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lfunc_lfunctions • Show schema
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{'Lhash': '2105828652872535617251739220178,3579115088153868300816977283365', 'a10': 2, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': -2, 'a6': 0, 'a7': -5, 'a8': -3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.82056271920522, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 2, 1]], [13, [1, 2, 1]]], 'bad_primes': [3, 5, 13], 'central_character': '585.1', 'coefficient_field': '1.1.1.1', 'conductor': 342225, 'conductor_radical': 195, 'degree': 4, 'euler_factors': [[1, 1, 0, 2, 4], [1], [1, 2, 1], [1, 5, 16, 35, 49], [1, 1, 18, 11, 121], [1, 2, 1], [1, -1, 30, -17, 289], [1, 2, 22, 38, 361], [1, 9, 62, 207, 529], [1, -6, 50, -174, 841], [1, -12, 98, -372, 961], [1, 9, 56, 333, 1369], [1, 3, 80, 123, 1681], [1, 2, 70, 86, 1849], [1, 14, 126, 658, 2209], [1, 3, 70, 159, 2809], [1, 24, 262, 1416, 3481], [1, 1, 84, 61, 3721], [1, -2, -18, -134, 4489], [1, 25, 294, 1775, 5041], [1, 12, 182, 876, 5329], [1, 3, 122, 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0.08304569574852282], 'positive_zeros': ['1.66120589734537228912904795572780', '2.82342396833124201444253741024316', '2.99613946156065026333088922267682', '3.46360417048540056927518683778991', '4.51937609989202770452600308295091', '4.54113818883496080611787069091953', '5.64656296920201328406111053153103', '6.30593074763065902148610787542384', '6.33191804757917848346117094712364', '6.83819828586910433106762194098759', '7.38527339122787260506101003182316', '7.925785096726287958543361634387944', '8.460648932664054176160298451417226', '8.536522635467047420772977550801559', '9.279297698324351119466275768764428', '9.693664612531849309713983016072602', '10.04323222908775155559777351236821', '10.25647380054202828006587558413755'], 'prelabel': '4-585e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.161307131863703, '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': 1533411340039759714, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66120589734537228912904795573', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82342396833124201444253741024', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99613946156065026333088922268', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.82056271920522, 'bad_primes': [3, 5, 13], 'central_character': '1.1', 'conductor': 342225, 'conductor_radical': 195, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 1, -2, 0, -5, -3, 0, 2, -1, 0, -2, 5, 0, 1, 1, 0, -2, -2, 0, 1, -9, 0, 3, 2, 0, -5, 6, 0, 12, 1, 0, -1, 10, 0, -9, 2, 0, 6, -3, 0, -2, -1, 0, 9, -14, 0, 9, -3, 0, -2, -3, 0, 2, 15, 0, -6, -24, 0, -1, -12, 0, 1, 4, 0, 2, 1, 0, -10, -25, 0, -12, 9, 0, -2, 5, 0, -3, -2, 0, 3, 0, 0, -2, 2, 0, 3, -9, 0, 10, -9, 0, 14, 4, 0, 5, -9, 0, 3], 'euler11': [1, 1, 18, 11, 121], 'euler13': [1, 2, 1, 0, 0], 'euler17': [1, -1, 30, -17, 289], 'euler19': [1, 2, 22, 38, 361], 'euler2': [1, 1, 0, 2, 4], 'euler23': [1, 9, 62, 207, 529], 'euler29': [1, -6, 50, -174, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -12, 98, -372, 961], 'euler37': [1, 9, 56, 333, 1369], 'euler41': [1, 3, 80, 123, 1681], 'euler43': [1, 2, 70, 86, 1849], 'euler47': [1, 14, 126, 658, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, 3, 70, 159, 2809], 'euler59': [1, 24, 262, 1416, 3481], 'euler61': [1, 1, 84, 61, 3721], 'euler67': [1, -2, -18, -134, 4489], 'euler7': [1, 5, 16, 35, 49], 'euler71': [1, 25, 294, 1775, 5041], 'euler73': [1, 12, 182, 876, 5329], 'euler79': [1, 3, 122, 237, 6241], 'euler83': [1, 0, -106, 0, 6889], 'euler89': [1, 9, 160, 801, 7921], 'euler97': [1, -5, -8, -485, 9409], 'euler_factors': [[1, 1, 0, 2, 4], [1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 5, 16, 35, 49], [1, 1, 18, 11, 121], [1, 2, 1, 0, 0], [1, -1, 30, -17, 289], [1, 2, 22, 38, 361], [1, 9, 62, 207, 529], [1, -6, 50, -174, 841], [1, -12, 98, -372, 961], [1, 9, 56, 333, 1369], [1, 3, 80, 123, 1681], [1, 2, 70, 86, 1849], [1, 14, 126, 658, 2209], [1, 3, 70, 159, 2809], [1, 24, 262, 1416, 3481], [1, 1, 84, 61, 3721], [1, -2, -18, -134, 4489], [1, 25, 294, 1775, 5041], [1, 12, 182, 876, 5329], [1, 3, 122, 237, 6241], [1, 0, -106, 0, 6889], [1, 9, 160, 801, 7921], [1, -5, -8, -485, 9409]], 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/a/j'], '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': '4-585e2-1.1-c1e2-0-29', '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': 2, 'prelabel': '4-585e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1533411340039759714, 'z1': {'__RealLiteral__': 0, 'data': '1.66120589734537228912904795573', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2105828652872535617251739220178,3579115088153868300816977283365', 'Lhash_array': ['2105828652872535617251739220178', '3579115088153868300816977283365'], 'label': '4-585e2-1.1-c1e2-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/a/j'}