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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': -3, 'A8': 0, 'A9': 1, 'Lhash': '1215614525264564798', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2623.56480881119, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [37, [1]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '328560.1', 'coefficient_field': '1.1.1.1', 'conductor': 328560, 'conductor_radical': 1110, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, 3, 7], [1, -2, 11], [1, 5, 13], [1, -2, 17], [1, 1, 19], [1, -2, 23], [1, 5, 29], [1, -4, 31], [1], [1, -10, 41], [1, -6, 43], [1, -12, 47], [1, -6, 53], [1, 10, 59], [1, 4, 61], [1, 2, 67], [1, -1, 71], [1, -6, 73], [1, 10, 79], [1, -13, 83], [1, -16, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 22, 'label': '2-328560-1.1-c1-0-22', 'leading_term': '3.32970759494', '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/328560/cn', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.329707594942453, 2.316076984618036, 0.08992715961255979, -1.29336697580476, -0.187043759371793, 2.535291942245282, 3.869460740017886, 2.206564005207514, -0.3469244379286885, -0.7357446850495097, 0.631565736358165, 0.7341902615515951, -0.8341992296674874, -1.016993536323829, 1.069266754561461, 1.836132467815826, -0.552917147061961, -2.094980898728411, 0.3149258989678418, 2.497863384702974, -0.2588767833429882, -4.242146375345865, -3.201235564904739, 0.6001549073526311, 0.7704691070738753, -1.362879137327883, -0.147576226863876, 2.739074692255582, 1.869106215911967, -0.7034109145736881, -0.1750287220800298, 0.2547423486467834, -3.789708191788266, -7.129247851908904, -4.060859066187852, 0.4828579751964909, 0.6883806215386264, -0.1421900940130074, 0.889665638371885, 0.3516927012574273, -1.351963365806702, 0.1574880879403573, 1.447834283984985, -2.525785492838439, -4.740659684912906, 1.526192868169555, 7.08583254487681, 3.405426985875445, -1.349942147795044, 0.07373646215680817, 1.453994419404296, -0.1048885679264035, 1.022935055652411, 3.218286932927072, 0.8894404570875355, -1.60048242330732, -0.0567218345399842, -0.03140648189857649, -2.469728904440149, -1.36757710813818, 0.5751809254427406, -1.639332920769278, -1.822881132695089, 2.631373204998185, 2.776959838223808, -1.396376519227477, -0.802741148512721, 1.561897302692925, -0.6508482136169293, -1.335352159895012, 0.9045764001284079, -2.820492916516752, -8.477584944082894, -5.125631481327799, 0.7217465379374047, -0.1564035700781067, -1.386677476847257, 0.5077818895830735, 0.05112261317692205, -0.4284617250354291, 1.726783543516575, 0.2744627012486237, -2.832340611322283, -0.04599219806289209, 2.403172213195929, -0.8875066654591462, -1.353258201402481, 1.601230808858832, 0.04681454958476526, -1.47106947961463, 0.9691319959631663, -0.09223422354138508, -1.66797511894185, 3.441435874474907, 4.537877080959792, -3.493798300322241, -5.909441478979997, -0.6435514572719186, 0.3436290982810863, -0.5888867849527492, 1.452443823171077, 0.5365735807068265, -1.530304038051266, 0.4178489166328074, 0.8318749556646741, -0.3982746722971827, 1.685440421756076, 0.8630755700522943, -3.290771171821778, -0.931229122362628, 2.526282034427626, -0.07477736322686873, 2.069314357170982, 8.688240144792731, 5.994000781958828, -0.07226932170083668, 0.4139403718425508, -0.2914934130395083, -2.812045470508397, -0.675149497206171, 0.2139851040760975], 'positive_zeros': ['0.5103380000604765', '1.019587536106739', '1.956569503259513', '2.388881095817125', '2.874778714074048', '3.385314309871609', '3.953451800165147', '4.477266620834771', '4.985990333578523', '5.701039086131736', '6.082391968218531', '6.511732851457640', '7.160375738082559', '7.526587744469960', '7.779880037560665', '8.709678899858338', '9.135209636056523', '9.308044443185269', '9.793139294595735', '10.23564607515954', '10.62314757341592', '11.20443112087202', '11.89360084166237', '12.24366514608743', '12.72741953059768', '12.88801686346999', '13.55907220469169', '14.00738820557370', '14.24626099367072', '14.87223679637290', '15.10636953207591', '15.60976956324320', '16.15647672200326', '16.56022782542709', '16.94781794935067', '17.37555474404809', '17.62670674715118', '18.44842186009094', '18.73592050213850', '19.17849370204344', '19.50777624788875', '19.80857162001750'], 'prelabel': '2-328560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.220745883003204, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1215614525264564798, 'z1': {'__RealLiteral__': 0, 'data': '0.5103380000604765', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.019587536106739', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.956569503259513', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2623.56480881119, 'bad_primes': [2, 3, 5, 37], 'central_character': '1.1', 'conductor': 328560, 'conductor_radical': 1110, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -3, 0, 1, 0, 2, 0, -5, 0, 1, 0, 2, 0, -1, 0, -3, 0, 2, 0, 1, 0, 1, 0, -5, 0, 4, 0, 2, 0, -3, 0, 0, 0, -5, 0, 10, 0, 6, 0, 1, 0, 12, 0, 2, 0, 2, 0, 6, 0, 2, 0, -1, 0, -10, 0, -4, 0, -3, 0, -5, 0, -2, 0, 2, 0, 1, 0, 6, 0, 1, 0, -6, 0, -10, 0, 1, 0, 13, 0, 2, 0, -5, 0, 16, 0, 15, 0, 4, 0, -1, 0, 10, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, 5, 13], 'euler17': [1, -2, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, 5, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 0, 0], 'euler41': [1, -10, 41], 'euler43': [1, -6, 43], 'euler47': [1, -12, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 10, 59], 'euler61': [1, 4, 61], 'euler67': [1, 2, 67], 'euler7': [1, 3, 7], 'euler71': [1, -1, 71], 'euler73': [1, -6, 73], 'euler79': [1, 10, 79], 'euler83': [1, -13, 83], 'euler89': [1, -16, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 3, 7], [1, -2, 11], [1, 5, 13], [1, -2, 17], [1, 1, 19], [1, -2, 23], [1, 5, 29], [1, -4, 31], [1, 0, 0], [1, -10, 41], [1, -6, 43], [1, -12, 47], [1, -6, 53], [1, 10, 59], [1, 4, 61], [1, 2, 67], [1, -1, 71], [1, -6, 73], [1, 10, 79], [1, -13, 83], [1, -16, 89], [1, -10, 97]], 'index': 22, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/328560/cn'], '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': '2-328560-1.1-c1-0-22', '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': '2-328560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.220745883003204, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1215614525264564798, 'z1': {'__RealLiteral__': 0, 'data': '0.5103380000604765', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1215614525264564798', 'Lhash_array': ['1215614525264564798'], 'label': '2-328560-1.1-c1-0-22', 'type': 'ECQ', 'url': 'EllipticCurve/Q/328560/cn'}