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Properties

Label 4830.2.a.l.1.1
Level $4830$
Weight $2$
Character 4830.1
Self dual yes
Analytic conductor $38.568$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4830,2,Mod(1,4830)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4830, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4830.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4830.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(38.5677441763\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4830.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} -4.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} +2.00000 q^{19} -1.00000 q^{20} +1.00000 q^{21} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} +6.00000 q^{29} +1.00000 q^{30} +2.00000 q^{31} -1.00000 q^{32} -1.00000 q^{35} +1.00000 q^{36} -10.0000 q^{37} -2.00000 q^{38} -4.00000 q^{39} +1.00000 q^{40} +6.00000 q^{41} -1.00000 q^{42} -4.00000 q^{43} -1.00000 q^{45} -1.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -4.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} -1.00000 q^{56} +2.00000 q^{57} -6.00000 q^{58} +12.0000 q^{59} -1.00000 q^{60} -10.0000 q^{61} -2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} -4.00000 q^{67} +1.00000 q^{69} +1.00000 q^{70} -1.00000 q^{72} +14.0000 q^{73} +10.0000 q^{74} +1.00000 q^{75} +2.00000 q^{76} +4.00000 q^{78} +8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} +6.00000 q^{83} +1.00000 q^{84} +4.00000 q^{86} +6.00000 q^{87} +1.00000 q^{90} -4.00000 q^{91} +1.00000 q^{92} +2.00000 q^{93} -6.00000 q^{94} -2.00000 q^{95} -1.00000 q^{96} +8.00000 q^{97} -1.00000 q^{98} +O(q^{100})\)

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
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) −4.00000 −1.10940 −0.554700 − 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −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 \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 4.00000 0.784465
\(27\) 1.00000 0.192450
\(28\) 1.00000 0.188982
\(29\) 6.00000 1.11417 0.557086 − 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 1.00000 0.182574
\(31\) 2.00000 0.359211 0.179605 − 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 1.00000 0.166667
\(37\) −10.0000 −1.64399 −0.821995 − 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −2.00000 −0.324443
\(39\) −4.00000 −0.640513
\(40\) 1.00000 0.158114
\(41\) 6.00000 0.937043 0.468521 − 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) −1.00000 −0.154303
\(43\) −4.00000 −0.609994 −0.304997 − 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) −1.00000 −0.147442
\(47\) 6.00000 0.875190 0.437595 − 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −4.00000 −0.554700
\(53\) −6.00000 −0.824163 −0.412082 − 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 2.00000 0.264906
\(58\) −6.00000 −0.787839
\(59\) 12.0000 1.56227 0.781133 − 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) −1.00000 −0.129099
\(61\) −10.0000 −1.28037 −0.640184 − 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) −2.00000 −0.254000
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) 4.00000 0.496139
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 1.00000 0.119523
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.00000 −0.117851
\(73\) 14.0000 1.63858 0.819288 − 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) 10.0000 1.16248
\(75\) 1.00000 0.115470
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) 4.00000 0.452911
\(79\) 8.00000 0.900070 0.450035 − 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −6.00000 −0.662589
\(83\) 6.00000 0.658586 0.329293 − 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 1.00000 0.109109
\(85\) 0 0
\(86\) 4.00000 0.431331
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 1.00000 0.105409
\(91\) −4.00000 −0.419314
\(92\) 1.00000 0.104257
\(93\) 2.00000 0.207390
\(94\) −6.00000 −0.618853
\(95\) −2.00000 −0.205196
\(96\) −1.00000 −0.102062
\(97\) 8.00000 0.812277 0.406138 − 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −4.00000 −0.394132 −0.197066 − 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 4.00000 0.392232
\(105\) −1.00000 −0.0975900
\(106\) 6.00000 0.582772
\(107\) 12.0000 1.16008 0.580042 − 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 1.00000 0.0962250
\(109\) 2.00000 0.191565 0.0957826 − 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) −10.0000 −0.949158
\(112\) 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
\(116\) 6.00000 0.557086
\(117\) −4.00000 −0.369800
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) −11.0000 −1.00000
\(122\) 10.0000 0.905357
\(123\) 6.00000 0.541002
\(124\) 2.00000 0.179605
\(125\) −1.00000 −0.0894427
\(126\) −1.00000 −0.0890871
\(127\) 8.00000 0.709885 0.354943 − 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.00000 −0.352180
\(130\) −4.00000 −0.350823
\(131\) 12.0000 1.04844 0.524222 − 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 2.00000 0.173422
\(134\) 4.00000 0.345547
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 6.00000 0.512615 0.256307 − 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) −1.00000 −0.0851257
\(139\) −16.0000 −1.35710 −0.678551 − 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −6.00000 −0.498273
\(146\) −14.0000 −1.15865
\(147\) 1.00000 0.0824786
\(148\) −10.0000 −0.821995
\(149\) −18.0000 −1.47462 −0.737309 − 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 20.0000 1.62758 0.813788 − 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) −2.00000 −0.162221
\(153\) 0 0
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) −4.00000 −0.320256
\(157\) 2.00000 0.159617 0.0798087 − 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −8.00000 −0.636446
\(159\) −6.00000 −0.475831
\(160\) 1.00000 0.0790569
\(161\) 1.00000 0.0788110
\(162\) −1.00000 −0.0785674
\(163\) −4.00000 −0.313304 −0.156652 − 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) −6.00000 −0.464294 −0.232147 − 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) −1.00000 −0.0771517
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 2.00000 0.152944
\(172\) −4.00000 −0.304997
\(173\) −12.0000 −0.912343 −0.456172 − 0.889892i \(-0.650780\pi\)
−0.456172 + 0.889892i \(0.650780\pi\)
\(174\) −6.00000 −0.454859
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 12.0000 0.901975
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 − 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 14.0000 1.04061 0.520306 − 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 4.00000 0.296500
\(183\) −10.0000 −0.739221
\(184\) −1.00000 −0.0737210
\(185\) 10.0000 0.735215
\(186\) −2.00000 −0.146647
\(187\) 0 0
\(188\) 6.00000 0.437595
\(189\) 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
\(193\) 14.0000 1.00774 0.503871 − 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −8.00000 −0.574367
\(195\) 4.00000 0.286446
\(196\) 1.00000 0.0714286
\(197\) −18.0000 −1.28245 −0.641223 − 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 − 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −4.00000 −0.282138
\(202\) 0 0
\(203\) 6.00000 0.421117
\(204\) 0 0
\(205\) −6.00000 −0.419058
\(206\) 4.00000 0.278693
\(207\) 1.00000 0.0695048
\(208\) −4.00000 −0.277350
\(209\) 0 0
\(210\) 1.00000 0.0690066
\(211\) 20.0000 1.37686 0.688428 − 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) 4.00000 0.272798
\(216\) −1.00000 −0.0680414
\(217\) 2.00000 0.135769
\(218\) −2.00000 −0.135457
\(219\) 14.0000 0.946032
\(220\) 0 0
\(221\) 0 0
\(222\) 10.0000 0.671156
\(223\) −22.0000 −1.47323 −0.736614 − 0.676313i \(-0.763577\pi\)
−0.736614 + 0.676313i \(0.763577\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 1.00000 0.0666667
\(226\) −18.0000 −1.19734
\(227\) −30.0000 −1.99117 −0.995585 − 0.0938647i \(-0.970078\pi\)
−0.995585 + 0.0938647i \(0.970078\pi\)
\(228\) 2.00000 0.132453
\(229\) 14.0000 0.925146 0.462573 − 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 1.00000 0.0659380
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 6.00000 0.393073 0.196537 − 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 4.00000 0.261488
\(235\) −6.00000 −0.391397
\(236\) 12.0000 0.781133
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 − 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −16.0000 −1.03065 −0.515325 − 0.856995i \(-0.672329\pi\)
−0.515325 + 0.856995i \(0.672329\pi\)
\(242\) 11.0000 0.707107
\(243\) 1.00000 0.0641500
\(244\) −10.0000 −0.640184
\(245\) −1.00000 −0.0638877
\(246\) −6.00000 −0.382546
\(247\) −8.00000 −0.509028
\(248\) −2.00000 −0.127000
\(249\) 6.00000 0.380235
\(250\) 1.00000 0.0632456
\(251\) −6.00000 −0.378717 −0.189358 − 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) 1.00000 0.0629941
\(253\) 0 0
\(254\) −8.00000 −0.501965
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 − 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 4.00000 0.249029
\(259\) −10.0000 −0.621370
\(260\) 4.00000 0.248069
\(261\) 6.00000 0.371391
\(262\) −12.0000 −0.741362
\(263\) 24.0000 1.47990 0.739952 − 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) −2.00000 −0.122628
\(267\) 0 0
\(268\) −4.00000 −0.244339
\(269\) 24.0000 1.46331 0.731653 − 0.681677i \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) 1.00000 0.0608581
\(271\) 2.00000 0.121491 0.0607457 − 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 0 0
\(273\) −4.00000 −0.242091
\(274\) −6.00000 −0.362473
\(275\) 0 0
\(276\) 1.00000 0.0601929
\(277\) 26.0000 1.56219 0.781094 − 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) 16.0000 0.959616
\(279\) 2.00000 0.119737
\(280\) 1.00000 0.0597614
\(281\) −6.00000 −0.357930 −0.178965 − 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) −6.00000 −0.357295
\(283\) 14.0000 0.832214 0.416107 − 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) 0 0
\(285\) −2.00000 −0.118470
\(286\) 0 0
\(287\) 6.00000 0.354169
\(288\) −1.00000 −0.0589256
\(289\) −17.0000 −1.00000
\(290\) 6.00000 0.352332
\(291\) 8.00000 0.468968
\(292\) 14.0000 0.819288
\(293\) −6.00000 −0.350524 −0.175262 − 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −12.0000 −0.698667
\(296\) 10.0000 0.581238
\(297\) 0 0
\(298\) 18.0000 1.04271
\(299\) −4.00000 −0.231326
\(300\) 1.00000 0.0577350
\(301\) −4.00000 −0.230556
\(302\) −20.0000 −1.15087
\(303\) 0 0
\(304\) 2.00000 0.114708
\(305\) 10.0000 0.572598
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 − 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 2.00000 0.113592
\(311\) 18.0000 1.02069 0.510343 − 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 4.00000 0.226455
\(313\) −4.00000 −0.226093 −0.113047 − 0.993590i \(-0.536061\pi\)
−0.113047 + 0.993590i \(0.536061\pi\)
\(314\) −2.00000 −0.112867
\(315\) −1.00000 −0.0563436
\(316\) 8.00000 0.450035
\(317\) −18.0000 −1.01098 −0.505490 − 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 6.00000 0.336463
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) 12.0000 0.669775
\(322\) −1.00000 −0.0557278
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −4.00000 −0.221880
\(326\) 4.00000 0.221540
\(327\) 2.00000 0.110600
\(328\) −6.00000 −0.331295
\(329\) 6.00000 0.330791
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 − 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 6.00000 0.329293
\(333\) −10.0000 −0.547997
\(334\) 6.00000 0.328305
\(335\) 4.00000 0.218543
\(336\) 1.00000 0.0545545
\(337\) −22.0000 −1.19842 −0.599208 − 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −3.00000 −0.163178
\(339\) 18.0000 0.977626
\(340\) 0 0
\(341\) 0 0
\(342\) −2.00000 −0.108148
\(343\) 1.00000 0.0539949
\(344\) 4.00000 0.215666
\(345\) −1.00000 −0.0538382
\(346\) 12.0000 0.645124
\(347\) −12.0000 −0.644194 −0.322097 − 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 6.00000 0.321634
\(349\) −28.0000 −1.49881 −0.749403 − 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) −1.00000 −0.0534522
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) 30.0000 1.59674 0.798369 − 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) −12.0000 −0.637793
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 24.0000 1.26667 0.633336 − 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 1.00000 0.0527046
\(361\) −15.0000 −0.789474
\(362\) −14.0000 −0.735824
\(363\) −11.0000 −0.577350
\(364\) −4.00000 −0.209657
\(365\) −14.0000 −0.732793
\(366\) 10.0000 0.522708
\(367\) −4.00000 −0.208798 −0.104399 − 0.994535i \(-0.533292\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(368\) 1.00000 0.0521286
\(369\) 6.00000 0.312348
\(370\) −10.0000 −0.519875
\(371\) −6.00000 −0.311504
\(372\) 2.00000 0.103695
\(373\) 14.0000 0.724893 0.362446 − 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) −6.00000 −0.309426
\(377\) −24.0000 −1.23606
\(378\) −1.00000 −0.0514344
\(379\) 20.0000 1.02733 0.513665 − 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −2.00000 −0.102598
\(381\) 8.00000 0.409852
\(382\) −24.0000 −1.22795
\(383\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) −4.00000 −0.203331
\(388\) 8.00000 0.406138
\(389\) −30.0000 −1.52106 −0.760530 − 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) −4.00000 −0.202548
\(391\) 0 0
\(392\) −1.00000 −0.0505076
\(393\) 12.0000 0.605320
\(394\) 18.0000 0.906827
\(395\) −8.00000 −0.402524
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 − 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) 4.00000 0.200502
\(399\) 2.00000 0.100125
\(400\) 1.00000 0.0500000
\(401\) 18.0000 0.898877 0.449439 − 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 4.00000 0.199502
\(403\) −8.00000 −0.398508
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) −6.00000 −0.297775
\(407\) 0 0
\(408\) 0 0
\(409\) −22.0000 −1.08783 −0.543915 − 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 6.00000 0.296319
\(411\) 6.00000 0.295958
\(412\) −4.00000 −0.197066
\(413\) 12.0000 0.590481
\(414\) −1.00000 −0.0491473
\(415\) −6.00000 −0.294528
\(416\) 4.00000 0.196116
\(417\) −16.0000 −0.783523
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 − 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) −1.00000 −0.0487950
\(421\) 26.0000 1.26716 0.633581 − 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) −20.0000 −0.973585
\(423\) 6.00000 0.291730
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) −10.0000 −0.483934
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) −4.00000 −0.192897
\(431\) −24.0000 −1.15604 −0.578020 − 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 1.00000 0.0481125
\(433\) −16.0000 −0.768911 −0.384455 − 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −2.00000 −0.0960031
\(435\) −6.00000 −0.287678
\(436\) 2.00000 0.0957826
\(437\) 2.00000 0.0956730
\(438\) −14.0000 −0.668946
\(439\) −34.0000 −1.62273 −0.811366 − 0.584539i \(-0.801275\pi\)
−0.811366 + 0.584539i \(0.801275\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 36.0000 1.71041 0.855206 − 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) −10.0000 −0.474579
\(445\) 0 0
\(446\) 22.0000 1.04173
\(447\) −18.0000 −0.851371
\(448\) 1.00000 0.0472456
\(449\) −18.0000 −0.849473 −0.424736 − 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 0 0
\(452\) 18.0000 0.846649
\(453\) 20.0000 0.939682
\(454\) 30.0000 1.40797
\(455\) 4.00000 0.187523
\(456\) −2.00000 −0.0936586
\(457\) 38.0000 1.77757 0.888783 − 0.458329i \(-0.151552\pi\)
0.888783 + 0.458329i \(0.151552\pi\)
\(458\) −14.0000 −0.654177
\(459\) 0 0
\(460\) −1.00000 −0.0466252
\(461\) 24.0000 1.11779 0.558896 − 0.829238i \(-0.311225\pi\)
0.558896 + 0.829238i \(0.311225\pi\)
\(462\) 0 0
\(463\) 20.0000 0.929479 0.464739 − 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) 6.00000 0.278543
\(465\) −2.00000 −0.0927478
\(466\) −6.00000 −0.277945
\(467\) −6.00000 −0.277647 −0.138823 − 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) −4.00000 −0.184900
\(469\) −4.00000 −0.184703
\(470\) 6.00000 0.276759
\(471\) 2.00000 0.0921551
\(472\) −12.0000 −0.552345
\(473\) 0 0
\(474\) −8.00000 −0.367452
\(475\) 2.00000 0.0917663
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) −24.0000 −1.09773
\(479\) 36.0000 1.64488 0.822441 − 0.568850i \(-0.192612\pi\)
0.822441 + 0.568850i \(0.192612\pi\)
\(480\) 1.00000 0.0456435
\(481\) 40.0000 1.82384
\(482\) 16.0000 0.728780
\(483\) 1.00000 0.0455016
\(484\) −11.0000 −0.500000
\(485\) −8.00000 −0.363261
\(486\) −1.00000 −0.0453609
\(487\) −28.0000 −1.26880 −0.634401 − 0.773004i \(-0.718753\pi\)
−0.634401 + 0.773004i \(0.718753\pi\)
\(488\) 10.0000 0.452679
\(489\) −4.00000 −0.180886
\(490\) 1.00000 0.0451754
\(491\) 36.0000 1.62466 0.812329 − 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 6.00000 0.270501
\(493\) 0 0
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) −6.00000 −0.268866
\(499\) −4.00000 −0.179065 −0.0895323 − 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −6.00000 −0.268060
\(502\) 6.00000 0.267793
\(503\) −24.0000 −1.07011 −0.535054 − 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 0 0
\(506\) 0 0
\(507\) 3.00000 0.133235
\(508\) 8.00000 0.354943
\(509\) 24.0000 1.06378 0.531891 − 0.846813i \(-0.321482\pi\)
0.531891 + 0.846813i \(0.321482\pi\)
\(510\) 0 0
\(511\) 14.0000 0.619324
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 0.0883022
\(514\) −18.0000 −0.793946
\(515\) 4.00000 0.176261
\(516\) −4.00000 −0.176090
\(517\) 0 0
\(518\) 10.0000 0.439375
\(519\) −12.0000 −0.526742
\(520\) −4.00000 −0.175412
\(521\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) −6.00000 −0.262613
\(523\) 14.0000 0.612177 0.306089 − 0.952003i \(-0.400980\pi\)
0.306089 + 0.952003i \(0.400980\pi\)
\(524\) 12.0000 0.524222
\(525\) 1.00000 0.0436436
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −6.00000 −0.260623
\(531\) 12.0000 0.520756
\(532\) 2.00000 0.0867110
\(533\) −24.0000 −1.03956
\(534\) 0 0
\(535\) −12.0000 −0.518805
\(536\) 4.00000 0.172774
\(537\) 12.0000 0.517838
\(538\) −24.0000 −1.03471
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) 38.0000 1.63375 0.816874 − 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −2.00000 −0.0859074
\(543\) 14.0000 0.600798
\(544\) 0 0
\(545\) −2.00000 −0.0856706
\(546\) 4.00000 0.171184
\(547\) −28.0000 −1.19719 −0.598597 − 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 6.00000 0.256307
\(549\) −10.0000 −0.426790
\(550\) 0 0
\(551\) 12.0000 0.511217
\(552\) −1.00000 −0.0425628
\(553\) 8.00000 0.340195
\(554\) −26.0000 −1.10463
\(555\) 10.0000 0.424476
\(556\) −16.0000 −0.678551
\(557\) −18.0000 −0.762684 −0.381342 − 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) −2.00000 −0.0846668
\(559\) 16.0000 0.676728
\(560\) −1.00000 −0.0422577
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) 6.00000 0.252870 0.126435 − 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) 6.00000 0.252646
\(565\) −18.0000 −0.757266
\(566\) −14.0000 −0.588464
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 − 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 2.00000 0.0837708
\(571\) 32.0000 1.33916 0.669579 − 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 0 0
\(573\) 24.0000 1.00261
\(574\) −6.00000 −0.250435
\(575\) 1.00000 0.0417029
\(576\) 1.00000 0.0416667
\(577\) 14.0000 0.582828 0.291414 − 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 17.0000 0.707107
\(579\) 14.0000 0.581820
\(580\) −6.00000 −0.249136
\(581\) 6.00000 0.248922
\(582\) −8.00000 −0.331611
\(583\) 0 0
\(584\) −14.0000 −0.579324
\(585\) 4.00000 0.165380
\(586\) 6.00000 0.247858
\(587\) −48.0000 −1.98117 −0.990586 − 0.136892i \(-0.956289\pi\)
−0.990586 + 0.136892i \(0.956289\pi\)
\(588\) 1.00000 0.0412393
\(589\) 4.00000 0.164817
\(590\) 12.0000 0.494032
\(591\) −18.0000 −0.740421
\(592\) −10.0000 −0.410997
\(593\) −30.0000 −1.23195 −0.615976 − 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) −4.00000 −0.163709
\(598\) 4.00000 0.163572
\(599\) −12.0000 −0.490307 −0.245153 − 0.969484i \(-0.578838\pi\)
−0.245153 + 0.969484i \(0.578838\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −10.0000 −0.407909 −0.203954 − 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 4.00000 0.163028
\(603\) −4.00000 −0.162893
\(604\) 20.0000 0.813788
\(605\) 11.0000 0.447214
\(606\) 0 0
\(607\) 14.0000 0.568242 0.284121 − 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 6.00000 0.243132
\(610\) −10.0000 −0.404888
\(611\) −24.0000 −0.970936
\(612\) 0 0
\(613\) 2.00000 0.0807792 0.0403896 − 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) −8.00000 −0.322854
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) 30.0000 1.20775 0.603877 − 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) 4.00000 0.160904
\(619\) 14.0000 0.562708 0.281354 − 0.959604i \(-0.409217\pi\)
0.281354 + 0.959604i \(0.409217\pi\)
\(620\) −2.00000 −0.0803219
\(621\) 1.00000 0.0401286
\(622\) −18.0000 −0.721734
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 1.00000 0.0400000
\(626\) 4.00000 0.159872
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) 0 0
\(630\) 1.00000 0.0398410
\(631\) −16.0000 −0.636950 −0.318475 − 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −8.00000 −0.318223
\(633\) 20.0000 0.794929
\(634\) 18.0000 0.714871
\(635\) −8.00000 −0.317470
\(636\) −6.00000 −0.237915
\(637\) −4.00000 −0.158486
\(638\) 0 0
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) 18.0000 0.710957 0.355479 − 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) −12.0000 −0.473602
\(643\) 2.00000 0.0788723 0.0394362 − 0.999222i \(-0.487444\pi\)
0.0394362 + 0.999222i \(0.487444\pi\)
\(644\) 1.00000 0.0394055
\(645\) 4.00000 0.157500
\(646\) 0 0
\(647\) 18.0000 0.707653 0.353827 − 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 4.00000 0.156893
\(651\) 2.00000 0.0783862
\(652\) −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
\(655\) −12.0000 −0.468879
\(656\) 6.00000 0.234261
\(657\) 14.0000 0.546192
\(658\) −6.00000 −0.233904
\(659\) −12.0000 −0.467454 −0.233727 − 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −10.0000 −0.388955 −0.194477 − 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) −20.0000 −0.777322
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) −2.00000 −0.0775567
\(666\) 10.0000 0.387492
\(667\) 6.00000 0.232321
\(668\) −6.00000 −0.232147
\(669\) −22.0000 −0.850569
\(670\) −4.00000 −0.154533
\(671\) 0 0
\(672\) −1.00000 −0.0385758
\(673\) 14.0000 0.539660 0.269830 − 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 22.0000 0.847408
\(675\) 1.00000 0.0384900
\(676\) 3.00000 0.115385
\(677\) 18.0000 0.691796 0.345898 − 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −18.0000 −0.691286
\(679\) 8.00000 0.307012
\(680\) 0 0
\(681\) −30.0000 −1.14960
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 − 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 2.00000 0.0764719
\(685\) −6.00000 −0.229248
\(686\) −1.00000 −0.0381802
\(687\) 14.0000 0.534133
\(688\) −4.00000 −0.152499
\(689\) 24.0000 0.914327
\(690\) 1.00000 0.0380693
\(691\) 8.00000 0.304334 0.152167 − 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) −12.0000 −0.456172
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 16.0000 0.606915
\(696\) −6.00000 −0.227429
\(697\) 0 0
\(698\) 28.0000 1.05982
\(699\) 6.00000 0.226941
\(700\) 1.00000 0.0377964
\(701\) 30.0000 1.13308 0.566542 − 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 4.00000 0.150970
\(703\) −20.0000 −0.754314
\(704\) 0 0
\(705\) −6.00000 −0.225973
\(706\) −30.0000 −1.12906
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) 14.0000 0.525781 0.262891 − 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 0 0
\(713\) 2.00000 0.0749006
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 24.0000 0.896296
\(718\) −24.0000 −0.895672
\(719\) −42.0000 −1.56634 −0.783168 − 0.621810i \(-0.786397\pi\)
−0.783168 + 0.621810i \(0.786397\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −4.00000 −0.148968
\(722\) 15.0000 0.558242
\(723\) −16.0000 −0.595046
\(724\) 14.0000 0.520306
\(725\) 6.00000 0.222834
\(726\) 11.0000 0.408248
\(727\) −28.0000 −1.03846 −0.519231 − 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 4.00000 0.148250
\(729\) 1.00000 0.0370370
\(730\) 14.0000 0.518163
\(731\) 0 0
\(732\) −10.0000 −0.369611
\(733\) 2.00000 0.0738717 0.0369358 − 0.999318i \(-0.488240\pi\)
0.0369358 + 0.999318i \(0.488240\pi\)
\(734\) 4.00000 0.147643
\(735\) −1.00000 −0.0368856
\(736\) −1.00000 −0.0368605
\(737\) 0 0
\(738\) −6.00000 −0.220863
\(739\) 44.0000 1.61857 0.809283 − 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) 10.0000 0.367607
\(741\) −8.00000 −0.293887
\(742\) 6.00000 0.220267
\(743\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) −2.00000 −0.0733236
\(745\) 18.0000 0.659469
\(746\) −14.0000 −0.512576
\(747\) 6.00000 0.219529
\(748\) 0 0
\(749\) 12.0000 0.438470
\(750\) 1.00000 0.0365148
\(751\) −16.0000 −0.583848 −0.291924 − 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) 6.00000 0.218797
\(753\) −6.00000 −0.218652
\(754\) 24.0000 0.874028
\(755\) −20.0000 −0.727875
\(756\) 1.00000 0.0363696
\(757\) −46.0000 −1.67190 −0.835949 − 0.548807i \(-0.815082\pi\)
−0.835949 + 0.548807i \(0.815082\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) 2.00000 0.0725476
\(761\) −30.0000 −1.08750 −0.543750 − 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) −8.00000 −0.289809
\(763\) 2.00000 0.0724049
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) 0 0
\(767\) −48.0000 −1.73318
\(768\) 1.00000 0.0360844
\(769\) −16.0000 −0.576975 −0.288487 − 0.957484i \(-0.593152\pi\)
−0.288487 + 0.957484i \(0.593152\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 14.0000 0.503871
\(773\) 54.0000 1.94225 0.971123 − 0.238581i \(-0.0766824\pi\)
0.971123 + 0.238581i \(0.0766824\pi\)
\(774\) 4.00000 0.143777
\(775\) 2.00000 0.0718421
\(776\) −8.00000 −0.287183
\(777\) −10.0000 −0.358748
\(778\) 30.0000 1.07555
\(779\) 12.0000 0.429945
\(780\) 4.00000 0.143223
\(781\) 0 0
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) 1.00000 0.0357143
\(785\) −2.00000 −0.0713831
\(786\) −12.0000 −0.428026
\(787\) 2.00000 0.0712923 0.0356462 − 0.999364i \(-0.488651\pi\)
0.0356462 + 0.999364i \(0.488651\pi\)
\(788\) −18.0000 −0.641223
\(789\) 24.0000 0.854423
\(790\) 8.00000 0.284627
\(791\) 18.0000 0.640006
\(792\) 0 0
\(793\) 40.0000 1.42044
\(794\) 4.00000 0.141955
\(795\) 6.00000 0.212798
\(796\) −4.00000 −0.141776
\(797\) −18.0000 −0.637593 −0.318796 − 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) −2.00000 −0.0707992
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) 0 0
\(802\) −18.0000 −0.635602
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) −1.00000 −0.0352454
\(806\) 8.00000 0.281788
\(807\) 24.0000 0.844840
\(808\) 0 0
\(809\) 54.0000 1.89854 0.949269 − 0.314464i \(-0.101825\pi\)
0.949269 + 0.314464i \(0.101825\pi\)
\(810\) 1.00000 0.0351364
\(811\) 20.0000 0.702295 0.351147 − 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 6.00000 0.210559
\(813\) 2.00000 0.0701431
\(814\) 0 0
\(815\) 4.00000 0.140114
\(816\) 0 0
\(817\) −8.00000 −0.279885
\(818\) 22.0000 0.769212
\(819\) −4.00000 −0.139771
\(820\) −6.00000 −0.209529
\(821\) −6.00000 −0.209401 −0.104701 − 0.994504i \(-0.533388\pi\)
−0.104701 + 0.994504i \(0.533388\pi\)
\(822\) −6.00000 −0.209274
\(823\) 32.0000 1.11545 0.557725 − 0.830026i \(-0.311674\pi\)
0.557725 + 0.830026i \(0.311674\pi\)
\(824\) 4.00000 0.139347
\(825\) 0 0
\(826\) −12.0000 −0.417533
\(827\) −12.0000 −0.417281 −0.208640 − 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 1.00000 0.0347524
\(829\) −16.0000 −0.555703 −0.277851 − 0.960624i \(-0.589622\pi\)
−0.277851 + 0.960624i \(0.589622\pi\)
\(830\) 6.00000 0.208263
\(831\) 26.0000 0.901930
\(832\) −4.00000 −0.138675
\(833\) 0 0
\(834\) 16.0000 0.554035
\(835\) 6.00000 0.207639
\(836\) 0 0
\(837\) 2.00000 0.0691301
\(838\) 30.0000 1.03633
\(839\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 1.00000 0.0345033
\(841\) 7.00000 0.241379
\(842\) −26.0000 −0.896019
\(843\) −6.00000 −0.206651
\(844\) 20.0000 0.688428
\(845\) −3.00000 −0.103203
\(846\) −6.00000 −0.206284
\(847\) −11.0000 −0.377964
\(848\) −6.00000 −0.206041
\(849\) 14.0000 0.480479
\(850\) 0 0
\(851\) −10.0000 −0.342796
\(852\) 0 0
\(853\) −52.0000 −1.78045 −0.890223 − 0.455525i \(-0.849452\pi\)
−0.890223 + 0.455525i \(0.849452\pi\)
\(854\) 10.0000 0.342193
\(855\) −2.00000 −0.0683986
\(856\) −12.0000 −0.410152
\(857\) −42.0000 −1.43469 −0.717346 − 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) 0 0
\(859\) −40.0000 −1.36478 −0.682391 − 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(860\) 4.00000 0.136399
\(861\) 6.00000 0.204479
\(862\) 24.0000 0.817443
\(863\) 12.0000 0.408485 0.204242 − 0.978920i \(-0.434527\pi\)
0.204242 + 0.978920i \(0.434527\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 12.0000 0.408012
\(866\) 16.0000 0.543702
\(867\) −17.0000 −0.577350
\(868\) 2.00000 0.0678844
\(869\) 0 0
\(870\) 6.00000 0.203419
\(871\) 16.0000 0.542139
\(872\) −2.00000 −0.0677285
\(873\) 8.00000 0.270759
\(874\) −2.00000 −0.0676510
\(875\) −1.00000 −0.0338062
\(876\) 14.0000 0.473016
\(877\) −10.0000 −0.337676 −0.168838 − 0.985644i \(-0.554001\pi\)
−0.168838 + 0.985644i \(0.554001\pi\)
\(878\) 34.0000 1.14744
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) 12.0000 0.404290 0.202145 − 0.979356i \(-0.435209\pi\)
0.202145 + 0.979356i \(0.435209\pi\)
\(882\) −1.00000 −0.0336718
\(883\) 20.0000 0.673054 0.336527 − 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 0 0
\(885\) −12.0000 −0.403376
\(886\) −36.0000 −1.20944
\(887\) −6.00000 −0.201460 −0.100730 − 0.994914i \(-0.532118\pi\)
−0.100730 + 0.994914i \(0.532118\pi\)
\(888\) 10.0000 0.335578
\(889\) 8.00000 0.268311
\(890\) 0 0
\(891\) 0 0
\(892\) −22.0000 −0.736614
\(893\) 12.0000 0.401565
\(894\) 18.0000 0.602010
\(895\) −12.0000 −0.401116
\(896\) −1.00000 −0.0334077
\(897\) −4.00000 −0.133556
\(898\) 18.0000 0.600668
\(899\) 12.0000 0.400222
\(900\) 1.00000 0.0333333
\(901\) 0 0
\(902\) 0 0
\(903\) −4.00000 −0.133112
\(904\) −18.0000 −0.598671
\(905\) −14.0000 −0.465376
\(906\) −20.0000 −0.664455
\(907\) −16.0000 −0.531271 −0.265636 − 0.964073i \(-0.585582\pi\)
−0.265636 + 0.964073i \(0.585582\pi\)
\(908\) −30.0000 −0.995585
\(909\) 0 0
\(910\) −4.00000 −0.132599
\(911\) −24.0000 −0.795155 −0.397578 − 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 2.00000 0.0662266
\(913\) 0 0
\(914\) −38.0000 −1.25693
\(915\) 10.0000 0.330590
\(916\) 14.0000 0.462573
\(917\) 12.0000 0.396275
\(918\) 0 0
\(919\) 8.00000 0.263896 0.131948 − 0.991257i \(-0.457877\pi\)
0.131948 + 0.991257i \(0.457877\pi\)
\(920\) 1.00000 0.0329690
\(921\) 8.00000 0.263609
\(922\) −24.0000 −0.790398
\(923\) 0 0
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) −20.0000 −0.657241
\(927\) −4.00000 −0.131377
\(928\) −6.00000 −0.196960
\(929\) −18.0000 −0.590561 −0.295280 − 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 2.00000 0.0655826
\(931\) 2.00000 0.0655474
\(932\) 6.00000 0.196537
\(933\) 18.0000 0.589294
\(934\) 6.00000 0.196326
\(935\) 0 0
\(936\) 4.00000 0.130744
\(937\) −4.00000 −0.130674 −0.0653372 − 0.997863i \(-0.520812\pi\)
−0.0653372 + 0.997863i \(0.520812\pi\)
\(938\) 4.00000 0.130605
\(939\) −4.00000 −0.130535
\(940\) −6.00000 −0.195698
\(941\) 18.0000 0.586783 0.293392 − 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 6.00000 0.195387
\(944\) 12.0000 0.390567
\(945\) −1.00000 −0.0325300
\(946\) 0 0
\(947\) −36.0000 −1.16984 −0.584921 − 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 8.00000 0.259828
\(949\) −56.0000 −1.81784
\(950\) −2.00000 −0.0648886
\(951\) −18.0000 −0.583690
\(952\) 0 0
\(953\) −54.0000 −1.74923 −0.874616 − 0.484817i \(-0.838886\pi\)
−0.874616 + 0.484817i \(0.838886\pi\)
\(954\) 6.00000 0.194257
\(955\) −24.0000 −0.776622
\(956\) 24.0000 0.776215
\(957\) 0 0
\(958\) −36.0000 −1.16311
\(959\) 6.00000 0.193750
\(960\) −1.00000 −0.0322749
\(961\) −27.0000 −0.870968
\(962\) −40.0000 −1.28965
\(963\) 12.0000 0.386695
\(964\) −16.0000 −0.515325
\(965\) −14.0000 −0.450676
\(966\) −1.00000 −0.0321745
\(967\) −4.00000 −0.128631 −0.0643157 − 0.997930i \(-0.520486\pi\)
−0.0643157 + 0.997930i \(0.520486\pi\)
\(968\) 11.0000 0.353553
\(969\) 0 0
\(970\) 8.00000 0.256865
\(971\) 42.0000 1.34784 0.673922 − 0.738802i \(-0.264608\pi\)
0.673922 + 0.738802i \(0.264608\pi\)
\(972\) 1.00000 0.0320750
\(973\) −16.0000 −0.512936
\(974\) 28.0000 0.897178
\(975\) −4.00000 −0.128103
\(976\) −10.0000 −0.320092
\(977\) −18.0000 −0.575871 −0.287936 − 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) 4.00000 0.127906
\(979\) 0 0
\(980\) −1.00000 −0.0319438
\(981\) 2.00000 0.0638551
\(982\) −36.0000 −1.14881
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) −6.00000 −0.191273
\(985\) 18.0000 0.573528
\(986\) 0 0
\(987\) 6.00000 0.190982
\(988\) −8.00000 −0.254514
\(989\) −4.00000 −0.127193
\(990\) 0 0
\(991\) −4.00000 −0.127064 −0.0635321 − 0.997980i \(-0.520237\pi\)
−0.0635321 + 0.997980i \(0.520237\pi\)
\(992\) −2.00000 −0.0635001
\(993\) 20.0000 0.634681
\(994\) 0 0
\(995\) 4.00000 0.126809
\(996\) 6.00000 0.190117
\(997\) −4.00000 −0.126681 −0.0633406 − 0.997992i \(-0.520175\pi\)
−0.0633406 + 0.997992i \(0.520175\pi\)
\(998\) 4.00000 0.126618
\(999\) −10.0000 −0.316386
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.l.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4830.2.a.l.1.1 ✓ 1 1.1 even 1 trivial