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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': 0, 'A8': 0, 'A9': 1, 'Lhash': '2081188681143931386', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1032.9448005472836, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [7, [1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '129360.1', 'coefficient_field': '1.1.1.1', 'conductor': 129360, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1], [1, 1], [1, 5, 13], [1, 0, 17], [1, -2, 19], [1, -3, 23], [1, -3, 29], [1, -8, 31], [1, -8, 37], [1, 3, 41], [1, 5, 43], [1, -3, 47], [1, 9, 53], [1, 0, 59], [1, 2, 61], [1, 14, 67], [1, 12, 71], [1, -10, 73], [1, 8, 79], [1, -6, 83], [1, 0, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 174, 'label': '2-129360-1.1-c1-0-174', 'leading_term': '9.35152047205', '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/129360/fy', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.113269488493471, 2.968631621146598, 1.919828816162543, -0.2930472221404653, -1.720687168737282, -0.9603400656411603, 1.137559316238274, 2.189129979274839, 1.116623555289659, -0.4297274261927045, -0.4028496666700002, 0.4627881803225111, -0.4712819085196486, -3.43912522681194, -5.031596195053106, -2.838538131103877, 0.5741904259085474, 1.097665244079374, -0.6955448665230028, -0.6096454393027881, 1.9229074111679, 2.416149665470649, -1.088357142256934, -3.979203335083076, -2.251038405882828, 0.7548551229954544, -0.03928719198520477, -2.862572390612243, -2.622782015370829, 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2.064630144204736, -0.6513938880277516, -0.09339903972340642, 2.299417498329718, 0.5750336066175312, -1.320484756661881, 0.8553397924483356, 1.317055870540225, -1.0932540336064, 0.4749779155213312, 3.050307362979975, -0.8211435993522384, -4.296415672472667, 0.01282088437422378, 3.088937244565911, -0.7995160522874898, -2.245470944945423, 1.332368045693836, 1.596374566637669, -0.5245111842992629, 0.6938284574518083, 1.388134942427993, -0.1618886011281485, 1.917726075816965, 5.113411179387369, 2.79868770475277, -0.1524361980636368, 0.7252193498001828, 0.3605418919766796, 0.3064224121997749, 5.902490449583853, 8.680038072680146, 2.087292487398911, -2.582546002001254, 0.04767942115271358, 0.2394282514577589, -2.012586639863996, 0.7667529055401986, 3.11236127853878, 0.3080163319916425, 0.02477447039966398], 'positive_zeros': ['0.9670726358137830', '1.617763746107591', '2.412594310047798', '2.852347261200019', '3.190564051396807', '4.197526465324909', '4.653783765705431', '5.070451439728456', '5.686619902475591', '6.415226549956316', '6.746383227356568', '7.517339068911325', '7.734061791810249', '8.348259824513653', '8.905563929051238', '9.453684278895167', '9.781289044680874', '10.27548517810044', '10.65258018242365', '11.42138539236503', '11.88202908337385', '12.31164892772877', '12.83451426573214', '13.36295610716303', '13.67008736243575', '14.21896599846601', '14.64889288931254', '15.10845255951226', '15.40603496103270', '16.10317273363006', '16.46825844951046', '17.03516136491907', '17.47247447636860', '17.76847152866852', '18.44895395438595', '18.75267125751690', '19.36814975665410', '19.58245955779410'], 'prelabel': '2-129360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.13945862249835, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2081188681143931386, 'z1': {'__RealLiteral__': 0, 'data': '0.9670726358137830', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.617763746107591', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.412594310047798', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1032.9448005472836, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 129360, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, -5, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 1, 0, 1, 0, 3, 0, 8, 0, -1, 0, 0, 0, 8, 0, -5, 0, -3, 0, -5, 0, 1, 0, 3, 0, 0, 0, 0, 0, -9, 0, -1, 0, 2, 0, 0, 0, -2, 0, 0, 0, -5, 0, -14, 0, 3, 0, -12, 0, 10, 0, 1, 0, 0, 0, -8, 0, 1, 0, 6, 0, 0, 0, 3, 0, 0, 0, 0, 0, 8, 0, 2, 0, -2, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 5, 13], 'euler17': [1, 0, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, -3, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -8, 37], 'euler41': [1, 3, 41], 'euler43': [1, 5, 43], 'euler47': [1, -3, 47], 'euler5': [1, -1, 0], 'euler53': [1, 9, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, 14, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, -10, 73], 'euler79': [1, 8, 79], 'euler83': [1, -6, 83], 'euler89': [1, 0, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 0, 0], [1, 1, 0], [1, 5, 13], [1, 0, 17], [1, -2, 19], [1, -3, 23], [1, -3, 29], [1, -8, 31], [1, -8, 37], [1, 3, 41], [1, 5, 43], [1, -3, 47], [1, 9, 53], [1, 0, 59], [1, 2, 61], [1, 14, 67], [1, 12, 71], [1, -10, 73], [1, 8, 79], [1, -6, 83], [1, 0, 89], [1, 2, 97]], 'index': 174, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/129360/fy'], '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': '2-129360-1.1-c1-0-174', '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': '2-129360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.13945862249835, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2081188681143931386, 'z1': {'__RealLiteral__': 0, 'data': '0.9670726358137830', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2081188681143931386', 'Lhash_array': ['2081188681143931386'], 'label': '2-129360-1.1-c1-0-174', 'type': 'ECQ', 'url': 'EllipticCurve/Q/129360/fy'}