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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '12569714191723724,741548168776098433', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.949654024266134, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '93312.1', 'coefficient_field': '1.1.1.1', 'conductor': 93312, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -6, 0, 25], [1, 0, 5, 0, 49], [1, -8, 38, -88, 121], [1, -2, 27, -26, 169], [1, 0, 18, 0, 289], [1, 0, 37, 0, 361], [1, -8, 62, -184, 529], [1, 0, 58, 0, 841], [1, 0, 46, 0, 961], [1, 18, 155, 666, 1369], [1, 0, 82, 0, 1681], [1, 0, 22, 0, 1849], [1, 24, 238, 1128, 2209], [1, 0, 42, 0, 2809], [1, -8, 134, -472, 3481], [1, 10, 147, 610, 3721], [1, 0, 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0.06919016523152359, -0.035268833414823085], 'positive_zeros': ['1.18156952361835473635888524724358', '1.81832624891237728767312244270248', '3.33304684468240638767778076252684', '3.36478379045069074059258347613155', '4.20575968417257290967879965799133', '5.10755730919050596352378085939177', '5.14859535448368711259372949904357', '6.44248673632066345518308551587175', '6.65045650092432229207532369717565', '6.71788542885177681871412514581762', '7.61689482228550235915151273027733', '8.285403607109998915279053043958487', '8.806587663978251937370981617555337', '9.093326194542073314647733546631281', '9.397687695952564808383582699780760'], 'prelabel': '4-93312-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5617910437660596, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 754117882967822157, 'z1': {'__RealLiteral__': 0, 'data': '1.18156952361835473635888524724358', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.81832624891237728767312244270248', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.33304684468240638767778076252684', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.949654024266134, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 93312, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0], 'euler11': [1, -8, 38, -88, 121], 'euler13': [1, -2, 27, -26, 169], 'euler17': [1, 0, 18, 0, 289], 'euler19': [1, 0, 37, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -8, 62, -184, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 18, 155, 666, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 24, 238, 1128, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, 0, 42, 0, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, 10, 147, 610, 3721], 'euler67': [1, 0, 13, 0, 4489], 'euler7': [1, 0, 5, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, -2, 147, -146, 5329], 'euler79': [1, 0, 133, 0, 6241], 'euler83': [1, -16, 230, -1328, 6889], 'euler89': [1, 0, 34, 0, 7921], 'euler97': [1, -10, 219, -970, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -6, 0, 25], [1, 0, 5, 0, 49], [1, -8, 38, -88, 121], [1, -2, 27, -26, 169], [1, 0, 18, 0, 289], [1, 0, 37, 0, 361], [1, -8, 62, -184, 529], [1, 0, 58, 0, 841], [1, 0, 46, 0, 961], [1, 18, 155, 666, 1369], [1, 0, 82, 0, 1681], [1, 0, 22, 0, 1849], [1, 24, 238, 1128, 2209], [1, 0, 42, 0, 2809], [1, -8, 134, -472, 3481], [1, 10, 147, 610, 3721], [1, 0, 13, 0, 4489], [1, -16, 206, -1136, 5041], [1, -2, 147, -146, 5329], [1, 0, 133, 0, 6241], [1, -16, 230, -1328, 6889], [1, 0, 34, 0, 7921], [1, -10, 219, -970, 9409]], 'index': 8, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.12.1/648.1/b', 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-648.1-b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-93312-1.1-c1e2-0-8', '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': '4-93312-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5617910437660596, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 754117882967822157, 'z1': {'__RealLiteral__': 0, 'data': '1.18156952361835473635888524724358', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9590788
{'Lhash': '12569714191723724,741548168776098433', 'Lhash_array': ['12569714191723724', '741548168776098433'], 'label': '4-93312-1.1-c1e2-0-8', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.12.1/holomorphic/2.2.12.1-648.1-b'}
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id: 9590597
{'Lhash': '12569714191723724,741548168776098433', 'Lhash_array': ['12569714191723724', '741548168776098433'], 'label': '4-93312-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.12.1/648.1/b'}