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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1879730697388037255', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 623.9829815550937, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [11, [1, -1]], [37, [1, 1]]], 'bad_primes': [2, 3, 11, 37], 'central_character': '78144.1', 'coefficient_field': '1.1.1.1', 'conductor': 78144, 'conductor_radical': 2442, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 2, 5], [1, 0, 7], [1, -1], [1, -2, 13], [1, -6, 17], [1, -4, 19], [1, -4, 23], [1, -6, 29], [1, 8, 31], [1, 1], [1, -2, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, -8, 59], [1, -10, 61], [1, -4, 67], [1, 8, 71], [1, -10, 73], [1, 0, 79], [1, -4, 83], [1, -6, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 62, 'label': '2-78144-1.1-c1-0-62', 'leading_term': '5.35687801647', '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/78144/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.204840843905255, 1.665236984454745, 1.049569279421211, -0.04315347391696043, -0.2060236875916363, 1.492936541842369, 4.081738741777681, 5.014488041370091, 2.659469369376132, -1.496683103726295, -3.914434436175046, -2.796356684498651, -0.1935525658014478, 0.6019542758515889, -0.6593743021513775, -1.05714090996946, 1.030036811207159, 3.251900115733209, 2.668740754703805, 0.3362147549797929, -0.1760719356724941, 1.574562892389629, 2.091637701881344, -0.2778519926676911, -2.241047668305235, -0.7172951897795401, 1.934908585650815, 1.656704936477208, -0.5581231148376615, -0.5695284493288267, 1.418741056273458, 1.205550720096434, -1.335529325932994, -1.18049329362142, 2.899415182736293, 5.164885771088476, 2.302143545574873, -0.6782651996721911, 0.9633270476845136, 3.517932711796595, 1.731646534105517, -1.808093675176296, -1.757299067634077, 0.4465864606511809, 0.2614485985139652, -1.196774987277978, -0.4473188248710821, 0.7115502860113286, -0.6240427180391882, -1.511152541765159, 0.8428606721620596, 1.897072341395222, -2.012480282929187, -5.021118670206526, -1.526060377613802, 2.955141528862443, 1.655846426503154, -1.155552431088423, 0.7135704573442204, 3.186431926595525, 0.652298585212785, -2.751629693542115, -1.811777514240855, 0.07983299923073225, -0.3848032349649621, 0.4290187511317332, 3.428990540276035, 3.222144316860573, -0.1426179515142783, -0.107773096654346, 2.843098529945961, 2.051900511289101, -1.107082204038198, -0.2237687916240653, 2.373690607928505, 1.124992252517875, -0.5106288377431234, 1.387586371549715, 1.33394861232454, -3.328331631097811, -4.961042786206127, -1.170440483646426, 0.02802407072205179, -2.495634799520755, -0.9628498362103021, 3.511491783173574, 2.789639864852711, -0.7951105173167389, 0.2008334777972012, 2.699672955015293, 1.175841349472557, -0.6455460807360729, 0.0951415771740853, -0.5617453145344212, -2.04550318718135, -0.347555086884165, 0.2774329133876252, -4.135347895731283, -6.093093564385645, -1.631825588314813, 0.4544710980586174, -2.1518791466322, -0.2953671530538029, 5.007216303311787, 3.34170220399743, -2.555312821388818, -2.530215118898321, 0.6303645605885045, 0.2790613343077174, -0.1606883652291279, 1.094999549201465, -0.648217608362771, -3.027113484197956, -0.8640356184742625, 0.7893981198572773, -1.673716095562501, -1.254201793431465, 2.756776730102419, 2.215325474199006, -0.6678247857251448], 'positive_zeros': ['0.9880632398007781', '1.303629784673920', '2.409367850846878', '3.274248317994365', '3.638764566984400', '4.152905747904451', '5.049675635355796', '5.287119879350307', '5.976697447842227', '6.559689906149565', '7.179179863566769', '7.575508389718153', '8.120395709165031', '8.587281429451231', '9.405600465135456', '9.669408957586779', '10.35957504907249', '10.93770183794146', '11.28967540597383', '11.81533776807307', '12.17063475750548', '12.67914359509730', '13.14748352025858', '13.81729476956507', '14.36522029261415', '14.69809204152793', '15.28744699142077', '15.97352073110297', '16.13063705379908', '16.45167573283149', '17.23676384879239', '17.51024386150890', '18.14558789547957', '18.51833404019829', '19.11289447849224', '19.35452353082304', '19.83550030794952'], 'prelabel': '2-78144-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.979651349750537, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1879730697388037255, 'z1': {'__RealLiteral__': 0, 'data': '0.9880632398007781', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.303629784673920', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.409367850846878', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 623.9829815550937, 'bad_primes': [2, 3, 11, 37], 'central_character': '1.1', 'conductor': 78144, 'conductor_radical': 2442, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -2, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 6, 0, 4, 0, 0, 0, 4, 0, -1, 0, -1, 0, 6, 0, -8, 0, -1, 0, 0, 0, -1, 0, -2, 0, 2, 0, 4, 0, -2, 0, 0, 0, -7, 0, -6, 0, -6, 0, -2, 0, -4, 0, 8, 0, 10, 0, 0, 0, -4, 0, 4, 0, -4, 0, -8, 0, 10, 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 0, -12, 0, -6, 0, 6, 0, 0, 0, 8, 0, -8, 0, -6, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 1, 0], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -8, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 0, 79], 'euler83': [1, -4, 83], 'euler89': [1, -6, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 2, 5], [1, 0, 7], [1, -1, 0], [1, -2, 13], [1, -6, 17], [1, -4, 19], [1, -4, 23], [1, -6, 29], [1, 8, 31], [1, 1, 0], [1, -2, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, -8, 59], [1, -10, 61], [1, -4, 67], [1, 8, 71], [1, -10, 73], [1, 0, 79], [1, -4, 83], [1, -6, 89], [1, 6, 97]], 'index': 62, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/78144/i'], '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': '2-78144-1.1-c1-0-62', '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': '2-78144-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.979651349750537, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1879730697388037255, 'z1': {'__RealLiteral__': 0, 'data': '0.9880632398007781', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1879730697388037255', 'Lhash_array': ['1879730697388037255'], 'factors': ['2-78144-1.1-c1-0-62'], 'label': '2-78144-1.1-c1-0-62', 'type': 'ECQ', 'url': 'EllipticCurve/Q/78144/i'}