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lfunc_lfunctions • Show schema
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{'Lhash': '1102653854887306683880456838721', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.0, 1.7320508075688772], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0366903928088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.0, -1.7320508075688772]]]], 'bad_primes': [2, 3, 7], 'central_character': '756.269', 'coefficient_field': 'CDF', 'conductor': 756, 'conductor_radical': 42, 'conjugate': '2013266749391546709087707402363', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [-2.0, -1.7320508075688772]], [[1.0, 0], [0, 0], [5.5, 9.526279441628825]], [[1.0, 0], [0, -5.196152422706632], [-13.0, 0]], [[1.0, 0], [0, 0], [-8.5, -14.722431864335457]], [[1.0, 0], [3.0, 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'2.47168693844004023704618418888209', '3.75286593814605939011564422897518', '4.78544808537332050285433725828250', '5.66803436863119794497106666483602', '6.79978912344790554746277743851859', '7.75945588857778625781650398968473', '8.304684175124121524246268673264205', '9.401251789733498716145497169871855', '10.38273259269943048516489025902406'], 'prelabel': '2-756-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': -0.31316038027938725, 'root_number': '0.5538440336596777 - 0.8326204335587601*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.15658019014', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.869840518111838942871331905076', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.47168693844004023704618418888', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75286593814605939011564422898', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0366903928088, 'bad_primes': [2, 3, 7], 'central_character': '21.17', 'conductor': 756, 'conductor_radical': 42, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/756/2/t/b/269/1'], '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': '2-756-21.17-c1-0-4', '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': '2-756-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4569677231923093, 'root_angle': -0.15658019013969363, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.869840518111838942871331905076', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1102653854887306683880456838721', 'Lhash_array': ['1102653854887306683880456838721'], 'label': '2-756-21.17-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/756/2/t/b/269/1'}