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lfunc_lfunctions • Show schema
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{'Lhash': '3345504690248704548278655925953', 'a10': [4.02450788191539, -3.3920920758264868], 'a2': [1.3299878716350146, 0.48076216708863817], 'a3': [-1.3163746939407006, -1.1256809784093034], 'a4': [1.5377354773924727, 1.2788157027377103], 'a5': [1.860878567454226, -3.2231362255467078], 'a6': [-1.2095775508378712, -2.1300051991741844], 'a7': [-2.4642858405443335, -0.9629617313749844], 'a8': [1.4303633261597068, 2.4400944152178496], 'a9': [0.46568466969494693, 2.9636359068568305], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3299878716350146, -0.48076216708863817]]], [3, [[1.0, 0], [1.3163746939407006, 1.1256809784093034]]], [7, [[1.0, 0], [2.4642858405443335, 0.9629617313749844]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'5.40394982530367621635167047112170', '6.33357032063199911161423096071626', '6.87661745399921300233181208550877', '9.432853044478742984186255192399914', '10.26454078800197126769109459053889', '10.75841332839223646265343357179095', '11.91110363395104464244328785706622', '12.76961904074527533967702372348489'], 'prelabel': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.154829393606534, 'root_number': '0.8840163021899613 + 0.46745607008828866*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0774146968033', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.63913785837073377663798864332', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77104268541213707809565127991', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.40394982530367621635167047112', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/v/a/107/26'], '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': '2-168-168.107-c1-0-21', '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': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.077414696803267, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.63913785837073377663798864332', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3345504690248704548278655925953', 'Lhash_array': ['3345504690248704548278655925953'], 'label': '2-168-168.107-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/v/a/107/26'}