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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': -1, 'Lhash': '992712763589978762965444429752', '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': [-0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.22777793843102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 1]], [17, [1, -2, 17]]], 'bad_primes': [2, 3, 17], 'central_character': '332928.1', 'coefficient_field': '1.1.1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1], [1, 0, 1], [1, 0, 6, 0, 25], [1, 0, -14, 0, 49], [1, 0, -6, 0, 121], [1, -4, 30, -52, 169], [1, -2, 17], [1, 0, 22, 0, 361], [1, 0, 18, 0, 529], [1, 0, 22, 0, 841], [1, 0, 2, 0, 961], [1, 0, 38, 0, 1369], [1, 0, 46, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, 94, 0, 2209], [1, 4, 110, 212, 2809], [1, 0, 102, 0, 3481], [1, 0, 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-0.1438645988222515, 0.43218327192531464, 1.0301523734130202, 1.5248740921474533], 'positive_zeros': ['0.78311228931004293601998866478684', '1.78167636969385998999361485962242', '2.45298205592555453445596963291561', '3.35388544215845361889643739923207', '3.63621771138967153396017329012765', '4.31959069849862984470207123436560', '4.87012711168870203371246944770269', '5.58922932010663702710475856403647', '5.92217351910696194047120005858331', '6.25743406259964716738067414408446', '6.94696833199936467814028970566167', '7.43349342323067272414894669087472', '7.85901936363461648715728367446125', '8.318706022162821746166836808676350', '8.771972578960312246988322339598093'], 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1309909154213698433, 'z1': {'__RealLiteral__': 0, 'data': '0.78311228931004293601998866478684', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.78167636969385998999361485962242', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.45298205592555453445596963291561', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.22777793843102, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -6, 0, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, -2, 17, 0, 0], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 18, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 0, 2, 0, 961], 'euler37': [1, 0, 38, 0, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, -14, 0, 49], 'euler71': [1, 0, -78, 0, 5041], 'euler73': [1, 0, 46, 0, 5329], 'euler79': [1, 0, -94, 0, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 0, 190, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, 6, 0, 25], [1, 0, -14, 0, 49], [1, 0, -6, 0, 121], [1, -4, 30, -52, 169], [1, -2, 17, 0, 0], [1, 0, 22, 0, 361], [1, 0, 18, 0, 529], [1, 0, 22, 0, 841], [1, 0, 2, 0, 961], [1, 0, 38, 0, 1369], [1, 0, 46, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, 94, 0, 2209], [1, 4, 110, 212, 2809], [1, 0, 102, 0, 3481], [1, 0, 118, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, -78, 0, 5041], [1, 0, 46, 0, 5329], [1, 0, -94, 0, 6241], [1, 0, 150, 0, 6889], [1, -12, 214, -1068, 7921], [1, 0, 190, 0, 9409]], 'index': 6, 'instance_types': ['BMF', 'BMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/20808.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/20808.3/a', 'EllipticCurve/2.0.4.1/20808.3/a', 'EllipticCurve/2.0.4.1/20808.1/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': '4-332928-1.1-c1e2-0-6', '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': '4-332928-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1309909154213698433, 'z1': {'__RealLiteral__': 0, 'data': '0.78311228931004293601998866478684', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9657182
{'Lhash': '992712763589978762965444429752', 'Lhash_array': ['992712763589978762965444429752'], 'label': '4-332928-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/20808.1/a'}
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id: 9656984
{'Lhash': '992712763589978762965444429752', 'Lhash_array': ['992712763589978762965444429752'], 'label': '4-332928-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/20808.3/a'}
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id: 9656892
{'Lhash': '992712763589978762965444429752', 'Lhash_array': ['992712763589978762965444429752'], 'label': '4-332928-1.1-c1e2-0-6', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/20808.3/a'}
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id: 9656667
{'Lhash': '992712763589978762965444429752', 'Lhash_array': ['992712763589978762965444429752'], 'label': '4-332928-1.1-c1e2-0-6', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/20808.1/a'}