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lfunc_lfunctions • Show schema
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{'A10': -8, 'A2': 2, 'A3': -3, 'A4': 0, 'A5': -4, 'A6': -6, 'A7': 0, 'A8': -4, 'A9': 3, 'Lhash': '75319482476166628', 'a10': [-0.08247422680412371, 0.0], 'a2': [0.020618556701030927, 0.0], 'a3': [-0.030927835051546393, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.041237113402061855, 0.0], 'a6': [-0.061855670103092786, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.041237113402061855, 0.0], 'a9': [0.030927835051546393, 0.0], 'algebraic': True, 'analytic_conductor': 52.32299637576201, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[29, [1, 5, 23, -29]], [28297, [1, 126, 28422, 28297]]], 'bad_primes': [29, 28297], 'central_character': '820613.1', 'coefficient_field': '1.1.1.1', 'conductor': 820613, 'conductor_radical': 820613, 'degree': 4, 'euler_factors': [[1, -2, 4, -4, 4], [1, 3, 6, 9, 9], [1, 4, 12, 20, 25], [1, 0, 8, 0, 49], [1, -4, 18, -44, 121], [1, -2, 2, -26, 169], [1, 3, 2, 51, 289], [1, 3, 6, 57, 361], [1, 0, -4, 0, 529], [1, 5, 23, -29], [1, -2, -12, -62, 961], [1, 1, -17, 37, 1369], [1, -9, 71, -369, 1681], [1, 7, 59, 301, 1849], [1, 0, -46, 0, 2209], [1, -12, 82, -636, 2809], [1, 3, 1, 177, 3481], [1, 5, 12, 305, 3721], [1, -3, 53, -201, 4489], [1, -5, 108, -355, 5041], [1, 0, -40, 0, 5329], [1, 3, 67, 237, 6241], [1, 5, 35, 415, 6889], [1, -10, 110, -890, 7921], [1, -7, 180, -679, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-820613-1.1-c1e2-0-0', 'leading_term': '2.15429742624', '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/820613/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.3808411855842022, 0.6074599928556248, 0.4658107024256059, -0.2979482216545465, -1.833209483587555, -3.95172590506453, -5.94884784037106, -6.688758349342186, 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-0.08295719907781636, -4.373554818503656, -1.924400280889598], 'positive_zeros': [0.6957436449523047, 1.904054302335477, 3.077265805022412, 3.667480259851149, 3.966013150236147, 4.294052756975969, 4.714292539848642, 5.162961861830115, 5.690866544796183, 6.163973933976486, 6.307946215790205, 6.963056600147425, 7.336193583452017, 8.015338274907911, 8.335264669321656, 8.895607329158391, 9.182806934626, 9.698634580205864, 10.39837559321493, 10.80633898867524, 11.24138354232382, 11.46927933492958, 11.74605119645805, 11.96211721231091, 12.44833992144153, 12.7759814097564, 13.04505710601695, 13.63179331336595, 13.81141552934589, 14.4310438396925, 14.70779857420337, 15.06058432265501, 15.38949583201719, 15.72444670283741, 16.21600645602345, 16.4376707014072, 16.90301532529292, 17.16095200015427, 17.54625075971783, 17.93299968739773, 18.1603578797534, 18.71618587307763, 18.98095263298019, 19.37922777270211, 19.78546825994894], 'prelabel': '4-820613-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.6895099274760903, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 75319482476166628, 'z1': {'__RealLiteral__': 0, 'data': '0.695743644952', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.90405430234', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.07726580502', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 52.32299637576201, 'bad_primes': [29, 28297], 'central_character': '1.1', 'conductor': 820613, 'conductor_radical': 820613, 'degree': 4, 'dirichlet_coefficients': [1, 2, -3, 0, -4, -6, 0, -4, 3, -8, 4, 0, 2, 0, 12, -4, -3, 6, -3, 0, 0, 8, 0, 12, 4, 4, 0, 0, -5, 24, 2, 0, -12, -6, 0, 0, -1, -6, -6, 16, 9, 0, -7, 0, -12, 0, 0, 12, -8, 8, 9, 0, 12, 0, -16, 0, 9, -10, -3, 0, -5, 4, 0, 0, -8, -24, 3, 0, 0, 0, 5, -12, 0, -2, -12, 0, 0, -12, -3, 16, 0, 18, -5, 0, 12, -14, 15, -16, 10, -24, 0, 0, -6, 0, 12, 0, 7, -16, 12, 0], 'euler11': [1, -4, 18, -44, 121], 'euler13': [1, -2, 2, -26, 169], 'euler17': [1, 3, 2, 51, 289], 'euler19': [1, 3, 6, 57, 361], 'euler2': [1, -2, 4, -4, 4], 'euler23': [1, 0, -4, 0, 529], 'euler29': [1, 5, 23, -29, 0], 'euler3': [1, 3, 6, 9, 9], 'euler31': [1, -2, -12, -62, 961], 'euler37': [1, 1, -17, 37, 1369], 'euler41': [1, -9, 71, -369, 1681], 'euler43': [1, 7, 59, 301, 1849], 'euler47': [1, 0, -46, 0, 2209], 'euler5': [1, 4, 12, 20, 25], 'euler53': [1, -12, 82, -636, 2809], 'euler59': [1, 3, 1, 177, 3481], 'euler61': [1, 5, 12, 305, 3721], 'euler67': [1, -3, 53, -201, 4489], 'euler7': [1, 0, 8, 0, 49], 'euler71': [1, -5, 108, -355, 5041], 'euler73': [1, 0, -40, 0, 5329], 'euler79': [1, 3, 67, 237, 6241], 'euler83': [1, 5, 35, 415, 6889], 'euler89': [1, -10, 110, -890, 7921], 'euler97': [1, -7, 180, -679, 9409], 'euler_factors': [[1, -2, 4, -4, 4], [1, 3, 6, 9, 9], [1, 4, 12, 20, 25], [1, 0, 8, 0, 49], [1, -4, 18, -44, 121], [1, -2, 2, -26, 169], [1, 3, 2, 51, 289], [1, 3, 6, 57, 361], [1, 0, -4, 0, 529], [1, 5, 23, -29, 0], [1, -2, -12, -62, 961], [1, 1, -17, 37, 1369], [1, -9, 71, -369, 1681], [1, 7, 59, 301, 1849], [1, 0, -46, 0, 2209], [1, -12, 82, -636, 2809], [1, 3, 1, 177, 3481], [1, 5, 12, 305, 3721], [1, -3, 53, -201, 4489], [1, -5, 108, -355, 5041], [1, 0, -40, 0, 5329], [1, 3, 67, 237, 6241], [1, 5, 35, 415, 6889], [1, -10, 110, -890, 7921], [1, -7, 180, -679, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/820613/a'], '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': '4-820613-1.1-c1e2-0-0', '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': '4-820613-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.6895099274760903, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 75319482476166628, 'z1': {'__RealLiteral__': 0, 'data': '0.695743644952', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': '75319482476166628', 'Lhash_array': ['75319482476166628'], 'label': '4-820613-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/820613/a'}