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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': 2, 'A8': 1, 'A9': 1, 'Lhash': '1096081487903298631', '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': [0.7559289460184544, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2214.6509000602127, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [5, [1]], [43, [1]]], 'bad_primes': [2, 3, 5, 43], 'central_character': '277350.1', 'coefficient_field': '1.1.1.1', 'conductor': 277350, 'conductor_radical': 1290, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1], [1, -2, 7], [1, -2, 11], [1, -2, 13], [1, 4, 17], [1, -2, 19], [1, 2, 23], [1, -6, 29], [1, -8, 31], [1, -2, 37], [1, -10, 41], [1], [1, 10, 47], [1, 10, 53], [1, -6, 59], [1, 0, 61], [1, -4, 67], [1, 0, 71], [1, -4, 73], [1, 16, 79], [1, 0, 83], [1, 2, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 85, 'label': '2-277350-1.1-c1-0-85', 'leading_term': '13.2510160109', '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/277350/cp', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.973316257119421, 4.117301517219748, 2.783754408052511, 0.4650767233733191, -0.2396121926817994, 1.378028294557298, 2.833746517933328, 1.513707012346366, -1.358403858625012, -1.922936013992548, 0.6967743787283237, 2.610201951683338, 0.7507095739988658, -2.350119314337575, -2.466635384924524, -0.209978217997536, 0.6080880552856825, -0.3424429553525564, -0.1613823863434462, 1.040962974813837, 0.279858591230977, -1.882879360790993, -1.753373480190485, 0.3295545173830802, 0.6093132025846348, -0.2866539333280405, 1.233139520161276, 3.019620076332068, 0.2976339466128219, -3.562810300937882, -1.742719284417555, 2.456414790129742, 1.278024538942223, -1.439281767158865, 2.920676635278131, 9.21469968473047, 6.47064288783004, -0.9566441903291147, -1.171635484247141, 3.126269400062231, 1.625755454920346, -3.179937158022984, -2.907454863815788, 0.0556125584912963, 0.18103758403192, 0.09974689215192403, 1.633337663473287, 0.8739654337090039, -1.150631657468433, 0.2509079823744729, 1.910442233602228, -0.5427295266349166, -2.184143852677728, 0.2090587451799872, 0.81984985676029, -1.482560200499831, -1.014228346140791, 0.3765146380502909, -2.084269608969577, -3.26716164680886, 0.4702920125269174, 2.040359980315162, -0.4038865983002567, -0.3780767777141324, -0.01719177170785493, -4.262395867231324, -5.934476313056572, -0.8392450564557031, 1.733968014882151, -0.2926202077879361, 0.7225011443081696, 1.474103987251952, -2.797593791009466, -1.998038141541739, 6.32382390381918, 7.408869024329691, 0.5293491873063346, 0.03684885171750868, 3.357344185161125, 0.07130816228494638, -2.754460901506461, 1.075597464538684, 2.54008497822339, -0.175792240863987, 0.1588739511017863, 0.7659247296750538, -1.822305589945328, -1.849038710014238, 0.3172403890761105, -0.5282326603115768, -0.8706821125075453, 0.9587355703627878, -0.0039540884564445, -1.071013593016848, 1.438666551032286, 1.779900932869242, -0.2757698446781605, 0.6492285743079571, 0.7032388427670344, -0.4971553520250508, 4.480459199207452, 8.1766120417172, 1.28305002286622, -2.598249759359629, 3.259418155305609, 2.966581210198549, -3.213673831533905, -0.7833298517262366, 2.964062535258352, -0.8524313256396395, -1.080431577628822, 3.077503686111821, 1.15340493459906, -1.166271292319002, 0.9001995072448113, -0.9780866506907806, -3.618303526979317, 0.05167933154833338, 1.760033067072862, -0.9451060658803453], 'positive_zeros': ['1.072639447960371', '1.312904071861931', '2.127542382521809', '2.694706083984700', '3.304804091452881', '4.026876662160745', '4.413736785961766', '4.783008166530794', '5.282704867416633', '5.955280362707983', '6.383552027877314', '6.605581073438419', '7.265808666527008', '7.839805356626752', '8.333006533127035', '8.636931292937823', '9.458231557974653', '9.814967064243383', '10.32757848559718', '10.99251916814077', '11.30555058299188', '11.47520852626937', '12.08793897228245', '12.47691522383961', '12.96013615469785', '13.48082950594113', '13.84253163259754', '14.37102541631085', '14.57565703572217', '15.22214802819664', '15.70598707604539', '16.06110454029116', '16.24789967350106', '17.03964670490415', '17.45655742098426', '17.67375967267967', '18.10285413946168', '18.56745025287017', '19.27675868547925', '19.49752982138114'], 'prelabel': '2-277350-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.060077561136815, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1096081487903298631, 'z1': {'__RealLiteral__': 0, 'data': '1.072639447960371', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.312904071861931', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.127542382521809', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2214.6509000602127, 'bad_primes': [2, 3, 5, 43], 'central_character': '1.1', 'conductor': 277350, 'conductor_radical': 1290, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 0, -1, 2, 1, 1, 0, 2, -1, 2, 2, 0, 1, -4, 1, 2, 0, -2, 2, -2, -1, 0, 2, -1, 2, 6, 0, 8, 1, -2, -4, 0, 1, 2, 2, -2, 0, 10, -2, 0, 2, 0, -2, -10, -1, -3, 0, 4, 2, -10, -1, 0, 2, -2, 6, 6, 0, 0, 8, 2, 1, 0, -2, 4, -4, 2, 0, 0, 1, 4, 2, 0, 2, 4, -2, -16, 0, 1, 10, 0, -2, 0, 0, -6, 2, -2, 0, 4, -2, -8, -10, 0, -1, -14, -3, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, -2, 13], 'euler17': [1, 4, 17], 'euler19': [1, -2, 19], 'euler2': [1, -1, 0], 'euler23': [1, 2, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -2, 37], 'euler41': [1, -10, 41], 'euler43': [1, 0, 0], 'euler47': [1, 10, 47], 'euler5': [1, 0, 0], 'euler53': [1, 10, 53], 'euler59': [1, -6, 59], 'euler61': [1, 0, 61], 'euler67': [1, -4, 67], 'euler7': [1, -2, 7], 'euler71': [1, 0, 71], 'euler73': [1, -4, 73], 'euler79': [1, 16, 79], 'euler83': [1, 0, 83], 'euler89': [1, 2, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 0, 0], [1, -2, 7], [1, -2, 11], [1, -2, 13], [1, 4, 17], [1, -2, 19], [1, 2, 23], [1, -6, 29], [1, -8, 31], [1, -2, 37], [1, -10, 41], [1, 0, 0], [1, 10, 47], [1, 10, 53], [1, -6, 59], [1, 0, 61], [1, -4, 67], [1, 0, 71], [1, -4, 73], [1, 16, 79], [1, 0, 83], [1, 2, 89], [1, 14, 97]], 'index': 85, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/277350/cp'], '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': '2-277350-1.1-c1-0-85', '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': '2-277350-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.060077561136815, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1096081487903298631, 'z1': {'__RealLiteral__': 0, 'data': '1.072639447960371', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1096081487903298631', 'Lhash_array': ['1096081487903298631'], 'label': '2-277350-1.1-c1-0-85', 'type': 'ECQ', 'url': 'EllipticCurve/Q/277350/cp'}