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lfunc_lfunctions • Show schema
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{'Lhash': '4077643281430473646039693100455', 'a10': [0.0, 0.0], 'a2': [1.2281016272920902, -2.127134415327917], 'a3': [0.7805223727225773, -1.3519044059997163], 'a4': [-2.0164672139149595, -3.4926236662975696], 'a5': [0.0, 0.0], 'a6': [-1.9171215921569609, -3.320552001903196], 'a7': [-4.505274079010705, 0.0], 'a8': [-4.993300157992075, 0.0], 'a9': [0.2815696513590363, 0.487692942023306], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-3.7980368652739958, 2.1389053204898247]]]], 'bad_primes': [5, 19], 'central_character': '475.201', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '1184119664968232930793144542683', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2281016272920902, 2.127134415327917], [-1.0, -1.7320508075688772]], [[1.0, 0], [-0.7805223727225773, 1.3519044059997163], [-1.5, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-475-19.11-c1-0-27', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/475/2/e/g/201/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.003713107708047, 2.3355276097885422, 2.710199235851386, 3.133594922238691, 3.6069774400982832, 4.126334049156469, 4.682180699907867, 5.259708878686089, 5.839206627126975, 6.396760166177654, 6.905280145664546, 7.335890830523372, 7.65968378322558, 7.849783907496847, 7.883616233772296, 7.745205342872686, 7.427293622258781, 6.933036971016356, 6.277033728253859, 5.485469535507939, 4.595219955936893, 3.6518427031267104, 2.706506646425139, 1.8120351359103068, 1.0183722682608536, 0.3678951900835703, -0.10892492757524758, -0.39698288696929895, -0.4986267940716714, 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'9.437302261584886238329526965426847', '10.18643917463953540024314812361868', '11.94248107191329901240153117013960'], 'prelabel': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.8976783131621969, 'root_number': '-0.9487773321604139 - 0.3159455237514334*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.448839156581', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.21669337015762043844747614566', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.85958298314530095996770122887', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82542413865052279038440116412', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.11', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/e/g/201/6'], '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': '2-475-19.11-c1-0-27', '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': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.44883915658109846, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.21669337015762043844747614566', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4077643281430473646039693100455', 'Lhash_array': ['4077643281430473646039693100455'], 'label': '2-475-19.11-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/e/g/201/6'}