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lfunc_lfunctions • Show schema
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{'Lhash': '1869050280226895362861830921826', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.994841846789825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '6762.1', 'coefficient_field': 'CDF', 'conductor': 6762, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0], [11.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [13.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [17.0, 0]], [[1.0, 0], [-3.414213562373095, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.7573593128807149, 0], [29.0, 0]], 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132, 'label': '2-6762-1.1-c1-0-132', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/6762/2/a/ca/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.3728312024109687e-60, 0.2530981596212003, 0.5050384138099681, 0.7546136411218535, 1.0005217798807116, 1.2413268365157883, 1.4754293974936272, 1.7010487849924087, 1.9162182751388144, 2.1187940564362857, 2.3064779042046823, 2.4768529256404843, 2.6274312110384477, 2.7557118141921277, 2.85924717126043, 2.935715838203697, 2.982999266480576, 2.999260231294772, 2.983020466496362, 2.9332350400365033, 2.849361022565778, 2.7314180614625774, 2.58003857736707, 2.396505455033105, 2.1827753095303173, 1.941485675856802, 1.6759447962915028, 1.3901030643857872, 1.088505623757142, 0.7762261073927914, 0.45878202979090066, 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'7.40171622104415464854761343330761'], 'prelabel': '2-6762-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.348118252096235, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47442069596337445812573067496', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33081473927780838828836060826', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25490929349754338752633539533', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.994841846789825, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 6762, 'conductor_radical': 966, 'degree': 2, 'index': 132, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6762/2/a/ca/1/1'], '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': '2-6762-1.1-c1-0-132', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6762-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.348118252096235, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47442069596337445812573067496', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1869050280226895362861830921826', 'Lhash_array': ['1869050280226895362861830921826'], 'label': '2-6762-1.1-c1-0-132', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6762/2/a/ca/1/1'}