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lfunc_lfunctions • Show schema
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{'Lhash': '1650668185876661750374657223347', 'a10': [0.0, 0.0], 'a2': [-1.3168617105478098, -2.280871389210867], 'a3': [0.0, 0.0], 'a4': [-2.468249529413807, 4.275133590702686], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.8987136442159585, -1.5566176932374196], 'a8': [7.733926347259531, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.389902136436429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.226', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '803239469669053835458224174505', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.3168617105478098, 2.280871389210867], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8987136442159585, 1.5566176932374196], [-3.5, 6.06217782649107]], [[1.0, 0], [-0.9040619935160362, -1.5658813059617795], 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0.9005056286749294, 'root_number': '-0.9515461833127806 + 0.30750587152586234*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.450252814337', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30214759933018876267573995103', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44947334884715984770508653217', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.09820050069709701411016862365', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.389902136436429, 'bad_primes': [3, 5], 'central_character': '9.4', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/2/e/c/226/1'], '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': '2-675-9.4-c1-0-8', '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': '2-675-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': 0.4502528143374647, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30214759933018876267573995103', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1650668185876661750374657223347', 'Lhash_array': ['1650668185876661750374657223347'], 'label': '2-675-9.4-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/2/e/c/226/1'}