Properties

Label 4019.2.a.a.1.8
Level $4019$
Weight $2$
Character 4019.1
Self dual yes
Analytic conductor $32.092$
Analytic rank $1$
Dimension $149$
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] = [4019,2,Mod(1,4019)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4019, 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("4019.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4019 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4019.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: \(32.0918765724\)
Analytic rank: \(1\)
Dimension: \(149\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 4019.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.57089 q^{2} +0.190612 q^{3} +4.60945 q^{4} -1.40475 q^{5} -0.490042 q^{6} +1.52623 q^{7} -6.70860 q^{8} -2.96367 q^{9} +O(q^{10})\) \(q-2.57089 q^{2} +0.190612 q^{3} +4.60945 q^{4} -1.40475 q^{5} -0.490042 q^{6} +1.52623 q^{7} -6.70860 q^{8} -2.96367 q^{9} +3.61144 q^{10} +4.90607 q^{11} +0.878618 q^{12} -2.99179 q^{13} -3.92377 q^{14} -0.267762 q^{15} +8.02813 q^{16} -0.189545 q^{17} +7.61925 q^{18} -0.111372 q^{19} -6.47510 q^{20} +0.290919 q^{21} -12.6130 q^{22} +5.98917 q^{23} -1.27874 q^{24} -3.02669 q^{25} +7.69154 q^{26} -1.13675 q^{27} +7.03509 q^{28} -8.54348 q^{29} +0.688385 q^{30} +4.85608 q^{31} -7.22221 q^{32} +0.935158 q^{33} +0.487299 q^{34} -2.14397 q^{35} -13.6609 q^{36} +2.51340 q^{37} +0.286325 q^{38} -0.570272 q^{39} +9.42387 q^{40} +3.73074 q^{41} -0.747919 q^{42} -12.4308 q^{43} +22.6143 q^{44} +4.16320 q^{45} -15.3975 q^{46} +7.35043 q^{47} +1.53026 q^{48} -4.67061 q^{49} +7.78127 q^{50} -0.0361297 q^{51} -13.7905 q^{52} +3.20655 q^{53} +2.92245 q^{54} -6.89178 q^{55} -10.2389 q^{56} -0.0212289 q^{57} +21.9643 q^{58} +3.87343 q^{59} -1.23423 q^{60} -6.93168 q^{61} -12.4844 q^{62} -4.52325 q^{63} +2.51120 q^{64} +4.20270 q^{65} -2.40418 q^{66} +2.31949 q^{67} -0.873699 q^{68} +1.14161 q^{69} +5.51190 q^{70} +4.63385 q^{71} +19.8820 q^{72} +13.4275 q^{73} -6.46166 q^{74} -0.576925 q^{75} -0.513363 q^{76} +7.48781 q^{77} +1.46610 q^{78} -14.6063 q^{79} -11.2775 q^{80} +8.67432 q^{81} -9.59130 q^{82} -12.6361 q^{83} +1.34098 q^{84} +0.266263 q^{85} +31.9582 q^{86} -1.62849 q^{87} -32.9129 q^{88} +10.0468 q^{89} -10.7031 q^{90} -4.56617 q^{91} +27.6068 q^{92} +0.925629 q^{93} -18.8971 q^{94} +0.156449 q^{95} -1.37664 q^{96} -7.10378 q^{97} +12.0076 q^{98} -14.5400 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57089 −1.81789 −0.908945 0.416916i \(-0.863111\pi\)
−0.908945 + 0.416916i \(0.863111\pi\)
\(3\) 0.190612 0.110050 0.0550250 0.998485i \(-0.482476\pi\)
0.0550250 + 0.998485i \(0.482476\pi\)
\(4\) 4.60945 2.30472
\(5\) −1.40475 −0.628221 −0.314111 0.949386i \(-0.601706\pi\)
−0.314111 + 0.949386i \(0.601706\pi\)
\(6\) −0.490042 −0.200059
\(7\) 1.52623 0.576862 0.288431 0.957501i \(-0.406866\pi\)
0.288431 + 0.957501i \(0.406866\pi\)
\(8\) −6.70860 −2.37185
\(9\) −2.96367 −0.987889
\(10\) 3.61144 1.14204
\(11\) 4.90607 1.47924 0.739619 0.673026i \(-0.235006\pi\)
0.739619 + 0.673026i \(0.235006\pi\)
\(12\) 0.878618 0.253635
\(13\) −2.99179 −0.829773 −0.414886 0.909873i \(-0.636179\pi\)
−0.414886 + 0.909873i \(0.636179\pi\)
\(14\) −3.92377 −1.04867
\(15\) −0.267762 −0.0691358
\(16\) 8.02813 2.00703
\(17\) −0.189545 −0.0459715 −0.0229857 0.999736i \(-0.507317\pi\)
−0.0229857 + 0.999736i \(0.507317\pi\)
\(18\) 7.61925 1.79587
\(19\) −0.111372 −0.0255505 −0.0127752 0.999918i \(-0.504067\pi\)
−0.0127752 + 0.999918i \(0.504067\pi\)
\(20\) −6.47510 −1.44788
\(21\) 0.290919 0.0634837
\(22\) −12.6130 −2.68909
\(23\) 5.98917 1.24883 0.624414 0.781094i \(-0.285338\pi\)
0.624414 + 0.781094i \(0.285338\pi\)
\(24\) −1.27874 −0.261022
\(25\) −3.02669 −0.605338
\(26\) 7.69154 1.50844
\(27\) −1.13675 −0.218767
\(28\) 7.03509 1.32951
\(29\) −8.54348 −1.58648 −0.793242 0.608906i \(-0.791609\pi\)
−0.793242 + 0.608906i \(0.791609\pi\)
\(30\) 0.688385 0.125681
\(31\) 4.85608 0.872178 0.436089 0.899904i \(-0.356363\pi\)
0.436089 + 0.899904i \(0.356363\pi\)
\(32\) −7.22221 −1.27672
\(33\) 0.935158 0.162790
\(34\) 0.487299 0.0835711
\(35\) −2.14397 −0.362397
\(36\) −13.6609 −2.27681
\(37\) 2.51340 0.413200 0.206600 0.978425i \(-0.433760\pi\)
0.206600 + 0.978425i \(0.433760\pi\)
\(38\) 0.286325 0.0464480
\(39\) −0.570272 −0.0913166
\(40\) 9.42387 1.49004
\(41\) 3.73074 0.582643 0.291322 0.956625i \(-0.405905\pi\)
0.291322 + 0.956625i \(0.405905\pi\)
\(42\) −0.747919 −0.115406
\(43\) −12.4308 −1.89568 −0.947841 0.318743i \(-0.896739\pi\)
−0.947841 + 0.318743i \(0.896739\pi\)
\(44\) 22.6143 3.40923
\(45\) 4.16320 0.620613
\(46\) −15.3975 −2.27023
\(47\) 7.35043 1.07217 0.536085 0.844164i \(-0.319902\pi\)
0.536085 + 0.844164i \(0.319902\pi\)
\(48\) 1.53026 0.220874
\(49\) −4.67061 −0.667231
\(50\) 7.78127 1.10044
\(51\) −0.0361297 −0.00505916
\(52\) −13.7905 −1.91240
\(53\) 3.20655 0.440453 0.220227 0.975449i \(-0.429320\pi\)
0.220227 + 0.975449i \(0.429320\pi\)
\(54\) 2.92245 0.397695
\(55\) −6.89178 −0.929288
\(56\) −10.2389 −1.36823
\(57\) −0.0212289 −0.00281183
\(58\) 21.9643 2.88406
\(59\) 3.87343 0.504277 0.252139 0.967691i \(-0.418866\pi\)
0.252139 + 0.967691i \(0.418866\pi\)
\(60\) −1.23423 −0.159339
\(61\) −6.93168 −0.887511 −0.443755 0.896148i \(-0.646354\pi\)
−0.443755 + 0.896148i \(0.646354\pi\)
\(62\) −12.4844 −1.58552
\(63\) −4.52325 −0.569875
\(64\) 2.51120 0.313900
\(65\) 4.20270 0.521281
\(66\) −2.40418 −0.295935
\(67\) 2.31949 0.283371 0.141685 0.989912i \(-0.454748\pi\)
0.141685 + 0.989912i \(0.454748\pi\)
\(68\) −0.873699 −0.105952
\(69\) 1.14161 0.137434
\(70\) 5.51190 0.658798
\(71\) 4.63385 0.549937 0.274968 0.961453i \(-0.411333\pi\)
0.274968 + 0.961453i \(0.411333\pi\)
\(72\) 19.8820 2.34312
\(73\) 13.4275 1.57157 0.785784 0.618501i \(-0.212260\pi\)
0.785784 + 0.618501i \(0.212260\pi\)
\(74\) −6.46166 −0.751153
\(75\) −0.576925 −0.0666175
\(76\) −0.513363 −0.0588868
\(77\) 7.48781 0.853315
\(78\) 1.46610 0.166004
\(79\) −14.6063 −1.64334 −0.821669 0.569965i \(-0.806957\pi\)
−0.821669 + 0.569965i \(0.806957\pi\)
\(80\) −11.2775 −1.26086
\(81\) 8.67432 0.963814
\(82\) −9.59130 −1.05918
\(83\) −12.6361 −1.38699 −0.693496 0.720461i \(-0.743930\pi\)
−0.693496 + 0.720461i \(0.743930\pi\)
\(84\) 1.34098 0.146312
\(85\) 0.266263 0.0288802
\(86\) 31.9582 3.44614
\(87\) −1.62849 −0.174593
\(88\) −32.9129 −3.50852
\(89\) 10.0468 1.06496 0.532480 0.846442i \(-0.321260\pi\)
0.532480 + 0.846442i \(0.321260\pi\)
\(90\) −10.7031 −1.12821
\(91\) −4.56617 −0.478664
\(92\) 27.6068 2.87820
\(93\) 0.925629 0.0959832
\(94\) −18.8971 −1.94909
\(95\) 0.156449 0.0160514
\(96\) −1.37664 −0.140503
\(97\) −7.10378 −0.721280 −0.360640 0.932705i \(-0.617442\pi\)
−0.360640 + 0.932705i \(0.617442\pi\)
\(98\) 12.0076 1.21295
\(99\) −14.5400 −1.46132
\(100\) −13.9514 −1.39514
\(101\) −7.37625 −0.733964 −0.366982 0.930228i \(-0.619609\pi\)
−0.366982 + 0.930228i \(0.619609\pi\)
\(102\) 0.0928852 0.00919700
\(103\) −10.1641 −1.00150 −0.500749 0.865593i \(-0.666942\pi\)
−0.500749 + 0.865593i \(0.666942\pi\)
\(104\) 20.0707 1.96809
\(105\) −0.408667 −0.0398818
\(106\) −8.24366 −0.800695
\(107\) −3.77084 −0.364540 −0.182270 0.983248i \(-0.558345\pi\)
−0.182270 + 0.983248i \(0.558345\pi\)
\(108\) −5.23979 −0.504199
\(109\) −16.7082 −1.60036 −0.800179 0.599761i \(-0.795262\pi\)
−0.800179 + 0.599761i \(0.795262\pi\)
\(110\) 17.7180 1.68934
\(111\) 0.479085 0.0454727
\(112\) 12.2528 1.15778
\(113\) 10.7160 1.00807 0.504037 0.863682i \(-0.331848\pi\)
0.504037 + 0.863682i \(0.331848\pi\)
\(114\) 0.0545770 0.00511160
\(115\) −8.41325 −0.784540
\(116\) −39.3808 −3.65641
\(117\) 8.86666 0.819723
\(118\) −9.95814 −0.916721
\(119\) −0.289290 −0.0265192
\(120\) 1.79631 0.163980
\(121\) 13.0696 1.18814
\(122\) 17.8206 1.61340
\(123\) 0.711125 0.0641200
\(124\) 22.3839 2.01013
\(125\) 11.2755 1.00851
\(126\) 11.6287 1.03597
\(127\) 20.1958 1.79209 0.896044 0.443965i \(-0.146429\pi\)
0.896044 + 0.443965i \(0.146429\pi\)
\(128\) 7.98840 0.706081
\(129\) −2.36947 −0.208620
\(130\) −10.8047 −0.947631
\(131\) 4.07458 0.355998 0.177999 0.984031i \(-0.443038\pi\)
0.177999 + 0.984031i \(0.443038\pi\)
\(132\) 4.31057 0.375187
\(133\) −0.169980 −0.0147391
\(134\) −5.96314 −0.515137
\(135\) 1.59684 0.137434
\(136\) 1.27158 0.109037
\(137\) −4.66449 −0.398514 −0.199257 0.979947i \(-0.563853\pi\)
−0.199257 + 0.979947i \(0.563853\pi\)
\(138\) −2.93495 −0.249839
\(139\) −4.14287 −0.351394 −0.175697 0.984444i \(-0.556218\pi\)
−0.175697 + 0.984444i \(0.556218\pi\)
\(140\) −9.88251 −0.835225
\(141\) 1.40108 0.117992
\(142\) −11.9131 −0.999725
\(143\) −14.6779 −1.22743
\(144\) −23.7927 −1.98273
\(145\) 12.0014 0.996663
\(146\) −34.5205 −2.85694
\(147\) −0.890277 −0.0734288
\(148\) 11.5854 0.952313
\(149\) −12.9993 −1.06495 −0.532474 0.846446i \(-0.678738\pi\)
−0.532474 + 0.846446i \(0.678738\pi\)
\(150\) 1.48321 0.121103
\(151\) −18.4497 −1.50142 −0.750710 0.660632i \(-0.770288\pi\)
−0.750710 + 0.660632i \(0.770288\pi\)
\(152\) 0.747149 0.0606018
\(153\) 0.561749 0.0454147
\(154\) −19.2503 −1.55123
\(155\) −6.82155 −0.547920
\(156\) −2.62864 −0.210460
\(157\) 1.30139 0.103862 0.0519310 0.998651i \(-0.483462\pi\)
0.0519310 + 0.998651i \(0.483462\pi\)
\(158\) 37.5511 2.98741
\(159\) 0.611207 0.0484719
\(160\) 10.1454 0.802061
\(161\) 9.14086 0.720401
\(162\) −22.3007 −1.75211
\(163\) 7.81357 0.612006 0.306003 0.952031i \(-0.401008\pi\)
0.306003 + 0.952031i \(0.401008\pi\)
\(164\) 17.1967 1.34283
\(165\) −1.31366 −0.102268
\(166\) 32.4859 2.52140
\(167\) −22.4883 −1.74020 −0.870098 0.492880i \(-0.835944\pi\)
−0.870098 + 0.492880i \(0.835944\pi\)
\(168\) −1.95166 −0.150574
\(169\) −4.04920 −0.311477
\(170\) −0.684531 −0.0525011
\(171\) 0.330069 0.0252410
\(172\) −57.2992 −4.36903
\(173\) 6.72968 0.511648 0.255824 0.966723i \(-0.417653\pi\)
0.255824 + 0.966723i \(0.417653\pi\)
\(174\) 4.18667 0.317391
\(175\) −4.61943 −0.349196
\(176\) 39.3866 2.96888
\(177\) 0.738323 0.0554958
\(178\) −25.8292 −1.93598
\(179\) −3.14792 −0.235286 −0.117643 0.993056i \(-0.537534\pi\)
−0.117643 + 0.993056i \(0.537534\pi\)
\(180\) 19.1900 1.43034
\(181\) 1.44134 0.107134 0.0535669 0.998564i \(-0.482941\pi\)
0.0535669 + 0.998564i \(0.482941\pi\)
\(182\) 11.7391 0.870159
\(183\) −1.32126 −0.0976706
\(184\) −40.1789 −2.96203
\(185\) −3.53069 −0.259581
\(186\) −2.37969 −0.174487
\(187\) −0.929923 −0.0680027
\(188\) 33.8815 2.47106
\(189\) −1.73494 −0.126199
\(190\) −0.402213 −0.0291796
\(191\) −1.27701 −0.0924013 −0.0462006 0.998932i \(-0.514711\pi\)
−0.0462006 + 0.998932i \(0.514711\pi\)
\(192\) 0.478666 0.0345447
\(193\) 25.6342 1.84519 0.922594 0.385772i \(-0.126065\pi\)
0.922594 + 0.385772i \(0.126065\pi\)
\(194\) 18.2630 1.31121
\(195\) 0.801087 0.0573670
\(196\) −21.5290 −1.53778
\(197\) −2.69630 −0.192103 −0.0960517 0.995376i \(-0.530621\pi\)
−0.0960517 + 0.995376i \(0.530621\pi\)
\(198\) 37.3806 2.65652
\(199\) −15.3839 −1.09054 −0.545270 0.838261i \(-0.683573\pi\)
−0.545270 + 0.838261i \(0.683573\pi\)
\(200\) 20.3048 1.43577
\(201\) 0.442123 0.0311850
\(202\) 18.9635 1.33427
\(203\) −13.0393 −0.915182
\(204\) −0.166538 −0.0116600
\(205\) −5.24074 −0.366029
\(206\) 26.1307 1.82061
\(207\) −17.7499 −1.23370
\(208\) −24.0185 −1.66538
\(209\) −0.546399 −0.0377952
\(210\) 1.05064 0.0725007
\(211\) −0.836067 −0.0575572 −0.0287786 0.999586i \(-0.509162\pi\)
−0.0287786 + 0.999586i \(0.509162\pi\)
\(212\) 14.7804 1.01512
\(213\) 0.883269 0.0605206
\(214\) 9.69439 0.662695
\(215\) 17.4621 1.19091
\(216\) 7.62599 0.518883
\(217\) 7.41151 0.503126
\(218\) 42.9549 2.90927
\(219\) 2.55944 0.172951
\(220\) −31.7673 −2.14175
\(221\) 0.567079 0.0381459
\(222\) −1.23167 −0.0826645
\(223\) 19.8521 1.32939 0.664697 0.747113i \(-0.268561\pi\)
0.664697 + 0.747113i \(0.268561\pi\)
\(224\) −11.0228 −0.736490
\(225\) 8.97010 0.598007
\(226\) −27.5495 −1.83257
\(227\) −21.7789 −1.44552 −0.722758 0.691101i \(-0.757126\pi\)
−0.722758 + 0.691101i \(0.757126\pi\)
\(228\) −0.0978534 −0.00648050
\(229\) 17.1392 1.13259 0.566297 0.824201i \(-0.308376\pi\)
0.566297 + 0.824201i \(0.308376\pi\)
\(230\) 21.6295 1.42621
\(231\) 1.42727 0.0939074
\(232\) 57.3148 3.76290
\(233\) −5.53066 −0.362326 −0.181163 0.983453i \(-0.557986\pi\)
−0.181163 + 0.983453i \(0.557986\pi\)
\(234\) −22.7952 −1.49017
\(235\) −10.3255 −0.673560
\(236\) 17.8544 1.16222
\(237\) −2.78414 −0.180849
\(238\) 0.743732 0.0482090
\(239\) 23.6992 1.53297 0.766487 0.642260i \(-0.222003\pi\)
0.766487 + 0.642260i \(0.222003\pi\)
\(240\) −2.14963 −0.138758
\(241\) 20.3636 1.31174 0.655869 0.754875i \(-0.272302\pi\)
0.655869 + 0.754875i \(0.272302\pi\)
\(242\) −33.6004 −2.15991
\(243\) 5.06368 0.324835
\(244\) −31.9512 −2.04547
\(245\) 6.56102 0.419168
\(246\) −1.82822 −0.116563
\(247\) 0.333201 0.0212011
\(248\) −32.5775 −2.06867
\(249\) −2.40860 −0.152639
\(250\) −28.9879 −1.83336
\(251\) −30.6631 −1.93544 −0.967718 0.252035i \(-0.918900\pi\)
−0.967718 + 0.252035i \(0.918900\pi\)
\(252\) −20.8497 −1.31341
\(253\) 29.3833 1.84731
\(254\) −51.9211 −3.25782
\(255\) 0.0507530 0.00317827
\(256\) −25.5597 −1.59748
\(257\) −9.07953 −0.566365 −0.283183 0.959066i \(-0.591390\pi\)
−0.283183 + 0.959066i \(0.591390\pi\)
\(258\) 6.09163 0.379248
\(259\) 3.83603 0.238360
\(260\) 19.3721 1.20141
\(261\) 25.3200 1.56727
\(262\) −10.4753 −0.647165
\(263\) 27.7582 1.71165 0.855823 0.517270i \(-0.173052\pi\)
0.855823 + 0.517270i \(0.173052\pi\)
\(264\) −6.27360 −0.386113
\(265\) −4.50438 −0.276702
\(266\) 0.436998 0.0267941
\(267\) 1.91505 0.117199
\(268\) 10.6916 0.653092
\(269\) 1.59950 0.0975232 0.0487616 0.998810i \(-0.484473\pi\)
0.0487616 + 0.998810i \(0.484473\pi\)
\(270\) −4.10530 −0.249840
\(271\) 25.9659 1.57732 0.788658 0.614833i \(-0.210776\pi\)
0.788658 + 0.614833i \(0.210776\pi\)
\(272\) −1.52169 −0.0922662
\(273\) −0.870368 −0.0526770
\(274\) 11.9919 0.724455
\(275\) −14.8492 −0.895439
\(276\) 5.26219 0.316747
\(277\) −24.3092 −1.46060 −0.730299 0.683127i \(-0.760619\pi\)
−0.730299 + 0.683127i \(0.760619\pi\)
\(278\) 10.6509 0.638796
\(279\) −14.3918 −0.861615
\(280\) 14.3830 0.859550
\(281\) 6.63221 0.395644 0.197822 0.980238i \(-0.436613\pi\)
0.197822 + 0.980238i \(0.436613\pi\)
\(282\) −3.60202 −0.214497
\(283\) 10.4707 0.622417 0.311208 0.950342i \(-0.399266\pi\)
0.311208 + 0.950342i \(0.399266\pi\)
\(284\) 21.3595 1.26745
\(285\) 0.0298212 0.00176645
\(286\) 37.7353 2.23133
\(287\) 5.69398 0.336105
\(288\) 21.4042 1.26126
\(289\) −16.9641 −0.997887
\(290\) −30.8543 −1.81182
\(291\) −1.35407 −0.0793769
\(292\) 61.8933 3.62203
\(293\) −1.48028 −0.0864787 −0.0432394 0.999065i \(-0.513768\pi\)
−0.0432394 + 0.999065i \(0.513768\pi\)
\(294\) 2.28880 0.133485
\(295\) −5.44118 −0.316798
\(296\) −16.8614 −0.980048
\(297\) −5.57697 −0.323609
\(298\) 33.4198 1.93596
\(299\) −17.9183 −1.03624
\(300\) −2.65931 −0.153535
\(301\) −18.9723 −1.09355
\(302\) 47.4322 2.72942
\(303\) −1.40600 −0.0807728
\(304\) −0.894108 −0.0512806
\(305\) 9.73725 0.557553
\(306\) −1.44419 −0.0825589
\(307\) −27.4938 −1.56915 −0.784576 0.620033i \(-0.787119\pi\)
−0.784576 + 0.620033i \(0.787119\pi\)
\(308\) 34.5147 1.96666
\(309\) −1.93740 −0.110215
\(310\) 17.5374 0.996059
\(311\) −33.3387 −1.89046 −0.945232 0.326399i \(-0.894165\pi\)
−0.945232 + 0.326399i \(0.894165\pi\)
\(312\) 3.82572 0.216589
\(313\) −26.3939 −1.49187 −0.745934 0.666019i \(-0.767997\pi\)
−0.745934 + 0.666019i \(0.767997\pi\)
\(314\) −3.34572 −0.188810
\(315\) 6.35401 0.358008
\(316\) −67.3270 −3.78744
\(317\) 6.96008 0.390917 0.195458 0.980712i \(-0.437381\pi\)
0.195458 + 0.980712i \(0.437381\pi\)
\(318\) −1.57134 −0.0881166
\(319\) −41.9150 −2.34679
\(320\) −3.52760 −0.197199
\(321\) −0.718768 −0.0401177
\(322\) −23.5001 −1.30961
\(323\) 0.0211100 0.00117459
\(324\) 39.9839 2.22133
\(325\) 9.05522 0.502293
\(326\) −20.0878 −1.11256
\(327\) −3.18479 −0.176120
\(328\) −25.0280 −1.38194
\(329\) 11.2185 0.618494
\(330\) 3.37727 0.185912
\(331\) 12.6989 0.697994 0.348997 0.937124i \(-0.386522\pi\)
0.348997 + 0.937124i \(0.386522\pi\)
\(332\) −58.2454 −3.19663
\(333\) −7.44888 −0.408196
\(334\) 57.8148 3.16348
\(335\) −3.25829 −0.178020
\(336\) 2.33553 0.127414
\(337\) −21.2437 −1.15722 −0.578608 0.815606i \(-0.696404\pi\)
−0.578608 + 0.815606i \(0.696404\pi\)
\(338\) 10.4100 0.566231
\(339\) 2.04260 0.110939
\(340\) 1.22732 0.0665610
\(341\) 23.8243 1.29016
\(342\) −0.848570 −0.0458854
\(343\) −17.8121 −0.961762
\(344\) 83.3934 4.49627
\(345\) −1.60367 −0.0863387
\(346\) −17.3012 −0.930120
\(347\) −4.94845 −0.265646 −0.132823 0.991140i \(-0.542404\pi\)
−0.132823 + 0.991140i \(0.542404\pi\)
\(348\) −7.50646 −0.402388
\(349\) −19.4692 −1.04216 −0.521082 0.853506i \(-0.674472\pi\)
−0.521082 + 0.853506i \(0.674472\pi\)
\(350\) 11.8760 0.634801
\(351\) 3.40091 0.181527
\(352\) −35.4327 −1.88857
\(353\) 20.2324 1.07686 0.538430 0.842670i \(-0.319018\pi\)
0.538430 + 0.842670i \(0.319018\pi\)
\(354\) −1.89814 −0.100885
\(355\) −6.50938 −0.345482
\(356\) 46.3103 2.45444
\(357\) −0.0551423 −0.00291844
\(358\) 8.09294 0.427725
\(359\) −4.31362 −0.227664 −0.113832 0.993500i \(-0.536313\pi\)
−0.113832 + 0.993500i \(0.536313\pi\)
\(360\) −27.9292 −1.47200
\(361\) −18.9876 −0.999347
\(362\) −3.70551 −0.194757
\(363\) 2.49122 0.130755
\(364\) −21.0475 −1.10319
\(365\) −18.8622 −0.987292
\(366\) 3.39682 0.177555
\(367\) 8.61722 0.449815 0.224908 0.974380i \(-0.427792\pi\)
0.224908 + 0.974380i \(0.427792\pi\)
\(368\) 48.0818 2.50644
\(369\) −11.0567 −0.575587
\(370\) 9.07699 0.471890
\(371\) 4.89394 0.254081
\(372\) 4.26664 0.221215
\(373\) −7.65555 −0.396389 −0.198195 0.980163i \(-0.563508\pi\)
−0.198195 + 0.980163i \(0.563508\pi\)
\(374\) 2.39072 0.123621
\(375\) 2.14924 0.110986
\(376\) −49.3111 −2.54302
\(377\) 25.5603 1.31642
\(378\) 4.46034 0.229415
\(379\) −3.24251 −0.166557 −0.0832783 0.996526i \(-0.526539\pi\)
−0.0832783 + 0.996526i \(0.526539\pi\)
\(380\) 0.721145 0.0369940
\(381\) 3.84957 0.197219
\(382\) 3.28305 0.167975
\(383\) 4.60080 0.235090 0.117545 0.993068i \(-0.462498\pi\)
0.117545 + 0.993068i \(0.462498\pi\)
\(384\) 1.52269 0.0777043
\(385\) −10.5185 −0.536071
\(386\) −65.9025 −3.35435
\(387\) 36.8408 1.87272
\(388\) −32.7445 −1.66235
\(389\) −4.43350 −0.224787 −0.112394 0.993664i \(-0.535852\pi\)
−0.112394 + 0.993664i \(0.535852\pi\)
\(390\) −2.05950 −0.104287
\(391\) −1.13522 −0.0574104
\(392\) 31.3333 1.58257
\(393\) 0.776665 0.0391776
\(394\) 6.93188 0.349223
\(395\) 20.5181 1.03238
\(396\) −67.0213 −3.36795
\(397\) −26.7763 −1.34386 −0.671932 0.740613i \(-0.734535\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(398\) 39.5504 1.98248
\(399\) −0.0324002 −0.00162204
\(400\) −24.2987 −1.21493
\(401\) 26.1492 1.30583 0.652913 0.757432i \(-0.273547\pi\)
0.652913 + 0.757432i \(0.273547\pi\)
\(402\) −1.13665 −0.0566909
\(403\) −14.5284 −0.723709
\(404\) −34.0004 −1.69159
\(405\) −12.1852 −0.605488
\(406\) 33.5226 1.66370
\(407\) 12.3309 0.611221
\(408\) 0.242379 0.0119996
\(409\) −29.8787 −1.47741 −0.738704 0.674030i \(-0.764562\pi\)
−0.738704 + 0.674030i \(0.764562\pi\)
\(410\) 13.4733 0.665400
\(411\) −0.889109 −0.0438565
\(412\) −46.8509 −2.30818
\(413\) 5.91175 0.290898
\(414\) 45.6329 2.24274
\(415\) 17.7505 0.871337
\(416\) 21.6073 1.05939
\(417\) −0.789683 −0.0386709
\(418\) 1.40473 0.0687076
\(419\) −17.2139 −0.840955 −0.420478 0.907303i \(-0.638138\pi\)
−0.420478 + 0.907303i \(0.638138\pi\)
\(420\) −1.88373 −0.0919166
\(421\) −11.9735 −0.583553 −0.291776 0.956487i \(-0.594246\pi\)
−0.291776 + 0.956487i \(0.594246\pi\)
\(422\) 2.14943 0.104633
\(423\) −21.7842 −1.05919
\(424\) −21.5114 −1.04469
\(425\) 0.573695 0.0278283
\(426\) −2.27078 −0.110020
\(427\) −10.5794 −0.511971
\(428\) −17.3815 −0.840166
\(429\) −2.79780 −0.135079
\(430\) −44.8931 −2.16494
\(431\) −34.2594 −1.65022 −0.825109 0.564973i \(-0.808886\pi\)
−0.825109 + 0.564973i \(0.808886\pi\)
\(432\) −9.12596 −0.439073
\(433\) −17.4810 −0.840083 −0.420041 0.907505i \(-0.637984\pi\)
−0.420041 + 0.907505i \(0.637984\pi\)
\(434\) −19.0541 −0.914628
\(435\) 2.28762 0.109683
\(436\) −77.0157 −3.68838
\(437\) −0.667025 −0.0319081
\(438\) −6.58003 −0.314406
\(439\) −7.02501 −0.335285 −0.167643 0.985848i \(-0.553615\pi\)
−0.167643 + 0.985848i \(0.553615\pi\)
\(440\) 46.2342 2.20413
\(441\) 13.8421 0.659150
\(442\) −1.45790 −0.0693450
\(443\) −24.7040 −1.17372 −0.586860 0.809688i \(-0.699636\pi\)
−0.586860 + 0.809688i \(0.699636\pi\)
\(444\) 2.20832 0.104802
\(445\) −14.1132 −0.669031
\(446\) −51.0374 −2.41669
\(447\) −2.47784 −0.117198
\(448\) 3.83268 0.181077
\(449\) −38.0305 −1.79477 −0.897384 0.441250i \(-0.854535\pi\)
−0.897384 + 0.441250i \(0.854535\pi\)
\(450\) −23.0611 −1.08711
\(451\) 18.3033 0.861868
\(452\) 49.3947 2.32333
\(453\) −3.51675 −0.165231
\(454\) 55.9911 2.62779
\(455\) 6.41430 0.300707
\(456\) 0.142416 0.00666924
\(457\) 1.66697 0.0779774 0.0389887 0.999240i \(-0.487586\pi\)
0.0389887 + 0.999240i \(0.487586\pi\)
\(458\) −44.0630 −2.05893
\(459\) 0.215465 0.0100571
\(460\) −38.7805 −1.80815
\(461\) −2.97689 −0.138648 −0.0693238 0.997594i \(-0.522084\pi\)
−0.0693238 + 0.997594i \(0.522084\pi\)
\(462\) −3.66935 −0.170713
\(463\) −22.9068 −1.06457 −0.532284 0.846566i \(-0.678666\pi\)
−0.532284 + 0.846566i \(0.678666\pi\)
\(464\) −68.5882 −3.18413
\(465\) −1.30027 −0.0602987
\(466\) 14.2187 0.658668
\(467\) 19.4041 0.897914 0.448957 0.893553i \(-0.351796\pi\)
0.448957 + 0.893553i \(0.351796\pi\)
\(468\) 40.8704 1.88924
\(469\) 3.54008 0.163466
\(470\) 26.5456 1.22446
\(471\) 0.248061 0.0114300
\(472\) −25.9853 −1.19607
\(473\) −60.9865 −2.80416
\(474\) 7.15771 0.328765
\(475\) 0.337088 0.0154667
\(476\) −1.33347 −0.0611194
\(477\) −9.50314 −0.435119
\(478\) −60.9279 −2.78678
\(479\) −33.5116 −1.53118 −0.765591 0.643328i \(-0.777553\pi\)
−0.765591 + 0.643328i \(0.777553\pi\)
\(480\) 1.93383 0.0882669
\(481\) −7.51956 −0.342863
\(482\) −52.3526 −2.38460
\(483\) 1.74236 0.0792802
\(484\) 60.2435 2.73834
\(485\) 9.97900 0.453123
\(486\) −13.0181 −0.590515
\(487\) 17.7440 0.804059 0.402030 0.915627i \(-0.368305\pi\)
0.402030 + 0.915627i \(0.368305\pi\)
\(488\) 46.5019 2.10504
\(489\) 1.48936 0.0673513
\(490\) −16.8676 −0.762002
\(491\) −38.8993 −1.75550 −0.877751 0.479117i \(-0.840957\pi\)
−0.877751 + 0.479117i \(0.840957\pi\)
\(492\) 3.27789 0.147779
\(493\) 1.61938 0.0729330
\(494\) −0.856622 −0.0385413
\(495\) 20.4250 0.918033
\(496\) 38.9852 1.75049
\(497\) 7.07233 0.317238
\(498\) 6.19222 0.277480
\(499\) −26.9134 −1.20481 −0.602405 0.798191i \(-0.705791\pi\)
−0.602405 + 0.798191i \(0.705791\pi\)
\(500\) 51.9736 2.32433
\(501\) −4.28654 −0.191509
\(502\) 78.8312 3.51841
\(503\) 16.9061 0.753806 0.376903 0.926253i \(-0.376989\pi\)
0.376903 + 0.926253i \(0.376989\pi\)
\(504\) 30.3446 1.35166
\(505\) 10.3617 0.461092
\(506\) −75.5411 −3.35821
\(507\) −0.771828 −0.0342781
\(508\) 93.0916 4.13027
\(509\) 13.9693 0.619180 0.309590 0.950870i \(-0.399808\pi\)
0.309590 + 0.950870i \(0.399808\pi\)
\(510\) −0.130480 −0.00577775
\(511\) 20.4935 0.906577
\(512\) 49.7342 2.19796
\(513\) 0.126602 0.00558961
\(514\) 23.3424 1.02959
\(515\) 14.2780 0.629162
\(516\) −10.9219 −0.480812
\(517\) 36.0618 1.58599
\(518\) −9.86200 −0.433311
\(519\) 1.28276 0.0563069
\(520\) −28.1942 −1.23640
\(521\) −16.1597 −0.707969 −0.353985 0.935251i \(-0.615173\pi\)
−0.353985 + 0.935251i \(0.615173\pi\)
\(522\) −65.0949 −2.84913
\(523\) −34.5524 −1.51087 −0.755436 0.655222i \(-0.772575\pi\)
−0.755436 + 0.655222i \(0.772575\pi\)
\(524\) 18.7816 0.820477
\(525\) −0.880521 −0.0384291
\(526\) −71.3632 −3.11158
\(527\) −0.920447 −0.0400953
\(528\) 7.50757 0.326725
\(529\) 12.8701 0.559571
\(530\) 11.5802 0.503014
\(531\) −11.4796 −0.498170
\(532\) −0.783512 −0.0339696
\(533\) −11.1616 −0.483462
\(534\) −4.92337 −0.213055
\(535\) 5.29706 0.229012
\(536\) −15.5605 −0.672112
\(537\) −0.600032 −0.0258933
\(538\) −4.11213 −0.177286
\(539\) −22.9144 −0.986992
\(540\) 7.36056 0.316748
\(541\) 3.32026 0.142749 0.0713747 0.997450i \(-0.477261\pi\)
0.0713747 + 0.997450i \(0.477261\pi\)
\(542\) −66.7553 −2.86739
\(543\) 0.274737 0.0117901
\(544\) 1.36893 0.0586926
\(545\) 23.4708 1.00538
\(546\) 2.23761 0.0957611
\(547\) −16.0509 −0.686285 −0.343142 0.939283i \(-0.611491\pi\)
−0.343142 + 0.939283i \(0.611491\pi\)
\(548\) −21.5007 −0.918466
\(549\) 20.5432 0.876762
\(550\) 38.1755 1.62781
\(551\) 0.951504 0.0405354
\(552\) −7.65860 −0.325971
\(553\) −22.2926 −0.947979
\(554\) 62.4962 2.65521
\(555\) −0.672993 −0.0285669
\(556\) −19.0964 −0.809867
\(557\) −4.99475 −0.211634 −0.105817 0.994386i \(-0.533746\pi\)
−0.105817 + 0.994386i \(0.533746\pi\)
\(558\) 36.9997 1.56632
\(559\) 37.1904 1.57299
\(560\) −17.2121 −0.727342
\(561\) −0.177255 −0.00748370
\(562\) −17.0506 −0.719238
\(563\) −18.6702 −0.786854 −0.393427 0.919356i \(-0.628711\pi\)
−0.393427 + 0.919356i \(0.628711\pi\)
\(564\) 6.45822 0.271940
\(565\) −15.0532 −0.633293
\(566\) −26.9189 −1.13149
\(567\) 13.2390 0.555987
\(568\) −31.0866 −1.30437
\(569\) −13.8393 −0.580175 −0.290088 0.957000i \(-0.593684\pi\)
−0.290088 + 0.957000i \(0.593684\pi\)
\(570\) −0.0766668 −0.00321122
\(571\) 46.4575 1.94419 0.972094 0.234594i \(-0.0753759\pi\)
0.972094 + 0.234594i \(0.0753759\pi\)
\(572\) −67.6572 −2.82889
\(573\) −0.243414 −0.0101688
\(574\) −14.6386 −0.611002
\(575\) −18.1274 −0.755963
\(576\) −7.44237 −0.310099
\(577\) −40.3325 −1.67906 −0.839531 0.543311i \(-0.817170\pi\)
−0.839531 + 0.543311i \(0.817170\pi\)
\(578\) 43.6127 1.81405
\(579\) 4.88619 0.203063
\(580\) 55.3199 2.29703
\(581\) −19.2856 −0.800102
\(582\) 3.48115 0.144298
\(583\) 15.7316 0.651535
\(584\) −90.0795 −3.72752
\(585\) −12.4554 −0.514968
\(586\) 3.80562 0.157209
\(587\) 23.8280 0.983485 0.491743 0.870741i \(-0.336360\pi\)
0.491743 + 0.870741i \(0.336360\pi\)
\(588\) −4.10369 −0.169233
\(589\) −0.540831 −0.0222846
\(590\) 13.9886 0.575904
\(591\) −0.513948 −0.0211410
\(592\) 20.1779 0.829307
\(593\) 4.01028 0.164682 0.0823412 0.996604i \(-0.473760\pi\)
0.0823412 + 0.996604i \(0.473760\pi\)
\(594\) 14.3378 0.588285
\(595\) 0.406379 0.0166599
\(596\) −59.9198 −2.45441
\(597\) −2.93237 −0.120014
\(598\) 46.0659 1.88378
\(599\) 19.4172 0.793366 0.396683 0.917956i \(-0.370161\pi\)
0.396683 + 0.917956i \(0.370161\pi\)
\(600\) 3.87035 0.158007
\(601\) 29.2910 1.19480 0.597402 0.801942i \(-0.296200\pi\)
0.597402 + 0.801942i \(0.296200\pi\)
\(602\) 48.7757 1.98795
\(603\) −6.87420 −0.279939
\(604\) −85.0432 −3.46036
\(605\) −18.3594 −0.746416
\(606\) 3.61467 0.146836
\(607\) −18.5559 −0.753161 −0.376581 0.926384i \(-0.622900\pi\)
−0.376581 + 0.926384i \(0.622900\pi\)
\(608\) 0.804351 0.0326207
\(609\) −2.48546 −0.100716
\(610\) −25.0333 −1.01357
\(611\) −21.9909 −0.889658
\(612\) 2.58935 0.104668
\(613\) −8.72673 −0.352469 −0.176235 0.984348i \(-0.556392\pi\)
−0.176235 + 0.984348i \(0.556392\pi\)
\(614\) 70.6833 2.85254
\(615\) −0.998949 −0.0402815
\(616\) −50.2327 −2.02393
\(617\) −25.5120 −1.02707 −0.513536 0.858068i \(-0.671665\pi\)
−0.513536 + 0.858068i \(0.671665\pi\)
\(618\) 4.98083 0.200359
\(619\) 37.7293 1.51647 0.758234 0.651982i \(-0.226062\pi\)
0.758234 + 0.651982i \(0.226062\pi\)
\(620\) −31.4436 −1.26281
\(621\) −6.80818 −0.273203
\(622\) 85.7100 3.43666
\(623\) 15.3338 0.614335
\(624\) −4.57822 −0.183275
\(625\) −0.705688 −0.0282275
\(626\) 67.8556 2.71205
\(627\) −0.104150 −0.00415937
\(628\) 5.99868 0.239373
\(629\) −0.476403 −0.0189954
\(630\) −16.3354 −0.650819
\(631\) −25.1965 −1.00305 −0.501527 0.865142i \(-0.667228\pi\)
−0.501527 + 0.865142i \(0.667228\pi\)
\(632\) 97.9878 3.89775
\(633\) −0.159365 −0.00633418
\(634\) −17.8936 −0.710644
\(635\) −28.3700 −1.12583
\(636\) 2.81733 0.111714
\(637\) 13.9735 0.553650
\(638\) 107.759 4.26620
\(639\) −13.7332 −0.543277
\(640\) −11.2217 −0.443575
\(641\) −2.24788 −0.0887860 −0.0443930 0.999014i \(-0.514135\pi\)
−0.0443930 + 0.999014i \(0.514135\pi\)
\(642\) 1.84787 0.0729296
\(643\) 14.7236 0.580644 0.290322 0.956929i \(-0.406238\pi\)
0.290322 + 0.956929i \(0.406238\pi\)
\(644\) 42.1344 1.66033
\(645\) 3.32850 0.131060
\(646\) −0.0542714 −0.00213528
\(647\) 37.9498 1.49196 0.745981 0.665968i \(-0.231981\pi\)
0.745981 + 0.665968i \(0.231981\pi\)
\(648\) −58.1925 −2.28602
\(649\) 19.0033 0.745946
\(650\) −23.2799 −0.913114
\(651\) 1.41272 0.0553691
\(652\) 36.0163 1.41051
\(653\) −31.0108 −1.21355 −0.606773 0.794875i \(-0.707536\pi\)
−0.606773 + 0.794875i \(0.707536\pi\)
\(654\) 8.18774 0.320166
\(655\) −5.72375 −0.223645
\(656\) 29.9509 1.16938
\(657\) −39.7946 −1.55253
\(658\) −28.8414 −1.12435
\(659\) −31.6736 −1.23383 −0.616913 0.787031i \(-0.711617\pi\)
−0.616913 + 0.787031i \(0.711617\pi\)
\(660\) −6.05525 −0.235700
\(661\) −35.0311 −1.36255 −0.681276 0.732026i \(-0.738575\pi\)
−0.681276 + 0.732026i \(0.738575\pi\)
\(662\) −32.6474 −1.26888
\(663\) 0.108092 0.00419796
\(664\) 84.7704 3.28973
\(665\) 0.238778 0.00925941
\(666\) 19.1502 0.742056
\(667\) −51.1683 −1.98125
\(668\) −103.659 −4.01067
\(669\) 3.78405 0.146300
\(670\) 8.37670 0.323620
\(671\) −34.0073 −1.31284
\(672\) −2.10108 −0.0810507
\(673\) 27.8738 1.07446 0.537229 0.843437i \(-0.319471\pi\)
0.537229 + 0.843437i \(0.319471\pi\)
\(674\) 54.6150 2.10369
\(675\) 3.44059 0.132428
\(676\) −18.6646 −0.717869
\(677\) −12.2263 −0.469895 −0.234947 0.972008i \(-0.575492\pi\)
−0.234947 + 0.972008i \(0.575492\pi\)
\(678\) −5.25128 −0.201674
\(679\) −10.8420 −0.416079
\(680\) −1.78625 −0.0684995
\(681\) −4.15133 −0.159079
\(682\) −61.2495 −2.34536
\(683\) −14.0620 −0.538069 −0.269034 0.963131i \(-0.586705\pi\)
−0.269034 + 0.963131i \(0.586705\pi\)
\(684\) 1.52144 0.0581736
\(685\) 6.55242 0.250355
\(686\) 45.7928 1.74838
\(687\) 3.26695 0.124642
\(688\) −99.7962 −3.80470
\(689\) −9.59331 −0.365476
\(690\) 4.12285 0.156954
\(691\) −44.7071 −1.70074 −0.850369 0.526186i \(-0.823621\pi\)
−0.850369 + 0.526186i \(0.823621\pi\)
\(692\) 31.0201 1.17921
\(693\) −22.1914 −0.842981
\(694\) 12.7219 0.482916
\(695\) 5.81968 0.220753
\(696\) 10.9249 0.414107
\(697\) −0.707144 −0.0267850
\(698\) 50.0532 1.89454
\(699\) −1.05421 −0.0398740
\(700\) −21.2931 −0.804802
\(701\) 18.8742 0.712870 0.356435 0.934320i \(-0.383992\pi\)
0.356435 + 0.934320i \(0.383992\pi\)
\(702\) −8.74335 −0.329997
\(703\) −0.279922 −0.0105575
\(704\) 12.3201 0.464333
\(705\) −1.96816 −0.0741254
\(706\) −52.0151 −1.95761
\(707\) −11.2579 −0.423396
\(708\) 3.40326 0.127903
\(709\) −45.3761 −1.70414 −0.852068 0.523431i \(-0.824652\pi\)
−0.852068 + 0.523431i \(0.824652\pi\)
\(710\) 16.7349 0.628048
\(711\) 43.2882 1.62344
\(712\) −67.4001 −2.52592
\(713\) 29.0839 1.08920
\(714\) 0.141764 0.00530540
\(715\) 20.6188 0.771098
\(716\) −14.5102 −0.542271
\(717\) 4.51736 0.168704
\(718\) 11.0898 0.413868
\(719\) 7.72346 0.288036 0.144018 0.989575i \(-0.453998\pi\)
0.144018 + 0.989575i \(0.453998\pi\)
\(720\) 33.4227 1.24559
\(721\) −15.5128 −0.577726
\(722\) 48.8149 1.81670
\(723\) 3.88156 0.144357
\(724\) 6.64377 0.246914
\(725\) 25.8585 0.960360
\(726\) −6.40464 −0.237699
\(727\) 3.75970 0.139439 0.0697197 0.997567i \(-0.477790\pi\)
0.0697197 + 0.997567i \(0.477790\pi\)
\(728\) 30.6326 1.13532
\(729\) −25.0578 −0.928065
\(730\) 48.4925 1.79479
\(731\) 2.35620 0.0871473
\(732\) −6.09030 −0.225104
\(733\) 45.6238 1.68516 0.842578 0.538575i \(-0.181037\pi\)
0.842578 + 0.538575i \(0.181037\pi\)
\(734\) −22.1539 −0.817715
\(735\) 1.25061 0.0461295
\(736\) −43.2550 −1.59440
\(737\) 11.3796 0.419173
\(738\) 28.4254 1.04635
\(739\) 9.77553 0.359599 0.179799 0.983703i \(-0.442455\pi\)
0.179799 + 0.983703i \(0.442455\pi\)
\(740\) −16.2745 −0.598263
\(741\) 0.0635123 0.00233318
\(742\) −12.5817 −0.461890
\(743\) −8.13920 −0.298598 −0.149299 0.988792i \(-0.547702\pi\)
−0.149299 + 0.988792i \(0.547702\pi\)
\(744\) −6.20967 −0.227658
\(745\) 18.2608 0.669023
\(746\) 19.6815 0.720593
\(747\) 37.4492 1.37019
\(748\) −4.28643 −0.156728
\(749\) −5.75517 −0.210289
\(750\) −5.52545 −0.201761
\(751\) −37.9081 −1.38329 −0.691643 0.722240i \(-0.743113\pi\)
−0.691643 + 0.722240i \(0.743113\pi\)
\(752\) 59.0102 2.15188
\(753\) −5.84476 −0.212995
\(754\) −65.7126 −2.39311
\(755\) 25.9172 0.943223
\(756\) −7.99713 −0.290853
\(757\) 10.5117 0.382054 0.191027 0.981585i \(-0.438818\pi\)
0.191027 + 0.981585i \(0.438818\pi\)
\(758\) 8.33612 0.302782
\(759\) 5.60082 0.203297
\(760\) −1.04955 −0.0380713
\(761\) −9.89394 −0.358655 −0.179328 0.983789i \(-0.557392\pi\)
−0.179328 + 0.983789i \(0.557392\pi\)
\(762\) −9.89680 −0.358523
\(763\) −25.5006 −0.923185
\(764\) −5.88632 −0.212960
\(765\) −0.789114 −0.0285305
\(766\) −11.8281 −0.427367
\(767\) −11.5885 −0.418436
\(768\) −4.87199 −0.175803
\(769\) 42.5087 1.53290 0.766452 0.642302i \(-0.222020\pi\)
0.766452 + 0.642302i \(0.222020\pi\)
\(770\) 27.0418 0.974518
\(771\) −1.73067 −0.0623286
\(772\) 118.159 4.25265
\(773\) 26.8577 0.966005 0.483003 0.875619i \(-0.339546\pi\)
0.483003 + 0.875619i \(0.339546\pi\)
\(774\) −94.7135 −3.40441
\(775\) −14.6979 −0.527962
\(776\) 47.6564 1.71077
\(777\) 0.731195 0.0262315
\(778\) 11.3980 0.408639
\(779\) −0.415500 −0.0148868
\(780\) 3.69257 0.132215
\(781\) 22.7340 0.813487
\(782\) 2.91851 0.104366
\(783\) 9.71179 0.347071
\(784\) −37.4963 −1.33915
\(785\) −1.82812 −0.0652483
\(786\) −1.99672 −0.0712205
\(787\) 31.6039 1.12656 0.563279 0.826267i \(-0.309539\pi\)
0.563279 + 0.826267i \(0.309539\pi\)
\(788\) −12.4285 −0.442746
\(789\) 5.29106 0.188367
\(790\) −52.7498 −1.87675
\(791\) 16.3551 0.581519
\(792\) 97.5428 3.46603
\(793\) 20.7381 0.736432
\(794\) 68.8388 2.44300
\(795\) −0.858591 −0.0304511
\(796\) −70.9115 −2.51339
\(797\) 24.1072 0.853921 0.426960 0.904270i \(-0.359584\pi\)
0.426960 + 0.904270i \(0.359584\pi\)
\(798\) 0.0832972 0.00294869
\(799\) −1.39324 −0.0492893
\(800\) 21.8594 0.772846
\(801\) −29.7754 −1.05206
\(802\) −67.2265 −2.37385
\(803\) 65.8762 2.32472
\(804\) 2.03795 0.0718728
\(805\) −12.8406 −0.452571
\(806\) 37.3508 1.31562
\(807\) 0.304884 0.0107324
\(808\) 49.4843 1.74085
\(809\) −1.16627 −0.0410038 −0.0205019 0.999790i \(-0.506526\pi\)
−0.0205019 + 0.999790i \(0.506526\pi\)
\(810\) 31.3268 1.10071
\(811\) −30.9429 −1.08655 −0.543275 0.839555i \(-0.682816\pi\)
−0.543275 + 0.839555i \(0.682816\pi\)
\(812\) −60.1042 −2.10924
\(813\) 4.94942 0.173584
\(814\) −31.7014 −1.11113
\(815\) −10.9761 −0.384475
\(816\) −0.290054 −0.0101539
\(817\) 1.38444 0.0484356
\(818\) 76.8148 2.68577
\(819\) 13.5326 0.472867
\(820\) −24.1569 −0.843596
\(821\) 20.8631 0.728127 0.364063 0.931374i \(-0.381389\pi\)
0.364063 + 0.931374i \(0.381389\pi\)
\(822\) 2.28580 0.0797263
\(823\) −5.86740 −0.204525 −0.102262 0.994757i \(-0.532608\pi\)
−0.102262 + 0.994757i \(0.532608\pi\)
\(824\) 68.1868 2.37540
\(825\) −2.83044 −0.0985431
\(826\) −15.1984 −0.528821
\(827\) 28.5448 0.992600 0.496300 0.868151i \(-0.334692\pi\)
0.496300 + 0.868151i \(0.334692\pi\)
\(828\) −81.8173 −2.84335
\(829\) 14.2365 0.494454 0.247227 0.968958i \(-0.420481\pi\)
0.247227 + 0.968958i \(0.420481\pi\)
\(830\) −45.6345 −1.58400
\(831\) −4.63364 −0.160739
\(832\) −7.51298 −0.260466
\(833\) 0.885292 0.0306736
\(834\) 2.03018 0.0702995
\(835\) 31.5903 1.09323
\(836\) −2.51860 −0.0871076
\(837\) −5.52014 −0.190804
\(838\) 44.2550 1.52876
\(839\) −48.8842 −1.68767 −0.843835 0.536603i \(-0.819707\pi\)
−0.843835 + 0.536603i \(0.819707\pi\)
\(840\) 2.74158 0.0945935
\(841\) 43.9911 1.51693
\(842\) 30.7825 1.06083
\(843\) 1.26418 0.0435407
\(844\) −3.85381 −0.132654
\(845\) 5.68810 0.195676
\(846\) 56.0048 1.92548
\(847\) 19.9472 0.685394
\(848\) 25.7426 0.884004
\(849\) 1.99584 0.0684970
\(850\) −1.47490 −0.0505888
\(851\) 15.0532 0.516016
\(852\) 4.07139 0.139483
\(853\) −31.6266 −1.08287 −0.541437 0.840741i \(-0.682120\pi\)
−0.541437 + 0.840741i \(0.682120\pi\)
\(854\) 27.1983 0.930707
\(855\) −0.463663 −0.0158570
\(856\) 25.2970 0.864634
\(857\) −4.11144 −0.140444 −0.0702221 0.997531i \(-0.522371\pi\)
−0.0702221 + 0.997531i \(0.522371\pi\)
\(858\) 7.19281 0.245559
\(859\) 31.5693 1.07713 0.538565 0.842584i \(-0.318967\pi\)
0.538565 + 0.842584i \(0.318967\pi\)
\(860\) 80.4908 2.74472
\(861\) 1.08534 0.0369884
\(862\) 88.0770 2.99992
\(863\) 28.6341 0.974716 0.487358 0.873202i \(-0.337961\pi\)
0.487358 + 0.873202i \(0.337961\pi\)
\(864\) 8.20983 0.279304
\(865\) −9.45348 −0.321428
\(866\) 44.9416 1.52718
\(867\) −3.23356 −0.109818
\(868\) 34.1630 1.15957
\(869\) −71.6596 −2.43089
\(870\) −5.88120 −0.199391
\(871\) −6.93942 −0.235133
\(872\) 112.089 3.79580
\(873\) 21.0532 0.712544
\(874\) 1.71485 0.0580055
\(875\) 17.2090 0.581769
\(876\) 11.7976 0.398605
\(877\) 32.0631 1.08269 0.541346 0.840800i \(-0.317915\pi\)
0.541346 + 0.840800i \(0.317915\pi\)
\(878\) 18.0605 0.609512
\(879\) −0.282159 −0.00951699
\(880\) −55.3281 −1.86511
\(881\) 49.3179 1.66156 0.830781 0.556599i \(-0.187894\pi\)
0.830781 + 0.556599i \(0.187894\pi\)
\(882\) −35.5866 −1.19826
\(883\) −33.0512 −1.11226 −0.556131 0.831095i \(-0.687715\pi\)
−0.556131 + 0.831095i \(0.687715\pi\)
\(884\) 2.61392 0.0879157
\(885\) −1.03716 −0.0348636
\(886\) 63.5110 2.13369
\(887\) −21.6937 −0.728405 −0.364202 0.931320i \(-0.618658\pi\)
−0.364202 + 0.931320i \(0.618658\pi\)
\(888\) −3.21399 −0.107854
\(889\) 30.8235 1.03379
\(890\) 36.2835 1.21622
\(891\) 42.5569 1.42571
\(892\) 91.5072 3.06389
\(893\) −0.818632 −0.0273945
\(894\) 6.37023 0.213052
\(895\) 4.42202 0.147812
\(896\) 12.1922 0.407311
\(897\) −3.41545 −0.114039
\(898\) 97.7719 3.26269
\(899\) −41.4878 −1.38370
\(900\) 41.3472 1.37824
\(901\) −0.607785 −0.0202483
\(902\) −47.0556 −1.56678
\(903\) −3.61636 −0.120345
\(904\) −71.8891 −2.39100
\(905\) −2.02471 −0.0673037
\(906\) 9.04116 0.300372
\(907\) 40.7646 1.35357 0.676783 0.736182i \(-0.263373\pi\)
0.676783 + 0.736182i \(0.263373\pi\)
\(908\) −100.389 −3.33152
\(909\) 21.8607 0.725075
\(910\) −16.4904 −0.546652
\(911\) 46.5196 1.54126 0.770632 0.637281i \(-0.219941\pi\)
0.770632 + 0.637281i \(0.219941\pi\)
\(912\) −0.170428 −0.00564344
\(913\) −61.9936 −2.05169
\(914\) −4.28558 −0.141754
\(915\) 1.85604 0.0613588
\(916\) 79.0025 2.61032
\(917\) 6.21876 0.205361
\(918\) −0.553936 −0.0182826
\(919\) −41.9645 −1.38428 −0.692141 0.721762i \(-0.743333\pi\)
−0.692141 + 0.721762i \(0.743333\pi\)
\(920\) 56.4411 1.86081
\(921\) −5.24065 −0.172685
\(922\) 7.65325 0.252046
\(923\) −13.8635 −0.456323
\(924\) 6.57893 0.216431
\(925\) −7.60729 −0.250126
\(926\) 58.8906 1.93527
\(927\) 30.1230 0.989368
\(928\) 61.7028 2.02549
\(929\) 26.2573 0.861474 0.430737 0.902477i \(-0.358254\pi\)
0.430737 + 0.902477i \(0.358254\pi\)
\(930\) 3.34285 0.109616
\(931\) 0.520175 0.0170481
\(932\) −25.4933 −0.835061
\(933\) −6.35477 −0.208046
\(934\) −49.8857 −1.63231
\(935\) 1.30630 0.0427207
\(936\) −59.4829 −1.94426
\(937\) −23.8821 −0.780193 −0.390097 0.920774i \(-0.627558\pi\)
−0.390097 + 0.920774i \(0.627558\pi\)
\(938\) −9.10114 −0.297163
\(939\) −5.03099 −0.164180
\(940\) −47.5948 −1.55237
\(941\) −6.69890 −0.218378 −0.109189 0.994021i \(-0.534825\pi\)
−0.109189 + 0.994021i \(0.534825\pi\)
\(942\) −0.637735 −0.0207785
\(943\) 22.3440 0.727621
\(944\) 31.0964 1.01210
\(945\) 2.43715 0.0792806
\(946\) 156.789 5.09766
\(947\) 43.3746 1.40949 0.704743 0.709463i \(-0.251062\pi\)
0.704743 + 0.709463i \(0.251062\pi\)
\(948\) −12.8334 −0.416808
\(949\) −40.1722 −1.30404
\(950\) −0.866616 −0.0281167
\(951\) 1.32668 0.0430204
\(952\) 1.94073 0.0628994
\(953\) −26.1479 −0.847015 −0.423507 0.905893i \(-0.639201\pi\)
−0.423507 + 0.905893i \(0.639201\pi\)
\(954\) 24.4315 0.790998
\(955\) 1.79388 0.0580484
\(956\) 109.240 3.53308
\(957\) −7.98951 −0.258264
\(958\) 86.1543 2.78352
\(959\) −7.11910 −0.229888
\(960\) −0.672404 −0.0217017
\(961\) −7.41849 −0.239306
\(962\) 19.3319 0.623286
\(963\) 11.1755 0.360126
\(964\) 93.8652 3.02319
\(965\) −36.0095 −1.15919
\(966\) −4.47941 −0.144123
\(967\) 33.0871 1.06401 0.532005 0.846741i \(-0.321439\pi\)
0.532005 + 0.846741i \(0.321439\pi\)
\(968\) −87.6785 −2.81809
\(969\) 0.00402383 0.000129264 0
\(970\) −25.6549 −0.823728
\(971\) −22.0121 −0.706403 −0.353202 0.935547i \(-0.614907\pi\)
−0.353202 + 0.935547i \(0.614907\pi\)
\(972\) 23.3408 0.748656
\(973\) −6.32299 −0.202706
\(974\) −45.6179 −1.46169
\(975\) 1.72604 0.0552774
\(976\) −55.6484 −1.78126
\(977\) 40.8260 1.30614 0.653070 0.757297i \(-0.273481\pi\)
0.653070 + 0.757297i \(0.273481\pi\)
\(978\) −3.82898 −0.122437
\(979\) 49.2905 1.57533
\(980\) 30.2427 0.966068
\(981\) 49.5176 1.58098
\(982\) 100.006 3.19131
\(983\) −18.4293 −0.587805 −0.293902 0.955835i \(-0.594954\pi\)
−0.293902 + 0.955835i \(0.594954\pi\)
\(984\) −4.77065 −0.152083
\(985\) 3.78761 0.120683
\(986\) −4.16323 −0.132584
\(987\) 2.13838 0.0680654
\(988\) 1.53587 0.0488627
\(989\) −74.4503 −2.36738
\(990\) −52.5102 −1.66888
\(991\) −9.16979 −0.291288 −0.145644 0.989337i \(-0.546525\pi\)
−0.145644 + 0.989337i \(0.546525\pi\)
\(992\) −35.0716 −1.11352
\(993\) 2.42057 0.0768143
\(994\) −18.1822 −0.576703
\(995\) 21.6105 0.685100
\(996\) −11.1023 −0.351790
\(997\) −19.3502 −0.612826 −0.306413 0.951899i \(-0.599129\pi\)
−0.306413 + 0.951899i \(0.599129\pi\)
\(998\) 69.1913 2.19021
\(999\) −2.85710 −0.0903948
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 4019.2.a.a.1.8 149
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4019.2.a.a.1.8 149 1.1 even 1 trivial