Properties

Label 8013.2.a.c.1.3
Level $8013$
Weight $2$
Character 8013.1
Self dual yes
Analytic conductor $63.984$
Analytic rank $1$
Dimension $116$
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] = [8013,2,Mod(1,8013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8013, 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("8013.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8013.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: \(63.9841271397\)
Analytic rank: \(1\)
Dimension: \(116\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 8013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.74646 q^{2} -1.00000 q^{3} +5.54305 q^{4} -2.85945 q^{5} +2.74646 q^{6} +1.69114 q^{7} -9.73084 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.74646 q^{2} -1.00000 q^{3} +5.54305 q^{4} -2.85945 q^{5} +2.74646 q^{6} +1.69114 q^{7} -9.73084 q^{8} +1.00000 q^{9} +7.85338 q^{10} +2.11017 q^{11} -5.54305 q^{12} +1.31830 q^{13} -4.64465 q^{14} +2.85945 q^{15} +15.6393 q^{16} +4.38429 q^{17} -2.74646 q^{18} -0.994689 q^{19} -15.8501 q^{20} -1.69114 q^{21} -5.79550 q^{22} -3.45019 q^{23} +9.73084 q^{24} +3.17647 q^{25} -3.62067 q^{26} -1.00000 q^{27} +9.37407 q^{28} -1.96936 q^{29} -7.85338 q^{30} +10.5424 q^{31} -23.4910 q^{32} -2.11017 q^{33} -12.0413 q^{34} -4.83574 q^{35} +5.54305 q^{36} -6.94781 q^{37} +2.73187 q^{38} -1.31830 q^{39} +27.8249 q^{40} +8.37730 q^{41} +4.64465 q^{42} +4.96606 q^{43} +11.6968 q^{44} -2.85945 q^{45} +9.47582 q^{46} -6.26352 q^{47} -15.6393 q^{48} -4.14004 q^{49} -8.72405 q^{50} -4.38429 q^{51} +7.30741 q^{52} -1.58492 q^{53} +2.74646 q^{54} -6.03393 q^{55} -16.4562 q^{56} +0.994689 q^{57} +5.40878 q^{58} -9.41363 q^{59} +15.8501 q^{60} -5.77156 q^{61} -28.9544 q^{62} +1.69114 q^{63} +33.2385 q^{64} -3.76962 q^{65} +5.79550 q^{66} +7.36669 q^{67} +24.3023 q^{68} +3.45019 q^{69} +13.2812 q^{70} -3.12053 q^{71} -9.73084 q^{72} -8.72593 q^{73} +19.0819 q^{74} -3.17647 q^{75} -5.51361 q^{76} +3.56859 q^{77} +3.62067 q^{78} +0.564522 q^{79} -44.7198 q^{80} +1.00000 q^{81} -23.0079 q^{82} -9.60777 q^{83} -9.37407 q^{84} -12.5367 q^{85} -13.6391 q^{86} +1.96936 q^{87} -20.5337 q^{88} -4.02539 q^{89} +7.85338 q^{90} +2.22943 q^{91} -19.1246 q^{92} -10.5424 q^{93} +17.2025 q^{94} +2.84427 q^{95} +23.4910 q^{96} -3.34692 q^{97} +11.3705 q^{98} +2.11017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74646 −1.94204 −0.971021 0.238996i \(-0.923182\pi\)
−0.971021 + 0.238996i \(0.923182\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.54305 2.77152
\(5\) −2.85945 −1.27879 −0.639393 0.768880i \(-0.720814\pi\)
−0.639393 + 0.768880i \(0.720814\pi\)
\(6\) 2.74646 1.12124
\(7\) 1.69114 0.639191 0.319596 0.947554i \(-0.396453\pi\)
0.319596 + 0.947554i \(0.396453\pi\)
\(8\) −9.73084 −3.44037
\(9\) 1.00000 0.333333
\(10\) 7.85338 2.48346
\(11\) 2.11017 0.636240 0.318120 0.948050i \(-0.396948\pi\)
0.318120 + 0.948050i \(0.396948\pi\)
\(12\) −5.54305 −1.60014
\(13\) 1.31830 0.365631 0.182816 0.983147i \(-0.441479\pi\)
0.182816 + 0.983147i \(0.441479\pi\)
\(14\) −4.64465 −1.24134
\(15\) 2.85945 0.738308
\(16\) 15.6393 3.90982
\(17\) 4.38429 1.06335 0.531673 0.846950i \(-0.321563\pi\)
0.531673 + 0.846950i \(0.321563\pi\)
\(18\) −2.74646 −0.647347
\(19\) −0.994689 −0.228197 −0.114099 0.993469i \(-0.536398\pi\)
−0.114099 + 0.993469i \(0.536398\pi\)
\(20\) −15.8501 −3.54419
\(21\) −1.69114 −0.369037
\(22\) −5.79550 −1.23560
\(23\) −3.45019 −0.719415 −0.359707 0.933065i \(-0.617123\pi\)
−0.359707 + 0.933065i \(0.617123\pi\)
\(24\) 9.73084 1.98630
\(25\) 3.17647 0.635294
\(26\) −3.62067 −0.710071
\(27\) −1.00000 −0.192450
\(28\) 9.37407 1.77153
\(29\) −1.96936 −0.365702 −0.182851 0.983141i \(-0.558533\pi\)
−0.182851 + 0.983141i \(0.558533\pi\)
\(30\) −7.85338 −1.43382
\(31\) 10.5424 1.89348 0.946740 0.322000i \(-0.104355\pi\)
0.946740 + 0.322000i \(0.104355\pi\)
\(32\) −23.4910 −4.15266
\(33\) −2.11017 −0.367333
\(34\) −12.0413 −2.06506
\(35\) −4.83574 −0.817389
\(36\) 5.54305 0.923841
\(37\) −6.94781 −1.14221 −0.571107 0.820876i \(-0.693486\pi\)
−0.571107 + 0.820876i \(0.693486\pi\)
\(38\) 2.73187 0.443169
\(39\) −1.31830 −0.211097
\(40\) 27.8249 4.39950
\(41\) 8.37730 1.30832 0.654158 0.756358i \(-0.273023\pi\)
0.654158 + 0.756358i \(0.273023\pi\)
\(42\) 4.64465 0.716685
\(43\) 4.96606 0.757317 0.378658 0.925537i \(-0.376386\pi\)
0.378658 + 0.925537i \(0.376386\pi\)
\(44\) 11.6968 1.76335
\(45\) −2.85945 −0.426262
\(46\) 9.47582 1.39713
\(47\) −6.26352 −0.913629 −0.456814 0.889562i \(-0.651010\pi\)
−0.456814 + 0.889562i \(0.651010\pi\)
\(48\) −15.6393 −2.25734
\(49\) −4.14004 −0.591435
\(50\) −8.72405 −1.23377
\(51\) −4.38429 −0.613923
\(52\) 7.30741 1.01336
\(53\) −1.58492 −0.217705 −0.108853 0.994058i \(-0.534718\pi\)
−0.108853 + 0.994058i \(0.534718\pi\)
\(54\) 2.74646 0.373746
\(55\) −6.03393 −0.813615
\(56\) −16.4562 −2.19905
\(57\) 0.994689 0.131750
\(58\) 5.40878 0.710208
\(59\) −9.41363 −1.22555 −0.612775 0.790257i \(-0.709947\pi\)
−0.612775 + 0.790257i \(0.709947\pi\)
\(60\) 15.8501 2.04624
\(61\) −5.77156 −0.738973 −0.369486 0.929236i \(-0.620466\pi\)
−0.369486 + 0.929236i \(0.620466\pi\)
\(62\) −28.9544 −3.67721
\(63\) 1.69114 0.213064
\(64\) 33.2385 4.15482
\(65\) −3.76962 −0.467564
\(66\) 5.79550 0.713377
\(67\) 7.36669 0.899984 0.449992 0.893033i \(-0.351427\pi\)
0.449992 + 0.893033i \(0.351427\pi\)
\(68\) 24.3023 2.94709
\(69\) 3.45019 0.415354
\(70\) 13.2812 1.58740
\(71\) −3.12053 −0.370339 −0.185170 0.982707i \(-0.559283\pi\)
−0.185170 + 0.982707i \(0.559283\pi\)
\(72\) −9.73084 −1.14679
\(73\) −8.72593 −1.02129 −0.510646 0.859791i \(-0.670594\pi\)
−0.510646 + 0.859791i \(0.670594\pi\)
\(74\) 19.0819 2.21823
\(75\) −3.17647 −0.366787
\(76\) −5.51361 −0.632454
\(77\) 3.56859 0.406679
\(78\) 3.62067 0.409960
\(79\) 0.564522 0.0635137 0.0317568 0.999496i \(-0.489890\pi\)
0.0317568 + 0.999496i \(0.489890\pi\)
\(80\) −44.7198 −4.99982
\(81\) 1.00000 0.111111
\(82\) −23.0079 −2.54080
\(83\) −9.60777 −1.05459 −0.527295 0.849682i \(-0.676794\pi\)
−0.527295 + 0.849682i \(0.676794\pi\)
\(84\) −9.37407 −1.02280
\(85\) −12.5367 −1.35979
\(86\) −13.6391 −1.47074
\(87\) 1.96936 0.211138
\(88\) −20.5337 −2.18890
\(89\) −4.02539 −0.426691 −0.213345 0.976977i \(-0.568436\pi\)
−0.213345 + 0.976977i \(0.568436\pi\)
\(90\) 7.85338 0.827818
\(91\) 2.22943 0.233708
\(92\) −19.1246 −1.99388
\(93\) −10.5424 −1.09320
\(94\) 17.2025 1.77430
\(95\) 2.84427 0.291816
\(96\) 23.4910 2.39754
\(97\) −3.34692 −0.339828 −0.169914 0.985459i \(-0.554349\pi\)
−0.169914 + 0.985459i \(0.554349\pi\)
\(98\) 11.3705 1.14859
\(99\) 2.11017 0.212080
\(100\) 17.6073 1.76073
\(101\) 5.62201 0.559411 0.279706 0.960086i \(-0.409763\pi\)
0.279706 + 0.960086i \(0.409763\pi\)
\(102\) 12.0413 1.19226
\(103\) −9.64887 −0.950731 −0.475366 0.879788i \(-0.657684\pi\)
−0.475366 + 0.879788i \(0.657684\pi\)
\(104\) −12.8282 −1.25791
\(105\) 4.83574 0.471920
\(106\) 4.35292 0.422793
\(107\) 14.8604 1.43661 0.718306 0.695727i \(-0.244918\pi\)
0.718306 + 0.695727i \(0.244918\pi\)
\(108\) −5.54305 −0.533380
\(109\) 8.27783 0.792872 0.396436 0.918062i \(-0.370247\pi\)
0.396436 + 0.918062i \(0.370247\pi\)
\(110\) 16.5720 1.58007
\(111\) 6.94781 0.659457
\(112\) 26.4482 2.49912
\(113\) −11.6422 −1.09520 −0.547602 0.836739i \(-0.684459\pi\)
−0.547602 + 0.836739i \(0.684459\pi\)
\(114\) −2.73187 −0.255863
\(115\) 9.86566 0.919978
\(116\) −10.9163 −1.01355
\(117\) 1.31830 0.121877
\(118\) 25.8542 2.38007
\(119\) 7.41445 0.679682
\(120\) −27.8249 −2.54005
\(121\) −6.54718 −0.595198
\(122\) 15.8514 1.43512
\(123\) −8.37730 −0.755356
\(124\) 58.4373 5.24782
\(125\) 5.21430 0.466381
\(126\) −4.64465 −0.413778
\(127\) 0.455510 0.0404200 0.0202100 0.999796i \(-0.493567\pi\)
0.0202100 + 0.999796i \(0.493567\pi\)
\(128\) −44.3063 −3.91616
\(129\) −4.96606 −0.437237
\(130\) 10.3531 0.908029
\(131\) −4.88141 −0.426491 −0.213245 0.976999i \(-0.568403\pi\)
−0.213245 + 0.976999i \(0.568403\pi\)
\(132\) −11.6968 −1.01807
\(133\) −1.68216 −0.145862
\(134\) −20.2323 −1.74781
\(135\) 2.85945 0.246103
\(136\) −42.6628 −3.65831
\(137\) −7.47667 −0.638775 −0.319388 0.947624i \(-0.603477\pi\)
−0.319388 + 0.947624i \(0.603477\pi\)
\(138\) −9.47582 −0.806635
\(139\) 15.5388 1.31798 0.658992 0.752150i \(-0.270983\pi\)
0.658992 + 0.752150i \(0.270983\pi\)
\(140\) −26.8047 −2.26541
\(141\) 6.26352 0.527484
\(142\) 8.57042 0.719214
\(143\) 2.78184 0.232629
\(144\) 15.6393 1.30327
\(145\) 5.63130 0.467654
\(146\) 23.9654 1.98339
\(147\) 4.14004 0.341465
\(148\) −38.5121 −3.16567
\(149\) 4.52115 0.370387 0.185194 0.982702i \(-0.440709\pi\)
0.185194 + 0.982702i \(0.440709\pi\)
\(150\) 8.72405 0.712316
\(151\) −4.08267 −0.332243 −0.166122 0.986105i \(-0.553124\pi\)
−0.166122 + 0.986105i \(0.553124\pi\)
\(152\) 9.67916 0.785084
\(153\) 4.38429 0.354449
\(154\) −9.80100 −0.789787
\(155\) −30.1456 −2.42136
\(156\) −7.30741 −0.585061
\(157\) −0.220306 −0.0175823 −0.00879117 0.999961i \(-0.502798\pi\)
−0.00879117 + 0.999961i \(0.502798\pi\)
\(158\) −1.55044 −0.123346
\(159\) 1.58492 0.125692
\(160\) 67.1714 5.31036
\(161\) −5.83476 −0.459844
\(162\) −2.74646 −0.215782
\(163\) −9.65358 −0.756126 −0.378063 0.925780i \(-0.623410\pi\)
−0.378063 + 0.925780i \(0.623410\pi\)
\(164\) 46.4358 3.62603
\(165\) 6.03393 0.469741
\(166\) 26.3874 2.04806
\(167\) 9.54341 0.738491 0.369246 0.929332i \(-0.379616\pi\)
0.369246 + 0.929332i \(0.379616\pi\)
\(168\) 16.4562 1.26962
\(169\) −11.2621 −0.866314
\(170\) 34.4315 2.64077
\(171\) −0.994689 −0.0760658
\(172\) 27.5271 2.09892
\(173\) −2.24820 −0.170928 −0.0854639 0.996341i \(-0.527237\pi\)
−0.0854639 + 0.996341i \(0.527237\pi\)
\(174\) −5.40878 −0.410039
\(175\) 5.37186 0.406074
\(176\) 33.0015 2.48758
\(177\) 9.41363 0.707572
\(178\) 11.0556 0.828651
\(179\) −22.6124 −1.69013 −0.845064 0.534665i \(-0.820438\pi\)
−0.845064 + 0.534665i \(0.820438\pi\)
\(180\) −15.8501 −1.18140
\(181\) 5.51831 0.410173 0.205086 0.978744i \(-0.434252\pi\)
0.205086 + 0.978744i \(0.434252\pi\)
\(182\) −6.12305 −0.453871
\(183\) 5.77156 0.426646
\(184\) 33.5733 2.47505
\(185\) 19.8669 1.46065
\(186\) 28.9544 2.12304
\(187\) 9.25160 0.676544
\(188\) −34.7190 −2.53214
\(189\) −1.69114 −0.123012
\(190\) −7.81167 −0.566718
\(191\) 21.0522 1.52328 0.761642 0.647998i \(-0.224394\pi\)
0.761642 + 0.647998i \(0.224394\pi\)
\(192\) −33.2385 −2.39878
\(193\) −0.181678 −0.0130775 −0.00653875 0.999979i \(-0.502081\pi\)
−0.00653875 + 0.999979i \(0.502081\pi\)
\(194\) 9.19218 0.659960
\(195\) 3.76962 0.269948
\(196\) −22.9485 −1.63918
\(197\) −2.81430 −0.200511 −0.100255 0.994962i \(-0.531966\pi\)
−0.100255 + 0.994962i \(0.531966\pi\)
\(198\) −5.79550 −0.411868
\(199\) −8.25008 −0.584833 −0.292416 0.956291i \(-0.594459\pi\)
−0.292416 + 0.956291i \(0.594459\pi\)
\(200\) −30.9097 −2.18565
\(201\) −7.36669 −0.519606
\(202\) −15.4406 −1.08640
\(203\) −3.33047 −0.233753
\(204\) −24.3023 −1.70150
\(205\) −23.9545 −1.67306
\(206\) 26.5002 1.84636
\(207\) −3.45019 −0.239805
\(208\) 20.6173 1.42955
\(209\) −2.09896 −0.145188
\(210\) −13.2812 −0.916487
\(211\) −4.88830 −0.336525 −0.168262 0.985742i \(-0.553816\pi\)
−0.168262 + 0.985742i \(0.553816\pi\)
\(212\) −8.78528 −0.603375
\(213\) 3.12053 0.213815
\(214\) −40.8136 −2.78996
\(215\) −14.2002 −0.968446
\(216\) 9.73084 0.662100
\(217\) 17.8288 1.21030
\(218\) −22.7347 −1.53979
\(219\) 8.72593 0.589644
\(220\) −33.4464 −2.25495
\(221\) 5.77982 0.388793
\(222\) −19.0819 −1.28069
\(223\) −17.2666 −1.15626 −0.578130 0.815945i \(-0.696217\pi\)
−0.578130 + 0.815945i \(0.696217\pi\)
\(224\) −39.7266 −2.65434
\(225\) 3.17647 0.211765
\(226\) 31.9748 2.12693
\(227\) −8.68134 −0.576201 −0.288100 0.957600i \(-0.593024\pi\)
−0.288100 + 0.957600i \(0.593024\pi\)
\(228\) 5.51361 0.365148
\(229\) −29.9412 −1.97857 −0.989285 0.145995i \(-0.953362\pi\)
−0.989285 + 0.145995i \(0.953362\pi\)
\(230\) −27.0957 −1.78663
\(231\) −3.56859 −0.234796
\(232\) 19.1636 1.25815
\(233\) 20.9419 1.37195 0.685974 0.727626i \(-0.259376\pi\)
0.685974 + 0.727626i \(0.259376\pi\)
\(234\) −3.62067 −0.236690
\(235\) 17.9102 1.16834
\(236\) −52.1802 −3.39664
\(237\) −0.564522 −0.0366697
\(238\) −20.3635 −1.31997
\(239\) 6.72716 0.435144 0.217572 0.976044i \(-0.430186\pi\)
0.217572 + 0.976044i \(0.430186\pi\)
\(240\) 44.7198 2.88665
\(241\) 27.1333 1.74781 0.873906 0.486095i \(-0.161579\pi\)
0.873906 + 0.486095i \(0.161579\pi\)
\(242\) 17.9816 1.15590
\(243\) −1.00000 −0.0641500
\(244\) −31.9920 −2.04808
\(245\) 11.8383 0.756319
\(246\) 23.0079 1.46693
\(247\) −1.31130 −0.0834361
\(248\) −102.587 −6.51427
\(249\) 9.60777 0.608868
\(250\) −14.3209 −0.905731
\(251\) −16.7055 −1.05444 −0.527221 0.849728i \(-0.676766\pi\)
−0.527221 + 0.849728i \(0.676766\pi\)
\(252\) 9.37407 0.590511
\(253\) −7.28049 −0.457721
\(254\) −1.25104 −0.0784973
\(255\) 12.5367 0.785077
\(256\) 55.2086 3.45053
\(257\) −7.13776 −0.445241 −0.222621 0.974905i \(-0.571461\pi\)
−0.222621 + 0.974905i \(0.571461\pi\)
\(258\) 13.6391 0.849132
\(259\) −11.7497 −0.730092
\(260\) −20.8952 −1.29587
\(261\) −1.96936 −0.121901
\(262\) 13.4066 0.828262
\(263\) −5.37160 −0.331227 −0.165613 0.986191i \(-0.552960\pi\)
−0.165613 + 0.986191i \(0.552960\pi\)
\(264\) 20.5337 1.26376
\(265\) 4.53200 0.278399
\(266\) 4.61998 0.283269
\(267\) 4.02539 0.246350
\(268\) 40.8339 2.49433
\(269\) 25.7170 1.56799 0.783997 0.620764i \(-0.213178\pi\)
0.783997 + 0.620764i \(0.213178\pi\)
\(270\) −7.85338 −0.477941
\(271\) 16.9470 1.02945 0.514727 0.857354i \(-0.327893\pi\)
0.514727 + 0.857354i \(0.327893\pi\)
\(272\) 68.5671 4.15749
\(273\) −2.22943 −0.134932
\(274\) 20.5344 1.24053
\(275\) 6.70289 0.404200
\(276\) 19.1246 1.15116
\(277\) −7.64851 −0.459555 −0.229777 0.973243i \(-0.573800\pi\)
−0.229777 + 0.973243i \(0.573800\pi\)
\(278\) −42.6767 −2.55958
\(279\) 10.5424 0.631160
\(280\) 47.0558 2.81212
\(281\) 3.16013 0.188518 0.0942588 0.995548i \(-0.469952\pi\)
0.0942588 + 0.995548i \(0.469952\pi\)
\(282\) −17.2025 −1.02440
\(283\) 21.4093 1.27265 0.636325 0.771421i \(-0.280454\pi\)
0.636325 + 0.771421i \(0.280454\pi\)
\(284\) −17.2973 −1.02640
\(285\) −2.84427 −0.168480
\(286\) −7.64022 −0.451776
\(287\) 14.1672 0.836263
\(288\) −23.4910 −1.38422
\(289\) 2.22200 0.130706
\(290\) −15.4662 −0.908204
\(291\) 3.34692 0.196200
\(292\) −48.3682 −2.83054
\(293\) −27.5891 −1.61177 −0.805887 0.592069i \(-0.798311\pi\)
−0.805887 + 0.592069i \(0.798311\pi\)
\(294\) −11.3705 −0.663139
\(295\) 26.9178 1.56722
\(296\) 67.6081 3.92964
\(297\) −2.11017 −0.122444
\(298\) −12.4172 −0.719307
\(299\) −4.54840 −0.263041
\(300\) −17.6073 −1.01656
\(301\) 8.39830 0.484070
\(302\) 11.2129 0.645230
\(303\) −5.62201 −0.322976
\(304\) −15.5562 −0.892210
\(305\) 16.5035 0.944988
\(306\) −12.0413 −0.688354
\(307\) −23.3751 −1.33409 −0.667044 0.745019i \(-0.732441\pi\)
−0.667044 + 0.745019i \(0.732441\pi\)
\(308\) 19.7809 1.12712
\(309\) 9.64887 0.548905
\(310\) 82.7938 4.70237
\(311\) 11.3883 0.645770 0.322885 0.946438i \(-0.395347\pi\)
0.322885 + 0.946438i \(0.395347\pi\)
\(312\) 12.8282 0.726253
\(313\) 31.5987 1.78606 0.893031 0.449995i \(-0.148574\pi\)
0.893031 + 0.449995i \(0.148574\pi\)
\(314\) 0.605062 0.0341456
\(315\) −4.83574 −0.272463
\(316\) 3.12917 0.176030
\(317\) 3.45277 0.193927 0.0969634 0.995288i \(-0.469087\pi\)
0.0969634 + 0.995288i \(0.469087\pi\)
\(318\) −4.35292 −0.244099
\(319\) −4.15569 −0.232674
\(320\) −95.0440 −5.31312
\(321\) −14.8604 −0.829428
\(322\) 16.0249 0.893035
\(323\) −4.36100 −0.242653
\(324\) 5.54305 0.307947
\(325\) 4.18755 0.232283
\(326\) 26.5132 1.46843
\(327\) −8.27783 −0.457765
\(328\) −81.5182 −4.50109
\(329\) −10.5925 −0.583983
\(330\) −16.5720 −0.912256
\(331\) 14.4247 0.792856 0.396428 0.918066i \(-0.370250\pi\)
0.396428 + 0.918066i \(0.370250\pi\)
\(332\) −53.2563 −2.92282
\(333\) −6.94781 −0.380738
\(334\) −26.2106 −1.43418
\(335\) −21.0647 −1.15089
\(336\) −26.4482 −1.44287
\(337\) 19.4647 1.06031 0.530154 0.847901i \(-0.322134\pi\)
0.530154 + 0.847901i \(0.322134\pi\)
\(338\) 30.9309 1.68242
\(339\) 11.6422 0.632317
\(340\) −69.4914 −3.76870
\(341\) 22.2464 1.20471
\(342\) 2.73187 0.147723
\(343\) −18.8394 −1.01723
\(344\) −48.3239 −2.60545
\(345\) −9.86566 −0.531149
\(346\) 6.17460 0.331949
\(347\) 11.9970 0.644032 0.322016 0.946734i \(-0.395639\pi\)
0.322016 + 0.946734i \(0.395639\pi\)
\(348\) 10.9163 0.585174
\(349\) 0.0640178 0.00342679 0.00171340 0.999999i \(-0.499455\pi\)
0.00171340 + 0.999999i \(0.499455\pi\)
\(350\) −14.7536 −0.788613
\(351\) −1.31830 −0.0703658
\(352\) −49.5700 −2.64209
\(353\) −8.53915 −0.454493 −0.227246 0.973837i \(-0.572972\pi\)
−0.227246 + 0.973837i \(0.572972\pi\)
\(354\) −25.8542 −1.37413
\(355\) 8.92302 0.473584
\(356\) −22.3130 −1.18258
\(357\) −7.41445 −0.392414
\(358\) 62.1040 3.28230
\(359\) 8.62463 0.455191 0.227595 0.973756i \(-0.426914\pi\)
0.227595 + 0.973756i \(0.426914\pi\)
\(360\) 27.8249 1.46650
\(361\) −18.0106 −0.947926
\(362\) −15.1558 −0.796572
\(363\) 6.54718 0.343638
\(364\) 12.3579 0.647728
\(365\) 24.9514 1.30601
\(366\) −15.8514 −0.828564
\(367\) 2.84408 0.148460 0.0742299 0.997241i \(-0.476350\pi\)
0.0742299 + 0.997241i \(0.476350\pi\)
\(368\) −53.9585 −2.81278
\(369\) 8.37730 0.436105
\(370\) −54.5638 −2.83664
\(371\) −2.68032 −0.139155
\(372\) −58.4373 −3.02983
\(373\) −20.4244 −1.05754 −0.528768 0.848766i \(-0.677346\pi\)
−0.528768 + 0.848766i \(0.677346\pi\)
\(374\) −25.4091 −1.31388
\(375\) −5.21430 −0.269265
\(376\) 60.9493 3.14322
\(377\) −2.59622 −0.133712
\(378\) 4.64465 0.238895
\(379\) −1.47694 −0.0758652 −0.0379326 0.999280i \(-0.512077\pi\)
−0.0379326 + 0.999280i \(0.512077\pi\)
\(380\) 15.7659 0.808774
\(381\) −0.455510 −0.0233365
\(382\) −57.8191 −2.95828
\(383\) −12.4669 −0.637030 −0.318515 0.947918i \(-0.603184\pi\)
−0.318515 + 0.947918i \(0.603184\pi\)
\(384\) 44.3063 2.26100
\(385\) −10.2042 −0.520055
\(386\) 0.498973 0.0253970
\(387\) 4.96606 0.252439
\(388\) −18.5521 −0.941841
\(389\) 14.1089 0.715351 0.357676 0.933846i \(-0.383569\pi\)
0.357676 + 0.933846i \(0.383569\pi\)
\(390\) −10.3531 −0.524251
\(391\) −15.1266 −0.764987
\(392\) 40.2861 2.03476
\(393\) 4.88141 0.246235
\(394\) 7.72937 0.389400
\(395\) −1.61422 −0.0812204
\(396\) 11.6968 0.587785
\(397\) 9.46892 0.475232 0.237616 0.971359i \(-0.423634\pi\)
0.237616 + 0.971359i \(0.423634\pi\)
\(398\) 22.6585 1.13577
\(399\) 1.68216 0.0842133
\(400\) 49.6777 2.48389
\(401\) 29.6367 1.47999 0.739993 0.672614i \(-0.234829\pi\)
0.739993 + 0.672614i \(0.234829\pi\)
\(402\) 20.2323 1.00910
\(403\) 13.8981 0.692315
\(404\) 31.1631 1.55042
\(405\) −2.85945 −0.142087
\(406\) 9.14701 0.453959
\(407\) −14.6611 −0.726722
\(408\) 42.6628 2.11212
\(409\) −20.5317 −1.01523 −0.507614 0.861585i \(-0.669472\pi\)
−0.507614 + 0.861585i \(0.669472\pi\)
\(410\) 65.7901 3.24914
\(411\) 7.47667 0.368797
\(412\) −53.4842 −2.63497
\(413\) −15.9198 −0.783361
\(414\) 9.47582 0.465711
\(415\) 27.4730 1.34859
\(416\) −30.9682 −1.51834
\(417\) −15.5388 −0.760938
\(418\) 5.76472 0.281962
\(419\) 4.17894 0.204154 0.102077 0.994776i \(-0.467451\pi\)
0.102077 + 0.994776i \(0.467451\pi\)
\(420\) 26.8047 1.30794
\(421\) 28.9145 1.40920 0.704602 0.709603i \(-0.251125\pi\)
0.704602 + 0.709603i \(0.251125\pi\)
\(422\) 13.4255 0.653545
\(423\) −6.26352 −0.304543
\(424\) 15.4226 0.748987
\(425\) 13.9266 0.675538
\(426\) −8.57042 −0.415238
\(427\) −9.76052 −0.472345
\(428\) 82.3721 3.98160
\(429\) −2.78184 −0.134309
\(430\) 39.0003 1.88076
\(431\) 38.3283 1.84621 0.923105 0.384547i \(-0.125642\pi\)
0.923105 + 0.384547i \(0.125642\pi\)
\(432\) −15.6393 −0.752445
\(433\) −8.93861 −0.429562 −0.214781 0.976662i \(-0.568904\pi\)
−0.214781 + 0.976662i \(0.568904\pi\)
\(434\) −48.9660 −2.35044
\(435\) −5.63130 −0.270000
\(436\) 45.8844 2.19746
\(437\) 3.43187 0.164169
\(438\) −23.9654 −1.14511
\(439\) −23.7305 −1.13260 −0.566298 0.824201i \(-0.691625\pi\)
−0.566298 + 0.824201i \(0.691625\pi\)
\(440\) 58.7152 2.79914
\(441\) −4.14004 −0.197145
\(442\) −15.8740 −0.755052
\(443\) −10.6949 −0.508128 −0.254064 0.967187i \(-0.581767\pi\)
−0.254064 + 0.967187i \(0.581767\pi\)
\(444\) 38.5121 1.82770
\(445\) 11.5104 0.545646
\(446\) 47.4222 2.24551
\(447\) −4.52115 −0.213843
\(448\) 56.2110 2.65572
\(449\) 13.9203 0.656942 0.328471 0.944514i \(-0.393467\pi\)
0.328471 + 0.944514i \(0.393467\pi\)
\(450\) −8.72405 −0.411256
\(451\) 17.6775 0.832403
\(452\) −64.5332 −3.03539
\(453\) 4.08267 0.191821
\(454\) 23.8430 1.11901
\(455\) −6.37496 −0.298863
\(456\) −9.67916 −0.453268
\(457\) −13.9019 −0.650303 −0.325152 0.945662i \(-0.605415\pi\)
−0.325152 + 0.945662i \(0.605415\pi\)
\(458\) 82.2324 3.84247
\(459\) −4.38429 −0.204641
\(460\) 54.6858 2.54974
\(461\) −10.8670 −0.506125 −0.253062 0.967450i \(-0.581438\pi\)
−0.253062 + 0.967450i \(0.581438\pi\)
\(462\) 9.80100 0.455984
\(463\) 1.70025 0.0790172 0.0395086 0.999219i \(-0.487421\pi\)
0.0395086 + 0.999219i \(0.487421\pi\)
\(464\) −30.7994 −1.42983
\(465\) 30.1456 1.39797
\(466\) −57.5161 −2.66438
\(467\) 13.4312 0.621520 0.310760 0.950488i \(-0.399416\pi\)
0.310760 + 0.950488i \(0.399416\pi\)
\(468\) 7.30741 0.337785
\(469\) 12.4581 0.575262
\(470\) −49.1898 −2.26896
\(471\) 0.220306 0.0101512
\(472\) 91.6026 4.21635
\(473\) 10.4792 0.481835
\(474\) 1.55044 0.0712140
\(475\) −3.15960 −0.144972
\(476\) 41.0986 1.88375
\(477\) −1.58492 −0.0725684
\(478\) −18.4759 −0.845067
\(479\) 22.3516 1.02127 0.510636 0.859797i \(-0.329410\pi\)
0.510636 + 0.859797i \(0.329410\pi\)
\(480\) −67.1714 −3.06594
\(481\) −9.15932 −0.417629
\(482\) −74.5206 −3.39432
\(483\) 5.83476 0.265491
\(484\) −36.2913 −1.64961
\(485\) 9.57035 0.434567
\(486\) 2.74646 0.124582
\(487\) 21.9576 0.994995 0.497497 0.867466i \(-0.334252\pi\)
0.497497 + 0.867466i \(0.334252\pi\)
\(488\) 56.1622 2.54234
\(489\) 9.65358 0.436550
\(490\) −32.5133 −1.46880
\(491\) −25.8543 −1.16679 −0.583393 0.812190i \(-0.698275\pi\)
−0.583393 + 0.812190i \(0.698275\pi\)
\(492\) −46.4358 −2.09349
\(493\) −8.63426 −0.388868
\(494\) 3.60144 0.162036
\(495\) −6.03393 −0.271205
\(496\) 164.876 7.40316
\(497\) −5.27726 −0.236717
\(498\) −26.3874 −1.18245
\(499\) −3.55903 −0.159324 −0.0796620 0.996822i \(-0.525384\pi\)
−0.0796620 + 0.996822i \(0.525384\pi\)
\(500\) 28.9031 1.29259
\(501\) −9.54341 −0.426368
\(502\) 45.8810 2.04777
\(503\) 10.8578 0.484126 0.242063 0.970261i \(-0.422176\pi\)
0.242063 + 0.970261i \(0.422176\pi\)
\(504\) −16.4562 −0.733018
\(505\) −16.0759 −0.715368
\(506\) 19.9956 0.888912
\(507\) 11.2621 0.500166
\(508\) 2.52492 0.112025
\(509\) −33.6865 −1.49313 −0.746565 0.665313i \(-0.768298\pi\)
−0.746565 + 0.665313i \(0.768298\pi\)
\(510\) −34.4315 −1.52465
\(511\) −14.7568 −0.652801
\(512\) −63.0155 −2.78492
\(513\) 0.994689 0.0439166
\(514\) 19.6036 0.864677
\(515\) 27.5905 1.21578
\(516\) −27.5271 −1.21181
\(517\) −13.2171 −0.581287
\(518\) 32.2702 1.41787
\(519\) 2.24820 0.0986852
\(520\) 36.6816 1.60859
\(521\) 17.9861 0.787987 0.393993 0.919113i \(-0.371093\pi\)
0.393993 + 0.919113i \(0.371093\pi\)
\(522\) 5.40878 0.236736
\(523\) −3.35948 −0.146900 −0.0734500 0.997299i \(-0.523401\pi\)
−0.0734500 + 0.997299i \(0.523401\pi\)
\(524\) −27.0579 −1.18203
\(525\) −5.37186 −0.234447
\(526\) 14.7529 0.643256
\(527\) 46.2211 2.01342
\(528\) −33.0015 −1.43621
\(529\) −11.0962 −0.482442
\(530\) −12.4470 −0.540661
\(531\) −9.41363 −0.408517
\(532\) −9.32429 −0.404259
\(533\) 11.0438 0.478361
\(534\) −11.0556 −0.478422
\(535\) −42.4927 −1.83712
\(536\) −71.6841 −3.09628
\(537\) 22.6124 0.975796
\(538\) −70.6308 −3.04511
\(539\) −8.73620 −0.376295
\(540\) 15.8501 0.682079
\(541\) −27.3714 −1.17679 −0.588393 0.808575i \(-0.700239\pi\)
−0.588393 + 0.808575i \(0.700239\pi\)
\(542\) −46.5442 −1.99924
\(543\) −5.51831 −0.236813
\(544\) −102.991 −4.41572
\(545\) −23.6701 −1.01391
\(546\) 6.12305 0.262043
\(547\) 13.4961 0.577053 0.288527 0.957472i \(-0.406835\pi\)
0.288527 + 0.957472i \(0.406835\pi\)
\(548\) −41.4435 −1.77038
\(549\) −5.77156 −0.246324
\(550\) −18.4092 −0.784972
\(551\) 1.95891 0.0834522
\(552\) −33.5733 −1.42897
\(553\) 0.954686 0.0405974
\(554\) 21.0063 0.892474
\(555\) −19.8669 −0.843305
\(556\) 86.1323 3.65282
\(557\) 4.55033 0.192804 0.0964019 0.995342i \(-0.469267\pi\)
0.0964019 + 0.995342i \(0.469267\pi\)
\(558\) −28.9544 −1.22574
\(559\) 6.54676 0.276899
\(560\) −75.6274 −3.19584
\(561\) −9.25160 −0.390603
\(562\) −8.67917 −0.366109
\(563\) −5.64962 −0.238103 −0.119052 0.992888i \(-0.537985\pi\)
−0.119052 + 0.992888i \(0.537985\pi\)
\(564\) 34.7190 1.46193
\(565\) 33.2903 1.40053
\(566\) −58.7998 −2.47154
\(567\) 1.69114 0.0710212
\(568\) 30.3654 1.27410
\(569\) 6.76448 0.283582 0.141791 0.989897i \(-0.454714\pi\)
0.141791 + 0.989897i \(0.454714\pi\)
\(570\) 7.81167 0.327195
\(571\) 29.5683 1.23739 0.618697 0.785630i \(-0.287661\pi\)
0.618697 + 0.785630i \(0.287661\pi\)
\(572\) 15.4199 0.644738
\(573\) −21.0522 −0.879468
\(574\) −38.9097 −1.62406
\(575\) −10.9594 −0.457040
\(576\) 33.2385 1.38494
\(577\) −16.1569 −0.672622 −0.336311 0.941751i \(-0.609179\pi\)
−0.336311 + 0.941751i \(0.609179\pi\)
\(578\) −6.10263 −0.253836
\(579\) 0.181678 0.00755030
\(580\) 31.2146 1.29612
\(581\) −16.2481 −0.674084
\(582\) −9.19218 −0.381028
\(583\) −3.34445 −0.138513
\(584\) 84.9106 3.51363
\(585\) −3.76962 −0.155855
\(586\) 75.7725 3.13013
\(587\) −29.0886 −1.20061 −0.600307 0.799770i \(-0.704955\pi\)
−0.600307 + 0.799770i \(0.704955\pi\)
\(588\) 22.9485 0.946379
\(589\) −10.4865 −0.432087
\(590\) −73.9288 −3.04360
\(591\) 2.81430 0.115765
\(592\) −108.659 −4.46585
\(593\) 14.8646 0.610415 0.305207 0.952286i \(-0.401274\pi\)
0.305207 + 0.952286i \(0.401274\pi\)
\(594\) 5.79550 0.237792
\(595\) −21.2013 −0.869167
\(596\) 25.0610 1.02654
\(597\) 8.25008 0.337653
\(598\) 12.4920 0.510836
\(599\) 15.7234 0.642442 0.321221 0.947004i \(-0.395907\pi\)
0.321221 + 0.947004i \(0.395907\pi\)
\(600\) 30.9097 1.26188
\(601\) −3.56659 −0.145484 −0.0727421 0.997351i \(-0.523175\pi\)
−0.0727421 + 0.997351i \(0.523175\pi\)
\(602\) −23.0656 −0.940084
\(603\) 7.36669 0.299995
\(604\) −22.6304 −0.920820
\(605\) 18.7214 0.761132
\(606\) 15.4406 0.627233
\(607\) 5.63249 0.228616 0.114308 0.993445i \(-0.463535\pi\)
0.114308 + 0.993445i \(0.463535\pi\)
\(608\) 23.3662 0.947626
\(609\) 3.33047 0.134958
\(610\) −45.3263 −1.83521
\(611\) −8.25722 −0.334051
\(612\) 24.3023 0.982363
\(613\) −33.3570 −1.34728 −0.673638 0.739062i \(-0.735269\pi\)
−0.673638 + 0.739062i \(0.735269\pi\)
\(614\) 64.1988 2.59085
\(615\) 23.9545 0.965939
\(616\) −34.7254 −1.39913
\(617\) −34.0842 −1.37218 −0.686088 0.727518i \(-0.740674\pi\)
−0.686088 + 0.727518i \(0.740674\pi\)
\(618\) −26.5002 −1.06600
\(619\) −22.6527 −0.910488 −0.455244 0.890367i \(-0.650448\pi\)
−0.455244 + 0.890367i \(0.650448\pi\)
\(620\) −167.099 −6.71084
\(621\) 3.45019 0.138451
\(622\) −31.2775 −1.25411
\(623\) −6.80751 −0.272737
\(624\) −20.6173 −0.825353
\(625\) −30.7924 −1.23170
\(626\) −86.7845 −3.46861
\(627\) 2.09896 0.0838245
\(628\) −1.22117 −0.0487299
\(629\) −30.4612 −1.21457
\(630\) 13.2812 0.529134
\(631\) 11.7492 0.467730 0.233865 0.972269i \(-0.424863\pi\)
0.233865 + 0.972269i \(0.424863\pi\)
\(632\) −5.49328 −0.218511
\(633\) 4.88830 0.194293
\(634\) −9.48289 −0.376614
\(635\) −1.30251 −0.0516885
\(636\) 8.78528 0.348359
\(637\) −5.45783 −0.216247
\(638\) 11.4134 0.451863
\(639\) −3.12053 −0.123446
\(640\) 126.692 5.00794
\(641\) −29.9914 −1.18459 −0.592294 0.805722i \(-0.701778\pi\)
−0.592294 + 0.805722i \(0.701778\pi\)
\(642\) 40.8136 1.61078
\(643\) −43.3144 −1.70815 −0.854076 0.520148i \(-0.825877\pi\)
−0.854076 + 0.520148i \(0.825877\pi\)
\(644\) −32.3424 −1.27447
\(645\) 14.2002 0.559132
\(646\) 11.9773 0.471242
\(647\) 33.9303 1.33394 0.666968 0.745086i \(-0.267592\pi\)
0.666968 + 0.745086i \(0.267592\pi\)
\(648\) −9.73084 −0.382264
\(649\) −19.8644 −0.779745
\(650\) −11.5009 −0.451104
\(651\) −17.8288 −0.698764
\(652\) −53.5102 −2.09562
\(653\) 31.4945 1.23248 0.616238 0.787560i \(-0.288656\pi\)
0.616238 + 0.787560i \(0.288656\pi\)
\(654\) 22.7347 0.888999
\(655\) 13.9582 0.545390
\(656\) 131.015 5.11528
\(657\) −8.72593 −0.340431
\(658\) 29.0919 1.13412
\(659\) −31.6154 −1.23156 −0.615780 0.787918i \(-0.711159\pi\)
−0.615780 + 0.787918i \(0.711159\pi\)
\(660\) 33.4464 1.30190
\(661\) −5.75734 −0.223935 −0.111967 0.993712i \(-0.535715\pi\)
−0.111967 + 0.993712i \(0.535715\pi\)
\(662\) −39.6170 −1.53976
\(663\) −5.77982 −0.224470
\(664\) 93.4917 3.62818
\(665\) 4.81005 0.186526
\(666\) 19.0819 0.739408
\(667\) 6.79469 0.263091
\(668\) 52.8996 2.04675
\(669\) 17.2666 0.667567
\(670\) 57.8534 2.23507
\(671\) −12.1790 −0.470164
\(672\) 39.7266 1.53249
\(673\) −38.2613 −1.47486 −0.737432 0.675421i \(-0.763962\pi\)
−0.737432 + 0.675421i \(0.763962\pi\)
\(674\) −53.4590 −2.05916
\(675\) −3.17647 −0.122262
\(676\) −62.4262 −2.40101
\(677\) −5.06528 −0.194674 −0.0973372 0.995251i \(-0.531033\pi\)
−0.0973372 + 0.995251i \(0.531033\pi\)
\(678\) −31.9748 −1.22799
\(679\) −5.66011 −0.217215
\(680\) 121.992 4.67819
\(681\) 8.68134 0.332670
\(682\) −61.0987 −2.33959
\(683\) −13.3896 −0.512337 −0.256169 0.966632i \(-0.582460\pi\)
−0.256169 + 0.966632i \(0.582460\pi\)
\(684\) −5.51361 −0.210818
\(685\) 21.3792 0.816857
\(686\) 51.7416 1.97550
\(687\) 29.9412 1.14233
\(688\) 77.6656 2.96097
\(689\) −2.08940 −0.0795999
\(690\) 27.0957 1.03151
\(691\) 3.29591 0.125382 0.0626912 0.998033i \(-0.480032\pi\)
0.0626912 + 0.998033i \(0.480032\pi\)
\(692\) −12.4619 −0.473730
\(693\) 3.56859 0.135560
\(694\) −32.9493 −1.25074
\(695\) −44.4324 −1.68542
\(696\) −19.1636 −0.726393
\(697\) 36.7285 1.39119
\(698\) −0.175822 −0.00665497
\(699\) −20.9419 −0.792095
\(700\) 29.7765 1.12544
\(701\) −43.1251 −1.62881 −0.814406 0.580295i \(-0.802937\pi\)
−0.814406 + 0.580295i \(0.802937\pi\)
\(702\) 3.62067 0.136653
\(703\) 6.91091 0.260650
\(704\) 70.1389 2.64346
\(705\) −17.9102 −0.674539
\(706\) 23.4524 0.882644
\(707\) 9.50762 0.357571
\(708\) 52.1802 1.96105
\(709\) −9.46629 −0.355514 −0.177757 0.984074i \(-0.556884\pi\)
−0.177757 + 0.984074i \(0.556884\pi\)
\(710\) −24.5067 −0.919721
\(711\) 0.564522 0.0211712
\(712\) 39.1705 1.46798
\(713\) −36.3735 −1.36220
\(714\) 20.3635 0.762085
\(715\) −7.95455 −0.297483
\(716\) −125.341 −4.68423
\(717\) −6.72716 −0.251230
\(718\) −23.6872 −0.883999
\(719\) 28.9236 1.07867 0.539335 0.842091i \(-0.318676\pi\)
0.539335 + 0.842091i \(0.318676\pi\)
\(720\) −44.7198 −1.66661
\(721\) −16.3176 −0.607699
\(722\) 49.4654 1.84091
\(723\) −27.1333 −1.00910
\(724\) 30.5883 1.13680
\(725\) −6.25563 −0.232328
\(726\) −17.9816 −0.667359
\(727\) 15.6425 0.580148 0.290074 0.957004i \(-0.406320\pi\)
0.290074 + 0.957004i \(0.406320\pi\)
\(728\) −21.6943 −0.804043
\(729\) 1.00000 0.0370370
\(730\) −68.5280 −2.53633
\(731\) 21.7726 0.805290
\(732\) 31.9920 1.18246
\(733\) −19.2180 −0.709834 −0.354917 0.934898i \(-0.615491\pi\)
−0.354917 + 0.934898i \(0.615491\pi\)
\(734\) −7.81116 −0.288315
\(735\) −11.8383 −0.436661
\(736\) 81.0484 2.98749
\(737\) 15.5450 0.572606
\(738\) −23.0079 −0.846934
\(739\) 12.5164 0.460424 0.230212 0.973140i \(-0.426058\pi\)
0.230212 + 0.973140i \(0.426058\pi\)
\(740\) 110.123 4.04822
\(741\) 1.31130 0.0481718
\(742\) 7.36139 0.270245
\(743\) 15.1423 0.555516 0.277758 0.960651i \(-0.410409\pi\)
0.277758 + 0.960651i \(0.410409\pi\)
\(744\) 102.587 3.76102
\(745\) −12.9280 −0.473646
\(746\) 56.0949 2.05378
\(747\) −9.60777 −0.351530
\(748\) 51.2820 1.87506
\(749\) 25.1311 0.918269
\(750\) 14.3209 0.522924
\(751\) −4.84471 −0.176786 −0.0883929 0.996086i \(-0.528173\pi\)
−0.0883929 + 0.996086i \(0.528173\pi\)
\(752\) −97.9570 −3.57212
\(753\) 16.7055 0.608782
\(754\) 7.13041 0.259674
\(755\) 11.6742 0.424868
\(756\) −9.37407 −0.340932
\(757\) −47.8734 −1.73999 −0.869994 0.493062i \(-0.835877\pi\)
−0.869994 + 0.493062i \(0.835877\pi\)
\(758\) 4.05635 0.147333
\(759\) 7.28049 0.264265
\(760\) −27.6771 −1.00395
\(761\) −5.82382 −0.211113 −0.105557 0.994413i \(-0.533662\pi\)
−0.105557 + 0.994413i \(0.533662\pi\)
\(762\) 1.25104 0.0453204
\(763\) 13.9990 0.506797
\(764\) 116.693 4.22182
\(765\) −12.5367 −0.453264
\(766\) 34.2399 1.23714
\(767\) −12.4100 −0.448100
\(768\) −55.2086 −1.99217
\(769\) 42.0154 1.51512 0.757558 0.652768i \(-0.226392\pi\)
0.757558 + 0.652768i \(0.226392\pi\)
\(770\) 28.0255 1.00997
\(771\) 7.13776 0.257060
\(772\) −1.00705 −0.0362446
\(773\) 14.8121 0.532755 0.266377 0.963869i \(-0.414173\pi\)
0.266377 + 0.963869i \(0.414173\pi\)
\(774\) −13.6391 −0.490247
\(775\) 33.4878 1.20292
\(776\) 32.5683 1.16913
\(777\) 11.7497 0.421519
\(778\) −38.7496 −1.38924
\(779\) −8.33281 −0.298554
\(780\) 20.8952 0.748168
\(781\) −6.58485 −0.235625
\(782\) 41.5447 1.48564
\(783\) 1.96936 0.0703793
\(784\) −64.7473 −2.31240
\(785\) 0.629955 0.0224841
\(786\) −13.4066 −0.478198
\(787\) 0.437405 0.0155918 0.00779590 0.999970i \(-0.497518\pi\)
0.00779590 + 0.999970i \(0.497518\pi\)
\(788\) −15.5998 −0.555720
\(789\) 5.37160 0.191234
\(790\) 4.43340 0.157733
\(791\) −19.6886 −0.700045
\(792\) −20.5337 −0.729634
\(793\) −7.60867 −0.270192
\(794\) −26.0060 −0.922919
\(795\) −4.53200 −0.160733
\(796\) −45.7306 −1.62088
\(797\) 55.9640 1.98235 0.991173 0.132573i \(-0.0423238\pi\)
0.991173 + 0.132573i \(0.0423238\pi\)
\(798\) −4.61998 −0.163546
\(799\) −27.4611 −0.971504
\(800\) −74.6184 −2.63816
\(801\) −4.02539 −0.142230
\(802\) −81.3961 −2.87419
\(803\) −18.4132 −0.649787
\(804\) −40.8339 −1.44010
\(805\) 16.6842 0.588042
\(806\) −38.1707 −1.34450
\(807\) −25.7170 −0.905282
\(808\) −54.7069 −1.92458
\(809\) −32.7203 −1.15038 −0.575192 0.818018i \(-0.695073\pi\)
−0.575192 + 0.818018i \(0.695073\pi\)
\(810\) 7.85338 0.275939
\(811\) −25.7291 −0.903471 −0.451736 0.892152i \(-0.649195\pi\)
−0.451736 + 0.892152i \(0.649195\pi\)
\(812\) −18.4610 −0.647853
\(813\) −16.9470 −0.594356
\(814\) 40.2660 1.41132
\(815\) 27.6039 0.966924
\(816\) −68.5671 −2.40033
\(817\) −4.93968 −0.172818
\(818\) 56.3895 1.97161
\(819\) 2.22943 0.0779027
\(820\) −132.781 −4.63691
\(821\) −21.5467 −0.751986 −0.375993 0.926622i \(-0.622698\pi\)
−0.375993 + 0.926622i \(0.622698\pi\)
\(822\) −20.5344 −0.716219
\(823\) −37.4937 −1.30695 −0.653475 0.756948i \(-0.726689\pi\)
−0.653475 + 0.756948i \(0.726689\pi\)
\(824\) 93.8916 3.27087
\(825\) −6.70289 −0.233365
\(826\) 43.7230 1.52132
\(827\) −29.9469 −1.04136 −0.520678 0.853753i \(-0.674321\pi\)
−0.520678 + 0.853753i \(0.674321\pi\)
\(828\) −19.1246 −0.664625
\(829\) −53.8651 −1.87081 −0.935407 0.353574i \(-0.884966\pi\)
−0.935407 + 0.353574i \(0.884966\pi\)
\(830\) −75.4534 −2.61903
\(831\) 7.64851 0.265324
\(832\) 43.8184 1.51913
\(833\) −18.1512 −0.628900
\(834\) 42.6767 1.47777
\(835\) −27.2889 −0.944372
\(836\) −11.6347 −0.402393
\(837\) −10.5424 −0.364400
\(838\) −11.4773 −0.396476
\(839\) 3.17579 0.109641 0.0548203 0.998496i \(-0.482541\pi\)
0.0548203 + 0.998496i \(0.482541\pi\)
\(840\) −47.0558 −1.62358
\(841\) −25.1216 −0.866262
\(842\) −79.4124 −2.73673
\(843\) −3.16013 −0.108841
\(844\) −27.0961 −0.932686
\(845\) 32.2034 1.10783
\(846\) 17.2025 0.591435
\(847\) −11.0722 −0.380446
\(848\) −24.7870 −0.851189
\(849\) −21.4093 −0.734765
\(850\) −38.2488 −1.31192
\(851\) 23.9713 0.821725
\(852\) 17.2973 0.592594
\(853\) −6.22163 −0.213025 −0.106512 0.994311i \(-0.533968\pi\)
−0.106512 + 0.994311i \(0.533968\pi\)
\(854\) 26.8069 0.917313
\(855\) 2.84427 0.0972719
\(856\) −144.604 −4.94248
\(857\) 43.6096 1.48967 0.744837 0.667246i \(-0.232527\pi\)
0.744837 + 0.667246i \(0.232527\pi\)
\(858\) 7.64022 0.260833
\(859\) 30.3020 1.03389 0.516945 0.856019i \(-0.327069\pi\)
0.516945 + 0.856019i \(0.327069\pi\)
\(860\) −78.7124 −2.68407
\(861\) −14.1672 −0.482817
\(862\) −105.267 −3.58542
\(863\) −3.10315 −0.105633 −0.0528163 0.998604i \(-0.516820\pi\)
−0.0528163 + 0.998604i \(0.516820\pi\)
\(864\) 23.4910 0.799180
\(865\) 6.42863 0.218580
\(866\) 24.5495 0.834227
\(867\) −2.22200 −0.0754630
\(868\) 98.8257 3.35436
\(869\) 1.19124 0.0404100
\(870\) 15.4662 0.524352
\(871\) 9.71152 0.329062
\(872\) −80.5503 −2.72778
\(873\) −3.34692 −0.113276
\(874\) −9.42549 −0.318822
\(875\) 8.81811 0.298106
\(876\) 48.3682 1.63421
\(877\) −24.8936 −0.840598 −0.420299 0.907386i \(-0.638075\pi\)
−0.420299 + 0.907386i \(0.638075\pi\)
\(878\) 65.1749 2.19955
\(879\) 27.5891 0.930558
\(880\) −94.3663 −3.18109
\(881\) −46.1780 −1.55578 −0.777888 0.628403i \(-0.783709\pi\)
−0.777888 + 0.628403i \(0.783709\pi\)
\(882\) 11.3705 0.382864
\(883\) −46.5572 −1.56677 −0.783387 0.621534i \(-0.786510\pi\)
−0.783387 + 0.621534i \(0.786510\pi\)
\(884\) 32.0378 1.07755
\(885\) −26.9178 −0.904833
\(886\) 29.3730 0.986806
\(887\) −44.5558 −1.49604 −0.748019 0.663677i \(-0.768995\pi\)
−0.748019 + 0.663677i \(0.768995\pi\)
\(888\) −67.6081 −2.26878
\(889\) 0.770332 0.0258361
\(890\) −31.6129 −1.05967
\(891\) 2.11017 0.0706934
\(892\) −95.7099 −3.20460
\(893\) 6.23026 0.208488
\(894\) 12.4172 0.415292
\(895\) 64.6590 2.16131
\(896\) −74.9282 −2.50318
\(897\) 4.54840 0.151867
\(898\) −38.2317 −1.27581
\(899\) −20.7619 −0.692449
\(900\) 17.6073 0.586911
\(901\) −6.94874 −0.231496
\(902\) −48.5507 −1.61656
\(903\) −8.39830 −0.279478
\(904\) 113.288 3.76791
\(905\) −15.7793 −0.524523
\(906\) −11.2129 −0.372524
\(907\) −27.9534 −0.928178 −0.464089 0.885789i \(-0.653618\pi\)
−0.464089 + 0.885789i \(0.653618\pi\)
\(908\) −48.1211 −1.59695
\(909\) 5.62201 0.186470
\(910\) 17.5086 0.580404
\(911\) 40.1941 1.33169 0.665845 0.746090i \(-0.268071\pi\)
0.665845 + 0.746090i \(0.268071\pi\)
\(912\) 15.5562 0.515118
\(913\) −20.2740 −0.670972
\(914\) 38.1810 1.26292
\(915\) −16.5035 −0.545589
\(916\) −165.966 −5.48366
\(917\) −8.25515 −0.272609
\(918\) 12.0413 0.397421
\(919\) 19.2051 0.633518 0.316759 0.948506i \(-0.397405\pi\)
0.316759 + 0.948506i \(0.397405\pi\)
\(920\) −96.0012 −3.16507
\(921\) 23.3751 0.770236
\(922\) 29.8457 0.982915
\(923\) −4.11381 −0.135408
\(924\) −19.7809 −0.650743
\(925\) −22.0695 −0.725641
\(926\) −4.66967 −0.153455
\(927\) −9.64887 −0.316910
\(928\) 46.2623 1.51864
\(929\) −35.9039 −1.17797 −0.588985 0.808144i \(-0.700472\pi\)
−0.588985 + 0.808144i \(0.700472\pi\)
\(930\) −82.7938 −2.71492
\(931\) 4.11806 0.134964
\(932\) 116.082 3.80239
\(933\) −11.3883 −0.372835
\(934\) −36.8882 −1.20702
\(935\) −26.4545 −0.865155
\(936\) −12.8282 −0.419303
\(937\) −42.9330 −1.40256 −0.701279 0.712887i \(-0.747387\pi\)
−0.701279 + 0.712887i \(0.747387\pi\)
\(938\) −34.2157 −1.11718
\(939\) −31.5987 −1.03118
\(940\) 99.2773 3.23807
\(941\) 60.2836 1.96519 0.982595 0.185761i \(-0.0594749\pi\)
0.982595 + 0.185761i \(0.0594749\pi\)
\(942\) −0.605062 −0.0197140
\(943\) −28.9033 −0.941221
\(944\) −147.222 −4.79168
\(945\) 4.83574 0.157307
\(946\) −28.7808 −0.935744
\(947\) −60.8483 −1.97730 −0.988652 0.150221i \(-0.952001\pi\)
−0.988652 + 0.150221i \(0.952001\pi\)
\(948\) −3.12917 −0.101631
\(949\) −11.5034 −0.373417
\(950\) 8.67772 0.281542
\(951\) −3.45277 −0.111964
\(952\) −72.1488 −2.33836
\(953\) −14.1760 −0.459206 −0.229603 0.973284i \(-0.573743\pi\)
−0.229603 + 0.973284i \(0.573743\pi\)
\(954\) 4.35292 0.140931
\(955\) −60.1978 −1.94795
\(956\) 37.2889 1.20601
\(957\) 4.15569 0.134334
\(958\) −61.3879 −1.98335
\(959\) −12.6441 −0.408299
\(960\) 95.0440 3.06753
\(961\) 80.1432 2.58526
\(962\) 25.1557 0.811052
\(963\) 14.8604 0.478871
\(964\) 150.401 4.84410
\(965\) 0.519501 0.0167233
\(966\) −16.0249 −0.515594
\(967\) −12.3841 −0.398247 −0.199124 0.979974i \(-0.563809\pi\)
−0.199124 + 0.979974i \(0.563809\pi\)
\(968\) 63.7096 2.04770
\(969\) 4.36100 0.140096
\(970\) −26.2846 −0.843947
\(971\) −12.1908 −0.391220 −0.195610 0.980682i \(-0.562669\pi\)
−0.195610 + 0.980682i \(0.562669\pi\)
\(972\) −5.54305 −0.177793
\(973\) 26.2783 0.842443
\(974\) −60.3057 −1.93232
\(975\) −4.18755 −0.134109
\(976\) −90.2631 −2.88925
\(977\) −40.0697 −1.28194 −0.640971 0.767565i \(-0.721468\pi\)
−0.640971 + 0.767565i \(0.721468\pi\)
\(978\) −26.5132 −0.847798
\(979\) −8.49427 −0.271478
\(980\) 65.6200 2.09616
\(981\) 8.27783 0.264291
\(982\) 71.0077 2.26595
\(983\) −3.57628 −0.114066 −0.0570329 0.998372i \(-0.518164\pi\)
−0.0570329 + 0.998372i \(0.518164\pi\)
\(984\) 81.5182 2.59871
\(985\) 8.04736 0.256410
\(986\) 23.7137 0.755197
\(987\) 10.5925 0.337163
\(988\) −7.26860 −0.231245
\(989\) −17.1339 −0.544825
\(990\) 16.5720 0.526691
\(991\) 9.72926 0.309060 0.154530 0.987988i \(-0.450614\pi\)
0.154530 + 0.987988i \(0.450614\pi\)
\(992\) −247.653 −7.86298
\(993\) −14.4247 −0.457755
\(994\) 14.4938 0.459715
\(995\) 23.5907 0.747876
\(996\) 53.2563 1.68749
\(997\) 59.0473 1.87005 0.935023 0.354586i \(-0.115378\pi\)
0.935023 + 0.354586i \(0.115378\pi\)
\(998\) 9.77473 0.309414
\(999\) 6.94781 0.219819
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 8013.2.a.c.1.3 116
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8013.2.a.c.1.3 116 1.1 even 1 trivial