Properties

Label 177.10.a.c.1.6
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
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: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-20.5236 q^{2} -81.0000 q^{3} -90.7810 q^{4} -622.721 q^{5} +1662.41 q^{6} +1394.83 q^{7} +12371.2 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-20.5236 q^{2} -81.0000 q^{3} -90.7810 q^{4} -622.721 q^{5} +1662.41 q^{6} +1394.83 q^{7} +12371.2 q^{8} +6561.00 q^{9} +12780.5 q^{10} +81914.7 q^{11} +7353.26 q^{12} +22151.8 q^{13} -28627.0 q^{14} +50440.4 q^{15} -207423. q^{16} +512258. q^{17} -134655. q^{18} +850265. q^{19} +56531.3 q^{20} -112982. q^{21} -1.68119e6 q^{22} +1.92743e6 q^{23} -1.00207e6 q^{24} -1.56534e6 q^{25} -454634. q^{26} -531441. q^{27} -126624. q^{28} -601830. q^{29} -1.03522e6 q^{30} -843126. q^{31} -2.07701e6 q^{32} -6.63509e6 q^{33} -1.05134e7 q^{34} -868593. q^{35} -595614. q^{36} +1.61227e7 q^{37} -1.74505e7 q^{38} -1.79429e6 q^{39} -7.70384e6 q^{40} +2.86947e7 q^{41} +2.31879e6 q^{42} +1.17712e7 q^{43} -7.43630e6 q^{44} -4.08567e6 q^{45} -3.95579e7 q^{46} +759231. q^{47} +1.68013e7 q^{48} -3.84080e7 q^{49} +3.21265e7 q^{50} -4.14929e7 q^{51} -2.01096e6 q^{52} -6.97578e7 q^{53} +1.09071e7 q^{54} -5.10101e7 q^{55} +1.72558e7 q^{56} -6.88715e7 q^{57} +1.23517e7 q^{58} +1.21174e7 q^{59} -4.57903e6 q^{60} +7.60079e7 q^{61} +1.73040e7 q^{62} +9.15151e6 q^{63} +1.48828e8 q^{64} -1.37944e7 q^{65} +1.36176e8 q^{66} -2.31398e8 q^{67} -4.65033e7 q^{68} -1.56122e8 q^{69} +1.78267e7 q^{70} -2.17666e7 q^{71} +8.11678e7 q^{72} +3.17363e8 q^{73} -3.30896e8 q^{74} +1.26793e8 q^{75} -7.71879e7 q^{76} +1.14257e8 q^{77} +3.68254e7 q^{78} +5.20051e7 q^{79} +1.29167e8 q^{80} +4.30467e7 q^{81} -5.88920e8 q^{82} -4.88211e8 q^{83} +1.02566e7 q^{84} -3.18994e8 q^{85} -2.41588e8 q^{86} +4.87482e7 q^{87} +1.01339e9 q^{88} +3.00615e8 q^{89} +8.38528e7 q^{90} +3.08980e7 q^{91} -1.74974e8 q^{92} +6.82932e7 q^{93} -1.55822e7 q^{94} -5.29478e8 q^{95} +1.68238e8 q^{96} +6.18576e7 q^{97} +7.88272e8 q^{98} +5.37443e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −20.5236 −0.907024 −0.453512 0.891250i \(-0.649829\pi\)
−0.453512 + 0.891250i \(0.649829\pi\)
\(3\) −81.0000 −0.577350
\(4\) −90.7810 −0.177307
\(5\) −622.721 −0.445583 −0.222792 0.974866i \(-0.571517\pi\)
−0.222792 + 0.974866i \(0.571517\pi\)
\(6\) 1662.41 0.523671
\(7\) 1394.83 0.219574 0.109787 0.993955i \(-0.464983\pi\)
0.109787 + 0.993955i \(0.464983\pi\)
\(8\) 12371.2 1.06785
\(9\) 6561.00 0.333333
\(10\) 12780.5 0.404155
\(11\) 81914.7 1.68692 0.843461 0.537190i \(-0.180514\pi\)
0.843461 + 0.537190i \(0.180514\pi\)
\(12\) 7353.26 0.102368
\(13\) 22151.8 0.215111 0.107556 0.994199i \(-0.465698\pi\)
0.107556 + 0.994199i \(0.465698\pi\)
\(14\) −28627.0 −0.199159
\(15\) 50440.4 0.257258
\(16\) −207423. −0.791256
\(17\) 512258. 1.48754 0.743769 0.668436i \(-0.233036\pi\)
0.743769 + 0.668436i \(0.233036\pi\)
\(18\) −134655. −0.302341
\(19\) 850265. 1.49680 0.748399 0.663249i \(-0.230823\pi\)
0.748399 + 0.663249i \(0.230823\pi\)
\(20\) 56531.3 0.0790049
\(21\) −112982. −0.126771
\(22\) −1.68119e6 −1.53008
\(23\) 1.92743e6 1.43616 0.718081 0.695959i \(-0.245021\pi\)
0.718081 + 0.695959i \(0.245021\pi\)
\(24\) −1.00207e6 −0.616521
\(25\) −1.56534e6 −0.801456
\(26\) −454634. −0.195111
\(27\) −531441. −0.192450
\(28\) −126624. −0.0389320
\(29\) −601830. −0.158009 −0.0790047 0.996874i \(-0.525174\pi\)
−0.0790047 + 0.996874i \(0.525174\pi\)
\(30\) −1.03522e6 −0.233339
\(31\) −843126. −0.163970 −0.0819851 0.996634i \(-0.526126\pi\)
−0.0819851 + 0.996634i \(0.526126\pi\)
\(32\) −2.07701e6 −0.350158
\(33\) −6.63509e6 −0.973945
\(34\) −1.05134e7 −1.34923
\(35\) −868593. −0.0978386
\(36\) −595614. −0.0591022
\(37\) 1.61227e7 1.41426 0.707130 0.707083i \(-0.249989\pi\)
0.707130 + 0.707083i \(0.249989\pi\)
\(38\) −1.74505e7 −1.35763
\(39\) −1.79429e6 −0.124195
\(40\) −7.70384e6 −0.475814
\(41\) 2.86947e7 1.58590 0.792948 0.609289i \(-0.208545\pi\)
0.792948 + 0.609289i \(0.208545\pi\)
\(42\) 2.31879e6 0.114985
\(43\) 1.17712e7 0.525066 0.262533 0.964923i \(-0.415442\pi\)
0.262533 + 0.964923i \(0.415442\pi\)
\(44\) −7.43630e6 −0.299103
\(45\) −4.08567e6 −0.148528
\(46\) −3.95579e7 −1.30263
\(47\) 759231. 0.0226952 0.0113476 0.999936i \(-0.496388\pi\)
0.0113476 + 0.999936i \(0.496388\pi\)
\(48\) 1.68013e7 0.456832
\(49\) −3.84080e7 −0.951787
\(50\) 3.21265e7 0.726940
\(51\) −4.14929e7 −0.858831
\(52\) −2.01096e6 −0.0381407
\(53\) −6.97578e7 −1.21437 −0.607186 0.794560i \(-0.707702\pi\)
−0.607186 + 0.794560i \(0.707702\pi\)
\(54\) 1.09071e7 0.174557
\(55\) −5.10101e7 −0.751664
\(56\) 1.72558e7 0.234471
\(57\) −6.88715e7 −0.864176
\(58\) 1.23517e7 0.143318
\(59\) 1.21174e7 0.130189
\(60\) −4.57903e6 −0.0456135
\(61\) 7.60079e7 0.702869 0.351435 0.936212i \(-0.385694\pi\)
0.351435 + 0.936212i \(0.385694\pi\)
\(62\) 1.73040e7 0.148725
\(63\) 9.15151e6 0.0731914
\(64\) 1.48828e8 1.10886
\(65\) −1.37944e7 −0.0958499
\(66\) 1.36176e8 0.883392
\(67\) −2.31398e8 −1.40289 −0.701444 0.712724i \(-0.747461\pi\)
−0.701444 + 0.712724i \(0.747461\pi\)
\(68\) −4.65033e7 −0.263751
\(69\) −1.56122e8 −0.829169
\(70\) 1.78267e7 0.0887420
\(71\) −2.17666e7 −0.101655 −0.0508274 0.998707i \(-0.516186\pi\)
−0.0508274 + 0.998707i \(0.516186\pi\)
\(72\) 8.11678e7 0.355949
\(73\) 3.17363e8 1.30799 0.653993 0.756500i \(-0.273092\pi\)
0.653993 + 0.756500i \(0.273092\pi\)
\(74\) −3.30896e8 −1.28277
\(75\) 1.26793e8 0.462721
\(76\) −7.71879e7 −0.265392
\(77\) 1.14257e8 0.370405
\(78\) 3.68254e7 0.112647
\(79\) 5.20051e7 0.150219 0.0751093 0.997175i \(-0.476069\pi\)
0.0751093 + 0.997175i \(0.476069\pi\)
\(80\) 1.29167e8 0.352570
\(81\) 4.30467e7 0.111111
\(82\) −5.88920e8 −1.43845
\(83\) −4.88211e8 −1.12916 −0.564581 0.825378i \(-0.690962\pi\)
−0.564581 + 0.825378i \(0.690962\pi\)
\(84\) 1.02566e7 0.0224774
\(85\) −3.18994e8 −0.662822
\(86\) −2.41588e8 −0.476247
\(87\) 4.87482e7 0.0912268
\(88\) 1.01339e9 1.80137
\(89\) 3.00615e8 0.507874 0.253937 0.967221i \(-0.418274\pi\)
0.253937 + 0.967221i \(0.418274\pi\)
\(90\) 8.38528e7 0.134718
\(91\) 3.08980e7 0.0472329
\(92\) −1.74974e8 −0.254641
\(93\) 6.82932e7 0.0946682
\(94\) −1.55822e7 −0.0205851
\(95\) −5.29478e8 −0.666948
\(96\) 1.68238e8 0.202164
\(97\) 6.18576e7 0.0709448 0.0354724 0.999371i \(-0.488706\pi\)
0.0354724 + 0.999371i \(0.488706\pi\)
\(98\) 7.88272e8 0.863294
\(99\) 5.37443e8 0.562307
\(100\) 1.42103e8 0.142103
\(101\) −6.13240e7 −0.0586387 −0.0293193 0.999570i \(-0.509334\pi\)
−0.0293193 + 0.999570i \(0.509334\pi\)
\(102\) 8.51584e8 0.778981
\(103\) −3.77156e8 −0.330182 −0.165091 0.986278i \(-0.552792\pi\)
−0.165091 + 0.986278i \(0.552792\pi\)
\(104\) 2.74045e8 0.229706
\(105\) 7.03560e7 0.0564871
\(106\) 1.43168e9 1.10146
\(107\) −7.46450e7 −0.0550521 −0.0275260 0.999621i \(-0.508763\pi\)
−0.0275260 + 0.999621i \(0.508763\pi\)
\(108\) 4.82448e7 0.0341227
\(109\) 1.11834e9 0.758849 0.379425 0.925223i \(-0.376122\pi\)
0.379425 + 0.925223i \(0.376122\pi\)
\(110\) 1.04691e9 0.681778
\(111\) −1.30594e9 −0.816524
\(112\) −2.89321e8 −0.173739
\(113\) 1.15233e9 0.664847 0.332424 0.943130i \(-0.392134\pi\)
0.332424 + 0.943130i \(0.392134\pi\)
\(114\) 1.41349e9 0.783829
\(115\) −1.20025e9 −0.639930
\(116\) 5.46348e7 0.0280161
\(117\) 1.45338e8 0.0717037
\(118\) −2.48692e8 −0.118085
\(119\) 7.14514e8 0.326625
\(120\) 6.24011e8 0.274711
\(121\) 4.35208e9 1.84571
\(122\) −1.55996e9 −0.637520
\(123\) −2.32427e9 −0.915618
\(124\) 7.65398e7 0.0290730
\(125\) 2.19103e9 0.802698
\(126\) −1.87822e8 −0.0663864
\(127\) 4.74924e9 1.61997 0.809986 0.586450i \(-0.199475\pi\)
0.809986 + 0.586450i \(0.199475\pi\)
\(128\) −1.99107e9 −0.655603
\(129\) −9.53469e8 −0.303147
\(130\) 2.83110e8 0.0869382
\(131\) 2.49512e9 0.740235 0.370118 0.928985i \(-0.379317\pi\)
0.370118 + 0.928985i \(0.379317\pi\)
\(132\) 6.02341e8 0.172687
\(133\) 1.18598e9 0.328658
\(134\) 4.74913e9 1.27245
\(135\) 3.30940e8 0.0857525
\(136\) 6.33727e9 1.58846
\(137\) −2.63323e9 −0.638625 −0.319312 0.947650i \(-0.603452\pi\)
−0.319312 + 0.947650i \(0.603452\pi\)
\(138\) 3.20419e9 0.752077
\(139\) −7.10811e9 −1.61506 −0.807528 0.589829i \(-0.799195\pi\)
−0.807528 + 0.589829i \(0.799195\pi\)
\(140\) 7.88518e7 0.0173474
\(141\) −6.14977e7 −0.0131031
\(142\) 4.46729e8 0.0922033
\(143\) 1.81456e9 0.362876
\(144\) −1.36090e9 −0.263752
\(145\) 3.74773e8 0.0704063
\(146\) −6.51344e9 −1.18638
\(147\) 3.11105e9 0.549515
\(148\) −1.46363e9 −0.250758
\(149\) 7.33933e9 1.21988 0.609942 0.792446i \(-0.291193\pi\)
0.609942 + 0.792446i \(0.291193\pi\)
\(150\) −2.60225e9 −0.419699
\(151\) −1.29484e9 −0.202683 −0.101342 0.994852i \(-0.532314\pi\)
−0.101342 + 0.994852i \(0.532314\pi\)
\(152\) 1.05188e10 1.59835
\(153\) 3.36092e9 0.495846
\(154\) −2.34498e9 −0.335966
\(155\) 5.25033e8 0.0730624
\(156\) 1.62888e8 0.0220205
\(157\) 6.63139e9 0.871077 0.435538 0.900170i \(-0.356558\pi\)
0.435538 + 0.900170i \(0.356558\pi\)
\(158\) −1.06733e9 −0.136252
\(159\) 5.65038e9 0.701118
\(160\) 1.29340e9 0.156024
\(161\) 2.68845e9 0.315344
\(162\) −8.83475e8 −0.100780
\(163\) 9.25376e9 1.02677 0.513386 0.858158i \(-0.328391\pi\)
0.513386 + 0.858158i \(0.328391\pi\)
\(164\) −2.60494e9 −0.281190
\(165\) 4.13182e9 0.433973
\(166\) 1.00199e10 1.02418
\(167\) 6.95721e9 0.692167 0.346083 0.938204i \(-0.387511\pi\)
0.346083 + 0.938204i \(0.387511\pi\)
\(168\) −1.39772e9 −0.135372
\(169\) −1.01138e10 −0.953727
\(170\) 6.54691e9 0.601196
\(171\) 5.57859e9 0.498932
\(172\) −1.06860e9 −0.0930977
\(173\) −1.69325e10 −1.43718 −0.718592 0.695431i \(-0.755213\pi\)
−0.718592 + 0.695431i \(0.755213\pi\)
\(174\) −1.00049e9 −0.0827449
\(175\) −2.18339e9 −0.175979
\(176\) −1.69910e10 −1.33479
\(177\) −9.81506e8 −0.0751646
\(178\) −6.16972e9 −0.460654
\(179\) 2.79100e9 0.203199 0.101599 0.994825i \(-0.467604\pi\)
0.101599 + 0.994825i \(0.467604\pi\)
\(180\) 3.70902e8 0.0263350
\(181\) −7.62877e9 −0.528325 −0.264162 0.964478i \(-0.585095\pi\)
−0.264162 + 0.964478i \(0.585095\pi\)
\(182\) −6.34139e8 −0.0428414
\(183\) −6.15664e9 −0.405802
\(184\) 2.38447e10 1.53360
\(185\) −1.00399e10 −0.630171
\(186\) −1.40162e9 −0.0858664
\(187\) 4.19615e10 2.50936
\(188\) −6.89238e7 −0.00402401
\(189\) −7.41272e8 −0.0422571
\(190\) 1.08668e10 0.604938
\(191\) −2.67707e10 −1.45549 −0.727746 0.685847i \(-0.759432\pi\)
−0.727746 + 0.685847i \(0.759432\pi\)
\(192\) −1.20551e10 −0.640199
\(193\) 1.34722e10 0.698923 0.349461 0.936951i \(-0.386365\pi\)
0.349461 + 0.936951i \(0.386365\pi\)
\(194\) −1.26954e9 −0.0643486
\(195\) 1.11734e9 0.0553390
\(196\) 3.48672e9 0.168758
\(197\) −1.23673e10 −0.585030 −0.292515 0.956261i \(-0.594492\pi\)
−0.292515 + 0.956261i \(0.594492\pi\)
\(198\) −1.10303e10 −0.510026
\(199\) −1.39648e10 −0.631241 −0.315620 0.948886i \(-0.602213\pi\)
−0.315620 + 0.948886i \(0.602213\pi\)
\(200\) −1.93652e10 −0.855831
\(201\) 1.87432e10 0.809958
\(202\) 1.25859e9 0.0531867
\(203\) −8.39453e8 −0.0346948
\(204\) 3.76677e9 0.152276
\(205\) −1.78688e10 −0.706649
\(206\) 7.74061e9 0.299483
\(207\) 1.26459e10 0.478721
\(208\) −4.59478e9 −0.170208
\(209\) 6.96492e10 2.52498
\(210\) −1.44396e9 −0.0512352
\(211\) 7.16560e9 0.248875 0.124438 0.992227i \(-0.460287\pi\)
0.124438 + 0.992227i \(0.460287\pi\)
\(212\) 6.33269e9 0.215316
\(213\) 1.76309e9 0.0586904
\(214\) 1.53198e9 0.0499336
\(215\) −7.33019e9 −0.233960
\(216\) −6.57459e9 −0.205507
\(217\) −1.17602e9 −0.0360036
\(218\) −2.29524e10 −0.688295
\(219\) −2.57064e10 −0.755167
\(220\) 4.63075e9 0.133275
\(221\) 1.13474e10 0.319986
\(222\) 2.68026e10 0.740607
\(223\) −1.21184e10 −0.328151 −0.164075 0.986448i \(-0.552464\pi\)
−0.164075 + 0.986448i \(0.552464\pi\)
\(224\) −2.89708e9 −0.0768856
\(225\) −1.02702e10 −0.267152
\(226\) −2.36499e10 −0.603033
\(227\) −5.58818e10 −1.39686 −0.698431 0.715677i \(-0.746118\pi\)
−0.698431 + 0.715677i \(0.746118\pi\)
\(228\) 6.25222e9 0.153224
\(229\) −1.38507e9 −0.0332823 −0.0166412 0.999862i \(-0.505297\pi\)
−0.0166412 + 0.999862i \(0.505297\pi\)
\(230\) 2.46335e10 0.580432
\(231\) −9.25486e9 −0.213853
\(232\) −7.44539e9 −0.168730
\(233\) −6.40947e10 −1.42469 −0.712345 0.701830i \(-0.752367\pi\)
−0.712345 + 0.701830i \(0.752367\pi\)
\(234\) −2.98286e9 −0.0650370
\(235\) −4.72789e8 −0.0101126
\(236\) −1.10003e9 −0.0230834
\(237\) −4.21241e9 −0.0867288
\(238\) −1.46644e10 −0.296257
\(239\) −3.09544e10 −0.613666 −0.306833 0.951763i \(-0.599269\pi\)
−0.306833 + 0.951763i \(0.599269\pi\)
\(240\) −1.04625e10 −0.203556
\(241\) −4.40383e10 −0.840919 −0.420459 0.907311i \(-0.638131\pi\)
−0.420459 + 0.907311i \(0.638131\pi\)
\(242\) −8.93204e10 −1.67410
\(243\) −3.48678e9 −0.0641500
\(244\) −6.90008e9 −0.124623
\(245\) 2.39175e10 0.424100
\(246\) 4.77025e10 0.830487
\(247\) 1.88349e10 0.321978
\(248\) −1.04305e10 −0.175095
\(249\) 3.95451e10 0.651921
\(250\) −4.49678e10 −0.728067
\(251\) −4.30727e10 −0.684968 −0.342484 0.939524i \(-0.611268\pi\)
−0.342484 + 0.939524i \(0.611268\pi\)
\(252\) −8.30783e8 −0.0129773
\(253\) 1.57885e11 2.42269
\(254\) −9.74716e10 −1.46935
\(255\) 2.58385e10 0.382681
\(256\) −3.53362e10 −0.514209
\(257\) −1.25399e11 −1.79306 −0.896530 0.442983i \(-0.853920\pi\)
−0.896530 + 0.442983i \(0.853920\pi\)
\(258\) 1.95686e10 0.274962
\(259\) 2.24885e10 0.310535
\(260\) 1.25227e9 0.0169948
\(261\) −3.94861e9 −0.0526698
\(262\) −5.12088e10 −0.671411
\(263\) −7.79571e10 −1.00474 −0.502372 0.864652i \(-0.667539\pi\)
−0.502372 + 0.864652i \(0.667539\pi\)
\(264\) −8.20844e10 −1.04002
\(265\) 4.34397e10 0.541103
\(266\) −2.43406e10 −0.298101
\(267\) −2.43498e10 −0.293221
\(268\) 2.10066e10 0.248742
\(269\) −4.10376e10 −0.477856 −0.238928 0.971037i \(-0.576796\pi\)
−0.238928 + 0.971037i \(0.576796\pi\)
\(270\) −6.79208e9 −0.0777796
\(271\) −2.74189e9 −0.0308807 −0.0154404 0.999881i \(-0.504915\pi\)
−0.0154404 + 0.999881i \(0.504915\pi\)
\(272\) −1.06254e11 −1.17702
\(273\) −2.50274e9 −0.0272699
\(274\) 5.40433e10 0.579248
\(275\) −1.28225e11 −1.35199
\(276\) 1.41729e10 0.147017
\(277\) 9.28261e10 0.947351 0.473676 0.880699i \(-0.342927\pi\)
0.473676 + 0.880699i \(0.342927\pi\)
\(278\) 1.45884e11 1.46490
\(279\) −5.53175e9 −0.0546567
\(280\) −1.07456e10 −0.104477
\(281\) 1.26706e11 1.21232 0.606161 0.795342i \(-0.292709\pi\)
0.606161 + 0.795342i \(0.292709\pi\)
\(282\) 1.26216e9 0.0118848
\(283\) 1.54310e11 1.43007 0.715033 0.699090i \(-0.246412\pi\)
0.715033 + 0.699090i \(0.246412\pi\)
\(284\) 1.97599e9 0.0180241
\(285\) 4.28877e10 0.385062
\(286\) −3.72412e10 −0.329137
\(287\) 4.00244e10 0.348222
\(288\) −1.36273e10 −0.116719
\(289\) 1.43820e11 1.21277
\(290\) −7.69169e9 −0.0638603
\(291\) −5.01047e9 −0.0409600
\(292\) −2.88105e10 −0.231915
\(293\) 8.19074e10 0.649260 0.324630 0.945841i \(-0.394760\pi\)
0.324630 + 0.945841i \(0.394760\pi\)
\(294\) −6.38500e10 −0.498423
\(295\) −7.54574e9 −0.0580100
\(296\) 1.99458e11 1.51021
\(297\) −4.35329e10 −0.324648
\(298\) −1.50630e11 −1.10646
\(299\) 4.26960e10 0.308935
\(300\) −1.15104e10 −0.0820435
\(301\) 1.64189e10 0.115291
\(302\) 2.65747e10 0.183839
\(303\) 4.96724e9 0.0338551
\(304\) −1.76364e11 −1.18435
\(305\) −4.73318e10 −0.313187
\(306\) −6.89783e10 −0.449745
\(307\) 5.97432e10 0.383854 0.191927 0.981409i \(-0.438526\pi\)
0.191927 + 0.981409i \(0.438526\pi\)
\(308\) −1.03724e10 −0.0656752
\(309\) 3.05496e10 0.190631
\(310\) −1.07756e10 −0.0662693
\(311\) 3.43145e10 0.207996 0.103998 0.994577i \(-0.466836\pi\)
0.103998 + 0.994577i \(0.466836\pi\)
\(312\) −2.21976e10 −0.132621
\(313\) −7.38980e10 −0.435194 −0.217597 0.976039i \(-0.569822\pi\)
−0.217597 + 0.976039i \(0.569822\pi\)
\(314\) −1.36100e11 −0.790088
\(315\) −5.69884e9 −0.0326129
\(316\) −4.72107e9 −0.0266348
\(317\) −1.09134e11 −0.607004 −0.303502 0.952831i \(-0.598156\pi\)
−0.303502 + 0.952831i \(0.598156\pi\)
\(318\) −1.15966e11 −0.635931
\(319\) −4.92988e10 −0.266550
\(320\) −9.26786e10 −0.494088
\(321\) 6.04624e9 0.0317843
\(322\) −5.51767e10 −0.286025
\(323\) 4.35555e11 2.22654
\(324\) −3.90783e9 −0.0197007
\(325\) −3.46751e10 −0.172402
\(326\) −1.89921e11 −0.931307
\(327\) −9.05857e10 −0.438122
\(328\) 3.54990e11 1.69349
\(329\) 1.05900e9 0.00498327
\(330\) −8.47998e10 −0.393624
\(331\) −8.21888e10 −0.376346 −0.188173 0.982136i \(-0.560257\pi\)
−0.188173 + 0.982136i \(0.560257\pi\)
\(332\) 4.43203e10 0.200208
\(333\) 1.05781e11 0.471420
\(334\) −1.42787e11 −0.627812
\(335\) 1.44097e11 0.625104
\(336\) 2.34350e10 0.100308
\(337\) 1.40309e11 0.592586 0.296293 0.955097i \(-0.404249\pi\)
0.296293 + 0.955097i \(0.404249\pi\)
\(338\) 2.07572e11 0.865054
\(339\) −9.33383e10 −0.383850
\(340\) 2.89586e10 0.117523
\(341\) −6.90645e10 −0.276605
\(342\) −1.14493e11 −0.452544
\(343\) −1.09859e11 −0.428562
\(344\) 1.45625e11 0.560689
\(345\) 9.72205e10 0.369464
\(346\) 3.47515e11 1.30356
\(347\) 6.18546e10 0.229029 0.114514 0.993422i \(-0.463469\pi\)
0.114514 + 0.993422i \(0.463469\pi\)
\(348\) −4.42542e9 −0.0161751
\(349\) −4.01370e11 −1.44821 −0.724103 0.689692i \(-0.757746\pi\)
−0.724103 + 0.689692i \(0.757746\pi\)
\(350\) 4.48111e10 0.159617
\(351\) −1.17724e10 −0.0413982
\(352\) −1.70138e11 −0.590689
\(353\) −1.75083e11 −0.600148 −0.300074 0.953916i \(-0.597011\pi\)
−0.300074 + 0.953916i \(0.597011\pi\)
\(354\) 2.01441e10 0.0681761
\(355\) 1.35545e10 0.0452956
\(356\) −2.72902e10 −0.0900495
\(357\) −5.78757e10 −0.188577
\(358\) −5.72814e10 −0.184306
\(359\) −1.97901e11 −0.628815 −0.314407 0.949288i \(-0.601806\pi\)
−0.314407 + 0.949288i \(0.601806\pi\)
\(360\) −5.05449e10 −0.158605
\(361\) 4.00263e11 1.24040
\(362\) 1.56570e11 0.479204
\(363\) −3.52518e11 −1.06562
\(364\) −2.80495e9 −0.00837471
\(365\) −1.97629e11 −0.582817
\(366\) 1.26357e11 0.368072
\(367\) 6.04032e11 1.73805 0.869025 0.494768i \(-0.164747\pi\)
0.869025 + 0.494768i \(0.164747\pi\)
\(368\) −3.99793e11 −1.13637
\(369\) 1.88266e11 0.528632
\(370\) 2.06056e11 0.571580
\(371\) −9.73006e10 −0.266645
\(372\) −6.19973e9 −0.0167853
\(373\) 4.45130e11 1.19069 0.595343 0.803472i \(-0.297016\pi\)
0.595343 + 0.803472i \(0.297016\pi\)
\(374\) −8.61201e11 −2.27605
\(375\) −1.77473e11 −0.463438
\(376\) 9.39263e9 0.0242349
\(377\) −1.33316e10 −0.0339896
\(378\) 1.52136e10 0.0383282
\(379\) 9.08604e10 0.226203 0.113101 0.993583i \(-0.463922\pi\)
0.113101 + 0.993583i \(0.463922\pi\)
\(380\) 4.80666e10 0.118254
\(381\) −3.84688e11 −0.935291
\(382\) 5.49432e11 1.32017
\(383\) −4.85742e11 −1.15348 −0.576741 0.816927i \(-0.695676\pi\)
−0.576741 + 0.816927i \(0.695676\pi\)
\(384\) 1.61276e11 0.378513
\(385\) −7.11506e10 −0.165046
\(386\) −2.76497e11 −0.633940
\(387\) 7.72310e10 0.175022
\(388\) −5.61550e9 −0.0125790
\(389\) 7.75466e11 1.71708 0.858538 0.512751i \(-0.171373\pi\)
0.858538 + 0.512751i \(0.171373\pi\)
\(390\) −2.29319e10 −0.0501938
\(391\) 9.87342e11 2.13635
\(392\) −4.75155e11 −1.01636
\(393\) −2.02104e11 −0.427375
\(394\) 2.53823e11 0.530637
\(395\) −3.23847e10 −0.0669349
\(396\) −4.87896e10 −0.0997008
\(397\) −9.45110e11 −1.90952 −0.954762 0.297372i \(-0.903890\pi\)
−0.954762 + 0.297372i \(0.903890\pi\)
\(398\) 2.86608e11 0.572551
\(399\) −9.60642e10 −0.189751
\(400\) 3.24688e11 0.634156
\(401\) 8.14221e11 1.57251 0.786254 0.617903i \(-0.212018\pi\)
0.786254 + 0.617903i \(0.212018\pi\)
\(402\) −3.84679e11 −0.734652
\(403\) −1.86767e10 −0.0352718
\(404\) 5.56706e9 0.0103970
\(405\) −2.68061e10 −0.0495092
\(406\) 1.72286e10 0.0314690
\(407\) 1.32069e12 2.38575
\(408\) −5.13319e11 −0.917099
\(409\) −1.23209e11 −0.217714 −0.108857 0.994057i \(-0.534719\pi\)
−0.108857 + 0.994057i \(0.534719\pi\)
\(410\) 3.66733e11 0.640947
\(411\) 2.13291e11 0.368710
\(412\) 3.42386e10 0.0585435
\(413\) 1.69017e10 0.0285861
\(414\) −2.59539e11 −0.434212
\(415\) 3.04019e11 0.503135
\(416\) −4.60094e10 −0.0753229
\(417\) 5.75757e11 0.932454
\(418\) −1.42945e12 −2.29022
\(419\) −1.88285e11 −0.298436 −0.149218 0.988804i \(-0.547676\pi\)
−0.149218 + 0.988804i \(0.547676\pi\)
\(420\) −6.38699e9 −0.0100155
\(421\) 6.21132e11 0.963639 0.481819 0.876271i \(-0.339976\pi\)
0.481819 + 0.876271i \(0.339976\pi\)
\(422\) −1.47064e11 −0.225736
\(423\) 4.98131e9 0.00756506
\(424\) −8.62992e11 −1.29676
\(425\) −8.01859e11 −1.19220
\(426\) −3.61850e10 −0.0532336
\(427\) 1.06018e11 0.154332
\(428\) 6.77635e9 0.00976110
\(429\) −1.46979e11 −0.209506
\(430\) 1.50442e11 0.212208
\(431\) 5.05784e11 0.706021 0.353010 0.935619i \(-0.385158\pi\)
0.353010 + 0.935619i \(0.385158\pi\)
\(432\) 1.10233e11 0.152277
\(433\) −7.19626e11 −0.983810 −0.491905 0.870649i \(-0.663699\pi\)
−0.491905 + 0.870649i \(0.663699\pi\)
\(434\) 2.41362e10 0.0326562
\(435\) −3.03566e10 −0.0406491
\(436\) −1.01524e11 −0.134549
\(437\) 1.63883e12 2.14964
\(438\) 5.27588e11 0.684955
\(439\) 1.85748e11 0.238690 0.119345 0.992853i \(-0.461921\pi\)
0.119345 + 0.992853i \(0.461921\pi\)
\(440\) −6.31058e11 −0.802661
\(441\) −2.51995e11 −0.317262
\(442\) −2.32890e11 −0.290235
\(443\) 4.70420e11 0.580321 0.290161 0.956978i \(-0.406291\pi\)
0.290161 + 0.956978i \(0.406291\pi\)
\(444\) 1.18554e11 0.144775
\(445\) −1.87200e11 −0.226300
\(446\) 2.48714e11 0.297641
\(447\) −5.94486e11 −0.704300
\(448\) 2.07591e11 0.243476
\(449\) −1.22800e12 −1.42590 −0.712951 0.701214i \(-0.752642\pi\)
−0.712951 + 0.701214i \(0.752642\pi\)
\(450\) 2.10782e11 0.242313
\(451\) 2.35052e12 2.67528
\(452\) −1.04609e11 −0.117882
\(453\) 1.04882e11 0.117019
\(454\) 1.14690e12 1.26699
\(455\) −1.92409e10 −0.0210462
\(456\) −8.52026e11 −0.922807
\(457\) 1.09592e12 1.17532 0.587659 0.809108i \(-0.300049\pi\)
0.587659 + 0.809108i \(0.300049\pi\)
\(458\) 2.84267e10 0.0301879
\(459\) −2.72235e11 −0.286277
\(460\) 1.08960e11 0.113464
\(461\) 3.49508e11 0.360415 0.180208 0.983629i \(-0.442323\pi\)
0.180208 + 0.983629i \(0.442323\pi\)
\(462\) 1.89943e11 0.193970
\(463\) 2.77251e11 0.280387 0.140194 0.990124i \(-0.455227\pi\)
0.140194 + 0.990124i \(0.455227\pi\)
\(464\) 1.24833e11 0.125026
\(465\) −4.25276e10 −0.0421826
\(466\) 1.31545e12 1.29223
\(467\) 5.83135e11 0.567340 0.283670 0.958922i \(-0.408448\pi\)
0.283670 + 0.958922i \(0.408448\pi\)
\(468\) −1.31939e10 −0.0127136
\(469\) −3.22762e11 −0.308038
\(470\) 9.70335e9 0.00917236
\(471\) −5.37143e11 −0.502916
\(472\) 1.49907e11 0.139022
\(473\) 9.64237e11 0.885745
\(474\) 8.64539e10 0.0786651
\(475\) −1.33096e12 −1.19962
\(476\) −6.48644e10 −0.0579128
\(477\) −4.57681e11 −0.404791
\(478\) 6.35296e11 0.556610
\(479\) −2.16228e12 −1.87673 −0.938367 0.345642i \(-0.887661\pi\)
−0.938367 + 0.345642i \(0.887661\pi\)
\(480\) −1.04765e11 −0.0900807
\(481\) 3.57146e11 0.304223
\(482\) 9.03826e11 0.762734
\(483\) −2.17764e11 −0.182064
\(484\) −3.95086e11 −0.327256
\(485\) −3.85201e10 −0.0316118
\(486\) 7.15614e10 0.0581856
\(487\) 1.78439e12 1.43750 0.718752 0.695266i \(-0.244714\pi\)
0.718752 + 0.695266i \(0.244714\pi\)
\(488\) 9.40313e11 0.750556
\(489\) −7.49554e11 −0.592807
\(490\) −4.90874e11 −0.384669
\(491\) 6.26155e11 0.486200 0.243100 0.970001i \(-0.421836\pi\)
0.243100 + 0.970001i \(0.421836\pi\)
\(492\) 2.11000e11 0.162345
\(493\) −3.08292e11 −0.235045
\(494\) −3.86560e11 −0.292042
\(495\) −3.34677e11 −0.250555
\(496\) 1.74884e11 0.129742
\(497\) −3.03608e10 −0.0223208
\(498\) −8.11608e11 −0.591309
\(499\) 6.26144e11 0.452087 0.226043 0.974117i \(-0.427421\pi\)
0.226043 + 0.974117i \(0.427421\pi\)
\(500\) −1.98904e11 −0.142324
\(501\) −5.63534e11 −0.399623
\(502\) 8.84008e11 0.621283
\(503\) 2.68291e12 1.86875 0.934373 0.356295i \(-0.115960\pi\)
0.934373 + 0.356295i \(0.115960\pi\)
\(504\) 1.13216e11 0.0781571
\(505\) 3.81878e10 0.0261284
\(506\) −3.24037e12 −2.19744
\(507\) 8.19218e11 0.550635
\(508\) −4.31141e11 −0.287232
\(509\) 2.90119e12 1.91578 0.957891 0.287133i \(-0.0927022\pi\)
0.957891 + 0.287133i \(0.0927022\pi\)
\(510\) −5.30300e11 −0.347101
\(511\) 4.42669e11 0.287200
\(512\) 1.74465e12 1.12200
\(513\) −4.51866e11 −0.288059
\(514\) 2.57364e12 1.62635
\(515\) 2.34863e11 0.147124
\(516\) 8.65569e10 0.0537500
\(517\) 6.21922e10 0.0382850
\(518\) −4.61545e11 −0.281663
\(519\) 1.37153e12 0.829759
\(520\) −1.70654e11 −0.102353
\(521\) −1.86142e12 −1.10682 −0.553408 0.832910i \(-0.686673\pi\)
−0.553408 + 0.832910i \(0.686673\pi\)
\(522\) 8.10397e10 0.0477728
\(523\) −3.02664e12 −1.76890 −0.884451 0.466634i \(-0.845467\pi\)
−0.884451 + 0.466634i \(0.845467\pi\)
\(524\) −2.26509e11 −0.131249
\(525\) 1.76855e11 0.101602
\(526\) 1.59996e12 0.911326
\(527\) −4.31898e11 −0.243912
\(528\) 1.37627e12 0.770639
\(529\) 1.91384e12 1.06256
\(530\) −8.91540e11 −0.490794
\(531\) 7.95020e10 0.0433963
\(532\) −1.07664e11 −0.0582733
\(533\) 6.35639e11 0.341144
\(534\) 4.99747e11 0.265959
\(535\) 4.64830e10 0.0245303
\(536\) −2.86268e12 −1.49807
\(537\) −2.26071e11 −0.117317
\(538\) 8.42241e11 0.433427
\(539\) −3.14619e12 −1.60559
\(540\) −3.00430e10 −0.0152045
\(541\) 1.90660e12 0.956913 0.478457 0.878111i \(-0.341196\pi\)
0.478457 + 0.878111i \(0.341196\pi\)
\(542\) 5.62734e10 0.0280096
\(543\) 6.17931e11 0.305028
\(544\) −1.06396e12 −0.520873
\(545\) −6.96416e11 −0.338130
\(546\) 5.13653e10 0.0247345
\(547\) −3.53996e12 −1.69066 −0.845328 0.534248i \(-0.820595\pi\)
−0.845328 + 0.534248i \(0.820595\pi\)
\(548\) 2.39047e11 0.113232
\(549\) 4.98688e11 0.234290
\(550\) 2.63163e12 1.22629
\(551\) −5.11715e11 −0.236508
\(552\) −1.93142e12 −0.885425
\(553\) 7.25384e10 0.0329841
\(554\) −1.90513e12 −0.859271
\(555\) 8.13235e11 0.363829
\(556\) 6.45282e11 0.286360
\(557\) −1.31009e12 −0.576704 −0.288352 0.957524i \(-0.593107\pi\)
−0.288352 + 0.957524i \(0.593107\pi\)
\(558\) 1.13532e11 0.0495750
\(559\) 2.60753e11 0.112948
\(560\) 1.80166e11 0.0774153
\(561\) −3.39888e12 −1.44878
\(562\) −2.60046e12 −1.09961
\(563\) 1.94733e12 0.816866 0.408433 0.912788i \(-0.366075\pi\)
0.408433 + 0.912788i \(0.366075\pi\)
\(564\) 5.58282e9 0.00232326
\(565\) −7.17577e11 −0.296245
\(566\) −3.16701e12 −1.29711
\(567\) 6.00430e10 0.0243971
\(568\) −2.69280e11 −0.108552
\(569\) −2.69619e12 −1.07831 −0.539156 0.842206i \(-0.681257\pi\)
−0.539156 + 0.842206i \(0.681257\pi\)
\(570\) −8.80211e11 −0.349261
\(571\) −2.34419e12 −0.922848 −0.461424 0.887180i \(-0.652661\pi\)
−0.461424 + 0.887180i \(0.652661\pi\)
\(572\) −1.64727e11 −0.0643403
\(573\) 2.16843e12 0.840329
\(574\) −8.21445e11 −0.315846
\(575\) −3.01709e12 −1.15102
\(576\) 9.76462e11 0.369619
\(577\) 2.78968e12 1.04776 0.523882 0.851791i \(-0.324483\pi\)
0.523882 + 0.851791i \(0.324483\pi\)
\(578\) −2.95171e12 −1.10001
\(579\) −1.09124e12 −0.403523
\(580\) −3.40222e10 −0.0124835
\(581\) −6.80973e11 −0.247935
\(582\) 1.02833e11 0.0371517
\(583\) −5.71420e12 −2.04855
\(584\) 3.92618e12 1.39673
\(585\) −9.05049e10 −0.0319500
\(586\) −1.68104e12 −0.588895
\(587\) −4.68401e12 −1.62834 −0.814172 0.580624i \(-0.802809\pi\)
−0.814172 + 0.580624i \(0.802809\pi\)
\(588\) −2.82424e11 −0.0974326
\(589\) −7.16880e11 −0.245430
\(590\) 1.54866e11 0.0526165
\(591\) 1.00175e12 0.337767
\(592\) −3.34421e12 −1.11904
\(593\) 1.28628e12 0.427159 0.213579 0.976926i \(-0.431488\pi\)
0.213579 + 0.976926i \(0.431488\pi\)
\(594\) 8.93452e11 0.294464
\(595\) −4.44943e11 −0.145539
\(596\) −6.66272e11 −0.216294
\(597\) 1.13115e12 0.364447
\(598\) −8.76276e11 −0.280211
\(599\) 3.76469e12 1.19484 0.597419 0.801929i \(-0.296193\pi\)
0.597419 + 0.801929i \(0.296193\pi\)
\(600\) 1.56859e12 0.494114
\(601\) 2.63327e12 0.823303 0.411652 0.911341i \(-0.364952\pi\)
0.411652 + 0.911341i \(0.364952\pi\)
\(602\) −3.36975e11 −0.104572
\(603\) −1.51820e12 −0.467630
\(604\) 1.17546e11 0.0359371
\(605\) −2.71013e12 −0.822415
\(606\) −1.01946e11 −0.0307074
\(607\) −1.72983e12 −0.517194 −0.258597 0.965985i \(-0.583260\pi\)
−0.258597 + 0.965985i \(0.583260\pi\)
\(608\) −1.76601e12 −0.524115
\(609\) 6.79957e10 0.0200311
\(610\) 9.71419e11 0.284068
\(611\) 1.68183e10 0.00488199
\(612\) −3.05108e11 −0.0879169
\(613\) 1.40396e12 0.401590 0.200795 0.979633i \(-0.435648\pi\)
0.200795 + 0.979633i \(0.435648\pi\)
\(614\) −1.22615e12 −0.348165
\(615\) 1.44737e12 0.407984
\(616\) 1.41351e12 0.395535
\(617\) −7.15165e12 −1.98666 −0.993329 0.115313i \(-0.963213\pi\)
−0.993329 + 0.115313i \(0.963213\pi\)
\(618\) −6.26989e11 −0.172907
\(619\) −2.44272e11 −0.0668754 −0.0334377 0.999441i \(-0.510646\pi\)
−0.0334377 + 0.999441i \(0.510646\pi\)
\(620\) −4.76630e10 −0.0129544
\(621\) −1.02432e12 −0.276390
\(622\) −7.04257e11 −0.188658
\(623\) 4.19309e11 0.111516
\(624\) 3.72177e11 0.0982696
\(625\) 1.69291e12 0.443787
\(626\) 1.51665e12 0.394732
\(627\) −5.64159e12 −1.45780
\(628\) −6.02005e11 −0.154448
\(629\) 8.25897e12 2.10377
\(630\) 1.16961e11 0.0295807
\(631\) 1.41979e12 0.356525 0.178263 0.983983i \(-0.442952\pi\)
0.178263 + 0.983983i \(0.442952\pi\)
\(632\) 6.43368e11 0.160410
\(633\) −5.80414e11 −0.143688
\(634\) 2.23982e12 0.550568
\(635\) −2.95745e12 −0.721832
\(636\) −5.12948e11 −0.124313
\(637\) −8.50806e11 −0.204740
\(638\) 1.01179e12 0.241767
\(639\) −1.42810e11 −0.0338849
\(640\) 1.23988e12 0.292126
\(641\) −4.08479e12 −0.955672 −0.477836 0.878449i \(-0.658579\pi\)
−0.477836 + 0.878449i \(0.658579\pi\)
\(642\) −1.24091e11 −0.0288292
\(643\) 3.67936e10 0.00848835 0.00424418 0.999991i \(-0.498649\pi\)
0.00424418 + 0.999991i \(0.498649\pi\)
\(644\) −2.44060e11 −0.0559127
\(645\) 5.93746e11 0.135077
\(646\) −8.93916e12 −2.01953
\(647\) 5.07128e12 1.13775 0.568877 0.822423i \(-0.307378\pi\)
0.568877 + 0.822423i \(0.307378\pi\)
\(648\) 5.32542e11 0.118650
\(649\) 9.92591e11 0.219619
\(650\) 7.11659e11 0.156373
\(651\) 9.52577e10 0.0207867
\(652\) −8.40066e11 −0.182054
\(653\) −3.13277e12 −0.674248 −0.337124 0.941460i \(-0.609454\pi\)
−0.337124 + 0.941460i \(0.609454\pi\)
\(654\) 1.85915e12 0.397387
\(655\) −1.55376e12 −0.329836
\(656\) −5.95194e12 −1.25485
\(657\) 2.08222e12 0.435996
\(658\) −2.17345e10 −0.00451995
\(659\) 7.60700e12 1.57119 0.785595 0.618741i \(-0.212357\pi\)
0.785595 + 0.618741i \(0.212357\pi\)
\(660\) −3.75090e11 −0.0769464
\(661\) 3.64344e11 0.0742344 0.0371172 0.999311i \(-0.488183\pi\)
0.0371172 + 0.999311i \(0.488183\pi\)
\(662\) 1.68681e12 0.341355
\(663\) −9.19140e11 −0.184744
\(664\) −6.03978e12 −1.20577
\(665\) −7.38534e11 −0.146445
\(666\) −2.17101e12 −0.427590
\(667\) −1.15999e12 −0.226927
\(668\) −6.31582e11 −0.122726
\(669\) 9.81591e11 0.189458
\(670\) −2.95738e12 −0.566984
\(671\) 6.22617e12 1.18569
\(672\) 2.34664e11 0.0443899
\(673\) −9.76993e12 −1.83579 −0.917896 0.396821i \(-0.870113\pi\)
−0.917896 + 0.396821i \(0.870113\pi\)
\(674\) −2.87965e12 −0.537490
\(675\) 8.31888e11 0.154240
\(676\) 9.18141e11 0.169102
\(677\) 8.73125e11 0.159745 0.0798725 0.996805i \(-0.474549\pi\)
0.0798725 + 0.996805i \(0.474549\pi\)
\(678\) 1.91564e12 0.348161
\(679\) 8.62811e10 0.0155776
\(680\) −3.94635e12 −0.707792
\(681\) 4.52642e12 0.806479
\(682\) 1.41745e12 0.250887
\(683\) 4.68690e10 0.00824123 0.00412062 0.999992i \(-0.498688\pi\)
0.00412062 + 0.999992i \(0.498688\pi\)
\(684\) −5.06430e11 −0.0884641
\(685\) 1.63977e12 0.284560
\(686\) 2.25471e12 0.388716
\(687\) 1.12191e11 0.0192155
\(688\) −2.44162e12 −0.415461
\(689\) −1.54526e12 −0.261225
\(690\) −1.99532e12 −0.335113
\(691\) 5.64962e12 0.942688 0.471344 0.881949i \(-0.343769\pi\)
0.471344 + 0.881949i \(0.343769\pi\)
\(692\) 1.53715e12 0.254822
\(693\) 7.49643e11 0.123468
\(694\) −1.26948e12 −0.207735
\(695\) 4.42637e12 0.719642
\(696\) 6.03077e11 0.0974162
\(697\) 1.46991e13 2.35908
\(698\) 8.23756e12 1.31356
\(699\) 5.19167e12 0.822545
\(700\) 1.98211e11 0.0312023
\(701\) 1.55240e12 0.242814 0.121407 0.992603i \(-0.461259\pi\)
0.121407 + 0.992603i \(0.461259\pi\)
\(702\) 2.41611e11 0.0375492
\(703\) 1.37085e13 2.11686
\(704\) 1.21912e13 1.87056
\(705\) 3.82959e10 0.00583850
\(706\) 3.59334e12 0.544349
\(707\) −8.55368e10 −0.0128755
\(708\) 8.91021e10 0.0133272
\(709\) −6.23477e12 −0.926643 −0.463322 0.886190i \(-0.653343\pi\)
−0.463322 + 0.886190i \(0.653343\pi\)
\(710\) −2.78188e11 −0.0410842
\(711\) 3.41205e11 0.0500729
\(712\) 3.71899e12 0.542331
\(713\) −1.62507e12 −0.235488
\(714\) 1.18782e12 0.171044
\(715\) −1.12996e12 −0.161691
\(716\) −2.53370e11 −0.0360285
\(717\) 2.50731e12 0.354300
\(718\) 4.06164e12 0.570350
\(719\) 4.36189e12 0.608689 0.304344 0.952562i \(-0.401563\pi\)
0.304344 + 0.952562i \(0.401563\pi\)
\(720\) 8.47463e11 0.117523
\(721\) −5.26070e11 −0.0724995
\(722\) −8.21484e12 −1.12508
\(723\) 3.56710e12 0.485505
\(724\) 6.92548e11 0.0936755
\(725\) 9.42071e11 0.126638
\(726\) 7.23495e12 0.966542
\(727\) 9.05985e12 1.20286 0.601432 0.798924i \(-0.294597\pi\)
0.601432 + 0.798924i \(0.294597\pi\)
\(728\) 3.82247e11 0.0504374
\(729\) 2.82430e11 0.0370370
\(730\) 4.05606e12 0.528629
\(731\) 6.02990e12 0.781056
\(732\) 5.58906e11 0.0719514
\(733\) 1.13791e13 1.45592 0.727962 0.685618i \(-0.240468\pi\)
0.727962 + 0.685618i \(0.240468\pi\)
\(734\) −1.23969e13 −1.57645
\(735\) −1.93732e12 −0.244854
\(736\) −4.00329e12 −0.502883
\(737\) −1.89549e13 −2.36656
\(738\) −3.86390e12 −0.479482
\(739\) −7.99980e12 −0.986686 −0.493343 0.869835i \(-0.664225\pi\)
−0.493343 + 0.869835i \(0.664225\pi\)
\(740\) 9.11436e11 0.111733
\(741\) −1.52562e12 −0.185894
\(742\) 1.99696e12 0.241853
\(743\) 6.88412e12 0.828702 0.414351 0.910117i \(-0.364009\pi\)
0.414351 + 0.910117i \(0.364009\pi\)
\(744\) 8.44872e11 0.101091
\(745\) −4.57036e12 −0.543560
\(746\) −9.13568e12 −1.07998
\(747\) −3.20315e12 −0.376387
\(748\) −3.80930e12 −0.444927
\(749\) −1.04117e11 −0.0120880
\(750\) 3.64239e12 0.420350
\(751\) 6.54436e12 0.750736 0.375368 0.926876i \(-0.377516\pi\)
0.375368 + 0.926876i \(0.377516\pi\)
\(752\) −1.57482e11 −0.0179577
\(753\) 3.48889e12 0.395467
\(754\) 2.73613e11 0.0308294
\(755\) 8.06321e11 0.0903123
\(756\) 6.72934e10 0.00749246
\(757\) −1.72596e12 −0.191029 −0.0955145 0.995428i \(-0.530450\pi\)
−0.0955145 + 0.995428i \(0.530450\pi\)
\(758\) −1.86478e12 −0.205171
\(759\) −1.27887e13 −1.39874
\(760\) −6.55031e12 −0.712197
\(761\) −1.30920e13 −1.41506 −0.707531 0.706682i \(-0.750191\pi\)
−0.707531 + 0.706682i \(0.750191\pi\)
\(762\) 7.89520e12 0.848332
\(763\) 1.55990e12 0.166624
\(764\) 2.43027e12 0.258069
\(765\) −2.09292e12 −0.220941
\(766\) 9.96918e12 1.04624
\(767\) 2.68421e11 0.0280051
\(768\) 2.86223e12 0.296879
\(769\) −9.00628e12 −0.928703 −0.464351 0.885651i \(-0.653713\pi\)
−0.464351 + 0.885651i \(0.653713\pi\)
\(770\) 1.46027e12 0.149701
\(771\) 1.01573e13 1.03522
\(772\) −1.22302e12 −0.123924
\(773\) 1.52547e13 1.53672 0.768362 0.640015i \(-0.221072\pi\)
0.768362 + 0.640015i \(0.221072\pi\)
\(774\) −1.58506e12 −0.158749
\(775\) 1.31978e12 0.131415
\(776\) 7.65256e11 0.0757581
\(777\) −1.82157e12 −0.179288
\(778\) −1.59154e13 −1.55743
\(779\) 2.43981e13 2.37377
\(780\) −1.01434e11 −0.00981197
\(781\) −1.78300e12 −0.171484
\(782\) −2.02638e13 −1.93772
\(783\) 3.19837e11 0.0304089
\(784\) 7.96671e12 0.753107
\(785\) −4.12951e12 −0.388137
\(786\) 4.14791e12 0.387640
\(787\) −1.59730e12 −0.148422 −0.0742112 0.997243i \(-0.523644\pi\)
−0.0742112 + 0.997243i \(0.523644\pi\)
\(788\) 1.12272e12 0.103730
\(789\) 6.31453e12 0.580089
\(790\) 6.64651e11 0.0607116
\(791\) 1.60730e12 0.145983
\(792\) 6.64884e12 0.600458
\(793\) 1.68371e12 0.151195
\(794\) 1.93971e13 1.73198
\(795\) −3.51862e12 −0.312406
\(796\) 1.26774e12 0.111923
\(797\) 8.04243e12 0.706033 0.353016 0.935617i \(-0.385156\pi\)
0.353016 + 0.935617i \(0.385156\pi\)
\(798\) 1.97159e12 0.172109
\(799\) 3.88922e11 0.0337600
\(800\) 3.25123e12 0.280636
\(801\) 1.97234e12 0.169291
\(802\) −1.67108e13 −1.42630
\(803\) 2.59967e13 2.20647
\(804\) −1.70153e12 −0.143611
\(805\) −1.67415e12 −0.140512
\(806\) 3.83314e11 0.0319924
\(807\) 3.32405e12 0.275890
\(808\) −7.58654e11 −0.0626171
\(809\) 3.37778e12 0.277245 0.138622 0.990345i \(-0.455733\pi\)
0.138622 + 0.990345i \(0.455733\pi\)
\(810\) 5.50158e11 0.0449061
\(811\) 1.01734e12 0.0825795 0.0412898 0.999147i \(-0.486853\pi\)
0.0412898 + 0.999147i \(0.486853\pi\)
\(812\) 7.62064e10 0.00615162
\(813\) 2.22093e11 0.0178290
\(814\) −2.71052e13 −2.16393
\(815\) −5.76251e12 −0.457512
\(816\) 8.60657e12 0.679555
\(817\) 1.00087e13 0.785917
\(818\) 2.52869e12 0.197472
\(819\) 2.02722e11 0.0157443
\(820\) 1.62215e12 0.125294
\(821\) 2.01419e13 1.54724 0.773618 0.633653i \(-0.218445\pi\)
0.773618 + 0.633653i \(0.218445\pi\)
\(822\) −4.37751e12 −0.334429
\(823\) −9.23318e12 −0.701539 −0.350770 0.936462i \(-0.614080\pi\)
−0.350770 + 0.936462i \(0.614080\pi\)
\(824\) −4.66589e12 −0.352584
\(825\) 1.03862e13 0.780574
\(826\) −3.46884e11 −0.0259283
\(827\) 1.65328e13 1.22906 0.614528 0.788895i \(-0.289346\pi\)
0.614528 + 0.788895i \(0.289346\pi\)
\(828\) −1.14801e12 −0.0848804
\(829\) −1.69704e13 −1.24795 −0.623973 0.781446i \(-0.714483\pi\)
−0.623973 + 0.781446i \(0.714483\pi\)
\(830\) −6.23958e12 −0.456356
\(831\) −7.51891e12 −0.546953
\(832\) 3.29681e12 0.238528
\(833\) −1.96748e13 −1.41582
\(834\) −1.18166e13 −0.845758
\(835\) −4.33240e12 −0.308418
\(836\) −6.32283e12 −0.447696
\(837\) 4.48072e11 0.0315561
\(838\) 3.86428e12 0.270689
\(839\) −2.03267e13 −1.41624 −0.708122 0.706090i \(-0.750458\pi\)
−0.708122 + 0.706090i \(0.750458\pi\)
\(840\) 8.70392e11 0.0603195
\(841\) −1.41449e13 −0.975033
\(842\) −1.27479e13 −0.874044
\(843\) −1.02632e13 −0.699935
\(844\) −6.50501e11 −0.0441273
\(845\) 6.29808e12 0.424965
\(846\) −1.02235e11 −0.00686169
\(847\) 6.07043e12 0.405269
\(848\) 1.44694e13 0.960878
\(849\) −1.24991e13 −0.825649
\(850\) 1.64571e13 1.08135
\(851\) 3.10754e13 2.03111
\(852\) −1.60055e11 −0.0104062
\(853\) −5.58034e12 −0.360903 −0.180451 0.983584i \(-0.557756\pi\)
−0.180451 + 0.983584i \(0.557756\pi\)
\(854\) −2.17588e12 −0.139983
\(855\) −3.47391e12 −0.222316
\(856\) −9.23451e11 −0.0587871
\(857\) 1.54397e13 0.977746 0.488873 0.872355i \(-0.337408\pi\)
0.488873 + 0.872355i \(0.337408\pi\)
\(858\) 3.01654e12 0.190028
\(859\) 6.97305e10 0.00436972 0.00218486 0.999998i \(-0.499305\pi\)
0.00218486 + 0.999998i \(0.499305\pi\)
\(860\) 6.65443e11 0.0414828
\(861\) −3.24197e12 −0.201046
\(862\) −1.03805e13 −0.640378
\(863\) 2.35934e13 1.44791 0.723955 0.689848i \(-0.242323\pi\)
0.723955 + 0.689848i \(0.242323\pi\)
\(864\) 1.10381e12 0.0673879
\(865\) 1.05442e13 0.640385
\(866\) 1.47693e13 0.892339
\(867\) −1.16494e13 −0.700194
\(868\) 1.06760e11 0.00638368
\(869\) 4.25998e12 0.253407
\(870\) 6.23027e11 0.0368697
\(871\) −5.12588e12 −0.301777
\(872\) 1.38353e13 0.810334
\(873\) 4.05848e11 0.0236483
\(874\) −3.36347e13 −1.94978
\(875\) 3.05612e12 0.176252
\(876\) 2.33365e12 0.133896
\(877\) −9.54680e12 −0.544954 −0.272477 0.962162i \(-0.587843\pi\)
−0.272477 + 0.962162i \(0.587843\pi\)
\(878\) −3.81222e12 −0.216497
\(879\) −6.63450e12 −0.374851
\(880\) 1.05807e13 0.594758
\(881\) 1.75702e13 0.982617 0.491308 0.870986i \(-0.336519\pi\)
0.491308 + 0.870986i \(0.336519\pi\)
\(882\) 5.17185e12 0.287765
\(883\) −2.87218e13 −1.58997 −0.794983 0.606632i \(-0.792520\pi\)
−0.794983 + 0.606632i \(0.792520\pi\)
\(884\) −1.03013e12 −0.0567357
\(885\) 6.11205e11 0.0334921
\(886\) −9.65471e12 −0.526366
\(887\) 3.24486e13 1.76011 0.880055 0.474872i \(-0.157506\pi\)
0.880055 + 0.474872i \(0.157506\pi\)
\(888\) −1.61561e13 −0.871922
\(889\) 6.62440e12 0.355704
\(890\) 3.84201e12 0.205260
\(891\) 3.52616e12 0.187436
\(892\) 1.10012e12 0.0581833
\(893\) 6.45547e11 0.0339701
\(894\) 1.22010e13 0.638818
\(895\) −1.73801e12 −0.0905419
\(896\) −2.77721e12 −0.143953
\(897\) −3.45838e12 −0.178364
\(898\) 2.52030e13 1.29333
\(899\) 5.07419e11 0.0259088
\(900\) 9.32341e11 0.0473678
\(901\) −3.57340e13 −1.80642
\(902\) −4.82412e13 −2.42655
\(903\) −1.32993e12 −0.0665632
\(904\) 1.42557e13 0.709955
\(905\) 4.75060e12 0.235413
\(906\) −2.15255e12 −0.106139
\(907\) 1.03571e13 0.508167 0.254083 0.967182i \(-0.418226\pi\)
0.254083 + 0.967182i \(0.418226\pi\)
\(908\) 5.07300e12 0.247673
\(909\) −4.02347e11 −0.0195462
\(910\) 3.94892e11 0.0190894
\(911\) −1.32787e13 −0.638739 −0.319369 0.947630i \(-0.603471\pi\)
−0.319369 + 0.947630i \(0.603471\pi\)
\(912\) 1.42855e13 0.683784
\(913\) −3.99917e13 −1.90481
\(914\) −2.24922e13 −1.06604
\(915\) 3.83387e12 0.180818
\(916\) 1.25738e11 0.00590117
\(917\) 3.48027e12 0.162537
\(918\) 5.58724e12 0.259660
\(919\) −4.00751e13 −1.85334 −0.926670 0.375877i \(-0.877342\pi\)
−0.926670 + 0.375877i \(0.877342\pi\)
\(920\) −1.48486e13 −0.683347
\(921\) −4.83920e12 −0.221618
\(922\) −7.17317e12 −0.326905
\(923\) −4.82168e11 −0.0218671
\(924\) 8.40165e11 0.0379176
\(925\) −2.52375e13 −1.13347
\(926\) −5.69019e12 −0.254318
\(927\) −2.47452e12 −0.110061
\(928\) 1.25001e12 0.0553282
\(929\) 8.42283e11 0.0371012 0.0185506 0.999828i \(-0.494095\pi\)
0.0185506 + 0.999828i \(0.494095\pi\)
\(930\) 8.72821e11 0.0382606
\(931\) −3.26570e13 −1.42463
\(932\) 5.81858e12 0.252607
\(933\) −2.77947e12 −0.120087
\(934\) −1.19680e13 −0.514591
\(935\) −2.61303e13 −1.11813
\(936\) 1.79801e12 0.0765686
\(937\) 2.55688e13 1.08363 0.541817 0.840497i \(-0.317737\pi\)
0.541817 + 0.840497i \(0.317737\pi\)
\(938\) 6.62424e12 0.279398
\(939\) 5.98574e12 0.251260
\(940\) 4.29203e10 0.00179303
\(941\) −2.70330e13 −1.12393 −0.561967 0.827160i \(-0.689955\pi\)
−0.561967 + 0.827160i \(0.689955\pi\)
\(942\) 1.10241e13 0.456157
\(943\) 5.53071e13 2.27760
\(944\) −2.51342e12 −0.103013
\(945\) 4.61606e11 0.0188290
\(946\) −1.97896e13 −0.803392
\(947\) −3.12375e13 −1.26212 −0.631062 0.775733i \(-0.717381\pi\)
−0.631062 + 0.775733i \(0.717381\pi\)
\(948\) 3.82407e11 0.0153776
\(949\) 7.03015e12 0.281363
\(950\) 2.73160e13 1.08808
\(951\) 8.83982e12 0.350454
\(952\) 8.83944e12 0.348785
\(953\) −3.49467e13 −1.37242 −0.686211 0.727402i \(-0.740727\pi\)
−0.686211 + 0.727402i \(0.740727\pi\)
\(954\) 9.39327e12 0.367155
\(955\) 1.66707e13 0.648543
\(956\) 2.81007e12 0.108807
\(957\) 3.99320e12 0.153892
\(958\) 4.43779e13 1.70224
\(959\) −3.67291e12 −0.140226
\(960\) 7.50696e12 0.285262
\(961\) −2.57288e13 −0.973114
\(962\) −7.32992e12 −0.275938
\(963\) −4.89746e11 −0.0183507
\(964\) 3.99784e12 0.149101
\(965\) −8.38940e12 −0.311428
\(966\) 4.46931e12 0.165137
\(967\) 2.47408e13 0.909903 0.454952 0.890516i \(-0.349657\pi\)
0.454952 + 0.890516i \(0.349657\pi\)
\(968\) 5.38406e13 1.97093
\(969\) −3.52799e13 −1.28550
\(970\) 7.90571e11 0.0286727
\(971\) 2.81788e13 1.01727 0.508634 0.860983i \(-0.330151\pi\)
0.508634 + 0.860983i \(0.330151\pi\)
\(972\) 3.16534e11 0.0113742
\(973\) −9.91464e12 −0.354625
\(974\) −3.66221e13 −1.30385
\(975\) 2.80868e12 0.0995364
\(976\) −1.57658e13 −0.556149
\(977\) 4.77088e13 1.67522 0.837612 0.546266i \(-0.183951\pi\)
0.837612 + 0.546266i \(0.183951\pi\)
\(978\) 1.53836e13 0.537690
\(979\) 2.46248e13 0.856744
\(980\) −2.17126e12 −0.0751958
\(981\) 7.33744e12 0.252950
\(982\) −1.28510e13 −0.440996
\(983\) 1.11374e13 0.380446 0.190223 0.981741i \(-0.439079\pi\)
0.190223 + 0.981741i \(0.439079\pi\)
\(984\) −2.87542e13 −0.977738
\(985\) 7.70141e12 0.260680
\(986\) 6.32727e12 0.213192
\(987\) −8.57791e10 −0.00287710
\(988\) −1.70985e12 −0.0570888
\(989\) 2.26882e13 0.754080
\(990\) 6.86878e12 0.227259
\(991\) −3.95333e13 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(992\) 1.75118e12 0.0574154
\(993\) 6.65730e12 0.217283
\(994\) 6.23113e11 0.0202455
\(995\) 8.69616e12 0.281270
\(996\) −3.58994e12 −0.115590
\(997\) 2.77111e12 0.0888230 0.0444115 0.999013i \(-0.485859\pi\)
0.0444115 + 0.999013i \(0.485859\pi\)
\(998\) −1.28507e13 −0.410054
\(999\) −8.56825e12 −0.272175
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.c.1.6 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.6 22 1.1 even 1 trivial