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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 1, 'A6': 0, 'A7': -1, 'A8': 1, 'A9': 0, 'Lhash': '1090020961878213233', 'a10': [0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 290.76725392029056, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [7, [1, 1]], [17, [1]]], 'bad_primes': [2, 3, 7, 17], 'central_character': '36414.1', 'coefficient_field': '1.1.1.1', 'conductor': 36414, 'conductor_radical': 714, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, -1, 5], [1, 1], [1, -3, 11], [1, 5, 13], [1], [1, 6, 19], [1, 8, 23], [1, -4, 29], [1, -6, 31], [1, -5, 37], [1, 4, 41], [1, -1, 43], [1, 2, 47], [1, -3, 53], [1, 4, 59], [1, -8, 61], [1, 1, 67], [1, -8, 71], [1, -5, 73], [1, 9, 79], [1, -9, 83], [1, -7, 89], [1, 3, 97]], 'gamma_factors': [[], [0]], 'index': 12, 'label': '2-36414-1.1-c1-0-12', 'leading_term': '2.98939556757', '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/36414/cj', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.989395567571674, 2.28857234779745, 0.3643813858029641, -2.096986863669882, -3.883865116528839, -3.907284834554304, -2.167208308463007, -0.0193481234795159, 0.856813983041148, 0.05589778375508774, -1.045391989257105, -0.6982863628324705, 1.19123696322733, 2.777246207493547, 2.351885340088556, 0.4654130836625146, -0.664063056477069, 0.03455034221591519, 1.049459467773496, 0.361930777350901, -1.590767605261098, -2.299620074260679, -0.6908643069304603, 1.195236526957728, 1.06914346922781, -0.2387127118754421, -0.1828045781408086, 1.148923469794878, 0.7081972747137474, -2.552447480283344, -5.023512017988185, -3.262511321565051, 0.2644328671812215, -0.0216809392578214, -4.499543264706945, -7.081871622131668, -3.833889837930393, 1.196315277870006, 2.070614088115725, -0.3780983841806643, -0.8701669728397211, 1.16612877625682, 0.8914170483946623, -3.136916185006558, -5.753193689820669, -3.286298069610538, 0.6190787898814294, 1.152822637276161, -0.3209620478157159, 0.04795104758520966, 1.386046171058815, 0.4144854799932199, -1.72884066923555, -1.328904815330174, 0.9184651821612559, 1.1880468948625, -0.3198938388932209, -0.1260960442010364, 1.4339203769368, 0.938029539379539, -0.7832054276655102, 0.2804863566583377, 2.997586866738905, 2.23051178030351, -1.330673234859653, -1.595316451857303, 1.790949840571498, 2.649673438867683, -0.04373809327148105, -0.5781009984281813, 1.433190520197963, -0.4796825521193875, -6.043753260392635, -6.118614140702297, 1.346377479178765, 6.381307425866403, 3.3989399678365, -0.5866841679158733, 0.1149067941219452, 1.088733187451063, -0.8353024438004295, -0.7517382521250429, 3.283198573563423, 4.998359798019618, 1.602453569702536, -1.207265453022351, -0.359802591276828, 0.2666341351483224, -0.6423675358874898, 0.09846776717292761, 1.59740611879307, 0.1528297327470456, -1.959409051960895, -0.4866421541589524, 1.504428372740018, -0.3632586714339863, -2.437191025823959, -0.6101161232472746, 1.0707862341454, -0.6570144695157937, -1.351441202392315, 0.7356357849603632, 0.4024512720049112, -2.16759062235589, -0.4477211442545244, 3.42739352412481, 0.8584469193167922, -5.103492470711232, -4.084338634091678, 1.143179616456769, 0.2132408862492984, -3.739116698227517, -0.9216021974224547, 4.741186657682816, 3.817330253872126, -0.007586211196050526, 0.981824117846553, 3.18687159073871, 1.45497058597257, -0.3054034272258621, 0.3290845811602279], 'positive_zeros': ['0.5379424174256485', '1.752803710610900', '2.260811270594709', '2.857081232736304', '3.816934905886888', '4.243169050775416', '4.800533422684612', '5.576543308939058', '6.196409871521924', '6.538802712132373', '7.069709022612900', '7.974353076272996', '8.248200870771146', '9.178389277065886', '9.710461400908999', '10.11458391040835', '10.57025515972169', '11.44829550603992', '11.93377190525211', '12.24169593726323', '12.79462773487516', '13.39324277483193', '13.94011200836572', '14.27108103113269', '14.86876223363718', '15.22291711060379', '15.90216696126421', '16.37508662573576', '16.99573126781118', '17.32298520020101', '17.72410020667849', '18.45995603360544', '19.18778075902047', '19.48574094428830', '19.90738319753684'], 'prelabel': '2-36414-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.05189883620855, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1090020961878213233, 'z1': {'__RealLiteral__': 0, 'data': '0.5379424174256485', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.752803710610900', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.260811270594709', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 290.76725392029056, 'bad_primes': [2, 3, 7, 17], 'central_character': '1.1', 'conductor': 36414, 'conductor_radical': 714, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 1, 0, -1, 1, 0, 1, 3, 0, -5, -1, 0, 1, 0, 0, -6, 1, 0, 3, -8, 0, -4, -5, 0, -1, 4, 0, 6, 1, 0, 0, -1, 0, 5, -6, 0, 1, -4, 0, 1, 3, 0, -8, -2, 0, 1, -4, 0, -5, 3, 0, 3, -1, 0, 4, -4, 0, 8, 6, 0, 1, -5, 0, -1, 0, 0, -1, 8, 0, 5, 5, 0, -6, -3, 0, -9, 1, 0, -4, 9, 0, 0, 1, 0, 3, 7, 0, 5, -8, 0, -2, -6, 0, -3, 1, 0, -4], 'euler11': [1, -3, 11], 'euler13': [1, 5, 13], 'euler17': [1, 0, 0], 'euler19': [1, 6, 19], 'euler2': [1, -1, 0], 'euler23': [1, 8, 23], 'euler29': [1, -4, 29], 'euler3': [1, 0, 0], 'euler31': [1, -6, 31], 'euler37': [1, -5, 37], 'euler41': [1, 4, 41], 'euler43': [1, -1, 43], 'euler47': [1, 2, 47], 'euler5': [1, -1, 5], 'euler53': [1, -3, 53], 'euler59': [1, 4, 59], 'euler61': [1, -8, 61], 'euler67': [1, 1, 67], 'euler7': [1, 1, 0], 'euler71': [1, -8, 71], 'euler73': [1, -5, 73], 'euler79': [1, 9, 79], 'euler83': [1, -9, 83], 'euler89': [1, -7, 89], 'euler97': [1, 3, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, -1, 5], [1, 1, 0], [1, -3, 11], [1, 5, 13], [1, 0, 0], [1, 6, 19], [1, 8, 23], [1, -4, 29], [1, -6, 31], [1, -5, 37], [1, 4, 41], [1, -1, 43], [1, 2, 47], [1, -3, 53], [1, 4, 59], [1, -8, 61], [1, 1, 67], [1, -8, 71], [1, -5, 73], [1, 9, 79], [1, -9, 83], [1, -7, 89], [1, 3, 97]], 'index': 12, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/36414/cj'], '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': '2-36414-1.1-c1-0-12', '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': '2-36414-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.05189883620855, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1090020961878213233, 'z1': {'__RealLiteral__': 0, 'data': '0.5379424174256485', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1090020961878213233', 'Lhash_array': ['1090020961878213233'], 'label': '2-36414-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/36414/cj'}