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  • lfunc_lfunctions • Show schema
    {'Lhash': '789722367844061124842779379690', 'a10': [0, 0], 'a2': [0, -2.0], 'a3': [0, 0], 'a4': [28.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 192.0], 'a8': [0, -120.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.08635945792065, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.199', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1948015277641400906319004996188', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.0], [-32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -192.0], [-16807.0, 0]], [[1.0, 0], [-148.0, 0], [161051.0, 0]], [[1.0, 0], [0, 286.0], [-371293.0, 0]], [[1.0, 0], [0, -1678.0], [-1419857.0, 0]], [[1.0, 0], [1060.0, 0], [2476099.0, 0]], [[1.0, 0], [0, -2976.0], [-6436343.0, 0]], [[1.0, 0], [3410.0, 0], [20511149.0, 0]], [[1.0, 0], [2448.0, 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'10.44596667286359341322326001091885', '11.10405029313746446887448562809602'], 'prelabel': '2-15e2-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.007192310715602, 'root_angle': -0.17620819117478337, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 57}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62298110197074692411003408939', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.13731800534778857489148889745', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.65966655599419577346465504890', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 36.08635945792065, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/6/b/e/199/1'], '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': '2-15e2-5.4-c5-0-10', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-15e2-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.007192310715602, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62298110197074692411003408939', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '789722367844061124842779379690', 'Lhash_array': ['789722367844061124842779379690'], 'factors': ['2-15e2-5.4-c5-0-10'], 'label': '2-15e2-5.4-c5-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/6/b/e/199/1'}