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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': 0, 'Lhash': '924950971322832410518158434768', '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': [0.0, 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, 0, 0, 9], [1, 0, 6, 0, 25], [1, 1], [1, -6, 30, -66, 121], [1, 0, 18, 0, 169], [1, 0, 2, 0, 289], [1, 0, -24, 0, 361], [1, 2, 38, 46, 529], [1, -4, 62, -116, 841], [1, 0, -10, 0, 961], [1, -8, 86, -296, 1369], [1, 0, -62, 0, 1681], [1, -14, 134, -602, 1849], [1, 0, -14, 0, 2209], [1, -6, 114, -318, 2809], [1, 0, 96, 0, 3481], [1, 0, -66, 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-1.519326454831777], 'positive_zeros': ['0.72965766052278370661407714692526', '1.36299850813920827589267426179132', '2.26861390332467851560893936650373', '2.60179529300555599455104946685830', '3.54867190725794325861079800663565', '3.84837293664482043821669858618259', '4.19721540899933601187892140421236', '4.72351915570667030998933327869541', '5.40533381932107717723736343106789', '5.90477584666526868227975885216542', '6.19922578082538972545274879674404', '6.63945337322056470396257157759144', '6.96896607652998296250929779978667', '7.53501780426551273067960397429087', '7.973154762079545303604438435229839'], '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': 934984924977893018, 'z1': {'__RealLiteral__': 0, 'data': '0.72965766052278370661407714692526', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.36299850813920827589267426179132', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.26861390332467851560893936650373', '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, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 16, 0, 0, 0, 0, 0, -6, 0, 12, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, -6, 30, -66, 121], 'euler13': [1, 0, 18, 0, 169], 'euler17': [1, 0, 2, 0, 289], 'euler19': [1, 0, -24, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 2, 38, 46, 529], 'euler29': [1, -4, 62, -116, 841], 'euler3': [1, 0, 0, 0, 9], 'euler31': [1, 0, -10, 0, 961], 'euler37': [1, -8, 86, -296, 1369], 'euler41': [1, 0, -62, 0, 1681], 'euler43': [1, -14, 134, -602, 1849], 'euler47': [1, 0, -14, 0, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, -6, 114, -318, 2809], 'euler59': [1, 0, 96, 0, 3481], 'euler61': [1, 0, -66, 0, 3721], 'euler67': [1, -8, 86, -536, 4489], 'euler7': [1, 1, 0, 0, 0], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 0, 38, 0, 5329], 'euler79': [1, -12, 158, -948, 6241], 'euler83': [1, 0, -72, 0, 6889], 'euler89': [1, 0, 70, 0, 7921], 'euler97': [1, 0, 58, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 9], [1, 0, 6, 0, 25], [1, 1, 0, 0, 0], [1, -6, 30, -66, 121], [1, 0, 18, 0, 169], [1, 0, 2, 0, 289], [1, 0, -24, 0, 361], [1, 2, 38, 46, 529], [1, -4, 62, -116, 841], [1, 0, -10, 0, 961], [1, -8, 86, -296, 1369], [1, 0, -62, 0, 1681], [1, -14, 134, -602, 1849], [1, 0, -14, 0, 2209], [1, -6, 114, -318, 2809], [1, 0, 96, 0, 3481], [1, 0, -66, 0, 3721], [1, -8, 86, -536, 4489], [1, -16, 206, -1136, 5041], [1, 0, 38, 0, 5329], [1, -12, 158, -948, 6241], [1, 0, -72, 0, 6889], [1, 0, 70, 0, 7921], [1, 0, 58, 0, 9409]], 'index': 7, 'instance_types': ['BMF', 'ECNF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.5/d', 'EllipticCurve/2.0.7.1/28672.5/d', 'EllipticCurve/2.0.7.1/28672.9/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.9/d'], '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-c1e2-0-7', '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': 934984924977893018, 'z1': {'__RealLiteral__': 0, 'data': '0.72965766052278370661407714692526', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9621006
{'Lhash': '924950971322832410518158434768', 'Lhash_array': ['924950971322832410518158434768'], 'label': '4-112e3-1.1-c1e2-0-7', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.9/d'}
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id: 9620870
{'Lhash': '924950971322832410518158434768', 'Lhash_array': ['924950971322832410518158434768'], 'label': '4-112e3-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.9/d'}
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id: 9620276
{'Lhash': '924950971322832410518158434768', 'Lhash_array': ['924950971322832410518158434768'], 'label': '4-112e3-1.1-c1e2-0-7', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.5/d'}
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id: 9619848
{'Lhash': '924950971322832410518158434768', 'Lhash_array': ['924950971322832410518158434768'], 'label': '4-112e3-1.1-c1e2-0-7', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.5/d'}