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lfunc_lfunctions • Show schema
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{'Lhash': '2325016406775526597658857342530', 'a10': [2.6718146237444933, 0.0], 'a2': [0.7922869913932613, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.3722813232690143, 0.0], 'a5': [3.3722813232690143, 0.0], 'a6': [0.7922869913932613, 0.0], 'a7': [2.5243377989621387, 0.0], 'a8': [-2.6718146237444933, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '363.1', 'coefficient_field': 'CDF', 'conductor': 363, 'conductor_radical': 33, 'conjugate': '2325016406775526597658857342530', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7922869913932613, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.3722813232690143, 0], [5.0, 0]], [[1.0, 0], [-2.5243377989621387, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.840962589317538, 0], [13.0, 0]], [[1.0, 0], 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'6.44663193842469751787444206692324', '7.79694174501864191774960110429941', '8.752974647539106053582913938069970', '9.734244861019423555355439770965859', '10.08291896927709444050110178214849', '11.62050949706971693175784826729666'], 'prelabel': '2-363-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.83411454730264611735408611709', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08416565161952874084754534841', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.76468449858083751139902884752', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 363, 'conductor_radical': 33, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/363/2/a/j/1/3'], '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': '2-363-1.1-c1-0-9', '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': '2-363-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83411454730264611735408611709', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2325016406775526597658857342530', 'Lhash_array': ['2325016406775526597658857342530'], 'factors': ['2-363-1.1-c1-0-9'], 'label': '2-363-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/363/2/a/j/1/3'}