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Properties

Label 6018.2.a.g.1.1
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
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] = [6018,2,Mod(1,6018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6018.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: \(48.0539719364\)
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 \(\chi\) \(=\) 6018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +3.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} +3.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -3.00000 q^{21} -2.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} -5.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +3.00000 q^{28} -6.00000 q^{29} -10.0000 q^{31} +1.00000 q^{32} +2.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} -1.00000 q^{38} +2.00000 q^{39} +3.00000 q^{41} -3.00000 q^{42} -2.00000 q^{43} -2.00000 q^{44} -1.00000 q^{46} +2.00000 q^{47} -1.00000 q^{48} +2.00000 q^{49} -5.00000 q^{50} -1.00000 q^{51} -2.00000 q^{52} -11.0000 q^{53} -1.00000 q^{54} +3.00000 q^{56} +1.00000 q^{57} -6.00000 q^{58} -1.00000 q^{59} +6.00000 q^{61} -10.0000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +2.00000 q^{66} -4.00000 q^{67} +1.00000 q^{68} +1.00000 q^{69} -8.00000 q^{71} +1.00000 q^{72} -7.00000 q^{73} -2.00000 q^{74} +5.00000 q^{75} -1.00000 q^{76} -6.00000 q^{77} +2.00000 q^{78} +16.0000 q^{79} +1.00000 q^{81} +3.00000 q^{82} -7.00000 q^{83} -3.00000 q^{84} -2.00000 q^{86} +6.00000 q^{87} -2.00000 q^{88} +5.00000 q^{89} -6.00000 q^{91} -1.00000 q^{92} +10.0000 q^{93} +2.00000 q^{94} -1.00000 q^{96} -7.00000 q^{97} +2.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)

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
\(5\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) −1.00000 −0.408248
\(7\) 3.00000 1.13389 0.566947 − 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 − 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.00000 −0.554700 −0.277350 − 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 3.00000 0.801784
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) 1.00000 0.235702
\(19\) −1.00000 −0.229416 −0.114708 − 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 0 0
\(21\) −3.00000 −0.654654
\(22\) −2.00000 −0.426401
\(23\) −1.00000 −0.208514 −0.104257 − 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) −1.00000 −0.204124
\(25\) −5.00000 −1.00000
\(26\) −2.00000 −0.392232
\(27\) −1.00000 −0.192450
\(28\) 3.00000 0.566947
\(29\) −6.00000 −1.11417 −0.557086 − 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −10.0000 −1.79605 −0.898027 − 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.00000 0.348155
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −1.00000 −0.162221
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) 3.00000 0.468521 0.234261 − 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) −3.00000 −0.462910
\(43\) −2.00000 −0.304997 −0.152499 − 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) −1.00000 −0.147442
\(47\) 2.00000 0.291730 0.145865 − 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.00000 0.285714
\(50\) −5.00000 −0.707107
\(51\) −1.00000 −0.140028
\(52\) −2.00000 −0.277350
\(53\) −11.0000 −1.51097 −0.755483 − 0.655168i \(-0.772598\pi\)
−0.755483 + 0.655168i \(0.772598\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 3.00000 0.400892
\(57\) 1.00000 0.132453
\(58\) −6.00000 −0.787839
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 − 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) −10.0000 −1.27000
\(63\) 3.00000 0.377964
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 2.00000 0.246183
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 1.00000 0.121268
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 − 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 1.00000 0.117851
\(73\) −7.00000 −0.819288 −0.409644 − 0.912245i \(-0.634347\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −2.00000 −0.232495
\(75\) 5.00000 0.577350
\(76\) −1.00000 −0.114708
\(77\) −6.00000 −0.683763
\(78\) 2.00000 0.226455
\(79\) 16.0000 1.80014 0.900070 − 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 3.00000 0.331295
\(83\) −7.00000 −0.768350 −0.384175 − 0.923260i \(-0.625514\pi\)
−0.384175 + 0.923260i \(0.625514\pi\)
\(84\) −3.00000 −0.327327
\(85\) 0 0
\(86\) −2.00000 −0.215666
\(87\) 6.00000 0.643268
\(88\) −2.00000 −0.213201
\(89\) 5.00000 0.529999 0.264999 − 0.964249i \(-0.414628\pi\)
0.264999 + 0.964249i \(0.414628\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) −1.00000 −0.104257
\(93\) 10.0000 1.03695
\(94\) 2.00000 0.206284
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −7.00000 −0.710742 −0.355371 − 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 2.00000 0.202031
\(99\) −2.00000 −0.201008
\(100\) −5.00000 −0.500000
\(101\) 4.00000 0.398015 0.199007 − 0.979998i \(-0.436228\pi\)
0.199007 + 0.979998i \(0.436228\pi\)
\(102\) −1.00000 −0.0990148
\(103\) −15.0000 −1.47799 −0.738997 − 0.673709i \(-0.764700\pi\)
−0.738997 + 0.673709i \(0.764700\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −11.0000 −1.06841
\(107\) −1.00000 −0.0966736 −0.0483368 − 0.998831i \(-0.515392\pi\)
−0.0483368 + 0.998831i \(0.515392\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 3.00000 0.283473
\(113\) 20.0000 1.88144 0.940721 − 0.339182i \(-0.110150\pi\)
0.940721 + 0.339182i \(0.110150\pi\)
\(114\) 1.00000 0.0936586
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) −2.00000 −0.184900
\(118\) −1.00000 −0.0920575
\(119\) 3.00000 0.275010
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 6.00000 0.543214
\(123\) −3.00000 −0.270501
\(124\) −10.0000 −0.898027
\(125\) 0 0
\(126\) 3.00000 0.267261
\(127\) 18.0000 1.59724 0.798621 − 0.601834i \(-0.205563\pi\)
0.798621 + 0.601834i \(0.205563\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.00000 0.176090
\(130\) 0 0
\(131\) 8.00000 0.698963 0.349482 − 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 2.00000 0.174078
\(133\) −3.00000 −0.260133
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 1.00000 0.0857493
\(137\) 10.0000 0.854358 0.427179 − 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 1.00000 0.0851257
\(139\) −14.0000 −1.18746 −0.593732 − 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) −8.00000 −0.671345
\(143\) 4.00000 0.334497
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −7.00000 −0.579324
\(147\) −2.00000 −0.164957
\(148\) −2.00000 −0.164399
\(149\) −8.00000 −0.655386 −0.327693 − 0.944784i \(-0.606271\pi\)
−0.327693 + 0.944784i \(0.606271\pi\)
\(150\) 5.00000 0.408248
\(151\) −5.00000 −0.406894 −0.203447 − 0.979086i \(-0.565214\pi\)
−0.203447 + 0.979086i \(0.565214\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 1.00000 0.0808452
\(154\) −6.00000 −0.483494
\(155\) 0 0
\(156\) 2.00000 0.160128
\(157\) 11.0000 0.877896 0.438948 − 0.898513i \(-0.355351\pi\)
0.438948 + 0.898513i \(0.355351\pi\)
\(158\) 16.0000 1.27289
\(159\) 11.0000 0.872357
\(160\) 0 0
\(161\) −3.00000 −0.236433
\(162\) 1.00000 0.0785674
\(163\) −10.0000 −0.783260 −0.391630 − 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) 3.00000 0.234261
\(165\) 0 0
\(166\) −7.00000 −0.543305
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) −3.00000 −0.231455
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −1.00000 −0.0764719
\(172\) −2.00000 −0.152499
\(173\) −2.00000 −0.152057 −0.0760286 − 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) 6.00000 0.454859
\(175\) −15.0000 −1.13389
\(176\) −2.00000 −0.150756
\(177\) 1.00000 0.0751646
\(178\) 5.00000 0.374766
\(179\) 15.0000 1.12115 0.560576 − 0.828103i \(-0.310580\pi\)
0.560576 + 0.828103i \(0.310580\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 − 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −6.00000 −0.444750
\(183\) −6.00000 −0.443533
\(184\) −1.00000 −0.0737210
\(185\) 0 0
\(186\) 10.0000 0.733236
\(187\) −2.00000 −0.146254
\(188\) 2.00000 0.145865
\(189\) −3.00000 −0.218218
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 − 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 22.0000 1.58359 0.791797 − 0.610784i \(-0.209146\pi\)
0.791797 + 0.610784i \(0.209146\pi\)
\(194\) −7.00000 −0.502571
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) −22.0000 −1.56744 −0.783718 − 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) −2.00000 −0.142134
\(199\) 15.0000 1.06332 0.531661 − 0.846957i \(-0.321568\pi\)
0.531661 + 0.846957i \(0.321568\pi\)
\(200\) −5.00000 −0.353553
\(201\) 4.00000 0.282138
\(202\) 4.00000 0.281439
\(203\) −18.0000 −1.26335
\(204\) −1.00000 −0.0700140
\(205\) 0 0
\(206\) −15.0000 −1.04510
\(207\) −1.00000 −0.0695048
\(208\) −2.00000 −0.138675
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 − 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −11.0000 −0.755483
\(213\) 8.00000 0.548151
\(214\) −1.00000 −0.0683586
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −30.0000 −2.03653
\(218\) 0 0
\(219\) 7.00000 0.473016
\(220\) 0 0
\(221\) −2.00000 −0.134535
\(222\) 2.00000 0.134231
\(223\) −14.0000 −0.937509 −0.468755 − 0.883328i \(-0.655297\pi\)
−0.468755 + 0.883328i \(0.655297\pi\)
\(224\) 3.00000 0.200446
\(225\) −5.00000 −0.333333
\(226\) 20.0000 1.33038
\(227\) 18.0000 1.19470 0.597351 − 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 1.00000 0.0662266
\(229\) −27.0000 −1.78421 −0.892105 − 0.451828i \(-0.850772\pi\)
−0.892105 + 0.451828i \(0.850772\pi\)
\(230\) 0 0
\(231\) 6.00000 0.394771
\(232\) −6.00000 −0.393919
\(233\) −18.0000 −1.17922 −0.589610 − 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) −1.00000 −0.0650945
\(237\) −16.0000 −1.03931
\(238\) 3.00000 0.194461
\(239\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 − 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −7.00000 −0.449977
\(243\) −1.00000 −0.0641500
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) −3.00000 −0.191273
\(247\) 2.00000 0.127257
\(248\) −10.0000 −0.635001
\(249\) 7.00000 0.443607
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 − 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 3.00000 0.188982
\(253\) 2.00000 0.125739
\(254\) 18.0000 1.12942
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −8.00000 −0.499026 −0.249513 − 0.968371i \(-0.580271\pi\)
−0.249513 + 0.968371i \(0.580271\pi\)
\(258\) 2.00000 0.124515
\(259\) −6.00000 −0.372822
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 8.00000 0.494242
\(263\) −11.0000 −0.678289 −0.339145 − 0.940734i \(-0.610138\pi\)
−0.339145 + 0.940734i \(0.610138\pi\)
\(264\) 2.00000 0.123091
\(265\) 0 0
\(266\) −3.00000 −0.183942
\(267\) −5.00000 −0.305995
\(268\) −4.00000 −0.244339
\(269\) 3.00000 0.182913 0.0914566 − 0.995809i \(-0.470848\pi\)
0.0914566 + 0.995809i \(0.470848\pi\)
\(270\) 0 0
\(271\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 1.00000 0.0606339
\(273\) 6.00000 0.363137
\(274\) 10.0000 0.604122
\(275\) 10.0000 0.603023
\(276\) 1.00000 0.0601929
\(277\) 17.0000 1.02143 0.510716 − 0.859750i \(-0.329381\pi\)
0.510716 + 0.859750i \(0.329381\pi\)
\(278\) −14.0000 −0.839664
\(279\) −10.0000 −0.598684
\(280\) 0 0
\(281\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) −2.00000 −0.119098
\(283\) 3.00000 0.178331 0.0891657 − 0.996017i \(-0.471580\pi\)
0.0891657 + 0.996017i \(0.471580\pi\)
\(284\) −8.00000 −0.474713
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 9.00000 0.531253
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 7.00000 0.410347
\(292\) −7.00000 −0.409644
\(293\) 30.0000 1.75262 0.876309 − 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) −2.00000 −0.116642
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 2.00000 0.116052
\(298\) −8.00000 −0.463428
\(299\) 2.00000 0.115663
\(300\) 5.00000 0.288675
\(301\) −6.00000 −0.345834
\(302\) −5.00000 −0.287718
\(303\) −4.00000 −0.229794
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) 1.00000 0.0571662
\(307\) 1.00000 0.0570730 0.0285365 − 0.999593i \(-0.490915\pi\)
0.0285365 + 0.999593i \(0.490915\pi\)
\(308\) −6.00000 −0.341882
\(309\) 15.0000 0.853320
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 − 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 2.00000 0.113228
\(313\) −26.0000 −1.46961 −0.734803 − 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 11.0000 0.620766
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) −4.00000 −0.224662 −0.112331 − 0.993671i \(-0.535832\pi\)
−0.112331 + 0.993671i \(0.535832\pi\)
\(318\) 11.0000 0.616849
\(319\) 12.0000 0.671871
\(320\) 0 0
\(321\) 1.00000 0.0558146
\(322\) −3.00000 −0.167183
\(323\) −1.00000 −0.0556415
\(324\) 1.00000 0.0555556
\(325\) 10.0000 0.554700
\(326\) −10.0000 −0.553849
\(327\) 0 0
\(328\) 3.00000 0.165647
\(329\) 6.00000 0.330791
\(330\) 0 0
\(331\) −25.0000 −1.37412 −0.687062 − 0.726599i \(-0.741100\pi\)
−0.687062 + 0.726599i \(0.741100\pi\)
\(332\) −7.00000 −0.384175
\(333\) −2.00000 −0.109599
\(334\) 0 0
\(335\) 0 0
\(336\) −3.00000 −0.163663
\(337\) −5.00000 −0.272367 −0.136184 − 0.990684i \(-0.543484\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) −9.00000 −0.489535
\(339\) −20.0000 −1.08625
\(340\) 0 0
\(341\) 20.0000 1.08306
\(342\) −1.00000 −0.0540738
\(343\) −15.0000 −0.809924
\(344\) −2.00000 −0.107833
\(345\) 0 0
\(346\) −2.00000 −0.107521
\(347\) 14.0000 0.751559 0.375780 − 0.926709i \(-0.377375\pi\)
0.375780 + 0.926709i \(0.377375\pi\)
\(348\) 6.00000 0.321634
\(349\) 15.0000 0.802932 0.401466 − 0.915874i \(-0.368501\pi\)
0.401466 + 0.915874i \(0.368501\pi\)
\(350\) −15.0000 −0.801784
\(351\) 2.00000 0.106752
\(352\) −2.00000 −0.106600
\(353\) 19.0000 1.01127 0.505634 − 0.862748i \(-0.331259\pi\)
0.505634 + 0.862748i \(0.331259\pi\)
\(354\) 1.00000 0.0531494
\(355\) 0 0
\(356\) 5.00000 0.264999
\(357\) −3.00000 −0.158777
\(358\) 15.0000 0.792775
\(359\) −11.0000 −0.580558 −0.290279 − 0.956942i \(-0.593748\pi\)
−0.290279 + 0.956942i \(0.593748\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) −10.0000 −0.525588
\(363\) 7.00000 0.367405
\(364\) −6.00000 −0.314485
\(365\) 0 0
\(366\) −6.00000 −0.313625
\(367\) 16.0000 0.835193 0.417597 − 0.908633i \(-0.362873\pi\)
0.417597 + 0.908633i \(0.362873\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 3.00000 0.156174
\(370\) 0 0
\(371\) −33.0000 −1.71327
\(372\) 10.0000 0.518476
\(373\) −14.0000 −0.724893 −0.362446 − 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) −2.00000 −0.103418
\(375\) 0 0
\(376\) 2.00000 0.103142
\(377\) 12.0000 0.618031
\(378\) −3.00000 −0.154303
\(379\) 10.0000 0.513665 0.256833 − 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(380\) 0 0
\(381\) −18.0000 −0.922168
\(382\) 12.0000 0.613973
\(383\) 7.00000 0.357683 0.178842 − 0.983878i \(-0.442765\pi\)
0.178842 + 0.983878i \(0.442765\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 22.0000 1.11977
\(387\) −2.00000 −0.101666
\(388\) −7.00000 −0.355371
\(389\) −26.0000 −1.31825 −0.659126 − 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) 0 0
\(391\) −1.00000 −0.0505722
\(392\) 2.00000 0.101015
\(393\) −8.00000 −0.403547
\(394\) −22.0000 −1.10834
\(395\) 0 0
\(396\) −2.00000 −0.100504
\(397\) −12.0000 −0.602263 −0.301131 − 0.953583i \(-0.597364\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(398\) 15.0000 0.751882
\(399\) 3.00000 0.150188
\(400\) −5.00000 −0.250000
\(401\) 20.0000 0.998752 0.499376 − 0.866385i \(-0.333563\pi\)
0.499376 + 0.866385i \(0.333563\pi\)
\(402\) 4.00000 0.199502
\(403\) 20.0000 0.996271
\(404\) 4.00000 0.199007
\(405\) 0 0
\(406\) −18.0000 −0.893325
\(407\) 4.00000 0.198273
\(408\) −1.00000 −0.0495074
\(409\) −10.0000 −0.494468 −0.247234 − 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) 0 0
\(411\) −10.0000 −0.493264
\(412\) −15.0000 −0.738997
\(413\) −3.00000 −0.147620
\(414\) −1.00000 −0.0491473
\(415\) 0 0
\(416\) −2.00000 −0.0980581
\(417\) 14.0000 0.685583
\(418\) 2.00000 0.0978232
\(419\) 20.0000 0.977064 0.488532 − 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) 29.0000 1.41337 0.706687 − 0.707527i \(-0.250189\pi\)
0.706687 + 0.707527i \(0.250189\pi\)
\(422\) −16.0000 −0.778868
\(423\) 2.00000 0.0972433
\(424\) −11.0000 −0.534207
\(425\) −5.00000 −0.242536
\(426\) 8.00000 0.387601
\(427\) 18.0000 0.871081
\(428\) −1.00000 −0.0483368
\(429\) −4.00000 −0.193122
\(430\) 0 0
\(431\) −3.00000 −0.144505 −0.0722525 − 0.997386i \(-0.523019\pi\)
−0.0722525 + 0.997386i \(0.523019\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −39.0000 −1.87422 −0.937110 − 0.349034i \(-0.886510\pi\)
−0.937110 + 0.349034i \(0.886510\pi\)
\(434\) −30.0000 −1.44005
\(435\) 0 0
\(436\) 0 0
\(437\) 1.00000 0.0478365
\(438\) 7.00000 0.334473
\(439\) −4.00000 −0.190910 −0.0954548 − 0.995434i \(-0.530431\pi\)
−0.0954548 + 0.995434i \(0.530431\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) −2.00000 −0.0951303
\(443\) −1.00000 −0.0475114 −0.0237557 − 0.999718i \(-0.507562\pi\)
−0.0237557 + 0.999718i \(0.507562\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) −14.0000 −0.662919
\(447\) 8.00000 0.378387
\(448\) 3.00000 0.141737
\(449\) 9.00000 0.424736 0.212368 − 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) −5.00000 −0.235702
\(451\) −6.00000 −0.282529
\(452\) 20.0000 0.940721
\(453\) 5.00000 0.234920
\(454\) 18.0000 0.844782
\(455\) 0 0
\(456\) 1.00000 0.0468293
\(457\) 8.00000 0.374224 0.187112 − 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) −27.0000 −1.26163
\(459\) −1.00000 −0.0466760
\(460\) 0 0
\(461\) −13.0000 −0.605470 −0.302735 − 0.953075i \(-0.597900\pi\)
−0.302735 + 0.953075i \(0.597900\pi\)
\(462\) 6.00000 0.279145
\(463\) −20.0000 −0.929479 −0.464739 − 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −18.0000 −0.833834
\(467\) −12.0000 −0.555294 −0.277647 − 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −2.00000 −0.0924500
\(469\) −12.0000 −0.554109
\(470\) 0 0
\(471\) −11.0000 −0.506853
\(472\) −1.00000 −0.0460287
\(473\) 4.00000 0.183920
\(474\) −16.0000 −0.734904
\(475\) 5.00000 0.229416
\(476\) 3.00000 0.137505
\(477\) −11.0000 −0.503655
\(478\) 0 0
\(479\) 18.0000 0.822441 0.411220 − 0.911536i \(-0.365103\pi\)
0.411220 + 0.911536i \(0.365103\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) −10.0000 −0.455488
\(483\) 3.00000 0.136505
\(484\) −7.00000 −0.318182
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 37.0000 1.67663 0.838315 − 0.545186i \(-0.183541\pi\)
0.838315 + 0.545186i \(0.183541\pi\)
\(488\) 6.00000 0.271607
\(489\) 10.0000 0.452216
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 − 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) −3.00000 −0.135250
\(493\) −6.00000 −0.270226
\(494\) 2.00000 0.0899843
\(495\) 0 0
\(496\) −10.0000 −0.449013
\(497\) −24.0000 −1.07655
\(498\) 7.00000 0.313678
\(499\) −12.0000 −0.537194 −0.268597 − 0.963253i \(-0.586560\pi\)
−0.268597 + 0.963253i \(0.586560\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −12.0000 −0.535586
\(503\) 9.00000 0.401290 0.200645 − 0.979664i \(-0.435696\pi\)
0.200645 + 0.979664i \(0.435696\pi\)
\(504\) 3.00000 0.133631
\(505\) 0 0
\(506\) 2.00000 0.0889108
\(507\) 9.00000 0.399704
\(508\) 18.0000 0.798621
\(509\) −30.0000 −1.32973 −0.664863 − 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 0 0
\(511\) −21.0000 −0.928985
\(512\) 1.00000 0.0441942
\(513\) 1.00000 0.0441511
\(514\) −8.00000 −0.352865
\(515\) 0 0
\(516\) 2.00000 0.0880451
\(517\) −4.00000 −0.175920
\(518\) −6.00000 −0.263625
\(519\) 2.00000 0.0877903
\(520\) 0 0
\(521\) −25.0000 −1.09527 −0.547635 − 0.836717i \(-0.684472\pi\)
−0.547635 + 0.836717i \(0.684472\pi\)
\(522\) −6.00000 −0.262613
\(523\) 20.0000 0.874539 0.437269 − 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 8.00000 0.349482
\(525\) 15.0000 0.654654
\(526\) −11.0000 −0.479623
\(527\) −10.0000 −0.435607
\(528\) 2.00000 0.0870388
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) −1.00000 −0.0433963
\(532\) −3.00000 −0.130066
\(533\) −6.00000 −0.259889
\(534\) −5.00000 −0.216371
\(535\) 0 0
\(536\) −4.00000 −0.172774
\(537\) −15.0000 −0.647298
\(538\) 3.00000 0.129339
\(539\) −4.00000 −0.172292
\(540\) 0 0
\(541\) 16.0000 0.687894 0.343947 − 0.938989i \(-0.388236\pi\)
0.343947 + 0.938989i \(0.388236\pi\)
\(542\) 0 0
\(543\) 10.0000 0.429141
\(544\) 1.00000 0.0428746
\(545\) 0 0
\(546\) 6.00000 0.256776
\(547\) −42.0000 −1.79579 −0.897895 − 0.440209i \(-0.854904\pi\)
−0.897895 + 0.440209i \(0.854904\pi\)
\(548\) 10.0000 0.427179
\(549\) 6.00000 0.256074
\(550\) 10.0000 0.426401
\(551\) 6.00000 0.255609
\(552\) 1.00000 0.0425628
\(553\) 48.0000 2.04117
\(554\) 17.0000 0.722261
\(555\) 0 0
\(556\) −14.0000 −0.593732
\(557\) −22.0000 −0.932170 −0.466085 − 0.884740i \(-0.654336\pi\)
−0.466085 + 0.884740i \(0.654336\pi\)
\(558\) −10.0000 −0.423334
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 2.00000 0.0844401
\(562\) 0 0
\(563\) 5.00000 0.210725 0.105362 − 0.994434i \(-0.466400\pi\)
0.105362 + 0.994434i \(0.466400\pi\)
\(564\) −2.00000 −0.0842152
\(565\) 0 0
\(566\) 3.00000 0.126099
\(567\) 3.00000 0.125988
\(568\) −8.00000 −0.335673
\(569\) −31.0000 −1.29959 −0.649794 − 0.760111i \(-0.725145\pi\)
−0.649794 + 0.760111i \(0.725145\pi\)
\(570\) 0 0
\(571\) −29.0000 −1.21361 −0.606806 − 0.794850i \(-0.707550\pi\)
−0.606806 + 0.794850i \(0.707550\pi\)
\(572\) 4.00000 0.167248
\(573\) −12.0000 −0.501307
\(574\) 9.00000 0.375653
\(575\) 5.00000 0.208514
\(576\) 1.00000 0.0416667
\(577\) 38.0000 1.58196 0.790980 − 0.611842i \(-0.209571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) 1.00000 0.0415945
\(579\) −22.0000 −0.914289
\(580\) 0 0
\(581\) −21.0000 −0.871227
\(582\) 7.00000 0.290159
\(583\) 22.0000 0.911147
\(584\) −7.00000 −0.289662
\(585\) 0 0
\(586\) 30.0000 1.23929
\(587\) 7.00000 0.288921 0.144460 − 0.989511i \(-0.453855\pi\)
0.144460 + 0.989511i \(0.453855\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 10.0000 0.412043
\(590\) 0 0
\(591\) 22.0000 0.904959
\(592\) −2.00000 −0.0821995
\(593\) 16.0000 0.657041 0.328521 − 0.944497i \(-0.393450\pi\)
0.328521 + 0.944497i \(0.393450\pi\)
\(594\) 2.00000 0.0820610
\(595\) 0 0
\(596\) −8.00000 −0.327693
\(597\) −15.0000 −0.613909
\(598\) 2.00000 0.0817861
\(599\) 39.0000 1.59350 0.796748 − 0.604311i \(-0.206552\pi\)
0.796748 + 0.604311i \(0.206552\pi\)
\(600\) 5.00000 0.204124
\(601\) 5.00000 0.203954 0.101977 − 0.994787i \(-0.467483\pi\)
0.101977 + 0.994787i \(0.467483\pi\)
\(602\) −6.00000 −0.244542
\(603\) −4.00000 −0.162893
\(604\) −5.00000 −0.203447
\(605\) 0 0
\(606\) −4.00000 −0.162489
\(607\) 33.0000 1.33943 0.669714 − 0.742619i \(-0.266417\pi\)
0.669714 + 0.742619i \(0.266417\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 18.0000 0.729397
\(610\) 0 0
\(611\) −4.00000 −0.161823
\(612\) 1.00000 0.0404226
\(613\) 29.0000 1.17130 0.585649 − 0.810564i \(-0.300840\pi\)
0.585649 + 0.810564i \(0.300840\pi\)
\(614\) 1.00000 0.0403567
\(615\) 0 0
\(616\) −6.00000 −0.241747
\(617\) −5.00000 −0.201292 −0.100646 − 0.994922i \(-0.532091\pi\)
−0.100646 + 0.994922i \(0.532091\pi\)
\(618\) 15.0000 0.603388
\(619\) −26.0000 −1.04503 −0.522514 − 0.852631i \(-0.675006\pi\)
−0.522514 + 0.852631i \(0.675006\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 8.00000 0.320771
\(623\) 15.0000 0.600962
\(624\) 2.00000 0.0800641
\(625\) 25.0000 1.00000
\(626\) −26.0000 −1.03917
\(627\) −2.00000 −0.0798723
\(628\) 11.0000 0.438948
\(629\) −2.00000 −0.0797452
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 − 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 16.0000 0.636446
\(633\) 16.0000 0.635943
\(634\) −4.00000 −0.158860
\(635\) 0 0
\(636\) 11.0000 0.436178
\(637\) −4.00000 −0.158486
\(638\) 12.0000 0.475085
\(639\) −8.00000 −0.316475
\(640\) 0 0
\(641\) −13.0000 −0.513469 −0.256735 − 0.966482i \(-0.582647\pi\)
−0.256735 + 0.966482i \(0.582647\pi\)
\(642\) 1.00000 0.0394669
\(643\) −20.0000 −0.788723 −0.394362 − 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) −3.00000 −0.118217
\(645\) 0 0
\(646\) −1.00000 −0.0393445
\(647\) 37.0000 1.45462 0.727310 − 0.686309i \(-0.240770\pi\)
0.727310 + 0.686309i \(0.240770\pi\)
\(648\) 1.00000 0.0392837
\(649\) 2.00000 0.0785069
\(650\) 10.0000 0.392232
\(651\) 30.0000 1.17579
\(652\) −10.0000 −0.391630
\(653\) 6.00000 0.234798 0.117399 − 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.00000 0.117130
\(657\) −7.00000 −0.273096
\(658\) 6.00000 0.233904
\(659\) 45.0000 1.75295 0.876476 − 0.481446i \(-0.159888\pi\)
0.876476 + 0.481446i \(0.159888\pi\)
\(660\) 0 0
\(661\) −32.0000 −1.24466 −0.622328 − 0.782757i \(-0.713813\pi\)
−0.622328 + 0.782757i \(0.713813\pi\)
\(662\) −25.0000 −0.971653
\(663\) 2.00000 0.0776736
\(664\) −7.00000 −0.271653
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 6.00000 0.232321
\(668\) 0 0
\(669\) 14.0000 0.541271
\(670\) 0 0
\(671\) −12.0000 −0.463255
\(672\) −3.00000 −0.115728
\(673\) −19.0000 −0.732396 −0.366198 − 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) −5.00000 −0.192593
\(675\) 5.00000 0.192450
\(676\) −9.00000 −0.346154
\(677\) 18.0000 0.691796 0.345898 − 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −20.0000 −0.768095
\(679\) −21.0000 −0.805906
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) 20.0000 0.765840
\(683\) 14.0000 0.535695 0.267848 − 0.963461i \(-0.413688\pi\)
0.267848 + 0.963461i \(0.413688\pi\)
\(684\) −1.00000 −0.0382360
\(685\) 0 0
\(686\) −15.0000 −0.572703
\(687\) 27.0000 1.03011
\(688\) −2.00000 −0.0762493
\(689\) 22.0000 0.838133
\(690\) 0 0
\(691\) 5.00000 0.190209 0.0951045 − 0.995467i \(-0.469681\pi\)
0.0951045 + 0.995467i \(0.469681\pi\)
\(692\) −2.00000 −0.0760286
\(693\) −6.00000 −0.227921
\(694\) 14.0000 0.531433
\(695\) 0 0
\(696\) 6.00000 0.227429
\(697\) 3.00000 0.113633
\(698\) 15.0000 0.567758
\(699\) 18.0000 0.680823
\(700\) −15.0000 −0.566947
\(701\) −24.0000 −0.906467 −0.453234 − 0.891392i \(-0.649730\pi\)
−0.453234 + 0.891392i \(0.649730\pi\)
\(702\) 2.00000 0.0754851
\(703\) 2.00000 0.0754314
\(704\) −2.00000 −0.0753778
\(705\) 0 0
\(706\) 19.0000 0.715074
\(707\) 12.0000 0.451306
\(708\) 1.00000 0.0375823
\(709\) −26.0000 −0.976450 −0.488225 − 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 0 0
\(711\) 16.0000 0.600047
\(712\) 5.00000 0.187383
\(713\) 10.0000 0.374503
\(714\) −3.00000 −0.112272
\(715\) 0 0
\(716\) 15.0000 0.560576
\(717\) 0 0
\(718\) −11.0000 −0.410516
\(719\) −16.0000 −0.596699 −0.298350 − 0.954457i \(-0.596436\pi\)
−0.298350 + 0.954457i \(0.596436\pi\)
\(720\) 0 0
\(721\) −45.0000 −1.67589
\(722\) −18.0000 −0.669891
\(723\) 10.0000 0.371904
\(724\) −10.0000 −0.371647
\(725\) 30.0000 1.11417
\(726\) 7.00000 0.259794
\(727\) −26.0000 −0.964287 −0.482143 − 0.876092i \(-0.660142\pi\)
−0.482143 + 0.876092i \(0.660142\pi\)
\(728\) −6.00000 −0.222375
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −2.00000 −0.0739727
\(732\) −6.00000 −0.221766
\(733\) 54.0000 1.99454 0.997268 − 0.0738717i \(-0.0235355\pi\)
0.997268 + 0.0738717i \(0.0235355\pi\)
\(734\) 16.0000 0.590571
\(735\) 0 0
\(736\) −1.00000 −0.0368605
\(737\) 8.00000 0.294684
\(738\) 3.00000 0.110432
\(739\) 44.0000 1.61857 0.809283 − 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) −33.0000 −1.21147
\(743\) 4.00000 0.146746 0.0733729 − 0.997305i \(-0.476624\pi\)
0.0733729 + 0.997305i \(0.476624\pi\)
\(744\) 10.0000 0.366618
\(745\) 0 0
\(746\) −14.0000 −0.512576
\(747\) −7.00000 −0.256117
\(748\) −2.00000 −0.0731272
\(749\) −3.00000 −0.109618
\(750\) 0 0
\(751\) −4.00000 −0.145962 −0.0729810 − 0.997333i \(-0.523251\pi\)
−0.0729810 + 0.997333i \(0.523251\pi\)
\(752\) 2.00000 0.0729325
\(753\) 12.0000 0.437304
\(754\) 12.0000 0.437014
\(755\) 0 0
\(756\) −3.00000 −0.109109
\(757\) 2.00000 0.0726912 0.0363456 − 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 10.0000 0.363216
\(759\) −2.00000 −0.0725954
\(760\) 0 0
\(761\) 18.0000 0.652499 0.326250 − 0.945284i \(-0.394215\pi\)
0.326250 + 0.945284i \(0.394215\pi\)
\(762\) −18.0000 −0.652071
\(763\) 0 0
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) 7.00000 0.252920
\(767\) 2.00000 0.0722158
\(768\) −1.00000 −0.0360844
\(769\) 32.0000 1.15395 0.576975 − 0.816762i \(-0.304233\pi\)
0.576975 + 0.816762i \(0.304233\pi\)
\(770\) 0 0
\(771\) 8.00000 0.288113
\(772\) 22.0000 0.791797
\(773\) −44.0000 −1.58257 −0.791285 − 0.611448i \(-0.790588\pi\)
−0.791285 + 0.611448i \(0.790588\pi\)
\(774\) −2.00000 −0.0718885
\(775\) 50.0000 1.79605
\(776\) −7.00000 −0.251285
\(777\) 6.00000 0.215249
\(778\) −26.0000 −0.932145
\(779\) −3.00000 −0.107486
\(780\) 0 0
\(781\) 16.0000 0.572525
\(782\) −1.00000 −0.0357599
\(783\) 6.00000 0.214423
\(784\) 2.00000 0.0714286
\(785\) 0 0
\(786\) −8.00000 −0.285351
\(787\) 40.0000 1.42585 0.712923 − 0.701242i \(-0.247371\pi\)
0.712923 + 0.701242i \(0.247371\pi\)
\(788\) −22.0000 −0.783718
\(789\) 11.0000 0.391610
\(790\) 0 0
\(791\) 60.0000 2.13335
\(792\) −2.00000 −0.0710669
\(793\) −12.0000 −0.426132
\(794\) −12.0000 −0.425864
\(795\) 0 0
\(796\) 15.0000 0.531661
\(797\) −6.00000 −0.212531 −0.106265 − 0.994338i \(-0.533889\pi\)
−0.106265 + 0.994338i \(0.533889\pi\)
\(798\) 3.00000 0.106199
\(799\) 2.00000 0.0707549
\(800\) −5.00000 −0.176777
\(801\) 5.00000 0.176666
\(802\) 20.0000 0.706225
\(803\) 14.0000 0.494049
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) 20.0000 0.704470
\(807\) −3.00000 −0.105605
\(808\) 4.00000 0.140720
\(809\) 28.0000 0.984428 0.492214 − 0.870474i \(-0.336188\pi\)
0.492214 + 0.870474i \(0.336188\pi\)
\(810\) 0 0
\(811\) 43.0000 1.50993 0.754967 − 0.655763i \(-0.227653\pi\)
0.754967 + 0.655763i \(0.227653\pi\)
\(812\) −18.0000 −0.631676
\(813\) 0 0
\(814\) 4.00000 0.140200
\(815\) 0 0
\(816\) −1.00000 −0.0350070
\(817\) 2.00000 0.0699711
\(818\) −10.0000 −0.349642
\(819\) −6.00000 −0.209657
\(820\) 0 0
\(821\) −11.0000 −0.383903 −0.191951 − 0.981404i \(-0.561482\pi\)
−0.191951 + 0.981404i \(0.561482\pi\)
\(822\) −10.0000 −0.348790
\(823\) 26.0000 0.906303 0.453152 − 0.891434i \(-0.350300\pi\)
0.453152 + 0.891434i \(0.350300\pi\)
\(824\) −15.0000 −0.522550
\(825\) −10.0000 −0.348155
\(826\) −3.00000 −0.104383
\(827\) −23.0000 −0.799788 −0.399894 − 0.916561i \(-0.630953\pi\)
−0.399894 + 0.916561i \(0.630953\pi\)
\(828\) −1.00000 −0.0347524
\(829\) −24.0000 −0.833554 −0.416777 − 0.909009i \(-0.636840\pi\)
−0.416777 + 0.909009i \(0.636840\pi\)
\(830\) 0 0
\(831\) −17.0000 −0.589723
\(832\) −2.00000 −0.0693375
\(833\) 2.00000 0.0692959
\(834\) 14.0000 0.484780
\(835\) 0 0
\(836\) 2.00000 0.0691714
\(837\) 10.0000 0.345651
\(838\) 20.0000 0.690889
\(839\) 28.0000 0.966667 0.483334 − 0.875436i \(-0.339426\pi\)
0.483334 + 0.875436i \(0.339426\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 29.0000 0.999406
\(843\) 0 0
\(844\) −16.0000 −0.550743
\(845\) 0 0
\(846\) 2.00000 0.0687614
\(847\) −21.0000 −0.721569
\(848\) −11.0000 −0.377742
\(849\) −3.00000 −0.102960
\(850\) −5.00000 −0.171499
\(851\) 2.00000 0.0685591
\(852\) 8.00000 0.274075
\(853\) 38.0000 1.30110 0.650548 − 0.759465i \(-0.274539\pi\)
0.650548 + 0.759465i \(0.274539\pi\)
\(854\) 18.0000 0.615947
\(855\) 0 0
\(856\) −1.00000 −0.0341793
\(857\) 20.0000 0.683187 0.341593 − 0.939848i \(-0.389033\pi\)
0.341593 + 0.939848i \(0.389033\pi\)
\(858\) −4.00000 −0.136558
\(859\) 20.0000 0.682391 0.341196 − 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 0 0
\(861\) −9.00000 −0.306719
\(862\) −3.00000 −0.102180
\(863\) 18.0000 0.612727 0.306364 − 0.951915i \(-0.400888\pi\)
0.306364 + 0.951915i \(0.400888\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) −39.0000 −1.32527
\(867\) −1.00000 −0.0339618
\(868\) −30.0000 −1.01827
\(869\) −32.0000 −1.08553
\(870\) 0 0
\(871\) 8.00000 0.271070
\(872\) 0 0
\(873\) −7.00000 −0.236914
\(874\) 1.00000 0.0338255
\(875\) 0 0
\(876\) 7.00000 0.236508
\(877\) 13.0000 0.438979 0.219489 − 0.975615i \(-0.429561\pi\)
0.219489 + 0.975615i \(0.429561\pi\)
\(878\) −4.00000 −0.134993
\(879\) −30.0000 −1.01187
\(880\) 0 0
\(881\) −28.0000 −0.943344 −0.471672 − 0.881774i \(-0.656349\pi\)
−0.471672 + 0.881774i \(0.656349\pi\)
\(882\) 2.00000 0.0673435
\(883\) −19.0000 −0.639401 −0.319700 − 0.947519i \(-0.603582\pi\)
−0.319700 + 0.947519i \(0.603582\pi\)
\(884\) −2.00000 −0.0672673
\(885\) 0 0
\(886\) −1.00000 −0.0335957
\(887\) 45.0000 1.51095 0.755476 − 0.655176i \(-0.227406\pi\)
0.755476 + 0.655176i \(0.227406\pi\)
\(888\) 2.00000 0.0671156
\(889\) 54.0000 1.81110
\(890\) 0 0
\(891\) −2.00000 −0.0670025
\(892\) −14.0000 −0.468755
\(893\) −2.00000 −0.0669274
\(894\) 8.00000 0.267560
\(895\) 0 0
\(896\) 3.00000 0.100223
\(897\) −2.00000 −0.0667781
\(898\) 9.00000 0.300334
\(899\) 60.0000 2.00111
\(900\) −5.00000 −0.166667
\(901\) −11.0000 −0.366463
\(902\) −6.00000 −0.199778
\(903\) 6.00000 0.199667
\(904\) 20.0000 0.665190
\(905\) 0 0
\(906\) 5.00000 0.166114
\(907\) −28.0000 −0.929725 −0.464862 − 0.885383i \(-0.653896\pi\)
−0.464862 + 0.885383i \(0.653896\pi\)
\(908\) 18.0000 0.597351
\(909\) 4.00000 0.132672
\(910\) 0 0
\(911\) 6.00000 0.198789 0.0993944 − 0.995048i \(-0.468309\pi\)
0.0993944 + 0.995048i \(0.468309\pi\)
\(912\) 1.00000 0.0331133
\(913\) 14.0000 0.463332
\(914\) 8.00000 0.264616
\(915\) 0 0
\(916\) −27.0000 −0.892105
\(917\) 24.0000 0.792550
\(918\) −1.00000 −0.0330049
\(919\) −8.00000 −0.263896 −0.131948 − 0.991257i \(-0.542123\pi\)
−0.131948 + 0.991257i \(0.542123\pi\)
\(920\) 0 0
\(921\) −1.00000 −0.0329511
\(922\) −13.0000 −0.428132
\(923\) 16.0000 0.526646
\(924\) 6.00000 0.197386
\(925\) 10.0000 0.328798
\(926\) −20.0000 −0.657241
\(927\) −15.0000 −0.492665
\(928\) −6.00000 −0.196960
\(929\) 38.0000 1.24674 0.623370 − 0.781927i \(-0.285763\pi\)
0.623370 + 0.781927i \(0.285763\pi\)
\(930\) 0 0
\(931\) −2.00000 −0.0655474
\(932\) −18.0000 −0.589610
\(933\) −8.00000 −0.261908
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) −2.00000 −0.0653720
\(937\) −8.00000 −0.261349 −0.130674 − 0.991425i \(-0.541714\pi\)
−0.130674 + 0.991425i \(0.541714\pi\)
\(938\) −12.0000 −0.391814
\(939\) 26.0000 0.848478
\(940\) 0 0
\(941\) 35.0000 1.14097 0.570484 − 0.821309i \(-0.306756\pi\)
0.570484 + 0.821309i \(0.306756\pi\)
\(942\) −11.0000 −0.358399
\(943\) −3.00000 −0.0976934
\(944\) −1.00000 −0.0325472
\(945\) 0 0
\(946\) 4.00000 0.130051
\(947\) 37.0000 1.20234 0.601169 − 0.799122i \(-0.294702\pi\)
0.601169 + 0.799122i \(0.294702\pi\)
\(948\) −16.0000 −0.519656
\(949\) 14.0000 0.454459
\(950\) 5.00000 0.162221
\(951\) 4.00000 0.129709
\(952\) 3.00000 0.0972306
\(953\) −2.00000 −0.0647864 −0.0323932 − 0.999475i \(-0.510313\pi\)
−0.0323932 + 0.999475i \(0.510313\pi\)
\(954\) −11.0000 −0.356138
\(955\) 0 0
\(956\) 0 0
\(957\) −12.0000 −0.387905
\(958\) 18.0000 0.581554
\(959\) 30.0000 0.968751
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) 4.00000 0.128965
\(963\) −1.00000 −0.0322245
\(964\) −10.0000 −0.322078
\(965\) 0 0
\(966\) 3.00000 0.0965234
\(967\) −55.0000 −1.76868 −0.884340 − 0.466843i \(-0.845391\pi\)
−0.884340 + 0.466843i \(0.845391\pi\)
\(968\) −7.00000 −0.224989
\(969\) 1.00000 0.0321246
\(970\) 0 0
\(971\) 14.0000 0.449281 0.224641 − 0.974442i \(-0.427879\pi\)
0.224641 + 0.974442i \(0.427879\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −42.0000 −1.34646
\(974\) 37.0000 1.18556
\(975\) −10.0000 −0.320256
\(976\) 6.00000 0.192055
\(977\) −30.0000 −0.959785 −0.479893 − 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 10.0000 0.319765
\(979\) −10.0000 −0.319601
\(980\) 0 0
\(981\) 0 0
\(982\) −24.0000 −0.765871
\(983\) 15.0000 0.478426 0.239213 − 0.970967i \(-0.423111\pi\)
0.239213 + 0.970967i \(0.423111\pi\)
\(984\) −3.00000 −0.0956365
\(985\) 0 0
\(986\) −6.00000 −0.191079
\(987\) −6.00000 −0.190982
\(988\) 2.00000 0.0636285
\(989\) 2.00000 0.0635963
\(990\) 0 0
\(991\) 10.0000 0.317660 0.158830 − 0.987306i \(-0.449228\pi\)
0.158830 + 0.987306i \(0.449228\pi\)
\(992\) −10.0000 −0.317500
\(993\) 25.0000 0.793351
\(994\) −24.0000 −0.761234
\(995\) 0 0
\(996\) 7.00000 0.221803
\(997\) −37.0000 −1.17180 −0.585901 − 0.810383i \(-0.699259\pi\)
−0.585901 + 0.810383i \(0.699259\pi\)
\(998\) −12.0000 −0.379853
\(999\) 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 6018.2.a.g.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.g.1.1 ✓ 1 1.1 even 1 trivial