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lfunc_lfunctions • Show schema
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{'Lhash': '4459756691718826748205068718628', 'a10': [1.5702338143899117, 3.7145527431262524], 'a2': [0.1744317384564385, -1.403414966650657], 'a3': [0.618109205827941, -1.6180052563792098], 'a4': [-1.9391471372381293, -0.4896002248173175], 'a5': [-2.4695801500447594, 1.4258127644136982], 'a6': [-2.1629149295935197, -1.149695180185365], 'a7': [-1.0203167421013688, -2.4410968325299285], 'a8': [-1.0253610894554226, 2.6360262965742183], 'a9': [-2.235882019341504, -2.0002078880919747], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.1744317384564385, 1.403414966650657]]], [3, [[1.0, 0], [-0.618109205827941, 1.6180052563792098]]], [7, [[1.0, 0], [1.0203167421013688, 2.4410968325299285]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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[0.5320281330877119, 0.9214997575639335], [-53.5, 92.66471820493493]], [[1.0, 0], [7.858740909850912, 4.537246179793948], [54.5, 94.39676901250381]], [[1.0, 0], [0, -16.812577504451276], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-168-168.101-c1-0-27', '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/168/2/ba/c/101/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9630306631697851, 1.1048000500138844, 1.2670499120760392, 1.4537793639323684, 1.667305518057004, 1.9081091622221682, 2.174792446298344, 2.4640777117965995, 2.770814818615044, 3.088002802068618, 3.4068541523445335, 3.7169366086550153, 4.006423720919334, 4.262476274425494, 4.471764551305203, 4.6211274500835735, 4.698349322065675, 4.693019677741517, 4.597425618676088, 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'5.53549813715434181180735773745345', '7.07312742223068903209976252968187', '8.277094138072261691484357728228808', '9.012555758003547177491952657521310', '9.736037450187798928979178102674020', '11.41571871617959118607790724170316', '12.36779620266598931176701661862953', '13.31553701967501104817411362434528'], 'prelabel': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.9012049763512808, 'root_number': '-0.9522194967155883 + 0.30541452171550676*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.450602488176', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.51812770089477855226107331126', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.50329988885137505341073685553', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.53549813715434181180735773745', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/14'], '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': '2-168-168.101-c1-0-27', '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': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.4506024881756404, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.51812770089477855226107331126', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4459756691718826748205068718628', 'Lhash_array': ['4459756691718826748205068718628'], 'label': '2-168-168.101-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/14'}