Properties

Label 8002.2.a.g.1.6
Level $8002$
Weight $2$
Character 8002.1
Self dual yes
Analytic conductor $63.896$
Analytic rank $0$
Dimension $95$
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] = [8002,2,Mod(1,8002)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8002, 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("8002.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8002.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: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(95\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 8002.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.80236 q^{3} +1.00000 q^{4} +1.73987 q^{5} -2.80236 q^{6} -0.386891 q^{7} +1.00000 q^{8} +4.85324 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.80236 q^{3} +1.00000 q^{4} +1.73987 q^{5} -2.80236 q^{6} -0.386891 q^{7} +1.00000 q^{8} +4.85324 q^{9} +1.73987 q^{10} -4.11288 q^{11} -2.80236 q^{12} +1.80933 q^{13} -0.386891 q^{14} -4.87575 q^{15} +1.00000 q^{16} +3.50517 q^{17} +4.85324 q^{18} -5.80916 q^{19} +1.73987 q^{20} +1.08421 q^{21} -4.11288 q^{22} -1.15032 q^{23} -2.80236 q^{24} -1.97284 q^{25} +1.80933 q^{26} -5.19344 q^{27} -0.386891 q^{28} -1.45658 q^{29} -4.87575 q^{30} -3.46348 q^{31} +1.00000 q^{32} +11.5258 q^{33} +3.50517 q^{34} -0.673141 q^{35} +4.85324 q^{36} +3.24261 q^{37} -5.80916 q^{38} -5.07039 q^{39} +1.73987 q^{40} +9.43456 q^{41} +1.08421 q^{42} +7.39336 q^{43} -4.11288 q^{44} +8.44402 q^{45} -1.15032 q^{46} -7.80327 q^{47} -2.80236 q^{48} -6.85032 q^{49} -1.97284 q^{50} -9.82276 q^{51} +1.80933 q^{52} -0.0764819 q^{53} -5.19344 q^{54} -7.15589 q^{55} -0.386891 q^{56} +16.2794 q^{57} -1.45658 q^{58} +14.6403 q^{59} -4.87575 q^{60} +2.69798 q^{61} -3.46348 q^{62} -1.87767 q^{63} +1.00000 q^{64} +3.14800 q^{65} +11.5258 q^{66} +2.31609 q^{67} +3.50517 q^{68} +3.22362 q^{69} -0.673141 q^{70} +9.43413 q^{71} +4.85324 q^{72} +2.25900 q^{73} +3.24261 q^{74} +5.52862 q^{75} -5.80916 q^{76} +1.59124 q^{77} -5.07039 q^{78} +4.01325 q^{79} +1.73987 q^{80} -0.00579824 q^{81} +9.43456 q^{82} -14.2396 q^{83} +1.08421 q^{84} +6.09855 q^{85} +7.39336 q^{86} +4.08187 q^{87} -4.11288 q^{88} +2.19901 q^{89} +8.44402 q^{90} -0.700012 q^{91} -1.15032 q^{92} +9.70593 q^{93} -7.80327 q^{94} -10.1072 q^{95} -2.80236 q^{96} -9.19795 q^{97} -6.85032 q^{98} -19.9608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 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
\(3\) −2.80236 −1.61794 −0.808972 0.587847i \(-0.799976\pi\)
−0.808972 + 0.587847i \(0.799976\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.73987 0.778095 0.389047 0.921218i \(-0.372804\pi\)
0.389047 + 0.921218i \(0.372804\pi\)
\(6\) −2.80236 −1.14406
\(7\) −0.386891 −0.146231 −0.0731155 0.997323i \(-0.523294\pi\)
−0.0731155 + 0.997323i \(0.523294\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.85324 1.61775
\(10\) 1.73987 0.550196
\(11\) −4.11288 −1.24008 −0.620040 0.784570i \(-0.712884\pi\)
−0.620040 + 0.784570i \(0.712884\pi\)
\(12\) −2.80236 −0.808972
\(13\) 1.80933 0.501817 0.250909 0.968011i \(-0.419271\pi\)
0.250909 + 0.968011i \(0.419271\pi\)
\(14\) −0.386891 −0.103401
\(15\) −4.87575 −1.25891
\(16\) 1.00000 0.250000
\(17\) 3.50517 0.850129 0.425064 0.905163i \(-0.360251\pi\)
0.425064 + 0.905163i \(0.360251\pi\)
\(18\) 4.85324 1.14392
\(19\) −5.80916 −1.33271 −0.666357 0.745633i \(-0.732147\pi\)
−0.666357 + 0.745633i \(0.732147\pi\)
\(20\) 1.73987 0.389047
\(21\) 1.08421 0.236594
\(22\) −4.11288 −0.876870
\(23\) −1.15032 −0.239859 −0.119929 0.992782i \(-0.538267\pi\)
−0.119929 + 0.992782i \(0.538267\pi\)
\(24\) −2.80236 −0.572030
\(25\) −1.97284 −0.394569
\(26\) 1.80933 0.354838
\(27\) −5.19344 −0.999479
\(28\) −0.386891 −0.0731155
\(29\) −1.45658 −0.270481 −0.135240 0.990813i \(-0.543181\pi\)
−0.135240 + 0.990813i \(0.543181\pi\)
\(30\) −4.87575 −0.890187
\(31\) −3.46348 −0.622059 −0.311030 0.950400i \(-0.600674\pi\)
−0.311030 + 0.950400i \(0.600674\pi\)
\(32\) 1.00000 0.176777
\(33\) 11.5258 2.00638
\(34\) 3.50517 0.601132
\(35\) −0.673141 −0.113782
\(36\) 4.85324 0.808873
\(37\) 3.24261 0.533082 0.266541 0.963824i \(-0.414119\pi\)
0.266541 + 0.963824i \(0.414119\pi\)
\(38\) −5.80916 −0.942371
\(39\) −5.07039 −0.811912
\(40\) 1.73987 0.275098
\(41\) 9.43456 1.47343 0.736715 0.676203i \(-0.236376\pi\)
0.736715 + 0.676203i \(0.236376\pi\)
\(42\) 1.08421 0.167297
\(43\) 7.39336 1.12748 0.563739 0.825953i \(-0.309363\pi\)
0.563739 + 0.825953i \(0.309363\pi\)
\(44\) −4.11288 −0.620040
\(45\) 8.44402 1.25876
\(46\) −1.15032 −0.169606
\(47\) −7.80327 −1.13822 −0.569112 0.822260i \(-0.692713\pi\)
−0.569112 + 0.822260i \(0.692713\pi\)
\(48\) −2.80236 −0.404486
\(49\) −6.85032 −0.978616
\(50\) −1.97284 −0.279002
\(51\) −9.82276 −1.37546
\(52\) 1.80933 0.250909
\(53\) −0.0764819 −0.0105056 −0.00525280 0.999986i \(-0.501672\pi\)
−0.00525280 + 0.999986i \(0.501672\pi\)
\(54\) −5.19344 −0.706738
\(55\) −7.15589 −0.964900
\(56\) −0.386891 −0.0517005
\(57\) 16.2794 2.15626
\(58\) −1.45658 −0.191259
\(59\) 14.6403 1.90601 0.953004 0.302956i \(-0.0979737\pi\)
0.953004 + 0.302956i \(0.0979737\pi\)
\(60\) −4.87575 −0.629457
\(61\) 2.69798 0.345441 0.172720 0.984971i \(-0.444744\pi\)
0.172720 + 0.984971i \(0.444744\pi\)
\(62\) −3.46348 −0.439862
\(63\) −1.87767 −0.236565
\(64\) 1.00000 0.125000
\(65\) 3.14800 0.390461
\(66\) 11.5258 1.41873
\(67\) 2.31609 0.282955 0.141477 0.989941i \(-0.454815\pi\)
0.141477 + 0.989941i \(0.454815\pi\)
\(68\) 3.50517 0.425064
\(69\) 3.22362 0.388078
\(70\) −0.673141 −0.0804557
\(71\) 9.43413 1.11963 0.559813 0.828619i \(-0.310873\pi\)
0.559813 + 0.828619i \(0.310873\pi\)
\(72\) 4.85324 0.571960
\(73\) 2.25900 0.264396 0.132198 0.991223i \(-0.457797\pi\)
0.132198 + 0.991223i \(0.457797\pi\)
\(74\) 3.24261 0.376946
\(75\) 5.52862 0.638390
\(76\) −5.80916 −0.666357
\(77\) 1.59124 0.181338
\(78\) −5.07039 −0.574109
\(79\) 4.01325 0.451526 0.225763 0.974182i \(-0.427512\pi\)
0.225763 + 0.974182i \(0.427512\pi\)
\(80\) 1.73987 0.194524
\(81\) −0.00579824 −0.000644249 0
\(82\) 9.43456 1.04187
\(83\) −14.2396 −1.56299 −0.781497 0.623909i \(-0.785544\pi\)
−0.781497 + 0.623909i \(0.785544\pi\)
\(84\) 1.08421 0.118297
\(85\) 6.09855 0.661481
\(86\) 7.39336 0.797247
\(87\) 4.08187 0.437623
\(88\) −4.11288 −0.438435
\(89\) 2.19901 0.233095 0.116547 0.993185i \(-0.462817\pi\)
0.116547 + 0.993185i \(0.462817\pi\)
\(90\) 8.44402 0.890077
\(91\) −0.700012 −0.0733812
\(92\) −1.15032 −0.119929
\(93\) 9.70593 1.00646
\(94\) −7.80327 −0.804846
\(95\) −10.1072 −1.03698
\(96\) −2.80236 −0.286015
\(97\) −9.19795 −0.933911 −0.466955 0.884281i \(-0.654649\pi\)
−0.466955 + 0.884281i \(0.654649\pi\)
\(98\) −6.85032 −0.691986
\(99\) −19.9608 −2.00614
\(100\) −1.97284 −0.197284
\(101\) 13.2816 1.32157 0.660784 0.750576i \(-0.270224\pi\)
0.660784 + 0.750576i \(0.270224\pi\)
\(102\) −9.82276 −0.972598
\(103\) 3.02225 0.297791 0.148896 0.988853i \(-0.452428\pi\)
0.148896 + 0.988853i \(0.452428\pi\)
\(104\) 1.80933 0.177419
\(105\) 1.88639 0.184092
\(106\) −0.0764819 −0.00742858
\(107\) −10.5944 −1.02420 −0.512102 0.858925i \(-0.671133\pi\)
−0.512102 + 0.858925i \(0.671133\pi\)
\(108\) −5.19344 −0.499739
\(109\) 11.8288 1.13299 0.566497 0.824064i \(-0.308298\pi\)
0.566497 + 0.824064i \(0.308298\pi\)
\(110\) −7.15589 −0.682288
\(111\) −9.08697 −0.862497
\(112\) −0.386891 −0.0365578
\(113\) 5.18957 0.488194 0.244097 0.969751i \(-0.421509\pi\)
0.244097 + 0.969751i \(0.421509\pi\)
\(114\) 16.2794 1.52470
\(115\) −2.00141 −0.186633
\(116\) −1.45658 −0.135240
\(117\) 8.78109 0.811812
\(118\) 14.6403 1.34775
\(119\) −1.35612 −0.124315
\(120\) −4.87575 −0.445093
\(121\) 5.91581 0.537801
\(122\) 2.69798 0.244264
\(123\) −26.4391 −2.38393
\(124\) −3.46348 −0.311030
\(125\) −12.1319 −1.08511
\(126\) −1.87767 −0.167276
\(127\) 13.1074 1.16310 0.581548 0.813512i \(-0.302447\pi\)
0.581548 + 0.813512i \(0.302447\pi\)
\(128\) 1.00000 0.0883883
\(129\) −20.7189 −1.82420
\(130\) 3.14800 0.276098
\(131\) −11.0039 −0.961413 −0.480707 0.876881i \(-0.659620\pi\)
−0.480707 + 0.876881i \(0.659620\pi\)
\(132\) 11.5258 1.00319
\(133\) 2.24751 0.194884
\(134\) 2.31609 0.200079
\(135\) −9.03593 −0.777689
\(136\) 3.50517 0.300566
\(137\) −10.9371 −0.934417 −0.467208 0.884147i \(-0.654740\pi\)
−0.467208 + 0.884147i \(0.654740\pi\)
\(138\) 3.22362 0.274413
\(139\) 1.06382 0.0902317 0.0451158 0.998982i \(-0.485634\pi\)
0.0451158 + 0.998982i \(0.485634\pi\)
\(140\) −0.673141 −0.0568908
\(141\) 21.8676 1.84158
\(142\) 9.43413 0.791695
\(143\) −7.44155 −0.622294
\(144\) 4.85324 0.404436
\(145\) −2.53427 −0.210460
\(146\) 2.25900 0.186956
\(147\) 19.1971 1.58335
\(148\) 3.24261 0.266541
\(149\) −9.80560 −0.803306 −0.401653 0.915792i \(-0.631564\pi\)
−0.401653 + 0.915792i \(0.631564\pi\)
\(150\) 5.52862 0.451410
\(151\) 21.5320 1.75225 0.876126 0.482081i \(-0.160119\pi\)
0.876126 + 0.482081i \(0.160119\pi\)
\(152\) −5.80916 −0.471185
\(153\) 17.0114 1.37529
\(154\) 1.59124 0.128226
\(155\) −6.02601 −0.484021
\(156\) −5.07039 −0.405956
\(157\) 13.2820 1.06002 0.530009 0.847992i \(-0.322189\pi\)
0.530009 + 0.847992i \(0.322189\pi\)
\(158\) 4.01325 0.319277
\(159\) 0.214330 0.0169975
\(160\) 1.73987 0.137549
\(161\) 0.445049 0.0350748
\(162\) −0.00579824 −0.000455553 0
\(163\) 9.48035 0.742558 0.371279 0.928521i \(-0.378919\pi\)
0.371279 + 0.928521i \(0.378919\pi\)
\(164\) 9.43456 0.736715
\(165\) 20.0534 1.56116
\(166\) −14.2396 −1.10520
\(167\) −21.4336 −1.65858 −0.829289 0.558820i \(-0.811254\pi\)
−0.829289 + 0.558820i \(0.811254\pi\)
\(168\) 1.08421 0.0836485
\(169\) −9.72634 −0.748180
\(170\) 6.09855 0.467737
\(171\) −28.1933 −2.15599
\(172\) 7.39336 0.563739
\(173\) 20.9886 1.59573 0.797867 0.602833i \(-0.205962\pi\)
0.797867 + 0.602833i \(0.205962\pi\)
\(174\) 4.08187 0.309446
\(175\) 0.763275 0.0576982
\(176\) −4.11288 −0.310020
\(177\) −41.0275 −3.08382
\(178\) 2.19901 0.164823
\(179\) 24.4083 1.82436 0.912182 0.409784i \(-0.134396\pi\)
0.912182 + 0.409784i \(0.134396\pi\)
\(180\) 8.44402 0.629380
\(181\) 22.5381 1.67525 0.837624 0.546248i \(-0.183944\pi\)
0.837624 + 0.546248i \(0.183944\pi\)
\(182\) −0.700012 −0.0518884
\(183\) −7.56072 −0.558904
\(184\) −1.15032 −0.0848028
\(185\) 5.64173 0.414788
\(186\) 9.70593 0.711673
\(187\) −14.4164 −1.05423
\(188\) −7.80327 −0.569112
\(189\) 2.00930 0.146155
\(190\) −10.1072 −0.733254
\(191\) 9.01860 0.652563 0.326282 0.945273i \(-0.394204\pi\)
0.326282 + 0.945273i \(0.394204\pi\)
\(192\) −2.80236 −0.202243
\(193\) 19.5799 1.40939 0.704697 0.709509i \(-0.251083\pi\)
0.704697 + 0.709509i \(0.251083\pi\)
\(194\) −9.19795 −0.660375
\(195\) −8.82183 −0.631745
\(196\) −6.85032 −0.489308
\(197\) −23.0988 −1.64572 −0.822861 0.568243i \(-0.807623\pi\)
−0.822861 + 0.568243i \(0.807623\pi\)
\(198\) −19.9608 −1.41855
\(199\) −6.50597 −0.461196 −0.230598 0.973049i \(-0.574068\pi\)
−0.230598 + 0.973049i \(0.574068\pi\)
\(200\) −1.97284 −0.139501
\(201\) −6.49051 −0.457806
\(202\) 13.2816 0.934489
\(203\) 0.563539 0.0395527
\(204\) −9.82276 −0.687731
\(205\) 16.4149 1.14647
\(206\) 3.02225 0.210570
\(207\) −5.58278 −0.388030
\(208\) 1.80933 0.125454
\(209\) 23.8924 1.65267
\(210\) 1.88639 0.130173
\(211\) −16.5607 −1.14009 −0.570043 0.821615i \(-0.693074\pi\)
−0.570043 + 0.821615i \(0.693074\pi\)
\(212\) −0.0764819 −0.00525280
\(213\) −26.4379 −1.81149
\(214\) −10.5944 −0.724221
\(215\) 12.8635 0.877284
\(216\) −5.19344 −0.353369
\(217\) 1.33999 0.0909644
\(218\) 11.8288 0.801148
\(219\) −6.33054 −0.427778
\(220\) −7.15589 −0.482450
\(221\) 6.34200 0.426609
\(222\) −9.08697 −0.609878
\(223\) −4.46460 −0.298971 −0.149486 0.988764i \(-0.547762\pi\)
−0.149486 + 0.988764i \(0.547762\pi\)
\(224\) −0.386891 −0.0258502
\(225\) −9.57467 −0.638312
\(226\) 5.18957 0.345205
\(227\) 6.05656 0.401988 0.200994 0.979592i \(-0.435583\pi\)
0.200994 + 0.979592i \(0.435583\pi\)
\(228\) 16.2794 1.07813
\(229\) −26.5917 −1.75723 −0.878616 0.477529i \(-0.841533\pi\)
−0.878616 + 0.477529i \(0.841533\pi\)
\(230\) −2.00141 −0.131969
\(231\) −4.45922 −0.293395
\(232\) −1.45658 −0.0956293
\(233\) −0.193795 −0.0126959 −0.00634796 0.999980i \(-0.502021\pi\)
−0.00634796 + 0.999980i \(0.502021\pi\)
\(234\) 8.78109 0.574038
\(235\) −13.5767 −0.885646
\(236\) 14.6403 0.953004
\(237\) −11.2466 −0.730545
\(238\) −1.35612 −0.0879041
\(239\) 13.5686 0.877678 0.438839 0.898566i \(-0.355390\pi\)
0.438839 + 0.898566i \(0.355390\pi\)
\(240\) −4.87575 −0.314729
\(241\) 15.6446 1.00776 0.503879 0.863774i \(-0.331906\pi\)
0.503879 + 0.863774i \(0.331906\pi\)
\(242\) 5.91581 0.380283
\(243\) 15.5966 1.00052
\(244\) 2.69798 0.172720
\(245\) −11.9187 −0.761456
\(246\) −26.4391 −1.68569
\(247\) −10.5107 −0.668778
\(248\) −3.46348 −0.219931
\(249\) 39.9044 2.52884
\(250\) −12.1319 −0.767286
\(251\) 7.81171 0.493071 0.246535 0.969134i \(-0.420708\pi\)
0.246535 + 0.969134i \(0.420708\pi\)
\(252\) −1.87767 −0.118282
\(253\) 4.73114 0.297444
\(254\) 13.1074 0.822434
\(255\) −17.0904 −1.07024
\(256\) 1.00000 0.0625000
\(257\) 28.3655 1.76939 0.884696 0.466168i \(-0.154366\pi\)
0.884696 + 0.466168i \(0.154366\pi\)
\(258\) −20.7189 −1.28990
\(259\) −1.25454 −0.0779531
\(260\) 3.14800 0.195231
\(261\) −7.06914 −0.437569
\(262\) −11.0039 −0.679822
\(263\) −2.05824 −0.126916 −0.0634582 0.997984i \(-0.520213\pi\)
−0.0634582 + 0.997984i \(0.520213\pi\)
\(264\) 11.5258 0.709363
\(265\) −0.133069 −0.00817435
\(266\) 2.24751 0.137804
\(267\) −6.16243 −0.377135
\(268\) 2.31609 0.141477
\(269\) 8.07102 0.492099 0.246049 0.969257i \(-0.420867\pi\)
0.246049 + 0.969257i \(0.420867\pi\)
\(270\) −9.03593 −0.549909
\(271\) 6.74968 0.410014 0.205007 0.978761i \(-0.434278\pi\)
0.205007 + 0.978761i \(0.434278\pi\)
\(272\) 3.50517 0.212532
\(273\) 1.96169 0.118727
\(274\) −10.9371 −0.660732
\(275\) 8.11407 0.489297
\(276\) 3.22362 0.194039
\(277\) −17.0790 −1.02618 −0.513089 0.858335i \(-0.671499\pi\)
−0.513089 + 0.858335i \(0.671499\pi\)
\(278\) 1.06382 0.0638034
\(279\) −16.8091 −1.00633
\(280\) −0.673141 −0.0402279
\(281\) −8.58496 −0.512136 −0.256068 0.966659i \(-0.582427\pi\)
−0.256068 + 0.966659i \(0.582427\pi\)
\(282\) 21.8676 1.30220
\(283\) −11.2073 −0.666205 −0.333103 0.942891i \(-0.608096\pi\)
−0.333103 + 0.942891i \(0.608096\pi\)
\(284\) 9.43413 0.559813
\(285\) 28.3241 1.67777
\(286\) −7.44155 −0.440028
\(287\) −3.65015 −0.215461
\(288\) 4.85324 0.285980
\(289\) −4.71378 −0.277281
\(290\) −2.53427 −0.148817
\(291\) 25.7760 1.51102
\(292\) 2.25900 0.132198
\(293\) 22.5845 1.31940 0.659699 0.751530i \(-0.270684\pi\)
0.659699 + 0.751530i \(0.270684\pi\)
\(294\) 19.1971 1.11960
\(295\) 25.4723 1.48306
\(296\) 3.24261 0.188473
\(297\) 21.3600 1.23943
\(298\) −9.80560 −0.568023
\(299\) −2.08131 −0.120365
\(300\) 5.52862 0.319195
\(301\) −2.86042 −0.164872
\(302\) 21.5320 1.23903
\(303\) −37.2198 −2.13822
\(304\) −5.80916 −0.333178
\(305\) 4.69414 0.268786
\(306\) 17.0114 0.972478
\(307\) 12.6918 0.724362 0.362181 0.932108i \(-0.382032\pi\)
0.362181 + 0.932108i \(0.382032\pi\)
\(308\) 1.59124 0.0906692
\(309\) −8.46944 −0.481810
\(310\) −6.02601 −0.342255
\(311\) −19.0415 −1.07974 −0.539872 0.841747i \(-0.681527\pi\)
−0.539872 + 0.841747i \(0.681527\pi\)
\(312\) −5.07039 −0.287054
\(313\) 15.9175 0.899713 0.449856 0.893101i \(-0.351475\pi\)
0.449856 + 0.893101i \(0.351475\pi\)
\(314\) 13.2820 0.749546
\(315\) −3.26691 −0.184070
\(316\) 4.01325 0.225763
\(317\) 5.17283 0.290535 0.145267 0.989392i \(-0.453596\pi\)
0.145267 + 0.989392i \(0.453596\pi\)
\(318\) 0.214330 0.0120190
\(319\) 5.99075 0.335418
\(320\) 1.73987 0.0972618
\(321\) 29.6895 1.65711
\(322\) 0.445049 0.0248016
\(323\) −20.3621 −1.13298
\(324\) −0.00579824 −0.000322125 0
\(325\) −3.56952 −0.198001
\(326\) 9.48035 0.525068
\(327\) −33.1486 −1.83312
\(328\) 9.43456 0.520936
\(329\) 3.01902 0.166444
\(330\) 20.0534 1.10390
\(331\) 12.9156 0.709908 0.354954 0.934884i \(-0.384497\pi\)
0.354954 + 0.934884i \(0.384497\pi\)
\(332\) −14.2396 −0.781497
\(333\) 15.7372 0.862391
\(334\) −21.4336 −1.17279
\(335\) 4.02969 0.220166
\(336\) 1.08421 0.0591484
\(337\) 13.9400 0.759362 0.379681 0.925117i \(-0.376034\pi\)
0.379681 + 0.925117i \(0.376034\pi\)
\(338\) −9.72634 −0.529043
\(339\) −14.5431 −0.789871
\(340\) 6.09855 0.330740
\(341\) 14.2449 0.771404
\(342\) −28.1933 −1.52452
\(343\) 5.35856 0.289335
\(344\) 7.39336 0.398623
\(345\) 5.60868 0.301961
\(346\) 20.9886 1.12835
\(347\) 32.9076 1.76657 0.883287 0.468833i \(-0.155326\pi\)
0.883287 + 0.468833i \(0.155326\pi\)
\(348\) 4.08187 0.218811
\(349\) 22.6923 1.21469 0.607344 0.794439i \(-0.292235\pi\)
0.607344 + 0.794439i \(0.292235\pi\)
\(350\) 0.763275 0.0407988
\(351\) −9.39664 −0.501555
\(352\) −4.11288 −0.219217
\(353\) 18.4688 0.982996 0.491498 0.870879i \(-0.336450\pi\)
0.491498 + 0.870879i \(0.336450\pi\)
\(354\) −41.0275 −2.18059
\(355\) 16.4142 0.871175
\(356\) 2.19901 0.116547
\(357\) 3.80034 0.201135
\(358\) 24.4083 1.29002
\(359\) −28.4244 −1.50018 −0.750092 0.661334i \(-0.769991\pi\)
−0.750092 + 0.661334i \(0.769991\pi\)
\(360\) 8.44402 0.445039
\(361\) 14.7464 0.776125
\(362\) 22.5381 1.18458
\(363\) −16.5782 −0.870132
\(364\) −0.700012 −0.0366906
\(365\) 3.93037 0.205725
\(366\) −7.56072 −0.395205
\(367\) 6.84530 0.357322 0.178661 0.983911i \(-0.442823\pi\)
0.178661 + 0.983911i \(0.442823\pi\)
\(368\) −1.15032 −0.0599646
\(369\) 45.7882 2.38364
\(370\) 5.64173 0.293300
\(371\) 0.0295901 0.00153624
\(372\) 9.70593 0.503229
\(373\) −13.5581 −0.702012 −0.351006 0.936373i \(-0.614160\pi\)
−0.351006 + 0.936373i \(0.614160\pi\)
\(374\) −14.4164 −0.745452
\(375\) 33.9979 1.75564
\(376\) −7.80327 −0.402423
\(377\) −2.63543 −0.135732
\(378\) 2.00930 0.103347
\(379\) 33.7983 1.73610 0.868051 0.496475i \(-0.165373\pi\)
0.868051 + 0.496475i \(0.165373\pi\)
\(380\) −10.1072 −0.518489
\(381\) −36.7318 −1.88183
\(382\) 9.01860 0.461432
\(383\) 0.153092 0.00782263 0.00391131 0.999992i \(-0.498755\pi\)
0.00391131 + 0.999992i \(0.498755\pi\)
\(384\) −2.80236 −0.143007
\(385\) 2.76855 0.141098
\(386\) 19.5799 0.996592
\(387\) 35.8817 1.82397
\(388\) −9.19795 −0.466955
\(389\) −10.8983 −0.552564 −0.276282 0.961077i \(-0.589102\pi\)
−0.276282 + 0.961077i \(0.589102\pi\)
\(390\) −8.82183 −0.446711
\(391\) −4.03207 −0.203911
\(392\) −6.85032 −0.345993
\(393\) 30.8369 1.55551
\(394\) −23.0988 −1.16370
\(395\) 6.98255 0.351330
\(396\) −19.9608 −1.00307
\(397\) 9.43226 0.473391 0.236696 0.971584i \(-0.423936\pi\)
0.236696 + 0.971584i \(0.423936\pi\)
\(398\) −6.50597 −0.326115
\(399\) −6.29835 −0.315312
\(400\) −1.97284 −0.0986421
\(401\) −9.90263 −0.494514 −0.247257 0.968950i \(-0.579529\pi\)
−0.247257 + 0.968950i \(0.579529\pi\)
\(402\) −6.49051 −0.323717
\(403\) −6.26657 −0.312160
\(404\) 13.2816 0.660784
\(405\) −0.0100882 −0.000501287 0
\(406\) 0.563539 0.0279680
\(407\) −13.3365 −0.661065
\(408\) −9.82276 −0.486299
\(409\) −30.5749 −1.51183 −0.755917 0.654668i \(-0.772809\pi\)
−0.755917 + 0.654668i \(0.772809\pi\)
\(410\) 16.4149 0.810676
\(411\) 30.6496 1.51183
\(412\) 3.02225 0.148896
\(413\) −5.66421 −0.278718
\(414\) −5.58278 −0.274379
\(415\) −24.7750 −1.21616
\(416\) 1.80933 0.0887096
\(417\) −2.98120 −0.145990
\(418\) 23.8924 1.16862
\(419\) 19.7963 0.967110 0.483555 0.875314i \(-0.339345\pi\)
0.483555 + 0.875314i \(0.339345\pi\)
\(420\) 1.88639 0.0920462
\(421\) −14.7606 −0.719386 −0.359693 0.933071i \(-0.617119\pi\)
−0.359693 + 0.933071i \(0.617119\pi\)
\(422\) −16.5607 −0.806163
\(423\) −37.8711 −1.84136
\(424\) −0.0764819 −0.00371429
\(425\) −6.91515 −0.335434
\(426\) −26.4379 −1.28092
\(427\) −1.04382 −0.0505142
\(428\) −10.5944 −0.512102
\(429\) 20.8539 1.00684
\(430\) 12.8635 0.620333
\(431\) 10.8736 0.523763 0.261882 0.965100i \(-0.415657\pi\)
0.261882 + 0.965100i \(0.415657\pi\)
\(432\) −5.19344 −0.249870
\(433\) −29.3690 −1.41138 −0.705691 0.708520i \(-0.749363\pi\)
−0.705691 + 0.708520i \(0.749363\pi\)
\(434\) 1.33999 0.0643215
\(435\) 7.10194 0.340512
\(436\) 11.8288 0.566497
\(437\) 6.68240 0.319663
\(438\) −6.33054 −0.302485
\(439\) 33.4954 1.59865 0.799324 0.600900i \(-0.205191\pi\)
0.799324 + 0.600900i \(0.205191\pi\)
\(440\) −7.15589 −0.341144
\(441\) −33.2462 −1.58315
\(442\) 6.34200 0.301658
\(443\) 5.91776 0.281161 0.140581 0.990069i \(-0.455103\pi\)
0.140581 + 0.990069i \(0.455103\pi\)
\(444\) −9.08697 −0.431249
\(445\) 3.82600 0.181370
\(446\) −4.46460 −0.211405
\(447\) 27.4789 1.29971
\(448\) −0.386891 −0.0182789
\(449\) 12.2918 0.580085 0.290042 0.957014i \(-0.406331\pi\)
0.290042 + 0.957014i \(0.406331\pi\)
\(450\) −9.57467 −0.451354
\(451\) −38.8032 −1.82717
\(452\) 5.18957 0.244097
\(453\) −60.3406 −2.83505
\(454\) 6.05656 0.284248
\(455\) −1.21793 −0.0570975
\(456\) 16.2794 0.762352
\(457\) 20.5618 0.961841 0.480920 0.876764i \(-0.340303\pi\)
0.480920 + 0.876764i \(0.340303\pi\)
\(458\) −26.5917 −1.24255
\(459\) −18.2039 −0.849686
\(460\) −2.00141 −0.0933163
\(461\) 15.8977 0.740428 0.370214 0.928947i \(-0.379284\pi\)
0.370214 + 0.928947i \(0.379284\pi\)
\(462\) −4.45922 −0.207462
\(463\) −12.0243 −0.558817 −0.279409 0.960172i \(-0.590138\pi\)
−0.279409 + 0.960172i \(0.590138\pi\)
\(464\) −1.45658 −0.0676201
\(465\) 16.8871 0.783119
\(466\) −0.193795 −0.00897737
\(467\) 26.3272 1.21828 0.609139 0.793064i \(-0.291515\pi\)
0.609139 + 0.793064i \(0.291515\pi\)
\(468\) 8.78109 0.405906
\(469\) −0.896073 −0.0413768
\(470\) −13.5767 −0.626247
\(471\) −37.2210 −1.71505
\(472\) 14.6403 0.673876
\(473\) −30.4080 −1.39816
\(474\) −11.2466 −0.516573
\(475\) 11.4606 0.525847
\(476\) −1.35612 −0.0621576
\(477\) −0.371185 −0.0169954
\(478\) 13.5686 0.620612
\(479\) 12.8252 0.585996 0.292998 0.956113i \(-0.405347\pi\)
0.292998 + 0.956113i \(0.405347\pi\)
\(480\) −4.87575 −0.222547
\(481\) 5.86694 0.267510
\(482\) 15.6446 0.712592
\(483\) −1.24719 −0.0567490
\(484\) 5.91581 0.268900
\(485\) −16.0033 −0.726671
\(486\) 15.5966 0.707475
\(487\) 32.0639 1.45295 0.726476 0.687191i \(-0.241157\pi\)
0.726476 + 0.687191i \(0.241157\pi\)
\(488\) 2.69798 0.122132
\(489\) −26.5674 −1.20142
\(490\) −11.9187 −0.538431
\(491\) −30.6227 −1.38198 −0.690991 0.722863i \(-0.742826\pi\)
−0.690991 + 0.722863i \(0.742826\pi\)
\(492\) −26.4391 −1.19197
\(493\) −5.10557 −0.229943
\(494\) −10.5107 −0.472898
\(495\) −34.7292 −1.56096
\(496\) −3.46348 −0.155515
\(497\) −3.64998 −0.163724
\(498\) 39.9044 1.78816
\(499\) 17.3833 0.778184 0.389092 0.921199i \(-0.372789\pi\)
0.389092 + 0.921199i \(0.372789\pi\)
\(500\) −12.1319 −0.542553
\(501\) 60.0646 2.68349
\(502\) 7.81171 0.348654
\(503\) −28.4946 −1.27051 −0.635255 0.772303i \(-0.719105\pi\)
−0.635255 + 0.772303i \(0.719105\pi\)
\(504\) −1.87767 −0.0836382
\(505\) 23.1083 1.02830
\(506\) 4.73114 0.210325
\(507\) 27.2567 1.21051
\(508\) 13.1074 0.581548
\(509\) 28.4529 1.26115 0.630576 0.776128i \(-0.282819\pi\)
0.630576 + 0.776128i \(0.282819\pi\)
\(510\) −17.0904 −0.756773
\(511\) −0.873987 −0.0386629
\(512\) 1.00000 0.0441942
\(513\) 30.1696 1.33202
\(514\) 28.3655 1.25115
\(515\) 5.25833 0.231710
\(516\) −20.7189 −0.912098
\(517\) 32.0940 1.41149
\(518\) −1.25454 −0.0551212
\(519\) −58.8177 −2.58181
\(520\) 3.14800 0.138049
\(521\) −16.1382 −0.707026 −0.353513 0.935430i \(-0.615013\pi\)
−0.353513 + 0.935430i \(0.615013\pi\)
\(522\) −7.06914 −0.309408
\(523\) 44.4285 1.94272 0.971362 0.237605i \(-0.0763624\pi\)
0.971362 + 0.237605i \(0.0763624\pi\)
\(524\) −11.0039 −0.480707
\(525\) −2.13897 −0.0933525
\(526\) −2.05824 −0.0897434
\(527\) −12.1401 −0.528830
\(528\) 11.5258 0.501596
\(529\) −21.6768 −0.942468
\(530\) −0.133069 −0.00578014
\(531\) 71.0530 3.08344
\(532\) 2.24751 0.0974420
\(533\) 17.0702 0.739393
\(534\) −6.16243 −0.266675
\(535\) −18.4330 −0.796927
\(536\) 2.31609 0.100040
\(537\) −68.4010 −2.95172
\(538\) 8.07102 0.347966
\(539\) 28.1745 1.21356
\(540\) −9.03593 −0.388845
\(541\) 16.8128 0.722840 0.361420 0.932403i \(-0.382292\pi\)
0.361420 + 0.932403i \(0.382292\pi\)
\(542\) 6.74968 0.289923
\(543\) −63.1601 −2.71046
\(544\) 3.50517 0.150283
\(545\) 20.5806 0.881577
\(546\) 1.96169 0.0839525
\(547\) 36.3759 1.55532 0.777660 0.628685i \(-0.216407\pi\)
0.777660 + 0.628685i \(0.216407\pi\)
\(548\) −10.9371 −0.467208
\(549\) 13.0939 0.558836
\(550\) 8.11407 0.345985
\(551\) 8.46153 0.360473
\(552\) 3.22362 0.137206
\(553\) −1.55269 −0.0660272
\(554\) −17.0790 −0.725617
\(555\) −15.8102 −0.671104
\(556\) 1.06382 0.0451158
\(557\) −9.03837 −0.382968 −0.191484 0.981496i \(-0.561330\pi\)
−0.191484 + 0.981496i \(0.561330\pi\)
\(558\) −16.8091 −0.711585
\(559\) 13.3770 0.565787
\(560\) −0.673141 −0.0284454
\(561\) 40.3999 1.70568
\(562\) −8.58496 −0.362135
\(563\) 10.2278 0.431049 0.215525 0.976498i \(-0.430854\pi\)
0.215525 + 0.976498i \(0.430854\pi\)
\(564\) 21.8676 0.920792
\(565\) 9.02919 0.379861
\(566\) −11.2073 −0.471078
\(567\) 0.00224329 9.42092e−5 0
\(568\) 9.43413 0.395847
\(569\) 27.3976 1.14857 0.574283 0.818657i \(-0.305281\pi\)
0.574283 + 0.818657i \(0.305281\pi\)
\(570\) 28.3241 1.18636
\(571\) −21.5018 −0.899823 −0.449912 0.893073i \(-0.648545\pi\)
−0.449912 + 0.893073i \(0.648545\pi\)
\(572\) −7.44155 −0.311147
\(573\) −25.2734 −1.05581
\(574\) −3.65015 −0.152354
\(575\) 2.26940 0.0946406
\(576\) 4.85324 0.202218
\(577\) −11.8311 −0.492533 −0.246267 0.969202i \(-0.579204\pi\)
−0.246267 + 0.969202i \(0.579204\pi\)
\(578\) −4.71378 −0.196067
\(579\) −54.8700 −2.28032
\(580\) −2.53427 −0.105230
\(581\) 5.50915 0.228558
\(582\) 25.7760 1.06845
\(583\) 0.314561 0.0130278
\(584\) 2.25900 0.0934781
\(585\) 15.2780 0.631667
\(586\) 22.5845 0.932955
\(587\) 34.7490 1.43425 0.717123 0.696946i \(-0.245458\pi\)
0.717123 + 0.696946i \(0.245458\pi\)
\(588\) 19.1971 0.791674
\(589\) 20.1199 0.829027
\(590\) 25.4723 1.04868
\(591\) 64.7312 2.66269
\(592\) 3.24261 0.133270
\(593\) 0.158235 0.00649795 0.00324897 0.999995i \(-0.498966\pi\)
0.00324897 + 0.999995i \(0.498966\pi\)
\(594\) 21.3600 0.876413
\(595\) −2.35947 −0.0967290
\(596\) −9.80560 −0.401653
\(597\) 18.2321 0.746189
\(598\) −2.08131 −0.0851110
\(599\) 25.6606 1.04846 0.524232 0.851576i \(-0.324353\pi\)
0.524232 + 0.851576i \(0.324353\pi\)
\(600\) 5.52862 0.225705
\(601\) −29.1463 −1.18890 −0.594450 0.804132i \(-0.702630\pi\)
−0.594450 + 0.804132i \(0.702630\pi\)
\(602\) −2.86042 −0.116582
\(603\) 11.2405 0.457749
\(604\) 21.5320 0.876126
\(605\) 10.2928 0.418460
\(606\) −37.2198 −1.51195
\(607\) −9.56400 −0.388191 −0.194095 0.980983i \(-0.562177\pi\)
−0.194095 + 0.980983i \(0.562177\pi\)
\(608\) −5.80916 −0.235593
\(609\) −1.57924 −0.0639940
\(610\) 4.69414 0.190060
\(611\) −14.1187 −0.571180
\(612\) 17.0114 0.687646
\(613\) 17.3910 0.702417 0.351209 0.936297i \(-0.385771\pi\)
0.351209 + 0.936297i \(0.385771\pi\)
\(614\) 12.6918 0.512201
\(615\) −46.0006 −1.85492
\(616\) 1.59124 0.0641128
\(617\) 43.3429 1.74492 0.872461 0.488684i \(-0.162523\pi\)
0.872461 + 0.488684i \(0.162523\pi\)
\(618\) −8.46944 −0.340691
\(619\) 37.2868 1.49868 0.749341 0.662184i \(-0.230370\pi\)
0.749341 + 0.662184i \(0.230370\pi\)
\(620\) −6.02601 −0.242011
\(621\) 5.97413 0.239734
\(622\) −19.0415 −0.763494
\(623\) −0.850778 −0.0340857
\(624\) −5.07039 −0.202978
\(625\) −11.2437 −0.449747
\(626\) 15.9175 0.636193
\(627\) −66.9552 −2.67393
\(628\) 13.2820 0.530009
\(629\) 11.3659 0.453188
\(630\) −3.26691 −0.130157
\(631\) −3.99272 −0.158948 −0.0794739 0.996837i \(-0.525324\pi\)
−0.0794739 + 0.996837i \(0.525324\pi\)
\(632\) 4.01325 0.159639
\(633\) 46.4091 1.84460
\(634\) 5.17283 0.205439
\(635\) 22.8053 0.905000
\(636\) 0.214330 0.00849874
\(637\) −12.3945 −0.491086
\(638\) 5.99075 0.237176
\(639\) 45.7861 1.81127
\(640\) 1.73987 0.0687745
\(641\) 26.2367 1.03629 0.518143 0.855294i \(-0.326623\pi\)
0.518143 + 0.855294i \(0.326623\pi\)
\(642\) 29.6895 1.17175
\(643\) −29.1591 −1.14992 −0.574962 0.818180i \(-0.694983\pi\)
−0.574962 + 0.818180i \(0.694983\pi\)
\(644\) 0.445049 0.0175374
\(645\) −36.0482 −1.41940
\(646\) −20.3621 −0.801136
\(647\) −31.9971 −1.25793 −0.628967 0.777432i \(-0.716522\pi\)
−0.628967 + 0.777432i \(0.716522\pi\)
\(648\) −0.00579824 −0.000227777 0
\(649\) −60.2140 −2.36361
\(650\) −3.56952 −0.140008
\(651\) −3.75513 −0.147175
\(652\) 9.48035 0.371279
\(653\) 7.21785 0.282456 0.141228 0.989977i \(-0.454895\pi\)
0.141228 + 0.989977i \(0.454895\pi\)
\(654\) −33.1486 −1.29621
\(655\) −19.1454 −0.748071
\(656\) 9.43456 0.368358
\(657\) 10.9635 0.427726
\(658\) 3.01902 0.117693
\(659\) 18.7844 0.731736 0.365868 0.930667i \(-0.380772\pi\)
0.365868 + 0.930667i \(0.380772\pi\)
\(660\) 20.0534 0.780578
\(661\) −12.5128 −0.486693 −0.243346 0.969939i \(-0.578245\pi\)
−0.243346 + 0.969939i \(0.578245\pi\)
\(662\) 12.9156 0.501980
\(663\) −17.7726 −0.690230
\(664\) −14.2396 −0.552602
\(665\) 3.91039 0.151638
\(666\) 15.7372 0.609802
\(667\) 1.67554 0.0648771
\(668\) −21.4336 −0.829289
\(669\) 12.5114 0.483719
\(670\) 4.02969 0.155681
\(671\) −11.0965 −0.428375
\(672\) 1.08421 0.0418243
\(673\) −21.3003 −0.821065 −0.410533 0.911846i \(-0.634657\pi\)
−0.410533 + 0.911846i \(0.634657\pi\)
\(674\) 13.9400 0.536950
\(675\) 10.2458 0.394363
\(676\) −9.72634 −0.374090
\(677\) 37.3958 1.43724 0.718618 0.695405i \(-0.244775\pi\)
0.718618 + 0.695405i \(0.244775\pi\)
\(678\) −14.5431 −0.558523
\(679\) 3.55860 0.136567
\(680\) 6.09855 0.233869
\(681\) −16.9727 −0.650395
\(682\) 14.2449 0.545465
\(683\) −1.67716 −0.0641747 −0.0320874 0.999485i \(-0.510215\pi\)
−0.0320874 + 0.999485i \(0.510215\pi\)
\(684\) −28.1933 −1.07800
\(685\) −19.0291 −0.727065
\(686\) 5.35856 0.204591
\(687\) 74.5197 2.84310
\(688\) 7.39336 0.281869
\(689\) −0.138381 −0.00527189
\(690\) 5.60868 0.213519
\(691\) −48.6176 −1.84950 −0.924750 0.380574i \(-0.875726\pi\)
−0.924750 + 0.380574i \(0.875726\pi\)
\(692\) 20.9886 0.797867
\(693\) 7.72265 0.293359
\(694\) 32.9076 1.24916
\(695\) 1.85090 0.0702088
\(696\) 4.08187 0.154723
\(697\) 33.0697 1.25261
\(698\) 22.6923 0.858915
\(699\) 0.543084 0.0205413
\(700\) 0.763275 0.0288491
\(701\) −14.5282 −0.548723 −0.274362 0.961627i \(-0.588466\pi\)
−0.274362 + 0.961627i \(0.588466\pi\)
\(702\) −9.39664 −0.354653
\(703\) −18.8369 −0.710445
\(704\) −4.11288 −0.155010
\(705\) 38.0468 1.43293
\(706\) 18.4688 0.695083
\(707\) −5.13853 −0.193254
\(708\) −41.0275 −1.54191
\(709\) −2.07261 −0.0778385 −0.0389193 0.999242i \(-0.512392\pi\)
−0.0389193 + 0.999242i \(0.512392\pi\)
\(710\) 16.4142 0.616014
\(711\) 19.4773 0.730455
\(712\) 2.19901 0.0824115
\(713\) 3.98411 0.149206
\(714\) 3.80034 0.142224
\(715\) −12.9474 −0.484203
\(716\) 24.4083 0.912182
\(717\) −38.0241 −1.42004
\(718\) −28.4244 −1.06079
\(719\) 18.9765 0.707703 0.353851 0.935302i \(-0.384872\pi\)
0.353851 + 0.935302i \(0.384872\pi\)
\(720\) 8.44402 0.314690
\(721\) −1.16928 −0.0435463
\(722\) 14.7464 0.548804
\(723\) −43.8418 −1.63050
\(724\) 22.5381 0.837624
\(725\) 2.87361 0.106723
\(726\) −16.5782 −0.615276
\(727\) 14.1840 0.526057 0.263029 0.964788i \(-0.415279\pi\)
0.263029 + 0.964788i \(0.415279\pi\)
\(728\) −0.700012 −0.0259442
\(729\) −43.6899 −1.61814
\(730\) 3.93037 0.145470
\(731\) 25.9150 0.958501
\(732\) −7.56072 −0.279452
\(733\) 28.5554 1.05472 0.527358 0.849643i \(-0.323183\pi\)
0.527358 + 0.849643i \(0.323183\pi\)
\(734\) 6.84530 0.252665
\(735\) 33.4005 1.23199
\(736\) −1.15032 −0.0424014
\(737\) −9.52579 −0.350887
\(738\) 45.7882 1.68549
\(739\) 49.9825 1.83864 0.919319 0.393514i \(-0.128741\pi\)
0.919319 + 0.393514i \(0.128741\pi\)
\(740\) 5.64173 0.207394
\(741\) 29.4547 1.08205
\(742\) 0.0295901 0.00108629
\(743\) −10.3475 −0.379611 −0.189806 0.981822i \(-0.560786\pi\)
−0.189806 + 0.981822i \(0.560786\pi\)
\(744\) 9.70593 0.355837
\(745\) −17.0605 −0.625048
\(746\) −13.5581 −0.496398
\(747\) −69.1079 −2.52853
\(748\) −14.4164 −0.527114
\(749\) 4.09889 0.149770
\(750\) 33.9979 1.24143
\(751\) −12.1440 −0.443142 −0.221571 0.975144i \(-0.571118\pi\)
−0.221571 + 0.975144i \(0.571118\pi\)
\(752\) −7.80327 −0.284556
\(753\) −21.8912 −0.797761
\(754\) −2.63543 −0.0959769
\(755\) 37.4630 1.36342
\(756\) 2.00930 0.0730774
\(757\) 6.34007 0.230434 0.115217 0.993340i \(-0.463244\pi\)
0.115217 + 0.993340i \(0.463244\pi\)
\(758\) 33.7983 1.22761
\(759\) −13.2584 −0.481248
\(760\) −10.1072 −0.366627
\(761\) −29.0587 −1.05338 −0.526689 0.850058i \(-0.676567\pi\)
−0.526689 + 0.850058i \(0.676567\pi\)
\(762\) −36.7318 −1.33065
\(763\) −4.57646 −0.165679
\(764\) 9.01860 0.326282
\(765\) 29.5977 1.07011
\(766\) 0.153092 0.00553143
\(767\) 26.4891 0.956468
\(768\) −2.80236 −0.101122
\(769\) −8.60300 −0.310232 −0.155116 0.987896i \(-0.549575\pi\)
−0.155116 + 0.987896i \(0.549575\pi\)
\(770\) 2.76855 0.0997716
\(771\) −79.4905 −2.86278
\(772\) 19.5799 0.704697
\(773\) −39.4896 −1.42034 −0.710171 0.704030i \(-0.751382\pi\)
−0.710171 + 0.704030i \(0.751382\pi\)
\(774\) 35.8817 1.28974
\(775\) 6.83290 0.245445
\(776\) −9.19795 −0.330187
\(777\) 3.51567 0.126124
\(778\) −10.8983 −0.390721
\(779\) −54.8069 −1.96366
\(780\) −8.82183 −0.315872
\(781\) −38.8015 −1.38843
\(782\) −4.03207 −0.144187
\(783\) 7.56468 0.270340
\(784\) −6.85032 −0.244654
\(785\) 23.1090 0.824795
\(786\) 30.8369 1.09991
\(787\) −43.8216 −1.56207 −0.781036 0.624486i \(-0.785308\pi\)
−0.781036 + 0.624486i \(0.785308\pi\)
\(788\) −23.0988 −0.822861
\(789\) 5.76793 0.205344
\(790\) 6.98255 0.248428
\(791\) −2.00780 −0.0713891
\(792\) −19.9608 −0.709276
\(793\) 4.88153 0.173348
\(794\) 9.43226 0.334738
\(795\) 0.372907 0.0132256
\(796\) −6.50597 −0.230598
\(797\) −19.5989 −0.694229 −0.347115 0.937823i \(-0.612839\pi\)
−0.347115 + 0.937823i \(0.612839\pi\)
\(798\) −6.29835 −0.222959
\(799\) −27.3518 −0.967637
\(800\) −1.97284 −0.0697505
\(801\) 10.6723 0.377088
\(802\) −9.90263 −0.349674
\(803\) −9.29101 −0.327872
\(804\) −6.49051 −0.228903
\(805\) 0.774328 0.0272915
\(806\) −6.26657 −0.220730
\(807\) −22.6179 −0.796189
\(808\) 13.2816 0.467245
\(809\) 8.58664 0.301890 0.150945 0.988542i \(-0.451768\pi\)
0.150945 + 0.988542i \(0.451768\pi\)
\(810\) −0.0100882 −0.000354463 0
\(811\) 29.3272 1.02982 0.514909 0.857245i \(-0.327826\pi\)
0.514909 + 0.857245i \(0.327826\pi\)
\(812\) 0.563539 0.0197763
\(813\) −18.9150 −0.663380
\(814\) −13.3365 −0.467443
\(815\) 16.4946 0.577781
\(816\) −9.82276 −0.343865
\(817\) −42.9492 −1.50260
\(818\) −30.5749 −1.06903
\(819\) −3.39733 −0.118712
\(820\) 16.4149 0.573234
\(821\) −6.41377 −0.223842 −0.111921 0.993717i \(-0.535700\pi\)
−0.111921 + 0.993717i \(0.535700\pi\)
\(822\) 30.6496 1.06903
\(823\) 35.2079 1.22727 0.613635 0.789590i \(-0.289707\pi\)
0.613635 + 0.789590i \(0.289707\pi\)
\(824\) 3.02225 0.105285
\(825\) −22.7386 −0.791656
\(826\) −5.66421 −0.197083
\(827\) −50.6697 −1.76196 −0.880978 0.473157i \(-0.843114\pi\)
−0.880978 + 0.473157i \(0.843114\pi\)
\(828\) −5.58278 −0.194015
\(829\) −19.0272 −0.660841 −0.330420 0.943834i \(-0.607191\pi\)
−0.330420 + 0.943834i \(0.607191\pi\)
\(830\) −24.7750 −0.859953
\(831\) 47.8616 1.66030
\(832\) 1.80933 0.0627271
\(833\) −24.0115 −0.831950
\(834\) −2.98120 −0.103230
\(835\) −37.2917 −1.29053
\(836\) 23.8924 0.826336
\(837\) 17.9874 0.621735
\(838\) 19.7963 0.683850
\(839\) −31.5069 −1.08774 −0.543869 0.839170i \(-0.683041\pi\)
−0.543869 + 0.839170i \(0.683041\pi\)
\(840\) 1.88639 0.0650865
\(841\) −26.8784 −0.926840
\(842\) −14.7606 −0.508683
\(843\) 24.0582 0.828607
\(844\) −16.5607 −0.570043
\(845\) −16.9226 −0.582155
\(846\) −37.8711 −1.30204
\(847\) −2.28877 −0.0786432
\(848\) −0.0764819 −0.00262640
\(849\) 31.4069 1.07788
\(850\) −6.91515 −0.237188
\(851\) −3.73004 −0.127864
\(852\) −26.4379 −0.905746
\(853\) 6.43711 0.220402 0.110201 0.993909i \(-0.464850\pi\)
0.110201 + 0.993909i \(0.464850\pi\)
\(854\) −1.04382 −0.0357189
\(855\) −49.0527 −1.67757
\(856\) −10.5944 −0.362111
\(857\) −20.9885 −0.716952 −0.358476 0.933539i \(-0.616704\pi\)
−0.358476 + 0.933539i \(0.616704\pi\)
\(858\) 20.8539 0.711941
\(859\) −33.2709 −1.13519 −0.567595 0.823308i \(-0.692126\pi\)
−0.567595 + 0.823308i \(0.692126\pi\)
\(860\) 12.8635 0.438642
\(861\) 10.2290 0.348605
\(862\) 10.8736 0.370357
\(863\) −38.9050 −1.32434 −0.662171 0.749353i \(-0.730365\pi\)
−0.662171 + 0.749353i \(0.730365\pi\)
\(864\) −5.19344 −0.176685
\(865\) 36.5175 1.24163
\(866\) −29.3690 −0.997998
\(867\) 13.2097 0.448626
\(868\) 1.33999 0.0454822
\(869\) −16.5060 −0.559929
\(870\) 7.10194 0.240778
\(871\) 4.19056 0.141992
\(872\) 11.8288 0.400574
\(873\) −44.6399 −1.51083
\(874\) 6.68240 0.226036
\(875\) 4.69371 0.158676
\(876\) −6.33054 −0.213889
\(877\) 26.1977 0.884632 0.442316 0.896859i \(-0.354157\pi\)
0.442316 + 0.896859i \(0.354157\pi\)
\(878\) 33.4954 1.13042
\(879\) −63.2898 −2.13471
\(880\) −7.15589 −0.241225
\(881\) −24.2765 −0.817895 −0.408948 0.912558i \(-0.634104\pi\)
−0.408948 + 0.912558i \(0.634104\pi\)
\(882\) −33.2462 −1.11946
\(883\) −13.9387 −0.469076 −0.234538 0.972107i \(-0.575358\pi\)
−0.234538 + 0.972107i \(0.575358\pi\)
\(884\) 6.34200 0.213305
\(885\) −71.3827 −2.39950
\(886\) 5.91776 0.198811
\(887\) 16.7014 0.560778 0.280389 0.959886i \(-0.409537\pi\)
0.280389 + 0.959886i \(0.409537\pi\)
\(888\) −9.08697 −0.304939
\(889\) −5.07115 −0.170081
\(890\) 3.82600 0.128248
\(891\) 0.0238475 0.000798921 0
\(892\) −4.46460 −0.149486
\(893\) 45.3305 1.51693
\(894\) 27.4789 0.919030
\(895\) 42.4674 1.41953
\(896\) −0.386891 −0.0129251
\(897\) 5.83258 0.194744
\(898\) 12.2918 0.410182
\(899\) 5.04484 0.168255
\(900\) −9.57467 −0.319156
\(901\) −0.268082 −0.00893111
\(902\) −38.8032 −1.29201
\(903\) 8.01595 0.266754
\(904\) 5.18957 0.172603
\(905\) 39.2135 1.30350
\(906\) −60.3406 −2.00468
\(907\) −34.8498 −1.15717 −0.578584 0.815623i \(-0.696395\pi\)
−0.578584 + 0.815623i \(0.696395\pi\)
\(908\) 6.05656 0.200994
\(909\) 64.4587 2.13796
\(910\) −1.21793 −0.0403741
\(911\) −18.4574 −0.611520 −0.305760 0.952109i \(-0.598910\pi\)
−0.305760 + 0.952109i \(0.598910\pi\)
\(912\) 16.2794 0.539064
\(913\) 58.5656 1.93824
\(914\) 20.5618 0.680124
\(915\) −13.1547 −0.434881
\(916\) −26.5917 −0.878616
\(917\) 4.25730 0.140588
\(918\) −18.2039 −0.600818
\(919\) −48.9446 −1.61453 −0.807266 0.590188i \(-0.799054\pi\)
−0.807266 + 0.590188i \(0.799054\pi\)
\(920\) −2.00141 −0.0659846
\(921\) −35.5672 −1.17198
\(922\) 15.8977 0.523562
\(923\) 17.0694 0.561847
\(924\) −4.45922 −0.146698
\(925\) −6.39716 −0.210337
\(926\) −12.0243 −0.395143
\(927\) 14.6677 0.481750
\(928\) −1.45658 −0.0478147
\(929\) 58.1360 1.90738 0.953690 0.300791i \(-0.0972505\pi\)
0.953690 + 0.300791i \(0.0972505\pi\)
\(930\) 16.8871 0.553749
\(931\) 39.7946 1.30422
\(932\) −0.193795 −0.00634796
\(933\) 53.3611 1.74697
\(934\) 26.3272 0.861452
\(935\) −25.0826 −0.820290
\(936\) 8.78109 0.287019
\(937\) −24.6344 −0.804771 −0.402386 0.915470i \(-0.631819\pi\)
−0.402386 + 0.915470i \(0.631819\pi\)
\(938\) −0.896073 −0.0292578
\(939\) −44.6067 −1.45569
\(940\) −13.5767 −0.442823
\(941\) 41.0314 1.33758 0.668792 0.743449i \(-0.266811\pi\)
0.668792 + 0.743449i \(0.266811\pi\)
\(942\) −37.2210 −1.21272
\(943\) −10.8528 −0.353415
\(944\) 14.6403 0.476502
\(945\) 3.49592 0.113722
\(946\) −30.4080 −0.988650
\(947\) 17.7566 0.577012 0.288506 0.957478i \(-0.406842\pi\)
0.288506 + 0.957478i \(0.406842\pi\)
\(948\) −11.2466 −0.365272
\(949\) 4.08727 0.132678
\(950\) 11.4606 0.371830
\(951\) −14.4961 −0.470069
\(952\) −1.35612 −0.0439521
\(953\) 7.20625 0.233433 0.116717 0.993165i \(-0.462763\pi\)
0.116717 + 0.993165i \(0.462763\pi\)
\(954\) −0.371185 −0.0120175
\(955\) 15.6912 0.507756
\(956\) 13.5686 0.438839
\(957\) −16.7883 −0.542688
\(958\) 12.8252 0.414362
\(959\) 4.23145 0.136641
\(960\) −4.87575 −0.157364
\(961\) −19.0043 −0.613042
\(962\) 5.86694 0.189158
\(963\) −51.4174 −1.65690
\(964\) 15.6446 0.503879
\(965\) 34.0666 1.09664
\(966\) −1.24719 −0.0401276
\(967\) −6.79547 −0.218528 −0.109264 0.994013i \(-0.534849\pi\)
−0.109264 + 0.994013i \(0.534849\pi\)
\(968\) 5.91581 0.190141
\(969\) 57.0620 1.83310
\(970\) −16.0033 −0.513834
\(971\) −11.0555 −0.354787 −0.177394 0.984140i \(-0.556767\pi\)
−0.177394 + 0.984140i \(0.556767\pi\)
\(972\) 15.5966 0.500261
\(973\) −0.411581 −0.0131947
\(974\) 32.0639 1.02739
\(975\) 10.0031 0.320355
\(976\) 2.69798 0.0863602
\(977\) −53.8767 −1.72367 −0.861834 0.507191i \(-0.830684\pi\)
−0.861834 + 0.507191i \(0.830684\pi\)
\(978\) −26.5674 −0.849531
\(979\) −9.04428 −0.289057
\(980\) −11.9187 −0.380728
\(981\) 57.4080 1.83290
\(982\) −30.6227 −0.977209
\(983\) 22.6631 0.722842 0.361421 0.932403i \(-0.382292\pi\)
0.361421 + 0.932403i \(0.382292\pi\)
\(984\) −26.4391 −0.842847
\(985\) −40.1890 −1.28053
\(986\) −5.10557 −0.162594
\(987\) −8.46038 −0.269297
\(988\) −10.5107 −0.334389
\(989\) −8.50474 −0.270435
\(990\) −34.7292 −1.10377
\(991\) 22.9896 0.730290 0.365145 0.930951i \(-0.381019\pi\)
0.365145 + 0.930951i \(0.381019\pi\)
\(992\) −3.46348 −0.109966
\(993\) −36.1943 −1.14859
\(994\) −3.64998 −0.115770
\(995\) −11.3196 −0.358854
\(996\) 39.9044 1.26442
\(997\) 32.0237 1.01420 0.507101 0.861887i \(-0.330717\pi\)
0.507101 + 0.861887i \(0.330717\pi\)
\(998\) 17.3833 0.550259
\(999\) −16.8403 −0.532804
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 8002.2.a.g.1.6 95
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8002.2.a.g.1.6 95 1.1 even 1 trivial