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  • lfunc_lfunctions • Show schema
    {'Lhash': '654784966860424810532369224849', 'a10': [0, 0], 'a2': [0, -2.8284271247461903], 'a3': [0, 0], 'a4': [-8.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-83.0, 0], 'a8': [0, 22.627416997969522], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.51648338772996, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 2.8284271247461903]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '450.251', 'coefficient_field': 'CDF', 'conductor': 450, 'conductor_radical': 30, 'conjugate': '781933276557768405012372252726', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.8284271247461903]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [83.0, 0], [2401.0, 0]], [[1.0, 0], [0, 80.61017305526642], [-14641.0, 0]], [[1.0, 0], [41.0, 0], [28561.0, 0]], [[1.0, 0], [0, -513.3595231414336], [-83521.0, 0]], [[1.0, 0], [139.0, 0], [130321.0, 0]], [[1.0, 0], [0, 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[141158161.0, 0]], [[1.0, 0], [0, 20466.49867466343], [-163047361.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-450-3.2-c4-0-8', 'leading_term': '1.076426725259420975770168258740462450757096500578730970', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/450/5/d/a/251/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.076426725259421, 1.0506916912673987, 0.9953770558402291, 0.9103733009617035, 0.7959426273031932, 0.6527259626217952, 0.48174798719069195, 0.2844197904619447, 0.0625386811058126, -0.1817154015891542, -0.44578747863676427, -0.7267597535362337, -1.0213690904099915, -1.3260303368300743, -1.636866011175103, -1.9497427723351881, -2.2603149552778907, -2.5640752913199, -2.8564127398857235, -3.1326771430743108, -3.3882501804806626, 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'4.95935506548344604362020961434674', '5.99295224600861205571582951397871', '6.97709441275613173985812448423260', '7.44434584397889287308884776917310', '8.964516087520742296047036227631296', '9.515893346906762112575587115334965', '10.21785883527478271901452652080605'], 'prelabel': '2-450-3.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8202993620316965, 'root_angle': 0.09795663800765181, 'root_number': '0.8164965809277260327324280249019637973219824935522233762 + 0.5773502691896257645091487805019574556476017512701268761*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09795663800765182', 'prec': 64}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51653426168262493240329966393', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59181272150738633398951179649', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71982074317332032159628536422', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 46.51648338772996, 'bad_primes': [2, 3, 5], 'central_character': '3.2', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/5/d/a/251/1'], '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': '2-450-3.2-c4-0-8', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-450-3.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.8202993620316965, 'root_angle': 0.09795663800765181, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51653426168262493240329966393', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '654784966860424810532369224849', 'Lhash_array': ['654784966860424810532369224849'], 'factors': ['2-450-3.2-c4-0-8'], 'label': '2-450-3.2-c4-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/5/d/a/251/1'}