Properties

Label 8035.2.a.b.1.3
Level $8035$
Weight $2$
Character 8035.1
Self dual yes
Analytic conductor $64.160$
Analytic rank $1$
Dimension $114$
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] = [8035,2,Mod(1,8035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8035, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("8035.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8035.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: \(64.1597980241\)
Analytic rank: \(1\)
Dimension: \(114\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 8035.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.71845 q^{2} -0.706981 q^{3} +5.38997 q^{4} +1.00000 q^{5} +1.92189 q^{6} -1.47518 q^{7} -9.21545 q^{8} -2.50018 q^{9} +O(q^{10})\) \(q-2.71845 q^{2} -0.706981 q^{3} +5.38997 q^{4} +1.00000 q^{5} +1.92189 q^{6} -1.47518 q^{7} -9.21545 q^{8} -2.50018 q^{9} -2.71845 q^{10} -4.87853 q^{11} -3.81061 q^{12} +1.58069 q^{13} +4.01021 q^{14} -0.706981 q^{15} +14.2718 q^{16} -5.03382 q^{17} +6.79661 q^{18} +0.358119 q^{19} +5.38997 q^{20} +1.04293 q^{21} +13.2620 q^{22} +5.10498 q^{23} +6.51515 q^{24} +1.00000 q^{25} -4.29702 q^{26} +3.88852 q^{27} -7.95119 q^{28} -1.87684 q^{29} +1.92189 q^{30} -3.56650 q^{31} -20.3663 q^{32} +3.44903 q^{33} +13.6842 q^{34} -1.47518 q^{35} -13.4759 q^{36} +9.21989 q^{37} -0.973528 q^{38} -1.11752 q^{39} -9.21545 q^{40} -7.76168 q^{41} -2.83514 q^{42} +1.91236 q^{43} -26.2951 q^{44} -2.50018 q^{45} -13.8776 q^{46} -5.66005 q^{47} -10.0899 q^{48} -4.82383 q^{49} -2.71845 q^{50} +3.55882 q^{51} +8.51986 q^{52} +11.8097 q^{53} -10.5708 q^{54} -4.87853 q^{55} +13.5945 q^{56} -0.253183 q^{57} +5.10210 q^{58} +8.68911 q^{59} -3.81061 q^{60} +0.0576245 q^{61} +9.69536 q^{62} +3.68822 q^{63} +26.8211 q^{64} +1.58069 q^{65} -9.37601 q^{66} +12.8902 q^{67} -27.1321 q^{68} -3.60912 q^{69} +4.01021 q^{70} +5.72097 q^{71} +23.0403 q^{72} +4.17106 q^{73} -25.0638 q^{74} -0.706981 q^{75} +1.93025 q^{76} +7.19673 q^{77} +3.03791 q^{78} +5.96417 q^{79} +14.2718 q^{80} +4.75142 q^{81} +21.0997 q^{82} -6.35712 q^{83} +5.62134 q^{84} -5.03382 q^{85} -5.19866 q^{86} +1.32689 q^{87} +44.9579 q^{88} +13.2929 q^{89} +6.79661 q^{90} -2.33181 q^{91} +27.5156 q^{92} +2.52145 q^{93} +15.3865 q^{94} +0.358119 q^{95} +14.3986 q^{96} -0.185315 q^{97} +13.1133 q^{98} +12.1972 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71845 −1.92223 −0.961117 0.276142i \(-0.910944\pi\)
−0.961117 + 0.276142i \(0.910944\pi\)
\(3\) −0.706981 −0.408176 −0.204088 0.978953i \(-0.565423\pi\)
−0.204088 + 0.978953i \(0.565423\pi\)
\(4\) 5.38997 2.69498
\(5\) 1.00000 0.447214
\(6\) 1.92189 0.784609
\(7\) −1.47518 −0.557567 −0.278784 0.960354i \(-0.589931\pi\)
−0.278784 + 0.960354i \(0.589931\pi\)
\(8\) −9.21545 −3.25815
\(9\) −2.50018 −0.833393
\(10\) −2.71845 −0.859649
\(11\) −4.87853 −1.47093 −0.735466 0.677562i \(-0.763037\pi\)
−0.735466 + 0.677562i \(0.763037\pi\)
\(12\) −3.81061 −1.10003
\(13\) 1.58069 0.438404 0.219202 0.975679i \(-0.429655\pi\)
0.219202 + 0.975679i \(0.429655\pi\)
\(14\) 4.01021 1.07177
\(15\) −0.706981 −0.182542
\(16\) 14.2718 3.56795
\(17\) −5.03382 −1.22088 −0.610440 0.792062i \(-0.709008\pi\)
−0.610440 + 0.792062i \(0.709008\pi\)
\(18\) 6.79661 1.60198
\(19\) 0.358119 0.0821581 0.0410791 0.999156i \(-0.486920\pi\)
0.0410791 + 0.999156i \(0.486920\pi\)
\(20\) 5.38997 1.20523
\(21\) 1.04293 0.227585
\(22\) 13.2620 2.82748
\(23\) 5.10498 1.06446 0.532230 0.846600i \(-0.321354\pi\)
0.532230 + 0.846600i \(0.321354\pi\)
\(24\) 6.51515 1.32990
\(25\) 1.00000 0.200000
\(26\) −4.29702 −0.842715
\(27\) 3.88852 0.748346
\(28\) −7.95119 −1.50263
\(29\) −1.87684 −0.348521 −0.174261 0.984700i \(-0.555753\pi\)
−0.174261 + 0.984700i \(0.555753\pi\)
\(30\) 1.92189 0.350888
\(31\) −3.56650 −0.640563 −0.320281 0.947322i \(-0.603777\pi\)
−0.320281 + 0.947322i \(0.603777\pi\)
\(32\) −20.3663 −3.60028
\(33\) 3.44903 0.600399
\(34\) 13.6842 2.34682
\(35\) −1.47518 −0.249352
\(36\) −13.4759 −2.24598
\(37\) 9.21989 1.51574 0.757870 0.652405i \(-0.226240\pi\)
0.757870 + 0.652405i \(0.226240\pi\)
\(38\) −0.973528 −0.157927
\(39\) −1.11752 −0.178946
\(40\) −9.21545 −1.45709
\(41\) −7.76168 −1.21217 −0.606085 0.795400i \(-0.707261\pi\)
−0.606085 + 0.795400i \(0.707261\pi\)
\(42\) −2.83514 −0.437472
\(43\) 1.91236 0.291633 0.145816 0.989312i \(-0.453419\pi\)
0.145816 + 0.989312i \(0.453419\pi\)
\(44\) −26.2951 −3.96414
\(45\) −2.50018 −0.372704
\(46\) −13.8776 −2.04614
\(47\) −5.66005 −0.825603 −0.412801 0.910821i \(-0.635450\pi\)
−0.412801 + 0.910821i \(0.635450\pi\)
\(48\) −10.0899 −1.45635
\(49\) −4.82383 −0.689119
\(50\) −2.71845 −0.384447
\(51\) 3.55882 0.498334
\(52\) 8.51986 1.18149
\(53\) 11.8097 1.62218 0.811092 0.584919i \(-0.198874\pi\)
0.811092 + 0.584919i \(0.198874\pi\)
\(54\) −10.5708 −1.43850
\(55\) −4.87853 −0.657821
\(56\) 13.5945 1.81664
\(57\) −0.253183 −0.0335350
\(58\) 5.10210 0.669939
\(59\) 8.68911 1.13123 0.565613 0.824671i \(-0.308640\pi\)
0.565613 + 0.824671i \(0.308640\pi\)
\(60\) −3.81061 −0.491947
\(61\) 0.0576245 0.00737806 0.00368903 0.999993i \(-0.498826\pi\)
0.00368903 + 0.999993i \(0.498826\pi\)
\(62\) 9.69536 1.23131
\(63\) 3.68822 0.464672
\(64\) 26.8211 3.35264
\(65\) 1.58069 0.196060
\(66\) −9.37601 −1.15411
\(67\) 12.8902 1.57479 0.787397 0.616447i \(-0.211428\pi\)
0.787397 + 0.616447i \(0.211428\pi\)
\(68\) −27.1321 −3.29025
\(69\) −3.60912 −0.434487
\(70\) 4.01021 0.479312
\(71\) 5.72097 0.678955 0.339477 0.940614i \(-0.389750\pi\)
0.339477 + 0.940614i \(0.389750\pi\)
\(72\) 23.0403 2.71532
\(73\) 4.17106 0.488186 0.244093 0.969752i \(-0.421510\pi\)
0.244093 + 0.969752i \(0.421510\pi\)
\(74\) −25.0638 −2.91361
\(75\) −0.706981 −0.0816352
\(76\) 1.93025 0.221415
\(77\) 7.19673 0.820143
\(78\) 3.03791 0.343976
\(79\) 5.96417 0.671021 0.335511 0.942036i \(-0.391091\pi\)
0.335511 + 0.942036i \(0.391091\pi\)
\(80\) 14.2718 1.59564
\(81\) 4.75142 0.527936
\(82\) 21.0997 2.33007
\(83\) −6.35712 −0.697784 −0.348892 0.937163i \(-0.613442\pi\)
−0.348892 + 0.937163i \(0.613442\pi\)
\(84\) 5.62134 0.613339
\(85\) −5.03382 −0.545995
\(86\) −5.19866 −0.560586
\(87\) 1.32689 0.142258
\(88\) 44.9579 4.79252
\(89\) 13.2929 1.40905 0.704524 0.709680i \(-0.251161\pi\)
0.704524 + 0.709680i \(0.251161\pi\)
\(90\) 6.79661 0.716425
\(91\) −2.33181 −0.244440
\(92\) 27.5156 2.86870
\(93\) 2.52145 0.261462
\(94\) 15.3865 1.58700
\(95\) 0.358119 0.0367422
\(96\) 14.3986 1.46955
\(97\) −0.185315 −0.0188159 −0.00940795 0.999956i \(-0.502995\pi\)
−0.00940795 + 0.999956i \(0.502995\pi\)
\(98\) 13.1133 1.32465
\(99\) 12.1972 1.22586
\(100\) 5.38997 0.538997
\(101\) −15.8166 −1.57381 −0.786906 0.617072i \(-0.788319\pi\)
−0.786906 + 0.617072i \(0.788319\pi\)
\(102\) −9.67446 −0.957915
\(103\) 7.77860 0.766449 0.383224 0.923655i \(-0.374814\pi\)
0.383224 + 0.923655i \(0.374814\pi\)
\(104\) −14.5668 −1.42839
\(105\) 1.04293 0.101779
\(106\) −32.1040 −3.11822
\(107\) −9.70917 −0.938621 −0.469310 0.883033i \(-0.655497\pi\)
−0.469310 + 0.883033i \(0.655497\pi\)
\(108\) 20.9590 2.01678
\(109\) 4.65543 0.445910 0.222955 0.974829i \(-0.428430\pi\)
0.222955 + 0.974829i \(0.428430\pi\)
\(110\) 13.2620 1.26449
\(111\) −6.51829 −0.618689
\(112\) −21.0535 −1.98937
\(113\) 6.86268 0.645587 0.322793 0.946469i \(-0.395378\pi\)
0.322793 + 0.946469i \(0.395378\pi\)
\(114\) 0.688266 0.0644620
\(115\) 5.10498 0.476041
\(116\) −10.1161 −0.939258
\(117\) −3.95200 −0.365363
\(118\) −23.6209 −2.17448
\(119\) 7.42581 0.680723
\(120\) 6.51515 0.594749
\(121\) 12.8001 1.16364
\(122\) −0.156649 −0.0141823
\(123\) 5.48736 0.494779
\(124\) −19.2233 −1.72631
\(125\) 1.00000 0.0894427
\(126\) −10.0262 −0.893209
\(127\) 3.18545 0.282663 0.141332 0.989962i \(-0.454862\pi\)
0.141332 + 0.989962i \(0.454862\pi\)
\(128\) −32.1792 −2.84427
\(129\) −1.35201 −0.119037
\(130\) −4.29702 −0.376874
\(131\) 6.42824 0.561638 0.280819 0.959761i \(-0.409394\pi\)
0.280819 + 0.959761i \(0.409394\pi\)
\(132\) 18.5902 1.61807
\(133\) −0.528291 −0.0458087
\(134\) −35.0415 −3.02712
\(135\) 3.88852 0.334671
\(136\) 46.3889 3.97782
\(137\) 14.1747 1.21102 0.605512 0.795836i \(-0.292968\pi\)
0.605512 + 0.795836i \(0.292968\pi\)
\(138\) 9.81121 0.835186
\(139\) 3.84558 0.326178 0.163089 0.986611i \(-0.447854\pi\)
0.163089 + 0.986611i \(0.447854\pi\)
\(140\) −7.95119 −0.671998
\(141\) 4.00155 0.336991
\(142\) −15.5522 −1.30511
\(143\) −7.71144 −0.644863
\(144\) −35.6821 −2.97350
\(145\) −1.87684 −0.155863
\(146\) −11.3388 −0.938407
\(147\) 3.41036 0.281282
\(148\) 49.6949 4.08490
\(149\) −24.0900 −1.97353 −0.986763 0.162166i \(-0.948152\pi\)
−0.986763 + 0.162166i \(0.948152\pi\)
\(150\) 1.92189 0.156922
\(151\) −3.04298 −0.247634 −0.123817 0.992305i \(-0.539514\pi\)
−0.123817 + 0.992305i \(0.539514\pi\)
\(152\) −3.30023 −0.267684
\(153\) 12.5854 1.01747
\(154\) −19.5639 −1.57651
\(155\) −3.56650 −0.286468
\(156\) −6.02338 −0.482256
\(157\) −23.1326 −1.84618 −0.923091 0.384581i \(-0.874346\pi\)
−0.923091 + 0.384581i \(0.874346\pi\)
\(158\) −16.2133 −1.28986
\(159\) −8.34922 −0.662136
\(160\) −20.3663 −1.61010
\(161\) −7.53078 −0.593508
\(162\) −12.9165 −1.01482
\(163\) −8.18237 −0.640892 −0.320446 0.947267i \(-0.603833\pi\)
−0.320446 + 0.947267i \(0.603833\pi\)
\(164\) −41.8352 −3.26678
\(165\) 3.44903 0.268507
\(166\) 17.2815 1.34130
\(167\) −6.93143 −0.536370 −0.268185 0.963367i \(-0.586424\pi\)
−0.268185 + 0.963367i \(0.586424\pi\)
\(168\) −9.61105 −0.741508
\(169\) −10.5014 −0.807802
\(170\) 13.6842 1.04953
\(171\) −0.895361 −0.0684700
\(172\) 10.3076 0.785945
\(173\) −1.39886 −0.106354 −0.0531768 0.998585i \(-0.516935\pi\)
−0.0531768 + 0.998585i \(0.516935\pi\)
\(174\) −3.60709 −0.273453
\(175\) −1.47518 −0.111513
\(176\) −69.6254 −5.24822
\(177\) −6.14304 −0.461739
\(178\) −36.1362 −2.70852
\(179\) 11.4579 0.856407 0.428203 0.903682i \(-0.359147\pi\)
0.428203 + 0.903682i \(0.359147\pi\)
\(180\) −13.4759 −1.00443
\(181\) 17.9619 1.33510 0.667550 0.744565i \(-0.267343\pi\)
0.667550 + 0.744565i \(0.267343\pi\)
\(182\) 6.33890 0.469870
\(183\) −0.0407394 −0.00301154
\(184\) −47.0447 −3.46818
\(185\) 9.21989 0.677860
\(186\) −6.85444 −0.502592
\(187\) 24.5576 1.79583
\(188\) −30.5075 −2.22499
\(189\) −5.73628 −0.417253
\(190\) −0.973528 −0.0706272
\(191\) −23.4796 −1.69893 −0.849463 0.527647i \(-0.823074\pi\)
−0.849463 + 0.527647i \(0.823074\pi\)
\(192\) −18.9620 −1.36846
\(193\) 13.9732 1.00581 0.502906 0.864341i \(-0.332264\pi\)
0.502906 + 0.864341i \(0.332264\pi\)
\(194\) 0.503770 0.0361686
\(195\) −1.11752 −0.0800271
\(196\) −26.0003 −1.85716
\(197\) 21.7177 1.54732 0.773659 0.633602i \(-0.218424\pi\)
0.773659 + 0.633602i \(0.218424\pi\)
\(198\) −33.1574 −2.35640
\(199\) −17.7517 −1.25839 −0.629194 0.777248i \(-0.716615\pi\)
−0.629194 + 0.777248i \(0.716615\pi\)
\(200\) −9.21545 −0.651631
\(201\) −9.11316 −0.642792
\(202\) 42.9967 3.02524
\(203\) 2.76869 0.194324
\(204\) 19.1819 1.34300
\(205\) −7.76168 −0.542099
\(206\) −21.1457 −1.47329
\(207\) −12.7633 −0.887114
\(208\) 22.5593 1.56420
\(209\) −1.74709 −0.120849
\(210\) −2.83514 −0.195644
\(211\) −6.92206 −0.476534 −0.238267 0.971200i \(-0.576579\pi\)
−0.238267 + 0.971200i \(0.576579\pi\)
\(212\) 63.6538 4.37176
\(213\) −4.04462 −0.277133
\(214\) 26.3939 1.80425
\(215\) 1.91236 0.130422
\(216\) −35.8345 −2.43823
\(217\) 5.26125 0.357157
\(218\) −12.6556 −0.857142
\(219\) −2.94886 −0.199266
\(220\) −26.2951 −1.77282
\(221\) −7.95690 −0.535239
\(222\) 17.7196 1.18926
\(223\) 20.7086 1.38675 0.693376 0.720576i \(-0.256123\pi\)
0.693376 + 0.720576i \(0.256123\pi\)
\(224\) 30.0440 2.00740
\(225\) −2.50018 −0.166679
\(226\) −18.6559 −1.24097
\(227\) 9.38692 0.623032 0.311516 0.950241i \(-0.399163\pi\)
0.311516 + 0.950241i \(0.399163\pi\)
\(228\) −1.36465 −0.0903762
\(229\) −17.5332 −1.15863 −0.579313 0.815105i \(-0.696679\pi\)
−0.579313 + 0.815105i \(0.696679\pi\)
\(230\) −13.8776 −0.915063
\(231\) −5.08795 −0.334763
\(232\) 17.2960 1.13554
\(233\) −6.11022 −0.400294 −0.200147 0.979766i \(-0.564142\pi\)
−0.200147 + 0.979766i \(0.564142\pi\)
\(234\) 10.7433 0.702313
\(235\) −5.66005 −0.369221
\(236\) 46.8340 3.04864
\(237\) −4.21656 −0.273895
\(238\) −20.1867 −1.30851
\(239\) −6.07982 −0.393271 −0.196635 0.980477i \(-0.563001\pi\)
−0.196635 + 0.980477i \(0.563001\pi\)
\(240\) −10.0899 −0.651300
\(241\) 10.0879 0.649818 0.324909 0.945745i \(-0.394666\pi\)
0.324909 + 0.945745i \(0.394666\pi\)
\(242\) −34.7963 −2.23679
\(243\) −15.0247 −0.963837
\(244\) 0.310594 0.0198837
\(245\) −4.82383 −0.308183
\(246\) −14.9171 −0.951080
\(247\) 0.566074 0.0360185
\(248\) 32.8669 2.08705
\(249\) 4.49436 0.284819
\(250\) −2.71845 −0.171930
\(251\) −13.7874 −0.870250 −0.435125 0.900370i \(-0.643296\pi\)
−0.435125 + 0.900370i \(0.643296\pi\)
\(252\) 19.8794 1.25228
\(253\) −24.9048 −1.56575
\(254\) −8.65949 −0.543345
\(255\) 3.55882 0.222862
\(256\) 33.8354 2.11471
\(257\) −10.7739 −0.672060 −0.336030 0.941851i \(-0.609084\pi\)
−0.336030 + 0.941851i \(0.609084\pi\)
\(258\) 3.67536 0.228818
\(259\) −13.6010 −0.845127
\(260\) 8.51986 0.528379
\(261\) 4.69244 0.290455
\(262\) −17.4749 −1.07960
\(263\) −4.40182 −0.271428 −0.135714 0.990748i \(-0.543333\pi\)
−0.135714 + 0.990748i \(0.543333\pi\)
\(264\) −31.7844 −1.95619
\(265\) 11.8097 0.725463
\(266\) 1.43613 0.0880550
\(267\) −9.39785 −0.575139
\(268\) 69.4780 4.24404
\(269\) 25.1991 1.53642 0.768209 0.640200i \(-0.221148\pi\)
0.768209 + 0.640200i \(0.221148\pi\)
\(270\) −10.5708 −0.643315
\(271\) −15.3734 −0.933867 −0.466933 0.884292i \(-0.654641\pi\)
−0.466933 + 0.884292i \(0.654641\pi\)
\(272\) −71.8417 −4.35604
\(273\) 1.64854 0.0997744
\(274\) −38.5331 −2.32787
\(275\) −4.87853 −0.294186
\(276\) −19.4530 −1.17094
\(277\) −7.92769 −0.476329 −0.238164 0.971225i \(-0.576546\pi\)
−0.238164 + 0.971225i \(0.576546\pi\)
\(278\) −10.4540 −0.626990
\(279\) 8.91689 0.533840
\(280\) 13.5945 0.812426
\(281\) −19.7785 −1.17989 −0.589943 0.807445i \(-0.700850\pi\)
−0.589943 + 0.807445i \(0.700850\pi\)
\(282\) −10.8780 −0.647775
\(283\) 22.0446 1.31042 0.655209 0.755448i \(-0.272581\pi\)
0.655209 + 0.755448i \(0.272581\pi\)
\(284\) 30.8359 1.82977
\(285\) −0.253183 −0.0149973
\(286\) 20.9631 1.23958
\(287\) 11.4499 0.675866
\(288\) 50.9193 3.00045
\(289\) 8.33935 0.490550
\(290\) 5.10210 0.299606
\(291\) 0.131014 0.00768020
\(292\) 22.4819 1.31565
\(293\) −11.6646 −0.681455 −0.340728 0.940162i \(-0.610673\pi\)
−0.340728 + 0.940162i \(0.610673\pi\)
\(294\) −9.27089 −0.540689
\(295\) 8.68911 0.505900
\(296\) −84.9655 −4.93852
\(297\) −18.9703 −1.10077
\(298\) 65.4874 3.79358
\(299\) 8.06938 0.466664
\(300\) −3.81061 −0.220005
\(301\) −2.82109 −0.162605
\(302\) 8.27219 0.476011
\(303\) 11.1821 0.642392
\(304\) 5.11100 0.293136
\(305\) 0.0576245 0.00329957
\(306\) −34.2129 −1.95582
\(307\) −8.49400 −0.484778 −0.242389 0.970179i \(-0.577931\pi\)
−0.242389 + 0.970179i \(0.577931\pi\)
\(308\) 38.7901 2.21027
\(309\) −5.49933 −0.312846
\(310\) 9.69536 0.550659
\(311\) −8.53645 −0.484058 −0.242029 0.970269i \(-0.577813\pi\)
−0.242029 + 0.970269i \(0.577813\pi\)
\(312\) 10.2984 0.583034
\(313\) −22.9002 −1.29440 −0.647198 0.762322i \(-0.724059\pi\)
−0.647198 + 0.762322i \(0.724059\pi\)
\(314\) 62.8848 3.54879
\(315\) 3.68822 0.207808
\(316\) 32.1467 1.80839
\(317\) −17.8009 −0.999797 −0.499898 0.866084i \(-0.666629\pi\)
−0.499898 + 0.866084i \(0.666629\pi\)
\(318\) 22.6969 1.27278
\(319\) 9.15624 0.512651
\(320\) 26.8211 1.49934
\(321\) 6.86420 0.383122
\(322\) 20.4720 1.14086
\(323\) −1.80271 −0.100305
\(324\) 25.6100 1.42278
\(325\) 1.58069 0.0876808
\(326\) 22.2433 1.23195
\(327\) −3.29130 −0.182009
\(328\) 71.5274 3.94944
\(329\) 8.34961 0.460329
\(330\) −9.37601 −0.516132
\(331\) 19.1065 1.05019 0.525094 0.851044i \(-0.324030\pi\)
0.525094 + 0.851044i \(0.324030\pi\)
\(332\) −34.2646 −1.88052
\(333\) −23.0514 −1.26321
\(334\) 18.8427 1.03103
\(335\) 12.8902 0.704269
\(336\) 14.8845 0.812014
\(337\) −31.4061 −1.71080 −0.855400 0.517968i \(-0.826689\pi\)
−0.855400 + 0.517968i \(0.826689\pi\)
\(338\) 28.5476 1.55278
\(339\) −4.85179 −0.263513
\(340\) −27.1321 −1.47145
\(341\) 17.3993 0.942225
\(342\) 2.43399 0.131615
\(343\) 17.4423 0.941797
\(344\) −17.6233 −0.950184
\(345\) −3.60912 −0.194309
\(346\) 3.80274 0.204437
\(347\) 25.2009 1.35286 0.676429 0.736508i \(-0.263527\pi\)
0.676429 + 0.736508i \(0.263527\pi\)
\(348\) 7.15191 0.383383
\(349\) 28.5847 1.53010 0.765051 0.643970i \(-0.222714\pi\)
0.765051 + 0.643970i \(0.222714\pi\)
\(350\) 4.01021 0.214355
\(351\) 6.14654 0.328078
\(352\) 99.3575 5.29577
\(353\) −18.5979 −0.989868 −0.494934 0.868931i \(-0.664808\pi\)
−0.494934 + 0.868931i \(0.664808\pi\)
\(354\) 16.6995 0.887571
\(355\) 5.72097 0.303638
\(356\) 71.6484 3.79736
\(357\) −5.24991 −0.277855
\(358\) −31.1478 −1.64621
\(359\) 7.82272 0.412868 0.206434 0.978461i \(-0.433814\pi\)
0.206434 + 0.978461i \(0.433814\pi\)
\(360\) 23.0403 1.21433
\(361\) −18.8718 −0.993250
\(362\) −48.8286 −2.56638
\(363\) −9.04940 −0.474970
\(364\) −12.5684 −0.658761
\(365\) 4.17106 0.218323
\(366\) 0.110748 0.00578889
\(367\) −14.3950 −0.751415 −0.375708 0.926738i \(-0.622600\pi\)
−0.375708 + 0.926738i \(0.622600\pi\)
\(368\) 72.8572 3.79795
\(369\) 19.4056 1.01021
\(370\) −25.0638 −1.30300
\(371\) −17.4214 −0.904476
\(372\) 13.5905 0.704636
\(373\) −33.1214 −1.71496 −0.857480 0.514517i \(-0.827971\pi\)
−0.857480 + 0.514517i \(0.827971\pi\)
\(374\) −66.7587 −3.45201
\(375\) −0.706981 −0.0365084
\(376\) 52.1599 2.68994
\(377\) −2.96670 −0.152793
\(378\) 15.5938 0.802058
\(379\) −3.04761 −0.156545 −0.0782725 0.996932i \(-0.524940\pi\)
−0.0782725 + 0.996932i \(0.524940\pi\)
\(380\) 1.93025 0.0990197
\(381\) −2.25206 −0.115376
\(382\) 63.8282 3.26574
\(383\) −16.8503 −0.861010 −0.430505 0.902588i \(-0.641664\pi\)
−0.430505 + 0.902588i \(0.641664\pi\)
\(384\) 22.7501 1.16096
\(385\) 7.19673 0.366779
\(386\) −37.9854 −1.93341
\(387\) −4.78125 −0.243044
\(388\) −0.998842 −0.0507085
\(389\) 30.5264 1.54775 0.773876 0.633337i \(-0.218315\pi\)
0.773876 + 0.633337i \(0.218315\pi\)
\(390\) 3.03791 0.153831
\(391\) −25.6975 −1.29958
\(392\) 44.4538 2.24526
\(393\) −4.54465 −0.229247
\(394\) −59.0383 −2.97431
\(395\) 5.96417 0.300090
\(396\) 65.7425 3.30368
\(397\) 23.0646 1.15758 0.578790 0.815476i \(-0.303525\pi\)
0.578790 + 0.815476i \(0.303525\pi\)
\(398\) 48.2572 2.41892
\(399\) 0.373492 0.0186980
\(400\) 14.2718 0.713590
\(401\) −1.86876 −0.0933216 −0.0466608 0.998911i \(-0.514858\pi\)
−0.0466608 + 0.998911i \(0.514858\pi\)
\(402\) 24.7737 1.23560
\(403\) −5.63753 −0.280825
\(404\) −85.2511 −4.24140
\(405\) 4.75142 0.236100
\(406\) −7.52654 −0.373536
\(407\) −44.9795 −2.22955
\(408\) −32.7961 −1.62365
\(409\) −23.0063 −1.13759 −0.568795 0.822479i \(-0.692590\pi\)
−0.568795 + 0.822479i \(0.692590\pi\)
\(410\) 21.0997 1.04204
\(411\) −10.0212 −0.494311
\(412\) 41.9264 2.06557
\(413\) −12.8180 −0.630734
\(414\) 34.6965 1.70524
\(415\) −6.35712 −0.312059
\(416\) −32.1927 −1.57838
\(417\) −2.71875 −0.133138
\(418\) 4.74939 0.232300
\(419\) 8.45864 0.413231 0.206616 0.978422i \(-0.433755\pi\)
0.206616 + 0.978422i \(0.433755\pi\)
\(420\) 5.62134 0.274293
\(421\) 13.2311 0.644846 0.322423 0.946596i \(-0.395503\pi\)
0.322423 + 0.946596i \(0.395503\pi\)
\(422\) 18.8173 0.916010
\(423\) 14.1511 0.688051
\(424\) −108.832 −5.28533
\(425\) −5.03382 −0.244176
\(426\) 10.9951 0.532714
\(427\) −0.0850067 −0.00411376
\(428\) −52.3321 −2.52957
\(429\) 5.45184 0.263217
\(430\) −5.19866 −0.250702
\(431\) −24.5279 −1.18147 −0.590733 0.806867i \(-0.701161\pi\)
−0.590733 + 0.806867i \(0.701161\pi\)
\(432\) 55.4962 2.67006
\(433\) −6.48827 −0.311806 −0.155903 0.987772i \(-0.549829\pi\)
−0.155903 + 0.987772i \(0.549829\pi\)
\(434\) −14.3024 −0.686539
\(435\) 1.32689 0.0636197
\(436\) 25.0926 1.20172
\(437\) 1.82819 0.0874541
\(438\) 8.01633 0.383035
\(439\) 19.5977 0.935347 0.467673 0.883901i \(-0.345092\pi\)
0.467673 + 0.883901i \(0.345092\pi\)
\(440\) 44.9579 2.14328
\(441\) 12.0604 0.574307
\(442\) 21.6304 1.02885
\(443\) −0.134618 −0.00639588 −0.00319794 0.999995i \(-0.501018\pi\)
−0.00319794 + 0.999995i \(0.501018\pi\)
\(444\) −35.1334 −1.66736
\(445\) 13.2929 0.630145
\(446\) −56.2953 −2.66566
\(447\) 17.0312 0.805546
\(448\) −39.5660 −1.86932
\(449\) −13.1854 −0.622256 −0.311128 0.950368i \(-0.600707\pi\)
−0.311128 + 0.950368i \(0.600707\pi\)
\(450\) 6.79661 0.320395
\(451\) 37.8656 1.78302
\(452\) 36.9896 1.73985
\(453\) 2.15133 0.101078
\(454\) −25.5179 −1.19761
\(455\) −2.33181 −0.109317
\(456\) 2.33320 0.109262
\(457\) −28.4708 −1.33181 −0.665904 0.746038i \(-0.731954\pi\)
−0.665904 + 0.746038i \(0.731954\pi\)
\(458\) 47.6631 2.22715
\(459\) −19.5741 −0.913642
\(460\) 27.5156 1.28292
\(461\) 3.73462 0.173939 0.0869693 0.996211i \(-0.472282\pi\)
0.0869693 + 0.996211i \(0.472282\pi\)
\(462\) 13.8313 0.643492
\(463\) 26.0760 1.21185 0.605927 0.795520i \(-0.292802\pi\)
0.605927 + 0.795520i \(0.292802\pi\)
\(464\) −26.7859 −1.24351
\(465\) 2.52145 0.116929
\(466\) 16.6103 0.769458
\(467\) 13.1441 0.608237 0.304118 0.952634i \(-0.401638\pi\)
0.304118 + 0.952634i \(0.401638\pi\)
\(468\) −21.3012 −0.984646
\(469\) −19.0155 −0.878053
\(470\) 15.3865 0.709729
\(471\) 16.3543 0.753567
\(472\) −80.0741 −3.68571
\(473\) −9.32952 −0.428972
\(474\) 11.4625 0.526490
\(475\) 0.358119 0.0164316
\(476\) 40.0249 1.83454
\(477\) −29.5263 −1.35192
\(478\) 16.5277 0.755958
\(479\) 35.2113 1.60885 0.804423 0.594056i \(-0.202474\pi\)
0.804423 + 0.594056i \(0.202474\pi\)
\(480\) 14.3986 0.657202
\(481\) 14.5738 0.664507
\(482\) −27.4234 −1.24910
\(483\) 5.32412 0.242256
\(484\) 68.9919 3.13599
\(485\) −0.185315 −0.00841473
\(486\) 40.8440 1.85272
\(487\) −31.7568 −1.43904 −0.719520 0.694472i \(-0.755638\pi\)
−0.719520 + 0.694472i \(0.755638\pi\)
\(488\) −0.531035 −0.0240388
\(489\) 5.78478 0.261597
\(490\) 13.1133 0.592401
\(491\) −40.2572 −1.81678 −0.908392 0.418120i \(-0.862689\pi\)
−0.908392 + 0.418120i \(0.862689\pi\)
\(492\) 29.5767 1.33342
\(493\) 9.44769 0.425503
\(494\) −1.53884 −0.0692359
\(495\) 12.1972 0.548223
\(496\) −50.9004 −2.28550
\(497\) −8.43949 −0.378563
\(498\) −12.2177 −0.547488
\(499\) 10.2506 0.458881 0.229441 0.973323i \(-0.426310\pi\)
0.229441 + 0.973323i \(0.426310\pi\)
\(500\) 5.38997 0.241047
\(501\) 4.90039 0.218933
\(502\) 37.4802 1.67282
\(503\) 40.3892 1.80086 0.900432 0.434996i \(-0.143250\pi\)
0.900432 + 0.434996i \(0.143250\pi\)
\(504\) −33.9886 −1.51397
\(505\) −15.8166 −0.703830
\(506\) 67.7024 3.00974
\(507\) 7.42431 0.329725
\(508\) 17.1695 0.761773
\(509\) 27.9511 1.23891 0.619456 0.785031i \(-0.287353\pi\)
0.619456 + 0.785031i \(0.287353\pi\)
\(510\) −9.67446 −0.428392
\(511\) −6.15308 −0.272196
\(512\) −27.6213 −1.22070
\(513\) 1.39255 0.0614827
\(514\) 29.2884 1.29186
\(515\) 7.77860 0.342766
\(516\) −7.28726 −0.320804
\(517\) 27.6127 1.21441
\(518\) 36.9737 1.62453
\(519\) 0.988971 0.0434110
\(520\) −14.5668 −0.638795
\(521\) 16.4776 0.721895 0.360947 0.932586i \(-0.382453\pi\)
0.360947 + 0.932586i \(0.382453\pi\)
\(522\) −12.7562 −0.558322
\(523\) −18.3490 −0.802347 −0.401174 0.916002i \(-0.631398\pi\)
−0.401174 + 0.916002i \(0.631398\pi\)
\(524\) 34.6480 1.51361
\(525\) 1.04293 0.0455171
\(526\) 11.9661 0.521748
\(527\) 17.9531 0.782051
\(528\) 49.2239 2.14219
\(529\) 3.06077 0.133077
\(530\) −32.1040 −1.39451
\(531\) −21.7243 −0.942756
\(532\) −2.84747 −0.123454
\(533\) −12.2688 −0.531420
\(534\) 25.5476 1.10555
\(535\) −9.70917 −0.419764
\(536\) −118.789 −5.13092
\(537\) −8.10055 −0.349565
\(538\) −68.5025 −2.95335
\(539\) 23.5332 1.01365
\(540\) 20.9590 0.901932
\(541\) −6.12390 −0.263287 −0.131644 0.991297i \(-0.542025\pi\)
−0.131644 + 0.991297i \(0.542025\pi\)
\(542\) 41.7918 1.79511
\(543\) −12.6988 −0.544956
\(544\) 102.520 4.39552
\(545\) 4.65543 0.199417
\(546\) −4.48148 −0.191790
\(547\) 39.2464 1.67806 0.839028 0.544088i \(-0.183124\pi\)
0.839028 + 0.544088i \(0.183124\pi\)
\(548\) 76.4010 3.26369
\(549\) −0.144071 −0.00614882
\(550\) 13.2620 0.565495
\(551\) −0.672133 −0.0286338
\(552\) 33.2597 1.41563
\(553\) −8.79824 −0.374139
\(554\) 21.5510 0.915616
\(555\) −6.51829 −0.276686
\(556\) 20.7275 0.879044
\(557\) 32.3225 1.36955 0.684775 0.728755i \(-0.259901\pi\)
0.684775 + 0.728755i \(0.259901\pi\)
\(558\) −24.2401 −1.02617
\(559\) 3.02285 0.127853
\(560\) −21.0535 −0.889674
\(561\) −17.3618 −0.733016
\(562\) 53.7669 2.26802
\(563\) 35.2490 1.48557 0.742784 0.669531i \(-0.233505\pi\)
0.742784 + 0.669531i \(0.233505\pi\)
\(564\) 21.5682 0.908185
\(565\) 6.86268 0.288715
\(566\) −59.9272 −2.51893
\(567\) −7.00922 −0.294359
\(568\) −52.7214 −2.21214
\(569\) −15.7040 −0.658347 −0.329174 0.944269i \(-0.606770\pi\)
−0.329174 + 0.944269i \(0.606770\pi\)
\(570\) 0.688266 0.0288283
\(571\) 0.859042 0.0359498 0.0179749 0.999838i \(-0.494278\pi\)
0.0179749 + 0.999838i \(0.494278\pi\)
\(572\) −41.5644 −1.73789
\(573\) 16.5997 0.693461
\(574\) −31.1260 −1.29917
\(575\) 5.10498 0.212892
\(576\) −67.0575 −2.79406
\(577\) −32.2001 −1.34051 −0.670253 0.742132i \(-0.733815\pi\)
−0.670253 + 0.742132i \(0.733815\pi\)
\(578\) −22.6701 −0.942952
\(579\) −9.87878 −0.410548
\(580\) −10.1161 −0.420049
\(581\) 9.37791 0.389061
\(582\) −0.356156 −0.0147631
\(583\) −57.6139 −2.38612
\(584\) −38.4382 −1.59058
\(585\) −3.95200 −0.163395
\(586\) 31.7097 1.30992
\(587\) −14.7665 −0.609477 −0.304739 0.952436i \(-0.598569\pi\)
−0.304739 + 0.952436i \(0.598569\pi\)
\(588\) 18.3817 0.758050
\(589\) −1.27723 −0.0526274
\(590\) −23.6209 −0.972458
\(591\) −15.3540 −0.631578
\(592\) 131.584 5.40809
\(593\) −33.1269 −1.36036 −0.680178 0.733047i \(-0.738098\pi\)
−0.680178 + 0.733047i \(0.738098\pi\)
\(594\) 51.5697 2.11593
\(595\) 7.42581 0.304429
\(596\) −129.844 −5.31862
\(597\) 12.5502 0.513643
\(598\) −21.9362 −0.897037
\(599\) −6.82450 −0.278841 −0.139421 0.990233i \(-0.544524\pi\)
−0.139421 + 0.990233i \(0.544524\pi\)
\(600\) 6.51515 0.265980
\(601\) 10.5329 0.429645 0.214822 0.976653i \(-0.431083\pi\)
0.214822 + 0.976653i \(0.431083\pi\)
\(602\) 7.66898 0.312564
\(603\) −32.2279 −1.31242
\(604\) −16.4016 −0.667371
\(605\) 12.8001 0.520396
\(606\) −30.3979 −1.23483
\(607\) 36.6944 1.48938 0.744690 0.667410i \(-0.232597\pi\)
0.744690 + 0.667410i \(0.232597\pi\)
\(608\) −7.29355 −0.295793
\(609\) −1.95741 −0.0793183
\(610\) −0.156649 −0.00634254
\(611\) −8.94677 −0.361948
\(612\) 67.8351 2.74207
\(613\) 23.9037 0.965460 0.482730 0.875769i \(-0.339645\pi\)
0.482730 + 0.875769i \(0.339645\pi\)
\(614\) 23.0905 0.931858
\(615\) 5.48736 0.221272
\(616\) −66.3211 −2.67215
\(617\) 18.4538 0.742923 0.371461 0.928448i \(-0.378857\pi\)
0.371461 + 0.928448i \(0.378857\pi\)
\(618\) 14.9496 0.601363
\(619\) −6.70657 −0.269560 −0.134780 0.990876i \(-0.543033\pi\)
−0.134780 + 0.990876i \(0.543033\pi\)
\(620\) −19.2233 −0.772028
\(621\) 19.8508 0.796586
\(622\) 23.2059 0.930472
\(623\) −19.6095 −0.785638
\(624\) −15.9490 −0.638471
\(625\) 1.00000 0.0400000
\(626\) 62.2530 2.48813
\(627\) 1.23516 0.0493276
\(628\) −124.684 −4.97543
\(629\) −46.4113 −1.85054
\(630\) −10.0262 −0.399455
\(631\) 8.09212 0.322142 0.161071 0.986943i \(-0.448505\pi\)
0.161071 + 0.986943i \(0.448505\pi\)
\(632\) −54.9625 −2.18629
\(633\) 4.89377 0.194510
\(634\) 48.3908 1.92184
\(635\) 3.18545 0.126411
\(636\) −45.0020 −1.78445
\(637\) −7.62498 −0.302113
\(638\) −24.8908 −0.985435
\(639\) −14.3035 −0.565836
\(640\) −32.1792 −1.27199
\(641\) −37.2110 −1.46975 −0.734874 0.678204i \(-0.762759\pi\)
−0.734874 + 0.678204i \(0.762759\pi\)
\(642\) −18.6600 −0.736451
\(643\) −5.32766 −0.210102 −0.105051 0.994467i \(-0.533501\pi\)
−0.105051 + 0.994467i \(0.533501\pi\)
\(644\) −40.5906 −1.59949
\(645\) −1.35201 −0.0532351
\(646\) 4.90057 0.192810
\(647\) −9.45277 −0.371627 −0.185813 0.982585i \(-0.559492\pi\)
−0.185813 + 0.982585i \(0.559492\pi\)
\(648\) −43.7865 −1.72010
\(649\) −42.3901 −1.66396
\(650\) −4.29702 −0.168543
\(651\) −3.71960 −0.145783
\(652\) −44.1027 −1.72719
\(653\) −12.7928 −0.500620 −0.250310 0.968166i \(-0.580533\pi\)
−0.250310 + 0.968166i \(0.580533\pi\)
\(654\) 8.94724 0.349865
\(655\) 6.42824 0.251172
\(656\) −110.773 −4.32497
\(657\) −10.4284 −0.406850
\(658\) −22.6980 −0.884859
\(659\) −47.1291 −1.83589 −0.917945 0.396707i \(-0.870153\pi\)
−0.917945 + 0.396707i \(0.870153\pi\)
\(660\) 18.5902 0.723621
\(661\) 46.0404 1.79077 0.895383 0.445298i \(-0.146902\pi\)
0.895383 + 0.445298i \(0.146902\pi\)
\(662\) −51.9400 −2.01871
\(663\) 5.62538 0.218472
\(664\) 58.5837 2.27349
\(665\) −0.528291 −0.0204863
\(666\) 62.6640 2.42818
\(667\) −9.58124 −0.370987
\(668\) −37.3602 −1.44551
\(669\) −14.6406 −0.566038
\(670\) −35.0415 −1.35377
\(671\) −0.281123 −0.0108526
\(672\) −21.2405 −0.819372
\(673\) −36.9987 −1.42620 −0.713098 0.701064i \(-0.752709\pi\)
−0.713098 + 0.701064i \(0.752709\pi\)
\(674\) 85.3759 3.28856
\(675\) 3.88852 0.149669
\(676\) −56.6023 −2.17701
\(677\) −30.5930 −1.17578 −0.587892 0.808939i \(-0.700042\pi\)
−0.587892 + 0.808939i \(0.700042\pi\)
\(678\) 13.1893 0.506534
\(679\) 0.273374 0.0104911
\(680\) 46.3889 1.77893
\(681\) −6.63637 −0.254306
\(682\) −47.2991 −1.81118
\(683\) −12.3008 −0.470675 −0.235338 0.971914i \(-0.575620\pi\)
−0.235338 + 0.971914i \(0.575620\pi\)
\(684\) −4.82597 −0.184525
\(685\) 14.1747 0.541587
\(686\) −47.4161 −1.81035
\(687\) 12.3956 0.472923
\(688\) 27.2929 1.04053
\(689\) 18.6674 0.711172
\(690\) 9.81121 0.373507
\(691\) −8.52828 −0.324431 −0.162216 0.986755i \(-0.551864\pi\)
−0.162216 + 0.986755i \(0.551864\pi\)
\(692\) −7.53983 −0.286621
\(693\) −17.9931 −0.683501
\(694\) −68.5075 −2.60051
\(695\) 3.84558 0.145871
\(696\) −12.2279 −0.463498
\(697\) 39.0709 1.47992
\(698\) −77.7060 −2.94121
\(699\) 4.31981 0.163390
\(700\) −7.95119 −0.300527
\(701\) −29.6545 −1.12004 −0.560018 0.828480i \(-0.689206\pi\)
−0.560018 + 0.828480i \(0.689206\pi\)
\(702\) −16.7091 −0.630643
\(703\) 3.30182 0.124530
\(704\) −130.847 −4.93150
\(705\) 4.00155 0.150707
\(706\) 50.5575 1.90276
\(707\) 23.3324 0.877506
\(708\) −33.1108 −1.24438
\(709\) 24.2556 0.910939 0.455470 0.890251i \(-0.349471\pi\)
0.455470 + 0.890251i \(0.349471\pi\)
\(710\) −15.5522 −0.583663
\(711\) −14.9115 −0.559224
\(712\) −122.500 −4.59089
\(713\) −18.2069 −0.681854
\(714\) 14.2716 0.534102
\(715\) −7.71144 −0.288391
\(716\) 61.7579 2.30800
\(717\) 4.29832 0.160524
\(718\) −21.2657 −0.793628
\(719\) −7.50727 −0.279974 −0.139987 0.990153i \(-0.544706\pi\)
−0.139987 + 0.990153i \(0.544706\pi\)
\(720\) −35.6821 −1.32979
\(721\) −11.4749 −0.427346
\(722\) 51.3019 1.90926
\(723\) −7.13195 −0.265240
\(724\) 96.8143 3.59807
\(725\) −1.87684 −0.0697042
\(726\) 24.6003 0.913004
\(727\) −42.2766 −1.56795 −0.783976 0.620792i \(-0.786811\pi\)
−0.783976 + 0.620792i \(0.786811\pi\)
\(728\) 21.4886 0.796422
\(729\) −3.63206 −0.134521
\(730\) −11.3388 −0.419668
\(731\) −9.62649 −0.356049
\(732\) −0.219584 −0.00811606
\(733\) 23.7618 0.877661 0.438830 0.898570i \(-0.355393\pi\)
0.438830 + 0.898570i \(0.355393\pi\)
\(734\) 39.1322 1.44440
\(735\) 3.41036 0.125793
\(736\) −103.969 −3.83236
\(737\) −62.8854 −2.31641
\(738\) −52.7531 −1.94187
\(739\) −35.8335 −1.31816 −0.659079 0.752074i \(-0.729054\pi\)
−0.659079 + 0.752074i \(0.729054\pi\)
\(740\) 49.6949 1.82682
\(741\) −0.400204 −0.0147019
\(742\) 47.3593 1.73861
\(743\) −14.3278 −0.525636 −0.262818 0.964845i \(-0.584652\pi\)
−0.262818 + 0.964845i \(0.584652\pi\)
\(744\) −23.2363 −0.851884
\(745\) −24.0900 −0.882588
\(746\) 90.0388 3.29655
\(747\) 15.8939 0.581528
\(748\) 132.365 4.83974
\(749\) 14.3228 0.523344
\(750\) 1.92189 0.0701776
\(751\) 33.8135 1.23387 0.616937 0.787013i \(-0.288374\pi\)
0.616937 + 0.787013i \(0.288374\pi\)
\(752\) −80.7791 −2.94571
\(753\) 9.74740 0.355215
\(754\) 8.06484 0.293704
\(755\) −3.04298 −0.110745
\(756\) −30.9184 −1.12449
\(757\) 26.3668 0.958317 0.479159 0.877728i \(-0.340942\pi\)
0.479159 + 0.877728i \(0.340942\pi\)
\(758\) 8.28477 0.300916
\(759\) 17.6072 0.639101
\(760\) −3.30023 −0.119712
\(761\) 28.8032 1.04411 0.522057 0.852910i \(-0.325165\pi\)
0.522057 + 0.852910i \(0.325165\pi\)
\(762\) 6.12210 0.221780
\(763\) −6.86762 −0.248624
\(764\) −126.554 −4.57858
\(765\) 12.5854 0.455028
\(766\) 45.8067 1.65506
\(767\) 13.7348 0.495934
\(768\) −23.9210 −0.863173
\(769\) −6.25033 −0.225393 −0.112696 0.993629i \(-0.535949\pi\)
−0.112696 + 0.993629i \(0.535949\pi\)
\(770\) −19.5639 −0.705035
\(771\) 7.61698 0.274319
\(772\) 75.3150 2.71065
\(773\) −31.4722 −1.13198 −0.565988 0.824414i \(-0.691505\pi\)
−0.565988 + 0.824414i \(0.691505\pi\)
\(774\) 12.9976 0.467188
\(775\) −3.56650 −0.128113
\(776\) 1.70776 0.0613051
\(777\) 9.61567 0.344960
\(778\) −82.9846 −2.97514
\(779\) −2.77960 −0.0995896
\(780\) −6.02338 −0.215672
\(781\) −27.9099 −0.998696
\(782\) 69.8574 2.49810
\(783\) −7.29815 −0.260814
\(784\) −68.8448 −2.45874
\(785\) −23.1326 −0.825638
\(786\) 12.3544 0.440667
\(787\) 10.8632 0.387231 0.193615 0.981077i \(-0.437979\pi\)
0.193615 + 0.981077i \(0.437979\pi\)
\(788\) 117.057 4.17000
\(789\) 3.11200 0.110790
\(790\) −16.2133 −0.576843
\(791\) −10.1237 −0.359958
\(792\) −112.403 −3.99405
\(793\) 0.0910863 0.00323457
\(794\) −62.7000 −2.22514
\(795\) −8.34922 −0.296116
\(796\) −95.6813 −3.39133
\(797\) 42.4536 1.50378 0.751892 0.659286i \(-0.229141\pi\)
0.751892 + 0.659286i \(0.229141\pi\)
\(798\) −1.01532 −0.0359419
\(799\) 28.4917 1.00796
\(800\) −20.3663 −0.720057
\(801\) −33.2347 −1.17429
\(802\) 5.08014 0.179386
\(803\) −20.3486 −0.718088
\(804\) −49.1196 −1.73232
\(805\) −7.53078 −0.265425
\(806\) 15.3253 0.539812
\(807\) −17.8153 −0.627128
\(808\) 145.757 5.12773
\(809\) −46.7224 −1.64267 −0.821336 0.570445i \(-0.806771\pi\)
−0.821336 + 0.570445i \(0.806771\pi\)
\(810\) −12.9165 −0.453839
\(811\) 14.2149 0.499151 0.249576 0.968355i \(-0.419709\pi\)
0.249576 + 0.968355i \(0.419709\pi\)
\(812\) 14.9231 0.523700
\(813\) 10.8687 0.381182
\(814\) 122.275 4.28572
\(815\) −8.18237 −0.286616
\(816\) 50.7907 1.77803
\(817\) 0.684854 0.0239600
\(818\) 62.5416 2.18671
\(819\) 5.82993 0.203714
\(820\) −41.8352 −1.46095
\(821\) −32.8769 −1.14741 −0.573705 0.819062i \(-0.694494\pi\)
−0.573705 + 0.819062i \(0.694494\pi\)
\(822\) 27.2422 0.950181
\(823\) −26.8886 −0.937279 −0.468639 0.883390i \(-0.655256\pi\)
−0.468639 + 0.883390i \(0.655256\pi\)
\(824\) −71.6834 −2.49721
\(825\) 3.44903 0.120080
\(826\) 34.8452 1.21242
\(827\) 18.4689 0.642227 0.321114 0.947041i \(-0.395943\pi\)
0.321114 + 0.947041i \(0.395943\pi\)
\(828\) −68.7940 −2.39076
\(829\) −34.0982 −1.18428 −0.592139 0.805836i \(-0.701716\pi\)
−0.592139 + 0.805836i \(0.701716\pi\)
\(830\) 17.2815 0.599850
\(831\) 5.60473 0.194426
\(832\) 42.3958 1.46981
\(833\) 24.2823 0.841332
\(834\) 7.39079 0.255922
\(835\) −6.93143 −0.239872
\(836\) −9.41678 −0.325686
\(837\) −13.8684 −0.479363
\(838\) −22.9944 −0.794327
\(839\) 11.5564 0.398971 0.199485 0.979901i \(-0.436073\pi\)
0.199485 + 0.979901i \(0.436073\pi\)
\(840\) −9.61105 −0.331613
\(841\) −25.4775 −0.878533
\(842\) −35.9682 −1.23955
\(843\) 13.9830 0.481601
\(844\) −37.3097 −1.28425
\(845\) −10.5014 −0.361260
\(846\) −38.4691 −1.32259
\(847\) −18.8824 −0.648808
\(848\) 168.545 5.78787
\(849\) −15.5851 −0.534881
\(850\) 13.6842 0.469364
\(851\) 47.0673 1.61345
\(852\) −21.8004 −0.746869
\(853\) −8.33383 −0.285345 −0.142672 0.989770i \(-0.545570\pi\)
−0.142672 + 0.989770i \(0.545570\pi\)
\(854\) 0.231086 0.00790761
\(855\) −0.895361 −0.0306207
\(856\) 89.4744 3.05817
\(857\) −34.9653 −1.19439 −0.597196 0.802095i \(-0.703719\pi\)
−0.597196 + 0.802095i \(0.703719\pi\)
\(858\) −14.8206 −0.505965
\(859\) 1.90243 0.0649101 0.0324551 0.999473i \(-0.489667\pi\)
0.0324551 + 0.999473i \(0.489667\pi\)
\(860\) 10.3076 0.351485
\(861\) −8.09486 −0.275872
\(862\) 66.6778 2.27105
\(863\) −43.2298 −1.47156 −0.735779 0.677222i \(-0.763184\pi\)
−0.735779 + 0.677222i \(0.763184\pi\)
\(864\) −79.1947 −2.69426
\(865\) −1.39886 −0.0475628
\(866\) 17.6380 0.599365
\(867\) −5.89576 −0.200231
\(868\) 28.3579 0.962531
\(869\) −29.0964 −0.987027
\(870\) −3.60709 −0.122292
\(871\) 20.3754 0.690396
\(872\) −42.9019 −1.45284
\(873\) 0.463321 0.0156810
\(874\) −4.96984 −0.168107
\(875\) −1.47518 −0.0498703
\(876\) −15.8943 −0.537017
\(877\) 46.0424 1.55474 0.777370 0.629043i \(-0.216553\pi\)
0.777370 + 0.629043i \(0.216553\pi\)
\(878\) −53.2753 −1.79796
\(879\) 8.24668 0.278154
\(880\) −69.6254 −2.34707
\(881\) 9.58560 0.322947 0.161473 0.986877i \(-0.448375\pi\)
0.161473 + 0.986877i \(0.448375\pi\)
\(882\) −32.7857 −1.10395
\(883\) −41.2914 −1.38956 −0.694782 0.719220i \(-0.744499\pi\)
−0.694782 + 0.719220i \(0.744499\pi\)
\(884\) −42.8874 −1.44246
\(885\) −6.14304 −0.206496
\(886\) 0.365951 0.0122944
\(887\) 52.1774 1.75195 0.875973 0.482360i \(-0.160220\pi\)
0.875973 + 0.482360i \(0.160220\pi\)
\(888\) 60.0690 2.01578
\(889\) −4.69913 −0.157604
\(890\) −36.1362 −1.21129
\(891\) −23.1799 −0.776557
\(892\) 111.619 3.73727
\(893\) −2.02697 −0.0678300
\(894\) −46.2983 −1.54845
\(895\) 11.4579 0.382997
\(896\) 47.4702 1.58587
\(897\) −5.70490 −0.190481
\(898\) 35.8438 1.19612
\(899\) 6.69377 0.223250
\(900\) −13.4759 −0.449196
\(901\) −59.4478 −1.98049
\(902\) −102.936 −3.42738
\(903\) 1.99446 0.0663713
\(904\) −63.2427 −2.10342
\(905\) 17.9619 0.597075
\(906\) −5.84829 −0.194296
\(907\) −18.5303 −0.615287 −0.307644 0.951502i \(-0.599540\pi\)
−0.307644 + 0.951502i \(0.599540\pi\)
\(908\) 50.5952 1.67906
\(909\) 39.5444 1.31160
\(910\) 6.33890 0.210132
\(911\) −34.2834 −1.13586 −0.567930 0.823077i \(-0.692255\pi\)
−0.567930 + 0.823077i \(0.692255\pi\)
\(912\) −3.61338 −0.119651
\(913\) 31.0134 1.02639
\(914\) 77.3964 2.56004
\(915\) −0.0407394 −0.00134680
\(916\) −94.5033 −3.12248
\(917\) −9.48284 −0.313151
\(918\) 53.2113 1.75623
\(919\) −12.2345 −0.403579 −0.201789 0.979429i \(-0.564676\pi\)
−0.201789 + 0.979429i \(0.564676\pi\)
\(920\) −47.0447 −1.55102
\(921\) 6.00510 0.197875
\(922\) −10.1524 −0.334351
\(923\) 9.04308 0.297657
\(924\) −27.4239 −0.902180
\(925\) 9.21989 0.303148
\(926\) −70.8863 −2.32947
\(927\) −19.4479 −0.638753
\(928\) 38.2243 1.25477
\(929\) −40.6051 −1.33221 −0.666105 0.745858i \(-0.732040\pi\)
−0.666105 + 0.745858i \(0.732040\pi\)
\(930\) −6.85444 −0.224766
\(931\) −1.72751 −0.0566167
\(932\) −32.9339 −1.07879
\(933\) 6.03511 0.197581
\(934\) −35.7316 −1.16917
\(935\) 24.5576 0.803121
\(936\) 36.4195 1.19041
\(937\) −24.9618 −0.815468 −0.407734 0.913101i \(-0.633681\pi\)
−0.407734 + 0.913101i \(0.633681\pi\)
\(938\) 51.6926 1.68782
\(939\) 16.1900 0.528341
\(940\) −30.5075 −0.995044
\(941\) 31.8445 1.03810 0.519050 0.854744i \(-0.326286\pi\)
0.519050 + 0.854744i \(0.326286\pi\)
\(942\) −44.4584 −1.44853
\(943\) −39.6232 −1.29031
\(944\) 124.009 4.03616
\(945\) −5.73628 −0.186601
\(946\) 25.3618 0.824584
\(947\) 44.3075 1.43980 0.719900 0.694078i \(-0.244188\pi\)
0.719900 + 0.694078i \(0.244188\pi\)
\(948\) −22.7271 −0.738142
\(949\) 6.59315 0.214023
\(950\) −0.973528 −0.0315854
\(951\) 12.5849 0.408093
\(952\) −68.4322 −2.21790
\(953\) −18.9388 −0.613488 −0.306744 0.951792i \(-0.599240\pi\)
−0.306744 + 0.951792i \(0.599240\pi\)
\(954\) 80.2657 2.59870
\(955\) −23.4796 −0.759783
\(956\) −32.7700 −1.05986
\(957\) −6.47329 −0.209252
\(958\) −95.7202 −3.09258
\(959\) −20.9103 −0.675227
\(960\) −18.9620 −0.611996
\(961\) −18.2801 −0.589679
\(962\) −39.6181 −1.27734
\(963\) 24.2746 0.782239
\(964\) 54.3734 1.75125
\(965\) 13.9732 0.449813
\(966\) −14.4733 −0.465672
\(967\) 54.2348 1.74408 0.872038 0.489439i \(-0.162798\pi\)
0.872038 + 0.489439i \(0.162798\pi\)
\(968\) −117.958 −3.79132
\(969\) 1.27448 0.0409422
\(970\) 0.503770 0.0161751
\(971\) −16.6494 −0.534303 −0.267152 0.963654i \(-0.586082\pi\)
−0.267152 + 0.963654i \(0.586082\pi\)
\(972\) −80.9828 −2.59752
\(973\) −5.67293 −0.181866
\(974\) 86.3293 2.76617
\(975\) −1.11752 −0.0357892
\(976\) 0.822405 0.0263245
\(977\) −34.0104 −1.08809 −0.544044 0.839057i \(-0.683108\pi\)
−0.544044 + 0.839057i \(0.683108\pi\)
\(978\) −15.7256 −0.502850
\(979\) −64.8500 −2.07261
\(980\) −26.0003 −0.830549
\(981\) −11.6394 −0.371618
\(982\) 109.437 3.49228
\(983\) 61.7051 1.96809 0.984044 0.177926i \(-0.0569387\pi\)
0.984044 + 0.177926i \(0.0569387\pi\)
\(984\) −50.5685 −1.61207
\(985\) 21.7177 0.691982
\(986\) −25.6831 −0.817916
\(987\) −5.90302 −0.187895
\(988\) 3.05112 0.0970691
\(989\) 9.76257 0.310432
\(990\) −33.1574 −1.05381
\(991\) 52.0963 1.65489 0.827447 0.561544i \(-0.189792\pi\)
0.827447 + 0.561544i \(0.189792\pi\)
\(992\) 72.6364 2.30621
\(993\) −13.5079 −0.428661
\(994\) 22.9423 0.727686
\(995\) −17.7517 −0.562768
\(996\) 24.2245 0.767581
\(997\) −26.8236 −0.849512 −0.424756 0.905308i \(-0.639640\pi\)
−0.424756 + 0.905308i \(0.639640\pi\)
\(998\) −27.8658 −0.882077
\(999\) 35.8517 1.13430
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 8035.2.a.b.1.3 114
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8035.2.a.b.1.3 114 1.1 even 1 trivial