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lfunc_lfunctions • Show schema
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{'Lhash': '1324525712189807926968289340537', 'a10': [0.0, 0.0], 'a2': [-4.0, 0.0], 'a3': [-19.30029761641144, 0.0], 'a4': [16.0, 0.0], 'a5': [0.0, 0.0], 'a6': [77.20119046564577, 0.0], 'a7': [-49.0, 0.0], 'a8': [-64.0, 0.0], 'a9': [129.50148808205722, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.134336934543235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [49.0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '350.1', 'coefficient_field': 'CDF', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.0, 0]], [[1.0, 0], [19.30029761641144, 0], [243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [49.0, 0]], [[1.0, 0], [10.903869013348753, 0], [161051.0, 0]], [[1.0, 0], [29.696726219474133, 0], [371293.0, 0]], [[1.0, 0], [-432.51934506674377, 0], [1419857.0, 0]], [[1.0, 0], [956.2339282709045, 0], [2476099.0, 0]], [[1.0, 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'4.26467838631811684402604213289922', '5.58787527741936466887580722341819', '6.28773082868192240715837114684674', '7.23563766348301664090699992769020', '8.355236588551091043266516771623550', '9.411075551449307212161340356311005', '10.38868304814197244864684583031586'], 'prelabel': '2-350-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.492285161053551, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04486655230655723200970365918', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64812041274584959464628672297', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26467838631811684402604213290', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.134336934543235, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/350/6/a/p/1/1'], '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': '2-350-1.1-c5-0-21', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-350-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.492285161053551, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04486655230655723200970365918', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1324525712189807926968289340537', 'Lhash_array': ['1324525712189807926968289340537'], 'factors': ['2-350-1.1-c5-0-21'], 'label': '2-350-1.1-c5-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/350/6/a/p/1/1'}