# Stored data for newform 48.23.e.a, downloaded from the LMFDB on 14 June 2024.
{"Nk2": 25392, "analytic_conductor": 147.21956872408825, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 3, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 2, "char_parity": -1, "char_values": [48, 2, [31, 37, 17], [2, 2, 1]], "cm_discs": [-3], "conrey_index": 17, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 0, "hecke_cutters": [[5, [0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 275263782960, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": false, "label": "48.23.e.a", "level": 48, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3], "level_radical": 6, "minimal_twist": "12.23.c.a", "nf_label": "1.1.1.1", "prim_orbit_index": 2, "qexp_display": "q+3^{11}q^{3}+3954581662q^{7}+3^{22}q^{9}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "22.2.1.d2", "self_twist_discs": [-3], "self_twist_type": 1, "space_label": "48.23.e", "trace_display": [0, 177147, 0, 3954581662], "trace_hash": 1224004077638057774, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.977", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.884", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.504", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 1, 0, 177147, 0, 0, 0, 3954581662, 0, 31381059609, 0, 0, 0, -3566264416198, 0, 0, 0, 0, 0, 211308066581014, 0, 700542277678314, 0, 0, 0, 2384185791015625, 0, 5559060566555523, 0, 0, 0, -11550498557326034, 0, 0, 0, 0, 0, 257128060064352074, 0, -631753042536227106, 0, 0, 0, -542156431674983642, 0, 0, 0, 0, 0, 11728895072843694195, 0, 0, 0, 0, 0, 0, 0, 37432590070626887058, 0, 0, 0, -67394602624928417446, 0, 124098962863880290158, 0, 0, 0, 5287275662394476662, 0, 0, 0, 0, 0, -235194739555780163854, 0, 422351360321044921875, 0, 0, 0, 414509648151065438542, 0, 984770902183611232881, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14103083862139746561076, 0, -2046136167934634944998, 0, 0, 0, -1618886660331792534142, 0, 0, 0, 0, 0, 22345726748523109190494, 0, 0, 0, 0, 0, 26518613812667723601146, 0, 45549464456219776852878, 0, 0, 0, 0, 0, -111913156226165023146582, 0, 0, 0, 81402749386839761113321, 0, 0, 0, 0, 0, 121296029839740252427246, 0, -96041385401928327229374, 0, 0, 0, 835635005133953001765268, 0, 0, 0, 0, 0, -572783790866399501650778, 0, 0, 0, 0, 0, 0, 0, 2077738575469041895561665, 0, 0, 0, -1671716651771127020236034, 0, 0, 0, 0, 0, -2541357050835456220574182, 0, 0, 0, 0, 0, 3223266518878810335026038, 0, 0, 0, 0, 0, 9506403008285206659617835, 0, 6631071033241341161663526, 0, 0, 0, 9428457407951354980468750, 0, 0, 0, 0, 0, 11618102909437065473992874, 0, -11938751671198194365306562, 0, 0, 0, 0, 0, 21983758974447801760619226, 0, 0, 0, 392181010196842561668482, 0, 0, 0, 0, 0, 35176217445621787621410334, 0, 936625021766194357243314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71232934099287005789122006, 0, 0, 0, 0, 0, -45677389781758989811588508, 0, -41664042528087788686244538, 0, 0, 0, -4787842736316088763618642, 0, 74818276426792144775390625, 0, 0, 0, -106248292973630273692958134, 0, 0, 0, 0, 0, 0, 0, 73429140641016789241399674, 0, 0, 0, 206285539140273775947061154, 0, 174449211009120179071170507, 0, 0, 0, -753580438703468006580864772, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1016833911116121251752066988, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1075828211346369024981518642, 0, -2498318996926469684054930172, 0, 0, 0, -948249400273832347913477782, 0, -362466883741116776601560706, 0, 0, 0, -1512309904508257317803157242, 0, 0, 0, 0, 0, 1174562876521148458974062689, 0, -286780915217796052045652874, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2144001882637246254803173004, 0, 0, 0, 0, 0, -2441835173825889744602111978, 0, 3958478456320623223768440618, 0, 0, 0, 3303161067224050732439392082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8502636948103904724121093750, 0, 4697692881072649232772210462, 0, 0, 0, 846525553051121798502080038, 0, 8068950980025964810156779066, 0, 0, 0, -7805427924944454350836914142, 0, 0, 0, 0, 0, 30921166750161931632142294652, 0, 0, 0, 0, 0, 10498238154134642474038937498, 0, -19825079885996455355347561554, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31081118584032154747623896235, 0, 14420252845630503161941475187, 0, 0, 0, -21701206965569561631856179698, 0, 0, 0, 0, 0, -26362866168453132750376272598, 0, 0, 0, 0, 0, -7371232303569164759813902586, 0, 21487227798020466496729347162, 0, 0, 0, 0, 0, -17013443299795397383701915978, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67948122591356303089689919418, 0, 148030234254464372403711930396, 0, 0, 0, 41192131994338169878956698732, 0, 0, 0, 0, 0, 17227290702054580863335933906, 0, 0, 0, 0, 0, 0, 0, -101466930200610072518930370366, 0, 0, 0, -146246019550328065702142331958, 0, 0, 0, 0, 0, -266517459658318983694632475252, 0, 0, 0, 0, 0, -98491925359235548166132184478, 0, 0, 0, 0, 0, -215816844773662240916142176066, 0, 368065155428614364673062269755, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -296139589711299838253752714998, 0, 0, 0, -168123075443366964642319580686, 0, 0, 0, 0, 0, -148492069249316856828063173426, 0, 0, 0, 0, 0, 20908963376444100417632172244, 0, -450193777484348563106054618754, 0, 0, 0, 503797689869437217712402343750, 0, 0, 0, 0, 0, -916986651013520827494740494652, 0, 0, 0, 0, 0, 114775432045667297311143188062, 0, 570991994019824614418857553586, 0, 0, 0, 0, 0, 0, 0, 0, 0, 270058948465753874387007418774, 0, 0, 0, 0, 0, 0, 0, 1684030773708699504131320616745, 0, 0, 0, -930096804046154262080383645348, 0, 1174674340325603862765208640322, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1197427700905823270395767309722, 0, 1670222944446358680725097656250, 0, 0, 0, 907846434775996175406740561329, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2298683668826705983775338833766, 0, 2058112076098047837521415650478, 0, 0, 0, -2199046427134684714770117222794, 0, -2114914042297746537230961538614, 0, 0, 0, 1639212253300275589020181216804, 0, 0, 0, 0, 0, 1933473190295376413318329833116, 0, 0, 0, 0, 0, 0, 0, 3894356951046504738488414028222, 0, 0, 0, 1417346504082764495129645905606, 0, 0, 0, 0, 0, 4664661796944360647064693733058, 0, 69473689413340069271886580854, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2440713518195355744776472318476, 0, 0, 0, 0, 0, 0, 0, 6231361391839562811769976437098, 0, 0, 0, -7122609411472158969541767914926, 0, 165920312730816031802581345158, 0, 0, 0, -8026523568789276738979670511314, 0, 0, 0, 0, 0, 2172349042237292758263832878026, 0, 0, 0, 0, 0, -9637988050149135565976383430426, 0, 0, 0, 0, 0, 5684341886080801486968994140625, 0, 0, 0, 0, 0, -1080522970077556083370201288514, 0, 12618700576886395214525595996882, 0, 0, 0, -41828341139602515762037316570610, 0, 0, 0, 0, 0, 6452873035441664291671270725814, 0, 0, 0, 0, 0, 0, 0, -8091612567669259768153469426676, 0, 0, 0, 0, 0, -7380660141723167502402161173086, 0, 0, 0, -17898786868842778135350200854678, 0, 0, 0, 0, 0, 0, 0, -848151977210186176208751574374, 0, 0, 0, 24224888723065085711729881138946, 0, 13253833214176948070526123046875, 0, 0, 0, -6402019499804529591106462104004, 0, 0, 0, 0, 0, 0, 0, -18821566355399682093886454563698, 0, 0, 0, -33479269723737489180523978749482, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54333233235925074990258339923036, 0, 0, 0, 0, 0, 45442926994333741138749942662666, 0, 13007751977134201163746228050078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88368001223772373187951237121028, 0, 36542864402082078587694042247638, 0, 0, 0, -32623060472934122381740192939778, 0, 30903154382632612361920641803529, 0, 0, 0, -47685087467664727843327995845734, 0, 0, 0, 0, 0, 68834397729433038256433596346422, 0, -133494513975003246961780451765484, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60304849984748953384008360505202, 0, 0, 0, 0, 0, 15735602856058490280477162573098, 0, 0, 0, 0, 0, 104870023885235683052376573784652, 0, 0, 0, 0, 0, -78010317715893666502714674080254, 0, 0, 0, 0, 0, -27538534539523205757141113281250, 0, 180129076852487531384123410723236, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30135950859528822282278544936938, 0, 0, 0, 0, 0, 240346973185086541004599228190308, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124854539476120816589616379912486, 0, -190579740155375233668401082874374, 0, 0, 0, -114562027361702410965865317772988, 0, -442569715348533325121278715179284, 0, 0, 0, 231079091778658325874357709784638, 0, 0, 0, 0, 0, -15991462208604175408599553435942, 0, -167979536510308578935828848647954, 0, 0, 0, 0, 0, -64209921054087613624636674385782, 0, 0, 0, 148852438543083302439338564577241, 0, 0, 0, 0, 0, 321913819961578263431199930519502, 0, -267901162653924259076875895948574, 0, 0, 0, -300873851129519961060830490158998, 0, 0, 0, 0, 0, -357193127029755577166549185586618, 0, 0, 0, 0, 0, 0, 0, 208070289887091886061878283168283, 0, 0, 0, -18855823053427132055787165771076, 0, -50802378788086917231731269670478, 0, 0, 0, -298836932452896163180239935111302, 0, 0, 0, 0, 0, -501425563826701445239006276960682, 0, 0, 0, 0, 0, 479675055277641601092038020762852, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -379803501503540262299617688139588, 0, 0, 0, -658679321723949192108963467522714, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -611950259693488798978790642780546, 0, -432563775537734890587030330566766, 0, 0, 0, 613041067276840386390686035156250, 0, 701232583101829442220907950156846, 0, 0, 0, 2478410140974182382494083009013730, 0, 0, 0, 0, 0, 952993020413645480786691090491378, 0, 585145073575538915099440989150054, 0, 0, 0, 0, 0, 0, 0, 0, 0, 838766630554735003903214091707092, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -512176681272347280294560865969405, 0, 0, 0, 0, 0, 838178084269445179618555256292766, 0, 0, 0, 0, 0, -2265120275651106561194105406833036, 0, -1506216627445762410163879394531250, 0, 0, 0, 0, 0, 832182200803376593637898766711914, 0, 0, 0, 0, 0, 0, 0, 0, 0, -457295843104690951603056386626514, 0, 149959462146347073239247972491586, 0, 0, 0, 1813068513468263875428280626069194, 0, 1429390459258659588224842941204702, 0], "weight": 23, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 0, 177147, 0, 0, 0, 3954581662, 0, 31381059609, 0, 0, 0, -3566264416198, 0, 0, 0, 0, 0, 211308066581014, 0, 700542277678314, 0, 0, 0, 2384185791015625, 0, 5559060566555523, 0, 0, 0, -11550498557326034, 0, 0, 0, 0, 0, 257128060064352074, 0, -631753042536227106, 0, 0, 0, -542156431674983642, 0, 0, 0, 0, 0, 11728895072843694195, 0, 0, 0, 0, 0, 0, 0, 37432590070626887058, 0, 0, 0, -67394602624928417446, 0, 124098962863880290158, 0, 0, 0, 5287275662394476662, 0, 0, 0, 0, 0, -235194739555780163854, 0, 422351360321044921875, 0, 0, 0, 414509648151065438542, 0, 984770902183611232881, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14103083862139746561076, 0, -2046136167934634944998, 0, 0, 0, -1618886660331792534142, 0, 0, 0, 0, 0, 22345726748523109190494, 0, 0, 0, 0, 0, 26518613812667723601146, 0, 45549464456219776852878, 0, 0, 0, 0, 0, -111913156226165023146582, 0, 0, 0, 81402749386839761113321, 0, 0, 0, 0, 0, 121296029839740252427246, 0, -96041385401928327229374, 0, 0, 0, 835635005133953001765268, 0, 0, 0, 0, 0, -572783790866399501650778, 0, 0, 0, 0, 0, 0, 0, 2077738575469041895561665, 0, 0, 0, -1671716651771127020236034, 0, 0, 0, 0, 0, -2541357050835456220574182, 0, 0, 0, 0, 0, 3223266518878810335026038, 0, 0, 0, 0, 0, 9506403008285206659617835, 0, 6631071033241341161663526, 0, 0, 0, 9428457407951354980468750, 0, 0, 0, 0, 0, 11618102909437065473992874, 0, -11938751671198194365306562, 0, 0, 0, 0, 0, 21983758974447801760619226, 0, 0, 0, 392181010196842561668482, 0, 0, 0, 0, 0, 35176217445621787621410334, 0, 936625021766194357243314, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71232934099287005789122006, 0, 0, 0, 0, 0, -45677389781758989811588508, 0, -41664042528087788686244538, 0, 0, 0, -4787842736316088763618642, 0, 74818276426792144775390625, 0, 0, 0, -106248292973630273692958134, 0, 0, 0, 0, 0, 0, 0, 73429140641016789241399674, 0, 0, 0, 206285539140273775947061154, 0, 174449211009120179071170507, 0, 0, 0, -753580438703468006580864772, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1016833911116121251752066988, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1075828211346369024981518642, 0, -2498318996926469684054930172, 0, 0, 0, -948249400273832347913477782, 0, -362466883741116776601560706, 0, 0, 0, -1512309904508257317803157242, 0, 0, 0, 0, 0, 1174562876521148458974062689, 0, -286780915217796052045652874, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2144001882637246254803173004, 0, 0, 0, 0, 0, -2441835173825889744602111978, 0, 3958478456320623223768440618, 0, 0, 0, 3303161067224050732439392082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8502636948103904724121093750, 0, 4697692881072649232772210462, 0, 0, 0, 846525553051121798502080038, 0, 8068950980025964810156779066, 0, 0, 0, -7805427924944454350836914142, 0, 0, 0, 0, 0, 30921166750161931632142294652, 0, 0, 0, 0, 0, 10498238154134642474038937498, 0, -19825079885996455355347561554, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31081118584032154747623896235, 0, 14420252845630503161941475187, 0, 0, 0, -21701206965569561631856179698, 0, 0, 0, 0, 0, -26362866168453132750376272598, 0, 0, 0, 0, 0, -7371232303569164759813902586, 0, 21487227798020466496729347162, 0, 0, 0, 0, 0, -17013443299795397383701915978, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67948122591356303089689919418, 0, 148030234254464372403711930396, 0, 0, 0, 41192131994338169878956698732, 0, 0, 0, 0, 0, 17227290702054580863335933906, 0, 0, 0, 0, 0, 0, 0, -101466930200610072518930370366, 0, 0, 0, -146246019550328065702142331958, 0, 0, 0, 0, 0, -266517459658318983694632475252, 0, 0, 0, 0, 0, -98491925359235548166132184478, 0, 0, 0, 0, 0, -215816844773662240916142176066, 0, 368065155428614364673062269755, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -296139589711299838253752714998, 0, 0, 0, -168123075443366964642319580686, 0, 0, 0, 0, 0, -148492069249316856828063173426, 0, 0, 0, 0, 0, 20908963376444100417632172244, 0, -450193777484348563106054618754, 0, 0, 0, 503797689869437217712402343750, 0, 0, 0, 0, 0, -916986651013520827494740494652, 0, 0, 0, 0, 0, 114775432045667297311143188062, 0, 570991994019824614418857553586, 0, 0, 0, 0, 0, 0, 0, 0, 0, 270058948465753874387007418774, 0, 0, 0, 0, 0, 0, 0, 1684030773708699504131320616745, 0, 0, 0, -930096804046154262080383645348, 0, 1174674340325603862765208640322, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1197427700905823270395767309722, 0, 1670222944446358680725097656250, 0, 0, 0, 907846434775996175406740561329, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2298683668826705983775338833766, 0, 2058112076098047837521415650478, 0, 0, 0, -2199046427134684714770117222794, 0, -2114914042297746537230961538614, 0, 0, 0, 1639212253300275589020181216804, 0, 0, 0, 0, 0, 1933473190295376413318329833116, 0, 0, 0, 0, 0, 0, 0, 3894356951046504738488414028222, 0, 0, 0, 1417346504082764495129645905606, 0, 0, 0, 0, 0, 4664661796944360647064693733058, 0, 69473689413340069271886580854, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2440713518195355744776472318476, 0, 0, 0, 0, 0, 0, 0, 6231361391839562811769976437098, 0, 0, 0, -7122609411472158969541767914926, 0, 165920312730816031802581345158, 0, 0, 0, -8026523568789276738979670511314, 0, 0, 0, 0, 0, 2172349042237292758263832878026, 0, 0, 0, 0, 0, -9637988050149135565976383430426, 0, 0, 0, 0, 0, 5684341886080801486968994140625, 0, 0, 0, 0, 0, -1080522970077556083370201288514, 0, 12618700576886395214525595996882, 0, 0, 0, -41828341139602515762037316570610, 0, 0, 0, 0, 0, 6452873035441664291671270725814, 0, 0, 0, 0, 0, 0, 0, -8091612567669259768153469426676, 0, 0, 0, 0, 0, -7380660141723167502402161173086, 0, 0, 0, -17898786868842778135350200854678, 0, 0, 0, 0, 0, 0, 0, -848151977210186176208751574374, 0, 0, 0, 24224888723065085711729881138946, 0, 13253833214176948070526123046875, 0, 0, 0, -6402019499804529591106462104004, 0, 0, 0, 0, 0, 0, 0, -18821566355399682093886454563698, 0, 0, 0, -33479269723737489180523978749482, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54333233235925074990258339923036, 0, 0, 0, 0, 0, 45442926994333741138749942662666, 0, 13007751977134201163746228050078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88368001223772373187951237121028, 0, 36542864402082078587694042247638, 0, 0, 0, -32623060472934122381740192939778, 0, 30903154382632612361920641803529, 0, 0, 0, -47685087467664727843327995845734, 0, 0, 0, 0, 0, 68834397729433038256433596346422, 0, -133494513975003246961780451765484, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60304849984748953384008360505202, 0, 0, 0, 0, 0, 15735602856058490280477162573098, 0, 0, 0, 0, 0, 104870023885235683052376573784652, 0, 0, 0, 0, 0, -78010317715893666502714674080254, 0, 0, 0, 0, 0, -27538534539523205757141113281250, 0, 180129076852487531384123410723236, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30135950859528822282278544936938, 0, 0, 0, 0, 0, 240346973185086541004599228190308, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124854539476120816589616379912486, 0, -190579740155375233668401082874374, 0, 0, 0, -114562027361702410965865317772988, 0, -442569715348533325121278715179284, 0, 0, 0, 231079091778658325874357709784638, 0, 0, 0, 0, 0, -15991462208604175408599553435942, 0, -167979536510308578935828848647954, 0, 0, 0, 0, 0, -64209921054087613624636674385782, 0, 0, 0, 148852438543083302439338564577241, 0, 0, 0, 0, 0, 321913819961578263431199930519502, 0, -267901162653924259076875895948574, 0, 0, 0, -300873851129519961060830490158998, 0, 0, 0, 0, 0, -357193127029755577166549185586618, 0, 0, 0, 0, 0, 0, 0, 208070289887091886061878283168283, 0, 0, 0, -18855823053427132055787165771076, 0, -50802378788086917231731269670478, 0, 0, 0, -298836932452896163180239935111302, 0, 0, 0, 0, 0, -501425563826701445239006276960682, 0, 0, 0, 0, 0, 479675055277641601092038020762852, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -379803501503540262299617688139588, 0, 0, 0, -658679321723949192108963467522714, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -611950259693488798978790642780546, 0, -432563775537734890587030330566766, 0, 0, 0, 613041067276840386390686035156250, 0, 701232583101829442220907950156846, 0, 0, 0, 2478410140974182382494083009013730, 0, 0, 0, 0, 0, 952993020413645480786691090491378, 0, 585145073575538915099440989150054, 0, 0, 0, 0, 0, 0, 0, 0, 0, 838766630554735003903214091707092, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -512176681272347280294560865969405, 0, 0, 0, 0, 0, 838178084269445179618555256292766, 0, 0, 0, 0, 0, -2265120275651106561194105406833036, 0, -1506216627445762410163879394531250, 0, 0, 0, 0, 0, 832182200803376593637898766711914, 0, 0, 0, 0, 0, 0, 0, 0, 0, -457295843104690951603056386626514, 0, 149959462146347073239247972491586, 0, 0, 0, 1813068513468263875428280626069194, 0, 1429390459258659588224842941204702, 0]}