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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': -1, 'A3': 0, 'A4': -1, 'A5': 2, 'A6': 0, 'A7': 1, 'A8': 3, 'A9': 0, 'Lhash': '1905477331691778678', 'a10': [-0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [1.0606601717798212, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1765.2288823638398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, -1]], [11, [1]], [29, [1, -1]]], 'bad_primes': [3, 7, 11, 29], 'central_character': '221067.1', 'coefficient_field': '1.1.1.1', 'conductor': 221067, 'conductor_radical': 6699, 'degree': 2, 'euler_factors': [[1, 1, 2], [1], [1, -2, 5], [1, -1], [1], [1, -4, 13], [1, 1, 17], [1, 7, 19], [1, -3, 23], [1, -1], [1, -3, 31], [1, 2, 37], [1, 7, 41], [1, 4, 43], [1, -13, 47], [1, -1, 53], [1, 0, 59], [1, -9, 61], [1, -3, 67], [1, 11, 71], [1, 2, 73], [1, -10, 79], [1, -6, 83], [1, 3, 89], [1, -1, 97]], 'gamma_factors': [[], [0]], 'index': 29, 'label': '2-221067-1.1-c1-0-29', 'leading_term': '6.02718527531', '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/221067/n', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.312004819889021, 1.601459512374326, 0.626207352078238, -0.5737153125224261, -0.5160441278366559, 0.8233774132317704, 1.592336886099506, 0.5721034125712576, -0.3817937962115885, 1.703881759611811, 6.093031155567949, 7.900519834096119, 4.41873221919915, -0.2802375882549099, -0.4541227911982309, 2.994754660966132, 4.055856959357647, 1.283039671606094, -0.1049287929901027, 2.446455933543246, 4.115922624564572, 1.323936964997485, -1.559785567948072, -0.05829225942764039, 2.085144011907939, -0.03952275490899056, -2.901492646107544, -0.9249678537242068, 2.706549891783634, 1.578890005676043, -2.294547123305163, -2.643708761108379, -0.1925064615412348, 0.4131196645394608, -0.1397052346828443, 0.723519159746127, 0.8094943729537778, -1.422389189614859, -2.23119102792167, -0.3027253392829253, 0.3055305042457323, -0.613612171474054, 0.8424864878606094, 2.297549196610821, -0.8576476518225993, -3.103612594428103, 2.191724793120103, 7.264997288832546, 2.677054517686033, -4.242694963642849, -3.220032099438657, 0.568158637231309, -0.1275413023701753, -0.7575576536007042, 1.290258161863791, 0.3710911043327833, -1.902504632610061, 1.382791147875622, 4.95090572123024, 0.8594377141614972, -3.270929004661531, 0.180493417890305, 2.113839291218768, -3.534928045302438, -6.680563390876446, -2.480477120511954, 0.524984948815506, -0.2902145280221077, 0.2082685201425431, 0.9960275444521243, -0.2408532388405905, -0.1236046222831097, 0.9986344675809591, -0.3820040320452938, -1.124889146525872, 0.5846466481129811, -0.3287298038537828, -1.895683091198754, 2.299607077273241, 5.722828004597033, 1.000042121644067, -2.997552719352026, -0.5575716357265735, -0.3996159316015553, -3.110722235107259, -0.7865534811776473, 1.780438552759108, -0.8525451974323481, -0.187021101606436, 4.193533975068365, 1.315770416469397, -4.388844483964965, -2.399908864661154, 0.364804133266231, -0.3371957219713793, 5.456475597940222, 13.68260961862128, 9.952207065273432, 0.7958937129495905, -0.7468944038594871, 0.2617284770392587, -0.9506259501836921, 0.4486040245831374, 1.831732231829991, -0.3703624505655206, -0.3404535331671373, 1.544530607826038, -0.4293219597452142, -1.836599842338599, 0.2546379261386466, -0.08104717209241909, -1.430717962845747, 0.2307226975281116, -0.04394634184039507, -1.61371094025874, 0.8406739660122841, 0.8579048860274525, -3.839289339489975, -2.931817406251571, 0.5720096978129903], 'positive_zeros': ['0.8653254174222407', '1.360384215842542', '2.097702158790839', '2.349447885367241', '3.478394215270333', '3.790453795268227', '4.636884703925662', '4.773967157067315', '5.584980855882989', '6.004821628333061', '6.497354725434956', '7.054482902560258', '7.597132841333213', '8.275605848915277', '8.639943538889671', '8.833068057159767', '9.356639478225032', '10.04240004875332', '10.32431662261623', '10.65993260676769', '11.20178956227052', '11.67500388829160', '12.33027136085052', '12.94072940573909', '13.23385667796210', '13.59914273414090', '14.03027995235955', '14.43333218780944', '15.03364062462378', '15.49106334501478', '15.86810071665789', '16.65452648258666', '16.92853103352209', '17.21224245433679', '17.70498094425418', '18.02179762734925', '18.45373255292307', '18.91129362610217', '19.21722220413119', '19.64908122747081'], 'prelabel': '2-221067-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.01462700493531, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1905477331691778678, 'z1': {'__RealLiteral__': 0, 'data': '0.8653254174222407', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.360384215842542', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.097702158790839', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1765.2288823638398, 'bad_primes': [3, 7, 11, 29], 'central_character': '1.1', 'conductor': 221067, 'conductor_radical': 6699, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, 2, 0, 1, 3, 0, -2, 0, 0, 4, -1, 0, -1, -1, 0, -7, -2, 0, 0, 3, 0, -1, -4, 0, -1, 1, 0, 3, -5, 0, 1, 2, 0, -2, 7, 0, 6, -7, 0, -4, 0, 0, -3, 13, 0, 1, 1, 0, -4, 1, 0, 0, 3, 0, -1, 0, 0, 9, -3, 0, 7, 8, 0, 3, 1, 0, -2, -11, 0, -2, 2, 0, 7, 0, 0, 10, -2, 0, 7, 6, 0, -2, 4, 0, 0, -3, 0, 4, -3, 0, -13, -14, 0, 1, -1, 0, 1], 'euler11': [1, 0, 0], 'euler13': [1, -4, 13], 'euler17': [1, 1, 17], 'euler19': [1, 7, 19], 'euler2': [1, 1, 2], 'euler23': [1, -3, 23], 'euler29': [1, -1, 0], 'euler3': [1, 0, 0], 'euler31': [1, -3, 31], 'euler37': [1, 2, 37], 'euler41': [1, 7, 41], 'euler43': [1, 4, 43], 'euler47': [1, -13, 47], 'euler5': [1, -2, 5], 'euler53': [1, -1, 53], 'euler59': [1, 0, 59], 'euler61': [1, -9, 61], 'euler67': [1, -3, 67], 'euler7': [1, -1, 0], 'euler71': [1, 11, 71], 'euler73': [1, 2, 73], 'euler79': [1, -10, 79], 'euler83': [1, -6, 83], 'euler89': [1, 3, 89], 'euler97': [1, -1, 97], 'euler_factors': [[1, 1, 2], [1, 0, 0], [1, -2, 5], [1, -1, 0], [1, 0, 0], [1, -4, 13], [1, 1, 17], [1, 7, 19], [1, -3, 23], [1, -1, 0], [1, -3, 31], [1, 2, 37], [1, 7, 41], [1, 4, 43], [1, -13, 47], [1, -1, 53], [1, 0, 59], [1, -9, 61], [1, -3, 67], [1, 11, 71], [1, 2, 73], [1, -10, 79], [1, -6, 83], [1, 3, 89], [1, -1, 97]], 'index': 29, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/221067/n'], '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': '2-221067-1.1-c1-0-29', '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': '2-221067-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.01462700493531, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1905477331691778678, 'z1': {'__RealLiteral__': 0, 'data': '0.8653254174222407', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1905477331691778678', 'Lhash_array': ['1905477331691778678'], 'label': '2-221067-1.1-c1-0-29', 'type': 'ECQ', 'url': 'EllipticCurve/Q/221067/n'}