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lfunc_lfunctions • Show schema
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{'Lhash': '1808751946575318348061251863808,1909285589909208922889587009160', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': 3, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 4, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6001.73415549938, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1]], [7, [1]], [11, [1, 2, 1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '9702.1', 'coefficient_field': '1.1.1.1', 'conductor': 94128804, 'conductor_radical': 462, 'degree': 4, 'euler_factors': [[1, -2, 1], [1], [1, 0, 10, 0, 25], [1], [1, 2, 1], [1, 0, 24, 0, 169], [1, -8, 50, -136, 289], [1, 8, 52, 152, 361], [1, 4, 18, 92, 529], [1, 0, 26, 0, 841], [1, 8, 28, 248, 961], [1, 4, 46, 148, 1369], [1, -8, 66, -328, 1681], [1, 20, 186, 860, 1849], [1, 0, 92, 0, 2209], [1, 4, 78, 212, 2809], [1, -8, 126, -472, 3481], [1, 0, 120, 0, 3721], [1, 0, 6, 0, 4489], [1, 16, 174, 1136, 5041], [1, 8, 162, 584, 5329], [1, 8, 142, 632, 6241], [1, 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'2.98583232802086492150019843370157', '3.43080771749806930262085326024249', '3.54888994758577472104825514633504', '4.08251615875410683537663548595292', '4.34411041864422905157916193890369', '4.62001275458236101101790794161385', '5.35782790963189340005352511643175', '5.38064030802644576590395019764729', '5.75617596550174521241084519877547', '5.92242279539087911123370123139703', '6.48213971345871216746309460409002', '6.62500836270285503258202784828694', '7.28107369343615028110287089325269', '7.29542208757960868442894179898919'], 'prelabel': '4-9702e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.80175323677313, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1703294219449588322, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42685369789567281596929366119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.50616075878121207401718628994', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.15734777430987458665248668046', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6001.73415549938, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 94128804, 'conductor_radical': 462, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, 3, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 5, 8, 0, -8, 0, 0, -4, -4, 0, -10, 0, 0, 0, 0, 0, -8, 6, 0, 16, 0, 0, -4, -16, 0, 0, 8, 0, -20, -6, 0, -8, 0, 0, 0, -20, 0, 0, -4, 0, 0, 0, 0, 0, 8, 0, 0, -16, 0, 7, 0, 0, 0, 24, 0, 0, -16, 0, -8, -8, 0, -24, 0, 0, -8, 0, 0, 16, -16, 0, 0, -40, 0, -8, 8, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -30], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 0, 24, 0, 169], 'euler17': [1, -8, 50, -136, 289], 'euler19': [1, 8, 52, 152, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 4, 18, 92, 529], 'euler29': [1, 0, 26, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 28, 248, 961], 'euler37': [1, 4, 46, 148, 1369], 'euler41': [1, -8, 66, -328, 1681], 'euler43': [1, 20, 186, 860, 1849], 'euler47': [1, 0, 92, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 4, 78, 212, 2809], 'euler59': [1, -8, 126, -472, 3481], 'euler61': [1, 0, 120, 0, 3721], 'euler67': [1, 0, 6, 0, 4489], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 16, 174, 1136, 5041], 'euler73': [1, 8, 162, 584, 5329], 'euler79': [1, 8, 142, 632, 6241], 'euler83': [1, 16, 180, 1328, 6889], 'euler89': [1, -8, 192, -712, 7921], 'euler97': [1, 0, 32, 0, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 10, 0, 25], [1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, 0, 24, 0, 169], [1, -8, 50, -136, 289], [1, 8, 52, 152, 361], [1, 4, 18, 92, 529], [1, 0, 26, 0, 841], [1, 8, 28, 248, 961], [1, 4, 46, 148, 1369], [1, -8, 66, -328, 1681], [1, 20, 186, 860, 1849], [1, 0, 92, 0, 2209], [1, 4, 78, 212, 2809], [1, -8, 126, -472, 3481], [1, 0, 120, 0, 3721], [1, 0, 6, 0, 4489], [1, 16, 174, 1136, 5041], [1, 8, 162, 584, 5329], [1, 8, 142, 632, 6241], [1, 16, 180, 1328, 6889], [1, -8, 192, -712, 7921], [1, 0, 32, 0, 9409]], 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9702/2/a/dl'], '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': '4-9702e2-1.1-c1e2-0-34', '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': 2, 'prelabel': '4-9702e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.80175323677313, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1703294219449588322, 'z1': {'__RealLiteral__': 0, 'data': '1.42685369789567281596929366119', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1808751946575318348061251863808,1909285589909208922889587009160', 'Lhash_array': ['1808751946575318348061251863808', '1909285589909208922889587009160'], 'label': '4-9702e2-1.1-c1e2-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9702/2/a/dl'}