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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1573.424', 'a10': [0.41541501300188644, -0.9096319953545183], 'a2': [0.057088810862767986, 0.9983691039261356], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [-0.9934817353485502, 0.11399140989054063], 'a5': [-0.8844329309978143, -0.4666673232256737], 'a6': [-0.9318640292114523, 0.362807705350641], 'a7': [-0.3892701063173915, -0.9211236531148501], 'a8': [-0.17052219263262378, -0.985353835847693], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 7.304981289215744, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '1573.424', 'coeff_info': ['x^220 - 1', '0.999592192828189 + 0.0285560507936963*I', '\\\\zeta_{220}'], 'conductor': 1573, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_1573.486', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^53', 'a^44', 'a^106', 'a^127', 'a^97', 'a^151', 'a^159', 'a^88', 'a^180', 0, 'a^150', 0, 'a^204', 'a^171', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-1573-1573.424-r0-0-0', 'leading_term': '0.0209357958032513135957695270956+0.708241044078278333598615647829*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/1573/424', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.7085504103894132, -1.3481661448571733, -1.5265385264780247, -0.16100634317577303, 3.175744577349992, 7.390768042028453, 10.239965752827722, 9.842684503169108, 6.247884021948105, 1.6205999670440352, -1.361640846146729, -1.6285169549309422, -0.3935511433835666, 0.3072296140099563, -0.25075909719980877, -0.9232047918411744, -0.3118008662343391, 1.3140650690024755, 2.1164603811907488, 0.8390854126809562, -1.5014404720506591, -2.557191887436768, -1.3035579145279022, 0.7419886697661149, 1.3247654562275506, 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'194.141729272245257353271826228503', '194.47234384960937082162000766002', '195.020328702339735472439158831672', '195.72294873192704895802949107294', '196.419153789926063121725336384441', '196.86013559221692191262066413940', '197.37783059466404423881346160670', '198.10483983446641666826852162677', '198.665762841975605720304989810297', '198.72041817907994107827057881522', '199.62446861578997198507907677931'], 'prelabel': '1-1573-1573.424-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.304981289215744, 'root_angle': -0.4905934133453117, 'root_number': '-0.998253906742264966677673279424-0.0590689230797833227531755767705*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.490593413345', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(220)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.597078697181122485045346752811+0.504349397260721923058275061659*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.957916470106', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.94871919184', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.86156808232', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 7.304981289215744, 'bad_primes': [11, 13], 'central_character': '1573.424', 'conductor': 1573, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1573/424'], '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': '1-1573-1573.424-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': '1-1573-1573.424-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.304981289215744, 'root_angle': -0.4905934133453117, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.957916470106', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1573.424', 'Lhash_array': ['dirichlet_L_1573.424'], 'factors': ['1-1573-1573.424-r0-0-0'], 'label': '1-1573-1573.424-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1573/424'}
Lfunction data - 1-1573-1573.424-r0-0-0