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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 3, 'A8': 0, 'A9': 1, 'Lhash': '1666828421983791826', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1841.6696722188117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [31, [1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '230640.1', 'coefficient_field': '1.1.1.1', 'conductor': 230640, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, -3, 7], [1, -3, 11], [1, -2, 13], [1, 0, 17], [1, 1, 19], [1, -1, 23], [1, -4, 29], [1], [1, 4, 37], [1, -12, 41], [1, -11, 43], [1, 6, 47], [1, 11, 53], [1, 6, 59], [1, -14, 61], [1, -2, 67], [1, -3, 71], [1, -13, 73], [1, -1, 79], [1, -12, 83], [1, -11, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 50, 'label': '2-230640-1.1-c1-0-50', 'leading_term': '6.70969586734', '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/230640/di', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [6.709695867340387, 5.557382452098656, 2.731198752050394, -0.01332554213159469, -0.8577619284340994, 0.2432275626812393, 1.265839702323366, 0.555809944799254, -0.8144192413953745, -0.4811803552755884, 1.394213463242971, 1.75895603403975, -0.7757926967162251, -3.185185502210276, -2.261650837372784, 0.1825014150801224, 0.02564970426687381, -2.27815951721843, -2.443833073369709, -0.1271702413005695, 0.06277766291480417, -2.926802870871465, -3.777742895129491, 0.007917883264728365, 3.100433618561058, 1.585785379337328, 0.007688429836652995, 2.650170776252465, 5.151862079151682, 2.698220830428579, -0.7532371466266764, -0.1073392985002399, 1.526676595716737, 0.008391636147503193, -1.483247843689747, 0.05897148165274353, 0.8445446819829127, -0.9753394895411923, -0.753127447092017, 1.900432005255897, 0.7101093684062867, -3.96040366128696, -4.35020762953699, -0.5432134594991643, 0.2634418858200944, -0.7261673645575183, 2.558891404739484, 6.054985885677, 3.150306270692936, -0.6370450250733538, 1.194852675104674, 2.586779451304633, -1.396077131722959, -3.712430321033972, -0.6673281337672, 1.044293621065913, -0.4788350805977257, -0.2943008659836146, 0.6230941193016266, -0.3280983543574454, 1.189455128201427, 5.268628735900593, 4.31317271707733, -0.0960150741472636, 0.6125187143046326, 2.474167287416058, -2.428364512530676, -6.925796167514971, -3.402484132794305, 0.4704643806473946, -0.3460052893648549, 0.3253221435596944, 1.8171515884713, -1.457429570803404, -3.717632732958741, 0.0544229848196933, 1.860541048941263, -0.7940441507853035, 0.009817932047762485, 2.464200469106292, -0.3484356058586539, -3.009467887619676, -0.5949063295340021, 0.6701311592103469, -0.198515440121886, 1.385249731445496, 1.466530824037663, -1.378456305739719, 0.4989274633035398, 4.028772742291365, 0.04429615872644789, -4.030504468789436, -0.6008063350692116, -0.2880746786885409, -6.428006096673384, -6.587601048561095, -1.098370442652481, -0.01546029607294044, -0.2132109716187816, 1.971789902495253, 0.7892094507830757, -1.634904108338689, -0.1124238805941476, -0.2938700390557951, -2.630859959575098, 0.3465324694686865, 3.702942207452428, 1.068468238396967, 0.2755596282616517, 2.854426674530712, 1.019541914115379, -1.100844045970414, 0.336624415276551, -2.566153183095739, -5.888965116041844, 0.4188989708725143, 5.904941163621809, 1.548097172707212, -0.9515981955178912, 1.574852975252123, 0.1188365070248533], 'positive_zeros': ['0.7483446712087173', '1.208872366093939', '1.840552525767091', '2.320975666303954', '2.939276029503944', '3.724298317195569', '4.003438628335519', '4.766201809237577', '5.007945742084847', '5.749575911511335', '6.453061737976205', '6.496038086076434', '7.420983798673990', '7.761959247205498', '8.250848344931767', '8.742939515551161', '9.129179685622938', '9.571641059858917', '10.04072288065056', '10.79905874169075', '11.04484928428462', '11.34861628835249', '12.17342972912052', '12.40517359331212', '12.92897017256895', '13.54895205101989', '13.92492513985047', '14.30160995201215', '14.66912083167133', '14.89956062520152', '15.74131035543252', '15.94763511276834', '16.40907567796270', '17.18605143890657', '17.43616581852065', '17.71237356650396', '18.16925993446830', '18.74699192776555', '19.17338102933649', '19.49922701855815', '19.98049972472371'], 'prelabel': '2-230640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.91467898305674, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1666828421983791826, 'z1': {'__RealLiteral__': 0, 'data': '0.7483446712087173', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.208872366093939', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.840552525767091', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1841.6696722188117, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 230640, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 3, 0, 2, 0, 1, 0, 0, 0, -1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 4, 0, 0, 0, 3, 0, 3, 0, -4, 0, 2, 0, 12, 0, 11, 0, 1, 0, -6, 0, 2, 0, 0, 0, -11, 0, 3, 0, -1, 0, -6, 0, 14, 0, 3, 0, 2, 0, 2, 0, 1, 0, 3, 0, 13, 0, 1, 0, 9, 0, 1, 0, 1, 0, 12, 0, 0, 0, 4, 0, 11, 0, 6, 0, 0, 0, -1, 0, 10, 0, 3, 0], 'euler11': [1, -3, 11], 'euler13': [1, -2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 23], 'euler29': [1, -4, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 0], 'euler37': [1, 4, 37], 'euler41': [1, -12, 41], 'euler43': [1, -11, 43], 'euler47': [1, 6, 47], 'euler5': [1, -1, 0], 'euler53': [1, 11, 53], 'euler59': [1, 6, 59], 'euler61': [1, -14, 61], 'euler67': [1, -2, 67], 'euler7': [1, -3, 7], 'euler71': [1, -3, 71], 'euler73': [1, -13, 73], 'euler79': [1, -1, 79], 'euler83': [1, -12, 83], 'euler89': [1, -11, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, -3, 7], [1, -3, 11], [1, -2, 13], [1, 0, 17], [1, 1, 19], [1, -1, 23], [1, -4, 29], [1, 0, 0], [1, 4, 37], [1, -12, 41], [1, -11, 43], [1, 6, 47], [1, 11, 53], [1, 6, 59], [1, -14, 61], [1, -2, 67], [1, -3, 71], [1, -13, 73], [1, -1, 79], [1, -12, 83], [1, -11, 89], [1, -10, 97]], 'index': 50, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/230640/di'], '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': '2-230640-1.1-c1-0-50', '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': '2-230640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.91467898305674, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1666828421983791826, 'z1': {'__RealLiteral__': 0, 'data': '0.7483446712087173', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1666828421983791826', 'Lhash_array': ['1666828421983791826'], 'label': '2-230640-1.1-c1-0-50', 'type': 'ECQ', 'url': 'EllipticCurve/Q/230640/di'}