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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': 1, 'A8': 1, 'A9': 1, 'Lhash': '1705358342476142783', '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': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 3026.7294886166346, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1]], [7, [1, -1]], [19, [1]]], 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '379050.1', 'coefficient_field': '1.1.1.1', 'conductor': 379050, 'conductor_radical': 3990, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1], [1, -1], [1, -1, 11], [1, -1, 13], [1, 3, 17], [1], [1, 3, 23], [1, -5, 29], [1, 4, 31], [1, -10, 37], [1, 9, 41], [1, -4, 43], [1, 6, 47], [1, 4, 53], [1, 15, 59], [1, 5, 61], [1, 13, 67], [1, -9, 71], [1, 10, 73], [1, -7, 79], [1, -11, 83], [1, 6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 223, 'label': '2-379050-1.1-c1-0-223', 'leading_term': '17.971227322', '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/379050/js', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 4.012132385566863, 5.422403976026993, 3.237045528312526, -0.6128423523011505, -2.586108041423978, -1.365283491827488, 0.4833956294183983, 0.03727552678695812, -1.77285442192849, -1.77012494616811, 0.190554966625038, 0.9244098683115507, -0.5543187980531956, -1.238740778203841, 0.3729181713859831, 1.391590944510631, -0.007038661915365253, -1.043846179938629, -0.08610953239980813, -0.5112903471627896, -3.901303960554374, -5.522118875528541, -2.566727868315163, 0.08587117591050193, -0.9768559594713077, -1.172454390066515, 2.168130028108646, 3.489966338901546, 0.3259217327852885, -0.9948858213994495, 1.739149751887409, 2.061560221694874, -0.8547465926458434, 0.06064860097345577, 3.923755516323147, 2.89047700730812, -0.4387898426902389, 2.190370692772071, 6.192029130682543, 2.914099904101641, -1.698298617272452, 0.6330088339624796, 3.466281380665509, 0.5733963452172629, -1.022632903468262, 2.018053164037474, 2.212680404810582, -0.8164170783834075, 0.1408067312051426, 2.783236036190908, 1.112364660996009, -0.6903167781220362, 1.128397678793974, 1.603386965422252, -0.1286066782175748, 0.2744283491500098, 0.6695699615627247, -1.379918177788298, -1.464013458978608, 0.2193863624270077, -0.9104358592840202, -1.276542219288451, 1.639528385317515, 0.812102357846103, -2.764894922083688, -0.3813784812245756, 2.106828146054084, -3.22491569452626, -4.82762184565152, 3.218941451161312, 5.878594695126648, 0.4349781446310261, 0.5290258521085962, 2.537187202032064, -3.667285017608256, -7.668706688523769, -2.102997452884742, 1.337802528980829, -0.320469889561459, 0.7676724252273459, 1.534860020881997, -0.9862594272856605, -0.5768182369025217, 0.7367040864656221, -2.080876520271486, -2.959232730702597, -0.3755569029987744, -0.3079896836399521, 0.8426274979326056, 5.091492510051124, 3.916536113421662, -0.4178579146853397, 0.9758203365304089, 2.500848684239611, -0.00177076612764394, 0.4991884309575968, 1.872774803238446, -0.6975763405593169, -0.6680695384067153, 1.689835490761969, 0.1285177752373614, 0.1989627659445892, 2.51351311564536, -1.345820702642358, -4.499498633560584, -0.647214470145824, -1.286352783822422, -4.823410843054543, 0.2713126302552813, 3.702544120516998, -0.1984344342547533, 3.340208989166124, 9.493029002489738, 3.667715555547495, -2.086481398326178, 0.2795529759229057, -1.449699678023824, -4.272481085210298, 0.345184894427841, 2.640288093885959], 'positive_zeros': ['0.9575678824331757', '1.661989415196432', '2.005610401722817', '2.725719233801802', '3.171924831543000', '3.703623081496403', '4.249062152062154', '4.772822249761146', '4.922851281988930', '5.974681368193559', '6.095806401662463', '6.605142815788875', '7.274077637030303', '7.608879259821442', '8.169411408551769', '8.495853508070450', '9.190375203099864', '9.371488358559697', '10.12406884342961', '10.46466754128037', '11.03836289769916', '11.35239116639130', '11.91982263114201', '12.23880420428459', '12.84734002345151', '13.12765010078051', '13.72345255036445', '13.94600957467996', '14.34714669845599', '14.94335804153230', '15.12501840172268', '15.61570648099246', '16.04964465946670', '16.51988974456798', '16.87794254611714', '17.41006189859230', '18.02818333824492', '18.21004950727592', '18.63383640567891', '19.33978417851549', '19.69441724142735', '19.91210604971403'], 'prelabel': '2-379050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.01572037714888, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1705358342476142783, 'z1': {'__RealLiteral__': 0, 'data': '0.9575678824331757', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.661989415196432', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.005610401722817', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3026.7294886166346, 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '1.1', 'conductor': 379050, 'conductor_radical': 3990, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, -3, 1, 0, 0, 1, 1, -3, 1, 0, 1, 1, 1, 5, 0, -4, 1, 1, -3, 0, 1, 10, 0, 1, 0, -9, 1, 4, 1, 0, -3, -6, 1, 1, 0, -3, 1, -4, 1, 0, 1, 0, 5, -15, 0, -5, -4, 1, 1, 0, 1, -13, -3, -3, 0, 9, 1, -10, 10, 0, 0, 1, 1, 7, 0, 1, -9, 11, 1, 0, 4, 5, 1, -6, 0, 1, -3, -4, -6, 0, 1, -2, 1, 1, 0], 'euler11': [1, -1, 11], 'euler13': [1, -1, 13], 'euler17': [1, 3, 17], 'euler19': [1, 0, 0], 'euler2': [1, -1, 0], 'euler23': [1, 3, 23], 'euler29': [1, -5, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -10, 37], 'euler41': [1, 9, 41], 'euler43': [1, -4, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 4, 53], 'euler59': [1, 15, 59], 'euler61': [1, 5, 61], 'euler67': [1, 13, 67], 'euler7': [1, -1, 0], 'euler71': [1, -9, 71], 'euler73': [1, 10, 73], 'euler79': [1, -7, 79], 'euler83': [1, -11, 83], 'euler89': [1, 6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 0, 0], [1, -1, 0], [1, -1, 11], [1, -1, 13], [1, 3, 17], [1, 0, 0], [1, 3, 23], [1, -5, 29], [1, 4, 31], [1, -10, 37], [1, 9, 41], [1, -4, 43], [1, 6, 47], [1, 4, 53], [1, 15, 59], [1, 5, 61], [1, 13, 67], [1, -9, 71], [1, 10, 73], [1, -7, 79], [1, -11, 83], [1, 6, 89], [1, 2, 97]], 'index': 223, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/379050/js'], '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': '2-379050-1.1-c1-0-223', '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': '2-379050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.01572037714888, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1705358342476142783, 'z1': {'__RealLiteral__': 0, 'data': '0.9575678824331757', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1705358342476142783', 'Lhash_array': ['1705358342476142783'], 'label': '2-379050-1.1-c1-0-223', 'type': 'ECQ', 'url': 'EllipticCurve/Q/379050/js'}