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Properties

Label 6018.2.a.c.1.1
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
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] = [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: \(0\)
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 \(\chi\) \(=\) 6018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} -4.00000 q^{21} +4.00000 q^{22} +8.00000 q^{23} +1.00000 q^{24} -5.00000 q^{25} -4.00000 q^{26} -1.00000 q^{27} +4.00000 q^{28} +8.00000 q^{29} -6.00000 q^{31} -1.00000 q^{32} +4.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} +4.00000 q^{37} -4.00000 q^{38} -4.00000 q^{39} -10.0000 q^{41} +4.00000 q^{42} +8.00000 q^{43} -4.00000 q^{44} -8.00000 q^{46} -4.00000 q^{47} -1.00000 q^{48} +9.00000 q^{49} +5.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} +1.00000 q^{54} -4.00000 q^{56} -4.00000 q^{57} -8.00000 q^{58} +1.00000 q^{59} +12.0000 q^{61} +6.00000 q^{62} +4.00000 q^{63} +1.00000 q^{64} -4.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} -8.00000 q^{69} +10.0000 q^{71} -1.00000 q^{72} +2.00000 q^{73} -4.00000 q^{74} +5.00000 q^{75} +4.00000 q^{76} -16.0000 q^{77} +4.00000 q^{78} +4.00000 q^{79} +1.00000 q^{81} +10.0000 q^{82} -12.0000 q^{83} -4.00000 q^{84} -8.00000 q^{86} -8.00000 q^{87} +4.00000 q^{88} +10.0000 q^{89} +16.0000 q^{91} +8.00000 q^{92} +6.00000 q^{93} +4.00000 q^{94} +1.00000 q^{96} -10.0000 q^{97} -9.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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
\(7\) 4.00000 1.51186 0.755929 − 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 − 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) −1.00000 −0.288675
\(13\) 4.00000 1.10940 0.554700 − 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) −4.00000 −1.06904
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) 4.00000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) −4.00000 −0.872872
\(22\) 4.00000 0.852803
\(23\) 8.00000 1.66812 0.834058 − 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 1.00000 0.204124
\(25\) −5.00000 −1.00000
\(26\) −4.00000 −0.784465
\(27\) −1.00000 −0.192450
\(28\) 4.00000 0.755929
\(29\) 8.00000 1.48556 0.742781 − 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) −6.00000 −1.07763 −0.538816 − 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.00000 0.696311
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 4.00000 0.657596 0.328798 − 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) −4.00000 −0.648886
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 − 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 4.00000 0.617213
\(43\) 8.00000 1.21999 0.609994 − 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) −8.00000 −1.17954
\(47\) −4.00000 −0.583460 −0.291730 − 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) −1.00000 −0.144338
\(49\) 9.00000 1.28571
\(50\) 5.00000 0.707107
\(51\) 1.00000 0.140028
\(52\) 4.00000 0.554700
\(53\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −4.00000 −0.534522
\(57\) −4.00000 −0.529813
\(58\) −8.00000 −1.05045
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) 12.0000 1.53644 0.768221 − 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 6.00000 0.762001
\(63\) 4.00000 0.503953
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −4.00000 −0.492366
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −1.00000 −0.121268
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) 10.0000 1.18678 0.593391 − 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.00000 0.234082 0.117041 − 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −4.00000 −0.464991
\(75\) 5.00000 0.577350
\(76\) 4.00000 0.458831
\(77\) −16.0000 −1.82337
\(78\) 4.00000 0.452911
\(79\) 4.00000 0.450035 0.225018 − 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 10.0000 1.10432
\(83\) −12.0000 −1.31717 −0.658586 − 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) −4.00000 −0.436436
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) −8.00000 −0.857690
\(88\) 4.00000 0.426401
\(89\) 10.0000 1.06000 0.529999 − 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0 0
\(91\) 16.0000 1.67726
\(92\) 8.00000 0.834058
\(93\) 6.00000 0.622171
\(94\) 4.00000 0.412568
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −10.0000 −1.01535 −0.507673 − 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) −9.00000 −0.909137
\(99\) −4.00000 −0.402015
\(100\) −5.00000 −0.500000
\(101\) 6.00000 0.597022 0.298511 − 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) −1.00000 −0.0990148
\(103\) 6.00000 0.591198 0.295599 − 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 0 0
\(107\) −16.0000 −1.54678 −0.773389 − 0.633932i \(-0.781440\pi\)
−0.773389 + 0.633932i \(0.781440\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 8.00000 0.766261 0.383131 − 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) 4.00000 0.377964
\(113\) −10.0000 −0.940721 −0.470360 − 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 4.00000 0.374634
\(115\) 0 0
\(116\) 8.00000 0.742781
\(117\) 4.00000 0.369800
\(118\) −1.00000 −0.0920575
\(119\) −4.00000 −0.366679
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) −12.0000 −1.08643
\(123\) 10.0000 0.901670
\(124\) −6.00000 −0.538816
\(125\) 0 0
\(126\) −4.00000 −0.356348
\(127\) 12.0000 1.06483 0.532414 − 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −8.00000 −0.704361
\(130\) 0 0
\(131\) 20.0000 1.74741 0.873704 − 0.486458i \(-0.161711\pi\)
0.873704 + 0.486458i \(0.161711\pi\)
\(132\) 4.00000 0.348155
\(133\) 16.0000 1.38738
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 1.00000 0.0857493
\(137\) 22.0000 1.87959 0.939793 − 0.341743i \(-0.111017\pi\)
0.939793 + 0.341743i \(0.111017\pi\)
\(138\) 8.00000 0.681005
\(139\) −4.00000 −0.339276 −0.169638 − 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 4.00000 0.336861
\(142\) −10.0000 −0.839181
\(143\) −16.0000 −1.33799
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −9.00000 −0.742307
\(148\) 4.00000 0.328798
\(149\) −22.0000 −1.80231 −0.901155 − 0.433497i \(-0.857280\pi\)
−0.901155 + 0.433497i \(0.857280\pi\)
\(150\) −5.00000 −0.408248
\(151\) 18.0000 1.46482 0.732410 − 0.680864i \(-0.238396\pi\)
0.732410 + 0.680864i \(0.238396\pi\)
\(152\) −4.00000 −0.324443
\(153\) −1.00000 −0.0808452
\(154\) 16.0000 1.28932
\(155\) 0 0
\(156\) −4.00000 −0.320256
\(157\) −20.0000 −1.59617 −0.798087 − 0.602542i \(-0.794154\pi\)
−0.798087 + 0.602542i \(0.794154\pi\)
\(158\) −4.00000 −0.318223
\(159\) 0 0
\(160\) 0 0
\(161\) 32.0000 2.52195
\(162\) −1.00000 −0.0785674
\(163\) 4.00000 0.313304 0.156652 − 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −10.0000 −0.780869
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) −10.0000 −0.773823 −0.386912 − 0.922117i \(-0.626458\pi\)
−0.386912 + 0.922117i \(0.626458\pi\)
\(168\) 4.00000 0.308607
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 4.00000 0.305888
\(172\) 8.00000 0.609994
\(173\) −22.0000 −1.67263 −0.836315 − 0.548250i \(-0.815294\pi\)
−0.836315 + 0.548250i \(0.815294\pi\)
\(174\) 8.00000 0.606478
\(175\) −20.0000 −1.51186
\(176\) −4.00000 −0.301511
\(177\) −1.00000 −0.0751646
\(178\) −10.0000 −0.749532
\(179\) −12.0000 −0.896922 −0.448461 − 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 − 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) −16.0000 −1.18600
\(183\) −12.0000 −0.887066
\(184\) −8.00000 −0.589768
\(185\) 0 0
\(186\) −6.00000 −0.439941
\(187\) 4.00000 0.292509
\(188\) −4.00000 −0.291730
\(189\) −4.00000 −0.290957
\(190\) 0 0
\(191\) 20.0000 1.44715 0.723575 − 0.690246i \(-0.242498\pi\)
0.723575 + 0.690246i \(0.242498\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 10.0000 0.719816 0.359908 − 0.932988i \(-0.382808\pi\)
0.359908 + 0.932988i \(0.382808\pi\)
\(194\) 10.0000 0.717958
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) −8.00000 −0.569976 −0.284988 − 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) 4.00000 0.284268
\(199\) −16.0000 −1.13421 −0.567105 − 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 5.00000 0.353553
\(201\) 4.00000 0.282138
\(202\) −6.00000 −0.422159
\(203\) 32.0000 2.24596
\(204\) 1.00000 0.0700140
\(205\) 0 0
\(206\) −6.00000 −0.418040
\(207\) 8.00000 0.556038
\(208\) 4.00000 0.277350
\(209\) −16.0000 −1.10674
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 − 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 0 0
\(213\) −10.0000 −0.685189
\(214\) 16.0000 1.09374
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −24.0000 −1.62923
\(218\) −8.00000 −0.541828
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) 4.00000 0.268462
\(223\) −24.0000 −1.60716 −0.803579 − 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) −4.00000 −0.267261
\(225\) −5.00000 −0.333333
\(226\) 10.0000 0.665190
\(227\) −12.0000 −0.796468 −0.398234 − 0.917284i \(-0.630377\pi\)
−0.398234 + 0.917284i \(0.630377\pi\)
\(228\) −4.00000 −0.264906
\(229\) 8.00000 0.528655 0.264327 − 0.964433i \(-0.414850\pi\)
0.264327 + 0.964433i \(0.414850\pi\)
\(230\) 0 0
\(231\) 16.0000 1.05272
\(232\) −8.00000 −0.525226
\(233\) 10.0000 0.655122 0.327561 − 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) −4.00000 −0.261488
\(235\) 0 0
\(236\) 1.00000 0.0650945
\(237\) −4.00000 −0.259828
\(238\) 4.00000 0.259281
\(239\) −14.0000 −0.905585 −0.452792 − 0.891616i \(-0.649572\pi\)
−0.452792 + 0.891616i \(0.649572\pi\)
\(240\) 0 0
\(241\) −2.00000 −0.128831 −0.0644157 − 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) −5.00000 −0.321412
\(243\) −1.00000 −0.0641500
\(244\) 12.0000 0.768221
\(245\) 0 0
\(246\) −10.0000 −0.637577
\(247\) 16.0000 1.01806
\(248\) 6.00000 0.381000
\(249\) 12.0000 0.760469
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 − 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 4.00000 0.251976
\(253\) −32.0000 −2.01182
\(254\) −12.0000 −0.752947
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 10.0000 0.623783 0.311891 − 0.950118i \(-0.399037\pi\)
0.311891 + 0.950118i \(0.399037\pi\)
\(258\) 8.00000 0.498058
\(259\) 16.0000 0.994192
\(260\) 0 0
\(261\) 8.00000 0.495188
\(262\) −20.0000 −1.23560
\(263\) 6.00000 0.369976 0.184988 − 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) −4.00000 −0.246183
\(265\) 0 0
\(266\) −16.0000 −0.981023
\(267\) −10.0000 −0.611990
\(268\) −4.00000 −0.244339
\(269\) −10.0000 −0.609711 −0.304855 − 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 0 0
\(271\) −24.0000 −1.45790 −0.728948 − 0.684569i \(-0.759990\pi\)
−0.728948 + 0.684569i \(0.759990\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −16.0000 −0.968364
\(274\) −22.0000 −1.32907
\(275\) 20.0000 1.20605
\(276\) −8.00000 −0.481543
\(277\) −2.00000 −0.120168 −0.0600842 − 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 4.00000 0.239904
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 − 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) −4.00000 −0.238197
\(283\) 24.0000 1.42665 0.713326 − 0.700832i \(-0.247188\pi\)
0.713326 + 0.700832i \(0.247188\pi\)
\(284\) 10.0000 0.593391
\(285\) 0 0
\(286\) 16.0000 0.946100
\(287\) −40.0000 −2.36113
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 10.0000 0.586210
\(292\) 2.00000 0.117041
\(293\) 28.0000 1.63578 0.817889 − 0.575376i \(-0.195144\pi\)
0.817889 + 0.575376i \(0.195144\pi\)
\(294\) 9.00000 0.524891
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 4.00000 0.232104
\(298\) 22.0000 1.27443
\(299\) 32.0000 1.85061
\(300\) 5.00000 0.288675
\(301\) 32.0000 1.84445
\(302\) −18.0000 −1.03578
\(303\) −6.00000 −0.344691
\(304\) 4.00000 0.229416
\(305\) 0 0
\(306\) 1.00000 0.0571662
\(307\) −4.00000 −0.228292 −0.114146 − 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) −16.0000 −0.911685
\(309\) −6.00000 −0.341328
\(310\) 0 0
\(311\) 30.0000 1.70114 0.850572 − 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 4.00000 0.226455
\(313\) 14.0000 0.791327 0.395663 − 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) 20.0000 1.12867
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 24.0000 1.34797 0.673987 − 0.738743i \(-0.264580\pi\)
0.673987 + 0.738743i \(0.264580\pi\)
\(318\) 0 0
\(319\) −32.0000 −1.79166
\(320\) 0 0
\(321\) 16.0000 0.893033
\(322\) −32.0000 −1.78329
\(323\) −4.00000 −0.222566
\(324\) 1.00000 0.0555556
\(325\) −20.0000 −1.10940
\(326\) −4.00000 −0.221540
\(327\) −8.00000 −0.442401
\(328\) 10.0000 0.552158
\(329\) −16.0000 −0.882109
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 − 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) −12.0000 −0.658586
\(333\) 4.00000 0.219199
\(334\) 10.0000 0.547176
\(335\) 0 0
\(336\) −4.00000 −0.218218
\(337\) 2.00000 0.108947 0.0544735 − 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) −3.00000 −0.163178
\(339\) 10.0000 0.543125
\(340\) 0 0
\(341\) 24.0000 1.29967
\(342\) −4.00000 −0.216295
\(343\) 8.00000 0.431959
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) 22.0000 1.18273
\(347\) −4.00000 −0.214731 −0.107366 − 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) −8.00000 −0.428845
\(349\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 20.0000 1.06904
\(351\) −4.00000 −0.213504
\(352\) 4.00000 0.213201
\(353\) −18.0000 −0.958043 −0.479022 − 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 1.00000 0.0531494
\(355\) 0 0
\(356\) 10.0000 0.529999
\(357\) 4.00000 0.211702
\(358\) 12.0000 0.634220
\(359\) 30.0000 1.58334 0.791670 − 0.610949i \(-0.209212\pi\)
0.791670 + 0.610949i \(0.209212\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 6.00000 0.315353
\(363\) −5.00000 −0.262432
\(364\) 16.0000 0.838628
\(365\) 0 0
\(366\) 12.0000 0.627250
\(367\) 30.0000 1.56599 0.782994 − 0.622030i \(-0.213692\pi\)
0.782994 + 0.622030i \(0.213692\pi\)
\(368\) 8.00000 0.417029
\(369\) −10.0000 −0.520579
\(370\) 0 0
\(371\) 0 0
\(372\) 6.00000 0.311086
\(373\) 22.0000 1.13912 0.569558 − 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) −4.00000 −0.206835
\(375\) 0 0
\(376\) 4.00000 0.206284
\(377\) 32.0000 1.64808
\(378\) 4.00000 0.205738
\(379\) −20.0000 −1.02733 −0.513665 − 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) −12.0000 −0.614779
\(382\) −20.0000 −1.02329
\(383\) 38.0000 1.94171 0.970855 − 0.239669i \(-0.0770389\pi\)
0.970855 + 0.239669i \(0.0770389\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 8.00000 0.406663
\(388\) −10.0000 −0.507673
\(389\) −4.00000 −0.202808 −0.101404 − 0.994845i \(-0.532333\pi\)
−0.101404 + 0.994845i \(0.532333\pi\)
\(390\) 0 0
\(391\) −8.00000 −0.404577
\(392\) −9.00000 −0.454569
\(393\) −20.0000 −1.00887
\(394\) 8.00000 0.403034
\(395\) 0 0
\(396\) −4.00000 −0.201008
\(397\) 8.00000 0.401508 0.200754 − 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(398\) 16.0000 0.802008
\(399\) −16.0000 −0.801002
\(400\) −5.00000 −0.250000
\(401\) 2.00000 0.0998752 0.0499376 − 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) −4.00000 −0.199502
\(403\) −24.0000 −1.19553
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) −32.0000 −1.58813
\(407\) −16.0000 −0.793091
\(408\) −1.00000 −0.0495074
\(409\) −18.0000 −0.890043 −0.445021 − 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) 0 0
\(411\) −22.0000 −1.08518
\(412\) 6.00000 0.295599
\(413\) 4.00000 0.196827
\(414\) −8.00000 −0.393179
\(415\) 0 0
\(416\) −4.00000 −0.196116
\(417\) 4.00000 0.195881
\(418\) 16.0000 0.782586
\(419\) 28.0000 1.36789 0.683945 − 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) −12.0000 −0.584844 −0.292422 − 0.956289i \(-0.594461\pi\)
−0.292422 + 0.956289i \(0.594461\pi\)
\(422\) −20.0000 −0.973585
\(423\) −4.00000 −0.194487
\(424\) 0 0
\(425\) 5.00000 0.242536
\(426\) 10.0000 0.484502
\(427\) 48.0000 2.32288
\(428\) −16.0000 −0.773389
\(429\) 16.0000 0.772487
\(430\) 0 0
\(431\) 8.00000 0.385346 0.192673 − 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 14.0000 0.672797 0.336399 − 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 24.0000 1.15204
\(435\) 0 0
\(436\) 8.00000 0.383131
\(437\) 32.0000 1.53077
\(438\) 2.00000 0.0955637
\(439\) −16.0000 −0.763638 −0.381819 − 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 4.00000 0.190261
\(443\) 20.0000 0.950229 0.475114 − 0.879924i \(-0.342407\pi\)
0.475114 + 0.879924i \(0.342407\pi\)
\(444\) −4.00000 −0.189832
\(445\) 0 0
\(446\) 24.0000 1.13643
\(447\) 22.0000 1.04056
\(448\) 4.00000 0.188982
\(449\) 14.0000 0.660701 0.330350 − 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 5.00000 0.235702
\(451\) 40.0000 1.88353
\(452\) −10.0000 −0.470360
\(453\) −18.0000 −0.845714
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −10.0000 −0.467780 −0.233890 − 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) −8.00000 −0.373815
\(459\) 1.00000 0.0466760
\(460\) 0 0
\(461\) −28.0000 −1.30409 −0.652045 − 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) −16.0000 −0.744387
\(463\) 14.0000 0.650635 0.325318 − 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) 8.00000 0.371391
\(465\) 0 0
\(466\) −10.0000 −0.463241
\(467\) 28.0000 1.29569 0.647843 − 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) 4.00000 0.184900
\(469\) −16.0000 −0.738811
\(470\) 0 0
\(471\) 20.0000 0.921551
\(472\) −1.00000 −0.0460287
\(473\) −32.0000 −1.47136
\(474\) 4.00000 0.183726
\(475\) −20.0000 −0.917663
\(476\) −4.00000 −0.183340
\(477\) 0 0
\(478\) 14.0000 0.640345
\(479\) 30.0000 1.37073 0.685367 − 0.728197i \(-0.259642\pi\)
0.685367 + 0.728197i \(0.259642\pi\)
\(480\) 0 0
\(481\) 16.0000 0.729537
\(482\) 2.00000 0.0910975
\(483\) −32.0000 −1.45605
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) −12.0000 −0.543214
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 10.0000 0.450835
\(493\) −8.00000 −0.360302
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) −6.00000 −0.269408
\(497\) 40.0000 1.79425
\(498\) −12.0000 −0.537733
\(499\) −4.00000 −0.179065 −0.0895323 − 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 10.0000 0.446767
\(502\) 12.0000 0.535586
\(503\) 32.0000 1.42681 0.713405 − 0.700752i \(-0.247152\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(504\) −4.00000 −0.178174
\(505\) 0 0
\(506\) 32.0000 1.42257
\(507\) −3.00000 −0.133235
\(508\) 12.0000 0.532414
\(509\) −18.0000 −0.797836 −0.398918 − 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) 0 0
\(511\) 8.00000 0.353899
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 −0.176604
\(514\) −10.0000 −0.441081
\(515\) 0 0
\(516\) −8.00000 −0.352180
\(517\) 16.0000 0.703679
\(518\) −16.0000 −0.703000
\(519\) 22.0000 0.965693
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 − 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −8.00000 −0.350150
\(523\) 4.00000 0.174908 0.0874539 − 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 20.0000 0.873704
\(525\) 20.0000 0.872872
\(526\) −6.00000 −0.261612
\(527\) 6.00000 0.261364
\(528\) 4.00000 0.174078
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) 1.00000 0.0433963
\(532\) 16.0000 0.693688
\(533\) −40.0000 −1.73259
\(534\) 10.0000 0.432742
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) 12.0000 0.517838
\(538\) 10.0000 0.431131
\(539\) −36.0000 −1.55063
\(540\) 0 0
\(541\) 32.0000 1.37579 0.687894 − 0.725811i \(-0.258536\pi\)
0.687894 + 0.725811i \(0.258536\pi\)
\(542\) 24.0000 1.03089
\(543\) 6.00000 0.257485
\(544\) 1.00000 0.0428746
\(545\) 0 0
\(546\) 16.0000 0.684737
\(547\) 28.0000 1.19719 0.598597 − 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 22.0000 0.939793
\(549\) 12.0000 0.512148
\(550\) −20.0000 −0.852803
\(551\) 32.0000 1.36325
\(552\) 8.00000 0.340503
\(553\) 16.0000 0.680389
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) −4.00000 −0.169638
\(557\) −20.0000 −0.847427 −0.423714 − 0.905796i \(-0.639274\pi\)
−0.423714 + 0.905796i \(0.639274\pi\)
\(558\) 6.00000 0.254000
\(559\) 32.0000 1.35346
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) −10.0000 −0.421825
\(563\) −12.0000 −0.505740 −0.252870 − 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 4.00000 0.168430
\(565\) 0 0
\(566\) −24.0000 −1.00880
\(567\) 4.00000 0.167984
\(568\) −10.0000 −0.419591
\(569\) −26.0000 −1.08998 −0.544988 − 0.838444i \(-0.683466\pi\)
−0.544988 + 0.838444i \(0.683466\pi\)
\(570\) 0 0
\(571\) 24.0000 1.00437 0.502184 − 0.864761i \(-0.332530\pi\)
0.502184 + 0.864761i \(0.332530\pi\)
\(572\) −16.0000 −0.668994
\(573\) −20.0000 −0.835512
\(574\) 40.0000 1.66957
\(575\) −40.0000 −1.66812
\(576\) 1.00000 0.0416667
\(577\) −2.00000 −0.0832611 −0.0416305 − 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −10.0000 −0.415586
\(580\) 0 0
\(581\) −48.0000 −1.99138
\(582\) −10.0000 −0.414513
\(583\) 0 0
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) −28.0000 −1.15667
\(587\) −36.0000 −1.48588 −0.742940 − 0.669359i \(-0.766569\pi\)
−0.742940 + 0.669359i \(0.766569\pi\)
\(588\) −9.00000 −0.371154
\(589\) −24.0000 −0.988903
\(590\) 0 0
\(591\) 8.00000 0.329076
\(592\) 4.00000 0.164399
\(593\) 34.0000 1.39621 0.698106 − 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) −22.0000 −0.901155
\(597\) 16.0000 0.654836
\(598\) −32.0000 −1.30858
\(599\) 18.0000 0.735460 0.367730 − 0.929933i \(-0.380135\pi\)
0.367730 + 0.929933i \(0.380135\pi\)
\(600\) −5.00000 −0.204124
\(601\) 10.0000 0.407909 0.203954 − 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) −32.0000 −1.30422
\(603\) −4.00000 −0.162893
\(604\) 18.0000 0.732410
\(605\) 0 0
\(606\) 6.00000 0.243733
\(607\) 8.00000 0.324710 0.162355 − 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) −4.00000 −0.162221
\(609\) −32.0000 −1.29671
\(610\) 0 0
\(611\) −16.0000 −0.647291
\(612\) −1.00000 −0.0404226
\(613\) 16.0000 0.646234 0.323117 − 0.946359i \(-0.395269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(614\) 4.00000 0.161427
\(615\) 0 0
\(616\) 16.0000 0.644658
\(617\) −14.0000 −0.563619 −0.281809 − 0.959470i \(-0.590935\pi\)
−0.281809 + 0.959470i \(0.590935\pi\)
\(618\) 6.00000 0.241355
\(619\) 28.0000 1.12542 0.562708 − 0.826656i \(-0.309760\pi\)
0.562708 + 0.826656i \(0.309760\pi\)
\(620\) 0 0
\(621\) −8.00000 −0.321029
\(622\) −30.0000 −1.20289
\(623\) 40.0000 1.60257
\(624\) −4.00000 −0.160128
\(625\) 25.0000 1.00000
\(626\) −14.0000 −0.559553
\(627\) 16.0000 0.638978
\(628\) −20.0000 −0.798087
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 − 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) −4.00000 −0.159111
\(633\) −20.0000 −0.794929
\(634\) −24.0000 −0.953162
\(635\) 0 0
\(636\) 0 0
\(637\) 36.0000 1.42637
\(638\) 32.0000 1.26689
\(639\) 10.0000 0.395594
\(640\) 0 0
\(641\) 30.0000 1.18493 0.592464 − 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) −16.0000 −0.631470
\(643\) 4.00000 0.157745 0.0788723 − 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 32.0000 1.26098
\(645\) 0 0
\(646\) 4.00000 0.157378
\(647\) −30.0000 −1.17942 −0.589711 − 0.807614i \(-0.700758\pi\)
−0.589711 + 0.807614i \(0.700758\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −4.00000 −0.157014
\(650\) 20.0000 0.784465
\(651\) 24.0000 0.940634
\(652\) 4.00000 0.156652
\(653\) 8.00000 0.313064 0.156532 − 0.987673i \(-0.449969\pi\)
0.156532 + 0.987673i \(0.449969\pi\)
\(654\) 8.00000 0.312825
\(655\) 0 0
\(656\) −10.0000 −0.390434
\(657\) 2.00000 0.0780274
\(658\) 16.0000 0.623745
\(659\) 36.0000 1.40236 0.701180 − 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 − 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 4.00000 0.155464
\(663\) 4.00000 0.155347
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) −4.00000 −0.154997
\(667\) 64.0000 2.47809
\(668\) −10.0000 −0.386912
\(669\) 24.0000 0.927894
\(670\) 0 0
\(671\) −48.0000 −1.85302
\(672\) 4.00000 0.154303
\(673\) 46.0000 1.77317 0.886585 − 0.462566i \(-0.153071\pi\)
0.886585 + 0.462566i \(0.153071\pi\)
\(674\) −2.00000 −0.0770371
\(675\) 5.00000 0.192450
\(676\) 3.00000 0.115385
\(677\) −52.0000 −1.99852 −0.999261 − 0.0384331i \(-0.987763\pi\)
−0.999261 + 0.0384331i \(0.987763\pi\)
\(678\) −10.0000 −0.384048
\(679\) −40.0000 −1.53506
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) −24.0000 −0.919007
\(683\) −4.00000 −0.153056 −0.0765279 − 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 4.00000 0.152944
\(685\) 0 0
\(686\) −8.00000 −0.305441
\(687\) −8.00000 −0.305219
\(688\) 8.00000 0.304997
\(689\) 0 0
\(690\) 0 0
\(691\) −44.0000 −1.67384 −0.836919 − 0.547326i \(-0.815646\pi\)
−0.836919 + 0.547326i \(0.815646\pi\)
\(692\) −22.0000 −0.836315
\(693\) −16.0000 −0.607790
\(694\) 4.00000 0.151838
\(695\) 0 0
\(696\) 8.00000 0.303239
\(697\) 10.0000 0.378777
\(698\) 0 0
\(699\) −10.0000 −0.378235
\(700\) −20.0000 −0.755929
\(701\) −18.0000 −0.679851 −0.339925 − 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 4.00000 0.150970
\(703\) 16.0000 0.603451
\(704\) −4.00000 −0.150756
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) 24.0000 0.902613
\(708\) −1.00000 −0.0375823
\(709\) −6.00000 −0.225335 −0.112667 − 0.993633i \(-0.535939\pi\)
−0.112667 + 0.993633i \(0.535939\pi\)
\(710\) 0 0
\(711\) 4.00000 0.150012
\(712\) −10.0000 −0.374766
\(713\) −48.0000 −1.79761
\(714\) −4.00000 −0.149696
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) 14.0000 0.522840
\(718\) −30.0000 −1.11959
\(719\) 40.0000 1.49175 0.745874 − 0.666087i \(-0.232032\pi\)
0.745874 + 0.666087i \(0.232032\pi\)
\(720\) 0 0
\(721\) 24.0000 0.893807
\(722\) 3.00000 0.111648
\(723\) 2.00000 0.0743808
\(724\) −6.00000 −0.222988
\(725\) −40.0000 −1.48556
\(726\) 5.00000 0.185567
\(727\) 20.0000 0.741759 0.370879 − 0.928681i \(-0.379056\pi\)
0.370879 + 0.928681i \(0.379056\pi\)
\(728\) −16.0000 −0.592999
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) −12.0000 −0.443533
\(733\) −14.0000 −0.517102 −0.258551 − 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) −30.0000 −1.10732
\(735\) 0 0
\(736\) −8.00000 −0.294884
\(737\) 16.0000 0.589368
\(738\) 10.0000 0.368105
\(739\) −24.0000 −0.882854 −0.441427 − 0.897297i \(-0.645528\pi\)
−0.441427 + 0.897297i \(0.645528\pi\)
\(740\) 0 0
\(741\) −16.0000 −0.587775
\(742\) 0 0
\(743\) −6.00000 −0.220119 −0.110059 − 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) −6.00000 −0.219971
\(745\) 0 0
\(746\) −22.0000 −0.805477
\(747\) −12.0000 −0.439057
\(748\) 4.00000 0.146254
\(749\) −64.0000 −2.33851
\(750\) 0 0
\(751\) −50.0000 −1.82453 −0.912263 − 0.409605i \(-0.865667\pi\)
−0.912263 + 0.409605i \(0.865667\pi\)
\(752\) −4.00000 −0.145865
\(753\) 12.0000 0.437304
\(754\) −32.0000 −1.16537
\(755\) 0 0
\(756\) −4.00000 −0.145479
\(757\) −2.00000 −0.0726912 −0.0363456 − 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 20.0000 0.726433
\(759\) 32.0000 1.16153
\(760\) 0 0
\(761\) −50.0000 −1.81250 −0.906249 − 0.422744i \(-0.861067\pi\)
−0.906249 + 0.422744i \(0.861067\pi\)
\(762\) 12.0000 0.434714
\(763\) 32.0000 1.15848
\(764\) 20.0000 0.723575
\(765\) 0 0
\(766\) −38.0000 −1.37300
\(767\) 4.00000 0.144432
\(768\) −1.00000 −0.0360844
\(769\) 30.0000 1.08183 0.540914 − 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) −10.0000 −0.360141
\(772\) 10.0000 0.359908
\(773\) 30.0000 1.07903 0.539513 − 0.841978i \(-0.318609\pi\)
0.539513 + 0.841978i \(0.318609\pi\)
\(774\) −8.00000 −0.287554
\(775\) 30.0000 1.07763
\(776\) 10.0000 0.358979
\(777\) −16.0000 −0.573997
\(778\) 4.00000 0.143407
\(779\) −40.0000 −1.43315
\(780\) 0 0
\(781\) −40.0000 −1.43131
\(782\) 8.00000 0.286079
\(783\) −8.00000 −0.285897
\(784\) 9.00000 0.321429
\(785\) 0 0
\(786\) 20.0000 0.713376
\(787\) −20.0000 −0.712923 −0.356462 − 0.934310i \(-0.616017\pi\)
−0.356462 + 0.934310i \(0.616017\pi\)
\(788\) −8.00000 −0.284988
\(789\) −6.00000 −0.213606
\(790\) 0 0
\(791\) −40.0000 −1.42224
\(792\) 4.00000 0.142134
\(793\) 48.0000 1.70453
\(794\) −8.00000 −0.283909
\(795\) 0 0
\(796\) −16.0000 −0.567105
\(797\) 26.0000 0.920967 0.460484 − 0.887668i \(-0.347676\pi\)
0.460484 + 0.887668i \(0.347676\pi\)
\(798\) 16.0000 0.566394
\(799\) 4.00000 0.141510
\(800\) 5.00000 0.176777
\(801\) 10.0000 0.353333
\(802\) −2.00000 −0.0706225
\(803\) −8.00000 −0.282314
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) 24.0000 0.845364
\(807\) 10.0000 0.352017
\(808\) −6.00000 −0.211079
\(809\) −30.0000 −1.05474 −0.527372 − 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 0 0
\(811\) −28.0000 −0.983213 −0.491606 − 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 32.0000 1.12298
\(813\) 24.0000 0.841717
\(814\) 16.0000 0.560800
\(815\) 0 0
\(816\) 1.00000 0.0350070
\(817\) 32.0000 1.11954
\(818\) 18.0000 0.629355
\(819\) 16.0000 0.559085
\(820\) 0 0
\(821\) −2.00000 −0.0698005 −0.0349002 − 0.999391i \(-0.511111\pi\)
−0.0349002 + 0.999391i \(0.511111\pi\)
\(822\) 22.0000 0.767338
\(823\) −2.00000 −0.0697156 −0.0348578 − 0.999392i \(-0.511098\pi\)
−0.0348578 + 0.999392i \(0.511098\pi\)
\(824\) −6.00000 −0.209020
\(825\) −20.0000 −0.696311
\(826\) −4.00000 −0.139178
\(827\) 12.0000 0.417281 0.208640 − 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 8.00000 0.278019
\(829\) −50.0000 −1.73657 −0.868286 − 0.496064i \(-0.834778\pi\)
−0.868286 + 0.496064i \(0.834778\pi\)
\(830\) 0 0
\(831\) 2.00000 0.0693792
\(832\) 4.00000 0.138675
\(833\) −9.00000 −0.311832
\(834\) −4.00000 −0.138509
\(835\) 0 0
\(836\) −16.0000 −0.553372
\(837\) 6.00000 0.207390
\(838\) −28.0000 −0.967244
\(839\) 32.0000 1.10476 0.552381 − 0.833592i \(-0.313719\pi\)
0.552381 + 0.833592i \(0.313719\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) 12.0000 0.413547
\(843\) −10.0000 −0.344418
\(844\) 20.0000 0.688428
\(845\) 0 0
\(846\) 4.00000 0.137523
\(847\) 20.0000 0.687208
\(848\) 0 0
\(849\) −24.0000 −0.823678
\(850\) −5.00000 −0.171499
\(851\) 32.0000 1.09695
\(852\) −10.0000 −0.342594
\(853\) −34.0000 −1.16414 −0.582069 − 0.813139i \(-0.697757\pi\)
−0.582069 + 0.813139i \(0.697757\pi\)
\(854\) −48.0000 −1.64253
\(855\) 0 0
\(856\) 16.0000 0.546869
\(857\) 42.0000 1.43469 0.717346 − 0.696717i \(-0.245357\pi\)
0.717346 + 0.696717i \(0.245357\pi\)
\(858\) −16.0000 −0.546231
\(859\) 28.0000 0.955348 0.477674 − 0.878537i \(-0.341480\pi\)
0.477674 + 0.878537i \(0.341480\pi\)
\(860\) 0 0
\(861\) 40.0000 1.36320
\(862\) −8.00000 −0.272481
\(863\) 4.00000 0.136162 0.0680808 − 0.997680i \(-0.478312\pi\)
0.0680808 + 0.997680i \(0.478312\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) −14.0000 −0.475739
\(867\) −1.00000 −0.0339618
\(868\) −24.0000 −0.814613
\(869\) −16.0000 −0.542763
\(870\) 0 0
\(871\) −16.0000 −0.542139
\(872\) −8.00000 −0.270914
\(873\) −10.0000 −0.338449
\(874\) −32.0000 −1.08242
\(875\) 0 0
\(876\) −2.00000 −0.0675737
\(877\) −58.0000 −1.95852 −0.979260 − 0.202606i \(-0.935059\pi\)
−0.979260 + 0.202606i \(0.935059\pi\)
\(878\) 16.0000 0.539974
\(879\) −28.0000 −0.944417
\(880\) 0 0
\(881\) −46.0000 −1.54978 −0.774890 − 0.632096i \(-0.782195\pi\)
−0.774890 + 0.632096i \(0.782195\pi\)
\(882\) −9.00000 −0.303046
\(883\) 36.0000 1.21150 0.605748 − 0.795656i \(-0.292874\pi\)
0.605748 + 0.795656i \(0.292874\pi\)
\(884\) −4.00000 −0.134535
\(885\) 0 0
\(886\) −20.0000 −0.671913
\(887\) 36.0000 1.20876 0.604381 − 0.796696i \(-0.293421\pi\)
0.604381 + 0.796696i \(0.293421\pi\)
\(888\) 4.00000 0.134231
\(889\) 48.0000 1.60987
\(890\) 0 0
\(891\) −4.00000 −0.134005
\(892\) −24.0000 −0.803579
\(893\) −16.0000 −0.535420
\(894\) −22.0000 −0.735790
\(895\) 0 0
\(896\) −4.00000 −0.133631
\(897\) −32.0000 −1.06845
\(898\) −14.0000 −0.467186
\(899\) −48.0000 −1.60089
\(900\) −5.00000 −0.166667
\(901\) 0 0
\(902\) −40.0000 −1.33185
\(903\) −32.0000 −1.06489
\(904\) 10.0000 0.332595
\(905\) 0 0
\(906\) 18.0000 0.598010
\(907\) 36.0000 1.19536 0.597680 − 0.801735i \(-0.296089\pi\)
0.597680 + 0.801735i \(0.296089\pi\)
\(908\) −12.0000 −0.398234
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) −30.0000 −0.993944 −0.496972 − 0.867766i \(-0.665555\pi\)
−0.496972 + 0.867766i \(0.665555\pi\)
\(912\) −4.00000 −0.132453
\(913\) 48.0000 1.58857
\(914\) 10.0000 0.330771
\(915\) 0 0
\(916\) 8.00000 0.264327
\(917\) 80.0000 2.64183
\(918\) −1.00000 −0.0330049
\(919\) −14.0000 −0.461817 −0.230909 − 0.972975i \(-0.574170\pi\)
−0.230909 + 0.972975i \(0.574170\pi\)
\(920\) 0 0
\(921\) 4.00000 0.131804
\(922\) 28.0000 0.922131
\(923\) 40.0000 1.31662
\(924\) 16.0000 0.526361
\(925\) −20.0000 −0.657596
\(926\) −14.0000 −0.460069
\(927\) 6.00000 0.197066
\(928\) −8.00000 −0.262613
\(929\) 58.0000 1.90292 0.951459 − 0.307775i \(-0.0995844\pi\)
0.951459 + 0.307775i \(0.0995844\pi\)
\(930\) 0 0
\(931\) 36.0000 1.17985
\(932\) 10.0000 0.327561
\(933\) −30.0000 −0.982156
\(934\) −28.0000 −0.916188
\(935\) 0 0
\(936\) −4.00000 −0.130744
\(937\) −46.0000 −1.50275 −0.751377 − 0.659873i \(-0.770610\pi\)
−0.751377 + 0.659873i \(0.770610\pi\)
\(938\) 16.0000 0.522419
\(939\) −14.0000 −0.456873
\(940\) 0 0
\(941\) −30.0000 −0.977972 −0.488986 − 0.872292i \(-0.662633\pi\)
−0.488986 + 0.872292i \(0.662633\pi\)
\(942\) −20.0000 −0.651635
\(943\) −80.0000 −2.60516
\(944\) 1.00000 0.0325472
\(945\) 0 0
\(946\) 32.0000 1.04041
\(947\) −8.00000 −0.259965 −0.129983 − 0.991516i \(-0.541492\pi\)
−0.129983 + 0.991516i \(0.541492\pi\)
\(948\) −4.00000 −0.129914
\(949\) 8.00000 0.259691
\(950\) 20.0000 0.648886
\(951\) −24.0000 −0.778253
\(952\) 4.00000 0.129641
\(953\) −2.00000 −0.0647864 −0.0323932 − 0.999475i \(-0.510313\pi\)
−0.0323932 + 0.999475i \(0.510313\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −14.0000 −0.452792
\(957\) 32.0000 1.03441
\(958\) −30.0000 −0.969256
\(959\) 88.0000 2.84167
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) −16.0000 −0.515861
\(963\) −16.0000 −0.515593
\(964\) −2.00000 −0.0644157
\(965\) 0 0
\(966\) 32.0000 1.02958
\(967\) −54.0000 −1.73652 −0.868261 − 0.496107i \(-0.834762\pi\)
−0.868261 + 0.496107i \(0.834762\pi\)
\(968\) −5.00000 −0.160706
\(969\) 4.00000 0.128499
\(970\) 0 0
\(971\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −16.0000 −0.512936
\(974\) 0 0
\(975\) 20.0000 0.640513
\(976\) 12.0000 0.384111
\(977\) 30.0000 0.959785 0.479893 − 0.877327i \(-0.340676\pi\)
0.479893 + 0.877327i \(0.340676\pi\)
\(978\) 4.00000 0.127906
\(979\) −40.0000 −1.27841
\(980\) 0 0
\(981\) 8.00000 0.255420
\(982\) 0 0
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) −10.0000 −0.318788
\(985\) 0 0
\(986\) 8.00000 0.254772
\(987\) 16.0000 0.509286
\(988\) 16.0000 0.509028
\(989\) 64.0000 2.03508
\(990\) 0 0
\(991\) 38.0000 1.20711 0.603555 − 0.797321i \(-0.293750\pi\)
0.603555 + 0.797321i \(0.293750\pi\)
\(992\) 6.00000 0.190500
\(993\) 4.00000 0.126936
\(994\) −40.0000 −1.26872
\(995\) 0 0
\(996\) 12.0000 0.380235
\(997\) −10.0000 −0.316703 −0.158352 − 0.987383i \(-0.550618\pi\)
−0.158352 + 0.987383i \(0.550618\pi\)
\(998\) 4.00000 0.126618
\(999\) −4.00000 −0.126554
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.c.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.c.1.1 ✓ 1 1.1 even 1 trivial