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lfunc_lfunctions • Show schema
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{'Lhash': '1297474292997111532882785488280', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [7.338204303841471, 4.236714230191344], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.06551863315638, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.901', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'conjugate': '1196313681364381332237290469997', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.338204303841471, -4.236714230191344], [12.5, 21.650635094610966]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.9497474683058327, -3.3770616770344914], [-60.5, 104.78907385791707]], [[1.0, 0], [0, 19.1885645666052], [-169.0, 0]], [[1.0, 0], [11.589719186508738, -6.69132749216299], [144.5, 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-0.06036767911354072, 'root_number': '0.98207015168574043229585629351832629483577927908335062278 - 0.18851582736721810527801782120667433294088172392099580958*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.030183839556770356', 'prec': 70}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02352674527469370218644912802', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88105076923645374814005268833', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90606272389745228064310109459', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.06551863315638, 'bad_primes': [2, 3, 7], 'central_character': '7.5', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/3/z/k/901/4'], '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': '2-42e2-7.5-c2-0-20', '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': '2-42e2-7.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.9329300179041455, 'root_angle': -0.03018383955677036, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02352674527469370218644912802', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1297474292997111532882785488280', 'Lhash_array': ['1297474292997111532882785488280'], 'label': '2-42e2-7.5-c2-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/3/z/k/901/4'}