LMFDB - Embedded newform 1.104.a.a.1.2

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			1.2
Root			$1.83024e14$ 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)

$f(q)$	$=$	$q-3.84396e15 q^{2} +3.76369e24 q^{3} +4.63479e30 q^{4} +1.31095e36 q^{5} -1.44675e40 q^{6} -5.54417e43 q^{7} +2.11664e46 q^{8} +2.50204e47 q^{9} +O(q^{10})$	\(q-3.84396e15 q^{2} +3.76369e24 q^{3} +4.63479e30 q^{4} +1.31095e36 q^{5} -1.44675e40 q^{6} -5.54417e43 q^{7} +2.11664e46 q^{8} +2.50204e47 q^{9} -5.03922e51 q^{10} -6.51768e53 q^{11} +1.74439e55 q^{12} -1.37266e57 q^{13} +2.13116e59 q^{14} +4.93400e60 q^{15} -1.28365e62 q^{16} +1.56950e63 q^{17} -9.61772e62 q^{18} +5.72587e65 q^{19} +6.07596e66 q^{20} -2.08666e68 q^{21} +2.50537e69 q^{22} +8.74183e69 q^{23} +7.96640e70 q^{24} +7.32506e71 q^{25} +5.27645e72 q^{26} -5.14308e73 q^{27} -2.56961e74 q^{28} +1.45955e75 q^{29} -1.89661e76 q^{30} +4.89378e76 q^{31} +2.78777e77 q^{32} -2.45306e78 q^{33} -6.03308e78 q^{34} -7.26812e79 q^{35} +1.15964e78 q^{36} -3.88581e80 q^{37} -2.20100e81 q^{38} -5.16628e81 q^{39} +2.77481e82 q^{40} -1.41013e83 q^{41} +8.02102e83 q^{42} +2.24257e84 q^{43} -3.02080e84 q^{44} +3.28004e83 q^{45} -3.36032e85 q^{46} -7.36419e85 q^{47} -4.83127e86 q^{48} +1.96436e87 q^{49} -2.81572e87 q^{50} +5.90711e87 q^{51} -6.36200e87 q^{52} +7.09567e88 q^{53} +1.97698e89 q^{54} -8.54433e89 q^{55} -1.17350e90 q^{56} +2.15504e90 q^{57} -5.61043e90 q^{58} +2.12206e91 q^{59} +2.28680e91 q^{60} +9.84700e91 q^{61} -1.88115e92 q^{62} -1.38717e91 q^{63} +2.30172e92 q^{64} -1.79949e93 q^{65} +9.42944e93 q^{66} +7.24139e93 q^{67} +7.27428e93 q^{68} +3.29016e94 q^{69} +2.79383e95 q^{70} -2.66545e93 q^{71} +5.29592e93 q^{72} +5.38053e95 q^{73} +1.49369e96 q^{74} +2.75693e96 q^{75} +2.65382e96 q^{76} +3.61351e97 q^{77} +1.98590e97 q^{78} -5.00820e97 q^{79} -1.68280e98 q^{80} -1.97052e98 q^{81} +5.42047e98 q^{82} -9.52399e98 q^{83} -9.67121e98 q^{84} +2.05753e99 q^{85} -8.62034e99 q^{86} +5.49328e99 q^{87} -1.37956e100 q^{88} -2.31148e100 q^{89} -1.26083e99 q^{90} +7.61028e100 q^{91} +4.05165e100 q^{92} +1.84187e101 q^{93} +2.83076e101 q^{94} +7.50631e101 q^{95} +1.04923e102 q^{96} +9.94437e101 q^{97} -7.55091e102 q^{98} -1.63075e101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.84396e15	−1.20707	−0.603536	−	0.797335i	$-0.706242\pi$
$2$	−3.84396e15	−1.20707	−0.603536	+	0.797335i	$0.706242\pi$
$3$	3.76369e24	1.00895	0.504475	−	0.863426i	$-0.331686\pi$
$3$	3.76369e24	1.00895	0.504475	+	0.863426i	$0.331686\pi$
$4$	4.63479e30	0.457025
$5$	1.31095e36	1.32017	0.660085	−	0.751191i	$-0.270520\pi$
$5$	1.31095e36	1.32017	0.660085	+	0.751191i	$0.270520\pi$
$6$	−1.44675e40	−1.21788
$7$	−5.54417e43	−1.66452	−0.832258	−	0.554389i	$-0.812952\pi$
$7$	−5.54417e43	−1.66452	−0.832258	+	0.554389i	$0.812952\pi$
$8$	2.11664e46	0.655410
$9$	2.50204e47	0.0179806
$10$	−5.03922e51	−1.59354
$11$	−6.51768e53	−1.52184	−0.760921	−	0.648844i	$-0.775253\pi$
$11$	−6.51768e53	−1.52184	−0.760921	+	0.648844i	$0.775253\pi$
$12$	1.74439e55	0.461116
$13$	−1.37266e57	−0.588141	−0.294070	−	0.955784i	$-0.595010\pi$
$13$	−1.37266e57	−0.588141	−0.294070	+	0.955784i	$0.595010\pi$
$14$	2.13116e59	2.00919
$15$	4.93400e60	1.33199
$16$	−1.28365e62	−1.24815
$17$	1.56950e63	0.672421	0.336210	−	0.941787i	$-0.390855\pi$
$17$	1.56950e63	0.672421	0.336210	+	0.941787i	$0.390855\pi$
$18$	−9.61772e62	−0.0217039
$19$	5.72587e65	0.798052	0.399026	−	0.916940i	$-0.369348\pi$
$19$	5.72587e65	0.798052	0.399026	+	0.916940i	$0.369348\pi$
$20$	6.07596e66	0.603351
$21$	−2.08666e68	−1.67941
$22$	2.50537e69	1.83697
$23$	8.74183e69	0.649559	0.324780	−	0.945790i	$-0.394710\pi$
$23$	8.74183e69	0.649559	0.324780	+	0.945790i	$0.394710\pi$
$24$	7.96640e70	0.661276
$25$	7.32506e71	0.742849
$26$	5.27645e72	0.709929
$27$	−5.14308e73	−0.990809
$28$	−2.56961e74	−0.760725
$29$	1.45955e75	0.709122	0.354561	−	0.935033i	$-0.384630\pi$
$29$	1.45955e75	0.709122	0.354561	+	0.935033i	$0.384630\pi$
$30$	−1.89661e76	−1.60780
$31$	4.89378e76	0.766508	0.383254	−	0.923643i	$-0.374803\pi$
$31$	4.89378e76	0.766508	0.383254	+	0.923643i	$0.374803\pi$
$32$	2.78777e77	0.851202
$33$	−2.45306e78	−1.53546
$34$	−6.03308e78	−0.811661
$35$	−7.26812e79	−2.19744
$36$	1.15964e78	0.00821760
$37$	−3.88581e80	−0.671573	−0.335786	−	0.941938i	$-0.609002\pi$
$37$	−3.88581e80	−0.671573	−0.335786	+	0.941938i	$0.609002\pi$
$38$	−2.20100e81	−0.963307
$39$	−5.16628e81	−0.593405
$40$	2.77481e82	0.865253
$41$	−1.41013e83	−1.23279	−0.616396	−	0.787437i	$-0.711408\pi$
$41$	−1.41013e83	−1.23279	−0.616396	+	0.787437i	$0.711408\pi$
$42$	8.02102e83	2.02717
$43$	2.24257e84	1.68702	0.843511	−	0.537112i	$-0.180485\pi$
$43$	2.24257e84	1.68702	0.843511	+	0.537112i	$0.180485\pi$
$44$	−3.02080e84	−0.695520
$45$	3.28004e83	0.0237375
$46$	−3.36032e85	−0.784066
$47$	−7.36419e85	−0.567656	−0.283828	−	0.958875i	$-0.591604\pi$
$47$	−7.36419e85	−0.567656	−0.283828	+	0.958875i	$0.591604\pi$
$48$	−4.83127e86	−1.25932
$49$	1.96436e87	1.77061
$50$	−2.81572e87	−0.896673
$51$	5.90711e87	0.678439
$52$	−6.36200e87	−0.268795
$53$	7.09567e88	1.12405	0.562026	−	0.827120i	$-0.310022\pi$
$53$	7.09567e88	1.12405	0.562026	+	0.827120i	$0.310022\pi$
$54$	1.97698e89	1.19598
$55$	−8.54433e89	−2.00909
$56$	−1.17350e90	−1.09094
$57$	2.15504e90	0.805195
$58$	−5.61043e90	−0.855962
$59$	2.12206e91	1.34239	0.671195	−	0.741281i	$-0.265781\pi$
$59$	2.12206e91	1.34239	0.671195	+	0.741281i	$0.265781\pi$
$60$	2.28680e91	0.608751
$61$	9.84700e91	1.11897	0.559484	−	0.828841i	$-0.311000\pi$
$61$	9.84700e91	1.11897	0.559484	+	0.828841i	$0.311000\pi$
$62$	−1.88115e92	−0.925232
$63$	−1.38717e91	−0.0299290
$64$	2.30172e92	0.220691
$65$	−1.79949e93	−0.776446
$66$	9.42944e93	1.85342
$67$	7.24139e93	0.656099	0.328050	−	0.944661i	$-0.393609\pi$
$67$	7.24139e93	0.656099	0.328050	+	0.944661i	$0.393609\pi$
$68$	7.27428e93	0.307313
$69$	3.29016e94	0.655373
$70$	2.79383e95	2.65247
$71$	−2.66545e93	−0.0121889	−0.00609446	−	0.999981i	$-0.501940\pi$
$71$	−2.66545e93	−0.0121889	−0.00609446	+	0.999981i	$0.501940\pi$
$72$	5.29592e93	0.0117847
$73$	5.38053e95	0.588434	0.294217	−	0.955739i	$-0.404941\pi$
$73$	5.38053e95	0.588434	0.294217	+	0.955739i	$0.404941\pi$
$74$	1.49369e96	0.810637
$75$	2.75693e96	0.749498
$76$	2.65382e96	0.364730
$77$	3.61351e97	2.53313
$78$	1.98590e97	0.716283
$79$	−5.00820e97	−0.937316	−0.468658	−	0.883380i	$-0.655262\pi$
$79$	−5.00820e97	−0.937316	−0.468658	+	0.883380i	$0.655262\pi$
$80$	−1.68280e98	−1.64777
$81$	−1.97052e98	−1.01766
$82$	5.42047e98	1.48807
$83$	−9.52399e98	−1.40055	−0.700273	−	0.713876i	$-0.746938\pi$
$83$	−9.52399e98	−1.40055	−0.700273	+	0.713876i	$0.746938\pi$
$84$	−9.67121e98	−0.767534
$85$	2.05753e99	0.887710
$86$	−8.62034e99	−2.03636
$87$	5.49328e99	0.715469
$88$	−1.37956e100	−0.997431
$89$	−2.31148e100	−0.933908	−0.466954	−	0.884282i	$-0.654649\pi$
$89$	−2.31148e100	−0.933908	−0.466954	+	0.884282i	$0.654649\pi$
$90$	−1.26083e99	−0.0286529
$91$	7.61028e100	0.978969
$92$	4.05165e100	0.296865
$93$	1.84187e101	0.773369
$94$	2.83076e101	0.685202
$95$	7.50631e101	1.05356
$96$	1.04923e102	0.858820
$97$	9.94437e101	0.477346	0.238673	−	0.971100i	$-0.423288\pi$
$97$	9.94437e101	0.477346	0.238673	+	0.971100i	$0.423288\pi$
$98$	−7.55091e102	−2.13726
$99$	−1.63075e101	−0.0273637
$100$	3.39501e102	0.339501
$101$	2.71280e102	0.162505	0.0812526	−	0.996694i	$-0.474108\pi$
$101$	2.71280e102	0.162505	0.0812526	+	0.996694i	$0.474108\pi$
$102$	−2.27067e103	−0.818925
$103$	4.58289e103	1.00005	0.500026	−	0.866010i	$-0.333324\pi$
$103$	4.58289e103	1.00005	0.500026	+	0.866010i	$0.333324\pi$
$104$	−2.90544e103	−0.385473
$105$	−2.73550e104	−2.21711
$106$	−2.72754e104	−1.35681
$107$	4.53430e104	1.39074	0.695369	−	0.718653i	$-0.255241\pi$
$107$	4.53430e104	1.39074	0.695369	+	0.718653i	$0.255241\pi$
$108$	−2.38371e104	−0.452824
$109$	2.64553e103	0.0312643	0.0156322	−	0.999878i	$-0.495024\pi$
$109$	2.64553e103	0.0312643	0.0156322	+	0.999878i	$0.495024\pi$
$110$	3.28440e105	2.42512
$111$	−1.46250e105	−0.677584
$112$	7.11678e105	2.07757
$113$	−3.33276e105	−0.615551	−0.307776	−	0.951459i	$-0.599585\pi$
$113$	−3.33276e105	−0.615551	−0.307776	+	0.951459i	$0.599585\pi$
$114$	−8.28389e105	−0.971929
$115$	1.14601e106	0.857529
$116$	6.76468e105	0.324086
$117$	−3.43445e104	−0.0105751
$118$	−8.15710e106	−1.62036
$119$	−8.70156e106	−1.11925
$120$	1.04435e107	0.872997
$121$	2.41382e107	1.31600
$122$	−3.78514e107	−1.35067
$123$	−5.30729e107	−1.24383
$124$	2.26816e107	0.350314
$125$	−3.32417e107	−0.339483
$126$	5.33223e106	0.0361265
$127$	3.90967e108	1.76298	0.881492	−	0.472200i	$-0.156540\pi$
$127$	3.90967e108	1.76298	0.881492	+	0.472200i	$0.156540\pi$
$128$	−3.71190e108	−1.11759
$129$	8.44035e108	1.70212
$130$	6.91715e108	0.937227
$131$	1.26327e109	1.15352	0.576760	−	0.816914i	$-0.304317\pi$
$131$	1.26327e109	1.15352	0.576760	+	0.816914i	$0.304317\pi$
$132$	−1.13694e109	−0.701745
$133$	−3.17452e109	−1.32837
$134$	−2.78356e109	−0.791960
$135$	−6.74231e109	−1.30804
$136$	3.32206e109	0.440711
$137$	7.01221e109	0.637890	0.318945	−	0.947773i	$-0.396671\pi$
$137$	7.01221e109	0.637890	0.318945	+	0.947773i	$0.396671\pi$
$138$	−1.26472e110	−0.791083
$139$	2.98456e110	1.28712	0.643559	−	0.765397i	$-0.277457\pi$
$139$	2.98456e110	1.28712	0.643559	+	0.765397i	$0.277457\pi$
$140$	−3.36862e110	−1.00429
$141$	−2.77165e110	−0.572736
$142$	1.02459e109	0.0147129
$143$	8.94658e110	0.895057
$144$	−3.21174e109	−0.0224426
$145$	1.91339e111	0.936161
$146$	−2.06825e111	−0.710282
$147$	7.39325e111	1.78646
$148$	−1.80099e111	−0.306926
$149$	4.61317e111	0.555784	0.277892	−	0.960612i	$-0.410364\pi$
$149$	4.61317e111	0.555784	0.277892	+	0.960612i	$0.410364\pi$
$150$	−1.05975e112	−0.904698
$151$	−1.32137e112	−0.801145	−0.400572	−	0.916265i	$-0.631189\pi$
$151$	−1.32137e112	−0.801145	−0.400572	+	0.916265i	$0.631189\pi$
$152$	1.21196e112	0.523052
$153$	3.92694e110	0.0120905
$154$	−1.38902e113	−3.05767
$155$	6.41548e112	1.01192
$156$	−2.39446e112	−0.271201
$157$	−5.76528e112	−0.469882	−0.234941	−	0.972010i	$-0.575490\pi$
$157$	−5.76528e112	−0.469882	−0.234941	+	0.972010i	$0.575490\pi$
$158$	1.92513e113	1.13141
$159$	2.67059e113	1.13411
$160$	3.65461e113	1.12373
$161$	−4.84662e113	−1.08120
$162$	7.57458e113	1.22839
$163$	−2.47052e113	−0.291827	−0.145914	−	0.989297i	$-0.546612\pi$
$163$	−2.47052e113	−0.291827	−0.145914	+	0.989297i	$0.546612\pi$
$164$	−6.53564e113	−0.563417
$165$	−3.21583e114	−2.02707
$166$	3.66098e114	1.69056
$167$	5.46207e114	1.85122	0.925612	−	0.378475i	$-0.123551\pi$
$167$	5.46207e114	1.85122	0.925612	+	0.378475i	$0.123551\pi$
$168$	−4.41671e114	−1.10070
$169$	−3.56290e114	−0.654091
$170$	−7.90904e114	−1.07153
$171$	1.43264e113	0.0143495
$172$	1.03938e115	0.771012
$173$	−1.85346e115	−1.02002	−0.510011	−	0.860168i	$-0.670359\pi$
$173$	−1.85346e115	−1.02002	−0.510011	+	0.860168i	$0.670359\pi$
$174$	−2.11159e115	−0.863623
$175$	−4.06114e115	−1.23648
$176$	8.36643e115	1.89949
$177$	7.98678e115	1.35441
$178$	8.88521e115	1.12729
$179$	6.25668e115	0.594857	0.297429	−	0.954744i	$-0.403871\pi$
$179$	6.25668e115	0.594857	0.297429	+	0.954744i	$0.403871\pi$
$180$	1.52023e114	0.0108486
$181$	−1.80631e116	−0.969048	−0.484524	−	0.874778i	$-0.661007\pi$
$181$	−1.80631e116	−0.969048	−0.484524	+	0.874778i	$0.661007\pi$
$182$	−2.92536e116	−1.18169
$183$	3.70611e116	1.12898
$184$	1.85033e116	0.425728
$185$	−5.09409e116	−0.886590
$186$	−7.08006e116	−0.933513
$187$	−1.02295e117	−1.02332
$188$	−3.41314e116	−0.259433
$189$	2.85142e117	1.64922
$190$	−2.88539e117	−1.27173
$191$	2.26140e117	0.760604	0.380302	−	0.924862i	$-0.375820\pi$
$191$	2.26140e117	0.760604	0.380302	+	0.924862i	$0.375820\pi$
$192$	8.66298e116	0.222666
$193$	5.94722e117	1.16980	0.584901	−	0.811104i	$-0.301133\pi$
$193$	5.94722e117	1.16980	0.584901	+	0.811104i	$0.301133\pi$
$194$	−3.82257e117	−0.576191
$195$	−6.77272e117	−0.783395
$196$	9.10439e117	0.809214
$197$	2.68054e117	0.183320	0.0916602	−	0.995790i	$-0.470783\pi$
$197$	2.68054e117	0.183320	0.0916602	+	0.995790i	$0.470783\pi$
$198$	6.26852e116	0.0330300
$199$	2.86888e117	0.116622	0.0583109	−	0.998298i	$-0.481429\pi$
$199$	2.86888e117	0.116622	0.0583109	+	0.998298i	$0.481429\pi$
$200$	1.55045e118	0.486871
$201$	2.72544e118	0.661971
$202$	−1.04279e118	−0.196156
$203$	−8.09197e118	−1.18034
$204$	2.73782e118	0.310064
$205$	−1.84860e119	−1.62749
$206$	−1.76164e119	−1.20714
$207$	2.18724e117	0.0116795
$208$	1.76202e119	0.734090
$209$	−3.73194e119	−1.21451
$210$	1.05151e120	2.67621
$211$	4.57220e119	0.911127	0.455564	−	0.890203i	$-0.349438\pi$
$211$	4.57220e119	0.911127	0.455564	+	0.890203i	$0.349438\pi$
$212$	3.28869e119	0.513720
$213$	−1.00319e118	−0.0122980
$214$	−1.74296e120	−1.67872
$215$	2.93989e120	2.22716
$216$	−1.08861e120	−0.649386
$217$	−2.71319e120	−1.27586
$218$	−1.01693e119	−0.0377383
$219$	2.02507e120	0.593700
$220$	−3.96011e120	−0.918205
$221$	−2.15439e120	−0.395478
$222$	5.62179e120	0.817893
$223$	1.34410e120	0.155143	0.0775714	−	0.996987i	$-0.475283\pi$
$223$	1.34410e120	0.155143	0.0775714	+	0.996987i	$0.475283\pi$
$224$	−1.54559e121	−1.41684
$225$	1.83276e119	0.0133569
$226$	1.28110e121	0.743015
$227$	−8.63345e120	−0.398889	−0.199445	−	0.979909i	$-0.563914\pi$
$227$	−8.63345e120	−0.398889	−0.199445	+	0.979909i	$0.563914\pi$
$228$	9.98816e120	0.367994
$229$	−5.04867e120	−0.148474	−0.0742369	−	0.997241i	$-0.523652\pi$
$229$	−5.04867e120	−0.148474	−0.0742369	+	0.997241i	$0.523652\pi$
$230$	−4.40520e121	−1.03510
$231$	1.36002e122	2.55580
$232$	3.08934e121	0.464766
$233$	−1.65761e121	−0.199826	−0.0999129	−	0.994996i	$-0.531856\pi$
$233$	−1.65761e121	−0.199826	−0.0999129	+	0.994996i	$0.531856\pi$
$234$	1.32019e120	0.0127650
$235$	−9.65406e121	−0.749402
$236$	9.83529e121	0.613506
$237$	−1.88493e122	−0.945705
$238$	3.34484e122	1.35102
$239$	3.17233e121	0.103249	0.0516245	−	0.998667i	$-0.483560\pi$
$239$	3.17233e121	0.103249	0.0516245	+	0.998667i	$0.483560\pi$
$240$	−6.33354e122	−1.66252
$241$	−6.34433e122	−1.34434	−0.672169	−	0.740398i	$-0.734637\pi$
$241$	−6.34433e122	−1.34434	−0.672169	+	0.740398i	$0.734637\pi$
$242$	−9.27860e122	−1.58851
$243$	−2.59720e121	−0.0359569
$244$	4.56387e122	0.511396
$245$	2.57517e123	2.33751
$246$	2.04010e123	1.50139
$247$	−7.85969e122	−0.469367
$248$	1.03584e123	0.502377
$249$	−3.58454e123	−1.41308
$250$	1.27780e123	0.409781
$251$	5.12794e123	1.33889	0.669447	−	0.742859i	$-0.266531\pi$
$251$	5.12794e123	1.33889	0.669447	+	0.742859i	$0.266531\pi$
$252$	−6.42925e121	−0.0136783
$253$	−5.69765e123	−0.988527
$254$	−1.50286e124	−2.12805
$255$	7.74390e123	0.895655
$256$	1.19342e124	1.12832
$257$	9.34587e123	0.722876	0.361438	−	0.932396i	$-0.382286\pi$
$257$	9.34587e123	0.722876	0.361438	+	0.932396i	$0.382286\pi$
$258$	−3.24443e124	−2.05459
$259$	2.15436e124	1.11784
$260$	−8.34024e123	−0.354855
$261$	3.65184e122	0.0127504
$262$	−4.85596e124	−1.39238
$263$	−2.43248e123	−0.0573230	−0.0286615	−	0.999589i	$-0.509124\pi$
$263$	−2.43248e123	−0.0573230	−0.0286615	+	0.999589i	$0.509124\pi$
$264$	−5.19224e124	−1.00636
$265$	9.30205e124	1.48394
$266$	1.22027e125	1.60344
$267$	−8.69969e124	−0.942267
$268$	3.35623e124	0.299854
$269$	8.90086e124	0.656432	0.328216	−	0.944603i	$-0.393553\pi$
$269$	8.90086e124	0.656432	0.328216	+	0.944603i	$0.393553\pi$
$270$	2.59171e125	1.57889
$271$	−1.33757e125	−0.673593	−0.336797	−	0.941577i	$-0.609343\pi$
$271$	−1.33757e125	−0.673593	−0.336797	+	0.941577i	$0.609343\pi$
$272$	−2.01469e125	−0.839284
$273$	2.86428e125	0.987731
$274$	−2.69546e125	−0.769980
$275$	−4.77424e125	−1.13050
$276$	1.52492e125	0.299522
$277$	4.56977e124	0.0745051	0.0372526	−	0.999306i	$-0.488139\pi$
$277$	4.56977e124	0.0745051	0.0372526	+	0.999306i	$0.488139\pi$
$278$	−1.14725e126	−1.55364
$279$	1.22444e124	0.0137823
$280$	−1.53840e126	−1.44023
$281$	1.95443e126	1.52281	0.761404	−	0.648278i	$-0.224511\pi$
$281$	1.95443e126	1.52281	0.761404	+	0.648278i	$0.224511\pi$
$282$	1.06541e126	0.691335
$283$	4.51389e125	0.244090	0.122045	−	0.992525i	$-0.461055\pi$
$283$	4.51389e125	0.244090	0.122045	+	0.992525i	$0.461055\pi$
$284$	−1.23538e124	−0.00557065
$285$	2.82515e126	1.06299
$286$	−3.43902e126	−1.08040
$287$	7.81799e126	2.05200
$288$	6.97510e124	0.0153051
$289$	−2.98470e126	−0.547850
$290$	−7.35497e126	−1.13001
$291$	3.74276e126	0.481618
$292$	2.49376e126	0.268929
$293$	−3.76777e126	−0.340724	−0.170362	−	0.985382i	$-0.554494\pi$
$293$	−3.76777e126	−0.340724	−0.170362	+	0.985382i	$0.554494\pi$
$294$	−2.84193e127	−2.15639
$295$	2.78191e127	1.77218
$296$	−8.22488e126	−0.440156
$297$	3.35210e127	1.50785
$298$	−1.77328e127	−0.670872
$299$	−1.19996e127	−0.382032
$300$	1.27778e127	0.342539
$301$	−1.24332e128	−2.80807
$302$	5.07928e127	0.967040
$303$	1.02102e127	0.163960
$304$	−7.35002e127	−0.996091
$305$	1.29089e128	1.47723
$306$	−1.50950e126	−0.0145942
$307$	2.21632e128	1.81136	0.905681	−	0.423960i	$-0.139360\pi$
$307$	2.21632e128	1.81136	0.905681	+	0.423960i	$0.139360\pi$
$308$	1.67479e128	1.15770
$309$	1.72486e128	1.00900
$310$	−2.46608e128	−1.22146
$311$	−2.08750e128	−0.875923	−0.437961	−	0.898994i	$-0.644299\pi$
$311$	−2.08750e128	−0.875923	−0.437961	+	0.898994i	$0.644299\pi$
$312$	−1.09352e128	−0.388923
$313$	−3.52356e128	−1.06279	−0.531397	−	0.847123i	$-0.678333\pi$
$313$	−3.52356e128	−1.06279	−0.531397	+	0.847123i	$0.678333\pi$
$314$	2.21615e128	0.567181
$315$	−1.81851e127	−0.0395114
$316$	−2.32119e128	−0.428377
$317$	4.86254e127	0.0762625	0.0381313	−	0.999273i	$-0.487860\pi$
$317$	4.86254e127	0.0762625	0.0381313	+	0.999273i	$0.487860\pi$
$318$	−1.02656e129	−1.36896
$319$	−9.51285e128	−1.07917
$320$	3.01743e128	0.291349
$321$	1.70657e129	1.40319
$322$	1.86302e129	1.30509
$323$	8.98674e128	0.536627
$324$	−9.13292e128	−0.465095
$325$	−1.00548e129	−0.436900
$326$	9.49655e128	0.352257
$327$	9.95699e127	0.0315441
$328$	−2.98474e129	−0.807984
$329$	4.08283e129	0.944872
$330$	1.23615e130	2.44682
$331$	−1.07244e130	−1.81649	−0.908243	−	0.418444i	$-0.862576\pi$
$331$	−1.07244e130	−1.81649	−0.908243	+	0.418444i	$0.862576\pi$
$332$	−4.41416e129	−0.640084
$333$	−9.72245e127	−0.0120753
$334$	−2.09959e130	−2.23456
$335$	9.49308e129	0.866162
$336$	2.67854e130	2.09616
$337$	−2.48592e130	−1.66935	−0.834675	−	0.550742i	$-0.814345\pi$
$337$	−2.48592e130	−1.66935	−0.834675	+	0.550742i	$0.814345\pi$
$338$	1.36956e130	0.789535
$339$	−1.25435e130	−0.621061
$340$	9.53620e129	0.405706
$341$	−3.18961e130	−1.16651
$342$	−5.50698e128	−0.0173209
$343$	−4.73991e130	−1.28269
$344$	4.74672e130	1.10569
$345$	4.31322e130	0.865204
$346$	7.12463e130	1.23124
$347$	−1.28443e131	−1.91312	−0.956558	−	0.291541i	$-0.905832\pi$
$347$	−1.28443e131	−1.91312	−0.956558	+	0.291541i	$0.905832\pi$
$348$	2.54602e130	0.326987
$349$	1.47483e131	1.63393	0.816965	−	0.576687i	$-0.195655\pi$
$349$	1.47483e131	1.63393	0.816965	+	0.576687i	$0.195655\pi$
$350$	1.56108e131	1.49253
$351$	7.05972e130	0.582735
$352$	−1.81698e131	−1.29539
$353$	6.40967e130	0.394855	0.197428	−	0.980317i	$-0.436741\pi$
$353$	6.40967e130	0.394855	0.197428	+	0.980317i	$0.436741\pi$
$354$	−3.07008e131	−1.63487
$355$	−3.49426e129	−0.0160915
$356$	−1.07132e131	−0.426819
$357$	−3.27500e131	−1.12927
$358$	−2.40504e131	−0.718036
$359$	−4.81724e130	−0.124576	−0.0622879	−	0.998058i	$-0.519840\pi$
$359$	−4.81724e130	−0.124576	−0.0622879	+	0.998058i	$0.519840\pi$
$360$	6.94267e129	0.0155578
$361$	−1.86923e131	−0.363113
$362$	6.94337e131	1.16971
$363$	9.08486e131	1.32778
$364$	3.52720e131	0.447413
$365$	7.05359e131	0.776833
$366$	−1.42461e132	−1.36276
$367$	1.10561e132	0.918969	0.459485	−	0.888186i	$-0.348034\pi$
$367$	1.10561e132	0.918969	0.459485	+	0.888186i	$0.348034\pi$
$368$	−1.12215e132	−0.810750
$369$	−3.52819e130	−0.0221664
$370$	1.95815e132	1.07018
$371$	−3.93396e132	−1.87100
$372$	8.53666e131	0.353449
$373$	2.38273e132	0.859153	0.429576	−	0.903030i	$-0.358663\pi$
$373$	2.38273e132	0.859153	0.429576	+	0.903030i	$0.358663\pi$
$374$	3.93217e132	1.23522
$375$	−1.25112e132	−0.342521
$376$	−1.55874e132	−0.372047
$377$	−2.00346e132	−0.417063
$378$	−1.09607e133	−1.99072
$379$	−5.06332e131	−0.0802631	−0.0401316	−	0.999194i	$-0.512778\pi$
$379$	−5.06332e131	−0.0802631	−0.0401316	+	0.999194i	$0.512778\pi$
$380$	3.47902e132	0.481505
$381$	1.47148e133	1.77876
$382$	−8.69272e132	−0.918105
$383$	−1.53557e133	−1.41753	−0.708767	−	0.705443i	$-0.750748\pi$
$383$	−1.53557e133	−1.41753	−0.708767	+	0.705443i	$0.750748\pi$
$384$	−1.39705e133	−1.12759
$385$	4.73713e133	3.34416
$386$	−2.28608e133	−1.41204
$387$	5.61100e131	0.0303337
$388$	4.60900e132	0.218159
$389$	−1.58353e133	−0.656479	−0.328240	−	0.944594i	$-0.606455\pi$
$389$	−1.58353e133	−0.656479	−0.328240	+	0.944594i	$0.606455\pi$
$390$	2.60340e133	0.945615
$391$	1.37203e133	0.436777
$392$	4.15785e133	1.16048
$393$	4.75457e133	1.16384
$394$	−1.03039e133	−0.221281
$395$	−6.56548e133	−1.23742
$396$	−7.55817e131	−0.0125059
$397$	−1.06791e133	−0.155176	−0.0775879	−	0.996986i	$-0.524722\pi$
$397$	−1.06791e133	−0.155176	−0.0775879	+	0.996986i	$0.524722\pi$
$398$	−1.10279e133	−0.140771
$399$	−1.19479e134	−1.34026
$400$	−9.40282e133	−0.927189
$401$	1.21033e134	1.04947	0.524735	−	0.851266i	$-0.324164\pi$
$401$	1.21033e134	1.04947	0.524735	+	0.851266i	$0.324164\pi$
$402$	−1.04765e134	−0.799048
$403$	−6.71750e133	−0.450815
$404$	1.25733e133	0.0742689
$405$	−2.58324e134	−1.34348
$406$	3.11052e134	1.42476
$407$	2.53265e134	1.02203
$408$	1.25032e134	0.444656
$409$	−5.37735e133	−0.168585	−0.0842923	−	0.996441i	$-0.526863\pi$
$409$	−5.37735e133	−0.168585	−0.0842923	+	0.996441i	$0.526863\pi$
$410$	7.10594e134	1.96450
$411$	2.63918e134	0.643599
$412$	2.12407e134	0.457049
$413$	−1.17651e135	−2.23443
$414$	−8.40765e132	−0.0140980
$415$	−1.24854e135	−1.84896
$416$	−3.82666e134	−0.500626
$417$	1.12330e135	1.29864
$418$	1.43454e135	1.46600
$419$	1.07138e135	0.968106	0.484053	−	0.875039i	$-0.339164\pi$
$419$	1.07138e135	0.968106	0.484053	+	0.875039i	$0.339164\pi$
$420$	−1.26784e135	−1.01328
$421$	−1.10685e135	−0.782639	−0.391320	−	0.920255i	$-0.627981\pi$
$421$	−1.10685e135	−0.782639	−0.391320	+	0.920255i	$0.627981\pi$
$422$	−1.75753e135	−1.09980
$423$	−1.84255e133	−0.0102068
$424$	1.50190e135	0.736715
$425$	1.14967e135	0.499507
$426$	3.85623e133	0.0148446
$427$	−5.45935e135	−1.86254
$428$	2.10155e135	0.635602
$429$	3.36722e135	0.903068
$430$	−1.13008e136	−2.68834
$431$	1.35915e135	0.286872	0.143436	−	0.989660i	$-0.454185\pi$
$431$	1.35915e135	0.286872	0.143436	+	0.989660i	$0.454185\pi$
$432$	6.60193e135	1.23668
$433$	2.47856e135	0.412166	0.206083	−	0.978535i	$-0.433928\pi$
$433$	2.47856e135	0.412166	0.206083	+	0.978535i	$0.433928\pi$
$434$	1.04294e136	1.54006
$435$	7.20140e135	0.944540
$436$	1.22615e134	0.0142886
$437$	5.00546e135	0.518382
$438$	−7.78426e135	−0.716640
$439$	3.71671e134	0.0304253	0.0152127	−	0.999884i	$-0.495157\pi$
$439$	3.71671e134	0.0304253	0.0152127	+	0.999884i	$0.495157\pi$
$440$	−1.80853e136	−1.31678
$441$	4.91491e134	0.0318367
$442$	8.28138e135	0.477371
$443$	−5.66929e135	−0.290895	−0.145448	−	0.989366i	$-0.546462\pi$
$443$	−5.66929e135	−0.290895	−0.145448	+	0.989366i	$0.546462\pi$
$444$	−6.77838e135	−0.309673
$445$	−3.03022e136	−1.23292
$446$	−5.16666e135	−0.187269
$447$	1.73625e136	0.560759
$448$	−1.27611e136	−0.367343
$449$	−4.49565e136	−1.15373	−0.576867	−	0.816838i	$-0.695725\pi$
$449$	−4.49565e136	−1.15373	−0.576867	+	0.816838i	$0.695725\pi$
$450$	−7.04504e134	−0.0161227
$451$	9.19076e136	1.87611
$452$	−1.54466e136	−0.281322
$453$	−4.97322e136	−0.808315
$454$	3.31866e136	0.481489
$455$	9.97667e136	1.29241
$456$	4.56146e136	0.527733
$457$	1.00591e137	1.03962	0.519812	−	0.854281i	$-0.326002\pi$
$457$	1.00591e137	1.03962	0.519812	+	0.854281i	$0.326002\pi$
$458$	1.94069e136	0.179219
$459$	−8.07206e136	−0.666240
$460$	5.31150e136	0.391912
$461$	4.39872e136	0.290221	0.145110	−	0.989415i	$-0.453646\pi$
$461$	4.39872e136	0.290221	0.145110	+	0.989415i	$0.453646\pi$
$462$	−5.22784e137	−3.08504
$463$	8.97464e136	0.473801	0.236901	−	0.971534i	$-0.423868\pi$
$463$	8.97464e136	0.473801	0.236901	+	0.971534i	$0.423868\pi$
$464$	−1.87355e137	−0.885092
$465$	2.41459e137	1.02098
$466$	6.37177e136	0.241204
$467$	1.46815e137	0.497682	0.248841	−	0.968544i	$-0.419950\pi$
$467$	1.46815e137	0.497682	0.248841	+	0.968544i	$0.419950\pi$
$468$	−1.59180e135	−0.00483310
$469$	−4.01475e137	−1.09209
$470$	3.71098e137	0.904583
$471$	−2.16988e137	−0.474087
$472$	4.49164e137	0.879816
$473$	−1.46164e138	−2.56738
$474$	7.24559e137	1.14154
$475$	4.19423e137	0.592832
$476$	−4.03299e137	−0.511527
$477$	1.77536e136	0.0202111
$478$	−1.21943e137	−0.124629
$479$	−8.59062e137	−0.788398	−0.394199	−	0.919025i	$-0.628978\pi$
$479$	−8.59062e137	−0.788398	−0.394199	+	0.919025i	$0.628978\pi$
$480$	1.37548e138	1.13379
$481$	5.33391e137	0.394979
$482$	2.43873e138	1.62271
$483$	−1.82412e138	−1.09088
$484$	1.11875e138	0.601447
$485$	1.30365e138	0.630177
$486$	9.98352e136	0.0434026
$487$	1.34506e138	0.526018	0.263009	−	0.964793i	$-0.415285\pi$
$487$	1.34506e138	0.526018	0.263009	+	0.964793i	$0.415285\pi$
$488$	2.08426e138	0.733383
$489$	−9.29826e137	−0.294439
$490$	−9.89885e138	−2.82154
$491$	−6.37468e138	−1.63592	−0.817959	−	0.575276i	$-0.804895\pi$
$491$	−6.37468e138	−1.63592	−0.817959	+	0.575276i	$0.804895\pi$
$492$	−2.45981e138	−0.568459
$493$	2.29075e138	0.476828
$494$	3.02123e138	0.566560
$495$	−2.13782e137	−0.0361247
$496$	−6.28190e138	−0.956720
$497$	1.47777e137	0.0202887
$498$	1.37788e139	1.70569
$499$	5.16841e138	0.577004	0.288502	−	0.957479i	$-0.406843\pi$
$499$	5.16841e138	0.577004	0.288502	+	0.957479i	$0.406843\pi$
$500$	−1.54068e138	−0.155152
$501$	2.05576e139	1.86779
$502$	−1.97116e139	−1.61614
$503$	−1.77422e137	−0.0131298	−0.00656488	−	0.999978i	$-0.502090\pi$
$503$	−1.77422e137	−0.0131298	−0.00656488	+	0.999978i	$0.502090\pi$
$504$	−2.93615e137	−0.0196158
$505$	3.55634e138	0.214534
$506$	2.19015e139	1.19322
$507$	−1.34097e139	−0.659945
$508$	1.81205e139	0.805728
$509$	1.49444e139	0.600501	0.300250	−	0.953860i	$-0.402930\pi$
$509$	1.49444e139	0.600501	0.300250	+	0.953860i	$0.402930\pi$
$510$	−2.97672e139	−1.08112
$511$	−2.98306e139	−0.979457
$512$	−8.23122e138	−0.244378
$513$	−2.94486e139	−0.790717
$514$	−3.59251e139	−0.872564
$515$	6.00793e139	1.32024
$516$	3.91192e139	0.777912
$517$	4.79974e139	0.863883
$518$	−8.28127e139	−1.34932
$519$	−6.97587e139	−1.02915
$520$	−3.80887e139	−0.508890
$521$	2.45826e139	0.297499	0.148750	−	0.988875i	$-0.452475\pi$
$521$	2.45826e139	0.297499	0.148750	+	0.988875i	$0.452475\pi$
$522$	−1.40375e138	−0.0153907
$523$	1.36972e140	1.36080	0.680402	−	0.732840i	$-0.261805\pi$
$523$	1.36972e140	1.36080	0.680402	+	0.732840i	$0.261805\pi$
$524$	5.85499e139	0.527187
$525$	−1.52849e140	−1.24755
$526$	9.35035e138	0.0691930
$527$	7.68077e139	0.515416
$528$	3.14887e140	1.91649
$529$	−1.04701e140	−0.578073
$530$	−3.57566e140	−1.79122
$531$	5.30947e138	0.0241370
$532$	−1.47132e140	−0.607098
$533$	1.93563e140	0.725055
$534$	3.34412e140	1.13738
$535$	5.94422e140	1.83601
$536$	1.53274e140	0.430014
$537$	2.35482e140	0.600182
$538$	−3.42145e140	−0.792361
$539$	−1.28031e141	−2.69459
$540$	−3.12492e140	−0.597805
$541$	−8.00457e140	−1.39213	−0.696064	−	0.717980i	$-0.745067\pi$
$541$	−8.00457e140	−1.39213	−0.696064	+	0.717980i	$0.745067\pi$
$542$	5.14156e140	0.813076
$543$	−6.79839e140	−0.977722
$544$	4.37539e140	0.572366
$545$	3.46816e139	0.0412742
$546$	−1.10102e141	−1.19226
$547$	9.42779e140	0.929100	0.464550	−	0.885547i	$-0.346216\pi$
$547$	9.42779e140	0.929100	0.464550	+	0.885547i	$0.346216\pi$
$548$	3.25001e140	0.291532
$549$	2.46376e139	0.0201197
$550$	1.83520e141	1.36460
$551$	8.35717e140	0.565916
$552$	6.96409e140	0.429538
$553$	2.77663e141	1.56018
$554$	−1.75660e140	−0.0899331
$555$	−1.91726e141	−0.894526
$556$	1.38328e141	0.588245
$557$	−4.54013e141	−1.76005	−0.880026	−	0.474925i	$-0.842475\pi$
$557$	−4.54013e141	−1.76005	−0.880026	+	0.474925i	$0.842475\pi$
$558$	−4.70670e139	−0.0166362
$559$	−3.07829e141	−0.992206
$560$	9.32973e141	2.74275
$561$	−3.85006e141	−1.03248
$562$	−7.51275e141	−1.83814
$563$	2.61229e141	0.583230	0.291615	−	0.956536i	$-0.405807\pi$
$563$	2.61229e141	0.583230	0.291615	+	0.956536i	$0.405807\pi$
$564$	−1.28460e141	−0.261755
$565$	−4.36907e141	−0.812632
$566$	−1.73512e141	−0.294634
$567$	1.09249e142	1.69391
$568$	−5.64181e139	−0.00798875
$569$	−3.10663e141	−0.401798	−0.200899	−	0.979612i	$-0.564386\pi$
$569$	−3.10663e141	−0.401798	−0.200899	+	0.979612i	$0.564386\pi$
$570$	−1.08597e142	−1.28311
$571$	1.42175e142	1.53484	0.767420	−	0.641145i	$-0.221540\pi$
$571$	1.42175e142	1.53484	0.767420	+	0.641145i	$0.221540\pi$
$572$	4.14655e141	0.409064
$573$	8.51121e141	0.767412
$574$	−3.00520e142	−2.47691
$575$	6.40344e141	0.482525
$576$	5.75899e139	0.00396816
$577$	−1.45001e142	−0.913725	−0.456863	−	0.889537i	$-0.651027\pi$
$577$	−1.45001e142	−0.913725	−0.456863	+	0.889537i	$0.651027\pi$
$578$	1.14731e142	0.661295
$579$	2.23835e142	1.18027
$580$	8.86814e141	0.427849
$581$	5.28026e142	2.33123
$582$	−1.43870e142	−0.581348
$583$	−4.62473e142	−1.71063
$584$	1.13887e142	0.385665
$585$	−4.50239e140	−0.0139610
$586$	1.44831e142	0.411278
$587$	−5.25666e142	−1.36725	−0.683625	−	0.729834i	$-0.739597\pi$
$587$	−5.25666e142	−1.36725	−0.683625	+	0.729834i	$0.739597\pi$
$588$	3.42661e142	0.816456
$589$	2.80211e142	0.611714
$590$	−1.06935e143	−2.13915
$591$	1.00887e142	0.184961
$592$	4.98803e142	0.838226
$593$	6.61885e142	1.01968	0.509842	−	0.860268i	$-0.329704\pi$
$593$	6.61885e142	1.01968	0.509842	+	0.860268i	$0.329704\pi$
$594$	−1.28853e143	−1.82009
$595$	−1.14073e143	−1.47761
$596$	2.13810e142	0.254007
$597$	1.07976e142	0.117666
$598$	4.61259e142	0.461141
$599$	−8.88243e142	−0.814798	−0.407399	−	0.913250i	$-0.633564\pi$
$599$	−8.88243e142	−0.814798	−0.407399	+	0.913250i	$0.633564\pi$
$600$	5.83543e142	0.491229
$601$	−1.86160e143	−1.43830	−0.719152	−	0.694853i	$-0.755469\pi$
$601$	−1.86160e143	−1.43830	−0.719152	+	0.694853i	$0.755469\pi$
$602$	4.77927e143	3.38955
$603$	1.81182e141	0.0117971
$604$	−6.12426e142	−0.366143
$605$	3.16438e143	1.73735
$606$	−3.92474e142	−0.197911
$607$	2.15377e143	0.997659	0.498830	−	0.866700i	$-0.333763\pi$
$607$	2.15377e143	0.997659	0.498830	+	0.866700i	$0.333763\pi$
$608$	1.59624e143	0.679303
$609$	−3.04557e143	−1.19091
$610$	−4.96212e143	−1.78312
$611$	1.01085e143	0.333861
$612$	1.82005e141	0.00552568
$613$	4.62414e143	1.29068	0.645338	−	0.763897i	$-0.276717\pi$
$613$	4.62414e143	1.29068	0.645338	+	0.763897i	$0.276717\pi$
$614$	−8.51942e143	−2.18645
$615$	−6.95757e143	−1.64206
$616$	7.64852e143	1.66024
$617$	−4.05236e143	−0.809137	−0.404568	−	0.914508i	$-0.632578\pi$
$617$	−4.05236e143	−0.809137	−0.404568	+	0.914508i	$0.632578\pi$
$618$	−6.63029e143	−1.21794
$619$	2.54979e143	0.430960	0.215480	−	0.976508i	$-0.430868\pi$
$619$	2.54979e143	0.430960	0.215480	+	0.976508i	$0.430868\pi$
$620$	2.97344e143	0.462473
$621$	−4.49600e143	−0.643589
$622$	8.02425e143	1.05730
$623$	1.28152e144	1.55450
$624$	6.63170e143	0.740660
$625$	−1.15809e144	−1.19102
$626$	1.35444e144	1.28287
$627$	−1.40459e144	−1.22538
$628$	−2.67208e143	−0.214748
$629$	−6.09877e143	−0.451579
$630$	6.99027e142	0.0476931
$631$	−7.65142e143	−0.481094	−0.240547	−	0.970638i	$-0.577327\pi$
$631$	−7.65142e143	−0.481094	−0.240547	+	0.970638i	$0.577327\pi$
$632$	−1.06006e144	−0.614327
$633$	1.72084e144	0.919282
$634$	−1.86914e143	−0.0920544
$635$	5.12537e144	2.32744
$636$	1.23776e144	0.518318
$637$	−2.69640e144	−1.04137
$638$	3.65670e144	1.30264
$639$	−6.66906e140	−0.000219165 0
$640$	−4.86611e144	−1.47541
$641$	3.53096e143	0.0987880	0.0493940	−	0.998779i	$-0.484271\pi$
$641$	3.53096e143	0.0987880	0.0493940	+	0.998779i	$0.484271\pi$
$642$	−6.55998e144	−1.69375
$643$	−2.19323e144	−0.522660	−0.261330	−	0.965249i	$-0.584161\pi$
$643$	−2.19323e144	−0.522660	−0.261330	+	0.965249i	$0.584161\pi$
$644$	−2.24631e144	−0.494136
$645$	1.10649e145	2.24709
$646$	−3.45446e144	−0.647748
$647$	3.54133e144	0.613191	0.306596	−	0.951840i	$-0.400810\pi$
$647$	3.54133e144	0.613191	0.306596	+	0.951840i	$0.400810\pi$
$648$	−4.17088e144	−0.666983
$649$	−1.38309e145	−2.04291
$650$	3.86503e144	0.527370
$651$	−1.02116e145	−1.28728
$652$	−1.14503e144	−0.133372
$653$	1.49140e145	1.60533	0.802666	−	0.596429i	$-0.203414\pi$
$653$	1.49140e145	1.60533	0.802666	+	0.596429i	$0.203414\pi$
$654$	−3.82742e143	−0.0380761
$655$	1.65608e145	1.52284
$656$	1.81011e145	1.53871
$657$	1.34623e143	0.0105804
$658$	−1.56942e145	−1.14053
$659$	1.65915e145	1.11503	0.557515	−	0.830167i	$-0.311755\pi$
$659$	1.65915e145	1.11503	0.557515	+	0.830167i	$0.311755\pi$
$660$	−1.49047e145	−0.926423
$661$	8.72748e143	0.0501780	0.0250890	−	0.999685i	$-0.492013\pi$
$661$	8.72748e143	0.0501780	0.0250890	+	0.999685i	$0.492013\pi$
$662$	4.12242e145	2.19263
$663$	−8.10847e144	−0.399018
$664$	−2.01589e145	−0.917932
$665$	−4.16163e145	−1.75367
$666$	3.73727e143	0.0145758
$667$	1.27591e145	0.460617
$668$	2.53155e145	0.846055
$669$	5.05879e144	0.156531
$670$	−3.64910e145	−1.04552
$671$	−6.41796e145	−1.70289
$672$	−5.81711e145	−1.42952
$673$	1.24310e145	0.282962	0.141481	−	0.989941i	$-0.454814\pi$
$673$	1.24310e145	0.282962	0.141481	+	0.989941i	$0.454814\pi$
$674$	9.55577e145	2.01503
$675$	−3.76734e145	−0.736021
$676$	−1.65133e145	−0.298936
$677$	4.41341e145	0.740386	0.370193	−	0.928955i	$-0.379292\pi$
$677$	4.41341e145	0.740386	0.370193	+	0.928955i	$0.379292\pi$
$678$	4.82166e145	0.749665
$679$	−5.51333e145	−0.794549
$680$	4.35505e145	0.581814
$681$	−3.24937e145	−0.402460
$682$	1.22607e146	1.40806
$683$	−1.69082e145	−0.180066	−0.0900328	−	0.995939i	$-0.528697\pi$
$683$	−1.69082e145	−0.180066	−0.0900328	+	0.995939i	$0.528697\pi$
$684$	6.63996e143	0.00655807
$685$	9.19264e145	0.842123
$686$	1.82200e146	1.54830
$687$	−1.90017e145	−0.149803
$688$	−2.87868e146	−2.10566
$689$	−9.73996e145	−0.661100
$690$	−1.65798e146	−1.04436
$691$	−2.14832e145	−0.125597	−0.0627986	−	0.998026i	$-0.520003\pi$
$691$	−2.14832e145	−0.125597	−0.0627986	+	0.998026i	$0.520003\pi$
$692$	−8.59041e145	−0.466176
$693$	9.04115e144	0.0455473
$694$	4.93728e146	2.30927
$695$	3.91260e146	1.69921
$696$	1.16273e146	0.468925
$697$	−2.21319e146	−0.828954
$698$	−5.66919e146	−1.97227
$699$	−6.23873e145	−0.201614
$700$	−1.88225e146	−0.565104
$701$	4.07353e146	1.13630	0.568149	−	0.822926i	$-0.307660\pi$
$701$	4.07353e146	1.13630	0.568149	+	0.822926i	$0.307660\pi$
$702$	−2.71372e146	−0.703403
$703$	−2.22497e146	−0.535950
$704$	−1.50019e146	−0.335857
$705$	−3.63349e146	−0.756109
$706$	−2.46385e146	−0.476619
$707$	−1.50402e146	−0.270492
$708$	3.70170e146	0.618997
$709$	1.12091e147	1.74297	0.871484	−	0.490423i	$-0.163158\pi$
$709$	1.12091e147	1.74297	0.871484	+	0.490423i	$0.163158\pi$
$710$	1.34318e145	0.0194236
$711$	−1.25307e145	−0.0168535
$712$	−4.89257e146	−0.612093
$713$	4.27806e146	0.497893
$714$	1.25890e147	1.36311
$715$	1.17285e147	1.18163
$716$	2.89984e146	0.271865
$717$	1.19397e146	0.104173
$718$	1.85172e146	0.150372
$719$	−4.57872e146	−0.346104	−0.173052	−	0.984913i	$-0.555363\pi$
$719$	−4.57872e146	−0.346104	−0.173052	+	0.984913i	$0.555363\pi$
$720$	−4.21043e145	−0.0296280
$721$	−2.54084e147	−1.66460
$722$	7.18524e146	0.438304
$723$	−2.38781e147	−1.35637
$724$	−8.37185e146	−0.442879
$725$	1.06913e147	0.526770
$726$	−3.49218e147	−1.60273
$727$	−1.12902e147	−0.482703	−0.241352	−	0.970438i	$-0.577591\pi$
$727$	−1.12902e147	−0.482703	−0.241352	+	0.970438i	$0.577591\pi$
$728$	1.61082e147	0.641626
$729$	2.64426e147	0.981379
$730$	−2.71137e147	−0.937694
$731$	3.51971e147	1.13439
$732$	1.71770e147	0.515973
$733$	−4.59740e147	−1.28723	−0.643617	−	0.765348i	$-0.722567\pi$
$733$	−4.59740e147	−1.28723	−0.643617	+	0.765348i	$0.722567\pi$
$734$	−4.24993e147	−1.10926
$735$	9.69216e147	2.35843
$736$	2.43702e147	0.552906
$737$	−4.71970e147	−0.998480
$738$	1.35622e146	0.0267564
$739$	4.38091e147	0.806075	0.403037	−	0.915183i	$-0.367954\pi$
$739$	4.38091e147	0.806075	0.403037	+	0.915183i	$0.367954\pi$
$740$	−2.36100e147	−0.405194
$741$	−2.95815e147	−0.473568
$742$	1.51220e148	2.25843
$743$	−3.72029e147	−0.518385	−0.259193	−	0.965826i	$-0.583456\pi$
$743$	−3.72029e147	−0.518385	−0.259193	+	0.965826i	$0.583456\pi$
$744$	3.89858e147	0.506874
$745$	6.04761e147	0.733730
$746$	−9.15912e147	−1.03706
$747$	−2.38294e146	−0.0251827
$748$	−4.74114e147	−0.467682
$749$	−2.51389e148	−2.31490
$750$	4.80924e147	0.413448
$751$	−5.97527e147	−0.479624	−0.239812	−	0.970819i	$-0.577086\pi$
$751$	−5.97527e147	−0.479624	−0.239812	+	0.970819i	$0.577086\pi$
$752$	9.45304e147	0.708521
$753$	1.93000e148	1.35088
$754$	7.70122e147	0.503426
$755$	−1.73224e148	−1.05765
$756$	1.32157e148	0.753733
$757$	−2.15898e148	−1.15030	−0.575150	−	0.818048i	$-0.695056\pi$
$757$	−2.15898e148	−1.15030	−0.575150	+	0.818048i	$0.695056\pi$
$758$	1.94632e147	0.0968834
$759$	−2.14442e148	−0.997375
$760$	1.58882e148	0.690517
$761$	2.06807e148	0.839952	0.419976	−	0.907535i	$-0.362039\pi$
$761$	2.06807e148	0.839952	0.419976	+	0.907535i	$0.362039\pi$
$762$	−5.65630e148	−2.14710
$763$	−1.46673e147	−0.0520399
$764$	1.04811e148	0.347615
$765$	5.14801e146	0.0159616
$766$	5.90267e148	1.71107
$767$	−2.91287e148	−0.789514
$768$	4.49165e148	1.13842
$769$	7.29288e148	1.72859	0.864296	−	0.502984i	$-0.167765\pi$
$769$	7.29288e148	1.72859	0.864296	+	0.502984i	$0.167765\pi$
$770$	−1.82093e149	−4.03665
$771$	3.51750e148	0.729346
$772$	2.75641e148	0.534629
$773$	5.84700e148	1.06094	0.530468	−	0.847705i	$-0.322016\pi$
$773$	5.84700e148	1.06094	0.530468	+	0.847705i	$0.322016\pi$
$774$	−2.15684e147	−0.0366150
$775$	3.58472e148	0.569400
$776$	2.10487e148	0.312857
$777$	8.10836e148	1.12785
$778$	6.08701e148	0.792418
$779$	−8.07421e148	−0.983832
$780$	−3.13901e148	−0.358031
$781$	1.73725e147	0.0185496
$782$	−5.27401e148	−0.527222
$783$	−7.50657e148	−0.702604
$784$	−2.52155e149	−2.20999
$785$	−7.55798e148	−0.620324
$786$	−1.82763e149	−1.40484
$787$	6.29281e148	0.453049	0.226525	−	0.974005i	$-0.427264\pi$
$787$	6.29281e148	0.453049	0.226525	+	0.974005i	$0.427264\pi$
$788$	1.24237e148	0.0837821
$789$	−9.15512e147	−0.0578360
$790$	2.52374e149	1.49365
$791$	1.84774e149	1.02459
$792$	−3.45171e147	−0.0179344
$793$	−1.35166e149	−0.658110
$794$	4.10500e148	0.187308
$795$	3.50101e149	1.49722
$796$	1.32967e148	0.0532991
$797$	−3.51456e148	−0.132059	−0.0660294	−	0.997818i	$-0.521033\pi$
$797$	−3.51456e148	−0.132059	−0.0660294	+	0.997818i	$0.521033\pi$
$798$	4.59273e149	1.61779
$799$	−1.15581e149	−0.381703
$800$	2.04205e149	0.632314
$801$	−5.78340e147	−0.0167922
$802$	−4.65247e149	−1.26679
$803$	−3.50686e149	−0.895503
$804$	1.26318e149	0.302538
$805$	−6.35367e149	−1.42737
$806$	2.58218e149	0.544166
$807$	3.35001e149	0.662307
$808$	5.74203e148	0.106508
$809$	−5.26882e149	−0.916989	−0.458495	−	0.888697i	$-0.651611\pi$
$809$	−5.26882e149	−0.916989	−0.458495	+	0.888697i	$0.651611\pi$
$810$	9.92987e149	1.62168
$811$	3.54979e149	0.544037	0.272019	−	0.962292i	$-0.412309\pi$
$811$	3.54979e149	0.544037	0.272019	+	0.962292i	$0.412309\pi$
$812$	−3.75046e149	−0.539447
$813$	−5.03420e149	−0.679622
$814$	−9.73539e149	−1.23366
$815$	−3.23871e149	−0.385262
$816$	−7.58266e149	−0.846796
$817$	1.28407e150	1.34633
$818$	2.06703e149	0.203494
$819$	1.90412e148	0.0176025
$820$	−8.56787e149	−0.743806
$821$	2.35660e150	1.92138	0.960689	−	0.277627i	$-0.0895481\pi$
$821$	2.35660e150	1.92138	0.960689	+	0.277627i	$0.0895481\pi$
$822$	−1.01449e150	−0.776871
$823$	−1.59227e150	−1.14532	−0.572659	−	0.819793i	$-0.694088\pi$
$823$	−1.59227e150	−1.14532	−0.572659	+	0.819793i	$0.694088\pi$
$824$	9.70035e149	0.655445
$825$	−1.79688e150	−1.14062
$826$	4.52244e150	2.69712
$827$	−3.02253e150	−1.69370	−0.846851	−	0.531831i	$-0.821504\pi$
$827$	−3.02253e150	−1.69370	−0.846851	+	0.531831i	$0.821504\pi$
$828$	1.01374e148	0.00533782
$829$	−1.41411e150	−0.699719	−0.349860	−	0.936802i	$-0.613771\pi$
$829$	−1.41411e150	−0.699719	−0.349860	+	0.936802i	$0.613771\pi$
$830$	4.79935e150	2.23183
$831$	1.71992e149	0.0751720
$832$	−3.15949e149	−0.129797
$833$	3.08306e150	1.19060
$834$	−4.31790e150	−1.56755
$835$	7.16048e150	2.44393
$836$	−1.72967e150	−0.555061
$837$	−2.51691e150	−0.759463
$838$	−4.11835e150	−1.16857
$839$	2.15421e150	0.574840	0.287420	−	0.957805i	$-0.407202\pi$
$839$	2.15421e150	0.574840	0.287420	+	0.957805i	$0.407202\pi$
$840$	−5.79007e150	−1.45312
$841$	−2.10610e150	−0.497146
$842$	4.25469e150	0.944703
$843$	7.35588e150	1.53644
$844$	2.11912e150	0.416408
$845$	−4.67077e150	−0.863511
$846$	7.08267e148	0.0123204
$847$	−1.33826e151	−2.19051
$848$	−9.10836e150	−1.40299
$849$	1.69889e150	0.246274
$850$	−4.41926e150	−0.602941
$851$	−3.39691e150	−0.436226
$852$	−4.64959e148	−0.00562051
$853$	9.16686e150	1.04315	0.521574	−	0.853206i	$-0.325345\pi$
$853$	9.16686e150	1.04315	0.521574	+	0.853206i	$0.325345\pi$
$854$	2.09855e151	2.24822
$855$	1.87811e149	0.0189437
$856$	9.59748e150	0.911504
$857$	−1.70515e150	−0.152493	−0.0762465	−	0.997089i	$-0.524294\pi$
$857$	−1.70515e150	−0.152493	−0.0762465	+	0.997089i	$0.524294\pi$
$858$	−1.29434e151	−1.09007
$859$	8.41943e150	0.667782	0.333891	−	0.942612i	$-0.391638\pi$
$859$	8.41943e150	0.667782	0.333891	+	0.942612i	$0.391638\pi$
$860$	1.36258e151	1.01787
$861$	2.94245e151	2.07037
$862$	−5.22451e150	−0.346275
$863$	4.44420e150	0.277484	0.138742	−	0.990329i	$-0.455694\pi$
$863$	4.44420e150	0.277484	0.138742	+	0.990329i	$0.455694\pi$
$864$	−1.43377e151	−0.843378
$865$	−2.42979e151	−1.34660
$866$	−9.52746e150	−0.497514
$867$	−1.12335e151	−0.552754
$868$	−1.25751e151	−0.583102
$869$	3.26418e151	1.42645
$870$	−2.76819e151	−1.14013
$871$	−9.93998e150	−0.385879
$872$	5.59965e149	0.0204910
$873$	2.48812e149	0.00858297
$874$	−1.92408e151	−0.625725
$875$	1.84298e151	0.565075
$876$	9.38575e150	0.271336
$877$	−5.66585e151	−1.54449	−0.772246	−	0.635323i	$-0.780867\pi$
$877$	−5.66585e151	−1.54449	−0.772246	+	0.635323i	$0.780867\pi$
$878$	−1.42869e150	−0.0367256
$879$	−1.41807e151	−0.343773
$880$	1.09679e152	2.50765
$881$	3.86876e151	0.834280	0.417140	−	0.908842i	$-0.363032\pi$
$881$	3.86876e151	0.834280	0.417140	+	0.908842i	$0.363032\pi$
$882$	−1.88927e150	−0.0384292
$883$	−7.05117e151	−1.35296	−0.676480	−	0.736461i	$-0.736496\pi$
$883$	−7.05117e151	−1.35296	−0.676480	+	0.736461i	$0.736496\pi$
$884$	−9.98513e150	−0.180743
$885$	1.04702e152	1.78805
$886$	2.17925e151	0.351132
$887$	−7.64125e151	−1.16171	−0.580855	−	0.814007i	$-0.697282\pi$
$887$	−7.64125e151	−1.16171	−0.580855	+	0.814007i	$0.697282\pi$
$888$	−3.09559e151	−0.444095
$889$	−2.16759e152	−2.93451
$890$	1.16480e152	1.48822
$891$	1.28432e152	1.54871
$892$	6.22962e150	0.0709041
$893$	−4.21664e151	−0.453019
$894$	−6.67408e151	−0.676877
$895$	8.20218e151	0.785313
$896$	2.05794e152	1.86025
$897$	−4.51628e151	−0.385452
$898$	1.72811e152	1.39264
$899$	7.14269e151	0.543548
$900$	8.49444e149	0.00610443
$901$	1.11366e152	0.755835
$902$	−3.53289e152	−2.26461
$903$	−4.67948e152	−2.83321
$904$	−7.05426e151	−0.403439
$905$	−2.36798e152	−1.27931
$906$	1.91169e152	0.975695
$907$	3.92186e152	1.89111	0.945554	−	0.325464i	$-0.105521\pi$
$907$	3.92186e152	1.89111	0.945554	+	0.325464i	$0.105521\pi$
$908$	−4.00142e151	−0.182303
$909$	6.78753e149	0.00292194
$910$	−3.83499e152	−1.56003
$911$	2.05812e151	0.0791177	0.0395589	−	0.999217i	$-0.487405\pi$
$911$	2.05812e151	0.0791177	0.0395589	+	0.999217i	$0.487405\pi$
$912$	−2.76632e152	−1.00501
$913$	6.20743e152	2.13141
$914$	−3.86669e152	−1.25490
$915$	4.85851e152	1.49045
$916$	−2.33995e151	−0.0678563
$917$	−7.00379e152	−1.92005
$918$	3.10286e152	0.804201
$919$	2.59673e152	0.636324	0.318162	−	0.948036i	$-0.396934\pi$
$919$	2.59673e152	0.636324	0.318162	+	0.948036i	$0.396934\pi$
$920$	2.42569e152	0.562033
$921$	8.34153e152	1.82757
$922$	−1.69085e152	−0.350317
$923$	3.65876e150	0.00716880
$924$	6.30338e152	1.16807
$925$	−2.84638e152	−0.498877
$926$	−3.44981e152	−0.571913
$927$	1.14666e151	0.0179816
$928$	4.06887e152	0.603606
$929$	−2.59624e152	−0.364364	−0.182182	−	0.983265i	$-0.558316\pi$
$929$	−2.59624e152	−0.364364	−0.182182	+	0.983265i	$0.558316\pi$
$930$	−9.28158e152	−1.23240
$931$	1.12477e153	1.41304
$932$	−7.68265e151	−0.0913254
$933$	−7.85670e152	−0.883763
$934$	−5.64351e152	−0.600739
$935$	−1.34103e153	−1.35095
$936$	−7.26951e150	−0.00693105
$937$	−1.02749e153	−0.927228	−0.463614	−	0.886037i	$-0.653448\pi$
$937$	−1.02749e153	−0.927228	−0.463614	+	0.886037i	$0.653448\pi$
$938$	1.54325e153	1.31823
$939$	−1.32616e153	−1.07231
$940$	−4.47445e152	−0.342496
$941$	7.21108e152	0.522558	0.261279	−	0.965263i	$-0.415856\pi$
$941$	7.21108e152	0.522558	0.261279	+	0.965263i	$0.415856\pi$
$942$	8.34091e152	0.572258
$943$	−1.23271e153	−0.800771
$944$	−2.72398e153	−1.67551
$945$	3.73805e153	2.17725
$946$	5.61846e153	3.09902
$947$	4.75065e151	0.0248158	0.0124079	−	0.999923i	$-0.496050\pi$
$947$	4.75065e151	0.0248158	0.0124079	+	0.999923i	$0.496050\pi$
$948$	−8.73625e152	−0.432211
$949$	−7.38565e152	−0.346082
$950$	−1.61224e153	−0.715592
$951$	1.83011e152	0.0769451
$952$	−1.84181e153	−0.733571
$953$	1.91062e153	0.720925	0.360462	−	0.932774i	$-0.382619\pi$
$953$	1.91062e153	0.720925	0.360462	+	0.932774i	$0.382619\pi$
$954$	−6.82442e151	−0.0243963
$955$	2.96457e153	1.00413
$956$	1.47031e152	0.0471874
$957$	−3.58035e153	−1.08883
$958$	3.30220e153	0.951654
$959$	−3.88769e153	−1.06178
$960$	1.13567e153	0.293957
$961$	−1.68129e153	−0.412465
$962$	−2.05033e153	−0.476769
$963$	1.13450e152	0.0250063
$964$	−2.94046e153	−0.614396
$965$	7.79649e153	1.54434
$966$	7.01184e153	1.31677
$967$	−8.30473e153	−1.47864	−0.739320	−	0.673355i	$-0.764853\pi$
$967$	−8.30473e153	−1.47864	−0.739320	+	0.673355i	$0.764853\pi$
$968$	5.10918e153	0.862523
$969$	3.38233e153	0.541430
$970$	−5.01119e153	−0.760670
$971$	2.58933e153	0.372732	0.186366	−	0.982480i	$-0.440329\pi$
$971$	2.58933e153	0.372732	0.186366	+	0.982480i	$0.440329\pi$
$972$	−1.20375e152	−0.0164332
$973$	−1.65469e154	−2.14243
$974$	−5.17036e153	−0.634943
$975$	−3.78433e153	−0.440810
$976$	−1.26401e154	−1.39664
$977$	−5.51224e153	−0.577774	−0.288887	−	0.957363i	$-0.593285\pi$
$977$	−5.51224e153	−0.577774	−0.288887	+	0.957363i	$0.593285\pi$
$978$	3.57421e153	0.355410
$979$	1.50655e154	1.42126
$980$	1.19354e154	1.06830
$981$	6.61923e150	0.000562152 0
$982$	2.45040e154	1.97467
$983$	−1.10834e153	−0.0847555	−0.0423778	−	0.999102i	$-0.513493\pi$
$983$	−1.10834e153	−0.0847555	−0.0423778	+	0.999102i	$0.513493\pi$
$984$	−1.12336e154	−0.815216
$985$	3.51404e153	0.242014
$986$	−8.80555e153	−0.575566
$987$	1.53665e154	0.953328
$988$	−3.64280e153	−0.214512
$989$	1.96042e154	1.09582
$990$	8.21770e152	0.0436052
$991$	2.95774e154	1.48993	0.744967	−	0.667101i	$-0.232465\pi$
$991$	2.95774e154	1.48993	0.744967	+	0.667101i	$0.232465\pi$
$992$	1.36427e154	0.652453
$993$	−4.03634e154	−1.83274
$994$	−5.68049e152	−0.0244899
$995$	3.76096e153	0.153961
$996$	−1.66136e154	−0.645813
$997$	−3.32744e154	−1.22832	−0.614158	−	0.789183i	$-0.710504\pi$
$997$	−3.32744e154	−1.22832	−0.614158	+	0.789183i	$0.710504\pi$
$998$	−1.98671e154	−0.696486
$999$	1.99851e154	0.665400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.104.a.a.1.2	✓	8
3.2	odd	2		9.104.a.a.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.104.a.a.1.2	✓	8	1.1	even	1	trivial
9.104.a.a.1.7		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)

\(f(q)\)	\(=\)	\(q-3.84396e15 q^{2} +3.76369e24 q^{3} +4.63479e30 q^{4} +1.31095e36 q^{5} -1.44675e40 q^{6} -5.54417e43 q^{7} +2.11664e46 q^{8} +2.50204e47 q^{9} +O(q^{10})\)	\(q-3.84396e15 q^{2} +3.76369e24 q^{3} +4.63479e30 q^{4} +1.31095e36 q^{5} -1.44675e40 q^{6} -5.54417e43 q^{7} +2.11664e46 q^{8} +2.50204e47 q^{9} -5.03922e51 q^{10} -6.51768e53 q^{11} +1.74439e55 q^{12} -1.37266e57 q^{13} +2.13116e59 q^{14} +4.93400e60 q^{15} -1.28365e62 q^{16} +1.56950e63 q^{17} -9.61772e62 q^{18} +5.72587e65 q^{19} +6.07596e66 q^{20} -2.08666e68 q^{21} +2.50537e69 q^{22} +8.74183e69 q^{23} +7.96640e70 q^{24} +7.32506e71 q^{25} +5.27645e72 q^{26} -5.14308e73 q^{27} -2.56961e74 q^{28} +1.45955e75 q^{29} -1.89661e76 q^{30} +4.89378e76 q^{31} +2.78777e77 q^{32} -2.45306e78 q^{33} -6.03308e78 q^{34} -7.26812e79 q^{35} +1.15964e78 q^{36} -3.88581e80 q^{37} -2.20100e81 q^{38} -5.16628e81 q^{39} +2.77481e82 q^{40} -1.41013e83 q^{41} +8.02102e83 q^{42} +2.24257e84 q^{43} -3.02080e84 q^{44} +3.28004e83 q^{45} -3.36032e85 q^{46} -7.36419e85 q^{47} -4.83127e86 q^{48} +1.96436e87 q^{49} -2.81572e87 q^{50} +5.90711e87 q^{51} -6.36200e87 q^{52} +7.09567e88 q^{53} +1.97698e89 q^{54} -8.54433e89 q^{55} -1.17350e90 q^{56} +2.15504e90 q^{57} -5.61043e90 q^{58} +2.12206e91 q^{59} +2.28680e91 q^{60} +9.84700e91 q^{61} -1.88115e92 q^{62} -1.38717e91 q^{63} +2.30172e92 q^{64} -1.79949e93 q^{65} +9.42944e93 q^{66} +7.24139e93 q^{67} +7.27428e93 q^{68} +3.29016e94 q^{69} +2.79383e95 q^{70} -2.66545e93 q^{71} +5.29592e93 q^{72} +5.38053e95 q^{73} +1.49369e96 q^{74} +2.75693e96 q^{75} +2.65382e96 q^{76} +3.61351e97 q^{77} +1.98590e97 q^{78} -5.00820e97 q^{79} -1.68280e98 q^{80} -1.97052e98 q^{81} +5.42047e98 q^{82} -9.52399e98 q^{83} -9.67121e98 q^{84} +2.05753e99 q^{85} -8.62034e99 q^{86} +5.49328e99 q^{87} -1.37956e100 q^{88} -2.31148e100 q^{89} -1.26083e99 q^{90} +7.61028e100 q^{91} +4.05165e100 q^{92} +1.84187e101 q^{93} +2.83076e101 q^{94} +7.50631e101 q^{95} +1.04923e102 q^{96} +9.94437e101 q^{97} -7.55091e102 q^{98} -1.63075e101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 43\!\cdots\!40 q^{2}+ \cdots + 35\!\cdots\!16 q^{9}+O(q^{10}) \) 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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