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Properties

Label 4830.2.a.g.1.1
Level $4830$
Weight $2$
Character 4830.1
Self dual yes
Analytic conductor $38.568$
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] = [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: \(1\)
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 \(\chi\) \(=\) 4830.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +2.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} -2.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} -2.00000 q^{22} -1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +1.00000 q^{30} -2.00000 q^{31} -1.00000 q^{32} -2.00000 q^{33} +1.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} +2.00000 q^{38} +2.00000 q^{39} -1.00000 q^{40} -6.00000 q^{41} +1.00000 q^{42} +2.00000 q^{43} +2.00000 q^{44} +1.00000 q^{45} +1.00000 q^{46} -2.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -2.00000 q^{52} -10.0000 q^{53} +1.00000 q^{54} +2.00000 q^{55} -1.00000 q^{56} +2.00000 q^{57} +4.00000 q^{59} -1.00000 q^{60} +2.00000 q^{61} +2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.00000 q^{65} +2.00000 q^{66} -14.0000 q^{67} +1.00000 q^{69} -1.00000 q^{70} -14.0000 q^{71} -1.00000 q^{72} -10.0000 q^{73} +2.00000 q^{74} -1.00000 q^{75} -2.00000 q^{76} +2.00000 q^{77} -2.00000 q^{78} +1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} +10.0000 q^{83} -1.00000 q^{84} -2.00000 q^{86} -2.00000 q^{88} +10.0000 q^{89} -1.00000 q^{90} -2.00000 q^{91} -1.00000 q^{92} +2.00000 q^{93} +2.00000 q^{94} -2.00000 q^{95} +1.00000 q^{96} -10.0000 q^{97} -1.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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
\(11\) 2.00000 0.603023 0.301511 − 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.00000 −0.554700 −0.277350 − 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −1.00000 −0.267261
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.00000 −0.458831 −0.229416 − 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 1.00000 0.223607
\(21\) −1.00000 −0.218218
\(22\) −2.00000 −0.426401
\(23\) −1.00000 −0.208514
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 2.00000 0.392232
\(27\) −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
\(31\) −2.00000 −0.359211 −0.179605 − 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.00000 −0.348155
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 1.00000 0.166667
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 2.00000 0.324443
\(39\) 2.00000 0.320256
\(40\) −1.00000 −0.158114
\(41\) −6.00000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 1.00000 0.154303
\(43\) 2.00000 0.304997 0.152499 − 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 2.00000 0.301511
\(45\) 1.00000 0.149071
\(46\) 1.00000 0.147442
\(47\) −2.00000 −0.291730 −0.145865 − 0.989305i \(-0.546597\pi\)
−0.145865 + 0.989305i \(0.546597\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) −10.0000 −1.37361 −0.686803 − 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 1.00000 0.136083
\(55\) 2.00000 0.269680
\(56\) −1.00000 −0.133631
\(57\) 2.00000 0.264906
\(58\) 0 0
\(59\) 4.00000 0.520756 0.260378 − 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) −1.00000 −0.129099
\(61\) 2.00000 0.256074 0.128037 − 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 2.00000 0.254000
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) −2.00000 −0.248069
\(66\) 2.00000 0.246183
\(67\) −14.0000 −1.71037 −0.855186 − 0.518321i \(-0.826557\pi\)
−0.855186 + 0.518321i \(0.826557\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) −1.00000 −0.119523
\(71\) −14.0000 −1.66149 −0.830747 − 0.556650i \(-0.812086\pi\)
−0.830747 + 0.556650i \(0.812086\pi\)
\(72\) −1.00000 −0.117851
\(73\) −10.0000 −1.17041 −0.585206 − 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 2.00000 0.232495
\(75\) −1.00000 −0.115470
\(76\) −2.00000 −0.229416
\(77\) 2.00000 0.227921
\(78\) −2.00000 −0.226455
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) 10.0000 1.09764 0.548821 − 0.835940i \(-0.315077\pi\)
0.548821 + 0.835940i \(0.315077\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) −2.00000 −0.215666
\(87\) 0 0
\(88\) −2.00000 −0.213201
\(89\) 10.0000 1.06000 0.529999 − 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −1.00000 −0.105409
\(91\) −2.00000 −0.209657
\(92\) −1.00000 −0.104257
\(93\) 2.00000 0.207390
\(94\) 2.00000 0.206284
\(95\) −2.00000 −0.205196
\(96\) 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
\(99\) 2.00000 0.201008
\(100\) 1.00000 0.100000
\(101\) 10.0000 0.995037 0.497519 − 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 − 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 2.00000 0.196116
\(105\) −1.00000 −0.0975900
\(106\) 10.0000 0.971286
\(107\) −20.0000 −1.93347 −0.966736 − 0.255774i \(-0.917670\pi\)
−0.966736 + 0.255774i \(0.917670\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 2.00000 0.191565 0.0957826 − 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −2.00000 −0.190693
\(111\) 2.00000 0.189832
\(112\) 1.00000 0.0944911
\(113\) 18.0000 1.69330 0.846649 − 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) −2.00000 −0.187317
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) −2.00000 −0.184900
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) −7.00000 −0.636364
\(122\) −2.00000 −0.181071
\(123\) 6.00000 0.541002
\(124\) −2.00000 −0.179605
\(125\) 1.00000 0.0894427
\(126\) −1.00000 −0.0890871
\(127\) −14.0000 −1.24230 −0.621150 − 0.783692i \(-0.713334\pi\)
−0.621150 + 0.783692i \(0.713334\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.00000 −0.176090
\(130\) 2.00000 0.175412
\(131\) 12.0000 1.04844 0.524222 − 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −2.00000 −0.174078
\(133\) −2.00000 −0.173422
\(134\) 14.0000 1.20942
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) −2.00000 −0.170872 −0.0854358 − 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) −1.00000 −0.0851257
\(139\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 1.00000 0.0845154
\(141\) 2.00000 0.168430
\(142\) 14.0000 1.17485
\(143\) −4.00000 −0.334497
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 10.0000 0.827606
\(147\) −1.00000 −0.0824786
\(148\) −2.00000 −0.164399
\(149\) −10.0000 −0.819232 −0.409616 − 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 1.00000 0.0816497
\(151\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 2.00000 0.162221
\(153\) 0 0
\(154\) −2.00000 −0.161165
\(155\) −2.00000 −0.160644
\(156\) 2.00000 0.160128
\(157\) 2.00000 0.159617 0.0798087 − 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) 10.0000 0.793052
\(160\) −1.00000 −0.0790569
\(161\) −1.00000 −0.0788110
\(162\) −1.00000 −0.0785674
\(163\) −16.0000 −1.25322 −0.626608 − 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) −6.00000 −0.468521
\(165\) −2.00000 −0.155700
\(166\) −10.0000 −0.776151
\(167\) 22.0000 1.70241 0.851206 − 0.524832i \(-0.175872\pi\)
0.851206 + 0.524832i \(0.175872\pi\)
\(168\) 1.00000 0.0771517
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −2.00000 −0.152944
\(172\) 2.00000 0.152499
\(173\) −12.0000 −0.912343 −0.456172 − 0.889892i \(-0.650780\pi\)
−0.456172 + 0.889892i \(0.650780\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 2.00000 0.150756
\(177\) −4.00000 −0.300658
\(178\) −10.0000 −0.749532
\(179\) 24.0000 1.79384 0.896922 − 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 1.00000 0.0745356
\(181\) −14.0000 −1.04061 −0.520306 − 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 2.00000 0.148250
\(183\) −2.00000 −0.147844
\(184\) 1.00000 0.0737210
\(185\) −2.00000 −0.147043
\(186\) −2.00000 −0.146647
\(187\) 0 0
\(188\) −2.00000 −0.145865
\(189\) −1.00000 −0.0727393
\(190\) 2.00000 0.145095
\(191\) 24.0000 1.73658 0.868290 − 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −6.00000 −0.431889 −0.215945 − 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) 10.0000 0.717958
\(195\) 2.00000 0.143223
\(196\) 1.00000 0.0714286
\(197\) 6.00000 0.427482 0.213741 − 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) −2.00000 −0.142134
\(199\) 16.0000 1.13421 0.567105 − 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 14.0000 0.987484
\(202\) −10.0000 −0.703598
\(203\) 0 0
\(204\) 0 0
\(205\) −6.00000 −0.419058
\(206\) −8.00000 −0.557386
\(207\) −1.00000 −0.0695048
\(208\) −2.00000 −0.138675
\(209\) −4.00000 −0.276686
\(210\) 1.00000 0.0690066
\(211\) 4.00000 0.275371 0.137686 − 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −10.0000 −0.686803
\(213\) 14.0000 0.959264
\(214\) 20.0000 1.36717
\(215\) 2.00000 0.136399
\(216\) 1.00000 0.0680414
\(217\) −2.00000 −0.135769
\(218\) −2.00000 −0.135457
\(219\) 10.0000 0.675737
\(220\) 2.00000 0.134840
\(221\) 0 0
\(222\) −2.00000 −0.134231
\(223\) −4.00000 −0.267860 −0.133930 − 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 1.00000 0.0666667
\(226\) −18.0000 −1.19734
\(227\) −6.00000 −0.398234 −0.199117 − 0.979976i \(-0.563807\pi\)
−0.199117 + 0.979976i \(0.563807\pi\)
\(228\) 2.00000 0.132453
\(229\) −6.00000 −0.396491 −0.198246 − 0.980152i \(-0.563524\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) 1.00000 0.0659380
\(231\) −2.00000 −0.131590
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 − 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 2.00000 0.130744
\(235\) −2.00000 −0.130466
\(236\) 4.00000 0.260378
\(237\) 0 0
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 − 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −20.0000 −1.28831 −0.644157 − 0.764894i \(-0.722792\pi\)
−0.644157 + 0.764894i \(0.722792\pi\)
\(242\) 7.00000 0.449977
\(243\) −1.00000 −0.0641500
\(244\) 2.00000 0.128037
\(245\) 1.00000 0.0638877
\(246\) −6.00000 −0.382546
\(247\) 4.00000 0.254514
\(248\) 2.00000 0.127000
\(249\) −10.0000 −0.633724
\(250\) −1.00000 −0.0632456
\(251\) −24.0000 −1.51487 −0.757433 − 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 1.00000 0.0629941
\(253\) −2.00000 −0.125739
\(254\) 14.0000 0.878438
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −6.00000 −0.374270 −0.187135 − 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) 2.00000 0.124515
\(259\) −2.00000 −0.124274
\(260\) −2.00000 −0.124035
\(261\) 0 0
\(262\) −12.0000 −0.741362
\(263\) −16.0000 −0.986602 −0.493301 − 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 2.00000 0.123091
\(265\) −10.0000 −0.614295
\(266\) 2.00000 0.122628
\(267\) −10.0000 −0.611990
\(268\) −14.0000 −0.855186
\(269\) −2.00000 −0.121942 −0.0609711 − 0.998140i \(-0.519420\pi\)
−0.0609711 + 0.998140i \(0.519420\pi\)
\(270\) 1.00000 0.0608581
\(271\) −2.00000 −0.121491 −0.0607457 − 0.998153i \(-0.519348\pi\)
−0.0607457 + 0.998153i \(0.519348\pi\)
\(272\) 0 0
\(273\) 2.00000 0.121046
\(274\) 2.00000 0.120824
\(275\) 2.00000 0.120605
\(276\) 1.00000 0.0601929
\(277\) 4.00000 0.240337 0.120168 − 0.992754i \(-0.461657\pi\)
0.120168 + 0.992754i \(0.461657\pi\)
\(278\) 0 0
\(279\) −2.00000 −0.119737
\(280\) −1.00000 −0.0597614
\(281\) 24.0000 1.43172 0.715860 − 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) −2.00000 −0.119098
\(283\) 24.0000 1.42665 0.713326 − 0.700832i \(-0.247188\pi\)
0.713326 + 0.700832i \(0.247188\pi\)
\(284\) −14.0000 −0.830747
\(285\) 2.00000 0.118470
\(286\) 4.00000 0.236525
\(287\) −6.00000 −0.354169
\(288\) −1.00000 −0.0589256
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 10.0000 0.586210
\(292\) −10.0000 −0.585206
\(293\) −18.0000 −1.05157 −0.525786 − 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 1.00000 0.0583212
\(295\) 4.00000 0.232889
\(296\) 2.00000 0.116248
\(297\) −2.00000 −0.116052
\(298\) 10.0000 0.579284
\(299\) 2.00000 0.115663
\(300\) −1.00000 −0.0577350
\(301\) 2.00000 0.115278
\(302\) 0 0
\(303\) −10.0000 −0.574485
\(304\) −2.00000 −0.114708
\(305\) 2.00000 0.114520
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 − 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 2.00000 0.113961
\(309\) −8.00000 −0.455104
\(310\) 2.00000 0.113592
\(311\) 16.0000 0.907277 0.453638 − 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) −2.00000 −0.113228
\(313\) −10.0000 −0.565233 −0.282617 − 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) −2.00000 −0.112867
\(315\) 1.00000 0.0563436
\(316\) 0 0
\(317\) −14.0000 −0.786318 −0.393159 − 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) −10.0000 −0.560772
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) 20.0000 1.11629
\(322\) 1.00000 0.0557278
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −2.00000 −0.110940
\(326\) 16.0000 0.886158
\(327\) −2.00000 −0.110600
\(328\) 6.00000 0.331295
\(329\) −2.00000 −0.110264
\(330\) 2.00000 0.110096
\(331\) −12.0000 −0.659580 −0.329790 − 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) 10.0000 0.548821
\(333\) −2.00000 −0.109599
\(334\) −22.0000 −1.20379
\(335\) −14.0000 −0.764902
\(336\) −1.00000 −0.0545545
\(337\) −8.00000 −0.435788 −0.217894 − 0.975972i \(-0.569919\pi\)
−0.217894 + 0.975972i \(0.569919\pi\)
\(338\) 9.00000 0.489535
\(339\) −18.0000 −0.977626
\(340\) 0 0
\(341\) −4.00000 −0.216612
\(342\) 2.00000 0.108148
\(343\) 1.00000 0.0539949
\(344\) −2.00000 −0.107833
\(345\) 1.00000 0.0538382
\(346\) 12.0000 0.645124
\(347\) −4.00000 −0.214731 −0.107366 − 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) 0 0
\(349\) 24.0000 1.28469 0.642345 − 0.766415i \(-0.277962\pi\)
0.642345 + 0.766415i \(0.277962\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 2.00000 0.106752
\(352\) −2.00000 −0.106600
\(353\) 14.0000 0.745145 0.372572 − 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 4.00000 0.212598
\(355\) −14.0000 −0.743043
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) −24.0000 −1.26844
\(359\) −32.0000 −1.68890 −0.844448 − 0.535638i \(-0.820071\pi\)
−0.844448 + 0.535638i \(0.820071\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −15.0000 −0.789474
\(362\) 14.0000 0.735824
\(363\) 7.00000 0.367405
\(364\) −2.00000 −0.104828
\(365\) −10.0000 −0.523424
\(366\) 2.00000 0.104542
\(367\) −32.0000 −1.67039 −0.835193 − 0.549957i \(-0.814644\pi\)
−0.835193 + 0.549957i \(0.814644\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −6.00000 −0.312348
\(370\) 2.00000 0.103975
\(371\) −10.0000 −0.519174
\(372\) 2.00000 0.103695
\(373\) 6.00000 0.310668 0.155334 − 0.987862i \(-0.450355\pi\)
0.155334 + 0.987862i \(0.450355\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 2.00000 0.103142
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) 28.0000 1.43826 0.719132 − 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) −2.00000 −0.102598
\(381\) 14.0000 0.717242
\(382\) −24.0000 −1.22795
\(383\) 16.0000 0.817562 0.408781 − 0.912633i \(-0.365954\pi\)
0.408781 + 0.912633i \(0.365954\pi\)
\(384\) 1.00000 0.0510310
\(385\) 2.00000 0.101929
\(386\) 6.00000 0.305392
\(387\) 2.00000 0.101666
\(388\) −10.0000 −0.507673
\(389\) 18.0000 0.912636 0.456318 − 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) −2.00000 −0.101274
\(391\) 0 0
\(392\) −1.00000 −0.0505076
\(393\) −12.0000 −0.605320
\(394\) −6.00000 −0.302276
\(395\) 0 0
\(396\) 2.00000 0.100504
\(397\) −10.0000 −0.501886 −0.250943 − 0.968002i \(-0.580741\pi\)
−0.250943 + 0.968002i \(0.580741\pi\)
\(398\) −16.0000 −0.802008
\(399\) 2.00000 0.100125
\(400\) 1.00000 0.0500000
\(401\) −36.0000 −1.79775 −0.898877 − 0.438201i \(-0.855616\pi\)
−0.898877 + 0.438201i \(0.855616\pi\)
\(402\) −14.0000 −0.698257
\(403\) 4.00000 0.199254
\(404\) 10.0000 0.497519
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −4.00000 −0.198273
\(408\) 0 0
\(409\) −30.0000 −1.48340 −0.741702 − 0.670729i \(-0.765981\pi\)
−0.741702 + 0.670729i \(0.765981\pi\)
\(410\) 6.00000 0.296319
\(411\) 2.00000 0.0986527
\(412\) 8.00000 0.394132
\(413\) 4.00000 0.196827
\(414\) 1.00000 0.0491473
\(415\) 10.0000 0.490881
\(416\) 2.00000 0.0980581
\(417\) 0 0
\(418\) 4.00000 0.195646
\(419\) 20.0000 0.977064 0.488532 − 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) −1.00000 −0.0487950
\(421\) −26.0000 −1.26716 −0.633581 − 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) −4.00000 −0.194717
\(423\) −2.00000 −0.0972433
\(424\) 10.0000 0.485643
\(425\) 0 0
\(426\) −14.0000 −0.678302
\(427\) 2.00000 0.0967868
\(428\) −20.0000 −0.966736
\(429\) 4.00000 0.193122
\(430\) −2.00000 −0.0964486
\(431\) 12.0000 0.578020 0.289010 − 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 14.0000 0.672797 0.336399 − 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 2.00000 0.0960031
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) 2.00000 0.0956730
\(438\) −10.0000 −0.477818
\(439\) −34.0000 −1.62273 −0.811366 − 0.584539i \(-0.801275\pi\)
−0.811366 + 0.584539i \(0.801275\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −28.0000 −1.33032 −0.665160 − 0.746701i \(-0.731637\pi\)
−0.665160 + 0.746701i \(0.731637\pi\)
\(444\) 2.00000 0.0949158
\(445\) 10.0000 0.474045
\(446\) 4.00000 0.189405
\(447\) 10.0000 0.472984
\(448\) 1.00000 0.0472456
\(449\) −2.00000 −0.0943858 −0.0471929 − 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −12.0000 −0.565058
\(452\) 18.0000 0.846649
\(453\) 0 0
\(454\) 6.00000 0.281594
\(455\) −2.00000 −0.0937614
\(456\) −2.00000 −0.0936586
\(457\) −40.0000 −1.87112 −0.935561 − 0.353166i \(-0.885105\pi\)
−0.935561 + 0.353166i \(0.885105\pi\)
\(458\) 6.00000 0.280362
\(459\) 0 0
\(460\) −1.00000 −0.0466252
\(461\) 10.0000 0.465746 0.232873 − 0.972507i \(-0.425187\pi\)
0.232873 + 0.972507i \(0.425187\pi\)
\(462\) 2.00000 0.0930484
\(463\) −22.0000 −1.02243 −0.511213 − 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) 0 0
\(465\) 2.00000 0.0927478
\(466\) 6.00000 0.277945
\(467\) 14.0000 0.647843 0.323921 − 0.946084i \(-0.394999\pi\)
0.323921 + 0.946084i \(0.394999\pi\)
\(468\) −2.00000 −0.0924500
\(469\) −14.0000 −0.646460
\(470\) 2.00000 0.0922531
\(471\) −2.00000 −0.0921551
\(472\) −4.00000 −0.184115
\(473\) 4.00000 0.183920
\(474\) 0 0
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) 6.00000 0.274434
\(479\) −16.0000 −0.731059 −0.365529 − 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 1.00000 0.0456435
\(481\) 4.00000 0.182384
\(482\) 20.0000 0.910975
\(483\) 1.00000 0.0455016
\(484\) −7.00000 −0.318182
\(485\) −10.0000 −0.454077
\(486\) 1.00000 0.0453609
\(487\) 10.0000 0.453143 0.226572 − 0.973995i \(-0.427248\pi\)
0.226572 + 0.973995i \(0.427248\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 16.0000 0.723545
\(490\) −1.00000 −0.0451754
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 6.00000 0.270501
\(493\) 0 0
\(494\) −4.00000 −0.179969
\(495\) 2.00000 0.0898933
\(496\) −2.00000 −0.0898027
\(497\) −14.0000 −0.627986
\(498\) 10.0000 0.448111
\(499\) −4.00000 −0.179065 −0.0895323 − 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 1.00000 0.0447214
\(501\) −22.0000 −0.982888
\(502\) 24.0000 1.07117
\(503\) 36.0000 1.60516 0.802580 − 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 10.0000 0.444994
\(506\) 2.00000 0.0889108
\(507\) 9.00000 0.399704
\(508\) −14.0000 −0.621150
\(509\) −14.0000 −0.620539 −0.310270 − 0.950649i \(-0.600419\pi\)
−0.310270 + 0.950649i \(0.600419\pi\)
\(510\) 0 0
\(511\) −10.0000 −0.442374
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 0.0883022
\(514\) 6.00000 0.264649
\(515\) 8.00000 0.352522
\(516\) −2.00000 −0.0880451
\(517\) −4.00000 −0.175920
\(518\) 2.00000 0.0878750
\(519\) 12.0000 0.526742
\(520\) 2.00000 0.0877058
\(521\) −22.0000 −0.963837 −0.481919 − 0.876216i \(-0.660060\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 − 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 12.0000 0.524222
\(525\) −1.00000 −0.0436436
\(526\) 16.0000 0.697633
\(527\) 0 0
\(528\) −2.00000 −0.0870388
\(529\) 1.00000 0.0434783
\(530\) 10.0000 0.434372
\(531\) 4.00000 0.173585
\(532\) −2.00000 −0.0867110
\(533\) 12.0000 0.519778
\(534\) 10.0000 0.432742
\(535\) −20.0000 −0.864675
\(536\) 14.0000 0.604708
\(537\) −24.0000 −1.03568
\(538\) 2.00000 0.0862261
\(539\) 2.00000 0.0861461
\(540\) −1.00000 −0.0430331
\(541\) 2.00000 0.0859867 0.0429934 − 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 2.00000 0.0859074
\(543\) 14.0000 0.600798
\(544\) 0 0
\(545\) 2.00000 0.0856706
\(546\) −2.00000 −0.0855921
\(547\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) −2.00000 −0.0854358
\(549\) 2.00000 0.0853579
\(550\) −2.00000 −0.0852803
\(551\) 0 0
\(552\) −1.00000 −0.0425628
\(553\) 0 0
\(554\) −4.00000 −0.169944
\(555\) 2.00000 0.0848953
\(556\) 0 0
\(557\) −42.0000 −1.77960 −0.889799 − 0.456354i \(-0.849155\pi\)
−0.889799 + 0.456354i \(0.849155\pi\)
\(558\) 2.00000 0.0846668
\(559\) −4.00000 −0.169182
\(560\) 1.00000 0.0422577
\(561\) 0 0
\(562\) −24.0000 −1.01238
\(563\) −14.0000 −0.590030 −0.295015 − 0.955493i \(-0.595325\pi\)
−0.295015 + 0.955493i \(0.595325\pi\)
\(564\) 2.00000 0.0842152
\(565\) 18.0000 0.757266
\(566\) −24.0000 −1.00880
\(567\) 1.00000 0.0419961
\(568\) 14.0000 0.587427
\(569\) −12.0000 −0.503066 −0.251533 − 0.967849i \(-0.580935\pi\)
−0.251533 + 0.967849i \(0.580935\pi\)
\(570\) −2.00000 −0.0837708
\(571\) 32.0000 1.33916 0.669579 − 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) −4.00000 −0.167248
\(573\) −24.0000 −1.00261
\(574\) 6.00000 0.250435
\(575\) −1.00000 −0.0417029
\(576\) 1.00000 0.0416667
\(577\) −38.0000 −1.58196 −0.790980 − 0.611842i \(-0.790429\pi\)
−0.790980 + 0.611842i \(0.790429\pi\)
\(578\) 17.0000 0.707107
\(579\) 6.00000 0.249351
\(580\) 0 0
\(581\) 10.0000 0.414870
\(582\) −10.0000 −0.414513
\(583\) −20.0000 −0.828315
\(584\) 10.0000 0.413803
\(585\) −2.00000 −0.0826898
\(586\) 18.0000 0.743573
\(587\) −20.0000 −0.825488 −0.412744 − 0.910847i \(-0.635430\pi\)
−0.412744 + 0.910847i \(0.635430\pi\)
\(588\) −1.00000 −0.0412393
\(589\) 4.00000 0.164817
\(590\) −4.00000 −0.164677
\(591\) −6.00000 −0.246807
\(592\) −2.00000 −0.0821995
\(593\) −6.00000 −0.246390 −0.123195 − 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 2.00000 0.0820610
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) −16.0000 −0.654836
\(598\) −2.00000 −0.0817861
\(599\) −38.0000 −1.55264 −0.776319 − 0.630340i \(-0.782915\pi\)
−0.776319 + 0.630340i \(0.782915\pi\)
\(600\) 1.00000 0.0408248
\(601\) 30.0000 1.22373 0.611863 − 0.790964i \(-0.290420\pi\)
0.611863 + 0.790964i \(0.290420\pi\)
\(602\) −2.00000 −0.0815139
\(603\) −14.0000 −0.570124
\(604\) 0 0
\(605\) −7.00000 −0.284590
\(606\) 10.0000 0.406222
\(607\) −8.00000 −0.324710 −0.162355 − 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) −2.00000 −0.0809776
\(611\) 4.00000 0.161823
\(612\) 0 0
\(613\) 26.0000 1.05013 0.525065 − 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 12.0000 0.484281
\(615\) 6.00000 0.241943
\(616\) −2.00000 −0.0805823
\(617\) −22.0000 −0.885687 −0.442843 − 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 8.00000 0.321807
\(619\) 2.00000 0.0803868 0.0401934 − 0.999192i \(-0.487203\pi\)
0.0401934 + 0.999192i \(0.487203\pi\)
\(620\) −2.00000 −0.0803219
\(621\) 1.00000 0.0401286
\(622\) −16.0000 −0.641542
\(623\) 10.0000 0.400642
\(624\) 2.00000 0.0800641
\(625\) 1.00000 0.0400000
\(626\) 10.0000 0.399680
\(627\) 4.00000 0.159745
\(628\) 2.00000 0.0798087
\(629\) 0 0
\(630\) −1.00000 −0.0398410
\(631\) 8.00000 0.318475 0.159237 − 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) −4.00000 −0.158986
\(634\) 14.0000 0.556011
\(635\) −14.0000 −0.555573
\(636\) 10.0000 0.396526
\(637\) −2.00000 −0.0792429
\(638\) 0 0
\(639\) −14.0000 −0.553831
\(640\) −1.00000 −0.0395285
\(641\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) −20.0000 −0.789337
\(643\) −36.0000 −1.41970 −0.709851 − 0.704352i \(-0.751238\pi\)
−0.709851 + 0.704352i \(0.751238\pi\)
\(644\) −1.00000 −0.0394055
\(645\) −2.00000 −0.0787499
\(646\) 0 0
\(647\) 50.0000 1.96570 0.982851 − 0.184399i \(-0.0590339\pi\)
0.982851 + 0.184399i \(0.0590339\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 8.00000 0.314027
\(650\) 2.00000 0.0784465
\(651\) 2.00000 0.0783862
\(652\) −16.0000 −0.626608
\(653\) −26.0000 −1.01746 −0.508729 − 0.860927i \(-0.669885\pi\)
−0.508729 + 0.860927i \(0.669885\pi\)
\(654\) 2.00000 0.0782062
\(655\) 12.0000 0.468879
\(656\) −6.00000 −0.234261
\(657\) −10.0000 −0.390137
\(658\) 2.00000 0.0779681
\(659\) 30.0000 1.16863 0.584317 − 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) −2.00000 −0.0778499
\(661\) 2.00000 0.0777910 0.0388955 − 0.999243i \(-0.487616\pi\)
0.0388955 + 0.999243i \(0.487616\pi\)
\(662\) 12.0000 0.466393
\(663\) 0 0
\(664\) −10.0000 −0.388075
\(665\) −2.00000 −0.0775567
\(666\) 2.00000 0.0774984
\(667\) 0 0
\(668\) 22.0000 0.851206
\(669\) 4.00000 0.154649
\(670\) 14.0000 0.540867
\(671\) 4.00000 0.154418
\(672\) 1.00000 0.0385758
\(673\) 14.0000 0.539660 0.269830 − 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 8.00000 0.308148
\(675\) −1.00000 −0.0384900
\(676\) −9.00000 −0.346154
\(677\) 6.00000 0.230599 0.115299 − 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 18.0000 0.691286
\(679\) −10.0000 −0.383765
\(680\) 0 0
\(681\) 6.00000 0.229920
\(682\) 4.00000 0.153168
\(683\) 44.0000 1.68361 0.841807 − 0.539779i \(-0.181492\pi\)
0.841807 + 0.539779i \(0.181492\pi\)
\(684\) −2.00000 −0.0764719
\(685\) −2.00000 −0.0764161
\(686\) −1.00000 −0.0381802
\(687\) 6.00000 0.228914
\(688\) 2.00000 0.0762493
\(689\) 20.0000 0.761939
\(690\) −1.00000 −0.0380693
\(691\) −12.0000 −0.456502 −0.228251 − 0.973602i \(-0.573301\pi\)
−0.228251 + 0.973602i \(0.573301\pi\)
\(692\) −12.0000 −0.456172
\(693\) 2.00000 0.0759737
\(694\) 4.00000 0.151838
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −24.0000 −0.908413
\(699\) 6.00000 0.226941
\(700\) 1.00000 0.0377964
\(701\) 34.0000 1.28416 0.642081 − 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) −2.00000 −0.0754851
\(703\) 4.00000 0.150863
\(704\) 2.00000 0.0753778
\(705\) 2.00000 0.0753244
\(706\) −14.0000 −0.526897
\(707\) 10.0000 0.376089
\(708\) −4.00000 −0.150329
\(709\) 38.0000 1.42712 0.713560 − 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) 14.0000 0.525411
\(711\) 0 0
\(712\) −10.0000 −0.374766
\(713\) 2.00000 0.0749006
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) 24.0000 0.896922
\(717\) 6.00000 0.224074
\(718\) 32.0000 1.19423
\(719\) 16.0000 0.596699 0.298350 − 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) 1.00000 0.0372678
\(721\) 8.00000 0.297936
\(722\) 15.0000 0.558242
\(723\) 20.0000 0.743808
\(724\) −14.0000 −0.520306
\(725\) 0 0
\(726\) −7.00000 −0.259794
\(727\) 24.0000 0.890111 0.445055 − 0.895503i \(-0.353184\pi\)
0.445055 + 0.895503i \(0.353184\pi\)
\(728\) 2.00000 0.0741249
\(729\) 1.00000 0.0370370
\(730\) 10.0000 0.370117
\(731\) 0 0
\(732\) −2.00000 −0.0739221
\(733\) −2.00000 −0.0738717 −0.0369358 − 0.999318i \(-0.511760\pi\)
−0.0369358 + 0.999318i \(0.511760\pi\)
\(734\) 32.0000 1.18114
\(735\) −1.00000 −0.0368856
\(736\) 1.00000 0.0368605
\(737\) −28.0000 −1.03139
\(738\) 6.00000 0.220863
\(739\) 4.00000 0.147142 0.0735712 − 0.997290i \(-0.476560\pi\)
0.0735712 + 0.997290i \(0.476560\pi\)
\(740\) −2.00000 −0.0735215
\(741\) −4.00000 −0.146944
\(742\) 10.0000 0.367112
\(743\) 32.0000 1.17397 0.586983 − 0.809599i \(-0.300316\pi\)
0.586983 + 0.809599i \(0.300316\pi\)
\(744\) −2.00000 −0.0733236
\(745\) −10.0000 −0.366372
\(746\) −6.00000 −0.219676
\(747\) 10.0000 0.365881
\(748\) 0 0
\(749\) −20.0000 −0.730784
\(750\) 1.00000 0.0365148
\(751\) −24.0000 −0.875772 −0.437886 − 0.899030i \(-0.644273\pi\)
−0.437886 + 0.899030i \(0.644273\pi\)
\(752\) −2.00000 −0.0729325
\(753\) 24.0000 0.874609
\(754\) 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 \(0.488428\pi\)
\(758\) −28.0000 −1.01701
\(759\) 2.00000 0.0725954
\(760\) 2.00000 0.0725476
\(761\) −10.0000 −0.362500 −0.181250 − 0.983437i \(-0.558014\pi\)
−0.181250 + 0.983437i \(0.558014\pi\)
\(762\) −14.0000 −0.507166
\(763\) 2.00000 0.0724049
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) −8.00000 −0.288863
\(768\) −1.00000 −0.0360844
\(769\) −40.0000 −1.44244 −0.721218 − 0.692708i \(-0.756418\pi\)
−0.721218 + 0.692708i \(0.756418\pi\)
\(770\) −2.00000 −0.0720750
\(771\) 6.00000 0.216085
\(772\) −6.00000 −0.215945
\(773\) −6.00000 −0.215805 −0.107903 − 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) −2.00000 −0.0718885
\(775\) −2.00000 −0.0718421
\(776\) 10.0000 0.358979
\(777\) 2.00000 0.0717496
\(778\) −18.0000 −0.645331
\(779\) 12.0000 0.429945
\(780\) 2.00000 0.0716115
\(781\) −28.0000 −1.00192
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 2.00000 0.0713831
\(786\) 12.0000 0.428026
\(787\) −4.00000 −0.142585 −0.0712923 − 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 6.00000 0.213741
\(789\) 16.0000 0.569615
\(790\) 0 0
\(791\) 18.0000 0.640006
\(792\) −2.00000 −0.0710669
\(793\) −4.00000 −0.142044
\(794\) 10.0000 0.354887
\(795\) 10.0000 0.354663
\(796\) 16.0000 0.567105
\(797\) −14.0000 −0.495905 −0.247953 − 0.968772i \(-0.579758\pi\)
−0.247953 + 0.968772i \(0.579758\pi\)
\(798\) −2.00000 −0.0707992
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) 10.0000 0.353333
\(802\) 36.0000 1.27120
\(803\) −20.0000 −0.705785
\(804\) 14.0000 0.493742
\(805\) −1.00000 −0.0352454
\(806\) −4.00000 −0.140894
\(807\) 2.00000 0.0704033
\(808\) −10.0000 −0.351799
\(809\) −30.0000 −1.05474 −0.527372 − 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 32.0000 1.12367 0.561836 − 0.827249i \(-0.310095\pi\)
0.561836 + 0.827249i \(0.310095\pi\)
\(812\) 0 0
\(813\) 2.00000 0.0701431
\(814\) 4.00000 0.140200
\(815\) −16.0000 −0.560456
\(816\) 0 0
\(817\) −4.00000 −0.139942
\(818\) 30.0000 1.04893
\(819\) −2.00000 −0.0698857
\(820\) −6.00000 −0.209529
\(821\) −48.0000 −1.67521 −0.837606 − 0.546275i \(-0.816045\pi\)
−0.837606 + 0.546275i \(0.816045\pi\)
\(822\) −2.00000 −0.0697580
\(823\) 34.0000 1.18517 0.592583 − 0.805510i \(-0.298108\pi\)
0.592583 + 0.805510i \(0.298108\pi\)
\(824\) −8.00000 −0.278693
\(825\) −2.00000 −0.0696311
\(826\) −4.00000 −0.139178
\(827\) −36.0000 −1.25184 −0.625921 − 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) −1.00000 −0.0347524
\(829\) −20.0000 −0.694629 −0.347314 − 0.937749i \(-0.612906\pi\)
−0.347314 + 0.937749i \(0.612906\pi\)
\(830\) −10.0000 −0.347105
\(831\) −4.00000 −0.138758
\(832\) −2.00000 −0.0693375
\(833\) 0 0
\(834\) 0 0
\(835\) 22.0000 0.761341
\(836\) −4.00000 −0.138343
\(837\) 2.00000 0.0691301
\(838\) −20.0000 −0.690889
\(839\) 48.0000 1.65714 0.828572 − 0.559883i \(-0.189154\pi\)
0.828572 + 0.559883i \(0.189154\pi\)
\(840\) 1.00000 0.0345033
\(841\) −29.0000 −1.00000
\(842\) 26.0000 0.896019
\(843\) −24.0000 −0.826604
\(844\) 4.00000 0.137686
\(845\) −9.00000 −0.309609
\(846\) 2.00000 0.0687614
\(847\) −7.00000 −0.240523
\(848\) −10.0000 −0.343401
\(849\) −24.0000 −0.823678
\(850\) 0 0
\(851\) 2.00000 0.0685591
\(852\) 14.0000 0.479632
\(853\) 30.0000 1.02718 0.513590 − 0.858036i \(-0.328315\pi\)
0.513590 + 0.858036i \(0.328315\pi\)
\(854\) −2.00000 −0.0684386
\(855\) −2.00000 −0.0683986
\(856\) 20.0000 0.683586
\(857\) −2.00000 −0.0683187 −0.0341593 − 0.999416i \(-0.510875\pi\)
−0.0341593 + 0.999416i \(0.510875\pi\)
\(858\) −4.00000 −0.136558
\(859\) 36.0000 1.22830 0.614152 − 0.789188i \(-0.289498\pi\)
0.614152 + 0.789188i \(0.289498\pi\)
\(860\) 2.00000 0.0681994
\(861\) 6.00000 0.204479
\(862\) −12.0000 −0.408722
\(863\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 1.00000 0.0340207
\(865\) −12.0000 −0.408012
\(866\) −14.0000 −0.475739
\(867\) 17.0000 0.577350
\(868\) −2.00000 −0.0678844
\(869\) 0 0
\(870\) 0 0
\(871\) 28.0000 0.948744
\(872\) −2.00000 −0.0677285
\(873\) −10.0000 −0.338449
\(874\) −2.00000 −0.0676510
\(875\) 1.00000 0.0338062
\(876\) 10.0000 0.337869
\(877\) −32.0000 −1.08056 −0.540282 − 0.841484i \(-0.681682\pi\)
−0.540282 + 0.841484i \(0.681682\pi\)
\(878\) 34.0000 1.14744
\(879\) 18.0000 0.607125
\(880\) 2.00000 0.0674200
\(881\) 30.0000 1.01073 0.505363 − 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) −1.00000 −0.0336718
\(883\) 40.0000 1.34611 0.673054 − 0.739594i \(-0.264982\pi\)
0.673054 + 0.739594i \(0.264982\pi\)
\(884\) 0 0
\(885\) −4.00000 −0.134459
\(886\) 28.0000 0.940678
\(887\) −30.0000 −1.00730 −0.503651 − 0.863907i \(-0.668010\pi\)
−0.503651 + 0.863907i \(0.668010\pi\)
\(888\) −2.00000 −0.0671156
\(889\) −14.0000 −0.469545
\(890\) −10.0000 −0.335201
\(891\) 2.00000 0.0670025
\(892\) −4.00000 −0.133930
\(893\) 4.00000 0.133855
\(894\) −10.0000 −0.334450
\(895\) 24.0000 0.802232
\(896\) −1.00000 −0.0334077
\(897\) −2.00000 −0.0667781
\(898\) 2.00000 0.0667409
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 0 0
\(902\) 12.0000 0.399556
\(903\) −2.00000 −0.0665558
\(904\) −18.0000 −0.598671
\(905\) −14.0000 −0.465376
\(906\) 0 0
\(907\) −10.0000 −0.332045 −0.166022 − 0.986122i \(-0.553092\pi\)
−0.166022 + 0.986122i \(0.553092\pi\)
\(908\) −6.00000 −0.199117
\(909\) 10.0000 0.331679
\(910\) 2.00000 0.0662994
\(911\) 4.00000 0.132526 0.0662630 − 0.997802i \(-0.478892\pi\)
0.0662630 + 0.997802i \(0.478892\pi\)
\(912\) 2.00000 0.0662266
\(913\) 20.0000 0.661903
\(914\) 40.0000 1.32308
\(915\) −2.00000 −0.0661180
\(916\) −6.00000 −0.198246
\(917\) 12.0000 0.396275
\(918\) 0 0
\(919\) 16.0000 0.527791 0.263896 − 0.964551i \(-0.414993\pi\)
0.263896 + 0.964551i \(0.414993\pi\)
\(920\) 1.00000 0.0329690
\(921\) 12.0000 0.395413
\(922\) −10.0000 −0.329332
\(923\) 28.0000 0.921631
\(924\) −2.00000 −0.0657952
\(925\) −2.00000 −0.0657596
\(926\) 22.0000 0.722965
\(927\) 8.00000 0.262754
\(928\) 0 0
\(929\) 14.0000 0.459325 0.229663 − 0.973270i \(-0.426238\pi\)
0.229663 + 0.973270i \(0.426238\pi\)
\(930\) −2.00000 −0.0655826
\(931\) −2.00000 −0.0655474
\(932\) −6.00000 −0.196537
\(933\) −16.0000 −0.523816
\(934\) −14.0000 −0.458094
\(935\) 0 0
\(936\) 2.00000 0.0653720
\(937\) 10.0000 0.326686 0.163343 − 0.986569i \(-0.447772\pi\)
0.163343 + 0.986569i \(0.447772\pi\)
\(938\) 14.0000 0.457116
\(939\) 10.0000 0.326338
\(940\) −2.00000 −0.0652328
\(941\) 46.0000 1.49956 0.749779 − 0.661689i \(-0.230160\pi\)
0.749779 + 0.661689i \(0.230160\pi\)
\(942\) 2.00000 0.0651635
\(943\) 6.00000 0.195387
\(944\) 4.00000 0.130189
\(945\) −1.00000 −0.0325300
\(946\) −4.00000 −0.130051
\(947\) 52.0000 1.68977 0.844886 − 0.534946i \(-0.179668\pi\)
0.844886 + 0.534946i \(0.179668\pi\)
\(948\) 0 0
\(949\) 20.0000 0.649227
\(950\) 2.00000 0.0648886
\(951\) 14.0000 0.453981
\(952\) 0 0
\(953\) 18.0000 0.583077 0.291539 − 0.956559i \(-0.405833\pi\)
0.291539 + 0.956559i \(0.405833\pi\)
\(954\) 10.0000 0.323762
\(955\) 24.0000 0.776622
\(956\) −6.00000 −0.194054
\(957\) 0 0
\(958\) 16.0000 0.516937
\(959\) −2.00000 −0.0645834
\(960\) −1.00000 −0.0322749
\(961\) −27.0000 −0.870968
\(962\) −4.00000 −0.128965
\(963\) −20.0000 −0.644491
\(964\) −20.0000 −0.644157
\(965\) −6.00000 −0.193147
\(966\) −1.00000 −0.0321745
\(967\) −46.0000 −1.47926 −0.739630 − 0.673014i \(-0.765000\pi\)
−0.739630 + 0.673014i \(0.765000\pi\)
\(968\) 7.00000 0.224989
\(969\) 0 0
\(970\) 10.0000 0.321081
\(971\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −10.0000 −0.320421
\(975\) 2.00000 0.0640513
\(976\) 2.00000 0.0640184
\(977\) 50.0000 1.59964 0.799821 − 0.600239i \(-0.204928\pi\)
0.799821 + 0.600239i \(0.204928\pi\)
\(978\) −16.0000 −0.511624
\(979\) 20.0000 0.639203
\(980\) 1.00000 0.0319438
\(981\) 2.00000 0.0638551
\(982\) 0 0
\(983\) −24.0000 −0.765481 −0.382741 − 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) −6.00000 −0.191273
\(985\) 6.00000 0.191176
\(986\) 0 0
\(987\) 2.00000 0.0636607
\(988\) 4.00000 0.127257
\(989\) −2.00000 −0.0635963
\(990\) −2.00000 −0.0635642
\(991\) 16.0000 0.508257 0.254128 − 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) 2.00000 0.0635001
\(993\) 12.0000 0.380808
\(994\) 14.0000 0.444053
\(995\) 16.0000 0.507234
\(996\) −10.0000 −0.316862
\(997\) −18.0000 −0.570066 −0.285033 − 0.958518i \(-0.592005\pi\)
−0.285033 + 0.958518i \(0.592005\pi\)
\(998\) 4.00000 0.126618
\(999\) 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 4830.2.a.g.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4830.2.a.g.1.1 ✓ 1 1.1 even 1 trivial