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lfunc_lfunctions • Show schema
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{'Lhash': '1915094173608476215980056431916', 'a10': [-1178.706750440013, 0.0], 'a2': [8.0, 0.0], 'a3': [40.56798697048388, 0.0], 'a4': [64.0, 0.0], 'a5': [-147.3383438050016, 0.0], 'a6': [324.54389576387103, 0.0], 'a7': [-419.9774473181119, 0.0], 'a8': [512.0, 0.0], 'a9': [-541.23843316265, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 168.06314371045758, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-8.0, 0]]], [269, [[1.0, 0], [19465109.0, 0]]]], 'bad_primes': [2, 269], 'central_character': '538.1', 'coefficient_field': 'CDF', 'conductor': 538, 'conductor_radical': 538, 'degree': 2, 'euler_factors': [[[1.0, 0], [-8.0, 0]], [[1.0, 0], [-40.56798697048388, 0], [2187.0, 0]], [[1.0, 0], [147.3383438050016, 0], [78125.0, 0]], [[1.0, 0], [419.9774473181119, 0], [823543.0, 0]], [[1.0, 0], [-240.1259665091907, 0], [19487171.0, 0]], [[1.0, 0], [-4978.404434514586, 0], [62748517.0, 0]], [[1.0, 0], 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0]], [[1.0, 0], [19465109.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 134, 'label': '2-538-1.1-c7-0-134', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/538/8/a/a/1/25', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-3.9185549327781877e-60, 0.5180349507763486, 1.0273575702516533, 1.5194173290947708, 1.9859843723779826, 2.4193025766426204, 2.812233992943791, 3.158392007392594, 3.452260723112373, 3.689298281048048, 3.8660220902123514, 3.980074228746548, 4.030265603095737, 4.016597810508605, 3.940262036137932, 3.80361472566574, 3.610130202247332, 3.364330836504602, 3.0716958233574787, 2.738550061976165, 2.3719350667125445, 1.9794642486202005, 1.56916528978856, 1.1493126766688961, 0.7282537543293537, 0.3142319018614977, -0.08478939878941157, 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'8.018085208648704216650687928609772', '9.225549655296827597592928801748455'], 'prelabel': '2-538-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.963916989492704, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51074292337626808425169444711', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73777898215251919490825151672', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52004418387981647549755471913', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 168.06314371045758, 'bad_primes': [2, 269], 'central_character': '1.1', 'conductor': 538, 'conductor_radical': 538, 'degree': 2, 'index': 134, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/538/8/a/a/1/25'], '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': '2-538-1.1-c7-0-134', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-538-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.963916989492704, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51074292337626808425169444711', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1915094173608476215980056431916', 'Lhash_array': ['1915094173608476215980056431916'], 'label': '2-538-1.1-c7-0-134', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/538/8/a/a/1/25'}