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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_73.3', 'a10': [2.9010907910729803e-30, -1.0], 'a2': [-0.5, -0.8660254037844386], 'a3': [-1.0, -1.4081532572346456e-30], 'a4': [-0.5, 0.8660254037844386], 'a5': [0.8660254037844386, 0.5], 'a6': [0.5, 0.8660254037844386], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 0.33901057476970714, 'analytic_normalization': 0, 'bad_lfactors': [[73, [1]]], 'bad_primes': [73], 'central_character': '73.3', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 73, 'conductor_radical': 73, 'conjugate': 'dirichlet_L_73.49', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^6', 'a^4', 'a^1', 'a^2', 'a^9', 'a^0', 'a^0', 'a^9', 'a^7', 'a^10', 'a^11', 'a^5', 'a^7', 'a^8', 'a^9', 'a^8', 'a^2', 'a^5', 'a^3', 'a^3', 'a^10', 'a^6', 'a^2', 'a^7', 'a^6', 'a^1', 'a^11', 'a^3', 'a^11', 'a^4', 'a^1', 'a^5', 'a^10', 'a^4', 'a^4', 'a^10', 'a^5', 'a^1', 'a^4', 'a^11', 'a^3', 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'191.215409393754400653225687714196', '192.4419748810270883036448495185', '193.302248925897706417950078642738', '193.81716861896467898973978103790', '194.6168718532162016183024827427', '194.93226270932422080677690790037', '196.397147937593648465758661775296', '197.462412693985749587746540762080', '198.11436480254117483105420927891', '199.02603667465974655258577121501', '199.82332609878947793551116122919'], 'prelabel': '1-73-73.3-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.33901057476970714, 'root_angle': -0.42898443235892364, 'root_number': '0.221255788116672359348510656188-0.975215810077374712767142757184*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.214492216179', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.620980760865638225647241861973-0.295521539622866623461735620877*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.1055481035', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.08827488262', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.86086835615', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.33901057476970714, 'bad_primes': [73], 'central_character': '73.3', 'conductor': 73, 'conductor_radical': 73, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/73/3'], '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': '1-73-73.3-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': '1-73-73.3-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.33901057476970714, 'root_angle': -0.21449221617946182, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.1055481035', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_73.3', 'Lhash_array': ['dirichlet_L_73.3'], 'label': '1-73-73.3-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/73/3'}