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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '1867471518961009641', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1, -1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, -1], [1, -1], [1, -2, 13], [1, -2, 17], [1, 4, 19], [1, 4, 23], [1, 6, 29], [1, 0, 31], [1, 6, 37], [1, -10, 41], [1, -4, 43], [1, 0, 47], [1, 2, 53], [1, 4, 59], [1, -10, 61], [1, -8, 67], [1, 0, 71], [1, 2, 73], [1, 8, 79], [1, 4, 83], [1, 2, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 127, 'label': '2-369600-1.1-c1-0-127', 'leading_term': '3.24251364478', '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/369600/ws', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.24251364478061, 2.065129578388828, -0.5999537958327646, -2.560865909164224, -2.028318485628397, 0.2301537193683452, 1.402551822726438, 0.2197256086692003, -1.100040998260792, -0.1213677338026791, 1.691340203774395, 0.9541649021215537, -1.90807790280874, -2.806501855604014, -0.6618193896774208, 0.7351746097470625, -0.3798340330531073, -0.4189218654533815, 2.336498521073602, 3.247986775451469, -0.4904208281098658, -3.539692040137373, -1.338091863723766, 1.397077315809387, -0.48833735501441, -2.64810052808847, 0.05324794299358304, 2.981220897116197, 0.690160865431485, -2.374990401195782, -1.076152041696517, 0.519101242007103, -1.342178595251113, -2.316655329076894, -0.2982213165472484, -0.05895936579151915, -1.761038883350667, -0.208022927952238, 2.568378833916028, 0.9441572711618867, -1.149610209656189, 1.65559091306391, 3.632504499950074, 0.2930934254734293, -1.38983165276843, 1.106787848771796, -0.07222007132935049, -4.476141258794531, -3.060212970596574, 1.734907197503286, 1.348526689928039, -0.3323692605141664, 2.381013688522449, 3.292473982745672, -0.3779892713540763, -1.130539898903885, 1.313486579958474, 0.6908265130827389, -0.40199088168886, 1.158785670867461, -0.06105825774813365, -3.36113149149219, -1.726094060776516, 0.8194384253565004, -1.351501566466925, -1.016494239239327, 3.740852290814572, 2.980569449734247, -1.466761988666007, 0.1200603468387457, 2.285807490884147, -1.295181813393076, -1.92312412505034, 2.251164068885761, 1.724681949654474, -1.116417930637395, 0.4282665979125141, 0.5897658675934818, -2.108935044269304, -0.3564058555783371, 2.211359822474689, -0.2406854561398072, -1.15947756908747, 0.8748332760015934, -0.425522284672955, -1.155115077195516, 1.195628223328808, -1.245858353253521, -5.072841196097295, -1.676186226388889, 0.2748859879268109, -4.090675858172721, -3.16926598967621, 1.682057983153043, -0.209287162163134, -2.071178946070378, 1.605633402334314, 1.69405397740878, -0.5938074298953825, 1.438433850360363, 1.054414288788896, -2.731364885906139, -1.423009335103825, 0.9859920962314509, 0.01043308564588598, 1.462247282422986, 1.871121344980413, -2.965607175404828, -3.108877861625896, 1.474288226315192, 0.7399583972111594, -0.3947702433086178, 1.646583268704954, -0.1721136939750106, 0.7499329854738546, 9.101746194837245, 9.256908821624014, 0.3453268106044065, -1.512949317172494, 0.5190028964898664, -0.8846291132123036], 'positive_zeros': ['0.4461640620063619', '1.224439464942377', '1.780106510257985', '2.265007611820221', '2.838021811560376', '3.571291664060047', '3.935120173594989', '4.301653018727691', '4.974118701854540', '5.589329623322149', '5.963235867131695', '6.496861148934620', '7.042200956856829', '7.610033613184850', '7.860009788179819', '8.542887302174546', '8.740092428964624', '9.265296502723060', '9.822136551678951', '10.14291043050380', '10.76851099749264', '11.14462683295945', '11.49569818304001', '12.14392050651807', '12.63231143448550', '12.81178678328819', '13.47400991892799', '13.86032153391871', '14.33851138883261', '14.58394247885705', '14.99563370147261', '15.61975248459326', '15.88318876948032', '16.30768744436069', '16.89687754298263', '17.24244018175833', '17.67539897373859', '18.11508732042218', '18.61951048500742', '18.95622766813882', '19.30362722215106', '19.77273535094831'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1867471518961009641, 'z1': {'__RealLiteral__': 0, 'data': '0.4461640620063619', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.224439464942377', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.780106510257985', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 0, -4, 0, 1, 0, -4, 0, 0, 0, 1, 0, -6, 0, 0, 0, 1, 0, 0, 0, -6, 0, 2, 0, 10, 0, 4, 0, 0, 0, 0, 0, 1, 0, 2, 0, -2, 0, 0, 0, -4, 0, -4, 0, 10, 0, 1, 0, 0, 0, 8, 0, -4, 0, 0, 0, -2, 0, 0, 0, 1, 0, -8, 0, 1, 0, -4, 0, 0, 0, -6, 0, -2, 0, 2, 0, 0, 0, 0, 0, -2, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, -2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 6, 37], 'euler41': [1, -10, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 4, 59], 'euler61': [1, -10, 61], 'euler67': [1, -8, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 2, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, -1, 0], [1, -1, 0], [1, -2, 13], [1, -2, 17], [1, 4, 19], [1, 4, 23], [1, 6, 29], [1, 0, 31], [1, 6, 37], [1, -10, 41], [1, -4, 43], [1, 0, 47], [1, 2, 53], [1, 4, 59], [1, -10, 61], [1, -8, 67], [1, 0, 71], [1, 2, 73], [1, 8, 79], [1, 4, 83], [1, 2, 89], [1, 2, 97]], 'index': 127, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/ws'], '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': '2-369600-1.1-c1-0-127', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1867471518961009641, 'z1': {'__RealLiteral__': 0, 'data': '0.4461640620063619', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1867471518961009641', 'Lhash_array': ['1867471518961009641'], 'label': '2-369600-1.1-c1-0-127', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/ws'}