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lfunc_lfunctions • Show schema
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{'Lhash': '1224069350576217992418363330031', 'a10': [2.432458234887408, -2.020679820141834], 'a2': [-1.411074343794321, -0.09417641045095253], 'a3': [0.4165191566224544, 1.6812233022910785], 'a4': [1.9822616074291475, 0.265779833155965], 'a5': [-1.621039517734604, 1.5402048181793104], 'a6': [-0.42940791983252347, -2.411557347106866], 'a7': [-0.36198928490127213, 0.36198928490127213], 'a8': [-2.7720883062748785, -0.5617173864267297], 'a9': [-2.6530235843330385, 1.4005234239285955], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.411074343794321, 0.09417641045095253]]], [3, [[1.0, 0], [-0.4165191566224544, -1.6812233022910785]]], [5, [[1.0, 0], [1.621039517734604, -1.5402048181793104]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': 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0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/53/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.6309584632271718, 0.5646608490518803, 0.501160387672857, 0.43644359878539385, 0.3663747148988625, 0.28706263634969864, 0.19515640226568892, 0.0880764804528084, -0.03579148538428072, -0.17691711388830506, -0.33445024429630277, -0.5060549508543379, -0.6877677239239659, -0.8739013600706796, -1.0570190520977436, -1.2280032640383833, -1.3762415220496296, -1.489946321776979, -1.556618953566193, -1.5636572707834224, -1.4990955552511187, -1.3524512033020732, -1.1156387831263788, -0.7838981878233824, -0.35667144403574386, 0.16164630795103413, 0.7611605855351526, 1.426213480120804, 2.1354705414663875, 2.8624112321632684, 3.576251700215072, 4.243297903618417, 4.828691151533273, 5.298469338745532, 5.621828722079416, 5.773436749487291, 5.735620198367905, 5.500238592083267, 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'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.5793197230347957, 'root_number': '-0.24661931028363532 - 0.969112437127511*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.289659861517', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.965620455948851374096445281244', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.08818423879855636304220805831', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.48994113794303824584628921110', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/w/c/53/1'], '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': '2-120-120.53-c1-0-2', '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': '2-120-120.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.28965986151739787, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.965620455948851374096445281244', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1224069350576217992418363330031', 'Lhash_array': ['1224069350576217992418363330031'], 'label': '2-120-120.53-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/53/1'}