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lfunc_lfunctions • Show schema
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{'Lhash': '1564987429663011454457259551889', 'a10': [240.16663785343422, 0.0], 'a2': [-9.606665514137369, 0.0], 'a3': [21.600001463731417, 0.0], 'a4': [60.2880223005162, 0.0], 'a5': [-25.0, 0.0], 'a6': [-207.5039891669453, 0.0], 'a7': [-51.16487560148463, 0.0], 'a8': [-271.75356829751775, 0.0], 'a9': [223.56006323319937, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 97.0322109868533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [25.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 11], 'central_character': '605.1', 'coefficient_field': 'CDF', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'euler_factors': [[[1.0, 0], [9.606665514137369, 0], [32.0, 0]], [[1.0, 0], [-21.600001463731417, 0], [243.0, 0]], [[1.0, 0], [25.0, 0]], [[1.0, 0], [51.16487560148463, 0], [16807.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [495.0376590060124, 0], [371293.0, 0]], [[1.0, 0], [155.80378142515832, 0], [1419857.0, 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['1.23455740042346775826500278630907', '2.48564598623346511984361481987193', '3.11841885563483704923936913500748', '4.55812715747432299586347177773171', '6.36267559289189473904757749227041', '7.39712953019000425263412133612765', '7.83022500536864379586930216982067', '8.642915239116640184387742291101620', '9.420140679529332289505498253503869'], 'prelabel': '2-605-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.850492931161025, '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': '1.23455740042346775826500278631', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48564598623346511984361481987', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11841885563483704923936913501', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 97.0322109868533, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 605, 'conductor_radical': 55, 'degree': 2, 'index': 129, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/605/6/a/p/1/3'], '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': '2-605-1.1-c5-0-129', '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': '2-605-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.850492931161025, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23455740042346775826500278631', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1564987429663011454457259551889', 'Lhash_array': ['1564987429663011454457259551889'], 'label': '2-605-1.1-c5-0-129', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/605/6/a/p/1/3'}