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lfunc_lfunctions • Show schema
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{'Lhash': '1030537998682195373936750633708', 'a10': [1.5107062301034488, 1.6485650385491697], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [-1.5817883970812843, -0.7056525114098449], 'a4': [0.0, 1.0], 'a5': [-2.2339421376720936, -0.09748089829826638], 'a6': [0.6195216259991566, 1.6174649779575943], 'a7': [-3.2595379389476746, 3.2595379389476746], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [2.004109066281958, 2.2323859098387224], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.072370503085302, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [1.5817883970812843, 0.7056525114098449]]], [5, [[1.0, 0], [2.2339421376720936, 0.09748089829826638]]], [17, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '510.443', 'coefficient_field': 'CDF', 'conductor': 510, 'conductor_radical': 510, 'conjugate': '779971847420044491548222341587', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [1.5817883970812843, 0.7056525114098449]], [[1.0, 0], [2.2339421376720936, 0.09748089829826638]], [[1.0, 0], [3.2595379389476746, -3.2595379389476746], [0, -7.0]], [[1.0, 0], [0, 3.9026934604303127], [-11.0, 0]], [[1.0, 0], [-2.892325047110851, -2.892325047110851], [0, 13.0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 5.280032625897036], [-19.0, 0]], [[1.0, 0], [-1.0871830869417511, 1.0871830869417511], [0, -23.0]], [[1.0, 0], [1.819418466154102, 0], [29.0, 0]], [[1.0, 0], [-7.470223989444654, 0], [31.0, 0]], [[1.0, 0], [3.8130072957230348, -3.8130072957230348], [0, -37.0]], [[1.0, 0], [0, -3.037822413869034], [-41.0, 0]], [[1.0, 0], [3.6650050867122252, 3.6650050867122252], [0, 43.0]], [[1.0, 0], [-3.797995815868891, -3.797995815868891], [0, 47.0]], [[1.0, 0], [-8.804745713306435, 8.804745713306435], [0, -53.0]], [[1.0, 0], [-8.477400335296094, 0], [59.0, 0]], [[1.0, 0], [-10.11687203595351, 0], [61.0, 0]], [[1.0, 0], [-4.291677907331129, 4.291677907331129], [0, -67.0]], [[1.0, 0], [0, 3.1916011570270797], [-71.0, 0]], [[1.0, 0], [-7.146473436167787, -7.146473436167787], [0, 73.0]], [[1.0, 0], [0, -3.971423410994588], [-79.0, 0]], [[1.0, 0], [-3.628001412034955, 3.628001412034955], [0, -83.0]], [[1.0, 0], [7.983623074784978, 0], [89.0, 0]], [[1.0, 0], [-9.409265304935795, 9.409265304935795], [0, -97.0]], [[1.0, 0], [0, -16.98951982832542], [-101.0, 0]], [[1.0, 0], [2.4691629769199928, 2.4691629769199928], [0, 103.0]], [[1.0, 0], [6.823470609991307, 6.823470609991307], [0, 107.0]], [[1.0, 0], [0, 4.734090465758405], [-109.0, 0]], [[1.0, 0], [8.889512845751149, -8.889512845751149], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-510-15.8-c1-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 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'rational': False, 'root_analytic_conductor': 2.018011522039778, 'root_angle': 0.3236567683391526, 'root_number': '0.5260919467668658 + 0.8504276944849863*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.16182838417', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.812951138505086513704700070289', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.60277955450784797593376067841', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26627134089209604858274498242', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.072370503085302, 'bad_primes': [2, 3, 5, 17], 'central_character': '15.8', 'conductor': 510, 'conductor_radical': 510, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/510/2/l/g/443/2'], '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': '2-510-15.8-c1-0-6', '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': '2-510-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.018011522039778, 'root_angle': 0.1618283841695763, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.812951138505086513704700070289', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1030537998682195373936750633708', 'Lhash_array': ['1030537998682195373936750633708'], 'label': '2-510-15.8-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/510/2/l/g/443/2'}