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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': '521594327105140936', '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': 105.40253066809017, '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': '13200.1', 'coefficient_field': '1.1.1.1', 'conductor': 13200, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 4, 7], [1, -1], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, 8, 23], [1, 10, 29], [1, 0, 31], [1, -10, 37], [1, 6, 41], [1, 8, 43], [1, 0, 47], [1, -2, 53], [1, 12, 59], [1, 2, 61], [1, 12, 67], [1, 8, 71], [1, -2, 73], [1, -8, 79], [1, 8, 83], [1, 6, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 72, 'label': '2-13200-1.1-c1-0-72', 'leading_term': '5.32665275032', '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': 2, 'origin': 'EllipticCurve/Q/13200/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.3279439824320418, -1.235738398503286, -2.414496731678532, -3.262159191131968, -3.115559032276655, -1.749349957794234, 0.237257123603805, 1.605268137748908, 1.318500952333232, -0.5130733490565816, -2.478050365307416, -2.892257632611532, -1.30108669454215, 0.9569027633121309, 1.89760634962564, 0.8493866642364103, -0.7528809394055351, -0.7778195153950541, 1.272676203263465, 3.55163143738683, 3.768597505040418, 1.72695760385297, -0.4551579837792749, -0.8367438187379995, 0.0915854241826925, 0.2592659433624324, -1.012560540821906, -1.861431363078241, -0.3964959225391552, 2.242673288298706, 2.66654198211543, -0.5409741584849576, -4.513981577676034, -5.183510437560741, -2.203844502888237, 0.6830591278729532, 0.4847226615860321, -1.415465301182349, -1.702568048166751, -0.05062972875117171, 0.592214796584574, -1.296489024108862, -3.228771140899711, -2.309092850360448, 0.2872891369665872, 0.8866981667892369, -1.218571078528036, -2.731650490611704, -1.436235674998163, 0.4706281770338819, 0.06574409437194331, -1.52388715096816, -1.177226184775063, 0.4814766578513108, -0.6038312442241937, -5.206006040792752, -8.36144707623681, -6.028493502524368, -1.146345836579089, 0.4997892781237575, -1.485028712775297, -2.374098688764754, -0.1866478138770193, 1.644247148056069, 0.543489251397019, -1.05299288277095, -0.5050585077659228, 0.1539190469077341, -1.875293895332769, -4.435915269909386, -3.546976078566344, -0.4298528456953316, 0.1253228701145824, -2.173035279409341, -2.599025206689859, 0.3347457507642795, 2.218904693106496, 0.4804780780886275, -1.259135075154063, -0.1777120691541488, 0.07960711611865218, -3.998960782440531, -8.210487900653524, -6.305632984465998, -0.1338049762605154, 3.025138401406788, 1.422631534430628, -0.2530916836292579, -0.002918723951796434, -0.6768708388059522, -2.670217220492202, -2.426914453013001, 0.188324130057825, 0.6508710398116743, -1.861558353646446, -2.445685415554798, 0.3864472019439625, 1.408586063695369, -1.737089242190893, -3.659555577177725, -0.7712020432189493, 2.117276482703417, 0.5943865964073552, -1.53026961353528, 0.05966894626904418, 1.917044615740453, -0.0747584359205967, -2.109709485693744, 0.6114394745113045, 4.425009938147613, 3.478179023800217, -0.006779156774280773, -0.5754894919623794, 0.5817822002398924, -0.529887796539629, -2.145016377536302, -0.874306205972584, 0.806562275002291, -0.1470086495160393, -0.3649753802395691], 'positive_zeros': ['1.719396231512600', '2.440905849008425', '3.388141190114969', '4.120841655776253', '4.617926002007811', '5.682931457420132', '6.225029529661103', '6.571411449369204', '7.287624164236929', '7.968417875534327', '8.917255673867525', '9.316361302628713', '10.00751782207997', '10.36053689636559', '11.21827275594741', '11.62686799929985', '12.41600058877774', '12.76039855460874', '13.41244406472001', '13.69660668234614', '14.83917504528131', '15.08947925518631', '15.76685873284434', '16.31620606222687', '16.85736137469615', '17.04531120072126', '18.04965201017888', '18.26986390140202', '18.97520483525527', '19.54642502636763'], 'prelabel': '2-13200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.266573462849724, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 521594327105140936, 'z1': {'__RealLiteral__': 0, 'data': '1.719396231512600', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.440905849008425', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.388141190114969', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 105.40253066809017, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 13200, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -4, 0, 1, 0, 1, 0, -2, 0, 0, 0, -6, 0, -4, 0, 4, 0, -8, 0, 0, 0, -1, 0, -10, 0, 0, 0, -1, 0, 0, 0, 10, 0, 2, 0, -6, 0, -8, 0, 0, 0, 0, 0, 9, 0, 6, 0, 2, 0, 0, 0, 4, 0, -12, 0, -2, 0, -4, 0, 0, 0, -12, 0, 8, 0, -8, 0, 2, 0, 0, 0, -4, 0, 8, 0, 1, 0, -8, 0, 0, 0, 10, 0, -6, 0, 8, 0, 0, 0, 0, 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, 8, 23], 'euler29': [1, 10, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -10, 37], 'euler41': [1, 6, 41], 'euler43': [1, 8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, 12, 59], 'euler61': [1, 2, 61], 'euler67': [1, 12, 67], 'euler7': [1, 4, 7], 'euler71': [1, 8, 71], 'euler73': [1, -2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 8, 83], 'euler89': [1, 6, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 4, 7], [1, -1, 0], [1, 2, 13], [1, 6, 17], [1, 4, 19], [1, 8, 23], [1, 10, 29], [1, 0, 31], [1, -10, 37], [1, 6, 41], [1, 8, 43], [1, 0, 47], [1, -2, 53], [1, 12, 59], [1, 2, 61], [1, 12, 67], [1, 8, 71], [1, -2, 73], [1, -8, 79], [1, 8, 83], [1, 6, 89], [1, -6, 97]], 'index': 72, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/13200/b'], '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': '2-13200-1.1-c1-0-72', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-13200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.266573462849724, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 521594327105140936, 'z1': {'__RealLiteral__': 0, 'data': '1.719396231512600', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '521594327105140936', 'Lhash_array': ['521594327105140936'], 'label': '2-13200-1.1-c1-0-72', 'type': 'ECQ', 'url': 'EllipticCurve/Q/13200/b'}