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lfunc_lfunctions • Show schema
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{'Lhash': '556690960333973361130150839093', 'a10': [0.7884019463191834, -1.1740623369481382], 'a2': [-1.1740623369481382, -0.7884019463191834], 'a3': [0, 0], 'a4': [0.7568447420802471, 1.851266063099922], 'a5': [0, 1.0], 'a6': [0, 0], 'a7': [0, 0.6250374810357419], 'a8': [0.5709588607089847, -2.770199628073381], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.68499407297962, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.1740623369481382, 0.7884019463191834]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '2340.1691', 'coefficient_field': 'CDF', 'conductor': 2340, 'conductor_radical': 390, 'conjugate': '1545714215085788294963416571651', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1740623369481382, 0.7884019463191834]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -0.6250374810357419], [-7.0, 0]], 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-4.881678560646659, -4.1571278157719505], 'positive_zeros': ['0.43915173489741260210682303948291', '1.59748511253193290966630894121110', '2.75703642450778456185161558605278', '4.17286663926048989713579695306805', '4.98924616344285586145543547329738', '5.83571581877776384582304515710087', '6.66636806058638326215626565606974', '7.34768356465446118663777166135250', '8.059042426994425573697359367427161', '8.988550929687078976298758546087261'], 'prelabel': '2-2340-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.322614263727406, 'root_angle': -0.4276200288435265, 'root_number': '0.2254339078353551221126407917587398785752313914877112541 - 0.9742584632417008736947112832356766245977296537294112451*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21381001442176326', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43915173489741260210682303948', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.59748511253193290966630894121', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75703642450778456185161558605', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.68499407297962, 'bad_primes': [2, 3, 5, 13], 'central_character': '12.11', 'conductor': 2340, 'conductor_radical': 390, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2340/2/g/a/1691/9'], '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': '2-2340-12.11-c1-0-17', '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': '2-2340-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.322614263727406, 'root_angle': -0.21381001442176326, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43915173489741260210682303948', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '556690960333973361130150839093', 'Lhash_array': ['556690960333973361130150839093'], 'label': '2-2340-12.11-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2340/2/g/a/1691/9'}