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lfunc_lfunctions • Show schema
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{'Lhash': '1313351814757624747370570096291', 'a10': [-0.8660254037844386, 0.5], 'a2': [0.9659258262890683, 0.25881904510252074], 'a3': [-1.0581408887153845, -1.3712541192749856], 'a4': [0.8660254037844386, 0.5], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [-0.6671789305190069, -1.5983967826142276], 'a7': [1.2710030035423212, 4.743447785792589], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [-0.7606757192572327, 2.90196010484853], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [3, [[1.0, 0], [1.0581408887153845, 1.3712541192749856]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [13, [[1.0, 0], [-0.5288859754122152, -3.5665501012900784]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.11', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 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[35.50704155516198, 20.5]], [[1.0, 0], [2.6386808787331373, 1.5234431156420951], [21.5, 37.239092362730865]], [[1.0, 0], [-4.773364401355432, -4.773364401355432], [0, 47.0]], [[1.0, 0], [0, 13.305480957759015], [-53.0, 0]], [[1.0, 0], [-0.8595645580497164, 0.2303196291718364], [51.09549882328188, -29.5]], [[1.0, 0], [-3.165914382738975, 5.483524563316966], [-30.5, -52.827549630850754]], [[1.0, 0], [-1.4737114997434333, 5.499966192741022], [-58.023702053557386, -33.5]], [[1.0, 0], [-3.5663313572349007, -13.309729821826721], [-61.48780366869514, 35.5]], [[1.0, 0], [-6.706068372228437, 6.706068372228437], [0, -73.0]], [[1.0, 0], [6.322161856406629, 0], [79.0, 0]], [[1.0, 0], [-3.442193261528941, 3.442193261528941], [0, -83.0]], [[1.0, 0], [-2.9743139469774946, 11.100290767780734], [-77.07626093681505, -44.5]], [[1.0, 0], [-10.571458059283172, 2.8326136498044097], [84.00446416709055, -48.5]], [[1.0, 0], [2.5353184771093193, 4.391300415721493], [-50.5, 87.4685657822283]], [[1.0, 0], [0, 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['1.03605190146335846958149703785679', '3.56542975911442150098538703352207', '4.12903229091127952366098128460291', '5.12803781161468778161508924277291', '6.14850306747177827072613703692323', '7.38155937438283627835994075753810', '8.268472337832233441592690164752869', '9.870156628547318103087480106384411', '10.50446998433516149653904493313881', '11.02212383531061754430465086594545'], 'prelabel': '2-390-39.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.2683514836930318, 'root_number': '0.6651877794897342 - 0.7466761131960208*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.134175741847', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03605190146335846958149703786', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.56542975911442150098538703352', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12903229091127952366098128460', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '39.11', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bh/b/11/7'], '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': '2-390-39.11-c1-0-6', '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': '2-390-39.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.1341757418465159, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03605190146335846958149703786', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1313351814757624747370570096291', 'Lhash_array': ['1313351814757624747370570096291'], 'label': '2-390-39.11-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bh/b/11/7'}