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lfunc_lfunctions • Show schema
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{'Lhash': '790727542514137381114801846500', 'a10': [144.60362898117717, 0.0], 'a2': [-5.784145159247087, 0.0], 'a3': [0.0, 0.0], 'a4': [1.456335223241511, 0.0], 'a5': [-25.0, 0.0], 'a6': [0.0, 0.0], 'a7': [17.6497628009752, 0.0], 'a8': [176.66899076415336, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 79.38999080742543, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [25.0, 0]]], [11, [[1.0, 0], [121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '495.1', 'coefficient_field': 'CDF', 'conductor': 495, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [5.784145159247087, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [25.0, 0]], [[1.0, 0], [-17.6497628009752, 0], [16807.0, 0]], [[1.0, 0], [121.0, 0]], [[1.0, 0], [-674.3958466376847, 0], [371293.0, 0]], [[1.0, 0], [-2117.621644109744, 0], [1419857.0, 0]], [[1.0, 0], [2307.7937103342424, 0], 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['0.62377404497088851152038135075275', '1.60921500684387199888985101615870', '3.26354768190471446030513561847565', '4.36400482999512249024689398845818', '5.48942556043060736269082089962018', '6.75875940176293052714813464676350', '7.77979711033930729970942349196294', '8.383053286391489149839130517579333', '9.119565993894597502881696095823882', '10.16635608756747259940231223861206'], 'prelabel': '2-495-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.910106105284349, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62377404497088851152038135075', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.60921500684387199888985101616', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.26354768190471446030513561848', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 79.38999080742543, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 495, 'conductor_radical': 165, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/495/6/a/b/1/1'], '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': '2-495-1.1-c5-0-19', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-495-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.910106105284349, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62377404497088851152038135075', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '790727542514137381114801846500', 'Lhash_array': ['790727542514137381114801846500'], 'label': '2-495-1.1-c5-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/495/6/a/b/1/1'}