Properties

Label 8043.2.a.s.1.7
Level $8043$
Weight $2$
Character 8043.1
Self dual yes
Analytic conductor $64.224$
Analytic rank $0$
Dimension $50$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8043,2,Mod(1,8043)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8043, 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("8043.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8043.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: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(50\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 8043.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.33165 q^{2} -1.00000 q^{3} +3.43661 q^{4} -1.59780 q^{5} +2.33165 q^{6} -1.00000 q^{7} -3.34969 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.33165 q^{2} -1.00000 q^{3} +3.43661 q^{4} -1.59780 q^{5} +2.33165 q^{6} -1.00000 q^{7} -3.34969 q^{8} +1.00000 q^{9} +3.72551 q^{10} -5.81283 q^{11} -3.43661 q^{12} -0.402462 q^{13} +2.33165 q^{14} +1.59780 q^{15} +0.937085 q^{16} +0.289318 q^{17} -2.33165 q^{18} +4.51626 q^{19} -5.49101 q^{20} +1.00000 q^{21} +13.5535 q^{22} +7.54020 q^{23} +3.34969 q^{24} -2.44704 q^{25} +0.938402 q^{26} -1.00000 q^{27} -3.43661 q^{28} +7.97204 q^{29} -3.72551 q^{30} +5.94230 q^{31} +4.51441 q^{32} +5.81283 q^{33} -0.674591 q^{34} +1.59780 q^{35} +3.43661 q^{36} -0.443031 q^{37} -10.5303 q^{38} +0.402462 q^{39} +5.35212 q^{40} -5.28630 q^{41} -2.33165 q^{42} +9.72378 q^{43} -19.9765 q^{44} -1.59780 q^{45} -17.5811 q^{46} +3.02531 q^{47} -0.937085 q^{48} +1.00000 q^{49} +5.70566 q^{50} -0.289318 q^{51} -1.38311 q^{52} -10.7576 q^{53} +2.33165 q^{54} +9.28773 q^{55} +3.34969 q^{56} -4.51626 q^{57} -18.5880 q^{58} -2.00386 q^{59} +5.49101 q^{60} +6.76064 q^{61} -13.8554 q^{62} -1.00000 q^{63} -12.4002 q^{64} +0.643052 q^{65} -13.5535 q^{66} -4.93512 q^{67} +0.994276 q^{68} -7.54020 q^{69} -3.72551 q^{70} -12.7643 q^{71} -3.34969 q^{72} +10.1541 q^{73} +1.03300 q^{74} +2.44704 q^{75} +15.5206 q^{76} +5.81283 q^{77} -0.938402 q^{78} +2.61238 q^{79} -1.49727 q^{80} +1.00000 q^{81} +12.3258 q^{82} -16.0045 q^{83} +3.43661 q^{84} -0.462272 q^{85} -22.6725 q^{86} -7.97204 q^{87} +19.4712 q^{88} -7.22871 q^{89} +3.72551 q^{90} +0.402462 q^{91} +25.9128 q^{92} -5.94230 q^{93} -7.05398 q^{94} -7.21606 q^{95} -4.51441 q^{96} -16.6173 q^{97} -2.33165 q^{98} -5.81283 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.33165 −1.64873 −0.824364 0.566059i \(-0.808467\pi\)
−0.824364 + 0.566059i \(0.808467\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.43661 1.71831
\(5\) −1.59780 −0.714557 −0.357278 0.933998i \(-0.616295\pi\)
−0.357278 + 0.933998i \(0.616295\pi\)
\(6\) 2.33165 0.951894
\(7\) −1.00000 −0.377964
\(8\) −3.34969 −1.18429
\(9\) 1.00000 0.333333
\(10\) 3.72551 1.17811
\(11\) −5.81283 −1.75264 −0.876318 0.481734i \(-0.840007\pi\)
−0.876318 + 0.481734i \(0.840007\pi\)
\(12\) −3.43661 −0.992065
\(13\) −0.402462 −0.111623 −0.0558114 0.998441i \(-0.517775\pi\)
−0.0558114 + 0.998441i \(0.517775\pi\)
\(14\) 2.33165 0.623161
\(15\) 1.59780 0.412549
\(16\) 0.937085 0.234271
\(17\) 0.289318 0.0701700 0.0350850 0.999384i \(-0.488830\pi\)
0.0350850 + 0.999384i \(0.488830\pi\)
\(18\) −2.33165 −0.549576
\(19\) 4.51626 1.03610 0.518050 0.855350i \(-0.326658\pi\)
0.518050 + 0.855350i \(0.326658\pi\)
\(20\) −5.49101 −1.22783
\(21\) 1.00000 0.218218
\(22\) 13.5535 2.88962
\(23\) 7.54020 1.57224 0.786120 0.618074i \(-0.212087\pi\)
0.786120 + 0.618074i \(0.212087\pi\)
\(24\) 3.34969 0.683752
\(25\) −2.44704 −0.489409
\(26\) 0.938402 0.184036
\(27\) −1.00000 −0.192450
\(28\) −3.43661 −0.649459
\(29\) 7.97204 1.48037 0.740185 0.672403i \(-0.234738\pi\)
0.740185 + 0.672403i \(0.234738\pi\)
\(30\) −3.72551 −0.680182
\(31\) 5.94230 1.06727 0.533635 0.845715i \(-0.320826\pi\)
0.533635 + 0.845715i \(0.320826\pi\)
\(32\) 4.51441 0.798043
\(33\) 5.81283 1.01188
\(34\) −0.674591 −0.115691
\(35\) 1.59780 0.270077
\(36\) 3.43661 0.572769
\(37\) −0.443031 −0.0728339 −0.0364169 0.999337i \(-0.511594\pi\)
−0.0364169 + 0.999337i \(0.511594\pi\)
\(38\) −10.5303 −1.70825
\(39\) 0.402462 0.0644455
\(40\) 5.35212 0.846244
\(41\) −5.28630 −0.825581 −0.412790 0.910826i \(-0.635446\pi\)
−0.412790 + 0.910826i \(0.635446\pi\)
\(42\) −2.33165 −0.359782
\(43\) 9.72378 1.48286 0.741431 0.671029i \(-0.234147\pi\)
0.741431 + 0.671029i \(0.234147\pi\)
\(44\) −19.9765 −3.01156
\(45\) −1.59780 −0.238186
\(46\) −17.5811 −2.59220
\(47\) 3.02531 0.441287 0.220643 0.975355i \(-0.429184\pi\)
0.220643 + 0.975355i \(0.429184\pi\)
\(48\) −0.937085 −0.135257
\(49\) 1.00000 0.142857
\(50\) 5.70566 0.806903
\(51\) −0.289318 −0.0405127
\(52\) −1.38311 −0.191802
\(53\) −10.7576 −1.47767 −0.738836 0.673885i \(-0.764624\pi\)
−0.738836 + 0.673885i \(0.764624\pi\)
\(54\) 2.33165 0.317298
\(55\) 9.28773 1.25236
\(56\) 3.34969 0.447621
\(57\) −4.51626 −0.598193
\(58\) −18.5880 −2.44073
\(59\) −2.00386 −0.260881 −0.130440 0.991456i \(-0.541639\pi\)
−0.130440 + 0.991456i \(0.541639\pi\)
\(60\) 5.49101 0.708886
\(61\) 6.76064 0.865612 0.432806 0.901487i \(-0.357524\pi\)
0.432806 + 0.901487i \(0.357524\pi\)
\(62\) −13.8554 −1.75964
\(63\) −1.00000 −0.125988
\(64\) −12.4002 −1.55003
\(65\) 0.643052 0.0797608
\(66\) −13.5535 −1.66832
\(67\) −4.93512 −0.602920 −0.301460 0.953479i \(-0.597474\pi\)
−0.301460 + 0.953479i \(0.597474\pi\)
\(68\) 0.994276 0.120574
\(69\) −7.54020 −0.907734
\(70\) −3.72551 −0.445284
\(71\) −12.7643 −1.51485 −0.757424 0.652923i \(-0.773543\pi\)
−0.757424 + 0.652923i \(0.773543\pi\)
\(72\) −3.34969 −0.394764
\(73\) 10.1541 1.18844 0.594221 0.804302i \(-0.297460\pi\)
0.594221 + 0.804302i \(0.297460\pi\)
\(74\) 1.03300 0.120083
\(75\) 2.44704 0.282560
\(76\) 15.5206 1.78034
\(77\) 5.81283 0.662434
\(78\) −0.938402 −0.106253
\(79\) 2.61238 0.293916 0.146958 0.989143i \(-0.453052\pi\)
0.146958 + 0.989143i \(0.453052\pi\)
\(80\) −1.49727 −0.167400
\(81\) 1.00000 0.111111
\(82\) 12.3258 1.36116
\(83\) −16.0045 −1.75672 −0.878362 0.477995i \(-0.841364\pi\)
−0.878362 + 0.477995i \(0.841364\pi\)
\(84\) 3.43661 0.374965
\(85\) −0.462272 −0.0501405
\(86\) −22.6725 −2.44484
\(87\) −7.97204 −0.854692
\(88\) 19.4712 2.07563
\(89\) −7.22871 −0.766241 −0.383121 0.923698i \(-0.625151\pi\)
−0.383121 + 0.923698i \(0.625151\pi\)
\(90\) 3.72551 0.392703
\(91\) 0.402462 0.0421895
\(92\) 25.9128 2.70159
\(93\) −5.94230 −0.616188
\(94\) −7.05398 −0.727562
\(95\) −7.21606 −0.740352
\(96\) −4.51441 −0.460750
\(97\) −16.6173 −1.68723 −0.843617 0.536946i \(-0.819578\pi\)
−0.843617 + 0.536946i \(0.819578\pi\)
\(98\) −2.33165 −0.235533
\(99\) −5.81283 −0.584212
\(100\) −8.40955 −0.840955
\(101\) −14.3690 −1.42977 −0.714886 0.699241i \(-0.753521\pi\)
−0.714886 + 0.699241i \(0.753521\pi\)
\(102\) 0.674591 0.0667944
\(103\) −0.298231 −0.0293856 −0.0146928 0.999892i \(-0.504677\pi\)
−0.0146928 + 0.999892i \(0.504677\pi\)
\(104\) 1.34812 0.132194
\(105\) −1.59780 −0.155929
\(106\) 25.0830 2.43628
\(107\) 14.1875 1.37156 0.685779 0.727809i \(-0.259461\pi\)
0.685779 + 0.727809i \(0.259461\pi\)
\(108\) −3.43661 −0.330688
\(109\) 4.30479 0.412324 0.206162 0.978518i \(-0.433903\pi\)
0.206162 + 0.978518i \(0.433903\pi\)
\(110\) −21.6558 −2.06480
\(111\) 0.443031 0.0420506
\(112\) −0.937085 −0.0885462
\(113\) −2.54672 −0.239575 −0.119788 0.992800i \(-0.538221\pi\)
−0.119788 + 0.992800i \(0.538221\pi\)
\(114\) 10.5303 0.986257
\(115\) −12.0477 −1.12345
\(116\) 27.3968 2.54373
\(117\) −0.402462 −0.0372076
\(118\) 4.67232 0.430122
\(119\) −0.289318 −0.0265218
\(120\) −5.35212 −0.488579
\(121\) 22.7890 2.07173
\(122\) −15.7635 −1.42716
\(123\) 5.28630 0.476649
\(124\) 20.4214 1.83390
\(125\) 11.8989 1.06427
\(126\) 2.33165 0.207720
\(127\) 1.10147 0.0977397 0.0488699 0.998805i \(-0.484438\pi\)
0.0488699 + 0.998805i \(0.484438\pi\)
\(128\) 19.8842 1.75753
\(129\) −9.72378 −0.856131
\(130\) −1.49938 −0.131504
\(131\) 5.65688 0.494244 0.247122 0.968984i \(-0.420515\pi\)
0.247122 + 0.968984i \(0.420515\pi\)
\(132\) 19.9765 1.73873
\(133\) −4.51626 −0.391609
\(134\) 11.5070 0.994052
\(135\) 1.59780 0.137516
\(136\) −0.969126 −0.0831019
\(137\) −15.7632 −1.34674 −0.673372 0.739304i \(-0.735155\pi\)
−0.673372 + 0.739304i \(0.735155\pi\)
\(138\) 17.5811 1.49661
\(139\) −2.20020 −0.186618 −0.0933091 0.995637i \(-0.529744\pi\)
−0.0933091 + 0.995637i \(0.529744\pi\)
\(140\) 5.49101 0.464075
\(141\) −3.02531 −0.254777
\(142\) 29.7620 2.49758
\(143\) 2.33944 0.195634
\(144\) 0.937085 0.0780904
\(145\) −12.7377 −1.05781
\(146\) −23.6757 −1.95942
\(147\) −1.00000 −0.0824786
\(148\) −1.52253 −0.125151
\(149\) 2.52281 0.206677 0.103338 0.994646i \(-0.467048\pi\)
0.103338 + 0.994646i \(0.467048\pi\)
\(150\) −5.70566 −0.465865
\(151\) 15.6399 1.27276 0.636379 0.771376i \(-0.280431\pi\)
0.636379 + 0.771376i \(0.280431\pi\)
\(152\) −15.1280 −1.22705
\(153\) 0.289318 0.0233900
\(154\) −13.5535 −1.09217
\(155\) −9.49459 −0.762624
\(156\) 1.38311 0.110737
\(157\) 5.94452 0.474424 0.237212 0.971458i \(-0.423766\pi\)
0.237212 + 0.971458i \(0.423766\pi\)
\(158\) −6.09117 −0.484587
\(159\) 10.7576 0.853135
\(160\) −7.21312 −0.570247
\(161\) −7.54020 −0.594251
\(162\) −2.33165 −0.183192
\(163\) −22.3137 −1.74774 −0.873870 0.486159i \(-0.838398\pi\)
−0.873870 + 0.486159i \(0.838398\pi\)
\(164\) −18.1670 −1.41860
\(165\) −9.28773 −0.723049
\(166\) 37.3170 2.89636
\(167\) −3.15606 −0.244223 −0.122112 0.992516i \(-0.538967\pi\)
−0.122112 + 0.992516i \(0.538967\pi\)
\(168\) −3.34969 −0.258434
\(169\) −12.8380 −0.987540
\(170\) 1.07786 0.0826680
\(171\) 4.51626 0.345367
\(172\) 33.4169 2.54801
\(173\) 6.29175 0.478353 0.239176 0.970976i \(-0.423123\pi\)
0.239176 + 0.970976i \(0.423123\pi\)
\(174\) 18.5880 1.40916
\(175\) 2.44704 0.184979
\(176\) −5.44712 −0.410592
\(177\) 2.00386 0.150620
\(178\) 16.8548 1.26332
\(179\) 5.45653 0.407840 0.203920 0.978988i \(-0.434632\pi\)
0.203920 + 0.978988i \(0.434632\pi\)
\(180\) −5.49101 −0.409276
\(181\) 8.75810 0.650985 0.325492 0.945545i \(-0.394470\pi\)
0.325492 + 0.945545i \(0.394470\pi\)
\(182\) −0.938402 −0.0695590
\(183\) −6.76064 −0.499761
\(184\) −25.2573 −1.86199
\(185\) 0.707874 0.0520439
\(186\) 13.8554 1.01593
\(187\) −1.68176 −0.122982
\(188\) 10.3968 0.758266
\(189\) 1.00000 0.0727393
\(190\) 16.8254 1.22064
\(191\) −17.9071 −1.29571 −0.647855 0.761764i \(-0.724334\pi\)
−0.647855 + 0.761764i \(0.724334\pi\)
\(192\) 12.4002 0.894909
\(193\) 19.3215 1.39079 0.695397 0.718625i \(-0.255228\pi\)
0.695397 + 0.718625i \(0.255228\pi\)
\(194\) 38.7459 2.78179
\(195\) −0.643052 −0.0460499
\(196\) 3.43661 0.245472
\(197\) −17.5692 −1.25175 −0.625875 0.779923i \(-0.715258\pi\)
−0.625875 + 0.779923i \(0.715258\pi\)
\(198\) 13.5535 0.963207
\(199\) 23.8610 1.69146 0.845731 0.533609i \(-0.179165\pi\)
0.845731 + 0.533609i \(0.179165\pi\)
\(200\) 8.19683 0.579604
\(201\) 4.93512 0.348096
\(202\) 33.5036 2.35730
\(203\) −7.97204 −0.559527
\(204\) −0.994276 −0.0696132
\(205\) 8.44643 0.589924
\(206\) 0.695371 0.0484488
\(207\) 7.54020 0.524080
\(208\) −0.377141 −0.0261500
\(209\) −26.2522 −1.81591
\(210\) 3.72551 0.257085
\(211\) 7.01306 0.482799 0.241399 0.970426i \(-0.422394\pi\)
0.241399 + 0.970426i \(0.422394\pi\)
\(212\) −36.9698 −2.53909
\(213\) 12.7643 0.874598
\(214\) −33.0804 −2.26133
\(215\) −15.5366 −1.05959
\(216\) 3.34969 0.227917
\(217\) −5.94230 −0.403390
\(218\) −10.0373 −0.679811
\(219\) −10.1541 −0.686147
\(220\) 31.9183 2.15193
\(221\) −0.116440 −0.00783258
\(222\) −1.03300 −0.0693301
\(223\) −23.9297 −1.60245 −0.801224 0.598364i \(-0.795818\pi\)
−0.801224 + 0.598364i \(0.795818\pi\)
\(224\) −4.51441 −0.301632
\(225\) −2.44704 −0.163136
\(226\) 5.93807 0.394995
\(227\) 25.0959 1.66567 0.832836 0.553520i \(-0.186716\pi\)
0.832836 + 0.553520i \(0.186716\pi\)
\(228\) −15.5206 −1.02788
\(229\) −21.0074 −1.38821 −0.694103 0.719876i \(-0.744199\pi\)
−0.694103 + 0.719876i \(0.744199\pi\)
\(230\) 28.0911 1.85227
\(231\) −5.81283 −0.382456
\(232\) −26.7038 −1.75319
\(233\) 17.9336 1.17487 0.587436 0.809271i \(-0.300137\pi\)
0.587436 + 0.809271i \(0.300137\pi\)
\(234\) 0.938402 0.0613453
\(235\) −4.83383 −0.315324
\(236\) −6.88651 −0.448274
\(237\) −2.61238 −0.169692
\(238\) 0.674591 0.0437272
\(239\) −26.3324 −1.70330 −0.851651 0.524109i \(-0.824399\pi\)
−0.851651 + 0.524109i \(0.824399\pi\)
\(240\) 1.49727 0.0966485
\(241\) 11.6061 0.747616 0.373808 0.927506i \(-0.378052\pi\)
0.373808 + 0.927506i \(0.378052\pi\)
\(242\) −53.1361 −3.41572
\(243\) −1.00000 −0.0641500
\(244\) 23.2337 1.48739
\(245\) −1.59780 −0.102080
\(246\) −12.3258 −0.785865
\(247\) −1.81762 −0.115652
\(248\) −19.9049 −1.26396
\(249\) 16.0045 1.01425
\(250\) −27.7440 −1.75469
\(251\) 15.5574 0.981973 0.490987 0.871167i \(-0.336636\pi\)
0.490987 + 0.871167i \(0.336636\pi\)
\(252\) −3.43661 −0.216486
\(253\) −43.8299 −2.75556
\(254\) −2.56825 −0.161146
\(255\) 0.462272 0.0289486
\(256\) −21.5627 −1.34767
\(257\) 10.4359 0.650976 0.325488 0.945546i \(-0.394471\pi\)
0.325488 + 0.945546i \(0.394471\pi\)
\(258\) 22.6725 1.41153
\(259\) 0.443031 0.0275286
\(260\) 2.20992 0.137054
\(261\) 7.97204 0.493457
\(262\) −13.1899 −0.814875
\(263\) −14.7946 −0.912274 −0.456137 0.889909i \(-0.650767\pi\)
−0.456137 + 0.889909i \(0.650767\pi\)
\(264\) −19.4712 −1.19837
\(265\) 17.1885 1.05588
\(266\) 10.5303 0.645657
\(267\) 7.22871 0.442390
\(268\) −16.9601 −1.03600
\(269\) −21.5132 −1.31168 −0.655840 0.754900i \(-0.727686\pi\)
−0.655840 + 0.754900i \(0.727686\pi\)
\(270\) −3.72551 −0.226727
\(271\) −20.9775 −1.27429 −0.637145 0.770744i \(-0.719885\pi\)
−0.637145 + 0.770744i \(0.719885\pi\)
\(272\) 0.271116 0.0164388
\(273\) −0.402462 −0.0243581
\(274\) 36.7544 2.22041
\(275\) 14.2243 0.857755
\(276\) −25.9128 −1.55976
\(277\) 9.97176 0.599145 0.299572 0.954074i \(-0.403156\pi\)
0.299572 + 0.954074i \(0.403156\pi\)
\(278\) 5.13010 0.307683
\(279\) 5.94230 0.355756
\(280\) −5.35212 −0.319850
\(281\) −22.6902 −1.35358 −0.676792 0.736174i \(-0.736630\pi\)
−0.676792 + 0.736174i \(0.736630\pi\)
\(282\) 7.05398 0.420058
\(283\) 6.26616 0.372485 0.186242 0.982504i \(-0.440369\pi\)
0.186242 + 0.982504i \(0.440369\pi\)
\(284\) −43.8661 −2.60298
\(285\) 7.21606 0.427442
\(286\) −5.45477 −0.322548
\(287\) 5.28630 0.312040
\(288\) 4.51441 0.266014
\(289\) −16.9163 −0.995076
\(290\) 29.6999 1.74404
\(291\) 16.6173 0.974125
\(292\) 34.8956 2.04211
\(293\) 23.3443 1.36379 0.681893 0.731452i \(-0.261157\pi\)
0.681893 + 0.731452i \(0.261157\pi\)
\(294\) 2.33165 0.135985
\(295\) 3.20177 0.186414
\(296\) 1.48402 0.0862566
\(297\) 5.81283 0.337295
\(298\) −5.88232 −0.340754
\(299\) −3.03464 −0.175498
\(300\) 8.40955 0.485525
\(301\) −9.72378 −0.560469
\(302\) −36.4669 −2.09843
\(303\) 14.3690 0.825479
\(304\) 4.23212 0.242729
\(305\) −10.8021 −0.618528
\(306\) −0.674591 −0.0385638
\(307\) 4.85883 0.277308 0.138654 0.990341i \(-0.455722\pi\)
0.138654 + 0.990341i \(0.455722\pi\)
\(308\) 19.9765 1.13826
\(309\) 0.298231 0.0169658
\(310\) 22.1381 1.25736
\(311\) −9.25092 −0.524571 −0.262286 0.964990i \(-0.584476\pi\)
−0.262286 + 0.964990i \(0.584476\pi\)
\(312\) −1.34812 −0.0763223
\(313\) 11.2008 0.633107 0.316554 0.948575i \(-0.397474\pi\)
0.316554 + 0.948575i \(0.397474\pi\)
\(314\) −13.8606 −0.782197
\(315\) 1.59780 0.0900257
\(316\) 8.97774 0.505037
\(317\) 11.4783 0.644687 0.322343 0.946623i \(-0.395529\pi\)
0.322343 + 0.946623i \(0.395529\pi\)
\(318\) −25.0830 −1.40659
\(319\) −46.3401 −2.59455
\(320\) 19.8130 1.10758
\(321\) −14.1875 −0.791870
\(322\) 17.5811 0.979759
\(323\) 1.30664 0.0727032
\(324\) 3.43661 0.190923
\(325\) 0.984842 0.0546292
\(326\) 52.0278 2.88155
\(327\) −4.30479 −0.238055
\(328\) 17.7074 0.977730
\(329\) −3.02531 −0.166791
\(330\) 21.6558 1.19211
\(331\) 15.6860 0.862180 0.431090 0.902309i \(-0.358129\pi\)
0.431090 + 0.902309i \(0.358129\pi\)
\(332\) −55.0014 −3.01859
\(333\) −0.443031 −0.0242780
\(334\) 7.35884 0.402658
\(335\) 7.88531 0.430821
\(336\) 0.937085 0.0511222
\(337\) 18.9502 1.03228 0.516141 0.856504i \(-0.327368\pi\)
0.516141 + 0.856504i \(0.327368\pi\)
\(338\) 29.9338 1.62819
\(339\) 2.54672 0.138319
\(340\) −1.58865 −0.0861567
\(341\) −34.5416 −1.87053
\(342\) −10.5303 −0.569416
\(343\) −1.00000 −0.0539949
\(344\) −32.5716 −1.75614
\(345\) 12.0477 0.648627
\(346\) −14.6702 −0.788674
\(347\) 31.9769 1.71661 0.858305 0.513140i \(-0.171518\pi\)
0.858305 + 0.513140i \(0.171518\pi\)
\(348\) −27.3968 −1.46862
\(349\) −17.5204 −0.937846 −0.468923 0.883239i \(-0.655358\pi\)
−0.468923 + 0.883239i \(0.655358\pi\)
\(350\) −5.70566 −0.304981
\(351\) 0.402462 0.0214818
\(352\) −26.2415 −1.39868
\(353\) 33.8568 1.80202 0.901008 0.433802i \(-0.142828\pi\)
0.901008 + 0.433802i \(0.142828\pi\)
\(354\) −4.67232 −0.248331
\(355\) 20.3948 1.08245
\(356\) −24.8423 −1.31664
\(357\) 0.289318 0.0153124
\(358\) −12.7227 −0.672418
\(359\) 25.5548 1.34873 0.674366 0.738398i \(-0.264417\pi\)
0.674366 + 0.738398i \(0.264417\pi\)
\(360\) 5.35212 0.282081
\(361\) 1.39656 0.0735034
\(362\) −20.4209 −1.07330
\(363\) −22.7890 −1.19611
\(364\) 1.38311 0.0724944
\(365\) −16.2241 −0.849209
\(366\) 15.7635 0.823970
\(367\) −31.6113 −1.65010 −0.825049 0.565061i \(-0.808853\pi\)
−0.825049 + 0.565061i \(0.808853\pi\)
\(368\) 7.06581 0.368331
\(369\) −5.28630 −0.275194
\(370\) −1.65052 −0.0858063
\(371\) 10.7576 0.558508
\(372\) −20.4214 −1.05880
\(373\) 6.60783 0.342141 0.171070 0.985259i \(-0.445277\pi\)
0.171070 + 0.985259i \(0.445277\pi\)
\(374\) 3.92128 0.202765
\(375\) −11.8989 −0.614455
\(376\) −10.1338 −0.522613
\(377\) −3.20844 −0.165243
\(378\) −2.33165 −0.119927
\(379\) −15.7343 −0.808216 −0.404108 0.914711i \(-0.632418\pi\)
−0.404108 + 0.914711i \(0.632418\pi\)
\(380\) −24.7988 −1.27215
\(381\) −1.10147 −0.0564301
\(382\) 41.7531 2.13627
\(383\) 1.00000 0.0510976
\(384\) −19.8842 −1.01471
\(385\) −9.28773 −0.473346
\(386\) −45.0512 −2.29304
\(387\) 9.72378 0.494287
\(388\) −57.1073 −2.89918
\(389\) 28.7760 1.45900 0.729500 0.683981i \(-0.239753\pi\)
0.729500 + 0.683981i \(0.239753\pi\)
\(390\) 1.49938 0.0759238
\(391\) 2.18152 0.110324
\(392\) −3.34969 −0.169185
\(393\) −5.65688 −0.285352
\(394\) 40.9652 2.06380
\(395\) −4.17405 −0.210019
\(396\) −19.9765 −1.00385
\(397\) 5.37667 0.269847 0.134924 0.990856i \(-0.456921\pi\)
0.134924 + 0.990856i \(0.456921\pi\)
\(398\) −55.6357 −2.78876
\(399\) 4.51626 0.226096
\(400\) −2.29309 −0.114654
\(401\) 22.1980 1.10852 0.554258 0.832345i \(-0.313002\pi\)
0.554258 + 0.832345i \(0.313002\pi\)
\(402\) −11.5070 −0.573916
\(403\) −2.39155 −0.119132
\(404\) −49.3808 −2.45679
\(405\) −1.59780 −0.0793952
\(406\) 18.5880 0.922509
\(407\) 2.57527 0.127651
\(408\) 0.969126 0.0479789
\(409\) 20.9907 1.03792 0.518961 0.854798i \(-0.326319\pi\)
0.518961 + 0.854798i \(0.326319\pi\)
\(410\) −19.6942 −0.972625
\(411\) 15.7632 0.777542
\(412\) −1.02490 −0.0504934
\(413\) 2.00386 0.0986037
\(414\) −17.5811 −0.864066
\(415\) 25.5720 1.25528
\(416\) −1.81688 −0.0890798
\(417\) 2.20020 0.107744
\(418\) 61.2112 2.99394
\(419\) −6.88529 −0.336368 −0.168184 0.985756i \(-0.553790\pi\)
−0.168184 + 0.985756i \(0.553790\pi\)
\(420\) −5.49101 −0.267934
\(421\) 23.7414 1.15709 0.578543 0.815652i \(-0.303621\pi\)
0.578543 + 0.815652i \(0.303621\pi\)
\(422\) −16.3520 −0.796004
\(423\) 3.02531 0.147096
\(424\) 36.0346 1.75000
\(425\) −0.707975 −0.0343418
\(426\) −29.7620 −1.44198
\(427\) −6.76064 −0.327170
\(428\) 48.7570 2.35676
\(429\) −2.33944 −0.112949
\(430\) 36.2260 1.74697
\(431\) −30.9196 −1.48934 −0.744671 0.667431i \(-0.767394\pi\)
−0.744671 + 0.667431i \(0.767394\pi\)
\(432\) −0.937085 −0.0450855
\(433\) −39.3270 −1.88994 −0.944968 0.327164i \(-0.893907\pi\)
−0.944968 + 0.327164i \(0.893907\pi\)
\(434\) 13.8554 0.665080
\(435\) 12.7377 0.610726
\(436\) 14.7939 0.708499
\(437\) 34.0535 1.62900
\(438\) 23.6757 1.13127
\(439\) −32.2271 −1.53812 −0.769058 0.639179i \(-0.779274\pi\)
−0.769058 + 0.639179i \(0.779274\pi\)
\(440\) −31.1110 −1.48316
\(441\) 1.00000 0.0476190
\(442\) 0.271497 0.0129138
\(443\) −4.09684 −0.194647 −0.0973233 0.995253i \(-0.531028\pi\)
−0.0973233 + 0.995253i \(0.531028\pi\)
\(444\) 1.52253 0.0722559
\(445\) 11.5500 0.547523
\(446\) 55.7957 2.64200
\(447\) −2.52281 −0.119325
\(448\) 12.4002 0.585856
\(449\) −17.5330 −0.827434 −0.413717 0.910406i \(-0.635770\pi\)
−0.413717 + 0.910406i \(0.635770\pi\)
\(450\) 5.70566 0.268968
\(451\) 30.7284 1.44694
\(452\) −8.75209 −0.411664
\(453\) −15.6399 −0.734827
\(454\) −58.5149 −2.74624
\(455\) −0.643052 −0.0301468
\(456\) 15.1280 0.708435
\(457\) 39.3588 1.84113 0.920564 0.390593i \(-0.127730\pi\)
0.920564 + 0.390593i \(0.127730\pi\)
\(458\) 48.9819 2.28878
\(459\) −0.289318 −0.0135042
\(460\) −41.4033 −1.93044
\(461\) 22.5425 1.04991 0.524954 0.851130i \(-0.324082\pi\)
0.524954 + 0.851130i \(0.324082\pi\)
\(462\) 13.5535 0.630567
\(463\) 5.00587 0.232643 0.116321 0.993212i \(-0.462890\pi\)
0.116321 + 0.993212i \(0.462890\pi\)
\(464\) 7.47048 0.346808
\(465\) 9.49459 0.440301
\(466\) −41.8151 −1.93705
\(467\) 38.8405 1.79733 0.898663 0.438640i \(-0.144540\pi\)
0.898663 + 0.438640i \(0.144540\pi\)
\(468\) −1.38311 −0.0639341
\(469\) 4.93512 0.227883
\(470\) 11.2708 0.519884
\(471\) −5.94452 −0.273909
\(472\) 6.71232 0.308960
\(473\) −56.5227 −2.59892
\(474\) 6.09117 0.279777
\(475\) −11.0515 −0.507077
\(476\) −0.994276 −0.0455726
\(477\) −10.7576 −0.492557
\(478\) 61.3981 2.80828
\(479\) −18.8144 −0.859651 −0.429826 0.902912i \(-0.641425\pi\)
−0.429826 + 0.902912i \(0.641425\pi\)
\(480\) 7.21312 0.329232
\(481\) 0.178303 0.00812992
\(482\) −27.0615 −1.23262
\(483\) 7.54020 0.343091
\(484\) 78.3171 3.55987
\(485\) 26.5511 1.20562
\(486\) 2.33165 0.105766
\(487\) −19.6799 −0.891780 −0.445890 0.895088i \(-0.647113\pi\)
−0.445890 + 0.895088i \(0.647113\pi\)
\(488\) −22.6460 −1.02514
\(489\) 22.3137 1.00906
\(490\) 3.72551 0.168301
\(491\) −29.4916 −1.33094 −0.665469 0.746425i \(-0.731769\pi\)
−0.665469 + 0.746425i \(0.731769\pi\)
\(492\) 18.1670 0.819030
\(493\) 2.30646 0.103878
\(494\) 4.23806 0.190679
\(495\) 9.28773 0.417452
\(496\) 5.56844 0.250031
\(497\) 12.7643 0.572559
\(498\) −37.3170 −1.67222
\(499\) −36.4429 −1.63141 −0.815705 0.578469i \(-0.803650\pi\)
−0.815705 + 0.578469i \(0.803650\pi\)
\(500\) 40.8918 1.82874
\(501\) 3.15606 0.141002
\(502\) −36.2745 −1.61901
\(503\) 7.29510 0.325272 0.162636 0.986686i \(-0.448000\pi\)
0.162636 + 0.986686i \(0.448000\pi\)
\(504\) 3.34969 0.149207
\(505\) 22.9588 1.02165
\(506\) 102.196 4.54318
\(507\) 12.8380 0.570157
\(508\) 3.78533 0.167947
\(509\) 1.85074 0.0820328 0.0410164 0.999158i \(-0.486940\pi\)
0.0410164 + 0.999158i \(0.486940\pi\)
\(510\) −1.07786 −0.0477284
\(511\) −10.1541 −0.449189
\(512\) 10.5083 0.464404
\(513\) −4.51626 −0.199398
\(514\) −24.3330 −1.07328
\(515\) 0.476512 0.0209976
\(516\) −33.4169 −1.47110
\(517\) −17.5856 −0.773415
\(518\) −1.03300 −0.0453872
\(519\) −6.29175 −0.276177
\(520\) −2.15402 −0.0944602
\(521\) −19.8621 −0.870175 −0.435087 0.900388i \(-0.643283\pi\)
−0.435087 + 0.900388i \(0.643283\pi\)
\(522\) −18.5880 −0.813576
\(523\) −17.2257 −0.753228 −0.376614 0.926370i \(-0.622912\pi\)
−0.376614 + 0.926370i \(0.622912\pi\)
\(524\) 19.4405 0.849263
\(525\) −2.44704 −0.106798
\(526\) 34.4959 1.50409
\(527\) 1.71922 0.0748903
\(528\) 5.44712 0.237055
\(529\) 33.8546 1.47194
\(530\) −40.0776 −1.74086
\(531\) −2.00386 −0.0869603
\(532\) −15.5206 −0.672904
\(533\) 2.12753 0.0921537
\(534\) −16.8548 −0.729381
\(535\) −22.6688 −0.980056
\(536\) 16.5311 0.714035
\(537\) −5.45653 −0.235467
\(538\) 50.1613 2.16261
\(539\) −5.81283 −0.250376
\(540\) 5.49101 0.236295
\(541\) −20.5841 −0.884979 −0.442489 0.896774i \(-0.645905\pi\)
−0.442489 + 0.896774i \(0.645905\pi\)
\(542\) 48.9122 2.10096
\(543\) −8.75810 −0.375846
\(544\) 1.30610 0.0559987
\(545\) −6.87818 −0.294629
\(546\) 0.938402 0.0401599
\(547\) −7.29507 −0.311915 −0.155957 0.987764i \(-0.549846\pi\)
−0.155957 + 0.987764i \(0.549846\pi\)
\(548\) −54.1721 −2.31412
\(549\) 6.76064 0.288537
\(550\) −33.1661 −1.41421
\(551\) 36.0038 1.53381
\(552\) 25.2573 1.07502
\(553\) −2.61238 −0.111090
\(554\) −23.2507 −0.987827
\(555\) −0.707874 −0.0300476
\(556\) −7.56122 −0.320667
\(557\) 1.15446 0.0489158 0.0244579 0.999701i \(-0.492214\pi\)
0.0244579 + 0.999701i \(0.492214\pi\)
\(558\) −13.8554 −0.586546
\(559\) −3.91345 −0.165521
\(560\) 1.49727 0.0632713
\(561\) 1.68176 0.0710040
\(562\) 52.9057 2.23169
\(563\) −13.8671 −0.584427 −0.292213 0.956353i \(-0.594392\pi\)
−0.292213 + 0.956353i \(0.594392\pi\)
\(564\) −10.3968 −0.437785
\(565\) 4.06914 0.171190
\(566\) −14.6105 −0.614126
\(567\) −1.00000 −0.0419961
\(568\) 42.7566 1.79403
\(569\) −30.8539 −1.29346 −0.646731 0.762719i \(-0.723864\pi\)
−0.646731 + 0.762719i \(0.723864\pi\)
\(570\) −16.8254 −0.704737
\(571\) 11.0429 0.462132 0.231066 0.972938i \(-0.425779\pi\)
0.231066 + 0.972938i \(0.425779\pi\)
\(572\) 8.03976 0.336159
\(573\) 17.9071 0.748078
\(574\) −12.3258 −0.514470
\(575\) −18.4512 −0.769469
\(576\) −12.4002 −0.516676
\(577\) −18.0509 −0.751471 −0.375735 0.926727i \(-0.622610\pi\)
−0.375735 + 0.926727i \(0.622610\pi\)
\(578\) 39.4430 1.64061
\(579\) −19.3215 −0.802976
\(580\) −43.7745 −1.81764
\(581\) 16.0045 0.663980
\(582\) −38.7459 −1.60607
\(583\) 62.5322 2.58982
\(584\) −34.0129 −1.40746
\(585\) 0.643052 0.0265869
\(586\) −54.4308 −2.24851
\(587\) 27.2619 1.12522 0.562610 0.826723i \(-0.309797\pi\)
0.562610 + 0.826723i \(0.309797\pi\)
\(588\) −3.43661 −0.141724
\(589\) 26.8370 1.10580
\(590\) −7.46542 −0.307346
\(591\) 17.5692 0.722699
\(592\) −0.415158 −0.0170629
\(593\) 39.4390 1.61956 0.809782 0.586731i \(-0.199585\pi\)
0.809782 + 0.586731i \(0.199585\pi\)
\(594\) −13.5535 −0.556108
\(595\) 0.462272 0.0189513
\(596\) 8.66992 0.355134
\(597\) −23.8610 −0.976566
\(598\) 7.07574 0.289348
\(599\) −3.94542 −0.161206 −0.0806028 0.996746i \(-0.525685\pi\)
−0.0806028 + 0.996746i \(0.525685\pi\)
\(600\) −8.19683 −0.334634
\(601\) −12.3453 −0.503573 −0.251787 0.967783i \(-0.581018\pi\)
−0.251787 + 0.967783i \(0.581018\pi\)
\(602\) 22.6725 0.924062
\(603\) −4.93512 −0.200973
\(604\) 53.7484 2.18699
\(605\) −36.4122 −1.48037
\(606\) −33.5036 −1.36099
\(607\) 19.8208 0.804502 0.402251 0.915529i \(-0.368228\pi\)
0.402251 + 0.915529i \(0.368228\pi\)
\(608\) 20.3882 0.826853
\(609\) 7.97204 0.323043
\(610\) 25.1868 1.01979
\(611\) −1.21757 −0.0492577
\(612\) 0.994276 0.0401912
\(613\) −24.7199 −0.998426 −0.499213 0.866479i \(-0.666377\pi\)
−0.499213 + 0.866479i \(0.666377\pi\)
\(614\) −11.3291 −0.457206
\(615\) −8.44643 −0.340593
\(616\) −19.4712 −0.784516
\(617\) 22.0279 0.886810 0.443405 0.896321i \(-0.353770\pi\)
0.443405 + 0.896321i \(0.353770\pi\)
\(618\) −0.695371 −0.0279719
\(619\) 21.0470 0.845950 0.422975 0.906141i \(-0.360986\pi\)
0.422975 + 0.906141i \(0.360986\pi\)
\(620\) −32.6292 −1.31042
\(621\) −7.54020 −0.302578
\(622\) 21.5699 0.864876
\(623\) 7.22871 0.289612
\(624\) 0.377141 0.0150977
\(625\) −6.77675 −0.271070
\(626\) −26.1164 −1.04382
\(627\) 26.2522 1.04841
\(628\) 20.4290 0.815206
\(629\) −0.128177 −0.00511075
\(630\) −3.72551 −0.148428
\(631\) 17.7033 0.704758 0.352379 0.935857i \(-0.385373\pi\)
0.352379 + 0.935857i \(0.385373\pi\)
\(632\) −8.75065 −0.348082
\(633\) −7.01306 −0.278744
\(634\) −26.7635 −1.06291
\(635\) −1.75993 −0.0698406
\(636\) 36.9698 1.46595
\(637\) −0.402462 −0.0159461
\(638\) 108.049 4.27771
\(639\) −12.7643 −0.504950
\(640\) −31.7709 −1.25586
\(641\) 24.5713 0.970509 0.485254 0.874373i \(-0.338727\pi\)
0.485254 + 0.874373i \(0.338727\pi\)
\(642\) 33.0804 1.30558
\(643\) 12.7318 0.502092 0.251046 0.967975i \(-0.419225\pi\)
0.251046 + 0.967975i \(0.419225\pi\)
\(644\) −25.9128 −1.02111
\(645\) 15.5366 0.611754
\(646\) −3.04662 −0.119868
\(647\) 22.9617 0.902719 0.451359 0.892342i \(-0.350939\pi\)
0.451359 + 0.892342i \(0.350939\pi\)
\(648\) −3.34969 −0.131588
\(649\) 11.6481 0.457229
\(650\) −2.29631 −0.0900687
\(651\) 5.94230 0.232897
\(652\) −76.6834 −3.00316
\(653\) 9.76257 0.382039 0.191019 0.981586i \(-0.438821\pi\)
0.191019 + 0.981586i \(0.438821\pi\)
\(654\) 10.0373 0.392489
\(655\) −9.03855 −0.353165
\(656\) −4.95371 −0.193410
\(657\) 10.1541 0.396147
\(658\) 7.05398 0.274993
\(659\) −18.5259 −0.721666 −0.360833 0.932630i \(-0.617508\pi\)
−0.360833 + 0.932630i \(0.617508\pi\)
\(660\) −31.9183 −1.24242
\(661\) −13.2466 −0.515231 −0.257616 0.966247i \(-0.582937\pi\)
−0.257616 + 0.966247i \(0.582937\pi\)
\(662\) −36.5743 −1.42150
\(663\) 0.116440 0.00452214
\(664\) 53.6101 2.08048
\(665\) 7.21606 0.279827
\(666\) 1.03300 0.0400278
\(667\) 60.1108 2.32750
\(668\) −10.8462 −0.419650
\(669\) 23.9297 0.925174
\(670\) −18.3858 −0.710307
\(671\) −39.2985 −1.51710
\(672\) 4.51441 0.174147
\(673\) 45.7730 1.76442 0.882210 0.470856i \(-0.156055\pi\)
0.882210 + 0.470856i \(0.156055\pi\)
\(674\) −44.1853 −1.70195
\(675\) 2.44704 0.0941868
\(676\) −44.1193 −1.69690
\(677\) −16.7208 −0.642632 −0.321316 0.946972i \(-0.604125\pi\)
−0.321316 + 0.946972i \(0.604125\pi\)
\(678\) −5.93807 −0.228050
\(679\) 16.6173 0.637714
\(680\) 1.54847 0.0593810
\(681\) −25.0959 −0.961676
\(682\) 80.5391 3.08400
\(683\) 26.0426 0.996493 0.498246 0.867035i \(-0.333978\pi\)
0.498246 + 0.867035i \(0.333978\pi\)
\(684\) 15.5206 0.593446
\(685\) 25.1864 0.962324
\(686\) 2.33165 0.0890230
\(687\) 21.0074 0.801481
\(688\) 9.11201 0.347392
\(689\) 4.32953 0.164942
\(690\) −28.0911 −1.06941
\(691\) −17.1943 −0.654102 −0.327051 0.945007i \(-0.606055\pi\)
−0.327051 + 0.945007i \(0.606055\pi\)
\(692\) 21.6223 0.821957
\(693\) 5.81283 0.220811
\(694\) −74.5591 −2.83022
\(695\) 3.51547 0.133349
\(696\) 26.7038 1.01221
\(697\) −1.52942 −0.0579310
\(698\) 40.8515 1.54625
\(699\) −17.9336 −0.678313
\(700\) 8.40955 0.317851
\(701\) 24.0669 0.908992 0.454496 0.890749i \(-0.349819\pi\)
0.454496 + 0.890749i \(0.349819\pi\)
\(702\) −0.938402 −0.0354177
\(703\) −2.00084 −0.0754632
\(704\) 72.0804 2.71663
\(705\) 4.83383 0.182053
\(706\) −78.9424 −2.97104
\(707\) 14.3690 0.540403
\(708\) 6.88651 0.258811
\(709\) 19.6823 0.739183 0.369591 0.929194i \(-0.379498\pi\)
0.369591 + 0.929194i \(0.379498\pi\)
\(710\) −47.5537 −1.78466
\(711\) 2.61238 0.0979719
\(712\) 24.2139 0.907454
\(713\) 44.8062 1.67800
\(714\) −0.674591 −0.0252459
\(715\) −3.73796 −0.139792
\(716\) 18.7520 0.700794
\(717\) 26.3324 0.983402
\(718\) −59.5850 −2.22369
\(719\) −32.5767 −1.21491 −0.607454 0.794355i \(-0.707809\pi\)
−0.607454 + 0.794355i \(0.707809\pi\)
\(720\) −1.49727 −0.0558000
\(721\) 0.298231 0.0111067
\(722\) −3.25630 −0.121187
\(723\) −11.6061 −0.431636
\(724\) 30.0982 1.11859
\(725\) −19.5079 −0.724506
\(726\) 53.1361 1.97207
\(727\) 13.6078 0.504684 0.252342 0.967638i \(-0.418799\pi\)
0.252342 + 0.967638i \(0.418799\pi\)
\(728\) −1.34812 −0.0499647
\(729\) 1.00000 0.0370370
\(730\) 37.8290 1.40012
\(731\) 2.81327 0.104052
\(732\) −23.2337 −0.858743
\(733\) 44.3774 1.63912 0.819558 0.572996i \(-0.194219\pi\)
0.819558 + 0.572996i \(0.194219\pi\)
\(734\) 73.7067 2.72057
\(735\) 1.59780 0.0589356
\(736\) 34.0396 1.25472
\(737\) 28.6870 1.05670
\(738\) 12.3258 0.453720
\(739\) −21.6585 −0.796720 −0.398360 0.917229i \(-0.630420\pi\)
−0.398360 + 0.917229i \(0.630420\pi\)
\(740\) 2.43269 0.0894274
\(741\) 1.81762 0.0667719
\(742\) −25.0830 −0.920828
\(743\) −13.6760 −0.501726 −0.250863 0.968023i \(-0.580714\pi\)
−0.250863 + 0.968023i \(0.580714\pi\)
\(744\) 19.9049 0.729747
\(745\) −4.03094 −0.147682
\(746\) −15.4072 −0.564097
\(747\) −16.0045 −0.585575
\(748\) −5.77956 −0.211322
\(749\) −14.1875 −0.518401
\(750\) 27.7440 1.01307
\(751\) 26.2599 0.958239 0.479119 0.877750i \(-0.340956\pi\)
0.479119 + 0.877750i \(0.340956\pi\)
\(752\) 2.83497 0.103381
\(753\) −15.5574 −0.566943
\(754\) 7.48097 0.272441
\(755\) −24.9894 −0.909458
\(756\) 3.43661 0.124988
\(757\) 14.9365 0.542876 0.271438 0.962456i \(-0.412501\pi\)
0.271438 + 0.962456i \(0.412501\pi\)
\(758\) 36.6869 1.33253
\(759\) 43.8299 1.59093
\(760\) 24.1715 0.876794
\(761\) 44.1733 1.60128 0.800641 0.599144i \(-0.204492\pi\)
0.800641 + 0.599144i \(0.204492\pi\)
\(762\) 2.56825 0.0930379
\(763\) −4.30479 −0.155844
\(764\) −61.5396 −2.22643
\(765\) −0.462272 −0.0167135
\(766\) −2.33165 −0.0842461
\(767\) 0.806479 0.0291203
\(768\) 21.5627 0.778076
\(769\) −5.04610 −0.181967 −0.0909836 0.995852i \(-0.529001\pi\)
−0.0909836 + 0.995852i \(0.529001\pi\)
\(770\) 21.6558 0.780420
\(771\) −10.4359 −0.375841
\(772\) 66.4007 2.38981
\(773\) −8.47679 −0.304889 −0.152444 0.988312i \(-0.548714\pi\)
−0.152444 + 0.988312i \(0.548714\pi\)
\(774\) −22.6725 −0.814946
\(775\) −14.5411 −0.522331
\(776\) 55.6628 1.99818
\(777\) −0.443031 −0.0158936
\(778\) −67.0957 −2.40550
\(779\) −23.8743 −0.855384
\(780\) −2.20992 −0.0791279
\(781\) 74.1970 2.65498
\(782\) −5.08655 −0.181895
\(783\) −7.97204 −0.284897
\(784\) 0.937085 0.0334673
\(785\) −9.49814 −0.339003
\(786\) 13.1899 0.470468
\(787\) 13.5247 0.482103 0.241051 0.970512i \(-0.422508\pi\)
0.241051 + 0.970512i \(0.422508\pi\)
\(788\) −60.3784 −2.15089
\(789\) 14.7946 0.526702
\(790\) 9.73245 0.346265
\(791\) 2.54672 0.0905509
\(792\) 19.4712 0.691878
\(793\) −2.72090 −0.0966220
\(794\) −12.5365 −0.444905
\(795\) −17.1885 −0.609613
\(796\) 82.0011 2.90645
\(797\) 50.0068 1.77133 0.885666 0.464324i \(-0.153703\pi\)
0.885666 + 0.464324i \(0.153703\pi\)
\(798\) −10.5303 −0.372770
\(799\) 0.875278 0.0309651
\(800\) −11.0470 −0.390569
\(801\) −7.22871 −0.255414
\(802\) −51.7582 −1.82764
\(803\) −59.0238 −2.08291
\(804\) 16.9601 0.598136
\(805\) 12.0477 0.424626
\(806\) 5.57627 0.196416
\(807\) 21.5132 0.757299
\(808\) 48.1317 1.69327
\(809\) −39.4153 −1.38577 −0.692883 0.721050i \(-0.743660\pi\)
−0.692883 + 0.721050i \(0.743660\pi\)
\(810\) 3.72551 0.130901
\(811\) −43.3030 −1.52057 −0.760286 0.649588i \(-0.774941\pi\)
−0.760286 + 0.649588i \(0.774941\pi\)
\(812\) −27.3968 −0.961440
\(813\) 20.9775 0.735711
\(814\) −6.00463 −0.210462
\(815\) 35.6527 1.24886
\(816\) −0.271116 −0.00949096
\(817\) 43.9151 1.53639
\(818\) −48.9430 −1.71125
\(819\) 0.402462 0.0140632
\(820\) 29.0271 1.01367
\(821\) 13.5554 0.473085 0.236543 0.971621i \(-0.423986\pi\)
0.236543 + 0.971621i \(0.423986\pi\)
\(822\) −36.7544 −1.28196
\(823\) −15.7731 −0.549815 −0.274907 0.961471i \(-0.588647\pi\)
−0.274907 + 0.961471i \(0.588647\pi\)
\(824\) 0.998980 0.0348011
\(825\) −14.2243 −0.495225
\(826\) −4.67232 −0.162571
\(827\) 22.8042 0.792980 0.396490 0.918039i \(-0.370228\pi\)
0.396490 + 0.918039i \(0.370228\pi\)
\(828\) 25.9128 0.900531
\(829\) 43.8904 1.52438 0.762188 0.647356i \(-0.224125\pi\)
0.762188 + 0.647356i \(0.224125\pi\)
\(830\) −59.6250 −2.06962
\(831\) −9.97176 −0.345916
\(832\) 4.99062 0.173018
\(833\) 0.289318 0.0100243
\(834\) −5.13010 −0.177641
\(835\) 5.04274 0.174511
\(836\) −90.2188 −3.12028
\(837\) −5.94230 −0.205396
\(838\) 16.0541 0.554580
\(839\) −32.3666 −1.11742 −0.558710 0.829363i \(-0.688703\pi\)
−0.558710 + 0.829363i \(0.688703\pi\)
\(840\) 5.35212 0.184666
\(841\) 34.5534 1.19150
\(842\) −55.3568 −1.90772
\(843\) 22.6902 0.781492
\(844\) 24.1012 0.829596
\(845\) 20.5126 0.705653
\(846\) −7.05398 −0.242521
\(847\) −22.7890 −0.783040
\(848\) −10.0808 −0.346176
\(849\) −6.26616 −0.215054
\(850\) 1.65075 0.0566204
\(851\) −3.34054 −0.114512
\(852\) 43.8661 1.50283
\(853\) 53.9608 1.84758 0.923791 0.382898i \(-0.125074\pi\)
0.923791 + 0.382898i \(0.125074\pi\)
\(854\) 15.7635 0.539415
\(855\) −7.21606 −0.246784
\(856\) −47.5237 −1.62433
\(857\) −6.64829 −0.227101 −0.113551 0.993532i \(-0.536222\pi\)
−0.113551 + 0.993532i \(0.536222\pi\)
\(858\) 5.45477 0.186223
\(859\) 17.0555 0.581926 0.290963 0.956734i \(-0.406024\pi\)
0.290963 + 0.956734i \(0.406024\pi\)
\(860\) −53.3934 −1.82070
\(861\) −5.28630 −0.180156
\(862\) 72.0937 2.45552
\(863\) 29.0399 0.988530 0.494265 0.869311i \(-0.335437\pi\)
0.494265 + 0.869311i \(0.335437\pi\)
\(864\) −4.51441 −0.153583
\(865\) −10.0529 −0.341810
\(866\) 91.6970 3.11599
\(867\) 16.9163 0.574507
\(868\) −20.4214 −0.693147
\(869\) −15.1853 −0.515127
\(870\) −29.6999 −1.00692
\(871\) 1.98620 0.0672997
\(872\) −14.4197 −0.488313
\(873\) −16.6173 −0.562411
\(874\) −79.4009 −2.68578
\(875\) −11.8989 −0.402255
\(876\) −34.8956 −1.17901
\(877\) 8.85278 0.298937 0.149469 0.988766i \(-0.452244\pi\)
0.149469 + 0.988766i \(0.452244\pi\)
\(878\) 75.1425 2.53594
\(879\) −23.3443 −0.787382
\(880\) 8.70339 0.293391
\(881\) −44.5240 −1.50005 −0.750026 0.661409i \(-0.769959\pi\)
−0.750026 + 0.661409i \(0.769959\pi\)
\(882\) −2.33165 −0.0785109
\(883\) 4.16684 0.140225 0.0701127 0.997539i \(-0.477664\pi\)
0.0701127 + 0.997539i \(0.477664\pi\)
\(884\) −0.400158 −0.0134588
\(885\) −3.20177 −0.107626
\(886\) 9.55241 0.320919
\(887\) 14.1528 0.475205 0.237602 0.971363i \(-0.423639\pi\)
0.237602 + 0.971363i \(0.423639\pi\)
\(888\) −1.48402 −0.0498003
\(889\) −1.10147 −0.0369421
\(890\) −26.9306 −0.902717
\(891\) −5.81283 −0.194737
\(892\) −82.2370 −2.75350
\(893\) 13.6631 0.457217
\(894\) 5.88232 0.196734
\(895\) −8.71842 −0.291425
\(896\) −19.8842 −0.664285
\(897\) 3.03464 0.101324
\(898\) 40.8809 1.36421
\(899\) 47.3723 1.57995
\(900\) −8.40955 −0.280318
\(901\) −3.11238 −0.103688
\(902\) −71.6479 −2.38561
\(903\) 9.72378 0.323587
\(904\) 8.53071 0.283727
\(905\) −13.9937 −0.465165
\(906\) 36.4669 1.21153
\(907\) −17.2412 −0.572483 −0.286242 0.958157i \(-0.592406\pi\)
−0.286242 + 0.958157i \(0.592406\pi\)
\(908\) 86.2448 2.86213
\(909\) −14.3690 −0.476590
\(910\) 1.49938 0.0497038
\(911\) 10.6056 0.351380 0.175690 0.984446i \(-0.443784\pi\)
0.175690 + 0.984446i \(0.443784\pi\)
\(912\) −4.23212 −0.140139
\(913\) 93.0316 3.07890
\(914\) −91.7711 −3.03552
\(915\) 10.8021 0.357108
\(916\) −72.1942 −2.38536
\(917\) −5.65688 −0.186807
\(918\) 0.674591 0.0222648
\(919\) −27.1277 −0.894861 −0.447431 0.894319i \(-0.647661\pi\)
−0.447431 + 0.894319i \(0.647661\pi\)
\(920\) 40.3561 1.33050
\(921\) −4.85883 −0.160104
\(922\) −52.5613 −1.73101
\(923\) 5.13716 0.169092
\(924\) −19.9765 −0.657177
\(925\) 1.08412 0.0356455
\(926\) −11.6720 −0.383565
\(927\) −0.298231 −0.00979518
\(928\) 35.9891 1.18140
\(929\) 23.0252 0.755431 0.377715 0.925922i \(-0.376710\pi\)
0.377715 + 0.925922i \(0.376710\pi\)
\(930\) −22.1381 −0.725937
\(931\) 4.51626 0.148014
\(932\) 61.6310 2.01879
\(933\) 9.25092 0.302861
\(934\) −90.5627 −2.96330
\(935\) 2.68711 0.0878779
\(936\) 1.34812 0.0440647
\(937\) 33.7275 1.10183 0.550915 0.834561i \(-0.314279\pi\)
0.550915 + 0.834561i \(0.314279\pi\)
\(938\) −11.5070 −0.375716
\(939\) −11.2008 −0.365525
\(940\) −16.6120 −0.541824
\(941\) −50.9437 −1.66072 −0.830359 0.557228i \(-0.811865\pi\)
−0.830359 + 0.557228i \(0.811865\pi\)
\(942\) 13.8606 0.451602
\(943\) −39.8597 −1.29801
\(944\) −1.87779 −0.0611169
\(945\) −1.59780 −0.0519763
\(946\) 131.791 4.28491
\(947\) −59.5145 −1.93396 −0.966980 0.254853i \(-0.917973\pi\)
−0.966980 + 0.254853i \(0.917973\pi\)
\(948\) −8.97774 −0.291583
\(949\) −4.08662 −0.132657
\(950\) 25.7682 0.836032
\(951\) −11.4783 −0.372210
\(952\) 0.969126 0.0314096
\(953\) −21.4127 −0.693625 −0.346812 0.937935i \(-0.612736\pi\)
−0.346812 + 0.937935i \(0.612736\pi\)
\(954\) 25.0830 0.812094
\(955\) 28.6118 0.925858
\(956\) −90.4944 −2.92680
\(957\) 46.3401 1.49796
\(958\) 43.8686 1.41733
\(959\) 15.7632 0.509021
\(960\) −19.8130 −0.639463
\(961\) 4.31096 0.139063
\(962\) −0.415741 −0.0134040
\(963\) 14.1875 0.457186
\(964\) 39.8858 1.28463
\(965\) −30.8719 −0.993802
\(966\) −17.5811 −0.565664
\(967\) −35.8832 −1.15392 −0.576962 0.816771i \(-0.695762\pi\)
−0.576962 + 0.816771i \(0.695762\pi\)
\(968\) −76.3361 −2.45353
\(969\) −1.30664 −0.0419752
\(970\) −61.9080 −1.98775
\(971\) 51.9947 1.66859 0.834295 0.551319i \(-0.185875\pi\)
0.834295 + 0.551319i \(0.185875\pi\)
\(972\) −3.43661 −0.110229
\(973\) 2.20020 0.0705350
\(974\) 45.8867 1.47030
\(975\) −0.984842 −0.0315402
\(976\) 6.33530 0.202788
\(977\) 24.4196 0.781252 0.390626 0.920550i \(-0.372259\pi\)
0.390626 + 0.920550i \(0.372259\pi\)
\(978\) −52.0278 −1.66366
\(979\) 42.0193 1.34294
\(980\) −5.49101 −0.175404
\(981\) 4.30479 0.137441
\(982\) 68.7643 2.19436
\(983\) 25.3920 0.809880 0.404940 0.914343i \(-0.367292\pi\)
0.404940 + 0.914343i \(0.367292\pi\)
\(984\) −17.7074 −0.564492
\(985\) 28.0720 0.894447
\(986\) −5.37786 −0.171266
\(987\) 3.02531 0.0962967
\(988\) −6.24646 −0.198726
\(989\) 73.3192 2.33142
\(990\) −21.6558 −0.688266
\(991\) 11.2458 0.357236 0.178618 0.983918i \(-0.442837\pi\)
0.178618 + 0.983918i \(0.442837\pi\)
\(992\) 26.8260 0.851727
\(993\) −15.6860 −0.497780
\(994\) −29.7620 −0.943995
\(995\) −38.1251 −1.20865
\(996\) 55.0014 1.74279
\(997\) 36.4242 1.15357 0.576783 0.816898i \(-0.304308\pi\)
0.576783 + 0.816898i \(0.304308\pi\)
\(998\) 84.9723 2.68975
\(999\) 0.443031 0.0140169
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 8043.2.a.s.1.7 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8043.2.a.s.1.7 50 1.1 even 1 trivial