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lfunc_lfunctions • Show schema
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{'Lhash': '1792585374827549516068026195831', 'a10': [-920543.0190917182, 531475.7598732343], 'a2': [-45.254833995939045, 78.38367176906169], 'a3': [2710.5161702900973, -1564.9172405598213], 'a4': [-4096.0, -7094.480107802121], 'a5': [10170.659549588929, 5872.033028791206], 'a6': [4.2703392396106835e-58, 283280.27975567087], 'a7': [552858.043234553, 610385.990075019], 'a8': [741455.2001894653, 0.0], 'a9': [2506447.4396027313, -4341294.311892856], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.406055541266845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [45.254833995939045, -78.38367176906169]]], [7, [[1.0, 0], [-552858.043234553, -610385.990075019]]]], 'bad_primes': [2, 7], 'central_character': '14.5', 'coefficient_field': 'CDF', 'conductor': 14, 'conductor_radical': 14, 'conjugate': '1624466086021895435991332381074', 'degree': 2, 'euler_factors': [[[1.0, 0], [45.254833995939045, -78.38367176906169]], [[1.0, 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'root_analytic_conductor': 4.1720565122331275, 'root_angle': -0.02725830522413955, 'root_number': '0.9963356070897998 - 0.08552986639180535*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0136291526121', 'prec': 54}, 'spectral_label': 'c14-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.41410052147240746022303207320', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.15054076467162020150596217155', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48753573526985722173593470632', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.406055541266845, 'bad_primes': [2, 7], 'central_character': '7.5', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/14/15/d/a/5/5'], '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': '2-14-7.5-c14-0-6', 'motivic_weight': 14, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [14], 'order_of_vanishing': 0, 'prelabel': '2-14-7.5-c14-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.1720565122331275, 'root_angle': -0.013629152612069775, 'self_dual': False, 'spectral_label': 'c14-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41410052147240746022303207320', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1792585374827549516068026195831', 'Lhash_array': ['1792585374827549516068026195831'], 'label': '2-14-7.5-c14-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/15/d/a/5/5'}