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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 0, 'Lhash': '346518381290366600,1489333638491333482', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.77285407260262, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1]], [7, [1, -1]]], 'bad_primes': [2, 3, 7], 'central_character': '1000188.1', 'coefficient_field': '1.1.1.1', 'conductor': 1000188, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, 0, -1], [1], [1, 0, 10, 0, 25], [1, -1], [1, 0, 22, 0, 121], [1, 0, 1, 0, 169], [1, -6, 43, -102, 289], [1, 0, 34, 0, 361], [1, 0, -35, 0, 529], [1, 0, 49, 0, 841], [1, 0, 37, 0, 961], [1, -4, 78, -148, 1369], [1, 12, 118, 492, 1681], [1, 2, 87, 86, 1849], [1, 12, 130, 564, 2209], [1, 0, 97, 0, 2809], [1, 6, 127, 354, 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0.06580682023138273, 0.27998143760740324, 0.4325301978733724, 0.450369477445809], 'positive_zeros': ['1.43423414088871078406280124120794', '1.68869994047015348511995782895005', '2.54401642319011399557920759888689', '3.34773629764867655679280376644618', '3.38877464404185294878323159151948', '4.30645127647783484429164317499182', '4.64577805751899849665319383092373', '5.36650684226892599309211492342136', '5.61879984028395623126782300752300', '6.29670817383847541122613475378689', '6.33738862277121156447234649391824', '7.21285497786280286801180495078762', '7.62887873867370361852526319091507', '7.66081859530557802153309309893230'], 'prelabel': '4-1000188-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.825914146012304, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1835852019781700082, 'z1': {'__RealLiteral__': 0, 'data': '1.43423414088871078406280124120794', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.68869994047015348511995782895005', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.54401642319011399557920759888689', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.77285407260262, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1000188, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -12, 0, -2, 0, 0, 0, -12, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 1, 0, 0, -26, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, -24, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, 1, 0, 169], 'euler17': [1, -6, 43, -102, 289], 'euler19': [1, 0, 34, 0, 361], 'euler2': [1, 0, -1, 0, 0], 'euler23': [1, 0, -35, 0, 529], 'euler29': [1, 0, 49, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 37, 0, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 2, 87, 86, 1849], 'euler47': [1, 12, 130, 564, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 97, 0, 2809], 'euler59': [1, 6, 127, 354, 3481], 'euler61': [1, 0, 22, 0, 3721], 'euler67': [1, 26, 303, 1742, 4489], 'euler7': [1, -1, 0, 0, 0], 'euler71': [1, 0, 61, 0, 5041], 'euler73': [1, 0, 142, 0, 5329], 'euler79': [1, 20, 258, 1580, 6241], 'euler83': [1, 24, 310, 1992, 6889], 'euler89': [1, -30, 403, -2670, 7921], 'euler97': [1, 0, 130, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 10, 0, 25], [1, -1, 0, 0, 0], [1, 0, 22, 0, 121], [1, 0, 1, 0, 169], [1, -6, 43, -102, 289], [1, 0, 34, 0, 361], [1, 0, -35, 0, 529], [1, 0, 49, 0, 841], [1, 0, 37, 0, 961], [1, -4, 78, -148, 1369], [1, 12, 118, 492, 1681], [1, 2, 87, 86, 1849], [1, 12, 130, 564, 2209], [1, 0, 97, 0, 2809], [1, 6, 127, 354, 3481], [1, 0, 22, 0, 3721], [1, 26, 303, 1742, 4489], [1, 0, 61, 0, 5041], [1, 0, 142, 0, 5329], [1, 20, 258, 1580, 6241], [1, 24, 310, 1992, 6889], [1, -30, 403, -2670, 7921], [1, 0, 130, 0, 9409]], 'index': 34, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.21.1/holomorphic/2.2.21.1-2268.1-v', 'EllipticCurve/2.2.21.1/2268.1/v'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-1000188-1.1-c1e2-0-34', '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': 1, 'prelabel': '4-1000188-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.825914146012304, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1835852019781700082, 'z1': {'__RealLiteral__': 0, 'data': '1.43423414088871078406280124120794', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9547157
{'Lhash': '346518381290366600,1489333638491333482', 'Lhash_array': ['346518381290366600', '1489333638491333482'], 'label': '4-1000188-1.1-c1e2-0-34', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.21.1/2268.1/v'}
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id: 9546877
{'Lhash': '346518381290366600,1489333638491333482', 'Lhash_array': ['346518381290366600', '1489333638491333482'], 'label': '4-1000188-1.1-c1e2-0-34', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.21.1/holomorphic/2.2.21.1-2268.1-v'}