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lfunc_lfunctions • Show schema
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{'Lhash': '862461144034793049801464819822', 'a10': [-1.9496858291468608, 3.3769549148794167], 'a2': [0.8660254037844386, -0.5], 'a3': [-0.6628271480711836, -0.3826834323650898], 'a4': [0.5, -0.8660254037844386], 'a5': [-3.3769549148794167, 1.9496858291468608], 'a6': [-0.7653668647301796, 0], 'a7': [0, 0], 'a8': [0, -1.0], 'a9': [-1.2071067811865475, -2.0907702751760278], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.607873337894029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-2.7588056345200664, -1.8409213646813747]]]], 'bad_primes': [2, 7, 11], 'central_character': '1078.1011', 'coefficient_field': 'CDF', 'conductor': 1078, 'conductor_radical': 154, 'conjugate': '1405643049688017886321955905501', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0.6628271480711836, 0.3826834323650898], [1.5, 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'group': 'GL2', 'index': 11, 'label': '2-1078-77.10-c1-0-11', 'leading_term': '1.406948955105163717357975712201140864441674560098752654', '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/1078/2/i/d/1011/11', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.4069489551051637, 1.3534027070764696, 1.289820323158814, 1.2155783473721367, 1.129862187765771, 1.0317170074597553, 0.9201073850764526, 0.7939824919075983, 0.6523436755255115, 0.49431172792672085, 0.31919161769081444, 0.1265329624167793, -0.08381506932559832, -0.3116554434888777, -0.5564023747654434, -0.8170486288438807, -1.0921417489269278, -1.379769942937587, -1.6775583607683653, -1.9826764534675503, -2.2918570230405404, -2.601427434129832, -2.9073532644893136, -3.205294421675793, -3.490673454075396, 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'7.46884554277099681179269564557303', '8.113966054921979678550699231083389', '8.692159979398577548997445345484793', '9.818061797033351496721294093319349'], 'prelabel': '2-1078-77.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.09241045938198307, 'root_number': '0.9581534609542300204553851522315327019862351540712284864 - 0.2862550353468577984990528065219292222510962676307059764*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.046205229690991535', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68036187880123629129468809227', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77672592247592585052915246223', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.02691167307305212927269343698', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.607873337894029, 'bad_primes': [2, 7, 11], 'central_character': '77.10', 'conductor': 1078, 'conductor_radical': 154, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1078/2/i/d/1011/11'], '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': '2-1078-77.10-c1-0-11', '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': '2-1078-77.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9339177455910432, 'root_angle': -0.046205229690991535, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68036187880123629129468809227', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '862461144034793049801464819822', 'Lhash_array': ['862461144034793049801464819822'], 'label': '2-1078-77.10-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1078/2/i/d/1011/11'}