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lfunc_lfunctions • Show schema
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{'Lhash': '1535883886497680075587213480692', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.7320508075688772], 'a4': [0, 0], 'a5': [0, 8.999382596297954], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.08735817754184, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.7320508075688772]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2352.97', 'coefficient_field': 'CDF', 'conductor': 2352, 'conductor_radical': 42, 'conjugate': '156791001876958385453959999132', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.7320508075688772]], [[1.0, 0], [0, -8.999382596297954], [-25.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.639335540393818, 0], [121.0, 0]], [[1.0, 0], [0, 15.77692327440411], [-169.0, 0]], [[1.0, 0], [0, -9.25506505839621], [-289.0, 0]], [[1.0, 0], [0, 27.54803671523222], [-361.0, 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'3.89977293997447852497226964094783', '4.08827343349176666303078326429760', '5.19637502495619038153205183212507', '5.61718825324875070515066670190198', '6.72069944080746821243809039351218', '7.76947105039343304384066406919161', '8.529499371129263714169711541540335', '9.144714240372616924436743711424669'], 'prelabel': '2-2352-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.00545802421959, 'root_angle': 0.7271855258285052, 'root_number': '-0.654653670707977143798292456246858355569208082395424558 + 0.755928946018454454429033072468360121631502623737842909*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3635927629142526', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21159875301692565548583230365', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11140632482874617533035104860', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89977293997447852497226964095', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.08735817754184, 'bad_primes': [2, 3, 7], 'central_character': '7.6', 'conductor': 2352, 'conductor_radical': 42, 'degree': 2, 'index': 64, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2352/3/f/k/97/4'], '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': '2-2352-7.6-c2-0-64', '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': '2-2352-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.00545802421959, 'root_angle': 0.3635927629142526, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21159875301692565548583230365', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1535883886497680075587213480692', 'Lhash_array': ['1535883886497680075587213480692'], 'label': '2-2352-7.6-c2-0-64', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2352/3/f/k/97/4'}