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lfunc_lfunctions • Show schema
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{'Lhash': '6307623411859315729371192025710', 'a10': [3.8284271247461903, -1.5857864376269049], 'a2': [0.0, -1.4142135623730951], 'a3': [-0.7071067811865476, -0.2928932188134525], 'a4': [-2.0, 0.0], 'a5': [1.1213203435596426, 2.7071067811865475], 'a6': [-0.41421356237309503, 1.0], 'a7': [1.0, -1.0], 'a8': [0.0, 2.8284271247461903], 'a9': [-1.7071067811865475, -1.7071067811865475], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.25552128646809735, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.4142135623730951]]]], 'bad_primes': [2], 'central_character': '32.29', 'coefficient_field': 'CDF', 'conductor': 32, 'conductor_radical': 2, 'conjugate': '3686787862036577043455628473985', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.4142135623730951]], [[1.0, 0], [0.7071067811865476, 0.2928932188134525], [2.1213203435596424, 2.1213203435596424]], [[1.0, 0], [-1.1213203435596426, -2.7071067811865475], 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0], [0, 6.343145750507619], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-2e5-32.29-c1-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/32/2/g/a/29/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6305548591730196, 0.6520419713913508, 0.686058221640753, 0.7330323418656399, 0.7931219758704101, 0.8662923727802087, 0.9523795816712115, 1.0511195445279031, 1.1621421800202165, 1.2849392948682237, 1.4188172581316039, 1.56284365461415, 1.715794630729243, 1.8761076968226758, 2.041843592532442, 2.210660260890182, 2.3798017413293273, 2.546104660407262, 2.7060248200443673, 2.855686060286059, 2.990953049810606, 3.1075289028230606, 3.2010775270953356, 3.2673693852985632, 3.3024479298869727, 3.302812399580096, 3.265611011791413, 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'14.82744530218702008272726686027095', '16.33197290303449701179261772819188', '16.68195039181042013865371882985349'], 'prelabel': '2-2e5-32.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5054911339164094, 'root_angle': 0.31250000000000006, 'root_number': '0.5555702330196021 + 0.8314696123025453*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.15625', 'prec': 24}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.97583751447258677706480813545', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.76679555433252604126019488759', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.039681780751416313585515708752', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.25552128646809735, 'bad_primes': [2], 'central_character': '32.29', 'conductor': 32, 'conductor_radical': 2, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/32/2/g/a/29/1'], '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': '2-2e5-32.29-c1-0-2', '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': '2-2e5-32.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5054911339164094, 'root_angle': 0.15625000000000003, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '4.97583751447258677706480813545', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '6307623411859315729371192025710', 'Lhash_array': ['6307623411859315729371192025710'], 'label': '2-2e5-32.29-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/32/2/g/a/29/1'}