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lfunc_lfunctions • Show schema
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{'Lhash': '1309853604992411712126388348049', 'a10': [1.3771259613472022, -2.846668945729999], 'a2': [-1.3098556537382124, -0.5331774248503404], 'a3': [-1.5983443223166098, -0.6673045986041588], 'a4': [1.4314436672599193, 1.3967709287715981], 'a5': [-0.14302830424727483, 2.231488943325543], 'a6': [1.7378085997322275, 1.7262738110440983], 'a7': [0.5827719754125508, 0.5827719754125508], 'a8': [-1.130257853659907, -2.592781746356623], 'a9': [2.1094091453634847, 2.133165032869443], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3098556537382124, 0.5331774248503404]]], [3, [[1.0, 0], [1.5983443223166098, 0.6673045986041588]]], [5, [[1.0, 0], [0.14302830424727483, -2.231488943325543]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.77', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': 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0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/77/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5653889519798774, 0.5340020447779826, 0.501102527682829, 0.46333809755239325, 0.4164991592463382, 0.3558239119014274, 0.27628170938295665, 0.172825053804454, 0.040626836584888255, -0.1246741115580847, -0.32670288897263333, -0.5680490198590676, -0.8499440053961498, -1.1719316291026625, -1.5315538931004913, -1.9240807009353496, -2.342314706184856, -2.7765038946100056, -3.2143931066046854, -3.641441467958228, -4.041225313607497, -4.396035594437732, -4.6876651642224365, -4.898365301270732, -5.011933239433104, -5.014874633529942, -4.897568339451219, -4.655347436912743, -4.2894019267617125, -3.8074067579513784, -3.223785240450048, -2.5595334183574554, -1.8415558273940384, -1.1014965658637303, -0.37409009469140536, 0.3048990362709212, 0.9010328690308979, 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'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.1607959078833974, 'root_number': '0.8750993561940678 - 0.483943299146427*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0803979539417', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03329230054131953142505625594', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.31734633457101120041564518952', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.70261692967966253596328939724', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.77', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/w/c/77/3'], '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': '2-120-120.77-c1-0-0', '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': '2-120-120.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.0803979539416987, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03329230054131953142505625594', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1309853604992411712126388348049', 'Lhash_array': ['1309853604992411712126388348049'], 'label': '2-120-120.77-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/w/c/77/3'}