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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': 1, 'A8': 0, 'A9': 1, 'Lhash': '1805207899297358716', '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': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 617.0839068204551, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [7, [1, -1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '77280.1', 'coefficient_field': '1.1.1.1', 'conductor': 77280, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, -1], [1, 0, 11], [1, 2, 13], [1, -2, 17], [1, 4, 19], [1, 1], [1, 10, 29], [1, 8, 31], [1, -6, 37], [1, -2, 41], [1, -4, 43], [1, -4, 47], [1, -6, 53], [1, -4, 59], [1, 10, 61], [1, -12, 67], [1, 12, 71], [1, -10, 73], [1, -8, 79], [1, 0, 83], [1, 2, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 30, 'label': '2-77280-1.1-c1-0-30', 'leading_term': '5.62116843744', '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/77280/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.253026586996396, 1.64658799480579, 0.712206005380571, -1.071772923895233, -2.302044524815817, -1.829084823278489, -0.1737776557049327, 0.6542241403306904, -0.6322810063744966, -2.649633730316236, -2.465759827242715, 0.8213860439726591, 4.382113571545776, 4.660422639536946, 1.831992893971501, -0.2708912239850806, 0.820574181905267, 2.960899289597055, 2.655548056014361, 0.1923371311293216, -1.071863256635883, -0.1318875971032454, 0.2649576739588682, -1.377867630016312, -2.35240088289762, -0.3287411750244278, 2.070845469986304, 1.162139214936083, -1.423064772725296, -1.238952674747081, 1.078785129341386, 0.4242085889579157, -3.710101631881622, -5.380139564782573, -1.775104485765855, 1.925760347480792, 1.227748469278148, -0.4679080791421336, 1.284877756443163, 3.783301035879753, 2.548489716122338, -0.2138545285688886, -0.07500538541808713, 1.19436372799735, -0.2650246745765389, -2.123944424840658, -0.3105308487979777, 2.420644232711606, 1.386998289434826, -0.9091385054550531, 0.04647816210426005, 1.472436118211433, -0.8146373317877874, -2.867910640480232, 0.2471694264597471, 4.015832297043512, 2.390350487270076, -0.8895953856080182, -0.2622986807000584, 0.6310360862160876, -2.463423974085965, -4.217785329186558, 0.09461750824884321, 4.402795145656814, 2.871169398308811, 0.05391486771876331, 0.5259999230113579, 0.7299068272791646, -1.206782863409721, -1.009806646678878, 1.248904311847324, 0.4597904814196939, -2.018591008629045, -1.121714420888984, 0.08171939802788718, -3.003351870264972, -4.696387852412907, 0.1568486686422933, 4.124217337257306, 1.220202774881949, -1.159733909646394, 2.200763823211641, 4.122717710668023, 0.9738439165031774, -0.4887292823581743, 1.32846932019719, 0.5458401580235417, -1.844016466699087, -0.9030751714227597, -0.1171491835130905, -3.19525550946288, -4.343411208553412, -0.8579879836031045, 0.4691252088969795, -1.593159456762746, -0.7846186488044925, 1.356252581115032, -0.5749268020368167, -1.959015846928516, 1.586355197554022, 2.9650054228606, -0.8275365857091501, -1.55270355528939, 1.410719378727162, -0.3699213820325177, -4.294718819270767, -1.747245361066131, 2.58240336786957, 1.060081379924283, -1.156370634661983, 0.2158624402269444, -0.2629578530951778, -2.416999404874036, -0.2561132225632208, 2.65372717733269, 0.7655835957556258, -0.8049657460006128, 0.9523851354410251, 0.5941063367833385, -0.7615676857635387], 'positive_zeros': ['0.8548326298546732', '1.777920555629518', '2.167436415222972', '2.949421250174845', '3.933435709184747', '4.142456710405856', '5.020542547199375', '5.527701898730486', '5.812496328692635', '6.527169241987819', '7.104402168146815', '7.628294056344158', '8.032142208660701', '8.844368370710638', '9.388945685920175', '9.628622189335495', '10.47127275745160', '10.76191918322979', '11.22386975889377', '11.77317981401307', '12.37551732107203', '12.74478952599730', '13.18940472757607', '13.73729532888186', '14.40804692122339', '14.78281900716103', '15.08008439554137', '15.74601545741143', '16.51272411015191', '16.63553237888937', '17.10296520900051', '17.60517371992436', '18.04118598937763', '18.64196036816900', '18.76778963150751', '19.49382000376995'], 'prelabel': '2-77280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.84117362002961, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1805207899297358716, 'z1': {'__RealLiteral__': 0, 'data': '0.8548326298546732', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.777920555629518', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.167436415222972', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 617.0839068204551, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 77280, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -2, 0, -1, 0, 2, 0, -4, 0, -1, 0, -1, 0, 1, 0, -1, 0, -10, 0, -8, 0, 0, 0, 1, 0, 6, 0, 2, 0, 2, 0, 4, 0, 1, 0, 4, 0, 1, 0, -2, 0, 6, 0, 0, 0, 4, 0, 4, 0, -10, 0, 1, 0, -2, 0, 12, 0, 1, 0, -12, 0, 10, 0, -1, 0, 0, 0, 8, 0, 1, 0, 0, 0, 2, 0, 10, 0, -2, 0, -2, 0, 8, 0, -4, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, 10, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -6, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, -4, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, -12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 12, 71], 'euler73': [1, -10, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, 2, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -1, 0], [1, 0, 11], [1, 2, 13], [1, -2, 17], [1, 4, 19], [1, 1, 0], [1, 10, 29], [1, 8, 31], [1, -6, 37], [1, -2, 41], [1, -4, 43], [1, -4, 47], [1, -6, 53], [1, -4, 59], [1, 10, 61], [1, -12, 67], [1, 12, 71], [1, -10, 73], [1, -8, 79], [1, 0, 83], [1, 2, 89], [1, -2, 97]], 'index': 30, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/77280/u'], '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': '2-77280-1.1-c1-0-30', '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': '2-77280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.84117362002961, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1805207899297358716, 'z1': {'__RealLiteral__': 0, 'data': '0.8548326298546732', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1805207899297358716', 'Lhash_array': ['1805207899297358716'], 'label': '2-77280-1.1-c1-0-30', 'type': 'ECQ', 'url': 'EllipticCurve/Q/77280/u'}