Properties

Label 4015.2.a.i.1.6
Level $4015$
Weight $2$
Character 4015.1
Self dual yes
Analytic conductor $32.060$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4015,2,Mod(1,4015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4015.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: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 4015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.26509 q^{2} +0.846807 q^{3} +3.13061 q^{4} +1.00000 q^{5} -1.91809 q^{6} -3.17432 q^{7} -2.56093 q^{8} -2.28292 q^{9} +O(q^{10})\) \(q-2.26509 q^{2} +0.846807 q^{3} +3.13061 q^{4} +1.00000 q^{5} -1.91809 q^{6} -3.17432 q^{7} -2.56093 q^{8} -2.28292 q^{9} -2.26509 q^{10} -1.00000 q^{11} +2.65102 q^{12} +0.106703 q^{13} +7.19011 q^{14} +0.846807 q^{15} -0.460493 q^{16} -6.41831 q^{17} +5.17100 q^{18} -4.21256 q^{19} +3.13061 q^{20} -2.68804 q^{21} +2.26509 q^{22} -5.49690 q^{23} -2.16862 q^{24} +1.00000 q^{25} -0.241691 q^{26} -4.47361 q^{27} -9.93757 q^{28} +5.93442 q^{29} -1.91809 q^{30} -2.85181 q^{31} +6.16492 q^{32} -0.846807 q^{33} +14.5380 q^{34} -3.17432 q^{35} -7.14693 q^{36} +6.54343 q^{37} +9.54181 q^{38} +0.0903567 q^{39} -2.56093 q^{40} -9.34825 q^{41} +6.08864 q^{42} -3.06128 q^{43} -3.13061 q^{44} -2.28292 q^{45} +12.4509 q^{46} +2.53298 q^{47} -0.389949 q^{48} +3.07633 q^{49} -2.26509 q^{50} -5.43507 q^{51} +0.334045 q^{52} +0.824356 q^{53} +10.1331 q^{54} -1.00000 q^{55} +8.12923 q^{56} -3.56723 q^{57} -13.4420 q^{58} +6.89047 q^{59} +2.65102 q^{60} +5.77749 q^{61} +6.45959 q^{62} +7.24672 q^{63} -13.0431 q^{64} +0.106703 q^{65} +1.91809 q^{66} -9.02101 q^{67} -20.0932 q^{68} -4.65481 q^{69} +7.19011 q^{70} +14.2526 q^{71} +5.84640 q^{72} -1.00000 q^{73} -14.8214 q^{74} +0.846807 q^{75} -13.1879 q^{76} +3.17432 q^{77} -0.204666 q^{78} +15.0952 q^{79} -0.460493 q^{80} +3.06047 q^{81} +21.1746 q^{82} -15.3194 q^{83} -8.41521 q^{84} -6.41831 q^{85} +6.93405 q^{86} +5.02530 q^{87} +2.56093 q^{88} +13.1552 q^{89} +5.17100 q^{90} -0.338709 q^{91} -17.2087 q^{92} -2.41493 q^{93} -5.73743 q^{94} -4.21256 q^{95} +5.22050 q^{96} +7.14280 q^{97} -6.96814 q^{98} +2.28292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9} + 4 q^{10} - 38 q^{11} + 12 q^{12} - q^{13} + 23 q^{14} + 5 q^{15} + 74 q^{16} + 26 q^{17} + 16 q^{18} - 10 q^{19} + 50 q^{20} + 21 q^{21} - 4 q^{22} + 10 q^{23} + 41 q^{24} + 38 q^{25} + 25 q^{26} + 5 q^{27} + 2 q^{28} + 28 q^{29} + 11 q^{30} + 24 q^{31} + 39 q^{32} - 5 q^{33} + 38 q^{34} + 111 q^{36} + 12 q^{37} + 19 q^{38} - 18 q^{39} + 15 q^{40} + 62 q^{41} - 17 q^{42} - 32 q^{43} - 50 q^{44} + 63 q^{45} - 9 q^{46} + 31 q^{47} + 53 q^{48} + 88 q^{49} + 4 q^{50} - 3 q^{51} - 21 q^{52} + 30 q^{53} + 49 q^{54} - 38 q^{55} + 32 q^{56} + 49 q^{57} + 12 q^{58} + 31 q^{59} + 12 q^{60} + 25 q^{61} + 12 q^{62} + 15 q^{63} + 137 q^{64} - q^{65} - 11 q^{66} + 20 q^{67} + 75 q^{68} + 92 q^{69} + 23 q^{70} + 32 q^{71} + 6 q^{72} - 38 q^{73} + 55 q^{74} + 5 q^{75} - 57 q^{76} - 17 q^{78} - 2 q^{79} + 74 q^{80} + 118 q^{81} + 14 q^{82} + 4 q^{83} + 22 q^{84} + 26 q^{85} + 5 q^{86} + 24 q^{87} - 15 q^{88} + 143 q^{89} + 16 q^{90} + 66 q^{91} + 29 q^{92} - 8 q^{93} - 7 q^{94} - 10 q^{95} + 59 q^{96} + 41 q^{97} - 10 q^{98} - 63 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26509 −1.60166 −0.800829 0.598894i \(-0.795607\pi\)
−0.800829 + 0.598894i \(0.795607\pi\)
\(3\) 0.846807 0.488904 0.244452 0.969661i \(-0.421392\pi\)
0.244452 + 0.969661i \(0.421392\pi\)
\(4\) 3.13061 1.56531
\(5\) 1.00000 0.447214
\(6\) −1.91809 −0.783057
\(7\) −3.17432 −1.19978 −0.599891 0.800082i \(-0.704789\pi\)
−0.599891 + 0.800082i \(0.704789\pi\)
\(8\) −2.56093 −0.905426
\(9\) −2.28292 −0.760973
\(10\) −2.26509 −0.716283
\(11\) −1.00000 −0.301511
\(12\) 2.65102 0.765285
\(13\) 0.106703 0.0295940 0.0147970 0.999891i \(-0.495290\pi\)
0.0147970 + 0.999891i \(0.495290\pi\)
\(14\) 7.19011 1.92164
\(15\) 0.846807 0.218645
\(16\) −0.460493 −0.115123
\(17\) −6.41831 −1.55667 −0.778334 0.627851i \(-0.783935\pi\)
−0.778334 + 0.627851i \(0.783935\pi\)
\(18\) 5.17100 1.21882
\(19\) −4.21256 −0.966428 −0.483214 0.875502i \(-0.660531\pi\)
−0.483214 + 0.875502i \(0.660531\pi\)
\(20\) 3.13061 0.700026
\(21\) −2.68804 −0.586578
\(22\) 2.26509 0.482918
\(23\) −5.49690 −1.14618 −0.573091 0.819492i \(-0.694256\pi\)
−0.573091 + 0.819492i \(0.694256\pi\)
\(24\) −2.16862 −0.442667
\(25\) 1.00000 0.200000
\(26\) −0.241691 −0.0473995
\(27\) −4.47361 −0.860947
\(28\) −9.93757 −1.87802
\(29\) 5.93442 1.10199 0.550997 0.834507i \(-0.314248\pi\)
0.550997 + 0.834507i \(0.314248\pi\)
\(30\) −1.91809 −0.350194
\(31\) −2.85181 −0.512200 −0.256100 0.966650i \(-0.582438\pi\)
−0.256100 + 0.966650i \(0.582438\pi\)
\(32\) 6.16492 1.08981
\(33\) −0.846807 −0.147410
\(34\) 14.5380 2.49325
\(35\) −3.17432 −0.536558
\(36\) −7.14693 −1.19115
\(37\) 6.54343 1.07573 0.537866 0.843030i \(-0.319231\pi\)
0.537866 + 0.843030i \(0.319231\pi\)
\(38\) 9.54181 1.54789
\(39\) 0.0903567 0.0144686
\(40\) −2.56093 −0.404919
\(41\) −9.34825 −1.45995 −0.729976 0.683473i \(-0.760469\pi\)
−0.729976 + 0.683473i \(0.760469\pi\)
\(42\) 6.08864 0.939497
\(43\) −3.06128 −0.466840 −0.233420 0.972376i \(-0.574992\pi\)
−0.233420 + 0.972376i \(0.574992\pi\)
\(44\) −3.13061 −0.471957
\(45\) −2.28292 −0.340317
\(46\) 12.4509 1.83579
\(47\) 2.53298 0.369474 0.184737 0.982788i \(-0.440857\pi\)
0.184737 + 0.982788i \(0.440857\pi\)
\(48\) −0.389949 −0.0562843
\(49\) 3.07633 0.439475
\(50\) −2.26509 −0.320331
\(51\) −5.43507 −0.761062
\(52\) 0.334045 0.0463237
\(53\) 0.824356 0.113234 0.0566170 0.998396i \(-0.481969\pi\)
0.0566170 + 0.998396i \(0.481969\pi\)
\(54\) 10.1331 1.37894
\(55\) −1.00000 −0.134840
\(56\) 8.12923 1.08631
\(57\) −3.56723 −0.472491
\(58\) −13.4420 −1.76502
\(59\) 6.89047 0.897063 0.448531 0.893767i \(-0.351947\pi\)
0.448531 + 0.893767i \(0.351947\pi\)
\(60\) 2.65102 0.342246
\(61\) 5.77749 0.739732 0.369866 0.929085i \(-0.379404\pi\)
0.369866 + 0.929085i \(0.379404\pi\)
\(62\) 6.45959 0.820369
\(63\) 7.24672 0.913001
\(64\) −13.0431 −1.63039
\(65\) 0.106703 0.0132348
\(66\) 1.91809 0.236101
\(67\) −9.02101 −1.10209 −0.551046 0.834475i \(-0.685771\pi\)
−0.551046 + 0.834475i \(0.685771\pi\)
\(68\) −20.0932 −2.43666
\(69\) −4.65481 −0.560374
\(70\) 7.19011 0.859383
\(71\) 14.2526 1.69147 0.845735 0.533602i \(-0.179162\pi\)
0.845735 + 0.533602i \(0.179162\pi\)
\(72\) 5.84640 0.689005
\(73\) −1.00000 −0.117041
\(74\) −14.8214 −1.72295
\(75\) 0.846807 0.0977809
\(76\) −13.1879 −1.51276
\(77\) 3.17432 0.361748
\(78\) −0.204666 −0.0231738
\(79\) 15.0952 1.69834 0.849172 0.528116i \(-0.177102\pi\)
0.849172 + 0.528116i \(0.177102\pi\)
\(80\) −0.460493 −0.0514847
\(81\) 3.06047 0.340052
\(82\) 21.1746 2.33834
\(83\) −15.3194 −1.68152 −0.840762 0.541405i \(-0.817893\pi\)
−0.840762 + 0.541405i \(0.817893\pi\)
\(84\) −8.41521 −0.918174
\(85\) −6.41831 −0.696163
\(86\) 6.93405 0.747718
\(87\) 5.02530 0.538769
\(88\) 2.56093 0.272996
\(89\) 13.1552 1.39444 0.697222 0.716856i \(-0.254419\pi\)
0.697222 + 0.716856i \(0.254419\pi\)
\(90\) 5.17100 0.545072
\(91\) −0.338709 −0.0355063
\(92\) −17.2087 −1.79413
\(93\) −2.41493 −0.250417
\(94\) −5.73743 −0.591770
\(95\) −4.21256 −0.432200
\(96\) 5.22050 0.532815
\(97\) 7.14280 0.725241 0.362621 0.931937i \(-0.381882\pi\)
0.362621 + 0.931937i \(0.381882\pi\)
\(98\) −6.96814 −0.703888
\(99\) 2.28292 0.229442
\(100\) 3.13061 0.313061
\(101\) −1.85103 −0.184185 −0.0920923 0.995750i \(-0.529355\pi\)
−0.0920923 + 0.995750i \(0.529355\pi\)
\(102\) 12.3109 1.21896
\(103\) 11.0094 1.08478 0.542392 0.840126i \(-0.317519\pi\)
0.542392 + 0.840126i \(0.317519\pi\)
\(104\) −0.273259 −0.0267952
\(105\) −2.68804 −0.262326
\(106\) −1.86724 −0.181362
\(107\) −9.27940 −0.897074 −0.448537 0.893764i \(-0.648055\pi\)
−0.448537 + 0.893764i \(0.648055\pi\)
\(108\) −14.0051 −1.34765
\(109\) −1.19923 −0.114866 −0.0574329 0.998349i \(-0.518292\pi\)
−0.0574329 + 0.998349i \(0.518292\pi\)
\(110\) 2.26509 0.215967
\(111\) 5.54102 0.525930
\(112\) 1.46175 0.138123
\(113\) 9.65051 0.907843 0.453922 0.891042i \(-0.350025\pi\)
0.453922 + 0.891042i \(0.350025\pi\)
\(114\) 8.08008 0.756768
\(115\) −5.49690 −0.512588
\(116\) 18.5783 1.72496
\(117\) −0.243594 −0.0225202
\(118\) −15.6075 −1.43679
\(119\) 20.3738 1.86766
\(120\) −2.16862 −0.197967
\(121\) 1.00000 0.0909091
\(122\) −13.0865 −1.18480
\(123\) −7.91617 −0.713777
\(124\) −8.92790 −0.801749
\(125\) 1.00000 0.0894427
\(126\) −16.4144 −1.46231
\(127\) 9.49076 0.842169 0.421084 0.907022i \(-0.361650\pi\)
0.421084 + 0.907022i \(0.361650\pi\)
\(128\) 17.2139 1.52150
\(129\) −2.59231 −0.228240
\(130\) −0.241691 −0.0211977
\(131\) 14.4570 1.26311 0.631555 0.775331i \(-0.282417\pi\)
0.631555 + 0.775331i \(0.282417\pi\)
\(132\) −2.65102 −0.230742
\(133\) 13.3720 1.15950
\(134\) 20.4334 1.76517
\(135\) −4.47361 −0.385027
\(136\) 16.4368 1.40945
\(137\) 17.7950 1.52033 0.760166 0.649729i \(-0.225118\pi\)
0.760166 + 0.649729i \(0.225118\pi\)
\(138\) 10.5435 0.897526
\(139\) −0.0888487 −0.00753605 −0.00376802 0.999993i \(-0.501199\pi\)
−0.00376802 + 0.999993i \(0.501199\pi\)
\(140\) −9.93757 −0.839878
\(141\) 2.14495 0.180637
\(142\) −32.2833 −2.70916
\(143\) −0.106703 −0.00892293
\(144\) 1.05127 0.0876057
\(145\) 5.93442 0.492826
\(146\) 2.26509 0.187460
\(147\) 2.60505 0.214861
\(148\) 20.4849 1.68385
\(149\) 12.9622 1.06190 0.530951 0.847402i \(-0.321835\pi\)
0.530951 + 0.847402i \(0.321835\pi\)
\(150\) −1.91809 −0.156611
\(151\) −11.7110 −0.953025 −0.476512 0.879168i \(-0.658099\pi\)
−0.476512 + 0.879168i \(0.658099\pi\)
\(152\) 10.7881 0.875029
\(153\) 14.6525 1.18458
\(154\) −7.19011 −0.579396
\(155\) −2.85181 −0.229063
\(156\) 0.282872 0.0226479
\(157\) 17.1979 1.37254 0.686272 0.727345i \(-0.259246\pi\)
0.686272 + 0.727345i \(0.259246\pi\)
\(158\) −34.1919 −2.72017
\(159\) 0.698071 0.0553606
\(160\) 6.16492 0.487380
\(161\) 17.4489 1.37517
\(162\) −6.93222 −0.544646
\(163\) −4.50983 −0.353237 −0.176619 0.984279i \(-0.556516\pi\)
−0.176619 + 0.984279i \(0.556516\pi\)
\(164\) −29.2657 −2.28527
\(165\) −0.846807 −0.0659238
\(166\) 34.6998 2.69323
\(167\) −18.6018 −1.43945 −0.719724 0.694261i \(-0.755731\pi\)
−0.719724 + 0.694261i \(0.755731\pi\)
\(168\) 6.88389 0.531103
\(169\) −12.9886 −0.999124
\(170\) 14.5380 1.11501
\(171\) 9.61693 0.735425
\(172\) −9.58366 −0.730748
\(173\) −9.42803 −0.716800 −0.358400 0.933568i \(-0.616678\pi\)
−0.358400 + 0.933568i \(0.616678\pi\)
\(174\) −11.3827 −0.862924
\(175\) −3.17432 −0.239956
\(176\) 0.460493 0.0347110
\(177\) 5.83490 0.438578
\(178\) −29.7975 −2.23342
\(179\) 4.43582 0.331549 0.165774 0.986164i \(-0.446988\pi\)
0.165774 + 0.986164i \(0.446988\pi\)
\(180\) −7.14693 −0.532701
\(181\) −9.38468 −0.697557 −0.348779 0.937205i \(-0.613404\pi\)
−0.348779 + 0.937205i \(0.613404\pi\)
\(182\) 0.767205 0.0568690
\(183\) 4.89242 0.361658
\(184\) 14.0772 1.03778
\(185\) 6.54343 0.481082
\(186\) 5.47003 0.401082
\(187\) 6.41831 0.469353
\(188\) 7.92979 0.578340
\(189\) 14.2007 1.03295
\(190\) 9.54181 0.692236
\(191\) 1.30115 0.0941478 0.0470739 0.998891i \(-0.485010\pi\)
0.0470739 + 0.998891i \(0.485010\pi\)
\(192\) −11.0450 −0.797103
\(193\) −15.7852 −1.13625 −0.568123 0.822944i \(-0.692330\pi\)
−0.568123 + 0.822944i \(0.692330\pi\)
\(194\) −16.1790 −1.16159
\(195\) 0.0903567 0.00647057
\(196\) 9.63078 0.687913
\(197\) 3.26661 0.232736 0.116368 0.993206i \(-0.462875\pi\)
0.116368 + 0.993206i \(0.462875\pi\)
\(198\) −5.17100 −0.367487
\(199\) 4.37603 0.310208 0.155104 0.987898i \(-0.450429\pi\)
0.155104 + 0.987898i \(0.450429\pi\)
\(200\) −2.56093 −0.181085
\(201\) −7.63905 −0.538817
\(202\) 4.19275 0.295001
\(203\) −18.8377 −1.32215
\(204\) −17.0151 −1.19129
\(205\) −9.34825 −0.652910
\(206\) −24.9371 −1.73745
\(207\) 12.5490 0.872214
\(208\) −0.0491359 −0.00340696
\(209\) 4.21256 0.291389
\(210\) 6.08864 0.420156
\(211\) −4.42716 −0.304779 −0.152389 0.988321i \(-0.548697\pi\)
−0.152389 + 0.988321i \(0.548697\pi\)
\(212\) 2.58074 0.177246
\(213\) 12.0692 0.826967
\(214\) 21.0186 1.43680
\(215\) −3.06128 −0.208777
\(216\) 11.4566 0.779524
\(217\) 9.05256 0.614528
\(218\) 2.71637 0.183976
\(219\) −0.846807 −0.0572219
\(220\) −3.13061 −0.211066
\(221\) −0.684851 −0.0460681
\(222\) −12.5509 −0.842360
\(223\) −25.3843 −1.69986 −0.849928 0.526899i \(-0.823355\pi\)
−0.849928 + 0.526899i \(0.823355\pi\)
\(224\) −19.5695 −1.30754
\(225\) −2.28292 −0.152195
\(226\) −21.8592 −1.45405
\(227\) −0.216301 −0.0143564 −0.00717819 0.999974i \(-0.502285\pi\)
−0.00717819 + 0.999974i \(0.502285\pi\)
\(228\) −11.1676 −0.739593
\(229\) −3.28796 −0.217275 −0.108637 0.994081i \(-0.534649\pi\)
−0.108637 + 0.994081i \(0.534649\pi\)
\(230\) 12.4509 0.820991
\(231\) 2.68804 0.176860
\(232\) −15.1976 −0.997774
\(233\) −13.3046 −0.871614 −0.435807 0.900040i \(-0.643537\pi\)
−0.435807 + 0.900040i \(0.643537\pi\)
\(234\) 0.551760 0.0360697
\(235\) 2.53298 0.165234
\(236\) 21.5714 1.40418
\(237\) 12.7827 0.830328
\(238\) −46.1483 −2.99135
\(239\) 23.6381 1.52902 0.764509 0.644613i \(-0.222981\pi\)
0.764509 + 0.644613i \(0.222981\pi\)
\(240\) −0.389949 −0.0251711
\(241\) −10.5637 −0.680467 −0.340234 0.940341i \(-0.610506\pi\)
−0.340234 + 0.940341i \(0.610506\pi\)
\(242\) −2.26509 −0.145605
\(243\) 16.0125 1.02720
\(244\) 18.0871 1.15791
\(245\) 3.07633 0.196539
\(246\) 17.9308 1.14323
\(247\) −0.449492 −0.0286005
\(248\) 7.30329 0.463759
\(249\) −12.9726 −0.822104
\(250\) −2.26509 −0.143257
\(251\) −23.8074 −1.50271 −0.751356 0.659897i \(-0.770600\pi\)
−0.751356 + 0.659897i \(0.770600\pi\)
\(252\) 22.6867 1.42913
\(253\) 5.49690 0.345587
\(254\) −21.4974 −1.34887
\(255\) −5.43507 −0.340357
\(256\) −12.9047 −0.806543
\(257\) −22.5855 −1.40885 −0.704423 0.709780i \(-0.748794\pi\)
−0.704423 + 0.709780i \(0.748794\pi\)
\(258\) 5.87180 0.365562
\(259\) −20.7709 −1.29064
\(260\) 0.334045 0.0207166
\(261\) −13.5478 −0.838587
\(262\) −32.7463 −2.02307
\(263\) −21.1197 −1.30230 −0.651148 0.758951i \(-0.725712\pi\)
−0.651148 + 0.758951i \(0.725712\pi\)
\(264\) 2.16862 0.133469
\(265\) 0.824356 0.0506398
\(266\) −30.2888 −1.85713
\(267\) 11.1399 0.681749
\(268\) −28.2413 −1.72511
\(269\) 27.8043 1.69526 0.847628 0.530591i \(-0.178030\pi\)
0.847628 + 0.530591i \(0.178030\pi\)
\(270\) 10.1331 0.616682
\(271\) −6.10517 −0.370863 −0.185431 0.982657i \(-0.559368\pi\)
−0.185431 + 0.982657i \(0.559368\pi\)
\(272\) 2.95559 0.179209
\(273\) −0.286821 −0.0173592
\(274\) −40.3072 −2.43505
\(275\) −1.00000 −0.0603023
\(276\) −14.5724 −0.877156
\(277\) −19.2588 −1.15715 −0.578575 0.815629i \(-0.696391\pi\)
−0.578575 + 0.815629i \(0.696391\pi\)
\(278\) 0.201250 0.0120702
\(279\) 6.51044 0.389770
\(280\) 8.12923 0.485814
\(281\) 13.1655 0.785387 0.392694 0.919669i \(-0.371543\pi\)
0.392694 + 0.919669i \(0.371543\pi\)
\(282\) −4.85849 −0.289319
\(283\) −27.1971 −1.61670 −0.808351 0.588701i \(-0.799640\pi\)
−0.808351 + 0.588701i \(0.799640\pi\)
\(284\) 44.6193 2.64767
\(285\) −3.56723 −0.211304
\(286\) 0.241691 0.0142915
\(287\) 29.6744 1.75162
\(288\) −14.0740 −0.829319
\(289\) 24.1946 1.42321
\(290\) −13.4420 −0.789339
\(291\) 6.04857 0.354574
\(292\) −3.13061 −0.183205
\(293\) 28.9691 1.69239 0.846197 0.532871i \(-0.178887\pi\)
0.846197 + 0.532871i \(0.178887\pi\)
\(294\) −5.90067 −0.344134
\(295\) 6.89047 0.401179
\(296\) −16.7573 −0.973996
\(297\) 4.47361 0.259585
\(298\) −29.3604 −1.70080
\(299\) −0.586534 −0.0339202
\(300\) 2.65102 0.153057
\(301\) 9.71748 0.560106
\(302\) 26.5263 1.52642
\(303\) −1.56747 −0.0900487
\(304\) 1.93986 0.111258
\(305\) 5.77749 0.330818
\(306\) −33.1891 −1.89729
\(307\) 11.9936 0.684509 0.342255 0.939607i \(-0.388809\pi\)
0.342255 + 0.939607i \(0.388809\pi\)
\(308\) 9.93757 0.566246
\(309\) 9.32280 0.530355
\(310\) 6.45959 0.366880
\(311\) 16.6020 0.941415 0.470707 0.882289i \(-0.343999\pi\)
0.470707 + 0.882289i \(0.343999\pi\)
\(312\) −0.231397 −0.0131003
\(313\) −32.0017 −1.80884 −0.904421 0.426640i \(-0.859697\pi\)
−0.904421 + 0.426640i \(0.859697\pi\)
\(314\) −38.9548 −2.19834
\(315\) 7.24672 0.408306
\(316\) 47.2572 2.65843
\(317\) 9.38752 0.527256 0.263628 0.964624i \(-0.415081\pi\)
0.263628 + 0.964624i \(0.415081\pi\)
\(318\) −1.58119 −0.0886687
\(319\) −5.93442 −0.332263
\(320\) −13.0431 −0.729131
\(321\) −7.85786 −0.438583
\(322\) −39.5233 −2.20255
\(323\) 27.0375 1.50441
\(324\) 9.58113 0.532285
\(325\) 0.106703 0.00591880
\(326\) 10.2151 0.565765
\(327\) −1.01552 −0.0561584
\(328\) 23.9402 1.32188
\(329\) −8.04051 −0.443288
\(330\) 1.91809 0.105587
\(331\) −19.1415 −1.05211 −0.526056 0.850450i \(-0.676330\pi\)
−0.526056 + 0.850450i \(0.676330\pi\)
\(332\) −47.9591 −2.63210
\(333\) −14.9381 −0.818603
\(334\) 42.1346 2.30550
\(335\) −9.02101 −0.492870
\(336\) 1.23782 0.0675289
\(337\) 19.4662 1.06039 0.530197 0.847874i \(-0.322118\pi\)
0.530197 + 0.847874i \(0.322118\pi\)
\(338\) 29.4203 1.60025
\(339\) 8.17212 0.443848
\(340\) −20.0932 −1.08971
\(341\) 2.85181 0.154434
\(342\) −21.7832 −1.17790
\(343\) 12.4550 0.672507
\(344\) 7.83972 0.422689
\(345\) −4.65481 −0.250607
\(346\) 21.3553 1.14807
\(347\) 1.02228 0.0548789 0.0274395 0.999623i \(-0.491265\pi\)
0.0274395 + 0.999623i \(0.491265\pi\)
\(348\) 15.7323 0.843339
\(349\) 13.4592 0.720454 0.360227 0.932865i \(-0.382699\pi\)
0.360227 + 0.932865i \(0.382699\pi\)
\(350\) 7.19011 0.384328
\(351\) −0.477347 −0.0254789
\(352\) −6.16492 −0.328591
\(353\) 16.1934 0.861885 0.430943 0.902379i \(-0.358181\pi\)
0.430943 + 0.902379i \(0.358181\pi\)
\(354\) −13.2165 −0.702451
\(355\) 14.2526 0.756449
\(356\) 41.1837 2.18273
\(357\) 17.2527 0.913107
\(358\) −10.0475 −0.531027
\(359\) −11.1725 −0.589664 −0.294832 0.955549i \(-0.595264\pi\)
−0.294832 + 0.955549i \(0.595264\pi\)
\(360\) 5.84640 0.308132
\(361\) −1.25431 −0.0660166
\(362\) 21.2571 1.11725
\(363\) 0.846807 0.0444458
\(364\) −1.06037 −0.0555783
\(365\) −1.00000 −0.0523424
\(366\) −11.0818 −0.579253
\(367\) 28.1766 1.47081 0.735404 0.677629i \(-0.236993\pi\)
0.735404 + 0.677629i \(0.236993\pi\)
\(368\) 2.53129 0.131952
\(369\) 21.3413 1.11098
\(370\) −14.8214 −0.770529
\(371\) −2.61677 −0.135856
\(372\) −7.56021 −0.391979
\(373\) 16.5111 0.854912 0.427456 0.904036i \(-0.359410\pi\)
0.427456 + 0.904036i \(0.359410\pi\)
\(374\) −14.5380 −0.751743
\(375\) 0.846807 0.0437289
\(376\) −6.48680 −0.334531
\(377\) 0.633218 0.0326124
\(378\) −32.1658 −1.65443
\(379\) 29.4953 1.51507 0.757537 0.652792i \(-0.226403\pi\)
0.757537 + 0.652792i \(0.226403\pi\)
\(380\) −13.1879 −0.676525
\(381\) 8.03684 0.411740
\(382\) −2.94721 −0.150793
\(383\) 24.2535 1.23929 0.619647 0.784880i \(-0.287276\pi\)
0.619647 + 0.784880i \(0.287276\pi\)
\(384\) 14.5768 0.743870
\(385\) 3.17432 0.161778
\(386\) 35.7549 1.81988
\(387\) 6.98864 0.355253
\(388\) 22.3613 1.13522
\(389\) 19.6390 0.995736 0.497868 0.867253i \(-0.334116\pi\)
0.497868 + 0.867253i \(0.334116\pi\)
\(390\) −0.204666 −0.0103636
\(391\) 35.2808 1.78423
\(392\) −7.87826 −0.397912
\(393\) 12.2423 0.617540
\(394\) −7.39914 −0.372763
\(395\) 15.0952 0.759523
\(396\) 7.14693 0.359147
\(397\) −5.46015 −0.274037 −0.137019 0.990568i \(-0.543752\pi\)
−0.137019 + 0.990568i \(0.543752\pi\)
\(398\) −9.91208 −0.496848
\(399\) 11.3235 0.566886
\(400\) −0.460493 −0.0230247
\(401\) −30.1486 −1.50555 −0.752776 0.658277i \(-0.771285\pi\)
−0.752776 + 0.658277i \(0.771285\pi\)
\(402\) 17.3031 0.863001
\(403\) −0.304296 −0.0151581
\(404\) −5.79487 −0.288305
\(405\) 3.06047 0.152076
\(406\) 42.6691 2.11763
\(407\) −6.54343 −0.324346
\(408\) 13.9188 0.689085
\(409\) −26.7960 −1.32498 −0.662489 0.749072i \(-0.730500\pi\)
−0.662489 + 0.749072i \(0.730500\pi\)
\(410\) 21.1746 1.04574
\(411\) 15.0689 0.743296
\(412\) 34.4660 1.69802
\(413\) −21.8726 −1.07628
\(414\) −28.4245 −1.39699
\(415\) −15.3194 −0.752000
\(416\) 0.657814 0.0322520
\(417\) −0.0752377 −0.00368441
\(418\) −9.54181 −0.466705
\(419\) 7.95612 0.388682 0.194341 0.980934i \(-0.437743\pi\)
0.194341 + 0.980934i \(0.437743\pi\)
\(420\) −8.41521 −0.410620
\(421\) 6.16353 0.300392 0.150196 0.988656i \(-0.452010\pi\)
0.150196 + 0.988656i \(0.452010\pi\)
\(422\) 10.0279 0.488151
\(423\) −5.78260 −0.281159
\(424\) −2.11112 −0.102525
\(425\) −6.41831 −0.311334
\(426\) −27.3377 −1.32452
\(427\) −18.3396 −0.887517
\(428\) −29.0502 −1.40419
\(429\) −0.0903567 −0.00436246
\(430\) 6.93405 0.334390
\(431\) −3.80907 −0.183477 −0.0917383 0.995783i \(-0.529242\pi\)
−0.0917383 + 0.995783i \(0.529242\pi\)
\(432\) 2.06007 0.0991151
\(433\) −29.1987 −1.40320 −0.701600 0.712571i \(-0.747531\pi\)
−0.701600 + 0.712571i \(0.747531\pi\)
\(434\) −20.5048 −0.984263
\(435\) 5.02530 0.240945
\(436\) −3.75434 −0.179800
\(437\) 23.1560 1.10770
\(438\) 1.91809 0.0916499
\(439\) −0.821251 −0.0391962 −0.0195981 0.999808i \(-0.506239\pi\)
−0.0195981 + 0.999808i \(0.506239\pi\)
\(440\) 2.56093 0.122088
\(441\) −7.02300 −0.334428
\(442\) 1.55125 0.0737852
\(443\) −10.6512 −0.506053 −0.253026 0.967459i \(-0.581426\pi\)
−0.253026 + 0.967459i \(0.581426\pi\)
\(444\) 17.3468 0.823242
\(445\) 13.1552 0.623614
\(446\) 57.4975 2.72259
\(447\) 10.9765 0.519169
\(448\) 41.4030 1.95611
\(449\) −2.51675 −0.118773 −0.0593864 0.998235i \(-0.518914\pi\)
−0.0593864 + 0.998235i \(0.518914\pi\)
\(450\) 5.17100 0.243763
\(451\) 9.34825 0.440192
\(452\) 30.2120 1.42105
\(453\) −9.91693 −0.465938
\(454\) 0.489940 0.0229940
\(455\) −0.338709 −0.0158789
\(456\) 9.13543 0.427806
\(457\) −18.8119 −0.879985 −0.439993 0.898001i \(-0.645019\pi\)
−0.439993 + 0.898001i \(0.645019\pi\)
\(458\) 7.44752 0.348000
\(459\) 28.7130 1.34021
\(460\) −17.2087 −0.802358
\(461\) 36.5827 1.70383 0.851914 0.523682i \(-0.175442\pi\)
0.851914 + 0.523682i \(0.175442\pi\)
\(462\) −6.08864 −0.283269
\(463\) 1.05788 0.0491641 0.0245820 0.999698i \(-0.492175\pi\)
0.0245820 + 0.999698i \(0.492175\pi\)
\(464\) −2.73276 −0.126865
\(465\) −2.41493 −0.111990
\(466\) 30.1361 1.39603
\(467\) −1.23362 −0.0570851 −0.0285426 0.999593i \(-0.509087\pi\)
−0.0285426 + 0.999593i \(0.509087\pi\)
\(468\) −0.762597 −0.0352511
\(469\) 28.6356 1.32227
\(470\) −5.73743 −0.264648
\(471\) 14.5633 0.671042
\(472\) −17.6460 −0.812224
\(473\) 3.06128 0.140758
\(474\) −28.9540 −1.32990
\(475\) −4.21256 −0.193286
\(476\) 63.7824 2.92346
\(477\) −1.88194 −0.0861680
\(478\) −53.5422 −2.44896
\(479\) 7.11688 0.325179 0.162589 0.986694i \(-0.448015\pi\)
0.162589 + 0.986694i \(0.448015\pi\)
\(480\) 5.22050 0.238282
\(481\) 0.698201 0.0318352
\(482\) 23.9277 1.08988
\(483\) 14.7759 0.672326
\(484\) 3.13061 0.142301
\(485\) 7.14280 0.324338
\(486\) −36.2696 −1.64522
\(487\) −39.5101 −1.79037 −0.895186 0.445693i \(-0.852957\pi\)
−0.895186 + 0.445693i \(0.852957\pi\)
\(488\) −14.7958 −0.669773
\(489\) −3.81895 −0.172699
\(490\) −6.96814 −0.314788
\(491\) 37.1038 1.67447 0.837235 0.546844i \(-0.184171\pi\)
0.837235 + 0.546844i \(0.184171\pi\)
\(492\) −24.7824 −1.11728
\(493\) −38.0889 −1.71544
\(494\) 1.01814 0.0458082
\(495\) 2.28292 0.102610
\(496\) 1.31324 0.0589662
\(497\) −45.2423 −2.02939
\(498\) 29.3840 1.31673
\(499\) −21.6772 −0.970404 −0.485202 0.874402i \(-0.661254\pi\)
−0.485202 + 0.874402i \(0.661254\pi\)
\(500\) 3.13061 0.140005
\(501\) −15.7521 −0.703752
\(502\) 53.9259 2.40683
\(503\) 7.26725 0.324031 0.162015 0.986788i \(-0.448201\pi\)
0.162015 + 0.986788i \(0.448201\pi\)
\(504\) −18.5584 −0.826655
\(505\) −1.85103 −0.0823699
\(506\) −12.4509 −0.553512
\(507\) −10.9989 −0.488476
\(508\) 29.7119 1.31825
\(509\) 26.1909 1.16089 0.580446 0.814299i \(-0.302878\pi\)
0.580446 + 0.814299i \(0.302878\pi\)
\(510\) 12.3109 0.545135
\(511\) 3.17432 0.140424
\(512\) −5.19749 −0.229699
\(513\) 18.8454 0.832044
\(514\) 51.1582 2.25649
\(515\) 11.0094 0.485130
\(516\) −8.11552 −0.357266
\(517\) −2.53298 −0.111401
\(518\) 47.0480 2.06717
\(519\) −7.98373 −0.350447
\(520\) −0.273259 −0.0119832
\(521\) 16.2995 0.714095 0.357047 0.934086i \(-0.383783\pi\)
0.357047 + 0.934086i \(0.383783\pi\)
\(522\) 30.6869 1.34313
\(523\) 39.0185 1.70616 0.853079 0.521781i \(-0.174732\pi\)
0.853079 + 0.521781i \(0.174732\pi\)
\(524\) 45.2591 1.97715
\(525\) −2.68804 −0.117316
\(526\) 47.8379 2.08583
\(527\) 18.3038 0.797325
\(528\) 0.389949 0.0169704
\(529\) 7.21590 0.313735
\(530\) −1.86724 −0.0811076
\(531\) −15.7304 −0.682640
\(532\) 41.8626 1.81498
\(533\) −0.997484 −0.0432058
\(534\) −25.2328 −1.09193
\(535\) −9.27940 −0.401184
\(536\) 23.1022 0.997863
\(537\) 3.75628 0.162096
\(538\) −62.9790 −2.71522
\(539\) −3.07633 −0.132507
\(540\) −14.0051 −0.602685
\(541\) 27.4700 1.18103 0.590514 0.807028i \(-0.298925\pi\)
0.590514 + 0.807028i \(0.298925\pi\)
\(542\) 13.8287 0.593995
\(543\) −7.94701 −0.341039
\(544\) −39.5683 −1.69648
\(545\) −1.19923 −0.0513695
\(546\) 0.649674 0.0278035
\(547\) 7.64867 0.327034 0.163517 0.986541i \(-0.447716\pi\)
0.163517 + 0.986541i \(0.447716\pi\)
\(548\) 55.7093 2.37978
\(549\) −13.1895 −0.562916
\(550\) 2.26509 0.0965836
\(551\) −24.9991 −1.06500
\(552\) 11.9207 0.507377
\(553\) −47.9171 −2.03764
\(554\) 43.6229 1.85336
\(555\) 5.54102 0.235203
\(556\) −0.278151 −0.0117962
\(557\) −1.94096 −0.0822411 −0.0411206 0.999154i \(-0.513093\pi\)
−0.0411206 + 0.999154i \(0.513093\pi\)
\(558\) −14.7467 −0.624278
\(559\) −0.326647 −0.0138157
\(560\) 1.46175 0.0617704
\(561\) 5.43507 0.229469
\(562\) −29.8210 −1.25792
\(563\) −24.0918 −1.01535 −0.507674 0.861549i \(-0.669495\pi\)
−0.507674 + 0.861549i \(0.669495\pi\)
\(564\) 6.71500 0.282753
\(565\) 9.65051 0.406000
\(566\) 61.6038 2.58940
\(567\) −9.71491 −0.407988
\(568\) −36.4999 −1.53150
\(569\) 28.1093 1.17840 0.589202 0.807986i \(-0.299442\pi\)
0.589202 + 0.807986i \(0.299442\pi\)
\(570\) 8.08008 0.338437
\(571\) 1.39775 0.0584940 0.0292470 0.999572i \(-0.490689\pi\)
0.0292470 + 0.999572i \(0.490689\pi\)
\(572\) −0.334045 −0.0139671
\(573\) 1.10182 0.0460293
\(574\) −67.2150 −2.80550
\(575\) −5.49690 −0.229237
\(576\) 29.7763 1.24068
\(577\) −15.7186 −0.654373 −0.327187 0.944960i \(-0.606101\pi\)
−0.327187 + 0.944960i \(0.606101\pi\)
\(578\) −54.8029 −2.27950
\(579\) −13.3670 −0.555515
\(580\) 18.5783 0.771424
\(581\) 48.6288 2.01746
\(582\) −13.7005 −0.567905
\(583\) −0.824356 −0.0341414
\(584\) 2.56093 0.105972
\(585\) −0.243594 −0.0100714
\(586\) −65.6175 −2.71063
\(587\) 16.4309 0.678177 0.339089 0.940754i \(-0.389881\pi\)
0.339089 + 0.940754i \(0.389881\pi\)
\(588\) 8.15541 0.336324
\(589\) 12.0134 0.495004
\(590\) −15.6075 −0.642551
\(591\) 2.76619 0.113786
\(592\) −3.01320 −0.123842
\(593\) 46.1092 1.89348 0.946738 0.322004i \(-0.104356\pi\)
0.946738 + 0.322004i \(0.104356\pi\)
\(594\) −10.1331 −0.415767
\(595\) 20.3738 0.835243
\(596\) 40.5795 1.66220
\(597\) 3.70565 0.151662
\(598\) 1.32855 0.0543285
\(599\) 15.4687 0.632034 0.316017 0.948753i \(-0.397654\pi\)
0.316017 + 0.948753i \(0.397654\pi\)
\(600\) −2.16862 −0.0885334
\(601\) 39.6969 1.61927 0.809634 0.586935i \(-0.199665\pi\)
0.809634 + 0.586935i \(0.199665\pi\)
\(602\) −22.0109 −0.897098
\(603\) 20.5942 0.838661
\(604\) −36.6625 −1.49178
\(605\) 1.00000 0.0406558
\(606\) 3.55045 0.144227
\(607\) 14.5226 0.589454 0.294727 0.955581i \(-0.404771\pi\)
0.294727 + 0.955581i \(0.404771\pi\)
\(608\) −25.9701 −1.05323
\(609\) −15.9519 −0.646405
\(610\) −13.0865 −0.529858
\(611\) 0.270276 0.0109342
\(612\) 45.8712 1.85423
\(613\) −22.2083 −0.896987 −0.448493 0.893786i \(-0.648039\pi\)
−0.448493 + 0.893786i \(0.648039\pi\)
\(614\) −27.1665 −1.09635
\(615\) −7.91617 −0.319211
\(616\) −8.12923 −0.327536
\(617\) 9.91147 0.399021 0.199510 0.979896i \(-0.436065\pi\)
0.199510 + 0.979896i \(0.436065\pi\)
\(618\) −21.1169 −0.849447
\(619\) −3.68563 −0.148138 −0.0740691 0.997253i \(-0.523599\pi\)
−0.0740691 + 0.997253i \(0.523599\pi\)
\(620\) −8.92790 −0.358553
\(621\) 24.5910 0.986803
\(622\) −37.6050 −1.50782
\(623\) −41.7587 −1.67303
\(624\) −0.0416086 −0.00166568
\(625\) 1.00000 0.0400000
\(626\) 72.4866 2.89715
\(627\) 3.56723 0.142461
\(628\) 53.8400 2.14845
\(629\) −41.9977 −1.67456
\(630\) −16.4144 −0.653967
\(631\) −26.2854 −1.04640 −0.523202 0.852209i \(-0.675263\pi\)
−0.523202 + 0.852209i \(0.675263\pi\)
\(632\) −38.6578 −1.53773
\(633\) −3.74895 −0.149008
\(634\) −21.2635 −0.844483
\(635\) 9.49076 0.376629
\(636\) 2.18539 0.0866563
\(637\) 0.328252 0.0130058
\(638\) 13.4420 0.532172
\(639\) −32.5375 −1.28716
\(640\) 17.2139 0.680438
\(641\) −35.0939 −1.38612 −0.693062 0.720878i \(-0.743739\pi\)
−0.693062 + 0.720878i \(0.743739\pi\)
\(642\) 17.7987 0.702460
\(643\) 34.6132 1.36501 0.682505 0.730881i \(-0.260891\pi\)
0.682505 + 0.730881i \(0.260891\pi\)
\(644\) 54.6258 2.15256
\(645\) −2.59231 −0.102072
\(646\) −61.2423 −2.40955
\(647\) −3.17606 −0.124864 −0.0624319 0.998049i \(-0.519886\pi\)
−0.0624319 + 0.998049i \(0.519886\pi\)
\(648\) −7.83765 −0.307892
\(649\) −6.89047 −0.270475
\(650\) −0.241691 −0.00947989
\(651\) 7.66577 0.300445
\(652\) −14.1185 −0.552924
\(653\) 26.0647 1.01999 0.509996 0.860177i \(-0.329647\pi\)
0.509996 + 0.860177i \(0.329647\pi\)
\(654\) 2.30024 0.0899465
\(655\) 14.4570 0.564880
\(656\) 4.30481 0.168075
\(657\) 2.28292 0.0890651
\(658\) 18.2124 0.709995
\(659\) −25.3185 −0.986269 −0.493135 0.869953i \(-0.664149\pi\)
−0.493135 + 0.869953i \(0.664149\pi\)
\(660\) −2.65102 −0.103191
\(661\) −47.9428 −1.86476 −0.932379 0.361482i \(-0.882271\pi\)
−0.932379 + 0.361482i \(0.882271\pi\)
\(662\) 43.3572 1.68512
\(663\) −0.579937 −0.0225229
\(664\) 39.2320 1.52250
\(665\) 13.3720 0.518545
\(666\) 33.8361 1.31112
\(667\) −32.6209 −1.26309
\(668\) −58.2349 −2.25318
\(669\) −21.4956 −0.831067
\(670\) 20.4334 0.789409
\(671\) −5.77749 −0.223038
\(672\) −16.5716 −0.639261
\(673\) −47.4326 −1.82839 −0.914196 0.405273i \(-0.867177\pi\)
−0.914196 + 0.405273i \(0.867177\pi\)
\(674\) −44.0927 −1.69839
\(675\) −4.47361 −0.172189
\(676\) −40.6623 −1.56393
\(677\) 36.7758 1.41341 0.706704 0.707510i \(-0.250181\pi\)
0.706704 + 0.707510i \(0.250181\pi\)
\(678\) −18.5105 −0.710893
\(679\) −22.6735 −0.870131
\(680\) 16.4368 0.630324
\(681\) −0.183165 −0.00701890
\(682\) −6.45959 −0.247350
\(683\) 27.1590 1.03921 0.519606 0.854406i \(-0.326079\pi\)
0.519606 + 0.854406i \(0.326079\pi\)
\(684\) 30.1069 1.15117
\(685\) 17.7950 0.679913
\(686\) −28.2117 −1.07713
\(687\) −2.78427 −0.106227
\(688\) 1.40970 0.0537442
\(689\) 0.0879611 0.00335105
\(690\) 10.5435 0.401386
\(691\) 16.3924 0.623598 0.311799 0.950148i \(-0.399068\pi\)
0.311799 + 0.950148i \(0.399068\pi\)
\(692\) −29.5155 −1.12201
\(693\) −7.24672 −0.275280
\(694\) −2.31555 −0.0878972
\(695\) −0.0888487 −0.00337022
\(696\) −12.8695 −0.487816
\(697\) 59.9999 2.27266
\(698\) −30.4862 −1.15392
\(699\) −11.2664 −0.426136
\(700\) −9.93757 −0.375605
\(701\) −17.4670 −0.659718 −0.329859 0.944030i \(-0.607001\pi\)
−0.329859 + 0.944030i \(0.607001\pi\)
\(702\) 1.08123 0.0408084
\(703\) −27.5646 −1.03962
\(704\) 13.0431 0.491580
\(705\) 2.14495 0.0807835
\(706\) −36.6793 −1.38044
\(707\) 5.87578 0.220981
\(708\) 18.2668 0.686509
\(709\) 16.4184 0.616606 0.308303 0.951288i \(-0.400239\pi\)
0.308303 + 0.951288i \(0.400239\pi\)
\(710\) −32.2833 −1.21157
\(711\) −34.4611 −1.29239
\(712\) −33.6894 −1.26257
\(713\) 15.6761 0.587075
\(714\) −39.0787 −1.46249
\(715\) −0.106703 −0.00399046
\(716\) 13.8868 0.518975
\(717\) 20.0169 0.747544
\(718\) 25.3067 0.944439
\(719\) −17.2489 −0.643275 −0.321638 0.946863i \(-0.604233\pi\)
−0.321638 + 0.946863i \(0.604233\pi\)
\(720\) 1.05127 0.0391785
\(721\) −34.9472 −1.30150
\(722\) 2.84113 0.105736
\(723\) −8.94541 −0.332683
\(724\) −29.3798 −1.09189
\(725\) 5.93442 0.220399
\(726\) −1.91809 −0.0711870
\(727\) −18.3674 −0.681210 −0.340605 0.940206i \(-0.610632\pi\)
−0.340605 + 0.940206i \(0.610632\pi\)
\(728\) 0.867411 0.0321484
\(729\) 4.37807 0.162151
\(730\) 2.26509 0.0838346
\(731\) 19.6482 0.726715
\(732\) 15.3163 0.566106
\(733\) 31.1376 1.15009 0.575047 0.818120i \(-0.304984\pi\)
0.575047 + 0.818120i \(0.304984\pi\)
\(734\) −63.8225 −2.35573
\(735\) 2.60505 0.0960889
\(736\) −33.8879 −1.24913
\(737\) 9.02101 0.332293
\(738\) −48.3398 −1.77941
\(739\) −29.5518 −1.08708 −0.543541 0.839383i \(-0.682917\pi\)
−0.543541 + 0.839383i \(0.682917\pi\)
\(740\) 20.4849 0.753041
\(741\) −0.380633 −0.0139829
\(742\) 5.92721 0.217595
\(743\) 19.6679 0.721547 0.360773 0.932653i \(-0.382513\pi\)
0.360773 + 0.932653i \(0.382513\pi\)
\(744\) 6.18448 0.226734
\(745\) 12.9622 0.474897
\(746\) −37.3990 −1.36928
\(747\) 34.9730 1.27959
\(748\) 20.0932 0.734681
\(749\) 29.4558 1.07629
\(750\) −1.91809 −0.0700388
\(751\) 25.5937 0.933928 0.466964 0.884276i \(-0.345348\pi\)
0.466964 + 0.884276i \(0.345348\pi\)
\(752\) −1.16642 −0.0425351
\(753\) −20.1603 −0.734682
\(754\) −1.43429 −0.0522339
\(755\) −11.7110 −0.426206
\(756\) 44.4568 1.61688
\(757\) −52.4842 −1.90757 −0.953785 0.300491i \(-0.902849\pi\)
−0.953785 + 0.300491i \(0.902849\pi\)
\(758\) −66.8095 −2.42663
\(759\) 4.65481 0.168959
\(760\) 10.7881 0.391325
\(761\) 33.1709 1.20244 0.601222 0.799082i \(-0.294681\pi\)
0.601222 + 0.799082i \(0.294681\pi\)
\(762\) −18.2041 −0.659466
\(763\) 3.80676 0.137814
\(764\) 4.07339 0.147370
\(765\) 14.6525 0.529761
\(766\) −54.9362 −1.98492
\(767\) 0.735232 0.0265477
\(768\) −10.9278 −0.394323
\(769\) −16.9060 −0.609646 −0.304823 0.952409i \(-0.598597\pi\)
−0.304823 + 0.952409i \(0.598597\pi\)
\(770\) −7.19011 −0.259114
\(771\) −19.1256 −0.688791
\(772\) −49.4174 −1.77857
\(773\) 15.5282 0.558511 0.279255 0.960217i \(-0.409912\pi\)
0.279255 + 0.960217i \(0.409912\pi\)
\(774\) −15.8299 −0.568993
\(775\) −2.85181 −0.102440
\(776\) −18.2922 −0.656652
\(777\) −17.5890 −0.631001
\(778\) −44.4840 −1.59483
\(779\) 39.3801 1.41094
\(780\) 0.282872 0.0101284
\(781\) −14.2526 −0.509998
\(782\) −79.9140 −2.85772
\(783\) −26.5483 −0.948758
\(784\) −1.41663 −0.0505938
\(785\) 17.1979 0.613820
\(786\) −27.7298 −0.989088
\(787\) 33.7886 1.20443 0.602216 0.798333i \(-0.294284\pi\)
0.602216 + 0.798333i \(0.294284\pi\)
\(788\) 10.2265 0.364303
\(789\) −17.8843 −0.636698
\(790\) −34.1919 −1.21649
\(791\) −30.6338 −1.08921
\(792\) −5.84640 −0.207743
\(793\) 0.616475 0.0218917
\(794\) 12.3677 0.438913
\(795\) 0.698071 0.0247580
\(796\) 13.6996 0.485571
\(797\) 34.8460 1.23431 0.617154 0.786843i \(-0.288286\pi\)
0.617154 + 0.786843i \(0.288286\pi\)
\(798\) −25.6488 −0.907957
\(799\) −16.2575 −0.575148
\(800\) 6.16492 0.217963
\(801\) −30.0321 −1.06113
\(802\) 68.2892 2.41138
\(803\) 1.00000 0.0352892
\(804\) −23.9149 −0.843414
\(805\) 17.4489 0.614994
\(806\) 0.689256 0.0242780
\(807\) 23.5449 0.828818
\(808\) 4.74037 0.166766
\(809\) −3.17918 −0.111774 −0.0558870 0.998437i \(-0.517799\pi\)
−0.0558870 + 0.998437i \(0.517799\pi\)
\(810\) −6.93222 −0.243573
\(811\) 27.1513 0.953411 0.476706 0.879063i \(-0.341831\pi\)
0.476706 + 0.879063i \(0.341831\pi\)
\(812\) −58.9737 −2.06957
\(813\) −5.16990 −0.181316
\(814\) 14.8214 0.519490
\(815\) −4.50983 −0.157972
\(816\) 2.50281 0.0876160
\(817\) 12.8958 0.451167
\(818\) 60.6952 2.12216
\(819\) 0.773245 0.0270194
\(820\) −29.2657 −1.02200
\(821\) −38.5388 −1.34501 −0.672507 0.740091i \(-0.734783\pi\)
−0.672507 + 0.740091i \(0.734783\pi\)
\(822\) −34.1325 −1.19051
\(823\) 3.34786 0.116699 0.0583495 0.998296i \(-0.481416\pi\)
0.0583495 + 0.998296i \(0.481416\pi\)
\(824\) −28.1942 −0.982191
\(825\) −0.846807 −0.0294820
\(826\) 49.5433 1.72383
\(827\) −47.2016 −1.64136 −0.820681 0.571387i \(-0.806406\pi\)
−0.820681 + 0.571387i \(0.806406\pi\)
\(828\) 39.2859 1.36528
\(829\) 8.59558 0.298537 0.149268 0.988797i \(-0.452308\pi\)
0.149268 + 0.988797i \(0.452308\pi\)
\(830\) 34.6998 1.20445
\(831\) −16.3085 −0.565736
\(832\) −1.39173 −0.0482497
\(833\) −19.7448 −0.684117
\(834\) 0.170420 0.00590115
\(835\) −18.6018 −0.643740
\(836\) 13.1879 0.456113
\(837\) 12.7579 0.440977
\(838\) −18.0213 −0.622535
\(839\) 16.5948 0.572915 0.286458 0.958093i \(-0.407522\pi\)
0.286458 + 0.958093i \(0.407522\pi\)
\(840\) 6.88389 0.237517
\(841\) 6.21728 0.214389
\(842\) −13.9609 −0.481125
\(843\) 11.1486 0.383979
\(844\) −13.8597 −0.477072
\(845\) −12.9886 −0.446822
\(846\) 13.0981 0.450321
\(847\) −3.17432 −0.109071
\(848\) −0.379611 −0.0130359
\(849\) −23.0307 −0.790413
\(850\) 14.5380 0.498650
\(851\) −35.9685 −1.23299
\(852\) 37.7840 1.29446
\(853\) 38.7402 1.32644 0.663219 0.748425i \(-0.269190\pi\)
0.663219 + 0.748425i \(0.269190\pi\)
\(854\) 41.5408 1.42150
\(855\) 9.61693 0.328892
\(856\) 23.7639 0.812234
\(857\) −9.09153 −0.310561 −0.155280 0.987870i \(-0.549628\pi\)
−0.155280 + 0.987870i \(0.549628\pi\)
\(858\) 0.204666 0.00698717
\(859\) 38.9948 1.33048 0.665242 0.746628i \(-0.268328\pi\)
0.665242 + 0.746628i \(0.268328\pi\)
\(860\) −9.58366 −0.326800
\(861\) 25.1285 0.856376
\(862\) 8.62787 0.293866
\(863\) −37.1356 −1.26411 −0.632055 0.774924i \(-0.717788\pi\)
−0.632055 + 0.774924i \(0.717788\pi\)
\(864\) −27.5795 −0.938273
\(865\) −9.42803 −0.320563
\(866\) 66.1375 2.24744
\(867\) 20.4882 0.695816
\(868\) 28.3400 0.961924
\(869\) −15.0952 −0.512070
\(870\) −11.3827 −0.385911
\(871\) −0.962566 −0.0326153
\(872\) 3.07116 0.104003
\(873\) −16.3064 −0.551889
\(874\) −52.4504 −1.77416
\(875\) −3.17432 −0.107312
\(876\) −2.65102 −0.0895698
\(877\) 16.0179 0.540885 0.270442 0.962736i \(-0.412830\pi\)
0.270442 + 0.962736i \(0.412830\pi\)
\(878\) 1.86020 0.0627788
\(879\) 24.5312 0.827418
\(880\) 0.460493 0.0155232
\(881\) 43.1627 1.45419 0.727095 0.686537i \(-0.240870\pi\)
0.727095 + 0.686537i \(0.240870\pi\)
\(882\) 15.9077 0.535640
\(883\) 24.2300 0.815404 0.407702 0.913115i \(-0.366330\pi\)
0.407702 + 0.913115i \(0.366330\pi\)
\(884\) −2.14400 −0.0721106
\(885\) 5.83490 0.196138
\(886\) 24.1258 0.810523
\(887\) −55.5713 −1.86590 −0.932951 0.360004i \(-0.882775\pi\)
−0.932951 + 0.360004i \(0.882775\pi\)
\(888\) −14.1902 −0.476191
\(889\) −30.1267 −1.01042
\(890\) −29.7975 −0.998816
\(891\) −3.06047 −0.102529
\(892\) −79.4683 −2.66079
\(893\) −10.6704 −0.357070
\(894\) −24.8626 −0.831530
\(895\) 4.43582 0.148273
\(896\) −54.6424 −1.82547
\(897\) −0.496681 −0.0165837
\(898\) 5.70066 0.190233
\(899\) −16.9238 −0.564441
\(900\) −7.14693 −0.238231
\(901\) −5.29097 −0.176268
\(902\) −21.1746 −0.705037
\(903\) 8.22883 0.273838
\(904\) −24.7143 −0.821985
\(905\) −9.38468 −0.311957
\(906\) 22.4627 0.746273
\(907\) 19.3917 0.643890 0.321945 0.946758i \(-0.395663\pi\)
0.321945 + 0.946758i \(0.395663\pi\)
\(908\) −0.677154 −0.0224721
\(909\) 4.22576 0.140159
\(910\) 0.767205 0.0254326
\(911\) −29.5602 −0.979375 −0.489687 0.871898i \(-0.662889\pi\)
−0.489687 + 0.871898i \(0.662889\pi\)
\(912\) 1.64269 0.0543947
\(913\) 15.3194 0.506999
\(914\) 42.6106 1.40943
\(915\) 4.89242 0.161739
\(916\) −10.2933 −0.340102
\(917\) −45.8911 −1.51546
\(918\) −65.0374 −2.14655
\(919\) −3.75963 −0.124019 −0.0620095 0.998076i \(-0.519751\pi\)
−0.0620095 + 0.998076i \(0.519751\pi\)
\(920\) 14.0772 0.464111
\(921\) 10.1562 0.334659
\(922\) −82.8630 −2.72895
\(923\) 1.52079 0.0500574
\(924\) 8.41521 0.276840
\(925\) 6.54343 0.215146
\(926\) −2.39620 −0.0787440
\(927\) −25.1334 −0.825490
\(928\) 36.5852 1.20097
\(929\) 49.2103 1.61454 0.807268 0.590185i \(-0.200945\pi\)
0.807268 + 0.590185i \(0.200945\pi\)
\(930\) 5.47003 0.179369
\(931\) −12.9592 −0.424721
\(932\) −41.6516 −1.36434
\(933\) 14.0587 0.460262
\(934\) 2.79426 0.0914308
\(935\) 6.41831 0.209901
\(936\) 0.623827 0.0203904
\(937\) 32.7620 1.07029 0.535144 0.844761i \(-0.320257\pi\)
0.535144 + 0.844761i \(0.320257\pi\)
\(938\) −64.8621 −2.11782
\(939\) −27.0993 −0.884351
\(940\) 7.92979 0.258641
\(941\) 54.8721 1.78878 0.894389 0.447289i \(-0.147611\pi\)
0.894389 + 0.447289i \(0.147611\pi\)
\(942\) −32.9872 −1.07478
\(943\) 51.3864 1.67337
\(944\) −3.17302 −0.103273
\(945\) 14.2007 0.461948
\(946\) −6.93405 −0.225445
\(947\) 26.0152 0.845379 0.422690 0.906275i \(-0.361086\pi\)
0.422690 + 0.906275i \(0.361086\pi\)
\(948\) 40.0178 1.29972
\(949\) −0.106703 −0.00346372
\(950\) 9.54181 0.309577
\(951\) 7.94942 0.257777
\(952\) −52.1759 −1.69103
\(953\) −6.79895 −0.220240 −0.110120 0.993918i \(-0.535123\pi\)
−0.110120 + 0.993918i \(0.535123\pi\)
\(954\) 4.26275 0.138012
\(955\) 1.30115 0.0421042
\(956\) 74.0016 2.39338
\(957\) −5.02530 −0.162445
\(958\) −16.1203 −0.520825
\(959\) −56.4871 −1.82406
\(960\) −11.0450 −0.356475
\(961\) −22.8672 −0.737651
\(962\) −1.58149 −0.0509892
\(963\) 21.1841 0.682648
\(964\) −33.0708 −1.06514
\(965\) −15.7852 −0.508144
\(966\) −33.4686 −1.07684
\(967\) 37.8667 1.21771 0.608856 0.793281i \(-0.291629\pi\)
0.608856 + 0.793281i \(0.291629\pi\)
\(968\) −2.56093 −0.0823115
\(969\) 22.8956 0.735511
\(970\) −16.1790 −0.519478
\(971\) −17.5825 −0.564251 −0.282125 0.959378i \(-0.591039\pi\)
−0.282125 + 0.959378i \(0.591039\pi\)
\(972\) 50.1288 1.60788
\(973\) 0.282034 0.00904161
\(974\) 89.4937 2.86756
\(975\) 0.0903567 0.00289373
\(976\) −2.66050 −0.0851605
\(977\) −14.4533 −0.462401 −0.231201 0.972906i \(-0.574265\pi\)
−0.231201 + 0.972906i \(0.574265\pi\)
\(978\) 8.65026 0.276605
\(979\) −13.1552 −0.420440
\(980\) 9.63078 0.307644
\(981\) 2.73775 0.0874097
\(982\) −84.0432 −2.68193
\(983\) 16.9165 0.539554 0.269777 0.962923i \(-0.413050\pi\)
0.269777 + 0.962923i \(0.413050\pi\)
\(984\) 20.2728 0.646272
\(985\) 3.26661 0.104083
\(986\) 86.2746 2.74754
\(987\) −6.80876 −0.216725
\(988\) −1.40719 −0.0447685
\(989\) 16.8275 0.535084
\(990\) −5.17100 −0.164345
\(991\) −29.9769 −0.952248 −0.476124 0.879378i \(-0.657959\pi\)
−0.476124 + 0.879378i \(0.657959\pi\)
\(992\) −17.5812 −0.558203
\(993\) −16.2092 −0.514383
\(994\) 102.478 3.25040
\(995\) 4.37603 0.138729
\(996\) −40.6121 −1.28684
\(997\) −14.0000 −0.443384 −0.221692 0.975117i \(-0.571158\pi\)
−0.221692 + 0.975117i \(0.571158\pi\)
\(998\) 49.1007 1.55426
\(999\) −29.2727 −0.926149
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 4015.2.a.i.1.6 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4015.2.a.i.1.6 38 1.1 even 1 trivial