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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '1527839464041466267', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1648.1122977192279, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [43, [1, 1]]], 'bad_primes': [2, 3, 5, 43], 'central_character': '206400.1', 'coefficient_field': '1.1.1.1', 'conductor': 206400, 'conductor_radical': 1290, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, 4, 7], [1, -3, 11], [1, -7, 13], [1, -5, 17], [1, -6, 19], [1, 4, 23], [1, -2, 29], [1, 4, 31], [1, -2, 37], [1, -6, 41], [1, 1], [1, 3, 47], [1, -6, 53], [1, -3, 59], [1, 0, 61], [1, -3, 67], [1, 6, 71], [1, -4, 73], [1, 17, 79], [1, 3, 83], [1, 0, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 117, 'label': '2-206400-1.1-c1-0-117', 'leading_term': '4.16208824484', '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/206400/fy', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.162088244835132, 3.230894306335999, 1.026740424082209, -0.8619206222301145, -0.9255833781057791, 0.5293591926164308, 1.20025129812312, -0.6565659537126023, -3.629911263946629, -4.401626282665254, -1.996872559990865, 0.7225249018894838, 0.9605507568195281, -0.2311752746927288, -0.2633003488498846, 0.3244818105681221, -0.8442065243191283, -2.409225797009519, 0.06976394777931881, 6.35849432405883, 9.732219441830365, 6.295476742470793, 1.09127304706756, 0.1633355190801924, 1.521820545686553, 0.3272134047673924, -1.774960400096987, -0.5779754490953104, 1.591294710376792, -0.001542573119632103, -2.796541944460774, -1.344023246793407, 2.012078833970247, 1.402781140445071, -1.356399162099415, -0.7993031547664602, 1.397987274545616, 0.7632963860327541, -0.5159456666969796, 0.6649178401137699, 0.754787454293797, -1.960145239606763, -1.527944736030911, 3.32861640543297, 4.144650005794084, -1.300819670309095, -3.765512793913181, -0.3953241152022688, 0.4772800750613057, -2.835163179020532, -2.685874335173399, 1.017297302334271, 1.411557966341341, -0.2125035389528217, 1.20066328273861, 2.412454099168937, 0.3499294633417177, -0.09596315615048737, 1.559037186692818, -1.204723087265637, -6.187026764786794, -4.976232531269934, -0.3474729939570927, 0.1011589401715612, -0.8209080535278349, 0.497717262737999, -0.08261059961621885, -0.9211388298837312, 4.616614685565591, 9.989317579438204, 5.011867812699153, -2.548108226309921, -1.779278821920309, 1.028619381502838, -0.8349604350608714, -1.351129487871409, 0.9240317488736411, -0.1132860636491953, -2.001622775966486, -0.1373780202350246, 0.716881638675389, -0.6178322154932192, 1.377227844109013, 3.215442045160184, -0.2500574212958464, -1.574225595724045, 2.486092840988833, 2.447902223921642, -1.572419835715845, -0.3115962962199774, 2.544759256941397, 0.5276745831223569, -0.2160979040338519, 1.357244555961269, -2.030733147207376, -4.772524280534649, 0.730822300380312, 4.339147694014388, -0.1385451861081146, -2.020386719472983, 0.9973174731768659, 0.6455464404127051, -1.097942404069437, -0.1879582955846535, -0.293206246107342, 0.4514926474587162, 4.437603472146271, 3.825400644434028, -0.8477831254796124, 1.08675670520676, 5.128935248503357, 2.102284785916275, 0.01833485677319674, 2.970247879596244, 1.865228673232111, -0.3332483269023507, 3.750249344042873, 5.290653738862017, 0.7486003759227778, 0.2504415880327852, 1.856469152086157], 'positive_zeros': ['0.6156260951192716', '1.167376712517239', '1.690190217753649', '2.665013636822929', '3.194104029637071', '3.583727471755805', '3.876525172402827', '4.496581335608483', '5.629656816315998', '5.706346991713175', '6.281701876777235', '6.802378495654150', '7.249883072311331', '7.838782787697953', '8.364510560369793', '8.829103219242009', '9.354828292195776', '9.648518076064397', '10.08012366824683', '10.58748388836177', '11.19550481803537', '11.77928859372902', '12.04538371656047', '12.67527066964262', '13.18768668507451', '13.35515404791972', '14.04294389817934', '14.26487298073035', '14.68893282851719', '15.53186011085972', '15.76693178507936', '16.16442270654590', '16.48966263588925', '16.82345581864773', '17.64227499889792', '18.11581074619088', '18.42237422156519', '18.88835946817433', '19.23962460276232', '19.76398537868985'], 'prelabel': '2-206400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.596949364690296, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1527839464041466267, 'z1': {'__RealLiteral__': 0, 'data': '0.6156260951192716', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.167376712517239', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.690190217753649', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1648.1122977192279, 'bad_primes': [2, 3, 5, 43], 'central_character': '1.1', 'conductor': 206400, 'conductor_radical': 1290, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -4, 0, 1, 0, 3, 0, 7, 0, 0, 0, 5, 0, 6, 0, -4, 0, -4, 0, 0, 0, 1, 0, 2, 0, -4, 0, 3, 0, 0, 0, 2, 0, 7, 0, 6, 0, -1, 0, 0, 0, -3, 0, 9, 0, 5, 0, 6, 0, 0, 0, 6, 0, 3, 0, 0, 0, -4, 0, 0, 0, 3, 0, -4, 0, -6, 0, 4, 0, 0, 0, -12, 0, -17, 0, 1, 0, -3, 0, 0, 0, 2, 0, 0, 0, -28, 0, -4, 0, 0, 0, 10, 0, 3, 0], 'euler11': [1, -3, 11], 'euler13': [1, -7, 13], 'euler17': [1, -5, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 1, 0], 'euler47': [1, 3, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, -3, 59], 'euler61': [1, 0, 61], 'euler67': [1, -3, 67], 'euler7': [1, 4, 7], 'euler71': [1, 6, 71], 'euler73': [1, -4, 73], 'euler79': [1, 17, 79], 'euler83': [1, 3, 83], 'euler89': [1, 0, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 4, 7], [1, -3, 11], [1, -7, 13], [1, -5, 17], [1, -6, 19], [1, 4, 23], [1, -2, 29], [1, 4, 31], [1, -2, 37], [1, -6, 41], [1, 1, 0], [1, 3, 47], [1, -6, 53], [1, -3, 59], [1, 0, 61], [1, -3, 67], [1, 6, 71], [1, -4, 73], [1, 17, 79], [1, 3, 83], [1, 0, 89], [1, -10, 97]], 'index': 117, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/206400/fy'], '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': '2-206400-1.1-c1-0-117', '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': '2-206400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.596949364690296, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1527839464041466267, 'z1': {'__RealLiteral__': 0, 'data': '0.6156260951192716', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1527839464041466267', 'Lhash_array': ['1527839464041466267'], 'label': '2-206400-1.1-c1-0-117', 'type': 'ECQ', 'url': 'EllipticCurve/Q/206400/fy'}