Properties

Label 8007.2.a.h.1.11
Level $8007$
Weight $2$
Character 8007.1
Self dual yes
Analytic conductor $63.936$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8007,2,Mod(1,8007)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8007, 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("8007.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8007.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 8007.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.81598 q^{2} +1.00000 q^{3} +1.29778 q^{4} -1.85785 q^{5} -1.81598 q^{6} -3.71645 q^{7} +1.27521 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.81598 q^{2} +1.00000 q^{3} +1.29778 q^{4} -1.85785 q^{5} -1.81598 q^{6} -3.71645 q^{7} +1.27521 q^{8} +1.00000 q^{9} +3.37381 q^{10} +2.48466 q^{11} +1.29778 q^{12} +3.08636 q^{13} +6.74901 q^{14} -1.85785 q^{15} -4.91132 q^{16} -1.00000 q^{17} -1.81598 q^{18} +3.85995 q^{19} -2.41109 q^{20} -3.71645 q^{21} -4.51209 q^{22} +9.02732 q^{23} +1.27521 q^{24} -1.54840 q^{25} -5.60476 q^{26} +1.00000 q^{27} -4.82316 q^{28} -6.29127 q^{29} +3.37381 q^{30} +11.0388 q^{31} +6.36845 q^{32} +2.48466 q^{33} +1.81598 q^{34} +6.90460 q^{35} +1.29778 q^{36} +6.78754 q^{37} -7.00960 q^{38} +3.08636 q^{39} -2.36914 q^{40} +1.22529 q^{41} +6.74901 q^{42} -1.24300 q^{43} +3.22455 q^{44} -1.85785 q^{45} -16.3934 q^{46} -3.57446 q^{47} -4.91132 q^{48} +6.81203 q^{49} +2.81187 q^{50} -1.00000 q^{51} +4.00542 q^{52} -10.3387 q^{53} -1.81598 q^{54} -4.61611 q^{55} -4.73926 q^{56} +3.85995 q^{57} +11.4248 q^{58} +14.2796 q^{59} -2.41109 q^{60} -12.5550 q^{61} -20.0463 q^{62} -3.71645 q^{63} -1.74233 q^{64} -5.73398 q^{65} -4.51209 q^{66} +2.94647 q^{67} -1.29778 q^{68} +9.02732 q^{69} -12.5386 q^{70} -7.48333 q^{71} +1.27521 q^{72} +11.4226 q^{73} -12.3260 q^{74} -1.54840 q^{75} +5.00939 q^{76} -9.23411 q^{77} -5.60476 q^{78} -10.4893 q^{79} +9.12449 q^{80} +1.00000 q^{81} -2.22511 q^{82} +7.82837 q^{83} -4.82316 q^{84} +1.85785 q^{85} +2.25727 q^{86} -6.29127 q^{87} +3.16846 q^{88} +6.91836 q^{89} +3.37381 q^{90} -11.4703 q^{91} +11.7155 q^{92} +11.0388 q^{93} +6.49115 q^{94} -7.17120 q^{95} +6.36845 q^{96} -13.1097 q^{97} -12.3705 q^{98} +2.48466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.81598 −1.28409 −0.642046 0.766666i \(-0.721914\pi\)
−0.642046 + 0.766666i \(0.721914\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.29778 0.648892
\(5\) −1.85785 −0.830855 −0.415427 0.909626i \(-0.636368\pi\)
−0.415427 + 0.909626i \(0.636368\pi\)
\(6\) −1.81598 −0.741371
\(7\) −3.71645 −1.40469 −0.702344 0.711838i \(-0.747863\pi\)
−0.702344 + 0.711838i \(0.747863\pi\)
\(8\) 1.27521 0.450855
\(9\) 1.00000 0.333333
\(10\) 3.37381 1.06689
\(11\) 2.48466 0.749152 0.374576 0.927196i \(-0.377788\pi\)
0.374576 + 0.927196i \(0.377788\pi\)
\(12\) 1.29778 0.374638
\(13\) 3.08636 0.856001 0.428000 0.903779i \(-0.359218\pi\)
0.428000 + 0.903779i \(0.359218\pi\)
\(14\) 6.74901 1.80375
\(15\) −1.85785 −0.479694
\(16\) −4.91132 −1.22783
\(17\) −1.00000 −0.242536
\(18\) −1.81598 −0.428031
\(19\) 3.85995 0.885534 0.442767 0.896637i \(-0.353997\pi\)
0.442767 + 0.896637i \(0.353997\pi\)
\(20\) −2.41109 −0.539135
\(21\) −3.71645 −0.810997
\(22\) −4.51209 −0.961980
\(23\) 9.02732 1.88233 0.941163 0.337954i \(-0.109735\pi\)
0.941163 + 0.337954i \(0.109735\pi\)
\(24\) 1.27521 0.260301
\(25\) −1.54840 −0.309681
\(26\) −5.60476 −1.09918
\(27\) 1.00000 0.192450
\(28\) −4.82316 −0.911491
\(29\) −6.29127 −1.16826 −0.584129 0.811661i \(-0.698564\pi\)
−0.584129 + 0.811661i \(0.698564\pi\)
\(30\) 3.37381 0.615971
\(31\) 11.0388 1.98264 0.991318 0.131487i \(-0.0419753\pi\)
0.991318 + 0.131487i \(0.0419753\pi\)
\(32\) 6.36845 1.12579
\(33\) 2.48466 0.432523
\(34\) 1.81598 0.311438
\(35\) 6.90460 1.16709
\(36\) 1.29778 0.216297
\(37\) 6.78754 1.11586 0.557932 0.829887i \(-0.311595\pi\)
0.557932 + 0.829887i \(0.311595\pi\)
\(38\) −7.00960 −1.13711
\(39\) 3.08636 0.494212
\(40\) −2.36914 −0.374595
\(41\) 1.22529 0.191359 0.0956794 0.995412i \(-0.469498\pi\)
0.0956794 + 0.995412i \(0.469498\pi\)
\(42\) 6.74901 1.04139
\(43\) −1.24300 −0.189556 −0.0947780 0.995498i \(-0.530214\pi\)
−0.0947780 + 0.995498i \(0.530214\pi\)
\(44\) 3.22455 0.486119
\(45\) −1.85785 −0.276952
\(46\) −16.3934 −2.41708
\(47\) −3.57446 −0.521389 −0.260694 0.965421i \(-0.583951\pi\)
−0.260694 + 0.965421i \(0.583951\pi\)
\(48\) −4.91132 −0.708889
\(49\) 6.81203 0.973147
\(50\) 2.81187 0.397658
\(51\) −1.00000 −0.140028
\(52\) 4.00542 0.555452
\(53\) −10.3387 −1.42012 −0.710062 0.704139i \(-0.751333\pi\)
−0.710062 + 0.704139i \(0.751333\pi\)
\(54\) −1.81598 −0.247124
\(55\) −4.61611 −0.622437
\(56\) −4.73926 −0.633310
\(57\) 3.85995 0.511263
\(58\) 11.4248 1.50015
\(59\) 14.2796 1.85904 0.929522 0.368768i \(-0.120220\pi\)
0.929522 + 0.368768i \(0.120220\pi\)
\(60\) −2.41109 −0.311270
\(61\) −12.5550 −1.60751 −0.803754 0.594962i \(-0.797167\pi\)
−0.803754 + 0.594962i \(0.797167\pi\)
\(62\) −20.0463 −2.54589
\(63\) −3.71645 −0.468229
\(64\) −1.74233 −0.217791
\(65\) −5.73398 −0.711212
\(66\) −4.51209 −0.555400
\(67\) 2.94647 0.359968 0.179984 0.983670i \(-0.442395\pi\)
0.179984 + 0.983670i \(0.442395\pi\)
\(68\) −1.29778 −0.157379
\(69\) 9.02732 1.08676
\(70\) −12.5386 −1.49865
\(71\) −7.48333 −0.888107 −0.444054 0.896000i \(-0.646460\pi\)
−0.444054 + 0.896000i \(0.646460\pi\)
\(72\) 1.27521 0.150285
\(73\) 11.4226 1.33692 0.668458 0.743750i \(-0.266955\pi\)
0.668458 + 0.743750i \(0.266955\pi\)
\(74\) −12.3260 −1.43287
\(75\) −1.54840 −0.178794
\(76\) 5.00939 0.574616
\(77\) −9.23411 −1.05232
\(78\) −5.60476 −0.634614
\(79\) −10.4893 −1.18014 −0.590069 0.807353i \(-0.700899\pi\)
−0.590069 + 0.807353i \(0.700899\pi\)
\(80\) 9.12449 1.02015
\(81\) 1.00000 0.111111
\(82\) −2.22511 −0.245722
\(83\) 7.82837 0.859275 0.429638 0.903001i \(-0.358641\pi\)
0.429638 + 0.903001i \(0.358641\pi\)
\(84\) −4.82316 −0.526249
\(85\) 1.85785 0.201512
\(86\) 2.25727 0.243407
\(87\) −6.29127 −0.674494
\(88\) 3.16846 0.337759
\(89\) 6.91836 0.733345 0.366672 0.930350i \(-0.380497\pi\)
0.366672 + 0.930350i \(0.380497\pi\)
\(90\) 3.37381 0.355631
\(91\) −11.4703 −1.20241
\(92\) 11.7155 1.22143
\(93\) 11.0388 1.14468
\(94\) 6.49115 0.669511
\(95\) −7.17120 −0.735750
\(96\) 6.36845 0.649977
\(97\) −13.1097 −1.33109 −0.665545 0.746358i \(-0.731801\pi\)
−0.665545 + 0.746358i \(0.731801\pi\)
\(98\) −12.3705 −1.24961
\(99\) 2.48466 0.249717
\(100\) −2.00949 −0.200949
\(101\) 11.4665 1.14095 0.570477 0.821313i \(-0.306758\pi\)
0.570477 + 0.821313i \(0.306758\pi\)
\(102\) 1.81598 0.179809
\(103\) −2.82872 −0.278722 −0.139361 0.990242i \(-0.544505\pi\)
−0.139361 + 0.990242i \(0.544505\pi\)
\(104\) 3.93575 0.385932
\(105\) 6.90460 0.673820
\(106\) 18.7748 1.82357
\(107\) −3.78434 −0.365846 −0.182923 0.983127i \(-0.558556\pi\)
−0.182923 + 0.983127i \(0.558556\pi\)
\(108\) 1.29778 0.124879
\(109\) 6.68734 0.640531 0.320266 0.947328i \(-0.396228\pi\)
0.320266 + 0.947328i \(0.396228\pi\)
\(110\) 8.38277 0.799266
\(111\) 6.78754 0.644244
\(112\) 18.2527 1.72472
\(113\) 12.1005 1.13832 0.569160 0.822227i \(-0.307269\pi\)
0.569160 + 0.822227i \(0.307269\pi\)
\(114\) −7.00960 −0.656509
\(115\) −16.7714 −1.56394
\(116\) −8.16471 −0.758074
\(117\) 3.08636 0.285334
\(118\) −25.9314 −2.38718
\(119\) 3.71645 0.340687
\(120\) −2.36914 −0.216272
\(121\) −4.82648 −0.438771
\(122\) 22.7997 2.06419
\(123\) 1.22529 0.110481
\(124\) 14.3260 1.28652
\(125\) 12.1659 1.08815
\(126\) 6.74901 0.601249
\(127\) −2.22421 −0.197367 −0.0986835 0.995119i \(-0.531463\pi\)
−0.0986835 + 0.995119i \(0.531463\pi\)
\(128\) −9.57286 −0.846129
\(129\) −1.24300 −0.109440
\(130\) 10.4128 0.913262
\(131\) −5.60301 −0.489537 −0.244768 0.969582i \(-0.578712\pi\)
−0.244768 + 0.969582i \(0.578712\pi\)
\(132\) 3.22455 0.280661
\(133\) −14.3453 −1.24390
\(134\) −5.35073 −0.462232
\(135\) −1.85785 −0.159898
\(136\) −1.27521 −0.109348
\(137\) −11.8173 −1.00962 −0.504810 0.863231i \(-0.668437\pi\)
−0.504810 + 0.863231i \(0.668437\pi\)
\(138\) −16.3934 −1.39550
\(139\) 7.98464 0.677249 0.338624 0.940922i \(-0.390038\pi\)
0.338624 + 0.940922i \(0.390038\pi\)
\(140\) 8.96069 0.757316
\(141\) −3.57446 −0.301024
\(142\) 13.5896 1.14041
\(143\) 7.66853 0.641275
\(144\) −4.91132 −0.409277
\(145\) 11.6882 0.970653
\(146\) −20.7432 −1.71672
\(147\) 6.81203 0.561847
\(148\) 8.80876 0.724075
\(149\) −16.3198 −1.33697 −0.668484 0.743726i \(-0.733056\pi\)
−0.668484 + 0.743726i \(0.733056\pi\)
\(150\) 2.81187 0.229588
\(151\) −16.1016 −1.31033 −0.655164 0.755487i \(-0.727400\pi\)
−0.655164 + 0.755487i \(0.727400\pi\)
\(152\) 4.92225 0.399247
\(153\) −1.00000 −0.0808452
\(154\) 16.7690 1.35128
\(155\) −20.5085 −1.64728
\(156\) 4.00542 0.320691
\(157\) −1.00000 −0.0798087
\(158\) 19.0484 1.51541
\(159\) −10.3387 −0.819909
\(160\) −11.8316 −0.935371
\(161\) −33.5496 −2.64408
\(162\) −1.81598 −0.142677
\(163\) −4.58586 −0.359192 −0.179596 0.983740i \(-0.557479\pi\)
−0.179596 + 0.983740i \(0.557479\pi\)
\(164\) 1.59017 0.124171
\(165\) −4.61611 −0.359364
\(166\) −14.2162 −1.10339
\(167\) 7.15609 0.553755 0.276877 0.960905i \(-0.410700\pi\)
0.276877 + 0.960905i \(0.410700\pi\)
\(168\) −4.73926 −0.365642
\(169\) −3.47441 −0.267262
\(170\) −3.37381 −0.258760
\(171\) 3.85995 0.295178
\(172\) −1.61315 −0.123001
\(173\) −22.4736 −1.70863 −0.854317 0.519753i \(-0.826024\pi\)
−0.854317 + 0.519753i \(0.826024\pi\)
\(174\) 11.4248 0.866113
\(175\) 5.75457 0.435005
\(176\) −12.2030 −0.919832
\(177\) 14.2796 1.07332
\(178\) −12.5636 −0.941682
\(179\) 10.4271 0.779360 0.389680 0.920950i \(-0.372586\pi\)
0.389680 + 0.920950i \(0.372586\pi\)
\(180\) −2.41109 −0.179712
\(181\) −12.4596 −0.926114 −0.463057 0.886328i \(-0.653248\pi\)
−0.463057 + 0.886328i \(0.653248\pi\)
\(182\) 20.8298 1.54401
\(183\) −12.5550 −0.928095
\(184\) 11.5117 0.848655
\(185\) −12.6102 −0.927121
\(186\) −20.0463 −1.46987
\(187\) −2.48466 −0.181696
\(188\) −4.63888 −0.338325
\(189\) −3.71645 −0.270332
\(190\) 13.0228 0.944771
\(191\) 21.2165 1.53517 0.767586 0.640946i \(-0.221458\pi\)
0.767586 + 0.640946i \(0.221458\pi\)
\(192\) −1.74233 −0.125742
\(193\) −23.0429 −1.65866 −0.829332 0.558756i \(-0.811279\pi\)
−0.829332 + 0.558756i \(0.811279\pi\)
\(194\) 23.8070 1.70924
\(195\) −5.73398 −0.410619
\(196\) 8.84054 0.631467
\(197\) 23.3293 1.66214 0.831071 0.556166i \(-0.187728\pi\)
0.831071 + 0.556166i \(0.187728\pi\)
\(198\) −4.51209 −0.320660
\(199\) −0.170206 −0.0120656 −0.00603280 0.999982i \(-0.501920\pi\)
−0.00603280 + 0.999982i \(0.501920\pi\)
\(200\) −1.97454 −0.139621
\(201\) 2.94647 0.207828
\(202\) −20.8228 −1.46509
\(203\) 23.3812 1.64104
\(204\) −1.29778 −0.0908631
\(205\) −2.27641 −0.158991
\(206\) 5.13690 0.357905
\(207\) 9.02732 0.627442
\(208\) −15.1581 −1.05102
\(209\) 9.59066 0.663400
\(210\) −12.5386 −0.865247
\(211\) 13.8948 0.956559 0.478280 0.878208i \(-0.341261\pi\)
0.478280 + 0.878208i \(0.341261\pi\)
\(212\) −13.4174 −0.921508
\(213\) −7.48333 −0.512749
\(214\) 6.87228 0.469780
\(215\) 2.30931 0.157493
\(216\) 1.27521 0.0867670
\(217\) −41.0254 −2.78498
\(218\) −12.1441 −0.822501
\(219\) 11.4226 0.771869
\(220\) −5.99072 −0.403894
\(221\) −3.08636 −0.207611
\(222\) −12.3260 −0.827269
\(223\) 20.1691 1.35062 0.675310 0.737534i \(-0.264010\pi\)
0.675310 + 0.737534i \(0.264010\pi\)
\(224\) −23.6680 −1.58139
\(225\) −1.54840 −0.103227
\(226\) −21.9743 −1.46171
\(227\) 21.7809 1.44565 0.722825 0.691031i \(-0.242843\pi\)
0.722825 + 0.691031i \(0.242843\pi\)
\(228\) 5.00939 0.331755
\(229\) −15.0518 −0.994650 −0.497325 0.867564i \(-0.665684\pi\)
−0.497325 + 0.867564i \(0.665684\pi\)
\(230\) 30.4565 2.00824
\(231\) −9.23411 −0.607560
\(232\) −8.02268 −0.526715
\(233\) 23.6200 1.54740 0.773699 0.633553i \(-0.218404\pi\)
0.773699 + 0.633553i \(0.218404\pi\)
\(234\) −5.60476 −0.366395
\(235\) 6.64080 0.433198
\(236\) 18.5318 1.20632
\(237\) −10.4893 −0.681353
\(238\) −6.74901 −0.437473
\(239\) 15.3534 0.993127 0.496563 0.868000i \(-0.334595\pi\)
0.496563 + 0.868000i \(0.334595\pi\)
\(240\) 9.12449 0.588983
\(241\) −0.0257356 −0.00165777 −0.000828887 1.00000i \(-0.500264\pi\)
−0.000828887 1.00000i \(0.500264\pi\)
\(242\) 8.76479 0.563422
\(243\) 1.00000 0.0641500
\(244\) −16.2937 −1.04310
\(245\) −12.6557 −0.808544
\(246\) −2.22511 −0.141868
\(247\) 11.9132 0.758018
\(248\) 14.0768 0.893881
\(249\) 7.82837 0.496103
\(250\) −22.0931 −1.39729
\(251\) 0.618199 0.0390204 0.0195102 0.999810i \(-0.493789\pi\)
0.0195102 + 0.999810i \(0.493789\pi\)
\(252\) −4.82316 −0.303830
\(253\) 22.4298 1.41015
\(254\) 4.03913 0.253437
\(255\) 1.85785 0.116343
\(256\) 20.8688 1.30430
\(257\) 6.60186 0.411813 0.205906 0.978572i \(-0.433986\pi\)
0.205906 + 0.978572i \(0.433986\pi\)
\(258\) 2.25727 0.140531
\(259\) −25.2256 −1.56744
\(260\) −7.44147 −0.461500
\(261\) −6.29127 −0.389420
\(262\) 10.1749 0.628610
\(263\) 12.7120 0.783854 0.391927 0.919996i \(-0.371809\pi\)
0.391927 + 0.919996i \(0.371809\pi\)
\(264\) 3.16846 0.195005
\(265\) 19.2077 1.17992
\(266\) 26.0509 1.59728
\(267\) 6.91836 0.423397
\(268\) 3.82388 0.233581
\(269\) 3.93410 0.239867 0.119933 0.992782i \(-0.461732\pi\)
0.119933 + 0.992782i \(0.461732\pi\)
\(270\) 3.37381 0.205324
\(271\) −4.94157 −0.300179 −0.150089 0.988672i \(-0.547956\pi\)
−0.150089 + 0.988672i \(0.547956\pi\)
\(272\) 4.91132 0.297793
\(273\) −11.4703 −0.694214
\(274\) 21.4600 1.29644
\(275\) −3.84725 −0.231998
\(276\) 11.7155 0.705191
\(277\) −28.9275 −1.73809 −0.869043 0.494736i \(-0.835265\pi\)
−0.869043 + 0.494736i \(0.835265\pi\)
\(278\) −14.5000 −0.869650
\(279\) 11.0388 0.660879
\(280\) 8.80482 0.526188
\(281\) −8.54227 −0.509589 −0.254795 0.966995i \(-0.582008\pi\)
−0.254795 + 0.966995i \(0.582008\pi\)
\(282\) 6.49115 0.386542
\(283\) −15.5300 −0.923165 −0.461583 0.887097i \(-0.652718\pi\)
−0.461583 + 0.887097i \(0.652718\pi\)
\(284\) −9.71174 −0.576286
\(285\) −7.17120 −0.424786
\(286\) −13.9259 −0.823456
\(287\) −4.55375 −0.268799
\(288\) 6.36845 0.375264
\(289\) 1.00000 0.0588235
\(290\) −21.2256 −1.24641
\(291\) −13.1097 −0.768505
\(292\) 14.8241 0.867514
\(293\) −9.19833 −0.537372 −0.268686 0.963228i \(-0.586589\pi\)
−0.268686 + 0.963228i \(0.586589\pi\)
\(294\) −12.3705 −0.721463
\(295\) −26.5293 −1.54459
\(296\) 8.65553 0.503093
\(297\) 2.48466 0.144174
\(298\) 29.6364 1.71679
\(299\) 27.8615 1.61127
\(300\) −2.00949 −0.116018
\(301\) 4.61956 0.266267
\(302\) 29.2402 1.68258
\(303\) 11.4665 0.658730
\(304\) −18.9575 −1.08729
\(305\) 23.3253 1.33561
\(306\) 1.81598 0.103813
\(307\) 10.6143 0.605791 0.302895 0.953024i \(-0.402047\pi\)
0.302895 + 0.953024i \(0.402047\pi\)
\(308\) −11.9839 −0.682845
\(309\) −2.82872 −0.160920
\(310\) 37.2430 2.11526
\(311\) 29.2727 1.65990 0.829950 0.557837i \(-0.188369\pi\)
0.829950 + 0.557837i \(0.188369\pi\)
\(312\) 3.93575 0.222818
\(313\) 24.2953 1.37325 0.686624 0.727012i \(-0.259092\pi\)
0.686624 + 0.727012i \(0.259092\pi\)
\(314\) 1.81598 0.102482
\(315\) 6.90460 0.389030
\(316\) −13.6128 −0.765782
\(317\) −10.0946 −0.566972 −0.283486 0.958976i \(-0.591491\pi\)
−0.283486 + 0.958976i \(0.591491\pi\)
\(318\) 18.7748 1.05284
\(319\) −15.6316 −0.875204
\(320\) 3.23698 0.180953
\(321\) −3.78434 −0.211221
\(322\) 60.9254 3.39524
\(323\) −3.85995 −0.214774
\(324\) 1.29778 0.0720991
\(325\) −4.77892 −0.265087
\(326\) 8.32782 0.461235
\(327\) 6.68734 0.369811
\(328\) 1.56251 0.0862750
\(329\) 13.2843 0.732388
\(330\) 8.38277 0.461456
\(331\) −8.02086 −0.440866 −0.220433 0.975402i \(-0.570747\pi\)
−0.220433 + 0.975402i \(0.570747\pi\)
\(332\) 10.1595 0.557577
\(333\) 6.78754 0.371955
\(334\) −12.9953 −0.711072
\(335\) −5.47409 −0.299081
\(336\) 18.2527 0.995767
\(337\) −17.1477 −0.934092 −0.467046 0.884233i \(-0.654682\pi\)
−0.467046 + 0.884233i \(0.654682\pi\)
\(338\) 6.30946 0.343189
\(339\) 12.1005 0.657209
\(340\) 2.41109 0.130759
\(341\) 27.4278 1.48530
\(342\) −7.00960 −0.379036
\(343\) 0.698588 0.0377202
\(344\) −1.58509 −0.0854622
\(345\) −16.7714 −0.902940
\(346\) 40.8116 2.19404
\(347\) −18.5049 −0.993396 −0.496698 0.867924i \(-0.665454\pi\)
−0.496698 + 0.867924i \(0.665454\pi\)
\(348\) −8.16471 −0.437674
\(349\) 0.565183 0.0302535 0.0151268 0.999886i \(-0.495185\pi\)
0.0151268 + 0.999886i \(0.495185\pi\)
\(350\) −10.4502 −0.558586
\(351\) 3.08636 0.164737
\(352\) 15.8234 0.843391
\(353\) 5.77035 0.307125 0.153562 0.988139i \(-0.450925\pi\)
0.153562 + 0.988139i \(0.450925\pi\)
\(354\) −25.9314 −1.37824
\(355\) 13.9029 0.737888
\(356\) 8.97854 0.475862
\(357\) 3.71645 0.196696
\(358\) −18.9355 −1.00077
\(359\) −7.28091 −0.384272 −0.192136 0.981368i \(-0.561541\pi\)
−0.192136 + 0.981368i \(0.561541\pi\)
\(360\) −2.36914 −0.124865
\(361\) −4.10076 −0.215829
\(362\) 22.6264 1.18922
\(363\) −4.82648 −0.253324
\(364\) −14.8860 −0.780237
\(365\) −21.2215 −1.11078
\(366\) 22.7997 1.19176
\(367\) 14.3613 0.749653 0.374826 0.927095i \(-0.377702\pi\)
0.374826 + 0.927095i \(0.377702\pi\)
\(368\) −44.3361 −2.31118
\(369\) 1.22529 0.0637862
\(370\) 22.8999 1.19051
\(371\) 38.4232 1.99483
\(372\) 14.3260 0.742771
\(373\) 19.2163 0.994981 0.497491 0.867469i \(-0.334255\pi\)
0.497491 + 0.867469i \(0.334255\pi\)
\(374\) 4.51209 0.233315
\(375\) 12.1659 0.628246
\(376\) −4.55819 −0.235071
\(377\) −19.4171 −1.00003
\(378\) 6.74901 0.347131
\(379\) 22.4576 1.15357 0.576784 0.816897i \(-0.304308\pi\)
0.576784 + 0.816897i \(0.304308\pi\)
\(380\) −9.30668 −0.477423
\(381\) −2.22421 −0.113950
\(382\) −38.5287 −1.97130
\(383\) 25.4733 1.30162 0.650812 0.759239i \(-0.274429\pi\)
0.650812 + 0.759239i \(0.274429\pi\)
\(384\) −9.57286 −0.488513
\(385\) 17.1556 0.874329
\(386\) 41.8454 2.12988
\(387\) −1.24300 −0.0631853
\(388\) −17.0136 −0.863733
\(389\) 30.2037 1.53139 0.765694 0.643205i \(-0.222395\pi\)
0.765694 + 0.643205i \(0.222395\pi\)
\(390\) 10.4128 0.527272
\(391\) −9.02732 −0.456531
\(392\) 8.68676 0.438748
\(393\) −5.60301 −0.282634
\(394\) −42.3655 −2.13434
\(395\) 19.4875 0.980523
\(396\) 3.22455 0.162040
\(397\) 32.0423 1.60816 0.804078 0.594524i \(-0.202659\pi\)
0.804078 + 0.594524i \(0.202659\pi\)
\(398\) 0.309091 0.0154933
\(399\) −14.3453 −0.718165
\(400\) 7.60471 0.380236
\(401\) −25.7052 −1.28366 −0.641829 0.766848i \(-0.721824\pi\)
−0.641829 + 0.766848i \(0.721824\pi\)
\(402\) −5.35073 −0.266870
\(403\) 34.0698 1.69714
\(404\) 14.8810 0.740356
\(405\) −1.85785 −0.0923172
\(406\) −42.4598 −2.10724
\(407\) 16.8647 0.835952
\(408\) −1.27521 −0.0631323
\(409\) 16.6542 0.823496 0.411748 0.911298i \(-0.364918\pi\)
0.411748 + 0.911298i \(0.364918\pi\)
\(410\) 4.13391 0.204159
\(411\) −11.8173 −0.582904
\(412\) −3.67107 −0.180861
\(413\) −53.0694 −2.61137
\(414\) −16.3934 −0.805693
\(415\) −14.5439 −0.713933
\(416\) 19.6553 0.963680
\(417\) 7.98464 0.391010
\(418\) −17.4165 −0.851866
\(419\) 13.2840 0.648966 0.324483 0.945892i \(-0.394810\pi\)
0.324483 + 0.945892i \(0.394810\pi\)
\(420\) 8.96069 0.437237
\(421\) 4.41988 0.215412 0.107706 0.994183i \(-0.465650\pi\)
0.107706 + 0.994183i \(0.465650\pi\)
\(422\) −25.2327 −1.22831
\(423\) −3.57446 −0.173796
\(424\) −13.1840 −0.640270
\(425\) 1.54840 0.0751086
\(426\) 13.5896 0.658417
\(427\) 46.6602 2.25805
\(428\) −4.91125 −0.237394
\(429\) 7.66853 0.370240
\(430\) −4.19366 −0.202236
\(431\) 21.6388 1.04231 0.521153 0.853463i \(-0.325502\pi\)
0.521153 + 0.853463i \(0.325502\pi\)
\(432\) −4.91132 −0.236296
\(433\) −8.20028 −0.394080 −0.197040 0.980395i \(-0.563133\pi\)
−0.197040 + 0.980395i \(0.563133\pi\)
\(434\) 74.5013 3.57617
\(435\) 11.6882 0.560407
\(436\) 8.67873 0.415636
\(437\) 34.8450 1.66686
\(438\) −20.7432 −0.991150
\(439\) 6.45795 0.308221 0.154111 0.988054i \(-0.450749\pi\)
0.154111 + 0.988054i \(0.450749\pi\)
\(440\) −5.88651 −0.280628
\(441\) 6.81203 0.324382
\(442\) 5.60476 0.266591
\(443\) 23.9380 1.13733 0.568663 0.822570i \(-0.307461\pi\)
0.568663 + 0.822570i \(0.307461\pi\)
\(444\) 8.80876 0.418045
\(445\) −12.8533 −0.609303
\(446\) −36.6266 −1.73432
\(447\) −16.3198 −0.771899
\(448\) 6.47529 0.305929
\(449\) −13.0183 −0.614372 −0.307186 0.951650i \(-0.599387\pi\)
−0.307186 + 0.951650i \(0.599387\pi\)
\(450\) 2.81187 0.132553
\(451\) 3.04443 0.143357
\(452\) 15.7038 0.738647
\(453\) −16.1016 −0.756518
\(454\) −39.5537 −1.85635
\(455\) 21.3101 0.999031
\(456\) 4.92225 0.230505
\(457\) 11.7973 0.551856 0.275928 0.961178i \(-0.411015\pi\)
0.275928 + 0.961178i \(0.411015\pi\)
\(458\) 27.3337 1.27722
\(459\) −1.00000 −0.0466760
\(460\) −21.7656 −1.01483
\(461\) −19.6307 −0.914291 −0.457146 0.889392i \(-0.651128\pi\)
−0.457146 + 0.889392i \(0.651128\pi\)
\(462\) 16.7690 0.780163
\(463\) −17.5000 −0.813293 −0.406646 0.913586i \(-0.633302\pi\)
−0.406646 + 0.913586i \(0.633302\pi\)
\(464\) 30.8984 1.43442
\(465\) −20.5085 −0.951059
\(466\) −42.8935 −1.98700
\(467\) 25.6935 1.18896 0.594478 0.804112i \(-0.297359\pi\)
0.594478 + 0.804112i \(0.297359\pi\)
\(468\) 4.00542 0.185151
\(469\) −10.9504 −0.505643
\(470\) −12.0596 −0.556266
\(471\) −1.00000 −0.0460776
\(472\) 18.2095 0.838158
\(473\) −3.08843 −0.142006
\(474\) 19.0484 0.874920
\(475\) −5.97677 −0.274233
\(476\) 4.82316 0.221069
\(477\) −10.3387 −0.473375
\(478\) −27.8814 −1.27527
\(479\) 41.8153 1.91059 0.955294 0.295658i \(-0.0955388\pi\)
0.955294 + 0.295658i \(0.0955388\pi\)
\(480\) −11.8316 −0.540036
\(481\) 20.9487 0.955181
\(482\) 0.0467353 0.00212873
\(483\) −33.5496 −1.52656
\(484\) −6.26373 −0.284715
\(485\) 24.3558 1.10594
\(486\) −1.81598 −0.0823745
\(487\) −28.3163 −1.28313 −0.641566 0.767067i \(-0.721715\pi\)
−0.641566 + 0.767067i \(0.721715\pi\)
\(488\) −16.0103 −0.724752
\(489\) −4.58586 −0.207380
\(490\) 22.9825 1.03824
\(491\) −22.4161 −1.01163 −0.505813 0.862643i \(-0.668807\pi\)
−0.505813 + 0.862643i \(0.668807\pi\)
\(492\) 1.59017 0.0716903
\(493\) 6.29127 0.283344
\(494\) −21.6341 −0.973365
\(495\) −4.61611 −0.207479
\(496\) −54.2154 −2.43434
\(497\) 27.8114 1.24751
\(498\) −14.2162 −0.637042
\(499\) 6.39303 0.286191 0.143096 0.989709i \(-0.454294\pi\)
0.143096 + 0.989709i \(0.454294\pi\)
\(500\) 15.7888 0.706095
\(501\) 7.15609 0.319710
\(502\) −1.12264 −0.0501057
\(503\) −16.8300 −0.750413 −0.375207 0.926941i \(-0.622428\pi\)
−0.375207 + 0.926941i \(0.622428\pi\)
\(504\) −4.73926 −0.211103
\(505\) −21.3029 −0.947967
\(506\) −40.7320 −1.81076
\(507\) −3.47441 −0.154304
\(508\) −2.88655 −0.128070
\(509\) −39.3748 −1.74526 −0.872629 0.488384i \(-0.837587\pi\)
−0.872629 + 0.488384i \(0.837587\pi\)
\(510\) −3.37381 −0.149395
\(511\) −42.4516 −1.87795
\(512\) −18.7516 −0.828711
\(513\) 3.85995 0.170421
\(514\) −11.9889 −0.528806
\(515\) 5.25533 0.231578
\(516\) −1.61315 −0.0710149
\(517\) −8.88131 −0.390600
\(518\) 45.8091 2.01274
\(519\) −22.4736 −0.986480
\(520\) −7.31202 −0.320653
\(521\) −4.16490 −0.182467 −0.0912337 0.995830i \(-0.529081\pi\)
−0.0912337 + 0.995830i \(0.529081\pi\)
\(522\) 11.4248 0.500050
\(523\) −13.4591 −0.588526 −0.294263 0.955724i \(-0.595074\pi\)
−0.294263 + 0.955724i \(0.595074\pi\)
\(524\) −7.27149 −0.317657
\(525\) 5.75457 0.251150
\(526\) −23.0847 −1.00654
\(527\) −11.0388 −0.480860
\(528\) −12.2030 −0.531066
\(529\) 58.4924 2.54315
\(530\) −34.8807 −1.51512
\(531\) 14.2796 0.619681
\(532\) −18.6172 −0.807156
\(533\) 3.78169 0.163803
\(534\) −12.5636 −0.543680
\(535\) 7.03072 0.303965
\(536\) 3.75736 0.162293
\(537\) 10.4271 0.449964
\(538\) −7.14426 −0.308011
\(539\) 16.9256 0.729035
\(540\) −2.41109 −0.103757
\(541\) −17.4282 −0.749297 −0.374648 0.927167i \(-0.622237\pi\)
−0.374648 + 0.927167i \(0.622237\pi\)
\(542\) 8.97379 0.385457
\(543\) −12.4596 −0.534692
\(544\) −6.36845 −0.273045
\(545\) −12.4241 −0.532188
\(546\) 20.8298 0.891435
\(547\) 3.60373 0.154084 0.0770421 0.997028i \(-0.475452\pi\)
0.0770421 + 0.997028i \(0.475452\pi\)
\(548\) −15.3363 −0.655134
\(549\) −12.5550 −0.535836
\(550\) 6.98653 0.297907
\(551\) −24.2840 −1.03453
\(552\) 11.5117 0.489971
\(553\) 38.9830 1.65772
\(554\) 52.5318 2.23186
\(555\) −12.6102 −0.535273
\(556\) 10.3623 0.439461
\(557\) −4.98862 −0.211375 −0.105687 0.994399i \(-0.533704\pi\)
−0.105687 + 0.994399i \(0.533704\pi\)
\(558\) −20.0463 −0.848629
\(559\) −3.83635 −0.162260
\(560\) −33.9107 −1.43299
\(561\) −2.48466 −0.104902
\(562\) 15.5126 0.654359
\(563\) −12.9858 −0.547287 −0.273644 0.961831i \(-0.588229\pi\)
−0.273644 + 0.961831i \(0.588229\pi\)
\(564\) −4.63888 −0.195332
\(565\) −22.4809 −0.945778
\(566\) 28.2023 1.18543
\(567\) −3.71645 −0.156076
\(568\) −9.54281 −0.400407
\(569\) 30.7135 1.28758 0.643789 0.765203i \(-0.277361\pi\)
0.643789 + 0.765203i \(0.277361\pi\)
\(570\) 13.0228 0.545464
\(571\) −0.927566 −0.0388174 −0.0194087 0.999812i \(-0.506178\pi\)
−0.0194087 + 0.999812i \(0.506178\pi\)
\(572\) 9.95210 0.416118
\(573\) 21.2165 0.886332
\(574\) 8.26952 0.345163
\(575\) −13.9779 −0.582920
\(576\) −1.74233 −0.0725971
\(577\) 34.1100 1.42002 0.710009 0.704192i \(-0.248691\pi\)
0.710009 + 0.704192i \(0.248691\pi\)
\(578\) −1.81598 −0.0755348
\(579\) −23.0429 −0.957630
\(580\) 15.1688 0.629849
\(581\) −29.0938 −1.20701
\(582\) 23.8070 0.986831
\(583\) −25.6880 −1.06389
\(584\) 14.5662 0.602755
\(585\) −5.73398 −0.237071
\(586\) 16.7040 0.690035
\(587\) 19.4587 0.803146 0.401573 0.915827i \(-0.368464\pi\)
0.401573 + 0.915827i \(0.368464\pi\)
\(588\) 8.84054 0.364578
\(589\) 42.6094 1.75569
\(590\) 48.1767 1.98340
\(591\) 23.3293 0.959639
\(592\) −33.3358 −1.37009
\(593\) −7.19389 −0.295417 −0.147709 0.989031i \(-0.547190\pi\)
−0.147709 + 0.989031i \(0.547190\pi\)
\(594\) −4.51209 −0.185133
\(595\) −6.90460 −0.283061
\(596\) −21.1796 −0.867548
\(597\) −0.170206 −0.00696607
\(598\) −50.5959 −2.06902
\(599\) −28.4340 −1.16178 −0.580892 0.813981i \(-0.697296\pi\)
−0.580892 + 0.813981i \(0.697296\pi\)
\(600\) −1.97454 −0.0806102
\(601\) 23.0662 0.940891 0.470446 0.882429i \(-0.344093\pi\)
0.470446 + 0.882429i \(0.344093\pi\)
\(602\) −8.38903 −0.341911
\(603\) 2.94647 0.119989
\(604\) −20.8964 −0.850262
\(605\) 8.96686 0.364555
\(606\) −20.8228 −0.845870
\(607\) −42.6536 −1.73126 −0.865628 0.500688i \(-0.833080\pi\)
−0.865628 + 0.500688i \(0.833080\pi\)
\(608\) 24.5819 0.996928
\(609\) 23.3812 0.947454
\(610\) −42.3584 −1.71504
\(611\) −11.0321 −0.446309
\(612\) −1.29778 −0.0524598
\(613\) 9.72973 0.392980 0.196490 0.980506i \(-0.437046\pi\)
0.196490 + 0.980506i \(0.437046\pi\)
\(614\) −19.2754 −0.777891
\(615\) −2.27641 −0.0917937
\(616\) −11.7754 −0.474446
\(617\) 17.2724 0.695359 0.347680 0.937613i \(-0.386970\pi\)
0.347680 + 0.937613i \(0.386970\pi\)
\(618\) 5.13690 0.206636
\(619\) −0.976399 −0.0392448 −0.0196224 0.999807i \(-0.506246\pi\)
−0.0196224 + 0.999807i \(0.506246\pi\)
\(620\) −26.6156 −1.06891
\(621\) 9.02732 0.362254
\(622\) −53.1586 −2.13147
\(623\) −25.7118 −1.03012
\(624\) −15.1581 −0.606809
\(625\) −14.8604 −0.594417
\(626\) −44.1197 −1.76338
\(627\) 9.59066 0.383014
\(628\) −1.29778 −0.0517872
\(629\) −6.78754 −0.270637
\(630\) −12.5386 −0.499551
\(631\) −7.08981 −0.282241 −0.141121 0.989992i \(-0.545071\pi\)
−0.141121 + 0.989992i \(0.545071\pi\)
\(632\) −13.3760 −0.532071
\(633\) 13.8948 0.552270
\(634\) 18.3317 0.728044
\(635\) 4.13225 0.163983
\(636\) −13.4174 −0.532033
\(637\) 21.0243 0.833015
\(638\) 28.3867 1.12384
\(639\) −7.48333 −0.296036
\(640\) 17.7849 0.703011
\(641\) 9.48668 0.374701 0.187351 0.982293i \(-0.440010\pi\)
0.187351 + 0.982293i \(0.440010\pi\)
\(642\) 6.87228 0.271227
\(643\) 6.57351 0.259234 0.129617 0.991564i \(-0.458625\pi\)
0.129617 + 0.991564i \(0.458625\pi\)
\(644\) −43.5402 −1.71572
\(645\) 2.30931 0.0909289
\(646\) 7.00960 0.275789
\(647\) 0.447485 0.0175925 0.00879623 0.999961i \(-0.497200\pi\)
0.00879623 + 0.999961i \(0.497200\pi\)
\(648\) 1.27521 0.0500950
\(649\) 35.4799 1.39271
\(650\) 8.67843 0.340396
\(651\) −41.0254 −1.60791
\(652\) −5.95145 −0.233077
\(653\) 26.4545 1.03525 0.517623 0.855609i \(-0.326817\pi\)
0.517623 + 0.855609i \(0.326817\pi\)
\(654\) −12.1441 −0.474871
\(655\) 10.4095 0.406734
\(656\) −6.01782 −0.234956
\(657\) 11.4226 0.445639
\(658\) −24.1241 −0.940454
\(659\) −36.1578 −1.40851 −0.704253 0.709949i \(-0.748718\pi\)
−0.704253 + 0.709949i \(0.748718\pi\)
\(660\) −5.99072 −0.233188
\(661\) 24.9296 0.969649 0.484824 0.874612i \(-0.338884\pi\)
0.484824 + 0.874612i \(0.338884\pi\)
\(662\) 14.5657 0.566113
\(663\) −3.08636 −0.119864
\(664\) 9.98281 0.387408
\(665\) 26.6515 1.03350
\(666\) −12.3260 −0.477624
\(667\) −56.7932 −2.19904
\(668\) 9.28706 0.359327
\(669\) 20.1691 0.779781
\(670\) 9.94083 0.384048
\(671\) −31.1950 −1.20427
\(672\) −23.6680 −0.913015
\(673\) −8.70737 −0.335644 −0.167822 0.985817i \(-0.553673\pi\)
−0.167822 + 0.985817i \(0.553673\pi\)
\(674\) 31.1398 1.19946
\(675\) −1.54840 −0.0595981
\(676\) −4.50904 −0.173424
\(677\) 50.9749 1.95912 0.979562 0.201143i \(-0.0644656\pi\)
0.979562 + 0.201143i \(0.0644656\pi\)
\(678\) −21.9743 −0.843917
\(679\) 48.7216 1.86976
\(680\) 2.36914 0.0908526
\(681\) 21.7809 0.834646
\(682\) −49.8083 −1.90726
\(683\) 35.9882 1.37705 0.688525 0.725213i \(-0.258259\pi\)
0.688525 + 0.725213i \(0.258259\pi\)
\(684\) 5.00939 0.191539
\(685\) 21.9547 0.838847
\(686\) −1.26862 −0.0484362
\(687\) −15.0518 −0.574261
\(688\) 6.10478 0.232743
\(689\) −31.9088 −1.21563
\(690\) 30.4565 1.15946
\(691\) −27.2666 −1.03727 −0.518636 0.854995i \(-0.673560\pi\)
−0.518636 + 0.854995i \(0.673560\pi\)
\(692\) −29.1658 −1.10872
\(693\) −9.23411 −0.350775
\(694\) 33.6046 1.27561
\(695\) −14.8342 −0.562695
\(696\) −8.02268 −0.304099
\(697\) −1.22529 −0.0464113
\(698\) −1.02636 −0.0388483
\(699\) 23.6200 0.893391
\(700\) 7.46819 0.282271
\(701\) 15.8638 0.599168 0.299584 0.954070i \(-0.403152\pi\)
0.299584 + 0.954070i \(0.403152\pi\)
\(702\) −5.60476 −0.211538
\(703\) 26.1996 0.988136
\(704\) −4.32909 −0.163159
\(705\) 6.64080 0.250107
\(706\) −10.4788 −0.394376
\(707\) −42.6145 −1.60268
\(708\) 18.5318 0.696468
\(709\) −35.9392 −1.34973 −0.674863 0.737943i \(-0.735797\pi\)
−0.674863 + 0.737943i \(0.735797\pi\)
\(710\) −25.2474 −0.947516
\(711\) −10.4893 −0.393379
\(712\) 8.82236 0.330632
\(713\) 99.6512 3.73197
\(714\) −6.74901 −0.252575
\(715\) −14.2470 −0.532806
\(716\) 13.5322 0.505721
\(717\) 15.3534 0.573382
\(718\) 13.2220 0.493440
\(719\) 7.28974 0.271862 0.135931 0.990718i \(-0.456598\pi\)
0.135931 + 0.990718i \(0.456598\pi\)
\(720\) 9.12449 0.340050
\(721\) 10.5128 0.391517
\(722\) 7.44689 0.277145
\(723\) −0.0257356 −0.000957116 0
\(724\) −16.1699 −0.600948
\(725\) 9.74142 0.361787
\(726\) 8.76479 0.325292
\(727\) 15.5564 0.576956 0.288478 0.957487i \(-0.406851\pi\)
0.288478 + 0.957487i \(0.406851\pi\)
\(728\) −14.6270 −0.542114
\(729\) 1.00000 0.0370370
\(730\) 38.5378 1.42635
\(731\) 1.24300 0.0459741
\(732\) −16.2937 −0.602234
\(733\) −2.94807 −0.108890 −0.0544448 0.998517i \(-0.517339\pi\)
−0.0544448 + 0.998517i \(0.517339\pi\)
\(734\) −26.0798 −0.962623
\(735\) −12.6557 −0.466813
\(736\) 57.4900 2.11911
\(737\) 7.32096 0.269671
\(738\) −2.22511 −0.0819074
\(739\) 23.6089 0.868468 0.434234 0.900800i \(-0.357019\pi\)
0.434234 + 0.900800i \(0.357019\pi\)
\(740\) −16.3653 −0.601601
\(741\) 11.9132 0.437642
\(742\) −69.7757 −2.56155
\(743\) 43.8295 1.60795 0.803974 0.594665i \(-0.202715\pi\)
0.803974 + 0.594665i \(0.202715\pi\)
\(744\) 14.0768 0.516082
\(745\) 30.3197 1.11083
\(746\) −34.8964 −1.27765
\(747\) 7.82837 0.286425
\(748\) −3.22455 −0.117901
\(749\) 14.0643 0.513899
\(750\) −22.0931 −0.806726
\(751\) 18.5276 0.676083 0.338042 0.941131i \(-0.390236\pi\)
0.338042 + 0.941131i \(0.390236\pi\)
\(752\) 17.5553 0.640177
\(753\) 0.618199 0.0225284
\(754\) 35.2610 1.28413
\(755\) 29.9143 1.08869
\(756\) −4.82316 −0.175416
\(757\) 34.9084 1.26877 0.634385 0.773018i \(-0.281254\pi\)
0.634385 + 0.773018i \(0.281254\pi\)
\(758\) −40.7825 −1.48129
\(759\) 22.4298 0.814150
\(760\) −9.14479 −0.331716
\(761\) −33.7526 −1.22353 −0.611766 0.791039i \(-0.709541\pi\)
−0.611766 + 0.791039i \(0.709541\pi\)
\(762\) 4.03913 0.146322
\(763\) −24.8532 −0.899746
\(764\) 27.5344 0.996161
\(765\) 1.85785 0.0671706
\(766\) −46.2590 −1.67140
\(767\) 44.0719 1.59134
\(768\) 20.8688 0.753038
\(769\) −40.4986 −1.46042 −0.730208 0.683224i \(-0.760577\pi\)
−0.730208 + 0.683224i \(0.760577\pi\)
\(770\) −31.1542 −1.12272
\(771\) 6.60186 0.237760
\(772\) −29.9047 −1.07629
\(773\) −33.4501 −1.20312 −0.601559 0.798829i \(-0.705453\pi\)
−0.601559 + 0.798829i \(0.705453\pi\)
\(774\) 2.25727 0.0811358
\(775\) −17.0926 −0.613984
\(776\) −16.7176 −0.600128
\(777\) −25.2256 −0.904962
\(778\) −54.8493 −1.96644
\(779\) 4.72958 0.169455
\(780\) −7.44147 −0.266447
\(781\) −18.5935 −0.665328
\(782\) 16.3934 0.586228
\(783\) −6.29127 −0.224831
\(784\) −33.4561 −1.19486
\(785\) 1.85785 0.0663094
\(786\) 10.1749 0.362928
\(787\) 12.7648 0.455015 0.227508 0.973776i \(-0.426942\pi\)
0.227508 + 0.973776i \(0.426942\pi\)
\(788\) 30.2764 1.07855
\(789\) 12.7120 0.452558
\(790\) −35.3889 −1.25908
\(791\) −44.9710 −1.59898
\(792\) 3.16846 0.112586
\(793\) −38.7493 −1.37603
\(794\) −58.1882 −2.06502
\(795\) 19.2077 0.681225
\(796\) −0.220891 −0.00782927
\(797\) 0.465613 0.0164929 0.00824644 0.999966i \(-0.497375\pi\)
0.00824644 + 0.999966i \(0.497375\pi\)
\(798\) 26.0509 0.922190
\(799\) 3.57446 0.126455
\(800\) −9.86093 −0.348636
\(801\) 6.91836 0.244448
\(802\) 46.6802 1.64833
\(803\) 28.3813 1.00155
\(804\) 3.82388 0.134858
\(805\) 62.3300 2.19685
\(806\) −61.8701 −2.17928
\(807\) 3.93410 0.138487
\(808\) 14.6221 0.514405
\(809\) 10.2849 0.361598 0.180799 0.983520i \(-0.442132\pi\)
0.180799 + 0.983520i \(0.442132\pi\)
\(810\) 3.37381 0.118544
\(811\) 17.8319 0.626164 0.313082 0.949726i \(-0.398639\pi\)
0.313082 + 0.949726i \(0.398639\pi\)
\(812\) 30.3438 1.06486
\(813\) −4.94157 −0.173308
\(814\) −30.6260 −1.07344
\(815\) 8.51982 0.298436
\(816\) 4.91132 0.171931
\(817\) −4.79793 −0.167858
\(818\) −30.2436 −1.05744
\(819\) −11.4703 −0.400805
\(820\) −2.95429 −0.103168
\(821\) 24.4931 0.854814 0.427407 0.904059i \(-0.359427\pi\)
0.427407 + 0.904059i \(0.359427\pi\)
\(822\) 21.4600 0.748502
\(823\) 5.88425 0.205112 0.102556 0.994727i \(-0.467298\pi\)
0.102556 + 0.994727i \(0.467298\pi\)
\(824\) −3.60721 −0.125663
\(825\) −3.84725 −0.133944
\(826\) 96.3730 3.35324
\(827\) 48.3976 1.68295 0.841474 0.540298i \(-0.181688\pi\)
0.841474 + 0.540298i \(0.181688\pi\)
\(828\) 11.7155 0.407142
\(829\) −27.4652 −0.953906 −0.476953 0.878929i \(-0.658259\pi\)
−0.476953 + 0.878929i \(0.658259\pi\)
\(830\) 26.4115 0.916756
\(831\) −28.9275 −1.00348
\(832\) −5.37745 −0.186429
\(833\) −6.81203 −0.236023
\(834\) −14.5000 −0.502092
\(835\) −13.2949 −0.460089
\(836\) 12.4466 0.430475
\(837\) 11.0388 0.381558
\(838\) −24.1235 −0.833332
\(839\) −8.25758 −0.285083 −0.142542 0.989789i \(-0.545527\pi\)
−0.142542 + 0.989789i \(0.545527\pi\)
\(840\) 8.80482 0.303795
\(841\) 10.5800 0.364828
\(842\) −8.02641 −0.276609
\(843\) −8.54227 −0.294211
\(844\) 18.0325 0.620704
\(845\) 6.45492 0.222056
\(846\) 6.49115 0.223170
\(847\) 17.9374 0.616336
\(848\) 50.7765 1.74367
\(849\) −15.5300 −0.532990
\(850\) −2.81187 −0.0964463
\(851\) 61.2732 2.10042
\(852\) −9.71174 −0.332719
\(853\) −29.7508 −1.01865 −0.509323 0.860575i \(-0.670104\pi\)
−0.509323 + 0.860575i \(0.670104\pi\)
\(854\) −84.7340 −2.89954
\(855\) −7.17120 −0.245250
\(856\) −4.82582 −0.164943
\(857\) 6.37210 0.217667 0.108833 0.994060i \(-0.465289\pi\)
0.108833 + 0.994060i \(0.465289\pi\)
\(858\) −13.9259 −0.475423
\(859\) 26.8962 0.917686 0.458843 0.888517i \(-0.348264\pi\)
0.458843 + 0.888517i \(0.348264\pi\)
\(860\) 2.99698 0.102196
\(861\) −4.55375 −0.155191
\(862\) −39.2957 −1.33842
\(863\) −50.1947 −1.70865 −0.854324 0.519741i \(-0.826028\pi\)
−0.854324 + 0.519741i \(0.826028\pi\)
\(864\) 6.36845 0.216659
\(865\) 41.7525 1.41963
\(866\) 14.8915 0.506035
\(867\) 1.00000 0.0339618
\(868\) −53.2421 −1.80715
\(869\) −26.0623 −0.884103
\(870\) −21.2256 −0.719614
\(871\) 9.09385 0.308133
\(872\) 8.52776 0.288786
\(873\) −13.1097 −0.443696
\(874\) −63.2779 −2.14041
\(875\) −45.2141 −1.52852
\(876\) 14.8241 0.500860
\(877\) −43.3499 −1.46382 −0.731911 0.681401i \(-0.761371\pi\)
−0.731911 + 0.681401i \(0.761371\pi\)
\(878\) −11.7275 −0.395784
\(879\) −9.19833 −0.310252
\(880\) 22.6712 0.764247
\(881\) −32.3313 −1.08927 −0.544635 0.838673i \(-0.683332\pi\)
−0.544635 + 0.838673i \(0.683332\pi\)
\(882\) −12.3705 −0.416537
\(883\) 23.2876 0.783691 0.391845 0.920031i \(-0.371837\pi\)
0.391845 + 0.920031i \(0.371837\pi\)
\(884\) −4.00542 −0.134717
\(885\) −26.5293 −0.891772
\(886\) −43.4708 −1.46043
\(887\) 18.2004 0.611111 0.305556 0.952174i \(-0.401158\pi\)
0.305556 + 0.952174i \(0.401158\pi\)
\(888\) 8.65553 0.290461
\(889\) 8.26619 0.277239
\(890\) 23.3413 0.782401
\(891\) 2.48466 0.0832391
\(892\) 26.1751 0.876407
\(893\) −13.7973 −0.461708
\(894\) 29.6364 0.991189
\(895\) −19.3720 −0.647535
\(896\) 35.5771 1.18855
\(897\) 27.8615 0.930269
\(898\) 23.6410 0.788910
\(899\) −69.4483 −2.31623
\(900\) −2.00949 −0.0669831
\(901\) 10.3387 0.344431
\(902\) −5.52863 −0.184083
\(903\) 4.61956 0.153729
\(904\) 15.4307 0.513217
\(905\) 23.1480 0.769466
\(906\) 29.2402 0.971439
\(907\) −10.0335 −0.333157 −0.166579 0.986028i \(-0.553272\pi\)
−0.166579 + 0.986028i \(0.553272\pi\)
\(908\) 28.2669 0.938071
\(909\) 11.4665 0.380318
\(910\) −38.6987 −1.28285
\(911\) 9.04286 0.299603 0.149802 0.988716i \(-0.452136\pi\)
0.149802 + 0.988716i \(0.452136\pi\)
\(912\) −18.9575 −0.627745
\(913\) 19.4508 0.643728
\(914\) −21.4237 −0.708634
\(915\) 23.3253 0.771112
\(916\) −19.5340 −0.645421
\(917\) 20.8233 0.687646
\(918\) 1.81598 0.0599363
\(919\) 9.36364 0.308878 0.154439 0.988002i \(-0.450643\pi\)
0.154439 + 0.988002i \(0.450643\pi\)
\(920\) −21.3870 −0.705109
\(921\) 10.6143 0.349753
\(922\) 35.6489 1.17403
\(923\) −23.0962 −0.760221
\(924\) −11.9839 −0.394241
\(925\) −10.5098 −0.345561
\(926\) 31.7796 1.04434
\(927\) −2.82872 −0.0929074
\(928\) −40.0656 −1.31522
\(929\) −18.2661 −0.599290 −0.299645 0.954051i \(-0.596868\pi\)
−0.299645 + 0.954051i \(0.596868\pi\)
\(930\) 37.2430 1.22125
\(931\) 26.2941 0.861755
\(932\) 30.6537 1.00410
\(933\) 29.2727 0.958344
\(934\) −46.6590 −1.52673
\(935\) 4.61611 0.150963
\(936\) 3.93575 0.128644
\(937\) 54.1527 1.76909 0.884546 0.466452i \(-0.154468\pi\)
0.884546 + 0.466452i \(0.154468\pi\)
\(938\) 19.8857 0.649292
\(939\) 24.2953 0.792846
\(940\) 8.61833 0.281099
\(941\) −40.3776 −1.31627 −0.658136 0.752899i \(-0.728655\pi\)
−0.658136 + 0.752899i \(0.728655\pi\)
\(942\) 1.81598 0.0591678
\(943\) 11.0611 0.360199
\(944\) −70.1317 −2.28259
\(945\) 6.90460 0.224607
\(946\) 5.60853 0.182349
\(947\) −8.88176 −0.288618 −0.144309 0.989533i \(-0.546096\pi\)
−0.144309 + 0.989533i \(0.546096\pi\)
\(948\) −13.6128 −0.442125
\(949\) 35.2542 1.14440
\(950\) 10.8537 0.352140
\(951\) −10.0946 −0.327341
\(952\) 4.73926 0.153600
\(953\) −21.9433 −0.710812 −0.355406 0.934712i \(-0.615657\pi\)
−0.355406 + 0.934712i \(0.615657\pi\)
\(954\) 18.7748 0.607857
\(955\) −39.4170 −1.27550
\(956\) 19.9254 0.644432
\(957\) −15.6316 −0.505299
\(958\) −75.9357 −2.45337
\(959\) 43.9184 1.41820
\(960\) 3.23698 0.104473
\(961\) 90.8562 2.93084
\(962\) −38.0425 −1.22654
\(963\) −3.78434 −0.121949
\(964\) −0.0333992 −0.00107572
\(965\) 42.8102 1.37811
\(966\) 60.9254 1.96024
\(967\) 9.73403 0.313025 0.156513 0.987676i \(-0.449975\pi\)
0.156513 + 0.987676i \(0.449975\pi\)
\(968\) −6.15477 −0.197822
\(969\) −3.85995 −0.124000
\(970\) −44.2297 −1.42013
\(971\) 34.2720 1.09984 0.549920 0.835218i \(-0.314658\pi\)
0.549920 + 0.835218i \(0.314658\pi\)
\(972\) 1.29778 0.0416265
\(973\) −29.6746 −0.951323
\(974\) 51.4218 1.64766
\(975\) −4.77892 −0.153048
\(976\) 61.6619 1.97375
\(977\) −4.82773 −0.154453 −0.0772264 0.997014i \(-0.524606\pi\)
−0.0772264 + 0.997014i \(0.524606\pi\)
\(978\) 8.32782 0.266294
\(979\) 17.1898 0.549387
\(980\) −16.4244 −0.524658
\(981\) 6.68734 0.213510
\(982\) 40.7072 1.29902
\(983\) 39.0588 1.24578 0.622891 0.782309i \(-0.285958\pi\)
0.622891 + 0.782309i \(0.285958\pi\)
\(984\) 1.56251 0.0498109
\(985\) −43.3423 −1.38100
\(986\) −11.4248 −0.363840
\(987\) 13.2843 0.422845
\(988\) 15.4608 0.491872
\(989\) −11.2210 −0.356806
\(990\) 8.38277 0.266422
\(991\) −34.8477 −1.10697 −0.553487 0.832858i \(-0.686703\pi\)
−0.553487 + 0.832858i \(0.686703\pi\)
\(992\) 70.3003 2.23204
\(993\) −8.02086 −0.254534
\(994\) −50.5050 −1.60192
\(995\) 0.316217 0.0100248
\(996\) 10.1595 0.321917
\(997\) 2.66730 0.0844742 0.0422371 0.999108i \(-0.486552\pi\)
0.0422371 + 0.999108i \(0.486552\pi\)
\(998\) −11.6096 −0.367496
\(999\) 6.78754 0.214748
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 8007.2.a.h.1.11 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.h.1.11 56 1.1 even 1 trivial