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lfunc_lfunctions • Show schema
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{'Lhash': '2126123715106108612519312880378', 'a10': [-4.318881752259641, -1.3965896880860372e-60], 'a2': [2.3454846872143755, 0.7620941720886282], 'a3': [-2.331830830015291, 1.6941742661201484], 'a4': [3.3024769020757696, 2.3993899171134423], 'a5': [-1.665525792839987, 0.541162134677639], 'a6': [-6.7603938396879455, 2.1965851128062184], 'a7': [1.3883724104367081, -1.9109306846060687], 'a8': [3.0181694177157152, 4.15415381946292], 'a9': [1.640157592701215, -5.047886021429524], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.14186074890431, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-3.3036414104485177, -0.2931781560241614]]], [13, [[1.0, 0], [-1.3332204885785215, -3.3500034520630644]]]], 'bad_primes': [11, 13], 'central_character': '143.64', 'coefficient_field': 'CDF', 'conductor': 143, 'conductor_radical': 143, 'conjugate': '4870851484791829364461113101601', 'degree': 2, 'euler_factors': [[[1.0, 0], 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{'__RealLiteral__': 0, 'data': '-0.253477296122', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67721587851046545190457218661', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.79597796815293413174016561846', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.15139645087005101737000342950', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.14186074890431, 'bad_primes': [11, 13], 'central_character': '143.64', 'conductor': 143, 'conductor_radical': 143, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/143/2/n/a/64/12'], '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': '2-143-143.64-c1-0-4', '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': '2-143-143.64-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0685788454317773, 'root_angle': -0.2534772961219368, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67721587851046545190457218661', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2126123715106108612519312880378', 'Lhash_array': ['2126123715106108612519312880378'], 'label': '2-143-143.64-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/143/2/n/a/64/12'}