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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': -1, 'A8': 0, 'A9': 0, 'Lhash': '1794205885924890048', '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': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2213.4531440298933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '277200.1', 'coefficient_field': '1.1.1.1', 'conductor': 277200, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 1], [1, -1], [1, 4, 13], [1, 2, 17], [1, 4, 19], [1, -2, 23], [1, 0, 29], [1, -2, 31], [1, -8, 37], [1, -6, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, -4, 59], [1, -6, 61], [1, -4, 67], [1, 0, 71], [1, -4, 73], [1, -14, 79], [1, -6, 83], [1, 0, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 93, 'label': '2-277200-1.1-c1-0-93', 'leading_term': '2.17827323527', '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/277200/ed', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.178273235273313, 1.403384210741548, -0.2254384405193182, -0.9762680437091436, 0.4645004549752626, 3.160134048951319, 4.310908800357492, 2.478958927687222, -0.2079519577501988, -0.6323202852891092, 0.8233851792680775, 0.7185115087337519, -1.905227648076232, -3.450986248595285, -1.360691391440456, 1.270333530013962, 0.4080493865649588, -2.16199741993248, -2.001899254426396, -0.0923348023465047, -1.054372391340939, -4.102797412144291, -3.709923494912508, 0.2755108497937928, 1.955502635239364, 0.1003580102162426, -0.07345212454797596, 2.396929004581005, 2.387683281786403, -0.3918546789567994, -0.319280642732732, 2.375559166982966, 1.49394420273207, -2.227059721780711, -1.932367163413449, 1.540797991209605, 1.421006995976374, -1.173163527725872, -0.4842118201301456, 1.116328904358094, -0.9794684415921185, -2.388783788984899, 0.9087513098830673, 2.95376154285865, 0.3586230585854956, -0.2639800563985761, 2.805384802770881, 2.280165152162631, -1.751164211279708, -1.761268214427075, 0.8272552138806187, 0.01855675564373398, -0.683498024579422, 2.1798974850316, 2.089816741849154, -2.552564673909765, -3.236297034477145, 0.300864192012704, 0.06654308144895801, -1.988558676232469, -0.1373707679479722, 0.588667487147874, -2.809787615113742, -2.743763114609575, 1.037929376149105, 0.1355708337383434, -2.973410657043404, -1.202958855848621, 0.6489452343274007, -1.100371148448026, -0.04303834630676909, 2.754510634911973, 0.1595591906833617, -2.278486440245688, 1.868257716604998, 4.219626200320457, 0.545514369673173, -0.9481904250497708, 0.0345597244318545, -1.626960989245185, -0.8823064805431823, 3.588929878388701, 2.839074642994766, -0.9324392193696251, 1.176489096127454, 3.260506732438639, -0.5677092639902513, -2.018587742177823, 0.426578392847706, -0.3778013802137833, -0.5591115961406784, 3.29525111549327, 3.004691732029429, -0.4061285444037682, 1.499041740079076, 2.981778169170897, -0.9864466237942614, -1.428805964351335, 1.675256085941801, -0.05657431499403209, -1.638117757178903, 0.9868154896721729, 0.003687780088555683, -2.219537837389183, 1.66257474441935, 3.826403605844494, 0.406241751810331, 0.2859663737969357, 1.33295905760453, -2.015936928281794, -1.998428091806322, 1.369393116611413, -1.030994157882524, -3.147275291312056, 0.819379752645183, 1.339373874680856, -1.509293811323135, 0.168324895871528, 0.5700519303633094, -2.453470509224607, -1.140537921518904], 'positive_zeros': ['0.4641289036987106', '0.9492748956348768', '1.974313946186011', '2.365780051081284', '2.834514424975515', '3.605733651189557', '4.038219118020308', '4.777351724257280', '4.855646195615932', '5.732272396040559', '6.263608666882597', '6.510025396047062', '7.209824334063312', '7.532012806810015', '8.096701685196378', '8.633090479090326', '9.124050286140111', '9.551324882913511', '9.919306092730823', '10.44586643650281', '11.03270183880614', '11.27816727631987', '11.88581616231735', '12.40015042133777', '12.75227965848139', '13.07849295788657', '13.61807951488446', '14.22332886311813', '14.50648109388709', '15.01268691696025', '15.30648501753678', '15.91990772255255', '16.25921938874973', '16.84819051942050', '17.11345365319383', '17.50319880351038', '18.00887027880772', '18.41327670018365', '19.03730049792116', '19.44794181438763', '19.52069241708387'], 'prelabel': '2-277200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.047350021333756, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1794205885924890048, 'z1': {'__RealLiteral__': 0, 'data': '0.4641289036987106', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9492748956348768', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.974313946186011', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2213.4531440298933, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 277200, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, -4, 0, 0, 0, -2, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 0, 0, 0, 0, 0, 4, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -1, 0, 14, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, 4, 13], 'euler17': [1, 2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, -8, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, -6, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -4, 73], 'euler79': [1, -14, 79], 'euler83': [1, -6, 83], 'euler89': [1, 0, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 4, 13], [1, 2, 17], [1, 4, 19], [1, -2, 23], [1, 0, 29], [1, -2, 31], [1, -8, 37], [1, -6, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, -4, 59], [1, -6, 61], [1, -4, 67], [1, 0, 71], [1, -4, 73], [1, -14, 79], [1, -6, 83], [1, 0, 89], [1, -10, 97]], 'index': 93, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/277200/ed'], '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': '2-277200-1.1-c1-0-93', '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': '2-277200-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.047350021333756, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1794205885924890048, 'z1': {'__RealLiteral__': 0, 'data': '0.4641289036987106', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1794205885924890048', 'Lhash_array': ['1794205885924890048'], 'label': '2-277200-1.1-c1-0-93', 'type': 'ECQ', 'url': 'EllipticCurve/Q/277200/ed'}