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  • lfunc_lfunctions • Show schema
    {'Lhash': '1864865982248888873833020805101', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.0, 1.0], 'a4': [0, 0], 'a5': [15.0, -20.0], 'a6': [0, 0], 'a7': [19.0, -19.0], 'a8': [0, 0], 'a9': [0, -79.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.078388186830196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-15.0, 20.0]]]], 'bad_primes': [2, 5], 'central_character': '320.193', 'coefficient_field': 'CDF', 'conductor': 320, 'conductor_radical': 10, 'conjugate': '1057424628060213363890053156773', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, -1.0], [0, 81.0]], [[1.0, 0], [-15.0, 20.0]], [[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], [-707281.0, 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'11.27391601029339718807031535637193'], 'prelabel': '2-320-5.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.751381415523595, 'root_angle': 0.19052047793695842, 'root_number': '0.3650819794101517821298309467416828934210223636658484366 + 0.9309753747065308441294595661161079291726391880535635544*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.19052047793695842', 'prec': 57}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47111986687272980984409109576', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.55746946151074549255495552373', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.93521824054533975124336756754', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 33.078388186830196, 'bad_primes': [2, 5], 'central_character': '5.3', 'conductor': 320, 'conductor_radical': 10, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/320/5/p/g/193/1'], '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': '2-320-5.3-c4-0-31', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-320-5.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.751381415523595, 'root_angle': 0.19052047793695842, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47111986687272980984409109576', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1864865982248888873833020805101', 'Lhash_array': ['1864865982248888873833020805101'], 'factors': ['2-320-5.3-c4-0-31'], 'label': '2-320-5.3-c4-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/320/5/p/g/193/1'}