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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': 3, 'A8': 1, 'A9': 1, 'Lhash': '1295675480717962284', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [1.1338934190276817, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 338.9649565803354, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1]], [283, [1, -1]]], 'bad_primes': [2, 3, 5, 283], 'central_character': '42450.1', 'coefficient_field': '1.1.1.1', 'conductor': 42450, 'conductor_radical': 8490, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1], [1, -3, 7], [1, 3, 11], [1, -7, 13], [1, -6, 17], [1, 0, 19], [1, -3, 23], [1, -3, 29], [1, 2, 31], [1, -8, 37], [1, -1, 41], [1, 2, 43], [1, -8, 47], [1, -6, 53], [1, 7, 59], [1, 11, 61], [1, 10, 67], [1, 12, 71], [1, -10, 73], [1, 6, 79], [1, -12, 83], [1, -9, 89], [1, -7, 97]], 'gamma_factors': [[], [0]], 'index': 14, 'label': '2-42450-1.1-c1-0-14', 'leading_term': '7.82889735973', '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/42450/bf', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [7.828897359728732, 7.070366643109845, 4.952404319609627, 2.145965118335412, -0.09805508796738086, -0.6451411463190782, 0.4807718512015214, 1.861763219638708, 1.8516833691524, 0.2247061059096786, -1.486424717859952, -1.619727582499154, -0.3275363581932121, 0.5501722487685644, -0.219468617307859, -1.597321224284664, -1.595048151049386, -0.06998848132012142, 0.8772374675808523, -0.2013483221983021, -1.847754953113809, -1.635225305152289, 0.1446265833491371, 0.6491666408477209, -1.149556217307132, -2.316000358721205, 0.04464724732149798, 4.044868382604038, 5.04065456255316, 2.123411420057191, -0.628584931309159, -0.354539644612007, 0.531491318923657, -0.9991290442801778, -2.916366368634, -1.439536384392363, 1.625802870106818, 0.4483747687157907, -5.443169954271901, -9.115711400699379, -6.068302228463739, -0.8438220809243357, 0.2743034744128625, -1.42887892473158, -0.7698191391039414, 1.826844218981506, 1.613853064015685, -1.309344361123383, -1.79806008849069, 1.169369997705751, 2.617630342973092, 0.3241322613262737, -1.700345371534483, -0.773545274772041, 0.2746784023762517, -0.6271288011499877, -0.9777794986399936, 0.5650275639836777, 1.139210665243112, -0.2876051808780803, -0.4986805974299158, 1.151617758783214, 0.824874127204475, -1.737152546318163, -1.663679156186083, 1.145722258255733, 0.4449106138159358, -3.925187828733696, -3.394606445819662, 4.087223372478917, 8.459137604157837, 4.008491283864499, -1.316382330921565, -0.7388049922592371, 0.5158765485430532, -2.152777994477765, -2.908276810480541, 2.092573272687347, 5.563568291333628, 2.033126158665174, -2.407230870819965, -1.815488807845002, 0.2366579353338899, -0.06262268253963998, -0.2590703077331045, 0.6058483467513804, -0.0972593742360838, -0.4508983282983948, 3.645223434739545, 8.15277715948967, 6.081419554313308, 0.4333516759624281, -1.196523171771609, 0.134881820047649, -0.381729252059676, -0.832624685472664, 1.081536353512758, 1.06463594213404, -2.350939719383726, -3.261620637792611, -0.4063966046070535, 0.288234955000267, -1.333839383623337, -0.2178547928540007, 0.9753444582410133, -2.821280345434369, -5.743678635054212, -1.423196625006859, 2.61904718348451, -0.8265001191051106, -4.011114705621068, -0.7016590164850564, 0.9257978153851222, -3.385574601181207, -4.391396795455551, 0.3772187188392553, 0.6274546586633422, -5.01277638339523, -5.951529383292726, -0.9223075966917618, 1.242207690969684], 'positive_zeros': ['0.9844221923833824', '1.419261172446508', '2.277877179731399', '3.060451201649624', '3.459486268382893', '4.260651549907905', '4.721672290462131', '5.478585303755913', '5.865440625015613', '6.497151710090068', '7.415397980851913', '7.816188540868598', '8.135782738656704', '8.855276431900721', '9.274780860417632', '10.32046778995143', '10.54702213423592', '11.07315358247591', '11.63973363595410', '12.16225746357793', '12.77691234416465', '13.37908851323667', '13.62045983789272', '14.16996673943942', '14.70313449909785', '15.08348447188293', '15.58427545951523', '16.14412421515033', '16.52917494052302', '17.12657445845034', '17.91080243294495', '18.32931858428893', '18.57775963098636', '19.16321157027278', '19.84210528397654'], 'prelabel': '2-42450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.411000966279246, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1295675480717962284, 'z1': {'__RealLiteral__': 0, 'data': '0.9844221923833824', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.419261172446508', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.277877179731399', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 338.9649565803354, 'bad_primes': [2, 3, 5, 283], 'central_character': '1.1', 'conductor': 42450, 'conductor_radical': 8490, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, 3, 1, 1, 0, -3, 1, 7, 3, 0, 1, 6, 1, 0, 0, 3, -3, 3, 1, 0, 7, 1, 3, 3, 0, -2, 1, -3, 6, 0, 1, 8, 0, 7, 0, 1, 3, -2, -3, 0, 3, 8, 1, 2, 0, 6, 7, 6, 1, 0, 3, 0, 3, -7, 0, -11, -2, 3, 1, 0, -3, -10, 6, 3, 0, -12, 1, 10, 8, 0, 0, -9, 7, -6, 0, 1, 1, 12, 3, 0, -2, 3, -3, 9, 0, 21, 3, -2, 8, 0, 1, 7, 2, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, -7, 13], 'euler17': [1, -6, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, -3, 23], 'euler29': [1, -3, 29], 'euler3': [1, -1, 0], 'euler31': [1, 2, 31], 'euler37': [1, -8, 37], 'euler41': [1, -1, 41], 'euler43': [1, 2, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 7, 59], 'euler61': [1, 11, 61], 'euler67': [1, 10, 67], 'euler7': [1, -3, 7], 'euler71': [1, 12, 71], 'euler73': [1, -10, 73], 'euler79': [1, 6, 79], 'euler83': [1, -12, 83], 'euler89': [1, -9, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 0, 0], [1, -3, 7], [1, 3, 11], [1, -7, 13], [1, -6, 17], [1, 0, 19], [1, -3, 23], [1, -3, 29], [1, 2, 31], [1, -8, 37], [1, -1, 41], [1, 2, 43], [1, -8, 47], [1, -6, 53], [1, 7, 59], [1, 11, 61], [1, 10, 67], [1, 12, 71], [1, -10, 73], [1, 6, 79], [1, -12, 83], [1, -9, 89], [1, -7, 97]], 'index': 14, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/42450/bf'], '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': '2-42450-1.1-c1-0-14', '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': '2-42450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.411000966279246, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1295675480717962284, 'z1': {'__RealLiteral__': 0, 'data': '0.9844221923833824', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1295675480717962284', 'Lhash_array': ['1295675480717962284'], 'factors': ['2-42450-1.1-c1-0-14'], 'label': '2-42450-1.1-c1-0-14', 'type': 'ECQ', 'url': 'EllipticCurve/Q/42450/bf'}