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lfunc_lfunctions • Show schema
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{'Lhash': '429024041548394853906737877777', 'a10': [10.7915619758885, -18.691533635267266], 'a2': [-2.1583123951777, -3.738306727053453], 'a3': [2.5, -4.330127018922194], 'a4': [-5.3166247903554, 9.208664261675784], 'a5': [2.5, 4.330127018922194], 'a6': [-21.583123951777, 5.910099029011399e-61], 'a7': [0.0, 0.0], 'a8': [11.3667504192892, 0.0], 'a9': [1.0, 1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.455467951406456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-2.5, -4.330127018922194]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 7], 'central_character': '245.116', 'coefficient_field': 'CDF', 'conductor': 245, 'conductor_radical': 35, 'conjugate': '2021438521935729287209633391500', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1583123951777, 3.738306727053453], [-4.0, 6.928203230275509]], [[1.0, 0], [-2.5, 4.330127018922194], [-13.5, -23.382685902179844]], [[1.0, 0], [-2.5, 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[0]], 'group': 'GL2', 'index': 3, 'label': '2-245-7.4-c3-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/245/4/e/k/116/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7160736822322212, 0.4939442514841723, 0.2218671114054696, -0.0985946881848239, -0.4645936154858951, -0.8716118590180203, -1.3130559641989825, -1.7798893378240237, -2.2603639262671584, -2.7399113386407636, -3.201247779228575, -3.624736349575036, -3.9890345187960916, -4.272033913323977, -4.45207448550521, -4.50938661076162, -4.427684482538457, -4.195804809333682, -3.8092593830783366, -3.2715520865913565, -2.595103880236086, -1.8016363917772666, -0.921888174930484, 0.005421628809056824, 0.9354105180382338, 1.819588766955664, 2.6090340651070005, 3.257984822655682, 3.727580490152926, 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'10.07064773681684615662496169504976', '11.43644783679691121236575044786405'], 'prelabel': '2-245-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.802034712020191, 'root_angle': -0.04034590610789225, 'root_number': '0.9919779164085226 - 0.12641128651274003*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0201729530539', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33844029377744374373785922247', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87427635825839520143647599459', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.63193146403438664272575340892', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.455467951406456, 'bad_primes': [5, 7], 'central_character': '7.4', 'conductor': 245, 'conductor_radical': 35, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/245/4/e/k/116/1'], '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': '2-245-7.4-c3-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-245-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.802034712020191, 'root_angle': -0.020172953053946126, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.33844029377744374373785922247', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '429024041548394853906737877777', 'Lhash_array': ['429024041548394853906737877777'], 'label': '2-245-7.4-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/245/4/e/k/116/1'}