Properties

Label 177.10.a.b.1.14
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 1.14
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+15.7099 q^{2} -81.0000 q^{3} -265.198 q^{4} -2481.38 q^{5} -1272.50 q^{6} +1632.53 q^{7} -12209.7 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+15.7099 q^{2} -81.0000 q^{3} -265.198 q^{4} -2481.38 q^{5} -1272.50 q^{6} +1632.53 q^{7} -12209.7 q^{8} +6561.00 q^{9} -38982.3 q^{10} +71994.6 q^{11} +21481.1 q^{12} +20979.3 q^{13} +25646.9 q^{14} +200992. q^{15} -56032.2 q^{16} -100423. q^{17} +103073. q^{18} +125554. q^{19} +658059. q^{20} -132235. q^{21} +1.13103e6 q^{22} +759888. q^{23} +988988. q^{24} +4.20414e6 q^{25} +329583. q^{26} -531441. q^{27} -432944. q^{28} -1.44179e6 q^{29} +3.15757e6 q^{30} -973200. q^{31} +5.37112e6 q^{32} -5.83156e6 q^{33} -1.57764e6 q^{34} -4.05093e6 q^{35} -1.73997e6 q^{36} +6.01928e6 q^{37} +1.97245e6 q^{38} -1.69932e6 q^{39} +3.02970e7 q^{40} +6.93821e6 q^{41} -2.07740e6 q^{42} +5.22977e6 q^{43} -1.90928e7 q^{44} -1.62804e7 q^{45} +1.19378e7 q^{46} -3.13303e7 q^{47} +4.53861e6 q^{48} -3.76885e7 q^{49} +6.60467e7 q^{50} +8.13429e6 q^{51} -5.56368e6 q^{52} +5.51922e7 q^{53} -8.34890e6 q^{54} -1.78646e8 q^{55} -1.99327e7 q^{56} -1.01699e7 q^{57} -2.26504e7 q^{58} -1.21174e7 q^{59} -5.33028e7 q^{60} -1.66783e8 q^{61} -1.52889e7 q^{62} +1.07110e7 q^{63} +1.13068e8 q^{64} -5.20577e7 q^{65} -9.16133e7 q^{66} +9.31844e7 q^{67} +2.66321e7 q^{68} -6.15509e7 q^{69} -6.36397e7 q^{70} -4.01312e7 q^{71} -8.01080e7 q^{72} -2.58311e8 q^{73} +9.45624e7 q^{74} -3.40536e8 q^{75} -3.32968e7 q^{76} +1.17533e8 q^{77} -2.66962e7 q^{78} -3.62808e8 q^{79} +1.39037e8 q^{80} +4.30467e7 q^{81} +1.08999e8 q^{82} +5.97676e8 q^{83} +3.50684e7 q^{84} +2.49189e8 q^{85} +8.21592e7 q^{86} +1.16785e8 q^{87} -8.79034e8 q^{88} +6.86238e8 q^{89} -2.55763e8 q^{90} +3.42493e7 q^{91} -2.01521e8 q^{92} +7.88292e7 q^{93} -4.92196e8 q^{94} -3.11548e8 q^{95} -4.35061e8 q^{96} +2.73324e7 q^{97} -5.92083e8 q^{98} +4.72356e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.7099 0.694287 0.347143 0.937812i \(-0.387152\pi\)
0.347143 + 0.937812i \(0.387152\pi\)
\(3\) −81.0000 −0.577350
\(4\) −265.198 −0.517966
\(5\) −2481.38 −1.77553 −0.887767 0.460293i \(-0.847744\pi\)
−0.887767 + 0.460293i \(0.847744\pi\)
\(6\) −1272.50 −0.400847
\(7\) 1632.53 0.256992 0.128496 0.991710i \(-0.458985\pi\)
0.128496 + 0.991710i \(0.458985\pi\)
\(8\) −12209.7 −1.05390
\(9\) 6561.00 0.333333
\(10\) −38982.3 −1.23273
\(11\) 71994.6 1.48263 0.741315 0.671158i \(-0.234203\pi\)
0.741315 + 0.671158i \(0.234203\pi\)
\(12\) 21481.1 0.299048
\(13\) 20979.3 0.203726 0.101863 0.994798i \(-0.467520\pi\)
0.101863 + 0.994798i \(0.467520\pi\)
\(14\) 25646.9 0.178426
\(15\) 200992. 1.02511
\(16\) −56032.2 −0.213746
\(17\) −100423. −0.291618 −0.145809 0.989313i \(-0.546579\pi\)
−0.145809 + 0.989313i \(0.546579\pi\)
\(18\) 103073. 0.231429
\(19\) 125554. 0.221024 0.110512 0.993875i \(-0.464751\pi\)
0.110512 + 0.993875i \(0.464751\pi\)
\(20\) 658059. 0.919666
\(21\) −132235. −0.148374
\(22\) 1.13103e6 1.02937
\(23\) 759888. 0.566206 0.283103 0.959090i \(-0.408636\pi\)
0.283103 + 0.959090i \(0.408636\pi\)
\(24\) 988988. 0.608472
\(25\) 4.20414e6 2.15252
\(26\) 329583. 0.141444
\(27\) −531441. −0.192450
\(28\) −432944. −0.133113
\(29\) −1.44179e6 −0.378539 −0.189269 0.981925i \(-0.560612\pi\)
−0.189269 + 0.981925i \(0.560612\pi\)
\(30\) 3.15757e6 0.711717
\(31\) −973200. −0.189267 −0.0946334 0.995512i \(-0.530168\pi\)
−0.0946334 + 0.995512i \(0.530168\pi\)
\(32\) 5.37112e6 0.905503
\(33\) −5.83156e6 −0.855997
\(34\) −1.57764e6 −0.202467
\(35\) −4.05093e6 −0.456298
\(36\) −1.73997e6 −0.172655
\(37\) 6.01928e6 0.528004 0.264002 0.964522i \(-0.414957\pi\)
0.264002 + 0.964522i \(0.414957\pi\)
\(38\) 1.97245e6 0.153454
\(39\) −1.69932e6 −0.117621
\(40\) 3.02970e7 1.87124
\(41\) 6.93821e6 0.383460 0.191730 0.981448i \(-0.438590\pi\)
0.191730 + 0.981448i \(0.438590\pi\)
\(42\) −2.07740e6 −0.103014
\(43\) 5.22977e6 0.233278 0.116639 0.993174i \(-0.462788\pi\)
0.116639 + 0.993174i \(0.462788\pi\)
\(44\) −1.90928e7 −0.767951
\(45\) −1.62804e7 −0.591845
\(46\) 1.19378e7 0.393109
\(47\) −3.13303e7 −0.936535 −0.468267 0.883587i \(-0.655122\pi\)
−0.468267 + 0.883587i \(0.655122\pi\)
\(48\) 4.53861e6 0.123406
\(49\) −3.76885e7 −0.933955
\(50\) 6.60467e7 1.49447
\(51\) 8.13429e6 0.168366
\(52\) −5.56368e6 −0.105523
\(53\) 5.51922e7 0.960807 0.480403 0.877048i \(-0.340490\pi\)
0.480403 + 0.877048i \(0.340490\pi\)
\(54\) −8.34890e6 −0.133616
\(55\) −1.78646e8 −2.63246
\(56\) −1.99327e7 −0.270845
\(57\) −1.01699e7 −0.127608
\(58\) −2.26504e7 −0.262815
\(59\) −1.21174e7 −0.130189
\(60\) −5.33028e7 −0.530969
\(61\) −1.66783e8 −1.54229 −0.771147 0.636658i \(-0.780317\pi\)
−0.771147 + 0.636658i \(0.780317\pi\)
\(62\) −1.52889e7 −0.131406
\(63\) 1.07110e7 0.0856639
\(64\) 1.13068e8 0.842425
\(65\) −5.20577e7 −0.361722
\(66\) −9.16133e7 −0.594307
\(67\) 9.31844e7 0.564945 0.282473 0.959275i \(-0.408845\pi\)
0.282473 + 0.959275i \(0.408845\pi\)
\(68\) 2.66321e7 0.151048
\(69\) −6.15509e7 −0.326899
\(70\) −6.36397e7 −0.316801
\(71\) −4.01312e7 −0.187422 −0.0937108 0.995599i \(-0.529873\pi\)
−0.0937108 + 0.995599i \(0.529873\pi\)
\(72\) −8.01080e7 −0.351301
\(73\) −2.58311e8 −1.06461 −0.532305 0.846553i \(-0.678674\pi\)
−0.532305 + 0.846553i \(0.678674\pi\)
\(74\) 9.45624e7 0.366586
\(75\) −3.40536e8 −1.24276
\(76\) −3.32968e7 −0.114483
\(77\) 1.17533e8 0.381024
\(78\) −2.66962e7 −0.0816628
\(79\) −3.62808e8 −1.04798 −0.523992 0.851723i \(-0.675558\pi\)
−0.523992 + 0.851723i \(0.675558\pi\)
\(80\) 1.39037e8 0.379513
\(81\) 4.30467e7 0.111111
\(82\) 1.08999e8 0.266231
\(83\) 5.97676e8 1.38234 0.691169 0.722693i \(-0.257096\pi\)
0.691169 + 0.722693i \(0.257096\pi\)
\(84\) 3.50684e7 0.0768528
\(85\) 2.49189e8 0.517778
\(86\) 8.21592e7 0.161962
\(87\) 1.16785e8 0.218549
\(88\) −8.79034e8 −1.56255
\(89\) 6.86238e8 1.15936 0.579682 0.814843i \(-0.303177\pi\)
0.579682 + 0.814843i \(0.303177\pi\)
\(90\) −2.55763e8 −0.410910
\(91\) 3.42493e7 0.0523559
\(92\) −2.01521e8 −0.293275
\(93\) 7.88292e7 0.109273
\(94\) −4.92196e8 −0.650224
\(95\) −3.11548e8 −0.392436
\(96\) −4.35061e8 −0.522792
\(97\) 2.73324e7 0.0313476 0.0156738 0.999877i \(-0.495011\pi\)
0.0156738 + 0.999877i \(0.495011\pi\)
\(98\) −5.92083e8 −0.648433
\(99\) 4.72356e8 0.494210
\(100\) −1.11493e9 −1.11493
\(101\) −1.63234e9 −1.56087 −0.780433 0.625240i \(-0.785001\pi\)
−0.780433 + 0.625240i \(0.785001\pi\)
\(102\) 1.27789e8 0.116894
\(103\) 1.28691e9 1.12663 0.563315 0.826242i \(-0.309526\pi\)
0.563315 + 0.826242i \(0.309526\pi\)
\(104\) −2.56152e8 −0.214707
\(105\) 3.28125e8 0.263444
\(106\) 8.67064e8 0.667075
\(107\) 8.46105e8 0.624018 0.312009 0.950079i \(-0.398998\pi\)
0.312009 + 0.950079i \(0.398998\pi\)
\(108\) 1.40937e8 0.0996825
\(109\) −6.07335e8 −0.412106 −0.206053 0.978541i \(-0.566062\pi\)
−0.206053 + 0.978541i \(0.566062\pi\)
\(110\) −2.80652e9 −1.82768
\(111\) −4.87562e8 −0.304843
\(112\) −9.14741e7 −0.0549309
\(113\) −1.20739e9 −0.696620 −0.348310 0.937379i \(-0.613244\pi\)
−0.348310 + 0.937379i \(0.613244\pi\)
\(114\) −1.59768e8 −0.0885969
\(115\) −1.88557e9 −1.00532
\(116\) 3.82360e8 0.196070
\(117\) 1.37645e8 0.0679086
\(118\) −1.90363e8 −0.0903885
\(119\) −1.63944e8 −0.0749435
\(120\) −2.45406e9 −1.08036
\(121\) 2.82527e9 1.19819
\(122\) −2.62014e9 −1.07079
\(123\) −5.61995e8 −0.221391
\(124\) 2.58091e8 0.0980338
\(125\) −5.58564e9 −2.04634
\(126\) 1.68269e8 0.0594753
\(127\) 4.29748e9 1.46587 0.732937 0.680296i \(-0.238149\pi\)
0.732937 + 0.680296i \(0.238149\pi\)
\(128\) −9.73718e8 −0.320618
\(129\) −4.23611e8 −0.134683
\(130\) −8.17823e8 −0.251139
\(131\) 6.42427e8 0.190591 0.0952956 0.995449i \(-0.469620\pi\)
0.0952956 + 0.995449i \(0.469620\pi\)
\(132\) 1.54652e9 0.443377
\(133\) 2.04971e8 0.0568015
\(134\) 1.46392e9 0.392234
\(135\) 1.31871e9 0.341702
\(136\) 1.22614e9 0.307337
\(137\) 4.33548e9 1.05146 0.525732 0.850650i \(-0.323792\pi\)
0.525732 + 0.850650i \(0.323792\pi\)
\(138\) −9.66960e8 −0.226962
\(139\) −3.46178e9 −0.786563 −0.393281 0.919418i \(-0.628660\pi\)
−0.393281 + 0.919418i \(0.628660\pi\)
\(140\) 1.07430e9 0.236347
\(141\) 2.53775e9 0.540709
\(142\) −6.30458e8 −0.130124
\(143\) 1.51040e9 0.302050
\(144\) −3.67627e8 −0.0712486
\(145\) 3.57763e9 0.672108
\(146\) −4.05805e9 −0.739145
\(147\) 3.05277e9 0.539219
\(148\) −1.59630e9 −0.273488
\(149\) −1.39148e9 −0.231280 −0.115640 0.993291i \(-0.536892\pi\)
−0.115640 + 0.993291i \(0.536892\pi\)
\(150\) −5.34979e9 −0.862831
\(151\) 4.41234e9 0.690673 0.345336 0.938479i \(-0.387765\pi\)
0.345336 + 0.938479i \(0.387765\pi\)
\(152\) −1.53298e9 −0.232938
\(153\) −6.58878e8 −0.0972061
\(154\) 1.84644e9 0.264540
\(155\) 2.41488e9 0.336050
\(156\) 4.50658e8 0.0609237
\(157\) −1.34294e10 −1.76404 −0.882021 0.471211i \(-0.843817\pi\)
−0.882021 + 0.471211i \(0.843817\pi\)
\(158\) −5.69968e9 −0.727602
\(159\) −4.47056e9 −0.554722
\(160\) −1.33278e10 −1.60775
\(161\) 1.24054e9 0.145510
\(162\) 6.76261e8 0.0771430
\(163\) 1.05500e10 1.17060 0.585298 0.810818i \(-0.300978\pi\)
0.585298 + 0.810818i \(0.300978\pi\)
\(164\) −1.84000e9 −0.198619
\(165\) 1.44703e10 1.51985
\(166\) 9.38943e9 0.959739
\(167\) 1.91306e9 0.190328 0.0951642 0.995462i \(-0.469662\pi\)
0.0951642 + 0.995462i \(0.469662\pi\)
\(168\) 1.61455e9 0.156372
\(169\) −1.01644e10 −0.958496
\(170\) 3.91474e9 0.359486
\(171\) 8.23761e8 0.0736748
\(172\) −1.38693e9 −0.120830
\(173\) −1.79045e10 −1.51969 −0.759846 0.650103i \(-0.774726\pi\)
−0.759846 + 0.650103i \(0.774726\pi\)
\(174\) 1.83468e9 0.151736
\(175\) 6.86338e9 0.553180
\(176\) −4.03401e9 −0.316906
\(177\) 9.81506e8 0.0751646
\(178\) 1.07807e10 0.804931
\(179\) −7.61767e9 −0.554605 −0.277302 0.960783i \(-0.589440\pi\)
−0.277302 + 0.960783i \(0.589440\pi\)
\(180\) 4.31753e9 0.306555
\(181\) −2.33571e10 −1.61758 −0.808788 0.588101i \(-0.799876\pi\)
−0.808788 + 0.588101i \(0.799876\pi\)
\(182\) 5.38054e8 0.0363500
\(183\) 1.35094e10 0.890443
\(184\) −9.27803e9 −0.596727
\(185\) −1.49362e10 −0.937489
\(186\) 1.23840e9 0.0758670
\(187\) −7.22994e9 −0.432362
\(188\) 8.30874e9 0.485093
\(189\) −8.67592e8 −0.0494581
\(190\) −4.89440e9 −0.272463
\(191\) −1.50832e10 −0.820057 −0.410029 0.912073i \(-0.634481\pi\)
−0.410029 + 0.912073i \(0.634481\pi\)
\(192\) −9.15853e9 −0.486374
\(193\) −1.68362e10 −0.873446 −0.436723 0.899596i \(-0.643861\pi\)
−0.436723 + 0.899596i \(0.643861\pi\)
\(194\) 4.29389e8 0.0217642
\(195\) 4.21667e9 0.208840
\(196\) 9.99492e9 0.483757
\(197\) −1.40072e10 −0.662601 −0.331301 0.943525i \(-0.607487\pi\)
−0.331301 + 0.943525i \(0.607487\pi\)
\(198\) 7.42068e9 0.343123
\(199\) 7.08429e9 0.320227 0.160113 0.987099i \(-0.448814\pi\)
0.160113 + 0.987099i \(0.448814\pi\)
\(200\) −5.13314e10 −2.26855
\(201\) −7.54794e9 −0.326171
\(202\) −2.56440e10 −1.08369
\(203\) −2.35376e9 −0.0972814
\(204\) −2.15720e9 −0.0872077
\(205\) −1.72164e10 −0.680847
\(206\) 2.02173e10 0.782205
\(207\) 4.98563e9 0.188735
\(208\) −1.17552e9 −0.0435455
\(209\) 9.03922e9 0.327697
\(210\) 5.15482e9 0.182905
\(211\) −1.28875e10 −0.447609 −0.223804 0.974634i \(-0.571848\pi\)
−0.223804 + 0.974634i \(0.571848\pi\)
\(212\) −1.46369e10 −0.497665
\(213\) 3.25063e9 0.108208
\(214\) 1.32922e10 0.433248
\(215\) −1.29771e10 −0.414194
\(216\) 6.48875e9 0.202824
\(217\) −1.58878e9 −0.0486400
\(218\) −9.54119e9 −0.286120
\(219\) 2.09232e10 0.614653
\(220\) 4.73767e10 1.36352
\(221\) −2.10681e9 −0.0594101
\(222\) −7.65956e9 −0.211649
\(223\) −1.54290e10 −0.417799 −0.208899 0.977937i \(-0.566988\pi\)
−0.208899 + 0.977937i \(0.566988\pi\)
\(224\) 8.76850e9 0.232707
\(225\) 2.75834e10 0.717507
\(226\) −1.89681e10 −0.483654
\(227\) 7.87485e9 0.196846 0.0984229 0.995145i \(-0.468620\pi\)
0.0984229 + 0.995145i \(0.468620\pi\)
\(228\) 2.69704e9 0.0660968
\(229\) 2.02461e10 0.486499 0.243250 0.969964i \(-0.421787\pi\)
0.243250 + 0.969964i \(0.421787\pi\)
\(230\) −2.96222e10 −0.697979
\(231\) −9.52018e9 −0.219984
\(232\) 1.76038e10 0.398943
\(233\) 1.16127e10 0.258126 0.129063 0.991636i \(-0.458803\pi\)
0.129063 + 0.991636i \(0.458803\pi\)
\(234\) 2.16240e9 0.0471481
\(235\) 7.77425e10 1.66285
\(236\) 3.21351e9 0.0674334
\(237\) 2.93874e10 0.605054
\(238\) −2.57554e9 −0.0520323
\(239\) 3.57480e10 0.708697 0.354349 0.935113i \(-0.384703\pi\)
0.354349 + 0.935113i \(0.384703\pi\)
\(240\) −1.12620e10 −0.219112
\(241\) 3.30065e10 0.630264 0.315132 0.949048i \(-0.397951\pi\)
0.315132 + 0.949048i \(0.397951\pi\)
\(242\) 4.43848e10 0.831888
\(243\) −3.48678e9 −0.0641500
\(244\) 4.42305e10 0.798855
\(245\) 9.35196e10 1.65827
\(246\) −8.82890e9 −0.153709
\(247\) 2.63404e9 0.0450284
\(248\) 1.18825e10 0.199469
\(249\) −4.84117e10 −0.798093
\(250\) −8.77499e10 −1.42075
\(251\) −1.11796e10 −0.177785 −0.0888926 0.996041i \(-0.528333\pi\)
−0.0888926 + 0.996041i \(0.528333\pi\)
\(252\) −2.84054e9 −0.0443710
\(253\) 5.47078e10 0.839474
\(254\) 6.75130e10 1.01774
\(255\) −2.01843e10 −0.298939
\(256\) −7.31880e10 −1.06503
\(257\) 6.82071e10 0.975283 0.487642 0.873044i \(-0.337857\pi\)
0.487642 + 0.873044i \(0.337857\pi\)
\(258\) −6.65490e9 −0.0935089
\(259\) 9.82664e9 0.135693
\(260\) 1.38056e10 0.187360
\(261\) −9.45957e9 −0.126180
\(262\) 1.00925e10 0.132325
\(263\) −1.28524e11 −1.65647 −0.828236 0.560379i \(-0.810655\pi\)
−0.828236 + 0.560379i \(0.810655\pi\)
\(264\) 7.12017e10 0.902138
\(265\) −1.36953e11 −1.70594
\(266\) 3.22007e9 0.0394365
\(267\) −5.55853e10 −0.669359
\(268\) −2.47124e10 −0.292622
\(269\) −1.82550e9 −0.0212567 −0.0106283 0.999944i \(-0.503383\pi\)
−0.0106283 + 0.999944i \(0.503383\pi\)
\(270\) 2.07168e10 0.237239
\(271\) 1.42806e11 1.60836 0.804182 0.594383i \(-0.202604\pi\)
0.804182 + 0.594383i \(0.202604\pi\)
\(272\) 5.62694e9 0.0623322
\(273\) −2.77419e9 −0.0302277
\(274\) 6.81100e10 0.730017
\(275\) 3.02675e11 3.19139
\(276\) 1.63232e10 0.169323
\(277\) −1.25742e11 −1.28328 −0.641640 0.767006i \(-0.721745\pi\)
−0.641640 + 0.767006i \(0.721745\pi\)
\(278\) −5.43843e10 −0.546100
\(279\) −6.38517e9 −0.0630890
\(280\) 4.94607e10 0.480894
\(281\) 6.80928e10 0.651513 0.325756 0.945454i \(-0.394381\pi\)
0.325756 + 0.945454i \(0.394381\pi\)
\(282\) 3.98679e10 0.375407
\(283\) −1.28817e11 −1.19381 −0.596904 0.802313i \(-0.703603\pi\)
−0.596904 + 0.802313i \(0.703603\pi\)
\(284\) 1.06427e10 0.0970780
\(285\) 2.52354e10 0.226573
\(286\) 2.37282e10 0.209709
\(287\) 1.13268e10 0.0985461
\(288\) 3.52399e10 0.301834
\(289\) −1.08503e11 −0.914959
\(290\) 5.62043e10 0.466636
\(291\) −2.21392e9 −0.0180986
\(292\) 6.85038e10 0.551432
\(293\) 1.18257e11 0.937394 0.468697 0.883359i \(-0.344724\pi\)
0.468697 + 0.883359i \(0.344724\pi\)
\(294\) 4.79587e10 0.374373
\(295\) 3.00678e10 0.231155
\(296\) −7.34938e10 −0.556465
\(297\) −3.82609e10 −0.285332
\(298\) −2.18600e10 −0.160575
\(299\) 1.59419e10 0.115351
\(300\) 9.03095e10 0.643706
\(301\) 8.53774e9 0.0599506
\(302\) 6.93174e10 0.479525
\(303\) 1.32220e11 0.901166
\(304\) −7.03508e9 −0.0472430
\(305\) 4.13852e11 2.73839
\(306\) −1.03509e10 −0.0674889
\(307\) 1.20165e11 0.772070 0.386035 0.922484i \(-0.373844\pi\)
0.386035 + 0.922484i \(0.373844\pi\)
\(308\) −3.11696e10 −0.197357
\(309\) −1.04240e11 −0.650461
\(310\) 3.79376e10 0.233315
\(311\) 1.52314e11 0.923246 0.461623 0.887076i \(-0.347267\pi\)
0.461623 + 0.887076i \(0.347267\pi\)
\(312\) 2.07483e10 0.123961
\(313\) −1.43895e11 −0.847416 −0.423708 0.905799i \(-0.639272\pi\)
−0.423708 + 0.905799i \(0.639272\pi\)
\(314\) −2.10975e11 −1.22475
\(315\) −2.65781e10 −0.152099
\(316\) 9.62161e10 0.542820
\(317\) 4.34701e10 0.241782 0.120891 0.992666i \(-0.461425\pi\)
0.120891 + 0.992666i \(0.461425\pi\)
\(318\) −7.02322e10 −0.385136
\(319\) −1.03801e11 −0.561233
\(320\) −2.80566e11 −1.49575
\(321\) −6.85345e10 −0.360277
\(322\) 1.94888e10 0.101026
\(323\) −1.26086e10 −0.0644547
\(324\) −1.14159e10 −0.0575517
\(325\) 8.82000e10 0.438524
\(326\) 1.65739e11 0.812729
\(327\) 4.91941e10 0.237930
\(328\) −8.47137e10 −0.404130
\(329\) −5.11475e10 −0.240682
\(330\) 2.27328e11 1.05521
\(331\) 1.33209e11 0.609968 0.304984 0.952358i \(-0.401349\pi\)
0.304984 + 0.952358i \(0.401349\pi\)
\(332\) −1.58503e11 −0.716003
\(333\) 3.94925e10 0.176001
\(334\) 3.00539e10 0.132142
\(335\) −2.31226e11 −1.00308
\(336\) 7.40940e9 0.0317144
\(337\) 4.38081e10 0.185020 0.0925102 0.995712i \(-0.470511\pi\)
0.0925102 + 0.995712i \(0.470511\pi\)
\(338\) −1.59681e11 −0.665471
\(339\) 9.77989e10 0.402194
\(340\) −6.60845e10 −0.268191
\(341\) −7.00651e10 −0.280613
\(342\) 1.29412e10 0.0511514
\(343\) −1.27406e11 −0.497011
\(344\) −6.38540e10 −0.245853
\(345\) 1.52732e11 0.580421
\(346\) −2.81279e11 −1.05510
\(347\) −2.17392e11 −0.804935 −0.402467 0.915434i \(-0.631847\pi\)
−0.402467 + 0.915434i \(0.631847\pi\)
\(348\) −3.09711e10 −0.113201
\(349\) 9.21736e10 0.332577 0.166288 0.986077i \(-0.446822\pi\)
0.166288 + 0.986077i \(0.446822\pi\)
\(350\) 1.07823e11 0.384066
\(351\) −1.11493e10 −0.0392070
\(352\) 3.86691e11 1.34253
\(353\) −4.92901e11 −1.68956 −0.844781 0.535113i \(-0.820269\pi\)
−0.844781 + 0.535113i \(0.820269\pi\)
\(354\) 1.54194e10 0.0521858
\(355\) 9.95810e10 0.332773
\(356\) −1.81989e11 −0.600511
\(357\) 1.32795e10 0.0432686
\(358\) −1.19673e11 −0.385055
\(359\) 1.26242e11 0.401123 0.200562 0.979681i \(-0.435723\pi\)
0.200562 + 0.979681i \(0.435723\pi\)
\(360\) 1.98779e11 0.623747
\(361\) −3.06924e11 −0.951148
\(362\) −3.66937e11 −1.12306
\(363\) −2.28847e11 −0.691775
\(364\) −9.08286e9 −0.0271185
\(365\) 6.40970e11 1.89025
\(366\) 2.12232e11 0.618223
\(367\) −4.99871e11 −1.43834 −0.719169 0.694835i \(-0.755477\pi\)
−0.719169 + 0.694835i \(0.755477\pi\)
\(368\) −4.25782e10 −0.121024
\(369\) 4.55216e10 0.127820
\(370\) −2.34646e11 −0.650886
\(371\) 9.01027e10 0.246919
\(372\) −2.09054e10 −0.0565998
\(373\) −3.99849e11 −1.06956 −0.534781 0.844991i \(-0.679606\pi\)
−0.534781 + 0.844991i \(0.679606\pi\)
\(374\) −1.13582e11 −0.300183
\(375\) 4.52437e11 1.18145
\(376\) 3.82534e11 0.987018
\(377\) −3.02477e10 −0.0771181
\(378\) −1.36298e10 −0.0343381
\(379\) 6.91858e11 1.72243 0.861213 0.508245i \(-0.169705\pi\)
0.861213 + 0.508245i \(0.169705\pi\)
\(380\) 8.26221e10 0.203269
\(381\) −3.48096e11 −0.846323
\(382\) −2.36956e11 −0.569355
\(383\) −2.13034e11 −0.505888 −0.252944 0.967481i \(-0.581399\pi\)
−0.252944 + 0.967481i \(0.581399\pi\)
\(384\) 7.88712e10 0.185109
\(385\) −2.91645e11 −0.676520
\(386\) −2.64495e11 −0.606422
\(387\) 3.43125e10 0.0777594
\(388\) −7.24850e9 −0.0162370
\(389\) 2.17993e11 0.482692 0.241346 0.970439i \(-0.422411\pi\)
0.241346 + 0.970439i \(0.422411\pi\)
\(390\) 6.62436e10 0.144995
\(391\) −7.63105e10 −0.165116
\(392\) 4.60166e11 0.984299
\(393\) −5.20366e10 −0.110038
\(394\) −2.20052e11 −0.460035
\(395\) 9.00266e11 1.86073
\(396\) −1.25268e11 −0.255984
\(397\) −1.38887e11 −0.280612 −0.140306 0.990108i \(-0.544809\pi\)
−0.140306 + 0.990108i \(0.544809\pi\)
\(398\) 1.11294e11 0.222329
\(399\) −1.66026e10 −0.0327943
\(400\) −2.35567e11 −0.460092
\(401\) −7.87148e11 −1.52022 −0.760111 0.649794i \(-0.774855\pi\)
−0.760111 + 0.649794i \(0.774855\pi\)
\(402\) −1.18577e11 −0.226457
\(403\) −2.04171e10 −0.0385585
\(404\) 4.32895e11 0.808475
\(405\) −1.06815e11 −0.197282
\(406\) −3.69773e10 −0.0675412
\(407\) 4.33356e11 0.782834
\(408\) −9.93175e10 −0.177441
\(409\) −1.03924e12 −1.83637 −0.918187 0.396148i \(-0.870347\pi\)
−0.918187 + 0.396148i \(0.870347\pi\)
\(410\) −2.70468e11 −0.472703
\(411\) −3.51174e11 −0.607063
\(412\) −3.41287e11 −0.583556
\(413\) −1.97819e10 −0.0334575
\(414\) 7.83238e10 0.131036
\(415\) −1.48306e12 −2.45439
\(416\) 1.12682e11 0.184474
\(417\) 2.80404e11 0.454122
\(418\) 1.42005e11 0.227516
\(419\) −1.85571e11 −0.294136 −0.147068 0.989126i \(-0.546984\pi\)
−0.147068 + 0.989126i \(0.546984\pi\)
\(420\) −8.70183e10 −0.136455
\(421\) −5.98397e11 −0.928368 −0.464184 0.885739i \(-0.653652\pi\)
−0.464184 + 0.885739i \(0.653652\pi\)
\(422\) −2.02462e11 −0.310769
\(423\) −2.05558e11 −0.312178
\(424\) −6.73881e11 −1.01260
\(425\) −4.22194e11 −0.627714
\(426\) 5.10671e10 0.0751274
\(427\) −2.72277e11 −0.396357
\(428\) −2.24386e11 −0.323220
\(429\) −1.22342e11 −0.174389
\(430\) −2.03869e11 −0.287569
\(431\) 1.23001e12 1.71696 0.858478 0.512850i \(-0.171410\pi\)
0.858478 + 0.512850i \(0.171410\pi\)
\(432\) 2.97778e10 0.0411354
\(433\) −5.20413e11 −0.711463 −0.355732 0.934588i \(-0.615768\pi\)
−0.355732 + 0.934588i \(0.615768\pi\)
\(434\) −2.49595e10 −0.0337701
\(435\) −2.89788e11 −0.388042
\(436\) 1.61064e11 0.213457
\(437\) 9.54072e10 0.125145
\(438\) 3.28702e11 0.426746
\(439\) −7.79982e11 −1.00229 −0.501146 0.865363i \(-0.667088\pi\)
−0.501146 + 0.865363i \(0.667088\pi\)
\(440\) 2.18122e12 2.77436
\(441\) −2.47274e11 −0.311318
\(442\) −3.30978e10 −0.0412477
\(443\) −1.51957e12 −1.87458 −0.937291 0.348548i \(-0.886675\pi\)
−0.937291 + 0.348548i \(0.886675\pi\)
\(444\) 1.29301e11 0.157898
\(445\) −1.70282e12 −2.05849
\(446\) −2.42389e11 −0.290072
\(447\) 1.12710e11 0.133530
\(448\) 1.84587e11 0.216496
\(449\) 9.46589e11 1.09914 0.549570 0.835448i \(-0.314792\pi\)
0.549570 + 0.835448i \(0.314792\pi\)
\(450\) 4.33333e11 0.498156
\(451\) 4.99514e11 0.568530
\(452\) 3.20199e11 0.360825
\(453\) −3.57399e11 −0.398760
\(454\) 1.23713e11 0.136667
\(455\) −8.49856e10 −0.0929596
\(456\) 1.24172e11 0.134487
\(457\) −1.31278e12 −1.40789 −0.703943 0.710256i \(-0.748579\pi\)
−0.703943 + 0.710256i \(0.748579\pi\)
\(458\) 3.18065e11 0.337770
\(459\) 5.33691e10 0.0561219
\(460\) 5.00051e11 0.520720
\(461\) −9.37640e10 −0.0966901 −0.0483450 0.998831i \(-0.515395\pi\)
−0.0483450 + 0.998831i \(0.515395\pi\)
\(462\) −1.49561e11 −0.152732
\(463\) −4.76737e11 −0.482131 −0.241065 0.970509i \(-0.577497\pi\)
−0.241065 + 0.970509i \(0.577497\pi\)
\(464\) 8.07865e10 0.0809111
\(465\) −1.95606e11 −0.194018
\(466\) 1.82435e11 0.179214
\(467\) 1.50733e12 1.46650 0.733249 0.679960i \(-0.238003\pi\)
0.733249 + 0.679960i \(0.238003\pi\)
\(468\) −3.65033e10 −0.0351743
\(469\) 1.52126e11 0.145186
\(470\) 1.22133e12 1.15449
\(471\) 1.08778e12 1.01847
\(472\) 1.47950e11 0.137207
\(473\) 3.76515e11 0.345865
\(474\) 4.61674e11 0.420081
\(475\) 5.27848e11 0.475760
\(476\) 4.34777e10 0.0388181
\(477\) 3.62116e11 0.320269
\(478\) 5.61598e11 0.492039
\(479\) −4.82675e11 −0.418933 −0.209467 0.977816i \(-0.567173\pi\)
−0.209467 + 0.977816i \(0.567173\pi\)
\(480\) 1.07955e12 0.928235
\(481\) 1.26280e11 0.107568
\(482\) 5.18529e11 0.437584
\(483\) −1.00484e11 −0.0840104
\(484\) −7.49257e11 −0.620621
\(485\) −6.78221e10 −0.0556588
\(486\) −5.47771e10 −0.0445385
\(487\) −1.54778e12 −1.24690 −0.623448 0.781865i \(-0.714269\pi\)
−0.623448 + 0.781865i \(0.714269\pi\)
\(488\) 2.03637e12 1.62543
\(489\) −8.54547e11 −0.675844
\(490\) 1.46918e12 1.15131
\(491\) 1.47468e12 1.14507 0.572534 0.819881i \(-0.305961\pi\)
0.572534 + 0.819881i \(0.305961\pi\)
\(492\) 1.49040e11 0.114673
\(493\) 1.44789e11 0.110389
\(494\) 4.13806e10 0.0312626
\(495\) −1.17210e12 −0.877486
\(496\) 5.45306e10 0.0404550
\(497\) −6.55153e10 −0.0481658
\(498\) −7.60544e11 −0.554105
\(499\) −8.77017e11 −0.633222 −0.316611 0.948556i \(-0.602545\pi\)
−0.316611 + 0.948556i \(0.602545\pi\)
\(500\) 1.48130e12 1.05993
\(501\) −1.54957e11 −0.109886
\(502\) −1.75631e11 −0.123434
\(503\) −1.48585e12 −1.03495 −0.517474 0.855699i \(-0.673128\pi\)
−0.517474 + 0.855699i \(0.673128\pi\)
\(504\) −1.30778e11 −0.0902815
\(505\) 4.05047e12 2.77137
\(506\) 8.59455e11 0.582836
\(507\) 8.23314e11 0.553388
\(508\) −1.13968e12 −0.759273
\(509\) −1.72731e12 −1.14062 −0.570308 0.821431i \(-0.693176\pi\)
−0.570308 + 0.821431i \(0.693176\pi\)
\(510\) −3.17094e11 −0.207550
\(511\) −4.21700e11 −0.273596
\(512\) −6.51234e11 −0.418815
\(513\) −6.67247e10 −0.0425362
\(514\) 1.07153e12 0.677126
\(515\) −3.19333e12 −2.00037
\(516\) 1.12341e11 0.0697613
\(517\) −2.25561e12 −1.38853
\(518\) 1.54376e11 0.0942096
\(519\) 1.45027e12 0.877395
\(520\) 6.35610e11 0.381220
\(521\) 7.82017e11 0.464993 0.232496 0.972597i \(-0.425311\pi\)
0.232496 + 0.972597i \(0.425311\pi\)
\(522\) −1.48609e11 −0.0876048
\(523\) −2.13367e12 −1.24701 −0.623504 0.781820i \(-0.714291\pi\)
−0.623504 + 0.781820i \(0.714291\pi\)
\(524\) −1.70371e11 −0.0987197
\(525\) −5.55934e11 −0.319379
\(526\) −2.01911e12 −1.15007
\(527\) 9.77320e10 0.0551937
\(528\) 3.26755e11 0.182966
\(529\) −1.22372e12 −0.679411
\(530\) −2.15152e12 −1.18442
\(531\) −7.95020e10 −0.0433963
\(532\) −5.43579e10 −0.0294212
\(533\) 1.45559e11 0.0781207
\(534\) −8.73240e11 −0.464727
\(535\) −2.09951e12 −1.10797
\(536\) −1.13776e12 −0.595398
\(537\) 6.17031e11 0.320201
\(538\) −2.86784e10 −0.0147582
\(539\) −2.71336e12 −1.38471
\(540\) −3.49720e11 −0.176990
\(541\) −8.84532e11 −0.443941 −0.221971 0.975053i \(-0.571249\pi\)
−0.221971 + 0.975053i \(0.571249\pi\)
\(542\) 2.24347e12 1.11667
\(543\) 1.89192e12 0.933907
\(544\) −5.39386e11 −0.264061
\(545\) 1.50703e12 0.731709
\(546\) −4.35823e10 −0.0209867
\(547\) 1.54270e12 0.736783 0.368391 0.929671i \(-0.379909\pi\)
0.368391 + 0.929671i \(0.379909\pi\)
\(548\) −1.14976e12 −0.544622
\(549\) −1.09426e12 −0.514098
\(550\) 4.75501e12 2.21574
\(551\) −1.81023e11 −0.0836663
\(552\) 7.51520e11 0.344520
\(553\) −5.92294e11 −0.269323
\(554\) −1.97540e12 −0.890964
\(555\) 1.20983e12 0.541259
\(556\) 9.18060e11 0.407412
\(557\) 2.50149e12 1.10116 0.550580 0.834782i \(-0.314406\pi\)
0.550580 + 0.834782i \(0.314406\pi\)
\(558\) −1.00310e11 −0.0438018
\(559\) 1.09717e11 0.0475248
\(560\) 2.26982e11 0.0975317
\(561\) 5.85625e11 0.249624
\(562\) 1.06973e12 0.452337
\(563\) 4.12189e12 1.72906 0.864528 0.502584i \(-0.167617\pi\)
0.864528 + 0.502584i \(0.167617\pi\)
\(564\) −6.73008e11 −0.280069
\(565\) 2.99601e12 1.23687
\(566\) −2.02371e12 −0.828845
\(567\) 7.02749e10 0.0285546
\(568\) 4.89991e11 0.197524
\(569\) −1.93214e12 −0.772738 −0.386369 0.922344i \(-0.626271\pi\)
−0.386369 + 0.922344i \(0.626271\pi\)
\(570\) 3.96446e11 0.157307
\(571\) 1.99421e12 0.785071 0.392536 0.919737i \(-0.371598\pi\)
0.392536 + 0.919737i \(0.371598\pi\)
\(572\) −4.00555e11 −0.156451
\(573\) 1.22174e12 0.473460
\(574\) 1.77944e11 0.0684193
\(575\) 3.19468e12 1.21877
\(576\) 7.41841e11 0.280808
\(577\) 1.57088e12 0.590001 0.295000 0.955497i \(-0.404680\pi\)
0.295000 + 0.955497i \(0.404680\pi\)
\(578\) −1.70457e12 −0.635244
\(579\) 1.36373e12 0.504284
\(580\) −9.48782e11 −0.348129
\(581\) 9.75722e11 0.355249
\(582\) −3.47805e10 −0.0125656
\(583\) 3.97354e12 1.42452
\(584\) 3.15391e12 1.12200
\(585\) −3.41551e11 −0.120574
\(586\) 1.85781e12 0.650820
\(587\) 1.24412e12 0.432504 0.216252 0.976338i \(-0.430617\pi\)
0.216252 + 0.976338i \(0.430617\pi\)
\(588\) −8.09589e11 −0.279297
\(589\) −1.22189e11 −0.0418326
\(590\) 4.72363e11 0.160488
\(591\) 1.13458e12 0.382553
\(592\) −3.37274e11 −0.112859
\(593\) −2.93383e12 −0.974292 −0.487146 0.873321i \(-0.661962\pi\)
−0.487146 + 0.873321i \(0.661962\pi\)
\(594\) −6.01075e11 −0.198102
\(595\) 4.06808e11 0.133065
\(596\) 3.69018e11 0.119795
\(597\) −5.73828e11 −0.184883
\(598\) 2.50446e11 0.0800865
\(599\) 2.07249e12 0.657767 0.328884 0.944370i \(-0.393328\pi\)
0.328884 + 0.944370i \(0.393328\pi\)
\(600\) 4.15785e12 1.30975
\(601\) −4.76700e12 −1.49043 −0.745213 0.666827i \(-0.767652\pi\)
−0.745213 + 0.666827i \(0.767652\pi\)
\(602\) 1.34127e11 0.0416229
\(603\) 6.11383e11 0.188315
\(604\) −1.17014e12 −0.357745
\(605\) −7.01058e12 −2.12743
\(606\) 2.07716e12 0.625668
\(607\) 3.17116e11 0.0948133 0.0474066 0.998876i \(-0.484904\pi\)
0.0474066 + 0.998876i \(0.484904\pi\)
\(608\) 6.74367e11 0.200138
\(609\) 1.90654e11 0.0561654
\(610\) 6.50158e12 1.90123
\(611\) −6.57288e11 −0.190796
\(612\) 1.74733e11 0.0503494
\(613\) −5.57634e12 −1.59506 −0.797530 0.603279i \(-0.793860\pi\)
−0.797530 + 0.603279i \(0.793860\pi\)
\(614\) 1.88779e12 0.536038
\(615\) 1.39453e12 0.393087
\(616\) −1.43505e12 −0.401562
\(617\) −4.78857e12 −1.33022 −0.665108 0.746747i \(-0.731615\pi\)
−0.665108 + 0.746747i \(0.731615\pi\)
\(618\) −1.63760e12 −0.451606
\(619\) 1.27618e12 0.349384 0.174692 0.984623i \(-0.444107\pi\)
0.174692 + 0.984623i \(0.444107\pi\)
\(620\) −6.40423e11 −0.174062
\(621\) −4.03836e11 −0.108966
\(622\) 2.39284e12 0.640998
\(623\) 1.12030e12 0.297947
\(624\) 9.52168e10 0.0251410
\(625\) 5.64890e12 1.48083
\(626\) −2.26058e12 −0.588350
\(627\) −7.32177e11 −0.189196
\(628\) 3.56146e12 0.913713
\(629\) −6.04477e11 −0.153975
\(630\) −4.17540e11 −0.105600
\(631\) 4.94728e12 1.24232 0.621161 0.783683i \(-0.286661\pi\)
0.621161 + 0.783683i \(0.286661\pi\)
\(632\) 4.42978e12 1.10447
\(633\) 1.04389e12 0.258427
\(634\) 6.82911e11 0.167866
\(635\) −1.06637e13 −2.60271
\(636\) 1.18559e12 0.287327
\(637\) −7.90678e11 −0.190271
\(638\) −1.63070e12 −0.389657
\(639\) −2.63301e11 −0.0624739
\(640\) 2.41617e12 0.569269
\(641\) 5.38898e12 1.26080 0.630399 0.776271i \(-0.282891\pi\)
0.630399 + 0.776271i \(0.282891\pi\)
\(642\) −1.07667e12 −0.250136
\(643\) −1.02124e12 −0.235602 −0.117801 0.993037i \(-0.537585\pi\)
−0.117801 + 0.993037i \(0.537585\pi\)
\(644\) −3.28989e11 −0.0753693
\(645\) 1.05114e12 0.239135
\(646\) −1.98080e11 −0.0447501
\(647\) −3.44500e12 −0.772895 −0.386447 0.922311i \(-0.626298\pi\)
−0.386447 + 0.922311i \(0.626298\pi\)
\(648\) −5.25589e11 −0.117100
\(649\) −8.72384e11 −0.193022
\(650\) 1.38561e12 0.304461
\(651\) 1.28691e11 0.0280823
\(652\) −2.79783e12 −0.606328
\(653\) 6.88490e12 1.48180 0.740898 0.671617i \(-0.234400\pi\)
0.740898 + 0.671617i \(0.234400\pi\)
\(654\) 7.72836e11 0.165191
\(655\) −1.59411e12 −0.338401
\(656\) −3.88763e11 −0.0819630
\(657\) −1.69478e12 −0.354870
\(658\) −8.03524e11 −0.167102
\(659\) −4.67100e12 −0.964773 −0.482386 0.875958i \(-0.660230\pi\)
−0.482386 + 0.875958i \(0.660230\pi\)
\(660\) −3.83751e12 −0.787231
\(661\) 3.71454e12 0.756830 0.378415 0.925636i \(-0.376469\pi\)
0.378415 + 0.925636i \(0.376469\pi\)
\(662\) 2.09270e12 0.423492
\(663\) 1.70652e11 0.0343005
\(664\) −7.29745e12 −1.45685
\(665\) −5.08611e11 −0.100853
\(666\) 6.20424e11 0.122195
\(667\) −1.09560e12 −0.214331
\(668\) −5.07339e11 −0.0985835
\(669\) 1.24975e12 0.241216
\(670\) −3.63255e12 −0.696425
\(671\) −1.20075e13 −2.28665
\(672\) −7.10248e11 −0.134353
\(673\) 1.00851e12 0.189502 0.0947511 0.995501i \(-0.469794\pi\)
0.0947511 + 0.995501i \(0.469794\pi\)
\(674\) 6.88221e11 0.128457
\(675\) −2.23425e12 −0.414253
\(676\) 2.69557e12 0.496468
\(677\) 9.99402e12 1.82848 0.914242 0.405168i \(-0.132787\pi\)
0.914242 + 0.405168i \(0.132787\pi\)
\(678\) 1.53641e12 0.279238
\(679\) 4.46208e10 0.00805608
\(680\) −3.04253e12 −0.545688
\(681\) −6.37863e11 −0.113649
\(682\) −1.10072e12 −0.194826
\(683\) −2.94151e12 −0.517222 −0.258611 0.965981i \(-0.583265\pi\)
−0.258611 + 0.965981i \(0.583265\pi\)
\(684\) −2.18460e11 −0.0381610
\(685\) −1.07580e13 −1.86691
\(686\) −2.00153e12 −0.345068
\(687\) −1.63994e12 −0.280881
\(688\) −2.93035e11 −0.0498623
\(689\) 1.15789e12 0.195741
\(690\) 2.39940e12 0.402978
\(691\) 5.36780e12 0.895664 0.447832 0.894118i \(-0.352196\pi\)
0.447832 + 0.894118i \(0.352196\pi\)
\(692\) 4.74826e12 0.787149
\(693\) 7.71135e11 0.127008
\(694\) −3.41521e12 −0.558856
\(695\) 8.59001e12 1.39657
\(696\) −1.42591e12 −0.230330
\(697\) −6.96759e11 −0.111824
\(698\) 1.44804e12 0.230904
\(699\) −9.40631e11 −0.149029
\(700\) −1.82016e12 −0.286528
\(701\) −6.20303e12 −0.970226 −0.485113 0.874451i \(-0.661222\pi\)
−0.485113 + 0.874451i \(0.661222\pi\)
\(702\) −1.75154e11 −0.0272209
\(703\) 7.55746e11 0.116702
\(704\) 8.14030e12 1.24900
\(705\) −6.29714e12 −0.960047
\(706\) −7.74344e12 −1.17304
\(707\) −2.66485e12 −0.401130
\(708\) −2.60294e11 −0.0389327
\(709\) 1.11494e13 1.65708 0.828541 0.559928i \(-0.189171\pi\)
0.828541 + 0.559928i \(0.189171\pi\)
\(710\) 1.56441e12 0.231040
\(711\) −2.38038e12 −0.349328
\(712\) −8.37878e12 −1.22186
\(713\) −7.39523e11 −0.107164
\(714\) 2.08619e11 0.0300408
\(715\) −3.74787e12 −0.536300
\(716\) 2.02019e12 0.287266
\(717\) −2.89558e12 −0.409166
\(718\) 1.98325e12 0.278495
\(719\) −1.13389e13 −1.58231 −0.791154 0.611616i \(-0.790520\pi\)
−0.791154 + 0.611616i \(0.790520\pi\)
\(720\) 9.12224e11 0.126504
\(721\) 2.10092e12 0.289535
\(722\) −4.82175e12 −0.660370
\(723\) −2.67352e12 −0.363883
\(724\) 6.19425e12 0.837848
\(725\) −6.06148e12 −0.814813
\(726\) −3.59517e12 −0.480291
\(727\) 9.02273e12 1.19793 0.598967 0.800773i \(-0.295578\pi\)
0.598967 + 0.800773i \(0.295578\pi\)
\(728\) −4.18174e11 −0.0551780
\(729\) 2.82430e11 0.0370370
\(730\) 1.00696e13 1.31238
\(731\) −5.25191e11 −0.0680282
\(732\) −3.58267e12 −0.461219
\(733\) −1.56301e12 −0.199984 −0.0999920 0.994988i \(-0.531882\pi\)
−0.0999920 + 0.994988i \(0.531882\pi\)
\(734\) −7.85294e12 −0.998619
\(735\) −7.57508e12 −0.957402
\(736\) 4.08145e12 0.512701
\(737\) 6.70877e12 0.837605
\(738\) 7.15141e11 0.0887438
\(739\) −5.73629e12 −0.707507 −0.353754 0.935339i \(-0.615095\pi\)
−0.353754 + 0.935339i \(0.615095\pi\)
\(740\) 3.96104e12 0.485587
\(741\) −2.13357e11 −0.0259971
\(742\) 1.41551e12 0.171433
\(743\) 5.90927e12 0.711352 0.355676 0.934609i \(-0.384251\pi\)
0.355676 + 0.934609i \(0.384251\pi\)
\(744\) −9.62483e11 −0.115164
\(745\) 3.45279e12 0.410645
\(746\) −6.28159e12 −0.742583
\(747\) 3.92135e12 0.460779
\(748\) 1.91737e12 0.223949
\(749\) 1.38129e12 0.160368
\(750\) 7.10774e12 0.820269
\(751\) 6.05076e11 0.0694113 0.0347056 0.999398i \(-0.488951\pi\)
0.0347056 + 0.999398i \(0.488951\pi\)
\(752\) 1.75550e12 0.200180
\(753\) 9.05550e11 0.102644
\(754\) −4.75189e11 −0.0535421
\(755\) −1.09487e13 −1.22631
\(756\) 2.30084e11 0.0256176
\(757\) 1.87357e12 0.207366 0.103683 0.994610i \(-0.466937\pi\)
0.103683 + 0.994610i \(0.466937\pi\)
\(758\) 1.08690e13 1.19586
\(759\) −4.43133e12 −0.484670
\(760\) 3.80392e12 0.413590
\(761\) 9.68739e12 1.04707 0.523535 0.852004i \(-0.324613\pi\)
0.523535 + 0.852004i \(0.324613\pi\)
\(762\) −5.46856e12 −0.587591
\(763\) −9.91491e11 −0.105908
\(764\) 4.00005e12 0.424762
\(765\) 1.63493e12 0.172593
\(766\) −3.34675e12 −0.351232
\(767\) −2.54214e11 −0.0265228
\(768\) 5.92823e12 0.614893
\(769\) −1.11147e13 −1.14611 −0.573057 0.819516i \(-0.694243\pi\)
−0.573057 + 0.819516i \(0.694243\pi\)
\(770\) −4.58172e12 −0.469699
\(771\) −5.52478e12 −0.563080
\(772\) 4.46493e12 0.452415
\(773\) 5.13307e12 0.517094 0.258547 0.965999i \(-0.416756\pi\)
0.258547 + 0.965999i \(0.416756\pi\)
\(774\) 5.39047e11 0.0539874
\(775\) −4.09147e12 −0.407401
\(776\) −3.33721e11 −0.0330374
\(777\) −7.95958e11 −0.0783422
\(778\) 3.42466e12 0.335127
\(779\) 8.71122e11 0.0847541
\(780\) −1.11826e12 −0.108172
\(781\) −2.88923e12 −0.277877
\(782\) −1.19883e12 −0.114638
\(783\) 7.66225e11 0.0728498
\(784\) 2.11177e12 0.199629
\(785\) 3.33235e13 3.13212
\(786\) −8.17491e11 −0.0763979
\(787\) −6.86470e12 −0.637875 −0.318937 0.947776i \(-0.603326\pi\)
−0.318937 + 0.947776i \(0.603326\pi\)
\(788\) 3.71468e12 0.343205
\(789\) 1.04105e13 0.956365
\(790\) 1.41431e13 1.29188
\(791\) −1.97110e12 −0.179026
\(792\) −5.76734e12 −0.520850
\(793\) −3.49899e12 −0.314205
\(794\) −2.18191e12 −0.194825
\(795\) 1.10932e13 0.984928
\(796\) −1.87874e12 −0.165866
\(797\) 9.50994e12 0.834863 0.417432 0.908708i \(-0.362930\pi\)
0.417432 + 0.908708i \(0.362930\pi\)
\(798\) −2.60826e11 −0.0227687
\(799\) 3.14629e12 0.273111
\(800\) 2.25809e13 1.94911
\(801\) 4.50241e12 0.386455
\(802\) −1.23660e13 −1.05547
\(803\) −1.85970e13 −1.57842
\(804\) 2.00170e12 0.168946
\(805\) −3.07825e12 −0.258358
\(806\) −3.20750e11 −0.0267707
\(807\) 1.47865e11 0.0122726
\(808\) 1.99305e13 1.64500
\(809\) −1.84582e13 −1.51503 −0.757516 0.652816i \(-0.773587\pi\)
−0.757516 + 0.652816i \(0.773587\pi\)
\(810\) −1.67806e12 −0.136970
\(811\) −7.97245e12 −0.647139 −0.323570 0.946204i \(-0.604883\pi\)
−0.323570 + 0.946204i \(0.604883\pi\)
\(812\) 6.24213e11 0.0503884
\(813\) −1.15673e13 −0.928589
\(814\) 6.80798e12 0.543511
\(815\) −2.61785e13 −2.07843
\(816\) −4.55782e11 −0.0359875
\(817\) 6.56620e11 0.0515602
\(818\) −1.63264e13 −1.27497
\(819\) 2.24710e11 0.0174520
\(820\) 4.56576e12 0.352655
\(821\) −1.51036e13 −1.16021 −0.580103 0.814543i \(-0.696988\pi\)
−0.580103 + 0.814543i \(0.696988\pi\)
\(822\) −5.51691e12 −0.421476
\(823\) −2.55362e13 −1.94025 −0.970125 0.242607i \(-0.921997\pi\)
−0.970125 + 0.242607i \(0.921997\pi\)
\(824\) −1.57129e13 −1.18736
\(825\) −2.45167e13 −1.84255
\(826\) −3.10772e11 −0.0232291
\(827\) 2.06767e13 1.53712 0.768558 0.639780i \(-0.220974\pi\)
0.768558 + 0.639780i \(0.220974\pi\)
\(828\) −1.32218e12 −0.0977584
\(829\) 2.61708e13 1.92452 0.962258 0.272137i \(-0.0877304\pi\)
0.962258 + 0.272137i \(0.0877304\pi\)
\(830\) −2.32988e13 −1.70405
\(831\) 1.01851e13 0.740902
\(832\) 2.37209e12 0.171624
\(833\) 3.78480e12 0.272358
\(834\) 4.40513e12 0.315291
\(835\) −4.74703e12 −0.337934
\(836\) −2.39719e12 −0.169736
\(837\) 5.17199e11 0.0364244
\(838\) −2.91531e12 −0.204214
\(839\) −1.97813e13 −1.37824 −0.689122 0.724645i \(-0.742004\pi\)
−0.689122 + 0.724645i \(0.742004\pi\)
\(840\) −4.00632e12 −0.277644
\(841\) −1.24284e13 −0.856708
\(842\) −9.40078e12 −0.644554
\(843\) −5.51552e12 −0.376151
\(844\) 3.41775e12 0.231846
\(845\) 2.52217e13 1.70184
\(846\) −3.22930e12 −0.216741
\(847\) 4.61233e12 0.307925
\(848\) −3.09254e12 −0.205368
\(849\) 1.04342e13 0.689246
\(850\) −6.63263e12 −0.435814
\(851\) 4.57398e12 0.298959
\(852\) −8.62062e11 −0.0560480
\(853\) −9.83550e12 −0.636101 −0.318050 0.948074i \(-0.603028\pi\)
−0.318050 + 0.948074i \(0.603028\pi\)
\(854\) −4.27746e12 −0.275185
\(855\) −2.04407e12 −0.130812
\(856\) −1.03307e13 −0.657655
\(857\) −2.31797e13 −1.46789 −0.733947 0.679207i \(-0.762324\pi\)
−0.733947 + 0.679207i \(0.762324\pi\)
\(858\) −1.92198e12 −0.121076
\(859\) −4.78226e12 −0.299684 −0.149842 0.988710i \(-0.547877\pi\)
−0.149842 + 0.988710i \(0.547877\pi\)
\(860\) 3.44150e12 0.214538
\(861\) −9.17473e11 −0.0568956
\(862\) 1.93233e13 1.19206
\(863\) −7.08844e11 −0.0435013 −0.0217506 0.999763i \(-0.506924\pi\)
−0.0217506 + 0.999763i \(0.506924\pi\)
\(864\) −2.85443e12 −0.174264
\(865\) 4.44281e13 2.69827
\(866\) −8.17564e12 −0.493960
\(867\) 8.78875e12 0.528252
\(868\) 4.21341e11 0.0251939
\(869\) −2.61202e13 −1.55377
\(870\) −4.55255e12 −0.269412
\(871\) 1.95494e12 0.115094
\(872\) 7.41540e12 0.434320
\(873\) 1.79328e11 0.0104492
\(874\) 1.49884e12 0.0868868
\(875\) −9.11871e12 −0.525893
\(876\) −5.54880e12 −0.318369
\(877\) −1.86698e13 −1.06572 −0.532859 0.846204i \(-0.678883\pi\)
−0.532859 + 0.846204i \(0.678883\pi\)
\(878\) −1.22535e13 −0.695878
\(879\) −9.57880e12 −0.541204
\(880\) 1.00099e13 0.562677
\(881\) −1.11188e12 −0.0621825 −0.0310912 0.999517i \(-0.509898\pi\)
−0.0310912 + 0.999517i \(0.509898\pi\)
\(882\) −3.88465e12 −0.216144
\(883\) −2.83915e13 −1.57169 −0.785843 0.618426i \(-0.787771\pi\)
−0.785843 + 0.618426i \(0.787771\pi\)
\(884\) 5.58723e11 0.0307724
\(885\) −2.43549e12 −0.133457
\(886\) −2.38723e13 −1.30150
\(887\) −2.15452e13 −1.16868 −0.584339 0.811510i \(-0.698646\pi\)
−0.584339 + 0.811510i \(0.698646\pi\)
\(888\) 5.95300e12 0.321275
\(889\) 7.01575e12 0.376718
\(890\) −2.67512e13 −1.42918
\(891\) 3.09913e12 0.164737
\(892\) 4.09176e12 0.216405
\(893\) −3.93365e12 −0.206997
\(894\) 1.77066e12 0.0927078
\(895\) 1.89024e13 0.984719
\(896\) −1.58962e12 −0.0823963
\(897\) −1.29130e12 −0.0665978
\(898\) 1.48708e13 0.763118
\(899\) 1.40315e12 0.0716449
\(900\) −7.31507e12 −0.371644
\(901\) −5.54258e12 −0.280189
\(902\) 7.84732e12 0.394723
\(903\) −6.91557e11 −0.0346125
\(904\) 1.47419e13 0.734170
\(905\) 5.79578e13 2.87206
\(906\) −5.61471e12 −0.276854
\(907\) 2.80098e13 1.37429 0.687143 0.726522i \(-0.258865\pi\)
0.687143 + 0.726522i \(0.258865\pi\)
\(908\) −2.08840e12 −0.101959
\(909\) −1.07098e13 −0.520288
\(910\) −1.33512e12 −0.0645406
\(911\) 1.11071e13 0.534281 0.267141 0.963658i \(-0.413921\pi\)
0.267141 + 0.963658i \(0.413921\pi\)
\(912\) 5.69841e11 0.0272758
\(913\) 4.30294e13 2.04949
\(914\) −2.06236e13 −0.977477
\(915\) −3.35220e13 −1.58101
\(916\) −5.36924e12 −0.251990
\(917\) 1.04878e12 0.0489804
\(918\) 8.38424e11 0.0389647
\(919\) −1.57365e13 −0.727758 −0.363879 0.931446i \(-0.618548\pi\)
−0.363879 + 0.931446i \(0.618548\pi\)
\(920\) 2.30223e13 1.05951
\(921\) −9.73339e12 −0.445755
\(922\) −1.47302e12 −0.0671307
\(923\) −8.41925e11 −0.0381826
\(924\) 2.52474e12 0.113944
\(925\) 2.53059e13 1.13654
\(926\) −7.48951e12 −0.334737
\(927\) 8.44344e12 0.375544
\(928\) −7.74401e12 −0.342768
\(929\) 2.12139e13 0.934435 0.467217 0.884142i \(-0.345257\pi\)
0.467217 + 0.884142i \(0.345257\pi\)
\(930\) −3.07295e12 −0.134704
\(931\) −4.73195e12 −0.206427
\(932\) −3.07968e12 −0.133701
\(933\) −1.23374e13 −0.533036
\(934\) 2.36800e13 1.01817
\(935\) 1.79402e13 0.767673
\(936\) −1.68061e12 −0.0715691
\(937\) 4.96097e12 0.210251 0.105126 0.994459i \(-0.466476\pi\)
0.105126 + 0.994459i \(0.466476\pi\)
\(938\) 2.38989e12 0.100801
\(939\) 1.16555e13 0.489256
\(940\) −2.06172e13 −0.861299
\(941\) 2.81479e13 1.17029 0.585143 0.810930i \(-0.301038\pi\)
0.585143 + 0.810930i \(0.301038\pi\)
\(942\) 1.70890e13 0.707110
\(943\) 5.27227e12 0.217117
\(944\) 6.78962e11 0.0278273
\(945\) 2.15283e12 0.0878145
\(946\) 5.91502e12 0.240130
\(947\) 3.56313e13 1.43965 0.719824 0.694156i \(-0.244222\pi\)
0.719824 + 0.694156i \(0.244222\pi\)
\(948\) −7.79350e12 −0.313397
\(949\) −5.41919e12 −0.216889
\(950\) 8.29245e12 0.330314
\(951\) −3.52108e12 −0.139593
\(952\) 2.00171e12 0.0789832
\(953\) 2.49292e13 0.979018 0.489509 0.871998i \(-0.337176\pi\)
0.489509 + 0.871998i \(0.337176\pi\)
\(954\) 5.68881e12 0.222358
\(955\) 3.74273e13 1.45604
\(956\) −9.48030e12 −0.367081
\(957\) 8.40787e12 0.324028
\(958\) −7.58278e12 −0.290860
\(959\) 7.07778e12 0.270218
\(960\) 2.27258e13 0.863574
\(961\) −2.54925e13 −0.964178
\(962\) 1.98385e12 0.0746830
\(963\) 5.55129e12 0.208006
\(964\) −8.75326e12 −0.326455
\(965\) 4.17771e13 1.55083
\(966\) −1.57859e12 −0.0583273
\(967\) −4.82176e13 −1.77332 −0.886659 0.462424i \(-0.846980\pi\)
−0.886659 + 0.462424i \(0.846980\pi\)
\(968\) −3.44958e13 −1.26278
\(969\) 1.02129e12 0.0372130
\(970\) −1.06548e12 −0.0386432
\(971\) 2.25803e12 0.0815161 0.0407580 0.999169i \(-0.487023\pi\)
0.0407580 + 0.999169i \(0.487023\pi\)
\(972\) 9.24690e11 0.0332275
\(973\) −5.65146e12 −0.202140
\(974\) −2.43156e13 −0.865703
\(975\) −7.14420e12 −0.253182
\(976\) 9.34521e12 0.329659
\(977\) 4.23005e13 1.48532 0.742660 0.669669i \(-0.233564\pi\)
0.742660 + 0.669669i \(0.233564\pi\)
\(978\) −1.34249e13 −0.469229
\(979\) 4.94054e13 1.71891
\(980\) −2.48012e13 −0.858927
\(981\) −3.98473e12 −0.137369
\(982\) 2.31671e13 0.795005
\(983\) 3.49372e13 1.19343 0.596716 0.802453i \(-0.296472\pi\)
0.596716 + 0.802453i \(0.296472\pi\)
\(984\) 6.86181e12 0.233325
\(985\) 3.47572e13 1.17647
\(986\) 2.27463e12 0.0766415
\(987\) 4.14295e12 0.138958
\(988\) −6.98543e11 −0.0233231
\(989\) 3.97404e12 0.132084
\(990\) −1.84136e13 −0.609227
\(991\) 4.83227e13 1.59155 0.795774 0.605594i \(-0.207064\pi\)
0.795774 + 0.605594i \(0.207064\pi\)
\(992\) −5.22717e12 −0.171382
\(993\) −1.07899e13 −0.352165
\(994\) −1.02924e12 −0.0334409
\(995\) −1.75788e13 −0.568573
\(996\) 1.28387e13 0.413385
\(997\) −1.14216e13 −0.366098 −0.183049 0.983104i \(-0.558597\pi\)
−0.183049 + 0.983104i \(0.558597\pi\)
\(998\) −1.37779e13 −0.439637
\(999\) −3.19889e12 −0.101614
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.1.14 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.14 21 1.1 even 1 trivial