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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': -2, 'A8': -1, 'A9': -2, 'Lhash': '245562724702776475', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [-0.7559289460184544, 0], 'a8': [-0.35355339059327373, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 546.5760018356644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '68450.1', 'coefficient_field': '1.1.1.1', 'conductor': 68450, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[1, 1], [1, 1, 3], [1], [1, 2, 7], [1, 3, 11], [1, 4, 13], [1, 3, 17], [1, 5, 19], [1, -6, 23], [1, 0, 29], [1, 2, 31], [1], [1, 3, 41], [1, 4, 43], [1, 12, 47], [1, 6, 53], [1, 0, 59], [1, 2, 61], [1, -13, 67], [1, -12, 71], [1, 11, 73], [1, -10, 79], [1, -9, 83], [1, 15, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 8, 'label': '2-68450-1.1-c1-0-8', 'leading_term': '1.58277436109', '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/68450/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.2820130501700323, -0.05381627511506123, -1.236319994903096, -2.683048849552773, -3.141045138547469, -1.773965196811438, 0.6612794928498541, 2.112060596599161, 1.29103151144036, -0.5934593678667462, -0.9465639265748448, 0.8814749080192301, 2.114210031526308, -0.3585276986448601, -5.472619729464977, -8.217209769289685, -5.410354842331754, 0.03505938801902591, 2.513620005850354, 0.80819146462774, -0.8175184924999253, 0.880004725427541, 3.514691520252846, 3.127195989782249, 0.4086215733235721, -0.7630979085043658, 0.1380825215857136, -0.3042338603475458, 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1.545642500089811, 0.4105807471960247, -2.190373795545615, 0.2556521515565437, 4.270668671414943, 1.904085384472003, -2.482428481131443, -0.5363685831662534, 2.8642580894791, 0.2886200705725392, -2.477322681842899, 0.5068951466801548, 2.538501220518904, -0.4416290325405648, -1.246934651271768, 1.571071770309637, 0.4204820279273168, -3.106884524927908, -0.5861013811146742, 4.342258172280657, 3.03398421925272, -0.1707354982816107, 1.695063143840471, 3.565015722159369, 0.973722388775086, -0.581588805386754, 0.512682938283718, -0.9432391780797257, -3.200172415010427, -1.228502153602386, 0.939637786354842, -0.7341632062570959, -1.091955273352057, 1.80463631539107, 2.223285042356031, 0.09853141095705392, 0.09066346744245643, 0.5025845065750089, -0.5947712009238743, -0.1687447035356783, -0.9145727831822458, -7.32956428355376], 'positive_zeros': ['0.4819357900718883', '1.681708023640057', '2.414951362198195', '2.899389985025451', '3.479136172551121', '4.498151041675857', '5.083250008622917', '5.418121619373889', '6.294149810449032', '6.713035025859479', '6.954141261172424', '7.959560767273526', '8.158458706523908', '8.872705551432373', '9.383597427199642', '9.838553051039779', '10.42536948024190', '10.87150840577458', '11.26819125718530', '11.76246439948684', '12.52264046550732', '12.77960690705417', '13.18757269776805', '13.91947905025749', '14.58608096263009', '15.04839347618544', '15.38308781022612', '16.05859151196925', '16.46957944666462', '16.96769187655014', '17.18388813834491', '17.80801556636284', '18.10386761208361', '18.80762119800776', '19.20535254245987', '19.55415677630812'], 'prelabel': '2-68450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.378964943633935, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 245562724702776475, 'z1': {'__RealLiteral__': 0, 'data': '0.4819357900718883', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.681708023640057', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.414951362198195', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 546.5760018356644, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 68450, 'conductor_radical': 370, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, -2, -1, -2, 0, -3, -1, -4, 2, 0, 1, -3, 2, -5, 0, 2, 3, 6, 1, 0, 4, 5, -2, 0, 0, -2, -1, 3, 3, 0, -2, 0, 5, 4, 0, -3, -2, -4, -3, 0, -6, -12, -1, -3, 0, 3, -4, -6, -5, 0, 2, 5, 0, 0, 0, -2, 2, 4, 1, 0, -3, 13, -3, -6, 0, 12, 2, -11, 0, 0, -5, 6, -4, 10, 0, 1, 3, 9, 2, 0, 4, 0, 3, -15, 0, 8, 6, 2, 12, 0, 1, 2, 3, 6, 0], 'euler11': [1, 3, 11], 'euler13': [1, 4, 13], 'euler17': [1, 3, 17], 'euler19': [1, 5, 19], 'euler2': [1, 1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 3], 'euler31': [1, 2, 31], 'euler37': [1, 0, 0], 'euler41': [1, 3, 41], 'euler43': [1, 4, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, -13, 67], 'euler7': [1, 2, 7], 'euler71': [1, -12, 71], 'euler73': [1, 11, 73], 'euler79': [1, -10, 79], 'euler83': [1, -9, 83], 'euler89': [1, 15, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 1, 0], [1, 1, 3], [1, 0, 0], [1, 2, 7], [1, 3, 11], [1, 4, 13], [1, 3, 17], [1, 5, 19], [1, -6, 23], [1, 0, 29], [1, 2, 31], [1, 0, 0], [1, 3, 41], [1, 4, 43], [1, 12, 47], [1, 6, 53], [1, 0, 59], [1, 2, 61], [1, -13, 67], [1, -12, 71], [1, 11, 73], [1, -10, 79], [1, -9, 83], [1, 15, 89], [1, -2, 97]], 'index': 8, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/68450/f'], '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': '2-68450-1.1-c1-0-8', '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': '2-68450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.378964943633935, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 245562724702776475, 'z1': {'__RealLiteral__': 0, 'data': '0.4819357900718883', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '245562724702776475', 'Lhash_array': ['245562724702776475'], 'factors': ['2-68450-1.1-c1-0-8'], 'label': '2-68450-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/68450/f'}