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lfunc_lfunctions • Show schema
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{'Lhash': '1784011487236497786944276806705', 'a10': [0, 0], 'a2': [0, 1.4625984229747742], 'a3': [0, 1.0], 'a4': [-0.13919414688829662, 0], 'a5': [0, 0], 'a6': [-1.4625984229747742, 0], 'a7': [0, -1.3234042760864777], 'a8': [0, 2.7216117062234066], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.367462439628493, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 29], 'central_character': '2175.349', 'coefficient_field': 'CDF', 'conductor': 2175, 'conductor_radical': 435, 'conjugate': '340744243593855776256802857426', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.4625984229747742], [-2.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.3234042760864777], [-7.0, 0]], [[1.0, 0], [5.323404276086477, 0], [11.0, 0]], [[1.0, 0], [0, 2.398207430136929], [-13.0, 0]], [[1.0, 0], [0, 5.045015982309884], 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'2.98741904847059349632911037728981', '3.97562649208654918004964523541195', '5.12785789919476738080718129907749', '5.99920056319391399024084540830170', '6.78686518101722973615468500502268', '7.67453919122002576909040422828673', '8.357715211075908363970591381339579', '9.221922859734647951064018647776740'], 'prelabel': '2-2175-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.167428756395062, 'root_angle': 0.07379180882521663, 'root_number': '0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07379180882521663', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40733691674606719290876071417', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24196874558558341165232043845', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98741904847059349632911037729', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.367462439628493, 'bad_primes': [3, 5, 29], 'central_character': '5.4', 'conductor': 2175, 'conductor_radical': 435, 'degree': 2, 'index': 62, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2175/2/c/l/349/4'], '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': '2-2175-5.4-c1-0-62', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2175-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.167428756395062, 'root_angle': 0.07379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40733691674606719290876071417', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1784011487236497786944276806705', 'Lhash_array': ['1784011487236497786944276806705'], 'factors': ['2-2175-5.4-c1-0-62'], 'label': '2-2175-5.4-c1-0-62', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2175/2/c/l/349/4'}