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Properties

Label 4730.2.a.d.1.1
Level $4730$
Weight $2$
Character 4730.1
Self dual yes
Analytic conductor $37.769$
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] = [4730,2,Mod(1,4730)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4730, 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("4730.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4730.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(37.7692401561\)
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 \(\chi\) \(=\) 4730.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -3.00000 q^{12} +1.00000 q^{14} -3.00000 q^{15} +1.00000 q^{16} -3.00000 q^{17} +6.00000 q^{18} -1.00000 q^{19} +1.00000 q^{20} -3.00000 q^{21} +1.00000 q^{22} -4.00000 q^{23} -3.00000 q^{24} +1.00000 q^{25} -9.00000 q^{27} +1.00000 q^{28} -5.00000 q^{29} -3.00000 q^{30} -3.00000 q^{31} +1.00000 q^{32} -3.00000 q^{33} -3.00000 q^{34} +1.00000 q^{35} +6.00000 q^{36} -11.0000 q^{37} -1.00000 q^{38} +1.00000 q^{40} -3.00000 q^{42} +1.00000 q^{43} +1.00000 q^{44} +6.00000 q^{45} -4.00000 q^{46} +6.00000 q^{47} -3.00000 q^{48} -6.00000 q^{49} +1.00000 q^{50} +9.00000 q^{51} -9.00000 q^{53} -9.00000 q^{54} +1.00000 q^{55} +1.00000 q^{56} +3.00000 q^{57} -5.00000 q^{58} +4.00000 q^{59} -3.00000 q^{60} +13.0000 q^{61} -3.00000 q^{62} +6.00000 q^{63} +1.00000 q^{64} -3.00000 q^{66} +12.0000 q^{67} -3.00000 q^{68} +12.0000 q^{69} +1.00000 q^{70} +9.00000 q^{71} +6.00000 q^{72} -10.0000 q^{73} -11.0000 q^{74} -3.00000 q^{75} -1.00000 q^{76} +1.00000 q^{77} -4.00000 q^{79} +1.00000 q^{80} +9.00000 q^{81} -3.00000 q^{84} -3.00000 q^{85} +1.00000 q^{86} +15.0000 q^{87} +1.00000 q^{88} -1.00000 q^{89} +6.00000 q^{90} -4.00000 q^{92} +9.00000 q^{93} +6.00000 q^{94} -1.00000 q^{95} -3.00000 q^{96} -6.00000 q^{98} +6.00000 q^{99} +O(q^{100})\)

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
\(3\) −3.00000 −1.73205 −0.866025 − 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −3.00000 −1.22474
\(7\) 1.00000 0.377964 0.188982 − 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.00000 2.00000
\(10\) 1.00000 0.316228
\(11\) 1.00000 0.301511
\(12\) −3.00000 −0.866025
\(13\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 1.00000 0.267261
\(15\) −3.00000 −0.774597
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 − 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 6.00000 1.41421
\(19\) −1.00000 −0.229416 −0.114708 − 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 1.00000 0.223607
\(21\) −3.00000 −0.654654
\(22\) 1.00000 0.213201
\(23\) −4.00000 −0.834058 −0.417029 − 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −3.00000 −0.612372
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −9.00000 −1.73205
\(28\) 1.00000 0.188982
\(29\) −5.00000 −0.928477 −0.464238 − 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) −3.00000 −0.547723
\(31\) −3.00000 −0.538816 −0.269408 − 0.963026i \(-0.586828\pi\)
−0.269408 + 0.963026i \(0.586828\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.00000 −0.522233
\(34\) −3.00000 −0.514496
\(35\) 1.00000 0.169031
\(36\) 6.00000 1.00000
\(37\) −11.0000 −1.80839 −0.904194 − 0.427121i \(-0.859528\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) −1.00000 −0.162221
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −3.00000 −0.462910
\(43\) 1.00000 0.152499
\(44\) 1.00000 0.150756
\(45\) 6.00000 0.894427
\(46\) −4.00000 −0.589768
\(47\) 6.00000 0.875190 0.437595 − 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) −3.00000 −0.433013
\(49\) −6.00000 −0.857143
\(50\) 1.00000 0.141421
\(51\) 9.00000 1.26025
\(52\) 0 0
\(53\) −9.00000 −1.23625 −0.618123 − 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) −9.00000 −1.22474
\(55\) 1.00000 0.134840
\(56\) 1.00000 0.133631
\(57\) 3.00000 0.397360
\(58\) −5.00000 −0.656532
\(59\) 4.00000 0.520756 0.260378 − 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) −3.00000 −0.387298
\(61\) 13.0000 1.66448 0.832240 − 0.554416i \(-0.187058\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) −3.00000 −0.381000
\(63\) 6.00000 0.755929
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.00000 −0.369274
\(67\) 12.0000 1.46603 0.733017 − 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) −3.00000 −0.363803
\(69\) 12.0000 1.44463
\(70\) 1.00000 0.119523
\(71\) 9.00000 1.06810 0.534052 − 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) 6.00000 0.707107
\(73\) −10.0000 −1.17041 −0.585206 − 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) −11.0000 −1.27872
\(75\) −3.00000 −0.346410
\(76\) −1.00000 −0.114708
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 − 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 1.00000 0.111803
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −3.00000 −0.327327
\(85\) −3.00000 −0.325396
\(86\) 1.00000 0.107833
\(87\) 15.0000 1.60817
\(88\) 1.00000 0.106600
\(89\) −1.00000 −0.106000 −0.0529999 − 0.998595i \(-0.516878\pi\)
−0.0529999 + 0.998595i \(0.516878\pi\)
\(90\) 6.00000 0.632456
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) 9.00000 0.933257
\(94\) 6.00000 0.618853
\(95\) −1.00000 −0.102598
\(96\) −3.00000 −0.306186
\(97\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) −6.00000 −0.606092
\(99\) 6.00000 0.603023
\(100\) 1.00000 0.100000
\(101\) −10.0000 −0.995037 −0.497519 − 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 9.00000 0.891133
\(103\) −8.00000 −0.788263 −0.394132 − 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) −3.00000 −0.292770
\(106\) −9.00000 −0.874157
\(107\) −4.00000 −0.386695 −0.193347 − 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) −9.00000 −0.866025
\(109\) −2.00000 −0.191565 −0.0957826 − 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 1.00000 0.0953463
\(111\) 33.0000 3.13222
\(112\) 1.00000 0.0944911
\(113\) −12.0000 −1.12887 −0.564433 − 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 3.00000 0.280976
\(115\) −4.00000 −0.373002
\(116\) −5.00000 −0.464238
\(117\) 0 0
\(118\) 4.00000 0.368230
\(119\) −3.00000 −0.275010
\(120\) −3.00000 −0.273861
\(121\) 1.00000 0.0909091
\(122\) 13.0000 1.17696
\(123\) 0 0
\(124\) −3.00000 −0.269408
\(125\) 1.00000 0.0894427
\(126\) 6.00000 0.534522
\(127\) −12.0000 −1.06483 −0.532414 − 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.00000 −0.264135
\(130\) 0 0
\(131\) −1.00000 −0.0873704 −0.0436852 − 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) −3.00000 −0.261116
\(133\) −1.00000 −0.0867110
\(134\) 12.0000 1.03664
\(135\) −9.00000 −0.774597
\(136\) −3.00000 −0.257248
\(137\) −2.00000 −0.170872 −0.0854358 − 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) 12.0000 1.02151
\(139\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 1.00000 0.0845154
\(141\) −18.0000 −1.51587
\(142\) 9.00000 0.755263
\(143\) 0 0
\(144\) 6.00000 0.500000
\(145\) −5.00000 −0.415227
\(146\) −10.0000 −0.827606
\(147\) 18.0000 1.48461
\(148\) −11.0000 −0.904194
\(149\) −11.0000 −0.901155 −0.450578 − 0.892737i \(-0.648782\pi\)
−0.450578 + 0.892737i \(0.648782\pi\)
\(150\) −3.00000 −0.244949
\(151\) −16.0000 −1.30206 −0.651031 − 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −18.0000 −1.45521
\(154\) 1.00000 0.0805823
\(155\) −3.00000 −0.240966
\(156\) 0 0
\(157\) −3.00000 −0.239426 −0.119713 − 0.992809i \(-0.538197\pi\)
−0.119713 + 0.992809i \(0.538197\pi\)
\(158\) −4.00000 −0.318223
\(159\) 27.0000 2.14124
\(160\) 1.00000 0.0790569
\(161\) −4.00000 −0.315244
\(162\) 9.00000 0.707107
\(163\) −11.0000 −0.861586 −0.430793 − 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) 0 0
\(165\) −3.00000 −0.233550
\(166\) 0 0
\(167\) 7.00000 0.541676 0.270838 − 0.962625i \(-0.412699\pi\)
0.270838 + 0.962625i \(0.412699\pi\)
\(168\) −3.00000 −0.231455
\(169\) −13.0000 −1.00000
\(170\) −3.00000 −0.230089
\(171\) −6.00000 −0.458831
\(172\) 1.00000 0.0762493
\(173\) 6.00000 0.456172 0.228086 − 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 15.0000 1.13715
\(175\) 1.00000 0.0755929
\(176\) 1.00000 0.0753778
\(177\) −12.0000 −0.901975
\(178\) −1.00000 −0.0749532
\(179\) 12.0000 0.896922 0.448461 − 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 6.00000 0.447214
\(181\) 14.0000 1.04061 0.520306 − 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) −39.0000 −2.88296
\(184\) −4.00000 −0.294884
\(185\) −11.0000 −0.808736
\(186\) 9.00000 0.659912
\(187\) −3.00000 −0.219382
\(188\) 6.00000 0.437595
\(189\) −9.00000 −0.654654
\(190\) −1.00000 −0.0725476
\(191\) −4.00000 −0.289430 −0.144715 − 0.989473i \(-0.546227\pi\)
−0.144715 + 0.989473i \(0.546227\pi\)
\(192\) −3.00000 −0.216506
\(193\) 5.00000 0.359908 0.179954 − 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) −12.0000 −0.854965 −0.427482 − 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 6.00000 0.426401
\(199\) 25.0000 1.77220 0.886102 − 0.463491i \(-0.153403\pi\)
0.886102 + 0.463491i \(0.153403\pi\)
\(200\) 1.00000 0.0707107
\(201\) −36.0000 −2.53924
\(202\) −10.0000 −0.703598
\(203\) −5.00000 −0.350931
\(204\) 9.00000 0.630126
\(205\) 0 0
\(206\) −8.00000 −0.557386
\(207\) −24.0000 −1.66812
\(208\) 0 0
\(209\) −1.00000 −0.0691714
\(210\) −3.00000 −0.207020
\(211\) 23.0000 1.58339 0.791693 − 0.610920i \(-0.209200\pi\)
0.791693 + 0.610920i \(0.209200\pi\)
\(212\) −9.00000 −0.618123
\(213\) −27.0000 −1.85001
\(214\) −4.00000 −0.273434
\(215\) 1.00000 0.0681994
\(216\) −9.00000 −0.612372
\(217\) −3.00000 −0.203653
\(218\) −2.00000 −0.135457
\(219\) 30.0000 2.02721
\(220\) 1.00000 0.0674200
\(221\) 0 0
\(222\) 33.0000 2.21481
\(223\) −28.0000 −1.87502 −0.937509 − 0.347960i \(-0.886874\pi\)
−0.937509 + 0.347960i \(0.886874\pi\)
\(224\) 1.00000 0.0668153
\(225\) 6.00000 0.400000
\(226\) −12.0000 −0.798228
\(227\) 18.0000 1.19470 0.597351 − 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 3.00000 0.198680
\(229\) −22.0000 −1.45380 −0.726900 − 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) −4.00000 −0.263752
\(231\) −3.00000 −0.197386
\(232\) −5.00000 −0.328266
\(233\) 3.00000 0.196537 0.0982683 − 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) 0 0
\(235\) 6.00000 0.391397
\(236\) 4.00000 0.260378
\(237\) 12.0000 0.779484
\(238\) −3.00000 −0.194461
\(239\) 2.00000 0.129369 0.0646846 − 0.997906i \(-0.479396\pi\)
0.0646846 + 0.997906i \(0.479396\pi\)
\(240\) −3.00000 −0.193649
\(241\) 4.00000 0.257663 0.128831 − 0.991667i \(-0.458877\pi\)
0.128831 + 0.991667i \(0.458877\pi\)
\(242\) 1.00000 0.0642824
\(243\) 0 0
\(244\) 13.0000 0.832240
\(245\) −6.00000 −0.383326
\(246\) 0 0
\(247\) 0 0
\(248\) −3.00000 −0.190500
\(249\) 0 0
\(250\) 1.00000 0.0632456
\(251\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 6.00000 0.377964
\(253\) −4.00000 −0.251478
\(254\) −12.0000 −0.752947
\(255\) 9.00000 0.563602
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 − 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) −3.00000 −0.186772
\(259\) −11.0000 −0.683507
\(260\) 0 0
\(261\) −30.0000 −1.85695
\(262\) −1.00000 −0.0617802
\(263\) −9.00000 −0.554964 −0.277482 − 0.960731i \(-0.589500\pi\)
−0.277482 + 0.960731i \(0.589500\pi\)
\(264\) −3.00000 −0.184637
\(265\) −9.00000 −0.552866
\(266\) −1.00000 −0.0613139
\(267\) 3.00000 0.183597
\(268\) 12.0000 0.733017
\(269\) 18.0000 1.09748 0.548740 − 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) −9.00000 −0.547723
\(271\) −22.0000 −1.33640 −0.668202 − 0.743980i \(-0.732936\pi\)
−0.668202 + 0.743980i \(0.732936\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 1.00000 0.0603023
\(276\) 12.0000 0.722315
\(277\) −2.00000 −0.120168 −0.0600842 − 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 0 0
\(279\) −18.0000 −1.07763
\(280\) 1.00000 0.0597614
\(281\) −12.0000 −0.715860 −0.357930 − 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) −18.0000 −1.07188
\(283\) −10.0000 −0.594438 −0.297219 − 0.954809i \(-0.596059\pi\)
−0.297219 + 0.954809i \(0.596059\pi\)
\(284\) 9.00000 0.534052
\(285\) 3.00000 0.177705
\(286\) 0 0
\(287\) 0 0
\(288\) 6.00000 0.353553
\(289\) −8.00000 −0.470588
\(290\) −5.00000 −0.293610
\(291\) 0 0
\(292\) −10.0000 −0.585206
\(293\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 18.0000 1.04978
\(295\) 4.00000 0.232889
\(296\) −11.0000 −0.639362
\(297\) −9.00000 −0.522233
\(298\) −11.0000 −0.637213
\(299\) 0 0
\(300\) −3.00000 −0.173205
\(301\) 1.00000 0.0576390
\(302\) −16.0000 −0.920697
\(303\) 30.0000 1.72345
\(304\) −1.00000 −0.0573539
\(305\) 13.0000 0.744378
\(306\) −18.0000 −1.02899
\(307\) −14.0000 −0.799022 −0.399511 − 0.916728i \(-0.630820\pi\)
−0.399511 + 0.916728i \(0.630820\pi\)
\(308\) 1.00000 0.0569803
\(309\) 24.0000 1.36531
\(310\) −3.00000 −0.170389
\(311\) −3.00000 −0.170114 −0.0850572 − 0.996376i \(-0.527107\pi\)
−0.0850572 + 0.996376i \(0.527107\pi\)
\(312\) 0 0
\(313\) −22.0000 −1.24351 −0.621757 − 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) −3.00000 −0.169300
\(315\) 6.00000 0.338062
\(316\) −4.00000 −0.225018
\(317\) −11.0000 −0.617822 −0.308911 − 0.951091i \(-0.599964\pi\)
−0.308911 + 0.951091i \(0.599964\pi\)
\(318\) 27.0000 1.51408
\(319\) −5.00000 −0.279946
\(320\) 1.00000 0.0559017
\(321\) 12.0000 0.669775
\(322\) −4.00000 −0.222911
\(323\) 3.00000 0.166924
\(324\) 9.00000 0.500000
\(325\) 0 0
\(326\) −11.0000 −0.609234
\(327\) 6.00000 0.331801
\(328\) 0 0
\(329\) 6.00000 0.330791
\(330\) −3.00000 −0.165145
\(331\) −4.00000 −0.219860 −0.109930 − 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 0 0
\(333\) −66.0000 −3.61678
\(334\) 7.00000 0.383023
\(335\) 12.0000 0.655630
\(336\) −3.00000 −0.163663
\(337\) −5.00000 −0.272367 −0.136184 − 0.990684i \(-0.543484\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) −13.0000 −0.707107
\(339\) 36.0000 1.95525
\(340\) −3.00000 −0.162698
\(341\) −3.00000 −0.162459
\(342\) −6.00000 −0.324443
\(343\) −13.0000 −0.701934
\(344\) 1.00000 0.0539164
\(345\) 12.0000 0.646058
\(346\) 6.00000 0.322562
\(347\) −30.0000 −1.61048 −0.805242 − 0.592946i \(-0.797965\pi\)
−0.805242 + 0.592946i \(0.797965\pi\)
\(348\) 15.0000 0.804084
\(349\) −14.0000 −0.749403 −0.374701 − 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 1.00000 0.0534522
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) −24.0000 −1.27739 −0.638696 − 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) −12.0000 −0.637793
\(355\) 9.00000 0.477670
\(356\) −1.00000 −0.0529999
\(357\) 9.00000 0.476331
\(358\) 12.0000 0.634220
\(359\) −4.00000 −0.211112 −0.105556 − 0.994413i \(-0.533662\pi\)
−0.105556 + 0.994413i \(0.533662\pi\)
\(360\) 6.00000 0.316228
\(361\) −18.0000 −0.947368
\(362\) 14.0000 0.735824
\(363\) −3.00000 −0.157459
\(364\) 0 0
\(365\) −10.0000 −0.523424
\(366\) −39.0000 −2.03856
\(367\) −10.0000 −0.521996 −0.260998 − 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) −4.00000 −0.208514
\(369\) 0 0
\(370\) −11.0000 −0.571863
\(371\) −9.00000 −0.467257
\(372\) 9.00000 0.466628
\(373\) −4.00000 −0.207112 −0.103556 − 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) −3.00000 −0.155126
\(375\) −3.00000 −0.154919
\(376\) 6.00000 0.309426
\(377\) 0 0
\(378\) −9.00000 −0.462910
\(379\) −12.0000 −0.616399 −0.308199 − 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) −1.00000 −0.0512989
\(381\) 36.0000 1.84434
\(382\) −4.00000 −0.204658
\(383\) −36.0000 −1.83951 −0.919757 − 0.392488i \(-0.871614\pi\)
−0.919757 + 0.392488i \(0.871614\pi\)
\(384\) −3.00000 −0.153093
\(385\) 1.00000 0.0509647
\(386\) 5.00000 0.254493
\(387\) 6.00000 0.304997
\(388\) 0 0
\(389\) −16.0000 −0.811232 −0.405616 − 0.914044i \(-0.632943\pi\)
−0.405616 + 0.914044i \(0.632943\pi\)
\(390\) 0 0
\(391\) 12.0000 0.606866
\(392\) −6.00000 −0.303046
\(393\) 3.00000 0.151330
\(394\) −12.0000 −0.604551
\(395\) −4.00000 −0.201262
\(396\) 6.00000 0.301511
\(397\) 6.00000 0.301131 0.150566 − 0.988600i \(-0.451890\pi\)
0.150566 + 0.988600i \(0.451890\pi\)
\(398\) 25.0000 1.25314
\(399\) 3.00000 0.150188
\(400\) 1.00000 0.0500000
\(401\) 31.0000 1.54807 0.774033 − 0.633145i \(-0.218236\pi\)
0.774033 + 0.633145i \(0.218236\pi\)
\(402\) −36.0000 −1.79552
\(403\) 0 0
\(404\) −10.0000 −0.497519
\(405\) 9.00000 0.447214
\(406\) −5.00000 −0.248146
\(407\) −11.0000 −0.545250
\(408\) 9.00000 0.445566
\(409\) 32.0000 1.58230 0.791149 − 0.611623i \(-0.209483\pi\)
0.791149 + 0.611623i \(0.209483\pi\)
\(410\) 0 0
\(411\) 6.00000 0.295958
\(412\) −8.00000 −0.394132
\(413\) 4.00000 0.196827
\(414\) −24.0000 −1.17954
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) −1.00000 −0.0489116
\(419\) 14.0000 0.683945 0.341972 − 0.939710i \(-0.388905\pi\)
0.341972 + 0.939710i \(0.388905\pi\)
\(420\) −3.00000 −0.146385
\(421\) −12.0000 −0.584844 −0.292422 − 0.956289i \(-0.594461\pi\)
−0.292422 + 0.956289i \(0.594461\pi\)
\(422\) 23.0000 1.11962
\(423\) 36.0000 1.75038
\(424\) −9.00000 −0.437079
\(425\) −3.00000 −0.145521
\(426\) −27.0000 −1.30815
\(427\) 13.0000 0.629114
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) 1.00000 0.0482243
\(431\) −2.00000 −0.0963366 −0.0481683 − 0.998839i \(-0.515338\pi\)
−0.0481683 + 0.998839i \(0.515338\pi\)
\(432\) −9.00000 −0.433013
\(433\) 28.0000 1.34559 0.672797 − 0.739827i \(-0.265093\pi\)
0.672797 + 0.739827i \(0.265093\pi\)
\(434\) −3.00000 −0.144005
\(435\) 15.0000 0.719195
\(436\) −2.00000 −0.0957826
\(437\) 4.00000 0.191346
\(438\) 30.0000 1.43346
\(439\) 34.0000 1.62273 0.811366 − 0.584539i \(-0.198725\pi\)
0.811366 + 0.584539i \(0.198725\pi\)
\(440\) 1.00000 0.0476731
\(441\) −36.0000 −1.71429
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 − 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 33.0000 1.56611
\(445\) −1.00000 −0.0474045
\(446\) −28.0000 −1.32584
\(447\) 33.0000 1.56085
\(448\) 1.00000 0.0472456
\(449\) 2.00000 0.0943858 0.0471929 − 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 6.00000 0.282843
\(451\) 0 0
\(452\) −12.0000 −0.564433
\(453\) 48.0000 2.25524
\(454\) 18.0000 0.844782
\(455\) 0 0
\(456\) 3.00000 0.140488
\(457\) 17.0000 0.795226 0.397613 − 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) −22.0000 −1.02799
\(459\) 27.0000 1.26025
\(460\) −4.00000 −0.186501
\(461\) −21.0000 −0.978068 −0.489034 − 0.872265i \(-0.662651\pi\)
−0.489034 + 0.872265i \(0.662651\pi\)
\(462\) −3.00000 −0.139573
\(463\) −26.0000 −1.20832 −0.604161 − 0.796862i \(-0.706492\pi\)
−0.604161 + 0.796862i \(0.706492\pi\)
\(464\) −5.00000 −0.232119
\(465\) 9.00000 0.417365
\(466\) 3.00000 0.138972
\(467\) 41.0000 1.89725 0.948627 − 0.316397i \(-0.102473\pi\)
0.948627 + 0.316397i \(0.102473\pi\)
\(468\) 0 0
\(469\) 12.0000 0.554109
\(470\) 6.00000 0.276759
\(471\) 9.00000 0.414698
\(472\) 4.00000 0.184115
\(473\) 1.00000 0.0459800
\(474\) 12.0000 0.551178
\(475\) −1.00000 −0.0458831
\(476\) −3.00000 −0.137505
\(477\) −54.0000 −2.47249
\(478\) 2.00000 0.0914779
\(479\) −24.0000 −1.09659 −0.548294 − 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) −3.00000 −0.136931
\(481\) 0 0
\(482\) 4.00000 0.182195
\(483\) 12.0000 0.546019
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) 0 0
\(487\) 26.0000 1.17817 0.589086 − 0.808070i \(-0.299488\pi\)
0.589086 + 0.808070i \(0.299488\pi\)
\(488\) 13.0000 0.588482
\(489\) 33.0000 1.49231
\(490\) −6.00000 −0.271052
\(491\) −5.00000 −0.225647 −0.112823 − 0.993615i \(-0.535989\pi\)
−0.112823 + 0.993615i \(0.535989\pi\)
\(492\) 0 0
\(493\) 15.0000 0.675566
\(494\) 0 0
\(495\) 6.00000 0.269680
\(496\) −3.00000 −0.134704
\(497\) 9.00000 0.403705
\(498\) 0 0
\(499\) 10.0000 0.447661 0.223831 − 0.974628i \(-0.428144\pi\)
0.223831 + 0.974628i \(0.428144\pi\)
\(500\) 1.00000 0.0447214
\(501\) −21.0000 −0.938211
\(502\) 0 0
\(503\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 6.00000 0.267261
\(505\) −10.0000 −0.444994
\(506\) −4.00000 −0.177822
\(507\) 39.0000 1.73205
\(508\) −12.0000 −0.532414
\(509\) 20.0000 0.886484 0.443242 − 0.896402i \(-0.353828\pi\)
0.443242 + 0.896402i \(0.353828\pi\)
\(510\) 9.00000 0.398527
\(511\) −10.0000 −0.442374
\(512\) 1.00000 0.0441942
\(513\) 9.00000 0.397360
\(514\) 6.00000 0.264649
\(515\) −8.00000 −0.352522
\(516\) −3.00000 −0.132068
\(517\) 6.00000 0.263880
\(518\) −11.0000 −0.483312
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) −10.0000 −0.438108 −0.219054 − 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) −30.0000 −1.31306
\(523\) 34.0000 1.48672 0.743358 − 0.668894i \(-0.233232\pi\)
0.743358 + 0.668894i \(0.233232\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −3.00000 −0.130931
\(526\) −9.00000 −0.392419
\(527\) 9.00000 0.392046
\(528\) −3.00000 −0.130558
\(529\) −7.00000 −0.304348
\(530\) −9.00000 −0.390935
\(531\) 24.0000 1.04151
\(532\) −1.00000 −0.0433555
\(533\) 0 0
\(534\) 3.00000 0.129823
\(535\) −4.00000 −0.172935
\(536\) 12.0000 0.518321
\(537\) −36.0000 −1.55351
\(538\) 18.0000 0.776035
\(539\) −6.00000 −0.258438
\(540\) −9.00000 −0.387298
\(541\) 17.0000 0.730887 0.365444 − 0.930834i \(-0.380917\pi\)
0.365444 + 0.930834i \(0.380917\pi\)
\(542\) −22.0000 −0.944981
\(543\) −42.0000 −1.80239
\(544\) −3.00000 −0.128624
\(545\) −2.00000 −0.0856706
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 − 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −2.00000 −0.0854358
\(549\) 78.0000 3.32896
\(550\) 1.00000 0.0426401
\(551\) 5.00000 0.213007
\(552\) 12.0000 0.510754
\(553\) −4.00000 −0.170097
\(554\) −2.00000 −0.0849719
\(555\) 33.0000 1.40077
\(556\) 0 0
\(557\) 26.0000 1.10166 0.550828 − 0.834619i \(-0.314312\pi\)
0.550828 + 0.834619i \(0.314312\pi\)
\(558\) −18.0000 −0.762001
\(559\) 0 0
\(560\) 1.00000 0.0422577
\(561\) 9.00000 0.379980
\(562\) −12.0000 −0.506189
\(563\) 4.00000 0.168580 0.0842900 − 0.996441i \(-0.473138\pi\)
0.0842900 + 0.996441i \(0.473138\pi\)
\(564\) −18.0000 −0.757937
\(565\) −12.0000 −0.504844
\(566\) −10.0000 −0.420331
\(567\) 9.00000 0.377964
\(568\) 9.00000 0.377632
\(569\) 10.0000 0.419222 0.209611 − 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 3.00000 0.125656
\(571\) −23.0000 −0.962520 −0.481260 − 0.876578i \(-0.659821\pi\)
−0.481260 + 0.876578i \(0.659821\pi\)
\(572\) 0 0
\(573\) 12.0000 0.501307
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 6.00000 0.250000
\(577\) 18.0000 0.749350 0.374675 − 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) −8.00000 −0.332756
\(579\) −15.0000 −0.623379
\(580\) −5.00000 −0.207614
\(581\) 0 0
\(582\) 0 0
\(583\) −9.00000 −0.372742
\(584\) −10.0000 −0.413803
\(585\) 0 0
\(586\) 0 0
\(587\) −21.0000 −0.866763 −0.433381 − 0.901211i \(-0.642680\pi\)
−0.433381 + 0.901211i \(0.642680\pi\)
\(588\) 18.0000 0.742307
\(589\) 3.00000 0.123613
\(590\) 4.00000 0.164677
\(591\) 36.0000 1.48084
\(592\) −11.0000 −0.452097
\(593\) 34.0000 1.39621 0.698106 − 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) −9.00000 −0.369274
\(595\) −3.00000 −0.122988
\(596\) −11.0000 −0.450578
\(597\) −75.0000 −3.06955
\(598\) 0 0
\(599\) 33.0000 1.34834 0.674172 − 0.738575i \(-0.264501\pi\)
0.674172 + 0.738575i \(0.264501\pi\)
\(600\) −3.00000 −0.122474
\(601\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 1.00000 0.0407570
\(603\) 72.0000 2.93207
\(604\) −16.0000 −0.651031
\(605\) 1.00000 0.0406558
\(606\) 30.0000 1.21867
\(607\) 27.0000 1.09590 0.547948 − 0.836512i \(-0.315409\pi\)
0.547948 + 0.836512i \(0.315409\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 15.0000 0.607831
\(610\) 13.0000 0.526355
\(611\) 0 0
\(612\) −18.0000 −0.727607
\(613\) 40.0000 1.61558 0.807792 − 0.589467i \(-0.200662\pi\)
0.807792 + 0.589467i \(0.200662\pi\)
\(614\) −14.0000 −0.564994
\(615\) 0 0
\(616\) 1.00000 0.0402911
\(617\) −26.0000 −1.04672 −0.523360 − 0.852111i \(-0.675322\pi\)
−0.523360 + 0.852111i \(0.675322\pi\)
\(618\) 24.0000 0.965422
\(619\) 18.0000 0.723481 0.361741 − 0.932279i \(-0.382183\pi\)
0.361741 + 0.932279i \(0.382183\pi\)
\(620\) −3.00000 −0.120483
\(621\) 36.0000 1.44463
\(622\) −3.00000 −0.120289
\(623\) −1.00000 −0.0400642
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −22.0000 −0.879297
\(627\) 3.00000 0.119808
\(628\) −3.00000 −0.119713
\(629\) 33.0000 1.31580
\(630\) 6.00000 0.239046
\(631\) −47.0000 −1.87104 −0.935520 − 0.353273i \(-0.885069\pi\)
−0.935520 + 0.353273i \(0.885069\pi\)
\(632\) −4.00000 −0.159111
\(633\) −69.0000 −2.74250
\(634\) −11.0000 −0.436866
\(635\) −12.0000 −0.476205
\(636\) 27.0000 1.07062
\(637\) 0 0
\(638\) −5.00000 −0.197952
\(639\) 54.0000 2.13621
\(640\) 1.00000 0.0395285
\(641\) 33.0000 1.30342 0.651711 − 0.758468i \(-0.274052\pi\)
0.651711 + 0.758468i \(0.274052\pi\)
\(642\) 12.0000 0.473602
\(643\) 7.00000 0.276053 0.138027 − 0.990429i \(-0.455924\pi\)
0.138027 + 0.990429i \(0.455924\pi\)
\(644\) −4.00000 −0.157622
\(645\) −3.00000 −0.118125
\(646\) 3.00000 0.118033
\(647\) 4.00000 0.157256 0.0786281 − 0.996904i \(-0.474946\pi\)
0.0786281 + 0.996904i \(0.474946\pi\)
\(648\) 9.00000 0.353553
\(649\) 4.00000 0.157014
\(650\) 0 0
\(651\) 9.00000 0.352738
\(652\) −11.0000 −0.430793
\(653\) 3.00000 0.117399 0.0586995 − 0.998276i \(-0.481305\pi\)
0.0586995 + 0.998276i \(0.481305\pi\)
\(654\) 6.00000 0.234619
\(655\) −1.00000 −0.0390732
\(656\) 0 0
\(657\) −60.0000 −2.34082
\(658\) 6.00000 0.233904
\(659\) 23.0000 0.895953 0.447976 − 0.894045i \(-0.352145\pi\)
0.447976 + 0.894045i \(0.352145\pi\)
\(660\) −3.00000 −0.116775
\(661\) 18.0000 0.700119 0.350059 − 0.936727i \(-0.386161\pi\)
0.350059 + 0.936727i \(0.386161\pi\)
\(662\) −4.00000 −0.155464
\(663\) 0 0
\(664\) 0 0
\(665\) −1.00000 −0.0387783
\(666\) −66.0000 −2.55745
\(667\) 20.0000 0.774403
\(668\) 7.00000 0.270838
\(669\) 84.0000 3.24763
\(670\) 12.0000 0.463600
\(671\) 13.0000 0.501859
\(672\) −3.00000 −0.115728
\(673\) −33.0000 −1.27206 −0.636028 − 0.771666i \(-0.719424\pi\)
−0.636028 + 0.771666i \(0.719424\pi\)
\(674\) −5.00000 −0.192593
\(675\) −9.00000 −0.346410
\(676\) −13.0000 −0.500000
\(677\) 6.00000 0.230599 0.115299 − 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 36.0000 1.38257
\(679\) 0 0
\(680\) −3.00000 −0.115045
\(681\) −54.0000 −2.06928
\(682\) −3.00000 −0.114876
\(683\) 33.0000 1.26271 0.631355 − 0.775494i \(-0.282499\pi\)
0.631355 + 0.775494i \(0.282499\pi\)
\(684\) −6.00000 −0.229416
\(685\) −2.00000 −0.0764161
\(686\) −13.0000 −0.496342
\(687\) 66.0000 2.51806
\(688\) 1.00000 0.0381246
\(689\) 0 0
\(690\) 12.0000 0.456832
\(691\) 20.0000 0.760836 0.380418 − 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 6.00000 0.228086
\(693\) 6.00000 0.227921
\(694\) −30.0000 −1.13878
\(695\) 0 0
\(696\) 15.0000 0.568574
\(697\) 0 0
\(698\) −14.0000 −0.529908
\(699\) −9.00000 −0.340411
\(700\) 1.00000 0.0377964
\(701\) −33.0000 −1.24639 −0.623196 − 0.782065i \(-0.714166\pi\)
−0.623196 + 0.782065i \(0.714166\pi\)
\(702\) 0 0
\(703\) 11.0000 0.414873
\(704\) 1.00000 0.0376889
\(705\) −18.0000 −0.677919
\(706\) −24.0000 −0.903252
\(707\) −10.0000 −0.376089
\(708\) −12.0000 −0.450988
\(709\) −32.0000 −1.20179 −0.600893 − 0.799330i \(-0.705188\pi\)
−0.600893 + 0.799330i \(0.705188\pi\)
\(710\) 9.00000 0.337764
\(711\) −24.0000 −0.900070
\(712\) −1.00000 −0.0374766
\(713\) 12.0000 0.449404
\(714\) 9.00000 0.336817
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −6.00000 −0.224074
\(718\) −4.00000 −0.149279
\(719\) 13.0000 0.484818 0.242409 − 0.970174i \(-0.422062\pi\)
0.242409 + 0.970174i \(0.422062\pi\)
\(720\) 6.00000 0.223607
\(721\) −8.00000 −0.297936
\(722\) −18.0000 −0.669891
\(723\) −12.0000 −0.446285
\(724\) 14.0000 0.520306
\(725\) −5.00000 −0.185695
\(726\) −3.00000 −0.111340
\(727\) −14.0000 −0.519231 −0.259616 − 0.965712i \(-0.583596\pi\)
−0.259616 + 0.965712i \(0.583596\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −10.0000 −0.370117
\(731\) −3.00000 −0.110959
\(732\) −39.0000 −1.44148
\(733\) −22.0000 −0.812589 −0.406294 − 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) −10.0000 −0.369107
\(735\) 18.0000 0.663940
\(736\) −4.00000 −0.147442
\(737\) 12.0000 0.442026
\(738\) 0 0
\(739\) 40.0000 1.47142 0.735712 − 0.677295i \(-0.236848\pi\)
0.735712 + 0.677295i \(0.236848\pi\)
\(740\) −11.0000 −0.404368
\(741\) 0 0
\(742\) −9.00000 −0.330400
\(743\) −19.0000 −0.697042 −0.348521 − 0.937301i \(-0.613316\pi\)
−0.348521 + 0.937301i \(0.613316\pi\)
\(744\) 9.00000 0.329956
\(745\) −11.0000 −0.403009
\(746\) −4.00000 −0.146450
\(747\) 0 0
\(748\) −3.00000 −0.109691
\(749\) −4.00000 −0.146157
\(750\) −3.00000 −0.109545
\(751\) 31.0000 1.13121 0.565603 − 0.824678i \(-0.308643\pi\)
0.565603 + 0.824678i \(0.308643\pi\)
\(752\) 6.00000 0.218797
\(753\) 0 0
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) −9.00000 −0.327327
\(757\) 2.00000 0.0726912 0.0363456 − 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −12.0000 −0.435860
\(759\) 12.0000 0.435572
\(760\) −1.00000 −0.0362738
\(761\) 20.0000 0.724999 0.362500 − 0.931984i \(-0.381923\pi\)
0.362500 + 0.931984i \(0.381923\pi\)
\(762\) 36.0000 1.30414
\(763\) −2.00000 −0.0724049
\(764\) −4.00000 −0.144715
\(765\) −18.0000 −0.650791
\(766\) −36.0000 −1.30073
\(767\) 0 0
\(768\) −3.00000 −0.108253
\(769\) −42.0000 −1.51456 −0.757279 − 0.653091i \(-0.773472\pi\)
−0.757279 + 0.653091i \(0.773472\pi\)
\(770\) 1.00000 0.0360375
\(771\) −18.0000 −0.648254
\(772\) 5.00000 0.179954
\(773\) −31.0000 −1.11499 −0.557496 − 0.830179i \(-0.688238\pi\)
−0.557496 + 0.830179i \(0.688238\pi\)
\(774\) 6.00000 0.215666
\(775\) −3.00000 −0.107763
\(776\) 0 0
\(777\) 33.0000 1.18387
\(778\) −16.0000 −0.573628
\(779\) 0 0
\(780\) 0 0
\(781\) 9.00000 0.322045
\(782\) 12.0000 0.429119
\(783\) 45.0000 1.60817
\(784\) −6.00000 −0.214286
\(785\) −3.00000 −0.107075
\(786\) 3.00000 0.107006
\(787\) −24.0000 −0.855508 −0.427754 − 0.903895i \(-0.640695\pi\)
−0.427754 + 0.903895i \(0.640695\pi\)
\(788\) −12.0000 −0.427482
\(789\) 27.0000 0.961225
\(790\) −4.00000 −0.142314
\(791\) −12.0000 −0.426671
\(792\) 6.00000 0.213201
\(793\) 0 0
\(794\) 6.00000 0.212932
\(795\) 27.0000 0.957591
\(796\) 25.0000 0.886102
\(797\) −42.0000 −1.48772 −0.743858 − 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 3.00000 0.106199
\(799\) −18.0000 −0.636794
\(800\) 1.00000 0.0353553
\(801\) −6.00000 −0.212000
\(802\) 31.0000 1.09465
\(803\) −10.0000 −0.352892
\(804\) −36.0000 −1.26962
\(805\) −4.00000 −0.140981
\(806\) 0 0
\(807\) −54.0000 −1.90089
\(808\) −10.0000 −0.351799
\(809\) −16.0000 −0.562530 −0.281265 − 0.959630i \(-0.590754\pi\)
−0.281265 + 0.959630i \(0.590754\pi\)
\(810\) 9.00000 0.316228
\(811\) −7.00000 −0.245803 −0.122902 − 0.992419i \(-0.539220\pi\)
−0.122902 + 0.992419i \(0.539220\pi\)
\(812\) −5.00000 −0.175466
\(813\) 66.0000 2.31472
\(814\) −11.0000 −0.385550
\(815\) −11.0000 −0.385313
\(816\) 9.00000 0.315063
\(817\) −1.00000 −0.0349856
\(818\) 32.0000 1.11885
\(819\) 0 0
\(820\) 0 0
\(821\) 38.0000 1.32621 0.663105 − 0.748527i \(-0.269238\pi\)
0.663105 + 0.748527i \(0.269238\pi\)
\(822\) 6.00000 0.209274
\(823\) −2.00000 −0.0697156 −0.0348578 − 0.999392i \(-0.511098\pi\)
−0.0348578 + 0.999392i \(0.511098\pi\)
\(824\) −8.00000 −0.278693
\(825\) −3.00000 −0.104447
\(826\) 4.00000 0.139178
\(827\) −12.0000 −0.417281 −0.208640 − 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) −24.0000 −0.834058
\(829\) −10.0000 −0.347314 −0.173657 − 0.984806i \(-0.555558\pi\)
−0.173657 + 0.984806i \(0.555558\pi\)
\(830\) 0 0
\(831\) 6.00000 0.208138
\(832\) 0 0
\(833\) 18.0000 0.623663
\(834\) 0 0
\(835\) 7.00000 0.242245
\(836\) −1.00000 −0.0345857
\(837\) 27.0000 0.933257
\(838\) 14.0000 0.483622
\(839\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) −3.00000 −0.103510
\(841\) −4.00000 −0.137931
\(842\) −12.0000 −0.413547
\(843\) 36.0000 1.23991
\(844\) 23.0000 0.791693
\(845\) −13.0000 −0.447214
\(846\) 36.0000 1.23771
\(847\) 1.00000 0.0343604
\(848\) −9.00000 −0.309061
\(849\) 30.0000 1.02960
\(850\) −3.00000 −0.102899
\(851\) 44.0000 1.50830
\(852\) −27.0000 −0.925005
\(853\) 56.0000 1.91740 0.958702 − 0.284413i \(-0.0917988\pi\)
0.958702 + 0.284413i \(0.0917988\pi\)
\(854\) 13.0000 0.444851
\(855\) −6.00000 −0.205196
\(856\) −4.00000 −0.136717
\(857\) 25.0000 0.853984 0.426992 − 0.904255i \(-0.359573\pi\)
0.426992 + 0.904255i \(0.359573\pi\)
\(858\) 0 0
\(859\) 34.0000 1.16007 0.580033 − 0.814593i \(-0.303040\pi\)
0.580033 + 0.814593i \(0.303040\pi\)
\(860\) 1.00000 0.0340997
\(861\) 0 0
\(862\) −2.00000 −0.0681203
\(863\) 10.0000 0.340404 0.170202 − 0.985409i \(-0.445558\pi\)
0.170202 + 0.985409i \(0.445558\pi\)
\(864\) −9.00000 −0.306186
\(865\) 6.00000 0.204006
\(866\) 28.0000 0.951479
\(867\) 24.0000 0.815083
\(868\) −3.00000 −0.101827
\(869\) −4.00000 −0.135691
\(870\) 15.0000 0.508548
\(871\) 0 0
\(872\) −2.00000 −0.0677285
\(873\) 0 0
\(874\) 4.00000 0.135302
\(875\) 1.00000 0.0338062
\(876\) 30.0000 1.01361
\(877\) −46.0000 −1.55331 −0.776655 − 0.629926i \(-0.783085\pi\)
−0.776655 + 0.629926i \(0.783085\pi\)
\(878\) 34.0000 1.14744
\(879\) 0 0
\(880\) 1.00000 0.0337100
\(881\) −42.0000 −1.41502 −0.707508 − 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) −36.0000 −1.21218
\(883\) −47.0000 −1.58168 −0.790838 − 0.612026i \(-0.790355\pi\)
−0.790838 + 0.612026i \(0.790355\pi\)
\(884\) 0 0
\(885\) −12.0000 −0.403376
\(886\) −4.00000 −0.134383
\(887\) −8.00000 −0.268614 −0.134307 − 0.990940i \(-0.542881\pi\)
−0.134307 + 0.990940i \(0.542881\pi\)
\(888\) 33.0000 1.10741
\(889\) −12.0000 −0.402467
\(890\) −1.00000 −0.0335201
\(891\) 9.00000 0.301511
\(892\) −28.0000 −0.937509
\(893\) −6.00000 −0.200782
\(894\) 33.0000 1.10369
\(895\) 12.0000 0.401116
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 2.00000 0.0667409
\(899\) 15.0000 0.500278
\(900\) 6.00000 0.200000
\(901\) 27.0000 0.899500
\(902\) 0 0
\(903\) −3.00000 −0.0998337
\(904\) −12.0000 −0.399114
\(905\) 14.0000 0.465376
\(906\) 48.0000 1.59469
\(907\) 19.0000 0.630885 0.315442 − 0.948945i \(-0.397847\pi\)
0.315442 + 0.948945i \(0.397847\pi\)
\(908\) 18.0000 0.597351
\(909\) −60.0000 −1.99007
\(910\) 0 0
\(911\) 9.00000 0.298183 0.149092 − 0.988823i \(-0.452365\pi\)
0.149092 + 0.988823i \(0.452365\pi\)
\(912\) 3.00000 0.0993399
\(913\) 0 0
\(914\) 17.0000 0.562310
\(915\) −39.0000 −1.28930
\(916\) −22.0000 −0.726900
\(917\) −1.00000 −0.0330229
\(918\) 27.0000 0.891133
\(919\) −4.00000 −0.131948 −0.0659739 − 0.997821i \(-0.521015\pi\)
−0.0659739 + 0.997821i \(0.521015\pi\)
\(920\) −4.00000 −0.131876
\(921\) 42.0000 1.38395
\(922\) −21.0000 −0.691598
\(923\) 0 0
\(924\) −3.00000 −0.0986928
\(925\) −11.0000 −0.361678
\(926\) −26.0000 −0.854413
\(927\) −48.0000 −1.57653
\(928\) −5.00000 −0.164133
\(929\) −43.0000 −1.41078 −0.705392 − 0.708817i \(-0.749229\pi\)
−0.705392 + 0.708817i \(0.749229\pi\)
\(930\) 9.00000 0.295122
\(931\) 6.00000 0.196642
\(932\) 3.00000 0.0982683
\(933\) 9.00000 0.294647
\(934\) 41.0000 1.34156
\(935\) −3.00000 −0.0981105
\(936\) 0 0
\(937\) 42.0000 1.37208 0.686040 − 0.727564i \(-0.259347\pi\)
0.686040 + 0.727564i \(0.259347\pi\)
\(938\) 12.0000 0.391814
\(939\) 66.0000 2.15383
\(940\) 6.00000 0.195698
\(941\) 25.0000 0.814977 0.407488 − 0.913210i \(-0.366405\pi\)
0.407488 + 0.913210i \(0.366405\pi\)
\(942\) 9.00000 0.293236
\(943\) 0 0
\(944\) 4.00000 0.130189
\(945\) −9.00000 −0.292770
\(946\) 1.00000 0.0325128
\(947\) 45.0000 1.46230 0.731152 − 0.682215i \(-0.238983\pi\)
0.731152 + 0.682215i \(0.238983\pi\)
\(948\) 12.0000 0.389742
\(949\) 0 0
\(950\) −1.00000 −0.0324443
\(951\) 33.0000 1.07010
\(952\) −3.00000 −0.0972306
\(953\) 9.00000 0.291539 0.145769 − 0.989319i \(-0.453434\pi\)
0.145769 + 0.989319i \(0.453434\pi\)
\(954\) −54.0000 −1.74831
\(955\) −4.00000 −0.129437
\(956\) 2.00000 0.0646846
\(957\) 15.0000 0.484881
\(958\) −24.0000 −0.775405
\(959\) −2.00000 −0.0645834
\(960\) −3.00000 −0.0968246
\(961\) −22.0000 −0.709677
\(962\) 0 0
\(963\) −24.0000 −0.773389
\(964\) 4.00000 0.128831
\(965\) 5.00000 0.160956
\(966\) 12.0000 0.386094
\(967\) −47.0000 −1.51142 −0.755709 − 0.654907i \(-0.772708\pi\)
−0.755709 + 0.654907i \(0.772708\pi\)
\(968\) 1.00000 0.0321412
\(969\) −9.00000 −0.289122
\(970\) 0 0
\(971\) −36.0000 −1.15529 −0.577647 − 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 26.0000 0.833094
\(975\) 0 0
\(976\) 13.0000 0.416120
\(977\) 12.0000 0.383914 0.191957 − 0.981403i \(-0.438517\pi\)
0.191957 + 0.981403i \(0.438517\pi\)
\(978\) 33.0000 1.05522
\(979\) −1.00000 −0.0319601
\(980\) −6.00000 −0.191663
\(981\) −12.0000 −0.383131
\(982\) −5.00000 −0.159556
\(983\) 32.0000 1.02064 0.510321 − 0.859984i \(-0.329527\pi\)
0.510321 + 0.859984i \(0.329527\pi\)
\(984\) 0 0
\(985\) −12.0000 −0.382352
\(986\) 15.0000 0.477697
\(987\) −18.0000 −0.572946
\(988\) 0 0
\(989\) −4.00000 −0.127193
\(990\) 6.00000 0.190693
\(991\) −16.0000 −0.508257 −0.254128 − 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) −3.00000 −0.0952501
\(993\) 12.0000 0.380808
\(994\) 9.00000 0.285463
\(995\) 25.0000 0.792553
\(996\) 0 0
\(997\) −24.0000 −0.760088 −0.380044 − 0.924968i \(-0.624091\pi\)
−0.380044 + 0.924968i \(0.624091\pi\)
\(998\) 10.0000 0.316544
\(999\) 99.0000 3.13222
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 4730.2.a.d.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.d.1.1 ✓ 1 1.1 even 1 trivial