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  • lfunc_lfunctions • Show schema
    {'Lhash': '1643927763584399236901988321839', 'a10': [0, 0], 'a2': [0, -2.641922871994017], 'a3': [0, 6.665343643170264], 'a4': [25.020243538434887, 0], 'a5': [0, 0], 'a6': [17.60932382059145, 0], 'a7': [0, 12.880167212877463], 'a8': [0, -150.64308557086017], 'a9': [198.57319411844975, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.10555044856968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [121.0, 0]]]], 'bad_primes': [5, 11], 'central_character': '275.199', 'coefficient_field': 'CDF', 'conductor': 275, 'conductor_radical': 55, 'conjugate': '974060561029353244925997690282', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.641922871994017], [-32.0, 0]], [[1.0, 0], [0, -6.665343643170264], [-243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -12.880167212877463], [-16807.0, 0]], [[1.0, 0], [121.0, 0]], [[1.0, 0], [0, 485.166703868196], [-371293.0, 0]], [[1.0, 0], [0, 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-0.7877724464572041, -0.24705771716509337, 0.35306763512673817], 'positive_zeros': ['1.29683034369914266890006526858282', '2.36109517289819793345399183755683', '3.93986942825683408782698337177988', '5.37760830299972027698839881883686', '6.45015087866668184470010792293551', '7.27027121300514872909793266185063', '7.922438866456434540363608900545456', '9.253963619401727689833901485734607', '10.32650941680355138577753020415523', '11.30279682461492255176931714029512'], 'prelabel': '2-275-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.641200979383901, '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': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29683034369914266890006526858', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.36109517289819793345399183756', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.93986942825683408782698337178', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 44.10555044856968, 'bad_primes': [5, 11], 'central_character': '5.4', 'conductor': 275, 'conductor_radical': 55, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/275/6/b/d/199/4'], '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': '2-275-5.4-c5-0-53', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-275-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.641200979383901, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29683034369914266890006526858', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1643927763584399236901988321839', 'Lhash_array': ['1643927763584399236901988321839'], 'factors': ['2-275-5.4-c5-0-53'], 'label': '2-275-5.4-c5-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/275/6/b/d/199/4'}