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lfunc_lfunctions • Show schema
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{'Lhash': '1511656924931436845590305820039', 'a10': [-55.6695817399367, 0.0], 'a2': [-4.671287618477067, 0.0], 'a3': [0.0, 0.0], 'a4': [13.82092801453715, 0.0], 'a5': [11.917395434984176, 0.0], 'a6': [0.0, 0.0], 'a7': [26.12220096898337, 0.0], 'a8': [-27.191228962353687, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.027292230878318, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-17.0, 0]]]], 'bad_primes': [3, 17], 'central_character': '153.1', 'coefficient_field': 'CDF', 'conductor': 153, 'conductor_radical': 51, 'conjugate': '1511656924931436845590305820039', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.671287618477067, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-11.917395434984176, 0], [125.0, 0]], [[1.0, 0], [-26.12220096898337, 0], [343.0, 0]], [[1.0, 0], [-3.2441156541810523, 0], [1331.0, 0]], [[1.0, 0], [20.051467097072695, 0], [2197.0, 0]], [[1.0, 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'4.92366682842881873154332931003638', '6.33393508384993200101546082743521', '7.66339150973919625829796199994583', '8.384103942534636298713570385177297', '9.526513657271677198750921965247866', '10.17207865755284213327310921790691', '11.17733506649139507468506665512124', '12.06355655455183979112984206493250'], 'prelabel': '2-153-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.004545261912078, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19248705018502435910495260381', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30137169809090431660128705933', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92366682842881873154332931004', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.027292230878318, 'bad_primes': [3, 17], 'central_character': '1.1', 'conductor': 153, 'conductor_radical': 51, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/153/4/a/g/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': '2-153-1.1-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-153-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.004545261912078, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19248705018502435910495260381', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1511656924931436845590305820039', 'Lhash_array': ['1511656924931436845590305820039'], 'label': '2-153-1.1-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/153/4/a/g/1/1'}