-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 3, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': -3, 'A6': 1, 'A7': 1, 'A8': -3, 'A9': 1, 'Lhash': '1013152907880901966', 'a10': [0.030927835051546393, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [-0.010309278350515464, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [-0.030927835051546393, 0.0], 'a6': [0.010309278350515464, 0.0], 'a7': [0.010309278350515464, 0.0], 'a8': [-0.030927835051546393, 0.0], 'a9': [0.010309278350515464, 0.0], 'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[3, [1, 1]], [13, [1, 3, 13]]], 'bad_primes': [3, 13], 'central_character': '13689.1', 'coefficient_field': '1.1.1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 1, 0, 2, 4], [1, 1], [1, 3, 10, 15, 25], [1, -1, 8, -7, 49], [1, -2, 10, -22, 121], [1, 3, 13], [1, -1, 18, -17, 289], [1, 1, -12, 19, 361], [1, 2, 30, 46, 529], [1, 9, 58, 261, 841], [1, 4, 6, 124, 961], [1, 2, 63, 74, 1369], [1, 1, 26, 41, 1681], [1, -2, 30, -86, 1849], [1, -2, -38, -94, 2209], [1, -3, 42, -159, 2809], [1, 8, 106, 472, 3481], [1, 4, 9, 244, 3721], [1, 5, 48, 335, 4489], [1, -6, 142, -426, 5041], [1, -2, -49, -146, 5329], [1, 3, 58, 237, 6241], [1, 2, -26, 166, 6889], [1, -2, -134, -178, 7921], [1, -11, 100, -1067, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 12, 'label': '4-117e2-1.1-c1e2-0-12', 'leading_term': '0.814361707675', 'load_key': 'G2Q', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'Genus2Curve/Q/13689/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.157020418077109, 0.3388381025195497, 0.5640966256949435, 0.8379317138213176, 1.143330383799422, 1.433135436352847, 1.626973510069977, 1.618954407872535, 1.301234730668551, 0.6040385324793759, -0.4557328864797673, -1.73539259775999, -2.961845756719556, -3.783288554253237, -3.881023599616636, -3.114060074707133, -1.636744269104147, 0.08404381446391382, 1.401456574628812, 1.754347766159382, 0.9642225889919576, -0.5951986716085026, -2.092485290102971, -2.615046723992297, -1.673613342704183, 0.4454715474142975, 2.735774605504869, 3.98290984376152, 3.485773200654462, 1.543937734056074, -0.6545237296729628, -1.750064943418128, -1.103286238669373, 0.7590898281301312, 2.509297608544214, 2.980408015703062, 2.021457536257113, 0.5644320311627669, -0.1846322089091562, 0.2172303993912125, 1.080028119608663, 1.244396688843564, 0.2225652928804305, -1.240246561404755, -1.784678256873594, -0.7400199737849693, 1.123308730507861, 2.214064071235257, 1.634829768989915, 0.1384187014543077, -0.5179936252312926, 0.6827833676362828, 2.880246551489426, 4.045619398151693, 2.948866144578269, 0.4184072399558135, -1.453364659900801, -1.384288777862569, -0.07477066732676776, 0.7657717387821396, 0.3985859071063364, -0.2658511917149525, -0.07708765257089661, 0.6510316432475532, 0.4574989508108938, -1.061888757820829, -1.966265148772815, 0.2051223207170345, 5.021921511995401, 8.28301981292477, 5.612548528552061, -2.675846549774203, -10.88437076893623, -12.88712326957643, -7.944028016708124, -1.199697386915542, 1.706447816660503, 0.02420818141957616, -2.436253283563236, -2.350679492749472, -0.3986082305625708, 0.5707491923739166, -0.2907544452925767, -0.9184856009973907, 0.4472960920692513, 2.609901338366645, 3.025680642464903, 1.340862659049399, -0.1552614730439638, 0.2164326059843056, 1.218715372776354, 0.6438650094494023, -1.31649116943963, -2.223863707831552, -0.9205777326464711, 0.7264651287125647, 0.5166542541623435, -0.8655761804050739, -0.9220123738296457, 0.8266931958876604, 2.034038166290472, 1.075678715053337, -0.4357501160366674, -0.1798129347943103, 1.093663712330726, 0.6118347045635844, -1.829232357750117, -2.996929777753402, -1.079251518932597, 0.9605186480818472, -0.6369456275933146, -4.404060689592774, -4.965152321768635, -0.675142755801114, 3.496323843024016, 2.695183046370866, -0.9146849870136508, -1.34741884555111, 2.438578828976724, 5.190999333600972, 3.343817104084856, 0.1777899927919778, 0.5132166948812918, 3.413447246716522, 4.083545140896049, 1.467236796784489, -0.5960691816266578, 0.09601685635855783, 1.011655372458873, 0.04014252111358395, -0.4706756049044455, 1.779423359130179, 3.662589160600527, 0.5427877868499107, -5.769366895726929, -8.272157343279266, -4.530882378361734, -0.1970466515683021, -0.7233464213108198, -3.952456592620272, -4.392619108804669, -1.517990404890326, 0.6661034270701169, 0.4196573071751515, -0.1819390157001493, 0.09976165094617781, 0.1085579228183115, -0.2822262403145991, 0.4164528737125274, 1.545567116834446, 0.3183401383515914, -2.832906881390711, -3.405904283059551, 0.2171807444038985, 3.370484564867536, 2.09192887710963, -0.6967664694508452, -0.5023300543163589, 1.1337099858799, 0.1960394606175276], 'positive_zeros': [1.98846463524503, 3.365393493637389, 4.058532298783233, 4.840020880958015, 5.751388707348107, 6.305184714343788, 7.230633920182169, 7.44430560246136, 8.090513077414982, 8.700705360677762, 9.394688668034071, 9.676111755979191, 10.53163226486427, 11.07310816244699, 11.53431943374611, 11.83327234880804, 12.25607947242685, 12.74000386895414, 13.44643201328255, 14.29592018868219, 14.62658654774544, 15.23083981933321, 15.51735377969231, 15.89714247425657, 16.65167112438955, 16.83458989691312, 17.31646443747978, 17.90192485419588, 18.25798898387899, 18.67237530664662, 19.24324040158494, 19.52643399169778, 19.9294020681061], 'prelabel': '4-117e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1013152907880901966, 'z1': {'__RealLiteral__': 0, 'data': '1.98846463525', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.36539349364', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.05853229878', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.8728225087682089, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 13689, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, -1, -1, 1, -3, 1, 1, -3, 1, 3, 2, -1, -3, -1, 3, 1, 1, -1, -1, -3, -1, -2, -2, 3, -1, 3, -1, 1, -9, -3, -4, 1, -2, -1, -3, 1, -2, 1, 3, 9, -1, 1, 2, 2, -3, 2, 2, -1, -7, 1, -1, -3, 3, 1, -6, -3, 1, 9, -8, 3, -4, 4, 1, 1, 9, 2, -5, 1, 2, 3, 6, -3, 2, 2, 1, -1, 2, -3, -3, -3, 1, 1, -2, -1, -3, -2, 9, -6, 2, 3, -3, -2, 4, -2, 3, -1, 11, 7, 2, -1], 'euler11': [1, -2, 10, -22, 121], 'euler13': [1, 3, 13, 0, 0], 'euler17': [1, -1, 18, -17, 289], 'euler19': [1, 1, -12, 19, 361], 'euler2': [1, 1, 0, 2, 4], 'euler23': [1, 2, 30, 46, 529], 'euler29': [1, 9, 58, 261, 841], 'euler3': [1, 1, 0, 0, 0], 'euler31': [1, 4, 6, 124, 961], 'euler37': [1, 2, 63, 74, 1369], 'euler41': [1, 1, 26, 41, 1681], 'euler43': [1, -2, 30, -86, 1849], 'euler47': [1, -2, -38, -94, 2209], 'euler5': [1, 3, 10, 15, 25], 'euler53': [1, -3, 42, -159, 2809], 'euler59': [1, 8, 106, 472, 3481], 'euler61': [1, 4, 9, 244, 3721], 'euler67': [1, 5, 48, 335, 4489], 'euler7': [1, -1, 8, -7, 49], 'euler71': [1, -6, 142, -426, 5041], 'euler73': [1, -2, -49, -146, 5329], 'euler79': [1, 3, 58, 237, 6241], 'euler83': [1, 2, -26, 166, 6889], 'euler89': [1, -2, -134, -178, 7921], 'euler97': [1, -11, 100, -1067, 9409], 'euler_factors': [[1, 1, 0, 2, 4], [1, 1, 0, 0, 0], [1, 3, 10, 15, 25], [1, -1, 8, -7, 49], [1, -2, 10, -22, 121], [1, 3, 13, 0, 0], [1, -1, 18, -17, 289], [1, 1, -12, 19, 361], [1, 2, 30, 46, 529], [1, 9, 58, 261, 841], [1, 4, 6, 124, 961], [1, 2, 63, 74, 1369], [1, 1, 26, 41, 1681], [1, -2, 30, -86, 1849], [1, -2, -38, -94, 2209], [1, -3, 42, -159, 2809], [1, 8, 106, 472, 3481], [1, 4, 9, 244, 3721], [1, 5, 48, 335, 4489], [1, -6, 142, -426, 5041], [1, -2, -49, -146, 5329], [1, 3, 58, 237, 6241], [1, 2, -26, 166, 6889], [1, -2, -134, -178, 7921], [1, -11, 100, -1067, 9409]], 'index': 12, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/13689/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-117e2-1.1-c1e2-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-117e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9665659334204683, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1013152907880901966, 'z1': {'__RealLiteral__': 0, 'data': '1.98846463525', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1013152907880901966', 'Lhash_array': ['1013152907880901966'], 'label': '4-117e2-1.1-c1e2-0-12', 'type': 'G2Q', 'url': 'Genus2Curve/Q/13689/c'}