Properties

Label 6018.2.a.h.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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} -1.00000 q^{12} -2.00000 q^{14} -2.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} +2.00000 q^{20} +2.00000 q^{21} +2.00000 q^{23} -1.00000 q^{24} -1.00000 q^{25} -1.00000 q^{27} -2.00000 q^{28} -6.00000 q^{29} -2.00000 q^{30} +1.00000 q^{32} -1.00000 q^{34} -4.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} -4.00000 q^{38} +2.00000 q^{40} -10.0000 q^{41} +2.00000 q^{42} +2.00000 q^{45} +2.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} -8.00000 q^{53} -1.00000 q^{54} -2.00000 q^{56} +4.00000 q^{57} -6.00000 q^{58} +1.00000 q^{59} -2.00000 q^{60} -2.00000 q^{61} -2.00000 q^{63} +1.00000 q^{64} -8.00000 q^{67} -1.00000 q^{68} -2.00000 q^{69} -4.00000 q^{70} +1.00000 q^{72} +10.0000 q^{73} -2.00000 q^{74} +1.00000 q^{75} -4.00000 q^{76} +10.0000 q^{79} +2.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} -12.0000 q^{83} +2.00000 q^{84} -2.00000 q^{85} +6.00000 q^{87} +6.00000 q^{89} +2.00000 q^{90} +2.00000 q^{92} +8.00000 q^{94} -8.00000 q^{95} -1.00000 q^{96} -2.00000 q^{97} -3.00000 q^{98} +O(q^{100})\)

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
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) −1.00000 −0.408248
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 2.00000 0.632456
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −2.00000 −0.534522
\(15\) −2.00000 −0.516398
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) 1.00000 0.235702
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 2.00000 0.447214
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) −1.00000 −0.204124
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −2.00000 −0.377964
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −2.00000 −0.365148
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −1.00000 −0.171499
\(35\) −4.00000 −0.676123
\(36\) 1.00000 0.166667
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −4.00000 −0.648886
\(39\) 0 0
\(40\) 2.00000 0.316228
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 2.00000 0.308607
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 2.00000 0.298142
\(46\) 2.00000 0.294884
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.00000 −0.428571
\(50\) −1.00000 −0.141421
\(51\) 1.00000 0.140028
\(52\) 0 0
\(53\) −8.00000 −1.09888 −0.549442 0.835532i \(-0.685160\pi\)
−0.549442 + 0.835532i \(0.685160\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) 4.00000 0.529813
\(58\) −6.00000 −0.787839
\(59\) 1.00000 0.130189
\(60\) −2.00000 −0.258199
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −8.00000 −0.977356 −0.488678 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) −1.00000 −0.121268
\(69\) −2.00000 −0.240772
\(70\) −4.00000 −0.478091
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000 0.117851
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) −2.00000 −0.232495
\(75\) 1.00000 0.115470
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 2.00000 0.223607
\(81\) 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 \(0.728845\pi\)
\(84\) 2.00000 0.218218
\(85\) −2.00000 −0.216930
\(86\) 0 0
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) 2.00000 0.208514
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) −8.00000 −0.820783
\(96\) −1.00000 −0.102062
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 1.00000 0.0990148
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) 0 0
\(105\) 4.00000 0.390360
\(106\) −8.00000 −0.777029
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −18.0000 −1.72409 −0.862044 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) −2.00000 −0.188982
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 4.00000 0.374634
\(115\) 4.00000 0.373002
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) 1.00000 0.0920575
\(119\) 2.00000 0.183340
\(120\) −2.00000 −0.182574
\(121\) −11.0000 −1.00000
\(122\) −2.00000 −0.181071
\(123\) 10.0000 0.901670
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) −2.00000 −0.178174
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 0 0
\(133\) 8.00000 0.693688
\(134\) −8.00000 −0.691095
\(135\) −2.00000 −0.172133
\(136\) −1.00000 −0.0857493
\(137\) 14.0000 1.19610 0.598050 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) −2.00000 −0.170251
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −4.00000 −0.338062
\(141\) −8.00000 −0.673722
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −12.0000 −0.996546
\(146\) 10.0000 0.827606
\(147\) 3.00000 0.247436
\(148\) −2.00000 −0.164399
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 1.00000 0.0816497
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) −4.00000 −0.324443
\(153\) −1.00000 −0.0808452
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 4.00000 0.319235 0.159617 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) 10.0000 0.795557
\(159\) 8.00000 0.634441
\(160\) 2.00000 0.158114
\(161\) −4.00000 −0.315244
\(162\) 1.00000 0.0785674
\(163\) 16.0000 1.25322 0.626608 0.779334i \(-0.284443\pi\)
0.626608 + 0.779334i \(0.284443\pi\)
\(164\) −10.0000 −0.780869
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) −24.0000 −1.85718 −0.928588 0.371113i \(-0.878976\pi\)
−0.928588 + 0.371113i \(0.878976\pi\)
\(168\) 2.00000 0.154303
\(169\) −13.0000 −1.00000
\(170\) −2.00000 −0.153393
\(171\) −4.00000 −0.305888
\(172\) 0 0
\(173\) −4.00000 −0.304114 −0.152057 0.988372i \(-0.548590\pi\)
−0.152057 + 0.988372i \(0.548590\pi\)
\(174\) 6.00000 0.454859
\(175\) 2.00000 0.151186
\(176\) 0 0
\(177\) −1.00000 −0.0751646
\(178\) 6.00000 0.449719
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 2.00000 0.149071
\(181\) −4.00000 −0.297318 −0.148659 0.988889i \(-0.547496\pi\)
−0.148659 + 0.988889i \(0.547496\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 2.00000 0.147442
\(185\) −4.00000 −0.294086
\(186\) 0 0
\(187\) 0 0
\(188\) 8.00000 0.583460
\(189\) 2.00000 0.145479
\(190\) −8.00000 −0.580381
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −18.0000 −1.29567 −0.647834 0.761781i \(-0.724325\pi\)
−0.647834 + 0.761781i \(0.724325\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −22.0000 −1.55954 −0.779769 0.626067i \(-0.784664\pi\)
−0.779769 + 0.626067i \(0.784664\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 8.00000 0.564276
\(202\) −10.0000 −0.703598
\(203\) 12.0000 0.842235
\(204\) 1.00000 0.0700140
\(205\) −20.0000 −1.39686
\(206\) 10.0000 0.696733
\(207\) 2.00000 0.139010
\(208\) 0 0
\(209\) 0 0
\(210\) 4.00000 0.276026
\(211\) 28.0000 1.92760 0.963800 0.266627i \(-0.0859092\pi\)
0.963800 + 0.266627i \(0.0859092\pi\)
\(212\) −8.00000 −0.549442
\(213\) 0 0
\(214\) −4.00000 −0.273434
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −18.0000 −1.21911
\(219\) −10.0000 −0.675737
\(220\) 0 0
\(221\) 0 0
\(222\) 2.00000 0.134231
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) −2.00000 −0.133631
\(225\) −1.00000 −0.0666667
\(226\) 2.00000 0.133038
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 4.00000 0.264906
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 4.00000 0.263752
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) 16.0000 1.04372
\(236\) 1.00000 0.0650945
\(237\) −10.0000 −0.649570
\(238\) 2.00000 0.129641
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −2.00000 −0.129099
\(241\) 22.0000 1.41714 0.708572 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) −11.0000 −0.707107
\(243\) −1.00000 −0.0641500
\(244\) −2.00000 −0.128037
\(245\) −6.00000 −0.383326
\(246\) 10.0000 0.637577
\(247\) 0 0
\(248\) 0 0
\(249\) 12.0000 0.760469
\(250\) −12.0000 −0.758947
\(251\) 8.00000 0.504956 0.252478 0.967603i \(-0.418755\pi\)
0.252478 + 0.967603i \(0.418755\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) 4.00000 0.250982
\(255\) 2.00000 0.125245
\(256\) 1.00000 0.0625000
\(257\) 10.0000 0.623783 0.311891 0.950118i \(-0.399037\pi\)
0.311891 + 0.950118i \(0.399037\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) −8.00000 −0.494242
\(263\) −6.00000 −0.369976 −0.184988 0.982741i \(-0.559225\pi\)
−0.184988 + 0.982741i \(0.559225\pi\)
\(264\) 0 0
\(265\) −16.0000 −0.982872
\(266\) 8.00000 0.490511
\(267\) −6.00000 −0.367194
\(268\) −8.00000 −0.488678
\(269\) 8.00000 0.487769 0.243884 0.969804i \(-0.421578\pi\)
0.243884 + 0.969804i \(0.421578\pi\)
\(270\) −2.00000 −0.121716
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 0 0
\(274\) 14.0000 0.845771
\(275\) 0 0
\(276\) −2.00000 −0.120386
\(277\) −28.0000 −1.68236 −0.841178 0.540758i \(-0.818138\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) −4.00000 −0.239904
\(279\) 0 0
\(280\) −4.00000 −0.239046
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) −8.00000 −0.476393
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 0 0
\(285\) 8.00000 0.473879
\(286\) 0 0
\(287\) 20.0000 1.18056
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) −12.0000 −0.704664
\(291\) 2.00000 0.117242
\(292\) 10.0000 0.585206
\(293\) −16.0000 −0.934730 −0.467365 0.884064i \(-0.654797\pi\)
−0.467365 + 0.884064i \(0.654797\pi\)
\(294\) 3.00000 0.174964
\(295\) 2.00000 0.116445
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) 10.0000 0.575435
\(303\) 10.0000 0.574485
\(304\) −4.00000 −0.229416
\(305\) −4.00000 −0.229039
\(306\) −1.00000 −0.0571662
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) −10.0000 −0.568880
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 4.00000 0.225733
\(315\) −4.00000 −0.225374
\(316\) 10.0000 0.562544
\(317\) −2.00000 −0.112331 −0.0561656 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) 8.00000 0.448618
\(319\) 0 0
\(320\) 2.00000 0.111803
\(321\) 4.00000 0.223258
\(322\) −4.00000 −0.222911
\(323\) 4.00000 0.222566
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 16.0000 0.886158
\(327\) 18.0000 0.995402
\(328\) −10.0000 −0.552158
\(329\) −16.0000 −0.882109
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) −12.0000 −0.658586
\(333\) −2.00000 −0.109599
\(334\) −24.0000 −1.31322
\(335\) −16.0000 −0.874173
\(336\) 2.00000 0.109109
\(337\) −30.0000 −1.63420 −0.817102 0.576493i \(-0.804421\pi\)
−0.817102 + 0.576493i \(0.804421\pi\)
\(338\) −13.0000 −0.707107
\(339\) −2.00000 −0.108625
\(340\) −2.00000 −0.108465
\(341\) 0 0
\(342\) −4.00000 −0.216295
\(343\) 20.0000 1.07990
\(344\) 0 0
\(345\) −4.00000 −0.215353
\(346\) −4.00000 −0.215041
\(347\) −36.0000 −1.93258 −0.966291 0.257454i \(-0.917117\pi\)
−0.966291 + 0.257454i \(0.917117\pi\)
\(348\) 6.00000 0.321634
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) 0 0
\(353\) −30.0000 −1.59674 −0.798369 0.602168i \(-0.794304\pi\)
−0.798369 + 0.602168i \(0.794304\pi\)
\(354\) −1.00000 −0.0531494
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) −2.00000 −0.105851
\(358\) 4.00000 0.211407
\(359\) 6.00000 0.316668 0.158334 0.987386i \(-0.449388\pi\)
0.158334 + 0.987386i \(0.449388\pi\)
\(360\) 2.00000 0.105409
\(361\) −3.00000 −0.157895
\(362\) −4.00000 −0.210235
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 20.0000 1.04685
\(366\) 2.00000 0.104542
\(367\) 28.0000 1.46159 0.730794 0.682598i \(-0.239150\pi\)
0.730794 + 0.682598i \(0.239150\pi\)
\(368\) 2.00000 0.104257
\(369\) −10.0000 −0.520579
\(370\) −4.00000 −0.207950
\(371\) 16.0000 0.830679
\(372\) 0 0
\(373\) −6.00000 −0.310668 −0.155334 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) 0 0
\(375\) 12.0000 0.619677
\(376\) 8.00000 0.412568
\(377\) 0 0
\(378\) 2.00000 0.102869
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) −8.00000 −0.410391
\(381\) −4.00000 −0.204926
\(382\) −8.00000 −0.409316
\(383\) −22.0000 −1.12415 −0.562074 0.827087i \(-0.689996\pi\)
−0.562074 + 0.827087i \(0.689996\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −18.0000 −0.916176
\(387\) 0 0
\(388\) −2.00000 −0.101535
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) −2.00000 −0.101144
\(392\) −3.00000 −0.151523
\(393\) 8.00000 0.403547
\(394\) −18.0000 −0.906827
\(395\) 20.0000 1.00631
\(396\) 0 0
\(397\) −6.00000 −0.301131 −0.150566 0.988600i \(-0.548110\pi\)
−0.150566 + 0.988600i \(0.548110\pi\)
\(398\) −22.0000 −1.10276
\(399\) −8.00000 −0.400501
\(400\) −1.00000 −0.0500000
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 8.00000 0.399004
\(403\) 0 0
\(404\) −10.0000 −0.497519
\(405\) 2.00000 0.0993808
\(406\) 12.0000 0.595550
\(407\) 0 0
\(408\) 1.00000 0.0495074
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) −20.0000 −0.987730
\(411\) −14.0000 −0.690569
\(412\) 10.0000 0.492665
\(413\) −2.00000 −0.0984136
\(414\) 2.00000 0.0982946
\(415\) −24.0000 −1.17811
\(416\) 0 0
\(417\) 4.00000 0.195881
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 4.00000 0.195180
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) 28.0000 1.36302
\(423\) 8.00000 0.388973
\(424\) −8.00000 −0.388514
\(425\) 1.00000 0.0485071
\(426\) 0 0
\(427\) 4.00000 0.193574
\(428\) −4.00000 −0.193347
\(429\) 0 0
\(430\) 0 0
\(431\) −38.0000 −1.83040 −0.915198 0.403005i \(-0.867966\pi\)
−0.915198 + 0.403005i \(0.867966\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 12.0000 0.575356
\(436\) −18.0000 −0.862044
\(437\) −8.00000 −0.382692
\(438\) −10.0000 −0.477818
\(439\) −30.0000 −1.43182 −0.715911 0.698192i \(-0.753988\pi\)
−0.715911 + 0.698192i \(0.753988\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) −12.0000 −0.570137 −0.285069 0.958507i \(-0.592016\pi\)
−0.285069 + 0.958507i \(0.592016\pi\)
\(444\) 2.00000 0.0949158
\(445\) 12.0000 0.568855
\(446\) −4.00000 −0.189405
\(447\) −6.00000 −0.283790
\(448\) −2.00000 −0.0944911
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 0 0
\(452\) 2.00000 0.0940721
\(453\) −10.0000 −0.469841
\(454\) 0 0
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 22.0000 1.02912 0.514558 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) 0 0
\(459\) 1.00000 0.0466760
\(460\) 4.00000 0.186501
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 18.0000 0.836531 0.418265 0.908325i \(-0.362638\pi\)
0.418265 + 0.908325i \(0.362638\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) 18.0000 0.833834
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) 16.0000 0.738811
\(470\) 16.0000 0.738025
\(471\) −4.00000 −0.184310
\(472\) 1.00000 0.0460287
\(473\) 0 0
\(474\) −10.0000 −0.459315
\(475\) 4.00000 0.183533
\(476\) 2.00000 0.0916698
\(477\) −8.00000 −0.366295
\(478\) 6.00000 0.274434
\(479\) −12.0000 −0.548294 −0.274147 0.961688i \(-0.588395\pi\)
−0.274147 + 0.961688i \(0.588395\pi\)
\(480\) −2.00000 −0.0912871
\(481\) 0 0
\(482\) 22.0000 1.00207
\(483\) 4.00000 0.182006
\(484\) −11.0000 −0.500000
\(485\) −4.00000 −0.181631
\(486\) −1.00000 −0.0453609
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) −2.00000 −0.0905357
\(489\) −16.0000 −0.723545
\(490\) −6.00000 −0.271052
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 10.0000 0.450835
\(493\) 6.00000 0.270226
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) 16.0000 0.716258 0.358129 0.933672i \(-0.383415\pi\)
0.358129 + 0.933672i \(0.383415\pi\)
\(500\) −12.0000 −0.536656
\(501\) 24.0000 1.07224
\(502\) 8.00000 0.357057
\(503\) 34.0000 1.51599 0.757993 0.652263i \(-0.226180\pi\)
0.757993 + 0.652263i \(0.226180\pi\)
\(504\) −2.00000 −0.0890871
\(505\) −20.0000 −0.889988
\(506\) 0 0
\(507\) 13.0000 0.577350
\(508\) 4.00000 0.177471
\(509\) 42.0000 1.86162 0.930809 0.365507i \(-0.119104\pi\)
0.930809 + 0.365507i \(0.119104\pi\)
\(510\) 2.00000 0.0885615
\(511\) −20.0000 −0.884748
\(512\) 1.00000 0.0441942
\(513\) 4.00000 0.176604
\(514\) 10.0000 0.441081
\(515\) 20.0000 0.881305
\(516\) 0 0
\(517\) 0 0
\(518\) 4.00000 0.175750
\(519\) 4.00000 0.175581
\(520\) 0 0
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −6.00000 −0.262613
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) −8.00000 −0.349482
\(525\) −2.00000 −0.0872872
\(526\) −6.00000 −0.261612
\(527\) 0 0
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) −16.0000 −0.694996
\(531\) 1.00000 0.0433963
\(532\) 8.00000 0.346844
\(533\) 0 0
\(534\) −6.00000 −0.259645
\(535\) −8.00000 −0.345870
\(536\) −8.00000 −0.345547
\(537\) −4.00000 −0.172613
\(538\) 8.00000 0.344904
\(539\) 0 0
\(540\) −2.00000 −0.0860663
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 8.00000 0.343629
\(543\) 4.00000 0.171656
\(544\) −1.00000 −0.0428746
\(545\) −36.0000 −1.54207
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 14.0000 0.598050
\(549\) −2.00000 −0.0853579
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) −2.00000 −0.0851257
\(553\) −20.0000 −0.850487
\(554\) −28.0000 −1.18961
\(555\) 4.00000 0.169791
\(556\) −4.00000 −0.169638
\(557\) 36.0000 1.52537 0.762684 0.646771i \(-0.223881\pi\)
0.762684 + 0.646771i \(0.223881\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −4.00000 −0.169031
\(561\) 0 0
\(562\) −6.00000 −0.253095
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) −8.00000 −0.336861
\(565\) 4.00000 0.168281
\(566\) −4.00000 −0.168133
\(567\) −2.00000 −0.0839921
\(568\) 0 0
\(569\) 22.0000 0.922288 0.461144 0.887325i \(-0.347439\pi\)
0.461144 + 0.887325i \(0.347439\pi\)
\(570\) 8.00000 0.335083
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 0 0
\(573\) 8.00000 0.334205
\(574\) 20.0000 0.834784
\(575\) −2.00000 −0.0834058
\(576\) 1.00000 0.0416667
\(577\) 22.0000 0.915872 0.457936 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) 1.00000 0.0415945
\(579\) 18.0000 0.748054
\(580\) −12.0000 −0.498273
\(581\) 24.0000 0.995688
\(582\) 2.00000 0.0829027
\(583\) 0 0
\(584\) 10.0000 0.413803
\(585\) 0 0
\(586\) −16.0000 −0.660954
\(587\) 28.0000 1.15568 0.577842 0.816149i \(-0.303895\pi\)
0.577842 + 0.816149i \(0.303895\pi\)
\(588\) 3.00000 0.123718
\(589\) 0 0
\(590\) 2.00000 0.0823387
\(591\) 18.0000 0.740421
\(592\) −2.00000 −0.0821995
\(593\) 2.00000 0.0821302 0.0410651 0.999156i \(-0.486925\pi\)
0.0410651 + 0.999156i \(0.486925\pi\)
\(594\) 0 0
\(595\) 4.00000 0.163984
\(596\) 6.00000 0.245770
\(597\) 22.0000 0.900400
\(598\) 0 0
\(599\) 26.0000 1.06233 0.531166 0.847268i \(-0.321754\pi\)
0.531166 + 0.847268i \(0.321754\pi\)
\(600\) 1.00000 0.0408248
\(601\) 30.0000 1.22373 0.611863 0.790964i \(-0.290420\pi\)
0.611863 + 0.790964i \(0.290420\pi\)
\(602\) 0 0
\(603\) −8.00000 −0.325785
\(604\) 10.0000 0.406894
\(605\) −22.0000 −0.894427
\(606\) 10.0000 0.406222
\(607\) −26.0000 −1.05531 −0.527654 0.849460i \(-0.676928\pi\)
−0.527654 + 0.849460i \(0.676928\pi\)
\(608\) −4.00000 −0.162221
\(609\) −12.0000 −0.486265
\(610\) −4.00000 −0.161955
\(611\) 0 0
\(612\) −1.00000 −0.0404226
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 20.0000 0.807134
\(615\) 20.0000 0.806478
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) −10.0000 −0.402259
\(619\) −44.0000 −1.76851 −0.884255 0.467005i \(-0.845333\pi\)
−0.884255 + 0.467005i \(0.845333\pi\)
\(620\) 0 0
\(621\) −2.00000 −0.0802572
\(622\) 24.0000 0.962312
\(623\) −12.0000 −0.480770
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) −10.0000 −0.399680
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) 2.00000 0.0797452
\(630\) −4.00000 −0.159364
\(631\) −12.0000 −0.477712 −0.238856 0.971055i \(-0.576772\pi\)
−0.238856 + 0.971055i \(0.576772\pi\)
\(632\) 10.0000 0.397779
\(633\) −28.0000 −1.11290
\(634\) −2.00000 −0.0794301
\(635\) 8.00000 0.317470
\(636\) 8.00000 0.317221
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 2.00000 0.0790569
\(641\) 46.0000 1.81689 0.908445 0.418004i \(-0.137270\pi\)
0.908445 + 0.418004i \(0.137270\pi\)
\(642\) 4.00000 0.157867
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) −4.00000 −0.157622
\(645\) 0 0
\(646\) 4.00000 0.157378
\(647\) −2.00000 −0.0786281 −0.0393141 0.999227i \(-0.512517\pi\)
−0.0393141 + 0.999227i \(0.512517\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 16.0000 0.626608
\(653\) 26.0000 1.01746 0.508729 0.860927i \(-0.330115\pi\)
0.508729 + 0.860927i \(0.330115\pi\)
\(654\) 18.0000 0.703856
\(655\) −16.0000 −0.625172
\(656\) −10.0000 −0.390434
\(657\) 10.0000 0.390137
\(658\) −16.0000 −0.623745
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 0 0
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) 4.00000 0.155464
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 16.0000 0.620453
\(666\) −2.00000 −0.0774984
\(667\) −12.0000 −0.464642
\(668\) −24.0000 −0.928588
\(669\) 4.00000 0.154649
\(670\) −16.0000 −0.618134
\(671\) 0 0
\(672\) 2.00000 0.0771517
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) −30.0000 −1.15556
\(675\) 1.00000 0.0384900
\(676\) −13.0000 −0.500000
\(677\) 2.00000 0.0768662 0.0384331 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) −2.00000 −0.0768095
\(679\) 4.00000 0.153506
\(680\) −2.00000 −0.0766965
\(681\) 0 0
\(682\) 0 0
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) −4.00000 −0.152944
\(685\) 28.0000 1.06983
\(686\) 20.0000 0.763604
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) −4.00000 −0.152277
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) −4.00000 −0.152057
\(693\) 0 0
\(694\) −36.0000 −1.36654
\(695\) −8.00000 −0.303457
\(696\) 6.00000 0.227429
\(697\) 10.0000 0.378777
\(698\) −28.0000 −1.05982
\(699\) −18.0000 −0.680823
\(700\) 2.00000 0.0755929
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) −16.0000 −0.602595
\(706\) −30.0000 −1.12906
\(707\) 20.0000 0.752177
\(708\) −1.00000 −0.0375823
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 10.0000 0.375029
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) −2.00000 −0.0748481
\(715\) 0 0
\(716\) 4.00000 0.149487
\(717\) −6.00000 −0.224074
\(718\) 6.00000 0.223918
\(719\) 22.0000 0.820462 0.410231 0.911982i \(-0.365448\pi\)
0.410231 + 0.911982i \(0.365448\pi\)
\(720\) 2.00000 0.0745356
\(721\) −20.0000 −0.744839
\(722\) −3.00000 −0.111648
\(723\) −22.0000 −0.818189
\(724\) −4.00000 −0.148659
\(725\) 6.00000 0.222834
\(726\) 11.0000 0.408248
\(727\) −44.0000 −1.63187 −0.815935 0.578144i \(-0.803777\pi\)
−0.815935 + 0.578144i \(0.803777\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 20.0000 0.740233
\(731\) 0 0
\(732\) 2.00000 0.0739221
\(733\) 22.0000 0.812589 0.406294 0.913742i \(-0.366821\pi\)
0.406294 + 0.913742i \(0.366821\pi\)
\(734\) 28.0000 1.03350
\(735\) 6.00000 0.221313
\(736\) 2.00000 0.0737210
\(737\) 0 0
\(738\) −10.0000 −0.368105
\(739\) −12.0000 −0.441427 −0.220714 0.975339i \(-0.570839\pi\)
−0.220714 + 0.975339i \(0.570839\pi\)
\(740\) −4.00000 −0.147043
\(741\) 0 0
\(742\) 16.0000 0.587378
\(743\) −12.0000 −0.440237 −0.220119 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 0 0
\(745\) 12.0000 0.439646
\(746\) −6.00000 −0.219676
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) 8.00000 0.292314
\(750\) 12.0000 0.438178
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) 8.00000 0.291730
\(753\) −8.00000 −0.291536
\(754\) 0 0
\(755\) 20.0000 0.727875
\(756\) 2.00000 0.0727393
\(757\) −42.0000 −1.52652 −0.763258 0.646094i \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) −8.00000 −0.290191
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) −4.00000 −0.144905
\(763\) 36.0000 1.30329
\(764\) −8.00000 −0.289430
\(765\) −2.00000 −0.0723102
\(766\) −22.0000 −0.794892
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) 0 0
\(771\) −10.0000 −0.360141
\(772\) −18.0000 −0.647834
\(773\) 2.00000 0.0719350 0.0359675 0.999353i \(-0.488549\pi\)
0.0359675 + 0.999353i \(0.488549\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −2.00000 −0.0717958
\(777\) −4.00000 −0.143499
\(778\) 0 0
\(779\) 40.0000 1.43315
\(780\) 0 0
\(781\) 0 0
\(782\) −2.00000 −0.0715199
\(783\) 6.00000 0.214423
\(784\) −3.00000 −0.107143
\(785\) 8.00000 0.285532
\(786\) 8.00000 0.285351
\(787\) 20.0000 0.712923 0.356462 0.934310i \(-0.383983\pi\)
0.356462 + 0.934310i \(0.383983\pi\)
\(788\) −18.0000 −0.641223
\(789\) 6.00000 0.213606
\(790\) 20.0000 0.711568
\(791\) −4.00000 −0.142224
\(792\) 0 0
\(793\) 0 0
\(794\) −6.00000 −0.212932
\(795\) 16.0000 0.567462
\(796\) −22.0000 −0.779769
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) −8.00000 −0.283197
\(799\) −8.00000 −0.283020
\(800\) −1.00000 −0.0353553
\(801\) 6.00000 0.212000
\(802\) 6.00000 0.211867
\(803\) 0 0
\(804\) 8.00000 0.282138
\(805\) −8.00000 −0.281963
\(806\) 0 0
\(807\) −8.00000 −0.281613
\(808\) −10.0000 −0.351799
\(809\) 30.0000 1.05474 0.527372 0.849635i \(-0.323177\pi\)
0.527372 + 0.849635i \(0.323177\pi\)
\(810\) 2.00000 0.0702728
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 12.0000 0.421117
\(813\) −8.00000 −0.280572
\(814\) 0 0
\(815\) 32.0000 1.12091
\(816\) 1.00000 0.0350070
\(817\) 0 0
\(818\) 14.0000 0.489499
\(819\) 0 0
\(820\) −20.0000 −0.698430
\(821\) 12.0000 0.418803 0.209401 0.977830i \(-0.432848\pi\)
0.209401 + 0.977830i \(0.432848\pi\)
\(822\) −14.0000 −0.488306
\(823\) −12.0000 −0.418294 −0.209147 0.977884i \(-0.567069\pi\)
−0.209147 + 0.977884i \(0.567069\pi\)
\(824\) 10.0000 0.348367
\(825\) 0 0
\(826\) −2.00000 −0.0695889
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 2.00000 0.0695048
\(829\) −10.0000 −0.347314 −0.173657 0.984806i \(-0.555558\pi\)
−0.173657 + 0.984806i \(0.555558\pi\)
\(830\) −24.0000 −0.833052
\(831\) 28.0000 0.971309
\(832\) 0 0
\(833\) 3.00000 0.103944
\(834\) 4.00000 0.138509
\(835\) −48.0000 −1.66111
\(836\) 0 0
\(837\) 0 0
\(838\) 24.0000 0.829066
\(839\) 22.0000 0.759524 0.379762 0.925084i \(-0.376006\pi\)
0.379762 + 0.925084i \(0.376006\pi\)
\(840\) 4.00000 0.138013
\(841\) 7.00000 0.241379
\(842\) 32.0000 1.10279
\(843\) 6.00000 0.206651
\(844\) 28.0000 0.963800
\(845\) −26.0000 −0.894427
\(846\) 8.00000 0.275046
\(847\) 22.0000 0.755929
\(848\) −8.00000 −0.274721
\(849\) 4.00000 0.137280
\(850\) 1.00000 0.0342997
\(851\) −4.00000 −0.137118
\(852\) 0 0
\(853\) −52.0000 −1.78045 −0.890223 0.455525i \(-0.849452\pi\)
−0.890223 + 0.455525i \(0.849452\pi\)
\(854\) 4.00000 0.136877
\(855\) −8.00000 −0.273594
\(856\) −4.00000 −0.136717
\(857\) −42.0000 −1.43469 −0.717346 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) 0 0
\(859\) 20.0000 0.682391 0.341196 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 0 0
\(861\) −20.0000 −0.681598
\(862\) −38.0000 −1.29429
\(863\) 4.00000 0.136162 0.0680808 0.997680i \(-0.478312\pi\)
0.0680808 + 0.997680i \(0.478312\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −8.00000 −0.272008
\(866\) −14.0000 −0.475739
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) 0 0
\(870\) 12.0000 0.406838
\(871\) 0 0
\(872\) −18.0000 −0.609557
\(873\) −2.00000 −0.0676897
\(874\) −8.00000 −0.270604
\(875\) 24.0000 0.811348
\(876\) −10.0000 −0.337869
\(877\) −36.0000 −1.21563 −0.607817 0.794077i \(-0.707955\pi\)
−0.607817 + 0.794077i \(0.707955\pi\)
\(878\) −30.0000 −1.01245
\(879\) 16.0000 0.539667
\(880\) 0 0
\(881\) −30.0000 −1.01073 −0.505363 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) −3.00000 −0.101015
\(883\) −52.0000 −1.74994 −0.874970 0.484178i \(-0.839119\pi\)
−0.874970 + 0.484178i \(0.839119\pi\)
\(884\) 0 0
\(885\) −2.00000 −0.0672293
\(886\) −12.0000 −0.403148
\(887\) 26.0000 0.872995 0.436497 0.899706i \(-0.356219\pi\)
0.436497 + 0.899706i \(0.356219\pi\)
\(888\) 2.00000 0.0671156
\(889\) −8.00000 −0.268311
\(890\) 12.0000 0.402241
\(891\) 0 0
\(892\) −4.00000 −0.133930
\(893\) −32.0000 −1.07084
\(894\) −6.00000 −0.200670
\(895\) 8.00000 0.267411
\(896\) −2.00000 −0.0668153
\(897\) 0 0
\(898\) −6.00000 −0.200223
\(899\) 0 0
\(900\) −1.00000 −0.0333333
\(901\) 8.00000 0.266519
\(902\) 0 0
\(903\) 0 0
\(904\) 2.00000 0.0665190
\(905\) −8.00000 −0.265929
\(906\) −10.0000 −0.332228
\(907\) 52.0000 1.72663 0.863316 0.504664i \(-0.168384\pi\)
0.863316 + 0.504664i \(0.168384\pi\)
\(908\) 0 0
\(909\) −10.0000 −0.331679
\(910\) 0 0
\(911\) −40.0000 −1.32526 −0.662630 0.748947i \(-0.730560\pi\)
−0.662630 + 0.748947i \(0.730560\pi\)
\(912\) 4.00000 0.132453
\(913\) 0 0
\(914\) 22.0000 0.727695
\(915\) 4.00000 0.132236
\(916\) 0 0
\(917\) 16.0000 0.528367
\(918\) 1.00000 0.0330049
\(919\) 50.0000 1.64935 0.824674 0.565608i \(-0.191359\pi\)
0.824674 + 0.565608i \(0.191359\pi\)
\(920\) 4.00000 0.131876
\(921\) −20.0000 −0.659022
\(922\) −12.0000 −0.395199
\(923\) 0 0
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) 18.0000 0.591517
\(927\) 10.0000 0.328443
\(928\) −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
\(931\) 12.0000 0.393284
\(932\) 18.0000 0.589610
\(933\) −24.0000 −0.785725
\(934\) 12.0000 0.392652
\(935\) 0 0
\(936\) 0 0
\(937\) 58.0000 1.89478 0.947389 0.320085i \(-0.103712\pi\)
0.947389 + 0.320085i \(0.103712\pi\)
\(938\) 16.0000 0.522419
\(939\) 10.0000 0.326338
\(940\) 16.0000 0.521862
\(941\) −8.00000 −0.260793 −0.130396 0.991462i \(-0.541625\pi\)
−0.130396 + 0.991462i \(0.541625\pi\)
\(942\) −4.00000 −0.130327
\(943\) −20.0000 −0.651290
\(944\) 1.00000 0.0325472
\(945\) 4.00000 0.130120
\(946\) 0 0
\(947\) −52.0000 −1.68977 −0.844886 0.534946i \(-0.820332\pi\)
−0.844886 + 0.534946i \(0.820332\pi\)
\(948\) −10.0000 −0.324785
\(949\) 0 0
\(950\) 4.00000 0.129777
\(951\) 2.00000 0.0648544
\(952\) 2.00000 0.0648204
\(953\) 30.0000 0.971795 0.485898 0.874016i \(-0.338493\pi\)
0.485898 + 0.874016i \(0.338493\pi\)
\(954\) −8.00000 −0.259010
\(955\) −16.0000 −0.517748
\(956\) 6.00000 0.194054
\(957\) 0 0
\(958\) −12.0000 −0.387702
\(959\) −28.0000 −0.904167
\(960\) −2.00000 −0.0645497
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) −4.00000 −0.128898
\(964\) 22.0000 0.708572
\(965\) −36.0000 −1.15888
\(966\) 4.00000 0.128698
\(967\) 54.0000 1.73652 0.868261 0.496107i \(-0.165238\pi\)
0.868261 + 0.496107i \(0.165238\pi\)
\(968\) −11.0000 −0.353553
\(969\) −4.00000 −0.128499
\(970\) −4.00000 −0.128432
\(971\) 56.0000 1.79713 0.898563 0.438845i \(-0.144612\pi\)
0.898563 + 0.438845i \(0.144612\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 8.00000 0.256468
\(974\) −2.00000 −0.0640841
\(975\) 0 0
\(976\) −2.00000 −0.0640184
\(977\) −34.0000 −1.08776 −0.543878 0.839164i \(-0.683045\pi\)
−0.543878 + 0.839164i \(0.683045\pi\)
\(978\) −16.0000 −0.511624
\(979\) 0 0
\(980\) −6.00000 −0.191663
\(981\) −18.0000 −0.574696
\(982\) −12.0000 −0.382935
\(983\) −2.00000 −0.0637901 −0.0318950 0.999491i \(-0.510154\pi\)
−0.0318950 + 0.999491i \(0.510154\pi\)
\(984\) 10.0000 0.318788
\(985\) −36.0000 −1.14706
\(986\) 6.00000 0.191079
\(987\) 16.0000 0.509286
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) −4.00000 −0.126936
\(994\) 0 0
\(995\) −44.0000 −1.39489
\(996\) 12.0000 0.380235
\(997\) −48.0000 −1.52018 −0.760088 0.649821i \(-0.774844\pi\)
−0.760088 + 0.649821i \(0.774844\pi\)
\(998\) 16.0000 0.506471
\(999\) 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.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.h.1.1 1 1.1 even 1 trivial