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lfunc_lfunctions • Show schema
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{'Lhash': '60724111846396378677203976385', 'a10': [48229.848764546405, 1.3534497266476288e-57], 'a2': [-9.234816478076006, 15.99517133860192], 'a3': [-68.08120508794933, -117.92010625284499], 'a4': [85.43632923251175, 147.98006304289245], 'a5': [-1305.652604982646, -2261.4566488646], 'a6': [2514.869738373866, 6.9966186385644635e-59], 'a7': [-1262.5719107754428, -2186.838697672386], 'a8': [-12612.407357640735, 0.0], 'a9': [571.3990275451661, -989.692147103676], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.05632593806331, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[37, [[1.0, 0], [5400190.031489795, -10039904.751484212]]]], 'bad_primes': [37], 'central_character': '37.10', 'coefficient_field': 'CDF', 'conductor': 37, 'conductor_radical': 37, 'conjugate': '1435509314366644158591082991412', 'degree': 2, 'euler_factors': [[[1.0, 0], [9.234816478076006, -15.99517133860192], [-256.0, -443.40500673763256]], [[1.0, 0], 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-4.837677883615117, -4.151752892140689, -3.0270567279872806], 'positive_zeros': ['0.04790287783989021386321762952617', '2.49237429124854029494798788772535', '3.84629365684922424716627761744772', '5.89640789431106152900894371533567', '7.35301934927845377253003784224685', '9.402919966989815826713047458743070', '10.58234530029911357765203570362945', '11.07658513377306223557199404773717', '12.04939102193924897296712920096028', '14.27889965175977755979996913617623'], 'prelabel': '2-37-37.10-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.365355190366909, 'root_angle': -0.7230763343809941, 'root_number': '-0.644840799176857 - 0.7643169131433324*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.36153816719', 'prec': 47}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.04790287783989021386321762953', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49237429124854029494798788773', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.84629365684922424716627761745', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.05632593806331, 'bad_primes': [37], 'central_character': '37.10', 'conductor': 37, 'conductor_radical': 37, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/37/10/c/a/10/10'], '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': '2-37-37.10-c9-0-0', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-37-37.10-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.365355190366909, 'root_angle': -0.36153816719049703, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.04790287783989021386321762953', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '60724111846396378677203976385', 'Lhash_array': ['60724111846396378677203976385'], 'label': '2-37-37.10-c9-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/37/10/c/a/10/10'}