Properties

Label 8042.2.a.a.1.63
Level $8042$
Weight $2$
Character 8042.1
Self dual yes
Analytic conductor $64.216$
Analytic rank $1$
Dimension $67$
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] = [8042,2,Mod(1,8042)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8042, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8042.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8042.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: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.63
Character \(\chi\) \(=\) 8042.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.47283 q^{3} +1.00000 q^{4} +0.183201 q^{5} +2.47283 q^{6} -1.10885 q^{7} +1.00000 q^{8} +3.11487 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.47283 q^{3} +1.00000 q^{4} +0.183201 q^{5} +2.47283 q^{6} -1.10885 q^{7} +1.00000 q^{8} +3.11487 q^{9} +0.183201 q^{10} -6.09305 q^{11} +2.47283 q^{12} +0.147267 q^{13} -1.10885 q^{14} +0.453025 q^{15} +1.00000 q^{16} -2.55699 q^{17} +3.11487 q^{18} -2.37200 q^{19} +0.183201 q^{20} -2.74200 q^{21} -6.09305 q^{22} -3.26269 q^{23} +2.47283 q^{24} -4.96644 q^{25} +0.147267 q^{26} +0.284055 q^{27} -1.10885 q^{28} +1.03517 q^{29} +0.453025 q^{30} +3.46406 q^{31} +1.00000 q^{32} -15.0671 q^{33} -2.55699 q^{34} -0.203143 q^{35} +3.11487 q^{36} +3.31986 q^{37} -2.37200 q^{38} +0.364165 q^{39} +0.183201 q^{40} -10.1172 q^{41} -2.74200 q^{42} -5.55485 q^{43} -6.09305 q^{44} +0.570648 q^{45} -3.26269 q^{46} +1.64994 q^{47} +2.47283 q^{48} -5.77045 q^{49} -4.96644 q^{50} -6.32298 q^{51} +0.147267 q^{52} +2.63040 q^{53} +0.284055 q^{54} -1.11625 q^{55} -1.10885 q^{56} -5.86554 q^{57} +1.03517 q^{58} -4.61993 q^{59} +0.453025 q^{60} +6.45638 q^{61} +3.46406 q^{62} -3.45393 q^{63} +1.00000 q^{64} +0.0269795 q^{65} -15.0671 q^{66} +8.78722 q^{67} -2.55699 q^{68} -8.06807 q^{69} -0.203143 q^{70} -0.468330 q^{71} +3.11487 q^{72} -13.3090 q^{73} +3.31986 q^{74} -12.2811 q^{75} -2.37200 q^{76} +6.75629 q^{77} +0.364165 q^{78} +8.13638 q^{79} +0.183201 q^{80} -8.64219 q^{81} -10.1172 q^{82} -10.0982 q^{83} -2.74200 q^{84} -0.468443 q^{85} -5.55485 q^{86} +2.55978 q^{87} -6.09305 q^{88} +17.2007 q^{89} +0.570648 q^{90} -0.163297 q^{91} -3.26269 q^{92} +8.56602 q^{93} +1.64994 q^{94} -0.434553 q^{95} +2.47283 q^{96} -9.50991 q^{97} -5.77045 q^{98} -18.9791 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9} - 20 q^{10} - 13 q^{11} - 11 q^{12} - 51 q^{13} - 40 q^{14} - 31 q^{15} + 67 q^{16} - 34 q^{17} + 24 q^{18} - 33 q^{19} - 20 q^{20} - 39 q^{21} - 13 q^{22} - 43 q^{23} - 11 q^{24} - 9 q^{25} - 51 q^{26} - 29 q^{27} - 40 q^{28} - 63 q^{29} - 31 q^{30} - 43 q^{31} + 67 q^{32} - 49 q^{33} - 34 q^{34} - 20 q^{35} + 24 q^{36} - 77 q^{37} - 33 q^{38} - 40 q^{39} - 20 q^{40} - 50 q^{41} - 39 q^{42} - 56 q^{43} - 13 q^{44} - 48 q^{45} - 43 q^{46} - 48 q^{47} - 11 q^{48} + q^{49} - 9 q^{50} - 18 q^{51} - 51 q^{52} - 91 q^{53} - 29 q^{54} - 58 q^{55} - 40 q^{56} - 65 q^{57} - 63 q^{58} - 17 q^{59} - 31 q^{60} - 45 q^{61} - 43 q^{62} - 67 q^{63} + 67 q^{64} - 65 q^{65} - 49 q^{66} - 112 q^{67} - 34 q^{68} - 57 q^{69} - 20 q^{70} - 75 q^{71} + 24 q^{72} - 79 q^{73} - 77 q^{74} - 5 q^{75} - 33 q^{76} - 85 q^{77} - 40 q^{78} - 80 q^{79} - 20 q^{80} - 77 q^{81} - 50 q^{82} - 22 q^{83} - 39 q^{84} - 134 q^{85} - 56 q^{86} - 49 q^{87} - 13 q^{88} - 77 q^{89} - 48 q^{90} - 17 q^{91} - 43 q^{92} - 97 q^{93} - 48 q^{94} - 73 q^{95} - 11 q^{96} - 87 q^{97} + q^{98} - 44 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 2.47283 1.42769 0.713843 0.700305i \(-0.246953\pi\)
0.713843 + 0.700305i \(0.246953\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.183201 0.0819301 0.0409650 0.999161i \(-0.486957\pi\)
0.0409650 + 0.999161i \(0.486957\pi\)
\(6\) 2.47283 1.00953
\(7\) −1.10885 −0.419107 −0.209553 0.977797i \(-0.567201\pi\)
−0.209553 + 0.977797i \(0.567201\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.11487 1.03829
\(10\) 0.183201 0.0579333
\(11\) −6.09305 −1.83712 −0.918562 0.395278i \(-0.870648\pi\)
−0.918562 + 0.395278i \(0.870648\pi\)
\(12\) 2.47283 0.713843
\(13\) 0.147267 0.0408445 0.0204222 0.999791i \(-0.493499\pi\)
0.0204222 + 0.999791i \(0.493499\pi\)
\(14\) −1.10885 −0.296353
\(15\) 0.453025 0.116970
\(16\) 1.00000 0.250000
\(17\) −2.55699 −0.620160 −0.310080 0.950710i \(-0.600356\pi\)
−0.310080 + 0.950710i \(0.600356\pi\)
\(18\) 3.11487 0.734182
\(19\) −2.37200 −0.544174 −0.272087 0.962273i \(-0.587714\pi\)
−0.272087 + 0.962273i \(0.587714\pi\)
\(20\) 0.183201 0.0409650
\(21\) −2.74200 −0.598353
\(22\) −6.09305 −1.29904
\(23\) −3.26269 −0.680318 −0.340159 0.940368i \(-0.610481\pi\)
−0.340159 + 0.940368i \(0.610481\pi\)
\(24\) 2.47283 0.504764
\(25\) −4.96644 −0.993287
\(26\) 0.147267 0.0288814
\(27\) 0.284055 0.0546664
\(28\) −1.10885 −0.209553
\(29\) 1.03517 0.192225 0.0961127 0.995370i \(-0.469359\pi\)
0.0961127 + 0.995370i \(0.469359\pi\)
\(30\) 0.453025 0.0827106
\(31\) 3.46406 0.622164 0.311082 0.950383i \(-0.399309\pi\)
0.311082 + 0.950383i \(0.399309\pi\)
\(32\) 1.00000 0.176777
\(33\) −15.0671 −2.62284
\(34\) −2.55699 −0.438520
\(35\) −0.203143 −0.0343374
\(36\) 3.11487 0.519145
\(37\) 3.31986 0.545781 0.272891 0.962045i \(-0.412020\pi\)
0.272891 + 0.962045i \(0.412020\pi\)
\(38\) −2.37200 −0.384789
\(39\) 0.364165 0.0583131
\(40\) 0.183201 0.0289667
\(41\) −10.1172 −1.58005 −0.790023 0.613077i \(-0.789931\pi\)
−0.790023 + 0.613077i \(0.789931\pi\)
\(42\) −2.74200 −0.423099
\(43\) −5.55485 −0.847107 −0.423553 0.905871i \(-0.639217\pi\)
−0.423553 + 0.905871i \(0.639217\pi\)
\(44\) −6.09305 −0.918562
\(45\) 0.570648 0.0850672
\(46\) −3.26269 −0.481058
\(47\) 1.64994 0.240669 0.120334 0.992733i \(-0.461603\pi\)
0.120334 + 0.992733i \(0.461603\pi\)
\(48\) 2.47283 0.356922
\(49\) −5.77045 −0.824350
\(50\) −4.96644 −0.702360
\(51\) −6.32298 −0.885395
\(52\) 0.147267 0.0204222
\(53\) 2.63040 0.361313 0.180657 0.983546i \(-0.442178\pi\)
0.180657 + 0.983546i \(0.442178\pi\)
\(54\) 0.284055 0.0386550
\(55\) −1.11625 −0.150516
\(56\) −1.10885 −0.148177
\(57\) −5.86554 −0.776910
\(58\) 1.03517 0.135924
\(59\) −4.61993 −0.601463 −0.300732 0.953709i \(-0.597231\pi\)
−0.300732 + 0.953709i \(0.597231\pi\)
\(60\) 0.453025 0.0584852
\(61\) 6.45638 0.826654 0.413327 0.910583i \(-0.364367\pi\)
0.413327 + 0.910583i \(0.364367\pi\)
\(62\) 3.46406 0.439936
\(63\) −3.45393 −0.435154
\(64\) 1.00000 0.125000
\(65\) 0.0269795 0.00334639
\(66\) −15.0671 −1.85463
\(67\) 8.78722 1.07353 0.536765 0.843732i \(-0.319646\pi\)
0.536765 + 0.843732i \(0.319646\pi\)
\(68\) −2.55699 −0.310080
\(69\) −8.06807 −0.971282
\(70\) −0.203143 −0.0242802
\(71\) −0.468330 −0.0555806 −0.0277903 0.999614i \(-0.508847\pi\)
−0.0277903 + 0.999614i \(0.508847\pi\)
\(72\) 3.11487 0.367091
\(73\) −13.3090 −1.55770 −0.778848 0.627213i \(-0.784196\pi\)
−0.778848 + 0.627213i \(0.784196\pi\)
\(74\) 3.31986 0.385926
\(75\) −12.2811 −1.41810
\(76\) −2.37200 −0.272087
\(77\) 6.75629 0.769950
\(78\) 0.364165 0.0412336
\(79\) 8.13638 0.915414 0.457707 0.889103i \(-0.348671\pi\)
0.457707 + 0.889103i \(0.348671\pi\)
\(80\) 0.183201 0.0204825
\(81\) −8.64219 −0.960244
\(82\) −10.1172 −1.11726
\(83\) −10.0982 −1.10842 −0.554211 0.832376i \(-0.686980\pi\)
−0.554211 + 0.832376i \(0.686980\pi\)
\(84\) −2.74200 −0.299176
\(85\) −0.468443 −0.0508098
\(86\) −5.55485 −0.598995
\(87\) 2.55978 0.274438
\(88\) −6.09305 −0.649521
\(89\) 17.2007 1.82327 0.911634 0.411004i \(-0.134822\pi\)
0.911634 + 0.411004i \(0.134822\pi\)
\(90\) 0.570648 0.0601516
\(91\) −0.163297 −0.0171182
\(92\) −3.26269 −0.340159
\(93\) 8.56602 0.888255
\(94\) 1.64994 0.170179
\(95\) −0.434553 −0.0445842
\(96\) 2.47283 0.252382
\(97\) −9.50991 −0.965585 −0.482793 0.875735i \(-0.660378\pi\)
−0.482793 + 0.875735i \(0.660378\pi\)
\(98\) −5.77045 −0.582903
\(99\) −18.9791 −1.90747
\(100\) −4.96644 −0.496644
\(101\) 16.1242 1.60442 0.802210 0.597042i \(-0.203657\pi\)
0.802210 + 0.597042i \(0.203657\pi\)
\(102\) −6.32298 −0.626069
\(103\) −5.38319 −0.530422 −0.265211 0.964190i \(-0.585442\pi\)
−0.265211 + 0.964190i \(0.585442\pi\)
\(104\) 0.147267 0.0144407
\(105\) −0.502337 −0.0490231
\(106\) 2.63040 0.255487
\(107\) −3.46803 −0.335267 −0.167634 0.985849i \(-0.553613\pi\)
−0.167634 + 0.985849i \(0.553613\pi\)
\(108\) 0.284055 0.0273332
\(109\) −7.14898 −0.684748 −0.342374 0.939564i \(-0.611231\pi\)
−0.342374 + 0.939564i \(0.611231\pi\)
\(110\) −1.11625 −0.106431
\(111\) 8.20943 0.779205
\(112\) −1.10885 −0.104777
\(113\) −4.43458 −0.417170 −0.208585 0.978004i \(-0.566886\pi\)
−0.208585 + 0.978004i \(0.566886\pi\)
\(114\) −5.86554 −0.549359
\(115\) −0.597729 −0.0557385
\(116\) 1.03517 0.0961127
\(117\) 0.458717 0.0424084
\(118\) −4.61993 −0.425299
\(119\) 2.83532 0.259913
\(120\) 0.453025 0.0413553
\(121\) 26.1252 2.37502
\(122\) 6.45638 0.584533
\(123\) −25.0182 −2.25581
\(124\) 3.46406 0.311082
\(125\) −1.82586 −0.163310
\(126\) −3.45393 −0.307700
\(127\) −20.5120 −1.82014 −0.910071 0.414453i \(-0.863973\pi\)
−0.910071 + 0.414453i \(0.863973\pi\)
\(128\) 1.00000 0.0883883
\(129\) −13.7362 −1.20940
\(130\) 0.0269795 0.00236626
\(131\) 9.46249 0.826742 0.413371 0.910563i \(-0.364351\pi\)
0.413371 + 0.910563i \(0.364351\pi\)
\(132\) −15.0671 −1.31142
\(133\) 2.63020 0.228067
\(134\) 8.78722 0.759100
\(135\) 0.0520392 0.00447882
\(136\) −2.55699 −0.219260
\(137\) 6.24595 0.533627 0.266814 0.963748i \(-0.414029\pi\)
0.266814 + 0.963748i \(0.414029\pi\)
\(138\) −8.06807 −0.686800
\(139\) 7.54672 0.640104 0.320052 0.947400i \(-0.396300\pi\)
0.320052 + 0.947400i \(0.396300\pi\)
\(140\) −0.203143 −0.0171687
\(141\) 4.08002 0.343600
\(142\) −0.468330 −0.0393014
\(143\) −0.897304 −0.0750363
\(144\) 3.11487 0.259573
\(145\) 0.189643 0.0157490
\(146\) −13.3090 −1.10146
\(147\) −14.2693 −1.17691
\(148\) 3.31986 0.272891
\(149\) 6.14251 0.503214 0.251607 0.967829i \(-0.419041\pi\)
0.251607 + 0.967829i \(0.419041\pi\)
\(150\) −12.2811 −1.00275
\(151\) 8.45338 0.687926 0.343963 0.938983i \(-0.388231\pi\)
0.343963 + 0.938983i \(0.388231\pi\)
\(152\) −2.37200 −0.192395
\(153\) −7.96468 −0.643906
\(154\) 6.75629 0.544437
\(155\) 0.634620 0.0509739
\(156\) 0.364165 0.0291566
\(157\) −14.5966 −1.16493 −0.582467 0.812855i \(-0.697912\pi\)
−0.582467 + 0.812855i \(0.697912\pi\)
\(158\) 8.13638 0.647295
\(159\) 6.50452 0.515842
\(160\) 0.183201 0.0144833
\(161\) 3.61784 0.285126
\(162\) −8.64219 −0.678995
\(163\) −3.38562 −0.265182 −0.132591 0.991171i \(-0.542330\pi\)
−0.132591 + 0.991171i \(0.542330\pi\)
\(164\) −10.1172 −0.790023
\(165\) −2.76030 −0.214889
\(166\) −10.0982 −0.783773
\(167\) 15.2464 1.17981 0.589903 0.807474i \(-0.299166\pi\)
0.589903 + 0.807474i \(0.299166\pi\)
\(168\) −2.74200 −0.211550
\(169\) −12.9783 −0.998332
\(170\) −0.468443 −0.0359279
\(171\) −7.38847 −0.565011
\(172\) −5.55485 −0.423553
\(173\) −6.34616 −0.482489 −0.241245 0.970464i \(-0.577556\pi\)
−0.241245 + 0.970464i \(0.577556\pi\)
\(174\) 2.55978 0.194057
\(175\) 5.50704 0.416293
\(176\) −6.09305 −0.459281
\(177\) −11.4243 −0.858701
\(178\) 17.2007 1.28924
\(179\) 11.4406 0.855109 0.427555 0.903990i \(-0.359375\pi\)
0.427555 + 0.903990i \(0.359375\pi\)
\(180\) 0.570648 0.0425336
\(181\) 7.37118 0.547896 0.273948 0.961745i \(-0.411670\pi\)
0.273948 + 0.961745i \(0.411670\pi\)
\(182\) −0.163297 −0.0121044
\(183\) 15.9655 1.18020
\(184\) −3.26269 −0.240529
\(185\) 0.608202 0.0447159
\(186\) 8.56602 0.628091
\(187\) 15.5798 1.13931
\(188\) 1.64994 0.120334
\(189\) −0.314975 −0.0229110
\(190\) −0.434553 −0.0315258
\(191\) 12.3229 0.891656 0.445828 0.895119i \(-0.352909\pi\)
0.445828 + 0.895119i \(0.352909\pi\)
\(192\) 2.47283 0.178461
\(193\) −23.3237 −1.67887 −0.839437 0.543457i \(-0.817115\pi\)
−0.839437 + 0.543457i \(0.817115\pi\)
\(194\) −9.50991 −0.682772
\(195\) 0.0667155 0.00477760
\(196\) −5.77045 −0.412175
\(197\) −17.6664 −1.25868 −0.629341 0.777130i \(-0.716675\pi\)
−0.629341 + 0.777130i \(0.716675\pi\)
\(198\) −18.9791 −1.34878
\(199\) −11.2536 −0.797748 −0.398874 0.917006i \(-0.630599\pi\)
−0.398874 + 0.917006i \(0.630599\pi\)
\(200\) −4.96644 −0.351180
\(201\) 21.7293 1.53266
\(202\) 16.1242 1.13450
\(203\) −1.14784 −0.0805629
\(204\) −6.32298 −0.442697
\(205\) −1.85349 −0.129453
\(206\) −5.38319 −0.375065
\(207\) −10.1629 −0.706368
\(208\) 0.147267 0.0102111
\(209\) 14.4527 0.999715
\(210\) −0.502337 −0.0346646
\(211\) 10.2433 0.705177 0.352588 0.935779i \(-0.385302\pi\)
0.352588 + 0.935779i \(0.385302\pi\)
\(212\) 2.63040 0.180657
\(213\) −1.15810 −0.0793517
\(214\) −3.46803 −0.237070
\(215\) −1.01766 −0.0694035
\(216\) 0.284055 0.0193275
\(217\) −3.84113 −0.260753
\(218\) −7.14898 −0.484190
\(219\) −32.9107 −2.22390
\(220\) −1.11625 −0.0752578
\(221\) −0.376559 −0.0253301
\(222\) 8.20943 0.550981
\(223\) 12.9734 0.868760 0.434380 0.900730i \(-0.356967\pi\)
0.434380 + 0.900730i \(0.356967\pi\)
\(224\) −1.10885 −0.0740883
\(225\) −15.4698 −1.03132
\(226\) −4.43458 −0.294984
\(227\) −22.7690 −1.51123 −0.755616 0.655015i \(-0.772662\pi\)
−0.755616 + 0.655015i \(0.772662\pi\)
\(228\) −5.86554 −0.388455
\(229\) −2.30148 −0.152086 −0.0760430 0.997105i \(-0.524229\pi\)
−0.0760430 + 0.997105i \(0.524229\pi\)
\(230\) −0.597729 −0.0394131
\(231\) 16.7071 1.09925
\(232\) 1.03517 0.0679619
\(233\) 21.4748 1.40686 0.703430 0.710764i \(-0.251651\pi\)
0.703430 + 0.710764i \(0.251651\pi\)
\(234\) 0.458717 0.0299873
\(235\) 0.302272 0.0197180
\(236\) −4.61993 −0.300732
\(237\) 20.1198 1.30692
\(238\) 2.83532 0.183786
\(239\) −7.14563 −0.462213 −0.231106 0.972929i \(-0.574235\pi\)
−0.231106 + 0.972929i \(0.574235\pi\)
\(240\) 0.453025 0.0292426
\(241\) 0.514479 0.0331405 0.0165703 0.999863i \(-0.494725\pi\)
0.0165703 + 0.999863i \(0.494725\pi\)
\(242\) 26.1252 1.67939
\(243\) −22.2228 −1.42559
\(244\) 6.45638 0.413327
\(245\) −1.05715 −0.0675390
\(246\) −25.0182 −1.59510
\(247\) −0.349317 −0.0222265
\(248\) 3.46406 0.219968
\(249\) −24.9711 −1.58248
\(250\) −1.82586 −0.115478
\(251\) −8.33417 −0.526048 −0.263024 0.964789i \(-0.584720\pi\)
−0.263024 + 0.964789i \(0.584720\pi\)
\(252\) −3.45393 −0.217577
\(253\) 19.8797 1.24983
\(254\) −20.5120 −1.28703
\(255\) −1.15838 −0.0725405
\(256\) 1.00000 0.0625000
\(257\) 28.2387 1.76148 0.880742 0.473596i \(-0.157044\pi\)
0.880742 + 0.473596i \(0.157044\pi\)
\(258\) −13.7362 −0.855177
\(259\) −3.68123 −0.228741
\(260\) 0.0269795 0.00167320
\(261\) 3.22441 0.199586
\(262\) 9.46249 0.584595
\(263\) 17.7534 1.09472 0.547360 0.836897i \(-0.315633\pi\)
0.547360 + 0.836897i \(0.315633\pi\)
\(264\) −15.0671 −0.927313
\(265\) 0.481893 0.0296024
\(266\) 2.63020 0.161268
\(267\) 42.5343 2.60306
\(268\) 8.78722 0.536765
\(269\) 6.26438 0.381946 0.190973 0.981595i \(-0.438836\pi\)
0.190973 + 0.981595i \(0.438836\pi\)
\(270\) 0.0520392 0.00316700
\(271\) 10.3591 0.629271 0.314636 0.949212i \(-0.398118\pi\)
0.314636 + 0.949212i \(0.398118\pi\)
\(272\) −2.55699 −0.155040
\(273\) −0.403805 −0.0244394
\(274\) 6.24595 0.377332
\(275\) 30.2607 1.82479
\(276\) −8.06807 −0.485641
\(277\) −23.9326 −1.43797 −0.718985 0.695026i \(-0.755393\pi\)
−0.718985 + 0.695026i \(0.755393\pi\)
\(278\) 7.54672 0.452622
\(279\) 10.7901 0.645986
\(280\) −0.203143 −0.0121401
\(281\) −7.88074 −0.470126 −0.235063 0.971980i \(-0.575530\pi\)
−0.235063 + 0.971980i \(0.575530\pi\)
\(282\) 4.08002 0.242962
\(283\) −9.88057 −0.587339 −0.293669 0.955907i \(-0.594876\pi\)
−0.293669 + 0.955907i \(0.594876\pi\)
\(284\) −0.468330 −0.0277903
\(285\) −1.07457 −0.0636523
\(286\) −0.897304 −0.0530587
\(287\) 11.2185 0.662208
\(288\) 3.11487 0.183546
\(289\) −10.4618 −0.615401
\(290\) 0.189643 0.0111362
\(291\) −23.5164 −1.37855
\(292\) −13.3090 −0.778848
\(293\) −1.56316 −0.0913210 −0.0456605 0.998957i \(-0.514539\pi\)
−0.0456605 + 0.998957i \(0.514539\pi\)
\(294\) −14.2693 −0.832203
\(295\) −0.846376 −0.0492779
\(296\) 3.31986 0.192963
\(297\) −1.73076 −0.100429
\(298\) 6.14251 0.355826
\(299\) −0.480486 −0.0277872
\(300\) −12.2811 −0.709052
\(301\) 6.15951 0.355028
\(302\) 8.45338 0.486437
\(303\) 39.8724 2.29061
\(304\) −2.37200 −0.136044
\(305\) 1.18282 0.0677278
\(306\) −7.96468 −0.455311
\(307\) −1.67312 −0.0954899 −0.0477450 0.998860i \(-0.515203\pi\)
−0.0477450 + 0.998860i \(0.515203\pi\)
\(308\) 6.75629 0.384975
\(309\) −13.3117 −0.757276
\(310\) 0.634620 0.0360440
\(311\) 8.55050 0.484854 0.242427 0.970170i \(-0.422056\pi\)
0.242427 + 0.970170i \(0.422056\pi\)
\(312\) 0.364165 0.0206168
\(313\) −5.99853 −0.339057 −0.169528 0.985525i \(-0.554224\pi\)
−0.169528 + 0.985525i \(0.554224\pi\)
\(314\) −14.5966 −0.823732
\(315\) −0.632764 −0.0356522
\(316\) 8.13638 0.457707
\(317\) −19.4961 −1.09501 −0.547505 0.836802i \(-0.684422\pi\)
−0.547505 + 0.836802i \(0.684422\pi\)
\(318\) 6.50452 0.364756
\(319\) −6.30731 −0.353142
\(320\) 0.183201 0.0102413
\(321\) −8.57584 −0.478657
\(322\) 3.61784 0.201614
\(323\) 6.06517 0.337475
\(324\) −8.64219 −0.480122
\(325\) −0.731392 −0.0405703
\(326\) −3.38562 −0.187512
\(327\) −17.6782 −0.977606
\(328\) −10.1172 −0.558631
\(329\) −1.82954 −0.100866
\(330\) −2.76030 −0.151950
\(331\) 3.23070 0.177575 0.0887876 0.996051i \(-0.471701\pi\)
0.0887876 + 0.996051i \(0.471701\pi\)
\(332\) −10.0982 −0.554211
\(333\) 10.3409 0.566679
\(334\) 15.2464 0.834248
\(335\) 1.60983 0.0879543
\(336\) −2.74200 −0.149588
\(337\) 12.9842 0.707292 0.353646 0.935379i \(-0.384942\pi\)
0.353646 + 0.935379i \(0.384942\pi\)
\(338\) −12.9783 −0.705927
\(339\) −10.9659 −0.595588
\(340\) −0.468443 −0.0254049
\(341\) −21.1067 −1.14299
\(342\) −7.38847 −0.399523
\(343\) 14.1605 0.764597
\(344\) −5.55485 −0.299497
\(345\) −1.47808 −0.0795772
\(346\) −6.34616 −0.341171
\(347\) −2.32541 −0.124834 −0.0624172 0.998050i \(-0.519881\pi\)
−0.0624172 + 0.998050i \(0.519881\pi\)
\(348\) 2.55978 0.137219
\(349\) 22.9593 1.22898 0.614491 0.788924i \(-0.289362\pi\)
0.614491 + 0.788924i \(0.289362\pi\)
\(350\) 5.50704 0.294364
\(351\) 0.0418318 0.00223282
\(352\) −6.09305 −0.324761
\(353\) −17.7095 −0.942581 −0.471291 0.881978i \(-0.656212\pi\)
−0.471291 + 0.881978i \(0.656212\pi\)
\(354\) −11.4243 −0.607193
\(355\) −0.0857987 −0.00455372
\(356\) 17.2007 0.911634
\(357\) 7.01125 0.371075
\(358\) 11.4406 0.604654
\(359\) 30.8355 1.62744 0.813719 0.581259i \(-0.197440\pi\)
0.813719 + 0.581259i \(0.197440\pi\)
\(360\) 0.570648 0.0300758
\(361\) −13.3736 −0.703875
\(362\) 7.37118 0.387421
\(363\) 64.6032 3.39079
\(364\) −0.163297 −0.00855909
\(365\) −2.43822 −0.127622
\(366\) 15.9655 0.834530
\(367\) 12.9844 0.677779 0.338889 0.940826i \(-0.389949\pi\)
0.338889 + 0.940826i \(0.389949\pi\)
\(368\) −3.26269 −0.170080
\(369\) −31.5139 −1.64055
\(370\) 0.608202 0.0316189
\(371\) −2.91672 −0.151429
\(372\) 8.56602 0.444128
\(373\) −16.8227 −0.871047 −0.435523 0.900177i \(-0.643437\pi\)
−0.435523 + 0.900177i \(0.643437\pi\)
\(374\) 15.5798 0.805615
\(375\) −4.51504 −0.233156
\(376\) 1.64994 0.0850893
\(377\) 0.152445 0.00785134
\(378\) −0.314975 −0.0162005
\(379\) 25.8009 1.32531 0.662653 0.748927i \(-0.269431\pi\)
0.662653 + 0.748927i \(0.269431\pi\)
\(380\) −0.434553 −0.0222921
\(381\) −50.7225 −2.59859
\(382\) 12.3229 0.630496
\(383\) 2.87242 0.146774 0.0733869 0.997304i \(-0.476619\pi\)
0.0733869 + 0.997304i \(0.476619\pi\)
\(384\) 2.47283 0.126191
\(385\) 1.23776 0.0630821
\(386\) −23.3237 −1.18714
\(387\) −17.3026 −0.879543
\(388\) −9.50991 −0.482793
\(389\) −31.4507 −1.59461 −0.797306 0.603575i \(-0.793742\pi\)
−0.797306 + 0.603575i \(0.793742\pi\)
\(390\) 0.0667155 0.00337827
\(391\) 8.34266 0.421906
\(392\) −5.77045 −0.291452
\(393\) 23.3991 1.18033
\(394\) −17.6664 −0.890022
\(395\) 1.49059 0.0749999
\(396\) −18.9791 −0.953733
\(397\) −1.11182 −0.0558008 −0.0279004 0.999611i \(-0.508882\pi\)
−0.0279004 + 0.999611i \(0.508882\pi\)
\(398\) −11.2536 −0.564093
\(399\) 6.50402 0.325608
\(400\) −4.96644 −0.248322
\(401\) −12.7527 −0.636839 −0.318419 0.947950i \(-0.603152\pi\)
−0.318419 + 0.947950i \(0.603152\pi\)
\(402\) 21.7293 1.08376
\(403\) 0.510141 0.0254119
\(404\) 16.1242 0.802210
\(405\) −1.58326 −0.0786728
\(406\) −1.14784 −0.0569666
\(407\) −20.2281 −1.00267
\(408\) −6.32298 −0.313034
\(409\) −27.3108 −1.35043 −0.675217 0.737620i \(-0.735950\pi\)
−0.675217 + 0.737620i \(0.735950\pi\)
\(410\) −1.85349 −0.0915373
\(411\) 15.4451 0.761853
\(412\) −5.38319 −0.265211
\(413\) 5.12281 0.252077
\(414\) −10.1629 −0.499477
\(415\) −1.85000 −0.0908132
\(416\) 0.147267 0.00722035
\(417\) 18.6617 0.913869
\(418\) 14.4527 0.706905
\(419\) −12.6594 −0.618454 −0.309227 0.950988i \(-0.600070\pi\)
−0.309227 + 0.950988i \(0.600070\pi\)
\(420\) −0.502337 −0.0245115
\(421\) 12.2017 0.594675 0.297337 0.954772i \(-0.403901\pi\)
0.297337 + 0.954772i \(0.403901\pi\)
\(422\) 10.2433 0.498635
\(423\) 5.13936 0.249884
\(424\) 2.63040 0.127744
\(425\) 12.6991 0.615998
\(426\) −1.15810 −0.0561101
\(427\) −7.15916 −0.346456
\(428\) −3.46803 −0.167634
\(429\) −2.21888 −0.107128
\(430\) −1.01766 −0.0490757
\(431\) −6.39065 −0.307827 −0.153913 0.988084i \(-0.549188\pi\)
−0.153913 + 0.988084i \(0.549188\pi\)
\(432\) 0.284055 0.0136666
\(433\) 8.54652 0.410720 0.205360 0.978687i \(-0.434164\pi\)
0.205360 + 0.978687i \(0.434164\pi\)
\(434\) −3.84113 −0.184380
\(435\) 0.468955 0.0224847
\(436\) −7.14898 −0.342374
\(437\) 7.73911 0.370212
\(438\) −32.9107 −1.57254
\(439\) −0.779523 −0.0372046 −0.0186023 0.999827i \(-0.505922\pi\)
−0.0186023 + 0.999827i \(0.505922\pi\)
\(440\) −1.11625 −0.0532153
\(441\) −17.9742 −0.855914
\(442\) −0.376559 −0.0179111
\(443\) −2.87892 −0.136782 −0.0683909 0.997659i \(-0.521786\pi\)
−0.0683909 + 0.997659i \(0.521786\pi\)
\(444\) 8.20943 0.389602
\(445\) 3.15118 0.149380
\(446\) 12.9734 0.614306
\(447\) 15.1894 0.718432
\(448\) −1.10885 −0.0523883
\(449\) 1.51382 0.0714418 0.0357209 0.999362i \(-0.488627\pi\)
0.0357209 + 0.999362i \(0.488627\pi\)
\(450\) −15.4698 −0.729254
\(451\) 61.6448 2.90274
\(452\) −4.43458 −0.208585
\(453\) 20.9037 0.982143
\(454\) −22.7690 −1.06860
\(455\) −0.0299162 −0.00140249
\(456\) −5.86554 −0.274679
\(457\) −5.83393 −0.272900 −0.136450 0.990647i \(-0.543569\pi\)
−0.136450 + 0.990647i \(0.543569\pi\)
\(458\) −2.30148 −0.107541
\(459\) −0.726324 −0.0339019
\(460\) −0.597729 −0.0278693
\(461\) −14.3110 −0.666530 −0.333265 0.942833i \(-0.608150\pi\)
−0.333265 + 0.942833i \(0.608150\pi\)
\(462\) 16.7071 0.777286
\(463\) −21.2913 −0.989490 −0.494745 0.869038i \(-0.664739\pi\)
−0.494745 + 0.869038i \(0.664739\pi\)
\(464\) 1.03517 0.0480563
\(465\) 1.56931 0.0727748
\(466\) 21.4748 0.994801
\(467\) −11.1190 −0.514528 −0.257264 0.966341i \(-0.582821\pi\)
−0.257264 + 0.966341i \(0.582821\pi\)
\(468\) 0.458717 0.0212042
\(469\) −9.74372 −0.449923
\(470\) 0.302272 0.0139427
\(471\) −36.0948 −1.66316
\(472\) −4.61993 −0.212649
\(473\) 33.8460 1.55624
\(474\) 20.1198 0.924135
\(475\) 11.7804 0.540521
\(476\) 2.83532 0.129957
\(477\) 8.19336 0.375148
\(478\) −7.14563 −0.326834
\(479\) 28.7405 1.31319 0.656593 0.754245i \(-0.271997\pi\)
0.656593 + 0.754245i \(0.271997\pi\)
\(480\) 0.453025 0.0206777
\(481\) 0.488905 0.0222922
\(482\) 0.514479 0.0234339
\(483\) 8.94629 0.407070
\(484\) 26.1252 1.18751
\(485\) −1.74223 −0.0791105
\(486\) −22.2228 −1.00805
\(487\) 16.5753 0.751100 0.375550 0.926802i \(-0.377454\pi\)
0.375550 + 0.926802i \(0.377454\pi\)
\(488\) 6.45638 0.292266
\(489\) −8.37205 −0.378597
\(490\) −1.05715 −0.0477573
\(491\) −29.4508 −1.32910 −0.664548 0.747246i \(-0.731376\pi\)
−0.664548 + 0.747246i \(0.731376\pi\)
\(492\) −25.0182 −1.12791
\(493\) −2.64690 −0.119211
\(494\) −0.349317 −0.0157165
\(495\) −3.47699 −0.156279
\(496\) 3.46406 0.155541
\(497\) 0.519309 0.0232942
\(498\) −24.9711 −1.11898
\(499\) −3.93211 −0.176026 −0.0880128 0.996119i \(-0.528052\pi\)
−0.0880128 + 0.996119i \(0.528052\pi\)
\(500\) −1.82586 −0.0816551
\(501\) 37.7018 1.68439
\(502\) −8.33417 −0.371972
\(503\) 38.5297 1.71796 0.858978 0.512013i \(-0.171100\pi\)
0.858978 + 0.512013i \(0.171100\pi\)
\(504\) −3.45393 −0.153850
\(505\) 2.95398 0.131450
\(506\) 19.8797 0.883762
\(507\) −32.0931 −1.42531
\(508\) −20.5120 −0.910071
\(509\) 35.2800 1.56376 0.781879 0.623430i \(-0.214261\pi\)
0.781879 + 0.623430i \(0.214261\pi\)
\(510\) −1.15838 −0.0512939
\(511\) 14.7577 0.652840
\(512\) 1.00000 0.0441942
\(513\) −0.673778 −0.0297480
\(514\) 28.2387 1.24556
\(515\) −0.986207 −0.0434575
\(516\) −13.7362 −0.604702
\(517\) −10.0532 −0.442138
\(518\) −3.68123 −0.161744
\(519\) −15.6929 −0.688844
\(520\) 0.0269795 0.00118313
\(521\) 23.9501 1.04927 0.524636 0.851326i \(-0.324201\pi\)
0.524636 + 0.851326i \(0.324201\pi\)
\(522\) 3.22441 0.141128
\(523\) −39.3010 −1.71851 −0.859257 0.511545i \(-0.829074\pi\)
−0.859257 + 0.511545i \(0.829074\pi\)
\(524\) 9.46249 0.413371
\(525\) 13.6180 0.594336
\(526\) 17.7534 0.774084
\(527\) −8.85756 −0.385841
\(528\) −15.0671 −0.655709
\(529\) −12.3548 −0.537167
\(530\) 0.481893 0.0209321
\(531\) −14.3905 −0.624493
\(532\) 2.63020 0.114033
\(533\) −1.48993 −0.0645361
\(534\) 42.5343 1.84064
\(535\) −0.635347 −0.0274685
\(536\) 8.78722 0.379550
\(537\) 28.2906 1.22083
\(538\) 6.26438 0.270077
\(539\) 35.1596 1.51443
\(540\) 0.0520392 0.00223941
\(541\) −29.7835 −1.28049 −0.640246 0.768170i \(-0.721168\pi\)
−0.640246 + 0.768170i \(0.721168\pi\)
\(542\) 10.3591 0.444962
\(543\) 18.2277 0.782224
\(544\) −2.55699 −0.109630
\(545\) −1.30970 −0.0561015
\(546\) −0.403805 −0.0172813
\(547\) −10.1833 −0.435408 −0.217704 0.976015i \(-0.569857\pi\)
−0.217704 + 0.976015i \(0.569857\pi\)
\(548\) 6.24595 0.266814
\(549\) 20.1108 0.858307
\(550\) 30.2607 1.29032
\(551\) −2.45541 −0.104604
\(552\) −8.06807 −0.343400
\(553\) −9.02203 −0.383656
\(554\) −23.9326 −1.01680
\(555\) 1.50398 0.0638403
\(556\) 7.54672 0.320052
\(557\) 22.8626 0.968718 0.484359 0.874869i \(-0.339053\pi\)
0.484359 + 0.874869i \(0.339053\pi\)
\(558\) 10.7901 0.456781
\(559\) −0.818045 −0.0345996
\(560\) −0.203143 −0.00858436
\(561\) 38.5263 1.62658
\(562\) −7.88074 −0.332429
\(563\) 9.38563 0.395557 0.197779 0.980247i \(-0.436627\pi\)
0.197779 + 0.980247i \(0.436627\pi\)
\(564\) 4.08002 0.171800
\(565\) −0.812420 −0.0341788
\(566\) −9.88057 −0.415311
\(567\) 9.58291 0.402444
\(568\) −0.468330 −0.0196507
\(569\) 22.8722 0.958851 0.479425 0.877583i \(-0.340845\pi\)
0.479425 + 0.877583i \(0.340845\pi\)
\(570\) −1.07457 −0.0450090
\(571\) 19.9195 0.833604 0.416802 0.908997i \(-0.363151\pi\)
0.416802 + 0.908997i \(0.363151\pi\)
\(572\) −0.897304 −0.0375182
\(573\) 30.4725 1.27301
\(574\) 11.2185 0.468251
\(575\) 16.2040 0.675752
\(576\) 3.11487 0.129786
\(577\) −26.3043 −1.09506 −0.547531 0.836786i \(-0.684432\pi\)
−0.547531 + 0.836786i \(0.684432\pi\)
\(578\) −10.4618 −0.435154
\(579\) −57.6754 −2.39691
\(580\) 0.189643 0.00787452
\(581\) 11.1974 0.464547
\(582\) −23.5164 −0.974785
\(583\) −16.0272 −0.663777
\(584\) −13.3090 −0.550729
\(585\) 0.0840375 0.00347452
\(586\) −1.56316 −0.0645737
\(587\) 0.955976 0.0394574 0.0197287 0.999805i \(-0.493720\pi\)
0.0197287 + 0.999805i \(0.493720\pi\)
\(588\) −14.2693 −0.588457
\(589\) −8.21675 −0.338565
\(590\) −0.846376 −0.0348447
\(591\) −43.6860 −1.79700
\(592\) 3.31986 0.136445
\(593\) −11.7470 −0.482393 −0.241197 0.970476i \(-0.577540\pi\)
−0.241197 + 0.970476i \(0.577540\pi\)
\(594\) −1.73076 −0.0710139
\(595\) 0.519434 0.0212947
\(596\) 6.14251 0.251607
\(597\) −27.8283 −1.13893
\(598\) −0.480486 −0.0196485
\(599\) 25.2248 1.03066 0.515329 0.856993i \(-0.327670\pi\)
0.515329 + 0.856993i \(0.327670\pi\)
\(600\) −12.2811 −0.501375
\(601\) −16.7051 −0.681417 −0.340709 0.940169i \(-0.610667\pi\)
−0.340709 + 0.940169i \(0.610667\pi\)
\(602\) 6.15951 0.251043
\(603\) 27.3710 1.11464
\(604\) 8.45338 0.343963
\(605\) 4.78618 0.194586
\(606\) 39.8724 1.61971
\(607\) −8.60323 −0.349194 −0.174597 0.984640i \(-0.555862\pi\)
−0.174597 + 0.984640i \(0.555862\pi\)
\(608\) −2.37200 −0.0961973
\(609\) −2.83842 −0.115019
\(610\) 1.18282 0.0478908
\(611\) 0.242982 0.00982999
\(612\) −7.96468 −0.321953
\(613\) −32.3558 −1.30684 −0.653420 0.756996i \(-0.726666\pi\)
−0.653420 + 0.756996i \(0.726666\pi\)
\(614\) −1.67312 −0.0675216
\(615\) −4.58336 −0.184819
\(616\) 6.75629 0.272219
\(617\) 19.6209 0.789908 0.394954 0.918701i \(-0.370761\pi\)
0.394954 + 0.918701i \(0.370761\pi\)
\(618\) −13.3117 −0.535475
\(619\) −0.598669 −0.0240626 −0.0120313 0.999928i \(-0.503830\pi\)
−0.0120313 + 0.999928i \(0.503830\pi\)
\(620\) 0.634620 0.0254870
\(621\) −0.926783 −0.0371905
\(622\) 8.55050 0.342844
\(623\) −19.0730 −0.764143
\(624\) 0.364165 0.0145783
\(625\) 24.4977 0.979907
\(626\) −5.99853 −0.239749
\(627\) 35.7390 1.42728
\(628\) −14.5966 −0.582467
\(629\) −8.48883 −0.338472
\(630\) −0.632764 −0.0252099
\(631\) 9.43387 0.375557 0.187778 0.982211i \(-0.439871\pi\)
0.187778 + 0.982211i \(0.439871\pi\)
\(632\) 8.13638 0.323648
\(633\) 25.3299 1.00677
\(634\) −19.4961 −0.774289
\(635\) −3.75781 −0.149124
\(636\) 6.50452 0.257921
\(637\) −0.849796 −0.0336701
\(638\) −6.30731 −0.249709
\(639\) −1.45879 −0.0577088
\(640\) 0.183201 0.00724166
\(641\) 24.6998 0.975583 0.487792 0.872960i \(-0.337803\pi\)
0.487792 + 0.872960i \(0.337803\pi\)
\(642\) −8.57584 −0.338461
\(643\) 16.3325 0.644091 0.322045 0.946724i \(-0.395630\pi\)
0.322045 + 0.946724i \(0.395630\pi\)
\(644\) 3.61784 0.142563
\(645\) −2.51649 −0.0990865
\(646\) 6.06517 0.238631
\(647\) −23.1810 −0.911339 −0.455670 0.890149i \(-0.650600\pi\)
−0.455670 + 0.890149i \(0.650600\pi\)
\(648\) −8.64219 −0.339497
\(649\) 28.1494 1.10496
\(650\) −0.731392 −0.0286875
\(651\) −9.49845 −0.372273
\(652\) −3.38562 −0.132591
\(653\) 32.5455 1.27360 0.636801 0.771028i \(-0.280257\pi\)
0.636801 + 0.771028i \(0.280257\pi\)
\(654\) −17.6782 −0.691272
\(655\) 1.73354 0.0677350
\(656\) −10.1172 −0.395011
\(657\) −41.4557 −1.61734
\(658\) −1.82954 −0.0713230
\(659\) −31.2204 −1.21618 −0.608088 0.793870i \(-0.708063\pi\)
−0.608088 + 0.793870i \(0.708063\pi\)
\(660\) −2.76030 −0.107445
\(661\) −17.0012 −0.661271 −0.330636 0.943759i \(-0.607263\pi\)
−0.330636 + 0.943759i \(0.607263\pi\)
\(662\) 3.23070 0.125565
\(663\) −0.931166 −0.0361635
\(664\) −10.0982 −0.391887
\(665\) 0.481855 0.0186855
\(666\) 10.3409 0.400703
\(667\) −3.37742 −0.130774
\(668\) 15.2464 0.589903
\(669\) 32.0809 1.24032
\(670\) 1.60983 0.0621931
\(671\) −39.3390 −1.51867
\(672\) −2.74200 −0.105775
\(673\) 5.41016 0.208546 0.104273 0.994549i \(-0.466748\pi\)
0.104273 + 0.994549i \(0.466748\pi\)
\(674\) 12.9842 0.500131
\(675\) −1.41074 −0.0542994
\(676\) −12.9783 −0.499166
\(677\) −6.64408 −0.255353 −0.127676 0.991816i \(-0.540752\pi\)
−0.127676 + 0.991816i \(0.540752\pi\)
\(678\) −10.9659 −0.421144
\(679\) 10.5451 0.404683
\(680\) −0.468443 −0.0179640
\(681\) −56.3038 −2.15757
\(682\) −21.1067 −0.808217
\(683\) 7.56452 0.289448 0.144724 0.989472i \(-0.453771\pi\)
0.144724 + 0.989472i \(0.453771\pi\)
\(684\) −7.38847 −0.282505
\(685\) 1.14427 0.0437201
\(686\) 14.1605 0.540652
\(687\) −5.69116 −0.217131
\(688\) −5.55485 −0.211777
\(689\) 0.387371 0.0147577
\(690\) −1.47808 −0.0562696
\(691\) −5.35303 −0.203639 −0.101819 0.994803i \(-0.532466\pi\)
−0.101819 + 0.994803i \(0.532466\pi\)
\(692\) −6.34616 −0.241245
\(693\) 21.0450 0.799432
\(694\) −2.32541 −0.0882712
\(695\) 1.38257 0.0524438
\(696\) 2.55978 0.0970283
\(697\) 25.8696 0.979882
\(698\) 22.9593 0.869021
\(699\) 53.1034 2.00856
\(700\) 5.50704 0.208147
\(701\) −21.3549 −0.806563 −0.403282 0.915076i \(-0.632131\pi\)
−0.403282 + 0.915076i \(0.632131\pi\)
\(702\) 0.0418318 0.00157884
\(703\) −7.87470 −0.297000
\(704\) −6.09305 −0.229640
\(705\) 0.747465 0.0281512
\(706\) −17.7095 −0.666506
\(707\) −17.8794 −0.672423
\(708\) −11.4243 −0.429350
\(709\) 49.1276 1.84503 0.922513 0.385965i \(-0.126132\pi\)
0.922513 + 0.385965i \(0.126132\pi\)
\(710\) −0.0857987 −0.00321997
\(711\) 25.3438 0.950465
\(712\) 17.2007 0.644622
\(713\) −11.3022 −0.423269
\(714\) 7.01125 0.262389
\(715\) −0.164387 −0.00614773
\(716\) 11.4406 0.427555
\(717\) −17.6699 −0.659895
\(718\) 30.8355 1.15077
\(719\) −23.2540 −0.867229 −0.433615 0.901098i \(-0.642762\pi\)
−0.433615 + 0.901098i \(0.642762\pi\)
\(720\) 0.570648 0.0212668
\(721\) 5.96916 0.222303
\(722\) −13.3736 −0.497714
\(723\) 1.27222 0.0473143
\(724\) 7.37118 0.273948
\(725\) −5.14108 −0.190935
\(726\) 64.6032 2.39765
\(727\) −10.5130 −0.389904 −0.194952 0.980813i \(-0.562455\pi\)
−0.194952 + 0.980813i \(0.562455\pi\)
\(728\) −0.163297 −0.00605219
\(729\) −29.0266 −1.07506
\(730\) −2.43822 −0.0902425
\(731\) 14.2037 0.525342
\(732\) 15.9655 0.590102
\(733\) −23.3493 −0.862427 −0.431214 0.902250i \(-0.641914\pi\)
−0.431214 + 0.902250i \(0.641914\pi\)
\(734\) 12.9844 0.479262
\(735\) −2.61416 −0.0964246
\(736\) −3.26269 −0.120264
\(737\) −53.5409 −1.97221
\(738\) −31.5139 −1.16004
\(739\) −5.69260 −0.209406 −0.104703 0.994504i \(-0.533389\pi\)
−0.104703 + 0.994504i \(0.533389\pi\)
\(740\) 0.608202 0.0223580
\(741\) −0.863800 −0.0317325
\(742\) −2.91672 −0.107076
\(743\) −3.76103 −0.137979 −0.0689894 0.997617i \(-0.521977\pi\)
−0.0689894 + 0.997617i \(0.521977\pi\)
\(744\) 8.56602 0.314046
\(745\) 1.12532 0.0412284
\(746\) −16.8227 −0.615923
\(747\) −31.4546 −1.15086
\(748\) 15.5798 0.569656
\(749\) 3.84553 0.140513
\(750\) −4.51504 −0.164866
\(751\) −23.6062 −0.861404 −0.430702 0.902494i \(-0.641734\pi\)
−0.430702 + 0.902494i \(0.641734\pi\)
\(752\) 1.64994 0.0601672
\(753\) −20.6089 −0.751032
\(754\) 0.152445 0.00555174
\(755\) 1.54867 0.0563618
\(756\) −0.314975 −0.0114555
\(757\) −33.0172 −1.20003 −0.600016 0.799988i \(-0.704839\pi\)
−0.600016 + 0.799988i \(0.704839\pi\)
\(758\) 25.8009 0.937132
\(759\) 49.1591 1.78436
\(760\) −0.434553 −0.0157629
\(761\) −27.7048 −1.00430 −0.502148 0.864782i \(-0.667457\pi\)
−0.502148 + 0.864782i \(0.667457\pi\)
\(762\) −50.7225 −1.83748
\(763\) 7.92716 0.286982
\(764\) 12.3229 0.445828
\(765\) −1.45914 −0.0527553
\(766\) 2.87242 0.103785
\(767\) −0.680362 −0.0245664
\(768\) 2.47283 0.0892304
\(769\) −21.3734 −0.770743 −0.385372 0.922761i \(-0.625927\pi\)
−0.385372 + 0.922761i \(0.625927\pi\)
\(770\) 1.23776 0.0446058
\(771\) 69.8295 2.51485
\(772\) −23.3237 −0.839437
\(773\) −22.4101 −0.806035 −0.403018 0.915192i \(-0.632039\pi\)
−0.403018 + 0.915192i \(0.632039\pi\)
\(774\) −17.3026 −0.621931
\(775\) −17.2040 −0.617987
\(776\) −9.50991 −0.341386
\(777\) −9.10304 −0.326570
\(778\) −31.4507 −1.12756
\(779\) 23.9981 0.859820
\(780\) 0.0667155 0.00238880
\(781\) 2.85356 0.102108
\(782\) 8.34266 0.298333
\(783\) 0.294044 0.0105083
\(784\) −5.77045 −0.206087
\(785\) −2.67411 −0.0954431
\(786\) 23.3991 0.834618
\(787\) −10.6122 −0.378285 −0.189143 0.981950i \(-0.560571\pi\)
−0.189143 + 0.981950i \(0.560571\pi\)
\(788\) −17.6664 −0.629341
\(789\) 43.9010 1.56292
\(790\) 1.49059 0.0530330
\(791\) 4.91729 0.174839
\(792\) −18.9791 −0.674391
\(793\) 0.950810 0.0337643
\(794\) −1.11182 −0.0394571
\(795\) 1.19164 0.0422630
\(796\) −11.2536 −0.398874
\(797\) −9.84951 −0.348888 −0.174444 0.984667i \(-0.555813\pi\)
−0.174444 + 0.984667i \(0.555813\pi\)
\(798\) 6.50402 0.230240
\(799\) −4.21888 −0.149253
\(800\) −4.96644 −0.175590
\(801\) 53.5779 1.89308
\(802\) −12.7527 −0.450313
\(803\) 81.0921 2.86168
\(804\) 21.7293 0.766332
\(805\) 0.662793 0.0233604
\(806\) 0.510141 0.0179690
\(807\) 15.4907 0.545300
\(808\) 16.1242 0.567248
\(809\) 27.9025 0.981001 0.490501 0.871441i \(-0.336814\pi\)
0.490501 + 0.871441i \(0.336814\pi\)
\(810\) −1.58326 −0.0556301
\(811\) 4.47359 0.157089 0.0785445 0.996911i \(-0.474973\pi\)
0.0785445 + 0.996911i \(0.474973\pi\)
\(812\) −1.14784 −0.0402814
\(813\) 25.6163 0.898403
\(814\) −20.2281 −0.708993
\(815\) −0.620250 −0.0217264
\(816\) −6.32298 −0.221349
\(817\) 13.1761 0.460974
\(818\) −27.3108 −0.954900
\(819\) −0.508649 −0.0177736
\(820\) −1.85349 −0.0647266
\(821\) −4.66110 −0.162673 −0.0813367 0.996687i \(-0.525919\pi\)
−0.0813367 + 0.996687i \(0.525919\pi\)
\(822\) 15.4451 0.538711
\(823\) −2.98327 −0.103990 −0.0519951 0.998647i \(-0.516558\pi\)
−0.0519951 + 0.998647i \(0.516558\pi\)
\(824\) −5.38319 −0.187532
\(825\) 74.8296 2.60523
\(826\) 5.12281 0.178245
\(827\) −39.6207 −1.37775 −0.688874 0.724881i \(-0.741895\pi\)
−0.688874 + 0.724881i \(0.741895\pi\)
\(828\) −10.1629 −0.353184
\(829\) −37.6711 −1.30837 −0.654186 0.756333i \(-0.726989\pi\)
−0.654186 + 0.756333i \(0.726989\pi\)
\(830\) −1.85000 −0.0642146
\(831\) −59.1811 −2.05297
\(832\) 0.147267 0.00510556
\(833\) 14.7550 0.511229
\(834\) 18.6617 0.646203
\(835\) 2.79317 0.0966615
\(836\) 14.4527 0.499857
\(837\) 0.983983 0.0340114
\(838\) −12.6594 −0.437313
\(839\) 44.0077 1.51932 0.759658 0.650323i \(-0.225366\pi\)
0.759658 + 0.650323i \(0.225366\pi\)
\(840\) −0.502337 −0.0173323
\(841\) −27.9284 −0.963049
\(842\) 12.2017 0.420499
\(843\) −19.4877 −0.671192
\(844\) 10.2433 0.352588
\(845\) −2.37764 −0.0817934
\(846\) 5.13936 0.176695
\(847\) −28.9690 −0.995387
\(848\) 2.63040 0.0903283
\(849\) −24.4329 −0.838536
\(850\) 12.6991 0.435576
\(851\) −10.8317 −0.371305
\(852\) −1.15810 −0.0396758
\(853\) −2.83934 −0.0972171 −0.0486086 0.998818i \(-0.515479\pi\)
−0.0486086 + 0.998818i \(0.515479\pi\)
\(854\) −7.15916 −0.244982
\(855\) −1.35358 −0.0462914
\(856\) −3.46803 −0.118535
\(857\) −2.26847 −0.0774894 −0.0387447 0.999249i \(-0.512336\pi\)
−0.0387447 + 0.999249i \(0.512336\pi\)
\(858\) −2.21888 −0.0757512
\(859\) 29.5917 1.00966 0.504828 0.863220i \(-0.331556\pi\)
0.504828 + 0.863220i \(0.331556\pi\)
\(860\) −1.01766 −0.0347018
\(861\) 27.7414 0.945425
\(862\) −6.39065 −0.217666
\(863\) 2.62119 0.0892263 0.0446132 0.999004i \(-0.485794\pi\)
0.0446132 + 0.999004i \(0.485794\pi\)
\(864\) 0.284055 0.00966374
\(865\) −1.16262 −0.0395304
\(866\) 8.54652 0.290423
\(867\) −25.8703 −0.878600
\(868\) −3.84113 −0.130376
\(869\) −49.5753 −1.68173
\(870\) 0.468955 0.0158991
\(871\) 1.29407 0.0438477
\(872\) −7.14898 −0.242095
\(873\) −29.6221 −1.00256
\(874\) 7.73911 0.261779
\(875\) 2.02461 0.0684444
\(876\) −32.9107 −1.11195
\(877\) 33.5166 1.13177 0.565887 0.824483i \(-0.308534\pi\)
0.565887 + 0.824483i \(0.308534\pi\)
\(878\) −0.779523 −0.0263076
\(879\) −3.86543 −0.130378
\(880\) −1.11625 −0.0376289
\(881\) 16.6790 0.561931 0.280966 0.959718i \(-0.409345\pi\)
0.280966 + 0.959718i \(0.409345\pi\)
\(882\) −17.9742 −0.605223
\(883\) 15.6322 0.526066 0.263033 0.964787i \(-0.415277\pi\)
0.263033 + 0.964787i \(0.415277\pi\)
\(884\) −0.376559 −0.0126651
\(885\) −2.09294 −0.0703534
\(886\) −2.87892 −0.0967193
\(887\) −1.39451 −0.0468229 −0.0234115 0.999726i \(-0.507453\pi\)
−0.0234115 + 0.999726i \(0.507453\pi\)
\(888\) 8.20943 0.275491
\(889\) 22.7447 0.762833
\(890\) 3.15118 0.105628
\(891\) 52.6573 1.76409
\(892\) 12.9734 0.434380
\(893\) −3.91366 −0.130966
\(894\) 15.1894 0.508008
\(895\) 2.09593 0.0700592
\(896\) −1.10885 −0.0370441
\(897\) −1.18816 −0.0396715
\(898\) 1.51382 0.0505170
\(899\) 3.58587 0.119596
\(900\) −15.4698 −0.515660
\(901\) −6.72590 −0.224072
\(902\) 61.6448 2.05255
\(903\) 15.2314 0.506869
\(904\) −4.43458 −0.147492
\(905\) 1.35041 0.0448891
\(906\) 20.9037 0.694480
\(907\) 42.4405 1.40921 0.704607 0.709597i \(-0.251123\pi\)
0.704607 + 0.709597i \(0.251123\pi\)
\(908\) −22.7690 −0.755616
\(909\) 50.2249 1.66585
\(910\) −0.0299162 −0.000991713 0
\(911\) 17.7487 0.588041 0.294020 0.955799i \(-0.405007\pi\)
0.294020 + 0.955799i \(0.405007\pi\)
\(912\) −5.86554 −0.194228
\(913\) 61.5289 2.03631
\(914\) −5.83393 −0.192969
\(915\) 2.92490 0.0966942
\(916\) −2.30148 −0.0760430
\(917\) −10.4925 −0.346493
\(918\) −0.726324 −0.0239723
\(919\) −46.2309 −1.52502 −0.762508 0.646979i \(-0.776032\pi\)
−0.762508 + 0.646979i \(0.776032\pi\)
\(920\) −0.597729 −0.0197065
\(921\) −4.13733 −0.136330
\(922\) −14.3110 −0.471308
\(923\) −0.0689695 −0.00227016
\(924\) 16.7071 0.549624
\(925\) −16.4879 −0.542118
\(926\) −21.2913 −0.699675
\(927\) −16.7679 −0.550732
\(928\) 1.03517 0.0339810
\(929\) −10.1976 −0.334573 −0.167286 0.985908i \(-0.553500\pi\)
−0.167286 + 0.985908i \(0.553500\pi\)
\(930\) 1.56931 0.0514596
\(931\) 13.6875 0.448590
\(932\) 21.4748 0.703430
\(933\) 21.1439 0.692220
\(934\) −11.1190 −0.363826
\(935\) 2.85425 0.0933438
\(936\) 0.458717 0.0149936
\(937\) 33.0387 1.07933 0.539664 0.841880i \(-0.318551\pi\)
0.539664 + 0.841880i \(0.318551\pi\)
\(938\) −9.74372 −0.318144
\(939\) −14.8333 −0.484067
\(940\) 0.302272 0.00985901
\(941\) −45.2092 −1.47378 −0.736890 0.676013i \(-0.763706\pi\)
−0.736890 + 0.676013i \(0.763706\pi\)
\(942\) −36.0948 −1.17603
\(943\) 33.0094 1.07493
\(944\) −4.61993 −0.150366
\(945\) −0.0577037 −0.00187710
\(946\) 33.8460 1.10043
\(947\) −8.73369 −0.283807 −0.141903 0.989881i \(-0.545322\pi\)
−0.141903 + 0.989881i \(0.545322\pi\)
\(948\) 20.1198 0.653462
\(949\) −1.95997 −0.0636233
\(950\) 11.7804 0.382206
\(951\) −48.2105 −1.56333
\(952\) 2.83532 0.0918932
\(953\) 50.7558 1.64414 0.822070 0.569386i \(-0.192819\pi\)
0.822070 + 0.569386i \(0.192819\pi\)
\(954\) 8.19336 0.265270
\(955\) 2.25758 0.0730535
\(956\) −7.14563 −0.231106
\(957\) −15.5969 −0.504176
\(958\) 28.7405 0.928563
\(959\) −6.92583 −0.223647
\(960\) 0.453025 0.0146213
\(961\) −19.0003 −0.612912
\(962\) 0.488905 0.0157629
\(963\) −10.8025 −0.348105
\(964\) 0.514479 0.0165703
\(965\) −4.27292 −0.137550
\(966\) 8.94629 0.287842
\(967\) −25.1397 −0.808437 −0.404218 0.914663i \(-0.632456\pi\)
−0.404218 + 0.914663i \(0.632456\pi\)
\(968\) 26.1252 0.839697
\(969\) 14.9981 0.481809
\(970\) −1.74223 −0.0559396
\(971\) 3.33687 0.107085 0.0535426 0.998566i \(-0.482949\pi\)
0.0535426 + 0.998566i \(0.482949\pi\)
\(972\) −22.2228 −0.712797
\(973\) −8.36819 −0.268272
\(974\) 16.5753 0.531108
\(975\) −1.80860 −0.0579217
\(976\) 6.45638 0.206664
\(977\) −31.8464 −1.01886 −0.509429 0.860513i \(-0.670143\pi\)
−0.509429 + 0.860513i \(0.670143\pi\)
\(978\) −8.37205 −0.267709
\(979\) −104.805 −3.34957
\(980\) −1.05715 −0.0337695
\(981\) −22.2682 −0.710967
\(982\) −29.4508 −0.939812
\(983\) −34.0752 −1.08683 −0.543415 0.839464i \(-0.682869\pi\)
−0.543415 + 0.839464i \(0.682869\pi\)
\(984\) −25.0182 −0.797550
\(985\) −3.23651 −0.103124
\(986\) −2.64690 −0.0842946
\(987\) −4.52414 −0.144005
\(988\) −0.349317 −0.0111133
\(989\) 18.1238 0.576302
\(990\) −3.47699 −0.110506
\(991\) 10.4713 0.332631 0.166315 0.986073i \(-0.446813\pi\)
0.166315 + 0.986073i \(0.446813\pi\)
\(992\) 3.46406 0.109984
\(993\) 7.98895 0.253522
\(994\) 0.519309 0.0164715
\(995\) −2.06168 −0.0653596
\(996\) −24.9711 −0.791240
\(997\) −19.2060 −0.608259 −0.304130 0.952631i \(-0.598366\pi\)
−0.304130 + 0.952631i \(0.598366\pi\)
\(998\) −3.93211 −0.124469
\(999\) 0.943021 0.0298359
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 8042.2.a.a.1.63 67
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8042.2.a.a.1.63 67 1.1 even 1 trivial