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lfunc_lfunctions • Show schema
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{'Lhash': '2712563941072186061739040957873', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.467046378507319, 1.7069511317826063], 'a4': [0.0, 0.0], 'a5': [2.198166086502583, -4.490886978777123], 'a6': [0.0, 0.0], 'a7': [2.814253950365616, -10.5029387281659], 'a8': [0.0, 0.0], 'a9': [3.1726356674121585, 8.422255215906498], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.904644758485345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-2.467046378507319, -1.7069511317826063]]], [5, [[1.0, 0], [-2.198166086502583, 4.490886978777123]]]], 'bad_primes': [2, 3, 5], 'central_character': '180.157', 'coefficient_field': 'CDF', 'conductor': 180, 'conductor_radical': 30, 'conjugate': '1772690272499196672442605564941', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.467046378507319, -1.7069511317826063]], [[1.0, 0], [-2.198166086502583, 4.490886978777123]], [[1.0, 0], 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[-11058.278380923497, 6384.5]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-180-45.22-c2-0-9', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/180/3/u/a/157/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0916829322735686, 2.1475727819431913, 2.1892987021768384, 2.2156709830282604, 2.224399441688517, 2.2123538267097493, 2.1759317135073304, 2.1115022555956893, 2.0158944414614073, 1.8869003138073823, 1.7237643111889458, 1.527628525130142, 1.3019007898849775, 1.0525095745286046, 0.7880083009879459, 0.5194934589795003, 0.26030682932346405, 0.02550287016272712, -0.16892207045846458, -0.30702210262089535, -0.3740759398588569, -0.35787847457293737, -0.2500616508725052, -0.047336280383278174, 0.24746732265944849, 0.6246864969335708, 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'10.44169466568377637411492656124581', '11.74337714229896729245412592664292', '12.44170348051363880370643208270628'], 'prelabel': '2-180-45.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2146432576117863, 'root_angle': 0.06589383674663302, 'root_number': '0.9155097250603677 + 0.4022958405451018*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0658938367466', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.13983564602408002090296326036', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.89791256981206328414950632258', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.94526416369292577374997547320', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.904644758485345, 'bad_primes': [2, 3, 5], 'central_character': '45.22', 'conductor': 180, 'conductor_radical': 30, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/180/3/u/a/157/10'], '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': '2-180-45.22-c2-0-9', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-180-45.22-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2146432576117863, 'root_angle': 0.06589383674663302, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.13983564602408002090296326036', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2712563941072186061739040957873', 'Lhash_array': ['2712563941072186061739040957873'], 'factors': ['2-180-45.22-c2-0-9'], 'label': '2-180-45.22-c2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/180/3/u/a/157/10'}