Properties

Label 197.14.a.a.1.6
Level $197$
Weight $14$
Character 197.1
Self dual yes
Analytic conductor $211.245$
Analytic rank $1$
Dimension $104$
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] = [197,14,Mod(1,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 197.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: \(211.244930035\)
Analytic rank: \(1\)
Dimension: \(104\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 197.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-164.231 q^{2} -1747.83 q^{3} +18780.0 q^{4} -30963.6 q^{5} +287048. q^{6} +120554. q^{7} -1.73888e6 q^{8} +1.46057e6 q^{9} +O(q^{10})\) \(q-164.231 q^{2} -1747.83 q^{3} +18780.0 q^{4} -30963.6 q^{5} +287048. q^{6} +120554. q^{7} -1.73888e6 q^{8} +1.46057e6 q^{9} +5.08520e6 q^{10} -1.02128e7 q^{11} -3.28241e7 q^{12} +5.41676e6 q^{13} -1.97988e7 q^{14} +5.41191e7 q^{15} +1.31733e8 q^{16} +1.78741e8 q^{17} -2.39872e8 q^{18} -2.67219e8 q^{19} -5.81496e8 q^{20} -2.10708e8 q^{21} +1.67726e9 q^{22} +5.02187e8 q^{23} +3.03926e9 q^{24} -2.61956e8 q^{25} -8.89602e8 q^{26} +2.33771e8 q^{27} +2.26401e9 q^{28} +3.45170e9 q^{29} -8.88805e9 q^{30} -8.65904e9 q^{31} -7.38982e9 q^{32} +1.78502e10 q^{33} -2.93549e10 q^{34} -3.73280e9 q^{35} +2.74295e10 q^{36} +7.60282e9 q^{37} +4.38857e10 q^{38} -9.46755e9 q^{39} +5.38420e10 q^{40} -4.48741e10 q^{41} +3.46049e10 q^{42} -7.21879e9 q^{43} -1.91796e11 q^{44} -4.52247e10 q^{45} -8.24749e10 q^{46} -7.77885e10 q^{47} -2.30247e11 q^{48} -8.23556e10 q^{49} +4.30214e10 q^{50} -3.12408e11 q^{51} +1.01727e11 q^{52} +8.12388e10 q^{53} -3.83925e10 q^{54} +3.16225e11 q^{55} -2.09630e11 q^{56} +4.67052e11 q^{57} -5.66877e11 q^{58} -1.94075e11 q^{59} +1.01635e12 q^{60} +2.64439e11 q^{61} +1.42209e12 q^{62} +1.76079e11 q^{63} +1.34484e11 q^{64} -1.67722e11 q^{65} -2.93156e12 q^{66} -1.30061e12 q^{67} +3.35675e12 q^{68} -8.77736e11 q^{69} +6.13044e11 q^{70} +1.46842e12 q^{71} -2.53976e12 q^{72} -1.62887e11 q^{73} -1.24862e12 q^{74} +4.57854e11 q^{75} -5.01836e12 q^{76} -1.23120e12 q^{77} +1.55487e12 q^{78} +9.21802e11 q^{79} -4.07894e12 q^{80} -2.73722e12 q^{81} +7.36974e12 q^{82} -5.40648e12 q^{83} -3.95710e12 q^{84} -5.53447e12 q^{85} +1.18555e12 q^{86} -6.03297e12 q^{87} +1.77588e13 q^{88} +3.99862e12 q^{89} +7.42731e12 q^{90} +6.53014e11 q^{91} +9.43106e12 q^{92} +1.51345e13 q^{93} +1.27753e13 q^{94} +8.27407e12 q^{95} +1.29161e13 q^{96} -8.17971e11 q^{97} +1.35254e13 q^{98} -1.49165e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9} - 9626347 q^{10} - 10688800 q^{11} - 68157440 q^{12} - 94762650 q^{13} - 52465903 q^{14} - 186128761 q^{15} + 1543503872 q^{16} - 109572251 q^{17} - 449658263 q^{18} - 1495268031 q^{19} - 1194030741 q^{20} - 832275538 q^{21} - 2695120703 q^{22} - 2632554532 q^{23} - 190649667 q^{24} + 22696779124 q^{25} - 2460454754 q^{26} - 16267542277 q^{27} - 18137835250 q^{28} + 47556769 q^{29} - 9613748117 q^{30} - 24774628288 q^{31} - 29246249180 q^{32} - 42367036666 q^{33} - 39395206606 q^{34} - 26216433864 q^{35} + 190013501626 q^{36} - 82419664050 q^{37} - 34593622142 q^{38} - 39498281801 q^{39} - 150303128514 q^{40} - 25862853768 q^{41} - 138889965149 q^{42} - 258164897781 q^{43} - 197365738094 q^{44} - 240782892021 q^{45} - 218441397971 q^{46} - 208905762731 q^{47} - 664063830814 q^{48} + 1113758315863 q^{49} - 1516068087607 q^{50} - 1019253294393 q^{51} - 1162941441840 q^{52} + 161684855900 q^{53} + 1679137315823 q^{54} - 557952233701 q^{55} + 2842561845328 q^{56} + 801593765429 q^{57} - 7249760433 q^{58} - 775487110641 q^{59} - 57598844627 q^{60} - 36786715662 q^{61} + 681529132643 q^{62} - 4349115033663 q^{63} + 4600420238797 q^{64} - 2531819073161 q^{65} - 3958922748734 q^{66} - 7314072405766 q^{67} - 10297353950393 q^{68} - 2089200206275 q^{69} - 14268943913713 q^{70} - 6055724651085 q^{71} - 26860198563805 q^{72} - 7572811533391 q^{73} - 11175265675817 q^{74} - 24431657592434 q^{75} - 26425925198106 q^{76} - 9735327037686 q^{77} - 35310017230907 q^{78} - 8981210762721 q^{79} - 25913753436330 q^{80} + 15437375349812 q^{81} - 19721330628227 q^{82} - 22209909714532 q^{83} - 18837805278768 q^{84} - 5905005171430 q^{85} - 8913876797772 q^{86} - 7341562344401 q^{87} - 35154329886441 q^{88} - 4646484034146 q^{89} + 9564902968095 q^{90} - 22752431457047 q^{91} - 13601121953458 q^{92} - 9615114240293 q^{93} + 15352521272967 q^{94} + 5258551767043 q^{95} + 87277848810881 q^{96} - 42298840804040 q^{97} + 27000102375354 q^{98} - 8666459567773 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −164.231 −1.81452 −0.907259 0.420572i \(-0.861829\pi\)
−0.907259 + 0.420572i \(0.861829\pi\)
\(3\) −1747.83 −1.38424 −0.692118 0.721784i \(-0.743322\pi\)
−0.692118 + 0.721784i \(0.743322\pi\)
\(4\) 18780.0 2.29248
\(5\) −30963.6 −0.886231 −0.443116 0.896465i \(-0.646127\pi\)
−0.443116 + 0.896465i \(0.646127\pi\)
\(6\) 287048. 2.51172
\(7\) 120554. 0.387299 0.193649 0.981071i \(-0.437968\pi\)
0.193649 + 0.981071i \(0.437968\pi\)
\(8\) −1.73888e6 −2.34522
\(9\) 1.46057e6 0.916109
\(10\) 5.08520e6 1.60808
\(11\) −1.02128e7 −1.73817 −0.869084 0.494665i \(-0.835291\pi\)
−0.869084 + 0.494665i \(0.835291\pi\)
\(12\) −3.28241e7 −3.17333
\(13\) 5.41676e6 0.311249 0.155624 0.987816i \(-0.450261\pi\)
0.155624 + 0.987816i \(0.450261\pi\)
\(14\) −1.97988e7 −0.702761
\(15\) 5.41191e7 1.22675
\(16\) 1.31733e8 1.96298
\(17\) 1.78741e8 1.79600 0.897999 0.439997i \(-0.145021\pi\)
0.897999 + 0.439997i \(0.145021\pi\)
\(18\) −2.39872e8 −1.66230
\(19\) −2.67219e8 −1.30307 −0.651536 0.758617i \(-0.725875\pi\)
−0.651536 + 0.758617i \(0.725875\pi\)
\(20\) −5.81496e8 −2.03166
\(21\) −2.10708e8 −0.536113
\(22\) 1.67726e9 3.15394
\(23\) 5.02187e8 0.707350 0.353675 0.935368i \(-0.384932\pi\)
0.353675 + 0.935368i \(0.384932\pi\)
\(24\) 3.03926e9 3.24634
\(25\) −2.61956e8 −0.214594
\(26\) −8.89602e8 −0.564766
\(27\) 2.33771e8 0.116125
\(28\) 2.26401e9 0.887874
\(29\) 3.45170e9 1.07757 0.538785 0.842443i \(-0.318883\pi\)
0.538785 + 0.842443i \(0.318883\pi\)
\(30\) −8.88805e9 −2.22597
\(31\) −8.65904e9 −1.75234 −0.876171 0.482001i \(-0.839910\pi\)
−0.876171 + 0.482001i \(0.839910\pi\)
\(32\) −7.38982e9 −1.21663
\(33\) 1.78502e10 2.40603
\(34\) −2.93549e10 −3.25887
\(35\) −3.73280e9 −0.343236
\(36\) 2.74295e10 2.10016
\(37\) 7.60282e9 0.487151 0.243576 0.969882i \(-0.421680\pi\)
0.243576 + 0.969882i \(0.421680\pi\)
\(38\) 4.38857e10 2.36445
\(39\) −9.46755e9 −0.430842
\(40\) 5.38420e10 2.07841
\(41\) −4.48741e10 −1.47537 −0.737685 0.675145i \(-0.764081\pi\)
−0.737685 + 0.675145i \(0.764081\pi\)
\(42\) 3.46049e10 0.972787
\(43\) −7.21879e9 −0.174148 −0.0870741 0.996202i \(-0.527752\pi\)
−0.0870741 + 0.996202i \(0.527752\pi\)
\(44\) −1.91796e11 −3.98471
\(45\) −4.52247e10 −0.811884
\(46\) −8.24749e10 −1.28350
\(47\) −7.77885e10 −1.05264 −0.526319 0.850287i \(-0.676428\pi\)
−0.526319 + 0.850287i \(0.676428\pi\)
\(48\) −2.30247e11 −2.71722
\(49\) −8.23556e10 −0.850000
\(50\) 4.30214e10 0.389386
\(51\) −3.12408e11 −2.48609
\(52\) 1.01727e11 0.713531
\(53\) 8.12388e10 0.503466 0.251733 0.967797i \(-0.419000\pi\)
0.251733 + 0.967797i \(0.419000\pi\)
\(54\) −3.83925e10 −0.210711
\(55\) 3.16225e11 1.54042
\(56\) −2.09630e11 −0.908302
\(57\) 4.67052e11 1.80376
\(58\) −5.66877e11 −1.95527
\(59\) −1.94075e11 −0.599005 −0.299503 0.954095i \(-0.596821\pi\)
−0.299503 + 0.954095i \(0.596821\pi\)
\(60\) 1.01635e12 2.81230
\(61\) 2.64439e11 0.657175 0.328588 0.944474i \(-0.393427\pi\)
0.328588 + 0.944474i \(0.393427\pi\)
\(62\) 1.42209e12 3.17966
\(63\) 1.76079e11 0.354808
\(64\) 1.34484e11 0.244625
\(65\) −1.67722e11 −0.275838
\(66\) −2.93156e12 −4.36579
\(67\) −1.30061e12 −1.75655 −0.878275 0.478157i \(-0.841305\pi\)
−0.878275 + 0.478157i \(0.841305\pi\)
\(68\) 3.35675e12 4.11729
\(69\) −8.77736e11 −0.979140
\(70\) 6.13044e11 0.622808
\(71\) 1.46842e12 1.36041 0.680206 0.733021i \(-0.261890\pi\)
0.680206 + 0.733021i \(0.261890\pi\)
\(72\) −2.53976e12 −2.14848
\(73\) −1.62887e11 −0.125976 −0.0629881 0.998014i \(-0.520063\pi\)
−0.0629881 + 0.998014i \(0.520063\pi\)
\(74\) −1.24862e12 −0.883945
\(75\) 4.57854e11 0.297049
\(76\) −5.01836e12 −2.98727
\(77\) −1.23120e12 −0.673190
\(78\) 1.55487e12 0.781770
\(79\) 9.21802e11 0.426640 0.213320 0.976982i \(-0.431572\pi\)
0.213320 + 0.976982i \(0.431572\pi\)
\(80\) −4.07894e12 −1.73965
\(81\) −2.73722e12 −1.07685
\(82\) 7.36974e12 2.67708
\(83\) −5.40648e12 −1.81513 −0.907564 0.419914i \(-0.862060\pi\)
−0.907564 + 0.419914i \(0.862060\pi\)
\(84\) −3.95710e12 −1.22903
\(85\) −5.53447e12 −1.59167
\(86\) 1.18555e12 0.315995
\(87\) −6.03297e12 −1.49161
\(88\) 1.77588e13 4.07639
\(89\) 3.99862e12 0.852855 0.426428 0.904522i \(-0.359772\pi\)
0.426428 + 0.904522i \(0.359772\pi\)
\(90\) 7.42731e12 1.47318
\(91\) 6.53014e11 0.120546
\(92\) 9.43106e12 1.62158
\(93\) 1.51345e13 2.42565
\(94\) 1.27753e13 1.91003
\(95\) 8.27407e12 1.15482
\(96\) 1.29161e13 1.68411
\(97\) −8.17971e11 −0.0997061 −0.0498530 0.998757i \(-0.515875\pi\)
−0.0498530 + 0.998757i \(0.515875\pi\)
\(98\) 1.35254e13 1.54234
\(99\) −1.49165e13 −1.59235
\(100\) −4.91953e12 −0.491953
\(101\) 9.96328e12 0.933928 0.466964 0.884276i \(-0.345348\pi\)
0.466964 + 0.884276i \(0.345348\pi\)
\(102\) 5.13072e13 4.51105
\(103\) 3.83298e12 0.316297 0.158148 0.987415i \(-0.449448\pi\)
0.158148 + 0.987415i \(0.449448\pi\)
\(104\) −9.41908e12 −0.729948
\(105\) 6.52429e12 0.475120
\(106\) −1.33420e13 −0.913548
\(107\) −1.46504e13 −0.943743 −0.471872 0.881667i \(-0.656421\pi\)
−0.471872 + 0.881667i \(0.656421\pi\)
\(108\) 4.39021e12 0.266214
\(109\) 2.24078e13 1.27975 0.639877 0.768477i \(-0.278985\pi\)
0.639877 + 0.768477i \(0.278985\pi\)
\(110\) −5.19341e13 −2.79512
\(111\) −1.32884e13 −0.674332
\(112\) 1.58810e13 0.760258
\(113\) 3.28909e12 0.148616 0.0743080 0.997235i \(-0.476325\pi\)
0.0743080 + 0.997235i \(0.476325\pi\)
\(114\) −7.67047e13 −3.27296
\(115\) −1.55495e13 −0.626876
\(116\) 6.48228e13 2.47031
\(117\) 7.91157e12 0.285138
\(118\) 3.18732e13 1.08691
\(119\) 2.15480e13 0.695588
\(120\) −9.41065e13 −2.87701
\(121\) 6.97783e13 2.02123
\(122\) −4.34292e13 −1.19246
\(123\) 7.84321e13 2.04226
\(124\) −1.62617e14 −4.01720
\(125\) 4.59085e13 1.07641
\(126\) −2.89177e13 −0.643805
\(127\) 1.31246e13 0.277564 0.138782 0.990323i \(-0.455681\pi\)
0.138782 + 0.990323i \(0.455681\pi\)
\(128\) 3.84509e13 0.772755
\(129\) 1.26172e13 0.241062
\(130\) 2.75453e13 0.500514
\(131\) 7.29776e13 1.26161 0.630806 0.775940i \(-0.282724\pi\)
0.630806 + 0.775940i \(0.282724\pi\)
\(132\) 3.35226e14 5.51578
\(133\) −3.22144e13 −0.504678
\(134\) 2.13601e14 3.18729
\(135\) −7.23840e12 −0.102914
\(136\) −3.10809e14 −4.21202
\(137\) 9.95397e13 1.28621 0.643106 0.765777i \(-0.277645\pi\)
0.643106 + 0.765777i \(0.277645\pi\)
\(138\) 1.44152e14 1.77667
\(139\) −1.04292e14 −1.22646 −0.613232 0.789903i \(-0.710131\pi\)
−0.613232 + 0.789903i \(0.710131\pi\)
\(140\) −7.01020e13 −0.786861
\(141\) 1.35961e14 1.45710
\(142\) −2.41160e14 −2.46849
\(143\) −5.53202e13 −0.541002
\(144\) 1.92406e14 1.79830
\(145\) −1.06877e14 −0.954977
\(146\) 2.67512e13 0.228586
\(147\) 1.43943e14 1.17660
\(148\) 1.42781e14 1.11678
\(149\) 1.55537e14 1.16445 0.582226 0.813027i \(-0.302182\pi\)
0.582226 + 0.813027i \(0.302182\pi\)
\(150\) −7.51940e13 −0.539002
\(151\) −4.80644e13 −0.329969 −0.164985 0.986296i \(-0.552757\pi\)
−0.164985 + 0.986296i \(0.552757\pi\)
\(152\) 4.64661e14 3.05600
\(153\) 2.61064e14 1.64533
\(154\) 2.02201e14 1.22152
\(155\) 2.68115e14 1.55298
\(156\) −1.77800e14 −0.987695
\(157\) 2.18884e14 1.16645 0.583226 0.812310i \(-0.301790\pi\)
0.583226 + 0.812310i \(0.301790\pi\)
\(158\) −1.51389e14 −0.774146
\(159\) −1.41991e14 −0.696916
\(160\) 2.28816e14 1.07822
\(161\) 6.05409e13 0.273956
\(162\) 4.49537e14 1.95397
\(163\) 1.30251e13 0.0543954 0.0271977 0.999630i \(-0.491342\pi\)
0.0271977 + 0.999630i \(0.491342\pi\)
\(164\) −8.42735e14 −3.38225
\(165\) −5.52706e14 −2.13230
\(166\) 8.87914e14 3.29358
\(167\) 3.04290e14 1.08550 0.542751 0.839893i \(-0.317383\pi\)
0.542751 + 0.839893i \(0.317383\pi\)
\(168\) 3.66396e14 1.25730
\(169\) −2.73534e14 −0.903124
\(170\) 9.08934e14 2.88811
\(171\) −3.90293e14 −1.19376
\(172\) −1.35569e14 −0.399231
\(173\) −4.56273e14 −1.29397 −0.646987 0.762501i \(-0.723971\pi\)
−0.646987 + 0.762501i \(0.723971\pi\)
\(174\) 9.90803e14 2.70656
\(175\) −3.15800e13 −0.0831122
\(176\) −1.34536e15 −3.41198
\(177\) 3.39209e14 0.829165
\(178\) −6.56699e14 −1.54752
\(179\) 6.65645e14 1.51251 0.756255 0.654277i \(-0.227027\pi\)
0.756255 + 0.654277i \(0.227027\pi\)
\(180\) −8.49318e14 −1.86123
\(181\) 1.83594e13 0.0388103 0.0194052 0.999812i \(-0.493823\pi\)
0.0194052 + 0.999812i \(0.493823\pi\)
\(182\) −1.07245e14 −0.218733
\(183\) −4.62193e14 −0.909685
\(184\) −8.73242e14 −1.65890
\(185\) −2.35411e14 −0.431729
\(186\) −2.48556e15 −4.40139
\(187\) −1.82544e15 −3.12175
\(188\) −1.46087e15 −2.41315
\(189\) 2.81821e13 0.0449751
\(190\) −1.35886e15 −2.09545
\(191\) −7.49221e14 −1.11659 −0.558294 0.829643i \(-0.688544\pi\)
−0.558294 + 0.829643i \(0.688544\pi\)
\(192\) −2.35054e14 −0.338618
\(193\) 1.22802e15 1.71034 0.855171 0.518346i \(-0.173452\pi\)
0.855171 + 0.518346i \(0.173452\pi\)
\(194\) 1.34337e14 0.180919
\(195\) 2.93150e14 0.381825
\(196\) −1.54664e15 −1.94861
\(197\) −5.84517e13 −0.0712470
\(198\) 2.44976e15 2.88935
\(199\) −1.04554e15 −1.19342 −0.596712 0.802456i \(-0.703526\pi\)
−0.596712 + 0.802456i \(0.703526\pi\)
\(200\) 4.55510e14 0.503272
\(201\) 2.27324e15 2.43148
\(202\) −1.63628e15 −1.69463
\(203\) 4.16118e14 0.417342
\(204\) −5.86702e15 −5.69930
\(205\) 1.38947e15 1.30752
\(206\) −6.29496e14 −0.573926
\(207\) 7.33481e14 0.648010
\(208\) 7.13566e14 0.610974
\(209\) 2.72905e15 2.26496
\(210\) −1.07149e15 −0.862114
\(211\) −1.41523e15 −1.10406 −0.552028 0.833825i \(-0.686146\pi\)
−0.552028 + 0.833825i \(0.686146\pi\)
\(212\) 1.52566e15 1.15418
\(213\) −2.56654e15 −1.88313
\(214\) 2.40605e15 1.71244
\(215\) 2.23520e14 0.154336
\(216\) −4.06499e14 −0.272339
\(217\) −1.04389e15 −0.678679
\(218\) −3.68006e15 −2.32214
\(219\) 2.84699e14 0.174381
\(220\) 5.93870e15 3.53137
\(221\) 9.68196e14 0.559002
\(222\) 2.18238e15 1.22359
\(223\) 9.57325e14 0.521288 0.260644 0.965435i \(-0.416065\pi\)
0.260644 + 0.965435i \(0.416065\pi\)
\(224\) −8.90876e14 −0.471200
\(225\) −3.82606e14 −0.196592
\(226\) −5.40172e14 −0.269667
\(227\) 2.20717e15 1.07070 0.535349 0.844631i \(-0.320180\pi\)
0.535349 + 0.844631i \(0.320180\pi\)
\(228\) 8.77123e15 4.13508
\(229\) −3.39090e15 −1.55376 −0.776880 0.629649i \(-0.783199\pi\)
−0.776880 + 0.629649i \(0.783199\pi\)
\(230\) 2.55372e15 1.13748
\(231\) 2.15192e15 0.931854
\(232\) −6.00208e15 −2.52715
\(233\) 2.78688e15 1.14105 0.570525 0.821280i \(-0.306740\pi\)
0.570525 + 0.821280i \(0.306740\pi\)
\(234\) −1.29933e15 −0.517388
\(235\) 2.40861e15 0.932881
\(236\) −3.64472e15 −1.37321
\(237\) −1.61115e15 −0.590571
\(238\) −3.53886e15 −1.26216
\(239\) 1.92839e15 0.669282 0.334641 0.942346i \(-0.391385\pi\)
0.334641 + 0.942346i \(0.391385\pi\)
\(240\) 7.12927e15 2.40809
\(241\) 9.64137e14 0.316977 0.158489 0.987361i \(-0.449338\pi\)
0.158489 + 0.987361i \(0.449338\pi\)
\(242\) −1.14598e16 −3.66756
\(243\) 4.41147e15 1.37449
\(244\) 4.96615e15 1.50656
\(245\) 2.55003e15 0.753296
\(246\) −1.28810e16 −3.70572
\(247\) −1.44746e15 −0.405580
\(248\) 1.50570e16 4.10963
\(249\) 9.44959e15 2.51256
\(250\) −7.53963e15 −1.95317
\(251\) 4.01969e14 0.101464 0.0507322 0.998712i \(-0.483845\pi\)
0.0507322 + 0.998712i \(0.483845\pi\)
\(252\) 3.30675e15 0.813389
\(253\) −5.12873e15 −1.22949
\(254\) −2.15548e15 −0.503645
\(255\) 9.67329e15 2.20325
\(256\) −7.41655e15 −1.64680
\(257\) −3.39614e15 −0.735225 −0.367613 0.929979i \(-0.619825\pi\)
−0.367613 + 0.929979i \(0.619825\pi\)
\(258\) −2.07214e15 −0.437412
\(259\) 9.16554e14 0.188673
\(260\) −3.14982e15 −0.632353
\(261\) 5.04146e15 0.987172
\(262\) −1.19852e16 −2.28922
\(263\) 7.87181e15 1.46677 0.733385 0.679813i \(-0.237939\pi\)
0.733385 + 0.679813i \(0.237939\pi\)
\(264\) −3.10393e16 −5.64269
\(265\) −2.51545e15 −0.446187
\(266\) 5.29062e15 0.915748
\(267\) −6.98890e15 −1.18055
\(268\) −2.44254e16 −4.02685
\(269\) −2.71709e15 −0.437234 −0.218617 0.975811i \(-0.570155\pi\)
−0.218617 + 0.975811i \(0.570155\pi\)
\(270\) 1.18877e15 0.186739
\(271\) 3.46996e15 0.532138 0.266069 0.963954i \(-0.414275\pi\)
0.266069 + 0.963954i \(0.414275\pi\)
\(272\) 2.35461e16 3.52550
\(273\) −1.14136e15 −0.166864
\(274\) −1.63476e16 −2.33386
\(275\) 2.67530e15 0.373001
\(276\) −1.64839e16 −2.24466
\(277\) 4.83696e15 0.643359 0.321680 0.946849i \(-0.395753\pi\)
0.321680 + 0.946849i \(0.395753\pi\)
\(278\) 1.71280e16 2.22544
\(279\) −1.26472e16 −1.60534
\(280\) 6.49090e15 0.804966
\(281\) 5.65710e15 0.685493 0.342747 0.939428i \(-0.388643\pi\)
0.342747 + 0.939428i \(0.388643\pi\)
\(282\) −2.23290e16 −2.64393
\(283\) −9.99162e15 −1.15618 −0.578088 0.815974i \(-0.696201\pi\)
−0.578088 + 0.815974i \(0.696201\pi\)
\(284\) 2.75768e16 3.11871
\(285\) −1.44616e16 −1.59855
\(286\) 9.08531e15 0.981659
\(287\) −5.40977e15 −0.571409
\(288\) −1.07934e16 −1.11457
\(289\) 2.20437e16 2.22561
\(290\) 1.75526e16 1.73282
\(291\) 1.42967e15 0.138017
\(292\) −3.05902e15 −0.288798
\(293\) −1.86990e16 −1.72655 −0.863274 0.504736i \(-0.831590\pi\)
−0.863274 + 0.504736i \(0.831590\pi\)
\(294\) −2.36400e16 −2.13496
\(295\) 6.00926e15 0.530857
\(296\) −1.32204e16 −1.14248
\(297\) −2.38745e15 −0.201845
\(298\) −2.55440e16 −2.11292
\(299\) 2.72022e15 0.220162
\(300\) 8.59848e15 0.680979
\(301\) −8.70257e14 −0.0674474
\(302\) 7.89368e15 0.598735
\(303\) −1.74141e16 −1.29278
\(304\) −3.52016e16 −2.55790
\(305\) −8.18798e15 −0.582409
\(306\) −4.28750e16 −2.98548
\(307\) 1.05970e16 0.722408 0.361204 0.932487i \(-0.382366\pi\)
0.361204 + 0.932487i \(0.382366\pi\)
\(308\) −2.31218e16 −1.54327
\(309\) −6.69939e15 −0.437829
\(310\) −4.40330e16 −2.81791
\(311\) 2.72333e16 1.70670 0.853351 0.521337i \(-0.174567\pi\)
0.853351 + 0.521337i \(0.174567\pi\)
\(312\) 1.64629e16 1.01042
\(313\) −9.42099e15 −0.566316 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(314\) −3.59477e16 −2.11655
\(315\) −5.45204e15 −0.314442
\(316\) 1.73114e16 0.978063
\(317\) 1.50841e15 0.0834902 0.0417451 0.999128i \(-0.486708\pi\)
0.0417451 + 0.999128i \(0.486708\pi\)
\(318\) 2.33194e16 1.26457
\(319\) −3.52515e16 −1.87300
\(320\) −4.16411e15 −0.216794
\(321\) 2.56063e16 1.30636
\(322\) −9.94272e15 −0.497098
\(323\) −4.77629e16 −2.34032
\(324\) −5.14049e16 −2.46866
\(325\) −1.41895e15 −0.0667922
\(326\) −2.13913e15 −0.0987015
\(327\) −3.91649e16 −1.77148
\(328\) 7.80306e16 3.46007
\(329\) −9.37775e15 −0.407685
\(330\) 9.07718e16 3.86910
\(331\) 2.65500e16 1.10964 0.554821 0.831970i \(-0.312787\pi\)
0.554821 + 0.831970i \(0.312787\pi\)
\(332\) −1.01534e17 −4.16114
\(333\) 1.11045e16 0.446284
\(334\) −4.99740e16 −1.96966
\(335\) 4.02716e16 1.55671
\(336\) −2.77572e16 −1.05238
\(337\) 3.97000e16 1.47637 0.738186 0.674597i \(-0.235683\pi\)
0.738186 + 0.674597i \(0.235683\pi\)
\(338\) 4.49229e16 1.63874
\(339\) −5.74876e15 −0.205720
\(340\) −1.03937e17 −3.64887
\(341\) 8.84329e16 3.04586
\(342\) 6.40984e16 2.16609
\(343\) −2.16087e16 −0.716502
\(344\) 1.25526e16 0.408417
\(345\) 2.71779e16 0.867744
\(346\) 7.49344e16 2.34794
\(347\) 3.08047e15 0.0947272 0.0473636 0.998878i \(-0.484918\pi\)
0.0473636 + 0.998878i \(0.484918\pi\)
\(348\) −1.13299e17 −3.41949
\(349\) 6.02974e16 1.78621 0.893106 0.449846i \(-0.148521\pi\)
0.893106 + 0.449846i \(0.148521\pi\)
\(350\) 5.18643e15 0.150809
\(351\) 1.26628e15 0.0361438
\(352\) 7.54707e16 2.11471
\(353\) 3.36289e16 0.925077 0.462538 0.886599i \(-0.346939\pi\)
0.462538 + 0.886599i \(0.346939\pi\)
\(354\) −5.57088e16 −1.50453
\(355\) −4.54676e16 −1.20564
\(356\) 7.50940e16 1.95515
\(357\) −3.76622e16 −0.962858
\(358\) −1.09320e17 −2.74448
\(359\) −4.89221e16 −1.20612 −0.603060 0.797695i \(-0.706052\pi\)
−0.603060 + 0.797695i \(0.706052\pi\)
\(360\) 7.86402e16 1.90405
\(361\) 2.93529e16 0.697999
\(362\) −3.01519e15 −0.0704220
\(363\) −1.21960e17 −2.79786
\(364\) 1.22636e16 0.276349
\(365\) 5.04358e15 0.111644
\(366\) 7.59066e16 1.65064
\(367\) 2.08663e16 0.445775 0.222888 0.974844i \(-0.428452\pi\)
0.222888 + 0.974844i \(0.428452\pi\)
\(368\) 6.61546e16 1.38851
\(369\) −6.55419e16 −1.35160
\(370\) 3.86619e16 0.783379
\(371\) 9.79369e15 0.194992
\(372\) 2.84225e17 5.56076
\(373\) −6.90621e16 −1.32780 −0.663899 0.747822i \(-0.731100\pi\)
−0.663899 + 0.747822i \(0.731100\pi\)
\(374\) 2.99795e17 5.66447
\(375\) −8.02401e16 −1.49001
\(376\) 1.35265e17 2.46867
\(377\) 1.86970e16 0.335392
\(378\) −4.62839e15 −0.0816081
\(379\) 4.82810e16 0.836800 0.418400 0.908263i \(-0.362591\pi\)
0.418400 + 0.908263i \(0.362591\pi\)
\(380\) 1.55387e17 2.64741
\(381\) −2.29396e16 −0.384214
\(382\) 1.23046e17 2.02607
\(383\) −7.25637e16 −1.17470 −0.587351 0.809333i \(-0.699829\pi\)
−0.587351 + 0.809333i \(0.699829\pi\)
\(384\) −6.72056e16 −1.06968
\(385\) 3.81223e16 0.596602
\(386\) −2.01680e17 −3.10345
\(387\) −1.05436e16 −0.159539
\(388\) −1.53615e16 −0.228574
\(389\) −9.04859e15 −0.132406 −0.0662031 0.997806i \(-0.521089\pi\)
−0.0662031 + 0.997806i \(0.521089\pi\)
\(390\) −4.81444e16 −0.692829
\(391\) 8.97614e16 1.27040
\(392\) 1.43206e17 1.99344
\(393\) −1.27552e17 −1.74637
\(394\) 9.59961e15 0.129279
\(395\) −2.85424e16 −0.378102
\(396\) −2.80132e17 −3.65043
\(397\) 5.87080e16 0.752591 0.376295 0.926500i \(-0.377198\pi\)
0.376295 + 0.926500i \(0.377198\pi\)
\(398\) 1.71710e17 2.16549
\(399\) 5.63052e16 0.698594
\(400\) −3.45083e16 −0.421244
\(401\) 7.57878e16 0.910251 0.455125 0.890427i \(-0.349594\pi\)
0.455125 + 0.890427i \(0.349594\pi\)
\(402\) −3.73337e17 −4.41196
\(403\) −4.69039e16 −0.545414
\(404\) 1.87110e17 2.14101
\(405\) 8.47542e16 0.954341
\(406\) −6.83396e16 −0.757274
\(407\) −7.76460e16 −0.846751
\(408\) 5.43240e17 5.83043
\(409\) −6.14465e16 −0.649076 −0.324538 0.945873i \(-0.605209\pi\)
−0.324538 + 0.945873i \(0.605209\pi\)
\(410\) −2.28194e17 −2.37252
\(411\) −1.73978e17 −1.78042
\(412\) 7.19833e16 0.725103
\(413\) −2.33966e16 −0.231994
\(414\) −1.20461e17 −1.17583
\(415\) 1.67404e17 1.60862
\(416\) −4.00289e16 −0.378675
\(417\) 1.82284e17 1.69772
\(418\) −4.48196e17 −4.10981
\(419\) 1.56464e17 1.41261 0.706306 0.707907i \(-0.250360\pi\)
0.706306 + 0.707907i \(0.250360\pi\)
\(420\) 1.22526e17 1.08920
\(421\) −1.28104e17 −1.12132 −0.560661 0.828045i \(-0.689453\pi\)
−0.560661 + 0.828045i \(0.689453\pi\)
\(422\) 2.32425e17 2.00333
\(423\) −1.13616e17 −0.964331
\(424\) −1.41264e17 −1.18074
\(425\) −4.68223e16 −0.385411
\(426\) 4.21506e17 3.41698
\(427\) 3.18793e16 0.254523
\(428\) −2.75133e17 −2.16351
\(429\) 9.66900e16 0.748875
\(430\) −3.67090e16 −0.280045
\(431\) 1.14344e17 0.859235 0.429617 0.903011i \(-0.358648\pi\)
0.429617 + 0.903011i \(0.358648\pi\)
\(432\) 3.07954e16 0.227951
\(433\) 2.25765e17 1.64621 0.823105 0.567889i \(-0.192240\pi\)
0.823105 + 0.567889i \(0.192240\pi\)
\(434\) 1.71439e17 1.23148
\(435\) 1.86803e17 1.32191
\(436\) 4.20817e17 2.93381
\(437\) −1.34194e17 −0.921729
\(438\) −4.67565e16 −0.316417
\(439\) −9.07134e16 −0.604856 −0.302428 0.953172i \(-0.597797\pi\)
−0.302428 + 0.953172i \(0.597797\pi\)
\(440\) −5.49877e17 −3.61263
\(441\) −1.20286e17 −0.778692
\(442\) −1.59008e17 −1.01432
\(443\) −2.41413e17 −1.51753 −0.758765 0.651365i \(-0.774197\pi\)
−0.758765 + 0.651365i \(0.774197\pi\)
\(444\) −2.49556e17 −1.54589
\(445\) −1.23812e17 −0.755827
\(446\) −1.57223e17 −0.945887
\(447\) −2.71851e17 −1.61188
\(448\) 1.62126e16 0.0947428
\(449\) 7.03138e16 0.404986 0.202493 0.979284i \(-0.435096\pi\)
0.202493 + 0.979284i \(0.435096\pi\)
\(450\) 6.28360e16 0.356720
\(451\) 4.58290e17 2.56444
\(452\) 6.17690e16 0.340699
\(453\) 8.40082e16 0.456755
\(454\) −3.62486e17 −1.94280
\(455\) −2.02197e16 −0.106832
\(456\) −8.12147e17 −4.23022
\(457\) −2.57859e16 −0.132412 −0.0662060 0.997806i \(-0.521089\pi\)
−0.0662060 + 0.997806i \(0.521089\pi\)
\(458\) 5.56892e17 2.81933
\(459\) 4.17844e16 0.208560
\(460\) −2.92020e17 −1.43710
\(461\) −7.49441e16 −0.363648 −0.181824 0.983331i \(-0.558200\pi\)
−0.181824 + 0.983331i \(0.558200\pi\)
\(462\) −3.53413e17 −1.69087
\(463\) 2.39300e17 1.12893 0.564464 0.825457i \(-0.309083\pi\)
0.564464 + 0.825457i \(0.309083\pi\)
\(464\) 4.54703e17 2.11525
\(465\) −4.68619e17 −2.14969
\(466\) −4.57694e17 −2.07046
\(467\) −2.99998e16 −0.133832 −0.0669158 0.997759i \(-0.521316\pi\)
−0.0669158 + 0.997759i \(0.521316\pi\)
\(468\) 1.48579e17 0.653672
\(469\) −1.56794e17 −0.680309
\(470\) −3.95570e17 −1.69273
\(471\) −3.82572e17 −1.61464
\(472\) 3.37472e17 1.40480
\(473\) 7.37239e16 0.302699
\(474\) 2.64602e17 1.07160
\(475\) 6.99996e16 0.279632
\(476\) 4.04671e17 1.59462
\(477\) 1.18655e17 0.461230
\(478\) −3.16703e17 −1.21442
\(479\) −2.32445e17 −0.879304 −0.439652 0.898168i \(-0.644898\pi\)
−0.439652 + 0.898168i \(0.644898\pi\)
\(480\) −3.99930e17 −1.49251
\(481\) 4.11826e16 0.151625
\(482\) −1.58342e17 −0.575161
\(483\) −1.05815e17 −0.379219
\(484\) 1.31043e18 4.63362
\(485\) 2.53274e16 0.0883626
\(486\) −7.24503e17 −2.49404
\(487\) 3.80963e17 1.29403 0.647016 0.762477i \(-0.276017\pi\)
0.647016 + 0.762477i \(0.276017\pi\)
\(488\) −4.59827e17 −1.54122
\(489\) −2.27656e16 −0.0752961
\(490\) −4.18795e17 −1.36687
\(491\) 2.77787e17 0.894711 0.447355 0.894356i \(-0.352366\pi\)
0.447355 + 0.894356i \(0.352366\pi\)
\(492\) 1.47295e18 4.68183
\(493\) 6.16960e17 1.93532
\(494\) 2.37718e17 0.735932
\(495\) 4.61870e17 1.41119
\(496\) −1.14068e18 −3.43980
\(497\) 1.77024e17 0.526886
\(498\) −1.55192e18 −4.55909
\(499\) 2.25995e16 0.0655308 0.0327654 0.999463i \(-0.489569\pi\)
0.0327654 + 0.999463i \(0.489569\pi\)
\(500\) 8.62161e17 2.46765
\(501\) −5.31846e17 −1.50259
\(502\) −6.60160e16 −0.184109
\(503\) 5.95996e16 0.164078 0.0820392 0.996629i \(-0.473857\pi\)
0.0820392 + 0.996629i \(0.473857\pi\)
\(504\) −3.06179e17 −0.832104
\(505\) −3.08499e17 −0.827676
\(506\) 8.42299e17 2.23094
\(507\) 4.78090e17 1.25014
\(508\) 2.46480e17 0.636309
\(509\) 3.04966e17 0.777294 0.388647 0.921387i \(-0.372943\pi\)
0.388647 + 0.921387i \(0.372943\pi\)
\(510\) −1.58866e18 −3.99783
\(511\) −1.96368e16 −0.0487904
\(512\) 9.03040e17 2.21540
\(513\) −6.24680e16 −0.151319
\(514\) 5.57753e17 1.33408
\(515\) −1.18683e17 −0.280312
\(516\) 2.36950e17 0.552630
\(517\) 7.94437e17 1.82966
\(518\) −1.50527e17 −0.342351
\(519\) 7.97486e17 1.79116
\(520\) 2.91649e17 0.646903
\(521\) −5.62230e17 −1.23160 −0.615799 0.787904i \(-0.711167\pi\)
−0.615799 + 0.787904i \(0.711167\pi\)
\(522\) −8.27966e17 −1.79124
\(523\) −5.72007e17 −1.22220 −0.611098 0.791555i \(-0.709272\pi\)
−0.611098 + 0.791555i \(0.709272\pi\)
\(524\) 1.37052e18 2.89222
\(525\) 5.51963e16 0.115047
\(526\) −1.29280e18 −2.66148
\(527\) −1.54772e18 −3.14720
\(528\) 2.35146e18 4.72299
\(529\) −2.51845e17 −0.499656
\(530\) 4.13116e17 0.809615
\(531\) −2.83460e17 −0.548754
\(532\) −6.04986e17 −1.15696
\(533\) −2.43072e17 −0.459207
\(534\) 1.14780e18 2.14213
\(535\) 4.53628e17 0.836374
\(536\) 2.26160e18 4.11950
\(537\) −1.16343e18 −2.09367
\(538\) 4.46232e17 0.793370
\(539\) 8.41080e17 1.47744
\(540\) −1.35937e17 −0.235927
\(541\) −5.51264e17 −0.945318 −0.472659 0.881245i \(-0.656706\pi\)
−0.472659 + 0.881245i \(0.656706\pi\)
\(542\) −5.69877e17 −0.965574
\(543\) −3.20890e16 −0.0537226
\(544\) −1.32086e18 −2.18507
\(545\) −6.93826e17 −1.13416
\(546\) 1.87446e17 0.302778
\(547\) 4.15668e16 0.0663481 0.0331741 0.999450i \(-0.489438\pi\)
0.0331741 + 0.999450i \(0.489438\pi\)
\(548\) 1.86935e18 2.94861
\(549\) 3.86232e17 0.602044
\(550\) −4.39369e17 −0.676818
\(551\) −9.22359e17 −1.40415
\(552\) 1.52628e18 2.29630
\(553\) 1.11127e17 0.165237
\(554\) −7.94380e17 −1.16739
\(555\) 4.11458e17 0.597614
\(556\) −1.95860e18 −2.81164
\(557\) −6.66203e17 −0.945252 −0.472626 0.881263i \(-0.656694\pi\)
−0.472626 + 0.881263i \(0.656694\pi\)
\(558\) 2.07706e18 2.91291
\(559\) −3.91024e16 −0.0542034
\(560\) −4.91734e17 −0.673764
\(561\) 3.19056e18 4.32123
\(562\) −9.29075e17 −1.24384
\(563\) −1.40923e18 −1.86499 −0.932495 0.361183i \(-0.882373\pi\)
−0.932495 + 0.361183i \(0.882373\pi\)
\(564\) 2.55334e18 3.34037
\(565\) −1.01842e17 −0.131708
\(566\) 1.64094e18 2.09790
\(567\) −3.29984e17 −0.417064
\(568\) −2.55340e18 −3.19047
\(569\) −1.10068e18 −1.35966 −0.679831 0.733369i \(-0.737947\pi\)
−0.679831 + 0.733369i \(0.737947\pi\)
\(570\) 2.37506e18 2.90060
\(571\) −4.64559e17 −0.560927 −0.280464 0.959865i \(-0.590488\pi\)
−0.280464 + 0.959865i \(0.590488\pi\)
\(572\) −1.03891e18 −1.24024
\(573\) 1.30951e18 1.54562
\(574\) 8.88455e17 1.03683
\(575\) −1.31551e17 −0.151793
\(576\) 1.96424e17 0.224103
\(577\) −2.50781e17 −0.282912 −0.141456 0.989945i \(-0.545178\pi\)
−0.141456 + 0.989945i \(0.545178\pi\)
\(578\) −3.62027e18 −4.03841
\(579\) −2.14637e18 −2.36752
\(580\) −2.00715e18 −2.18926
\(581\) −6.51775e17 −0.702996
\(582\) −2.34797e17 −0.250434
\(583\) −8.29674e17 −0.875108
\(584\) 2.83241e17 0.295443
\(585\) −2.44971e17 −0.252698
\(586\) 3.07096e18 3.13285
\(587\) −1.08453e17 −0.109419 −0.0547096 0.998502i \(-0.517423\pi\)
−0.0547096 + 0.998502i \(0.517423\pi\)
\(588\) 2.70325e18 2.69733
\(589\) 2.31386e18 2.28343
\(590\) −9.86909e17 −0.963250
\(591\) 1.02163e17 0.0986227
\(592\) 1.00154e18 0.956266
\(593\) −1.11060e18 −1.04883 −0.524413 0.851464i \(-0.675715\pi\)
−0.524413 + 0.851464i \(0.675715\pi\)
\(594\) 3.92095e17 0.366251
\(595\) −6.67205e17 −0.616452
\(596\) 2.92097e18 2.66948
\(597\) 1.82742e18 1.65198
\(598\) −4.46746e17 −0.399488
\(599\) 1.09969e18 0.972742 0.486371 0.873752i \(-0.338320\pi\)
0.486371 + 0.873752i \(0.338320\pi\)
\(600\) −7.96152e17 −0.696648
\(601\) −1.58647e18 −1.37324 −0.686621 0.727015i \(-0.740907\pi\)
−0.686621 + 0.727015i \(0.740907\pi\)
\(602\) 1.42924e17 0.122385
\(603\) −1.89963e18 −1.60919
\(604\) −9.02648e17 −0.756447
\(605\) −2.16059e18 −1.79128
\(606\) 2.85994e18 2.34577
\(607\) −6.04036e17 −0.490158 −0.245079 0.969503i \(-0.578814\pi\)
−0.245079 + 0.969503i \(0.578814\pi\)
\(608\) 1.97470e18 1.58536
\(609\) −7.27301e17 −0.577699
\(610\) 1.34472e18 1.05679
\(611\) −4.21361e17 −0.327632
\(612\) 4.90278e18 3.77188
\(613\) 5.37012e17 0.408781 0.204391 0.978889i \(-0.434479\pi\)
0.204391 + 0.978889i \(0.434479\pi\)
\(614\) −1.74036e18 −1.31082
\(615\) −2.42854e18 −1.80991
\(616\) 2.14090e18 1.57878
\(617\) −1.55039e18 −1.13132 −0.565662 0.824637i \(-0.691379\pi\)
−0.565662 + 0.824637i \(0.691379\pi\)
\(618\) 1.10025e18 0.794450
\(619\) 8.75786e17 0.625762 0.312881 0.949792i \(-0.398706\pi\)
0.312881 + 0.949792i \(0.398706\pi\)
\(620\) 5.03520e18 3.56017
\(621\) 1.17397e17 0.0821411
\(622\) −4.47256e18 −3.09684
\(623\) 4.82052e17 0.330310
\(624\) −1.24719e18 −0.845732
\(625\) −1.10172e18 −0.739355
\(626\) 1.54722e18 1.02759
\(627\) −4.76990e18 −3.13524
\(628\) 4.11064e18 2.67406
\(629\) 1.35894e18 0.874923
\(630\) 8.95396e17 0.570560
\(631\) −5.68638e17 −0.358629 −0.179314 0.983792i \(-0.557388\pi\)
−0.179314 + 0.983792i \(0.557388\pi\)
\(632\) −1.60290e18 −1.00057
\(633\) 2.47358e18 1.52827
\(634\) −2.47729e17 −0.151494
\(635\) −4.06387e17 −0.245986
\(636\) −2.66659e18 −1.59766
\(637\) −4.46100e17 −0.264561
\(638\) 5.78940e18 3.39859
\(639\) 2.14473e18 1.24629
\(640\) −1.19058e18 −0.684840
\(641\) 2.67922e18 1.52557 0.762784 0.646654i \(-0.223832\pi\)
0.762784 + 0.646654i \(0.223832\pi\)
\(642\) −4.20536e18 −2.37042
\(643\) −1.98256e17 −0.110626 −0.0553128 0.998469i \(-0.517616\pi\)
−0.0553128 + 0.998469i \(0.517616\pi\)
\(644\) 1.13696e18 0.628038
\(645\) −3.90674e17 −0.213637
\(646\) 7.84418e18 4.24655
\(647\) 1.70529e18 0.913945 0.456973 0.889481i \(-0.348934\pi\)
0.456973 + 0.889481i \(0.348934\pi\)
\(648\) 4.75969e18 2.52546
\(649\) 1.98204e18 1.04117
\(650\) 2.33037e17 0.121196
\(651\) 1.82453e18 0.939452
\(652\) 2.44611e17 0.124700
\(653\) −2.26552e18 −1.14349 −0.571746 0.820431i \(-0.693734\pi\)
−0.571746 + 0.820431i \(0.693734\pi\)
\(654\) 6.43211e18 3.21439
\(655\) −2.25965e18 −1.11808
\(656\) −5.91140e18 −2.89611
\(657\) −2.37909e17 −0.115408
\(658\) 1.54012e18 0.739753
\(659\) 1.06435e18 0.506210 0.253105 0.967439i \(-0.418548\pi\)
0.253105 + 0.967439i \(0.418548\pi\)
\(660\) −1.03798e19 −4.88826
\(661\) −2.82204e18 −1.31599 −0.657996 0.753021i \(-0.728596\pi\)
−0.657996 + 0.753021i \(0.728596\pi\)
\(662\) −4.36035e18 −2.01347
\(663\) −1.69224e18 −0.773791
\(664\) 9.40122e18 4.25688
\(665\) 9.97476e17 0.447262
\(666\) −1.82371e18 −0.809790
\(667\) 1.73340e18 0.762220
\(668\) 5.71456e18 2.48849
\(669\) −1.67324e18 −0.721586
\(670\) −6.61386e18 −2.82468
\(671\) −2.70066e18 −1.14228
\(672\) 1.55710e18 0.652252
\(673\) 2.07422e18 0.860511 0.430255 0.902707i \(-0.358424\pi\)
0.430255 + 0.902707i \(0.358424\pi\)
\(674\) −6.51998e18 −2.67890
\(675\) −6.12377e16 −0.0249198
\(676\) −5.13696e18 −2.07039
\(677\) 4.05470e18 1.61857 0.809286 0.587415i \(-0.199854\pi\)
0.809286 + 0.587415i \(0.199854\pi\)
\(678\) 9.44127e17 0.373282
\(679\) −9.86101e16 −0.0386160
\(680\) 9.62377e18 3.73282
\(681\) −3.85775e18 −1.48210
\(682\) −1.45235e19 −5.52678
\(683\) −1.88066e18 −0.708886 −0.354443 0.935078i \(-0.615330\pi\)
−0.354443 + 0.935078i \(0.615330\pi\)
\(684\) −7.32969e18 −2.73666
\(685\) −3.08211e18 −1.13988
\(686\) 3.54884e18 1.30011
\(687\) 5.92670e18 2.15077
\(688\) −9.50953e17 −0.341849
\(689\) 4.40050e17 0.156703
\(690\) −4.46346e18 −1.57454
\(691\) −1.84402e18 −0.644406 −0.322203 0.946671i \(-0.604423\pi\)
−0.322203 + 0.946671i \(0.604423\pi\)
\(692\) −8.56880e18 −2.96640
\(693\) −1.79825e18 −0.616716
\(694\) −5.05910e17 −0.171884
\(695\) 3.22926e18 1.08693
\(696\) 1.04906e19 3.49817
\(697\) −8.02084e18 −2.64976
\(698\) −9.90272e18 −3.24111
\(699\) −4.87098e18 −1.57948
\(700\) −5.93071e17 −0.190533
\(701\) 1.05721e18 0.336507 0.168253 0.985744i \(-0.446187\pi\)
0.168253 + 0.985744i \(0.446187\pi\)
\(702\) −2.07963e17 −0.0655835
\(703\) −2.03162e18 −0.634793
\(704\) −1.37345e18 −0.425199
\(705\) −4.20984e18 −1.29133
\(706\) −5.52293e18 −1.67857
\(707\) 1.20112e18 0.361709
\(708\) 6.37033e18 1.90084
\(709\) −3.47406e18 −1.02716 −0.513579 0.858042i \(-0.671681\pi\)
−0.513579 + 0.858042i \(0.671681\pi\)
\(710\) 7.46720e18 2.18765
\(711\) 1.34636e18 0.390849
\(712\) −6.95312e18 −2.00014
\(713\) −4.34846e18 −1.23952
\(714\) 6.18532e18 1.74712
\(715\) 1.71291e18 0.479453
\(716\) 1.25008e19 3.46740
\(717\) −3.37049e18 −0.926444
\(718\) 8.03454e18 2.18853
\(719\) 3.18904e18 0.860839 0.430420 0.902629i \(-0.358366\pi\)
0.430420 + 0.902629i \(0.358366\pi\)
\(720\) −5.95759e18 −1.59371
\(721\) 4.62083e17 0.122501
\(722\) −4.82067e18 −1.26653
\(723\) −1.68514e18 −0.438771
\(724\) 3.44789e17 0.0889718
\(725\) −9.04194e17 −0.231241
\(726\) 2.00297e19 5.07676
\(727\) 6.45840e18 1.62238 0.811188 0.584786i \(-0.198821\pi\)
0.811188 + 0.584786i \(0.198821\pi\)
\(728\) −1.13551e18 −0.282708
\(729\) −3.34648e18 −0.825770
\(730\) −8.28315e17 −0.202580
\(731\) −1.29029e18 −0.312770
\(732\) −8.67997e18 −2.08543
\(733\) −3.06499e18 −0.729883 −0.364941 0.931031i \(-0.618911\pi\)
−0.364941 + 0.931031i \(0.618911\pi\)
\(734\) −3.42690e18 −0.808867
\(735\) −4.45701e18 −1.04274
\(736\) −3.71107e18 −0.860585
\(737\) 1.32828e19 3.05318
\(738\) 1.07640e19 2.45250
\(739\) −2.66860e18 −0.602691 −0.301345 0.953515i \(-0.597436\pi\)
−0.301345 + 0.953515i \(0.597436\pi\)
\(740\) −4.42102e18 −0.989728
\(741\) 2.52991e18 0.561418
\(742\) −1.60843e18 −0.353816
\(743\) 1.17551e18 0.256330 0.128165 0.991753i \(-0.459091\pi\)
0.128165 + 0.991753i \(0.459091\pi\)
\(744\) −2.63171e19 −5.68870
\(745\) −4.81598e18 −1.03197
\(746\) 1.13422e19 2.40932
\(747\) −7.89656e18 −1.66285
\(748\) −3.42818e19 −7.15654
\(749\) −1.76617e18 −0.365510
\(750\) 1.31780e19 2.70365
\(751\) −7.80250e18 −1.58699 −0.793495 0.608577i \(-0.791741\pi\)
−0.793495 + 0.608577i \(0.791741\pi\)
\(752\) −1.02473e19 −2.06630
\(753\) −7.02572e17 −0.140451
\(754\) −3.07064e18 −0.608576
\(755\) 1.48825e18 0.292429
\(756\) 5.29260e17 0.103104
\(757\) −1.89110e18 −0.365251 −0.182625 0.983183i \(-0.558460\pi\)
−0.182625 + 0.983183i \(0.558460\pi\)
\(758\) −7.92926e18 −1.51839
\(759\) 8.96413e18 1.70191
\(760\) −1.43876e19 −2.70832
\(761\) 4.11499e18 0.768014 0.384007 0.923330i \(-0.374544\pi\)
0.384007 + 0.923330i \(0.374544\pi\)
\(762\) 3.76740e18 0.697163
\(763\) 2.70136e18 0.495647
\(764\) −1.40703e19 −2.55975
\(765\) −8.08350e18 −1.45814
\(766\) 1.19172e19 2.13152
\(767\) −1.05126e18 −0.186440
\(768\) 1.29628e19 2.27957
\(769\) 5.53905e18 0.965860 0.482930 0.875659i \(-0.339572\pi\)
0.482930 + 0.875659i \(0.339572\pi\)
\(770\) −6.26089e18 −1.08255
\(771\) 5.93586e18 1.01772
\(772\) 2.30622e19 3.92092
\(773\) −1.59242e18 −0.268466 −0.134233 0.990950i \(-0.542857\pi\)
−0.134233 + 0.990950i \(0.542857\pi\)
\(774\) 1.73159e18 0.289486
\(775\) 2.26829e18 0.376043
\(776\) 1.42235e18 0.233833
\(777\) −1.60198e18 −0.261168
\(778\) 1.48606e18 0.240254
\(779\) 1.19912e19 1.92251
\(780\) 5.50535e18 0.875326
\(781\) −1.49966e19 −2.36462
\(782\) −1.47416e19 −2.30516
\(783\) 8.06906e17 0.125133
\(784\) −1.08490e19 −1.66853
\(785\) −6.77745e18 −1.03375
\(786\) 2.09481e19 3.16882
\(787\) 1.13209e19 1.69842 0.849211 0.528054i \(-0.177078\pi\)
0.849211 + 0.528054i \(0.177078\pi\)
\(788\) −1.09772e18 −0.163332
\(789\) −1.37586e19 −2.03036
\(790\) 4.68755e18 0.686073
\(791\) 3.96514e17 0.0575588
\(792\) 2.59380e19 3.73442
\(793\) 1.43240e18 0.204545
\(794\) −9.64170e18 −1.36559
\(795\) 4.39656e18 0.617628
\(796\) −1.96352e19 −2.73590
\(797\) 5.73943e18 0.793212 0.396606 0.917989i \(-0.370188\pi\)
0.396606 + 0.917989i \(0.370188\pi\)
\(798\) −9.24709e18 −1.26761
\(799\) −1.39040e19 −1.89054
\(800\) 1.93581e18 0.261082
\(801\) 5.84028e18 0.781308
\(802\) −1.24467e19 −1.65167
\(803\) 1.66353e18 0.218968
\(804\) 4.26913e19 5.57411
\(805\) −1.87457e18 −0.242788
\(806\) 7.70310e18 0.989663
\(807\) 4.74900e18 0.605236
\(808\) −1.73249e19 −2.19027
\(809\) 5.01001e18 0.628309 0.314155 0.949372i \(-0.398279\pi\)
0.314155 + 0.949372i \(0.398279\pi\)
\(810\) −1.39193e19 −1.73167
\(811\) −2.87604e18 −0.354944 −0.177472 0.984126i \(-0.556792\pi\)
−0.177472 + 0.984126i \(0.556792\pi\)
\(812\) 7.81468e18 0.956747
\(813\) −6.06489e18 −0.736604
\(814\) 1.27519e19 1.53644
\(815\) −4.03305e17 −0.0482069
\(816\) −4.11545e19 −4.88013
\(817\) 1.92900e18 0.226928
\(818\) 1.00914e19 1.17776
\(819\) 9.53775e17 0.110433
\(820\) 2.60941e19 2.99746
\(821\) −3.04163e18 −0.346638 −0.173319 0.984866i \(-0.555449\pi\)
−0.173319 + 0.984866i \(0.555449\pi\)
\(822\) 2.85727e19 3.23061
\(823\) 8.88153e18 0.996297 0.498148 0.867092i \(-0.334013\pi\)
0.498148 + 0.867092i \(0.334013\pi\)
\(824\) −6.66509e18 −0.741787
\(825\) −4.67596e18 −0.516322
\(826\) 3.84245e18 0.420957
\(827\) 1.32121e19 1.43610 0.718050 0.695992i \(-0.245035\pi\)
0.718050 + 0.695992i \(0.245035\pi\)
\(828\) 1.37748e19 1.48555
\(829\) −1.05788e19 −1.13196 −0.565979 0.824419i \(-0.691502\pi\)
−0.565979 + 0.824419i \(0.691502\pi\)
\(830\) −2.74931e19 −2.91887
\(831\) −8.45416e18 −0.890561
\(832\) 7.28466e17 0.0761391
\(833\) −1.47203e19 −1.52660
\(834\) −2.99368e19 −3.08054
\(835\) −9.42193e18 −0.962006
\(836\) 5.12515e19 5.19237
\(837\) −2.02423e18 −0.203491
\(838\) −2.56963e19 −2.56321
\(839\) 3.91972e18 0.387974 0.193987 0.981004i \(-0.437858\pi\)
0.193987 + 0.981004i \(0.437858\pi\)
\(840\) −1.13450e19 −1.11426
\(841\) 1.65359e18 0.161159
\(842\) 2.10388e19 2.03466
\(843\) −9.88764e18 −0.948884
\(844\) −2.65780e19 −2.53103
\(845\) 8.46960e18 0.800377
\(846\) 1.86593e19 1.74980
\(847\) 8.41208e18 0.782819
\(848\) 1.07018e19 0.988291
\(849\) 1.74636e19 1.60042
\(850\) 7.68969e18 0.699336
\(851\) 3.81804e18 0.344587
\(852\) −4.81995e19 −4.31703
\(853\) −1.56876e19 −1.39440 −0.697200 0.716876i \(-0.745571\pi\)
−0.697200 + 0.716876i \(0.745571\pi\)
\(854\) −5.23558e18 −0.461837
\(855\) 1.20849e19 1.05794
\(856\) 2.54752e19 2.21329
\(857\) −1.02998e19 −0.888083 −0.444041 0.896006i \(-0.646456\pi\)
−0.444041 + 0.896006i \(0.646456\pi\)
\(858\) −1.58795e19 −1.35885
\(859\) 8.47145e18 0.719453 0.359726 0.933058i \(-0.382870\pi\)
0.359726 + 0.933058i \(0.382870\pi\)
\(860\) 4.19770e18 0.353811
\(861\) 9.45534e18 0.790964
\(862\) −1.87789e19 −1.55910
\(863\) −3.58662e18 −0.295539 −0.147770 0.989022i \(-0.547209\pi\)
−0.147770 + 0.989022i \(0.547209\pi\)
\(864\) −1.72753e18 −0.141281
\(865\) 1.41279e19 1.14676
\(866\) −3.70777e19 −2.98708
\(867\) −3.85286e19 −3.08077
\(868\) −1.96041e19 −1.55586
\(869\) −9.41417e18 −0.741572
\(870\) −3.06789e19 −2.39864
\(871\) −7.04508e18 −0.546724
\(872\) −3.89644e19 −3.00131
\(873\) −1.19471e18 −0.0913416
\(874\) 2.20388e19 1.67249
\(875\) 5.53448e18 0.416893
\(876\) 5.34664e18 0.399764
\(877\) −2.00115e19 −1.48519 −0.742594 0.669742i \(-0.766405\pi\)
−0.742594 + 0.669742i \(0.766405\pi\)
\(878\) 1.48980e19 1.09752
\(879\) 3.26826e19 2.38995
\(880\) 4.16573e19 3.02380
\(881\) −2.31276e19 −1.66643 −0.833216 0.552947i \(-0.813503\pi\)
−0.833216 + 0.552947i \(0.813503\pi\)
\(882\) 1.97548e19 1.41295
\(883\) 4.18896e18 0.297414 0.148707 0.988881i \(-0.452489\pi\)
0.148707 + 0.988881i \(0.452489\pi\)
\(884\) 1.81827e19 1.28150
\(885\) −1.05031e19 −0.734832
\(886\) 3.96477e19 2.75359
\(887\) 1.02860e19 0.709156 0.354578 0.935026i \(-0.384625\pi\)
0.354578 + 0.935026i \(0.384625\pi\)
\(888\) 2.31069e19 1.58146
\(889\) 1.58223e18 0.107500
\(890\) 2.03338e19 1.37146
\(891\) 2.79546e19 1.87175
\(892\) 1.79785e19 1.19504
\(893\) 2.07865e19 1.37166
\(894\) 4.46465e19 2.92478
\(895\) −2.06108e19 −1.34043
\(896\) 4.63543e18 0.299287
\(897\) −4.75448e18 −0.304756
\(898\) −1.15477e19 −0.734854
\(899\) −2.98884e19 −1.88827
\(900\) −7.18534e18 −0.450683
\(901\) 1.45207e19 0.904224
\(902\) −7.52656e19 −4.65322
\(903\) 1.52106e18 0.0933631
\(904\) −5.71933e18 −0.348538
\(905\) −5.68473e17 −0.0343949
\(906\) −1.37968e19 −0.828790
\(907\) −2.94735e18 −0.175786 −0.0878929 0.996130i \(-0.528013\pi\)
−0.0878929 + 0.996130i \(0.528013\pi\)
\(908\) 4.14506e19 2.45455
\(909\) 1.45521e19 0.855580
\(910\) 3.32071e18 0.193848
\(911\) 8.76223e18 0.507861 0.253931 0.967222i \(-0.418276\pi\)
0.253931 + 0.967222i \(0.418276\pi\)
\(912\) 6.15262e19 3.54074
\(913\) 5.52152e19 3.15500
\(914\) 4.23486e18 0.240264
\(915\) 1.43112e19 0.806191
\(916\) −6.36810e19 −3.56196
\(917\) 8.79777e18 0.488621
\(918\) −6.86232e18 −0.378437
\(919\) 2.22512e19 1.21844 0.609218 0.793003i \(-0.291484\pi\)
0.609218 + 0.793003i \(0.291484\pi\)
\(920\) 2.70388e19 1.47016
\(921\) −1.85217e19 −0.999983
\(922\) 1.23082e19 0.659846
\(923\) 7.95406e18 0.423426
\(924\) 4.04130e19 2.13625
\(925\) −1.99161e18 −0.104540
\(926\) −3.93006e19 −2.04846
\(927\) 5.59835e18 0.289762
\(928\) −2.55074e19 −1.31101
\(929\) 2.18098e19 1.11314 0.556570 0.830801i \(-0.312117\pi\)
0.556570 + 0.830801i \(0.312117\pi\)
\(930\) 7.69620e19 3.90065
\(931\) 2.20070e19 1.10761
\(932\) 5.23376e19 2.61583
\(933\) −4.75991e19 −2.36248
\(934\) 4.92691e18 0.242840
\(935\) 5.65223e19 2.76659
\(936\) −1.37573e19 −0.668712
\(937\) 3.47028e18 0.167517 0.0837583 0.996486i \(-0.473308\pi\)
0.0837583 + 0.996486i \(0.473308\pi\)
\(938\) 2.57505e19 1.23443
\(939\) 1.64663e19 0.783914
\(940\) 4.52337e19 2.13861
\(941\) −9.03591e18 −0.424267 −0.212134 0.977241i \(-0.568041\pi\)
−0.212134 + 0.977241i \(0.568041\pi\)
\(942\) 6.28303e19 2.92980
\(943\) −2.25352e19 −1.04360
\(944\) −2.55661e19 −1.17583
\(945\) −8.72621e17 −0.0398583
\(946\) −1.21078e19 −0.549253
\(947\) −2.42336e18 −0.109180 −0.0545901 0.998509i \(-0.517385\pi\)
−0.0545901 + 0.998509i \(0.517385\pi\)
\(948\) −3.02574e19 −1.35387
\(949\) −8.82321e17 −0.0392099
\(950\) −1.14961e19 −0.507398
\(951\) −2.63645e18 −0.115570
\(952\) −3.74694e19 −1.63131
\(953\) −2.10889e18 −0.0911907 −0.0455954 0.998960i \(-0.514518\pi\)
−0.0455954 + 0.998960i \(0.514518\pi\)
\(954\) −1.94869e19 −0.836910
\(955\) 2.31986e19 0.989555
\(956\) 3.62152e19 1.53431
\(957\) 6.16134e19 2.59267
\(958\) 3.81748e19 1.59551
\(959\) 1.20000e19 0.498148
\(960\) 7.27814e18 0.300094
\(961\) 5.05614e19 2.07070
\(962\) −6.76349e18 −0.275127
\(963\) −2.13979e19 −0.864571
\(964\) 1.81065e19 0.726663
\(965\) −3.80240e19 −1.51576
\(966\) 1.73781e19 0.688101
\(967\) 2.53391e19 0.996596 0.498298 0.867006i \(-0.333959\pi\)
0.498298 + 0.867006i \(0.333959\pi\)
\(968\) −1.21336e20 −4.74023
\(969\) 8.34813e19 3.23955
\(970\) −4.15955e18 −0.160336
\(971\) −2.98802e19 −1.14408 −0.572042 0.820224i \(-0.693849\pi\)
−0.572042 + 0.820224i \(0.693849\pi\)
\(972\) 8.28474e19 3.15100
\(973\) −1.25729e19 −0.475008
\(974\) −6.25661e19 −2.34804
\(975\) 2.48008e18 0.0924562
\(976\) 3.48353e19 1.29002
\(977\) −5.02894e18 −0.184996 −0.0924979 0.995713i \(-0.529485\pi\)
−0.0924979 + 0.995713i \(0.529485\pi\)
\(978\) 3.73884e18 0.136626
\(979\) −4.08371e19 −1.48241
\(980\) 4.78895e19 1.72691
\(981\) 3.27282e19 1.17239
\(982\) −4.56214e19 −1.62347
\(983\) 6.49435e18 0.229582 0.114791 0.993390i \(-0.463380\pi\)
0.114791 + 0.993390i \(0.463380\pi\)
\(984\) −1.36384e20 −4.78956
\(985\) 1.80988e18 0.0631413
\(986\) −1.01324e20 −3.51167
\(987\) 1.63907e19 0.564333
\(988\) −2.71833e19 −0.929782
\(989\) −3.62518e18 −0.123184
\(990\) −7.58536e19 −2.56063
\(991\) 3.22546e19 1.08172 0.540858 0.841114i \(-0.318100\pi\)
0.540858 + 0.841114i \(0.318100\pi\)
\(992\) 6.39887e19 2.13195
\(993\) −4.64048e19 −1.53601
\(994\) −2.90730e19 −0.956044
\(995\) 3.23736e19 1.05765
\(996\) 1.77463e20 5.76000
\(997\) 8.49999e17 0.0274094 0.0137047 0.999906i \(-0.495638\pi\)
0.0137047 + 0.999906i \(0.495638\pi\)
\(998\) −3.71155e18 −0.118907
\(999\) 1.77732e18 0.0565705
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 197.14.a.a.1.6 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.14.a.a.1.6 104 1.1 even 1 trivial