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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 1, 'Lhash': '1519048130197854551', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1295.4929223932536, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [13, [1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '162240.1', 'coefficient_field': '1.1.1.1', 'conductor': 162240, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, -4, 7], [1, -4, 11], [1], [1, -2, 17], [1, -4, 19], [1, 0, 23], [1, 10, 29], [1, -4, 31], [1, 10, 37], [1, 2, 41], [1, -4, 43], [1, 8, 47], [1, 2, 53], [1, -12, 59], [1, -10, 61], [1, -12, 67], [1, 0, 71], [1, 10, 73], [1, 4, 79], [1, -4, 83], [1, -6, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 93, 'label': '2-162240-1.1-c1-0-93', 'leading_term': '4.9278988067', '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/162240/gd', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.927898806701993, 3.960357749795317, 1.561909684864038, -0.8198450551256456, -1.578804737611307, -0.5094839929122612, 0.6789134314306638, 0.2417020005246535, -1.172609563373989, -1.017042451424376, 1.636482030601762, 4.211887059987227, 3.721347418746225, 1.014215244497059, -0.3065155849837976, 0.7472710164231936, 1.173249643418387, -0.7903194761602758, -2.323831120313177, -0.7775260320619729, 1.221652902708728, -0.05289022432269981, -2.267120891816031, -0.1172177631244837, 5.105682231475392, 6.213961813256003, 1.452325644405437, -2.492088650285521, -1.36139637455599, 0.6580726427637346, -0.385513066847826, -1.572014032089603, -0.1256738190798695, 0.912904055133785, -0.4302252969382733, -0.5957393586245229, 1.619012951373324, 1.577867277268156, -1.5135041696962, -1.653393151621036, 2.056288657564365, 2.298666562717263, -2.569690669936343, -4.648307938346116, -1.206664641467849, 0.9891869202740112, -0.3888596703772013, -0.346123793487374, 0.6742768635690423, -2.355579581583599, -5.987981026456015, -3.304295819327449, 1.313236227363159, -0.3149261201969658, -4.357383227981396, -3.22437974900082, 0.0198602065392123, 0.1025959210394674, -0.1774870715644189, 0.8940055463520988, -0.276213291300615, -1.887751347303996, 0.8741752390684104, 3.465156209126381, 0.44805756064262, -1.459106873751455, 3.006576007193404, 5.528487774145974, 1.477915312904918, -0.8598813026715494, 0.8628644606006016, -0.7973852220651896, -4.240529176144962, -1.942309052346682, 1.844431977831147, 0.4854989384074238, -0.620036530712352, 2.136159979946536, 2.180435718890567, -0.8560959829769641, -0.1049037602794189, 2.277116771362248, 0.990152172860445, -0.1759724999207832, 0.2034752561041449, -3.071414321156677, -6.420425611875346, -3.065617485053446, 0.224304554875626, -2.516732090150039, -2.896012614219031, 1.078541015377663, -0.7710396965670896, -6.204770814524259, -4.102790470169185, 1.202224695799954, 0.8451787722003588, -0.4366195803865911, 0.8082521882824034, 0.1313462671674194, 0.2752055670184782, 4.307053593880502, 4.217052003749532, -1.08144340642813, -1.330315410422822, 2.097118211038263, 0.6565690143376974, -1.204246813783158, 1.099013640976507, 1.30604934071824, -0.5554959994113863, 0.4426325572873867, 0.183210464797978, -0.7207685195923069, 5.92861914158178, 12.06344784526566, 5.004882211545404, -3.832258990859057, -1.434261592694167, 2.274013675609655, 0.3140013969826979], 'positive_zeros': ['0.6515013460831608', '1.335550426996025', '1.794067898259685', '2.366879717302456', '3.375307319771311', '3.612449008757296', '4.169580825669497', '4.824508051063875', '5.245091882484470', '5.756179029960649', '6.566364577648306', '7.132290672667551', '7.449861004297624', '8.015725742178591', '8.434553003571329', '8.828262307135347', '9.381704693246664', '9.868177039683620', '10.37963414087780', '11.08273625764425', '11.44077417877020', '11.80544549595621', '12.10188745889976', '12.90389485259096', '13.23203388087442', '13.99734880923461', '14.27663678280250', '14.54558381128175', '14.97088317913540', '15.44714904430522', '16.02662068288697', '16.36077356302683', '17.08828784869799', '17.38093764991432', '17.69587551702290', '18.35111532044612', '18.79560091727446', '19.07477274238354', '19.66757856756515'], 'prelabel': '2-162240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.992956566434685, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1519048130197854551, 'z1': {'__RealLiteral__': 0, 'data': '0.6515013460831608', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.335550426996025', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.794067898259685', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1295.4929223932536, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 162240, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 4, 0, 1, 0, 4, 0, 0, 0, -1, 0, 2, 0, 4, 0, 4, 0, 0, 0, 1, 0, 1, 0, -10, 0, 4, 0, 4, 0, -4, 0, -10, 0, 0, 0, -2, 0, 4, 0, -1, 0, -8, 0, 9, 0, 2, 0, -2, 0, -4, 0, 4, 0, 12, 0, 10, 0, 4, 0, 0, 0, 12, 0, 0, 0, 0, 0, -10, 0, 1, 0, 16, 0, -4, 0, 1, 0, 4, 0, -2, 0, -10, 0, 6, 0, 0, 0, 4, 0, -4, 0, 14, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 0, 0], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 10, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 10, 37], 'euler41': [1, 2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, 2, 53], 'euler59': [1, -12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -12, 67], 'euler7': [1, -4, 7], 'euler71': [1, 0, 71], 'euler73': [1, 10, 73], 'euler79': [1, 4, 79], 'euler83': [1, -4, 83], 'euler89': [1, -6, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -4, 7], [1, -4, 11], [1, 0, 0], [1, -2, 17], [1, -4, 19], [1, 0, 23], [1, 10, 29], [1, -4, 31], [1, 10, 37], [1, 2, 41], [1, -4, 43], [1, 8, 47], [1, 2, 53], [1, -12, 59], [1, -10, 61], [1, -12, 67], [1, 0, 71], [1, 10, 73], [1, 4, 79], [1, -4, 83], [1, -6, 89], [1, -14, 97]], 'index': 93, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/162240/gd'], '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': '2-162240-1.1-c1-0-93', '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': '2-162240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 35.992956566434685, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1519048130197854551, 'z1': {'__RealLiteral__': 0, 'data': '0.6515013460831608', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1519048130197854551', 'Lhash_array': ['1519048130197854551'], 'factors': ['2-162240-1.1-c1-0-93'], 'label': '2-162240-1.1-c1-0-93', 'type': 'ECQ', 'url': 'EllipticCurve/Q/162240/gd'}