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lfunc_lfunctions • Show schema
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{'Lhash': '2182651315780299023116201067836,2460431282612645528427343744600', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 119.32361682000412, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -2, 1]]], 'bad_primes': [2, 3, 19], 'central_character': '1368.1', 'coefficient_field': '1.1.1.1', 'conductor': 1871424, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 1, 6, 5, 25], [1, -1, 10, -7, 49], [1, 7, 30, 77, 121], [1, 2, 10, 26, 169], [1, 1, -4, 17, 289], [1, -2, 1], [1, 10, 54, 230, 529], [1, 0, -10, 0, 841], [1, 4, 66, 124, 961], [1, 16, 138, 592, 1369], [1, -2, 66, -82, 1681], [1, -1, 82, -43, 1849], [1, -1, 56, -47, 2209], [1, -8, 54, -424, 2809], [1, 24, 262, 1416, 3481], [1, -1, 84, -61, 3721], [1, 4, 70, 268, 4489], [1, 0, 142, 0, 5041], [1, 5, -56, 365, 5329], [1, 2, 6, 158, 6241], [1, 8, 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'2.80203519824726207782574024181350', '3.06940715612023451468291156546010', '4.00395169995047673255636676435221', '4.02883090227823545932008734573623', '4.98739524312174120048643645785075', '5.05819907741072692268536925855682', '5.58047950761476600184648104996604', '5.98630505389494854275615366728085', '6.50324011812014693129658106225258', '7.12119993922417367778747557958997', '7.65332501703342613470881963731633', '7.66190770990152056405132713218627', '8.084711086656233871244845227047455', '8.411515746775814653294218273640538', '9.149236607541663322133941012393570', '9.202662513579733759431425021263649'], 'prelabel': '4-1368e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.305077154396121, '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': 1979306482424672449, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72180829274827917643095105983', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.94093804883590667586111335914', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80203519824726207782574024181', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 119.32361682000412, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 1871424, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -7, 0, -2, 0, 0, 0, -1, 0, 2, 0, 0, 0, -10, 0, -5, 0, 0, 0, 0, 0, -4, 0, 0, 0, -1, 0, -16, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, -9, 0, 0, 0, 8, 0, 7, 0, 0, 0, -24, 0, 1, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, -5, 0, 0, 0, -7, 0, -2, 0, 0, 0, -8, 0, 1, 0, 0, 0, 12, 0, -2, 0, 0, 0, -2, 0, -8, 0, 0, 0], 'euler11': [1, 7, 30, 77, 121], 'euler13': [1, 2, 10, 26, 169], 'euler17': [1, 1, -4, 17, 289], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 10, 54, 230, 529], 'euler29': [1, 0, -10, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 4, 66, 124, 961], 'euler37': [1, 16, 138, 592, 1369], 'euler41': [1, -2, 66, -82, 1681], 'euler43': [1, -1, 82, -43, 1849], 'euler47': [1, -1, 56, -47, 2209], 'euler5': [1, 1, 6, 5, 25], 'euler53': [1, -8, 54, -424, 2809], 'euler59': [1, 24, 262, 1416, 3481], 'euler61': [1, -1, 84, -61, 3721], 'euler67': [1, 4, 70, 268, 4489], 'euler7': [1, -1, 10, -7, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 5, -56, 365, 5329], 'euler79': [1, 2, 6, 158, 6241], 'euler83': [1, 8, 182, 664, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 8, 142, 776, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 1, 6, 5, 25], [1, -1, 10, -7, 49], [1, 7, 30, 77, 121], [1, 2, 10, 26, 169], [1, 1, -4, 17, 289], [1, -2, 1, 0, 0], [1, 10, 54, 230, 529], [1, 0, -10, 0, 841], [1, 4, 66, 124, 961], [1, 16, 138, 592, 1369], [1, -2, 66, -82, 1681], [1, -1, 82, -43, 1849], [1, -1, 56, -47, 2209], [1, -8, 54, -424, 2809], [1, 24, 262, 1416, 3481], [1, -1, 84, -61, 3721], [1, 4, 70, 268, 4489], [1, 0, 142, 0, 5041], [1, 5, -56, 365, 5329], [1, 2, 6, 158, 6241], [1, 8, 182, 664, 6889], [1, -12, 214, -1068, 7921], [1, 8, 142, 776, 9409]], 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1368/2/a/k'], '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': '4-1368e2-1.1-c1e2-0-25', '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': '4-1368e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.305077154396121, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1979306482424672449, 'z1': {'__RealLiteral__': 0, 'data': '1.72180829274827917643095105983', 'prec': 103}}
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{'Lhash': '2182651315780299023116201067836,2460431282612645528427343744600', 'Lhash_array': ['2182651315780299023116201067836', '2460431282612645528427343744600'], 'label': '4-1368e2-1.1-c1e2-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1368/2/a/k'}