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lfunc_lfunctions • Show schema
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{'Lhash': '1164488404424482127280820349601,1378061675488418090613190274318', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1353.876826855227, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '4608.1', 'coefficient_field': '1.1.1.1', 'conductor': 21233664, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, -4, 12, -20, 25], [1, -4, 16, -28, 49], [1, -4, 26, -44, 121], [1, 0, 18, 0, 169], [1, -4, 6, -68, 289], [1, 0, 6, 0, 361], [1, 8, 54, 184, 529], [1, -4, 60, -116, 841], [1, -12, 96, -372, 961], [1, -8, 58, -296, 1369], [1, -12, 86, -492, 1681], [1, -8, 70, -344, 1849], [1, 8, 38, 376, 2209], [1, -4, 12, -212, 2809], [1, 8, 134, 472, 3481], [1, -8, 106, -488, 3721], [1, -16, 198, -1072, 4489], [1, 24, 278, 1704, 5041], [1, -8, 130, -584, 5329], [1, -20, 240, -1580, 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0.42247220817070924, -0.15858001370427166, -0.5867466981968195, -0.8428964570239325], 'positive_zeros': ['0.918619376833668659725951051311368', '1.08709898077617771084790018005681', '1.83619650703641114579002383233867', '1.93723054310808572352251286323592', '2.70841013164296153844322149236246', '2.75837890263118224056386816817018', '3.78443940346819520216077468929915', '3.96683080443626455630115761002133', '4.61692563488086584660718316132658', '4.64301621794781698873241075285851', '5.30034851041620303420082673159649', '5.61020677836677848325583594989888', '6.10361659804626254678279783841170', '6.15238525488398953993879243620331', '6.51938349739942481526667437843792', '6.91975511187405688868801555273906', '7.73767693179721289177421371332628', '7.76286562195232263396088706111407', '8.115986525583857272656340209958661', '8.331855736467897710675438440363027'], 'prelabel': '4-4608e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.065893606996913, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1312526666428280606, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.918619376833668659725951051311', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.08709898077617771084790018006', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.83619650703641114579002383234', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1353.876826855227, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 21233664, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -8, 0, 4, 0, 0, 0, 4, 0, 12, 0, 0, 0, 16, 0, 8, 0, 0, 0, 12, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 4, 0, 16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 16, 0, 0, 0, -24, 0, 8, 0, 0, 0, 16, 0, 20, 0, 0, 0, -4, 0, 16, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, -4, 26, -44, 121], 'euler13': [1, 0, 18, 0, 169], 'euler17': [1, -4, 6, -68, 289], 'euler19': [1, 0, 6, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 8, 54, 184, 529], 'euler29': [1, -4, 60, -116, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -12, 96, -372, 961], 'euler37': [1, -8, 58, -296, 1369], 'euler41': [1, -12, 86, -492, 1681], 'euler43': [1, -8, 70, -344, 1849], 'euler47': [1, 8, 38, 376, 2209], 'euler5': [1, -4, 12, -20, 25], 'euler53': [1, -4, 12, -212, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, -8, 106, -488, 3721], 'euler67': [1, -16, 198, -1072, 4489], 'euler7': [1, -4, 16, -28, 49], 'euler71': [1, 24, 278, 1704, 5041], 'euler73': [1, -8, 130, -584, 5329], 'euler79': [1, -20, 240, -1580, 6241], 'euler83': [1, 4, 42, 332, 6889], 'euler89': [1, 4, 182, 356, 7921], 'euler97': [1, -4, 70, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -4, 12, -20, 25], [1, -4, 16, -28, 49], [1, -4, 26, -44, 121], [1, 0, 18, 0, 169], [1, -4, 6, -68, 289], [1, 0, 6, 0, 361], [1, 8, 54, 184, 529], [1, -4, 60, -116, 841], [1, -12, 96, -372, 961], [1, -8, 58, -296, 1369], [1, -12, 86, -492, 1681], [1, -8, 70, -344, 1849], [1, 8, 38, 376, 2209], [1, -4, 12, -212, 2809], [1, 8, 134, 472, 3481], [1, -8, 106, -488, 3721], [1, -16, 198, -1072, 4489], [1, 24, 278, 1704, 5041], [1, -8, 130, -584, 5329], [1, -20, 240, -1580, 6241], [1, 4, 42, 332, 6889], [1, 4, 182, 356, 7921], [1, -4, 70, -388, 9409]], 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4608/2/a/r'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '4-4608e2-1.1-c1e2-0-44', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-4608e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.065893606996913, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1312526666428280606, 'z1': {'__RealLiteral__': 0, 'data': '0.918619376833668659725951051311', 'prec': 107}}
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{'Lhash': '1164488404424482127280820349601,1378061675488418090613190274318', 'Lhash_array': ['1164488404424482127280820349601', '1378061675488418090613190274318'], 'label': '4-4608e2-1.1-c1e2-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4608/2/a/r'}