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lfunc_lfunctions • Show schema
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{'Lhash': '3209281425749842807460471640942', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0420835613735244, -1.383496241814582], 'a4': [0.0, 0.0], 'a5': [-0.0619692644413602, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.6368934278613039, -2.0786004680612558], 'a8': [0.0, 0.0], 'a9': [-0.8281237022301441, 2.883437381634052], '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], [1.0420835613735244, 1.383496241814582]]], [7, [[1.0, 0], [1.6368934278613039, 2.0786004680612558]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.193', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '85693434921529622137843880360', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0420835613735244, 1.383496241814582]], [[1.0, 0], [0.0619692644413602, 0], [5.0, 0]], [[1.0, 0], [1.6368934278613039, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-504-63.4-c1-0-21', '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/193/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.11265673815477664, 0.33032726393795275, 0.564510380130136, 0.8193902597714263, 1.0968032722817047, 1.3952263104805316, 1.7092050407567034, 2.0291921712663585, 2.341754079341967, 2.6301294927357675, 2.8751446214746132, 3.0564862168146303, 3.1543068729532946, 3.1510927828256436, 3.0336722772971116, 2.795192947778534, 2.4368547925182567, 1.9691649585562738, 1.4124835300064098, 0.7966646863110477, 0.15966555012867242, -0.4549058544093252, -1.0012087618320344, -1.435323389779091, -1.7197776192616692, -1.8279747562093307, -1.747983747195188, -1.4851465282031804, 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'9.984812242873323205593241195895263', '10.23295029040486172516781855615558', '11.65189443723025222733212939801553'], 'prelabel': '2-504-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': -0.825361946843222, 'root_number': '-0.8532337406604356 - 0.5215286989213543*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.412680973422', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.53167665062600038268030748476', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.73330259203713821202953283256', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.97418448480802350585478024563', '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': '63.4', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/2/t/c/193/4'], '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': '2-504-63.4-c1-0-21', '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': '2-504-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': -0.412680973421611, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.53167665062600038268030748476', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3209281425749842807460471640942', 'Lhash_array': ['3209281425749842807460471640942'], 'label': '2-504-63.4-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/2/t/c/193/4'}