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Properties

Label 4650.2.a.br.1.1
Level $4650$
Weight $2$
Character 4650.1
Self dual yes
Analytic conductor $37.130$
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] = [4650,2,Mod(1,4650)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4650, 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("4650.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4650.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: \(37.1304369399\)
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 \(\chi\) \(=\) 4650.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +5.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +1.00000 q^{18} +1.00000 q^{21} +5.00000 q^{22} +6.00000 q^{23} +1.00000 q^{24} +1.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -2.00000 q^{29} +1.00000 q^{31} +1.00000 q^{32} +5.00000 q^{33} +1.00000 q^{36} -7.00000 q^{37} +1.00000 q^{39} -9.00000 q^{41} +1.00000 q^{42} +11.0000 q^{43} +5.00000 q^{44} +6.00000 q^{46} +3.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} +1.00000 q^{52} -13.0000 q^{53} +1.00000 q^{54} +1.00000 q^{56} -2.00000 q^{58} +1.00000 q^{61} +1.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +5.00000 q^{66} +4.00000 q^{67} +6.00000 q^{69} +1.00000 q^{71} +1.00000 q^{72} -4.00000 q^{73} -7.00000 q^{74} +5.00000 q^{77} +1.00000 q^{78} +10.0000 q^{79} +1.00000 q^{81} -9.00000 q^{82} +1.00000 q^{83} +1.00000 q^{84} +11.0000 q^{86} -2.00000 q^{87} +5.00000 q^{88} -2.00000 q^{89} +1.00000 q^{91} +6.00000 q^{92} +1.00000 q^{93} +3.00000 q^{94} +1.00000 q^{96} +2.00000 q^{97} -6.00000 q^{98} +5.00000 q^{99} +O(q^{100})\)

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
\(6\) 1.00000 0.408248
\(7\) 1.00000 0.377964 0.188982 − 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.00000 1.50756 0.753778 − 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000 0.277350 0.138675 − 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 1.00000 0.235702
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 5.00000 1.06600
\(23\) 6.00000 1.25109 0.625543 − 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 1.00000 0.204124
\(25\) 0 0
\(26\) 1.00000 0.196116
\(27\) 1.00000 0.192450
\(28\) 1.00000 0.188982
\(29\) −2.00000 −0.371391 −0.185695 − 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 1.00000 0.179605
\(32\) 1.00000 0.176777
\(33\) 5.00000 0.870388
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −7.00000 −1.15079 −0.575396 − 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) −9.00000 −1.40556 −0.702782 − 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 1.00000 0.154303
\(43\) 11.0000 1.67748 0.838742 − 0.544529i \(-0.183292\pi\)
0.838742 + 0.544529i \(0.183292\pi\)
\(44\) 5.00000 0.753778
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 3.00000 0.437595 0.218797 − 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 1.00000 0.138675
\(53\) −13.0000 −1.78569 −0.892844 − 0.450367i \(-0.851293\pi\)
−0.892844 + 0.450367i \(0.851293\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −2.00000 −0.262613
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037 0.0640184 − 0.997949i \(-0.479608\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 1.00000 0.127000
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 5.00000 0.615457
\(67\) 4.00000 0.488678 0.244339 − 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 1.00000 0.118678 0.0593391 − 0.998238i \(-0.481101\pi\)
0.0593391 + 0.998238i \(0.481101\pi\)
\(72\) 1.00000 0.117851
\(73\) −4.00000 −0.468165 −0.234082 − 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) −7.00000 −0.813733
\(75\) 0 0
\(76\) 0 0
\(77\) 5.00000 0.569803
\(78\) 1.00000 0.113228
\(79\) 10.0000 1.12509 0.562544 − 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −9.00000 −0.993884
\(83\) 1.00000 0.109764 0.0548821 − 0.998493i \(-0.482522\pi\)
0.0548821 + 0.998493i \(0.482522\pi\)
\(84\) 1.00000 0.109109
\(85\) 0 0
\(86\) 11.0000 1.18616
\(87\) −2.00000 −0.214423
\(88\) 5.00000 0.533002
\(89\) −2.00000 −0.212000 −0.106000 − 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 6.00000 0.625543
\(93\) 1.00000 0.103695
\(94\) 3.00000 0.309426
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 2.00000 0.203069 0.101535 − 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −6.00000 −0.606092
\(99\) 5.00000 0.502519
\(100\) 0 0
\(101\) 8.00000 0.796030 0.398015 − 0.917379i \(-0.369699\pi\)
0.398015 + 0.917379i \(0.369699\pi\)
\(102\) 0 0
\(103\) 13.0000 1.28093 0.640464 − 0.767988i \(-0.278742\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −13.0000 −1.26267
\(107\) −14.0000 −1.35343 −0.676716 − 0.736245i \(-0.736597\pi\)
−0.676716 + 0.736245i \(0.736597\pi\)
\(108\) 1.00000 0.0962250
\(109\) −12.0000 −1.14939 −0.574696 − 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 0 0
\(111\) −7.00000 −0.664411
\(112\) 1.00000 0.0944911
\(113\) 18.0000 1.69330 0.846649 − 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.00000 −0.185695
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 1.00000 0.0905357
\(123\) −9.00000 −0.811503
\(124\) 1.00000 0.0898027
\(125\) 0 0
\(126\) 1.00000 0.0890871
\(127\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 1.00000 0.0883883
\(129\) 11.0000 0.968496
\(130\) 0 0
\(131\) 14.0000 1.22319 0.611593 − 0.791173i \(-0.290529\pi\)
0.611593 + 0.791173i \(0.290529\pi\)
\(132\) 5.00000 0.435194
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 0 0
\(137\) −18.0000 −1.53784 −0.768922 − 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 6.00000 0.510754
\(139\) −9.00000 −0.763370 −0.381685 − 0.924292i \(-0.624656\pi\)
−0.381685 + 0.924292i \(0.624656\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) 1.00000 0.0839181
\(143\) 5.00000 0.418121
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −4.00000 −0.331042
\(147\) −6.00000 −0.494872
\(148\) −7.00000 −0.575396
\(149\) 2.00000 0.163846 0.0819232 − 0.996639i \(-0.473894\pi\)
0.0819232 + 0.996639i \(0.473894\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 − 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 5.00000 0.402911
\(155\) 0 0
\(156\) 1.00000 0.0800641
\(157\) 18.0000 1.43656 0.718278 − 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 10.0000 0.795557
\(159\) −13.0000 −1.03097
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 1.00000 0.0785674
\(163\) −6.00000 −0.469956 −0.234978 − 0.972001i \(-0.575502\pi\)
−0.234978 + 0.972001i \(0.575502\pi\)
\(164\) −9.00000 −0.702782
\(165\) 0 0
\(166\) 1.00000 0.0776151
\(167\) 6.00000 0.464294 0.232147 − 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 1.00000 0.0771517
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 11.0000 0.838742
\(173\) 24.0000 1.82469 0.912343 − 0.409426i \(-0.134271\pi\)
0.912343 + 0.409426i \(0.134271\pi\)
\(174\) −2.00000 −0.151620
\(175\) 0 0
\(176\) 5.00000 0.376889
\(177\) 0 0
\(178\) −2.00000 −0.149906
\(179\) −1.00000 −0.0747435 −0.0373718 − 0.999301i \(-0.511899\pi\)
−0.0373718 + 0.999301i \(0.511899\pi\)
\(180\) 0 0
\(181\) −3.00000 −0.222988 −0.111494 − 0.993765i \(-0.535564\pi\)
−0.111494 + 0.993765i \(0.535564\pi\)
\(182\) 1.00000 0.0741249
\(183\) 1.00000 0.0739221
\(184\) 6.00000 0.442326
\(185\) 0 0
\(186\) 1.00000 0.0733236
\(187\) 0 0
\(188\) 3.00000 0.218797
\(189\) 1.00000 0.0727393
\(190\) 0 0
\(191\) 8.00000 0.578860 0.289430 − 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 1.00000 0.0721688
\(193\) −7.00000 −0.503871 −0.251936 − 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) −5.00000 −0.356235 −0.178118 − 0.984009i \(-0.557001\pi\)
−0.178118 + 0.984009i \(0.557001\pi\)
\(198\) 5.00000 0.355335
\(199\) −6.00000 −0.425329 −0.212664 − 0.977125i \(-0.568214\pi\)
−0.212664 + 0.977125i \(0.568214\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) 8.00000 0.562878
\(203\) −2.00000 −0.140372
\(204\) 0 0
\(205\) 0 0
\(206\) 13.0000 0.905753
\(207\) 6.00000 0.417029
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 − 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) −13.0000 −0.892844
\(213\) 1.00000 0.0685189
\(214\) −14.0000 −0.957020
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 1.00000 0.0678844
\(218\) −12.0000 −0.812743
\(219\) −4.00000 −0.270295
\(220\) 0 0
\(221\) 0 0
\(222\) −7.00000 −0.469809
\(223\) 26.0000 1.74109 0.870544 − 0.492090i \(-0.163767\pi\)
0.870544 + 0.492090i \(0.163767\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 18.0000 1.19734
\(227\) −20.0000 −1.32745 −0.663723 − 0.747978i \(-0.731025\pi\)
−0.663723 + 0.747978i \(0.731025\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 − 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 5.00000 0.328976
\(232\) −2.00000 −0.131306
\(233\) 9.00000 0.589610 0.294805 − 0.955557i \(-0.404745\pi\)
0.294805 + 0.955557i \(0.404745\pi\)
\(234\) 1.00000 0.0653720
\(235\) 0 0
\(236\) 0 0
\(237\) 10.0000 0.649570
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 − 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −26.0000 −1.67481 −0.837404 − 0.546585i \(-0.815928\pi\)
−0.837404 + 0.546585i \(0.815928\pi\)
\(242\) 14.0000 0.899954
\(243\) 1.00000 0.0641500
\(244\) 1.00000 0.0640184
\(245\) 0 0
\(246\) −9.00000 −0.573819
\(247\) 0 0
\(248\) 1.00000 0.0635001
\(249\) 1.00000 0.0633724
\(250\) 0 0
\(251\) 17.0000 1.07303 0.536515 − 0.843891i \(-0.319740\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(252\) 1.00000 0.0629941
\(253\) 30.0000 1.88608
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −7.00000 −0.436648 −0.218324 − 0.975876i \(-0.570059\pi\)
−0.218324 + 0.975876i \(0.570059\pi\)
\(258\) 11.0000 0.684830
\(259\) −7.00000 −0.434959
\(260\) 0 0
\(261\) −2.00000 −0.123797
\(262\) 14.0000 0.864923
\(263\) 12.0000 0.739952 0.369976 − 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 5.00000 0.307729
\(265\) 0 0
\(266\) 0 0
\(267\) −2.00000 −0.122398
\(268\) 4.00000 0.244339
\(269\) 18.0000 1.09748 0.548740 − 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 1.00000 0.0605228
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 6.00000 0.361158
\(277\) −22.0000 −1.32185 −0.660926 − 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) −9.00000 −0.539784
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) 27.0000 1.61068 0.805342 − 0.592810i \(-0.201981\pi\)
0.805342 + 0.592810i \(0.201981\pi\)
\(282\) 3.00000 0.178647
\(283\) 16.0000 0.951101 0.475551 − 0.879688i \(-0.342249\pi\)
0.475551 + 0.879688i \(0.342249\pi\)
\(284\) 1.00000 0.0593391
\(285\) 0 0
\(286\) 5.00000 0.295656
\(287\) −9.00000 −0.531253
\(288\) 1.00000 0.0589256
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 2.00000 0.117242
\(292\) −4.00000 −0.234082
\(293\) −14.0000 −0.817889 −0.408944 − 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) −6.00000 −0.349927
\(295\) 0 0
\(296\) −7.00000 −0.406867
\(297\) 5.00000 0.290129
\(298\) 2.00000 0.115857
\(299\) 6.00000 0.346989
\(300\) 0 0
\(301\) 11.0000 0.634029
\(302\) −10.0000 −0.575435
\(303\) 8.00000 0.459588
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 22.0000 1.25561 0.627803 − 0.778372i \(-0.283954\pi\)
0.627803 + 0.778372i \(0.283954\pi\)
\(308\) 5.00000 0.284901
\(309\) 13.0000 0.739544
\(310\) 0 0
\(311\) −3.00000 −0.170114 −0.0850572 − 0.996376i \(-0.527107\pi\)
−0.0850572 + 0.996376i \(0.527107\pi\)
\(312\) 1.00000 0.0566139
\(313\) −14.0000 −0.791327 −0.395663 − 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) 18.0000 1.01580
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 4.00000 0.224662 0.112331 − 0.993671i \(-0.464168\pi\)
0.112331 + 0.993671i \(0.464168\pi\)
\(318\) −13.0000 −0.729004
\(319\) −10.0000 −0.559893
\(320\) 0 0
\(321\) −14.0000 −0.781404
\(322\) 6.00000 0.334367
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.00000 −0.332309
\(327\) −12.0000 −0.663602
\(328\) −9.00000 −0.496942
\(329\) 3.00000 0.165395
\(330\) 0 0
\(331\) −19.0000 −1.04433 −0.522167 − 0.852843i \(-0.674876\pi\)
−0.522167 + 0.852843i \(0.674876\pi\)
\(332\) 1.00000 0.0548821
\(333\) −7.00000 −0.383598
\(334\) 6.00000 0.328305
\(335\) 0 0
\(336\) 1.00000 0.0545545
\(337\) −8.00000 −0.435788 −0.217894 − 0.975972i \(-0.569919\pi\)
−0.217894 + 0.975972i \(0.569919\pi\)
\(338\) −12.0000 −0.652714
\(339\) 18.0000 0.977626
\(340\) 0 0
\(341\) 5.00000 0.270765
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 11.0000 0.593080
\(345\) 0 0
\(346\) 24.0000 1.29025
\(347\) 17.0000 0.912608 0.456304 − 0.889824i \(-0.349173\pi\)
0.456304 + 0.889824i \(0.349173\pi\)
\(348\) −2.00000 −0.107211
\(349\) −16.0000 −0.856460 −0.428230 − 0.903670i \(-0.640863\pi\)
−0.428230 + 0.903670i \(0.640863\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 5.00000 0.266501
\(353\) 26.0000 1.38384 0.691920 − 0.721974i \(-0.256765\pi\)
0.691920 + 0.721974i \(0.256765\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −2.00000 −0.106000
\(357\) 0 0
\(358\) −1.00000 −0.0528516
\(359\) −24.0000 −1.26667 −0.633336 − 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) −3.00000 −0.157676
\(363\) 14.0000 0.734809
\(364\) 1.00000 0.0524142
\(365\) 0 0
\(366\) 1.00000 0.0522708
\(367\) 18.0000 0.939592 0.469796 − 0.882775i \(-0.344327\pi\)
0.469796 + 0.882775i \(0.344327\pi\)
\(368\) 6.00000 0.312772
\(369\) −9.00000 −0.468521
\(370\) 0 0
\(371\) −13.0000 −0.674926
\(372\) 1.00000 0.0518476
\(373\) −24.0000 −1.24267 −0.621336 − 0.783544i \(-0.713410\pi\)
−0.621336 + 0.783544i \(0.713410\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) −2.00000 −0.103005
\(378\) 1.00000 0.0514344
\(379\) −26.0000 −1.33553 −0.667765 − 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 8.00000 0.409316
\(383\) 12.0000 0.613171 0.306586 − 0.951843i \(-0.400813\pi\)
0.306586 + 0.951843i \(0.400813\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −7.00000 −0.356291
\(387\) 11.0000 0.559161
\(388\) 2.00000 0.101535
\(389\) −6.00000 −0.304212 −0.152106 − 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −6.00000 −0.303046
\(393\) 14.0000 0.706207
\(394\) −5.00000 −0.251896
\(395\) 0 0
\(396\) 5.00000 0.251259
\(397\) −18.0000 −0.903394 −0.451697 − 0.892171i \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) −6.00000 −0.300753
\(399\) 0 0
\(400\) 0 0
\(401\) −10.0000 −0.499376 −0.249688 − 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) 4.00000 0.199502
\(403\) 1.00000 0.0498135
\(404\) 8.00000 0.398015
\(405\) 0 0
\(406\) −2.00000 −0.0992583
\(407\) −35.0000 −1.73489
\(408\) 0 0
\(409\) 12.0000 0.593362 0.296681 − 0.954977i \(-0.404120\pi\)
0.296681 + 0.954977i \(0.404120\pi\)
\(410\) 0 0
\(411\) −18.0000 −0.887875
\(412\) 13.0000 0.640464
\(413\) 0 0
\(414\) 6.00000 0.294884
\(415\) 0 0
\(416\) 1.00000 0.0490290
\(417\) −9.00000 −0.440732
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 − 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 0 0
\(421\) −6.00000 −0.292422 −0.146211 − 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) −8.00000 −0.389434
\(423\) 3.00000 0.145865
\(424\) −13.0000 −0.631336
\(425\) 0 0
\(426\) 1.00000 0.0484502
\(427\) 1.00000 0.0483934
\(428\) −14.0000 −0.676716
\(429\) 5.00000 0.241402
\(430\) 0 0
\(431\) −7.00000 −0.337178 −0.168589 − 0.985686i \(-0.553921\pi\)
−0.168589 + 0.985686i \(0.553921\pi\)
\(432\) 1.00000 0.0481125
\(433\) −26.0000 −1.24948 −0.624740 − 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 1.00000 0.0480015
\(435\) 0 0
\(436\) −12.0000 −0.574696
\(437\) 0 0
\(438\) −4.00000 −0.191127
\(439\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) 18.0000 0.855206 0.427603 − 0.903967i \(-0.359358\pi\)
0.427603 + 0.903967i \(0.359358\pi\)
\(444\) −7.00000 −0.332205
\(445\) 0 0
\(446\) 26.0000 1.23114
\(447\) 2.00000 0.0945968
\(448\) 1.00000 0.0472456
\(449\) −34.0000 −1.60456 −0.802280 − 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 0 0
\(451\) −45.0000 −2.11897
\(452\) 18.0000 0.846649
\(453\) −10.0000 −0.469841
\(454\) −20.0000 −0.938647
\(455\) 0 0
\(456\) 0 0
\(457\) −2.00000 −0.0935561 −0.0467780 − 0.998905i \(-0.514895\pi\)
−0.0467780 + 0.998905i \(0.514895\pi\)
\(458\) −14.0000 −0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) −9.00000 −0.419172 −0.209586 − 0.977790i \(-0.567212\pi\)
−0.209586 + 0.977790i \(0.567212\pi\)
\(462\) 5.00000 0.232621
\(463\) −30.0000 −1.39422 −0.697109 − 0.716965i \(-0.745531\pi\)
−0.697109 + 0.716965i \(0.745531\pi\)
\(464\) −2.00000 −0.0928477
\(465\) 0 0
\(466\) 9.00000 0.416917
\(467\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 1.00000 0.0462250
\(469\) 4.00000 0.184703
\(470\) 0 0
\(471\) 18.0000 0.829396
\(472\) 0 0
\(473\) 55.0000 2.52890
\(474\) 10.0000 0.459315
\(475\) 0 0
\(476\) 0 0
\(477\) −13.0000 −0.595229
\(478\) −16.0000 −0.731823
\(479\) 4.00000 0.182765 0.0913823 − 0.995816i \(-0.470871\pi\)
0.0913823 + 0.995816i \(0.470871\pi\)
\(480\) 0 0
\(481\) −7.00000 −0.319173
\(482\) −26.0000 −1.18427
\(483\) 6.00000 0.273009
\(484\) 14.0000 0.636364
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 34.0000 1.54069 0.770344 − 0.637629i \(-0.220085\pi\)
0.770344 + 0.637629i \(0.220085\pi\)
\(488\) 1.00000 0.0452679
\(489\) −6.00000 −0.271329
\(490\) 0 0
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) −9.00000 −0.405751
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.00000 0.0449013
\(497\) 1.00000 0.0448561
\(498\) 1.00000 0.0448111
\(499\) −4.00000 −0.179065 −0.0895323 − 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 6.00000 0.268060
\(502\) 17.0000 0.758747
\(503\) 27.0000 1.20387 0.601935 − 0.798545i \(-0.294397\pi\)
0.601935 + 0.798545i \(0.294397\pi\)
\(504\) 1.00000 0.0445435
\(505\) 0 0
\(506\) 30.0000 1.33366
\(507\) −12.0000 −0.532939
\(508\) 0 0
\(509\) 15.0000 0.664863 0.332432 − 0.943127i \(-0.392131\pi\)
0.332432 + 0.943127i \(0.392131\pi\)
\(510\) 0 0
\(511\) −4.00000 −0.176950
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −7.00000 −0.308757
\(515\) 0 0
\(516\) 11.0000 0.484248
\(517\) 15.0000 0.659699
\(518\) −7.00000 −0.307562
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) −21.0000 −0.920027 −0.460013 − 0.887912i \(-0.652155\pi\)
−0.460013 + 0.887912i \(0.652155\pi\)
\(522\) −2.00000 −0.0875376
\(523\) 12.0000 0.524723 0.262362 − 0.964970i \(-0.415499\pi\)
0.262362 + 0.964970i \(0.415499\pi\)
\(524\) 14.0000 0.611593
\(525\) 0 0
\(526\) 12.0000 0.523225
\(527\) 0 0
\(528\) 5.00000 0.217597
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −9.00000 −0.389833
\(534\) −2.00000 −0.0865485
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) −1.00000 −0.0431532
\(538\) 18.0000 0.776035
\(539\) −30.0000 −1.29219
\(540\) 0 0
\(541\) −30.0000 −1.28980 −0.644900 − 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) 0 0
\(543\) −3.00000 −0.128742
\(544\) 0 0
\(545\) 0 0
\(546\) 1.00000 0.0427960
\(547\) 26.0000 1.11168 0.555840 − 0.831289i \(-0.312397\pi\)
0.555840 + 0.831289i \(0.312397\pi\)
\(548\) −18.0000 −0.768922
\(549\) 1.00000 0.0426790
\(550\) 0 0
\(551\) 0 0
\(552\) 6.00000 0.255377
\(553\) 10.0000 0.425243
\(554\) −22.0000 −0.934690
\(555\) 0 0
\(556\) −9.00000 −0.381685
\(557\) −18.0000 −0.762684 −0.381342 − 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 1.00000 0.0423334
\(559\) 11.0000 0.465250
\(560\) 0 0
\(561\) 0 0
\(562\) 27.0000 1.13893
\(563\) −44.0000 −1.85438 −0.927189 − 0.374593i \(-0.877783\pi\)
−0.927189 + 0.374593i \(0.877783\pi\)
\(564\) 3.00000 0.126323
\(565\) 0 0
\(566\) 16.0000 0.672530
\(567\) 1.00000 0.0419961
\(568\) 1.00000 0.0419591
\(569\) 34.0000 1.42535 0.712677 − 0.701492i \(-0.247483\pi\)
0.712677 + 0.701492i \(0.247483\pi\)
\(570\) 0 0
\(571\) 5.00000 0.209243 0.104622 − 0.994512i \(-0.466637\pi\)
0.104622 + 0.994512i \(0.466637\pi\)
\(572\) 5.00000 0.209061
\(573\) 8.00000 0.334205
\(574\) −9.00000 −0.375653
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 18.0000 0.749350 0.374675 − 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) −17.0000 −0.707107
\(579\) −7.00000 −0.290910
\(580\) 0 0
\(581\) 1.00000 0.0414870
\(582\) 2.00000 0.0829027
\(583\) −65.0000 −2.69202
\(584\) −4.00000 −0.165521
\(585\) 0 0
\(586\) −14.0000 −0.578335
\(587\) 39.0000 1.60970 0.804851 − 0.593477i \(-0.202245\pi\)
0.804851 + 0.593477i \(0.202245\pi\)
\(588\) −6.00000 −0.247436
\(589\) 0 0
\(590\) 0 0
\(591\) −5.00000 −0.205673
\(592\) −7.00000 −0.287698
\(593\) −5.00000 −0.205325 −0.102663 − 0.994716i \(-0.532736\pi\)
−0.102663 + 0.994716i \(0.532736\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) 2.00000 0.0819232
\(597\) −6.00000 −0.245564
\(598\) 6.00000 0.245358
\(599\) −9.00000 −0.367730 −0.183865 − 0.982952i \(-0.558861\pi\)
−0.183865 + 0.982952i \(0.558861\pi\)
\(600\) 0 0
\(601\) −2.00000 −0.0815817 −0.0407909 − 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) 11.0000 0.448327
\(603\) 4.00000 0.162893
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 8.00000 0.324978
\(607\) 13.0000 0.527654 0.263827 − 0.964570i \(-0.415015\pi\)
0.263827 + 0.964570i \(0.415015\pi\)
\(608\) 0 0
\(609\) −2.00000 −0.0810441
\(610\) 0 0
\(611\) 3.00000 0.121367
\(612\) 0 0
\(613\) −6.00000 −0.242338 −0.121169 − 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) 22.0000 0.887848
\(615\) 0 0
\(616\) 5.00000 0.201456
\(617\) −41.0000 −1.65060 −0.825299 − 0.564696i \(-0.808993\pi\)
−0.825299 + 0.564696i \(0.808993\pi\)
\(618\) 13.0000 0.522937
\(619\) −29.0000 −1.16561 −0.582804 − 0.812613i \(-0.698045\pi\)
−0.582804 + 0.812613i \(0.698045\pi\)
\(620\) 0 0
\(621\) 6.00000 0.240772
\(622\) −3.00000 −0.120289
\(623\) −2.00000 −0.0801283
\(624\) 1.00000 0.0400320
\(625\) 0 0
\(626\) −14.0000 −0.559553
\(627\) 0 0
\(628\) 18.0000 0.718278
\(629\) 0 0
\(630\) 0 0
\(631\) −14.0000 −0.557331 −0.278666 − 0.960388i \(-0.589892\pi\)
−0.278666 + 0.960388i \(0.589892\pi\)
\(632\) 10.0000 0.397779
\(633\) −8.00000 −0.317971
\(634\) 4.00000 0.158860
\(635\) 0 0
\(636\) −13.0000 −0.515484
\(637\) −6.00000 −0.237729
\(638\) −10.0000 −0.395904
\(639\) 1.00000 0.0395594
\(640\) 0 0
\(641\) −42.0000 −1.65890 −0.829450 − 0.558581i \(-0.811346\pi\)
−0.829450 + 0.558581i \(0.811346\pi\)
\(642\) −14.0000 −0.552536
\(643\) 5.00000 0.197181 0.0985904 − 0.995128i \(-0.468567\pi\)
0.0985904 + 0.995128i \(0.468567\pi\)
\(644\) 6.00000 0.236433
\(645\) 0 0
\(646\) 0 0
\(647\) 10.0000 0.393141 0.196570 − 0.980490i \(-0.437020\pi\)
0.196570 + 0.980490i \(0.437020\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 1.00000 0.0391931
\(652\) −6.00000 −0.234978
\(653\) 28.0000 1.09572 0.547862 − 0.836569i \(-0.315442\pi\)
0.547862 + 0.836569i \(0.315442\pi\)
\(654\) −12.0000 −0.469237
\(655\) 0 0
\(656\) −9.00000 −0.351391
\(657\) −4.00000 −0.156055
\(658\) 3.00000 0.116952
\(659\) −10.0000 −0.389545 −0.194772 − 0.980848i \(-0.562397\pi\)
−0.194772 + 0.980848i \(0.562397\pi\)
\(660\) 0 0
\(661\) 48.0000 1.86698 0.933492 − 0.358599i \(-0.116745\pi\)
0.933492 + 0.358599i \(0.116745\pi\)
\(662\) −19.0000 −0.738456
\(663\) 0 0
\(664\) 1.00000 0.0388075
\(665\) 0 0
\(666\) −7.00000 −0.271244
\(667\) −12.0000 −0.464642
\(668\) 6.00000 0.232147
\(669\) 26.0000 1.00522
\(670\) 0 0
\(671\) 5.00000 0.193023
\(672\) 1.00000 0.0385758
\(673\) −2.00000 −0.0770943 −0.0385472 − 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) −8.00000 −0.308148
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) 31.0000 1.19143 0.595713 − 0.803197i \(-0.296869\pi\)
0.595713 + 0.803197i \(0.296869\pi\)
\(678\) 18.0000 0.691286
\(679\) 2.00000 0.0767530
\(680\) 0 0
\(681\) −20.0000 −0.766402
\(682\) 5.00000 0.191460
\(683\) 8.00000 0.306111 0.153056 − 0.988218i \(-0.451089\pi\)
0.153056 + 0.988218i \(0.451089\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −13.0000 −0.496342
\(687\) −14.0000 −0.534133
\(688\) 11.0000 0.419371
\(689\) −13.0000 −0.495261
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 − 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 24.0000 0.912343
\(693\) 5.00000 0.189934
\(694\) 17.0000 0.645311
\(695\) 0 0
\(696\) −2.00000 −0.0758098
\(697\) 0 0
\(698\) −16.0000 −0.605609
\(699\) 9.00000 0.340411
\(700\) 0 0
\(701\) 44.0000 1.66186 0.830929 − 0.556379i \(-0.187810\pi\)
0.830929 + 0.556379i \(0.187810\pi\)
\(702\) 1.00000 0.0377426
\(703\) 0 0
\(704\) 5.00000 0.188445
\(705\) 0 0
\(706\) 26.0000 0.978523
\(707\) 8.00000 0.300871
\(708\) 0 0
\(709\) 38.0000 1.42712 0.713560 − 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) 0 0
\(711\) 10.0000 0.375029
\(712\) −2.00000 −0.0749532
\(713\) 6.00000 0.224702
\(714\) 0 0
\(715\) 0 0
\(716\) −1.00000 −0.0373718
\(717\) −16.0000 −0.597531
\(718\) −24.0000 −0.895672
\(719\) −40.0000 −1.49175 −0.745874 − 0.666087i \(-0.767968\pi\)
−0.745874 + 0.666087i \(0.767968\pi\)
\(720\) 0 0
\(721\) 13.0000 0.484145
\(722\) −19.0000 −0.707107
\(723\) −26.0000 −0.966950
\(724\) −3.00000 −0.111494
\(725\) 0 0
\(726\) 14.0000 0.519589
\(727\) −9.00000 −0.333792 −0.166896 − 0.985975i \(-0.553374\pi\)
−0.166896 + 0.985975i \(0.553374\pi\)
\(728\) 1.00000 0.0370625
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 1.00000 0.0369611
\(733\) −34.0000 −1.25582 −0.627909 − 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) 18.0000 0.664392
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 20.0000 0.736709
\(738\) −9.00000 −0.331295
\(739\) −20.0000 −0.735712 −0.367856 − 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −13.0000 −0.477245
\(743\) −8.00000 −0.293492 −0.146746 − 0.989174i \(-0.546880\pi\)
−0.146746 + 0.989174i \(0.546880\pi\)
\(744\) 1.00000 0.0366618
\(745\) 0 0
\(746\) −24.0000 −0.878702
\(747\) 1.00000 0.0365881
\(748\) 0 0
\(749\) −14.0000 −0.511549
\(750\) 0 0
\(751\) 13.0000 0.474377 0.237188 − 0.971464i \(-0.423774\pi\)
0.237188 + 0.971464i \(0.423774\pi\)
\(752\) 3.00000 0.109399
\(753\) 17.0000 0.619514
\(754\) −2.00000 −0.0728357
\(755\) 0 0
\(756\) 1.00000 0.0363696
\(757\) 15.0000 0.545184 0.272592 − 0.962130i \(-0.412119\pi\)
0.272592 + 0.962130i \(0.412119\pi\)
\(758\) −26.0000 −0.944363
\(759\) 30.0000 1.08893
\(760\) 0 0
\(761\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) −12.0000 −0.434429
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) 12.0000 0.433578
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 15.0000 0.540914 0.270457 − 0.962732i \(-0.412825\pi\)
0.270457 + 0.962732i \(0.412825\pi\)
\(770\) 0 0
\(771\) −7.00000 −0.252099
\(772\) −7.00000 −0.251936
\(773\) −42.0000 −1.51064 −0.755318 − 0.655359i \(-0.772517\pi\)
−0.755318 + 0.655359i \(0.772517\pi\)
\(774\) 11.0000 0.395387
\(775\) 0 0
\(776\) 2.00000 0.0717958
\(777\) −7.00000 −0.251124
\(778\) −6.00000 −0.215110
\(779\) 0 0
\(780\) 0 0
\(781\) 5.00000 0.178914
\(782\) 0 0
\(783\) −2.00000 −0.0714742
\(784\) −6.00000 −0.214286
\(785\) 0 0
\(786\) 14.0000 0.499363
\(787\) 37.0000 1.31891 0.659454 − 0.751745i \(-0.270788\pi\)
0.659454 + 0.751745i \(0.270788\pi\)
\(788\) −5.00000 −0.178118
\(789\) 12.0000 0.427211
\(790\) 0 0
\(791\) 18.0000 0.640006
\(792\) 5.00000 0.177667
\(793\) 1.00000 0.0355110
\(794\) −18.0000 −0.638796
\(795\) 0 0
\(796\) −6.00000 −0.212664
\(797\) 18.0000 0.637593 0.318796 − 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −2.00000 −0.0706665
\(802\) −10.0000 −0.353112
\(803\) −20.0000 −0.705785
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) 1.00000 0.0352235
\(807\) 18.0000 0.633630
\(808\) 8.00000 0.281439
\(809\) 50.0000 1.75791 0.878953 − 0.476908i \(-0.158243\pi\)
0.878953 + 0.476908i \(0.158243\pi\)
\(810\) 0 0
\(811\) −40.0000 −1.40459 −0.702295 − 0.711886i \(-0.747841\pi\)
−0.702295 + 0.711886i \(0.747841\pi\)
\(812\) −2.00000 −0.0701862
\(813\) 0 0
\(814\) −35.0000 −1.22675
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 12.0000 0.419570
\(819\) 1.00000 0.0349428
\(820\) 0 0
\(821\) −27.0000 −0.942306 −0.471153 − 0.882051i \(-0.656162\pi\)
−0.471153 + 0.882051i \(0.656162\pi\)
\(822\) −18.0000 −0.627822
\(823\) −32.0000 −1.11545 −0.557725 − 0.830026i \(-0.688326\pi\)
−0.557725 + 0.830026i \(0.688326\pi\)
\(824\) 13.0000 0.452876
\(825\) 0 0
\(826\) 0 0
\(827\) 4.00000 0.139094 0.0695468 − 0.997579i \(-0.477845\pi\)
0.0695468 + 0.997579i \(0.477845\pi\)
\(828\) 6.00000 0.208514
\(829\) 29.0000 1.00721 0.503606 − 0.863934i \(-0.332006\pi\)
0.503606 + 0.863934i \(0.332006\pi\)
\(830\) 0 0
\(831\) −22.0000 −0.763172
\(832\) 1.00000 0.0346688
\(833\) 0 0
\(834\) −9.00000 −0.311645
\(835\) 0 0
\(836\) 0 0
\(837\) 1.00000 0.0345651
\(838\) −30.0000 −1.03633
\(839\) 29.0000 1.00119 0.500596 − 0.865681i \(-0.333114\pi\)
0.500596 + 0.865681i \(0.333114\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −6.00000 −0.206774
\(843\) 27.0000 0.929929
\(844\) −8.00000 −0.275371
\(845\) 0 0
\(846\) 3.00000 0.103142
\(847\) 14.0000 0.481046
\(848\) −13.0000 −0.446422
\(849\) 16.0000 0.549119
\(850\) 0 0
\(851\) −42.0000 −1.43974
\(852\) 1.00000 0.0342594
\(853\) −24.0000 −0.821744 −0.410872 − 0.911693i \(-0.634776\pi\)
−0.410872 + 0.911693i \(0.634776\pi\)
\(854\) 1.00000 0.0342193
\(855\) 0 0
\(856\) −14.0000 −0.478510
\(857\) −45.0000 −1.53717 −0.768585 − 0.639747i \(-0.779039\pi\)
−0.768585 + 0.639747i \(0.779039\pi\)
\(858\) 5.00000 0.170697
\(859\) −5.00000 −0.170598 −0.0852989 − 0.996355i \(-0.527185\pi\)
−0.0852989 + 0.996355i \(0.527185\pi\)
\(860\) 0 0
\(861\) −9.00000 −0.306719
\(862\) −7.00000 −0.238421
\(863\) −36.0000 −1.22545 −0.612727 − 0.790295i \(-0.709928\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) −26.0000 −0.883516
\(867\) −17.0000 −0.577350
\(868\) 1.00000 0.0339422
\(869\) 50.0000 1.69613
\(870\) 0 0
\(871\) 4.00000 0.135535
\(872\) −12.0000 −0.406371
\(873\) 2.00000 0.0676897
\(874\) 0 0
\(875\) 0 0
\(876\) −4.00000 −0.135147
\(877\) −36.0000 −1.21563 −0.607817 − 0.794077i \(-0.707955\pi\)
−0.607817 + 0.794077i \(0.707955\pi\)
\(878\) 0 0
\(879\) −14.0000 −0.472208
\(880\) 0 0
\(881\) 16.0000 0.539054 0.269527 − 0.962993i \(-0.413133\pi\)
0.269527 + 0.962993i \(0.413133\pi\)
\(882\) −6.00000 −0.202031
\(883\) −7.00000 −0.235569 −0.117784 − 0.993039i \(-0.537579\pi\)
−0.117784 + 0.993039i \(0.537579\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 18.0000 0.604722
\(887\) 3.00000 0.100730 0.0503651 − 0.998731i \(-0.483962\pi\)
0.0503651 + 0.998731i \(0.483962\pi\)
\(888\) −7.00000 −0.234905
\(889\) 0 0
\(890\) 0 0
\(891\) 5.00000 0.167506
\(892\) 26.0000 0.870544
\(893\) 0 0
\(894\) 2.00000 0.0668900
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 6.00000 0.200334
\(898\) −34.0000 −1.13459
\(899\) −2.00000 −0.0667037
\(900\) 0 0
\(901\) 0 0
\(902\) −45.0000 −1.49834
\(903\) 11.0000 0.366057
\(904\) 18.0000 0.598671
\(905\) 0 0
\(906\) −10.0000 −0.332228
\(907\) −16.0000 −0.531271 −0.265636 − 0.964073i \(-0.585582\pi\)
−0.265636 + 0.964073i \(0.585582\pi\)
\(908\) −20.0000 −0.663723
\(909\) 8.00000 0.265343
\(910\) 0 0
\(911\) 8.00000 0.265052 0.132526 − 0.991180i \(-0.457691\pi\)
0.132526 + 0.991180i \(0.457691\pi\)
\(912\) 0 0
\(913\) 5.00000 0.165476
\(914\) −2.00000 −0.0661541
\(915\) 0 0
\(916\) −14.0000 −0.462573
\(917\) 14.0000 0.462321
\(918\) 0 0
\(919\) −33.0000 −1.08857 −0.544285 − 0.838901i \(-0.683199\pi\)
−0.544285 + 0.838901i \(0.683199\pi\)
\(920\) 0 0
\(921\) 22.0000 0.724925
\(922\) −9.00000 −0.296399
\(923\) 1.00000 0.0329154
\(924\) 5.00000 0.164488
\(925\) 0 0
\(926\) −30.0000 −0.985861
\(927\) 13.0000 0.426976
\(928\) −2.00000 −0.0656532
\(929\) 54.0000 1.77168 0.885841 − 0.463988i \(-0.153582\pi\)
0.885841 + 0.463988i \(0.153582\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 9.00000 0.294805
\(933\) −3.00000 −0.0982156
\(934\) 0 0
\(935\) 0 0
\(936\) 1.00000 0.0326860
\(937\) −34.0000 −1.11073 −0.555366 − 0.831606i \(-0.687422\pi\)
−0.555366 + 0.831606i \(0.687422\pi\)
\(938\) 4.00000 0.130605
\(939\) −14.0000 −0.456873
\(940\) 0 0
\(941\) −18.0000 −0.586783 −0.293392 − 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) 18.0000 0.586472
\(943\) −54.0000 −1.75848
\(944\) 0 0
\(945\) 0 0
\(946\) 55.0000 1.78820
\(947\) −5.00000 −0.162478 −0.0812391 − 0.996695i \(-0.525888\pi\)
−0.0812391 + 0.996695i \(0.525888\pi\)
\(948\) 10.0000 0.324785
\(949\) −4.00000 −0.129845
\(950\) 0 0
\(951\) 4.00000 0.129709
\(952\) 0 0
\(953\) −22.0000 −0.712650 −0.356325 − 0.934362i \(-0.615970\pi\)
−0.356325 + 0.934362i \(0.615970\pi\)
\(954\) −13.0000 −0.420891
\(955\) 0 0
\(956\) −16.0000 −0.517477
\(957\) −10.0000 −0.323254
\(958\) 4.00000 0.129234
\(959\) −18.0000 −0.581250
\(960\) 0 0
\(961\) 1.00000 0.0322581
\(962\) −7.00000 −0.225689
\(963\) −14.0000 −0.451144
\(964\) −26.0000 −0.837404
\(965\) 0 0
\(966\) 6.00000 0.193047
\(967\) 10.0000 0.321578 0.160789 − 0.986989i \(-0.448596\pi\)
0.160789 + 0.986989i \(0.448596\pi\)
\(968\) 14.0000 0.449977
\(969\) 0 0
\(970\) 0 0
\(971\) 12.0000 0.385098 0.192549 − 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) 1.00000 0.0320750
\(973\) −9.00000 −0.288527
\(974\) 34.0000 1.08943
\(975\) 0 0
\(976\) 1.00000 0.0320092
\(977\) −3.00000 −0.0959785 −0.0479893 − 0.998848i \(-0.515281\pi\)
−0.0479893 + 0.998848i \(0.515281\pi\)
\(978\) −6.00000 −0.191859
\(979\) −10.0000 −0.319601
\(980\) 0 0
\(981\) −12.0000 −0.383131
\(982\) 0 0
\(983\) 18.0000 0.574111 0.287055 − 0.957914i \(-0.407324\pi\)
0.287055 + 0.957914i \(0.407324\pi\)
\(984\) −9.00000 −0.286910
\(985\) 0 0
\(986\) 0 0
\(987\) 3.00000 0.0954911
\(988\) 0 0
\(989\) 66.0000 2.09868
\(990\) 0 0
\(991\) 2.00000 0.0635321 0.0317660 − 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) 1.00000 0.0317500
\(993\) −19.0000 −0.602947
\(994\) 1.00000 0.0317181
\(995\) 0 0
\(996\) 1.00000 0.0316862
\(997\) −48.0000 −1.52018 −0.760088 − 0.649821i \(-0.774844\pi\)
−0.760088 + 0.649821i \(0.774844\pi\)
\(998\) −4.00000 −0.126618
\(999\) −7.00000 −0.221470
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 4650.2.a.br.1.1 yes 1
5.2 odd 4 4650.2.d.bb.3349.2 2
5.3 odd 4 4650.2.d.bb.3349.1 2
5.4 even 2 4650.2.a.g.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4650.2.a.g.1.1 ✓ 1 5.4 even 2
4650.2.a.br.1.1 yes 1 1.1 even 1 trivial
4650.2.d.bb.3349.1 2 5.3 odd 4
4650.2.d.bb.3349.2 2 5.2 odd 4