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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 3, 'A8': 0, 'A9': 1, 'Lhash': '604454464259390447', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 269.89435883192783, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '33800.1', 'coefficient_field': '1.1.1.1', 'conductor': 33800, 'conductor_radical': 130, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1], [1, -3, 7], [1, -5, 11], [1], [1, -2, 17], [1, 5, 19], [1, -8, 23], [1, 0, 29], [1, 8, 31], [1, 9, 37], [1, -2, 41], [1, -6, 43], [1, 7, 47], [1, -13, 53], [1, 0, 59], [1, -4, 61], [1, 0, 67], [1, 14, 71], [1, -10, 73], [1, 4, 79], [1, 18, 83], [1, 9, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 19, 'label': '2-33800-1.1-c1-0-19', 'leading_term': '4.8161528831', '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/33800/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.117424228259868, 1.725750305661803, 1.465012175335161, 0.4869560509088524, -0.359545321351877, -0.04997410224532193, 1.549689092662976, 3.092337407985723, 2.61523495991425, -0.5037774112702618, -4.384881515130501, -5.929121775036465, -3.775968373311181, 0.08562033512126632, 2.164429527209955, 1.094842975893631, -1.052682831425693, -1.451626003742368, 0.04314581163692269, 1.074695789137608, 0.2794961583850998, -0.7921942290889581, -0.1281391581618011, 1.495758393914884, 1.512951145058142, -0.4003672193472841, -1.518244993781804, -0.2867419303128561, 0.7235376017969596, -1.626792710369418, -5.726258874461932, -6.657144968857175, -3.194099922885649, 0.09347105453745715, -0.5100265020247193, -2.271571689234873, -0.4011823269623393, 4.071840046664827, 5.410594905971543, 1.82183355432109, -1.901132920619417, -1.718069517971451, 0.2786696047732496, 0.4798171417139277, -0.3884230741005614, 0.06760905065990672, 0.7515311300439752, -0.5330461032996298, -1.99898845486543, -0.7812493371059018, 0.756808093829284, -1.919288021042726, -6.792121691304681, -6.894970908927875, -1.418044259890785, 2.43396908639996, 0.8187056954245069, -1.438518595412533, -0.4858424059257835, -0.2303763571044945, -3.975023651762679, -6.820312070913663, -3.598214675636469, 1.783041543177172, 2.665725457671646, 0.1186246493200918, -0.6953921505395968, 0.2055234453780072, -0.095509613822207, -0.4850744507109368, 0.901463625955303, 1.203975627304794, -1.556371639852089, -2.804794981152809, 0.6495861160443662, 3.406605441388867, 0.8857221931078931, -1.446973470467096, 1.931856764191583, 5.392357359056661, 2.005243916558918, -3.40012846649738, -2.866775465922792, 0.8317639625643997, 0.9387091059245184, -0.5604622630715446, 1.225848277907808, 3.452884524163824, 1.83860614947645, -0.4682563109186951, 0.05811729626439466, 0.2721151171633997, -1.755167282834779, -1.936303269718533, 0.6211617176271413, 1.036891391263655, -0.6902588254168197, 0.6336409436489551, 3.404018390030812, 1.528215323014914, -1.961367101944451, 0.0816497929551391, 3.22112507480502, -1.370222665421831, -8.687145049601723, -7.539948719257274, -0.4625420752279425, 2.12165032209004, 0.1252174206580611, -0.2642048169247069, 0.4198050363749279, -0.06119285017730168, 1.385480900041095, 4.795818241894376, 4.420974907180044, 0.4771600149104687, -0.6894154395736499, 0.4750949494497894, -0.805459944910279, -1.735453864592217], 'positive_zeros': ['1.118284734298373', '1.511472939513795', '2.468010591750609', '3.493901982336878', '4.119238740226385', '4.743694927656337', '5.300472109012798', '5.770159478358567', '6.452775394658959', '7.040174947439041', '7.375806415282176', '8.485339421828971', '8.681176285517727', '9.274322055668707', '10.10020493949668', '10.70647003319954', '11.12153455162737', '11.48392786091232', '11.93064099089028', '12.58706188808052', '12.87802688020442', '13.81226683477943', '14.31616091728874', '14.83790173008374', '14.96152050786642', '15.90452174993881', '16.51335426329098', '16.93247708213495', '17.22251644028910', '17.61442654381761', '18.12862960099887', '18.71390852395228', '19.30763349376146', '19.64869887094293'], 'prelabel': '2-33800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.428461852283306, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 604454464259390447, 'z1': {'__RealLiteral__': 0, 'data': '1.118284734298373', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.511472939513795', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.468010591750609', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 269.89435883192783, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 33800, 'conductor_radical': 130, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 3, 0, 1, 0, 5, 0, 0, 0, 0, 0, 2, 0, -5, 0, -6, 0, 8, 0, 0, 0, 4, 0, 0, 0, -8, 0, -10, 0, 0, 0, -9, 0, 0, 0, 2, 0, 6, 0, 0, 0, -7, 0, 2, 0, -4, 0, 13, 0, 0, 0, 10, 0, 0, 0, 4, 0, 3, 0, 0, 0, 0, 0, -16, 0, -14, 0, 10, 0, 0, 0, 15, 0, -4, 0, -11, 0, -18, 0, 0, 0, 0, 0, -9, 0, 0, 0, 16, 0, 0, 0, 2, 0, 5, 0], 'euler11': [1, -5, 11], 'euler13': [1, 0, 0], 'euler17': [1, -2, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, -8, 23], 'euler29': [1, 0, 29], 'euler3': [1, 2, 3], 'euler31': [1, 8, 31], 'euler37': [1, 9, 37], 'euler41': [1, -2, 41], 'euler43': [1, -6, 43], 'euler47': [1, 7, 47], 'euler5': [1, 0, 0], 'euler53': [1, -13, 53], 'euler59': [1, 0, 59], 'euler61': [1, -4, 61], 'euler67': [1, 0, 67], 'euler7': [1, -3, 7], 'euler71': [1, 14, 71], 'euler73': [1, -10, 73], 'euler79': [1, 4, 79], 'euler83': [1, 18, 83], 'euler89': [1, 9, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 0, 0], [1, -3, 7], [1, -5, 11], [1, 0, 0], [1, -2, 17], [1, 5, 19], [1, -8, 23], [1, 0, 29], [1, 8, 31], [1, 9, 37], [1, -2, 41], [1, -6, 43], [1, 7, 47], [1, -13, 53], [1, 0, 59], [1, -4, 61], [1, 0, 67], [1, 14, 71], [1, -10, 73], [1, 4, 79], [1, 18, 83], [1, 9, 89], [1, -2, 97]], 'index': 19, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/33800/h'], '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': '2-33800-1.1-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': 1, 'prelabel': '2-33800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.428461852283306, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 604454464259390447, 'z1': {'__RealLiteral__': 0, 'data': '1.118284734298373', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '604454464259390447', 'Lhash_array': ['604454464259390447'], 'label': '2-33800-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/33800/h'}