Formats: - HTML - YAML - JSON - 2026-09-07T15:32:50.374853
  • lfunc_lfunctions • Show schema
    {'Lhash': '1492533306685050617429454832866', 'a10': [2.587992468425066, -0.1031200141875692], 'a2': [-1.1583038249052717, 0.0], 'a3': [0.15047324954909191, 1.7255021881093449], 'a4': [-0.6583322492098175, 0.0], 'a5': [-2.2342950206839878, 0.08902674062740193], 'a6': [-0.17429374049863863, -1.99865578436947], 'a7': [-0.1899941311199394, -0.10969316274654607], 'a8': [3.0791564121287656, 0.0], 'a9': [-2.9547156023402734, 0.5192838426977632], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.7130436939895395, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [-0.15047324954909191, -1.7255021881093449]]], [5, [[1.0, 0], [2.2342950206839878, -0.08902674062740193]]], [31, [[1.0, 0], [-5.530552837511598, -0.6426393323571274]]]], 'bad_primes': [3, 5, 31], 'central_character': '465.119', 'coefficient_field': 'CDF', 'conductor': 465, 'conductor_radical': 465, 'conjugate': '536393922005280485259175030201', 'degree': 2, 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[109.0, 0]], [[1.0, 0], [-8.344344242602254, -14.452828184031945], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-465-465.119-c1-0-25', '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/465/2/t/d/119/15', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.43465273959260203, 0.510163976546527, 0.5661743410494529, 0.6012957250585306, 0.611718409191628, 0.5918990799297404, 0.53552725445479, 0.43663016654531767, 0.29072142649793337, 0.0959263194019013, -0.14598368282286228, -0.42873191514685677, -0.7409572300642231, -1.0660290926333482, -1.3823663274568194, -1.6643440944198045, -1.8838289309539056, -2.012318711564884, -2.023587645456779, -1.8966532334813442, -1.6188022195977205, -1.1883475873887595, -0.6167507799860793, 0.07025619739861202, 0.8328668818905696, 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'8.103974789234819993544184762512918', '9.241046041416487452332046070658173', '10.17265688850855217824902041139060', '11.06229248313102966349503322787942'], 'prelabel': '2-465-465.119-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9269259700334986, 'root_angle': 0.12054650807234181, 'root_number': '0.7266137286700298 + 0.6870462060940562*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.120546508072', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17740117538407906078380871358', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.86294985617475270369117813819', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.38754059869340980357745106222', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.7130436939895395, 'bad_primes': [3, 5, 31], 'central_character': '465.119', 'conductor': 465, 'conductor_radical': 465, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/465/2/t/d/119/15'], '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': '2-465-465.119-c1-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-465-465.119-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9269259700334986, 'root_angle': 0.12054650807234181, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17740117538407906078380871358', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1492533306685050617429454832866', 'Lhash_array': ['1492533306685050617429454832866'], 'factors': ['2-465-465.119-c1-0-25'], 'label': '2-465-465.119-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/465/2/t/d/119/15'}