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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 0, 'Lhash': '931711696899953919', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.010309278350515464, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.020618556701030927, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'algebraic': True, 'analytic_conductor': 3.765015437230913, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '59049.1', 'coefficient_field': '1.1.1.1', 'conductor': 59049, 'conductor_radical': 3, 'degree': 4, 'euler_factors': [[1, 0, 1, 0, 4], [1], [1, 0, 7, 0, 25], [1, 2, -3, 14, 49], [1, 0, 10, 0, 121], [1, -1, -12, -13, 169], [1, 0, 7, 0, 289], [1, 2, -15, 38, 361], [1, 0, 34, 0, 529], [1, 0, 55, 0, 841], [1, 8, 33, 248, 961], [1, -7, 12, -259, 1369], [1, 0, 34, 0, 1681], [1, 2, -39, 86, 1849], [1, 0, 46, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, -74, 0, 3481], [1, 14, 171, 854, 3721], [1, 20, 234, 1340, 4489], [1, 0, 34, 0, 5041], [1, 14, 195, 1022, 5329], [1, 2, -75, 158, 6241], [1, 0, -26, 0, 6889], [1, 0, 151, 0, 7921], [1, 2, -93, 194, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 5, 'label': '4-3e10-1.1-c1e2-0-5', 'leading_term': '1.91390394014', '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/59049/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.3656618368534354, 0.7673031798363776, 1.21708188717129, 1.682391261539519, 2.074013109524669, 2.253489899954397, 2.069597638124365, 1.424895880944691, 0.3550136183704321, -0.917775062542793, -2.004558042798754, -2.472732998756532, -2.049385294885229, -0.815655908195775, 0.736287808176957, 1.876025579202374, 2.006427456042941, 1.046775808226622, 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6.488675851333633, 7.203840997347658, 7.614433716584894, 8.211580338331286, 8.993705612559378, 9.096515183502946, 9.604149027405192, 10.22166020238685, 10.61329945794473, 11.14038050659062, 11.77241458979417, 11.97582763138094, 12.74186992431322, 13.09115951736398, 13.38673001027105, 13.79525887527246, 14.32221571819515, 14.78345386418989, 15.28210320090934, 15.61956214547442, 16.14712997776427, 16.48838827100892, 16.86168467447784, 17.37307018059307, 17.85455814026515, 18.25505742244872, 18.44680264336983, 18.98806852757729, 19.51409456164386, 19.66945402840087], 'prelabel': '4-3e10-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.392969766045593, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'J(E_3)', 'trace_hash': 931711696899953919, 'z1': {'__RealLiteral__': 0, 'data': '1.74070911643', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.72297727784', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.50737832038', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.765015437230913, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 59049, 'conductor_radical': 3, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0, 0, -7, 0, 0, 2, 0, 0, -8, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 7, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 7, 0, 0, -20, 0, 0, 0, 0, 0, -14, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 7], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, -1, -12, -13, 169], 'euler17': [1, 0, 7, 0, 289], 'euler19': [1, 2, -15, 38, 361], 'euler2': [1, 0, 1, 0, 4], 'euler23': [1, 0, 34, 0, 529], 'euler29': [1, 0, 55, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 33, 248, 961], 'euler37': [1, -7, 12, -259, 1369], 'euler41': [1, 0, 34, 0, 1681], 'euler43': [1, 2, -39, 86, 1849], 'euler47': [1, 0, 46, 0, 2209], 'euler5': [1, 0, 7, 0, 25], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, 0, -74, 0, 3481], 'euler61': [1, 14, 171, 854, 3721], 'euler67': [1, 20, 234, 1340, 4489], 'euler7': [1, 2, -3, 14, 49], 'euler71': [1, 0, 34, 0, 5041], 'euler73': [1, 14, 195, 1022, 5329], 'euler79': [1, 2, -75, 158, 6241], 'euler83': [1, 0, -26, 0, 6889], 'euler89': [1, 0, 151, 0, 7921], 'euler97': [1, 2, -93, 194, 9409], 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, 0, 0, 0], [1, 0, 7, 0, 25], [1, 2, -3, 14, 49], [1, 0, 10, 0, 121], [1, -1, -12, -13, 169], [1, 0, 7, 0, 289], [1, 2, -15, 38, 361], [1, 0, 34, 0, 529], [1, 0, 55, 0, 841], [1, 8, 33, 248, 961], [1, -7, 12, -259, 1369], [1, 0, 34, 0, 1681], [1, 2, -39, 86, 1849], [1, 0, 46, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, -74, 0, 3481], [1, 14, 171, 854, 3721], [1, 20, 234, 1340, 4489], [1, 0, 34, 0, 5041], [1, 14, 195, 1022, 5329], [1, 2, -75, 158, 6241], [1, 0, -26, 0, 6889], [1, 0, 151, 0, 7921], [1, 2, -93, 194, 9409]], 'index': 5, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/59049/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': '4-3e10-1.1-c1e2-0-5', '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': '4-3e10-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.392969766045593, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 931711696899953919, 'z1': {'__RealLiteral__': 0, 'data': '1.74070911643', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '931711696899953919', 'Lhash_array': ['931711696899953919'], 'factors': ['4-3e10-1.1-c1e2-0-5'], 'label': '4-3e10-1.1-c1e2-0-5', 'type': 'G2Q', 'url': 'Genus2Curve/Q/59049/a'}