Properties

Label 5610.2.a.d.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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} -1.00000 q^{20} -1.00000 q^{21} +1.00000 q^{22} +5.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{27} +1.00000 q^{28} +9.00000 q^{29} -1.00000 q^{30} -7.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} -1.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} -4.00000 q^{38} +1.00000 q^{40} +1.00000 q^{42} -5.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} -5.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} -6.00000 q^{49} -1.00000 q^{50} -1.00000 q^{51} +12.0000 q^{53} +1.00000 q^{54} +1.00000 q^{55} -1.00000 q^{56} -4.00000 q^{57} -9.00000 q^{58} -6.00000 q^{59} +1.00000 q^{60} -14.0000 q^{61} +7.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -1.00000 q^{66} +8.00000 q^{67} +1.00000 q^{68} -5.00000 q^{69} +1.00000 q^{70} -6.00000 q^{71} -1.00000 q^{72} -14.0000 q^{73} +2.00000 q^{74} -1.00000 q^{75} +4.00000 q^{76} -1.00000 q^{77} +8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +16.0000 q^{83} -1.00000 q^{84} -1.00000 q^{85} +5.00000 q^{86} -9.00000 q^{87} +1.00000 q^{88} +1.00000 q^{90} +5.00000 q^{92} +7.00000 q^{93} -8.00000 q^{94} -4.00000 q^{95} +1.00000 q^{96} +7.00000 q^{97} +6.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) −1.00000 −0.288675
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −1.00000 −0.267261
\(15\) 1.00000 0.258199
\(16\) 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 \(0.348268\pi\)
\(20\) −1.00000 −0.223607
\(21\) −1.00000 −0.218218
\(22\) 1.00000 0.213201
\(23\) 5.00000 1.04257 0.521286 0.853382i \(-0.325452\pi\)
0.521286 + 0.853382i \(0.325452\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.00000 0.188982
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) −1.00000 −0.182574
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) −1.00000 −0.171499
\(35\) −1.00000 −0.169031
\(36\) 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
\(40\) 1.00000 0.158114
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 1.00000 0.154303
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) −1.00000 −0.150756
\(45\) −1.00000 −0.149071
\(46\) −5.00000 −0.737210
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.00000 −0.857143
\(50\) −1.00000 −0.141421
\(51\) −1.00000 −0.140028
\(52\) 0 0
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 1.00000 0.136083
\(55\) 1.00000 0.134840
\(56\) −1.00000 −0.133631
\(57\) −4.00000 −0.529813
\(58\) −9.00000 −1.18176
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) 1.00000 0.129099
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 7.00000 0.889001
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −1.00000 −0.123091
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 1.00000 0.121268
\(69\) −5.00000 −0.601929
\(70\) 1.00000 0.119523
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) −1.00000 −0.117851
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 2.00000 0.232495
\(75\) −1.00000 −0.115470
\(76\) 4.00000 0.458831
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 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
\(83\) 16.0000 1.75623 0.878114 0.478451i \(-0.158802\pi\)
0.878114 + 0.478451i \(0.158802\pi\)
\(84\) −1.00000 −0.109109
\(85\) −1.00000 −0.108465
\(86\) 5.00000 0.539164
\(87\) −9.00000 −0.964901
\(88\) 1.00000 0.106600
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) 5.00000 0.521286
\(93\) 7.00000 0.725866
\(94\) −8.00000 −0.825137
\(95\) −4.00000 −0.410391
\(96\) 1.00000 0.102062
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 6.00000 0.606092
\(99\) −1.00000 −0.100504
\(100\) 1.00000 0.100000
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 1.00000 0.0990148
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) 0 0
\(105\) 1.00000 0.0975900
\(106\) −12.0000 −1.16554
\(107\) −5.00000 −0.483368 −0.241684 0.970355i \(-0.577700\pi\)
−0.241684 + 0.970355i \(0.577700\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 2.00000 0.189832
\(112\) 1.00000 0.0944911
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 4.00000 0.374634
\(115\) −5.00000 −0.466252
\(116\) 9.00000 0.835629
\(117\) 0 0
\(118\) 6.00000 0.552345
\(119\) 1.00000 0.0916698
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 0.0909091
\(122\) 14.0000 1.26750
\(123\) 0 0
\(124\) −7.00000 −0.628619
\(125\) −1.00000 −0.0894427
\(126\) −1.00000 −0.0890871
\(127\) −18.0000 −1.59724 −0.798621 0.601834i \(-0.794437\pi\)
−0.798621 + 0.601834i \(0.794437\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 5.00000 0.440225
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 1.00000 0.0870388
\(133\) 4.00000 0.346844
\(134\) −8.00000 −0.691095
\(135\) 1.00000 0.0860663
\(136\) −1.00000 −0.0857493
\(137\) 9.00000 0.768922 0.384461 0.923141i \(-0.374387\pi\)
0.384461 + 0.923141i \(0.374387\pi\)
\(138\) 5.00000 0.425628
\(139\) −1.00000 −0.0848189 −0.0424094 0.999100i \(-0.513503\pi\)
−0.0424094 + 0.999100i \(0.513503\pi\)
\(140\) −1.00000 −0.0845154
\(141\) −8.00000 −0.673722
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −9.00000 −0.747409
\(146\) 14.0000 1.15865
\(147\) 6.00000 0.494872
\(148\) −2.00000 −0.164399
\(149\) −8.00000 −0.655386 −0.327693 0.944784i \(-0.606271\pi\)
−0.327693 + 0.944784i \(0.606271\pi\)
\(150\) 1.00000 0.0816497
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) −4.00000 −0.324443
\(153\) 1.00000 0.0808452
\(154\) 1.00000 0.0805823
\(155\) 7.00000 0.562254
\(156\) 0 0
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) −8.00000 −0.636446
\(159\) −12.0000 −0.951662
\(160\) 1.00000 0.0790569
\(161\) 5.00000 0.394055
\(162\) −1.00000 −0.0785674
\(163\) 5.00000 0.391630 0.195815 0.980641i \(-0.437265\pi\)
0.195815 + 0.980641i \(0.437265\pi\)
\(164\) 0 0
\(165\) −1.00000 −0.0778499
\(166\) −16.0000 −1.24184
\(167\) 18.0000 1.39288 0.696441 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) 1.00000 0.0771517
\(169\) −13.0000 −1.00000
\(170\) 1.00000 0.0766965
\(171\) 4.00000 0.305888
\(172\) −5.00000 −0.381246
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 9.00000 0.682288
\(175\) 1.00000 0.0755929
\(176\) −1.00000 −0.0753778
\(177\) 6.00000 0.450988
\(178\) 0 0
\(179\) 2.00000 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) −5.00000 −0.368605
\(185\) 2.00000 0.147043
\(186\) −7.00000 −0.513265
\(187\) −1.00000 −0.0731272
\(188\) 8.00000 0.583460
\(189\) −1.00000 −0.0727393
\(190\) 4.00000 0.290191
\(191\) −3.00000 −0.217072 −0.108536 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 22.0000 1.58359 0.791797 0.610784i \(-0.209146\pi\)
0.791797 + 0.610784i \(0.209146\pi\)
\(194\) −7.00000 −0.502571
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) −8.00000 −0.569976 −0.284988 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) 1.00000 0.0710669
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −8.00000 −0.564276
\(202\) −10.0000 −0.703598
\(203\) 9.00000 0.631676
\(204\) −1.00000 −0.0700140
\(205\) 0 0
\(206\) 1.00000 0.0696733
\(207\) 5.00000 0.347524
\(208\) 0 0
\(209\) −4.00000 −0.276686
\(210\) −1.00000 −0.0690066
\(211\) 17.0000 1.17033 0.585164 0.810915i \(-0.301030\pi\)
0.585164 + 0.810915i \(0.301030\pi\)
\(212\) 12.0000 0.824163
\(213\) 6.00000 0.411113
\(214\) 5.00000 0.341793
\(215\) 5.00000 0.340997
\(216\) 1.00000 0.0680414
\(217\) −7.00000 −0.475191
\(218\) 4.00000 0.270914
\(219\) 14.0000 0.946032
\(220\) 1.00000 0.0674200
\(221\) 0 0
\(222\) −2.00000 −0.134231
\(223\) −9.00000 −0.602685 −0.301342 0.953516i \(-0.597435\pi\)
−0.301342 + 0.953516i \(0.597435\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 1.00000 0.0666667
\(226\) −6.00000 −0.399114
\(227\) −29.0000 −1.92480 −0.962399 0.271640i \(-0.912434\pi\)
−0.962399 + 0.271640i \(0.912434\pi\)
\(228\) −4.00000 −0.264906
\(229\) 4.00000 0.264327 0.132164 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 5.00000 0.329690
\(231\) 1.00000 0.0657952
\(232\) −9.00000 −0.590879
\(233\) −15.0000 −0.982683 −0.491341 0.870967i \(-0.663493\pi\)
−0.491341 + 0.870967i \(0.663493\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) −6.00000 −0.390567
\(237\) −8.00000 −0.519656
\(238\) −1.00000 −0.0648204
\(239\) −2.00000 −0.129369 −0.0646846 0.997906i \(-0.520604\pi\)
−0.0646846 + 0.997906i \(0.520604\pi\)
\(240\) 1.00000 0.0645497
\(241\) 1.00000 0.0644157 0.0322078 0.999481i \(-0.489746\pi\)
0.0322078 + 0.999481i \(0.489746\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) −14.0000 −0.896258
\(245\) 6.00000 0.383326
\(246\) 0 0
\(247\) 0 0
\(248\) 7.00000 0.444500
\(249\) −16.0000 −1.01396
\(250\) 1.00000 0.0632456
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 1.00000 0.0629941
\(253\) −5.00000 −0.314347
\(254\) 18.0000 1.12942
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) −17.0000 −1.06043 −0.530215 0.847863i \(-0.677889\pi\)
−0.530215 + 0.847863i \(0.677889\pi\)
\(258\) −5.00000 −0.311286
\(259\) −2.00000 −0.124274
\(260\) 0 0
\(261\) 9.00000 0.557086
\(262\) 8.00000 0.494242
\(263\) 7.00000 0.431638 0.215819 0.976433i \(-0.430758\pi\)
0.215819 + 0.976433i \(0.430758\pi\)
\(264\) −1.00000 −0.0615457
\(265\) −12.0000 −0.737154
\(266\) −4.00000 −0.245256
\(267\) 0 0
\(268\) 8.00000 0.488678
\(269\) 30.0000 1.82913 0.914566 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 27.0000 1.64013 0.820067 0.572268i \(-0.193936\pi\)
0.820067 + 0.572268i \(0.193936\pi\)
\(272\) 1.00000 0.0606339
\(273\) 0 0
\(274\) −9.00000 −0.543710
\(275\) −1.00000 −0.0603023
\(276\) −5.00000 −0.300965
\(277\) 14.0000 0.841178 0.420589 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 1.00000 0.0599760
\(279\) −7.00000 −0.419079
\(280\) 1.00000 0.0597614
\(281\) −3.00000 −0.178965 −0.0894825 0.995988i \(-0.528521\pi\)
−0.0894825 + 0.995988i \(0.528521\pi\)
\(282\) 8.00000 0.476393
\(283\) 22.0000 1.30776 0.653882 0.756596i \(-0.273139\pi\)
0.653882 + 0.756596i \(0.273139\pi\)
\(284\) −6.00000 −0.356034
\(285\) 4.00000 0.236940
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 9.00000 0.528498
\(291\) −7.00000 −0.410347
\(292\) −14.0000 −0.819288
\(293\) 33.0000 1.92788 0.963940 0.266119i \(-0.0857413\pi\)
0.963940 + 0.266119i \(0.0857413\pi\)
\(294\) −6.00000 −0.349927
\(295\) 6.00000 0.349334
\(296\) 2.00000 0.116248
\(297\) 1.00000 0.0580259
\(298\) 8.00000 0.463428
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) −5.00000 −0.288195
\(302\) −20.0000 −1.15087
\(303\) −10.0000 −0.574485
\(304\) 4.00000 0.229416
\(305\) 14.0000 0.801638
\(306\) −1.00000 −0.0571662
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) −1.00000 −0.0569803
\(309\) 1.00000 0.0568880
\(310\) −7.00000 −0.397573
\(311\) 20.0000 1.13410 0.567048 0.823685i \(-0.308085\pi\)
0.567048 + 0.823685i \(0.308085\pi\)
\(312\) 0 0
\(313\) 25.0000 1.41308 0.706542 0.707671i \(-0.250254\pi\)
0.706542 + 0.707671i \(0.250254\pi\)
\(314\) −10.0000 −0.564333
\(315\) −1.00000 −0.0563436
\(316\) 8.00000 0.450035
\(317\) 27.0000 1.51647 0.758236 0.651981i \(-0.226062\pi\)
0.758236 + 0.651981i \(0.226062\pi\)
\(318\) 12.0000 0.672927
\(319\) −9.00000 −0.503903
\(320\) −1.00000 −0.0559017
\(321\) 5.00000 0.279073
\(322\) −5.00000 −0.278639
\(323\) 4.00000 0.222566
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −5.00000 −0.276924
\(327\) 4.00000 0.221201
\(328\) 0 0
\(329\) 8.00000 0.441054
\(330\) 1.00000 0.0550482
\(331\) −19.0000 −1.04433 −0.522167 0.852843i \(-0.674876\pi\)
−0.522167 + 0.852843i \(0.674876\pi\)
\(332\) 16.0000 0.878114
\(333\) −2.00000 −0.109599
\(334\) −18.0000 −0.984916
\(335\) −8.00000 −0.437087
\(336\) −1.00000 −0.0545545
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) 13.0000 0.707107
\(339\) −6.00000 −0.325875
\(340\) −1.00000 −0.0542326
\(341\) 7.00000 0.379071
\(342\) −4.00000 −0.216295
\(343\) −13.0000 −0.701934
\(344\) 5.00000 0.269582
\(345\) 5.00000 0.269191
\(346\) 18.0000 0.967686
\(347\) 28.0000 1.50312 0.751559 0.659665i \(-0.229302\pi\)
0.751559 + 0.659665i \(0.229302\pi\)
\(348\) −9.00000 −0.482451
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) −7.00000 −0.372572 −0.186286 0.982496i \(-0.559645\pi\)
−0.186286 + 0.982496i \(0.559645\pi\)
\(354\) −6.00000 −0.318896
\(355\) 6.00000 0.318447
\(356\) 0 0
\(357\) −1.00000 −0.0529256
\(358\) −2.00000 −0.105703
\(359\) 18.0000 0.950004 0.475002 0.879985i \(-0.342447\pi\)
0.475002 + 0.879985i \(0.342447\pi\)
\(360\) 1.00000 0.0527046
\(361\) −3.00000 −0.157895
\(362\) 7.00000 0.367912
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) 14.0000 0.732793
\(366\) −14.0000 −0.731792
\(367\) 18.0000 0.939592 0.469796 0.882775i \(-0.344327\pi\)
0.469796 + 0.882775i \(0.344327\pi\)
\(368\) 5.00000 0.260643
\(369\) 0 0
\(370\) −2.00000 −0.103975
\(371\) 12.0000 0.623009
\(372\) 7.00000 0.362933
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 1.00000 0.0517088
\(375\) 1.00000 0.0516398
\(376\) −8.00000 −0.412568
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −4.00000 −0.205196
\(381\) 18.0000 0.922168
\(382\) 3.00000 0.153493
\(383\) 8.00000 0.408781 0.204390 0.978889i \(-0.434479\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(384\) 1.00000 0.0510310
\(385\) 1.00000 0.0509647
\(386\) −22.0000 −1.11977
\(387\) −5.00000 −0.254164
\(388\) 7.00000 0.355371
\(389\) −22.0000 −1.11544 −0.557722 0.830028i \(-0.688325\pi\)
−0.557722 + 0.830028i \(0.688325\pi\)
\(390\) 0 0
\(391\) 5.00000 0.252861
\(392\) 6.00000 0.303046
\(393\) 8.00000 0.403547
\(394\) 8.00000 0.403034
\(395\) −8.00000 −0.402524
\(396\) −1.00000 −0.0502519
\(397\) 22.0000 1.10415 0.552074 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 0 0
\(399\) −4.00000 −0.200250
\(400\) 1.00000 0.0500000
\(401\) 3.00000 0.149813 0.0749064 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) 8.00000 0.399004
\(403\) 0 0
\(404\) 10.0000 0.497519
\(405\) −1.00000 −0.0496904
\(406\) −9.00000 −0.446663
\(407\) 2.00000 0.0991363
\(408\) 1.00000 0.0495074
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) −9.00000 −0.443937
\(412\) −1.00000 −0.0492665
\(413\) −6.00000 −0.295241
\(414\) −5.00000 −0.245737
\(415\) −16.0000 −0.785409
\(416\) 0 0
\(417\) 1.00000 0.0489702
\(418\) 4.00000 0.195646
\(419\) −23.0000 −1.12362 −0.561812 0.827265i \(-0.689895\pi\)
−0.561812 + 0.827265i \(0.689895\pi\)
\(420\) 1.00000 0.0487950
\(421\) 12.0000 0.584844 0.292422 0.956289i \(-0.405539\pi\)
0.292422 + 0.956289i \(0.405539\pi\)
\(422\) −17.0000 −0.827547
\(423\) 8.00000 0.388973
\(424\) −12.0000 −0.582772
\(425\) 1.00000 0.0485071
\(426\) −6.00000 −0.290701
\(427\) −14.0000 −0.677507
\(428\) −5.00000 −0.241684
\(429\) 0 0
\(430\) −5.00000 −0.241121
\(431\) 39.0000 1.87856 0.939282 0.343146i \(-0.111493\pi\)
0.939282 + 0.343146i \(0.111493\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −4.00000 −0.192228 −0.0961139 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) 7.00000 0.336011
\(435\) 9.00000 0.431517
\(436\) −4.00000 −0.191565
\(437\) 20.0000 0.956730
\(438\) −14.0000 −0.668946
\(439\) −38.0000 −1.81364 −0.906821 0.421517i \(-0.861498\pi\)
−0.906821 + 0.421517i \(0.861498\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) 13.0000 0.617649 0.308824 0.951119i \(-0.400064\pi\)
0.308824 + 0.951119i \(0.400064\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) 9.00000 0.426162
\(447\) 8.00000 0.378387
\(448\) 1.00000 0.0472456
\(449\) −15.0000 −0.707894 −0.353947 0.935266i \(-0.615161\pi\)
−0.353947 + 0.935266i \(0.615161\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) −20.0000 −0.939682
\(454\) 29.0000 1.36104
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 22.0000 1.02912 0.514558 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) −4.00000 −0.186908
\(459\) −1.00000 −0.0466760
\(460\) −5.00000 −0.233126
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) −1.00000 −0.0465242
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 9.00000 0.417815
\(465\) −7.00000 −0.324617
\(466\) 15.0000 0.694862
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) 0 0
\(469\) 8.00000 0.369406
\(470\) 8.00000 0.369012
\(471\) −10.0000 −0.460776
\(472\) 6.00000 0.276172
\(473\) 5.00000 0.229900
\(474\) 8.00000 0.367452
\(475\) 4.00000 0.183533
\(476\) 1.00000 0.0458349
\(477\) 12.0000 0.549442
\(478\) 2.00000 0.0914779
\(479\) −39.0000 −1.78196 −0.890978 0.454047i \(-0.849980\pi\)
−0.890978 + 0.454047i \(0.849980\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 0 0
\(482\) −1.00000 −0.0455488
\(483\) −5.00000 −0.227508
\(484\) 1.00000 0.0454545
\(485\) −7.00000 −0.317854
\(486\) 1.00000 0.0453609
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) 14.0000 0.633750
\(489\) −5.00000 −0.226108
\(490\) −6.00000 −0.271052
\(491\) 40.0000 1.80517 0.902587 0.430507i \(-0.141665\pi\)
0.902587 + 0.430507i \(0.141665\pi\)
\(492\) 0 0
\(493\) 9.00000 0.405340
\(494\) 0 0
\(495\) 1.00000 0.0449467
\(496\) −7.00000 −0.314309
\(497\) −6.00000 −0.269137
\(498\) 16.0000 0.716977
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −18.0000 −0.804181
\(502\) 8.00000 0.357057
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) −1.00000 −0.0445435
\(505\) −10.0000 −0.444994
\(506\) 5.00000 0.222277
\(507\) 13.0000 0.577350
\(508\) −18.0000 −0.798621
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) −1.00000 −0.0442807
\(511\) −14.0000 −0.619324
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 −0.176604
\(514\) 17.0000 0.749838
\(515\) 1.00000 0.0440653
\(516\) 5.00000 0.220113
\(517\) −8.00000 −0.351840
\(518\) 2.00000 0.0878750
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −9.00000 −0.393919
\(523\) 19.0000 0.830812 0.415406 0.909636i \(-0.363640\pi\)
0.415406 + 0.909636i \(0.363640\pi\)
\(524\) −8.00000 −0.349482
\(525\) −1.00000 −0.0436436
\(526\) −7.00000 −0.305215
\(527\) −7.00000 −0.304925
\(528\) 1.00000 0.0435194
\(529\) 2.00000 0.0869565
\(530\) 12.0000 0.521247
\(531\) −6.00000 −0.260378
\(532\) 4.00000 0.173422
\(533\) 0 0
\(534\) 0 0
\(535\) 5.00000 0.216169
\(536\) −8.00000 −0.345547
\(537\) −2.00000 −0.0863064
\(538\) −30.0000 −1.29339
\(539\) 6.00000 0.258438
\(540\) 1.00000 0.0430331
\(541\) 8.00000 0.343947 0.171973 0.985102i \(-0.444986\pi\)
0.171973 + 0.985102i \(0.444986\pi\)
\(542\) −27.0000 −1.15975
\(543\) 7.00000 0.300399
\(544\) −1.00000 −0.0428746
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) 38.0000 1.62476 0.812381 0.583127i \(-0.198171\pi\)
0.812381 + 0.583127i \(0.198171\pi\)
\(548\) 9.00000 0.384461
\(549\) −14.0000 −0.597505
\(550\) 1.00000 0.0426401
\(551\) 36.0000 1.53365
\(552\) 5.00000 0.212814
\(553\) 8.00000 0.340195
\(554\) −14.0000 −0.594803
\(555\) −2.00000 −0.0848953
\(556\) −1.00000 −0.0424094
\(557\) 23.0000 0.974541 0.487271 0.873251i \(-0.337993\pi\)
0.487271 + 0.873251i \(0.337993\pi\)
\(558\) 7.00000 0.296334
\(559\) 0 0
\(560\) −1.00000 −0.0422577
\(561\) 1.00000 0.0422200
\(562\) 3.00000 0.126547
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) −8.00000 −0.336861
\(565\) −6.00000 −0.252422
\(566\) −22.0000 −0.924729
\(567\) 1.00000 0.0419961
\(568\) 6.00000 0.251754
\(569\) −2.00000 −0.0838444 −0.0419222 0.999121i \(-0.513348\pi\)
−0.0419222 + 0.999121i \(0.513348\pi\)
\(570\) −4.00000 −0.167542
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 3.00000 0.125327
\(574\) 0 0
\(575\) 5.00000 0.208514
\(576\) 1.00000 0.0416667
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −22.0000 −0.914289
\(580\) −9.00000 −0.373705
\(581\) 16.0000 0.663792
\(582\) 7.00000 0.290159
\(583\) −12.0000 −0.496989
\(584\) 14.0000 0.579324
\(585\) 0 0
\(586\) −33.0000 −1.36322
\(587\) 35.0000 1.44460 0.722302 0.691577i \(-0.243084\pi\)
0.722302 + 0.691577i \(0.243084\pi\)
\(588\) 6.00000 0.247436
\(589\) −28.0000 −1.15372
\(590\) −6.00000 −0.247016
\(591\) 8.00000 0.329076
\(592\) −2.00000 −0.0821995
\(593\) 42.0000 1.72473 0.862367 0.506284i \(-0.168981\pi\)
0.862367 + 0.506284i \(0.168981\pi\)
\(594\) −1.00000 −0.0410305
\(595\) −1.00000 −0.0409960
\(596\) −8.00000 −0.327693
\(597\) 0 0
\(598\) 0 0
\(599\) −13.0000 −0.531166 −0.265583 0.964088i \(-0.585564\pi\)
−0.265583 + 0.964088i \(0.585564\pi\)
\(600\) 1.00000 0.0408248
\(601\) −42.0000 −1.71322 −0.856608 0.515968i \(-0.827432\pi\)
−0.856608 + 0.515968i \(0.827432\pi\)
\(602\) 5.00000 0.203785
\(603\) 8.00000 0.325785
\(604\) 20.0000 0.813788
\(605\) −1.00000 −0.0406558
\(606\) 10.0000 0.406222
\(607\) −16.0000 −0.649420 −0.324710 0.945814i \(-0.605267\pi\)
−0.324710 + 0.945814i \(0.605267\pi\)
\(608\) −4.00000 −0.162221
\(609\) −9.00000 −0.364698
\(610\) −14.0000 −0.566843
\(611\) 0 0
\(612\) 1.00000 0.0404226
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) 28.0000 1.12999
\(615\) 0 0
\(616\) 1.00000 0.0402911
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 42.0000 1.68812 0.844061 0.536247i \(-0.180158\pi\)
0.844061 + 0.536247i \(0.180158\pi\)
\(620\) 7.00000 0.281127
\(621\) −5.00000 −0.200643
\(622\) −20.0000 −0.801927
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −25.0000 −0.999201
\(627\) 4.00000 0.159745
\(628\) 10.0000 0.399043
\(629\) −2.00000 −0.0797452
\(630\) 1.00000 0.0398410
\(631\) 14.0000 0.557331 0.278666 0.960388i \(-0.410108\pi\)
0.278666 + 0.960388i \(0.410108\pi\)
\(632\) −8.00000 −0.318223
\(633\) −17.0000 −0.675689
\(634\) −27.0000 −1.07231
\(635\) 18.0000 0.714308
\(636\) −12.0000 −0.475831
\(637\) 0 0
\(638\) 9.00000 0.356313
\(639\) −6.00000 −0.237356
\(640\) 1.00000 0.0395285
\(641\) −27.0000 −1.06644 −0.533218 0.845978i \(-0.679017\pi\)
−0.533218 + 0.845978i \(0.679017\pi\)
\(642\) −5.00000 −0.197334
\(643\) −13.0000 −0.512670 −0.256335 0.966588i \(-0.582515\pi\)
−0.256335 + 0.966588i \(0.582515\pi\)
\(644\) 5.00000 0.197028
\(645\) −5.00000 −0.196875
\(646\) −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
\(649\) 6.00000 0.235521
\(650\) 0 0
\(651\) 7.00000 0.274352
\(652\) 5.00000 0.195815
\(653\) −37.0000 −1.44792 −0.723961 0.689841i \(-0.757680\pi\)
−0.723961 + 0.689841i \(0.757680\pi\)
\(654\) −4.00000 −0.156412
\(655\) 8.00000 0.312586
\(656\) 0 0
\(657\) −14.0000 −0.546192
\(658\) −8.00000 −0.311872
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) −1.00000 −0.0389249
\(661\) 36.0000 1.40024 0.700119 0.714026i \(-0.253130\pi\)
0.700119 + 0.714026i \(0.253130\pi\)
\(662\) 19.0000 0.738456
\(663\) 0 0
\(664\) −16.0000 −0.620920
\(665\) −4.00000 −0.155113
\(666\) 2.00000 0.0774984
\(667\) 45.0000 1.74241
\(668\) 18.0000 0.696441
\(669\) 9.00000 0.347960
\(670\) 8.00000 0.309067
\(671\) 14.0000 0.540464
\(672\) 1.00000 0.0385758
\(673\) −8.00000 −0.308377 −0.154189 0.988041i \(-0.549276\pi\)
−0.154189 + 0.988041i \(0.549276\pi\)
\(674\) −22.0000 −0.847408
\(675\) −1.00000 −0.0384900
\(676\) −13.0000 −0.500000
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 6.00000 0.230429
\(679\) 7.00000 0.268635
\(680\) 1.00000 0.0383482
\(681\) 29.0000 1.11128
\(682\) −7.00000 −0.268044
\(683\) −8.00000 −0.306111 −0.153056 0.988218i \(-0.548911\pi\)
−0.153056 + 0.988218i \(0.548911\pi\)
\(684\) 4.00000 0.152944
\(685\) −9.00000 −0.343872
\(686\) 13.0000 0.496342
\(687\) −4.00000 −0.152610
\(688\) −5.00000 −0.190623
\(689\) 0 0
\(690\) −5.00000 −0.190347
\(691\) 12.0000 0.456502 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) −18.0000 −0.684257
\(693\) −1.00000 −0.0379869
\(694\) −28.0000 −1.06287
\(695\) 1.00000 0.0379322
\(696\) 9.00000 0.341144
\(697\) 0 0
\(698\) −2.00000 −0.0757011
\(699\) 15.0000 0.567352
\(700\) 1.00000 0.0377964
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) −8.00000 −0.301726
\(704\) −1.00000 −0.0376889
\(705\) 8.00000 0.301297
\(706\) 7.00000 0.263448
\(707\) 10.0000 0.376089
\(708\) 6.00000 0.225494
\(709\) −26.0000 −0.976450 −0.488225 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) −6.00000 −0.225176
\(711\) 8.00000 0.300023
\(712\) 0 0
\(713\) −35.0000 −1.31076
\(714\) 1.00000 0.0374241
\(715\) 0 0
\(716\) 2.00000 0.0747435
\(717\) 2.00000 0.0746914
\(718\) −18.0000 −0.671754
\(719\) −14.0000 −0.522112 −0.261056 0.965324i \(-0.584071\pi\)
−0.261056 + 0.965324i \(0.584071\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −1.00000 −0.0372419
\(722\) 3.00000 0.111648
\(723\) −1.00000 −0.0371904
\(724\) −7.00000 −0.260153
\(725\) 9.00000 0.334252
\(726\) 1.00000 0.0371135
\(727\) 23.0000 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −14.0000 −0.518163
\(731\) −5.00000 −0.184932
\(732\) 14.0000 0.517455
\(733\) −36.0000 −1.32969 −0.664845 0.746981i \(-0.731502\pi\)
−0.664845 + 0.746981i \(0.731502\pi\)
\(734\) −18.0000 −0.664392
\(735\) −6.00000 −0.221313
\(736\) −5.00000 −0.184302
\(737\) −8.00000 −0.294684
\(738\) 0 0
\(739\) 26.0000 0.956425 0.478213 0.878244i \(-0.341285\pi\)
0.478213 + 0.878244i \(0.341285\pi\)
\(740\) 2.00000 0.0735215
\(741\) 0 0
\(742\) −12.0000 −0.440534
\(743\) 8.00000 0.293492 0.146746 0.989174i \(-0.453120\pi\)
0.146746 + 0.989174i \(0.453120\pi\)
\(744\) −7.00000 −0.256632
\(745\) 8.00000 0.293097
\(746\) −14.0000 −0.512576
\(747\) 16.0000 0.585409
\(748\) −1.00000 −0.0365636
\(749\) −5.00000 −0.182696
\(750\) −1.00000 −0.0365148
\(751\) −17.0000 −0.620339 −0.310169 0.950681i \(-0.600386\pi\)
−0.310169 + 0.950681i \(0.600386\pi\)
\(752\) 8.00000 0.291730
\(753\) 8.00000 0.291536
\(754\) 0 0
\(755\) −20.0000 −0.727875
\(756\) −1.00000 −0.0363696
\(757\) −45.0000 −1.63555 −0.817776 0.575536i \(-0.804793\pi\)
−0.817776 + 0.575536i \(0.804793\pi\)
\(758\) −20.0000 −0.726433
\(759\) 5.00000 0.181489
\(760\) 4.00000 0.145095
\(761\) −37.0000 −1.34125 −0.670624 0.741797i \(-0.733974\pi\)
−0.670624 + 0.741797i \(0.733974\pi\)
\(762\) −18.0000 −0.652071
\(763\) −4.00000 −0.144810
\(764\) −3.00000 −0.108536
\(765\) −1.00000 −0.0361551
\(766\) −8.00000 −0.289052
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) −1.00000 −0.0360375
\(771\) 17.0000 0.612240
\(772\) 22.0000 0.791797
\(773\) 36.0000 1.29483 0.647415 0.762138i \(-0.275850\pi\)
0.647415 + 0.762138i \(0.275850\pi\)
\(774\) 5.00000 0.179721
\(775\) −7.00000 −0.251447
\(776\) −7.00000 −0.251285
\(777\) 2.00000 0.0717496
\(778\) 22.0000 0.788738
\(779\) 0 0
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) −5.00000 −0.178800
\(783\) −9.00000 −0.321634
\(784\) −6.00000 −0.214286
\(785\) −10.0000 −0.356915
\(786\) −8.00000 −0.285351
\(787\) −28.0000 −0.998092 −0.499046 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) −8.00000 −0.284988
\(789\) −7.00000 −0.249207
\(790\) 8.00000 0.284627
\(791\) 6.00000 0.213335
\(792\) 1.00000 0.0355335
\(793\) 0 0
\(794\) −22.0000 −0.780751
\(795\) 12.0000 0.425596
\(796\) 0 0
\(797\) 8.00000 0.283375 0.141687 0.989911i \(-0.454747\pi\)
0.141687 + 0.989911i \(0.454747\pi\)
\(798\) 4.00000 0.141598
\(799\) 8.00000 0.283020
\(800\) −1.00000 −0.0353553
\(801\) 0 0
\(802\) −3.00000 −0.105934
\(803\) 14.0000 0.494049
\(804\) −8.00000 −0.282138
\(805\) −5.00000 −0.176227
\(806\) 0 0
\(807\) −30.0000 −1.05605
\(808\) −10.0000 −0.351799
\(809\) 26.0000 0.914111 0.457056 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) 1.00000 0.0351364
\(811\) 24.0000 0.842754 0.421377 0.906886i \(-0.361547\pi\)
0.421377 + 0.906886i \(0.361547\pi\)
\(812\) 9.00000 0.315838
\(813\) −27.0000 −0.946931
\(814\) −2.00000 −0.0701000
\(815\) −5.00000 −0.175142
\(816\) −1.00000 −0.0350070
\(817\) −20.0000 −0.699711
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 27.0000 0.942306 0.471153 0.882051i \(-0.343838\pi\)
0.471153 + 0.882051i \(0.343838\pi\)
\(822\) 9.00000 0.313911
\(823\) −22.0000 −0.766872 −0.383436 0.923567i \(-0.625259\pi\)
−0.383436 + 0.923567i \(0.625259\pi\)
\(824\) 1.00000 0.0348367
\(825\) 1.00000 0.0348155
\(826\) 6.00000 0.208767
\(827\) −11.0000 −0.382507 −0.191254 0.981541i \(-0.561255\pi\)
−0.191254 + 0.981541i \(0.561255\pi\)
\(828\) 5.00000 0.173762
\(829\) −50.0000 −1.73657 −0.868286 0.496064i \(-0.834778\pi\)
−0.868286 + 0.496064i \(0.834778\pi\)
\(830\) 16.0000 0.555368
\(831\) −14.0000 −0.485655
\(832\) 0 0
\(833\) −6.00000 −0.207888
\(834\) −1.00000 −0.0346272
\(835\) −18.0000 −0.622916
\(836\) −4.00000 −0.138343
\(837\) 7.00000 0.241955
\(838\) 23.0000 0.794522
\(839\) 30.0000 1.03572 0.517858 0.855467i \(-0.326730\pi\)
0.517858 + 0.855467i \(0.326730\pi\)
\(840\) −1.00000 −0.0345033
\(841\) 52.0000 1.79310
\(842\) −12.0000 −0.413547
\(843\) 3.00000 0.103325
\(844\) 17.0000 0.585164
\(845\) 13.0000 0.447214
\(846\) −8.00000 −0.275046
\(847\) 1.00000 0.0343604
\(848\) 12.0000 0.412082
\(849\) −22.0000 −0.755038
\(850\) −1.00000 −0.0342997
\(851\) −10.0000 −0.342796
\(852\) 6.00000 0.205557
\(853\) 49.0000 1.67773 0.838864 0.544341i \(-0.183220\pi\)
0.838864 + 0.544341i \(0.183220\pi\)
\(854\) 14.0000 0.479070
\(855\) −4.00000 −0.136797
\(856\) 5.00000 0.170896
\(857\) −9.00000 −0.307434 −0.153717 0.988115i \(-0.549124\pi\)
−0.153717 + 0.988115i \(0.549124\pi\)
\(858\) 0 0
\(859\) 3.00000 0.102359 0.0511793 0.998689i \(-0.483702\pi\)
0.0511793 + 0.998689i \(0.483702\pi\)
\(860\) 5.00000 0.170499
\(861\) 0 0
\(862\) −39.0000 −1.32835
\(863\) −8.00000 −0.272323 −0.136162 0.990687i \(-0.543477\pi\)
−0.136162 + 0.990687i \(0.543477\pi\)
\(864\) 1.00000 0.0340207
\(865\) 18.0000 0.612018
\(866\) 4.00000 0.135926
\(867\) −1.00000 −0.0339618
\(868\) −7.00000 −0.237595
\(869\) −8.00000 −0.271381
\(870\) −9.00000 −0.305129
\(871\) 0 0
\(872\) 4.00000 0.135457
\(873\) 7.00000 0.236914
\(874\) −20.0000 −0.676510
\(875\) −1.00000 −0.0338062
\(876\) 14.0000 0.473016
\(877\) 9.00000 0.303908 0.151954 0.988388i \(-0.451443\pi\)
0.151954 + 0.988388i \(0.451443\pi\)
\(878\) 38.0000 1.28244
\(879\) −33.0000 −1.11306
\(880\) 1.00000 0.0337100
\(881\) −29.0000 −0.977035 −0.488517 0.872554i \(-0.662462\pi\)
−0.488517 + 0.872554i \(0.662462\pi\)
\(882\) 6.00000 0.202031
\(883\) 56.0000 1.88455 0.942275 0.334840i \(-0.108682\pi\)
0.942275 + 0.334840i \(0.108682\pi\)
\(884\) 0 0
\(885\) −6.00000 −0.201688
\(886\) −13.0000 −0.436744
\(887\) −44.0000 −1.47738 −0.738688 0.674048i \(-0.764554\pi\)
−0.738688 + 0.674048i \(0.764554\pi\)
\(888\) −2.00000 −0.0671156
\(889\) −18.0000 −0.603701
\(890\) 0 0
\(891\) −1.00000 −0.0335013
\(892\) −9.00000 −0.301342
\(893\) 32.0000 1.07084
\(894\) −8.00000 −0.267560
\(895\) −2.00000 −0.0668526
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 15.0000 0.500556
\(899\) −63.0000 −2.10117
\(900\) 1.00000 0.0333333
\(901\) 12.0000 0.399778
\(902\) 0 0
\(903\) 5.00000 0.166390
\(904\) −6.00000 −0.199557
\(905\) 7.00000 0.232688
\(906\) 20.0000 0.664455
\(907\) −5.00000 −0.166022 −0.0830111 0.996549i \(-0.526454\pi\)
−0.0830111 + 0.996549i \(0.526454\pi\)
\(908\) −29.0000 −0.962399
\(909\) 10.0000 0.331679
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) −4.00000 −0.132453
\(913\) −16.0000 −0.529523
\(914\) −22.0000 −0.727695
\(915\) −14.0000 −0.462826
\(916\) 4.00000 0.132164
\(917\) −8.00000 −0.264183
\(918\) 1.00000 0.0330049
\(919\) −11.0000 −0.362857 −0.181428 0.983404i \(-0.558072\pi\)
−0.181428 + 0.983404i \(0.558072\pi\)
\(920\) 5.00000 0.164845
\(921\) 28.0000 0.922631
\(922\) 18.0000 0.592798
\(923\) 0 0
\(924\) 1.00000 0.0328976
\(925\) −2.00000 −0.0657596
\(926\) 8.00000 0.262896
\(927\) −1.00000 −0.0328443
\(928\) −9.00000 −0.295439
\(929\) −47.0000 −1.54202 −0.771010 0.636823i \(-0.780248\pi\)
−0.771010 + 0.636823i \(0.780248\pi\)
\(930\) 7.00000 0.229539
\(931\) −24.0000 −0.786568
\(932\) −15.0000 −0.491341
\(933\) −20.0000 −0.654771
\(934\) −36.0000 −1.17796
\(935\) 1.00000 0.0327035
\(936\) 0 0
\(937\) 30.0000 0.980057 0.490029 0.871706i \(-0.336986\pi\)
0.490029 + 0.871706i \(0.336986\pi\)
\(938\) −8.00000 −0.261209
\(939\) −25.0000 −0.815844
\(940\) −8.00000 −0.260931
\(941\) 30.0000 0.977972 0.488986 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) 10.0000 0.325818
\(943\) 0 0
\(944\) −6.00000 −0.195283
\(945\) 1.00000 0.0325300
\(946\) −5.00000 −0.162564
\(947\) −6.00000 −0.194974 −0.0974869 0.995237i \(-0.531080\pi\)
−0.0974869 + 0.995237i \(0.531080\pi\)
\(948\) −8.00000 −0.259828
\(949\) 0 0
\(950\) −4.00000 −0.129777
\(951\) −27.0000 −0.875535
\(952\) −1.00000 −0.0324102
\(953\) −38.0000 −1.23094 −0.615470 0.788160i \(-0.711034\pi\)
−0.615470 + 0.788160i \(0.711034\pi\)
\(954\) −12.0000 −0.388514
\(955\) 3.00000 0.0970777
\(956\) −2.00000 −0.0646846
\(957\) 9.00000 0.290929
\(958\) 39.0000 1.26003
\(959\) 9.00000 0.290625
\(960\) 1.00000 0.0322749
\(961\) 18.0000 0.580645
\(962\) 0 0
\(963\) −5.00000 −0.161123
\(964\) 1.00000 0.0322078
\(965\) −22.0000 −0.708205
\(966\) 5.00000 0.160872
\(967\) 42.0000 1.35063 0.675314 0.737530i \(-0.264008\pi\)
0.675314 + 0.737530i \(0.264008\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −4.00000 −0.128499
\(970\) 7.00000 0.224756
\(971\) 28.0000 0.898563 0.449281 0.893390i \(-0.351680\pi\)
0.449281 + 0.893390i \(0.351680\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −1.00000 −0.0320585
\(974\) −2.00000 −0.0640841
\(975\) 0 0
\(976\) −14.0000 −0.448129
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 5.00000 0.159882
\(979\) 0 0
\(980\) 6.00000 0.191663
\(981\) −4.00000 −0.127710
\(982\) −40.0000 −1.27645
\(983\) −19.0000 −0.606006 −0.303003 0.952990i \(-0.597989\pi\)
−0.303003 + 0.952990i \(0.597989\pi\)
\(984\) 0 0
\(985\) 8.00000 0.254901
\(986\) −9.00000 −0.286618
\(987\) −8.00000 −0.254643
\(988\) 0 0
\(989\) −25.0000 −0.794954
\(990\) −1.00000 −0.0317821
\(991\) 3.00000 0.0952981 0.0476491 0.998864i \(-0.484827\pi\)
0.0476491 + 0.998864i \(0.484827\pi\)
\(992\) 7.00000 0.222250
\(993\) 19.0000 0.602947
\(994\) 6.00000 0.190308
\(995\) 0 0
\(996\) −16.0000 −0.506979
\(997\) −21.0000 −0.665077 −0.332538 0.943090i \(-0.607905\pi\)
−0.332538 + 0.943090i \(0.607905\pi\)
\(998\) −28.0000 −0.886325
\(999\) 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.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.d.1.1 1 1.1 even 1 trivial