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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_311.185', 'a10': [-0.8743466161445821, -0.48530196253108104], 'a2': [0.15142777750457667, -0.9884683243281114], 'a3': [0.15142777750457667, 0.9884683243281114], 'a4': [-0.9541392564000488, -0.29936312297335793], 'a5': [0.3473052528448203, -0.9377521321470804], 'a6': [1.0, 0.0], 'a7': [-0.25065253225872053, 0.9680771188662043], 'a8': [-0.4403941515576343, 0.8978045395707417], 'a9': [-0.9541392564000488, 0.29936312297335793], 'algebraic': True, 'analytic_conductor': 33.421591611128385, 'analytic_normalization': 0, 'bad_lfactors': [[311, [1]]], 'bad_primes': [311], 'central_character': '311.185', 'coeff_info': ['x^62 - 1', '0.994869323391895 + 0.101168321987432*I', '\\\\zeta_{62}'], 'conductor': 311, 'conductor_radical': 311, 'conjugate': 'dirichlet_L_311.116', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^48', 'a^14', 'a^34', 'a^50', 'a^0', 'a^18', 'a^20', 'a^28', 'a^36', 'a^55', 'a^48', 'a^28', 'a^4', 'a^2', 'a^6', 'a^5', 'a^14', 'a^43', 'a^22', 'a^32', 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[[1], []], 'index': 0, 'label': '1-311-311.185-r1-0-0', 'leading_term': '0.635025248017788636418606337077-1.21527560656191467470087593633*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/311/185', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.3711862986204624, 0.36010095667271097, -0.7643195293413613, -1.6653064414935124, -2.0079202471543294, -1.6219489275675705, -0.6574043159945381, 0.41601245109944085, 1.0250218269605726, 0.8307108173500846, -0.023696996200588148, -0.9547963309929812, -1.3011591718990507, -0.7991600729682209, 0.1698305006578671, 0.8018936431465211, 0.4851673204331648, -0.6034409834647785, -1.4091527812004836, -0.609702539499388, 2.4010672846358068, 6.846960659962487, 10.794747401167278, 12.25223298793135, 10.447280599512595, 6.372750341530845, 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'192.5505985965008613767440808171', '193.05427449798470394695991332527', '193.49539450786722692755602294481', '194.41367490028518282001202998047', '194.950225341098899537954070554019', '196.04441347785685848174909676996', '196.36807449659026661318643343722', '197.227377060025181616557333030346', '198.12265693754322158060128065983', '198.98677549471441860758041906348', '199.365008515609989642689993376914'], 'prelabel': '1-311-311.185-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 33.421591611128385, 'root_angle': -0.6934590253968594, 'root_number': '-0.571037773049718891849876966883-0.820923785591828092233497872187*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.346729512698', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(62)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.944637588158553214973792086135-0.403769578139627704739953562551*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.411845635069', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.0590926341', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.11768005224', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.421591611128385, 'bad_primes': [311], 'central_character': '311.185', 'conductor': 311, 'conductor_radical': 311, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/311/185'], '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': '1-311-311.185-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-311-311.185-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 33.421591611128385, 'root_angle': -0.3467295126984297, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.411845635069', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_311.185', 'Lhash_array': ['dirichlet_L_311.185'], 'label': '1-311-311.185-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/311/185'}