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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1776626527369863285', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1042.3352078249861, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]], [37, [1, 1]]], 'bad_primes': [2, 3, 7, 37], 'central_character': '130536.1', 'coefficient_field': '1.1.1.1', 'conductor': 130536, 'conductor_radical': 1554, 'degree': 2, 'euler_factors': [[1], [1], [1, 2, 5], [1], [1, 4, 11], [1, -6, 13], [1, 4, 17], [1, 4, 19], [1, 0, 23], [1, -10, 29], [1, 2, 31], [1, 1], [1, 2, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, -14, 61], [1, -12, 67], [1, -8, 71], [1, -14, 73], [1, -12, 79], [1, -6, 83], [1, 0, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 10, 'label': '2-130536-1.1-c1-0-10', 'leading_term': '1.34942897276', '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/130536/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.349428972755553, 0.7478873400691946, -0.5980845797535381, -1.439742248782383, -0.5389411082224257, 1.920213903436202, 3.910400699850573, 3.385010942003926, 0.8221428925568635, -0.8314451486755531, 0.4485104659366156, 3.004531011571403, 3.455038562306243, 1.280775290152374, -0.431223172172929, 0.3971443683962938, 1.629556206172855, 0.4187349455349375, -1.852484911122067, -1.587010394543079, 0.7296675099642603, 0.6707711417177133, -2.783013472228562, -4.832012597141071, -2.355462774408518, 0.8795000861340849, 0.6118687085542291, -0.6700201135197701, 1.458012585170352, 4.927676875931299, 4.548260632847306, 1.190963452133759, -0.1329390948947243, 0.6199121879538518, -0.2019007956211481, -1.312695835451393, 1.288577725357285, 4.737444416803826, 2.554047616545588, -3.243528388237787, -4.517357559804824, -0.8786107867263433, 0.6609334563350725, -1.055163865740037, -1.007792266820293, 0.4977380716295164, -0.8497665588130413, -2.741534938614109, -0.2225548034138292, 3.264645722328069, 1.943430734908615, -0.7817320878152992, 0.2869385045742153, 1.358342383265818, -1.331133572884151, -2.511895537241137, 0.5013754804198443, 0.5425784739166563, -4.858303405927677, -7.17891494310147, -3.068301793279692, 0.1962907392674088, -0.1611200527195759, 0.3136432450674351, 0.9976322094486493, -0.9583914243338539, -0.7783867450659265, 4.163897803303019, 5.632043366883783, 0.09505814935257657, -3.148261081617822, -0.3128995552021768, 0.6939712538126563, -1.641495338429518, -0.8025392861496194, 1.453350731632847, -0.4560019238629578, -2.24276357182356, 0.07765502013570463, 0.4282039258153521, -2.870463688513814, -2.752349397775569, -0.0412785767157344, -1.388399577500277, -3.215868596333852, -0.5870668182371983, 0.2042480220031117, -3.01356747331711, -1.319936182974551, 4.835128931423654, 4.763101711699152, -0.177762095534881, -0.932694482608124, 0.4392747553698591, -0.4847620160786376, -0.2899219452828423, -0.1236168052149926, -4.420049240839981, -6.345302693502277, -0.3131834215302749, 3.77067364696569, 0.5788839650999053, -0.6884314490770349, 1.392335279527433, -0.768246591901184, -3.555147834837809, -1.032767724479899, 0.462566519776345, -1.431119326346575, 0.3227160657833389, 3.291551867178947, 1.002013120361379, -0.8303479490793032, 1.302600157811538, 0.4618613475567323, -2.005104011139769, -0.09071035139195081, -0.4943185987631252, -6.484682351047167, -6.774357380250653, -0.4904548774653529], 'positive_zeros': ['0.3934363828338999', '1.064315075128757', '2.084505042798851', '2.451813593343937', '3.396359046110890', '3.686154372075476', '4.292569420049374', '4.917285080785747', '5.312916907248689', '6.159287172407338', '6.584993911288065', '6.884591170212539', '7.894747206339661', '8.058469003568075', '8.470343961152749', '8.916854846327836', '9.607772958503252', '10.31888824784096', '10.61226992402444', '11.14153403501099', '11.41109059155622', '12.01282453049464', '12.64850388030583', '12.96828211513810', '13.40007661635175', '13.96105088876577', '14.28456361859988', '15.21206081828737', '15.44377503041871', '15.68596270619367', '16.14890619981321', '16.55153008188749', '17.25381400502443', '17.77447619548484', '18.07982601766966', '18.56792231593760', '18.96462633018277', '19.49277004959357', '19.78967113166995'], 'prelabel': '2-130536-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.2852165522393, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1776626527369863285, 'z1': {'__RealLiteral__': 0, 'data': '0.3934363828338999', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.064315075128757', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.084505042798851', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1042.3352078249861, 'bad_primes': [2, 3, 7, 37], 'central_character': '1.1', 'conductor': 130536, 'conductor_radical': 1554, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 6, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 10, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 8, 0, 0, 0, 0, 0, 14, 0, 0, 0, -12, 0, 12, 0, 0, 0, 8, 0, 14, 0, 0, 0, 0, 0, 12, 0, 0, 0, 6, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0], 'euler11': [1, 4, 11], 'euler13': [1, -6, 13], 'euler17': [1, 4, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, 1, 0], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 2, 5], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -14, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 0], 'euler71': [1, -8, 71], 'euler73': [1, -14, 73], 'euler79': [1, -12, 79], 'euler83': [1, -6, 83], 'euler89': [1, 0, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 2, 5], [1, 0, 0], [1, 4, 11], [1, -6, 13], [1, 4, 17], [1, 4, 19], [1, 0, 23], [1, -10, 29], [1, 2, 31], [1, 1, 0], [1, 2, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, -14, 61], [1, -12, 67], [1, -8, 71], [1, -14, 73], [1, -12, 79], [1, -6, 83], [1, 0, 89], [1, -8, 97]], 'index': 10, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/130536/o'], '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': '2-130536-1.1-c1-0-10', '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': '2-130536-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.2852165522393, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1776626527369863285, 'z1': {'__RealLiteral__': 0, 'data': '0.3934363828338999', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1776626527369863285', 'Lhash_array': ['1776626527369863285'], 'label': '2-130536-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/130536/o'}