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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 0, 'Lhash': '1046622627348219633', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 3176.448992406535, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [13, [1, -1]], [17, [1, -1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '397800.1', 'coefficient_field': '1.1.1.1', 'conductor': 397800, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 2, 7], [1, 0, 11], [1, -1], [1, -1], [1, -8, 19], [1, -6, 23], [1, -7, 29], [1, -3, 31], [1, -2, 37], [1, -12, 41], [1, -8, 43], [1, 6, 47], [1, 9, 53], [1, 9, 59], [1, -2, 61], [1, 1, 67], [1, 2, 71], [1, 2, 73], [1, 6, 79], [1, -12, 83], [1, 1, 89], [1, 4, 97]], 'gamma_factors': [[], [0]], 'index': 40, 'label': '2-397800-1.1-c1-0-40', 'leading_term': '3.06201112661', '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': 0, 'origin': 'EllipticCurve/Q/397800/bi', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.062011126609598, 2.114161829165803, 0.06071333143633116, -1.221341045946835, -0.5510741525870916, 0.7042962163412351, -0.2450733049005758, -3.717140874043631, -6.194666718969625, -4.664635534763984, -1.097940147316666, 0.266199027669525, -0.6547787849893891, -0.2095873965916015, 1.954804615418389, 1.743453007676563, -1.667841355944017, -3.197575060326377, -0.4833301573828214, 1.503332346499461, -0.6097057122314048, -2.25208157481302, 0.2856227949377707, 2.565657004255813, 0.8054829451421067, -0.6596645737669635, 1.424859585968884, 2.331596713235017, -0.4495388386464176, -1.395695708650805, 1.378521943909168, 1.82768545706606, -0.7381173249862223, 0.5343192282786609, 5.044499032544235, 4.813079655818943, 0.563075521257848, -0.467499791872892, 0.3960762969253631, -1.475015301470075, -1.975390898572262, 1.77120939785552, 2.946622018778263, -0.311234866896255, -0.308641748438083, 2.780151541765808, 1.31649755347483, -1.924863248299119, -0.04327239321109049, 2.074861934041928, -0.4324455204911374, -1.245509598071484, 1.263670796510734, 0.1542916443176059, -2.546837819004043, -0.4641700256909, 1.375595446307293, -0.8211553951736882, 0.2978457330339519, 4.386676533924357, 2.206872595469527, -2.628575415082823, -1.235455511178694, 1.334518870310618, 0.07386688539426685, 0.259717055920729, 0.5000374158129649, -4.208781062899365, -6.362218620078543, -1.609551000720243, 0.4924549706552743, -1.071675826544881, 1.614093927738484, 3.662006071812071, -0.4618046574890143, -2.204714695514709, 0.289644373600975, -0.8386843932741116, -2.175685487665149, 0.5514809340694949, -0.149610312822539, -3.27438164488664, -0.4989124797948358, 2.188747196415665, -0.4216617264729541, 0.1774321312394984, 2.747463658470974, -1.085258046367861, -4.025015089684311, -0.5161853886545896, 0.455196040406846, -1.23780502848932, 0.07978751044322788, -1.090755655443431, -3.716041182970521, 0.6793055443560811, 4.41832116430402, 0.4303509686668665, -0.8377436006399772, 1.883327887664662, 0.2675202369931126, -0.1708078792201986, 3.056542853115663, 1.015040533425007, -2.220585362804183, -0.03561397974344111, -0.07989792521217412, -1.657041353574536, 1.918946417364069, 2.526414716600278, -1.250926608745908, 1.216776556993244, 3.983561374491521, -0.4692570540575923, -1.914328851051075, 0.6601578972040993, -0.5363030084232457, -0.6911590670526527, -0.2037339850645403, -5.161438213657595, -5.919735679522562], 'positive_zeros': ['0.5076240489910886', '1.092744880544564', '1.474247924398358', '2.623171951634170', '2.845710843560881', '3.277557156411874', '3.887912659308609', '4.535621762025264', '4.949864002836018', '5.480084382174023', '6.078944855941612', '6.363525026574557', '6.964092116254019', '7.387813819339338', '7.919150394535738', '8.214734264492319', '9.046741922067933', '9.342958951751219', '9.591763460558755', '10.14492804161084', '10.72444372505263', '11.02567498102914', '11.58026602835247', '12.00298423861138', '12.46586855616870', '12.87206507613722', '13.26134492501547', '13.78331726533702', '14.16486731548052', '14.48112999546594', '15.09540023217818', '15.58375764101382', '16.01332268069988', '16.20376352688340', '16.54308660316200', '17.34647546071972', '17.57303270693376', '17.90008771834877', '18.47621641226983', '18.96076572764304', '19.16915249241849', '19.69994613170830', '19.98933192100897'], 'prelabel': '2-397800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 56.35999460970996, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1046622627348219633, 'z1': {'__RealLiteral__': 0, 'data': '0.5076240489910886', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.092744880544564', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.474247924398358', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3176.448992406535, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 397800, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 8, 0, 0, 0, 6, 0, 0, 0, 0, 0, 7, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 12, 0, 8, 0, 0, 0, -6, 0, -3, 0, 0, 0, -9, 0, 0, 0, 0, 0, -9, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, -6, 0, 0, 0, 12, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -1, 0], 'euler17': [1, -1, 0], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -7, 29], 'euler3': [1, 0, 0], 'euler31': [1, -3, 31], 'euler37': [1, -2, 37], 'euler41': [1, -12, 41], 'euler43': [1, -8, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 9, 53], 'euler59': [1, 9, 59], 'euler61': [1, -2, 61], 'euler67': [1, 1, 67], 'euler7': [1, 2, 7], 'euler71': [1, 2, 71], 'euler73': [1, 2, 73], 'euler79': [1, 6, 79], 'euler83': [1, -12, 83], 'euler89': [1, 1, 89], 'euler97': [1, 4, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 2, 7], [1, 0, 11], [1, -1, 0], [1, -1, 0], [1, -8, 19], [1, -6, 23], [1, -7, 29], [1, -3, 31], [1, -2, 37], [1, -12, 41], [1, -8, 43], [1, 6, 47], [1, 9, 53], [1, 9, 59], [1, -2, 61], [1, 1, 67], [1, 2, 71], [1, 2, 73], [1, 6, 79], [1, -12, 83], [1, 1, 89], [1, 4, 97]], 'index': 40, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/397800/bi'], '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': '2-397800-1.1-c1-0-40', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-397800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 56.35999460970996, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1046622627348219633, 'z1': {'__RealLiteral__': 0, 'data': '0.5076240489910886', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1046622627348219633', 'Lhash_array': ['1046622627348219633'], 'label': '2-397800-1.1-c1-0-40', 'type': 'ECQ', 'url': 'EllipticCurve/Q/397800/bi'}