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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1412133098782038872', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 563.4244366621547, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '70560.1', 'coefficient_field': '1.1.1.1', 'conductor': 70560, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1], [1, -2, 11], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, 1, 23], [1, -1, 29], [1, -2, 31], [1, -4, 37], [1, -5, 41], [1, -11, 43], [1, -8, 47], [1, -8, 53], [1, 4, 59], [1, -5, 61], [1, 1, 67], [1, -12, 71], [1, 6, 73], [1, -4, 79], [1, -13, 83], [1, 3, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 30, 'label': '2-70560-1.1-c1-0-30', 'leading_term': '2.24772660384', '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/70560/bi', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.247726603841829, 1.697605656655191, 0.3488141834275374, -0.8815174681819613, -0.8344233726115567, 0.8695229852334476, 3.072537154047658, 3.815435733801084, 2.332143681553551, 0.2042035322153036, -0.1107029221955673, 1.821047888638376, 3.601559964372597, 2.806738099268392, 0.1815330624713534, -1.182402858531673, -0.01791715366256434, 1.320279389742645, 0.3721287770999556, -1.468469868704385, -0.7841840280878843, 2.447180777322418, 4.203319144283834, 2.250740534617037, -0.2536906999296371, 0.5408872417665793, 3.175514092425377, 3.279660968688595, 0.7197239861892893, -0.3241962381248377, 1.38401759559451, 1.990912559819604, -0.5052825654800962, -2.34794226461274, -0.4767241037391299, 1.861847956519928, 0.7391628177925791, -1.377001836138417, -0.1953591005636979, 2.159906884501549, 0.6909311048463598, -3.094775713980748, -3.433451814683953, -0.5701448313214162, -0.09031639335932859, -2.489445851738104, -2.625332180084298, 0.1516195897555051, 0.9790596599234769, -0.6025384317835567, 0.1760569529755887, 3.078457689614575, 2.486873198662262, -1.315306985367126, -1.72136210513298, 1.806923282717592, 2.679053588129927, -0.1350327361924839, -0.7138302432171953, 1.497048050867644, 0.8956435044253708, -2.251764209199483, -2.259966348552371, -0.03210431994897715, -1.11591608812148, -3.642379481841308, -1.949762092524553, 1.308952720342919, 0.468673455308737, -1.299046369633638, 0.9862790775834807, 3.042990192868336, 0.4095113426156665, -1.429988380568838, 1.807315951774105, 4.019409301251088, 1.194455757187041, -0.9097496663598719, 0.4471537457097113, 0.2016753070331715, -1.781891979265202, -0.2138038749873621, 2.494333565994557, 0.3071014591378387, -2.663724513459496, -0.05086003019299285, 3.030705984948341, 0.6047472635769993, -1.942922126935419, -0.2728833636378165, 0.0984001686126804, -2.416549547757203, -1.533620081167355, 1.870550602403964, 0.9287691562121815, -1.777704510850875, 0.02790820098192823, 2.289580118435012, 0.3972421659157447, -0.3297120282902214, 1.954050035997198, 0.3194365718139167, -4.376710737972384, -3.721958397520543, -0.02492472030885011, -1.207574974314594, -3.602894031784795, -1.349258476431537, 0.417058563470508, -1.418224545436819, -0.8955111506757941, 1.731104464144858, 0.3521374419296154, -1.350790032800338, 2.156372092284931, 4.388278374910016, 1.074728454401336, -0.07795591225956366, 2.539106262270922, 1.058706980153111, -2.697010862061011], 'positive_zeros': ['0.5595006913753286', '1.146187527216308', '2.286562947177916', '2.524424130310923', '3.518545476635661', '4.002438476437809', '4.545353624149431', '5.070307518676580', '5.956945649483204', '6.186267091889372', '7.085261389374178', '7.322516462130442', '7.959251253799874', '8.538831613988592', '9.070421063812783', '9.517653745019028', '10.04548885732440', '10.82121992455825', '10.98513178883845', '11.73562930270986', '12.15233630869415', '12.48267159578905', '13.16045911738981', '13.62929405760025', '14.23750164406171', '14.58611004928557', '15.07165807184249', '15.75737666568881', '15.86770093811763', '16.62766026711037', '17.04486914105111', '17.42765716316497', '18.02833020666642', '18.39128539363416', '19.08866666415302', '19.43263368385671', '19.77428081571932'], 'prelabel': '2-70560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.73656328667136, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1412133098782038872, 'z1': {'__RealLiteral__': 0, 'data': '0.5595006913753286', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.146187527216308', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.286562947177916', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 563.4244366621547, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 70560, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 5, 0, 11, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, -2, 0, 0, 0, -4, 0, 5, 0, 0, 0, 2, 0, -1, 0, 0, 0, 12, 0, -6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 13, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, 2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 23], 'euler29': [1, -1, 29], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, -4, 37], 'euler41': [1, -5, 41], 'euler43': [1, -11, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -8, 53], 'euler59': [1, 4, 59], 'euler61': [1, -5, 61], 'euler67': [1, 1, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, 6, 73], 'euler79': [1, -4, 79], 'euler83': [1, -13, 83], 'euler89': [1, 3, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -2, 11], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, 1, 23], [1, -1, 29], [1, -2, 31], [1, -4, 37], [1, -5, 41], [1, -11, 43], [1, -8, 47], [1, -8, 53], [1, 4, 59], [1, -5, 61], [1, 1, 67], [1, -12, 71], [1, 6, 73], [1, -4, 79], [1, -13, 83], [1, 3, 89], [1, -2, 97]], 'index': 30, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/70560/bi'], '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': '2-70560-1.1-c1-0-30', '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': '2-70560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.73656328667136, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1412133098782038872, 'z1': {'__RealLiteral__': 0, 'data': '0.5595006913753286', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1412133098782038872', 'Lhash_array': ['1412133098782038872'], 'label': '2-70560-1.1-c1-0-30', 'type': 'ECQ', 'url': 'EllipticCurve/Q/70560/bi'}