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lfunc_lfunctions • Show schema
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{'Lhash': '2698816407002466715579525067002', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.123440174278894, -2.712224505258899], 'a6': [0, 0], 'a7': [-3.031502686810599, -3.031502686810599], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.1007', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '303663147660521810719398300054', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.123440174278894, 2.712224505258899], [-3.5355339059327378, 3.5355339059327378]], [[1.0, 0], [3.031502686810599, 3.031502686810599], [0, 7.0]], [[1.0, 0], [0.6168468814919061, 1.4892001072053092], [-7.7781745930520225, 7.7781745930520225]], [[1.0, 0], [-3.3513254765752944, 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'leading_term': '0.5426188731888521921613303997336233609817184202380391854', '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/1152/2/w/b/1007/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.5426188731888522, 0.6936321049759203, 0.8488965296992846, 1.0085274191508915, 1.1724720986369666, 1.340437440331322, 1.5118312879751479, 1.6857203187856142, 1.860805468388978, 2.035414939550585, 2.2075140723427915, 2.37473094916865, 2.534396451513805, 2.68359746325977, 2.819241927112915, 2.9381344352213383, 3.0370609344355226, 3.1128809410158134, 3.1626253990195923, 3.18359800353663, 3.1734774730976523, 3.130417925862252, 3.053144222123707, 2.9410389098539866, 2.7942172761669153, 2.613586987823041, 2.4008889161477067, 2.158715999072602, 1.8905074030876323, 1.6005158123137295, 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'8.643156806713661948298445371348607', '9.512814183022408099901516656049722', '10.17951202658702656022853882212073'], 'prelabel': '2-1152-96.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.9356692602124123, 'root_number': '-0.97964701489126263393360681359327385539928711193189333425 - 0.20072799061077218674620882438361761161680679605683099760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.46783463010620613', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.12899075385328451707085135930', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26690337079042026861182885081', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67086843590937665434297882500', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '96.83', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/w/b/1007/2'], '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': '2-1152-96.83-c1-0-14', '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': '2-1152-96.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.46783463010620613, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.12899075385328451707085135930', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2698816407002466715579525067002', 'Lhash_array': ['2698816407002466715579525067002'], 'label': '2-1152-96.83-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/w/b/1007/2'}