Formats: - HTML - YAML - JSON - 2026-10-12T16:14:50.992569
  • lfunc_lfunctions • Show schema
    {'Lhash': '87676578220107244387252460350', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.5307337294603591, 0], 'a6': [0, 0], 'a7': [0, 0.585786437626905], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.795065251406015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '4608.2303', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'conjugate': '1270563860319397106552899089164', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5307337294603591, 0], [5.0, 0]], [[1.0, 0], [0, -0.585786437626905], [-7.0, 0]], [[1.0, 0], [0, 5.226251859505506], [-11.0, 0]], [[1.0, 0], [0, 5.226251859505506], [-13.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-17.0, 0]], [[1.0, 0], [3.0614674589207183, 0], [19.0, 0]], [[1.0, 0], [0.8284271247461901, 0], 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-6.585786437626905], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-4608-24.11-c1-0-0', 'leading_term': '0.223022200442800058346096612444299998250143369108103702', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4608/2/f/o/2303/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [0.22302220044280005, 0.07359290720788639, -0.0829444633350756, -0.2458633823818516, -0.41439077334153046, -0.5876722898232674, -0.7647399564631259, -0.9444841898042018, -1.1256319148892748, -1.3067321245169334, -1.4861498318161994, -1.662068976063837, -1.832504479685923, -1.9953233336339997, -2.148274312064522, -2.289025682224821, -2.4152100749057945, -2.5244755071410325, -2.614541395435034, -2.6832582602618134, -2.7286696990343007, -2.7490750958382946, -2.7430914446780403, -2.7097125930573154, 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'4.21389774279863200097987256510758', '4.88060232086837637760179269003030', '5.96115189349710794153641894476173', '6.81969028244980689605400717209896', '7.32576587720803607484447781294427', '7.905174193550910954542991716325414'], 'prelabel': '2-4608-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': -0.3479566380076518, 'root_number': '-0.5773502691896257645091487805019574556476017512701268761 - 0.8164965809277260327324280249019637973219824935522233762*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3479566380076518', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.06916462486139464884913268747', 'prec': 94}, 'z2': {'__RealLiteral__': 0, 'data': '1.73602605631198394780791844237', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.36044586121742563949562274375', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 36.795065251406015, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 4608, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4608/2/f/o/2303/4'], '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': '2-4608-24.11-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-4608-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': -0.3479566380076518, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.06916462486139464884913268747', 'prec': 94}}
  • lfunc_instances • Show schema
    {'Lhash': '87676578220107244387252460350', 'Lhash_array': ['87676578220107244387252460350'], 'factors': ['2-4608-24.11-c1-0-0'], 'label': '2-4608-24.11-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4608/2/f/o/2303/4'}