Properties

Label 2671.2.a.b.1.80
Level $2671$
Weight $2$
Character 2671.1
Self dual yes
Analytic conductor $21.328$
Analytic rank $0$
Dimension $122$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2671,2,Mod(1,2671)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2671, 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("2671.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2671 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2671.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: \(21.3280423799\)
Analytic rank: \(0\)
Dimension: \(122\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.80
Character \(\chi\) \(=\) 2671.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.22085 q^{2} -3.14093 q^{3} -0.509528 q^{4} -0.946195 q^{5} -3.83460 q^{6} -0.0224945 q^{7} -3.06375 q^{8} +6.86545 q^{9} +O(q^{10})\) \(q+1.22085 q^{2} -3.14093 q^{3} -0.509528 q^{4} -0.946195 q^{5} -3.83460 q^{6} -0.0224945 q^{7} -3.06375 q^{8} +6.86545 q^{9} -1.15516 q^{10} -6.33640 q^{11} +1.60039 q^{12} +0.358954 q^{13} -0.0274624 q^{14} +2.97193 q^{15} -2.72133 q^{16} -0.0188727 q^{17} +8.38168 q^{18} -6.65643 q^{19} +0.482113 q^{20} +0.0706537 q^{21} -7.73579 q^{22} +1.13749 q^{23} +9.62304 q^{24} -4.10472 q^{25} +0.438229 q^{26} -12.1411 q^{27} +0.0114616 q^{28} -7.65975 q^{29} +3.62828 q^{30} -8.09110 q^{31} +2.80518 q^{32} +19.9022 q^{33} -0.0230407 q^{34} +0.0212842 q^{35} -3.49814 q^{36} +0.639087 q^{37} -8.12650 q^{38} -1.12745 q^{39} +2.89891 q^{40} -2.68215 q^{41} +0.0862575 q^{42} +10.9076 q^{43} +3.22857 q^{44} -6.49605 q^{45} +1.38870 q^{46} +7.99169 q^{47} +8.54750 q^{48} -6.99949 q^{49} -5.01124 q^{50} +0.0592778 q^{51} -0.182897 q^{52} -5.97511 q^{53} -14.8225 q^{54} +5.99547 q^{55} +0.0689176 q^{56} +20.9074 q^{57} -9.35140 q^{58} -9.74596 q^{59} -1.51428 q^{60} +9.04821 q^{61} -9.87801 q^{62} -0.154435 q^{63} +8.86735 q^{64} -0.339641 q^{65} +24.2976 q^{66} -6.76683 q^{67} +0.00961615 q^{68} -3.57277 q^{69} +0.0259848 q^{70} +5.84470 q^{71} -21.0341 q^{72} -4.58304 q^{73} +0.780229 q^{74} +12.8926 q^{75} +3.39164 q^{76} +0.142534 q^{77} -1.37645 q^{78} -15.1903 q^{79} +2.57490 q^{80} +17.5381 q^{81} -3.27450 q^{82} -2.35275 q^{83} -0.0360000 q^{84} +0.0178572 q^{85} +13.3165 q^{86} +24.0587 q^{87} +19.4132 q^{88} +15.1594 q^{89} -7.93070 q^{90} -0.00807450 q^{91} -0.579582 q^{92} +25.4136 q^{93} +9.75664 q^{94} +6.29828 q^{95} -8.81088 q^{96} +12.9716 q^{97} -8.54532 q^{98} -43.5022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22085 0.863271 0.431635 0.902048i \(-0.357937\pi\)
0.431635 + 0.902048i \(0.357937\pi\)
\(3\) −3.14093 −1.81342 −0.906709 0.421757i \(-0.861413\pi\)
−0.906709 + 0.421757i \(0.861413\pi\)
\(4\) −0.509528 −0.254764
\(5\) −0.946195 −0.423151 −0.211576 0.977362i \(-0.567859\pi\)
−0.211576 + 0.977362i \(0.567859\pi\)
\(6\) −3.83460 −1.56547
\(7\) −0.0224945 −0.00850212 −0.00425106 0.999991i \(-0.501353\pi\)
−0.00425106 + 0.999991i \(0.501353\pi\)
\(8\) −3.06375 −1.08320
\(9\) 6.86545 2.28848
\(10\) −1.15516 −0.365294
\(11\) −6.33640 −1.91050 −0.955248 0.295806i \(-0.904412\pi\)
−0.955248 + 0.295806i \(0.904412\pi\)
\(12\) 1.60039 0.461993
\(13\) 0.358954 0.0995561 0.0497780 0.998760i \(-0.484149\pi\)
0.0497780 + 0.998760i \(0.484149\pi\)
\(14\) −0.0274624 −0.00733963
\(15\) 2.97193 0.767350
\(16\) −2.72133 −0.680331
\(17\) −0.0188727 −0.00457730 −0.00228865 0.999997i \(-0.500728\pi\)
−0.00228865 + 0.999997i \(0.500728\pi\)
\(18\) 8.38168 1.97558
\(19\) −6.65643 −1.52709 −0.763545 0.645755i \(-0.776543\pi\)
−0.763545 + 0.645755i \(0.776543\pi\)
\(20\) 0.482113 0.107804
\(21\) 0.0706537 0.0154179
\(22\) −7.73579 −1.64928
\(23\) 1.13749 0.237183 0.118591 0.992943i \(-0.462162\pi\)
0.118591 + 0.992943i \(0.462162\pi\)
\(24\) 9.62304 1.96430
\(25\) −4.10472 −0.820943
\(26\) 0.438229 0.0859438
\(27\) −12.1411 −2.33656
\(28\) 0.0114616 0.00216603
\(29\) −7.65975 −1.42238 −0.711190 0.703000i \(-0.751843\pi\)
−0.711190 + 0.703000i \(0.751843\pi\)
\(30\) 3.62828 0.662431
\(31\) −8.09110 −1.45320 −0.726602 0.687058i \(-0.758902\pi\)
−0.726602 + 0.687058i \(0.758902\pi\)
\(32\) 2.80518 0.495891
\(33\) 19.9022 3.46453
\(34\) −0.0230407 −0.00395144
\(35\) 0.0212842 0.00359768
\(36\) −3.49814 −0.583023
\(37\) 0.639087 0.105065 0.0525326 0.998619i \(-0.483271\pi\)
0.0525326 + 0.998619i \(0.483271\pi\)
\(38\) −8.12650 −1.31829
\(39\) −1.12745 −0.180537
\(40\) 2.89891 0.458358
\(41\) −2.68215 −0.418881 −0.209441 0.977821i \(-0.567164\pi\)
−0.209441 + 0.977821i \(0.567164\pi\)
\(42\) 0.0862575 0.0133098
\(43\) 10.9076 1.66339 0.831697 0.555230i \(-0.187370\pi\)
0.831697 + 0.555230i \(0.187370\pi\)
\(44\) 3.22857 0.486725
\(45\) −6.49605 −0.968375
\(46\) 1.38870 0.204753
\(47\) 7.99169 1.16571 0.582854 0.812577i \(-0.301936\pi\)
0.582854 + 0.812577i \(0.301936\pi\)
\(48\) 8.54750 1.23373
\(49\) −6.99949 −0.999928
\(50\) −5.01124 −0.708696
\(51\) 0.0592778 0.00830055
\(52\) −0.182897 −0.0253633
\(53\) −5.97511 −0.820744 −0.410372 0.911918i \(-0.634601\pi\)
−0.410372 + 0.911918i \(0.634601\pi\)
\(54\) −14.8225 −2.01708
\(55\) 5.99547 0.808429
\(56\) 0.0689176 0.00920951
\(57\) 20.9074 2.76925
\(58\) −9.35140 −1.22790
\(59\) −9.74596 −1.26882 −0.634408 0.772999i \(-0.718756\pi\)
−0.634408 + 0.772999i \(0.718756\pi\)
\(60\) −1.51428 −0.195493
\(61\) 9.04821 1.15850 0.579252 0.815148i \(-0.303345\pi\)
0.579252 + 0.815148i \(0.303345\pi\)
\(62\) −9.87801 −1.25451
\(63\) −0.154435 −0.0194570
\(64\) 8.86735 1.10842
\(65\) −0.339641 −0.0421273
\(66\) 24.2976 2.99082
\(67\) −6.76683 −0.826700 −0.413350 0.910572i \(-0.635641\pi\)
−0.413350 + 0.910572i \(0.635641\pi\)
\(68\) 0.00961615 0.00116613
\(69\) −3.57277 −0.430111
\(70\) 0.0259848 0.00310577
\(71\) 5.84470 0.693638 0.346819 0.937932i \(-0.387262\pi\)
0.346819 + 0.937932i \(0.387262\pi\)
\(72\) −21.0341 −2.47889
\(73\) −4.58304 −0.536404 −0.268202 0.963363i \(-0.586430\pi\)
−0.268202 + 0.963363i \(0.586430\pi\)
\(74\) 0.780229 0.0906997
\(75\) 12.8926 1.48871
\(76\) 3.39164 0.389047
\(77\) 0.142534 0.0162433
\(78\) −1.37645 −0.155852
\(79\) −15.1903 −1.70905 −0.854523 0.519414i \(-0.826150\pi\)
−0.854523 + 0.519414i \(0.826150\pi\)
\(80\) 2.57490 0.287883
\(81\) 17.5381 1.94867
\(82\) −3.27450 −0.361608
\(83\) −2.35275 −0.258248 −0.129124 0.991628i \(-0.541216\pi\)
−0.129124 + 0.991628i \(0.541216\pi\)
\(84\) −0.0360000 −0.00392792
\(85\) 0.0178572 0.00193689
\(86\) 13.3165 1.43596
\(87\) 24.0587 2.57937
\(88\) 19.4132 2.06945
\(89\) 15.1594 1.60689 0.803446 0.595378i \(-0.202998\pi\)
0.803446 + 0.595378i \(0.202998\pi\)
\(90\) −7.93070 −0.835969
\(91\) −0.00807450 −0.000846438 0
\(92\) −0.579582 −0.0604256
\(93\) 25.4136 2.63527
\(94\) 9.75664 1.00632
\(95\) 6.29828 0.646190
\(96\) −8.81088 −0.899257
\(97\) 12.9716 1.31707 0.658534 0.752551i \(-0.271177\pi\)
0.658534 + 0.752551i \(0.271177\pi\)
\(98\) −8.54532 −0.863208
\(99\) −43.5022 −4.37214
\(100\) 2.09147 0.209147
\(101\) 16.4512 1.63695 0.818476 0.574540i \(-0.194819\pi\)
0.818476 + 0.574540i \(0.194819\pi\)
\(102\) 0.0723692 0.00716562
\(103\) −2.78791 −0.274701 −0.137350 0.990523i \(-0.543859\pi\)
−0.137350 + 0.990523i \(0.543859\pi\)
\(104\) −1.09975 −0.107839
\(105\) −0.0668522 −0.00652410
\(106\) −7.29470 −0.708524
\(107\) 3.75751 0.363252 0.181626 0.983368i \(-0.441864\pi\)
0.181626 + 0.983368i \(0.441864\pi\)
\(108\) 6.18624 0.595271
\(109\) 3.69023 0.353460 0.176730 0.984259i \(-0.443448\pi\)
0.176730 + 0.984259i \(0.443448\pi\)
\(110\) 7.31956 0.697893
\(111\) −2.00733 −0.190527
\(112\) 0.0612149 0.00578426
\(113\) 0.0599889 0.00564329 0.00282164 0.999996i \(-0.499102\pi\)
0.00282164 + 0.999996i \(0.499102\pi\)
\(114\) 25.5248 2.39061
\(115\) −1.07629 −0.100364
\(116\) 3.90285 0.362371
\(117\) 2.46438 0.227832
\(118\) −11.8983 −1.09533
\(119\) 0.000424531 0 3.89167e−5 0
\(120\) −9.10527 −0.831194
\(121\) 29.1500 2.65000
\(122\) 11.0465 1.00010
\(123\) 8.42445 0.759607
\(124\) 4.12264 0.370224
\(125\) 8.61483 0.770534
\(126\) −0.188542 −0.0167966
\(127\) 10.4771 0.929692 0.464846 0.885392i \(-0.346110\pi\)
0.464846 + 0.885392i \(0.346110\pi\)
\(128\) 5.21534 0.460975
\(129\) −34.2600 −3.01643
\(130\) −0.414650 −0.0363672
\(131\) −5.26636 −0.460124 −0.230062 0.973176i \(-0.573893\pi\)
−0.230062 + 0.973176i \(0.573893\pi\)
\(132\) −10.1407 −0.882637
\(133\) 0.149733 0.0129835
\(134\) −8.26128 −0.713666
\(135\) 11.4879 0.988718
\(136\) 0.0578212 0.00495813
\(137\) −3.92989 −0.335753 −0.167877 0.985808i \(-0.553691\pi\)
−0.167877 + 0.985808i \(0.553691\pi\)
\(138\) −4.36182 −0.371302
\(139\) 1.53103 0.129860 0.0649299 0.997890i \(-0.479318\pi\)
0.0649299 + 0.997890i \(0.479318\pi\)
\(140\) −0.0108449 −0.000916560 0
\(141\) −25.1013 −2.11391
\(142\) 7.13549 0.598797
\(143\) −2.27448 −0.190201
\(144\) −18.6831 −1.55693
\(145\) 7.24761 0.601882
\(146\) −5.59520 −0.463062
\(147\) 21.9849 1.81329
\(148\) −0.325633 −0.0267668
\(149\) 7.53174 0.617024 0.308512 0.951220i \(-0.400169\pi\)
0.308512 + 0.951220i \(0.400169\pi\)
\(150\) 15.7400 1.28516
\(151\) 18.0198 1.46643 0.733215 0.679997i \(-0.238019\pi\)
0.733215 + 0.679997i \(0.238019\pi\)
\(152\) 20.3937 1.65414
\(153\) −0.129569 −0.0104751
\(154\) 0.174013 0.0140223
\(155\) 7.65576 0.614925
\(156\) 0.574468 0.0459942
\(157\) −3.27134 −0.261082 −0.130541 0.991443i \(-0.541671\pi\)
−0.130541 + 0.991443i \(0.541671\pi\)
\(158\) −18.5451 −1.47537
\(159\) 18.7674 1.48835
\(160\) −2.65425 −0.209837
\(161\) −0.0255872 −0.00201656
\(162\) 21.4113 1.68223
\(163\) −24.3816 −1.90971 −0.954856 0.297068i \(-0.903991\pi\)
−0.954856 + 0.297068i \(0.903991\pi\)
\(164\) 1.36663 0.106716
\(165\) −18.8314 −1.46602
\(166\) −2.87235 −0.222938
\(167\) 12.9593 1.00282 0.501411 0.865209i \(-0.332814\pi\)
0.501411 + 0.865209i \(0.332814\pi\)
\(168\) −0.216466 −0.0167007
\(169\) −12.8712 −0.990089
\(170\) 0.0218010 0.00167206
\(171\) −45.6994 −3.49472
\(172\) −5.55773 −0.423773
\(173\) −2.28681 −0.173863 −0.0869314 0.996214i \(-0.527706\pi\)
−0.0869314 + 0.996214i \(0.527706\pi\)
\(174\) 29.3721 2.22669
\(175\) 0.0923335 0.00697976
\(176\) 17.2434 1.29977
\(177\) 30.6114 2.30089
\(178\) 18.5073 1.38718
\(179\) −12.8359 −0.959399 −0.479700 0.877433i \(-0.659254\pi\)
−0.479700 + 0.877433i \(0.659254\pi\)
\(180\) 3.30992 0.246707
\(181\) 0.576179 0.0428271 0.0214135 0.999771i \(-0.493183\pi\)
0.0214135 + 0.999771i \(0.493183\pi\)
\(182\) −0.00985775 −0.000730705 0
\(183\) −28.4198 −2.10085
\(184\) −3.48498 −0.256916
\(185\) −0.604701 −0.0444585
\(186\) 31.0262 2.27495
\(187\) 0.119585 0.00874491
\(188\) −4.07199 −0.296980
\(189\) 0.273108 0.0198657
\(190\) 7.68925 0.557837
\(191\) −14.3322 −1.03704 −0.518520 0.855065i \(-0.673517\pi\)
−0.518520 + 0.855065i \(0.673517\pi\)
\(192\) −27.8518 −2.01003
\(193\) −6.85980 −0.493779 −0.246890 0.969044i \(-0.579409\pi\)
−0.246890 + 0.969044i \(0.579409\pi\)
\(194\) 15.8364 1.13699
\(195\) 1.06679 0.0763943
\(196\) 3.56644 0.254745
\(197\) 11.3893 0.811457 0.405728 0.913994i \(-0.367018\pi\)
0.405728 + 0.913994i \(0.367018\pi\)
\(198\) −53.1097 −3.77434
\(199\) −25.2042 −1.78668 −0.893339 0.449383i \(-0.851644\pi\)
−0.893339 + 0.449383i \(0.851644\pi\)
\(200\) 12.5758 0.889246
\(201\) 21.2541 1.49915
\(202\) 20.0844 1.41313
\(203\) 0.172302 0.0120932
\(204\) −0.0302037 −0.00211468
\(205\) 2.53784 0.177250
\(206\) −3.40362 −0.237141
\(207\) 7.80937 0.542789
\(208\) −0.976832 −0.0677311
\(209\) 42.1778 2.91750
\(210\) −0.0816164 −0.00563207
\(211\) −8.73149 −0.601101 −0.300550 0.953766i \(-0.597170\pi\)
−0.300550 + 0.953766i \(0.597170\pi\)
\(212\) 3.04448 0.209096
\(213\) −18.3578 −1.25786
\(214\) 4.58735 0.313585
\(215\) −10.3207 −0.703867
\(216\) 37.1974 2.53096
\(217\) 0.182005 0.0123553
\(218\) 4.50522 0.305132
\(219\) 14.3950 0.972725
\(220\) −3.05486 −0.205958
\(221\) −0.00677443 −0.000455698 0
\(222\) −2.45064 −0.164476
\(223\) −15.0962 −1.01092 −0.505459 0.862851i \(-0.668677\pi\)
−0.505459 + 0.862851i \(0.668677\pi\)
\(224\) −0.0631011 −0.00421612
\(225\) −28.1807 −1.87871
\(226\) 0.0732374 0.00487168
\(227\) −6.50073 −0.431468 −0.215734 0.976452i \(-0.569214\pi\)
−0.215734 + 0.976452i \(0.569214\pi\)
\(228\) −10.6529 −0.705505
\(229\) −13.3493 −0.882146 −0.441073 0.897471i \(-0.645402\pi\)
−0.441073 + 0.897471i \(0.645402\pi\)
\(230\) −1.31398 −0.0866414
\(231\) −0.447690 −0.0294558
\(232\) 23.4676 1.54072
\(233\) 27.3005 1.78852 0.894258 0.447551i \(-0.147704\pi\)
0.894258 + 0.447551i \(0.147704\pi\)
\(234\) 3.00864 0.196681
\(235\) −7.56169 −0.493270
\(236\) 4.96584 0.323248
\(237\) 47.7118 3.09921
\(238\) 0.000518289 0 3.35957e−5 0
\(239\) −12.4180 −0.803251 −0.401625 0.915804i \(-0.631555\pi\)
−0.401625 + 0.915804i \(0.631555\pi\)
\(240\) −8.08760 −0.522052
\(241\) −3.98664 −0.256802 −0.128401 0.991722i \(-0.540984\pi\)
−0.128401 + 0.991722i \(0.540984\pi\)
\(242\) 35.5877 2.28766
\(243\) −18.6625 −1.19720
\(244\) −4.61032 −0.295145
\(245\) 6.62289 0.423121
\(246\) 10.2850 0.655746
\(247\) −2.38936 −0.152031
\(248\) 24.7891 1.57411
\(249\) 7.38982 0.468311
\(250\) 10.5174 0.665180
\(251\) −10.2676 −0.648084 −0.324042 0.946043i \(-0.605042\pi\)
−0.324042 + 0.946043i \(0.605042\pi\)
\(252\) 0.0786889 0.00495693
\(253\) −7.20758 −0.453137
\(254\) 12.7909 0.802576
\(255\) −0.0560883 −0.00351239
\(256\) −11.3676 −0.710473
\(257\) 9.95019 0.620676 0.310338 0.950626i \(-0.399558\pi\)
0.310338 + 0.950626i \(0.399558\pi\)
\(258\) −41.8263 −2.60399
\(259\) −0.0143759 −0.000893278 0
\(260\) 0.173056 0.0107325
\(261\) −52.5876 −3.25509
\(262\) −6.42943 −0.397212
\(263\) −4.10482 −0.253114 −0.126557 0.991959i \(-0.540393\pi\)
−0.126557 + 0.991959i \(0.540393\pi\)
\(264\) −60.9754 −3.75278
\(265\) 5.65362 0.347299
\(266\) 0.182801 0.0112083
\(267\) −47.6146 −2.91397
\(268\) 3.44789 0.210613
\(269\) −3.11361 −0.189840 −0.0949200 0.995485i \(-0.530260\pi\)
−0.0949200 + 0.995485i \(0.530260\pi\)
\(270\) 14.0249 0.853531
\(271\) 6.43569 0.390941 0.195470 0.980710i \(-0.437377\pi\)
0.195470 + 0.980710i \(0.437377\pi\)
\(272\) 0.0513587 0.00311408
\(273\) 0.0253615 0.00153495
\(274\) −4.79781 −0.289846
\(275\) 26.0091 1.56841
\(276\) 1.82043 0.109577
\(277\) −12.8651 −0.772991 −0.386496 0.922291i \(-0.626315\pi\)
−0.386496 + 0.922291i \(0.626315\pi\)
\(278\) 1.86915 0.112104
\(279\) −55.5490 −3.32563
\(280\) −0.0652095 −0.00389701
\(281\) 7.36315 0.439249 0.219624 0.975585i \(-0.429517\pi\)
0.219624 + 0.975585i \(0.429517\pi\)
\(282\) −30.6449 −1.82488
\(283\) 9.49154 0.564214 0.282107 0.959383i \(-0.408967\pi\)
0.282107 + 0.959383i \(0.408967\pi\)
\(284\) −2.97804 −0.176714
\(285\) −19.7825 −1.17181
\(286\) −2.77680 −0.164195
\(287\) 0.0603336 0.00356138
\(288\) 19.2588 1.13484
\(289\) −16.9996 −0.999979
\(290\) 8.84824 0.519587
\(291\) −40.7429 −2.38839
\(292\) 2.33519 0.136656
\(293\) 11.5436 0.674385 0.337193 0.941436i \(-0.390523\pi\)
0.337193 + 0.941436i \(0.390523\pi\)
\(294\) 26.8403 1.56536
\(295\) 9.22157 0.536901
\(296\) −1.95801 −0.113807
\(297\) 76.9310 4.46399
\(298\) 9.19511 0.532659
\(299\) 0.408306 0.0236130
\(300\) −6.56915 −0.379270
\(301\) −0.245361 −0.0141424
\(302\) 21.9994 1.26593
\(303\) −51.6720 −2.96848
\(304\) 18.1143 1.03893
\(305\) −8.56137 −0.490223
\(306\) −0.158185 −0.00904282
\(307\) −13.2120 −0.754049 −0.377025 0.926203i \(-0.623053\pi\)
−0.377025 + 0.926203i \(0.623053\pi\)
\(308\) −0.0726251 −0.00413820
\(309\) 8.75663 0.498147
\(310\) 9.34652 0.530847
\(311\) 21.2986 1.20773 0.603867 0.797085i \(-0.293626\pi\)
0.603867 + 0.797085i \(0.293626\pi\)
\(312\) 3.45423 0.195558
\(313\) −14.1808 −0.801547 −0.400774 0.916177i \(-0.631259\pi\)
−0.400774 + 0.916177i \(0.631259\pi\)
\(314\) −3.99382 −0.225384
\(315\) 0.146125 0.00823324
\(316\) 7.73989 0.435403
\(317\) −28.8514 −1.62046 −0.810229 0.586113i \(-0.800657\pi\)
−0.810229 + 0.586113i \(0.800657\pi\)
\(318\) 22.9122 1.28485
\(319\) 48.5352 2.71745
\(320\) −8.39024 −0.469029
\(321\) −11.8021 −0.658727
\(322\) −0.0312381 −0.00174083
\(323\) 0.125625 0.00698994
\(324\) −8.93613 −0.496452
\(325\) −1.47341 −0.0817299
\(326\) −29.7662 −1.64860
\(327\) −11.5908 −0.640971
\(328\) 8.21745 0.453733
\(329\) −0.179769 −0.00991099
\(330\) −22.9902 −1.26557
\(331\) 29.5040 1.62169 0.810843 0.585264i \(-0.199009\pi\)
0.810843 + 0.585264i \(0.199009\pi\)
\(332\) 1.19879 0.0657922
\(333\) 4.38762 0.240440
\(334\) 15.8214 0.865707
\(335\) 6.40274 0.349819
\(336\) −0.192272 −0.0104893
\(337\) −30.9951 −1.68841 −0.844205 0.536021i \(-0.819927\pi\)
−0.844205 + 0.536021i \(0.819927\pi\)
\(338\) −15.7137 −0.854714
\(339\) −0.188421 −0.0102336
\(340\) −0.00909875 −0.000493449 0
\(341\) 51.2684 2.77634
\(342\) −55.7921 −3.01689
\(343\) 0.314912 0.0170036
\(344\) −33.4182 −1.80179
\(345\) 3.38054 0.182002
\(346\) −2.79185 −0.150091
\(347\) −30.5123 −1.63799 −0.818993 0.573804i \(-0.805467\pi\)
−0.818993 + 0.573804i \(0.805467\pi\)
\(348\) −12.2586 −0.657130
\(349\) −18.7502 −1.00367 −0.501837 0.864962i \(-0.667342\pi\)
−0.501837 + 0.864962i \(0.667342\pi\)
\(350\) 0.112725 0.00602542
\(351\) −4.35811 −0.232619
\(352\) −17.7747 −0.947397
\(353\) 3.35416 0.178524 0.0892621 0.996008i \(-0.471549\pi\)
0.0892621 + 0.996008i \(0.471549\pi\)
\(354\) 37.3719 1.98629
\(355\) −5.53022 −0.293514
\(356\) −7.72413 −0.409378
\(357\) −0.00133342 −7.05723e−5 0
\(358\) −15.6707 −0.828221
\(359\) 1.98616 0.104826 0.0524128 0.998626i \(-0.483309\pi\)
0.0524128 + 0.998626i \(0.483309\pi\)
\(360\) 19.9023 1.04894
\(361\) 25.3081 1.33200
\(362\) 0.703428 0.0369713
\(363\) −91.5580 −4.80555
\(364\) 0.00411418 0.000215642 0
\(365\) 4.33645 0.226980
\(366\) −34.6963 −1.81360
\(367\) 20.9339 1.09274 0.546369 0.837544i \(-0.316010\pi\)
0.546369 + 0.837544i \(0.316010\pi\)
\(368\) −3.09548 −0.161363
\(369\) −18.4142 −0.958603
\(370\) −0.738248 −0.0383797
\(371\) 0.134407 0.00697807
\(372\) −12.9489 −0.671371
\(373\) −7.22722 −0.374211 −0.187106 0.982340i \(-0.559911\pi\)
−0.187106 + 0.982340i \(0.559911\pi\)
\(374\) 0.145995 0.00754922
\(375\) −27.0586 −1.39730
\(376\) −24.4846 −1.26270
\(377\) −2.74950 −0.141607
\(378\) 0.333424 0.0171495
\(379\) 14.5494 0.747352 0.373676 0.927559i \(-0.378097\pi\)
0.373676 + 0.927559i \(0.378097\pi\)
\(380\) −3.20915 −0.164626
\(381\) −32.9078 −1.68592
\(382\) −17.4974 −0.895247
\(383\) 33.4698 1.71023 0.855114 0.518439i \(-0.173487\pi\)
0.855114 + 0.518439i \(0.173487\pi\)
\(384\) −16.3810 −0.835940
\(385\) −0.134865 −0.00687336
\(386\) −8.37478 −0.426265
\(387\) 74.8856 3.80665
\(388\) −6.60940 −0.335541
\(389\) 0.947467 0.0480385 0.0240192 0.999711i \(-0.492354\pi\)
0.0240192 + 0.999711i \(0.492354\pi\)
\(390\) 1.30239 0.0659490
\(391\) −0.0214674 −0.00108566
\(392\) 21.4447 1.08312
\(393\) 16.5413 0.834397
\(394\) 13.9047 0.700507
\(395\) 14.3730 0.723184
\(396\) 22.1656 1.11386
\(397\) −24.8447 −1.24692 −0.623460 0.781855i \(-0.714274\pi\)
−0.623460 + 0.781855i \(0.714274\pi\)
\(398\) −30.7705 −1.54239
\(399\) −0.470301 −0.0235445
\(400\) 11.1703 0.558513
\(401\) 15.9321 0.795613 0.397807 0.917469i \(-0.369771\pi\)
0.397807 + 0.917469i \(0.369771\pi\)
\(402\) 25.9481 1.29417
\(403\) −2.90434 −0.144675
\(404\) −8.38233 −0.417036
\(405\) −16.5944 −0.824583
\(406\) 0.210355 0.0104397
\(407\) −4.04951 −0.200727
\(408\) −0.181613 −0.00899116
\(409\) 6.85730 0.339071 0.169536 0.985524i \(-0.445773\pi\)
0.169536 + 0.985524i \(0.445773\pi\)
\(410\) 3.09831 0.153015
\(411\) 12.3435 0.608861
\(412\) 1.42052 0.0699838
\(413\) 0.219230 0.0107876
\(414\) 9.53406 0.468573
\(415\) 2.22616 0.109278
\(416\) 1.00693 0.0493689
\(417\) −4.80885 −0.235490
\(418\) 51.4927 2.51859
\(419\) 25.8878 1.26470 0.632352 0.774681i \(-0.282090\pi\)
0.632352 + 0.774681i \(0.282090\pi\)
\(420\) 0.0340630 0.00166211
\(421\) 40.0558 1.95220 0.976100 0.217322i \(-0.0697320\pi\)
0.976100 + 0.217322i \(0.0697320\pi\)
\(422\) −10.6598 −0.518913
\(423\) 54.8665 2.66770
\(424\) 18.3063 0.889031
\(425\) 0.0774670 0.00375770
\(426\) −22.4121 −1.08587
\(427\) −0.203535 −0.00984975
\(428\) −1.91455 −0.0925434
\(429\) 7.14398 0.344915
\(430\) −12.6000 −0.607628
\(431\) −16.3544 −0.787762 −0.393881 0.919161i \(-0.628868\pi\)
−0.393881 + 0.919161i \(0.628868\pi\)
\(432\) 33.0399 1.58963
\(433\) −0.620336 −0.0298114 −0.0149057 0.999889i \(-0.504745\pi\)
−0.0149057 + 0.999889i \(0.504745\pi\)
\(434\) 0.222201 0.0106660
\(435\) −22.7643 −1.09146
\(436\) −1.88028 −0.0900489
\(437\) −7.57161 −0.362199
\(438\) 17.5741 0.839725
\(439\) 26.1015 1.24575 0.622877 0.782319i \(-0.285964\pi\)
0.622877 + 0.782319i \(0.285964\pi\)
\(440\) −18.3686 −0.875691
\(441\) −48.0547 −2.28832
\(442\) −0.00827056 −0.000393390 0
\(443\) −17.1496 −0.814800 −0.407400 0.913250i \(-0.633564\pi\)
−0.407400 + 0.913250i \(0.633564\pi\)
\(444\) 1.02279 0.0485394
\(445\) −14.3437 −0.679958
\(446\) −18.4302 −0.872695
\(447\) −23.6567 −1.11892
\(448\) −0.199467 −0.00942392
\(449\) 17.4659 0.824265 0.412132 0.911124i \(-0.364784\pi\)
0.412132 + 0.911124i \(0.364784\pi\)
\(450\) −34.4044 −1.62184
\(451\) 16.9952 0.800271
\(452\) −0.0305660 −0.00143771
\(453\) −56.5989 −2.65925
\(454\) −7.93641 −0.372474
\(455\) 0.00764005 0.000358171 0
\(456\) −64.0551 −2.99966
\(457\) 17.3283 0.810583 0.405291 0.914188i \(-0.367170\pi\)
0.405291 + 0.914188i \(0.367170\pi\)
\(458\) −16.2975 −0.761531
\(459\) 0.229135 0.0106951
\(460\) 0.548397 0.0255692
\(461\) −4.65508 −0.216809 −0.108404 0.994107i \(-0.534574\pi\)
−0.108404 + 0.994107i \(0.534574\pi\)
\(462\) −0.546562 −0.0254284
\(463\) 11.5407 0.536343 0.268171 0.963371i \(-0.413581\pi\)
0.268171 + 0.963371i \(0.413581\pi\)
\(464\) 20.8447 0.967690
\(465\) −24.0462 −1.11512
\(466\) 33.3298 1.54397
\(467\) 12.1981 0.564460 0.282230 0.959347i \(-0.408926\pi\)
0.282230 + 0.959347i \(0.408926\pi\)
\(468\) −1.25567 −0.0580435
\(469\) 0.152216 0.00702870
\(470\) −9.23168 −0.425826
\(471\) 10.2751 0.473450
\(472\) 29.8592 1.37438
\(473\) −69.1149 −3.17791
\(474\) 58.2489 2.67546
\(475\) 27.3228 1.25365
\(476\) −0.000216311 0 −9.91458e−6 0
\(477\) −41.0218 −1.87826
\(478\) −15.1605 −0.693423
\(479\) 9.03674 0.412899 0.206450 0.978457i \(-0.433809\pi\)
0.206450 + 0.978457i \(0.433809\pi\)
\(480\) 8.33681 0.380522
\(481\) 0.229403 0.0104599
\(482\) −4.86708 −0.221690
\(483\) 0.0803677 0.00365686
\(484\) −14.8527 −0.675123
\(485\) −12.2737 −0.557319
\(486\) −22.7841 −1.03351
\(487\) −3.89191 −0.176359 −0.0881796 0.996105i \(-0.528105\pi\)
−0.0881796 + 0.996105i \(0.528105\pi\)
\(488\) −27.7215 −1.25489
\(489\) 76.5809 3.46311
\(490\) 8.08554 0.365268
\(491\) −39.6501 −1.78938 −0.894691 0.446686i \(-0.852604\pi\)
−0.894691 + 0.446686i \(0.852604\pi\)
\(492\) −4.29249 −0.193520
\(493\) 0.144560 0.00651065
\(494\) −2.91704 −0.131244
\(495\) 41.1616 1.85008
\(496\) 22.0185 0.988661
\(497\) −0.131474 −0.00589739
\(498\) 9.02185 0.404279
\(499\) −5.98204 −0.267793 −0.133896 0.990995i \(-0.542749\pi\)
−0.133896 + 0.990995i \(0.542749\pi\)
\(500\) −4.38950 −0.196304
\(501\) −40.7043 −1.81854
\(502\) −12.5352 −0.559472
\(503\) −30.5397 −1.36170 −0.680849 0.732424i \(-0.738389\pi\)
−0.680849 + 0.732424i \(0.738389\pi\)
\(504\) 0.473151 0.0210758
\(505\) −15.5660 −0.692678
\(506\) −8.79936 −0.391179
\(507\) 40.4274 1.79544
\(508\) −5.33837 −0.236852
\(509\) 34.8350 1.54404 0.772018 0.635601i \(-0.219248\pi\)
0.772018 + 0.635601i \(0.219248\pi\)
\(510\) −0.0684754 −0.00303214
\(511\) 0.103093 0.00456058
\(512\) −24.3088 −1.07431
\(513\) 80.8165 3.56814
\(514\) 12.1477 0.535811
\(515\) 2.63790 0.116240
\(516\) 17.4564 0.768477
\(517\) −50.6385 −2.22708
\(518\) −0.0175509 −0.000771140 0
\(519\) 7.18271 0.315286
\(520\) 1.04058 0.0456323
\(521\) −12.7551 −0.558810 −0.279405 0.960173i \(-0.590137\pi\)
−0.279405 + 0.960173i \(0.590137\pi\)
\(522\) −64.2015 −2.81003
\(523\) −29.5165 −1.29066 −0.645332 0.763902i \(-0.723281\pi\)
−0.645332 + 0.763902i \(0.723281\pi\)
\(524\) 2.68336 0.117223
\(525\) −0.290013 −0.0126572
\(526\) −5.01137 −0.218506
\(527\) 0.152701 0.00665175
\(528\) −54.1604 −2.35703
\(529\) −21.7061 −0.943744
\(530\) 6.90221 0.299813
\(531\) −66.9104 −2.90366
\(532\) −0.0762932 −0.00330773
\(533\) −0.962770 −0.0417022
\(534\) −58.1302 −2.51554
\(535\) −3.55533 −0.153710
\(536\) 20.7319 0.895482
\(537\) 40.3166 1.73979
\(538\) −3.80124 −0.163883
\(539\) 44.3516 1.91036
\(540\) −5.85338 −0.251890
\(541\) 20.4901 0.880940 0.440470 0.897767i \(-0.354812\pi\)
0.440470 + 0.897767i \(0.354812\pi\)
\(542\) 7.85701 0.337488
\(543\) −1.80974 −0.0776633
\(544\) −0.0529413 −0.00226984
\(545\) −3.49168 −0.149567
\(546\) 0.0309625 0.00132507
\(547\) −36.3056 −1.55231 −0.776157 0.630540i \(-0.782834\pi\)
−0.776157 + 0.630540i \(0.782834\pi\)
\(548\) 2.00239 0.0855378
\(549\) 62.1201 2.65122
\(550\) 31.7532 1.35396
\(551\) 50.9866 2.17210
\(552\) 10.9461 0.465897
\(553\) 0.341699 0.0145305
\(554\) −15.7064 −0.667301
\(555\) 1.89932 0.0806218
\(556\) −0.780100 −0.0330836
\(557\) −18.1871 −0.770614 −0.385307 0.922788i \(-0.625904\pi\)
−0.385307 + 0.922788i \(0.625904\pi\)
\(558\) −67.8170 −2.87092
\(559\) 3.91533 0.165601
\(560\) −0.0579212 −0.00244762
\(561\) −0.375608 −0.0158582
\(562\) 8.98929 0.379191
\(563\) 11.2207 0.472895 0.236448 0.971644i \(-0.424017\pi\)
0.236448 + 0.971644i \(0.424017\pi\)
\(564\) 12.7898 0.538549
\(565\) −0.0567612 −0.00238796
\(566\) 11.5877 0.487069
\(567\) −0.394510 −0.0165679
\(568\) −17.9067 −0.751349
\(569\) 41.0440 1.72066 0.860328 0.509741i \(-0.170259\pi\)
0.860328 + 0.509741i \(0.170259\pi\)
\(570\) −24.1514 −1.01159
\(571\) −25.4279 −1.06412 −0.532062 0.846705i \(-0.678583\pi\)
−0.532062 + 0.846705i \(0.678583\pi\)
\(572\) 1.15891 0.0484565
\(573\) 45.0164 1.88059
\(574\) 0.0736582 0.00307444
\(575\) −4.66906 −0.194713
\(576\) 60.8784 2.53660
\(577\) 27.6682 1.15184 0.575922 0.817505i \(-0.304643\pi\)
0.575922 + 0.817505i \(0.304643\pi\)
\(578\) −20.7540 −0.863252
\(579\) 21.5462 0.895428
\(580\) −3.69286 −0.153338
\(581\) 0.0529239 0.00219565
\(582\) −49.7410 −2.06183
\(583\) 37.8607 1.56803
\(584\) 14.0413 0.581034
\(585\) −2.33179 −0.0964076
\(586\) 14.0930 0.582177
\(587\) 34.0275 1.40447 0.702234 0.711947i \(-0.252186\pi\)
0.702234 + 0.711947i \(0.252186\pi\)
\(588\) −11.2019 −0.461960
\(589\) 53.8578 2.21917
\(590\) 11.2581 0.463491
\(591\) −35.7731 −1.47151
\(592\) −1.73916 −0.0714792
\(593\) −48.2166 −1.98002 −0.990009 0.141003i \(-0.954967\pi\)
−0.990009 + 0.141003i \(0.954967\pi\)
\(594\) 93.9211 3.85363
\(595\) −0.000401689 0 −1.64677e−5 0
\(596\) −3.83763 −0.157195
\(597\) 79.1647 3.23999
\(598\) 0.498480 0.0203844
\(599\) −30.8669 −1.26119 −0.630593 0.776113i \(-0.717188\pi\)
−0.630593 + 0.776113i \(0.717188\pi\)
\(600\) −39.4999 −1.61257
\(601\) 24.3388 0.992801 0.496400 0.868094i \(-0.334655\pi\)
0.496400 + 0.868094i \(0.334655\pi\)
\(602\) −0.299549 −0.0122087
\(603\) −46.4573 −1.89189
\(604\) −9.18159 −0.373593
\(605\) −27.5815 −1.12135
\(606\) −63.0837 −2.56260
\(607\) 28.5189 1.15755 0.578773 0.815488i \(-0.303532\pi\)
0.578773 + 0.815488i \(0.303532\pi\)
\(608\) −18.6725 −0.757270
\(609\) −0.541189 −0.0219301
\(610\) −10.4521 −0.423195
\(611\) 2.86865 0.116053
\(612\) 0.0660192 0.00266867
\(613\) −14.2204 −0.574358 −0.287179 0.957877i \(-0.592717\pi\)
−0.287179 + 0.957877i \(0.592717\pi\)
\(614\) −16.1299 −0.650949
\(615\) −7.97117 −0.321429
\(616\) −0.436690 −0.0175947
\(617\) −37.4279 −1.50679 −0.753395 0.657568i \(-0.771585\pi\)
−0.753395 + 0.657568i \(0.771585\pi\)
\(618\) 10.6905 0.430036
\(619\) −30.1790 −1.21300 −0.606498 0.795085i \(-0.707426\pi\)
−0.606498 + 0.795085i \(0.707426\pi\)
\(620\) −3.90082 −0.156661
\(621\) −13.8104 −0.554191
\(622\) 26.0024 1.04260
\(623\) −0.341003 −0.0136620
\(624\) 3.06816 0.122825
\(625\) 12.3723 0.494891
\(626\) −17.3126 −0.691952
\(627\) −132.478 −5.29064
\(628\) 1.66684 0.0665142
\(629\) −0.0120613 −0.000480915 0
\(630\) 0.178397 0.00710751
\(631\) −11.3900 −0.453429 −0.226715 0.973961i \(-0.572798\pi\)
−0.226715 + 0.973961i \(0.572798\pi\)
\(632\) 46.5394 1.85124
\(633\) 27.4250 1.09005
\(634\) −35.2233 −1.39889
\(635\) −9.91337 −0.393400
\(636\) −9.56251 −0.379178
\(637\) −2.51250 −0.0995489
\(638\) 59.2542 2.34590
\(639\) 40.1265 1.58738
\(640\) −4.93473 −0.195062
\(641\) −35.9168 −1.41863 −0.709315 0.704892i \(-0.750996\pi\)
−0.709315 + 0.704892i \(0.750996\pi\)
\(642\) −14.4085 −0.568660
\(643\) −11.7899 −0.464947 −0.232474 0.972603i \(-0.574682\pi\)
−0.232474 + 0.972603i \(0.574682\pi\)
\(644\) 0.0130374 0.000513746 0
\(645\) 32.4167 1.27641
\(646\) 0.153369 0.00603421
\(647\) −8.51966 −0.334942 −0.167471 0.985877i \(-0.553560\pi\)
−0.167471 + 0.985877i \(0.553560\pi\)
\(648\) −53.7323 −2.11080
\(649\) 61.7543 2.42407
\(650\) −1.79881 −0.0705550
\(651\) −0.571666 −0.0224054
\(652\) 12.4231 0.486526
\(653\) 11.9568 0.467905 0.233952 0.972248i \(-0.424834\pi\)
0.233952 + 0.972248i \(0.424834\pi\)
\(654\) −14.1506 −0.553331
\(655\) 4.98300 0.194702
\(656\) 7.29900 0.284978
\(657\) −31.4646 −1.22755
\(658\) −0.219471 −0.00855586
\(659\) −9.67627 −0.376934 −0.188467 0.982080i \(-0.560352\pi\)
−0.188467 + 0.982080i \(0.560352\pi\)
\(660\) 9.59510 0.373489
\(661\) 10.2307 0.397926 0.198963 0.980007i \(-0.436243\pi\)
0.198963 + 0.980007i \(0.436243\pi\)
\(662\) 36.0199 1.39995
\(663\) 0.0212780 0.000826370 0
\(664\) 7.20824 0.279734
\(665\) −0.141677 −0.00549399
\(666\) 5.35662 0.207565
\(667\) −8.71287 −0.337364
\(668\) −6.60314 −0.255483
\(669\) 47.4162 1.83322
\(670\) 7.81678 0.301988
\(671\) −57.3331 −2.21332
\(672\) 0.198196 0.00764559
\(673\) −21.1798 −0.816422 −0.408211 0.912888i \(-0.633847\pi\)
−0.408211 + 0.912888i \(0.633847\pi\)
\(674\) −37.8403 −1.45755
\(675\) 49.8358 1.91818
\(676\) 6.55821 0.252239
\(677\) −48.9082 −1.87969 −0.939847 0.341596i \(-0.889032\pi\)
−0.939847 + 0.341596i \(0.889032\pi\)
\(678\) −0.230034 −0.00883439
\(679\) −0.291790 −0.0111979
\(680\) −0.0547102 −0.00209804
\(681\) 20.4183 0.782432
\(682\) 62.5910 2.39673
\(683\) 31.5927 1.20886 0.604430 0.796658i \(-0.293401\pi\)
0.604430 + 0.796658i \(0.293401\pi\)
\(684\) 23.2851 0.890329
\(685\) 3.71844 0.142074
\(686\) 0.384460 0.0146787
\(687\) 41.9292 1.59970
\(688\) −29.6831 −1.13166
\(689\) −2.14479 −0.0817100
\(690\) 4.12713 0.157117
\(691\) −15.7644 −0.599708 −0.299854 0.953985i \(-0.596938\pi\)
−0.299854 + 0.953985i \(0.596938\pi\)
\(692\) 1.16519 0.0442940
\(693\) 0.978561 0.0371725
\(694\) −37.2509 −1.41402
\(695\) −1.44865 −0.0549504
\(696\) −73.7101 −2.79397
\(697\) 0.0506193 0.00191734
\(698\) −22.8911 −0.866442
\(699\) −85.7491 −3.24333
\(700\) −0.0470465 −0.00177819
\(701\) 11.1194 0.419972 0.209986 0.977704i \(-0.432658\pi\)
0.209986 + 0.977704i \(0.432658\pi\)
\(702\) −5.32059 −0.200813
\(703\) −4.25404 −0.160444
\(704\) −56.1871 −2.11763
\(705\) 23.7508 0.894505
\(706\) 4.09493 0.154115
\(707\) −0.370061 −0.0139176
\(708\) −15.5974 −0.586184
\(709\) −31.4261 −1.18023 −0.590116 0.807319i \(-0.700918\pi\)
−0.590116 + 0.807319i \(0.700918\pi\)
\(710\) −6.75156 −0.253382
\(711\) −104.288 −3.91112
\(712\) −46.4446 −1.74059
\(713\) −9.20353 −0.344675
\(714\) −0.00162791 −6.09230e−5 0
\(715\) 2.15210 0.0804840
\(716\) 6.54024 0.244420
\(717\) 39.0040 1.45663
\(718\) 2.42481 0.0904929
\(719\) 48.6905 1.81585 0.907925 0.419133i \(-0.137666\pi\)
0.907925 + 0.419133i \(0.137666\pi\)
\(720\) 17.6779 0.658816
\(721\) 0.0627126 0.00233554
\(722\) 30.8973 1.14988
\(723\) 12.5218 0.465689
\(724\) −0.293579 −0.0109108
\(725\) 31.4411 1.16769
\(726\) −111.779 −4.14849
\(727\) 44.7373 1.65921 0.829607 0.558348i \(-0.188565\pi\)
0.829607 + 0.558348i \(0.188565\pi\)
\(728\) 0.0247383 0.000916862 0
\(729\) 6.00345 0.222350
\(730\) 5.29415 0.195945
\(731\) −0.205856 −0.00761385
\(732\) 14.4807 0.535222
\(733\) −4.39845 −0.162460 −0.0812302 0.996695i \(-0.525885\pi\)
−0.0812302 + 0.996695i \(0.525885\pi\)
\(734\) 25.5571 0.943329
\(735\) −20.8020 −0.767294
\(736\) 3.19086 0.117617
\(737\) 42.8773 1.57941
\(738\) −22.4809 −0.827534
\(739\) −29.7684 −1.09505 −0.547523 0.836790i \(-0.684429\pi\)
−0.547523 + 0.836790i \(0.684429\pi\)
\(740\) 0.308112 0.0113264
\(741\) 7.50480 0.275696
\(742\) 0.164091 0.00602396
\(743\) 0.325683 0.0119481 0.00597407 0.999982i \(-0.498098\pi\)
0.00597407 + 0.999982i \(0.498098\pi\)
\(744\) −77.8610 −2.85452
\(745\) −7.12649 −0.261094
\(746\) −8.82334 −0.323045
\(747\) −16.1527 −0.590995
\(748\) −0.0609318 −0.00222789
\(749\) −0.0845232 −0.00308841
\(750\) −33.0345 −1.20625
\(751\) −6.81255 −0.248593 −0.124297 0.992245i \(-0.539667\pi\)
−0.124297 + 0.992245i \(0.539667\pi\)
\(752\) −21.7480 −0.793067
\(753\) 32.2498 1.17525
\(754\) −3.35673 −0.122245
\(755\) −17.0502 −0.620522
\(756\) −0.139156 −0.00506107
\(757\) 13.6442 0.495905 0.247953 0.968772i \(-0.420242\pi\)
0.247953 + 0.968772i \(0.420242\pi\)
\(758\) 17.7626 0.645167
\(759\) 22.6385 0.821726
\(760\) −19.2964 −0.699953
\(761\) 0.601384 0.0218002 0.0109001 0.999941i \(-0.496530\pi\)
0.0109001 + 0.999941i \(0.496530\pi\)
\(762\) −40.1755 −1.45540
\(763\) −0.0830099 −0.00300516
\(764\) 7.30265 0.264200
\(765\) 0.122598 0.00443254
\(766\) 40.8616 1.47639
\(767\) −3.49835 −0.126318
\(768\) 35.7048 1.28838
\(769\) −3.34733 −0.120708 −0.0603538 0.998177i \(-0.519223\pi\)
−0.0603538 + 0.998177i \(0.519223\pi\)
\(770\) −0.164650 −0.00593357
\(771\) −31.2529 −1.12554
\(772\) 3.49526 0.125797
\(773\) −9.87620 −0.355222 −0.177611 0.984101i \(-0.556837\pi\)
−0.177611 + 0.984101i \(0.556837\pi\)
\(774\) 91.4240 3.28617
\(775\) 33.2117 1.19300
\(776\) −39.7418 −1.42665
\(777\) 0.0451538 0.00161989
\(778\) 1.15671 0.0414702
\(779\) 17.8535 0.639670
\(780\) −0.543559 −0.0194625
\(781\) −37.0343 −1.32519
\(782\) −0.0262085 −0.000937214 0
\(783\) 92.9979 3.32347
\(784\) 19.0479 0.680282
\(785\) 3.09533 0.110477
\(786\) 20.1944 0.720311
\(787\) 15.9163 0.567355 0.283677 0.958920i \(-0.408446\pi\)
0.283677 + 0.958920i \(0.408446\pi\)
\(788\) −5.80318 −0.206730
\(789\) 12.8930 0.459001
\(790\) 17.5473 0.624304
\(791\) −0.00134942 −4.79799e−5 0
\(792\) 133.280 4.73590
\(793\) 3.24790 0.115336
\(794\) −30.3316 −1.07643
\(795\) −17.7576 −0.629798
\(796\) 12.8422 0.455181
\(797\) 38.7987 1.37432 0.687161 0.726505i \(-0.258857\pi\)
0.687161 + 0.726505i \(0.258857\pi\)
\(798\) −0.574167 −0.0203253
\(799\) −0.150824 −0.00533579
\(800\) −11.5145 −0.407098
\(801\) 104.076 3.67735
\(802\) 19.4507 0.686830
\(803\) 29.0400 1.02480
\(804\) −10.8296 −0.381930
\(805\) 0.0242105 0.000853308 0
\(806\) −3.54576 −0.124894
\(807\) 9.77963 0.344259
\(808\) −50.4023 −1.77315
\(809\) −0.684369 −0.0240611 −0.0120306 0.999928i \(-0.503830\pi\)
−0.0120306 + 0.999928i \(0.503830\pi\)
\(810\) −20.2593 −0.711839
\(811\) 34.2689 1.20334 0.601672 0.798743i \(-0.294502\pi\)
0.601672 + 0.798743i \(0.294502\pi\)
\(812\) −0.0877928 −0.00308092
\(813\) −20.2141 −0.708939
\(814\) −4.94384 −0.173282
\(815\) 23.0697 0.808097
\(816\) −0.161314 −0.00564712
\(817\) −72.6057 −2.54015
\(818\) 8.37172 0.292710
\(819\) −0.0554351 −0.00193706
\(820\) −1.29310 −0.0451569
\(821\) −16.1277 −0.562861 −0.281431 0.959582i \(-0.590809\pi\)
−0.281431 + 0.959582i \(0.590809\pi\)
\(822\) 15.0696 0.525612
\(823\) 26.7045 0.930861 0.465430 0.885084i \(-0.345900\pi\)
0.465430 + 0.885084i \(0.345900\pi\)
\(824\) 8.54147 0.297556
\(825\) −81.6928 −2.84418
\(826\) 0.267647 0.00931264
\(827\) 1.68571 0.0586178 0.0293089 0.999570i \(-0.490669\pi\)
0.0293089 + 0.999570i \(0.490669\pi\)
\(828\) −3.97909 −0.138283
\(829\) 47.5517 1.65154 0.825770 0.564007i \(-0.190741\pi\)
0.825770 + 0.564007i \(0.190741\pi\)
\(830\) 2.71780 0.0943363
\(831\) 40.4085 1.40176
\(832\) 3.18298 0.110350
\(833\) 0.132099 0.00457696
\(834\) −5.87087 −0.203292
\(835\) −12.2620 −0.424346
\(836\) −21.4908 −0.743274
\(837\) 98.2350 3.39550
\(838\) 31.6051 1.09178
\(839\) 27.8988 0.963174 0.481587 0.876398i \(-0.340061\pi\)
0.481587 + 0.876398i \(0.340061\pi\)
\(840\) 0.204819 0.00706691
\(841\) 29.6717 1.02316
\(842\) 48.9021 1.68528
\(843\) −23.1272 −0.796541
\(844\) 4.44894 0.153139
\(845\) 12.1786 0.418957
\(846\) 66.9837 2.30295
\(847\) −0.655714 −0.0225306
\(848\) 16.2602 0.558378
\(849\) −29.8123 −1.02316
\(850\) 0.0945754 0.00324391
\(851\) 0.726954 0.0249197
\(852\) 9.35380 0.320456
\(853\) 21.6002 0.739578 0.369789 0.929116i \(-0.379430\pi\)
0.369789 + 0.929116i \(0.379430\pi\)
\(854\) −0.248486 −0.00850300
\(855\) 43.2405 1.47879
\(856\) −11.5121 −0.393475
\(857\) 6.86410 0.234473 0.117237 0.993104i \(-0.462596\pi\)
0.117237 + 0.993104i \(0.462596\pi\)
\(858\) 8.72172 0.297755
\(859\) 24.6814 0.842119 0.421059 0.907033i \(-0.361658\pi\)
0.421059 + 0.907033i \(0.361658\pi\)
\(860\) 5.25869 0.179320
\(861\) −0.189504 −0.00645827
\(862\) −19.9662 −0.680052
\(863\) 50.3396 1.71358 0.856789 0.515667i \(-0.172456\pi\)
0.856789 + 0.515667i \(0.172456\pi\)
\(864\) −34.0580 −1.15868
\(865\) 2.16377 0.0735703
\(866\) −0.757336 −0.0257353
\(867\) 53.3947 1.81338
\(868\) −0.0927367 −0.00314769
\(869\) 96.2520 3.26512
\(870\) −27.7917 −0.942228
\(871\) −2.42898 −0.0823030
\(872\) −11.3060 −0.382868
\(873\) 89.0559 3.01409
\(874\) −9.24379 −0.312676
\(875\) −0.193786 −0.00655118
\(876\) −7.33466 −0.247815
\(877\) −8.51355 −0.287482 −0.143741 0.989615i \(-0.545913\pi\)
−0.143741 + 0.989615i \(0.545913\pi\)
\(878\) 31.8659 1.07542
\(879\) −36.2577 −1.22294
\(880\) −16.3156 −0.550000
\(881\) −32.6365 −1.09955 −0.549776 0.835312i \(-0.685287\pi\)
−0.549776 + 0.835312i \(0.685287\pi\)
\(882\) −58.6675 −1.97544
\(883\) 1.56632 0.0527108 0.0263554 0.999653i \(-0.491610\pi\)
0.0263554 + 0.999653i \(0.491610\pi\)
\(884\) 0.00345176 0.000116095 0
\(885\) −28.9643 −0.973625
\(886\) −20.9370 −0.703393
\(887\) −30.1670 −1.01291 −0.506454 0.862267i \(-0.669044\pi\)
−0.506454 + 0.862267i \(0.669044\pi\)
\(888\) 6.14996 0.206379
\(889\) −0.235677 −0.00790435
\(890\) −17.5115 −0.586988
\(891\) −111.128 −3.72293
\(892\) 7.69194 0.257545
\(893\) −53.1961 −1.78014
\(894\) −28.8812 −0.965932
\(895\) 12.1452 0.405971
\(896\) −0.117316 −0.00391927
\(897\) −1.28246 −0.0428202
\(898\) 21.3232 0.711563
\(899\) 61.9758 2.06701
\(900\) 14.3589 0.478629
\(901\) 0.112766 0.00375679
\(902\) 20.7485 0.690851
\(903\) 0.770662 0.0256460
\(904\) −0.183791 −0.00611281
\(905\) −0.545178 −0.0181223
\(906\) −69.0987 −2.29565
\(907\) 26.9452 0.894700 0.447350 0.894359i \(-0.352368\pi\)
0.447350 + 0.894359i \(0.352368\pi\)
\(908\) 3.31230 0.109923
\(909\) 112.945 3.74614
\(910\) 0.00932735 0.000309199 0
\(911\) 32.9757 1.09253 0.546266 0.837612i \(-0.316049\pi\)
0.546266 + 0.837612i \(0.316049\pi\)
\(912\) −56.8958 −1.88401
\(913\) 14.9080 0.493381
\(914\) 21.1552 0.699752
\(915\) 26.8907 0.888979
\(916\) 6.80184 0.224739
\(917\) 0.118464 0.00391203
\(918\) 0.279740 0.00923278
\(919\) 45.6169 1.50476 0.752381 0.658728i \(-0.228905\pi\)
0.752381 + 0.658728i \(0.228905\pi\)
\(920\) 3.29747 0.108714
\(921\) 41.4980 1.36741
\(922\) −5.68315 −0.187164
\(923\) 2.09798 0.0690558
\(924\) 0.228110 0.00750428
\(925\) −2.62327 −0.0862526
\(926\) 14.0895 0.463009
\(927\) −19.1402 −0.628648
\(928\) −21.4870 −0.705345
\(929\) 20.3305 0.667023 0.333511 0.942746i \(-0.391766\pi\)
0.333511 + 0.942746i \(0.391766\pi\)
\(930\) −29.3568 −0.962647
\(931\) 46.5916 1.52698
\(932\) −13.9104 −0.455649
\(933\) −66.8975 −2.19013
\(934\) 14.8920 0.487282
\(935\) −0.113151 −0.00370042
\(936\) −7.55027 −0.246788
\(937\) −15.7936 −0.515953 −0.257976 0.966151i \(-0.583056\pi\)
−0.257976 + 0.966151i \(0.583056\pi\)
\(938\) 0.185833 0.00606767
\(939\) 44.5410 1.45354
\(940\) 3.85289 0.125668
\(941\) −11.8889 −0.387568 −0.193784 0.981044i \(-0.562076\pi\)
−0.193784 + 0.981044i \(0.562076\pi\)
\(942\) 12.5443 0.408716
\(943\) −3.05091 −0.0993514
\(944\) 26.5219 0.863215
\(945\) −0.258414 −0.00840620
\(946\) −84.3789 −2.74339
\(947\) 11.8570 0.385302 0.192651 0.981267i \(-0.438291\pi\)
0.192651 + 0.981267i \(0.438291\pi\)
\(948\) −24.3105 −0.789567
\(949\) −1.64510 −0.0534023
\(950\) 33.3570 1.08224
\(951\) 90.6204 2.93857
\(952\) −0.00130066 −4.21546e−5 0
\(953\) −3.90429 −0.126472 −0.0632361 0.997999i \(-0.520142\pi\)
−0.0632361 + 0.997999i \(0.520142\pi\)
\(954\) −50.0814 −1.62145
\(955\) 13.5610 0.438825
\(956\) 6.32729 0.204639
\(957\) −152.446 −4.92787
\(958\) 11.0325 0.356444
\(959\) 0.0884010 0.00285462
\(960\) 26.3532 0.850545
\(961\) 34.4659 1.11180
\(962\) 0.280067 0.00902971
\(963\) 25.7970 0.831296
\(964\) 2.03130 0.0654239
\(965\) 6.49071 0.208943
\(966\) 0.0981169 0.00315686
\(967\) 11.9696 0.384916 0.192458 0.981305i \(-0.438354\pi\)
0.192458 + 0.981305i \(0.438354\pi\)
\(968\) −89.3083 −2.87048
\(969\) −0.394578 −0.0126757
\(970\) −14.9843 −0.481117
\(971\) −43.3466 −1.39106 −0.695529 0.718498i \(-0.744830\pi\)
−0.695529 + 0.718498i \(0.744830\pi\)
\(972\) 9.50906 0.305003
\(973\) −0.0344396 −0.00110408
\(974\) −4.75143 −0.152246
\(975\) 4.62787 0.148210
\(976\) −24.6231 −0.788167
\(977\) 54.7469 1.75151 0.875754 0.482757i \(-0.160365\pi\)
0.875754 + 0.482757i \(0.160365\pi\)
\(978\) 93.4937 2.98960
\(979\) −96.0559 −3.06996
\(980\) −3.37454 −0.107796
\(981\) 25.3351 0.808888
\(982\) −48.4067 −1.54472
\(983\) −2.64257 −0.0842847 −0.0421424 0.999112i \(-0.513418\pi\)
−0.0421424 + 0.999112i \(0.513418\pi\)
\(984\) −25.8104 −0.822807
\(985\) −10.7765 −0.343369
\(986\) 0.176486 0.00562045
\(987\) 0.564642 0.0179728
\(988\) 1.21744 0.0387320
\(989\) 12.4073 0.394528
\(990\) 50.2521 1.59712
\(991\) 36.7064 1.16602 0.583009 0.812465i \(-0.301875\pi\)
0.583009 + 0.812465i \(0.301875\pi\)
\(992\) −22.6970 −0.720630
\(993\) −92.6700 −2.94079
\(994\) −0.160509 −0.00509105
\(995\) 23.8481 0.756035
\(996\) −3.76532 −0.119309
\(997\) 39.6303 1.25510 0.627552 0.778575i \(-0.284057\pi\)
0.627552 + 0.778575i \(0.284057\pi\)
\(998\) −7.30317 −0.231178
\(999\) −7.75923 −0.245491
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 2671.2.a.b.1.80 122
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2671.2.a.b.1.80 122 1.1 even 1 trivial