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lfunc_lfunctions • Show schema
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{'Lhash': '1584030456831339759889926430866', 'a10': [-1.0957347321569986, 1.8978682277137968], 'a2': [-0.8660254037844386, -0.5], 'a3': [0, 0], 'a4': [0.5, 0.8660254037844386], 'a5': [0, -2.191469464313997], 'a6': [0, 0], 'a7': [0.8660254037844386, -0.5], 'a8': [0, -1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.079495851085733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.8660254037844386, 0.5]]], [13, [[1.0, 0], [-3.5355715214637495, -0.7069186775114281]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '1638.1135', 'coefficient_field': 'CDF', 'conductor': 1638, 'conductor_radical': 546, 'conjugate': '875273056847322206022448395935', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.191469464313997], [-5.0, 0]], [[1.0, 0], [-0.8660254037844386, 0.5]], 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'1.262193076142605106985976627206567658214915835096224768', '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/1638/2/bj/h/1135/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.262193076142605, 1.3383067428363264, 1.4081892985647255, 1.4712296319401534, 1.5266041857518386, 1.5732722521667106, 1.6099882202236007, 1.6353297853818938, 1.647740293416362, 1.645582877940842, 1.627203825796047, 1.5910025855489924, 1.5355059277998178, 1.4594438922033612, 1.3618252624277094, 1.2420103728766103, 1.09977906976096, 0.9353916396921531, 0.749640505278374, 0.5438904954325126, 0.32010555281128006, 0.08085986263732835, -0.17066840832073113, -0.4307222765717878, -0.6950111300449038, -0.9587765685273898, -1.216878945203613, -1.4639039999284436, -1.6942882552255822, 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'7.904955142515421507871672871516825', '8.689881531342553825310705619964625', '9.781317412627081726174908603863005'], 'prelabel': '2-1638-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6165585645867444, 'root_angle': 0.558734120213177, 'root_number': '-0.1834734059297918332537728456698794618633738793079588614 + 0.9830246738086088482669829240062965730536577546328519418*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2793670601065885', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24957970007362354644070963289', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64710374567470565514554430844', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37852648310366344705700059731', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.079495851085733, 'bad_primes': [2, 3, 7, 13], 'central_character': '13.4', 'conductor': 1638, 'conductor_radical': 546, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1638/2/bj/h/1135/1'], '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': '2-1638-13.4-c1-0-25', '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': '2-1638-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6165585645867444, 'root_angle': 0.2793670601065885, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24957970007362354644070963289', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1584030456831339759889926430866', 'Lhash_array': ['1584030456831339759889926430866'], 'label': '2-1638-13.4-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1638/2/bj/h/1135/1'}