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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': '1231730779077315318', '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': 513.8373370069395, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1]], [11, [1, -1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '64350.1', 'coefficient_field': '1.1.1.1', 'conductor': 64350, 'conductor_radical': 4290, 'degree': 2, 'euler_factors': [[1, 1], [1], [1], [1, 1, 7], [1, -1], [1, -1], [1, 1, 17], [1, 4, 19], [1, 8, 23], [1, -8, 29], [1, 0, 31], [1, 7, 37], [1, -8, 41], [1, 11, 43], [1, 1, 47], [1, -2, 53], [1, 14, 59], [1, 8, 61], [1, 8, 67], [1, 9, 71], [1, -4, 73], [1, -2, 79], [1, 0, 83], [1, -4, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 1, 'label': '2-64350-1.1-c1-0-1', 'leading_term': '0.512208349224', '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/64350/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.5122083492238642, 0.05731924760264134, -1.057104865990891, -2.088333194323893, -2.136875548745204, -0.9757620126121195, 0.4023282502162273, 0.4977894087652675, -1.027386340790374, -2.571606422140949, -2.135059604422694, 0.1120607641829886, 1.495726498997314, -0.09295556454004653, -3.139521059512807, -3.875877632897414, -1.181447910697421, 1.345374754220297, -0.2154138626654353, -4.468597893015953, -5.89384289562743, -2.095899327238683, 2.734319735464632, 3.393109704846485, 0.5240134665902632, -1.147766776224555, -0.2164462911155571, -0.07573691004675218, -2.532270565153647, 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0.7060318019223606, -0.2483074654119587, 0.8251107953580137, 5.009950929696491, 5.391184877168439, 1.098616933132132, 0.1505888866461646, 2.7974488331198, 1.126595570305961, -2.793429077245041, -0.1534591066259905, 5.11193062353922, 3.213572847230474, -1.290892290438606, 0.7315806791370321, 3.800113369206364, 0.1792829480569736, -3.541784843217768, -1.0805381736633, 0.6793635720238712, -2.313899876705703, -3.127809472762688, -0.07448105995283412, 0.3689657261258142, -1.403795548794141, -0.4389230993176447, 0.622568736635025, -1.169227615709343, -1.068207675352165, 1.966803350139629, 1.914602951247525, -0.7742124555512349, -0.5444460631707349, 0.5430992047660029, -0.9207151115794694, -0.5939074741651421, 2.483197532718162, 2.000232661793934, -1.05112830484637, -0.3990551326450812, 0.5874615088591632, -2.472031658611481], 'positive_zeros': ['0.2660740739984768', '1.413209931671082', '1.855156079023228', '2.738204300541557', '3.241897845569760', '4.088587166604232', '4.484955508906177', '5.346276583202277', '6.046220883628081', '6.549013127871183', '6.734555399715045', '7.762719875299828', '7.992922138581272', '8.663726461198447', '9.043345415369789', '9.675356758223257', '10.16769647113140', '10.59850221173978', '11.03616429073975', '11.79019919148981', '12.19848079512232', '12.48007936225048', '13.34256827367924', '13.69743193899020', '14.22515928934373', '14.85586825600696', '15.26732617161722', '15.88787405676119', '16.22358294938693', '16.58120444370052', '17.32004546311246', '17.62437420068619', '18.03799951128316', '18.60916157888280', '19.03567047489639', '19.58068370362424', '19.94452091688164'], 'prelabel': '2-64350-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.667980435119038, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1231730779077315318, 'z1': {'__RealLiteral__': 0, 'data': '0.2660740739984768', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.413209931671082', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.855156079023228', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 513.8373370069395, 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '1.1', 'conductor': 64350, 'conductor_radical': 4290, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, -1, -1, 0, 0, 1, 0, 1, 1, 0, 1, -1, 0, -4, 0, 0, -1, -8, 0, 0, -1, 0, -1, 8, 0, 0, -1, 0, 1, 0, 0, -7, 4, 0, 0, 8, 0, -11, 1, 0, 8, -1, 0, -6, 0, 0, 1, 2, 0, 0, 1, 0, -8, -14, 0, -8, 0, 0, 1, 0, 0, -8, -1, 0, 0, -9, 0, 4, 7, 0, -4, -1, 0, 2, 0, 0, -8, 0, 0, 0, 11, 0, -1, 4, 0, -1, -8, 0, 1, 0, 0, -8, 6, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, -1, 0], 'euler17': [1, 1, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 8, 23], 'euler29': [1, -8, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, 7, 37], 'euler41': [1, -8, 41], 'euler43': [1, 11, 43], 'euler47': [1, 1, 47], 'euler5': [1, 0, 0], 'euler53': [1, -2, 53], 'euler59': [1, 14, 59], 'euler61': [1, 8, 61], 'euler67': [1, 8, 67], 'euler7': [1, 1, 7], 'euler71': [1, 9, 71], 'euler73': [1, -4, 73], 'euler79': [1, -2, 79], 'euler83': [1, 0, 83], 'euler89': [1, -4, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 0, 0], [1, 1, 7], [1, -1, 0], [1, -1, 0], [1, 1, 17], [1, 4, 19], [1, 8, 23], [1, -8, 29], [1, 0, 31], [1, 7, 37], [1, -8, 41], [1, 11, 43], [1, 1, 47], [1, -2, 53], [1, 14, 59], [1, 8, 61], [1, 8, 67], [1, 9, 71], [1, -4, 73], [1, -2, 79], [1, 0, 83], [1, -4, 89], [1, 8, 97]], 'index': 1, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/64350/y'], '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': '2-64350-1.1-c1-0-1', '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': '2-64350-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.667980435119038, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1231730779077315318, 'z1': {'__RealLiteral__': 0, 'data': '0.2660740739984768', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1231730779077315318', 'Lhash_array': ['1231730779077315318'], 'factors': ['2-64350-1.1-c1-0-1'], 'label': '2-64350-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/64350/y'}