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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '1272318018683447594', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 421.61012267236066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '52800.1', 'coefficient_field': '1.1.1.1', 'conductor': 52800, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 4, 7], [1, 1], [1, 2, 13], [1, -2, 17], [1, 0, 19], [1, 8, 23], [1, -6, 29], [1, 8, 31], [1, -6, 37], [1, 2, 41], [1, 0, 43], [1, 8, 47], [1, -6, 53], [1, -4, 59], [1, 6, 61], [1, 4, 67], [1, 0, 71], [1, -14, 73], [1, 4, 79], [1, -12, 83], [1, 6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 63, 'label': '2-52800-1.1-c1-0-63', 'leading_term': '3.25959633538', '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/52800/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.6897516241751266, 0.6715880881431272, -0.4455132408419749, -2.248504448842882, -3.436523911435913, -2.726879277764211, -0.2418115667068729, 2.12590361333572, 2.270175126811162, 0.1268929075198698, -1.956470188496814, -1.677079639987121, 0.4639781450233659, 1.623540071717181, 0.197116404303428, -1.896044434502813, -1.567460717886887, 1.183675187369117, 2.971359183342167, 1.513882223542426, -1.196899041788956, -1.742429766663541, -0.1445778389803418, 0.5223494974199321, -0.8217890639412788, -1.607940442074217, -0.1936672261331994, 0.897078324150149, -0.9676089776794908, -3.494839137450398, -2.529429252779317, 0.8101351624516778, 0.9474033936606162, -3.467879126247986, -6.773651106626787, -4.624699883829821, -0.3858909436311528, 0.675335155386421, -0.5633897547386097, -0.09591816284347322, 1.421150631351475, 0.4472703992402445, -1.767384365696891, -0.5874710260540552, 3.374272367585175, 4.503652284979234, 1.642200054659778, -0.2777730367607922, 0.6988550774931049, 0.8006533770365339, -1.193248603291765, -1.369749150827505, 0.8379958057122321, 0.465560109177818, -3.110247827033717, -3.492436570553312, 1.106977163258382, 3.422734378590369, -0.2833592848793676, -3.33853513839832, -0.6100560195683643, 2.845066778153625, 1.873693386682035, -0.1325406381208439, 0.482289341702951, 0.8574245838860929, -0.4915636062878181, 0.5346758822548939, 4.274125329643045, 4.749728274208413, 1.050951277240786, -0.5076347653408948, 1.187228988725279, 0.3942014645427745, -2.825076850714833, -2.325053647980892, 1.167637626234964, 1.434112252539501, -0.2316770844352522, 1.466868812322244, 3.006468888209382, -1.401898128508643, -6.183338870221516, -3.403577351928462, 2.158996950777563, 2.227732882583319, -0.3170726164442618, 0.1857085589021725, 0.8090249536734403, -1.25895659781583, -1.824021720566726, 0.1223791021074479, -0.2107120073058527, -1.89636568611911, 0.04840304070645653, 2.409773731430072, -0.0635727351946805, -2.009138055330013, 2.217035799851023, 5.839102653806332, 2.86746105542092, -0.3372677165555854, 0.5148561139337443, -0.4125272311237727, -3.927699300044124, -3.124361780367583, 0.3154791690760606, -1.274143151639312, -4.642228711503786, -2.497571450296163, 0.6924539768009608, -1.132859440494363, -2.828377815701205, -0.3741649183564268, 0.99830453873806, -0.1630281563823604, 0.5496122156604224, 1.343391446866871, -0.8414100634124774, -0.7172230841324057], 'positive_zeros': ['0.6750611742928177', '1.771334806841168', '2.512134435758316', '3.198404523096050', '3.770888063849795', '4.402195027140824', '5.130799897107314', '5.772655780519693', '6.123800990136777', '6.775512363133880', '7.161460094699055', '7.933156653708424', '8.321040311416481', '9.283585528624298', '9.634370668082810', '10.01452192893950', '10.54509515567021', '11.04078955811806', '11.91315722457256', '12.11994723550853', '12.60969112414061', '13.15457494416960', '13.53905331459395', '14.19609416530022', '14.73572378873991', '15.28386819777731', '15.96485334224080', '16.14877628970371', '16.65638341426610', '16.95111671129869', '17.83505264689278', '18.09059186163412', '18.53180096170999', '19.15934339367931', '19.68517141629542', '19.85119833199995'], 'prelabel': '2-52800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.533146925699448, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1272318018683447594, 'z1': {'__RealLiteral__': 0, 'data': '0.6750611742928177', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.771334806841168', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.512134435758316', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 421.61012267236066, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 52800, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -4, 0, 1, 0, -1, 0, -2, 0, 0, 0, 2, 0, 0, 0, 4, 0, -8, 0, 0, 0, -1, 0, 6, 0, -8, 0, 1, 0, 0, 0, 6, 0, 2, 0, -2, 0, 0, 0, 0, 0, -8, 0, 9, 0, -2, 0, 6, 0, 0, 0, 0, 0, 4, 0, -6, 0, -4, 0, 0, 0, -4, 0, 8, 0, 0, 0, 14, 0, 0, 0, 4, 0, -4, 0, 1, 0, 12, 0, 0, 0, -6, 0, -6, 0, 8, 0, 8, 0, 0, 0, -2, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 0, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 6, 61], 'euler67': [1, 4, 67], 'euler7': [1, 4, 7], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, 4, 79], 'euler83': [1, -12, 83], 'euler89': [1, 6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 4, 7], [1, 1, 0], [1, 2, 13], [1, -2, 17], [1, 0, 19], [1, 8, 23], [1, -6, 29], [1, 8, 31], [1, -6, 37], [1, 2, 41], [1, 0, 43], [1, 8, 47], [1, -6, 53], [1, -4, 59], [1, 6, 61], [1, 4, 67], [1, 0, 71], [1, -14, 73], [1, 4, 79], [1, -12, 83], [1, 6, 89], [1, 2, 97]], 'index': 63, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/52800/d'], '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': '2-52800-1.1-c1-0-63', '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': '2-52800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.533146925699448, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1272318018683447594, 'z1': {'__RealLiteral__': 0, 'data': '0.6750611742928177', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1272318018683447594', 'Lhash_array': ['1272318018683447594'], 'label': '2-52800-1.1-c1-0-63', 'type': 'ECQ', 'url': 'EllipticCurve/Q/52800/d'}