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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': '829660901099740334', '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, 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': 189, 'label': '2-369600-1.1-c1-0-189', 'leading_term': '3.88420361906', '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/vd', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.884203619055533, 2.75513324554346, 0.226357271212398, -1.544552873348472, -0.8419901770689844, 1.457810500034401, 2.437833535566473, 0.7959030154963951, -1.145293138990835, -0.6978494746528836, 0.9887071507002424, 0.7340789042230919, -1.12485780193164, -0.9379202961080998, 1.74249268810071, 2.648532267122264, 0.04886891371552051, -1.817333733360484, -0.2541026373289599, 0.8158859934158545, -1.482834928908514, -2.724623456533955, 0.4332737361078563, 2.578119829500183, -1.084062559698384, -4.998746598454758, -2.829856163729003, 1.102484279371269, 0.578126003792253, -1.165278018003708, 0.3470510463191604, 1.389044362746831, -0.8997834834729845, -1.667967050568727, 0.7986468952497427, 0.8613287682035033, -2.015436519767868, -1.984126952566994, 0.09354208423469292, -0.8265047959325913, -1.433401166821935, 2.383658273110426, 4.240315673882198, 0.2678079958685699, -1.285053626857787, 2.692912800262516, 3.524962555131496, 0.09050029521758413, 0.5318634961054027, 2.978937655043815, 0.3802292934173981, -2.194847781921262, 1.016380553847035, 3.038100735038418, 0.2300512779311286, -0.3678063661183329, 1.46928191302895, -0.2421817918472391, -2.247270735551139, -0.5672146630513591, -0.2481139358277273, -1.298351608614675, 1.772006785805741, 3.840275591442054, -0.3427870736257281, -2.032298692954969, 1.912315969907917, 1.477730111681703, -2.398653227317621, -0.5043790957108749, 1.953098470707688, -1.132345933700172, -1.497234810582976, 2.219944327539815, 1.001630817374746, -1.55358858036489, 1.612316113190497, 3.353124084187195, 0.4255349376671202, 0.1867291014888271, 1.045276213226604, -1.180921859962312, -0.7533441239127168, 1.512154835211632, -1.315078049741756, -3.33801952807365, 0.07934846039380437, 0.4422844483501467, -1.581277665691888, 1.238970526688566, 1.948756514818518, -1.912328496797643, 1.024427240860673, 6.782970982904984, 3.198061893140837, -1.395523250273706, 0.8945814842615246, 1.050612866339173, -1.399424005323813, -0.09920421634890912, 0.02915975978676508, -1.105563405543852, 2.61291517321077, 4.075653018304078, -0.568334490621869, -1.242675324127361, 1.11595659643239, -0.4239065665907749, -0.3601702817405968, 1.384471943226896, -0.5260962610637286, 1.609785668129894, 7.697220094386751, 4.696141083241024, -1.317063061692095, 0.5714833635899892, 0.5947121865818579, -3.151759626507768, -0.5524176482358433, 1.484963521839923, -2.486468962775563], 'positive_zeros': ['0.5224764355646214', '1.096300849931958', '1.833647445386811', '2.346800036012836', '2.849027166901404', '3.347969796389265', '4.003864706112105', '4.528356624051130', '4.869818864999878', '5.473509684156486', '5.948590190864068', '6.657601025822708', '7.059878808301439', '7.463310719642290', '7.918274623211606', '8.422912910022086', '8.829123546144333', '9.478626806536643', '9.632369142015169', '10.11799352123184', '10.76521254884490', '11.09846373292906', '11.75935422495317', '11.94925345506615', '12.52189363846295', '12.94221882368654', '13.52080754708197', '13.79661255956877', '14.23078081833814', '14.84639722882407', '14.94425569462134', '15.39370366866421', '15.98290903484343', '16.38571345446710', '16.83319653336102', '17.27992916366671', '17.67591607079135', '18.09741039043556', '18.56449266163239', '18.90698982186737', '19.55000489386596', '19.71909919214576'], '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': 829660901099740334, 'z1': {'__RealLiteral__': 0, 'data': '0.5224764355646214', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.096300849931958', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.833647445386811', '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, -4, 0, 0, 0, -2, 0, 4, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 8, 0, -4, 0, -6, 0, 4, 0, 0, 0, 0, 0, 1, 0, -2, 0, 6, 0, 0, 0, 4, 0, 4, 0, -6, 0, 1, 0, 0, 0, 4, 0, 2, 0, 0, 0, -4, 0, 0, 0, 1, 0, 14, 0, 1, 0, -6, 0, 0, 0, 0, 0, 0, 0, -4, 0, 2, 0, 0, 0, -10, 0, 1, 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, -1, 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, -1, 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': 189, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/vd'], '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-c1-0-189', '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': 829660901099740334, 'z1': {'__RealLiteral__': 0, 'data': '0.5224764355646214', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '829660901099740334', 'Lhash_array': ['829660901099740334'], 'label': '2-369600-1.1-c1-0-189', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/vd'}