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lfunc_lfunctions • Show schema
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{'Lhash': '691348577615735495523201353754', 'a10': [-7.696829165957008, 0.0], 'a2': [2.0517530329829596, 0.0], 'a3': [0.0, 0.0], 'a4': [2.209690508354773, 0.0], 'a5': [-3.751342896648192, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.359987960645276, 0.0], 'a8': [0.4302331365046445, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.934196333374636, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1', 'coefficient_field': 'CDF', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0517530329829596, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.751342896648192, 0], [5.0, 0]], [[1.0, 0], [2.359987960645276, 0], [7.0, 0]], [[1.0, 0], [3.2723063090260793, 0], [11.0, 0]], [[1.0, 0], [-4.294950835347535, 0], [13.0, 0]], [[1.0, 0], 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'3.85700285550375146797464498455267', '4.07616682819754024632201320990302', '5.20577924142763704729792136553703', '5.73244207973470314808500784093681', '6.59605401279776112983189566401855', '7.16195930015222248047276213140743', '7.980770823062418929435409141810475'], 'prelabel': '2-6003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.923452630976444, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.54537786476120804254674032466', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35784776078108947060045585141', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22800026791352467723251386521', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.934196333374636, 'bad_primes': [3, 23, 29], 'central_character': '1.1', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6003/2/a/p/1/12'], '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': '2-6003-1.1-c1-0-44', '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': '2-6003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.923452630976444, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54537786476120804254674032466', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '691348577615735495523201353754', 'Lhash_array': ['691348577615735495523201353754'], 'label': '2-6003-1.1-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6003/2/a/p/1/12'}