Properties

Label 177.14.a.b.1.6
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 1.6
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-135.114 q^{2} -729.000 q^{3} +10063.7 q^{4} -36751.1 q^{5} +98497.9 q^{6} -177254. q^{7} -252896. q^{8} +531441. q^{9} +O(q^{10})\) \(q-135.114 q^{2} -729.000 q^{3} +10063.7 q^{4} -36751.1 q^{5} +98497.9 q^{6} -177254. q^{7} -252896. q^{8} +531441. q^{9} +4.96558e6 q^{10} -8.38008e6 q^{11} -7.33646e6 q^{12} +4.85093e6 q^{13} +2.39495e7 q^{14} +2.67916e7 q^{15} -4.82723e7 q^{16} +1.51868e7 q^{17} -7.18050e7 q^{18} -1.04615e8 q^{19} -3.69853e8 q^{20} +1.29218e8 q^{21} +1.13226e9 q^{22} +5.03097e8 q^{23} +1.84361e8 q^{24} +1.29940e8 q^{25} -6.55428e8 q^{26} -3.87420e8 q^{27} -1.78384e9 q^{28} -4.08283e9 q^{29} -3.61991e9 q^{30} -6.12832e9 q^{31} +8.59398e9 q^{32} +6.10907e9 q^{33} -2.05195e9 q^{34} +6.51428e9 q^{35} +5.34828e9 q^{36} +9.81095e9 q^{37} +1.41349e10 q^{38} -3.53633e9 q^{39} +9.29421e9 q^{40} +3.36959e10 q^{41} -1.74592e10 q^{42} -3.54505e10 q^{43} -8.43348e10 q^{44} -1.95310e10 q^{45} -6.79753e10 q^{46} +6.44491e10 q^{47} +3.51905e10 q^{48} -6.54700e10 q^{49} -1.75567e10 q^{50} -1.10712e10 q^{51} +4.88185e10 q^{52} -1.40446e11 q^{53} +5.23458e10 q^{54} +3.07977e11 q^{55} +4.48269e10 q^{56} +7.62642e10 q^{57} +5.51646e11 q^{58} -4.21805e10 q^{59} +2.69623e11 q^{60} -7.41838e11 q^{61} +8.28020e11 q^{62} -9.42001e10 q^{63} -7.65718e11 q^{64} -1.78277e11 q^{65} -8.25420e11 q^{66} +9.59565e11 q^{67} +1.52836e11 q^{68} -3.66757e11 q^{69} -8.80169e11 q^{70} -7.60819e11 q^{71} -1.34399e11 q^{72} -5.28101e11 q^{73} -1.32559e12 q^{74} -9.47263e10 q^{75} -1.05281e12 q^{76} +1.48540e12 q^{77} +4.77807e11 q^{78} +1.53934e11 q^{79} +1.77406e12 q^{80} +2.82430e11 q^{81} -4.55278e12 q^{82} +4.32516e12 q^{83} +1.30042e12 q^{84} -5.58132e11 q^{85} +4.78985e12 q^{86} +2.97638e12 q^{87} +2.11929e12 q^{88} +3.47028e12 q^{89} +2.63891e12 q^{90} -8.59848e11 q^{91} +5.06303e12 q^{92} +4.46755e12 q^{93} -8.70796e12 q^{94} +3.84471e12 q^{95} -6.26501e12 q^{96} +5.67818e12 q^{97} +8.84590e12 q^{98} -4.45352e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −135.114 −1.49281 −0.746405 0.665492i \(-0.768222\pi\)
−0.746405 + 0.665492i \(0.768222\pi\)
\(3\) −729.000 −0.577350
\(4\) 10063.7 1.22848
\(5\) −36751.1 −1.05188 −0.525939 0.850522i \(-0.676286\pi\)
−0.525939 + 0.850522i \(0.676286\pi\)
\(6\) 98497.9 0.861874
\(7\) −177254. −0.569454 −0.284727 0.958609i \(-0.591903\pi\)
−0.284727 + 0.958609i \(0.591903\pi\)
\(8\) −252896. −0.341081
\(9\) 531441. 0.333333
\(10\) 4.96558e6 1.57025
\(11\) −8.38008e6 −1.42625 −0.713125 0.701037i \(-0.752721\pi\)
−0.713125 + 0.701037i \(0.752721\pi\)
\(12\) −7.33646e6 −0.709265
\(13\) 4.85093e6 0.278736 0.139368 0.990241i \(-0.455493\pi\)
0.139368 + 0.990241i \(0.455493\pi\)
\(14\) 2.39495e7 0.850087
\(15\) 2.67916e7 0.607302
\(16\) −4.82723e7 −0.719313
\(17\) 1.51868e7 0.152598 0.0762989 0.997085i \(-0.475690\pi\)
0.0762989 + 0.997085i \(0.475690\pi\)
\(18\) −7.18050e7 −0.497603
\(19\) −1.04615e8 −0.510146 −0.255073 0.966922i \(-0.582100\pi\)
−0.255073 + 0.966922i \(0.582100\pi\)
\(20\) −3.69853e8 −1.29221
\(21\) 1.29218e8 0.328775
\(22\) 1.13226e9 2.12912
\(23\) 5.03097e8 0.708632 0.354316 0.935126i \(-0.384714\pi\)
0.354316 + 0.935126i \(0.384714\pi\)
\(24\) 1.84361e8 0.196923
\(25\) 1.29940e8 0.106447
\(26\) −6.55428e8 −0.416100
\(27\) −3.87420e8 −0.192450
\(28\) −1.78384e9 −0.699565
\(29\) −4.08283e9 −1.27460 −0.637300 0.770616i \(-0.719949\pi\)
−0.637300 + 0.770616i \(0.719949\pi\)
\(30\) −3.61991e9 −0.906587
\(31\) −6.12832e9 −1.24020 −0.620098 0.784524i \(-0.712907\pi\)
−0.620098 + 0.784524i \(0.712907\pi\)
\(32\) 8.59398e9 1.41488
\(33\) 6.10907e9 0.823445
\(34\) −2.05195e9 −0.227800
\(35\) 6.51428e9 0.598996
\(36\) 5.34828e9 0.409494
\(37\) 9.81095e9 0.628637 0.314318 0.949318i \(-0.398224\pi\)
0.314318 + 0.949318i \(0.398224\pi\)
\(38\) 1.41349e10 0.761551
\(39\) −3.53633e9 −0.160928
\(40\) 9.29421e9 0.358775
\(41\) 3.36959e10 1.10785 0.553927 0.832565i \(-0.313129\pi\)
0.553927 + 0.832565i \(0.313129\pi\)
\(42\) −1.74592e10 −0.490798
\(43\) −3.54505e10 −0.855219 −0.427609 0.903964i \(-0.640644\pi\)
−0.427609 + 0.903964i \(0.640644\pi\)
\(44\) −8.43348e10 −1.75212
\(45\) −1.95310e10 −0.350626
\(46\) −6.79753e10 −1.05785
\(47\) 6.44491e10 0.872129 0.436065 0.899915i \(-0.356372\pi\)
0.436065 + 0.899915i \(0.356372\pi\)
\(48\) 3.51905e10 0.415296
\(49\) −6.54700e10 −0.675722
\(50\) −1.75567e10 −0.158905
\(51\) −1.10712e10 −0.0881024
\(52\) 4.88185e10 0.342423
\(53\) −1.40446e11 −0.870393 −0.435196 0.900336i \(-0.643321\pi\)
−0.435196 + 0.900336i \(0.643321\pi\)
\(54\) 5.23458e10 0.287291
\(55\) 3.07977e11 1.50024
\(56\) 4.48269e10 0.194230
\(57\) 7.62642e10 0.294533
\(58\) 5.51646e11 1.90274
\(59\) −4.21805e10 −0.130189
\(60\) 2.69623e11 0.746060
\(61\) −7.41838e11 −1.84359 −0.921797 0.387674i \(-0.873279\pi\)
−0.921797 + 0.387674i \(0.873279\pi\)
\(62\) 8.28020e11 1.85138
\(63\) −9.42001e10 −0.189818
\(64\) −7.65718e11 −1.39283
\(65\) −1.78277e11 −0.293197
\(66\) −8.25420e11 −1.22925
\(67\) 9.59565e11 1.29595 0.647975 0.761662i \(-0.275616\pi\)
0.647975 + 0.761662i \(0.275616\pi\)
\(68\) 1.52836e11 0.187464
\(69\) −3.66757e11 −0.409129
\(70\) −8.80169e11 −0.894188
\(71\) −7.60819e11 −0.704859 −0.352429 0.935838i \(-0.614644\pi\)
−0.352429 + 0.935838i \(0.614644\pi\)
\(72\) −1.34399e11 −0.113694
\(73\) −5.28101e11 −0.408430 −0.204215 0.978926i \(-0.565464\pi\)
−0.204215 + 0.978926i \(0.565464\pi\)
\(74\) −1.32559e12 −0.938435
\(75\) −9.47263e10 −0.0614572
\(76\) −1.05281e12 −0.626706
\(77\) 1.48540e12 0.812184
\(78\) 4.77807e11 0.240236
\(79\) 1.53934e11 0.0712457 0.0356229 0.999365i \(-0.488658\pi\)
0.0356229 + 0.999365i \(0.488658\pi\)
\(80\) 1.77406e12 0.756630
\(81\) 2.82430e11 0.111111
\(82\) −4.55278e12 −1.65382
\(83\) 4.32516e12 1.45210 0.726048 0.687644i \(-0.241355\pi\)
0.726048 + 0.687644i \(0.241355\pi\)
\(84\) 1.30042e12 0.403894
\(85\) −5.58132e11 −0.160514
\(86\) 4.78985e12 1.27668
\(87\) 2.97638e12 0.735891
\(88\) 2.11929e12 0.486466
\(89\) 3.47028e12 0.740166 0.370083 0.928999i \(-0.379329\pi\)
0.370083 + 0.928999i \(0.379329\pi\)
\(90\) 2.63891e12 0.523418
\(91\) −8.59848e11 −0.158728
\(92\) 5.06303e12 0.870541
\(93\) 4.46755e12 0.716028
\(94\) −8.70796e12 −1.30192
\(95\) 3.84471e12 0.536611
\(96\) −6.26501e12 −0.816881
\(97\) 5.67818e12 0.692138 0.346069 0.938209i \(-0.387516\pi\)
0.346069 + 0.938209i \(0.387516\pi\)
\(98\) 8.84590e12 1.00872
\(99\) −4.45352e12 −0.475416
\(100\) 1.30768e12 0.130768
\(101\) 2.43651e12 0.228391 0.114196 0.993458i \(-0.463571\pi\)
0.114196 + 0.993458i \(0.463571\pi\)
\(102\) 1.49587e12 0.131520
\(103\) 4.75427e12 0.392321 0.196161 0.980572i \(-0.437153\pi\)
0.196161 + 0.980572i \(0.437153\pi\)
\(104\) −1.22678e12 −0.0950716
\(105\) −4.74891e12 −0.345831
\(106\) 1.89761e13 1.29933
\(107\) 1.94033e13 1.24992 0.624958 0.780658i \(-0.285116\pi\)
0.624958 + 0.780658i \(0.285116\pi\)
\(108\) −3.89889e12 −0.236422
\(109\) 3.10438e13 1.77297 0.886487 0.462754i \(-0.153139\pi\)
0.886487 + 0.462754i \(0.153139\pi\)
\(110\) −4.16119e13 −2.23957
\(111\) −7.15218e12 −0.362944
\(112\) 8.55646e12 0.409616
\(113\) 2.47488e13 1.11826 0.559132 0.829078i \(-0.311134\pi\)
0.559132 + 0.829078i \(0.311134\pi\)
\(114\) −1.03043e13 −0.439682
\(115\) −1.84894e13 −0.745394
\(116\) −4.10885e13 −1.56582
\(117\) 2.57798e12 0.0929121
\(118\) 5.69917e12 0.194347
\(119\) −2.69192e12 −0.0868975
\(120\) −6.77548e12 −0.207139
\(121\) 3.57029e13 1.03419
\(122\) 1.00233e14 2.75213
\(123\) −2.45643e13 −0.639620
\(124\) −6.16737e13 −1.52356
\(125\) 4.00867e13 0.939909
\(126\) 1.27277e13 0.283362
\(127\) 9.17463e13 1.94028 0.970140 0.242545i \(-0.0779822\pi\)
0.970140 + 0.242545i \(0.0779822\pi\)
\(128\) 3.30572e13 0.664356
\(129\) 2.58434e13 0.493761
\(130\) 2.40877e13 0.437687
\(131\) 2.51976e12 0.0435607 0.0217804 0.999763i \(-0.493067\pi\)
0.0217804 + 0.999763i \(0.493067\pi\)
\(132\) 6.14801e13 1.01159
\(133\) 1.85434e13 0.290505
\(134\) −1.29650e14 −1.93461
\(135\) 1.42381e13 0.202434
\(136\) −3.84068e12 −0.0520482
\(137\) 1.51614e12 0.0195909 0.00979545 0.999952i \(-0.496882\pi\)
0.00979545 + 0.999952i \(0.496882\pi\)
\(138\) 4.95540e13 0.610751
\(139\) 8.90817e13 1.04759 0.523796 0.851844i \(-0.324515\pi\)
0.523796 + 0.851844i \(0.324515\pi\)
\(140\) 6.55580e13 0.735857
\(141\) −4.69834e13 −0.503524
\(142\) 1.02797e14 1.05222
\(143\) −4.06512e13 −0.397547
\(144\) −2.56539e13 −0.239771
\(145\) 1.50048e14 1.34072
\(146\) 7.13537e13 0.609709
\(147\) 4.77276e13 0.390128
\(148\) 9.87347e13 0.772269
\(149\) 1.99945e14 1.49692 0.748462 0.663177i \(-0.230792\pi\)
0.748462 + 0.663177i \(0.230792\pi\)
\(150\) 1.27988e13 0.0917439
\(151\) −1.57341e14 −1.08017 −0.540086 0.841610i \(-0.681608\pi\)
−0.540086 + 0.841610i \(0.681608\pi\)
\(152\) 2.64567e13 0.174001
\(153\) 8.07089e12 0.0508660
\(154\) −2.00698e14 −1.21244
\(155\) 2.25222e14 1.30453
\(156\) −3.55887e13 −0.197698
\(157\) 1.30345e13 0.0694618 0.0347309 0.999397i \(-0.488943\pi\)
0.0347309 + 0.999397i \(0.488943\pi\)
\(158\) −2.07986e13 −0.106356
\(159\) 1.02385e14 0.502521
\(160\) −3.15838e14 −1.48828
\(161\) −8.91759e13 −0.403533
\(162\) −3.81601e13 −0.165868
\(163\) −3.61627e14 −1.51023 −0.755113 0.655595i \(-0.772418\pi\)
−0.755113 + 0.655595i \(0.772418\pi\)
\(164\) 3.39107e14 1.36098
\(165\) −2.24515e14 −0.866164
\(166\) −5.84389e14 −2.16770
\(167\) −5.37036e14 −1.91578 −0.957892 0.287130i \(-0.907299\pi\)
−0.957892 + 0.287130i \(0.907299\pi\)
\(168\) −3.26788e13 −0.112139
\(169\) −2.79344e14 −0.922306
\(170\) 7.54113e13 0.239617
\(171\) −5.55966e13 −0.170049
\(172\) −3.56764e14 −1.05062
\(173\) −5.14188e14 −1.45822 −0.729108 0.684398i \(-0.760065\pi\)
−0.729108 + 0.684398i \(0.760065\pi\)
\(174\) −4.02150e14 −1.09855
\(175\) −2.30324e13 −0.0606167
\(176\) 4.04526e14 1.02592
\(177\) 3.07496e13 0.0751646
\(178\) −4.68882e14 −1.10493
\(179\) 4.60252e14 1.04581 0.522903 0.852392i \(-0.324849\pi\)
0.522903 + 0.852392i \(0.324849\pi\)
\(180\) −1.96555e14 −0.430738
\(181\) 2.21457e14 0.468143 0.234072 0.972219i \(-0.424795\pi\)
0.234072 + 0.972219i \(0.424795\pi\)
\(182\) 1.16177e14 0.236950
\(183\) 5.40800e14 1.06440
\(184\) −1.27231e14 −0.241701
\(185\) −3.60563e14 −0.661249
\(186\) −6.03627e14 −1.06889
\(187\) −1.27267e14 −0.217643
\(188\) 6.48598e14 1.07140
\(189\) 6.86719e13 0.109592
\(190\) −5.19473e14 −0.801059
\(191\) 7.56917e14 1.12806 0.564029 0.825755i \(-0.309251\pi\)
0.564029 + 0.825755i \(0.309251\pi\)
\(192\) 5.58208e14 0.804152
\(193\) −1.80083e14 −0.250813 −0.125407 0.992105i \(-0.540024\pi\)
−0.125407 + 0.992105i \(0.540024\pi\)
\(194\) −7.67200e14 −1.03323
\(195\) 1.29964e14 0.169277
\(196\) −6.58872e14 −0.830112
\(197\) 9.49115e14 1.15688 0.578440 0.815725i \(-0.303662\pi\)
0.578440 + 0.815725i \(0.303662\pi\)
\(198\) 6.01731e14 0.709707
\(199\) 3.59484e14 0.410331 0.205166 0.978727i \(-0.434227\pi\)
0.205166 + 0.978727i \(0.434227\pi\)
\(200\) −3.28614e13 −0.0363070
\(201\) −6.99523e14 −0.748217
\(202\) −3.29206e14 −0.340945
\(203\) 7.23698e14 0.725827
\(204\) −1.11417e14 −0.108232
\(205\) −1.23836e15 −1.16533
\(206\) −6.42367e14 −0.585661
\(207\) 2.67366e14 0.236211
\(208\) −2.34166e14 −0.200499
\(209\) 8.76680e14 0.727596
\(210\) 6.41643e14 0.516260
\(211\) −1.32993e15 −1.03751 −0.518755 0.854923i \(-0.673604\pi\)
−0.518755 + 0.854923i \(0.673604\pi\)
\(212\) −1.41341e15 −1.06926
\(213\) 5.54637e14 0.406950
\(214\) −2.62165e15 −1.86589
\(215\) 1.30284e15 0.899586
\(216\) 9.79772e13 0.0656410
\(217\) 1.08627e15 0.706235
\(218\) −4.19444e15 −2.64671
\(219\) 3.84985e14 0.235807
\(220\) 3.09940e15 1.84302
\(221\) 7.36702e13 0.0425346
\(222\) 9.66358e14 0.541806
\(223\) −1.66917e15 −0.908907 −0.454454 0.890770i \(-0.650165\pi\)
−0.454454 + 0.890770i \(0.650165\pi\)
\(224\) −1.52332e15 −0.805709
\(225\) 6.90555e13 0.0354823
\(226\) −3.34391e15 −1.66936
\(227\) 2.67853e15 1.29935 0.649677 0.760210i \(-0.274904\pi\)
0.649677 + 0.760210i \(0.274904\pi\)
\(228\) 7.67502e14 0.361829
\(229\) 2.33451e15 1.06971 0.534853 0.844945i \(-0.320367\pi\)
0.534853 + 0.844945i \(0.320367\pi\)
\(230\) 2.49817e15 1.11273
\(231\) −1.08286e15 −0.468915
\(232\) 1.03253e15 0.434742
\(233\) 5.83561e14 0.238931 0.119466 0.992838i \(-0.461882\pi\)
0.119466 + 0.992838i \(0.461882\pi\)
\(234\) −3.48321e14 −0.138700
\(235\) −2.36857e15 −0.917373
\(236\) −4.24493e14 −0.159935
\(237\) −1.12218e14 −0.0411337
\(238\) 3.63716e14 0.129722
\(239\) −2.79102e15 −0.968670 −0.484335 0.874883i \(-0.660938\pi\)
−0.484335 + 0.874883i \(0.660938\pi\)
\(240\) −1.29329e15 −0.436840
\(241\) 8.64348e14 0.284170 0.142085 0.989854i \(-0.454619\pi\)
0.142085 + 0.989854i \(0.454619\pi\)
\(242\) −4.82396e15 −1.54385
\(243\) −2.05891e14 −0.0641500
\(244\) −7.46566e15 −2.26482
\(245\) 2.40609e15 0.710777
\(246\) 3.31898e15 0.954831
\(247\) −5.07479e14 −0.142196
\(248\) 1.54983e15 0.423007
\(249\) −3.15305e15 −0.838367
\(250\) −5.41627e15 −1.40311
\(251\) 1.93339e15 0.488023 0.244011 0.969772i \(-0.421537\pi\)
0.244011 + 0.969772i \(0.421537\pi\)
\(252\) −9.48004e14 −0.233188
\(253\) −4.21599e15 −1.01069
\(254\) −1.23962e16 −2.89647
\(255\) 4.06878e14 0.0926730
\(256\) 1.80628e15 0.401076
\(257\) 5.14069e15 1.11290 0.556450 0.830881i \(-0.312163\pi\)
0.556450 + 0.830881i \(0.312163\pi\)
\(258\) −3.49180e15 −0.737091
\(259\) −1.73903e15 −0.357980
\(260\) −1.79413e15 −0.360187
\(261\) −2.16978e15 −0.424867
\(262\) −3.40454e14 −0.0650279
\(263\) −5.52213e15 −1.02895 −0.514475 0.857505i \(-0.672013\pi\)
−0.514475 + 0.857505i \(0.672013\pi\)
\(264\) −1.54496e15 −0.280861
\(265\) 5.16153e15 0.915547
\(266\) −2.50547e15 −0.433669
\(267\) −2.52983e15 −0.427335
\(268\) 9.65680e15 1.59205
\(269\) −5.12039e15 −0.823974 −0.411987 0.911190i \(-0.635165\pi\)
−0.411987 + 0.911190i \(0.635165\pi\)
\(270\) −1.92377e15 −0.302196
\(271\) −1.04149e16 −1.59718 −0.798589 0.601876i \(-0.794420\pi\)
−0.798589 + 0.601876i \(0.794420\pi\)
\(272\) −7.33102e14 −0.109766
\(273\) 6.26829e14 0.0916414
\(274\) −2.04851e14 −0.0292455
\(275\) −1.08891e15 −0.151820
\(276\) −3.69095e15 −0.502607
\(277\) −6.95643e15 −0.925268 −0.462634 0.886549i \(-0.653096\pi\)
−0.462634 + 0.886549i \(0.653096\pi\)
\(278\) −1.20362e16 −1.56386
\(279\) −3.25684e15 −0.413399
\(280\) −1.64744e15 −0.204306
\(281\) −3.47038e15 −0.420520 −0.210260 0.977646i \(-0.567431\pi\)
−0.210260 + 0.977646i \(0.567431\pi\)
\(282\) 6.34810e15 0.751666
\(283\) 6.56657e15 0.759848 0.379924 0.925018i \(-0.375950\pi\)
0.379924 + 0.925018i \(0.375950\pi\)
\(284\) −7.65668e15 −0.865907
\(285\) −2.80279e15 −0.309813
\(286\) 5.49253e15 0.593463
\(287\) −5.97274e15 −0.630872
\(288\) 4.56719e15 0.471626
\(289\) −9.67394e15 −0.976714
\(290\) −2.02736e16 −2.00145
\(291\) −4.13939e15 −0.399606
\(292\) −5.31466e15 −0.501750
\(293\) 1.71602e16 1.58446 0.792232 0.610221i \(-0.208919\pi\)
0.792232 + 0.610221i \(0.208919\pi\)
\(294\) −6.44866e15 −0.582387
\(295\) 1.55018e15 0.136943
\(296\) −2.48115e15 −0.214416
\(297\) 3.24661e15 0.274482
\(298\) −2.70153e16 −2.23462
\(299\) 2.44049e15 0.197521
\(300\) −9.53300e14 −0.0754990
\(301\) 6.28374e15 0.487008
\(302\) 2.12590e16 1.61249
\(303\) −1.77622e15 −0.131862
\(304\) 5.05000e15 0.366955
\(305\) 2.72634e16 1.93923
\(306\) −1.09049e15 −0.0759332
\(307\) 1.11248e15 0.0758390 0.0379195 0.999281i \(-0.487927\pi\)
0.0379195 + 0.999281i \(0.487927\pi\)
\(308\) 1.49487e16 0.997754
\(309\) −3.46586e15 −0.226507
\(310\) −3.04307e16 −1.94742
\(311\) −1.98978e16 −1.24699 −0.623493 0.781829i \(-0.714287\pi\)
−0.623493 + 0.781829i \(0.714287\pi\)
\(312\) 8.94324e14 0.0548896
\(313\) −1.75088e15 −0.105249 −0.0526246 0.998614i \(-0.516759\pi\)
−0.0526246 + 0.998614i \(0.516759\pi\)
\(314\) −1.76114e15 −0.103693
\(315\) 3.46196e15 0.199665
\(316\) 1.54915e15 0.0875241
\(317\) 4.90894e15 0.271708 0.135854 0.990729i \(-0.456622\pi\)
0.135854 + 0.990729i \(0.456622\pi\)
\(318\) −1.38336e16 −0.750169
\(319\) 3.42144e16 1.81790
\(320\) 2.81410e16 1.46509
\(321\) −1.41450e16 −0.721640
\(322\) 1.20489e16 0.602399
\(323\) −1.58876e15 −0.0778472
\(324\) 2.84229e15 0.136498
\(325\) 6.30331e14 0.0296706
\(326\) 4.88608e16 2.25448
\(327\) −2.26309e16 −1.02363
\(328\) −8.52157e15 −0.377868
\(329\) −1.14239e16 −0.496638
\(330\) 3.03351e16 1.29302
\(331\) 1.20282e16 0.502710 0.251355 0.967895i \(-0.419124\pi\)
0.251355 + 0.967895i \(0.419124\pi\)
\(332\) 4.35273e16 1.78387
\(333\) 5.21394e15 0.209546
\(334\) 7.25610e16 2.85990
\(335\) −3.52651e16 −1.36318
\(336\) −6.23766e15 −0.236492
\(337\) −2.09057e16 −0.777447 −0.388723 0.921355i \(-0.627084\pi\)
−0.388723 + 0.921355i \(0.627084\pi\)
\(338\) 3.77432e16 1.37683
\(339\) −1.80419e16 −0.645630
\(340\) −5.61689e15 −0.197189
\(341\) 5.13558e16 1.76883
\(342\) 7.51186e15 0.253850
\(343\) 2.87788e16 0.954247
\(344\) 8.96529e15 0.291699
\(345\) 1.34787e16 0.430353
\(346\) 6.94738e16 2.17684
\(347\) 2.79978e16 0.860959 0.430479 0.902600i \(-0.358345\pi\)
0.430479 + 0.902600i \(0.358345\pi\)
\(348\) 2.99535e16 0.904029
\(349\) −9.68362e15 −0.286862 −0.143431 0.989660i \(-0.545813\pi\)
−0.143431 + 0.989660i \(0.545813\pi\)
\(350\) 3.11200e15 0.0904892
\(351\) −1.87935e15 −0.0536428
\(352\) −7.20182e16 −2.01797
\(353\) −4.80443e16 −1.32162 −0.660809 0.750554i \(-0.729787\pi\)
−0.660809 + 0.750554i \(0.729787\pi\)
\(354\) −4.15470e15 −0.112206
\(355\) 2.79609e16 0.741425
\(356\) 3.49239e16 0.909280
\(357\) 1.96241e15 0.0501703
\(358\) −6.21864e16 −1.56119
\(359\) −4.48117e16 −1.10478 −0.552392 0.833584i \(-0.686285\pi\)
−0.552392 + 0.833584i \(0.686285\pi\)
\(360\) 4.93933e15 0.119592
\(361\) −3.11087e16 −0.739751
\(362\) −2.99219e16 −0.698849
\(363\) −2.60274e16 −0.597088
\(364\) −8.65327e15 −0.194994
\(365\) 1.94083e16 0.429619
\(366\) −7.30695e16 −1.58895
\(367\) 1.97937e16 0.422861 0.211430 0.977393i \(-0.432188\pi\)
0.211430 + 0.977393i \(0.432188\pi\)
\(368\) −2.42856e16 −0.509728
\(369\) 1.79074e16 0.369285
\(370\) 4.87170e16 0.987119
\(371\) 2.48946e16 0.495649
\(372\) 4.49602e16 0.879627
\(373\) 6.21356e16 1.19463 0.597315 0.802007i \(-0.296234\pi\)
0.597315 + 0.802007i \(0.296234\pi\)
\(374\) 1.71955e16 0.324899
\(375\) −2.92232e16 −0.542657
\(376\) −1.62989e16 −0.297466
\(377\) −1.98055e16 −0.355277
\(378\) −9.27851e15 −0.163599
\(379\) −2.69500e16 −0.467094 −0.233547 0.972345i \(-0.575033\pi\)
−0.233547 + 0.972345i \(0.575033\pi\)
\(380\) 3.86921e16 0.659218
\(381\) −6.68831e16 −1.12022
\(382\) −1.02270e17 −1.68398
\(383\) −2.91675e16 −0.472179 −0.236089 0.971731i \(-0.575866\pi\)
−0.236089 + 0.971731i \(0.575866\pi\)
\(384\) −2.40987e16 −0.383566
\(385\) −5.45902e16 −0.854318
\(386\) 2.43317e16 0.374417
\(387\) −1.88398e16 −0.285073
\(388\) 5.71436e16 0.850279
\(389\) 9.35821e16 1.36937 0.684684 0.728840i \(-0.259940\pi\)
0.684684 + 0.728840i \(0.259940\pi\)
\(390\) −1.75599e16 −0.252699
\(391\) 7.64043e15 0.108136
\(392\) 1.65571e16 0.230476
\(393\) −1.83690e15 −0.0251498
\(394\) −1.28238e17 −1.72700
\(395\) −5.65725e15 −0.0749418
\(396\) −4.48190e16 −0.584041
\(397\) −2.26960e16 −0.290945 −0.145473 0.989362i \(-0.546470\pi\)
−0.145473 + 0.989362i \(0.546470\pi\)
\(398\) −4.85712e16 −0.612546
\(399\) −1.35181e16 −0.167723
\(400\) −6.27251e15 −0.0765687
\(401\) 6.63148e16 0.796475 0.398238 0.917282i \(-0.369622\pi\)
0.398238 + 0.917282i \(0.369622\pi\)
\(402\) 9.45151e16 1.11695
\(403\) −2.97281e16 −0.345688
\(404\) 2.45204e16 0.280574
\(405\) −1.03796e16 −0.116875
\(406\) −9.77815e16 −1.08352
\(407\) −8.22165e16 −0.896593
\(408\) 2.79986e15 0.0300500
\(409\) 3.74208e16 0.395286 0.197643 0.980274i \(-0.436671\pi\)
0.197643 + 0.980274i \(0.436671\pi\)
\(410\) 1.67320e17 1.73961
\(411\) −1.10526e15 −0.0113108
\(412\) 4.78457e16 0.481960
\(413\) 7.47667e15 0.0741366
\(414\) −3.61249e16 −0.352617
\(415\) −1.58955e17 −1.52743
\(416\) 4.16888e16 0.394378
\(417\) −6.49406e16 −0.604828
\(418\) −1.18451e17 −1.08616
\(419\) −2.41263e16 −0.217821 −0.108910 0.994052i \(-0.534736\pi\)
−0.108910 + 0.994052i \(0.534736\pi\)
\(420\) −4.77917e16 −0.424847
\(421\) 2.19706e16 0.192313 0.0961563 0.995366i \(-0.469345\pi\)
0.0961563 + 0.995366i \(0.469345\pi\)
\(422\) 1.79692e17 1.54881
\(423\) 3.42509e16 0.290710
\(424\) 3.55182e16 0.296874
\(425\) 1.97337e15 0.0162436
\(426\) −7.49391e16 −0.607500
\(427\) 1.31494e17 1.04984
\(428\) 1.95270e17 1.53550
\(429\) 2.96347e16 0.229524
\(430\) −1.76032e17 −1.34291
\(431\) 7.37220e16 0.553981 0.276991 0.960873i \(-0.410663\pi\)
0.276991 + 0.960873i \(0.410663\pi\)
\(432\) 1.87017e16 0.138432
\(433\) 9.16974e16 0.668630 0.334315 0.942461i \(-0.391495\pi\)
0.334315 + 0.942461i \(0.391495\pi\)
\(434\) −1.46770e17 −1.05428
\(435\) −1.09385e17 −0.774067
\(436\) 3.12416e17 2.17807
\(437\) −5.26313e16 −0.361506
\(438\) −5.20168e16 −0.352016
\(439\) 1.77992e17 1.18681 0.593404 0.804905i \(-0.297784\pi\)
0.593404 + 0.804905i \(0.297784\pi\)
\(440\) −7.78862e16 −0.511703
\(441\) −3.47934e16 −0.225241
\(442\) −9.95385e15 −0.0634960
\(443\) 1.71435e17 1.07765 0.538823 0.842419i \(-0.318869\pi\)
0.538823 + 0.842419i \(0.318869\pi\)
\(444\) −7.19776e16 −0.445870
\(445\) −1.27536e17 −0.778564
\(446\) 2.25528e17 1.35683
\(447\) −1.45760e17 −0.864250
\(448\) 1.35727e17 0.793155
\(449\) 1.55418e17 0.895158 0.447579 0.894244i \(-0.352286\pi\)
0.447579 + 0.894244i \(0.352286\pi\)
\(450\) −9.33035e15 −0.0529684
\(451\) −2.82374e17 −1.58008
\(452\) 2.49065e17 1.37377
\(453\) 1.14702e17 0.623637
\(454\) −3.61906e17 −1.93969
\(455\) 3.16003e16 0.166962
\(456\) −1.92869e16 −0.100460
\(457\) −1.55484e17 −0.798417 −0.399208 0.916860i \(-0.630715\pi\)
−0.399208 + 0.916860i \(0.630715\pi\)
\(458\) −3.15424e17 −1.59687
\(459\) −5.88368e15 −0.0293675
\(460\) −1.86072e17 −0.915703
\(461\) 1.69476e17 0.822342 0.411171 0.911558i \(-0.365120\pi\)
0.411171 + 0.911558i \(0.365120\pi\)
\(462\) 1.46309e17 0.700001
\(463\) −5.34879e16 −0.252336 −0.126168 0.992009i \(-0.540268\pi\)
−0.126168 + 0.992009i \(0.540268\pi\)
\(464\) 1.97087e17 0.916837
\(465\) −1.64187e17 −0.753174
\(466\) −7.88471e16 −0.356679
\(467\) −7.43957e16 −0.331885 −0.165943 0.986135i \(-0.553067\pi\)
−0.165943 + 0.986135i \(0.553067\pi\)
\(468\) 2.59441e16 0.114141
\(469\) −1.70087e17 −0.737984
\(470\) 3.20027e17 1.36946
\(471\) −9.50214e15 −0.0401038
\(472\) 1.06673e16 0.0444049
\(473\) 2.97078e17 1.21976
\(474\) 1.51622e16 0.0614049
\(475\) −1.35937e16 −0.0543035
\(476\) −2.70908e16 −0.106752
\(477\) −7.46386e16 −0.290131
\(478\) 3.77105e17 1.44604
\(479\) −3.24024e17 −1.22573 −0.612867 0.790186i \(-0.709984\pi\)
−0.612867 + 0.790186i \(0.709984\pi\)
\(480\) 2.30246e17 0.859259
\(481\) 4.75922e16 0.175224
\(482\) −1.16785e17 −0.424212
\(483\) 6.50093e16 0.232980
\(484\) 3.59305e17 1.27048
\(485\) −2.08679e17 −0.728045
\(486\) 2.78187e16 0.0957638
\(487\) −4.34696e17 −1.47655 −0.738274 0.674501i \(-0.764359\pi\)
−0.738274 + 0.674501i \(0.764359\pi\)
\(488\) 1.87608e17 0.628814
\(489\) 2.63626e17 0.871929
\(490\) −3.25096e17 −1.06105
\(491\) −1.57154e17 −0.506170 −0.253085 0.967444i \(-0.581445\pi\)
−0.253085 + 0.967444i \(0.581445\pi\)
\(492\) −2.47209e17 −0.785761
\(493\) −6.20051e16 −0.194501
\(494\) 6.85674e16 0.212272
\(495\) 1.63672e17 0.500080
\(496\) 2.95828e17 0.892090
\(497\) 1.34858e17 0.401385
\(498\) 4.26020e17 1.25152
\(499\) 1.37480e17 0.398643 0.199322 0.979934i \(-0.436126\pi\)
0.199322 + 0.979934i \(0.436126\pi\)
\(500\) 4.03422e17 1.15466
\(501\) 3.91499e17 1.10608
\(502\) −2.61227e17 −0.728525
\(503\) −2.33300e17 −0.642278 −0.321139 0.947032i \(-0.604066\pi\)
−0.321139 + 0.947032i \(0.604066\pi\)
\(504\) 2.38228e16 0.0647433
\(505\) −8.95444e16 −0.240240
\(506\) 5.69638e17 1.50876
\(507\) 2.03641e17 0.532494
\(508\) 9.23310e17 2.38360
\(509\) 3.95297e16 0.100753 0.0503765 0.998730i \(-0.483958\pi\)
0.0503765 + 0.998730i \(0.483958\pi\)
\(510\) −5.49748e16 −0.138343
\(511\) 9.36080e16 0.232583
\(512\) −5.14858e17 −1.26309
\(513\) 4.05299e16 0.0981777
\(514\) −6.94578e17 −1.66135
\(515\) −1.74725e17 −0.412674
\(516\) 2.60081e17 0.606577
\(517\) −5.40088e17 −1.24387
\(518\) 2.34967e17 0.534396
\(519\) 3.74843e17 0.841902
\(520\) 4.50856e16 0.100004
\(521\) 7.26203e17 1.59079 0.795395 0.606092i \(-0.207263\pi\)
0.795395 + 0.606092i \(0.207263\pi\)
\(522\) 2.93167e17 0.634245
\(523\) −3.14235e17 −0.671419 −0.335709 0.941966i \(-0.608976\pi\)
−0.335709 + 0.941966i \(0.608976\pi\)
\(524\) 2.53581e16 0.0535136
\(525\) 1.67906e16 0.0349970
\(526\) 7.46116e17 1.53603
\(527\) −9.30696e16 −0.189251
\(528\) −2.94899e17 −0.592315
\(529\) −2.50930e17 −0.497841
\(530\) −6.97394e17 −1.36674
\(531\) −2.24165e16 −0.0433963
\(532\) 1.86616e17 0.356880
\(533\) 1.63457e17 0.308799
\(534\) 3.41815e17 0.637930
\(535\) −7.13093e17 −1.31476
\(536\) −2.42670e17 −0.442023
\(537\) −3.35524e17 −0.603796
\(538\) 6.91836e17 1.23004
\(539\) 5.48644e17 0.963748
\(540\) 1.43289e17 0.248687
\(541\) 1.07834e17 0.184915 0.0924574 0.995717i \(-0.470528\pi\)
0.0924574 + 0.995717i \(0.470528\pi\)
\(542\) 1.40719e18 2.38429
\(543\) −1.61442e17 −0.270283
\(544\) 1.30515e17 0.215908
\(545\) −1.14089e18 −1.86495
\(546\) −8.46932e16 −0.136803
\(547\) −1.07320e18 −1.71302 −0.856509 0.516132i \(-0.827371\pi\)
−0.856509 + 0.516132i \(0.827371\pi\)
\(548\) 1.52580e16 0.0240671
\(549\) −3.94243e17 −0.614531
\(550\) 1.47126e17 0.226638
\(551\) 4.27124e17 0.650232
\(552\) 9.27516e16 0.139546
\(553\) −2.72855e16 −0.0405712
\(554\) 9.39909e17 1.38125
\(555\) 2.62850e17 0.381772
\(556\) 8.96494e17 1.28695
\(557\) 2.97270e17 0.421787 0.210893 0.977509i \(-0.432363\pi\)
0.210893 + 0.977509i \(0.432363\pi\)
\(558\) 4.40044e17 0.617126
\(559\) −1.71968e17 −0.238381
\(560\) −3.14459e17 −0.430866
\(561\) 9.27773e16 0.125656
\(562\) 4.68897e17 0.627756
\(563\) −9.38201e17 −1.24163 −0.620814 0.783958i \(-0.713198\pi\)
−0.620814 + 0.783958i \(0.713198\pi\)
\(564\) −4.72828e17 −0.618570
\(565\) −9.09546e17 −1.17628
\(566\) −8.87234e17 −1.13431
\(567\) −5.00618e16 −0.0632727
\(568\) 1.92408e17 0.240414
\(569\) −2.02313e17 −0.249916 −0.124958 0.992162i \(-0.539880\pi\)
−0.124958 + 0.992162i \(0.539880\pi\)
\(570\) 3.78696e17 0.462492
\(571\) 8.75809e17 1.05749 0.528743 0.848782i \(-0.322664\pi\)
0.528743 + 0.848782i \(0.322664\pi\)
\(572\) −4.09102e17 −0.488380
\(573\) −5.51792e17 −0.651284
\(574\) 8.06999e17 0.941772
\(575\) 6.53724e16 0.0754317
\(576\) −4.06934e17 −0.464278
\(577\) 1.28222e17 0.144651 0.0723254 0.997381i \(-0.476958\pi\)
0.0723254 + 0.997381i \(0.476958\pi\)
\(578\) 1.30708e18 1.45805
\(579\) 1.31281e17 0.144807
\(580\) 1.51005e18 1.64706
\(581\) −7.66653e17 −0.826902
\(582\) 5.59289e17 0.596536
\(583\) 1.17695e18 1.24140
\(584\) 1.33555e17 0.139308
\(585\) −9.47438e16 −0.0977322
\(586\) −2.31858e18 −2.36530
\(587\) 1.30462e18 1.31624 0.658122 0.752911i \(-0.271351\pi\)
0.658122 + 0.752911i \(0.271351\pi\)
\(588\) 4.80318e17 0.479266
\(589\) 6.41113e17 0.632681
\(590\) −2.09451e17 −0.204430
\(591\) −6.91905e17 −0.667925
\(592\) −4.73597e17 −0.452187
\(593\) 6.13712e17 0.579575 0.289787 0.957091i \(-0.406415\pi\)
0.289787 + 0.957091i \(0.406415\pi\)
\(594\) −4.38662e17 −0.409749
\(595\) 9.89311e16 0.0914056
\(596\) 2.01219e18 1.83895
\(597\) −2.62064e17 −0.236905
\(598\) −3.29744e17 −0.294862
\(599\) −1.94525e18 −1.72068 −0.860340 0.509721i \(-0.829749\pi\)
−0.860340 + 0.509721i \(0.829749\pi\)
\(600\) 2.39559e16 0.0209619
\(601\) 1.80265e18 1.56036 0.780182 0.625552i \(-0.215126\pi\)
0.780182 + 0.625552i \(0.215126\pi\)
\(602\) −8.49020e17 −0.727011
\(603\) 5.09952e17 0.431983
\(604\) −1.58344e18 −1.32697
\(605\) −1.31212e18 −1.08784
\(606\) 2.39991e17 0.196844
\(607\) −4.92005e17 −0.399248 −0.199624 0.979873i \(-0.563972\pi\)
−0.199624 + 0.979873i \(0.563972\pi\)
\(608\) −8.99057e17 −0.721795
\(609\) −5.27576e17 −0.419056
\(610\) −3.68366e18 −2.89491
\(611\) 3.12638e17 0.243094
\(612\) 8.12233e16 0.0624879
\(613\) 6.31596e17 0.480780 0.240390 0.970676i \(-0.422725\pi\)
0.240390 + 0.970676i \(0.422725\pi\)
\(614\) −1.50311e17 −0.113213
\(615\) 9.02766e17 0.672802
\(616\) −3.75653e17 −0.277020
\(617\) 6.34814e17 0.463226 0.231613 0.972808i \(-0.425600\pi\)
0.231613 + 0.972808i \(0.425600\pi\)
\(618\) 4.68286e17 0.338131
\(619\) −1.99491e18 −1.42539 −0.712694 0.701475i \(-0.752525\pi\)
−0.712694 + 0.701475i \(0.752525\pi\)
\(620\) 2.26658e18 1.60260
\(621\) −1.94910e17 −0.136376
\(622\) 2.68846e18 1.86151
\(623\) −6.15120e17 −0.421491
\(624\) 1.70707e17 0.115758
\(625\) −1.63185e18 −1.09512
\(626\) 2.36568e17 0.157117
\(627\) −6.39100e17 −0.420078
\(628\) 1.31176e17 0.0853326
\(629\) 1.48997e17 0.0959286
\(630\) −4.67758e17 −0.298063
\(631\) 3.26786e16 0.0206098 0.0103049 0.999947i \(-0.496720\pi\)
0.0103049 + 0.999947i \(0.496720\pi\)
\(632\) −3.89294e16 −0.0243006
\(633\) 9.69518e17 0.599007
\(634\) −6.63266e17 −0.405609
\(635\) −3.37178e18 −2.04094
\(636\) 1.03037e18 0.617339
\(637\) −3.17591e17 −0.188348
\(638\) −4.62284e18 −2.71378
\(639\) −4.04330e17 −0.234953
\(640\) −1.21489e18 −0.698821
\(641\) 5.86346e17 0.333869 0.166935 0.985968i \(-0.446613\pi\)
0.166935 + 0.985968i \(0.446613\pi\)
\(642\) 1.91119e18 1.07727
\(643\) 1.70659e18 0.952267 0.476133 0.879373i \(-0.342038\pi\)
0.476133 + 0.879373i \(0.342038\pi\)
\(644\) −8.97442e17 −0.495734
\(645\) −9.49774e17 −0.519376
\(646\) 2.14664e17 0.116211
\(647\) −2.16639e18 −1.16107 −0.580537 0.814234i \(-0.697157\pi\)
−0.580537 + 0.814234i \(0.697157\pi\)
\(648\) −7.14253e16 −0.0378979
\(649\) 3.53476e17 0.185682
\(650\) −8.51663e16 −0.0442926
\(651\) −7.91891e17 −0.407745
\(652\) −3.63932e18 −1.85529
\(653\) 1.60954e16 0.00812394 0.00406197 0.999992i \(-0.498707\pi\)
0.00406197 + 0.999992i \(0.498707\pi\)
\(654\) 3.05775e18 1.52808
\(655\) −9.26038e16 −0.0458206
\(656\) −1.62658e18 −0.796894
\(657\) −2.80654e17 −0.136143
\(658\) 1.54352e18 0.741386
\(659\) 2.79209e18 1.32793 0.663965 0.747764i \(-0.268873\pi\)
0.663965 + 0.747764i \(0.268873\pi\)
\(660\) −2.25946e18 −1.06407
\(661\) −3.90908e18 −1.82291 −0.911455 0.411401i \(-0.865040\pi\)
−0.911455 + 0.411401i \(0.865040\pi\)
\(662\) −1.62517e18 −0.750451
\(663\) −5.37056e16 −0.0245573
\(664\) −1.09382e18 −0.495282
\(665\) −6.81490e17 −0.305576
\(666\) −7.04475e17 −0.312812
\(667\) −2.05406e18 −0.903222
\(668\) −5.40459e18 −2.35351
\(669\) 1.21683e18 0.524758
\(670\) 4.76479e18 2.03497
\(671\) 6.21666e18 2.62942
\(672\) 1.11050e18 0.465176
\(673\) −4.15377e18 −1.72323 −0.861617 0.507559i \(-0.830548\pi\)
−0.861617 + 0.507559i \(0.830548\pi\)
\(674\) 2.82465e18 1.16058
\(675\) −5.03415e16 −0.0204857
\(676\) −2.81124e18 −1.13304
\(677\) −2.72367e18 −1.08725 −0.543624 0.839329i \(-0.682948\pi\)
−0.543624 + 0.839329i \(0.682948\pi\)
\(678\) 2.43771e18 0.963804
\(679\) −1.00648e18 −0.394141
\(680\) 1.41149e17 0.0547484
\(681\) −1.95265e18 −0.750183
\(682\) −6.93887e18 −2.64053
\(683\) 2.96098e18 1.11609 0.558046 0.829810i \(-0.311551\pi\)
0.558046 + 0.829810i \(0.311551\pi\)
\(684\) −5.59509e17 −0.208902
\(685\) −5.57196e16 −0.0206072
\(686\) −3.88841e18 −1.42451
\(687\) −1.70186e18 −0.617595
\(688\) 1.71128e18 0.615170
\(689\) −6.81293e17 −0.242610
\(690\) −1.82116e18 −0.642436
\(691\) 3.39708e18 1.18713 0.593566 0.804785i \(-0.297720\pi\)
0.593566 + 0.804785i \(0.297720\pi\)
\(692\) −5.17464e18 −1.79139
\(693\) 7.89404e17 0.270728
\(694\) −3.78289e18 −1.28525
\(695\) −3.27385e18 −1.10194
\(696\) −7.52715e17 −0.250998
\(697\) 5.11734e17 0.169056
\(698\) 1.30839e18 0.428230
\(699\) −4.25416e17 −0.137947
\(700\) −2.31792e17 −0.0744665
\(701\) −3.98665e18 −1.26894 −0.634470 0.772947i \(-0.718782\pi\)
−0.634470 + 0.772947i \(0.718782\pi\)
\(702\) 2.53926e17 0.0800786
\(703\) −1.02637e18 −0.320697
\(704\) 6.41677e18 1.98653
\(705\) 1.72669e18 0.529646
\(706\) 6.49144e18 1.97293
\(707\) −4.31881e17 −0.130058
\(708\) 3.09456e17 0.0923384
\(709\) −2.82310e18 −0.834692 −0.417346 0.908748i \(-0.637040\pi\)
−0.417346 + 0.908748i \(0.637040\pi\)
\(710\) −3.77791e18 −1.10681
\(711\) 8.18069e16 0.0237486
\(712\) −8.77619e17 −0.252456
\(713\) −3.08314e18 −0.878842
\(714\) −2.65149e17 −0.0748947
\(715\) 1.49398e18 0.418171
\(716\) 4.63185e18 1.28475
\(717\) 2.03465e18 0.559262
\(718\) 6.05468e18 1.64923
\(719\) 1.65057e17 0.0445551 0.0222775 0.999752i \(-0.492908\pi\)
0.0222775 + 0.999752i \(0.492908\pi\)
\(720\) 9.42808e17 0.252210
\(721\) −8.42713e17 −0.223409
\(722\) 4.20322e18 1.10431
\(723\) −6.30110e17 −0.164066
\(724\) 2.22868e18 0.575106
\(725\) −5.30523e17 −0.135677
\(726\) 3.51667e18 0.891339
\(727\) 4.92778e18 1.23788 0.618938 0.785440i \(-0.287563\pi\)
0.618938 + 0.785440i \(0.287563\pi\)
\(728\) 2.17452e17 0.0541389
\(729\) 1.50095e17 0.0370370
\(730\) −2.62233e18 −0.641340
\(731\) −5.38380e17 −0.130505
\(732\) 5.44246e18 1.30760
\(733\) −2.75180e18 −0.655301 −0.327651 0.944799i \(-0.606257\pi\)
−0.327651 + 0.944799i \(0.606257\pi\)
\(734\) −2.67440e18 −0.631251
\(735\) −1.75404e18 −0.410367
\(736\) 4.32360e18 1.00263
\(737\) −8.04122e18 −1.84835
\(738\) −2.41954e18 −0.551272
\(739\) 3.04067e18 0.686722 0.343361 0.939204i \(-0.388435\pi\)
0.343361 + 0.939204i \(0.388435\pi\)
\(740\) −3.62861e18 −0.812333
\(741\) 3.69952e17 0.0820970
\(742\) −3.36360e18 −0.739910
\(743\) −7.85000e17 −0.171176 −0.0855879 0.996331i \(-0.527277\pi\)
−0.0855879 + 0.996331i \(0.527277\pi\)
\(744\) −1.12982e18 −0.244223
\(745\) −7.34820e18 −1.57458
\(746\) −8.39538e18 −1.78336
\(747\) 2.29857e18 0.484032
\(748\) −1.28078e18 −0.267370
\(749\) −3.43931e18 −0.711771
\(750\) 3.94846e18 0.810083
\(751\) −6.27619e18 −1.27655 −0.638273 0.769810i \(-0.720351\pi\)
−0.638273 + 0.769810i \(0.720351\pi\)
\(752\) −3.11111e18 −0.627334
\(753\) −1.40944e18 −0.281760
\(754\) 2.67600e18 0.530362
\(755\) 5.78246e18 1.13621
\(756\) 6.91095e17 0.134631
\(757\) 5.40715e18 1.04435 0.522174 0.852839i \(-0.325121\pi\)
0.522174 + 0.852839i \(0.325121\pi\)
\(758\) 3.64132e18 0.697283
\(759\) 3.07346e18 0.583519
\(760\) −9.72312e17 −0.183028
\(761\) −4.05663e18 −0.757121 −0.378561 0.925577i \(-0.623581\pi\)
−0.378561 + 0.925577i \(0.623581\pi\)
\(762\) 9.03682e18 1.67228
\(763\) −5.50263e18 −1.00963
\(764\) 7.61740e18 1.38580
\(765\) −2.96614e17 −0.0535048
\(766\) 3.94092e18 0.704873
\(767\) −2.04615e17 −0.0362884
\(768\) −1.31678e18 −0.231561
\(769\) −4.92529e18 −0.858837 −0.429419 0.903106i \(-0.641281\pi\)
−0.429419 + 0.903106i \(0.641281\pi\)
\(770\) 7.37588e18 1.27534
\(771\) −3.74757e18 −0.642533
\(772\) −1.81231e18 −0.308120
\(773\) 1.58560e18 0.267318 0.133659 0.991027i \(-0.457327\pi\)
0.133659 + 0.991027i \(0.457327\pi\)
\(774\) 2.54552e18 0.425560
\(775\) −7.96314e17 −0.132015
\(776\) −1.43599e18 −0.236075
\(777\) 1.26775e18 0.206680
\(778\) −1.26442e19 −2.04421
\(779\) −3.52509e18 −0.565167
\(780\) 1.30792e18 0.207954
\(781\) 6.37572e18 1.00530
\(782\) −1.03233e18 −0.161426
\(783\) 1.58177e18 0.245297
\(784\) 3.16039e18 0.486056
\(785\) −4.79032e17 −0.0730653
\(786\) 2.48191e17 0.0375439
\(787\) 3.72631e17 0.0559041 0.0279521 0.999609i \(-0.491101\pi\)
0.0279521 + 0.999609i \(0.491101\pi\)
\(788\) 9.55163e18 1.42121
\(789\) 4.02563e18 0.594065
\(790\) 7.64372e17 0.111874
\(791\) −4.38683e18 −0.636801
\(792\) 1.12628e18 0.162155
\(793\) −3.59861e18 −0.513876
\(794\) 3.06654e18 0.434326
\(795\) −3.76276e18 −0.528591
\(796\) 3.61775e18 0.504084
\(797\) 1.14973e19 1.58897 0.794484 0.607285i \(-0.207741\pi\)
0.794484 + 0.607285i \(0.207741\pi\)
\(798\) 1.82649e18 0.250379
\(799\) 9.78776e17 0.133085
\(800\) 1.11670e18 0.150610
\(801\) 1.84425e18 0.246722
\(802\) −8.96005e18 −1.18899
\(803\) 4.42552e18 0.582524
\(804\) −7.03980e18 −0.919171
\(805\) 3.27731e18 0.424468
\(806\) 4.01667e18 0.516046
\(807\) 3.73277e18 0.475722
\(808\) −6.16184e17 −0.0778998
\(809\) −1.08696e19 −1.36317 −0.681585 0.731739i \(-0.738709\pi\)
−0.681585 + 0.731739i \(0.738709\pi\)
\(810\) 1.40243e18 0.174473
\(811\) −9.14789e17 −0.112898 −0.0564489 0.998405i \(-0.517978\pi\)
−0.0564489 + 0.998405i \(0.517978\pi\)
\(812\) 7.28310e18 0.891665
\(813\) 7.59244e18 0.922132
\(814\) 1.11086e19 1.33844
\(815\) 1.32902e19 1.58857
\(816\) 5.34431e17 0.0633733
\(817\) 3.70865e18 0.436287
\(818\) −5.05606e18 −0.590087
\(819\) −4.56958e17 −0.0529092
\(820\) −1.24625e19 −1.43158
\(821\) 1.18804e19 1.35394 0.676972 0.736009i \(-0.263292\pi\)
0.676972 + 0.736009i \(0.263292\pi\)
\(822\) 1.49336e17 0.0168849
\(823\) 1.10207e18 0.123627 0.0618133 0.998088i \(-0.480312\pi\)
0.0618133 + 0.998088i \(0.480312\pi\)
\(824\) −1.20234e18 −0.133813
\(825\) 7.93814e17 0.0876532
\(826\) −1.01020e18 −0.110672
\(827\) 5.65393e18 0.614561 0.307280 0.951619i \(-0.400581\pi\)
0.307280 + 0.951619i \(0.400581\pi\)
\(828\) 2.69070e18 0.290180
\(829\) 6.06514e18 0.648987 0.324494 0.945888i \(-0.394806\pi\)
0.324494 + 0.945888i \(0.394806\pi\)
\(830\) 2.14769e19 2.28016
\(831\) 5.07124e18 0.534204
\(832\) −3.71445e18 −0.388233
\(833\) −9.94280e17 −0.103114
\(834\) 8.77436e18 0.902893
\(835\) 1.97367e19 2.01517
\(836\) 8.82267e18 0.893838
\(837\) 2.37424e18 0.238676
\(838\) 3.25980e18 0.325165
\(839\) 1.37363e19 1.35962 0.679812 0.733387i \(-0.262062\pi\)
0.679812 + 0.733387i \(0.262062\pi\)
\(840\) 1.20098e18 0.117956
\(841\) 6.40885e18 0.624606
\(842\) −2.96853e18 −0.287086
\(843\) 2.52991e18 0.242787
\(844\) −1.33840e19 −1.27456
\(845\) 1.02662e19 0.970153
\(846\) −4.62777e18 −0.433974
\(847\) −6.32849e18 −0.588922
\(848\) 6.77964e18 0.626085
\(849\) −4.78703e18 −0.438698
\(850\) −2.66630e17 −0.0242486
\(851\) 4.93585e18 0.445472
\(852\) 5.58172e18 0.499931
\(853\) −3.26824e18 −0.290499 −0.145250 0.989395i \(-0.546399\pi\)
−0.145250 + 0.989395i \(0.546399\pi\)
\(854\) −1.77666e19 −1.56722
\(855\) 2.04324e18 0.178870
\(856\) −4.90702e18 −0.426323
\(857\) 4.29308e18 0.370164 0.185082 0.982723i \(-0.440745\pi\)
0.185082 + 0.982723i \(0.440745\pi\)
\(858\) −4.00406e18 −0.342636
\(859\) −8.04363e18 −0.683119 −0.341560 0.939860i \(-0.610955\pi\)
−0.341560 + 0.939860i \(0.610955\pi\)
\(860\) 1.31115e19 1.10513
\(861\) 4.35413e18 0.364234
\(862\) −9.96086e18 −0.826989
\(863\) 2.89038e18 0.238169 0.119084 0.992884i \(-0.462004\pi\)
0.119084 + 0.992884i \(0.462004\pi\)
\(864\) −3.32948e18 −0.272294
\(865\) 1.88970e19 1.53387
\(866\) −1.23896e19 −0.998138
\(867\) 7.05230e18 0.563906
\(868\) 1.09319e19 0.867597
\(869\) −1.28998e18 −0.101614
\(870\) 1.47795e19 1.15554
\(871\) 4.65478e18 0.361228
\(872\) −7.85085e18 −0.604727
\(873\) 3.01762e18 0.230713
\(874\) 7.11122e18 0.539659
\(875\) −7.10554e18 −0.535235
\(876\) 3.87439e18 0.289685
\(877\) 1.94577e19 1.44409 0.722043 0.691848i \(-0.243203\pi\)
0.722043 + 0.691848i \(0.243203\pi\)
\(878\) −2.40491e19 −1.77168
\(879\) −1.25098e19 −0.914790
\(880\) −1.48668e19 −1.07914
\(881\) −7.85383e18 −0.565898 −0.282949 0.959135i \(-0.591313\pi\)
−0.282949 + 0.959135i \(0.591313\pi\)
\(882\) 4.70107e18 0.336241
\(883\) −2.26828e19 −1.61047 −0.805234 0.592957i \(-0.797960\pi\)
−0.805234 + 0.592957i \(0.797960\pi\)
\(884\) 7.41397e17 0.0522530
\(885\) −1.13008e18 −0.0790640
\(886\) −2.31633e19 −1.60872
\(887\) 8.05272e18 0.555187 0.277593 0.960699i \(-0.410463\pi\)
0.277593 + 0.960699i \(0.410463\pi\)
\(888\) 1.80876e18 0.123793
\(889\) −1.62624e19 −1.10490
\(890\) 1.72319e19 1.16225
\(891\) −2.36678e18 −0.158472
\(892\) −1.67981e19 −1.11658
\(893\) −6.74233e18 −0.444913
\(894\) 1.96942e19 1.29016
\(895\) −1.69148e19 −1.10006
\(896\) −5.85952e18 −0.378320
\(897\) −1.77912e18 −0.114039
\(898\) −2.09991e19 −1.33630
\(899\) 2.50209e19 1.58075
\(900\) 6.94956e17 0.0435894
\(901\) −2.13292e18 −0.132820
\(902\) 3.81527e19 2.35875
\(903\) −4.58085e18 −0.281174
\(904\) −6.25888e18 −0.381419
\(905\) −8.13879e18 −0.492430
\(906\) −1.54978e19 −0.930972
\(907\) −1.59480e18 −0.0951170 −0.0475585 0.998868i \(-0.515144\pi\)
−0.0475585 + 0.998868i \(0.515144\pi\)
\(908\) 2.69560e19 1.59623
\(909\) 1.29486e18 0.0761304
\(910\) −4.26964e18 −0.249243
\(911\) −8.38863e18 −0.486208 −0.243104 0.970000i \(-0.578166\pi\)
−0.243104 + 0.970000i \(0.578166\pi\)
\(912\) −3.68145e18 −0.211862
\(913\) −3.62452e19 −2.07105
\(914\) 2.10080e19 1.19188
\(915\) −1.98750e19 −1.11962
\(916\) 2.34938e19 1.31412
\(917\) −4.46637e17 −0.0248059
\(918\) 7.94966e17 0.0438401
\(919\) 3.45407e19 1.89139 0.945693 0.325062i \(-0.105385\pi\)
0.945693 + 0.325062i \(0.105385\pi\)
\(920\) 4.67589e18 0.254240
\(921\) −8.10998e17 −0.0437857
\(922\) −2.28986e19 −1.22760
\(923\) −3.69068e18 −0.196470
\(924\) −1.08976e19 −0.576053
\(925\) 1.27484e18 0.0669164
\(926\) 7.22695e18 0.376690
\(927\) 2.52661e18 0.130774
\(928\) −3.50877e19 −1.80341
\(929\) −1.60387e19 −0.818593 −0.409297 0.912401i \(-0.634226\pi\)
−0.409297 + 0.912401i \(0.634226\pi\)
\(930\) 2.21839e19 1.12435
\(931\) 6.84913e18 0.344717
\(932\) 5.87280e18 0.293523
\(933\) 1.45055e19 0.719948
\(934\) 1.00519e19 0.495442
\(935\) 4.67719e18 0.228933
\(936\) −6.51962e17 −0.0316905
\(937\) 1.46031e19 0.704917 0.352458 0.935827i \(-0.385346\pi\)
0.352458 + 0.935827i \(0.385346\pi\)
\(938\) 2.29811e19 1.10167
\(939\) 1.27639e18 0.0607656
\(940\) −2.38367e19 −1.12698
\(941\) 1.53211e19 0.719377 0.359689 0.933072i \(-0.382883\pi\)
0.359689 + 0.933072i \(0.382883\pi\)
\(942\) 1.28387e18 0.0598674
\(943\) 1.69523e19 0.785060
\(944\) 2.03615e18 0.0936466
\(945\) −2.52377e18 −0.115277
\(946\) −4.01393e19 −1.82086
\(947\) −2.81915e19 −1.27012 −0.635058 0.772465i \(-0.719024\pi\)
−0.635058 + 0.772465i \(0.719024\pi\)
\(948\) −1.12933e18 −0.0505321
\(949\) −2.56178e18 −0.113844
\(950\) 1.83669e18 0.0810648
\(951\) −3.57862e18 −0.156871
\(952\) 6.80777e17 0.0296391
\(953\) −6.50868e18 −0.281442 −0.140721 0.990049i \(-0.544942\pi\)
−0.140721 + 0.990049i \(0.544942\pi\)
\(954\) 1.00847e19 0.433110
\(955\) −2.78175e19 −1.18658
\(956\) −2.80880e19 −1.18999
\(957\) −2.49423e19 −1.04956
\(958\) 4.37801e19 1.82979
\(959\) −2.68741e17 −0.0111561
\(960\) −2.05148e19 −0.845870
\(961\) 1.31388e19 0.538087
\(962\) −6.43037e18 −0.261576
\(963\) 1.03117e19 0.416639
\(964\) 8.69856e18 0.349098
\(965\) 6.61825e18 0.263825
\(966\) −8.78364e18 −0.347795
\(967\) −1.04592e19 −0.411365 −0.205683 0.978619i \(-0.565941\pi\)
−0.205683 + 0.978619i \(0.565941\pi\)
\(968\) −9.02914e18 −0.352741
\(969\) 1.15821e18 0.0449451
\(970\) 2.81954e19 1.08683
\(971\) −1.64057e19 −0.628158 −0.314079 0.949397i \(-0.601696\pi\)
−0.314079 + 0.949397i \(0.601696\pi\)
\(972\) −2.07203e18 −0.0788072
\(973\) −1.57901e19 −0.596556
\(974\) 5.87334e19 2.20421
\(975\) −4.59511e17 −0.0171303
\(976\) 3.58102e19 1.32612
\(977\) 3.21003e19 1.18085 0.590424 0.807093i \(-0.298960\pi\)
0.590424 + 0.807093i \(0.298960\pi\)
\(978\) −3.56196e19 −1.30163
\(979\) −2.90812e19 −1.05566
\(980\) 2.42143e19 0.873177
\(981\) 1.64979e19 0.590991
\(982\) 2.12337e19 0.755615
\(983\) −2.01546e19 −0.712486 −0.356243 0.934393i \(-0.615942\pi\)
−0.356243 + 0.934393i \(0.615942\pi\)
\(984\) 6.21223e18 0.218162
\(985\) −3.48810e19 −1.21690
\(986\) 8.37774e18 0.290353
\(987\) 8.32800e18 0.286734
\(988\) −5.10713e18 −0.174686
\(989\) −1.78350e19 −0.606035
\(990\) −2.21143e19 −0.746525
\(991\) 4.63111e19 1.55313 0.776563 0.630040i \(-0.216961\pi\)
0.776563 + 0.630040i \(0.216961\pi\)
\(992\) −5.26666e19 −1.75473
\(993\) −8.76854e18 −0.290240
\(994\) −1.82212e19 −0.599191
\(995\) −1.32114e19 −0.431618
\(996\) −3.17314e19 −1.02992
\(997\) 1.23578e19 0.398494 0.199247 0.979949i \(-0.436150\pi\)
0.199247 + 0.979949i \(0.436150\pi\)
\(998\) −1.85754e19 −0.595099
\(999\) −3.80096e18 −0.120981
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.1.6 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.6 31 1.1 even 1 trivial