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lfunc_lfunctions • Show schema
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{'Lhash': '722597392471137462842758283787,1024259628995052031772785596744', 'a10': 0, 'a2': 0, 'a3': -24, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 333, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 948.2515534652371, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 24, 243]]], 'bad_primes': [2, 3], 'central_character': '192.1', 'coefficient_field': '1.1.1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 24, 243], [1, 0, 86, 0, 9765625], [1, 0, -1538, 0, 282475249], [1, 1296, 742006, 208722096, 25937424601], [1, -484, 801150, -179705812, 137858491849], [1, 0, -2738338, 0, 2015993900449], [1, 0, -3380474, 0, 6131066257801], [1, -2592, 14552302, -16683001056, 41426511213649], [1, 0, -37062298, 0, 420707233300201], [1, 0, -45678866, 0, 819628286980801], [1, -24116, 284083278, -1672298867012, 4808584372417849], [1, 0, -12512146, 0, 13422659310152401], [1, 0, 33190390, 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True, 'root_analytic_conductor': 5.549206556264805, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e2-0', 'trace_hash': 1782484034480045769, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57002883313512423961339566119', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.807998378110374456120912133353', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.30576158348564855887970448708', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 948.2515534652371, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 36864, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, -24, 0, 0, 0, 0, 0, 333, 0, -1296, 0, 484, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2592, 0, -86, 0, -2160, 0, 0, 0, 0, 0, 31104, 0, 0, 0, 24116, 0, -11616, 0, 0, 0, 0, 0, 0, 0, 25920, 0, 1538, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16848, 0, 51524, 0, 0, 0, 0, 0, 0, 0, -62208, 0, 111456, 0, 52052, 0, 2064, 0, 0, 0, 0, 0, -29079, 0, 156816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 206180, 0, -431568, 0], 'euler11': [1, 1296, 742006, 208722096, 25937424601], 'euler13': [1, -484, 801150, -179705812, 137858491849], 'euler17': [1, 0, -2738338, 0, 2015993900449], 'euler19': [1, 0, -3380474, 0, 6131066257801], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -2592, 14552302, -16683001056, 41426511213649], 'euler29': [1, 0, -37062298, 0, 420707233300201], 'euler3': [1, 24, 243, 0, 0], 'euler31': [1, 0, -45678866, 0, 819628286980801], 'euler37': [1, -24116, 284083278, -1672298867012, 4808584372417849], 'euler41': [1, 0, -12512146, 0, 13422659310152401], 'euler43': [1, 0, 33190390, 0, 21611482313284249], 'euler47': [1, -25920, 626651614, -5944622581440, 52599132235830049], 'euler5': [1, 0, 86, 0, 9765625], 'euler53': [1, 0, -108251530, 0, 174887470365513049], 'euler59': [1, 16848, 1500812374, 12045044589552, 511116753300641401], 'euler61': [1, -51524, 2352873246, -43516979812724, 713342911662882601], 'euler67': [1, 0, -2596035290, 0, 1822837804551761449], 'euler7': [1, 0, -1538, 0, 282475249], 'euler71': [1, -111456, 6714068686, -201092186545056, 3255243551009881201], 'euler73': [1, -52052, 4823495862, -107907522558836, 4297625829703557649], 'euler79': [1, 0, -5786874674, 0, 9468276082626847201], 'euler83': [1, -156816, 14025895750, -617704597472688, 15516041187205853449], 'euler89': [1, 0, -4075828594, 0, 31181719929966183601], 'euler97': [1, -206180, 27802228614, -1770537814188260, 73742412689492826049], 'euler_factors': [[1, 0, 0, 0, 0], [1, 24, 243, 0, 0], [1, 0, 86, 0, 9765625], [1, 0, -1538, 0, 282475249], [1, 1296, 742006, 208722096, 25937424601], [1, -484, 801150, -179705812, 137858491849], [1, 0, -2738338, 0, 2015993900449], [1, 0, -3380474, 0, 6131066257801], [1, -2592, 14552302, -16683001056, 41426511213649], [1, 0, -37062298, 0, 420707233300201], [1, 0, -45678866, 0, 819628286980801], [1, -24116, 284083278, -1672298867012, 4808584372417849], [1, 0, -12512146, 0, 13422659310152401], [1, 0, 33190390, 0, 21611482313284249], [1, -25920, 626651614, -5944622581440, 52599132235830049], [1, 0, -108251530, 0, 174887470365513049], [1, 16848, 1500812374, 12045044589552, 511116753300641401], [1, -51524, 2352873246, -43516979812724, 713342911662882601], [1, 0, -2596035290, 0, 1822837804551761449], [1, -111456, 6714068686, -201092186545056, 3255243551009881201], [1, -52052, 4823495862, -107907522558836, 4297625829703557649], [1, 0, -5786874674, 0, 9468276082626847201], [1, -156816, 14025895750, -617704597472688, 15516041187205853449], [1, 0, -4075828594, 0, 31181719929966183601], [1, -206180, 27802228614, -1770537814188260, 73742412689492826049]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/6/c/a'], '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': '4-192e2-1.1-c5e2-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'prelabel': '4-192e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.549206556264805, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 1782484034480045769, 'z1': {'__RealLiteral__': 0, 'data': '0.57002883313512423961339566119', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '722597392471137462842758283787,1024259628995052031772785596744', 'Lhash_array': ['722597392471137462842758283787', '1024259628995052031772785596744'], 'label': '4-192e2-1.1-c5e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/6/c/a'}