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lfunc_lfunctions • Show schema
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{'Lhash': '1084887399289802637896538976633,1154157908690534271645458371644', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 477.2944672800165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, 8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -5, 0, 25], [1, 0, -11, 0, 49], [1, 0, -22, 0, 121], [1, -9, 40, -117, 169], [1, 0, -17, 0, 289], [1, 8, 19], [1, 0, 23, 0, 529], [1, 0, 29, 0, 841], [1, -14, 111, -434, 961], [1, 0, -47, 0, 1369], [1, 0, 41, 0, 1681], [1, -3, 46, -129, 1849], [1, 0, 47, 0, 2209], [1, 0, 53, 0, 2809], [1, 0, -59, 0, 3481], [1, 1, -60, 61, 3721], [1, -11, 54, -737, 4489], [1, 0, -71, 0, 5041], [1, -17, 216, -1241, 5329], [1, 17, 210, 1343, 6241], [1, 0, -166, 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['0.855825255866622988987925164972721', '0.910470052617604753593672075840570', '1.98287532879091870427986315871272', '2.20334430234549329988242126215881', '3.13815437477491998902486821029668', '3.19214276063401651569658488838466', '4.03817414099960516379896148426284', '4.12763693954251826797621201516733', '4.65295640390820777370049660403332', '5.03376896420342561840532107718423', '5.83454040499677930876511298497051', '5.93118469062646253544049786025522', '6.43428391563242308233867846327009', '6.48565859301277859419015297690745', '7.18380769215877349521827336957647', '7.35411392181660839900008508373606', '8.295281912548680510010605338663840', '8.306474864771470966562884629387858', '8.551437021430137707522251499780255', '8.719140888055867441608011788355647'], 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1404790978718803488, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.855825255866622988987925164973', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.910470052617604753593672075841', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.98287532879091870427986315871', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 477.2944672800165, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, -9, 40, -117, 169], 'euler17': [1, 0, -17, 0, 289], 'euler19': [1, 8, 19, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 23, 0, 529], 'euler29': [1, 0, 29, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -14, 111, -434, 961], 'euler37': [1, 0, -47, 0, 1369], 'euler41': [1, 0, 41, 0, 1681], 'euler43': [1, -3, 46, -129, 1849], 'euler47': [1, 0, 47, 0, 2209], 'euler5': [1, 0, -5, 0, 25], 'euler53': [1, 0, 53, 0, 2809], 'euler59': [1, 0, -59, 0, 3481], 'euler61': [1, 1, -60, 61, 3721], 'euler67': [1, -11, 54, -737, 4489], 'euler7': [1, 0, -11, 0, 49], 'euler71': [1, 0, -71, 0, 5041], 'euler73': [1, -17, 216, -1241, 5329], 'euler79': [1, 17, 210, 1343, 6241], 'euler83': [1, 0, -166, 0, 6889], 'euler89': [1, 0, 89, 0, 7921], 'euler97': [1, -24, 289, -2328, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -5, 0, 25], [1, 0, -11, 0, 49], [1, 0, -22, 0, 121], [1, -9, 40, -117, 169], [1, 0, -17, 0, 289], [1, 8, 19, 0, 0], [1, 0, 23, 0, 529], [1, 0, 29, 0, 841], [1, -14, 111, -434, 961], [1, 0, -47, 0, 1369], [1, 0, 41, 0, 1681], [1, -3, 46, -129, 1849], [1, 0, 47, 0, 2209], [1, 0, 53, 0, 2809], [1, 0, -59, 0, 3481], [1, 1, -60, 61, 3721], [1, -11, 54, -737, 4489], [1, 0, -71, 0, 5041], [1, -17, 216, -1241, 5329], [1, 17, 210, 1343, 6241], [1, 0, -166, 0, 6889], [1, 0, 89, 0, 7921], [1, -24, 289, -2328, 9409]], 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/bm/e'], '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': '4-2736e2-1.1-c1e2-0-37', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2736e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1404790978718803488, 'z1': {'__RealLiteral__': 0, 'data': '0.855825255866622988987925164973', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1084887399289802637896538976633,1154157908690534271645458371644', 'Lhash_array': ['1084887399289802637896538976633', '1154157908690534271645458371644'], 'label': '4-2736e2-1.1-c1e2-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/bm/e'}