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lfunc_lfunctions • Show schema
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{'Lhash': '1511285805515947547160237150308,1719392740346553514980735741763', 'a10': 4, 'a2': 2, 'a3': -2, 'a4': 3, 'a5': 2, 'a6': -4, 'a7': 1, 'a8': 4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.14677389390195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, 2, 1]], [5, [1, -2, 1]], [31, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.1', 'coefficient_field': '1.1.1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 2, 1], [1, -2, 1], [1, -1, 10, -7, 49], [1, -1, 18, -11, 121], [1, -4, 30, -52, 169], [1, -2, 18, -34, 289], [1, 3, 2, 57, 361], [1, -7, 54, -161, 529], [1, -6, 50, -174, 841], [1, -2, 1], [1, -2, 58, -74, 1369], [1, -6, 74, -246, 1681], [1, -5, -14, -215, 1849], [1, -2, 78, -94, 2209], [1, -19, 192, -1007, 2809], [1, 18, 182, 1062, 3481], [1, -12, 158, -732, 3721], [1, 6, -10, 402, 4489], [1, 3, 106, 213, 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8.092803122061406, 5.687509300762324], 'positive_zeros': ['1.19219428858697637835555291852712', '1.35636171358021831321444547882852', '2.50779933605166344714653458320336', '2.82179157383162195127400833663955', '3.69405827722768577241665985395139', '4.18573751729956530611062536604780', '4.59322043530120736241495437637831', '5.06919548701767731828346583917417', '5.56865023429522812415694669481090', '5.82657404658869598588534061457397', '6.36442623568392223854921019560991', '6.48159766284164875326425405870519', '7.25349638059761408898454286541958', '7.27109803947625248603649878617351', '8.269220544903797731966262923998452', '8.454113429484776346681778764310507', '9.135189465923416730781059868944353', '9.560176306576161195048511404639075', '10.07896814888613568901950952351934', '10.58369742668169622881392498136657'], 'prelabel': '4-930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1541584574229225816, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19219428858697637835555291853', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.35636171358021831321444547883', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.50779933605166344714653458320', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55.14677389390195, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'dirichlet_coefficients': [1, 2, -2, 3, 2, -4, 1, 4, 3, 4, 1, -6, 4, 2, -4, 5, 2, 6, -3, 6, -2, 2, 7, -8, 3, 8, -4, 3, 6, -8, 2, 6, -2, 4, 2, 9, 2, -6, -8, 8, 6, -4, 5, 3, 6, 14, 2, -10, -9, 6, -4, 12, 19, -8, 2, 4, 6, 12, -18, -12, 12, 4, 3, 7, 8, -4, -6, 6, -14, 4, -3, 12, -1, 4, -6, -9, 1, -16, -21, 10, 5, 12, 12, -6, 4, 10, -12, 4, -15, 12, 4, 21, -4, 4, -6, -12, -12, -18, 3, 9], 'euler11': [1, -1, 18, -11, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, -2, 18, -34, 289], 'euler19': [1, 3, 2, 57, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, -7, 54, -161, 529], 'euler29': [1, -6, 50, -174, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -2, 1, 0, 0], 'euler37': [1, -2, 58, -74, 1369], 'euler41': [1, -6, 74, -246, 1681], 'euler43': [1, -5, -14, -215, 1849], 'euler47': [1, -2, 78, -94, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -19, 192, -1007, 2809], 'euler59': [1, 18, 182, 1062, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, 6, -10, 402, 4489], 'euler7': [1, -1, 10, -7, 49], 'euler71': [1, 3, 106, 213, 5041], 'euler73': [1, 1, 40, 73, 5329], 'euler79': [1, 21, 230, 1659, 6241], 'euler83': [1, -12, 134, -996, 6889], 'euler89': [1, 15, 196, 1335, 7921], 'euler97': [1, 12, 230, 1164, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, -1, 10, -7, 49], [1, -1, 18, -11, 121], [1, -4, 30, -52, 169], [1, -2, 18, -34, 289], [1, 3, 2, 57, 361], [1, -7, 54, -161, 529], [1, -6, 50, -174, 841], [1, -2, 1, 0, 0], [1, -2, 58, -74, 1369], [1, -6, 74, -246, 1681], [1, -5, -14, -215, 1849], [1, -2, 78, -94, 2209], [1, -19, 192, -1007, 2809], [1, 18, 182, 1062, 3481], [1, -12, 158, -732, 3721], [1, 6, -10, 402, 4489], [1, 3, 106, 213, 5041], [1, 1, 40, 73, 5329], [1, 21, 230, 1659, 6241], [1, -12, 134, -996, 6889], [1, 15, 196, 1335, 7921], [1, 12, 230, 1164, 9409]], 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/a/p'], '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': '4-930e2-1.1-c1e2-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-930e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1541584574229225816, 'z1': {'__RealLiteral__': 0, 'data': '1.19219428858697637835555291853', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1511285805515947547160237150308,1719392740346553514980735741763', 'Lhash_array': ['1511285805515947547160237150308', '1719392740346553514980735741763'], 'label': '4-930e2-1.1-c1e2-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/a/p'}