LMFDB - Embedded newform 1.104.a.a.1.1

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			1.1
Root			$2.50366e14$ 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)

$f(q)$	$=$	$q-5.46018e15 q^{2} -1.30099e24 q^{3} +1.96724e31 q^{4} -5.30727e35 q^{5} +7.10366e39 q^{6} +2.61912e43 q^{7} -5.20418e46 q^{8} -1.22226e49 q^{9} +O(q^{10})$	\(q-5.46018e15 q^{2} -1.30099e24 q^{3} +1.96724e31 q^{4} -5.30727e35 q^{5} +7.10366e39 q^{6} +2.61912e43 q^{7} -5.20418e46 q^{8} -1.22226e49 q^{9} +2.89786e51 q^{10} +4.50261e53 q^{11} -2.55936e55 q^{12} +2.00188e57 q^{13} -1.43009e59 q^{14} +6.90472e59 q^{15} +8.46561e61 q^{16} +3.55342e63 q^{17} +6.67376e64 q^{18} +1.06089e66 q^{19} -1.04406e67 q^{20} -3.40746e67 q^{21} -2.45850e69 q^{22} +1.51243e70 q^{23} +6.77060e70 q^{24} -7.04405e71 q^{25} -1.09306e73 q^{26} +3.40051e73 q^{27} +5.15243e74 q^{28} -1.95550e75 q^{29} -3.77010e75 q^{30} -6.33189e76 q^{31} +6.55289e76 q^{32} -5.85786e77 q^{33} -1.94023e79 q^{34} -1.39004e79 q^{35} -2.40447e80 q^{36} -3.73954e80 q^{37} -5.79264e81 q^{38} -2.60443e81 q^{39} +2.76200e82 q^{40} +1.79903e83 q^{41} +1.86054e83 q^{42} -4.86424e83 q^{43} +8.85768e84 q^{44} +6.48686e84 q^{45} -8.25816e85 q^{46} -1.62041e86 q^{47} -1.10137e86 q^{48} -4.23445e86 q^{49} +3.84618e87 q^{50} -4.62298e87 q^{51} +3.93817e88 q^{52} +7.08477e88 q^{53} -1.85674e89 q^{54} -2.38965e89 q^{55} -1.36304e90 q^{56} -1.38021e90 q^{57} +1.06774e91 q^{58} -2.20029e90 q^{59} +1.35832e91 q^{60} +4.53670e91 q^{61} +3.45732e92 q^{62} -3.20125e92 q^{63} -1.21631e93 q^{64} -1.06245e93 q^{65} +3.19850e93 q^{66} +1.42797e94 q^{67} +6.99042e94 q^{68} -1.96767e94 q^{69} +7.58986e94 q^{70} +1.63302e95 q^{71} +6.36086e95 q^{72} -1.05405e96 q^{73} +2.04186e96 q^{74} +9.16427e95 q^{75} +2.08702e97 q^{76} +1.17929e97 q^{77} +1.42207e97 q^{78} -7.93552e97 q^{79} -4.49292e97 q^{80} +1.25840e98 q^{81} -9.82303e98 q^{82} +5.44480e98 q^{83} -6.70328e98 q^{84} -1.88590e99 q^{85} +2.65596e99 q^{86} +2.54410e99 q^{87} -2.34324e100 q^{88} -3.14467e100 q^{89} -3.54194e100 q^{90} +5.24317e100 q^{91} +2.97532e101 q^{92} +8.23775e100 q^{93} +8.84774e101 q^{94} -5.63042e101 q^{95} -8.52526e100 q^{96} +6.67281e101 q^{97} +2.31208e102 q^{98} -5.50336e102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.46018e15	−1.71460	−0.857299	−	0.514819i	$-0.827859\pi$
$2$	−5.46018e15	−1.71460	−0.857299	+	0.514819i	$0.827859\pi$
$3$	−1.30099e24	−0.348763	−0.174382	−	0.984678i	$-0.555793\pi$
$3$	−1.30099e24	−0.348763	−0.174382	+	0.984678i	$0.555793\pi$
$4$	1.96724e31	1.93984
$5$	−5.30727e35	−0.534461	−0.267230	−	0.963633i	$-0.586108\pi$
$5$	−5.30727e35	−0.534461	−0.267230	+	0.963633i	$0.586108\pi$
$6$	7.10366e39	0.597988
$7$	2.61912e43	0.786334	0.393167	−	0.919467i	$-0.371379\pi$
$7$	2.61912e43	0.786334	0.393167	+	0.919467i	$0.371379\pi$
$8$	−5.20418e46	−1.61145
$9$	−1.22226e49	−0.878364
$10$	2.89786e51	0.916385
$11$	4.50261e53	1.05133	0.525667	−	0.850691i	$-0.323816\pi$
$11$	4.50261e53	1.05133	0.525667	+	0.850691i	$0.323816\pi$
$12$	−2.55936e55	−0.676546
$13$	2.00188e57	0.857739	0.428870	−	0.903366i	$-0.358912\pi$
$13$	2.00188e57	0.857739	0.428870	+	0.903366i	$0.358912\pi$
$14$	−1.43009e59	−1.34825
$15$	6.90472e59	0.186400
$16$	8.46561e61	0.823150
$17$	3.55342e63	1.52239	0.761197	−	0.648520i	$-0.224612\pi$
$17$	3.55342e63	1.52239	0.761197	+	0.648520i	$0.224612\pi$
$18$	6.67376e64	1.50604
$19$	1.06089e66	1.47863	0.739315	−	0.673360i	$-0.235149\pi$
$19$	1.06089e66	1.47863	0.739315	+	0.673360i	$0.235149\pi$
$20$	−1.04406e67	−1.03677
$21$	−3.40746e67	−0.274244
$22$	−2.45850e69	−1.80261
$23$	1.51243e70	1.12381	0.561905	−	0.827202i	$-0.310069\pi$
$23$	1.51243e70	1.12381	0.561905	+	0.827202i	$0.310069\pi$
$24$	6.77060e70	0.562016
$25$	−7.04405e71	−0.714352
$26$	−1.09306e73	−1.47068
$27$	3.40051e73	0.655104
$28$	5.15243e74	1.52536
$29$	−1.95550e75	−0.950084	−0.475042	−	0.879963i	$-0.657567\pi$
$29$	−1.95550e75	−0.950084	−0.475042	+	0.879963i	$0.657567\pi$
$30$	−3.77010e75	−0.319601
$31$	−6.33189e76	−0.991759	−0.495879	−	0.868391i	$-0.665154\pi$
$31$	−6.33189e76	−0.991759	−0.495879	+	0.868391i	$0.665154\pi$
$32$	6.55289e76	0.200082
$33$	−5.85786e77	−0.366666
$34$	−1.94023e79	−2.61029
$35$	−1.39004e79	−0.420264
$36$	−2.40447e80	−1.70389
$37$	−3.73954e80	−0.646293	−0.323147	−	0.946349i	$-0.604741\pi$
$37$	−3.73954e80	−0.646293	−0.323147	+	0.946349i	$0.604741\pi$
$38$	−5.79264e81	−2.53526
$39$	−2.60443e81	−0.299148
$40$	2.76200e82	0.861258
$41$	1.79903e83	1.57279	0.786394	−	0.617725i	$-0.211946\pi$
$41$	1.79903e83	1.57279	0.786394	+	0.617725i	$0.211946\pi$
$42$	1.86054e83	0.470218
$43$	−4.86424e83	−0.365923	−0.182961	−	0.983120i	$-0.558568\pi$
$43$	−4.86424e83	−0.365923	−0.182961	+	0.983120i	$0.558568\pi$
$44$	8.85768e84	2.03942
$45$	6.48686e84	0.469451
$46$	−8.25816e85	−1.92688
$47$	−1.62041e86	−1.24907	−0.624534	−	0.780998i	$-0.714711\pi$
$47$	−1.62041e86	−1.24907	−0.624534	+	0.780998i	$0.714711\pi$
$48$	−1.10137e86	−0.287085
$49$	−4.23445e86	−0.381679
$50$	3.84618e87	1.22483
$51$	−4.62298e87	−0.530955
$52$	3.93817e88	1.66388
$53$	7.08477e88	1.12232	0.561162	−	0.827706i	$-0.310355\pi$
$53$	7.08477e88	1.12232	0.561162	+	0.827706i	$0.310355\pi$
$54$	−1.85674e89	−1.12324
$55$	−2.38965e89	−0.561896
$56$	−1.36304e90	−1.26714
$57$	−1.38021e90	−0.515692
$58$	1.06774e91	1.62901
$59$	−2.20029e90	−0.139188	−0.0695941	−	0.997575i	$-0.522170\pi$
$59$	−2.20029e90	−0.139188	−0.0695941	+	0.997575i	$0.522170\pi$
$60$	1.35832e91	0.361587
$61$	4.53670e91	0.515529	0.257765	−	0.966208i	$-0.417014\pi$
$61$	4.53670e91	0.515529	0.257765	+	0.966208i	$0.417014\pi$
$62$	3.45732e92	1.70047
$63$	−3.20125e92	−0.690688
$64$	−1.21631e93	−1.16621
$65$	−1.06245e93	−0.458428
$66$	3.19850e93	0.628685
$67$	1.42797e94	1.29379	0.646897	−	0.762577i	$-0.276066\pi$
$67$	1.42797e94	1.29379	0.646897	+	0.762577i	$0.276066\pi$
$68$	6.99042e94	2.95321
$69$	−1.96767e94	−0.391944
$70$	7.58986e94	0.720584
$71$	1.63302e95	0.746771	0.373386	−	0.927676i	$-0.378197\pi$
$71$	1.63302e95	0.746771	0.373386	+	0.927676i	$0.378197\pi$
$72$	6.36086e95	1.41544
$73$	−1.05405e96	−1.15275	−0.576374	−	0.817186i	$-0.695533\pi$
$73$	−1.05405e96	−1.15275	−0.576374	+	0.817186i	$0.695533\pi$
$74$	2.04186e96	1.10813
$75$	9.16427e95	0.249140
$76$	2.08702e97	2.86831
$77$	1.17929e97	0.826699
$78$	1.42207e97	0.512918
$79$	−7.93552e97	−1.48518	−0.742592	−	0.669744i	$-0.766404\pi$
$79$	−7.93552e97	−1.48518	−0.742592	+	0.669744i	$0.766404\pi$
$80$	−4.49292e97	−0.439941
$81$	1.25840e98	0.649888
$82$	−9.82303e98	−2.69670
$83$	5.44480e98	0.800682	0.400341	−	0.916366i	$-0.368892\pi$
$83$	5.44480e98	0.800682	0.400341	+	0.916366i	$0.368892\pi$
$84$	−6.70328e98	−0.531991
$85$	−1.88590e99	−0.813660
$86$	2.65596e99	0.627410
$87$	2.54410e99	0.331354
$88$	−2.34324e100	−1.69418
$89$	−3.14467e100	−1.27054	−0.635272	−	0.772289i	$-0.719112\pi$
$89$	−3.14467e100	−1.27054	−0.635272	+	0.772289i	$0.719112\pi$
$90$	−3.54194e100	−0.804919
$91$	5.24317e100	0.674470
$92$	2.97532e101	2.18002
$93$	8.23775e100	0.345889
$94$	8.84774e101	2.14165
$95$	−5.63042e101	−0.790269
$96$	−8.52526e100	−0.0697813
$97$	6.67281e101	0.320305	0.160153	−	0.987092i	$-0.448801\pi$
$97$	6.67281e101	0.320305	0.160153	+	0.987092i	$0.448801\pi$
$98$	2.31208e102	0.654426
$99$	−5.50336e102	−0.923454
$100$	−1.38573e103	−1.38573
$101$	9.58727e102	0.574307	0.287154	−	0.957885i	$-0.407291\pi$
$101$	9.58727e102	0.574307	0.287154	+	0.957885i	$0.407291\pi$
$102$	2.52423e103	0.910374
$103$	−3.71510e102	−0.0810688	−0.0405344	−	0.999178i	$-0.512906\pi$
$103$	−3.71510e102	−0.0810688	−0.0405344	+	0.999178i	$0.512906\pi$
$104$	−1.04181e104	−1.38221
$105$	1.80843e103	0.146573
$106$	−3.86841e104	−1.92433
$107$	−3.82474e104	−1.17311	−0.586553	−	0.809911i	$-0.699516\pi$
$107$	−3.82474e104	−1.17311	−0.586553	+	0.809911i	$0.699516\pi$
$108$	6.68961e104	1.27080
$109$	8.09300e104	0.956411	0.478206	−	0.878248i	$-0.341287\pi$
$109$	8.09300e104	0.956411	0.478206	+	0.878248i	$0.341287\pi$
$110$	1.30479e105	0.963426
$111$	4.86512e104	0.225403
$112$	2.21725e105	0.647271
$113$	4.33478e105	0.800621	0.400311	−	0.916379i	$-0.368902\pi$
$113$	4.33478e105	0.800621	0.400311	+	0.916379i	$0.368902\pi$
$114$	7.53619e105	0.884204
$115$	−8.02689e105	−0.600632
$116$	−3.84694e106	−1.84301
$117$	−2.44682e106	−0.753408
$118$	1.20140e106	0.238652
$119$	9.30685e106	1.19711
$120$	−3.59334e106	−0.300375
$121$	1.93146e106	0.105302
$122$	−2.47712e107	−0.883925
$123$	−2.34053e107	−0.548530
$124$	−1.24563e108	−1.92386
$125$	8.97184e107	0.916253
$126$	1.74794e108	1.18425
$127$	−8.30922e107	−0.374687	−0.187344	−	0.982294i	$-0.559988\pi$
$127$	−8.30922e107	−0.374687	−0.187344	+	0.982294i	$0.559988\pi$
$128$	5.97675e108	1.79950
$129$	6.32834e107	0.127620
$130$	5.80117e108	0.786019
$131$	3.82011e108	0.348823	0.174411	−	0.984673i	$-0.444198\pi$
$131$	3.82011e108	0.348823	0.174411	+	0.984673i	$0.444198\pi$
$132$	−1.15238e109	−0.711276
$133$	2.77860e109	1.16270
$134$	−7.79695e109	−2.21834
$135$	−1.80474e109	−0.350127
$136$	−1.84926e110	−2.45327
$137$	1.58709e110	1.44375	0.721874	−	0.692024i	$-0.243281\pi$
$137$	1.58709e110	1.44375	0.721874	+	0.692024i	$0.243281\pi$
$138$	1.07438e110	0.672026
$139$	1.90197e110	0.820242	0.410121	−	0.912031i	$-0.365487\pi$
$139$	1.90197e110	0.820242	0.410121	+	0.912031i	$0.365487\pi$
$140$	−2.73453e110	−0.815247
$141$	2.10815e110	0.435629
$142$	−8.91660e110	−1.28041
$143$	9.01367e110	0.901770
$144$	−1.03472e111	−0.723026
$145$	1.03784e111	0.507782
$146$	5.75531e111	1.97650
$147$	5.50899e110	0.133116
$148$	−7.35656e111	−1.25371
$149$	1.31408e112	1.58317	0.791585	−	0.611059i	$-0.209256\pi$
$149$	1.31408e112	1.58317	0.791585	+	0.611059i	$0.209256\pi$
$150$	−5.00386e111	−0.427174
$151$	2.22106e112	1.34663	0.673314	−	0.739357i	$-0.264870\pi$
$151$	2.22106e112	1.34663	0.673314	+	0.739357i	$0.264870\pi$
$152$	−5.52106e112	−2.38274
$153$	−4.34321e112	−1.33722
$154$	−6.43912e112	−1.41746
$155$	3.36050e112	0.530056
$156$	−5.12353e112	−0.580300
$157$	1.03035e113	0.839755	0.419878	−	0.907581i	$-0.362073\pi$
$157$	1.03035e113	0.839755	0.419878	+	0.907581i	$0.362073\pi$
$158$	4.33294e113	2.54649
$159$	−9.21723e112	−0.391425
$160$	−3.47779e112	−0.106936
$161$	3.96125e113	0.883690
$162$	−6.87106e113	−1.11430
$163$	−1.34400e114	−1.58759	−0.793796	−	0.608184i	$-0.791898\pi$
$163$	−1.34400e114	−1.58759	−0.793796	+	0.608184i	$0.791898\pi$
$164$	3.53912e114	3.05096
$165$	3.10892e113	0.195969
$166$	−2.97296e114	−1.37285
$167$	−2.30653e114	−0.781737	−0.390868	−	0.920447i	$-0.627825\pi$
$167$	−2.30653e114	−0.781737	−0.390868	+	0.920447i	$0.627825\pi$
$168$	1.77330e114	0.441932
$169$	−1.43958e114	−0.264283
$170$	1.02973e115	1.39510
$171$	−1.29668e115	−1.29878
$172$	−9.56910e114	−0.709833
$173$	−6.66123e114	−0.366589	−0.183295	−	0.983058i	$-0.558676\pi$
$173$	−6.66123e114	−0.366589	−0.183295	+	0.983058i	$0.558676\pi$
$174$	−1.38912e115	−0.568139
$175$	−1.84492e115	−0.561719
$176$	3.81173e115	0.865406
$177$	2.86257e114	0.0485437
$178$	1.71705e116	2.17847
$179$	9.46546e115	0.899934	0.449967	−	0.893045i	$-0.351436\pi$
$179$	9.46546e115	0.899934	0.449967	+	0.893045i	$0.351436\pi$
$180$	1.27612e116	0.910662
$181$	−6.71300e115	−0.360139	−0.180069	−	0.983654i	$-0.557632\pi$
$181$	−6.71300e115	−0.360139	−0.180069	+	0.983654i	$0.557632\pi$
$182$	−2.86287e116	−1.15644
$183$	−5.90221e115	−0.179798
$184$	−7.87098e116	−1.81097
$185$	1.98467e116	0.345418
$186$	−4.49796e116	−0.593060
$187$	1.59997e117	1.60054
$188$	−3.18773e117	−2.42300
$189$	8.90636e116	0.515131
$190$	3.07431e117	1.35499
$191$	−1.50316e117	−0.505577	−0.252789	−	0.967522i	$-0.581348\pi$
$191$	−1.50316e117	−0.505577	−0.252789	+	0.967522i	$0.581348\pi$
$192$	1.58242e117	0.406731
$193$	3.67640e117	0.723138	0.361569	−	0.932345i	$-0.382241\pi$
$193$	3.67640e117	0.723138	0.361569	+	0.932345i	$0.382241\pi$
$194$	−3.64347e117	−0.549195
$195$	1.38224e117	0.159883
$196$	−8.33015e117	−0.740398
$197$	−1.11233e118	−0.760716	−0.380358	−	0.924839i	$-0.624199\pi$
$197$	−1.11233e118	−0.760716	−0.380358	+	0.924839i	$0.624199\pi$
$198$	3.00493e118	1.58335
$199$	2.74913e118	1.11754	0.558768	−	0.829324i	$-0.311274\pi$
$199$	2.74913e118	1.11754	0.558768	+	0.829324i	$0.311274\pi$
$200$	3.66585e118	1.15115
$201$	−1.85777e118	−0.451228
$202$	−5.23482e118	−0.984706
$203$	−5.12171e118	−0.747083
$204$	−9.09449e118	−1.02997
$205$	−9.54794e118	−0.840593
$206$	2.02851e118	0.139000
$207$	−1.84859e119	−0.987115
$208$	1.69471e119	0.706049
$209$	4.77676e119	1.55453
$210$	−9.87436e118	−0.251313
$211$	−5.77832e119	−1.15148	−0.575738	−	0.817634i	$-0.695285\pi$
$211$	−5.77832e119	−1.15148	−0.575738	+	0.817634i	$0.695285\pi$
$212$	1.39374e120	2.17713
$213$	−2.12455e119	−0.260446
$214$	2.08838e120	2.01141
$215$	2.58158e119	0.195571
$216$	−1.76969e120	−1.05567
$217$	−1.65840e120	−0.779853
$218$	−4.41892e120	−1.63986
$219$	1.37131e120	0.402036
$220$	−4.70101e120	−1.08999
$221$	7.11352e120	1.30582
$222$	−2.65644e120	−0.386476
$223$	6.96461e120	0.803889	0.401944	−	0.915664i	$-0.368334\pi$
$223$	6.96461e120	0.803889	0.401944	+	0.915664i	$0.368334\pi$
$224$	1.71628e120	0.157331
$225$	8.60967e120	0.627461
$226$	−2.36687e121	−1.37274
$227$	−2.51778e121	−1.16329	−0.581643	−	0.813444i	$-0.697590\pi$
$227$	−2.51778e121	−1.16329	−0.581643	+	0.813444i	$0.697590\pi$
$228$	−2.71520e121	−1.00036
$229$	5.94832e121	1.74931	0.874656	−	0.484745i	$-0.161088\pi$
$229$	5.94832e121	1.74931	0.874656	+	0.484745i	$0.161088\pi$
$230$	4.38283e121	1.02984
$231$	−1.53425e121	−0.288322
$232$	1.01768e122	1.53102
$233$	−1.21145e122	−1.46041	−0.730207	−	0.683226i	$-0.760576\pi$
$233$	−1.21145e122	−1.46041	−0.730207	+	0.683226i	$0.760576\pi$
$234$	1.33601e122	1.29179
$235$	8.59996e121	0.667577
$236$	−4.32850e121	−0.270003
$237$	1.03241e122	0.517977
$238$	−5.08171e122	−2.05256
$239$	−2.55458e122	−0.831434	−0.415717	−	0.909494i	$-0.636469\pi$
$239$	−2.55458e122	−0.831434	−0.415717	+	0.909494i	$0.636469\pi$
$240$	5.84527e121	0.153435
$241$	−4.59650e122	−0.973980	−0.486990	−	0.873408i	$-0.661905\pi$
$241$	−4.59650e122	−0.973980	−0.486990	+	0.873408i	$0.661905\pi$
$242$	−1.05461e122	−0.180551
$243$	−6.36904e122	−0.881761
$244$	8.92475e122	1.00005
$245$	2.24733e122	0.203992
$246$	1.27797e123	0.940509
$247$	2.12377e123	1.26828
$248$	3.29523e123	1.59817
$249$	−7.08365e122	−0.279248
$250$	−4.89878e123	−1.57101
$251$	−8.18914e122	−0.213817	−0.106908	−	0.994269i	$-0.534095\pi$
$251$	−8.18914e122	−0.213817	−0.106908	+	0.994269i	$0.534095\pi$
$252$	−6.29762e123	−1.33983
$253$	6.80990e123	1.18150
$254$	4.53698e123	0.642437
$255$	2.45354e123	0.283775
$256$	−2.02992e124	−1.91921
$257$	1.57942e124	1.22163	0.610817	−	0.791772i	$-0.290841\pi$
$257$	1.57942e124	1.22163	0.610817	+	0.791772i	$0.290841\pi$
$258$	−3.45539e123	−0.218817
$259$	−9.79432e123	−0.508202
$260$	−2.09009e124	−0.889278
$261$	2.39014e124	0.834520
$262$	−2.08585e124	−0.598090
$263$	2.58576e124	0.609351	0.304675	−	0.952456i	$-0.401452\pi$
$263$	2.58576e124	0.609351	0.304675	+	0.952456i	$0.401452\pi$
$264$	3.04854e124	0.590866
$265$	−3.76007e124	−0.599838
$266$	−1.51717e125	−1.99356
$267$	4.09120e124	0.443119
$268$	2.80914e125	2.50976
$269$	−9.10642e124	−0.671592	−0.335796	−	0.941935i	$-0.609005\pi$
$269$	−9.10642e124	−0.671592	−0.335796	+	0.941935i	$0.609005\pi$
$270$	9.85421e124	0.600327
$271$	3.36714e125	1.69567	0.847837	−	0.530256i	$-0.177904\pi$
$271$	3.36714e125	1.69567	0.847837	+	0.530256i	$0.177904\pi$
$272$	3.00819e125	1.25316
$273$	−6.82133e124	−0.235230
$274$	−8.66578e125	−2.47545
$275$	−3.17166e125	−0.751022
$276$	−3.87087e125	−0.760310
$277$	−4.58923e125	−0.748224	−0.374112	−	0.927384i	$-0.622052\pi$
$277$	−4.58923e125	−0.748224	−0.374112	+	0.927384i	$0.622052\pi$
$278$	−1.03851e126	−1.40638
$279$	7.73922e125	0.871125
$280$	7.23401e125	0.677237
$281$	1.57573e126	1.22774	0.613871	−	0.789406i	$-0.289611\pi$
$281$	1.57573e126	1.22774	0.613871	+	0.789406i	$0.289611\pi$
$282$	−1.15109e126	−0.746928
$283$	3.29385e125	0.178116	0.0890579	−	0.996026i	$-0.471614\pi$
$283$	3.29385e125	0.178116	0.0890579	+	0.996026i	$0.471614\pi$
$284$	3.21254e126	1.44862
$285$	7.32514e125	0.275617
$286$	−4.92163e126	−1.54617
$287$	4.71189e126	1.23674
$288$	−8.00934e125	−0.175745
$289$	7.17878e126	1.31769
$290$	−5.66678e126	−0.870642
$291$	−8.68128e125	−0.111711
$292$	−2.07357e127	−2.23615
$293$	1.39826e127	1.26446	0.632229	−	0.774781i	$-0.282140\pi$
$293$	1.39826e127	1.26446	0.632229	+	0.774781i	$0.282140\pi$
$294$	−3.00801e126	−0.228240
$295$	1.16775e126	0.0743906
$296$	1.94612e127	1.04147
$297$	1.53112e127	0.688733
$298$	−7.17509e127	−2.71450
$299$	3.02771e127	0.963937
$300$	1.80283e127	0.483292
$301$	−1.27400e127	−0.287737
$302$	−1.21274e128	−2.30892
$303$	−1.24730e127	−0.200297
$304$	8.98107e127	1.21713
$305$	−2.40774e127	−0.275530
$306$	2.37147e128	2.29279
$307$	−2.54064e127	−0.207643	−0.103822	−	0.994596i	$-0.533107\pi$
$307$	−2.54064e127	−0.207643	−0.103822	+	0.994596i	$0.533107\pi$
$308$	2.31994e128	1.60367
$309$	4.83333e126	0.0282738
$310$	−1.83489e128	−0.908832
$311$	−1.19727e127	−0.0502379	−0.0251190	−	0.999684i	$-0.507996\pi$
$311$	−1.19727e127	−0.0502379	−0.0251190	+	0.999684i	$0.507996\pi$
$312$	1.35539e128	0.482063
$313$	2.34857e127	0.0708387	0.0354193	−	0.999373i	$-0.488723\pi$
$313$	2.34857e127	0.0708387	0.0354193	+	0.999373i	$0.488723\pi$
$314$	−5.62590e128	−1.43984
$315$	1.69899e128	0.369145
$316$	−1.56110e129	−2.88102
$317$	4.05413e128	0.635837	0.317919	−	0.948118i	$-0.397016\pi$
$317$	4.05413e128	0.635837	0.317919	+	0.948118i	$0.397016\pi$
$318$	5.03278e128	0.671137
$319$	−8.80486e128	−0.998855
$320$	6.45530e128	0.623294
$321$	4.97597e128	0.409136
$322$	−2.16292e129	−1.51517
$323$	3.76979e129	2.25106
$324$	2.47556e129	1.26068
$325$	−1.41014e129	−0.612728
$326$	7.33850e129	2.72208
$327$	−1.05289e129	−0.333561
$328$	−9.36248e129	−2.53447
$329$	−4.24406e129	−0.982184
$330$	−1.69753e129	−0.336007
$331$	−3.80412e129	−0.644336	−0.322168	−	0.946682i	$-0.604412\pi$
$331$	−3.80412e129	−0.644336	−0.322168	+	0.946682i	$0.604412\pi$
$332$	1.07112e130	1.55320
$333$	4.57070e129	0.567681
$334$	1.25941e130	1.34036
$335$	−7.57859e129	−0.691482
$336$	−2.88463e129	−0.225744
$337$	−1.67977e130	−1.12800	−0.564001	−	0.825774i	$-0.690739\pi$
$337$	−1.67977e130	−1.12800	−0.564001	+	0.825774i	$0.690739\pi$
$338$	7.86034e129	0.453139
$339$	−5.63952e129	−0.279227
$340$	−3.71000e130	−1.57837
$341$	−2.85100e130	−1.04267
$342$	7.08012e130	2.22688
$343$	−4.01478e130	−1.08646
$344$	2.53144e130	0.589667
$345$	1.04429e130	0.209478
$346$	3.63715e130	0.628553
$347$	2.25423e130	0.335760	0.167880	−	0.985807i	$-0.446308\pi$
$347$	2.25423e130	0.335760	0.167880	+	0.985807i	$0.446308\pi$
$348$	5.00484e130	0.642775
$349$	−5.83015e130	−0.645908	−0.322954	−	0.946415i	$-0.604676\pi$
$349$	−5.83015e130	−0.645908	−0.322954	+	0.946415i	$0.604676\pi$
$350$	1.00736e131	0.963122
$351$	6.80742e130	0.561909
$352$	2.95051e130	0.210353
$353$	1.98835e130	0.122489	0.0612444	−	0.998123i	$-0.480493\pi$
$353$	1.98835e130	0.122489	0.0612444	+	0.998123i	$0.480493\pi$
$354$	−1.56301e130	−0.0832329
$355$	−8.66689e130	−0.399120
$356$	−6.18631e131	−2.46466
$357$	−1.21082e131	−0.417508
$358$	−5.16831e131	−1.54302
$359$	3.69274e131	0.954960	0.477480	−	0.878643i	$-0.341550\pi$
$359$	3.69274e131	0.954960	0.477480	+	0.878643i	$0.341550\pi$
$360$	−3.37588e131	−0.756499
$361$	6.10707e131	1.18635
$362$	3.66542e131	0.617493
$363$	−2.51281e130	−0.0367256
$364$	1.03146e132	1.30837
$365$	5.59413e131	0.616099
$366$	3.22271e131	0.308280
$367$	−1.08880e132	−0.904998	−0.452499	−	0.891765i	$-0.649467\pi$
$367$	−1.08880e132	−0.904998	−0.452499	+	0.891765i	$0.649467\pi$
$368$	1.28037e132	0.925065
$369$	−2.19889e132	−1.38148
$370$	−1.08367e132	−0.592253
$371$	1.85559e132	0.882521
$372$	1.62056e132	0.670970
$373$	3.00190e132	1.08241	0.541205	−	0.840891i	$-0.317968\pi$
$373$	3.00190e132	1.08241	0.541205	+	0.840891i	$0.317968\pi$
$374$	−8.73610e132	−2.74429
$375$	−1.16723e132	−0.319555
$376$	8.43292e132	2.01281
$377$	−3.91468e132	−0.814924
$378$	−4.86303e132	−0.883242
$379$	9.93644e132	1.57511	0.787556	−	0.616243i	$-0.211346\pi$
$379$	9.93644e132	1.57511	0.787556	+	0.616243i	$0.211346\pi$
$380$	−1.10764e133	−1.53300
$381$	1.08102e132	0.130677
$382$	8.20753e132	0.866861
$383$	−3.74392e132	−0.345613	−0.172806	−	0.984956i	$-0.555283\pi$
$383$	−3.74392e132	−0.345613	−0.172806	+	0.984956i	$0.555283\pi$
$384$	−7.77572e132	−0.627599
$385$	−6.25879e132	−0.441838
$386$	−2.00738e133	−1.23989
$387$	5.94537e132	0.321413
$388$	1.31270e133	0.621342
$389$	2.61673e133	1.08481	0.542406	−	0.840116i	$-0.317513\pi$
$389$	2.61673e133	1.08481	0.542406	+	0.840116i	$0.317513\pi$
$390$	−7.54729e132	−0.274135
$391$	5.37432e133	1.71088
$392$	2.20368e133	0.615058
$393$	−4.96995e132	−0.121656
$394$	6.07352e133	1.30432
$395$	4.21159e133	0.793772
$396$	−1.08264e134	−1.79136
$397$	−7.05323e133	−1.02489	−0.512444	−	0.858720i	$-0.671260\pi$
$397$	−7.05323e133	−1.02489	−0.512444	+	0.858720i	$0.671260\pi$
$398$	−1.50107e134	−1.91612
$399$	−3.61494e133	−0.405506
$400$	−5.96322e133	−0.588019
$401$	9.04492e132	0.0784277	0.0392138	−	0.999231i	$-0.487515\pi$
$401$	9.04492e132	0.0784277	0.0392138	+	0.999231i	$0.487515\pi$
$402$	1.01438e134	0.773674
$403$	−1.26757e134	−0.850671
$404$	1.88604e134	1.11407
$405$	−6.67864e133	−0.347340
$406$	2.79654e134	1.28095
$407$	−1.68377e134	−0.679470
$408$	2.40588e134	0.855610
$409$	−1.98753e134	−0.623107	−0.311554	−	0.950229i	$-0.600849\pi$
$409$	−1.98753e134	−0.623107	−0.311554	+	0.950229i	$0.600849\pi$
$410$	5.21335e134	1.44128
$411$	−2.06479e134	−0.503526
$412$	−7.30849e133	−0.157261
$413$	−5.76284e133	−0.109448
$414$	1.00936e135	1.69250
$415$	−2.88970e134	−0.427933
$416$	1.31181e134	0.171618
$417$	−2.47445e134	−0.286070
$418$	−2.60820e135	−2.66540
$419$	−1.34542e135	−1.21573	−0.607865	−	0.794040i	$-0.707974\pi$
$419$	−1.34542e135	−1.21573	−0.607865	+	0.794040i	$0.707974\pi$
$420$	3.55761e134	0.284328
$421$	2.13498e135	1.50961	0.754807	−	0.655947i	$-0.227730\pi$
$421$	2.13498e135	1.50961	0.754807	+	0.655947i	$0.227730\pi$
$422$	3.15507e135	1.97432
$423$	1.98057e135	1.09714
$424$	−3.68704e135	−1.80857
$425$	−2.50305e135	−1.08753
$426$	1.16004e135	0.446560
$427$	1.18822e135	0.405378
$428$	−7.52417e135	−2.27564
$429$	−1.17267e135	−0.314504
$430$	−1.40959e135	−0.335326
$431$	9.22168e135	1.94639	0.973196	−	0.229976i	$-0.0738648\pi$
$431$	9.22168e135	1.94639	0.973196	+	0.229976i	$0.0738648\pi$
$432$	2.87874e135	0.539249
$433$	−8.87148e135	−1.47526	−0.737632	−	0.675203i	$-0.764056\pi$
$433$	−8.87148e135	−1.47526	−0.737632	+	0.675203i	$0.764056\pi$
$434$	9.05516e135	1.33713
$435$	−1.35022e135	−0.177096
$436$	1.59208e136	1.85529
$437$	1.60453e136	1.66170
$438$	−7.48762e135	−0.689330
$439$	−1.83247e136	−1.50008	−0.750041	−	0.661391i	$-0.769966\pi$
$439$	−1.83247e136	−1.50008	−0.750041	+	0.661391i	$0.769966\pi$
$440$	1.24362e136	0.905470
$441$	5.17560e135	0.335253
$442$	−3.88411e136	−2.23895
$443$	−1.12684e136	−0.578188	−0.289094	−	0.957301i	$-0.593354\pi$
$443$	−1.12684e136	−0.578188	−0.289094	+	0.957301i	$0.593354\pi$
$444$	9.57084e135	0.437247
$445$	1.66896e136	0.679056
$446$	−3.80280e136	−1.37835
$447$	−1.70960e136	−0.552151
$448$	−3.18568e136	−0.917031
$449$	1.86589e135	0.0478849	0.0239425	−	0.999713i	$-0.492378\pi$
$449$	1.86589e135	0.0478849	0.0239425	+	0.999713i	$0.492378\pi$
$450$	−4.70104e136	−1.07584
$451$	8.10033e136	1.65352
$452$	8.52753e136	1.55308
$453$	−2.88959e136	−0.469654
$454$	1.37475e137	1.99457
$455$	−2.78269e136	−0.360477
$456$	7.18286e136	0.831013
$457$	1.50996e137	1.56056	0.780281	−	0.625429i	$-0.215076\pi$
$457$	1.50996e137	1.56056	0.780281	+	0.625429i	$0.215076\pi$
$458$	−3.24789e137	−2.99936
$459$	1.20835e137	0.997327
$460$	−1.57908e137	−1.16513
$461$	−5.70758e136	−0.376577	−0.188289	−	0.982114i	$-0.560294\pi$
$461$	−5.70758e136	−0.376577	−0.188289	+	0.982114i	$0.560294\pi$
$462$	8.37726e136	0.494356
$463$	−1.56763e137	−0.827602	−0.413801	−	0.910367i	$-0.635799\pi$
$463$	−1.56763e137	−0.827602	−0.413801	+	0.910367i	$0.635799\pi$
$464$	−1.65545e137	−0.782062
$465$	−4.37199e136	−0.184864
$466$	6.61474e137	2.50402
$467$	1.07059e137	0.362913	0.181456	−	0.983399i	$-0.441919\pi$
$467$	1.07059e137	0.362913	0.181456	+	0.983399i	$0.441919\pi$
$468$	−4.81347e137	−1.46149
$469$	3.74002e137	1.01735
$470$	−4.69573e137	−1.14463
$471$	−1.34048e137	−0.292876
$472$	1.14507e137	0.224295
$473$	−2.19017e137	−0.384707
$474$	−5.63712e137	−0.888123
$475$	−7.47296e137	−1.05626
$476$	1.83088e138	2.32221
$477$	−8.65943e137	−0.985809
$478$	1.39485e138	1.42557
$479$	−3.24976e137	−0.298244	−0.149122	−	0.988819i	$-0.547645\pi$
$479$	−3.24976e137	−0.298244	−0.149122	+	0.988819i	$0.547645\pi$
$480$	4.52458e136	0.0372954
$481$	−7.48611e137	−0.554351
$482$	2.50977e138	1.66998
$483$	−5.15357e137	−0.308199
$484$	3.79963e137	0.204270
$485$	−3.54144e137	−0.171191
$486$	3.47761e138	1.51187
$487$	−1.50996e138	−0.590504	−0.295252	−	0.955419i	$-0.595404\pi$
$487$	−1.50996e138	−0.590504	−0.295252	+	0.955419i	$0.595404\pi$
$488$	−2.36098e138	−0.830751
$489$	1.74854e138	0.553694
$490$	−1.22708e138	−0.349765
$491$	1.86965e138	0.479804	0.239902	−	0.970797i	$-0.422885\pi$
$491$	1.86965e138	0.479804	0.239902	+	0.970797i	$0.422885\pi$
$492$	−4.60437e138	−1.06406
$493$	−6.94873e138	−1.44640
$494$	−1.15962e139	−2.17459
$495$	2.92078e138	0.493550
$496$	−5.36033e138	−0.816367
$497$	4.27709e138	0.587211
$498$	3.86780e138	0.478799
$499$	1.11104e139	1.24037	0.620184	−	0.784456i	$-0.287058\pi$
$499$	1.11104e139	1.24037	0.620184	+	0.784456i	$0.287058\pi$
$500$	1.76497e139	1.77739
$501$	3.00078e138	0.272641
$502$	4.47142e138	0.366610
$503$	5.25435e138	0.388837	0.194419	−	0.980919i	$-0.437718\pi$
$503$	5.25435e138	0.388837	0.194419	+	0.980919i	$0.437718\pi$
$504$	1.66599e139	1.11301
$505$	−5.08822e138	−0.306945
$506$	−3.71833e139	−2.02580
$507$	1.87288e138	0.0921722
$508$	−1.63462e139	−0.726834
$509$	1.69031e139	0.679204	0.339602	−	0.940569i	$-0.389708\pi$
$509$	1.69031e139	0.679204	0.339602	+	0.940569i	$0.389708\pi$
$510$	−1.33968e139	−0.486559
$511$	−2.76069e139	−0.906445
$512$	5.02261e139	1.49117
$513$	3.60757e139	0.968657
$514$	−8.62390e139	−2.09461
$515$	1.97170e138	0.0433281
$516$	1.24493e139	0.247564
$517$	−7.29608e139	−1.31319
$518$	5.34788e139	0.871362
$519$	8.66621e138	0.127853
$520$	5.52918e139	0.738735
$521$	−1.49839e139	−0.181335	−0.0906677	−	0.995881i	$-0.528900\pi$
$521$	−1.49839e139	−0.181335	−0.0906677	+	0.995881i	$0.528900\pi$
$522$	−1.30506e140	−1.43087
$523$	1.48013e140	1.47049	0.735244	−	0.677802i	$-0.237067\pi$
$523$	1.48013e140	1.47049	0.735244	+	0.677802i	$0.237067\pi$
$524$	7.51507e139	0.676661
$525$	2.40024e139	0.195907
$526$	−1.41187e140	−1.04479
$527$	−2.24999e140	−1.50985
$528$	−4.95904e139	−0.301822
$529$	4.76256e139	0.262950
$530$	2.05307e140	1.02848
$531$	2.68933e139	0.122258
$532$	5.46616e140	2.25545
$533$	3.60144e140	1.34904
$534$	−2.23387e140	−0.759770
$535$	2.02989e140	0.626979
$536$	−7.43138e140	−2.08489
$537$	−1.23145e140	−0.313864
$538$	4.97227e140	1.15151
$539$	−1.90660e140	−0.401272
$540$	−3.55035e140	−0.679192
$541$	−2.50038e140	−0.434858	−0.217429	−	0.976076i	$-0.569767\pi$
$541$	−2.50038e140	−0.434858	−0.217429	+	0.976076i	$0.569767\pi$
$542$	−1.83852e141	−2.90740
$543$	8.73357e139	0.125603
$544$	2.32852e140	0.304604
$545$	−4.29517e140	−0.511164
$546$	3.72457e140	0.403325
$547$	1.55005e140	0.152756	0.0763781	−	0.997079i	$-0.475664\pi$
$547$	1.55005e140	0.152756	0.0763781	+	0.997079i	$0.475664\pi$
$548$	3.12217e141	2.80065
$549$	−5.54503e140	−0.452822
$550$	1.73178e141	1.28770
$551$	−2.07457e141	−1.40482
$552$	1.02401e141	0.631599
$553$	−2.07841e141	−1.16785
$554$	2.50580e141	1.28290
$555$	−2.58205e140	−0.120469
$556$	3.74163e141	1.59114
$557$	2.89920e141	1.12392	0.561959	−	0.827165i	$-0.310048\pi$
$557$	2.89920e141	1.12392	0.561959	+	0.827165i	$0.310048\pi$
$558$	−4.22575e141	−1.49363
$559$	−9.73762e140	−0.313866
$560$	−1.17675e141	−0.345941
$561$	−2.08154e141	−0.558211
$562$	−8.60378e141	−2.10508
$563$	6.09221e139	0.0136017	0.00680084	−	0.999977i	$-0.497835\pi$
$563$	6.09221e139	0.0136017	0.00680084	+	0.999977i	$0.497835\pi$
$564$	4.14722e141	0.845052
$565$	−2.30058e141	−0.427901
$566$	−1.79850e141	−0.305397
$567$	3.29589e141	0.511029
$568$	−8.49855e141	−1.20339
$569$	1.48496e142	1.92058	0.960289	−	0.279006i	$-0.0900048\pi$
$569$	1.48496e142	1.92058	0.960289	+	0.279006i	$0.0900048\pi$
$570$	−3.99966e141	−0.472572
$571$	5.27044e141	0.568968	0.284484	−	0.958681i	$-0.408178\pi$
$571$	5.27044e141	0.568968	0.284484	+	0.958681i	$0.408178\pi$
$572$	1.77320e142	1.74929
$573$	1.95560e141	0.176327
$574$	−2.57277e142	−2.12050
$575$	−1.06537e142	−0.802796
$576$	1.48665e142	1.02436
$577$	8.50107e141	0.535697	0.267849	−	0.963461i	$-0.413687\pi$
$577$	8.50107e141	0.535697	0.267849	+	0.963461i	$0.413687\pi$
$578$	−3.91974e142	−2.25930
$579$	−4.78297e141	−0.252204
$580$	2.04167e142	0.985018
$581$	1.42606e142	0.629604
$582$	4.74013e141	0.191539
$583$	3.18999e142	1.17994
$584$	5.48547e142	1.85760
$585$	1.29859e142	0.402667
$586$	−7.63474e142	−2.16804
$587$	2.15480e142	0.560460	0.280230	−	0.959933i	$-0.409589\pi$
$587$	2.15480e142	0.560460	0.280230	+	0.959933i	$0.409589\pi$
$588$	1.08375e142	0.258224
$589$	−6.71743e142	−1.46644
$590$	−6.37615e141	−0.127550
$591$	1.44713e142	0.265310
$592$	−3.16575e142	−0.531996
$593$	−9.57113e142	−1.47451	−0.737253	−	0.675617i	$-0.763877\pi$
$593$	−9.57113e142	−1.47451	−0.737253	+	0.675617i	$0.763877\pi$
$594$	−8.36017e142	−1.18090
$595$	−4.93939e142	−0.639808
$596$	2.58510e143	3.07110
$597$	−3.57660e142	−0.389755
$598$	−1.65319e143	−1.65276
$599$	9.42752e142	0.864801	0.432401	−	0.901682i	$-0.357667\pi$
$599$	9.42752e142	0.864801	0.432401	+	0.901682i	$0.357667\pi$
$600$	−4.76925e142	−0.401477
$601$	1.35464e143	1.04662	0.523310	−	0.852142i	$-0.324697\pi$
$601$	1.35464e143	1.04662	0.523310	+	0.852142i	$0.324697\pi$
$602$	6.95629e142	0.493354
$603$	−1.74535e143	−1.13642
$604$	4.36935e143	2.61225
$605$	−1.02508e142	−0.0562800
$606$	6.81047e142	0.343429
$607$	1.82567e143	0.845679	0.422839	−	0.906205i	$-0.361033\pi$
$607$	1.82567e143	0.845679	0.422839	+	0.906205i	$0.361033\pi$
$608$	6.95188e142	0.295848
$609$	6.66331e142	0.260555
$610$	1.31467e143	0.472423
$611$	−3.24387e143	−1.07137
$612$	−8.54411e143	−2.59399
$613$	−4.77180e143	−1.33189	−0.665945	−	0.746001i	$-0.731971\pi$
$613$	−4.77180e143	−1.33189	−0.665945	+	0.746001i	$0.731971\pi$
$614$	1.38724e143	0.356024
$615$	1.24218e143	0.293168
$616$	−6.13723e143	−1.33219
$617$	2.49860e143	0.498896	0.249448	−	0.968388i	$-0.419751\pi$
$617$	2.49860e143	0.498896	0.249448	+	0.968388i	$0.419751\pi$
$618$	−2.63908e142	−0.0484782
$619$	4.34805e143	0.734896	0.367448	−	0.930044i	$-0.380232\pi$
$619$	4.34805e143	0.734896	0.367448	+	0.930044i	$0.380232\pi$
$620$	6.61090e143	1.02823
$621$	5.14305e143	0.736213
$622$	6.53730e142	0.0861378
$623$	−8.23628e143	−0.999072
$624$	−2.20481e143	−0.246244
$625$	2.18438e143	0.224651
$626$	−1.28236e143	−0.121460
$627$	−6.21454e143	−0.542164
$628$	2.02694e144	1.62899
$629$	−1.32882e144	−0.983913
$630$	−9.27679e143	−0.632935
$631$	−2.31627e143	−0.145639	−0.0728196	−	0.997345i	$-0.523200\pi$
$631$	−2.31627e143	−0.145639	−0.0728196	+	0.997345i	$0.523200\pi$
$632$	4.12979e144	2.39331
$633$	7.51756e143	0.401593
$634$	−2.21363e144	−1.09021
$635$	4.40992e143	0.200255
$636$	−1.81325e144	−0.759304
$637$	−8.47685e143	−0.327381
$638$	4.80761e144	1.71263
$639$	−1.99598e144	−0.655937
$640$	−3.17202e144	−0.961762
$641$	1.76803e144	0.494655	0.247327	−	0.968932i	$-0.420448\pi$
$641$	1.76803e144	0.494655	0.247327	+	0.968932i	$0.420448\pi$
$642$	−2.71697e144	−0.701504
$643$	5.06126e144	1.20613	0.603064	−	0.797692i	$-0.293946\pi$
$643$	5.06126e144	1.20613	0.603064	+	0.797692i	$0.293946\pi$
$644$	7.79272e144	1.71422
$645$	−3.35862e143	−0.0682080
$646$	−2.05837e145	−3.85966
$647$	3.35045e144	0.580140	0.290070	−	0.957005i	$-0.406321\pi$
$647$	3.35045e144	0.580140	0.290070	+	0.957005i	$0.406321\pi$
$648$	−6.54891e144	−1.04726
$649$	−9.90706e143	−0.146333
$650$	7.69959e144	1.05058
$651$	2.15757e144	0.271984
$652$	−2.64397e145	−3.07968
$653$	1.16215e145	1.25093	0.625465	−	0.780252i	$-0.284909\pi$
$653$	1.16215e145	1.25093	0.625465	+	0.780252i	$0.284909\pi$
$654$	5.74899e144	0.571923
$655$	−2.02744e144	−0.186432
$656$	1.52299e145	1.29464
$657$	1.28833e145	1.01253
$658$	2.31733e145	1.68405
$659$	6.04023e144	0.405933	0.202967	−	0.979186i	$-0.434942\pi$
$659$	6.04023e144	0.405933	0.202967	+	0.979186i	$0.434942\pi$
$660$	6.11598e144	0.380149
$661$	−1.76758e144	−0.101626	−0.0508129	−	0.998708i	$-0.516181\pi$
$661$	−1.76758e144	−0.101626	−0.0508129	+	0.998708i	$0.516181\pi$
$662$	2.07712e145	1.10478
$663$	−9.25465e144	−0.455421
$664$	−2.83357e145	−1.29026
$665$	−1.47468e145	−0.621416
$666$	−2.49568e145	−0.973344
$667$	−2.95757e145	−1.06771
$668$	−4.53748e145	−1.51645
$669$	−9.06091e144	−0.280367
$670$	4.13805e145	1.18561
$671$	2.04269e145	0.541993
$672$	−2.23287e144	−0.0548714
$673$	−3.31245e145	−0.754004	−0.377002	−	0.926212i	$-0.623045\pi$
$673$	−3.31245e145	−0.754004	−0.377002	+	0.926212i	$0.623045\pi$
$674$	9.17185e145	1.93407
$675$	−2.39534e145	−0.467975
$676$	−2.83198e145	−0.512668
$677$	−8.09936e145	−1.35873	−0.679367	−	0.733799i	$-0.737746\pi$
$677$	−8.09936e145	−1.35873	−0.679367	+	0.733799i	$0.737746\pi$
$678$	3.07928e145	0.478762
$679$	1.74769e145	0.251867
$680$	9.81454e145	1.31118
$681$	3.27562e145	0.405711
$682$	1.55670e146	1.78776
$683$	7.49413e144	0.0798096	0.0399048	−	0.999203i	$-0.487295\pi$
$683$	7.49413e144	0.0798096	0.0399048	+	0.999203i	$0.487295\pi$
$684$	−2.55088e146	−2.51942
$685$	−8.42309e145	−0.771627
$686$	2.19214e146	1.86284
$687$	−7.73873e145	−0.610095
$688$	−4.11787e145	−0.301209
$689$	1.41828e146	0.962661
$690$	−5.70203e145	−0.359171
$691$	1.42862e146	0.835215	0.417608	−	0.908628i	$-0.362869\pi$
$691$	1.42862e146	0.835215	0.417608	+	0.908628i	$0.362869\pi$
$692$	−1.31042e146	−0.711126
$693$	−1.44140e146	−0.726143
$694$	−1.23085e146	−0.575694
$695$	−1.00943e146	−0.438387
$696$	−1.32399e146	−0.533962
$697$	6.39272e146	2.39440
$698$	3.18337e146	1.10747
$699$	1.57609e146	0.509339
$700$	−3.62940e146	−1.08965
$701$	−1.30604e146	−0.364317	−0.182158	−	0.983269i	$-0.558308\pi$
$701$	−1.30604e146	−0.364317	−0.182158	+	0.983269i	$0.558308\pi$
$702$	−3.71697e146	−0.963447
$703$	−3.96724e146	−0.955629
$704$	−5.47658e146	−1.22608
$705$	−1.11885e146	−0.232826
$706$	−1.08568e146	−0.210019
$707$	2.51103e146	0.451597
$708$	5.63135e145	0.0941672
$709$	−1.50306e146	−0.233719	−0.116860	−	0.993148i	$-0.537283\pi$
$709$	−1.50306e146	−0.233719	−0.116860	+	0.993148i	$0.537283\pi$
$710$	4.73228e146	0.684330
$711$	9.69928e146	1.30453
$712$	1.63654e147	2.04742
$713$	−9.57657e146	−1.11455
$714$	6.61127e146	0.715858
$715$	−4.78380e146	−0.481961
$716$	1.86208e147	1.74573
$717$	3.32349e146	0.289974
$718$	−2.01630e147	−1.63737
$719$	4.52946e146	0.342380	0.171190	−	0.985238i	$-0.445239\pi$
$719$	4.52946e146	0.342380	0.171190	+	0.985238i	$0.445239\pi$
$720$	5.49153e146	0.386429
$721$	−9.73032e145	−0.0637472
$722$	−3.33457e147	−2.03411
$723$	5.98002e146	0.339688
$724$	−1.32060e147	−0.698613
$725$	1.37747e147	0.678694
$726$	1.37204e146	0.0629697
$727$	−7.96559e146	−0.340562	−0.170281	−	0.985396i	$-0.554468\pi$
$727$	−7.96559e146	−0.340562	−0.170281	+	0.985396i	$0.554468\pi$
$728$	−2.72864e147	−1.08688
$729$	−9.22473e146	−0.342362
$730$	−3.05450e147	−1.05636
$731$	−1.72847e147	−0.557079
$732$	−1.16110e147	−0.348779
$733$	3.53939e147	0.990999	0.495500	−	0.868608i	$-0.334985\pi$
$733$	3.53939e147	0.990999	0.495500	+	0.868608i	$0.334985\pi$
$734$	5.94507e147	1.55171
$735$	−2.92377e146	−0.0711450
$736$	9.91081e146	0.224855
$737$	6.42956e147	1.36021
$738$	1.20063e148	2.36868
$739$	−4.95197e147	−0.911150	−0.455575	−	0.890198i	$-0.650566\pi$
$739$	−4.95197e147	−0.911150	−0.455575	+	0.890198i	$0.650566\pi$
$740$	3.90432e147	0.670057
$741$	−2.76301e147	−0.442329
$742$	−1.01318e148	−1.51317
$743$	5.33251e147	0.743033	0.371516	−	0.928426i	$-0.378838\pi$
$743$	5.33251e147	0.743033	0.371516	+	0.928426i	$0.378838\pi$
$744$	−4.28707e147	−0.557384
$745$	−6.97415e147	−0.846142
$746$	−1.63909e148	−1.85590
$747$	−6.65497e147	−0.703291
$748$	3.14751e148	3.10481
$749$	−1.00175e148	−0.922454
$750$	6.37329e147	0.547909
$751$	5.96070e147	0.478454	0.239227	−	0.970964i	$-0.423106\pi$
$751$	5.96070e147	0.478454	0.239227	+	0.970964i	$0.423106\pi$
$752$	−1.37178e148	−1.02817
$753$	1.06540e147	0.0745714
$754$	2.13749e148	1.39727
$755$	−1.17878e148	−0.719719
$756$	1.75209e148	0.999273
$757$	8.31494e147	0.443018	0.221509	−	0.975158i	$-0.428902\pi$
$757$	8.31494e147	0.443018	0.221509	+	0.975158i	$0.428902\pi$
$758$	−5.42547e148	−2.70068
$759$	−8.85963e147	−0.412064
$760$	2.93017e148	1.27348
$761$	−4.38910e148	−1.78265	−0.891325	−	0.453365i	$-0.850223\pi$
$761$	−4.38910e148	−1.78265	−0.891325	+	0.453365i	$0.850223\pi$
$762$	−5.90259e147	−0.224058
$763$	2.11966e148	0.752059
$764$	−2.95707e148	−0.980741
$765$	2.30506e148	0.714690
$766$	2.04425e148	0.592586
$767$	−4.40473e147	−0.119387
$768$	2.64092e148	0.669349
$769$	−9.80404e147	−0.232380	−0.116190	−	0.993227i	$-0.537068\pi$
$769$	−9.80404e147	−0.232380	−0.116190	+	0.993227i	$0.537068\pi$
$770$	3.41741e148	0.757574
$771$	−2.05481e148	−0.426061
$772$	7.23234e148	1.40277
$773$	3.27776e148	0.594748	0.297374	−	0.954761i	$-0.403889\pi$
$773$	3.27776e148	0.594748	0.297374	+	0.954761i	$0.403889\pi$
$774$	−3.24628e148	−0.551095
$775$	4.46022e148	0.708465
$776$	−3.47265e148	−0.516157
$777$	1.27424e148	0.177242
$778$	−1.42878e149	−1.86002
$779$	1.90857e149	2.32557
$780$	2.71920e148	0.310148
$781$	7.35286e148	0.785106
$782$	−2.93447e149	−2.93348
$783$	−6.64972e148	−0.622404
$784$	−3.58472e148	−0.314179
$785$	−5.46834e148	−0.448816
$786$	2.71368e148	0.208592
$787$	−2.62026e148	−0.188645	−0.0943225	−	0.995542i	$-0.530068\pi$
$787$	−2.62026e148	−0.188645	−0.0943225	+	0.995542i	$0.530068\pi$
$788$	−2.18821e149	−1.47567
$789$	−3.36406e148	−0.212519
$790$	−2.29960e149	−1.36100
$791$	1.13533e149	0.629556
$792$	2.86405e149	1.48810
$793$	9.08192e148	0.442190
$794$	3.85119e149	1.75727
$795$	4.89183e148	0.209201
$796$	5.40818e149	2.16784
$797$	−8.15941e148	−0.306588	−0.153294	−	0.988181i	$-0.548988\pi$
$797$	−8.15941e148	−0.306588	−0.153294	+	0.988181i	$0.548988\pi$
$798$	1.97382e149	0.695279
$799$	−5.75801e149	−1.90157
$800$	−4.61589e148	−0.142929
$801$	3.84361e149	1.11600
$802$	−4.93869e148	−0.134472
$803$	−4.74598e149	−1.21192
$804$	−3.65468e149	−0.875311
$805$	−2.10234e149	−0.472297
$806$	6.92115e149	1.45856
$807$	1.18474e149	0.234226
$808$	−4.98939e149	−0.925470
$809$	−3.06884e149	−0.534104	−0.267052	−	0.963682i	$-0.586050\pi$
$809$	−3.06884e149	−0.534104	−0.267052	+	0.963682i	$0.586050\pi$
$810$	3.64666e149	0.595547
$811$	1.75625e149	0.269161	0.134580	−	0.990903i	$-0.457031\pi$
$811$	1.75625e149	0.269161	0.134580	+	0.990903i	$0.457031\pi$
$812$	−1.00756e150	−1.44922
$813$	−4.38063e149	−0.591389
$814$	9.19367e149	1.16502
$815$	7.13299e149	0.848505
$816$	−3.91363e149	−0.437056
$817$	−5.16042e149	−0.541064
$818$	1.08523e150	1.06838
$819$	−6.40852e149	−0.592430
$820$	−1.87830e150	−1.63062
$821$	8.24093e149	0.671898	0.335949	−	0.941880i	$-0.390943\pi$
$821$	8.24093e149	0.671898	0.335949	+	0.941880i	$0.390943\pi$
$822$	1.12741e150	0.863345
$823$	−1.47424e149	−0.106042	−0.0530210	−	0.998593i	$-0.516885\pi$
$823$	−1.47424e149	−0.106042	−0.0530210	+	0.998593i	$0.516885\pi$
$824$	1.93341e149	0.130639
$825$	4.12631e149	0.261929
$826$	3.14662e149	0.187660
$827$	4.73345e149	0.265243	0.132622	−	0.991167i	$-0.457661\pi$
$827$	4.73345e149	0.265243	0.132622	+	0.991167i	$0.457661\pi$
$828$	−3.63661e150	−1.91485
$829$	1.42057e150	0.702918	0.351459	−	0.936203i	$-0.385686\pi$
$829$	1.42057e150	0.702918	0.351459	+	0.936203i	$0.385686\pi$
$830$	1.57783e150	0.733733
$831$	5.97056e149	0.260953
$832$	−2.43492e150	−1.00031
$833$	−1.50468e150	−0.581066
$834$	1.35110e150	0.490495
$835$	1.22414e150	0.417807
$836$	9.39702e150	3.01555
$837$	−2.15317e150	−0.649705
$838$	7.34626e150	2.08449
$839$	−1.36874e150	−0.365242	−0.182621	−	0.983183i	$-0.558458\pi$
$839$	−1.36874e150	−0.365242	−0.182621	+	0.983183i	$0.558458\pi$
$840$	−9.41140e149	−0.236195
$841$	−4.12372e149	−0.0973409
$842$	−1.16574e151	−2.58838
$843$	−2.05002e150	−0.428191
$844$	−1.13673e151	−2.23369
$845$	7.64021e149	0.141249
$846$	−1.08143e151	−1.88115
$847$	5.05873e149	0.0828029
$848$	5.99769e150	0.923841
$849$	−4.28528e149	−0.0621202
$850$	1.36671e151	1.86467
$851$	−5.65581e150	−0.726311
$852$	−4.17950e150	−0.505225
$853$	7.71668e150	0.878123	0.439062	−	0.898457i	$-0.355311\pi$
$853$	7.71668e150	0.878123	0.439062	+	0.898457i	$0.355311\pi$
$854$	−6.48788e150	−0.695060
$855$	6.88184e150	0.694144
$856$	1.99046e151	1.89041
$857$	1.36517e151	1.22088	0.610440	−	0.792063i	$-0.290993\pi$
$857$	1.36517e151	1.22088	0.610440	+	0.792063i	$0.290993\pi$
$858$	6.40301e150	0.539248
$859$	−4.88128e150	−0.387156	−0.193578	−	0.981085i	$-0.562009\pi$
$859$	−4.88128e150	−0.387156	−0.193578	+	0.981085i	$0.562009\pi$
$860$	5.07858e150	0.379378
$861$	−6.13013e150	−0.431328
$862$	−5.03520e151	−3.33728
$863$	2.58884e151	1.61640	0.808201	−	0.588906i	$-0.200441\pi$
$863$	2.58884e151	1.61640	0.808201	+	0.588906i	$0.200441\pi$
$864$	2.22832e150	0.131075
$865$	3.53529e150	0.195928
$866$	4.84399e151	2.52948
$867$	−9.33955e150	−0.459560
$868$	−3.26246e151	−1.51279
$869$	−3.57305e151	−1.56142
$870$	7.37245e150	0.303648
$871$	2.85861e151	1.10974
$872$	−4.21174e151	−1.54121
$873$	−8.15591e150	−0.281345
$874$	−8.76100e151	−2.84915
$875$	2.34983e151	0.720481
$876$	2.69770e151	0.779888
$877$	5.48140e150	0.149421	0.0747107	−	0.997205i	$-0.476197\pi$
$877$	5.48140e150	0.149421	0.0747107	+	0.997205i	$0.476197\pi$
$878$	1.00056e152	2.57204
$879$	−1.81912e151	−0.440997
$880$	−2.02299e151	−0.462525
$881$	3.41155e151	0.735685	0.367843	−	0.929888i	$-0.380097\pi$
$881$	3.41155e151	0.735685	0.367843	+	0.929888i	$0.380097\pi$
$882$	−2.82597e151	−0.574824
$883$	−8.15917e151	−1.56556	−0.782780	−	0.622299i	$-0.786199\pi$
$883$	−8.15917e151	−1.56556	−0.782780	+	0.622299i	$0.786199\pi$
$884$	1.39940e152	2.53308
$885$	−1.51924e150	−0.0259447
$886$	6.15273e151	0.991359
$887$	−9.60570e151	−1.46037	−0.730184	−	0.683250i	$-0.760566\pi$
$887$	−9.60570e151	−1.46037	−0.730184	+	0.683250i	$0.760566\pi$
$888$	−2.53190e151	−0.363227
$889$	−2.17629e151	−0.294629
$890$	−9.11282e151	−1.16431
$891$	5.66606e151	0.683249
$892$	1.37010e152	1.55942
$893$	−1.71908e152	−1.84691
$894$	9.33474e151	0.946717
$895$	−5.02357e151	−0.480979
$896$	1.56539e152	1.41501
$897$	−3.93904e151	−0.336186
$898$	−1.01881e151	−0.0821034
$899$	1.23820e152	0.942254
$900$	1.69373e152	1.21718
$901$	2.51752e152	1.70862
$902$	−4.42292e152	−2.83513
$903$	1.65747e151	0.100352
$904$	−2.25590e152	−1.29016
$905$	3.56277e151	0.192480
$906$	1.57777e152	0.805268
$907$	−2.92428e152	−1.41008	−0.705039	−	0.709168i	$-0.749071\pi$
$907$	−2.92428e152	−1.41008	−0.705039	+	0.709168i	$0.749071\pi$
$908$	−4.95307e152	−2.25659
$909$	−1.17181e152	−0.504451
$910$	1.51940e152	0.618073
$911$	3.06739e152	1.17916	0.589580	−	0.807710i	$-0.299293\pi$
$911$	3.06739e152	1.17916	0.589580	+	0.807710i	$0.299293\pi$
$912$	−1.16843e152	−0.424492
$913$	2.45158e152	0.841784
$914$	−8.24465e152	−2.67573
$915$	3.13246e151	0.0960947
$916$	1.17017e153	3.39339
$917$	1.00054e152	0.274291
$918$	−6.59778e152	−1.71001
$919$	2.60238e152	0.637709	0.318854	−	0.947804i	$-0.396702\pi$
$919$	2.60238e152	0.637709	0.318854	+	0.947804i	$0.396702\pi$
$920$	4.17734e152	0.967891
$921$	3.30536e151	0.0724182
$922$	3.11644e152	0.645678
$923$	3.26912e152	0.640535
$924$	−3.01822e152	−0.559300
$925$	2.63415e152	0.461681
$926$	8.55952e152	1.41900
$927$	4.54083e151	0.0712080
$928$	−1.28142e152	−0.190095
$929$	−1.69956e152	−0.238521	−0.119260	−	0.992863i	$-0.538052\pi$
$929$	−1.69956e152	−0.238521	−0.119260	+	0.992863i	$0.538052\pi$
$930$	2.38719e152	0.316967
$931$	−4.49228e152	−0.564362
$932$	−2.38321e153	−2.83298
$933$	1.55764e151	0.0175211
$934$	−5.84560e152	−0.622250
$935$	−8.49144e152	−0.855428
$936$	1.27337e153	1.21408
$937$	−1.54910e153	−1.39794	−0.698971	−	0.715150i	$-0.746359\pi$
$937$	−1.54910e153	−1.39794	−0.698971	+	0.715150i	$0.746359\pi$
$938$	−2.04212e153	−1.74435
$939$	−3.05548e151	−0.0247059
$940$	1.69181e153	1.29500
$941$	1.95873e153	1.41941	0.709707	−	0.704497i	$-0.248827\pi$
$941$	1.95873e153	1.41941	0.709707	+	0.704497i	$0.248827\pi$
$942$	7.31926e152	0.502164
$943$	2.72092e153	1.76752
$944$	−1.86268e152	−0.114573
$945$	−4.72684e152	−0.275317
$946$	1.19587e153	0.659617
$947$	−3.18920e153	−1.66594	−0.832968	−	0.553321i	$-0.813360\pi$
$947$	−3.18920e153	−1.66594	−0.832968	+	0.553321i	$0.813360\pi$
$948$	2.03099e153	1.00480
$949$	−2.11008e153	−0.988758
$950$	4.08037e153	1.81106
$951$	−5.27440e152	−0.221757
$952$	−4.84345e153	−1.92909
$953$	−1.81979e153	−0.686654	−0.343327	−	0.939216i	$-0.611554\pi$
$953$	−1.81979e153	−0.686654	−0.343327	+	0.939216i	$0.611554\pi$
$954$	4.72820e153	1.69027
$955$	7.97768e152	0.270211
$956$	−5.02546e153	−1.61285
$957$	1.14551e153	0.348364
$958$	1.77442e153	0.511368
$959$	4.15678e153	1.13527
$960$	−8.39831e152	−0.217382
$961$	−6.69097e151	−0.0164148
$962$	4.08755e153	0.950489
$963$	4.67483e153	1.03042
$964$	−9.04240e153	−1.88937
$965$	−1.95116e153	−0.386489
$966$	2.81394e153	0.528436
$967$	−4.30897e153	−0.767202	−0.383601	−	0.923499i	$-0.625316\pi$
$967$	−4.30897e153	−0.767202	−0.383601	+	0.923499i	$0.625316\pi$
$968$	−1.00517e153	−0.169690
$969$	−4.90447e153	−0.785086
$970$	1.93369e153	0.293523
$971$	7.26145e152	0.104528	0.0522641	−	0.998633i	$-0.483356\pi$
$971$	7.26145e152	0.104528	0.0522641	+	0.998633i	$0.483356\pi$
$972$	−1.25294e154	−1.71048
$973$	4.98150e153	0.644984
$974$	8.24463e153	1.01248
$975$	1.83458e153	0.213697
$976$	3.84059e153	0.424358
$977$	4.14163e153	0.434112	0.217056	−	0.976159i	$-0.430355\pi$
$977$	4.14163e153	0.434112	0.217056	+	0.976159i	$0.430355\pi$
$978$	−9.54735e153	−0.949362
$979$	−1.41592e154	−1.33577
$980$	4.42103e153	0.395713
$981$	−9.89175e153	−0.840078
$982$	−1.02086e154	−0.822671
$983$	−4.71221e153	−0.360345	−0.180172	−	0.983635i	$-0.557666\pi$
$983$	−4.71221e153	−0.360345	−0.180172	+	0.983635i	$0.557666\pi$
$984$	1.21805e154	0.883931
$985$	5.90343e153	0.406573
$986$	3.79413e154	2.48000
$987$	5.52150e153	0.342550
$988$	4.17796e154	2.46026
$989$	−7.35684e153	−0.411228
$990$	−1.59480e154	−0.846239
$991$	2.54041e154	1.27971	0.639854	−	0.768497i	$-0.278995\pi$
$991$	2.54041e154	1.27971	0.639854	+	0.768497i	$0.278995\pi$
$992$	−4.14921e153	−0.198433
$993$	4.94914e153	0.224721
$994$	−2.33537e154	−1.00683
$995$	−1.45903e154	−0.597279
$996$	−1.39352e154	−0.541698
$997$	1.47094e154	0.542991	0.271496	−	0.962440i	$-0.412482\pi$
$997$	1.47094e154	0.542991	0.271496	+	0.962440i	$0.412482\pi$
$998$	−6.06646e154	−2.12673
$999$	−1.27164e154	−0.423389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.104.a.a.1.1	✓	8
3.2	odd	2		9.104.a.a.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.104.a.a.1.1	✓	8	1.1	even	1	trivial
9.104.a.a.1.8		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)

\(f(q)\)	\(=\)	\(q-5.46018e15 q^{2} -1.30099e24 q^{3} +1.96724e31 q^{4} -5.30727e35 q^{5} +7.10366e39 q^{6} +2.61912e43 q^{7} -5.20418e46 q^{8} -1.22226e49 q^{9} +O(q^{10})\)	\(q-5.46018e15 q^{2} -1.30099e24 q^{3} +1.96724e31 q^{4} -5.30727e35 q^{5} +7.10366e39 q^{6} +2.61912e43 q^{7} -5.20418e46 q^{8} -1.22226e49 q^{9} +2.89786e51 q^{10} +4.50261e53 q^{11} -2.55936e55 q^{12} +2.00188e57 q^{13} -1.43009e59 q^{14} +6.90472e59 q^{15} +8.46561e61 q^{16} +3.55342e63 q^{17} +6.67376e64 q^{18} +1.06089e66 q^{19} -1.04406e67 q^{20} -3.40746e67 q^{21} -2.45850e69 q^{22} +1.51243e70 q^{23} +6.77060e70 q^{24} -7.04405e71 q^{25} -1.09306e73 q^{26} +3.40051e73 q^{27} +5.15243e74 q^{28} -1.95550e75 q^{29} -3.77010e75 q^{30} -6.33189e76 q^{31} +6.55289e76 q^{32} -5.85786e77 q^{33} -1.94023e79 q^{34} -1.39004e79 q^{35} -2.40447e80 q^{36} -3.73954e80 q^{37} -5.79264e81 q^{38} -2.60443e81 q^{39} +2.76200e82 q^{40} +1.79903e83 q^{41} +1.86054e83 q^{42} -4.86424e83 q^{43} +8.85768e84 q^{44} +6.48686e84 q^{45} -8.25816e85 q^{46} -1.62041e86 q^{47} -1.10137e86 q^{48} -4.23445e86 q^{49} +3.84618e87 q^{50} -4.62298e87 q^{51} +3.93817e88 q^{52} +7.08477e88 q^{53} -1.85674e89 q^{54} -2.38965e89 q^{55} -1.36304e90 q^{56} -1.38021e90 q^{57} +1.06774e91 q^{58} -2.20029e90 q^{59} +1.35832e91 q^{60} +4.53670e91 q^{61} +3.45732e92 q^{62} -3.20125e92 q^{63} -1.21631e93 q^{64} -1.06245e93 q^{65} +3.19850e93 q^{66} +1.42797e94 q^{67} +6.99042e94 q^{68} -1.96767e94 q^{69} +7.58986e94 q^{70} +1.63302e95 q^{71} +6.36086e95 q^{72} -1.05405e96 q^{73} +2.04186e96 q^{74} +9.16427e95 q^{75} +2.08702e97 q^{76} +1.17929e97 q^{77} +1.42207e97 q^{78} -7.93552e97 q^{79} -4.49292e97 q^{80} +1.25840e98 q^{81} -9.82303e98 q^{82} +5.44480e98 q^{83} -6.70328e98 q^{84} -1.88590e99 q^{85} +2.65596e99 q^{86} +2.54410e99 q^{87} -2.34324e100 q^{88} -3.14467e100 q^{89} -3.54194e100 q^{90} +5.24317e100 q^{91} +2.97532e101 q^{92} +8.23775e100 q^{93} +8.84774e101 q^{94} -5.63042e101 q^{95} -8.52526e100 q^{96} +6.67281e101 q^{97} +2.31208e102 q^{98} -5.50336e102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 43\!\cdots\!40 q^{2}+ \cdots + 35\!\cdots\!16 q^{9}+O(q^{10}) \) 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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