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lfunc_lfunctions • Show schema
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{'Lhash': '3465381897746155296751773579159', 'a10': [-6.537076907723678, -3.774183112387552], 'a2': [1.3660254037844386, -0.36602540378443865], 'a3': [0.0, 0.0], 'a4': [1.7320508075688772, -1.0], 'a5': [-3.774183112387552, -3.774183112387552], 'a6': [0.0, 0.0], 'a7': [-9.910946123632202, -2.655630010055615], 'a8': [2.0, -2.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.376038186030948, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3660254037844386, 0.36602540378443865]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [8.185129236019755, -10.099686103520973]]]], 'bad_primes': [2, 3, 13], 'central_character': '234.163', 'coefficient_field': 'CDF', 'conductor': 234, 'conductor_radical': 78, 'conjugate': '606204576615915343807381056300', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3660254037844386, 0.36602540378443865]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.774183112387552, 3.774183112387552], 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[34.940465421474165, 60.518661350096764], [-6384.5, 11058.278380923497]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-234-13.7-c2-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/234/3/bb/f/163/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1605268648919085, 1.4484368258587708, 1.7312328179725542, 2.0082198405645757, 2.277187879416098, 2.5341820263753245, 2.7734669958210656, 2.9876877537559183, 3.168215664066807, 3.3056619628814836, 3.390534542603159, 3.414007222019132, 3.3687615772902832, 3.249850293587399, 3.055519359841274, 2.787916433879566, 2.4536067283608363, 2.0638180426405968, 1.6343448957880549, 1.185059221307617, 0.7390019696265637, 0.3210653296398861, -0.04368299662001009, -0.3319372997468208, -0.5242136726833285, 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'8.084365977506067500647349740104052', '9.681325538428329901224066543959638', '10.38083722982226693433648961786003', '11.63148448372788101022945827361121', '12.48942827004608062896038793989854'], 'prelabel': '2-234-13.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.525081817690458, 'root_angle': 0.7919156813951961, 'root_number': '-0.7938293332733292 + 0.608140600219079*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.395957840698', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.73370430079253983732814759687', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.57257279253405429913361839705', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.02627076530616436354339244585', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.376038186030948, 'bad_primes': [2, 3, 13], 'central_character': '13.7', 'conductor': 234, 'conductor_radical': 78, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/234/3/bb/f/163/1'], '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': '2-234-13.7-c2-0-10', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-234-13.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.525081817690458, 'root_angle': 0.39595784069759804, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.73370430079253983732814759687', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3465381897746155296751773579159', 'Lhash_array': ['3465381897746155296751773579159'], 'label': '2-234-13.7-c2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/234/3/bb/f/163/1'}