Formats: - HTML - YAML - JSON - 2026-10-15T21:17:30.799002
  • lfunc_lfunctions • Show schema
    {'Lhash': '1545482321096160259169002117147', 'a10': [0, 0], 'a2': [0, 8.0], 'a3': [0, 0], 'a4': [-64.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -1174.0], 'a8': [0, -512.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 140.57326146785485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, -8.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '450.199', 'coefficient_field': 'CDF', 'conductor': 450, 'conductor_radical': 30, 'conjugate': '672312135537313958616998033212', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -8.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1174.0], [-823543.0, 0]], [[1.0, 0], [-7563.0, 0], [19487171.0, 0]], [[1.0, 0], [0, 5372.0], [-62748517.0, 0]], [[1.0, 0], [0, 24021.0], [-410338673.0, 0]], [[1.0, 0], [-51235.0, 0], [893871739.0, 0]], [[1.0, 0], [0, 57618.0], [-3404825447.0, 0]], [[1.0, 0], [-47040.0, 0], 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0], [0, -20783607.0], [-235260548044817.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 45, 'label': '2-450-5.4-c7-0-45', 'leading_term': '2.308117870055721558542743835690207232495041598451246430', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/450/8/c/q/199/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [2.3081178700557214, 2.489821535502736, 2.6393032738817417, 2.7535934162060385, 2.830505250698637, 2.8686704422123444, 2.8675584420791083, 2.8274795653792344, 2.74957168061528, 2.6357707289782657, 2.488765563938003, 2.3119378736662286, 2.109288215437887, 1.8853494490046323, 1.6450891010798854, 1.3938024213573283, 1.1369980975463627, 0.8802787782558888, 0.6292187036492433, 0.3892408601398415, 0.16549615268624351, -0.037252877524264656, -0.21474127458520212, -0.3633013750562444, 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'6.18286103332631702848611466222788', '7.39465321681355895676386792605971', '8.723000558343305132376587159243808', '9.187059666983558371329088601495338', '9.923374914748787078762963026551540'], 'prelabel': '2-450-5.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.856359536883776, 'root_angle': 0.17620819117478337, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17620819117478337', 'prec': 57}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21917058282298741209046473426', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.93555770967744663444818122795', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.25826170708675744754859853191', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 140.57326146785485, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'index': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/8/c/q/199/2'], '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': '2-450-5.4-c7-0-45', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-450-5.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.856359536883776, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21917058282298741209046473426', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1545482321096160259169002117147', 'Lhash_array': ['1545482321096160259169002117147'], 'factors': ['2-450-5.4-c7-0-45'], 'label': '2-450-5.4-c7-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/8/c/q/199/2'}