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lfunc_lfunctions • Show schema
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{'Lhash': '1108372037519535300209452058006', 'a10': [-225.57550765359255, -1.2757854291098066e-59], 'a2': [2.0, 3.4641016151377544], 'a3': [-14.696938456699069, 5.196152422706632], 'a4': [-8.0, 13.856406460551018], 'a5': [-28.19693845669907, 48.838530024895555], 'a6': [-47.39387691339814, -40.51938340001816], 'a7': [11.151530771650465, 19.315017878666374], 'a8': [-64.0, 0.0], 'a9': [189.0, -152.73506473629428], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, -3.4641016151377544]]], [3, [[1.0, 0], [14.696938456699069, -5.196152422706632]]]], 'bad_primes': [2, 3], 'central_character': '18.13', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '5240189150003096383311417560431', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, -3.4641016151377544]], [[1.0, 0], [14.696938456699069, -5.196152422706632]], [[1.0, 0], 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'6.13022856964328002006875292662276', '8.486321866727081155140317189704447', '10.57559409097599858330115099373997', '11.83865182996358570874042275610539', '12.69221572029100091838100060267416', '14.18963639247044396136160532301201', '16.21422977660534182139442444075603', '16.98047680108832992097513354982523'], 'prelabel': '2-18-9.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.699090567519475, 'root_angle': -0.771902451494341, 'root_number': '-0.7540501295809626 - 0.6568168710370749*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.385951225747', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.874351368839317877182743688301', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '4.34834546863170708381835743615', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.13022856964328002006875292662', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/6/c/a/13/1'], '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': '2-18-9.4-c5-0-0', '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': '2-18-9.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.699090567519475, 'root_angle': -0.3859512257471705, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.874351368839317877182743688301', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1108372037519535300209452058006', 'Lhash_array': ['1108372037519535300209452058006'], 'label': '2-18-9.4-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/6/c/a/13/1'}