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lfunc_lfunctions • Show schema
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{'Lhash': '116966754895675322114080382172', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-2.6457513110645907, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.19568209498026, '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], [2.6457513110645907, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '4032.3905', 'coefficient_field': 'CDF', 'conductor': 4032, 'conductor_radical': 42, 'conjugate': '1350229690198692303109598201668', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [2.6457513110645907, 0]], [[1.0, 0], [0, 6.570084511520132], [-11.0, 0]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [0, 0], [-19.0, 0]], [[1.0, 0], [0, 1.9151968627184388], [-23.0, 0]], [[1.0, 0], [0, -8.897528335920978], 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'2-4032-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': -0.6959132760153036, 'root_number': '-0.5773502691896257645091487805019574556476017512701268761 - 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3479566380076518', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.092270500147766648861724307336', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.76028861041294364612386140118', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.51505388792759405527698783706', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.19568209498026, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 4032, 'conductor_radical': 42, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4032/2/k/c/3905/1'], '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': '2-4032-21.20-c1-0-3', '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': '2-4032-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.674123905501206, 'root_angle': -0.3479566380076518, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.092270500147766648861724307336', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '116966754895675322114080382172', 'Lhash_array': ['116966754895675322114080382172'], 'label': '2-4032-21.20-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4032/2/k/c/3905/1'}