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Properties

Label 6006.2.a.p.1.1
Level $6006$
Weight $2$
Character 6006.1
Self dual yes
Analytic conductor $47.958$
Analytic rank $1$
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] = [6006,2,Mod(1,6006)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6006, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6006.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6006 = 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6006.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: \(47.9581514540\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 6006.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} -1.00000 q^{18} -4.00000 q^{19} +1.00000 q^{21} -1.00000 q^{22} -1.00000 q^{24} -5.00000 q^{25} -1.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} +6.00000 q^{29} +2.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} +6.00000 q^{34} +1.00000 q^{36} -4.00000 q^{37} +4.00000 q^{38} +1.00000 q^{39} -6.00000 q^{41} -1.00000 q^{42} -10.0000 q^{43} +1.00000 q^{44} +12.0000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +5.00000 q^{50} -6.00000 q^{51} +1.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} -1.00000 q^{56} -4.00000 q^{57} -6.00000 q^{58} -6.00000 q^{59} -10.0000 q^{61} -2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -1.00000 q^{66} -10.0000 q^{67} -6.00000 q^{68} -6.00000 q^{71} -1.00000 q^{72} +2.00000 q^{73} +4.00000 q^{74} -5.00000 q^{75} -4.00000 q^{76} +1.00000 q^{77} -1.00000 q^{78} -4.00000 q^{79} +1.00000 q^{81} +6.00000 q^{82} +1.00000 q^{84} +10.0000 q^{86} +6.00000 q^{87} -1.00000 q^{88} -6.00000 q^{89} +1.00000 q^{91} +2.00000 q^{93} -12.0000 q^{94} -1.00000 q^{96} -16.0000 q^{97} -1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) −1.00000 −0.408248
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) 1.00000 0.277350
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −6.00000 −1.45521 −0.727607 − 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) −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
\(22\) −1.00000 −0.213201
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.00000 −0.204124
\(25\) −5.00000 −1.00000
\(26\) −1.00000 −0.196116
\(27\) 1.00000 0.192450
\(28\) 1.00000 0.188982
\(29\) 6.00000 1.11417 0.557086 − 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 − 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −4.00000 −0.657596 −0.328798 − 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 4.00000 0.648886
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) −1.00000 −0.154303
\(43\) −10.0000 −1.52499 −0.762493 − 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 1.00000 0.150756
\(45\) 0 0
\(46\) 0 0
\(47\) 12.0000 1.75038 0.875190 − 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) 5.00000 0.707107
\(51\) −6.00000 −0.840168
\(52\) 1.00000 0.138675
\(53\) 6.00000 0.824163 0.412082 − 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) −4.00000 −0.529813
\(58\) −6.00000 −0.787839
\(59\) −6.00000 −0.781133 −0.390567 − 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 − 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) −2.00000 −0.254000
\(63\) 1.00000 0.125988
\(64\) 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 \(0.709171\pi\)
\(68\) −6.00000 −0.727607
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 − 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.00000 0.234082 0.117041 − 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 4.00000 0.464991
\(75\) −5.00000 −0.577350
\(76\) −4.00000 −0.458831
\(77\) 1.00000 0.113961
\(78\) −1.00000 −0.113228
\(79\) −4.00000 −0.450035 −0.225018 − 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 1.00000 0.109109
\(85\) 0 0
\(86\) 10.0000 1.07833
\(87\) 6.00000 0.643268
\(88\) −1.00000 −0.106600
\(89\) −6.00000 −0.635999 −0.317999 − 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 2.00000 0.207390
\(94\) −12.0000 −1.23771
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −16.0000 −1.62455 −0.812277 − 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) −1.00000 −0.101015
\(99\) 1.00000 0.100504
\(100\) −5.00000 −0.500000
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 6.00000 0.594089
\(103\) −4.00000 −0.394132 −0.197066 − 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −12.0000 −1.16008 −0.580042 − 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 1.00000 0.0962250
\(109\) 2.00000 0.191565 0.0957826 − 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) 1.00000 0.0944911
\(113\) 18.0000 1.69330 0.846649 − 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 4.00000 0.374634
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 1.00000 0.0924500
\(118\) 6.00000 0.552345
\(119\) −6.00000 −0.550019
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 10.0000 0.905357
\(123\) −6.00000 −0.541002
\(124\) 2.00000 0.179605
\(125\) 0 0
\(126\) −1.00000 −0.0890871
\(127\) −16.0000 −1.41977 −0.709885 − 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −10.0000 −0.880451
\(130\) 0 0
\(131\) −6.00000 −0.524222 −0.262111 − 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) 1.00000 0.0870388
\(133\) −4.00000 −0.346844
\(134\) 10.0000 0.863868
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 8.00000 0.678551 0.339276 − 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) 6.00000 0.503509
\(143\) 1.00000 0.0836242
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 1.00000 0.0824786
\(148\) −4.00000 −0.328798
\(149\) 6.00000 0.491539 0.245770 − 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 5.00000 0.408248
\(151\) 8.00000 0.651031 0.325515 − 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 4.00000 0.324443
\(153\) −6.00000 −0.485071
\(154\) −1.00000 −0.0805823
\(155\) 0 0
\(156\) 1.00000 0.0800641
\(157\) 14.0000 1.11732 0.558661 − 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 4.00000 0.318223
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 2.00000 0.156652 0.0783260 − 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 0 0
\(167\) 24.0000 1.85718 0.928588 − 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) −1.00000 −0.0771517
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) −10.0000 −0.762493
\(173\) 12.0000 0.912343 0.456172 − 0.889892i \(-0.349220\pi\)
0.456172 + 0.889892i \(0.349220\pi\)
\(174\) −6.00000 −0.454859
\(175\) −5.00000 −0.377964
\(176\) 1.00000 0.0753778
\(177\) −6.00000 −0.450988
\(178\) 6.00000 0.449719
\(179\) −12.0000 −0.896922 −0.448461 − 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 − 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −1.00000 −0.0741249
\(183\) −10.0000 −0.739221
\(184\) 0 0
\(185\) 0 0
\(186\) −2.00000 −0.146647
\(187\) −6.00000 −0.438763
\(188\) 12.0000 0.875190
\(189\) 1.00000 0.0727393
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 − 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 1.00000 0.0721688
\(193\) −22.0000 −1.58359 −0.791797 − 0.610784i \(-0.790854\pi\)
−0.791797 + 0.610784i \(0.790854\pi\)
\(194\) 16.0000 1.14873
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −18.0000 −1.28245 −0.641223 − 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) −1.00000 −0.0710669
\(199\) 8.00000 0.567105 0.283552 − 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 5.00000 0.353553
\(201\) −10.0000 −0.705346
\(202\) 0 0
\(203\) 6.00000 0.421117
\(204\) −6.00000 −0.420084
\(205\) 0 0
\(206\) 4.00000 0.278693
\(207\) 0 0
\(208\) 1.00000 0.0693375
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −10.0000 −0.688428 −0.344214 − 0.938891i \(-0.611855\pi\)
−0.344214 + 0.938891i \(0.611855\pi\)
\(212\) 6.00000 0.412082
\(213\) −6.00000 −0.411113
\(214\) 12.0000 0.820303
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 2.00000 0.135769
\(218\) −2.00000 −0.135457
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) −6.00000 −0.403604
\(222\) 4.00000 0.268462
\(223\) 26.0000 1.74109 0.870544 − 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −5.00000 −0.333333
\(226\) −18.0000 −1.19734
\(227\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) −4.00000 −0.264906
\(229\) −10.0000 −0.660819 −0.330409 − 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 1.00000 0.0657952
\(232\) −6.00000 −0.393919
\(233\) −24.0000 −1.57229 −0.786146 − 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 0 0
\(236\) −6.00000 −0.390567
\(237\) −4.00000 −0.259828
\(238\) 6.00000 0.388922
\(239\) 12.0000 0.776215 0.388108 − 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 − 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) −4.00000 −0.254514
\(248\) −2.00000 −0.127000
\(249\) 0 0
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 − 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 1.00000 0.0629941
\(253\) 0 0
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 30.0000 1.87135 0.935674 − 0.352865i \(-0.114792\pi\)
0.935674 + 0.352865i \(0.114792\pi\)
\(258\) 10.0000 0.622573
\(259\) −4.00000 −0.248548
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 6.00000 0.370681
\(263\) −6.00000 −0.369976 −0.184988 − 0.982741i \(-0.559225\pi\)
−0.184988 + 0.982741i \(0.559225\pi\)
\(264\) −1.00000 −0.0615457
\(265\) 0 0
\(266\) 4.00000 0.245256
\(267\) −6.00000 −0.367194
\(268\) −10.0000 −0.610847
\(269\) −30.0000 −1.82913 −0.914566 − 0.404436i \(-0.867468\pi\)
−0.914566 + 0.404436i \(0.867468\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 − 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −6.00000 −0.363803
\(273\) 1.00000 0.0605228
\(274\) 0 0
\(275\) −5.00000 −0.301511
\(276\) 0 0
\(277\) −4.00000 −0.240337 −0.120168 − 0.992754i \(-0.538343\pi\)
−0.120168 + 0.992754i \(0.538343\pi\)
\(278\) −8.00000 −0.479808
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 − 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) −12.0000 −0.714590
\(283\) −4.00000 −0.237775 −0.118888 − 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) −1.00000 −0.0591312
\(287\) −6.00000 −0.354169
\(288\) −1.00000 −0.0589256
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) −16.0000 −0.937937
\(292\) 2.00000 0.117041
\(293\) 18.0000 1.05157 0.525786 − 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 0 0
\(296\) 4.00000 0.232495
\(297\) 1.00000 0.0580259
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) −5.00000 −0.288675
\(301\) −10.0000 −0.576390
\(302\) −8.00000 −0.460348
\(303\) 0 0
\(304\) −4.00000 −0.229416
\(305\) 0 0
\(306\) 6.00000 0.342997
\(307\) −4.00000 −0.228292 −0.114146 − 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 1.00000 0.0569803
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 − 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −10.0000 −0.565233 −0.282617 − 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 18.0000 1.01098 0.505490 − 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) −6.00000 −0.336463
\(319\) 6.00000 0.335936
\(320\) 0 0
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 24.0000 1.33540
\(324\) 1.00000 0.0555556
\(325\) −5.00000 −0.277350
\(326\) −2.00000 −0.110770
\(327\) 2.00000 0.110600
\(328\) 6.00000 0.331295
\(329\) 12.0000 0.661581
\(330\) 0 0
\(331\) −10.0000 −0.549650 −0.274825 − 0.961494i \(-0.588620\pi\)
−0.274825 + 0.961494i \(0.588620\pi\)
\(332\) 0 0
\(333\) −4.00000 −0.219199
\(334\) −24.0000 −1.31322
\(335\) 0 0
\(336\) 1.00000 0.0545545
\(337\) −22.0000 −1.19842 −0.599208 − 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 18.0000 0.977626
\(340\) 0 0
\(341\) 2.00000 0.108306
\(342\) 4.00000 0.216295
\(343\) 1.00000 0.0539949
\(344\) 10.0000 0.539164
\(345\) 0 0
\(346\) −12.0000 −0.645124
\(347\) −12.0000 −0.644194 −0.322097 − 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 6.00000 0.321634
\(349\) 2.00000 0.107058 0.0535288 − 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 5.00000 0.267261
\(351\) 1.00000 0.0533761
\(352\) −1.00000 −0.0533002
\(353\) 6.00000 0.319348 0.159674 − 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 6.00000 0.318896
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) −6.00000 −0.317554
\(358\) 12.0000 0.634220
\(359\) −24.0000 −1.26667 −0.633336 − 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −2.00000 −0.105118
\(363\) 1.00000 0.0524864
\(364\) 1.00000 0.0524142
\(365\) 0 0
\(366\) 10.0000 0.522708
\(367\) −28.0000 −1.46159 −0.730794 − 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 6.00000 0.311504
\(372\) 2.00000 0.103695
\(373\) 8.00000 0.414224 0.207112 − 0.978317i \(-0.433593\pi\)
0.207112 + 0.978317i \(0.433593\pi\)
\(374\) 6.00000 0.310253
\(375\) 0 0
\(376\) −12.0000 −0.618853
\(377\) 6.00000 0.309016
\(378\) −1.00000 −0.0514344
\(379\) −22.0000 −1.13006 −0.565032 − 0.825069i \(-0.691136\pi\)
−0.565032 + 0.825069i \(0.691136\pi\)
\(380\) 0 0
\(381\) −16.0000 −0.819705
\(382\) 12.0000 0.613973
\(383\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 22.0000 1.11977
\(387\) −10.0000 −0.508329
\(388\) −16.0000 −0.812277
\(389\) −6.00000 −0.304212 −0.152106 − 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.00000 −0.0505076
\(393\) −6.00000 −0.302660
\(394\) 18.0000 0.906827
\(395\) 0 0
\(396\) 1.00000 0.0502519
\(397\) 2.00000 0.100377 0.0501886 − 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) −8.00000 −0.401004
\(399\) −4.00000 −0.200250
\(400\) −5.00000 −0.250000
\(401\) −12.0000 −0.599251 −0.299626 − 0.954057i \(-0.596862\pi\)
−0.299626 + 0.954057i \(0.596862\pi\)
\(402\) 10.0000 0.498755
\(403\) 2.00000 0.0996271
\(404\) 0 0
\(405\) 0 0
\(406\) −6.00000 −0.297775
\(407\) −4.00000 −0.198273
\(408\) 6.00000 0.297044
\(409\) −22.0000 −1.08783 −0.543915 − 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.00000 −0.197066
\(413\) −6.00000 −0.295241
\(414\) 0 0
\(415\) 0 0
\(416\) −1.00000 −0.0490290
\(417\) 8.00000 0.391762
\(418\) 4.00000 0.195646
\(419\) 36.0000 1.75872 0.879358 − 0.476162i \(-0.157972\pi\)
0.879358 + 0.476162i \(0.157972\pi\)
\(420\) 0 0
\(421\) 32.0000 1.55958 0.779792 − 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) 10.0000 0.486792
\(423\) 12.0000 0.583460
\(424\) −6.00000 −0.291386
\(425\) 30.0000 1.45521
\(426\) 6.00000 0.290701
\(427\) −10.0000 −0.483934
\(428\) −12.0000 −0.580042
\(429\) 1.00000 0.0482805
\(430\) 0 0
\(431\) 24.0000 1.15604 0.578020 − 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 1.00000 0.0481125
\(433\) 2.00000 0.0961139 0.0480569 − 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) −2.00000 −0.0960031
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) 0 0
\(438\) −2.00000 −0.0955637
\(439\) 14.0000 0.668184 0.334092 − 0.942541i \(-0.391570\pi\)
0.334092 + 0.942541i \(0.391570\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 6.00000 0.285391
\(443\) 12.0000 0.570137 0.285069 − 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) −4.00000 −0.189832
\(445\) 0 0
\(446\) −26.0000 −1.23114
\(447\) 6.00000 0.283790
\(448\) 1.00000 0.0472456
\(449\) −12.0000 −0.566315 −0.283158 − 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 5.00000 0.235702
\(451\) −6.00000 −0.282529
\(452\) 18.0000 0.846649
\(453\) 8.00000 0.375873
\(454\) 0 0
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 14.0000 0.654892 0.327446 − 0.944870i \(-0.393812\pi\)
0.327446 + 0.944870i \(0.393812\pi\)
\(458\) 10.0000 0.467269
\(459\) −6.00000 −0.280056
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 − 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) −1.00000 −0.0465242
\(463\) 32.0000 1.48717 0.743583 − 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) 24.0000 1.11178
\(467\) 36.0000 1.66588 0.832941 − 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) 1.00000 0.0462250
\(469\) −10.0000 −0.461757
\(470\) 0 0
\(471\) 14.0000 0.645086
\(472\) 6.00000 0.276172
\(473\) −10.0000 −0.459800
\(474\) 4.00000 0.183726
\(475\) 20.0000 0.917663
\(476\) −6.00000 −0.275010
\(477\) 6.00000 0.274721
\(478\) −12.0000 −0.548867
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −4.00000 −0.182384
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 20.0000 0.906287 0.453143 − 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) 10.0000 0.452679
\(489\) 2.00000 0.0904431
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 − 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) −6.00000 −0.270501
\(493\) −36.0000 −1.62136
\(494\) 4.00000 0.179969
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) −6.00000 −0.269137
\(498\) 0 0
\(499\) 2.00000 0.0895323 0.0447661 − 0.998997i \(-0.485746\pi\)
0.0447661 + 0.998997i \(0.485746\pi\)
\(500\) 0 0
\(501\) 24.0000 1.07224
\(502\) 12.0000 0.535586
\(503\) −24.0000 −1.07011 −0.535054 − 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) −16.0000 −0.709885
\(509\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 −0.176604
\(514\) −30.0000 −1.32324
\(515\) 0 0
\(516\) −10.0000 −0.440225
\(517\) 12.0000 0.527759
\(518\) 4.00000 0.175750
\(519\) 12.0000 0.526742
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 − 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −6.00000 −0.262613
\(523\) −16.0000 −0.699631 −0.349816 − 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −6.00000 −0.262111
\(525\) −5.00000 −0.218218
\(526\) 6.00000 0.261612
\(527\) −12.0000 −0.522728
\(528\) 1.00000 0.0435194
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) −4.00000 −0.173422
\(533\) −6.00000 −0.259889
\(534\) 6.00000 0.259645
\(535\) 0 0
\(536\) 10.0000 0.431934
\(537\) −12.0000 −0.517838
\(538\) 30.0000 1.29339
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −34.0000 −1.46177 −0.730887 − 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) −8.00000 −0.343629
\(543\) 2.00000 0.0858282
\(544\) 6.00000 0.257248
\(545\) 0 0
\(546\) −1.00000 −0.0427960
\(547\) 2.00000 0.0855138 0.0427569 − 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 0 0
\(549\) −10.0000 −0.426790
\(550\) 5.00000 0.213201
\(551\) −24.0000 −1.02243
\(552\) 0 0
\(553\) −4.00000 −0.170097
\(554\) 4.00000 0.169944
\(555\) 0 0
\(556\) 8.00000 0.339276
\(557\) 18.0000 0.762684 0.381342 − 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) −2.00000 −0.0846668
\(559\) −10.0000 −0.422955
\(560\) 0 0
\(561\) −6.00000 −0.253320
\(562\) −18.0000 −0.759284
\(563\) −30.0000 −1.26435 −0.632175 − 0.774826i \(-0.717837\pi\)
−0.632175 + 0.774826i \(0.717837\pi\)
\(564\) 12.0000 0.505291
\(565\) 0 0
\(566\) 4.00000 0.168133
\(567\) 1.00000 0.0419961
\(568\) 6.00000 0.251754
\(569\) −24.0000 −1.00613 −0.503066 − 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) −22.0000 −0.920671 −0.460336 − 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) 1.00000 0.0418121
\(573\) −12.0000 −0.501307
\(574\) 6.00000 0.250435
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −16.0000 −0.666089 −0.333044 − 0.942911i \(-0.608076\pi\)
−0.333044 + 0.942911i \(0.608076\pi\)
\(578\) −19.0000 −0.790296
\(579\) −22.0000 −0.914289
\(580\) 0 0
\(581\) 0 0
\(582\) 16.0000 0.663221
\(583\) 6.00000 0.248495
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) −18.0000 −0.743573
\(587\) 30.0000 1.23823 0.619116 − 0.785299i \(-0.287491\pi\)
0.619116 + 0.785299i \(0.287491\pi\)
\(588\) 1.00000 0.0412393
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) −18.0000 −0.740421
\(592\) −4.00000 −0.164399
\(593\) −6.00000 −0.246390 −0.123195 − 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) 8.00000 0.327418
\(598\) 0 0
\(599\) 12.0000 0.490307 0.245153 − 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 5.00000 0.204124
\(601\) 8.00000 0.326327 0.163163 − 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 10.0000 0.407570
\(603\) −10.0000 −0.407231
\(604\) 8.00000 0.325515
\(605\) 0 0
\(606\) 0 0
\(607\) −10.0000 −0.405887 −0.202944 − 0.979190i \(-0.565051\pi\)
−0.202944 + 0.979190i \(0.565051\pi\)
\(608\) 4.00000 0.162221
\(609\) 6.00000 0.243132
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) −6.00000 −0.242536
\(613\) −10.0000 −0.403896 −0.201948 − 0.979396i \(-0.564727\pi\)
−0.201948 + 0.979396i \(0.564727\pi\)
\(614\) 4.00000 0.161427
\(615\) 0 0
\(616\) −1.00000 −0.0402911
\(617\) −12.0000 −0.483102 −0.241551 − 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) 4.00000 0.160904
\(619\) −28.0000 −1.12542 −0.562708 − 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) −6.00000 −0.240385
\(624\) 1.00000 0.0400320
\(625\) 25.0000 1.00000
\(626\) 10.0000 0.399680
\(627\) −4.00000 −0.159745
\(628\) 14.0000 0.558661
\(629\) 24.0000 0.956943
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 − 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 4.00000 0.159111
\(633\) −10.0000 −0.397464
\(634\) −18.0000 −0.714871
\(635\) 0 0
\(636\) 6.00000 0.237915
\(637\) 1.00000 0.0396214
\(638\) −6.00000 −0.237542
\(639\) −6.00000 −0.237356
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 − 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 12.0000 0.473602
\(643\) −4.00000 −0.157745 −0.0788723 − 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −24.0000 −0.944267
\(647\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −6.00000 −0.235521
\(650\) 5.00000 0.196116
\(651\) 2.00000 0.0783862
\(652\) 2.00000 0.0783260
\(653\) 18.0000 0.704394 0.352197 − 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) −2.00000 −0.0782062
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) 2.00000 0.0780274
\(658\) −12.0000 −0.467809
\(659\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −34.0000 −1.32245 −0.661223 − 0.750189i \(-0.729962\pi\)
−0.661223 + 0.750189i \(0.729962\pi\)
\(662\) 10.0000 0.388661
\(663\) −6.00000 −0.233021
\(664\) 0 0
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 0 0
\(668\) 24.0000 0.928588
\(669\) 26.0000 1.00522
\(670\) 0 0
\(671\) −10.0000 −0.386046
\(672\) −1.00000 −0.0385758
\(673\) −46.0000 −1.77317 −0.886585 − 0.462566i \(-0.846929\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) 22.0000 0.847408
\(675\) −5.00000 −0.192450
\(676\) 1.00000 0.0384615
\(677\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) −18.0000 −0.691286
\(679\) −16.0000 −0.614024
\(680\) 0 0
\(681\) 0 0
\(682\) −2.00000 −0.0765840
\(683\) 48.0000 1.83667 0.918334 − 0.395805i \(-0.129534\pi\)
0.918334 + 0.395805i \(0.129534\pi\)
\(684\) −4.00000 −0.152944
\(685\) 0 0
\(686\) −1.00000 −0.0381802
\(687\) −10.0000 −0.381524
\(688\) −10.0000 −0.381246
\(689\) 6.00000 0.228582
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 − 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 12.0000 0.456172
\(693\) 1.00000 0.0379869
\(694\) 12.0000 0.455514
\(695\) 0 0
\(696\) −6.00000 −0.227429
\(697\) 36.0000 1.36360
\(698\) −2.00000 −0.0757011
\(699\) −24.0000 −0.907763
\(700\) −5.00000 −0.188982
\(701\) 30.0000 1.13308 0.566542 − 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) −1.00000 −0.0377426
\(703\) 16.0000 0.603451
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) −6.00000 −0.225813
\(707\) 0 0
\(708\) −6.00000 −0.225494
\(709\) 44.0000 1.65245 0.826227 − 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) 0 0
\(711\) −4.00000 −0.150012
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) 6.00000 0.224544
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) 12.0000 0.448148
\(718\) 24.0000 0.895672
\(719\) −48.0000 −1.79010 −0.895049 − 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 0 0
\(721\) −4.00000 −0.148968
\(722\) 3.00000 0.111648
\(723\) −10.0000 −0.371904
\(724\) 2.00000 0.0743294
\(725\) −30.0000 −1.11417
\(726\) −1.00000 −0.0371135
\(727\) −28.0000 −1.03846 −0.519231 − 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) −1.00000 −0.0370625
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 60.0000 2.21918
\(732\) −10.0000 −0.369611
\(733\) −46.0000 −1.69905 −0.849524 − 0.527549i \(-0.823111\pi\)
−0.849524 + 0.527549i \(0.823111\pi\)
\(734\) 28.0000 1.03350
\(735\) 0 0
\(736\) 0 0
\(737\) −10.0000 −0.368355
\(738\) 6.00000 0.220863
\(739\) 20.0000 0.735712 0.367856 − 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 0 0
\(741\) −4.00000 −0.146944
\(742\) −6.00000 −0.220267
\(743\) −48.0000 −1.76095 −0.880475 − 0.474093i \(-0.842776\pi\)
−0.880475 + 0.474093i \(0.842776\pi\)
\(744\) −2.00000 −0.0733236
\(745\) 0 0
\(746\) −8.00000 −0.292901
\(747\) 0 0
\(748\) −6.00000 −0.219382
\(749\) −12.0000 −0.438470
\(750\) 0 0
\(751\) −40.0000 −1.45962 −0.729810 − 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) 12.0000 0.437595
\(753\) −12.0000 −0.437304
\(754\) −6.00000 −0.218507
\(755\) 0 0
\(756\) 1.00000 0.0363696
\(757\) 2.00000 0.0726912 0.0363456 − 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 22.0000 0.799076
\(759\) 0 0
\(760\) 0 0
\(761\) −42.0000 −1.52250 −0.761249 − 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 16.0000 0.579619
\(763\) 2.00000 0.0724049
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) 0 0
\(767\) −6.00000 −0.216647
\(768\) 1.00000 0.0360844
\(769\) 38.0000 1.37032 0.685158 − 0.728395i \(-0.259733\pi\)
0.685158 + 0.728395i \(0.259733\pi\)
\(770\) 0 0
\(771\) 30.0000 1.08042
\(772\) −22.0000 −0.791797
\(773\) −24.0000 −0.863220 −0.431610 − 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 10.0000 0.359443
\(775\) −10.0000 −0.359211
\(776\) 16.0000 0.574367
\(777\) −4.00000 −0.143499
\(778\) 6.00000 0.215110
\(779\) 24.0000 0.859889
\(780\) 0 0
\(781\) −6.00000 −0.214697
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 6.00000 0.214013
\(787\) −28.0000 −0.998092 −0.499046 − 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) −18.0000 −0.641223
\(789\) −6.00000 −0.213606
\(790\) 0 0
\(791\) 18.0000 0.640006
\(792\) −1.00000 −0.0355335
\(793\) −10.0000 −0.355110
\(794\) −2.00000 −0.0709773
\(795\) 0 0
\(796\) 8.00000 0.283552
\(797\) 42.0000 1.48772 0.743858 − 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 4.00000 0.141598
\(799\) −72.0000 −2.54718
\(800\) 5.00000 0.176777
\(801\) −6.00000 −0.212000
\(802\) 12.0000 0.423735
\(803\) 2.00000 0.0705785
\(804\) −10.0000 −0.352673
\(805\) 0 0
\(806\) −2.00000 −0.0704470
\(807\) −30.0000 −1.05605
\(808\) 0 0
\(809\) −12.0000 −0.421898 −0.210949 − 0.977497i \(-0.567655\pi\)
−0.210949 + 0.977497i \(0.567655\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 − 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 6.00000 0.210559
\(813\) 8.00000 0.280572
\(814\) 4.00000 0.140200
\(815\) 0 0
\(816\) −6.00000 −0.210042
\(817\) 40.0000 1.39942
\(818\) 22.0000 0.769212
\(819\) 1.00000 0.0349428
\(820\) 0 0
\(821\) −6.00000 −0.209401 −0.104701 − 0.994504i \(-0.533388\pi\)
−0.104701 + 0.994504i \(0.533388\pi\)
\(822\) 0 0
\(823\) 32.0000 1.11545 0.557725 − 0.830026i \(-0.311674\pi\)
0.557725 + 0.830026i \(0.311674\pi\)
\(824\) 4.00000 0.139347
\(825\) −5.00000 −0.174078
\(826\) 6.00000 0.208767
\(827\) 36.0000 1.25184 0.625921 − 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 0 0
\(829\) 2.00000 0.0694629 0.0347314 − 0.999397i \(-0.488942\pi\)
0.0347314 + 0.999397i \(0.488942\pi\)
\(830\) 0 0
\(831\) −4.00000 −0.138758
\(832\) 1.00000 0.0346688
\(833\) −6.00000 −0.207888
\(834\) −8.00000 −0.277017
\(835\) 0 0
\(836\) −4.00000 −0.138343
\(837\) 2.00000 0.0691301
\(838\) −36.0000 −1.24360
\(839\) 24.0000 0.828572 0.414286 − 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −32.0000 −1.10279
\(843\) 18.0000 0.619953
\(844\) −10.0000 −0.344214
\(845\) 0 0
\(846\) −12.0000 −0.412568
\(847\) 1.00000 0.0343604
\(848\) 6.00000 0.206041
\(849\) −4.00000 −0.137280
\(850\) −30.0000 −1.02899
\(851\) 0 0
\(852\) −6.00000 −0.205557
\(853\) −22.0000 −0.753266 −0.376633 − 0.926363i \(-0.622918\pi\)
−0.376633 + 0.926363i \(0.622918\pi\)
\(854\) 10.0000 0.342193
\(855\) 0 0
\(856\) 12.0000 0.410152
\(857\) 54.0000 1.84460 0.922302 − 0.386469i \(-0.126305\pi\)
0.922302 + 0.386469i \(0.126305\pi\)
\(858\) −1.00000 −0.0341394
\(859\) 20.0000 0.682391 0.341196 − 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 0 0
\(861\) −6.00000 −0.204479
\(862\) −24.0000 −0.817443
\(863\) 6.00000 0.204242 0.102121 − 0.994772i \(-0.467437\pi\)
0.102121 + 0.994772i \(0.467437\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) −2.00000 −0.0679628
\(867\) 19.0000 0.645274
\(868\) 2.00000 0.0678844
\(869\) −4.00000 −0.135691
\(870\) 0 0
\(871\) −10.0000 −0.338837
\(872\) −2.00000 −0.0677285
\(873\) −16.0000 −0.541518
\(874\) 0 0
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) −22.0000 −0.742887 −0.371444 − 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) −14.0000 −0.472477
\(879\) 18.0000 0.607125
\(880\) 0 0
\(881\) 30.0000 1.01073 0.505363 − 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) −1.00000 −0.0336718
\(883\) 20.0000 0.673054 0.336527 − 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) −6.00000 −0.201802
\(885\) 0 0
\(886\) −12.0000 −0.403148
\(887\) −36.0000 −1.20876 −0.604381 − 0.796696i \(-0.706579\pi\)
−0.604381 + 0.796696i \(0.706579\pi\)
\(888\) 4.00000 0.134231
\(889\) −16.0000 −0.536623
\(890\) 0 0
\(891\) 1.00000 0.0335013
\(892\) 26.0000 0.870544
\(893\) −48.0000 −1.60626
\(894\) −6.00000 −0.200670
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 12.0000 0.400445
\(899\) 12.0000 0.400222
\(900\) −5.00000 −0.166667
\(901\) −36.0000 −1.19933
\(902\) 6.00000 0.199778
\(903\) −10.0000 −0.332779
\(904\) −18.0000 −0.598671
\(905\) 0 0
\(906\) −8.00000 −0.265782
\(907\) 32.0000 1.06254 0.531271 − 0.847202i \(-0.321714\pi\)
0.531271 + 0.847202i \(0.321714\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 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
\(913\) 0 0
\(914\) −14.0000 −0.463079
\(915\) 0 0
\(916\) −10.0000 −0.330409
\(917\) −6.00000 −0.198137
\(918\) 6.00000 0.198030
\(919\) −4.00000 −0.131948 −0.0659739 − 0.997821i \(-0.521015\pi\)
−0.0659739 + 0.997821i \(0.521015\pi\)
\(920\) 0 0
\(921\) −4.00000 −0.131804
\(922\) −30.0000 −0.987997
\(923\) −6.00000 −0.197492
\(924\) 1.00000 0.0328976
\(925\) 20.0000 0.657596
\(926\) −32.0000 −1.05159
\(927\) −4.00000 −0.131377
\(928\) −6.00000 −0.196960
\(929\) 6.00000 0.196854 0.0984268 − 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) 0 0
\(931\) −4.00000 −0.131095
\(932\) −24.0000 −0.786146
\(933\) −24.0000 −0.785725
\(934\) −36.0000 −1.17796
\(935\) 0 0
\(936\) −1.00000 −0.0326860
\(937\) −16.0000 −0.522697 −0.261349 − 0.965244i \(-0.584167\pi\)
−0.261349 + 0.965244i \(0.584167\pi\)
\(938\) 10.0000 0.326512
\(939\) −10.0000 −0.326338
\(940\) 0 0
\(941\) 54.0000 1.76035 0.880175 − 0.474650i \(-0.157425\pi\)
0.880175 + 0.474650i \(0.157425\pi\)
\(942\) −14.0000 −0.456145
\(943\) 0 0
\(944\) −6.00000 −0.195283
\(945\) 0 0
\(946\) 10.0000 0.325128
\(947\) −48.0000 −1.55979 −0.779895 − 0.625910i \(-0.784728\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(948\) −4.00000 −0.129914
\(949\) 2.00000 0.0649227
\(950\) −20.0000 −0.648886
\(951\) 18.0000 0.583690
\(952\) 6.00000 0.194461
\(953\) −12.0000 −0.388718 −0.194359 − 0.980930i \(-0.562263\pi\)
−0.194359 + 0.980930i \(0.562263\pi\)
\(954\) −6.00000 −0.194257
\(955\) 0 0
\(956\) 12.0000 0.388108
\(957\) 6.00000 0.193952
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 4.00000 0.128965
\(963\) −12.0000 −0.386695
\(964\) −10.0000 −0.322078
\(965\) 0 0
\(966\) 0 0
\(967\) 32.0000 1.02905 0.514525 − 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 24.0000 0.770991
\(970\) 0 0
\(971\) −24.0000 −0.770197 −0.385098 − 0.922876i \(-0.625832\pi\)
−0.385098 + 0.922876i \(0.625832\pi\)
\(972\) 1.00000 0.0320750
\(973\) 8.00000 0.256468
\(974\) −20.0000 −0.640841
\(975\) −5.00000 −0.160128
\(976\) −10.0000 −0.320092
\(977\) −12.0000 −0.383914 −0.191957 − 0.981403i \(-0.561483\pi\)
−0.191957 + 0.981403i \(0.561483\pi\)
\(978\) −2.00000 −0.0639529
\(979\) −6.00000 −0.191761
\(980\) 0 0
\(981\) 2.00000 0.0638551
\(982\) 36.0000 1.14881
\(983\) 24.0000 0.765481 0.382741 − 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) 6.00000 0.191273
\(985\) 0 0
\(986\) 36.0000 1.14647
\(987\) 12.0000 0.381964
\(988\) −4.00000 −0.127257
\(989\) 0 0
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 − 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) −2.00000 −0.0635001
\(993\) −10.0000 −0.317340
\(994\) 6.00000 0.190308
\(995\) 0 0
\(996\) 0 0
\(997\) −10.0000 −0.316703 −0.158352 − 0.987383i \(-0.550618\pi\)
−0.158352 + 0.987383i \(0.550618\pi\)
\(998\) −2.00000 −0.0633089
\(999\) −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 6006.2.a.p.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6006.2.a.p.1.1 ✓ 1 1.1 even 1 trivial