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lfunc_lfunctions • Show schema
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{'Lhash': '2010563107503551267022980255990', 'a10': [0, 0], 'a2': [1.4142135623730951, 0], 'a3': [0, 1.7320508075688772], 'a4': [2.0, 0], 'a5': [0, 0], 'a6': [0, 2.449489742783178], 'a7': [4.63050413065874, -5.249612509124112], 'a8': [2.8284271247461903, 0], 'a9': [-3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.4142135623730951, 0]]], [3, [[1.0, 0], [0, -1.7320508075688772]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-4.63050413065874, 5.249612509124112]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.601', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '1003575728425625990147850747155', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4142135623730951, 0]], [[1.0, 0], [0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.63050413065874, 5.249612509124112]], [[1.0, 0], 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-1.1198659527845714, -1.6187135643253472, -2.1320860389876115], 'positive_zeros': ['1.58605463298922192550122003363513', '2.17278193079190356343473892131012', '3.74428871846536144642825723302402', '4.46483638047201134340311729367152', '5.70075146973881700860938747153928', '6.26709198026135341550150160707040', '7.19492067138098299148218896159782', '8.000702566195762859314000070038459', '9.044796212920003988792352714596782', '9.593946009965993533512256452543177'], 'prelabel': '2-1050-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.23008009430494344, 'root_number': '0.74994464416058735815819039767211249885162538438508158397 + 0.66150059009410566487602576235431062707586129572661434153*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.11504004715247172', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.58605463298922192550122003364', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17278193079190356343473892131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74428871846536144642825723302', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '7.6', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/f/e/601/16'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '2-1050-7.6-c2-0-45', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1050-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.11504004715247172, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58605463298922192550122003364', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2010563107503551267022980255990', 'Lhash_array': ['2010563107503551267022980255990'], 'label': '2-1050-7.6-c2-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/f/e/601/16'}