Properties

Label 17.10.a.a.1.5
Level $17$
Weight $10$
Character 17.1
Self dual yes
Analytic conductor $8.756$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.75560921479\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - 2 x^{4} - 1596 x^{3} + 5754 x^{2} + 488987 x - 2711704\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(33.6330\) of defining polynomial
Character \(\chi\) \(=\) 17.1

$q$-expansion

\(f(q)\) \(=\) \(q+26.6330 q^{2} -85.9747 q^{3} +197.318 q^{4} -1460.58 q^{5} -2289.77 q^{6} -446.232 q^{7} -8380.94 q^{8} -12291.3 q^{9} +O(q^{10})\) \(q+26.6330 q^{2} -85.9747 q^{3} +197.318 q^{4} -1460.58 q^{5} -2289.77 q^{6} -446.232 q^{7} -8380.94 q^{8} -12291.3 q^{9} -38899.6 q^{10} +2565.20 q^{11} -16964.3 q^{12} +70467.9 q^{13} -11884.5 q^{14} +125573. q^{15} -324236. q^{16} -83521.0 q^{17} -327356. q^{18} -474111. q^{19} -288198. q^{20} +38364.6 q^{21} +68319.0 q^{22} +1.74586e6 q^{23} +720549. q^{24} +180168. q^{25} +1.87677e6 q^{26} +2.74899e6 q^{27} -88049.4 q^{28} +501157. q^{29} +3.34439e6 q^{30} -510635. q^{31} -4.34435e6 q^{32} -220542. q^{33} -2.22442e6 q^{34} +651757. q^{35} -2.42530e6 q^{36} -3.74847e6 q^{37} -1.26270e7 q^{38} -6.05845e6 q^{39} +1.22410e7 q^{40} -3.04327e7 q^{41} +1.02177e6 q^{42} -2.15222e7 q^{43} +506159. q^{44} +1.79525e7 q^{45} +4.64976e7 q^{46} +3.43306e6 q^{47} +2.78761e7 q^{48} -4.01545e7 q^{49} +4.79842e6 q^{50} +7.18069e6 q^{51} +1.39046e7 q^{52} -2.87800e7 q^{53} +7.32138e7 q^{54} -3.74668e6 q^{55} +3.73984e6 q^{56} +4.07615e7 q^{57} +1.33473e7 q^{58} -1.37313e8 q^{59} +2.47778e7 q^{60} +1.21854e8 q^{61} -1.35997e7 q^{62} +5.48479e6 q^{63} +5.03058e7 q^{64} -1.02924e8 q^{65} -5.87371e6 q^{66} -8.31665e7 q^{67} -1.64802e7 q^{68} -1.50100e8 q^{69} +1.73583e7 q^{70} +1.48492e8 q^{71} +1.03013e8 q^{72} +1.45029e8 q^{73} -9.98331e7 q^{74} -1.54899e7 q^{75} -9.35504e7 q^{76} -1.14467e6 q^{77} -1.61355e8 q^{78} -4.22172e8 q^{79} +4.73573e8 q^{80} +5.58742e6 q^{81} -8.10515e8 q^{82} -5.36072e7 q^{83} +7.57002e6 q^{84} +1.21989e8 q^{85} -5.73201e8 q^{86} -4.30868e7 q^{87} -2.14988e7 q^{88} +9.26167e8 q^{89} +4.78129e8 q^{90} -3.14450e7 q^{91} +3.44490e8 q^{92} +4.39017e7 q^{93} +9.14328e7 q^{94} +6.92477e8 q^{95} +3.73504e8 q^{96} +1.44334e9 q^{97} -1.06944e9 q^{98} -3.15298e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 33q^{2} - 236q^{3} + 853q^{4} + 1480q^{5} + 7578q^{6} - 13202q^{7} - 42423q^{8} + 10981q^{9} + O(q^{10}) \) \( 5q - 33q^{2} - 236q^{3} + 853q^{4} + 1480q^{5} + 7578q^{6} - 13202q^{7} - 42423q^{8} + 10981q^{9} - 89328q^{10} - 68036q^{11} - 406010q^{12} - 158862q^{13} - 84700q^{14} - 687324q^{15} + 350225q^{16} - 417605q^{17} - 1911585q^{18} - 370992q^{19} + 1632640q^{20} + 1783880q^{21} + 122290q^{22} + 1645870q^{23} + 9678702q^{24} + 3270239q^{25} + 734846q^{26} - 2998268q^{27} + 183372q^{28} + 3668616q^{29} + 17048544q^{30} - 7262362q^{31} - 5605919q^{32} - 11334900q^{33} + 2756193q^{34} - 26503988q^{35} + 49782133q^{36} - 31420708q^{37} + 18513700q^{38} - 42449884q^{39} - 53930464q^{40} - 7996938q^{41} - 44519496q^{42} - 56908268q^{43} + 43323054q^{44} + 12799536q^{45} - 32063472q^{46} - 16903336q^{47} - 102794498q^{48} - 11784059q^{49} + 85921093q^{50} + 19710956q^{51} + 173619082q^{52} - 83362982q^{53} + 386329164q^{54} + 6363364q^{55} + 317409372q^{56} + 136615904q^{57} + 64577488q^{58} - 37946604q^{59} - 223158912q^{60} - 77685452q^{61} + 324855300q^{62} - 191945278q^{63} + 131623105q^{64} - 40321288q^{65} + 298037676q^{66} - 304503600q^{67} - 71243413q^{68} - 333409272q^{69} - 122787392q^{70} - 476602922q^{71} - 1301701911q^{72} - 289980486q^{73} + 262289012q^{74} - 153685772q^{75} - 1031276084q^{76} - 143385648q^{77} + 691646196q^{78} - 828240610q^{79} + 912750944q^{80} + 891328609q^{81} - 1109615654q^{82} + 194681148q^{83} + 1541719592q^{84} - 123611080q^{85} + 1164707144q^{86} + 158149884q^{87} - 1017979978q^{88} + 376848106q^{89} - 2240087472q^{90} + 194543664q^{91} + 2506713088q^{92} + 3494835920q^{93} - 2244811104q^{94} + 1498679864q^{95} + 2935047582q^{96} + 692035246q^{97} + 871744055q^{98} + 2027106408q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 26.6330 1.17702 0.588512 0.808488i \(-0.299714\pi\)
0.588512 + 0.808488i \(0.299714\pi\)
\(3\) −85.9747 −0.612809 −0.306404 0.951901i \(-0.599126\pi\)
−0.306404 + 0.951901i \(0.599126\pi\)
\(4\) 197.318 0.385386
\(5\) −1460.58 −1.04511 −0.522553 0.852607i \(-0.675020\pi\)
−0.522553 + 0.852607i \(0.675020\pi\)
\(6\) −2289.77 −0.721291
\(7\) −446.232 −0.0702456 −0.0351228 0.999383i \(-0.511182\pi\)
−0.0351228 + 0.999383i \(0.511182\pi\)
\(8\) −8380.94 −0.723416
\(9\) −12291.3 −0.624465
\(10\) −38899.6 −1.23011
\(11\) 2565.20 0.0528268 0.0264134 0.999651i \(-0.491591\pi\)
0.0264134 + 0.999651i \(0.491591\pi\)
\(12\) −16964.3 −0.236168
\(13\) 70467.9 0.684299 0.342150 0.939645i \(-0.388845\pi\)
0.342150 + 0.939645i \(0.388845\pi\)
\(14\) −11884.5 −0.0826808
\(15\) 125573. 0.640450
\(16\) −324236. −1.23686
\(17\) −83521.0 −0.242536
\(18\) −327356. −0.735011
\(19\) −474111. −0.834620 −0.417310 0.908764i \(-0.637027\pi\)
−0.417310 + 0.908764i \(0.637027\pi\)
\(20\) −288198. −0.402769
\(21\) 38364.6 0.0430471
\(22\) 68319.0 0.0621784
\(23\) 1.74586e6 1.30087 0.650437 0.759561i \(-0.274586\pi\)
0.650437 + 0.759561i \(0.274586\pi\)
\(24\) 720549. 0.443315
\(25\) 180168. 0.0922461
\(26\) 1.87677e6 0.805437
\(27\) 2.74899e6 0.995487
\(28\) −88049.4 −0.0270717
\(29\) 501157. 0.131578 0.0657889 0.997834i \(-0.479044\pi\)
0.0657889 + 0.997834i \(0.479044\pi\)
\(30\) 3.34439e6 0.753825
\(31\) −510635. −0.0993077 −0.0496538 0.998766i \(-0.515812\pi\)
−0.0496538 + 0.998766i \(0.515812\pi\)
\(32\) −4.34435e6 −0.732403
\(33\) −220542. −0.0323727
\(34\) −2.22442e6 −0.285470
\(35\) 651757. 0.0734141
\(36\) −2.42530e6 −0.240660
\(37\) −3.74847e6 −0.328811 −0.164406 0.986393i \(-0.552571\pi\)
−0.164406 + 0.986393i \(0.552571\pi\)
\(38\) −1.26270e7 −0.982368
\(39\) −6.05845e6 −0.419345
\(40\) 1.22410e7 0.756046
\(41\) −3.04327e7 −1.68195 −0.840975 0.541074i \(-0.818018\pi\)
−0.840975 + 0.541074i \(0.818018\pi\)
\(42\) 1.02177e6 0.0506675
\(43\) −2.15222e7 −0.960017 −0.480008 0.877264i \(-0.659366\pi\)
−0.480008 + 0.877264i \(0.659366\pi\)
\(44\) 506159. 0.0203587
\(45\) 1.79525e7 0.652632
\(46\) 4.64976e7 1.53116
\(47\) 3.43306e6 0.102622 0.0513111 0.998683i \(-0.483660\pi\)
0.0513111 + 0.998683i \(0.483660\pi\)
\(48\) 2.78761e7 0.757961
\(49\) −4.01545e7 −0.995066
\(50\) 4.79842e6 0.108576
\(51\) 7.18069e6 0.148628
\(52\) 1.39046e7 0.263719
\(53\) −2.87800e7 −0.501013 −0.250506 0.968115i \(-0.580597\pi\)
−0.250506 + 0.968115i \(0.580597\pi\)
\(54\) 7.32138e7 1.17171
\(55\) −3.74668e6 −0.0552096
\(56\) 3.73984e6 0.0508168
\(57\) 4.07615e7 0.511462
\(58\) 1.33473e7 0.154870
\(59\) −1.37313e8 −1.47529 −0.737643 0.675191i \(-0.764061\pi\)
−0.737643 + 0.675191i \(0.764061\pi\)
\(60\) 2.47778e7 0.246821
\(61\) 1.21854e8 1.12682 0.563410 0.826177i \(-0.309489\pi\)
0.563410 + 0.826177i \(0.309489\pi\)
\(62\) −1.35997e7 −0.116888
\(63\) 5.48479e6 0.0438659
\(64\) 5.03058e7 0.374808
\(65\) −1.02924e8 −0.715165
\(66\) −5.87371e6 −0.0381035
\(67\) −8.31665e7 −0.504210 −0.252105 0.967700i \(-0.581123\pi\)
−0.252105 + 0.967700i \(0.581123\pi\)
\(68\) −1.64802e7 −0.0934698
\(69\) −1.50100e8 −0.797187
\(70\) 1.73583e7 0.0864102
\(71\) 1.48492e8 0.693490 0.346745 0.937960i \(-0.387287\pi\)
0.346745 + 0.937960i \(0.387287\pi\)
\(72\) 1.03013e8 0.451748
\(73\) 1.45029e8 0.597726 0.298863 0.954296i \(-0.403393\pi\)
0.298863 + 0.954296i \(0.403393\pi\)
\(74\) −9.98331e7 −0.387019
\(75\) −1.54899e7 −0.0565292
\(76\) −9.35504e7 −0.321651
\(77\) −1.14467e6 −0.00371085
\(78\) −1.61355e8 −0.493579
\(79\) −4.22172e8 −1.21946 −0.609729 0.792610i \(-0.708722\pi\)
−0.609729 + 0.792610i \(0.708722\pi\)
\(80\) 4.73573e8 1.29265
\(81\) 5.58742e6 0.0144221
\(82\) −8.10515e8 −1.97970
\(83\) −5.36072e7 −0.123986 −0.0619929 0.998077i \(-0.519746\pi\)
−0.0619929 + 0.998077i \(0.519746\pi\)
\(84\) 7.57002e6 0.0165898
\(85\) 1.21989e8 0.253475
\(86\) −5.73201e8 −1.12996
\(87\) −4.30868e7 −0.0806321
\(88\) −2.14988e7 −0.0382157
\(89\) 9.26167e8 1.56471 0.782355 0.622832i \(-0.214018\pi\)
0.782355 + 0.622832i \(0.214018\pi\)
\(90\) 4.78129e8 0.768164
\(91\) −3.14450e7 −0.0480690
\(92\) 3.44490e8 0.501338
\(93\) 4.39017e7 0.0608566
\(94\) 9.14328e7 0.120789
\(95\) 6.92477e8 0.872266
\(96\) 3.73504e8 0.448823
\(97\) 1.44334e9 1.65538 0.827688 0.561189i \(-0.189656\pi\)
0.827688 + 0.561189i \(0.189656\pi\)
\(98\) −1.06944e9 −1.17122
\(99\) −3.15298e7 −0.0329885
\(100\) 3.55504e7 0.0355504
\(101\) 1.73497e9 1.65900 0.829498 0.558510i \(-0.188627\pi\)
0.829498 + 0.558510i \(0.188627\pi\)
\(102\) 1.91244e8 0.174939
\(103\) −1.15796e9 −1.01374 −0.506871 0.862022i \(-0.669198\pi\)
−0.506871 + 0.862022i \(0.669198\pi\)
\(104\) −5.90587e8 −0.495033
\(105\) −5.60346e7 −0.0449888
\(106\) −7.66498e8 −0.589704
\(107\) 6.18767e8 0.456352 0.228176 0.973620i \(-0.426724\pi\)
0.228176 + 0.973620i \(0.426724\pi\)
\(108\) 5.42423e8 0.383647
\(109\) −1.81586e9 −1.23215 −0.616074 0.787688i \(-0.711278\pi\)
−0.616074 + 0.787688i \(0.711278\pi\)
\(110\) −9.97854e7 −0.0649830
\(111\) 3.22274e8 0.201498
\(112\) 1.44685e8 0.0868842
\(113\) −2.89208e9 −1.66862 −0.834310 0.551296i \(-0.814134\pi\)
−0.834310 + 0.551296i \(0.814134\pi\)
\(114\) 1.08560e9 0.602004
\(115\) −2.54997e9 −1.35955
\(116\) 9.88871e7 0.0507083
\(117\) −8.66145e8 −0.427321
\(118\) −3.65705e9 −1.73645
\(119\) 3.72697e7 0.0170371
\(120\) −1.05242e9 −0.463312
\(121\) −2.35137e9 −0.997209
\(122\) 3.24533e9 1.32629
\(123\) 2.61644e9 1.03071
\(124\) −1.00757e8 −0.0382718
\(125\) 2.58954e9 0.948699
\(126\) 1.46076e8 0.0516313
\(127\) 1.38692e9 0.473081 0.236540 0.971622i \(-0.423986\pi\)
0.236540 + 0.971622i \(0.423986\pi\)
\(128\) 3.56410e9 1.17356
\(129\) 1.85037e9 0.588307
\(130\) −2.74118e9 −0.841767
\(131\) 5.87855e9 1.74401 0.872006 0.489496i \(-0.162819\pi\)
0.872006 + 0.489496i \(0.162819\pi\)
\(132\) −4.35169e7 −0.0124760
\(133\) 2.11563e8 0.0586284
\(134\) −2.21497e9 −0.593468
\(135\) −4.01511e9 −1.04039
\(136\) 6.99985e8 0.175454
\(137\) 2.25574e9 0.547075 0.273538 0.961861i \(-0.411806\pi\)
0.273538 + 0.961861i \(0.411806\pi\)
\(138\) −3.99762e9 −0.938308
\(139\) −2.06541e9 −0.469289 −0.234645 0.972081i \(-0.575393\pi\)
−0.234645 + 0.972081i \(0.575393\pi\)
\(140\) 1.28603e8 0.0282928
\(141\) −2.95156e8 −0.0628878
\(142\) 3.95479e9 0.816254
\(143\) 1.80764e8 0.0361493
\(144\) 3.98530e9 0.772378
\(145\) −7.31980e8 −0.137513
\(146\) 3.86256e9 0.703538
\(147\) 3.45227e9 0.609785
\(148\) −7.39640e8 −0.126719
\(149\) −3.00126e9 −0.498845 −0.249422 0.968395i \(-0.580241\pi\)
−0.249422 + 0.968395i \(0.580241\pi\)
\(150\) −4.12543e8 −0.0665363
\(151\) −1.05501e10 −1.65143 −0.825714 0.564089i \(-0.809227\pi\)
−0.825714 + 0.564089i \(0.809227\pi\)
\(152\) 3.97349e9 0.603777
\(153\) 1.02659e9 0.151455
\(154\) −3.04861e7 −0.00436776
\(155\) 7.45823e8 0.103787
\(156\) −1.19544e9 −0.161610
\(157\) 8.51695e9 1.11876 0.559378 0.828912i \(-0.311040\pi\)
0.559378 + 0.828912i \(0.311040\pi\)
\(158\) −1.12437e10 −1.43533
\(159\) 2.47435e9 0.307025
\(160\) 6.34527e9 0.765439
\(161\) −7.79059e8 −0.0913806
\(162\) 1.48810e8 0.0169752
\(163\) −6.90475e9 −0.766133 −0.383066 0.923721i \(-0.625132\pi\)
−0.383066 + 0.923721i \(0.625132\pi\)
\(164\) −6.00491e9 −0.648200
\(165\) 3.22120e8 0.0338329
\(166\) −1.42772e9 −0.145934
\(167\) −8.18088e9 −0.813909 −0.406954 0.913448i \(-0.633409\pi\)
−0.406954 + 0.913448i \(0.633409\pi\)
\(168\) −3.21532e8 −0.0311410
\(169\) −5.63878e9 −0.531735
\(170\) 3.24894e9 0.298347
\(171\) 5.82746e9 0.521191
\(172\) −4.24671e9 −0.369977
\(173\) 1.96517e9 0.166799 0.0833995 0.996516i \(-0.473422\pi\)
0.0833995 + 0.996516i \(0.473422\pi\)
\(174\) −1.14753e9 −0.0949059
\(175\) −8.03968e7 −0.00647988
\(176\) −8.31731e8 −0.0653395
\(177\) 1.18054e10 0.904069
\(178\) 2.46666e10 1.84170
\(179\) −2.51083e10 −1.82801 −0.914006 0.405701i \(-0.867028\pi\)
−0.914006 + 0.405701i \(0.867028\pi\)
\(180\) 3.54234e9 0.251515
\(181\) −3.03563e9 −0.210230 −0.105115 0.994460i \(-0.533521\pi\)
−0.105115 + 0.994460i \(0.533521\pi\)
\(182\) −8.37475e8 −0.0565784
\(183\) −1.04763e10 −0.690526
\(184\) −1.46320e10 −0.941072
\(185\) 5.47494e9 0.343642
\(186\) 1.16923e9 0.0716297
\(187\) −2.14248e8 −0.0128124
\(188\) 6.77404e8 0.0395491
\(189\) −1.22668e9 −0.0699286
\(190\) 1.84427e10 1.02668
\(191\) −3.15580e10 −1.71577 −0.857885 0.513841i \(-0.828222\pi\)
−0.857885 + 0.513841i \(0.828222\pi\)
\(192\) −4.32503e9 −0.229685
\(193\) 2.29526e9 0.119076 0.0595379 0.998226i \(-0.481037\pi\)
0.0595379 + 0.998226i \(0.481037\pi\)
\(194\) 3.84406e10 1.94842
\(195\) 8.84886e9 0.438260
\(196\) −7.92319e9 −0.383484
\(197\) 2.65359e10 1.25527 0.627633 0.778509i \(-0.284024\pi\)
0.627633 + 0.778509i \(0.284024\pi\)
\(198\) −8.39733e8 −0.0388283
\(199\) −1.45778e10 −0.658949 −0.329475 0.944164i \(-0.606872\pi\)
−0.329475 + 0.944164i \(0.606872\pi\)
\(200\) −1.50998e9 −0.0667323
\(201\) 7.15021e9 0.308985
\(202\) 4.62074e10 1.95268
\(203\) −2.23632e8 −0.00924276
\(204\) 1.41688e9 0.0572792
\(205\) 4.44494e10 1.75782
\(206\) −3.08401e10 −1.19320
\(207\) −2.14590e10 −0.812350
\(208\) −2.28482e10 −0.846385
\(209\) −1.21619e9 −0.0440903
\(210\) −1.49237e9 −0.0529529
\(211\) 4.31184e10 1.49759 0.748793 0.662804i \(-0.230634\pi\)
0.748793 + 0.662804i \(0.230634\pi\)
\(212\) −5.67880e9 −0.193083
\(213\) −1.27665e10 −0.424977
\(214\) 1.64796e10 0.537137
\(215\) 3.14349e10 1.00332
\(216\) −2.30391e10 −0.720151
\(217\) 2.27861e8 0.00697593
\(218\) −4.83618e10 −1.45027
\(219\) −1.24688e10 −0.366292
\(220\) −7.39286e8 −0.0212770
\(221\) −5.88555e9 −0.165967
\(222\) 8.58312e9 0.237169
\(223\) −3.81093e10 −1.03195 −0.515975 0.856604i \(-0.672570\pi\)
−0.515975 + 0.856604i \(0.672570\pi\)
\(224\) 1.93859e9 0.0514481
\(225\) −2.21451e9 −0.0576045
\(226\) −7.70248e10 −1.96401
\(227\) −2.78123e10 −0.695216 −0.347608 0.937640i \(-0.613006\pi\)
−0.347608 + 0.937640i \(0.613006\pi\)
\(228\) 8.04297e9 0.197110
\(229\) 3.54756e10 0.852452 0.426226 0.904617i \(-0.359843\pi\)
0.426226 + 0.904617i \(0.359843\pi\)
\(230\) −6.79135e10 −1.60022
\(231\) 9.84130e7 0.00227404
\(232\) −4.20017e9 −0.0951854
\(233\) 4.62674e10 1.02843 0.514213 0.857662i \(-0.328084\pi\)
0.514213 + 0.857662i \(0.328084\pi\)
\(234\) −2.30681e10 −0.502967
\(235\) −5.01426e9 −0.107251
\(236\) −2.70942e10 −0.568555
\(237\) 3.62961e10 0.747295
\(238\) 9.92605e8 0.0200530
\(239\) 8.33772e10 1.65294 0.826469 0.562982i \(-0.190346\pi\)
0.826469 + 0.562982i \(0.190346\pi\)
\(240\) −4.07153e10 −0.792149
\(241\) −7.31412e9 −0.139664 −0.0698321 0.997559i \(-0.522246\pi\)
−0.0698321 + 0.997559i \(0.522246\pi\)
\(242\) −6.26240e10 −1.17374
\(243\) −5.45887e10 −1.00432
\(244\) 2.40439e10 0.434261
\(245\) 5.86488e10 1.03995
\(246\) 6.96838e10 1.21318
\(247\) −3.34096e10 −0.571130
\(248\) 4.27960e9 0.0718407
\(249\) 4.60886e9 0.0759795
\(250\) 6.89674e10 1.11664
\(251\) 9.50519e10 1.51157 0.755786 0.654818i \(-0.227255\pi\)
0.755786 + 0.654818i \(0.227255\pi\)
\(252\) 1.08225e9 0.0169053
\(253\) 4.47849e9 0.0687210
\(254\) 3.69379e10 0.556827
\(255\) −1.04880e10 −0.155332
\(256\) 6.91663e10 1.00650
\(257\) −7.20648e10 −1.03044 −0.515222 0.857057i \(-0.672290\pi\)
−0.515222 + 0.857057i \(0.672290\pi\)
\(258\) 4.92808e10 0.692451
\(259\) 1.67269e9 0.0230975
\(260\) −2.03087e10 −0.275615
\(261\) −6.15989e9 −0.0821658
\(262\) 1.56564e11 2.05274
\(263\) −1.71832e10 −0.221464 −0.110732 0.993850i \(-0.535320\pi\)
−0.110732 + 0.993850i \(0.535320\pi\)
\(264\) 1.84835e9 0.0234189
\(265\) 4.20354e10 0.523612
\(266\) 5.63457e9 0.0690070
\(267\) −7.96269e10 −0.958869
\(268\) −1.64102e10 −0.194316
\(269\) 1.10544e10 0.128721 0.0643605 0.997927i \(-0.479499\pi\)
0.0643605 + 0.997927i \(0.479499\pi\)
\(270\) −1.06935e11 −1.22456
\(271\) −1.41142e11 −1.58963 −0.794813 0.606855i \(-0.792431\pi\)
−0.794813 + 0.606855i \(0.792431\pi\)
\(272\) 2.70805e10 0.299983
\(273\) 2.70347e9 0.0294571
\(274\) 6.00773e10 0.643921
\(275\) 4.62168e8 0.00487307
\(276\) −2.96174e10 −0.307225
\(277\) −1.12712e11 −1.15030 −0.575151 0.818047i \(-0.695057\pi\)
−0.575151 + 0.818047i \(0.695057\pi\)
\(278\) −5.50082e10 −0.552365
\(279\) 6.27639e9 0.0620142
\(280\) −5.46234e9 −0.0531089
\(281\) 4.86687e10 0.465662 0.232831 0.972517i \(-0.425201\pi\)
0.232831 + 0.972517i \(0.425201\pi\)
\(282\) −7.86091e9 −0.0740204
\(283\) −1.21207e11 −1.12328 −0.561640 0.827382i \(-0.689829\pi\)
−0.561640 + 0.827382i \(0.689829\pi\)
\(284\) 2.93001e10 0.267261
\(285\) −5.95355e10 −0.534532
\(286\) 4.81430e9 0.0425486
\(287\) 1.35800e10 0.118150
\(288\) 5.33979e10 0.457360
\(289\) 6.97576e9 0.0588235
\(290\) −1.94948e10 −0.161856
\(291\) −1.24091e11 −1.01443
\(292\) 2.86168e10 0.230355
\(293\) 9.65141e10 0.765044 0.382522 0.923946i \(-0.375056\pi\)
0.382522 + 0.923946i \(0.375056\pi\)
\(294\) 9.19444e10 0.717732
\(295\) 2.00556e11 1.54183
\(296\) 3.14157e10 0.237867
\(297\) 7.05170e9 0.0525884
\(298\) −7.99326e10 −0.587153
\(299\) 1.23027e11 0.890187
\(300\) −3.05643e9 −0.0217856
\(301\) 9.60389e9 0.0674370
\(302\) −2.80981e11 −1.94377
\(303\) −1.49163e11 −1.01665
\(304\) 1.53724e11 1.03231
\(305\) −1.77977e11 −1.17765
\(306\) 2.73411e10 0.178266
\(307\) −1.31572e11 −0.845360 −0.422680 0.906279i \(-0.638911\pi\)
−0.422680 + 0.906279i \(0.638911\pi\)
\(308\) −2.25864e8 −0.00143011
\(309\) 9.95556e10 0.621230
\(310\) 1.98635e10 0.122160
\(311\) 3.19848e9 0.0193875 0.00969376 0.999953i \(-0.496914\pi\)
0.00969376 + 0.999953i \(0.496914\pi\)
\(312\) 5.07755e10 0.303360
\(313\) −1.59936e11 −0.941882 −0.470941 0.882165i \(-0.656086\pi\)
−0.470941 + 0.882165i \(0.656086\pi\)
\(314\) 2.26832e11 1.31680
\(315\) −8.01097e9 −0.0458445
\(316\) −8.33019e10 −0.469962
\(317\) 6.77437e10 0.376792 0.188396 0.982093i \(-0.439671\pi\)
0.188396 + 0.982093i \(0.439671\pi\)
\(318\) 6.58994e10 0.361376
\(319\) 1.28557e9 0.00695083
\(320\) −7.34757e10 −0.391714
\(321\) −5.31983e10 −0.279657
\(322\) −2.07487e10 −0.107557
\(323\) 3.95982e10 0.202425
\(324\) 1.10250e9 0.00555808
\(325\) 1.26961e10 0.0631239
\(326\) −1.83894e11 −0.901757
\(327\) 1.56118e11 0.755071
\(328\) 2.55055e11 1.21675
\(329\) −1.53194e9 −0.00720876
\(330\) 8.57902e9 0.0398222
\(331\) 1.23890e11 0.567295 0.283647 0.958929i \(-0.408456\pi\)
0.283647 + 0.958929i \(0.408456\pi\)
\(332\) −1.05776e10 −0.0477824
\(333\) 4.60738e10 0.205331
\(334\) −2.17881e11 −0.957990
\(335\) 1.21471e11 0.526953
\(336\) −1.24392e10 −0.0532434
\(337\) −1.66091e11 −0.701476 −0.350738 0.936474i \(-0.614069\pi\)
−0.350738 + 0.936474i \(0.614069\pi\)
\(338\) −1.50178e11 −0.625865
\(339\) 2.48646e11 1.02254
\(340\) 2.40706e10 0.0976859
\(341\) −1.30988e9 −0.00524611
\(342\) 1.55203e11 0.613454
\(343\) 3.59253e10 0.140145
\(344\) 1.80376e11 0.694491
\(345\) 2.19233e11 0.833144
\(346\) 5.23385e10 0.196327
\(347\) −3.59340e11 −1.33052 −0.665262 0.746610i \(-0.731680\pi\)
−0.665262 + 0.746610i \(0.731680\pi\)
\(348\) −8.50179e9 −0.0310745
\(349\) 4.55698e11 1.64423 0.822116 0.569321i \(-0.192794\pi\)
0.822116 + 0.569321i \(0.192794\pi\)
\(350\) −2.14121e9 −0.00762698
\(351\) 1.93715e11 0.681211
\(352\) −1.11441e10 −0.0386905
\(353\) −2.35070e11 −0.805772 −0.402886 0.915250i \(-0.631993\pi\)
−0.402886 + 0.915250i \(0.631993\pi\)
\(354\) 3.14414e11 1.06411
\(355\) −2.16884e11 −0.724770
\(356\) 1.82749e11 0.603018
\(357\) −3.20425e9 −0.0104405
\(358\) −6.68710e11 −2.15161
\(359\) 8.46696e10 0.269031 0.134516 0.990911i \(-0.457052\pi\)
0.134516 + 0.990911i \(0.457052\pi\)
\(360\) −1.50459e11 −0.472124
\(361\) −9.79067e10 −0.303410
\(362\) −8.08479e10 −0.247446
\(363\) 2.02158e11 0.611099
\(364\) −6.20465e9 −0.0185251
\(365\) −2.11827e11 −0.624687
\(366\) −2.79017e11 −0.812765
\(367\) 3.10781e10 0.0894246 0.0447123 0.999000i \(-0.485763\pi\)
0.0447123 + 0.999000i \(0.485763\pi\)
\(368\) −5.66072e11 −1.60900
\(369\) 3.74059e11 1.05032
\(370\) 1.45814e11 0.404476
\(371\) 1.28425e10 0.0351940
\(372\) 8.66258e9 0.0234533
\(373\) −6.64364e11 −1.77712 −0.888559 0.458763i \(-0.848293\pi\)
−0.888559 + 0.458763i \(0.848293\pi\)
\(374\) −5.70607e9 −0.0150805
\(375\) −2.22635e11 −0.581371
\(376\) −2.87723e10 −0.0742385
\(377\) 3.53155e10 0.0900386
\(378\) −3.26703e10 −0.0823076
\(379\) −1.05029e11 −0.261475 −0.130738 0.991417i \(-0.541735\pi\)
−0.130738 + 0.991417i \(0.541735\pi\)
\(380\) 1.36638e11 0.336159
\(381\) −1.19240e11 −0.289908
\(382\) −8.40485e11 −2.01950
\(383\) 6.90072e11 1.63870 0.819351 0.573293i \(-0.194334\pi\)
0.819351 + 0.573293i \(0.194334\pi\)
\(384\) −3.06423e11 −0.719168
\(385\) 1.67189e9 0.00387823
\(386\) 6.11297e10 0.140155
\(387\) 2.64537e11 0.599497
\(388\) 2.84797e11 0.637959
\(389\) 1.43485e11 0.317712 0.158856 0.987302i \(-0.449219\pi\)
0.158856 + 0.987302i \(0.449219\pi\)
\(390\) 2.35672e11 0.515842
\(391\) −1.45816e11 −0.315508
\(392\) 3.36532e11 0.719846
\(393\) −5.05407e11 −1.06875
\(394\) 7.06731e11 1.47748
\(395\) 6.16615e11 1.27446
\(396\) −6.22138e9 −0.0127133
\(397\) −4.59121e11 −0.927620 −0.463810 0.885935i \(-0.653518\pi\)
−0.463810 + 0.885935i \(0.653518\pi\)
\(398\) −3.88250e11 −0.775599
\(399\) −1.81891e10 −0.0359280
\(400\) −5.84171e10 −0.114096
\(401\) −1.18477e11 −0.228815 −0.114408 0.993434i \(-0.536497\pi\)
−0.114408 + 0.993434i \(0.536497\pi\)
\(402\) 1.90432e11 0.363682
\(403\) −3.59834e10 −0.0679562
\(404\) 3.42340e11 0.639354
\(405\) −8.16088e9 −0.0150726
\(406\) −5.95600e9 −0.0108790
\(407\) −9.61558e9 −0.0173700
\(408\) −6.01810e10 −0.107520
\(409\) 3.44816e11 0.609301 0.304651 0.952464i \(-0.401460\pi\)
0.304651 + 0.952464i \(0.401460\pi\)
\(410\) 1.18382e12 2.06899
\(411\) −1.93937e11 −0.335253
\(412\) −2.28487e11 −0.390682
\(413\) 6.12732e10 0.103632
\(414\) −5.71518e11 −0.956156
\(415\) 7.82976e10 0.129578
\(416\) −3.06137e11 −0.501183
\(417\) 1.77573e11 0.287585
\(418\) −3.23908e10 −0.0518953
\(419\) 1.06432e12 1.68697 0.843487 0.537150i \(-0.180499\pi\)
0.843487 + 0.537150i \(0.180499\pi\)
\(420\) −1.10566e10 −0.0173381
\(421\) 8.40482e11 1.30394 0.651972 0.758243i \(-0.273942\pi\)
0.651972 + 0.758243i \(0.273942\pi\)
\(422\) 1.14837e12 1.76269
\(423\) −4.21970e10 −0.0640840
\(424\) 2.41203e11 0.362441
\(425\) −1.50478e10 −0.0223730
\(426\) −3.40012e11 −0.500208
\(427\) −5.43750e10 −0.0791542
\(428\) 1.22094e11 0.175872
\(429\) −1.55411e10 −0.0221526
\(430\) 8.37206e11 1.18093
\(431\) −7.86921e11 −1.09846 −0.549229 0.835672i \(-0.685078\pi\)
−0.549229 + 0.835672i \(0.685078\pi\)
\(432\) −8.91321e11 −1.23128
\(433\) −7.27832e11 −0.995029 −0.497514 0.867456i \(-0.665754\pi\)
−0.497514 + 0.867456i \(0.665754\pi\)
\(434\) 6.06864e9 0.00821084
\(435\) 6.29317e10 0.0842690
\(436\) −3.58301e11 −0.474853
\(437\) −8.27733e11 −1.08573
\(438\) −3.32083e11 −0.431135
\(439\) −5.63619e11 −0.724261 −0.362130 0.932127i \(-0.617950\pi\)
−0.362130 + 0.932127i \(0.617950\pi\)
\(440\) 3.14007e10 0.0399395
\(441\) 4.93553e11 0.621384
\(442\) −1.56750e11 −0.195347
\(443\) 2.48083e11 0.306041 0.153021 0.988223i \(-0.451100\pi\)
0.153021 + 0.988223i \(0.451100\pi\)
\(444\) 6.35903e10 0.0776547
\(445\) −1.35274e12 −1.63529
\(446\) −1.01496e12 −1.21463
\(447\) 2.58033e11 0.305697
\(448\) −2.24481e10 −0.0263286
\(449\) −1.36225e12 −1.58178 −0.790891 0.611957i \(-0.790383\pi\)
−0.790891 + 0.611957i \(0.790383\pi\)
\(450\) −5.89791e10 −0.0678019
\(451\) −7.80660e10 −0.0888520
\(452\) −5.70658e11 −0.643063
\(453\) 9.07040e11 1.01201
\(454\) −7.40724e11 −0.818286
\(455\) 4.59279e10 0.0502372
\(456\) −3.41620e11 −0.370000
\(457\) 9.81977e11 1.05312 0.526560 0.850138i \(-0.323481\pi\)
0.526560 + 0.850138i \(0.323481\pi\)
\(458\) 9.44822e11 1.00336
\(459\) −2.29598e11 −0.241441
\(460\) −5.03155e11 −0.523952
\(461\) 7.36336e11 0.759314 0.379657 0.925127i \(-0.376042\pi\)
0.379657 + 0.925127i \(0.376042\pi\)
\(462\) 2.62103e9 0.00267660
\(463\) 1.79548e11 0.181579 0.0907894 0.995870i \(-0.471061\pi\)
0.0907894 + 0.995870i \(0.471061\pi\)
\(464\) −1.62493e11 −0.162744
\(465\) −6.41219e10 −0.0636016
\(466\) 1.23224e12 1.21048
\(467\) 1.13676e11 0.110596 0.0552982 0.998470i \(-0.482389\pi\)
0.0552982 + 0.998470i \(0.482389\pi\)
\(468\) −1.70906e11 −0.164684
\(469\) 3.71115e10 0.0354186
\(470\) −1.33545e11 −0.126237
\(471\) −7.32242e11 −0.685584
\(472\) 1.15081e12 1.06724
\(473\) −5.52088e10 −0.0507146
\(474\) 9.66674e11 0.879584
\(475\) −8.54197e10 −0.0769904
\(476\) 7.35397e9 0.00656585
\(477\) 3.53745e11 0.312865
\(478\) 2.22059e12 1.94555
\(479\) −5.35347e11 −0.464649 −0.232325 0.972638i \(-0.574633\pi\)
−0.232325 + 0.972638i \(0.574633\pi\)
\(480\) −5.45533e11 −0.469068
\(481\) −2.64147e11 −0.225005
\(482\) −1.94797e11 −0.164388
\(483\) 6.69794e10 0.0559989
\(484\) −4.63966e11 −0.384311
\(485\) −2.10812e12 −1.73004
\(486\) −1.45386e12 −1.18211
\(487\) 9.30784e11 0.749840 0.374920 0.927057i \(-0.377670\pi\)
0.374920 + 0.927057i \(0.377670\pi\)
\(488\) −1.02125e12 −0.815159
\(489\) 5.93634e11 0.469493
\(490\) 1.56200e12 1.22404
\(491\) 1.40150e12 1.08824 0.544122 0.839006i \(-0.316863\pi\)
0.544122 + 0.839006i \(0.316863\pi\)
\(492\) 5.16270e11 0.397223
\(493\) −4.18571e10 −0.0319123
\(494\) −8.89798e11 −0.672233
\(495\) 4.60517e10 0.0344765
\(496\) 1.65566e11 0.122830
\(497\) −6.62617e10 −0.0487146
\(498\) 1.22748e11 0.0894298
\(499\) 9.65319e11 0.696977 0.348488 0.937313i \(-0.386695\pi\)
0.348488 + 0.937313i \(0.386695\pi\)
\(500\) 5.10963e11 0.365615
\(501\) 7.03348e11 0.498771
\(502\) 2.53152e12 1.77916
\(503\) −1.35251e12 −0.942076 −0.471038 0.882113i \(-0.656121\pi\)
−0.471038 + 0.882113i \(0.656121\pi\)
\(504\) −4.59677e10 −0.0317333
\(505\) −2.53406e12 −1.73383
\(506\) 1.19276e11 0.0808862
\(507\) 4.84792e11 0.325852
\(508\) 2.73664e11 0.182319
\(509\) −1.24943e12 −0.825053 −0.412527 0.910946i \(-0.635354\pi\)
−0.412527 + 0.910946i \(0.635354\pi\)
\(510\) −2.79326e11 −0.182829
\(511\) −6.47166e10 −0.0419876
\(512\) 1.72851e10 0.0111162
\(513\) −1.30332e12 −0.830853
\(514\) −1.91930e12 −1.21286
\(515\) 1.69130e12 1.05947
\(516\) 3.65110e11 0.226725
\(517\) 8.80649e9 0.00542120
\(518\) 4.45487e10 0.0271864
\(519\) −1.68955e11 −0.102216
\(520\) 8.62599e11 0.517361
\(521\) 2.83113e11 0.168341 0.0841706 0.996451i \(-0.473176\pi\)
0.0841706 + 0.996451i \(0.473176\pi\)
\(522\) −1.64057e11 −0.0967111
\(523\) 6.03608e11 0.352774 0.176387 0.984321i \(-0.443559\pi\)
0.176387 + 0.984321i \(0.443559\pi\)
\(524\) 1.15994e12 0.672118
\(525\) 6.91209e9 0.00397093
\(526\) −4.57640e11 −0.260668
\(527\) 4.26487e10 0.0240857
\(528\) 7.15078e10 0.0400406
\(529\) 1.24689e12 0.692271
\(530\) 1.11953e12 0.616303
\(531\) 1.68776e12 0.921265
\(532\) 4.17452e10 0.0225946
\(533\) −2.14453e12 −1.15096
\(534\) −2.12070e12 −1.12861
\(535\) −9.03758e11 −0.476936
\(536\) 6.97013e11 0.364754
\(537\) 2.15868e12 1.12022
\(538\) 2.94412e11 0.151508
\(539\) −1.03004e11 −0.0525661
\(540\) −7.92253e11 −0.400951
\(541\) −7.92682e11 −0.397843 −0.198921 0.980015i \(-0.563744\pi\)
−0.198921 + 0.980015i \(0.563744\pi\)
\(542\) −3.75904e12 −1.87103
\(543\) 2.60987e11 0.128831
\(544\) 3.62845e11 0.177634
\(545\) 2.65221e12 1.28773
\(546\) 7.20017e10 0.0346717
\(547\) 5.81013e10 0.0277487 0.0138744 0.999904i \(-0.495584\pi\)
0.0138744 + 0.999904i \(0.495584\pi\)
\(548\) 4.45098e11 0.210835
\(549\) −1.49775e12 −0.703660
\(550\) 1.23089e10 0.00573572
\(551\) −2.37604e11 −0.109817
\(552\) 1.25798e12 0.576697
\(553\) 1.88386e11 0.0856616
\(554\) −3.00187e12 −1.35393
\(555\) −4.70707e11 −0.210587
\(556\) −4.07543e11 −0.180857
\(557\) −8.04975e11 −0.354351 −0.177176 0.984179i \(-0.556696\pi\)
−0.177176 + 0.984179i \(0.556696\pi\)
\(558\) 1.67159e11 0.0729922
\(559\) −1.51662e12 −0.656939
\(560\) −2.11323e11 −0.0908032
\(561\) 1.84199e10 0.00785154
\(562\) 1.29619e12 0.548096
\(563\) −3.22746e12 −1.35386 −0.676929 0.736048i \(-0.736690\pi\)
−0.676929 + 0.736048i \(0.736690\pi\)
\(564\) −5.82396e10 −0.0242361
\(565\) 4.22411e12 1.74388
\(566\) −3.22810e12 −1.32213
\(567\) −2.49329e9 −0.00101309
\(568\) −1.24450e12 −0.501681
\(569\) −2.00792e12 −0.803048 −0.401524 0.915848i \(-0.631519\pi\)
−0.401524 + 0.915848i \(0.631519\pi\)
\(570\) −1.58561e12 −0.629157
\(571\) 3.16004e11 0.124403 0.0622013 0.998064i \(-0.480188\pi\)
0.0622013 + 0.998064i \(0.480188\pi\)
\(572\) 3.56680e10 0.0139314
\(573\) 2.71319e12 1.05144
\(574\) 3.61677e11 0.139065
\(575\) 3.14549e11 0.120001
\(576\) −6.18327e11 −0.234054
\(577\) −1.81033e12 −0.679932 −0.339966 0.940438i \(-0.610416\pi\)
−0.339966 + 0.940438i \(0.610416\pi\)
\(578\) 1.85785e11 0.0692367
\(579\) −1.97334e11 −0.0729707
\(580\) −1.44432e11 −0.0529955
\(581\) 2.39212e10 0.00870945
\(582\) −3.30492e12 −1.19401
\(583\) −7.38264e10 −0.0264669
\(584\) −1.21548e12 −0.432404
\(585\) 1.26507e12 0.446596
\(586\) 2.57046e12 0.900475
\(587\) 2.94820e12 1.02491 0.512455 0.858714i \(-0.328736\pi\)
0.512455 + 0.858714i \(0.328736\pi\)
\(588\) 6.81194e11 0.235003
\(589\) 2.42098e11 0.0828842
\(590\) 5.34141e12 1.81477
\(591\) −2.28142e12 −0.769238
\(592\) 1.21539e12 0.406695
\(593\) 4.46478e12 1.48270 0.741350 0.671118i \(-0.234186\pi\)
0.741350 + 0.671118i \(0.234186\pi\)
\(594\) 1.87808e11 0.0618978
\(595\) −5.44354e10 −0.0178055
\(596\) −5.92202e11 −0.192248
\(597\) 1.25332e12 0.403810
\(598\) 3.27659e12 1.04777
\(599\) 3.15817e12 1.00234 0.501170 0.865349i \(-0.332903\pi\)
0.501170 + 0.865349i \(0.332903\pi\)
\(600\) 1.29820e11 0.0408941
\(601\) 5.98536e12 1.87135 0.935675 0.352863i \(-0.114792\pi\)
0.935675 + 0.352863i \(0.114792\pi\)
\(602\) 2.55781e11 0.0793749
\(603\) 1.02223e12 0.314862
\(604\) −2.08172e12 −0.636437
\(605\) 3.43436e12 1.04219
\(606\) −3.97267e12 −1.19662
\(607\) 1.60857e11 0.0480939 0.0240469 0.999711i \(-0.492345\pi\)
0.0240469 + 0.999711i \(0.492345\pi\)
\(608\) 2.05970e12 0.611278
\(609\) 1.92267e10 0.00566405
\(610\) −4.74007e12 −1.38612
\(611\) 2.41920e11 0.0702243
\(612\) 2.02564e11 0.0583687
\(613\) −4.87119e12 −1.39336 −0.696679 0.717383i \(-0.745340\pi\)
−0.696679 + 0.717383i \(0.745340\pi\)
\(614\) −3.50417e12 −0.995009
\(615\) −3.82152e12 −1.07721
\(616\) 9.59344e9 0.00268449
\(617\) 3.48094e12 0.966970 0.483485 0.875353i \(-0.339371\pi\)
0.483485 + 0.875353i \(0.339371\pi\)
\(618\) 2.65147e12 0.731203
\(619\) 2.25847e12 0.618310 0.309155 0.951012i \(-0.399954\pi\)
0.309155 + 0.951012i \(0.399954\pi\)
\(620\) 1.47164e11 0.0399981
\(621\) 4.79935e12 1.29500
\(622\) 8.51852e10 0.0228196
\(623\) −4.13285e11 −0.109914
\(624\) 1.96437e12 0.518672
\(625\) −4.13413e12 −1.08374
\(626\) −4.25958e12 −1.10862
\(627\) 1.04561e11 0.0270189
\(628\) 1.68054e12 0.431153
\(629\) 3.13076e11 0.0797484
\(630\) −2.13356e11 −0.0539601
\(631\) −6.76730e12 −1.69935 −0.849676 0.527305i \(-0.823203\pi\)
−0.849676 + 0.527305i \(0.823203\pi\)
\(632\) 3.53819e12 0.882175
\(633\) −3.70709e12 −0.917734
\(634\) 1.80422e12 0.443494
\(635\) −2.02571e12 −0.494419
\(636\) 4.88233e11 0.118323
\(637\) −2.82960e12 −0.680923
\(638\) 3.42385e10 0.00818130
\(639\) −1.82516e12 −0.433060
\(640\) −5.20566e12 −1.22649
\(641\) 7.28070e12 1.70338 0.851691 0.524045i \(-0.175578\pi\)
0.851691 + 0.524045i \(0.175578\pi\)
\(642\) −1.41683e12 −0.329163
\(643\) −6.62565e12 −1.52855 −0.764274 0.644892i \(-0.776902\pi\)
−0.764274 + 0.644892i \(0.776902\pi\)
\(644\) −1.53722e11 −0.0352168
\(645\) −2.70261e12 −0.614843
\(646\) 1.05462e12 0.238259
\(647\) −6.36313e12 −1.42758 −0.713792 0.700358i \(-0.753024\pi\)
−0.713792 + 0.700358i \(0.753024\pi\)
\(648\) −4.68279e10 −0.0104332
\(649\) −3.52234e11 −0.0779346
\(650\) 3.38135e11 0.0742984
\(651\) −1.95903e10 −0.00427491
\(652\) −1.36243e12 −0.295257
\(653\) 5.95209e12 1.28103 0.640516 0.767945i \(-0.278720\pi\)
0.640516 + 0.767945i \(0.278720\pi\)
\(654\) 4.15789e12 0.888737
\(655\) −8.58609e12 −1.82268
\(656\) 9.86739e12 2.08034
\(657\) −1.78260e12 −0.373259
\(658\) −4.08002e10 −0.00848488
\(659\) −5.45445e12 −1.12659 −0.563296 0.826255i \(-0.690467\pi\)
−0.563296 + 0.826255i \(0.690467\pi\)
\(660\) 6.35599e10 0.0130387
\(661\) −2.82523e12 −0.575634 −0.287817 0.957685i \(-0.592930\pi\)
−0.287817 + 0.957685i \(0.592930\pi\)
\(662\) 3.29955e12 0.667720
\(663\) 5.06008e11 0.101706
\(664\) 4.49279e11 0.0896932
\(665\) −3.09005e11 −0.0612728
\(666\) 1.22708e12 0.241680
\(667\) 8.74951e11 0.171166
\(668\) −1.61423e12 −0.313669
\(669\) 3.27643e12 0.632388
\(670\) 3.23515e12 0.620237
\(671\) 3.12579e11 0.0595263
\(672\) −1.66669e11 −0.0315278
\(673\) −2.66233e12 −0.500259 −0.250129 0.968212i \(-0.580473\pi\)
−0.250129 + 0.968212i \(0.580473\pi\)
\(674\) −4.42352e12 −0.825654
\(675\) 4.95280e11 0.0918298
\(676\) −1.11263e12 −0.204923
\(677\) −6.37169e12 −1.16575 −0.582875 0.812562i \(-0.698072\pi\)
−0.582875 + 0.812562i \(0.698072\pi\)
\(678\) 6.62219e12 1.20356
\(679\) −6.44065e11 −0.116283
\(680\) −1.02238e12 −0.183368
\(681\) 2.39115e12 0.426035
\(682\) −3.48861e10 −0.00617479
\(683\) 7.29274e12 1.28232 0.641161 0.767406i \(-0.278453\pi\)
0.641161 + 0.767406i \(0.278453\pi\)
\(684\) 1.14986e12 0.200860
\(685\) −3.29469e12 −0.571752
\(686\) 9.56798e11 0.164954
\(687\) −3.05000e12 −0.522390
\(688\) 6.97828e12 1.18741
\(689\) −2.02806e12 −0.342843
\(690\) 5.83884e12 0.980631
\(691\) 8.91264e12 1.48715 0.743576 0.668652i \(-0.233128\pi\)
0.743576 + 0.668652i \(0.233128\pi\)
\(692\) 3.87764e11 0.0642820
\(693\) 1.40696e10 0.00231730
\(694\) −9.57030e12 −1.56606
\(695\) 3.01670e12 0.490457
\(696\) 3.61108e11 0.0583305
\(697\) 2.54177e12 0.407933
\(698\) 1.21366e13 1.93530
\(699\) −3.97782e12 −0.630229
\(700\) −1.58637e10 −0.00249726
\(701\) 3.09782e12 0.484534 0.242267 0.970210i \(-0.422109\pi\)
0.242267 + 0.970210i \(0.422109\pi\)
\(702\) 5.15922e12 0.801802
\(703\) 1.77719e12 0.274432
\(704\) 1.29045e11 0.0197999
\(705\) 4.31099e11 0.0657244
\(706\) −6.26064e12 −0.948413
\(707\) −7.74197e11 −0.116537
\(708\) 2.32942e12 0.348415
\(709\) 5.42374e12 0.806104 0.403052 0.915177i \(-0.367949\pi\)
0.403052 + 0.915177i \(0.367949\pi\)
\(710\) −5.77628e12 −0.853072
\(711\) 5.18906e12 0.761509
\(712\) −7.76215e12 −1.13194
\(713\) −8.91499e11 −0.129187
\(714\) −8.53389e10 −0.0122887
\(715\) −2.64020e11 −0.0377799
\(716\) −4.95432e12 −0.704490
\(717\) −7.16833e12 −1.01294
\(718\) 2.25501e12 0.316656
\(719\) −5.08993e12 −0.710284 −0.355142 0.934812i \(-0.615567\pi\)
−0.355142 + 0.934812i \(0.615567\pi\)
\(720\) −5.82085e12 −0.807217
\(721\) 5.16720e11 0.0712109
\(722\) −2.60755e12 −0.357121
\(723\) 6.28829e11 0.0855875
\(724\) −5.98982e11 −0.0810197
\(725\) 9.02925e10 0.0121375
\(726\) 5.38408e12 0.719278
\(727\) 8.07173e12 1.07167 0.535836 0.844322i \(-0.319997\pi\)
0.535836 + 0.844322i \(0.319997\pi\)
\(728\) 2.63539e11 0.0347739
\(729\) 4.58327e12 0.601037
\(730\) −5.64158e12 −0.735272
\(731\) 1.79756e12 0.232838
\(732\) −2.06717e12 −0.266119
\(733\) 6.29376e12 0.805272 0.402636 0.915360i \(-0.368094\pi\)
0.402636 + 0.915360i \(0.368094\pi\)
\(734\) 8.27703e11 0.105255
\(735\) −5.04232e12 −0.637290
\(736\) −7.58464e12 −0.952763
\(737\) −2.13339e11 −0.0266358
\(738\) 9.96232e12 1.23625
\(739\) −9.33473e11 −0.115134 −0.0575668 0.998342i \(-0.518334\pi\)
−0.0575668 + 0.998342i \(0.518334\pi\)
\(740\) 1.08030e12 0.132435
\(741\) 2.87238e12 0.349993
\(742\) 3.42035e11 0.0414241
\(743\) −1.42665e13 −1.71739 −0.858694 0.512489i \(-0.828724\pi\)
−0.858694 + 0.512489i \(0.828724\pi\)
\(744\) −3.67937e11 −0.0440246
\(745\) 4.38358e12 0.521346
\(746\) −1.76940e13 −2.09171
\(747\) 6.58905e11 0.0774248
\(748\) −4.22749e10 −0.00493771
\(749\) −2.76113e11 −0.0320567
\(750\) −5.92945e12 −0.684288
\(751\) 1.42997e13 1.64039 0.820197 0.572081i \(-0.193864\pi\)
0.820197 + 0.572081i \(0.193864\pi\)
\(752\) −1.11312e12 −0.126930
\(753\) −8.17206e12 −0.926305
\(754\) 9.40557e11 0.105978
\(755\) 1.54092e13 1.72592
\(756\) −2.42046e11 −0.0269495
\(757\) −6.04819e12 −0.669413 −0.334706 0.942322i \(-0.608637\pi\)
−0.334706 + 0.942322i \(0.608637\pi\)
\(758\) −2.79723e12 −0.307763
\(759\) −3.85037e11 −0.0421128
\(760\) −5.80361e12 −0.631011
\(761\) 5.22191e12 0.564414 0.282207 0.959353i \(-0.408933\pi\)
0.282207 + 0.959353i \(0.408933\pi\)
\(762\) −3.17573e12 −0.341229
\(763\) 8.10294e11 0.0865530
\(764\) −6.22695e12 −0.661234
\(765\) −1.49941e12 −0.158287
\(766\) 1.83787e13 1.92879
\(767\) −9.67612e12 −1.00954
\(768\) −5.94655e12 −0.616793
\(769\) −8.85529e12 −0.913134 −0.456567 0.889689i \(-0.650921\pi\)
−0.456567 + 0.889689i \(0.650921\pi\)
\(770\) 4.45274e10 0.00456477
\(771\) 6.19575e12 0.631465
\(772\) 4.52895e11 0.0458902
\(773\) 5.21750e12 0.525599 0.262799 0.964850i \(-0.415354\pi\)
0.262799 + 0.964850i \(0.415354\pi\)
\(774\) 7.04542e12 0.705623
\(775\) −9.20002e10 −0.00916075
\(776\) −1.20966e13 −1.19752
\(777\) −1.43809e11 −0.0141544
\(778\) 3.82144e12 0.373955
\(779\) 1.44285e13 1.40379
\(780\) 1.74604e12 0.168899
\(781\) 3.80911e11 0.0366348
\(782\) −3.88353e12 −0.371361
\(783\) 1.37767e12 0.130984
\(784\) 1.30195e13 1.23076
\(785\) −1.24397e13 −1.16922
\(786\) −1.34605e13 −1.25794
\(787\) −1.22879e13 −1.14181 −0.570903 0.821017i \(-0.693407\pi\)
−0.570903 + 0.821017i \(0.693407\pi\)
\(788\) 5.23600e12 0.483762
\(789\) 1.47732e12 0.135715
\(790\) 1.64223e13 1.50007
\(791\) 1.29054e12 0.117213
\(792\) 2.64249e11 0.0238644
\(793\) 8.58678e12 0.771082
\(794\) −1.22278e13 −1.09183
\(795\) −3.61399e12 −0.320874
\(796\) −2.87645e12 −0.253950
\(797\) 1.04691e13 0.919063 0.459532 0.888161i \(-0.348017\pi\)
0.459532 + 0.888161i \(0.348017\pi\)
\(798\) −4.84430e11 −0.0422881
\(799\) −2.86733e11 −0.0248895
\(800\) −7.82714e11 −0.0675613
\(801\) −1.13838e13 −0.977107
\(802\) −3.15540e12 −0.269321
\(803\) 3.72029e11 0.0315760
\(804\) 1.41086e12 0.119078
\(805\) 1.13788e12 0.0955024
\(806\) −9.58345e11 −0.0799861
\(807\) −9.50398e11 −0.0788814
\(808\) −1.45407e13 −1.20014
\(809\) −1.43675e13 −1.17927 −0.589634 0.807671i \(-0.700728\pi\)
−0.589634 + 0.807671i \(0.700728\pi\)
\(810\) −2.17349e11 −0.0177409
\(811\) −1.55011e12 −0.125825 −0.0629127 0.998019i \(-0.520039\pi\)
−0.0629127 + 0.998019i \(0.520039\pi\)
\(812\) −4.41265e10 −0.00356203
\(813\) 1.21347e13 0.974137
\(814\) −2.56092e11 −0.0204450
\(815\) 1.00849e13 0.800690
\(816\) −2.32824e12 −0.183833
\(817\) 1.02039e13 0.801249
\(818\) 9.18348e12 0.717163
\(819\) 3.86501e11 0.0300174
\(820\) 8.77065e12 0.677438
\(821\) −1.37949e13 −1.05968 −0.529839 0.848098i \(-0.677748\pi\)
−0.529839 + 0.848098i \(0.677748\pi\)
\(822\) −5.16513e12 −0.394601
\(823\) −1.07251e13 −0.814899 −0.407449 0.913228i \(-0.633582\pi\)
−0.407449 + 0.913228i \(0.633582\pi\)
\(824\) 9.70482e12 0.733357
\(825\) −3.97347e10 −0.00298626
\(826\) 1.63189e12 0.121978
\(827\) 1.65480e13 1.23019 0.615093 0.788454i \(-0.289118\pi\)
0.615093 + 0.788454i \(0.289118\pi\)
\(828\) −4.23424e12 −0.313068
\(829\) 1.03812e13 0.763398 0.381699 0.924287i \(-0.375339\pi\)
0.381699 + 0.924287i \(0.375339\pi\)
\(830\) 2.08530e12 0.152517
\(831\) 9.69040e12 0.704916
\(832\) 3.54494e12 0.256481
\(833\) 3.35374e12 0.241339
\(834\) 4.72931e12 0.338494
\(835\) 1.19488e13 0.850621
\(836\) −2.39976e11 −0.0169918
\(837\) −1.40373e12 −0.0988595
\(838\) 2.83460e13 1.98561
\(839\) −6.25038e12 −0.435489 −0.217745 0.976006i \(-0.569870\pi\)
−0.217745 + 0.976006i \(0.569870\pi\)
\(840\) 4.69623e11 0.0325456
\(841\) −1.42560e13 −0.982687
\(842\) 2.23846e13 1.53477
\(843\) −4.18428e12 −0.285362
\(844\) 8.50802e12 0.577149
\(845\) 8.23589e12 0.555719
\(846\) −1.12383e12 −0.0754284
\(847\) 1.04925e12 0.0700496
\(848\) 9.33151e12 0.619685
\(849\) 1.04207e13 0.688356
\(850\) −4.00769e11 −0.0263335
\(851\) −6.54432e12 −0.427742
\(852\) −2.51906e12 −0.163780
\(853\) −2.08264e13 −1.34693 −0.673464 0.739220i \(-0.735194\pi\)
−0.673464 + 0.739220i \(0.735194\pi\)
\(854\) −1.44817e12 −0.0931664
\(855\) −8.51147e12 −0.544700
\(856\) −5.18585e12 −0.330132
\(857\) 2.34103e12 0.148249 0.0741246 0.997249i \(-0.476384\pi\)
0.0741246 + 0.997249i \(0.476384\pi\)
\(858\) −4.13908e11 −0.0260742
\(859\) −1.14439e13 −0.717139 −0.358569 0.933503i \(-0.616735\pi\)
−0.358569 + 0.933503i \(0.616735\pi\)
\(860\) 6.20266e12 0.386665
\(861\) −1.16754e12 −0.0724031
\(862\) −2.09581e13 −1.29291
\(863\) −1.65044e13 −1.01286 −0.506431 0.862281i \(-0.669035\pi\)
−0.506431 + 0.862281i \(0.669035\pi\)
\(864\) −1.19426e13 −0.729097
\(865\) −2.87029e12 −0.174323
\(866\) −1.93844e13 −1.17117
\(867\) −5.99739e11 −0.0360476
\(868\) 4.49611e10 0.00268843
\(869\) −1.08295e12 −0.0644201
\(870\) 1.67606e12 0.0991867
\(871\) −5.86056e12 −0.345031
\(872\) 1.52186e13 0.891355
\(873\) −1.77406e13 −1.03372
\(874\) −2.20450e13 −1.27794
\(875\) −1.15554e12 −0.0666419
\(876\) −2.46032e12 −0.141164
\(877\) −1.42710e11 −0.00814620 −0.00407310 0.999992i \(-0.501297\pi\)
−0.00407310 + 0.999992i \(0.501297\pi\)
\(878\) −1.50109e13 −0.852473
\(879\) −8.29777e12 −0.468826
\(880\) 1.21481e12 0.0682867
\(881\) 2.11785e13 1.18441 0.592206 0.805786i \(-0.298257\pi\)
0.592206 + 0.805786i \(0.298257\pi\)
\(882\) 1.31448e13 0.731384
\(883\) 1.83970e13 1.01841 0.509207 0.860644i \(-0.329939\pi\)
0.509207 + 0.860644i \(0.329939\pi\)
\(884\) −1.16132e12 −0.0639613
\(885\) −1.72427e13 −0.944847
\(886\) 6.60720e12 0.360218
\(887\) −1.18951e13 −0.645225 −0.322613 0.946531i \(-0.604561\pi\)
−0.322613 + 0.946531i \(0.604561\pi\)
\(888\) −2.70096e12 −0.145767
\(889\) −6.18888e11 −0.0332318
\(890\) −3.60276e13 −1.92477
\(891\) 1.43329e10 0.000761874 0
\(892\) −7.51963e12 −0.397699
\(893\) −1.62765e12 −0.0856505
\(894\) 6.87219e12 0.359812
\(895\) 3.66727e13 1.91047
\(896\) −1.59042e12 −0.0824375
\(897\) −1.05772e13 −0.545514
\(898\) −3.62807e13 −1.86180
\(899\) −2.55908e11 −0.0130667
\(900\) −4.36962e11 −0.0222000
\(901\) 2.40373e12 0.121513
\(902\) −2.07913e12 −0.104581
\(903\) −8.25692e11 −0.0413260
\(904\) 2.42384e13 1.20711
\(905\) 4.43377e12 0.219713
\(906\) 2.41572e13 1.19116
\(907\) 3.91571e13 1.92122 0.960612 0.277893i \(-0.0896361\pi\)
0.960612 + 0.277893i \(0.0896361\pi\)
\(908\) −5.48785e12 −0.267927
\(909\) −2.13251e13 −1.03599
\(910\) 1.22320e12 0.0591304
\(911\) −2.83393e13 −1.36319 −0.681595 0.731730i \(-0.738713\pi\)
−0.681595 + 0.731730i \(0.738713\pi\)
\(912\) −1.32164e13 −0.632609
\(913\) −1.37513e11 −0.00654977
\(914\) 2.61530e13 1.23955
\(915\) 1.53015e13 0.721672
\(916\) 6.99996e12 0.328523
\(917\) −2.62319e12 −0.122509
\(918\) −6.11489e12 −0.284182
\(919\) −1.73995e13 −0.804668 −0.402334 0.915493i \(-0.631801\pi\)
−0.402334 + 0.915493i \(0.631801\pi\)
\(920\) 2.13712e13 0.983520
\(921\) 1.13119e13 0.518044
\(922\) 1.96108e13 0.893731
\(923\) 1.04639e13 0.474554
\(924\) 1.94186e10 0.000876384 0
\(925\) −6.75356e11 −0.0303316
\(926\) 4.78189e12 0.213723
\(927\) 1.42329e13 0.633047
\(928\) −2.17720e12 −0.0963680
\(929\) −3.95509e13 −1.74215 −0.871074 0.491151i \(-0.836576\pi\)
−0.871074 + 0.491151i \(0.836576\pi\)
\(930\) −1.70776e12 −0.0748607
\(931\) 1.90377e13 0.830501
\(932\) 9.12937e12 0.396341
\(933\) −2.74988e11 −0.0118808
\(934\) 3.02752e12 0.130175
\(935\) 3.12926e11 0.0133903
\(936\) 7.25911e12 0.309131
\(937\) 4.31185e13 1.82741 0.913704 0.406381i \(-0.133210\pi\)
0.913704 + 0.406381i \(0.133210\pi\)
\(938\) 9.88392e11 0.0416885
\(939\) 1.37504e13 0.577194
\(940\) −9.89402e11 −0.0413330
\(941\) 1.23028e13 0.511505 0.255753 0.966742i \(-0.417677\pi\)
0.255753 + 0.966742i \(0.417677\pi\)
\(942\) −1.95018e13 −0.806949
\(943\) −5.31313e13 −2.18800
\(944\) 4.45217e13 1.82473
\(945\) 1.79167e12 0.0730828
\(946\) −1.47038e12 −0.0596923
\(947\) 3.99251e13 1.61314 0.806568 0.591142i \(-0.201323\pi\)
0.806568 + 0.591142i \(0.201323\pi\)
\(948\) 7.16186e12 0.287997
\(949\) 1.02199e13 0.409024
\(950\) −2.27498e12 −0.0906196
\(951\) −5.82424e12 −0.230902
\(952\) −3.12355e11 −0.0123249
\(953\) −4.12885e13 −1.62148 −0.810739 0.585408i \(-0.800934\pi\)
−0.810739 + 0.585408i \(0.800934\pi\)
\(954\) 9.42129e12 0.368250
\(955\) 4.60930e13 1.79316
\(956\) 1.64518e13 0.637019
\(957\) −1.10526e11 −0.00425953
\(958\) −1.42579e13 −0.546904
\(959\) −1.00658e12 −0.0384296
\(960\) 6.31705e12 0.240046
\(961\) −2.61789e13 −0.990138
\(962\) −7.03503e12 −0.264837
\(963\) −7.60548e12 −0.284976
\(964\) −1.44320e12 −0.0538246
\(965\) −3.35241e12 −0.124447
\(966\) 1.78386e12 0.0659120
\(967\) −3.74952e13 −1.37898 −0.689488 0.724297i \(-0.742164\pi\)
−0.689488 + 0.724297i \(0.742164\pi\)
\(968\) 1.97067e13 0.721397
\(969\) −3.40444e12 −0.124048
\(970\) −5.61455e13 −2.03630
\(971\) −1.85734e13 −0.670508 −0.335254 0.942128i \(-0.608822\pi\)
−0.335254 + 0.942128i \(0.608822\pi\)
\(972\) −1.07713e13 −0.387053
\(973\) 9.21653e11 0.0329655
\(974\) 2.47896e13 0.882580
\(975\) −1.09154e12 −0.0386829
\(976\) −3.95094e13 −1.39372
\(977\) −5.09643e13 −1.78954 −0.894769 0.446530i \(-0.852660\pi\)
−0.894769 + 0.446530i \(0.852660\pi\)
\(978\) 1.58103e13 0.552604
\(979\) 2.37580e12 0.0826586
\(980\) 1.15724e13 0.400782
\(981\) 2.23194e13 0.769434
\(982\) 3.73262e13 1.28089
\(983\) 1.27845e12 0.0436710 0.0218355 0.999762i \(-0.493049\pi\)
0.0218355 + 0.999762i \(0.493049\pi\)
\(984\) −2.19283e13 −0.745635
\(985\) −3.87578e13 −1.31189
\(986\) −1.11478e12 −0.0375616
\(987\) 1.31708e11 0.00441759
\(988\) −6.59230e12 −0.220105
\(989\) −3.75748e13 −1.24886
\(990\) 1.22650e12 0.0405796
\(991\) 1.53850e13 0.506719 0.253360 0.967372i \(-0.418464\pi\)
0.253360 + 0.967372i \(0.418464\pi\)
\(992\) 2.21838e12 0.0727332
\(993\) −1.06514e13 −0.347643
\(994\) −1.76475e12 −0.0573383
\(995\) 2.12920e13 0.688672
\(996\) 9.09410e11 0.0292815
\(997\) 3.56093e13 1.14139 0.570696 0.821162i \(-0.306674\pi\)
0.570696 + 0.821162i \(0.306674\pi\)
\(998\) 2.57094e13 0.820359
\(999\) −1.03045e13 −0.327327
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 17.10.a.a.1.5 5
3.2 odd 2 153.10.a.c.1.1 5
4.3 odd 2 272.10.a.f.1.4 5
17.16 even 2 289.10.a.a.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.a.a.1.5 5 1.1 even 1 trivial
153.10.a.c.1.1 5 3.2 odd 2
272.10.a.f.1.4 5 4.3 odd 2
289.10.a.a.1.5 5 17.16 even 2