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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': -1, 'A8': 0, 'A9': 1, 'Lhash': '2131232534164002392', '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': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, 1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 1], [1, 1], [1, -6, 13], [1, -5, 17], [1, 5, 19], [1, -1, 23], [1, 3, 29], [1, 0, 31], [1, 6, 37], [1, -4, 41], [1, 11, 43], [1, 4, 47], [1, -1, 53], [1, -15, 59], [1, -15, 61], [1, -10, 67], [1, 12, 71], [1, 4, 73], [1, -2, 79], [1, 15, 83], [1, 7, 89], [1, 5, 97]], 'gamma_factors': [[], [0]], 'index': 106, 'label': '2-369600-1.1-c1-0-106', 'leading_term': '1.81079083946', '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/369600/de', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.810790839464674, 1.02650466862879, -0.5985505617157051, -1.356127695192849, -0.2155906464362873, 1.517952878518224, 1.32984210019975, -0.8943356308172618, -1.804679544585312, 1.022681731339417, 4.799312166040365, 4.689446329927913, 0.9481137033961617, -1.197630361544037, 0.3165885060632436, 1.399776629561319, -0.5469593809311246, -1.645921053881623, 1.288009772726211, 4.199923166753987, 2.574235698419213, -0.5538125232049697, -0.5169926106914022, 0.5596612668702503, -0.8253614247191354, -1.880228336868354, 0.2005892885133615, 1.525404813163962, -0.1821510684018857, 0.4278048504134783, 5.272799118644185, 7.023920383262578, 2.782268905188071, -0.06939836608697086, 1.074491381027513, -0.4876371139194738, -4.819381182805727, -3.762820790289885, 1.707430527140625, 2.667266978025049, -0.08069692440603393, 0.3766315063280351, 1.712387342005414, -0.5851237192012969, -1.975126917098264, 0.1170022101837537, 0.1278083575621352, -1.681342115825097, 0.8096886907697572, 4.290898537822813, 2.334858899387833, -0.4067648577366453, 0.3222431364350001, -0.8289100361986144, -3.366121385111532, -0.2999509211545813, 3.417902061099752, -0.296639661184403, -3.705540230112873, 0.1175137943411764, 1.982171152178145, -1.863252703996769, -2.001502074250387, 1.556931828632408, 1.008268916861548, -0.5563365596722327, 0.6427948985346671, -0.7454711066483592, -3.398957723506596, -1.117525863323698, 0.753216872301441, -2.08581841912842, -1.934062470347313, 1.631356617358183, 0.9660464249330128, -0.4975144650780243, 1.162242847839902, -0.4963909688636599, -2.644382262364831, 3.283743053904412, 8.011869673437745, 2.513367651490193, -1.872334495500091, 0.3149091917836621, 0.07931896504916072, -1.044288281512484, 1.630517292598285, 0.473806553076827, -4.159452532972326, -2.555790420003231, 0.792534608130213, -0.8852382496810937, -1.223391731692753, 0.6219268541158516, -0.2494705702502732, 0.1374693848217883, 0.5029160435673224, -5.586520748869419, -8.679358704445773, -1.933363752224046, 1.771602325041034, -0.4520641605000732, 1.28087437899912, 2.390071899109745, -1.0221870674382, -0.0650444390897996, 1.314704799670189, -4.258033403220012, -5.339548370955469, 1.180007065838362, 2.283426202006955, -0.4171419495163022, 0.2885604885547453, -0.34330164993622, -0.7928369102912189, 2.436225246301335, 1.313858691741557, -2.554549195711998, -0.3976129281120741, 1.376938511533102, -0.3192426848702996], 'positive_zeros': ['0.4075549568739809', '1.028462416791092', '1.657387667232039', '2.185644877092381', '3.067359748316643', '3.464437295164452', '3.946237450705272', '4.417711579671813', '5.189676053590833', '5.585323489678113', '5.896756914576112', '6.481472271931419', '6.974851752424170', '7.214203044623079', '8.216338077889277', '8.301791950047389', '8.718333166937741', '9.416574637223673', '9.989217215907615', '10.20174290022601', '10.70302928166572', '11.23598667927315', '11.51571762971279', '11.95308098579162', '12.67703046102222', '12.92667251011158', '13.16978899383138', '13.76377163170965', '14.23738260550574', '14.74408055248601', '15.13912806215454', '15.63004759115394', '16.10638767398890', '16.38238908957151', '16.68829526659915', '17.32984286643382', '17.59048685624263', '18.12533747869457', '18.59763879124102', '18.84178494452612', '19.21646371691434', '19.64599513117387'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2131232534164002392, 'z1': {'__RealLiteral__': 0, 'data': '0.4075549568739809', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.028462416791092', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.657387667232039', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -1, 0, 1, 0, -1, 0, 6, 0, 0, 0, 5, 0, -5, 0, 1, 0, 1, 0, 0, 0, -1, 0, -3, 0, 0, 0, 1, 0, 0, 0, -6, 0, -6, 0, 4, 0, -11, 0, 0, 0, -4, 0, 1, 0, -5, 0, 1, 0, 0, 0, 5, 0, 15, 0, 15, 0, -1, 0, 0, 0, 10, 0, -1, 0, -12, 0, -4, 0, 0, 0, 1, 0, 2, 0, 1, 0, -15, 0, 0, 0, 3, 0, -7, 0, -6, 0, 0, 0, 0, 0, -5, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -6, 13], 'euler17': [1, -5, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 23], 'euler29': [1, 3, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 6, 37], 'euler41': [1, -4, 41], 'euler43': [1, 11, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 0], 'euler53': [1, -1, 53], 'euler59': [1, -15, 59], 'euler61': [1, -15, 61], 'euler67': [1, -10, 67], 'euler7': [1, 1, 0], 'euler71': [1, 12, 71], 'euler73': [1, 4, 73], 'euler79': [1, -2, 79], 'euler83': [1, 15, 83], 'euler89': [1, 7, 89], 'euler97': [1, 5, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 1, 0], [1, -6, 13], [1, -5, 17], [1, 5, 19], [1, -1, 23], [1, 3, 29], [1, 0, 31], [1, 6, 37], [1, -4, 41], [1, 11, 43], [1, 4, 47], [1, -1, 53], [1, -15, 59], [1, -15, 61], [1, -10, 67], [1, 12, 71], [1, 4, 73], [1, -2, 79], [1, 15, 83], [1, 7, 89], [1, 5, 97]], 'index': 106, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/de'], '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': '2-369600-1.1-c1-0-106', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2131232534164002392, 'z1': {'__RealLiteral__': 0, 'data': '0.4075549568739809', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2131232534164002392', 'Lhash_array': ['2131232534164002392'], 'label': '2-369600-1.1-c1-0-106', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/de'}