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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': -1, 'A6': 1, 'A7': -3, 'A8': -1, 'A9': 1, 'Lhash': '286820491007052591', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [-1.1338934190276817, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 688.2306150214159, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1, 1]], [13, [1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '86190.1', 'coefficient_field': '1.1.1.1', 'conductor': 86190, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, 1], [1, 3, 7], [1, 1, 11], [1], [1, 1], [1, 4, 19], [1, 1, 23], [1, 6, 29], [1, 4, 31], [1, 0, 37], [1, -10, 41], [1, 11, 43], [1, 2, 47], [1, 14, 53], [1, -6, 59], [1, 3, 61], [1, -7, 67], [1, 6, 71], [1, 1, 73], [1, -16, 79], [1, 9, 83], [1, -11, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 15, 'label': '2-86190-1.1-c1-0-15', 'leading_term': '1.91185591599', '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': 1, 'origin': 'EllipticCurve/Q/86190/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.3585882083717677, 0.07918720009531628, -1.024817061267937, -2.267851357904338, -2.377402115558018, -0.774010763516664, 1.32381423312362, 1.674977174364977, -0.4835332827653545, -2.997905636028601, -2.853854729149458, 0.0393120177693631, 2.239803090597493, 1.013124047403839, -1.68401137385704, -1.428018369741283, 2.397152455523404, 5.05350030553148, 2.730313260857096, -1.794255763974483, -2.717882232037499, 0.6714679548892252, 3.316715655533606, 2.131913228207156, 0.07964310122722298, 0.5066720605438507, 1.600636015560821, 0.2465683048201773, -1.922831269257484, -1.377792693098479, 0.5807103741267698, -0.202151398472051, -3.065512699033646, -3.242894268507445, -0.2733868062696984, 1.073997902327328, -0.7293725255446777, -1.641427796604424, 0.000263242088314341, 0.5327209801477109, -1.482211935619108, -2.291020463603364, -0.542064428393101, -0.02043713978843412, -1.629844594779452, -1.127302051306312, 1.875829639387463, 2.060681210217936, -1.167956144872822, -1.915074376851386, 0.5159224708909899, 0.3922248420760849, -1.137994197079955, 3.868345676671794, 13.15494820837632, 13.95415969368512, 4.456049131368544, -1.876344910563571, 1.304013405650494, 4.563317810035615, 1.629664338107482, -1.273420216901634, -0.05567414616611889, 0.6338503429372538, -0.894496468655207, -0.792856809280631, 0.3248322241326791, -1.017226352445742, -2.223602181821295, -0.00961513440886914, 1.575098675885894, -0.5359630093817587, -1.691610196918369, 0.3590833375951605, 0.9842696791337029, -0.4838190196480221, 0.2076434459719471, 1.441153402164675, -0.5870508084125672, -1.715726498863209, 1.214669841875923, 1.394386806721612, -3.615945483787163, -4.51013637449627, 0.8000630668411002, 1.757695065809591, -3.11018655461653, -3.524263960715705, 0.5152582509018065, 0.1490635579590084, -2.233523050902136, 0.3285356647570709, 2.77541970928762, 0.07437187615877448, -1.037459781118586, 1.54366436107315, -0.2154823418466671, -5.017518058051574, -3.395647147499036, 1.527748063729941, 0.7326226576912469, -1.791663773677511, 0.1536844405403225, 1.360017040148061, -1.047539321148438, -1.288321090045595, 0.2096259301202182, -1.746834625340585, -3.52731393890547, -0.8776839585800249, 1.092815480250228, 0.05746384423147767, 0.5078615254468778, 1.267789136957288, -0.9506929823327809, -1.874242728897911, -0.07549800798062697, -0.8273233436769258, -2.031741398509719, 0.6928685602661452], 'positive_zeros': ['0.5256757219549161', '1.585490617118284', '2.207437992673308', '2.996984750792540', '3.587569595883237', '4.109039054132729', '4.893169686157925', '5.458499500277860', '6.273875860880180', '6.385984920737771', '7.024655288384513', '7.658717614675143', '7.979023079397595', '8.773703976361651', '9.168563593983003', '9.749963924047997', '10.08563147990582', '10.84325457751582', '10.99481074875348', '11.59738327364488', '12.16258868981871', '12.69384747484839', '13.04449640027538', '13.36032072419543', '14.37700702660694', '14.68756704818444', '15.34976895101377', '15.75726316318168', '16.11336094183539', '16.63879924709759', '16.86909878623792', '17.50080534807972', '17.95152452531346', '18.46109668477416', '18.90793911380401', '19.22170254713970', '19.69835210732535'], 'prelabel': '2-86190-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.234149786517115, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 286820491007052591, 'z1': {'__RealLiteral__': 0, 'data': '0.5256757219549161', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.585490617118284', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.207437992673308', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 688.2306150214159, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 86190, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, -1, 1, -3, -1, 1, 1, -1, -1, 0, 3, 1, 1, -1, -1, -4, -1, 3, 1, -1, 1, 1, 0, -1, -3, -6, -1, -4, -1, 1, 1, 3, 1, 0, 4, 0, 1, 10, -3, -11, -1, -1, 1, -2, -1, 2, -1, 1, 0, -14, 1, 1, 3, 4, 6, 6, 1, -3, 4, -3, 1, 0, -1, 7, -1, 1, -3, -6, -1, -1, 0, -1, -4, 3, 0, 16, -1, 1, -10, -9, 3, 1, 11, 6, 1, 11, 1, 0, -1, 4, 2, 4, 1, 2, -2, -1, 1], 'euler11': [1, 1, 11], 'euler13': [1, 0, 0], 'euler17': [1, 1, 0], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 1, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 0, 37], 'euler41': [1, -10, 41], 'euler43': [1, 11, 43], 'euler47': [1, 2, 47], 'euler5': [1, 1, 0], 'euler53': [1, 14, 53], 'euler59': [1, -6, 59], 'euler61': [1, 3, 61], 'euler67': [1, -7, 67], 'euler7': [1, 3, 7], 'euler71': [1, 6, 71], 'euler73': [1, 1, 73], 'euler79': [1, -16, 79], 'euler83': [1, 9, 83], 'euler89': [1, -11, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 1, 0], [1, 3, 7], [1, 1, 11], [1, 0, 0], [1, 1, 0], [1, 4, 19], [1, 1, 23], [1, 6, 29], [1, 4, 31], [1, 0, 37], [1, -10, 41], [1, 11, 43], [1, 2, 47], [1, 14, 53], [1, -6, 59], [1, 3, 61], [1, -7, 67], [1, 6, 71], [1, 1, 73], [1, -16, 79], [1, 9, 83], [1, -11, 89], [1, -2, 97]], 'index': 15, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/86190/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': '2-86190-1.1-c1-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-86190-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.234149786517115, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 286820491007052591, 'z1': {'__RealLiteral__': 0, 'data': '0.5256757219549161', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '286820491007052591', 'Lhash_array': ['286820491007052591'], 'label': '2-86190-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/86190/c'}