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lfunc_lfunctions • Show schema
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{'Lhash': '836711681373416934364707414419,1728175322835472347431092004506', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 477.2944672800165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, 2, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, -4, 14, -20, 25], [1, 0, -6, 0, 49], [1, 0, -20, 0, 121], [1, 0, -18, 0, 169], [1, -4, 38, -68, 289], [1, 2, 19], [1, 0, -44, 0, 529], [1, 0, -8, 0, 841], [1, -12, 98, -372, 961], [1, 0, 54, 0, 1369], [1, 0, -64, 0, 1681], [1, 0, -86, 0, 1849], [1, 0, -44, 0, 2209], [1, 0, -8, 0, 2809], [1, -16, 182, -944, 3481], [1, 16, 186, 976, 3721], [1, 4, 138, 268, 4489], [1, -16, 206, -1136, 5041], [1, 0, 146, 0, 5329], [1, 16, 222, 1264, 6241], [1, 0, -4, 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'5.62177203256154037941756271806186', '5.62804488175347957839789838601944', '6.51730782226577339672886193518652', '6.54422947909739461180924384448945', '6.93046491031248673035674699290414', '7.57928460845954272202522472185351', '7.979024601144416548478720392696396', '8.247950402571882068434279879201635', '8.628418519873205653505689124770595', '9.113230658535619010469194486065739'], 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1242657380285942124, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66004913437722848509469054681', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.36328994955260503026483027157', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.83543257837750060927044170708', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 477.2944672800165, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, -4, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0], 'euler11': [1, 0, -20, 0, 121], 'euler13': [1, 0, -18, 0, 169], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, 2, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -44, 0, 529], 'euler29': [1, 0, -8, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -12, 98, -372, 961], 'euler37': [1, 0, 54, 0, 1369], 'euler41': [1, 0, -64, 0, 1681], 'euler43': [1, 0, -86, 0, 1849], 'euler47': [1, 0, -44, 0, 2209], 'euler5': [1, -4, 14, -20, 25], 'euler53': [1, 0, -8, 0, 2809], 'euler59': [1, -16, 182, -944, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, 4, 138, 268, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 0, 146, 0, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 0, -4, 0, 6889], 'euler89': [1, 0, -80, 0, 7921], 'euler97': [1, 0, -186, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -4, 14, -20, 25], [1, 0, -6, 0, 49], [1, 0, -20, 0, 121], [1, 0, -18, 0, 169], [1, -4, 38, -68, 289], [1, 2, 19, 0, 0], [1, 0, -44, 0, 529], [1, 0, -8, 0, 841], [1, -12, 98, -372, 961], [1, 0, 54, 0, 1369], [1, 0, -64, 0, 1681], [1, 0, -86, 0, 1849], [1, 0, -44, 0, 2209], [1, 0, -8, 0, 2809], [1, -16, 182, -944, 3481], [1, 16, 186, 976, 3721], [1, 4, 138, 268, 4489], [1, -16, 206, -1136, 5041], [1, 0, 146, 0, 5329], [1, 16, 222, 1264, 6241], [1, 0, -4, 0, 6889], [1, 0, -80, 0, 7921], [1, 0, -186, 0, 9409]], 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/k/h'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-2736e2-1.1-c1e2-0-31', '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': 0, 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1242657380285942124, 'z1': {'__RealLiteral__': 0, 'data': '0.66004913437722848509469054681', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '836711681373416934364707414419,1728175322835472347431092004506', 'Lhash_array': ['836711681373416934364707414419', '1728175322835472347431092004506'], 'label': '4-2736e2-1.1-c1e2-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/k/h'}