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lfunc_lfunctions • Show schema
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{'Lhash': '731447489833701320900096784575', 'a10': [4.3747159281142185, 0.0], 'a2': [-1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-4.3747159281142185, 0.0], 'a6': [1.0, 0.0], 'a7': [-0.773392696596388, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.24561290125763, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]], [53, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 19, 53], 'central_character': '6042.1', 'coefficient_field': 'CDF', 'conductor': 6042, 'conductor_radical': 6042, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.3747159281142185, 0], [5.0, 0]], [[1.0, 0], [0.773392696596388, 0], [7.0, 0]], [[1.0, 0], [-4.420794446961094, 0], [11.0, 0]], [[1.0, 0], [-0.6484616804545299, 0], [13.0, 0]], [[1.0, 0], [-6.40302052208195, 0], [17.0, 0]], [[1.0, 0], 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[[1.0, 0], [17.250594095008083, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-6042-1.1-c1-0-12', 'leading_term': '0.72307347110019658696414075822401', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/6042/2/a/z/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.7230734711001966, 0.7178208508668641, 0.7020855373033624, 0.6759389949239584, 0.639512801325164, 0.5930164189261825, 0.536760291977403, 0.4711826660333517, 0.3968782954004594, 0.31462709511846787, 0.22542079708000043, 0.13048576575126267, 0.03130029515083995, -0.07039507613963758, -0.17259544863301268, -0.27303859546474907, -0.3692218200778193, -0.4584290277462676, -0.5377681096757211, -0.6042184415318232, -0.6546879960459496, -0.6860792635356119, 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'4.14137818865433176387528873030361', '5.26100921358101257249734043158667', '6.13297291308769948447616071661162', '6.90229339966232610613274046671676', '7.45822945142754266431844267599677', '7.906586555814756173109529190052987'], 'prelabel': '2-6042-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.945906197268837, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57701032895185045379696906840', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.34645643144581499011267084480', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.94898464155020677121386096018', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.24561290125763, 'bad_primes': [2, 3, 19, 53], 'central_character': '1.1', 'conductor': 6042, 'conductor_radical': 6042, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6042/2/a/z/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': '2-6042-1.1-c1-0-12', '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': '2-6042-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.945906197268837, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57701032895185045379696906840', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '731447489833701320900096784575', 'Lhash_array': ['731447489833701320900096784575'], 'label': '2-6042-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6042/2/a/z/1/1'}