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lfunc_lfunctions • Show schema
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{'Lhash': '701883333015615075274498568060', 'a10': [6.006613101926062, -3.731031900663699], 'a2': [0.36602540378443865, 1.3660254037844386], 'a3': [0.0, 0.0], 'a4': [-1.7320508075688772, 1.0], 'a5': [-1.449055686313682, -4.78541927295425], 'a6': [0.0, 0.0], 'a7': [1.6126701951164808, 6.0185671040267215], 'a8': [-2.0, -2.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.3569671377280175, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.36602540378443865, -1.3660254037844386]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.449055686313682, 4.78541927295425]]]], 'bad_primes': [2, 3, 5], 'central_character': '270.73', 'coefficient_field': 'CDF', 'conductor': 270, 'conductor_radical': 30, 'conjugate': '2470684897964510387619241586870', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.36602540378443865, -1.3660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.449055686313682, 4.78541927295425]], [[1.0, 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'6.23926068056757842523793235301515', '7.58058769544714976393541803739237', '8.269590628655325899073361737243109', '9.867278829720148609462592136877958', '10.74665700473149163727435393732136', '10.91478541607051162053823335176868'], 'prelabel': '2-270-45.43-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.712372971721997, 'root_angle': -0.38431834091046735, 'root_number': '-0.7472718059247272 - 0.6645185084480317*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.38431834091', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55368832144223899003086666249', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72954624807512661199148186853', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58256881649687878036469093883', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.3569671377280175, 'bad_primes': [2, 3, 5], 'central_character': '45.43', 'conductor': 270, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/270/3/l/a/73/3'], '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': '2-270-45.43-c2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-270-45.43-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.712372971721997, 'root_angle': -0.38431834091046735, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55368832144223899003086666249', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '701883333015615075274498568060', 'Lhash_array': ['701883333015615075274498568060'], 'factors': ['2-270-45.43-c2-0-2'], 'label': '2-270-45.43-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/270/3/l/a/73/3'}