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lfunc_lfunctions • Show schema
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{'Lhash': '1326358884513316988469159618326,1838466768974716830897598870124', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 24, 'a8': 0, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 150.6117350274592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [13, [1, -91, 2197]]], 'bad_primes': [2, 13], 'central_character': '208.1', 'coefficient_field': '1.1.1.1', 'conductor': 43264, 'conductor_radical': 26, 'degree': 4, 'euler_factors': [[1], [1, -2, -23, -54, 729], [1, 0, -247, 0, 15625], [1, -24, 535, -8232, 117649], [1, 24, 1523, 31944, 1771561], [1, -91, 2197], [1, 117, 8776, 574821, 24137569], [1, -198, 19927, -1358082, 47045881], [1, 78, -6083, 949026, 148035889], [1, -141, -4508, -3438849, 594823321], [1, 0, -35282, 0, 887503681], [1, 249, 71320, 12612597, 2565726409], [1, -471, 142868, -32461791, 4750104241], [1, -104, -68691, -8268728, 6321363049], [1, 0, -116818, 0, 10779215329], [1, -186, 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'3.24767138576359516999663601720891', '4.34095374656694777953470558090436', '4.43817892699905125639082933181429', '5.35594562269790954217406331365111', '5.77872364940037632261564910583372', '6.89956670413125727925317936517731', '6.92495851557559707457824789906969', '7.72567831698769910932769734206828', '8.283761099719966662700360282901299', '8.727149893366397299792231971337761', '8.934129358721195011190726339742282', '9.835781014522031616098884338933135', '10.25109597878612378579809896785783', '10.89733847083912375357617703906064', '11.09267344104038232102105219268890', '11.56885243740790785001834536092410', '12.14674524305745409670587747740939'], 'prelabel': '4-208e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.503198150432552, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3e2-0', 'trace_hash': 1630244405572346455, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04631267028510669576583039583', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.45029455959214390114118125828', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.60138688882169316357273968957', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 150.6117350274592, 'bad_primes': [2, 13], 'central_character': '1.1', 'conductor': 43264, 'conductor_radical': 26, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 24, 0, 27, 0, -24, 0, 91, 0, 0, 0, -117, 0, 198, 0, 48, 0, -78, 0, 247, 0, 154, 0, 141, 0, 0, 0, -48, 0, 0, 0, -249, 0, 182, 0, 471, 0, 104, 0, 0, 0, 0, 0, 41, 0, -234, 0, 186, 0, 0, 0, 396, 0, 492, 0, -145, 0, 648, 0, 0, 0, 1362, 0, -156, 0, -1830, 0, 0, 0, 494, 0, -576, 0, -2552, 0, 308, 0, 0, 0, 0, 0, 282, 0, -1692, 0, 2184, 0, 0, 0, 0, 0, 348, 0, -648, 0], 'euler11': [1, 24, 1523, 31944, 1771561], 'euler13': [1, -91, 2197, 0, 0], 'euler17': [1, 117, 8776, 574821, 24137569], 'euler19': [1, -198, 19927, -1358082, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 78, -6083, 949026, 148035889], 'euler29': [1, -141, -4508, -3438849, 594823321], 'euler3': [1, -2, -23, -54, 729], 'euler31': [1, 0, -35282, 0, 887503681], 'euler37': [1, 249, 71320, 12612597, 2565726409], 'euler41': [1, -471, 142868, -32461791, 4750104241], 'euler43': [1, -104, -68691, -8268728, 6321363049], 'euler47': [1, 0, -116818, 0, 10779215329], 'euler5': [1, 0, -247, 0, 15625], 'euler53': [1, -186, 306403, -27691122, 22164361129], 'euler59': [1, -492, 286067, -101046468, 42180533641], 'euler61': [1, 145, -205956, 32912245, 51520374361], 'euler67': [1, -1362, 919111, -409639206, 90458382169], 'euler7': [1, -24, 535, -8232, 117649], 'euler71': [1, 1830, 1474211, 654977130, 128100283921], 'euler73': [1, 0, -567359, 0, 151334226289], 'euler79': [1, 2552, 2614254, 1258235528, 243087455521], 'euler83': [1, 0, -519766, 0, 326940373369], 'euler89': [1, 1692, 1659257, 1192807548, 496981290961], 'euler97': [1, -348, 953041, -317610204, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, -23, -54, 729], [1, 0, -247, 0, 15625], [1, -24, 535, -8232, 117649], [1, 24, 1523, 31944, 1771561], [1, -91, 2197, 0, 0], [1, 117, 8776, 574821, 24137569], [1, -198, 19927, -1358082, 47045881], [1, 78, -6083, 949026, 148035889], [1, -141, -4508, -3438849, 594823321], [1, 0, -35282, 0, 887503681], [1, 249, 71320, 12612597, 2565726409], [1, -471, 142868, -32461791, 4750104241], [1, -104, -68691, -8268728, 6321363049], [1, 0, -116818, 0, 10779215329], [1, -186, 306403, -27691122, 22164361129], [1, -492, 286067, -101046468, 42180533641], [1, 145, -205956, 32912245, 51520374361], [1, -1362, 919111, -409639206, 90458382169], [1, 1830, 1474211, 654977130, 128100283921], [1, 0, -567359, 0, 151334226289], [1, 2552, 2614254, 1258235528, 243087455521], [1, 0, -519766, 0, 326940373369], [1, 1692, 1659257, 1192807548, 496981290961], [1, -348, 953041, -317610204, 832972004929]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/208/4/w/b'], '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': '4-208e2-1.1-c3e2-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-208e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.503198150432552, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1630244405572346455, 'z1': {'__RealLiteral__': 0, 'data': '1.04631267028510669576583039583', 'prec': 103}}
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{'Lhash': '1326358884513316988469159618326,1838466768974716830897598870124', 'Lhash_array': ['1326358884513316988469159618326', '1838466768974716830897598870124'], 'label': '4-208e2-1.1-c3e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/208/4/w/b'}