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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': 1, 'A8': 0, 'A9': 2, 'Lhash': '1027876684260852116453735454928', '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': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.57942739416335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]]], 'bad_primes': [2, 7], 'central_character': '1404928.1', 'coefficient_field': '1.1.1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, -2, 0, 9], [1, 0, -6, 0, 25], [1, -1], [1, 4, 22, 44, 121], [1, 0, 2, 0, 169], [1, 0, 6, 0, 289], [1, 0, -18, 0, 361], [1, -4, 46, -92, 529], [1, -16, 118, -464, 841], [1, 0, -50, 0, 961], [1, -8, 54, -296, 1369], [1, 0, 6, 0, 1681], [1, -12, 118, -516, 1849], [1, 0, 30, 0, 2209], [1, -4, 46, -212, 2809], [1, 0, 78, 0, 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3.0966704350838294, 1.8169192300021197, 0.683654795886807], 'positive_zeros': ['0.810851731601587938385971351198947', '1.25985139020924222725570342394993', '2.38682896528902303409865720604725', '2.69646086029005397649121999910602', '3.10928311745819888460525767719489', '3.98804946472276595480203988763978', '4.52888646732450766791406891014211', '4.70557549370005929953803756175194', '5.24699196417129412925415384478303', '5.69483165949111729900547756683607', '6.27369448907204373654297099637169', '6.72004791321776142968750236016293', '7.06041050174913625098611822083221', '7.58252574174644448721066256413373', '7.88141621718185587197034632049577'], 'prelabel': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 250444637455671242, 'z1': {'__RealLiteral__': 0, 'data': '0.810851731601587938385971351198947', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.25985139020924222725570342394993', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.38682896528902303409865720604725', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.57942739416335, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 1, 0, 2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0], 'euler11': [1, 4, 22, 44, 121], 'euler13': [1, 0, 2, 0, 169], 'euler17': [1, 0, 6, 0, 289], 'euler19': [1, 0, -18, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -4, 46, -92, 529], 'euler29': [1, -16, 118, -464, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, -50, 0, 961], 'euler37': [1, -8, 54, -296, 1369], 'euler41': [1, 0, 6, 0, 1681], 'euler43': [1, -12, 118, -516, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, -4, 46, -212, 2809], 'euler59': [1, 0, 78, 0, 3481], 'euler61': [1, 0, -38, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, -1, 0, 0, 0], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, 0, -114, 0, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, -18, 0, 6889], 'euler89': [1, 0, 110, 0, 7921], 'euler97': [1, 0, -170, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -2, 0, 9], [1, 0, -6, 0, 25], [1, -1, 0, 0, 0], [1, 4, 22, 44, 121], [1, 0, 2, 0, 169], [1, 0, 6, 0, 289], [1, 0, -18, 0, 361], [1, -4, 46, -92, 529], [1, -16, 118, -464, 841], [1, 0, -50, 0, 961], [1, -8, 54, -296, 1369], [1, 0, 6, 0, 1681], [1, -12, 118, -516, 1849], [1, 0, 30, 0, 2209], [1, -4, 46, -212, 2809], [1, 0, 78, 0, 3481], [1, 0, -38, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, 78, 0, 5041], [1, 0, -114, 0, 5329], [1, 0, 94, 0, 6241], [1, 0, -18, 0, 6889], [1, 0, 110, 0, 7921], [1, 0, -170, 0, 9409]], 'index': 12, 'instance_types': ['ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.0.7.1/28672.7/u', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.7/s', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.7/u', 'EllipticCurve/2.0.7.1/28672.7/s'], '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': '4-112e3-1.1-c1e2-0-12', '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': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 250444637455671242, 'z1': {'__RealLiteral__': 0, 'data': '0.810851731601587938385971351198947', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9620528
{'Lhash': '1027876684260852116453735454928', 'Lhash_array': ['1027876684260852116453735454928'], 'label': '4-112e3-1.1-c1e2-0-12', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.7/s'}
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id: 9620413
{'Lhash': '1027876684260852116453735454928', 'Lhash_array': ['1027876684260852116453735454928'], 'label': '4-112e3-1.1-c1e2-0-12', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.7/u'}
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id: 9620117
{'Lhash': '1027876684260852116453735454928', 'Lhash_array': ['1027876684260852116453735454928'], 'label': '4-112e3-1.1-c1e2-0-12', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.7/s'}
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id: 9619659
{'Lhash': '1027876684260852116453735454928', 'Lhash_array': ['1027876684260852116453735454928'], 'label': '4-112e3-1.1-c1e2-0-12', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.7/u'}