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Properties

Label 6762.2.a.z.1.1
Level $6762$
Weight $2$
Character 6762.1
Self dual yes
Analytic conductor $53.995$
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] = [6762,2,Mod(1,6762)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6762, 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("6762.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6762.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: \(53.9948418468\)
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 \(\chi\) \(=\) 6762.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} +6.00000 q^{19} -4.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} -5.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} -2.00000 q^{29} -2.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} +6.00000 q^{38} -2.00000 q^{39} +8.00000 q^{41} +4.00000 q^{43} -4.00000 q^{44} +1.00000 q^{46} +6.00000 q^{47} -1.00000 q^{48} -5.00000 q^{50} +2.00000 q^{51} +2.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} -6.00000 q^{57} -2.00000 q^{58} +4.00000 q^{59} -2.00000 q^{62} +1.00000 q^{64} +4.00000 q^{66} -4.00000 q^{67} -2.00000 q^{68} -1.00000 q^{69} +1.00000 q^{72} +4.00000 q^{73} -2.00000 q^{74} +5.00000 q^{75} +6.00000 q^{76} -2.00000 q^{78} -12.0000 q^{79} +1.00000 q^{81} +8.00000 q^{82} +6.00000 q^{83} +4.00000 q^{86} +2.00000 q^{87} -4.00000 q^{88} +10.0000 q^{89} +1.00000 q^{92} +2.00000 q^{93} +6.00000 q^{94} -1.00000 q^{96} -6.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 − 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −2.00000 −0.485071 −0.242536 − 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 1.00000 0.235702
\(19\) 6.00000 1.37649 0.688247 − 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.00000 −0.852803
\(23\) 1.00000 0.208514
\(24\) −1.00000 −0.204124
\(25\) −5.00000 −1.00000
\(26\) 2.00000 0.392232
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 − 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 − 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.00000 0.696311
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 6.00000 0.973329
\(39\) −2.00000 −0.320256
\(40\) 0 0
\(41\) 8.00000 1.24939 0.624695 − 0.780869i \(-0.285223\pi\)
0.624695 + 0.780869i \(0.285223\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 − 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) 6.00000 0.875190 0.437595 − 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) −5.00000 −0.707107
\(51\) 2.00000 0.280056
\(52\) 2.00000 0.277350
\(53\) 6.00000 0.824163 0.412082 − 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 0 0
\(57\) −6.00000 −0.794719
\(58\) −2.00000 −0.262613
\(59\) 4.00000 0.520756 0.260378 − 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 4.00000 0.492366
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −2.00000 −0.242536
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000 0.117851
\(73\) 4.00000 0.468165 0.234082 − 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) −2.00000 −0.232495
\(75\) 5.00000 0.577350
\(76\) 6.00000 0.688247
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) −12.0000 −1.35011 −0.675053 − 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 8.00000 0.883452
\(83\) 6.00000 0.658586 0.329293 − 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 4.00000 0.431331
\(87\) 2.00000 0.214423
\(88\) −4.00000 −0.426401
\(89\) 10.0000 1.06000 0.529999 − 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.00000 0.104257
\(93\) 2.00000 0.207390
\(94\) 6.00000 0.618853
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −6.00000 −0.609208 −0.304604 − 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) −5.00000 −0.500000
\(101\) 14.0000 1.39305 0.696526 − 0.717532i \(-0.254728\pi\)
0.696526 + 0.717532i \(0.254728\pi\)
\(102\) 2.00000 0.198030
\(103\) −4.00000 −0.394132 −0.197066 − 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) 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
\(109\) 2.00000 0.191565 0.0957826 − 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 − 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) −6.00000 −0.561951
\(115\) 0 0
\(116\) −2.00000 −0.185695
\(117\) 2.00000 0.184900
\(118\) 4.00000 0.368230
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) −8.00000 −0.721336
\(124\) −2.00000 −0.179605
\(125\) 0 0
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 − 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 − 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 4.00000 0.348155
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) −2.00000 −0.171499
\(137\) −6.00000 −0.512615 −0.256307 − 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) −1.00000 −0.0851257
\(139\) −8.00000 −0.678551 −0.339276 − 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −8.00000 −0.668994
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) 10.0000 0.819232 0.409616 − 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 5.00000 0.408248
\(151\) −16.0000 −1.30206 −0.651031 − 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 6.00000 0.486664
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) −2.00000 −0.160128
\(157\) −4.00000 −0.319235 −0.159617 − 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) −12.0000 −0.954669
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −8.00000 −0.626608 −0.313304 − 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 8.00000 0.624695
\(165\) 0 0
\(166\) 6.00000 0.465690
\(167\) 10.0000 0.773823 0.386912 − 0.922117i \(-0.373542\pi\)
0.386912 + 0.922117i \(0.373542\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 6.00000 0.458831
\(172\) 4.00000 0.304997
\(173\) 6.00000 0.456172 0.228086 − 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 2.00000 0.151620
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) −4.00000 −0.300658
\(178\) 10.0000 0.749532
\(179\) 12.0000 0.896922 0.448461 − 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 16.0000 1.18927 0.594635 − 0.803996i \(-0.297296\pi\)
0.594635 + 0.803996i \(0.297296\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.00000 0.0737210
\(185\) 0 0
\(186\) 2.00000 0.146647
\(187\) 8.00000 0.585018
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) 20.0000 1.44715 0.723575 − 0.690246i \(-0.242498\pi\)
0.723575 + 0.690246i \(0.242498\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 6.00000 0.431889 0.215945 − 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 − 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −4.00000 −0.284268
\(199\) 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
\(202\) 14.0000 0.985037
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) 0 0
\(206\) −4.00000 −0.278693
\(207\) 1.00000 0.0695048
\(208\) 2.00000 0.138675
\(209\) −24.0000 −1.66011
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 − 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) 12.0000 0.820303
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) 2.00000 0.134231
\(223\) −14.0000 −0.937509 −0.468755 − 0.883328i \(-0.655297\pi\)
−0.468755 + 0.883328i \(0.655297\pi\)
\(224\) 0 0
\(225\) −5.00000 −0.333333
\(226\) −2.00000 −0.133038
\(227\) −6.00000 −0.398234 −0.199117 − 0.979976i \(-0.563807\pi\)
−0.199117 + 0.979976i \(0.563807\pi\)
\(228\) −6.00000 −0.397360
\(229\) 16.0000 1.05731 0.528655 − 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) 10.0000 0.655122 0.327561 − 0.944830i \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) 2.00000 0.130744
\(235\) 0 0
\(236\) 4.00000 0.260378
\(237\) 12.0000 0.779484
\(238\) 0 0
\(239\) 8.00000 0.517477 0.258738 − 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) 22.0000 1.41714 0.708572 − 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) 5.00000 0.321412
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) −8.00000 −0.510061
\(247\) 12.0000 0.763542
\(248\) −2.00000 −0.127000
\(249\) −6.00000 −0.380235
\(250\) 0 0
\(251\) −26.0000 −1.64111 −0.820553 − 0.571571i \(-0.806334\pi\)
−0.820553 + 0.571571i \(0.806334\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 28.0000 1.74659 0.873296 − 0.487190i \(-0.161978\pi\)
0.873296 + 0.487190i \(0.161978\pi\)
\(258\) −4.00000 −0.249029
\(259\) 0 0
\(260\) 0 0
\(261\) −2.00000 −0.123797
\(262\) 12.0000 0.741362
\(263\) 8.00000 0.493301 0.246651 − 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(264\) 4.00000 0.246183
\(265\) 0 0
\(266\) 0 0
\(267\) −10.0000 −0.611990
\(268\) −4.00000 −0.244339
\(269\) 6.00000 0.365826 0.182913 − 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) 30.0000 1.82237 0.911185 − 0.411997i \(-0.135169\pi\)
0.911185 + 0.411997i \(0.135169\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 20.0000 1.20605
\(276\) −1.00000 −0.0601929
\(277\) 30.0000 1.80253 0.901263 − 0.433273i \(-0.142641\pi\)
0.901263 + 0.433273i \(0.142641\pi\)
\(278\) −8.00000 −0.479808
\(279\) −2.00000 −0.119737
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 − 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) −6.00000 −0.357295
\(283\) −10.0000 −0.594438 −0.297219 − 0.954809i \(-0.596059\pi\)
−0.297219 + 0.954809i \(0.596059\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 6.00000 0.351726
\(292\) 4.00000 0.234082
\(293\) −16.0000 −0.934730 −0.467365 − 0.884064i \(-0.654797\pi\)
−0.467365 + 0.884064i \(0.654797\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 4.00000 0.232104
\(298\) 10.0000 0.579284
\(299\) 2.00000 0.115663
\(300\) 5.00000 0.288675
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) −14.0000 −0.804279
\(304\) 6.00000 0.344124
\(305\) 0 0
\(306\) −2.00000 −0.114332
\(307\) −8.00000 −0.456584 −0.228292 − 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 − 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) −2.00000 −0.113228
\(313\) 22.0000 1.24351 0.621757 − 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −12.0000 −0.675053
\(317\) −22.0000 −1.23564 −0.617822 − 0.786318i \(-0.711985\pi\)
−0.617822 + 0.786318i \(0.711985\pi\)
\(318\) −6.00000 −0.336463
\(319\) 8.00000 0.447914
\(320\) 0 0
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) 1.00000 0.0555556
\(325\) −10.0000 −0.554700
\(326\) −8.00000 −0.443079
\(327\) −2.00000 −0.110600
\(328\) 8.00000 0.441726
\(329\) 0 0
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 − 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 6.00000 0.329293
\(333\) −2.00000 −0.109599
\(334\) 10.0000 0.547176
\(335\) 0 0
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 − 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −9.00000 −0.489535
\(339\) 2.00000 0.108625
\(340\) 0 0
\(341\) 8.00000 0.433224
\(342\) 6.00000 0.324443
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) −16.0000 −0.858925 −0.429463 − 0.903085i \(-0.641297\pi\)
−0.429463 + 0.903085i \(0.641297\pi\)
\(348\) 2.00000 0.107211
\(349\) −10.0000 −0.535288 −0.267644 − 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) −4.00000 −0.213201
\(353\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) −4.00000 −0.212598
\(355\) 0 0
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −4.00000 −0.211112 −0.105556 − 0.994413i \(-0.533662\pi\)
−0.105556 + 0.994413i \(0.533662\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 16.0000 0.840941
\(363\) −5.00000 −0.262432
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −20.0000 −1.04399 −0.521996 − 0.852948i \(-0.674812\pi\)
−0.521996 + 0.852948i \(0.674812\pi\)
\(368\) 1.00000 0.0521286
\(369\) 8.00000 0.416463
\(370\) 0 0
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) 2.00000 0.103556 0.0517780 − 0.998659i \(-0.483511\pi\)
0.0517780 + 0.998659i \(0.483511\pi\)
\(374\) 8.00000 0.413670
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 − 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 0 0
\(381\) −16.0000 −0.819705
\(382\) 20.0000 1.02329
\(383\) −24.0000 −1.22634 −0.613171 − 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 6.00000 0.305392
\(387\) 4.00000 0.203331
\(388\) −6.00000 −0.304604
\(389\) −30.0000 −1.52106 −0.760530 − 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) −2.00000 −0.101144
\(392\) 0 0
\(393\) −12.0000 −0.605320
\(394\) 18.0000 0.906827
\(395\) 0 0
\(396\) −4.00000 −0.201008
\(397\) 2.00000 0.100377 0.0501886 − 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 10.0000 0.499376 0.249688 − 0.968326i \(-0.419672\pi\)
0.249688 + 0.968326i \(0.419672\pi\)
\(402\) 4.00000 0.199502
\(403\) −4.00000 −0.199254
\(404\) 14.0000 0.696526
\(405\) 0 0
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 2.00000 0.0990148
\(409\) 24.0000 1.18672 0.593362 − 0.804936i \(-0.297800\pi\)
0.593362 + 0.804936i \(0.297800\pi\)
\(410\) 0 0
\(411\) 6.00000 0.295958
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) 1.00000 0.0491473
\(415\) 0 0
\(416\) 2.00000 0.0980581
\(417\) 8.00000 0.391762
\(418\) −24.0000 −1.17388
\(419\) −34.0000 −1.66101 −0.830504 − 0.557012i \(-0.811948\pi\)
−0.830504 + 0.557012i \(0.811948\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 − 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) −8.00000 −0.389434
\(423\) 6.00000 0.291730
\(424\) 6.00000 0.291386
\(425\) 10.0000 0.485071
\(426\) 0 0
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 8.00000 0.386244
\(430\) 0 0
\(431\) 8.00000 0.385346 0.192673 − 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −6.00000 −0.288342 −0.144171 − 0.989553i \(-0.546051\pi\)
−0.144171 + 0.989553i \(0.546051\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) 6.00000 0.287019
\(438\) −4.00000 −0.191127
\(439\) 10.0000 0.477274 0.238637 − 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −4.00000 −0.190261
\(443\) 8.00000 0.380091 0.190046 − 0.981775i \(-0.439136\pi\)
0.190046 + 0.981775i \(0.439136\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) −14.0000 −0.662919
\(447\) −10.0000 −0.472984
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 − 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) −5.00000 −0.235702
\(451\) −32.0000 −1.50682
\(452\) −2.00000 −0.0940721
\(453\) 16.0000 0.751746
\(454\) −6.00000 −0.281594
\(455\) 0 0
\(456\) −6.00000 −0.280976
\(457\) −22.0000 −1.02912 −0.514558 − 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 16.0000 0.747631
\(459\) 2.00000 0.0933520
\(460\) 0 0
\(461\) 6.00000 0.279448 0.139724 − 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 − 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) −2.00000 −0.0928477
\(465\) 0 0
\(466\) 10.0000 0.463241
\(467\) 18.0000 0.832941 0.416470 − 0.909149i \(-0.363267\pi\)
0.416470 + 0.909149i \(0.363267\pi\)
\(468\) 2.00000 0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) 4.00000 0.184310
\(472\) 4.00000 0.184115
\(473\) −16.0000 −0.735681
\(474\) 12.0000 0.551178
\(475\) −30.0000 −1.37649
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 8.00000 0.365911
\(479\) 4.00000 0.182765 0.0913823 − 0.995816i \(-0.470871\pi\)
0.0913823 + 0.995816i \(0.470871\pi\)
\(480\) 0 0
\(481\) −4.00000 −0.182384
\(482\) 22.0000 1.00207
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 16.0000 0.725029 0.362515 − 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 0 0
\(489\) 8.00000 0.361773
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 − 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) −8.00000 −0.360668
\(493\) 4.00000 0.180151
\(494\) 12.0000 0.539906
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) −6.00000 −0.268866
\(499\) −8.00000 −0.358129 −0.179065 − 0.983837i \(-0.557307\pi\)
−0.179065 + 0.983837i \(0.557307\pi\)
\(500\) 0 0
\(501\) −10.0000 −0.446767
\(502\) −26.0000 −1.16044
\(503\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −4.00000 −0.177822
\(507\) 9.00000 0.399704
\(508\) 16.0000 0.709885
\(509\) 22.0000 0.975133 0.487566 − 0.873086i \(-0.337885\pi\)
0.487566 + 0.873086i \(0.337885\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −6.00000 −0.264906
\(514\) 28.0000 1.23503
\(515\) 0 0
\(516\) −4.00000 −0.176090
\(517\) −24.0000 −1.05552
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 10.0000 0.438108 0.219054 − 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) −2.00000 −0.0875376
\(523\) 14.0000 0.612177 0.306089 − 0.952003i \(-0.400980\pi\)
0.306089 + 0.952003i \(0.400980\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 4.00000 0.174243
\(528\) 4.00000 0.174078
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) 16.0000 0.693037
\(534\) −10.0000 −0.432742
\(535\) 0 0
\(536\) −4.00000 −0.172774
\(537\) −12.0000 −0.517838
\(538\) 6.00000 0.258678
\(539\) 0 0
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 − 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 30.0000 1.28861
\(543\) −16.0000 −0.686626
\(544\) −2.00000 −0.0857493
\(545\) 0 0
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 − 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) −6.00000 −0.256307
\(549\) 0 0
\(550\) 20.0000 0.852803
\(551\) −12.0000 −0.511217
\(552\) −1.00000 −0.0425628
\(553\) 0 0
\(554\) 30.0000 1.27458
\(555\) 0 0
\(556\) −8.00000 −0.339276
\(557\) 18.0000 0.762684 0.381342 − 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) −2.00000 −0.0846668
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −8.00000 −0.337760
\(562\) 18.0000 0.759284
\(563\) 6.00000 0.252870 0.126435 − 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) −6.00000 −0.252646
\(565\) 0 0
\(566\) −10.0000 −0.420331
\(567\) 0 0
\(568\) 0 0
\(569\) 26.0000 1.08998 0.544988 − 0.838444i \(-0.316534\pi\)
0.544988 + 0.838444i \(0.316534\pi\)
\(570\) 0 0
\(571\) −28.0000 −1.17176 −0.585882 − 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) −8.00000 −0.334497
\(573\) −20.0000 −0.835512
\(574\) 0 0
\(575\) −5.00000 −0.208514
\(576\) 1.00000 0.0416667
\(577\) 28.0000 1.16566 0.582828 − 0.812596i \(-0.301946\pi\)
0.582828 + 0.812596i \(0.301946\pi\)
\(578\) −13.0000 −0.540729
\(579\) −6.00000 −0.249351
\(580\) 0 0
\(581\) 0 0
\(582\) 6.00000 0.248708
\(583\) −24.0000 −0.993978
\(584\) 4.00000 0.165521
\(585\) 0 0
\(586\) −16.0000 −0.660954
\(587\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) −18.0000 −0.740421
\(592\) −2.00000 −0.0821995
\(593\) −12.0000 −0.492781 −0.246390 − 0.969171i \(-0.579245\pi\)
−0.246390 + 0.969171i \(0.579245\pi\)
\(594\) 4.00000 0.164122
\(595\) 0 0
\(596\) 10.0000 0.409616
\(597\) −4.00000 −0.163709
\(598\) 2.00000 0.0817861
\(599\) −40.0000 −1.63436 −0.817178 − 0.576386i \(-0.804463\pi\)
−0.817178 + 0.576386i \(0.804463\pi\)
\(600\) 5.00000 0.204124
\(601\) 28.0000 1.14214 0.571072 − 0.820900i \(-0.306528\pi\)
0.571072 + 0.820900i \(0.306528\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) −16.0000 −0.651031
\(605\) 0 0
\(606\) −14.0000 −0.568711
\(607\) 14.0000 0.568242 0.284121 − 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) 6.00000 0.243332
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) −2.00000 −0.0808452
\(613\) 42.0000 1.69636 0.848182 − 0.529705i \(-0.177697\pi\)
0.848182 + 0.529705i \(0.177697\pi\)
\(614\) −8.00000 −0.322854
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 0.0805170 0.0402585 − 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) 4.00000 0.160904
\(619\) 26.0000 1.04503 0.522514 − 0.852631i \(-0.324994\pi\)
0.522514 + 0.852631i \(0.324994\pi\)
\(620\) 0 0
\(621\) −1.00000 −0.0401286
\(622\) −18.0000 −0.721734
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) 25.0000 1.00000
\(626\) 22.0000 0.879297
\(627\) 24.0000 0.958468
\(628\) −4.00000 −0.159617
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) −12.0000 −0.477712 −0.238856 − 0.971055i \(-0.576772\pi\)
−0.238856 + 0.971055i \(0.576772\pi\)
\(632\) −12.0000 −0.477334
\(633\) 8.00000 0.317971
\(634\) −22.0000 −0.873732
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) 0 0
\(638\) 8.00000 0.316723
\(639\) 0 0
\(640\) 0 0
\(641\) 2.00000 0.0789953 0.0394976 − 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) −12.0000 −0.473602
\(643\) 34.0000 1.34083 0.670415 − 0.741987i \(-0.266116\pi\)
0.670415 + 0.741987i \(0.266116\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12.0000 −0.472134
\(647\) 10.0000 0.393141 0.196570 − 0.980490i \(-0.437020\pi\)
0.196570 + 0.980490i \(0.437020\pi\)
\(648\) 1.00000 0.0392837
\(649\) −16.0000 −0.628055
\(650\) −10.0000 −0.392232
\(651\) 0 0
\(652\) −8.00000 −0.313304
\(653\) 6.00000 0.234798 0.117399 − 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) −2.00000 −0.0782062
\(655\) 0 0
\(656\) 8.00000 0.312348
\(657\) 4.00000 0.156055
\(658\) 0 0
\(659\) −4.00000 −0.155818 −0.0779089 − 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 0 0
\(661\) −16.0000 −0.622328 −0.311164 − 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) −20.0000 −0.777322
\(663\) 4.00000 0.155347
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) −2.00000 −0.0774403
\(668\) 10.0000 0.386912
\(669\) 14.0000 0.541271
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 − 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) 14.0000 0.539260
\(675\) 5.00000 0.192450
\(676\) −9.00000 −0.346154
\(677\) −40.0000 −1.53732 −0.768662 − 0.639655i \(-0.779077\pi\)
−0.768662 + 0.639655i \(0.779077\pi\)
\(678\) 2.00000 0.0768095
\(679\) 0 0
\(680\) 0 0
\(681\) 6.00000 0.229920
\(682\) 8.00000 0.306336
\(683\) 8.00000 0.306111 0.153056 − 0.988218i \(-0.451089\pi\)
0.153056 + 0.988218i \(0.451089\pi\)
\(684\) 6.00000 0.229416
\(685\) 0 0
\(686\) 0 0
\(687\) −16.0000 −0.610438
\(688\) 4.00000 0.152499
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) −48.0000 −1.82601 −0.913003 − 0.407953i \(-0.866243\pi\)
−0.913003 + 0.407953i \(0.866243\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −16.0000 −0.607352
\(695\) 0 0
\(696\) 2.00000 0.0758098
\(697\) −16.0000 −0.606043
\(698\) −10.0000 −0.378506
\(699\) −10.0000 −0.378235
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 − 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) −2.00000 −0.0754851
\(703\) −12.0000 −0.452589
\(704\) −4.00000 −0.150756
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) −4.00000 −0.150329
\(709\) −50.0000 −1.87779 −0.938895 − 0.344204i \(-0.888149\pi\)
−0.938895 + 0.344204i \(0.888149\pi\)
\(710\) 0 0
\(711\) −12.0000 −0.450035
\(712\) 10.0000 0.374766
\(713\) −2.00000 −0.0749006
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −8.00000 −0.298765
\(718\) −4.00000 −0.149279
\(719\) 2.00000 0.0745874 0.0372937 − 0.999304i \(-0.488126\pi\)
0.0372937 + 0.999304i \(0.488126\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 17.0000 0.632674
\(723\) −22.0000 −0.818189
\(724\) 16.0000 0.594635
\(725\) 10.0000 0.371391
\(726\) −5.00000 −0.185567
\(727\) −12.0000 −0.445055 −0.222528 − 0.974926i \(-0.571431\pi\)
−0.222528 + 0.974926i \(0.571431\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 0 0
\(733\) 20.0000 0.738717 0.369358 − 0.929287i \(-0.379577\pi\)
0.369358 + 0.929287i \(0.379577\pi\)
\(734\) −20.0000 −0.738213
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) 16.0000 0.589368
\(738\) 8.00000 0.294484
\(739\) 16.0000 0.588570 0.294285 − 0.955718i \(-0.404919\pi\)
0.294285 + 0.955718i \(0.404919\pi\)
\(740\) 0 0
\(741\) −12.0000 −0.440831
\(742\) 0 0
\(743\) −52.0000 −1.90769 −0.953847 − 0.300291i \(-0.902916\pi\)
−0.953847 + 0.300291i \(0.902916\pi\)
\(744\) 2.00000 0.0733236
\(745\) 0 0
\(746\) 2.00000 0.0732252
\(747\) 6.00000 0.219529
\(748\) 8.00000 0.292509
\(749\) 0 0
\(750\) 0 0
\(751\) −40.0000 −1.45962 −0.729810 − 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) 6.00000 0.218797
\(753\) 26.0000 0.947493
\(754\) −4.00000 −0.145671
\(755\) 0 0
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 − 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 4.00000 0.145287
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) 36.0000 1.30500 0.652499 − 0.757789i \(-0.273720\pi\)
0.652499 + 0.757789i \(0.273720\pi\)
\(762\) −16.0000 −0.579619
\(763\) 0 0
\(764\) 20.0000 0.723575
\(765\) 0 0
\(766\) −24.0000 −0.867155
\(767\) 8.00000 0.288863
\(768\) −1.00000 −0.0360844
\(769\) −50.0000 −1.80305 −0.901523 − 0.432731i \(-0.857550\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 0 0
\(771\) −28.0000 −1.00840
\(772\) 6.00000 0.215945
\(773\) −36.0000 −1.29483 −0.647415 − 0.762138i \(-0.724150\pi\)
−0.647415 + 0.762138i \(0.724150\pi\)
\(774\) 4.00000 0.143777
\(775\) 10.0000 0.359211
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) −30.0000 −1.07555
\(779\) 48.0000 1.71978
\(780\) 0 0
\(781\) 0 0
\(782\) −2.00000 −0.0715199
\(783\) 2.00000 0.0714742
\(784\) 0 0
\(785\) 0 0
\(786\) −12.0000 −0.428026
\(787\) −46.0000 −1.63972 −0.819861 − 0.572562i \(-0.805950\pi\)
−0.819861 + 0.572562i \(0.805950\pi\)
\(788\) 18.0000 0.641223
\(789\) −8.00000 −0.284808
\(790\) 0 0
\(791\) 0 0
\(792\) −4.00000 −0.142134
\(793\) 0 0
\(794\) 2.00000 0.0709773
\(795\) 0 0
\(796\) 4.00000 0.141776
\(797\) −28.0000 −0.991811 −0.495905 − 0.868377i \(-0.665164\pi\)
−0.495905 + 0.868377i \(0.665164\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529
\(800\) −5.00000 −0.176777
\(801\) 10.0000 0.353333
\(802\) 10.0000 0.353112
\(803\) −16.0000 −0.564628
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) −6.00000 −0.211210
\(808\) 14.0000 0.492518
\(809\) −26.0000 −0.914111 −0.457056 − 0.889438i \(-0.651096\pi\)
−0.457056 + 0.889438i \(0.651096\pi\)
\(810\) 0 0
\(811\) 12.0000 0.421377 0.210688 − 0.977553i \(-0.432429\pi\)
0.210688 + 0.977553i \(0.432429\pi\)
\(812\) 0 0
\(813\) −30.0000 −1.05215
\(814\) 8.00000 0.280400
\(815\) 0 0
\(816\) 2.00000 0.0700140
\(817\) 24.0000 0.839654
\(818\) 24.0000 0.839140
\(819\) 0 0
\(820\) 0 0
\(821\) 10.0000 0.349002 0.174501 − 0.984657i \(-0.444169\pi\)
0.174501 + 0.984657i \(0.444169\pi\)
\(822\) 6.00000 0.209274
\(823\) 24.0000 0.836587 0.418294 − 0.908312i \(-0.362628\pi\)
0.418294 + 0.908312i \(0.362628\pi\)
\(824\) −4.00000 −0.139347
\(825\) −20.0000 −0.696311
\(826\) 0 0
\(827\) 12.0000 0.417281 0.208640 − 0.977992i \(-0.433096\pi\)
0.208640 + 0.977992i \(0.433096\pi\)
\(828\) 1.00000 0.0347524
\(829\) 18.0000 0.625166 0.312583 − 0.949890i \(-0.398806\pi\)
0.312583 + 0.949890i \(0.398806\pi\)
\(830\) 0 0
\(831\) −30.0000 −1.04069
\(832\) 2.00000 0.0693375
\(833\) 0 0
\(834\) 8.00000 0.277017
\(835\) 0 0
\(836\) −24.0000 −0.830057
\(837\) 2.00000 0.0691301
\(838\) −34.0000 −1.17451
\(839\) 32.0000 1.10476 0.552381 − 0.833592i \(-0.313719\pi\)
0.552381 + 0.833592i \(0.313719\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 6.00000 0.206774
\(843\) −18.0000 −0.619953
\(844\) −8.00000 −0.275371
\(845\) 0 0
\(846\) 6.00000 0.206284
\(847\) 0 0
\(848\) 6.00000 0.206041
\(849\) 10.0000 0.343199
\(850\) 10.0000 0.342997
\(851\) −2.00000 −0.0685591
\(852\) 0 0
\(853\) −46.0000 −1.57501 −0.787505 − 0.616308i \(-0.788628\pi\)
−0.787505 + 0.616308i \(0.788628\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 12.0000 0.410152
\(857\) −40.0000 −1.36637 −0.683187 − 0.730243i \(-0.739407\pi\)
−0.683187 + 0.730243i \(0.739407\pi\)
\(858\) 8.00000 0.273115
\(859\) −48.0000 −1.63774 −0.818869 − 0.573980i \(-0.805399\pi\)
−0.818869 + 0.573980i \(0.805399\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 8.00000 0.272481
\(863\) 16.0000 0.544646 0.272323 − 0.962206i \(-0.412208\pi\)
0.272323 + 0.962206i \(0.412208\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) −6.00000 −0.203888
\(867\) 13.0000 0.441503
\(868\) 0 0
\(869\) 48.0000 1.62829
\(870\) 0 0
\(871\) −8.00000 −0.271070
\(872\) 2.00000 0.0677285
\(873\) −6.00000 −0.203069
\(874\) 6.00000 0.202953
\(875\) 0 0
\(876\) −4.00000 −0.135147
\(877\) −46.0000 −1.55331 −0.776655 − 0.629926i \(-0.783085\pi\)
−0.776655 + 0.629926i \(0.783085\pi\)
\(878\) 10.0000 0.337484
\(879\) 16.0000 0.539667
\(880\) 0 0
\(881\) −18.0000 −0.606435 −0.303218 − 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) −24.0000 −0.807664 −0.403832 − 0.914833i \(-0.632322\pi\)
−0.403832 + 0.914833i \(0.632322\pi\)
\(884\) −4.00000 −0.134535
\(885\) 0 0
\(886\) 8.00000 0.268765
\(887\) −22.0000 −0.738688 −0.369344 − 0.929293i \(-0.620418\pi\)
−0.369344 + 0.929293i \(0.620418\pi\)
\(888\) 2.00000 0.0671156
\(889\) 0 0
\(890\) 0 0
\(891\) −4.00000 −0.134005
\(892\) −14.0000 −0.468755
\(893\) 36.0000 1.20469
\(894\) −10.0000 −0.334450
\(895\) 0 0
\(896\) 0 0
\(897\) −2.00000 −0.0667781
\(898\) 14.0000 0.467186
\(899\) 4.00000 0.133407
\(900\) −5.00000 −0.166667
\(901\) −12.0000 −0.399778
\(902\) −32.0000 −1.06548
\(903\) 0 0
\(904\) −2.00000 −0.0665190
\(905\) 0 0
\(906\) 16.0000 0.531564
\(907\) −4.00000 −0.132818 −0.0664089 − 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) −6.00000 −0.199117
\(909\) 14.0000 0.464351
\(910\) 0 0
\(911\) −36.0000 −1.19273 −0.596367 − 0.802712i \(-0.703390\pi\)
−0.596367 + 0.802712i \(0.703390\pi\)
\(912\) −6.00000 −0.198680
\(913\) −24.0000 −0.794284
\(914\) −22.0000 −0.727695
\(915\) 0 0
\(916\) 16.0000 0.528655
\(917\) 0 0
\(918\) 2.00000 0.0660098
\(919\) −20.0000 −0.659739 −0.329870 − 0.944027i \(-0.607005\pi\)
−0.329870 + 0.944027i \(0.607005\pi\)
\(920\) 0 0
\(921\) 8.00000 0.263609
\(922\) 6.00000 0.197599
\(923\) 0 0
\(924\) 0 0
\(925\) 10.0000 0.328798
\(926\) −8.00000 −0.262896
\(927\) −4.00000 −0.131377
\(928\) −2.00000 −0.0656532
\(929\) 24.0000 0.787414 0.393707 − 0.919236i \(-0.371192\pi\)
0.393707 + 0.919236i \(0.371192\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 10.0000 0.327561
\(933\) 18.0000 0.589294
\(934\) 18.0000 0.588978
\(935\) 0 0
\(936\) 2.00000 0.0653720
\(937\) −2.00000 −0.0653372 −0.0326686 − 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) 0 0
\(939\) −22.0000 −0.717943
\(940\) 0 0
\(941\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 4.00000 0.130327
\(943\) 8.00000 0.260516
\(944\) 4.00000 0.130189
\(945\) 0 0
\(946\) −16.0000 −0.520205
\(947\) 24.0000 0.779895 0.389948 − 0.920837i \(-0.372493\pi\)
0.389948 + 0.920837i \(0.372493\pi\)
\(948\) 12.0000 0.389742
\(949\) 8.00000 0.259691
\(950\) −30.0000 −0.973329
\(951\) 22.0000 0.713399
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 − 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 6.00000 0.194257
\(955\) 0 0
\(956\) 8.00000 0.258738
\(957\) −8.00000 −0.258603
\(958\) 4.00000 0.129234
\(959\) 0 0
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) −4.00000 −0.128965
\(963\) 12.0000 0.386695
\(964\) 22.0000 0.708572
\(965\) 0 0
\(966\) 0 0
\(967\) 40.0000 1.28631 0.643157 − 0.765735i \(-0.277624\pi\)
0.643157 + 0.765735i \(0.277624\pi\)
\(968\) 5.00000 0.160706
\(969\) 12.0000 0.385496
\(970\) 0 0
\(971\) −50.0000 −1.60458 −0.802288 − 0.596937i \(-0.796384\pi\)
−0.802288 + 0.596937i \(0.796384\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) 16.0000 0.512673
\(975\) 10.0000 0.320256
\(976\) 0 0
\(977\) −38.0000 −1.21573 −0.607864 − 0.794041i \(-0.707973\pi\)
−0.607864 + 0.794041i \(0.707973\pi\)
\(978\) 8.00000 0.255812
\(979\) −40.0000 −1.27841
\(980\) 0 0
\(981\) 2.00000 0.0638551
\(982\) 24.0000 0.765871
\(983\) −48.0000 −1.53096 −0.765481 − 0.643458i \(-0.777499\pi\)
−0.765481 + 0.643458i \(0.777499\pi\)
\(984\) −8.00000 −0.255031
\(985\) 0 0
\(986\) 4.00000 0.127386
\(987\) 0 0
\(988\) 12.0000 0.381771
\(989\) 4.00000 0.127193
\(990\) 0 0
\(991\) −40.0000 −1.27064 −0.635321 − 0.772248i \(-0.719132\pi\)
−0.635321 + 0.772248i \(0.719132\pi\)
\(992\) −2.00000 −0.0635001
\(993\) 20.0000 0.634681
\(994\) 0 0
\(995\) 0 0
\(996\) −6.00000 −0.190117
\(997\) −22.0000 −0.696747 −0.348373 − 0.937356i \(-0.613266\pi\)
−0.348373 + 0.937356i \(0.613266\pi\)
\(998\) −8.00000 −0.253236
\(999\) 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 6762.2.a.z.1.1 ✓ 1
7.6 odd 2 6762.2.a.bj.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6762.2.a.z.1.1 ✓ 1 1.1 even 1 trivial
6762.2.a.bj.1.1 yes 1 7.6 odd 2