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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': '1956188706163126592', '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': 2582.362001368209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '323400.1', 'coefficient_field': '1.1.1.1', 'conductor': 323400, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1], [1, -1], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, 2, 29], [1, -4, 31], [1, 6, 37], [1, 6, 41], [1, 12, 43], [1, -4, 47], [1, 6, 53], [1, -4, 59], [1, -10, 61], [1, -4, 67], [1, -8, 71], [1, 2, 73], [1, 0, 79], [1, 16, 83], [1, -6, 89], [1, 6, 97]], 'gamma_factors': [[], [0]], 'index': 122, 'label': '2-323400-1.1-c1-0-122', 'leading_term': '5.50986934313', '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/323400/cz', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.113800777007601, 0.8820777061110393, -0.8486554193626865, -2.452225677679766, -1.964512425451856, 0.2357498605337975, 1.254919927263715, -0.536342246550819, -2.566580546624055, -1.212646102312144, 2.481029070344977, 3.569800517848705, 0.6023674187427737, -1.736894767820614, 0.0872652831268028, 2.699071096851521, 1.619601256674875, -1.068742600635168, -0.7956806141377026, 1.125548873559629, 0.5035417905507413, -1.191616521909707, 0.2802197817190272, 3.006883992898467, 2.164822011654824, -0.4978623535694776, -0.387067260702234, 0.3461483819719149, -2.151777319888504, -3.831584767840836, -0.168903434358741, 3.448407661033432, 1.423170107683353, -0.751490417551254, 2.198204420808967, 4.105153638555718, 0.1525236181093646, -2.955396415103855, -0.9411156406285327, 0.0634558008283575, -2.050676740455872, -1.208074154840207, 2.130322067558333, 1.481604319919051, -1.152981906177068, -0.2127385572610414, 0.9507779393712206, -0.8693382879563688, -0.5492438060987529, 2.419788641307542, 1.570058137880523, -0.8818362620327799, 1.681015678160105, 4.195607497393624, 1.066033168687888, -0.1546151675376225, 3.940639492408465, 3.96817988751894, -0.8289195876056352, -0.7911467002160274, 2.168364495523432, 0.4710709258315078, -0.8890039794765763, 2.355323916184391, 2.668441500157827, -1.020248021049669, -1.031703947743578, 0.7276355723489573, -0.689922368137234, -0.6837013452259995, 1.196126362605248, -1.236440402385331, -3.788164836179524, -0.740408771167064, 0.6305904601342208, -1.985407403137349, -0.1673159135014386, 2.943905308937745, -0.5446344677994936, -2.952525754366668, 0.4541219755575447, -0.09802063898992497, -3.665648626085101, -0.4468100473219674, 3.411561459223368, 0.4355334051105851, -1.362538559018332, 0.3153156211364185, -1.097784169564615, -1.99771351910279, 0.4624608353099098, -0.5950583125062137, -2.83911683000291, 0.005377264431430841, 1.200640944160312, -1.483498922763377, -0.1787524983758699, 1.457002963610726, -1.619558451334078, -1.213659450059802, 1.4833041733196, -2.645354130730521, -5.080520269769632, 0.7410328669930965, 2.208783537097539, -2.024906271194399, -0.9347275116671433, 1.105656074215862, -0.5314243967730016, 1.787569520516236, 4.754881774205034, 1.325387329858499, -0.8574841031717899, 0.2964766834315417, -1.382562685080204, -0.7858460320152946, 3.429225518781595, 2.40915287660971, -0.142264407740381, 0.9527864405686065], 'positive_zeros': ['0.6439446946514768', '1.473382231048823', '1.947772002032142', '2.584453096371655', '3.291988497500363', '3.743227834487525', '4.385537057938573', '4.843451365389975', '5.310086225844110', '5.726264457284209', '6.439036589107633', '6.818579094954310', '7.064688397957064', '7.758133587575256', '8.354313344336566', '8.605077900526506', '9.257446671026033', '9.854554921083573', '10.01178445801066', '10.58455081018634', '11.11903483929478', '11.52398466193155', '11.89766957504998', '12.29755663448500', '12.87271614083151', '13.14263747157209', '13.82780780991454', '14.01509491486575', '14.70000190934862', '15.05694676948653', '15.53772049511608', '15.83982067758924', '16.42455025211455', '16.85911339887088', '17.16296857340155', '17.57501846744980', '17.92183309255184', '18.55132148809557', '18.81681731586380', '19.25942364518278', '19.72368374482783'], 'prelabel': '2-323400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 50.816946005916265, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1956188706163126592, 'z1': {'__RealLiteral__': 0, 'data': '0.6439446946514768', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.473382231048823', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.947772002032142', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2582.362001368209, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 323400, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 4, 0, -1, 0, 0, 0, -6, 0, 2, 0, -6, 0, -12, 0, 0, 0, 4, 0, 0, 0, 2, 0, -6, 0, 0, 0, 0, 0, 4, 0, 10, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, -16, 0, 0, 0, 2, 0, 6, 0, 0, 0, -4, 0, 0, 0, -6, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, 2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 6, 37], 'euler41': [1, 6, 41], 'euler43': [1, 12, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -8, 71], 'euler73': [1, 2, 73], 'euler79': [1, 0, 79], 'euler83': [1, 16, 83], 'euler89': [1, -6, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, 0, 23], [1, 2, 29], [1, -4, 31], [1, 6, 37], [1, 6, 41], [1, 12, 43], [1, -4, 47], [1, 6, 53], [1, -4, 59], [1, -10, 61], [1, -4, 67], [1, -8, 71], [1, 2, 73], [1, 0, 79], [1, 16, 83], [1, -6, 89], [1, 6, 97]], 'index': 122, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/323400/cz'], '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': '2-323400-1.1-c1-0-122', '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': '2-323400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 50.816946005916265, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1956188706163126592, 'z1': {'__RealLiteral__': 0, 'data': '0.6439446946514768', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1956188706163126592', 'Lhash_array': ['1956188706163126592'], 'label': '2-323400-1.1-c1-0-122', 'type': 'ECQ', 'url': 'EllipticCurve/Q/323400/cz'}