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Properties

Label 3234.2.a.c.1.1
Level $3234$
Weight $2$
Character 3234.1
Self dual yes
Analytic conductor $25.824$
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] = [3234,2,Mod(1,3234)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3234, 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("3234.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.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: \(25.8236200137\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 3234.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -3.00000 q^{19} +1.00000 q^{22} -1.00000 q^{23} +1.00000 q^{24} -5.00000 q^{25} -4.00000 q^{26} -1.00000 q^{27} -1.00000 q^{29} +6.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} -3.00000 q^{37} +3.00000 q^{38} -4.00000 q^{39} -6.00000 q^{41} +1.00000 q^{43} -1.00000 q^{44} +1.00000 q^{46} -1.00000 q^{47} -1.00000 q^{48} +5.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} +1.00000 q^{54} +3.00000 q^{57} +1.00000 q^{58} +7.00000 q^{59} +6.00000 q^{61} -6.00000 q^{62} +1.00000 q^{64} -1.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} +1.00000 q^{69} -15.0000 q^{71} -1.00000 q^{72} +12.0000 q^{73} +3.00000 q^{74} +5.00000 q^{75} -3.00000 q^{76} +4.00000 q^{78} +1.00000 q^{81} +6.00000 q^{82} -16.0000 q^{83} -1.00000 q^{86} +1.00000 q^{87} +1.00000 q^{88} -8.00000 q^{89} -1.00000 q^{92} -6.00000 q^{93} +1.00000 q^{94} +1.00000 q^{96} +7.00000 q^{97} -1.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) −1.00000 −0.288675
\(13\) 4.00000 1.10940 0.554700 − 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536 −0.121268 − 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) −1.00000 −0.235702
\(19\) −3.00000 −0.688247 −0.344124 − 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −1.00000 −0.208514 −0.104257 − 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 1.00000 0.204124
\(25\) −5.00000 −1.00000
\(26\) −4.00000 −0.784465
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695 −0.0928477 − 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 0 0
\(31\) 6.00000 1.07763 0.538816 − 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −3.00000 −0.493197 −0.246598 − 0.969118i \(-0.579313\pi\)
−0.246598 + 0.969118i \(0.579313\pi\)
\(38\) 3.00000 0.486664
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 − 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) −1.00000 −0.145865 −0.0729325 − 0.997337i \(-0.523236\pi\)
−0.0729325 + 0.997337i \(0.523236\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 5.00000 0.707107
\(51\) 1.00000 0.140028
\(52\) 4.00000 0.554700
\(53\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) 1.00000 0.131306
\(59\) 7.00000 0.911322 0.455661 − 0.890153i \(-0.349403\pi\)
0.455661 + 0.890153i \(0.349403\pi\)
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 − 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −1.00000 −0.123091
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −1.00000 −0.121268
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −15.0000 −1.78017 −0.890086 − 0.455792i \(-0.849356\pi\)
−0.890086 + 0.455792i \(0.849356\pi\)
\(72\) −1.00000 −0.117851
\(73\) 12.0000 1.40449 0.702247 − 0.711934i \(-0.252180\pi\)
0.702247 + 0.711934i \(0.252180\pi\)
\(74\) 3.00000 0.348743
\(75\) 5.00000 0.577350
\(76\) −3.00000 −0.344124
\(77\) 0 0
\(78\) 4.00000 0.452911
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) −16.0000 −1.75623 −0.878114 − 0.478451i \(-0.841198\pi\)
−0.878114 + 0.478451i \(0.841198\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.00000 −0.107833
\(87\) 1.00000 0.107211
\(88\) 1.00000 0.106600
\(89\) −8.00000 −0.847998 −0.423999 − 0.905663i \(-0.639374\pi\)
−0.423999 + 0.905663i \(0.639374\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.00000 −0.104257
\(93\) −6.00000 −0.622171
\(94\) 1.00000 0.103142
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 7.00000 0.710742 0.355371 − 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) −5.00000 −0.500000
\(101\) 15.0000 1.49256 0.746278 − 0.665635i \(-0.231839\pi\)
0.746278 + 0.665635i \(0.231839\pi\)
\(102\) −1.00000 −0.0990148
\(103\) 4.00000 0.394132 0.197066 − 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 0 0
\(107\) 2.00000 0.193347 0.0966736 − 0.995316i \(-0.469180\pi\)
0.0966736 + 0.995316i \(0.469180\pi\)
\(108\) −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
\(111\) 3.00000 0.284747
\(112\) 0 0
\(113\) 4.00000 0.376288 0.188144 − 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) −3.00000 −0.280976
\(115\) 0 0
\(116\) −1.00000 −0.0928477
\(117\) 4.00000 0.369800
\(118\) −7.00000 −0.644402
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −6.00000 −0.543214
\(123\) 6.00000 0.541002
\(124\) 6.00000 0.538816
\(125\) 0 0
\(126\) 0 0
\(127\) −7.00000 −0.621150 −0.310575 − 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.00000 −0.0880451
\(130\) 0 0
\(131\) −2.00000 −0.174741 −0.0873704 − 0.996176i \(-0.527846\pi\)
−0.0873704 + 0.996176i \(0.527846\pi\)
\(132\) 1.00000 0.0870388
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 1.00000 0.0857493
\(137\) −4.00000 −0.341743 −0.170872 − 0.985293i \(-0.554658\pi\)
−0.170872 + 0.985293i \(0.554658\pi\)
\(138\) −1.00000 −0.0851257
\(139\) −17.0000 −1.44192 −0.720961 − 0.692976i \(-0.756299\pi\)
−0.720961 + 0.692976i \(0.756299\pi\)
\(140\) 0 0
\(141\) 1.00000 0.0842152
\(142\) 15.0000 1.25877
\(143\) −4.00000 −0.334497
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −12.0000 −0.993127
\(147\) 0 0
\(148\) −3.00000 −0.246598
\(149\) 1.00000 0.0819232 0.0409616 − 0.999161i \(-0.486958\pi\)
0.0409616 + 0.999161i \(0.486958\pi\)
\(150\) −5.00000 −0.408248
\(151\) 11.0000 0.895167 0.447584 − 0.894242i \(-0.352285\pi\)
0.447584 + 0.894242i \(0.352285\pi\)
\(152\) 3.00000 0.243332
\(153\) −1.00000 −0.0808452
\(154\) 0 0
\(155\) 0 0
\(156\) −4.00000 −0.320256
\(157\) −9.00000 −0.718278 −0.359139 − 0.933284i \(-0.616930\pi\)
−0.359139 + 0.933284i \(0.616930\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −18.0000 −1.40987 −0.704934 − 0.709273i \(-0.749024\pi\)
−0.704934 + 0.709273i \(0.749024\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 16.0000 1.24184
\(167\) −12.0000 −0.928588 −0.464294 − 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −3.00000 −0.229416
\(172\) 1.00000 0.0762493
\(173\) −6.00000 −0.456172 −0.228086 − 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) −1.00000 −0.0758098
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) −7.00000 −0.526152
\(178\) 8.00000 0.599625
\(179\) −25.0000 −1.86859 −0.934294 − 0.356504i \(-0.883969\pi\)
−0.934294 + 0.356504i \(0.883969\pi\)
\(180\) 0 0
\(181\) 22.0000 1.63525 0.817624 − 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) −6.00000 −0.443533
\(184\) 1.00000 0.0737210
\(185\) 0 0
\(186\) 6.00000 0.439941
\(187\) 1.00000 0.0731272
\(188\) −1.00000 −0.0729325
\(189\) 0 0
\(190\) 0 0
\(191\) −24.0000 −1.73658 −0.868290 − 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 14.0000 1.00774 0.503871 − 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −7.00000 −0.502571
\(195\) 0 0
\(196\) 0 0
\(197\) 27.0000 1.92367 0.961835 − 0.273629i \(-0.0882242\pi\)
0.961835 + 0.273629i \(0.0882242\pi\)
\(198\) 1.00000 0.0710669
\(199\) 4.00000 0.283552 0.141776 − 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 5.00000 0.353553
\(201\) 4.00000 0.282138
\(202\) −15.0000 −1.05540
\(203\) 0 0
\(204\) 1.00000 0.0700140
\(205\) 0 0
\(206\) −4.00000 −0.278693
\(207\) −1.00000 −0.0695048
\(208\) 4.00000 0.277350
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 − 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 0 0
\(213\) 15.0000 1.02778
\(214\) −2.00000 −0.136717
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 18.0000 1.21911
\(219\) −12.0000 −0.810885
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) −3.00000 −0.201347
\(223\) 16.0000 1.07144 0.535720 − 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) −5.00000 −0.333333
\(226\) −4.00000 −0.266076
\(227\) −2.00000 −0.132745 −0.0663723 − 0.997795i \(-0.521143\pi\)
−0.0663723 + 0.997795i \(0.521143\pi\)
\(228\) 3.00000 0.198680
\(229\) −6.00000 −0.396491 −0.198246 − 0.980152i \(-0.563524\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.00000 0.0656532
\(233\) −11.0000 −0.720634 −0.360317 − 0.932830i \(-0.617331\pi\)
−0.360317 + 0.932830i \(0.617331\pi\)
\(234\) −4.00000 −0.261488
\(235\) 0 0
\(236\) 7.00000 0.455661
\(237\) 0 0
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 − 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) −4.00000 −0.257663 −0.128831 − 0.991667i \(-0.541123\pi\)
−0.128831 + 0.991667i \(0.541123\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) −12.0000 −0.763542
\(248\) −6.00000 −0.381000
\(249\) 16.0000 1.01396
\(250\) 0 0
\(251\) −7.00000 −0.441836 −0.220918 − 0.975292i \(-0.570905\pi\)
−0.220918 + 0.975292i \(0.570905\pi\)
\(252\) 0 0
\(253\) 1.00000 0.0628695
\(254\) 7.00000 0.439219
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −12.0000 −0.748539 −0.374270 − 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) 1.00000 0.0622573
\(259\) 0 0
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 2.00000 0.123560
\(263\) −14.0000 −0.863277 −0.431638 − 0.902047i \(-0.642064\pi\)
−0.431638 + 0.902047i \(0.642064\pi\)
\(264\) −1.00000 −0.0615457
\(265\) 0 0
\(266\) 0 0
\(267\) 8.00000 0.489592
\(268\) −4.00000 −0.244339
\(269\) −18.0000 −1.09748 −0.548740 − 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 − 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 0 0
\(274\) 4.00000 0.241649
\(275\) 5.00000 0.301511
\(276\) 1.00000 0.0601929
\(277\) −16.0000 −0.961347 −0.480673 − 0.876900i \(-0.659608\pi\)
−0.480673 + 0.876900i \(0.659608\pi\)
\(278\) 17.0000 1.01959
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) −27.0000 −1.61068 −0.805342 − 0.592810i \(-0.798019\pi\)
−0.805342 + 0.592810i \(0.798019\pi\)
\(282\) −1.00000 −0.0595491
\(283\) 20.0000 1.18888 0.594438 − 0.804141i \(-0.297374\pi\)
0.594438 + 0.804141i \(0.297374\pi\)
\(284\) −15.0000 −0.890086
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) −7.00000 −0.410347
\(292\) 12.0000 0.702247
\(293\) −15.0000 −0.876309 −0.438155 − 0.898900i \(-0.644368\pi\)
−0.438155 + 0.898900i \(0.644368\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.00000 0.174371
\(297\) 1.00000 0.0580259
\(298\) −1.00000 −0.0579284
\(299\) −4.00000 −0.231326
\(300\) 5.00000 0.288675
\(301\) 0 0
\(302\) −11.0000 −0.632979
\(303\) −15.0000 −0.861727
\(304\) −3.00000 −0.172062
\(305\) 0 0
\(306\) 1.00000 0.0571662
\(307\) −20.0000 −1.14146 −0.570730 − 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) −31.0000 −1.75785 −0.878924 − 0.476961i \(-0.841738\pi\)
−0.878924 + 0.476961i \(0.841738\pi\)
\(312\) 4.00000 0.226455
\(313\) −33.0000 −1.86527 −0.932635 − 0.360821i \(-0.882497\pi\)
−0.932635 + 0.360821i \(0.882497\pi\)
\(314\) 9.00000 0.507899
\(315\) 0 0
\(316\) 0 0
\(317\) 12.0000 0.673987 0.336994 − 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 0 0
\(319\) 1.00000 0.0559893
\(320\) 0 0
\(321\) −2.00000 −0.111629
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) 1.00000 0.0555556
\(325\) −20.0000 −1.10940
\(326\) 18.0000 0.996928
\(327\) 18.0000 0.995402
\(328\) 6.00000 0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) 10.0000 0.549650 0.274825 − 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) −16.0000 −0.878114
\(333\) −3.00000 −0.164399
\(334\) 12.0000 0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) −26.0000 −1.41631 −0.708155 − 0.706057i \(-0.750472\pi\)
−0.708155 + 0.706057i \(0.750472\pi\)
\(338\) −3.00000 −0.163178
\(339\) −4.00000 −0.217250
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) 3.00000 0.162221
\(343\) 0 0
\(344\) −1.00000 −0.0539164
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) −20.0000 −1.07366 −0.536828 − 0.843692i \(-0.680378\pi\)
−0.536828 + 0.843692i \(0.680378\pi\)
\(348\) 1.00000 0.0536056
\(349\) 32.0000 1.71292 0.856460 − 0.516213i \(-0.172659\pi\)
0.856460 + 0.516213i \(0.172659\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 1.00000 0.0533002
\(353\) −8.00000 −0.425797 −0.212899 − 0.977074i \(-0.568290\pi\)
−0.212899 + 0.977074i \(0.568290\pi\)
\(354\) 7.00000 0.372046
\(355\) 0 0
\(356\) −8.00000 −0.423999
\(357\) 0 0
\(358\) 25.0000 1.32129
\(359\) 2.00000 0.105556 0.0527780 − 0.998606i \(-0.483192\pi\)
0.0527780 + 0.998606i \(0.483192\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) −22.0000 −1.15629
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) 0 0
\(366\) 6.00000 0.313625
\(367\) 20.0000 1.04399 0.521996 − 0.852948i \(-0.325188\pi\)
0.521996 + 0.852948i \(0.325188\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 0 0
\(372\) −6.00000 −0.311086
\(373\) 34.0000 1.76045 0.880227 − 0.474554i \(-0.157390\pi\)
0.880227 + 0.474554i \(0.157390\pi\)
\(374\) −1.00000 −0.0517088
\(375\) 0 0
\(376\) 1.00000 0.0515711
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) −22.0000 −1.13006 −0.565032 − 0.825069i \(-0.691136\pi\)
−0.565032 + 0.825069i \(0.691136\pi\)
\(380\) 0 0
\(381\) 7.00000 0.358621
\(382\) 24.0000 1.22795
\(383\) 29.0000 1.48183 0.740915 − 0.671598i \(-0.234392\pi\)
0.740915 + 0.671598i \(0.234392\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 1.00000 0.0508329
\(388\) 7.00000 0.355371
\(389\) −28.0000 −1.41966 −0.709828 − 0.704375i \(-0.751227\pi\)
−0.709828 + 0.704375i \(0.751227\pi\)
\(390\) 0 0
\(391\) 1.00000 0.0505722
\(392\) 0 0
\(393\) 2.00000 0.100887
\(394\) −27.0000 −1.36024
\(395\) 0 0
\(396\) −1.00000 −0.0502519
\(397\) 23.0000 1.15434 0.577168 − 0.816625i \(-0.304158\pi\)
0.577168 + 0.816625i \(0.304158\pi\)
\(398\) −4.00000 −0.200502
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 2.00000 0.0998752 0.0499376 − 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) −4.00000 −0.199502
\(403\) 24.0000 1.19553
\(404\) 15.0000 0.746278
\(405\) 0 0
\(406\) 0 0
\(407\) 3.00000 0.148704
\(408\) −1.00000 −0.0495074
\(409\) 6.00000 0.296681 0.148340 − 0.988936i \(-0.452607\pi\)
0.148340 + 0.988936i \(0.452607\pi\)
\(410\) 0 0
\(411\) 4.00000 0.197305
\(412\) 4.00000 0.197066
\(413\) 0 0
\(414\) 1.00000 0.0491473
\(415\) 0 0
\(416\) −4.00000 −0.196116
\(417\) 17.0000 0.832494
\(418\) −3.00000 −0.146735
\(419\) −17.0000 −0.830504 −0.415252 − 0.909706i \(-0.636307\pi\)
−0.415252 + 0.909706i \(0.636307\pi\)
\(420\) 0 0
\(421\) −3.00000 −0.146211 −0.0731055 − 0.997324i \(-0.523291\pi\)
−0.0731055 + 0.997324i \(0.523291\pi\)
\(422\) 20.0000 0.973585
\(423\) −1.00000 −0.0486217
\(424\) 0 0
\(425\) 5.00000 0.242536
\(426\) −15.0000 −0.726752
\(427\) 0 0
\(428\) 2.00000 0.0966736
\(429\) 4.00000 0.193122
\(430\) 0 0
\(431\) −28.0000 −1.34871 −0.674356 − 0.738406i \(-0.735579\pi\)
−0.674356 + 0.738406i \(0.735579\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −19.0000 −0.913082 −0.456541 − 0.889702i \(-0.650912\pi\)
−0.456541 + 0.889702i \(0.650912\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −18.0000 −0.862044
\(437\) 3.00000 0.143509
\(438\) 12.0000 0.573382
\(439\) −11.0000 −0.525001 −0.262501 − 0.964932i \(-0.584547\pi\)
−0.262501 + 0.964932i \(0.584547\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.00000 0.190261
\(443\) −3.00000 −0.142534 −0.0712672 − 0.997457i \(-0.522704\pi\)
−0.0712672 + 0.997457i \(0.522704\pi\)
\(444\) 3.00000 0.142374
\(445\) 0 0
\(446\) −16.0000 −0.757622
\(447\) −1.00000 −0.0472984
\(448\) 0 0
\(449\) −8.00000 −0.377543 −0.188772 − 0.982021i \(-0.560451\pi\)
−0.188772 + 0.982021i \(0.560451\pi\)
\(450\) 5.00000 0.235702
\(451\) 6.00000 0.282529
\(452\) 4.00000 0.188144
\(453\) −11.0000 −0.516825
\(454\) 2.00000 0.0938647
\(455\) 0 0
\(456\) −3.00000 −0.140488
\(457\) 18.0000 0.842004 0.421002 − 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(458\) 6.00000 0.280362
\(459\) 1.00000 0.0466760
\(460\) 0 0
\(461\) 21.0000 0.978068 0.489034 − 0.872265i \(-0.337349\pi\)
0.489034 + 0.872265i \(0.337349\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 − 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 0 0
\(466\) 11.0000 0.509565
\(467\) −23.0000 −1.06431 −0.532157 − 0.846646i \(-0.678618\pi\)
−0.532157 + 0.846646i \(0.678618\pi\)
\(468\) 4.00000 0.184900
\(469\) 0 0
\(470\) 0 0
\(471\) 9.00000 0.414698
\(472\) −7.00000 −0.322201
\(473\) −1.00000 −0.0459800
\(474\) 0 0
\(475\) 15.0000 0.688247
\(476\) 0 0
\(477\) 0 0
\(478\) −16.0000 −0.731823
\(479\) 10.0000 0.456912 0.228456 − 0.973554i \(-0.426632\pi\)
0.228456 + 0.973554i \(0.426632\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) 4.00000 0.182195
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 20.0000 0.906287 0.453143 − 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) −6.00000 −0.271607
\(489\) 18.0000 0.813988
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 − 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 6.00000 0.270501
\(493\) 1.00000 0.0450377
\(494\) 12.0000 0.539906
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) 0 0
\(498\) −16.0000 −0.716977
\(499\) 10.0000 0.447661 0.223831 − 0.974628i \(-0.428144\pi\)
0.223831 + 0.974628i \(0.428144\pi\)
\(500\) 0 0
\(501\) 12.0000 0.536120
\(502\) 7.00000 0.312425
\(503\) 2.00000 0.0891756 0.0445878 − 0.999005i \(-0.485803\pi\)
0.0445878 + 0.999005i \(0.485803\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −1.00000 −0.0444554
\(507\) −3.00000 −0.133235
\(508\) −7.00000 −0.310575
\(509\) 4.00000 0.177297 0.0886484 − 0.996063i \(-0.471745\pi\)
0.0886484 + 0.996063i \(0.471745\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 3.00000 0.132453
\(514\) 12.0000 0.529297
\(515\) 0 0
\(516\) −1.00000 −0.0440225
\(517\) 1.00000 0.0439799
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 − 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 1.00000 0.0437688
\(523\) 44.0000 1.92399 0.961993 − 0.273075i \(-0.0880406\pi\)
0.961993 + 0.273075i \(0.0880406\pi\)
\(524\) −2.00000 −0.0873704
\(525\) 0 0
\(526\) 14.0000 0.610429
\(527\) −6.00000 −0.261364
\(528\) 1.00000 0.0435194
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) 7.00000 0.303774
\(532\) 0 0
\(533\) −24.0000 −1.03956
\(534\) −8.00000 −0.346194
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) 25.0000 1.07883
\(538\) 18.0000 0.776035
\(539\) 0 0
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 − 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 16.0000 0.687259
\(543\) −22.0000 −0.944110
\(544\) 1.00000 0.0428746
\(545\) 0 0
\(546\) 0 0
\(547\) 7.00000 0.299298 0.149649 − 0.988739i \(-0.452186\pi\)
0.149649 + 0.988739i \(0.452186\pi\)
\(548\) −4.00000 −0.170872
\(549\) 6.00000 0.256074
\(550\) −5.00000 −0.213201
\(551\) 3.00000 0.127804
\(552\) −1.00000 −0.0425628
\(553\) 0 0
\(554\) 16.0000 0.679775
\(555\) 0 0
\(556\) −17.0000 −0.720961
\(557\) −3.00000 −0.127114 −0.0635570 − 0.997978i \(-0.520244\pi\)
−0.0635570 + 0.997978i \(0.520244\pi\)
\(558\) −6.00000 −0.254000
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) −1.00000 −0.0422200
\(562\) 27.0000 1.13893
\(563\) 12.0000 0.505740 0.252870 − 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 1.00000 0.0421076
\(565\) 0 0
\(566\) −20.0000 −0.840663
\(567\) 0 0
\(568\) 15.0000 0.629386
\(569\) 39.0000 1.63497 0.817483 − 0.575953i \(-0.195369\pi\)
0.817483 + 0.575953i \(0.195369\pi\)
\(570\) 0 0
\(571\) 7.00000 0.292941 0.146470 − 0.989215i \(-0.453209\pi\)
0.146470 + 0.989215i \(0.453209\pi\)
\(572\) −4.00000 −0.167248
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) 5.00000 0.208514
\(576\) 1.00000 0.0416667
\(577\) −22.0000 −0.915872 −0.457936 − 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) 16.0000 0.665512
\(579\) −14.0000 −0.581820
\(580\) 0 0
\(581\) 0 0
\(582\) 7.00000 0.290159
\(583\) 0 0
\(584\) −12.0000 −0.496564
\(585\) 0 0
\(586\) 15.0000 0.619644
\(587\) 4.00000 0.165098 0.0825488 − 0.996587i \(-0.473694\pi\)
0.0825488 + 0.996587i \(0.473694\pi\)
\(588\) 0 0
\(589\) −18.0000 −0.741677
\(590\) 0 0
\(591\) −27.0000 −1.11063
\(592\) −3.00000 −0.123299
\(593\) −19.0000 −0.780236 −0.390118 − 0.920765i \(-0.627566\pi\)
−0.390118 + 0.920765i \(0.627566\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) 1.00000 0.0409616
\(597\) −4.00000 −0.163709
\(598\) 4.00000 0.163572
\(599\) −40.0000 −1.63436 −0.817178 − 0.576386i \(-0.804463\pi\)
−0.817178 + 0.576386i \(0.804463\pi\)
\(600\) −5.00000 −0.204124
\(601\) 22.0000 0.897399 0.448699 − 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 11.0000 0.447584
\(605\) 0 0
\(606\) 15.0000 0.609333
\(607\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 3.00000 0.121666
\(609\) 0 0
\(610\) 0 0
\(611\) −4.00000 −0.161823
\(612\) −1.00000 −0.0404226
\(613\) 40.0000 1.61558 0.807792 − 0.589467i \(-0.200662\pi\)
0.807792 + 0.589467i \(0.200662\pi\)
\(614\) 20.0000 0.807134
\(615\) 0 0
\(616\) 0 0
\(617\) 26.0000 1.04672 0.523360 − 0.852111i \(-0.324678\pi\)
0.523360 + 0.852111i \(0.324678\pi\)
\(618\) 4.00000 0.160904
\(619\) −30.0000 −1.20580 −0.602901 − 0.797816i \(-0.705989\pi\)
−0.602901 + 0.797816i \(0.705989\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 31.0000 1.24299
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 25.0000 1.00000
\(626\) 33.0000 1.31895
\(627\) −3.00000 −0.119808
\(628\) −9.00000 −0.359139
\(629\) 3.00000 0.119618
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 − 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 0 0
\(633\) 20.0000 0.794929
\(634\) −12.0000 −0.476581
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −1.00000 −0.0395904
\(639\) −15.0000 −0.593391
\(640\) 0 0
\(641\) 34.0000 1.34292 0.671460 − 0.741041i \(-0.265668\pi\)
0.671460 + 0.741041i \(0.265668\pi\)
\(642\) 2.00000 0.0789337
\(643\) −10.0000 −0.394362 −0.197181 − 0.980367i \(-0.563179\pi\)
−0.197181 + 0.980367i \(0.563179\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.00000 −0.118033
\(647\) 8.00000 0.314512 0.157256 − 0.987558i \(-0.449735\pi\)
0.157256 + 0.987558i \(0.449735\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −7.00000 −0.274774
\(650\) 20.0000 0.784465
\(651\) 0 0
\(652\) −18.0000 −0.704934
\(653\) 48.0000 1.87839 0.939193 − 0.343391i \(-0.111576\pi\)
0.939193 + 0.343391i \(0.111576\pi\)
\(654\) −18.0000 −0.703856
\(655\) 0 0
\(656\) −6.00000 −0.234261
\(657\) 12.0000 0.468165
\(658\) 0 0
\(659\) 50.0000 1.94772 0.973862 − 0.227142i \(-0.0729380\pi\)
0.973862 + 0.227142i \(0.0729380\pi\)
\(660\) 0 0
\(661\) −41.0000 −1.59472 −0.797358 − 0.603507i \(-0.793769\pi\)
−0.797358 + 0.603507i \(0.793769\pi\)
\(662\) −10.0000 −0.388661
\(663\) 4.00000 0.155347
\(664\) 16.0000 0.620920
\(665\) 0 0
\(666\) 3.00000 0.116248
\(667\) 1.00000 0.0387202
\(668\) −12.0000 −0.464294
\(669\) −16.0000 −0.618596
\(670\) 0 0
\(671\) −6.00000 −0.231627
\(672\) 0 0
\(673\) −28.0000 −1.07932 −0.539660 − 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) 26.0000 1.00148
\(675\) 5.00000 0.192450
\(676\) 3.00000 0.115385
\(677\) −9.00000 −0.345898 −0.172949 − 0.984931i \(-0.555330\pi\)
−0.172949 + 0.984931i \(0.555330\pi\)
\(678\) 4.00000 0.153619
\(679\) 0 0
\(680\) 0 0
\(681\) 2.00000 0.0766402
\(682\) 6.00000 0.229752
\(683\) 39.0000 1.49229 0.746147 − 0.665782i \(-0.231902\pi\)
0.746147 + 0.665782i \(0.231902\pi\)
\(684\) −3.00000 −0.114708
\(685\) 0 0
\(686\) 0 0
\(687\) 6.00000 0.228914
\(688\) 1.00000 0.0381246
\(689\) 0 0
\(690\) 0 0
\(691\) −34.0000 −1.29342 −0.646710 − 0.762736i \(-0.723856\pi\)
−0.646710 + 0.762736i \(0.723856\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 20.0000 0.759190
\(695\) 0 0
\(696\) −1.00000 −0.0379049
\(697\) 6.00000 0.227266
\(698\) −32.0000 −1.21122
\(699\) 11.0000 0.416058
\(700\) 0 0
\(701\) 29.0000 1.09531 0.547657 − 0.836703i \(-0.315520\pi\)
0.547657 + 0.836703i \(0.315520\pi\)
\(702\) 4.00000 0.150970
\(703\) 9.00000 0.339441
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 8.00000 0.301084
\(707\) 0 0
\(708\) −7.00000 −0.263076
\(709\) −9.00000 −0.338002 −0.169001 − 0.985616i \(-0.554054\pi\)
−0.169001 + 0.985616i \(0.554054\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 8.00000 0.299813
\(713\) −6.00000 −0.224702
\(714\) 0 0
\(715\) 0 0
\(716\) −25.0000 −0.934294
\(717\) −16.0000 −0.597531
\(718\) −2.00000 −0.0746393
\(719\) −37.0000 −1.37987 −0.689934 − 0.723873i \(-0.742360\pi\)
−0.689934 + 0.723873i \(0.742360\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 10.0000 0.372161
\(723\) 4.00000 0.148762
\(724\) 22.0000 0.817624
\(725\) 5.00000 0.185695
\(726\) 1.00000 0.0371135
\(727\) 14.0000 0.519231 0.259616 − 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −1.00000 −0.0369863
\(732\) −6.00000 −0.221766
\(733\) −10.0000 −0.369358 −0.184679 − 0.982799i \(-0.559125\pi\)
−0.184679 + 0.982799i \(0.559125\pi\)
\(734\) −20.0000 −0.738213
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) 4.00000 0.147342
\(738\) 6.00000 0.220863
\(739\) −20.0000 −0.735712 −0.367856 − 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) 12.0000 0.440831
\(742\) 0 0
\(743\) −6.00000 −0.220119 −0.110059 − 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 6.00000 0.219971
\(745\) 0 0
\(746\) −34.0000 −1.24483
\(747\) −16.0000 −0.585409
\(748\) 1.00000 0.0365636
\(749\) 0 0
\(750\) 0 0
\(751\) −34.0000 −1.24068 −0.620339 − 0.784334i \(-0.713005\pi\)
−0.620339 + 0.784334i \(0.713005\pi\)
\(752\) −1.00000 −0.0364662
\(753\) 7.00000 0.255094
\(754\) 4.00000 0.145671
\(755\) 0 0
\(756\) 0 0
\(757\) 29.0000 1.05402 0.527011 − 0.849858i \(-0.323312\pi\)
0.527011 + 0.849858i \(0.323312\pi\)
\(758\) 22.0000 0.799076
\(759\) −1.00000 −0.0362977
\(760\) 0 0
\(761\) −18.0000 −0.652499 −0.326250 − 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) −7.00000 −0.253583
\(763\) 0 0
\(764\) −24.0000 −0.868290
\(765\) 0 0
\(766\) −29.0000 −1.04781
\(767\) 28.0000 1.01102
\(768\) −1.00000 −0.0360844
\(769\) −22.0000 −0.793340 −0.396670 − 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 12.0000 0.432169
\(772\) 14.0000 0.503871
\(773\) 14.0000 0.503545 0.251773 − 0.967786i \(-0.418987\pi\)
0.251773 + 0.967786i \(0.418987\pi\)
\(774\) −1.00000 −0.0359443
\(775\) −30.0000 −1.07763
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) 28.0000 1.00385
\(779\) 18.0000 0.644917
\(780\) 0 0
\(781\) 15.0000 0.536742
\(782\) −1.00000 −0.0357599
\(783\) 1.00000 0.0357371
\(784\) 0 0
\(785\) 0 0
\(786\) −2.00000 −0.0713376
\(787\) −11.0000 −0.392108 −0.196054 − 0.980593i \(-0.562813\pi\)
−0.196054 + 0.980593i \(0.562813\pi\)
\(788\) 27.0000 0.961835
\(789\) 14.0000 0.498413
\(790\) 0 0
\(791\) 0 0
\(792\) 1.00000 0.0355335
\(793\) 24.0000 0.852265
\(794\) −23.0000 −0.816239
\(795\) 0 0
\(796\) 4.00000 0.141776
\(797\) 42.0000 1.48772 0.743858 − 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 0 0
\(799\) 1.00000 0.0353775
\(800\) 5.00000 0.176777
\(801\) −8.00000 −0.282666
\(802\) −2.00000 −0.0706225
\(803\) −12.0000 −0.423471
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) −24.0000 −0.845364
\(807\) 18.0000 0.633630
\(808\) −15.0000 −0.527698
\(809\) 42.0000 1.47664 0.738321 − 0.674450i \(-0.235619\pi\)
0.738321 + 0.674450i \(0.235619\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 − 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 0 0
\(813\) 16.0000 0.561144
\(814\) −3.00000 −0.105150
\(815\) 0 0
\(816\) 1.00000 0.0350070
\(817\) −3.00000 −0.104957
\(818\) −6.00000 −0.209785
\(819\) 0 0
\(820\) 0 0
\(821\) 10.0000 0.349002 0.174501 − 0.984657i \(-0.444169\pi\)
0.174501 + 0.984657i \(0.444169\pi\)
\(822\) −4.00000 −0.139516
\(823\) 50.0000 1.74289 0.871445 − 0.490493i \(-0.163183\pi\)
0.871445 + 0.490493i \(0.163183\pi\)
\(824\) −4.00000 −0.139347
\(825\) −5.00000 −0.174078
\(826\) 0 0
\(827\) 30.0000 1.04320 0.521601 − 0.853189i \(-0.325335\pi\)
0.521601 + 0.853189i \(0.325335\pi\)
\(828\) −1.00000 −0.0347524
\(829\) −7.00000 −0.243120 −0.121560 − 0.992584i \(-0.538790\pi\)
−0.121560 + 0.992584i \(0.538790\pi\)
\(830\) 0 0
\(831\) 16.0000 0.555034
\(832\) 4.00000 0.138675
\(833\) 0 0
\(834\) −17.0000 −0.588662
\(835\) 0 0
\(836\) 3.00000 0.103757
\(837\) −6.00000 −0.207390
\(838\) 17.0000 0.587255
\(839\) −4.00000 −0.138095 −0.0690477 − 0.997613i \(-0.521996\pi\)
−0.0690477 + 0.997613i \(0.521996\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) 3.00000 0.103387
\(843\) 27.0000 0.929929
\(844\) −20.0000 −0.688428
\(845\) 0 0
\(846\) 1.00000 0.0343807
\(847\) 0 0
\(848\) 0 0
\(849\) −20.0000 −0.686398
\(850\) −5.00000 −0.171499
\(851\) 3.00000 0.102839
\(852\) 15.0000 0.513892
\(853\) −36.0000 −1.23262 −0.616308 − 0.787505i \(-0.711372\pi\)
−0.616308 + 0.787505i \(0.711372\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −2.00000 −0.0683586
\(857\) 51.0000 1.74213 0.871063 − 0.491171i \(-0.163431\pi\)
0.871063 + 0.491171i \(0.163431\pi\)
\(858\) −4.00000 −0.136558
\(859\) 8.00000 0.272956 0.136478 − 0.990643i \(-0.456422\pi\)
0.136478 + 0.990643i \(0.456422\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 28.0000 0.953684
\(863\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) 19.0000 0.645646
\(867\) 16.0000 0.543388
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −16.0000 −0.542139
\(872\) 18.0000 0.609557
\(873\) 7.00000 0.236914
\(874\) −3.00000 −0.101477
\(875\) 0 0
\(876\) −12.0000 −0.405442
\(877\) 32.0000 1.08056 0.540282 − 0.841484i \(-0.318318\pi\)
0.540282 + 0.841484i \(0.318318\pi\)
\(878\) 11.0000 0.371232
\(879\) 15.0000 0.505937
\(880\) 0 0
\(881\) −12.0000 −0.404290 −0.202145 − 0.979356i \(-0.564791\pi\)
−0.202145 + 0.979356i \(0.564791\pi\)
\(882\) 0 0
\(883\) 14.0000 0.471138 0.235569 − 0.971858i \(-0.424305\pi\)
0.235569 + 0.971858i \(0.424305\pi\)
\(884\) −4.00000 −0.134535
\(885\) 0 0
\(886\) 3.00000 0.100787
\(887\) 8.00000 0.268614 0.134307 − 0.990940i \(-0.457119\pi\)
0.134307 + 0.990940i \(0.457119\pi\)
\(888\) −3.00000 −0.100673
\(889\) 0 0
\(890\) 0 0
\(891\) −1.00000 −0.0335013
\(892\) 16.0000 0.535720
\(893\) 3.00000 0.100391
\(894\) 1.00000 0.0334450
\(895\) 0 0
\(896\) 0 0
\(897\) 4.00000 0.133556
\(898\) 8.00000 0.266963
\(899\) −6.00000 −0.200111
\(900\) −5.00000 −0.166667
\(901\) 0 0
\(902\) −6.00000 −0.199778
\(903\) 0 0
\(904\) −4.00000 −0.133038
\(905\) 0 0
\(906\) 11.0000 0.365451
\(907\) −8.00000 −0.265636 −0.132818 − 0.991140i \(-0.542403\pi\)
−0.132818 + 0.991140i \(0.542403\pi\)
\(908\) −2.00000 −0.0663723
\(909\) 15.0000 0.497519
\(910\) 0 0
\(911\) −21.0000 −0.695761 −0.347881 − 0.937539i \(-0.613099\pi\)
−0.347881 + 0.937539i \(0.613099\pi\)
\(912\) 3.00000 0.0993399
\(913\) 16.0000 0.529523
\(914\) −18.0000 −0.595387
\(915\) 0 0
\(916\) −6.00000 −0.198246
\(917\) 0 0
\(918\) −1.00000 −0.0330049
\(919\) −33.0000 −1.08857 −0.544285 − 0.838901i \(-0.683199\pi\)
−0.544285 + 0.838901i \(0.683199\pi\)
\(920\) 0 0
\(921\) 20.0000 0.659022
\(922\) −21.0000 −0.691598
\(923\) −60.0000 −1.97492
\(924\) 0 0
\(925\) 15.0000 0.493197
\(926\) 32.0000 1.05159
\(927\) 4.00000 0.131377
\(928\) 1.00000 0.0328266
\(929\) 54.0000 1.77168 0.885841 − 0.463988i \(-0.153582\pi\)
0.885841 + 0.463988i \(0.153582\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −11.0000 −0.360317
\(933\) 31.0000 1.01489
\(934\) 23.0000 0.752583
\(935\) 0 0
\(936\) −4.00000 −0.130744
\(937\) 8.00000 0.261349 0.130674 − 0.991425i \(-0.458286\pi\)
0.130674 + 0.991425i \(0.458286\pi\)
\(938\) 0 0
\(939\) 33.0000 1.07691
\(940\) 0 0
\(941\) −45.0000 −1.46696 −0.733479 − 0.679712i \(-0.762105\pi\)
−0.733479 + 0.679712i \(0.762105\pi\)
\(942\) −9.00000 −0.293236
\(943\) 6.00000 0.195387
\(944\) 7.00000 0.227831
\(945\) 0 0
\(946\) 1.00000 0.0325128
\(947\) −51.0000 −1.65728 −0.828639 − 0.559784i \(-0.810884\pi\)
−0.828639 + 0.559784i \(0.810884\pi\)
\(948\) 0 0
\(949\) 48.0000 1.55815
\(950\) −15.0000 −0.486664
\(951\) −12.0000 −0.389127
\(952\) 0 0
\(953\) 14.0000 0.453504 0.226752 − 0.973952i \(-0.427189\pi\)
0.226752 + 0.973952i \(0.427189\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 16.0000 0.517477
\(957\) −1.00000 −0.0323254
\(958\) −10.0000 −0.323085
\(959\) 0 0
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) 12.0000 0.386896
\(963\) 2.00000 0.0644491
\(964\) −4.00000 −0.128831
\(965\) 0 0
\(966\) 0 0
\(967\) −35.0000 −1.12552 −0.562762 − 0.826619i \(-0.690261\pi\)
−0.562762 + 0.826619i \(0.690261\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −3.00000 −0.0963739
\(970\) 0 0
\(971\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −20.0000 −0.640841
\(975\) 20.0000 0.640513
\(976\) 6.00000 0.192055
\(977\) 12.0000 0.383914 0.191957 − 0.981403i \(-0.438517\pi\)
0.191957 + 0.981403i \(0.438517\pi\)
\(978\) −18.0000 −0.575577
\(979\) 8.00000 0.255681
\(980\) 0 0
\(981\) −18.0000 −0.574696
\(982\) −12.0000 −0.382935
\(983\) 19.0000 0.606006 0.303003 − 0.952990i \(-0.402011\pi\)
0.303003 + 0.952990i \(0.402011\pi\)
\(984\) −6.00000 −0.191273
\(985\) 0 0
\(986\) −1.00000 −0.0318465
\(987\) 0 0
\(988\) −12.0000 −0.381771
\(989\) −1.00000 −0.0317982
\(990\) 0 0
\(991\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) −6.00000 −0.190500
\(993\) −10.0000 −0.317340
\(994\) 0 0
\(995\) 0 0
\(996\) 16.0000 0.506979
\(997\) −44.0000 −1.39349 −0.696747 − 0.717317i \(-0.745370\pi\)
−0.696747 + 0.717317i \(0.745370\pi\)
\(998\) −10.0000 −0.316544
\(999\) 3.00000 0.0949158
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 3234.2.a.c.1.1 1
3.2 odd 2 9702.2.a.bv.1.1 1
7.2 even 3 462.2.i.d.67.1 ✓ 2
7.4 even 3 462.2.i.d.331.1 yes 2
7.6 odd 2 3234.2.a.j.1.1 1
21.2 odd 6 1386.2.k.f.991.1 2
21.11 odd 6 1386.2.k.f.793.1 2
21.20 even 2 9702.2.a.bq.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.i.d.67.1 ✓ 2 7.2 even 3
462.2.i.d.331.1 yes 2 7.4 even 3
1386.2.k.f.793.1 2 21.11 odd 6
1386.2.k.f.991.1 2 21.2 odd 6
3234.2.a.c.1.1 1 1.1 even 1 trivial
3234.2.a.j.1.1 1 7.6 odd 2
9702.2.a.bq.1.1 1 21.20 even 2
9702.2.a.bv.1.1 1 3.2 odd 2