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lfunc_lfunctions • Show schema
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{'Lhash': '491771322335786173143665384099', 'a10': [0.0, 15.985866738256664], 'a2': [0.0, -2.869689012330993], 'a3': [-2.762781262772798, 4.400799892527669], 'a4': [-0.23511502749322827, 0.0], 'a5': [-5.570592029159165, 0.0], 'a6': [12.628927097054065, 7.928323033253044], 'a7': [0.0, 0.0], 'a8': [0.0, -22.282805087616726], 'a9': [-11.734079388143085, -24.316894968575976], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.673280770843874, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.762781262772798, -4.400799892527669]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.146', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'conjugate': '2384246982811341353819732952477', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.869689012330993], [-8.0, 0]], [[1.0, 0], [2.762781262772798, -4.400799892527669]], [[1.0, 0], [5.570592029159165, 0], [125.0, 0]], [[1.0, 0], [0, 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5.75353078628108, 4.6278880245055944, 3.170564752627877, 1.6959383539110375], 'positive_zeros': ['0.38793917049954226223174378913057', '2.70524828251052004824558219844611', '4.97218746500877538950427790748939', '6.07220130057295433152083140784751', '6.86305154989930638573449370233930', '8.014636512528265839697242580662858', '8.552137109009901569508418067451613', '10.75115466145677001689826192124774', '11.26646159033208090388083108115139', '12.46298494565159743965547458870789'], 'prelabel': '2-147-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9450434242713426, 'root_angle': -0.45571363708195994, 'root_number': '0.13868128920273606 - 0.9903370638449654*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.227856818541', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.38793917049954226223174378913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70524828251052004824558219845', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.97218746500877538950427790749', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.673280770843874, 'bad_primes': [3, 7], 'central_character': '21.20', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/4/c/b/146/7'], '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': '2-147-21.20-c3-0-3', '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': '2-147-21.20-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9450434242713426, 'root_angle': -0.22785681854097997, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.38793917049954226223174378913', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '491771322335786173143665384099', 'Lhash_array': ['491771322335786173143665384099'], 'label': '2-147-21.20-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/4/c/b/146/7'}