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lfunc_lfunctions • Show schema
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{'Lhash': '749529148787592804632910414570', 'a10': [1.374409137263511, -0.3331659097305293], 'a2': [-1.0236902731983895, 0.975734710133347], 'a3': [-0.9929265869450131, 0.5732664322582397], 'a4': [0.09588355088198663, -1.9977002639711148], 'a5': [-0.8660254037844386, -0.5], 'a6': [0.45709333294701343, -1.5556802061503894], 'a7': [2.644184886199814, -0.09102904806969811], 'a8': [1.8510704296015539, 2.1385832377194767], 'a9': [-0.8427311952918182, 1.459653247368679], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.2358112565958517, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0236902731983895, -0.975734710133347]]], [5, [[1.0, 0], [0.8660254037844386, 0.5]]], [7, [[1.0, 0], [-2.644184886199814, 0.09102904806969811]]]], 'bad_primes': [2, 5, 7], 'central_character': '280.261', 'coefficient_field': 'CDF', 'conductor': 280, 'conductor_radical': 70, 'conjugate': '2280713931137136429486477907737', 'degree': 2, 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[7.612184319487936, -4.394896665977408], [54.5, -94.39676901250381]], [[1.0, 0], [5.11334612516368, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-280-56.37-c1-0-5', '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': 'ModularForm/GL2/Q/holomorphic/280/2/bl/b/261/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5683295513763731, 0.4605886316720582, 0.34940275437048046, 0.23101026383836992, 0.10208596568218897, -0.03951002138896583, -0.19417822958290593, -0.36022136762540735, -0.5336580436985924, -0.7081944683942419, -0.8753592504762914, -1.0248198218192666, -1.144900804259018, -1.2233150222940585, -1.2480992347337254, -1.2087217925363465, -1.0973012343316002, -0.9098464595800518, -0.6474040756794103, -0.31698057423151454, 0.06790007009446393, 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'5.41094809171192787130496060565537', '6.75009628425993135810950935662793', '7.963190730090135907865252470837076', '8.400458160352815227854765765704531', '9.824894099896418180682493490349015', '10.76897488101710600898175599212572', '11.39450795515661701090680590730419'], 'prelabel': '2-280-56.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4952629389494851, 'root_angle': -0.758227514691283, 'root_number': '-0.7251454949799361 - 0.6885956804325043*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.379113757346', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59127424280211490301646791085', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47893359912998706754088448377', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93707990248823545682205783644', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.2358112565958517, 'bad_primes': [2, 5, 7], 'central_character': '56.37', 'conductor': 280, 'conductor_radical': 70, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/280/2/bl/b/261/7'], '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': '2-280-56.37-c1-0-5', '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': '2-280-56.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4952629389494851, 'root_angle': -0.3791137573456415, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59127424280211490301646791085', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '749529148787592804632910414570', 'Lhash_array': ['749529148787592804632910414570'], 'label': '2-280-56.37-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/280/2/bl/b/261/7'}