Properties

Label 177.10.a.b.1.15
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 1.15
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+16.0816 q^{2} -81.0000 q^{3} -253.381 q^{4} +2048.36 q^{5} -1302.61 q^{6} -8880.78 q^{7} -12308.6 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+16.0816 q^{2} -81.0000 q^{3} -253.381 q^{4} +2048.36 q^{5} -1302.61 q^{6} -8880.78 q^{7} -12308.6 q^{8} +6561.00 q^{9} +32940.9 q^{10} +70959.2 q^{11} +20523.9 q^{12} -57764.1 q^{13} -142817. q^{14} -165917. q^{15} -68210.6 q^{16} +574690. q^{17} +105512. q^{18} -675543. q^{19} -519016. q^{20} +719343. q^{21} +1.14114e6 q^{22} +325234. q^{23} +996995. q^{24} +2.24265e6 q^{25} -928941. q^{26} -531441. q^{27} +2.25022e6 q^{28} -2.59800e6 q^{29} -2.66822e6 q^{30} +3.69152e6 q^{31} +5.20505e6 q^{32} -5.74770e6 q^{33} +9.24195e6 q^{34} -1.81910e7 q^{35} -1.66244e6 q^{36} -1.59909e7 q^{37} -1.08638e7 q^{38} +4.67889e6 q^{39} -2.52124e7 q^{40} +2.01221e7 q^{41} +1.15682e7 q^{42} -2.99619e7 q^{43} -1.79797e7 q^{44} +1.34393e7 q^{45} +5.23028e6 q^{46} +1.30817e7 q^{47} +5.52506e6 q^{48} +3.85146e7 q^{49} +3.60654e7 q^{50} -4.65499e7 q^{51} +1.46364e7 q^{52} -4.33294e7 q^{53} -8.54643e6 q^{54} +1.45350e8 q^{55} +1.09310e8 q^{56} +5.47190e7 q^{57} -4.17801e7 q^{58} -1.21174e7 q^{59} +4.20403e7 q^{60} +1.48079e8 q^{61} +5.93656e7 q^{62} -5.82668e7 q^{63} +1.18630e8 q^{64} -1.18322e8 q^{65} -9.24323e7 q^{66} +2.62228e7 q^{67} -1.45616e8 q^{68} -2.63439e7 q^{69} -2.92541e8 q^{70} -3.59885e8 q^{71} -8.07566e7 q^{72} -3.34147e8 q^{73} -2.57160e8 q^{74} -1.81654e8 q^{75} +1.71170e8 q^{76} -6.30173e8 q^{77} +7.52442e7 q^{78} -6.43140e8 q^{79} -1.39720e8 q^{80} +4.30467e7 q^{81} +3.23596e8 q^{82} -3.84290e8 q^{83} -1.82268e8 q^{84} +1.17717e9 q^{85} -4.81835e8 q^{86} +2.10438e8 q^{87} -8.73407e8 q^{88} +3.95175e8 q^{89} +2.16125e8 q^{90} +5.12990e8 q^{91} -8.24081e7 q^{92} -2.99013e8 q^{93} +2.10374e8 q^{94} -1.38375e9 q^{95} -4.21609e8 q^{96} -3.41540e8 q^{97} +6.19377e8 q^{98} +4.65564e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 16.0816 0.710714 0.355357 0.934731i \(-0.384359\pi\)
0.355357 + 0.934731i \(0.384359\pi\)
\(3\) −81.0000 −0.577350
\(4\) −253.381 −0.494885
\(5\) 2048.36 1.46569 0.732843 0.680398i \(-0.238193\pi\)
0.732843 + 0.680398i \(0.238193\pi\)
\(6\) −1302.61 −0.410331
\(7\) −8880.78 −1.39801 −0.699004 0.715118i \(-0.746373\pi\)
−0.699004 + 0.715118i \(0.746373\pi\)
\(8\) −12308.6 −1.06244
\(9\) 6561.00 0.333333
\(10\) 32940.9 1.04168
\(11\) 70959.2 1.46131 0.730654 0.682748i \(-0.239215\pi\)
0.730654 + 0.682748i \(0.239215\pi\)
\(12\) 20523.9 0.285722
\(13\) −57764.1 −0.560936 −0.280468 0.959863i \(-0.590490\pi\)
−0.280468 + 0.959863i \(0.590490\pi\)
\(14\) −142817. −0.993584
\(15\) −165917. −0.846214
\(16\) −68210.6 −0.260203
\(17\) 574690. 1.66884 0.834418 0.551132i \(-0.185804\pi\)
0.834418 + 0.551132i \(0.185804\pi\)
\(18\) 105512. 0.236905
\(19\) −675543. −1.18922 −0.594610 0.804015i \(-0.702693\pi\)
−0.594610 + 0.804015i \(0.702693\pi\)
\(20\) −519016. −0.725347
\(21\) 719343. 0.807141
\(22\) 1.14114e6 1.03857
\(23\) 325234. 0.242337 0.121169 0.992632i \(-0.461336\pi\)
0.121169 + 0.992632i \(0.461336\pi\)
\(24\) 996995. 0.613398
\(25\) 2.24265e6 1.14823
\(26\) −928941. −0.398665
\(27\) −531441. −0.192450
\(28\) 2.25022e6 0.691854
\(29\) −2.59800e6 −0.682101 −0.341050 0.940045i \(-0.610783\pi\)
−0.341050 + 0.940045i \(0.610783\pi\)
\(30\) −2.66822e6 −0.601416
\(31\) 3.69152e6 0.717922 0.358961 0.933352i \(-0.383131\pi\)
0.358961 + 0.933352i \(0.383131\pi\)
\(32\) 5.20505e6 0.877506
\(33\) −5.74770e6 −0.843687
\(34\) 9.24195e6 1.18607
\(35\) −1.81910e7 −2.04904
\(36\) −1.66244e6 −0.164962
\(37\) −1.59909e7 −1.40271 −0.701353 0.712814i \(-0.747420\pi\)
−0.701353 + 0.712814i \(0.747420\pi\)
\(38\) −1.08638e7 −0.845195
\(39\) 4.67889e6 0.323856
\(40\) −2.52124e7 −1.55720
\(41\) 2.01221e7 1.11210 0.556052 0.831147i \(-0.312316\pi\)
0.556052 + 0.831147i \(0.312316\pi\)
\(42\) 1.15682e7 0.573646
\(43\) −2.99619e7 −1.33647 −0.668237 0.743948i \(-0.732951\pi\)
−0.668237 + 0.743948i \(0.732951\pi\)
\(44\) −1.79797e7 −0.723180
\(45\) 1.34393e7 0.488562
\(46\) 5.23028e6 0.172232
\(47\) 1.30817e7 0.391041 0.195521 0.980700i \(-0.437360\pi\)
0.195521 + 0.980700i \(0.437360\pi\)
\(48\) 5.52506e6 0.150228
\(49\) 3.85146e7 0.954428
\(50\) 3.60654e7 0.816067
\(51\) −4.65499e7 −0.963503
\(52\) 1.46364e7 0.277599
\(53\) −4.33294e7 −0.754295 −0.377148 0.926153i \(-0.623095\pi\)
−0.377148 + 0.926153i \(0.623095\pi\)
\(54\) −8.54643e6 −0.136777
\(55\) 1.45350e8 2.14182
\(56\) 1.09310e8 1.48529
\(57\) 5.47190e7 0.686596
\(58\) −4.17801e7 −0.484779
\(59\) −1.21174e7 −0.130189
\(60\) 4.20403e7 0.418779
\(61\) 1.48079e8 1.36934 0.684668 0.728855i \(-0.259947\pi\)
0.684668 + 0.728855i \(0.259947\pi\)
\(62\) 5.93656e7 0.510238
\(63\) −5.82668e7 −0.466003
\(64\) 1.18630e8 0.883859
\(65\) −1.18322e8 −0.822156
\(66\) −9.24323e7 −0.599620
\(67\) 2.62228e7 0.158980 0.0794899 0.996836i \(-0.474671\pi\)
0.0794899 + 0.996836i \(0.474671\pi\)
\(68\) −1.45616e8 −0.825883
\(69\) −2.63439e7 −0.139913
\(70\) −2.92541e8 −1.45628
\(71\) −3.59885e8 −1.68074 −0.840372 0.542010i \(-0.817663\pi\)
−0.840372 + 0.542010i \(0.817663\pi\)
\(72\) −8.07566e7 −0.354145
\(73\) −3.34147e8 −1.37716 −0.688580 0.725160i \(-0.741766\pi\)
−0.688580 + 0.725160i \(0.741766\pi\)
\(74\) −2.57160e8 −0.996922
\(75\) −1.81654e8 −0.662934
\(76\) 1.71170e8 0.588527
\(77\) −6.30173e8 −2.04292
\(78\) 7.52442e7 0.230169
\(79\) −6.43140e8 −1.85773 −0.928867 0.370413i \(-0.879216\pi\)
−0.928867 + 0.370413i \(0.879216\pi\)
\(80\) −1.39720e8 −0.381376
\(81\) 4.30467e7 0.111111
\(82\) 3.23596e8 0.790388
\(83\) −3.84290e8 −0.888808 −0.444404 0.895826i \(-0.646585\pi\)
−0.444404 + 0.895826i \(0.646585\pi\)
\(84\) −1.82268e8 −0.399442
\(85\) 1.17717e9 2.44599
\(86\) −4.81835e8 −0.949852
\(87\) 2.10438e8 0.393811
\(88\) −8.73407e8 −1.55255
\(89\) 3.95175e8 0.667628 0.333814 0.942639i \(-0.391664\pi\)
0.333814 + 0.942639i \(0.391664\pi\)
\(90\) 2.16125e8 0.347228
\(91\) 5.12990e8 0.784193
\(92\) −8.24081e7 −0.119929
\(93\) −2.99013e8 −0.414493
\(94\) 2.10374e8 0.277918
\(95\) −1.38375e9 −1.74302
\(96\) −4.21609e8 −0.506628
\(97\) −3.41540e8 −0.391714 −0.195857 0.980632i \(-0.562749\pi\)
−0.195857 + 0.980632i \(0.562749\pi\)
\(98\) 6.19377e8 0.678325
\(99\) 4.65564e8 0.487103
\(100\) −5.68245e8 −0.568245
\(101\) −1.26167e9 −1.20643 −0.603213 0.797580i \(-0.706113\pi\)
−0.603213 + 0.797580i \(0.706113\pi\)
\(102\) −7.48598e8 −0.684775
\(103\) −3.05119e8 −0.267117 −0.133559 0.991041i \(-0.542640\pi\)
−0.133559 + 0.991041i \(0.542640\pi\)
\(104\) 7.10994e8 0.595958
\(105\) 1.47347e9 1.18301
\(106\) −6.96807e8 −0.536088
\(107\) −1.23762e9 −0.912769 −0.456385 0.889783i \(-0.650856\pi\)
−0.456385 + 0.889783i \(0.650856\pi\)
\(108\) 1.34657e8 0.0952407
\(109\) −9.06241e8 −0.614928 −0.307464 0.951560i \(-0.599480\pi\)
−0.307464 + 0.951560i \(0.599480\pi\)
\(110\) 2.33746e9 1.52222
\(111\) 1.29527e9 0.809852
\(112\) 6.05764e8 0.363766
\(113\) −1.77528e9 −1.02427 −0.512135 0.858905i \(-0.671145\pi\)
−0.512135 + 0.858905i \(0.671145\pi\)
\(114\) 8.79970e8 0.487973
\(115\) 6.66195e8 0.355190
\(116\) 6.58285e8 0.337562
\(117\) −3.78990e8 −0.186979
\(118\) −1.94867e8 −0.0925271
\(119\) −5.10370e9 −2.33305
\(120\) 2.04220e9 0.899048
\(121\) 2.67727e9 1.13542
\(122\) 2.38136e9 0.973207
\(123\) −1.62989e9 −0.642074
\(124\) −9.35362e8 −0.355289
\(125\) 5.93043e8 0.217266
\(126\) −9.37024e8 −0.331195
\(127\) 4.23992e9 1.44624 0.723120 0.690722i \(-0.242707\pi\)
0.723120 + 0.690722i \(0.242707\pi\)
\(128\) −7.57231e8 −0.249335
\(129\) 2.42691e9 0.771614
\(130\) −1.90280e9 −0.584318
\(131\) −1.60747e9 −0.476895 −0.238447 0.971155i \(-0.576638\pi\)
−0.238447 + 0.971155i \(0.576638\pi\)
\(132\) 1.45636e9 0.417528
\(133\) 5.99935e9 1.66254
\(134\) 4.21705e8 0.112989
\(135\) −1.08858e9 −0.282071
\(136\) −7.07362e9 −1.77303
\(137\) −6.17427e9 −1.49742 −0.748709 0.662899i \(-0.769326\pi\)
−0.748709 + 0.662899i \(0.769326\pi\)
\(138\) −4.23653e8 −0.0994384
\(139\) −6.22009e9 −1.41329 −0.706643 0.707571i \(-0.749791\pi\)
−0.706643 + 0.707571i \(0.749791\pi\)
\(140\) 4.60926e9 1.01404
\(141\) −1.05961e9 −0.225768
\(142\) −5.78754e9 −1.19453
\(143\) −4.09890e9 −0.819700
\(144\) −4.47530e8 −0.0867343
\(145\) −5.32164e9 −0.999746
\(146\) −5.37363e9 −0.978768
\(147\) −3.11968e9 −0.551039
\(148\) 4.05181e9 0.694178
\(149\) 1.18843e10 1.97531 0.987657 0.156630i \(-0.0500630\pi\)
0.987657 + 0.156630i \(0.0500630\pi\)
\(150\) −2.92130e9 −0.471156
\(151\) −7.78951e9 −1.21931 −0.609654 0.792667i \(-0.708692\pi\)
−0.609654 + 0.792667i \(0.708692\pi\)
\(152\) 8.31497e9 1.26347
\(153\) 3.77054e9 0.556279
\(154\) −1.01342e10 −1.45193
\(155\) 7.56155e9 1.05225
\(156\) −1.18554e9 −0.160272
\(157\) 9.52831e9 1.25161 0.625803 0.779981i \(-0.284771\pi\)
0.625803 + 0.779981i \(0.284771\pi\)
\(158\) −1.03427e10 −1.32032
\(159\) 3.50968e9 0.435492
\(160\) 1.06618e10 1.28615
\(161\) −2.88833e9 −0.338789
\(162\) 6.92261e8 0.0789682
\(163\) −6.42572e9 −0.712981 −0.356490 0.934299i \(-0.616027\pi\)
−0.356490 + 0.934299i \(0.616027\pi\)
\(164\) −5.09856e9 −0.550364
\(165\) −1.17733e10 −1.23658
\(166\) −6.18001e9 −0.631688
\(167\) 1.74275e9 0.173385 0.0866925 0.996235i \(-0.472370\pi\)
0.0866925 + 0.996235i \(0.472370\pi\)
\(168\) −8.85409e9 −0.857535
\(169\) −7.26781e9 −0.685351
\(170\) 1.89308e10 1.73840
\(171\) −4.43224e9 −0.396406
\(172\) 7.59178e9 0.661402
\(173\) −1.30581e9 −0.110834 −0.0554168 0.998463i \(-0.517649\pi\)
−0.0554168 + 0.998463i \(0.517649\pi\)
\(174\) 3.38419e9 0.279887
\(175\) −1.99164e10 −1.60524
\(176\) −4.84017e9 −0.380237
\(177\) 9.81506e8 0.0751646
\(178\) 6.35506e9 0.474493
\(179\) −9.50453e9 −0.691978 −0.345989 0.938239i \(-0.612456\pi\)
−0.345989 + 0.938239i \(0.612456\pi\)
\(180\) −3.40526e9 −0.241782
\(181\) 6.40309e9 0.443441 0.221721 0.975110i \(-0.428833\pi\)
0.221721 + 0.975110i \(0.428833\pi\)
\(182\) 8.24972e9 0.557337
\(183\) −1.19944e10 −0.790587
\(184\) −4.00316e9 −0.257468
\(185\) −3.27552e10 −2.05593
\(186\) −4.80862e9 −0.294586
\(187\) 4.07796e10 2.43868
\(188\) −3.31465e9 −0.193521
\(189\) 4.71961e9 0.269047
\(190\) −2.22530e10 −1.23879
\(191\) 2.35967e10 1.28293 0.641463 0.767154i \(-0.278328\pi\)
0.641463 + 0.767154i \(0.278328\pi\)
\(192\) −9.60899e9 −0.510296
\(193\) −1.82705e9 −0.0947857 −0.0473928 0.998876i \(-0.515091\pi\)
−0.0473928 + 0.998876i \(0.515091\pi\)
\(194\) −5.49253e9 −0.278397
\(195\) 9.58405e9 0.474672
\(196\) −9.75888e9 −0.472332
\(197\) 1.08956e10 0.515409 0.257705 0.966224i \(-0.417034\pi\)
0.257705 + 0.966224i \(0.417034\pi\)
\(198\) 7.48702e9 0.346191
\(199\) 3.90626e10 1.76572 0.882862 0.469633i \(-0.155614\pi\)
0.882862 + 0.469633i \(0.155614\pi\)
\(200\) −2.76038e10 −1.21993
\(201\) −2.12405e9 −0.0917871
\(202\) −2.02898e10 −0.857424
\(203\) 2.30723e10 0.953583
\(204\) 1.17949e10 0.476824
\(205\) 4.12172e10 1.63000
\(206\) −4.90681e9 −0.189844
\(207\) 2.13386e9 0.0807791
\(208\) 3.94013e9 0.145957
\(209\) −4.79360e10 −1.73782
\(210\) 2.36958e10 0.840785
\(211\) −1.23713e10 −0.429678 −0.214839 0.976649i \(-0.568923\pi\)
−0.214839 + 0.976649i \(0.568923\pi\)
\(212\) 1.09789e10 0.373290
\(213\) 2.91507e10 0.970378
\(214\) −1.99030e10 −0.648718
\(215\) −6.13726e10 −1.95885
\(216\) 6.54128e9 0.204466
\(217\) −3.27836e10 −1.00366
\(218\) −1.45738e10 −0.437038
\(219\) 2.70659e10 0.795104
\(220\) −3.68290e10 −1.05995
\(221\) −3.31965e10 −0.936110
\(222\) 2.08300e10 0.575573
\(223\) 8.76793e9 0.237424 0.118712 0.992929i \(-0.462123\pi\)
0.118712 + 0.992929i \(0.462123\pi\)
\(224\) −4.62249e10 −1.22676
\(225\) 1.47140e10 0.382745
\(226\) −2.85494e10 −0.727963
\(227\) 1.40496e10 0.351195 0.175597 0.984462i \(-0.443814\pi\)
0.175597 + 0.984462i \(0.443814\pi\)
\(228\) −1.38648e10 −0.339786
\(229\) 5.68805e10 1.36680 0.683398 0.730046i \(-0.260501\pi\)
0.683398 + 0.730046i \(0.260501\pi\)
\(230\) 1.07135e10 0.252439
\(231\) 5.10440e10 1.17948
\(232\) 3.19777e10 0.724689
\(233\) −7.66188e10 −1.70307 −0.851537 0.524294i \(-0.824329\pi\)
−0.851537 + 0.524294i \(0.824329\pi\)
\(234\) −6.09478e9 −0.132888
\(235\) 2.67959e10 0.573143
\(236\) 3.07031e9 0.0644286
\(237\) 5.20943e10 1.07256
\(238\) −8.20757e10 −1.65813
\(239\) −2.35739e9 −0.0467348 −0.0233674 0.999727i \(-0.507439\pi\)
−0.0233674 + 0.999727i \(0.507439\pi\)
\(240\) 1.13173e10 0.220187
\(241\) −6.47507e10 −1.23642 −0.618212 0.786011i \(-0.712143\pi\)
−0.618212 + 0.786011i \(0.712143\pi\)
\(242\) 4.30548e10 0.806960
\(243\) −3.48678e9 −0.0641500
\(244\) −3.75205e10 −0.677665
\(245\) 7.88917e10 1.39889
\(246\) −2.62113e10 −0.456331
\(247\) 3.90222e10 0.667075
\(248\) −4.54373e10 −0.762747
\(249\) 3.11275e10 0.513154
\(250\) 9.53710e9 0.154414
\(251\) 7.83882e10 1.24658 0.623288 0.781992i \(-0.285796\pi\)
0.623288 + 0.781992i \(0.285796\pi\)
\(252\) 1.47637e10 0.230618
\(253\) 2.30783e10 0.354129
\(254\) 6.81848e10 1.02786
\(255\) −9.53509e10 −1.41219
\(256\) −7.29158e10 −1.06107
\(257\) 1.12417e11 1.60743 0.803716 0.595013i \(-0.202853\pi\)
0.803716 + 0.595013i \(0.202853\pi\)
\(258\) 3.90287e10 0.548397
\(259\) 1.42012e11 1.96099
\(260\) 2.99805e10 0.406873
\(261\) −1.70455e10 −0.227367
\(262\) −2.58508e10 −0.338936
\(263\) −3.79023e10 −0.488501 −0.244250 0.969712i \(-0.578542\pi\)
−0.244250 + 0.969712i \(0.578542\pi\)
\(264\) 7.07460e10 0.896363
\(265\) −8.87541e10 −1.10556
\(266\) 9.64793e10 1.18159
\(267\) −3.20092e10 −0.385455
\(268\) −6.64436e9 −0.0786768
\(269\) −4.07264e10 −0.474232 −0.237116 0.971481i \(-0.576202\pi\)
−0.237116 + 0.971481i \(0.576202\pi\)
\(270\) −1.75062e10 −0.200472
\(271\) −9.29803e10 −1.04720 −0.523599 0.851965i \(-0.675411\pi\)
−0.523599 + 0.851965i \(0.675411\pi\)
\(272\) −3.92000e10 −0.434236
\(273\) −4.15522e10 −0.452754
\(274\) −9.92923e10 −1.06424
\(275\) 1.59136e11 1.67793
\(276\) 6.67506e9 0.0692411
\(277\) 6.68436e10 0.682183 0.341091 0.940030i \(-0.389203\pi\)
0.341091 + 0.940030i \(0.389203\pi\)
\(278\) −1.00029e11 −1.00444
\(279\) 2.42201e10 0.239307
\(280\) 2.23905e11 2.17698
\(281\) 1.78845e11 1.71119 0.855595 0.517647i \(-0.173192\pi\)
0.855595 + 0.517647i \(0.173192\pi\)
\(282\) −1.70403e10 −0.160456
\(283\) 8.69585e10 0.805885 0.402943 0.915225i \(-0.367987\pi\)
0.402943 + 0.915225i \(0.367987\pi\)
\(284\) 9.11882e10 0.831776
\(285\) 1.12084e11 1.00633
\(286\) −6.59169e10 −0.582572
\(287\) −1.78700e11 −1.55473
\(288\) 3.41504e10 0.292502
\(289\) 2.11681e11 1.78501
\(290\) −8.55806e10 −0.710533
\(291\) 2.76648e10 0.226156
\(292\) 8.46666e10 0.681537
\(293\) −1.40207e11 −1.11139 −0.555693 0.831387i \(-0.687547\pi\)
−0.555693 + 0.831387i \(0.687547\pi\)
\(294\) −5.01696e10 −0.391631
\(295\) −2.48207e10 −0.190816
\(296\) 1.96826e11 1.49028
\(297\) −3.77106e10 −0.281229
\(298\) 1.91119e11 1.40388
\(299\) −1.87868e10 −0.135936
\(300\) 4.60278e10 0.328076
\(301\) 2.66085e11 1.86840
\(302\) −1.25268e11 −0.866580
\(303\) 1.02196e11 0.696531
\(304\) 4.60792e10 0.309438
\(305\) 3.03319e11 2.00702
\(306\) 6.06365e10 0.395355
\(307\) −1.99661e11 −1.28283 −0.641417 0.767192i \(-0.721653\pi\)
−0.641417 + 0.767192i \(0.721653\pi\)
\(308\) 1.59674e11 1.01101
\(309\) 2.47147e10 0.154220
\(310\) 1.21602e11 0.747848
\(311\) −1.99334e11 −1.20826 −0.604130 0.796886i \(-0.706479\pi\)
−0.604130 + 0.796886i \(0.706479\pi\)
\(312\) −5.75905e10 −0.344077
\(313\) −1.31175e11 −0.772508 −0.386254 0.922393i \(-0.626231\pi\)
−0.386254 + 0.922393i \(0.626231\pi\)
\(314\) 1.53231e11 0.889534
\(315\) −1.19351e11 −0.683014
\(316\) 1.62960e11 0.919366
\(317\) 8.58630e10 0.477573 0.238786 0.971072i \(-0.423250\pi\)
0.238786 + 0.971072i \(0.423250\pi\)
\(318\) 5.64414e10 0.309511
\(319\) −1.84352e11 −0.996760
\(320\) 2.42996e11 1.29546
\(321\) 1.00247e11 0.526987
\(322\) −4.64490e10 −0.240782
\(323\) −3.88228e11 −1.98461
\(324\) −1.09072e10 −0.0549873
\(325\) −1.29544e11 −0.644086
\(326\) −1.03336e11 −0.506725
\(327\) 7.34055e10 0.355029
\(328\) −2.47674e11 −1.18154
\(329\) −1.16175e11 −0.546679
\(330\) −1.89335e11 −0.878855
\(331\) −8.30618e10 −0.380343 −0.190171 0.981751i \(-0.560904\pi\)
−0.190171 + 0.981751i \(0.560904\pi\)
\(332\) 9.73720e10 0.439858
\(333\) −1.04917e11 −0.467568
\(334\) 2.80263e10 0.123227
\(335\) 5.37136e10 0.233015
\(336\) −4.90668e10 −0.210020
\(337\) −1.49661e11 −0.632083 −0.316042 0.948745i \(-0.602354\pi\)
−0.316042 + 0.948745i \(0.602354\pi\)
\(338\) −1.16878e11 −0.487089
\(339\) 1.43798e11 0.591362
\(340\) −2.98273e11 −1.21048
\(341\) 2.61947e11 1.04911
\(342\) −7.12776e10 −0.281732
\(343\) 1.63318e10 0.0637104
\(344\) 3.68788e11 1.41992
\(345\) −5.39618e10 −0.205069
\(346\) −2.09995e10 −0.0787710
\(347\) −2.38151e11 −0.881801 −0.440900 0.897556i \(-0.645341\pi\)
−0.440900 + 0.897556i \(0.645341\pi\)
\(348\) −5.33211e10 −0.194891
\(349\) 2.91117e11 1.05040 0.525199 0.850980i \(-0.323991\pi\)
0.525199 + 0.850980i \(0.323991\pi\)
\(350\) −3.20289e11 −1.14087
\(351\) 3.06982e10 0.107952
\(352\) 3.69347e11 1.28231
\(353\) 4.63430e11 1.58854 0.794270 0.607565i \(-0.207854\pi\)
0.794270 + 0.607565i \(0.207854\pi\)
\(354\) 1.57842e10 0.0534205
\(355\) −7.37174e11 −2.46344
\(356\) −1.00130e11 −0.330399
\(357\) 4.13399e11 1.34699
\(358\) −1.52848e11 −0.491798
\(359\) −3.43784e11 −1.09235 −0.546173 0.837672i \(-0.683916\pi\)
−0.546173 + 0.837672i \(0.683916\pi\)
\(360\) −1.65418e11 −0.519066
\(361\) 1.33671e11 0.414242
\(362\) 1.02972e11 0.315160
\(363\) −2.16859e11 −0.655536
\(364\) −1.29982e11 −0.388086
\(365\) −6.84453e11 −2.01849
\(366\) −1.92890e11 −0.561881
\(367\) −5.88441e11 −1.69319 −0.846595 0.532237i \(-0.821352\pi\)
−0.846595 + 0.532237i \(0.821352\pi\)
\(368\) −2.21844e10 −0.0630568
\(369\) 1.32021e11 0.370701
\(370\) −5.26757e11 −1.46118
\(371\) 3.84799e11 1.05451
\(372\) 7.57643e10 0.205126
\(373\) −4.80252e11 −1.28463 −0.642317 0.766439i \(-0.722027\pi\)
−0.642317 + 0.766439i \(0.722027\pi\)
\(374\) 6.55802e11 1.73321
\(375\) −4.80365e10 −0.125438
\(376\) −1.61017e11 −0.415456
\(377\) 1.50071e11 0.382615
\(378\) 7.58990e10 0.191215
\(379\) 7.91147e10 0.196961 0.0984806 0.995139i \(-0.468602\pi\)
0.0984806 + 0.995139i \(0.468602\pi\)
\(380\) 3.50618e11 0.862596
\(381\) −3.43433e11 −0.834988
\(382\) 3.79474e11 0.911793
\(383\) 5.13977e11 1.22053 0.610266 0.792197i \(-0.291063\pi\)
0.610266 + 0.792197i \(0.291063\pi\)
\(384\) 6.13357e10 0.143954
\(385\) −1.29082e12 −2.99428
\(386\) −2.93819e10 −0.0673655
\(387\) −1.96580e11 −0.445492
\(388\) 8.65400e10 0.193854
\(389\) 5.24137e11 1.16057 0.580286 0.814413i \(-0.302941\pi\)
0.580286 + 0.814413i \(0.302941\pi\)
\(390\) 1.54127e11 0.337356
\(391\) 1.86909e11 0.404421
\(392\) −4.74060e11 −1.01402
\(393\) 1.30205e11 0.275335
\(394\) 1.75219e11 0.366309
\(395\) −1.31738e12 −2.72286
\(396\) −1.17965e11 −0.241060
\(397\) 1.37630e11 0.278071 0.139036 0.990287i \(-0.455600\pi\)
0.139036 + 0.990287i \(0.455600\pi\)
\(398\) 6.28191e11 1.25492
\(399\) −4.85947e11 −0.959867
\(400\) −1.52972e11 −0.298774
\(401\) 9.21929e11 1.78052 0.890261 0.455450i \(-0.150522\pi\)
0.890261 + 0.455450i \(0.150522\pi\)
\(402\) −3.41581e10 −0.0652344
\(403\) −2.13237e11 −0.402708
\(404\) 3.19685e11 0.597043
\(405\) 8.81751e10 0.162854
\(406\) 3.71040e11 0.677725
\(407\) −1.13471e12 −2.04978
\(408\) 5.72963e11 1.02366
\(409\) −2.01994e11 −0.356931 −0.178466 0.983946i \(-0.557113\pi\)
−0.178466 + 0.983946i \(0.557113\pi\)
\(410\) 6.62840e11 1.15846
\(411\) 5.00116e11 0.864535
\(412\) 7.73115e10 0.132192
\(413\) 1.07612e11 0.182005
\(414\) 3.43159e10 0.0574108
\(415\) −7.87164e11 −1.30271
\(416\) −3.00665e11 −0.492225
\(417\) 5.03827e11 0.815961
\(418\) −7.70889e11 −1.23509
\(419\) 5.01944e11 0.795596 0.397798 0.917473i \(-0.369775\pi\)
0.397798 + 0.917473i \(0.369775\pi\)
\(420\) −3.73350e11 −0.585457
\(421\) −7.66121e11 −1.18858 −0.594289 0.804251i \(-0.702567\pi\)
−0.594289 + 0.804251i \(0.702567\pi\)
\(422\) −1.98950e11 −0.305379
\(423\) 8.58287e10 0.130347
\(424\) 5.33323e11 0.801390
\(425\) 1.28883e12 1.91622
\(426\) 4.68791e11 0.689661
\(427\) −1.31506e12 −1.91434
\(428\) 3.13590e11 0.451716
\(429\) 3.32011e11 0.473254
\(430\) −9.86972e11 −1.39218
\(431\) −2.97428e11 −0.415177 −0.207589 0.978216i \(-0.566562\pi\)
−0.207589 + 0.978216i \(0.566562\pi\)
\(432\) 3.62499e10 0.0500761
\(433\) 1.09804e12 1.50114 0.750569 0.660792i \(-0.229779\pi\)
0.750569 + 0.660792i \(0.229779\pi\)
\(434\) −5.27213e11 −0.713316
\(435\) 4.31053e11 0.577203
\(436\) 2.29625e11 0.304319
\(437\) −2.19709e11 −0.288192
\(438\) 4.35264e11 0.565092
\(439\) −8.54029e11 −1.09744 −0.548722 0.836005i \(-0.684886\pi\)
−0.548722 + 0.836005i \(0.684886\pi\)
\(440\) −1.78905e12 −2.27555
\(441\) 2.52694e11 0.318143
\(442\) −5.33853e11 −0.665307
\(443\) −3.63618e11 −0.448568 −0.224284 0.974524i \(-0.572004\pi\)
−0.224284 + 0.974524i \(0.572004\pi\)
\(444\) −3.28196e11 −0.400784
\(445\) 8.09460e11 0.978533
\(446\) 1.41003e11 0.168741
\(447\) −9.62630e11 −1.14045
\(448\) −1.05352e12 −1.23564
\(449\) −2.76604e11 −0.321181 −0.160590 0.987021i \(-0.551340\pi\)
−0.160590 + 0.987021i \(0.551340\pi\)
\(450\) 2.36625e11 0.272022
\(451\) 1.42785e12 1.62513
\(452\) 4.49823e11 0.506896
\(453\) 6.30950e11 0.703968
\(454\) 2.25941e11 0.249599
\(455\) 1.05079e12 1.14938
\(456\) −6.73513e11 −0.729464
\(457\) −2.71605e11 −0.291283 −0.145642 0.989337i \(-0.546525\pi\)
−0.145642 + 0.989337i \(0.546525\pi\)
\(458\) 9.14731e11 0.971402
\(459\) −3.05414e11 −0.321168
\(460\) −1.68801e11 −0.175778
\(461\) 5.93856e11 0.612388 0.306194 0.951969i \(-0.400944\pi\)
0.306194 + 0.951969i \(0.400944\pi\)
\(462\) 8.20871e11 0.838274
\(463\) −1.90507e11 −0.192662 −0.0963310 0.995349i \(-0.530711\pi\)
−0.0963310 + 0.995349i \(0.530711\pi\)
\(464\) 1.77211e11 0.177485
\(465\) −6.12486e11 −0.607516
\(466\) −1.23215e12 −1.21040
\(467\) −6.17353e11 −0.600631 −0.300315 0.953840i \(-0.597092\pi\)
−0.300315 + 0.953840i \(0.597092\pi\)
\(468\) 9.60291e10 0.0925330
\(469\) −2.32879e11 −0.222255
\(470\) 4.30922e11 0.407341
\(471\) −7.71793e11 −0.722615
\(472\) 1.49147e11 0.138317
\(473\) −2.12607e12 −1.95300
\(474\) 8.37762e11 0.762286
\(475\) −1.51500e12 −1.36550
\(476\) 1.29318e12 1.15459
\(477\) −2.84284e11 −0.251432
\(478\) −3.79107e10 −0.0332151
\(479\) −2.05297e11 −0.178186 −0.0890928 0.996023i \(-0.528397\pi\)
−0.0890928 + 0.996023i \(0.528397\pi\)
\(480\) −8.63607e11 −0.742558
\(481\) 9.23703e11 0.786828
\(482\) −1.04130e12 −0.878745
\(483\) 2.33954e11 0.195600
\(484\) −6.78369e11 −0.561904
\(485\) −6.99597e11 −0.574130
\(486\) −5.60732e10 −0.0455923
\(487\) −1.89086e12 −1.52328 −0.761640 0.648001i \(-0.775605\pi\)
−0.761640 + 0.648001i \(0.775605\pi\)
\(488\) −1.82265e12 −1.45483
\(489\) 5.20484e11 0.411640
\(490\) 1.26871e12 0.994212
\(491\) 1.01893e12 0.791187 0.395594 0.918426i \(-0.370539\pi\)
0.395594 + 0.918426i \(0.370539\pi\)
\(492\) 4.12983e11 0.317753
\(493\) −1.49305e12 −1.13831
\(494\) 6.27540e11 0.474100
\(495\) 9.53641e11 0.713940
\(496\) −2.51801e11 −0.186805
\(497\) 3.19606e12 2.34969
\(498\) 5.00581e11 0.364705
\(499\) 1.51606e12 1.09462 0.547311 0.836929i \(-0.315651\pi\)
0.547311 + 0.836929i \(0.315651\pi\)
\(500\) −1.50266e11 −0.107522
\(501\) −1.41163e11 −0.100104
\(502\) 1.26061e12 0.885959
\(503\) −2.25319e12 −1.56943 −0.784713 0.619859i \(-0.787190\pi\)
−0.784713 + 0.619859i \(0.787190\pi\)
\(504\) 7.17181e11 0.495098
\(505\) −2.58436e12 −1.76824
\(506\) 3.71137e11 0.251685
\(507\) 5.88692e11 0.395688
\(508\) −1.07432e12 −0.715724
\(509\) −1.89541e11 −0.125162 −0.0625812 0.998040i \(-0.519933\pi\)
−0.0625812 + 0.998040i \(0.519933\pi\)
\(510\) −1.53340e12 −1.00367
\(511\) 2.96748e12 1.92528
\(512\) −7.84903e11 −0.504779
\(513\) 3.59011e11 0.228865
\(514\) 1.80785e12 1.14242
\(515\) −6.24993e11 −0.391510
\(516\) −6.14934e11 −0.381861
\(517\) 9.28264e11 0.571431
\(518\) 2.28378e12 1.39371
\(519\) 1.05770e11 0.0639898
\(520\) 1.45637e12 0.873488
\(521\) 2.48369e11 0.147682 0.0738411 0.997270i \(-0.476474\pi\)
0.0738411 + 0.997270i \(0.476474\pi\)
\(522\) −2.74119e11 −0.161593
\(523\) −2.94791e11 −0.172289 −0.0861443 0.996283i \(-0.527455\pi\)
−0.0861443 + 0.996283i \(0.527455\pi\)
\(524\) 4.07303e11 0.236008
\(525\) 1.61323e12 0.926787
\(526\) −6.09531e11 −0.347184
\(527\) 2.12148e12 1.19809
\(528\) 3.92054e11 0.219530
\(529\) −1.69538e12 −0.941273
\(530\) −1.42731e12 −0.785737
\(531\) −7.95020e10 −0.0433963
\(532\) −1.52012e12 −0.822766
\(533\) −1.16233e12 −0.623819
\(534\) −5.14760e11 −0.273948
\(535\) −2.53509e12 −1.33783
\(536\) −3.22765e11 −0.168906
\(537\) 7.69867e11 0.399513
\(538\) −6.54947e11 −0.337044
\(539\) 2.73297e12 1.39471
\(540\) 2.75826e11 0.139593
\(541\) 2.55667e11 0.128318 0.0641590 0.997940i \(-0.479564\pi\)
0.0641590 + 0.997940i \(0.479564\pi\)
\(542\) −1.49527e12 −0.744259
\(543\) −5.18650e11 −0.256021
\(544\) 2.99129e12 1.46441
\(545\) −1.85631e12 −0.901292
\(546\) −6.68227e11 −0.321779
\(547\) −2.11030e12 −1.00786 −0.503932 0.863743i \(-0.668114\pi\)
−0.503932 + 0.863743i \(0.668114\pi\)
\(548\) 1.56445e12 0.741051
\(549\) 9.71548e11 0.456445
\(550\) 2.55917e12 1.19253
\(551\) 1.75506e12 0.811167
\(552\) 3.24256e11 0.148649
\(553\) 5.71158e12 2.59713
\(554\) 1.07495e12 0.484837
\(555\) 2.65317e12 1.18699
\(556\) 1.57605e12 0.699414
\(557\) −4.44566e12 −1.95699 −0.978493 0.206279i \(-0.933865\pi\)
−0.978493 + 0.206279i \(0.933865\pi\)
\(558\) 3.89498e11 0.170079
\(559\) 1.73072e12 0.749677
\(560\) 1.24082e12 0.533167
\(561\) −3.30315e12 −1.40798
\(562\) 2.87612e12 1.21617
\(563\) 4.54146e12 1.90506 0.952528 0.304452i \(-0.0984732\pi\)
0.952528 + 0.304452i \(0.0984732\pi\)
\(564\) 2.68486e11 0.111729
\(565\) −3.63641e12 −1.50126
\(566\) 1.39843e12 0.572754
\(567\) −3.82288e11 −0.155334
\(568\) 4.42967e12 1.78568
\(569\) −3.69150e12 −1.47638 −0.738190 0.674593i \(-0.764319\pi\)
−0.738190 + 0.674593i \(0.764319\pi\)
\(570\) 1.80249e12 0.715216
\(571\) 2.45410e10 0.00966117 0.00483058 0.999988i \(-0.498462\pi\)
0.00483058 + 0.999988i \(0.498462\pi\)
\(572\) 1.03858e12 0.405658
\(573\) −1.91133e12 −0.740697
\(574\) −2.87378e12 −1.10497
\(575\) 7.29384e11 0.278260
\(576\) 7.78328e11 0.294620
\(577\) 2.34560e12 0.880974 0.440487 0.897759i \(-0.354806\pi\)
0.440487 + 0.897759i \(0.354806\pi\)
\(578\) 3.40418e12 1.26864
\(579\) 1.47991e11 0.0547245
\(580\) 1.34840e12 0.494760
\(581\) 3.41280e12 1.24256
\(582\) 4.44895e11 0.160733
\(583\) −3.07462e12 −1.10226
\(584\) 4.11287e12 1.46315
\(585\) −7.76308e11 −0.274052
\(586\) −2.25475e12 −0.789878
\(587\) −2.42490e12 −0.842990 −0.421495 0.906831i \(-0.638495\pi\)
−0.421495 + 0.906831i \(0.638495\pi\)
\(588\) 7.90469e11 0.272701
\(589\) −2.49378e12 −0.853767
\(590\) −3.99157e11 −0.135616
\(591\) −8.82542e11 −0.297572
\(592\) 1.09075e12 0.364988
\(593\) 2.29186e12 0.761101 0.380551 0.924760i \(-0.375734\pi\)
0.380551 + 0.924760i \(0.375734\pi\)
\(594\) −6.06448e11 −0.199873
\(595\) −1.04542e13 −3.41951
\(596\) −3.01127e12 −0.977555
\(597\) −3.16407e12 −1.01944
\(598\) −3.02123e11 −0.0966113
\(599\) −5.21413e12 −1.65486 −0.827430 0.561569i \(-0.810198\pi\)
−0.827430 + 0.561569i \(0.810198\pi\)
\(600\) 2.23591e12 0.704325
\(601\) 1.28472e12 0.401674 0.200837 0.979625i \(-0.435634\pi\)
0.200837 + 0.979625i \(0.435634\pi\)
\(602\) 4.27907e12 1.32790
\(603\) 1.72048e11 0.0529933
\(604\) 1.97372e12 0.603418
\(605\) 5.48400e12 1.66417
\(606\) 1.64347e12 0.495034
\(607\) 1.50667e12 0.450474 0.225237 0.974304i \(-0.427684\pi\)
0.225237 + 0.974304i \(0.427684\pi\)
\(608\) −3.51624e12 −1.04355
\(609\) −1.86886e12 −0.550551
\(610\) 4.87787e12 1.42642
\(611\) −7.55650e11 −0.219349
\(612\) −9.55385e11 −0.275294
\(613\) 7.34445e11 0.210081 0.105041 0.994468i \(-0.466503\pi\)
0.105041 + 0.994468i \(0.466503\pi\)
\(614\) −3.21087e12 −0.911728
\(615\) −3.33859e12 −0.941078
\(616\) 7.75653e12 2.17047
\(617\) 6.90093e11 0.191701 0.0958505 0.995396i \(-0.469443\pi\)
0.0958505 + 0.995396i \(0.469443\pi\)
\(618\) 3.97452e11 0.109606
\(619\) −2.37314e12 −0.649704 −0.324852 0.945765i \(-0.605314\pi\)
−0.324852 + 0.945765i \(0.605314\pi\)
\(620\) −1.91596e12 −0.520742
\(621\) −1.72842e11 −0.0466378
\(622\) −3.20562e12 −0.858727
\(623\) −3.50946e12 −0.933349
\(624\) −3.19150e11 −0.0842684
\(625\) −3.16540e12 −0.829792
\(626\) −2.10951e12 −0.549032
\(627\) 3.88282e12 1.00333
\(628\) −2.41430e12 −0.619401
\(629\) −9.18984e12 −2.34089
\(630\) −1.91936e12 −0.485427
\(631\) 3.82877e12 0.961450 0.480725 0.876871i \(-0.340374\pi\)
0.480725 + 0.876871i \(0.340374\pi\)
\(632\) 7.91614e12 1.97372
\(633\) 1.00207e12 0.248075
\(634\) 1.38082e12 0.339418
\(635\) 8.68487e12 2.11973
\(636\) −8.89288e11 −0.215519
\(637\) −2.22476e12 −0.535373
\(638\) −2.96468e12 −0.708411
\(639\) −2.36121e12 −0.560248
\(640\) −1.55108e12 −0.365447
\(641\) −8.41400e12 −1.96853 −0.984263 0.176708i \(-0.943455\pi\)
−0.984263 + 0.176708i \(0.943455\pi\)
\(642\) 1.61214e12 0.374537
\(643\) 6.56454e12 1.51445 0.757225 0.653155i \(-0.226555\pi\)
0.757225 + 0.653155i \(0.226555\pi\)
\(644\) 7.31848e11 0.167662
\(645\) 4.97118e12 1.13094
\(646\) −6.24334e12 −1.41049
\(647\) −1.08070e12 −0.242458 −0.121229 0.992625i \(-0.538684\pi\)
−0.121229 + 0.992625i \(0.538684\pi\)
\(648\) −5.29844e11 −0.118048
\(649\) −8.59839e11 −0.190246
\(650\) −2.08329e12 −0.457761
\(651\) 2.65547e12 0.579464
\(652\) 1.62816e12 0.352844
\(653\) 4.48631e12 0.965562 0.482781 0.875741i \(-0.339627\pi\)
0.482781 + 0.875741i \(0.339627\pi\)
\(654\) 1.18048e12 0.252324
\(655\) −3.29268e12 −0.698978
\(656\) −1.37254e12 −0.289373
\(657\) −2.19234e12 −0.459054
\(658\) −1.86829e12 −0.388532
\(659\) −2.37848e12 −0.491264 −0.245632 0.969363i \(-0.578995\pi\)
−0.245632 + 0.969363i \(0.578995\pi\)
\(660\) 2.98315e12 0.611965
\(661\) −7.15743e12 −1.45831 −0.729157 0.684347i \(-0.760087\pi\)
−0.729157 + 0.684347i \(0.760087\pi\)
\(662\) −1.33577e12 −0.270315
\(663\) 2.68892e12 0.540463
\(664\) 4.73007e12 0.944302
\(665\) 1.22888e13 2.43676
\(666\) −1.68723e12 −0.332307
\(667\) −8.44958e11 −0.165298
\(668\) −4.41581e11 −0.0858057
\(669\) −7.10202e11 −0.137077
\(670\) 8.63803e11 0.165607
\(671\) 1.05076e13 2.00102
\(672\) 3.74422e12 0.708271
\(673\) 3.34043e12 0.627675 0.313838 0.949477i \(-0.398385\pi\)
0.313838 + 0.949477i \(0.398385\pi\)
\(674\) −2.40679e12 −0.449231
\(675\) −1.19183e12 −0.220978
\(676\) 1.84153e12 0.339170
\(677\) 1.16108e10 0.00212429 0.00106214 0.999999i \(-0.499662\pi\)
0.00106214 + 0.999999i \(0.499662\pi\)
\(678\) 2.31250e12 0.420290
\(679\) 3.03315e12 0.547620
\(680\) −1.44893e13 −2.59871
\(681\) −1.13802e12 −0.202763
\(682\) 4.21254e12 0.745614
\(683\) −2.75359e12 −0.484179 −0.242090 0.970254i \(-0.577833\pi\)
−0.242090 + 0.970254i \(0.577833\pi\)
\(684\) 1.12305e12 0.196176
\(685\) −1.26471e13 −2.19474
\(686\) 2.62642e11 0.0452799
\(687\) −4.60732e12 −0.789120
\(688\) 2.04372e12 0.347755
\(689\) 2.50288e12 0.423111
\(690\) −8.67793e11 −0.145746
\(691\) 3.09917e12 0.517124 0.258562 0.965995i \(-0.416751\pi\)
0.258562 + 0.965995i \(0.416751\pi\)
\(692\) 3.30867e11 0.0548499
\(693\) −4.13457e12 −0.680974
\(694\) −3.82986e12 −0.626708
\(695\) −1.27410e13 −2.07143
\(696\) −2.59019e12 −0.418399
\(697\) 1.15640e13 1.85592
\(698\) 4.68164e12 0.746532
\(699\) 6.20612e12 0.983270
\(700\) 5.04645e12 0.794411
\(701\) 2.89435e12 0.452710 0.226355 0.974045i \(-0.427319\pi\)
0.226355 + 0.974045i \(0.427319\pi\)
\(702\) 4.93677e11 0.0767231
\(703\) 1.08026e13 1.66812
\(704\) 8.41786e12 1.29159
\(705\) −2.17047e12 −0.330904
\(706\) 7.45271e12 1.12900
\(707\) 1.12046e13 1.68659
\(708\) −2.48695e11 −0.0371979
\(709\) −3.07176e12 −0.456540 −0.228270 0.973598i \(-0.573307\pi\)
−0.228270 + 0.973598i \(0.573307\pi\)
\(710\) −1.18550e13 −1.75080
\(711\) −4.21964e12 −0.619245
\(712\) −4.86404e12 −0.709312
\(713\) 1.20061e12 0.173979
\(714\) 6.64813e12 0.957322
\(715\) −8.39601e12 −1.20142
\(716\) 2.40827e12 0.342450
\(717\) 1.90949e11 0.0269824
\(718\) −5.52860e12 −0.776346
\(719\) −7.37377e12 −1.02899 −0.514493 0.857495i \(-0.672020\pi\)
−0.514493 + 0.857495i \(0.672020\pi\)
\(720\) −9.16702e11 −0.127125
\(721\) 2.70970e12 0.373432
\(722\) 2.14964e12 0.294408
\(723\) 5.24481e12 0.713850
\(724\) −1.62242e12 −0.219453
\(725\) −5.82640e12 −0.783212
\(726\) −3.48744e12 −0.465899
\(727\) 1.76907e11 0.0234877 0.0117438 0.999931i \(-0.496262\pi\)
0.0117438 + 0.999931i \(0.496262\pi\)
\(728\) −6.31418e12 −0.833155
\(729\) 2.82430e11 0.0370370
\(730\) −1.10071e13 −1.43457
\(731\) −1.72188e13 −2.23036
\(732\) 3.03916e12 0.391250
\(733\) 7.53574e12 0.964180 0.482090 0.876122i \(-0.339878\pi\)
0.482090 + 0.876122i \(0.339878\pi\)
\(734\) −9.46309e12 −1.20337
\(735\) −6.39023e12 −0.807650
\(736\) 1.69286e12 0.212652
\(737\) 1.86075e12 0.232319
\(738\) 2.12311e12 0.263463
\(739\) 9.74013e12 1.20134 0.600669 0.799498i \(-0.294901\pi\)
0.600669 + 0.799498i \(0.294901\pi\)
\(740\) 8.29955e12 1.01745
\(741\) −3.16079e12 −0.385136
\(742\) 6.18819e12 0.749456
\(743\) −6.04164e12 −0.727286 −0.363643 0.931538i \(-0.618467\pi\)
−0.363643 + 0.931538i \(0.618467\pi\)
\(744\) 3.68042e12 0.440372
\(745\) 2.43434e13 2.89519
\(746\) −7.72323e12 −0.913007
\(747\) −2.52133e12 −0.296269
\(748\) −1.03328e13 −1.20687
\(749\) 1.09910e13 1.27606
\(750\) −7.72505e11 −0.0891508
\(751\) −1.86477e12 −0.213917 −0.106958 0.994264i \(-0.534111\pi\)
−0.106958 + 0.994264i \(0.534111\pi\)
\(752\) −8.92308e11 −0.101750
\(753\) −6.34944e12 −0.719711
\(754\) 2.41339e12 0.271930
\(755\) −1.59557e13 −1.78712
\(756\) −1.19586e12 −0.133147
\(757\) −1.42975e13 −1.58244 −0.791222 0.611528i \(-0.790555\pi\)
−0.791222 + 0.611528i \(0.790555\pi\)
\(758\) 1.27229e12 0.139983
\(759\) −1.86934e12 −0.204457
\(760\) 1.70320e13 1.85185
\(761\) 7.40971e11 0.0800885 0.0400442 0.999198i \(-0.487250\pi\)
0.0400442 + 0.999198i \(0.487250\pi\)
\(762\) −5.52297e12 −0.593437
\(763\) 8.04813e12 0.859675
\(764\) −5.97897e12 −0.634901
\(765\) 7.72342e12 0.815330
\(766\) 8.26559e12 0.867449
\(767\) 6.99949e11 0.0730276
\(768\) 5.90618e12 0.612606
\(769\) −2.78398e12 −0.287076 −0.143538 0.989645i \(-0.545848\pi\)
−0.143538 + 0.989645i \(0.545848\pi\)
\(770\) −2.07585e13 −2.12808
\(771\) −9.10577e12 −0.928051
\(772\) 4.62941e11 0.0469080
\(773\) 7.72432e11 0.0778131 0.0389065 0.999243i \(-0.487613\pi\)
0.0389065 + 0.999243i \(0.487613\pi\)
\(774\) −3.16132e12 −0.316617
\(775\) 8.27877e12 0.824343
\(776\) 4.20388e12 0.416171
\(777\) −1.15030e13 −1.13218
\(778\) 8.42898e12 0.824835
\(779\) −1.35933e13 −1.32254
\(780\) −2.42842e12 −0.234908
\(781\) −2.55372e13 −2.45608
\(782\) 3.00579e12 0.287428
\(783\) 1.38069e12 0.131270
\(784\) −2.62711e12 −0.248345
\(785\) 1.95174e13 1.83446
\(786\) 2.09391e12 0.195685
\(787\) −1.05342e12 −0.0978851 −0.0489425 0.998802i \(-0.515585\pi\)
−0.0489425 + 0.998802i \(0.515585\pi\)
\(788\) −2.76074e12 −0.255068
\(789\) 3.07009e12 0.282036
\(790\) −2.11856e13 −1.93517
\(791\) 1.57659e13 1.43194
\(792\) −5.73042e12 −0.517516
\(793\) −8.55367e12 −0.768110
\(794\) 2.21331e12 0.197629
\(795\) 7.18908e12 0.638295
\(796\) −9.89774e12 −0.873831
\(797\) −5.36649e12 −0.471116 −0.235558 0.971860i \(-0.575692\pi\)
−0.235558 + 0.971860i \(0.575692\pi\)
\(798\) −7.81482e12 −0.682191
\(799\) 7.51790e12 0.652583
\(800\) 1.16731e13 1.00758
\(801\) 2.59274e12 0.222543
\(802\) 1.48261e13 1.26544
\(803\) −2.37108e13 −2.01246
\(804\) 5.38193e11 0.0454241
\(805\) −5.91633e12 −0.496559
\(806\) −3.42920e12 −0.286210
\(807\) 3.29884e12 0.273798
\(808\) 1.55294e13 1.28175
\(809\) 6.93954e12 0.569590 0.284795 0.958589i \(-0.408075\pi\)
0.284795 + 0.958589i \(0.408075\pi\)
\(810\) 1.41800e12 0.115743
\(811\) −1.68670e12 −0.136913 −0.0684565 0.997654i \(-0.521807\pi\)
−0.0684565 + 0.997654i \(0.521807\pi\)
\(812\) −5.84609e12 −0.471914
\(813\) 7.53141e12 0.604601
\(814\) −1.82479e13 −1.45681
\(815\) −1.31622e13 −1.04501
\(816\) 3.17520e12 0.250706
\(817\) 2.02405e13 1.58936
\(818\) −3.24840e12 −0.253676
\(819\) 3.36573e12 0.261398
\(820\) −1.04437e13 −0.806661
\(821\) 2.02395e13 1.55473 0.777365 0.629050i \(-0.216556\pi\)
0.777365 + 0.629050i \(0.216556\pi\)
\(822\) 8.04268e12 0.614437
\(823\) 8.31956e11 0.0632123 0.0316061 0.999500i \(-0.489938\pi\)
0.0316061 + 0.999500i \(0.489938\pi\)
\(824\) 3.75558e12 0.283795
\(825\) −1.28901e13 −0.968751
\(826\) 1.73057e12 0.129354
\(827\) 1.16197e13 0.863813 0.431906 0.901918i \(-0.357841\pi\)
0.431906 + 0.901918i \(0.357841\pi\)
\(828\) −5.40680e11 −0.0399764
\(829\) 2.32301e13 1.70827 0.854135 0.520051i \(-0.174087\pi\)
0.854135 + 0.520051i \(0.174087\pi\)
\(830\) −1.26589e13 −0.925857
\(831\) −5.41433e12 −0.393858
\(832\) −6.85253e12 −0.495788
\(833\) 2.21340e13 1.59278
\(834\) 8.10236e12 0.579915
\(835\) 3.56978e12 0.254128
\(836\) 1.21461e13 0.860020
\(837\) −1.96182e12 −0.138164
\(838\) 8.07208e12 0.565441
\(839\) 1.50688e13 1.04990 0.524952 0.851132i \(-0.324083\pi\)
0.524952 + 0.851132i \(0.324083\pi\)
\(840\) −1.81363e13 −1.25688
\(841\) −7.75753e12 −0.534738
\(842\) −1.23205e13 −0.844739
\(843\) −1.44864e13 −0.987955
\(844\) 3.13465e12 0.212642
\(845\) −1.48871e13 −1.00451
\(846\) 1.38027e12 0.0926395
\(847\) −2.37762e13 −1.58733
\(848\) 2.95553e12 0.196270
\(849\) −7.04364e12 −0.465278
\(850\) 2.07264e13 1.36188
\(851\) −5.20079e12 −0.339928
\(852\) −7.38625e12 −0.480226
\(853\) −2.01905e13 −1.30580 −0.652900 0.757444i \(-0.726448\pi\)
−0.652900 + 0.757444i \(0.726448\pi\)
\(854\) −2.11483e13 −1.36055
\(855\) −9.07881e12 −0.581007
\(856\) 1.52334e13 0.969759
\(857\) −5.74789e11 −0.0363994 −0.0181997 0.999834i \(-0.505793\pi\)
−0.0181997 + 0.999834i \(0.505793\pi\)
\(858\) 5.33927e12 0.336348
\(859\) 1.93738e13 1.21407 0.607037 0.794674i \(-0.292358\pi\)
0.607037 + 0.794674i \(0.292358\pi\)
\(860\) 1.55507e13 0.969407
\(861\) 1.44747e13 0.897624
\(862\) −4.78312e12 −0.295072
\(863\) −4.19691e12 −0.257562 −0.128781 0.991673i \(-0.541106\pi\)
−0.128781 + 0.991673i \(0.541106\pi\)
\(864\) −2.76618e12 −0.168876
\(865\) −2.67476e12 −0.162447
\(866\) 1.76582e13 1.06688
\(867\) −1.71462e13 −1.03058
\(868\) 8.30674e12 0.496697
\(869\) −4.56367e13 −2.71472
\(870\) 6.93203e12 0.410227
\(871\) −1.51474e12 −0.0891775
\(872\) 1.11545e13 0.653322
\(873\) −2.24085e12 −0.130571
\(874\) −3.53328e12 −0.204822
\(875\) −5.26668e12 −0.303739
\(876\) −6.85800e12 −0.393485
\(877\) 1.32466e13 0.756148 0.378074 0.925775i \(-0.376586\pi\)
0.378074 + 0.925775i \(0.376586\pi\)
\(878\) −1.37342e13 −0.779969
\(879\) 1.13568e13 0.641659
\(880\) −9.91441e12 −0.557308
\(881\) 2.43165e13 1.35991 0.679955 0.733254i \(-0.261999\pi\)
0.679955 + 0.733254i \(0.261999\pi\)
\(882\) 4.06373e12 0.226108
\(883\) 1.97916e13 1.09562 0.547809 0.836604i \(-0.315462\pi\)
0.547809 + 0.836604i \(0.315462\pi\)
\(884\) 8.41137e12 0.463267
\(885\) 2.01048e12 0.110168
\(886\) −5.84757e12 −0.318804
\(887\) −5.09160e12 −0.276184 −0.138092 0.990419i \(-0.544097\pi\)
−0.138092 + 0.990419i \(0.544097\pi\)
\(888\) −1.59429e13 −0.860416
\(889\) −3.76538e13 −2.02186
\(890\) 1.30174e13 0.695457
\(891\) 3.05456e12 0.162368
\(892\) −2.22163e12 −0.117498
\(893\) −8.83722e12 −0.465033
\(894\) −1.54807e13 −0.810533
\(895\) −1.94687e13 −1.01422
\(896\) 6.72480e12 0.348573
\(897\) 1.52173e12 0.0784824
\(898\) −4.44823e12 −0.228268
\(899\) −9.59058e12 −0.489695
\(900\) −3.72825e12 −0.189415
\(901\) −2.49010e13 −1.25879
\(902\) 2.29621e13 1.15500
\(903\) −2.15529e13 −1.07872
\(904\) 2.18512e13 1.08822
\(905\) 1.31158e13 0.649945
\(906\) 1.01467e13 0.500320
\(907\) 3.51115e12 0.172273 0.0861364 0.996283i \(-0.472548\pi\)
0.0861364 + 0.996283i \(0.472548\pi\)
\(908\) −3.55991e12 −0.173801
\(909\) −8.27784e12 −0.402142
\(910\) 1.68984e13 0.816881
\(911\) −5.93968e12 −0.285713 −0.142857 0.989743i \(-0.545629\pi\)
−0.142857 + 0.989743i \(0.545629\pi\)
\(912\) −3.73242e12 −0.178654
\(913\) −2.72689e13 −1.29882
\(914\) −4.36786e12 −0.207019
\(915\) −2.45689e13 −1.15875
\(916\) −1.44125e13 −0.676408
\(917\) 1.42756e13 0.666703
\(918\) −4.91155e12 −0.228258
\(919\) −1.16149e12 −0.0537151 −0.0268576 0.999639i \(-0.508550\pi\)
−0.0268576 + 0.999639i \(0.508550\pi\)
\(920\) −8.19991e12 −0.377367
\(921\) 1.61725e13 0.740645
\(922\) 9.55016e12 0.435233
\(923\) 2.07885e13 0.942789
\(924\) −1.29336e13 −0.583708
\(925\) −3.58620e13 −1.61064
\(926\) −3.06366e12 −0.136928
\(927\) −2.00189e12 −0.0890391
\(928\) −1.35227e13 −0.598548
\(929\) −7.37213e12 −0.324730 −0.162365 0.986731i \(-0.551912\pi\)
−0.162365 + 0.986731i \(0.551912\pi\)
\(930\) −9.84977e12 −0.431770
\(931\) −2.60183e13 −1.13502
\(932\) 1.94138e13 0.842827
\(933\) 1.61461e13 0.697589
\(934\) −9.92804e12 −0.426877
\(935\) 8.35312e13 3.57435
\(936\) 4.66483e12 0.198653
\(937\) 3.78723e13 1.60507 0.802534 0.596606i \(-0.203485\pi\)
0.802534 + 0.596606i \(0.203485\pi\)
\(938\) −3.74507e12 −0.157960
\(939\) 1.06252e13 0.446008
\(940\) −6.78958e12 −0.283640
\(941\) −6.80763e12 −0.283037 −0.141518 0.989936i \(-0.545198\pi\)
−0.141518 + 0.989936i \(0.545198\pi\)
\(942\) −1.24117e13 −0.513573
\(943\) 6.54437e12 0.269504
\(944\) 8.26533e11 0.0338755
\(945\) 9.66745e12 0.394338
\(946\) −3.41907e13 −1.38803
\(947\) −3.21838e12 −0.130036 −0.0650179 0.997884i \(-0.520710\pi\)
−0.0650179 + 0.997884i \(0.520710\pi\)
\(948\) −1.31997e13 −0.530796
\(949\) 1.93017e13 0.772499
\(950\) −2.43637e13 −0.970482
\(951\) −6.95491e12 −0.275727
\(952\) 6.28192e13 2.47871
\(953\) 2.57077e13 1.00959 0.504796 0.863239i \(-0.331568\pi\)
0.504796 + 0.863239i \(0.331568\pi\)
\(954\) −4.57175e12 −0.178696
\(955\) 4.83345e13 1.88037
\(956\) 5.97319e11 0.0231284
\(957\) 1.49325e13 0.575480
\(958\) −3.30151e12 −0.126639
\(959\) 5.48323e13 2.09340
\(960\) −1.96827e13 −0.747934
\(961\) −1.28123e13 −0.484588
\(962\) 1.48546e13 0.559209
\(963\) −8.12004e12 −0.304256
\(964\) 1.64066e13 0.611889
\(965\) −3.74245e12 −0.138926
\(966\) 3.76237e12 0.139016
\(967\) 8.66214e12 0.318571 0.159285 0.987233i \(-0.449081\pi\)
0.159285 + 0.987233i \(0.449081\pi\)
\(968\) −3.29533e13 −1.20631
\(969\) 3.14465e13 1.14582
\(970\) −1.12507e13 −0.408042
\(971\) −2.16854e12 −0.0782852 −0.0391426 0.999234i \(-0.512463\pi\)
−0.0391426 + 0.999234i \(0.512463\pi\)
\(972\) 8.83486e11 0.0317469
\(973\) 5.52392e13 1.97579
\(974\) −3.04081e13 −1.08262
\(975\) 1.04931e13 0.371863
\(976\) −1.01006e13 −0.356305
\(977\) −4.24310e13 −1.48990 −0.744951 0.667120i \(-0.767527\pi\)
−0.744951 + 0.667120i \(0.767527\pi\)
\(978\) 8.37022e12 0.292558
\(979\) 2.80413e13 0.975610
\(980\) −1.99897e13 −0.692291
\(981\) −5.94585e12 −0.204976
\(982\) 1.63861e13 0.562308
\(983\) −5.52491e13 −1.88727 −0.943635 0.330987i \(-0.892618\pi\)
−0.943635 + 0.330987i \(0.892618\pi\)
\(984\) 2.00616e13 0.682162
\(985\) 2.23180e13 0.755428
\(986\) −2.40106e13 −0.809016
\(987\) 9.41020e12 0.315625
\(988\) −9.88749e12 −0.330126
\(989\) −9.74460e12 −0.323878
\(990\) 1.53361e13 0.507407
\(991\) 2.15925e13 0.711167 0.355584 0.934644i \(-0.384282\pi\)
0.355584 + 0.934644i \(0.384282\pi\)
\(992\) 1.92145e13 0.629981
\(993\) 6.72801e12 0.219591
\(994\) 5.13978e13 1.66996
\(995\) 8.00143e13 2.58800
\(996\) −7.88713e12 −0.253952
\(997\) 3.54323e12 0.113572 0.0567860 0.998386i \(-0.481915\pi\)
0.0567860 + 0.998386i \(0.481915\pi\)
\(998\) 2.43807e13 0.777964
\(999\) 8.49825e12 0.269951
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.b.1.15 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.15 21 1.1 even 1 trivial