Properties

Label 177.10.a.a.1.6
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-26.8579 q^{2} +81.0000 q^{3} +209.348 q^{4} -2742.53 q^{5} -2175.49 q^{6} -8878.91 q^{7} +8128.61 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-26.8579 q^{2} +81.0000 q^{3} +209.348 q^{4} -2742.53 q^{5} -2175.49 q^{6} -8878.91 q^{7} +8128.61 q^{8} +6561.00 q^{9} +73658.6 q^{10} -61766.0 q^{11} +16957.2 q^{12} -93410.5 q^{13} +238469. q^{14} -222145. q^{15} -325504. q^{16} +540545. q^{17} -176215. q^{18} +591646. q^{19} -574143. q^{20} -719191. q^{21} +1.65891e6 q^{22} +571277. q^{23} +658417. q^{24} +5.56834e6 q^{25} +2.50881e6 q^{26} +531441. q^{27} -1.85878e6 q^{28} -1.20821e6 q^{29} +5.96635e6 q^{30} -3.72946e6 q^{31} +4.58050e6 q^{32} -5.00304e6 q^{33} -1.45179e7 q^{34} +2.43506e7 q^{35} +1.37353e6 q^{36} +1.40983e7 q^{37} -1.58904e7 q^{38} -7.56625e6 q^{39} -2.22929e7 q^{40} -7.71359e6 q^{41} +1.93160e7 q^{42} +3.91142e6 q^{43} -1.29306e7 q^{44} -1.79937e7 q^{45} -1.53433e7 q^{46} -5.70269e7 q^{47} -2.63658e7 q^{48} +3.84813e7 q^{49} -1.49554e8 q^{50} +4.37842e7 q^{51} -1.95553e7 q^{52} +4.11217e7 q^{53} -1.42734e7 q^{54} +1.69395e8 q^{55} -7.21731e7 q^{56} +4.79233e7 q^{57} +3.24500e7 q^{58} +1.21174e7 q^{59} -4.65055e7 q^{60} +5.31961e7 q^{61} +1.00165e8 q^{62} -5.82545e7 q^{63} +4.36350e7 q^{64} +2.56181e8 q^{65} +1.34371e8 q^{66} +2.25785e8 q^{67} +1.13162e8 q^{68} +4.62735e7 q^{69} -6.54008e8 q^{70} -2.29743e8 q^{71} +5.33318e7 q^{72} +1.11661e8 q^{73} -3.78651e8 q^{74} +4.51035e8 q^{75} +1.23860e8 q^{76} +5.48414e8 q^{77} +2.03214e8 q^{78} +7.39558e7 q^{79} +8.92703e8 q^{80} +4.30467e7 q^{81} +2.07171e8 q^{82} +1.07859e8 q^{83} -1.50561e8 q^{84} -1.48246e9 q^{85} -1.05053e8 q^{86} -9.78651e7 q^{87} -5.02071e8 q^{88} -6.13295e8 q^{89} +4.83274e8 q^{90} +8.29383e8 q^{91} +1.19596e8 q^{92} -3.02086e8 q^{93} +1.53162e9 q^{94} -1.62261e9 q^{95} +3.71021e8 q^{96} +6.55776e8 q^{97} -1.03353e9 q^{98} -4.05247e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −26.8579 −1.18696 −0.593482 0.804847i \(-0.702247\pi\)
−0.593482 + 0.804847i \(0.702247\pi\)
\(3\) 81.0000 0.577350
\(4\) 209.348 0.408883
\(5\) −2742.53 −1.96239 −0.981197 0.193011i \(-0.938175\pi\)
−0.981197 + 0.193011i \(0.938175\pi\)
\(6\) −2175.49 −0.685294
\(7\) −8878.91 −1.39771 −0.698857 0.715262i \(-0.746308\pi\)
−0.698857 + 0.715262i \(0.746308\pi\)
\(8\) 8128.61 0.701635
\(9\) 6561.00 0.333333
\(10\) 73658.6 2.32929
\(11\) −61766.0 −1.27199 −0.635993 0.771695i \(-0.719409\pi\)
−0.635993 + 0.771695i \(0.719409\pi\)
\(12\) 16957.2 0.236069
\(13\) −93410.5 −0.907090 −0.453545 0.891233i \(-0.649841\pi\)
−0.453545 + 0.891233i \(0.649841\pi\)
\(14\) 238469. 1.65904
\(15\) −222145. −1.13299
\(16\) −325504. −1.24170
\(17\) 540545. 1.56968 0.784841 0.619697i \(-0.212744\pi\)
0.784841 + 0.619697i \(0.212744\pi\)
\(18\) −176215. −0.395655
\(19\) 591646. 1.04153 0.520764 0.853701i \(-0.325647\pi\)
0.520764 + 0.853701i \(0.325647\pi\)
\(20\) −574143. −0.802389
\(21\) −719191. −0.806970
\(22\) 1.65891e6 1.50980
\(23\) 571277. 0.425669 0.212834 0.977088i \(-0.431731\pi\)
0.212834 + 0.977088i \(0.431731\pi\)
\(24\) 658417. 0.405089
\(25\) 5.56834e6 2.85099
\(26\) 2.50881e6 1.07668
\(27\) 531441. 0.192450
\(28\) −1.85878e6 −0.571501
\(29\) −1.20821e6 −0.317213 −0.158607 0.987342i \(-0.550700\pi\)
−0.158607 + 0.987342i \(0.550700\pi\)
\(30\) 5.96635e6 1.34482
\(31\) −3.72946e6 −0.725301 −0.362650 0.931925i \(-0.618128\pi\)
−0.362650 + 0.931925i \(0.618128\pi\)
\(32\) 4.58050e6 0.772215
\(33\) −5.00304e6 −0.734381
\(34\) −1.45179e7 −1.86316
\(35\) 2.43506e7 2.74286
\(36\) 1.37353e6 0.136294
\(37\) 1.40983e7 1.23668 0.618342 0.785910i \(-0.287805\pi\)
0.618342 + 0.785910i \(0.287805\pi\)
\(38\) −1.58904e7 −1.23626
\(39\) −7.56625e6 −0.523709
\(40\) −2.22929e7 −1.37688
\(41\) −7.71359e6 −0.426314 −0.213157 0.977018i \(-0.568375\pi\)
−0.213157 + 0.977018i \(0.568375\pi\)
\(42\) 1.93160e7 0.957845
\(43\) 3.91142e6 0.174472 0.0872362 0.996188i \(-0.472197\pi\)
0.0872362 + 0.996188i \(0.472197\pi\)
\(44\) −1.29306e7 −0.520093
\(45\) −1.79937e7 −0.654131
\(46\) −1.53433e7 −0.505253
\(47\) −5.70269e7 −1.70467 −0.852333 0.523000i \(-0.824813\pi\)
−0.852333 + 0.523000i \(0.824813\pi\)
\(48\) −2.63658e7 −0.716894
\(49\) 3.84813e7 0.953604
\(50\) −1.49554e8 −3.38402
\(51\) 4.37842e7 0.906257
\(52\) −1.95553e7 −0.370894
\(53\) 4.11217e7 0.715863 0.357932 0.933748i \(-0.383482\pi\)
0.357932 + 0.933748i \(0.383482\pi\)
\(54\) −1.42734e7 −0.228431
\(55\) 1.69395e8 2.49614
\(56\) −7.21731e7 −0.980685
\(57\) 4.79233e7 0.601326
\(58\) 3.24500e7 0.376521
\(59\) 1.21174e7 0.130189
\(60\) −4.65055e7 −0.463259
\(61\) 5.31961e7 0.491921 0.245961 0.969280i \(-0.420897\pi\)
0.245961 + 0.969280i \(0.420897\pi\)
\(62\) 1.00165e8 0.860906
\(63\) −5.82545e7 −0.465905
\(64\) 4.36350e7 0.325106
\(65\) 2.56181e8 1.78007
\(66\) 1.34371e8 0.871684
\(67\) 2.25785e8 1.36886 0.684430 0.729079i \(-0.260051\pi\)
0.684430 + 0.729079i \(0.260051\pi\)
\(68\) 1.13162e8 0.641816
\(69\) 4.62735e7 0.245760
\(70\) −6.54008e8 −3.25568
\(71\) −2.29743e8 −1.07295 −0.536476 0.843916i \(-0.680245\pi\)
−0.536476 + 0.843916i \(0.680245\pi\)
\(72\) 5.33318e7 0.233878
\(73\) 1.11661e8 0.460201 0.230100 0.973167i \(-0.426095\pi\)
0.230100 + 0.973167i \(0.426095\pi\)
\(74\) −3.78651e8 −1.46790
\(75\) 4.51035e8 1.64602
\(76\) 1.23860e8 0.425863
\(77\) 5.48414e8 1.77787
\(78\) 2.03214e8 0.621623
\(79\) 7.39558e7 0.213624 0.106812 0.994279i \(-0.465936\pi\)
0.106812 + 0.994279i \(0.465936\pi\)
\(80\) 8.92703e8 2.43670
\(81\) 4.30467e7 0.111111
\(82\) 2.07171e8 0.506019
\(83\) 1.07859e8 0.249463 0.124732 0.992191i \(-0.460193\pi\)
0.124732 + 0.992191i \(0.460193\pi\)
\(84\) −1.50561e8 −0.329956
\(85\) −1.48246e9 −3.08033
\(86\) −1.05053e8 −0.207092
\(87\) −9.78651e7 −0.183143
\(88\) −5.02071e8 −0.892470
\(89\) −6.13295e8 −1.03613 −0.518065 0.855341i \(-0.673347\pi\)
−0.518065 + 0.855341i \(0.673347\pi\)
\(90\) 4.83274e8 0.776430
\(91\) 8.29383e8 1.26785
\(92\) 1.19596e8 0.174049
\(93\) −3.02086e8 −0.418753
\(94\) 1.53162e9 2.02338
\(95\) −1.62261e9 −2.04389
\(96\) 3.71021e8 0.445839
\(97\) 6.55776e8 0.752112 0.376056 0.926597i \(-0.377280\pi\)
0.376056 + 0.926597i \(0.377280\pi\)
\(98\) −1.03353e9 −1.13189
\(99\) −4.05247e8 −0.423995
\(100\) 1.16572e9 1.16572
\(101\) 4.54527e7 0.0434624 0.0217312 0.999764i \(-0.493082\pi\)
0.0217312 + 0.999764i \(0.493082\pi\)
\(102\) −1.17595e9 −1.07569
\(103\) −1.48991e9 −1.30435 −0.652174 0.758070i \(-0.726143\pi\)
−0.652174 + 0.758070i \(0.726143\pi\)
\(104\) −7.59297e8 −0.636446
\(105\) 1.97240e9 1.58359
\(106\) −1.10444e9 −0.849704
\(107\) −8.57527e7 −0.0632442 −0.0316221 0.999500i \(-0.510067\pi\)
−0.0316221 + 0.999500i \(0.510067\pi\)
\(108\) 1.11256e8 0.0786895
\(109\) 2.78093e9 1.88700 0.943499 0.331375i \(-0.107513\pi\)
0.943499 + 0.331375i \(0.107513\pi\)
\(110\) −4.54960e9 −2.96282
\(111\) 1.14196e9 0.713999
\(112\) 2.89012e9 1.73554
\(113\) 1.75843e9 1.01455 0.507274 0.861785i \(-0.330653\pi\)
0.507274 + 0.861785i \(0.330653\pi\)
\(114\) −1.28712e9 −0.713753
\(115\) −1.56674e9 −0.835330
\(116\) −2.52936e8 −0.129703
\(117\) −6.12866e8 −0.302363
\(118\) −3.25447e8 −0.154530
\(119\) −4.79945e9 −2.19397
\(120\) −1.80573e9 −0.794944
\(121\) 1.45709e9 0.617948
\(122\) −1.42874e9 −0.583892
\(123\) −6.24801e8 −0.246132
\(124\) −7.80754e8 −0.296563
\(125\) −9.91482e9 −3.63237
\(126\) 1.56459e9 0.553012
\(127\) 3.48699e9 1.18942 0.594709 0.803941i \(-0.297267\pi\)
0.594709 + 0.803941i \(0.297267\pi\)
\(128\) −3.51716e9 −1.15810
\(129\) 3.16825e8 0.100732
\(130\) −6.88049e9 −2.11288
\(131\) −5.58769e9 −1.65772 −0.828860 0.559456i \(-0.811010\pi\)
−0.828860 + 0.559456i \(0.811010\pi\)
\(132\) −1.04738e9 −0.300276
\(133\) −5.25317e9 −1.45576
\(134\) −6.06412e9 −1.62479
\(135\) −1.45749e9 −0.377663
\(136\) 4.39388e9 1.10134
\(137\) 7.07450e9 1.71575 0.857873 0.513861i \(-0.171785\pi\)
0.857873 + 0.513861i \(0.171785\pi\)
\(138\) −1.24281e9 −0.291708
\(139\) −7.81032e9 −1.77461 −0.887304 0.461186i \(-0.847424\pi\)
−0.887304 + 0.461186i \(0.847424\pi\)
\(140\) 5.09776e9 1.12151
\(141\) −4.61918e9 −0.984189
\(142\) 6.17043e9 1.27355
\(143\) 5.76959e9 1.15381
\(144\) −2.13563e9 −0.413899
\(145\) 3.31355e9 0.622498
\(146\) −2.99897e9 −0.546242
\(147\) 3.11699e9 0.550563
\(148\) 2.95145e9 0.505658
\(149\) 3.65520e9 0.607537 0.303768 0.952746i \(-0.401755\pi\)
0.303768 + 0.952746i \(0.401755\pi\)
\(150\) −1.21139e10 −1.95376
\(151\) 5.30736e9 0.830774 0.415387 0.909645i \(-0.363646\pi\)
0.415387 + 0.909645i \(0.363646\pi\)
\(152\) 4.80926e9 0.730772
\(153\) 3.54652e9 0.523228
\(154\) −1.47293e10 −2.11027
\(155\) 1.02281e10 1.42333
\(156\) −1.58398e9 −0.214135
\(157\) −7.06139e9 −0.927560 −0.463780 0.885950i \(-0.653507\pi\)
−0.463780 + 0.885950i \(0.653507\pi\)
\(158\) −1.98630e9 −0.253564
\(159\) 3.33086e9 0.413304
\(160\) −1.25622e10 −1.51539
\(161\) −5.07232e9 −0.594963
\(162\) −1.15615e9 −0.131885
\(163\) −7.27115e9 −0.806787 −0.403393 0.915027i \(-0.632169\pi\)
−0.403393 + 0.915027i \(0.632169\pi\)
\(164\) −1.61482e9 −0.174312
\(165\) 1.37210e10 1.44115
\(166\) −2.89688e9 −0.296104
\(167\) −8.95764e9 −0.891189 −0.445594 0.895235i \(-0.647008\pi\)
−0.445594 + 0.895235i \(0.647008\pi\)
\(168\) −5.84602e9 −0.566198
\(169\) −1.87898e9 −0.177187
\(170\) 3.98158e10 3.65625
\(171\) 3.88179e9 0.347176
\(172\) 8.18848e8 0.0713387
\(173\) −7.27592e9 −0.617562 −0.308781 0.951133i \(-0.599921\pi\)
−0.308781 + 0.951133i \(0.599921\pi\)
\(174\) 2.62845e9 0.217384
\(175\) −4.94407e10 −3.98486
\(176\) 2.01050e10 1.57942
\(177\) 9.81506e8 0.0751646
\(178\) 1.64718e10 1.22985
\(179\) −2.08457e10 −1.51767 −0.758836 0.651281i \(-0.774232\pi\)
−0.758836 + 0.651281i \(0.774232\pi\)
\(180\) −3.76695e9 −0.267463
\(181\) 1.27240e10 0.881192 0.440596 0.897706i \(-0.354767\pi\)
0.440596 + 0.897706i \(0.354767\pi\)
\(182\) −2.22755e10 −1.50489
\(183\) 4.30888e9 0.284011
\(184\) 4.64369e9 0.298664
\(185\) −3.86649e10 −2.42686
\(186\) 8.11340e9 0.497044
\(187\) −3.33873e10 −1.99661
\(188\) −1.19385e10 −0.697008
\(189\) −4.71861e9 −0.268990
\(190\) 4.35798e10 2.42602
\(191\) 2.88968e10 1.57108 0.785541 0.618809i \(-0.212385\pi\)
0.785541 + 0.618809i \(0.212385\pi\)
\(192\) 3.53444e9 0.187700
\(193\) 1.58940e10 0.824564 0.412282 0.911056i \(-0.364732\pi\)
0.412282 + 0.911056i \(0.364732\pi\)
\(194\) −1.76128e10 −0.892729
\(195\) 2.07507e10 1.02772
\(196\) 8.05599e9 0.389912
\(197\) −1.71196e10 −0.809835 −0.404917 0.914353i \(-0.632700\pi\)
−0.404917 + 0.914353i \(0.632700\pi\)
\(198\) 1.08841e10 0.503267
\(199\) −3.69899e10 −1.67203 −0.836015 0.548707i \(-0.815120\pi\)
−0.836015 + 0.548707i \(0.815120\pi\)
\(200\) 4.52628e10 2.00035
\(201\) 1.82886e10 0.790312
\(202\) −1.22077e9 −0.0515883
\(203\) 1.07276e10 0.443374
\(204\) 9.16612e9 0.370553
\(205\) 2.11547e10 0.836595
\(206\) 4.00160e10 1.54821
\(207\) 3.74815e9 0.141890
\(208\) 3.04054e10 1.12633
\(209\) −3.65436e10 −1.32481
\(210\) −5.29746e10 −1.87967
\(211\) 2.82074e10 0.979697 0.489848 0.871808i \(-0.337052\pi\)
0.489848 + 0.871808i \(0.337052\pi\)
\(212\) 8.60875e9 0.292704
\(213\) −1.86092e10 −0.619469
\(214\) 2.30314e9 0.0750686
\(215\) −1.07272e10 −0.342383
\(216\) 4.31987e9 0.135030
\(217\) 3.31135e10 1.01376
\(218\) −7.46901e10 −2.23980
\(219\) 9.04452e9 0.265697
\(220\) 3.54625e10 1.02063
\(221\) −5.04926e10 −1.42384
\(222\) −3.06707e10 −0.847491
\(223\) −2.75802e10 −0.746837 −0.373419 0.927663i \(-0.621815\pi\)
−0.373419 + 0.927663i \(0.621815\pi\)
\(224\) −4.06699e10 −1.07934
\(225\) 3.65338e10 0.950329
\(226\) −4.72278e10 −1.20423
\(227\) −2.76405e10 −0.690922 −0.345461 0.938433i \(-0.612277\pi\)
−0.345461 + 0.938433i \(0.612277\pi\)
\(228\) 1.00327e10 0.245872
\(229\) 3.15202e10 0.757407 0.378704 0.925518i \(-0.376370\pi\)
0.378704 + 0.925518i \(0.376370\pi\)
\(230\) 4.20795e10 0.991506
\(231\) 4.44216e10 1.02645
\(232\) −9.82107e9 −0.222568
\(233\) 3.03425e10 0.674450 0.337225 0.941424i \(-0.390512\pi\)
0.337225 + 0.941424i \(0.390512\pi\)
\(234\) 1.64603e10 0.358894
\(235\) 1.56398e11 3.34522
\(236\) 2.53674e9 0.0532320
\(237\) 5.99042e9 0.123336
\(238\) 1.28903e11 2.60416
\(239\) −3.01660e10 −0.598036 −0.299018 0.954247i \(-0.596659\pi\)
−0.299018 + 0.954247i \(0.596659\pi\)
\(240\) 7.23089e10 1.40683
\(241\) 2.56192e10 0.489203 0.244601 0.969624i \(-0.421343\pi\)
0.244601 + 0.969624i \(0.421343\pi\)
\(242\) −3.91344e10 −0.733482
\(243\) 3.48678e9 0.0641500
\(244\) 1.11365e10 0.201138
\(245\) −1.05536e11 −1.87135
\(246\) 1.67809e10 0.292150
\(247\) −5.52660e10 −0.944760
\(248\) −3.03153e10 −0.508896
\(249\) 8.73661e9 0.144028
\(250\) 2.66291e11 4.31149
\(251\) 1.93681e10 0.308003 0.154002 0.988071i \(-0.450784\pi\)
0.154002 + 0.988071i \(0.450784\pi\)
\(252\) −1.21955e10 −0.190500
\(253\) −3.52855e10 −0.541445
\(254\) −9.36534e10 −1.41180
\(255\) −1.20079e11 −1.77843
\(256\) 7.21226e10 1.04952
\(257\) 1.20699e11 1.72585 0.862926 0.505330i \(-0.168629\pi\)
0.862926 + 0.505330i \(0.168629\pi\)
\(258\) −8.50927e9 −0.119565
\(259\) −1.25177e11 −1.72853
\(260\) 5.36309e10 0.727839
\(261\) −7.92707e9 −0.105738
\(262\) 1.50074e11 1.96765
\(263\) 1.68684e10 0.217407 0.108703 0.994074i \(-0.465330\pi\)
0.108703 + 0.994074i \(0.465330\pi\)
\(264\) −4.06678e10 −0.515268
\(265\) −1.12778e11 −1.40481
\(266\) 1.41089e11 1.72793
\(267\) −4.96769e10 −0.598210
\(268\) 4.72677e10 0.559703
\(269\) 1.17255e11 1.36535 0.682676 0.730721i \(-0.260816\pi\)
0.682676 + 0.730721i \(0.260816\pi\)
\(270\) 3.91452e10 0.448272
\(271\) −3.54818e9 −0.0399617 −0.0199808 0.999800i \(-0.506361\pi\)
−0.0199808 + 0.999800i \(0.506361\pi\)
\(272\) −1.75949e11 −1.94907
\(273\) 6.71800e10 0.731995
\(274\) −1.90006e11 −2.03653
\(275\) −3.43934e11 −3.62642
\(276\) 9.68726e9 0.100487
\(277\) 8.36832e10 0.854042 0.427021 0.904242i \(-0.359563\pi\)
0.427021 + 0.904242i \(0.359563\pi\)
\(278\) 2.09769e11 2.10639
\(279\) −2.44690e10 −0.241767
\(280\) 1.97937e11 1.92449
\(281\) −3.07370e10 −0.294092 −0.147046 0.989130i \(-0.546977\pi\)
−0.147046 + 0.989130i \(0.546977\pi\)
\(282\) 1.24061e11 1.16820
\(283\) −1.78139e11 −1.65090 −0.825449 0.564477i \(-0.809078\pi\)
−0.825449 + 0.564477i \(0.809078\pi\)
\(284\) −4.80963e10 −0.438711
\(285\) −1.31431e11 −1.18004
\(286\) −1.54959e11 −1.36953
\(287\) 6.84883e10 0.595865
\(288\) 3.00527e10 0.257405
\(289\) 1.73601e11 1.46390
\(290\) −8.89951e10 −0.738882
\(291\) 5.31178e10 0.434232
\(292\) 2.33759e10 0.188168
\(293\) −1.81919e11 −1.44203 −0.721014 0.692921i \(-0.756324\pi\)
−0.721014 + 0.692921i \(0.756324\pi\)
\(294\) −8.37159e10 −0.653499
\(295\) −3.32322e10 −0.255482
\(296\) 1.14599e11 0.867700
\(297\) −3.28250e10 −0.244794
\(298\) −9.81710e10 −0.721124
\(299\) −5.33633e10 −0.386120
\(300\) 9.44233e10 0.673028
\(301\) −3.47291e10 −0.243862
\(302\) −1.42545e11 −0.986098
\(303\) 3.68167e9 0.0250930
\(304\) −1.92583e11 −1.29326
\(305\) −1.45892e11 −0.965343
\(306\) −9.52521e10 −0.621052
\(307\) 2.35783e11 1.51492 0.757460 0.652882i \(-0.226440\pi\)
0.757460 + 0.652882i \(0.226440\pi\)
\(308\) 1.14809e11 0.726941
\(309\) −1.20683e11 −0.753065
\(310\) −2.74707e11 −1.68944
\(311\) 8.77054e10 0.531624 0.265812 0.964025i \(-0.414360\pi\)
0.265812 + 0.964025i \(0.414360\pi\)
\(312\) −6.15031e10 −0.367452
\(313\) 1.15319e11 0.679126 0.339563 0.940583i \(-0.389721\pi\)
0.339563 + 0.940583i \(0.389721\pi\)
\(314\) 1.89654e11 1.10098
\(315\) 1.59765e11 0.914288
\(316\) 1.54825e10 0.0873472
\(317\) −2.91934e11 −1.62374 −0.811872 0.583835i \(-0.801551\pi\)
−0.811872 + 0.583835i \(0.801551\pi\)
\(318\) −8.94600e10 −0.490577
\(319\) 7.46263e10 0.403491
\(320\) −1.19670e11 −0.637986
\(321\) −6.94597e9 −0.0365141
\(322\) 1.36232e11 0.706200
\(323\) 3.19812e11 1.63487
\(324\) 9.01174e9 0.0454314
\(325\) −5.20141e11 −2.58610
\(326\) 1.95288e11 0.957627
\(327\) 2.25256e11 1.08946
\(328\) −6.27008e10 −0.299117
\(329\) 5.06336e11 2.38263
\(330\) −3.68517e11 −1.71059
\(331\) 3.45536e11 1.58222 0.791110 0.611674i \(-0.209504\pi\)
0.791110 + 0.611674i \(0.209504\pi\)
\(332\) 2.25801e10 0.102001
\(333\) 9.24988e10 0.412228
\(334\) 2.40584e11 1.05781
\(335\) −6.19223e11 −2.68624
\(336\) 2.34099e11 1.00201
\(337\) 2.55218e11 1.07789 0.538947 0.842340i \(-0.318822\pi\)
0.538947 + 0.842340i \(0.318822\pi\)
\(338\) 5.04655e10 0.210315
\(339\) 1.42433e11 0.585749
\(340\) −3.10350e11 −1.25950
\(341\) 2.30354e11 0.922572
\(342\) −1.04257e11 −0.412085
\(343\) 1.66236e10 0.0648488
\(344\) 3.17944e10 0.122416
\(345\) −1.26906e11 −0.482278
\(346\) 1.95416e11 0.733024
\(347\) 2.89107e11 1.07047 0.535237 0.844702i \(-0.320222\pi\)
0.535237 + 0.844702i \(0.320222\pi\)
\(348\) −2.04878e10 −0.0748841
\(349\) 5.91146e10 0.213295 0.106647 0.994297i \(-0.465988\pi\)
0.106647 + 0.994297i \(0.465988\pi\)
\(350\) 1.32787e12 4.72989
\(351\) −4.96422e10 −0.174570
\(352\) −2.82919e11 −0.982247
\(353\) −2.63011e11 −0.901547 −0.450774 0.892638i \(-0.648852\pi\)
−0.450774 + 0.892638i \(0.648852\pi\)
\(354\) −2.63612e10 −0.0892176
\(355\) 6.30077e11 2.10555
\(356\) −1.28392e11 −0.423655
\(357\) −3.88755e11 −1.26669
\(358\) 5.59873e11 1.80142
\(359\) −3.28022e11 −1.04226 −0.521132 0.853476i \(-0.674490\pi\)
−0.521132 + 0.853476i \(0.674490\pi\)
\(360\) −1.46264e11 −0.458961
\(361\) 2.73576e10 0.0847804
\(362\) −3.41740e11 −1.04594
\(363\) 1.18024e11 0.356772
\(364\) 1.73630e11 0.518403
\(365\) −3.06233e11 −0.903095
\(366\) −1.15728e11 −0.337110
\(367\) 2.02654e11 0.583121 0.291560 0.956552i \(-0.405826\pi\)
0.291560 + 0.956552i \(0.405826\pi\)
\(368\) −1.85953e11 −0.528552
\(369\) −5.06089e10 −0.142105
\(370\) 1.03846e12 2.88059
\(371\) −3.65116e11 −1.00057
\(372\) −6.32411e10 −0.171221
\(373\) 6.72717e11 1.79946 0.899731 0.436446i \(-0.143763\pi\)
0.899731 + 0.436446i \(0.143763\pi\)
\(374\) 8.96714e11 2.36991
\(375\) −8.03100e11 −2.09715
\(376\) −4.63549e11 −1.19605
\(377\) 1.12860e11 0.287741
\(378\) 1.26732e11 0.319282
\(379\) 5.61509e11 1.39791 0.698956 0.715164i \(-0.253648\pi\)
0.698956 + 0.715164i \(0.253648\pi\)
\(380\) −3.39689e11 −0.835710
\(381\) 2.82446e11 0.686711
\(382\) −7.76107e11 −1.86482
\(383\) 2.38068e11 0.565335 0.282668 0.959218i \(-0.408781\pi\)
0.282668 + 0.959218i \(0.408781\pi\)
\(384\) −2.84890e11 −0.668632
\(385\) −1.50404e12 −3.48888
\(386\) −4.26879e11 −0.978727
\(387\) 2.56628e10 0.0581575
\(388\) 1.37285e11 0.307526
\(389\) 5.45633e10 0.120817 0.0604084 0.998174i \(-0.480760\pi\)
0.0604084 + 0.998174i \(0.480760\pi\)
\(390\) −5.57319e11 −1.21987
\(391\) 3.08801e11 0.668165
\(392\) 3.12800e11 0.669082
\(393\) −4.52603e11 −0.957085
\(394\) 4.59798e11 0.961245
\(395\) −2.02826e11 −0.419215
\(396\) −8.48375e10 −0.173364
\(397\) −2.81399e11 −0.568546 −0.284273 0.958743i \(-0.591752\pi\)
−0.284273 + 0.958743i \(0.591752\pi\)
\(398\) 9.93471e11 1.98464
\(399\) −4.25507e11 −0.840482
\(400\) −1.81251e12 −3.54006
\(401\) −5.46924e11 −1.05628 −0.528138 0.849159i \(-0.677110\pi\)
−0.528138 + 0.849159i \(0.677110\pi\)
\(402\) −4.91194e11 −0.938071
\(403\) 3.48370e11 0.657913
\(404\) 9.51544e9 0.0177710
\(405\) −1.18057e11 −0.218044
\(406\) −2.88121e11 −0.526268
\(407\) −8.70794e11 −1.57304
\(408\) 3.55904e11 0.635861
\(409\) −4.16938e11 −0.736745 −0.368372 0.929678i \(-0.620085\pi\)
−0.368372 + 0.929678i \(0.620085\pi\)
\(410\) −5.68172e11 −0.993008
\(411\) 5.73035e11 0.990587
\(412\) −3.11910e11 −0.533325
\(413\) −1.07589e11 −0.181967
\(414\) −1.00668e11 −0.168418
\(415\) −2.95807e11 −0.489545
\(416\) −4.27867e11 −0.700469
\(417\) −6.32636e11 −1.02457
\(418\) 9.81486e11 1.57250
\(419\) −2.29898e10 −0.0364395 −0.0182197 0.999834i \(-0.505800\pi\)
−0.0182197 + 0.999834i \(0.505800\pi\)
\(420\) 4.12918e11 0.647504
\(421\) −1.12164e12 −1.74013 −0.870066 0.492935i \(-0.835924\pi\)
−0.870066 + 0.492935i \(0.835924\pi\)
\(422\) −7.57591e11 −1.16286
\(423\) −3.74153e11 −0.568222
\(424\) 3.34262e11 0.502275
\(425\) 3.00994e12 4.47515
\(426\) 4.99805e11 0.735287
\(427\) −4.72323e11 −0.687565
\(428\) −1.79522e10 −0.0258595
\(429\) 4.67337e11 0.666150
\(430\) 2.88110e11 0.406397
\(431\) 3.60756e11 0.503577 0.251789 0.967782i \(-0.418981\pi\)
0.251789 + 0.967782i \(0.418981\pi\)
\(432\) −1.72986e11 −0.238965
\(433\) −6.41294e11 −0.876721 −0.438361 0.898799i \(-0.644441\pi\)
−0.438361 + 0.898799i \(0.644441\pi\)
\(434\) −8.89360e11 −1.20330
\(435\) 2.68398e11 0.359399
\(436\) 5.82183e11 0.771561
\(437\) 3.37994e11 0.443346
\(438\) −2.42917e11 −0.315373
\(439\) 6.52702e11 0.838735 0.419368 0.907816i \(-0.362252\pi\)
0.419368 + 0.907816i \(0.362252\pi\)
\(440\) 1.37694e12 1.75138
\(441\) 2.52476e11 0.317868
\(442\) 1.35613e12 1.69005
\(443\) 1.30215e11 0.160636 0.0803182 0.996769i \(-0.474406\pi\)
0.0803182 + 0.996769i \(0.474406\pi\)
\(444\) 2.39067e11 0.291942
\(445\) 1.68198e12 2.03329
\(446\) 7.40748e11 0.886469
\(447\) 2.96071e11 0.350761
\(448\) −3.87431e11 −0.454406
\(449\) −8.31004e11 −0.964927 −0.482463 0.875916i \(-0.660258\pi\)
−0.482463 + 0.875916i \(0.660258\pi\)
\(450\) −9.81223e11 −1.12801
\(451\) 4.76438e11 0.542265
\(452\) 3.68124e11 0.414831
\(453\) 4.29897e11 0.479647
\(454\) 7.42366e11 0.820099
\(455\) −2.27461e12 −2.48803
\(456\) 3.89550e11 0.421912
\(457\) −6.65343e11 −0.713547 −0.356773 0.934191i \(-0.616123\pi\)
−0.356773 + 0.934191i \(0.616123\pi\)
\(458\) −8.46567e11 −0.899015
\(459\) 2.87268e11 0.302086
\(460\) −3.27995e11 −0.341552
\(461\) −1.11231e12 −1.14702 −0.573512 0.819197i \(-0.694419\pi\)
−0.573512 + 0.819197i \(0.694419\pi\)
\(462\) −1.19307e12 −1.21836
\(463\) −9.99926e11 −1.01124 −0.505619 0.862757i \(-0.668736\pi\)
−0.505619 + 0.862757i \(0.668736\pi\)
\(464\) 3.93277e11 0.393883
\(465\) 8.28480e11 0.821757
\(466\) −8.14937e11 −0.800548
\(467\) −1.02910e12 −1.00123 −0.500614 0.865671i \(-0.666892\pi\)
−0.500614 + 0.865671i \(0.666892\pi\)
\(468\) −1.28302e11 −0.123631
\(469\) −2.00473e12 −1.91327
\(470\) −4.20052e12 −3.97066
\(471\) −5.71973e11 −0.535527
\(472\) 9.84972e10 0.0913451
\(473\) −2.41593e11 −0.221926
\(474\) −1.60890e11 −0.146395
\(475\) 3.29448e12 2.96938
\(476\) −1.00475e12 −0.897075
\(477\) 2.69800e11 0.238621
\(478\) 8.10196e11 0.709847
\(479\) 7.17132e10 0.0622429 0.0311214 0.999516i \(-0.490092\pi\)
0.0311214 + 0.999516i \(0.490092\pi\)
\(480\) −1.01753e12 −0.874911
\(481\) −1.31693e12 −1.12178
\(482\) −6.88078e11 −0.580666
\(483\) −4.10858e11 −0.343502
\(484\) 3.05039e11 0.252668
\(485\) −1.79848e12 −1.47594
\(486\) −9.36478e10 −0.0761438
\(487\) −1.95850e12 −1.57777 −0.788884 0.614542i \(-0.789341\pi\)
−0.788884 + 0.614542i \(0.789341\pi\)
\(488\) 4.32410e11 0.345149
\(489\) −5.88963e11 −0.465799
\(490\) 2.83448e12 2.22122
\(491\) −9.39570e11 −0.729563 −0.364781 0.931093i \(-0.618856\pi\)
−0.364781 + 0.931093i \(0.618856\pi\)
\(492\) −1.30801e11 −0.100639
\(493\) −6.53092e11 −0.497924
\(494\) 1.48433e12 1.12140
\(495\) 1.11140e12 0.832046
\(496\) 1.21395e12 0.900604
\(497\) 2.03987e12 1.49968
\(498\) −2.34647e11 −0.170956
\(499\) 1.84042e12 1.32881 0.664406 0.747372i \(-0.268684\pi\)
0.664406 + 0.747372i \(0.268684\pi\)
\(500\) −2.07565e12 −1.48521
\(501\) −7.25569e11 −0.514528
\(502\) −5.20187e11 −0.365589
\(503\) 1.93179e12 1.34556 0.672781 0.739842i \(-0.265100\pi\)
0.672781 + 0.739842i \(0.265100\pi\)
\(504\) −4.73528e11 −0.326895
\(505\) −1.24655e11 −0.0852904
\(506\) 9.47696e11 0.642675
\(507\) −1.52197e11 −0.102299
\(508\) 7.29995e11 0.486332
\(509\) 1.57321e12 1.03886 0.519430 0.854513i \(-0.326144\pi\)
0.519430 + 0.854513i \(0.326144\pi\)
\(510\) 3.22508e12 2.11093
\(511\) −9.91425e11 −0.643229
\(512\) −1.36275e11 −0.0876395
\(513\) 3.14425e11 0.200442
\(514\) −3.24172e12 −2.04852
\(515\) 4.08613e12 2.55964
\(516\) 6.63267e10 0.0411874
\(517\) 3.52232e12 2.16831
\(518\) 3.36200e12 2.05170
\(519\) −5.89350e11 −0.356550
\(520\) 2.08239e12 1.24896
\(521\) −1.47553e12 −0.877362 −0.438681 0.898643i \(-0.644554\pi\)
−0.438681 + 0.898643i \(0.644554\pi\)
\(522\) 2.12905e11 0.125507
\(523\) 1.84774e11 0.107990 0.0539951 0.998541i \(-0.482804\pi\)
0.0539951 + 0.998541i \(0.482804\pi\)
\(524\) −1.16977e12 −0.677813
\(525\) −4.00470e12 −2.30066
\(526\) −4.53050e11 −0.258054
\(527\) −2.01594e12 −1.13849
\(528\) 1.62851e12 0.911880
\(529\) −1.47479e12 −0.818806
\(530\) 3.02897e12 1.66745
\(531\) 7.95020e10 0.0433963
\(532\) −1.09974e12 −0.595234
\(533\) 7.20530e11 0.386705
\(534\) 1.33422e12 0.710053
\(535\) 2.35179e11 0.124110
\(536\) 1.83532e12 0.960440
\(537\) −1.68850e12 −0.876229
\(538\) −3.14922e12 −1.62062
\(539\) −2.37684e12 −1.21297
\(540\) −3.05123e11 −0.154420
\(541\) −6.52891e11 −0.327682 −0.163841 0.986487i \(-0.552388\pi\)
−0.163841 + 0.986487i \(0.552388\pi\)
\(542\) 9.52967e10 0.0474330
\(543\) 1.03064e12 0.508756
\(544\) 2.47597e12 1.21213
\(545\) −7.62679e12 −3.70303
\(546\) −1.80432e12 −0.868852
\(547\) 3.32658e12 1.58875 0.794375 0.607428i \(-0.207799\pi\)
0.794375 + 0.607428i \(0.207799\pi\)
\(548\) 1.48103e12 0.701539
\(549\) 3.49020e11 0.163974
\(550\) 9.23734e12 4.30442
\(551\) −7.14833e11 −0.330387
\(552\) 3.76139e11 0.172434
\(553\) −6.56647e11 −0.298585
\(554\) −2.24756e12 −1.01372
\(555\) −3.13186e12 −1.40115
\(556\) −1.63507e12 −0.725606
\(557\) 1.94559e12 0.856453 0.428226 0.903672i \(-0.359139\pi\)
0.428226 + 0.903672i \(0.359139\pi\)
\(558\) 6.57186e11 0.286969
\(559\) −3.65368e11 −0.158262
\(560\) −7.92622e12 −3.40581
\(561\) −2.70437e12 −1.15275
\(562\) 8.25533e11 0.349077
\(563\) 2.30080e12 0.965144 0.482572 0.875856i \(-0.339703\pi\)
0.482572 + 0.875856i \(0.339703\pi\)
\(564\) −9.67015e11 −0.402418
\(565\) −4.82255e12 −1.99094
\(566\) 4.78444e12 1.95956
\(567\) −3.82208e11 −0.155302
\(568\) −1.86749e12 −0.752820
\(569\) 9.87978e11 0.395132 0.197566 0.980290i \(-0.436696\pi\)
0.197566 + 0.980290i \(0.436696\pi\)
\(570\) 3.52997e12 1.40066
\(571\) −8.55231e11 −0.336683 −0.168341 0.985729i \(-0.553841\pi\)
−0.168341 + 0.985729i \(0.553841\pi\)
\(572\) 1.20785e12 0.471771
\(573\) 2.34064e12 0.907065
\(574\) −1.83945e12 −0.707270
\(575\) 3.18106e12 1.21358
\(576\) 2.86289e11 0.108369
\(577\) −1.50266e12 −0.564378 −0.282189 0.959359i \(-0.591061\pi\)
−0.282189 + 0.959359i \(0.591061\pi\)
\(578\) −4.66257e12 −1.73760
\(579\) 1.28741e12 0.476062
\(580\) 6.93685e11 0.254528
\(581\) −9.57673e11 −0.348678
\(582\) −1.42663e12 −0.515418
\(583\) −2.53993e12 −0.910568
\(584\) 9.07646e11 0.322893
\(585\) 1.68080e12 0.593356
\(586\) 4.88596e12 1.71163
\(587\) 5.14820e12 1.78972 0.894858 0.446351i \(-0.147277\pi\)
0.894858 + 0.446351i \(0.147277\pi\)
\(588\) 6.52535e11 0.225116
\(589\) −2.20652e12 −0.755421
\(590\) 8.92548e11 0.303248
\(591\) −1.38669e12 −0.467558
\(592\) −4.58904e12 −1.53559
\(593\) 2.46084e11 0.0817218 0.0408609 0.999165i \(-0.486990\pi\)
0.0408609 + 0.999165i \(0.486990\pi\)
\(594\) 8.81611e11 0.290561
\(595\) 1.31626e13 4.30543
\(596\) 7.65208e11 0.248411
\(597\) −2.99618e12 −0.965347
\(598\) 1.43323e12 0.458310
\(599\) 4.30285e12 1.36564 0.682819 0.730588i \(-0.260754\pi\)
0.682819 + 0.730588i \(0.260754\pi\)
\(600\) 3.66629e12 1.15490
\(601\) −8.32379e11 −0.260247 −0.130124 0.991498i \(-0.541537\pi\)
−0.130124 + 0.991498i \(0.541537\pi\)
\(602\) 9.32753e11 0.289456
\(603\) 1.48138e12 0.456287
\(604\) 1.11109e12 0.339689
\(605\) −3.99611e12 −1.21266
\(606\) −9.88821e10 −0.0297845
\(607\) −4.24000e12 −1.26770 −0.633850 0.773456i \(-0.718526\pi\)
−0.633850 + 0.773456i \(0.718526\pi\)
\(608\) 2.71004e12 0.804284
\(609\) 8.68935e11 0.255982
\(610\) 3.91835e12 1.14583
\(611\) 5.32691e12 1.54629
\(612\) 7.42456e11 0.213939
\(613\) −2.49618e11 −0.0714008 −0.0357004 0.999363i \(-0.511366\pi\)
−0.0357004 + 0.999363i \(0.511366\pi\)
\(614\) −6.33264e12 −1.79815
\(615\) 1.71353e12 0.483008
\(616\) 4.45784e12 1.24742
\(617\) −6.24706e12 −1.73537 −0.867686 0.497113i \(-0.834394\pi\)
−0.867686 + 0.497113i \(0.834394\pi\)
\(618\) 3.24129e12 0.893861
\(619\) −2.45716e12 −0.672707 −0.336354 0.941736i \(-0.609194\pi\)
−0.336354 + 0.941736i \(0.609194\pi\)
\(620\) 2.14124e12 0.581973
\(621\) 3.03600e11 0.0819200
\(622\) −2.35558e12 −0.631018
\(623\) 5.44538e12 1.44821
\(624\) 2.46284e12 0.650288
\(625\) 1.63160e13 4.27714
\(626\) −3.09722e12 −0.806098
\(627\) −2.96003e12 −0.764879
\(628\) −1.47829e12 −0.379263
\(629\) 7.62076e12 1.94120
\(630\) −4.29094e12 −1.08523
\(631\) −3.57158e12 −0.896867 −0.448434 0.893816i \(-0.648018\pi\)
−0.448434 + 0.893816i \(0.648018\pi\)
\(632\) 6.01158e11 0.149886
\(633\) 2.28480e12 0.565628
\(634\) 7.84074e12 1.92733
\(635\) −9.56318e12 −2.33411
\(636\) 6.97309e11 0.168993
\(637\) −3.59456e12 −0.865005
\(638\) −2.00431e12 −0.478929
\(639\) −1.50735e12 −0.357651
\(640\) 9.64592e12 2.27266
\(641\) −2.29585e12 −0.537133 −0.268567 0.963261i \(-0.586550\pi\)
−0.268567 + 0.963261i \(0.586550\pi\)
\(642\) 1.86554e11 0.0433409
\(643\) 3.40634e12 0.785848 0.392924 0.919571i \(-0.371464\pi\)
0.392924 + 0.919571i \(0.371464\pi\)
\(644\) −1.06188e12 −0.243270
\(645\) −8.68902e11 −0.197675
\(646\) −8.58947e12 −1.94053
\(647\) 5.01929e12 1.12609 0.563045 0.826426i \(-0.309630\pi\)
0.563045 + 0.826426i \(0.309630\pi\)
\(648\) 3.49910e11 0.0779594
\(649\) −7.48441e11 −0.165598
\(650\) 1.39699e13 3.06961
\(651\) 2.68219e12 0.585296
\(652\) −1.52220e12 −0.329881
\(653\) −3.46316e12 −0.745354 −0.372677 0.927961i \(-0.621560\pi\)
−0.372677 + 0.927961i \(0.621560\pi\)
\(654\) −6.04990e12 −1.29315
\(655\) 1.53244e13 3.25310
\(656\) 2.51080e12 0.529353
\(657\) 7.32606e11 0.153400
\(658\) −1.35991e13 −2.82810
\(659\) 1.58198e12 0.326751 0.163376 0.986564i \(-0.447762\pi\)
0.163376 + 0.986564i \(0.447762\pi\)
\(660\) 2.87246e12 0.589259
\(661\) 2.53721e12 0.516951 0.258476 0.966018i \(-0.416780\pi\)
0.258476 + 0.966018i \(0.416780\pi\)
\(662\) −9.28037e12 −1.87804
\(663\) −4.08990e12 −0.822057
\(664\) 8.76746e11 0.175032
\(665\) 1.44070e13 2.85677
\(666\) −2.48433e12 −0.489299
\(667\) −6.90223e11 −0.135028
\(668\) −1.87526e12 −0.364392
\(669\) −2.23400e12 −0.431187
\(670\) 1.66310e13 3.18847
\(671\) −3.28571e12 −0.625717
\(672\) −3.29426e12 −0.623155
\(673\) −4.06419e12 −0.763672 −0.381836 0.924230i \(-0.624708\pi\)
−0.381836 + 0.924230i \(0.624708\pi\)
\(674\) −6.85461e12 −1.27942
\(675\) 2.95924e12 0.548673
\(676\) −3.93361e11 −0.0724487
\(677\) 5.16546e11 0.0945061 0.0472531 0.998883i \(-0.484953\pi\)
0.0472531 + 0.998883i \(0.484953\pi\)
\(678\) −3.82545e12 −0.695263
\(679\) −5.82257e12 −1.05124
\(680\) −1.20503e13 −2.16127
\(681\) −2.23888e12 −0.398904
\(682\) −6.18682e12 −1.09506
\(683\) −6.87660e12 −1.20915 −0.604576 0.796548i \(-0.706657\pi\)
−0.604576 + 0.796548i \(0.706657\pi\)
\(684\) 8.12645e11 0.141954
\(685\) −1.94020e13 −3.36697
\(686\) −4.46476e11 −0.0769731
\(687\) 2.55314e12 0.437289
\(688\) −1.27318e12 −0.216642
\(689\) −3.84120e12 −0.649353
\(690\) 3.40844e12 0.572446
\(691\) −3.00307e12 −0.501089 −0.250544 0.968105i \(-0.580610\pi\)
−0.250544 + 0.968105i \(0.580610\pi\)
\(692\) −1.52320e12 −0.252510
\(693\) 3.59815e12 0.592624
\(694\) −7.76481e12 −1.27061
\(695\) 2.14200e13 3.48248
\(696\) −7.95506e11 −0.128500
\(697\) −4.16955e12 −0.669177
\(698\) −1.58769e12 −0.253173
\(699\) 2.45774e12 0.389394
\(700\) −1.03503e13 −1.62934
\(701\) 2.97144e12 0.464768 0.232384 0.972624i \(-0.425347\pi\)
0.232384 + 0.972624i \(0.425347\pi\)
\(702\) 1.33329e12 0.207208
\(703\) 8.34120e12 1.28804
\(704\) −2.69516e12 −0.413531
\(705\) 1.26682e13 1.93137
\(706\) 7.06394e12 1.07010
\(707\) −4.03571e11 −0.0607480
\(708\) 2.05476e11 0.0307335
\(709\) 7.47955e12 1.11165 0.555824 0.831300i \(-0.312403\pi\)
0.555824 + 0.831300i \(0.312403\pi\)
\(710\) −1.69226e13 −2.49922
\(711\) 4.85224e11 0.0712081
\(712\) −4.98523e12 −0.726985
\(713\) −2.13056e12 −0.308738
\(714\) 1.04412e13 1.50351
\(715\) −1.58233e13 −2.26422
\(716\) −4.36401e12 −0.620550
\(717\) −2.44345e12 −0.345276
\(718\) 8.80999e12 1.23713
\(719\) −8.56748e12 −1.19556 −0.597782 0.801659i \(-0.703951\pi\)
−0.597782 + 0.801659i \(0.703951\pi\)
\(720\) 5.85702e12 0.812233
\(721\) 1.32288e13 1.82310
\(722\) −7.34768e11 −0.100631
\(723\) 2.07516e12 0.282441
\(724\) 2.66374e12 0.360304
\(725\) −6.72772e12 −0.904372
\(726\) −3.16989e12 −0.423476
\(727\) −8.91360e12 −1.18345 −0.591723 0.806142i \(-0.701552\pi\)
−0.591723 + 0.806142i \(0.701552\pi\)
\(728\) 6.74173e12 0.889570
\(729\) 2.82430e11 0.0370370
\(730\) 8.22477e12 1.07194
\(731\) 2.11430e12 0.273866
\(732\) 9.02056e11 0.116127
\(733\) −1.54952e12 −0.198258 −0.0991290 0.995075i \(-0.531606\pi\)
−0.0991290 + 0.995075i \(0.531606\pi\)
\(734\) −5.44287e12 −0.692143
\(735\) −8.54843e12 −1.08042
\(736\) 2.61674e12 0.328708
\(737\) −1.39459e13 −1.74117
\(738\) 1.35925e12 0.168673
\(739\) −1.32347e13 −1.63236 −0.816178 0.577800i \(-0.803911\pi\)
−0.816178 + 0.577800i \(0.803911\pi\)
\(740\) −8.09442e12 −0.992300
\(741\) −4.47654e12 −0.545457
\(742\) 9.80626e12 1.18764
\(743\) −3.83362e12 −0.461487 −0.230743 0.973015i \(-0.574116\pi\)
−0.230743 + 0.973015i \(0.574116\pi\)
\(744\) −2.45554e12 −0.293811
\(745\) −1.00245e13 −1.19223
\(746\) −1.80678e13 −2.13590
\(747\) 7.07665e11 0.0831544
\(748\) −6.98956e12 −0.816381
\(749\) 7.61390e11 0.0883973
\(750\) 2.15696e13 2.48924
\(751\) −7.32602e12 −0.840404 −0.420202 0.907431i \(-0.638041\pi\)
−0.420202 + 0.907431i \(0.638041\pi\)
\(752\) 1.85624e13 2.11668
\(753\) 1.56882e12 0.177826
\(754\) −3.03117e12 −0.341538
\(755\) −1.45556e13 −1.63030
\(756\) −9.87832e11 −0.109985
\(757\) 7.43989e11 0.0823446 0.0411723 0.999152i \(-0.486891\pi\)
0.0411723 + 0.999152i \(0.486891\pi\)
\(758\) −1.50810e13 −1.65927
\(759\) −2.85813e12 −0.312603
\(760\) −1.31895e13 −1.43406
\(761\) 1.54943e13 1.67472 0.837359 0.546653i \(-0.184098\pi\)
0.837359 + 0.546653i \(0.184098\pi\)
\(762\) −7.58592e12 −0.815100
\(763\) −2.46916e13 −2.63748
\(764\) 6.04948e12 0.642388
\(765\) −9.72642e12 −1.02678
\(766\) −6.39400e12 −0.671032
\(767\) −1.13189e12 −0.118093
\(768\) 5.84193e12 0.605942
\(769\) 1.38198e13 1.42506 0.712532 0.701639i \(-0.247548\pi\)
0.712532 + 0.701639i \(0.247548\pi\)
\(770\) 4.03954e13 4.14118
\(771\) 9.77659e12 0.996421
\(772\) 3.32737e12 0.337150
\(773\) −1.14859e13 −1.15706 −0.578531 0.815660i \(-0.696374\pi\)
−0.578531 + 0.815660i \(0.696374\pi\)
\(774\) −6.89251e11 −0.0690308
\(775\) −2.07669e13 −2.06782
\(776\) 5.33054e12 0.527708
\(777\) −1.01394e13 −0.997967
\(778\) −1.46546e12 −0.143405
\(779\) −4.56372e12 −0.444018
\(780\) 4.34411e12 0.420218
\(781\) 1.41903e13 1.36478
\(782\) −8.29376e12 −0.793087
\(783\) −6.42093e11 −0.0610478
\(784\) −1.25258e13 −1.18409
\(785\) 1.93661e13 1.82024
\(786\) 1.21560e13 1.13603
\(787\) −1.14994e13 −1.06853 −0.534265 0.845317i \(-0.679412\pi\)
−0.534265 + 0.845317i \(0.679412\pi\)
\(788\) −3.58396e12 −0.331127
\(789\) 1.36634e12 0.125520
\(790\) 5.44748e12 0.497593
\(791\) −1.56129e13 −1.41805
\(792\) −3.29409e12 −0.297490
\(793\) −4.96907e12 −0.446217
\(794\) 7.55779e12 0.674843
\(795\) −9.13498e12 −0.811065
\(796\) −7.74375e12 −0.683664
\(797\) −3.89098e11 −0.0341583 −0.0170792 0.999854i \(-0.505437\pi\)
−0.0170792 + 0.999854i \(0.505437\pi\)
\(798\) 1.14282e13 0.997622
\(799\) −3.08256e13 −2.67578
\(800\) 2.55058e13 2.20158
\(801\) −4.02383e12 −0.345377
\(802\) 1.46892e13 1.25376
\(803\) −6.89683e12 −0.585369
\(804\) 3.82868e12 0.323145
\(805\) 1.39110e13 1.16755
\(806\) −9.35651e12 −0.780919
\(807\) 9.49763e12 0.788287
\(808\) 3.69467e11 0.0304947
\(809\) −1.48311e13 −1.21732 −0.608661 0.793430i \(-0.708293\pi\)
−0.608661 + 0.793430i \(0.708293\pi\)
\(810\) 3.17076e12 0.258810
\(811\) −2.16295e13 −1.75571 −0.877855 0.478926i \(-0.841026\pi\)
−0.877855 + 0.478926i \(0.841026\pi\)
\(812\) 2.24580e12 0.181288
\(813\) −2.87402e11 −0.0230719
\(814\) 2.33877e13 1.86715
\(815\) 1.99413e13 1.58323
\(816\) −1.42519e13 −1.12530
\(817\) 2.31418e12 0.181718
\(818\) 1.11981e13 0.874489
\(819\) 5.44158e12 0.422618
\(820\) 4.42870e12 0.342069
\(821\) 4.44081e12 0.341129 0.170564 0.985347i \(-0.445441\pi\)
0.170564 + 0.985347i \(0.445441\pi\)
\(822\) −1.53905e13 −1.17579
\(823\) 1.73705e13 1.31982 0.659908 0.751347i \(-0.270595\pi\)
0.659908 + 0.751347i \(0.270595\pi\)
\(824\) −1.21109e13 −0.915176
\(825\) −2.78586e13 −2.09371
\(826\) 2.88961e12 0.215988
\(827\) −9.92279e12 −0.737665 −0.368832 0.929496i \(-0.620242\pi\)
−0.368832 + 0.929496i \(0.620242\pi\)
\(828\) 7.84668e11 0.0580162
\(829\) 4.10308e12 0.301728 0.150864 0.988555i \(-0.451795\pi\)
0.150864 + 0.988555i \(0.451795\pi\)
\(830\) 7.94477e12 0.581072
\(831\) 6.77834e12 0.493081
\(832\) −4.07597e12 −0.294901
\(833\) 2.08009e13 1.49686
\(834\) 1.69913e13 1.21613
\(835\) 2.45666e13 1.74886
\(836\) −7.65033e12 −0.541691
\(837\) −1.98199e12 −0.139584
\(838\) 6.17458e11 0.0432523
\(839\) 9.17820e12 0.639483 0.319741 0.947505i \(-0.396404\pi\)
0.319741 + 0.947505i \(0.396404\pi\)
\(840\) 1.60329e13 1.11110
\(841\) −1.30474e13 −0.899376
\(842\) 3.01248e13 2.06547
\(843\) −2.48970e12 −0.169794
\(844\) 5.90516e12 0.400581
\(845\) 5.15316e12 0.347711
\(846\) 1.00490e13 0.674459
\(847\) −1.29374e13 −0.863715
\(848\) −1.33853e13 −0.888886
\(849\) −1.44293e13 −0.953146
\(850\) −8.08406e13 −5.31183
\(851\) 8.05403e12 0.526417
\(852\) −3.89580e12 −0.253290
\(853\) 1.05675e13 0.683444 0.341722 0.939801i \(-0.388990\pi\)
0.341722 + 0.939801i \(0.388990\pi\)
\(854\) 1.26856e13 0.816114
\(855\) −1.06459e13 −0.681296
\(856\) −6.97050e11 −0.0443743
\(857\) 9.21033e12 0.583259 0.291629 0.956531i \(-0.405803\pi\)
0.291629 + 0.956531i \(0.405803\pi\)
\(858\) −1.25517e13 −0.790696
\(859\) −1.86736e12 −0.117020 −0.0585099 0.998287i \(-0.518635\pi\)
−0.0585099 + 0.998287i \(0.518635\pi\)
\(860\) −2.24571e12 −0.139995
\(861\) 5.54755e12 0.344023
\(862\) −9.68916e12 −0.597728
\(863\) −2.25160e13 −1.38179 −0.690896 0.722954i \(-0.742784\pi\)
−0.690896 + 0.722954i \(0.742784\pi\)
\(864\) 2.43427e12 0.148613
\(865\) 1.99544e13 1.21190
\(866\) 1.72238e13 1.04064
\(867\) 1.40617e13 0.845185
\(868\) 6.93224e12 0.414510
\(869\) −4.56795e12 −0.271727
\(870\) −7.20860e12 −0.426594
\(871\) −2.10907e13 −1.24168
\(872\) 2.26051e13 1.32398
\(873\) 4.30254e12 0.250704
\(874\) −9.07782e12 −0.526236
\(875\) 8.80327e13 5.07701
\(876\) 1.89345e12 0.108639
\(877\) −3.32866e13 −1.90008 −0.950039 0.312130i \(-0.898957\pi\)
−0.950039 + 0.312130i \(0.898957\pi\)
\(878\) −1.75302e13 −0.995548
\(879\) −1.47354e13 −0.832555
\(880\) −5.51387e13 −3.09945
\(881\) 8.33047e12 0.465884 0.232942 0.972491i \(-0.425165\pi\)
0.232942 + 0.972491i \(0.425165\pi\)
\(882\) −6.78098e12 −0.377298
\(883\) −8.05324e12 −0.445808 −0.222904 0.974840i \(-0.571554\pi\)
−0.222904 + 0.974840i \(0.571554\pi\)
\(884\) −1.05705e13 −0.582185
\(885\) −2.69181e12 −0.147503
\(886\) −3.49730e12 −0.190670
\(887\) 1.49443e13 0.810626 0.405313 0.914178i \(-0.367162\pi\)
0.405313 + 0.914178i \(0.367162\pi\)
\(888\) 9.28255e12 0.500967
\(889\) −3.09607e13 −1.66247
\(890\) −4.51744e13 −2.41345
\(891\) −2.65882e12 −0.141332
\(892\) −5.77386e12 −0.305369
\(893\) −3.37397e13 −1.77546
\(894\) −7.95185e12 −0.416341
\(895\) 5.71700e13 2.97827
\(896\) 3.12286e13 1.61870
\(897\) −4.32243e12 −0.222927
\(898\) 2.23190e13 1.14533
\(899\) 4.50597e12 0.230075
\(900\) 7.64829e12 0.388573
\(901\) 2.22282e13 1.12368
\(902\) −1.27961e13 −0.643649
\(903\) −2.81306e12 −0.140794
\(904\) 1.42936e13 0.711842
\(905\) −3.48960e13 −1.72924
\(906\) −1.15461e13 −0.569324
\(907\) −2.42002e13 −1.18737 −0.593686 0.804697i \(-0.702328\pi\)
−0.593686 + 0.804697i \(0.702328\pi\)
\(908\) −5.78647e12 −0.282506
\(909\) 2.98215e11 0.0144875
\(910\) 6.10912e13 2.95320
\(911\) 6.28371e12 0.302262 0.151131 0.988514i \(-0.451708\pi\)
0.151131 + 0.988514i \(0.451708\pi\)
\(912\) −1.55992e13 −0.746666
\(913\) −6.66204e12 −0.317314
\(914\) 1.78697e13 0.846954
\(915\) −1.18172e13 −0.557341
\(916\) 6.59869e12 0.309691
\(917\) 4.96125e13 2.31702
\(918\) −7.71542e12 −0.358565
\(919\) −8.71865e12 −0.403208 −0.201604 0.979467i \(-0.564615\pi\)
−0.201604 + 0.979467i \(0.564615\pi\)
\(920\) −1.27354e13 −0.586096
\(921\) 1.90984e13 0.874639
\(922\) 2.98744e13 1.36147
\(923\) 2.14604e13 0.973264
\(924\) 9.29956e12 0.419700
\(925\) 7.85040e13 3.52577
\(926\) 2.68559e13 1.20030
\(927\) −9.77532e12 −0.434783
\(928\) −5.53421e12 −0.244957
\(929\) 2.66041e13 1.17186 0.585932 0.810360i \(-0.300728\pi\)
0.585932 + 0.810360i \(0.300728\pi\)
\(930\) −2.22512e13 −0.975396
\(931\) 2.27673e13 0.993205
\(932\) 6.35214e12 0.275771
\(933\) 7.10414e12 0.306933
\(934\) 2.76395e13 1.18842
\(935\) 9.15656e13 3.91814
\(936\) −4.98175e12 −0.212149
\(937\) −1.41793e13 −0.600933 −0.300466 0.953792i \(-0.597142\pi\)
−0.300466 + 0.953792i \(0.597142\pi\)
\(938\) 5.38428e13 2.27099
\(939\) 9.34082e12 0.392094
\(940\) 3.27415e13 1.36780
\(941\) −1.47256e13 −0.612238 −0.306119 0.951993i \(-0.599031\pi\)
−0.306119 + 0.951993i \(0.599031\pi\)
\(942\) 1.53620e13 0.635651
\(943\) −4.40660e12 −0.181468
\(944\) −3.94424e12 −0.161655
\(945\) 1.29409e13 0.527864
\(946\) 6.48868e12 0.263419
\(947\) −1.08853e13 −0.439812 −0.219906 0.975521i \(-0.570575\pi\)
−0.219906 + 0.975521i \(0.570575\pi\)
\(948\) 1.25408e12 0.0504299
\(949\) −1.04303e13 −0.417444
\(950\) −8.84830e13 −3.52455
\(951\) −2.36466e13 −0.937469
\(952\) −3.90128e13 −1.53936
\(953\) 2.18030e12 0.0856244 0.0428122 0.999083i \(-0.486368\pi\)
0.0428122 + 0.999083i \(0.486368\pi\)
\(954\) −7.24626e12 −0.283235
\(955\) −7.92502e13 −3.08308
\(956\) −6.31519e12 −0.244527
\(957\) 6.04473e12 0.232956
\(958\) −1.92607e12 −0.0738800
\(959\) −6.28138e13 −2.39812
\(960\) −9.69329e12 −0.368342
\(961\) −1.25308e13 −0.473939
\(962\) 3.53699e13 1.33152
\(963\) −5.62623e11 −0.0210814
\(964\) 5.36333e12 0.200027
\(965\) −4.35896e13 −1.61812
\(966\) 1.10348e13 0.407725
\(967\) 1.05073e13 0.386431 0.193215 0.981156i \(-0.438108\pi\)
0.193215 + 0.981156i \(0.438108\pi\)
\(968\) 1.18441e13 0.433574
\(969\) 2.59047e13 0.943892
\(970\) 4.83035e13 1.75189
\(971\) −3.59410e13 −1.29749 −0.648745 0.761006i \(-0.724706\pi\)
−0.648745 + 0.761006i \(0.724706\pi\)
\(972\) 7.29951e11 0.0262298
\(973\) 6.93471e13 2.48039
\(974\) 5.26012e13 1.87275
\(975\) −4.21314e13 −1.49309
\(976\) −1.73155e13 −0.610817
\(977\) 2.61860e13 0.919484 0.459742 0.888053i \(-0.347942\pi\)
0.459742 + 0.888053i \(0.347942\pi\)
\(978\) 1.58183e13 0.552886
\(979\) 3.78807e13 1.31794
\(980\) −2.20938e13 −0.765161
\(981\) 1.82457e13 0.628999
\(982\) 2.52349e13 0.865964
\(983\) −7.35083e11 −0.0251099 −0.0125550 0.999921i \(-0.503996\pi\)
−0.0125550 + 0.999921i \(0.503996\pi\)
\(984\) −5.07876e12 −0.172695
\(985\) 4.69511e13 1.58921
\(986\) 1.75407e13 0.591018
\(987\) 4.10132e13 1.37561
\(988\) −1.15698e13 −0.386296
\(989\) 2.23451e12 0.0742674
\(990\) −2.98499e13 −0.987608
\(991\) 1.94771e13 0.641493 0.320747 0.947165i \(-0.396066\pi\)
0.320747 + 0.947165i \(0.396066\pi\)
\(992\) −1.70828e13 −0.560088
\(993\) 2.79884e13 0.913495
\(994\) −5.47866e13 −1.78006
\(995\) 1.01446e14 3.28118
\(996\) 1.82899e12 0.0588904
\(997\) −5.96015e13 −1.91042 −0.955210 0.295930i \(-0.904371\pi\)
−0.955210 + 0.295930i \(0.904371\pi\)
\(998\) −4.94298e13 −1.57725
\(999\) 7.49240e12 0.238000
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 177.10.a.a.1.6 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.6 21 1.1 even 1 trivial