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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': -1, 'A8': -1, 'A9': 0, 'Lhash': '827562833426597742', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1816.0376931699807, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, 1]], [7, [1, 1]], [19, [1]]], 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '227430.1', 'coefficient_field': '1.1.1.1', 'conductor': 227430, 'conductor_radical': 3990, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 1], [1, 1], [1, 3, 11], [1, 6, 13], [1, 2, 17], [1], [1, -1, 23], [1, -1, 29], [1, 2, 31], [1, 2, 37], [1, 3, 41], [1, -7, 43], [1, 6, 47], [1, -2, 53], [1, -6, 59], [1, -10, 61], [1, 9, 67], [1, -8, 71], [1, -5, 73], [1, -5, 79], [1, 5, 83], [1, -15, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 16, 'label': '2-227430-1.1-c1-0-16', 'leading_term': '0.589516723087', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/227430/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.5895167230867614, 0.1362453287634855, -0.7050222598705413, -0.6902474472519201, 0.9908611359491973, 3.363758687230153, 4.12683085877421, 2.302063494958709, -0.07258751990988414, -0.2590904386846185, 1.281996699339175, 1.34038869887932, -0.9097696338312993, -1.834626452730199, 1.16175983009206, 4.438000429526997, 2.702615416830031, -2.386278282786953, -3.910109698015982, -0.4295077927151111, 1.703212567043858, -0.7968363812279173, -2.371601065204262, 1.469974936180177, 5.67361536285145, 4.034786702678577, -0.2826933604165323, -0.8507437468841361, 1.081156493764977, 0.6780505078846321, -0.8572551741281988, -0.06794037710860282, 0.7955022063452868, -1.188155555222095, -2.629295960975644, -0.5827773485620655, 0.9304615075743363, -0.9107638496128196, -1.876733286783691, 0.1617627340149315, 0.8609832269475418, -0.6480782465374558, 0.103677313206666, 2.09125020107509, 0.2694770866152063, -2.567909988873067, -0.8261596699858352, 1.469203930757239, -0.8236870401529648, -2.307588369051728, 0.8725116260355916, 1.886335242240485, -0.715647536197152, 1.997813130469609, 8.54193126027103, 6.473516339983208, -2.165449202901054, -3.333069269671729, 1.843458191058836, 1.719348207555537, -1.624219685677854, -0.2082082758248897, 1.811807240785698, -0.06044662164618843, -0.2249026686021078, 2.286363606572545, 1.392497814607283, -0.8036134018261629, 0.8206899784989578, 1.733396478197749, -0.9826244836401142, -1.363987694869977, 0.6402009152425127, -0.8460236985824403, -2.718804021042719, -0.2521119537584047, 1.471004204616386, 0.03619486057893471, 0.2359952480868094, 0.5698216197483527, -1.938478808333604, -1.67462204645698, 1.566024453044454, -0.002125520766780505, -2.38931689781855, 2.155650988202845, 4.945035309622497, -0.03006134968782909, -1.393922829721345, 2.568187630433722, 0.2759128427833915, -3.76770659525825, 0.6002271886395943, 3.670595622815396, -1.560123066118716, -3.387295944494411, 0.51377982030578, 0.5660295541057961, 0.1473631571579901, 4.029812921936159, 3.832468901103739, -0.5834675713354507, 0.1807898255787293, 2.424901420737968, -0.074701185797825, -1.180585190145598, 0.5338396632344072, -0.396741617980941, -1.054748209292877, 0.3067093043372416, -1.209351738490521, -2.011414829064124, 1.972275712931997, 3.096588694561671, 0.1895572774131027, 0.6093696988238003, 1.250355164486268, -0.8811047582090672, 0.2939737926266477, 1.266383734225801, -2.758706024610877], 'positive_zeros': ['0.2901307390476283', '0.8817557617966769', '1.988807736980323', '2.300046684685977', '2.909769949512471', '3.428225422678837', '4.131833922310945', '4.777176472095401', '5.191669369206050', '5.680510581445057', '6.478238200536209', '6.855595551330128', '7.340937865933046', '7.760329767354832', '8.134214282713762', '8.804699601286448', '9.155901711281767', '9.732083299011760', '10.14018198599974', '10.48852846971166', '11.01855459050227', '11.56020041730295', '11.93926449703259', '12.44186266675528', '12.91808190244486', '13.15540274664902', '13.93045274260255', '14.40541519333982', '14.85987946939921', '15.26601709332335', '15.74319964811063', '16.02495838589831', '16.62190855742348', '16.91995734262287', '17.41722247863179', '17.89864920070417', '18.17439560897695', '18.76905399106609', '19.25747174813497', '19.44993143654493', '19.82330812079535'], 'prelabel': '2-227430-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.61499376006033, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 827562833426597742, 'z1': {'__RealLiteral__': 0, 'data': '0.2901307390476283', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.8817557617966769', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.988807736980323', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1816.0376931699807, 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '1.1', 'conductor': 227430, 'conductor_radical': 3990, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, -1, -1, 0, 1, -3, 0, -6, 1, 0, 1, -2, 0, 0, -1, 0, 3, 1, 0, 1, 6, 0, -1, 1, 0, -2, -1, 0, 2, 1, 0, -2, 0, 0, 1, -3, 0, 7, -3, 0, -1, -6, 0, 1, -1, 0, -6, 2, 0, 3, 1, 0, -1, 6, 0, 10, 2, 0, 1, 6, 0, -9, -2, 0, -1, 8, 0, 5, 2, 0, 0, 3, 0, 5, -1, 0, 3, -5, 0, 2, -7, 0, 3, 15, 0, 6, 1, 0, 6, 0, 0, 2, -1, 0, 1], 'euler11': [1, 3, 11], 'euler13': [1, 6, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 0], 'euler2': [1, 1, 0], 'euler23': [1, -1, 23], 'euler29': [1, -1, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, 2, 37], 'euler41': [1, 3, 41], 'euler43': [1, -7, 43], 'euler47': [1, 6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, -6, 59], 'euler61': [1, -10, 61], 'euler67': [1, 9, 67], 'euler7': [1, 1, 0], 'euler71': [1, -8, 71], 'euler73': [1, -5, 73], 'euler79': [1, -5, 79], 'euler83': [1, 5, 83], 'euler89': [1, -15, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 3, 11], [1, 6, 13], [1, 2, 17], [1, 0, 0], [1, -1, 23], [1, -1, 29], [1, 2, 31], [1, 2, 37], [1, 3, 41], [1, -7, 43], [1, 6, 47], [1, -2, 53], [1, -6, 59], [1, -10, 61], [1, 9, 67], [1, -8, 71], [1, -5, 73], [1, -5, 79], [1, 5, 83], [1, -15, 89], [1, -2, 97]], 'index': 16, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/227430/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-227430-1.1-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-227430-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.61499376006033, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 827562833426597742, 'z1': {'__RealLiteral__': 0, 'data': '0.2901307390476283', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '827562833426597742', 'Lhash_array': ['827562833426597742'], 'label': '2-227430-1.1-c1-0-16', 'type': 'ECQ', 'url': 'EllipticCurve/Q/227430/c'}