Properties

Label 5610.2.a.t.1.1
Level $5610$
Weight $2$
Character 5610.1
Self dual yes
Analytic conductor $44.796$
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] = [5610,2,Mod(1,5610)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5610, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5610.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5610.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: \(44.7960755339\)
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 \(\chi\) \(=\) 5610.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} -2.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +8.00000 q^{19} +1.00000 q^{20} +2.00000 q^{21} +1.00000 q^{22} -1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} +2.00000 q^{28} +6.00000 q^{29} -1.00000 q^{30} +8.00000 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +2.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -8.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} -2.00000 q^{42} -10.0000 q^{43} -1.00000 q^{44} +1.00000 q^{45} +1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} -4.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} -1.00000 q^{55} -2.00000 q^{56} +8.00000 q^{57} -6.00000 q^{58} -6.00000 q^{59} +1.00000 q^{60} +2.00000 q^{61} -8.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} +1.00000 q^{66} +2.00000 q^{67} +1.00000 q^{68} -2.00000 q^{70} -6.00000 q^{71} -1.00000 q^{72} +8.00000 q^{73} -2.00000 q^{74} +1.00000 q^{75} +8.00000 q^{76} -2.00000 q^{77} +4.00000 q^{78} +8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{84} +1.00000 q^{85} +10.0000 q^{86} +6.00000 q^{87} +1.00000 q^{88} +6.00000 q^{89} -1.00000 q^{90} -8.00000 q^{91} +8.00000 q^{93} +8.00000 q^{95} -1.00000 q^{96} +8.00000 q^{97} +3.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
\(5\) 1.00000 0.447214
\(6\) −1.00000 −0.408248
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) −1.00000 −0.301511
\(12\) 1.00000 0.288675
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −2.00000 −0.534522
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) −1.00000 −0.235702
\(19\) 8.00000 1.83533 0.917663 0.397360i \(-0.130073\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 1.00000 0.223607
\(21\) 2.00000 0.436436
\(22\) 1.00000 0.213201
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 4.00000 0.784465
\(27\) 1.00000 0.192450
\(28\) 2.00000 0.377964
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) −1.00000 −0.182574
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) −1.00000 −0.171499
\(35\) 2.00000 0.338062
\(36\) 1.00000 0.166667
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −8.00000 −1.29777
\(39\) −4.00000 −0.640513
\(40\) −1.00000 −0.158114
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −2.00000 −0.308607
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) −1.00000 −0.150756
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) −1.00000 −0.141421
\(51\) 1.00000 0.140028
\(52\) −4.00000 −0.554700
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −1.00000 −0.136083
\(55\) −1.00000 −0.134840
\(56\) −2.00000 −0.267261
\(57\) 8.00000 1.05963
\(58\) −6.00000 −0.787839
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 1.00000 0.129099
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −8.00000 −1.01600
\(63\) 2.00000 0.251976
\(64\) 1.00000 0.125000
\(65\) −4.00000 −0.496139
\(66\) 1.00000 0.123091
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 1.00000 0.121268
\(69\) 0 0
\(70\) −2.00000 −0.239046
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) −1.00000 −0.117851
\(73\) 8.00000 0.936329 0.468165 0.883641i \(-0.344915\pi\)
0.468165 + 0.883641i \(0.344915\pi\)
\(74\) −2.00000 −0.232495
\(75\) 1.00000 0.115470
\(76\) 8.00000 0.917663
\(77\) −2.00000 −0.227921
\(78\) 4.00000 0.452911
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 2.00000 0.218218
\(85\) 1.00000 0.108465
\(86\) 10.0000 1.07833
\(87\) 6.00000 0.643268
\(88\) 1.00000 0.106600
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −1.00000 −0.105409
\(91\) −8.00000 −0.838628
\(92\) 0 0
\(93\) 8.00000 0.829561
\(94\) 0 0
\(95\) 8.00000 0.820783
\(96\) −1.00000 −0.102062
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 3.00000 0.303046
\(99\) −1.00000 −0.100504
\(100\) 1.00000 0.100000
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) −1.00000 −0.0990148
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 4.00000 0.392232
\(105\) 2.00000 0.195180
\(106\) 6.00000 0.582772
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 1.00000 0.0962250
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 1.00000 0.0953463
\(111\) 2.00000 0.189832
\(112\) 2.00000 0.188982
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) −8.00000 −0.749269
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) −4.00000 −0.369800
\(118\) 6.00000 0.552345
\(119\) 2.00000 0.183340
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 0.0909091
\(122\) −2.00000 −0.181071
\(123\) 0 0
\(124\) 8.00000 0.718421
\(125\) 1.00000 0.0894427
\(126\) −2.00000 −0.178174
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −10.0000 −0.880451
\(130\) 4.00000 0.350823
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 16.0000 1.38738
\(134\) −2.00000 −0.172774
\(135\) 1.00000 0.0860663
\(136\) −1.00000 −0.0857493
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 2.00000 0.169031
\(141\) 0 0
\(142\) 6.00000 0.503509
\(143\) 4.00000 0.334497
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) −8.00000 −0.662085
\(147\) −3.00000 −0.247436
\(148\) 2.00000 0.164399
\(149\) −12.0000 −0.983078 −0.491539 0.870855i \(-0.663566\pi\)
−0.491539 + 0.870855i \(0.663566\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −8.00000 −0.648886
\(153\) 1.00000 0.0808452
\(154\) 2.00000 0.161165
\(155\) 8.00000 0.642575
\(156\) −4.00000 −0.320256
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) −8.00000 −0.636446
\(159\) −6.00000 −0.475831
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 8.00000 0.626608 0.313304 0.949653i \(-0.398564\pi\)
0.313304 + 0.949653i \(0.398564\pi\)
\(164\) 0 0
\(165\) −1.00000 −0.0778499
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) −2.00000 −0.154303
\(169\) 3.00000 0.230769
\(170\) −1.00000 −0.0766965
\(171\) 8.00000 0.611775
\(172\) −10.0000 −0.762493
\(173\) 18.0000 1.36851 0.684257 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) −6.00000 −0.454859
\(175\) 2.00000 0.151186
\(176\) −1.00000 −0.0753778
\(177\) −6.00000 −0.450988
\(178\) −6.00000 −0.449719
\(179\) −18.0000 −1.34538 −0.672692 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 1.00000 0.0745356
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 8.00000 0.592999
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 2.00000 0.147043
\(186\) −8.00000 −0.586588
\(187\) −1.00000 −0.0731272
\(188\) 0 0
\(189\) 2.00000 0.145479
\(190\) −8.00000 −0.580381
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 1.00000 0.0721688
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) −8.00000 −0.574367
\(195\) −4.00000 −0.286446
\(196\) −3.00000 −0.214286
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 1.00000 0.0710669
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 2.00000 0.141069
\(202\) −12.0000 −0.844317
\(203\) 12.0000 0.842235
\(204\) 1.00000 0.0700140
\(205\) 0 0
\(206\) 4.00000 0.278693
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) −8.00000 −0.553372
\(210\) −2.00000 −0.138013
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −6.00000 −0.412082
\(213\) −6.00000 −0.411113
\(214\) −12.0000 −0.820303
\(215\) −10.0000 −0.681994
\(216\) −1.00000 −0.0680414
\(217\) 16.0000 1.08615
\(218\) −14.0000 −0.948200
\(219\) 8.00000 0.540590
\(220\) −1.00000 −0.0674200
\(221\) −4.00000 −0.269069
\(222\) −2.00000 −0.134231
\(223\) −28.0000 −1.87502 −0.937509 0.347960i \(-0.886874\pi\)
−0.937509 + 0.347960i \(0.886874\pi\)
\(224\) −2.00000 −0.133631
\(225\) 1.00000 0.0666667
\(226\) 6.00000 0.399114
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 8.00000 0.529813
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) −2.00000 −0.131590
\(232\) −6.00000 −0.393919
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 4.00000 0.261488
\(235\) 0 0
\(236\) −6.00000 −0.390567
\(237\) 8.00000 0.519656
\(238\) −2.00000 −0.129641
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 1.00000 0.0645497
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) 2.00000 0.128037
\(245\) −3.00000 −0.191663
\(246\) 0 0
\(247\) −32.0000 −2.03611
\(248\) −8.00000 −0.508001
\(249\) 0 0
\(250\) −1.00000 −0.0632456
\(251\) −6.00000 −0.378717 −0.189358 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) 4.00000 0.250982
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 10.0000 0.622573
\(259\) 4.00000 0.248548
\(260\) −4.00000 −0.248069
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 1.00000 0.0615457
\(265\) −6.00000 −0.368577
\(266\) −16.0000 −0.981023
\(267\) 6.00000 0.367194
\(268\) 2.00000 0.122169
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 1.00000 0.0606339
\(273\) −8.00000 −0.484182
\(274\) 6.00000 0.362473
\(275\) −1.00000 −0.0603023
\(276\) 0 0
\(277\) 14.0000 0.841178 0.420589 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 4.00000 0.239904
\(279\) 8.00000 0.478947
\(280\) −2.00000 −0.119523
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 20.0000 1.18888 0.594438 0.804141i \(-0.297374\pi\)
0.594438 + 0.804141i \(0.297374\pi\)
\(284\) −6.00000 −0.356034
\(285\) 8.00000 0.473879
\(286\) −4.00000 −0.236525
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −6.00000 −0.352332
\(291\) 8.00000 0.468968
\(292\) 8.00000 0.468165
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 3.00000 0.174964
\(295\) −6.00000 −0.349334
\(296\) −2.00000 −0.116248
\(297\) −1.00000 −0.0580259
\(298\) 12.0000 0.695141
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) −20.0000 −1.15278
\(302\) −8.00000 −0.460348
\(303\) 12.0000 0.689382
\(304\) 8.00000 0.458831
\(305\) 2.00000 0.114520
\(306\) −1.00000 −0.0571662
\(307\) 14.0000 0.799022 0.399511 0.916728i \(-0.369180\pi\)
0.399511 + 0.916728i \(0.369180\pi\)
\(308\) −2.00000 −0.113961
\(309\) −4.00000 −0.227552
\(310\) −8.00000 −0.454369
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 4.00000 0.226455
\(313\) 8.00000 0.452187 0.226093 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) −8.00000 −0.451466
\(315\) 2.00000 0.112687
\(316\) 8.00000 0.450035
\(317\) −30.0000 −1.68497 −0.842484 0.538721i \(-0.818908\pi\)
−0.842484 + 0.538721i \(0.818908\pi\)
\(318\) 6.00000 0.336463
\(319\) −6.00000 −0.335936
\(320\) 1.00000 0.0559017
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 1.00000 0.0555556
\(325\) −4.00000 −0.221880
\(326\) −8.00000 −0.443079
\(327\) 14.0000 0.774202
\(328\) 0 0
\(329\) 0 0
\(330\) 1.00000 0.0550482
\(331\) 32.0000 1.75888 0.879440 0.476011i \(-0.157918\pi\)
0.879440 + 0.476011i \(0.157918\pi\)
\(332\) 0 0
\(333\) 2.00000 0.109599
\(334\) 0 0
\(335\) 2.00000 0.109272
\(336\) 2.00000 0.109109
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) −3.00000 −0.163178
\(339\) −6.00000 −0.325875
\(340\) 1.00000 0.0542326
\(341\) −8.00000 −0.433224
\(342\) −8.00000 −0.432590
\(343\) −20.0000 −1.07990
\(344\) 10.0000 0.539164
\(345\) 0 0
\(346\) −18.0000 −0.967686
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 6.00000 0.321634
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) −2.00000 −0.106904
\(351\) −4.00000 −0.213504
\(352\) 1.00000 0.0533002
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 6.00000 0.318896
\(355\) −6.00000 −0.318447
\(356\) 6.00000 0.317999
\(357\) 2.00000 0.105851
\(358\) 18.0000 0.951330
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 45.0000 2.36842
\(362\) −14.0000 −0.735824
\(363\) 1.00000 0.0524864
\(364\) −8.00000 −0.419314
\(365\) 8.00000 0.418739
\(366\) −2.00000 −0.104542
\(367\) 26.0000 1.35719 0.678594 0.734513i \(-0.262589\pi\)
0.678594 + 0.734513i \(0.262589\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −2.00000 −0.103975
\(371\) −12.0000 −0.623009
\(372\) 8.00000 0.414781
\(373\) −16.0000 −0.828449 −0.414224 0.910175i \(-0.635947\pi\)
−0.414224 + 0.910175i \(0.635947\pi\)
\(374\) 1.00000 0.0517088
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) −2.00000 −0.102869
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 8.00000 0.410391
\(381\) −4.00000 −0.204926
\(382\) 12.0000 0.613973
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −2.00000 −0.101929
\(386\) 4.00000 0.203595
\(387\) −10.0000 −0.508329
\(388\) 8.00000 0.406138
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 4.00000 0.202548
\(391\) 0 0
\(392\) 3.00000 0.151523
\(393\) 0 0
\(394\) 6.00000 0.302276
\(395\) 8.00000 0.402524
\(396\) −1.00000 −0.0502519
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) −8.00000 −0.401004
\(399\) 16.0000 0.801002
\(400\) 1.00000 0.0500000
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) −2.00000 −0.0997509
\(403\) −32.0000 −1.59403
\(404\) 12.0000 0.597022
\(405\) 1.00000 0.0496904
\(406\) −12.0000 −0.595550
\(407\) −2.00000 −0.0991363
\(408\) −1.00000 −0.0495074
\(409\) 38.0000 1.87898 0.939490 0.342578i \(-0.111300\pi\)
0.939490 + 0.342578i \(0.111300\pi\)
\(410\) 0 0
\(411\) −6.00000 −0.295958
\(412\) −4.00000 −0.197066
\(413\) −12.0000 −0.590481
\(414\) 0 0
\(415\) 0 0
\(416\) 4.00000 0.196116
\(417\) −4.00000 −0.195881
\(418\) 8.00000 0.391293
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 2.00000 0.0975900
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 4.00000 0.194717
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 1.00000 0.0485071
\(426\) 6.00000 0.290701
\(427\) 4.00000 0.193574
\(428\) 12.0000 0.580042
\(429\) 4.00000 0.193122
\(430\) 10.0000 0.482243
\(431\) −30.0000 −1.44505 −0.722525 0.691345i \(-0.757018\pi\)
−0.722525 + 0.691345i \(0.757018\pi\)
\(432\) 1.00000 0.0481125
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) −16.0000 −0.768025
\(435\) 6.00000 0.287678
\(436\) 14.0000 0.670478
\(437\) 0 0
\(438\) −8.00000 −0.382255
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 1.00000 0.0476731
\(441\) −3.00000 −0.142857
\(442\) 4.00000 0.190261
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 2.00000 0.0949158
\(445\) 6.00000 0.284427
\(446\) 28.0000 1.32584
\(447\) −12.0000 −0.567581
\(448\) 2.00000 0.0944911
\(449\) 24.0000 1.13263 0.566315 0.824189i \(-0.308369\pi\)
0.566315 + 0.824189i \(0.308369\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) 8.00000 0.375873
\(454\) −12.0000 −0.563188
\(455\) −8.00000 −0.375046
\(456\) −8.00000 −0.374634
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) −14.0000 −0.654177
\(459\) 1.00000 0.0466760
\(460\) 0 0
\(461\) −24.0000 −1.11779 −0.558896 0.829238i \(-0.688775\pi\)
−0.558896 + 0.829238i \(0.688775\pi\)
\(462\) 2.00000 0.0930484
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 6.00000 0.278543
\(465\) 8.00000 0.370991
\(466\) −18.0000 −0.833834
\(467\) −24.0000 −1.11059 −0.555294 0.831654i \(-0.687394\pi\)
−0.555294 + 0.831654i \(0.687394\pi\)
\(468\) −4.00000 −0.184900
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) 8.00000 0.368621
\(472\) 6.00000 0.276172
\(473\) 10.0000 0.459800
\(474\) −8.00000 −0.367452
\(475\) 8.00000 0.367065
\(476\) 2.00000 0.0916698
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) 30.0000 1.37073 0.685367 0.728197i \(-0.259642\pi\)
0.685367 + 0.728197i \(0.259642\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −8.00000 −0.364769
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 8.00000 0.363261
\(486\) −1.00000 −0.0453609
\(487\) −34.0000 −1.54069 −0.770344 0.637629i \(-0.779915\pi\)
−0.770344 + 0.637629i \(0.779915\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 8.00000 0.361773
\(490\) 3.00000 0.135526
\(491\) 18.0000 0.812329 0.406164 0.913800i \(-0.366866\pi\)
0.406164 + 0.913800i \(0.366866\pi\)
\(492\) 0 0
\(493\) 6.00000 0.270226
\(494\) 32.0000 1.43975
\(495\) −1.00000 −0.0449467
\(496\) 8.00000 0.359211
\(497\) −12.0000 −0.538274
\(498\) 0 0
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 1.00000 0.0447214
\(501\) 0 0
\(502\) 6.00000 0.267793
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 12.0000 0.533993
\(506\) 0 0
\(507\) 3.00000 0.133235
\(508\) −4.00000 −0.177471
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) −1.00000 −0.0442807
\(511\) 16.0000 0.707798
\(512\) −1.00000 −0.0441942
\(513\) 8.00000 0.353209
\(514\) −6.00000 −0.264649
\(515\) −4.00000 −0.176261
\(516\) −10.0000 −0.440225
\(517\) 0 0
\(518\) −4.00000 −0.175750
\(519\) 18.0000 0.790112
\(520\) 4.00000 0.175412
\(521\) −24.0000 −1.05146 −0.525730 0.850652i \(-0.676208\pi\)
−0.525730 + 0.850652i \(0.676208\pi\)
\(522\) −6.00000 −0.262613
\(523\) 26.0000 1.13690 0.568450 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(524\) 0 0
\(525\) 2.00000 0.0872872
\(526\) −24.0000 −1.04645
\(527\) 8.00000 0.348485
\(528\) −1.00000 −0.0435194
\(529\) −23.0000 −1.00000
\(530\) 6.00000 0.260623
\(531\) −6.00000 −0.260378
\(532\) 16.0000 0.693688
\(533\) 0 0
\(534\) −6.00000 −0.259645
\(535\) 12.0000 0.518805
\(536\) −2.00000 −0.0863868
\(537\) −18.0000 −0.776757
\(538\) −6.00000 −0.258678
\(539\) 3.00000 0.129219
\(540\) 1.00000 0.0430331
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 16.0000 0.687259
\(543\) 14.0000 0.600798
\(544\) −1.00000 −0.0428746
\(545\) 14.0000 0.599694
\(546\) 8.00000 0.342368
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −6.00000 −0.256307
\(549\) 2.00000 0.0853579
\(550\) 1.00000 0.0426401
\(551\) 48.0000 2.04487
\(552\) 0 0
\(553\) 16.0000 0.680389
\(554\) −14.0000 −0.594803
\(555\) 2.00000 0.0848953
\(556\) −4.00000 −0.169638
\(557\) −18.0000 −0.762684 −0.381342 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) −8.00000 −0.338667
\(559\) 40.0000 1.69182
\(560\) 2.00000 0.0845154
\(561\) −1.00000 −0.0422200
\(562\) 18.0000 0.759284
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) 0 0
\(565\) −6.00000 −0.252422
\(566\) −20.0000 −0.840663
\(567\) 2.00000 0.0839921
\(568\) 6.00000 0.251754
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) −8.00000 −0.335083
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 4.00000 0.167248
\(573\) −12.0000 −0.501307
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −4.00000 −0.166234
\(580\) 6.00000 0.249136
\(581\) 0 0
\(582\) −8.00000 −0.331611
\(583\) 6.00000 0.248495
\(584\) −8.00000 −0.331042
\(585\) −4.00000 −0.165380
\(586\) 30.0000 1.23929
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) −3.00000 −0.123718
\(589\) 64.0000 2.63707
\(590\) 6.00000 0.247016
\(591\) −6.00000 −0.246807
\(592\) 2.00000 0.0821995
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 1.00000 0.0410305
\(595\) 2.00000 0.0819920
\(596\) −12.0000 −0.491539
\(597\) 8.00000 0.327418
\(598\) 0 0
\(599\) −36.0000 −1.47092 −0.735460 0.677568i \(-0.763034\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −46.0000 −1.87638 −0.938190 0.346122i \(-0.887498\pi\)
−0.938190 + 0.346122i \(0.887498\pi\)
\(602\) 20.0000 0.815139
\(603\) 2.00000 0.0814463
\(604\) 8.00000 0.325515
\(605\) 1.00000 0.0406558
\(606\) −12.0000 −0.487467
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) −8.00000 −0.324443
\(609\) 12.0000 0.486265
\(610\) −2.00000 −0.0809776
\(611\) 0 0
\(612\) 1.00000 0.0404226
\(613\) −40.0000 −1.61558 −0.807792 0.589467i \(-0.799338\pi\)
−0.807792 + 0.589467i \(0.799338\pi\)
\(614\) −14.0000 −0.564994
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 4.00000 0.160904
\(619\) 44.0000 1.76851 0.884255 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(620\) 8.00000 0.321288
\(621\) 0 0
\(622\) −30.0000 −1.20289
\(623\) 12.0000 0.480770
\(624\) −4.00000 −0.160128
\(625\) 1.00000 0.0400000
\(626\) −8.00000 −0.319744
\(627\) −8.00000 −0.319489
\(628\) 8.00000 0.319235
\(629\) 2.00000 0.0797452
\(630\) −2.00000 −0.0796819
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −8.00000 −0.318223
\(633\) −4.00000 −0.158986
\(634\) 30.0000 1.19145
\(635\) −4.00000 −0.158735
\(636\) −6.00000 −0.237915
\(637\) 12.0000 0.475457
\(638\) 6.00000 0.237542
\(639\) −6.00000 −0.237356
\(640\) −1.00000 −0.0395285
\(641\) −24.0000 −0.947943 −0.473972 0.880540i \(-0.657180\pi\)
−0.473972 + 0.880540i \(0.657180\pi\)
\(642\) −12.0000 −0.473602
\(643\) −16.0000 −0.630978 −0.315489 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(644\) 0 0
\(645\) −10.0000 −0.393750
\(646\) −8.00000 −0.314756
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 6.00000 0.235521
\(650\) 4.00000 0.156893
\(651\) 16.0000 0.627089
\(652\) 8.00000 0.313304
\(653\) −18.0000 −0.704394 −0.352197 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) −14.0000 −0.547443
\(655\) 0 0
\(656\) 0 0
\(657\) 8.00000 0.312110
\(658\) 0 0
\(659\) −6.00000 −0.233727 −0.116863 0.993148i \(-0.537284\pi\)
−0.116863 + 0.993148i \(0.537284\pi\)
\(660\) −1.00000 −0.0389249
\(661\) 26.0000 1.01128 0.505641 0.862744i \(-0.331256\pi\)
0.505641 + 0.862744i \(0.331256\pi\)
\(662\) −32.0000 −1.24372
\(663\) −4.00000 −0.155347
\(664\) 0 0
\(665\) 16.0000 0.620453
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) 0 0
\(669\) −28.0000 −1.08254
\(670\) −2.00000 −0.0772667
\(671\) −2.00000 −0.0772091
\(672\) −2.00000 −0.0771517
\(673\) −4.00000 −0.154189 −0.0770943 0.997024i \(-0.524564\pi\)
−0.0770943 + 0.997024i \(0.524564\pi\)
\(674\) −8.00000 −0.308148
\(675\) 1.00000 0.0384900
\(676\) 3.00000 0.115385
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 6.00000 0.230429
\(679\) 16.0000 0.614024
\(680\) −1.00000 −0.0383482
\(681\) 12.0000 0.459841
\(682\) 8.00000 0.306336
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 8.00000 0.305888
\(685\) −6.00000 −0.229248
\(686\) 20.0000 0.763604
\(687\) 14.0000 0.534133
\(688\) −10.0000 −0.381246
\(689\) 24.0000 0.914327
\(690\) 0 0
\(691\) −52.0000 −1.97817 −0.989087 0.147335i \(-0.952930\pi\)
−0.989087 + 0.147335i \(0.952930\pi\)
\(692\) 18.0000 0.684257
\(693\) −2.00000 −0.0759737
\(694\) 12.0000 0.455514
\(695\) −4.00000 −0.151729
\(696\) −6.00000 −0.227429
\(697\) 0 0
\(698\) −14.0000 −0.529908
\(699\) 18.0000 0.680823
\(700\) 2.00000 0.0755929
\(701\) −24.0000 −0.906467 −0.453234 0.891392i \(-0.649730\pi\)
−0.453234 + 0.891392i \(0.649730\pi\)
\(702\) 4.00000 0.150970
\(703\) 16.0000 0.603451
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) 24.0000 0.902613
\(708\) −6.00000 −0.225494
\(709\) −46.0000 −1.72757 −0.863783 0.503864i \(-0.831911\pi\)
−0.863783 + 0.503864i \(0.831911\pi\)
\(710\) 6.00000 0.225176
\(711\) 8.00000 0.300023
\(712\) −6.00000 −0.224860
\(713\) 0 0
\(714\) −2.00000 −0.0748481
\(715\) 4.00000 0.149592
\(716\) −18.0000 −0.672692
\(717\) 0 0
\(718\) −12.0000 −0.447836
\(719\) −6.00000 −0.223762 −0.111881 0.993722i \(-0.535688\pi\)
−0.111881 + 0.993722i \(0.535688\pi\)
\(720\) 1.00000 0.0372678
\(721\) −8.00000 −0.297936
\(722\) −45.0000 −1.67473
\(723\) −10.0000 −0.371904
\(724\) 14.0000 0.520306
\(725\) 6.00000 0.222834
\(726\) −1.00000 −0.0371135
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 8.00000 0.296500
\(729\) 1.00000 0.0370370
\(730\) −8.00000 −0.296093
\(731\) −10.0000 −0.369863
\(732\) 2.00000 0.0739221
\(733\) 32.0000 1.18195 0.590973 0.806691i \(-0.298744\pi\)
0.590973 + 0.806691i \(0.298744\pi\)
\(734\) −26.0000 −0.959678
\(735\) −3.00000 −0.110657
\(736\) 0 0
\(737\) −2.00000 −0.0736709
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 2.00000 0.0735215
\(741\) −32.0000 −1.17555
\(742\) 12.0000 0.440534
\(743\) −48.0000 −1.76095 −0.880475 0.474093i \(-0.842776\pi\)
−0.880475 + 0.474093i \(0.842776\pi\)
\(744\) −8.00000 −0.293294
\(745\) −12.0000 −0.439646
\(746\) 16.0000 0.585802
\(747\) 0 0
\(748\) −1.00000 −0.0365636
\(749\) 24.0000 0.876941
\(750\) −1.00000 −0.0365148
\(751\) −4.00000 −0.145962 −0.0729810 0.997333i \(-0.523251\pi\)
−0.0729810 + 0.997333i \(0.523251\pi\)
\(752\) 0 0
\(753\) −6.00000 −0.218652
\(754\) 24.0000 0.874028
\(755\) 8.00000 0.291150
\(756\) 2.00000 0.0727393
\(757\) 8.00000 0.290765 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) −8.00000 −0.290191
\(761\) 42.0000 1.52250 0.761249 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 4.00000 0.144905
\(763\) 28.0000 1.01367
\(764\) −12.0000 −0.434145
\(765\) 1.00000 0.0361551
\(766\) 24.0000 0.867155
\(767\) 24.0000 0.866590
\(768\) 1.00000 0.0360844
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 2.00000 0.0720750
\(771\) 6.00000 0.216085
\(772\) −4.00000 −0.143963
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 10.0000 0.359443
\(775\) 8.00000 0.287368
\(776\) −8.00000 −0.287183
\(777\) 4.00000 0.143499
\(778\) 0 0
\(779\) 0 0
\(780\) −4.00000 −0.143223
\(781\) 6.00000 0.214697
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) −3.00000 −0.107143
\(785\) 8.00000 0.285532
\(786\) 0 0
\(787\) 32.0000 1.14068 0.570338 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) −6.00000 −0.213741
\(789\) 24.0000 0.854423
\(790\) −8.00000 −0.284627
\(791\) −12.0000 −0.426671
\(792\) 1.00000 0.0355335
\(793\) −8.00000 −0.284088
\(794\) −2.00000 −0.0709773
\(795\) −6.00000 −0.212798
\(796\) 8.00000 0.283552
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) −16.0000 −0.566394
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) 6.00000 0.212000
\(802\) 0 0
\(803\) −8.00000 −0.282314
\(804\) 2.00000 0.0705346
\(805\) 0 0
\(806\) 32.0000 1.12715
\(807\) 6.00000 0.211210
\(808\) −12.0000 −0.422159
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 12.0000 0.421117
\(813\) −16.0000 −0.561144
\(814\) 2.00000 0.0701000
\(815\) 8.00000 0.280228
\(816\) 1.00000 0.0350070
\(817\) −80.0000 −2.79885
\(818\) −38.0000 −1.32864
\(819\) −8.00000 −0.279543
\(820\) 0 0
\(821\) 18.0000 0.628204 0.314102 0.949389i \(-0.398297\pi\)
0.314102 + 0.949389i \(0.398297\pi\)
\(822\) 6.00000 0.209274
\(823\) 26.0000 0.906303 0.453152 0.891434i \(-0.350300\pi\)
0.453152 + 0.891434i \(0.350300\pi\)
\(824\) 4.00000 0.139347
\(825\) −1.00000 −0.0348155
\(826\) 12.0000 0.417533
\(827\) 12.0000 0.417281 0.208640 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 0 0
\(829\) 26.0000 0.903017 0.451509 0.892267i \(-0.350886\pi\)
0.451509 + 0.892267i \(0.350886\pi\)
\(830\) 0 0
\(831\) 14.0000 0.485655
\(832\) −4.00000 −0.138675
\(833\) −3.00000 −0.103944
\(834\) 4.00000 0.138509
\(835\) 0 0
\(836\) −8.00000 −0.276686
\(837\) 8.00000 0.276520
\(838\) 24.0000 0.829066
\(839\) 30.0000 1.03572 0.517858 0.855467i \(-0.326730\pi\)
0.517858 + 0.855467i \(0.326730\pi\)
\(840\) −2.00000 −0.0690066
\(841\) 7.00000 0.241379
\(842\) 10.0000 0.344623
\(843\) −18.0000 −0.619953
\(844\) −4.00000 −0.137686
\(845\) 3.00000 0.103203
\(846\) 0 0
\(847\) 2.00000 0.0687208
\(848\) −6.00000 −0.206041
\(849\) 20.0000 0.686398
\(850\) −1.00000 −0.0342997
\(851\) 0 0
\(852\) −6.00000 −0.205557
\(853\) 38.0000 1.30110 0.650548 0.759465i \(-0.274539\pi\)
0.650548 + 0.759465i \(0.274539\pi\)
\(854\) −4.00000 −0.136877
\(855\) 8.00000 0.273594
\(856\) −12.0000 −0.410152
\(857\) −6.00000 −0.204956 −0.102478 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) −4.00000 −0.136558
\(859\) 8.00000 0.272956 0.136478 0.990643i \(-0.456422\pi\)
0.136478 + 0.990643i \(0.456422\pi\)
\(860\) −10.0000 −0.340997
\(861\) 0 0
\(862\) 30.0000 1.02180
\(863\) −24.0000 −0.816970 −0.408485 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 18.0000 0.612018
\(866\) −14.0000 −0.475739
\(867\) 1.00000 0.0339618
\(868\) 16.0000 0.543075
\(869\) −8.00000 −0.271381
\(870\) −6.00000 −0.203419
\(871\) −8.00000 −0.271070
\(872\) −14.0000 −0.474100
\(873\) 8.00000 0.270759
\(874\) 0 0
\(875\) 2.00000 0.0676123
\(876\) 8.00000 0.270295
\(877\) 14.0000 0.472746 0.236373 0.971662i \(-0.424041\pi\)
0.236373 + 0.971662i \(0.424041\pi\)
\(878\) −8.00000 −0.269987
\(879\) −30.0000 −1.01187
\(880\) −1.00000 −0.0337100
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 3.00000 0.101015
\(883\) −10.0000 −0.336527 −0.168263 0.985742i \(-0.553816\pi\)
−0.168263 + 0.985742i \(0.553816\pi\)
\(884\) −4.00000 −0.134535
\(885\) −6.00000 −0.201688
\(886\) −36.0000 −1.20944
\(887\) 36.0000 1.20876 0.604381 0.796696i \(-0.293421\pi\)
0.604381 + 0.796696i \(0.293421\pi\)
\(888\) −2.00000 −0.0671156
\(889\) −8.00000 −0.268311
\(890\) −6.00000 −0.201120
\(891\) −1.00000 −0.0335013
\(892\) −28.0000 −0.937509
\(893\) 0 0
\(894\) 12.0000 0.401340
\(895\) −18.0000 −0.601674
\(896\) −2.00000 −0.0668153
\(897\) 0 0
\(898\) −24.0000 −0.800890
\(899\) 48.0000 1.60089
\(900\) 1.00000 0.0333333
\(901\) −6.00000 −0.199889
\(902\) 0 0
\(903\) −20.0000 −0.665558
\(904\) 6.00000 0.199557
\(905\) 14.0000 0.465376
\(906\) −8.00000 −0.265782
\(907\) 32.0000 1.06254 0.531271 0.847202i \(-0.321714\pi\)
0.531271 + 0.847202i \(0.321714\pi\)
\(908\) 12.0000 0.398234
\(909\) 12.0000 0.398015
\(910\) 8.00000 0.265197
\(911\) 42.0000 1.39152 0.695761 0.718273i \(-0.255067\pi\)
0.695761 + 0.718273i \(0.255067\pi\)
\(912\) 8.00000 0.264906
\(913\) 0 0
\(914\) 10.0000 0.330771
\(915\) 2.00000 0.0661180
\(916\) 14.0000 0.462573
\(917\) 0 0
\(918\) −1.00000 −0.0330049
\(919\) 8.00000 0.263896 0.131948 0.991257i \(-0.457877\pi\)
0.131948 + 0.991257i \(0.457877\pi\)
\(920\) 0 0
\(921\) 14.0000 0.461316
\(922\) 24.0000 0.790398
\(923\) 24.0000 0.789970
\(924\) −2.00000 −0.0657952
\(925\) 2.00000 0.0657596
\(926\) 4.00000 0.131448
\(927\) −4.00000 −0.131377
\(928\) −6.00000 −0.196960
\(929\) 36.0000 1.18112 0.590561 0.806993i \(-0.298907\pi\)
0.590561 + 0.806993i \(0.298907\pi\)
\(930\) −8.00000 −0.262330
\(931\) −24.0000 −0.786568
\(932\) 18.0000 0.589610
\(933\) 30.0000 0.982156
\(934\) 24.0000 0.785304
\(935\) −1.00000 −0.0327035
\(936\) 4.00000 0.130744
\(937\) −10.0000 −0.326686 −0.163343 0.986569i \(-0.552228\pi\)
−0.163343 + 0.986569i \(0.552228\pi\)
\(938\) −4.00000 −0.130605
\(939\) 8.00000 0.261070
\(940\) 0 0
\(941\) 18.0000 0.586783 0.293392 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) −8.00000 −0.260654
\(943\) 0 0
\(944\) −6.00000 −0.195283
\(945\) 2.00000 0.0650600
\(946\) −10.0000 −0.325128
\(947\) 60.0000 1.94974 0.974869 0.222779i \(-0.0715128\pi\)
0.974869 + 0.222779i \(0.0715128\pi\)
\(948\) 8.00000 0.259828
\(949\) −32.0000 −1.03876
\(950\) −8.00000 −0.259554
\(951\) −30.0000 −0.972817
\(952\) −2.00000 −0.0648204
\(953\) −54.0000 −1.74923 −0.874616 0.484817i \(-0.838886\pi\)
−0.874616 + 0.484817i \(0.838886\pi\)
\(954\) 6.00000 0.194257
\(955\) −12.0000 −0.388311
\(956\) 0 0
\(957\) −6.00000 −0.193952
\(958\) −30.0000 −0.969256
\(959\) −12.0000 −0.387500
\(960\) 1.00000 0.0322749
\(961\) 33.0000 1.06452
\(962\) 8.00000 0.257930
\(963\) 12.0000 0.386695
\(964\) −10.0000 −0.322078
\(965\) −4.00000 −0.128765
\(966\) 0 0
\(967\) 8.00000 0.257263 0.128631 0.991692i \(-0.458942\pi\)
0.128631 + 0.991692i \(0.458942\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 8.00000 0.256997
\(970\) −8.00000 −0.256865
\(971\) 6.00000 0.192549 0.0962746 0.995355i \(-0.469307\pi\)
0.0962746 + 0.995355i \(0.469307\pi\)
\(972\) 1.00000 0.0320750
\(973\) −8.00000 −0.256468
\(974\) 34.0000 1.08943
\(975\) −4.00000 −0.128103
\(976\) 2.00000 0.0640184
\(977\) −18.0000 −0.575871 −0.287936 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) −8.00000 −0.255812
\(979\) −6.00000 −0.191761
\(980\) −3.00000 −0.0958315
\(981\) 14.0000 0.446986
\(982\) −18.0000 −0.574403
\(983\) 12.0000 0.382741 0.191370 0.981518i \(-0.438707\pi\)
0.191370 + 0.981518i \(0.438707\pi\)
\(984\) 0 0
\(985\) −6.00000 −0.191176
\(986\) −6.00000 −0.191079
\(987\) 0 0
\(988\) −32.0000 −1.01806
\(989\) 0 0
\(990\) 1.00000 0.0317821
\(991\) 56.0000 1.77890 0.889449 0.457034i \(-0.151088\pi\)
0.889449 + 0.457034i \(0.151088\pi\)
\(992\) −8.00000 −0.254000
\(993\) 32.0000 1.01549
\(994\) 12.0000 0.380617
\(995\) 8.00000 0.253617
\(996\) 0 0
\(997\) 2.00000 0.0633406 0.0316703 0.999498i \(-0.489917\pi\)
0.0316703 + 0.999498i \(0.489917\pi\)
\(998\) 4.00000 0.126618
\(999\) 2.00000 0.0632772
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 5610.2.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.t.1.1 1 1.1 even 1 trivial