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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': 0, 'A8': 1, 'A9': 0, 'Lhash': '1736500182296444227', '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': [0.0, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 176.07013645692334, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '22050.1', 'coefficient_field': '1.1.1.1', 'conductor': 22050, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1, -1], [1], [1], [1], [1, 2, 11], [1, -2, 13], [1, 2, 17], [1, 6, 19], [1, 4, 23], [1, 0, 29], [1, -2, 31], [1, 2, 37], [1, -10, 41], [1, -8, 43], [1, -8, 47], [1, 2, 53], [1, -4, 59], [1, 8, 61], [1, -4, 67], [1, 6, 71], [1, 2, 73], [1, 8, 79], [1, 4, 83], [1, 10, 89], [1, -18, 97]], 'gamma_factors': [[], [0]], 'index': 120, 'label': '2-22050-1.1-c1-0-120', 'leading_term': '7.7556838301', '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/22050/ds', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.846322950253868, 3.108166701505223, 3.18677550360281, 1.824159082188033, -0.4504346220536293, -2.385148313922534, -2.804975452048069, -1.616734368920798, -0.05218359772707537, 0.3266819382034258, -0.878626245282926, -2.406655542901573, -2.560409686860185, -1.041256041056698, 0.6447252631888638, 0.8656816075439618, -0.1859657455958662, -0.6896144862733827, 0.4865514208811529, 2.180160173148684, 2.289318068496816, 0.5617591581592521, -0.9190568913003451, -0.5094310266155876, 0.591252148996541, -0.09319773064455635, -2.586673543936862, -3.935173172774653, -2.226649789959676, 0.2736604660369274, -0.143944434608906, -3.280949803919429, -4.865320285270531, -2.56870750160565, 0.1798183114782779, -1.287618991257939, -5.911115612820339, -7.765018373971859, -4.13821129172721, 0.6607750468462483, 1.417105544524542, -0.9445615226268098, -1.675504162775552, 0.1881428502276669, 0.879120802373506, -1.381298697950572, -3.245383229611214, -1.731726374767457, 0.9423169681922559, 1.175234365156156, -0.2159792880883484, 0.003778088285747994, 1.545534044649688, 1.296349046481696, -0.7560040250768125, -1.279748640039625, 0.293306917548626, 0.4865520046605423, -1.914908794123271, -3.318732140793325, -1.576318827835741, 0.1731103414452511, -0.5897099932048631, -0.8971643765778388, 1.914922491712465, 4.14277713533604, 1.641192168845498, -2.011520918725039, -0.7870321509231802, 3.125240461456388, 2.619095142487803, -1.781300921716421, -2.401168440367093, 2.196059031403993, 4.541723685883368, 1.267905496931791, -1.390580754218427, 0.874678707475532, 3.096450299470237, 0.702943508203069, -2.281171259458864, -1.158254117073528, 1.15692647602277, 0.5943282399730211, -0.4708528331425709, 1.024714478767836, 2.200726675923416, 0.2135699003057015, -1.60495469593011, -0.1817599448622309, 1.24578453351015, -0.2596584843936435, -1.566461488407829, -0.2199224342144197, 0.5025094323478644, -1.144076326497038, -1.277511216662558, 1.186184030803391, 1.189853192873479, -2.389179742430549, -3.519300885793598, -0.5241923291633251, 0.5750380183077648, -1.538985287832863, -0.6703315158451687, 3.183111370774069, 1.839837587165671, -4.914062385644913, -6.760237046578031, -1.057654812024598, 2.562636680892134, 0.1730903505501939, -0.6599444748913972, 2.860894169544308, 3.737019866762934, 0.1387175314857601, -1.09907089891313, 1.408423573035413, 1.652413224701639, -0.7426748493477486], 'positive_zeros': ['1.202427350110003', '2.261352901383471', '2.599002685301950', '3.638133563884158', '4.209731327973886', '4.677641478971687', '5.571676768576951', '6.100006235901599', '6.487447668125782', '7.460338167161260', '7.733470020749383', '8.717820684687492', '8.887896977874266', '9.954790194394287', '10.40573082947548', '10.97708871994197', '11.37449129445990', '12.14781707152569', '12.70288359460159', '12.99929821205196', '13.65870135044399', '14.20538597851438', '14.56778617781014', '15.44494014511506', '15.63249228869362', '16.10698482339354', '16.84368285239795', '17.29882772987101', '17.89826956289130', '18.39362124696107', '19.07748107284926', '19.43682733268019'], 'prelabel': '2-22050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.269142265305748, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1736500182296444227, 'z1': {'__RealLiteral__': 0, 'data': '1.202427350110003', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.261352901383471', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.599002685301950', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 176.07013645692334, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 22050, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, 2, 0, 0, 1, -2, 0, -6, 0, 0, -2, -4, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, -2, 0, 0, -2, -6, 0, 0, 10, 0, 8, -2, 0, -4, 8, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 4, 0, -8, 2, 0, 1, 0, 0, 4, -2, 0, 0, -6, 0, -2, -2, 0, -6, 0, 0, -8, 0, 0, 10, -4, 0, 0, 8, 0, -2, -10, 0, 0, -4, 0, 8, 0, 0, 18, 0, 0, 0], 'euler11': [1, 2, 11], 'euler13': [1, -2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 6, 19], 'euler2': [1, -1, 0], 'euler23': [1, 4, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, 2, 37], 'euler41': [1, -10, 41], 'euler43': [1, -8, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, -4, 59], 'euler61': [1, 8, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 6, 71], 'euler73': [1, 2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 10, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 2, 11], [1, -2, 13], [1, 2, 17], [1, 6, 19], [1, 4, 23], [1, 0, 29], [1, -2, 31], [1, 2, 37], [1, -10, 41], [1, -8, 43], [1, -8, 47], [1, 2, 53], [1, -4, 59], [1, 8, 61], [1, -4, 67], [1, 6, 71], [1, 2, 73], [1, 8, 79], [1, 4, 83], [1, 10, 89], [1, -18, 97]], 'index': 120, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/22050/ds'], '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': '2-22050-1.1-c1-0-120', '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': '2-22050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.269142265305748, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1736500182296444227, 'z1': {'__RealLiteral__': 0, 'data': '1.202427350110003', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1736500182296444227', 'Lhash_array': ['1736500182296444227'], 'label': '2-22050-1.1-c1-0-120', 'type': 'ECQ', 'url': 'EllipticCurve/Q/22050/ds'}