pi\)
\(692\) 10.0000 0.380143
\(693\) 0 0
\(694\) 20.0000 0.759190
\(695\) −4.00000 −0.151729
\(696\) −8.00000 −0.303239
\(697\) 60.0000 2.27266
\(698\) 2.00000 0.0757011
\(699\) 14.0000 0.529529
\(700\) −2.00000 −0.0755929
\(701\) 30.0000 1.13308 0.566542 − 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) −4.00000 −0.150970
\(703\) 0 0
\(704\) 0 0
\(705\) −4.00000 −0.150649
\(706\) 14.0000 0.526897
\(707\) 12.0000 0.451306
\(708\) −14.0000 −0.526152
\(709\) 46.0000 1.72757 0.863783 − 0.503864i \(-0.168089\pi\)
0.863783 + 0.503864i \(0.168089\pi\)
\(710\) −6.00000 −0.225176
\(711\) 8.00000 0.300023
\(712\) 16.0000 0.599625
\(713\) 0 0
\(714\) 12.0000 0.449089
\(715\) 0 0
\(716\) 0 0
\(717\) 12.0000 0.448148
\(718\) 18.0000 0.671754
\(719\) −40.0000 −1.49175 −0.745874 − 0.666087i \(-0.767968\pi\)
−0.745874 + 0.666087i \(0.767968\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 12.0000 0.446903
\(722\) −19.0000 −0.707107
\(723\) 14.0000 0.520666
\(724\) −6.00000 −0.222988
\(725\) 8.00000 0.297113
\(726\) 11.0000 0.408248
\(727\) −10.0000 −0.370879 −0.185440 − 0.982656i \(-0.559371\pi\)
−0.185440 + 0.982656i \(0.559371\pi\)
\(728\) −8.00000 −0.296500
\(729\) 1.00000 0.0370370
\(730\) 8.00000 0.296093
\(731\) 48.0000 1.77534
\(732\) 6.00000 0.221766
\(733\) −22.0000 −0.812589 −0.406294 − 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) −36.0000 −1.32878
\(735\) −3.00000 −0.110657
\(736\) 0 0
\(737\) 0 0
\(738\) 10.0000 0.368105
\(739\) 20.0000 0.735712 0.367856 − 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) −4.00000 −0.147043
\(741\) 0 0
\(742\) 28.0000 1.02791
\(743\) 24.0000 0.880475 0.440237 − 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 1.00000 0.0366618
\(745\) −18.0000 −0.659469
\(746\) 6.00000 0.219676
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) −16.0000 −0.584627
\(750\) 1.00000 0.0365148
\(751\) −32.0000 −1.16770 −0.583848 − 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) −4.00000 −0.145865
\(753\) 0 0
\(754\) 32.0000 1.16537
\(755\) 8.00000 0.291150
\(756\) 2.00000 0.0727393
\(757\) −12.0000 −0.436147 −0.218074 − 0.975932i \(-0.569977\pi\)
−0.218074 + 0.975932i \(0.569977\pi\)
\(758\) 8.00000 0.290573
\(759\) 0 0
\(760\) 0 0
\(761\) −20.0000 −0.724999 −0.362500 − 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(762\) 0 0
\(763\) −36.0000 −1.30329
\(764\) −14.0000 −0.506502
\(765\) −6.00000 −0.216930
\(766\) 0 0
\(767\) 56.0000 2.02204
\(768\) −1.00000 −0.0360844
\(769\) 30.0000 1.08183 0.540914 − 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) −2.00000 −0.0720282
\(772\) −2.00000 −0.0719816
\(773\) −46.0000 −1.65451 −0.827253 − 0.561830i \(-0.810097\pi\)
−0.827253 + 0.561830i \(0.810097\pi\)
\(774\) 8.00000 0.287554
\(775\) −1.00000 −0.0359211
\(776\) −10.0000 −0.358979
\(777\) 8.00000 0.286998
\(778\) −32.0000 −1.14726
\(779\) 0 0
\(780\) 4.00000 0.143223
\(781\) 0 0
\(782\) 0 0
\(783\) −8.00000 −0.285897
\(784\) −3.00000 −0.107143
\(785\) 18.0000 0.642448
\(786\) 18.0000 0.642039
\(787\) 44.0000 1.56843 0.784215 − 0.620489i \(-0.213066\pi\)
0.784215 + 0.620489i \(0.213066\pi\)
\(788\) −2.00000 −0.0712470
\(789\) −16.0000 −0.569615
\(790\) −8.00000 −0.284627
\(791\) −28.0000 −0.995565
\(792\) 0 0
\(793\) −24.0000 −0.852265
\(794\) 18.0000 0.638796
\(795\) −14.0000 −0.496529
\(796\) −24.0000 −0.850657
\(797\) −2.00000 −0.0708436 −0.0354218 − 0.999372i \(-0.511277\pi\)
−0.0354218 + 0.999372i \(0.511277\pi\)
\(798\) 0 0
\(799\) −24.0000 −0.849059
\(800\) 1.00000 0.0353553
\(801\) 16.0000 0.565332
\(802\) 4.00000 0.141245
\(803\) 0 0
\(804\) 10.0000 0.352673
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) −24.0000 −0.844840
\(808\) −6.00000 −0.211079
\(809\) 4.00000 0.140633 0.0703163 − 0.997525i \(-0.477599\pi\)
0.0703163 + 0.997525i \(0.477599\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 56.0000 1.96643 0.983213 − 0.182462i \(-0.0584065\pi\)
0.983213 + 0.182462i \(0.0584065\pi\)
\(812\) −16.0000 −0.561490
\(813\) 16.0000 0.561144
\(814\) 0 0
\(815\) −6.00000 −0.210171
\(816\) −6.00000 −0.210042
\(817\) 0 0
\(818\) 30.0000 1.04893
\(819\) −8.00000 −0.279543
\(820\) −10.0000 −0.349215
\(821\) −48.0000 −1.67521 −0.837606 − 0.546275i \(-0.816045\pi\)
−0.837606 + 0.546275i \(0.816045\pi\)
\(822\) 6.00000 0.209274
\(823\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) −6.00000 −0.209020
\(825\) 0 0
\(826\) −28.0000 −0.974245
\(827\) 12.0000 0.417281 0.208640 − 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 0 0
\(829\) 2.00000 0.0694629 0.0347314 − 0.999397i \(-0.488942\pi\)
0.0347314 + 0.999397i \(0.488942\pi\)
\(830\) 12.0000 0.416526
\(831\) −16.0000 −0.555034
\(832\) 4.00000 0.138675
\(833\) −18.0000 −0.623663
\(834\) −4.00000 −0.138509
\(835\) 8.00000 0.276851
\(836\) 0 0
\(837\) 1.00000 0.0345651
\(838\) −6.00000 −0.207267
\(839\) −30.0000 −1.03572 −0.517858 − 0.855467i \(-0.673270\pi\)
−0.517858 + 0.855467i \(0.673270\pi\)
\(840\) −2.00000 −0.0690066
\(841\) 35.0000 1.20690
\(842\) −6.00000 −0.206774
\(843\) −30.0000 −1.03325
\(844\) 16.0000 0.550743
\(845\) −3.00000 −0.103203
\(846\) −4.00000 −0.137523
\(847\) 22.0000 0.755929
\(848\) −14.0000 −0.480762
\(849\) −14.0000 −0.480479
\(850\) 6.00000 0.205798
\(851\) 0 0
\(852\) −6.00000 −0.205557
\(853\) 18.0000 0.616308 0.308154 − 0.951336i \(-0.400289\pi\)
0.308154 + 0.951336i \(0.400289\pi\)
\(854\) 12.0000 0.410632
\(855\) 0 0
\(856\) 8.00000 0.273434
\(857\) −10.0000 −0.341593 −0.170797 − 0.985306i \(-0.554634\pi\)
−0.170797 + 0.985306i \(0.554634\pi\)
\(858\) 0 0
\(859\) −20.0000 −0.682391 −0.341196 − 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) −8.00000 −0.272798
\(861\) 20.0000 0.681598
\(862\) −6.00000 −0.204361
\(863\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −10.0000 −0.340010
\(866\) −16.0000 −0.543702
\(867\) −19.0000 −0.645274
\(868\) 2.00000 0.0678844
\(869\) 0 0
\(870\) 8.00000 0.271225
\(871\) −40.0000 −1.35535
\(872\) 18.0000 0.609557
\(873\) −10.0000 −0.338449
\(874\) 0 0
\(875\) 2.00000 0.0676123
\(876\) 8.00000 0.270295
\(877\) −6.00000 −0.202606 −0.101303 − 0.994856i \(-0.532301\pi\)
−0.101303 + 0.994856i \(0.532301\pi\)
\(878\) 24.0000 0.809961
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) −48.0000 −1.61716 −0.808581 − 0.588386i \(-0.799764\pi\)
−0.808581 + 0.588386i \(0.799764\pi\)
\(882\) −3.00000 −0.101015
\(883\) −12.0000 −0.403832 −0.201916 − 0.979403i \(-0.564717\pi\)
−0.201916 + 0.979403i \(0.564717\pi\)
\(884\) 24.0000 0.807207
\(885\) 14.0000 0.470605
\(886\) −36.0000 −1.20944
\(887\) −56.0000 −1.88030 −0.940148 − 0.340766i \(-0.889313\pi\)
−0.940148 + 0.340766i \(0.889313\pi\)
\(888\) −4.00000 −0.134231
\(889\) 0 0
\(890\) −16.0000 −0.536321
\(891\) 0 0
\(892\) −20.0000 −0.669650
\(893\) 0 0
\(894\) −18.0000 −0.602010
\(895\) 0 0
\(896\) −2.00000 −0.0668153
\(897\) 0 0
\(898\) −20.0000 −0.667409
\(899\) −8.00000 −0.266815
\(900\) 1.00000 0.0333333
\(901\) −84.0000 −2.79845
\(902\) 0 0
\(903\) 16.0000 0.532447
\(904\) 14.0000 0.465633
\(905\) 6.00000 0.199447
\(906\) 8.00000 0.265782
\(907\) 2.00000 0.0664089 0.0332045 − 0.999449i \(-0.489429\pi\)
0.0332045 + 0.999449i \(0.489429\pi\)
\(908\) 12.0000 0.398234
\(909\) −6.00000 −0.199007
\(910\) 8.00000 0.265197
\(911\) −24.0000 −0.795155 −0.397578 − 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 8.00000 0.264616
\(915\) −6.00000 −0.198354
\(916\) −10.0000 −0.330409
\(917\) 36.0000 1.18882
\(918\) −6.00000 −0.198030
\(919\) −60.0000 −1.97922 −0.989609 − 0.143787i \(-0.954072\pi\)
−0.989609 + 0.143787i \(0.954072\pi\)
\(920\) 0 0
\(921\) −10.0000 −0.329511
\(922\) −12.0000 −0.395199
\(923\) 24.0000 0.789970
\(924\) 0 0
\(925\) 4.00000 0.131519
\(926\) 0 0
\(927\) −6.00000 −0.197066
\(928\) 8.00000 0.262613
\(929\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) −1.00000 −0.0327913
\(931\) 0 0
\(932\) −14.0000 −0.458585
\(933\) −18.0000 −0.589294
\(934\) −32.0000 −1.04707
\(935\) 0 0
\(936\) 4.00000 0.130744
\(937\) −42.0000 −1.37208 −0.686040 − 0.727564i \(-0.740653\pi\)
−0.686040 + 0.727564i \(0.740653\pi\)
\(938\) 20.0000 0.653023
\(939\) 16.0000 0.522140
\(940\) 4.00000 0.130466
\(941\) −8.00000 −0.260793 −0.130396 − 0.991462i \(-0.541625\pi\)
−0.130396 + 0.991462i \(0.541625\pi\)
\(942\) 18.0000 0.586472
\(943\) 0 0
\(944\) 14.0000 0.455661
\(945\) −2.00000 −0.0650600
\(946\) 0 0
\(947\) −28.0000 −0.909878 −0.454939 − 0.890523i \(-0.650339\pi\)
−0.454939 + 0.890523i \(0.650339\pi\)
\(948\) −8.00000 −0.259828
\(949\) −32.0000 −1.03876
\(950\) 0 0
\(951\) 10.0000 0.324272
\(952\) −12.0000 −0.388922
\(953\) −46.0000 −1.49009 −0.745043 − 0.667016i \(-0.767571\pi\)
−0.745043 + 0.667016i \(0.767571\pi\)
\(954\) −14.0000 −0.453267
\(955\) 14.0000 0.453029
\(956\) −12.0000 −0.388108
\(957\) 0 0
\(958\) −42.0000 −1.35696
\(959\) 12.0000 0.387500
\(960\) 1.00000 0.0322749
\(961\) 1.00000 0.0322581
\(962\) 16.0000 0.515861
\(963\) 8.00000 0.257796
\(964\) −14.0000 −0.450910
\(965\) 2.00000 0.0643823
\(966\) 0 0
\(967\) 52.0000 1.67221 0.836104 − 0.548572i \(-0.184828\pi\)
0.836104 + 0.548572i \(0.184828\pi\)
\(968\) −11.0000 −0.353553
\(969\) 0 0
\(970\) 10.0000 0.321081
\(971\) 18.0000 0.577647 0.288824 − 0.957382i \(-0.406736\pi\)
0.288824 + 0.957382i \(0.406736\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −8.00000 −0.256468
\(974\) −8.00000 −0.256337
\(975\) −4.00000 −0.128103
\(976\) −6.00000 −0.192055
\(977\) −18.0000 −0.575871 −0.287936 − 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) −6.00000 −0.191859
\(979\) 0 0
\(980\) 3.00000 0.0958315
\(981\) 18.0000 0.574696
\(982\) 36.0000 1.14881
\(983\) −40.0000 −1.27580 −0.637901 − 0.770118i \(-0.720197\pi\)
−0.637901 + 0.770118i \(0.720197\pi\)
\(984\) −10.0000 −0.318788
\(985\) 2.00000 0.0637253
\(986\) 48.0000 1.52863
\(987\) −8.00000 −0.254643
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 − 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 12.0000 0.380808
\(994\) −12.0000 −0.380617
\(995\) 24.0000 0.760851
\(996\) 12.0000 0.380235
\(997\) 6.00000 0.190022 0.0950110 − 0.995476i \(-0.469711\pi\)
0.0950110 + 0.995476i \(0.469711\pi\)
\(998\) 20.0000 0.633089
\(999\) −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 930.2.a.k.1.1 ✓ 1
3.2 odd 2 2790.2.a.f.1.1 1
4.3 odd 2 7440.2.a.u.1.1 1
5.2 odd 4 4650.2.d.g.3349.2 2
5.3 odd 4 4650.2.d.g.3349.1 2
5.4 even 2 4650.2.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.a.k.1.1 ✓ 1 1.1 even 1 trivial
2790.2.a.f.1.1 1 3.2 odd 2
4650.2.a.t.1.1 1 5.4 even 2
4650.2.d.g.3349.1 2 5.3 odd 4
4650.2.d.g.3349.2 2 5.2 odd 4
7440.2.a.u.1.1 1 4.3 odd 2