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lfunc_lfunctions • Show schema
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{'Lhash': '70014523958499879641309857675,1993109076650620095824756929074', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -18, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9622.216082775107, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '3600.1', 'coefficient_field': '1.1.1.1', 'conductor': 12960000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1], [1, 18, 179, 882, 2401], [1, 0, 96, 0, 14641], [1, 2, 339, 338, 28561], [1, 0, 144, 0, 83521], [1, 50, 1347, 18050, 130321], [1, 0, -1040, 0, 279841], [1, 0, -960, 0, 707281], [1, -78, 3443, -74958, 923521], [1, 64, 3762, 87616, 1874161], [1, 0, -3330, 0, 2825761], [1, 46, 4227, 85054, 3418801], [1, 0, -3360, 0, 4879681], [1, 0, 3630, 0, 7890481], [1, 0, -6864, 0, 12117361], [1, -146, 12771, -543266, 13845841], [1, -126, 12947, -565614, 20151121], [1, 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'6.38316475790437159515744164871817', '6.65997258995402939772140314163791', '6.98561126807676597054637360868096', '7.17135805382902305190067607424684', '7.997636132580568519118650313442370', '8.252796158568762970501735270186883', '8.776138061745164346003530987261725'], 'prelabel': '4-60e4-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.904185739863065, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e2-0', 'trace_hash': 1572401390343374753, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.05523172074852043384134555270', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.77087749458354807650065673550', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.57228583041082317301656131480', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9622.216082775107, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 12960000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, 145, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 146, 0, 0, 0, 0, 0, 126, 0, 0, 0, 0, 0, -272, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 14, 0, 0, 0], 'euler11': [1, 0, 96, 0, 14641], 'euler13': [1, 2, 339, 338, 28561], 'euler17': [1, 0, 144, 0, 83521], 'euler19': [1, 50, 1347, 18050, 130321], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -1040, 0, 279841], 'euler29': [1, 0, -960, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -78, 3443, -74958, 923521], 'euler37': [1, 64, 3762, 87616, 1874161], 'euler41': [1, 0, -3330, 0, 2825761], 'euler43': [1, 46, 4227, 85054, 3418801], 'euler47': [1, 0, -3360, 0, 4879681], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 3630, 0, 7890481], 'euler59': [1, 0, -6864, 0, 12117361], 'euler61': [1, -146, 12771, -543266, 13845841], 'euler67': [1, -126, 12947, -565614, 20151121], 'euler7': [1, 18, 179, 882, 2401], 'euler71': [1, 0, -6210, 0, 25411681], 'euler73': [1, 272, 29154, 1449488, 28398241], 'euler79': [1, -48, 13058, -299568, 38950081], 'euler83': [1, 0, -11600, 0, 47458321], 'euler89': [1, 0, -5474, 0, 62742241], 'euler97': [1, -14, 18867, -131726, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 18, 179, 882, 2401], [1, 0, 96, 0, 14641], [1, 2, 339, 338, 28561], [1, 0, 144, 0, 83521], [1, 50, 1347, 18050, 130321], [1, 0, -1040, 0, 279841], [1, 0, -960, 0, 707281], [1, -78, 3443, -74958, 923521], [1, 64, 3762, 87616, 1874161], [1, 0, -3330, 0, 2825761], [1, 46, 4227, 85054, 3418801], [1, 0, -3360, 0, 4879681], [1, 0, 3630, 0, 7890481], [1, 0, -6864, 0, 12117361], [1, -146, 12771, -543266, 13845841], [1, -126, 12947, -565614, 20151121], [1, 0, -6210, 0, 25411681], [1, 272, 29154, 1449488, 28398241], [1, -48, 13058, -299568, 38950081], [1, 0, -11600, 0, 47458321], [1, 0, -5474, 0, 62742241], [1, -14, 18867, -131726, 88529281]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3600/3/l/b'], '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': '4-60e4-1.1-c2e2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-60e4-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 9.904185739863065, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 1572401390343374753, 'z1': {'__RealLiteral__': 0, 'data': '0.05523172074852043384134555270', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '70014523958499879641309857675,1993109076650620095824756929074', 'Lhash_array': ['70014523958499879641309857675', '1993109076650620095824756929074'], 'factors': ['2-60e2-3.2-c2-0-2', '2-60e2-3.2-c2-0-75'], 'label': '4-60e4-1.1-c2e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3600/3/l/b'}