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Properties

Label 4290.2.a.y.1.1
Level $4290$
Weight $2$
Character 4290.1
Self dual yes
Analytic conductor $34.256$
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] = [4290,2,Mod(1,4290)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4290, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4290.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4290 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4290.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: \(34.2558224671\)
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 \(\chi\) \(=\) 4290.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} -1.00000 q^{20} -1.00000 q^{22} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{26} +1.00000 q^{27} -6.00000 q^{29} -1.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} +6.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} +4.00000 q^{38} +1.00000 q^{39} -1.00000 q^{40} +2.00000 q^{41} -8.00000 q^{43} -1.00000 q^{44} -1.00000 q^{45} +8.00000 q^{47} +1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} +6.00000 q^{51} +1.00000 q^{52} +6.00000 q^{53} +1.00000 q^{54} +1.00000 q^{55} +4.00000 q^{57} -6.00000 q^{58} +12.0000 q^{59} -1.00000 q^{60} +6.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} -1.00000 q^{65} -1.00000 q^{66} -8.00000 q^{67} +6.00000 q^{68} -8.00000 q^{71} +1.00000 q^{72} -6.00000 q^{73} -2.00000 q^{74} +1.00000 q^{75} +4.00000 q^{76} +1.00000 q^{78} +4.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +12.0000 q^{83} -6.00000 q^{85} -8.00000 q^{86} -6.00000 q^{87} -1.00000 q^{88} -2.00000 q^{89} -1.00000 q^{90} +4.00000 q^{93} +8.00000 q^{94} -4.00000 q^{95} +1.00000 q^{96} +10.0000 q^{97} -7.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.00000 0.408248
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) −1.00000 −0.301511
\(12\) 1.00000 0.288675
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) 6.00000 1.45521 0.727607 − 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 1.00000 0.235702
\(19\) 4.00000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 1.00000 0.196116
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 − 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −1.00000 −0.182574
\(31\) 4.00000 0.718421 0.359211 − 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.00000 −0.174078
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 4.00000 0.648886
\(39\) 1.00000 0.160128
\(40\) −1.00000 −0.158114
\(41\) 2.00000 0.312348 0.156174 − 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 − 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −1.00000 −0.150756
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 8.00000 1.16692 0.583460 − 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 1.00000 0.144338
\(49\) −7.00000 −1.00000
\(50\) 1.00000 0.141421
\(51\) 6.00000 0.840168
\(52\) 1.00000 0.138675
\(53\) 6.00000 0.824163 0.412082 − 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 1.00000 0.136083
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) −6.00000 −0.787839
\(59\) 12.0000 1.56227 0.781133 − 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) −1.00000 −0.129099
\(61\) 6.00000 0.768221 0.384111 − 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) −1.00000 −0.123091
\(67\) −8.00000 −0.977356 −0.488678 − 0.872464i \(-0.662521\pi\)
−0.488678 + 0.872464i \(0.662521\pi\)
\(68\) 6.00000 0.727607
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 − 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 1.00000 0.117851
\(73\) −6.00000 −0.702247 −0.351123 − 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −2.00000 −0.232495
\(75\) 1.00000 0.115470
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) 4.00000 0.450035 0.225018 − 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 2.00000 0.220863
\(83\) 12.0000 1.31717 0.658586 − 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) −8.00000 −0.862662
\(87\) −6.00000 −0.643268
\(88\) −1.00000 −0.106600
\(89\) −2.00000 −0.212000 −0.106000 − 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) 0 0
\(93\) 4.00000 0.414781
\(94\) 8.00000 0.825137
\(95\) −4.00000 −0.410391
\(96\) 1.00000 0.102062
\(97\) 10.0000 1.01535 0.507673 − 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) −7.00000 −0.707107
\(99\) −1.00000 −0.100504
\(100\) 1.00000 0.100000
\(101\) 18.0000 1.79107 0.895533 − 0.444994i \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) 6.00000 0.594089
\(103\) 16.0000 1.57653 0.788263 − 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −12.0000 −1.16008 −0.580042 − 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 1.00000 0.0962250
\(109\) 14.0000 1.34096 0.670478 − 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 1.00000 0.0953463
\(111\) −2.00000 −0.189832
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 − 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 4.00000 0.374634
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 1.00000 0.0924500
\(118\) 12.0000 1.10469
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 0.0909091
\(122\) 6.00000 0.543214
\(123\) 2.00000 0.180334
\(124\) 4.00000 0.359211
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 − 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 1.00000 0.0883883
\(129\) −8.00000 −0.704361
\(130\) −1.00000 −0.0877058
\(131\) 20.0000 1.74741 0.873704 − 0.486458i \(-0.161711\pi\)
0.873704 + 0.486458i \(0.161711\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) −1.00000 −0.0860663
\(136\) 6.00000 0.514496
\(137\) 14.0000 1.19610 0.598050 − 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) 0 0
\(139\) 8.00000 0.678551 0.339276 − 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) −8.00000 −0.671345
\(143\) −1.00000 −0.0836242
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) −6.00000 −0.496564
\(147\) −7.00000 −0.577350
\(148\) −2.00000 −0.164399
\(149\) −10.0000 −0.819232 −0.409616 − 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 1.00000 0.0816497
\(151\) −8.00000 −0.651031 −0.325515 − 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 4.00000 0.324443
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 1.00000 0.0800641
\(157\) −2.00000 −0.159617 −0.0798087 − 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 4.00000 0.318223
\(159\) 6.00000 0.475831
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −16.0000 −1.25322 −0.626608 − 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 2.00000 0.156174
\(165\) 1.00000 0.0778499
\(166\) 12.0000 0.931381
\(167\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −6.00000 −0.460179
\(171\) 4.00000 0.305888
\(172\) −8.00000 −0.609994
\(173\) −6.00000 −0.456172 −0.228086 − 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) −6.00000 −0.454859
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 12.0000 0.901975
\(178\) −2.00000 −0.149906
\(179\) 12.0000 0.896922 0.448461 − 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −10.0000 −0.743294 −0.371647 − 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 6.00000 0.443533
\(184\) 0 0
\(185\) 2.00000 0.147043
\(186\) 4.00000 0.293294
\(187\) −6.00000 −0.438763
\(188\) 8.00000 0.583460
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) −16.0000 −1.15772 −0.578860 − 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 1.00000 0.0721688
\(193\) 2.00000 0.143963 0.0719816 − 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 10.0000 0.717958
\(195\) −1.00000 −0.0716115
\(196\) −7.00000 −0.500000
\(197\) 6.00000 0.427482 0.213741 − 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) −1.00000 −0.0710669
\(199\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 1.00000 0.0707107
\(201\) −8.00000 −0.564276
\(202\) 18.0000 1.26648
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) −2.00000 −0.139686
\(206\) 16.0000 1.11477
\(207\) 0 0
\(208\) 1.00000 0.0693375
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 − 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 6.00000 0.412082
\(213\) −8.00000 −0.548151
\(214\) −12.0000 −0.820303
\(215\) 8.00000 0.545595
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 14.0000 0.948200
\(219\) −6.00000 −0.405442
\(220\) 1.00000 0.0674200
\(221\) 6.00000 0.403604
\(222\) −2.00000 −0.134231
\(223\) −20.0000 −1.33930 −0.669650 − 0.742677i \(-0.733556\pi\)
−0.669650 + 0.742677i \(0.733556\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 2.00000 0.133038
\(227\) 4.00000 0.265489 0.132745 − 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(228\) 4.00000 0.264906
\(229\) 6.00000 0.396491 0.198246 − 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 14.0000 0.917170 0.458585 − 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 1.00000 0.0653720
\(235\) −8.00000 −0.521862
\(236\) 12.0000 0.781133
\(237\) 4.00000 0.259828
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 − 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −30.0000 −1.93247 −0.966235 − 0.257663i \(-0.917048\pi\)
−0.966235 + 0.257663i \(0.917048\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) 6.00000 0.384111
\(245\) 7.00000 0.447214
\(246\) 2.00000 0.127515
\(247\) 4.00000 0.254514
\(248\) 4.00000 0.254000
\(249\) 12.0000 0.760469
\(250\) −1.00000 −0.0632456
\(251\) −4.00000 −0.252478 −0.126239 − 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −4.00000 −0.250982
\(255\) −6.00000 −0.375735
\(256\) 1.00000 0.0625000
\(257\) −6.00000 −0.374270 −0.187135 − 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) −8.00000 −0.498058
\(259\) 0 0
\(260\) −1.00000 −0.0620174
\(261\) −6.00000 −0.371391
\(262\) 20.0000 1.23560
\(263\) −32.0000 −1.97320 −0.986602 − 0.163144i \(-0.947836\pi\)
−0.986602 + 0.163144i \(0.947836\pi\)
\(264\) −1.00000 −0.0615457
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) −2.00000 −0.122398
\(268\) −8.00000 −0.488678
\(269\) 6.00000 0.365826 0.182913 − 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −32.0000 −1.94386 −0.971931 − 0.235267i \(-0.924404\pi\)
−0.971931 + 0.235267i \(0.924404\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) 14.0000 0.845771
\(275\) −1.00000 −0.0603023
\(276\) 0 0
\(277\) −10.0000 −0.600842 −0.300421 − 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) 8.00000 0.479808
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) −14.0000 −0.835170 −0.417585 − 0.908638i \(-0.637123\pi\)
−0.417585 + 0.908638i \(0.637123\pi\)
\(282\) 8.00000 0.476393
\(283\) 32.0000 1.90220 0.951101 − 0.308879i \(-0.0999539\pi\)
0.951101 + 0.308879i \(0.0999539\pi\)
\(284\) −8.00000 −0.474713
\(285\) −4.00000 −0.236940
\(286\) −1.00000 −0.0591312
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 19.0000 1.11765
\(290\) 6.00000 0.352332
\(291\) 10.0000 0.586210
\(292\) −6.00000 −0.351123
\(293\) −26.0000 −1.51894 −0.759468 − 0.650545i \(-0.774541\pi\)
−0.759468 + 0.650545i \(0.774541\pi\)
\(294\) −7.00000 −0.408248
\(295\) −12.0000 −0.698667
\(296\) −2.00000 −0.116248
\(297\) −1.00000 −0.0580259
\(298\) −10.0000 −0.579284
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 0 0
\(302\) −8.00000 −0.460348
\(303\) 18.0000 1.03407
\(304\) 4.00000 0.229416
\(305\) −6.00000 −0.343559
\(306\) 6.00000 0.342997
\(307\) −12.0000 −0.684876 −0.342438 − 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) −4.00000 −0.227185
\(311\) 16.0000 0.907277 0.453638 − 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) 1.00000 0.0566139
\(313\) −22.0000 −1.24351 −0.621757 − 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) −14.0000 −0.786318 −0.393159 − 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) 6.00000 0.336463
\(319\) 6.00000 0.335936
\(320\) −1.00000 −0.0559017
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 24.0000 1.33540
\(324\) 1.00000 0.0555556
\(325\) 1.00000 0.0554700
\(326\) −16.0000 −0.886158
\(327\) 14.0000 0.774202
\(328\) 2.00000 0.110432
\(329\) 0 0
\(330\) 1.00000 0.0550482
\(331\) 8.00000 0.439720 0.219860 − 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 12.0000 0.658586
\(333\) −2.00000 −0.109599
\(334\) 0 0
\(335\) 8.00000 0.437087
\(336\) 0 0
\(337\) 10.0000 0.544735 0.272367 − 0.962193i \(-0.412193\pi\)
0.272367 + 0.962193i \(0.412193\pi\)
\(338\) 1.00000 0.0543928
\(339\) 2.00000 0.108625
\(340\) −6.00000 −0.325396
\(341\) −4.00000 −0.216612
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) 28.0000 1.50312 0.751559 − 0.659665i \(-0.229302\pi\)
0.751559 + 0.659665i \(0.229302\pi\)
\(348\) −6.00000 −0.321634
\(349\) −18.0000 −0.963518 −0.481759 − 0.876304i \(-0.660002\pi\)
−0.481759 + 0.876304i \(0.660002\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) −1.00000 −0.0533002
\(353\) 14.0000 0.745145 0.372572 − 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 12.0000 0.637793
\(355\) 8.00000 0.424596
\(356\) −2.00000 −0.106000
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −8.00000 −0.422224 −0.211112 − 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −3.00000 −0.157895
\(362\) −10.0000 −0.525588
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 6.00000 0.313625
\(367\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 2.00000 0.104116
\(370\) 2.00000 0.103975
\(371\) 0 0
\(372\) 4.00000 0.207390
\(373\) 14.0000 0.724893 0.362446 − 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) −6.00000 −0.310253
\(375\) −1.00000 −0.0516398
\(376\) 8.00000 0.412568
\(377\) −6.00000 −0.309016
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 − 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) −4.00000 −0.205196
\(381\) −4.00000 −0.204926
\(382\) −16.0000 −0.818631
\(383\) −32.0000 −1.63512 −0.817562 − 0.575841i \(-0.804675\pi\)
−0.817562 + 0.575841i \(0.804675\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 2.00000 0.101797
\(387\) −8.00000 −0.406663
\(388\) 10.0000 0.507673
\(389\) 14.0000 0.709828 0.354914 − 0.934899i \(-0.384510\pi\)
0.354914 + 0.934899i \(0.384510\pi\)
\(390\) −1.00000 −0.0506370
\(391\) 0 0
\(392\) −7.00000 −0.353553
\(393\) 20.0000 1.00887
\(394\) 6.00000 0.302276
\(395\) −4.00000 −0.201262
\(396\) −1.00000 −0.0502519
\(397\) 22.0000 1.10415 0.552074 − 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 14.0000 0.699127 0.349563 − 0.936913i \(-0.386330\pi\)
0.349563 + 0.936913i \(0.386330\pi\)
\(402\) −8.00000 −0.399004
\(403\) 4.00000 0.199254
\(404\) 18.0000 0.895533
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 2.00000 0.0991363
\(408\) 6.00000 0.297044
\(409\) −22.0000 −1.08783 −0.543915 − 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) −2.00000 −0.0987730
\(411\) 14.0000 0.690569
\(412\) 16.0000 0.788263
\(413\) 0 0
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) 1.00000 0.0490290
\(417\) 8.00000 0.391762
\(418\) −4.00000 −0.195646
\(419\) 12.0000 0.586238 0.293119 − 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 − 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −8.00000 −0.389434
\(423\) 8.00000 0.388973
\(424\) 6.00000 0.291386
\(425\) 6.00000 0.291043
\(426\) −8.00000 −0.387601
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) −1.00000 −0.0482805
\(430\) 8.00000 0.385794
\(431\) −40.0000 −1.92673 −0.963366 − 0.268190i \(-0.913575\pi\)
−0.963366 + 0.268190i \(0.913575\pi\)
\(432\) 1.00000 0.0481125
\(433\) −14.0000 −0.672797 −0.336399 − 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 6.00000 0.287678
\(436\) 14.0000 0.670478
\(437\) 0 0
\(438\) −6.00000 −0.286691
\(439\) 4.00000 0.190910 0.0954548 − 0.995434i \(-0.469569\pi\)
0.0954548 + 0.995434i \(0.469569\pi\)
\(440\) 1.00000 0.0476731
\(441\) −7.00000 −0.333333
\(442\) 6.00000 0.285391
\(443\) −4.00000 −0.190046 −0.0950229 − 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) −2.00000 −0.0949158
\(445\) 2.00000 0.0948091
\(446\) −20.0000 −0.947027
\(447\) −10.0000 −0.472984
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 − 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 1.00000 0.0471405
\(451\) −2.00000 −0.0941763
\(452\) 2.00000 0.0940721
\(453\) −8.00000 −0.375873
\(454\) 4.00000 0.187729
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 10.0000 0.467780 0.233890 − 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 6.00000 0.280362
\(459\) 6.00000 0.280056
\(460\) 0 0
\(461\) −42.0000 −1.95614 −0.978068 − 0.208288i \(-0.933211\pi\)
−0.978068 + 0.208288i \(0.933211\pi\)
\(462\) 0 0
\(463\) −36.0000 −1.67306 −0.836531 − 0.547920i \(-0.815420\pi\)
−0.836531 + 0.547920i \(0.815420\pi\)
\(464\) −6.00000 −0.278543
\(465\) −4.00000 −0.185496
\(466\) 14.0000 0.648537
\(467\) −4.00000 −0.185098 −0.0925490 − 0.995708i \(-0.529501\pi\)
−0.0925490 + 0.995708i \(0.529501\pi\)
\(468\) 1.00000 0.0462250
\(469\) 0 0
\(470\) −8.00000 −0.369012
\(471\) −2.00000 −0.0921551
\(472\) 12.0000 0.552345
\(473\) 8.00000 0.367840
\(474\) 4.00000 0.183726
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) −16.0000 −0.731823
\(479\) 16.0000 0.731059 0.365529 − 0.930800i \(-0.380888\pi\)
0.365529 + 0.930800i \(0.380888\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −2.00000 −0.0911922
\(482\) −30.0000 −1.36646
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −10.0000 −0.454077
\(486\) 1.00000 0.0453609
\(487\) −20.0000 −0.906287 −0.453143 − 0.891438i \(-0.649697\pi\)
−0.453143 + 0.891438i \(0.649697\pi\)
\(488\) 6.00000 0.271607
\(489\) −16.0000 −0.723545
\(490\) 7.00000 0.316228
\(491\) 12.0000 0.541552 0.270776 − 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 2.00000 0.0901670
\(493\) −36.0000 −1.62136
\(494\) 4.00000 0.179969
\(495\) 1.00000 0.0449467
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) −24.0000 −1.07439 −0.537194 − 0.843459i \(-0.680516\pi\)
−0.537194 + 0.843459i \(0.680516\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 0 0
\(502\) −4.00000 −0.178529
\(503\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) −4.00000 −0.177471
\(509\) −6.00000 −0.265945 −0.132973 − 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) −6.00000 −0.265684
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 4.00000 0.176604
\(514\) −6.00000 −0.264649
\(515\) −16.0000 −0.705044
\(516\) −8.00000 −0.352180
\(517\) −8.00000 −0.351840
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) −1.00000 −0.0438529
\(521\) −6.00000 −0.262865 −0.131432 − 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −6.00000 −0.262613
\(523\) −16.0000 −0.699631 −0.349816 − 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 20.0000 0.873704
\(525\) 0 0
\(526\) −32.0000 −1.39527
\(527\) 24.0000 1.04546
\(528\) −1.00000 −0.0435194
\(529\) −23.0000 −1.00000
\(530\) −6.00000 −0.260623
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) 2.00000 0.0866296
\(534\) −2.00000 −0.0865485
\(535\) 12.0000 0.518805
\(536\) −8.00000 −0.345547
\(537\) 12.0000 0.517838
\(538\) 6.00000 0.258678
\(539\) 7.00000 0.301511
\(540\) −1.00000 −0.0430331
\(541\) 30.0000 1.28980 0.644900 − 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) −32.0000 −1.37452
\(543\) −10.0000 −0.429141
\(544\) 6.00000 0.257248
\(545\) −14.0000 −0.599694
\(546\) 0 0
\(547\) 40.0000 1.71028 0.855138 − 0.518400i \(-0.173472\pi\)
0.855138 + 0.518400i \(0.173472\pi\)
\(548\) 14.0000 0.598050
\(549\) 6.00000 0.256074
\(550\) −1.00000 −0.0426401
\(551\) −24.0000 −1.02243
\(552\) 0 0
\(553\) 0 0
\(554\) −10.0000 −0.424859
\(555\) 2.00000 0.0848953
\(556\) 8.00000 0.339276
\(557\) 14.0000 0.593199 0.296600 − 0.955002i \(-0.404147\pi\)
0.296600 + 0.955002i \(0.404147\pi\)
\(558\) 4.00000 0.169334
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) −6.00000 −0.253320
\(562\) −14.0000 −0.590554
\(563\) 20.0000 0.842900 0.421450 − 0.906852i \(-0.361521\pi\)
0.421450 + 0.906852i \(0.361521\pi\)
\(564\) 8.00000 0.336861
\(565\) −2.00000 −0.0841406
\(566\) 32.0000 1.34506
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) −10.0000 −0.419222 −0.209611 − 0.977785i \(-0.567220\pi\)
−0.209611 + 0.977785i \(0.567220\pi\)
\(570\) −4.00000 −0.167542
\(571\) 32.0000 1.33916 0.669579 − 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) −1.00000 −0.0418121
\(573\) −16.0000 −0.668410
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 2.00000 0.0832611 0.0416305 − 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 19.0000 0.790296
\(579\) 2.00000 0.0831172
\(580\) 6.00000 0.249136
\(581\) 0 0
\(582\) 10.0000 0.414513
\(583\) −6.00000 −0.248495
\(584\) −6.00000 −0.248282
\(585\) −1.00000 −0.0413449
\(586\) −26.0000 −1.07405
\(587\) 12.0000 0.495293 0.247647 − 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) −7.00000 −0.288675
\(589\) 16.0000 0.659269
\(590\) −12.0000 −0.494032
\(591\) 6.00000 0.246807
\(592\) −2.00000 −0.0821995
\(593\) 18.0000 0.739171 0.369586 − 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) 0 0
\(598\) 0 0
\(599\) 40.0000 1.63436 0.817178 − 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 1.00000 0.0408248
\(601\) −6.00000 −0.244745 −0.122373 − 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 0 0
\(603\) −8.00000 −0.325785
\(604\) −8.00000 −0.325515
\(605\) −1.00000 −0.0406558
\(606\) 18.0000 0.731200
\(607\) −4.00000 −0.162355 −0.0811775 − 0.996700i \(-0.525868\pi\)
−0.0811775 + 0.996700i \(0.525868\pi\)
\(608\) 4.00000 0.162221
\(609\) 0 0
\(610\) −6.00000 −0.242933
\(611\) 8.00000 0.323645
\(612\) 6.00000 0.242536
\(613\) −42.0000 −1.69636 −0.848182 − 0.529705i \(-0.822303\pi\)
−0.848182 + 0.529705i \(0.822303\pi\)
\(614\) −12.0000 −0.484281
\(615\) −2.00000 −0.0806478
\(616\) 0 0
\(617\) 30.0000 1.20775 0.603877 − 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) 16.0000 0.643614
\(619\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) −4.00000 −0.160644
\(621\) 0 0
\(622\) 16.0000 0.641542
\(623\) 0 0
\(624\) 1.00000 0.0400320
\(625\) 1.00000 0.0400000
\(626\) −22.0000 −0.879297
\(627\) −4.00000 −0.159745
\(628\) −2.00000 −0.0798087
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −28.0000 −1.11466 −0.557331 − 0.830290i \(-0.688175\pi\)
−0.557331 + 0.830290i \(0.688175\pi\)
\(632\) 4.00000 0.159111
\(633\) −8.00000 −0.317971
\(634\) −14.0000 −0.556011
\(635\) 4.00000 0.158735
\(636\) 6.00000 0.237915
\(637\) −7.00000 −0.277350
\(638\) 6.00000 0.237542
\(639\) −8.00000 −0.316475
\(640\) −1.00000 −0.0395285
\(641\) 18.0000 0.710957 0.355479 − 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) −12.0000 −0.473602
\(643\) −48.0000 −1.89294 −0.946468 − 0.322799i \(-0.895376\pi\)
−0.946468 + 0.322799i \(0.895376\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 24.0000 0.944267
\(647\) −8.00000 −0.314512 −0.157256 − 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(648\) 1.00000 0.0392837
\(649\) −12.0000 −0.471041
\(650\) 1.00000 0.0392232
\(651\) 0 0
\(652\) −16.0000 −0.626608
\(653\) −26.0000 −1.01746 −0.508729 − 0.860927i \(-0.669885\pi\)
−0.508729 + 0.860927i \(0.669885\pi\)
\(654\) 14.0000 0.547443
\(655\) −20.0000 −0.781465
\(656\) 2.00000 0.0780869
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) −20.0000 −0.779089 −0.389545 − 0.921008i \(-0.627368\pi\)
−0.389545 + 0.921008i \(0.627368\pi\)
\(660\) 1.00000 0.0389249
\(661\) 14.0000 0.544537 0.272268 − 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 8.00000 0.310929
\(663\) 6.00000 0.233021
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) 0 0
\(669\) −20.0000 −0.773245
\(670\) 8.00000 0.309067
\(671\) −6.00000 −0.231627
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 − 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) 10.0000 0.385186
\(675\) 1.00000 0.0384900
\(676\) 1.00000 0.0384615
\(677\) 42.0000 1.61419 0.807096 − 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) 2.00000 0.0768095
\(679\) 0 0
\(680\) −6.00000 −0.230089
\(681\) 4.00000 0.153280
\(682\) −4.00000 −0.153168
\(683\) −4.00000 −0.153056 −0.0765279 − 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 4.00000 0.152944
\(685\) −14.0000 −0.534913
\(686\) 0 0
\(687\) 6.00000 0.228914
\(688\) −8.00000 −0.304997
\(689\) 6.00000 0.228582
\(690\) 0 0
\(691\) −16.0000 −0.608669 −0.304334 − 0.952565i \(-0.598434\pi\)
−0.304334 + 0.952565i \(0.598434\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) −8.00000 −0.303457
\(696\) −6.00000 −0.227429
\(697\) 12.0000 0.454532
\(698\) −18.0000 −0.681310
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) −22.0000 −0.830929 −0.415464 − 0.909610i \(-0.636381\pi\)
−0.415464 + 0.909610i \(0.636381\pi\)
\(702\) 1.00000 0.0377426
\(703\) −8.00000 −0.301726
\(704\) −1.00000 −0.0376889
\(705\) −8.00000 −0.301297
\(706\) 14.0000 0.526897
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) 22.0000 0.826227 0.413114 − 0.910679i \(-0.364441\pi\)
0.413114 + 0.910679i \(0.364441\pi\)
\(710\) 8.00000 0.300235
\(711\) 4.00000 0.150012
\(712\) −2.00000 −0.0749532
\(713\) 0 0
\(714\) 0 0
\(715\) 1.00000 0.0373979
\(716\) 12.0000 0.448461
\(717\) −16.0000 −0.597531
\(718\) −8.00000 −0.298557
\(719\) 16.0000 0.596699 0.298350 − 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 0 0
\(722\) −3.00000 −0.111648
\(723\) −30.0000 −1.11571
\(724\) −10.0000 −0.371647
\(725\) −6.00000 −0.222834
\(726\) 1.00000 0.0371135
\(727\) 48.0000 1.78022 0.890111 − 0.455744i \(-0.150627\pi\)
0.890111 + 0.455744i \(0.150627\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 6.00000 0.222070
\(731\) −48.0000 −1.77534
\(732\) 6.00000 0.221766
\(733\) 30.0000 1.10808 0.554038 − 0.832492i \(-0.313086\pi\)
0.554038 + 0.832492i \(0.313086\pi\)
\(734\) 0 0
\(735\) 7.00000 0.258199
\(736\) 0 0
\(737\) 8.00000 0.294684
\(738\) 2.00000 0.0736210
\(739\) 28.0000 1.03000 0.514998 − 0.857191i \(-0.327793\pi\)
0.514998 + 0.857191i \(0.327793\pi\)
\(740\) 2.00000 0.0735215
\(741\) 4.00000 0.146944
\(742\) 0 0
\(743\) 16.0000 0.586983 0.293492 − 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) 4.00000 0.146647
\(745\) 10.0000 0.366372
\(746\) 14.0000 0.512576
\(747\) 12.0000 0.439057
\(748\) −6.00000 −0.219382
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) −32.0000 −1.16770 −0.583848 − 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 8.00000 0.291730
\(753\) −4.00000 −0.145768
\(754\) −6.00000 −0.218507
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) −42.0000 −1.52652 −0.763258 − 0.646094i \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(758\) −16.0000 −0.581146
\(759\) 0 0
\(760\) −4.00000 −0.145095
\(761\) 26.0000 0.942499 0.471250 − 0.882000i \(-0.343803\pi\)
0.471250 + 0.882000i \(0.343803\pi\)
\(762\) −4.00000 −0.144905
\(763\) 0 0
\(764\) −16.0000 −0.578860
\(765\) −6.00000 −0.216930
\(766\) −32.0000 −1.15621
\(767\) 12.0000 0.433295
\(768\) 1.00000 0.0360844
\(769\) 18.0000 0.649097 0.324548 − 0.945869i \(-0.394788\pi\)
0.324548 + 0.945869i \(0.394788\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 2.00000 0.0719816
\(773\) −6.00000 −0.215805 −0.107903 − 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) −8.00000 −0.287554
\(775\) 4.00000 0.143684
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) 14.0000 0.501924
\(779\) 8.00000 0.286630
\(780\) −1.00000 −0.0358057
\(781\) 8.00000 0.286263
\(782\) 0 0
\(783\) −6.00000 −0.214423
\(784\) −7.00000 −0.250000
\(785\) 2.00000 0.0713831
\(786\) 20.0000 0.713376
\(787\) 28.0000 0.998092 0.499046 − 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) 6.00000 0.213741
\(789\) −32.0000 −1.13923
\(790\) −4.00000 −0.142314
\(791\) 0 0
\(792\) −1.00000 −0.0355335
\(793\) 6.00000 0.213066
\(794\) 22.0000 0.780751
\(795\) −6.00000 −0.212798
\(796\) 0 0
\(797\) −26.0000 −0.920967 −0.460484 − 0.887668i \(-0.652324\pi\)
−0.460484 + 0.887668i \(0.652324\pi\)
\(798\) 0 0
\(799\) 48.0000 1.69812
\(800\) 1.00000 0.0353553
\(801\) −2.00000 −0.0706665
\(802\) 14.0000 0.494357
\(803\) 6.00000 0.211735
\(804\) −8.00000 −0.282138
\(805\) 0 0
\(806\) 4.00000 0.140894
\(807\) 6.00000 0.211210
\(808\) 18.0000 0.633238
\(809\) 6.00000 0.210949 0.105474 − 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −4.00000 −0.140459 −0.0702295 − 0.997531i \(-0.522373\pi\)
−0.0702295 + 0.997531i \(0.522373\pi\)
\(812\) 0 0
\(813\) −32.0000 −1.12229
\(814\) 2.00000 0.0701000
\(815\) 16.0000 0.560456
\(816\) 6.00000 0.210042
\(817\) −32.0000 −1.11954
\(818\) −22.0000 −0.769212
\(819\) 0 0
\(820\) −2.00000 −0.0698430
\(821\) 30.0000 1.04701 0.523504 − 0.852023i \(-0.324625\pi\)
0.523504 + 0.852023i \(0.324625\pi\)
\(822\) 14.0000 0.488306
\(823\) 16.0000 0.557725 0.278862 − 0.960331i \(-0.410043\pi\)
0.278862 + 0.960331i \(0.410043\pi\)
\(824\) 16.0000 0.557386
\(825\) −1.00000 −0.0348155
\(826\) 0 0
\(827\) −20.0000 −0.695468 −0.347734 − 0.937593i \(-0.613049\pi\)
−0.347734 + 0.937593i \(0.613049\pi\)
\(828\) 0 0
\(829\) −34.0000 −1.18087 −0.590434 − 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) −12.0000 −0.416526
\(831\) −10.0000 −0.346896
\(832\) 1.00000 0.0346688
\(833\) −42.0000 −1.45521
\(834\) 8.00000 0.277017
\(835\) 0 0
\(836\) −4.00000 −0.138343
\(837\) 4.00000 0.138260
\(838\) 12.0000 0.414533
\(839\) −32.0000 −1.10476 −0.552381 − 0.833592i \(-0.686281\pi\)
−0.552381 + 0.833592i \(0.686281\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −10.0000 −0.344623
\(843\) −14.0000 −0.482186
\(844\) −8.00000 −0.275371
\(845\) −1.00000 −0.0344010
\(846\) 8.00000 0.275046
\(847\) 0 0
\(848\) 6.00000 0.206041
\(849\) 32.0000 1.09824
\(850\) 6.00000 0.205798
\(851\) 0 0
\(852\) −8.00000 −0.274075
\(853\) 6.00000 0.205436 0.102718 − 0.994711i \(-0.467246\pi\)
0.102718 + 0.994711i \(0.467246\pi\)
\(854\) 0 0
\(855\) −4.00000 −0.136797
\(856\) −12.0000 −0.410152
\(857\) 6.00000 0.204956 0.102478 − 0.994735i \(-0.467323\pi\)
0.102478 + 0.994735i \(0.467323\pi\)
\(858\) −1.00000 −0.0341394
\(859\) −28.0000 −0.955348 −0.477674 − 0.878537i \(-0.658520\pi\)
−0.477674 + 0.878537i \(0.658520\pi\)
\(860\) 8.00000 0.272798
\(861\) 0 0
\(862\) −40.0000 −1.36241
\(863\) −32.0000 −1.08929 −0.544646 − 0.838666i \(-0.683336\pi\)
−0.544646 + 0.838666i \(0.683336\pi\)
\(864\) 1.00000 0.0340207
\(865\) 6.00000 0.204006
\(866\) −14.0000 −0.475739
\(867\) 19.0000 0.645274
\(868\) 0 0
\(869\) −4.00000 −0.135691
\(870\) 6.00000 0.203419
\(871\) −8.00000 −0.271070
\(872\) 14.0000 0.474100
\(873\) 10.0000 0.338449
\(874\) 0 0
\(875\) 0 0
\(876\) −6.00000 −0.202721
\(877\) 14.0000 0.472746 0.236373 − 0.971662i \(-0.424041\pi\)
0.236373 + 0.971662i \(0.424041\pi\)
\(878\) 4.00000 0.134993
\(879\) −26.0000 −0.876958
\(880\) 1.00000 0.0337100
\(881\) 50.0000 1.68454 0.842271 − 0.539054i \(-0.181218\pi\)
0.842271 + 0.539054i \(0.181218\pi\)
\(882\) −7.00000 −0.235702
\(883\) 12.0000 0.403832 0.201916 − 0.979403i \(-0.435283\pi\)
0.201916 + 0.979403i \(0.435283\pi\)
\(884\) 6.00000 0.201802
\(885\) −12.0000 −0.403376
\(886\) −4.00000 −0.134383
\(887\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) −2.00000 −0.0671156
\(889\) 0 0
\(890\) 2.00000 0.0670402
\(891\) −1.00000 −0.0335013
\(892\) −20.0000 −0.669650
\(893\) 32.0000 1.07084
\(894\) −10.0000 −0.334450
\(895\) −12.0000 −0.401116
\(896\) 0 0
\(897\) 0 0
\(898\) −10.0000 −0.333704
\(899\) −24.0000 −0.800445
\(900\) 1.00000 0.0333333
\(901\) 36.0000 1.19933
\(902\) −2.00000 −0.0665927
\(903\) 0 0
\(904\) 2.00000 0.0665190
\(905\) 10.0000 0.332411
\(906\) −8.00000 −0.265782
\(907\) 44.0000 1.46100 0.730498 − 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) 4.00000 0.132745
\(909\) 18.0000 0.597022
\(910\) 0 0
\(911\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 4.00000 0.132453
\(913\) −12.0000 −0.397142
\(914\) 10.0000 0.330771
\(915\) −6.00000 −0.198354
\(916\) 6.00000 0.198246
\(917\) 0 0
\(918\) 6.00000 0.198030
\(919\) 20.0000 0.659739 0.329870 − 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) 0 0
\(921\) −12.0000 −0.395413
\(922\) −42.0000 −1.38320
\(923\) −8.00000 −0.263323
\(924\) 0 0
\(925\) −2.00000 −0.0657596
\(926\) −36.0000 −1.18303
\(927\) 16.0000 0.525509
\(928\) −6.00000 −0.196960
\(929\) 38.0000 1.24674 0.623370 − 0.781927i \(-0.285763\pi\)
0.623370 + 0.781927i \(0.285763\pi\)
\(930\) −4.00000 −0.131165
\(931\) −28.0000 −0.917663
\(932\) 14.0000 0.458585
\(933\) 16.0000 0.523816
\(934\) −4.00000 −0.130884
\(935\) 6.00000 0.196221
\(936\) 1.00000 0.0326860
\(937\) −22.0000 −0.718709 −0.359354 − 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) −22.0000 −0.717943
\(940\) −8.00000 −0.260931
\(941\) 6.00000 0.195594 0.0977972 − 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 0 0
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) 8.00000 0.260102
\(947\) 12.0000 0.389948 0.194974 − 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 4.00000 0.129914
\(949\) −6.00000 −0.194768
\(950\) 4.00000 0.129777
\(951\) −14.0000 −0.453981
\(952\) 0 0
\(953\) 54.0000 1.74923 0.874616 − 0.484817i \(-0.161114\pi\)
0.874616 + 0.484817i \(0.161114\pi\)
\(954\) 6.00000 0.194257
\(955\) 16.0000 0.517748
\(956\) −16.0000 −0.517477
\(957\) 6.00000 0.193952
\(958\) 16.0000 0.516937
\(959\) 0 0
\(960\) −1.00000 −0.0322749
\(961\) −15.0000 −0.483871
\(962\) −2.00000 −0.0644826
\(963\) −12.0000 −0.386695
\(964\) −30.0000 −0.966235
\(965\) −2.00000 −0.0643823
\(966\) 0 0
\(967\) 16.0000 0.514525 0.257263 − 0.966342i \(-0.417179\pi\)
0.257263 + 0.966342i \(0.417179\pi\)
\(968\) 1.00000 0.0321412
\(969\) 24.0000 0.770991
\(970\) −10.0000 −0.321081
\(971\) −60.0000 −1.92549 −0.962746 − 0.270408i \(-0.912841\pi\)
−0.962746 + 0.270408i \(0.912841\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) −20.0000 −0.640841
\(975\) 1.00000 0.0320256
\(976\) 6.00000 0.192055
\(977\) −18.0000 −0.575871 −0.287936 − 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) −16.0000 −0.511624
\(979\) 2.00000 0.0639203
\(980\) 7.00000 0.223607
\(981\) 14.0000 0.446986
\(982\) 12.0000 0.382935
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 2.00000 0.0637577
\(985\) −6.00000 −0.191176
\(986\) −36.0000 −1.14647
\(987\) 0 0
\(988\) 4.00000 0.127257
\(989\) 0 0
\(990\) 1.00000 0.0317821
\(991\) −40.0000 −1.27064 −0.635321 − 0.772248i \(-0.719132\pi\)
−0.635321 + 0.772248i \(0.719132\pi\)
\(992\) 4.00000 0.127000
\(993\) 8.00000 0.253872
\(994\) 0 0
\(995\) 0 0
\(996\) 12.0000 0.380235
\(997\) 14.0000 0.443384 0.221692 − 0.975117i \(-0.428842\pi\)
0.221692 + 0.975117i \(0.428842\pi\)
\(998\) −24.0000 −0.759707
\(999\) −2.00000 −0.0632772
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4290.2.a.y.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4290.2.a.y.1.1 ✓ 1 1.1 even 1 trivial