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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.51596464537423928475349764277', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.52662309714559379852450488702', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.59890707293714280763495544046', 'prec': 103}}
-
lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4141007165682.879, 'bad_primes': [2, 5, 11, 43], 'central_character': '1.1', 'conductor': 250546953241043972448100000000, 'conductor_radical': 4730, 'degree': 16, 'dirichlet_coefficients': [1, -8, 3, 36, 8, -24, 11, -120, -6, -64, -8, 108, 6, -88, 24, 330, 9, 48, 9, 288, 33, 64, -2, -360, 36, -48, -22, 396, -10, -192, 6, -792, -24, -72, 88, -216, 16, -72, 18, -960, -4, -264, -8, -288, -48, 16, -11, 990, 38, -288, 27, 216, -15, 176, -64, -1320, 27, 80, -7, 864, 2, -48, -66, 1716, 48, 192, 4, 324, -6, -704, -3, 720, 32, -128, 108, 324, -88, -144, 45, 2640, 29, 32, 39, 1188, 72, 64, -30, 960, -22, 384, 66, -72, 18, 88, 72, -2376, 30, -304, 48, 1296], 'euler11': [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler13': [1, -6, 56, -198, 812, -562, -5096, 52030, -217882, 676390, -861224, -1234714, 23191532, -73516014, 270301304, -376491102, 815730721], 'euler17': [1, -9, 87, -601, 3904, -21757, 112362, -522986, 2280891, -8890762, 32472618, -106892141, 326065984, -853334057, 2099968503, -3693048057, 6975757441], 'euler19': [1, -9, 117, -767, 5924, -32115, 186316, -864248, 4124941, -16420712, 67260076, -220276785, 772021604, -1899167933, 5504368077, -8044845651, 16983563041], 'euler2': [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 2, 96, 126, 3588, -818, 67120, -218798, 1067670, -5032354, 35506480, -9952606, 1004069508, 810979218, 14211445344, 6809650894, 78310985281], 'euler29': [1, 10, 189, 1466, 16362, 104346, 861411, 4575426, 30229322, 132687354, 724446651, 2544894594, 11572531722, 30069344434, 112421607669, 172498763090, 500246412961], 'euler3': [1, -3, 15, -41, 118, -267, 596, -1136, 2099, -3408, 5364, -7209, 9558, -9963, 10935, -6561, 6561], 'euler31': [1, -6, 169, -842, 13550, -58090, 695239, -2593702, 25290434, -80404762, 668124679, -1730559190, 12513709550, -24105745142, 149988122089, -165075684666, 852891037441], 'euler37': [1, -16, 321, -3518, 41066, -344554, 2954111, -19874912, 134955402, -735371744, 4044177959, -17452693762, 76964295626, -243952040726, 823598177289, -1518910034128, 3512479453921], 'euler41': [1, 4, 184, 944, 17684, 98904, 1151320, 6165204, 54805686, 252773364, 1935368920, 6816562584, 49970757524, 109368253744, 874019180344, 779017095524, 7984925229121], 'euler43': [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler47': [1, 11, 290, 2678, 40016, 308551, 3390883, 21891232, 192450008, 1028887904, 7490460547, 32034690473, 195265314896, 614185928746, 3125972445410, 5572854325093, 23811286661761], 'euler5': [1, -8, 28, -56, 70, -56, 28, -8, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 15, 359, 4191, 58688, 550765, 5725974, 44240966, 368327611, 2344771198, 16084260966, 81996240905, 463076548928, 1752657311163, 7957005645311, 17620667097555, 62259690411361], 'euler59': [1, 7, 310, 1870, 48406, 256023, 4863943, 22258856, 340193048, 1313272504, 16931385583, 52581747717, 586552976566, 1336908439130, 13075965428710, 17420560393733, 146830437604321], 'euler61': [1, -2, 173, -258, 13146, -48466, 722187, -6226362, 40704730, -379808082, 2687257827, -11000861146, 182017425786, -217905845658, 8913024764453, -6285485672042, 191707312997281], 'euler67': [1, -4, 296, -1092, 39900, -144516, 3458392, -12643748, 242751078, -847131116, 15524721688, -43465065708, 804029727900, -1474336616844, 26775681122024, -24242846421292, 406067677556641], 'euler7': [1, -11, 83, -465, 2140, -8471, 29454, -91492, 255259, -640444, 1443246, -2905553, 5138140, -7815255, 9764867, -9058973, 5764801], 'euler71': [1, 3, 251, 817, 34524, 118515, 3534502, 12628708, 283024187, 896638268, 17817424582, 42417822165, 877312874844, 1474055379767, 32153171264171, 27285360475173, 645753531245761], 'euler73': [1, -32, 704, -10628, 137164, -1496452, 15474608, -144995000, 1303399494, -10584635000, 82464186032, -582145267684, 3895216328524, -22032604890404, 106539295307456, -353516752611104, 806460091894081], 'euler79': [1, -45, 1264, -24352, 368254, -4481047, 47083561, -442336508, 3997142488, -34944584132, 293848504201, -2209330931833, 14343523128574, -74932477428448, 307262543778544, -864175904377155, 1517108809906561], 'euler83': [1, -39, 902, -14594, 198374, -2399223, 27273811, -284037900, 2724078224, -23575145700, 187889283979, -1371844521501, 9414496970054, -57486359143942, 294900216778838, -1058305988595453, 2252292232139041], 'euler89': [1, 22, 489, 7894, 127750, 1616582, 19871335, 209703870, 2155136002, 18663644430, 157400844535, 1139640195958, 8015321287750, 44080565290406, 243023851279929, 973089367701638, 3936588805702081], 'euler97': [1, -30, 972, -18646, 355644, -5057418, 70504772, -786673474, 8582427558, -76307326978, 663379399748, -4615768858314, 31484907611964, -160119546432022, 809648788790988, -2423948534343390, 7837433594376961], 'euler_factors': [[1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -3, 15, -41, 118, -267, 596, -1136, 2099, -3408, 5364, -7209, 9558, -9963, 10935, -6561, 6561], [1, -8, 28, -56, 70, -56, 28, -8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -11, 83, -465, 2140, -8471, 29454, -91492, 255259, -640444, 1443246, -2905553, 5138140, -7815255, 9764867, -9058973, 5764801], [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -6, 56, -198, 812, -562, -5096, 52030, -217882, 676390, -861224, -1234714, 23191532, -73516014, 270301304, -376491102, 815730721], [1, -9, 87, -601, 3904, -21757, 112362, -522986, 2280891, -8890762, 32472618, -106892141, 326065984, -853334057, 2099968503, -3693048057, 6975757441], [1, -9, 117, -767, 5924, -32115, 186316, -864248, 4124941, -16420712, 67260076, -220276785, 772021604, -1899167933, 5504368077, -8044845651, 16983563041], [1, 2, 96, 126, 3588, -818, 67120, -218798, 1067670, -5032354, 35506480, -9952606, 1004069508, 810979218, 14211445344, 6809650894, 78310985281], [1, 10, 189, 1466, 16362, 104346, 861411, 4575426, 30229322, 132687354, 724446651, 2544894594, 11572531722, 30069344434, 112421607669, 172498763090, 500246412961], [1, -6, 169, 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52581747717, 586552976566, 1336908439130, 13075965428710, 17420560393733, 146830437604321], [1, -2, 173, -258, 13146, -48466, 722187, -6226362, 40704730, -379808082, 2687257827, -11000861146, 182017425786, -217905845658, 8913024764453, -6285485672042, 191707312997281], [1, -4, 296, -1092, 39900, -144516, 3458392, -12643748, 242751078, -847131116, 15524721688, -43465065708, 804029727900, -1474336616844, 26775681122024, -24242846421292, 406067677556641], [1, 3, 251, 817, 34524, 118515, 3534502, 12628708, 283024187, 896638268, 17817424582, 42417822165, 877312874844, 1474055379767, 32153171264171, 27285360475173, 645753531245761], [1, -32, 704, -10628, 137164, -1496452, 15474608, -144995000, 1303399494, -10584635000, 82464186032, -582145267684, 3895216328524, -22032604890404, 106539295307456, -353516752611104, 806460091894081], [1, -45, 1264, -24352, 368254, -4481047, 47083561, -442336508, 3997142488, -34944584132, 293848504201, -2209330931833, 14343523128574, -74932477428448, 307262543778544, -864175904377155, 1517108809906561], [1, -39, 902, -14594, 198374, -2399223, 27273811, -284037900, 2724078224, -23575145700, 187889283979, -1371844521501, 9414496970054, -57486359143942, 294900216778838, -1058305988595453, 2252292232139041], [1, 22, 489, 7894, 127750, 1616582, 19871335, 209703870, 2155136002, 18663644430, 157400844535, 1139640195958, 8015321287750, 44080565290406, 243023851279929, 973089367701638, 3936588805702081], [1, -30, 972, -18646, 355644, -5057418, 70504772, -786673474, 8582427558, -76307326978, 663379399748, -4615768858314, 31484907611964, -160119546432022, 809648788790988, -2423948534343390, 7837433594376961]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4730/2/a/y'], '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': '16-4730e8-1.1-c1e8-0-0', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '16-4730e8-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.145668405964126, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e8-0', 'trace_hash': 2020965882734056916, 'z1': {'__RealLiteral__': 0, 'data': '0.51596464537423928475349764277', 'prec': 103}}
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{'Lhash': '654062892405199956068563484961,667574085190661140331746797534,759204910489701045192722321555,787170411746866988795863135217,1078598447486076058620180764285,1190285793697337253814780505614,1448444253817998984823041263597,1699360859638052611566697317074', 'Lhash_array': ['654062892405199956068563484961', '667574085190661140331746797534', '759204910489701045192722321555', '787170411746866988795863135217', '1078598447486076058620180764285', '1190285793697337253814780505614', '1448444253817998984823041263597', '1699360859638052611566697317074'], 'label': '16-4730e8-1.1-c1e8-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4730/2/a/y'}