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lfunc_lfunctions • Show schema
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{'Lhash': '1612282470321395136042246210189', 'a10': [7.126126397028421e-61, -5.464101615137754], 'a2': [-1.3660254037844386, -0.36602540378443865], 'a3': [-0.8660254037844386, -1.5], 'a4': [1.7320508075688772, 1.0], 'a5': [1.0, 3.732050807568877], 'a6': [0.6339745962155614, 2.366025403784439], 'a7': [0.6339745962155614, -0.36602540378443865], 'a8': [-2.0, -2.0], 'a9': [-1.5, 2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.149845789106438, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3660254037844386, 0.36602540378443865]]], [3, [[1.0, 0], [0.8660254037844386, 1.5]]]], 'bad_primes': [2, 3], 'central_character': '144.13', 'coefficient_field': 'CDF', 'conductor': 144, 'conductor_radical': 6, 'conjugate': '2213022673763867857914327347620', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3660254037844386, 0.36602540378443865]], [[1.0, 0], [0.8660254037844386, 1.5]], [[1.0, 0], [-1.0, 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'11.05200634195610041229649991239009', '11.68774020176796013091594321488673', '12.94690318904039083142615001477110'], 'prelabel': '2-12e2-144.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.072308625865911, 'root_angle': -0.013888888888888888, 'root_number': '0.9990482215818578 - 0.043619387365336*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00694444444444', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27186660900970486748029768107', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.17803090641290544437846190947', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.54086619136761879072610801135', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.149845789106438, 'bad_primes': [2, 3], 'central_character': '144.13', 'conductor': 144, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/144/2/x/c/13/1'], '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': '2-12e2-144.13-c1-0-3', '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': '2-12e2-144.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.072308625865911, 'root_angle': -0.006944444444444444, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27186660900970486748029768107', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1612282470321395136042246210189', 'Lhash_array': ['1612282470321395136042246210189'], 'label': '2-12e2-144.13-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/144/2/x/c/13/1'}