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Properties

Label 4650.2.a.o.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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.00000 q^{11} +1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -1.00000 q^{18} -6.00000 q^{19} -1.00000 q^{21} +3.00000 q^{22} -1.00000 q^{24} +1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +2.00000 q^{29} -1.00000 q^{31} -1.00000 q^{32} -3.00000 q^{33} +1.00000 q^{36} +11.0000 q^{37} +6.00000 q^{38} -1.00000 q^{39} -5.00000 q^{41} +1.00000 q^{42} -5.00000 q^{43} -3.00000 q^{44} +13.0000 q^{47} +1.00000 q^{48} -6.00000 q^{49} -1.00000 q^{52} +5.00000 q^{53} -1.00000 q^{54} +1.00000 q^{56} -6.00000 q^{57} -2.00000 q^{58} +14.0000 q^{59} +3.00000 q^{61} +1.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.00000 q^{66} -2.00000 q^{67} +15.0000 q^{71} -1.00000 q^{72} +2.00000 q^{73} -11.0000 q^{74} -6.00000 q^{76} +3.00000 q^{77} +1.00000 q^{78} +8.00000 q^{79} +1.00000 q^{81} +5.00000 q^{82} -3.00000 q^{83} -1.00000 q^{84} +5.00000 q^{86} +2.00000 q^{87} +3.00000 q^{88} -14.0000 q^{89} +1.00000 q^{91} -1.00000 q^{93} -13.0000 q^{94} -1.00000 q^{96} +10.0000 q^{97} +6.00000 q^{98} -3.00000 q^{99} +O(q^{100})\)

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 \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 − 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.00000 −0.277350 −0.138675 − 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 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
\(19\) −6.00000 −1.37649 −0.688247 − 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 3.00000 0.639602
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −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 \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605
\(32\) −1.00000 −0.176777
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 11.0000 1.80839 0.904194 − 0.427121i \(-0.140472\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 6.00000 0.973329
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −5.00000 −0.780869 −0.390434 − 0.920631i \(-0.627675\pi\)
−0.390434 + 0.920631i \(0.627675\pi\)
\(42\) 1.00000 0.154303
\(43\) −5.00000 −0.762493 −0.381246 − 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) 0 0
\(47\) 13.0000 1.89624 0.948122 − 0.317905i \(-0.102979\pi\)
0.948122 + 0.317905i \(0.102979\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) −1.00000 −0.138675
\(53\) 5.00000 0.686803 0.343401 − 0.939189i \(-0.388421\pi\)
0.343401 + 0.939189i \(0.388421\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) −6.00000 −0.794719
\(58\) −2.00000 −0.262613
\(59\) 14.0000 1.82264 0.911322 − 0.411693i \(-0.135063\pi\)
0.911322 + 0.411693i \(0.135063\pi\)
\(60\) 0 0
\(61\) 3.00000 0.384111 0.192055 − 0.981384i \(-0.438485\pi\)
0.192055 + 0.981384i \(0.438485\pi\)
\(62\) 1.00000 0.127000
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.00000 0.369274
\(67\) −2.00000 −0.244339 −0.122169 − 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 15.0000 1.78017 0.890086 − 0.455792i \(-0.150644\pi\)
0.890086 + 0.455792i \(0.150644\pi\)
\(72\) −1.00000 −0.117851
\(73\) 2.00000 0.234082 0.117041 − 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −11.0000 −1.27872
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) 3.00000 0.341882
\(78\) 1.00000 0.113228
\(79\) 8.00000 0.900070 0.450035 − 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 5.00000 0.552158
\(83\) −3.00000 −0.329293 −0.164646 − 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) 5.00000 0.539164
\(87\) 2.00000 0.214423
\(88\) 3.00000 0.319801
\(89\) −14.0000 −1.48400 −0.741999 − 0.670402i \(-0.766122\pi\)
−0.741999 + 0.670402i \(0.766122\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −1.00000 −0.103695
\(94\) −13.0000 −1.34085
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 10.0000 1.01535 0.507673 − 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 6.00000 0.606092
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 15.0000 1.47799 0.738997 − 0.673709i \(-0.235300\pi\)
0.738997 + 0.673709i \(0.235300\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −5.00000 −0.485643
\(107\) 16.0000 1.54678 0.773389 − 0.633932i \(-0.218560\pi\)
0.773389 + 0.633932i \(0.218560\pi\)
\(108\) 1.00000 0.0962250
\(109\) −18.0000 −1.72409 −0.862044 − 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) 0 0
\(111\) 11.0000 1.04407
\(112\) −1.00000 −0.0944911
\(113\) 10.0000 0.940721 0.470360 − 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 6.00000 0.561951
\(115\) 0 0
\(116\) 2.00000 0.185695
\(117\) −1.00000 −0.0924500
\(118\) −14.0000 −1.28880
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −3.00000 −0.271607
\(123\) −5.00000 −0.450835
\(124\) −1.00000 −0.0898027
\(125\) 0 0
\(126\) 1.00000 0.0890871
\(127\) 12.0000 1.06483 0.532414 − 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −5.00000 −0.440225
\(130\) 0 0
\(131\) 18.0000 1.57267 0.786334 − 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) −3.00000 −0.261116
\(133\) 6.00000 0.520266
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 0 0
\(137\) −12.0000 −1.02523 −0.512615 − 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 0 0
\(139\) −5.00000 −0.424094 −0.212047 − 0.977259i \(-0.568013\pi\)
−0.212047 + 0.977259i \(0.568013\pi\)
\(140\) 0 0
\(141\) 13.0000 1.09480
\(142\) −15.0000 −1.25877
\(143\) 3.00000 0.250873
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −6.00000 −0.494872
\(148\) 11.0000 0.904194
\(149\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) 4.00000 0.325515 0.162758 − 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) 6.00000 0.486664
\(153\) 0 0
\(154\) −3.00000 −0.241747
\(155\) 0 0
\(156\) −1.00000 −0.0800641
\(157\) 6.00000 0.478852 0.239426 − 0.970915i \(-0.423041\pi\)
0.239426 + 0.970915i \(0.423041\pi\)
\(158\) −8.00000 −0.636446
\(159\) 5.00000 0.396526
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −6.00000 −0.469956 −0.234978 − 0.972001i \(-0.575502\pi\)
−0.234978 + 0.972001i \(0.575502\pi\)
\(164\) −5.00000 −0.390434
\(165\) 0 0
\(166\) 3.00000 0.232845
\(167\) −16.0000 −1.23812 −0.619059 − 0.785345i \(-0.712486\pi\)
−0.619059 + 0.785345i \(0.712486\pi\)
\(168\) 1.00000 0.0771517
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −6.00000 −0.458831
\(172\) −5.00000 −0.381246
\(173\) 2.00000 0.152057 0.0760286 − 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) −2.00000 −0.151620
\(175\) 0 0
\(176\) −3.00000 −0.226134
\(177\) 14.0000 1.05230
\(178\) 14.0000 1.04934
\(179\) 15.0000 1.12115 0.560576 − 0.828103i \(-0.310580\pi\)
0.560576 + 0.828103i \(0.310580\pi\)
\(180\) 0 0
\(181\) 15.0000 1.11494 0.557471 − 0.830197i \(-0.311772\pi\)
0.557471 + 0.830197i \(0.311772\pi\)
\(182\) −1.00000 −0.0741249
\(183\) 3.00000 0.221766
\(184\) 0 0
\(185\) 0 0
\(186\) 1.00000 0.0733236
\(187\) 0 0
\(188\) 13.0000 0.948122
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) 4.00000 0.289430 0.144715 − 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) 1.00000 0.0721688
\(193\) 5.00000 0.359908 0.179954 − 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) 17.0000 1.21120 0.605600 − 0.795769i \(-0.292933\pi\)
0.605600 + 0.795769i \(0.292933\pi\)
\(198\) 3.00000 0.213201
\(199\) −6.00000 −0.425329 −0.212664 − 0.977125i \(-0.568214\pi\)
−0.212664 + 0.977125i \(0.568214\pi\)
\(200\) 0 0
\(201\) −2.00000 −0.141069
\(202\) 0 0
\(203\) −2.00000 −0.140372
\(204\) 0 0
\(205\) 0 0
\(206\) −15.0000 −1.04510
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) 18.0000 1.24509
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 − 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 5.00000 0.343401
\(213\) 15.0000 1.02778
\(214\) −16.0000 −1.09374
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 1.00000 0.0678844
\(218\) 18.0000 1.21911
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) 0 0
\(222\) −11.0000 −0.738272
\(223\) −10.0000 −0.669650 −0.334825 − 0.942280i \(-0.608677\pi\)
−0.334825 + 0.942280i \(0.608677\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −10.0000 −0.665190
\(227\) 24.0000 1.59294 0.796468 − 0.604681i \(-0.206699\pi\)
0.796468 + 0.604681i \(0.206699\pi\)
\(228\) −6.00000 −0.397360
\(229\) −10.0000 −0.660819 −0.330409 − 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 3.00000 0.197386
\(232\) −2.00000 −0.131306
\(233\) −19.0000 −1.24473 −0.622366 − 0.782727i \(-0.713828\pi\)
−0.622366 + 0.782727i \(0.713828\pi\)
\(234\) 1.00000 0.0653720
\(235\) 0 0
\(236\) 14.0000 0.911322
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 − 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −2.00000 −0.128831 −0.0644157 − 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 2.00000 0.128565
\(243\) 1.00000 0.0641500
\(244\) 3.00000 0.192055
\(245\) 0 0
\(246\) 5.00000 0.318788
\(247\) 6.00000 0.381771
\(248\) 1.00000 0.0635001
\(249\) −3.00000 −0.190117
\(250\) 0 0
\(251\) −3.00000 −0.189358 −0.0946792 − 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 0 0
\(254\) −12.0000 −0.752947
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 25.0000 1.55946 0.779729 − 0.626118i \(-0.215357\pi\)
0.779729 + 0.626118i \(0.215357\pi\)
\(258\) 5.00000 0.311286
\(259\) −11.0000 −0.683507
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) −18.0000 −1.11204
\(263\) 26.0000 1.60323 0.801614 − 0.597841i \(-0.203975\pi\)
0.801614 + 0.597841i \(0.203975\pi\)
\(264\) 3.00000 0.184637
\(265\) 0 0
\(266\) −6.00000 −0.367884
\(267\) −14.0000 −0.856786
\(268\) −2.00000 −0.122169
\(269\) −18.0000 −1.09748 −0.548740 − 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 − 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) 1.00000 0.0605228
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 − 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 5.00000 0.299880
\(279\) −1.00000 −0.0598684
\(280\) 0 0
\(281\) 3.00000 0.178965 0.0894825 − 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) −13.0000 −0.774139
\(283\) 16.0000 0.951101 0.475551 − 0.879688i \(-0.342249\pi\)
0.475551 + 0.879688i \(0.342249\pi\)
\(284\) 15.0000 0.890086
\(285\) 0 0
\(286\) −3.00000 −0.177394
\(287\) 5.00000 0.295141
\(288\) −1.00000 −0.0589256
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 10.0000 0.586210
\(292\) 2.00000 0.117041
\(293\) −12.0000 −0.701047 −0.350524 − 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) 6.00000 0.349927
\(295\) 0 0
\(296\) −11.0000 −0.639362
\(297\) −3.00000 −0.174078
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 5.00000 0.288195
\(302\) −4.00000 −0.230174
\(303\) 0 0
\(304\) −6.00000 −0.344124
\(305\) 0 0
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 − 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 3.00000 0.170941
\(309\) 15.0000 0.853320
\(310\) 0 0
\(311\) −9.00000 −0.510343 −0.255172 − 0.966896i \(-0.582132\pi\)
−0.255172 + 0.966896i \(0.582132\pi\)
\(312\) 1.00000 0.0566139
\(313\) −14.0000 −0.791327 −0.395663 − 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) −6.00000 −0.338600
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −8.00000 −0.449325 −0.224662 − 0.974437i \(-0.572128\pi\)
−0.224662 + 0.974437i \(0.572128\pi\)
\(318\) −5.00000 −0.280386
\(319\) −6.00000 −0.335936
\(320\) 0 0
\(321\) 16.0000 0.893033
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 6.00000 0.332309
\(327\) −18.0000 −0.995402
\(328\) 5.00000 0.276079
\(329\) −13.0000 −0.716713
\(330\) 0 0
\(331\) 33.0000 1.81384 0.906922 − 0.421299i \(-0.138426\pi\)
0.906922 + 0.421299i \(0.138426\pi\)
\(332\) −3.00000 −0.164646
\(333\) 11.0000 0.602796
\(334\) 16.0000 0.875481
\(335\) 0 0
\(336\) −1.00000 −0.0545545
\(337\) 14.0000 0.762629 0.381314 − 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 12.0000 0.652714
\(339\) 10.0000 0.543125
\(340\) 0 0
\(341\) 3.00000 0.162459
\(342\) 6.00000 0.324443
\(343\) 13.0000 0.701934
\(344\) 5.00000 0.269582
\(345\) 0 0
\(346\) −2.00000 −0.107521
\(347\) −23.0000 −1.23470 −0.617352 − 0.786687i \(-0.711795\pi\)
−0.617352 + 0.786687i \(0.711795\pi\)
\(348\) 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
\(351\) −1.00000 −0.0533761
\(352\) 3.00000 0.159901
\(353\) 16.0000 0.851594 0.425797 − 0.904819i \(-0.359994\pi\)
0.425797 + 0.904819i \(0.359994\pi\)
\(354\) −14.0000 −0.744092
\(355\) 0 0
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) −15.0000 −0.792775
\(359\) −12.0000 −0.633336 −0.316668 − 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) −15.0000 −0.788382
\(363\) −2.00000 −0.104973
\(364\) 1.00000 0.0524142
\(365\) 0 0
\(366\) −3.00000 −0.156813
\(367\) 36.0000 1.87918 0.939592 − 0.342296i \(-0.111204\pi\)
0.939592 + 0.342296i \(0.111204\pi\)
\(368\) 0 0
\(369\) −5.00000 −0.260290
\(370\) 0 0
\(371\) −5.00000 −0.259587
\(372\) −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
\(376\) −13.0000 −0.670424
\(377\) −2.00000 −0.103005
\(378\) 1.00000 0.0514344
\(379\) −10.0000 −0.513665 −0.256833 − 0.966456i \(-0.582679\pi\)
−0.256833 + 0.966456i \(0.582679\pi\)
\(380\) 0 0
\(381\) 12.0000 0.614779
\(382\) −4.00000 −0.204658
\(383\) 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
\(386\) −5.00000 −0.254493
\(387\) −5.00000 −0.254164
\(388\) 10.0000 0.507673
\(389\) 22.0000 1.11544 0.557722 − 0.830028i \(-0.311675\pi\)
0.557722 + 0.830028i \(0.311675\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 6.00000 0.303046
\(393\) 18.0000 0.907980
\(394\) −17.0000 −0.856448
\(395\) 0 0
\(396\) −3.00000 −0.150756
\(397\) 6.00000 0.301131 0.150566 − 0.988600i \(-0.451890\pi\)
0.150566 + 0.988600i \(0.451890\pi\)
\(398\) 6.00000 0.300753
\(399\) 6.00000 0.300376
\(400\) 0 0
\(401\) −20.0000 −0.998752 −0.499376 − 0.866385i \(-0.666437\pi\)
−0.499376 + 0.866385i \(0.666437\pi\)
\(402\) 2.00000 0.0997509
\(403\) 1.00000 0.0498135
\(404\) 0 0
\(405\) 0 0
\(406\) 2.00000 0.0992583
\(407\) −33.0000 −1.63575
\(408\) 0 0
\(409\) −6.00000 −0.296681 −0.148340 − 0.988936i \(-0.547393\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) 15.0000 0.738997
\(413\) −14.0000 −0.688895
\(414\) 0 0
\(415\) 0 0
\(416\) 1.00000 0.0490290
\(417\) −5.00000 −0.244851
\(418\) −18.0000 −0.880409
\(419\) 12.0000 0.586238 0.293119 − 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 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
\(423\) 13.0000 0.632082
\(424\) −5.00000 −0.242821
\(425\) 0 0
\(426\) −15.0000 −0.726752
\(427\) −3.00000 −0.145180
\(428\) 16.0000 0.773389
\(429\) 3.00000 0.144841
\(430\) 0 0
\(431\) 15.0000 0.722525 0.361262 − 0.932464i \(-0.382346\pi\)
0.361262 + 0.932464i \(0.382346\pi\)
\(432\) 1.00000 0.0481125
\(433\) 16.0000 0.768911 0.384455 − 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(434\) −1.00000 −0.0480015
\(435\) 0 0
\(436\) −18.0000 −0.862044
\(437\) 0 0
\(438\) −2.00000 −0.0955637
\(439\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 0 0
\(443\) 6.00000 0.285069 0.142534 − 0.989790i \(-0.454475\pi\)
0.142534 + 0.989790i \(0.454475\pi\)
\(444\) 11.0000 0.522037
\(445\) 0 0
\(446\) 10.0000 0.473514
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) 22.0000 1.03824 0.519122 − 0.854700i \(-0.326259\pi\)
0.519122 + 0.854700i \(0.326259\pi\)
\(450\) 0 0
\(451\) 15.0000 0.706322
\(452\) 10.0000 0.470360
\(453\) 4.00000 0.187936
\(454\) −24.0000 −1.12638
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) 40.0000 1.87112 0.935561 − 0.353166i \(-0.114895\pi\)
0.935561 + 0.353166i \(0.114895\pi\)
\(458\) 10.0000 0.467269
\(459\) 0 0
\(460\) 0 0
\(461\) 21.0000 0.978068 0.489034 − 0.872265i \(-0.337349\pi\)
0.489034 + 0.872265i \(0.337349\pi\)
\(462\) −3.00000 −0.139573
\(463\) −36.0000 −1.67306 −0.836531 − 0.547920i \(-0.815420\pi\)
−0.836531 + 0.547920i \(0.815420\pi\)
\(464\) 2.00000 0.0928477
\(465\) 0 0
\(466\) 19.0000 0.880158
\(467\) 2.00000 0.0925490 0.0462745 − 0.998929i \(-0.485265\pi\)
0.0462745 + 0.998929i \(0.485265\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 2.00000 0.0923514
\(470\) 0 0
\(471\) 6.00000 0.276465
\(472\) −14.0000 −0.644402
\(473\) 15.0000 0.689701
\(474\) −8.00000 −0.367452
\(475\) 0 0
\(476\) 0 0
\(477\) 5.00000 0.228934
\(478\) −6.00000 −0.274434
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −11.0000 −0.501557
\(482\) 2.00000 0.0910975
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −16.0000 −0.725029 −0.362515 − 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −3.00000 −0.135804
\(489\) −6.00000 −0.271329
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 − 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) −5.00000 −0.225417
\(493\) 0 0
\(494\) −6.00000 −0.269953
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) −15.0000 −0.672842
\(498\) 3.00000 0.134433
\(499\) 32.0000 1.43252 0.716258 − 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 0 0
\(501\) −16.0000 −0.714827
\(502\) 3.00000 0.133897
\(503\) −19.0000 −0.847168 −0.423584 − 0.905857i \(-0.639228\pi\)
−0.423584 + 0.905857i \(0.639228\pi\)
\(504\) 1.00000 0.0445435
\(505\) 0 0
\(506\) 0 0
\(507\) −12.0000 −0.532939
\(508\) 12.0000 0.532414
\(509\) 37.0000 1.64000 0.819998 − 0.572366i \(-0.193974\pi\)
0.819998 + 0.572366i \(0.193974\pi\)
\(510\) 0 0
\(511\) −2.00000 −0.0884748
\(512\) −1.00000 −0.0441942
\(513\) −6.00000 −0.264906
\(514\) −25.0000 −1.10270
\(515\) 0 0
\(516\) −5.00000 −0.220113
\(517\) −39.0000 −1.71522
\(518\) 11.0000 0.483312
\(519\) 2.00000 0.0877903
\(520\) 0 0
\(521\) 15.0000 0.657162 0.328581 − 0.944476i \(-0.393430\pi\)
0.328581 + 0.944476i \(0.393430\pi\)
\(522\) −2.00000 −0.0875376
\(523\) 36.0000 1.57417 0.787085 − 0.616844i \(-0.211589\pi\)
0.787085 + 0.616844i \(0.211589\pi\)
\(524\) 18.0000 0.786334
\(525\) 0 0
\(526\) −26.0000 −1.13365
\(527\) 0 0
\(528\) −3.00000 −0.130558
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 14.0000 0.607548
\(532\) 6.00000 0.260133
\(533\) 5.00000 0.216574
\(534\) 14.0000 0.605839
\(535\) 0 0
\(536\) 2.00000 0.0863868
\(537\) 15.0000 0.647298
\(538\) 18.0000 0.776035
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) −6.00000 −0.257960 −0.128980 − 0.991647i \(-0.541170\pi\)
−0.128980 + 0.991647i \(0.541170\pi\)
\(542\) 16.0000 0.687259
\(543\) 15.0000 0.643712
\(544\) 0 0
\(545\) 0 0
\(546\) −1.00000 −0.0427960
\(547\) 12.0000 0.513083 0.256541 − 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) −12.0000 −0.512615
\(549\) 3.00000 0.128037
\(550\) 0 0
\(551\) −12.0000 −0.511217
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 22.0000 0.934690
\(555\) 0 0
\(556\) −5.00000 −0.212047
\(557\) 6.00000 0.254228 0.127114 − 0.991888i \(-0.459429\pi\)
0.127114 + 0.991888i \(0.459429\pi\)
\(558\) 1.00000 0.0423334
\(559\) 5.00000 0.211477
\(560\) 0 0
\(561\) 0 0
\(562\) −3.00000 −0.126547
\(563\) −16.0000 −0.674320 −0.337160 − 0.941447i \(-0.609466\pi\)
−0.337160 + 0.941447i \(0.609466\pi\)
\(564\) 13.0000 0.547399
\(565\) 0 0
\(566\) −16.0000 −0.672530
\(567\) −1.00000 −0.0419961
\(568\) −15.0000 −0.629386
\(569\) 16.0000 0.670755 0.335377 − 0.942084i \(-0.391136\pi\)
0.335377 + 0.942084i \(0.391136\pi\)
\(570\) 0 0
\(571\) −19.0000 −0.795125 −0.397563 − 0.917575i \(-0.630144\pi\)
−0.397563 + 0.917575i \(0.630144\pi\)
\(572\) 3.00000 0.125436
\(573\) 4.00000 0.167102
\(574\) −5.00000 −0.208696
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −6.00000 −0.249783 −0.124892 − 0.992170i \(-0.539858\pi\)
−0.124892 + 0.992170i \(0.539858\pi\)
\(578\) 17.0000 0.707107
\(579\) 5.00000 0.207793
\(580\) 0 0
\(581\) 3.00000 0.124461
\(582\) −10.0000 −0.414513
\(583\) −15.0000 −0.621237
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 12.0000 0.495715
\(587\) 39.0000 1.60970 0.804851 − 0.593477i \(-0.202245\pi\)
0.804851 + 0.593477i \(0.202245\pi\)
\(588\) −6.00000 −0.247436
\(589\) 6.00000 0.247226
\(590\) 0 0
\(591\) 17.0000 0.699287
\(592\) 11.0000 0.452097
\(593\) −21.0000 −0.862367 −0.431183 − 0.902264i \(-0.641904\pi\)
−0.431183 + 0.902264i \(0.641904\pi\)
\(594\) 3.00000 0.123091
\(595\) 0 0
\(596\) 0 0
\(597\) −6.00000 −0.245564
\(598\) 0 0
\(599\) 33.0000 1.34834 0.674172 − 0.738575i \(-0.264501\pi\)
0.674172 + 0.738575i \(0.264501\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 − 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) −5.00000 −0.203785
\(603\) −2.00000 −0.0814463
\(604\) 4.00000 0.162758
\(605\) 0 0
\(606\) 0 0
\(607\) 7.00000 0.284121 0.142061 − 0.989858i \(-0.454627\pi\)
0.142061 + 0.989858i \(0.454627\pi\)
\(608\) 6.00000 0.243332
\(609\) −2.00000 −0.0810441
\(610\) 0 0
\(611\) −13.0000 −0.525924
\(612\) 0 0
\(613\) −34.0000 −1.37325 −0.686624 − 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 16.0000 0.645707
\(615\) 0 0
\(616\) −3.00000 −0.120873
\(617\) −5.00000 −0.201292 −0.100646 − 0.994922i \(-0.532091\pi\)
−0.100646 + 0.994922i \(0.532091\pi\)
\(618\) −15.0000 −0.603388
\(619\) 43.0000 1.72832 0.864158 − 0.503221i \(-0.167852\pi\)
0.864158 + 0.503221i \(0.167852\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 9.00000 0.360867
\(623\) 14.0000 0.560898
\(624\) −1.00000 −0.0400320
\(625\) 0 0
\(626\) 14.0000 0.559553
\(627\) 18.0000 0.718851
\(628\) 6.00000 0.239426
\(629\) 0 0
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 − 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) −8.00000 −0.318223
\(633\) −8.00000 −0.317971
\(634\) 8.00000 0.317721
\(635\) 0 0
\(636\) 5.00000 0.198263
\(637\) 6.00000 0.237729
\(638\) 6.00000 0.237542
\(639\) 15.0000 0.593391
\(640\) 0 0
\(641\) 10.0000 0.394976 0.197488 − 0.980305i \(-0.436722\pi\)
0.197488 + 0.980305i \(0.436722\pi\)
\(642\) −16.0000 −0.631470
\(643\) −23.0000 −0.907031 −0.453516 − 0.891248i \(-0.649830\pi\)
−0.453516 + 0.891248i \(0.649830\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −32.0000 −1.25805 −0.629025 − 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −42.0000 −1.64864
\(650\) 0 0
\(651\) 1.00000 0.0391931
\(652\) −6.00000 −0.234978
\(653\) 22.0000 0.860927 0.430463 − 0.902608i \(-0.358350\pi\)
0.430463 + 0.902608i \(0.358350\pi\)
\(654\) 18.0000 0.703856
\(655\) 0 0
\(656\) −5.00000 −0.195217
\(657\) 2.00000 0.0780274
\(658\) 13.0000 0.506793
\(659\) 36.0000 1.40236 0.701180 − 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) 36.0000 1.40024 0.700119 − 0.714026i \(-0.253130\pi\)
0.700119 + 0.714026i \(0.253130\pi\)
\(662\) −33.0000 −1.28258
\(663\) 0 0
\(664\) 3.00000 0.116423
\(665\) 0 0
\(666\) −11.0000 −0.426241
\(667\) 0 0
\(668\) −16.0000 −0.619059
\(669\) −10.0000 −0.386622
\(670\) 0 0
\(671\) −9.00000 −0.347441
\(672\) 1.00000 0.0385758
\(673\) −10.0000 −0.385472 −0.192736 − 0.981251i \(-0.561736\pi\)
−0.192736 + 0.981251i \(0.561736\pi\)
\(674\) −14.0000 −0.539260
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) −23.0000 −0.883962 −0.441981 − 0.897024i \(-0.645724\pi\)
−0.441981 + 0.897024i \(0.645724\pi\)
\(678\) −10.0000 −0.384048
\(679\) −10.0000 −0.383765
\(680\) 0 0
\(681\) 24.0000 0.919682
\(682\) −3.00000 −0.114876
\(683\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) −6.00000 −0.229416
\(685\) 0 0
\(686\) −13.0000 −0.496342
\(687\) −10.0000 −0.381524
\(688\) −5.00000 −0.190623
\(689\) −5.00000 −0.190485
\(690\) 0 0
\(691\) 44.0000 1.67384 0.836919 − 0.547326i \(-0.184354\pi\)
0.836919 + 0.547326i \(0.184354\pi\)
\(692\) 2.00000 0.0760286
\(693\) 3.00000 0.113961
\(694\) 23.0000 0.873068
\(695\) 0 0
\(696\) −2.00000 −0.0758098
\(697\) 0 0
\(698\) 10.0000 0.378506
\(699\) −19.0000 −0.718646
\(700\) 0 0
\(701\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 1.00000 0.0377426
\(703\) −66.0000 −2.48924
\(704\) −3.00000 −0.113067
\(705\) 0 0
\(706\) −16.0000 −0.602168
\(707\) 0 0
\(708\) 14.0000 0.526152
\(709\) 10.0000 0.375558 0.187779 − 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 14.0000 0.524672
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 15.0000 0.560576
\(717\) 6.00000 0.224074
\(718\) 12.0000 0.447836
\(719\) 20.0000 0.745874 0.372937 − 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 0 0
\(721\) −15.0000 −0.558629
\(722\) −17.0000 −0.632674
\(723\) −2.00000 −0.0743808
\(724\) 15.0000 0.557471
\(725\) 0 0
\(726\) 2.00000 0.0742270
\(727\) 1.00000 0.0370879 0.0185440 − 0.999828i \(-0.494097\pi\)
0.0185440 + 0.999828i \(0.494097\pi\)
\(728\) −1.00000 −0.0370625
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 3.00000 0.110883
\(733\) −8.00000 −0.295487 −0.147743 − 0.989026i \(-0.547201\pi\)
−0.147743 + 0.989026i \(0.547201\pi\)
\(734\) −36.0000 −1.32878
\(735\) 0 0
\(736\) 0 0
\(737\) 6.00000 0.221013
\(738\) 5.00000 0.184053
\(739\) −28.0000 −1.03000 −0.514998 − 0.857191i \(-0.672207\pi\)
−0.514998 + 0.857191i \(0.672207\pi\)
\(740\) 0 0
\(741\) 6.00000 0.220416
\(742\) 5.00000 0.183556
\(743\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 1.00000 0.0366618
\(745\) 0 0
\(746\) 24.0000 0.878702
\(747\) −3.00000 −0.109764
\(748\) 0 0
\(749\) −16.0000 −0.584627
\(750\) 0 0
\(751\) −53.0000 −1.93400 −0.966999 − 0.254781i \(-0.917997\pi\)
−0.966999 + 0.254781i \(0.917997\pi\)
\(752\) 13.0000 0.474061
\(753\) −3.00000 −0.109326
\(754\) 2.00000 0.0728357
\(755\) 0 0
\(756\) −1.00000 −0.0363696
\(757\) −15.0000 −0.545184 −0.272592 − 0.962130i \(-0.587881\pi\)
−0.272592 + 0.962130i \(0.587881\pi\)
\(758\) 10.0000 0.363216
\(759\) 0 0
\(760\) 0 0
\(761\) −14.0000 −0.507500 −0.253750 − 0.967270i \(-0.581664\pi\)
−0.253750 + 0.967270i \(0.581664\pi\)
\(762\) −12.0000 −0.434714
\(763\) 18.0000 0.651644
\(764\) 4.00000 0.144715
\(765\) 0 0
\(766\) −12.0000 −0.433578
\(767\) −14.0000 −0.505511
\(768\) 1.00000 0.0360844
\(769\) −45.0000 −1.62274 −0.811371 − 0.584532i \(-0.801278\pi\)
−0.811371 + 0.584532i \(0.801278\pi\)
\(770\) 0 0
\(771\) 25.0000 0.900353
\(772\) 5.00000 0.179954
\(773\) −26.0000 −0.935155 −0.467578 − 0.883952i \(-0.654873\pi\)
−0.467578 + 0.883952i \(0.654873\pi\)
\(774\) 5.00000 0.179721
\(775\) 0 0
\(776\) −10.0000 −0.358979
\(777\) −11.0000 −0.394623
\(778\) −22.0000 −0.788738
\(779\) 30.0000 1.07486
\(780\) 0 0
\(781\) −45.0000 −1.61023
\(782\) 0 0
\(783\) 2.00000 0.0714742
\(784\) −6.00000 −0.214286
\(785\) 0 0
\(786\) −18.0000 −0.642039
\(787\) 13.0000 0.463400 0.231700 − 0.972787i \(-0.425571\pi\)
0.231700 + 0.972787i \(0.425571\pi\)
\(788\) 17.0000 0.605600
\(789\) 26.0000 0.925625
\(790\) 0 0
\(791\) −10.0000 −0.355559
\(792\) 3.00000 0.106600
\(793\) −3.00000 −0.106533
\(794\) −6.00000 −0.212932
\(795\) 0 0
\(796\) −6.00000 −0.212664
\(797\) 2.00000 0.0708436 0.0354218 − 0.999372i \(-0.488723\pi\)
0.0354218 + 0.999372i \(0.488723\pi\)
\(798\) −6.00000 −0.212398
\(799\) 0 0
\(800\) 0 0
\(801\) −14.0000 −0.494666
\(802\) 20.0000 0.706225
\(803\) −6.00000 −0.211735
\(804\) −2.00000 −0.0705346
\(805\) 0 0
\(806\) −1.00000 −0.0352235
\(807\) −18.0000 −0.633630
\(808\) 0 0
\(809\) 34.0000 1.19538 0.597688 − 0.801729i \(-0.296086\pi\)
0.597688 + 0.801729i \(0.296086\pi\)
\(810\) 0 0
\(811\) 50.0000 1.75574 0.877869 − 0.478901i \(-0.158965\pi\)
0.877869 + 0.478901i \(0.158965\pi\)
\(812\) −2.00000 −0.0701862
\(813\) −16.0000 −0.561144
\(814\) 33.0000 1.15665
\(815\) 0 0
\(816\) 0 0
\(817\) 30.0000 1.04957
\(818\) 6.00000 0.209785
\(819\) 1.00000 0.0349428
\(820\) 0 0
\(821\) 3.00000 0.104701 0.0523504 − 0.998629i \(-0.483329\pi\)
0.0523504 + 0.998629i \(0.483329\pi\)
\(822\) 12.0000 0.418548
\(823\) −24.0000 −0.836587 −0.418294 − 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) −15.0000 −0.522550
\(825\) 0 0
\(826\) 14.0000 0.487122
\(827\) 36.0000 1.25184 0.625921 − 0.779886i \(-0.284723\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(828\) 0 0
\(829\) 35.0000 1.21560 0.607800 − 0.794090i \(-0.292052\pi\)
0.607800 + 0.794090i \(0.292052\pi\)
\(830\) 0 0
\(831\) −22.0000 −0.763172
\(832\) −1.00000 −0.0346688
\(833\) 0 0
\(834\) 5.00000 0.173136
\(835\) 0 0
\(836\) 18.0000 0.622543
\(837\) −1.00000 −0.0345651
\(838\) −12.0000 −0.414533
\(839\) −21.0000 −0.725001 −0.362500 − 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −6.00000 −0.206774
\(843\) 3.00000 0.103325
\(844\) −8.00000 −0.275371
\(845\) 0 0
\(846\) −13.0000 −0.446949
\(847\) 2.00000 0.0687208
\(848\) 5.00000 0.171701
\(849\) 16.0000 0.549119
\(850\) 0 0
\(851\) 0 0
\(852\) 15.0000 0.513892
\(853\) 30.0000 1.02718 0.513590 − 0.858036i \(-0.328315\pi\)
0.513590 + 0.858036i \(0.328315\pi\)
\(854\) 3.00000 0.102658
\(855\) 0 0
\(856\) −16.0000 −0.546869
\(857\) 7.00000 0.239115 0.119558 − 0.992827i \(-0.461852\pi\)
0.119558 + 0.992827i \(0.461852\pi\)
\(858\) −3.00000 −0.102418
\(859\) −17.0000 −0.580033 −0.290016 − 0.957022i \(-0.593661\pi\)
−0.290016 + 0.957022i \(0.593661\pi\)
\(860\) 0 0
\(861\) 5.00000 0.170400
\(862\) −15.0000 −0.510902
\(863\) −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
\(866\) −16.0000 −0.543702
\(867\) −17.0000 −0.577350
\(868\) 1.00000 0.0339422
\(869\) −24.0000 −0.814144
\(870\) 0 0
\(871\) 2.00000 0.0677674
\(872\) 18.0000 0.609557
\(873\) 10.0000 0.338449
\(874\) 0 0
\(875\) 0 0
\(876\) 2.00000 0.0675737
\(877\) 48.0000 1.62084 0.810422 − 0.585846i \(-0.199238\pi\)
0.810422 + 0.585846i \(0.199238\pi\)
\(878\) 0 0
\(879\) −12.0000 −0.404750
\(880\) 0 0
\(881\) −18.0000 −0.606435 −0.303218 − 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) 6.00000 0.202031
\(883\) −15.0000 −0.504790 −0.252395 − 0.967624i \(-0.581218\pi\)
−0.252395 + 0.967624i \(0.581218\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −6.00000 −0.201574
\(887\) 5.00000 0.167884 0.0839418 − 0.996471i \(-0.473249\pi\)
0.0839418 + 0.996471i \(0.473249\pi\)
\(888\) −11.0000 −0.369136
\(889\) −12.0000 −0.402467
\(890\) 0 0
\(891\) −3.00000 −0.100504
\(892\) −10.0000 −0.334825
\(893\) −78.0000 −2.61017
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −22.0000 −0.734150
\(899\) −2.00000 −0.0667037
\(900\) 0 0
\(901\) 0 0
\(902\) −15.0000 −0.499445
\(903\) 5.00000 0.166390
\(904\) −10.0000 −0.332595
\(905\) 0 0
\(906\) −4.00000 −0.132891
\(907\) 16.0000 0.531271 0.265636 − 0.964073i \(-0.414418\pi\)
0.265636 + 0.964073i \(0.414418\pi\)
\(908\) 24.0000 0.796468
\(909\) 0 0
\(910\) 0 0
\(911\) 54.0000 1.78910 0.894550 − 0.446968i \(-0.147496\pi\)
0.894550 + 0.446968i \(0.147496\pi\)
\(912\) −6.00000 −0.198680
\(913\) 9.00000 0.297857
\(914\) −40.0000 −1.32308
\(915\) 0 0
\(916\) −10.0000 −0.330409
\(917\) −18.0000 −0.594412
\(918\) 0 0
\(919\) −15.0000 −0.494804 −0.247402 − 0.968913i \(-0.579577\pi\)
−0.247402 + 0.968913i \(0.579577\pi\)
\(920\) 0 0
\(921\) −16.0000 −0.527218
\(922\) −21.0000 −0.691598
\(923\) −15.0000 −0.493731
\(924\) 3.00000 0.0986928
\(925\) 0 0
\(926\) 36.0000 1.18303
\(927\) 15.0000 0.492665
\(928\) −2.00000 −0.0656532
\(929\) −6.00000 −0.196854 −0.0984268 − 0.995144i \(-0.531381\pi\)
−0.0984268 + 0.995144i \(0.531381\pi\)
\(930\) 0 0
\(931\) 36.0000 1.17985
\(932\) −19.0000 −0.622366
\(933\) −9.00000 −0.294647
\(934\) −2.00000 −0.0654420
\(935\) 0 0
\(936\) 1.00000 0.0326860
\(937\) 42.0000 1.37208 0.686040 − 0.727564i \(-0.259347\pi\)
0.686040 + 0.727564i \(0.259347\pi\)
\(938\) −2.00000 −0.0653023
\(939\) −14.0000 −0.456873
\(940\) 0 0
\(941\) 46.0000 1.49956 0.749779 − 0.661689i \(-0.230160\pi\)
0.749779 + 0.661689i \(0.230160\pi\)
\(942\) −6.00000 −0.195491
\(943\) 0 0
\(944\) 14.0000 0.455661
\(945\) 0 0
\(946\) −15.0000 −0.487692
\(947\) −41.0000 −1.33232 −0.666160 − 0.745808i \(-0.732063\pi\)
−0.666160 + 0.745808i \(0.732063\pi\)
\(948\) 8.00000 0.259828
\(949\) −2.00000 −0.0649227
\(950\) 0 0
\(951\) −8.00000 −0.259418
\(952\) 0 0
\(953\) 28.0000 0.907009 0.453504 − 0.891254i \(-0.350174\pi\)
0.453504 + 0.891254i \(0.350174\pi\)
\(954\) −5.00000 −0.161881
\(955\) 0 0
\(956\) 6.00000 0.194054
\(957\) −6.00000 −0.193952
\(958\) 0 0
\(959\) 12.0000 0.387500
\(960\) 0 0
\(961\) 1.00000 0.0322581
\(962\) 11.0000 0.354654
\(963\) 16.0000 0.515593
\(964\) −2.00000 −0.0644157
\(965\) 0 0
\(966\) 0 0
\(967\) −22.0000 −0.707472 −0.353736 − 0.935345i \(-0.615089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(968\) 2.00000 0.0642824
\(969\) 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
\(973\) 5.00000 0.160293
\(974\) 16.0000 0.512673
\(975\) 0 0
\(976\) 3.00000 0.0960277
\(977\) 9.00000 0.287936 0.143968 − 0.989582i \(-0.454014\pi\)
0.143968 + 0.989582i \(0.454014\pi\)
\(978\) 6.00000 0.191859
\(979\) 42.0000 1.34233
\(980\) 0 0
\(981\) −18.0000 −0.574696
\(982\) 12.0000 0.382935
\(983\) −14.0000 −0.446531 −0.223265 − 0.974758i \(-0.571672\pi\)
−0.223265 + 0.974758i \(0.571672\pi\)
\(984\) 5.00000 0.159394
\(985\) 0 0
\(986\) 0 0
\(987\) −13.0000 −0.413795
\(988\) 6.00000 0.190885
\(989\) 0 0
\(990\) 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
\(993\) 33.0000 1.04722
\(994\) 15.0000 0.475771
\(995\) 0 0
\(996\) −3.00000 −0.0950586
\(997\) 24.0000 0.760088 0.380044 − 0.924968i \(-0.375909\pi\)
0.380044 + 0.924968i \(0.375909\pi\)
\(998\) −32.0000 −1.01294
\(999\) 11.0000 0.348025
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.o.1.1 ✓ 1
5.2 odd 4 4650.2.d.e.3349.1 2
5.3 odd 4 4650.2.d.e.3349.2 2
5.4 even 2 4650.2.a.be.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4650.2.a.o.1.1 ✓ 1 1.1 even 1 trivial
4650.2.a.be.1.1 yes 1 5.4 even 2
4650.2.d.e.3349.1 2 5.2 odd 4
4650.2.d.e.3349.2 2 5.3 odd 4