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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 4, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '1518704932308205652', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 246.83356272818205, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [7, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '30912.1', 'coefficient_field': '1.1.1.1', 'conductor': 30912, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -4, 5], [1, 1], [1, -2, 11], [1, 2, 13], [1, -2, 17], [1, 2, 19], [1, 1], [1, -6, 29], [1, 0, 31], [1, 4, 37], [1, 10, 41], [1, 10, 43], [1, -8, 47], [1, 0, 53], [1, 0, 59], [1, -4, 61], [1, -2, 67], [1, 8, 71], [1, 2, 73], [1, -8, 79], [1, 6, 83], [1, -6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 17, 'label': '2-30912-1.1-c1-0-17', 'leading_term': '2.63935774768', '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/30912/bf', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.639357747676816, 2.174753009051504, 0.9133287917733908, -0.6504943412086136, -1.682285436638884, -1.516241092192463, -0.3513087040413581, 0.6574344511626005, 0.3374143375726347, -1.205290137566783, -2.353492425168906, -1.482378976321767, 1.056862889228235, 2.772247658571108, 1.419074326750833, -2.33603560522857, -5.173448196059118, -4.516079850848791, -1.375451292268736, 0.8580477094699538, 0.4025111422998929, -1.080165319357025, -1.10600772464976, 0.1974652607469642, 0.6450523416236136, -0.406049012258083, -1.011164150946947, -0.04012938102163611, 0.2662665047485878, -2.643472082146229, -6.838519227420567, -7.162523533280765, -2.081170175417982, 3.450860555348846, 4.034237520230119, 0.7236750078434419, -1.081106205539692, 0.540844318706681, 2.185254253643282, 1.30065649027877, -0.0998790333380238, 0.111829256122188, -0.04780516518236216, -2.8289905579096, -5.553017997638797, -4.037662956174645, 0.24960148479578, 1.775471073203415, -0.5056244789225072, -1.801233143538926, 0.2677426883954506, 1.941072569679526, 0.3765025381122209, -1.286538914936944, 0.09928217496195114, 1.847581921434229, 0.7407405923184294, -0.453665574365797, 1.883916991639749, 4.489906663863799, 2.192609185006932, -2.185062339207657, -1.440240264868543, 3.914129746254225, 6.171521442919931, 2.907685224124752, -0.1784947737618548, 0.2464342205982148, 0.9400573297813299, 0.02752377522069354, 0.1744992940461869, 1.652043937734513, 1.003768139783051, -1.245230413331046, -0.5578724898798293, 2.127017973361942, 0.8092032378778667, -3.76251604655796, -3.791704843524577, 1.496939503139334, 3.445309343655296, -0.9847899871876056, -4.112220066959787, -1.575916106884302, 0.9411195049124316, -0.5235492660589334, -1.860849325445466, -0.5382708052980693, 0.1430029436925303, -0.3076861134610996, 1.640943302074813, 4.310582959574643, 2.4929540701828, -1.37727490925242, -0.545119261254214, 2.814002556740842, 1.289455539645115, -3.352280578180929, -3.60758105783234, -0.3965058484241003, 0.2511214646365533, -0.5423227798388615, 0.9469695838873795, 1.370621699383093, -2.058362166488182, -3.494159369106985, 0.2846710400329659, 2.08261946796931, -1.755734352911075, -3.41125496543015, 1.052846076780402, 3.861043836798466, 0.8991238586821121, -1.317801543037507, 0.3464690071455064, 0.9848292195535893, -0.3926080213115887, 0.0841799350991369, 1.191377050834511, -0.0233258223309187, -0.5078074539954708], 'positive_zeros': ['0.6440254825650223', '1.568183472242722', '2.066594322990921', '2.902666256761587', '3.603386048688958', '4.619896714793823', '5.064262865987873', '5.711976949682093', '6.170384579651069', '6.758224816417108', '7.044894641283240', '8.080919078520068', '8.807595058997936', '9.192511984807795', '9.967035495583828', '10.20600132614857', '10.49139287342206', '11.48366549775537', '11.95462855631337', '12.47583170998624', '13.03833761289225', '13.48959633278780', '14.09562501844634', '14.34181452912047', '15.11250493123680', '15.57527317818292', '16.46945525396706', '16.70166901408209', '17.25787512326027', '17.46099797279247', '18.10356472251435', '18.54957464469254', '19.04641321217435', '19.68272809604292'], 'prelabel': '2-30912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.710937678196743, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1518704932308205652, 'z1': {'__RealLiteral__': 0, 'data': '0.6440254825650223', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.568183472242722', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.066594322990921', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 246.83356272818205, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 30912, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 4, 0, -1, 0, 1, 0, 2, 0, -2, 0, -4, 0, 2, 0, -2, 0, 1, 0, -1, 0, 11, 0, -1, 0, 6, 0, 0, 0, -2, 0, -4, 0, -4, 0, 2, 0, -10, 0, -10, 0, 4, 0, 8, 0, 1, 0, -2, 0, 0, 0, 8, 0, 2, 0, 0, 0, 4, 0, -1, 0, -8, 0, 2, 0, 1, 0, -8, 0, -2, 0, -11, 0, -2, 0, 8, 0, 1, 0, -6, 0, 8, 0, -6, 0, 6, 0, 2, 0, 0, 0, -8, 0, -2, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 4, 37], 'euler41': [1, 10, 41], 'euler43': [1, 10, 43], 'euler47': [1, -8, 47], 'euler5': [1, -4, 5], 'euler53': [1, 0, 53], 'euler59': [1, 0, 59], 'euler61': [1, -4, 61], 'euler67': [1, -2, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 6, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -4, 5], [1, 1, 0], [1, -2, 11], [1, 2, 13], [1, -2, 17], [1, 2, 19], [1, 1, 0], [1, -6, 29], [1, 0, 31], [1, 4, 37], [1, 10, 41], [1, 10, 43], [1, -8, 47], [1, 0, 53], [1, 0, 59], [1, -4, 61], [1, -2, 67], [1, 8, 71], [1, 2, 73], [1, -8, 79], [1, 6, 83], [1, -6, 89], [1, 2, 97]], 'index': 17, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/30912/bf'], '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': '2-30912-1.1-c1-0-17', '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': '2-30912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.710937678196743, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1518704932308205652, 'z1': {'__RealLiteral__': 0, 'data': '0.6440254825650223', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1518704932308205652', 'Lhash_array': ['1518704932308205652'], 'factors': ['2-30912-1.1-c1-0-17'], 'label': '2-30912-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/30912/bf'}