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lfunc_lfunctions • Show schema
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{'Lhash': '1528637640294388300931522793042', 'a10': [1.5076480221109079, -0.1078291146752006], 'a2': [0.5406408174555976, -0.8412535328311812], 'a3': [0.0, 0.0], 'a4': [-0.41541501300188644, -0.9096319953545183], 'a5': [0.9058076827719271, 1.2100174041632301], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.9898214418809327, -0.14231483827328514], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5406408174555976, 0.8412535328311812]]], [3, [[1.0, 0], [0, 0]]], [89, [[1.0, 0], [0.8005412409243604, 0.599277666511347]]]], 'bad_primes': [2, 3, 89], 'central_character': '3204.359', 'coefficient_field': 'CDF', 'conductor': 3204, 'conductor_radical': 534, 'conjugate': '1652873899756874316265675113730', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5406408174555976, 0.8412535328311812]], [[1.0, 0], [0, 0]], [[1.0, 0], 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['1.20588247267754258619604068578267', '2.47375158258991812598094119225989', '3.75887556355572554959240766587535', '4.35071476391316458220303539859251', '5.48294217580497736916931205700872', '5.67890267909895910224410982970901', '6.42437013497291988318308494987597', '7.45365199260709808475174833154002', '8.430641299377378742247000241488312', '8.519857517662735942655288730131727'], 'prelabel': '2-3204-1068.359-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': 0.22737267543667827, 'root_number': '0.75554391317705399384886727024769 + 0.65509800431775419683463265268533*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.11368633771833912', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20588247267754258619604068578', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47375158258991812598094119226', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75887556355572554959240766588', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'bad_primes': [2, 3, 89], 'central_character': '1068.359', 'conductor': 3204, 'conductor_radical': 534, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3204/1/cd/b/359/1'], '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': '2-3204-1068.359-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3204-1068.359-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': 0.11368633771833914, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20588247267754258619604068578', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1528637640294388300931522793042', 'Lhash_array': ['1528637640294388300931522793042'], 'label': '2-3204-1068.359-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3204/1/cd/b/359/1'}