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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3381.1235', 'a10': [0.7512790933133434, 0.6599846391775195], 'a2': [-0.15576280242346308, 0.9877944874219481], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9514758987623784, -0.3077232751585818], 'a5': [0.5349078513860724, -0.8449104038450086], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.45217190728268575, -0.8919308080026939], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.701297990361368, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [23, [1]]], 'bad_primes': [3, 7, 23], 'central_character': '3381.1235', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 3381, 'conductor_radical': 483, 'conjugate': 'dirichlet_L_3381.887', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^127', 0, 'a^254', 'a^388', 0, 0, 'a^381', 0, 'a^53', 'a^71', 0, 'a^141', 0, 0, 'a^46', 'a^362', 0, 'a^133', 'a^180', 0, 'a^198', 0, 0, 'a^314', 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'198.98506324270309875228001818710', '199.81360919543565383975686588493'], 'prelabel': '1-3381-3381.1235-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': -0.6289804672285179, 'root_number': '-0.394206330210954124508710851114-0.919021963405452131914513892189*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(462)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.760230079558721810691641107403+0.261072442856422993624027554026*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0557024260723', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.45341710556', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.95312281501', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.701297990361368, 'bad_primes': [3, 7, 23], 'central_character': '3381.1235', 'conductor': 3381, 'conductor_radical': 483, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3381/1235'], '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': '1-3381-3381.1235-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': '1-3381-3381.1235-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.701297990361368, 'root_angle': -0.31449023361425893, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0557024260723', 'prec': 50}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3381.1235', 'Lhash_array': ['dirichlet_L_3381.1235'], 'label': '1-3381-3381.1235-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3381/1235'}
Lfunction data - 1-3381-3381.1235-r0-0-0