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lfunc_lfunctions • Show schema
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{'Lhash': '2944572981510765413162901216424', 'a10': [0.0, 0.0], 'a2': [0.0, -2.124885419764574], 'a3': [0.0, -1.0], 'a4': [-2.5151380471280707, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.124885419764574, 0.0], 'a7': [0.0, -3.6400234668926448], 'a8': [0.0, 1.094609325508433], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.587658166755635, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.199', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'conjugate': '719328052047318861690741103259', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.124885419764574], [-2.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.6400234668926448], [-7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, -1.5151380471280704], [-13.0, 0]], [[1.0, 0], [0, 1.1551615140207152], [-17.0, 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'6.25420744733698131452314451540942', '7.38926996729282910680261481347551', '8.243922113188058498243258141922061', '8.957452143185897948066623279840730', '9.491270156066729688650409678288708', '10.68654892140462194465546155142649'], 'prelabel': '2-825-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.566643365712431, 'root_angle': -0.6475836176504333, 'root_number': '-0.4472135954999579 - 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.323791808825', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.32285850768391606188067586596', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77309870844691475126191373343', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.98381156796781296434293067236', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.587658166755635, 'bad_primes': [3, 5, 11], 'central_character': '5.4', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/2/c/f/199/2'], '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': '2-825-5.4-c1-0-27', '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': '2-825-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.566643365712431, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.32285850768391606188067586596', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2944572981510765413162901216424', 'Lhash_array': ['2944572981510765413162901216424'], 'label': '2-825-5.4-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/c/f/199/2'}