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lfunc_lfunctions • Show schema
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{'Lhash': '2493683264185896851492136366872', 'a10': [0.19661967140038972, 4.795102322398145e-61], 'a2': [0.09830983570019486, 0.17027763031648613], 'a3': [0.9942156567906841, -1.4182860176255947], 'a4': [0.9806703524092014, -1.6985708758492128], 'a5': [0.5, -0.8660254037844386], 'a6': [0.33924356006194584, 0.0298612206932107], 'a7': [0.5661670001161083, 0.980630009769954], 'a8': [0.7788775076863825, 0.0], 'a9': [-1.0230704555845371, -2.820164329061349], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.8272093728194765, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.9942156567906841, 1.4182860176255947]]], [5, [[1.0, 0], [-0.5, 0.8660254037844386]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '855.571', 'coefficient_field': 'CDF', 'conductor': 855, 'conductor_radical': 285, 'conjugate': '1424899041118253796606545929539', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-5.624814300721935, 9.742464151990397], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 57, 'label': '2-855-9.4-c1-0-57', '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/855/2/i/d/571/13', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.330876752741048, 2.5321069904309157, 2.73282784434781, 2.927922993593597, 3.106811509201803, 3.254472091519207, 3.353147012651127, 3.3844171571641515, 3.3314340738602253, 3.181157920699701, 2.926453187686413, 2.5678606619760473, 2.114828800667321, 1.5861767415739034, 1.009589512111533, 0.420018976238356, -0.14302092836272184, -0.6391291118370861, -1.031364912097789, -1.2908168465495287, -1.4008215744145613, -1.3602038814614035, -1.1849340580726941, -0.9077219734374637, -0.5752877578778675, 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'5.95345714931357345899982297223009', '7.40692227245883256358993810853747', '7.65718354251554748346527724601072', '8.751614318271310938232860323828592', '9.583726471370372201091817093660727', '10.42218574926420551126778073487510'], 'prelabel': '2-855-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.612892912619933, 'root_angle': 0.5003375412110596, 'root_number': '-0.0010604167902114694 + 0.9999994377579574*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.250168770606', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96716923712017411884747484608', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23378675440457427536344627453', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65497657875539818900022440760', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.8272093728194765, 'bad_primes': [3, 5, 19], 'central_character': '9.4', 'conductor': 855, 'conductor_radical': 285, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/855/2/i/d/571/13'], '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': '2-855-9.4-c1-0-57', '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': '2-855-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.612892912619933, 'root_angle': 0.2501687706055298, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96716923712017411884747484608', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2493683264185896851492136366872', 'Lhash_array': ['2493683264185896851492136366872'], 'label': '2-855-9.4-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/855/2/i/d/571/13'}