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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1987344658084575295', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1032.9448005472836, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [7, [1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '129360.1', 'coefficient_field': '1.1.1.1', 'conductor': 129360, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1], [1, 1], [1, -2, 13], [1, 4, 17], [1, 0, 19], [1, -2, 23], [1, 0, 29], [1, 8, 31], [1, 12, 37], [1, 2, 41], [1, -12, 43], [1, 0, 47], [1, 12, 53], [1, -6, 59], [1, -10, 61], [1, -8, 67], [1, 8, 71], [1, 0, 73], [1, -14, 79], [1, -14, 83], [1, -4, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 169, 'label': '2-129360-1.1-c1-0-169', 'leading_term': '9.37129536907', '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/129360/gm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.114780936918542, 2.949272337396531, 1.828320397867365, -0.5407966032560383, -2.23110459697129, -1.828981643414508, -0.1184715500980704, 0.6468475066099854, -0.4362331614871551, -1.552978652868762, -0.5808597709152195, 1.657886922782401, 2.246062960060548, 0.532841960626187, -0.4910243304800764, 1.341099882360655, 3.530553587399832, 2.359490464233611, -1.027537523067811, -1.931288742528875, 0.4179121194802099, 1.35404253837688, -1.510664557400192, -3.963762850309757, -2.11578603795086, 0.9086219636698714, 0.3755624220824477, -1.799744311810181, -0.7805218608140271, 2.092248350091213, 1.639643672809343, -1.510511852781574, -2.02033637075613, 0.3564143322582518, 0.9098067008008097, -0.6286510022116437, -0.2188596759206773, 1.37528770364579, -0.2891684297072471, -3.549695832615765, -2.766964528703792, 0.6353242788178717, 0.8402021346343502, -0.4398180903899179, 2.420438960700228, 6.052499707885626, 3.092135998175553, -3.052413962689327, -3.42482410956756, 0.4688169367737055, 0.9404420662425927, -1.025716390971915, -0.00988490292989046, 1.806679078118743, 0.5947129098036537, -0.06785020932261457, 2.271598560012834, 2.717650796364283, 0.1304688140536035, 0.4423458141369355, 3.474620703514423, 2.710419262946027, -0.4694775787144839, -0.1434369108619268, 0.1394030684513727, -4.716880977937611, -8.01493501245102, -3.846114883970121, 0.271378987639448, -1.269525029131415, -1.919622136597551, 0.8005622526074453, 0.08355089483685516, -3.483807496622975, -2.683945877750607, 0.05311716485442799, -1.085136609278195, -1.510841084299389, 2.469452458568517, 4.02581102609935, 0.7963911243984423, -0.5180119669996573, 0.2468304291492427, -1.442865828477419, -1.720385381203546, 2.213019175218166, 3.143147719932465, -0.3261391042760042, -0.5025960713244104, 0.5599656129110967, -4.258003112432635, -8.119378458793259, -3.504855229480372, 0.6957912679307017, -1.687571641866231, -2.243334650986745, 0.9912006745583639, 0.2785601373355751, -2.116028324907971, 0.06556170250334799, 1.86455367068448, -0.06029819684712455, 0.01378470401540853, 1.409821092935896, -0.54061575236927, -1.226517280834371, 1.266367470163601, -0.3979859127902398, -4.109052673769159, -1.461179802778837, 1.741996751374748, -1.233880503049427, -1.696606035531883, 3.218622636742984, 3.157747800552543, -0.9432407244494027, -0.4340753122459522, 0.08928319955486612, -3.262580058645714, -2.241489883399073], 'positive_zeros': ['0.9447183687712321', '1.769002996287453', '2.177823715617141', '2.815959089729028', '3.572353865521882', '3.859449989551529', '4.670210115493731', '5.210652440833554', '5.644773869920494', '6.403603505432331', '6.789117169342659', '7.313974826501361', '7.879263212493456', '8.461533218401072', '8.894786105305710', '9.279644402533633', '9.728466811642369', '10.44394956110197', '10.86610622741266', '11.08645321473269', '11.86595440961708', '12.46481354158474', '12.85687436971885', '13.25101773048140', '13.83837355929473', '14.01311283968740', '14.76675992070114', '14.95196645462704', '15.69912174908491', '16.02085126861473', '16.26374872383754', '17.20764539673448', '17.37065233668493', '17.92323925567136', '18.25609761435964', '18.98806194359221', '19.10848056988359', '19.61275028997034'], 'prelabel': '2-129360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.13945862249835, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1987344658084575295, 'z1': {'__RealLiteral__': 0, 'data': '0.9447183687712321', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.769002996287453', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.177823715617141', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1032.9448005472836, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 129360, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 2, 0, 1, 0, -4, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, -8, 0, -1, 0, 0, 0, -12, 0, 2, 0, -2, 0, 12, 0, 1, 0, 0, 0, 0, 0, -4, 0, -12, 0, -1, 0, 0, 0, 6, 0, 10, 0, 0, 0, 2, 0, 8, 0, 2, 0, -8, 0, 0, 0, 1, 0, 0, 0, 14, 0, 1, 0, 14, 0, -4, 0, 0, 0, 4, 0, 0, 0, -8, 0, 0, 0, -14, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -2, 13], 'euler17': [1, 4, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 12, 37], 'euler41': [1, 2, 41], 'euler43': [1, -12, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, 12, 53], 'euler59': [1, -6, 59], 'euler61': [1, -10, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 8, 71], 'euler73': [1, 0, 73], 'euler79': [1, -14, 79], 'euler83': [1, -14, 83], 'euler89': [1, -4, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 0, 0], [1, 1, 0], [1, -2, 13], [1, 4, 17], [1, 0, 19], [1, -2, 23], [1, 0, 29], [1, 8, 31], [1, 12, 37], [1, 2, 41], [1, -12, 43], [1, 0, 47], [1, 12, 53], [1, -6, 59], [1, -10, 61], [1, -8, 67], [1, 8, 71], [1, 0, 73], [1, -14, 79], [1, -14, 83], [1, -4, 89], [1, 14, 97]], 'index': 169, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/129360/gm'], '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': '2-129360-1.1-c1-0-169', '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': '2-129360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.13945862249835, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1987344658084575295, 'z1': {'__RealLiteral__': 0, 'data': '0.9447183687712321', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1987344658084575295', 'Lhash_array': ['1987344658084575295'], 'label': '2-129360-1.1-c1-0-169', 'type': 'ECQ', 'url': 'EllipticCurve/Q/129360/gm'}