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lfunc_lfunctions • Show schema
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{'Lhash': '3174033294188126746598496187718', 'a10': [2.622385737870664, -1.7472073017910734], 'a2': [1.3784345511540061, 0.29299530868045576], 'a3': [1.6345628771948373, -0.5728910895593813], 'a4': [-0.012855354378810909, -0.0057235725292533145], 'a5': [1.5624249553941556, -1.5996337889534502], 'a6': [2.4209923475848, -0.31077361713560003], 'a7': [-2.486518000131135, 4.306775510161682], 'a8': [-2.296224673892545, -1.668304879438175], 'a9': [2.34359159900693, -1.8728530153389351], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.6345628771948373, 0.5728910895593813]]], [5, [[1.0, 0], [-1.5624249553941556, 1.5996337889534502]]]], 'bad_primes': [3, 5], 'central_character': '225.106', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '2762996011952850377490173223178', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0], [8.797119282199855, -3.916729852516215], [55.53784032778523, -61.68102051462372]], [[1.0, 0], [-0.845142299264562, -2.6010805410169837], [-72.00251249937033, 52.31288745403011]], [[1.0, 0], [-1.0272454981855392, -9.773588053696665], [-94.88031727117915, 20.167434009322655]], [[1.0, 0], [3.7698710228825165, -6.529608149614172], [-50.5, -87.4685657822283]], [[1.0, 0], [-0.2823021277329331, -0.12568900519033624], [68.9204524549624, 76.5439170241716]], [[1.0, 0], [-10.609181974307722, 0], [107.0, 0]], [[1.0, 0], [-2.7254580954009273, 8.388097511476454], [-88.18285238686927, -64.06859249987957]], [[1.0, 0], [-8.587467917729747, 1.8253226540442593], [103.2306367136139, -45.96124066756542]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 22, 'label': '2-15e2-225.106-c1-0-22', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 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'0.989216290600288 + 0.14646204426747014*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0233943114168', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.50387077765487573436184945049', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.76457528462634113470042137279', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26245835247463382675933003873', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '225.106', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/q/a/106/20'], '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': '2-15e2-225.106-c1-0-22', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-15e2-225.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.023394311416819073, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.50387077765487573436184945049', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3174033294188126746598496187718', 'Lhash_array': ['3174033294188126746598496187718'], 'label': '2-15e2-225.106-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/q/a/106/20'}