LMFDB - Embedded newform 1.104.a.a.1.8

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			1.8
Root			$-2.30156e14$ 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)

$f(q)$	$=$	$q+6.07235e15 q^{2} +6.42408e24 q^{3} +2.67322e31 q^{4} -2.83827e35 q^{5} +3.90093e40 q^{6} -2.16284e43 q^{7} +1.00747e47 q^{8} +2.73537e49 q^{9} +O(q^{10})$	\(q+6.07235e15 q^{2} +6.42408e24 q^{3} +2.67322e31 q^{4} -2.83827e35 q^{5} +3.90093e40 q^{6} -2.16284e43 q^{7} +1.00747e47 q^{8} +2.73537e49 q^{9} -1.72350e51 q^{10} +2.34754e53 q^{11} +1.71730e56 q^{12} -1.57075e57 q^{13} -1.31335e59 q^{14} -1.82333e60 q^{15} +3.40672e62 q^{16} -1.46066e63 q^{17} +1.66101e65 q^{18} +1.14769e66 q^{19} -7.58734e66 q^{20} -1.38943e68 q^{21} +1.42551e69 q^{22} +3.42022e69 q^{23} +6.47205e71 q^{24} -9.05518e71 q^{25} -9.53817e72 q^{26} +8.63299e73 q^{27} -5.78176e74 q^{28} +3.20038e74 q^{29} -1.10719e76 q^{30} +5.53588e76 q^{31} +1.04699e78 q^{32} +1.50808e78 q^{33} -8.86962e78 q^{34} +6.13873e78 q^{35} +7.31225e80 q^{36} -8.68560e79 q^{37} +6.96915e81 q^{38} -1.00907e82 q^{39} -2.85946e82 q^{40} +6.58025e82 q^{41} -8.43709e83 q^{42} -2.31883e84 q^{43} +6.27549e84 q^{44} -7.76372e84 q^{45} +2.07688e85 q^{46} -2.37719e86 q^{47} +2.18850e87 q^{48} -6.41638e86 q^{49} -5.49862e87 q^{50} -9.38338e87 q^{51} -4.19898e88 q^{52} -1.71359e88 q^{53} +5.24225e89 q^{54} -6.66295e88 q^{55} -2.17899e90 q^{56} +7.37283e90 q^{57} +1.94338e90 q^{58} -1.30001e91 q^{59} -4.87417e91 q^{60} -6.15903e91 q^{61} +3.36158e92 q^{62} -5.91616e92 q^{63} +2.90285e93 q^{64} +4.45823e92 q^{65} +9.15757e93 q^{66} +6.14223e92 q^{67} -3.90466e94 q^{68} +2.19718e94 q^{69} +3.72765e94 q^{70} +1.58406e95 q^{71} +2.75579e96 q^{72} -1.01581e96 q^{73} -5.27420e95 q^{74} -5.81713e96 q^{75} +3.06802e97 q^{76} -5.07734e96 q^{77} -6.12740e97 q^{78} +8.88387e97 q^{79} -9.66920e97 q^{80} +1.73959e98 q^{81} +3.99576e98 q^{82} -4.44747e98 q^{83} -3.71425e99 q^{84} +4.14574e98 q^{85} -1.40807e100 q^{86} +2.05595e99 q^{87} +2.36506e100 q^{88} +2.52929e100 q^{89} -4.71440e100 q^{90} +3.39729e100 q^{91} +9.14300e100 q^{92} +3.55630e101 q^{93} -1.44352e102 q^{94} -3.25745e101 q^{95} +6.72593e102 q^{96} +6.67584e101 q^{97} -3.89625e102 q^{98} +6.42137e102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	6.07235e15	1.90683	0.953415	−	0.301661i	$-0.0975410\pi$
$2$	6.07235e15	1.90683	0.953415	+	0.301661i	$0.0975410\pi$
$3$	6.42408e24	1.72213	0.861066	−	0.508493i	$-0.169797\pi$
$3$	6.42408e24	1.72213	0.861066	+	0.508493i	$0.169797\pi$
$4$	2.67322e31	2.63600
$5$	−2.83827e35	−0.285824	−0.142912	−	0.989735i	$-0.545647\pi$
$5$	−2.83827e35	−0.285824	−0.142912	+	0.989735i	$0.545647\pi$
$6$	3.90093e40	3.28382
$7$	−2.16284e43	−0.649345	−0.324672	−	0.945827i	$-0.605254\pi$
$7$	−2.16284e43	−0.649345	−0.324672	+	0.945827i	$0.605254\pi$
$8$	1.00747e47	3.11958
$9$	2.73537e49	1.96574
$10$	−1.72350e51	−0.545018
$11$	2.34754e53	0.548137	0.274068	−	0.961710i	$-0.411631\pi$
$11$	2.34754e53	0.548137	0.274068	+	0.961710i	$0.411631\pi$
$12$	1.71730e56	4.53955
$13$	−1.57075e57	−0.673016	−0.336508	−	0.941681i	$-0.609246\pi$
$13$	−1.57075e57	−0.673016	−0.336508	+	0.941681i	$0.609246\pi$
$14$	−1.31335e59	−1.23819
$15$	−1.82333e60	−0.492227
$16$	3.40672e62	3.31251
$17$	−1.46066e63	−0.625790	−0.312895	−	0.949788i	$-0.601299\pi$
$17$	−1.46066e63	−0.625790	−0.312895	+	0.949788i	$0.601299\pi$
$18$	1.66101e65	3.74833
$19$	1.14769e66	1.59960	0.799802	−	0.600263i	$-0.204938\pi$
$19$	1.14769e66	1.59960	0.799802	+	0.600263i	$0.204938\pi$
$20$	−7.58734e66	−0.753433
$21$	−1.38943e68	−1.11826
$22$	1.42551e69	1.04520
$23$	3.42022e69	0.254138	0.127069	−	0.991894i	$-0.459443\pi$
$23$	3.42022e69	0.254138	0.127069	+	0.991894i	$0.459443\pi$
$24$	6.47205e71	5.37233
$25$	−9.05518e71	−0.918305
$26$	−9.53817e72	−1.28333
$27$	8.63299e73	1.66313
$28$	−5.78176e74	−1.71167
$29$	3.20038e74	0.155491	0.0777455	−	0.996973i	$-0.475228\pi$
$29$	3.20038e74	0.155491	0.0777455	+	0.996973i	$0.475228\pi$
$30$	−1.10719e76	−0.938594
$31$	5.53588e76	0.867080	0.433540	−	0.901134i	$-0.357264\pi$
$31$	5.53588e76	0.867080	0.433540	+	0.901134i	$0.357264\pi$
$32$	1.04699e78	3.19681
$33$	1.50808e78	0.943964
$34$	−8.86962e78	−1.19328
$35$	6.13873e78	0.185598
$36$	7.31225e80	5.18170
$37$	−8.68560e79	−0.150111	−0.0750553	−	0.997179i	$-0.523913\pi$
$37$	−8.68560e79	−0.150111	−0.0750553	+	0.997179i	$0.523913\pi$
$38$	6.96915e81	3.05018
$39$	−1.00907e82	−1.15902
$40$	−2.85946e82	−0.891652
$41$	6.58025e82	0.575273	0.287636	−	0.957740i	$-0.407131\pi$
$41$	6.58025e82	0.575273	0.287636	+	0.957740i	$0.407131\pi$
$42$	−8.43709e83	−2.13233
$43$	−2.31883e84	−1.74439	−0.872194	−	0.489160i	$-0.837303\pi$
$43$	−2.31883e84	−1.74439	−0.872194	+	0.489160i	$0.837303\pi$
$44$	6.27549e84	1.44489
$45$	−7.76372e84	−0.561856
$46$	2.07688e85	0.484598
$47$	−2.37719e86	−1.83242	−0.916210	−	0.400700i	$-0.868767\pi$
$47$	−2.37719e86	−1.83242	−0.916210	+	0.400700i	$0.868767\pi$
$48$	2.18850e87	5.70458
$49$	−6.41638e86	−0.578351
$50$	−5.49862e87	−1.75105
$51$	−9.38338e87	−1.07769
$52$	−4.19898e88	−1.77407
$53$	−1.71359e88	−0.271457	−0.135728	−	0.990746i	$-0.543337\pi$
$53$	−1.71359e88	−0.271457	−0.135728	+	0.990746i	$0.543337\pi$
$54$	5.24225e89	3.17131
$55$	−6.66295e88	−0.156671
$56$	−2.17899e90	−2.02568
$57$	7.37283e90	2.75473
$58$	1.94338e90	0.296495
$59$	−1.30001e91	−0.822374	−0.411187	−	0.911551i	$-0.634886\pi$
$59$	−1.30001e91	−0.822374	−0.411187	+	0.911551i	$0.634886\pi$
$60$	−4.87417e91	−1.29751
$61$	−6.15903e91	−0.699884	−0.349942	−	0.936771i	$-0.613799\pi$
$61$	−6.15903e91	−0.699884	−0.349942	+	0.936771i	$0.613799\pi$
$62$	3.36158e92	1.65338
$63$	−5.91616e92	−1.27644
$64$	2.90285e93	2.78327
$65$	4.45823e92	0.192364
$66$	9.15757e93	1.79998
$67$	6.14223e92	0.0556511	0.0278256	−	0.999613i	$-0.491142\pi$
$67$	6.14223e92	0.0556511	0.0278256	+	0.999613i	$0.491142\pi$
$68$	−3.90466e94	−1.64958
$69$	2.19718e94	0.437660
$70$	3.72765e94	0.353905
$71$	1.58406e95	0.724381	0.362191	−	0.932104i	$-0.382029\pi$
$71$	1.58406e95	0.724381	0.362191	+	0.932104i	$0.382029\pi$
$72$	2.75579e96	6.13229
$73$	−1.01581e96	−1.11093	−0.555463	−	0.831541i	$-0.687459\pi$
$73$	−1.01581e96	−1.11093	−0.555463	+	0.831541i	$0.687459\pi$
$74$	−5.27420e95	−0.286235
$75$	−5.81713e96	−1.58144
$76$	3.06802e97	4.21656
$77$	−5.07734e96	−0.355930
$78$	−6.12740e97	−2.21006
$79$	8.88387e97	1.66267	0.831336	−	0.555769i	$-0.187576\pi$
$79$	8.88387e97	1.66267	0.831336	+	0.555769i	$0.187576\pi$
$80$	−9.66920e97	−0.946795
$81$	1.73959e98	0.898396
$82$	3.99576e98	1.09695
$83$	−4.44747e98	−0.654021	−0.327011	−	0.945021i	$-0.606041\pi$
$83$	−4.44747e98	−0.654021	−0.327011	+	0.945021i	$0.606041\pi$
$84$	−3.71425e99	−2.94773
$85$	4.14574e98	0.178866
$86$	−1.40807e100	−3.32625
$87$	2.05595e99	0.267776
$88$	2.36506e100	1.70996
$89$	2.52929e100	1.02191	0.510956	−	0.859607i	$-0.329292\pi$
$89$	2.52929e100	1.02191	0.510956	+	0.859607i	$0.329292\pi$
$90$	−4.71440e100	−1.07136
$91$	3.39729e100	0.437020
$92$	9.14300e100	0.669909
$93$	3.55630e101	1.49323
$94$	−1.44352e102	−3.49411
$95$	−3.25745e101	−0.457206
$96$	6.72593e102	5.50534
$97$	6.67584e101	0.320451	0.160225	−	0.987080i	$-0.448778\pi$
$97$	6.67584e101	0.320451	0.160225	+	0.987080i	$0.448778\pi$
$98$	−3.89625e102	−1.10282
$99$	6.42137e102	1.07749
$100$	−2.42065e103	−2.42065
$101$	8.99196e102	0.538646	0.269323	−	0.963050i	$-0.413200\pi$
$101$	8.99196e102	0.538646	0.269323	+	0.963050i	$0.413200\pi$
$102$	−5.69792e103	−2.05498
$103$	6.61718e103	1.44396	0.721981	−	0.691912i	$-0.243232\pi$
$103$	6.61718e103	1.44396	0.721981	+	0.691912i	$0.243232\pi$
$104$	−1.58248e104	−2.09953
$105$	3.94357e103	0.319625
$106$	−1.04055e104	−0.517622
$107$	−4.76733e104	−1.46221	−0.731106	−	0.682263i	$-0.760996\pi$
$107$	−4.76733e104	−1.46221	−0.731106	+	0.682263i	$0.760996\pi$
$108$	2.30779e105	4.38403
$109$	−3.85797e104	−0.455926	−0.227963	−	0.973670i	$-0.573207\pi$
$109$	−3.85797e104	−0.455926	−0.227963	+	0.973670i	$0.573207\pi$
$110$	−4.04597e104	−0.298744
$111$	−5.57970e104	−0.258510
$112$	−7.36819e105	−2.15096
$113$	−2.60806e105	−0.481701	−0.240851	−	0.970562i	$-0.577426\pi$
$113$	−2.60806e105	−0.481701	−0.240851	+	0.970562i	$0.577426\pi$
$114$	4.47704e106	5.25281
$115$	−9.70750e104	−0.0726388
$116$	8.55534e105	0.409875
$117$	−4.29659e106	−1.32298
$118$	−7.89414e106	−1.56813
$119$	3.15917e106	0.406353
$120$	−1.83694e107	−1.53554
$121$	−1.28311e107	−0.699546
$122$	−3.73998e107	−1.33456
$123$	4.22721e107	0.990696
$124$	1.47986e108	2.28563
$125$	5.36886e107	0.548298
$126$	−3.59250e108	−2.43396
$127$	3.81611e108	1.72079	0.860397	−	0.509624i	$-0.170215\pi$
$127$	3.81611e108	1.72079	0.860397	+	0.509624i	$0.170215\pi$
$128$	7.00941e108	2.11042
$129$	−1.48963e109	−3.00407
$130$	2.70719e108	0.366806
$131$	3.01807e108	0.275587	0.137793	−	0.990461i	$-0.455999\pi$
$131$	3.01807e108	0.275587	0.137793	+	0.990461i	$0.455999\pi$
$132$	4.03143e109	2.48829
$133$	−2.48226e109	−1.03870
$134$	3.72978e108	0.106117
$135$	−2.45028e109	−0.475364
$136$	−1.47156e110	−1.95220
$137$	6.13919e109	0.558472	0.279236	−	0.960222i	$-0.409919\pi$
$137$	6.13919e109	0.558472	0.279236	+	0.960222i	$0.409919\pi$
$138$	1.33420e110	0.834543
$139$	−3.55156e110	−1.53164	−0.765820	−	0.643056i	$-0.777666\pi$
$139$	−3.55156e110	−1.53164	−0.765820	+	0.643056i	$0.777666\pi$
$140$	1.64102e110	0.489238
$141$	−1.52713e111	−3.15567
$142$	9.61898e110	1.38127
$143$	−3.68740e110	−0.368905
$144$	9.31862e111	6.51153
$145$	−9.08356e109	−0.0444431
$146$	−6.16836e111	−2.11835
$147$	−4.12193e111	−0.995998
$148$	−2.32186e111	−0.395692
$149$	9.90515e111	1.19335	0.596675	−	0.802483i	$-0.296488\pi$
$149$	9.90515e111	1.19335	0.596675	+	0.802483i	$0.296488\pi$
$150$	−3.53236e112	−3.01554
$151$	−1.40577e112	−0.852318	−0.426159	−	0.904648i	$-0.640134\pi$
$151$	−1.40577e112	−0.852318	−0.426159	+	0.904648i	$0.640134\pi$
$152$	1.15626e113	4.99010
$153$	−3.99543e112	−1.23014
$154$	−3.08314e112	−0.678698
$155$	−1.57123e112	−0.247833
$156$	−2.69746e113	−3.05519
$157$	−1.75912e112	−0.143371	−0.0716857	−	0.997427i	$-0.522838\pi$
$157$	−1.75912e112	−0.143371	−0.0716857	+	0.997427i	$0.522838\pi$
$158$	5.39460e113	3.17044
$159$	−1.10083e113	−0.467485
$160$	−2.97163e113	−0.913726
$161$	−7.39738e112	−0.165023
$162$	1.05634e114	1.71309
$163$	5.67002e113	0.669765	0.334883	−	0.942260i	$-0.391303\pi$
$163$	5.67002e113	0.669765	0.334883	+	0.942260i	$0.391303\pi$
$164$	1.75905e114	1.51642
$165$	−4.28033e113	−0.269808
$166$	−2.70066e114	−1.24711
$167$	3.13107e114	1.06119	0.530597	−	0.847624i	$-0.321968\pi$
$167$	3.13107e114	1.06119	0.530597	+	0.847624i	$0.321968\pi$
$168$	−1.39980e115	−3.48850
$169$	−2.97983e114	−0.547049
$170$	2.51744e114	0.341067
$171$	3.13934e115	3.14441
$172$	−6.19875e115	−4.59821
$173$	2.61537e115	1.43933	0.719663	−	0.694323i	$-0.244296\pi$
$173$	2.61537e115	1.43933	0.719663	+	0.694323i	$0.244296\pi$
$174$	1.24845e115	0.510603
$175$	1.95849e115	0.596296
$176$	7.99739e115	1.81571
$177$	−8.35140e115	−1.41624
$178$	1.53587e116	1.94861
$179$	−1.66512e116	−1.58312	−0.791559	−	0.611093i	$-0.790730\pi$
$179$	−1.66512e116	−1.58312	−0.791559	+	0.611093i	$0.790730\pi$
$180$	−2.07542e116	−1.48105
$181$	2.26806e116	1.21677	0.608383	−	0.793643i	$-0.291818\pi$
$181$	2.26806e116	1.21677	0.608383	+	0.793643i	$0.291818\pi$
$182$	2.06295e116	0.833322
$183$	−3.95662e116	−1.20529
$184$	3.44575e116	0.792805
$185$	2.46521e115	0.0429052
$186$	2.15951e117	2.84733
$187$	−3.42894e116	−0.343018
$188$	−6.35477e117	−4.83026
$189$	−1.86718e117	−1.07995
$190$	−1.97804e117	−0.871814
$191$	−2.97607e117	−1.00098	−0.500489	−	0.865743i	$-0.666847\pi$
$191$	−2.97607e117	−1.00098	−0.500489	+	0.865743i	$0.666847\pi$
$192$	1.86481e118	4.79316
$193$	4.66441e117	0.917477	0.458738	−	0.888571i	$-0.348302\pi$
$193$	4.66441e117	0.917477	0.458738	+	0.888571i	$0.348302\pi$
$194$	4.05380e117	0.611045
$195$	2.86400e117	0.331277
$196$	−1.71524e118	−1.52454
$197$	−1.03884e118	−0.710456	−0.355228	−	0.934780i	$-0.615597\pi$
$197$	−1.03884e118	−0.710456	−0.355228	+	0.934780i	$0.615597\pi$
$198$	3.89928e118	2.05460
$199$	1.79886e118	0.731248	0.365624	−	0.930763i	$-0.380856\pi$
$199$	1.79886e118	0.731248	0.365624	+	0.930763i	$0.380856\pi$
$200$	−9.12279e118	−2.86473
$201$	3.94582e117	0.0958386
$202$	5.46023e118	1.02711
$203$	−6.92192e117	−0.100967
$204$	−2.50839e119	−2.84080
$205$	−1.86766e118	−0.164427
$206$	4.01819e119	2.75339
$207$	9.35554e118	0.499570
$208$	−5.35112e119	−2.22937
$209$	2.69423e119	0.876802
$210$	2.39468e119	0.609471
$211$	−1.36386e118	−0.0271784	−0.0135892	−	0.999908i	$-0.504326\pi$
$211$	−1.36386e118	−0.0271784	−0.0135892	+	0.999908i	$0.504326\pi$
$212$	−4.58082e119	−0.715561
$213$	1.01761e120	1.24748
$214$	−2.89489e120	−2.78819
$215$	6.58147e119	0.498588
$216$	8.69744e120	5.18828
$217$	−1.19732e120	−0.563034
$218$	−2.34270e120	−0.869374
$219$	−6.52565e120	−1.91316
$220$	−1.78116e120	−0.412984
$221$	2.29433e120	0.421167
$222$	−3.38819e120	−0.492935
$223$	9.08196e120	1.04828	0.524142	−	0.851631i	$-0.324386\pi$
$223$	9.08196e120	1.04828	0.524142	+	0.851631i	$0.324386\pi$
$224$	−2.26446e121	−2.07583
$225$	−2.47692e121	−1.80515
$226$	−1.58371e121	−0.918523
$227$	−9.69741e120	−0.448048	−0.224024	−	0.974584i	$-0.571919\pi$
$227$	−9.69741e120	−0.448048	−0.224024	+	0.974584i	$0.571919\pi$
$228$	1.97092e122	7.26148
$229$	−1.97339e121	−0.580344	−0.290172	−	0.956975i	$-0.593713\pi$
$229$	−1.97339e121	−0.580344	−0.290172	+	0.956975i	$0.593713\pi$
$230$	−5.89474e120	−0.138510
$231$	−3.26173e121	−0.612958
$232$	3.22428e121	0.485067
$233$	−2.49838e121	−0.301182	−0.150591	−	0.988596i	$-0.548118\pi$
$233$	−2.49838e121	−0.301182	−0.150591	+	0.988596i	$0.548118\pi$
$234$	−2.60904e122	−2.52269
$235$	6.74712e121	0.523750
$236$	−3.47523e122	−2.16778
$237$	5.70707e122	2.86334
$238$	1.91836e122	0.774847
$239$	9.67351e121	0.314842	0.157421	−	0.987532i	$-0.449682\pi$
$239$	9.67351e121	0.314842	0.157421	+	0.987532i	$0.449682\pi$
$240$	−6.21157e122	−1.63051
$241$	5.26856e122	1.11639	0.558193	−	0.829711i	$-0.311495\pi$
$241$	5.26856e122	1.11639	0.558193	+	0.829711i	$0.311495\pi$
$242$	−7.79148e122	−1.33392
$243$	−8.37710e121	−0.115977
$244$	−1.64645e123	−1.84490
$245$	1.82114e122	0.165307
$246$	2.56691e123	1.88909
$247$	−1.80273e123	−1.07656
$248$	5.57721e123	2.70493
$249$	−2.85710e123	−1.12631
$250$	3.26016e123	1.04551
$251$	3.48139e123	0.908983	0.454492	−	0.890751i	$-0.349821\pi$
$251$	3.48139e123	0.908983	0.454492	+	0.890751i	$0.349821\pi$
$252$	−1.58152e124	−3.36471
$253$	8.02908e122	0.139302
$254$	2.31727e124	3.28126
$255$	2.66326e123	0.308031
$256$	1.31252e124	1.24093
$257$	−1.41120e124	−1.09152	−0.545762	−	0.837940i	$-0.683760\pi$
$257$	−1.41120e124	−1.09152	−0.545762	+	0.837940i	$0.683760\pi$
$258$	−9.04558e124	−5.72825
$259$	1.87856e123	0.0974735
$260$	1.19178e124	0.507073
$261$	8.75422e123	0.305655
$262$	1.83268e124	0.525497
$263$	−2.05011e123	−0.0483122	−0.0241561	−	0.999708i	$-0.507690\pi$
$263$	−2.05011e123	−0.0483122	−0.0241561	+	0.999708i	$0.507690\pi$
$264$	1.51934e125	2.94477
$265$	4.86365e123	0.0775889
$266$	−1.50732e125	−1.98062
$267$	1.62484e125	1.75987
$268$	1.64196e124	0.146697
$269$	1.31086e125	0.966752	0.483376	−	0.875413i	$-0.339410\pi$
$269$	1.31086e125	0.966752	0.483376	+	0.875413i	$0.339410\pi$
$270$	−1.48789e125	−0.906438
$271$	−1.56703e125	−0.789147	−0.394573	−	0.918864i	$-0.629108\pi$
$271$	−1.56703e125	−0.789147	−0.394573	+	0.918864i	$0.629108\pi$
$272$	−4.97604e125	−2.07293
$273$	2.18245e125	0.752606
$274$	3.72793e125	1.06491
$275$	−2.12574e125	−0.503356
$276$	5.87354e125	1.15367
$277$	2.76619e125	0.450997	0.225499	−	0.974243i	$-0.427599\pi$
$277$	2.76619e125	0.450997	0.225499	+	0.974243i	$0.427599\pi$
$278$	−2.15663e126	−2.92058
$279$	1.51427e126	1.70446
$280$	6.18456e125	0.578989
$281$	2.18795e126	1.70475	0.852376	−	0.522929i	$-0.175161\pi$
$281$	2.18795e126	1.70475	0.852376	+	0.522929i	$0.175161\pi$
$282$	−9.27326e126	−6.01733
$283$	1.87218e126	1.01239	0.506193	−	0.862420i	$-0.331052\pi$
$283$	1.87218e126	1.01239	0.506193	+	0.862420i	$0.331052\pi$
$284$	4.23455e126	1.90947
$285$	−2.09261e126	−0.787369
$286$	−2.23912e126	−0.703439
$287$	−1.42320e126	−0.373550
$288$	2.86389e127	6.28411
$289$	−3.31451e126	−0.608387
$290$	−5.51586e125	−0.0847454
$291$	4.28861e126	0.551859
$292$	−2.71549e127	−2.92841
$293$	−3.41873e126	−0.309159	−0.154580	−	0.987980i	$-0.549402\pi$
$293$	−3.41873e126	−0.309159	−0.154580	+	0.987980i	$0.549402\pi$
$294$	−2.50298e127	−1.89920
$295$	3.68979e126	0.235054
$296$	−8.75045e126	−0.468282
$297$	2.02662e127	0.911625
$298$	6.01475e127	2.27552
$299$	−5.37232e126	−0.171039
$300$	−1.55505e128	−4.16869
$301$	5.01525e127	1.13271
$302$	−8.53633e127	−1.62523
$303$	5.77651e127	0.927620
$304$	3.90984e128	5.29871
$305$	1.74810e127	0.200044
$306$	−2.42617e128	−2.34567
$307$	−1.50661e127	−0.123133	−0.0615666	−	0.998103i	$-0.519610\pi$
$307$	−1.50661e127	−0.123133	−0.0615666	+	0.998103i	$0.519610\pi$
$308$	−1.35729e128	−0.938232
$309$	4.25093e128	2.48670
$310$	−9.54108e127	−0.472575
$311$	3.45522e127	0.144983	0.0724913	−	0.997369i	$-0.476905\pi$
$311$	3.45522e127	0.144983	0.0724913	+	0.997369i	$0.476905\pi$
$312$	−1.01660e129	−3.61567
$313$	8.59988e127	0.259394	0.129697	−	0.991554i	$-0.458600\pi$
$313$	8.59988e127	0.259394	0.129697	+	0.991554i	$0.458600\pi$
$314$	−1.06820e128	−0.273385
$315$	1.67917e128	0.364838
$316$	2.37486e129	4.38281
$317$	−6.92172e128	−1.08558	−0.542790	−	0.839868i	$-0.682632\pi$
$317$	−6.92172e128	−1.08558	−0.542790	+	0.839868i	$0.682632\pi$
$318$	−6.68461e128	−0.891414
$319$	7.51301e127	0.0852303
$320$	−8.23908e128	−0.795526
$321$	−3.06257e129	−2.51812
$322$	−4.49195e128	−0.314671
$323$	−1.67637e129	−1.00102
$324$	4.65031e129	2.36817
$325$	1.42235e129	0.618034
$326$	3.44303e129	1.27713
$327$	−2.47839e129	−0.785166
$328$	6.62938e129	1.79461
$329$	5.14149e129	1.18987
$330$	−2.59917e129	−0.514478
$331$	−1.41905e129	−0.240357	−0.120179	−	0.992752i	$-0.538347\pi$
$331$	−1.41905e129	−0.240357	−0.120179	+	0.992752i	$0.538347\pi$
$332$	−1.18891e130	−1.72400
$333$	−2.37583e129	−0.295078
$334$	1.90130e130	2.02352
$335$	−1.74333e128	−0.0159064
$336$	−4.73339e130	−3.70424
$337$	−1.22765e129	−0.0824394	−0.0412197	−	0.999150i	$-0.513124\pi$
$337$	−1.22765e129	−0.0824394	−0.0412197	+	0.999150i	$0.513124\pi$
$338$	−1.80946e130	−1.04313
$339$	−1.67544e130	−0.829554
$340$	1.10825e130	0.471491
$341$	1.29957e130	0.475279
$342$	1.90632e131	5.99585
$343$	3.78727e130	1.02489
$344$	−2.33614e131	−5.44176
$345$	−6.23618e129	−0.125094
$346$	1.58815e131	2.74455
$347$	−1.12977e131	−1.68277	−0.841383	−	0.540439i	$-0.818258\pi$
$347$	−1.12977e131	−1.68277	−0.841383	+	0.540439i	$0.818258\pi$
$348$	5.49602e130	0.705858
$349$	−8.78345e130	−0.973095	−0.486548	−	0.873654i	$-0.661744\pi$
$349$	−8.78345e130	−0.973095	−0.486548	+	0.873654i	$0.661744\pi$
$350$	1.18926e131	1.13704
$351$	−1.35603e131	−1.11932
$352$	2.45784e131	1.75229
$353$	8.51890e130	0.524791	0.262395	−	0.964960i	$-0.415488\pi$
$353$	8.51890e130	0.524791	0.262395	+	0.964960i	$0.415488\pi$
$354$	−5.07126e131	−2.70053
$355$	−4.49600e130	−0.207046
$356$	6.76136e131	2.69376
$357$	2.02947e131	0.699794
$358$	−1.01112e132	−3.01874
$359$	−2.80558e131	−0.725534	−0.362767	−	0.931880i	$-0.618168\pi$
$359$	−2.80558e131	−0.725534	−0.362767	+	0.931880i	$0.618168\pi$
$360$	−7.82168e131	−1.75276
$361$	8.02404e131	1.55874
$362$	1.37724e132	2.32017
$363$	−8.24279e131	−1.20471
$364$	9.08172e131	1.15199
$365$	2.88315e131	0.317530
$366$	−2.40260e132	−2.29829
$367$	−1.42800e132	−1.18693	−0.593465	−	0.804859i	$-0.702241\pi$
$367$	−1.42800e132	−1.18693	−0.593465	+	0.804859i	$0.702241\pi$
$368$	1.16517e132	0.841835
$369$	1.79994e132	1.13084
$370$	1.49696e131	0.0818130
$371$	3.70623e131	0.176269
$372$	9.50678e132	3.93615
$373$	2.12769e132	0.767192	0.383596	−	0.923501i	$-0.374685\pi$
$373$	2.12769e132	0.767192	0.383596	+	0.923501i	$0.374685\pi$
$374$	−2.08217e132	−0.654078
$375$	3.44900e132	0.944241
$376$	−2.39494e133	−5.71638
$377$	−5.02701e131	−0.104648
$378$	−1.13382e133	−2.05928
$379$	5.03313e132	0.797846	0.398923	−	0.916984i	$-0.369384\pi$
$379$	5.03313e132	0.797846	0.398923	+	0.916984i	$0.369384\pi$
$380$	−8.70789e132	−1.20520
$381$	2.45150e133	2.96344
$382$	−1.80717e133	−1.90870
$383$	−3.06972e132	−0.283375	−0.141688	−	0.989911i	$-0.545253\pi$
$383$	−3.06972e132	−0.283375	−0.141688	+	0.989911i	$0.545253\pi$
$384$	4.50290e133	3.63442
$385$	1.44109e132	0.101733
$386$	2.83239e133	1.74947
$387$	−6.34284e133	−3.42901
$388$	1.78460e133	0.844709
$389$	2.00588e133	0.831575	0.415788	−	0.909462i	$-0.363506\pi$
$389$	2.00588e133	0.831575	0.415788	+	0.909462i	$0.363506\pi$
$390$	1.73912e133	0.631689
$391$	−4.99576e132	−0.159037
$392$	−6.46428e133	−1.80421
$393$	1.93884e133	0.474597
$394$	−6.30819e133	−1.35472
$395$	−2.52148e133	−0.475232
$396$	1.71658e134	2.84028
$397$	1.69968e133	0.246977	0.123489	−	0.992346i	$-0.460592\pi$
$397$	1.69968e133	0.246977	0.123489	+	0.992346i	$0.460592\pi$
$398$	1.09233e134	1.39437
$399$	−1.59463e134	−1.78877
$400$	−3.08485e134	−3.04189
$401$	1.71989e134	1.49130	0.745651	−	0.666337i	$-0.232139\pi$
$401$	1.71989e134	1.49130	0.745651	+	0.666337i	$0.232139\pi$
$402$	2.39604e133	0.182748
$403$	−8.69550e133	−0.583559
$404$	2.40375e134	1.41987
$405$	−4.93742e133	−0.256783
$406$	−4.20323e133	−0.192527
$407$	−2.03898e133	−0.0822811
$408$	−9.45344e134	−3.36195
$409$	3.22329e134	1.01053	0.505265	−	0.862964i	$-0.331395\pi$
$409$	3.22329e134	1.01053	0.505265	+	0.862964i	$0.331395\pi$
$410$	−1.13411e134	−0.313534
$411$	3.94387e134	0.961763
$412$	1.76892e135	3.80629
$413$	2.81172e134	0.534004
$414$	5.68101e134	0.952595
$415$	1.26231e134	0.186935
$416$	−1.64456e135	−2.15151
$417$	−2.28155e135	−2.63769
$418$	1.63603e135	1.67191
$419$	−1.14412e135	−1.03383	−0.516917	−	0.856036i	$-0.672920\pi$
$419$	−1.14412e135	−1.03383	−0.516917	+	0.856036i	$0.672920\pi$
$420$	1.05421e135	0.842533
$421$	1.87609e135	1.32655	0.663277	−	0.748374i	$-0.269165\pi$
$421$	1.87609e135	1.32655	0.663277	+	0.748374i	$0.269165\pi$
$422$	−8.28185e133	−0.0518246
$423$	−6.50249e135	−3.60206
$424$	−1.72639e135	−0.846832
$425$	1.32265e135	0.574666
$426$	6.17931e135	2.37873
$427$	1.33210e135	0.454466
$428$	−1.27441e136	−3.85440
$429$	−2.36882e135	−0.635303
$430$	3.99650e135	0.950723
$431$	7.69548e135	1.62426	0.812132	−	0.583474i	$-0.198307\pi$
$431$	7.69548e135	1.62426	0.812132	+	0.583474i	$0.198307\pi$
$432$	2.94101e136	5.50915
$433$	−3.63186e135	−0.603953	−0.301976	−	0.953315i	$-0.597646\pi$
$433$	−3.63186e135	−0.603953	−0.301976	+	0.953315i	$0.597646\pi$
$434$	−7.27056e135	−1.07361
$435$	−5.83535e134	−0.0765368
$436$	−1.03132e136	−1.20182
$437$	3.92533e135	0.406521
$438$	−3.96260e136	−3.64808
$439$	2.27855e136	1.86524	0.932620	−	0.360859i	$-0.117516\pi$
$439$	2.27855e136	1.86524	0.932620	+	0.360859i	$0.117516\pi$
$440$	−6.71269e135	−0.488747
$441$	−1.75511e136	−1.13689
$442$	1.39320e136	0.803094
$443$	2.02196e136	1.03748	0.518740	−	0.854932i	$-0.326401\pi$
$443$	2.02196e136	1.03748	0.518740	+	0.854932i	$0.326401\pi$
$444$	−1.49158e136	−0.681434
$445$	−7.17881e135	−0.292087
$446$	5.51488e136	1.99890
$447$	6.36315e136	2.05511
$448$	−6.27840e136	−1.80730
$449$	2.46399e136	0.632341	0.316171	−	0.948702i	$-0.397603\pi$
$449$	2.46399e136	0.632341	0.316171	+	0.948702i	$0.397603\pi$
$450$	−1.50408e137	−3.44211
$451$	1.54474e136	0.315328
$452$	−6.97193e136	−1.26977
$453$	−9.03079e136	−1.46780
$454$	−5.88861e136	−0.854351
$455$	−9.64244e135	−0.124911
$456$	7.42788e137	8.59361
$457$	−2.78919e136	−0.288266	−0.144133	−	0.989558i	$-0.546039\pi$
$457$	−2.78919e136	−0.288266	−0.144133	+	0.989558i	$0.546039\pi$
$458$	−1.19831e137	−1.10662
$459$	−1.26098e137	−1.04077
$460$	−2.59503e136	−0.191476
$461$	1.22798e136	0.0810205	0.0405102	−	0.999179i	$-0.487102\pi$
$461$	1.22798e136	0.0810205	0.0405102	+	0.999179i	$0.487102\pi$
$462$	−1.98064e137	−1.16881
$463$	2.40728e137	1.27088	0.635441	−	0.772149i	$-0.280818\pi$
$463$	2.40728e137	1.27088	0.635441	+	0.772149i	$0.280818\pi$
$464$	1.09028e137	0.515065
$465$	−1.00937e137	−0.426800
$466$	−1.51710e137	−0.574303
$467$	2.49513e137	0.845812	0.422906	−	0.906174i	$-0.361010\pi$
$467$	2.49513e137	0.845812	0.422906	+	0.906174i	$0.361010\pi$
$468$	−1.14857e138	−3.48737
$469$	−1.32847e136	−0.0361368
$470$	4.09709e137	0.998702
$471$	−1.13007e137	−0.246905
$472$	−1.30972e138	−2.56546
$473$	−5.44353e137	−0.956163
$474$	3.46553e138	5.45991
$475$	−1.03925e138	−1.46892
$476$	8.44516e137	1.07115
$477$	−4.68731e137	−0.533614
$478$	5.87410e137	0.600350
$479$	1.49339e138	1.37055	0.685274	−	0.728285i	$-0.259682\pi$
$479$	1.49339e138	1.37055	0.685274	+	0.728285i	$0.259682\pi$
$480$	−1.90900e138	−1.57356
$481$	1.36429e137	0.101027
$482$	3.19926e138	2.12876
$483$	−4.75214e137	−0.284192
$484$	−3.43003e138	−1.84401
$485$	−1.89478e137	−0.0915926
$486$	−5.08687e137	−0.221148
$487$	1.78412e138	0.697721	0.348860	−	0.937175i	$-0.386569\pi$
$487$	1.78412e138	0.697721	0.348860	+	0.937175i	$0.386569\pi$
$488$	−6.20502e138	−2.18334
$489$	3.64247e138	1.15342
$490$	1.10586e138	0.315212
$491$	−7.24097e138	−1.85823	−0.929115	−	0.369790i	$-0.879430\pi$
$491$	−7.24097e138	−1.85823	−0.929115	+	0.369790i	$0.879430\pi$
$492$	1.13003e139	2.61148
$493$	−4.67466e137	−0.0973046
$494$	−1.09468e139	−2.05282
$495$	−1.82256e138	−0.307974
$496$	1.88592e139	2.87221
$497$	−3.42607e138	−0.470373
$498$	−1.73493e139	−2.14768
$499$	−1.04278e139	−1.16416	−0.582082	−	0.813130i	$-0.697762\pi$
$499$	−1.04278e139	−1.16416	−0.582082	+	0.813130i	$0.697762\pi$
$500$	1.43522e139	1.44531
$501$	2.01143e139	1.82752
$502$	2.11402e139	1.73328
$503$	−7.60937e138	−0.563116	−0.281558	−	0.959544i	$-0.590851\pi$
$503$	−7.60937e138	−0.563116	−0.281558	+	0.959544i	$0.590851\pi$
$504$	−5.96033e139	−3.98197
$505$	−2.55216e138	−0.153958
$506$	4.87554e138	0.265626
$507$	−1.91427e139	−0.942091
$508$	1.02013e140	4.53602
$509$	−1.47324e138	−0.0591980	−0.0295990	−	0.999562i	$-0.509423\pi$
$509$	−1.47324e138	−0.0591980	−0.0295990	+	0.999562i	$0.509423\pi$
$510$	1.61722e139	0.587362
$511$	2.19704e139	0.721374
$512$	8.61709e138	0.255834
$513$	9.90796e139	2.66036
$514$	−8.56931e139	−2.08135
$515$	−1.87814e139	−0.412719
$516$	−3.98213e140	−7.91873
$517$	−5.58055e139	−1.00442
$518$	1.14073e139	0.185865
$519$	1.68014e140	2.47871
$520$	4.49152e139	0.600096
$521$	1.28966e140	1.56075	0.780374	−	0.625313i	$-0.215029\pi$
$521$	1.28966e140	1.56075	0.780374	+	0.625313i	$0.215029\pi$
$522$	5.31587e139	0.582832
$523$	−7.41732e139	−0.736903	−0.368451	−	0.929647i	$-0.620112\pi$
$523$	−7.41732e139	−0.736903	−0.368451	+	0.929647i	$0.620112\pi$
$524$	8.06799e139	0.726447
$525$	1.25815e140	1.02690
$526$	−1.24490e139	−0.0921232
$527$	−8.08602e139	−0.542610
$528$	5.13759e140	3.12689
$529$	−1.69422e140	−0.935414
$530$	2.95338e139	0.147949
$531$	−3.55602e140	−1.61657
$532$	−6.63564e140	−2.73800
$533$	−1.03360e140	−0.387168
$534$	9.86658e140	3.35577
$535$	1.35310e140	0.417936
$536$	6.18809e139	0.173608
$537$	−1.06968e141	−2.72634
$538$	7.96002e140	1.84343
$539$	−1.50627e140	−0.317016
$540$	−6.55014e140	−1.25306
$541$	1.69600e140	0.294962	0.147481	−	0.989065i	$-0.452883\pi$
$541$	1.69600e140	0.294962	0.147481	+	0.989065i	$0.452883\pi$
$542$	−9.51553e140	−1.50477
$543$	1.45702e141	2.09543
$544$	−1.52929e141	−2.00053
$545$	1.09500e140	0.130315
$546$	1.32526e141	1.43509
$547$	3.25568e140	0.320844	0.160422	−	0.987049i	$-0.448715\pi$
$547$	3.25568e140	0.320844	0.160422	+	0.987049i	$0.448715\pi$
$548$	1.64114e141	1.47213
$549$	−1.68472e141	−1.37579
$550$	−1.29082e141	−0.959815
$551$	3.67304e140	0.248724
$552$	2.21358e141	1.36531
$553$	−1.92144e141	−1.07965
$554$	1.67973e141	0.859976
$555$	1.58367e140	0.0738885
$556$	−9.49411e141	−4.03741
$557$	3.01092e141	1.16723	0.583615	−	0.812031i	$-0.301638\pi$
$557$	3.01092e141	1.16723	0.583615	+	0.812031i	$0.301638\pi$
$558$	9.19515e141	3.25011
$559$	3.64231e141	1.17400
$560$	2.09129e141	0.614796
$561$	−2.20278e141	−0.590723
$562$	1.32860e142	3.25067
$563$	−2.26836e141	−0.506443	−0.253221	−	0.967408i	$-0.581490\pi$
$563$	−2.26836e141	−0.506443	−0.253221	+	0.967408i	$0.581490\pi$
$564$	−4.08236e142	−8.31835
$565$	7.40239e140	0.137682
$566$	1.13685e142	1.93045
$567$	−3.76245e141	−0.583369
$568$	1.59589e142	2.25977
$569$	2.47710e141	0.320377	0.160189	−	0.987086i	$-0.448790\pi$
$569$	2.47710e141	0.320377	0.160189	+	0.987086i	$0.448790\pi$
$570$	−1.27071e142	−1.50138
$571$	2.61303e140	0.0282088	0.0141044	−	0.999901i	$-0.495510\pi$
$571$	2.61303e140	0.0282088	0.0141044	+	0.999901i	$0.495510\pi$
$572$	−9.85725e141	−0.972434
$573$	−1.91185e142	−1.72382
$574$	−8.64219e141	−0.712298
$575$	−3.09707e141	−0.233376
$576$	7.94035e142	5.47119
$577$	1.49135e142	0.939779	0.469889	−	0.882725i	$-0.344294\pi$
$577$	1.49135e142	0.939779	0.469889	+	0.882725i	$0.344294\pi$
$578$	−2.01268e142	−1.16009
$579$	2.99645e142	1.58002
$580$	−2.42824e141	−0.117152
$581$	9.61918e141	0.424685
$582$	2.60420e142	1.05230
$583$	−4.02272e141	−0.148795
$584$	−1.02339e143	−3.46563
$585$	1.21949e142	0.378138
$586$	−2.07597e142	−0.589514
$587$	3.23347e141	0.0841021	0.0420510	−	0.999115i	$-0.486611\pi$
$587$	3.23347e141	0.0841021	0.0420510	+	0.999115i	$0.486611\pi$
$588$	−1.10189e143	−2.62545
$589$	6.35345e142	1.38699
$590$	2.24057e142	0.448209
$591$	−6.67358e142	−1.22350
$592$	−2.95894e142	−0.497243
$593$	1.18014e141	0.0181810	0.00909050	−	0.999959i	$-0.497106\pi$
$593$	1.18014e141	0.0181810	0.00909050	+	0.999959i	$0.497106\pi$
$594$	1.23064e143	1.73831
$595$	−8.96657e141	−0.116146
$596$	2.64787e143	3.14568
$597$	1.15560e143	1.25931
$598$	−3.26226e142	−0.326143
$599$	−1.75272e143	−1.60780	−0.803899	−	0.594766i	$-0.797245\pi$
$599$	−1.75272e143	−1.60780	−0.803899	+	0.594766i	$0.797245\pi$
$600$	−5.86056e143	−4.93344
$601$	8.75727e142	0.676602	0.338301	−	0.941038i	$-0.390148\pi$
$601$	8.75727e142	0.676602	0.338301	+	0.941038i	$0.390148\pi$
$602$	3.04544e143	2.15988
$603$	1.68013e142	0.109396
$604$	−3.75794e143	−2.24671
$605$	3.64181e142	0.199947
$606$	3.50770e143	1.76881
$607$	−2.73108e143	−1.26508	−0.632539	−	0.774528i	$-0.717987\pi$
$607$	−2.73108e143	−1.26508	−0.632539	+	0.774528i	$0.717987\pi$
$608$	1.20161e144	5.11364
$609$	−4.44670e142	−0.173879
$610$	1.06151e143	0.381450
$611$	3.73399e143	1.23325
$612$	−1.06807e144	−3.24265
$613$	−4.94136e143	−1.37921	−0.689607	−	0.724184i	$-0.742217\pi$
$613$	−4.94136e143	−1.37921	−0.689607	+	0.724184i	$0.742217\pi$
$614$	−9.14868e142	−0.234794
$615$	−1.19980e143	−0.283165
$616$	−5.11525e143	−1.11035
$617$	−9.09473e143	−1.81595	−0.907975	−	0.419024i	$-0.862372\pi$
$617$	−9.09473e143	−1.81595	−0.907975	+	0.419024i	$0.862372\pi$
$618$	2.58132e144	4.74171
$619$	−4.19400e143	−0.708860	−0.354430	−	0.935083i	$-0.615325\pi$
$619$	−4.19400e143	−0.708860	−0.354430	+	0.935083i	$0.615325\pi$
$620$	−4.20026e143	−0.653287
$621$	2.95267e143	0.422666
$622$	2.09813e143	0.276457
$623$	−5.47045e143	−0.663573
$624$	−3.43760e144	−3.83928
$625$	7.40527e143	0.761588
$626$	5.22215e143	0.494620
$627$	1.73080e144	1.50997
$628$	−4.70252e143	−0.377928
$629$	1.26867e143	0.0939377
$630$	1.01965e144	0.695685
$631$	−4.19504e142	−0.0263769	−0.0131885	−	0.999913i	$-0.504198\pi$
$631$	−4.19504e142	−0.0263769	−0.0131885	+	0.999913i	$0.504198\pi$
$632$	8.95020e144	5.18684
$633$	−8.76156e142	−0.0468048
$634$	−4.20311e144	−2.07002
$635$	−1.08312e144	−0.491845
$636$	−2.94276e144	−1.23229
$637$	1.00785e144	0.389240
$638$	4.56217e143	0.162520
$639$	4.33299e144	1.42395
$640$	−1.98946e144	−0.603208
$641$	−2.63806e144	−0.738067	−0.369033	−	0.929416i	$-0.620311\pi$
$641$	−2.63806e144	−0.738067	−0.369033	+	0.929416i	$0.620311\pi$
$642$	−1.85970e145	−4.80164
$643$	4.23252e144	1.00863	0.504317	−	0.863519i	$-0.331744\pi$
$643$	4.23252e144	1.00863	0.504317	+	0.863519i	$0.331744\pi$
$644$	−1.97749e144	−0.435002
$645$	4.22799e144	0.858635
$646$	−1.01795e145	−1.90877
$647$	1.01709e145	1.76113	0.880564	−	0.473928i	$-0.157164\pi$
$647$	1.01709e145	1.76113	0.880564	+	0.473928i	$0.157164\pi$
$648$	1.75258e145	2.80262
$649$	−3.05183e144	−0.450774
$650$	8.63699e144	1.17849
$651$	−7.69170e144	−0.969619
$652$	1.51572e145	1.76550
$653$	−1.38607e145	−1.49196	−0.745981	−	0.665967i	$-0.768019\pi$
$653$	−1.38607e145	−1.49196	−0.745981	+	0.665967i	$0.768019\pi$
$654$	−1.50497e145	−1.49718
$655$	−8.56612e143	−0.0787693
$656$	2.24171e145	1.90560
$657$	−2.77861e145	−2.18379
$658$	3.12209e145	2.26888
$659$	−7.27509e143	−0.0488922	−0.0244461	−	0.999701i	$-0.507782\pi$
$659$	−7.27509e143	−0.0488922	−0.0244461	+	0.999701i	$0.507782\pi$
$660$	−1.14423e145	−0.711214
$661$	7.66825e144	0.440881	0.220440	−	0.975400i	$-0.429251\pi$
$661$	7.66825e144	0.440881	0.220440	+	0.975400i	$0.429251\pi$
$662$	−8.61699e144	−0.458320
$663$	1.47390e145	0.725305
$664$	−4.48068e145	−2.04027
$665$	7.04534e144	0.296884
$666$	−1.44269e145	−0.562665
$667$	1.09460e144	0.0395162
$668$	8.37006e145	2.79731
$669$	5.83433e145	1.80528
$670$	−1.05861e144	−0.0303309
$671$	−1.44586e145	−0.383632
$672$	−1.45471e146	−3.57486
$673$	5.62431e145	1.28025	0.640123	−	0.768273i	$-0.278883\pi$
$673$	5.62431e145	1.28025	0.640123	+	0.768273i	$0.278883\pi$
$674$	−7.45472e144	−0.157198
$675$	−7.81733e145	−1.52726
$676$	−7.96576e145	−1.44202
$677$	4.97394e145	0.834419	0.417209	−	0.908810i	$-0.363008\pi$
$677$	4.97394e145	0.834419	0.417209	+	0.908810i	$0.363008\pi$
$678$	−1.01739e146	−1.58182
$679$	−1.44388e145	−0.208083
$680$	4.17669e145	0.557987
$681$	−6.22970e145	−0.771598
$682$	7.89143e145	0.906276
$683$	−9.66317e145	−1.02909	−0.514545	−	0.857463i	$-0.672039\pi$
$683$	−9.66317e145	−1.02909	−0.514545	+	0.857463i	$0.672039\pi$
$684$	8.39217e146	8.28867
$685$	−1.74247e145	−0.159625
$686$	2.29976e146	1.95430
$687$	−1.26772e146	−0.999429
$688$	−7.89959e146	−5.77830
$689$	2.69164e145	0.182695
$690$	−3.78683e145	−0.238532
$691$	−8.71251e144	−0.0509359	−0.0254680	−	0.999676i	$-0.508108\pi$
$691$	−8.71251e144	−0.0509359	−0.0254680	+	0.999676i	$0.508108\pi$
$692$	6.99148e146	3.79407
$693$	−1.38884e146	−0.699666
$694$	−6.86039e146	−3.20875
$695$	1.00803e146	0.437779
$696$	2.07130e146	0.835349
$697$	−9.61149e145	−0.360000
$698$	−5.33362e146	−1.85553
$699$	−1.60498e146	−0.518675
$700$	5.23549e146	1.57184
$701$	1.95548e146	0.545475	0.272738	−	0.962088i	$-0.412071\pi$
$701$	1.95548e146	0.545475	0.272738	+	0.962088i	$0.412071\pi$
$702$	−8.23429e146	−2.13435
$703$	−9.96835e145	−0.240118
$704$	6.81454e146	1.52561
$705$	4.33441e146	0.901966
$706$	5.17298e146	1.00069
$707$	−1.94482e146	−0.349767
$708$	−2.23252e147	−3.73321
$709$	2.04480e146	0.317958	0.158979	−	0.987282i	$-0.449180\pi$
$709$	2.04480e146	0.317958	0.158979	+	0.987282i	$0.449180\pi$
$710$	−2.73013e146	−0.394801
$711$	2.43006e147	3.26838
$712$	2.54817e147	3.18793
$713$	1.89339e146	0.220358
$714$	1.23237e147	1.33439
$715$	1.04658e146	0.105442
$716$	−4.45123e147	−4.17310
$717$	6.21434e146	0.542199
$718$	−1.70364e147	−1.38347
$719$	−2.59082e147	−1.95839	−0.979194	−	0.202925i	$-0.934955\pi$
$719$	−2.59082e147	−1.95839	−0.979194	+	0.202925i	$0.934955\pi$
$720$	−2.64488e147	−1.86115
$721$	−1.43119e147	−0.937630
$722$	4.87248e147	2.97224
$723$	3.38457e147	1.92256
$724$	6.06303e147	3.20740
$725$	−2.89800e146	−0.142788
$726$	−5.00531e147	−2.29718
$727$	−1.53001e147	−0.654144	−0.327072	−	0.944999i	$-0.606062\pi$
$727$	−1.53001e147	−0.654144	−0.327072	+	0.944999i	$0.606062\pi$
$728$	3.42266e147	1.36332
$729$	−2.95882e147	−1.09812
$730$	1.75075e147	0.605475
$731$	3.38701e147	1.09162
$732$	−1.05769e148	−3.17716
$733$	−2.07608e147	−0.581284	−0.290642	−	0.956832i	$-0.593869\pi$
$733$	−2.07608e147	−0.581284	−0.290642	+	0.956832i	$0.593869\pi$
$734$	−8.67131e147	−2.26328
$735$	1.16992e147	0.284680
$736$	3.58092e147	0.812432
$737$	1.44191e146	0.0305044
$738$	1.09299e148	2.15632
$739$	9.03589e147	1.66258	0.831290	−	0.555840i	$-0.187603\pi$
$739$	9.03589e147	1.66258	0.831290	+	0.555840i	$0.187603\pi$
$740$	6.59006e146	0.113098
$741$	−1.15809e148	−1.85398
$742$	2.25055e147	0.336115
$743$	−1.31649e148	−1.83440	−0.917201	−	0.398425i	$-0.869557\pi$
$743$	−1.31649e148	−1.83440	−0.917201	+	0.398425i	$0.869557\pi$
$744$	3.58285e148	4.65824
$745$	−2.81135e147	−0.341088
$746$	1.29201e148	1.46291
$747$	−1.21655e148	−1.28564
$748$	−9.16633e147	−0.904198
$749$	1.03110e148	0.949480
$750$	2.09435e148	1.80051
$751$	−1.42830e147	−0.114647	−0.0573235	−	0.998356i	$-0.518257\pi$
$751$	−1.42830e147	−0.114647	−0.0573235	+	0.998356i	$0.518257\pi$
$752$	−8.09843e148	−6.06991
$753$	2.23647e148	1.56539
$754$	−3.05258e147	−0.199546
$755$	3.98996e147	0.243613
$756$	−4.99138e148	−2.84674
$757$	−1.00223e148	−0.533987	−0.266994	−	0.963698i	$-0.586030\pi$
$757$	−1.00223e148	−0.533987	−0.266994	+	0.963698i	$0.586030\pi$
$758$	3.05629e148	1.52136
$759$	5.15795e147	0.239897
$760$	−3.28177e148	−1.42629
$761$	−1.21467e148	−0.493342	−0.246671	−	0.969099i	$-0.579337\pi$
$761$	−1.21467e148	−0.493342	−0.246671	+	0.969099i	$0.579337\pi$
$762$	1.48864e149	5.65077
$763$	8.34418e147	0.296053
$764$	−7.95571e148	−2.63858
$765$	1.13401e148	0.351604
$766$	−1.86404e148	−0.540348
$767$	2.04200e148	0.553471
$768$	8.43175e148	2.13705
$769$	2.62336e148	0.621800	0.310900	−	0.950443i	$-0.399370\pi$
$769$	2.62336e148	0.621800	0.310900	+	0.950443i	$0.399370\pi$
$770$	8.75080e147	0.193988
$771$	−9.06567e148	−1.87975
$772$	1.24690e149	2.41847
$773$	5.95078e148	1.07977	0.539884	−	0.841740i	$-0.318468\pi$
$773$	5.95078e148	1.07977	0.539884	+	0.841740i	$0.318468\pi$
$774$	−3.85160e149	−6.53855
$775$	−5.01284e148	−0.796244
$776$	6.72568e148	0.999672
$777$	1.20680e148	0.167862
$778$	1.21804e149	1.58567
$779$	7.55206e148	0.920209
$780$	7.65612e148	0.873247
$781$	3.71864e148	0.397060
$782$	−3.03360e148	−0.303257
$783$	2.76289e148	0.258602
$784$	−2.18588e149	−1.91579
$785$	4.99286e147	0.0409790
$786$	1.17733e149	0.904975
$787$	−2.18892e149	−1.57591	−0.787956	−	0.615732i	$-0.788861\pi$
$787$	−2.18892e149	−1.57591	−0.787956	+	0.615732i	$0.788861\pi$
$788$	−2.77705e149	−1.87276
$789$	−1.31701e148	−0.0832001
$790$	−1.53113e149	−0.906187
$791$	5.64082e148	0.312790
$792$	6.46931e149	3.36133
$793$	9.67433e148	0.471033
$794$	1.03211e149	0.470943
$795$	3.12445e148	0.133618
$796$	4.80876e149	1.92757
$797$	−4.44733e149	−1.67107	−0.835537	−	0.549433i	$-0.814844\pi$
$797$	−4.44733e149	−1.67107	−0.835537	+	0.549433i	$0.814844\pi$
$798$	−9.68313e149	−3.41088
$799$	3.47226e149	1.14671
$800$	−9.48066e149	−2.93565
$801$	6.91853e149	2.00881
$802$	1.04438e150	2.84366
$803$	−2.38465e149	−0.608940
$804$	1.05481e149	0.252631
$805$	2.09958e148	0.0471676
$806$	−5.28022e149	−1.11275
$807$	8.42109e149	1.66487
$808$	9.05909e149	1.68035
$809$	2.32924e149	0.405383	0.202691	−	0.979243i	$-0.435031\pi$
$809$	2.32924e149	0.405383	0.202691	+	0.979243i	$0.435031\pi$
$810$	−2.99818e149	−0.489642
$811$	−2.31909e149	−0.355421	−0.177710	−	0.984083i	$-0.556869\pi$
$811$	−2.31909e149	−0.355421	−0.177710	+	0.984083i	$0.556869\pi$
$812$	−1.85038e149	−0.266150
$813$	−1.00667e150	−1.35902
$814$	−1.23814e149	−0.156896
$815$	−1.60931e149	−0.191435
$816$	−3.19665e150	−3.56987
$817$	−2.66129e150	−2.79033
$818$	1.95729e150	1.92691
$819$	9.29283e149	0.859067
$820$	−4.99266e149	−0.433430
$821$	−1.03815e150	−0.846421	−0.423211	−	0.906031i	$-0.639097\pi$
$821$	−1.03815e150	−0.846421	−0.423211	+	0.906031i	$0.639097\pi$
$822$	2.39485e150	1.83392
$823$	−6.33395e149	−0.455600	−0.227800	−	0.973708i	$-0.573153\pi$
$823$	−6.33395e149	−0.455600	−0.227800	+	0.973708i	$0.573153\pi$
$824$	6.66659e150	4.50456
$825$	−1.36559e150	−0.866847
$826$	1.70738e150	1.01826
$827$	−1.60869e150	−0.901444	−0.450722	−	0.892664i	$-0.648834\pi$
$827$	−1.60869e150	−0.901444	−0.450722	+	0.892664i	$0.648834\pi$
$828$	2.50095e150	1.31687
$829$	1.85985e150	0.920277	0.460138	−	0.887847i	$-0.347800\pi$
$829$	1.85985e150	0.920277	0.460138	+	0.887847i	$0.347800\pi$
$830$	7.66522e149	0.356453
$831$	1.77702e150	0.776677
$832$	−4.55966e150	−1.87319
$833$	9.37212e149	0.361926
$834$	−1.38544e151	−5.02962
$835$	−8.88683e149	−0.303315
$836$	7.20229e150	2.31125
$837$	4.77912e150	1.44207
$838$	−6.94752e150	−1.97135
$839$	−5.46889e150	−1.45935	−0.729673	−	0.683796i	$-0.760328\pi$
$839$	−5.46889e150	−1.45935	−0.729673	+	0.683796i	$0.760328\pi$
$840$	3.97302e150	0.997096
$841$	−4.13394e150	−0.975823
$842$	1.13923e151	2.52952
$843$	1.40556e151	2.93581
$844$	−3.64591e149	−0.0716423
$845$	8.45757e149	0.156360
$846$	−3.94854e151	−6.86852
$847$	2.77516e150	0.454247
$848$	−5.83773e150	−0.899203
$849$	1.20270e151	1.74346
$850$	8.03160e150	1.09579
$851$	−2.97066e149	−0.0381488
$852$	2.72031e151	3.28836
$853$	6.42324e150	0.730935	0.365467	−	0.930824i	$-0.380909\pi$
$853$	6.42324e150	0.730935	0.365467	+	0.930824i	$0.380909\pi$
$854$	8.08898e150	0.866590
$855$	−8.91031e150	−0.898748
$856$	−4.80292e151	−4.56149
$857$	−1.30840e150	−0.117011	−0.0585057	−	0.998287i	$-0.518634\pi$
$857$	−1.30840e150	−0.117011	−0.0585057	+	0.998287i	$0.518634\pi$
$858$	−1.43843e151	−1.21142
$859$	−3.61292e150	−0.286556	−0.143278	−	0.989682i	$-0.545764\pi$
$859$	−3.61292e150	−0.286556	−0.143278	+	0.989682i	$0.545764\pi$
$860$	1.75937e151	1.31428
$861$	−9.14278e150	−0.643303
$862$	4.67297e151	3.09720
$863$	−1.74253e151	−1.08799	−0.543993	−	0.839089i	$-0.683088\pi$
$863$	−1.74253e151	−1.08799	−0.543993	+	0.839089i	$0.683088\pi$
$864$	9.03862e151	5.31673
$865$	−7.42314e150	−0.411394
$866$	−2.20540e151	−1.15164
$867$	−2.12927e151	−1.04772
$868$	−3.20071e151	−1.48416
$869$	2.08552e151	0.911372
$870$	−3.54343e150	−0.145943
$871$	−9.64794e149	−0.0374541
$872$	−3.88678e151	−1.42230
$873$	1.82609e151	0.629923
$874$	2.38360e151	0.775166
$875$	−1.16120e151	−0.356034
$876$	−1.74445e152	−5.04310
$877$	2.37084e151	0.646283	0.323142	−	0.946351i	$-0.395261\pi$
$877$	2.37084e151	0.646283	0.323142	+	0.946351i	$0.395261\pi$
$878$	1.38361e152	3.55670
$879$	−2.19622e151	−0.532413
$880$	−2.26988e151	−0.518973
$881$	1.12244e151	0.242049	0.121025	−	0.992650i	$-0.461382\pi$
$881$	1.12244e151	0.242049	0.121025	+	0.992650i	$0.461382\pi$
$882$	−1.06577e152	−2.16785
$883$	−8.50352e150	−0.163163	−0.0815817	−	0.996667i	$-0.525997\pi$
$883$	−8.50352e150	−0.163163	−0.0815817	+	0.996667i	$0.525997\pi$
$884$	6.13326e151	1.11020
$885$	2.37036e151	0.404795
$886$	1.22780e152	1.97830
$887$	7.81398e151	1.18797	0.593986	−	0.804476i	$-0.297554\pi$
$887$	7.81398e151	1.18797	0.593986	+	0.804476i	$0.297554\pi$
$888$	−5.62136e151	−0.806444
$889$	−8.25363e151	−1.11739
$890$	−4.35923e151	−0.556960
$891$	4.08374e151	0.492444
$892$	2.42781e152	2.76328
$893$	−2.72827e152	−2.93115
$894$	3.86393e152	3.91874
$895$	4.72605e151	0.452493
$896$	−1.51602e152	−1.37039
$897$	−3.45122e151	−0.294552
$898$	1.49622e152	1.20577
$899$	1.77169e151	0.134823
$900$	−6.62137e152	−4.75838
$901$	2.50297e151	0.169875
$902$	9.38019e151	0.601277
$903$	3.22184e152	1.95068
$904$	−2.62753e152	−1.50271
$905$	−6.43736e151	−0.347781
$906$	−5.48381e152	−2.79885
$907$	−2.30723e152	−1.11254	−0.556271	−	0.831001i	$-0.687768\pi$
$907$	−2.30723e152	−1.11254	−0.556271	+	0.831001i	$0.687768\pi$
$908$	−2.59234e152	−1.18106
$909$	2.45963e152	1.05884
$910$	−5.85523e151	−0.238184
$911$	4.80563e151	0.184737	0.0923685	−	0.995725i	$-0.470556\pi$
$911$	4.80563e151	0.184737	0.0923685	+	0.995725i	$0.470556\pi$
$912$	2.51172e153	9.12507
$913$	−1.04406e152	−0.358493
$914$	−1.69369e152	−0.549675
$915$	1.12300e152	0.344502
$916$	−5.27531e152	−1.52979
$917$	−6.52761e151	−0.178951
$918$	−7.65713e152	−1.98458
$919$	−5.78053e152	−1.41651	−0.708254	−	0.705958i	$-0.750517\pi$
$919$	−5.78053e152	−1.41651	−0.708254	+	0.705958i	$0.750517\pi$
$920$	−9.77998e151	−0.226603
$921$	−9.67861e151	−0.212052
$922$	7.45675e151	0.154492
$923$	−2.48817e152	−0.487520
$924$	−8.71933e152	−1.61576
$925$	7.86497e151	0.137847
$926$	1.46178e153	2.42336
$927$	1.81004e153	2.83846
$928$	3.35076e152	0.497075
$929$	7.00190e152	0.982667	0.491334	−	0.870971i	$-0.336510\pi$
$929$	7.00190e152	0.982667	0.491334	+	0.870971i	$0.336510\pi$
$930$	−6.12927e152	−0.813836
$931$	−7.36399e152	−0.925134
$932$	−6.67873e152	−0.793916
$933$	2.21966e152	0.249679
$934$	1.51513e153	1.61282
$935$	9.73227e151	0.0980429
$936$	−4.32867e153	−4.12713
$937$	4.71217e152	0.425238	0.212619	−	0.977135i	$-0.431801\pi$
$937$	4.71217e152	0.425238	0.212619	+	0.977135i	$0.431801\pi$
$938$	−8.06692e151	−0.0689067
$939$	5.52464e152	0.446710
$940$	1.80366e153	1.38061
$941$	−2.36978e153	−1.71729	−0.858644	−	0.512572i	$-0.828693\pi$
$941$	−2.36978e153	−1.71729	−0.858644	+	0.512572i	$0.828693\pi$
$942$	−6.86219e152	−0.470805
$943$	2.25059e152	0.146199
$944$	−4.42878e153	−2.72412
$945$	5.29956e152	0.308675
$946$	−3.30550e153	−1.82324
$947$	7.71500e152	0.403007	0.201503	−	0.979488i	$-0.435417\pi$
$947$	7.71500e152	0.403007	0.201503	+	0.979488i	$0.435417\pi$
$948$	1.52563e154	7.54778
$949$	1.59559e153	0.747672
$950$	−6.31070e153	−2.80099
$951$	−4.44657e153	−1.86951
$952$	3.18275e153	1.26765
$953$	2.70635e153	1.02117	0.510586	−	0.859826i	$-0.329428\pi$
$953$	2.70635e153	1.02117	0.510586	+	0.859826i	$0.329428\pi$
$954$	−2.84630e153	−1.01751
$955$	8.44690e152	0.286104
$956$	2.58595e153	0.829924
$957$	4.82642e152	0.146778
$958$	9.06839e153	2.61340
$959$	−1.32781e153	−0.362641
$960$	−5.29285e153	−1.37000
$961$	−1.01159e153	−0.248172
$962$	8.28448e152	0.192641
$963$	−1.30404e154	−2.87433
$964$	1.40840e154	2.94280
$965$	−1.32389e153	−0.262237
$966$	−2.88567e153	−0.541906
$967$	−7.05479e153	−1.25609	−0.628045	−	0.778177i	$-0.716144\pi$
$967$	−7.05479e153	−1.25609	−0.628045	+	0.778177i	$0.716144\pi$
$968$	−1.29269e154	−2.18229
$969$	−1.07692e154	−1.72388
$970$	−1.15058e153	−0.174652
$971$	1.03219e154	1.48584	0.742918	−	0.669383i	$-0.233441\pi$
$971$	1.03219e154	1.48584	0.742918	+	0.669383i	$0.233441\pi$
$972$	−2.23939e153	−0.305715
$973$	7.68145e153	0.994562
$974$	1.08338e154	1.33044
$975$	9.13727e153	1.06434
$976$	−2.09821e154	−2.31837
$977$	6.20051e153	0.649916	0.324958	−	0.945728i	$-0.394650\pi$
$977$	6.20051e153	0.649916	0.324958	+	0.945728i	$0.394650\pi$
$978$	2.21183e154	2.19939
$979$	5.93760e153	0.560147
$980$	4.86832e153	0.435749
$981$	−1.05530e154	−0.896233
$982$	−4.39697e154	−3.54333
$983$	2.83564e153	0.216843	0.108421	−	0.994105i	$-0.465420\pi$
$983$	2.83564e153	0.216843	0.108421	+	0.994105i	$0.465420\pi$
$984$	4.25877e154	3.09056
$985$	2.94850e153	0.203065
$986$	−2.83862e153	−0.185543
$987$	3.30294e154	2.04912
$988$	−4.81911e154	−2.83782
$989$	−7.93089e153	−0.443316
$990$	−1.10672e154	−0.587254
$991$	2.99812e154	1.51027	0.755137	−	0.655566i	$-0.227570\pi$
$991$	2.99812e154	1.51027	0.755137	+	0.655566i	$0.227570\pi$
$992$	5.79599e154	2.77189
$993$	−9.11611e153	−0.413927
$994$	−2.08043e154	−0.896922
$995$	−5.10566e153	−0.209008
$996$	−7.63766e154	−2.96896
$997$	−1.67081e154	−0.616773	−0.308387	−	0.951261i	$-0.599789\pi$
$997$	−1.67081e154	−0.616773	−0.308387	+	0.951261i	$0.599789\pi$
$998$	−6.33212e154	−2.21986
$999$	−7.49827e153	−0.249654

Twists

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

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

\(f(q)\)	\(=\)	\(q+6.07235e15 q^{2} +6.42408e24 q^{3} +2.67322e31 q^{4} -2.83827e35 q^{5} +3.90093e40 q^{6} -2.16284e43 q^{7} +1.00747e47 q^{8} +2.73537e49 q^{9} +O(q^{10})\)	\(q+6.07235e15 q^{2} +6.42408e24 q^{3} +2.67322e31 q^{4} -2.83827e35 q^{5} +3.90093e40 q^{6} -2.16284e43 q^{7} +1.00747e47 q^{8} +2.73537e49 q^{9} -1.72350e51 q^{10} +2.34754e53 q^{11} +1.71730e56 q^{12} -1.57075e57 q^{13} -1.31335e59 q^{14} -1.82333e60 q^{15} +3.40672e62 q^{16} -1.46066e63 q^{17} +1.66101e65 q^{18} +1.14769e66 q^{19} -7.58734e66 q^{20} -1.38943e68 q^{21} +1.42551e69 q^{22} +3.42022e69 q^{23} +6.47205e71 q^{24} -9.05518e71 q^{25} -9.53817e72 q^{26} +8.63299e73 q^{27} -5.78176e74 q^{28} +3.20038e74 q^{29} -1.10719e76 q^{30} +5.53588e76 q^{31} +1.04699e78 q^{32} +1.50808e78 q^{33} -8.86962e78 q^{34} +6.13873e78 q^{35} +7.31225e80 q^{36} -8.68560e79 q^{37} +6.96915e81 q^{38} -1.00907e82 q^{39} -2.85946e82 q^{40} +6.58025e82 q^{41} -8.43709e83 q^{42} -2.31883e84 q^{43} +6.27549e84 q^{44} -7.76372e84 q^{45} +2.07688e85 q^{46} -2.37719e86 q^{47} +2.18850e87 q^{48} -6.41638e86 q^{49} -5.49862e87 q^{50} -9.38338e87 q^{51} -4.19898e88 q^{52} -1.71359e88 q^{53} +5.24225e89 q^{54} -6.66295e88 q^{55} -2.17899e90 q^{56} +7.37283e90 q^{57} +1.94338e90 q^{58} -1.30001e91 q^{59} -4.87417e91 q^{60} -6.15903e91 q^{61} +3.36158e92 q^{62} -5.91616e92 q^{63} +2.90285e93 q^{64} +4.45823e92 q^{65} +9.15757e93 q^{66} +6.14223e92 q^{67} -3.90466e94 q^{68} +2.19718e94 q^{69} +3.72765e94 q^{70} +1.58406e95 q^{71} +2.75579e96 q^{72} -1.01581e96 q^{73} -5.27420e95 q^{74} -5.81713e96 q^{75} +3.06802e97 q^{76} -5.07734e96 q^{77} -6.12740e97 q^{78} +8.88387e97 q^{79} -9.66920e97 q^{80} +1.73959e98 q^{81} +3.99576e98 q^{82} -4.44747e98 q^{83} -3.71425e99 q^{84} +4.14574e98 q^{85} -1.40807e100 q^{86} +2.05595e99 q^{87} +2.36506e100 q^{88} +2.52929e100 q^{89} -4.71440e100 q^{90} +3.39729e100 q^{91} +9.14300e100 q^{92} +3.55630e101 q^{93} -1.44352e102 q^{94} -3.25745e101 q^{95} +6.72593e102 q^{96} +6.67584e101 q^{97} -3.89625e102 q^{98} +6.42137e102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 43\!\cdots\!40 q^{2}+ \cdots + 35\!\cdots\!16 q^{9}+O(q^{10}) \) 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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