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lfunc_lfunctions • Show schema
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{'A10': -4, 'A2': 2, 'A3': -1, 'A4': 2, 'A5': -2, 'A6': -2, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '230314114763331982', 'a10': [-1.2649110640673518, 0], 'a2': [1.414213562373095, 0], 'a3': [-0.5773502691896258, 0], 'a4': [1.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [-0.8164965809277261, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 259.4100010465337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [7, [1]], [13, [1, 1]], [17, [1, 1]]], 'bad_primes': [3, 7, 13, 17], 'central_character': '32487.1', 'coefficient_field': '1.1.1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'euler_factors': [[1, -2, 2], [1, 1], [1, 2, 5], [1], [1, -5, 11], [1, 1], [1, 1], [1, 6, 19], [1, 4, 23], [1, -8, 29], [1, -1, 31], [1, -1, 37], [1, 3, 41], [1, -11, 43], [1, -2, 47], [1, 3, 53], [1, 4, 59], [1, 0, 61], [1, -2, 67], [1, 11, 71], [1, 14, 73], [1, 4, 79], [1, -14, 83], [1, -2, 89], [1, 13, 97]], 'gamma_factors': [[], [0]], 'index': 3, 'label': '2-32487-1.1-c1-0-3', 'leading_term': '2.2766200916', '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/32487/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.276620091602557, 1.573821560563513, -0.3406614127506045, -2.728150927814481, -4.277423288204753, -3.773761638293117, -1.17009653378961, 1.974763931099368, 3.452066316573867, 2.233548330475247, -0.4889702261987015, -2.296819502106674, -1.819756479835537, 0.01949687557947973, 1.194946594516979, 0.8646511684891381, 0.04057132941009822, -0.09648632027730399, 0.114002045613066, -0.4870191716068965, -1.797736158253501, -2.217568507796659, -0.9387561520135798, 0.5680656422916552, 0.4869515549154455, -0.5693598046838514, -0.443340903530485, 0.8388177154417518, 0.4543990119199917, -2.699678701568302, -4.906105191212881, -2.015683803550731, 3.768992969486888, 5.400147229525619, 0.5547744805966968, -4.117972904790597, -1.681171133049465, 4.849702594754962, 6.035633936566625, -0.7745528522371564, -7.515229120266332, -6.601749404789934, -0.8319424837388377, 1.908523217535904, -0.09939339478569323, -1.990202416374573, -1.08305881070339, 0.1625638652488368, -0.0747731042312881, -0.1581008196026299, 0.6568537992421531, 0.2656288337929831, -1.763702380605194, -2.413058760517838, -0.4838288151785072, 0.8325307875710325, -0.5005328998723734, -1.775616767568943, -0.7798964412754528, 0.09594182096966027, -1.117796634019968, -1.745279929587677, 0.1647818414771176, 1.41647080486918, -0.06178164494788134, -0.1647795095285334, 3.734435000286613, 6.179581867951344, 2.625685219316366, -1.323326858902423, 0.5444742886835691, 2.623728062830145, -3.259340719881292, -11.58497956424475, -10.39811985253299, -1.281491812292, 3.220527256613156, 0.2317266403988523, -1.251672381907261, 1.697164638811053, 2.003441002838528, -2.110589846199008, -3.390200397818711, 0.3954859721862088, 2.588209449772288, 0.2987637606474157, -1.54067781571318, -0.5073354223141378, 0.1904322181023733, -0.3865715580915792, 0.1211765527515324, 1.173780749169503, 0.6479065912314745, -0.1415266607672904, 0.2757804853825368, -0.02303716087342766, -1.19560259710672, -0.1911322929673644, 1.843486462870371, 0.7133623092537166, -0.6995871351586131, 3.150385022283631, 6.387976485016067, -0.5495415531476503, -10.617553414873, -8.481517507492399, 2.841094745263542, 6.638717715204843, 0.9398476827685721, -1.937630854899176, -0.04901729932996283, -1.120514248232082, -2.651543827984787, 2.82544108856825, 9.345286308648252, 6.876534743976618, 0.3921349294691791, -0.09799296110136484, 2.561657022264767, 1.457751342571721, -0.7186434996230123], 'positive_zeros': ['0.4627658944599375', '1.588588304597067', '2.455301975108319', '3.247317924433207', '4.018684266431482', '4.336704377012972', '4.605589963104482', '5.635582846337481', '6.112079676551136', '6.589551469748986', '7.049201562384342', '7.836721245978190', '8.521912573548510', '9.065329753915546', '9.727445973125200', '10.54168071438841', '10.99136856386567', '11.69039634230206', '11.96664504762622', '12.30769732772658', '12.78978939930530', '13.55499756154794', '13.93576496748881', '14.65395756142947', '14.79789729039036', '15.48270318174338', '15.99138620782853', '16.26762652408080', '17.13145448821626', '17.46355434106488', '17.90213105148240', '18.78901727466737', '19.26540991363502', '19.62291723103051'], 'prelabel': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 230314114763331982, 'z1': {'__RealLiteral__': 0, 'data': '0.4627658944599375', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.588588304597067', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.455301975108319', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 259.4100010465337, 'bad_primes': [3, 7, 13, 17], 'central_character': '1.1', 'conductor': 32487, 'conductor_radical': 4641, 'degree': 2, 'dirichlet_coefficients': [1, 2, -1, 2, -2, -2, 0, 0, 1, -4, 5, -2, -1, 0, 2, -4, -1, 2, -6, -4, 0, 10, -4, 0, -1, -2, -1, 0, 8, 4, 1, -8, -5, -2, 0, 2, 1, -12, 1, 0, -3, 0, 11, 10, -2, -8, 2, 4, 0, -2, 1, -2, -3, -2, -10, 0, 6, 16, -4, 4, 0, 2, 0, -8, 2, -10, 2, -2, 4, 0, -11, 0, -14, 2, 1, -12, 0, 2, -4, 8, 1, -6, 14, 0, 2, 22, -8, 0, 2, -4, 0, -8, -1, 4, 12, 8, -13, 0, 5, -2], 'euler11': [1, -5, 11], 'euler13': [1, 1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 6, 19], 'euler2': [1, -2, 2], 'euler23': [1, 4, 23], 'euler29': [1, -8, 29], 'euler3': [1, 1, 0], 'euler31': [1, -1, 31], 'euler37': [1, -1, 37], 'euler41': [1, 3, 41], 'euler43': [1, -11, 43], 'euler47': [1, -2, 47], 'euler5': [1, 2, 5], 'euler53': [1, 3, 53], 'euler59': [1, 4, 59], 'euler61': [1, 0, 61], 'euler67': [1, -2, 67], 'euler7': [1, 0, 0], 'euler71': [1, 11, 71], 'euler73': [1, 14, 73], 'euler79': [1, 4, 79], 'euler83': [1, -14, 83], 'euler89': [1, -2, 89], 'euler97': [1, 13, 97], 'euler_factors': [[1, -2, 2], [1, 1, 0], [1, 2, 5], [1, 0, 0], [1, -5, 11], [1, 1, 0], [1, 1, 0], [1, 6, 19], [1, 4, 23], [1, -8, 29], [1, -1, 31], [1, -1, 37], [1, 3, 41], [1, -11, 43], [1, -2, 47], [1, 3, 53], [1, 4, 59], [1, 0, 61], [1, -2, 67], [1, 11, 71], [1, 14, 73], [1, 4, 79], [1, -14, 83], [1, -2, 89], [1, 13, 97]], 'index': 3, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32487/k'], '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': '2-32487-1.1-c1-0-3', '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': '2-32487-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106210014976636, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 230314114763331982, 'z1': {'__RealLiteral__': 0, 'data': '0.4627658944599375', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '230314114763331982', 'Lhash_array': ['230314114763331982'], 'label': '2-32487-1.1-c1-0-3', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32487/k'}