Formats: - HTML - YAML - JSON - 2026-08-15T01:59:53.101769
  • lfunc_lfunctions • Show schema
    {'Lhash': '1746959287744145937027372633520', 'a10': [0, 0], 'a2': [2.0, 2.0], 'a3': [0, 0], 'a4': [0, 8.0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [19.0, 19.0], 'a8': [-16.0, 16.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.51648338772996, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, -2.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '450.307', 'coefficient_field': 'CDF', 'conductor': 450, 'conductor_radical': 30, 'conjugate': '326313283472238434229601649799', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, -2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-19.0, -19.0], [0, 2401.0]], [[1.0, 0], [202.0, 0], [14641.0, 0]], [[1.0, 0], [-99.0, 99.0], [0, -28561.0]], [[1.0, 0], [239.0, 239.0], [0, 83521.0]], [[1.0, 0], [0, -40.0], [-130321.0, 0]], [[1.0, 0], [-541.0, 541.0], [0, -279841.0]], [[1.0, 0], [0, -200.0], 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'10.01396631993002159022651932297195', '10.96999253601733227639599294480401'], 'prelabel': '2-450-5.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8202993620316965, 'root_angle': 0.21310409558739168, 'root_number': '0.2297529205473611835239373693814627187159909372855097265 + 0.9732489894677301637880577483081525807410411271519101104*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21310409558739168', 'prec': 57}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37810788511410099850060729833', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.57544236264127434810592184589', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.80570161603564770186637160346', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 46.51648338772996, 'bad_primes': [2, 3, 5], 'central_character': '5.2', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/5/g/b/307/1'], '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': '2-450-5.2-c4-0-26', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-450-5.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8202993620316965, 'root_angle': 0.21310409558739168, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37810788511410099850060729833', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1746959287744145937027372633520', 'Lhash_array': ['1746959287744145937027372633520'], 'factors': ['2-450-5.2-c4-0-26'], 'label': '2-450-5.2-c4-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/5/g/b/307/1'}