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lfunc_lfunctions • Show schema
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{'Lhash': '1451372809347135491279805271829', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.541196100146197, -0.541196100146197], 'a4': [0.0, 1.0], 'a5': [-0.9238795325112867, -0.3826834323650898], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, -0.41421356237309503], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3449802090459415, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.9238795325112867, 0.3826834323650898]]], [7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 7, 11], 'central_character': '2695.1077', 'coefficient_field': 'CDF', 'conductor': 2695, 'conductor_radical': 385, 'conjugate': '825856171572765128289723183651', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0.541196100146197, 0.541196100146197], [0, 1.0]], [[1.0, 0], [0.9238795325112867, 0.3826834323650898]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, 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'6.02541173257438844321099711560960', '6.79491145926447764683391492565887', '7.47058828481620615165567331588965', '8.545017068767187893133630167509380', '9.160644570047581590475061664389514'], 'prelabel': '2-2695-385.307-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.159732817956766, 'root_angle': 0.3146325045297363, 'root_number': '0.54998740909119195361389699404130 + 0.83517294606635688508507434525203*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.15731625226486814', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14493126819474428772790972595', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51204201488154730844977811619', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79709261951104349019791321619', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3449802090459415, 'bad_primes': [5, 7, 11], 'central_character': '385.307', 'conductor': 2695, 'conductor_radical': 385, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2695/1/l/b/1077/2'], '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': '2-2695-385.307-c0-0-5', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2695-385.307-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.159732817956766, 'root_angle': 0.15731625226486814, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14493126819474428772790972595', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1451372809347135491279805271829', 'Lhash_array': ['1451372809347135491279805271829'], 'label': '2-2695-385.307-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2695/1/l/b/1077/2'}