Properties

Label 177.14.a.b.1.9
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(1\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-80.4989 q^{2} -729.000 q^{3} -1711.93 q^{4} -19074.6 q^{5} +58683.7 q^{6} -213612. q^{7} +797255. q^{8} +531441. q^{9} +O(q^{10})\) \(q-80.4989 q^{2} -729.000 q^{3} -1711.93 q^{4} -19074.6 q^{5} +58683.7 q^{6} -213612. q^{7} +797255. q^{8} +531441. q^{9} +1.53548e6 q^{10} +8.17809e6 q^{11} +1.24800e6 q^{12} +1.28272e7 q^{13} +1.71955e7 q^{14} +1.39054e7 q^{15} -5.01540e7 q^{16} -1.73178e8 q^{17} -4.27804e7 q^{18} -1.17963e8 q^{19} +3.26545e7 q^{20} +1.55723e8 q^{21} -6.58327e8 q^{22} -4.16120e8 q^{23} -5.81199e8 q^{24} -8.56862e8 q^{25} -1.03257e9 q^{26} -3.87420e8 q^{27} +3.65690e8 q^{28} -1.55997e8 q^{29} -1.11937e9 q^{30} -3.96240e9 q^{31} -2.49378e9 q^{32} -5.96182e9 q^{33} +1.39407e10 q^{34} +4.07457e9 q^{35} -9.09792e8 q^{36} +1.91396e10 q^{37} +9.49589e9 q^{38} -9.35103e9 q^{39} -1.52073e10 q^{40} +4.39945e10 q^{41} -1.25355e10 q^{42} +5.38432e10 q^{43} -1.40003e10 q^{44} -1.01370e10 q^{45} +3.34972e10 q^{46} -9.05033e10 q^{47} +3.65622e10 q^{48} -5.12589e10 q^{49} +6.89764e10 q^{50} +1.26247e11 q^{51} -2.19593e10 q^{52} +3.89797e10 q^{53} +3.11869e10 q^{54} -1.55994e11 q^{55} -1.70303e11 q^{56} +8.59951e10 q^{57} +1.25576e10 q^{58} -4.21805e10 q^{59} -2.38051e10 q^{60} +1.44043e11 q^{61} +3.18969e11 q^{62} -1.13522e11 q^{63} +6.11608e11 q^{64} -2.44674e11 q^{65} +4.79920e11 q^{66} +3.53590e11 q^{67} +2.96470e11 q^{68} +3.03351e11 q^{69} -3.27998e11 q^{70} +8.31665e11 q^{71} +4.23694e11 q^{72} +1.24104e11 q^{73} -1.54072e12 q^{74} +6.24653e11 q^{75} +2.01945e11 q^{76} -1.74694e12 q^{77} +7.52747e11 q^{78} +1.36968e12 q^{79} +9.56668e11 q^{80} +2.82430e11 q^{81} -3.54151e12 q^{82} -2.42824e12 q^{83} -2.66588e11 q^{84} +3.30331e12 q^{85} -4.33431e12 q^{86} +1.13722e11 q^{87} +6.52002e12 q^{88} +1.71038e12 q^{89} +8.16019e11 q^{90} -2.74004e12 q^{91} +7.12370e11 q^{92} +2.88859e12 q^{93} +7.28541e12 q^{94} +2.25010e12 q^{95} +1.81796e12 q^{96} +1.14861e13 q^{97} +4.12628e12 q^{98} +4.34617e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −80.4989 −0.889395 −0.444698 0.895681i \(-0.646689\pi\)
−0.444698 + 0.895681i \(0.646689\pi\)
\(3\) −729.000 −0.577350
\(4\) −1711.93 −0.208976
\(5\) −19074.6 −0.545947 −0.272974 0.962022i \(-0.588007\pi\)
−0.272974 + 0.962022i \(0.588007\pi\)
\(6\) 58683.7 0.513492
\(7\) −213612. −0.686260 −0.343130 0.939288i \(-0.611487\pi\)
−0.343130 + 0.939288i \(0.611487\pi\)
\(8\) 797255. 1.07526
\(9\) 531441. 0.333333
\(10\) 1.53548e6 0.485563
\(11\) 8.17809e6 1.39187 0.695936 0.718104i \(-0.254990\pi\)
0.695936 + 0.718104i \(0.254990\pi\)
\(12\) 1.24800e6 0.120653
\(13\) 1.28272e7 0.737055 0.368528 0.929617i \(-0.379862\pi\)
0.368528 + 0.929617i \(0.379862\pi\)
\(14\) 1.71955e7 0.610356
\(15\) 1.39054e7 0.315203
\(16\) −5.01540e7 −0.747352
\(17\) −1.73178e8 −1.74010 −0.870052 0.492959i \(-0.835915\pi\)
−0.870052 + 0.492959i \(0.835915\pi\)
\(18\) −4.27804e7 −0.296465
\(19\) −1.17963e8 −0.575238 −0.287619 0.957745i \(-0.592864\pi\)
−0.287619 + 0.957745i \(0.592864\pi\)
\(20\) 3.26545e7 0.114090
\(21\) 1.55723e8 0.396212
\(22\) −6.58327e8 −1.23792
\(23\) −4.16120e8 −0.586121 −0.293061 0.956094i \(-0.594674\pi\)
−0.293061 + 0.956094i \(0.594674\pi\)
\(24\) −5.81199e8 −0.620800
\(25\) −8.56862e8 −0.701942
\(26\) −1.03257e9 −0.655533
\(27\) −3.87420e8 −0.192450
\(28\) 3.65690e8 0.143412
\(29\) −1.55997e8 −0.0487000 −0.0243500 0.999703i \(-0.507752\pi\)
−0.0243500 + 0.999703i \(0.507752\pi\)
\(30\) −1.11937e9 −0.280340
\(31\) −3.96240e9 −0.801877 −0.400939 0.916105i \(-0.631316\pi\)
−0.400939 + 0.916105i \(0.631316\pi\)
\(32\) −2.49378e9 −0.410566
\(33\) −5.96182e9 −0.803598
\(34\) 1.39407e10 1.54764
\(35\) 4.07457e9 0.374661
\(36\) −9.09792e8 −0.0696588
\(37\) 1.91396e10 1.22637 0.613186 0.789938i \(-0.289888\pi\)
0.613186 + 0.789938i \(0.289888\pi\)
\(38\) 9.49589e9 0.511614
\(39\) −9.35103e9 −0.425539
\(40\) −1.52073e10 −0.587034
\(41\) 4.39945e10 1.44645 0.723225 0.690613i \(-0.242659\pi\)
0.723225 + 0.690613i \(0.242659\pi\)
\(42\) −1.25355e10 −0.352389
\(43\) 5.38432e10 1.29893 0.649465 0.760392i \(-0.274993\pi\)
0.649465 + 0.760392i \(0.274993\pi\)
\(44\) −1.40003e10 −0.290868
\(45\) −1.01370e10 −0.181982
\(46\) 3.34972e10 0.521293
\(47\) −9.05033e10 −1.22470 −0.612348 0.790588i \(-0.709775\pi\)
−0.612348 + 0.790588i \(0.709775\pi\)
\(48\) 3.65622e10 0.431484
\(49\) −5.12589e10 −0.529048
\(50\) 6.89764e10 0.624303
\(51\) 1.26247e11 1.00465
\(52\) −2.19593e10 −0.154027
\(53\) 3.89797e10 0.241571 0.120786 0.992679i \(-0.461459\pi\)
0.120786 + 0.992679i \(0.461459\pi\)
\(54\) 3.11869e10 0.171164
\(55\) −1.55994e11 −0.759888
\(56\) −1.70303e11 −0.737906
\(57\) 8.59951e10 0.332114
\(58\) 1.25576e10 0.0433136
\(59\) −4.21805e10 −0.130189
\(60\) −2.38051e10 −0.0658699
\(61\) 1.44043e11 0.357972 0.178986 0.983852i \(-0.442718\pi\)
0.178986 + 0.983852i \(0.442718\pi\)
\(62\) 3.18969e11 0.713185
\(63\) −1.13522e11 −0.228753
\(64\) 6.11608e11 1.11251
\(65\) −2.44674e11 −0.402393
\(66\) 4.79920e11 0.714716
\(67\) 3.53590e11 0.477545 0.238772 0.971076i \(-0.423255\pi\)
0.238772 + 0.971076i \(0.423255\pi\)
\(68\) 2.96470e11 0.363641
\(69\) 3.03351e11 0.338397
\(70\) −3.27998e11 −0.333222
\(71\) 8.31665e11 0.770494 0.385247 0.922814i \(-0.374116\pi\)
0.385247 + 0.922814i \(0.374116\pi\)
\(72\) 4.23694e11 0.358419
\(73\) 1.24104e11 0.0959811 0.0479905 0.998848i \(-0.484718\pi\)
0.0479905 + 0.998848i \(0.484718\pi\)
\(74\) −1.54072e12 −1.09073
\(75\) 6.24653e11 0.405266
\(76\) 2.01945e11 0.120211
\(77\) −1.74694e12 −0.955185
\(78\) 7.52747e11 0.378472
\(79\) 1.36968e12 0.633932 0.316966 0.948437i \(-0.397336\pi\)
0.316966 + 0.948437i \(0.397336\pi\)
\(80\) 9.56668e11 0.408015
\(81\) 2.82430e11 0.111111
\(82\) −3.54151e12 −1.28646
\(83\) −2.42824e12 −0.815237 −0.407618 0.913152i \(-0.633641\pi\)
−0.407618 + 0.913152i \(0.633641\pi\)
\(84\) −2.66588e11 −0.0827990
\(85\) 3.30331e12 0.950005
\(86\) −4.33431e12 −1.15526
\(87\) 1.13722e11 0.0281170
\(88\) 6.52002e12 1.49662
\(89\) 1.71038e12 0.364802 0.182401 0.983224i \(-0.441613\pi\)
0.182401 + 0.983224i \(0.441613\pi\)
\(90\) 8.16019e11 0.161854
\(91\) −2.74004e12 −0.505811
\(92\) 7.12370e11 0.122486
\(93\) 2.88859e12 0.462964
\(94\) 7.28541e12 1.08924
\(95\) 2.25010e12 0.314050
\(96\) 1.81796e12 0.237040
\(97\) 1.14861e13 1.40009 0.700045 0.714098i \(-0.253163\pi\)
0.700045 + 0.714098i \(0.253163\pi\)
\(98\) 4.12628e12 0.470532
\(99\) 4.34617e12 0.463957
\(100\) 1.46689e12 0.146689
\(101\) 2.63942e12 0.247411 0.123706 0.992319i \(-0.460522\pi\)
0.123706 + 0.992319i \(0.460522\pi\)
\(102\) −1.01627e13 −0.893531
\(103\) −3.88934e12 −0.320948 −0.160474 0.987040i \(-0.551302\pi\)
−0.160474 + 0.987040i \(0.551302\pi\)
\(104\) 1.02266e13 0.792524
\(105\) −2.97036e12 −0.216311
\(106\) −3.13782e12 −0.214852
\(107\) −1.65551e13 −1.06644 −0.533222 0.845975i \(-0.679019\pi\)
−0.533222 + 0.845975i \(0.679019\pi\)
\(108\) 6.63239e11 0.0402175
\(109\) −1.37664e13 −0.786228 −0.393114 0.919490i \(-0.628602\pi\)
−0.393114 + 0.919490i \(0.628602\pi\)
\(110\) 1.25573e13 0.675841
\(111\) −1.39528e13 −0.708046
\(112\) 1.07135e13 0.512878
\(113\) −1.07861e13 −0.487363 −0.243682 0.969855i \(-0.578355\pi\)
−0.243682 + 0.969855i \(0.578355\pi\)
\(114\) −6.92251e12 −0.295380
\(115\) 7.93732e12 0.319991
\(116\) 2.67057e11 0.0101772
\(117\) 6.81690e12 0.245685
\(118\) 3.39548e12 0.115789
\(119\) 3.69930e13 1.19416
\(120\) 1.10861e13 0.338924
\(121\) 3.23584e13 0.937307
\(122\) −1.15953e13 −0.318379
\(123\) −3.20720e13 −0.835108
\(124\) 6.78338e12 0.167573
\(125\) 3.96288e13 0.929170
\(126\) 9.13841e12 0.203452
\(127\) 2.31937e13 0.490509 0.245254 0.969459i \(-0.421129\pi\)
0.245254 + 0.969459i \(0.421129\pi\)
\(128\) −2.88047e13 −0.578893
\(129\) −3.92517e13 −0.749938
\(130\) 1.96960e13 0.357887
\(131\) −1.11690e13 −0.193086 −0.0965429 0.995329i \(-0.530778\pi\)
−0.0965429 + 0.995329i \(0.530778\pi\)
\(132\) 1.02063e13 0.167933
\(133\) 2.51983e13 0.394763
\(134\) −2.84636e13 −0.424726
\(135\) 7.38989e12 0.105068
\(136\) −1.38067e14 −1.87106
\(137\) 1.20494e14 1.55697 0.778485 0.627663i \(-0.215989\pi\)
0.778485 + 0.627663i \(0.215989\pi\)
\(138\) −2.44194e13 −0.300969
\(139\) 1.61914e14 1.90410 0.952048 0.305947i \(-0.0989732\pi\)
0.952048 + 0.305947i \(0.0989732\pi\)
\(140\) −6.97539e12 −0.0782954
\(141\) 6.59769e13 0.707079
\(142\) −6.69481e13 −0.685273
\(143\) 1.04902e14 1.02589
\(144\) −2.66539e13 −0.249117
\(145\) 2.97558e12 0.0265877
\(146\) −9.99019e12 −0.0853651
\(147\) 3.73678e13 0.305446
\(148\) −3.27658e13 −0.256283
\(149\) −9.37466e11 −0.00701850 −0.00350925 0.999994i \(-0.501117\pi\)
−0.00350925 + 0.999994i \(0.501117\pi\)
\(150\) −5.02838e13 −0.360442
\(151\) −1.24838e14 −0.857030 −0.428515 0.903535i \(-0.640963\pi\)
−0.428515 + 0.903535i \(0.640963\pi\)
\(152\) −9.40467e13 −0.618529
\(153\) −9.20340e13 −0.580035
\(154\) 1.40626e14 0.849537
\(155\) 7.55813e13 0.437783
\(156\) 1.60084e13 0.0889276
\(157\) −2.14585e14 −1.14354 −0.571771 0.820413i \(-0.693744\pi\)
−0.571771 + 0.820413i \(0.693744\pi\)
\(158\) −1.10258e14 −0.563816
\(159\) −2.84162e13 −0.139471
\(160\) 4.75679e13 0.224147
\(161\) 8.88882e13 0.402231
\(162\) −2.27353e13 −0.0988217
\(163\) 2.45085e14 1.02352 0.511761 0.859128i \(-0.328993\pi\)
0.511761 + 0.859128i \(0.328993\pi\)
\(164\) −7.53157e13 −0.302274
\(165\) 1.13719e14 0.438722
\(166\) 1.95470e14 0.725068
\(167\) −1.53043e14 −0.545955 −0.272977 0.962020i \(-0.588008\pi\)
−0.272977 + 0.962020i \(0.588008\pi\)
\(168\) 1.24151e14 0.426030
\(169\) −1.38338e14 −0.456749
\(170\) −2.65913e14 −0.844930
\(171\) −6.26904e13 −0.191746
\(172\) −9.21760e13 −0.271446
\(173\) 5.15002e14 1.46053 0.730264 0.683166i \(-0.239397\pi\)
0.730264 + 0.683166i \(0.239397\pi\)
\(174\) −9.15448e12 −0.0250071
\(175\) 1.83036e14 0.481714
\(176\) −4.10164e14 −1.04022
\(177\) 3.07496e13 0.0751646
\(178\) −1.37684e14 −0.324453
\(179\) 6.31949e14 1.43594 0.717972 0.696072i \(-0.245071\pi\)
0.717972 + 0.696072i \(0.245071\pi\)
\(180\) 1.73539e13 0.0380300
\(181\) −4.63932e13 −0.0980717 −0.0490359 0.998797i \(-0.515615\pi\)
−0.0490359 + 0.998797i \(0.515615\pi\)
\(182\) 2.20570e14 0.449866
\(183\) −1.05008e14 −0.206675
\(184\) −3.31754e14 −0.630231
\(185\) −3.65081e14 −0.669534
\(186\) −2.32528e14 −0.411758
\(187\) −1.41627e15 −2.42200
\(188\) 1.54936e14 0.255933
\(189\) 8.27577e13 0.132071
\(190\) −1.81130e14 −0.279314
\(191\) 6.06776e14 0.904298 0.452149 0.891942i \(-0.350658\pi\)
0.452149 + 0.891942i \(0.350658\pi\)
\(192\) −4.45862e14 −0.642307
\(193\) −2.92079e14 −0.406797 −0.203398 0.979096i \(-0.565199\pi\)
−0.203398 + 0.979096i \(0.565199\pi\)
\(194\) −9.24617e14 −1.24523
\(195\) 1.78367e14 0.232322
\(196\) 8.77519e13 0.110559
\(197\) 8.20582e14 1.00021 0.500106 0.865964i \(-0.333295\pi\)
0.500106 + 0.865964i \(0.333295\pi\)
\(198\) −3.49862e14 −0.412641
\(199\) −8.75439e14 −0.999266 −0.499633 0.866237i \(-0.666532\pi\)
−0.499633 + 0.866237i \(0.666532\pi\)
\(200\) −6.83138e14 −0.754768
\(201\) −2.57767e14 −0.275711
\(202\) −2.12470e14 −0.220046
\(203\) 3.33228e13 0.0334209
\(204\) −2.16127e14 −0.209948
\(205\) −8.39178e14 −0.789685
\(206\) 3.13088e14 0.285449
\(207\) −2.21143e14 −0.195374
\(208\) −6.43335e14 −0.550840
\(209\) −9.64712e14 −0.800658
\(210\) 2.39110e14 0.192386
\(211\) −3.01341e14 −0.235083 −0.117542 0.993068i \(-0.537501\pi\)
−0.117542 + 0.993068i \(0.537501\pi\)
\(212\) −6.67306e13 −0.0504827
\(213\) −6.06284e14 −0.444845
\(214\) 1.33267e15 0.948490
\(215\) −1.02704e15 −0.709147
\(216\) −3.08873e14 −0.206933
\(217\) 8.46417e14 0.550296
\(218\) 1.10818e15 0.699267
\(219\) −9.04715e13 −0.0554147
\(220\) 2.67051e14 0.158799
\(221\) −2.22139e15 −1.28255
\(222\) 1.12318e15 0.629733
\(223\) 7.48486e14 0.407570 0.203785 0.979016i \(-0.434676\pi\)
0.203785 + 0.979016i \(0.434676\pi\)
\(224\) 5.32701e14 0.281755
\(225\) −4.55372e14 −0.233981
\(226\) 8.68265e14 0.433458
\(227\) −1.73311e15 −0.840731 −0.420365 0.907355i \(-0.638098\pi\)
−0.420365 + 0.907355i \(0.638098\pi\)
\(228\) −1.47218e14 −0.0694040
\(229\) −1.83370e15 −0.840231 −0.420116 0.907471i \(-0.638010\pi\)
−0.420116 + 0.907471i \(0.638010\pi\)
\(230\) −6.38945e14 −0.284599
\(231\) 1.27352e15 0.551476
\(232\) −1.24369e14 −0.0523651
\(233\) −1.82157e15 −0.745818 −0.372909 0.927868i \(-0.621640\pi\)
−0.372909 + 0.927868i \(0.621640\pi\)
\(234\) −5.48753e14 −0.218511
\(235\) 1.72632e15 0.668620
\(236\) 7.22103e13 0.0272064
\(237\) −9.98496e14 −0.366001
\(238\) −2.97789e15 −1.06208
\(239\) 4.32444e15 1.50087 0.750435 0.660944i \(-0.229844\pi\)
0.750435 + 0.660944i \(0.229844\pi\)
\(240\) −6.97411e14 −0.235568
\(241\) 2.79473e15 0.918818 0.459409 0.888225i \(-0.348061\pi\)
0.459409 + 0.888225i \(0.348061\pi\)
\(242\) −2.60481e15 −0.833636
\(243\) −2.05891e14 −0.0641500
\(244\) −2.46593e14 −0.0748078
\(245\) 9.77744e14 0.288832
\(246\) 2.58176e15 0.742741
\(247\) −1.51314e15 −0.423982
\(248\) −3.15905e15 −0.862224
\(249\) 1.77019e15 0.470677
\(250\) −3.19007e15 −0.826399
\(251\) 1.43836e15 0.363068 0.181534 0.983385i \(-0.441894\pi\)
0.181534 + 0.983385i \(0.441894\pi\)
\(252\) 1.94343e14 0.0478040
\(253\) −3.40306e15 −0.815806
\(254\) −1.86707e15 −0.436256
\(255\) −2.40811e15 −0.548486
\(256\) −2.69155e15 −0.597643
\(257\) −4.98081e15 −1.07829 −0.539143 0.842214i \(-0.681252\pi\)
−0.539143 + 0.842214i \(0.681252\pi\)
\(258\) 3.15971e15 0.666991
\(259\) −4.08845e15 −0.841610
\(260\) 4.18866e14 0.0840907
\(261\) −8.29032e13 −0.0162333
\(262\) 8.99090e14 0.171730
\(263\) −6.11475e14 −0.113937 −0.0569687 0.998376i \(-0.518144\pi\)
−0.0569687 + 0.998376i \(0.518144\pi\)
\(264\) −4.75310e15 −0.864074
\(265\) −7.43522e14 −0.131885
\(266\) −2.02844e15 −0.351100
\(267\) −1.24687e15 −0.210619
\(268\) −6.05323e14 −0.0997956
\(269\) −1.10305e16 −1.77502 −0.887512 0.460785i \(-0.847568\pi\)
−0.887512 + 0.460785i \(0.847568\pi\)
\(270\) −5.94878e14 −0.0934466
\(271\) −4.71700e15 −0.723378 −0.361689 0.932299i \(-0.617800\pi\)
−0.361689 + 0.932299i \(0.617800\pi\)
\(272\) 8.68558e15 1.30047
\(273\) 1.99749e15 0.292030
\(274\) −9.69959e15 −1.38476
\(275\) −7.00749e15 −0.977013
\(276\) −5.19318e14 −0.0707170
\(277\) −7.70626e15 −1.02500 −0.512502 0.858686i \(-0.671281\pi\)
−0.512502 + 0.858686i \(0.671281\pi\)
\(278\) −1.30339e16 −1.69349
\(279\) −2.10578e15 −0.267292
\(280\) 3.24847e15 0.402858
\(281\) 1.10133e15 0.133453 0.0667263 0.997771i \(-0.478745\pi\)
0.0667263 + 0.997771i \(0.478745\pi\)
\(282\) −5.31107e15 −0.628872
\(283\) 1.00903e16 1.16760 0.583798 0.811899i \(-0.301566\pi\)
0.583798 + 0.811899i \(0.301566\pi\)
\(284\) −1.42376e15 −0.161015
\(285\) −1.64032e15 −0.181317
\(286\) −8.44449e15 −0.912418
\(287\) −9.39775e15 −0.992640
\(288\) −1.32530e15 −0.136855
\(289\) 2.00861e16 2.02797
\(290\) −2.39531e14 −0.0236469
\(291\) −8.37336e15 −0.808343
\(292\) −2.12457e14 −0.0200578
\(293\) 4.10282e14 0.0378829 0.0189415 0.999821i \(-0.493970\pi\)
0.0189415 + 0.999821i \(0.493970\pi\)
\(294\) −3.00806e15 −0.271662
\(295\) 8.04577e14 0.0710763
\(296\) 1.52592e16 1.31867
\(297\) −3.16836e15 −0.267866
\(298\) 7.54649e13 0.00624222
\(299\) −5.33765e15 −0.432004
\(300\) −1.06936e15 −0.0846911
\(301\) −1.15016e16 −0.891403
\(302\) 1.00493e16 0.762238
\(303\) −1.92413e15 −0.142843
\(304\) 5.91632e15 0.429906
\(305\) −2.74757e15 −0.195434
\(306\) 7.40863e15 0.515880
\(307\) −9.89210e15 −0.674356 −0.337178 0.941441i \(-0.609472\pi\)
−0.337178 + 0.941441i \(0.609472\pi\)
\(308\) 2.99064e15 0.199611
\(309\) 2.83533e15 0.185299
\(310\) −6.08421e15 −0.389362
\(311\) 2.68530e16 1.68287 0.841434 0.540360i \(-0.181712\pi\)
0.841434 + 0.540360i \(0.181712\pi\)
\(312\) −7.45516e15 −0.457564
\(313\) −2.91390e15 −0.175161 −0.0875803 0.996157i \(-0.527913\pi\)
−0.0875803 + 0.996157i \(0.527913\pi\)
\(314\) 1.72739e16 1.01706
\(315\) 2.16539e15 0.124887
\(316\) −2.34480e15 −0.132477
\(317\) −1.30073e16 −0.719948 −0.359974 0.932962i \(-0.617214\pi\)
−0.359974 + 0.932962i \(0.617214\pi\)
\(318\) 2.28747e15 0.124045
\(319\) −1.27576e15 −0.0677842
\(320\) −1.16662e16 −0.607371
\(321\) 1.20687e16 0.615712
\(322\) −7.15540e15 −0.357743
\(323\) 2.04286e16 1.00097
\(324\) −4.83501e14 −0.0232196
\(325\) −1.09911e16 −0.517370
\(326\) −1.97290e16 −0.910315
\(327\) 1.00357e16 0.453929
\(328\) 3.50748e16 1.55531
\(329\) 1.93326e16 0.840460
\(330\) −9.15429e15 −0.390197
\(331\) 8.56049e15 0.357780 0.178890 0.983869i \(-0.442749\pi\)
0.178890 + 0.983869i \(0.442749\pi\)
\(332\) 4.15699e15 0.170365
\(333\) 1.01716e16 0.408791
\(334\) 1.23198e16 0.485569
\(335\) −6.74460e15 −0.260714
\(336\) −7.81014e15 −0.296110
\(337\) −4.26634e15 −0.158658 −0.0793289 0.996848i \(-0.525278\pi\)
−0.0793289 + 0.996848i \(0.525278\pi\)
\(338\) 1.11361e16 0.406231
\(339\) 7.86303e15 0.281379
\(340\) −5.65505e15 −0.198529
\(341\) −3.24049e16 −1.11611
\(342\) 5.04651e15 0.170538
\(343\) 3.16462e16 1.04932
\(344\) 4.29268e16 1.39668
\(345\) −5.78631e15 −0.184747
\(346\) −4.14571e16 −1.29899
\(347\) 1.84443e16 0.567178 0.283589 0.958946i \(-0.408475\pi\)
0.283589 + 0.958946i \(0.408475\pi\)
\(348\) −1.94684e14 −0.00587579
\(349\) 1.37643e16 0.407744 0.203872 0.978998i \(-0.434647\pi\)
0.203872 + 0.978998i \(0.434647\pi\)
\(350\) −1.47342e16 −0.428434
\(351\) −4.96952e15 −0.141846
\(352\) −2.03943e16 −0.571455
\(353\) 1.10794e16 0.304775 0.152388 0.988321i \(-0.451304\pi\)
0.152388 + 0.988321i \(0.451304\pi\)
\(354\) −2.47531e15 −0.0668510
\(355\) −1.58637e16 −0.420649
\(356\) −2.92806e15 −0.0762351
\(357\) −2.69679e16 −0.689451
\(358\) −5.08712e16 −1.27712
\(359\) 7.87950e16 1.94261 0.971304 0.237843i \(-0.0764405\pi\)
0.971304 + 0.237843i \(0.0764405\pi\)
\(360\) −8.08180e15 −0.195678
\(361\) −2.81377e16 −0.669101
\(362\) 3.73460e15 0.0872245
\(363\) −2.35893e16 −0.541154
\(364\) 4.69078e15 0.105703
\(365\) −2.36723e15 −0.0524006
\(366\) 8.45300e15 0.183816
\(367\) −5.97301e16 −1.27604 −0.638019 0.770020i \(-0.720246\pi\)
−0.638019 + 0.770020i \(0.720246\pi\)
\(368\) 2.08701e16 0.438039
\(369\) 2.33805e16 0.482150
\(370\) 2.93886e16 0.595481
\(371\) −8.32652e15 −0.165780
\(372\) −4.94508e15 −0.0967485
\(373\) −2.86827e16 −0.551458 −0.275729 0.961235i \(-0.588919\pi\)
−0.275729 + 0.961235i \(0.588919\pi\)
\(374\) 1.14008e17 2.15412
\(375\) −2.88894e16 −0.536457
\(376\) −7.21543e16 −1.31686
\(377\) −2.00101e15 −0.0358946
\(378\) −6.66190e15 −0.117463
\(379\) 5.49980e16 0.953218 0.476609 0.879115i \(-0.341866\pi\)
0.476609 + 0.879115i \(0.341866\pi\)
\(380\) −3.85202e15 −0.0656290
\(381\) −1.69082e16 −0.283195
\(382\) −4.88448e16 −0.804278
\(383\) −2.75953e16 −0.446729 −0.223364 0.974735i \(-0.571704\pi\)
−0.223364 + 0.974735i \(0.571704\pi\)
\(384\) 2.09986e16 0.334224
\(385\) 3.33221e16 0.521481
\(386\) 2.35120e16 0.361803
\(387\) 2.86145e16 0.432977
\(388\) −1.96634e16 −0.292586
\(389\) −3.35993e14 −0.00491652 −0.00245826 0.999997i \(-0.500782\pi\)
−0.00245826 + 0.999997i \(0.500782\pi\)
\(390\) −1.43584e16 −0.206626
\(391\) 7.20629e16 1.01991
\(392\) −4.08664e16 −0.568863
\(393\) 8.14219e15 0.111478
\(394\) −6.60559e16 −0.889583
\(395\) −2.61261e16 −0.346093
\(396\) −7.44036e15 −0.0969561
\(397\) −9.99384e16 −1.28113 −0.640566 0.767903i \(-0.721300\pi\)
−0.640566 + 0.767903i \(0.721300\pi\)
\(398\) 7.04719e16 0.888742
\(399\) −1.83696e16 −0.227916
\(400\) 4.29751e16 0.524598
\(401\) 1.36815e17 1.64322 0.821610 0.570050i \(-0.193076\pi\)
0.821610 + 0.570050i \(0.193076\pi\)
\(402\) 2.07500e16 0.245216
\(403\) −5.08266e16 −0.591028
\(404\) −4.51851e15 −0.0517031
\(405\) −5.38723e15 −0.0606608
\(406\) −2.68245e15 −0.0297244
\(407\) 1.56526e17 1.70695
\(408\) 1.00651e17 1.08026
\(409\) 6.83409e16 0.721904 0.360952 0.932584i \(-0.382452\pi\)
0.360952 + 0.932584i \(0.382452\pi\)
\(410\) 6.75528e16 0.702342
\(411\) −8.78398e16 −0.898917
\(412\) 6.65830e15 0.0670705
\(413\) 9.01027e15 0.0893434
\(414\) 1.78018e16 0.173764
\(415\) 4.63177e16 0.445076
\(416\) −3.19882e16 −0.302610
\(417\) −1.18036e17 −1.09933
\(418\) 7.76582e16 0.712101
\(419\) −8.94425e16 −0.807519 −0.403759 0.914865i \(-0.632297\pi\)
−0.403759 + 0.914865i \(0.632297\pi\)
\(420\) 5.08506e15 0.0452039
\(421\) −7.32844e16 −0.641472 −0.320736 0.947169i \(-0.603930\pi\)
−0.320736 + 0.947169i \(0.603930\pi\)
\(422\) 2.42576e16 0.209082
\(423\) −4.80972e16 −0.408232
\(424\) 3.10767e16 0.259751
\(425\) 1.48390e17 1.22145
\(426\) 4.88051e16 0.395643
\(427\) −3.07694e16 −0.245662
\(428\) 2.83413e16 0.222862
\(429\) −7.64735e16 −0.592296
\(430\) 8.26754e16 0.630712
\(431\) −1.36306e17 −1.02426 −0.512132 0.858907i \(-0.671144\pi\)
−0.512132 + 0.858907i \(0.671144\pi\)
\(432\) 1.94307e16 0.143828
\(433\) 1.44267e17 1.05195 0.525976 0.850500i \(-0.323700\pi\)
0.525976 + 0.850500i \(0.323700\pi\)
\(434\) −6.81356e16 −0.489430
\(435\) −2.16920e15 −0.0153504
\(436\) 2.35672e16 0.164303
\(437\) 4.90868e16 0.337159
\(438\) 7.28285e15 0.0492856
\(439\) −2.35753e17 −1.57195 −0.785975 0.618259i \(-0.787838\pi\)
−0.785975 + 0.618259i \(0.787838\pi\)
\(440\) −1.24367e17 −0.817076
\(441\) −2.72411e16 −0.176349
\(442\) 1.78820e17 1.14070
\(443\) −2.55727e17 −1.60750 −0.803752 0.594964i \(-0.797166\pi\)
−0.803752 + 0.594964i \(0.797166\pi\)
\(444\) 2.38863e16 0.147965
\(445\) −3.26248e16 −0.199163
\(446\) −6.02522e16 −0.362490
\(447\) 6.83412e14 0.00405214
\(448\) −1.30647e17 −0.763469
\(449\) 2.25571e16 0.129922 0.0649609 0.997888i \(-0.479308\pi\)
0.0649609 + 0.997888i \(0.479308\pi\)
\(450\) 3.66569e16 0.208101
\(451\) 3.59791e17 2.01327
\(452\) 1.84650e16 0.101847
\(453\) 9.10068e16 0.494806
\(454\) 1.39513e17 0.747742
\(455\) 5.22653e16 0.276146
\(456\) 6.85600e16 0.357108
\(457\) −9.18133e16 −0.471466 −0.235733 0.971818i \(-0.575749\pi\)
−0.235733 + 0.971818i \(0.575749\pi\)
\(458\) 1.47611e17 0.747297
\(459\) 6.70928e16 0.334883
\(460\) −1.35882e16 −0.0668706
\(461\) 1.21412e17 0.589125 0.294562 0.955632i \(-0.404826\pi\)
0.294562 + 0.955632i \(0.404826\pi\)
\(462\) −1.02517e17 −0.490480
\(463\) −1.82524e17 −0.861081 −0.430541 0.902571i \(-0.641677\pi\)
−0.430541 + 0.902571i \(0.641677\pi\)
\(464\) 7.82387e15 0.0363961
\(465\) −5.50988e16 −0.252754
\(466\) 1.46635e17 0.663327
\(467\) 7.60620e16 0.339319 0.169659 0.985503i \(-0.445733\pi\)
0.169659 + 0.985503i \(0.445733\pi\)
\(468\) −1.16701e16 −0.0513424
\(469\) −7.55311e16 −0.327720
\(470\) −1.38966e17 −0.594667
\(471\) 1.56433e17 0.660225
\(472\) −3.36287e16 −0.139987
\(473\) 4.40334e17 1.80794
\(474\) 8.03778e16 0.325519
\(475\) 1.01078e17 0.403784
\(476\) −6.33295e16 −0.249552
\(477\) 2.07154e16 0.0805237
\(478\) −3.48112e17 −1.33487
\(479\) 6.08627e16 0.230235 0.115117 0.993352i \(-0.463276\pi\)
0.115117 + 0.993352i \(0.463276\pi\)
\(480\) −3.46770e16 −0.129412
\(481\) 2.45508e17 0.903904
\(482\) −2.24973e17 −0.817192
\(483\) −6.47995e16 −0.232228
\(484\) −5.53954e16 −0.195875
\(485\) −2.19093e17 −0.764376
\(486\) 1.65740e16 0.0570547
\(487\) −1.79972e17 −0.611317 −0.305659 0.952141i \(-0.598877\pi\)
−0.305659 + 0.952141i \(0.598877\pi\)
\(488\) 1.14839e17 0.384913
\(489\) −1.78667e17 −0.590930
\(490\) −7.87073e16 −0.256886
\(491\) −3.07934e17 −0.991809 −0.495905 0.868377i \(-0.665163\pi\)
−0.495905 + 0.868377i \(0.665163\pi\)
\(492\) 5.49051e16 0.174518
\(493\) 2.70153e16 0.0847432
\(494\) 1.21806e17 0.377088
\(495\) −8.29015e16 −0.253296
\(496\) 1.98730e17 0.599285
\(497\) −1.77654e17 −0.528759
\(498\) −1.42498e17 −0.418618
\(499\) −3.50911e17 −1.01752 −0.508760 0.860908i \(-0.669896\pi\)
−0.508760 + 0.860908i \(0.669896\pi\)
\(500\) −6.78418e16 −0.194175
\(501\) 1.11568e17 0.315207
\(502\) −1.15786e17 −0.322911
\(503\) 3.57981e17 0.985526 0.492763 0.870164i \(-0.335987\pi\)
0.492763 + 0.870164i \(0.335987\pi\)
\(504\) −9.05062e16 −0.245969
\(505\) −5.03458e16 −0.135073
\(506\) 2.73943e17 0.725574
\(507\) 1.00848e17 0.263704
\(508\) −3.97062e16 −0.102505
\(509\) 4.62471e17 1.17874 0.589371 0.807863i \(-0.299376\pi\)
0.589371 + 0.807863i \(0.299376\pi\)
\(510\) 1.93850e17 0.487821
\(511\) −2.65100e16 −0.0658679
\(512\) 4.52634e17 1.11043
\(513\) 4.57013e16 0.110705
\(514\) 4.00949e17 0.959023
\(515\) 7.41877e16 0.175221
\(516\) 6.71963e16 0.156719
\(517\) −7.40144e17 −1.70462
\(518\) 3.29116e17 0.748524
\(519\) −3.75437e17 −0.843236
\(520\) −1.95068e17 −0.432676
\(521\) 4.25083e17 0.931170 0.465585 0.885003i \(-0.345844\pi\)
0.465585 + 0.885003i \(0.345844\pi\)
\(522\) 6.67361e15 0.0144379
\(523\) 1.34418e17 0.287208 0.143604 0.989635i \(-0.454131\pi\)
0.143604 + 0.989635i \(0.454131\pi\)
\(524\) 1.91206e16 0.0403504
\(525\) −1.33433e17 −0.278118
\(526\) 4.92230e16 0.101335
\(527\) 6.86202e17 1.39535
\(528\) 2.99009e17 0.600571
\(529\) −3.30881e17 −0.656462
\(530\) 5.98527e16 0.117298
\(531\) −2.24165e16 −0.0433963
\(532\) −4.31379e16 −0.0824961
\(533\) 5.64326e17 1.06611
\(534\) 1.00371e17 0.187323
\(535\) 3.15783e17 0.582222
\(536\) 2.81902e17 0.513484
\(537\) −4.60691e17 −0.829042
\(538\) 8.87940e17 1.57870
\(539\) −4.19200e17 −0.736367
\(540\) −1.26510e16 −0.0219566
\(541\) −1.30229e17 −0.223320 −0.111660 0.993746i \(-0.535617\pi\)
−0.111660 + 0.993746i \(0.535617\pi\)
\(542\) 3.79713e17 0.643369
\(543\) 3.38207e16 0.0566217
\(544\) 4.31868e17 0.714428
\(545\) 2.62589e17 0.429239
\(546\) −1.60796e17 −0.259730
\(547\) −1.28017e17 −0.204339 −0.102169 0.994767i \(-0.532578\pi\)
−0.102169 + 0.994767i \(0.532578\pi\)
\(548\) −2.06277e17 −0.325370
\(549\) 7.65506e16 0.119324
\(550\) 5.64095e17 0.868950
\(551\) 1.84019e16 0.0280141
\(552\) 2.41849e17 0.363864
\(553\) −2.92580e17 −0.435042
\(554\) 6.20345e17 0.911633
\(555\) 2.66144e17 0.386556
\(556\) −2.77187e17 −0.397911
\(557\) 6.55367e17 0.929878 0.464939 0.885343i \(-0.346076\pi\)
0.464939 + 0.885343i \(0.346076\pi\)
\(558\) 1.69513e17 0.237728
\(559\) 6.90657e17 0.957383
\(560\) −2.04356e17 −0.280004
\(561\) 1.03246e18 1.39834
\(562\) −8.86560e16 −0.118692
\(563\) −5.69437e16 −0.0753600 −0.0376800 0.999290i \(-0.511997\pi\)
−0.0376800 + 0.999290i \(0.511997\pi\)
\(564\) −1.12948e17 −0.147763
\(565\) 2.05740e17 0.266074
\(566\) −8.12259e17 −1.03845
\(567\) −6.03303e16 −0.0762511
\(568\) 6.63049e17 0.828479
\(569\) −3.58343e17 −0.442659 −0.221329 0.975199i \(-0.571040\pi\)
−0.221329 + 0.975199i \(0.571040\pi\)
\(570\) 1.32044e17 0.161262
\(571\) −1.30154e18 −1.57153 −0.785766 0.618524i \(-0.787731\pi\)
−0.785766 + 0.618524i \(0.787731\pi\)
\(572\) −1.79585e17 −0.214386
\(573\) −4.42340e17 −0.522097
\(574\) 7.56508e17 0.882849
\(575\) 3.56557e17 0.411423
\(576\) 3.25033e17 0.370836
\(577\) −1.26412e18 −1.42609 −0.713043 0.701120i \(-0.752684\pi\)
−0.713043 + 0.701120i \(0.752684\pi\)
\(578\) −1.61691e18 −1.80366
\(579\) 2.12926e17 0.234864
\(580\) −5.09400e15 −0.00555619
\(581\) 5.18701e17 0.559464
\(582\) 6.74046e17 0.718936
\(583\) 3.18779e17 0.336236
\(584\) 9.89422e16 0.103204
\(585\) −1.30030e17 −0.134131
\(586\) −3.30273e16 −0.0336929
\(587\) −1.20369e18 −1.21442 −0.607210 0.794542i \(-0.707711\pi\)
−0.607210 + 0.794542i \(0.707711\pi\)
\(588\) −6.39711e16 −0.0638310
\(589\) 4.67417e17 0.461270
\(590\) −6.47675e16 −0.0632149
\(591\) −5.98205e17 −0.577472
\(592\) −9.59928e17 −0.916532
\(593\) −1.50625e18 −1.42247 −0.711234 0.702956i \(-0.751863\pi\)
−0.711234 + 0.702956i \(0.751863\pi\)
\(594\) 2.55049e17 0.238239
\(595\) −7.05626e17 −0.651950
\(596\) 1.60488e15 0.00146670
\(597\) 6.38195e17 0.576926
\(598\) 4.29675e17 0.384222
\(599\) −5.52771e17 −0.488957 −0.244479 0.969655i \(-0.578617\pi\)
−0.244479 + 0.969655i \(0.578617\pi\)
\(600\) 4.98008e17 0.435766
\(601\) −1.44492e18 −1.25072 −0.625360 0.780337i \(-0.715048\pi\)
−0.625360 + 0.780337i \(0.715048\pi\)
\(602\) 9.25862e17 0.792810
\(603\) 1.87912e17 0.159182
\(604\) 2.13714e17 0.179099
\(605\) −6.17223e17 −0.511720
\(606\) 1.54891e17 0.127044
\(607\) 7.08095e17 0.574600 0.287300 0.957841i \(-0.407242\pi\)
0.287300 + 0.957841i \(0.407242\pi\)
\(608\) 2.94174e17 0.236173
\(609\) −2.42923e16 −0.0192955
\(610\) 2.21176e17 0.173818
\(611\) −1.16090e18 −0.902669
\(612\) 1.57556e17 0.121214
\(613\) 4.16918e17 0.317364 0.158682 0.987330i \(-0.449276\pi\)
0.158682 + 0.987330i \(0.449276\pi\)
\(614\) 7.96303e17 0.599769
\(615\) 6.11761e17 0.455925
\(616\) −1.39276e18 −1.02707
\(617\) −1.42371e18 −1.03889 −0.519444 0.854505i \(-0.673861\pi\)
−0.519444 + 0.854505i \(0.673861\pi\)
\(618\) −2.28241e17 −0.164804
\(619\) −2.13246e17 −0.152367 −0.0761836 0.997094i \(-0.524274\pi\)
−0.0761836 + 0.997094i \(0.524274\pi\)
\(620\) −1.29390e17 −0.0914862
\(621\) 1.61213e17 0.112799
\(622\) −2.16163e18 −1.49673
\(623\) −3.65358e17 −0.250349
\(624\) 4.68991e17 0.318028
\(625\) 2.90072e17 0.194664
\(626\) 2.34566e17 0.155787
\(627\) 7.03275e17 0.462260
\(628\) 3.67356e17 0.238973
\(629\) −3.31457e18 −2.13402
\(630\) −1.74312e17 −0.111074
\(631\) −1.54439e18 −0.974013 −0.487007 0.873398i \(-0.661911\pi\)
−0.487007 + 0.873398i \(0.661911\pi\)
\(632\) 1.09198e18 0.681640
\(633\) 2.19677e17 0.135725
\(634\) 1.04707e18 0.640318
\(635\) −4.42412e17 −0.267792
\(636\) 4.86466e16 0.0291462
\(637\) −6.57508e17 −0.389937
\(638\) 1.02697e17 0.0602869
\(639\) 4.41981e17 0.256831
\(640\) 5.49438e17 0.316045
\(641\) 1.32543e18 0.754707 0.377354 0.926069i \(-0.376834\pi\)
0.377354 + 0.926069i \(0.376834\pi\)
\(642\) −9.71516e17 −0.547611
\(643\) −2.70013e18 −1.50665 −0.753326 0.657647i \(-0.771552\pi\)
−0.753326 + 0.657647i \(0.771552\pi\)
\(644\) −1.52171e17 −0.0840569
\(645\) 7.48710e17 0.409426
\(646\) −1.64448e18 −0.890262
\(647\) −1.72588e18 −0.924983 −0.462491 0.886624i \(-0.653044\pi\)
−0.462491 + 0.886624i \(0.653044\pi\)
\(648\) 2.25168e17 0.119473
\(649\) −3.44956e17 −0.181206
\(650\) 8.84775e17 0.460146
\(651\) −6.17038e17 −0.317713
\(652\) −4.19569e17 −0.213892
\(653\) −6.14833e17 −0.310329 −0.155164 0.987889i \(-0.549591\pi\)
−0.155164 + 0.987889i \(0.549591\pi\)
\(654\) −8.07863e17 −0.403722
\(655\) 2.13044e17 0.105415
\(656\) −2.20650e18 −1.08101
\(657\) 6.59537e16 0.0319937
\(658\) −1.55625e18 −0.747501
\(659\) −4.49875e17 −0.213962 −0.106981 0.994261i \(-0.534118\pi\)
−0.106981 + 0.994261i \(0.534118\pi\)
\(660\) −1.94680e17 −0.0916825
\(661\) −8.57866e17 −0.400046 −0.200023 0.979791i \(-0.564102\pi\)
−0.200023 + 0.979791i \(0.564102\pi\)
\(662\) −6.89109e17 −0.318208
\(663\) 1.61940e18 0.740483
\(664\) −1.93593e18 −0.876590
\(665\) −4.80648e17 −0.215520
\(666\) −8.18801e17 −0.363576
\(667\) 6.49135e16 0.0285441
\(668\) 2.62000e17 0.114092
\(669\) −5.45646e17 −0.235310
\(670\) 5.42932e17 0.231878
\(671\) 1.17800e18 0.498252
\(672\) −3.88339e17 −0.162671
\(673\) 2.84588e18 1.18064 0.590321 0.807168i \(-0.299001\pi\)
0.590321 + 0.807168i \(0.299001\pi\)
\(674\) 3.43436e17 0.141109
\(675\) 3.31966e17 0.135089
\(676\) 2.36826e17 0.0954499
\(677\) 9.37510e17 0.374239 0.187120 0.982337i \(-0.440085\pi\)
0.187120 + 0.982337i \(0.440085\pi\)
\(678\) −6.32965e17 −0.250257
\(679\) −2.45357e18 −0.960826
\(680\) 2.63358e18 1.02150
\(681\) 1.26343e18 0.485396
\(682\) 2.60856e18 0.992663
\(683\) 1.83395e18 0.691279 0.345639 0.938367i \(-0.387662\pi\)
0.345639 + 0.938367i \(0.387662\pi\)
\(684\) 1.07322e17 0.0400704
\(685\) −2.29837e18 −0.850023
\(686\) −2.54748e18 −0.933263
\(687\) 1.33677e18 0.485108
\(688\) −2.70045e18 −0.970758
\(689\) 5.00000e17 0.178051
\(690\) 4.65791e17 0.164313
\(691\) −5.18222e18 −1.81096 −0.905479 0.424391i \(-0.860488\pi\)
−0.905479 + 0.424391i \(0.860488\pi\)
\(692\) −8.81651e17 −0.305216
\(693\) −9.28394e17 −0.318395
\(694\) −1.48474e18 −0.504446
\(695\) −3.08845e18 −1.03954
\(696\) 9.06653e16 0.0302330
\(697\) −7.61889e18 −2.51697
\(698\) −1.10801e18 −0.362646
\(699\) 1.32793e18 0.430598
\(700\) −3.13346e17 −0.100667
\(701\) −2.74774e18 −0.874598 −0.437299 0.899316i \(-0.644065\pi\)
−0.437299 + 0.899316i \(0.644065\pi\)
\(702\) 4.00041e17 0.126157
\(703\) −2.25777e18 −0.705456
\(704\) 5.00178e18 1.54847
\(705\) −1.25848e18 −0.386028
\(706\) −8.91877e17 −0.271066
\(707\) −5.63811e17 −0.169788
\(708\) −5.26413e16 −0.0157076
\(709\) 1.84861e18 0.546569 0.273284 0.961933i \(-0.411890\pi\)
0.273284 + 0.961933i \(0.411890\pi\)
\(710\) 1.27701e18 0.374123
\(711\) 7.27903e17 0.211311
\(712\) 1.36361e18 0.392256
\(713\) 1.64884e18 0.469997
\(714\) 2.17088e18 0.613194
\(715\) −2.00096e18 −0.560080
\(716\) −1.08186e18 −0.300078
\(717\) −3.15251e18 −0.866528
\(718\) −6.34291e18 −1.72775
\(719\) −1.08067e18 −0.291713 −0.145856 0.989306i \(-0.546594\pi\)
−0.145856 + 0.989306i \(0.546594\pi\)
\(720\) 5.08412e17 0.136005
\(721\) 8.30810e17 0.220253
\(722\) 2.26505e18 0.595095
\(723\) −2.03736e18 −0.530480
\(724\) 7.94222e16 0.0204947
\(725\) 1.33668e17 0.0341846
\(726\) 1.89891e18 0.481300
\(727\) 5.54684e18 1.39339 0.696694 0.717368i \(-0.254654\pi\)
0.696694 + 0.717368i \(0.254654\pi\)
\(728\) −2.18451e18 −0.543877
\(729\) 1.50095e17 0.0370370
\(730\) 1.90559e17 0.0466048
\(731\) −9.32447e18 −2.26027
\(732\) 1.79766e17 0.0431903
\(733\) 1.45102e18 0.345539 0.172770 0.984962i \(-0.444728\pi\)
0.172770 + 0.984962i \(0.444728\pi\)
\(734\) 4.80820e18 1.13490
\(735\) −7.12775e17 −0.166757
\(736\) 1.03771e18 0.240642
\(737\) 2.89169e18 0.664681
\(738\) −1.88210e18 −0.428822
\(739\) 1.54915e18 0.349868 0.174934 0.984580i \(-0.444029\pi\)
0.174934 + 0.984580i \(0.444029\pi\)
\(740\) 6.24995e17 0.139917
\(741\) 1.10308e18 0.244786
\(742\) 6.70276e17 0.147444
\(743\) 1.60773e18 0.350579 0.175289 0.984517i \(-0.443914\pi\)
0.175289 + 0.984517i \(0.443914\pi\)
\(744\) 2.30295e18 0.497806
\(745\) 1.78818e16 0.00383173
\(746\) 2.30893e18 0.490464
\(747\) −1.29047e18 −0.271746
\(748\) 2.42456e18 0.506141
\(749\) 3.53637e18 0.731857
\(750\) 2.32556e18 0.477122
\(751\) 1.29902e17 0.0264214 0.0132107 0.999913i \(-0.495795\pi\)
0.0132107 + 0.999913i \(0.495795\pi\)
\(752\) 4.53910e18 0.915280
\(753\) −1.04856e18 −0.209617
\(754\) 1.61079e17 0.0319245
\(755\) 2.38123e18 0.467893
\(756\) −1.41676e17 −0.0275997
\(757\) −3.65956e18 −0.706815 −0.353407 0.935470i \(-0.614977\pi\)
−0.353407 + 0.935470i \(0.614977\pi\)
\(758\) −4.42728e18 −0.847787
\(759\) 2.48083e18 0.471006
\(760\) 1.79390e18 0.337684
\(761\) −3.82973e18 −0.714772 −0.357386 0.933957i \(-0.616332\pi\)
−0.357386 + 0.933957i \(0.616332\pi\)
\(762\) 1.36109e18 0.251873
\(763\) 2.94067e18 0.539556
\(764\) −1.03876e18 −0.188977
\(765\) 1.75551e18 0.316668
\(766\) 2.22139e18 0.397318
\(767\) −5.41058e17 −0.0959564
\(768\) 1.96214e18 0.345050
\(769\) −3.84684e18 −0.670785 −0.335392 0.942079i \(-0.608869\pi\)
−0.335392 + 0.942079i \(0.608869\pi\)
\(770\) −2.68239e18 −0.463802
\(771\) 3.63101e18 0.622549
\(772\) 5.00020e17 0.0850110
\(773\) 3.24278e18 0.546702 0.273351 0.961914i \(-0.411868\pi\)
0.273351 + 0.961914i \(0.411868\pi\)
\(774\) −2.30343e18 −0.385087
\(775\) 3.39524e18 0.562871
\(776\) 9.15735e18 1.50546
\(777\) 2.98048e18 0.485904
\(778\) 2.70471e16 0.00437273
\(779\) −5.18973e18 −0.832053
\(780\) −3.05353e17 −0.0485498
\(781\) 6.80143e18 1.07243
\(782\) −5.80098e18 −0.907105
\(783\) 6.04364e16 0.00937233
\(784\) 2.57084e18 0.395385
\(785\) 4.09313e18 0.624314
\(786\) −6.55437e17 −0.0991481
\(787\) 1.66449e18 0.249716 0.124858 0.992175i \(-0.460152\pi\)
0.124858 + 0.992175i \(0.460152\pi\)
\(788\) −1.40478e18 −0.209021
\(789\) 4.45765e17 0.0657818
\(790\) 2.10312e18 0.307814
\(791\) 2.30403e18 0.334458
\(792\) 3.46501e18 0.498874
\(793\) 1.84767e18 0.263845
\(794\) 8.04493e18 1.13943
\(795\) 5.42027e17 0.0761439
\(796\) 1.49870e18 0.208823
\(797\) −7.59643e18 −1.04986 −0.524929 0.851146i \(-0.675908\pi\)
−0.524929 + 0.851146i \(0.675908\pi\)
\(798\) 1.47873e18 0.202708
\(799\) 1.56732e19 2.13110
\(800\) 2.13683e18 0.288193
\(801\) 9.08966e17 0.121601
\(802\) −1.10135e19 −1.46147
\(803\) 1.01493e18 0.133593
\(804\) 4.41281e17 0.0576170
\(805\) −1.69551e18 −0.219597
\(806\) 4.09148e18 0.525657
\(807\) 8.04121e18 1.02481
\(808\) 2.10429e18 0.266031
\(809\) −8.74663e17 −0.109692 −0.0548460 0.998495i \(-0.517467\pi\)
−0.0548460 + 0.998495i \(0.517467\pi\)
\(810\) 4.33666e17 0.0539514
\(811\) −1.26322e19 −1.55899 −0.779495 0.626409i \(-0.784524\pi\)
−0.779495 + 0.626409i \(0.784524\pi\)
\(812\) −5.70465e16 −0.00698417
\(813\) 3.43869e18 0.417642
\(814\) −1.26001e19 −1.51816
\(815\) −4.67490e18 −0.558789
\(816\) −6.33179e18 −0.750828
\(817\) −6.35151e18 −0.747194
\(818\) −5.50136e18 −0.642057
\(819\) −1.45617e18 −0.168604
\(820\) 1.43662e18 0.165026
\(821\) 8.64806e18 0.985572 0.492786 0.870151i \(-0.335979\pi\)
0.492786 + 0.870151i \(0.335979\pi\)
\(822\) 7.07100e18 0.799492
\(823\) −1.67852e19 −1.88291 −0.941453 0.337144i \(-0.890539\pi\)
−0.941453 + 0.337144i \(0.890539\pi\)
\(824\) −3.10080e18 −0.345102
\(825\) 5.10846e18 0.564079
\(826\) −7.25316e17 −0.0794616
\(827\) −3.84411e18 −0.417840 −0.208920 0.977933i \(-0.566995\pi\)
−0.208920 + 0.977933i \(0.566995\pi\)
\(828\) 3.78583e17 0.0408285
\(829\) 2.24354e17 0.0240065 0.0120033 0.999928i \(-0.496179\pi\)
0.0120033 + 0.999928i \(0.496179\pi\)
\(830\) −3.72852e18 −0.395849
\(831\) 5.61786e18 0.591786
\(832\) 7.84521e18 0.819980
\(833\) 8.87693e18 0.920599
\(834\) 9.50172e18 0.977739
\(835\) 2.91924e18 0.298062
\(836\) 1.65152e18 0.167319
\(837\) 1.53512e18 0.154321
\(838\) 7.20002e18 0.718203
\(839\) 1.12129e19 1.10985 0.554927 0.831899i \(-0.312746\pi\)
0.554927 + 0.831899i \(0.312746\pi\)
\(840\) −2.36813e18 −0.232590
\(841\) −1.02363e19 −0.997628
\(842\) 5.89931e18 0.570522
\(843\) −8.02871e17 −0.0770489
\(844\) 5.15875e17 0.0491269
\(845\) 2.63874e18 0.249361
\(846\) 3.87177e18 0.363080
\(847\) −6.91214e18 −0.643236
\(848\) −1.95499e18 −0.180539
\(849\) −7.35584e18 −0.674112
\(850\) −1.19452e19 −1.08635
\(851\) −7.96438e18 −0.718803
\(852\) 1.03792e18 0.0929621
\(853\) 8.41030e18 0.747554 0.373777 0.927519i \(-0.378063\pi\)
0.373777 + 0.927519i \(0.378063\pi\)
\(854\) 2.47690e18 0.218491
\(855\) 1.19580e18 0.104683
\(856\) −1.31987e19 −1.14670
\(857\) 1.58581e19 1.36734 0.683668 0.729793i \(-0.260384\pi\)
0.683668 + 0.729793i \(0.260384\pi\)
\(858\) 6.15603e18 0.526785
\(859\) 1.82988e19 1.55406 0.777029 0.629465i \(-0.216726\pi\)
0.777029 + 0.629465i \(0.216726\pi\)
\(860\) 1.75822e18 0.148195
\(861\) 6.85096e18 0.573101
\(862\) 1.09724e19 0.910975
\(863\) 2.15593e18 0.177650 0.0888250 0.996047i \(-0.471689\pi\)
0.0888250 + 0.996047i \(0.471689\pi\)
\(864\) 9.66141e17 0.0790135
\(865\) −9.82347e18 −0.797371
\(866\) −1.16133e19 −0.935600
\(867\) −1.46428e19 −1.17085
\(868\) −1.44901e18 −0.114999
\(869\) 1.12014e19 0.882352
\(870\) 1.74618e17 0.0136526
\(871\) 4.53557e18 0.351977
\(872\) −1.09753e19 −0.845397
\(873\) 6.10418e18 0.466697
\(874\) −3.95143e18 −0.299868
\(875\) −8.46518e18 −0.637652
\(876\) 1.54881e17 0.0115804
\(877\) −1.47003e19 −1.09101 −0.545505 0.838108i \(-0.683662\pi\)
−0.545505 + 0.838108i \(0.683662\pi\)
\(878\) 1.89779e19 1.39808
\(879\) −2.99096e17 −0.0218717
\(880\) 7.82371e18 0.567905
\(881\) 2.66615e19 1.92106 0.960531 0.278174i \(-0.0897292\pi\)
0.960531 + 0.278174i \(0.0897292\pi\)
\(882\) 2.19288e18 0.156844
\(883\) 1.91984e19 1.36308 0.681538 0.731783i \(-0.261312\pi\)
0.681538 + 0.731783i \(0.261312\pi\)
\(884\) 3.80288e18 0.268023
\(885\) −5.86537e17 −0.0410359
\(886\) 2.05857e19 1.42971
\(887\) −2.08261e19 −1.43583 −0.717916 0.696130i \(-0.754904\pi\)
−0.717916 + 0.696130i \(0.754904\pi\)
\(888\) −1.11239e19 −0.761332
\(889\) −4.95446e18 −0.336616
\(890\) 2.62626e18 0.177134
\(891\) 2.30973e18 0.154652
\(892\) −1.28136e18 −0.0851724
\(893\) 1.06761e19 0.704492
\(894\) −5.50139e16 −0.00360395
\(895\) −1.20542e19 −0.783949
\(896\) 6.15303e18 0.397271
\(897\) 3.89115e18 0.249418
\(898\) −1.81582e18 −0.115552
\(899\) 6.18123e17 0.0390514
\(900\) 7.79567e17 0.0488964
\(901\) −6.75043e18 −0.420359
\(902\) −2.89627e19 −1.79059
\(903\) 8.38463e18 0.514652
\(904\) −8.59924e18 −0.524041
\(905\) 8.84933e17 0.0535420
\(906\) −7.32594e18 −0.440078
\(907\) 7.30186e18 0.435498 0.217749 0.976005i \(-0.430129\pi\)
0.217749 + 0.976005i \(0.430129\pi\)
\(908\) 2.96696e18 0.175693
\(909\) 1.40269e18 0.0824703
\(910\) −4.20729e18 −0.245603
\(911\) 1.45485e19 0.843235 0.421618 0.906774i \(-0.361462\pi\)
0.421618 + 0.906774i \(0.361462\pi\)
\(912\) −4.31300e18 −0.248206
\(913\) −1.98583e19 −1.13471
\(914\) 7.39086e18 0.419319
\(915\) 2.00298e18 0.112834
\(916\) 3.13918e18 0.175588
\(917\) 2.38583e18 0.132507
\(918\) −5.40089e18 −0.297844
\(919\) 3.07202e19 1.68218 0.841091 0.540893i \(-0.181914\pi\)
0.841091 + 0.540893i \(0.181914\pi\)
\(920\) 6.32807e18 0.344073
\(921\) 7.21134e18 0.389339
\(922\) −9.77357e18 −0.523965
\(923\) 1.06679e19 0.567897
\(924\) −2.18018e18 −0.115246
\(925\) −1.64000e19 −0.860842
\(926\) 1.46930e19 0.765841
\(927\) −2.06696e18 −0.106983
\(928\) 3.89022e17 0.0199946
\(929\) 3.14728e19 1.60633 0.803163 0.595759i \(-0.203149\pi\)
0.803163 + 0.595759i \(0.203149\pi\)
\(930\) 4.43539e18 0.224798
\(931\) 6.04666e18 0.304328
\(932\) 3.11841e18 0.155858
\(933\) −1.95758e19 −0.971604
\(934\) −6.12290e18 −0.301789
\(935\) 2.70147e19 1.32229
\(936\) 5.43481e18 0.264175
\(937\) −3.26697e19 −1.57702 −0.788511 0.615021i \(-0.789147\pi\)
−0.788511 + 0.615021i \(0.789147\pi\)
\(938\) 6.08017e18 0.291472
\(939\) 2.12423e18 0.101129
\(940\) −2.95534e18 −0.139726
\(941\) −8.38611e18 −0.393757 −0.196878 0.980428i \(-0.563080\pi\)
−0.196878 + 0.980428i \(0.563080\pi\)
\(942\) −1.25927e19 −0.587201
\(943\) −1.83070e19 −0.847795
\(944\) 2.11552e18 0.0972970
\(945\) −1.57857e18 −0.0721036
\(946\) −3.54464e19 −1.60798
\(947\) 6.26802e18 0.282394 0.141197 0.989982i \(-0.454905\pi\)
0.141197 + 0.989982i \(0.454905\pi\)
\(948\) 1.70936e18 0.0764855
\(949\) 1.59190e18 0.0707434
\(950\) −8.13667e18 −0.359123
\(951\) 9.48230e18 0.415662
\(952\) 2.94928e19 1.28403
\(953\) 3.46589e19 1.49869 0.749343 0.662183i \(-0.230370\pi\)
0.749343 + 0.662183i \(0.230370\pi\)
\(954\) −1.66757e18 −0.0716174
\(955\) −1.15740e19 −0.493699
\(956\) −7.40315e18 −0.313646
\(957\) 9.30027e17 0.0391352
\(958\) −4.89938e18 −0.204769
\(959\) −2.57389e19 −1.06849
\(960\) 8.50464e18 0.350666
\(961\) −8.71690e18 −0.356993
\(962\) −1.97631e19 −0.803928
\(963\) −8.79808e18 −0.355481
\(964\) −4.78440e18 −0.192011
\(965\) 5.57129e18 0.222090
\(966\) 5.21629e18 0.206543
\(967\) 4.76538e18 0.187424 0.0937121 0.995599i \(-0.470127\pi\)
0.0937121 + 0.995599i \(0.470127\pi\)
\(968\) 2.57979e19 1.00785
\(969\) −1.48925e19 −0.577913
\(970\) 1.76367e19 0.679832
\(971\) −4.11037e19 −1.57382 −0.786912 0.617066i \(-0.788321\pi\)
−0.786912 + 0.617066i \(0.788321\pi\)
\(972\) 3.52472e17 0.0134058
\(973\) −3.45868e19 −1.30670
\(974\) 1.44875e19 0.543703
\(975\) 8.01254e18 0.298704
\(976\) −7.22435e18 −0.267532
\(977\) 1.21988e19 0.448747 0.224373 0.974503i \(-0.427966\pi\)
0.224373 + 0.974503i \(0.427966\pi\)
\(978\) 1.43825e19 0.525571
\(979\) 1.39876e19 0.507758
\(980\) −1.67383e18 −0.0603591
\(981\) −7.31603e18 −0.262076
\(982\) 2.47883e19 0.882110
\(983\) 4.85533e19 1.71641 0.858204 0.513309i \(-0.171580\pi\)
0.858204 + 0.513309i \(0.171580\pi\)
\(984\) −2.55696e19 −0.897956
\(985\) −1.56523e19 −0.546063
\(986\) −2.17470e18 −0.0753702
\(987\) −1.40935e19 −0.485240
\(988\) 2.59039e18 0.0886023
\(989\) −2.24052e19 −0.761330
\(990\) 6.67348e18 0.225280
\(991\) −1.09206e19 −0.366242 −0.183121 0.983090i \(-0.558620\pi\)
−0.183121 + 0.983090i \(0.558620\pi\)
\(992\) 9.88136e18 0.329224
\(993\) −6.24060e18 −0.206565
\(994\) 1.43009e19 0.470275
\(995\) 1.66987e19 0.545546
\(996\) −3.03044e18 −0.0983604
\(997\) −1.56931e19 −0.506046 −0.253023 0.967460i \(-0.581425\pi\)
−0.253023 + 0.967460i \(0.581425\pi\)
\(998\) 2.82479e19 0.904978
\(999\) −7.41508e18 −0.236015
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 177.14.a.b.1.9 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.9 31 1.1 even 1 trivial