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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -6, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 21, 'Lhash': '700956291542315619,1934663668760385422', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-3.4641016151377544, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [7.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.14019429926089, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [19, [1, -2, 1]]], 'bad_primes': [2, 19], 'central_character': '739328.1', 'coefficient_field': '1.1.1.1', 'conductor': 739328, 'conductor_radical': 38, 'degree': 4, 'euler_factors': [[1], [1, 6, 15, 18, 9], [1, 0, 10, 0, 25], [1, 0, 13, 0, 49], [1, 4, 26, 44, 121], [1, 0, 25, 0, 169], [1, -6, 43, -102, 289], [1, -2, 1], [1, 0, 37, 0, 529], [1, 0, 49, 0, 841], [1, 0, -2, 0, 961], [1, 0, -26, 0, 1369], [1, 24, 226, 984, 1681], [1, 16, 150, 688, 1849], [1, 0, 30, 0, 2209], [1, 0, 25, 0, 2809], [1, -10, 143, -590, 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-1.2207868450469221, -0.892861026259472, -0.5769323785432177, -0.305252268095913, -0.1030743420154815], 'positive_zeros': ['1.37942708011457790071691730372484', '1.71114737147421549133826699878577', '3.11827862407422559284554596551673', '3.69177683782741766976501946645311', '4.39011552338323920878309071486365', '5.05677384969689549249862504577401', '5.22289133265133441977616849928471', '5.40675236139494372245760564829746', '5.91824238738469752095279165719534', '6.48093639487009967007655018619734', '6.61303503651954034437075836395682', '7.34354802745880252390609982428063', '7.47536575646542499937872009351946'], 'prelabel': '4-739328-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6202808450938764, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 329776951089007090, 'z1': {'__RealLiteral__': 0, 'data': '1.37942708011457790071691730372484', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.71114737147421549133826699878577', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.11827862407422559284554596551673', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.14019429926089, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 739328, 'conductor_radical': 38, 'degree': 4, 'dirichlet_coefficients': [1, 0, -6, 0, 0, 0, 0, 0, 21, 0, -4, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, -10, 0, -54, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -24, 0, -16, 0, 0, 0, 0, 0, -13, 0, -36, 0, 0, 0, 0, 0, -12, 0, 10, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 2, 0, 60, 0, 0, 0, 0, 0, 108, 0, -12, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -12, 0, -84, 0], 'euler11': [1, 4, 26, 44, 121], 'euler13': [1, 0, 25, 0, 169], 'euler17': [1, -6, 43, -102, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 37, 0, 529], 'euler29': [1, 0, 49, 0, 841], 'euler3': [1, 6, 15, 18, 9], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 24, 226, 984, 1681], 'euler43': [1, 16, 150, 688, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 25, 0, 2809], 'euler59': [1, -10, 143, -590, 3481], 'euler61': [1, 0, 22, 0, 3721], 'euler67': [1, 14, 183, 938, 4489], 'euler7': [1, 0, 13, 0, 49], 'euler71': [1, 0, 42, 0, 5041], 'euler73': [1, -2, 147, -146, 5329], 'euler79': [1, 0, -38, 0, 6241], 'euler83': [1, 12, 202, 996, 6889], 'euler89': [1, 8, 194, 712, 7921], 'euler97': [1, 12, 230, 1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 6, 15, 18, 9], [1, 0, 10, 0, 25], [1, 0, 13, 0, 49], [1, 4, 26, 44, 121], [1, 0, 25, 0, 169], [1, -6, 43, -102, 289], [1, -2, 1, 0, 0], [1, 0, 37, 0, 529], [1, 0, 49, 0, 841], [1, 0, -2, 0, 961], [1, 0, -26, 0, 1369], [1, 24, 226, 984, 1681], [1, 16, 150, 688, 1849], [1, 0, 30, 0, 2209], [1, 0, 25, 0, 2809], [1, -10, 143, -590, 3481], [1, 0, 22, 0, 3721], [1, 14, 183, 938, 4489], [1, 0, 42, 0, 5041], [1, -2, 147, -146, 5329], [1, 0, -38, 0, 6241], [1, 12, 202, 996, 6889], [1, 8, 194, 712, 7921], [1, 12, 230, 1164, 9409]], 'index': 9, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/11552.2/a', 'EllipticCurve/2.0.8.1/11552.2/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-739328-1.1-c1e2-0-9', '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': 2, 'prelabel': '4-739328-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.6202808450938764, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 329776951089007090, 'z1': {'__RealLiteral__': 0, 'data': '1.37942708011457790071691730372484', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9817294
{'Lhash': '700956291542315619,1934663668760385422', 'Lhash_array': ['700956291542315619', '1934663668760385422'], 'label': '4-739328-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/11552.2/a'}
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id: 9816872
{'Lhash': '700956291542315619,1934663668760385422', 'Lhash_array': ['700956291542315619', '1934663668760385422'], 'label': '4-739328-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/11552.2/a'}