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lfunc_lfunctions • Show schema
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{'Lhash': '1814546374575769377514909915304', 'a10': [-4.244793292060503, 2.8815027125443775], 'a2': [-1.6223849103934136, -1.6223849103934136], 'a3': [-1.4999846680444144, 0.8660519589676406], 'a4': [0.0, 3.2642655949444896], 'a5': [0.42015016620979906, -2.196240842401825], 'a6': [3.8386221211024876, 1.0284828614109756], 'a7': [-0.8409126279500722, 0.225321859564355], 'a8': [2.0511254239674916, -2.0511254239674916], 'a9': [1.499908008736624, -2.5981293203625824], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.4999846680444144, -0.8660519589676406]]], [5, [[1.0, 0], [-0.42015016620979906, 2.196240842401825]]], [13, [[1.0, 0], [3.594118653808208, 0.28689911527900425]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.59', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '437378283856490038597023754134', 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'3.40433233418198040314288554997774', '5.36053238739459767103717600734811', '6.03452671552486388915262264570842', '6.86079564594797352681701817094366', '7.35710691709483485191895314864022', '8.240741978974871327487473893614754', '9.468221829638358491996698090087239', '10.09643189790255032958492406759386', '10.87637996239642882146671932166159'], 'prelabel': '2-585-585.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.978253790204485, 'root_number': '-0.9976672512006086 - 0.06826460196779721*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.489126895102', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43142469561334659246599596161', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.40433233418198040314288554998', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.36053238739459767103717600735', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '585.59', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/cn/a/59/10'], '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': '2-585-585.59-c1-0-42', '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': '2-585-585.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.4891268951022425, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43142469561334659246599596161', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1814546374575769377514909915304', 'Lhash_array': ['1814546374575769377514909915304'], 'label': '2-585-585.59-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/cn/a/59/10'}