# Stored data for newform 29.9.c.a, downloaded from the LMFDB on 25 April 2024.
{"label": "29.9.c.a", "space_label": "29.9.c", "level": 29, "weight": 9, "hecke_orbit": 1, "hecke_orbit_code": 137589948445, "dim": 38, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 29, "char_orbit_label": "c", "char_is_real": false, "Nk2": 2349, "analytic_conductor": 11.813979691772689, "level_radical": 29, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [29, 4, [2], [1]], "inner_twist_count": 2, "level_primes": [29], "conrey_indexes": [12, 17], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 19, "sato_tate_group": "8.2.3.c4", "trace_display": [-8, -2, 0, -4], "traces": [38, -8, -2, 0, 0, 0, -4, -3678, 0, 15870, -8390, 5022, 0, 12728, -35530, -245912, 76234, -465022, -164488, 4092, -514620, 0, 733568, -482376, -1528354, 1405470, -1279754, 0, 1420996, 3659852, 291062, 1592134, 0, 0, 0, -10223688, 7994574, 0, -309930, 9093994, 9561658, 0, -5181022, -11400526, 9526060, -32561820, 5445034, -17683542, 45106458, 3122002, 0, 56198616, -25331452, -42307016, 3037606, -25661184, 0, -33846328, 27333008, 30592014, -49572406, 0, 0, 0, -121974972, 133443354, 0, 21192980, -28739184, -17976124, 0, -186114192, 45787870, 91919252, -159074460, 243795016, 59851916, 163580208, -99827470, 0, -75138586, -18178416, -177270160, -9436684, 156307616, 0, -20584526, 563433236, -388451858, 306402752, 0, 0, 0, 81569204, -44386260, 0, -121157834, -129908712, -216447384, 0, -286613342, 294756412, 641835140, -52996962, 810930168, 358921762, -455979244, -283726998, 0, -2229619128, -431882832, -1208763540, -77931290, 1012021484, 0, -257207940, 2716264080, -2041979992, 1533584492, 0, 0, 0, 638482828, 363345314, 0, -2460950944, -716393240, -1980560190, 0, -1076590958, 471903904, 3639966660, -262075576, 3272058096, 2596025110, -990226880, -1094640086, 0, -2218758896, 1100851764, -3175407004, 295221680, 2032168686, 0, -938982864, 5835172076, -3434615118, 364224056, 0, 0, 0, -736399236, 1129375170, 0, 129178302, 1359605286, -1607332002, 0, -1762802730, 1832804146, 1860067288, -4521272576, 3007931590, -166652552, -1902869496, 1351396016, 0, -2978812212, -4915310402, -3808473192, 2290572056, 3921929042, 0, -2587812716, 2826262576, -649316642, 2911906196, 0, 0, 0, -875712940, 12287957724, 0, 674346248, 648513804, -7824501930, 0, -12301262, -5735011452, -5267087260, -1413277988, -5560392382, 1403732846, 5530848008, -295697502, 0, 11577675668, -11367049668, -4678402412, 2596584144, -94602040, 0, -4738811248, 7138451216, -3119634808, -8331412972, 0, 0, 0, 5630349164, 7248108150, 0, 13947396312, -7298145420, 8574144606, 0, 9339032536, 151450086, 1186148152, 1183079958, -9598589256, -16116525604, -10042190556, 16699838840, 0, 8940383512, -5298844804, -7060234252, -4142223606, 4364049048, 0, -4106623750, -22603811476, 33279440844, 9774570354, 0, 0, 0, 8892598904, 15902423298, 0, 2461162418, -4763326696, -1097273672, 0, 56668291152, -8611322172, -49005076620, 23097828700, -42818507078, -21876081398, -32429022992, 5278475620, 0, 18630955416, -11662306136, -24576379132, 12898035922, 25993965008, 0, -33670101698, -1479162436, 8797165486, 15231706194, 0, 0, 0, 25620869208, -13359885254, 0, 25692074582, -46270456196, 9024158832, 0, 70849931740, 16475208052, -40863191080, 24236480660, -61638219820, -47882988556, -18115913956, 43397934618, 0, -9464729124, -77659660756, -33290042308, 19185546704, 41812271396, 0, -23876863998, -1999627036, 44794465544, 28539132262, 0, 0, 0, 78898339500, 40732607126, 0, 86465568636, -31900653084, -34547835888, 0, 127581643448, -17006227884, -121761394876, 44985434690, -108803296796, -79950391444, -34017060792, 48787407556, 0, 71889507628, -43282352752, -103052970432, 37713825702, 34584418990, 0, -69128136726, 71598250524, 38984834712, 22498928636, 0, 0, 0, 96720539252, 127981300990, 0, 88838708120, -117504438726, 7747323142, 0, 117731135046, -40712373212, -81247095192, -21806502860, -73534946746, -143429502470, -111967870540, 108804237556, 0, 132705756304, -161825658992, -218403012732, 24196198980, 151820315844, 0, -253970643650, 55101706332, 47645969408, 70820193486, 0, 0, 0, 67344397284, 322095269636, 0, 93078027740, -38528739086, -136688007672, 0, 231056905814, -4112009912, -70963971492, -101498812620, -153926235768, -82025215540, -180974937688, 127612492330, 0, 56185470628, -486043668524, -290785337676, 144851206792, 229398906890, 0, -107540662992, 323907917188, 36740791012, 110750290356, 0, 0, 0, 209665455960, 278706590600, 0, 90425343160, -141920345024, -144799147778, 0, 178936431108, -20891355690, -76392019140, -70453421020, -74336004354, -177507325896, -87169020612, 123339151832, 0, 49046607680, -200814514708, -709655747872, 138401210034, 369313296320, 0, -448393447612, 430773370280, -54280899888, 177669409266, 0, 0, 0, 151286501296, 638725491772, 0, 214586059830, -280554430920, -317372564940, 0, 780146104232, 2785786634, -185496442804, -17132847892, -199627152054, -135267495002, -475167949916, 133186879468, 0, -258590096916, -735425516536, -407072457040, 341911178298, 330286958610, 0, -413240614038, 726818395380, -56572197844, 640092135148, 0, 0, 0, 550170864400, 547396744492, 0, 74972443844, -334756475656, -481180631498, 0, 459685018414, -41445026130, -102142145148, 77500400236, -291892248260, -244948075828, -604897040292, 478546774620, 0, -97240314640, -747462364152, -1302905727128, -9585380690, 1179494598120, 0, -826329063896, 936141067184, -133355667094, 188684199574, 0, 0, 0, 717852450492, 771357234124, 0, 468544916190, -389136343416, -546686159276, 0, 926653641296, 171385245694, -409208585620, 64241007672, -383395827810, -635145275356, -924904221504, 231806651592, 0, 97685815676, -1237400297136, -1127978619908, 311802403026, 470853242902, 0, -484751607858, 644108970612, 5252720868, 769255818538, 0, 0, 0, 1086554478540, 975649928900, 0, 231827646562, -951872155824, -393758135908, 0, 1007275494580, 91622748104, -530910718156, 33929974672, -617054756472, -638663145134, -402865448060, 620426412002, 0, 466723250164, -677093530616, -1728542905400, 473619308504, 1235565161206, 0, -1545347964386, 633954637320, 671273971696, 498807567192, 0, 0, 0, 565021746802, 1410368635830, 0, 1070710809712, -621484744932, -200802667852, 0, 1842954534120, -239885311356, -1080582834220, 175450699398, -1790026655406, -837020607070, -886799222824, 1047354162066, 0, 710807639184, -2303194973364, -539427651956, 457247647076, 738490518430, 0, -855876002156, 1229947321272, 780043624744, 533254518560, 0, 0, 0, 1091698540572, 1102538617198, 0, 1037014493340, -995345618634, -672327184550, 0, 1453409214708, -343703061432, -1501497629364, -505571514996, -588687153614, -1895132225608, -368220031064, 692005490742, 0, 997347036576, -1394068824664, -2742714035804, 605350557030, 1163291896808, 0, -1636751191132, 749887812664, 879874354760, 253096922862, 0, 0, 0, 156246152240, 2626926989202, 0, 1677732616260, -423676212936, -333608889940, 0, 3598696100010, -360609151204, -1766795051496, 45232129716, -2167226517244, -1004576116574, -1461951144144, 756639275446, 0, 1263118905232, -2796361452140, -1885894374828, 1110379845684, 384567288542, 0, -1502774149392, 326826107056, 1010687387718, 790983741008, 0, 0, 0, 1806162086692, 1019233012522, 0, 334917737882, -1004966182902, 129600425436, 0, 1988897662448, -429217730838, -1472417474162, 741758617394, -2277801368856, -2328145581684, -501430565788, 2030454268880, 0, 1778716655304, -1834332346188, -1413279301004, 270348176820, 2034419170930, 0, -1975037295480, -1024018820664, 1266417590974, 815200505326, 0, 0, 0, 1795571189176, 2017320294772, 0, 1704435558078, -1505805054640, -430935175392, 0, 2903190713722, 235175391514, -1434983290172, 309099634300, -1901835655772, -1378256069978, -2202320751164, 241185757798, 0, 360601958936, -1191527313220, -1225396384872, 853111310868, 838994422848, 0, -478573169940, 1142654051748, 1081677777256, 596082738048, 0, 0, 0, 2400614195828, 1392596200764, 0, 1762593764578, -2294186966704, -946583486888, 0, 1685783966068, -526079099094, -1173084790432, 764942034608, -742338039368, -1132533033968, -2661315183540, 1743371252582, 0, -784879083824, -1625545155832, -2992783777320, 578212258560, 2049950167116, 0, -1654848805428, 1331276726212, -354010013638, 1015471875618, 0, 0, 0, 2926819179848, 2422893478358, 0, -205715419568, 441057103400, -2508665024736, 0, 3023128606440, 856170620364, -915043394788, 697459833584, -2297842473956, 260691261446, -2771570853060, 1770435006708, 0, 78345059276, -1946590129452, -2037966276408, -215735606056, 1785144499010, 0, -2409230978036, 3241518327364, -1671743207620, 706555513212, 0, 0, 0, 1090233524336, -700112311826, 0, 722131085922, -1309343048660, -247228713504, 0, 1825388813714, 116855795940, -666572267436, -488705298404, 1429091427688, -793942845126, 1167910284772, -841156829842, 0, -2183444024208, -2014684658672, -1258855995820, 700562912244, 1460594783518, 0, 32827492646, 394803893916, -520749503780, 2519951363050, 0, 0, 0, -1886491539544, 1856523420532, 0, 140194633028, -799933299900, -1873515770176, 0, -348698939594, 559732375302, 343800398772, -1553250448086, -153138852492, -147408626978, -200666780500, 317575991724, 0, -1075952001128, 2063324268172, -2145353188648, 2355314374746, 1326711280428, 0, -1085761485474, 3018350435256, -1008748433124, -142686276956, 0, 0, 0, -1191481097812, 2050805700668, 0, -810574698644, 1469275123298, -1162059682938, 0, -1281008241446, -208369273912, 1191422673784, 612349030492, 1514154367646, 1422079945094, -2061299244880, -870524165400, 0, 899912273364, -3552430298656, -1249301853776, -2309345272394, 319433793350, 0, -279705789012, 2735699410656, 511520641092, -543024931998, 0, 0, 0, 253891455864, 1302657914696, 0, -2650933001520, 2370167100952, 930770811600, 0, -4149903382356, -577835497070, 6692333623856, -2081733127094, 3951387633108, 2935527786808, 4227602866304, -1954333740594, 0, 1584327661780, 2613666192580, 321352656580, 1079279642760, -1535964737750, 0, 704510645466, 3401143250324, -3124264256538, -1896023256046, 0, 0, 0, -2656548586228, -2294015598420, 0, 268457943584, -1395592133588, 1963593059362, 0, -5870813737408, -1527613903700, -64219386652, -5848009183194, 1700854729498, 2764105456878, 8972422616408, -2465559379316, 0, -3417148094288, -727244880512, -2295652959532, -682084234894, -1455751831520, 0, 5120098015632, -755822750384, -2745785363406, 2869038208310, 0, 0, 0, -4485061411908, -861120391644, 0, -3466879959470, 1591427261926, 3554968347870, 0, -3577892748504, 1295695794160, 5767166059060, 3498102389242, 4828538085540, -1401111553184, -4957996723284, -221363989518, 0, 2366786033660, 3998339577496, 8487398944124, -6039102433560, -5423199296760, 0, 1007214908302, -4796443314780, 353302233796, -7395917567488, 0, 0, 0, -5826581919604, -1636951570132, 0, -4155346562202, 866175910616, -2374531083830, 0, -7301508671088, 822312499536, 830769369904, -1103422806312, 8540911831928, 5016977589992, 4522982816780, -5800533222564, 0, -5444825633512, 9434692517868, 15475959908028, -2491773276510, -2190061554504, 0, 5909166006458, -3122642482216, -765511040190, -1186090012368, 0, 0, 0, -3075327319872, -12846812611176, 0, 1470484199784, 7406456437650, 5222975323162, 0, -8572171032948, 351805327628, -80624854864, 1601242376976, 236884583434, 4960585146514, 9631228033056, -576009682520, 0, -5709962296072, 9938848683248, 62013285716, -1350816036200, -6037321318480, 0, 10553328684804, -11091659156744, -20271106528, -4808790081142, 0, 0, 0, -2779225965084, -9697356263460, 0, -3889654466054, 8120485416192, 4984302798076, 0, -3622299567188, 1932188244336, -435722942936, 7236187377296, 1084142190972, 9214241833992, 3528498303932, -6960596279922, 0, -2224514220588, 7392210292652, 15549394624072, 275142046678, -9022816472592, 0, 4782944580624, -12041633392772, -5106883697508, -2624712542500, 0, 0, 0, -3727300331860, -16641275233300, 0, -10745094563448, -1880232503810, 8169517178772, 0, -11253862760562], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": true, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 29, 3, -1, 4, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "29.9.c.a", "char_is_minimal": true, "conrey_index": 12, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}