Properties

Label 177.14.a.b.1.12
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 1.12
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-63.8588 q^{2} -729.000 q^{3} -4114.05 q^{4} +18414.6 q^{5} +46553.1 q^{6} +120263. q^{7} +785850. q^{8} +531441. q^{9} +O(q^{10})\) \(q-63.8588 q^{2} -729.000 q^{3} -4114.05 q^{4} +18414.6 q^{5} +46553.1 q^{6} +120263. q^{7} +785850. q^{8} +531441. q^{9} -1.17593e6 q^{10} -3.91572e6 q^{11} +2.99914e6 q^{12} -9.55466e6 q^{13} -7.67982e6 q^{14} -1.34242e7 q^{15} -1.64811e7 q^{16} +4.69357e6 q^{17} -3.39372e7 q^{18} +3.61757e8 q^{19} -7.57586e7 q^{20} -8.76714e7 q^{21} +2.50053e8 q^{22} +1.17374e9 q^{23} -5.72885e8 q^{24} -8.81606e8 q^{25} +6.10149e8 q^{26} -3.87420e8 q^{27} -4.94766e8 q^{28} -4.59818e9 q^{29} +8.57256e8 q^{30} -5.94328e9 q^{31} -5.38522e9 q^{32} +2.85456e9 q^{33} -2.99726e8 q^{34} +2.21459e9 q^{35} -2.18638e9 q^{36} -1.48917e10 q^{37} -2.31014e10 q^{38} +6.96535e9 q^{39} +1.44711e10 q^{40} -1.83734e10 q^{41} +5.59859e9 q^{42} +1.62479e10 q^{43} +1.61095e10 q^{44} +9.78627e9 q^{45} -7.49535e10 q^{46} +1.36551e9 q^{47} +1.20147e10 q^{48} -8.24259e10 q^{49} +5.62983e10 q^{50} -3.42161e9 q^{51} +3.93084e10 q^{52} +1.60234e11 q^{53} +2.47402e10 q^{54} -7.21065e10 q^{55} +9.45083e10 q^{56} -2.63721e11 q^{57} +2.93635e11 q^{58} -4.21805e10 q^{59} +5.52280e10 q^{60} +2.01713e11 q^{61} +3.79531e11 q^{62} +6.39124e10 q^{63} +4.78907e11 q^{64} -1.75945e11 q^{65} -1.82289e11 q^{66} +5.67639e11 q^{67} -1.93096e10 q^{68} -8.55654e11 q^{69} -1.41421e11 q^{70} -2.83595e11 q^{71} +4.17633e11 q^{72} +2.34947e12 q^{73} +9.50965e11 q^{74} +6.42690e11 q^{75} -1.48829e12 q^{76} -4.70915e11 q^{77} -4.44799e11 q^{78} +1.78071e12 q^{79} -3.03493e11 q^{80} +2.82430e11 q^{81} +1.17330e12 q^{82} +1.42768e12 q^{83} +3.60685e11 q^{84} +8.64303e10 q^{85} -1.03757e12 q^{86} +3.35208e12 q^{87} -3.07717e12 q^{88} -5.50543e12 q^{89} -6.24940e11 q^{90} -1.14907e12 q^{91} -4.82882e12 q^{92} +4.33265e12 q^{93} -8.72001e10 q^{94} +6.66162e12 q^{95} +3.92582e12 q^{96} +1.04921e13 q^{97} +5.26362e12 q^{98} -2.08097e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −63.8588 −0.705547 −0.352773 0.935709i \(-0.614761\pi\)
−0.352773 + 0.935709i \(0.614761\pi\)
\(3\) −729.000 −0.577350
\(4\) −4114.05 −0.502204
\(5\) 18414.6 0.527057 0.263528 0.964652i \(-0.415114\pi\)
0.263528 + 0.964652i \(0.415114\pi\)
\(6\) 46553.1 0.407348
\(7\) 120263. 0.386361 0.193180 0.981163i \(-0.438120\pi\)
0.193180 + 0.981163i \(0.438120\pi\)
\(8\) 785850. 1.05988
\(9\) 531441. 0.333333
\(10\) −1.17593e6 −0.371863
\(11\) −3.91572e6 −0.666437 −0.333219 0.942850i \(-0.608135\pi\)
−0.333219 + 0.942850i \(0.608135\pi\)
\(12\) 2.99914e6 0.289947
\(13\) −9.55466e6 −0.549014 −0.274507 0.961585i \(-0.588515\pi\)
−0.274507 + 0.961585i \(0.588515\pi\)
\(14\) −7.67982e6 −0.272596
\(15\) −1.34242e7 −0.304296
\(16\) −1.64811e7 −0.245588
\(17\) 4.69357e6 0.0471613 0.0235806 0.999722i \(-0.492493\pi\)
0.0235806 + 0.999722i \(0.492493\pi\)
\(18\) −3.39372e7 −0.235182
\(19\) 3.61757e8 1.76408 0.882041 0.471172i \(-0.156169\pi\)
0.882041 + 0.471172i \(0.156169\pi\)
\(20\) −7.57586e7 −0.264690
\(21\) −8.76714e7 −0.223066
\(22\) 2.50053e8 0.470203
\(23\) 1.17374e9 1.65326 0.826628 0.562749i \(-0.190256\pi\)
0.826628 + 0.562749i \(0.190256\pi\)
\(24\) −5.72885e8 −0.611919
\(25\) −8.81606e8 −0.722211
\(26\) 6.10149e8 0.387355
\(27\) −3.87420e8 −0.192450
\(28\) −4.94766e8 −0.194032
\(29\) −4.59818e9 −1.43549 −0.717744 0.696307i \(-0.754825\pi\)
−0.717744 + 0.696307i \(0.754825\pi\)
\(30\) 8.57256e8 0.214695
\(31\) −5.94328e9 −1.20275 −0.601375 0.798967i \(-0.705380\pi\)
−0.601375 + 0.798967i \(0.705380\pi\)
\(32\) −5.38522e9 −0.886601
\(33\) 2.85456e9 0.384768
\(34\) −2.99726e8 −0.0332745
\(35\) 2.21459e9 0.203634
\(36\) −2.18638e9 −0.167401
\(37\) −1.48917e10 −0.954185 −0.477093 0.878853i \(-0.658309\pi\)
−0.477093 + 0.878853i \(0.658309\pi\)
\(38\) −2.31014e10 −1.24464
\(39\) 6.96535e9 0.316973
\(40\) 1.44711e10 0.558614
\(41\) −1.83734e10 −0.604080 −0.302040 0.953295i \(-0.597668\pi\)
−0.302040 + 0.953295i \(0.597668\pi\)
\(42\) 5.59859e9 0.157383
\(43\) 1.62479e10 0.391970 0.195985 0.980607i \(-0.437210\pi\)
0.195985 + 0.980607i \(0.437210\pi\)
\(44\) 1.61095e10 0.334687
\(45\) 9.78627e9 0.175686
\(46\) −7.49535e10 −1.16645
\(47\) 1.36551e9 0.0184782 0.00923911 0.999957i \(-0.497059\pi\)
0.00923911 + 0.999957i \(0.497059\pi\)
\(48\) 1.20147e10 0.141790
\(49\) −8.24259e10 −0.850725
\(50\) 5.62983e10 0.509554
\(51\) −3.42161e9 −0.0272286
\(52\) 3.93084e10 0.275717
\(53\) 1.60234e11 0.993026 0.496513 0.868029i \(-0.334614\pi\)
0.496513 + 0.868029i \(0.334614\pi\)
\(54\) 2.47402e10 0.135783
\(55\) −7.21065e10 −0.351250
\(56\) 9.45083e10 0.409494
\(57\) −2.63721e11 −1.01849
\(58\) 2.93635e11 1.01280
\(59\) −4.21805e10 −0.130189
\(60\) 5.52280e10 0.152819
\(61\) 2.01713e11 0.501291 0.250646 0.968079i \(-0.419357\pi\)
0.250646 + 0.968079i \(0.419357\pi\)
\(62\) 3.79531e11 0.848596
\(63\) 6.39124e10 0.128787
\(64\) 4.78907e11 0.871127
\(65\) −1.75945e11 −0.289362
\(66\) −1.82289e11 −0.271472
\(67\) 5.67639e11 0.766631 0.383315 0.923618i \(-0.374782\pi\)
0.383315 + 0.923618i \(0.374782\pi\)
\(68\) −1.93096e10 −0.0236846
\(69\) −8.55654e11 −0.954507
\(70\) −1.41421e11 −0.143673
\(71\) −2.83595e11 −0.262736 −0.131368 0.991334i \(-0.541937\pi\)
−0.131368 + 0.991334i \(0.541937\pi\)
\(72\) 4.17633e11 0.353292
\(73\) 2.34947e12 1.81707 0.908534 0.417812i \(-0.137203\pi\)
0.908534 + 0.417812i \(0.137203\pi\)
\(74\) 9.50965e11 0.673222
\(75\) 6.42690e11 0.416969
\(76\) −1.48829e12 −0.885929
\(77\) −4.70915e11 −0.257485
\(78\) −4.44799e11 −0.223640
\(79\) 1.78071e12 0.824170 0.412085 0.911145i \(-0.364801\pi\)
0.412085 + 0.911145i \(0.364801\pi\)
\(80\) −3.03493e11 −0.129439
\(81\) 2.82430e11 0.111111
\(82\) 1.17330e12 0.426207
\(83\) 1.42768e12 0.479319 0.239659 0.970857i \(-0.422964\pi\)
0.239659 + 0.970857i \(0.422964\pi\)
\(84\) 3.60685e11 0.112024
\(85\) 8.64303e10 0.0248567
\(86\) −1.03757e12 −0.276553
\(87\) 3.35208e12 0.828779
\(88\) −3.07717e12 −0.706340
\(89\) −5.50543e12 −1.17424 −0.587119 0.809500i \(-0.699738\pi\)
−0.587119 + 0.809500i \(0.699738\pi\)
\(90\) −6.24940e11 −0.123954
\(91\) −1.14907e12 −0.212118
\(92\) −4.82882e12 −0.830271
\(93\) 4.33265e12 0.694408
\(94\) −8.72001e10 −0.0130372
\(95\) 6.66162e12 0.929771
\(96\) 3.92582e12 0.511880
\(97\) 1.04921e13 1.27893 0.639465 0.768820i \(-0.279156\pi\)
0.639465 + 0.768820i \(0.279156\pi\)
\(98\) 5.26362e12 0.600227
\(99\) −2.08097e12 −0.222146
\(100\) 3.62697e12 0.362697
\(101\) 1.03017e13 0.965648 0.482824 0.875717i \(-0.339611\pi\)
0.482824 + 0.875717i \(0.339611\pi\)
\(102\) 2.18500e11 0.0192110
\(103\) 1.10824e13 0.914518 0.457259 0.889334i \(-0.348831\pi\)
0.457259 + 0.889334i \(0.348831\pi\)
\(104\) −7.50853e12 −0.581886
\(105\) −1.61443e12 −0.117568
\(106\) −1.02323e13 −0.700626
\(107\) −8.17553e11 −0.0526649 −0.0263325 0.999653i \(-0.508383\pi\)
−0.0263325 + 0.999653i \(0.508383\pi\)
\(108\) 1.59387e12 0.0966491
\(109\) −1.99066e13 −1.13691 −0.568455 0.822715i \(-0.692458\pi\)
−0.568455 + 0.822715i \(0.692458\pi\)
\(110\) 4.60463e12 0.247824
\(111\) 1.08560e13 0.550899
\(112\) −1.98206e12 −0.0948855
\(113\) 1.70793e12 0.0771723 0.0385861 0.999255i \(-0.487715\pi\)
0.0385861 + 0.999255i \(0.487715\pi\)
\(114\) 1.68409e13 0.718595
\(115\) 2.16139e13 0.871359
\(116\) 1.89172e13 0.720907
\(117\) −5.07774e12 −0.183005
\(118\) 2.69360e12 0.0918544
\(119\) 5.64461e11 0.0182213
\(120\) −1.05494e13 −0.322516
\(121\) −1.91898e13 −0.555861
\(122\) −1.28812e13 −0.353684
\(123\) 1.33942e13 0.348766
\(124\) 2.44510e13 0.604025
\(125\) −3.87132e13 −0.907703
\(126\) −4.08137e12 −0.0908652
\(127\) −3.27440e13 −0.692479 −0.346240 0.938146i \(-0.612542\pi\)
−0.346240 + 0.938146i \(0.612542\pi\)
\(128\) 1.35333e13 0.271981
\(129\) −1.18447e13 −0.226304
\(130\) 1.12357e13 0.204158
\(131\) −4.51213e13 −0.780043 −0.390022 0.920806i \(-0.627532\pi\)
−0.390022 + 0.920806i \(0.627532\pi\)
\(132\) −1.17438e13 −0.193232
\(133\) 4.35058e13 0.681572
\(134\) −3.62488e13 −0.540894
\(135\) −7.13419e12 −0.101432
\(136\) 3.68844e12 0.0499851
\(137\) −1.29786e14 −1.67705 −0.838524 0.544865i \(-0.816581\pi\)
−0.838524 + 0.544865i \(0.816581\pi\)
\(138\) 5.46411e13 0.673450
\(139\) 8.14124e13 0.957402 0.478701 0.877978i \(-0.341108\pi\)
0.478701 + 0.877978i \(0.341108\pi\)
\(140\) −9.11093e12 −0.102266
\(141\) −9.95459e11 −0.0106684
\(142\) 1.81100e13 0.185372
\(143\) 3.74134e13 0.365884
\(144\) −8.75874e12 −0.0818626
\(145\) −8.46737e13 −0.756583
\(146\) −1.50034e14 −1.28203
\(147\) 6.00885e13 0.491166
\(148\) 6.12652e13 0.479195
\(149\) 8.63226e13 0.646270 0.323135 0.946353i \(-0.395263\pi\)
0.323135 + 0.946353i \(0.395263\pi\)
\(150\) −4.10414e13 −0.294191
\(151\) 2.12012e14 1.45550 0.727748 0.685845i \(-0.240567\pi\)
0.727748 + 0.685845i \(0.240567\pi\)
\(152\) 2.84287e14 1.86971
\(153\) 2.49436e12 0.0157204
\(154\) 3.00720e13 0.181668
\(155\) −1.09443e14 −0.633917
\(156\) −2.86558e13 −0.159185
\(157\) −1.66693e14 −0.888321 −0.444161 0.895947i \(-0.646498\pi\)
−0.444161 + 0.895947i \(0.646498\pi\)
\(158\) −1.13714e14 −0.581491
\(159\) −1.16810e14 −0.573324
\(160\) −9.91666e13 −0.467289
\(161\) 1.41157e14 0.638753
\(162\) −1.80356e13 −0.0783941
\(163\) −4.64988e13 −0.194188 −0.0970940 0.995275i \(-0.530955\pi\)
−0.0970940 + 0.995275i \(0.530955\pi\)
\(164\) 7.55891e13 0.303371
\(165\) 5.25656e13 0.202794
\(166\) −9.11702e13 −0.338182
\(167\) 3.31583e14 1.18287 0.591433 0.806354i \(-0.298562\pi\)
0.591433 + 0.806354i \(0.298562\pi\)
\(168\) −6.88965e13 −0.236422
\(169\) −2.11584e14 −0.698584
\(170\) −5.51933e12 −0.0175375
\(171\) 1.92253e14 0.588027
\(172\) −6.68448e13 −0.196849
\(173\) 6.09235e13 0.172777 0.0863883 0.996262i \(-0.472467\pi\)
0.0863883 + 0.996262i \(0.472467\pi\)
\(174\) −2.14060e14 −0.584743
\(175\) −1.06024e14 −0.279034
\(176\) 6.45355e13 0.163669
\(177\) 3.07496e13 0.0751646
\(178\) 3.51570e14 0.828481
\(179\) 2.22302e14 0.505125 0.252563 0.967581i \(-0.418727\pi\)
0.252563 + 0.967581i \(0.418727\pi\)
\(180\) −4.02612e13 −0.0882299
\(181\) −3.90444e14 −0.825368 −0.412684 0.910874i \(-0.635409\pi\)
−0.412684 + 0.910874i \(0.635409\pi\)
\(182\) 7.33781e13 0.149659
\(183\) −1.47049e14 −0.289421
\(184\) 9.22381e14 1.75224
\(185\) −2.74224e14 −0.502910
\(186\) −2.76678e14 −0.489937
\(187\) −1.83787e13 −0.0314300
\(188\) −5.61779e12 −0.00927983
\(189\) −4.65922e13 −0.0743552
\(190\) −4.25403e14 −0.655997
\(191\) −2.60963e14 −0.388922 −0.194461 0.980910i \(-0.562296\pi\)
−0.194461 + 0.980910i \(0.562296\pi\)
\(192\) −3.49123e14 −0.502945
\(193\) 1.06191e14 0.147899 0.0739496 0.997262i \(-0.476440\pi\)
0.0739496 + 0.997262i \(0.476440\pi\)
\(194\) −6.70014e14 −0.902345
\(195\) 1.28264e14 0.167063
\(196\) 3.39105e14 0.427237
\(197\) −7.48053e14 −0.911804 −0.455902 0.890030i \(-0.650683\pi\)
−0.455902 + 0.890030i \(0.650683\pi\)
\(198\) 1.32889e14 0.156734
\(199\) −9.12192e14 −1.04122 −0.520608 0.853796i \(-0.674295\pi\)
−0.520608 + 0.853796i \(0.674295\pi\)
\(200\) −6.92810e14 −0.765454
\(201\) −4.13809e14 −0.442614
\(202\) −6.57853e14 −0.681310
\(203\) −5.52989e14 −0.554616
\(204\) 1.40767e13 0.0136743
\(205\) −3.38339e14 −0.318384
\(206\) −7.07710e14 −0.645235
\(207\) 6.23772e14 0.551085
\(208\) 1.57472e14 0.134831
\(209\) −1.41654e15 −1.17565
\(210\) 1.03096e14 0.0829498
\(211\) 1.88689e15 1.47201 0.736005 0.676976i \(-0.236710\pi\)
0.736005 + 0.676976i \(0.236710\pi\)
\(212\) −6.59209e14 −0.498701
\(213\) 2.06741e14 0.151691
\(214\) 5.22080e13 0.0371576
\(215\) 2.99199e14 0.206590
\(216\) −3.04454e14 −0.203973
\(217\) −7.14754e14 −0.464695
\(218\) 1.27121e15 0.802143
\(219\) −1.71276e15 −1.04908
\(220\) 2.96650e14 0.176399
\(221\) −4.48455e13 −0.0258922
\(222\) −6.93254e14 −0.388685
\(223\) 6.28777e14 0.342385 0.171193 0.985238i \(-0.445238\pi\)
0.171193 + 0.985238i \(0.445238\pi\)
\(224\) −6.47640e14 −0.342548
\(225\) −4.68521e14 −0.240737
\(226\) −1.09067e14 −0.0544487
\(227\) 1.17064e15 0.567879 0.283939 0.958842i \(-0.408359\pi\)
0.283939 + 0.958842i \(0.408359\pi\)
\(228\) 1.08496e15 0.511491
\(229\) −2.26275e14 −0.103683 −0.0518414 0.998655i \(-0.516509\pi\)
−0.0518414 + 0.998655i \(0.516509\pi\)
\(230\) −1.38024e15 −0.614785
\(231\) 3.43297e14 0.148659
\(232\) −3.61348e15 −1.52144
\(233\) −2.85646e15 −1.16954 −0.584770 0.811199i \(-0.698815\pi\)
−0.584770 + 0.811199i \(0.698815\pi\)
\(234\) 3.24258e14 0.129118
\(235\) 2.51454e13 0.00973906
\(236\) 1.73533e14 0.0653813
\(237\) −1.29814e15 −0.475835
\(238\) −3.60458e13 −0.0128560
\(239\) 1.01593e15 0.352596 0.176298 0.984337i \(-0.443588\pi\)
0.176298 + 0.984337i \(0.443588\pi\)
\(240\) 2.21247e14 0.0747315
\(241\) −8.99146e14 −0.295610 −0.147805 0.989016i \(-0.547221\pi\)
−0.147805 + 0.989016i \(0.547221\pi\)
\(242\) 1.22544e15 0.392186
\(243\) −2.05891e14 −0.0641500
\(244\) −8.29858e14 −0.251750
\(245\) −1.51784e15 −0.448380
\(246\) −8.55338e14 −0.246071
\(247\) −3.45647e15 −0.968506
\(248\) −4.67053e15 −1.27476
\(249\) −1.04078e15 −0.276735
\(250\) 2.47218e15 0.640427
\(251\) −6.61525e15 −1.66981 −0.834905 0.550393i \(-0.814478\pi\)
−0.834905 + 0.550393i \(0.814478\pi\)
\(252\) −2.62939e14 −0.0646773
\(253\) −4.59603e15 −1.10179
\(254\) 2.09099e15 0.488577
\(255\) −6.30077e13 −0.0143510
\(256\) −4.78742e15 −1.06302
\(257\) 2.15487e15 0.466504 0.233252 0.972416i \(-0.425063\pi\)
0.233252 + 0.972416i \(0.425063\pi\)
\(258\) 7.56391e14 0.159668
\(259\) −1.79091e15 −0.368660
\(260\) 7.23848e14 0.145318
\(261\) −2.44366e15 −0.478496
\(262\) 2.88140e15 0.550357
\(263\) 6.52155e15 1.21517 0.607587 0.794253i \(-0.292137\pi\)
0.607587 + 0.794253i \(0.292137\pi\)
\(264\) 2.24326e15 0.407806
\(265\) 2.95064e15 0.523381
\(266\) −2.77823e15 −0.480881
\(267\) 4.01346e15 0.677947
\(268\) −2.33530e15 −0.385005
\(269\) −5.06945e15 −0.815776 −0.407888 0.913032i \(-0.633735\pi\)
−0.407888 + 0.913032i \(0.633735\pi\)
\(270\) 4.55581e14 0.0715651
\(271\) −1.22251e16 −1.87478 −0.937392 0.348275i \(-0.886767\pi\)
−0.937392 + 0.348275i \(0.886767\pi\)
\(272\) −7.73553e13 −0.0115822
\(273\) 8.37670e14 0.122466
\(274\) 8.28800e15 1.18324
\(275\) 3.45212e15 0.481309
\(276\) 3.52021e15 0.479357
\(277\) −2.00845e15 −0.267142 −0.133571 0.991039i \(-0.542644\pi\)
−0.133571 + 0.991039i \(0.542644\pi\)
\(278\) −5.19890e15 −0.675492
\(279\) −3.15850e15 −0.400917
\(280\) 1.74033e15 0.215827
\(281\) 3.49015e15 0.422915 0.211457 0.977387i \(-0.432179\pi\)
0.211457 + 0.977387i \(0.432179\pi\)
\(282\) 6.35688e13 0.00752706
\(283\) 1.96381e15 0.227242 0.113621 0.993524i \(-0.463755\pi\)
0.113621 + 0.993524i \(0.463755\pi\)
\(284\) 1.16673e15 0.131947
\(285\) −4.85632e15 −0.536804
\(286\) −2.38917e15 −0.258148
\(287\) −2.20963e15 −0.233393
\(288\) −2.86193e15 −0.295534
\(289\) −9.88255e15 −0.997776
\(290\) 5.40716e15 0.533805
\(291\) −7.64875e15 −0.738390
\(292\) −9.66584e15 −0.912538
\(293\) 1.34590e16 1.24272 0.621358 0.783526i \(-0.286581\pi\)
0.621358 + 0.783526i \(0.286581\pi\)
\(294\) −3.83718e15 −0.346541
\(295\) −7.76738e14 −0.0686169
\(296\) −1.17026e16 −1.01132
\(297\) 1.51703e15 0.128256
\(298\) −5.51246e15 −0.455974
\(299\) −1.12147e16 −0.907660
\(300\) −2.64406e15 −0.209403
\(301\) 1.95402e15 0.151442
\(302\) −1.35389e16 −1.02692
\(303\) −7.50992e15 −0.557517
\(304\) −5.96216e15 −0.433237
\(305\) 3.71446e15 0.264209
\(306\) −1.59287e14 −0.0110915
\(307\) −1.54157e16 −1.05090 −0.525452 0.850823i \(-0.676104\pi\)
−0.525452 + 0.850823i \(0.676104\pi\)
\(308\) 1.93737e15 0.129310
\(309\) −8.07908e15 −0.527997
\(310\) 6.98891e15 0.447258
\(311\) 2.06399e16 1.29349 0.646747 0.762705i \(-0.276129\pi\)
0.646747 + 0.762705i \(0.276129\pi\)
\(312\) 5.47372e15 0.335952
\(313\) 1.07125e16 0.643948 0.321974 0.946748i \(-0.395654\pi\)
0.321974 + 0.946748i \(0.395654\pi\)
\(314\) 1.06448e16 0.626752
\(315\) 1.17692e15 0.0678780
\(316\) −7.32593e15 −0.413901
\(317\) 7.10976e15 0.393523 0.196761 0.980451i \(-0.436958\pi\)
0.196761 + 0.980451i \(0.436958\pi\)
\(318\) 7.45937e15 0.404507
\(319\) 1.80052e16 0.956663
\(320\) 8.81888e15 0.459133
\(321\) 5.95996e14 0.0304061
\(322\) −9.01409e15 −0.450670
\(323\) 1.69793e15 0.0831964
\(324\) −1.16193e15 −0.0558004
\(325\) 8.42344e15 0.396504
\(326\) 2.96936e15 0.137009
\(327\) 1.45119e16 0.656395
\(328\) −1.44387e16 −0.640249
\(329\) 1.64220e14 0.00713926
\(330\) −3.35678e15 −0.143081
\(331\) −4.63238e16 −1.93607 −0.968037 0.250806i \(-0.919304\pi\)
−0.968037 + 0.250806i \(0.919304\pi\)
\(332\) −5.87356e15 −0.240716
\(333\) −7.91405e15 −0.318062
\(334\) −2.11745e16 −0.834567
\(335\) 1.04529e16 0.404058
\(336\) 1.44492e15 0.0547822
\(337\) 1.40598e16 0.522860 0.261430 0.965222i \(-0.415806\pi\)
0.261430 + 0.965222i \(0.415806\pi\)
\(338\) 1.35115e16 0.492883
\(339\) −1.24508e15 −0.0445554
\(340\) −3.55579e14 −0.0124831
\(341\) 2.32722e16 0.801557
\(342\) −1.22770e16 −0.414881
\(343\) −2.15649e16 −0.715048
\(344\) 1.27684e16 0.415439
\(345\) −1.57565e16 −0.503079
\(346\) −3.89050e15 −0.121902
\(347\) −3.96808e16 −1.22022 −0.610111 0.792316i \(-0.708875\pi\)
−0.610111 + 0.792316i \(0.708875\pi\)
\(348\) −1.37906e16 −0.416216
\(349\) −4.08458e16 −1.20999 −0.604996 0.796229i \(-0.706825\pi\)
−0.604996 + 0.796229i \(0.706825\pi\)
\(350\) 6.77057e15 0.196872
\(351\) 3.70167e15 0.105658
\(352\) 2.10870e16 0.590864
\(353\) 5.54402e16 1.52507 0.762534 0.646948i \(-0.223955\pi\)
0.762534 + 0.646948i \(0.223955\pi\)
\(354\) −1.96363e15 −0.0530321
\(355\) −5.22229e15 −0.138477
\(356\) 2.26496e16 0.589707
\(357\) −4.11492e14 −0.0105201
\(358\) −1.41960e16 −0.356390
\(359\) −7.48019e16 −1.84416 −0.922080 0.386998i \(-0.873512\pi\)
−0.922080 + 0.386998i \(0.873512\pi\)
\(360\) 7.69054e15 0.186205
\(361\) 8.88153e16 2.11199
\(362\) 2.49333e16 0.582336
\(363\) 1.39894e16 0.320927
\(364\) 4.72732e15 0.106526
\(365\) 4.32645e16 0.957697
\(366\) 9.39036e15 0.204200
\(367\) 2.69332e16 0.575384 0.287692 0.957723i \(-0.407112\pi\)
0.287692 + 0.957723i \(0.407112\pi\)
\(368\) −1.93445e16 −0.406019
\(369\) −9.76438e15 −0.201360
\(370\) 1.75116e16 0.354826
\(371\) 1.92701e16 0.383666
\(372\) −1.78248e16 −0.348734
\(373\) 5.13785e15 0.0987812 0.0493906 0.998780i \(-0.484272\pi\)
0.0493906 + 0.998780i \(0.484272\pi\)
\(374\) 1.17364e15 0.0221754
\(375\) 2.82219e16 0.524063
\(376\) 1.07309e15 0.0195846
\(377\) 4.39341e16 0.788103
\(378\) 2.97532e15 0.0524611
\(379\) −5.72424e15 −0.0992117 −0.0496058 0.998769i \(-0.515797\pi\)
−0.0496058 + 0.998769i \(0.515797\pi\)
\(380\) −2.74062e16 −0.466935
\(381\) 2.38703e16 0.399803
\(382\) 1.66648e16 0.274403
\(383\) −6.23726e16 −1.00972 −0.504861 0.863201i \(-0.668456\pi\)
−0.504861 + 0.863201i \(0.668456\pi\)
\(384\) −9.86576e15 −0.157028
\(385\) −8.67170e15 −0.135709
\(386\) −6.78124e15 −0.104350
\(387\) 8.63481e15 0.130657
\(388\) −4.31651e16 −0.642283
\(389\) −1.15033e15 −0.0168325 −0.00841625 0.999965i \(-0.502679\pi\)
−0.00841625 + 0.999965i \(0.502679\pi\)
\(390\) −8.19079e15 −0.117871
\(391\) 5.50902e15 0.0779696
\(392\) −6.47744e16 −0.901663
\(393\) 3.28935e16 0.450358
\(394\) 4.77697e16 0.643321
\(395\) 3.27910e16 0.434384
\(396\) 8.56124e15 0.111562
\(397\) −7.66690e16 −0.982837 −0.491418 0.870924i \(-0.663521\pi\)
−0.491418 + 0.870924i \(0.663521\pi\)
\(398\) 5.82515e16 0.734627
\(399\) −3.17158e16 −0.393506
\(400\) 1.45298e16 0.177366
\(401\) 2.78495e16 0.334487 0.167243 0.985916i \(-0.446513\pi\)
0.167243 + 0.985916i \(0.446513\pi\)
\(402\) 2.64254e16 0.312285
\(403\) 5.67860e16 0.660327
\(404\) −4.23816e16 −0.484952
\(405\) 5.20083e15 0.0585618
\(406\) 3.53132e16 0.391308
\(407\) 5.83117e16 0.635905
\(408\) −2.68887e15 −0.0288589
\(409\) −8.47371e16 −0.895101 −0.447550 0.894259i \(-0.647703\pi\)
−0.447550 + 0.894259i \(0.647703\pi\)
\(410\) 2.16059e16 0.224635
\(411\) 9.46143e16 0.968244
\(412\) −4.55936e16 −0.459274
\(413\) −5.07274e15 −0.0502999
\(414\) −3.98333e16 −0.388816
\(415\) 2.62902e16 0.252628
\(416\) 5.14539e16 0.486757
\(417\) −5.93496e16 −0.552756
\(418\) 9.04586e16 0.829476
\(419\) −2.15791e16 −0.194824 −0.0974118 0.995244i \(-0.531056\pi\)
−0.0974118 + 0.995244i \(0.531056\pi\)
\(420\) 6.64186e15 0.0590432
\(421\) −5.87309e15 −0.0514083 −0.0257042 0.999670i \(-0.508183\pi\)
−0.0257042 + 0.999670i \(0.508183\pi\)
\(422\) −1.20495e17 −1.03857
\(423\) 7.25690e14 0.00615940
\(424\) 1.25920e17 1.05248
\(425\) −4.13788e15 −0.0340604
\(426\) −1.32022e16 −0.107025
\(427\) 2.42585e16 0.193679
\(428\) 3.36346e15 0.0264485
\(429\) −2.72744e16 −0.211243
\(430\) −1.91065e16 −0.145759
\(431\) 2.09721e17 1.57594 0.787970 0.615713i \(-0.211132\pi\)
0.787970 + 0.615713i \(0.211132\pi\)
\(432\) 6.38512e15 0.0472634
\(433\) −1.91663e17 −1.39755 −0.698775 0.715342i \(-0.746271\pi\)
−0.698775 + 0.715342i \(0.746271\pi\)
\(434\) 4.56433e16 0.327864
\(435\) 6.17272e16 0.436814
\(436\) 8.18970e16 0.570960
\(437\) 4.24608e17 2.91648
\(438\) 1.09375e17 0.740178
\(439\) 5.54766e16 0.369905 0.184952 0.982747i \(-0.440787\pi\)
0.184952 + 0.982747i \(0.440787\pi\)
\(440\) −5.66648e16 −0.372281
\(441\) −4.38045e16 −0.283575
\(442\) 2.86378e15 0.0182682
\(443\) −1.61504e17 −1.01521 −0.507607 0.861589i \(-0.669470\pi\)
−0.507607 + 0.861589i \(0.669470\pi\)
\(444\) −4.46623e16 −0.276664
\(445\) −1.01380e17 −0.618890
\(446\) −4.01529e16 −0.241569
\(447\) −6.29292e16 −0.373124
\(448\) 5.75946e16 0.336569
\(449\) −8.58276e16 −0.494340 −0.247170 0.968972i \(-0.579501\pi\)
−0.247170 + 0.968972i \(0.579501\pi\)
\(450\) 2.99192e16 0.169851
\(451\) 7.19451e16 0.402581
\(452\) −7.02653e15 −0.0387562
\(453\) −1.54557e17 −0.840331
\(454\) −7.47557e16 −0.400665
\(455\) −2.11596e16 −0.111798
\(456\) −2.07245e17 −1.07948
\(457\) −2.08369e17 −1.06998 −0.534992 0.844857i \(-0.679686\pi\)
−0.534992 + 0.844857i \(0.679686\pi\)
\(458\) 1.44497e16 0.0731531
\(459\) −1.81839e15 −0.00907619
\(460\) −8.89207e16 −0.437600
\(461\) 8.06039e16 0.391111 0.195555 0.980693i \(-0.437349\pi\)
0.195555 + 0.980693i \(0.437349\pi\)
\(462\) −2.19225e16 −0.104886
\(463\) −3.05515e17 −1.44131 −0.720653 0.693296i \(-0.756158\pi\)
−0.720653 + 0.693296i \(0.756158\pi\)
\(464\) 7.57832e16 0.352538
\(465\) 7.97841e16 0.365992
\(466\) 1.82410e17 0.825165
\(467\) −3.37157e16 −0.150408 −0.0752042 0.997168i \(-0.523961\pi\)
−0.0752042 + 0.997168i \(0.523961\pi\)
\(468\) 2.08901e16 0.0919056
\(469\) 6.82657e16 0.296196
\(470\) −1.60575e15 −0.00687137
\(471\) 1.21519e17 0.512873
\(472\) −3.31476e16 −0.137984
\(473\) −6.36224e16 −0.261224
\(474\) 8.28975e16 0.335724
\(475\) −3.18927e17 −1.27404
\(476\) −2.32222e15 −0.00915079
\(477\) 8.51547e16 0.331009
\(478\) −6.48760e16 −0.248773
\(479\) 1.85402e17 0.701350 0.350675 0.936497i \(-0.385952\pi\)
0.350675 + 0.936497i \(0.385952\pi\)
\(480\) 7.22925e16 0.269790
\(481\) 1.42285e17 0.523861
\(482\) 5.74184e16 0.208567
\(483\) −1.02903e17 −0.368784
\(484\) 7.89480e16 0.279156
\(485\) 1.93208e17 0.674068
\(486\) 1.31480e16 0.0452609
\(487\) −5.28050e17 −1.79365 −0.896824 0.442388i \(-0.854131\pi\)
−0.896824 + 0.442388i \(0.854131\pi\)
\(488\) 1.58516e17 0.531306
\(489\) 3.38976e16 0.112115
\(490\) 9.69275e16 0.316353
\(491\) 9.57612e16 0.308432 0.154216 0.988037i \(-0.450715\pi\)
0.154216 + 0.988037i \(0.450715\pi\)
\(492\) −5.51045e16 −0.175151
\(493\) −2.15819e16 −0.0676994
\(494\) 2.20726e17 0.683326
\(495\) −3.83203e16 −0.117083
\(496\) 9.79519e16 0.295381
\(497\) −3.41059e16 −0.101511
\(498\) 6.64631e16 0.195249
\(499\) −1.14773e17 −0.332801 −0.166401 0.986058i \(-0.553215\pi\)
−0.166401 + 0.986058i \(0.553215\pi\)
\(500\) 1.59268e17 0.455852
\(501\) −2.41724e17 −0.682928
\(502\) 4.22442e17 1.17813
\(503\) 9.36677e16 0.257868 0.128934 0.991653i \(-0.458844\pi\)
0.128934 + 0.991653i \(0.458844\pi\)
\(504\) 5.02256e16 0.136498
\(505\) 1.89701e17 0.508951
\(506\) 2.93497e17 0.777365
\(507\) 1.54244e17 0.403327
\(508\) 1.34710e17 0.347766
\(509\) −6.74000e17 −1.71789 −0.858943 0.512071i \(-0.828879\pi\)
−0.858943 + 0.512071i \(0.828879\pi\)
\(510\) 4.02359e15 0.0101253
\(511\) 2.82553e17 0.702044
\(512\) 1.94855e17 0.478031
\(513\) −1.40152e17 −0.339498
\(514\) −1.37607e17 −0.329141
\(515\) 2.04078e17 0.482003
\(516\) 4.87299e16 0.113651
\(517\) −5.34697e15 −0.0123146
\(518\) 1.14365e17 0.260107
\(519\) −4.44132e16 −0.0997526
\(520\) −1.38267e17 −0.306687
\(521\) 4.53485e17 0.993385 0.496693 0.867927i \(-0.334548\pi\)
0.496693 + 0.867927i \(0.334548\pi\)
\(522\) 1.56049e17 0.337601
\(523\) 8.66889e17 1.85226 0.926132 0.377201i \(-0.123113\pi\)
0.926132 + 0.377201i \(0.123113\pi\)
\(524\) 1.85632e17 0.391740
\(525\) 7.72916e16 0.161100
\(526\) −4.16459e17 −0.857363
\(527\) −2.78952e16 −0.0567232
\(528\) −4.70464e16 −0.0944943
\(529\) 8.73622e17 1.73325
\(530\) −1.88424e17 −0.369270
\(531\) −2.24165e16 −0.0433963
\(532\) −1.78985e17 −0.342288
\(533\) 1.75552e17 0.331648
\(534\) −2.56295e17 −0.478323
\(535\) −1.50549e16 −0.0277574
\(536\) 4.46079e17 0.812533
\(537\) −1.62058e17 −0.291634
\(538\) 3.23729e17 0.575568
\(539\) 3.22757e17 0.566955
\(540\) 2.93504e16 0.0509396
\(541\) −6.69887e17 −1.14873 −0.574367 0.818598i \(-0.694752\pi\)
−0.574367 + 0.818598i \(0.694752\pi\)
\(542\) 7.80679e17 1.32275
\(543\) 2.84633e17 0.476526
\(544\) −2.52759e16 −0.0418132
\(545\) −3.66573e17 −0.599215
\(546\) −5.34926e16 −0.0864056
\(547\) 7.81136e17 1.24683 0.623417 0.781889i \(-0.285744\pi\)
0.623417 + 0.781889i \(0.285744\pi\)
\(548\) 5.33948e17 0.842220
\(549\) 1.07199e17 0.167097
\(550\) −2.20448e17 −0.339586
\(551\) −1.66343e18 −2.53232
\(552\) −6.72416e17 −1.01166
\(553\) 2.14153e17 0.318427
\(554\) 1.28257e17 0.188481
\(555\) 1.99910e17 0.290355
\(556\) −3.34935e17 −0.480811
\(557\) 4.27554e17 0.606642 0.303321 0.952888i \(-0.401905\pi\)
0.303321 + 0.952888i \(0.401905\pi\)
\(558\) 2.01698e17 0.282865
\(559\) −1.55243e17 −0.215197
\(560\) −3.64989e16 −0.0500100
\(561\) 1.33981e16 0.0181461
\(562\) −2.22877e17 −0.298386
\(563\) 8.65471e16 0.114538 0.0572688 0.998359i \(-0.481761\pi\)
0.0572688 + 0.998359i \(0.481761\pi\)
\(564\) 4.09537e15 0.00535771
\(565\) 3.14509e16 0.0406742
\(566\) −1.25407e17 −0.160330
\(567\) 3.39657e16 0.0429290
\(568\) −2.22863e17 −0.278467
\(569\) −1.27671e16 −0.0157712 −0.00788558 0.999969i \(-0.502510\pi\)
−0.00788558 + 0.999969i \(0.502510\pi\)
\(570\) 3.10119e17 0.378740
\(571\) −1.88068e17 −0.227080 −0.113540 0.993533i \(-0.536219\pi\)
−0.113540 + 0.993533i \(0.536219\pi\)
\(572\) −1.53921e17 −0.183748
\(573\) 1.90242e17 0.224544
\(574\) 1.41104e17 0.164670
\(575\) −1.03477e18 −1.19400
\(576\) 2.54511e17 0.290376
\(577\) 1.05926e18 1.19498 0.597491 0.801876i \(-0.296164\pi\)
0.597491 + 0.801876i \(0.296164\pi\)
\(578\) 6.31088e17 0.703978
\(579\) −7.74133e16 −0.0853896
\(580\) 3.48352e17 0.379959
\(581\) 1.71697e17 0.185190
\(582\) 4.88440e17 0.520969
\(583\) −6.27430e17 −0.661789
\(584\) 1.84633e18 1.92586
\(585\) −9.35045e16 −0.0964538
\(586\) −8.59474e17 −0.876795
\(587\) 1.21775e18 1.22860 0.614301 0.789072i \(-0.289438\pi\)
0.614301 + 0.789072i \(0.289438\pi\)
\(588\) −2.47207e17 −0.246666
\(589\) −2.15003e18 −2.12175
\(590\) 4.96015e16 0.0484125
\(591\) 5.45330e17 0.526430
\(592\) 2.45432e17 0.234336
\(593\) −5.86979e17 −0.554328 −0.277164 0.960823i \(-0.589395\pi\)
−0.277164 + 0.960823i \(0.589395\pi\)
\(594\) −9.68758e16 −0.0904906
\(595\) 1.03943e16 0.00960364
\(596\) −3.55136e17 −0.324559
\(597\) 6.64988e17 0.601147
\(598\) 7.16155e17 0.640397
\(599\) −1.74292e18 −1.54171 −0.770854 0.637012i \(-0.780170\pi\)
−0.770854 + 0.637012i \(0.780170\pi\)
\(600\) 5.05058e17 0.441935
\(601\) −6.26376e17 −0.542189 −0.271095 0.962553i \(-0.587386\pi\)
−0.271095 + 0.962553i \(0.587386\pi\)
\(602\) −1.24781e17 −0.106849
\(603\) 3.01667e17 0.255544
\(604\) −8.72230e17 −0.730955
\(605\) −3.53373e17 −0.292970
\(606\) 4.79575e17 0.393354
\(607\) −1.70636e18 −1.38466 −0.692331 0.721580i \(-0.743416\pi\)
−0.692331 + 0.721580i \(0.743416\pi\)
\(608\) −1.94814e18 −1.56404
\(609\) 4.03129e17 0.320208
\(610\) −2.37201e17 −0.186412
\(611\) −1.30470e16 −0.0101448
\(612\) −1.02619e16 −0.00789485
\(613\) −3.36839e17 −0.256407 −0.128203 0.991748i \(-0.540921\pi\)
−0.128203 + 0.991748i \(0.540921\pi\)
\(614\) 9.84427e17 0.741462
\(615\) 2.46649e17 0.183819
\(616\) −3.70068e17 −0.272902
\(617\) −3.34927e17 −0.244397 −0.122199 0.992506i \(-0.538995\pi\)
−0.122199 + 0.992506i \(0.538995\pi\)
\(618\) 5.15920e17 0.372527
\(619\) −2.03089e18 −1.45110 −0.725550 0.688169i \(-0.758415\pi\)
−0.725550 + 0.688169i \(0.758415\pi\)
\(620\) 4.50255e17 0.318356
\(621\) −4.54730e17 −0.318169
\(622\) −1.31804e18 −0.912621
\(623\) −6.62097e17 −0.453680
\(624\) −1.14797e17 −0.0778448
\(625\) 3.63291e17 0.243800
\(626\) −6.84085e17 −0.454336
\(627\) 1.03266e18 0.678762
\(628\) 6.85785e17 0.446118
\(629\) −6.98952e16 −0.0450006
\(630\) −7.51568e16 −0.0478911
\(631\) −1.93258e18 −1.21884 −0.609421 0.792847i \(-0.708598\pi\)
−0.609421 + 0.792847i \(0.708598\pi\)
\(632\) 1.39937e18 0.873517
\(633\) −1.37554e18 −0.849865
\(634\) −4.54021e17 −0.277649
\(635\) −6.02967e17 −0.364976
\(636\) 4.80564e17 0.287925
\(637\) 7.87552e17 0.467060
\(638\) −1.14979e18 −0.674970
\(639\) −1.50714e17 −0.0875786
\(640\) 2.49210e17 0.143349
\(641\) −3.17896e18 −1.81012 −0.905060 0.425283i \(-0.860175\pi\)
−0.905060 + 0.425283i \(0.860175\pi\)
\(642\) −3.80596e16 −0.0214529
\(643\) 1.99242e18 1.11176 0.555879 0.831263i \(-0.312382\pi\)
0.555879 + 0.831263i \(0.312382\pi\)
\(644\) −5.80726e17 −0.320784
\(645\) −2.18116e17 −0.119275
\(646\) −1.08428e17 −0.0586989
\(647\) −1.34205e18 −0.719267 −0.359634 0.933094i \(-0.617098\pi\)
−0.359634 + 0.933094i \(0.617098\pi\)
\(648\) 2.21947e17 0.117764
\(649\) 1.65167e17 0.0867628
\(650\) −5.37911e17 −0.279752
\(651\) 5.21056e17 0.268292
\(652\) 1.91299e17 0.0975220
\(653\) −2.21477e18 −1.11787 −0.558937 0.829210i \(-0.688791\pi\)
−0.558937 + 0.829210i \(0.688791\pi\)
\(654\) −9.26715e17 −0.463117
\(655\) −8.30892e17 −0.411127
\(656\) 3.02814e17 0.148355
\(657\) 1.24860e18 0.605689
\(658\) −1.04869e16 −0.00503708
\(659\) −2.98710e18 −1.42068 −0.710338 0.703861i \(-0.751458\pi\)
−0.710338 + 0.703861i \(0.751458\pi\)
\(660\) −2.16258e17 −0.101844
\(661\) −1.01538e18 −0.473498 −0.236749 0.971571i \(-0.576082\pi\)
−0.236749 + 0.971571i \(0.576082\pi\)
\(662\) 2.95818e18 1.36599
\(663\) 3.26924e16 0.0149489
\(664\) 1.12194e18 0.508018
\(665\) 8.01143e17 0.359227
\(666\) 5.05382e17 0.224407
\(667\) −5.39706e18 −2.37323
\(668\) −1.36415e18 −0.594040
\(669\) −4.58378e17 −0.197676
\(670\) −6.67507e17 −0.285082
\(671\) −7.89852e17 −0.334079
\(672\) 4.72129e17 0.197770
\(673\) −5.60114e17 −0.232369 −0.116185 0.993228i \(-0.537066\pi\)
−0.116185 + 0.993228i \(0.537066\pi\)
\(674\) −8.97843e17 −0.368902
\(675\) 3.41552e17 0.138990
\(676\) 8.70466e17 0.350831
\(677\) −8.13286e17 −0.324651 −0.162326 0.986737i \(-0.551899\pi\)
−0.162326 + 0.986737i \(0.551899\pi\)
\(678\) 7.95096e16 0.0314360
\(679\) 1.26181e18 0.494128
\(680\) 6.79212e16 0.0263450
\(681\) −8.53397e17 −0.327865
\(682\) −1.48614e18 −0.565536
\(683\) 2.98829e18 1.12639 0.563195 0.826324i \(-0.309572\pi\)
0.563195 + 0.826324i \(0.309572\pi\)
\(684\) −7.90937e17 −0.295310
\(685\) −2.38996e18 −0.883899
\(686\) 1.37711e18 0.504500
\(687\) 1.64955e17 0.0598613
\(688\) −2.67784e17 −0.0962631
\(689\) −1.53098e18 −0.545185
\(690\) 1.00619e18 0.354946
\(691\) −3.41593e18 −1.19372 −0.596858 0.802347i \(-0.703585\pi\)
−0.596858 + 0.802347i \(0.703585\pi\)
\(692\) −2.50642e17 −0.0867690
\(693\) −2.50263e17 −0.0858284
\(694\) 2.53397e18 0.860924
\(695\) 1.49918e18 0.504605
\(696\) 2.63423e18 0.878402
\(697\) −8.62369e16 −0.0284892
\(698\) 2.60836e18 0.853705
\(699\) 2.08236e18 0.675234
\(700\) 4.36189e17 0.140132
\(701\) −6.57222e17 −0.209192 −0.104596 0.994515i \(-0.533355\pi\)
−0.104596 + 0.994515i \(0.533355\pi\)
\(702\) −2.36384e17 −0.0745465
\(703\) −5.38718e18 −1.68326
\(704\) −1.87527e18 −0.580551
\(705\) −1.83310e16 −0.00562285
\(706\) −3.54035e18 −1.07601
\(707\) 1.23891e18 0.373089
\(708\) −1.26506e17 −0.0377479
\(709\) −1.79482e17 −0.0530665 −0.0265333 0.999648i \(-0.508447\pi\)
−0.0265333 + 0.999648i \(0.508447\pi\)
\(710\) 3.33489e17 0.0977018
\(711\) 9.46342e17 0.274723
\(712\) −4.32644e18 −1.24455
\(713\) −6.97585e18 −1.98845
\(714\) 2.62774e16 0.00742239
\(715\) 6.88953e17 0.192841
\(716\) −9.14563e17 −0.253676
\(717\) −7.40612e17 −0.203571
\(718\) 4.77676e18 1.30114
\(719\) 4.97080e18 1.34180 0.670902 0.741546i \(-0.265907\pi\)
0.670902 + 0.741546i \(0.265907\pi\)
\(720\) −1.61289e17 −0.0431462
\(721\) 1.33280e18 0.353334
\(722\) −5.67164e18 −1.49011
\(723\) 6.55478e17 0.170671
\(724\) 1.60631e18 0.414503
\(725\) 4.05379e18 1.03673
\(726\) −8.93346e17 −0.226429
\(727\) 7.59211e17 0.190717 0.0953583 0.995443i \(-0.469600\pi\)
0.0953583 + 0.995443i \(0.469600\pi\)
\(728\) −9.02995e17 −0.224818
\(729\) 1.50095e17 0.0370370
\(730\) −2.76282e18 −0.675700
\(731\) 7.62608e16 0.0184858
\(732\) 6.04966e17 0.145348
\(733\) 6.71055e18 1.59802 0.799010 0.601318i \(-0.205357\pi\)
0.799010 + 0.601318i \(0.205357\pi\)
\(734\) −1.71992e18 −0.405960
\(735\) 1.10651e18 0.258873
\(736\) −6.32083e18 −1.46578
\(737\) −2.22272e18 −0.510911
\(738\) 6.23541e17 0.142069
\(739\) −5.57650e18 −1.25943 −0.629713 0.776828i \(-0.716827\pi\)
−0.629713 + 0.776828i \(0.716827\pi\)
\(740\) 1.12817e18 0.252563
\(741\) 2.51977e18 0.559167
\(742\) −1.23057e18 −0.270694
\(743\) 8.17239e18 1.78206 0.891029 0.453946i \(-0.149984\pi\)
0.891029 + 0.453946i \(0.149984\pi\)
\(744\) 3.40481e18 0.735986
\(745\) 1.58960e18 0.340621
\(746\) −3.28097e17 −0.0696948
\(747\) 7.58730e17 0.159773
\(748\) 7.56110e16 0.0157843
\(749\) −9.83210e16 −0.0203477
\(750\) −1.80222e18 −0.369751
\(751\) −5.17756e18 −1.05309 −0.526545 0.850147i \(-0.676513\pi\)
−0.526545 + 0.850147i \(0.676513\pi\)
\(752\) −2.25052e16 −0.00453802
\(753\) 4.82252e18 0.964066
\(754\) −2.80558e18 −0.556044
\(755\) 3.90412e18 0.767129
\(756\) 1.91683e17 0.0373414
\(757\) −9.33308e17 −0.180261 −0.0901305 0.995930i \(-0.528728\pi\)
−0.0901305 + 0.995930i \(0.528728\pi\)
\(758\) 3.65543e17 0.0699985
\(759\) 3.35050e18 0.636119
\(760\) 5.23503e18 0.985441
\(761\) 6.65862e18 1.24275 0.621375 0.783513i \(-0.286574\pi\)
0.621375 + 0.783513i \(0.286574\pi\)
\(762\) −1.52433e18 −0.282080
\(763\) −2.39402e18 −0.439257
\(764\) 1.07362e18 0.195318
\(765\) 4.59326e16 0.00828555
\(766\) 3.98304e18 0.712406
\(767\) 4.03021e17 0.0714755
\(768\) 3.49003e18 0.613736
\(769\) −5.49304e18 −0.957836 −0.478918 0.877860i \(-0.658971\pi\)
−0.478918 + 0.877860i \(0.658971\pi\)
\(770\) 5.53765e17 0.0957493
\(771\) −1.57090e18 −0.269336
\(772\) −4.36876e17 −0.0742755
\(773\) −4.56545e18 −0.769692 −0.384846 0.922981i \(-0.625745\pi\)
−0.384846 + 0.922981i \(0.625745\pi\)
\(774\) −5.51409e17 −0.0921844
\(775\) 5.23963e18 0.868639
\(776\) 8.24523e18 1.35551
\(777\) 1.30557e18 0.212846
\(778\) 7.34584e16 0.0118761
\(779\) −6.64671e18 −1.06565
\(780\) −5.27685e17 −0.0838996
\(781\) 1.11048e18 0.175097
\(782\) −3.51799e17 −0.0550112
\(783\) 1.78143e18 0.276260
\(784\) 1.35847e18 0.208928
\(785\) −3.06959e18 −0.468196
\(786\) −2.10054e18 −0.317749
\(787\) −8.58589e18 −1.28810 −0.644050 0.764983i \(-0.722747\pi\)
−0.644050 + 0.764983i \(0.722747\pi\)
\(788\) 3.07753e18 0.457911
\(789\) −4.75421e18 −0.701581
\(790\) −2.09400e18 −0.306478
\(791\) 2.05401e17 0.0298163
\(792\) −1.63533e18 −0.235447
\(793\) −1.92730e18 −0.275216
\(794\) 4.89599e18 0.693437
\(795\) −2.15101e18 −0.302174
\(796\) 3.75280e18 0.522903
\(797\) 6.84451e18 0.945939 0.472970 0.881079i \(-0.343182\pi\)
0.472970 + 0.881079i \(0.343182\pi\)
\(798\) 2.02533e18 0.277637
\(799\) 6.40914e15 0.000871456 0
\(800\) 4.74764e18 0.640313
\(801\) −2.92581e18 −0.391413
\(802\) −1.77843e18 −0.235996
\(803\) −9.19986e18 −1.21096
\(804\) 1.70243e18 0.222283
\(805\) 2.59934e18 0.336659
\(806\) −3.62629e18 −0.465891
\(807\) 3.69563e18 0.470989
\(808\) 8.09557e18 1.02347
\(809\) 1.01211e19 1.26930 0.634650 0.772800i \(-0.281144\pi\)
0.634650 + 0.772800i \(0.281144\pi\)
\(810\) −3.32119e17 −0.0413181
\(811\) −5.21041e18 −0.643037 −0.321519 0.946903i \(-0.604193\pi\)
−0.321519 + 0.946903i \(0.604193\pi\)
\(812\) 2.27503e18 0.278530
\(813\) 8.91208e18 1.08241
\(814\) −3.72372e18 −0.448661
\(815\) −8.56257e17 −0.102348
\(816\) 5.63920e16 0.00668700
\(817\) 5.87781e18 0.691468
\(818\) 5.41121e18 0.631536
\(819\) −6.10662e17 −0.0707058
\(820\) 1.39194e18 0.159894
\(821\) 2.25361e18 0.256831 0.128416 0.991720i \(-0.459011\pi\)
0.128416 + 0.991720i \(0.459011\pi\)
\(822\) −6.04195e18 −0.683141
\(823\) 1.04493e19 1.17217 0.586085 0.810250i \(-0.300669\pi\)
0.586085 + 0.810250i \(0.300669\pi\)
\(824\) 8.70911e18 0.969275
\(825\) −2.51660e18 −0.277884
\(826\) 3.23939e17 0.0354889
\(827\) 1.23524e19 1.34265 0.671327 0.741162i \(-0.265725\pi\)
0.671327 + 0.741162i \(0.265725\pi\)
\(828\) −2.56623e18 −0.276757
\(829\) −7.88948e18 −0.844197 −0.422098 0.906550i \(-0.638706\pi\)
−0.422098 + 0.906550i \(0.638706\pi\)
\(830\) −1.67886e18 −0.178241
\(831\) 1.46416e18 0.154235
\(832\) −4.57579e18 −0.478261
\(833\) −3.86872e17 −0.0401213
\(834\) 3.79000e18 0.389995
\(835\) 6.10597e18 0.623437
\(836\) 5.82772e18 0.590416
\(837\) 2.30255e18 0.231469
\(838\) 1.37801e18 0.137457
\(839\) 1.36386e19 1.34995 0.674975 0.737841i \(-0.264155\pi\)
0.674975 + 0.737841i \(0.264155\pi\)
\(840\) −1.26870e18 −0.124608
\(841\) 1.08827e19 1.06062
\(842\) 3.75049e17 0.0362710
\(843\) −2.54432e18 −0.244170
\(844\) −7.76277e18 −0.739249
\(845\) −3.89623e18 −0.368193
\(846\) −4.63417e16 −0.00434575
\(847\) −2.30782e18 −0.214763
\(848\) −2.64083e18 −0.243875
\(849\) −1.43162e18 −0.131198
\(850\) 2.64240e17 0.0240312
\(851\) −1.74789e19 −1.57751
\(852\) −8.50543e17 −0.0761796
\(853\) 4.63570e18 0.412047 0.206023 0.978547i \(-0.433948\pi\)
0.206023 + 0.978547i \(0.433948\pi\)
\(854\) −1.54912e18 −0.136650
\(855\) 3.54026e18 0.309924
\(856\) −6.42474e17 −0.0558182
\(857\) 6.54102e18 0.563988 0.281994 0.959416i \(-0.409004\pi\)
0.281994 + 0.959416i \(0.409004\pi\)
\(858\) 1.74171e18 0.149042
\(859\) 4.55967e18 0.387238 0.193619 0.981077i \(-0.437977\pi\)
0.193619 + 0.981077i \(0.437977\pi\)
\(860\) −1.23092e18 −0.103750
\(861\) 1.61082e18 0.134749
\(862\) −1.33925e19 −1.11190
\(863\) −1.50526e19 −1.24035 −0.620173 0.784465i \(-0.712937\pi\)
−0.620173 + 0.784465i \(0.712937\pi\)
\(864\) 2.08634e18 0.170627
\(865\) 1.12188e18 0.0910631
\(866\) 1.22394e19 0.986037
\(867\) 7.20438e18 0.576066
\(868\) 2.94054e18 0.233372
\(869\) −6.97276e18 −0.549258
\(870\) −3.94182e18 −0.308192
\(871\) −5.42360e18 −0.420891
\(872\) −1.56436e19 −1.20498
\(873\) 5.57594e18 0.426310
\(874\) −2.71150e19 −2.05771
\(875\) −4.65574e18 −0.350701
\(876\) 7.04639e18 0.526854
\(877\) 7.32647e18 0.543748 0.271874 0.962333i \(-0.412357\pi\)
0.271874 + 0.962333i \(0.412357\pi\)
\(878\) −3.54267e18 −0.260985
\(879\) −9.81159e18 −0.717483
\(880\) 1.18840e18 0.0862628
\(881\) −7.90227e18 −0.569388 −0.284694 0.958618i \(-0.591892\pi\)
−0.284694 + 0.958618i \(0.591892\pi\)
\(882\) 2.79730e18 0.200076
\(883\) 1.84667e19 1.31113 0.655563 0.755140i \(-0.272431\pi\)
0.655563 + 0.755140i \(0.272431\pi\)
\(884\) 1.84497e17 0.0130032
\(885\) 5.66242e17 0.0396160
\(886\) 1.03134e19 0.716281
\(887\) 1.78491e19 1.23059 0.615295 0.788297i \(-0.289037\pi\)
0.615295 + 0.788297i \(0.289037\pi\)
\(888\) 8.53122e18 0.583884
\(889\) −3.93787e18 −0.267547
\(890\) 6.47403e18 0.436656
\(891\) −1.10592e18 −0.0740486
\(892\) −2.58682e18 −0.171947
\(893\) 4.93984e17 0.0325971
\(894\) 4.01858e18 0.263257
\(895\) 4.09361e18 0.266230
\(896\) 1.62755e18 0.105083
\(897\) 8.17549e18 0.524038
\(898\) 5.48085e18 0.348780
\(899\) 2.73283e19 1.72653
\(900\) 1.92752e18 0.120899
\(901\) 7.52068e17 0.0468323
\(902\) −4.59433e18 −0.284040
\(903\) −1.42448e18 −0.0874350
\(904\) 1.34218e18 0.0817930
\(905\) −7.18986e18 −0.435016
\(906\) 9.86982e18 0.592893
\(907\) −1.78793e18 −0.106636 −0.0533178 0.998578i \(-0.516980\pi\)
−0.0533178 + 0.998578i \(0.516980\pi\)
\(908\) −4.81608e18 −0.285191
\(909\) 5.47473e18 0.321883
\(910\) 1.35123e18 0.0788787
\(911\) 1.31518e19 0.762283 0.381142 0.924517i \(-0.375531\pi\)
0.381142 + 0.924517i \(0.375531\pi\)
\(912\) 4.34642e18 0.250130
\(913\) −5.59041e18 −0.319436
\(914\) 1.33062e19 0.754924
\(915\) −2.70784e18 −0.152541
\(916\) 9.30909e17 0.0520699
\(917\) −5.42641e18 −0.301378
\(918\) 1.16120e17 0.00640368
\(919\) −2.87717e19 −1.57549 −0.787743 0.616004i \(-0.788750\pi\)
−0.787743 + 0.616004i \(0.788750\pi\)
\(920\) 1.69853e19 0.923532
\(921\) 1.12380e19 0.606740
\(922\) −5.14727e18 −0.275947
\(923\) 2.70965e18 0.144246
\(924\) −1.41234e18 −0.0746572
\(925\) 1.31286e19 0.689123
\(926\) 1.95098e19 1.01691
\(927\) 5.88965e18 0.304839
\(928\) 2.47622e19 1.27271
\(929\) 9.56512e18 0.488190 0.244095 0.969751i \(-0.421509\pi\)
0.244095 + 0.969751i \(0.421509\pi\)
\(930\) −5.09492e18 −0.258225
\(931\) −2.98182e19 −1.50075
\(932\) 1.17516e19 0.587347
\(933\) −1.50465e19 −0.746799
\(934\) 2.15304e18 0.106120
\(935\) −3.38437e17 −0.0165654
\(936\) −3.99034e18 −0.193962
\(937\) −2.37281e19 −1.14540 −0.572698 0.819766i \(-0.694103\pi\)
−0.572698 + 0.819766i \(0.694103\pi\)
\(938\) −4.35937e18 −0.208980
\(939\) −7.80938e18 −0.371784
\(940\) −1.03449e17 −0.00489099
\(941\) 5.14891e18 0.241759 0.120880 0.992667i \(-0.461429\pi\)
0.120880 + 0.992667i \(0.461429\pi\)
\(942\) −7.76008e18 −0.361856
\(943\) −2.15655e19 −0.998698
\(944\) 6.95182e17 0.0319728
\(945\) −8.57976e17 −0.0391894
\(946\) 4.06285e18 0.184305
\(947\) 2.30511e19 1.03852 0.519262 0.854615i \(-0.326207\pi\)
0.519262 + 0.854615i \(0.326207\pi\)
\(948\) 5.34060e18 0.238966
\(949\) −2.24484e19 −0.997596
\(950\) 2.03663e19 0.898895
\(951\) −5.18302e18 −0.227201
\(952\) 4.43581e17 0.0193123
\(953\) 5.07741e18 0.219552 0.109776 0.993956i \(-0.464987\pi\)
0.109776 + 0.993956i \(0.464987\pi\)
\(954\) −5.43788e18 −0.233542
\(955\) −4.80554e18 −0.204984
\(956\) −4.17959e18 −0.177075
\(957\) −1.31258e19 −0.552329
\(958\) −1.18396e19 −0.494835
\(959\) −1.56084e19 −0.647946
\(960\) −6.42896e18 −0.265081
\(961\) 1.09050e19 0.446607
\(962\) −9.08615e18 −0.369609
\(963\) −4.34481e17 −0.0175550
\(964\) 3.69914e18 0.148457
\(965\) 1.95547e18 0.0779512
\(966\) 6.57127e18 0.260195
\(967\) −4.68899e19 −1.84420 −0.922099 0.386954i \(-0.873527\pi\)
−0.922099 + 0.386954i \(0.873527\pi\)
\(968\) −1.50803e19 −0.589143
\(969\) −1.23779e18 −0.0480334
\(970\) −1.23380e19 −0.475587
\(971\) −1.11617e19 −0.427371 −0.213686 0.976902i \(-0.568547\pi\)
−0.213686 + 0.976902i \(0.568547\pi\)
\(972\) 8.47047e17 0.0322164
\(973\) 9.79086e18 0.369902
\(974\) 3.37207e19 1.26550
\(975\) −6.14069e18 −0.228922
\(976\) −3.32446e18 −0.123111
\(977\) −4.19466e19 −1.54306 −0.771529 0.636194i \(-0.780508\pi\)
−0.771529 + 0.636194i \(0.780508\pi\)
\(978\) −2.16466e18 −0.0791021
\(979\) 2.15577e19 0.782557
\(980\) 6.24448e18 0.225178
\(981\) −1.05792e19 −0.378970
\(982\) −6.11520e18 −0.217613
\(983\) −3.57397e19 −1.26344 −0.631718 0.775198i \(-0.717650\pi\)
−0.631718 + 0.775198i \(0.717650\pi\)
\(984\) 1.05258e19 0.369648
\(985\) −1.37751e19 −0.480573
\(986\) 1.37820e18 0.0477651
\(987\) −1.19716e17 −0.00412185
\(988\) 1.42201e19 0.486387
\(989\) 1.90708e19 0.648027
\(990\) 2.44709e18 0.0826078
\(991\) −1.75515e19 −0.588620 −0.294310 0.955710i \(-0.595090\pi\)
−0.294310 + 0.955710i \(0.595090\pi\)
\(992\) 3.20059e19 1.06636
\(993\) 3.37700e19 1.11779
\(994\) 2.17796e18 0.0716207
\(995\) −1.67976e19 −0.548780
\(996\) 4.28183e18 0.138977
\(997\) 5.23492e18 0.168807 0.0844036 0.996432i \(-0.473101\pi\)
0.0844036 + 0.996432i \(0.473101\pi\)
\(998\) 7.32925e18 0.234807
\(999\) 5.76934e18 0.183633
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.1.12 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.12 31 1.1 even 1 trivial