Properties

Label 177.14.a.b.1.3
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 1.3
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-159.673 q^{2} -729.000 q^{3} +17303.4 q^{4} -10788.6 q^{5} +116402. q^{6} +188818. q^{7} -1.45485e6 q^{8} +531441. q^{9} +O(q^{10})\) \(q-159.673 q^{2} -729.000 q^{3} +17303.4 q^{4} -10788.6 q^{5} +116402. q^{6} +188818. q^{7} -1.45485e6 q^{8} +531441. q^{9} +1.72264e6 q^{10} +7.69789e6 q^{11} -1.26142e7 q^{12} +8.10554e6 q^{13} -3.01492e7 q^{14} +7.86486e6 q^{15} +9.05501e7 q^{16} -3.84238e7 q^{17} -8.48567e7 q^{18} +2.90246e8 q^{19} -1.86679e8 q^{20} -1.37649e8 q^{21} -1.22914e9 q^{22} +6.02860e8 q^{23} +1.06058e9 q^{24} -1.10431e9 q^{25} -1.29424e9 q^{26} -3.87420e8 q^{27} +3.26720e9 q^{28} +6.20361e9 q^{29} -1.25581e9 q^{30} -4.12563e9 q^{31} -2.54027e9 q^{32} -5.61176e9 q^{33} +6.13525e9 q^{34} -2.03708e9 q^{35} +9.19575e9 q^{36} +2.05036e9 q^{37} -4.63444e10 q^{38} -5.90894e9 q^{39} +1.56957e10 q^{40} -1.51019e10 q^{41} +2.19787e10 q^{42} -8.13939e10 q^{43} +1.33200e11 q^{44} -5.73348e9 q^{45} -9.62605e10 q^{46} -3.75187e10 q^{47} -6.60110e10 q^{48} -6.12366e10 q^{49} +1.76328e11 q^{50} +2.80110e10 q^{51} +1.40254e11 q^{52} -4.24339e10 q^{53} +6.18605e10 q^{54} -8.30491e10 q^{55} -2.74702e11 q^{56} -2.11589e11 q^{57} -9.90549e11 q^{58} -4.21805e10 q^{59} +1.36089e11 q^{60} -7.71030e11 q^{61} +6.58751e11 q^{62} +1.00346e11 q^{63} -3.36173e11 q^{64} -8.74472e10 q^{65} +8.96046e11 q^{66} +2.56447e10 q^{67} -6.64864e11 q^{68} -4.39485e11 q^{69} +3.25266e11 q^{70} -1.41029e12 q^{71} -7.73166e11 q^{72} -1.45810e12 q^{73} -3.27386e11 q^{74} +8.05042e11 q^{75} +5.02224e12 q^{76} +1.45350e12 q^{77} +9.43498e11 q^{78} +3.78082e12 q^{79} -9.76905e11 q^{80} +2.82430e11 q^{81} +2.41136e12 q^{82} -1.30021e12 q^{83} -2.38179e12 q^{84} +4.14538e11 q^{85} +1.29964e13 q^{86} -4.52244e12 q^{87} -1.11993e13 q^{88} +8.93336e11 q^{89} +9.15482e11 q^{90} +1.53048e12 q^{91} +1.04316e13 q^{92} +3.00758e12 q^{93} +5.99072e12 q^{94} -3.13133e12 q^{95} +1.85186e12 q^{96} +9.58195e12 q^{97} +9.77783e12 q^{98} +4.09097e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −159.673 −1.76415 −0.882076 0.471106i \(-0.843855\pi\)
−0.882076 + 0.471106i \(0.843855\pi\)
\(3\) −729.000 −0.577350
\(4\) 17303.4 2.11223
\(5\) −10788.6 −0.308787 −0.154393 0.988009i \(-0.549342\pi\)
−0.154393 + 0.988009i \(0.549342\pi\)
\(6\) 116402. 1.01853
\(7\) 188818. 0.606606 0.303303 0.952894i \(-0.401911\pi\)
0.303303 + 0.952894i \(0.401911\pi\)
\(8\) −1.45485e6 −1.96215
\(9\) 531441. 0.333333
\(10\) 1.72264e6 0.544747
\(11\) 7.69789e6 1.31014 0.655072 0.755566i \(-0.272638\pi\)
0.655072 + 0.755566i \(0.272638\pi\)
\(12\) −1.26142e7 −1.21950
\(13\) 8.10554e6 0.465747 0.232874 0.972507i \(-0.425187\pi\)
0.232874 + 0.972507i \(0.425187\pi\)
\(14\) −3.01492e7 −1.07015
\(15\) 7.86486e6 0.178278
\(16\) 9.05501e7 1.34930
\(17\) −3.84238e7 −0.386085 −0.193042 0.981190i \(-0.561836\pi\)
−0.193042 + 0.981190i \(0.561836\pi\)
\(18\) −8.48567e7 −0.588051
\(19\) 2.90246e8 1.41536 0.707681 0.706532i \(-0.249742\pi\)
0.707681 + 0.706532i \(0.249742\pi\)
\(20\) −1.86679e8 −0.652230
\(21\) −1.37649e8 −0.350224
\(22\) −1.22914e9 −2.31129
\(23\) 6.02860e8 0.849153 0.424576 0.905392i \(-0.360423\pi\)
0.424576 + 0.905392i \(0.360423\pi\)
\(24\) 1.06058e9 1.13285
\(25\) −1.10431e9 −0.904651
\(26\) −1.29424e9 −0.821649
\(27\) −3.87420e8 −0.192450
\(28\) 3.26720e9 1.28129
\(29\) 6.20361e9 1.93668 0.968340 0.249635i \(-0.0803107\pi\)
0.968340 + 0.249635i \(0.0803107\pi\)
\(30\) −1.25581e9 −0.314510
\(31\) −4.12563e9 −0.834909 −0.417455 0.908698i \(-0.637078\pi\)
−0.417455 + 0.908698i \(0.637078\pi\)
\(32\) −2.54027e9 −0.418221
\(33\) −5.61176e9 −0.756412
\(34\) 6.13525e9 0.681113
\(35\) −2.03708e9 −0.187312
\(36\) 9.19575e9 0.704078
\(37\) 2.05036e9 0.131377 0.0656883 0.997840i \(-0.479076\pi\)
0.0656883 + 0.997840i \(0.479076\pi\)
\(38\) −4.63444e10 −2.49691
\(39\) −5.90894e9 −0.268899
\(40\) 1.56957e10 0.605886
\(41\) −1.51019e10 −0.496520 −0.248260 0.968693i \(-0.579859\pi\)
−0.248260 + 0.968693i \(0.579859\pi\)
\(42\) 2.19787e10 0.617849
\(43\) −8.13939e10 −1.96357 −0.981786 0.189992i \(-0.939154\pi\)
−0.981786 + 0.189992i \(0.939154\pi\)
\(44\) 1.33200e11 2.76733
\(45\) −5.73348e9 −0.102929
\(46\) −9.62605e10 −1.49804
\(47\) −3.75187e10 −0.507705 −0.253853 0.967243i \(-0.581698\pi\)
−0.253853 + 0.967243i \(0.581698\pi\)
\(48\) −6.60110e10 −0.779019
\(49\) −6.12366e10 −0.632029
\(50\) 1.76328e11 1.59594
\(51\) 2.80110e10 0.222906
\(52\) 1.40254e11 0.983768
\(53\) −4.24339e10 −0.262978 −0.131489 0.991318i \(-0.541976\pi\)
−0.131489 + 0.991318i \(0.541976\pi\)
\(54\) 6.18605e10 0.339511
\(55\) −8.30491e10 −0.404555
\(56\) −2.74702e11 −1.19025
\(57\) −2.11589e11 −0.817159
\(58\) −9.90549e11 −3.41660
\(59\) −4.21805e10 −0.130189
\(60\) 1.36089e11 0.376565
\(61\) −7.71030e11 −1.91614 −0.958070 0.286535i \(-0.907497\pi\)
−0.958070 + 0.286535i \(0.907497\pi\)
\(62\) 6.58751e11 1.47291
\(63\) 1.00346e11 0.202202
\(64\) −3.36173e11 −0.611495
\(65\) −8.74472e10 −0.143817
\(66\) 8.96046e11 1.33443
\(67\) 2.56447e10 0.0346347 0.0173174 0.999850i \(-0.494487\pi\)
0.0173174 + 0.999850i \(0.494487\pi\)
\(68\) −6.64864e11 −0.815502
\(69\) −4.39485e11 −0.490259
\(70\) 3.25266e11 0.330447
\(71\) −1.41029e12 −1.30656 −0.653282 0.757115i \(-0.726608\pi\)
−0.653282 + 0.757115i \(0.726608\pi\)
\(72\) −7.73166e11 −0.654051
\(73\) −1.45810e12 −1.12769 −0.563844 0.825881i \(-0.690678\pi\)
−0.563844 + 0.825881i \(0.690678\pi\)
\(74\) −3.27386e11 −0.231768
\(75\) 8.05042e11 0.522300
\(76\) 5.02224e12 2.98958
\(77\) 1.45350e12 0.794742
\(78\) 9.43498e11 0.474380
\(79\) 3.78082e12 1.74989 0.874943 0.484227i \(-0.160899\pi\)
0.874943 + 0.484227i \(0.160899\pi\)
\(80\) −9.76905e11 −0.416646
\(81\) 2.82430e11 0.111111
\(82\) 2.41136e12 0.875937
\(83\) −1.30021e12 −0.436521 −0.218261 0.975891i \(-0.570038\pi\)
−0.218261 + 0.975891i \(0.570038\pi\)
\(84\) −2.38179e12 −0.739756
\(85\) 4.14538e11 0.119218
\(86\) 1.29964e13 3.46404
\(87\) −4.52244e12 −1.11814
\(88\) −1.11993e13 −2.57070
\(89\) 8.93336e11 0.190537 0.0952686 0.995452i \(-0.469629\pi\)
0.0952686 + 0.995452i \(0.469629\pi\)
\(90\) 9.15482e11 0.181582
\(91\) 1.53048e12 0.282525
\(92\) 1.04316e13 1.79361
\(93\) 3.00758e12 0.482035
\(94\) 5.99072e12 0.895669
\(95\) −3.13133e12 −0.437045
\(96\) 1.85186e12 0.241460
\(97\) 9.58195e12 1.16799 0.583993 0.811759i \(-0.301490\pi\)
0.583993 + 0.811759i \(0.301490\pi\)
\(98\) 9.77783e12 1.11500
\(99\) 4.09097e12 0.436715
\(100\) −1.91083e13 −1.91083
\(101\) 1.29711e12 0.121587 0.0607936 0.998150i \(-0.480637\pi\)
0.0607936 + 0.998150i \(0.480637\pi\)
\(102\) −4.47259e12 −0.393241
\(103\) −8.37017e12 −0.690704 −0.345352 0.938473i \(-0.612241\pi\)
−0.345352 + 0.938473i \(0.612241\pi\)
\(104\) −1.17923e13 −0.913867
\(105\) 1.48503e12 0.108145
\(106\) 6.77555e12 0.463934
\(107\) −1.60096e11 −0.0103130 −0.00515652 0.999987i \(-0.501641\pi\)
−0.00515652 + 0.999987i \(0.501641\pi\)
\(108\) −6.70370e12 −0.406500
\(109\) −4.01913e12 −0.229541 −0.114770 0.993392i \(-0.536613\pi\)
−0.114770 + 0.993392i \(0.536613\pi\)
\(110\) 1.32607e13 0.713697
\(111\) −1.49471e12 −0.0758503
\(112\) 1.70975e13 0.818494
\(113\) −1.96393e13 −0.887394 −0.443697 0.896177i \(-0.646333\pi\)
−0.443697 + 0.896177i \(0.646333\pi\)
\(114\) 3.37850e13 1.44159
\(115\) −6.50400e12 −0.262207
\(116\) 1.07344e14 4.09072
\(117\) 4.30762e12 0.155249
\(118\) 6.73509e12 0.229673
\(119\) −7.25513e12 −0.234202
\(120\) −1.14422e13 −0.349809
\(121\) 2.47347e13 0.716477
\(122\) 1.23113e14 3.38036
\(123\) 1.10093e13 0.286666
\(124\) −7.13875e13 −1.76352
\(125\) 2.50835e13 0.588131
\(126\) −1.60225e13 −0.356715
\(127\) −6.34911e13 −1.34273 −0.671365 0.741127i \(-0.734292\pi\)
−0.671365 + 0.741127i \(0.734292\pi\)
\(128\) 7.44877e13 1.49699
\(129\) 5.93361e13 1.13367
\(130\) 1.39629e13 0.253714
\(131\) 9.15084e13 1.58197 0.790984 0.611837i \(-0.209569\pi\)
0.790984 + 0.611837i \(0.209569\pi\)
\(132\) −9.71027e13 −1.59772
\(133\) 5.48037e13 0.858567
\(134\) −4.09476e12 −0.0611009
\(135\) 4.17971e12 0.0594260
\(136\) 5.59008e13 0.757557
\(137\) 1.26357e14 1.63273 0.816367 0.577534i \(-0.195985\pi\)
0.816367 + 0.577534i \(0.195985\pi\)
\(138\) 7.01739e13 0.864891
\(139\) −2.79722e13 −0.328950 −0.164475 0.986381i \(-0.552593\pi\)
−0.164475 + 0.986381i \(0.552593\pi\)
\(140\) −3.52484e13 −0.395647
\(141\) 2.73511e13 0.293124
\(142\) 2.25186e14 2.30498
\(143\) 6.23956e13 0.610196
\(144\) 4.81220e13 0.449767
\(145\) −6.69281e13 −0.598021
\(146\) 2.32819e14 1.98941
\(147\) 4.46415e13 0.364902
\(148\) 3.54782e13 0.277498
\(149\) −2.51209e14 −1.88072 −0.940361 0.340177i \(-0.889513\pi\)
−0.940361 + 0.340177i \(0.889513\pi\)
\(150\) −1.28543e14 −0.921418
\(151\) 2.18580e14 1.50058 0.750291 0.661108i \(-0.229913\pi\)
0.750291 + 0.661108i \(0.229913\pi\)
\(152\) −4.22263e14 −2.77715
\(153\) −2.04200e13 −0.128695
\(154\) −2.32085e14 −1.40205
\(155\) 4.45096e13 0.257809
\(156\) −1.02245e14 −0.567979
\(157\) −7.47896e13 −0.398560 −0.199280 0.979943i \(-0.563860\pi\)
−0.199280 + 0.979943i \(0.563860\pi\)
\(158\) −6.03694e14 −3.08706
\(159\) 3.09343e13 0.151831
\(160\) 2.74059e13 0.129141
\(161\) 1.13831e14 0.515101
\(162\) −4.50963e13 −0.196017
\(163\) −4.02010e14 −1.67887 −0.839436 0.543459i \(-0.817115\pi\)
−0.839436 + 0.543459i \(0.817115\pi\)
\(164\) −2.61315e14 −1.04877
\(165\) 6.05428e13 0.233570
\(166\) 2.07608e14 0.770090
\(167\) 3.79547e14 1.35397 0.676984 0.735998i \(-0.263287\pi\)
0.676984 + 0.735998i \(0.263287\pi\)
\(168\) 2.00258e14 0.687193
\(169\) −2.37175e14 −0.783079
\(170\) −6.61905e13 −0.210319
\(171\) 1.54248e14 0.471787
\(172\) −1.40839e15 −4.14752
\(173\) −5.55455e14 −1.57525 −0.787624 0.616156i \(-0.788689\pi\)
−0.787624 + 0.616156i \(0.788689\pi\)
\(174\) 7.22110e14 1.97257
\(175\) −2.08514e14 −0.548767
\(176\) 6.97044e14 1.76778
\(177\) 3.07496e13 0.0751646
\(178\) −1.42641e14 −0.336137
\(179\) 5.64535e14 1.28276 0.641381 0.767222i \(-0.278362\pi\)
0.641381 + 0.767222i \(0.278362\pi\)
\(180\) −9.92089e13 −0.217410
\(181\) 3.34847e14 0.707840 0.353920 0.935276i \(-0.384849\pi\)
0.353920 + 0.935276i \(0.384849\pi\)
\(182\) −2.44375e14 −0.498418
\(183\) 5.62081e14 1.10628
\(184\) −8.77070e14 −1.66617
\(185\) −2.21204e13 −0.0405673
\(186\) −4.80230e14 −0.850383
\(187\) −2.95782e14 −0.505827
\(188\) −6.49202e14 −1.07239
\(189\) −7.31521e13 −0.116741
\(190\) 4.99989e14 0.771013
\(191\) −3.68079e14 −0.548559 −0.274280 0.961650i \(-0.588439\pi\)
−0.274280 + 0.961650i \(0.588439\pi\)
\(192\) 2.45070e14 0.353047
\(193\) −1.19941e14 −0.167049 −0.0835244 0.996506i \(-0.526618\pi\)
−0.0835244 + 0.996506i \(0.526618\pi\)
\(194\) −1.52998e15 −2.06051
\(195\) 6.37490e13 0.0830325
\(196\) −1.05960e15 −1.33499
\(197\) −1.52574e15 −1.85974 −0.929868 0.367894i \(-0.880079\pi\)
−0.929868 + 0.367894i \(0.880079\pi\)
\(198\) −6.53217e14 −0.770431
\(199\) 2.96360e14 0.338279 0.169140 0.985592i \(-0.445901\pi\)
0.169140 + 0.985592i \(0.445901\pi\)
\(200\) 1.60660e15 1.77506
\(201\) −1.86950e13 −0.0199964
\(202\) −2.07113e14 −0.214498
\(203\) 1.17136e15 1.17480
\(204\) 4.84686e14 0.470830
\(205\) 1.62928e14 0.153319
\(206\) 1.33649e15 1.21851
\(207\) 3.20385e14 0.283051
\(208\) 7.33958e14 0.628433
\(209\) 2.23428e15 1.85433
\(210\) −2.37119e14 −0.190784
\(211\) −2.99534e14 −0.233674 −0.116837 0.993151i \(-0.537275\pi\)
−0.116837 + 0.993151i \(0.537275\pi\)
\(212\) −7.34252e14 −0.555472
\(213\) 1.02810e15 0.754345
\(214\) 2.55630e13 0.0181938
\(215\) 8.78123e14 0.606325
\(216\) 5.63638e14 0.377616
\(217\) −7.78994e14 −0.506461
\(218\) 6.41746e14 0.404945
\(219\) 1.06296e15 0.651071
\(220\) −1.43703e15 −0.854515
\(221\) −3.11446e14 −0.179818
\(222\) 2.38665e14 0.133812
\(223\) −2.32263e14 −0.126473 −0.0632367 0.997999i \(-0.520142\pi\)
−0.0632367 + 0.997999i \(0.520142\pi\)
\(224\) −4.79650e14 −0.253695
\(225\) −5.86876e14 −0.301550
\(226\) 3.13586e15 1.56550
\(227\) −7.29458e14 −0.353861 −0.176930 0.984223i \(-0.556617\pi\)
−0.176930 + 0.984223i \(0.556617\pi\)
\(228\) −3.66122e15 −1.72603
\(229\) −1.84328e15 −0.844620 −0.422310 0.906451i \(-0.638781\pi\)
−0.422310 + 0.906451i \(0.638781\pi\)
\(230\) 1.03851e15 0.462573
\(231\) −1.05960e15 −0.458844
\(232\) −9.02532e15 −3.80006
\(233\) −2.70339e15 −1.10687 −0.553434 0.832893i \(-0.686683\pi\)
−0.553434 + 0.832893i \(0.686683\pi\)
\(234\) −6.87810e14 −0.273883
\(235\) 4.04773e14 0.156773
\(236\) −7.29868e14 −0.274990
\(237\) −2.75622e15 −1.01030
\(238\) 1.15845e15 0.413167
\(239\) 2.63090e15 0.913100 0.456550 0.889698i \(-0.349085\pi\)
0.456550 + 0.889698i \(0.349085\pi\)
\(240\) 7.12164e14 0.240551
\(241\) −5.27704e15 −1.73492 −0.867460 0.497507i \(-0.834249\pi\)
−0.867460 + 0.497507i \(0.834249\pi\)
\(242\) −3.94947e15 −1.26398
\(243\) −2.05891e14 −0.0641500
\(244\) −1.33415e16 −4.04734
\(245\) 6.60655e14 0.195162
\(246\) −1.75788e15 −0.505722
\(247\) 2.35260e15 0.659201
\(248\) 6.00216e15 1.63822
\(249\) 9.47852e14 0.252026
\(250\) −4.00516e15 −1.03755
\(251\) 3.52800e15 0.890531 0.445265 0.895399i \(-0.353109\pi\)
0.445265 + 0.895399i \(0.353109\pi\)
\(252\) 1.73633e15 0.427098
\(253\) 4.64075e15 1.11251
\(254\) 1.01378e16 2.36878
\(255\) −3.02198e14 −0.0688305
\(256\) −9.13973e15 −2.02943
\(257\) −2.69146e15 −0.582669 −0.291335 0.956621i \(-0.594099\pi\)
−0.291335 + 0.956621i \(0.594099\pi\)
\(258\) −9.47437e15 −1.99996
\(259\) 3.87145e14 0.0796939
\(260\) −1.51314e15 −0.303774
\(261\) 3.29686e15 0.645560
\(262\) −1.46114e16 −2.79083
\(263\) −2.03595e15 −0.379363 −0.189682 0.981846i \(-0.560746\pi\)
−0.189682 + 0.981846i \(0.560746\pi\)
\(264\) 8.16426e15 1.48420
\(265\) 4.57801e14 0.0812042
\(266\) −8.75066e15 −1.51464
\(267\) −6.51242e14 −0.110007
\(268\) 4.43741e14 0.0731566
\(269\) −4.93105e15 −0.793504 −0.396752 0.917926i \(-0.629863\pi\)
−0.396752 + 0.917926i \(0.629863\pi\)
\(270\) −6.67386e14 −0.104837
\(271\) 1.06198e16 1.62860 0.814301 0.580443i \(-0.197121\pi\)
0.814301 + 0.580443i \(0.197121\pi\)
\(272\) −3.47928e15 −0.520945
\(273\) −1.11572e15 −0.163116
\(274\) −2.01758e16 −2.88039
\(275\) −8.50085e15 −1.18522
\(276\) −7.60460e15 −1.03554
\(277\) 6.73410e15 0.895697 0.447849 0.894109i \(-0.352190\pi\)
0.447849 + 0.894109i \(0.352190\pi\)
\(278\) 4.46640e15 0.580319
\(279\) −2.19253e15 −0.278303
\(280\) 2.96364e15 0.367534
\(281\) 7.63531e15 0.925200 0.462600 0.886567i \(-0.346917\pi\)
0.462600 + 0.886567i \(0.346917\pi\)
\(282\) −4.36723e15 −0.517115
\(283\) 2.87879e15 0.333118 0.166559 0.986031i \(-0.446734\pi\)
0.166559 + 0.986031i \(0.446734\pi\)
\(284\) −2.44029e16 −2.75977
\(285\) 2.28274e15 0.252328
\(286\) −9.96288e15 −1.07648
\(287\) −2.85152e15 −0.301192
\(288\) −1.35001e15 −0.139407
\(289\) −8.42819e15 −0.850938
\(290\) 1.06866e16 1.05500
\(291\) −6.98524e15 −0.674337
\(292\) −2.52301e16 −2.38194
\(293\) 3.05609e15 0.282181 0.141090 0.989997i \(-0.454939\pi\)
0.141090 + 0.989997i \(0.454939\pi\)
\(294\) −7.12804e15 −0.643743
\(295\) 4.55067e14 0.0402006
\(296\) −2.98296e15 −0.257781
\(297\) −2.98232e15 −0.252137
\(298\) 4.01113e16 3.31788
\(299\) 4.88651e15 0.395491
\(300\) 1.39300e16 1.10322
\(301\) −1.53687e16 −1.19111
\(302\) −3.49013e16 −2.64726
\(303\) −9.45593e14 −0.0701984
\(304\) 2.62818e16 1.90975
\(305\) 8.31830e15 0.591678
\(306\) 3.26052e15 0.227038
\(307\) 2.36580e16 1.61279 0.806397 0.591375i \(-0.201415\pi\)
0.806397 + 0.591375i \(0.201415\pi\)
\(308\) 2.51506e16 1.67868
\(309\) 6.10185e15 0.398778
\(310\) −7.10698e15 −0.454814
\(311\) −3.10338e16 −1.94488 −0.972438 0.233162i \(-0.925093\pi\)
−0.972438 + 0.233162i \(0.925093\pi\)
\(312\) 8.59661e15 0.527621
\(313\) −2.34297e16 −1.40841 −0.704205 0.709997i \(-0.748696\pi\)
−0.704205 + 0.709997i \(0.748696\pi\)
\(314\) 1.19419e16 0.703120
\(315\) −1.08259e15 −0.0624373
\(316\) 6.54211e16 3.69617
\(317\) −1.29438e16 −0.716435 −0.358218 0.933638i \(-0.616615\pi\)
−0.358218 + 0.933638i \(0.616615\pi\)
\(318\) −4.93937e15 −0.267852
\(319\) 4.77547e16 2.53733
\(320\) 3.62682e15 0.188822
\(321\) 1.16710e14 0.00595423
\(322\) −1.81757e16 −0.908718
\(323\) −1.11524e16 −0.546450
\(324\) 4.88700e15 0.234693
\(325\) −8.95103e15 −0.421339
\(326\) 6.41901e16 2.96179
\(327\) 2.92994e15 0.132525
\(328\) 2.19710e16 0.974247
\(329\) −7.08422e15 −0.307977
\(330\) −9.66704e15 −0.412053
\(331\) −4.31442e16 −1.80319 −0.901593 0.432584i \(-0.857602\pi\)
−0.901593 + 0.432584i \(0.857602\pi\)
\(332\) −2.24981e16 −0.922035
\(333\) 1.08964e15 0.0437922
\(334\) −6.06034e16 −2.38861
\(335\) −2.76670e14 −0.0106947
\(336\) −1.24641e16 −0.472558
\(337\) 3.15609e16 1.17369 0.586847 0.809698i \(-0.300369\pi\)
0.586847 + 0.809698i \(0.300369\pi\)
\(338\) 3.78705e16 1.38147
\(339\) 1.43171e16 0.512337
\(340\) 7.17293e15 0.251816
\(341\) −3.17586e16 −1.09385
\(342\) −2.46293e16 −0.832304
\(343\) −2.98570e16 −0.989999
\(344\) 1.18416e17 3.85283
\(345\) 4.74141e15 0.151385
\(346\) 8.86910e16 2.77898
\(347\) 1.98681e16 0.610962 0.305481 0.952198i \(-0.401183\pi\)
0.305481 + 0.952198i \(0.401183\pi\)
\(348\) −7.82536e16 −2.36178
\(349\) 5.59919e16 1.65867 0.829334 0.558753i \(-0.188720\pi\)
0.829334 + 0.558753i \(0.188720\pi\)
\(350\) 3.32940e16 0.968109
\(351\) −3.14025e15 −0.0896331
\(352\) −1.95547e16 −0.547930
\(353\) 3.58540e16 0.986284 0.493142 0.869949i \(-0.335848\pi\)
0.493142 + 0.869949i \(0.335848\pi\)
\(354\) −4.90988e15 −0.132602
\(355\) 1.52151e16 0.403449
\(356\) 1.54578e16 0.402459
\(357\) 5.28899e15 0.135216
\(358\) −9.01410e16 −2.26299
\(359\) 4.28853e16 1.05729 0.528646 0.848843i \(-0.322700\pi\)
0.528646 + 0.848843i \(0.322700\pi\)
\(360\) 8.34135e15 0.201962
\(361\) 4.21895e16 1.00325
\(362\) −5.34659e16 −1.24874
\(363\) −1.80316e16 −0.413658
\(364\) 2.64825e16 0.596760
\(365\) 1.57308e16 0.348215
\(366\) −8.97490e16 −1.95165
\(367\) −3.10176e16 −0.662642 −0.331321 0.943518i \(-0.607494\pi\)
−0.331321 + 0.943518i \(0.607494\pi\)
\(368\) 5.45891e16 1.14576
\(369\) −8.02577e15 −0.165507
\(370\) 3.53203e15 0.0715670
\(371\) −8.01230e15 −0.159524
\(372\) 5.20415e16 1.01817
\(373\) −1.79979e15 −0.0346030 −0.0173015 0.999850i \(-0.505508\pi\)
−0.0173015 + 0.999850i \(0.505508\pi\)
\(374\) 4.72284e16 0.892356
\(375\) −1.82859e16 −0.339557
\(376\) 5.45840e16 0.996195
\(377\) 5.02837e16 0.902004
\(378\) 1.16804e16 0.205950
\(379\) −7.40780e16 −1.28391 −0.641955 0.766743i \(-0.721876\pi\)
−0.641955 + 0.766743i \(0.721876\pi\)
\(380\) −5.41828e16 −0.923141
\(381\) 4.62850e16 0.775226
\(382\) 5.87722e16 0.967743
\(383\) 1.40044e16 0.226712 0.113356 0.993554i \(-0.463840\pi\)
0.113356 + 0.993554i \(0.463840\pi\)
\(384\) −5.43015e16 −0.864289
\(385\) −1.56812e16 −0.245406
\(386\) 1.91512e16 0.294700
\(387\) −4.32560e16 −0.654524
\(388\) 1.65801e17 2.46706
\(389\) −1.46668e16 −0.214617 −0.107308 0.994226i \(-0.534223\pi\)
−0.107308 + 0.994226i \(0.534223\pi\)
\(390\) −1.01790e16 −0.146482
\(391\) −2.31642e16 −0.327845
\(392\) 8.90900e16 1.24014
\(393\) −6.67096e16 −0.913350
\(394\) 2.43620e17 3.28086
\(395\) −4.07896e16 −0.540341
\(396\) 7.07878e16 0.922444
\(397\) −1.34858e17 −1.72878 −0.864390 0.502823i \(-0.832295\pi\)
−0.864390 + 0.502823i \(0.832295\pi\)
\(398\) −4.73207e16 −0.596776
\(399\) −3.99519e16 −0.495694
\(400\) −9.99953e16 −1.22065
\(401\) −9.96784e16 −1.19719 −0.598595 0.801052i \(-0.704274\pi\)
−0.598595 + 0.801052i \(0.704274\pi\)
\(402\) 2.98508e15 0.0352766
\(403\) −3.34405e16 −0.388857
\(404\) 2.24444e16 0.256821
\(405\) −3.04701e15 −0.0343096
\(406\) −1.87034e17 −2.07253
\(407\) 1.57834e16 0.172122
\(408\) −4.07517e16 −0.437376
\(409\) −8.75972e16 −0.925313 −0.462656 0.886538i \(-0.653104\pi\)
−0.462656 + 0.886538i \(0.653104\pi\)
\(410\) −2.60151e16 −0.270478
\(411\) −9.21142e16 −0.942659
\(412\) −1.44833e17 −1.45893
\(413\) −7.96446e15 −0.0789734
\(414\) −5.11568e16 −0.499345
\(415\) 1.40274e16 0.134792
\(416\) −2.05903e16 −0.194785
\(417\) 2.03917e16 0.189920
\(418\) −3.56754e17 −3.27132
\(419\) 2.19132e16 0.197841 0.0989203 0.995095i \(-0.468461\pi\)
0.0989203 + 0.995095i \(0.468461\pi\)
\(420\) 2.56961e16 0.228427
\(421\) 2.77673e16 0.243052 0.121526 0.992588i \(-0.461221\pi\)
0.121526 + 0.992588i \(0.461221\pi\)
\(422\) 4.78274e16 0.412236
\(423\) −1.99390e16 −0.169235
\(424\) 6.17349e16 0.516003
\(425\) 4.24318e16 0.349272
\(426\) −1.64160e17 −1.33078
\(427\) −1.45585e17 −1.16234
\(428\) −2.77021e15 −0.0217835
\(429\) −4.54864e16 −0.352297
\(430\) −1.40212e17 −1.06965
\(431\) 2.11622e17 1.59023 0.795114 0.606460i \(-0.207411\pi\)
0.795114 + 0.606460i \(0.207411\pi\)
\(432\) −3.50809e16 −0.259673
\(433\) −2.12581e17 −1.55008 −0.775040 0.631912i \(-0.782270\pi\)
−0.775040 + 0.631912i \(0.782270\pi\)
\(434\) 1.24384e17 0.893475
\(435\) 4.87906e16 0.345268
\(436\) −6.95447e16 −0.484844
\(437\) 1.74978e17 1.20186
\(438\) −1.69725e17 −1.14859
\(439\) 1.48280e16 0.0988695 0.0494347 0.998777i \(-0.484258\pi\)
0.0494347 + 0.998777i \(0.484258\pi\)
\(440\) 1.20824e17 0.793798
\(441\) −3.25437e16 −0.210676
\(442\) 4.97295e16 0.317226
\(443\) 1.33915e17 0.841790 0.420895 0.907109i \(-0.361716\pi\)
0.420895 + 0.907109i \(0.361716\pi\)
\(444\) −2.58636e16 −0.160214
\(445\) −9.63781e15 −0.0588353
\(446\) 3.70862e16 0.223118
\(447\) 1.83132e17 1.08584
\(448\) −6.34756e16 −0.370937
\(449\) −9.57945e16 −0.551746 −0.275873 0.961194i \(-0.588967\pi\)
−0.275873 + 0.961194i \(0.588967\pi\)
\(450\) 9.37081e16 0.531981
\(451\) −1.16253e17 −0.650512
\(452\) −3.39827e17 −1.87438
\(453\) −1.59345e17 −0.866361
\(454\) 1.16475e17 0.624264
\(455\) −1.65116e16 −0.0872400
\(456\) 3.07830e17 1.60339
\(457\) 2.24606e17 1.15336 0.576681 0.816969i \(-0.304348\pi\)
0.576681 + 0.816969i \(0.304348\pi\)
\(458\) 2.94322e17 1.49004
\(459\) 1.48862e16 0.0743021
\(460\) −1.12541e17 −0.553843
\(461\) 1.30695e17 0.634166 0.317083 0.948398i \(-0.397297\pi\)
0.317083 + 0.948398i \(0.397297\pi\)
\(462\) 1.69190e17 0.809471
\(463\) 5.86683e16 0.276775 0.138387 0.990378i \(-0.455808\pi\)
0.138387 + 0.990378i \(0.455808\pi\)
\(464\) 5.61738e17 2.61316
\(465\) −3.24475e16 −0.148846
\(466\) 4.31659e17 1.95268
\(467\) 3.78140e17 1.68692 0.843458 0.537196i \(-0.180516\pi\)
0.843458 + 0.537196i \(0.180516\pi\)
\(468\) 7.45366e16 0.327923
\(469\) 4.84219e15 0.0210096
\(470\) −6.46312e16 −0.276571
\(471\) 5.45216e16 0.230109
\(472\) 6.13663e16 0.255450
\(473\) −6.26561e17 −2.57256
\(474\) 4.40093e17 1.78232
\(475\) −3.20521e17 −1.28041
\(476\) −1.25539e17 −0.494689
\(477\) −2.25511e16 −0.0876594
\(478\) −4.20084e17 −1.61085
\(479\) 2.31664e17 0.876350 0.438175 0.898890i \(-0.355625\pi\)
0.438175 + 0.898890i \(0.355625\pi\)
\(480\) −1.99789e16 −0.0745596
\(481\) 1.66192e16 0.0611883
\(482\) 8.42600e17 3.06066
\(483\) −8.29829e16 −0.297394
\(484\) 4.27996e17 1.51337
\(485\) −1.03375e17 −0.360658
\(486\) 3.28752e16 0.113170
\(487\) 2.94479e17 1.00027 0.500134 0.865948i \(-0.333284\pi\)
0.500134 + 0.865948i \(0.333284\pi\)
\(488\) 1.12173e18 3.75976
\(489\) 2.93065e17 0.969297
\(490\) −1.05489e17 −0.344296
\(491\) −3.67443e17 −1.18348 −0.591739 0.806130i \(-0.701558\pi\)
−0.591739 + 0.806130i \(0.701558\pi\)
\(492\) 1.90498e17 0.605505
\(493\) −2.38367e17 −0.747723
\(494\) −3.75646e17 −1.16293
\(495\) −4.41357e16 −0.134852
\(496\) −3.73576e17 −1.12654
\(497\) −2.66290e17 −0.792570
\(498\) −1.51346e17 −0.444612
\(499\) 8.41582e16 0.244030 0.122015 0.992528i \(-0.461064\pi\)
0.122015 + 0.992528i \(0.461064\pi\)
\(500\) 4.34031e17 1.24227
\(501\) −2.76690e17 −0.781714
\(502\) −5.63325e17 −1.57103
\(503\) −1.88108e17 −0.517863 −0.258932 0.965896i \(-0.583370\pi\)
−0.258932 + 0.965896i \(0.583370\pi\)
\(504\) −1.45988e17 −0.396751
\(505\) −1.39939e16 −0.0375445
\(506\) −7.41002e17 −1.96264
\(507\) 1.72901e17 0.452111
\(508\) −1.09861e18 −2.83616
\(509\) −1.17080e17 −0.298413 −0.149206 0.988806i \(-0.547672\pi\)
−0.149206 + 0.988806i \(0.547672\pi\)
\(510\) 4.82529e16 0.121427
\(511\) −2.75316e17 −0.684063
\(512\) 8.49164e17 2.08323
\(513\) −1.12447e17 −0.272386
\(514\) 4.29753e17 1.02792
\(515\) 9.03021e16 0.213280
\(516\) 1.02672e18 2.39457
\(517\) −2.88815e17 −0.665167
\(518\) −6.18165e16 −0.140592
\(519\) 4.04926e17 0.909470
\(520\) 1.27222e17 0.282190
\(521\) −2.25724e17 −0.494461 −0.247230 0.968957i \(-0.579520\pi\)
−0.247230 + 0.968957i \(0.579520\pi\)
\(522\) −5.26418e17 −1.13887
\(523\) 1.23001e17 0.262814 0.131407 0.991328i \(-0.458050\pi\)
0.131407 + 0.991328i \(0.458050\pi\)
\(524\) 1.58341e18 3.34149
\(525\) 1.52007e17 0.316831
\(526\) 3.25086e17 0.669254
\(527\) 1.58523e17 0.322346
\(528\) −5.08145e17 −1.02063
\(529\) −1.40596e17 −0.278939
\(530\) −7.30984e16 −0.143257
\(531\) −2.24165e16 −0.0433963
\(532\) 9.48292e17 1.81350
\(533\) −1.22409e17 −0.231253
\(534\) 1.03986e17 0.194069
\(535\) 1.72721e15 0.00318453
\(536\) −3.73091e16 −0.0679586
\(537\) −4.11546e17 −0.740604
\(538\) 7.87354e17 1.39986
\(539\) −4.71393e17 −0.828049
\(540\) 7.23233e16 0.125522
\(541\) −4.04571e17 −0.693765 −0.346883 0.937909i \(-0.612760\pi\)
−0.346883 + 0.937909i \(0.612760\pi\)
\(542\) −1.69569e18 −2.87310
\(543\) −2.44103e17 −0.408672
\(544\) 9.76071e16 0.161469
\(545\) 4.33606e16 0.0708791
\(546\) 1.78150e17 0.287762
\(547\) −1.11019e18 −1.77206 −0.886032 0.463624i \(-0.846549\pi\)
−0.886032 + 0.463624i \(0.846549\pi\)
\(548\) 2.18641e18 3.44872
\(549\) −4.09757e17 −0.638713
\(550\) 1.35736e18 2.09091
\(551\) 1.80057e18 2.74110
\(552\) 6.39384e17 0.961962
\(553\) 7.13888e17 1.06149
\(554\) −1.07525e18 −1.58015
\(555\) 1.61258e16 0.0234216
\(556\) −4.84015e17 −0.694820
\(557\) 4.52746e17 0.642385 0.321193 0.947014i \(-0.395916\pi\)
0.321193 + 0.947014i \(0.395916\pi\)
\(558\) 3.50087e17 0.490969
\(559\) −6.59742e17 −0.914528
\(560\) −1.84458e17 −0.252740
\(561\) 2.15625e17 0.292039
\(562\) −1.21915e18 −1.63219
\(563\) −1.39911e18 −1.85160 −0.925799 0.378017i \(-0.876606\pi\)
−0.925799 + 0.378017i \(0.876606\pi\)
\(564\) 4.73268e17 0.619146
\(565\) 2.11880e17 0.274015
\(566\) −4.59665e17 −0.587671
\(567\) 5.33279e16 0.0674007
\(568\) 2.05176e18 2.56368
\(569\) −8.98613e16 −0.111005 −0.0555026 0.998459i \(-0.517676\pi\)
−0.0555026 + 0.998459i \(0.517676\pi\)
\(570\) −3.64492e17 −0.445145
\(571\) −8.09016e16 −0.0976838 −0.0488419 0.998807i \(-0.515553\pi\)
−0.0488419 + 0.998807i \(0.515553\pi\)
\(572\) 1.07966e18 1.28888
\(573\) 2.68329e17 0.316711
\(574\) 4.55310e17 0.531349
\(575\) −6.65745e17 −0.768187
\(576\) −1.78656e17 −0.203832
\(577\) −1.57286e15 −0.00177438 −0.000887190 1.00000i \(-0.500282\pi\)
−0.000887190 1.00000i \(0.500282\pi\)
\(578\) 1.34575e18 1.50119
\(579\) 8.74366e16 0.0964457
\(580\) −1.15809e18 −1.26316
\(581\) −2.45503e17 −0.264797
\(582\) 1.11535e18 1.18963
\(583\) −3.26651e17 −0.344539
\(584\) 2.12132e18 2.21270
\(585\) −4.64730e16 −0.0479389
\(586\) −4.87975e17 −0.497810
\(587\) −5.97841e17 −0.603167 −0.301584 0.953440i \(-0.597515\pi\)
−0.301584 + 0.953440i \(0.597515\pi\)
\(588\) 7.72451e17 0.770759
\(589\) −1.19745e18 −1.18170
\(590\) −7.26619e16 −0.0709200
\(591\) 1.11227e18 1.07372
\(592\) 1.85660e17 0.177267
\(593\) 5.99958e17 0.566585 0.283292 0.959034i \(-0.408573\pi\)
0.283292 + 0.959034i \(0.408573\pi\)
\(594\) 4.76195e17 0.444809
\(595\) 7.82724e16 0.0723183
\(596\) −4.34678e18 −3.97253
\(597\) −2.16047e17 −0.195306
\(598\) −7.80243e17 −0.697706
\(599\) −2.68993e17 −0.237939 −0.118970 0.992898i \(-0.537959\pi\)
−0.118970 + 0.992898i \(0.537959\pi\)
\(600\) −1.17121e18 −1.02483
\(601\) −3.33071e17 −0.288306 −0.144153 0.989555i \(-0.546046\pi\)
−0.144153 + 0.989555i \(0.546046\pi\)
\(602\) 2.45396e18 2.10131
\(603\) 1.36286e16 0.0115449
\(604\) 3.78218e18 3.16958
\(605\) −2.66852e17 −0.221239
\(606\) 1.50986e17 0.123841
\(607\) 3.32104e17 0.269493 0.134747 0.990880i \(-0.456978\pi\)
0.134747 + 0.990880i \(0.456978\pi\)
\(608\) −7.37304e17 −0.591934
\(609\) −8.53919e17 −0.678272
\(610\) −1.32821e18 −1.04381
\(611\) −3.04109e17 −0.236462
\(612\) −3.53336e17 −0.271834
\(613\) −6.68632e17 −0.508972 −0.254486 0.967076i \(-0.581906\pi\)
−0.254486 + 0.967076i \(0.581906\pi\)
\(614\) −3.77754e18 −2.84521
\(615\) −1.18774e17 −0.0885186
\(616\) −2.11462e18 −1.55940
\(617\) −2.07671e18 −1.51538 −0.757691 0.652613i \(-0.773673\pi\)
−0.757691 + 0.652613i \(0.773673\pi\)
\(618\) −9.74300e17 −0.703506
\(619\) −2.42821e18 −1.73499 −0.867495 0.497446i \(-0.834271\pi\)
−0.867495 + 0.497446i \(0.834271\pi\)
\(620\) 7.70169e17 0.544553
\(621\) −2.33561e17 −0.163420
\(622\) 4.95525e18 3.43106
\(623\) 1.68678e17 0.115581
\(624\) −5.35055e17 −0.362826
\(625\) 1.07742e18 0.723044
\(626\) 3.74109e18 2.48465
\(627\) −1.62879e18 −1.07060
\(628\) −1.29412e18 −0.841852
\(629\) −7.87825e16 −0.0507225
\(630\) 1.72860e17 0.110149
\(631\) 1.99224e18 1.25647 0.628234 0.778024i \(-0.283778\pi\)
0.628234 + 0.778024i \(0.283778\pi\)
\(632\) −5.50051e18 −3.43354
\(633\) 2.18360e17 0.134911
\(634\) 2.06678e18 1.26390
\(635\) 6.84978e17 0.414617
\(636\) 5.35270e17 0.320702
\(637\) −4.96356e17 −0.294366
\(638\) −7.62513e18 −4.47624
\(639\) −7.49488e17 −0.435521
\(640\) −8.03615e17 −0.462251
\(641\) 1.44405e18 0.822254 0.411127 0.911578i \(-0.365135\pi\)
0.411127 + 0.911578i \(0.365135\pi\)
\(642\) −1.86354e16 −0.0105042
\(643\) −3.04746e18 −1.70046 −0.850230 0.526411i \(-0.823537\pi\)
−0.850230 + 0.526411i \(0.823537\pi\)
\(644\) 1.96967e18 1.08802
\(645\) −6.40151e17 −0.350062
\(646\) 1.78073e18 0.964021
\(647\) −2.39541e18 −1.28381 −0.641907 0.766783i \(-0.721856\pi\)
−0.641907 + 0.766783i \(0.721856\pi\)
\(648\) −4.10892e17 −0.218017
\(649\) −3.24701e17 −0.170566
\(650\) 1.42924e18 0.743306
\(651\) 5.67887e17 0.292405
\(652\) −6.95615e18 −3.54617
\(653\) 1.00343e18 0.506466 0.253233 0.967405i \(-0.418506\pi\)
0.253233 + 0.967405i \(0.418506\pi\)
\(654\) −4.67833e17 −0.233795
\(655\) −9.87244e17 −0.488491
\(656\) −1.36748e18 −0.669954
\(657\) −7.74895e17 −0.375896
\(658\) 1.13116e18 0.543319
\(659\) −2.20142e18 −1.04700 −0.523502 0.852024i \(-0.675375\pi\)
−0.523502 + 0.852024i \(0.675375\pi\)
\(660\) 1.04760e18 0.493355
\(661\) 1.93163e18 0.900772 0.450386 0.892834i \(-0.351286\pi\)
0.450386 + 0.892834i \(0.351286\pi\)
\(662\) 6.88896e18 3.18110
\(663\) 2.27044e17 0.103818
\(664\) 1.89161e18 0.856521
\(665\) −5.91253e17 −0.265114
\(666\) −1.73986e17 −0.0772561
\(667\) 3.73991e18 1.64454
\(668\) 6.56746e18 2.85990
\(669\) 1.69320e17 0.0730194
\(670\) 4.41766e16 0.0188671
\(671\) −5.93530e18 −2.51042
\(672\) 3.49665e17 0.146471
\(673\) 1.18529e18 0.491729 0.245865 0.969304i \(-0.420928\pi\)
0.245865 + 0.969304i \(0.420928\pi\)
\(674\) −5.03942e18 −2.07057
\(675\) 4.27832e17 0.174100
\(676\) −4.10394e18 −1.65405
\(677\) −2.82296e18 −1.12688 −0.563440 0.826157i \(-0.690522\pi\)
−0.563440 + 0.826157i \(0.690522\pi\)
\(678\) −2.28605e18 −0.903841
\(679\) 1.80925e18 0.708508
\(680\) −6.03090e17 −0.233924
\(681\) 5.31775e17 0.204302
\(682\) 5.07099e18 1.92972
\(683\) 1.91965e18 0.723580 0.361790 0.932260i \(-0.382166\pi\)
0.361790 + 0.932260i \(0.382166\pi\)
\(684\) 2.66903e18 0.996525
\(685\) −1.36321e18 −0.504166
\(686\) 4.76736e18 1.74651
\(687\) 1.34375e18 0.487642
\(688\) −7.37022e18 −2.64945
\(689\) −3.43950e17 −0.122481
\(690\) −7.57075e17 −0.267067
\(691\) −5.30676e18 −1.85448 −0.927240 0.374468i \(-0.877825\pi\)
−0.927240 + 0.374468i \(0.877825\pi\)
\(692\) −9.61127e18 −3.32729
\(693\) 7.72451e17 0.264914
\(694\) −3.17239e18 −1.07783
\(695\) 3.01780e17 0.101575
\(696\) 6.57946e18 2.19397
\(697\) 5.80273e17 0.191699
\(698\) −8.94038e18 −2.92615
\(699\) 1.97077e18 0.639050
\(700\) −3.60801e18 −1.15912
\(701\) 1.94249e18 0.618288 0.309144 0.951015i \(-0.399958\pi\)
0.309144 + 0.951015i \(0.399958\pi\)
\(702\) 5.01413e17 0.158127
\(703\) 5.95107e17 0.185945
\(704\) −2.58782e18 −0.801147
\(705\) −2.95079e17 −0.0905127
\(706\) −5.72491e18 −1.73996
\(707\) 2.44918e17 0.0737555
\(708\) 5.32074e17 0.158765
\(709\) 1.39382e18 0.412105 0.206052 0.978541i \(-0.433938\pi\)
0.206052 + 0.978541i \(0.433938\pi\)
\(710\) −2.42943e18 −0.711746
\(711\) 2.00928e18 0.583295
\(712\) −1.29967e18 −0.373863
\(713\) −2.48718e18 −0.708965
\(714\) −8.44508e17 −0.238542
\(715\) −6.73158e17 −0.188420
\(716\) 9.76840e18 2.70950
\(717\) −1.91793e18 −0.527178
\(718\) −6.84762e18 −1.86522
\(719\) −1.25268e18 −0.338143 −0.169072 0.985604i \(-0.554077\pi\)
−0.169072 + 0.985604i \(0.554077\pi\)
\(720\) −5.19167e17 −0.138882
\(721\) −1.58044e18 −0.418986
\(722\) −6.73653e18 −1.76988
\(723\) 3.84696e18 1.00166
\(724\) 5.79399e18 1.49512
\(725\) −6.85071e18 −1.75202
\(726\) 2.87916e18 0.729757
\(727\) 1.06674e18 0.267970 0.133985 0.990983i \(-0.457223\pi\)
0.133985 + 0.990983i \(0.457223\pi\)
\(728\) −2.22661e18 −0.554358
\(729\) 1.50095e17 0.0370370
\(730\) −2.51178e18 −0.614305
\(731\) 3.12746e18 0.758105
\(732\) 9.72592e18 2.33673
\(733\) 5.83547e17 0.138963 0.0694816 0.997583i \(-0.477865\pi\)
0.0694816 + 0.997583i \(0.477865\pi\)
\(734\) 4.95267e18 1.16900
\(735\) −4.81618e17 −0.112677
\(736\) −1.53143e18 −0.355134
\(737\) 1.97410e17 0.0453765
\(738\) 1.28150e18 0.291979
\(739\) 6.34195e18 1.43230 0.716150 0.697946i \(-0.245902\pi\)
0.716150 + 0.697946i \(0.245902\pi\)
\(740\) −3.82758e17 −0.0856877
\(741\) −1.71504e18 −0.380590
\(742\) 1.27935e18 0.281425
\(743\) −1.18973e17 −0.0259430 −0.0129715 0.999916i \(-0.504129\pi\)
−0.0129715 + 0.999916i \(0.504129\pi\)
\(744\) −4.37558e18 −0.945826
\(745\) 2.71019e18 0.580742
\(746\) 2.87377e17 0.0610450
\(747\) −6.90984e17 −0.145507
\(748\) −5.11805e18 −1.06843
\(749\) −3.02291e16 −0.00625595
\(750\) 2.91976e18 0.599031
\(751\) 3.88050e18 0.789274 0.394637 0.918837i \(-0.370870\pi\)
0.394637 + 0.918837i \(0.370870\pi\)
\(752\) −3.39732e18 −0.685047
\(753\) −2.57191e18 −0.514148
\(754\) −8.02894e18 −1.59127
\(755\) −2.35816e18 −0.463360
\(756\) −1.26578e18 −0.246585
\(757\) 3.34912e18 0.646857 0.323428 0.946253i \(-0.395165\pi\)
0.323428 + 0.946253i \(0.395165\pi\)
\(758\) 1.18282e19 2.26501
\(759\) −3.38311e18 −0.642309
\(760\) 4.55561e18 0.857548
\(761\) 7.46644e18 1.39352 0.696760 0.717304i \(-0.254624\pi\)
0.696760 + 0.717304i \(0.254624\pi\)
\(762\) −7.39047e18 −1.36762
\(763\) −7.58885e17 −0.139241
\(764\) −6.36902e18 −1.15869
\(765\) 2.20302e17 0.0397393
\(766\) −2.23613e18 −0.399954
\(767\) −3.41896e17 −0.0606351
\(768\) 6.66286e18 1.17169
\(769\) 4.87854e18 0.850686 0.425343 0.905032i \(-0.360154\pi\)
0.425343 + 0.905032i \(0.360154\pi\)
\(770\) 2.50386e18 0.432933
\(771\) 1.96207e18 0.336404
\(772\) −2.07538e18 −0.352846
\(773\) −3.71918e18 −0.627020 −0.313510 0.949585i \(-0.601505\pi\)
−0.313510 + 0.949585i \(0.601505\pi\)
\(774\) 6.90682e18 1.15468
\(775\) 4.55597e18 0.755301
\(776\) −1.39403e19 −2.29177
\(777\) −2.82228e17 −0.0460113
\(778\) 2.34189e18 0.378617
\(779\) −4.38326e18 −0.702755
\(780\) 1.10308e18 0.175384
\(781\) −1.08563e19 −1.71179
\(782\) 3.69870e18 0.578369
\(783\) −2.40341e18 −0.372714
\(784\) −5.54498e18 −0.852797
\(785\) 8.06872e17 0.123070
\(786\) 1.06517e19 1.61129
\(787\) −8.05087e17 −0.120783 −0.0603916 0.998175i \(-0.519235\pi\)
−0.0603916 + 0.998175i \(0.519235\pi\)
\(788\) −2.64006e19 −3.92820
\(789\) 1.48421e18 0.219025
\(790\) 6.51299e18 0.953244
\(791\) −3.70826e18 −0.538299
\(792\) −5.95174e18 −0.856901
\(793\) −6.24962e18 −0.892437
\(794\) 2.15332e19 3.04983
\(795\) −3.33737e17 −0.0468833
\(796\) 5.12805e18 0.714525
\(797\) 8.26045e16 0.0114163 0.00570814 0.999984i \(-0.498183\pi\)
0.00570814 + 0.999984i \(0.498183\pi\)
\(798\) 6.37923e18 0.874480
\(799\) 1.44161e18 0.196017
\(800\) 2.80525e18 0.378344
\(801\) 4.74755e17 0.0635124
\(802\) 1.59159e19 2.11202
\(803\) −1.12243e19 −1.47743
\(804\) −3.23487e17 −0.0422370
\(805\) −1.22807e18 −0.159056
\(806\) 5.33954e18 0.686003
\(807\) 3.59473e18 0.458130
\(808\) −1.88710e18 −0.238572
\(809\) 1.38254e19 1.73385 0.866925 0.498439i \(-0.166093\pi\)
0.866925 + 0.498439i \(0.166093\pi\)
\(810\) 4.86525e17 0.0605274
\(811\) 4.71473e18 0.581864 0.290932 0.956744i \(-0.406035\pi\)
0.290932 + 0.956744i \(0.406035\pi\)
\(812\) 2.02685e19 2.48146
\(813\) −7.74181e18 −0.940273
\(814\) −2.52018e18 −0.303650
\(815\) 4.33711e18 0.518413
\(816\) 2.53640e18 0.300768
\(817\) −2.36242e19 −2.77916
\(818\) 1.39869e19 1.63239
\(819\) 8.13357e17 0.0941751
\(820\) 2.81921e18 0.323845
\(821\) 3.15464e18 0.359516 0.179758 0.983711i \(-0.442468\pi\)
0.179758 + 0.983711i \(0.442468\pi\)
\(822\) 1.47081e19 1.66299
\(823\) 6.03428e18 0.676903 0.338452 0.940984i \(-0.390097\pi\)
0.338452 + 0.940984i \(0.390097\pi\)
\(824\) 1.21773e19 1.35527
\(825\) 6.19712e18 0.684289
\(826\) 1.27171e18 0.139321
\(827\) 1.18728e19 1.29053 0.645265 0.763958i \(-0.276747\pi\)
0.645265 + 0.763958i \(0.276747\pi\)
\(828\) 5.54375e18 0.597870
\(829\) 2.32766e17 0.0249067 0.0124533 0.999922i \(-0.496036\pi\)
0.0124533 + 0.999922i \(0.496036\pi\)
\(830\) −2.23979e18 −0.237794
\(831\) −4.90916e18 −0.517131
\(832\) −2.72487e18 −0.284802
\(833\) 2.35295e18 0.244017
\(834\) −3.25601e18 −0.335047
\(835\) −4.09477e18 −0.418087
\(836\) 3.86607e19 3.91677
\(837\) 1.59835e18 0.160678
\(838\) −3.49895e18 −0.349021
\(839\) 7.84977e18 0.776970 0.388485 0.921455i \(-0.372999\pi\)
0.388485 + 0.921455i \(0.372999\pi\)
\(840\) −2.16049e18 −0.212196
\(841\) 2.82242e19 2.75073
\(842\) −4.43368e18 −0.428781
\(843\) −5.56614e18 −0.534165
\(844\) −5.18296e18 −0.493573
\(845\) 2.55878e18 0.241804
\(846\) 3.18371e18 0.298556
\(847\) 4.67037e18 0.434620
\(848\) −3.84239e18 −0.354837
\(849\) −2.09864e18 −0.192326
\(850\) −6.77521e18 −0.616169
\(851\) 1.23608e18 0.111559
\(852\) 1.77897e19 1.59335
\(853\) −3.39791e18 −0.302025 −0.151013 0.988532i \(-0.548253\pi\)
−0.151013 + 0.988532i \(0.548253\pi\)
\(854\) 2.32459e19 2.05055
\(855\) −1.66412e18 −0.145682
\(856\) 2.32916e17 0.0202357
\(857\) 1.52503e18 0.131493 0.0657467 0.997836i \(-0.479057\pi\)
0.0657467 + 0.997836i \(0.479057\pi\)
\(858\) 7.26294e18 0.621506
\(859\) 7.91165e17 0.0671911 0.0335955 0.999436i \(-0.489304\pi\)
0.0335955 + 0.999436i \(0.489304\pi\)
\(860\) 1.51945e19 1.28070
\(861\) 2.07875e18 0.173893
\(862\) −3.37904e19 −2.80540
\(863\) −5.10763e18 −0.420871 −0.210436 0.977608i \(-0.567488\pi\)
−0.210436 + 0.977608i \(0.567488\pi\)
\(864\) 9.84154e17 0.0804867
\(865\) 5.99256e18 0.486416
\(866\) 3.39435e19 2.73458
\(867\) 6.14415e18 0.491290
\(868\) −1.34793e19 −1.06976
\(869\) 2.91043e19 2.29260
\(870\) −7.79053e18 −0.609105
\(871\) 2.07864e17 0.0161310
\(872\) 5.84722e18 0.450394
\(873\) 5.09224e18 0.389329
\(874\) −2.79392e19 −2.12026
\(875\) 4.73623e18 0.356764
\(876\) 1.83928e19 1.37522
\(877\) 1.59731e19 1.18547 0.592735 0.805398i \(-0.298048\pi\)
0.592735 + 0.805398i \(0.298048\pi\)
\(878\) −2.36762e18 −0.174421
\(879\) −2.22789e18 −0.162917
\(880\) −7.52010e18 −0.545866
\(881\) −5.20802e18 −0.375257 −0.187629 0.982240i \(-0.560080\pi\)
−0.187629 + 0.982240i \(0.560080\pi\)
\(882\) 5.19634e18 0.371665
\(883\) −6.44610e18 −0.457670 −0.228835 0.973465i \(-0.573492\pi\)
−0.228835 + 0.973465i \(0.573492\pi\)
\(884\) −5.38909e18 −0.379818
\(885\) −3.31744e17 −0.0232098
\(886\) −2.13825e19 −1.48505
\(887\) −7.23479e18 −0.498795 −0.249398 0.968401i \(-0.580233\pi\)
−0.249398 + 0.968401i \(0.580233\pi\)
\(888\) 2.17457e18 0.148830
\(889\) −1.19883e19 −0.814509
\(890\) 1.53890e18 0.103794
\(891\) 2.17411e18 0.145572
\(892\) −4.01895e18 −0.267141
\(893\) −1.08896e19 −0.718586
\(894\) −2.92411e19 −1.91558
\(895\) −6.09052e18 −0.396100
\(896\) 1.40646e19 0.908085
\(897\) −3.56227e18 −0.228337
\(898\) 1.52958e19 0.973364
\(899\) −2.55938e19 −1.61695
\(900\) −1.01550e19 −0.636945
\(901\) 1.63047e18 0.101532
\(902\) 1.85624e19 1.14760
\(903\) 1.12037e19 0.687690
\(904\) 2.85722e19 1.74120
\(905\) −3.61251e18 −0.218572
\(906\) 2.54430e19 1.52839
\(907\) 1.89021e18 0.112736 0.0563680 0.998410i \(-0.482048\pi\)
0.0563680 + 0.998410i \(0.482048\pi\)
\(908\) −1.26221e19 −0.747437
\(909\) 6.89337e17 0.0405291
\(910\) 2.63646e18 0.153905
\(911\) −2.22775e19 −1.29121 −0.645605 0.763671i \(-0.723395\pi\)
−0.645605 + 0.763671i \(0.723395\pi\)
\(912\) −1.91594e19 −1.10259
\(913\) −1.00089e19 −0.571906
\(914\) −3.58634e19 −2.03471
\(915\) −6.06404e18 −0.341606
\(916\) −3.18951e19 −1.78404
\(917\) 1.72785e19 0.959632
\(918\) −2.37692e18 −0.131080
\(919\) 1.55361e19 0.850727 0.425363 0.905023i \(-0.360146\pi\)
0.425363 + 0.905023i \(0.360146\pi\)
\(920\) 9.46233e18 0.514490
\(921\) −1.72467e19 −0.931147
\(922\) −2.08684e19 −1.11877
\(923\) −1.14312e19 −0.608529
\(924\) −1.83348e19 −0.969187
\(925\) −2.26423e18 −0.118850
\(926\) −9.36773e18 −0.488273
\(927\) −4.44825e18 −0.230235
\(928\) −1.57589e19 −0.809960
\(929\) 5.57626e18 0.284604 0.142302 0.989823i \(-0.454550\pi\)
0.142302 + 0.989823i \(0.454550\pi\)
\(930\) 5.18099e18 0.262587
\(931\) −1.77737e19 −0.894549
\(932\) −4.67780e19 −2.33796
\(933\) 2.26236e19 1.12287
\(934\) −6.03787e19 −2.97598
\(935\) 3.19107e18 0.156193
\(936\) −6.26693e18 −0.304622
\(937\) −1.53589e19 −0.741402 −0.370701 0.928752i \(-0.620883\pi\)
−0.370701 + 0.928752i \(0.620883\pi\)
\(938\) −7.73167e17 −0.0370642
\(939\) 1.70803e19 0.813146
\(940\) 7.00395e18 0.331140
\(941\) −8.38429e18 −0.393671 −0.196836 0.980437i \(-0.563067\pi\)
−0.196836 + 0.980437i \(0.563067\pi\)
\(942\) −8.70562e18 −0.405947
\(943\) −9.10434e18 −0.421621
\(944\) −3.81945e18 −0.175664
\(945\) 7.89206e17 0.0360482
\(946\) 1.00045e20 4.53839
\(947\) 2.70215e19 1.21740 0.608702 0.793399i \(-0.291691\pi\)
0.608702 + 0.793399i \(0.291691\pi\)
\(948\) −4.76920e19 −2.13398
\(949\) −1.18187e19 −0.525218
\(950\) 5.11785e19 2.25883
\(951\) 9.43604e18 0.413634
\(952\) 1.05551e19 0.459539
\(953\) −1.64697e19 −0.712168 −0.356084 0.934454i \(-0.615888\pi\)
−0.356084 + 0.934454i \(0.615888\pi\)
\(954\) 3.60080e18 0.154645
\(955\) 3.97104e18 0.169388
\(956\) 4.55236e19 1.92868
\(957\) −3.48132e19 −1.46493
\(958\) −3.69904e19 −1.54601
\(959\) 2.38585e19 0.990426
\(960\) −2.64395e18 −0.109016
\(961\) −7.39673e18 −0.302927
\(962\) −2.65364e18 −0.107945
\(963\) −8.50817e16 −0.00343768
\(964\) −9.13108e19 −3.66456
\(965\) 1.29399e18 0.0515824
\(966\) 1.32501e19 0.524648
\(967\) 3.71084e19 1.45949 0.729743 0.683721i \(-0.239639\pi\)
0.729743 + 0.683721i \(0.239639\pi\)
\(968\) −3.59853e19 −1.40584
\(969\) 8.13007e18 0.315493
\(970\) 1.65063e19 0.636257
\(971\) 4.23409e19 1.62119 0.810597 0.585604i \(-0.199143\pi\)
0.810597 + 0.585604i \(0.199143\pi\)
\(972\) −3.56262e18 −0.135500
\(973\) −5.28166e18 −0.199543
\(974\) −4.70204e19 −1.76463
\(975\) 6.52530e18 0.243260
\(976\) −6.98168e19 −2.58545
\(977\) −4.15029e19 −1.52673 −0.763367 0.645964i \(-0.776455\pi\)
−0.763367 + 0.645964i \(0.776455\pi\)
\(978\) −4.67946e19 −1.70999
\(979\) 6.87680e18 0.249631
\(980\) 1.14316e19 0.412228
\(981\) −2.13593e18 −0.0765135
\(982\) 5.86707e19 2.08784
\(983\) −1.04911e19 −0.370873 −0.185436 0.982656i \(-0.559370\pi\)
−0.185436 + 0.982656i \(0.559370\pi\)
\(984\) −1.60168e19 −0.562482
\(985\) 1.64606e19 0.574261
\(986\) 3.80607e19 1.31910
\(987\) 5.16439e18 0.177811
\(988\) 4.07080e19 1.39239
\(989\) −4.90691e19 −1.66737
\(990\) 7.04728e18 0.237899
\(991\) −2.39742e19 −0.804017 −0.402009 0.915636i \(-0.631688\pi\)
−0.402009 + 0.915636i \(0.631688\pi\)
\(992\) 1.04802e19 0.349176
\(993\) 3.14521e19 1.04107
\(994\) 4.25192e19 1.39821
\(995\) −3.19730e18 −0.104456
\(996\) 1.64011e19 0.532337
\(997\) 3.65502e18 0.117861 0.0589307 0.998262i \(-0.481231\pi\)
0.0589307 + 0.998262i \(0.481231\pi\)
\(998\) −1.34378e19 −0.430506
\(999\) −7.94350e17 −0.0252834
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.1.3 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.3 31 1.1 even 1 trivial