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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_833.61', 'a10': [0.9789183458976485, -0.20425198178968035], 'a2': [-0.9165622558699762, 0.39989202431974097], 'a3': [-0.949894146672846, 0.3125717679456445], 'a4': [0.6801727377709194, -0.7330518718298263], 'a5': [-0.9789183458976485, -0.20425198178968035], 'a6': [0.7456421648831656, -0.6663465779520039], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.3302790619551671, 0.9438833303083676], 'a9': [0.8045977797666684, -0.5938201855735016], 'algebraic': True, 'analytic_conductor': 3.8684357367556994, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [17, [1]]], 'bad_primes': [7, 17], 'central_character': '833.61', 'coeff_info': ['x^336 - 1', '0.999825160912746 + 0.0186988664309023*I', '\\\\zeta_{336}'], 'conductor': 833, 'conductor_radical': 119, 'conjugate': 'dirichlet_L_833.437', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^146', 'a^151', 'a^292', 'a^179', 'a^297', 0, 'a^102', 'a^302', 'a^325', 'a^265', 'a^107', 'a^132', 0, 'a^330', 'a^248', 0, 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-833-833.61-r0-0-0', 'leading_term': '0.0841110414078308671059444066893-0.168302189690384373161673554490*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/833/61', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.18814965942378944, -0.17773815511297983, -0.5684330631550994, -0.5629128581340976, 0.3510079358770875, 2.1671832712237546, 4.053149202672503, 4.679347117107768, 3.1213154389824442, -0.2623068944647034, -3.756280580301741, -5.310165789862438, -4.03438751316468, -0.9798962594984273, 1.5792158606395774, 1.9193103930062239, 0.24117300325496113, -1.5977773841656489, -1.8125369429866467, -0.3097069588314237, 1.3432088524896622, 1.5724670804260024, 0.4151067627670329, -0.5733667142846696, -0.042963297202748996, 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'191.2040526405019979467554860307', '191.850967772710636546111019750539', '192.42819543319474496785271550095', '192.99935110985196986372252769090', '193.65508633399273119128881204671', '194.5943265585801635349075244145', '195.07515496803581634104489473139', '195.51529587947471264440262882215', '196.19485453328272902953851869163', '196.94616816070444064039511576784', '197.59316208172813401300144747291', '198.36028475677280467047642418649', '198.82140202116152343497282299948', '199.317269563974144012384603056428', '199.779182366407170683684682836401'], 'prelabel': '1-833-833.61-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8684357367556994, 'root_angle': -0.3524769905626423, 'root_number': '-0.600304606594271478498423037558-0.799771454417883654520975210227*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.352476990563', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(336)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.397453280852346873928547976364+0.0142320607124596510814624312315*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.170028592292', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.16543550618', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.79090299851', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8684357367556994, 'bad_primes': [7, 17], 'central_character': '833.61', 'conductor': 833, 'conductor_radical': 119, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/833/61'], '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': '1-833-833.61-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': '1-833-833.61-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8684357367556994, 'root_angle': -0.3524769905626423, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.170028592292', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_833.61', 'Lhash_array': ['dirichlet_L_833.61'], 'factors': ['1-833-833.61-r0-0-0'], 'label': '1-833-833.61-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/833/61'}
Lfunction data - 1-833-833.61-r0-0-0