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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': 0, 'A8': 0, 'A9': 1, 'Lhash': '468534060971667460', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2850.0844292651577, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [11, [1, -1]], [13, [1]]], 'bad_primes': [2, 3, 11, 13], 'central_character': '356928.1', 'coefficient_field': '1.1.1.1', 'conductor': 356928, 'conductor_radical': 858, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 0, 5], [1, 0, 7], [1, -1], [1], [1, 4, 17], [1, 8, 19], [1, 0, 23], [1, 4, 29], [1, -6, 31], [1, 6, 37], [1, 6, 41], [1, -2, 43], [1, -8, 47], [1, 6, 53], [1, 0, 59], [1, -14, 61], [1, -14, 67], [1, -4, 71], [1, 6, 73], [1, 10, 79], [1, 12, 83], [1, 12, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 114, 'label': '2-356928-1.1-c1-0-114', 'leading_term': '8.42952320676', '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': 1, 'origin': 'EllipticCurve/Q/356928/gi', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.75640576628959, 1.673640077320257, -0.6852564838924466, -3.480316527630158, -4.016758412427439, -1.898553974791226, 0.1810441498378601, -0.01277795212988373, -0.9847128894825128, 0.08484412344245157, 2.397489067607381, 2.346516335416698, -0.3872299552580298, -1.743871591929861, 0.02357094265312376, 1.324878822845531, -0.03557058749374792, -0.4720497907217182, 2.278539386118049, 3.471966227189717, -0.5501015045467844, -4.4554015034444, -2.42334944909181, 1.409326788432887, 0.591036754274597, -2.000318869319672, -0.8899131116950022, 0.7955818432745831, -1.52546092820804, -3.561498785660515, -0.685008797994086, 2.397157621184335, 1.256013935064335, -0.02946450933530652, 0.9146323549763774, -0.2356431624100428, -3.117880877283635, -1.972631196355032, 1.286043314119798, 0.5259245432574625, -0.8216003655261657, 2.476218167034753, 4.541576024939915, 0.76781364336677, -1.48288175404409, 0.7281369194951897, -0.8622487141910218, -6.324596911201747, -5.92646383636589, -0.9074263303291331, 0.006352699608558172, -0.6766414769874423, 2.158844431257598, 3.121021003227401, -0.02467075581808249, -0.544741549072055, 0.9284028582841986, -1.343362337614402, -3.100990501991184, -0.2492495697017627, 0.9711555353782813, -0.5839759116338648, 0.5896567432375729, 0.1291035360703302, -6.243820001843218, -8.52503904415319, -2.740914308826983, 0.1648391335263652, -1.099430100609483, 1.252957836215066, 2.303038354292037, -2.644431364115175, -3.48964192395896, 1.947964139709648, 2.832888738033178, -0.1079657537373699, 0.1321817473048689, -0.512413174969749, -3.05227344376983, -1.159468973555133, 1.168793458044423, -1.109250544996284, -1.074610985305674, 1.721104216308757, 0.1145336916935922, -1.010933804772935, 2.385598620855675, 1.809338741326878, -1.151759327989766, 1.945641062219082, 3.100124071005561, -2.817390232671983, -3.771938163405246, 0.4823490738037191, -0.646277523709077, -1.83458866861225, 1.874869558294407, 1.463806060527641, -1.738463483612658, 0.06130117294563499, 1.009169985820343, -1.109779401817628, 0.4647873217138736, 1.607200758621907, -0.8714045861339992, 0.612016214455165, 2.920437003392574, -0.3086427369665746, -1.070402034367954, 1.267623946767972, -1.306728368323291, -1.836700085708961, 2.779217509236275, 0.9364370527753304, -2.951278860321821, 1.382575158741878, 3.348011804648414, -1.073289785785712, -0.5503997725684949, 1.561421634728642], 'positive_zeros': ['0.6922024418480748', '1.713204951612716', '1.997149711005976', '2.490356007220721', '3.216523410511790', '3.747478143989912', '4.244967415053531', '4.562752798520020', '5.224573843794646', '5.886270994142694', '6.297876948409512', '6.837349987450916', '7.131608634119194', '7.790032985751517', '8.446153949067623', '8.521567617914091', '8.979085674133286', '9.632846838365516', '10.05307568169363', '10.34735646111833', '11.04341207691706', '11.42087567729672', '11.70104921233088', '12.57987357170329', '12.75120818304188', '13.08664666733045', '13.74785833285628', '14.07105386101991', '14.39834306305885', '15.01938900105702', '15.39099356557356', '15.67780492091365', '16.00779561592265', '16.91506591573580', '17.04181514515891', '17.41094532609729', '17.88133502339899', '18.41131023392215', '18.98486691856161', '19.21934485331128', '19.44169774069440'], 'prelabel': '2-356928-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 53.38618200681856, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 468534060971667460, 'z1': {'__RealLiteral__': 0, 'data': '0.6922024418480748', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.713204951612716', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.997149711005976', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2850.0844292651577, 'bad_primes': [2, 3, 11, 13], 'central_character': '1.1', 'conductor': 356928, 'conductor_radical': 858, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, -5, 0, 1, 0, -4, 0, 6, 0, 1, 0, 0, 0, -6, 0, 0, 0, -6, 0, 2, 0, 0, 0, 8, 0, -7, 0, -4, 0, -6, 0, 0, 0, -8, 0, 0, 0, 14, 0, 0, 0, 0, 0, 14, 0, 0, 0, 4, 0, -6, 0, -5, 0, 0, 0, -10, 0, 1, 0, -12, 0, 0, 0, -4, 0, -12, 0, 0, 0, 6, 0, 0, 0, 2, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, 0, 0], 'euler17': [1, 4, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 4, 29], 'euler3': [1, -1, 0], 'euler31': [1, -6, 31], 'euler37': [1, 6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -2, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 5], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -14, 61], 'euler67': [1, -14, 67], 'euler7': [1, 0, 7], 'euler71': [1, -4, 71], 'euler73': [1, 6, 73], 'euler79': [1, 10, 79], 'euler83': [1, 12, 83], 'euler89': [1, 12, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 5], [1, 0, 7], [1, -1, 0], [1, 0, 0], [1, 4, 17], [1, 8, 19], [1, 0, 23], [1, 4, 29], [1, -6, 31], [1, 6, 37], [1, 6, 41], [1, -2, 43], [1, -8, 47], [1, 6, 53], [1, 0, 59], [1, -14, 61], [1, -14, 67], [1, -4, 71], [1, 6, 73], [1, 10, 79], [1, 12, 83], [1, 12, 89], [1, -2, 97]], 'index': 114, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/356928/gi'], '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': '2-356928-1.1-c1-0-114', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-356928-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 53.38618200681856, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 468534060971667460, 'z1': {'__RealLiteral__': 0, 'data': '0.6922024418480748', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '468534060971667460', 'Lhash_array': ['468534060971667460'], 'label': '2-356928-1.1-c1-0-114', 'type': 'ECQ', 'url': 'EllipticCurve/Q/356928/gi'}