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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': 0, 'A8': -1, 'A9': 1, 'Lhash': '142092254904262659', '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': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 762.9705913133345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1]], [7, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '95550.1', 'coefficient_field': '1.1.1.1', 'conductor': 95550, 'conductor_radical': 2730, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1], [1], [1, -4, 11], [1, 1], [1, -8, 17], [1, -6, 19], [1, 6, 23], [1, 4, 29], [1, 0, 31], [1, -2, 37], [1, -2, 41], [1, -4, 43], [1, 0, 47], [1, -10, 53], [1, 4, 59], [1, -10, 61], [1, 12, 67], [1, 8, 71], [1, 8, 73], [1, -8, 79], [1, -12, 83], [1, -14, 89], [1, 16, 97]], 'gamma_factors': [[], [0]], 'index': 54, 'label': '2-95550-1.1-c1-0-54', 'leading_term': '1.78538841692', '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/95550/co', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.785388416920741, 1.338580764339871, 0.2799324922603117, -0.6106572491384705, -0.5522996221241764, 0.3183495481824099, 0.6924216860204293, -0.6049979079452072, -2.803534436242189, -3.350288586541596, -0.7567647315163083, 2.946555068517891, 3.910272202809629, 1.190183274944382, -1.557024615368057, -0.6091890043622556, 2.474627961947355, 2.521799391561939, -1.965284977933732, -6.12681621645072, -5.212370780413719, -1.159222109353798, 0.5950852321059302, -0.7773664764212559, -1.108442188005673, 1.189573537934804, 2.4177988685859, 0.2406503075744848, -2.032917063895507, -1.180981364432246, 0.4291514919672598, -0.3869954410322626, -1.340605021561227, 1.126329909418168, 4.54893736258968, 3.993381769354497, 0.592750544351933, -0.5817133381359348, 0.6228836121527253, 0.3130015124213948, -1.270530829458009, -0.6957513242158097, 0.7974802758682739, -0.8520669187196163, -3.97642037678412, -3.573947002788686, -0.680244074805752, 0.1198304109331015, -0.1344434716393326, 1.532272985866191, 1.3260058214477, -4.292925631752097, -8.180778673327133, -2.963260161353657, 4.194579581780055, 2.563414514835365, -3.504425354103364, -3.455562370525835, 0.1216790094947855, -1.22371998238647, -3.996508824366132, -0.4042180404480803, 5.176662226644629, 4.456994533774507, 0.4206420937299567, -0.3883041319309317, 0.09165691772564331, -1.185981360139234, -1.169102707254237, 0.8835187081545356, 0.802466163813108, -0.861109841559756, -0.06472644685600622, 1.043266247478644, -0.9450904207888294, -2.198504179981153, -0.1921480832212917, 0.07614158538102334, -2.239507024478935, -1.093625980852839, 2.303046107592949, 1.122074724736402, -1.503460131843603, 0.9598841764583715, 2.895117629059574, -1.669478075966333, -4.803253160643905, -0.9656727643338059, 1.50894563910962, -0.7046801051891939, 0.3333623978683978, 3.856704503447729, 1.435194385976811, -2.717151539636452, 0.0001180127691085583, 3.429484385891017, 0.3805084315943741, -2.070197441143434, 0.3537362329110732, 0.4171106798616154, -2.29346545935559, -0.902857183355475, 1.220959375097358, -1.850605420792405, -4.0083304701394, -1.000586539514928, 0.0365290336577902, -2.485132197438353, -1.728729034343891, 1.138089292571706, 0.7451657970793408, -0.2076975815527506, 0.272120319255481, -1.264253477825997, -2.468599600203669, 0.4130030033551671, 1.85153562600142, -0.818963259952663, -1.014151384085046, 1.018463832992966, -0.0649788981689368], 'positive_zeros': ['0.5635371654678414', '1.166073717451803', '1.669334634032827', '2.548759464057457', '3.335431208620378', '3.800698299305128', '4.408040460557867', '5.346728010207325', '5.637224630071349', '6.137942597437229', '6.769556199789096', '7.401793990800578', '7.689786858108362', '8.171832963629551', '9.057193474583628', '9.379185072505910', '9.797309320659902', '10.34181303107336', '10.67745184781601', '11.59959800722575', '11.80353524638011', '12.03811578497620', '12.57972610085808', '13.33609257513024', '13.84794995635352', '14.48487092503938', '14.65049795462648', '15.26572586499462', '16.04161269141533', '16.36569992868326', '16.53508839067718', '17.14099852148448', '17.60627351224560', '18.00858257078929', '18.41135446762420', '19.02382804093703', '19.26008475452095', '19.82189207884316'], 'prelabel': '2-95550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.621922295765994, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 142092254904262659, 'z1': {'__RealLiteral__': 0, 'data': '0.5635371654678414', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.166073717451803', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.669334634032827', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 762.9705913133345, 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '1.1', 'conductor': 95550, 'conductor_radical': 2730, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, 0, -1, 1, 0, 4, -1, -1, 0, 0, 1, 8, -1, 6, 0, 0, -4, -6, 1, 0, 1, -1, 0, -4, 0, 0, -1, -4, -8, 0, 1, 2, -6, 1, 0, 2, 0, 4, 4, 0, 6, 0, -1, 0, 0, -8, -1, 10, 1, 0, 0, -6, 4, -4, 0, 10, 0, 0, 1, 0, 4, -12, 8, 6, 0, -8, -1, -8, -2, 0, 6, 0, -1, 8, 0, 1, -2, 12, 0, 0, -4, 4, -4, 14, 0, 0, -6, 0, 0, 0, 1, -16, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 1, 0], 'euler17': [1, -8, 17], 'euler19': [1, -6, 19], 'euler2': [1, 1, 0], 'euler23': [1, 6, 23], 'euler29': [1, 4, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, 4, 59], 'euler61': [1, -10, 61], 'euler67': [1, 12, 67], 'euler7': [1, 0, 0], 'euler71': [1, 8, 71], 'euler73': [1, 8, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -14, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 0, 0], [1, -4, 11], [1, 1, 0], [1, -8, 17], [1, -6, 19], [1, 6, 23], [1, 4, 29], [1, 0, 31], [1, -2, 37], [1, -2, 41], [1, -4, 43], [1, 0, 47], [1, -10, 53], [1, 4, 59], [1, -10, 61], [1, 12, 67], [1, 8, 71], [1, 8, 73], [1, -8, 79], [1, -12, 83], [1, -14, 89], [1, 16, 97]], 'index': 54, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/95550/co'], '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': '2-95550-1.1-c1-0-54', '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': '2-95550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.621922295765994, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 142092254904262659, 'z1': {'__RealLiteral__': 0, 'data': '0.5635371654678414', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '142092254904262659', 'Lhash_array': ['142092254904262659'], 'label': '2-95550-1.1-c1-0-54', 'type': 'ECQ', 'url': 'EllipticCurve/Q/95550/co'}