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lfunc_lfunctions • Show schema
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{'Lhash': '2188358106618421795541950776855', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.449489742783178, 4.58257569495584], 'a4': [0, 0], 'a5': [-2.3146441975848298, 0], 'a6': [0, 0], 'a7': [0, -29.663568003794833], 'a8': [0, 0], 'a9': [-15.0, 22.44994432064365], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.656733442204406, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-2.449489742783178, -4.58257569495584]]]], 'bad_primes': [2, 3], 'central_character': '384.191', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '335338223122751794711554442822', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.449489742783178, -4.58257569495584]], [[1.0, 0], [2.3146441975848298, 0], [125.0, 0]], [[1.0, 0], [0, 29.663568003794833], [-343.0, 0]], [[1.0, 0], [0, -22.83484861008832], [-1331.0, 0]], [[1.0, 0], [0, 8.66060555964672], [-2197.0, 0]], [[1.0, 0], 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-0.6233996402987358, -0.09501542979590233, 0.40785826220346266], 'positive_zeros': ['1.72631015693474768333407764614231', '2.69859829696648727389772793428625', '4.02488526074733755609183165296142', '5.88955573795951463806507885788605', '6.14133389421716299519781644810857', '7.64408192591979163812349114311559', '8.519301196027412857556618816213039', '8.924022183824225753139877470121568', '10.22806910786470177981546215592565', '11.57286346153625284928903426548717'], 'prelabel': '2-384-24.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.759908974151124, 'root_angle': 0.593747190544135, 'root_number': '-0.290276231128990230930624788719424883626003301296454491 + 0.956942897795656897597291455386091550292669967963121158*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2968735952720675', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72631015693474768333407764614', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69859829696648727389772793429', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.02488526074733755609183165296', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.656733442204406, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/4/f/g/191/8'], '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': '2-384-24.11-c3-0-39', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-384-24.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.759908974151124, 'root_angle': 0.2968735952720675, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72631015693474768333407764614', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2188358106618421795541950776855', 'Lhash_array': ['2188358106618421795541950776855'], 'label': '2-384-24.11-c3-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/4/f/g/191/8'}