LMFDB - Embedded newform 1.104.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,104,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 104, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 104);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 104 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$67.1843880807$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3 x^{7} + \cdots + 10\!\cdots\!50 $ x^8 - 3x^7 - 110283155023106816031125934721x^6 - 277756125200616111944957306998121362507407x^5 + 3615145056187152647091917675184148606484802560193938764821x^4 - 4774138117848826898639724516318231553744017867877724139494624739712905x^3 - 36334369037932662462346573394466943229349842004727405236161831501966195279473330193275x^2 + 172728417031650434910498074262630444968168617983190890654058108274285387537868605493689180015974875*x + 101461061269920389859822710291212890633390824429836134060111062767619447438513563789688253635879869357294426723750
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{104}\cdot 3^{40}\cdot 5^{12}\cdot 7^{8}\cdot 11\cdot 13^{3}\cdot 17^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$8.06342e13$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.38660e15 q^{2} +4.94875e24 q^{3} -8.21853e30 q^{4} -1.47562e36 q^{5} -6.86195e39 q^{6} +3.27966e43 q^{7} +2.54577e46 q^{8} +1.05749e49 q^{9} +O(q^{10})$	\(q-1.38660e15 q^{2} +4.94875e24 q^{3} -8.21853e30 q^{4} -1.47562e36 q^{5} -6.86195e39 q^{6} +3.27966e43 q^{7} +2.54577e46 q^{8} +1.05749e49 q^{9} +2.04610e51 q^{10} -1.87140e52 q^{11} -4.06714e55 q^{12} -1.80976e57 q^{13} -4.54760e58 q^{14} -7.30247e60 q^{15} +4.80460e61 q^{16} +4.46350e61 q^{17} -1.46632e64 q^{18} -1.38718e66 q^{19} +1.21274e67 q^{20} +1.62302e68 q^{21} +2.59489e67 q^{22} +1.24176e70 q^{23} +1.25984e71 q^{24} +1.19138e72 q^{25} +2.50942e72 q^{26} -1.65303e73 q^{27} -2.69540e74 q^{28} -3.27288e75 q^{29} +1.01256e76 q^{30} +9.03121e76 q^{31} -3.24793e77 q^{32} -9.26107e76 q^{33} -6.18911e76 q^{34} -4.83954e79 q^{35} -8.69101e79 q^{36} +3.03788e80 q^{37} +1.92347e81 q^{38} -8.95602e81 q^{39} -3.75659e82 q^{40} +1.50080e83 q^{41} -2.25049e83 q^{42} +2.40163e84 q^{43} +1.53801e83 q^{44} -1.56045e85 q^{45} -1.72184e85 q^{46} -3.60725e84 q^{47} +2.37768e86 q^{48} -3.38056e85 q^{49} -1.65197e87 q^{50} +2.20887e86 q^{51} +1.48735e88 q^{52} -9.21270e87 q^{53} +2.29210e88 q^{54} +2.76147e88 q^{55} +8.34927e89 q^{56} -6.86481e90 q^{57} +4.53819e90 q^{58} +1.63460e91 q^{59} +6.00156e91 q^{60} -9.20037e91 q^{61} -1.25227e92 q^{62} +3.46821e92 q^{63} -3.68858e91 q^{64} +2.67051e93 q^{65} +1.28414e92 q^{66} +1.05409e94 q^{67} -3.66834e92 q^{68} +6.14518e94 q^{69} +6.71053e94 q^{70} +3.92423e95 q^{71} +2.69212e95 q^{72} +2.83774e95 q^{73} -4.21234e95 q^{74} +5.89582e96 q^{75} +1.14006e97 q^{76} -6.13755e95 q^{77} +1.24185e97 q^{78} +2.16532e97 q^{79} -7.08977e97 q^{80} -2.28956e98 q^{81} -2.08102e98 q^{82} +4.78462e98 q^{83} -1.33389e99 q^{84} -6.58643e97 q^{85} -3.33011e99 q^{86} -1.61966e100 q^{87} -4.76415e98 q^{88} +3.22127e100 q^{89} +2.16373e100 q^{90} -5.93539e100 q^{91} -1.02055e101 q^{92} +4.46932e101 q^{93} +5.00183e99 q^{94} +2.04695e102 q^{95} -1.60732e102 q^{96} +7.81604e101 q^{97} +4.68750e100 q^{98} -1.97898e101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 43\!\cdots\!40 q^{2}+ \cdots + 35\!\cdots\!16 q^{9}+O(q^{10}) $ 8 * q + 4388929556680440 * q^2 + 5087569706910766050323040 * q^3 + 48324394003700265820897106483264 * q^4 + 551645266991094947988587979858507120 * q^5 + 2626953258123361256046267420263544594336 * q^6 + 41737594138377573148159523392718424208446400 * q^7 + 109882609245772353721829965115065527112449646080 * q^8 + 35934061358184471683999399496530848001601644543016 * q^9	$ 8 q + 43\!\cdots\!40 q^{2}+ \cdots - 72\!\cdots\!88 q^{99}+O(q^{100}) $ 8 * q + 4388929556680440 * q^2 + 5087569706910766050323040 * q^3 + 48324394003700265820897106483264 * q^4 + 551645266991094947988587979858507120 * q^5 + 2626953258123361256046267420263544594336 * q^6 + 41737594138377573148159523392718424208446400 * q^7 + 109882609245772353721829965115065527112449646080 * q^8 + 35934061358184471683999399496530848001601644543016 * q^9 + 2027618525260516073181410940373995286751686815077520 * q^10 - 53564255892798621618914292149029865323976089024126944 * q^11 + 25633960574085217446823189913789134273379599963259585280 * q^12 - 1551327849817932010092927923451244764349197489311375245520 * q^13 + 204985531745225680495392627955462650660602632112553429561408 * q^14 - 3020750766469193774466110593818157380300334453782433876013760 * q^15 + 361863449936885119768267973598726020537150452888847981908594688 * q^16 + 2015497649979997361336875976150254045164880842011155416684792720 * q^17 + 267307540106838323861864757930082029915233950378733807409255489240 * q^18 + 1484734834072313889071781871918609444991921518407889999862194156000 * q^19 + 2550001838610112272657033084622870492091806723524425439331785816960 * q^20 - 468651934282513875675935203933822637725944475261560345505782668354304 * q^21 - 137605849219876342207658729678467678698030207344807412231509580517920 * q^22 + 40599619287653938731347770176481184954623812150658724038701540865523520 * q^23 + 417632054269801118353552142462197805319757108882280256182409075047884800 * q^24 - 362937074225983688614876200177837163768974389374609498487470358942710600 * q^25 - 14030741852054819908281579342280387163553452467847954283089945570102881584 * q^26 + 6310451948770981419229340353143176080605163694982014782921106225679184320 * q^27 + 514148330168929069137279753066565726408108706760021137474482330032788078080 * q^28 - 1109314641409183093552976605346965837461990086922169583222454360155329880400 * q^29 - 31780974033428375753830150804412858338763487684738816318474129735272931696960 * q^30 + 104264780455232531257795764608297281101784409237357406959070797687652099233536 * q^31 + 1028908566996694821915427200010950055520054418022728660586770754660435042467840 * q^32 + 1637064370206527961191840416792241672318252830384788267847230786245723880401280 * q^33 - 16880249585595311287790910689090067879202031794055262067512201336945927884230032 * q^34 - 15809814583992711056872904141791269441389432991285782813731594074561867170321280 * q^35 + 805787623574605247165419461734624389987695467909486995221520106404473098849425728 * q^36 - 92541276402281504667713648425023541514489587998355774759921151431265396409265040 * q^37 + 1971300306790799032342240078744393153702898113403645290763243656535920191023423520 * q^38 - 7885389189078955664633112105466856010714545616525346076007201630144160874672246208 * q^39 + 1977015288844745924714331362379506784318231603612597717318543376316436008269440000 * q^40 + 222749082810191111691395557742339640725571297200098840306597511963716166910016506576 * q^41 - 1883267638769361387897797057480679095562739407538640601371566884432999969422842010880 * q^42 + 968895197607192930930940008787782675398644318852140770090896736295885033488529690400 * q^43 + 2615800371528018307641663183711908967442008589707371423475870586505299691562914926848 * q^44 - 1473010112873063959626609346390652156643077000013339776241472977560123315435112983760 * q^45 + 27446065195956198075877779014773406391109527885085904763819008268953431741208364616896 * q^46 - 293609653174290525998217973440321639247924396408373610899942779596119844480753010677120 * q^47 + 1240474483651634936656271628196732975278107731060035918088958893365811804822813860741120 * q^48 + 2668551616424529602044449137134709537764999196283756605526691963266904852724306068111944 * q^49 - 6521555021853481798089331632691717210870069276041958186139599024744619050092391455132600 * q^50 - 20813334460690950021193410586099062172982223916797529091846346968717683910092635969470784 * q^51 - 36075131888471074369144062637736452287512569193963836276062247375366142706627591324022400 * q^52 + 161574805302535676592212552212935130219348465152378468526413124882553154054403888166112240 * q^53 + 244996591061285005233721911255171344371445084231598513861031145908120404974069967807566400 * q^54 - 607939909864004614075356036982415128356301156312798815333086681706442442074797191568452160 * q^55 - 503347948801547505295544537202800039798463622449253526436143518261972796907682627548672000 * q^56 + 5585281202236608576148075500959180617113370740733374350303663601038337658261844358331674240 * q^57 + 10803107862759337782251611301310445432173113486135052277293695910012872510635542918433350480 * q^58 - 3763669177454952719015429893224775020266577352512033436736083012099637155611183545807925600 * q^59 - 44516663894047516283340986041100025029890327265561963837781098524475428602375001706220910080 * q^60 + 56147145392217940296237629782250660517556168142847888898434987753570576599200638389784423856 * q^61 + 708807506014393204305112275358657132745269481108345030482782405369277364762268787441349556480 * q^62 + 1004547917742295582189356352643083605257294414907733584799000902948644764606451215157969453760 * q^63 + 2689955130199770090919426143081142657167991663226807770013236363849718691785612797260291375104 * q^64 + 5124254892052438764657504605348539922002660919805937289990918847816257298286298313919564321440 * q^65 + 36460770617845857205288107920138564493995889702559578221696109246179691643034860902124792436352 * q^66 + 36212058392130762275437269862682052845105568281986303679248701513796303582516933489238204852320 * q^67 + 121871257184262948410168536656451503789769474779037040449473211419440774288140532505483576282240 * q^68 + 146171714897241059447510875608282423246804848799861315408644138710655320106224092813159842449152 * q^69 + 853756690279911250368037438486434151435346605497824981233696852732671552949658306872737406389120 * q^70 + 1323027110921369091114059758958942708535901440060160919331826835683096477433051757156908929999296 * q^71 + 5635474260733453081095589332277842775365114507654390044914919885310203213431471309882290635036160 * q^72 + 4434337224305117877569754735641925591340191550850949206294860286939824237219014387268913705824720 * q^73 + 9446978778046296456470116730008064896416484139132353834625710442657435714245141545863045630195088 * q^74 + 15788198796594475882673542236654839411090926672421130688549340631916075230881024844909417441328800 * q^75 + 62208878575567502646775884731743768059494074065603793769837837917746101674437608641395557819334400 * q^76 + 37781769005935846521801726968449743374817416956894448777845288067504206491843901930831867790380800 * q^77 + 44019466816742377243458217012569984532155201470078975456308994008831948835905199650013699349604800 * q^78 + 24360542002769992615028834274408332054107188048024574794369918904382062971902552671267968844374400 * q^79 - 257406550547438596244863901420403525688280266364441018588431059738298545930906704910071981299015680 * q^80 - 319858452590968976040706219061802261896767071034600475754637194160339936835204759950912194010523832 * q^81 - 347037715568344180193612732627815416282275947315627995720995526007231252178377268346955612809946320 * q^82 - 2589709199921534719789158381824365674651513931126861560377010891589296789100538920269990341311172640 * q^83 - 14763276600099218032093350675578467421653757870459793949112274722608304409453274353718894336536287232 * q^84 - 7750041700239420480976421024168094692666091522883832659906501732615678081854865932331016250083918880 * q^85 - 22862474248159310408090160685058395474537452344937345785285404938278205476818797847965682857887379744 * q^86 - 19667171614563900919678037177279936924594588506587176946944336641584005321373812755132416018759906240 * q^87 - 40280517105348128384004030315972727789809528309384337508840799111515821927415232196104998546661181440 * q^88 - 2411931583959929374872883405418443793306523554844108736778614462710442635343758894445178420208577200 * q^89 + 19218417888800936875567136220118837811145582599884634713838228828686741391845969008376636752235577040 * q^90 + 157061027064080129827172588737919758324770125960416982485587688356910129161874310994817267624768962176 * q^91 + 773615141308510753640652909662430286328720511338068191045295874258285130068299519150171249463376222720 * q^92 + 1017145077013570534640298063884056653140131362969292242328097944460668594729564068877620396903861703680 * q^93 + 727087863890952033548300791290895488242032063484702253117314469808013304697569232190083038540113931648 * q^94 + 2743732154506646909406097298325321408379587730896118185195801036752841998424162414172669753574660712000 * q^95 + 8873312662336745259606299368794125872185792644230053366160730387846004935345208576954549405340151709696 * q^96 + 5002945503247003905009597326381275147828980571278924405638622881444475469921369111184405290832776414480 * q^97 + 8807510378044686174684586237206775917067603624837914322579837506936931417303594998092206302439262913720 * q^98 - 7247372384990122262319746951941725843983906615680409319965154257589720777414294443683699540960522497888 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.38660e15	−0.435420	−0.217710	−	0.976014i	$-0.569859\pi$
$2$	−1.38660e15	−0.435420	−0.217710	+	0.976014i	$0.569859\pi$
$3$	4.94875e24	1.32663	0.663316	−	0.748339i	$-0.269148\pi$
$3$	4.94875e24	1.32663	0.663316	+	0.748339i	$0.269148\pi$
$4$	−8.21853e30	−0.810410
$5$	−1.47562e36	−1.48600	−0.743001	−	0.669291i	$-0.766598\pi$
$5$	−1.47562e36	−1.48600	−0.743001	+	0.669291i	$0.766598\pi$
$6$	−6.86195e39	−0.577642
$7$	3.27966e43	0.984647	0.492323	−	0.870412i	$-0.336148\pi$
$7$	3.27966e43	0.984647	0.492323	+	0.870412i	$0.336148\pi$
$8$	2.54577e46	0.788288
$9$	1.05749e49	0.759953
$10$	2.04610e51	0.647034
$11$	−1.87140e52	−0.0436961	−0.0218480	−	0.999761i	$-0.506955\pi$
$11$	−1.87140e52	−0.0436961	−0.0218480	+	0.999761i	$0.506955\pi$
$12$	−4.06714e55	−1.07512
$13$	−1.80976e57	−0.775421	−0.387710	−	0.921781i	$-0.626734\pi$
$13$	−1.80976e57	−0.775421	−0.387710	+	0.921781i	$0.626734\pi$
$14$	−4.54760e58	−0.428734
$15$	−7.30247e60	−1.97138
$16$	4.80460e61	0.467174
$17$	4.46350e61	0.0191230	0.00956151	−	0.999954i	$-0.496956\pi$
$17$	4.46350e61	0.0191230	0.00956151	+	0.999954i	$0.496956\pi$
$18$	−1.46632e64	−0.330898
$19$	−1.38718e66	−1.93340	−0.966702	−	0.255904i	$-0.917627\pi$
$19$	−1.38718e66	−1.93340	−0.966702	+	0.255904i	$0.917627\pi$
$20$	1.21274e67	1.20427
$21$	1.62302e68	1.30626
$22$	2.59489e67	0.0190261
$23$	1.24176e70	0.922689	0.461345	−	0.887221i	$-0.347367\pi$
$23$	1.24176e70	0.922689	0.461345	+	0.887221i	$0.347367\pi$
$24$	1.25984e71	1.04577
$25$	1.19138e72	1.20820
$26$	2.50942e72	0.337633
$27$	−1.65303e73	−0.318454
$28$	−2.69540e74	−0.797967
$29$	−3.27288e75	−1.59013	−0.795065	−	0.606524i	$-0.792563\pi$
$29$	−3.27288e75	−1.59013	−0.795065	+	0.606524i	$0.792563\pi$
$30$	1.01256e76	0.858376
$31$	9.03121e76	1.41455	0.707276	−	0.706938i	$-0.249924\pi$
$31$	9.03121e76	1.41455	0.707276	+	0.706938i	$0.249924\pi$
$32$	−3.24793e77	−0.991704
$33$	−9.26107e76	−0.0579686
$34$	−6.18911e76	−0.00832653
$35$	−4.83954e79	−1.46319
$36$	−8.69101e79	−0.615873
$37$	3.03788e80	0.525027	0.262513	−	0.964928i	$-0.415449\pi$
$37$	3.03788e80	0.525027	0.262513	+	0.964928i	$0.415449\pi$
$38$	1.92347e81	0.841842
$39$	−8.95602e81	−1.02870
$40$	−3.75659e82	−1.17140
$41$	1.50080e83	1.31206	0.656031	−	0.754734i	$-0.272234\pi$
$41$	1.50080e83	1.31206	0.656031	+	0.754734i	$0.272234\pi$
$42$	−2.25049e83	−0.568773
$43$	2.40163e84	1.80668	0.903338	−	0.428930i	$-0.141109\pi$
$43$	2.40163e84	1.80668	0.903338	+	0.428930i	$0.141109\pi$
$44$	1.53801e83	0.0354117
$45$	−1.56045e85	−1.12929
$46$	−1.72184e85	−0.401757
$47$	−3.60725e84	−0.0278059	−0.0139029	−	0.999903i	$-0.504426\pi$
$47$	−3.60725e84	−0.0278059	−0.0139029	+	0.999903i	$0.504426\pi$
$48$	2.37768e86	0.619768
$49$	−3.38056e85	−0.0304712
$50$	−1.65197e87	−0.526074
$51$	2.20887e86	0.0253692
$52$	1.48735e88	0.628408
$53$	−9.21270e87	−0.145942	−0.0729709	−	0.997334i	$-0.523248\pi$
$53$	−9.21270e87	−0.145942	−0.0729709	+	0.997334i	$0.523248\pi$
$54$	2.29210e88	0.138661
$55$	2.76147e88	0.0649325
$56$	8.34927e89	0.776185
$57$	−6.86481e90	−2.56492
$58$	4.53819e90	0.692374
$59$	1.63460e91	1.03403	0.517015	−	0.855977i	$-0.327043\pi$
$59$	1.63460e91	1.03403	0.517015	+	0.855977i	$0.327043\pi$
$60$	6.00156e91	1.59762
$61$	−9.20037e91	−1.04549	−0.522744	−	0.852490i	$-0.675092\pi$
$61$	−9.20037e91	−1.04549	−0.522744	+	0.852490i	$0.675092\pi$
$62$	−1.25227e92	−0.615923
$63$	3.46821e92	0.748285
$64$	−3.68858e91	−0.0353664
$65$	2.67051e93	1.15228
$66$	1.28414e92	0.0252407
$67$	1.05409e94	0.955045	0.477522	−	0.878620i	$-0.341535\pi$
$67$	1.05409e94	0.955045	0.477522	+	0.878620i	$0.341535\pi$
$68$	−3.66834e92	−0.0154975
$69$	6.14518e94	1.22407
$70$	6.71053e94	0.637100
$71$	3.92423e95	1.79452	0.897261	−	0.441500i	$-0.145553\pi$
$71$	3.92423e95	1.79452	0.897261	+	0.441500i	$0.145553\pi$
$72$	2.69212e95	0.599062
$73$	2.83774e95	0.310345	0.155173	−	0.987887i	$-0.450407\pi$
$73$	2.83774e95	0.310345	0.155173	+	0.987887i	$0.450407\pi$
$74$	−4.21234e95	−0.228607
$75$	5.89582e96	1.60284
$76$	1.14006e97	1.56685
$77$	−6.13755e95	−0.0430252
$78$	1.24185e97	0.447915
$79$	2.16532e97	0.405254	0.202627	−	0.979256i	$-0.435052\pi$
$79$	2.16532e97	0.405254	0.202627	+	0.979256i	$0.435052\pi$
$80$	−7.08977e97	−0.694221
$81$	−2.28956e98	−1.18242
$82$	−2.08102e98	−0.571297
$83$	4.78462e98	0.703600	0.351800	−	0.936075i	$-0.385570\pi$
$83$	4.78462e98	0.703600	0.351800	+	0.936075i	$0.385570\pi$
$84$	−1.33389e99	−1.05861
$85$	−6.58643e97	−0.0284168
$86$	−3.33011e99	−0.786662
$87$	−1.61966e100	−2.10952
$88$	−4.76415e98	−0.0344451
$89$	3.22127e100	1.30149	0.650747	−	0.759295i	$-0.274456\pi$
$89$	3.22127e100	1.30149	0.650747	+	0.759295i	$0.274456\pi$
$90$	2.16373e100	0.491716
$91$	−5.93539e100	−0.763515
$92$	−1.02055e101	−0.747757
$93$	4.46932e101	1.87659
$94$	5.00183e99	0.0121072
$95$	2.04695e102	2.87304
$96$	−1.60732e102	−1.31563
$97$	7.81604e101	0.375182	0.187591	−	0.982247i	$-0.439932\pi$
$97$	7.81604e101	0.375182	0.187591	+	0.982247i	$0.439932\pi$
$98$	4.68750e100	0.0132678
$99$	−1.97898e101	−0.0332070
$100$	−9.79137e102	−0.979137
$101$	3.84808e101	0.0230512	0.0115256	−	0.999934i	$-0.496331\pi$
$101$	3.84808e101	0.0230512	0.0115256	+	0.999934i	$0.496331\pi$
$102$	−3.06284e101	−0.0110462
$103$	6.60422e102	0.144113	0.0720567	−	0.997401i	$-0.477044\pi$
$103$	6.60422e102	0.144113	0.0720567	+	0.997401i	$0.477044\pi$
$104$	−4.60722e103	−0.611255
$105$	−2.39496e104	−1.94111
$106$	1.27744e103	0.0635459
$107$	−5.35561e103	−0.164265	−0.0821323	−	0.996621i	$-0.526173\pi$
$107$	−5.35561e103	−0.164265	−0.0821323	+	0.996621i	$0.526173\pi$
$108$	1.35855e104	0.258078
$109$	1.12941e105	1.33471	0.667356	−	0.744739i	$-0.267426\pi$
$109$	1.12941e105	1.33471	0.667356	+	0.744739i	$0.267426\pi$
$110$	−3.82907e103	−0.0282729
$111$	1.50337e105	0.696517
$112$	1.57575e105	0.460001
$113$	−2.39902e104	−0.0443092	−0.0221546	−	0.999755i	$-0.507053\pi$
$113$	−2.39902e104	−0.0443092	−0.0221546	+	0.999755i	$0.507053\pi$
$114$	9.51877e105	1.11681
$115$	−1.83237e106	−1.37112
$116$	2.68982e106	1.28866
$117$	−1.91380e106	−0.589283
$118$	−2.26654e106	−0.450237
$119$	1.46388e105	0.0188294
$120$	−1.85904e107	−1.55401
$121$	−1.83070e107	−0.998091
$122$	1.27573e107	0.455226
$123$	7.42708e107	1.74062
$124$	−7.42233e107	−1.14637
$125$	−3.02946e107	−0.309385
$126$	−4.80904e107	−0.325818
$127$	−9.06897e105	−0.00408946	−0.00204473	−	0.999998i	$-0.500651\pi$
$127$	−9.06897e105	−0.00408946	−0.00204473	+	0.999998i	$0.500651\pi$
$128$	3.34493e108	1.00710
$129$	1.18850e109	2.39679
$130$	−3.70294e108	−0.501723
$131$	5.86233e108	0.535302	0.267651	−	0.963516i	$-0.413753\pi$
$131$	5.86233e108	0.535302	0.267651	+	0.963516i	$0.413753\pi$
$132$	7.61124e107	0.0469784
$133$	−4.54949e109	−1.90372
$134$	−1.46160e109	−0.415845
$135$	2.43924e109	0.473223
$136$	1.13630e108	0.0150744
$137$	−7.10352e109	−0.646196	−0.323098	−	0.946365i	$-0.604724\pi$
$137$	−7.10352e109	−0.646196	−0.323098	+	0.946365i	$0.604724\pi$
$138$	−8.52093e109	−0.532984
$139$	−1.49203e110	−0.643451	−0.321726	−	0.946833i	$-0.604263\pi$
$139$	−1.49203e110	−0.643451	−0.321726	+	0.946833i	$0.604263\pi$
$140$	3.97739e110	1.18578
$141$	−1.78514e109	−0.0368882
$142$	−5.44135e110	−0.781370
$143$	3.38677e109	0.0338829
$144$	5.08082e110	0.355030
$145$	4.82952e111	2.36294
$146$	−3.93482e110	−0.135130
$147$	−1.67295e110	−0.0404241
$148$	−2.49669e111	−0.425487
$149$	3.48025e110	0.0419293	0.0209646	−	0.999780i	$-0.493326\pi$
$149$	3.48025e110	0.0419293	0.0209646	+	0.999780i	$0.493326\pi$
$150$	−8.17517e111	−0.697906
$151$	1.86956e112	1.13351	0.566757	−	0.823885i	$-0.308198\pi$
$151$	1.86956e112	1.13351	0.566757	+	0.823885i	$0.308198\pi$
$152$	−3.53144e112	−1.52408
$153$	4.72011e110	0.0145326
$154$	8.51036e110	0.0187340
$155$	−1.33266e113	−2.10202
$156$	7.36054e112	0.833667
$157$	5.49138e112	0.447558	0.223779	−	0.974640i	$-0.428161\pi$
$157$	5.49138e112	0.447558	0.223779	+	0.974640i	$0.428161\pi$
$158$	−3.00244e112	−0.176455
$159$	−4.55913e112	−0.193611
$160$	4.79270e113	1.47367
$161$	4.07257e113	0.908523
$162$	3.17471e113	0.514851
$163$	−1.91395e113	−0.226083	−0.113042	−	0.993590i	$-0.536059\pi$
$163$	−1.91395e113	−0.226083	−0.113042	+	0.993590i	$0.536059\pi$
$164$	−1.23344e114	−1.06331
$165$	1.36658e113	0.0861415
$166$	−6.63438e113	−0.306361
$167$	1.92884e113	0.0653729	0.0326864	−	0.999466i	$-0.489594\pi$
$167$	1.92884e113	0.0653729	0.0326864	+	0.999466i	$0.489594\pi$
$168$	4.13184e114	1.02971
$169$	−2.17188e114	−0.398723
$170$	9.13278e112	0.0123732
$171$	−1.46693e115	−1.46930
$172$	−1.97378e115	−1.46415
$173$	−5.88175e114	−0.323692	−0.161846	−	0.986816i	$-0.551745\pi$
$173$	−5.88175e114	−0.323692	−0.161846	+	0.986816i	$0.551745\pi$
$174$	2.24583e115	0.918525
$175$	3.90732e115	1.18965
$176$	−8.99132e113	−0.0204137
$177$	8.08922e115	1.37178
$178$	−4.46663e115	−0.566696
$179$	−4.29767e115	−0.408604	−0.204302	−	0.978908i	$-0.565492\pi$
$179$	−4.29767e115	−0.408604	−0.204302	+	0.978908i	$0.565492\pi$
$180$	1.28246e116	0.915189
$181$	7.62899e115	0.409280	0.204640	−	0.978837i	$-0.434398\pi$
$181$	7.62899e115	0.409280	0.204640	+	0.978837i	$0.434398\pi$
$182$	8.23004e115	0.332449
$183$	−4.55303e116	−1.38698
$184$	3.16125e116	0.727345
$185$	−4.48275e116	−0.780190
$186$	−6.19717e116	−0.817104
$187$	−8.35298e113	−0.000835601 0
$188$	2.96463e115	0.0225342
$189$	−5.42138e116	−0.313565
$190$	−2.83831e117	−1.25098
$191$	4.26603e117	1.43485	0.717424	−	0.696637i	$-0.245321\pi$
$191$	4.26603e117	1.43485	0.717424	+	0.696637i	$0.245321\pi$
$192$	−1.82539e116	−0.0469182
$193$	2.59015e117	0.509477	0.254738	−	0.967010i	$-0.418011\pi$
$193$	2.59015e117	0.509477	0.254738	+	0.967010i	$0.418011\pi$
$194$	−1.08378e117	−0.163362
$195$	1.32157e118	1.52865
$196$	2.77832e116	0.0246942
$197$	−8.46442e117	−0.578877	−0.289439	−	0.957197i	$-0.593469\pi$
$197$	−8.46442e117	−0.578877	−0.289439	+	0.957197i	$0.593469\pi$
$198$	2.74407e116	0.0144590
$199$	−2.51940e118	−1.02415	−0.512076	−	0.858940i	$-0.671123\pi$
$199$	−2.51940e118	−1.02415	−0.512076	+	0.858940i	$0.671123\pi$
$200$	3.03297e118	0.952409
$201$	5.21640e118	1.26699
$202$	−5.33576e116	−0.0100369
$203$	−1.07339e119	−1.56572
$204$	−1.81537e117	−0.0205595
$205$	−2.21461e119	−1.94972
$206$	−9.15744e117	−0.0627498
$207$	1.31315e119	0.701201
$208$	−8.69516e118	−0.362256
$209$	2.59597e118	0.0844822
$210$	3.32087e119	0.845197
$211$	2.08083e119	0.414659	0.207329	−	0.978271i	$-0.433523\pi$
$211$	2.08083e119	0.414659	0.207329	+	0.978271i	$0.433523\pi$
$212$	7.57149e118	0.118273
$213$	1.94200e120	2.38067
$214$	7.42611e118	0.0715241
$215$	−3.54389e120	−2.68472
$216$	−4.20823e119	−0.251033
$217$	2.96193e120	1.39283
$218$	−1.56605e120	−0.581160
$219$	1.40433e120	0.411714
$220$	−2.26952e119	−0.0526219
$221$	−8.07785e118	−0.0148284
$222$	−2.08458e120	−0.303277
$223$	−1.43517e121	−1.65654	−0.828271	−	0.560328i	$-0.810675\pi$
$223$	−1.43517e121	−1.65654	−0.828271	+	0.560328i	$0.810675\pi$
$224$	−1.06521e121	−0.976478
$225$	1.25987e121	0.918175
$226$	3.32649e119	0.0192931
$227$	6.21977e120	0.287371	0.143685	−	0.989623i	$-0.454105\pi$
$227$	6.21977e120	0.287371	0.143685	+	0.989623i	$0.454105\pi$
$228$	5.64186e121	2.07863
$229$	−3.79949e121	−1.11737	−0.558687	−	0.829379i	$-0.688695\pi$
$229$	−3.79949e121	−1.11737	−0.558687	+	0.829379i	$0.688695\pi$
$230$	2.54077e121	0.597011
$231$	−3.03732e120	−0.0570786
$232$	−8.33199e121	−1.25348
$233$	1.58774e122	1.91403	0.957017	−	0.290031i	$-0.0936657\pi$
$233$	1.58774e122	1.91403	0.957017	+	0.290031i	$0.0936657\pi$
$234$	2.65368e121	0.256585
$235$	5.32293e120	0.0413196
$236$	−1.34340e122	−0.837987
$237$	1.07156e122	0.537622
$238$	−2.02982e120	−0.00819869
$239$	−4.28019e122	−1.39306	−0.696532	−	0.717526i	$-0.745274\pi$
$239$	−4.28019e122	−1.39306	−0.696532	+	0.717526i	$0.745274\pi$
$240$	−3.50855e122	−0.920976
$241$	7.98661e121	0.169233	0.0846165	−	0.996414i	$-0.473033\pi$
$241$	7.98661e121	0.169233	0.0846165	+	0.996414i	$0.473033\pi$
$242$	2.53845e122	0.434588
$243$	−9.03022e122	−1.25019
$244$	7.56136e122	0.847274
$245$	4.98842e121	0.0452803
$246$	−1.02984e123	−0.757901
$247$	2.51046e123	1.49920
$248$	2.29914e123	1.11507
$249$	2.36779e123	0.933418
$250$	4.20066e122	0.134712
$251$	−4.21130e123	−1.09956	−0.549780	−	0.835309i	$-0.685289\pi$
$251$	−4.21130e123	−1.09956	−0.549780	+	0.835309i	$0.685289\pi$
$252$	−2.85036e123	−0.606418
$253$	−2.32383e122	−0.0403179
$254$	1.25751e121	0.00178063
$255$	−3.25946e122	−0.0376987
$256$	−4.26404e123	−0.403146
$257$	1.69032e124	1.30741	0.653706	−	0.756749i	$-0.273213\pi$
$257$	1.69032e124	1.30741	0.653706	+	0.756749i	$0.273213\pi$
$258$	−1.64799e124	−1.04361
$259$	9.96322e123	0.516966
$260$	−2.19477e124	−0.933816
$261$	−3.46103e124	−1.20842
$262$	−8.12874e123	−0.233081
$263$	2.34782e124	0.553278	0.276639	−	0.960974i	$-0.410779\pi$
$263$	2.34782e124	0.553278	0.276639	+	0.960974i	$0.410779\pi$
$264$	−2.35765e123	−0.0456960
$265$	1.35944e124	0.216870
$266$	6.30834e124	0.828917
$267$	1.59413e125	1.72660
$268$	−8.66304e124	−0.773978
$269$	5.04713e124	0.372222	0.186111	−	0.982529i	$-0.440412\pi$
$269$	5.04713e124	0.372222	0.186111	+	0.982529i	$0.440412\pi$
$270$	−3.38226e124	−0.206050
$271$	8.90355e124	0.448379	0.224189	−	0.974546i	$-0.428027\pi$
$271$	8.90355e124	0.448379	0.224189	+	0.974546i	$0.428027\pi$
$272$	2.14454e123	0.00893377
$273$	−2.93727e125	−1.01290
$274$	9.84978e124	0.281367
$275$	−2.22954e124	−0.0527936
$276$	−5.05043e125	−0.991998
$277$	−1.89004e125	−0.308150	−0.154075	−	0.988059i	$-0.549240\pi$
$277$	−1.89004e125	−0.308150	−0.154075	+	0.988059i	$0.549240\pi$
$278$	2.06886e125	0.280171
$279$	9.55041e125	1.07499
$280$	−1.23203e126	−1.15341
$281$	−1.93020e126	−1.50393	−0.751965	−	0.659203i	$-0.770894\pi$
$281$	−1.93020e126	−1.50393	−0.751965	+	0.659203i	$0.770894\pi$
$282$	2.47528e124	0.0160618
$283$	1.67149e126	0.903863	0.451932	−	0.892053i	$-0.350735\pi$
$283$	1.67149e126	0.903863	0.451932	+	0.892053i	$0.350735\pi$
$284$	−3.22514e126	−1.45430
$285$	1.01298e127	3.81147
$286$	−4.69611e124	−0.0147533
$287$	4.92212e126	1.29192
$288$	−3.43465e126	−0.753649
$289$	−5.44603e126	−0.999634
$290$	−6.69664e126	−1.02887
$291$	3.86796e126	0.497729
$292$	−2.33221e126	−0.251507
$293$	1.21150e127	1.09557	0.547787	−	0.836618i	$-0.315470\pi$
$293$	1.21150e127	1.09557	0.547787	+	0.836618i	$0.315470\pi$
$294$	2.31972e125	0.0176015
$295$	−2.41205e127	−1.53657
$296$	7.73374e126	0.413872
$297$	3.09347e125	0.0139152
$298$	−4.82573e125	−0.0182568
$299$	−2.24729e127	−0.715472
$300$	−4.84550e127	−1.29895
$301$	7.87653e127	1.77894
$302$	−2.59234e127	−0.493554
$303$	1.90432e126	0.0305804
$304$	−6.66486e127	−0.903236
$305$	1.35763e128	1.55360
$306$	−6.54492e125	−0.00632778
$307$	1.18403e128	0.967694	0.483847	−	0.875153i	$-0.339239\pi$
$307$	1.18403e128	0.967694	0.483847	+	0.875153i	$0.339239\pi$
$308$	5.04417e126	0.0348680
$309$	3.26826e127	0.191185
$310$	1.84788e128	0.915263
$311$	1.43730e128	0.603097	0.301548	−	0.953451i	$-0.402496\pi$
$311$	1.43730e128	0.603097	0.301548	+	0.953451i	$0.402496\pi$
$312$	−2.28000e128	−0.810910
$313$	−5.98680e128	−1.80576	−0.902882	−	0.429888i	$-0.858553\pi$
$313$	−5.98680e128	−1.80576	−0.902882	+	0.429888i	$0.858553\pi$
$314$	−7.61437e127	−0.194875
$315$	−5.11776e128	−1.11195
$316$	−1.77957e128	−0.328421
$317$	7.02009e128	1.10101	0.550504	−	0.834833i	$-0.314436\pi$
$317$	7.02009e128	1.10101	0.550504	+	0.834833i	$0.314436\pi$
$318$	6.32171e127	0.0843021
$319$	6.12485e127	0.0694825
$320$	5.44294e127	0.0525545
$321$	−2.65035e128	−0.217919
$322$	−5.64704e128	−0.395589
$323$	−6.19168e127	−0.0369725
$324$	1.88168e129	0.958248
$325$	−2.15610e129	−0.936863
$326$	2.65389e128	0.0984410
$327$	5.58917e129	1.77067
$328$	3.82069e129	1.03428
$329$	−1.18306e128	−0.0273790
$330$	−1.89491e128	−0.0375077
$331$	−6.53510e129	−1.10690	−0.553452	−	0.832881i	$-0.686690\pi$
$331$	−6.53510e129	−1.10690	−0.553452	+	0.832881i	$0.686690\pi$
$332$	−3.93225e129	−0.570204
$333$	3.21252e129	0.398996
$334$	−2.67454e128	−0.0284646
$335$	−1.55543e130	−1.41920
$336$	7.79798e129	0.610252
$337$	−7.88857e129	−0.529735	−0.264867	−	0.964285i	$-0.585328\pi$
$337$	−7.88857e129	−0.529735	−0.264867	+	0.964285i	$0.585328\pi$
$338$	3.01154e129	0.173612
$339$	−1.18721e129	−0.0587820
$340$	5.41308e128	0.0230293
$341$	−1.69010e129	−0.0618104
$342$	2.03405e130	0.639760
$343$	−3.74941e130	−1.01465
$344$	6.11399e130	1.42418
$345$	−9.06794e130	−1.81897
$346$	8.15567e129	0.140942
$347$	5.14091e130	0.765724	0.382862	−	0.923806i	$-0.374938\pi$
$347$	5.14091e130	0.765724	0.382862	+	0.923806i	$0.374938\pi$
$348$	1.33113e131	1.70957
$349$	4.76696e130	0.528119	0.264059	−	0.964506i	$-0.414938\pi$
$349$	4.76696e130	0.528119	0.264059	+	0.964506i	$0.414938\pi$
$350$	−5.41790e130	−0.517997
$351$	2.99158e130	0.246936
$352$	6.07816e129	0.0433336
$353$	2.17977e131	1.34281	0.671405	−	0.741091i	$-0.265691\pi$
$353$	2.17977e131	1.34281	0.671405	+	0.741091i	$0.265691\pi$
$354$	−1.12165e131	−0.597298
$355$	−5.79066e131	−2.66666
$356$	−2.64741e131	−1.05474
$357$	7.24437e129	0.0249797
$358$	5.95917e130	0.177914
$359$	2.57415e129	0.00665685	0.00332843	−	0.999994i	$-0.498941\pi$
$359$	2.57415e129	0.00665685	0.00332843	+	0.999994i	$0.498941\pi$
$360$	−3.97255e131	−0.890207
$361$	1.40949e132	2.73805
$362$	−1.05784e131	−0.178209
$363$	−9.05966e131	−1.32410
$364$	4.87802e131	0.618760
$365$	−4.18743e131	−0.461174
$366$	6.31325e131	0.603917
$367$	6.71409e130	0.0558065	0.0279033	−	0.999611i	$-0.491117\pi$
$367$	6.71409e130	0.0558065	0.0279033	+	0.999611i	$0.491117\pi$
$368$	5.96619e131	0.431056
$369$	1.58708e132	0.997105
$370$	6.21580e131	0.339710
$371$	−3.02146e131	−0.143701
$372$	−3.67312e132	−1.52081
$373$	1.68779e132	0.608574	0.304287	−	0.952580i	$-0.401582\pi$
$373$	1.68779e132	0.608574	0.304287	+	0.952580i	$0.401582\pi$
$374$	1.15823e129	0.000363837 0
$375$	−1.49920e132	−0.410440
$376$	−9.18323e130	−0.0219190
$377$	5.92311e132	1.23302
$378$	7.51731e131	0.136532
$379$	−6.30987e132	−1.00023	−0.500116	−	0.865958i	$-0.666709\pi$
$379$	−6.30987e132	−1.00023	−0.500116	+	0.865958i	$0.666709\pi$
$380$	−1.68229e133	−2.32834
$381$	−4.48800e130	−0.00542522
$382$	−5.91530e132	−0.624761
$383$	7.18637e132	0.663396	0.331698	−	0.943386i	$-0.392379\pi$
$383$	7.18637e132	0.663396	0.331698	+	0.943386i	$0.392379\pi$
$384$	1.65532e133	1.33606
$385$	9.05669e131	0.0639355
$386$	−3.59152e132	−0.221836
$387$	2.53970e133	1.37299
$388$	−6.42363e132	−0.304051
$389$	1.02193e133	0.423660	0.211830	−	0.977306i	$-0.432058\pi$
$389$	1.02193e133	0.423660	0.211830	+	0.977306i	$0.432058\pi$
$390$	−1.83249e133	−0.665603
$391$	5.54262e131	0.0176446
$392$	−8.60612e131	−0.0240201
$393$	2.90112e133	0.710148
$394$	1.17368e133	0.252054
$395$	−3.19519e133	−0.602207
$396$	1.62643e132	0.0269113
$397$	9.23396e133	1.34177	0.670883	−	0.741563i	$-0.265915\pi$
$397$	9.23396e133	1.34177	0.670883	+	0.741563i	$0.265915\pi$
$398$	3.49342e133	0.445936
$399$	−2.25143e134	−2.52554
$400$	5.72410e133	0.564439
$401$	−1.78505e134	−1.54780	−0.773899	−	0.633310i	$-0.781696\pi$
$401$	−1.78505e134	−1.54780	−0.773899	+	0.633310i	$0.781696\pi$
$402$	−7.23309e133	−0.551674
$403$	−1.63443e134	−1.09687
$404$	−3.16256e132	−0.0186809
$405$	3.37852e134	1.75708
$406$	1.48837e134	0.681743
$407$	−5.68507e132	−0.0229416
$408$	5.62328e132	0.0199982
$409$	2.98366e134	0.935402	0.467701	−	0.883887i	$-0.345082\pi$
$409$	2.98366e134	0.935402	0.467701	+	0.883887i	$0.345082\pi$
$410$	3.07079e134	0.848948
$411$	−3.51535e134	−0.857265
$412$	−5.42770e133	−0.116791
$413$	5.36094e134	1.01815
$414$	−1.82082e134	−0.305317
$415$	−7.06028e134	−1.04555
$416$	5.87795e134	0.768988
$417$	−7.38368e134	−0.853623
$418$	−3.59958e133	−0.0367852
$419$	−1.13134e134	−0.102228	−0.0511140	−	0.998693i	$-0.516277\pi$
$419$	−1.13134e134	−0.102228	−0.0511140	+	0.998693i	$0.516277\pi$
$420$	1.96831e135	1.57309
$421$	−1.67287e135	−1.18286	−0.591431	−	0.806355i	$-0.701437\pi$
$421$	−1.67287e135	−1.18286	−0.591431	+	0.806355i	$0.701437\pi$
$422$	−2.88529e134	−0.180551
$423$	−3.81463e133	−0.0211312
$424$	−2.34534e134	−0.115044
$425$	5.31771e133	0.0231044
$426$	−2.69279e135	−1.03659
$427$	−3.01741e135	−1.02944
$428$	4.40152e134	0.133122
$429$	1.67603e134	0.0449501
$430$	4.91397e135	1.16898
$431$	2.20865e135	0.466173	0.233087	−	0.972456i	$-0.425117\pi$
$431$	2.20865e135	0.466173	0.233087	+	0.972456i	$0.425117\pi$
$432$	−7.94215e134	−0.148773
$433$	6.14291e135	1.02152	0.510760	−	0.859723i	$-0.329364\pi$
$433$	6.14291e135	1.02152	0.510760	+	0.859723i	$0.329364\pi$
$434$	−4.10703e135	−0.606467
$435$	2.39001e136	3.13475
$436$	−9.28211e135	−1.08166
$437$	−1.72255e136	−1.78393
$438$	−1.94724e135	−0.179268
$439$	9.09548e135	0.744565	0.372283	−	0.928119i	$-0.378575\pi$
$439$	9.09548e135	0.744565	0.372283	+	0.928119i	$0.378575\pi$
$440$	7.03007e134	0.0511855
$441$	−3.57490e134	−0.0231567
$442$	1.12008e134	0.00645657
$443$	9.73657e134	0.0499590	0.0249795	−	0.999688i	$-0.492048\pi$
$443$	9.73657e134	0.0499590	0.0249795	+	0.999688i	$0.492048\pi$
$444$	−1.23555e136	−0.564465
$445$	−4.75337e136	−1.93402
$446$	1.99001e136	0.721291
$447$	1.72229e135	0.0556247
$448$	−1.20973e135	−0.0348234
$449$	−5.76893e135	−0.148050	−0.0740251	−	0.997256i	$-0.523584\pi$
$449$	−5.76893e135	−0.148050	−0.0740251	+	0.997256i	$0.523584\pi$
$450$	−1.74694e136	−0.399791
$451$	−2.80859e135	−0.0573319
$452$	1.97164e135	0.0359086
$453$	9.25198e136	1.50376
$454$	−8.62436e135	−0.125127
$455$	8.75838e136	1.13458
$456$	−1.74762e137	−2.02189
$457$	1.14703e137	1.18547	0.592733	−	0.805399i	$-0.298049\pi$
$457$	1.14703e137	1.18547	0.592733	+	0.805399i	$0.298049\pi$
$458$	5.26840e136	0.486526
$459$	−7.37830e134	−0.00608980
$460$	1.50594e137	1.11117
$461$	−4.28772e136	−0.282897	−0.141449	−	0.989946i	$-0.545176\pi$
$461$	−4.28772e136	−0.282897	−0.141449	+	0.989946i	$0.545176\pi$
$462$	4.21156e135	0.0248531
$463$	1.83388e137	0.968165	0.484083	−	0.875022i	$-0.339153\pi$
$463$	1.83388e137	0.968165	0.484083	+	0.875022i	$0.339153\pi$
$464$	−1.57249e137	−0.742867
$465$	−6.59501e137	−2.78861
$466$	−2.20157e137	−0.833408
$467$	−3.86590e136	−0.131048	−0.0655241	−	0.997851i	$-0.520872\pi$
$467$	−3.86590e136	−0.131048	−0.0655241	+	0.997851i	$0.520872\pi$
$468$	1.57286e137	0.477561
$469$	3.45705e137	0.940381
$470$	−7.38080e135	−0.0179914
$471$	2.71754e137	0.593745
$472$	4.16131e137	0.815113
$473$	−4.49440e136	−0.0789447
$474$	−1.48583e137	−0.234091
$475$	−1.65266e138	−2.33594
$476$	−1.20309e136	−0.0152595
$477$	−9.74233e136	−0.110909
$478$	5.93493e137	0.606567
$479$	2.45895e137	0.225668	0.112834	−	0.993614i	$-0.464007\pi$
$479$	2.45895e137	0.225668	0.112834	+	0.993614i	$0.464007\pi$
$480$	2.37179e138	1.95502
$481$	−5.49782e137	−0.407117
$482$	−1.10743e137	−0.0736873
$483$	2.01541e138	1.20528
$484$	1.50456e138	0.808862
$485$	−1.15335e138	−0.557521
$486$	1.25214e138	0.544356
$487$	−3.14432e138	−1.22966	−0.614830	−	0.788660i	$-0.710775\pi$
$487$	−3.14432e138	−1.22966	−0.614830	+	0.788660i	$0.710775\pi$
$488$	−2.34220e138	−0.824145
$489$	−9.47164e137	−0.299929
$490$	−6.91696e136	−0.0197159
$491$	2.43959e137	0.0626065	0.0313033	−	0.999510i	$-0.490034\pi$
$491$	2.43959e137	0.0626065	0.0313033	+	0.999510i	$0.490034\pi$
$492$	−6.10397e138	−1.41062
$493$	−1.46085e137	−0.0304081
$494$	−3.48101e138	−0.652782
$495$	2.92023e137	0.0493456
$496$	4.33914e138	0.660841
$497$	1.28701e139	1.76697
$498$	−3.28318e138	−0.406428
$499$	−9.51286e138	−1.06202	−0.531010	−	0.847365i	$-0.678187\pi$
$499$	−9.51286e138	−1.06202	−0.531010	+	0.847365i	$0.678187\pi$
$500$	2.48977e138	0.250729
$501$	9.54533e137	0.0867258
$502$	5.83940e138	0.478770
$503$	7.69347e138	0.569339	0.284669	−	0.958626i	$-0.408116\pi$
$503$	7.69347e138	0.569339	0.284669	+	0.958626i	$0.408116\pi$
$504$	8.82927e138	0.589864
$505$	−5.67830e137	−0.0342541
$506$	3.22224e137	0.0175552
$507$	−1.07481e139	−0.528959
$508$	7.45336e136	0.00331414
$509$	1.68209e139	0.675900	0.337950	−	0.941164i	$-0.390267\pi$
$509$	1.68209e139	0.675900	0.337950	+	0.941164i	$0.390267\pi$
$510$	4.51958e137	0.0164147
$511$	9.30684e138	0.305581
$512$	−2.80091e139	−0.831566
$513$	2.29305e139	0.615700
$514$	−2.34380e139	−0.569272
$515$	−9.74531e138	−0.214153
$516$	−9.76776e139	−1.94239
$517$	6.75060e136	0.00121501
$518$	−1.38150e139	−0.225097
$519$	−2.91073e139	−0.429421
$520$	6.79851e139	0.908325
$521$	1.00938e140	1.22156	0.610778	−	0.791802i	$-0.290857\pi$
$521$	1.00938e140	1.22156	0.610778	+	0.791802i	$0.290857\pi$
$522$	4.79908e139	0.526172
$523$	−1.31642e140	−1.30785	−0.653923	−	0.756561i	$-0.726878\pi$
$523$	−1.31642e140	−1.30785	−0.653923	+	0.756561i	$0.726878\pi$
$524$	−4.81798e139	−0.433814
$525$	1.93363e140	1.57823
$526$	−3.25550e139	−0.240908
$527$	4.03108e138	0.0270505
$528$	−4.44958e138	−0.0270814
$529$	−2.69225e139	−0.148644
$530$	−1.88501e139	−0.0944293
$531$	1.72857e140	0.785814
$532$	3.73901e140	1.54279
$533$	−2.71608e140	−1.01740
$534$	−2.21042e140	−0.751797
$535$	7.90284e139	0.244098
$536$	2.68346e140	0.752850
$537$	−2.12681e140	−0.542067
$538$	−6.99838e139	−0.162073
$539$	6.32637e137	0.00133147
$540$	−2.00470e140	−0.383504
$541$	−6.09215e140	−1.05953	−0.529763	−	0.848146i	$-0.677719\pi$
$541$	−6.09215e140	−1.05953	−0.529763	+	0.848146i	$0.677719\pi$
$542$	−1.23457e140	−0.195233
$543$	3.77540e140	0.542964
$544$	−1.44971e139	−0.0189644
$545$	−1.66658e141	−1.98338
$546$	4.07284e140	0.441038
$547$	4.40996e139	0.0434598	0.0217299	−	0.999764i	$-0.493083\pi$
$547$	4.40996e139	0.0434598	0.0217299	+	0.999764i	$0.493083\pi$
$548$	5.83805e140	0.523684
$549$	−9.72930e140	−0.794522
$550$	3.09149e139	0.0229874
$551$	4.54007e141	3.07436
$552$	1.56442e141	0.964919
$553$	7.10152e140	0.399031
$554$	2.62074e140	0.134175
$555$	−2.21840e141	−1.03503
$556$	1.22623e141	0.521459
$557$	−1.16444e141	−0.451415	−0.225707	−	0.974195i	$-0.572469\pi$
$557$	−1.16444e141	−0.451415	−0.225707	+	0.974195i	$0.572469\pi$
$558$	−1.32426e141	−0.468073
$559$	−4.34636e141	−1.40093
$560$	−2.32521e141	−0.683562
$561$	−4.13368e138	−0.00110854
$562$	2.67643e141	0.654840
$563$	5.53026e141	1.23471	0.617353	−	0.786687i	$-0.288205\pi$
$563$	5.53026e141	1.23471	0.617353	+	0.786687i	$0.288205\pi$
$564$	1.46712e140	0.0298946
$565$	3.54004e140	0.0658435
$566$	−2.31770e141	−0.393560
$567$	−7.50899e141	−1.16427
$568$	9.99017e141	1.41460
$569$	−6.18794e141	−0.800322	−0.400161	−	0.916445i	$-0.631046\pi$
$569$	−6.18794e141	−0.800322	−0.400161	+	0.916445i	$0.631046\pi$
$570$	−1.40461e142	−1.65959
$571$	−9.18082e141	−0.991110	−0.495555	−	0.868576i	$-0.665035\pi$
$571$	−9.18082e141	−0.991110	−0.495555	+	0.868576i	$0.665035\pi$
$572$	−2.78343e140	−0.0274590
$573$	2.11115e142	1.90351
$574$	−6.82503e141	−0.562526
$575$	1.47941e142	1.11479
$576$	−3.90064e140	−0.0268768
$577$	1.84227e142	1.16091	0.580457	−	0.814291i	$-0.302874\pi$
$577$	1.84227e142	1.16091	0.580457	+	0.814291i	$0.302874\pi$
$578$	7.55149e141	0.435260
$579$	1.28180e142	0.675888
$580$	−3.96916e142	−1.91495
$581$	1.56919e142	0.692797
$582$	−5.36333e141	−0.216721
$583$	1.72406e140	0.00637709
$584$	7.22423e141	0.244642
$585$	2.82404e142	0.875676
$586$	−1.67988e142	−0.477035
$587$	1.27209e142	0.330869	0.165435	−	0.986221i	$-0.447097\pi$
$587$	1.27209e142	0.330869	0.165435	+	0.986221i	$0.447097\pi$
$588$	1.37492e141	0.0327601
$589$	−1.25279e143	−2.73490
$590$	3.34456e142	0.669052
$591$	−4.18883e142	−0.767957
$592$	1.45958e142	0.245279
$593$	6.22106e142	0.958402	0.479201	−	0.877705i	$-0.340926\pi$
$593$	6.22106e142	0.958402	0.479201	+	0.877705i	$0.340926\pi$
$594$	−4.28942e140	−0.00605895
$595$	−2.16013e141	−0.0279805
$596$	−2.86025e141	−0.0339799
$597$	−1.24679e143	−1.35867
$598$	3.11610e142	0.311531
$599$	−1.82276e143	−1.67204	−0.836022	−	0.548696i	$-0.815125\pi$
$599$	−1.82276e143	−1.67204	−0.836022	+	0.548696i	$0.815125\pi$
$600$	1.50094e143	1.26350
$601$	2.43541e143	1.88164	0.940819	−	0.338910i	$-0.110058\pi$
$601$	2.43541e143	1.88164	0.940819	+	0.338910i	$0.110058\pi$
$602$	−1.09216e143	−0.774584
$603$	1.11468e143	0.725789
$604$	−1.53650e143	−0.918611
$605$	2.70141e143	1.48316
$606$	−2.64053e141	−0.0133153
$607$	2.14879e143	0.995349	0.497675	−	0.867364i	$-0.334187\pi$
$607$	2.14879e143	0.995349	0.497675	+	0.867364i	$0.334187\pi$
$608$	4.50546e143	1.91737
$609$	−5.31195e143	−2.07713
$610$	−1.88249e143	−0.676466
$611$	6.52825e141	0.0215613
$612$	−3.87923e141	−0.0117774
$613$	2.20584e143	0.615685	0.307843	−	0.951437i	$-0.400393\pi$
$613$	2.20584e143	0.615685	0.307843	+	0.951437i	$0.400393\pi$
$614$	−1.64179e143	−0.421353
$615$	−1.09595e144	−2.58657
$616$	−1.56248e142	−0.0339162
$617$	1.93858e143	0.387077	0.193538	−	0.981093i	$-0.438004\pi$
$617$	1.93858e143	0.387077	0.193538	+	0.981093i	$0.438004\pi$
$618$	−4.53178e142	−0.0832459
$619$	−5.57066e143	−0.941538	−0.470769	−	0.882256i	$-0.656024\pi$
$619$	−5.57066e143	−0.941538	−0.470769	+	0.882256i	$0.656024\pi$
$620$	1.09525e144	1.70350
$621$	−2.05267e143	−0.293834
$622$	−1.99297e143	−0.262600
$623$	1.05647e144	1.28151
$624$	−4.30301e143	−0.480581
$625$	−7.27756e143	−0.748453
$626$	8.30132e143	0.786265
$627$	1.28468e143	0.112077
$628$	−4.51311e143	−0.362705
$629$	1.35596e142	0.0100401
$630$	7.09631e143	0.484166
$631$	3.61771e142	0.0227469	0.0113734	−	0.999935i	$-0.496380\pi$
$631$	3.61771e142	0.0227469	0.0113734	+	0.999935i	$0.496380\pi$
$632$	5.51241e143	0.319456
$633$	1.02975e144	0.550100
$634$	−9.73408e143	−0.479400
$635$	1.33824e142	0.00607695
$636$	3.74694e143	0.156904
$637$	6.11798e142	0.0236280
$638$	−8.49275e142	−0.0302540
$639$	4.14983e144	1.36375
$640$	−4.93585e144	−1.49656
$641$	3.83328e144	1.07246	0.536231	−	0.844072i	$-0.319848\pi$
$641$	3.83328e144	1.07246	0.536231	+	0.844072i	$0.319848\pi$
$642$	3.67499e143	0.0948861
$643$	−3.54930e143	−0.0845820	−0.0422910	−	0.999105i	$-0.513466\pi$
$643$	−3.54930e143	−0.0845820	−0.0422910	+	0.999105i	$0.513466\pi$
$644$	−3.34705e144	−0.736276
$645$	−1.75378e145	−3.56164
$646$	8.58542e142	0.0160986
$647$	5.81862e144	1.00751	0.503755	−	0.863847i	$-0.331951\pi$
$647$	5.81862e144	1.00751	0.503755	+	0.863847i	$0.331951\pi$
$648$	−5.82869e144	−0.932091
$649$	−3.05898e143	−0.0451830
$650$	2.98966e144	0.407928
$651$	1.46579e145	1.84778
$652$	1.57298e144	0.183220
$653$	1.39255e145	1.49894	0.749468	−	0.662040i	$-0.230309\pi$
$653$	1.39255e145	1.49894	0.749468	+	0.662040i	$0.230309\pi$
$654$	−7.74997e144	−0.770985
$655$	−8.65057e144	−0.795459
$656$	7.21075e144	0.612961
$657$	3.00088e144	0.235848
$658$	1.64043e143	0.0119213
$659$	7.91052e144	0.531626	0.265813	−	0.964025i	$-0.414360\pi$
$659$	7.91052e144	0.531626	0.265813	+	0.964025i	$0.414360\pi$
$660$	−1.12313e144	−0.0698099
$661$	−2.97341e145	−1.70954	−0.854771	−	0.519005i	$-0.826302\pi$
$661$	−2.97341e145	−1.70954	−0.854771	+	0.519005i	$0.826302\pi$
$662$	9.06160e144	0.481968
$663$	−3.99752e143	−0.0196718
$664$	1.21805e145	0.554639
$665$	6.71331e145	2.82893
$666$	−4.45450e144	−0.173731
$667$	−4.06414e145	−1.46720
$668$	−1.58522e144	−0.0529788
$669$	−7.10229e145	−2.19762
$670$	2.15677e145	0.617946
$671$	1.72176e144	0.0456837
$672$	−5.27146e145	−1.29543
$673$	−5.07205e145	−1.15454	−0.577268	−	0.816555i	$-0.695881\pi$
$673$	−5.07205e145	−1.15454	−0.577268	+	0.816555i	$0.695881\pi$
$674$	1.09383e145	0.230657
$675$	−1.96938e145	−0.384756
$676$	1.78497e145	0.323129
$677$	1.16550e146	1.95522	0.977608	−	0.210435i	$-0.0674881\pi$
$677$	1.16550e146	1.95522	0.977608	+	0.210435i	$0.0674881\pi$
$678$	1.64620e144	0.0255948
$679$	2.56340e145	0.369422
$680$	−1.67675e144	−0.0224006
$681$	3.07801e145	0.381235
$682$	2.34350e144	0.0269134
$683$	−1.33029e146	−1.41671	−0.708353	−	0.705858i	$-0.750561\pi$
$683$	−1.33029e146	−1.41671	−0.708353	+	0.705858i	$0.750561\pi$
$684$	1.20560e146	1.19073
$685$	1.04821e146	0.960249
$686$	5.19896e145	0.441798
$687$	−1.88027e146	−1.48234
$688$	1.15389e146	0.844032
$689$	1.66727e145	0.113166
$690$	1.25736e146	0.792015
$691$	−2.87961e146	−1.68350	−0.841752	−	0.539865i	$-0.818475\pi$
$691$	−2.87961e146	−1.68350	−0.841752	+	0.539865i	$0.818475\pi$
$692$	4.83394e145	0.262324
$693$	−6.49040e144	−0.0326971
$694$	−7.12841e145	−0.333411
$695$	2.20167e146	0.956169
$696$	−4.12329e146	−1.66291
$697$	6.69882e144	0.0250906
$698$	−6.60988e145	−0.229953
$699$	7.85733e146	2.53922
$700$	−3.21124e146	−0.964104
$701$	−3.12479e146	−0.871651	−0.435826	−	0.900031i	$-0.643544\pi$
$701$	−3.12479e146	−0.871651	−0.435826	+	0.900031i	$0.643544\pi$
$702$	−4.14814e145	−0.107521
$703$	−4.21409e146	−1.01509
$704$	6.90280e143	0.00154537
$705$	2.63418e145	0.0548159
$706$	−3.02249e146	−0.584685
$707$	1.26204e145	0.0226973
$708$	−6.64815e146	−1.11170
$709$	6.99651e146	1.08793	0.543964	−	0.839108i	$-0.316923\pi$
$709$	6.99651e146	1.08793	0.543964	+	0.839108i	$0.316923\pi$
$710$	8.02936e146	1.16112
$711$	2.28980e146	0.307974
$712$	8.20062e146	1.02595
$713$	1.12146e147	1.30519
$714$	−1.00451e145	−0.0108766
$715$	−4.99759e145	−0.0503500
$716$	3.53206e146	0.331136
$717$	−2.11816e147	−1.84808
$718$	−3.56932e144	−0.00289852
$719$	1.97740e147	1.49471	0.747356	−	0.664424i	$-0.231323\pi$
$719$	1.97740e147	1.49471	0.747356	+	0.664424i	$0.231323\pi$
$720$	−7.49736e146	−0.527575
$721$	2.16596e146	0.141901
$722$	−1.95441e147	−1.19220
$723$	3.95237e146	0.224510
$724$	−6.26991e146	−0.331685
$725$	−3.89923e147	−1.92119
$726$	1.25622e147	0.576539
$727$	1.38347e147	0.591489	0.295744	−	0.955267i	$-0.404432\pi$
$727$	1.38347e147	0.591489	0.295744	+	0.955267i	$0.404432\pi$
$728$	−1.51101e147	−0.601870
$729$	−1.28286e147	−0.476116
$730$	5.80630e146	0.200804
$731$	1.07197e146	0.0345491
$732$	3.74192e147	1.12402
$733$	7.02841e146	0.196790	0.0983949	−	0.995147i	$-0.468629\pi$
$733$	7.02841e146	0.196790	0.0983949	+	0.995147i	$0.468629\pi$
$734$	−9.30979e145	−0.0242993
$735$	2.46864e146	0.0600703
$736$	−4.03316e147	−0.915035
$737$	−1.97261e146	−0.0417317
$738$	−2.20065e147	−0.434159
$739$	1.70762e147	0.314197	0.157099	−	0.987583i	$-0.449786\pi$
$739$	1.70762e147	0.314197	0.157099	+	0.987583i	$0.449786\pi$
$740$	3.68416e147	0.632274
$741$	1.24236e148	1.98889
$742$	4.18957e146	0.0625703
$743$	−1.26492e148	−1.76255	−0.881274	−	0.472606i	$-0.843313\pi$
$743$	−1.26492e148	−1.76255	−0.881274	+	0.472606i	$0.843313\pi$
$744$	1.13778e148	1.47929
$745$	−5.13552e146	−0.0623070
$746$	−2.34030e147	−0.264985
$747$	5.05968e147	0.534703
$748$	6.86493e144	0.000677179 0
$749$	−1.75646e147	−0.161743
$750$	2.07880e147	0.178714
$751$	−4.73492e147	−0.380063	−0.190032	−	0.981778i	$-0.560859\pi$
$751$	−4.73492e147	−0.380063	−0.190032	+	0.981778i	$0.560859\pi$
$752$	−1.73314e146	−0.0129902
$753$	−2.08406e148	−1.45871
$754$	−8.21301e147	−0.536881
$755$	−2.75876e148	−1.68440
$756$	4.45558e147	0.254116
$757$	7.89892e147	0.420852	0.210426	−	0.977610i	$-0.432515\pi$
$757$	7.89892e147	0.420852	0.210426	+	0.977610i	$0.432515\pi$
$758$	8.74929e147	0.435521
$759$	−1.15001e147	−0.0534871
$760$	5.21107e148	2.26478
$761$	−2.42437e148	−0.984666	−0.492333	−	0.870407i	$-0.663856\pi$
$761$	−2.42437e148	−0.984666	−0.492333	+	0.870407i	$0.663856\pi$
$762$	6.22309e145	0.00236224
$763$	3.70409e148	1.31422
$764$	−3.50605e148	−1.16281
$765$	−6.96508e146	−0.0215955
$766$	−9.96466e147	−0.288856
$767$	−2.95823e148	−0.801808
$768$	−2.11016e148	−0.534827
$769$	1.14358e148	0.271057	0.135528	−	0.990773i	$-0.456727\pi$
$769$	1.14358e148	0.271057	0.135528	+	0.990773i	$0.456727\pi$
$770$	−1.25581e147	−0.0278388
$771$	8.36495e148	1.73445
$772$	−2.12873e148	−0.412885
$773$	8.37268e148	1.51922	0.759610	−	0.650379i	$-0.225390\pi$
$773$	8.37268e148	1.51922	0.759610	+	0.650379i	$0.225390\pi$
$774$	−3.52155e148	−0.597826
$775$	1.07596e149	1.70906
$776$	1.98978e148	0.295752
$777$	4.93054e148	0.685823
$778$	−1.41702e148	−0.184470
$779$	−2.08188e149	−2.53674
$780$	−1.08614e149	−1.23883
$781$	−7.34378e147	−0.0784136
$782$	−7.68542e146	−0.00768280
$783$	5.41016e148	0.506383
$784$	−1.62422e147	−0.0142354
$785$	−8.10318e148	−0.665072
$786$	−4.02270e148	−0.309213
$787$	−2.20240e149	−1.58561	−0.792807	−	0.609473i	$-0.791381\pi$
$787$	−2.20240e149	−1.58561	−0.792807	+	0.609473i	$0.791381\pi$
$788$	6.95651e148	0.469128
$789$	1.16188e149	0.733997
$790$	4.43046e148	0.262213
$791$	−7.86798e147	−0.0436289
$792$	−5.03803e147	−0.0261767
$793$	1.66504e149	0.810693
$794$	−1.28039e149	−0.584231
$795$	6.72754e148	0.287706
$796$	2.07058e149	0.829983
$797$	6.88399e148	0.258664	0.129332	−	0.991601i	$-0.458717\pi$
$797$	6.88399e148	0.258664	0.129332	+	0.991601i	$0.458717\pi$
$798$	3.12184e149	1.09967
$799$	−1.61010e146	−0.000531732 0
$800$	−3.86950e149	−1.19818
$801$	3.40646e149	0.989075
$802$	2.47515e149	0.673941
$803$	−5.31054e147	−0.0135609
$804$	−4.28712e149	−1.02678
$805$	−6.00956e149	−1.35007
$806$	2.26631e149	0.477600
$807$	2.49770e149	0.493802
$808$	9.79632e147	0.0181710
$809$	−1.39930e149	−0.243534	−0.121767	−	0.992559i	$-0.538856\pi$
$809$	−1.39930e149	−0.243534	−0.121767	+	0.992559i	$0.538856\pi$
$810$	−4.68467e149	−0.765069
$811$	−2.40080e149	−0.367944	−0.183972	−	0.982932i	$-0.558896\pi$
$811$	−2.40080e149	−0.367944	−0.183972	+	0.982932i	$0.558896\pi$
$812$	8.82172e149	1.26887
$813$	4.40614e149	0.594833
$814$	7.88295e147	0.00998923
$815$	2.82426e149	0.335960
$816$	1.06128e148	0.0118518
$817$	−3.33149e150	−3.49303
$818$	−4.13715e149	−0.407292
$819$	−6.27661e149	−0.580236
$820$	1.82008e150	1.58008
$821$	−8.20174e149	−0.668703	−0.334351	−	0.942448i	$-0.608517\pi$
$821$	−8.20174e149	−0.668703	−0.334351	+	0.942448i	$0.608517\pi$
$822$	4.87441e149	0.373270
$823$	2.02435e150	1.45611	0.728054	−	0.685520i	$-0.240425\pi$
$823$	2.02435e150	1.45611	0.728054	+	0.685520i	$0.240425\pi$
$824$	1.68128e149	0.113603
$825$	−1.10334e149	−0.0700377
$826$	−7.43350e149	−0.443324
$827$	3.27114e150	1.83301	0.916507	−	0.400018i	$-0.130996\pi$
$827$	3.27114e150	1.83301	0.916507	+	0.400018i	$0.130996\pi$
$828$	−1.07922e150	−0.568260
$829$	6.39157e149	0.316264	0.158132	−	0.987418i	$-0.449453\pi$
$829$	6.39157e149	0.316264	0.158132	+	0.987418i	$0.449453\pi$
$830$	9.78982e149	0.455253
$831$	−9.35333e149	−0.408802
$832$	6.67543e148	0.0274238
$833$	−1.50891e147	−0.000582702 0
$834$	1.02382e150	0.371684
$835$	−2.84623e149	−0.0971442
$836$	−2.13350e149	−0.0684652
$837$	−1.49288e150	−0.450469
$838$	1.56872e149	0.0445121
$839$	4.63238e149	0.123613	0.0618063	−	0.998088i	$-0.480314\pi$
$839$	4.63238e149	0.123613	0.0618063	+	0.998088i	$0.480314\pi$
$840$	−6.09703e150	−1.53015
$841$	6.47535e150	1.52851
$842$	2.31961e150	0.515042
$843$	−9.55209e150	−1.99516
$844$	−1.71014e150	−0.336044
$845$	3.20487e150	0.592503
$846$	5.28939e148	0.00920093
$847$	−6.00407e150	−0.982766
$848$	−4.42634e149	−0.0681802
$849$	8.27179e150	1.19909
$850$	−7.37357e148	−0.0100601
$851$	3.77233e150	0.484437
$852$	−1.59604e151	−1.92932
$853$	−1.40317e151	−1.59674	−0.798372	−	0.602165i	$-0.794305\pi$
$853$	−1.40317e151	−1.59674	−0.798372	+	0.602165i	$0.794305\pi$
$854$	4.18396e150	0.448237
$855$	2.16463e151	2.18338
$856$	−1.36341e150	−0.129488
$857$	4.00172e150	0.357878	0.178939	−	0.983860i	$-0.442734\pi$
$857$	4.00172e150	0.357878	0.178939	+	0.983860i	$0.442734\pi$
$858$	−2.32399e149	−0.0195721
$859$	−3.74195e150	−0.296790	−0.148395	−	0.988928i	$-0.547411\pi$
$859$	−3.74195e150	−0.296790	−0.148395	+	0.988928i	$0.547411\pi$
$860$	2.91256e151	2.17572
$861$	2.43583e151	1.71390
$862$	−3.06252e150	−0.202981
$863$	−1.41102e151	−0.881003	−0.440502	−	0.897752i	$-0.645199\pi$
$863$	−1.41102e151	−0.881003	−0.440502	+	0.897752i	$0.645199\pi$
$864$	5.36892e150	0.315812
$865$	8.67923e150	0.481007
$866$	−8.51778e150	−0.444790
$867$	−2.69510e151	−1.32615
$868$	−2.43427e151	−1.12877
$869$	−4.05217e149	−0.0177080
$870$	−3.31399e151	−1.36493
$871$	−1.90764e151	−0.740561
$872$	2.87522e151	1.05214
$873$	8.26538e150	0.285121
$874$	2.38850e151	0.776759
$875$	−9.93561e150	−0.304635
$876$	−1.15415e151	−0.333657
$877$	−1.57159e151	−0.428410	−0.214205	−	0.976789i	$-0.568716\pi$
$877$	−1.57159e151	−0.428410	−0.214205	+	0.976789i	$0.568716\pi$
$878$	−1.26118e151	−0.324198
$879$	5.99542e151	1.45342
$880$	1.32678e150	0.0303347
$881$	9.81411e150	0.211637	0.105818	−	0.994385i	$-0.466254\pi$
$881$	9.81411e150	0.211637	0.105818	+	0.994385i	$0.466254\pi$
$882$	4.95698e149	0.0100829
$883$	−1.00914e151	−0.193631	−0.0968153	−	0.995302i	$-0.530866\pi$
$883$	−1.00914e151	−0.193631	−0.0968153	+	0.995302i	$0.530866\pi$
$884$	6.63881e149	0.0120171
$885$	−1.19366e152	−2.03846
$886$	−1.35008e150	−0.0217531
$887$	3.85045e151	0.585390	0.292695	−	0.956206i	$-0.405448\pi$
$887$	3.85045e151	0.585390	0.292695	+	0.956206i	$0.405448\pi$
$888$	3.82723e151	0.549056
$889$	−2.97432e149	−0.00402668
$890$	6.59105e151	0.842111
$891$	4.28467e150	0.0516673
$892$	1.17950e152	1.34248
$893$	5.00391e150	0.0537600
$894$	−2.38813e150	−0.0242201
$895$	6.34173e151	0.607186
$896$	1.09703e152	0.991641
$897$	−1.11213e152	−0.949169
$898$	7.99923e150	0.0644639
$899$	−2.95580e152	−2.24932
$900$	−1.03543e152	−0.744098
$901$	−4.11209e149	−0.00279085
$902$	3.89441e150	0.0249635
$903$	3.89789e152	2.35999
$904$	−6.10735e150	−0.0349284
$905$	−1.12575e152	−0.608191
$906$	−1.28288e152	−0.654765
$907$	−3.01371e152	−1.45320	−0.726602	−	0.687058i	$-0.758902\pi$
$907$	−3.01371e152	−1.45320	−0.726602	+	0.687058i	$0.758902\pi$
$908$	−5.11174e151	−0.232888
$909$	4.06930e150	0.0175178
$910$	−1.21444e152	−0.494020
$911$	2.13545e152	0.820907	0.410453	−	0.911882i	$-0.365370\pi$
$911$	2.13545e152	0.820907	0.410453	+	0.911882i	$0.365370\pi$
$912$	−3.29827e152	−1.19826
$913$	−8.95392e150	−0.0307446
$914$	−1.59047e152	−0.516175
$915$	6.71854e152	2.06105
$916$	3.12263e152	0.905531
$917$	1.92265e152	0.527083
$918$	1.02308e150	0.00265162
$919$	2.05675e152	0.504002	0.252001	−	0.967727i	$-0.418911\pi$
$919$	2.05675e152	0.504002	0.252001	+	0.967727i	$0.418911\pi$
$920$	−4.66480e152	−1.08084
$921$	5.85949e152	1.28377
$922$	5.94537e151	0.123179
$923$	−7.10189e152	−1.39151
$924$	2.49623e151	0.0462571
$925$	3.61926e152	0.634337
$926$	−2.54287e152	−0.421558
$927$	6.98389e151	0.109519
$928$	1.06301e153	1.57694
$929$	−1.09687e153	−1.53939	−0.769693	−	0.638414i	$-0.779591\pi$
$929$	−1.09687e153	−1.53939	−0.769693	+	0.638414i	$0.779591\pi$
$930$	9.14467e152	1.21422
$931$	4.68945e151	0.0589132
$932$	−1.30489e153	−1.55115
$933$	7.11283e152	0.800088
$934$	5.36048e151	0.0570610
$935$	1.23258e150	0.00124170
$936$	−4.87209e152	−0.464525
$937$	−5.52863e152	−0.498917	−0.249459	−	0.968385i	$-0.580253\pi$
$937$	−5.52863e152	−0.498917	−0.249459	+	0.968385i	$0.580253\pi$
$938$	−4.79356e152	−0.409460
$939$	−2.96271e153	−2.39559
$940$	−4.37467e151	−0.0334858
$941$	1.10236e152	0.0798834	0.0399417	−	0.999202i	$-0.487283\pi$
$941$	1.10236e152	0.0798834	0.0399417	+	0.999202i	$0.487283\pi$
$942$	−3.76816e152	−0.258528
$943$	1.86364e153	1.21062
$944$	7.85361e152	0.483071
$945$	7.99989e152	0.465957
$946$	6.23195e151	0.0343740
$947$	1.56209e153	0.815987	0.407994	−	0.912985i	$-0.366229\pi$
$947$	1.56209e153	0.815987	0.407994	+	0.912985i	$0.366229\pi$
$948$	−8.80666e152	−0.435694
$949$	−5.13562e152	−0.240648
$950$	2.29158e153	1.01711
$951$	3.47406e153	1.46063
$952$	3.72670e151	0.0148430
$953$	−1.11248e153	−0.419766	−0.209883	−	0.977726i	$-0.567308\pi$
$953$	−1.11248e153	−0.419766	−0.209883	+	0.977726i	$0.567308\pi$
$954$	1.35088e152	0.0482919
$955$	−6.29504e153	−2.13218
$956$	3.51769e153	1.12895
$957$	3.03103e152	0.0921777
$958$	−3.40959e152	−0.0982603
$959$	−2.32972e153	−0.636275
$960$	2.69358e152	0.0697205
$961$	4.08008e153	1.00095
$962$	7.62330e152	0.177267
$963$	−5.66350e152	−0.124833
$964$	−6.56382e152	−0.137148
$965$	−3.82208e153	−0.757083
$966$	−2.79458e153	−0.524801
$967$	6.73826e153	1.19973	0.599866	−	0.800100i	$-0.295221\pi$
$967$	6.73826e153	1.19973	0.599866	+	0.800100i	$0.295221\pi$
$968$	−4.66053e153	−0.786783
$969$	−3.06411e152	−0.0490489
$970$	1.59924e153	0.242756
$971$	−5.16901e153	−0.744075	−0.372037	−	0.928218i	$-0.621341\pi$
$971$	−5.16901e153	−0.744075	−0.372037	+	0.928218i	$0.621341\pi$
$972$	7.42152e153	1.01316
$973$	−4.89336e153	−0.633572
$974$	4.35992e153	0.535418
$975$	−1.06700e154	−1.24287
$976$	−4.42042e153	−0.488425
$977$	−1.45504e154	−1.52513	−0.762564	−	0.646913i	$-0.776060\pi$
$977$	−1.45504e154	−1.52513	−0.762564	+	0.646913i	$0.776060\pi$
$978$	1.31334e153	0.130595
$979$	−6.02828e152	−0.0568702
$980$	−4.09975e152	−0.0366956
$981$	1.19434e154	1.01432
$982$	−3.38274e152	−0.0272601
$983$	2.41089e154	1.84362	0.921812	−	0.387638i	$-0.126709\pi$
$983$	2.41089e154	1.84362	0.921812	+	0.387638i	$0.126709\pi$
$984$	1.89076e154	1.37211
$985$	1.24903e154	0.860212
$986$	2.02562e152	0.0132403
$987$	−5.85465e152	−0.0363218
$988$	−2.06323e154	−1.21497
$989$	2.98225e154	1.66700
$990$	−4.04920e152	−0.0214860
$991$	3.44196e153	0.173385	0.0866926	−	0.996235i	$-0.472370\pi$
$991$	3.44196e153	0.173385	0.0866926	+	0.996235i	$0.472370\pi$
$992$	−2.93327e154	−1.40282
$993$	−3.23405e154	−1.46846
$994$	−1.78458e154	−0.769374
$995$	3.71768e154	1.52189
$996$	−1.94597e154	−0.756451
$997$	−8.30556e153	−0.306597	−0.153299	−	0.988180i	$-0.548990\pi$
$997$	−8.30556e153	−0.306597	−0.153299	+	0.988180i	$0.548990\pi$
$998$	1.31906e154	0.462424
$999$	−5.02170e153	−0.167197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.104.a.a.1.4	✓	8
3.2	odd	2		9.104.a.a.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.104.a.a.1.4	✓	8	1.1	even	1	trivial
9.104.a.a.1.5		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 104 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-1.38660e15 q^{2} +4.94875e24 q^{3} -8.21853e30 q^{4} -1.47562e36 q^{5} -6.86195e39 q^{6} +3.27966e43 q^{7} +2.54577e46 q^{8} +1.05749e49 q^{9} +O(q^{10})\)	\(q-1.38660e15 q^{2} +4.94875e24 q^{3} -8.21853e30 q^{4} -1.47562e36 q^{5} -6.86195e39 q^{6} +3.27966e43 q^{7} +2.54577e46 q^{8} +1.05749e49 q^{9} +2.04610e51 q^{10} -1.87140e52 q^{11} -4.06714e55 q^{12} -1.80976e57 q^{13} -4.54760e58 q^{14} -7.30247e60 q^{15} +4.80460e61 q^{16} +4.46350e61 q^{17} -1.46632e64 q^{18} -1.38718e66 q^{19} +1.21274e67 q^{20} +1.62302e68 q^{21} +2.59489e67 q^{22} +1.24176e70 q^{23} +1.25984e71 q^{24} +1.19138e72 q^{25} +2.50942e72 q^{26} -1.65303e73 q^{27} -2.69540e74 q^{28} -3.27288e75 q^{29} +1.01256e76 q^{30} +9.03121e76 q^{31} -3.24793e77 q^{32} -9.26107e76 q^{33} -6.18911e76 q^{34} -4.83954e79 q^{35} -8.69101e79 q^{36} +3.03788e80 q^{37} +1.92347e81 q^{38} -8.95602e81 q^{39} -3.75659e82 q^{40} +1.50080e83 q^{41} -2.25049e83 q^{42} +2.40163e84 q^{43} +1.53801e83 q^{44} -1.56045e85 q^{45} -1.72184e85 q^{46} -3.60725e84 q^{47} +2.37768e86 q^{48} -3.38056e85 q^{49} -1.65197e87 q^{50} +2.20887e86 q^{51} +1.48735e88 q^{52} -9.21270e87 q^{53} +2.29210e88 q^{54} +2.76147e88 q^{55} +8.34927e89 q^{56} -6.86481e90 q^{57} +4.53819e90 q^{58} +1.63460e91 q^{59} +6.00156e91 q^{60} -9.20037e91 q^{61} -1.25227e92 q^{62} +3.46821e92 q^{63} -3.68858e91 q^{64} +2.67051e93 q^{65} +1.28414e92 q^{66} +1.05409e94 q^{67} -3.66834e92 q^{68} +6.14518e94 q^{69} +6.71053e94 q^{70} +3.92423e95 q^{71} +2.69212e95 q^{72} +2.83774e95 q^{73} -4.21234e95 q^{74} +5.89582e96 q^{75} +1.14006e97 q^{76} -6.13755e95 q^{77} +1.24185e97 q^{78} +2.16532e97 q^{79} -7.08977e97 q^{80} -2.28956e98 q^{81} -2.08102e98 q^{82} +4.78462e98 q^{83} -1.33389e99 q^{84} -6.58643e97 q^{85} -3.33011e99 q^{86} -1.61966e100 q^{87} -4.76415e98 q^{88} +3.22127e100 q^{89} +2.16373e100 q^{90} -5.93539e100 q^{91} -1.02055e101 q^{92} +4.46932e101 q^{93} +5.00183e99 q^{94} +2.04695e102 q^{95} -1.60732e102 q^{96} +7.81604e101 q^{97} +4.68750e100 q^{98} -1.97898e101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 43\!\cdots\!40 q^{2}+ \cdots + 35\!\cdots\!16 q^{9}+O(q^{10}) \) 8 * q + 4388929556680440 * q^2 + 5087569706910766050323040 * q^3 + 48324394003700265820897106483264 * q^4 + 551645266991094947988587979858507120 * q^5 + 2626953258123361256046267420263544594336 * q^6 + 41737594138377573148159523392718424208446400 * q^7 + 109882609245772353721829965115065527112449646080 * q^8 + 35934061358184471683999399496530848001601644543016 * q^9	\( 8 q + 43\!\cdots\!40 q^{2}+ \cdots - 72\!\cdots\!88 q^{99}+O(q^{100}) \) 8 * q + 4388929556680440 * q^2 + 5087569706910766050323040 * q^3 + 48324394003700265820897106483264 * q^4 + 551645266991094947988587979858507120 * q^5 + 2626953258123361256046267420263544594336 * q^6 + 41737594138377573148159523392718424208446400 * q^7 + 109882609245772353721829965115065527112449646080 * q^8 + 35934061358184471683999399496530848001601644543016 * q^9 + 2027618525260516073181410940373995286751686815077520 * q^10 - 53564255892798621618914292149029865323976089024126944 * q^11 + 25633960574085217446823189913789134273379599963259585280 * q^12 - 1551327849817932010092927923451244764349197489311375245520 * q^13 + 204985531745225680495392627955462650660602632112553429561408 * q^14 - 3020750766469193774466110593818157380300334453782433876013760 * q^15 + 361863449936885119768267973598726020537150452888847981908594688 * q^16 + 2015497649979997361336875976150254045164880842011155416684792720 * q^17 + 267307540106838323861864757930082029915233950378733807409255489240 * q^18 + 1484734834072313889071781871918609444991921518407889999862194156000 * q^19 + 2550001838610112272657033084622870492091806723524425439331785816960 * q^20 - 468651934282513875675935203933822637725944475261560345505782668354304 * q^21 - 137605849219876342207658729678467678698030207344807412231509580517920 * q^22 + 40599619287653938731347770176481184954623812150658724038701540865523520 * q^23 + 417632054269801118353552142462197805319757108882280256182409075047884800 * q^24 - 362937074225983688614876200177837163768974389374609498487470358942710600 * q^25 - 14030741852054819908281579342280387163553452467847954283089945570102881584 * q^26 + 6310451948770981419229340353143176080605163694982014782921106225679184320 * q^27 + 514148330168929069137279753066565726408108706760021137474482330032788078080 * q^28 - 1109314641409183093552976605346965837461990086922169583222454360155329880400 * q^29 - 31780974033428375753830150804412858338763487684738816318474129735272931696960 * q^30 + 104264780455232531257795764608297281101784409237357406959070797687652099233536 * q^31 + 1028908566996694821915427200010950055520054418022728660586770754660435042467840 * q^32 + 1637064370206527961191840416792241672318252830384788267847230786245723880401280 * q^33 - 16880249585595311287790910689090067879202031794055262067512201336945927884230032 * q^34 - 15809814583992711056872904141791269441389432991285782813731594074561867170321280 * q^35 + 805787623574605247165419461734624389987695467909486995221520106404473098849425728 * q^36 - 92541276402281504667713648425023541514489587998355774759921151431265396409265040 * q^37 + 1971300306790799032342240078744393153702898113403645290763243656535920191023423520 * q^38 - 7885389189078955664633112105466856010714545616525346076007201630144160874672246208 * q^39 + 1977015288844745924714331362379506784318231603612597717318543376316436008269440000 * q^40 + 222749082810191111691395557742339640725571297200098840306597511963716166910016506576 * q^41 - 1883267638769361387897797057480679095562739407538640601371566884432999969422842010880 * q^42 + 968895197607192930930940008787782675398644318852140770090896736295885033488529690400 * q^43 + 2615800371528018307641663183711908967442008589707371423475870586505299691562914926848 * q^44 - 1473010112873063959626609346390652156643077000013339776241472977560123315435112983760 * q^45 + 27446065195956198075877779014773406391109527885085904763819008268953431741208364616896 * q^46 - 293609653174290525998217973440321639247924396408373610899942779596119844480753010677120 * q^47 + 1240474483651634936656271628196732975278107731060035918088958893365811804822813860741120 * q^48 + 2668551616424529602044449137134709537764999196283756605526691963266904852724306068111944 * q^49 - 6521555021853481798089331632691717210870069276041958186139599024744619050092391455132600 * q^50 - 20813334460690950021193410586099062172982223916797529091846346968717683910092635969470784 * q^51 - 36075131888471074369144062637736452287512569193963836276062247375366142706627591324022400 * q^52 + 161574805302535676592212552212935130219348465152378468526413124882553154054403888166112240 * q^53 + 244996591061285005233721911255171344371445084231598513861031145908120404974069967807566400 * q^54 - 607939909864004614075356036982415128356301156312798815333086681706442442074797191568452160 * q^55 - 503347948801547505295544537202800039798463622449253526436143518261972796907682627548672000 * q^56 + 5585281202236608576148075500959180617113370740733374350303663601038337658261844358331674240 * q^57 + 10803107862759337782251611301310445432173113486135052277293695910012872510635542918433350480 * q^58 - 3763669177454952719015429893224775020266577352512033436736083012099637155611183545807925600 * q^59 - 44516663894047516283340986041100025029890327265561963837781098524475428602375001706220910080 * q^60 + 56147145392217940296237629782250660517556168142847888898434987753570576599200638389784423856 * q^61 + 708807506014393204305112275358657132745269481108345030482782405369277364762268787441349556480 * q^62 + 1004547917742295582189356352643083605257294414907733584799000902948644764606451215157969453760 * q^63 + 2689955130199770090919426143081142657167991663226807770013236363849718691785612797260291375104 * q^64 + 5124254892052438764657504605348539922002660919805937289990918847816257298286298313919564321440 * q^65 + 36460770617845857205288107920138564493995889702559578221696109246179691643034860902124792436352 * q^66 + 36212058392130762275437269862682052845105568281986303679248701513796303582516933489238204852320 * q^67 + 121871257184262948410168536656451503789769474779037040449473211419440774288140532505483576282240 * q^68 + 146171714897241059447510875608282423246804848799861315408644138710655320106224092813159842449152 * q^69 + 853756690279911250368037438486434151435346605497824981233696852732671552949658306872737406389120 * q^70 + 1323027110921369091114059758958942708535901440060160919331826835683096477433051757156908929999296 * q^71 + 5635474260733453081095589332277842775365114507654390044914919885310203213431471309882290635036160 * q^72 + 4434337224305117877569754735641925591340191550850949206294860286939824237219014387268913705824720 * q^73 + 9446978778046296456470116730008064896416484139132353834625710442657435714245141545863045630195088 * q^74 + 15788198796594475882673542236654839411090926672421130688549340631916075230881024844909417441328800 * q^75 + 62208878575567502646775884731743768059494074065603793769837837917746101674437608641395557819334400 * q^76 + 37781769005935846521801726968449743374817416956894448777845288067504206491843901930831867790380800 * q^77 + 44019466816742377243458217012569984532155201470078975456308994008831948835905199650013699349604800 * q^78 + 24360542002769992615028834274408332054107188048024574794369918904382062971902552671267968844374400 * q^79 - 257406550547438596244863901420403525688280266364441018588431059738298545930906704910071981299015680 * q^80 - 319858452590968976040706219061802261896767071034600475754637194160339936835204759950912194010523832 * q^81 - 347037715568344180193612732627815416282275947315627995720995526007231252178377268346955612809946320 * q^82 - 2589709199921534719789158381824365674651513931126861560377010891589296789100538920269990341311172640 * q^83 - 14763276600099218032093350675578467421653757870459793949112274722608304409453274353718894336536287232 * q^84 - 7750041700239420480976421024168094692666091522883832659906501732615678081854865932331016250083918880 * q^85 - 22862474248159310408090160685058395474537452344937345785285404938278205476818797847965682857887379744 * q^86 - 19667171614563900919678037177279936924594588506587176946944336641584005321373812755132416018759906240 * q^87 - 40280517105348128384004030315972727789809528309384337508840799111515821927415232196104998546661181440 * q^88 - 2411931583959929374872883405418443793306523554844108736778614462710442635343758894445178420208577200 * q^89 + 19218417888800936875567136220118837811145582599884634713838228828686741391845969008376636752235577040 * q^90 + 157061027064080129827172588737919758324770125960416982485587688356910129161874310994817267624768962176 * q^91 + 773615141308510753640652909662430286328720511338068191045295874258285130068299519150171249463376222720 * q^92 + 1017145077013570534640298063884056653140131362969292242328097944460668594729564068877620396903861703680 * q^93 + 727087863890952033548300791290895488242032063484702253117314469808013304697569232190083038540113931648 * q^94 + 2743732154506646909406097298325321408379587730896118185195801036752841998424162414172669753574660712000 * q^95 + 8873312662336745259606299368794125872185792644230053366160730387846004935345208576954549405340151709696 * q^96 + 5002945503247003905009597326381275147828980571278924405638622881444475469921369111184405290832776414480 * q^97 + 8807510378044686174684586237206775917067603624837914322579837506936931417303594998092206302439262913720 * q^98 - 7247372384990122262319746951941725843983906615680409319965154257589720777414294443683699540960522497888 * q^99

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