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lfunc_lfunctions • Show schema
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{'Lhash': '1083568725724651502556968083254', 'a10': [-1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.44756819804406434, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.44756819804406434, 0.0], 'a7': [1.8651506764628814, 0.0], 'a8': [1.0, 0.0], 'a9': [-2.799682708099589, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.17971201457601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 13, 31], 'central_character': '4030.1', 'coefficient_field': 'CDF', 'conductor': 4030, 'conductor_radical': 4030, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.44756819804406434, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.8651506764628814, 0], [7.0, 0]], [[1.0, 0], [4.77230490488839, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.7786581671146523, 0], [17.0, 0]], [[1.0, 0], 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'4.81067055822541395898596609112565', '5.31648814249654893504315857915926', '5.98496444403688986664534046403248', '7.18735764263874096947848312627976', '7.61946538554596665882339629273761', '8.318477914587690933476880408649095'], 'prelabel': '2-4030-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.672716458150893, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.854785005844326845476791014616', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.47929094525654821875115895068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79817729689008600843588397467', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.17971201457601, 'bad_primes': [2, 5, 13, 31], 'central_character': '1.1', 'conductor': 4030, 'conductor_radical': 4030, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4030/2/a/n/1/6'], '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': '2-4030-1.1-c1-0-35', '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': '2-4030-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.672716458150893, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.854785005844326845476791014616', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1083568725724651502556968083254', 'Lhash_array': ['1083568725724651502556968083254'], 'label': '2-4030-1.1-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4030/2/a/n/1/6'}