Formats: - HTML - YAML - JSON - 2026-10-14T19:33:15.726248
  • lfunc_lfunctions • Show schema
    {'Lhash': '2394612915683615318820450756669', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0.5, -2.598076211353316], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.048920523745066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5, 2.598076211353316]]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.865', 'coefficient_field': 'CDF', 'conductor': 1008, 'conductor_radical': 42, 'conjugate': '429897489483500141243514988395', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [-0.5, 2.598076211353316]], [[1.0, 0], [0, 0], [-5.5, -9.526279441628825]], [[1.0, 0], [7.0, 0], [13.0, 0]], [[1.0, 0], [0, 0], [-8.5, -14.722431864335457]], [[1.0, 0], [3.5, 6.06217782649107], [-9.5, 16.454482671904334]], [[1.0, 0], 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'5.18893701315880067251559790015579', '5.84779876966750141570473531862359', '6.99022875816697026822061597234220', '7.79694550440379629369947205092522', '8.625070940816977595190755931454620', '9.522503565607493123660424770731565', '10.09483885543316872585529127791386'], 'prelabel': '2-1008-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': 0.3736792394412256, 'root_number': '-0.7012145161459063422881052853594033060275307273817210712 + 0.7129503505478221262538366779721476646448806805958393603*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3736792394412256', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.88901651232010319783404348713', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.80204972038659717137231396963', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.14987164623491398145971295562', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 8.048920523745066, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 1008, 'conductor_radical': 42, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/2/s/j/865/1'], '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': '2-1008-7.4-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1008-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.837061952750603, 'root_angle': 0.3736792394412256, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.88901651232010319783404348713', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2394612915683615318820450756669', 'Lhash_array': ['2394612915683615318820450756669'], 'factors': ['2-1008-7.4-c1-0-16'], 'label': '2-1008-7.4-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/2/s/j/865/1'}