Formats: - HTML - YAML - JSON - 2026-10-13T01:57:28.916287
  • lfunc_lfunctions • Show schema
    {'Lhash': '1861851432878191779408263837137', 'a10': [2.6915904671607827, 0.0], 'a2': [2.6915904671607827, 0.0], 'a3': [1.0, 0.0], 'a4': [5.2446592429108, 0.0], 'a5': [1.0, 0.0], 'a6': [2.6915904671607827, 0.0], 'a7': [-0.797044177332249, 0.0], 'a8': [8.733293887403832, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.23899269452335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '5415.1', 'coefficient_field': 'CDF', 'conductor': 5415, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.6915904671607827, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.797044177332249, 0], [7.0, 0]], [[1.0, 0], [-2.592247733863472, 0], [11.0, 0]], [[1.0, 0], [-2.797044177332249, 0], [13.0, 0]], [[1.0, 0], [5.772472845517286, 0], [17.0, 0]], 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[109.0, 0]], [[1.0, 0], [8.26042364868175, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 196, 'label': '2-5415-1.1-c1-0-196', 'leading_term': '9.9193373108627836418708143013', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5415/2/a/z/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [9.919337310862783, 9.908995698019517, 9.877713799841516, 9.82473773482172, 9.748867510215302, 9.648537746236146, 9.521923200873651, 9.367062647453288, 9.181994062092894, 8.96489407691744, 8.71421512307287, 8.428814464740727, 8.10807025418225, 7.751980691817982, 7.361243271392371, 6.937311888361879, 6.482430284149291, 5.999640906540457, 5.49276881463236, 4.9663807741361765, 4.425720199477279, 3.876619118883275, 3.325388874125431, 2.7786918154659657, 2.2433968046113524, 1.7264218778898928, 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'5.05617677625977594549169227074503', '6.08094901000050350774999152359614', '6.64121121842086762463026515303795', '6.83880392662720164780696900962071', '8.138525380168549397938070725807282'], 'prelabel': '2-5415-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.575636295790952, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46874180672732826845638630457', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.22627011020930451794773391698', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.09725519347025551541663215355', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 43.23899269452335, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 5415, 'conductor_radical': 285, 'degree': 2, 'index': 196, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5415/2/a/z/1/5'], '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': '2-5415-1.1-c1-0-196', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-5415-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.575636295790952, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46874180672732826845638630457', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1861851432878191779408263837137', 'Lhash_array': ['1861851432878191779408263837137'], 'factors': ['2-5415-1.1-c1-0-196'], 'label': '2-5415-1.1-c1-0-196', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5415/2/a/z/1/5'}