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lfunc_lfunctions • Show schema
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{'Lhash': '2914798688184230337098589555138,3500621788617137721645860569314', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 2, 'a5': 1, 'a6': 0, 'a7': -8, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5754418249421496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -1, 1]], [19, [1, 7, 19]]], 'bad_primes': [5, 19], 'central_character': '95.1', 'coefficient_field': '1.1.1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'euler_factors': [[1, 0, -2, 0, 4], [1, -2, 1, -6, 9], [1, -1, 1], [1, 8, 30, 56, 49], [1, -6, 31, -66, 121], [1, 2, -9, 26, 169], [1, 6, 19, 102, 289], [1, 7, 19], [1, 0, -23, 0, 529], [1, -3, -20, -87, 841], [1, 14, 111, 434, 961], [1, -16, 138, -592, 1369], [1, -6, -5, -246, 1681], [1, -4, -27, -172, 1849], [1, 6, -11, 282, 2209], [1, -6, -17, -318, 2809], [1, -15, 166, -885, 3481], [1, 5, -36, 305, 3721], [1, 2, -63, 134, 4489], [1, -3, -62, -213, 5041], [1, 8, -9, 584, 5329], [1, 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-2.21656944970917], 'positive_zeros': ['2.29937073169802967093938323200187', '2.76150367300491270317309970663239', '3.77337017171378786291803365909954', '4.25245972936901947248198134347836', '6.12009696796375254811739836850817', '6.33318627269780152687854974749063', '6.93957105375992591277788891737302', '7.03575539981179466954492587891707', '8.323530410914496101847811241859227', '9.239927903917167007568240168427275', '9.280394832524382960342480921885495', '9.547593772168487256781364363023718', '10.55286062112174331753025360207693', '10.80327490361199919615475316805588', '11.74685280654655406145570868760454', '12.40959478732948953346559269489836', '12.79406976587063842094663671018311', '13.23941662520608353357695345489412', '13.46187718623727369698285947221612', '14.45727815431112247704379615371689'], 'prelabel': '4-95e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8709643042066444, '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': 646349333082974348, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.29937073169802967093938323200', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.76150367300491270317309970663', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77337017171378786291803365910', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5754418249421496, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 2, 1, 0, -8, 0, 3, 0, 6, 4, -2, 0, 2, 0, -6, 0, -7, 2, -16, 0, 0, 0, 0, 0, 10, -16, 3, 0, -14, 0, 12, 0, -8, 6, 16, 0, -4, 0, 6, 0, 4, 12, 3, 0, -6, 0, 34, 0, -12, -4, 6, 0, 6, 0, -14, 0, 15, 4, -5, 0, -24, -8, -2, 0, -2, -12, 0, 0, 3, 0, -8, 0, 0, -14, -48, 0, -5, 0, 20, 0, 24, -32, -6, 0, 6, 0, 15, 0, 16, 0, -28, 0, -7, 0, -8, 0, 18, 0], 'euler11': [1, -6, 31, -66, 121], 'euler13': [1, 2, -9, 26, 169], 'euler17': [1, 6, 19, 102, 289], 'euler19': [1, 7, 19, 0, 0], 'euler2': [1, 0, -2, 0, 4], 'euler23': [1, 0, -23, 0, 529], 'euler29': [1, -3, -20, -87, 841], 'euler3': [1, -2, 1, -6, 9], 'euler31': [1, 14, 111, 434, 961], 'euler37': [1, -16, 138, -592, 1369], 'euler41': [1, -6, -5, -246, 1681], 'euler43': [1, -4, -27, -172, 1849], 'euler47': [1, 6, -11, 282, 2209], 'euler5': [1, -1, 1, 0, 0], 'euler53': [1, -6, -17, -318, 2809], 'euler59': [1, -15, 166, -885, 3481], 'euler61': [1, 5, -36, 305, 3721], 'euler67': [1, 2, -63, 134, 4489], 'euler7': [1, 8, 30, 56, 49], 'euler71': [1, -3, -62, -213, 5041], 'euler73': [1, 8, -9, 584, 5329], 'euler79': [1, 5, -54, 395, 6241], 'euler83': [1, -24, 310, -1992, 6889], 'euler89': [1, -15, 136, -1335, 7921], 'euler97': [1, 8, -33, 776, 9409], 'euler_factors': [[1, 0, -2, 0, 4], [1, -2, 1, -6, 9], [1, -1, 1, 0, 0], [1, 8, 30, 56, 49], [1, -6, 31, -66, 121], [1, 2, -9, 26, 169], [1, 6, 19, 102, 289], [1, 7, 19, 0, 0], [1, 0, -23, 0, 529], [1, -3, -20, -87, 841], [1, 14, 111, 434, 961], [1, -16, 138, -592, 1369], [1, -6, -5, -246, 1681], [1, -4, -27, -172, 1849], [1, 6, -11, 282, 2209], [1, -6, -17, -318, 2809], [1, -15, 166, -885, 3481], [1, 5, -36, 305, 3721], [1, 2, -63, 134, 4489], [1, -3, -62, -213, 5041], [1, 8, -9, 584, 5329], [1, 5, -54, 395, 6241], [1, -24, 310, -1992, 6889], [1, -15, 136, -1335, 7921], [1, 8, -33, 776, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/95/2/e/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': '4-95e2-1.1-c1e2-0-3', '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': '4-95e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8709643042066444, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 646349333082974348, 'z1': {'__RealLiteral__': 0, 'data': '2.29937073169802967093938323200', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2914798688184230337098589555138,3500621788617137721645860569314', 'Lhash_array': ['2914798688184230337098589555138', '3500621788617137721645860569314'], 'label': '4-95e2-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/95/2/e/a'}