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lfunc_lfunctions • Show schema
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{'Lhash': '2258544694661433520375295680611', 'a10': [0.0, 0.0], 'a2': [0.6234898018587335, -0.7818314824680298], 'a3': [1.6234898018587336, 0.7818314824680298], 'a4': [-0.2225209339563144, -0.9749279121818236], 'a5': [0.0, 0.0], 'a6': [1.6234898018587336, -0.7818314824680298], 'a7': [-0.9009688679024191, -0.4338837391175581], 'a8': [-0.9009688679024191, -0.4338837391175581], 'a9': [1.400968867902419, 1.7567593946498534], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6234898018587335, 0.7818314824680298]]], [7, [[1.0, 0], [0.9009688679024191, 0.4338837391175581]]], [17, [[1.0, 0], [0.2225209339563144, -0.9749279121818236]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.2787', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1638098572882497237244470331304', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[[1.0, 0], [-0.40096886790241915, -1.7567593946498534], [-0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [-0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.40096886790241915, -1.7567593946498534], [-0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [-1.246979603717467, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [1.1234898018587336, 1.4088116512993818], [-0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.1234898018587336, 0.5410441730642654], [0.6234898018587335, 0.7818314824680298]], [[1.0, 0], [0, 0], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0.2774790660436856, 0.3479477433504717], [-0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [0, 0], [0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-3332-3332.2787-c0-0-3', 'leading_term': '2.7944726369871329233481779854937', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/be/b/2787/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.794472636987133, 2.855724648596572, 2.9381523885267584, 3.0409766965466747, 3.162168658862214, 3.2986924488243257, 3.4467877827836952, 3.602236583711537, 3.7605829989450132, 3.9172991567311986, 4.067903675949792, 4.2080457615607045, 4.333567734048368, 4.440556183946612, 4.525388665396131, 4.584779930391106, 4.615829464329684, 4.6160704953238465, 4.5835195858567594, 4.516725238242988, 4.414813544255928, 4.277528705940158, 4.105266197647238, 3.8990963965240653, 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'6.33066190217200478284695899442965', '6.81375933264209262423243254518631', '7.27780830565181572790483934943711', '8.073406986954312727797597961171538', '8.969187130111730971453306582358262'], 'prelabel': '2-3332-3332.2787-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.32653061224489793, 'root_number': '0.51839256831052503153847431467515 + 0.85514276300534616571883696203789*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.16326530612244897', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78167761231273215605079634324', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57563752139687124372397925501', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.59836164524781691976066744660', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '3332.2787', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/be/b/2787/1'], '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': '2-3332-3332.2787-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-3332.2787-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.16326530612244897, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78167761231273215605079634324', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2258544694661433520375295680611', 'Lhash_array': ['2258544694661433520375295680611'], 'label': '2-3332-3332.2787-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/be/b/2787/1'}