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lfunc_lfunctions • Show schema
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{'Lhash': '2440437083543819212840436389896', 'a10': [0.1253367738593787, -0.07236322012707154], 'a2': [0.14723151417312436, 0.03945056532310007], 'a3': [0.0, 0.0], 'a4': [-1.7119300359074785, -0.9883832670649885], 'a5': [0.671391566869243, -0.671391566869243], 'a6': [0.0, 0.0], 'a7': [0.3834983549481273, 1.4312353452854945], 'a8': [-0.4286196704035514, -0.4286196704035514], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8027491109469427, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0.563386559872526, 3.561263200629097]]]], 'bad_primes': [3, 13], 'central_character': '351.323', 'coefficient_field': 'CDF', 'conductor': 351, 'conductor_radical': 39, 'conjugate': '1050112028867782615407366299598', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.14723151417312436, -0.03945056532310007], [1.7320508075688772, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.671391566869243, 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[56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-351-39.11-c1-0-12', '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/351/2/bd/e/323/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.136647654387391, 1.258839681582355, 1.381474710266359, 1.5038128334181238, 1.6219050058638336, 1.7289414247147372, 1.815866760542256, 1.8721415423444243, 1.8865912559994706, 1.8483282770224112, 1.7477409232354597, 1.5775276587709464, 1.333727010820637, 1.0166658496731773, 0.6317270020601666, 0.18982586529815684, -0.2925124265026712, -0.7935668318288546, -1.2873841772867534, -1.745304391837808, -2.1379991798586695, -2.43790930559027, -2.621898381277291, -2.6738816650038135, -2.587146052167042, -2.3660610931253765, -2.0268978468823553, 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'9.794213392634675771061677316099712', '10.59452454135947790143431278011777', '11.97657128824486910828645159562500'], 'prelabel': '2-351-39.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6741413055494876, 'root_angle': 0.43776659540591, 'root_number': '0.19426881250331537 + 0.980948331202287*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.218883297703', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92516540685930323722544721102', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.80766849935747611306102626558', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42082147972383250278610821701', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8027491109469427, 'bad_primes': [3, 13], 'central_character': '39.11', 'conductor': 351, 'conductor_radical': 39, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/351/2/bd/e/323/3'], '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': '2-351-39.11-c1-0-12', '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': '2-351-39.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6741413055494876, 'root_angle': 0.218883297702955, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92516540685930323722544721102', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2440437083543819212840436389896', 'Lhash_array': ['2440437083543819212840436389896'], 'label': '2-351-39.11-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/351/2/bd/e/323/3'}