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Properties

Label 5610.2.a.bh.1.1
Level $5610$
Weight $2$
Character 5610.1
Self dual yes
Analytic conductor $44.796$
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] = [5610,2,Mod(1,5610)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5610, 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("5610.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5610.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: \(44.7960755339\)
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 \(\chi\) \(=\) 5610.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -6.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -1.00000 q^{20} +1.00000 q^{22} -8.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.00000 q^{26} +1.00000 q^{27} -6.00000 q^{29} -1.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} +2.00000 q^{37} -6.00000 q^{39} -1.00000 q^{40} +2.00000 q^{41} -8.00000 q^{43} +1.00000 q^{44} -1.00000 q^{45} -8.00000 q^{46} +1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} +1.00000 q^{51} -6.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -6.00000 q^{58} -8.00000 q^{59} -1.00000 q^{60} +2.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +1.00000 q^{66} +12.0000 q^{67} +1.00000 q^{68} -8.00000 q^{69} +8.00000 q^{71} +1.00000 q^{72} -2.00000 q^{73} +2.00000 q^{74} +1.00000 q^{75} -6.00000 q^{78} -1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +12.0000 q^{83} -1.00000 q^{85} -8.00000 q^{86} -6.00000 q^{87} +1.00000 q^{88} +2.00000 q^{89} -1.00000 q^{90} -8.00000 q^{92} -4.00000 q^{93} +1.00000 q^{96} -6.00000 q^{97} -7.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

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
\(5\) −1.00000 −0.447214
\(6\) 1.00000 0.408248
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) −6.00000 −1.66410 −0.832050 − 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) 1.00000 0.235702
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −8.00000 −1.66812 −0.834058 − 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) −6.00000 −1.17670
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 − 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −1.00000 −0.182574
\(31\) −4.00000 −0.718421 −0.359211 − 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 2.00000 0.328798 0.164399 − 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) −6.00000 −0.960769
\(40\) −1.00000 −0.158114
\(41\) 2.00000 0.312348 0.156174 − 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 − 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 1.00000 0.150756
\(45\) −1.00000 −0.149071
\(46\) −8.00000 −1.17954
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000 0.144338
\(49\) −7.00000 −1.00000
\(50\) 1.00000 0.141421
\(51\) 1.00000 0.140028
\(52\) −6.00000 −0.832050
\(53\) −6.00000 −0.824163 −0.412082 − 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 1.00000 0.136083
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) −8.00000 −1.04151 −0.520756 − 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) −1.00000 −0.129099
\(61\) 2.00000 0.256074 0.128037 − 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) 1.00000 0.123091
\(67\) 12.0000 1.46603 0.733017 − 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 1.00000 0.121268
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 − 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 1.00000 0.117851
\(73\) −2.00000 −0.234082 −0.117041 − 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 2.00000 0.232495
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) 0 0
\(78\) −6.00000 −0.679366
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 2.00000 0.220863
\(83\) 12.0000 1.31717 0.658586 − 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −1.00000 −0.108465
\(86\) −8.00000 −0.862662
\(87\) −6.00000 −0.643268
\(88\) 1.00000 0.106600
\(89\) 2.00000 0.212000 0.106000 − 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −8.00000 −0.834058
\(93\) −4.00000 −0.414781
\(94\) 0 0
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −6.00000 −0.609208 −0.304604 − 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) −7.00000 −0.707107
\(99\) 1.00000 0.100504
\(100\) 1.00000 0.100000
\(101\) −2.00000 −0.199007 −0.0995037 − 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 1.00000 0.0990148
\(103\) −8.00000 −0.788263 −0.394132 − 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) −6.00000 −0.588348
\(105\) 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 \(0.469465\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 − 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) 8.00000 0.746004
\(116\) −6.00000 −0.557086
\(117\) −6.00000 −0.554700
\(118\) −8.00000 −0.736460
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 0.0909091
\(122\) 2.00000 0.181071
\(123\) 2.00000 0.180334
\(124\) −4.00000 −0.359211
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 − 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 1.00000 0.0883883
\(129\) −8.00000 −0.704361
\(130\) 6.00000 0.526235
\(131\) 4.00000 0.349482 0.174741 − 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 1.00000 0.0870388
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) −1.00000 −0.0860663
\(136\) 1.00000 0.0857493
\(137\) 2.00000 0.170872 0.0854358 − 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) −8.00000 −0.681005
\(139\) 4.00000 0.339276 0.169638 − 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.00000 0.671345
\(143\) −6.00000 −0.501745
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) −2.00000 −0.165521
\(147\) −7.00000 −0.577350
\(148\) 2.00000 0.164399
\(149\) −2.00000 −0.163846 −0.0819232 − 0.996639i \(-0.526106\pi\)
−0.0819232 + 0.996639i \(0.526106\pi\)
\(150\) 1.00000 0.0816497
\(151\) 16.0000 1.30206 0.651031 − 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) 1.00000 0.0808452
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) −6.00000 −0.480384
\(157\) −2.00000 −0.159617 −0.0798087 − 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 0 0
\(159\) −6.00000 −0.475831
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −4.00000 −0.313304 −0.156652 − 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 2.00000 0.156174
\(165\) −1.00000 −0.0778499
\(166\) 12.0000 0.931381
\(167\) 4.00000 0.309529 0.154765 − 0.987951i \(-0.450538\pi\)
0.154765 + 0.987951i \(0.450538\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) −1.00000 −0.0766965
\(171\) 0 0
\(172\) −8.00000 −0.609994
\(173\) 2.00000 0.152057 0.0760286 − 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) −6.00000 −0.454859
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) −8.00000 −0.601317
\(178\) 2.00000 0.149906
\(179\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −6.00000 −0.445976 −0.222988 − 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) −8.00000 −0.589768
\(185\) −2.00000 −0.147043
\(186\) −4.00000 −0.293294
\(187\) 1.00000 0.0731272
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −24.0000 −1.73658 −0.868290 − 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 1.00000 0.0721688
\(193\) 6.00000 0.431889 0.215945 − 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) −6.00000 −0.430775
\(195\) 6.00000 0.429669
\(196\) −7.00000 −0.500000
\(197\) 2.00000 0.142494 0.0712470 − 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 1.00000 0.0710669
\(199\) 12.0000 0.850657 0.425329 − 0.905039i \(-0.360158\pi\)
0.425329 + 0.905039i \(0.360158\pi\)
\(200\) 1.00000 0.0707107
\(201\) 12.0000 0.846415
\(202\) −2.00000 −0.140720
\(203\) 0 0
\(204\) 1.00000 0.0700140
\(205\) −2.00000 −0.139686
\(206\) −8.00000 −0.557386
\(207\) −8.00000 −0.556038
\(208\) −6.00000 −0.416025
\(209\) 0 0
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 − 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) −6.00000 −0.412082
\(213\) 8.00000 0.548151
\(214\) −12.0000 −0.820303
\(215\) 8.00000 0.545595
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) −2.00000 −0.135147
\(220\) −1.00000 −0.0674200
\(221\) −6.00000 −0.403604
\(222\) 2.00000 0.134231
\(223\) −24.0000 −1.60716 −0.803579 − 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) −10.0000 −0.665190
\(227\) 12.0000 0.796468 0.398234 − 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 0 0
\(229\) −2.00000 −0.132164 −0.0660819 − 0.997814i \(-0.521050\pi\)
−0.0660819 + 0.997814i \(0.521050\pi\)
\(230\) 8.00000 0.527504
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −6.00000 −0.393073 −0.196537 − 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −6.00000 −0.392232
\(235\) 0 0
\(236\) −8.00000 −0.520756
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 14.0000 0.901819 0.450910 − 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) 2.00000 0.128037
\(245\) 7.00000 0.447214
\(246\) 2.00000 0.127515
\(247\) 0 0
\(248\) −4.00000 −0.254000
\(249\) 12.0000 0.760469
\(250\) −1.00000 −0.0632456
\(251\) −8.00000 −0.504956 −0.252478 − 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) −16.0000 −1.00393
\(255\) −1.00000 −0.0626224
\(256\) 1.00000 0.0625000
\(257\) −6.00000 −0.374270 −0.187135 − 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) −8.00000 −0.498058
\(259\) 0 0
\(260\) 6.00000 0.372104
\(261\) −6.00000 −0.371391
\(262\) 4.00000 0.247121
\(263\) −8.00000 −0.493301 −0.246651 − 0.969104i \(-0.579330\pi\)
−0.246651 + 0.969104i \(0.579330\pi\)
\(264\) 1.00000 0.0615457
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 2.00000 0.122398
\(268\) 12.0000 0.733017
\(269\) 18.0000 1.09748 0.548740 − 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −16.0000 −0.971931 −0.485965 − 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 1.00000 0.0606339
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 1.00000 0.0603023
\(276\) −8.00000 −0.481543
\(277\) −22.0000 −1.32185 −0.660926 − 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 4.00000 0.239904
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) 26.0000 1.55103 0.775515 − 0.631329i \(-0.217490\pi\)
0.775515 + 0.631329i \(0.217490\pi\)
\(282\) 0 0
\(283\) −4.00000 −0.237775 −0.118888 − 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 8.00000 0.474713
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) 6.00000 0.352332
\(291\) −6.00000 −0.351726
\(292\) −2.00000 −0.117041
\(293\) 22.0000 1.28525 0.642627 − 0.766179i \(-0.277845\pi\)
0.642627 + 0.766179i \(0.277845\pi\)
\(294\) −7.00000 −0.408248
\(295\) 8.00000 0.465778
\(296\) 2.00000 0.116248
\(297\) 1.00000 0.0580259
\(298\) −2.00000 −0.115857
\(299\) 48.0000 2.77591
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) 16.0000 0.920697
\(303\) −2.00000 −0.114897
\(304\) 0 0
\(305\) −2.00000 −0.114520
\(306\) 1.00000 0.0571662
\(307\) −24.0000 −1.36975 −0.684876 − 0.728659i \(-0.740144\pi\)
−0.684876 + 0.728659i \(0.740144\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 4.00000 0.227185
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) −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
\(315\) 0 0
\(316\) 0 0
\(317\) 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
\(320\) −1.00000 −0.0559017
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −6.00000 −0.332820
\(326\) −4.00000 −0.221540
\(327\) 2.00000 0.110600
\(328\) 2.00000 0.110432
\(329\) 0 0
\(330\) −1.00000 −0.0550482
\(331\) 28.0000 1.53902 0.769510 − 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 12.0000 0.658586
\(333\) 2.00000 0.109599
\(334\) 4.00000 0.218870
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 6.00000 0.326841 0.163420 − 0.986557i \(-0.447747\pi\)
0.163420 + 0.986557i \(0.447747\pi\)
\(338\) 23.0000 1.25104
\(339\) −10.0000 −0.543125
\(340\) −1.00000 −0.0542326
\(341\) −4.00000 −0.216612
\(342\) 0 0
\(343\) 0 0
\(344\) −8.00000 −0.431331
\(345\) 8.00000 0.430706
\(346\) 2.00000 0.107521
\(347\) 20.0000 1.07366 0.536828 − 0.843692i \(-0.319622\pi\)
0.536828 + 0.843692i \(0.319622\pi\)
\(348\) −6.00000 −0.321634
\(349\) 26.0000 1.39175 0.695874 − 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) −6.00000 −0.320256
\(352\) 1.00000 0.0533002
\(353\) 10.0000 0.532246 0.266123 − 0.963939i \(-0.414257\pi\)
0.266123 + 0.963939i \(0.414257\pi\)
\(354\) −8.00000 −0.425195
\(355\) −8.00000 −0.424596
\(356\) 2.00000 0.106000
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −19.0000 −1.00000
\(362\) −6.00000 −0.315353
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) 2.00000 0.104685
\(366\) 2.00000 0.104542
\(367\) −28.0000 −1.46159 −0.730794 − 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) −8.00000 −0.417029
\(369\) 2.00000 0.104116
\(370\) −2.00000 −0.103975
\(371\) 0 0
\(372\) −4.00000 −0.207390
\(373\) −14.0000 −0.724893 −0.362446 − 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 1.00000 0.0517088
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 36.0000 1.85409
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 − 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) −16.0000 −0.819705
\(382\) −24.0000 −1.22795
\(383\) 8.00000 0.408781 0.204390 − 0.978889i \(-0.434479\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 6.00000 0.305392
\(387\) −8.00000 −0.406663
\(388\) −6.00000 −0.304604
\(389\) −22.0000 −1.11544 −0.557722 − 0.830028i \(-0.688325\pi\)
−0.557722 + 0.830028i \(0.688325\pi\)
\(390\) 6.00000 0.303822
\(391\) −8.00000 −0.404577
\(392\) −7.00000 −0.353553
\(393\) 4.00000 0.201773
\(394\) 2.00000 0.100759
\(395\) 0 0
\(396\) 1.00000 0.0502519
\(397\) 10.0000 0.501886 0.250943 − 0.968002i \(-0.419259\pi\)
0.250943 + 0.968002i \(0.419259\pi\)
\(398\) 12.0000 0.601506
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 22.0000 1.09863 0.549314 − 0.835616i \(-0.314889\pi\)
0.549314 + 0.835616i \(0.314889\pi\)
\(402\) 12.0000 0.598506
\(403\) 24.0000 1.19553
\(404\) −2.00000 −0.0995037
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 2.00000 0.0991363
\(408\) 1.00000 0.0495074
\(409\) −14.0000 −0.692255 −0.346128 − 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) −2.00000 −0.0987730
\(411\) 2.00000 0.0986527
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) −8.00000 −0.393179
\(415\) −12.0000 −0.589057
\(416\) −6.00000 −0.294174
\(417\) 4.00000 0.195881
\(418\) 0 0
\(419\) −4.00000 −0.195413 −0.0977064 − 0.995215i \(-0.531151\pi\)
−0.0977064 + 0.995215i \(0.531151\pi\)
\(420\) 0 0
\(421\) −18.0000 −0.877266 −0.438633 − 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(422\) −20.0000 −0.973585
\(423\) 0 0
\(424\) −6.00000 −0.291386
\(425\) 1.00000 0.0485071
\(426\) 8.00000 0.387601
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) −6.00000 −0.289683
\(430\) 8.00000 0.385794
\(431\) −20.0000 −0.963366 −0.481683 − 0.876346i \(-0.659974\pi\)
−0.481683 + 0.876346i \(0.659974\pi\)
\(432\) 1.00000 0.0481125
\(433\) 2.00000 0.0961139 0.0480569 − 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 6.00000 0.287678
\(436\) 2.00000 0.0957826
\(437\) 0 0
\(438\) −2.00000 −0.0955637
\(439\) −16.0000 −0.763638 −0.381819 − 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −7.00000 −0.333333
\(442\) −6.00000 −0.285391
\(443\) 24.0000 1.14027 0.570137 − 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) 2.00000 0.0949158
\(445\) −2.00000 −0.0948091
\(446\) −24.0000 −1.13643
\(447\) −2.00000 −0.0945968
\(448\) 0 0
\(449\) −2.00000 −0.0943858 −0.0471929 − 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 1.00000 0.0471405
\(451\) 2.00000 0.0941763
\(452\) −10.0000 −0.470360
\(453\) 16.0000 0.751746
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 0 0
\(457\) 10.0000 0.467780 0.233890 − 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) −2.00000 −0.0934539
\(459\) 1.00000 0.0466760
\(460\) 8.00000 0.373002
\(461\) 14.0000 0.652045 0.326023 − 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 − 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −6.00000 −0.278543
\(465\) 4.00000 0.185496
\(466\) −6.00000 −0.277945
\(467\) −32.0000 −1.48078 −0.740392 − 0.672176i \(-0.765360\pi\)
−0.740392 + 0.672176i \(0.765360\pi\)
\(468\) −6.00000 −0.277350
\(469\) 0 0
\(470\) 0 0
\(471\) −2.00000 −0.0921551
\(472\) −8.00000 −0.368230
\(473\) −8.00000 −0.367840
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) 12.0000 0.548294 0.274147 − 0.961688i \(-0.411605\pi\)
0.274147 + 0.961688i \(0.411605\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −12.0000 −0.547153
\(482\) 14.0000 0.637683
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 6.00000 0.272446
\(486\) 1.00000 0.0453609
\(487\) 12.0000 0.543772 0.271886 − 0.962329i \(-0.412353\pi\)
0.271886 + 0.962329i \(0.412353\pi\)
\(488\) 2.00000 0.0905357
\(489\) −4.00000 −0.180886
\(490\) 7.00000 0.316228
\(491\) 36.0000 1.62466 0.812329 − 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 2.00000 0.0901670
\(493\) −6.00000 −0.270226
\(494\) 0 0
\(495\) −1.00000 −0.0449467
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) −28.0000 −1.25345 −0.626726 − 0.779240i \(-0.715605\pi\)
−0.626726 + 0.779240i \(0.715605\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 4.00000 0.178707
\(502\) −8.00000 −0.357057
\(503\) 28.0000 1.24846 0.624229 − 0.781241i \(-0.285413\pi\)
0.624229 + 0.781241i \(0.285413\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) −8.00000 −0.355643
\(507\) 23.0000 1.02147
\(508\) −16.0000 −0.709885
\(509\) 2.00000 0.0886484 0.0443242 − 0.999017i \(-0.485887\pi\)
0.0443242 + 0.999017i \(0.485887\pi\)
\(510\) −1.00000 −0.0442807
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) 8.00000 0.352522
\(516\) −8.00000 −0.352180
\(517\) 0 0
\(518\) 0 0
\(519\) 2.00000 0.0877903
\(520\) 6.00000 0.263117
\(521\) −18.0000 −0.788594 −0.394297 − 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −6.00000 −0.262613
\(523\) −8.00000 −0.349816 −0.174908 − 0.984585i \(-0.555963\pi\)
−0.174908 + 0.984585i \(0.555963\pi\)
\(524\) 4.00000 0.174741
\(525\) 0 0
\(526\) −8.00000 −0.348817
\(527\) −4.00000 −0.174243
\(528\) 1.00000 0.0435194
\(529\) 41.0000 1.78261
\(530\) 6.00000 0.260623
\(531\) −8.00000 −0.347170
\(532\) 0 0
\(533\) −12.0000 −0.519778
\(534\) 2.00000 0.0865485
\(535\) 12.0000 0.518805
\(536\) 12.0000 0.518321
\(537\) 0 0
\(538\) 18.0000 0.776035
\(539\) −7.00000 −0.301511
\(540\) −1.00000 −0.0430331
\(541\) −30.0000 −1.28980 −0.644900 − 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) −16.0000 −0.687259
\(543\) −6.00000 −0.257485
\(544\) 1.00000 0.0428746
\(545\) −2.00000 −0.0856706
\(546\) 0 0
\(547\) 12.0000 0.513083 0.256541 − 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) 2.00000 0.0854358
\(549\) 2.00000 0.0853579
\(550\) 1.00000 0.0426401
\(551\) 0 0
\(552\) −8.00000 −0.340503
\(553\) 0 0
\(554\) −22.0000 −0.934690
\(555\) −2.00000 −0.0848953
\(556\) 4.00000 0.169638
\(557\) 38.0000 1.61011 0.805056 − 0.593199i \(-0.202135\pi\)
0.805056 + 0.593199i \(0.202135\pi\)
\(558\) −4.00000 −0.169334
\(559\) 48.0000 2.03018
\(560\) 0 0
\(561\) 1.00000 0.0422200
\(562\) 26.0000 1.09674
\(563\) −4.00000 −0.168580 −0.0842900 − 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 0 0
\(565\) 10.0000 0.420703
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) 8.00000 0.335673
\(569\) −22.0000 −0.922288 −0.461144 − 0.887325i \(-0.652561\pi\)
−0.461144 + 0.887325i \(0.652561\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 − 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) −6.00000 −0.250873
\(573\) −24.0000 −1.00261
\(574\) 0 0
\(575\) −8.00000 −0.333623
\(576\) 1.00000 0.0416667
\(577\) 18.0000 0.749350 0.374675 − 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) 1.00000 0.0415945
\(579\) 6.00000 0.249351
\(580\) 6.00000 0.249136
\(581\) 0 0
\(582\) −6.00000 −0.248708
\(583\) −6.00000 −0.248495
\(584\) −2.00000 −0.0827606
\(585\) 6.00000 0.248069
\(586\) 22.0000 0.908812
\(587\) 40.0000 1.65098 0.825488 − 0.564419i \(-0.190900\pi\)
0.825488 + 0.564419i \(0.190900\pi\)
\(588\) −7.00000 −0.288675
\(589\) 0 0
\(590\) 8.00000 0.329355
\(591\) 2.00000 0.0822690
\(592\) 2.00000 0.0821995
\(593\) −30.0000 −1.23195 −0.615976 − 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 1.00000 0.0410305
\(595\) 0 0
\(596\) −2.00000 −0.0819232
\(597\) 12.0000 0.491127
\(598\) 48.0000 1.96287
\(599\) −24.0000 −0.980613 −0.490307 − 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 1.00000 0.0408248
\(601\) 22.0000 0.897399 0.448699 − 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 16.0000 0.651031
\(605\) −1.00000 −0.0406558
\(606\) −2.00000 −0.0812444
\(607\) 16.0000 0.649420 0.324710 − 0.945814i \(-0.394733\pi\)
0.324710 + 0.945814i \(0.394733\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −2.00000 −0.0809776
\(611\) 0 0
\(612\) 1.00000 0.0404226
\(613\) 10.0000 0.403896 0.201948 − 0.979396i \(-0.435273\pi\)
0.201948 + 0.979396i \(0.435273\pi\)
\(614\) −24.0000 −0.968561
\(615\) −2.00000 −0.0806478
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 − 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) −8.00000 −0.321807
\(619\) 36.0000 1.44696 0.723481 − 0.690344i \(-0.242541\pi\)
0.723481 + 0.690344i \(0.242541\pi\)
\(620\) 4.00000 0.160644
\(621\) −8.00000 −0.321029
\(622\) 0 0
\(623\) 0 0
\(624\) −6.00000 −0.240192
\(625\) 1.00000 0.0400000
\(626\) −14.0000 −0.559553
\(627\) 0 0
\(628\) −2.00000 −0.0798087
\(629\) 2.00000 0.0797452
\(630\) 0 0
\(631\) −24.0000 −0.955425 −0.477712 − 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) 0 0
\(633\) −20.0000 −0.794929
\(634\) 18.0000 0.714871
\(635\) 16.0000 0.634941
\(636\) −6.00000 −0.237915
\(637\) 42.0000 1.66410
\(638\) −6.00000 −0.237542
\(639\) 8.00000 0.316475
\(640\) −1.00000 −0.0395285
\(641\) 6.00000 0.236986 0.118493 − 0.992955i \(-0.462194\pi\)
0.118493 + 0.992955i \(0.462194\pi\)
\(642\) −12.0000 −0.473602
\(643\) −44.0000 −1.73519 −0.867595 − 0.497271i \(-0.834335\pi\)
−0.867595 + 0.497271i \(0.834335\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 0 0
\(647\) 8.00000 0.314512 0.157256 − 0.987558i \(-0.449735\pi\)
0.157256 + 0.987558i \(0.449735\pi\)
\(648\) 1.00000 0.0392837
\(649\) −8.00000 −0.314027
\(650\) −6.00000 −0.235339
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) 18.0000 0.704394 0.352197 − 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 2.00000 0.0782062
\(655\) −4.00000 −0.156293
\(656\) 2.00000 0.0780869
\(657\) −2.00000 −0.0780274
\(658\) 0 0
\(659\) 20.0000 0.779089 0.389545 − 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) −1.00000 −0.0389249
\(661\) −10.0000 −0.388955 −0.194477 − 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) 28.0000 1.08825
\(663\) −6.00000 −0.233021
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) 2.00000 0.0774984
\(667\) 48.0000 1.85857
\(668\) 4.00000 0.154765
\(669\) −24.0000 −0.927894
\(670\) −12.0000 −0.463600
\(671\) 2.00000 0.0772091
\(672\) 0 0
\(673\) 22.0000 0.848038 0.424019 − 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) 6.00000 0.231111
\(675\) 1.00000 0.0384900
\(676\) 23.0000 0.884615
\(677\) 18.0000 0.691796 0.345898 − 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −10.0000 −0.384048
\(679\) 0 0
\(680\) −1.00000 −0.0383482
\(681\) 12.0000 0.459841
\(682\) −4.00000 −0.153168
\(683\) 12.0000 0.459167 0.229584 − 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) 0 0
\(687\) −2.00000 −0.0763048
\(688\) −8.00000 −0.304997
\(689\) 36.0000 1.37149
\(690\) 8.00000 0.304555
\(691\) 44.0000 1.67384 0.836919 − 0.547326i \(-0.184354\pi\)
0.836919 + 0.547326i \(0.184354\pi\)
\(692\) 2.00000 0.0760286
\(693\) 0 0
\(694\) 20.0000 0.759190
\(695\) −4.00000 −0.151729
\(696\) −6.00000 −0.227429
\(697\) 2.00000 0.0757554
\(698\) 26.0000 0.984115
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 − 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) −6.00000 −0.226455
\(703\) 0 0
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) 10.0000 0.376355
\(707\) 0 0
\(708\) −8.00000 −0.300658
\(709\) −46.0000 −1.72757 −0.863783 − 0.503864i \(-0.831911\pi\)
−0.863783 + 0.503864i \(0.831911\pi\)
\(710\) −8.00000 −0.300235
\(711\) 0 0
\(712\) 2.00000 0.0749532
\(713\) 32.0000 1.19841
\(714\) 0 0
\(715\) 6.00000 0.224387
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 40.0000 1.49175 0.745874 − 0.666087i \(-0.232032\pi\)
0.745874 + 0.666087i \(0.232032\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 0 0
\(722\) −19.0000 −0.707107
\(723\) 14.0000 0.520666
\(724\) −6.00000 −0.222988
\(725\) −6.00000 −0.222834
\(726\) 1.00000 0.0371135
\(727\) −48.0000 −1.78022 −0.890111 − 0.455744i \(-0.849373\pi\)
−0.890111 + 0.455744i \(0.849373\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 2.00000 0.0740233
\(731\) −8.00000 −0.295891
\(732\) 2.00000 0.0739221
\(733\) −22.0000 −0.812589 −0.406294 − 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) −28.0000 −1.03350
\(735\) 7.00000 0.258199
\(736\) −8.00000 −0.294884
\(737\) 12.0000 0.442026
\(738\) 2.00000 0.0736210
\(739\) 16.0000 0.588570 0.294285 − 0.955718i \(-0.404919\pi\)
0.294285 + 0.955718i \(0.404919\pi\)
\(740\) −2.00000 −0.0735215
\(741\) 0 0
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 − 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) −4.00000 −0.146647
\(745\) 2.00000 0.0732743
\(746\) −14.0000 −0.512576
\(747\) 12.0000 0.439057
\(748\) 1.00000 0.0365636
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) 28.0000 1.02173 0.510867 − 0.859660i \(-0.329324\pi\)
0.510867 + 0.859660i \(0.329324\pi\)
\(752\) 0 0
\(753\) −8.00000 −0.291536
\(754\) 36.0000 1.31104
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) −34.0000 −1.23575 −0.617876 − 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) −4.00000 −0.145287
\(759\) −8.00000 −0.290382
\(760\) 0 0
\(761\) −6.00000 −0.217500 −0.108750 − 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) −16.0000 −0.579619
\(763\) 0 0
\(764\) −24.0000 −0.868290
\(765\) −1.00000 −0.0361551
\(766\) 8.00000 0.289052
\(767\) 48.0000 1.73318
\(768\) 1.00000 0.0360844
\(769\) 34.0000 1.22607 0.613036 − 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 6.00000 0.215945
\(773\) 10.0000 0.359675 0.179838 − 0.983696i \(-0.442443\pi\)
0.179838 + 0.983696i \(0.442443\pi\)
\(774\) −8.00000 −0.287554
\(775\) −4.00000 −0.143684
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) −22.0000 −0.788738
\(779\) 0 0
\(780\) 6.00000 0.214834
\(781\) 8.00000 0.286263
\(782\) −8.00000 −0.286079
\(783\) −6.00000 −0.214423
\(784\) −7.00000 −0.250000
\(785\) 2.00000 0.0713831
\(786\) 4.00000 0.142675
\(787\) −4.00000 −0.142585 −0.0712923 − 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 2.00000 0.0712470
\(789\) −8.00000 −0.284808
\(790\) 0 0
\(791\) 0 0
\(792\) 1.00000 0.0355335
\(793\) −12.0000 −0.426132
\(794\) 10.0000 0.354887
\(795\) 6.00000 0.212798
\(796\) 12.0000 0.425329
\(797\) −30.0000 −1.06265 −0.531327 − 0.847167i \(-0.678307\pi\)
−0.531327 + 0.847167i \(0.678307\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000 0.0353553
\(801\) 2.00000 0.0706665
\(802\) 22.0000 0.776847
\(803\) −2.00000 −0.0705785
\(804\) 12.0000 0.423207
\(805\) 0 0
\(806\) 24.0000 0.845364
\(807\) 18.0000 0.633630
\(808\) −2.00000 −0.0703598
\(809\) 26.0000 0.914111 0.457056 − 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −12.0000 −0.421377 −0.210688 − 0.977553i \(-0.567571\pi\)
−0.210688 + 0.977553i \(0.567571\pi\)
\(812\) 0 0
\(813\) −16.0000 −0.561144
\(814\) 2.00000 0.0701000
\(815\) 4.00000 0.140114
\(816\) 1.00000 0.0350070
\(817\) 0 0
\(818\) −14.0000 −0.489499
\(819\) 0 0
\(820\) −2.00000 −0.0698430
\(821\) 42.0000 1.46581 0.732905 − 0.680331i \(-0.238164\pi\)
0.732905 + 0.680331i \(0.238164\pi\)
\(822\) 2.00000 0.0697580
\(823\) 4.00000 0.139431 0.0697156 − 0.997567i \(-0.477791\pi\)
0.0697156 + 0.997567i \(0.477791\pi\)
\(824\) −8.00000 −0.278693
\(825\) 1.00000 0.0348155
\(826\) 0 0
\(827\) 4.00000 0.139094 0.0695468 − 0.997579i \(-0.477845\pi\)
0.0695468 + 0.997579i \(0.477845\pi\)
\(828\) −8.00000 −0.278019
\(829\) −2.00000 −0.0694629 −0.0347314 − 0.999397i \(-0.511058\pi\)
−0.0347314 + 0.999397i \(0.511058\pi\)
\(830\) −12.0000 −0.416526
\(831\) −22.0000 −0.763172
\(832\) −6.00000 −0.208013
\(833\) −7.00000 −0.242536
\(834\) 4.00000 0.138509
\(835\) −4.00000 −0.138426
\(836\) 0 0
\(837\) −4.00000 −0.138260
\(838\) −4.00000 −0.138178
\(839\) 40.0000 1.38095 0.690477 − 0.723355i \(-0.257401\pi\)
0.690477 + 0.723355i \(0.257401\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −18.0000 −0.620321
\(843\) 26.0000 0.895488
\(844\) −20.0000 −0.688428
\(845\) −23.0000 −0.791224
\(846\) 0 0
\(847\) 0 0
\(848\) −6.00000 −0.206041
\(849\) −4.00000 −0.137280
\(850\) 1.00000 0.0342997
\(851\) −16.0000 −0.548473
\(852\) 8.00000 0.274075
\(853\) −22.0000 −0.753266 −0.376633 − 0.926363i \(-0.622918\pi\)
−0.376633 + 0.926363i \(0.622918\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) 10.0000 0.341593 0.170797 − 0.985306i \(-0.445366\pi\)
0.170797 + 0.985306i \(0.445366\pi\)
\(858\) −6.00000 −0.204837
\(859\) −4.00000 −0.136478 −0.0682391 − 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) 8.00000 0.272798
\(861\) 0 0
\(862\) −20.0000 −0.681203
\(863\) −32.0000 −1.08929 −0.544646 − 0.838666i \(-0.683336\pi\)
−0.544646 + 0.838666i \(0.683336\pi\)
\(864\) 1.00000 0.0340207
\(865\) −2.00000 −0.0680020
\(866\) 2.00000 0.0679628
\(867\) 1.00000 0.0339618
\(868\) 0 0
\(869\) 0 0
\(870\) 6.00000 0.203419
\(871\) −72.0000 −2.43963
\(872\) 2.00000 0.0677285
\(873\) −6.00000 −0.203069
\(874\) 0 0
\(875\) 0 0
\(876\) −2.00000 −0.0675737
\(877\) −46.0000 −1.55331 −0.776655 − 0.629926i \(-0.783085\pi\)
−0.776655 + 0.629926i \(0.783085\pi\)
\(878\) −16.0000 −0.539974
\(879\) 22.0000 0.742042
\(880\) −1.00000 −0.0337100
\(881\) 6.00000 0.202145 0.101073 − 0.994879i \(-0.467773\pi\)
0.101073 + 0.994879i \(0.467773\pi\)
\(882\) −7.00000 −0.235702
\(883\) −28.0000 −0.942275 −0.471138 − 0.882060i \(-0.656156\pi\)
−0.471138 + 0.882060i \(0.656156\pi\)
\(884\) −6.00000 −0.201802
\(885\) 8.00000 0.268917
\(886\) 24.0000 0.806296
\(887\) 44.0000 1.47738 0.738688 − 0.674048i \(-0.235446\pi\)
0.738688 + 0.674048i \(0.235446\pi\)
\(888\) 2.00000 0.0671156
\(889\) 0 0
\(890\) −2.00000 −0.0670402
\(891\) 1.00000 0.0335013
\(892\) −24.0000 −0.803579
\(893\) 0 0
\(894\) −2.00000 −0.0668900
\(895\) 0 0
\(896\) 0 0
\(897\) 48.0000 1.60267
\(898\) −2.00000 −0.0667409
\(899\) 24.0000 0.800445
\(900\) 1.00000 0.0333333
\(901\) −6.00000 −0.199889
\(902\) 2.00000 0.0665927
\(903\) 0 0
\(904\) −10.0000 −0.332595
\(905\) 6.00000 0.199447
\(906\) 16.0000 0.531564
\(907\) −12.0000 −0.398453 −0.199227 − 0.979953i \(-0.563843\pi\)
−0.199227 + 0.979953i \(0.563843\pi\)
\(908\) 12.0000 0.398234
\(909\) −2.00000 −0.0663358
\(910\) 0 0
\(911\) 16.0000 0.530104 0.265052 − 0.964234i \(-0.414611\pi\)
0.265052 + 0.964234i \(0.414611\pi\)
\(912\) 0 0
\(913\) 12.0000 0.397142
\(914\) 10.0000 0.330771
\(915\) −2.00000 −0.0661180
\(916\) −2.00000 −0.0660819
\(917\) 0 0
\(918\) 1.00000 0.0330049
\(919\) 16.0000 0.527791 0.263896 − 0.964551i \(-0.414993\pi\)
0.263896 + 0.964551i \(0.414993\pi\)
\(920\) 8.00000 0.263752
\(921\) −24.0000 −0.790827
\(922\) 14.0000 0.461065
\(923\) −48.0000 −1.57994
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) 8.00000 0.262896
\(927\) −8.00000 −0.262754
\(928\) −6.00000 −0.196960
\(929\) −34.0000 −1.11550 −0.557752 − 0.830008i \(-0.688336\pi\)
−0.557752 + 0.830008i \(0.688336\pi\)
\(930\) 4.00000 0.131165
\(931\) 0 0
\(932\) −6.00000 −0.196537
\(933\) 0 0
\(934\) −32.0000 −1.04707
\(935\) −1.00000 −0.0327035
\(936\) −6.00000 −0.196116
\(937\) −38.0000 −1.24141 −0.620703 − 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(938\) 0 0
\(939\) −14.0000 −0.456873
\(940\) 0 0
\(941\) 18.0000 0.586783 0.293392 − 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) −2.00000 −0.0651635
\(943\) −16.0000 −0.521032
\(944\) −8.00000 −0.260378
\(945\) 0 0
\(946\) −8.00000 −0.260102
\(947\) 36.0000 1.16984 0.584921 − 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) 0 0
\(949\) 12.0000 0.389536
\(950\) 0 0
\(951\) 18.0000 0.583690
\(952\) 0 0
\(953\) −22.0000 −0.712650 −0.356325 − 0.934362i \(-0.615970\pi\)
−0.356325 + 0.934362i \(0.615970\pi\)
\(954\) −6.00000 −0.194257
\(955\) 24.0000 0.776622
\(956\) 0 0
\(957\) −6.00000 −0.193952
\(958\) 12.0000 0.387702
\(959\) 0 0
\(960\) −1.00000 −0.0322749
\(961\) −15.0000 −0.483871
\(962\) −12.0000 −0.386896
\(963\) −12.0000 −0.386695
\(964\) 14.0000 0.450910
\(965\) −6.00000 −0.193147
\(966\) 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
\(969\) 0 0
\(970\) 6.00000 0.192648
\(971\) −8.00000 −0.256732 −0.128366 − 0.991727i \(-0.540973\pi\)
−0.128366 + 0.991727i \(0.540973\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) 12.0000 0.384505
\(975\) −6.00000 −0.192154
\(976\) 2.00000 0.0640184
\(977\) −38.0000 −1.21573 −0.607864 − 0.794041i \(-0.707973\pi\)
−0.607864 + 0.794041i \(0.707973\pi\)
\(978\) −4.00000 −0.127906
\(979\) 2.00000 0.0639203
\(980\) 7.00000 0.223607
\(981\) 2.00000 0.0638551
\(982\) 36.0000 1.14881
\(983\) 48.0000 1.53096 0.765481 − 0.643458i \(-0.222501\pi\)
0.765481 + 0.643458i \(0.222501\pi\)
\(984\) 2.00000 0.0637577
\(985\) −2.00000 −0.0637253
\(986\) −6.00000 −0.191079
\(987\) 0 0
\(988\) 0 0
\(989\) 64.0000 2.03508
\(990\) −1.00000 −0.0317821
\(991\) −20.0000 −0.635321 −0.317660 − 0.948205i \(-0.602897\pi\)
−0.317660 + 0.948205i \(0.602897\pi\)
\(992\) −4.00000 −0.127000
\(993\) 28.0000 0.888553
\(994\) 0 0
\(995\) −12.0000 −0.380426
\(996\) 12.0000 0.380235
\(997\) 42.0000 1.33015 0.665077 − 0.746775i \(-0.268399\pi\)
0.665077 + 0.746775i \(0.268399\pi\)
\(998\) −28.0000 −0.886325
\(999\) 2.00000 0.0632772
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 5610.2.a.bh.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.bh.1.1 ✓ 1 1.1 even 1 trivial