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lfunc_lfunctions • Show schema
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{'Lhash': '5154042977573172874925767420006', 'a10': [-578.2396337690775, 0.0], 'a2': [5.916627816819124, 0.0], 'a3': [-18.28284053687604, 0.0], 'a4': [3.0064847227578393, 0.0], 'a5': [-97.73128404753176, 0.0], 'a6': [-108.17276289094909, 0.0], 'a7': [139.55833902746903, 0.0], 'a8': [-171.54383899670123, 0.0], 'a9': [91.26225809683783, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.65113077457644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[29, [[1.0, 0], [841.0, 0]]]], 'bad_primes': [29], 'central_character': '29.1', 'coefficient_field': 'CDF', 'conductor': 29, 'conductor_radical': 29, 'conjugate': '5154042977573172874925767420006', 'degree': 2, 'euler_factors': [[[1.0, 0], [-5.916627816819124, 0], [32.0, 0]], [[1.0, 0], [18.28284053687604, 0], [243.0, 0]], [[1.0, 0], [97.73128404753176, 0], [3125.0, 0]], [[1.0, 0], [-139.55833902746903, 0], [16807.0, 0]], [[1.0, 0], [-533.092386742604, 0], [161051.0, 0]], [[1.0, 0], 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'positive_zeros': ['4.06582300883637220147848087199185', '4.97366964083269778478972425767756', '6.79019200518989928730526496807612', '8.549307801629179520181945231379333', '11.12418386082560822681824002023393', '11.80070269425034457392820771437841', '12.51840770723615562574405252373157', '14.58240123089896895347008893515885', '15.06651560583581579760084873537396'], 'prelabel': '2-29-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.156648041423644, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.06582300883637220147848087199', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.97366964083269778478972425768', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.79019200518989928730526496808', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.65113077457644, 'bad_primes': [29], 'central_character': '1.1', 'conductor': 29, 'conductor_radical': 29, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/29/6/a/a/1/4'], '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': '2-29-1.1-c5-0-10', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-29-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.156648041423644, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '4.06582300883637220147848087199', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5154042977573172874925767420006', 'Lhash_array': ['5154042977573172874925767420006'], 'label': '2-29-1.1-c5-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/29/6/a/a/1/4'}