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lfunc_lfunctions • Show schema
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{'Lhash': '892535242580755552804940303938', 'a10': [1.714974177442458, 1.4348740609215724], 'a2': [-0.5, -0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, 0.8660254037844386], 'a5': [-2.100124476710651, 0.7677741740387042], 'a6': [0, 0], 'a7': [0.8230627601526622, -1.4255865184022878], 'a8': [1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.34249703648981, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.100124476710651, -0.7677741740387042]]], [13, [[1.0, 0], [3.5964328992149888, 0.2562623683728636]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1170.829', 'coefficient_field': 'CDF', 'conductor': 1170, 'conductor_radical': 390, 'conjugate': '1103280496229334188304281638214', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.100124476710651, 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'group': 'GL2', 'index': 11, 'label': '2-1170-65.49-c1-0-11', 'leading_term': '0.980100411967956225566495041261374369348321019122300691', '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/1170/2/bj/c/829/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.9801004119679563, 0.9633054411130817, 0.9369325482964079, 0.9005251996344817, 0.8534682623324154, 0.7950232364988841, 0.7243736693865516, 0.6406781564425033, 0.5431282279687967, 0.43100855974974217, 0.30375723227611157, 0.16102409784411284, 0.0027256227749401832, -0.1709051889852573, -0.3592750260447933, -0.5613937995943274, -0.7758465762918778, -1.0007749923853682, -1.2338691951867606, -1.4723712966293683, -1.713091217404301, -1.9524356390879012, -2.1864505609457145, -2.410877677441798, -2.621224455457555, 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'7.58356077007524557947730605289260', '7.948372826797698136277953452421788', '9.042262225715370975134152524010321', '9.420699568258027531482783999986364'], 'prelabel': '2-1170-65.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': 0.08182657481295691, 'root_number': '0.9671401512966958876551901991009469334411855860371885065 + 0.2542438352247782383506111832133015556143592174573984336*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.040913287406478455', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70408615940391018632584839452', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48769828230872838315769937020', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73054984427531087639604943651', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.34249703648981, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.49', 'conductor': 1170, 'conductor_radical': 390, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1170/2/bj/c/829/1'], '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': '2-1170-65.49-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': '2-1170-65.49-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0565498583353437, 'root_angle': 0.040913287406478455, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70408615940391018632584839452', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '892535242580755552804940303938', 'Lhash_array': ['892535242580755552804940303938'], 'label': '2-1170-65.49-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1170/2/bj/c/829/1'}