Properties

Label 177.14.a.b.1.1
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 1.1
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-169.906 q^{2} -729.000 q^{3} +20675.9 q^{4} +41498.5 q^{5} +123861. q^{6} +222317. q^{7} -2.12109e6 q^{8} +531441. q^{9} +O(q^{10})\) \(q-169.906 q^{2} -729.000 q^{3} +20675.9 q^{4} +41498.5 q^{5} +123861. q^{6} +222317. q^{7} -2.12109e6 q^{8} +531441. q^{9} -7.05083e6 q^{10} -1.07727e7 q^{11} -1.50728e7 q^{12} +2.00397e7 q^{13} -3.77728e7 q^{14} -3.02524e7 q^{15} +1.91008e8 q^{16} +1.01659e8 q^{17} -9.02948e7 q^{18} -3.33309e8 q^{19} +8.58021e8 q^{20} -1.62069e8 q^{21} +1.83034e9 q^{22} +1.06894e9 q^{23} +1.54628e9 q^{24} +5.01424e8 q^{25} -3.40486e9 q^{26} -3.87420e8 q^{27} +4.59660e9 q^{28} +5.94950e9 q^{29} +5.14006e9 q^{30} -6.31398e9 q^{31} -1.50774e10 q^{32} +7.85331e9 q^{33} -1.72724e10 q^{34} +9.22581e9 q^{35} +1.09880e10 q^{36} -1.05289e10 q^{37} +5.66310e10 q^{38} -1.46089e10 q^{39} -8.80222e10 q^{40} -3.83957e10 q^{41} +2.75364e10 q^{42} +1.84687e10 q^{43} -2.22736e11 q^{44} +2.20540e10 q^{45} -1.81619e11 q^{46} +2.22256e10 q^{47} -1.39245e11 q^{48} -4.74644e10 q^{49} -8.51948e10 q^{50} -7.41094e10 q^{51} +4.14339e11 q^{52} +1.89641e10 q^{53} +6.58249e10 q^{54} -4.47052e11 q^{55} -4.71554e11 q^{56} +2.42982e11 q^{57} -1.01085e12 q^{58} -4.21805e10 q^{59} -6.25497e11 q^{60} +3.61171e11 q^{61} +1.07278e12 q^{62} +1.18148e11 q^{63} +9.96998e11 q^{64} +8.31617e11 q^{65} -1.33432e12 q^{66} -1.10019e12 q^{67} +2.10190e12 q^{68} -7.79257e11 q^{69} -1.56752e12 q^{70} -5.32591e11 q^{71} -1.12724e12 q^{72} +8.30365e11 q^{73} +1.78893e12 q^{74} -3.65538e11 q^{75} -6.89147e12 q^{76} -2.39495e12 q^{77} +2.48214e12 q^{78} -2.73593e12 q^{79} +7.92656e12 q^{80} +2.82430e11 q^{81} +6.52364e12 q^{82} +3.89497e12 q^{83} -3.35092e12 q^{84} +4.21870e12 q^{85} -3.13794e12 q^{86} -4.33718e12 q^{87} +2.28499e13 q^{88} -6.16283e12 q^{89} -3.74710e12 q^{90} +4.45516e12 q^{91} +2.21013e13 q^{92} +4.60289e12 q^{93} -3.77625e12 q^{94} -1.38318e13 q^{95} +1.09914e13 q^{96} -1.11435e13 q^{97} +8.06446e12 q^{98} -5.72506e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −169.906 −1.87721 −0.938605 0.344993i \(-0.887881\pi\)
−0.938605 + 0.344993i \(0.887881\pi\)
\(3\) −729.000 −0.577350
\(4\) 20675.9 2.52392
\(5\) 41498.5 1.18776 0.593878 0.804555i \(-0.297596\pi\)
0.593878 + 0.804555i \(0.297596\pi\)
\(6\) 123861. 1.08381
\(7\) 222317. 0.714224 0.357112 0.934062i \(-0.383761\pi\)
0.357112 + 0.934062i \(0.383761\pi\)
\(8\) −2.12109e6 −2.86072
\(9\) 531441. 0.333333
\(10\) −7.05083e6 −2.22967
\(11\) −1.07727e7 −1.83346 −0.916732 0.399502i \(-0.869183\pi\)
−0.916732 + 0.399502i \(0.869183\pi\)
\(12\) −1.50728e7 −1.45719
\(13\) 2.00397e7 1.15149 0.575744 0.817630i \(-0.304713\pi\)
0.575744 + 0.817630i \(0.304713\pi\)
\(14\) −3.77728e7 −1.34075
\(15\) −3.02524e7 −0.685752
\(16\) 1.91008e8 2.84625
\(17\) 1.01659e8 1.02148 0.510738 0.859737i \(-0.329372\pi\)
0.510738 + 0.859737i \(0.329372\pi\)
\(18\) −9.02948e7 −0.625737
\(19\) −3.33309e8 −1.62535 −0.812677 0.582714i \(-0.801991\pi\)
−0.812677 + 0.582714i \(0.801991\pi\)
\(20\) 8.58021e8 2.99780
\(21\) −1.62069e8 −0.412358
\(22\) 1.83034e9 3.44180
\(23\) 1.06894e9 1.50564 0.752822 0.658224i \(-0.228692\pi\)
0.752822 + 0.658224i \(0.228692\pi\)
\(24\) 1.54628e9 1.65163
\(25\) 5.01424e8 0.410766
\(26\) −3.40486e9 −2.16158
\(27\) −3.87420e8 −0.192450
\(28\) 4.59660e9 1.80264
\(29\) 5.94950e9 1.85735 0.928674 0.370897i \(-0.120950\pi\)
0.928674 + 0.370897i \(0.120950\pi\)
\(30\) 5.14006e9 1.28730
\(31\) −6.31398e9 −1.27777 −0.638884 0.769303i \(-0.720604\pi\)
−0.638884 + 0.769303i \(0.720604\pi\)
\(32\) −1.50774e10 −2.48229
\(33\) 7.85331e9 1.05855
\(34\) −1.72724e10 −1.91752
\(35\) 9.22581e9 0.848325
\(36\) 1.09880e10 0.841306
\(37\) −1.05289e10 −0.674643 −0.337321 0.941390i \(-0.609521\pi\)
−0.337321 + 0.941390i \(0.609521\pi\)
\(38\) 5.66310e10 3.05113
\(39\) −1.46089e10 −0.664812
\(40\) −8.80222e10 −3.39783
\(41\) −3.83957e10 −1.26237 −0.631185 0.775632i \(-0.717431\pi\)
−0.631185 + 0.775632i \(0.717431\pi\)
\(42\) 2.75364e10 0.774082
\(43\) 1.84687e10 0.445546 0.222773 0.974870i \(-0.428489\pi\)
0.222773 + 0.974870i \(0.428489\pi\)
\(44\) −2.22736e11 −4.62752
\(45\) 2.20540e10 0.395919
\(46\) −1.81619e11 −2.82641
\(47\) 2.22256e10 0.300758 0.150379 0.988628i \(-0.451951\pi\)
0.150379 + 0.988628i \(0.451951\pi\)
\(48\) −1.39245e11 −1.64328
\(49\) −4.74644e10 −0.489884
\(50\) −8.51948e10 −0.771095
\(51\) −7.41094e10 −0.589749
\(52\) 4.14339e11 2.90626
\(53\) 1.89641e10 0.117527 0.0587637 0.998272i \(-0.481284\pi\)
0.0587637 + 0.998272i \(0.481284\pi\)
\(54\) 6.58249e10 0.361269
\(55\) −4.47052e11 −2.17771
\(56\) −4.71554e11 −2.04319
\(57\) 2.42982e11 0.938399
\(58\) −1.01085e12 −3.48663
\(59\) −4.21805e10 −0.130189
\(60\) −6.25497e11 −1.73078
\(61\) 3.61171e11 0.897572 0.448786 0.893639i \(-0.351857\pi\)
0.448786 + 0.893639i \(0.351857\pi\)
\(62\) 1.07278e12 2.39864
\(63\) 1.18148e11 0.238075
\(64\) 9.96998e11 1.81353
\(65\) 8.31617e11 1.36769
\(66\) −1.33432e12 −1.98712
\(67\) −1.10019e12 −1.48587 −0.742937 0.669362i \(-0.766568\pi\)
−0.742937 + 0.669362i \(0.766568\pi\)
\(68\) 2.10190e12 2.57812
\(69\) −7.79257e11 −0.869284
\(70\) −1.56752e12 −1.59248
\(71\) −5.32591e11 −0.493418 −0.246709 0.969090i \(-0.579349\pi\)
−0.246709 + 0.969090i \(0.579349\pi\)
\(72\) −1.12724e12 −0.953572
\(73\) 8.30365e11 0.642200 0.321100 0.947045i \(-0.395947\pi\)
0.321100 + 0.947045i \(0.395947\pi\)
\(74\) 1.78893e12 1.26645
\(75\) −3.65538e11 −0.237156
\(76\) −6.89147e12 −4.10226
\(77\) −2.39495e12 −1.30950
\(78\) 2.48214e12 1.24799
\(79\) −2.73593e12 −1.26628 −0.633139 0.774038i \(-0.718234\pi\)
−0.633139 + 0.774038i \(0.718234\pi\)
\(80\) 7.92656e12 3.38065
\(81\) 2.82430e11 0.111111
\(82\) 6.52364e12 2.36974
\(83\) 3.89497e12 1.30766 0.653832 0.756640i \(-0.273160\pi\)
0.653832 + 0.756640i \(0.273160\pi\)
\(84\) −3.35092e12 −1.04076
\(85\) 4.21870e12 1.21326
\(86\) −3.13794e12 −0.836383
\(87\) −4.33718e12 −1.07234
\(88\) 2.28499e13 5.24502
\(89\) −6.16283e12 −1.31445 −0.657227 0.753693i \(-0.728271\pi\)
−0.657227 + 0.753693i \(0.728271\pi\)
\(90\) −3.74710e12 −0.743223
\(91\) 4.45516e12 0.822420
\(92\) 2.21013e13 3.80012
\(93\) 4.60289e12 0.737720
\(94\) −3.77625e12 −0.564585
\(95\) −1.38318e13 −1.93053
\(96\) 1.09914e13 1.43315
\(97\) −1.11435e13 −1.35833 −0.679164 0.733987i \(-0.737657\pi\)
−0.679164 + 0.733987i \(0.737657\pi\)
\(98\) 8.06446e12 0.919615
\(99\) −5.72506e12 −0.611155
\(100\) 1.03674e13 1.03674
\(101\) −3.08647e12 −0.289316 −0.144658 0.989482i \(-0.546208\pi\)
−0.144658 + 0.989482i \(0.546208\pi\)
\(102\) 1.25916e13 1.10708
\(103\) −1.71321e12 −0.141374 −0.0706869 0.997499i \(-0.522519\pi\)
−0.0706869 + 0.997499i \(0.522519\pi\)
\(104\) −4.25060e13 −3.29408
\(105\) −6.72561e12 −0.489780
\(106\) −3.22211e12 −0.220624
\(107\) −2.62326e12 −0.168985 −0.0844923 0.996424i \(-0.526927\pi\)
−0.0844923 + 0.996424i \(0.526927\pi\)
\(108\) −8.01028e12 −0.485728
\(109\) −8.90261e12 −0.508446 −0.254223 0.967146i \(-0.581820\pi\)
−0.254223 + 0.967146i \(0.581820\pi\)
\(110\) 7.59566e13 4.08802
\(111\) 7.67560e12 0.389505
\(112\) 4.24643e13 2.03286
\(113\) 2.18781e13 0.988553 0.494277 0.869305i \(-0.335433\pi\)
0.494277 + 0.869305i \(0.335433\pi\)
\(114\) −4.12840e13 −1.76157
\(115\) 4.43594e13 1.78834
\(116\) 1.23011e14 4.68779
\(117\) 1.06499e13 0.383829
\(118\) 7.16671e12 0.244392
\(119\) 2.26005e13 0.729562
\(120\) 6.41682e13 1.96174
\(121\) 8.15286e13 2.36159
\(122\) −6.13651e13 −1.68493
\(123\) 2.79904e13 0.728830
\(124\) −1.30547e14 −3.22498
\(125\) −2.98490e13 −0.699866
\(126\) −2.00740e13 −0.446916
\(127\) −2.92834e13 −0.619295 −0.309647 0.950851i \(-0.600211\pi\)
−0.309647 + 0.950851i \(0.600211\pi\)
\(128\) −4.58814e13 −0.922088
\(129\) −1.34637e13 −0.257236
\(130\) −1.41297e14 −2.56744
\(131\) −1.01661e13 −0.175748 −0.0878739 0.996132i \(-0.528007\pi\)
−0.0878739 + 0.996132i \(0.528007\pi\)
\(132\) 1.62374e14 2.67170
\(133\) −7.41000e13 −1.16087
\(134\) 1.86929e14 2.78930
\(135\) −1.60774e13 −0.228584
\(136\) −2.15628e14 −2.92215
\(137\) 1.16359e14 1.50355 0.751774 0.659421i \(-0.229199\pi\)
0.751774 + 0.659421i \(0.229199\pi\)
\(138\) 1.32400e14 1.63183
\(139\) 1.06667e14 1.25440 0.627200 0.778858i \(-0.284201\pi\)
0.627200 + 0.778858i \(0.284201\pi\)
\(140\) 1.90752e14 2.14110
\(141\) −1.62024e13 −0.173642
\(142\) 9.04903e13 0.926249
\(143\) −2.15882e14 −2.11121
\(144\) 1.01510e14 0.948749
\(145\) 2.46895e14 2.20608
\(146\) −1.41084e14 −1.20554
\(147\) 3.46015e13 0.282835
\(148\) −2.17696e14 −1.70274
\(149\) −2.04918e14 −1.53416 −0.767078 0.641554i \(-0.778290\pi\)
−0.767078 + 0.641554i \(0.778290\pi\)
\(150\) 6.21070e13 0.445192
\(151\) −9.14387e12 −0.0627740 −0.0313870 0.999507i \(-0.509992\pi\)
−0.0313870 + 0.999507i \(0.509992\pi\)
\(152\) 7.06978e14 4.64968
\(153\) 5.40258e13 0.340492
\(154\) 4.06916e14 2.45822
\(155\) −2.62021e14 −1.51768
\(156\) −3.02053e14 −1.67793
\(157\) −2.59828e14 −1.38464 −0.692322 0.721589i \(-0.743412\pi\)
−0.692322 + 0.721589i \(0.743412\pi\)
\(158\) 4.64850e14 2.37707
\(159\) −1.38248e13 −0.0678545
\(160\) −6.25690e14 −2.94835
\(161\) 2.37643e14 1.07537
\(162\) −4.79864e13 −0.208579
\(163\) 2.09548e14 0.875111 0.437556 0.899191i \(-0.355844\pi\)
0.437556 + 0.899191i \(0.355844\pi\)
\(164\) −7.93866e14 −3.18612
\(165\) 3.25901e14 1.25730
\(166\) −6.61777e14 −2.45476
\(167\) −4.71310e14 −1.68132 −0.840658 0.541567i \(-0.817831\pi\)
−0.840658 + 0.541567i \(0.817831\pi\)
\(168\) 3.43763e14 1.17964
\(169\) 9.87141e13 0.325923
\(170\) −7.16781e14 −2.27755
\(171\) −1.77134e14 −0.541785
\(172\) 3.81859e14 1.12452
\(173\) 3.58466e14 1.01660 0.508298 0.861181i \(-0.330275\pi\)
0.508298 + 0.861181i \(0.330275\pi\)
\(174\) 7.36912e14 2.01301
\(175\) 1.11475e14 0.293379
\(176\) −2.05768e15 −5.21849
\(177\) 3.07496e13 0.0751646
\(178\) 1.04710e15 2.46751
\(179\) −8.11876e14 −1.84478 −0.922391 0.386258i \(-0.873767\pi\)
−0.922391 + 0.386258i \(0.873767\pi\)
\(180\) 4.55987e14 0.999267
\(181\) 1.02697e14 0.217093 0.108546 0.994091i \(-0.465380\pi\)
0.108546 + 0.994091i \(0.465380\pi\)
\(182\) −7.56956e14 −1.54386
\(183\) −2.63294e14 −0.518213
\(184\) −2.26732e15 −4.30722
\(185\) −4.36936e14 −0.801312
\(186\) −7.82057e14 −1.38486
\(187\) −1.09514e15 −1.87284
\(188\) 4.59534e14 0.759088
\(189\) −8.61300e13 −0.137453
\(190\) 2.35010e15 3.62400
\(191\) 7.72970e14 1.15198 0.575991 0.817456i \(-0.304616\pi\)
0.575991 + 0.817456i \(0.304616\pi\)
\(192\) −7.26811e14 −1.04704
\(193\) −9.59978e13 −0.133702 −0.0668511 0.997763i \(-0.521295\pi\)
−0.0668511 + 0.997763i \(0.521295\pi\)
\(194\) 1.89334e15 2.54987
\(195\) −6.06249e14 −0.789635
\(196\) −9.81370e14 −1.23643
\(197\) 7.21801e14 0.879806 0.439903 0.898045i \(-0.355013\pi\)
0.439903 + 0.898045i \(0.355013\pi\)
\(198\) 9.72720e14 1.14727
\(199\) −4.25273e14 −0.485426 −0.242713 0.970098i \(-0.578037\pi\)
−0.242713 + 0.970098i \(0.578037\pi\)
\(200\) −1.06357e15 −1.17509
\(201\) 8.02039e14 0.857869
\(202\) 5.24408e14 0.543107
\(203\) 1.32267e15 1.32656
\(204\) −1.53228e15 −1.48848
\(205\) −1.59336e15 −1.49939
\(206\) 2.91084e14 0.265388
\(207\) 5.68079e14 0.501881
\(208\) 3.82775e15 3.27742
\(209\) 3.59064e15 2.98003
\(210\) 1.14272e15 0.919421
\(211\) −4.88535e14 −0.381118 −0.190559 0.981676i \(-0.561030\pi\)
−0.190559 + 0.981676i \(0.561030\pi\)
\(212\) 3.92101e14 0.296630
\(213\) 3.88259e14 0.284875
\(214\) 4.45707e14 0.317220
\(215\) 7.66425e14 0.529200
\(216\) 8.21755e14 0.550545
\(217\) −1.40370e15 −0.912613
\(218\) 1.51260e15 0.954460
\(219\) −6.05336e14 −0.370774
\(220\) −9.24321e15 −5.49636
\(221\) 2.03722e15 1.17622
\(222\) −1.30413e15 −0.731183
\(223\) 2.42274e15 1.31925 0.659623 0.751596i \(-0.270716\pi\)
0.659623 + 0.751596i \(0.270716\pi\)
\(224\) −3.35196e15 −1.77291
\(225\) 2.66477e14 0.136922
\(226\) −3.71722e15 −1.85572
\(227\) 4.93812e14 0.239548 0.119774 0.992801i \(-0.461783\pi\)
0.119774 + 0.992801i \(0.461783\pi\)
\(228\) 5.02388e15 2.36844
\(229\) 4.26781e14 0.195557 0.0977786 0.995208i \(-0.468826\pi\)
0.0977786 + 0.995208i \(0.468826\pi\)
\(230\) −7.53692e15 −3.35709
\(231\) 1.74592e15 0.756043
\(232\) −1.26194e16 −5.31334
\(233\) −1.10492e15 −0.452394 −0.226197 0.974082i \(-0.572629\pi\)
−0.226197 + 0.974082i \(0.572629\pi\)
\(234\) −1.80948e15 −0.720528
\(235\) 9.22328e14 0.357227
\(236\) −8.72122e14 −0.328586
\(237\) 1.99449e15 0.731086
\(238\) −3.83995e15 −1.36954
\(239\) 2.55175e15 0.885629 0.442815 0.896613i \(-0.353980\pi\)
0.442815 + 0.896613i \(0.353980\pi\)
\(240\) −5.77846e15 −1.95182
\(241\) −5.07400e14 −0.166817 −0.0834084 0.996515i \(-0.526581\pi\)
−0.0834084 + 0.996515i \(0.526581\pi\)
\(242\) −1.38522e16 −4.43321
\(243\) −2.05891e14 −0.0641500
\(244\) 7.46756e15 2.26540
\(245\) −1.96970e15 −0.581863
\(246\) −4.75573e15 −1.36817
\(247\) −6.67940e15 −1.87158
\(248\) 1.33925e16 3.65533
\(249\) −2.83943e15 −0.754980
\(250\) 5.07152e15 1.31380
\(251\) −2.50939e15 −0.633416 −0.316708 0.948523i \(-0.602578\pi\)
−0.316708 + 0.948523i \(0.602578\pi\)
\(252\) 2.44282e15 0.600881
\(253\) −1.15154e16 −2.76055
\(254\) 4.97542e15 1.16255
\(255\) −3.07543e15 −0.700479
\(256\) −3.71890e14 −0.0825762
\(257\) 2.31866e15 0.501963 0.250982 0.967992i \(-0.419247\pi\)
0.250982 + 0.967992i \(0.419247\pi\)
\(258\) 2.28756e15 0.482886
\(259\) −2.34076e15 −0.481846
\(260\) 1.71945e16 3.45193
\(261\) 3.16181e15 0.619116
\(262\) 1.72727e15 0.329916
\(263\) −5.55745e15 −1.03553 −0.517766 0.855522i \(-0.673236\pi\)
−0.517766 + 0.855522i \(0.673236\pi\)
\(264\) −1.66576e16 −3.02821
\(265\) 7.86982e14 0.139594
\(266\) 1.25900e16 2.17919
\(267\) 4.49270e15 0.758900
\(268\) −2.27475e16 −3.75022
\(269\) −4.98044e15 −0.801453 −0.400726 0.916198i \(-0.631242\pi\)
−0.400726 + 0.916198i \(0.631242\pi\)
\(270\) 2.73164e15 0.429100
\(271\) −6.85334e15 −1.05100 −0.525499 0.850794i \(-0.676121\pi\)
−0.525499 + 0.850794i \(0.676121\pi\)
\(272\) 1.94177e16 2.90737
\(273\) −3.24781e15 −0.474825
\(274\) −1.97701e16 −2.82247
\(275\) −5.40169e15 −0.753126
\(276\) −1.61119e16 −2.19400
\(277\) 6.46709e15 0.860182 0.430091 0.902786i \(-0.358481\pi\)
0.430091 + 0.902786i \(0.358481\pi\)
\(278\) −1.81234e16 −2.35477
\(279\) −3.35551e15 −0.425923
\(280\) −1.95688e16 −2.42682
\(281\) 1.61187e16 1.95316 0.976581 0.215148i \(-0.0690234\pi\)
0.976581 + 0.215148i \(0.0690234\pi\)
\(282\) 2.75288e15 0.325963
\(283\) −1.04420e16 −1.20830 −0.604148 0.796872i \(-0.706486\pi\)
−0.604148 + 0.796872i \(0.706486\pi\)
\(284\) −1.10118e16 −1.24535
\(285\) 1.00834e16 1.11459
\(286\) 3.66795e16 3.96319
\(287\) −8.53599e15 −0.901616
\(288\) −8.01276e15 −0.827429
\(289\) 4.29979e14 0.0434121
\(290\) −4.19489e16 −4.14127
\(291\) 8.12360e15 0.784231
\(292\) 1.71686e16 1.62086
\(293\) 6.23910e15 0.576079 0.288040 0.957619i \(-0.406997\pi\)
0.288040 + 0.957619i \(0.406997\pi\)
\(294\) −5.87899e15 −0.530940
\(295\) −1.75043e15 −0.154633
\(296\) 2.23329e16 1.92996
\(297\) 4.17357e15 0.352850
\(298\) 3.48167e16 2.87993
\(299\) 2.14212e16 1.73373
\(300\) −7.55784e15 −0.598563
\(301\) 4.10591e15 0.318219
\(302\) 1.55360e15 0.117840
\(303\) 2.25003e15 0.167037
\(304\) −6.36647e16 −4.62616
\(305\) 1.49881e16 1.06610
\(306\) −9.17929e15 −0.639175
\(307\) −3.51073e15 −0.239330 −0.119665 0.992814i \(-0.538182\pi\)
−0.119665 + 0.992814i \(0.538182\pi\)
\(308\) −4.95179e16 −3.30508
\(309\) 1.24893e15 0.0816222
\(310\) 4.45188e16 2.84900
\(311\) 5.47784e15 0.343295 0.171647 0.985158i \(-0.445091\pi\)
0.171647 + 0.985158i \(0.445091\pi\)
\(312\) 3.09869e16 1.90184
\(313\) 1.64788e16 0.990574 0.495287 0.868729i \(-0.335063\pi\)
0.495287 + 0.868729i \(0.335063\pi\)
\(314\) 4.41462e16 2.59927
\(315\) 4.90297e15 0.282775
\(316\) −5.65680e16 −3.19598
\(317\) 5.74438e15 0.317950 0.158975 0.987283i \(-0.449181\pi\)
0.158975 + 0.987283i \(0.449181\pi\)
\(318\) 2.34892e15 0.127377
\(319\) −6.40922e16 −3.40538
\(320\) 4.13739e16 2.15403
\(321\) 1.91236e15 0.0975633
\(322\) −4.03769e16 −2.01869
\(323\) −3.38838e16 −1.66026
\(324\) 5.83950e15 0.280435
\(325\) 1.00484e16 0.472992
\(326\) −3.56033e16 −1.64277
\(327\) 6.49000e15 0.293552
\(328\) 8.14407e16 3.61128
\(329\) 4.94111e15 0.214808
\(330\) −5.53724e16 −2.36022
\(331\) 1.62670e16 0.679869 0.339934 0.940449i \(-0.389595\pi\)
0.339934 + 0.940449i \(0.389595\pi\)
\(332\) 8.05321e16 3.30044
\(333\) −5.59552e15 −0.224881
\(334\) 8.00782e16 3.15618
\(335\) −4.56563e16 −1.76486
\(336\) −3.09565e16 −1.17367
\(337\) 5.00718e16 1.86208 0.931041 0.364914i \(-0.118901\pi\)
0.931041 + 0.364914i \(0.118901\pi\)
\(338\) −1.67721e16 −0.611827
\(339\) −1.59491e16 −0.570742
\(340\) 8.72256e16 3.06218
\(341\) 6.80187e16 2.34274
\(342\) 3.00960e16 1.01704
\(343\) −3.20921e16 −1.06411
\(344\) −3.91739e16 −1.27458
\(345\) −3.23380e16 −1.03250
\(346\) −6.09054e16 −1.90836
\(347\) 1.83010e16 0.562774 0.281387 0.959594i \(-0.409205\pi\)
0.281387 + 0.959594i \(0.409205\pi\)
\(348\) −8.96753e16 −2.70650
\(349\) −3.68256e16 −1.09090 −0.545449 0.838144i \(-0.683641\pi\)
−0.545449 + 0.838144i \(0.683641\pi\)
\(350\) −1.89402e16 −0.550735
\(351\) −7.76379e15 −0.221604
\(352\) 1.62425e17 4.55119
\(353\) −5.65039e16 −1.55433 −0.777165 0.629297i \(-0.783343\pi\)
−0.777165 + 0.629297i \(0.783343\pi\)
\(354\) −5.22453e15 −0.141100
\(355\) −2.21018e16 −0.586060
\(356\) −1.27422e17 −3.31757
\(357\) −1.64758e16 −0.421213
\(358\) 1.37942e17 3.46304
\(359\) 2.96902e16 0.731980 0.365990 0.930619i \(-0.380730\pi\)
0.365990 + 0.930619i \(0.380730\pi\)
\(360\) −4.67786e16 −1.13261
\(361\) 6.90416e16 1.64178
\(362\) −1.74487e16 −0.407529
\(363\) −5.94343e16 −1.36347
\(364\) 9.21145e16 2.07572
\(365\) 3.44589e16 0.762778
\(366\) 4.47351e16 0.972796
\(367\) 2.27563e16 0.486151 0.243076 0.970007i \(-0.421844\pi\)
0.243076 + 0.970007i \(0.421844\pi\)
\(368\) 2.04176e17 4.28543
\(369\) −2.04050e16 −0.420790
\(370\) 7.42379e16 1.50423
\(371\) 4.21603e15 0.0839409
\(372\) 9.51691e16 1.86195
\(373\) 8.01528e16 1.54103 0.770516 0.637421i \(-0.219999\pi\)
0.770516 + 0.637421i \(0.219999\pi\)
\(374\) 1.86071e17 3.51571
\(375\) 2.17599e16 0.404068
\(376\) −4.71425e16 −0.860382
\(377\) 1.19226e17 2.13871
\(378\) 1.46340e16 0.258027
\(379\) −2.97541e15 −0.0515694 −0.0257847 0.999668i \(-0.508208\pi\)
−0.0257847 + 0.999668i \(0.508208\pi\)
\(380\) −2.85986e17 −4.87249
\(381\) 2.13476e16 0.357550
\(382\) −1.31332e17 −2.16251
\(383\) −3.32467e16 −0.538217 −0.269108 0.963110i \(-0.586729\pi\)
−0.269108 + 0.963110i \(0.586729\pi\)
\(384\) 3.34476e16 0.532368
\(385\) −9.93869e16 −1.55537
\(386\) 1.63106e16 0.250987
\(387\) 9.81504e15 0.148515
\(388\) −2.30402e17 −3.42831
\(389\) 4.92225e16 0.720263 0.360131 0.932902i \(-0.382732\pi\)
0.360131 + 0.932902i \(0.382732\pi\)
\(390\) 1.03005e17 1.48231
\(391\) 1.08667e17 1.53798
\(392\) 1.00676e17 1.40142
\(393\) 7.41107e15 0.101468
\(394\) −1.22638e17 −1.65158
\(395\) −1.13537e17 −1.50403
\(396\) −1.18371e17 −1.54251
\(397\) −9.44825e16 −1.21119 −0.605596 0.795772i \(-0.707065\pi\)
−0.605596 + 0.795772i \(0.707065\pi\)
\(398\) 7.22563e16 0.911246
\(399\) 5.40189e16 0.670227
\(400\) 9.57761e16 1.16914
\(401\) 3.07168e16 0.368925 0.184462 0.982840i \(-0.440946\pi\)
0.184462 + 0.982840i \(0.440946\pi\)
\(402\) −1.36271e17 −1.61040
\(403\) −1.26530e17 −1.47133
\(404\) −6.38156e16 −0.730210
\(405\) 1.17204e16 0.131973
\(406\) −2.24729e17 −2.49024
\(407\) 1.13425e17 1.23693
\(408\) 1.57193e17 1.68710
\(409\) −6.13389e16 −0.647940 −0.323970 0.946067i \(-0.605018\pi\)
−0.323970 + 0.946067i \(0.605018\pi\)
\(410\) 2.70721e17 2.81467
\(411\) −8.48259e16 −0.868074
\(412\) −3.54223e16 −0.356816
\(413\) −9.37743e15 −0.0929841
\(414\) −9.65198e16 −0.942137
\(415\) 1.61635e17 1.55319
\(416\) −3.02147e17 −2.85832
\(417\) −7.77606e16 −0.724228
\(418\) −6.10069e17 −5.59414
\(419\) 1.31663e16 0.118870 0.0594350 0.998232i \(-0.481070\pi\)
0.0594350 + 0.998232i \(0.481070\pi\)
\(420\) −1.39058e17 −1.23617
\(421\) −1.64531e17 −1.44018 −0.720088 0.693883i \(-0.755898\pi\)
−0.720088 + 0.693883i \(0.755898\pi\)
\(422\) 8.30049e16 0.715439
\(423\) 1.18116e16 0.100253
\(424\) −4.02246e16 −0.336212
\(425\) 5.09743e16 0.419588
\(426\) −6.59674e16 −0.534770
\(427\) 8.02944e16 0.641068
\(428\) −5.42384e16 −0.426503
\(429\) 1.57378e17 1.21891
\(430\) −1.30220e17 −0.993420
\(431\) −1.06355e17 −0.799202 −0.399601 0.916689i \(-0.630851\pi\)
−0.399601 + 0.916689i \(0.630851\pi\)
\(432\) −7.40005e16 −0.547760
\(433\) 1.21678e17 0.887239 0.443619 0.896215i \(-0.353694\pi\)
0.443619 + 0.896215i \(0.353694\pi\)
\(434\) 2.38497e17 1.71317
\(435\) −1.79987e17 −1.27368
\(436\) −1.84070e17 −1.28328
\(437\) −3.56287e17 −2.44721
\(438\) 1.02850e17 0.696022
\(439\) −2.38736e17 −1.59184 −0.795920 0.605402i \(-0.793012\pi\)
−0.795920 + 0.605402i \(0.793012\pi\)
\(440\) 9.48238e17 6.22981
\(441\) −2.52245e16 −0.163295
\(442\) −3.46134e17 −2.20801
\(443\) −2.57387e17 −1.61794 −0.808970 0.587850i \(-0.799975\pi\)
−0.808970 + 0.587850i \(0.799975\pi\)
\(444\) 1.58700e17 0.983079
\(445\) −2.55748e17 −1.56125
\(446\) −4.11638e17 −2.47650
\(447\) 1.49385e17 0.885745
\(448\) 2.21649e17 1.29527
\(449\) 2.94292e17 1.69503 0.847516 0.530770i \(-0.178097\pi\)
0.847516 + 0.530770i \(0.178097\pi\)
\(450\) −4.52760e16 −0.257032
\(451\) 4.13625e17 2.31451
\(452\) 4.52351e17 2.49503
\(453\) 6.66588e15 0.0362426
\(454\) −8.39014e16 −0.449683
\(455\) 1.84882e17 0.976835
\(456\) −5.15387e17 −2.68449
\(457\) −2.48129e17 −1.27416 −0.637078 0.770800i \(-0.719857\pi\)
−0.637078 + 0.770800i \(0.719857\pi\)
\(458\) −7.25124e16 −0.367102
\(459\) −3.93848e16 −0.196583
\(460\) 9.17173e17 4.51362
\(461\) −2.54644e17 −1.23560 −0.617801 0.786335i \(-0.711976\pi\)
−0.617801 + 0.786335i \(0.711976\pi\)
\(462\) −2.96642e17 −1.41925
\(463\) 3.82962e16 0.180667 0.0903337 0.995912i \(-0.471207\pi\)
0.0903337 + 0.995912i \(0.471207\pi\)
\(464\) 1.13640e18 5.28647
\(465\) 1.91013e17 0.876232
\(466\) 1.87732e17 0.849238
\(467\) −3.09661e16 −0.138142 −0.0690711 0.997612i \(-0.522004\pi\)
−0.0690711 + 0.997612i \(0.522004\pi\)
\(468\) 2.20197e17 0.968754
\(469\) −2.44591e17 −1.06125
\(470\) −1.56709e17 −0.670590
\(471\) 1.89414e17 0.799424
\(472\) 8.94688e16 0.372433
\(473\) −1.98958e17 −0.816892
\(474\) −3.38876e17 −1.37240
\(475\) −1.67129e17 −0.667641
\(476\) 4.67286e17 1.84136
\(477\) 1.00783e16 0.0391758
\(478\) −4.33557e17 −1.66251
\(479\) 4.11777e17 1.55769 0.778846 0.627215i \(-0.215805\pi\)
0.778846 + 0.627215i \(0.215805\pi\)
\(480\) 4.56128e17 1.70223
\(481\) −2.10997e17 −0.776843
\(482\) 8.62102e16 0.313150
\(483\) −1.73242e17 −0.620864
\(484\) 1.68568e18 5.96047
\(485\) −4.62438e17 −1.61336
\(486\) 3.49821e16 0.120423
\(487\) −3.38591e17 −1.15010 −0.575052 0.818117i \(-0.695018\pi\)
−0.575052 + 0.818117i \(0.695018\pi\)
\(488\) −7.66078e17 −2.56770
\(489\) −1.52760e17 −0.505246
\(490\) 3.34663e17 1.09228
\(491\) −5.96980e16 −0.192278 −0.0961391 0.995368i \(-0.530649\pi\)
−0.0961391 + 0.995368i \(0.530649\pi\)
\(492\) 5.78729e17 1.83951
\(493\) 6.04820e17 1.89724
\(494\) 1.13487e18 3.51334
\(495\) −2.37581e17 −0.725903
\(496\) −1.20602e18 −3.63684
\(497\) −1.18404e17 −0.352411
\(498\) 4.82436e17 1.41726
\(499\) 1.33164e16 0.0386130 0.0193065 0.999814i \(-0.493854\pi\)
0.0193065 + 0.999814i \(0.493854\pi\)
\(500\) −6.17157e17 −1.76641
\(501\) 3.43585e17 0.970708
\(502\) 4.26360e17 1.18906
\(503\) −3.31781e17 −0.913397 −0.456699 0.889621i \(-0.650968\pi\)
−0.456699 + 0.889621i \(0.650968\pi\)
\(504\) −2.50603e17 −0.681064
\(505\) −1.28084e17 −0.343637
\(506\) 1.95653e18 5.18212
\(507\) −7.19626e16 −0.188172
\(508\) −6.05462e17 −1.56305
\(509\) −5.66799e17 −1.44465 −0.722326 0.691552i \(-0.756927\pi\)
−0.722326 + 0.691552i \(0.756927\pi\)
\(510\) 5.22533e17 1.31495
\(511\) 1.84604e17 0.458675
\(512\) 4.39047e17 1.07710
\(513\) 1.29131e17 0.312800
\(514\) −3.93954e17 −0.942290
\(515\) −7.10957e16 −0.167918
\(516\) −2.78375e17 −0.649242
\(517\) −2.39429e17 −0.551428
\(518\) 3.97708e17 0.904527
\(519\) −2.61322e17 −0.586932
\(520\) −1.76394e18 −3.91256
\(521\) −2.81915e17 −0.617550 −0.308775 0.951135i \(-0.599919\pi\)
−0.308775 + 0.951135i \(0.599919\pi\)
\(522\) −5.37209e17 −1.16221
\(523\) −5.36927e17 −1.14724 −0.573620 0.819121i \(-0.694462\pi\)
−0.573620 + 0.819121i \(0.694462\pi\)
\(524\) −2.10193e17 −0.443573
\(525\) −8.12652e16 −0.169383
\(526\) 9.44243e17 1.94391
\(527\) −6.41873e17 −1.30521
\(528\) 1.50005e18 3.01290
\(529\) 6.38596e17 1.26696
\(530\) −1.33713e17 −0.262047
\(531\) −2.24165e16 −0.0433963
\(532\) −1.53209e18 −2.92993
\(533\) −7.69437e17 −1.45360
\(534\) −7.63336e17 −1.42462
\(535\) −1.08861e17 −0.200713
\(536\) 2.33361e18 4.25066
\(537\) 5.91857e17 1.06509
\(538\) 8.46205e17 1.50450
\(539\) 5.11320e17 0.898185
\(540\) −3.32415e17 −0.576927
\(541\) −1.11950e18 −1.91974 −0.959868 0.280452i \(-0.909516\pi\)
−0.959868 + 0.280452i \(0.909516\pi\)
\(542\) 1.16442e18 1.97295
\(543\) −7.48658e16 −0.125339
\(544\) −1.53276e18 −2.53560
\(545\) −3.69445e17 −0.603910
\(546\) 5.51821e17 0.891345
\(547\) 8.41696e17 1.34350 0.671750 0.740778i \(-0.265543\pi\)
0.671750 + 0.740778i \(0.265543\pi\)
\(548\) 2.40584e18 3.79483
\(549\) 1.91941e17 0.299191
\(550\) 9.17779e17 1.41378
\(551\) −1.98302e18 −3.01885
\(552\) 1.65288e18 2.48677
\(553\) −6.08243e17 −0.904406
\(554\) −1.09880e18 −1.61474
\(555\) 3.18526e17 0.462637
\(556\) 2.20545e18 3.16600
\(557\) −1.54092e17 −0.218636 −0.109318 0.994007i \(-0.534867\pi\)
−0.109318 + 0.994007i \(0.534867\pi\)
\(558\) 5.70120e17 0.799547
\(559\) 3.70108e17 0.513040
\(560\) 1.76221e18 2.41454
\(561\) 7.98359e17 1.08128
\(562\) −2.73866e18 −3.66650
\(563\) 3.23193e17 0.427717 0.213859 0.976865i \(-0.431397\pi\)
0.213859 + 0.976865i \(0.431397\pi\)
\(564\) −3.35000e17 −0.438259
\(565\) 9.07909e17 1.17416
\(566\) 1.77416e18 2.26822
\(567\) 6.27888e16 0.0793582
\(568\) 1.12968e18 1.41153
\(569\) −3.00730e17 −0.371490 −0.185745 0.982598i \(-0.559470\pi\)
−0.185745 + 0.982598i \(0.559470\pi\)
\(570\) −1.71323e18 −2.09232
\(571\) −2.63499e17 −0.318159 −0.159079 0.987266i \(-0.550853\pi\)
−0.159079 + 0.987266i \(0.550853\pi\)
\(572\) −4.46356e18 −5.32853
\(573\) −5.63495e17 −0.665097
\(574\) 1.45031e18 1.69252
\(575\) 5.35992e17 0.618468
\(576\) 5.29846e17 0.604510
\(577\) −8.70812e17 −0.982385 −0.491192 0.871051i \(-0.663439\pi\)
−0.491192 + 0.871051i \(0.663439\pi\)
\(578\) −7.30558e16 −0.0814937
\(579\) 6.99824e16 0.0771931
\(580\) 5.10479e18 5.56796
\(581\) 8.65916e17 0.933966
\(582\) −1.38025e18 −1.47217
\(583\) −2.04295e17 −0.215482
\(584\) −1.76128e18 −1.83715
\(585\) 4.41956e17 0.455896
\(586\) −1.06006e18 −1.08142
\(587\) −1.15068e18 −1.16093 −0.580467 0.814284i \(-0.697130\pi\)
−0.580467 + 0.814284i \(0.697130\pi\)
\(588\) 7.15419e17 0.713851
\(589\) 2.10450e18 2.07683
\(590\) 2.97408e17 0.290278
\(591\) −5.26193e17 −0.507956
\(592\) −2.01112e18 −1.92020
\(593\) −6.40296e17 −0.604679 −0.302340 0.953200i \(-0.597768\pi\)
−0.302340 + 0.953200i \(0.597768\pi\)
\(594\) −7.09113e17 −0.662374
\(595\) 9.37887e17 0.866543
\(596\) −4.23687e18 −3.87208
\(597\) 3.10024e17 0.280261
\(598\) −3.63959e18 −3.25458
\(599\) −6.09215e17 −0.538886 −0.269443 0.963016i \(-0.586840\pi\)
−0.269443 + 0.963016i \(0.586840\pi\)
\(600\) 7.75340e17 0.678436
\(601\) −1.59761e18 −1.38289 −0.691443 0.722431i \(-0.743025\pi\)
−0.691443 + 0.722431i \(0.743025\pi\)
\(602\) −6.97617e17 −0.597365
\(603\) −5.84687e17 −0.495291
\(604\) −1.89058e17 −0.158437
\(605\) 3.38331e18 2.80500
\(606\) −3.82294e17 −0.313563
\(607\) −1.52598e17 −0.123829 −0.0619145 0.998081i \(-0.519721\pi\)
−0.0619145 + 0.998081i \(0.519721\pi\)
\(608\) 5.02543e18 4.03460
\(609\) −9.64228e17 −0.765891
\(610\) −2.54656e18 −2.00129
\(611\) 4.45393e17 0.346319
\(612\) 1.11703e18 0.859374
\(613\) −5.78338e17 −0.440239 −0.220120 0.975473i \(-0.570645\pi\)
−0.220120 + 0.975473i \(0.570645\pi\)
\(614\) 5.96492e17 0.449273
\(615\) 1.16156e18 0.865673
\(616\) 5.07991e18 3.74612
\(617\) 1.27830e18 0.932777 0.466388 0.884580i \(-0.345555\pi\)
0.466388 + 0.884580i \(0.345555\pi\)
\(618\) −2.12201e17 −0.153222
\(619\) −1.25526e18 −0.896902 −0.448451 0.893807i \(-0.648024\pi\)
−0.448451 + 0.893807i \(0.648024\pi\)
\(620\) −5.41753e18 −3.83050
\(621\) −4.14129e17 −0.289761
\(622\) −9.30717e17 −0.644436
\(623\) −1.37010e18 −0.938815
\(624\) −2.79043e18 −1.89222
\(625\) −1.85078e18 −1.24204
\(626\) −2.79984e18 −1.85952
\(627\) −2.61757e18 −1.72052
\(628\) −5.37218e18 −3.49473
\(629\) −1.07036e18 −0.689131
\(630\) −8.33043e17 −0.530828
\(631\) 4.25601e17 0.268418 0.134209 0.990953i \(-0.457151\pi\)
0.134209 + 0.990953i \(0.457151\pi\)
\(632\) 5.80316e18 3.62246
\(633\) 3.56142e17 0.220039
\(634\) −9.76003e17 −0.596858
\(635\) −1.21522e18 −0.735571
\(636\) −2.85841e17 −0.171259
\(637\) −9.51171e17 −0.564095
\(638\) 1.08896e19 6.39262
\(639\) −2.83041e17 −0.164473
\(640\) −1.90401e18 −1.09522
\(641\) −2.52388e18 −1.43712 −0.718558 0.695467i \(-0.755197\pi\)
−0.718558 + 0.695467i \(0.755197\pi\)
\(642\) −3.24920e17 −0.183147
\(643\) −2.66994e17 −0.148981 −0.0744903 0.997222i \(-0.523733\pi\)
−0.0744903 + 0.997222i \(0.523733\pi\)
\(644\) 4.91349e18 2.71414
\(645\) −5.58724e17 −0.305534
\(646\) 5.75705e18 3.11666
\(647\) −2.91487e18 −1.56222 −0.781108 0.624395i \(-0.785345\pi\)
−0.781108 + 0.624395i \(0.785345\pi\)
\(648\) −5.99059e17 −0.317857
\(649\) 4.54399e17 0.238697
\(650\) −1.70728e18 −0.887906
\(651\) 1.02330e18 0.526897
\(652\) 4.33259e18 2.20871
\(653\) 9.19067e17 0.463886 0.231943 0.972729i \(-0.425492\pi\)
0.231943 + 0.972729i \(0.425492\pi\)
\(654\) −1.10269e18 −0.551058
\(655\) −4.21877e17 −0.208746
\(656\) −7.33389e18 −3.59302
\(657\) 4.41290e17 0.214067
\(658\) −8.39522e17 −0.403240
\(659\) −2.20480e17 −0.104861 −0.0524306 0.998625i \(-0.516697\pi\)
−0.0524306 + 0.998625i \(0.516697\pi\)
\(660\) 6.73830e18 3.17333
\(661\) 3.51365e18 1.63851 0.819255 0.573430i \(-0.194388\pi\)
0.819255 + 0.573430i \(0.194388\pi\)
\(662\) −2.76385e18 −1.27626
\(663\) −1.48513e18 −0.679089
\(664\) −8.26159e18 −3.74086
\(665\) −3.07504e18 −1.37883
\(666\) 9.50710e17 0.422149
\(667\) 6.35966e18 2.79651
\(668\) −9.74477e18 −4.24350
\(669\) −1.76618e18 −0.761667
\(670\) 7.75726e18 3.31301
\(671\) −3.89079e18 −1.64567
\(672\) 2.44358e18 1.02359
\(673\) −1.15268e18 −0.478200 −0.239100 0.970995i \(-0.576852\pi\)
−0.239100 + 0.970995i \(0.576852\pi\)
\(674\) −8.50749e18 −3.49552
\(675\) −1.94262e17 −0.0790520
\(676\) 2.04101e18 0.822604
\(677\) −4.04894e18 −1.61627 −0.808136 0.588995i \(-0.799524\pi\)
−0.808136 + 0.588995i \(0.799524\pi\)
\(678\) 2.70985e18 1.07140
\(679\) −2.47738e18 −0.970150
\(680\) −8.94825e18 −3.47080
\(681\) −3.59989e17 −0.138303
\(682\) −1.15568e19 −4.39782
\(683\) 1.80682e17 0.0681052 0.0340526 0.999420i \(-0.489159\pi\)
0.0340526 + 0.999420i \(0.489159\pi\)
\(684\) −3.66241e18 −1.36742
\(685\) 4.82874e18 1.78585
\(686\) 5.45264e18 1.99756
\(687\) −3.11123e17 −0.112905
\(688\) 3.52768e18 1.26813
\(689\) 3.80035e17 0.135331
\(690\) 5.49441e18 1.93822
\(691\) 5.20396e18 1.81855 0.909277 0.416191i \(-0.136635\pi\)
0.909277 + 0.416191i \(0.136635\pi\)
\(692\) 7.41162e18 2.56581
\(693\) −1.27278e18 −0.436502
\(694\) −3.10945e18 −1.05645
\(695\) 4.42654e18 1.48992
\(696\) 9.19957e18 3.06766
\(697\) −3.90326e18 −1.28948
\(698\) 6.25687e18 2.04784
\(699\) 8.05485e17 0.261190
\(700\) 2.30485e18 0.740466
\(701\) 1.05851e18 0.336920 0.168460 0.985708i \(-0.446121\pi\)
0.168460 + 0.985708i \(0.446121\pi\)
\(702\) 1.31911e18 0.415997
\(703\) 3.50939e18 1.09653
\(704\) −1.07404e19 −3.32504
\(705\) −6.72377e17 −0.206245
\(706\) 9.60034e18 2.91780
\(707\) −6.86173e17 −0.206637
\(708\) 6.35777e17 0.189709
\(709\) −7.68395e17 −0.227187 −0.113594 0.993527i \(-0.536236\pi\)
−0.113594 + 0.993527i \(0.536236\pi\)
\(710\) 3.75521e18 1.10016
\(711\) −1.45399e18 −0.422093
\(712\) 1.30719e19 3.76028
\(713\) −6.74927e18 −1.92387
\(714\) 2.79932e18 0.790706
\(715\) −8.95877e18 −2.50761
\(716\) −1.67863e19 −4.65608
\(717\) −1.86023e18 −0.511318
\(718\) −5.04453e18 −1.37408
\(719\) 1.35722e18 0.366364 0.183182 0.983079i \(-0.441360\pi\)
0.183182 + 0.983079i \(0.441360\pi\)
\(720\) 4.21250e18 1.12688
\(721\) −3.80875e17 −0.100973
\(722\) −1.17306e19 −3.08196
\(723\) 3.69895e17 0.0963117
\(724\) 2.12335e18 0.547924
\(725\) 2.98322e18 0.762936
\(726\) 1.00982e19 2.55951
\(727\) 1.76674e18 0.443813 0.221906 0.975068i \(-0.428772\pi\)
0.221906 + 0.975068i \(0.428772\pi\)
\(728\) −9.44980e18 −2.35271
\(729\) 1.50095e17 0.0370370
\(730\) −5.85477e18 −1.43189
\(731\) 1.87751e18 0.455114
\(732\) −5.44385e18 −1.30793
\(733\) −5.71590e18 −1.36116 −0.680580 0.732674i \(-0.738272\pi\)
−0.680580 + 0.732674i \(0.738272\pi\)
\(734\) −3.86642e18 −0.912608
\(735\) 1.43591e18 0.335939
\(736\) −1.61169e19 −3.73744
\(737\) 1.18520e19 2.72430
\(738\) 3.46693e18 0.789912
\(739\) 1.38377e18 0.312518 0.156259 0.987716i \(-0.450056\pi\)
0.156259 + 0.987716i \(0.450056\pi\)
\(740\) −9.03406e18 −2.02245
\(741\) 4.86928e18 1.08055
\(742\) −7.16328e17 −0.157575
\(743\) −1.50693e18 −0.328598 −0.164299 0.986411i \(-0.552536\pi\)
−0.164299 + 0.986411i \(0.552536\pi\)
\(744\) −9.76316e18 −2.11041
\(745\) −8.50379e18 −1.82220
\(746\) −1.36184e19 −2.89284
\(747\) 2.06995e18 0.435888
\(748\) −2.26431e19 −4.72689
\(749\) −5.83194e17 −0.120693
\(750\) −3.69714e18 −0.758521
\(751\) 2.94298e18 0.598587 0.299294 0.954161i \(-0.403249\pi\)
0.299294 + 0.954161i \(0.403249\pi\)
\(752\) 4.24527e18 0.856030
\(753\) 1.82935e18 0.365703
\(754\) −2.02572e19 −4.01481
\(755\) −3.79457e17 −0.0745603
\(756\) −1.78082e18 −0.346919
\(757\) 1.83281e18 0.353992 0.176996 0.984212i \(-0.443362\pi\)
0.176996 + 0.984212i \(0.443362\pi\)
\(758\) 5.05539e17 0.0968066
\(759\) 8.39471e18 1.59380
\(760\) 2.93385e19 5.52268
\(761\) 5.44048e18 1.01540 0.507700 0.861534i \(-0.330496\pi\)
0.507700 + 0.861534i \(0.330496\pi\)
\(762\) −3.62708e18 −0.671196
\(763\) −1.97920e18 −0.363145
\(764\) 1.59819e19 2.90751
\(765\) 2.24199e18 0.404422
\(766\) 5.64881e18 1.01035
\(767\) −8.45285e17 −0.149911
\(768\) 2.71108e17 0.0476754
\(769\) −5.22162e18 −0.910509 −0.455255 0.890361i \(-0.650452\pi\)
−0.455255 + 0.890361i \(0.650452\pi\)
\(770\) 1.68864e19 2.91976
\(771\) −1.69030e18 −0.289809
\(772\) −1.98485e18 −0.337454
\(773\) −4.14804e18 −0.699321 −0.349661 0.936876i \(-0.613703\pi\)
−0.349661 + 0.936876i \(0.613703\pi\)
\(774\) −1.66763e18 −0.278794
\(775\) −3.16598e18 −0.524864
\(776\) 2.36363e19 3.88579
\(777\) 1.70641e18 0.278194
\(778\) −8.36318e18 −1.35208
\(779\) 1.27976e19 2.05180
\(780\) −1.25348e19 −1.99297
\(781\) 5.73745e18 0.904664
\(782\) −1.84632e19 −2.88711
\(783\) −2.30496e18 −0.357447
\(784\) −9.06609e18 −1.39433
\(785\) −1.07825e19 −1.64462
\(786\) −1.25918e18 −0.190477
\(787\) −2.74707e17 −0.0412130 −0.0206065 0.999788i \(-0.506560\pi\)
−0.0206065 + 0.999788i \(0.506560\pi\)
\(788\) 1.49239e19 2.22056
\(789\) 4.05138e18 0.597864
\(790\) 1.92906e19 2.82338
\(791\) 4.86387e18 0.706049
\(792\) 1.21434e19 1.74834
\(793\) 7.23776e18 1.03354
\(794\) 1.60531e19 2.27366
\(795\) −5.73710e17 −0.0805946
\(796\) −8.79292e18 −1.22518
\(797\) −9.11974e18 −1.26039 −0.630193 0.776439i \(-0.717024\pi\)
−0.630193 + 0.776439i \(0.717024\pi\)
\(798\) −9.17812e18 −1.25816
\(799\) 2.25943e18 0.307216
\(800\) −7.56018e18 −1.01964
\(801\) −3.27518e18 −0.438151
\(802\) −5.21896e18 −0.692549
\(803\) −8.94528e18 −1.17745
\(804\) 1.65829e19 2.16519
\(805\) 9.86184e18 1.27728
\(806\) 2.14982e19 2.76200
\(807\) 3.63074e18 0.462719
\(808\) 6.54668e18 0.827651
\(809\) −1.69025e18 −0.211976 −0.105988 0.994367i \(-0.533801\pi\)
−0.105988 + 0.994367i \(0.533801\pi\)
\(810\) −1.99136e18 −0.247741
\(811\) −3.21503e18 −0.396780 −0.198390 0.980123i \(-0.563571\pi\)
−0.198390 + 0.980123i \(0.563571\pi\)
\(812\) 2.73475e19 3.34814
\(813\) 4.99609e18 0.606794
\(814\) −1.92716e19 −2.32198
\(815\) 8.69591e18 1.03942
\(816\) −1.41555e19 −1.67857
\(817\) −6.15579e18 −0.724170
\(818\) 1.04218e19 1.21632
\(819\) 2.36765e18 0.274140
\(820\) −3.29443e19 −3.78434
\(821\) 5.39563e18 0.614911 0.307455 0.951563i \(-0.400523\pi\)
0.307455 + 0.951563i \(0.400523\pi\)
\(822\) 1.44124e19 1.62956
\(823\) 6.17768e18 0.692989 0.346494 0.938052i \(-0.387372\pi\)
0.346494 + 0.938052i \(0.387372\pi\)
\(824\) 3.63388e18 0.404430
\(825\) 3.93784e18 0.434817
\(826\) 1.59328e18 0.174551
\(827\) 7.42446e18 0.807010 0.403505 0.914977i \(-0.367792\pi\)
0.403505 + 0.914977i \(0.367792\pi\)
\(828\) 1.17456e19 1.26671
\(829\) 4.12318e18 0.441192 0.220596 0.975365i \(-0.429200\pi\)
0.220596 + 0.975365i \(0.429200\pi\)
\(830\) −2.74628e19 −2.91566
\(831\) −4.71451e18 −0.496626
\(832\) 1.99795e19 2.08826
\(833\) −4.82518e18 −0.500404
\(834\) 1.32120e19 1.35953
\(835\) −1.95586e19 −1.99699
\(836\) 7.42398e19 7.52135
\(837\) 2.44617e18 0.245907
\(838\) −2.23703e18 −0.223144
\(839\) 1.29446e19 1.28126 0.640630 0.767849i \(-0.278673\pi\)
0.640630 + 0.767849i \(0.278673\pi\)
\(840\) 1.42656e19 1.40112
\(841\) 2.51359e19 2.44974
\(842\) 2.79548e19 2.70351
\(843\) −1.17505e19 −1.12766
\(844\) −1.01009e19 −0.961912
\(845\) 4.09649e18 0.387118
\(846\) −2.00685e18 −0.188195
\(847\) 1.81252e19 1.68671
\(848\) 3.62230e18 0.334512
\(849\) 7.61224e18 0.697610
\(850\) −8.66082e18 −0.787655
\(851\) −1.12548e19 −1.01577
\(852\) 8.02762e18 0.719001
\(853\) 1.06609e19 0.947603 0.473801 0.880632i \(-0.342881\pi\)
0.473801 + 0.880632i \(0.342881\pi\)
\(854\) −1.36425e19 −1.20342
\(855\) −7.35079e18 −0.643509
\(856\) 5.56418e18 0.483417
\(857\) −1.58162e19 −1.36373 −0.681864 0.731479i \(-0.738830\pi\)
−0.681864 + 0.731479i \(0.738830\pi\)
\(858\) −2.67394e19 −2.28815
\(859\) −1.52986e18 −0.129926 −0.0649632 0.997888i \(-0.520693\pi\)
−0.0649632 + 0.997888i \(0.520693\pi\)
\(860\) 1.58466e19 1.33566
\(861\) 6.22274e18 0.520548
\(862\) 1.80704e19 1.50027
\(863\) −2.83497e18 −0.233603 −0.116801 0.993155i \(-0.537264\pi\)
−0.116801 + 0.993155i \(0.537264\pi\)
\(864\) 5.84130e18 0.477716
\(865\) 1.48758e19 1.20747
\(866\) −2.06738e19 −1.66553
\(867\) −3.13454e17 −0.0250640
\(868\) −2.90229e19 −2.30336
\(869\) 2.94734e19 2.32168
\(870\) 3.05808e19 2.39096
\(871\) −2.20475e19 −1.71096
\(872\) 1.88833e19 1.45452
\(873\) −5.92210e18 −0.452776
\(874\) 6.05352e19 4.59392
\(875\) −6.63593e18 −0.499861
\(876\) −1.25159e19 −0.935805
\(877\) −8.45969e18 −0.627852 −0.313926 0.949447i \(-0.601644\pi\)
−0.313926 + 0.949447i \(0.601644\pi\)
\(878\) 4.05627e19 2.98822
\(879\) −4.54830e18 −0.332599
\(880\) −8.53906e19 −6.19830
\(881\) 1.94438e19 1.40100 0.700501 0.713651i \(-0.252960\pi\)
0.700501 + 0.713651i \(0.252960\pi\)
\(882\) 4.28579e18 0.306538
\(883\) 8.34134e18 0.592231 0.296115 0.955152i \(-0.404309\pi\)
0.296115 + 0.955152i \(0.404309\pi\)
\(884\) 4.21213e19 2.96867
\(885\) 1.27606e18 0.0892773
\(886\) 4.37315e19 3.03721
\(887\) −1.84638e19 −1.27297 −0.636486 0.771289i \(-0.719612\pi\)
−0.636486 + 0.771289i \(0.719612\pi\)
\(888\) −1.62807e19 −1.11426
\(889\) −6.51018e18 −0.442315
\(890\) 4.34531e19 2.93080
\(891\) −3.04253e18 −0.203718
\(892\) 5.00925e19 3.32967
\(893\) −7.40797e18 −0.488838
\(894\) −2.53814e19 −1.66273
\(895\) −3.36916e19 −2.19115
\(896\) −1.02002e19 −0.658577
\(897\) −1.56161e19 −1.00097
\(898\) −5.00020e19 −3.18193
\(899\) −3.75650e19 −2.37326
\(900\) 5.50967e18 0.345580
\(901\) 1.92787e18 0.120051
\(902\) −7.02773e19 −4.34483
\(903\) −2.99321e18 −0.183724
\(904\) −4.64055e19 −2.82797
\(905\) 4.26176e18 0.257853
\(906\) −1.13257e18 −0.0680350
\(907\) 1.60702e19 0.958461 0.479231 0.877689i \(-0.340916\pi\)
0.479231 + 0.877689i \(0.340916\pi\)
\(908\) 1.02100e19 0.604601
\(909\) −1.64027e18 −0.0964387
\(910\) −3.14126e19 −1.83373
\(911\) −2.89298e19 −1.67678 −0.838390 0.545070i \(-0.816503\pi\)
−0.838390 + 0.545070i \(0.816503\pi\)
\(912\) 4.64116e19 2.67091
\(913\) −4.19594e19 −2.39756
\(914\) 4.21585e19 2.39186
\(915\) −1.09263e19 −0.615512
\(916\) 8.82409e18 0.493571
\(917\) −2.26009e18 −0.125523
\(918\) 6.69170e18 0.369028
\(919\) −2.54475e19 −1.39346 −0.696731 0.717333i \(-0.745363\pi\)
−0.696731 + 0.717333i \(0.745363\pi\)
\(920\) −9.40904e19 −5.11593
\(921\) 2.55932e18 0.138177
\(922\) 4.32655e19 2.31948
\(923\) −1.06730e19 −0.568164
\(924\) 3.60985e19 1.90819
\(925\) −5.27947e18 −0.277121
\(926\) −6.50675e18 −0.339151
\(927\) −9.10471e17 −0.0471246
\(928\) −8.97030e19 −4.61047
\(929\) −3.42006e19 −1.74555 −0.872774 0.488125i \(-0.837681\pi\)
−0.872774 + 0.488125i \(0.837681\pi\)
\(930\) −3.24542e19 −1.64487
\(931\) 1.58203e19 0.796235
\(932\) −2.28452e19 −1.14180
\(933\) −3.99335e18 −0.198201
\(934\) 5.26131e18 0.259322
\(935\) −4.54468e19 −2.22448
\(936\) −2.25895e19 −1.09803
\(937\) 7.36987e18 0.355756 0.177878 0.984053i \(-0.443077\pi\)
0.177878 + 0.984053i \(0.443077\pi\)
\(938\) 4.15573e19 1.99218
\(939\) −1.20130e19 −0.571908
\(940\) 1.90700e19 0.901611
\(941\) 2.27720e19 1.06922 0.534611 0.845098i \(-0.320458\pi\)
0.534611 + 0.845098i \(0.320458\pi\)
\(942\) −3.21826e19 −1.50069
\(943\) −4.10427e19 −1.90068
\(944\) −8.05683e18 −0.370550
\(945\) −3.57427e18 −0.163260
\(946\) 3.38042e19 1.53348
\(947\) 4.25430e18 0.191670 0.0958349 0.995397i \(-0.469448\pi\)
0.0958349 + 0.995397i \(0.469448\pi\)
\(948\) 4.12380e19 1.84520
\(949\) 1.66403e19 0.739486
\(950\) 2.83961e19 1.25330
\(951\) −4.18766e18 −0.183568
\(952\) −4.79377e19 −2.08707
\(953\) −1.23523e19 −0.534126 −0.267063 0.963679i \(-0.586053\pi\)
−0.267063 + 0.963679i \(0.586053\pi\)
\(954\) −1.71236e18 −0.0735412
\(955\) 3.20771e19 1.36827
\(956\) 5.27599e19 2.23526
\(957\) 4.67232e19 1.96610
\(958\) −6.99633e19 −2.92411
\(959\) 2.58686e19 1.07387
\(960\) −3.01616e19 −1.24363
\(961\) 1.54488e19 0.632693
\(962\) 3.58496e19 1.45830
\(963\) −1.39411e18 −0.0563282
\(964\) −1.04910e19 −0.421032
\(965\) −3.98377e18 −0.158806
\(966\) 2.94348e19 1.16549
\(967\) −5.84975e18 −0.230073 −0.115036 0.993361i \(-0.536698\pi\)
−0.115036 + 0.993361i \(0.536698\pi\)
\(968\) −1.72930e20 −6.75584
\(969\) 2.47013e19 0.958551
\(970\) 7.85708e19 3.02862
\(971\) 3.23007e19 1.23677 0.618383 0.785877i \(-0.287788\pi\)
0.618383 + 0.785877i \(0.287788\pi\)
\(972\) −4.25699e18 −0.161909
\(973\) 2.37139e19 0.895922
\(974\) 5.75286e19 2.15899
\(975\) −7.32527e18 −0.273082
\(976\) 6.89867e19 2.55471
\(977\) 3.22016e19 1.18457 0.592287 0.805727i \(-0.298225\pi\)
0.592287 + 0.805727i \(0.298225\pi\)
\(978\) 2.59548e19 0.948452
\(979\) 6.63904e19 2.41000
\(980\) −4.07254e19 −1.46857
\(981\) −4.73121e18 −0.169482
\(982\) 1.01430e19 0.360947
\(983\) 1.37394e19 0.485700 0.242850 0.970064i \(-0.421918\pi\)
0.242850 + 0.970064i \(0.421918\pi\)
\(984\) −5.93703e19 −2.08498
\(985\) 2.99537e19 1.04500
\(986\) −1.02762e20 −3.56151
\(987\) −3.60207e18 −0.124020
\(988\) −1.38103e20 −4.72370
\(989\) 1.97420e19 0.670833
\(990\) 4.03664e19 1.36267
\(991\) −6.20738e18 −0.208176 −0.104088 0.994568i \(-0.533192\pi\)
−0.104088 + 0.994568i \(0.533192\pi\)
\(992\) 9.51985e19 3.17179
\(993\) −1.18586e19 −0.392522
\(994\) 2.01175e19 0.661549
\(995\) −1.76482e19 −0.576568
\(996\) −5.87079e19 −1.90551
\(997\) −2.64598e18 −0.0853234 −0.0426617 0.999090i \(-0.513584\pi\)
−0.0426617 + 0.999090i \(0.513584\pi\)
\(998\) −2.26254e18 −0.0724848
\(999\) 4.07913e18 0.129835
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.1.1 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.1 31 1.1 even 1 trivial