Properties

Label 8041.2.a.f.1.18
Level $8041$
Weight $2$
Character 8041.1
Self dual yes
Analytic conductor $64.208$
Analytic rank $0$
Dimension $66$
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] = [8041,2,Mod(1,8041)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8041, 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("8041.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8041.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(66\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 8041.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.25548 q^{2} -0.219421 q^{3} -0.423759 q^{4} +4.17472 q^{5} +0.275480 q^{6} -0.198048 q^{7} +3.04299 q^{8} -2.95185 q^{9} +O(q^{10})\) \(q-1.25548 q^{2} -0.219421 q^{3} -0.423759 q^{4} +4.17472 q^{5} +0.275480 q^{6} -0.198048 q^{7} +3.04299 q^{8} -2.95185 q^{9} -5.24130 q^{10} -1.00000 q^{11} +0.0929815 q^{12} +0.262830 q^{13} +0.248646 q^{14} -0.916021 q^{15} -2.97291 q^{16} +1.00000 q^{17} +3.70601 q^{18} -5.47442 q^{19} -1.76907 q^{20} +0.0434558 q^{21} +1.25548 q^{22} +5.47926 q^{23} -0.667696 q^{24} +12.4283 q^{25} -0.329979 q^{26} +1.30596 q^{27} +0.0839245 q^{28} +1.57962 q^{29} +1.15005 q^{30} -0.491859 q^{31} -2.35354 q^{32} +0.219421 q^{33} -1.25548 q^{34} -0.826794 q^{35} +1.25087 q^{36} -4.40751 q^{37} +6.87304 q^{38} -0.0576705 q^{39} +12.7036 q^{40} +2.47972 q^{41} -0.0545581 q^{42} -1.00000 q^{43} +0.423759 q^{44} -12.3232 q^{45} -6.87913 q^{46} +1.03795 q^{47} +0.652319 q^{48} -6.96078 q^{49} -15.6035 q^{50} -0.219421 q^{51} -0.111377 q^{52} -1.96523 q^{53} -1.63961 q^{54} -4.17472 q^{55} -0.602658 q^{56} +1.20120 q^{57} -1.98319 q^{58} +4.48629 q^{59} +0.388172 q^{60} +0.162668 q^{61} +0.617522 q^{62} +0.584608 q^{63} +8.90065 q^{64} +1.09724 q^{65} -0.275480 q^{66} +5.02953 q^{67} -0.423759 q^{68} -1.20227 q^{69} +1.03803 q^{70} -4.99462 q^{71} -8.98247 q^{72} +15.8803 q^{73} +5.53356 q^{74} -2.72703 q^{75} +2.31983 q^{76} +0.198048 q^{77} +0.0724044 q^{78} +6.86933 q^{79} -12.4111 q^{80} +8.56901 q^{81} -3.11325 q^{82} +0.608284 q^{83} -0.0184148 q^{84} +4.17472 q^{85} +1.25548 q^{86} -0.346603 q^{87} -3.04299 q^{88} -16.7625 q^{89} +15.4715 q^{90} -0.0520530 q^{91} -2.32189 q^{92} +0.107924 q^{93} -1.30313 q^{94} -22.8542 q^{95} +0.516416 q^{96} -16.8484 q^{97} +8.73915 q^{98} +2.95185 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25548 −0.887762 −0.443881 0.896086i \(-0.646399\pi\)
−0.443881 + 0.896086i \(0.646399\pi\)
\(3\) −0.219421 −0.126683 −0.0633414 0.997992i \(-0.520176\pi\)
−0.0633414 + 0.997992i \(0.520176\pi\)
\(4\) −0.423759 −0.211879
\(5\) 4.17472 1.86699 0.933496 0.358588i \(-0.116742\pi\)
0.933496 + 0.358588i \(0.116742\pi\)
\(6\) 0.275480 0.112464
\(7\) −0.198048 −0.0748551 −0.0374275 0.999299i \(-0.511916\pi\)
−0.0374275 + 0.999299i \(0.511916\pi\)
\(8\) 3.04299 1.07586
\(9\) −2.95185 −0.983951
\(10\) −5.24130 −1.65744
\(11\) −1.00000 −0.301511
\(12\) 0.0929815 0.0268415
\(13\) 0.262830 0.0728960 0.0364480 0.999336i \(-0.488396\pi\)
0.0364480 + 0.999336i \(0.488396\pi\)
\(14\) 0.248646 0.0664534
\(15\) −0.916021 −0.236516
\(16\) −2.97291 −0.743228
\(17\) 1.00000 0.242536
\(18\) 3.70601 0.873514
\(19\) −5.47442 −1.25592 −0.627959 0.778247i \(-0.716109\pi\)
−0.627959 + 0.778247i \(0.716109\pi\)
\(20\) −1.76907 −0.395577
\(21\) 0.0434558 0.00948284
\(22\) 1.25548 0.267670
\(23\) 5.47926 1.14251 0.571253 0.820774i \(-0.306458\pi\)
0.571253 + 0.820774i \(0.306458\pi\)
\(24\) −0.667696 −0.136293
\(25\) 12.4283 2.48566
\(26\) −0.329979 −0.0647143
\(27\) 1.30596 0.251332
\(28\) 0.0839245 0.0158602
\(29\) 1.57962 0.293329 0.146664 0.989186i \(-0.453146\pi\)
0.146664 + 0.989186i \(0.453146\pi\)
\(30\) 1.15005 0.209969
\(31\) −0.491859 −0.0883405 −0.0441703 0.999024i \(-0.514064\pi\)
−0.0441703 + 0.999024i \(0.514064\pi\)
\(32\) −2.35354 −0.416051
\(33\) 0.219421 0.0381963
\(34\) −1.25548 −0.215314
\(35\) −0.826794 −0.139754
\(36\) 1.25087 0.208479
\(37\) −4.40751 −0.724590 −0.362295 0.932063i \(-0.618007\pi\)
−0.362295 + 0.932063i \(0.618007\pi\)
\(38\) 6.87304 1.11496
\(39\) −0.0576705 −0.00923467
\(40\) 12.7036 2.00862
\(41\) 2.47972 0.387267 0.193633 0.981074i \(-0.437973\pi\)
0.193633 + 0.981074i \(0.437973\pi\)
\(42\) −0.0545581 −0.00841850
\(43\) −1.00000 −0.152499
\(44\) 0.423759 0.0638840
\(45\) −12.3232 −1.83703
\(46\) −6.87913 −1.01427
\(47\) 1.03795 0.151400 0.0757001 0.997131i \(-0.475881\pi\)
0.0757001 + 0.997131i \(0.475881\pi\)
\(48\) 0.652319 0.0941541
\(49\) −6.96078 −0.994397
\(50\) −15.6035 −2.20667
\(51\) −0.219421 −0.0307251
\(52\) −0.111377 −0.0154452
\(53\) −1.96523 −0.269945 −0.134973 0.990849i \(-0.543095\pi\)
−0.134973 + 0.990849i \(0.543095\pi\)
\(54\) −1.63961 −0.223123
\(55\) −4.17472 −0.562919
\(56\) −0.602658 −0.0805336
\(57\) 1.20120 0.159103
\(58\) −1.98319 −0.260406
\(59\) 4.48629 0.584065 0.292032 0.956408i \(-0.405669\pi\)
0.292032 + 0.956408i \(0.405669\pi\)
\(60\) 0.388172 0.0501128
\(61\) 0.162668 0.0208275 0.0104137 0.999946i \(-0.496685\pi\)
0.0104137 + 0.999946i \(0.496685\pi\)
\(62\) 0.617522 0.0784253
\(63\) 0.584608 0.0736537
\(64\) 8.90065 1.11258
\(65\) 1.09724 0.136096
\(66\) −0.275480 −0.0339092
\(67\) 5.02953 0.614455 0.307228 0.951636i \(-0.400599\pi\)
0.307228 + 0.951636i \(0.400599\pi\)
\(68\) −0.423759 −0.0513883
\(69\) −1.20227 −0.144736
\(70\) 1.03803 0.124068
\(71\) −4.99462 −0.592752 −0.296376 0.955071i \(-0.595778\pi\)
−0.296376 + 0.955071i \(0.595778\pi\)
\(72\) −8.98247 −1.05859
\(73\) 15.8803 1.85864 0.929322 0.369271i \(-0.120393\pi\)
0.929322 + 0.369271i \(0.120393\pi\)
\(74\) 5.53356 0.643263
\(75\) −2.72703 −0.314890
\(76\) 2.31983 0.266103
\(77\) 0.198048 0.0225696
\(78\) 0.0724044 0.00819818
\(79\) 6.86933 0.772859 0.386430 0.922319i \(-0.373708\pi\)
0.386430 + 0.922319i \(0.373708\pi\)
\(80\) −12.4111 −1.38760
\(81\) 8.56901 0.952112
\(82\) −3.11325 −0.343800
\(83\) 0.608284 0.0667679 0.0333839 0.999443i \(-0.489372\pi\)
0.0333839 + 0.999443i \(0.489372\pi\)
\(84\) −0.0184148 −0.00200922
\(85\) 4.17472 0.452812
\(86\) 1.25548 0.135382
\(87\) −0.346603 −0.0371597
\(88\) −3.04299 −0.324384
\(89\) −16.7625 −1.77683 −0.888413 0.459045i \(-0.848192\pi\)
−0.888413 + 0.459045i \(0.848192\pi\)
\(90\) 15.4715 1.63084
\(91\) −0.0520530 −0.00545664
\(92\) −2.32189 −0.242073
\(93\) 0.107924 0.0111912
\(94\) −1.30313 −0.134407
\(95\) −22.8542 −2.34479
\(96\) 0.516416 0.0527065
\(97\) −16.8484 −1.71070 −0.855349 0.518052i \(-0.826657\pi\)
−0.855349 + 0.518052i \(0.826657\pi\)
\(98\) 8.73915 0.882787
\(99\) 2.95185 0.296673
\(100\) −5.26660 −0.526660
\(101\) 0.894331 0.0889893 0.0444946 0.999010i \(-0.485832\pi\)
0.0444946 + 0.999010i \(0.485832\pi\)
\(102\) 0.275480 0.0272765
\(103\) 1.97313 0.194419 0.0972094 0.995264i \(-0.469008\pi\)
0.0972094 + 0.995264i \(0.469008\pi\)
\(104\) 0.799791 0.0784259
\(105\) 0.181416 0.0177044
\(106\) 2.46732 0.239647
\(107\) 6.29149 0.608222 0.304111 0.952637i \(-0.401641\pi\)
0.304111 + 0.952637i \(0.401641\pi\)
\(108\) −0.553413 −0.0532521
\(109\) −4.93109 −0.472312 −0.236156 0.971715i \(-0.575888\pi\)
−0.236156 + 0.971715i \(0.575888\pi\)
\(110\) 5.24130 0.499738
\(111\) 0.967100 0.0917930
\(112\) 0.588779 0.0556344
\(113\) 13.1299 1.23516 0.617578 0.786509i \(-0.288114\pi\)
0.617578 + 0.786509i \(0.288114\pi\)
\(114\) −1.50809 −0.141246
\(115\) 22.8744 2.13305
\(116\) −0.669379 −0.0621503
\(117\) −0.775837 −0.0717262
\(118\) −5.63246 −0.518510
\(119\) −0.198048 −0.0181550
\(120\) −2.78744 −0.254458
\(121\) 1.00000 0.0909091
\(122\) −0.204227 −0.0184898
\(123\) −0.544102 −0.0490600
\(124\) 0.208430 0.0187175
\(125\) 31.0110 2.77371
\(126\) −0.733967 −0.0653870
\(127\) 14.7165 1.30587 0.652937 0.757412i \(-0.273536\pi\)
0.652937 + 0.757412i \(0.273536\pi\)
\(128\) −6.46755 −0.571656
\(129\) 0.219421 0.0193189
\(130\) −1.37757 −0.120821
\(131\) 19.2655 1.68323 0.841617 0.540075i \(-0.181604\pi\)
0.841617 + 0.540075i \(0.181604\pi\)
\(132\) −0.0929815 −0.00809300
\(133\) 1.08420 0.0940118
\(134\) −6.31450 −0.545490
\(135\) 5.45202 0.469235
\(136\) 3.04299 0.260934
\(137\) 9.71081 0.829650 0.414825 0.909901i \(-0.363843\pi\)
0.414825 + 0.909901i \(0.363843\pi\)
\(138\) 1.50943 0.128491
\(139\) 1.88200 0.159629 0.0798147 0.996810i \(-0.474567\pi\)
0.0798147 + 0.996810i \(0.474567\pi\)
\(140\) 0.350361 0.0296109
\(141\) −0.227748 −0.0191798
\(142\) 6.27066 0.526222
\(143\) −0.262830 −0.0219790
\(144\) 8.77560 0.731300
\(145\) 6.59449 0.547642
\(146\) −19.9374 −1.65003
\(147\) 1.52734 0.125973
\(148\) 1.86772 0.153526
\(149\) −22.4773 −1.84142 −0.920708 0.390253i \(-0.872387\pi\)
−0.920708 + 0.390253i \(0.872387\pi\)
\(150\) 3.42374 0.279547
\(151\) 20.0317 1.63016 0.815079 0.579350i \(-0.196694\pi\)
0.815079 + 0.579350i \(0.196694\pi\)
\(152\) −16.6586 −1.35119
\(153\) −2.95185 −0.238643
\(154\) −0.248646 −0.0200365
\(155\) −2.05337 −0.164931
\(156\) 0.0244384 0.00195664
\(157\) 21.5385 1.71896 0.859481 0.511168i \(-0.170787\pi\)
0.859481 + 0.511168i \(0.170787\pi\)
\(158\) −8.62433 −0.686115
\(159\) 0.431213 0.0341974
\(160\) −9.82537 −0.776764
\(161\) −1.08516 −0.0855223
\(162\) −10.7583 −0.845248
\(163\) 2.91228 0.228107 0.114054 0.993475i \(-0.463616\pi\)
0.114054 + 0.993475i \(0.463616\pi\)
\(164\) −1.05080 −0.0820538
\(165\) 0.916021 0.0713121
\(166\) −0.763691 −0.0592740
\(167\) 23.6474 1.82989 0.914946 0.403575i \(-0.132233\pi\)
0.914946 + 0.403575i \(0.132233\pi\)
\(168\) 0.132236 0.0102022
\(169\) −12.9309 −0.994686
\(170\) −5.24130 −0.401989
\(171\) 16.1597 1.23576
\(172\) 0.423759 0.0323113
\(173\) 3.99111 0.303438 0.151719 0.988424i \(-0.451519\pi\)
0.151719 + 0.988424i \(0.451519\pi\)
\(174\) 0.435154 0.0329889
\(175\) −2.46140 −0.186064
\(176\) 2.97291 0.224092
\(177\) −0.984385 −0.0739909
\(178\) 21.0451 1.57740
\(179\) −9.55519 −0.714189 −0.357094 0.934068i \(-0.616233\pi\)
−0.357094 + 0.934068i \(0.616233\pi\)
\(180\) 5.22205 0.389229
\(181\) −1.14049 −0.0847719 −0.0423860 0.999101i \(-0.513496\pi\)
−0.0423860 + 0.999101i \(0.513496\pi\)
\(182\) 0.0653517 0.00484419
\(183\) −0.0356927 −0.00263848
\(184\) 16.6734 1.22918
\(185\) −18.4001 −1.35280
\(186\) −0.135497 −0.00993513
\(187\) −1.00000 −0.0731272
\(188\) −0.439840 −0.0320786
\(189\) −0.258643 −0.0188135
\(190\) 28.6930 2.08161
\(191\) 17.2310 1.24679 0.623397 0.781905i \(-0.285752\pi\)
0.623397 + 0.781905i \(0.285752\pi\)
\(192\) −1.95299 −0.140945
\(193\) −3.30315 −0.237766 −0.118883 0.992908i \(-0.537931\pi\)
−0.118883 + 0.992908i \(0.537931\pi\)
\(194\) 21.1529 1.51869
\(195\) −0.240758 −0.0172410
\(196\) 2.94969 0.210692
\(197\) 8.69059 0.619179 0.309590 0.950870i \(-0.399808\pi\)
0.309590 + 0.950870i \(0.399808\pi\)
\(198\) −3.70601 −0.263374
\(199\) 3.17087 0.224777 0.112388 0.993664i \(-0.464150\pi\)
0.112388 + 0.993664i \(0.464150\pi\)
\(200\) 37.8192 2.67422
\(201\) −1.10358 −0.0778408
\(202\) −1.12282 −0.0790013
\(203\) −0.312841 −0.0219571
\(204\) 0.0929815 0.00651001
\(205\) 10.3521 0.723024
\(206\) −2.47724 −0.172597
\(207\) −16.1740 −1.12417
\(208\) −0.781371 −0.0541784
\(209\) 5.47442 0.378673
\(210\) −0.227765 −0.0157173
\(211\) 6.68616 0.460294 0.230147 0.973156i \(-0.426079\pi\)
0.230147 + 0.973156i \(0.426079\pi\)
\(212\) 0.832784 0.0571958
\(213\) 1.09592 0.0750914
\(214\) −7.89887 −0.539956
\(215\) −4.17472 −0.284714
\(216\) 3.97403 0.270398
\(217\) 0.0974117 0.00661273
\(218\) 6.19090 0.419301
\(219\) −3.48446 −0.235458
\(220\) 1.76907 0.119271
\(221\) 0.262830 0.0176799
\(222\) −1.21418 −0.0814903
\(223\) 4.16096 0.278639 0.139319 0.990247i \(-0.455509\pi\)
0.139319 + 0.990247i \(0.455509\pi\)
\(224\) 0.466113 0.0311435
\(225\) −36.6865 −2.44577
\(226\) −16.4844 −1.09652
\(227\) −18.7600 −1.24514 −0.622571 0.782563i \(-0.713912\pi\)
−0.622571 + 0.782563i \(0.713912\pi\)
\(228\) −0.509020 −0.0337106
\(229\) −7.01865 −0.463806 −0.231903 0.972739i \(-0.574495\pi\)
−0.231903 + 0.972739i \(0.574495\pi\)
\(230\) −28.7184 −1.89364
\(231\) −0.0434558 −0.00285918
\(232\) 4.80678 0.315581
\(233\) −14.2957 −0.936543 −0.468272 0.883585i \(-0.655123\pi\)
−0.468272 + 0.883585i \(0.655123\pi\)
\(234\) 0.974051 0.0636757
\(235\) 4.33314 0.282663
\(236\) −1.90110 −0.123751
\(237\) −1.50727 −0.0979079
\(238\) 0.248646 0.0161173
\(239\) −17.0906 −1.10550 −0.552749 0.833348i \(-0.686421\pi\)
−0.552749 + 0.833348i \(0.686421\pi\)
\(240\) 2.72325 0.175785
\(241\) −11.2551 −0.725002 −0.362501 0.931983i \(-0.618077\pi\)
−0.362501 + 0.931983i \(0.618077\pi\)
\(242\) −1.25548 −0.0807056
\(243\) −5.79810 −0.371949
\(244\) −0.0689318 −0.00441291
\(245\) −29.0593 −1.85653
\(246\) 0.683111 0.0435536
\(247\) −1.43884 −0.0915514
\(248\) −1.49672 −0.0950420
\(249\) −0.133470 −0.00845834
\(250\) −38.9339 −2.46239
\(251\) −18.2278 −1.15053 −0.575264 0.817968i \(-0.695101\pi\)
−0.575264 + 0.817968i \(0.695101\pi\)
\(252\) −0.247733 −0.0156057
\(253\) −5.47926 −0.344478
\(254\) −18.4763 −1.15931
\(255\) −0.916021 −0.0573635
\(256\) −9.68139 −0.605087
\(257\) 21.0290 1.31175 0.655876 0.754868i \(-0.272299\pi\)
0.655876 + 0.754868i \(0.272299\pi\)
\(258\) −0.275480 −0.0171506
\(259\) 0.872898 0.0542392
\(260\) −0.464966 −0.0288360
\(261\) −4.66282 −0.288621
\(262\) −24.1875 −1.49431
\(263\) 2.84048 0.175152 0.0875759 0.996158i \(-0.472088\pi\)
0.0875759 + 0.996158i \(0.472088\pi\)
\(264\) 0.667696 0.0410938
\(265\) −8.20429 −0.503985
\(266\) −1.36119 −0.0834600
\(267\) 3.67805 0.225093
\(268\) −2.13131 −0.130190
\(269\) −13.5930 −0.828780 −0.414390 0.910099i \(-0.636005\pi\)
−0.414390 + 0.910099i \(0.636005\pi\)
\(270\) −6.84493 −0.416569
\(271\) 10.4699 0.636000 0.318000 0.948091i \(-0.396989\pi\)
0.318000 + 0.948091i \(0.396989\pi\)
\(272\) −2.97291 −0.180259
\(273\) 0.0114215 0.000691262 0
\(274\) −12.1918 −0.736532
\(275\) −12.4283 −0.749454
\(276\) 0.509470 0.0306665
\(277\) 13.2330 0.795092 0.397546 0.917582i \(-0.369862\pi\)
0.397546 + 0.917582i \(0.369862\pi\)
\(278\) −2.36282 −0.141713
\(279\) 1.45190 0.0869228
\(280\) −2.51593 −0.150355
\(281\) −7.82870 −0.467021 −0.233511 0.972354i \(-0.575021\pi\)
−0.233511 + 0.972354i \(0.575021\pi\)
\(282\) 0.285933 0.0170271
\(283\) 28.6242 1.70153 0.850767 0.525543i \(-0.176138\pi\)
0.850767 + 0.525543i \(0.176138\pi\)
\(284\) 2.11651 0.125592
\(285\) 5.01468 0.297044
\(286\) 0.329979 0.0195121
\(287\) −0.491103 −0.0289889
\(288\) 6.94731 0.409374
\(289\) 1.00000 0.0588235
\(290\) −8.27928 −0.486176
\(291\) 3.69690 0.216716
\(292\) −6.72940 −0.393808
\(293\) 5.23654 0.305922 0.152961 0.988232i \(-0.451119\pi\)
0.152961 + 0.988232i \(0.451119\pi\)
\(294\) −1.91755 −0.111834
\(295\) 18.7290 1.09044
\(296\) −13.4120 −0.779557
\(297\) −1.30596 −0.0757796
\(298\) 28.2199 1.63474
\(299\) 1.44012 0.0832841
\(300\) 1.15560 0.0667187
\(301\) 0.198048 0.0114153
\(302\) −25.1495 −1.44719
\(303\) −0.196235 −0.0112734
\(304\) 16.2750 0.933433
\(305\) 0.679092 0.0388847
\(306\) 3.70601 0.211858
\(307\) 13.8668 0.791422 0.395711 0.918375i \(-0.370498\pi\)
0.395711 + 0.918375i \(0.370498\pi\)
\(308\) −0.0839245 −0.00478204
\(309\) −0.432947 −0.0246295
\(310\) 2.57798 0.146419
\(311\) −21.6256 −1.22628 −0.613138 0.789976i \(-0.710093\pi\)
−0.613138 + 0.789976i \(0.710093\pi\)
\(312\) −0.175491 −0.00993521
\(313\) 23.6956 1.33935 0.669676 0.742653i \(-0.266433\pi\)
0.669676 + 0.742653i \(0.266433\pi\)
\(314\) −27.0413 −1.52603
\(315\) 2.44058 0.137511
\(316\) −2.91094 −0.163753
\(317\) 27.9898 1.57206 0.786032 0.618185i \(-0.212132\pi\)
0.786032 + 0.618185i \(0.212132\pi\)
\(318\) −0.541381 −0.0303591
\(319\) −1.57962 −0.0884420
\(320\) 37.1577 2.07718
\(321\) −1.38049 −0.0770512
\(322\) 1.36240 0.0759234
\(323\) −5.47442 −0.304605
\(324\) −3.63119 −0.201733
\(325\) 3.26653 0.181195
\(326\) −3.65632 −0.202505
\(327\) 1.08198 0.0598338
\(328\) 7.54576 0.416645
\(329\) −0.205563 −0.0113331
\(330\) −1.15005 −0.0633082
\(331\) 20.5936 1.13193 0.565965 0.824430i \(-0.308504\pi\)
0.565965 + 0.824430i \(0.308504\pi\)
\(332\) −0.257766 −0.0141467
\(333\) 13.0103 0.712961
\(334\) −29.6890 −1.62451
\(335\) 20.9969 1.14718
\(336\) −0.129190 −0.00704791
\(337\) −11.0382 −0.601289 −0.300644 0.953736i \(-0.597202\pi\)
−0.300644 + 0.953736i \(0.597202\pi\)
\(338\) 16.2346 0.883044
\(339\) −2.88097 −0.156473
\(340\) −1.76907 −0.0959415
\(341\) 0.491859 0.0266357
\(342\) −20.2882 −1.09706
\(343\) 2.76490 0.149291
\(344\) −3.04299 −0.164067
\(345\) −5.01912 −0.270220
\(346\) −5.01078 −0.269381
\(347\) 10.0228 0.538054 0.269027 0.963133i \(-0.413298\pi\)
0.269027 + 0.963133i \(0.413298\pi\)
\(348\) 0.146876 0.00787337
\(349\) −16.3768 −0.876631 −0.438315 0.898821i \(-0.644425\pi\)
−0.438315 + 0.898821i \(0.644425\pi\)
\(350\) 3.09024 0.165181
\(351\) 0.343246 0.0183211
\(352\) 2.35354 0.125444
\(353\) −25.6068 −1.36291 −0.681456 0.731859i \(-0.738653\pi\)
−0.681456 + 0.731859i \(0.738653\pi\)
\(354\) 1.23588 0.0656863
\(355\) −20.8511 −1.10666
\(356\) 7.10328 0.376473
\(357\) 0.0434558 0.00229993
\(358\) 11.9964 0.634029
\(359\) −19.4853 −1.02840 −0.514198 0.857672i \(-0.671910\pi\)
−0.514198 + 0.857672i \(0.671910\pi\)
\(360\) −37.4993 −1.97639
\(361\) 10.9692 0.577328
\(362\) 1.43187 0.0752573
\(363\) −0.219421 −0.0115166
\(364\) 0.0220579 0.00115615
\(365\) 66.2956 3.47007
\(366\) 0.0448116 0.00234234
\(367\) 31.7509 1.65738 0.828692 0.559705i \(-0.189086\pi\)
0.828692 + 0.559705i \(0.189086\pi\)
\(368\) −16.2894 −0.849142
\(369\) −7.31976 −0.381052
\(370\) 23.1011 1.20097
\(371\) 0.389210 0.0202068
\(372\) −0.0457338 −0.00237119
\(373\) −4.50240 −0.233125 −0.116563 0.993183i \(-0.537188\pi\)
−0.116563 + 0.993183i \(0.537188\pi\)
\(374\) 1.25548 0.0649196
\(375\) −6.80447 −0.351381
\(376\) 3.15847 0.162886
\(377\) 0.415173 0.0213825
\(378\) 0.324722 0.0167019
\(379\) −31.7529 −1.63104 −0.815519 0.578731i \(-0.803548\pi\)
−0.815519 + 0.578731i \(0.803548\pi\)
\(380\) 9.68465 0.496812
\(381\) −3.22910 −0.165432
\(382\) −21.6333 −1.10686
\(383\) 0.324770 0.0165950 0.00829749 0.999966i \(-0.497359\pi\)
0.00829749 + 0.999966i \(0.497359\pi\)
\(384\) 1.41912 0.0724190
\(385\) 0.826794 0.0421373
\(386\) 4.14706 0.211080
\(387\) 2.95185 0.150051
\(388\) 7.13967 0.362462
\(389\) −35.2287 −1.78617 −0.893084 0.449890i \(-0.851463\pi\)
−0.893084 + 0.449890i \(0.851463\pi\)
\(390\) 0.302268 0.0153059
\(391\) 5.47926 0.277098
\(392\) −21.1816 −1.06983
\(393\) −4.22725 −0.213237
\(394\) −10.9109 −0.549684
\(395\) 28.6775 1.44292
\(396\) −1.25087 −0.0628588
\(397\) −0.994514 −0.0499132 −0.0249566 0.999689i \(-0.507945\pi\)
−0.0249566 + 0.999689i \(0.507945\pi\)
\(398\) −3.98098 −0.199548
\(399\) −0.237895 −0.0119097
\(400\) −36.9482 −1.84741
\(401\) −11.5538 −0.576972 −0.288486 0.957484i \(-0.593152\pi\)
−0.288486 + 0.957484i \(0.593152\pi\)
\(402\) 1.38553 0.0691041
\(403\) −0.129276 −0.00643967
\(404\) −0.378981 −0.0188550
\(405\) 35.7732 1.77759
\(406\) 0.392767 0.0194927
\(407\) 4.40751 0.218472
\(408\) −0.667696 −0.0330559
\(409\) 27.1171 1.34085 0.670426 0.741976i \(-0.266111\pi\)
0.670426 + 0.741976i \(0.266111\pi\)
\(410\) −12.9969 −0.641873
\(411\) −2.13075 −0.105102
\(412\) −0.836133 −0.0411933
\(413\) −0.888499 −0.0437202
\(414\) 20.3062 0.997995
\(415\) 2.53942 0.124655
\(416\) −0.618582 −0.0303285
\(417\) −0.412951 −0.0202223
\(418\) −6.87304 −0.336172
\(419\) −17.8829 −0.873636 −0.436818 0.899550i \(-0.643895\pi\)
−0.436818 + 0.899550i \(0.643895\pi\)
\(420\) −0.0768766 −0.00375119
\(421\) 6.20436 0.302382 0.151191 0.988505i \(-0.451689\pi\)
0.151191 + 0.988505i \(0.451689\pi\)
\(422\) −8.39436 −0.408631
\(423\) −3.06387 −0.148971
\(424\) −5.98018 −0.290423
\(425\) 12.4283 0.602861
\(426\) −1.37591 −0.0666633
\(427\) −0.0322160 −0.00155904
\(428\) −2.66608 −0.128870
\(429\) 0.0576705 0.00278436
\(430\) 5.24130 0.252758
\(431\) 24.1398 1.16277 0.581387 0.813627i \(-0.302510\pi\)
0.581387 + 0.813627i \(0.302510\pi\)
\(432\) −3.88251 −0.186797
\(433\) −19.4029 −0.932442 −0.466221 0.884668i \(-0.654385\pi\)
−0.466221 + 0.884668i \(0.654385\pi\)
\(434\) −0.122299 −0.00587053
\(435\) −1.44697 −0.0693768
\(436\) 2.08959 0.100073
\(437\) −29.9958 −1.43489
\(438\) 4.37469 0.209031
\(439\) 9.20578 0.439368 0.219684 0.975571i \(-0.429497\pi\)
0.219684 + 0.975571i \(0.429497\pi\)
\(440\) −12.7036 −0.605622
\(441\) 20.5472 0.978438
\(442\) −0.329979 −0.0156955
\(443\) 12.3157 0.585138 0.292569 0.956244i \(-0.405490\pi\)
0.292569 + 0.956244i \(0.405490\pi\)
\(444\) −0.409817 −0.0194491
\(445\) −69.9789 −3.31732
\(446\) −5.22403 −0.247365
\(447\) 4.93200 0.233275
\(448\) −1.76276 −0.0832824
\(449\) 21.5655 1.01774 0.508869 0.860844i \(-0.330064\pi\)
0.508869 + 0.860844i \(0.330064\pi\)
\(450\) 46.0593 2.17126
\(451\) −2.47972 −0.116765
\(452\) −5.56391 −0.261704
\(453\) −4.39538 −0.206513
\(454\) 23.5528 1.10539
\(455\) −0.217307 −0.0101875
\(456\) 3.65525 0.171173
\(457\) 0.729361 0.0341181 0.0170590 0.999854i \(-0.494570\pi\)
0.0170590 + 0.999854i \(0.494570\pi\)
\(458\) 8.81181 0.411749
\(459\) 1.30596 0.0609571
\(460\) −9.69323 −0.451949
\(461\) −28.7517 −1.33910 −0.669549 0.742768i \(-0.733513\pi\)
−0.669549 + 0.742768i \(0.733513\pi\)
\(462\) 0.0545581 0.00253827
\(463\) 30.2490 1.40579 0.702894 0.711294i \(-0.251891\pi\)
0.702894 + 0.711294i \(0.251891\pi\)
\(464\) −4.69608 −0.218010
\(465\) 0.450553 0.0208939
\(466\) 17.9480 0.831427
\(467\) −19.5618 −0.905211 −0.452606 0.891711i \(-0.649505\pi\)
−0.452606 + 0.891711i \(0.649505\pi\)
\(468\) 0.328768 0.0151973
\(469\) −0.996088 −0.0459951
\(470\) −5.44019 −0.250937
\(471\) −4.72600 −0.217763
\(472\) 13.6517 0.628372
\(473\) 1.00000 0.0459800
\(474\) 1.89236 0.0869189
\(475\) −68.0376 −3.12178
\(476\) 0.0839245 0.00384667
\(477\) 5.80107 0.265613
\(478\) 21.4570 0.981419
\(479\) −12.0797 −0.551933 −0.275967 0.961167i \(-0.588998\pi\)
−0.275967 + 0.961167i \(0.588998\pi\)
\(480\) 2.15589 0.0984025
\(481\) −1.15843 −0.0528197
\(482\) 14.1306 0.643629
\(483\) 0.238106 0.0108342
\(484\) −0.423759 −0.0192618
\(485\) −70.3375 −3.19386
\(486\) 7.27943 0.330202
\(487\) 24.9364 1.12997 0.564987 0.825100i \(-0.308881\pi\)
0.564987 + 0.825100i \(0.308881\pi\)
\(488\) 0.494996 0.0224074
\(489\) −0.639015 −0.0288973
\(490\) 36.4835 1.64816
\(491\) −12.8485 −0.579844 −0.289922 0.957050i \(-0.593629\pi\)
−0.289922 + 0.957050i \(0.593629\pi\)
\(492\) 0.230568 0.0103948
\(493\) 1.57962 0.0711427
\(494\) 1.80645 0.0812758
\(495\) 12.3232 0.553885
\(496\) 1.46225 0.0656571
\(497\) 0.989173 0.0443705
\(498\) 0.167570 0.00750899
\(499\) −5.85117 −0.261934 −0.130967 0.991387i \(-0.541808\pi\)
−0.130967 + 0.991387i \(0.541808\pi\)
\(500\) −13.1412 −0.587692
\(501\) −5.18874 −0.231816
\(502\) 22.8847 1.02139
\(503\) 18.8977 0.842608 0.421304 0.906919i \(-0.361572\pi\)
0.421304 + 0.906919i \(0.361572\pi\)
\(504\) 1.77896 0.0792411
\(505\) 3.73358 0.166142
\(506\) 6.87913 0.305815
\(507\) 2.83731 0.126010
\(508\) −6.23623 −0.276688
\(509\) 33.7919 1.49780 0.748899 0.662684i \(-0.230583\pi\)
0.748899 + 0.662684i \(0.230583\pi\)
\(510\) 1.15005 0.0509251
\(511\) −3.14505 −0.139129
\(512\) 25.0899 1.10883
\(513\) −7.14938 −0.315653
\(514\) −26.4016 −1.16452
\(515\) 8.23729 0.362978
\(516\) −0.0929815 −0.00409328
\(517\) −1.03795 −0.0456489
\(518\) −1.09591 −0.0481515
\(519\) −0.875733 −0.0384404
\(520\) 3.33890 0.146421
\(521\) 23.6466 1.03598 0.517989 0.855388i \(-0.326681\pi\)
0.517989 + 0.855388i \(0.326681\pi\)
\(522\) 5.85410 0.256227
\(523\) 9.70761 0.424484 0.212242 0.977217i \(-0.431923\pi\)
0.212242 + 0.977217i \(0.431923\pi\)
\(524\) −8.16392 −0.356642
\(525\) 0.540082 0.0235711
\(526\) −3.56618 −0.155493
\(527\) −0.491859 −0.0214257
\(528\) −0.652319 −0.0283885
\(529\) 7.02234 0.305319
\(530\) 10.3004 0.447419
\(531\) −13.2429 −0.574691
\(532\) −0.459438 −0.0199192
\(533\) 0.651745 0.0282302
\(534\) −4.61774 −0.199829
\(535\) 26.2652 1.13554
\(536\) 15.3048 0.661068
\(537\) 2.09661 0.0904754
\(538\) 17.0658 0.735759
\(539\) 6.96078 0.299822
\(540\) −2.31034 −0.0994213
\(541\) −9.46586 −0.406969 −0.203485 0.979078i \(-0.565227\pi\)
−0.203485 + 0.979078i \(0.565227\pi\)
\(542\) −13.1448 −0.564616
\(543\) 0.250247 0.0107391
\(544\) −2.35354 −0.100907
\(545\) −20.5859 −0.881803
\(546\) −0.0143395 −0.000613676 0
\(547\) 16.8704 0.721327 0.360663 0.932696i \(-0.382550\pi\)
0.360663 + 0.932696i \(0.382550\pi\)
\(548\) −4.11504 −0.175786
\(549\) −0.480171 −0.0204932
\(550\) 15.6035 0.665336
\(551\) −8.64752 −0.368397
\(552\) −3.65848 −0.155715
\(553\) −1.36046 −0.0578524
\(554\) −16.6138 −0.705852
\(555\) 4.03737 0.171377
\(556\) −0.797515 −0.0338222
\(557\) 29.1365 1.23455 0.617277 0.786746i \(-0.288236\pi\)
0.617277 + 0.786746i \(0.288236\pi\)
\(558\) −1.82283 −0.0771667
\(559\) −0.262830 −0.0111165
\(560\) 2.45799 0.103869
\(561\) 0.219421 0.00926396
\(562\) 9.82881 0.414603
\(563\) 22.9194 0.965936 0.482968 0.875638i \(-0.339559\pi\)
0.482968 + 0.875638i \(0.339559\pi\)
\(564\) 0.0965100 0.00406380
\(565\) 54.8136 2.30603
\(566\) −35.9373 −1.51056
\(567\) −1.69707 −0.0712704
\(568\) −15.1986 −0.637718
\(569\) 28.3524 1.18860 0.594298 0.804245i \(-0.297430\pi\)
0.594298 + 0.804245i \(0.297430\pi\)
\(570\) −6.29585 −0.263704
\(571\) −12.3064 −0.515009 −0.257504 0.966277i \(-0.582900\pi\)
−0.257504 + 0.966277i \(0.582900\pi\)
\(572\) 0.111377 0.00465689
\(573\) −3.78085 −0.157947
\(574\) 0.616572 0.0257352
\(575\) 68.0979 2.83988
\(576\) −26.2734 −1.09473
\(577\) 1.38978 0.0578574 0.0289287 0.999581i \(-0.490790\pi\)
0.0289287 + 0.999581i \(0.490790\pi\)
\(578\) −1.25548 −0.0522213
\(579\) 0.724780 0.0301208
\(580\) −2.79447 −0.116034
\(581\) −0.120469 −0.00499791
\(582\) −4.64140 −0.192392
\(583\) 1.96523 0.0813915
\(584\) 48.3235 1.99964
\(585\) −3.23890 −0.133912
\(586\) −6.57439 −0.271586
\(587\) −0.186409 −0.00769394 −0.00384697 0.999993i \(-0.501225\pi\)
−0.00384697 + 0.999993i \(0.501225\pi\)
\(588\) −0.647224 −0.0266911
\(589\) 2.69264 0.110948
\(590\) −23.5140 −0.968054
\(591\) −1.90690 −0.0784393
\(592\) 13.1031 0.538535
\(593\) 26.3400 1.08165 0.540826 0.841134i \(-0.318112\pi\)
0.540826 + 0.841134i \(0.318112\pi\)
\(594\) 1.63961 0.0672742
\(595\) −0.826794 −0.0338953
\(596\) 9.52497 0.390158
\(597\) −0.695755 −0.0284753
\(598\) −1.80804 −0.0739365
\(599\) 40.5886 1.65840 0.829202 0.558949i \(-0.188795\pi\)
0.829202 + 0.558949i \(0.188795\pi\)
\(600\) −8.29832 −0.338777
\(601\) 1.05716 0.0431225 0.0215612 0.999768i \(-0.493136\pi\)
0.0215612 + 0.999768i \(0.493136\pi\)
\(602\) −0.248646 −0.0101341
\(603\) −14.8464 −0.604594
\(604\) −8.48861 −0.345397
\(605\) 4.17472 0.169727
\(606\) 0.246370 0.0100081
\(607\) 24.8145 1.00719 0.503594 0.863940i \(-0.332011\pi\)
0.503594 + 0.863940i \(0.332011\pi\)
\(608\) 12.8843 0.522526
\(609\) 0.0686439 0.00278159
\(610\) −0.852589 −0.0345203
\(611\) 0.272804 0.0110365
\(612\) 1.25087 0.0505636
\(613\) −41.2735 −1.66702 −0.833511 0.552504i \(-0.813673\pi\)
−0.833511 + 0.552504i \(0.813673\pi\)
\(614\) −17.4096 −0.702594
\(615\) −2.27147 −0.0915946
\(616\) 0.602658 0.0242818
\(617\) 23.9969 0.966079 0.483040 0.875599i \(-0.339533\pi\)
0.483040 + 0.875599i \(0.339533\pi\)
\(618\) 0.543558 0.0218651
\(619\) 23.9276 0.961733 0.480867 0.876794i \(-0.340322\pi\)
0.480867 + 0.876794i \(0.340322\pi\)
\(620\) 0.870135 0.0349455
\(621\) 7.15571 0.287149
\(622\) 27.1506 1.08864
\(623\) 3.31979 0.133004
\(624\) 0.171449 0.00686346
\(625\) 67.3209 2.69284
\(626\) −29.7494 −1.18903
\(627\) −1.20120 −0.0479714
\(628\) −9.12714 −0.364212
\(629\) −4.40751 −0.175739
\(630\) −3.06411 −0.122077
\(631\) −2.18475 −0.0869733 −0.0434867 0.999054i \(-0.513847\pi\)
−0.0434867 + 0.999054i \(0.513847\pi\)
\(632\) 20.9033 0.831489
\(633\) −1.46708 −0.0583113
\(634\) −35.1408 −1.39562
\(635\) 61.4371 2.43806
\(636\) −0.182730 −0.00724572
\(637\) −1.82950 −0.0724876
\(638\) 1.98319 0.0785154
\(639\) 14.7434 0.583239
\(640\) −27.0002 −1.06728
\(641\) −8.17441 −0.322870 −0.161435 0.986883i \(-0.551612\pi\)
−0.161435 + 0.986883i \(0.551612\pi\)
\(642\) 1.73318 0.0684031
\(643\) −8.45652 −0.333493 −0.166746 0.986000i \(-0.553326\pi\)
−0.166746 + 0.986000i \(0.553326\pi\)
\(644\) 0.459845 0.0181204
\(645\) 0.916021 0.0360683
\(646\) 6.87304 0.270416
\(647\) −20.3019 −0.798150 −0.399075 0.916918i \(-0.630669\pi\)
−0.399075 + 0.916918i \(0.630669\pi\)
\(648\) 26.0754 1.02434
\(649\) −4.48629 −0.176102
\(650\) −4.10108 −0.160858
\(651\) −0.0213742 −0.000837719 0
\(652\) −1.23410 −0.0483313
\(653\) −20.4317 −0.799555 −0.399778 0.916612i \(-0.630913\pi\)
−0.399778 + 0.916612i \(0.630913\pi\)
\(654\) −1.35841 −0.0531182
\(655\) 80.4280 3.14258
\(656\) −7.37198 −0.287827
\(657\) −46.8762 −1.82881
\(658\) 0.258082 0.0100611
\(659\) 18.0598 0.703511 0.351755 0.936092i \(-0.385585\pi\)
0.351755 + 0.936092i \(0.385585\pi\)
\(660\) −0.388172 −0.0151096
\(661\) 8.33527 0.324204 0.162102 0.986774i \(-0.448173\pi\)
0.162102 + 0.986774i \(0.448173\pi\)
\(662\) −25.8550 −1.00488
\(663\) −0.0576705 −0.00223974
\(664\) 1.85100 0.0718329
\(665\) 4.52622 0.175519
\(666\) −16.3343 −0.632940
\(667\) 8.65518 0.335130
\(668\) −10.0208 −0.387717
\(669\) −0.913003 −0.0352987
\(670\) −26.3613 −1.01842
\(671\) −0.162668 −0.00627971
\(672\) −0.102275 −0.00394535
\(673\) 14.5473 0.560758 0.280379 0.959889i \(-0.409540\pi\)
0.280379 + 0.959889i \(0.409540\pi\)
\(674\) 13.8583 0.533801
\(675\) 16.2309 0.624726
\(676\) 5.47959 0.210753
\(677\) −38.9940 −1.49866 −0.749331 0.662195i \(-0.769625\pi\)
−0.749331 + 0.662195i \(0.769625\pi\)
\(678\) 3.61702 0.138911
\(679\) 3.33680 0.128054
\(680\) 12.7036 0.487162
\(681\) 4.11633 0.157738
\(682\) −0.617522 −0.0236461
\(683\) −5.40974 −0.206998 −0.103499 0.994630i \(-0.533004\pi\)
−0.103499 + 0.994630i \(0.533004\pi\)
\(684\) −6.84781 −0.261832
\(685\) 40.5399 1.54895
\(686\) −3.47129 −0.132535
\(687\) 1.54004 0.0587562
\(688\) 2.97291 0.113341
\(689\) −0.516522 −0.0196779
\(690\) 6.30143 0.239891
\(691\) 16.8797 0.642132 0.321066 0.947057i \(-0.395959\pi\)
0.321066 + 0.947057i \(0.395959\pi\)
\(692\) −1.69127 −0.0642924
\(693\) −0.584608 −0.0222074
\(694\) −12.5835 −0.477664
\(695\) 7.85683 0.298027
\(696\) −1.05471 −0.0399786
\(697\) 2.47972 0.0939260
\(698\) 20.5608 0.778239
\(699\) 3.13678 0.118644
\(700\) 1.04304 0.0394231
\(701\) 33.0451 1.24809 0.624047 0.781387i \(-0.285487\pi\)
0.624047 + 0.781387i \(0.285487\pi\)
\(702\) −0.430940 −0.0162648
\(703\) 24.1285 0.910025
\(704\) −8.90065 −0.335456
\(705\) −0.950782 −0.0358085
\(706\) 32.1489 1.20994
\(707\) −0.177120 −0.00666130
\(708\) 0.417142 0.0156771
\(709\) 45.6191 1.71326 0.856631 0.515929i \(-0.172553\pi\)
0.856631 + 0.515929i \(0.172553\pi\)
\(710\) 26.1783 0.982453
\(711\) −20.2772 −0.760456
\(712\) −51.0083 −1.91162
\(713\) −2.69503 −0.100930
\(714\) −0.0545581 −0.00204179
\(715\) −1.09724 −0.0410346
\(716\) 4.04910 0.151322
\(717\) 3.75003 0.140048
\(718\) 24.4635 0.912970
\(719\) 35.9360 1.34019 0.670094 0.742277i \(-0.266254\pi\)
0.670094 + 0.742277i \(0.266254\pi\)
\(720\) 36.6357 1.36533
\(721\) −0.390775 −0.0145532
\(722\) −13.7717 −0.512530
\(723\) 2.46960 0.0918453
\(724\) 0.483293 0.0179614
\(725\) 19.6320 0.729115
\(726\) 0.275480 0.0102240
\(727\) −36.2870 −1.34581 −0.672905 0.739729i \(-0.734954\pi\)
−0.672905 + 0.739729i \(0.734954\pi\)
\(728\) −0.158397 −0.00587058
\(729\) −24.4348 −0.904993
\(730\) −83.2331 −3.08060
\(731\) −1.00000 −0.0369863
\(732\) 0.0151251 0.000559039 0
\(733\) 24.6054 0.908821 0.454410 0.890792i \(-0.349850\pi\)
0.454410 + 0.890792i \(0.349850\pi\)
\(734\) −39.8628 −1.47136
\(735\) 6.37622 0.235190
\(736\) −12.8957 −0.475341
\(737\) −5.02953 −0.185265
\(738\) 9.18985 0.338283
\(739\) −27.7395 −1.02041 −0.510207 0.860052i \(-0.670431\pi\)
−0.510207 + 0.860052i \(0.670431\pi\)
\(740\) 7.79721 0.286631
\(741\) 0.315712 0.0115980
\(742\) −0.488647 −0.0179388
\(743\) 35.3944 1.29849 0.649247 0.760577i \(-0.275084\pi\)
0.649247 + 0.760577i \(0.275084\pi\)
\(744\) 0.328412 0.0120402
\(745\) −93.8366 −3.43791
\(746\) 5.65269 0.206960
\(747\) −1.79557 −0.0656963
\(748\) 0.423759 0.0154942
\(749\) −1.24602 −0.0455285
\(750\) 8.54290 0.311943
\(751\) 8.13716 0.296929 0.148465 0.988918i \(-0.452567\pi\)
0.148465 + 0.988918i \(0.452567\pi\)
\(752\) −3.08573 −0.112525
\(753\) 3.99956 0.145752
\(754\) −0.521243 −0.0189826
\(755\) 83.6268 3.04349
\(756\) 0.109602 0.00398619
\(757\) −10.2325 −0.371906 −0.185953 0.982559i \(-0.559537\pi\)
−0.185953 + 0.982559i \(0.559537\pi\)
\(758\) 39.8653 1.44797
\(759\) 1.20227 0.0436395
\(760\) −69.5450 −2.52266
\(761\) 30.3022 1.09845 0.549227 0.835673i \(-0.314922\pi\)
0.549227 + 0.835673i \(0.314922\pi\)
\(762\) 4.05408 0.146864
\(763\) 0.976591 0.0353550
\(764\) −7.30180 −0.264170
\(765\) −12.3232 −0.445545
\(766\) −0.407744 −0.0147324
\(767\) 1.17913 0.0425760
\(768\) 2.12430 0.0766541
\(769\) 3.84778 0.138755 0.0693773 0.997590i \(-0.477899\pi\)
0.0693773 + 0.997590i \(0.477899\pi\)
\(770\) −1.03803 −0.0374079
\(771\) −4.61420 −0.166176
\(772\) 1.39974 0.0503777
\(773\) 5.66585 0.203787 0.101893 0.994795i \(-0.467510\pi\)
0.101893 + 0.994795i \(0.467510\pi\)
\(774\) −3.70601 −0.133210
\(775\) −6.11297 −0.219584
\(776\) −51.2696 −1.84047
\(777\) −0.191532 −0.00687117
\(778\) 44.2291 1.58569
\(779\) −13.5750 −0.486375
\(780\) 0.102023 0.00365302
\(781\) 4.99462 0.178721
\(782\) −6.87913 −0.245997
\(783\) 2.06293 0.0737230
\(784\) 20.6938 0.739063
\(785\) 89.9173 3.20929
\(786\) 5.30725 0.189303
\(787\) 9.40645 0.335304 0.167652 0.985846i \(-0.446382\pi\)
0.167652 + 0.985846i \(0.446382\pi\)
\(788\) −3.68272 −0.131191
\(789\) −0.623262 −0.0221887
\(790\) −36.0042 −1.28097
\(791\) −2.60035 −0.0924577
\(792\) 8.98247 0.319178
\(793\) 0.0427540 0.00151824
\(794\) 1.24860 0.0443111
\(795\) 1.80019 0.0638462
\(796\) −1.34368 −0.0476256
\(797\) −43.9783 −1.55779 −0.778895 0.627154i \(-0.784220\pi\)
−0.778895 + 0.627154i \(0.784220\pi\)
\(798\) 0.298674 0.0105729
\(799\) 1.03795 0.0367200
\(800\) −29.2505 −1.03416
\(801\) 49.4806 1.74831
\(802\) 14.5057 0.512213
\(803\) −15.8803 −0.560402
\(804\) 0.467654 0.0164929
\(805\) −4.53023 −0.159669
\(806\) 0.162303 0.00571689
\(807\) 2.98259 0.104992
\(808\) 2.72144 0.0957400
\(809\) −14.1277 −0.496704 −0.248352 0.968670i \(-0.579889\pi\)
−0.248352 + 0.968670i \(0.579889\pi\)
\(810\) −44.9127 −1.57807
\(811\) −42.2820 −1.48472 −0.742360 0.670001i \(-0.766294\pi\)
−0.742360 + 0.670001i \(0.766294\pi\)
\(812\) 0.132569 0.00465227
\(813\) −2.29731 −0.0805702
\(814\) −5.53356 −0.193951
\(815\) 12.1580 0.425875
\(816\) 0.652319 0.0228357
\(817\) 5.47442 0.191526
\(818\) −34.0451 −1.19036
\(819\) 0.153653 0.00536907
\(820\) −4.38680 −0.153194
\(821\) 25.3616 0.885128 0.442564 0.896737i \(-0.354069\pi\)
0.442564 + 0.896737i \(0.354069\pi\)
\(822\) 2.67513 0.0933058
\(823\) 7.98785 0.278439 0.139219 0.990262i \(-0.455541\pi\)
0.139219 + 0.990262i \(0.455541\pi\)
\(824\) 6.00423 0.209167
\(825\) 2.72703 0.0949429
\(826\) 1.11550 0.0388131
\(827\) −33.2617 −1.15662 −0.578311 0.815816i \(-0.696288\pi\)
−0.578311 + 0.815816i \(0.696288\pi\)
\(828\) 6.85387 0.238188
\(829\) 28.0611 0.974602 0.487301 0.873234i \(-0.337981\pi\)
0.487301 + 0.873234i \(0.337981\pi\)
\(830\) −3.18820 −0.110664
\(831\) −2.90359 −0.100724
\(832\) 2.33936 0.0811028
\(833\) −6.96078 −0.241177
\(834\) 0.518453 0.0179526
\(835\) 98.7214 3.41639
\(836\) −2.31983 −0.0802331
\(837\) −0.642349 −0.0222028
\(838\) 22.4517 0.775581
\(839\) 37.4342 1.29237 0.646187 0.763179i \(-0.276363\pi\)
0.646187 + 0.763179i \(0.276363\pi\)
\(840\) 0.552047 0.0190474
\(841\) −26.5048 −0.913958
\(842\) −7.78948 −0.268443
\(843\) 1.71778 0.0591635
\(844\) −2.83332 −0.0975268
\(845\) −53.9830 −1.85707
\(846\) 3.84664 0.132250
\(847\) −0.198048 −0.00680501
\(848\) 5.84245 0.200631
\(849\) −6.28076 −0.215555
\(850\) −15.6035 −0.535196
\(851\) −24.1499 −0.827848
\(852\) −0.464407 −0.0159103
\(853\) 28.2181 0.966170 0.483085 0.875573i \(-0.339516\pi\)
0.483085 + 0.875573i \(0.339516\pi\)
\(854\) 0.0404467 0.00138406
\(855\) 67.4621 2.30716
\(856\) 19.1450 0.654361
\(857\) −7.20776 −0.246213 −0.123106 0.992393i \(-0.539286\pi\)
−0.123106 + 0.992393i \(0.539286\pi\)
\(858\) −0.0724044 −0.00247185
\(859\) −22.9052 −0.781514 −0.390757 0.920494i \(-0.627787\pi\)
−0.390757 + 0.920494i \(0.627787\pi\)
\(860\) 1.76907 0.0603249
\(861\) 0.107758 0.00367239
\(862\) −30.3072 −1.03227
\(863\) −22.4308 −0.763552 −0.381776 0.924255i \(-0.624687\pi\)
−0.381776 + 0.924255i \(0.624687\pi\)
\(864\) −3.07363 −0.104567
\(865\) 16.6618 0.566517
\(866\) 24.3600 0.827786
\(867\) −0.219421 −0.00745192
\(868\) −0.0412790 −0.00140110
\(869\) −6.86933 −0.233026
\(870\) 1.81665 0.0615901
\(871\) 1.32191 0.0447913
\(872\) −15.0053 −0.508142
\(873\) 49.7341 1.68324
\(874\) 37.6592 1.27384
\(875\) −6.14167 −0.207626
\(876\) 1.47657 0.0498887
\(877\) 26.0520 0.879713 0.439856 0.898068i \(-0.355029\pi\)
0.439856 + 0.898068i \(0.355029\pi\)
\(878\) −11.5577 −0.390054
\(879\) −1.14901 −0.0387550
\(880\) 12.4111 0.418377
\(881\) −32.9724 −1.11087 −0.555434 0.831561i \(-0.687448\pi\)
−0.555434 + 0.831561i \(0.687448\pi\)
\(882\) −25.7967 −0.868620
\(883\) 31.3018 1.05339 0.526694 0.850055i \(-0.323431\pi\)
0.526694 + 0.850055i \(0.323431\pi\)
\(884\) −0.111377 −0.00374600
\(885\) −4.10953 −0.138140
\(886\) −15.4622 −0.519463
\(887\) −7.60261 −0.255271 −0.127635 0.991821i \(-0.540739\pi\)
−0.127635 + 0.991821i \(0.540739\pi\)
\(888\) 2.94288 0.0987565
\(889\) −2.91456 −0.0977513
\(890\) 87.8575 2.94499
\(891\) −8.56901 −0.287073
\(892\) −1.76324 −0.0590378
\(893\) −5.68216 −0.190146
\(894\) −6.19205 −0.207093
\(895\) −39.8903 −1.33338
\(896\) 1.28089 0.0427914
\(897\) −0.315992 −0.0105507
\(898\) −27.0751 −0.903509
\(899\) −0.776952 −0.0259128
\(900\) 15.5462 0.518207
\(901\) −1.96523 −0.0654713
\(902\) 3.11325 0.103660
\(903\) −0.0434558 −0.00144612
\(904\) 39.9542 1.32886
\(905\) −4.76123 −0.158268
\(906\) 5.51833 0.183334
\(907\) 39.5886 1.31452 0.657259 0.753664i \(-0.271716\pi\)
0.657259 + 0.753664i \(0.271716\pi\)
\(908\) 7.94970 0.263820
\(909\) −2.63994 −0.0875611
\(910\) 0.272825 0.00904407
\(911\) 25.4149 0.842034 0.421017 0.907053i \(-0.361673\pi\)
0.421017 + 0.907053i \(0.361673\pi\)
\(912\) −3.57107 −0.118250
\(913\) −0.608284 −0.0201313
\(914\) −0.915702 −0.0302887
\(915\) −0.149007 −0.00492602
\(916\) 2.97422 0.0982708
\(917\) −3.81549 −0.125999
\(918\) −1.63961 −0.0541153
\(919\) −50.7219 −1.67316 −0.836580 0.547845i \(-0.815448\pi\)
−0.836580 + 0.547845i \(0.815448\pi\)
\(920\) 69.6066 2.29486
\(921\) −3.04267 −0.100260
\(922\) 36.0973 1.18880
\(923\) −1.31274 −0.0432093
\(924\) 0.0184148 0.000605802 0
\(925\) −54.7778 −1.80108
\(926\) −37.9771 −1.24800
\(927\) −5.82441 −0.191299
\(928\) −3.71771 −0.122040
\(929\) −4.82556 −0.158322 −0.0791608 0.996862i \(-0.525224\pi\)
−0.0791608 + 0.996862i \(0.525224\pi\)
\(930\) −0.565663 −0.0185488
\(931\) 38.1062 1.24888
\(932\) 6.05793 0.198434
\(933\) 4.74511 0.155348
\(934\) 24.5595 0.803612
\(935\) −4.17472 −0.136528
\(936\) −2.36087 −0.0771673
\(937\) −19.6040 −0.640435 −0.320218 0.947344i \(-0.603756\pi\)
−0.320218 + 0.947344i \(0.603756\pi\)
\(938\) 1.25057 0.0408327
\(939\) −5.19930 −0.169673
\(940\) −1.83621 −0.0598905
\(941\) −25.6887 −0.837427 −0.418714 0.908118i \(-0.637519\pi\)
−0.418714 + 0.908118i \(0.637519\pi\)
\(942\) 5.93342 0.193321
\(943\) 13.5870 0.442454
\(944\) −13.3373 −0.434093
\(945\) −1.07976 −0.0351246
\(946\) −1.25548 −0.0408193
\(947\) 9.84383 0.319882 0.159941 0.987127i \(-0.448870\pi\)
0.159941 + 0.987127i \(0.448870\pi\)
\(948\) 0.638720 0.0207447
\(949\) 4.17381 0.135488
\(950\) 85.4202 2.77140
\(951\) −6.14155 −0.199153
\(952\) −0.602658 −0.0195323
\(953\) 50.3340 1.63048 0.815239 0.579125i \(-0.196606\pi\)
0.815239 + 0.579125i \(0.196606\pi\)
\(954\) −7.28316 −0.235801
\(955\) 71.9348 2.32775
\(956\) 7.24229 0.234232
\(957\) 0.346603 0.0112041
\(958\) 15.1658 0.489985
\(959\) −1.92320 −0.0621035
\(960\) −8.15319 −0.263143
\(961\) −30.7581 −0.992196
\(962\) 1.45439 0.0468913
\(963\) −18.5716 −0.598461
\(964\) 4.76943 0.153613
\(965\) −13.7897 −0.443907
\(966\) −0.298938 −0.00961819
\(967\) 38.3721 1.23396 0.616981 0.786978i \(-0.288356\pi\)
0.616981 + 0.786978i \(0.288356\pi\)
\(968\) 3.04299 0.0978055
\(969\) 1.20120 0.0385882
\(970\) 88.3076 2.83539
\(971\) −55.0151 −1.76552 −0.882759 0.469827i \(-0.844316\pi\)
−0.882759 + 0.469827i \(0.844316\pi\)
\(972\) 2.45700 0.0788082
\(973\) −0.372727 −0.0119491
\(974\) −31.3072 −1.00315
\(975\) −0.716745 −0.0229542
\(976\) −0.483596 −0.0154795
\(977\) −4.72353 −0.151119 −0.0755596 0.997141i \(-0.524074\pi\)
−0.0755596 + 0.997141i \(0.524074\pi\)
\(978\) 0.802274 0.0256539
\(979\) 16.7625 0.535733
\(980\) 12.3141 0.393360
\(981\) 14.5559 0.464733
\(982\) 16.1311 0.514763
\(983\) −11.4263 −0.364444 −0.182222 0.983257i \(-0.558329\pi\)
−0.182222 + 0.983257i \(0.558329\pi\)
\(984\) −1.65570 −0.0527817
\(985\) 36.2808 1.15600
\(986\) −1.98319 −0.0631577
\(987\) 0.0451049 0.00143571
\(988\) 0.609722 0.0193979
\(989\) −5.47926 −0.174230
\(990\) −15.4715 −0.491718
\(991\) −28.7124 −0.912081 −0.456040 0.889959i \(-0.650733\pi\)
−0.456040 + 0.889959i \(0.650733\pi\)
\(992\) 1.15761 0.0367541
\(993\) −4.51868 −0.143396
\(994\) −1.24189 −0.0393904
\(995\) 13.2375 0.419657
\(996\) 0.0565592 0.00179215
\(997\) 0.0920907 0.00291654 0.00145827 0.999999i \(-0.499536\pi\)
0.00145827 + 0.999999i \(0.499536\pi\)
\(998\) 7.34605 0.232535
\(999\) −5.75604 −0.182113
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 8041.2.a.f.1.18 66
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8041.2.a.f.1.18 66 1.1 even 1 trivial