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  • lfunc_lfunctions • Show schema
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3.4682540976655027, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e4-0', 'trace_hash': 374300113739372064, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46942097395760816159121276717', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.877850360441859825708411064560', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.36530432482200037396190724604', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 20935.689300513717, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 31640625, 'conductor_radical': 15, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1673, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32608, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 139208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -59049, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -644204, 0, 155624547606, 0, -16708992677662604, 0, 672749994932560009201], 'euler13': [1, 0, 0, 0, 275716983698, 0, 0, 0, 19004963774880799438801], 'euler17': [1, 0, 0, 0, 1820608576898, 0, 0, 0, 4064231406647572522401601], 'euler19': [1, 0, -538604, 0, 12334656082806, 0, -3302216810716649804, 0, 37589973457545958193355601], 'euler2': [1, 0, 0, 0, 1673, 0, 0, 0, 1048576], 'euler23': [1, 0, 0, 0, 37064501443298, 0, 0, 0, 1716155831334586342923895201], 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0, 0, 5437943429267472574499737549036572950401], 'euler_factors': [[1, 0, 0, 0, 1673, 0, 0, 0, 1048576], [1, 0, 0, 0, 59049, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 564950498, 0, 0, 0, 79792266297612001], [1, 0, -644204, 0, 155624547606, 0, -16708992677662604, 0, 672749994932560009201], [1, 0, 0, 0, 275716983698, 0, 0, 0, 19004963774880799438801], [1, 0, 0, 0, 1820608576898, 0, 0, 0, 4064231406647572522401601], [1, 0, -538604, 0, 12334656082806, 0, -3302216810716649804, 0, 37589973457545958193355601], [1, 0, 0, 0, 37064501443298, 0, 0, 0, 1716155831334586342923895201], [1, 0, 82044596, 0, 2524243399801206, 0, 34516754990392737763796, 0, 176994576151109753197786640401], [1, -32608, 513247228, -4967586098656, 32164689055176070, -142217772523923521056, 420671946283284602469628, -765155263030071518803842208, 671790528819082282036142601601], [1, 0, 0, 0, 9617168744835698, 0, 0, 0, 23122483666661158726686253786801], [1, 0, -463424804, 0, 80535955860914406, 0, 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89648251976843595444986830377401534401], [1, 0, 0, 0, -24050685636765349102, 0, 0, 0, 240747534123068430155382383568465195601], [1, 0, 22336237796, 0, 187090319579797101606, 0, 696482311243997143150531583396, 0, 972299657790850297934682879408841327201], [1, 0, 0, 0, 147484825378985652098, 0, 0, 0, 5437943429267472574499737549036572950401]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/6/e/b'], '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': '8-75e4-1.1-c5e4-0-2', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [5, 5, 5, 5], 'order_of_vanishing': 0, 'prelabel': '8-75e4-1.1-c5e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.4682540976655027, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e4-0', 'trace_hash': 374300113739372064, 'z1': {'__RealLiteral__': 0, 'data': '0.46942097395760816159121276717', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '595061779397082028542342231581,1112807536324691135542473562256,1730728846854806256168021709016,3037926928005456211037412096547', 'Lhash_array': ['595061779397082028542342231581', '1112807536324691135542473562256', '1730728846854806256168021709016', '3037926928005456211037412096547'], 'factors': ['2-75-15.8-c5-0-3', '2-75-15.2-c5-0-9', '2-75-15.2-c5-0-17', '2-75-15.8-c5-0-27'], 'label': '8-75e4-1.1-c5e4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/6/e/b'}