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Properties

Label 4830.2.a.bb.1.1
Level $4830$
Weight $2$
Character 4830.1
Self dual yes
Analytic conductor $38.568$
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] = [4830,2,Mod(1,4830)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4830, 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("4830.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4830.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: \(38.5677441763\)
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 \(\chi\) \(=\) 4830.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +4.00000 q^{11} +1.00000 q^{12} +6.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -4.00000 q^{17} +1.00000 q^{18} -1.00000 q^{20} -1.00000 q^{21} +4.00000 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +6.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} -1.00000 q^{30} +1.00000 q^{32} +4.00000 q^{33} -4.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} +6.00000 q^{39} -1.00000 q^{40} -1.00000 q^{42} +4.00000 q^{44} -1.00000 q^{45} +1.00000 q^{46} +8.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -4.00000 q^{51} +6.00000 q^{52} +8.00000 q^{53} +1.00000 q^{54} -4.00000 q^{55} -1.00000 q^{56} -1.00000 q^{60} +10.0000 q^{61} -1.00000 q^{63} +1.00000 q^{64} -6.00000 q^{65} +4.00000 q^{66} -8.00000 q^{67} -4.00000 q^{68} +1.00000 q^{69} +1.00000 q^{70} +1.00000 q^{72} +4.00000 q^{73} -6.00000 q^{74} +1.00000 q^{75} -4.00000 q^{77} +6.00000 q^{78} -4.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +16.0000 q^{83} -1.00000 q^{84} +4.00000 q^{85} +4.00000 q^{88} +10.0000 q^{89} -1.00000 q^{90} -6.00000 q^{91} +1.00000 q^{92} +8.00000 q^{94} +1.00000 q^{96} -10.0000 q^{97} +1.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

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
\(5\) −1.00000 −0.447214
\(6\) 1.00000 0.408248
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 4.00000 1.20605 0.603023 − 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 1.00000 0.288675
\(13\) 6.00000 1.66410 0.832050 − 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) −1.00000 −0.267261
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −4.00000 −0.970143 −0.485071 − 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) 1.00000 0.235702
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −1.00000 −0.223607
\(21\) −1.00000 −0.218218
\(22\) 4.00000 0.852803
\(23\) 1.00000 0.208514
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 6.00000 1.17670
\(27\) 1.00000 0.192450
\(28\) −1.00000 −0.188982
\(29\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −1.00000 −0.182574
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.00000 0.696311
\(34\) −4.00000 −0.685994
\(35\) 1.00000 0.169031
\(36\) 1.00000 0.166667
\(37\) −6.00000 −0.986394 −0.493197 − 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 6.00000 0.960769
\(40\) −1.00000 −0.158114
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −1.00000 −0.154303
\(43\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 4.00000 0.603023
\(45\) −1.00000 −0.149071
\(46\) 1.00000 0.147442
\(47\) 8.00000 1.16692 0.583460 − 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) 1.00000 0.141421
\(51\) −4.00000 −0.560112
\(52\) 6.00000 0.832050
\(53\) 8.00000 1.09888 0.549442 − 0.835532i \(-0.314840\pi\)
0.549442 + 0.835532i \(0.314840\pi\)
\(54\) 1.00000 0.136083
\(55\) −4.00000 −0.539360
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −1.00000 −0.129099
\(61\) 10.0000 1.28037 0.640184 − 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 0 0
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) −6.00000 −0.744208
\(66\) 4.00000 0.492366
\(67\) −8.00000 −0.977356 −0.488678 − 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) −4.00000 −0.485071
\(69\) 1.00000 0.120386
\(70\) 1.00000 0.119523
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000 0.117851
\(73\) 4.00000 0.468165 0.234082 − 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) −6.00000 −0.697486
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) −4.00000 −0.455842
\(78\) 6.00000 0.679366
\(79\) −4.00000 −0.450035 −0.225018 − 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 16.0000 1.75623 0.878114 − 0.478451i \(-0.158802\pi\)
0.878114 + 0.478451i \(0.158802\pi\)
\(84\) −1.00000 −0.109109
\(85\) 4.00000 0.433861
\(86\) 0 0
\(87\) 0 0
\(88\) 4.00000 0.426401
\(89\) 10.0000 1.06000 0.529999 − 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −1.00000 −0.105409
\(91\) −6.00000 −0.628971
\(92\) 1.00000 0.104257
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −10.0000 −1.01535 −0.507673 − 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 1.00000 0.101015
\(99\) 4.00000 0.402015
\(100\) 1.00000 0.100000
\(101\) 10.0000 0.995037 0.497519 − 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) −4.00000 −0.396059
\(103\) −4.00000 −0.394132 −0.197066 − 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 6.00000 0.588348
\(105\) 1.00000 0.0975900
\(106\) 8.00000 0.777029
\(107\) −10.0000 −0.966736 −0.483368 − 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) 1.00000 0.0962250
\(109\) −12.0000 −1.14939 −0.574696 − 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) −4.00000 −0.381385
\(111\) −6.00000 −0.569495
\(112\) −1.00000 −0.0944911
\(113\) −6.00000 −0.564433 −0.282216 − 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 6.00000 0.554700
\(118\) 0 0
\(119\) 4.00000 0.366679
\(120\) −1.00000 −0.0912871
\(121\) 5.00000 0.454545
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) −1.00000 −0.0890871
\(127\) 4.00000 0.354943 0.177471 − 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −6.00000 −0.526235
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) −1.00000 −0.0860663
\(136\) −4.00000 −0.342997
\(137\) 18.0000 1.53784 0.768922 − 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 1.00000 0.0851257
\(139\) 12.0000 1.01783 0.508913 − 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 1.00000 0.0845154
\(141\) 8.00000 0.673722
\(142\) 0 0
\(143\) 24.0000 2.00698
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) 1.00000 0.0824786
\(148\) −6.00000 −0.493197
\(149\) −14.0000 −1.14692 −0.573462 − 0.819232i \(-0.694400\pi\)
−0.573462 + 0.819232i \(0.694400\pi\)
\(150\) 1.00000 0.0816497
\(151\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) −4.00000 −0.322329
\(155\) 0 0
\(156\) 6.00000 0.480384
\(157\) −2.00000 −0.159617 −0.0798087 − 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) −4.00000 −0.318223
\(159\) 8.00000 0.634441
\(160\) −1.00000 −0.0790569
\(161\) −1.00000 −0.0788110
\(162\) 1.00000 0.0785674
\(163\) 10.0000 0.783260 0.391630 − 0.920123i \(-0.371911\pi\)
0.391630 + 0.920123i \(0.371911\pi\)
\(164\) 0 0
\(165\) −4.00000 −0.311400
\(166\) 16.0000 1.24184
\(167\) −20.0000 −1.54765 −0.773823 − 0.633402i \(-0.781658\pi\)
−0.773823 + 0.633402i \(0.781658\pi\)
\(168\) −1.00000 −0.0771517
\(169\) 23.0000 1.76923
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) 0 0
\(173\) −18.0000 −1.36851 −0.684257 − 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) 10.0000 0.749532
\(179\) −2.00000 −0.149487 −0.0747435 − 0.997203i \(-0.523814\pi\)
−0.0747435 + 0.997203i \(0.523814\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 22.0000 1.63525 0.817624 − 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) −6.00000 −0.444750
\(183\) 10.0000 0.739221
\(184\) 1.00000 0.0737210
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) −16.0000 −1.17004
\(188\) 8.00000 0.583460
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000 0.0721688
\(193\) 22.0000 1.58359 0.791797 − 0.610784i \(-0.209146\pi\)
0.791797 + 0.610784i \(0.209146\pi\)
\(194\) −10.0000 −0.717958
\(195\) −6.00000 −0.429669
\(196\) 1.00000 0.0714286
\(197\) −2.00000 −0.142494 −0.0712470 − 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 4.00000 0.284268
\(199\) −2.00000 −0.141776 −0.0708881 − 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 1.00000 0.0707107
\(201\) −8.00000 −0.564276
\(202\) 10.0000 0.703598
\(203\) 0 0
\(204\) −4.00000 −0.280056
\(205\) 0 0
\(206\) −4.00000 −0.278693
\(207\) 1.00000 0.0695048
\(208\) 6.00000 0.416025
\(209\) 0 0
\(210\) 1.00000 0.0690066
\(211\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 8.00000 0.549442
\(213\) 0 0
\(214\) −10.0000 −0.683586
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) −12.0000 −0.812743
\(219\) 4.00000 0.270295
\(220\) −4.00000 −0.269680
\(221\) −24.0000 −1.61441
\(222\) −6.00000 −0.402694
\(223\) −2.00000 −0.133930 −0.0669650 − 0.997755i \(-0.521332\pi\)
−0.0669650 + 0.997755i \(0.521332\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 1.00000 0.0666667
\(226\) −6.00000 −0.399114
\(227\) 20.0000 1.32745 0.663723 − 0.747978i \(-0.268975\pi\)
0.663723 + 0.747978i \(0.268975\pi\)
\(228\) 0 0
\(229\) −18.0000 −1.18947 −0.594737 − 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) −1.00000 −0.0659380
\(231\) −4.00000 −0.263181
\(232\) 0 0
\(233\) −10.0000 −0.655122 −0.327561 − 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) 6.00000 0.392232
\(235\) −8.00000 −0.521862
\(236\) 0 0
\(237\) −4.00000 −0.259828
\(238\) 4.00000 0.259281
\(239\) 24.0000 1.55243 0.776215 − 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 4.00000 0.257663 0.128831 − 0.991667i \(-0.458877\pi\)
0.128831 + 0.991667i \(0.458877\pi\)
\(242\) 5.00000 0.321412
\(243\) 1.00000 0.0641500
\(244\) 10.0000 0.640184
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 16.0000 1.01396
\(250\) −1.00000 −0.0632456
\(251\) 28.0000 1.76734 0.883672 − 0.468106i \(-0.155064\pi\)
0.883672 + 0.468106i \(0.155064\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 4.00000 0.251478
\(254\) 4.00000 0.250982
\(255\) 4.00000 0.250490
\(256\) 1.00000 0.0625000
\(257\) 22.0000 1.37232 0.686161 − 0.727450i \(-0.259294\pi\)
0.686161 + 0.727450i \(0.259294\pi\)
\(258\) 0 0
\(259\) 6.00000 0.372822
\(260\) −6.00000 −0.372104
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 4.00000 0.246183
\(265\) −8.00000 −0.491436
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) −8.00000 −0.488678
\(269\) 30.0000 1.82913 0.914566 − 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 8.00000 0.485965 0.242983 − 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −4.00000 −0.242536
\(273\) −6.00000 −0.363137
\(274\) 18.0000 1.08742
\(275\) 4.00000 0.241209
\(276\) 1.00000 0.0601929
\(277\) 8.00000 0.480673 0.240337 − 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 12.0000 0.719712
\(279\) 0 0
\(280\) 1.00000 0.0597614
\(281\) −22.0000 −1.31241 −0.656205 − 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 8.00000 0.476393
\(283\) −12.0000 −0.713326 −0.356663 − 0.934233i \(-0.616086\pi\)
−0.356663 + 0.934233i \(0.616086\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 24.0000 1.41915
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) −10.0000 −0.586210
\(292\) 4.00000 0.234082
\(293\) −6.00000 −0.350524 −0.175262 − 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 1.00000 0.0583212
\(295\) 0 0
\(296\) −6.00000 −0.348743
\(297\) 4.00000 0.232104
\(298\) −14.0000 −0.810998
\(299\) 6.00000 0.346989
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) 0 0
\(303\) 10.0000 0.574485
\(304\) 0 0
\(305\) −10.0000 −0.572598
\(306\) −4.00000 −0.228665
\(307\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) −4.00000 −0.227921
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) −10.0000 −0.567048 −0.283524 − 0.958965i \(-0.591504\pi\)
−0.283524 + 0.958965i \(0.591504\pi\)
\(312\) 6.00000 0.339683
\(313\) −14.0000 −0.791327 −0.395663 − 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) −2.00000 −0.112867
\(315\) 1.00000 0.0563436
\(316\) −4.00000 −0.225018
\(317\) 2.00000 0.112331 0.0561656 − 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) 8.00000 0.448618
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) −10.0000 −0.558146
\(322\) −1.00000 −0.0557278
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 6.00000 0.332820
\(326\) 10.0000 0.553849
\(327\) −12.0000 −0.663602
\(328\) 0 0
\(329\) −8.00000 −0.441054
\(330\) −4.00000 −0.220193
\(331\) −28.0000 −1.53902 −0.769510 − 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) 16.0000 0.878114
\(333\) −6.00000 −0.328798
\(334\) −20.0000 −1.09435
\(335\) 8.00000 0.437087
\(336\) −1.00000 −0.0545545
\(337\) −6.00000 −0.326841 −0.163420 − 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) 23.0000 1.25104
\(339\) −6.00000 −0.325875
\(340\) 4.00000 0.216930
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −1.00000 −0.0538382
\(346\) −18.0000 −0.967686
\(347\) −28.0000 −1.50312 −0.751559 − 0.659665i \(-0.770698\pi\)
−0.751559 + 0.659665i \(0.770698\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 − 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 6.00000 0.320256
\(352\) 4.00000 0.213201
\(353\) −26.0000 −1.38384 −0.691920 − 0.721974i \(-0.743235\pi\)
−0.691920 + 0.721974i \(0.743235\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 10.0000 0.529999
\(357\) 4.00000 0.211702
\(358\) −2.00000 −0.105703
\(359\) 32.0000 1.68890 0.844448 − 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −19.0000 −1.00000
\(362\) 22.0000 1.15629
\(363\) 5.00000 0.262432
\(364\) −6.00000 −0.314485
\(365\) −4.00000 −0.209370
\(366\) 10.0000 0.522708
\(367\) −32.0000 −1.67039 −0.835193 − 0.549957i \(-0.814644\pi\)
−0.835193 + 0.549957i \(0.814644\pi\)
\(368\) 1.00000 0.0521286
\(369\) 0 0
\(370\) 6.00000 0.311925
\(371\) −8.00000 −0.415339
\(372\) 0 0
\(373\) −26.0000 −1.34623 −0.673114 − 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) −16.0000 −0.827340
\(375\) −1.00000 −0.0516398
\(376\) 8.00000 0.412568
\(377\) 0 0
\(378\) −1.00000 −0.0514344
\(379\) −34.0000 −1.74646 −0.873231 − 0.487306i \(-0.837980\pi\)
−0.873231 + 0.487306i \(0.837980\pi\)
\(380\) 0 0
\(381\) 4.00000 0.204926
\(382\) 0 0
\(383\) 6.00000 0.306586 0.153293 − 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 1.00000 0.0510310
\(385\) 4.00000 0.203859
\(386\) 22.0000 1.11977
\(387\) 0 0
\(388\) −10.0000 −0.507673
\(389\) −18.0000 −0.912636 −0.456318 − 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) −6.00000 −0.303822
\(391\) −4.00000 −0.202289
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) −2.00000 −0.100759
\(395\) 4.00000 0.201262
\(396\) 4.00000 0.201008
\(397\) −26.0000 −1.30490 −0.652451 − 0.757831i \(-0.726259\pi\)
−0.652451 + 0.757831i \(0.726259\pi\)
\(398\) −2.00000 −0.100251
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −10.0000 −0.499376 −0.249688 − 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) −8.00000 −0.399004
\(403\) 0 0
\(404\) 10.0000 0.497519
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) −4.00000 −0.198030
\(409\) −14.0000 −0.692255 −0.346128 − 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 0 0
\(411\) 18.0000 0.887875
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) 1.00000 0.0491473
\(415\) −16.0000 −0.785409
\(416\) 6.00000 0.294174
\(417\) 12.0000 0.587643
\(418\) 0 0
\(419\) −4.00000 −0.195413 −0.0977064 − 0.995215i \(-0.531151\pi\)
−0.0977064 + 0.995215i \(0.531151\pi\)
\(420\) 1.00000 0.0487950
\(421\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 8.00000 0.388973
\(424\) 8.00000 0.388514
\(425\) −4.00000 −0.194029
\(426\) 0 0
\(427\) −10.0000 −0.483934
\(428\) −10.0000 −0.483368
\(429\) 24.0000 1.15873
\(430\) 0 0
\(431\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 1.00000 0.0481125
\(433\) −10.0000 −0.480569 −0.240285 − 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −12.0000 −0.574696
\(437\) 0 0
\(438\) 4.00000 0.191127
\(439\) 8.00000 0.381819 0.190910 − 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) −4.00000 −0.190693
\(441\) 1.00000 0.0476190
\(442\) −24.0000 −1.14156
\(443\) −20.0000 −0.950229 −0.475114 − 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) −6.00000 −0.284747
\(445\) −10.0000 −0.474045
\(446\) −2.00000 −0.0947027
\(447\) −14.0000 −0.662177
\(448\) −1.00000 −0.0472456
\(449\) 6.00000 0.283158 0.141579 − 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) 0 0
\(454\) 20.0000 0.938647
\(455\) 6.00000 0.281284
\(456\) 0 0
\(457\) 18.0000 0.842004 0.421002 − 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(458\) −18.0000 −0.841085
\(459\) −4.00000 −0.186704
\(460\) −1.00000 −0.0466252
\(461\) 14.0000 0.652045 0.326023 − 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) −4.00000 −0.186097
\(463\) 4.00000 0.185896 0.0929479 − 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −10.0000 −0.463241
\(467\) −20.0000 −0.925490 −0.462745 − 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 6.00000 0.277350
\(469\) 8.00000 0.369406
\(470\) −8.00000 −0.369012
\(471\) −2.00000 −0.0921551
\(472\) 0 0
\(473\) 0 0
\(474\) −4.00000 −0.183726
\(475\) 0 0
\(476\) 4.00000 0.183340
\(477\) 8.00000 0.366295
\(478\) 24.0000 1.09773
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −36.0000 −1.64146
\(482\) 4.00000 0.182195
\(483\) −1.00000 −0.0455016
\(484\) 5.00000 0.227273
\(485\) 10.0000 0.454077
\(486\) 1.00000 0.0453609
\(487\) −32.0000 −1.45006 −0.725029 − 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) 10.0000 0.452679
\(489\) 10.0000 0.452216
\(490\) −1.00000 −0.0451754
\(491\) −30.0000 −1.35388 −0.676941 − 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −4.00000 −0.179787
\(496\) 0 0
\(497\) 0 0
\(498\) 16.0000 0.716977
\(499\) −8.00000 −0.358129 −0.179065 − 0.983837i \(-0.557307\pi\)
−0.179065 + 0.983837i \(0.557307\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −20.0000 −0.893534
\(502\) 28.0000 1.24970
\(503\) 6.00000 0.267527 0.133763 − 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) −1.00000 −0.0445435
\(505\) −10.0000 −0.444994
\(506\) 4.00000 0.177822
\(507\) 23.0000 1.02147
\(508\) 4.00000 0.177471
\(509\) −10.0000 −0.443242 −0.221621 − 0.975133i \(-0.571135\pi\)
−0.221621 + 0.975133i \(0.571135\pi\)
\(510\) 4.00000 0.177123
\(511\) −4.00000 −0.176950
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 22.0000 0.970378
\(515\) 4.00000 0.176261
\(516\) 0 0
\(517\) 32.0000 1.40736
\(518\) 6.00000 0.263625
\(519\) −18.0000 −0.790112
\(520\) −6.00000 −0.263117
\(521\) 6.00000 0.262865 0.131432 − 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) −36.0000 −1.57417 −0.787085 − 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) 0 0
\(525\) −1.00000 −0.0436436
\(526\) 0 0
\(527\) 0 0
\(528\) 4.00000 0.174078
\(529\) 1.00000 0.0434783
\(530\) −8.00000 −0.347498
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 10.0000 0.432742
\(535\) 10.0000 0.432338
\(536\) −8.00000 −0.345547
\(537\) −2.00000 −0.0863064
\(538\) 30.0000 1.29339
\(539\) 4.00000 0.172292
\(540\) −1.00000 −0.0430331
\(541\) −10.0000 −0.429934 −0.214967 − 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 8.00000 0.343629
\(543\) 22.0000 0.944110
\(544\) −4.00000 −0.171499
\(545\) 12.0000 0.514024
\(546\) −6.00000 −0.256776
\(547\) −2.00000 −0.0855138 −0.0427569 − 0.999086i \(-0.513614\pi\)
−0.0427569 + 0.999086i \(0.513614\pi\)
\(548\) 18.0000 0.768922
\(549\) 10.0000 0.426790
\(550\) 4.00000 0.170561
\(551\) 0 0
\(552\) 1.00000 0.0425628
\(553\) 4.00000 0.170097
\(554\) 8.00000 0.339887
\(555\) 6.00000 0.254686
\(556\) 12.0000 0.508913
\(557\) 12.0000 0.508456 0.254228 − 0.967144i \(-0.418179\pi\)
0.254228 + 0.967144i \(0.418179\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.00000 0.0422577
\(561\) −16.0000 −0.675521
\(562\) −22.0000 −0.928014
\(563\) −36.0000 −1.51722 −0.758610 − 0.651546i \(-0.774121\pi\)
−0.758610 + 0.651546i \(0.774121\pi\)
\(564\) 8.00000 0.336861
\(565\) 6.00000 0.252422
\(566\) −12.0000 −0.504398
\(567\) −1.00000 −0.0419961
\(568\) 0 0
\(569\) −34.0000 −1.42535 −0.712677 − 0.701492i \(-0.752517\pi\)
−0.712677 + 0.701492i \(0.752517\pi\)
\(570\) 0 0
\(571\) −26.0000 −1.08807 −0.544033 − 0.839064i \(-0.683103\pi\)
−0.544033 + 0.839064i \(0.683103\pi\)
\(572\) 24.0000 1.00349
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 1.00000 0.0416667
\(577\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 22.0000 0.914289
\(580\) 0 0
\(581\) −16.0000 −0.663792
\(582\) −10.0000 −0.414513
\(583\) 32.0000 1.32530
\(584\) 4.00000 0.165521
\(585\) −6.00000 −0.248069
\(586\) −6.00000 −0.247858
\(587\) 36.0000 1.48588 0.742940 − 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 1.00000 0.0412393
\(589\) 0 0
\(590\) 0 0
\(591\) −2.00000 −0.0822690
\(592\) −6.00000 −0.246598
\(593\) 14.0000 0.574911 0.287456 − 0.957794i \(-0.407191\pi\)
0.287456 + 0.957794i \(0.407191\pi\)
\(594\) 4.00000 0.164122
\(595\) −4.00000 −0.163984
\(596\) −14.0000 −0.573462
\(597\) −2.00000 −0.0818546
\(598\) 6.00000 0.245358
\(599\) 44.0000 1.79779 0.898896 − 0.438163i \(-0.144371\pi\)
0.898896 + 0.438163i \(0.144371\pi\)
\(600\) 1.00000 0.0408248
\(601\) −22.0000 −0.897399 −0.448699 − 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) −8.00000 −0.325785
\(604\) 0 0
\(605\) −5.00000 −0.203279
\(606\) 10.0000 0.406222
\(607\) 18.0000 0.730597 0.365299 − 0.930890i \(-0.380967\pi\)
0.365299 + 0.930890i \(0.380967\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −10.0000 −0.404888
\(611\) 48.0000 1.94187
\(612\) −4.00000 −0.161690
\(613\) 46.0000 1.85792 0.928961 − 0.370177i \(-0.120703\pi\)
0.928961 + 0.370177i \(0.120703\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −4.00000 −0.161165
\(617\) −18.0000 −0.724653 −0.362326 − 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) −4.00000 −0.160904
\(619\) −16.0000 −0.643094 −0.321547 − 0.946894i \(-0.604203\pi\)
−0.321547 + 0.946894i \(0.604203\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) −10.0000 −0.400963
\(623\) −10.0000 −0.400642
\(624\) 6.00000 0.240192
\(625\) 1.00000 0.0400000
\(626\) −14.0000 −0.559553
\(627\) 0 0
\(628\) −2.00000 −0.0798087
\(629\) 24.0000 0.956943
\(630\) 1.00000 0.0398410
\(631\) −20.0000 −0.796187 −0.398094 − 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) −4.00000 −0.159111
\(633\) 0 0
\(634\) 2.00000 0.0794301
\(635\) −4.00000 −0.158735
\(636\) 8.00000 0.317221
\(637\) 6.00000 0.237729
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 −0.0395285
\(641\) 18.0000 0.710957 0.355479 − 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) −10.0000 −0.394669
\(643\) 4.00000 0.157745 0.0788723 − 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) −1.00000 −0.0394055
\(645\) 0 0
\(646\) 0 0
\(647\) 12.0000 0.471769 0.235884 − 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 6.00000 0.235339
\(651\) 0 0
\(652\) 10.0000 0.391630
\(653\) −2.00000 −0.0782660 −0.0391330 − 0.999234i \(-0.512460\pi\)
−0.0391330 + 0.999234i \(0.512460\pi\)
\(654\) −12.0000 −0.469237
\(655\) 0 0
\(656\) 0 0
\(657\) 4.00000 0.156055
\(658\) −8.00000 −0.311872
\(659\) 24.0000 0.934907 0.467454 − 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) −4.00000 −0.155700
\(661\) −14.0000 −0.544537 −0.272268 − 0.962221i \(-0.587774\pi\)
−0.272268 + 0.962221i \(0.587774\pi\)
\(662\) −28.0000 −1.08825
\(663\) −24.0000 −0.932083
\(664\) 16.0000 0.620920
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) 0 0
\(668\) −20.0000 −0.773823
\(669\) −2.00000 −0.0773245
\(670\) 8.00000 0.309067
\(671\) 40.0000 1.54418
\(672\) −1.00000 −0.0385758
\(673\) 10.0000 0.385472 0.192736 − 0.981251i \(-0.438264\pi\)
0.192736 + 0.981251i \(0.438264\pi\)
\(674\) −6.00000 −0.231111
\(675\) 1.00000 0.0384900
\(676\) 23.0000 0.884615
\(677\) −50.0000 −1.92166 −0.960828 − 0.277145i \(-0.910612\pi\)
−0.960828 + 0.277145i \(0.910612\pi\)
\(678\) −6.00000 −0.230429
\(679\) 10.0000 0.383765
\(680\) 4.00000 0.153393
\(681\) 20.0000 0.766402
\(682\) 0 0
\(683\) −4.00000 −0.153056 −0.0765279 − 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0 0
\(685\) −18.0000 −0.687745
\(686\) −1.00000 −0.0381802
\(687\) −18.0000 −0.686743
\(688\) 0 0
\(689\) 48.0000 1.82865
\(690\) −1.00000 −0.0380693
\(691\) −20.0000 −0.760836 −0.380418 − 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) −18.0000 −0.684257
\(693\) −4.00000 −0.151947
\(694\) −28.0000 −1.06287
\(695\) −12.0000 −0.455186
\(696\) 0 0
\(697\) 0 0
\(698\) −2.00000 −0.0757011
\(699\) −10.0000 −0.378235
\(700\) −1.00000 −0.0377964
\(701\) 30.0000 1.13308 0.566542 − 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 6.00000 0.226455
\(703\) 0 0
\(704\) 4.00000 0.150756
\(705\) −8.00000 −0.301297
\(706\) −26.0000 −0.978523
\(707\) −10.0000 −0.376089
\(708\) 0 0
\(709\) −4.00000 −0.150223 −0.0751116 − 0.997175i \(-0.523931\pi\)
−0.0751116 + 0.997175i \(0.523931\pi\)
\(710\) 0 0
\(711\) −4.00000 −0.150012
\(712\) 10.0000 0.374766
\(713\) 0 0
\(714\) 4.00000 0.149696
\(715\) −24.0000 −0.897549
\(716\) −2.00000 −0.0747435
\(717\) 24.0000 0.896296
\(718\) 32.0000 1.19423
\(719\) −10.0000 −0.372937 −0.186469 − 0.982461i \(-0.559704\pi\)
−0.186469 + 0.982461i \(0.559704\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 4.00000 0.148968
\(722\) −19.0000 −0.707107
\(723\) 4.00000 0.148762
\(724\) 22.0000 0.817624
\(725\) 0 0
\(726\) 5.00000 0.185567
\(727\) 52.0000 1.92857 0.964287 − 0.264861i \(-0.0853260\pi\)
0.964287 + 0.264861i \(0.0853260\pi\)
\(728\) −6.00000 −0.222375
\(729\) 1.00000 0.0370370
\(730\) −4.00000 −0.148047
\(731\) 0 0
\(732\) 10.0000 0.369611
\(733\) −46.0000 −1.69905 −0.849524 − 0.527549i \(-0.823111\pi\)
−0.849524 + 0.527549i \(0.823111\pi\)
\(734\) −32.0000 −1.18114
\(735\) −1.00000 −0.0368856
\(736\) 1.00000 0.0368605
\(737\) −32.0000 −1.17874
\(738\) 0 0
\(739\) −40.0000 −1.47142 −0.735712 − 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) 6.00000 0.220564
\(741\) 0 0
\(742\) −8.00000 −0.293689
\(743\) −32.0000 −1.17397 −0.586983 − 0.809599i \(-0.699684\pi\)
−0.586983 + 0.809599i \(0.699684\pi\)
\(744\) 0 0
\(745\) 14.0000 0.512920
\(746\) −26.0000 −0.951928
\(747\) 16.0000 0.585409
\(748\) −16.0000 −0.585018
\(749\) 10.0000 0.365392
\(750\) −1.00000 −0.0365148
\(751\) 32.0000 1.16770 0.583848 − 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 8.00000 0.291730
\(753\) 28.0000 1.02038
\(754\) 0 0
\(755\) 0 0
\(756\) −1.00000 −0.0363696
\(757\) 2.00000 0.0726912 0.0363456 − 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −34.0000 −1.23494
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 4.00000 0.144905
\(763\) 12.0000 0.434429
\(764\) 0 0
\(765\) 4.00000 0.144620
\(766\) 6.00000 0.216789
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 32.0000 1.15395 0.576975 − 0.816762i \(-0.304233\pi\)
0.576975 + 0.816762i \(0.304233\pi\)
\(770\) 4.00000 0.144150
\(771\) 22.0000 0.792311
\(772\) 22.0000 0.791797
\(773\) −14.0000 −0.503545 −0.251773 − 0.967786i \(-0.581013\pi\)
−0.251773 + 0.967786i \(0.581013\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −10.0000 −0.358979
\(777\) 6.00000 0.215249
\(778\) −18.0000 −0.645331
\(779\) 0 0
\(780\) −6.00000 −0.214834
\(781\) 0 0
\(782\) −4.00000 −0.143040
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 2.00000 0.0713831
\(786\) 0 0
\(787\) −28.0000 −0.998092 −0.499046 − 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) −2.00000 −0.0712470
\(789\) 0 0
\(790\) 4.00000 0.142314
\(791\) 6.00000 0.213335
\(792\) 4.00000 0.142134
\(793\) 60.0000 2.13066
\(794\) −26.0000 −0.922705
\(795\) −8.00000 −0.283731
\(796\) −2.00000 −0.0708881
\(797\) −34.0000 −1.20434 −0.602171 − 0.798367i \(-0.705697\pi\)
−0.602171 + 0.798367i \(0.705697\pi\)
\(798\) 0 0
\(799\) −32.0000 −1.13208
\(800\) 1.00000 0.0353553
\(801\) 10.0000 0.353333
\(802\) −10.0000 −0.353112
\(803\) 16.0000 0.564628
\(804\) −8.00000 −0.282138
\(805\) 1.00000 0.0352454
\(806\) 0 0
\(807\) 30.0000 1.05605
\(808\) 10.0000 0.351799
\(809\) −34.0000 −1.19538 −0.597688 − 0.801729i \(-0.703914\pi\)
−0.597688 + 0.801729i \(0.703914\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −36.0000 −1.26413 −0.632065 − 0.774915i \(-0.717793\pi\)
−0.632065 + 0.774915i \(0.717793\pi\)
\(812\) 0 0
\(813\) 8.00000 0.280572
\(814\) −24.0000 −0.841200
\(815\) −10.0000 −0.350285
\(816\) −4.00000 −0.140028
\(817\) 0 0
\(818\) −14.0000 −0.489499
\(819\) −6.00000 −0.209657
\(820\) 0 0
\(821\) −48.0000 −1.67521 −0.837606 − 0.546275i \(-0.816045\pi\)
−0.837606 + 0.546275i \(0.816045\pi\)
\(822\) 18.0000 0.627822
\(823\) 4.00000 0.139431 0.0697156 − 0.997567i \(-0.477791\pi\)
0.0697156 + 0.997567i \(0.477791\pi\)
\(824\) −4.00000 −0.139347
\(825\) 4.00000 0.139262
\(826\) 0 0
\(827\) −30.0000 −1.04320 −0.521601 − 0.853189i \(-0.674665\pi\)
−0.521601 + 0.853189i \(0.674665\pi\)
\(828\) 1.00000 0.0347524
\(829\) 2.00000 0.0694629 0.0347314 − 0.999397i \(-0.488942\pi\)
0.0347314 + 0.999397i \(0.488942\pi\)
\(830\) −16.0000 −0.555368
\(831\) 8.00000 0.277517
\(832\) 6.00000 0.208013
\(833\) −4.00000 −0.138592
\(834\) 12.0000 0.415526
\(835\) 20.0000 0.692129
\(836\) 0 0
\(837\) 0 0
\(838\) −4.00000 −0.138178
\(839\) 36.0000 1.24286 0.621429 − 0.783470i \(-0.286552\pi\)
0.621429 + 0.783470i \(0.286552\pi\)
\(840\) 1.00000 0.0345033
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) −22.0000 −0.757720
\(844\) 0 0
\(845\) −23.0000 −0.791224
\(846\) 8.00000 0.275046
\(847\) −5.00000 −0.171802
\(848\) 8.00000 0.274721
\(849\) −12.0000 −0.411839
\(850\) −4.00000 −0.137199
\(851\) −6.00000 −0.205677
\(852\) 0 0
\(853\) 22.0000 0.753266 0.376633 − 0.926363i \(-0.377082\pi\)
0.376633 + 0.926363i \(0.377082\pi\)
\(854\) −10.0000 −0.342193
\(855\) 0 0
\(856\) −10.0000 −0.341793
\(857\) 18.0000 0.614868 0.307434 − 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 24.0000 0.819346
\(859\) −20.0000 −0.682391 −0.341196 − 0.939992i \(-0.610832\pi\)
−0.341196 + 0.939992i \(0.610832\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 16.0000 0.544646 0.272323 − 0.962206i \(-0.412208\pi\)
0.272323 + 0.962206i \(0.412208\pi\)
\(864\) 1.00000 0.0340207
\(865\) 18.0000 0.612018
\(866\) −10.0000 −0.339814
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) −16.0000 −0.542763
\(870\) 0 0
\(871\) −48.0000 −1.62642
\(872\) −12.0000 −0.406371
\(873\) −10.0000 −0.338449
\(874\) 0 0
\(875\) 1.00000 0.0338062
\(876\) 4.00000 0.135147
\(877\) −12.0000 −0.405211 −0.202606 − 0.979260i \(-0.564941\pi\)
−0.202606 + 0.979260i \(0.564941\pi\)
\(878\) 8.00000 0.269987
\(879\) −6.00000 −0.202375
\(880\) −4.00000 −0.134840
\(881\) 42.0000 1.41502 0.707508 − 0.706705i \(-0.249819\pi\)
0.707508 + 0.706705i \(0.249819\pi\)
\(882\) 1.00000 0.0336718
\(883\) 18.0000 0.605748 0.302874 − 0.953031i \(-0.402054\pi\)
0.302874 + 0.953031i \(0.402054\pi\)
\(884\) −24.0000 −0.807207
\(885\) 0 0
\(886\) −20.0000 −0.671913
\(887\) 48.0000 1.61168 0.805841 − 0.592132i \(-0.201714\pi\)
0.805841 + 0.592132i \(0.201714\pi\)
\(888\) −6.00000 −0.201347
\(889\) −4.00000 −0.134156
\(890\) −10.0000 −0.335201
\(891\) 4.00000 0.134005
\(892\) −2.00000 −0.0669650
\(893\) 0 0
\(894\) −14.0000 −0.468230
\(895\) 2.00000 0.0668526
\(896\) −1.00000 −0.0334077
\(897\) 6.00000 0.200334
\(898\) 6.00000 0.200223
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) −32.0000 −1.06607
\(902\) 0 0
\(903\) 0 0
\(904\) −6.00000 −0.199557
\(905\) −22.0000 −0.731305
\(906\) 0 0
\(907\) −8.00000 −0.265636 −0.132818 − 0.991140i \(-0.542403\pi\)
−0.132818 + 0.991140i \(0.542403\pi\)
\(908\) 20.0000 0.663723
\(909\) 10.0000 0.331679
\(910\) 6.00000 0.198898
\(911\) 8.00000 0.265052 0.132526 − 0.991180i \(-0.457691\pi\)
0.132526 + 0.991180i \(0.457691\pi\)
\(912\) 0 0
\(913\) 64.0000 2.11809
\(914\) 18.0000 0.595387
\(915\) −10.0000 −0.330590
\(916\) −18.0000 −0.594737
\(917\) 0 0
\(918\) −4.00000 −0.132020
\(919\) 24.0000 0.791687 0.395843 − 0.918318i \(-0.370452\pi\)
0.395843 + 0.918318i \(0.370452\pi\)
\(920\) −1.00000 −0.0329690
\(921\) 0 0
\(922\) 14.0000 0.461065
\(923\) 0 0
\(924\) −4.00000 −0.131590
\(925\) −6.00000 −0.197279
\(926\) 4.00000 0.131448
\(927\) −4.00000 −0.131377
\(928\) 0 0
\(929\) −36.0000 −1.18112 −0.590561 − 0.806993i \(-0.701093\pi\)
−0.590561 + 0.806993i \(0.701093\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −10.0000 −0.327561
\(933\) −10.0000 −0.327385
\(934\) −20.0000 −0.654420
\(935\) 16.0000 0.523256
\(936\) 6.00000 0.196116
\(937\) −38.0000 −1.24141 −0.620703 − 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(938\) 8.00000 0.261209
\(939\) −14.0000 −0.456873
\(940\) −8.00000 −0.260931
\(941\) 54.0000 1.76035 0.880175 − 0.474650i \(-0.157425\pi\)
0.880175 + 0.474650i \(0.157425\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 0 0
\(944\) 0 0
\(945\) 1.00000 0.0325300
\(946\) 0 0
\(947\) 8.00000 0.259965 0.129983 − 0.991516i \(-0.458508\pi\)
0.129983 + 0.991516i \(0.458508\pi\)
\(948\) −4.00000 −0.129914
\(949\) 24.0000 0.779073
\(950\) 0 0
\(951\) 2.00000 0.0648544
\(952\) 4.00000 0.129641
\(953\) −50.0000 −1.61966 −0.809829 − 0.586665i \(-0.800440\pi\)
−0.809829 + 0.586665i \(0.800440\pi\)
\(954\) 8.00000 0.259010
\(955\) 0 0
\(956\) 24.0000 0.776215
\(957\) 0 0
\(958\) 0 0
\(959\) −18.0000 −0.581250
\(960\) −1.00000 −0.0322749
\(961\) −31.0000 −1.00000
\(962\) −36.0000 −1.16069
\(963\) −10.0000 −0.322245
\(964\) 4.00000 0.128831
\(965\) −22.0000 −0.708205
\(966\) −1.00000 −0.0321745
\(967\) −8.00000 −0.257263 −0.128631 − 0.991692i \(-0.541058\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(968\) 5.00000 0.160706
\(969\) 0 0
\(970\) 10.0000 0.321081
\(971\) 36.0000 1.15529 0.577647 − 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 1.00000 0.0320750
\(973\) −12.0000 −0.384702
\(974\) −32.0000 −1.02535
\(975\) 6.00000 0.192154
\(976\) 10.0000 0.320092
\(977\) −38.0000 −1.21573 −0.607864 − 0.794041i \(-0.707973\pi\)
−0.607864 + 0.794041i \(0.707973\pi\)
\(978\) 10.0000 0.319765
\(979\) 40.0000 1.27841
\(980\) −1.00000 −0.0319438
\(981\) −12.0000 −0.383131
\(982\) −30.0000 −0.957338
\(983\) 54.0000 1.72233 0.861166 − 0.508323i \(-0.169735\pi\)
0.861166 + 0.508323i \(0.169735\pi\)
\(984\) 0 0
\(985\) 2.00000 0.0637253
\(986\) 0 0
\(987\) −8.00000 −0.254643
\(988\) 0 0
\(989\) 0 0
\(990\) −4.00000 −0.127128
\(991\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) −28.0000 −0.888553
\(994\) 0 0
\(995\) 2.00000 0.0634043
\(996\) 16.0000 0.506979
\(997\) −22.0000 −0.696747 −0.348373 − 0.937356i \(-0.613266\pi\)
−0.348373 + 0.937356i \(0.613266\pi\)
\(998\) −8.00000 −0.253236
\(999\) −6.00000 −0.189832
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 4830.2.a.bb.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4830.2.a.bb.1.1 ✓ 1 1.1 even 1 trivial