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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': '1652446565799557818', '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': 2615.8991702171465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [7, [1, -1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '327600.1', 'coefficient_field': '1.1.1.1', 'conductor': 327600, 'conductor_radical': 2730, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, -1], [1, -3, 11], [1, 1], [1, 3, 17], [1, -7, 19], [1, 9, 23], [1, -9, 29], [1, -4, 31], [1, -7, 37], [1, 12, 41], [1, 1, 43], [1, 0, 47], [1, 6, 53], [1, -12, 59], [1, 1, 61], [1, -14, 67], [1, -12, 71], [1, -7, 73], [1, -10, 79], [1, -6, 83], [1, -6, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 142, 'label': '2-327600-1.1-c1-0-142', 'leading_term': '3.49282503546', '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/327600/ms', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.492825035458341, 2.542938539659732, 0.4349059449749371, -0.9833600090111813, -0.3002546095510459, 1.592231761303302, 2.083973179207447, 0.2225354627195571, -1.511822311035287, -0.4924437440558268, 1.76256033488939, 1.340836710455127, -1.893661253736816, -3.518018748401758, -1.449320210751021, 0.4957973435516797, -0.9551307224899955, -2.79512279267154, -1.243517235072777, 1.123313650497761, 0.197645885531877, -1.466625804116396, 0.7560468903000345, 4.163380077953153, 3.123693462992065, -0.3654163230267832, -0.7273373874626027, 0.2301408821375173, -2.312506570593722, -5.220949068940264, -3.045234108047816, 0.7080540882160355, 0.4458264254159871, -0.4837613307731258, 1.988518772404242, 2.987203987877222, -0.8164294680092854, -3.097681542612962, -0.6164501571486212, 0.6097128171533026, -0.7310288376126753, 1.340805694405493, 5.076393933205842, 3.084914380659093, -1.464132141151565, -0.8141708888924588, 1.731695938814576, 0.6150816841827805, -0.3012436129077469, 0.4283336574266309, -3.030416975319897, -8.03856471520731, -5.740865932080035, -0.0138651063190816, -0.01476877957899057, -1.994313712485697, -0.3703714317440466, 0.09752039264498048, -1.287002028719335, 1.735427634524621, 5.4368805548119, 2.640139674715666, -0.6907931989067566, 0.73145321044149, 0.08008909440456613, -3.262898625298571, -1.585495604841072, 1.370533467945044, -1.477891559462009, -3.551007450593639, -0.5164203691924482, 0.3798539416281798, -0.7101671095987416, 1.665561812270787, 1.814906632210922, -2.784168250492918, -2.173137189060198, 3.227952970990688, 2.900002592517842, -0.1630311370180079, 0.6833917577671518, 0.4887108356187915, -0.3716422738124293, 4.239448472690308, 6.976735435103414, 1.670816933341312, -1.492507160159031, 0.757183221772417, 0.2368335212139284, -0.7771518431898711, 0.9978088041026001, -1.648481550513856, -5.829402696650302, -2.287353813008578, 1.47591163638495, -1.303850487190916, -1.697110100987424, 0.8870818683043141, -0.8374572884032788, -1.843382131463859, 0.03728305193067334, -2.382286665668872, -4.041036617166381, 0.6248774869216112, 1.018671437689023, -3.951022976529876, -2.929389954805158, 0.3788125586191751, -0.4670975667055786, 0.5886669766158114, 1.228511484191223, -3.864069429941078, -5.046546434656009, -0.3656020824461893, -0.06909586268532003, -0.7047966244931076, 1.704782508259159, -1.420366794900591, -5.762311314852711, -1.645553681543442, 1.860947646935327], 'positive_zeros': ['0.5539770868698499', '1.042429774076317', '1.773198530827646', '2.301199303275998', '2.863688157322583', '3.641123559866578', '3.895716217863216', '4.607001017552949', '5.021244984805128', '5.449360691331366', '6.216206010914783', '6.627375779462712', '6.807557442789777', '7.683651402880347', '8.062045499556725', '8.328815273036390', '8.955304991713839', '9.556084274510375', '9.858664864076558', '10.15741903345667', '10.90066484943771', '11.31352956929444', '11.83219207315013', '12.07893573128784', '12.32511515229606', '13.25098935447195', '13.49857319365912', '14.04716447303727', '14.26601412304558', '14.65568424818030', '15.40408234798075', '15.66139846595823', '16.00609352527900', '16.59554789506897', '16.91254935971602', '17.54488756881003', '17.81081472456286', '18.11113011921918', '18.60423146093470', '19.09669540460319', '19.72139695529163', '19.89171389381755'], 'prelabel': '2-327600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.14586171155147, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1652446565799557818, 'z1': {'__RealLiteral__': 0, 'data': '0.5539770868698499', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.042429774076317', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.773198530827646', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2615.8991702171465, 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '1.1', 'conductor': 327600, 'conductor_radical': 2730, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, -1, 0, 0, 0, -3, 0, 7, 0, 0, 0, -9, 0, 0, 0, 0, 0, 9, 0, 4, 0, 0, 0, 0, 0, 7, 0, 0, 0, -12, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 0, 0, 0, 0, 0, 12, 0, -1, 0, 0, 0, 0, 0, 14, 0, 0, 0, 12, 0, 7, 0, 0, 0, 3, 0, 10, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, -1, 0, 0, 0, 0, 0, 10, 0, 0, 0], 'euler11': [1, -3, 11], 'euler13': [1, 1, 0], 'euler17': [1, 3, 17], 'euler19': [1, -7, 19], 'euler2': [1, 0, 0], 'euler23': [1, 9, 23], 'euler29': [1, -9, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -7, 37], 'euler41': [1, 12, 41], 'euler43': [1, 1, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -12, 59], 'euler61': [1, 1, 61], 'euler67': [1, -14, 67], 'euler7': [1, -1, 0], 'euler71': [1, -12, 71], 'euler73': [1, -7, 73], 'euler79': [1, -10, 79], 'euler83': [1, -6, 83], 'euler89': [1, -6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -1, 0], [1, -3, 11], [1, 1, 0], [1, 3, 17], [1, -7, 19], [1, 9, 23], [1, -9, 29], [1, -4, 31], [1, -7, 37], [1, 12, 41], [1, 1, 43], [1, 0, 47], [1, 6, 53], [1, -12, 59], [1, 1, 61], [1, -14, 67], [1, -12, 71], [1, -7, 73], [1, -10, 79], [1, -6, 83], [1, -6, 89], [1, -10, 97]], 'index': 142, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/327600/ms'], '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': '2-327600-1.1-c1-0-142', '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': '2-327600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.14586171155147, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1652446565799557818, 'z1': {'__RealLiteral__': 0, 'data': '0.5539770868698499', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1652446565799557818', 'Lhash_array': ['1652446565799557818'], 'label': '2-327600-1.1-c1-0-142', 'type': 'ECQ', 'url': 'EllipticCurve/Q/327600/ms'}