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Properties

Label 567.2.a.a.1.1
Level $567$
Weight $2$
Character 567.1
Self dual yes
Analytic conductor $4.528$
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] = [567,2,Mod(1,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("567.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.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: \(4.52751779461\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 567.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} +3.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} +3.00000 q^{8} -1.00000 q^{10} -2.00000 q^{11} -5.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} +3.00000 q^{17} -2.00000 q^{19} -1.00000 q^{20} +2.00000 q^{22} +6.00000 q^{23} -4.00000 q^{25} +5.00000 q^{26} +1.00000 q^{28} -5.00000 q^{29} -6.00000 q^{31} -5.00000 q^{32} -3.00000 q^{34} -1.00000 q^{35} -3.00000 q^{37} +2.00000 q^{38} +3.00000 q^{40} -10.0000 q^{41} -4.00000 q^{43} +2.00000 q^{44} -6.00000 q^{46} -6.00000 q^{47} +1.00000 q^{49} +4.00000 q^{50} +5.00000 q^{52} -6.00000 q^{53} -2.00000 q^{55} -3.00000 q^{56} +5.00000 q^{58} +6.00000 q^{59} +7.00000 q^{61} +6.00000 q^{62} +7.00000 q^{64} -5.00000 q^{65} -2.00000 q^{67} -3.00000 q^{68} +1.00000 q^{70} -12.0000 q^{71} -15.0000 q^{73} +3.00000 q^{74} +2.00000 q^{76} +2.00000 q^{77} +14.0000 q^{79} -1.00000 q^{80} +10.0000 q^{82} +18.0000 q^{83} +3.00000 q^{85} +4.00000 q^{86} -6.00000 q^{88} -5.00000 q^{89} +5.00000 q^{91} -6.00000 q^{92} +6.00000 q^{94} -2.00000 q^{95} -18.0000 q^{97} -1.00000 q^{98} +O(q^{100})\)

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 −0.353553 − 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 1.00000 0.447214 0.223607 − 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) −1.00000 −0.316228
\(11\) −2.00000 −0.603023 −0.301511 − 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −5.00000 −1.38675 −0.693375 − 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 3.00000 0.727607 0.363803 − 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 − 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) 2.00000 0.426401
\(23\) 6.00000 1.25109 0.625543 − 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 5.00000 0.980581
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) −5.00000 −0.928477 −0.464238 − 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 0 0
\(31\) −6.00000 −1.07763 −0.538816 − 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) −3.00000 −0.493197 −0.246598 − 0.969118i \(-0.579313\pi\)
−0.246598 + 0.969118i \(0.579313\pi\)
\(38\) 2.00000 0.324443
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) −10.0000 −1.56174 −0.780869 − 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 − 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) −6.00000 −0.875190 −0.437595 − 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) 5.00000 0.693375
\(53\) −6.00000 −0.824163 −0.412082 − 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) −3.00000 −0.400892
\(57\) 0 0
\(58\) 5.00000 0.656532
\(59\) 6.00000 0.781133 0.390567 − 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 0 0
\(61\) 7.00000 0.896258 0.448129 − 0.893969i \(-0.352090\pi\)
0.448129 + 0.893969i \(0.352090\pi\)
\(62\) 6.00000 0.762001
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −5.00000 −0.620174
\(66\) 0 0
\(67\) −2.00000 −0.244339 −0.122169 − 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) −3.00000 −0.363803
\(69\) 0 0
\(70\) 1.00000 0.119523
\(71\) −12.0000 −1.42414 −0.712069 − 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) −15.0000 −1.75562 −0.877809 − 0.479012i \(-0.840995\pi\)
−0.877809 + 0.479012i \(0.840995\pi\)
\(74\) 3.00000 0.348743
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 2.00000 0.227921
\(78\) 0 0
\(79\) 14.0000 1.57512 0.787562 − 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) 10.0000 1.10432
\(83\) 18.0000 1.97576 0.987878 − 0.155230i \(-0.0496119\pi\)
0.987878 + 0.155230i \(0.0496119\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) 4.00000 0.431331
\(87\) 0 0
\(88\) −6.00000 −0.639602
\(89\) −5.00000 −0.529999 −0.264999 − 0.964249i \(-0.585372\pi\)
−0.264999 + 0.964249i \(0.585372\pi\)
\(90\) 0 0
\(91\) 5.00000 0.524142
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) 6.00000 0.618853
\(95\) −2.00000 −0.205196
\(96\) 0 0
\(97\) −18.0000 −1.82762 −0.913812 − 0.406138i \(-0.866875\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) 14.0000 1.39305 0.696526 − 0.717532i \(-0.254728\pi\)
0.696526 + 0.717532i \(0.254728\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 − 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −15.0000 −1.47087
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −8.00000 −0.773389 −0.386695 − 0.922208i \(-0.626383\pi\)
−0.386695 + 0.922208i \(0.626383\pi\)
\(108\) 0 0
\(109\) 9.00000 0.862044 0.431022 − 0.902342i \(-0.358153\pi\)
0.431022 + 0.902342i \(0.358153\pi\)
\(110\) 2.00000 0.190693
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) 1.00000 0.0940721 0.0470360 − 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) 0 0
\(115\) 6.00000 0.559503
\(116\) 5.00000 0.464238
\(117\) 0 0
\(118\) −6.00000 −0.552345
\(119\) −3.00000 −0.275010
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) −7.00000 −0.633750
\(123\) 0 0
\(124\) 6.00000 0.538816
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 12.0000 1.06483 0.532414 − 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) 3.00000 0.265165
\(129\) 0 0
\(130\) 5.00000 0.438529
\(131\) 16.0000 1.39793 0.698963 − 0.715158i \(-0.253645\pi\)
0.698963 + 0.715158i \(0.253645\pi\)
\(132\) 0 0
\(133\) 2.00000 0.173422
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 9.00000 0.771744
\(137\) 21.0000 1.79415 0.897076 − 0.441877i \(-0.145687\pi\)
0.897076 + 0.441877i \(0.145687\pi\)
\(138\) 0 0
\(139\) −6.00000 −0.508913 −0.254457 − 0.967084i \(-0.581897\pi\)
−0.254457 + 0.967084i \(0.581897\pi\)
\(140\) 1.00000 0.0845154
\(141\) 0 0
\(142\) 12.0000 1.00702
\(143\) 10.0000 0.836242
\(144\) 0 0
\(145\) −5.00000 −0.415227
\(146\) 15.0000 1.24141
\(147\) 0 0
\(148\) 3.00000 0.246598
\(149\) 15.0000 1.22885 0.614424 − 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 − 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −6.00000 −0.486664
\(153\) 0 0
\(154\) −2.00000 −0.161165
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) −5.00000 −0.399043 −0.199522 − 0.979893i \(-0.563939\pi\)
−0.199522 + 0.979893i \(0.563939\pi\)
\(158\) −14.0000 −1.11378
\(159\) 0 0
\(160\) −5.00000 −0.395285
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) 16.0000 1.25322 0.626608 − 0.779334i \(-0.284443\pi\)
0.626608 + 0.779334i \(0.284443\pi\)
\(164\) 10.0000 0.780869
\(165\) 0 0
\(166\) −18.0000 −1.39707
\(167\) −14.0000 −1.08335 −0.541676 − 0.840587i \(-0.682210\pi\)
−0.541676 + 0.840587i \(0.682210\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) −3.00000 −0.230089
\(171\) 0 0
\(172\) 4.00000 0.304997
\(173\) 5.00000 0.380143 0.190071 − 0.981770i \(-0.439128\pi\)
0.190071 + 0.981770i \(0.439128\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) 2.00000 0.150756
\(177\) 0 0
\(178\) 5.00000 0.374766
\(179\) 2.00000 0.149487 0.0747435 − 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 − 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) −5.00000 −0.370625
\(183\) 0 0
\(184\) 18.0000 1.32698
\(185\) −3.00000 −0.220564
\(186\) 0 0
\(187\) −6.00000 −0.438763
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 2.00000 0.145095
\(191\) −14.0000 −1.01300 −0.506502 − 0.862239i \(-0.669062\pi\)
−0.506502 + 0.862239i \(0.669062\pi\)
\(192\) 0 0
\(193\) −13.0000 −0.935760 −0.467880 − 0.883792i \(-0.654982\pi\)
−0.467880 + 0.883792i \(0.654982\pi\)
\(194\) 18.0000 1.29232
\(195\) 0 0
\(196\) −1.00000 −0.0714286
\(197\) −5.00000 −0.356235 −0.178118 − 0.984009i \(-0.557001\pi\)
−0.178118 + 0.984009i \(0.557001\pi\)
\(198\) 0 0
\(199\) −6.00000 −0.425329 −0.212664 − 0.977125i \(-0.568214\pi\)
−0.212664 + 0.977125i \(0.568214\pi\)
\(200\) −12.0000 −0.848528
\(201\) 0 0
\(202\) −14.0000 −0.985037
\(203\) 5.00000 0.350931
\(204\) 0 0
\(205\) −10.0000 −0.698430
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 5.00000 0.346688
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 22.0000 1.51454 0.757271 − 0.653101i \(-0.226532\pi\)
0.757271 + 0.653101i \(0.226532\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) 8.00000 0.546869
\(215\) −4.00000 −0.272798
\(216\) 0 0
\(217\) 6.00000 0.407307
\(218\) −9.00000 −0.609557
\(219\) 0 0
\(220\) 2.00000 0.134840
\(221\) −15.0000 −1.00901
\(222\) 0 0
\(223\) 4.00000 0.267860 0.133930 − 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 5.00000 0.334077
\(225\) 0 0
\(226\) −1.00000 −0.0665190
\(227\) −24.0000 −1.59294 −0.796468 − 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) 0 0
\(229\) 11.0000 0.726900 0.363450 − 0.931614i \(-0.381599\pi\)
0.363450 + 0.931614i \(0.381599\pi\)
\(230\) −6.00000 −0.395628
\(231\) 0 0
\(232\) −15.0000 −0.984798
\(233\) 21.0000 1.37576 0.687878 − 0.725826i \(-0.258542\pi\)
0.687878 + 0.725826i \(0.258542\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) −6.00000 −0.390567
\(237\) 0 0
\(238\) 3.00000 0.194461
\(239\) 30.0000 1.94054 0.970269 − 0.242028i \(-0.0778125\pi\)
0.970269 + 0.242028i \(0.0778125\pi\)
\(240\) 0 0
\(241\) −19.0000 −1.22390 −0.611949 − 0.790897i \(-0.709614\pi\)
−0.611949 + 0.790897i \(0.709614\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) −7.00000 −0.448129
\(245\) 1.00000 0.0638877
\(246\) 0 0
\(247\) 10.0000 0.636285
\(248\) −18.0000 −1.14300
\(249\) 0 0
\(250\) 9.00000 0.569210
\(251\) −2.00000 −0.126239 −0.0631194 − 0.998006i \(-0.520105\pi\)
−0.0631194 + 0.998006i \(0.520105\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) −12.0000 −0.752947
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) −13.0000 −0.810918 −0.405459 − 0.914113i \(-0.632888\pi\)
−0.405459 + 0.914113i \(0.632888\pi\)
\(258\) 0 0
\(259\) 3.00000 0.186411
\(260\) 5.00000 0.310087
\(261\) 0 0
\(262\) −16.0000 −0.988483
\(263\) 10.0000 0.616626 0.308313 − 0.951285i \(-0.400236\pi\)
0.308313 + 0.951285i \(0.400236\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) −2.00000 −0.122628
\(267\) 0 0
\(268\) 2.00000 0.122169
\(269\) 9.00000 0.548740 0.274370 − 0.961624i \(-0.411531\pi\)
0.274370 + 0.961624i \(0.411531\pi\)
\(270\) 0 0
\(271\) −14.0000 −0.850439 −0.425220 − 0.905090i \(-0.639803\pi\)
−0.425220 + 0.905090i \(0.639803\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −21.0000 −1.26866
\(275\) 8.00000 0.482418
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 − 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 6.00000 0.359856
\(279\) 0 0
\(280\) −3.00000 −0.179284
\(281\) 5.00000 0.298275 0.149137 − 0.988816i \(-0.452350\pi\)
0.149137 + 0.988816i \(0.452350\pi\)
\(282\) 0 0
\(283\) −8.00000 −0.475551 −0.237775 − 0.971320i \(-0.576418\pi\)
−0.237775 + 0.971320i \(0.576418\pi\)
\(284\) 12.0000 0.712069
\(285\) 0 0
\(286\) −10.0000 −0.591312
\(287\) 10.0000 0.590281
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 5.00000 0.293610
\(291\) 0 0
\(292\) 15.0000 0.877809
\(293\) −31.0000 −1.81104 −0.905520 − 0.424304i \(-0.860519\pi\)
−0.905520 + 0.424304i \(0.860519\pi\)
\(294\) 0 0
\(295\) 6.00000 0.349334
\(296\) −9.00000 −0.523114
\(297\) 0 0
\(298\) −15.0000 −0.868927
\(299\) −30.0000 −1.73494
\(300\) 0 0
\(301\) 4.00000 0.230556
\(302\) 10.0000 0.575435
\(303\) 0 0
\(304\) 2.00000 0.114708
\(305\) 7.00000 0.400819
\(306\) 0 0
\(307\) −8.00000 −0.456584 −0.228292 − 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) −2.00000 −0.113961
\(309\) 0 0
\(310\) 6.00000 0.340777
\(311\) 6.00000 0.340229 0.170114 − 0.985424i \(-0.445586\pi\)
0.170114 + 0.985424i \(0.445586\pi\)
\(312\) 0 0
\(313\) −19.0000 −1.07394 −0.536972 − 0.843600i \(-0.680432\pi\)
−0.536972 + 0.843600i \(0.680432\pi\)
\(314\) 5.00000 0.282166
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) −9.00000 −0.505490 −0.252745 − 0.967533i \(-0.581333\pi\)
−0.252745 + 0.967533i \(0.581333\pi\)
\(318\) 0 0
\(319\) 10.0000 0.559893
\(320\) 7.00000 0.391312
\(321\) 0 0
\(322\) 6.00000 0.334367
\(323\) −6.00000 −0.333849
\(324\) 0 0
\(325\) 20.0000 1.10940
\(326\) −16.0000 −0.886158
\(327\) 0 0
\(328\) −30.0000 −1.65647
\(329\) 6.00000 0.330791
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 − 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) −18.0000 −0.987878
\(333\) 0 0
\(334\) 14.0000 0.766046
\(335\) −2.00000 −0.109272
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 − 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) −12.0000 −0.652714
\(339\) 0 0
\(340\) −3.00000 −0.162698
\(341\) 12.0000 0.649836
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −12.0000 −0.646997
\(345\) 0 0
\(346\) −5.00000 −0.268802
\(347\) −4.00000 −0.214731 −0.107366 − 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 − 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) 10.0000 0.533002
\(353\) −14.0000 −0.745145 −0.372572 − 0.928003i \(-0.621524\pi\)
−0.372572 + 0.928003i \(0.621524\pi\)
\(354\) 0 0
\(355\) −12.0000 −0.636894
\(356\) 5.00000 0.264999
\(357\) 0 0
\(358\) −2.00000 −0.105703
\(359\) 8.00000 0.422224 0.211112 − 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 14.0000 0.735824
\(363\) 0 0
\(364\) −5.00000 −0.262071
\(365\) −15.0000 −0.785136
\(366\) 0 0
\(367\) −30.0000 −1.56599 −0.782994 − 0.622030i \(-0.786308\pi\)
−0.782994 + 0.622030i \(0.786308\pi\)
\(368\) −6.00000 −0.312772
\(369\) 0 0
\(370\) 3.00000 0.155963
\(371\) 6.00000 0.311504
\(372\) 0 0
\(373\) −22.0000 −1.13912 −0.569558 − 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 6.00000 0.310253
\(375\) 0 0
\(376\) −18.0000 −0.928279
\(377\) 25.0000 1.28757
\(378\) 0 0
\(379\) 6.00000 0.308199 0.154100 − 0.988055i \(-0.450752\pi\)
0.154100 + 0.988055i \(0.450752\pi\)
\(380\) 2.00000 0.102598
\(381\) 0 0
\(382\) 14.0000 0.716302
\(383\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 2.00000 0.101929
\(386\) 13.0000 0.661683
\(387\) 0 0
\(388\) 18.0000 0.913812
\(389\) 18.0000 0.912636 0.456318 − 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 3.00000 0.151523
\(393\) 0 0
\(394\) 5.00000 0.251896
\(395\) 14.0000 0.704416
\(396\) 0 0
\(397\) 15.0000 0.752828 0.376414 − 0.926451i \(-0.377157\pi\)
0.376414 + 0.926451i \(0.377157\pi\)
\(398\) 6.00000 0.300753
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) −3.00000 −0.149813 −0.0749064 − 0.997191i \(-0.523866\pi\)
−0.0749064 + 0.997191i \(0.523866\pi\)
\(402\) 0 0
\(403\) 30.0000 1.49441
\(404\) −14.0000 −0.696526
\(405\) 0 0
\(406\) −5.00000 −0.248146
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) 5.00000 0.247234 0.123617 − 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(410\) 10.0000 0.493865
\(411\) 0 0
\(412\) −8.00000 −0.394132
\(413\) −6.00000 −0.295241
\(414\) 0 0
\(415\) 18.0000 0.883585
\(416\) 25.0000 1.22573
\(417\) 0 0
\(418\) −4.00000 −0.195646
\(419\) 36.0000 1.75872 0.879358 − 0.476162i \(-0.157972\pi\)
0.879358 + 0.476162i \(0.157972\pi\)
\(420\) 0 0
\(421\) 29.0000 1.41337 0.706687 − 0.707527i \(-0.250189\pi\)
0.706687 + 0.707527i \(0.250189\pi\)
\(422\) −22.0000 −1.07094
\(423\) 0 0
\(424\) −18.0000 −0.874157
\(425\) −12.0000 −0.582086
\(426\) 0 0
\(427\) −7.00000 −0.338754
\(428\) 8.00000 0.386695
\(429\) 0 0
\(430\) 4.00000 0.192897
\(431\) 12.0000 0.578020 0.289010 − 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 0 0
\(433\) 1.00000 0.0480569 0.0240285 − 0.999711i \(-0.492351\pi\)
0.0240285 + 0.999711i \(0.492351\pi\)
\(434\) −6.00000 −0.288009
\(435\) 0 0
\(436\) −9.00000 −0.431022
\(437\) −12.0000 −0.574038
\(438\) 0 0
\(439\) 36.0000 1.71819 0.859093 − 0.511819i \(-0.171028\pi\)
0.859093 + 0.511819i \(0.171028\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) 15.0000 0.713477
\(443\) 6.00000 0.285069 0.142534 − 0.989790i \(-0.454475\pi\)
0.142534 + 0.989790i \(0.454475\pi\)
\(444\) 0 0
\(445\) −5.00000 −0.237023
\(446\) −4.00000 −0.189405
\(447\) 0 0
\(448\) −7.00000 −0.330719
\(449\) 18.0000 0.849473 0.424736 − 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) 20.0000 0.941763
\(452\) −1.00000 −0.0470360
\(453\) 0 0
\(454\) 24.0000 1.12638
\(455\) 5.00000 0.234404
\(456\) 0 0
\(457\) −17.0000 −0.795226 −0.397613 − 0.917553i \(-0.630161\pi\)
−0.397613 + 0.917553i \(0.630161\pi\)
\(458\) −11.0000 −0.513996
\(459\) 0 0
\(460\) −6.00000 −0.279751
\(461\) 38.0000 1.76984 0.884918 − 0.465746i \(-0.154214\pi\)
0.884918 + 0.465746i \(0.154214\pi\)
\(462\) 0 0
\(463\) −2.00000 −0.0929479 −0.0464739 − 0.998920i \(-0.514798\pi\)
−0.0464739 + 0.998920i \(0.514798\pi\)
\(464\) 5.00000 0.232119
\(465\) 0 0
\(466\) −21.0000 −0.972806
\(467\) −18.0000 −0.832941 −0.416470 − 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) 0 0
\(469\) 2.00000 0.0923514
\(470\) 6.00000 0.276759
\(471\) 0 0
\(472\) 18.0000 0.828517
\(473\) 8.00000 0.367840
\(474\) 0 0
\(475\) 8.00000 0.367065
\(476\) 3.00000 0.137505
\(477\) 0 0
\(478\) −30.0000 −1.37217
\(479\) −34.0000 −1.55350 −0.776750 − 0.629809i \(-0.783133\pi\)
−0.776750 + 0.629809i \(0.783133\pi\)
\(480\) 0 0
\(481\) 15.0000 0.683941
\(482\) 19.0000 0.865426
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) −18.0000 −0.817338
\(486\) 0 0
\(487\) 34.0000 1.54069 0.770344 − 0.637629i \(-0.220085\pi\)
0.770344 + 0.637629i \(0.220085\pi\)
\(488\) 21.0000 0.950625
\(489\) 0 0
\(490\) −1.00000 −0.0451754
\(491\) −28.0000 −1.26362 −0.631811 − 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) 0 0
\(493\) −15.0000 −0.675566
\(494\) −10.0000 −0.449921
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) 12.0000 0.538274
\(498\) 0 0
\(499\) 10.0000 0.447661 0.223831 − 0.974628i \(-0.428144\pi\)
0.223831 + 0.974628i \(0.428144\pi\)
\(500\) 9.00000 0.402492
\(501\) 0 0
\(502\) 2.00000 0.0892644
\(503\) −18.0000 −0.802580 −0.401290 − 0.915951i \(-0.631438\pi\)
−0.401290 + 0.915951i \(0.631438\pi\)
\(504\) 0 0
\(505\) 14.0000 0.622992
\(506\) 12.0000 0.533465
\(507\) 0 0
\(508\) −12.0000 −0.532414
\(509\) −34.0000 −1.50702 −0.753512 − 0.657434i \(-0.771642\pi\)
−0.753512 + 0.657434i \(0.771642\pi\)
\(510\) 0 0
\(511\) 15.0000 0.663561
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) 13.0000 0.573405
\(515\) 8.00000 0.352522
\(516\) 0 0
\(517\) 12.0000 0.527759
\(518\) −3.00000 −0.131812
\(519\) 0 0
\(520\) −15.0000 −0.657794
\(521\) −6.00000 −0.262865 −0.131432 − 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 − 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) −16.0000 −0.698963
\(525\) 0 0
\(526\) −10.0000 −0.436021
\(527\) −18.0000 −0.784092
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 6.00000 0.260623
\(531\) 0 0
\(532\) −2.00000 −0.0867110
\(533\) 50.0000 2.16574
\(534\) 0 0
\(535\) −8.00000 −0.345870
\(536\) −6.00000 −0.259161
\(537\) 0 0
\(538\) −9.00000 −0.388018
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) 17.0000 0.730887 0.365444 − 0.930834i \(-0.380917\pi\)
0.365444 + 0.930834i \(0.380917\pi\)
\(542\) 14.0000 0.601351
\(543\) 0 0
\(544\) −15.0000 −0.643120
\(545\) 9.00000 0.385518
\(546\) 0 0
\(547\) 22.0000 0.940652 0.470326 − 0.882493i \(-0.344136\pi\)
0.470326 + 0.882493i \(0.344136\pi\)
\(548\) −21.0000 −0.897076
\(549\) 0 0
\(550\) −8.00000 −0.341121
\(551\) 10.0000 0.426014
\(552\) 0 0
\(553\) −14.0000 −0.595341
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) 6.00000 0.254457
\(557\) −29.0000 −1.22877 −0.614385 − 0.789007i \(-0.710596\pi\)
−0.614385 + 0.789007i \(0.710596\pi\)
\(558\) 0 0
\(559\) 20.0000 0.845910
\(560\) 1.00000 0.0422577
\(561\) 0 0
\(562\) −5.00000 −0.210912
\(563\) −32.0000 −1.34864 −0.674320 − 0.738440i \(-0.735563\pi\)
−0.674320 + 0.738440i \(0.735563\pi\)
\(564\) 0 0
\(565\) 1.00000 0.0420703
\(566\) 8.00000 0.336265
\(567\) 0 0
\(568\) −36.0000 −1.51053
\(569\) −11.0000 −0.461144 −0.230572 − 0.973055i \(-0.574060\pi\)
−0.230572 + 0.973055i \(0.574060\pi\)
\(570\) 0 0
\(571\) 38.0000 1.59025 0.795125 − 0.606445i \(-0.207405\pi\)
0.795125 + 0.606445i \(0.207405\pi\)
\(572\) −10.0000 −0.418121
\(573\) 0 0
\(574\) −10.0000 −0.417392
\(575\) −24.0000 −1.00087
\(576\) 0 0
\(577\) −23.0000 −0.957503 −0.478751 − 0.877951i \(-0.658910\pi\)
−0.478751 + 0.877951i \(0.658910\pi\)
\(578\) 8.00000 0.332756
\(579\) 0 0
\(580\) 5.00000 0.207614
\(581\) −18.0000 −0.746766
\(582\) 0 0
\(583\) 12.0000 0.496989
\(584\) −45.0000 −1.86211
\(585\) 0 0
\(586\) 31.0000 1.28060
\(587\) −26.0000 −1.07313 −0.536567 − 0.843857i \(-0.680279\pi\)
−0.536567 + 0.843857i \(0.680279\pi\)
\(588\) 0 0
\(589\) 12.0000 0.494451
\(590\) −6.00000 −0.247016
\(591\) 0 0
\(592\) 3.00000 0.123299
\(593\) 27.0000 1.10876 0.554379 − 0.832265i \(-0.312956\pi\)
0.554379 + 0.832265i \(0.312956\pi\)
\(594\) 0 0
\(595\) −3.00000 −0.122988
\(596\) −15.0000 −0.614424
\(597\) 0 0
\(598\) 30.0000 1.22679
\(599\) 30.0000 1.22577 0.612883 − 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 0 0
\(601\) 33.0000 1.34610 0.673049 − 0.739598i \(-0.264984\pi\)
0.673049 + 0.739598i \(0.264984\pi\)
\(602\) −4.00000 −0.163028
\(603\) 0 0
\(604\) 10.0000 0.406894
\(605\) −7.00000 −0.284590
\(606\) 0 0
\(607\) 14.0000 0.568242 0.284121 − 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) 10.0000 0.405554
\(609\) 0 0
\(610\) −7.00000 −0.283422
\(611\) 30.0000 1.21367
\(612\) 0 0
\(613\) −2.00000 −0.0807792 −0.0403896 − 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 8.00000 0.322854
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) −15.0000 −0.603877 −0.301939 − 0.953327i \(-0.597634\pi\)
−0.301939 + 0.953327i \(0.597634\pi\)
\(618\) 0 0
\(619\) 4.00000 0.160774 0.0803868 − 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 6.00000 0.240966
\(621\) 0 0
\(622\) −6.00000 −0.240578
\(623\) 5.00000 0.200321
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 19.0000 0.759393
\(627\) 0 0
\(628\) 5.00000 0.199522
\(629\) −9.00000 −0.358854
\(630\) 0 0
\(631\) −22.0000 −0.875806 −0.437903 − 0.899022i \(-0.644279\pi\)
−0.437903 + 0.899022i \(0.644279\pi\)
\(632\) 42.0000 1.67067
\(633\) 0 0
\(634\) 9.00000 0.357436
\(635\) 12.0000 0.476205
\(636\) 0 0
\(637\) −5.00000 −0.198107
\(638\) −10.0000 −0.395904
\(639\) 0 0
\(640\) 3.00000 0.118585
\(641\) −15.0000 −0.592464 −0.296232 − 0.955116i \(-0.595730\pi\)
−0.296232 + 0.955116i \(0.595730\pi\)
\(642\) 0 0
\(643\) 14.0000 0.552106 0.276053 − 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 6.00000 0.236433
\(645\) 0 0
\(646\) 6.00000 0.236067
\(647\) 8.00000 0.314512 0.157256 − 0.987558i \(-0.449735\pi\)
0.157256 + 0.987558i \(0.449735\pi\)
\(648\) 0 0
\(649\) −12.0000 −0.471041
\(650\) −20.0000 −0.784465
\(651\) 0 0
\(652\) −16.0000 −0.626608
\(653\) −30.0000 −1.17399 −0.586995 − 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) 0 0
\(655\) 16.0000 0.625172
\(656\) 10.0000 0.390434
\(657\) 0 0
\(658\) −6.00000 −0.233904
\(659\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −41.0000 −1.59472 −0.797358 − 0.603507i \(-0.793769\pi\)
−0.797358 + 0.603507i \(0.793769\pi\)
\(662\) 4.00000 0.155464
\(663\) 0 0
\(664\) 54.0000 2.09561
\(665\) 2.00000 0.0775567
\(666\) 0 0
\(667\) −30.0000 −1.16160
\(668\) 14.0000 0.541676
\(669\) 0 0
\(670\) 2.00000 0.0772667
\(671\) −14.0000 −0.540464
\(672\) 0 0
\(673\) −41.0000 −1.58043 −0.790217 − 0.612827i \(-0.790032\pi\)
−0.790217 + 0.612827i \(0.790032\pi\)
\(674\) 2.00000 0.0770371
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) −6.00000 −0.230599 −0.115299 − 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 0 0
\(679\) 18.0000 0.690777
\(680\) 9.00000 0.345134
\(681\) 0 0
\(682\) −12.0000 −0.459504
\(683\) −12.0000 −0.459167 −0.229584 − 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 0 0
\(685\) 21.0000 0.802369
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) 4.00000 0.152499
\(689\) 30.0000 1.14291
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 − 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) −5.00000 −0.190071
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) −6.00000 −0.227593
\(696\) 0 0
\(697\) −30.0000 −1.13633
\(698\) −10.0000 −0.378506
\(699\) 0 0
\(700\) −4.00000 −0.151186
\(701\) −9.00000 −0.339925 −0.169963 − 0.985451i \(-0.554365\pi\)
−0.169963 + 0.985451i \(0.554365\pi\)
\(702\) 0 0
\(703\) 6.00000 0.226294
\(704\) −14.0000 −0.527645
\(705\) 0 0
\(706\) 14.0000 0.526897
\(707\) −14.0000 −0.526524
\(708\) 0 0
\(709\) −39.0000 −1.46468 −0.732338 − 0.680941i \(-0.761571\pi\)
−0.732338 + 0.680941i \(0.761571\pi\)
\(710\) 12.0000 0.450352
\(711\) 0 0
\(712\) −15.0000 −0.562149
\(713\) −36.0000 −1.34821
\(714\) 0 0
\(715\) 10.0000 0.373979
\(716\) −2.00000 −0.0747435
\(717\) 0 0
\(718\) −8.00000 −0.298557
\(719\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 15.0000 0.558242
\(723\) 0 0
\(724\) 14.0000 0.520306
\(725\) 20.0000 0.742781
\(726\) 0 0
\(727\) 8.00000 0.296704 0.148352 − 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 15.0000 0.555937
\(729\) 0 0
\(730\) 15.0000 0.555175
\(731\) −12.0000 −0.443836
\(732\) 0 0
\(733\) −6.00000 −0.221615 −0.110808 − 0.993842i \(-0.535344\pi\)
−0.110808 + 0.993842i \(0.535344\pi\)
\(734\) 30.0000 1.10732
\(735\) 0 0
\(736\) −30.0000 −1.10581
\(737\) 4.00000 0.147342
\(738\) 0 0
\(739\) 54.0000 1.98642 0.993211 − 0.116326i \(-0.0371118\pi\)
0.993211 + 0.116326i \(0.0371118\pi\)
\(740\) 3.00000 0.110282
\(741\) 0 0
\(742\) −6.00000 −0.220267
\(743\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 15.0000 0.549557
\(746\) 22.0000 0.805477
\(747\) 0 0
\(748\) 6.00000 0.219382
\(749\) 8.00000 0.292314
\(750\) 0 0
\(751\) −44.0000 −1.60558 −0.802791 − 0.596260i \(-0.796653\pi\)
−0.802791 + 0.596260i \(0.796653\pi\)
\(752\) 6.00000 0.218797
\(753\) 0 0
\(754\) −25.0000 −0.910446
\(755\) −10.0000 −0.363937
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 − 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −6.00000 −0.217930
\(759\) 0 0
\(760\) −6.00000 −0.217643
\(761\) −33.0000 −1.19625 −0.598125 − 0.801403i \(-0.704087\pi\)
−0.598125 + 0.801403i \(0.704087\pi\)
\(762\) 0 0
\(763\) −9.00000 −0.325822
\(764\) 14.0000 0.506502
\(765\) 0 0
\(766\) 0 0
\(767\) −30.0000 −1.08324
\(768\) 0 0
\(769\) 5.00000 0.180305 0.0901523 − 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) −2.00000 −0.0720750
\(771\) 0 0
\(772\) 13.0000 0.467880
\(773\) 29.0000 1.04306 0.521529 − 0.853234i \(-0.325362\pi\)
0.521529 + 0.853234i \(0.325362\pi\)
\(774\) 0 0
\(775\) 24.0000 0.862105
\(776\) −54.0000 −1.93849
\(777\) 0 0
\(778\) −18.0000 −0.645331
\(779\) 20.0000 0.716574
\(780\) 0 0
\(781\) 24.0000 0.858788
\(782\) −18.0000 −0.643679
\(783\) 0 0
\(784\) −1.00000 −0.0357143
\(785\) −5.00000 −0.178458
\(786\) 0 0
\(787\) 16.0000 0.570338 0.285169 − 0.958477i \(-0.407950\pi\)
0.285169 + 0.958477i \(0.407950\pi\)
\(788\) 5.00000 0.178118
\(789\) 0 0
\(790\) −14.0000 −0.498098
\(791\) −1.00000 −0.0355559
\(792\) 0 0
\(793\) −35.0000 −1.24289
\(794\) −15.0000 −0.532330
\(795\) 0 0
\(796\) 6.00000 0.212664
\(797\) 37.0000 1.31061 0.655304 − 0.755366i \(-0.272541\pi\)
0.655304 + 0.755366i \(0.272541\pi\)
\(798\) 0 0
\(799\) −18.0000 −0.636794
\(800\) 20.0000 0.707107
\(801\) 0 0
\(802\) 3.00000 0.105934
\(803\) 30.0000 1.05868
\(804\) 0 0
\(805\) −6.00000 −0.211472
\(806\) −30.0000 −1.05670
\(807\) 0 0
\(808\) 42.0000 1.47755
\(809\) 9.00000 0.316423 0.158212 − 0.987405i \(-0.449427\pi\)
0.158212 + 0.987405i \(0.449427\pi\)
\(810\) 0 0
\(811\) 14.0000 0.491606 0.245803 − 0.969320i \(-0.420948\pi\)
0.245803 + 0.969320i \(0.420948\pi\)
\(812\) −5.00000 −0.175466
\(813\) 0 0
\(814\) −6.00000 −0.210300
\(815\) 16.0000 0.560456
\(816\) 0 0
\(817\) 8.00000 0.279885
\(818\) −5.00000 −0.174821
\(819\) 0 0
\(820\) 10.0000 0.349215
\(821\) 47.0000 1.64031 0.820156 − 0.572140i \(-0.193887\pi\)
0.820156 + 0.572140i \(0.193887\pi\)
\(822\) 0 0
\(823\) −24.0000 −0.836587 −0.418294 − 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) 24.0000 0.836080
\(825\) 0 0
\(826\) 6.00000 0.208767
\(827\) 24.0000 0.834562 0.417281 − 0.908778i \(-0.362983\pi\)
0.417281 + 0.908778i \(0.362983\pi\)
\(828\) 0 0
\(829\) −34.0000 −1.18087 −0.590434 − 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) −18.0000 −0.624789
\(831\) 0 0
\(832\) −35.0000 −1.21341
\(833\) 3.00000 0.103944
\(834\) 0 0
\(835\) −14.0000 −0.484490
\(836\) −4.00000 −0.138343
\(837\) 0 0
\(838\) −36.0000 −1.24360
\(839\) −8.00000 −0.276191 −0.138095 − 0.990419i \(-0.544098\pi\)
−0.138095 + 0.990419i \(0.544098\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) −29.0000 −0.999406
\(843\) 0 0
\(844\) −22.0000 −0.757271
\(845\) 12.0000 0.412813
\(846\) 0 0
\(847\) 7.00000 0.240523
\(848\) 6.00000 0.206041
\(849\) 0 0
\(850\) 12.0000 0.411597
\(851\) −18.0000 −0.617032
\(852\) 0 0
\(853\) −10.0000 −0.342393 −0.171197 − 0.985237i \(-0.554763\pi\)
−0.171197 + 0.985237i \(0.554763\pi\)
\(854\) 7.00000 0.239535
\(855\) 0 0
\(856\) −24.0000 −0.820303
\(857\) −41.0000 −1.40053 −0.700267 − 0.713881i \(-0.746936\pi\)
−0.700267 + 0.713881i \(0.746936\pi\)
\(858\) 0 0
\(859\) −52.0000 −1.77422 −0.887109 − 0.461561i \(-0.847290\pi\)
−0.887109 + 0.461561i \(0.847290\pi\)
\(860\) 4.00000 0.136399
\(861\) 0 0
\(862\) −12.0000 −0.408722
\(863\) 54.0000 1.83818 0.919091 − 0.394046i \(-0.128925\pi\)
0.919091 + 0.394046i \(0.128925\pi\)
\(864\) 0 0
\(865\) 5.00000 0.170005
\(866\) −1.00000 −0.0339814
\(867\) 0 0
\(868\) −6.00000 −0.203653
\(869\) −28.0000 −0.949835
\(870\) 0 0
\(871\) 10.0000 0.338837
\(872\) 27.0000 0.914335
\(873\) 0 0
\(874\) 12.0000 0.405906
\(875\) 9.00000 0.304256
\(876\) 0 0
\(877\) −11.0000 −0.371444 −0.185722 − 0.982602i \(-0.559462\pi\)
−0.185722 + 0.982602i \(0.559462\pi\)
\(878\) −36.0000 −1.21494
\(879\) 0 0
\(880\) 2.00000 0.0674200
\(881\) −18.0000 −0.606435 −0.303218 − 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 0 0
\(883\) 26.0000 0.874970 0.437485 − 0.899226i \(-0.355869\pi\)
0.437485 + 0.899226i \(0.355869\pi\)
\(884\) 15.0000 0.504505
\(885\) 0 0
\(886\) −6.00000 −0.201574
\(887\) 38.0000 1.27592 0.637958 − 0.770072i \(-0.279780\pi\)
0.637958 + 0.770072i \(0.279780\pi\)
\(888\) 0 0
\(889\) −12.0000 −0.402467
\(890\) 5.00000 0.167600
\(891\) 0 0
\(892\) −4.00000 −0.133930
\(893\) 12.0000 0.401565
\(894\) 0 0
\(895\) 2.00000 0.0668526
\(896\) −3.00000 −0.100223
\(897\) 0 0
\(898\) −18.0000 −0.600668
\(899\) 30.0000 1.00056
\(900\) 0 0
\(901\) −18.0000 −0.599667
\(902\) −20.0000 −0.665927
\(903\) 0 0
\(904\) 3.00000 0.0997785
\(905\) −14.0000 −0.465376
\(906\) 0 0
\(907\) −4.00000 −0.132818 −0.0664089 − 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) 24.0000 0.796468
\(909\) 0 0
\(910\) −5.00000 −0.165748
\(911\) 12.0000 0.397578 0.198789 − 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 0 0
\(913\) −36.0000 −1.19143
\(914\) 17.0000 0.562310
\(915\) 0 0
\(916\) −11.0000 −0.363450
\(917\) −16.0000 −0.528367
\(918\) 0 0
\(919\) −34.0000 −1.12156 −0.560778 − 0.827966i \(-0.689498\pi\)
−0.560778 + 0.827966i \(0.689498\pi\)
\(920\) 18.0000 0.593442
\(921\) 0 0
\(922\) −38.0000 −1.25146
\(923\) 60.0000 1.97492
\(924\) 0 0
\(925\) 12.0000 0.394558
\(926\) 2.00000 0.0657241
\(927\) 0 0
\(928\) 25.0000 0.820665
\(929\) −37.0000 −1.21393 −0.606965 − 0.794728i \(-0.707613\pi\)
−0.606965 + 0.794728i \(0.707613\pi\)
\(930\) 0 0
\(931\) −2.00000 −0.0655474
\(932\) −21.0000 −0.687878
\(933\) 0 0
\(934\) 18.0000 0.588978
\(935\) −6.00000 −0.196221
\(936\) 0 0
\(937\) 33.0000 1.07806 0.539032 − 0.842286i \(-0.318790\pi\)
0.539032 + 0.842286i \(0.318790\pi\)
\(938\) −2.00000 −0.0653023
\(939\) 0 0
\(940\) 6.00000 0.195698
\(941\) 41.0000 1.33656 0.668281 − 0.743909i \(-0.267030\pi\)
0.668281 + 0.743909i \(0.267030\pi\)
\(942\) 0 0
\(943\) −60.0000 −1.95387
\(944\) −6.00000 −0.195283
\(945\) 0 0
\(946\) −8.00000 −0.260102
\(947\) −4.00000 −0.129983 −0.0649913 − 0.997886i \(-0.520702\pi\)
−0.0649913 + 0.997886i \(0.520702\pi\)
\(948\) 0 0
\(949\) 75.0000 2.43460
\(950\) −8.00000 −0.259554
\(951\) 0 0
\(952\) −9.00000 −0.291692
\(953\) 5.00000 0.161966 0.0809829 − 0.996715i \(-0.474194\pi\)
0.0809829 + 0.996715i \(0.474194\pi\)
\(954\) 0 0
\(955\) −14.0000 −0.453029
\(956\) −30.0000 −0.970269
\(957\) 0 0
\(958\) 34.0000 1.09849
\(959\) −21.0000 −0.678125
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) −15.0000 −0.483619
\(963\) 0 0
\(964\) 19.0000 0.611949
\(965\) −13.0000 −0.418485
\(966\) 0 0
\(967\) −26.0000 −0.836104 −0.418052 − 0.908423i \(-0.637287\pi\)
−0.418052 + 0.908423i \(0.637287\pi\)
\(968\) −21.0000 −0.674966
\(969\) 0 0
\(970\) 18.0000 0.577945
\(971\) −54.0000 −1.73294 −0.866471 − 0.499227i \(-0.833617\pi\)
−0.866471 + 0.499227i \(0.833617\pi\)
\(972\) 0 0
\(973\) 6.00000 0.192351
\(974\) −34.0000 −1.08943
\(975\) 0 0
\(976\) −7.00000 −0.224065
\(977\) 18.0000 0.575871 0.287936 − 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 0 0
\(979\) 10.0000 0.319601
\(980\) −1.00000 −0.0319438
\(981\) 0 0
\(982\) 28.0000 0.893516
\(983\) 12.0000 0.382741 0.191370 − 0.981518i \(-0.438707\pi\)
0.191370 + 0.981518i \(0.438707\pi\)
\(984\) 0 0
\(985\) −5.00000 −0.159313
\(986\) 15.0000 0.477697
\(987\) 0 0
\(988\) −10.0000 −0.318142
\(989\) −24.0000 −0.763156
\(990\) 0 0
\(991\) 2.00000 0.0635321 0.0317660 − 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) 30.0000 0.952501
\(993\) 0 0
\(994\) −12.0000 −0.380617
\(995\) −6.00000 −0.190213
\(996\) 0 0
\(997\) 7.00000 0.221692 0.110846 − 0.993838i \(-0.464644\pi\)
0.110846 + 0.993838i \(0.464644\pi\)
\(998\) −10.0000 −0.316544
\(999\) 0 0
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 567.2.a.a.1.1 ✓ 1
3.2 odd 2 567.2.a.b.1.1 yes 1
4.3 odd 2 9072.2.a.q.1.1 1
7.6 odd 2 3969.2.a.b.1.1 1
9.2 odd 6 567.2.f.c.190.1 2
9.4 even 3 567.2.f.f.379.1 2
9.5 odd 6 567.2.f.c.379.1 2
9.7 even 3 567.2.f.f.190.1 2
12.11 even 2 9072.2.a.j.1.1 1
21.20 even 2 3969.2.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
567.2.a.a.1.1 ✓ 1 1.1 even 1 trivial
567.2.a.b.1.1 yes 1 3.2 odd 2
567.2.f.c.190.1 2 9.2 odd 6
567.2.f.c.379.1 2 9.5 odd 6
567.2.f.f.190.1 2 9.7 even 3
567.2.f.f.379.1 2 9.4 even 3
3969.2.a.b.1.1 1 7.6 odd 2
3969.2.a.e.1.1 1 21.20 even 2
9072.2.a.j.1.1 1 12.11 even 2
9072.2.a.q.1.1 1 4.3 odd 2