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{'Lhash': '982281980933246530774040138892,1150940219174059012507543849854,1802418985784573369727234596893,2139248908366798507636787109514,2315231098711857116814406280939,2862277257528964811154095382844', 'a10': 0, 'a2': 0, 'a3': 8, 'a4': -4, 'a5': 6, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 26, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17318.05984582416, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1]], [13, [1, -6, 15, -20, 15, -6, 1]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': '1.1.1.1', 'conductor': 66809249633371609, 'conductor_radical': 91, 'degree': 12, 'euler_factors': [[1, 0, 4, 0, 10, 4, 22, 8, 40, 0, 64, 0, 64], [1, -8, 38, -132, 363, -820, 1550, -2460, 3267, -3564, 3078, -1944, 729], [1, -6, 35, -126, 444, -1166, 2971, -5830, 11100, -15750, 21875, -18750, 15625], [1], [1, -4, 28, -64, 329, -384, 2562, -4224, 39809, -85184, 409948, -644204, 1771561], [1, -6, 15, -20, 15, -6, 1], [1, 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'10.66354676703402963636632321490258', '10.67802031495921849066054587245660'], 'prelabel': '12-637e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e6-0', 'trace_hash': 1764270333158169428, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77488385266128951688398560546', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.907931743152917920890736717421', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.42185787271355655763855117191', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 17318.05984582416, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 66809249633371609, 'conductor_radical': 91, 'degree': 12, 'dirichlet_coefficients': [1, 0, 8, -4, 6, 0, 0, 0, 26, 0, 4, -32, 6, 0, 48, 6, 16, 0, 2, -24, 0, 0, -6, 0, 1, 0, 36, 0, -6, 0, 6, -4, 32, 0, 0, -104, 0, 0, 48, 0, -8, 0, 2, -16, 156, 0, 30, 48, 0, 0, 128, -24, -14, 0, 24, 0, 16, 0, 24, -192, 0, 0, 0, -6, 36, 0, 16, -64, -48, 0, 8, 0, -6, 0, 8, -8, 0, 0, -22, 36, -7, 0, 50, 0, 96, 0, -48, 0, 26, 0, 0, 24, 48, 0, 12, -32, -14, 0, 104, -4], 'euler11': [1, -4, 28, -64, 329, -384, 2562, -4224, 39809, -85184, 409948, -644204, 1771561], 'euler13': [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], 'euler17': [1, -16, 158, -1036, 5351, -22924, 95142, -389708, 1546439, -5089868, 13196318, -22717712, 24137569], 'euler19': [1, -2, 97, -174, 4206, -6314, 103439, -119966, 1518366, -1193466, 12641137, -4952198, 47045881], 'euler2': [1, 0, 4, 0, 10, 4, 22, 8, 40, 0, 64, 0, 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3030, 35490, 288526, 2479717, 15291878, 99691410, 451097310, 2217225161, 5854736902, 22164361129], 'euler59': [1, -24, 500, -7036, 85435, -826892, 7012620, -48786628, 297399235, -1445046644, 6058680500, -17158183176, 42180533641], 'euler61': [1, 0, 120, 112, 12043, -272, 813584, -16592, 44812003, 25421872, 1661500920, 0, 51520374361], 'euler67': [1, -16, 402, -4560, 65351, -561152, 5755516, -37597184, 293360639, -1371479280, 8100750642, -21602001712, 90458382169], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, -8, 110, -984, 19145, -111980, 1119230, -7950580, 96509945, -352184424, 2795284910, -14433834808, 128100283921], 'euler73': [1, 6, 197, 1382, 21574, 165022, 1685555, 12046606, 114967846, 537621494, 5594453477, 12438429558, 151334226289], 'euler79': [1, 22, 409, 5518, 61946, 630742, 5676321, 49828618, 386604986, 2720589202, 15930583129, 67695240778, 243087455521], 'euler83': [1, -50, 1439, -28742, 441892, -5421474, 54504063, -449982342, 3044193988, -16434301954, 68292523919, -196952032150, 326940373369], 'euler89': [1, -26, 665, -10382, 156398, -1742290, 18723811, -155063810, 1238828558, -7318988158, 41723590265, -145185545674, 496981290961], 'euler97': [1, 14, 321, 3170, 53038, 457742, 6291427, 44400974, 499034542, 2893173410, 28417899201, 120222763598, 832972004929], 'euler_factors': [[1, 0, 4, 0, 10, 4, 22, 8, 40, 0, 64, 0, 64], [1, -8, 38, -132, 363, -820, 1550, -2460, 3267, -3564, 3078, -1944, 729], [1, -6, 35, -126, 444, -1166, 2971, -5830, 11100, -15750, 21875, -18750, 15625], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 28, -64, 329, -384, 2562, -4224, 39809, -85184, 409948, -644204, 1771561], [1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0], [1, -16, 158, -1036, 5351, -22924, 95142, -389708, 1546439, -5089868, 13196318, -22717712, 24137569], [1, -2, 97, -174, 4206, -6314, 103439, -119966, 1518366, -1193466, 12641137, -4952198, 47045881], [1, 6, 101, 418, 4362, 13846, 118657, 318458, 2307498, 5085806, 28263941, 38618058, 148035889], [1, 6, 141, 602, 8386, 27374, 298533, 793846, 7052626, 14682178, 99726621, 123066894, 594823321], [1, -6, 71, -422, 4336, -20462, 147703, -634322, 4166896, -12571802, 65569991, -171774906, 887503681], [1, 0, 140, 236, 8777, 25480, 367738, 942760, 12015713, 11954108, 262382540, 0, 2565726409], [1, 8, 126, 672, 7255, 35160, 337924, 1441560, 12195655, 46314912, 356045886, 926849608, 4750104241], [1, -2, 97, -618, 6618, -32018, 404609, -1376774, 12236682, -49135326, 331623697, -294016886, 6321363049], [1, -30, 497, -5570, 47934, -346670, 2382079, -16293490, 105886206, -578294110, 2425201457, -6880350210, 10779215329], [1, 14, 281, 3030, 35490, 288526, 2479717, 15291878, 99691410, 451097310, 2217225161, 5854736902, 22164361129], [1, -24, 500, -7036, 85435, -826892, 7012620, -48786628, 297399235, -1445046644, 6058680500, -17158183176, 42180533641], [1, 0, 120, 112, 12043, -272, 813584, -16592, 44812003, 25421872, 1661500920, 0, 51520374361], [1, -16, 402, -4560, 65351, -561152, 5755516, -37597184, 293360639, -1371479280, 8100750642, -21602001712, 90458382169], [1, -8, 110, -984, 19145, -111980, 1119230, -7950580, 96509945, -352184424, 2795284910, -14433834808, 128100283921], [1, 6, 197, 1382, 21574, 165022, 1685555, 12046606, 114967846, 537621494, 5594453477, 12438429558, 151334226289], [1, 22, 409, 5518, 61946, 630742, 5676321, 49828618, 386604986, 2720589202, 15930583129, 67695240778, 243087455521], [1, -50, 1439, -28742, 441892, -5421474, 54504063, -449982342, 3044193988, -16434301954, 68292523919, -196952032150, 326940373369], [1, -26, 665, -10382, 156398, -1742290, 18723811, -155063810, 1238828558, -7318988158, 41723590265, -145185545674, 496981290961], [1, 14, 321, 3170, 53038, 457742, 6291427, 44400974, 499034542, 2893173410, 28417899201, 120222763598, 832972004929]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/a/n'], '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': '12-637e6-1.1-c1e6-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-637e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 1764270333158169428, 'z1': {'__RealLiteral__': 0, 'data': '0.77488385266128951688398560546', 'prec': 103}}
-
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{'Lhash': '982281980933246530774040138892,1150940219174059012507543849854,1802418985784573369727234596893,2139248908366798507636787109514,2315231098711857116814406280939,2862277257528964811154095382844', 'Lhash_array': ['982281980933246530774040138892', '1150940219174059012507543849854', '1802418985784573369727234596893', '2139248908366798507636787109514', '2315231098711857116814406280939', '2862277257528964811154095382844'], 'label': '12-637e6-1.1-c1e6-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/n'}