Properties

Label 177.14.a.b.1.7
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 1.7
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-117.761 q^{2} -729.000 q^{3} +5675.60 q^{4} -28297.1 q^{5} +85847.6 q^{6} +297580. q^{7} +296333. q^{8} +531441. q^{9} +O(q^{10})\) \(q-117.761 q^{2} -729.000 q^{3} +5675.60 q^{4} -28297.1 q^{5} +85847.6 q^{6} +297580. q^{7} +296333. q^{8} +531441. q^{9} +3.33229e6 q^{10} +6.74053e6 q^{11} -4.13751e6 q^{12} +1.09553e7 q^{13} -3.50432e7 q^{14} +2.06286e7 q^{15} -8.13909e7 q^{16} +1.25092e8 q^{17} -6.25829e7 q^{18} +5.93564e7 q^{19} -1.60603e8 q^{20} -2.16936e8 q^{21} -7.93770e8 q^{22} -2.24559e8 q^{23} -2.16027e8 q^{24} -4.19977e8 q^{25} -1.29011e9 q^{26} -3.87420e8 q^{27} +1.68894e9 q^{28} -3.59989e9 q^{29} -2.42924e9 q^{30} +2.51758e9 q^{31} +7.15710e9 q^{32} -4.91384e9 q^{33} -1.47309e10 q^{34} -8.42065e9 q^{35} +3.01625e9 q^{36} -9.31650e9 q^{37} -6.98985e9 q^{38} -7.98643e9 q^{39} -8.38537e9 q^{40} -2.88329e10 q^{41} +2.55465e10 q^{42} +6.45299e10 q^{43} +3.82565e10 q^{44} -1.50382e10 q^{45} +2.64442e10 q^{46} -3.47238e9 q^{47} +5.93340e10 q^{48} -8.33535e9 q^{49} +4.94568e10 q^{50} -9.11920e10 q^{51} +6.21780e10 q^{52} -6.81644e10 q^{53} +4.56229e10 q^{54} -1.90737e11 q^{55} +8.81827e10 q^{56} -4.32708e10 q^{57} +4.23926e11 q^{58} -4.21805e10 q^{59} +1.17080e11 q^{60} -2.72876e11 q^{61} -2.96473e11 q^{62} +1.58146e11 q^{63} -1.76071e11 q^{64} -3.10004e11 q^{65} +5.78658e11 q^{66} -1.27218e12 q^{67} +7.09972e11 q^{68} +1.63703e11 q^{69} +9.91622e11 q^{70} +2.97964e11 q^{71} +1.57484e11 q^{72} -7.41056e11 q^{73} +1.09712e12 q^{74} +3.06163e11 q^{75} +3.36883e11 q^{76} +2.00584e12 q^{77} +9.40488e11 q^{78} -2.93932e12 q^{79} +2.30313e12 q^{80} +2.82430e11 q^{81} +3.39538e12 q^{82} +3.27472e12 q^{83} -1.23124e12 q^{84} -3.53974e12 q^{85} -7.59909e12 q^{86} +2.62432e12 q^{87} +1.99744e12 q^{88} +1.53034e12 q^{89} +1.77092e12 q^{90} +3.26008e12 q^{91} -1.27450e12 q^{92} -1.83532e12 q^{93} +4.08910e11 q^{94} -1.67961e12 q^{95} -5.21753e12 q^{96} -6.38006e12 q^{97} +9.81577e11 q^{98} +3.58219e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −117.761 −1.30109 −0.650543 0.759470i \(-0.725458\pi\)
−0.650543 + 0.759470i \(0.725458\pi\)
\(3\) −729.000 −0.577350
\(4\) 5675.60 0.692822
\(5\) −28297.1 −0.809911 −0.404955 0.914336i \(-0.632713\pi\)
−0.404955 + 0.914336i \(0.632713\pi\)
\(6\) 85847.6 0.751182
\(7\) 297580. 0.956018 0.478009 0.878355i \(-0.341359\pi\)
0.478009 + 0.878355i \(0.341359\pi\)
\(8\) 296333. 0.399664
\(9\) 531441. 0.333333
\(10\) 3.33229e6 1.05376
\(11\) 6.74053e6 1.14721 0.573603 0.819133i \(-0.305545\pi\)
0.573603 + 0.819133i \(0.305545\pi\)
\(12\) −4.13751e6 −0.400001
\(13\) 1.09553e7 0.629496 0.314748 0.949175i \(-0.398080\pi\)
0.314748 + 0.949175i \(0.398080\pi\)
\(14\) −3.50432e7 −1.24386
\(15\) 2.06286e7 0.467602
\(16\) −8.13909e7 −1.21282
\(17\) 1.25092e8 1.25693 0.628465 0.777838i \(-0.283683\pi\)
0.628465 + 0.777838i \(0.283683\pi\)
\(18\) −6.25829e7 −0.433695
\(19\) 5.93564e7 0.289447 0.144723 0.989472i \(-0.453771\pi\)
0.144723 + 0.989472i \(0.453771\pi\)
\(20\) −1.60603e8 −0.561124
\(21\) −2.16936e8 −0.551957
\(22\) −7.93770e8 −1.49261
\(23\) −2.24559e8 −0.316300 −0.158150 0.987415i \(-0.550553\pi\)
−0.158150 + 0.987415i \(0.550553\pi\)
\(24\) −2.16027e8 −0.230746
\(25\) −4.19977e8 −0.344045
\(26\) −1.29011e9 −0.819028
\(27\) −3.87420e8 −0.192450
\(28\) 1.68894e9 0.662351
\(29\) −3.59989e9 −1.12383 −0.561917 0.827194i \(-0.689936\pi\)
−0.561917 + 0.827194i \(0.689936\pi\)
\(30\) −2.42924e9 −0.608390
\(31\) 2.51758e9 0.509487 0.254743 0.967009i \(-0.418009\pi\)
0.254743 + 0.967009i \(0.418009\pi\)
\(32\) 7.15710e9 1.17832
\(33\) −4.91384e9 −0.662340
\(34\) −1.47309e10 −1.63537
\(35\) −8.42065e9 −0.774289
\(36\) 3.01625e9 0.230941
\(37\) −9.31650e9 −0.596955 −0.298477 0.954417i \(-0.596479\pi\)
−0.298477 + 0.954417i \(0.596479\pi\)
\(38\) −6.98985e9 −0.376595
\(39\) −7.98643e9 −0.363440
\(40\) −8.38537e9 −0.323692
\(41\) −2.88329e10 −0.947966 −0.473983 0.880534i \(-0.657184\pi\)
−0.473983 + 0.880534i \(0.657184\pi\)
\(42\) 2.55465e10 0.718143
\(43\) 6.45299e10 1.55674 0.778370 0.627806i \(-0.216047\pi\)
0.778370 + 0.627806i \(0.216047\pi\)
\(44\) 3.82565e10 0.794810
\(45\) −1.50382e10 −0.269970
\(46\) 2.64442e10 0.411533
\(47\) −3.47238e9 −0.0469884 −0.0234942 0.999724i \(-0.507479\pi\)
−0.0234942 + 0.999724i \(0.507479\pi\)
\(48\) 5.93340e10 0.700222
\(49\) −8.33535e9 −0.0860299
\(50\) 4.94568e10 0.447632
\(51\) −9.11920e10 −0.725689
\(52\) 6.21780e10 0.436129
\(53\) −6.81644e10 −0.422440 −0.211220 0.977439i \(-0.567744\pi\)
−0.211220 + 0.977439i \(0.567744\pi\)
\(54\) 4.56229e10 0.250394
\(55\) −1.90737e11 −0.929134
\(56\) 8.81827e10 0.382086
\(57\) −4.32708e10 −0.167112
\(58\) 4.23926e11 1.46220
\(59\) −4.21805e10 −0.130189
\(60\) 1.17080e11 0.323965
\(61\) −2.72876e11 −0.678144 −0.339072 0.940760i \(-0.610113\pi\)
−0.339072 + 0.940760i \(0.610113\pi\)
\(62\) −2.96473e11 −0.662886
\(63\) 1.58146e11 0.318673
\(64\) −1.76071e11 −0.320271
\(65\) −3.10004e11 −0.509836
\(66\) 5.78658e11 0.861760
\(67\) −1.27218e12 −1.71815 −0.859077 0.511847i \(-0.828962\pi\)
−0.859077 + 0.511847i \(0.828962\pi\)
\(68\) 7.09972e11 0.870830
\(69\) 1.63703e11 0.182616
\(70\) 9.91622e11 1.00742
\(71\) 2.97964e11 0.276048 0.138024 0.990429i \(-0.455925\pi\)
0.138024 + 0.990429i \(0.455925\pi\)
\(72\) 1.57484e11 0.133221
\(73\) −7.41056e11 −0.573129 −0.286564 0.958061i \(-0.592513\pi\)
−0.286564 + 0.958061i \(0.592513\pi\)
\(74\) 1.09712e12 0.776689
\(75\) 3.06163e11 0.198634
\(76\) 3.36883e11 0.200535
\(77\) 2.00584e12 1.09675
\(78\) 9.40488e11 0.472866
\(79\) −2.93932e12 −1.36041 −0.680207 0.733020i \(-0.738110\pi\)
−0.680207 + 0.733020i \(0.738110\pi\)
\(80\) 2.30313e12 0.982275
\(81\) 2.82430e11 0.111111
\(82\) 3.39538e12 1.23338
\(83\) 3.27472e12 1.09943 0.549714 0.835353i \(-0.314737\pi\)
0.549714 + 0.835353i \(0.314737\pi\)
\(84\) −1.23124e12 −0.382408
\(85\) −3.53974e12 −1.01800
\(86\) −7.59909e12 −2.02545
\(87\) 2.62432e12 0.648846
\(88\) 1.99744e12 0.458497
\(89\) 1.53034e12 0.326402 0.163201 0.986593i \(-0.447818\pi\)
0.163201 + 0.986593i \(0.447818\pi\)
\(90\) 1.77092e12 0.351254
\(91\) 3.26008e12 0.601810
\(92\) −1.27450e12 −0.219139
\(93\) −1.83532e12 −0.294152
\(94\) 4.08910e11 0.0611359
\(95\) −1.67961e12 −0.234426
\(96\) −5.21753e12 −0.680302
\(97\) −6.38006e12 −0.777694 −0.388847 0.921302i \(-0.627127\pi\)
−0.388847 + 0.921302i \(0.627127\pi\)
\(98\) 9.81577e11 0.111932
\(99\) 3.58219e12 0.382402
\(100\) −2.38362e12 −0.238362
\(101\) −9.05475e12 −0.848765 −0.424383 0.905483i \(-0.639509\pi\)
−0.424383 + 0.905483i \(0.639509\pi\)
\(102\) 1.07388e13 0.944184
\(103\) 1.75266e13 1.44629 0.723144 0.690697i \(-0.242696\pi\)
0.723144 + 0.690697i \(0.242696\pi\)
\(104\) 3.24642e12 0.251587
\(105\) 6.13865e12 0.447036
\(106\) 8.02710e12 0.549630
\(107\) 3.27589e12 0.211026 0.105513 0.994418i \(-0.466352\pi\)
0.105513 + 0.994418i \(0.466352\pi\)
\(108\) −2.19884e12 −0.133334
\(109\) −9.70937e12 −0.554522 −0.277261 0.960795i \(-0.589427\pi\)
−0.277261 + 0.960795i \(0.589427\pi\)
\(110\) 2.24614e13 1.20888
\(111\) 6.79173e12 0.344652
\(112\) −2.42203e13 −1.15948
\(113\) 2.39339e13 1.08144 0.540721 0.841202i \(-0.318151\pi\)
0.540721 + 0.841202i \(0.318151\pi\)
\(114\) 5.09560e12 0.217427
\(115\) 6.35436e12 0.256174
\(116\) −2.04315e13 −0.778617
\(117\) 5.82210e12 0.209832
\(118\) 4.96721e12 0.169387
\(119\) 3.72248e13 1.20165
\(120\) 6.11294e12 0.186884
\(121\) 1.09120e13 0.316082
\(122\) 3.21341e13 0.882323
\(123\) 2.10192e13 0.547308
\(124\) 1.42888e13 0.352984
\(125\) 4.64265e13 1.08856
\(126\) −1.86234e13 −0.414620
\(127\) −1.10493e13 −0.233674 −0.116837 0.993151i \(-0.537275\pi\)
−0.116837 + 0.993151i \(0.537275\pi\)
\(128\) −3.78967e13 −0.761617
\(129\) −4.70423e13 −0.898784
\(130\) 3.65063e13 0.663340
\(131\) 7.94265e13 1.37310 0.686550 0.727083i \(-0.259124\pi\)
0.686550 + 0.727083i \(0.259124\pi\)
\(132\) −2.78890e13 −0.458884
\(133\) 1.76632e13 0.276716
\(134\) 1.49813e14 2.23546
\(135\) 1.09629e13 0.155867
\(136\) 3.70689e13 0.502350
\(137\) −1.29017e13 −0.166711 −0.0833553 0.996520i \(-0.526564\pi\)
−0.0833553 + 0.996520i \(0.526564\pi\)
\(138\) −1.92778e13 −0.237599
\(139\) 1.05554e14 1.24131 0.620653 0.784086i \(-0.286868\pi\)
0.620653 + 0.784086i \(0.286868\pi\)
\(140\) −4.77922e13 −0.536445
\(141\) 2.53136e12 0.0271288
\(142\) −3.50884e13 −0.359162
\(143\) 7.38446e13 0.722162
\(144\) −4.32545e13 −0.404273
\(145\) 1.01866e14 0.910205
\(146\) 8.72673e13 0.745690
\(147\) 6.07647e12 0.0496694
\(148\) −5.28767e13 −0.413584
\(149\) −1.53169e14 −1.14672 −0.573362 0.819302i \(-0.694361\pi\)
−0.573362 + 0.819302i \(0.694361\pi\)
\(150\) −3.60540e13 −0.258440
\(151\) −2.16491e14 −1.48624 −0.743121 0.669157i \(-0.766655\pi\)
−0.743121 + 0.669157i \(0.766655\pi\)
\(152\) 1.75893e13 0.115682
\(153\) 6.64790e13 0.418977
\(154\) −2.36210e14 −1.42696
\(155\) −7.12404e13 −0.412639
\(156\) −4.53278e13 −0.251799
\(157\) 1.48745e14 0.792675 0.396338 0.918105i \(-0.370281\pi\)
0.396338 + 0.918105i \(0.370281\pi\)
\(158\) 3.46137e14 1.77001
\(159\) 4.96919e13 0.243896
\(160\) −2.02525e14 −0.954332
\(161\) −6.68241e13 −0.302388
\(162\) −3.32591e13 −0.144565
\(163\) −2.47866e14 −1.03513 −0.517567 0.855642i \(-0.673162\pi\)
−0.517567 + 0.855642i \(0.673162\pi\)
\(164\) −1.63644e14 −0.656772
\(165\) 1.39048e14 0.536436
\(166\) −3.85633e14 −1.43045
\(167\) 4.58344e13 0.163506 0.0817532 0.996653i \(-0.473948\pi\)
0.0817532 + 0.996653i \(0.473948\pi\)
\(168\) −6.42852e13 −0.220598
\(169\) −1.82856e14 −0.603735
\(170\) 4.16843e14 1.32451
\(171\) 3.15444e13 0.0964823
\(172\) 3.66246e14 1.07854
\(173\) 2.10806e14 0.597838 0.298919 0.954279i \(-0.403374\pi\)
0.298919 + 0.954279i \(0.403374\pi\)
\(174\) −3.09042e14 −0.844203
\(175\) −1.24977e14 −0.328913
\(176\) −5.48618e14 −1.39135
\(177\) 3.07496e13 0.0751646
\(178\) −1.80214e14 −0.424676
\(179\) −5.78992e14 −1.31561 −0.657807 0.753187i \(-0.728516\pi\)
−0.657807 + 0.753187i \(0.728516\pi\)
\(180\) −8.53511e13 −0.187041
\(181\) −8.43273e14 −1.78261 −0.891307 0.453400i \(-0.850211\pi\)
−0.891307 + 0.453400i \(0.850211\pi\)
\(182\) −3.83909e14 −0.783006
\(183\) 1.98927e14 0.391527
\(184\) −6.65441e13 −0.126414
\(185\) 2.63630e14 0.483480
\(186\) 2.16129e14 0.382717
\(187\) 8.43186e14 1.44196
\(188\) −1.97078e13 −0.0325546
\(189\) −1.15288e14 −0.183986
\(190\) 1.97793e14 0.305008
\(191\) 5.90563e14 0.880135 0.440068 0.897965i \(-0.354954\pi\)
0.440068 + 0.897965i \(0.354954\pi\)
\(192\) 1.28356e14 0.184909
\(193\) −7.89365e14 −1.09940 −0.549699 0.835363i \(-0.685258\pi\)
−0.549699 + 0.835363i \(0.685258\pi\)
\(194\) 7.51321e14 1.01185
\(195\) 2.25993e14 0.294354
\(196\) −4.73081e13 −0.0596034
\(197\) −8.09274e14 −0.986428 −0.493214 0.869908i \(-0.664178\pi\)
−0.493214 + 0.869908i \(0.664178\pi\)
\(198\) −4.21842e14 −0.497538
\(199\) −3.81549e14 −0.435517 −0.217759 0.976003i \(-0.569875\pi\)
−0.217759 + 0.976003i \(0.569875\pi\)
\(200\) −1.24453e14 −0.137502
\(201\) 9.27418e14 0.991976
\(202\) 1.06629e15 1.10432
\(203\) −1.07125e15 −1.07441
\(204\) −5.17570e14 −0.502774
\(205\) 8.15887e14 0.767768
\(206\) −2.06394e15 −1.88174
\(207\) −1.19340e14 −0.105433
\(208\) −8.91663e14 −0.763465
\(209\) 4.00093e14 0.332055
\(210\) −7.22892e14 −0.581632
\(211\) 4.82454e14 0.376374 0.188187 0.982133i \(-0.439739\pi\)
0.188187 + 0.982133i \(0.439739\pi\)
\(212\) −3.86874e14 −0.292676
\(213\) −2.17216e14 −0.159376
\(214\) −3.85772e14 −0.274562
\(215\) −1.82601e15 −1.26082
\(216\) −1.14806e14 −0.0769154
\(217\) 7.49182e14 0.487079
\(218\) 1.14338e15 0.721480
\(219\) 5.40230e14 0.330896
\(220\) −1.08255e15 −0.643725
\(221\) 1.37042e15 0.791233
\(222\) −7.99799e14 −0.448422
\(223\) −4.81615e14 −0.262252 −0.131126 0.991366i \(-0.541859\pi\)
−0.131126 + 0.991366i \(0.541859\pi\)
\(224\) 2.12981e15 1.12649
\(225\) −2.23193e14 −0.114682
\(226\) −2.81847e15 −1.40705
\(227\) 1.33786e15 0.648996 0.324498 0.945886i \(-0.394805\pi\)
0.324498 + 0.945886i \(0.394805\pi\)
\(228\) −2.45588e14 −0.115779
\(229\) 1.86755e14 0.0855737 0.0427869 0.999084i \(-0.486376\pi\)
0.0427869 + 0.999084i \(0.486376\pi\)
\(230\) −7.48294e14 −0.333305
\(231\) −1.46226e15 −0.633209
\(232\) −1.06677e15 −0.449156
\(233\) 1.75469e15 0.718434 0.359217 0.933254i \(-0.383044\pi\)
0.359217 + 0.933254i \(0.383044\pi\)
\(234\) −6.85616e14 −0.273009
\(235\) 9.82582e13 0.0380564
\(236\) −2.39400e14 −0.0901978
\(237\) 2.14276e15 0.785435
\(238\) −4.38362e15 −1.56345
\(239\) −8.29366e14 −0.287846 −0.143923 0.989589i \(-0.545972\pi\)
−0.143923 + 0.989589i \(0.545972\pi\)
\(240\) −1.67898e15 −0.567117
\(241\) −3.96498e15 −1.30356 −0.651779 0.758409i \(-0.725977\pi\)
−0.651779 + 0.758409i \(0.725977\pi\)
\(242\) −1.28501e15 −0.411249
\(243\) −2.05891e14 −0.0641500
\(244\) −1.54874e15 −0.469834
\(245\) 2.35866e14 0.0696765
\(246\) −2.47523e15 −0.712095
\(247\) 6.50268e14 0.182206
\(248\) 7.46044e14 0.203624
\(249\) −2.38727e15 −0.634755
\(250\) −5.46722e15 −1.41630
\(251\) −3.63989e15 −0.918774 −0.459387 0.888236i \(-0.651931\pi\)
−0.459387 + 0.888236i \(0.651931\pi\)
\(252\) 8.97574e14 0.220784
\(253\) −1.51364e15 −0.362861
\(254\) 1.30117e15 0.304029
\(255\) 2.58047e15 0.587743
\(256\) 5.90512e15 1.31120
\(257\) −2.52357e15 −0.546323 −0.273162 0.961968i \(-0.588069\pi\)
−0.273162 + 0.961968i \(0.588069\pi\)
\(258\) 5.53974e15 1.16939
\(259\) −2.77240e15 −0.570699
\(260\) −1.75946e15 −0.353226
\(261\) −1.91313e15 −0.374611
\(262\) −9.35332e15 −1.78652
\(263\) 7.92683e15 1.47702 0.738512 0.674241i \(-0.235529\pi\)
0.738512 + 0.674241i \(0.235529\pi\)
\(264\) −1.45613e15 −0.264713
\(265\) 1.92886e15 0.342138
\(266\) −2.08004e15 −0.360032
\(267\) −1.11562e15 −0.188448
\(268\) −7.22038e15 −1.19038
\(269\) −1.79820e15 −0.289367 −0.144684 0.989478i \(-0.546216\pi\)
−0.144684 + 0.989478i \(0.546216\pi\)
\(270\) −1.29100e15 −0.202797
\(271\) −1.92526e15 −0.295249 −0.147625 0.989043i \(-0.547163\pi\)
−0.147625 + 0.989043i \(0.547163\pi\)
\(272\) −1.01814e16 −1.52443
\(273\) −2.37660e15 −0.347455
\(274\) 1.51931e15 0.216905
\(275\) −2.83086e15 −0.394690
\(276\) 9.29114e14 0.126520
\(277\) −1.51421e15 −0.201404 −0.100702 0.994917i \(-0.532109\pi\)
−0.100702 + 0.994917i \(0.532109\pi\)
\(278\) −1.24301e16 −1.61504
\(279\) 1.33795e15 0.169829
\(280\) −2.49532e15 −0.309456
\(281\) −6.62527e15 −0.802810 −0.401405 0.915901i \(-0.631478\pi\)
−0.401405 + 0.915901i \(0.631478\pi\)
\(282\) −2.98095e14 −0.0352968
\(283\) −9.24844e15 −1.07018 −0.535090 0.844795i \(-0.679722\pi\)
−0.535090 + 0.844795i \(0.679722\pi\)
\(284\) 1.69112e15 0.191252
\(285\) 1.22444e15 0.135346
\(286\) −8.69600e15 −0.939594
\(287\) −8.58007e15 −0.906272
\(288\) 3.80358e15 0.392772
\(289\) 5.74342e15 0.579875
\(290\) −1.19959e16 −1.18425
\(291\) 4.65107e15 0.449002
\(292\) −4.20594e15 −0.397077
\(293\) −1.32961e16 −1.22767 −0.613837 0.789433i \(-0.710375\pi\)
−0.613837 + 0.789433i \(0.710375\pi\)
\(294\) −7.15570e14 −0.0646241
\(295\) 1.19359e15 0.105441
\(296\) −2.76079e15 −0.238581
\(297\) −2.61142e15 −0.220780
\(298\) 1.80373e16 1.49199
\(299\) −2.46011e15 −0.199109
\(300\) 1.73766e15 0.137618
\(301\) 1.92028e16 1.48827
\(302\) 2.54941e16 1.93373
\(303\) 6.60091e15 0.490035
\(304\) −4.83107e15 −0.351047
\(305\) 7.72162e15 0.549236
\(306\) −7.82862e15 −0.545125
\(307\) −7.15787e15 −0.487960 −0.243980 0.969780i \(-0.578453\pi\)
−0.243980 + 0.969780i \(0.578453\pi\)
\(308\) 1.13844e16 0.759853
\(309\) −1.27769e16 −0.835015
\(310\) 8.38932e15 0.536878
\(311\) 1.06496e16 0.667408 0.333704 0.942678i \(-0.391701\pi\)
0.333704 + 0.942678i \(0.391701\pi\)
\(312\) −2.36664e15 −0.145254
\(313\) 2.71914e16 1.63453 0.817266 0.576261i \(-0.195489\pi\)
0.817266 + 0.576261i \(0.195489\pi\)
\(314\) −1.75164e16 −1.03134
\(315\) −4.47508e15 −0.258096
\(316\) −1.66824e16 −0.942525
\(317\) −9.02585e14 −0.0499578 −0.0249789 0.999688i \(-0.507952\pi\)
−0.0249789 + 0.999688i \(0.507952\pi\)
\(318\) −5.85175e15 −0.317329
\(319\) −2.42651e16 −1.28927
\(320\) 4.98230e15 0.259391
\(321\) −2.38812e15 −0.121836
\(322\) 7.86926e15 0.393433
\(323\) 7.42500e15 0.363815
\(324\) 1.60296e15 0.0769803
\(325\) −4.60098e15 −0.216575
\(326\) 2.91888e16 1.34680
\(327\) 7.07813e15 0.320153
\(328\) −8.54413e15 −0.378868
\(329\) −1.03331e15 −0.0449218
\(330\) −1.63744e16 −0.697949
\(331\) 4.49271e16 1.87770 0.938851 0.344323i \(-0.111891\pi\)
0.938851 + 0.344323i \(0.111891\pi\)
\(332\) 1.85860e16 0.761708
\(333\) −4.95117e15 −0.198985
\(334\) −5.39750e15 −0.212736
\(335\) 3.59990e16 1.39155
\(336\) 1.76566e16 0.669424
\(337\) −7.55357e15 −0.280904 −0.140452 0.990087i \(-0.544856\pi\)
−0.140452 + 0.990087i \(0.544856\pi\)
\(338\) 2.15333e16 0.785510
\(339\) −1.74478e16 −0.624371
\(340\) −2.00902e16 −0.705294
\(341\) 1.69698e16 0.584486
\(342\) −3.71469e15 −0.125532
\(343\) −3.13126e16 −1.03826
\(344\) 1.91223e16 0.622173
\(345\) −4.63233e15 −0.147902
\(346\) −2.48247e16 −0.777838
\(347\) −4.10435e15 −0.126213 −0.0631063 0.998007i \(-0.520101\pi\)
−0.0631063 + 0.998007i \(0.520101\pi\)
\(348\) 1.48946e16 0.449535
\(349\) 1.63887e16 0.485488 0.242744 0.970090i \(-0.421952\pi\)
0.242744 + 0.970090i \(0.421952\pi\)
\(350\) 1.47173e16 0.427944
\(351\) −4.24431e15 −0.121147
\(352\) 4.82426e16 1.35177
\(353\) 4.19774e16 1.15473 0.577365 0.816486i \(-0.304081\pi\)
0.577365 + 0.816486i \(0.304081\pi\)
\(354\) −3.62110e15 −0.0977955
\(355\) −8.43151e15 −0.223574
\(356\) 8.68559e15 0.226138
\(357\) −2.71369e16 −0.693772
\(358\) 6.81826e16 1.71172
\(359\) 2.40099e15 0.0591939 0.0295970 0.999562i \(-0.490578\pi\)
0.0295970 + 0.999562i \(0.490578\pi\)
\(360\) −4.45633e15 −0.107897
\(361\) −3.85298e16 −0.916220
\(362\) 9.93045e16 2.31933
\(363\) −7.95485e15 −0.182490
\(364\) 1.85029e16 0.416947
\(365\) 2.09697e16 0.464183
\(366\) −2.34258e16 −0.509410
\(367\) −2.70476e16 −0.577829 −0.288915 0.957355i \(-0.593294\pi\)
−0.288915 + 0.957355i \(0.593294\pi\)
\(368\) 1.82770e16 0.383614
\(369\) −1.53230e16 −0.315989
\(370\) −3.10453e16 −0.629049
\(371\) −2.02844e16 −0.403860
\(372\) −1.04165e16 −0.203795
\(373\) −8.72842e16 −1.67814 −0.839070 0.544023i \(-0.816900\pi\)
−0.839070 + 0.544023i \(0.816900\pi\)
\(374\) −9.92942e16 −1.87611
\(375\) −3.38449e16 −0.628478
\(376\) −1.02898e15 −0.0187796
\(377\) −3.94379e16 −0.707449
\(378\) 1.35765e16 0.239381
\(379\) 2.75110e16 0.476818 0.238409 0.971165i \(-0.423374\pi\)
0.238409 + 0.971165i \(0.423374\pi\)
\(380\) −9.53282e15 −0.162416
\(381\) 8.05492e15 0.134912
\(382\) −6.95452e16 −1.14513
\(383\) 8.86617e16 1.43530 0.717652 0.696402i \(-0.245217\pi\)
0.717652 + 0.696402i \(0.245217\pi\)
\(384\) 2.76267e16 0.439720
\(385\) −5.67596e16 −0.888269
\(386\) 9.29562e16 1.43041
\(387\) 3.42938e16 0.518913
\(388\) −3.62107e16 −0.538804
\(389\) 2.30974e15 0.0337980 0.0168990 0.999857i \(-0.494621\pi\)
0.0168990 + 0.999857i \(0.494621\pi\)
\(390\) −2.66131e16 −0.382979
\(391\) −2.80905e16 −0.397567
\(392\) −2.47004e15 −0.0343831
\(393\) −5.79019e16 −0.792759
\(394\) 9.53008e16 1.28343
\(395\) 8.31743e16 1.10181
\(396\) 2.03311e16 0.264937
\(397\) 8.90985e16 1.14217 0.571087 0.820890i \(-0.306522\pi\)
0.571087 + 0.820890i \(0.306522\pi\)
\(398\) 4.49315e16 0.566645
\(399\) −1.28765e16 −0.159762
\(400\) 3.41823e16 0.417264
\(401\) −4.54579e16 −0.545973 −0.272986 0.962018i \(-0.588011\pi\)
−0.272986 + 0.962018i \(0.588011\pi\)
\(402\) −1.09214e17 −1.29065
\(403\) 2.75809e16 0.320720
\(404\) −5.13912e16 −0.588044
\(405\) −7.99194e15 −0.0899901
\(406\) 1.26152e17 1.39789
\(407\) −6.27981e16 −0.684830
\(408\) −2.70232e16 −0.290032
\(409\) 2.24076e16 0.236698 0.118349 0.992972i \(-0.462240\pi\)
0.118349 + 0.992972i \(0.462240\pi\)
\(410\) −9.60795e16 −0.998931
\(411\) 9.40534e15 0.0962505
\(412\) 9.94738e16 1.00202
\(413\) −1.25521e16 −0.124463
\(414\) 1.40535e16 0.137178
\(415\) −9.26651e16 −0.890438
\(416\) 7.84083e16 0.741746
\(417\) −7.69489e16 −0.716668
\(418\) −4.71153e16 −0.432032
\(419\) 1.54773e16 0.139735 0.0698673 0.997556i \(-0.477742\pi\)
0.0698673 + 0.997556i \(0.477742\pi\)
\(420\) 3.48405e16 0.309717
\(421\) −1.50058e17 −1.31348 −0.656742 0.754115i \(-0.728066\pi\)
−0.656742 + 0.754115i \(0.728066\pi\)
\(422\) −5.68142e16 −0.489695
\(423\) −1.84536e15 −0.0156628
\(424\) −2.01994e16 −0.168834
\(425\) −5.25357e16 −0.432441
\(426\) 2.55795e16 0.207362
\(427\) −8.12025e16 −0.648318
\(428\) 1.85927e16 0.146203
\(429\) −5.38327e16 −0.416940
\(430\) 2.15032e17 1.64043
\(431\) 5.05907e16 0.380162 0.190081 0.981768i \(-0.439125\pi\)
0.190081 + 0.981768i \(0.439125\pi\)
\(432\) 3.15325e16 0.233407
\(433\) −1.65677e17 −1.20807 −0.604033 0.796959i \(-0.706441\pi\)
−0.604033 + 0.796959i \(0.706441\pi\)
\(434\) −8.82242e16 −0.633731
\(435\) −7.42606e16 −0.525507
\(436\) −5.51065e16 −0.384185
\(437\) −1.33290e16 −0.0915520
\(438\) −6.36179e16 −0.430524
\(439\) 2.59250e17 1.72862 0.864309 0.502961i \(-0.167756\pi\)
0.864309 + 0.502961i \(0.167756\pi\)
\(440\) −5.65218e16 −0.371342
\(441\) −4.42975e15 −0.0286766
\(442\) −1.61382e17 −1.02946
\(443\) 3.12166e17 1.96228 0.981141 0.193291i \(-0.0619163\pi\)
0.981141 + 0.193291i \(0.0619163\pi\)
\(444\) 3.85471e16 0.238783
\(445\) −4.33041e16 −0.264356
\(446\) 5.67154e16 0.341212
\(447\) 1.11660e17 0.662062
\(448\) −5.23952e16 −0.306185
\(449\) 7.88485e16 0.454142 0.227071 0.973878i \(-0.427085\pi\)
0.227071 + 0.973878i \(0.427085\pi\)
\(450\) 2.62834e16 0.149211
\(451\) −1.94349e17 −1.08751
\(452\) 1.35839e17 0.749247
\(453\) 1.57822e17 0.858082
\(454\) −1.57547e17 −0.844399
\(455\) −9.22508e16 −0.487412
\(456\) −1.28226e16 −0.0667888
\(457\) 2.47908e17 1.27302 0.636511 0.771267i \(-0.280377\pi\)
0.636511 + 0.771267i \(0.280377\pi\)
\(458\) −2.19924e16 −0.111339
\(459\) −4.84632e16 −0.241896
\(460\) 3.60648e16 0.177483
\(461\) −1.42944e17 −0.693602 −0.346801 0.937939i \(-0.612732\pi\)
−0.346801 + 0.937939i \(0.612732\pi\)
\(462\) 1.72197e17 0.823858
\(463\) −3.17250e17 −1.49667 −0.748333 0.663323i \(-0.769146\pi\)
−0.748333 + 0.663323i \(0.769146\pi\)
\(464\) 2.92998e17 1.36301
\(465\) 5.19342e16 0.238237
\(466\) −2.06634e17 −0.934744
\(467\) 2.64421e17 1.17961 0.589803 0.807548i \(-0.299206\pi\)
0.589803 + 0.807548i \(0.299206\pi\)
\(468\) 3.30439e16 0.145376
\(469\) −3.78575e17 −1.64259
\(470\) −1.15710e16 −0.0495146
\(471\) −1.08435e17 −0.457651
\(472\) −1.24995e16 −0.0520318
\(473\) 4.34966e17 1.78590
\(474\) −2.52334e17 −1.02192
\(475\) −2.49283e16 −0.0995827
\(476\) 2.11273e17 0.832529
\(477\) −3.62254e16 −0.140813
\(478\) 9.76668e16 0.374512
\(479\) 3.00162e17 1.13547 0.567734 0.823212i \(-0.307820\pi\)
0.567734 + 0.823212i \(0.307820\pi\)
\(480\) 1.47641e17 0.550984
\(481\) −1.02065e17 −0.375781
\(482\) 4.66919e17 1.69604
\(483\) 4.87148e16 0.174584
\(484\) 6.19321e16 0.218988
\(485\) 1.80537e17 0.629863
\(486\) 2.42459e16 0.0834646
\(487\) 3.73898e17 1.27003 0.635016 0.772499i \(-0.280994\pi\)
0.635016 + 0.772499i \(0.280994\pi\)
\(488\) −8.08623e16 −0.271030
\(489\) 1.80694e17 0.597635
\(490\) −2.77758e16 −0.0906551
\(491\) 2.38789e17 0.769102 0.384551 0.923104i \(-0.374356\pi\)
0.384551 + 0.923104i \(0.374356\pi\)
\(492\) 1.19296e17 0.379187
\(493\) −4.50317e17 −1.41258
\(494\) −7.65760e16 −0.237065
\(495\) −1.01366e17 −0.309711
\(496\) −2.04909e17 −0.617916
\(497\) 8.86680e16 0.263907
\(498\) 2.81127e17 0.825870
\(499\) −1.66895e17 −0.483937 −0.241969 0.970284i \(-0.577793\pi\)
−0.241969 + 0.970284i \(0.577793\pi\)
\(500\) 2.63498e17 0.754176
\(501\) −3.34133e16 −0.0944005
\(502\) 4.28636e17 1.19540
\(503\) −5.06854e17 −1.39538 −0.697688 0.716402i \(-0.745788\pi\)
−0.697688 + 0.716402i \(0.745788\pi\)
\(504\) 4.68639e16 0.127362
\(505\) 2.56223e17 0.687424
\(506\) 1.78248e17 0.472113
\(507\) 1.33302e17 0.348566
\(508\) −6.27113e16 −0.161894
\(509\) 2.37315e17 0.604867 0.302434 0.953170i \(-0.402201\pi\)
0.302434 + 0.953170i \(0.402201\pi\)
\(510\) −3.03878e17 −0.764704
\(511\) −2.20523e17 −0.547922
\(512\) −3.84942e17 −0.944366
\(513\) −2.29959e16 −0.0557041
\(514\) 2.97177e17 0.710813
\(515\) −4.95951e17 −1.17136
\(516\) −2.66993e17 −0.622698
\(517\) −2.34056e16 −0.0539054
\(518\) 3.26480e17 0.742528
\(519\) −1.53678e17 −0.345162
\(520\) −9.18644e16 −0.203763
\(521\) −3.55489e17 −0.778719 −0.389360 0.921086i \(-0.627304\pi\)
−0.389360 + 0.921086i \(0.627304\pi\)
\(522\) 2.25291e17 0.487401
\(523\) −1.66098e17 −0.354897 −0.177449 0.984130i \(-0.556784\pi\)
−0.177449 + 0.984130i \(0.556784\pi\)
\(524\) 4.50793e17 0.951314
\(525\) 9.11079e16 0.189898
\(526\) −9.33470e17 −1.92173
\(527\) 3.14930e17 0.640390
\(528\) 3.99942e17 0.803299
\(529\) −4.53610e17 −0.899955
\(530\) −2.27144e17 −0.445151
\(531\) −2.24165e16 −0.0433963
\(532\) 1.00250e17 0.191715
\(533\) −3.15873e17 −0.596741
\(534\) 1.31376e17 0.245187
\(535\) −9.26983e16 −0.170912
\(536\) −3.76989e17 −0.686685
\(537\) 4.22086e17 0.759570
\(538\) 2.11758e17 0.376491
\(539\) −5.61846e16 −0.0986940
\(540\) 6.22209e16 0.107988
\(541\) 5.99966e17 1.02883 0.514416 0.857541i \(-0.328009\pi\)
0.514416 + 0.857541i \(0.328009\pi\)
\(542\) 2.26720e17 0.384144
\(543\) 6.14746e17 1.02919
\(544\) 8.95296e17 1.48106
\(545\) 2.74747e17 0.449113
\(546\) 2.79870e17 0.452068
\(547\) 6.07266e17 0.969306 0.484653 0.874706i \(-0.338946\pi\)
0.484653 + 0.874706i \(0.338946\pi\)
\(548\) −7.32249e16 −0.115501
\(549\) −1.45018e17 −0.226048
\(550\) 3.33365e17 0.513526
\(551\) −2.13676e17 −0.325290
\(552\) 4.85107e16 0.0729850
\(553\) −8.74682e17 −1.30058
\(554\) 1.78315e17 0.262044
\(555\) −1.92186e17 −0.279137
\(556\) 5.99083e17 0.860004
\(557\) −5.93798e17 −0.842519 −0.421260 0.906940i \(-0.638412\pi\)
−0.421260 + 0.906940i \(0.638412\pi\)
\(558\) −1.57558e17 −0.220962
\(559\) 7.06945e17 0.979962
\(560\) 6.85364e17 0.939073
\(561\) −6.14682e17 −0.832515
\(562\) 7.80197e17 1.04452
\(563\) 1.46670e18 1.94106 0.970528 0.240989i \(-0.0774718\pi\)
0.970528 + 0.240989i \(0.0774718\pi\)
\(564\) 1.43670e16 0.0187954
\(565\) −6.77260e17 −0.875871
\(566\) 1.08910e18 1.39239
\(567\) 8.40453e16 0.106224
\(568\) 8.82965e16 0.110326
\(569\) −2.96505e17 −0.366270 −0.183135 0.983088i \(-0.558625\pi\)
−0.183135 + 0.983088i \(0.558625\pi\)
\(570\) −1.44191e17 −0.176097
\(571\) −9.45165e17 −1.14123 −0.570615 0.821218i \(-0.693295\pi\)
−0.570615 + 0.821218i \(0.693295\pi\)
\(572\) 4.19113e17 0.500330
\(573\) −4.30520e17 −0.508146
\(574\) 1.01040e18 1.17914
\(575\) 9.43094e16 0.108821
\(576\) −9.35714e16 −0.106757
\(577\) 5.97695e16 0.0674274 0.0337137 0.999432i \(-0.489267\pi\)
0.0337137 + 0.999432i \(0.489267\pi\)
\(578\) −6.76349e17 −0.754467
\(579\) 5.75447e17 0.634738
\(580\) 5.78153e17 0.630610
\(581\) 9.74490e17 1.05107
\(582\) −5.47713e17 −0.584190
\(583\) −4.59464e17 −0.484625
\(584\) −2.19599e17 −0.229059
\(585\) −1.64749e17 −0.169945
\(586\) 1.56575e18 1.59731
\(587\) −1.05773e18 −1.06716 −0.533578 0.845751i \(-0.679153\pi\)
−0.533578 + 0.845751i \(0.679153\pi\)
\(588\) 3.44876e16 0.0344120
\(589\) 1.49435e17 0.147469
\(590\) −1.40558e17 −0.137188
\(591\) 5.89961e17 0.569514
\(592\) 7.58278e17 0.723998
\(593\) −1.24219e18 −1.17309 −0.586545 0.809917i \(-0.699512\pi\)
−0.586545 + 0.809917i \(0.699512\pi\)
\(594\) 3.07523e17 0.287253
\(595\) −1.05335e18 −0.973228
\(596\) −8.69324e17 −0.794477
\(597\) 2.78149e17 0.251446
\(598\) 2.89705e17 0.259058
\(599\) 4.08031e17 0.360927 0.180463 0.983582i \(-0.442240\pi\)
0.180463 + 0.983582i \(0.442240\pi\)
\(600\) 9.07262e16 0.0793871
\(601\) −1.38737e18 −1.20091 −0.600453 0.799660i \(-0.705013\pi\)
−0.600453 + 0.799660i \(0.705013\pi\)
\(602\) −2.26134e18 −1.93637
\(603\) −6.76088e17 −0.572718
\(604\) −1.22872e18 −1.02970
\(605\) −3.08778e17 −0.255998
\(606\) −7.77329e17 −0.637577
\(607\) −1.70509e17 −0.138363 −0.0691816 0.997604i \(-0.522039\pi\)
−0.0691816 + 0.997604i \(0.522039\pi\)
\(608\) 4.24819e17 0.341060
\(609\) 7.80944e17 0.620308
\(610\) −9.09303e17 −0.714603
\(611\) −3.80410e16 −0.0295790
\(612\) 3.77308e17 0.290277
\(613\) 2.03409e16 0.0154838 0.00774189 0.999970i \(-0.497536\pi\)
0.00774189 + 0.999970i \(0.497536\pi\)
\(614\) 8.42917e17 0.634878
\(615\) −5.94781e17 −0.443271
\(616\) 5.94398e17 0.438332
\(617\) −2.02104e18 −1.47476 −0.737380 0.675478i \(-0.763937\pi\)
−0.737380 + 0.675478i \(0.763937\pi\)
\(618\) 1.50461e18 1.08643
\(619\) −5.19853e17 −0.371442 −0.185721 0.982602i \(-0.559462\pi\)
−0.185721 + 0.982602i \(0.559462\pi\)
\(620\) −4.04332e17 −0.285885
\(621\) 8.69986e16 0.0608719
\(622\) −1.25411e18 −0.868354
\(623\) 4.55397e17 0.312046
\(624\) 6.50023e17 0.440787
\(625\) −8.01069e17 −0.537588
\(626\) −3.20208e18 −2.12666
\(627\) −2.91668e17 −0.191712
\(628\) 8.44219e17 0.549183
\(629\) −1.16542e18 −0.750331
\(630\) 5.26988e17 0.335805
\(631\) −2.04962e18 −1.29266 −0.646328 0.763060i \(-0.723696\pi\)
−0.646328 + 0.763060i \(0.723696\pi\)
\(632\) −8.71018e17 −0.543709
\(633\) −3.51709e17 −0.217300
\(634\) 1.06289e17 0.0649993
\(635\) 3.12663e17 0.189255
\(636\) 2.82031e17 0.168976
\(637\) −9.13164e16 −0.0541555
\(638\) 2.85748e18 1.67745
\(639\) 1.58350e17 0.0920159
\(640\) 1.07237e18 0.616842
\(641\) −1.02725e18 −0.584924 −0.292462 0.956277i \(-0.594474\pi\)
−0.292462 + 0.956277i \(0.594474\pi\)
\(642\) 2.81227e17 0.158519
\(643\) 2.56040e18 1.42869 0.714343 0.699795i \(-0.246725\pi\)
0.714343 + 0.699795i \(0.246725\pi\)
\(644\) −3.79267e17 −0.209501
\(645\) 1.33116e18 0.727935
\(646\) −8.74374e17 −0.473354
\(647\) −1.82578e17 −0.0978523 −0.0489262 0.998802i \(-0.515580\pi\)
−0.0489262 + 0.998802i \(0.515580\pi\)
\(648\) 8.36932e16 0.0444071
\(649\) −2.84319e17 −0.149354
\(650\) 5.41815e17 0.281782
\(651\) −5.46154e17 −0.281215
\(652\) −1.40679e18 −0.717164
\(653\) −5.14885e15 −0.00259881 −0.00129941 0.999999i \(-0.500414\pi\)
−0.00129941 + 0.999999i \(0.500414\pi\)
\(654\) −8.33526e17 −0.416547
\(655\) −2.24754e18 −1.11209
\(656\) 2.34673e18 1.14971
\(657\) −3.93827e17 −0.191043
\(658\) 1.21683e17 0.0584470
\(659\) 8.96066e17 0.426172 0.213086 0.977033i \(-0.431649\pi\)
0.213086 + 0.977033i \(0.431649\pi\)
\(660\) 7.89179e17 0.371655
\(661\) −2.05762e18 −0.959523 −0.479762 0.877399i \(-0.659277\pi\)
−0.479762 + 0.877399i \(0.659277\pi\)
\(662\) −5.29066e18 −2.44305
\(663\) −9.99038e17 −0.456819
\(664\) 9.70408e17 0.439402
\(665\) −4.99819e17 −0.224116
\(666\) 5.83053e17 0.258896
\(667\) 8.08386e17 0.355468
\(668\) 2.60138e17 0.113281
\(669\) 3.51097e17 0.151411
\(670\) −4.23927e18 −1.81053
\(671\) −1.83933e18 −0.777971
\(672\) −1.55263e18 −0.650381
\(673\) −2.65917e18 −1.10319 −0.551593 0.834113i \(-0.685980\pi\)
−0.551593 + 0.834113i \(0.685980\pi\)
\(674\) 8.89514e17 0.365480
\(675\) 1.62708e17 0.0662115
\(676\) −1.03782e18 −0.418281
\(677\) −9.92748e16 −0.0396289 −0.0198145 0.999804i \(-0.506308\pi\)
−0.0198145 + 0.999804i \(0.506308\pi\)
\(678\) 2.05467e18 0.812360
\(679\) −1.89858e18 −0.743489
\(680\) −1.04894e18 −0.406859
\(681\) −9.75299e17 −0.374698
\(682\) −1.99838e18 −0.760467
\(683\) −4.11610e18 −1.55150 −0.775748 0.631042i \(-0.782627\pi\)
−0.775748 + 0.631042i \(0.782627\pi\)
\(684\) 1.79033e17 0.0668451
\(685\) 3.65081e17 0.135021
\(686\) 3.68740e18 1.35087
\(687\) −1.36144e17 −0.0494060
\(688\) −5.25215e18 −1.88804
\(689\) −7.46763e17 −0.265924
\(690\) 5.45507e17 0.192434
\(691\) −5.22830e17 −0.182706 −0.0913530 0.995819i \(-0.529119\pi\)
−0.0913530 + 0.995819i \(0.529119\pi\)
\(692\) 1.19645e18 0.414195
\(693\) 1.06599e18 0.365583
\(694\) 4.83331e17 0.164213
\(695\) −2.98687e18 −1.00535
\(696\) 7.77673e17 0.259320
\(697\) −3.60676e18 −1.19153
\(698\) −1.92994e18 −0.631662
\(699\) −1.27917e18 −0.414788
\(700\) −7.09317e17 −0.227878
\(701\) 9.28005e16 0.0295382 0.0147691 0.999891i \(-0.495299\pi\)
0.0147691 + 0.999891i \(0.495299\pi\)
\(702\) 4.99814e17 0.157622
\(703\) −5.52993e17 −0.172787
\(704\) −1.18681e18 −0.367417
\(705\) −7.16302e16 −0.0219719
\(706\) −4.94329e18 −1.50240
\(707\) −2.69451e18 −0.811435
\(708\) 1.74523e17 0.0520757
\(709\) 1.08498e18 0.320791 0.160395 0.987053i \(-0.448723\pi\)
0.160395 + 0.987053i \(0.448723\pi\)
\(710\) 9.92902e17 0.290889
\(711\) −1.56208e18 −0.453471
\(712\) 4.53490e17 0.130451
\(713\) −5.65345e17 −0.161151
\(714\) 3.19566e18 0.902656
\(715\) −2.08959e18 −0.584887
\(716\) −3.28613e18 −0.911486
\(717\) 6.04608e17 0.166188
\(718\) −2.82743e17 −0.0770163
\(719\) −1.43557e18 −0.387514 −0.193757 0.981050i \(-0.562067\pi\)
−0.193757 + 0.981050i \(0.562067\pi\)
\(720\) 1.22398e18 0.327425
\(721\) 5.21555e18 1.38268
\(722\) 4.53730e18 1.19208
\(723\) 2.89047e18 0.752610
\(724\) −4.78608e18 −1.23503
\(725\) 1.51187e18 0.386649
\(726\) 9.36769e17 0.237435
\(727\) 3.01211e18 0.756654 0.378327 0.925672i \(-0.376499\pi\)
0.378327 + 0.925672i \(0.376499\pi\)
\(728\) 9.66069e17 0.240522
\(729\) 1.50095e17 0.0370370
\(730\) −2.46941e18 −0.603942
\(731\) 8.07217e18 1.95671
\(732\) 1.12903e18 0.271259
\(733\) 1.04077e18 0.247845 0.123922 0.992292i \(-0.460453\pi\)
0.123922 + 0.992292i \(0.460453\pi\)
\(734\) 3.18515e18 0.751805
\(735\) −1.71947e17 −0.0402277
\(736\) −1.60719e18 −0.372701
\(737\) −8.57516e18 −1.97108
\(738\) 1.80444e18 0.411128
\(739\) 6.59981e18 1.49054 0.745268 0.666765i \(-0.232322\pi\)
0.745268 + 0.666765i \(0.232322\pi\)
\(740\) 1.49626e18 0.334966
\(741\) −4.74045e17 −0.105197
\(742\) 2.38870e18 0.525456
\(743\) −6.39379e18 −1.39422 −0.697110 0.716964i \(-0.745531\pi\)
−0.697110 + 0.716964i \(0.745531\pi\)
\(744\) −5.43866e17 −0.117562
\(745\) 4.33423e18 0.928745
\(746\) 1.02787e19 2.18340
\(747\) 1.74032e18 0.366476
\(748\) 4.78559e18 0.999021
\(749\) 9.74839e17 0.201744
\(750\) 3.98560e18 0.817704
\(751\) −2.96633e18 −0.603336 −0.301668 0.953413i \(-0.597543\pi\)
−0.301668 + 0.953413i \(0.597543\pi\)
\(752\) 2.82620e17 0.0569885
\(753\) 2.65348e18 0.530454
\(754\) 4.64424e18 0.920451
\(755\) 6.12607e18 1.20372
\(756\) −6.54331e17 −0.127469
\(757\) −1.36828e18 −0.264272 −0.132136 0.991232i \(-0.542184\pi\)
−0.132136 + 0.991232i \(0.542184\pi\)
\(758\) −3.23972e18 −0.620380
\(759\) 1.10345e18 0.209498
\(760\) −4.97725e17 −0.0936917
\(761\) 3.65930e18 0.682965 0.341482 0.939888i \(-0.389071\pi\)
0.341482 + 0.939888i \(0.389071\pi\)
\(762\) −9.48554e17 −0.175531
\(763\) −2.88931e18 −0.530133
\(764\) 3.35180e18 0.609777
\(765\) −1.88116e18 −0.339334
\(766\) −1.04409e19 −1.86745
\(767\) −4.62101e17 −0.0819534
\(768\) −4.30483e18 −0.757022
\(769\) 8.16747e18 1.42418 0.712092 0.702086i \(-0.247748\pi\)
0.712092 + 0.702086i \(0.247748\pi\)
\(770\) 6.68405e18 1.15571
\(771\) 1.83968e18 0.315420
\(772\) −4.48012e18 −0.761688
\(773\) −9.87665e18 −1.66511 −0.832555 0.553942i \(-0.813123\pi\)
−0.832555 + 0.553942i \(0.813123\pi\)
\(774\) −4.03847e18 −0.675150
\(775\) −1.05733e18 −0.175286
\(776\) −1.89062e18 −0.310817
\(777\) 2.02108e18 0.329493
\(778\) −2.71997e17 −0.0439740
\(779\) −1.71141e18 −0.274386
\(780\) 1.28264e18 0.203935
\(781\) 2.00843e18 0.316684
\(782\) 3.30796e18 0.517268
\(783\) 1.39467e18 0.216282
\(784\) 6.78422e17 0.104339
\(785\) −4.20906e18 −0.641996
\(786\) 6.81857e18 1.03145
\(787\) −1.02120e17 −0.0153206 −0.00766029 0.999971i \(-0.502438\pi\)
−0.00766029 + 0.999971i \(0.502438\pi\)
\(788\) −4.59312e18 −0.683419
\(789\) −5.77866e18 −0.852760
\(790\) −9.79467e18 −1.43355
\(791\) 7.12224e18 1.03388
\(792\) 1.06152e18 0.152832
\(793\) −2.98945e18 −0.426889
\(794\) −1.04923e19 −1.48606
\(795\) −1.40614e18 −0.197534
\(796\) −2.16552e18 −0.301736
\(797\) −3.18508e18 −0.440191 −0.220095 0.975478i \(-0.570637\pi\)
−0.220095 + 0.975478i \(0.570637\pi\)
\(798\) 1.51635e18 0.207864
\(799\) −4.34366e17 −0.0590612
\(800\) −3.00581e18 −0.405394
\(801\) 8.13284e17 0.108801
\(802\) 5.35316e18 0.710357
\(803\) −4.99511e18 −0.657497
\(804\) 5.26366e18 0.687264
\(805\) 1.89093e18 0.244907
\(806\) −3.24795e18 −0.417284
\(807\) 1.31089e18 0.167066
\(808\) −2.68322e18 −0.339221
\(809\) 3.36804e18 0.422388 0.211194 0.977444i \(-0.432265\pi\)
0.211194 + 0.977444i \(0.432265\pi\)
\(810\) 9.41137e17 0.117085
\(811\) 1.45522e19 1.79595 0.897975 0.440046i \(-0.145038\pi\)
0.897975 + 0.440046i \(0.145038\pi\)
\(812\) −6.08001e18 −0.744372
\(813\) 1.40351e18 0.170462
\(814\) 7.39515e18 0.891022
\(815\) 7.01388e18 0.838366
\(816\) 7.42221e18 0.880130
\(817\) 3.83026e18 0.450593
\(818\) −2.63874e18 −0.307964
\(819\) 1.73254e18 0.200603
\(820\) 4.63065e18 0.531927
\(821\) 7.95100e18 0.906132 0.453066 0.891477i \(-0.350330\pi\)
0.453066 + 0.891477i \(0.350330\pi\)
\(822\) −1.10758e18 −0.125230
\(823\) 4.31928e18 0.484521 0.242261 0.970211i \(-0.422111\pi\)
0.242261 + 0.970211i \(0.422111\pi\)
\(824\) 5.19370e18 0.578030
\(825\) 2.06370e18 0.227875
\(826\) 1.47814e18 0.161937
\(827\) 4.40647e18 0.478966 0.239483 0.970901i \(-0.423022\pi\)
0.239483 + 0.970901i \(0.423022\pi\)
\(828\) −6.77324e17 −0.0730465
\(829\) −5.62494e18 −0.601885 −0.300943 0.953642i \(-0.597301\pi\)
−0.300943 + 0.953642i \(0.597301\pi\)
\(830\) 1.09123e19 1.15854
\(831\) 1.10386e18 0.116281
\(832\) −1.92891e18 −0.201610
\(833\) −1.04268e18 −0.108134
\(834\) 9.06156e18 0.932446
\(835\) −1.29698e18 −0.132426
\(836\) 2.27077e18 0.230055
\(837\) −9.75364e17 −0.0980508
\(838\) −1.82262e18 −0.181807
\(839\) 6.34005e18 0.627538 0.313769 0.949499i \(-0.398408\pi\)
0.313769 + 0.949499i \(0.398408\pi\)
\(840\) 1.81909e18 0.178664
\(841\) 2.69857e18 0.263002
\(842\) 1.76709e19 1.70895
\(843\) 4.82982e18 0.463503
\(844\) 2.73822e18 0.260761
\(845\) 5.17430e18 0.488971
\(846\) 2.17311e17 0.0203786
\(847\) 3.24719e18 0.302180
\(848\) 5.54797e18 0.512343
\(849\) 6.74211e18 0.617868
\(850\) 6.18664e18 0.562642
\(851\) 2.09210e18 0.188817
\(852\) −1.23283e18 −0.110419
\(853\) −1.82493e19 −1.62210 −0.811049 0.584978i \(-0.801103\pi\)
−0.811049 + 0.584978i \(0.801103\pi\)
\(854\) 9.56247e18 0.843517
\(855\) −8.92616e17 −0.0781420
\(856\) 9.70755e17 0.0843393
\(857\) 3.55069e18 0.306152 0.153076 0.988214i \(-0.451082\pi\)
0.153076 + 0.988214i \(0.451082\pi\)
\(858\) 6.33938e18 0.542475
\(859\) 1.25671e18 0.106728 0.0533642 0.998575i \(-0.483006\pi\)
0.0533642 + 0.998575i \(0.483006\pi\)
\(860\) −1.03637e19 −0.873524
\(861\) 6.25487e18 0.523237
\(862\) −5.95760e18 −0.494623
\(863\) 1.66156e19 1.36914 0.684568 0.728949i \(-0.259991\pi\)
0.684568 + 0.728949i \(0.259991\pi\)
\(864\) −2.77281e18 −0.226767
\(865\) −5.96520e18 −0.484195
\(866\) 1.95102e19 1.57180
\(867\) −4.18695e18 −0.334791
\(868\) 4.25206e18 0.337459
\(869\) −1.98126e19 −1.56067
\(870\) 8.74499e18 0.683729
\(871\) −1.39371e19 −1.08157
\(872\) −2.87721e18 −0.221623
\(873\) −3.39063e18 −0.259231
\(874\) 1.56963e18 0.119117
\(875\) 1.38156e19 1.04068
\(876\) 3.06613e18 0.229252
\(877\) −2.23539e19 −1.65904 −0.829519 0.558479i \(-0.811385\pi\)
−0.829519 + 0.558479i \(0.811385\pi\)
\(878\) −3.05295e19 −2.24908
\(879\) 9.69282e18 0.708798
\(880\) 1.55243e19 1.12687
\(881\) −1.82829e18 −0.131735 −0.0658677 0.997828i \(-0.520982\pi\)
−0.0658677 + 0.997828i \(0.520982\pi\)
\(882\) 5.21650e17 0.0373107
\(883\) 9.26249e18 0.657632 0.328816 0.944394i \(-0.393350\pi\)
0.328816 + 0.944394i \(0.393350\pi\)
\(884\) 7.77797e18 0.548184
\(885\) −8.70125e17 −0.0608766
\(886\) −3.67609e19 −2.55310
\(887\) 1.52083e19 1.04852 0.524261 0.851558i \(-0.324342\pi\)
0.524261 + 0.851558i \(0.324342\pi\)
\(888\) 2.01261e18 0.137745
\(889\) −3.28804e18 −0.223396
\(890\) 5.09953e18 0.343950
\(891\) 1.90372e18 0.127467
\(892\) −2.73345e18 −0.181694
\(893\) −2.06108e17 −0.0136006
\(894\) −1.31492e19 −0.861399
\(895\) 1.63838e19 1.06553
\(896\) −1.12773e19 −0.728119
\(897\) 1.79342e18 0.114956
\(898\) −9.28525e18 −0.590878
\(899\) −9.06302e18 −0.572579
\(900\) −1.26675e18 −0.0794540
\(901\) −8.52682e18 −0.530977
\(902\) 2.28867e19 1.41495
\(903\) −1.39988e19 −0.859254
\(904\) 7.09240e18 0.432214
\(905\) 2.38622e19 1.44376
\(906\) −1.85852e19 −1.11644
\(907\) 1.57518e19 0.939467 0.469733 0.882808i \(-0.344350\pi\)
0.469733 + 0.882808i \(0.344350\pi\)
\(908\) 7.59315e18 0.449639
\(909\) −4.81207e18 −0.282922
\(910\) 1.08635e19 0.634164
\(911\) −3.62535e18 −0.210127 −0.105063 0.994466i \(-0.533505\pi\)
−0.105063 + 0.994466i \(0.533505\pi\)
\(912\) 3.52185e18 0.202677
\(913\) 2.20733e19 1.26127
\(914\) −2.91939e19 −1.65631
\(915\) −5.62906e18 −0.317102
\(916\) 1.05994e18 0.0592874
\(917\) 2.36357e19 1.31271
\(918\) 5.70706e18 0.314728
\(919\) −3.56210e19 −1.95054 −0.975270 0.221018i \(-0.929062\pi\)
−0.975270 + 0.221018i \(0.929062\pi\)
\(920\) 1.88301e18 0.102384
\(921\) 5.21809e18 0.281724
\(922\) 1.68332e19 0.902436
\(923\) 3.26429e18 0.173771
\(924\) −8.29921e18 −0.438701
\(925\) 3.91271e18 0.205379
\(926\) 3.73596e19 1.94729
\(927\) 9.31434e18 0.482096
\(928\) −2.57648e19 −1.32423
\(929\) −1.54882e18 −0.0790494 −0.0395247 0.999219i \(-0.512584\pi\)
−0.0395247 + 0.999219i \(0.512584\pi\)
\(930\) −6.11581e18 −0.309967
\(931\) −4.94756e17 −0.0249011
\(932\) 9.95892e18 0.497747
\(933\) −7.76357e18 −0.385328
\(934\) −3.11385e19 −1.53477
\(935\) −2.38597e19 −1.16786
\(936\) 1.72528e18 0.0838624
\(937\) −2.69360e19 −1.30025 −0.650124 0.759828i \(-0.725283\pi\)
−0.650124 + 0.759828i \(0.725283\pi\)
\(938\) 4.45812e19 2.13714
\(939\) −1.98225e19 −0.943697
\(940\) 5.57674e17 0.0263663
\(941\) 5.50527e18 0.258491 0.129246 0.991613i \(-0.458744\pi\)
0.129246 + 0.991613i \(0.458744\pi\)
\(942\) 1.27694e19 0.595443
\(943\) 6.47467e18 0.299841
\(944\) 3.43311e18 0.157896
\(945\) 3.26233e18 0.149012
\(946\) −5.12219e19 −2.32361
\(947\) 3.46328e18 0.156032 0.0780158 0.996952i \(-0.475142\pi\)
0.0780158 + 0.996952i \(0.475142\pi\)
\(948\) 1.21615e19 0.544167
\(949\) −8.11850e18 −0.360783
\(950\) 2.93557e18 0.129566
\(951\) 6.57984e17 0.0288431
\(952\) 1.10309e19 0.480256
\(953\) −9.28755e18 −0.401603 −0.200802 0.979632i \(-0.564355\pi\)
−0.200802 + 0.979632i \(0.564355\pi\)
\(954\) 4.26593e18 0.183210
\(955\) −1.67112e19 −0.712831
\(956\) −4.70715e18 −0.199426
\(957\) 1.76893e19 0.744360
\(958\) −3.53473e19 −1.47734
\(959\) −3.83929e18 −0.159378
\(960\) −3.63210e18 −0.149760
\(961\) −1.80793e19 −0.740423
\(962\) 1.20193e19 0.488923
\(963\) 1.74094e18 0.0703418
\(964\) −2.25037e19 −0.903135
\(965\) 2.23367e19 0.890414
\(966\) −5.73669e18 −0.227148
\(967\) −2.33632e18 −0.0918882 −0.0459441 0.998944i \(-0.514630\pi\)
−0.0459441 + 0.998944i \(0.514630\pi\)
\(968\) 3.23359e18 0.126327
\(969\) −5.41283e18 −0.210049
\(970\) −2.12602e19 −0.819505
\(971\) −7.87518e18 −0.301534 −0.150767 0.988569i \(-0.548174\pi\)
−0.150767 + 0.988569i \(0.548174\pi\)
\(972\) −1.16856e18 −0.0444446
\(973\) 3.14107e19 1.18671
\(974\) −4.40305e19 −1.65242
\(975\) 3.35411e18 0.125040
\(976\) 2.22097e19 0.822467
\(977\) −1.02952e19 −0.378723 −0.189362 0.981907i \(-0.560642\pi\)
−0.189362 + 0.981907i \(0.560642\pi\)
\(978\) −2.12787e19 −0.777574
\(979\) 1.03153e19 0.374450
\(980\) 1.33868e18 0.0482734
\(981\) −5.15996e18 −0.184841
\(982\) −2.81199e19 −1.00067
\(983\) −3.04604e19 −1.07681 −0.538403 0.842687i \(-0.680972\pi\)
−0.538403 + 0.842687i \(0.680972\pi\)
\(984\) 6.22867e18 0.218740
\(985\) 2.29001e19 0.798918
\(986\) 5.30297e19 1.83789
\(987\) 7.53282e17 0.0259356
\(988\) 3.69066e18 0.126236
\(989\) −1.44907e19 −0.492396
\(990\) 1.19369e19 0.402961
\(991\) −1.84904e19 −0.620108 −0.310054 0.950719i \(-0.600347\pi\)
−0.310054 + 0.950719i \(0.600347\pi\)
\(992\) 1.80186e19 0.600337
\(993\) −3.27519e19 −1.08409
\(994\) −1.04416e19 −0.343365
\(995\) 1.07967e19 0.352730
\(996\) −1.35492e19 −0.439772
\(997\) −3.53403e19 −1.13960 −0.569799 0.821784i \(-0.692979\pi\)
−0.569799 + 0.821784i \(0.692979\pi\)
\(998\) 1.96537e19 0.629644
\(999\) 3.60940e18 0.114884
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.1.7 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.7 31 1.1 even 1 trivial