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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': 4, 'A8': 0, 'A9': 1, 'Lhash': '1628608426376710178', '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': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1096.1863189481376, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [11, [1, 1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '137280.1', 'coefficient_field': '1.1.1.1', 'conductor': 137280, 'conductor_radical': 4290, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, -4, 7], [1, 1], [1, -1], [1, 1, 17], [1, 1, 19], [1, 6, 23], [1, 0, 29], [1, 6, 31], [1, -11, 37], [1, -11, 41], [1, -5, 43], [1, 1, 47], [1, -12, 53], [1, -6, 59], [1, -10, 61], [1, 7, 67], [1, 14, 71], [1, -12, 73], [1, 10, 79], [1, -6, 83], [1, 6, 89], [1, 17, 97]], 'gamma_factors': [[], [0]], 'index': 133, 'label': '2-137280-1.1-c1-0-133', 'leading_term': '6.51244935811', '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/137280/bs', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.440937979619888, 1.865270794111638, 0.8926214745607398, -0.6076133507917028, -0.9507787185593478, 0.5758157737722297, 2.452161993928662, 2.366202006997469, 0.3456691716865622, -0.5294945854951502, 2.218574556312729, 6.612105395115354, 7.91299151127206, 4.57407423408922, 0.3924855993463286, -0.6628786452151496, 0.3323250139280302, -0.1807652137078896, -2.12018234697227, -2.189463779418819, -0.047695310541693, 0.7703670600283766, -0.7214249213455975, -0.7423484381857905, 2.364035736190629, 4.171557091453247, 1.303412438168307, -2.318096468322618, -1.81288341966395, 0.5842623354565027, 0.3595148277104658, -0.7651732298694421, 0.9722671863461648, 2.835289526890103, 0.4898466037485812, -2.337790150057929, 0.4470841060979436, 5.343800867130696, 4.412799577983977, -0.6915088657263979, -1.93912357252995, 0.8698577469284121, 1.543035789266186, -0.2151294774620906, -0.2825252357601861, 0.2734681190162977, -1.212812404383588, -1.554023939164819, 1.366284194910584, 2.353008714594147, -0.6626669416597732, -1.010935209962054, 3.146429638986264, 3.682025828770631, -1.446209105827803, -3.500072915813299, -0.1319427031576667, 1.011244667109054, -1.104288095916732, -0.1243650734009808, 2.306564908217863, 0.02000805341797914, -3.296178182228944, -1.616268036841141, 0.6126630483785515, -0.9151271521827724, -0.7068034187405196, 3.26195061864803, 4.008435291149635, 0.5700678390553244, -0.6167055854064846, 0.09344430645205606, -0.8143953954159115, 0.5647006619541022, 5.212505985401844, 5.025598425735673, -0.06438695431805681, 0.05886769017714334, 4.434834618405345, 3.072499191384864, -1.44013972404292, -0.7915544358989643, 0.7196671861935363, -2.035384275198588, -2.849917292788953, 0.02595473660793904, -0.4176389349950839, -2.437904044395353, 0.2894350683989234, 2.410474998314455, -1.243157422471689, -3.311705871693286, -0.4877388300477186, 0.4764348774411624, -0.4995012629554571, 0.933543128502319, 1.242151411487734, -0.3592120002891453, 2.117964671278634, 4.377765375807111, -1.419985344201603, -6.385367733300728, -1.922398949059586, 1.20961521524537, -3.292777685731543, -4.538579262814456, -0.2182237321309634, 0.3481755390116536, -1.387536289251088, 0.1202241730418132, 0.6209498961156702, -0.6947729165069984, 0.7821370888947226, 0.8253986682714513, -3.079378873811016, -2.352077251338562, 2.511966776181435, 1.412747611442799, -2.062653551114791, -0.06237852165840985], 'positive_zeros': ['0.8918201954354565', '1.428827206011377', '2.294082398489712', '2.586083026787373', '3.787045956747067', '4.162354384657410', '4.471317829550411', '5.255725351002384', '5.644677357113257', '6.077565542040338', '6.824209395378164', '7.423523794045411', '7.806558789374983', '8.156408125766043', '8.781184699327740', '9.228515539030099', '9.961976448183623', '10.42546443000182', '10.96431087337787', '11.32137752680818', '11.57700714977904', '12.14713111434349', '12.69899307715249', '13.07282648964992', '13.68459228173909', '14.25952194884558', '14.61914262406475', '15.01039551072019', '15.50116744951578', '16.13169604567261', '16.39129982092944', '16.80353729894513', '17.55064497750488', '17.92222439054468', '18.05897379895364', '18.45999744795356', '19.24592209333536', '19.49622043996213'], 'prelabel': '2-137280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.10870457973458, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1628608426376710178, 'z1': {'__RealLiteral__': 0, 'data': '0.8918201954354565', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.428827206011377', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.294082398489712', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1096.1863189481376, 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '1.1', 'conductor': 137280, 'conductor_radical': 4290, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 4, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -4, 0, -6, 0, 1, 0, -1, 0, 0, 0, -6, 0, 1, 0, -4, 0, 11, 0, -1, 0, 11, 0, 5, 0, -1, 0, -1, 0, 9, 0, 1, 0, 12, 0, 1, 0, 1, 0, 6, 0, 10, 0, 4, 0, -1, 0, -7, 0, 6, 0, -14, 0, 12, 0, -1, 0, -4, 0, -10, 0, 1, 0, 6, 0, 1, 0, 0, 0, -6, 0, 4, 0, 6, 0, 1, 0, -17, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -1, 0], 'euler17': [1, 1, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, 6, 31], 'euler37': [1, -11, 37], 'euler41': [1, -11, 41], 'euler43': [1, -5, 43], 'euler47': [1, 1, 47], 'euler5': [1, 1, 0], 'euler53': [1, -12, 53], 'euler59': [1, -6, 59], 'euler61': [1, -10, 61], 'euler67': [1, 7, 67], 'euler7': [1, -4, 7], 'euler71': [1, 14, 71], 'euler73': [1, -12, 73], 'euler79': [1, 10, 79], 'euler83': [1, -6, 83], 'euler89': [1, 6, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, -4, 7], [1, 1, 0], [1, -1, 0], [1, 1, 17], [1, 1, 19], [1, 6, 23], [1, 0, 29], [1, 6, 31], [1, -11, 37], [1, -11, 41], [1, -5, 43], [1, 1, 47], [1, -12, 53], [1, -6, 59], [1, -10, 61], [1, 7, 67], [1, 14, 71], [1, -12, 73], [1, 10, 79], [1, -6, 83], [1, 6, 89], [1, 17, 97]], 'index': 133, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/137280/bs'], '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': '2-137280-1.1-c1-0-133', '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': '2-137280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.10870457973458, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1628608426376710178, 'z1': {'__RealLiteral__': 0, 'data': '0.8918201954354565', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1628608426376710178', 'Lhash_array': ['1628608426376710178'], 'label': '2-137280-1.1-c1-0-133', 'type': 'ECQ', 'url': 'EllipticCurve/Q/137280/bs'}