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lfunc_lfunctions • Show schema
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{'Lhash': '2424102512515320338703943472638', 'a10': [-10.103814834775646, 5.833440214699853], 'a2': [-1.7320508075688772, -1.0], 'a3': [0, 0], 'a4': [2.0, 3.4641016151377544], 'a5': [2.9167201073499265, -5.051907417387823], 'a6': [0, 0], 'a7': [-2.668510781608583, -18.327003306826754], 'a8': [0, -8.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.302721982169963, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.7320508075688772, 1.0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.668510781608583, 18.327003306826754]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.215', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '157281786485817669965732315189', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7320508075688772, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.9167201073499265, 5.051907417387823], [-62.5, -108.25317547305482]], [[1.0, 0], [2.668510781608583, 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'8.640264069170264911843335105748166', '9.702778463217390855613345987411035', '10.24161916363805316710851910075961', '11.57084651827039672906506682976010'], 'prelabel': '2-378-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.722575778340667, 'root_angle': -0.8390116344851914, 'root_number': '-0.87480659277493841057736340201328282012401703953783733134 - 0.4844723162756599402774977105363687864571934026121975140*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4195058172425957', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91227970237136470154901766268', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.03201386326309063762743375210', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83890693444946822708871502186', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.302721982169963, 'bad_primes': [2, 3, 7], 'central_character': '21.5', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/4/k/a/215/2'], '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': '2-378-21.5-c3-0-30', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-378-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.722575778340667, 'root_angle': -0.4195058172425957, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91227970237136470154901766268', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2424102512515320338703943472638', 'Lhash_array': ['2424102512515320338703943472638'], 'label': '2-378-21.5-c3-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/4/k/a/215/2'}