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  • lfunc_lfunctions • Show schema
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'8.617506485191786541322690274082490', '8.739100997259001296618798265341668', '9.416488223765838367064657334144098', '9.506710814602415565983123694024909', '9.747225826089862165706865860618529', '10.07175209376578307857858067619987', '10.20524524408134718734106209255037', '10.29130766873002452587857503701699', '10.61080730296115361101711821500238', '10.65893706578457776771152062712630', '10.89157441437072401433054066801519', '11.28836633852854281732621410812500', '11.70852398378159037070945200786835', '11.91871493687861706509599897547585', '12.20603725897311012268859178484428', '12.68034143927252445119929055234238', '12.83657326647230114823033878324525'], 'prelabel': '8-230e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 1318541043501008871, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63326505294999348003538572031', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.41485660603361830762438369361', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.03867292215223658109292997604', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 11.376790797644762, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 2798410000, 'conductor_radical': 230, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 0, 0, 9, 0, -18, 0, 0, 0, 0, 3, 0, 0, 14, 0, 0, 0, 0, 0, 10, 0, 0, 0, 12, 0, -22, 0, 0, 0, 0, -18, 0, 0, 0, 0, -18, 0, 0, 36, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -28, 0, 0, 4, 0, 44, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -162, -20], 'euler11': [1, 18, 163, 936, 3705, 10296, 19723, 23958, 14641], 'euler13': [1, 0, -45, 0, 833, 0, -7605, 0, 28561], 'euler17': [1, 0, -33, 0, 569, 0, -9537, 0, 83521], 'euler19': [1, -14, 127, -812, 4105, -15428, 45847, -96026, 130321], 'euler2': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler23': [1, 0, 2, 0, 1, 0, 0, 0, 0], 'euler29': [1, -12, 80, -612, 4254, -17748, 67280, -292668, 707281], 'euler3': [1, 0, -9, 0, 37, 0, -81, 0, 81], 'euler31': [1, 22, 283, 2464, 15985, 76384, 271963, 655402, 923521], 'euler37': [1, 0, -40, 0, 1518, 0, -54760, 0, 1874161], 'euler41': [1, 18, 283, 2556, 20205, 104796, 475723, 1240578, 2825761], 'euler43': [1, 0, 0, 0, 2078, 0, 0, 0, 3418801], 'euler47': [1, 0, -48, 0, 494, 0, -106032, 0, 4879681], 'euler5': [1, 0, -10, 0, 25, 0, 0, 0, 0], 'euler53': [1, 0, -204, 0, 16022, 0, -573036, 0, 7890481], 'euler59': [1, -24, 452, -5112, 47670, -301608, 1573412, -4929096, 12117361], 'euler61': [1, 2, 223, 344, 19885, 20984, 829783, 453962, 13845841], 'euler67': [1, 0, -240, 0, 23198, 0, -1077360, 0, 20151121], 'euler7': [1, 0, -1, 0, -3, 0, -49, 0, 2401], 'euler71': [1, -6, 295, -1284, 31809, -91164, 1487095, -2147466, 25411681], 'euler73': [1, 0, 36, 0, -538, 0, 191844, 0, 28398241], 'euler79': [1, -4, 232, -772, 26110, -60988, 1447912, -1972156, 38950081], 'euler83': [1, 0, -240, 0, 27998, 0, -1653360, 0, 47458321], 'euler89': [1, -12, 320, -2772, 42414, -246708, 2534720, -8459628, 62742241], 'euler97': [1, 0, 39, 0, 17297, 0, 366951, 0, 88529281], 'euler_factors': [[1, 0, 2, 0, 1, 0, 0, 0, 0], [1, 0, -9, 0, 37, 0, -81, 0, 81], [1, 0, -10, 0, 25, 0, 0, 0, 0], [1, 0, -1, 0, -3, 0, -49, 0, 2401], [1, 18, 163, 936, 3705, 10296, 19723, 23958, 14641], [1, 0, -45, 0, 833, 0, -7605, 0, 28561], [1, 0, -33, 0, 569, 0, -9537, 0, 83521], [1, -14, 127, -812, 4105, -15428, 45847, -96026, 130321], [1, 0, 2, 0, 1, 0, 0, 0, 0], [1, -12, 80, -612, 4254, -17748, 67280, -292668, 707281], [1, 22, 283, 2464, 15985, 76384, 271963, 655402, 923521], [1, 0, -40, 0, 1518, 0, -54760, 0, 1874161], [1, 18, 283, 2556, 20205, 104796, 475723, 1240578, 2825761], [1, 0, 0, 0, 2078, 0, 0, 0, 3418801], [1, 0, -48, 0, 494, 0, -106032, 0, 4879681], [1, 0, -204, 0, 16022, 0, -573036, 0, 7890481], [1, -24, 452, -5112, 47670, -301608, 1573412, -4929096, 12117361], [1, 2, 223, 344, 19885, 20984, 829783, 453962, 13845841], [1, 0, -240, 0, 23198, 0, -1077360, 0, 20151121], [1, -6, 295, -1284, 31809, -91164, 1487095, -2147466, 25411681], [1, 0, 36, 0, -538, 0, 191844, 0, 28398241], [1, -4, 232, -772, 26110, -60988, 1447912, -1972156, 38950081], [1, 0, -240, 0, 27998, 0, -1653360, 0, 47458321], [1, -12, 320, -2772, 42414, -246708, 2534720, -8459628, 62742241], [1, 0, 39, 0, 17297, 0, 366951, 0, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/b/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '8-230e4-1.1-c1e4-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-230e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.355197124587213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1318541043501008871, 'z1': {'__RealLiteral__': 0, 'data': '0.63326505294999348003538572031', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '802758824475620708986499806139,1793543825875391744229744067416,2584324953435321094234741300739,3918130343674362646334175492594', 'Lhash_array': ['802758824475620708986499806139', '1793543825875391744229744067416', '2584324953435321094234741300739', '3918130343674362646334175492594'], 'factors': ['2-230-5.4-c1-0-0', '2-230-5.4-c1-0-5', '2-230-5.4-c1-0-6', '2-230-5.4-c1-0-11'], 'label': '8-230e4-1.1-c1e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/b/a'}