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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '1704173802937808798', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1121.0996443787772, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '140400.1', 'coefficient_field': '1.1.1.1', 'conductor': 140400, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 4, 7], [1, -6, 11], [1, 1], [1, 6, 17], [1, 5, 19], [1, 6, 23], [1, -9, 29], [1, -4, 31], [1, 2, 37], [1, 9, 41], [1, -2, 43], [1, 9, 47], [1, -9, 53], [1, 0, 59], [1, -8, 61], [1, 13, 67], [1, 0, 71], [1, -4, 73], [1, -16, 79], [1, -6, 83], [1, -15, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 110, 'label': '2-140400-1.1-c1-0-110', 'leading_term': '5.28567572428', '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/140400/p', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.114316526926589, 1.107402541922533, -0.4268671947861807, -2.494637282003567, -3.145742353003305, -1.416149869663716, 1.167672919370788, 1.883377749935528, 0.07899065498612537, -1.682493369589163, -0.7722065300425007, 1.823623368999904, 2.697141321272969, 0.9242043505837751, -0.5535263668415024, 0.3674829500653573, 1.39050990950883, -0.3000033212806818, -2.524820270752464, -0.7211104668568088, 4.405564241546961, 6.830355639509267, 3.921277663388367, 0.08643361030510475, -0.5775648431565498, 0.1188117833043852, -0.162605316361718, 0.9628053625765493, 4.990071746437623, 6.989588902034264, 2.768828185126528, -2.912944401362807, -3.196548723172341, -0.0508405697507165, 0.282503655108064, -1.471580140200579, -0.635902304573504, 1.320723423693005, 0.1802790160070396, -1.731667381647076, -0.4341494778691888, 0.4913579520292447, -3.225927903151936, -6.519102026707652, -3.510670744605178, 1.104936853392799, 0.8790882186738948, -0.8469228810904244, 0.49595666212057, 1.056608535144494, -1.908298097067074, -2.945706267562554, 0.1126196102540339, 1.319939687946979, -0.3427113790336631, 1.14469913733193, 4.628258773132512, 3.01450080736745, -1.384814167376048, -1.092979367535354, 1.064403438485021, -1.176343244801623, -3.665765424534397, -1.438392192262495, 0.4632710140573891, -0.941786150751737, -0.110802369320039, 3.05662704097897, 2.197433379419162, -0.4911577521980505, 0.8774362722460824, 1.190862976088715, -4.668798058265469, -8.34740721385592, -3.908553073193245, 0.5604641201222204, 0.0534770328581456, -0.2086347675842533, 0.5085973587034444, -0.5893070273441059, 1.014645417672638, 6.201988409896383, 5.203292768038058, -2.600816967525496, -4.780589426028255, 0.04678587168908631, 1.54615139123388, -0.4055317838421819, 0.02170937409769048, -0.08472586361556415, -1.970866659884927, -0.1573286728607446, 2.2747921115196, -1.197066911420977, -3.686373009882168, 0.9098994759154648, 3.506611506613573, -0.04619211657791075, -0.8898709382285148, 1.455866534643829, 0.1752754745746089, -1.011406712633069, 1.607858859214029, 1.493020956303243, -1.008888020913642, 1.270036055691729, 3.637146256529749, 0.3454777475725826, -0.8919422704956025, 2.082519875648256, 0.3957507124672148, -3.486692642741537, -1.467855758960723, 0.5537262948440915, -2.10223575545867, -1.947617577189182, 0.7723005297629577, -0.7362990715587573, -1.914074228959996, 0.4938877891401933], 'positive_zeros': ['0.6969337561441926', '1.629786310854005', '2.258313714338138', '2.827013955446967', '3.613459154081345', '3.941907001933028', '4.472434482309896', '5.039819211495831', '6.009144921201053', '6.428606802926654', '6.650539863388253', '6.876466809853879', '7.856999313601329', '8.505329490715065', '8.790607445810612', '9.316609493440515', '9.767888877979919', '10.29932555857484', '10.55952057440732', '11.41961767877783', '11.84503126805971', '12.19045120139147', '12.60871387452448', '13.24135178441073', '13.68735974505145', '13.90437888184574', '14.65624212254519', '15.09612771872295', '15.41773045166956', '16.12531187957577', '16.36084802082432', '16.75906560854239', '17.42585664077972', '17.66020598754299', '18.07158032480488', '18.94090769397489', '19.25999076887372', '19.55084119432327', '19.88610886761762'], 'prelabel': '2-140400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.482826110989755, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1704173802937808798, 'z1': {'__RealLiteral__': 0, 'data': '0.6969337561441926', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.629786310854005', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.258313714338138', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1121.0996443787772, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 140400, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 6, 0, -1, 0, 0, 0, -6, 0, -5, 0, 0, 0, -6, 0, 0, 0, 0, 0, 9, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, -9, 0, 2, 0, 0, 0, -9, 0, 9, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 4, 0, 0, 0, -24, 0, 16, 0, 0, 0, 6, 0, 0, 0, 0, 0, 15, 0, 4, 0, 0, 0, 0, 0, -8, 0, 0, 0], 'euler11': [1, -6, 11], 'euler13': [1, 1, 0], 'euler17': [1, 6, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -9, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 9, 41], 'euler43': [1, -2, 43], 'euler47': [1, 9, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, 0, 59], 'euler61': [1, -8, 61], 'euler67': [1, 13, 67], 'euler7': [1, 4, 7], 'euler71': [1, 0, 71], 'euler73': [1, -4, 73], 'euler79': [1, -16, 79], 'euler83': [1, -6, 83], 'euler89': [1, -15, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 4, 7], [1, -6, 11], [1, 1, 0], [1, 6, 17], [1, 5, 19], [1, 6, 23], [1, -9, 29], [1, -4, 31], [1, 2, 37], [1, 9, 41], [1, -2, 43], [1, 9, 47], [1, -9, 53], [1, 0, 59], [1, -8, 61], [1, 13, 67], [1, 0, 71], [1, -4, 73], [1, -16, 79], [1, -6, 83], [1, -15, 89], [1, 8, 97]], 'index': 110, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/140400/p'], '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': '2-140400-1.1-c1-0-110', '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': '2-140400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.482826110989755, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1704173802937808798, 'z1': {'__RealLiteral__': 0, 'data': '0.6969337561441926', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1704173802937808798', 'Lhash_array': ['1704173802937808798'], 'factors': ['2-140400-1.1-c1-0-110'], 'label': '2-140400-1.1-c1-0-110', 'type': 'ECQ', 'url': 'EllipticCurve/Q/140400/p'}