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lfunc_lfunctions • Show schema
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{'Lhash': '554250493369076325279617565677', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [2.0, 3.4641016151377544], 'a6': [0.0, 0.0], 'a7': [-3.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.461767498255581, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [4.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '684.577', 'coefficient_field': 'CDF', 'conductor': 684, 'conductor_radical': 114, 'conjugate': '3087835453214137293812128320399', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0, -3.4641016151377544], [-2.5, 4.330127018922194]], [[1.0, 0], [3.0, 0], [7.0, 0]], [[1.0, 0], [4.0, 0], [11.0, 0]], [[1.0, 0], [2.5, -4.330127018922194], [-6.5, -11.258330249197702]], [[1.0, 0], [0, 0], [-8.5, 14.722431864335457]], [[1.0, 0], 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1.0975273984031355, 1.386825986841594, 1.198516982328], 'positive_zeros': ['0.43722654591832195116399434118880', '2.14170392074495020242443445663693', '3.39349154255150084750148568179123', '4.99254866738420551500185459251770', '5.38482928820182145468782345512260', '6.39737234569397275903182508423762', '7.64666404494160553927137108341045', '8.562220068111626520122914371121565', '9.276500448455116606976406422019652', '10.14223655608284798734247874257368'], 'prelabel': '2-684-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.337042468218235, 'root_angle': -0.8021732427912203, 'root_number': '-0.8130111781688403 - 0.5822480778607295*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.401086621396', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43722654591832195116399434119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14170392074495020242443445664', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39349154255150084750148568179', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.461767498255581, 'bad_primes': [2, 3, 19], 'central_character': '19.7', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/684/2/k/e/577/1'], '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': '2-684-19.7-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': '2-684-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.337042468218235, 'root_angle': -0.40108662139561013, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43722654591832195116399434119', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '554250493369076325279617565677', 'Lhash_array': ['554250493369076325279617565677'], 'label': '2-684-19.7-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/684/2/k/e/577/1'}