Formats: - HTML - YAML - JSON - 2026-09-11T02:35:15.334987
  • lfunc_lfunctions • Show schema
    {'Lhash': '1088873371455047208795430434436', 'a10': [0.0, 0.0], 'a2': [0.5718181187980719, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.6730240390142341, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.313068769364532, 0.0], 'a8': [-2.100301696289215, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.47545968271595, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 37], 'central_character': '8325.1', 'coefficient_field': 'CDF', 'conductor': 8325, 'conductor_radical': 555, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5718181187980719, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.313068769364532, 0], [7.0, 0]], [[1.0, 0], [-0.7784030893146946, 0], [11.0, 0]], [[1.0, 0], [-3.692140260983219, 0], [13.0, 0]], [[1.0, 0], [-4.201359417952508, 0], [17.0, 0]], [[1.0, 0], [-5.469570213254022, 0], 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0], [-11.337585802120064, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 109, 'label': '2-8325-1.1-c1-0-109', 'leading_term': '2.78200415101981650508813239739', '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/8325/2/a/cx/1/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [2.7820041510198164, 2.7725495226939345, 2.744172539352646, 2.69684107982741, 2.630525025575405, 2.5452296953958857, 2.441039433636103, 2.3181684783731518, 2.1770158475330197, 2.0182208237129715, 1.8427156690014836, 1.65177241939639, 1.4470409485239837, 1.2305759088834418, 1.0048506205781411, 0.7727564576632245, 0.537586766015101, 0.30300482700038517, 0.07299585613230128, -0.1481965045386761, -0.35614827734334037, -0.5463464430806247, -0.7142916122062605, -0.8556098194639259, -0.9661707887923275, -1.0422096558736946, 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'5.50535177002706067536119444661311', '6.18203326165017206677581824420636', '7.22429574533067243147837799161814', '7.966194055133375394470025487265169'], 'prelabel': '2-8325-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.15324841291592, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.858969633477083577638122943354', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.57452852044673620194609452458', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.84638951981782107103663234275', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 66.47545968271595, 'bad_primes': [3, 5, 37], 'central_character': '1.1', 'conductor': 8325, 'conductor_radical': 555, 'degree': 2, 'index': 109, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8325/2/a/cx/1/9'], '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': '2-8325-1.1-c1-0-109', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-8325-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.15324841291592, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.858969633477083577638122943354', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1088873371455047208795430434436', 'Lhash_array': ['1088873371455047208795430434436'], 'factors': ['2-8325-1.1-c1-0-109'], 'label': '2-8325-1.1-c1-0-109', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8325/2/a/cx/1/9'}