-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1333252817995196750', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1295.8762043229558, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '162288.1', 'coefficient_field': '1.1.1.1', 'conductor': 162288, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1], [1], [1, 4, 5], [1], [1, -2, 11], [1, 5, 13], [1, 0, 17], [1, 4, 19], [1, -1], [1, -3, 29], [1, -5, 31], [1, -4, 37], [1, -5, 41], [1, -4, 43], [1, -11, 47], [1, 0, 53], [1, -12, 59], [1, -6, 61], [1, -16, 67], [1, -7, 71], [1, 7, 73], [1, 16, 79], [1, 8, 83], [1, 12, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 63, 'label': '2-162288-1.1-c1-0-63', 'leading_term': '1.80725528633', '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/162288/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.807255286334411, 1.286071106779317, 0.2245013017936069, -0.08635872982351207, 1.420939076104749, 4.080973299781714, 5.391874876926023, 3.414232032720742, -0.5801141567401403, -2.931057986822583, -1.807601738041014, 0.3694881315187473, 0.0967888144997412, -2.350552875711394, -3.439711868873594, -1.775540485069977, -0.03435361765930672, -0.2218845753089343, -0.2500267941133317, 1.848979062812722, 3.263775138380723, 0.6131185087522313, -3.114283482573786, -1.865482225520297, 3.646321646921517, 6.208008210663279, 3.182795209244745, 0.02543058446225666, 0.5162512799761911, 1.296041384186288, -0.314046378182692, -1.099507000978731, 0.8330877904726512, 1.754271463946027, 0.2599498893488764, 0.8584794375294394, 4.389505836117881, 4.632206922842399, 0.09572880776106384, -1.783123291764049, 1.810075266318941, 3.468578169698347, -0.3845419079422948, -3.009062994057731, -0.7538343220501955, 0.8909081639847202, -0.5590264298980947, -0.6520957460426469, 1.019036805389954, 0.4122390360463056, -0.780858680587147, 0.7163164818875913, -0.03717100687922543, -6.555031523268378, -10.14375132727942, -4.286809499327668, 2.386264084472337, 1.81565515677427, -0.3222701113113627, 1.074430855235202, 1.30198765589282, -0.9957357206334573, -0.8101942699940675, 0.534435866798511, -1.318967829926863, -2.240929437906361, 1.162824012643823, 2.473506870322331, -0.4365849006774663, -0.4246646966031284, 1.434024370206206, -3.102741956616602, -9.328115994495798, -6.63648737896339, 0.06606631096945435, 0.7601381553442503, -1.127717023693783, -0.2474272439593985, -0.1133643548367471, -1.128362682670493, 0.07901495719887688, -0.4173703919607001, -4.321625424830226, -3.340450982068794, 2.380541200319303, 1.576989937359789, -4.015413395084256, -2.872414946338559, 1.668206005792689, 0.6119396449933163, -1.022291660983505, 1.460992888961627, 1.76213001063356, -0.4829358376015088, 0.4482087362921488, 1.209119257620581, -1.101521031574705, -0.4245187253926218, 2.179957501747489, 0.3126141606480496, -0.1698046849467605, 5.152798602205878, 5.329530919271662, -1.865508122531674, -2.969434253371761, 2.371405205470307, 2.720678572956869, 0.03526063627446887, 0.5519942415256667, 0.4024453610453967, -0.6648675498469439, 0.913664361857969, 0.1973270205976556, -3.214657682046327, -0.9965693529147069, 2.383300420156378, -2.013112611429098, -4.850490067969336, 0.9234493988069733, 3.5941749679767, -0.1555182477479273], 'positive_zeros': ['0.5694148037325393', '0.7830439858422918', '1.962891891353296', '2.693341198880580', '3.012834989696982', '4.012306107779578', '4.163261889633123', '4.547303477865270', '5.285215859846969', '5.841707809440199', '6.755130397420573', '6.903104601182127', '7.461391580949494', '7.910470152825296', '8.580727473818485', '8.607683429987155', '9.505210621101659', '9.895504145714220', '10.47970635610826', '11.06513981007820', '11.42024242998783', '11.84297807128151', '12.30630033351837', '12.65801482665865', '12.99771834302407', '13.88358041452255', '14.41835556099938', '14.60962642442809', '15.13963882079804', '15.60778996313618', '15.86934002763055', '16.42697688634561', '16.96138138184064', '17.29124529484692', '17.62998169091253', '18.49628845565345', '18.83043972205935', '19.30342136851194', '19.47278229976750', '19.98726306030675'], 'prelabel': '2-162288-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.998280574535165, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1333252817995196750, 'z1': {'__RealLiteral__': 0, 'data': '0.5694148037325393', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.7830439858422918', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.962891891353296', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1295.8762043229558, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 162288, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, -5, 0, 0, 0, 0, 0, -4, 0, 0, 0, 1, 0, 11, 0, 0, 0, 3, 0, 5, 0, 0, 0, 0, 0, 4, 0, 0, 0, 5, 0, 4, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 12, 0, 6, 0, 0, 0, 20, 0, 16, 0, 0, 0, 7, 0, -7, 0, 0, 0, 0, 0, -16, 0, 0, 0, -8, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 16, 0, -6, 0, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, 5, 13], 'euler17': [1, 0, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, -3, 29], 'euler3': [1, 0, 0], 'euler31': [1, -5, 31], 'euler37': [1, -4, 37], 'euler41': [1, -5, 41], 'euler43': [1, -4, 43], 'euler47': [1, -11, 47], 'euler5': [1, 4, 5], 'euler53': [1, 0, 53], 'euler59': [1, -12, 59], 'euler61': [1, -6, 61], 'euler67': [1, -16, 67], 'euler7': [1, 0, 0], 'euler71': [1, -7, 71], 'euler73': [1, 7, 73], 'euler79': [1, 16, 79], 'euler83': [1, 8, 83], 'euler89': [1, 12, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 4, 5], [1, 0, 0], [1, -2, 11], [1, 5, 13], [1, 0, 17], [1, 4, 19], [1, -1, 0], [1, -3, 29], [1, -5, 31], [1, -4, 37], [1, -5, 41], [1, -4, 43], [1, -11, 47], [1, 0, 53], [1, -12, 59], [1, -6, 61], [1, -16, 67], [1, -7, 71], [1, 7, 73], [1, 16, 79], [1, 8, 83], [1, 12, 89], [1, 6, 97]], 'index': 63, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/162288/f'], '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': '2-162288-1.1-c1-0-63', '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': '2-162288-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.998280574535165, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1333252817995196750, 'z1': {'__RealLiteral__': 0, 'data': '0.5694148037325393', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1333252817995196750', 'Lhash_array': ['1333252817995196750'], 'label': '2-162288-1.1-c1-0-63', 'type': 'ECQ', 'url': 'EllipticCurve/Q/162288/f'}