Properties

Label 430.2.a.d.1.1
Level $430$
Weight $2$
Character 430.1
Self dual yes
Analytic conductor $3.434$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [430,2,Mod(1,430)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(430, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("430.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 430.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: \(3.43356728692\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 430.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} -5.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} -5.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -2.00000 q^{11} -2.00000 q^{12} -5.00000 q^{13} -5.00000 q^{14} -2.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} +3.00000 q^{19} +1.00000 q^{20} +10.0000 q^{21} -2.00000 q^{22} -6.00000 q^{23} -2.00000 q^{24} +1.00000 q^{25} -5.00000 q^{26} +4.00000 q^{27} -5.00000 q^{28} -1.00000 q^{29} -2.00000 q^{30} -11.0000 q^{31} +1.00000 q^{32} +4.00000 q^{33} +2.00000 q^{34} -5.00000 q^{35} +1.00000 q^{36} -10.0000 q^{37} +3.00000 q^{38} +10.0000 q^{39} +1.00000 q^{40} +5.00000 q^{41} +10.0000 q^{42} -1.00000 q^{43} -2.00000 q^{44} +1.00000 q^{45} -6.00000 q^{46} +4.00000 q^{47} -2.00000 q^{48} +18.0000 q^{49} +1.00000 q^{50} -4.00000 q^{51} -5.00000 q^{52} +10.0000 q^{53} +4.00000 q^{54} -2.00000 q^{55} -5.00000 q^{56} -6.00000 q^{57} -1.00000 q^{58} +8.00000 q^{59} -2.00000 q^{60} -3.00000 q^{61} -11.0000 q^{62} -5.00000 q^{63} +1.00000 q^{64} -5.00000 q^{65} +4.00000 q^{66} -3.00000 q^{67} +2.00000 q^{68} +12.0000 q^{69} -5.00000 q^{70} -8.00000 q^{71} +1.00000 q^{72} +7.00000 q^{73} -10.0000 q^{74} -2.00000 q^{75} +3.00000 q^{76} +10.0000 q^{77} +10.0000 q^{78} +7.00000 q^{79} +1.00000 q^{80} -11.0000 q^{81} +5.00000 q^{82} +10.0000 q^{84} +2.00000 q^{85} -1.00000 q^{86} +2.00000 q^{87} -2.00000 q^{88} +6.00000 q^{89} +1.00000 q^{90} +25.0000 q^{91} -6.00000 q^{92} +22.0000 q^{93} +4.00000 q^{94} +3.00000 q^{95} -2.00000 q^{96} +12.0000 q^{97} +18.0000 q^{98} -2.00000 q^{99} +O(q^{100})\)

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
\(3\) −2.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −2.00000 −0.816497
\(7\) −5.00000 −1.88982 −0.944911 0.327327i \(-0.893852\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) −2.00000 −0.577350
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) −5.00000 −1.33631
\(15\) −2.00000 −0.516398
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 1.00000 0.235702
\(19\) 3.00000 0.688247 0.344124 0.938924i \(-0.388176\pi\)
0.344124 + 0.938924i \(0.388176\pi\)
\(20\) 1.00000 0.223607
\(21\) 10.0000 2.18218
\(22\) −2.00000 −0.426401
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) −2.00000 −0.408248
\(25\) 1.00000 0.200000
\(26\) −5.00000 −0.980581
\(27\) 4.00000 0.769800
\(28\) −5.00000 −0.944911
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) −2.00000 −0.365148
\(31\) −11.0000 −1.97566 −0.987829 0.155543i \(-0.950287\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.00000 0.696311
\(34\) 2.00000 0.342997
\(35\) −5.00000 −0.845154
\(36\) 1.00000 0.166667
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 3.00000 0.486664
\(39\) 10.0000 1.60128
\(40\) 1.00000 0.158114
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 10.0000 1.54303
\(43\) −1.00000 −0.152499
\(44\) −2.00000 −0.301511
\(45\) 1.00000 0.149071
\(46\) −6.00000 −0.884652
\(47\) 4.00000 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) −2.00000 −0.288675
\(49\) 18.0000 2.57143
\(50\) 1.00000 0.141421
\(51\) −4.00000 −0.560112
\(52\) −5.00000 −0.693375
\(53\) 10.0000 1.37361 0.686803 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) 4.00000 0.544331
\(55\) −2.00000 −0.269680
\(56\) −5.00000 −0.668153
\(57\) −6.00000 −0.794719
\(58\) −1.00000 −0.131306
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) −2.00000 −0.258199
\(61\) −3.00000 −0.384111 −0.192055 0.981384i \(-0.561515\pi\)
−0.192055 + 0.981384i \(0.561515\pi\)
\(62\) −11.0000 −1.39700
\(63\) −5.00000 −0.629941
\(64\) 1.00000 0.125000
\(65\) −5.00000 −0.620174
\(66\) 4.00000 0.492366
\(67\) −3.00000 −0.366508 −0.183254 0.983066i \(-0.558663\pi\)
−0.183254 + 0.983066i \(0.558663\pi\)
\(68\) 2.00000 0.242536
\(69\) 12.0000 1.44463
\(70\) −5.00000 −0.597614
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 1.00000 0.117851
\(73\) 7.00000 0.819288 0.409644 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) −10.0000 −1.16248
\(75\) −2.00000 −0.230940
\(76\) 3.00000 0.344124
\(77\) 10.0000 1.13961
\(78\) 10.0000 1.13228
\(79\) 7.00000 0.787562 0.393781 0.919204i \(-0.371167\pi\)
0.393781 + 0.919204i \(0.371167\pi\)
\(80\) 1.00000 0.111803
\(81\) −11.0000 −1.22222
\(82\) 5.00000 0.552158
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 10.0000 1.09109
\(85\) 2.00000 0.216930
\(86\) −1.00000 −0.107833
\(87\) 2.00000 0.214423
\(88\) −2.00000 −0.213201
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 1.00000 0.105409
\(91\) 25.0000 2.62071
\(92\) −6.00000 −0.625543
\(93\) 22.0000 2.28129
\(94\) 4.00000 0.412568
\(95\) 3.00000 0.307794
\(96\) −2.00000 −0.204124
\(97\) 12.0000 1.21842 0.609208 0.793011i \(-0.291488\pi\)
0.609208 + 0.793011i \(0.291488\pi\)
\(98\) 18.0000 1.81827
\(99\) −2.00000 −0.201008
\(100\) 1.00000 0.100000
\(101\) −14.0000 −1.39305 −0.696526 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) −4.00000 −0.396059
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) −5.00000 −0.490290
\(105\) 10.0000 0.975900
\(106\) 10.0000 0.971286
\(107\) −7.00000 −0.676716 −0.338358 0.941018i \(-0.609871\pi\)
−0.338358 + 0.941018i \(0.609871\pi\)
\(108\) 4.00000 0.384900
\(109\) −8.00000 −0.766261 −0.383131 0.923694i \(-0.625154\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(110\) −2.00000 −0.190693
\(111\) 20.0000 1.89832
\(112\) −5.00000 −0.472456
\(113\) −15.0000 −1.41108 −0.705541 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) −6.00000 −0.561951
\(115\) −6.00000 −0.559503
\(116\) −1.00000 −0.0928477
\(117\) −5.00000 −0.462250
\(118\) 8.00000 0.736460
\(119\) −10.0000 −0.916698
\(120\) −2.00000 −0.182574
\(121\) −7.00000 −0.636364
\(122\) −3.00000 −0.271607
\(123\) −10.0000 −0.901670
\(124\) −11.0000 −0.987829
\(125\) 1.00000 0.0894427
\(126\) −5.00000 −0.445435
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.00000 0.176090
\(130\) −5.00000 −0.438529
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 4.00000 0.348155
\(133\) −15.0000 −1.30066
\(134\) −3.00000 −0.259161
\(135\) 4.00000 0.344265
\(136\) 2.00000 0.171499
\(137\) −19.0000 −1.62328 −0.811640 0.584158i \(-0.801425\pi\)
−0.811640 + 0.584158i \(0.801425\pi\)
\(138\) 12.0000 1.02151
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) −5.00000 −0.422577
\(141\) −8.00000 −0.673722
\(142\) −8.00000 −0.671345
\(143\) 10.0000 0.836242
\(144\) 1.00000 0.0833333
\(145\) −1.00000 −0.0830455
\(146\) 7.00000 0.579324
\(147\) −36.0000 −2.96923
\(148\) −10.0000 −0.821995
\(149\) −23.0000 −1.88423 −0.942117 0.335285i \(-0.891167\pi\)
−0.942117 + 0.335285i \(0.891167\pi\)
\(150\) −2.00000 −0.163299
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) 3.00000 0.243332
\(153\) 2.00000 0.161690
\(154\) 10.0000 0.805823
\(155\) −11.0000 −0.883541
\(156\) 10.0000 0.800641
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) 7.00000 0.556890
\(159\) −20.0000 −1.58610
\(160\) 1.00000 0.0790569
\(161\) 30.0000 2.36433
\(162\) −11.0000 −0.864242
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 5.00000 0.390434
\(165\) 4.00000 0.311400
\(166\) 0 0
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 10.0000 0.771517
\(169\) 12.0000 0.923077
\(170\) 2.00000 0.153393
\(171\) 3.00000 0.229416
\(172\) −1.00000 −0.0762493
\(173\) −9.00000 −0.684257 −0.342129 0.939653i \(-0.611148\pi\)
−0.342129 + 0.939653i \(0.611148\pi\)
\(174\) 2.00000 0.151620
\(175\) −5.00000 −0.377964
\(176\) −2.00000 −0.150756
\(177\) −16.0000 −1.20263
\(178\) 6.00000 0.449719
\(179\) −15.0000 −1.12115 −0.560576 0.828103i \(-0.689420\pi\)
−0.560576 + 0.828103i \(0.689420\pi\)
\(180\) 1.00000 0.0745356
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 25.0000 1.85312
\(183\) 6.00000 0.443533
\(184\) −6.00000 −0.442326
\(185\) −10.0000 −0.735215
\(186\) 22.0000 1.61312
\(187\) −4.00000 −0.292509
\(188\) 4.00000 0.291730
\(189\) −20.0000 −1.45479
\(190\) 3.00000 0.217643
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) −2.00000 −0.144338
\(193\) 8.00000 0.575853 0.287926 0.957653i \(-0.407034\pi\)
0.287926 + 0.957653i \(0.407034\pi\)
\(194\) 12.0000 0.861550
\(195\) 10.0000 0.716115
\(196\) 18.0000 1.28571
\(197\) 7.00000 0.498729 0.249365 0.968410i \(-0.419778\pi\)
0.249365 + 0.968410i \(0.419778\pi\)
\(198\) −2.00000 −0.142134
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 1.00000 0.0707107
\(201\) 6.00000 0.423207
\(202\) −14.0000 −0.985037
\(203\) 5.00000 0.350931
\(204\) −4.00000 −0.280056
\(205\) 5.00000 0.349215
\(206\) −14.0000 −0.975426
\(207\) −6.00000 −0.417029
\(208\) −5.00000 −0.346688
\(209\) −6.00000 −0.415029
\(210\) 10.0000 0.690066
\(211\) −28.0000 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 10.0000 0.686803
\(213\) 16.0000 1.09630
\(214\) −7.00000 −0.478510
\(215\) −1.00000 −0.0681994
\(216\) 4.00000 0.272166
\(217\) 55.0000 3.73364
\(218\) −8.00000 −0.541828
\(219\) −14.0000 −0.946032
\(220\) −2.00000 −0.134840
\(221\) −10.0000 −0.672673
\(222\) 20.0000 1.34231
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) −5.00000 −0.334077
\(225\) 1.00000 0.0666667
\(226\) −15.0000 −0.997785
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) −6.00000 −0.397360
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −6.00000 −0.395628
\(231\) −20.0000 −1.31590
\(232\) −1.00000 −0.0656532
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) −5.00000 −0.326860
\(235\) 4.00000 0.260931
\(236\) 8.00000 0.520756
\(237\) −14.0000 −0.909398
\(238\) −10.0000 −0.648204
\(239\) 11.0000 0.711531 0.355765 0.934575i \(-0.384220\pi\)
0.355765 + 0.934575i \(0.384220\pi\)
\(240\) −2.00000 −0.129099
\(241\) −12.0000 −0.772988 −0.386494 0.922292i \(-0.626314\pi\)
−0.386494 + 0.922292i \(0.626314\pi\)
\(242\) −7.00000 −0.449977
\(243\) 10.0000 0.641500
\(244\) −3.00000 −0.192055
\(245\) 18.0000 1.14998
\(246\) −10.0000 −0.637577
\(247\) −15.0000 −0.954427
\(248\) −11.0000 −0.698501
\(249\) 0 0
\(250\) 1.00000 0.0632456
\(251\) 2.00000 0.126239 0.0631194 0.998006i \(-0.479895\pi\)
0.0631194 + 0.998006i \(0.479895\pi\)
\(252\) −5.00000 −0.314970
\(253\) 12.0000 0.754434
\(254\) 16.0000 1.00393
\(255\) −4.00000 −0.250490
\(256\) 1.00000 0.0625000
\(257\) 1.00000 0.0623783 0.0311891 0.999514i \(-0.490071\pi\)
0.0311891 + 0.999514i \(0.490071\pi\)
\(258\) 2.00000 0.124515
\(259\) 50.0000 3.10685
\(260\) −5.00000 −0.310087
\(261\) −1.00000 −0.0618984
\(262\) −12.0000 −0.741362
\(263\) −3.00000 −0.184988 −0.0924940 0.995713i \(-0.529484\pi\)
−0.0924940 + 0.995713i \(0.529484\pi\)
\(264\) 4.00000 0.246183
\(265\) 10.0000 0.614295
\(266\) −15.0000 −0.919709
\(267\) −12.0000 −0.734388
\(268\) −3.00000 −0.183254
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 4.00000 0.243432
\(271\) 3.00000 0.182237 0.0911185 0.995840i \(-0.470956\pi\)
0.0911185 + 0.995840i \(0.470956\pi\)
\(272\) 2.00000 0.121268
\(273\) −50.0000 −3.02614
\(274\) −19.0000 −1.14783
\(275\) −2.00000 −0.120605
\(276\) 12.0000 0.722315
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 14.0000 0.839664
\(279\) −11.0000 −0.658553
\(280\) −5.00000 −0.298807
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) −8.00000 −0.476393
\(283\) −29.0000 −1.72387 −0.861936 0.507018i \(-0.830748\pi\)
−0.861936 + 0.507018i \(0.830748\pi\)
\(284\) −8.00000 −0.474713
\(285\) −6.00000 −0.355409
\(286\) 10.0000 0.591312
\(287\) −25.0000 −1.47570
\(288\) 1.00000 0.0589256
\(289\) −13.0000 −0.764706
\(290\) −1.00000 −0.0587220
\(291\) −24.0000 −1.40690
\(292\) 7.00000 0.409644
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) −36.0000 −2.09956
\(295\) 8.00000 0.465778
\(296\) −10.0000 −0.581238
\(297\) −8.00000 −0.464207
\(298\) −23.0000 −1.33235
\(299\) 30.0000 1.73494
\(300\) −2.00000 −0.115470
\(301\) 5.00000 0.288195
\(302\) 10.0000 0.575435
\(303\) 28.0000 1.60856
\(304\) 3.00000 0.172062
\(305\) −3.00000 −0.171780
\(306\) 2.00000 0.114332
\(307\) 3.00000 0.171219 0.0856095 0.996329i \(-0.472716\pi\)
0.0856095 + 0.996329i \(0.472716\pi\)
\(308\) 10.0000 0.569803
\(309\) 28.0000 1.59286
\(310\) −11.0000 −0.624758
\(311\) 25.0000 1.41762 0.708810 0.705399i \(-0.249232\pi\)
0.708810 + 0.705399i \(0.249232\pi\)
\(312\) 10.0000 0.566139
\(313\) 22.0000 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) −10.0000 −0.564333
\(315\) −5.00000 −0.281718
\(316\) 7.00000 0.393781
\(317\) −1.00000 −0.0561656 −0.0280828 0.999606i \(-0.508940\pi\)
−0.0280828 + 0.999606i \(0.508940\pi\)
\(318\) −20.0000 −1.12154
\(319\) 2.00000 0.111979
\(320\) 1.00000 0.0559017
\(321\) 14.0000 0.781404
\(322\) 30.0000 1.67183
\(323\) 6.00000 0.333849
\(324\) −11.0000 −0.611111
\(325\) −5.00000 −0.277350
\(326\) 4.00000 0.221540
\(327\) 16.0000 0.884802
\(328\) 5.00000 0.276079
\(329\) −20.0000 −1.10264
\(330\) 4.00000 0.220193
\(331\) −16.0000 −0.879440 −0.439720 0.898135i \(-0.644922\pi\)
−0.439720 + 0.898135i \(0.644922\pi\)
\(332\) 0 0
\(333\) −10.0000 −0.547997
\(334\) 6.00000 0.328305
\(335\) −3.00000 −0.163908
\(336\) 10.0000 0.545545
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 12.0000 0.652714
\(339\) 30.0000 1.62938
\(340\) 2.00000 0.108465
\(341\) 22.0000 1.19137
\(342\) 3.00000 0.162221
\(343\) −55.0000 −2.96972
\(344\) −1.00000 −0.0539164
\(345\) 12.0000 0.646058
\(346\) −9.00000 −0.483843
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 2.00000 0.107211
\(349\) −6.00000 −0.321173 −0.160586 0.987022i \(-0.551338\pi\)
−0.160586 + 0.987022i \(0.551338\pi\)
\(350\) −5.00000 −0.267261
\(351\) −20.0000 −1.06752
\(352\) −2.00000 −0.106600
\(353\) −16.0000 −0.851594 −0.425797 0.904819i \(-0.640006\pi\)
−0.425797 + 0.904819i \(0.640006\pi\)
\(354\) −16.0000 −0.850390
\(355\) −8.00000 −0.424596
\(356\) 6.00000 0.317999
\(357\) 20.0000 1.05851
\(358\) −15.0000 −0.792775
\(359\) 9.00000 0.475002 0.237501 0.971387i \(-0.423672\pi\)
0.237501 + 0.971387i \(0.423672\pi\)
\(360\) 1.00000 0.0527046
\(361\) −10.0000 −0.526316
\(362\) 10.0000 0.525588
\(363\) 14.0000 0.734809
\(364\) 25.0000 1.31036
\(365\) 7.00000 0.366397
\(366\) 6.00000 0.313625
\(367\) 28.0000 1.46159 0.730794 0.682598i \(-0.239150\pi\)
0.730794 + 0.682598i \(0.239150\pi\)
\(368\) −6.00000 −0.312772
\(369\) 5.00000 0.260290
\(370\) −10.0000 −0.519875
\(371\) −50.0000 −2.59587
\(372\) 22.0000 1.14065
\(373\) 2.00000 0.103556 0.0517780 0.998659i \(-0.483511\pi\)
0.0517780 + 0.998659i \(0.483511\pi\)
\(374\) −4.00000 −0.206835
\(375\) −2.00000 −0.103280
\(376\) 4.00000 0.206284
\(377\) 5.00000 0.257513
\(378\) −20.0000 −1.02869
\(379\) −14.0000 −0.719132 −0.359566 0.933120i \(-0.617075\pi\)
−0.359566 + 0.933120i \(0.617075\pi\)
\(380\) 3.00000 0.153897
\(381\) −32.0000 −1.63941
\(382\) 4.00000 0.204658
\(383\) 27.0000 1.37964 0.689818 0.723983i \(-0.257691\pi\)
0.689818 + 0.723983i \(0.257691\pi\)
\(384\) −2.00000 −0.102062
\(385\) 10.0000 0.509647
\(386\) 8.00000 0.407189
\(387\) −1.00000 −0.0508329
\(388\) 12.0000 0.609208
\(389\) −34.0000 −1.72387 −0.861934 0.507020i \(-0.830747\pi\)
−0.861934 + 0.507020i \(0.830747\pi\)
\(390\) 10.0000 0.506370
\(391\) −12.0000 −0.606866
\(392\) 18.0000 0.909137
\(393\) 24.0000 1.21064
\(394\) 7.00000 0.352655
\(395\) 7.00000 0.352208
\(396\) −2.00000 −0.100504
\(397\) 14.0000 0.702640 0.351320 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) 4.00000 0.200502
\(399\) 30.0000 1.50188
\(400\) 1.00000 0.0500000
\(401\) 15.0000 0.749064 0.374532 0.927214i \(-0.377803\pi\)
0.374532 + 0.927214i \(0.377803\pi\)
\(402\) 6.00000 0.299253
\(403\) 55.0000 2.73975
\(404\) −14.0000 −0.696526
\(405\) −11.0000 −0.546594
\(406\) 5.00000 0.248146
\(407\) 20.0000 0.991363
\(408\) −4.00000 −0.198030
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 5.00000 0.246932
\(411\) 38.0000 1.87440
\(412\) −14.0000 −0.689730
\(413\) −40.0000 −1.96827
\(414\) −6.00000 −0.294884
\(415\) 0 0
\(416\) −5.00000 −0.245145
\(417\) −28.0000 −1.37117
\(418\) −6.00000 −0.293470
\(419\) 7.00000 0.341972 0.170986 0.985273i \(-0.445305\pi\)
0.170986 + 0.985273i \(0.445305\pi\)
\(420\) 10.0000 0.487950
\(421\) 35.0000 1.70580 0.852898 0.522078i \(-0.174843\pi\)
0.852898 + 0.522078i \(0.174843\pi\)
\(422\) −28.0000 −1.36302
\(423\) 4.00000 0.194487
\(424\) 10.0000 0.485643
\(425\) 2.00000 0.0970143
\(426\) 16.0000 0.775203
\(427\) 15.0000 0.725901
\(428\) −7.00000 −0.338358
\(429\) −20.0000 −0.965609
\(430\) −1.00000 −0.0482243
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 4.00000 0.192450
\(433\) 23.0000 1.10531 0.552655 0.833410i \(-0.313615\pi\)
0.552655 + 0.833410i \(0.313615\pi\)
\(434\) 55.0000 2.64008
\(435\) 2.00000 0.0958927
\(436\) −8.00000 −0.383131
\(437\) −18.0000 −0.861057
\(438\) −14.0000 −0.668946
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 18.0000 0.857143
\(442\) −10.0000 −0.475651
\(443\) 31.0000 1.47285 0.736427 0.676517i \(-0.236511\pi\)
0.736427 + 0.676517i \(0.236511\pi\)
\(444\) 20.0000 0.949158
\(445\) 6.00000 0.284427
\(446\) −8.00000 −0.378811
\(447\) 46.0000 2.17573
\(448\) −5.00000 −0.236228
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 1.00000 0.0471405
\(451\) −10.0000 −0.470882
\(452\) −15.0000 −0.705541
\(453\) −20.0000 −0.939682
\(454\) −4.00000 −0.187729
\(455\) 25.0000 1.17202
\(456\) −6.00000 −0.280976
\(457\) 42.0000 1.96468 0.982339 0.187112i \(-0.0599128\pi\)
0.982339 + 0.187112i \(0.0599128\pi\)
\(458\) 10.0000 0.467269
\(459\) 8.00000 0.373408
\(460\) −6.00000 −0.279751
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) −20.0000 −0.930484
\(463\) 9.00000 0.418265 0.209133 0.977887i \(-0.432936\pi\)
0.209133 + 0.977887i \(0.432936\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 22.0000 1.02023
\(466\) −14.0000 −0.648537
\(467\) −34.0000 −1.57333 −0.786666 0.617379i \(-0.788195\pi\)
−0.786666 + 0.617379i \(0.788195\pi\)
\(468\) −5.00000 −0.231125
\(469\) 15.0000 0.692636
\(470\) 4.00000 0.184506
\(471\) 20.0000 0.921551
\(472\) 8.00000 0.368230
\(473\) 2.00000 0.0919601
\(474\) −14.0000 −0.643041
\(475\) 3.00000 0.137649
\(476\) −10.0000 −0.458349
\(477\) 10.0000 0.457869
\(478\) 11.0000 0.503128
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) −2.00000 −0.0912871
\(481\) 50.0000 2.27980
\(482\) −12.0000 −0.546585
\(483\) −60.0000 −2.73009
\(484\) −7.00000 −0.318182
\(485\) 12.0000 0.544892
\(486\) 10.0000 0.453609
\(487\) 36.0000 1.63132 0.815658 0.578535i \(-0.196375\pi\)
0.815658 + 0.578535i \(0.196375\pi\)
\(488\) −3.00000 −0.135804
\(489\) −8.00000 −0.361773
\(490\) 18.0000 0.813157
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) −10.0000 −0.450835
\(493\) −2.00000 −0.0900755
\(494\) −15.0000 −0.674882
\(495\) −2.00000 −0.0898933
\(496\) −11.0000 −0.493915
\(497\) 40.0000 1.79425
\(498\) 0 0
\(499\) −13.0000 −0.581960 −0.290980 0.956729i \(-0.593981\pi\)
−0.290980 + 0.956729i \(0.593981\pi\)
\(500\) 1.00000 0.0447214
\(501\) −12.0000 −0.536120
\(502\) 2.00000 0.0892644
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) −5.00000 −0.222718
\(505\) −14.0000 −0.622992
\(506\) 12.0000 0.533465
\(507\) −24.0000 −1.06588
\(508\) 16.0000 0.709885
\(509\) 20.0000 0.886484 0.443242 0.896402i \(-0.353828\pi\)
0.443242 + 0.896402i \(0.353828\pi\)
\(510\) −4.00000 −0.177123
\(511\) −35.0000 −1.54831
\(512\) 1.00000 0.0441942
\(513\) 12.0000 0.529813
\(514\) 1.00000 0.0441081
\(515\) −14.0000 −0.616914
\(516\) 2.00000 0.0880451
\(517\) −8.00000 −0.351840
\(518\) 50.0000 2.19687
\(519\) 18.0000 0.790112
\(520\) −5.00000 −0.219265
\(521\) −16.0000 −0.700973 −0.350486 0.936568i \(-0.613984\pi\)
−0.350486 + 0.936568i \(0.613984\pi\)
\(522\) −1.00000 −0.0437688
\(523\) −8.00000 −0.349816 −0.174908 0.984585i \(-0.555963\pi\)
−0.174908 + 0.984585i \(0.555963\pi\)
\(524\) −12.0000 −0.524222
\(525\) 10.0000 0.436436
\(526\) −3.00000 −0.130806
\(527\) −22.0000 −0.958335
\(528\) 4.00000 0.174078
\(529\) 13.0000 0.565217
\(530\) 10.0000 0.434372
\(531\) 8.00000 0.347170
\(532\) −15.0000 −0.650332
\(533\) −25.0000 −1.08287
\(534\) −12.0000 −0.519291
\(535\) −7.00000 −0.302636
\(536\) −3.00000 −0.129580
\(537\) 30.0000 1.29460
\(538\) 0 0
\(539\) −36.0000 −1.55063
\(540\) 4.00000 0.172133
\(541\) 6.00000 0.257960 0.128980 0.991647i \(-0.458830\pi\)
0.128980 + 0.991647i \(0.458830\pi\)
\(542\) 3.00000 0.128861
\(543\) −20.0000 −0.858282
\(544\) 2.00000 0.0857493
\(545\) −8.00000 −0.342682
\(546\) −50.0000 −2.13980
\(547\) −4.00000 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) −19.0000 −0.811640
\(549\) −3.00000 −0.128037
\(550\) −2.00000 −0.0852803
\(551\) −3.00000 −0.127804
\(552\) 12.0000 0.510754
\(553\) −35.0000 −1.48835
\(554\) 8.00000 0.339887
\(555\) 20.0000 0.848953
\(556\) 14.0000 0.593732
\(557\) −23.0000 −0.974541 −0.487271 0.873251i \(-0.662007\pi\)
−0.487271 + 0.873251i \(0.662007\pi\)
\(558\) −11.0000 −0.465667
\(559\) 5.00000 0.211477
\(560\) −5.00000 −0.211289
\(561\) 8.00000 0.337760
\(562\) 9.00000 0.379642
\(563\) −3.00000 −0.126435 −0.0632175 0.998000i \(-0.520136\pi\)
−0.0632175 + 0.998000i \(0.520136\pi\)
\(564\) −8.00000 −0.336861
\(565\) −15.0000 −0.631055
\(566\) −29.0000 −1.21896
\(567\) 55.0000 2.30978
\(568\) −8.00000 −0.335673
\(569\) −43.0000 −1.80265 −0.901327 0.433140i \(-0.857406\pi\)
−0.901327 + 0.433140i \(0.857406\pi\)
\(570\) −6.00000 −0.251312
\(571\) 31.0000 1.29731 0.648655 0.761083i \(-0.275332\pi\)
0.648655 + 0.761083i \(0.275332\pi\)
\(572\) 10.0000 0.418121
\(573\) −8.00000 −0.334205
\(574\) −25.0000 −1.04348
\(575\) −6.00000 −0.250217
\(576\) 1.00000 0.0416667
\(577\) 5.00000 0.208153 0.104076 0.994569i \(-0.466811\pi\)
0.104076 + 0.994569i \(0.466811\pi\)
\(578\) −13.0000 −0.540729
\(579\) −16.0000 −0.664937
\(580\) −1.00000 −0.0415227
\(581\) 0 0
\(582\) −24.0000 −0.994832
\(583\) −20.0000 −0.828315
\(584\) 7.00000 0.289662
\(585\) −5.00000 −0.206725
\(586\) −6.00000 −0.247858
\(587\) 42.0000 1.73353 0.866763 0.498721i \(-0.166197\pi\)
0.866763 + 0.498721i \(0.166197\pi\)
\(588\) −36.0000 −1.48461
\(589\) −33.0000 −1.35974
\(590\) 8.00000 0.329355
\(591\) −14.0000 −0.575883
\(592\) −10.0000 −0.410997
\(593\) 9.00000 0.369586 0.184793 0.982777i \(-0.440839\pi\)
0.184793 + 0.982777i \(0.440839\pi\)
\(594\) −8.00000 −0.328244
\(595\) −10.0000 −0.409960
\(596\) −23.0000 −0.942117
\(597\) −8.00000 −0.327418
\(598\) 30.0000 1.22679
\(599\) −36.0000 −1.47092 −0.735460 0.677568i \(-0.763034\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) −2.00000 −0.0816497
\(601\) −4.00000 −0.163163 −0.0815817 0.996667i \(-0.525997\pi\)
−0.0815817 + 0.996667i \(0.525997\pi\)
\(602\) 5.00000 0.203785
\(603\) −3.00000 −0.122169
\(604\) 10.0000 0.406894
\(605\) −7.00000 −0.284590
\(606\) 28.0000 1.13742
\(607\) 16.0000 0.649420 0.324710 0.945814i \(-0.394733\pi\)
0.324710 + 0.945814i \(0.394733\pi\)
\(608\) 3.00000 0.121666
\(609\) −10.0000 −0.405220
\(610\) −3.00000 −0.121466
\(611\) −20.0000 −0.809113
\(612\) 2.00000 0.0808452
\(613\) −13.0000 −0.525065 −0.262533 0.964923i \(-0.584558\pi\)
−0.262533 + 0.964923i \(0.584558\pi\)
\(614\) 3.00000 0.121070
\(615\) −10.0000 −0.403239
\(616\) 10.0000 0.402911
\(617\) 44.0000 1.77137 0.885687 0.464283i \(-0.153688\pi\)
0.885687 + 0.464283i \(0.153688\pi\)
\(618\) 28.0000 1.12633
\(619\) −14.0000 −0.562708 −0.281354 0.959604i \(-0.590783\pi\)
−0.281354 + 0.959604i \(0.590783\pi\)
\(620\) −11.0000 −0.441771
\(621\) −24.0000 −0.963087
\(622\) 25.0000 1.00241
\(623\) −30.0000 −1.20192
\(624\) 10.0000 0.400320
\(625\) 1.00000 0.0400000
\(626\) 22.0000 0.879297
\(627\) 12.0000 0.479234
\(628\) −10.0000 −0.399043
\(629\) −20.0000 −0.797452
\(630\) −5.00000 −0.199205
\(631\) 34.0000 1.35352 0.676759 0.736204i \(-0.263384\pi\)
0.676759 + 0.736204i \(0.263384\pi\)
\(632\) 7.00000 0.278445
\(633\) 56.0000 2.22580
\(634\) −1.00000 −0.0397151
\(635\) 16.0000 0.634941
\(636\) −20.0000 −0.793052
\(637\) −90.0000 −3.56593
\(638\) 2.00000 0.0791808
\(639\) −8.00000 −0.316475
\(640\) 1.00000 0.0395285
\(641\) 22.0000 0.868948 0.434474 0.900684i \(-0.356934\pi\)
0.434474 + 0.900684i \(0.356934\pi\)
\(642\) 14.0000 0.552536
\(643\) 39.0000 1.53801 0.769005 0.639243i \(-0.220752\pi\)
0.769005 + 0.639243i \(0.220752\pi\)
\(644\) 30.0000 1.18217
\(645\) 2.00000 0.0787499
\(646\) 6.00000 0.236067
\(647\) 33.0000 1.29736 0.648682 0.761060i \(-0.275321\pi\)
0.648682 + 0.761060i \(0.275321\pi\)
\(648\) −11.0000 −0.432121
\(649\) −16.0000 −0.628055
\(650\) −5.00000 −0.196116
\(651\) −110.000 −4.31124
\(652\) 4.00000 0.156652
\(653\) −24.0000 −0.939193 −0.469596 0.882881i \(-0.655601\pi\)
−0.469596 + 0.882881i \(0.655601\pi\)
\(654\) 16.0000 0.625650
\(655\) −12.0000 −0.468879
\(656\) 5.00000 0.195217
\(657\) 7.00000 0.273096
\(658\) −20.0000 −0.779681
\(659\) 26.0000 1.01282 0.506408 0.862294i \(-0.330973\pi\)
0.506408 + 0.862294i \(0.330973\pi\)
\(660\) 4.00000 0.155700
\(661\) −24.0000 −0.933492 −0.466746 0.884391i \(-0.654574\pi\)
−0.466746 + 0.884391i \(0.654574\pi\)
\(662\) −16.0000 −0.621858
\(663\) 20.0000 0.776736
\(664\) 0 0
\(665\) −15.0000 −0.581675
\(666\) −10.0000 −0.387492
\(667\) 6.00000 0.232321
\(668\) 6.00000 0.232147
\(669\) 16.0000 0.618596
\(670\) −3.00000 −0.115900
\(671\) 6.00000 0.231627
\(672\) 10.0000 0.385758
\(673\) −21.0000 −0.809491 −0.404745 0.914429i \(-0.632640\pi\)
−0.404745 + 0.914429i \(0.632640\pi\)
\(674\) −18.0000 −0.693334
\(675\) 4.00000 0.153960
\(676\) 12.0000 0.461538
\(677\) 14.0000 0.538064 0.269032 0.963131i \(-0.413296\pi\)
0.269032 + 0.963131i \(0.413296\pi\)
\(678\) 30.0000 1.15214
\(679\) −60.0000 −2.30259
\(680\) 2.00000 0.0766965
\(681\) 8.00000 0.306561
\(682\) 22.0000 0.842424
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 3.00000 0.114708
\(685\) −19.0000 −0.725953
\(686\) −55.0000 −2.09991
\(687\) −20.0000 −0.763048
\(688\) −1.00000 −0.0381246
\(689\) −50.0000 −1.90485
\(690\) 12.0000 0.456832
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) −9.00000 −0.342129
\(693\) 10.0000 0.379869
\(694\) −12.0000 −0.455514
\(695\) 14.0000 0.531050
\(696\) 2.00000 0.0758098
\(697\) 10.0000 0.378777
\(698\) −6.00000 −0.227103
\(699\) 28.0000 1.05906
\(700\) −5.00000 −0.188982
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) −20.0000 −0.754851
\(703\) −30.0000 −1.13147
\(704\) −2.00000 −0.0753778
\(705\) −8.00000 −0.301297
\(706\) −16.0000 −0.602168
\(707\) 70.0000 2.63262
\(708\) −16.0000 −0.601317
\(709\) 44.0000 1.65245 0.826227 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) −8.00000 −0.300235
\(711\) 7.00000 0.262521
\(712\) 6.00000 0.224860
\(713\) 66.0000 2.47172
\(714\) 20.0000 0.748481
\(715\) 10.0000 0.373979
\(716\) −15.0000 −0.560576
\(717\) −22.0000 −0.821605
\(718\) 9.00000 0.335877
\(719\) −12.0000 −0.447524 −0.223762 0.974644i \(-0.571834\pi\)
−0.223762 + 0.974644i \(0.571834\pi\)
\(720\) 1.00000 0.0372678
\(721\) 70.0000 2.60694
\(722\) −10.0000 −0.372161
\(723\) 24.0000 0.892570
\(724\) 10.0000 0.371647
\(725\) −1.00000 −0.0371391
\(726\) 14.0000 0.519589
\(727\) −4.00000 −0.148352 −0.0741759 0.997245i \(-0.523633\pi\)
−0.0741759 + 0.997245i \(0.523633\pi\)
\(728\) 25.0000 0.926562
\(729\) 13.0000 0.481481
\(730\) 7.00000 0.259082
\(731\) −2.00000 −0.0739727
\(732\) 6.00000 0.221766
\(733\) −28.0000 −1.03420 −0.517102 0.855924i \(-0.672989\pi\)
−0.517102 + 0.855924i \(0.672989\pi\)
\(734\) 28.0000 1.03350
\(735\) −36.0000 −1.32788
\(736\) −6.00000 −0.221163
\(737\) 6.00000 0.221013
\(738\) 5.00000 0.184053
\(739\) −25.0000 −0.919640 −0.459820 0.888012i \(-0.652086\pi\)
−0.459820 + 0.888012i \(0.652086\pi\)
\(740\) −10.0000 −0.367607
\(741\) 30.0000 1.10208
\(742\) −50.0000 −1.83556
\(743\) 1.00000 0.0366864 0.0183432 0.999832i \(-0.494161\pi\)
0.0183432 + 0.999832i \(0.494161\pi\)
\(744\) 22.0000 0.806559
\(745\) −23.0000 −0.842655
\(746\) 2.00000 0.0732252
\(747\) 0 0
\(748\) −4.00000 −0.146254
\(749\) 35.0000 1.27887
\(750\) −2.00000 −0.0730297
\(751\) −46.0000 −1.67856 −0.839282 0.543696i \(-0.817024\pi\)
−0.839282 + 0.543696i \(0.817024\pi\)
\(752\) 4.00000 0.145865
\(753\) −4.00000 −0.145768
\(754\) 5.00000 0.182089
\(755\) 10.0000 0.363937
\(756\) −20.0000 −0.727393
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −14.0000 −0.508503
\(759\) −24.0000 −0.871145
\(760\) 3.00000 0.108821
\(761\) −30.0000 −1.08750 −0.543750 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) −32.0000 −1.15924
\(763\) 40.0000 1.44810
\(764\) 4.00000 0.144715
\(765\) 2.00000 0.0723102
\(766\) 27.0000 0.975550
\(767\) −40.0000 −1.44432
\(768\) −2.00000 −0.0721688
\(769\) 3.00000 0.108183 0.0540914 0.998536i \(-0.482774\pi\)
0.0540914 + 0.998536i \(0.482774\pi\)
\(770\) 10.0000 0.360375
\(771\) −2.00000 −0.0720282
\(772\) 8.00000 0.287926
\(773\) −14.0000 −0.503545 −0.251773 0.967786i \(-0.581013\pi\)
−0.251773 + 0.967786i \(0.581013\pi\)
\(774\) −1.00000 −0.0359443
\(775\) −11.0000 −0.395132
\(776\) 12.0000 0.430775
\(777\) −100.000 −3.58748
\(778\) −34.0000 −1.21896
\(779\) 15.0000 0.537431
\(780\) 10.0000 0.358057
\(781\) 16.0000 0.572525
\(782\) −12.0000 −0.429119
\(783\) −4.00000 −0.142948
\(784\) 18.0000 0.642857
\(785\) −10.0000 −0.356915
\(786\) 24.0000 0.856052
\(787\) −11.0000 −0.392108 −0.196054 0.980593i \(-0.562813\pi\)
−0.196054 + 0.980593i \(0.562813\pi\)
\(788\) 7.00000 0.249365
\(789\) 6.00000 0.213606
\(790\) 7.00000 0.249049
\(791\) 75.0000 2.66669
\(792\) −2.00000 −0.0710669
\(793\) 15.0000 0.532666
\(794\) 14.0000 0.496841
\(795\) −20.0000 −0.709327
\(796\) 4.00000 0.141776
\(797\) 3.00000 0.106265 0.0531327 0.998587i \(-0.483079\pi\)
0.0531327 + 0.998587i \(0.483079\pi\)
\(798\) 30.0000 1.06199
\(799\) 8.00000 0.283020
\(800\) 1.00000 0.0353553
\(801\) 6.00000 0.212000
\(802\) 15.0000 0.529668
\(803\) −14.0000 −0.494049
\(804\) 6.00000 0.211604
\(805\) 30.0000 1.05736
\(806\) 55.0000 1.93729
\(807\) 0 0
\(808\) −14.0000 −0.492518
\(809\) −19.0000 −0.668004 −0.334002 0.942572i \(-0.608399\pi\)
−0.334002 + 0.942572i \(0.608399\pi\)
\(810\) −11.0000 −0.386501
\(811\) 1.00000 0.0351147 0.0175574 0.999846i \(-0.494411\pi\)
0.0175574 + 0.999846i \(0.494411\pi\)
\(812\) 5.00000 0.175466
\(813\) −6.00000 −0.210429
\(814\) 20.0000 0.701000
\(815\) 4.00000 0.140114
\(816\) −4.00000 −0.140028
\(817\) −3.00000 −0.104957
\(818\) −14.0000 −0.489499
\(819\) 25.0000 0.873571
\(820\) 5.00000 0.174608
\(821\) 14.0000 0.488603 0.244302 0.969699i \(-0.421441\pi\)
0.244302 + 0.969699i \(0.421441\pi\)
\(822\) 38.0000 1.32540
\(823\) −46.0000 −1.60346 −0.801730 0.597687i \(-0.796087\pi\)
−0.801730 + 0.597687i \(0.796087\pi\)
\(824\) −14.0000 −0.487713
\(825\) 4.00000 0.139262
\(826\) −40.0000 −1.39178
\(827\) −41.0000 −1.42571 −0.712855 0.701312i \(-0.752598\pi\)
−0.712855 + 0.701312i \(0.752598\pi\)
\(828\) −6.00000 −0.208514
\(829\) −11.0000 −0.382046 −0.191023 0.981586i \(-0.561180\pi\)
−0.191023 + 0.981586i \(0.561180\pi\)
\(830\) 0 0
\(831\) −16.0000 −0.555034
\(832\) −5.00000 −0.173344
\(833\) 36.0000 1.24733
\(834\) −28.0000 −0.969561
\(835\) 6.00000 0.207639
\(836\) −6.00000 −0.207514
\(837\) −44.0000 −1.52086
\(838\) 7.00000 0.241811
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 10.0000 0.345033
\(841\) −28.0000 −0.965517
\(842\) 35.0000 1.20618
\(843\) −18.0000 −0.619953
\(844\) −28.0000 −0.963800
\(845\) 12.0000 0.412813
\(846\) 4.00000 0.137523
\(847\) 35.0000 1.20261
\(848\) 10.0000 0.343401
\(849\) 58.0000 1.99055
\(850\) 2.00000 0.0685994
\(851\) 60.0000 2.05677
\(852\) 16.0000 0.548151
\(853\) −34.0000 −1.16414 −0.582069 0.813139i \(-0.697757\pi\)
−0.582069 + 0.813139i \(0.697757\pi\)
\(854\) 15.0000 0.513289
\(855\) 3.00000 0.102598
\(856\) −7.00000 −0.239255
\(857\) 10.0000 0.341593 0.170797 0.985306i \(-0.445366\pi\)
0.170797 + 0.985306i \(0.445366\pi\)
\(858\) −20.0000 −0.682789
\(859\) 13.0000 0.443554 0.221777 0.975097i \(-0.428814\pi\)
0.221777 + 0.975097i \(0.428814\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 50.0000 1.70400
\(862\) 24.0000 0.817443
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 4.00000 0.136083
\(865\) −9.00000 −0.306009
\(866\) 23.0000 0.781572
\(867\) 26.0000 0.883006
\(868\) 55.0000 1.86682
\(869\) −14.0000 −0.474917
\(870\) 2.00000 0.0678064
\(871\) 15.0000 0.508256
\(872\) −8.00000 −0.270914
\(873\) 12.0000 0.406138
\(874\) −18.0000 −0.608859
\(875\) −5.00000 −0.169031
\(876\) −14.0000 −0.473016
\(877\) −34.0000 −1.14810 −0.574049 0.818821i \(-0.694628\pi\)
−0.574049 + 0.818821i \(0.694628\pi\)
\(878\) −8.00000 −0.269987
\(879\) 12.0000 0.404750
\(880\) −2.00000 −0.0674200
\(881\) −33.0000 −1.11180 −0.555899 0.831250i \(-0.687626\pi\)
−0.555899 + 0.831250i \(0.687626\pi\)
\(882\) 18.0000 0.606092
\(883\) 1.00000 0.0336527 0.0168263 0.999858i \(-0.494644\pi\)
0.0168263 + 0.999858i \(0.494644\pi\)
\(884\) −10.0000 −0.336336
\(885\) −16.0000 −0.537834
\(886\) 31.0000 1.04147
\(887\) −17.0000 −0.570804 −0.285402 0.958408i \(-0.592127\pi\)
−0.285402 + 0.958408i \(0.592127\pi\)
\(888\) 20.0000 0.671156
\(889\) −80.0000 −2.68311
\(890\) 6.00000 0.201120
\(891\) 22.0000 0.737028
\(892\) −8.00000 −0.267860
\(893\) 12.0000 0.401565
\(894\) 46.0000 1.53847
\(895\) −15.0000 −0.501395
\(896\) −5.00000 −0.167038
\(897\) −60.0000 −2.00334
\(898\) 10.0000 0.333704
\(899\) 11.0000 0.366871
\(900\) 1.00000 0.0333333
\(901\) 20.0000 0.666297
\(902\) −10.0000 −0.332964
\(903\) −10.0000 −0.332779
\(904\) −15.0000 −0.498893
\(905\) 10.0000 0.332411
\(906\) −20.0000 −0.664455
\(907\) −33.0000 −1.09575 −0.547874 0.836561i \(-0.684562\pi\)
−0.547874 + 0.836561i \(0.684562\pi\)
\(908\) −4.00000 −0.132745
\(909\) −14.0000 −0.464351
\(910\) 25.0000 0.828742
\(911\) −52.0000 −1.72284 −0.861418 0.507896i \(-0.830423\pi\)
−0.861418 + 0.507896i \(0.830423\pi\)
\(912\) −6.00000 −0.198680
\(913\) 0 0
\(914\) 42.0000 1.38924
\(915\) 6.00000 0.198354
\(916\) 10.0000 0.330409
\(917\) 60.0000 1.98137
\(918\) 8.00000 0.264039
\(919\) 11.0000 0.362857 0.181428 0.983404i \(-0.441928\pi\)
0.181428 + 0.983404i \(0.441928\pi\)
\(920\) −6.00000 −0.197814
\(921\) −6.00000 −0.197707
\(922\) −30.0000 −0.987997
\(923\) 40.0000 1.31662
\(924\) −20.0000 −0.657952
\(925\) −10.0000 −0.328798
\(926\) 9.00000 0.295758
\(927\) −14.0000 −0.459820
\(928\) −1.00000 −0.0328266
\(929\) 34.0000 1.11550 0.557752 0.830008i \(-0.311664\pi\)
0.557752 + 0.830008i \(0.311664\pi\)
\(930\) 22.0000 0.721408
\(931\) 54.0000 1.76978
\(932\) −14.0000 −0.458585
\(933\) −50.0000 −1.63693
\(934\) −34.0000 −1.11251
\(935\) −4.00000 −0.130814
\(936\) −5.00000 −0.163430
\(937\) −18.0000 −0.588034 −0.294017 0.955800i \(-0.594992\pi\)
−0.294017 + 0.955800i \(0.594992\pi\)
\(938\) 15.0000 0.489767
\(939\) −44.0000 −1.43589
\(940\) 4.00000 0.130466
\(941\) −12.0000 −0.391189 −0.195594 0.980685i \(-0.562664\pi\)
−0.195594 + 0.980685i \(0.562664\pi\)
\(942\) 20.0000 0.651635
\(943\) −30.0000 −0.976934
\(944\) 8.00000 0.260378
\(945\) −20.0000 −0.650600
\(946\) 2.00000 0.0650256
\(947\) −33.0000 −1.07236 −0.536178 0.844105i \(-0.680132\pi\)
−0.536178 + 0.844105i \(0.680132\pi\)
\(948\) −14.0000 −0.454699
\(949\) −35.0000 −1.13615
\(950\) 3.00000 0.0973329
\(951\) 2.00000 0.0648544
\(952\) −10.0000 −0.324102
\(953\) −13.0000 −0.421111 −0.210556 0.977582i \(-0.567527\pi\)
−0.210556 + 0.977582i \(0.567527\pi\)
\(954\) 10.0000 0.323762
\(955\) 4.00000 0.129437
\(956\) 11.0000 0.355765
\(957\) −4.00000 −0.129302
\(958\) −24.0000 −0.775405
\(959\) 95.0000 3.06771
\(960\) −2.00000 −0.0645497
\(961\) 90.0000 2.90323
\(962\) 50.0000 1.61206
\(963\) −7.00000 −0.225572
\(964\) −12.0000 −0.386494
\(965\) 8.00000 0.257529
\(966\) −60.0000 −1.93047
\(967\) 52.0000 1.67221 0.836104 0.548572i \(-0.184828\pi\)
0.836104 + 0.548572i \(0.184828\pi\)
\(968\) −7.00000 −0.224989
\(969\) −12.0000 −0.385496
\(970\) 12.0000 0.385297
\(971\) 62.0000 1.98967 0.994837 0.101482i \(-0.0323585\pi\)
0.994837 + 0.101482i \(0.0323585\pi\)
\(972\) 10.0000 0.320750
\(973\) −70.0000 −2.24410
\(974\) 36.0000 1.15351
\(975\) 10.0000 0.320256
\(976\) −3.00000 −0.0960277
\(977\) −36.0000 −1.15174 −0.575871 0.817541i \(-0.695337\pi\)
−0.575871 + 0.817541i \(0.695337\pi\)
\(978\) −8.00000 −0.255812
\(979\) −12.0000 −0.383522
\(980\) 18.0000 0.574989
\(981\) −8.00000 −0.255420
\(982\) −36.0000 −1.14881
\(983\) 61.0000 1.94560 0.972799 0.231651i \(-0.0744128\pi\)
0.972799 + 0.231651i \(0.0744128\pi\)
\(984\) −10.0000 −0.318788
\(985\) 7.00000 0.223039
\(986\) −2.00000 −0.0636930
\(987\) 40.0000 1.27321
\(988\) −15.0000 −0.477214
\(989\) 6.00000 0.190789
\(990\) −2.00000 −0.0635642
\(991\) −8.00000 −0.254128 −0.127064 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) −11.0000 −0.349250
\(993\) 32.0000 1.01549
\(994\) 40.0000 1.26872
\(995\) 4.00000 0.126809
\(996\) 0 0
\(997\) −16.0000 −0.506725 −0.253363 0.967371i \(-0.581537\pi\)
−0.253363 + 0.967371i \(0.581537\pi\)
\(998\) −13.0000 −0.411508
\(999\) −40.0000 −1.26554
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 430.2.a.d.1.1 1
3.2 odd 2 3870.2.a.a.1.1 1
4.3 odd 2 3440.2.a.f.1.1 1
5.2 odd 4 2150.2.b.d.1549.2 2
5.3 odd 4 2150.2.b.d.1549.1 2
5.4 even 2 2150.2.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
430.2.a.d.1.1 1 1.1 even 1 trivial
2150.2.a.g.1.1 1 5.4 even 2
2150.2.b.d.1549.1 2 5.3 odd 4
2150.2.b.d.1549.2 2 5.2 odd 4
3440.2.a.f.1.1 1 4.3 odd 2
3870.2.a.a.1.1 1 3.2 odd 2