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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 1, 'A9': 0, 'Lhash': '21954388669931774', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 600.0757711899224, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1]], [167, [1, 1]]], 'bad_primes': [2, 3, 5, 167], 'central_character': '75150.1', 'coefficient_field': '1.1.1.1', 'conductor': 75150, 'conductor_radical': 5010, 'degree': 2, 'euler_factors': [[1, -1], [1], [1], [1, 1, 7], [1, 0, 11], [1, -2, 13], [1, 2, 17], [1, -2, 19], [1, -2, 23], [1, -4, 29], [1, -1, 31], [1, -3, 37], [1, 2, 41], [1, 4, 43], [1, 1, 47], [1, 11, 53], [1, -3, 59], [1, 4, 61], [1, -3, 67], [1, 6, 71], [1, -4, 73], [1, 12, 79], [1, -7, 83], [1, 3, 89], [1, 7, 97]], 'gamma_factors': [[], [0]], 'index': 28, 'label': '2-75150-1.1-c1-0-28', 'leading_term': '10.247210402', '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/75150/bg', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.367193396753562, 3.601073267415525, 2.931615499709084, 0.6916494046394969, -1.438482628852573, -1.59884231201919, 0.3924231789214601, 2.550987365329719, 2.64153698514627, 0.6857328200422945, -1.004367586965309, -0.6682253832380373, 0.6498910891011778, 0.5956936388150982, -1.069404133061732, -2.005636458000847, -0.7620104755963205, 0.8661670531662261, 0.4610639276611026, -1.150965082552901, -1.026246022523378, 1.13135572674123, 2.232950861458138, 0.7430931071067786, -0.7085198193269748, 0.1722036801570125, 1.134905980354872, -0.7299677565766611, -3.156078411109839, -1.771546688296871, 2.010237076698823, 2.296138272204363, -1.462657328434329, -2.78948549228152, 1.119840116268889, 4.110294585735869, 1.170823691395097, -2.891487040593217, -1.605755162498661, 2.106116637535893, 1.416888317043151, -2.330336767309283, -2.567647316824372, 0.5475013458375732, 1.239282073379182, -0.7356921139695874, -0.3567925018423555, 2.321102135886634, 2.350437091703526, -0.2438876314209047, -0.7738169292053996, 0.7483760928597865, 0.3529513191985381, -1.214461306435475, -0.3483391376644938, 1.211421173378565, -0.1542778993788192, -1.76538206576473, 0.2289860014241798, 2.463462858686414, 0.8656701877204942, -1.044744683177782, 0.1681064066152803, 0.5154359701105213, -2.111413693539199, -2.283965886037943, 1.015488660941572, 0.3086448516824904, -5.11809195319388, -5.950421636562294, -1.048115689687959, -0.3768503804167027, -4.990237951346785, -4.680979692915397, 1.274103331399134, 2.812620286308001, -0.574703829966359, -0.1579451525140401, 3.33089205963915, 2.477583304687993, -0.5318440002375382, 0.3377084688849825, 1.638352996202453, -0.8747038902603549, -2.339140842334507, 0.07537453500854165, 0.9576943397743624, -0.9263826077228904, -0.5154563657262459, 1.302461437039369, 0.05122412544706555, -1.575184186112992, -0.3548017736418184, -0.3650757377265431, -2.693898536897141, -1.905608507743877, 0.9511490803304927, -0.2051881452710613, -2.447882033379408, -0.4258425790697215, 1.023001463367787, -1.432445871578427, -0.9651172711556311, 2.910290283590137, 1.546510572246146, -2.577567952036731, 0.0573642774215605, 4.001737404121003, 0.1175184409134195, -3.058331302481995, 2.827358813768068, 7.273618127236585, 2.929674542613349, -0.642401781724124, 0.6932770082298112, -0.2774973230314069, -2.341953103310858, 0.4757382631914004, 2.947369315869361, 0.2550102949630919], 'positive_zeros': ['1.069093644039577', '1.710698527026169', '2.578506346847799', '3.120235754822049', '3.603453570134553', '4.347610114464212', '4.820709914296853', '5.379766482421044', '6.092610961750576', '6.472976909701590', '6.935243956468317', '7.613265649840013', '8.160236477952573', '8.693079023090246', '9.308272784182983', '9.847396798891196', '10.34331895438444', '10.95380636574190', '11.40504161724156', '11.78654956633383', '12.47390936017634', '12.87492667232042', '13.29950729729166', '13.79194903722925', '14.23414444105645', '14.73196401725836', '15.32898017067130', '15.72690955533887', '16.06310420572903', '16.67002324389249', '17.01752522411054', '17.82624106754079', '17.96658481492771', '18.69469849947423', '19.20289836605844', '19.51178263070663'], 'prelabel': '2-75150-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.496444051941957, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 21954388669931774, 'z1': {'__RealLiteral__': 0, 'data': '1.069093644039577', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.710698527026169', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.578506346847799', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 600.0757711899224, 'bad_primes': [2, 3, 5, 167], 'central_character': '1.1', 'conductor': 75150, 'conductor_radical': 5010, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0, 2, -1, 0, 1, -2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, -1, 4, 0, 1, 1, 0, -2, 0, 0, 3, 2, 0, 0, -2, 0, -4, 0, 0, 2, -1, 0, -6, 0, 0, 2, -11, 0, 0, -1, 0, 4, 3, 0, -4, 1, 0, 1, 0, 0, 3, -2, 0, 0, -6, 0, 4, 3, 0, 2, 0, 0, -12, 0, 0, -2, 7, 0, 0, -4, 0, 0, -3, 0, -2, 2, 0, -1, 0, 0, -7, -6, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, 2, 17], 'euler19': [1, -2, 19], 'euler2': [1, -1, 0], 'euler23': [1, -2, 23], 'euler29': [1, -4, 29], 'euler3': [1, 0, 0], 'euler31': [1, -1, 31], 'euler37': [1, -3, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 1, 47], 'euler5': [1, 0, 0], 'euler53': [1, 11, 53], 'euler59': [1, -3, 59], 'euler61': [1, 4, 61], 'euler67': [1, -3, 67], 'euler7': [1, 1, 7], 'euler71': [1, 6, 71], 'euler73': [1, -4, 73], 'euler79': [1, 12, 79], 'euler83': [1, -7, 83], 'euler89': [1, 3, 89], 'euler97': [1, 7, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 1, 7], [1, 0, 11], [1, -2, 13], [1, 2, 17], [1, -2, 19], [1, -2, 23], [1, -4, 29], [1, -1, 31], [1, -3, 37], [1, 2, 41], [1, 4, 43], [1, 1, 47], [1, 11, 53], [1, -3, 59], [1, 4, 61], [1, -3, 67], [1, 6, 71], [1, -4, 73], [1, 12, 79], [1, -7, 83], [1, 3, 89], [1, 7, 97]], 'index': 28, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/75150/bg'], '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': '2-75150-1.1-c1-0-28', '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': '2-75150-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.496444051941957, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 21954388669931774, 'z1': {'__RealLiteral__': 0, 'data': '1.069093644039577', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '21954388669931774', 'Lhash_array': ['21954388669931774'], 'label': '2-75150-1.1-c1-0-28', 'type': 'ECQ', 'url': 'EllipticCurve/Q/75150/bg'}