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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '687309794283386739', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1027.674674013879, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [11, [1, 1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '128700.1', 'coefficient_field': '1.1.1.1', 'conductor': 128700, 'conductor_radical': 4290, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 0, 7], [1, 1], [1, -1], [1, 4, 17], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, -4, 43], [1, -12, 47], [1, -10, 53], [1, 8, 59], [1, -6, 61], [1, 2, 67], [1, 0, 71], [1, 10, 73], [1, -10, 79], [1, -6, 83], [1, 0, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 34, 'label': '2-128700-1.1-c1-0-34', 'leading_term': '6.11013819643', '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/128700/bc', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.322494572223514, 1.519507115042891, 0.1122914080954987, -2.040562445004503, -3.060413617325449, -1.835740477040452, 0.4426412284051234, 1.293701668865096, -0.03656977757345208, -1.30804569594589, -0.08077978679732765, 2.670976439040004, 3.450345986815477, 1.109985539640642, -1.223885185425464, -0.6205103376354637, 1.160097249384882, 0.4440206947287106, -2.213703861690232, -2.601092608757443, 0.1852989956331169, 1.884280800349077, 0.0368777516024221, -1.806881678574632, -0.2826858410589317, 1.741894598763542, 0.293588827046078, -2.289113435834188, -1.421900337685177, 1.165985748877677, 0.425359574238497, -2.505797347768273, -2.189666101880626, 0.9720700950749703, 1.649376905634283, -0.05356519213011142, 0.8812040236590657, 3.734594487413683, 2.713189596072907, -1.553534766465741, -2.522390579279931, 0.1034053953695392, 0.5679175590875472, -1.025242701923835, 0.3660388635443312, 3.07286262923065, 1.377133867706973, -2.262410778874571, -1.385457453274596, 1.593453272826307, 0.5045976814244247, -2.073010118541255, -1.101802468912253, -0.09583690626385331, -2.715723325681768, -3.592789471865361, 0.4755394183005893, 2.825396348892001, 0.3362036805235922, -0.5152714381753964, 2.014698403669701, 1.765139991389418, -0.8140976096800487, 0.4320657156487176, 2.91509832906424, 0.5991271863897606, -2.164883921012547, 0.1286850046436559, 2.10152328757399, -0.1587024406070401, -0.5208234417492071, 2.450024808265912, 1.726012454266851, -1.937514376695942, -1.524914061129263, 0.2126528022650077, -2.309963430687068, -3.803818342907906, -0.2644703286059584, 1.238900585621166, -1.409843303593444, -0.8859315127541582, 2.064878362075425, 0.6911366636981876, -1.306442218986229, 1.298614942087776, 2.286207432651682, -1.30807335818185, -1.8568750164094, 0.8385305279875377, -0.5159589897471845, -2.638060977192115, 0.4754074822589903, 2.60296802400657, -0.2254837985762093, -0.8860134570212811, 0.8811591897976223, -1.620269611531256, -4.120618509005931, -0.7936495346806468, 1.197183184340693, -1.619278488828185, -1.271659913363582, 1.896634610201207, 0.7825516319420128, -0.5314342655682773, 2.05370315385772, 1.126943561135086, -3.602441836292034, -2.939389487701854, 0.5825758747985857, -0.1470595254653822, 0.2122552587268427, 3.988576217557411, 2.991968243806437, -1.133051708570105, -0.575031639022067, -0.1573038887613274, -3.539071059503285, -2.618606407206314], 'positive_zeros': ['0.7635646126831167', '1.696994082124980', '2.245034310660496', '2.758004904005645', '3.594020495054251', '4.077154275324348', '4.545066936026939', '5.235230207322398', '5.753348439251508', '6.276069721508203', '6.774465263850420', '7.372850835407893', '7.786703069607118', '8.420343819361329', '8.988099372485711', '9.145734010097009', '9.906063520678862', '10.48928182925139', '10.83301653630736', '11.21938069917714', '11.83266574901098', '12.35019518794668', '12.79029905629393', '13.43300973798522', '13.46229982168805', '14.22489021331175', '14.78039878702104', '15.06227166153277', '15.65290203488370', '15.96475846717985', '16.53680282281531', '16.99110719461570', '17.48500694830618', '17.80028696678521', '18.35920535017890', '18.91436785983492', '19.05661545652808', '19.76695431431473'], 'prelabel': '2-128700-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.05736536295331, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 687309794283386739, 'z1': {'__RealLiteral__': 0, 'data': '0.7635646126831167', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.696994082124980', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.245034310660496', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1027.674674013879, 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '1.1', 'conductor': 128700, 'conductor_radical': 4290, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 12, 0, -7, 0, 0, 0, 10, 0, 0, 0, 0, 0, -8, 0, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 10, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0], 'euler11': [1, 1, 0], 'euler13': [1, -1, 0], 'euler17': [1, 4, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, -12, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, 8, 59], 'euler61': [1, -6, 61], 'euler67': [1, 2, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 10, 73], 'euler79': [1, -10, 79], 'euler83': [1, -6, 83], 'euler89': [1, 0, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 7], [1, 1, 0], [1, -1, 0], [1, 4, 17], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, -4, 43], [1, -12, 47], [1, -10, 53], [1, 8, 59], [1, -6, 61], [1, 2, 67], [1, 0, 71], [1, 10, 73], [1, -10, 79], [1, -6, 83], [1, 0, 89], [1, -14, 97]], 'index': 34, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/128700/bc'], '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': '2-128700-1.1-c1-0-34', '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': '2-128700-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.05736536295331, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 687309794283386739, 'z1': {'__RealLiteral__': 0, 'data': '0.7635646126831167', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '687309794283386739', 'Lhash_array': ['687309794283386739'], 'factors': ['2-128700-1.1-c1-0-34'], 'label': '2-128700-1.1-c1-0-34', 'type': 'ECQ', 'url': 'EllipticCurve/Q/128700/bc'}