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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_173.40', 'a10': [0.10937120837787438, -0.9940009752399459], 'a2': [0.03652202305765884, 0.9993328483702394], 'a3': [-0.8339978178898779, -0.5517677407704459], 'a4': [-0.9973322836635516, 0.07299531466090753], 'a5': [-0.9893433680751103, -0.14560116773500487], 'a6': [0.5209403404879303, -0.8535930890373464], 'a7': [0.3228804047714462, 0.9464397731576093], 'a8': [-0.10937120837787438, -0.9940009752399459], 'a9': [0.391104720490156, 0.9203461835691594], 'algebraic': True, 'analytic_conductor': 0.803408622399443, 'analytic_normalization': 0, 'bad_lfactors': [[173, [1]]], 'bad_primes': [173], 'central_character': '173.40', 'coeff_info': ['x^86 - 1', '0.997332283663552 + 0.0729953146609075*I', '\\\\zeta_{86}'], 'conductor': 173, 'conductor_radical': 173, 'conjugate': 'dirichlet_L_173.13', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^21', 'a^51', 'a^42', 'a^45', 'a^72', 'a^17', 'a^63', 'a^16', 'a^66', 'a^53', 'a^7', 'a^64', 'a^38', 'a^10', 'a^84', 'a^71', 'a^37', 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'186.56032978560172503510482418765', '187.077683541752202428401102345647', '187.68748684036609904711129823337', '188.8305332042917239479263323674', '189.0103333964849344936649160909', '189.61687390540815797697944979841', '190.504197431352618075058759072730', '191.369787150875766068293571639058', '191.66267068706844897696969112013', '193.22826004669600453642667041090', '193.795810200781156146050184228892', '194.703786535433988895107559842570', '195.190296779001092542591234904850', '195.74963689340386204767794063962', '196.54127014063378163902526515295', '196.82752977909228015388475138204', '198.17698648635664284431844289057', '198.92532666370495422507442693568', '199.42839447929670428558331181032', '199.76761071165238727745593562059'], 'prelabel': '1-173-173.40-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.803408622399443, 'root_angle': -0.03971642401265319, 'root_number': '0.992225964496107590620604772521-0.124449328562949824584311520646*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0198582120063', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(86)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.633447253156855878855475785071+0.127635897183508955403706540378*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.641165896644', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '3.14980596845', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.06176405887', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.803408622399443, 'bad_primes': [173], 'central_character': '173.40', 'conductor': 173, 'conductor_radical': 173, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/173/40'], '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': '1-173-173.40-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': '1-173-173.40-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.803408622399443, 'root_angle': -0.019858212006326596, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.641165896644', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_173.40', 'Lhash_array': ['dirichlet_L_173.40'], 'label': '1-173-173.40-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/173/40'}
Lfunction data - 1-173-173.40-r0-0-0