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lfunc_lfunctions • Show schema
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{'Lhash': '2203833933310969236284703964229', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.7225228522263947, 0.18142498052320688], 'a4': [0.0, 0.0], 'a5': [2.104397124298905, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.7847489110437182, -1.953118359067945], 'a8': [0.0, 0.0], 'a9': [2.934169952884308, 0.6250173498319048], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.024460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.7225228522263947, -0.18142498052320688]]], [7, [[1.0, 0], [1.7847489110437182, 1.953118359067945]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.457', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '1997346473719835938351202346781', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7225228522263947, -0.18142498052320688]], [[1.0, 0], [-2.104397124298905, 0], [5.0, 0]], [[1.0, 0], [1.7847489110437182, 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[-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-504-63.16-c1-0-17', '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/504/2/t/c/457/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.2104359487468006, 2.2275513401513214, 2.2437884031684106, 2.253452422107547, 2.2478025086291176, 2.216460100976842, 2.1489220957802684, 2.0359949935328654, 1.8710747784560016, 1.651242958299283, 1.3781415145754434, 1.0585609469304884, 0.704652128757163, 0.3336677098044176, -0.03284318470330804, -0.3704225706774468, -0.6536492056309147, -0.8585443371491711, -0.9652607903454477, -0.9608043261004621, -0.8414782416061994, -0.6147123236562968, -0.2999459172461221, 0.07171077011575339, 0.45921078014252165, 0.8147278129581685, 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'8.342726729612328186710607236677161', '9.333171723822275546739914549405357', '9.728052661974204243433894626917155', '10.66404212400800237259833932233601'], 'prelabel': '2-504-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.033183382065011015, 'root_number': '0.9945710268884431 + 0.1040599465407694*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0165916910325', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73851843158847415459139872757', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.85173688046901277572882723468', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.87278047328155861178029353761', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.024460261872533, 'bad_primes': [2, 3, 7], 'central_character': '63.16', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/2/t/c/457/11'], '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': '2-504-63.16-c1-0-17', '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': '2-504-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.016591691032505507, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73851843158847415459139872757', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2203833933310969236284703964229', 'Lhash_array': ['2203833933310969236284703964229'], 'label': '2-504-63.16-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/2/t/c/457/11'}