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lfunc_lfunctions • Show schema
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{'Lhash': '440797924881178732338188274557', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.2614299281353234, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.07224668490505, 0.0], 'a8': [0.0, 0.0], 'a9': [7.636925176136781, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.34315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.1', 'coefficient_field': 'CDF', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.2614299281353234, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.07224668490505, 0], [7.0, 0]], [[1.0, 0], [0.7863662711582616, 0], [11.0, 0]], [[1.0, 0], [1.0797435455306719, 0], [13.0, 0]], [[1.0, 0], [-1.9079284516500181, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-1.4138346829348232, 0], 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'5.57521110486776199541678524993541', '6.21877437173903329080020564038601', '6.92635585998282557249227662701875', '7.27220979164578819313465357989245', '8.545631826970720253296483961784939'], 'prelabel': '2-3800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5084619239935355, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34772825004131021745878878768', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.68321993376562308574504357026', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16105278521843829131378944880', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.34315276808656, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/2/a/ba/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': '2-3800-1.1-c1-0-1', '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': '2-3800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5084619239935355, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34772825004131021745878878768', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '440797924881178732338188274557', 'Lhash_array': ['440797924881178732338188274557'], 'label': '2-3800-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/2/a/ba/1/1'}