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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': -1, 'A9': 0, 'Lhash': '766237298065976571', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 578.5161626441767, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1]], [7, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '72450.1', 'coefficient_field': '1.1.1.1', 'conductor': 72450, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1, 1], [1], [1], [1, 1], [1, -1, 11], [1, -2, 13], [1, 6, 17], [1, -5, 19], [1, 1], [1, 8, 29], [1, -4, 31], [1, -6, 37], [1, -11, 41], [1, -2, 43], [1, 3, 47], [1, -9, 53], [1, -4, 59], [1, -10, 61], [1, 6, 67], [1, -6, 71], [1, -2, 73], [1, 2, 79], [1, 4, 83], [1, 6, 89], [1, 17, 97]], 'gamma_factors': [[], [0]], 'index': 19, 'label': '2-72450-1.1-c1-0-19', 'leading_term': '1.54272672907', '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/72450/t', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.542726729073731, 1.100738921846575, 0.0372567910284948, -0.8792195278984754, -0.7540497779049955, 0.5548798050389231, 1.928193000506225, 1.843500973521081, 0.131939688822152, -1.406039276154357, -0.8441930684115372, 1.28288033729219, 2.099818184619537, -0.1304290806473757, -3.296090998334484, -3.691170169695126, -1.10556194279289, 0.2135765380583962, -2.94157331215523, -7.773911995832031, -8.555294243361882, -4.308461343034938, -0.2805621849899815, -0.6723611951517874, -3.07065170607083, -2.774654955146874, -0.09962678612673122, 0.7882281411251159, -0.8592848932333244, -1.303282648786284, 0.9284316721467518, 2.346156031553422, 0.6622117559528922, -1.101252814078779, 0.04670350415692421, 1.861139576755313, 1.167454386998326, -0.4370366719415345, -0.1306029105330324, 0.3574850533929775, -1.726800608485711, -3.963595746182083, -2.585193549884292, 0.2755206971512456, 0.2763503031971028, -0.988291668646673, 0.4601295953645593, 2.228860333483135, -0.2979853544242567, -3.817288810004052, -1.803064610193337, 3.07701888252547, 3.094276349901012, -0.2759857385125439, 0.5654097944702378, 4.049918058126226, 1.923741806917233, -4.352177660564429, -5.28060118243237, -0.6484162399604666, 0.64222967882738, -2.656850939717704, -3.289636144762335, -0.3143788519441896, 0.5681632023033522, -0.4293319087849318, 1.180454284471793, 3.3027602138701, 1.485381738162283, -1.130104581601216, -0.08177736321741261, 1.451202101618393, 0.1794562404197985, -0.3768530354923736, 1.330325695659376, 0.8101969769098412, -2.12017987591069, -2.110672642733109, 0.2548323089426685, -0.0293441625374628, -1.088499404219837, 0.9846133145357528, 2.162995370426004, -0.3897906244111398, -0.2090926801207605, 4.562215264671709, 4.902174168957888, -0.9063087215920377, -2.740673782464892, 0.7876440611745512, 0.5206045467811665, -2.315625852933955, 0.9453404132566777, 5.531242401513783, 1.586471365173611, -4.822018100274766, -3.513453298473405, 0.5452585021998198, 0.2914029448439712, 0.5173751263597898, 3.72789033378897, 3.427939398853253, -0.3103624447554115, -0.5034481766950512, 1.475579540980588, 0.4556901860167914, -0.6492606668497456, 0.4400201393920157, -0.8096507504173465, -3.662357933590158, -2.294409688779756, 0.5910745128220595, -0.4659532626474194, -1.664904379499025, 0.002119477139174989, -0.193171470837427, -1.788482966768231, 0.351398295765431, 2.191485235495941, -0.8156128572310042, -1.764823377771515], 'positive_zeros': ['0.5081002832933931', '1.161114365359734', '2.016273888813850', '2.605126924963585', '3.240197572938230', '4.121070652893595', '4.292382335180900', '5.546156262635734', '5.650818252996850', '6.510537491340142', '6.886878909249254', '7.412302025762816', '8.067236679495057', '8.494709096596969', '9.160027261826778', '9.530726354533786', '9.826175831948530', '10.71616787521467', '11.04417773288047', '11.45419279937778', '11.98253487480226', '12.58615500909114', '13.22169347177304', '13.45539025701685', '14.07670404024910', '14.79139790770149', '15.06259882749548', '15.78112453132347', '16.11844385961979', '16.37843564375747', '17.11285508810549', '17.50885314664067', '18.02623609699809', '18.31784219540890', '18.82113404797305', '19.46394790795146', '19.74555524363773'], 'prelabel': '2-72450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.052362932655424, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 766237298065976571, 'z1': {'__RealLiteral__': 0, 'data': '0.5081002832933931', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.161114365359734', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.016273888813850', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 578.5161626441767, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 72450, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, -1, -1, 0, 0, 1, 0, 2, 1, 0, 1, -6, 0, 5, 0, 0, -1, -1, 0, 0, -2, 0, -1, -8, 0, 4, -1, 0, 6, 0, 0, 6, -5, 0, 0, 11, 0, 2, 1, 0, 1, -3, 0, 1, 0, 0, 2, 9, 0, 0, 1, 0, 8, 4, 0, 10, -4, 0, 1, 0, 0, -6, -6, 0, 0, 6, 0, 2, -6, 0, 5, -1, 0, -2, 0, 0, -11, -4, 0, 0, -2, 0, -1, -6, 0, -2, -1, 0, 3, 0, 0, -17, -1, 0, 0], 'euler11': [1, -1, 11], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, -5, 19], 'euler2': [1, 1, 0], 'euler23': [1, 1, 0], 'euler29': [1, 8, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, -11, 41], 'euler43': [1, -2, 43], 'euler47': [1, 3, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, -4, 59], 'euler61': [1, -10, 61], 'euler67': [1, 6, 67], 'euler7': [1, 1, 0], 'euler71': [1, -6, 71], 'euler73': [1, -2, 73], 'euler79': [1, 2, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -1, 11], [1, -2, 13], [1, 6, 17], [1, -5, 19], [1, 1, 0], [1, 8, 29], [1, -4, 31], [1, -6, 37], [1, -11, 41], [1, -2, 43], [1, 3, 47], [1, -9, 53], [1, -4, 59], [1, -10, 61], [1, 6, 67], [1, -6, 71], [1, -2, 73], [1, 2, 79], [1, 4, 83], [1, 6, 89], [1, 17, 97]], 'index': 19, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/72450/t'], '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': '2-72450-1.1-c1-0-19', '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': '2-72450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.052362932655424, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 766237298065976571, 'z1': {'__RealLiteral__': 0, 'data': '0.5081002832933931', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '766237298065976571', 'Lhash_array': ['766237298065976571'], 'label': '2-72450-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/72450/t'}