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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 3, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 6, 'Lhash': '1539346183761410459', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.7320508075688774, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'algebraic': True, 'analytic_conductor': 3064.5945492551255, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [17, [1]], [83, [1, -1]]], 'bad_primes': [2, 17, 83], 'central_character': '383792.1', 'coefficient_field': '1.1.1.1', 'conductor': 383792, 'conductor_radical': 2822, 'degree': 2, 'euler_factors': [[1], [1, -3, 3], [1, -2, 5], [1, 2, 7], [1, 1, 11], [1, -7, 13], [1], [1, -7, 19], [1, 6, 23], [1, -3, 29], [1, -2, 31], [1, -6, 37], [1, 6, 41], [1, 7, 43], [1, 8, 47], [1, 6, 53], [1, -14, 59], [1, 15, 61], [1, -12, 67], [1, -5, 71], [1, 1, 73], [1, 8, 79], [1, -1], [1, -8, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 15, 'label': '2-383792-1.1-c1-0-15', 'leading_term': '8.02595874388', '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/383792/t', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [8.025958743882487, 6.279285594838321, 2.031349152493258, -2.033055933996249, -3.262008025471739, -1.676159843115011, -0.08047403940267246, -0.5379574531093285, -1.69667461147317, -1.151479126329236, 0.558981464691326, 0.9053414164241507, -0.175402546294328, -0.329900823071605, 0.4535030138896166, -0.2913903967686214, -1.712268464299947, 0.4280448497096258, 5.354197716586013, 5.877920953268715, 0.008751154537474399, -3.929522813871158, -0.3324643673011865, 4.161459499125568, 2.520346816671162, -0.7506197244052414, 0.3649997463115291, 1.522026610962115, -2.353934423219283, -5.930247676657717, -3.629079909888987, -0.1391706383540192, -0.3983971445274377, -0.9665347444131531, 0.4821453988696471, 0.2732086966499303, -1.68854400960019, -1.361952935656525, -0.0185689241480755, -0.6122828493222316, -0.379557677504433, 0.6537881920305434, -3.25737599384139, -8.309263022355319, -3.546008654720158, 5.719953331601167, 4.143650450165424, -3.679484623666538, -1.335442458050068, 7.323005163102583, 7.201321715354814, 0.8388851782094335, -0.9979575551771197, 0.08070178716148144, -0.2931619865817526, 0.02350394692522707, 0.4067740302948067, -0.7788617438541545, 0.3155971709996451, 2.713871847287586, 0.1748448870354382, -3.55571847129998, -1.842542767214609, 0.2608213589958237, -0.1949411648648253, 2.267101962576545, 2.561221881875088, -6.593584628138047, -11.57487526251151, -1.425436549930119, 7.505216157965494, 3.515759947964236, -0.7651145513800341, 0.6779393318790539, 0.2146519996824119, -0.1650624752287348, 3.073845142913669, 2.698710139947359, -1.332031426868914, -1.317366062866658, 0.1896724674128425, -0.4784888144783217, 0.6378325094395338, 1.778530870859362, -0.002947937245922841, 0.4051188242326662, 1.512168154416457, -1.483379239819598, -0.5720228880980048, 5.040034854582344, 1.691266080640677, -5.23690046783366, -0.5121479029338721, 4.233205771723709, -2.630191477264789, -5.289376661587406, 1.41485678785943, 2.158118852025328, -1.749664234553401, -0.2471731047690875, 1.389299472177122, -0.138105507764994, -0.1648269064316019, -0.140058729841358, -0.4215671494399728, 0.8828007368876921, 0.1466820782902306, 0.1218171863444802, 4.387103910490711, 2.324588273300404, -5.143600569542248, -1.211152930323129, 6.651008892961953, 1.908986365222184, -3.087010545092629, 0.2975819526815103, -0.5129528938268367, -1.888767365799562, 4.95956183747196, 7.286874265669359, 1.577139458004381], 'positive_zeros': ['0.6117963335793934', '1.551135736504678', '1.581534987696501', '2.412895592705980', '2.958433329892097', '3.347785084245027', '3.704127531921953', '4.224786910419382', '5.000327418211123', '5.514155476288039', '6.164238853527821', '6.463610920793334', '6.881039439251348', '7.774100268197916', '7.919143871583044', '8.421662747958489', '8.786228211375522', '9.515681787586843', '9.555461064502619', '10.05967893873203', '10.33732008583468', '11.08537120605732', '11.61957392102384', '12.03802953667157', '12.79704882946515', '13.21368626334744', '13.38007571440983', '13.74380465897710', '14.09600929987315', '14.47080773815986', '15.00910222375301', '15.66971635639801', '15.87505938217875', '16.05414577729691', '16.59281198645973', '17.27659872037824', '17.90534150999118', '18.16006703520174', '18.53031578977222', '18.76904901369478', '19.40721572737538', '19.92473016838579'], 'prelabel': '2-383792-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.35878023633763, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1539346183761410459, 'z1': {'__RealLiteral__': 0, 'data': '0.6117963335793934', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.551135736504678', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.581534987696501', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3064.5945492551255, 'bad_primes': [2, 17, 83], 'central_character': '1.1', 'conductor': 383792, 'conductor_radical': 2822, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, 2, 0, -2, 0, 6, 0, -1, 0, 7, 0, 6, 0, 0, 0, 7, 0, -6, 0, -6, 0, -1, 0, 9, 0, 3, 0, 2, 0, -3, 0, -4, 0, 6, 0, 21, 0, -6, 0, -7, 0, 12, 0, -8, 0, -3, 0, 0, 0, -6, 0, -2, 0, 21, 0, 14, 0, -15, 0, -12, 0, 14, 0, 12, 0, -18, 0, 5, 0, -1, 0, -3, 0, 2, 0, -8, 0, 9, 0, 1, 0, 0, 0, 9, 0, 8, 0, -14, 0, 6, 0, 14, 0, 2, 0, -6, 0], 'euler11': [1, 1, 11], 'euler13': [1, -7, 13], 'euler17': [1, 0, 0], 'euler19': [1, -7, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -3, 29], 'euler3': [1, -3, 3], 'euler31': [1, -2, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, 7, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -14, 59], 'euler61': [1, 15, 61], 'euler67': [1, -12, 67], 'euler7': [1, 2, 7], 'euler71': [1, -5, 71], 'euler73': [1, 1, 73], 'euler79': [1, 8, 79], 'euler83': [1, -1, 0], 'euler89': [1, -8, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, -3, 3], [1, -2, 5], [1, 2, 7], [1, 1, 11], [1, -7, 13], [1, 0, 0], [1, -7, 19], [1, 6, 23], [1, -3, 29], [1, -2, 31], [1, -6, 37], [1, 6, 41], [1, 7, 43], [1, 8, 47], [1, 6, 53], [1, -14, 59], [1, 15, 61], [1, -12, 67], [1, -5, 71], [1, 1, 73], [1, 8, 79], [1, -1, 0], [1, -8, 89], [1, -2, 97]], 'index': 15, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/383792/t'], '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': '2-383792-1.1-c1-0-15', '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': '2-383792-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.35878023633763, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1539346183761410459, 'z1': {'__RealLiteral__': 0, 'data': '0.6117963335793934', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1539346183761410459', 'Lhash_array': ['1539346183761410459'], 'factors': ['2-383792-1.1-c1-0-15'], 'label': '2-383792-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/383792/t'}