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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_953.952', 'a10': [-1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 4.425713393911383, 'analytic_normalization': 0, 'bad_lfactors': [[953, [1]]], 'bad_primes': [953], 'central_character': '953.952', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 953, 'conductor_radical': 953, 'conjugate': 'dirichlet_L_953.952', 'degree': 1, 'dirichlet_coefficients': [1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1], 'euler_factors': [[1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], 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'186.6817084334418416793739416230', '187.150731818546938826224873173892', '187.88152286351747621786682276802', '188.09037490769431455109053607513', '188.90149966991049781771684746175', '189.266291566188146836672205934313', '190.11159978068206103976551470857', '190.83478097029672534681010586064', '191.7903577855929006296206559265', '192.20838635970838890610176447383', '192.486961779575629225076929677838', '193.71073543190420166659896479178', '193.97540259014136418134061422276', '194.55077327881756744112456926598', '195.016325560401047027893383099708', '195.60474897299165872356629500161', '196.08706969944158154144389180261', '196.55821337061149546165154321198', '197.45687583742173510154134771588', '198.44739507533922810364177576437', '198.689242802823228727427323960600', '199.2020956038568480827937199240'], 'prelabel': '1-953-953.952-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.425713393911383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2)', 'symmetry_type': 'orthogonal', 'types': ['DIR'], 'values': [[1, '1.45295536414148277191441519392']], 'z1': {'__RealLiteral__': 0, 'data': '0.981526206314', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.16488559636', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.57237339675', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.425713393911383, 'bad_primes': [953], 'central_character': '953.952', 'conductor': 953, 'conductor_radical': 953, 'degree': 1, 'dirichlet_coefficients': [1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1], 'euler11': [1, -1], 'euler13': [1, 1], 'euler17': [1, 1], 'euler19': [1, -1], 'euler2': [1, 1], 'euler23': [1, -1], 'euler29': [1, 1], 'euler3': [1, -1], 'euler31': [1, -1], 'euler37': [1, 1], 'euler41': [1, 1], 'euler43': [1, -1], 'euler47': [1, -1], 'euler5': [1, -1], 'euler53': [1, 1], 'euler59': [1, 1], 'euler61': [1, -1], 'euler67': [1, 1], 'euler7': [1, 1], 'euler71': [1, 1], 'euler73': [1, 1], 'euler79': [1, 1], 'euler83': [1, 1], 'euler89': [1, -1], 'euler97': [1, -1], 'euler_factors': [[1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, -1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/953/952'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-953-953.952-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-953-953.952-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.425713393911383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.981526206314', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_953.952', 'Lhash_array': ['dirichlet_L_953.952'], 'factors': ['1-953-953.952-r0-0-0'], 'label': '1-953-953.952-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/953/952'}