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lfunc_lfunctions • Show schema
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{'Lhash': '1211805425690427331942417543336,1975886960100369945112558458729', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 145.76652359452027, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -4, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '1512.1', 'coefficient_field': '1.1.1.1', 'conductor': 2286144, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1], [1, -4, 11, -20, 25], [1, -4, 7], [1, 2, -7, 22, 121], [1, -10, 51, -130, 169], [1, 6, 19, 102, 289], [1, -4, -3, -76, 361], [1, 6, 13, 138, 529], [1, -12, 94, -348, 841], [1, -7, 18, -217, 961], [1, 7, 12, 259, 1369], [1, -4, 86, -164, 1681], [1, 14, 135, 602, 1849], [1, -2, -43, -94, 2209], [1, 6, -17, 318, 2809], [1, 6, -23, 354, 3481], [1, -9, 20, -549, 3721], [1, -7, -18, -469, 4489], [1, 16, 206, 1136, 5041], [1, 10, 27, 730, 5329], [1, 1, -78, 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'7.12570850932302715700973426988253', '7.984971492146270062353283586741365', '8.196760255591124082067706619074136', '8.508385544461882300850942521956955', '8.720055336694627882912932059129359', '9.188433984246528729469153003988593', '10.01700425014403252979344240696543'], 'prelabel': '4-1512e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.474677076451508, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1905231129334022540, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.955945925061884059852400536299', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.55869997595917107007756803860', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.87784844181740957651219037248', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 145.76652359452027, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 2286144, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 4, 0, 0, 0, -2, 0, 10, 0, 0, 0, -6, 0, 4, 0, 0, 0, -6, 0, 5, 0, 0, 0, 12, 0, 7, 0, 0, 0, 16, 0, -7, 0, 0, 0, 4, 0, -14, 0, 0, 0, 2, 0, 9, 0, 0, 0, -6, 0, -8, 0, 0, 0, -6, 0, 9, 0, 0, 0, 40, 0, 7, 0, 0, 0, -16, 0, -10, 0, 0, 0, -8, 0, -1, 0, 0, 0, 28, 0, -24, 0, 0, 0, -12, 0, 40, 0, 0, 0, 16, 0, -30, 0, 0, 0], 'euler11': [1, 2, -7, 22, 121], 'euler13': [1, -10, 51, -130, 169], 'euler17': [1, 6, 19, 102, 289], 'euler19': [1, -4, -3, -76, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 6, 13, 138, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -7, 18, -217, 961], 'euler37': [1, 7, 12, 259, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 14, 135, 602, 1849], 'euler47': [1, -2, -43, -94, 2209], 'euler5': [1, -4, 11, -20, 25], 'euler53': [1, 6, -17, 318, 2809], 'euler59': [1, 6, -23, 354, 3481], 'euler61': [1, -9, 20, -549, 3721], 'euler67': [1, -7, -18, -469, 4489], 'euler7': [1, -4, 7, 0, 0], 'euler71': [1, 16, 206, 1136, 5041], 'euler73': [1, 10, 27, 730, 5329], 'euler79': [1, 1, -78, 79, 6241], 'euler83': [1, -28, 362, -2324, 6889], 'euler89': [1, 12, 55, 1068, 7921], 'euler97': [1, 30, 419, 2910, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -4, 11, -20, 25], [1, -4, 7, 0, 0], [1, 2, -7, 22, 121], [1, -10, 51, -130, 169], [1, 6, 19, 102, 289], [1, -4, -3, -76, 361], [1, 6, 13, 138, 529], [1, -12, 94, -348, 841], [1, -7, 18, -217, 961], [1, 7, 12, 259, 1369], [1, -4, 86, -164, 1681], [1, 14, 135, 602, 1849], [1, -2, -43, -94, 2209], [1, 6, -17, 318, 2809], [1, 6, -23, 354, 3481], [1, -9, 20, -549, 3721], [1, -7, -18, -469, 4489], [1, 16, 206, 1136, 5041], [1, 10, 27, 730, 5329], [1, 1, -78, 79, 6241], [1, -28, 362, -2324, 6889], [1, 12, 55, 1068, 7921], [1, 30, 419, 2910, 9409]], 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1512/2/s/j'], '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': '4-1512e2-1.1-c1e2-0-21', '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': '4-1512e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.474677076451508, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1905231129334022540, 'z1': {'__RealLiteral__': 0, 'data': '0.955945925061884059852400536299', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1211805425690427331942417543336,1975886960100369945112558458729', 'Lhash_array': ['1211805425690427331942417543336', '1975886960100369945112558458729'], 'label': '4-1512e2-1.1-c1e2-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1512/2/s/j'}