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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': '136846690127704743', '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': 974.9734086798339, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [11, [1, 1]], [37, [1, -1]]], 'bad_primes': [2, 3, 5, 11, 37], 'central_character': '122100.1', 'coefficient_field': '1.1.1.1', 'conductor': 122100, 'conductor_radical': 12210, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, 0, 7], [1, 1], [1, 0, 13], [1, 0, 17], [1, -8, 19], [1, -6, 23], [1, 0, 29], [1, 2, 31], [1, -1], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, -10, 59], [1, -12, 61], [1, 0, 67], [1, 16, 71], [1, 14, 73], [1, -8, 79], [1, 4, 83], [1, 14, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 10, 'label': '2-122100-1.1-c1-0-10', 'leading_term': '3.61091089876', '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/122100/x', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.610910898760116, 2.79160333096731, 0.76951539290799, -1.178360722585359, -1.566778438489377, -0.1105831183393831, 1.577140615488757, 1.423420964567532, -0.6465219738035367, -2.315031981321632, -1.622694130156285, 0.4049195434812993, 1.117267281080015, 0.1378586420986551, 0.0719112625139365, 2.378779771007504, 4.478429744459755, 3.261784580842641, 0.2198552707744603, -0.3057582884489887, 2.120128945333616, 3.134169480785994, 0.8280382565903069, -0.5701137350981718, 2.458938620411854, 6.239821389871964, 5.267760826373519, 1.046984608253053, -0.6386306013271001, 0.6609133163993293, 0.3730803813149506, -1.999979585199183, -2.114021962950565, 0.4521310261844289, 1.049656654398472, -1.07567813464094, -1.284729265586825, 1.231842937759902, 1.8482773327734, 0.05326958346485751, 0.6671924018139, 3.464835823444672, 2.547044565900157, -1.755394053530012, -2.34297452662558, 1.222496831513808, 1.804030867978698, -1.082174092624569, -0.3532408847453382, 3.984704008454761, 4.329193724502684, 0.3182043939575065, -1.121195050520196, 0.1919228808453606, -1.099145584105494, -3.402934375848576, -1.854632906778219, 0.6214848464036236, -0.2386217476860647, -0.575237290512597, 2.469619333578255, 3.471075988320916, 0.4379378935921112, -0.5035816584700283, 1.284812251763136, -0.2364176088953378, -2.946775709516786, 0.06000399793830926, 4.364378205672194, 1.898922853238766, -2.253454153398345, -0.4975052770528732, 1.910983305649269, -0.4133083553119527, -1.498077341034918, 1.441162453064326, 1.818179699589814, -0.6971100491257755, 0.1665173948633146, 2.096745428902904, -0.3359556098810542, -2.704686163142655, -0.9433748742303573, 0.1084174549646961, -0.1086903890673112, 3.610490343818931, 7.2425217140698, 4.047983048206752, -0.03825132543330026, 0.7143158881805985, -0.4226581644686256, -4.995495767666198, -3.765497571720932, 1.965715956848998, 2.067569447877874, -0.5406063113611546, 1.805873658543306, 3.638882100344291, 0.4187866209832809, -0.7667625474528162, 1.446269069904917, 0.789446797228899, -0.07505054148685017, 3.078875837918322, 3.928026969702539, 0.3401928188570008, -0.4924010346317307, 0.6944900434098086, -0.9272306899735049, -0.331263708826569, 3.687296791206991, 2.027241973710342, -3.245203662277824, -1.551600882626126, 2.414017047582655, 0.2275055951633654, -1.269184918045943, 1.404507387670649, -0.04362703405393211, -3.336558319063908, 0.1199533288693463], 'positive_zeros': ['0.5869624225968860', '1.264030773665160', '1.931852191998098', '2.696351425527709', '3.286102309838792', '3.484057273826683', '4.524572964189027', '4.794373695141436', '5.580158728841769', '5.835535940693234', '6.834079619748814', '7.139162507191618', '7.544476407178419', '8.205311996407883', '8.632416640723394', '9.134729318544819', '9.760597792004149', '9.914537249778401', '10.64569449272333', '11.16613372347675', '11.65296428116649', '12.02325505827683', '12.77246080352533', '13.19827056383078', '13.37604821747138', '14.15550180121902', '14.46542212066581', '14.81440142054261', '15.53894750087489', '15.82245775864618', '16.23270305818276', '16.74725003756610', '17.34008840789575', '17.78294336543895', '18.21786298389744', '18.63890072274708', '19.16799212809348', '19.48422310293809', '19.97771991229288'], 'prelabel': '2-122100-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.224564187188168, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 136846690127704743, 'z1': {'__RealLiteral__': 0, 'data': '0.5869624225968860', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.264030773665160', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.931852191998098', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 974.9734086798339, 'bad_primes': [2, 3, 5, 11, 37], 'central_character': '1.1', 'conductor': 122100, 'conductor_radical': 12210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 6, 0, 0, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 1, 0, 0, 0, -6, 0, 4, 0, 0, 0, 0, 0, -7, 0, 0, 0, -6, 0, 0, 0, 8, 0, 10, 0, 12, 0, 0, 0, 0, 0, 0, 0, 6, 0, -16, 0, -14, 0, 0, 0, 0, 0, 8, 0, 1, 0, -4, 0, 0, 0, 0, 0, -14, 0, 0, 0, -2, 0, 0, 0, 10, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 0, 13], 'euler17': [1, 0, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, 0, 29], 'euler3': [1, -1, 0], 'euler31': [1, 2, 31], 'euler37': [1, -1, 0], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -10, 59], 'euler61': [1, -12, 61], 'euler67': [1, 0, 67], 'euler7': [1, 0, 7], 'euler71': [1, 16, 71], 'euler73': [1, 14, 73], 'euler79': [1, -8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 14, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 0, 7], [1, 1, 0], [1, 0, 13], [1, 0, 17], [1, -8, 19], [1, -6, 23], [1, 0, 29], [1, 2, 31], [1, -1, 0], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 6, 53], [1, -10, 59], [1, -12, 61], [1, 0, 67], [1, 16, 71], [1, 14, 73], [1, -8, 79], [1, 4, 83], [1, 14, 89], [1, -10, 97]], 'index': 10, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/122100/x'], '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': '2-122100-1.1-c1-0-10', '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': '2-122100-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.224564187188168, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 136846690127704743, 'z1': {'__RealLiteral__': 0, 'data': '0.5869624225968860', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '136846690127704743', 'Lhash_array': ['136846690127704743'], 'label': '2-122100-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/122100/x'}