LMFDB - Embedded newform 1.104.a.a.1.7

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			1.7
Root			$-2.04878e14$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.46569e15 q^{2} -5.92176e24 q^{3} +1.97326e31 q^{4} +6.19706e35 q^{5} -3.23665e40 q^{6} +6.38506e43 q^{7} +5.24235e46 q^{8} +2.11521e49 q^{9} +O(q^{10})$	\(q+5.46569e15 q^{2} -5.92176e24 q^{3} +1.97326e31 q^{4} +6.19706e35 q^{5} -3.23665e40 q^{6} +6.38506e43 q^{7} +5.24235e46 q^{8} +2.11521e49 q^{9} +3.38712e51 q^{10} -3.56369e53 q^{11} -1.16852e56 q^{12} -1.22872e57 q^{13} +3.48988e59 q^{14} -3.66975e60 q^{15} +8.64183e61 q^{16} +1.95760e63 q^{17} +1.15611e65 q^{18} -1.27427e65 q^{19} +1.22284e67 q^{20} -3.78108e68 q^{21} -1.94780e69 q^{22} +1.72828e70 q^{23} -3.10439e71 q^{24} -6.02041e71 q^{25} -6.71578e72 q^{26} -4.28550e73 q^{27} +1.25994e75 q^{28} +5.38742e74 q^{29} -2.00577e76 q^{30} +4.50113e76 q^{31} -5.93010e76 q^{32} +2.11033e78 q^{33} +1.06996e79 q^{34} +3.95686e79 q^{35} +4.17385e80 q^{36} +2.11547e80 q^{37} -6.96479e80 q^{38} +7.27616e81 q^{39} +3.24871e82 q^{40} +1.19842e83 q^{41} -2.06662e84 q^{42} +1.22330e84 q^{43} -7.03208e84 q^{44} +1.31081e85 q^{45} +9.44625e85 q^{46} +1.73935e85 q^{47} -5.11749e86 q^{48} +2.96748e87 q^{49} -3.29057e87 q^{50} -1.15924e88 q^{51} -2.42457e88 q^{52} +8.89924e88 q^{53} -2.34232e89 q^{54} -2.20844e89 q^{55} +3.34727e90 q^{56} +7.54594e89 q^{57} +2.94460e90 q^{58} -2.03072e91 q^{59} -7.24136e91 q^{60} -2.35768e91 q^{61} +2.46018e92 q^{62} +1.35057e93 q^{63} -1.20051e93 q^{64} -7.61442e92 q^{65} +1.15344e94 q^{66} -5.83119e93 q^{67} +3.86284e94 q^{68} -1.02345e95 q^{69} +2.16270e95 q^{70} -1.13221e94 q^{71} +1.10886e96 q^{72} +1.69770e96 q^{73} +1.15625e96 q^{74} +3.56514e96 q^{75} -2.51447e96 q^{76} -2.27544e97 q^{77} +3.97692e97 q^{78} +4.56875e96 q^{79} +5.35540e97 q^{80} -4.05580e97 q^{81} +6.55017e98 q^{82} -4.40271e98 q^{83} -7.46105e99 q^{84} +1.21313e99 q^{85} +6.68618e99 q^{86} -3.19030e99 q^{87} -1.86821e100 q^{88} -4.93939e99 q^{89} +7.16446e100 q^{90} -7.84542e100 q^{91} +3.41034e101 q^{92} -2.66546e101 q^{93} +9.50676e100 q^{94} -7.89675e100 q^{95} +3.51167e101 q^{96} -2.79258e101 q^{97} +1.62193e103 q^{98} -7.53794e102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 43\!\cdots\!40 q^{2}+ \cdots + 35\!\cdots\!16 q^{9}+O(q^{10}) $ 8 * q + 4388929556680440 * q^2 + 5087569706910766050323040 * q^3 + 48324394003700265820897106483264 * q^4 + 551645266991094947988587979858507120 * q^5 + 2626953258123361256046267420263544594336 * q^6 + 41737594138377573148159523392718424208446400 * q^7 + 109882609245772353721829965115065527112449646080 * q^8 + 35934061358184471683999399496530848001601644543016 * q^9	$ 8 q + 43\!\cdots\!40 q^{2}+ \cdots - 72\!\cdots\!88 q^{99}+O(q^{100}) $ 8 * q + 4388929556680440 * q^2 + 5087569706910766050323040 * q^3 + 48324394003700265820897106483264 * q^4 + 551645266991094947988587979858507120 * q^5 + 2626953258123361256046267420263544594336 * q^6 + 41737594138377573148159523392718424208446400 * q^7 + 109882609245772353721829965115065527112449646080 * q^8 + 35934061358184471683999399496530848001601644543016 * q^9 + 2027618525260516073181410940373995286751686815077520 * q^10 - 53564255892798621618914292149029865323976089024126944 * q^11 + 25633960574085217446823189913789134273379599963259585280 * q^12 - 1551327849817932010092927923451244764349197489311375245520 * q^13 + 204985531745225680495392627955462650660602632112553429561408 * q^14 - 3020750766469193774466110593818157380300334453782433876013760 * q^15 + 361863449936885119768267973598726020537150452888847981908594688 * q^16 + 2015497649979997361336875976150254045164880842011155416684792720 * q^17 + 267307540106838323861864757930082029915233950378733807409255489240 * q^18 + 1484734834072313889071781871918609444991921518407889999862194156000 * q^19 + 2550001838610112272657033084622870492091806723524425439331785816960 * q^20 - 468651934282513875675935203933822637725944475261560345505782668354304 * q^21 - 137605849219876342207658729678467678698030207344807412231509580517920 * q^22 + 40599619287653938731347770176481184954623812150658724038701540865523520 * q^23 + 417632054269801118353552142462197805319757108882280256182409075047884800 * q^24 - 362937074225983688614876200177837163768974389374609498487470358942710600 * q^25 - 14030741852054819908281579342280387163553452467847954283089945570102881584 * q^26 + 6310451948770981419229340353143176080605163694982014782921106225679184320 * q^27 + 514148330168929069137279753066565726408108706760021137474482330032788078080 * q^28 - 1109314641409183093552976605346965837461990086922169583222454360155329880400 * q^29 - 31780974033428375753830150804412858338763487684738816318474129735272931696960 * q^30 + 104264780455232531257795764608297281101784409237357406959070797687652099233536 * q^31 + 1028908566996694821915427200010950055520054418022728660586770754660435042467840 * q^32 + 1637064370206527961191840416792241672318252830384788267847230786245723880401280 * q^33 - 16880249585595311287790910689090067879202031794055262067512201336945927884230032 * q^34 - 15809814583992711056872904141791269441389432991285782813731594074561867170321280 * q^35 + 805787623574605247165419461734624389987695467909486995221520106404473098849425728 * q^36 - 92541276402281504667713648425023541514489587998355774759921151431265396409265040 * q^37 + 1971300306790799032342240078744393153702898113403645290763243656535920191023423520 * q^38 - 7885389189078955664633112105466856010714545616525346076007201630144160874672246208 * q^39 + 1977015288844745924714331362379506784318231603612597717318543376316436008269440000 * q^40 + 222749082810191111691395557742339640725571297200098840306597511963716166910016506576 * q^41 - 1883267638769361387897797057480679095562739407538640601371566884432999969422842010880 * q^42 + 968895197607192930930940008787782675398644318852140770090896736295885033488529690400 * q^43 + 2615800371528018307641663183711908967442008589707371423475870586505299691562914926848 * q^44 - 1473010112873063959626609346390652156643077000013339776241472977560123315435112983760 * q^45 + 27446065195956198075877779014773406391109527885085904763819008268953431741208364616896 * q^46 - 293609653174290525998217973440321639247924396408373610899942779596119844480753010677120 * q^47 + 1240474483651634936656271628196732975278107731060035918088958893365811804822813860741120 * q^48 + 2668551616424529602044449137134709537764999196283756605526691963266904852724306068111944 * q^49 - 6521555021853481798089331632691717210870069276041958186139599024744619050092391455132600 * q^50 - 20813334460690950021193410586099062172982223916797529091846346968717683910092635969470784 * q^51 - 36075131888471074369144062637736452287512569193963836276062247375366142706627591324022400 * q^52 + 161574805302535676592212552212935130219348465152378468526413124882553154054403888166112240 * q^53 + 244996591061285005233721911255171344371445084231598513861031145908120404974069967807566400 * q^54 - 607939909864004614075356036982415128356301156312798815333086681706442442074797191568452160 * q^55 - 503347948801547505295544537202800039798463622449253526436143518261972796907682627548672000 * q^56 + 5585281202236608576148075500959180617113370740733374350303663601038337658261844358331674240 * q^57 + 10803107862759337782251611301310445432173113486135052277293695910012872510635542918433350480 * q^58 - 3763669177454952719015429893224775020266577352512033436736083012099637155611183545807925600 * q^59 - 44516663894047516283340986041100025029890327265561963837781098524475428602375001706220910080 * q^60 + 56147145392217940296237629782250660517556168142847888898434987753570576599200638389784423856 * q^61 + 708807506014393204305112275358657132745269481108345030482782405369277364762268787441349556480 * q^62 + 1004547917742295582189356352643083605257294414907733584799000902948644764606451215157969453760 * q^63 + 2689955130199770090919426143081142657167991663226807770013236363849718691785612797260291375104 * q^64 + 5124254892052438764657504605348539922002660919805937289990918847816257298286298313919564321440 * q^65 + 36460770617845857205288107920138564493995889702559578221696109246179691643034860902124792436352 * q^66 + 36212058392130762275437269862682052845105568281986303679248701513796303582516933489238204852320 * q^67 + 121871257184262948410168536656451503789769474779037040449473211419440774288140532505483576282240 * q^68 + 146171714897241059447510875608282423246804848799861315408644138710655320106224092813159842449152 * q^69 + 853756690279911250368037438486434151435346605497824981233696852732671552949658306872737406389120 * q^70 + 1323027110921369091114059758958942708535901440060160919331826835683096477433051757156908929999296 * q^71 + 5635474260733453081095589332277842775365114507654390044914919885310203213431471309882290635036160 * q^72 + 4434337224305117877569754735641925591340191550850949206294860286939824237219014387268913705824720 * q^73 + 9446978778046296456470116730008064896416484139132353834625710442657435714245141545863045630195088 * q^74 + 15788198796594475882673542236654839411090926672421130688549340631916075230881024844909417441328800 * q^75 + 62208878575567502646775884731743768059494074065603793769837837917746101674437608641395557819334400 * q^76 + 37781769005935846521801726968449743374817416956894448777845288067504206491843901930831867790380800 * q^77 + 44019466816742377243458217012569984532155201470078975456308994008831948835905199650013699349604800 * q^78 + 24360542002769992615028834274408332054107188048024574794369918904382062971902552671267968844374400 * q^79 - 257406550547438596244863901420403525688280266364441018588431059738298545930906704910071981299015680 * q^80 - 319858452590968976040706219061802261896767071034600475754637194160339936835204759950912194010523832 * q^81 - 347037715568344180193612732627815416282275947315627995720995526007231252178377268346955612809946320 * q^82 - 2589709199921534719789158381824365674651513931126861560377010891589296789100538920269990341311172640 * q^83 - 14763276600099218032093350675578467421653757870459793949112274722608304409453274353718894336536287232 * q^84 - 7750041700239420480976421024168094692666091522883832659906501732615678081854865932331016250083918880 * q^85 - 22862474248159310408090160685058395474537452344937345785285404938278205476818797847965682857887379744 * q^86 - 19667171614563900919678037177279936924594588506587176946944336641584005321373812755132416018759906240 * q^87 - 40280517105348128384004030315972727789809528309384337508840799111515821927415232196104998546661181440 * q^88 - 2411931583959929374872883405418443793306523554844108736778614462710442635343758894445178420208577200 * q^89 + 19218417888800936875567136220118837811145582599884634713838228828686741391845969008376636752235577040 * q^90 + 157061027064080129827172588737919758324770125960416982485587688356910129161874310994817267624768962176 * q^91 + 773615141308510753640652909662430286328720511338068191045295874258285130068299519150171249463376222720 * q^92 + 1017145077013570534640298063884056653140131362969292242328097944460668594729564068877620396903861703680 * q^93 + 727087863890952033548300791290895488242032063484702253117314469808013304697569232190083038540113931648 * q^94 + 2743732154506646909406097298325321408379587730896118185195801036752841998424162414172669753574660712000 * q^95 + 8873312662336745259606299368794125872185792644230053366160730387846004935345208576954549405340151709696 * q^96 + 5002945503247003905009597326381275147828980571278924405638622881444475469921369111184405290832776414480 * q^97 + 8807510378044686174684586237206775917067603624837914322579837506936931417303594998092206302439262913720 * q^98 - 7247372384990122262319746951941725843983906615680409319965154257589720777414294443683699540960522497888 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	5.46569e15	1.71633	0.858164	−	0.513376i	$-0.171605\pi$
$2$	5.46569e15	1.71633	0.858164	+	0.513376i	$0.171605\pi$
$3$	−5.92176e24	−1.58747	−0.793736	−	0.608262i	$-0.791867\pi$
$3$	−5.92176e24	−1.58747	−0.793736	+	0.608262i	$0.791867\pi$
$4$	1.97326e31	1.94578
$5$	6.19706e35	0.624066	0.312033	−	0.950071i	$-0.398990\pi$
$5$	6.19706e35	0.624066	0.312033	+	0.950071i	$0.398990\pi$
$6$	−3.23665e40	−2.72462
$7$	6.38506e43	1.91697	0.958487	−	0.285137i	$-0.0920392\pi$
$7$	6.38506e43	1.91697	0.958487	+	0.285137i	$0.0920392\pi$
$8$	5.24235e46	1.62327
$9$	2.11521e49	1.52007
$10$	3.38712e51	1.07110
$11$	−3.56369e53	−0.832103	−0.416051	−	0.909341i	$-0.636586\pi$
$11$	−3.56369e53	−0.832103	−0.416051	+	0.909341i	$0.636586\pi$
$12$	−1.16852e56	−3.08888
$13$	−1.22872e57	−0.526464	−0.263232	−	0.964733i	$-0.584788\pi$
$13$	−1.22872e57	−0.526464	−0.263232	+	0.964733i	$0.584788\pi$
$14$	3.48988e59	3.29016
$15$	−3.66975e60	−0.990688
$16$	8.64183e61	0.840285
$17$	1.95760e63	0.838694	0.419347	−	0.907826i	$-0.362259\pi$
$17$	1.95760e63	0.838694	0.419347	+	0.907826i	$0.362259\pi$
$18$	1.15611e65	2.60894
$19$	−1.27427e65	−0.177604	−0.0888019	−	0.996049i	$-0.528304\pi$
$19$	−1.27427e65	−0.177604	−0.0888019	+	0.996049i	$0.528304\pi$
$20$	1.22284e67	1.21430
$21$	−3.78108e68	−3.04314
$22$	−1.94780e69	−1.42816
$23$	1.72828e70	1.28419	0.642097	−	0.766623i	$-0.278065\pi$
$23$	1.72828e70	1.28419	0.642097	+	0.766623i	$0.278065\pi$
$24$	−3.10439e71	−2.57690
$25$	−6.02041e71	−0.610542
$26$	−6.71578e72	−0.903585
$27$	−4.28550e73	−0.825596
$28$	1.25994e75	3.73001
$29$	5.38742e74	0.261748	0.130874	−	0.991399i	$-0.458222\pi$
$29$	5.38742e74	0.261748	0.130874	+	0.991399i	$0.458222\pi$
$30$	−2.00577e76	−1.70035
$31$	4.50113e76	0.705009	0.352505	−	0.935810i	$-0.385330\pi$
$31$	4.50113e76	0.705009	0.352505	+	0.935810i	$0.385330\pi$
$32$	−5.93010e76	−0.181067
$33$	2.11033e78	1.32094
$34$	1.06996e79	1.43947
$35$	3.95686e79	1.19632
$36$	4.17385e80	2.95772
$37$	2.11547e80	0.365611	0.182805	−	0.983149i	$-0.441482\pi$
$37$	2.11547e80	0.365611	0.182805	+	0.983149i	$0.441482\pi$
$38$	−6.96479e80	−0.304826
$39$	7.27616e81	0.835747
$40$	3.24871e82	1.01303
$41$	1.19842e83	1.04770	0.523852	−	0.851809i	$-0.324494\pi$
$41$	1.19842e83	1.04770	0.523852	+	0.851809i	$0.324494\pi$
$42$	−2.06662e84	−5.22303
$43$	1.22330e84	0.920254	0.460127	−	0.887853i	$-0.347804\pi$
$43$	1.22330e84	0.920254	0.460127	+	0.887853i	$0.347804\pi$
$44$	−7.03208e84	−1.61909
$45$	1.31081e85	0.948624
$46$	9.44625e85	2.20410
$47$	1.73935e85	0.134075	0.0670375	−	0.997750i	$-0.478645\pi$
$47$	1.73935e85	0.134075	0.0670375	+	0.997750i	$0.478645\pi$
$48$	−5.11749e86	−1.33393
$49$	2.96748e87	2.67479
$50$	−3.29057e87	−1.04789
$51$	−1.15924e88	−1.33140
$52$	−2.42457e88	−1.02438
$53$	8.89924e88	1.40976	0.704881	−	0.709326i	$-0.251000\pi$
$53$	8.89924e88	1.40976	0.704881	+	0.709326i	$0.251000\pi$
$54$	−2.34232e89	−1.41699
$55$	−2.20844e89	−0.519287
$56$	3.34727e90	3.11177
$57$	7.54594e89	0.281941
$58$	2.94460e90	0.449246
$59$	−2.03072e91	−1.28461	−0.642305	−	0.766449i	$-0.722022\pi$
$59$	−2.03072e91	−1.28461	−0.642305	+	0.766449i	$0.722022\pi$
$60$	−7.24136e91	−1.92766
$61$	−2.35768e91	−0.267916	−0.133958	−	0.990987i	$-0.542769\pi$
$61$	−2.35768e91	−0.267916	−0.133958	+	0.990987i	$0.542769\pi$
$62$	2.46018e92	1.21003
$63$	1.35057e93	2.91393
$64$	−1.20051e93	−1.15106
$65$	−7.61442e92	−0.328548
$66$	1.15344e94	2.26717
$67$	−5.83119e93	−0.528330	−0.264165	−	0.964478i	$-0.585096\pi$
$67$	−5.83119e93	−0.528330	−0.264165	+	0.964478i	$0.585096\pi$
$68$	3.86284e94	1.63192
$69$	−1.02345e95	−2.03862
$70$	2.16270e95	2.05327
$71$	−1.13221e94	−0.0517754	−0.0258877	−	0.999665i	$-0.508241\pi$
$71$	−1.13221e94	−0.0517754	−0.0258877	+	0.999665i	$0.508241\pi$
$72$	1.10886e96	2.46749
$73$	1.69770e96	1.85667	0.928334	−	0.371748i	$-0.121241\pi$
$73$	1.69770e96	1.85667	0.928334	+	0.371748i	$0.121241\pi$
$74$	1.15625e96	0.627508
$75$	3.56514e96	0.969218
$76$	−2.51447e96	−0.345578
$77$	−2.27544e97	−1.59512
$78$	3.97692e97	1.43442
$79$	4.56875e96	0.0855071	0.0427536	−	0.999086i	$-0.486387\pi$
$79$	4.56875e96	0.0855071	0.0427536	+	0.999086i	$0.486387\pi$
$80$	5.35540e97	0.524394
$81$	−4.05580e97	−0.209459
$82$	6.55017e98	1.79820
$83$	−4.40271e98	−0.647438	−0.323719	−	0.946153i	$-0.604933\pi$
$83$	−4.40271e98	−0.647438	−0.323719	+	0.946153i	$0.604933\pi$
$84$	−7.46105e99	−5.92129
$85$	1.21313e99	0.523401
$86$	6.68618e99	1.57946
$87$	−3.19030e99	−0.415518
$88$	−1.86821e100	−1.35073
$89$	−4.93939e99	−0.199567	−0.0997834	−	0.995009i	$-0.531815\pi$
$89$	−4.93939e99	−0.199567	−0.0997834	+	0.995009i	$0.531815\pi$
$90$	7.16446e100	1.62815
$91$	−7.84542e100	−1.00922
$92$	3.41034e101	2.49876
$93$	−2.66546e101	−1.11918
$94$	9.50676e100	0.230117
$95$	−7.89675e100	−0.110837
$96$	3.51167e101	0.287438
$97$	−2.79258e101	−0.134048	−0.0670240	−	0.997751i	$-0.521350\pi$
$97$	−2.79258e101	−0.134048	−0.0670240	+	0.997751i	$0.521350\pi$
$98$	1.62193e103	4.59081
$99$	−7.53794e102	−1.26485
$100$	−1.18798e103	−1.18798
$101$	−1.93439e103	−1.15876	−0.579380	−	0.815058i	$-0.696705\pi$
$101$	−1.93439e103	−1.15876	−0.579380	+	0.815058i	$0.696705\pi$
$102$	−6.33606e103	−2.28513
$103$	5.36250e103	1.17017	0.585087	−	0.810971i	$-0.301061\pi$
$103$	5.36250e103	1.17017	0.585087	+	0.810971i	$0.301061\pi$
$104$	−6.44135e103	−0.854594
$105$	−2.34316e104	−1.89912
$106$	4.86405e104	2.41961
$107$	3.95193e104	1.21212	0.606058	−	0.795420i	$-0.292750\pi$
$107$	3.95193e104	1.21212	0.606058	+	0.795420i	$0.292750\pi$
$108$	−8.45639e104	−1.60643
$109$	8.53955e104	1.00918	0.504592	−	0.863358i	$-0.331643\pi$
$109$	8.53955e104	1.00918	0.504592	+	0.863358i	$0.331643\pi$
$110$	−1.20707e105	−0.891267
$111$	−1.25273e105	−0.580397
$112$	5.51787e105	1.61080
$113$	3.04693e105	0.562759	0.281379	−	0.959597i	$-0.409208\pi$
$113$	3.04693e105	0.562759	0.281379	+	0.959597i	$0.409208\pi$
$114$	4.12438e105	0.483904
$115$	1.07103e106	0.801422
$116$	1.06308e106	0.509305
$117$	−2.59899e106	−0.800262
$118$	−1.10993e107	−2.20481
$119$	1.24994e107	1.60775
$120$	−1.92381e107	−1.60816
$121$	−5.64209e106	−0.307605
$122$	−1.28864e107	−0.459832
$123$	−7.09673e107	−1.66320
$124$	8.88190e107	1.37179
$125$	−9.84166e107	−1.00508
$126$	7.38181e108	5.00126
$127$	1.65440e107	0.0746020	0.0373010	−	0.999304i	$-0.488124\pi$
$127$	1.65440e107	0.0746020	0.0373010	+	0.999304i	$0.488124\pi$
$128$	−5.96022e108	−1.79452
$129$	−7.24409e108	−1.46088
$130$	−4.16181e108	−0.563897
$131$	1.13774e109	1.03889	0.519446	−	0.854503i	$-0.326138\pi$
$131$	1.13774e109	1.03889	0.519446	+	0.854503i	$0.326138\pi$
$132$	4.16423e109	2.57026
$133$	−8.13632e108	−0.340462
$134$	−3.18715e109	−0.906787
$135$	−2.65575e109	−0.515226
$136$	1.02624e110	1.36143
$137$	−1.51469e110	−1.37789	−0.688943	−	0.724815i	$-0.741925\pi$
$137$	−1.51469e110	−1.37789	−0.688943	+	0.724815i	$0.741925\pi$
$138$	−5.59384e110	−3.49895
$139$	−2.07034e109	−0.0892853	−0.0446427	−	0.999003i	$-0.514215\pi$
$139$	−2.07034e109	−0.0892853	−0.0446427	+	0.999003i	$0.514215\pi$
$140$	7.80791e110	2.32777
$141$	−1.03000e110	−0.212840
$142$	−6.18833e109	−0.0888635
$143$	4.37876e110	0.438072
$144$	1.82793e111	1.27729
$145$	3.33862e110	0.163348
$146$	9.27911e111	3.18665
$147$	−1.75727e112	−4.24615
$148$	4.17437e111	0.711399
$149$	−5.24925e111	−0.632419	−0.316209	−	0.948689i	$-0.602410\pi$
$149$	−5.24925e111	−0.632419	−0.316209	+	0.948689i	$0.602410\pi$
$150$	1.94860e112	1.66350
$151$	−2.47519e112	−1.50071	−0.750355	−	0.661036i	$-0.770117\pi$
$151$	−2.47519e112	−1.50071	−0.750355	+	0.661036i	$0.770117\pi$
$152$	−6.68018e111	−0.288299
$153$	4.14072e112	1.27487
$154$	−1.24368e113	−2.73775
$155$	2.78938e112	0.439972
$156$	1.43577e113	1.62618
$157$	−4.05697e112	−0.330651	−0.165325	−	0.986239i	$-0.552867\pi$
$157$	−4.05697e112	−0.330651	−0.165325	+	0.986239i	$0.552867\pi$
$158$	2.49714e112	0.146758
$159$	−5.26992e113	−2.23796
$160$	−3.67492e112	−0.112998
$161$	1.10352e114	2.46177
$162$	−2.21678e113	−0.359500
$163$	4.69441e113	0.554523	0.277262	−	0.960794i	$-0.410573\pi$
$163$	4.69441e113	0.554523	0.277262	+	0.960794i	$0.410573\pi$
$164$	2.36478e114	2.03860
$165$	1.30779e114	0.824354
$166$	−2.40639e114	−1.11122
$167$	2.39699e114	0.812395	0.406198	−	0.913785i	$-0.366854\pi$
$167$	2.39699e114	0.812395	0.406198	+	0.913785i	$0.366854\pi$
$168$	−1.98217e115	−4.93985
$169$	−3.93736e114	−0.722836
$170$	6.63062e114	0.898327
$171$	−2.69535e114	−0.269970
$172$	2.41389e115	1.79061
$173$	2.38070e115	1.31018	0.655089	−	0.755552i	$-0.272631\pi$
$173$	2.38070e115	1.31018	0.655089	+	0.755552i	$0.272631\pi$
$174$	−1.74372e115	−0.713165
$175$	−3.84407e115	−1.17039
$176$	−3.07968e115	−0.699204
$177$	1.20254e116	2.03928
$178$	−2.69972e115	−0.342522
$179$	−2.35520e115	−0.223922	−0.111961	−	0.993713i	$-0.535713\pi$
$179$	−2.35520e115	−0.223922	−0.111961	+	0.993713i	$0.535713\pi$
$180$	2.58656e116	1.84581
$181$	−1.24792e116	−0.669485	−0.334743	−	0.942310i	$-0.608649\pi$
$181$	−1.24792e116	−0.669485	−0.334743	+	0.942310i	$0.608649\pi$
$182$	−4.28807e116	−1.73215
$183$	1.39616e116	0.425309
$184$	9.06024e116	2.08460
$185$	1.31097e116	0.228165
$186$	−1.45686e117	−1.92088
$187$	−6.97627e116	−0.697880
$188$	3.43219e116	0.260881
$189$	−2.73632e117	−1.58265
$190$	−4.31612e116	−0.190232
$191$	8.62903e116	0.290231	0.145115	−	0.989415i	$-0.453645\pi$
$191$	8.62903e116	0.290231	0.145115	+	0.989415i	$0.453645\pi$
$192$	7.10912e117	1.82727
$193$	−6.94577e117	−1.36622	−0.683108	−	0.730318i	$-0.739372\pi$
$193$	−6.94577e117	−1.36622	−0.683108	+	0.730318i	$0.739372\pi$
$194$	−1.52634e117	−0.230070
$195$	4.50908e117	0.521561
$196$	5.85560e118	5.20455
$197$	−2.26547e118	−1.54935	−0.774673	−	0.632362i	$-0.782085\pi$
$197$	−2.26547e118	−1.54935	−0.774673	+	0.632362i	$0.782085\pi$
$198$	−4.12001e118	−2.17090
$199$	2.10252e118	0.854688	0.427344	−	0.904089i	$-0.359449\pi$
$199$	2.10252e118	0.854688	0.427344	+	0.904089i	$0.359449\pi$
$200$	−3.15610e118	−0.991075
$201$	3.45309e118	0.838709
$202$	−1.05728e119	−1.98881
$203$	3.43990e118	0.501764
$204$	−2.28748e119	−2.59062
$205$	7.42665e118	0.653837
$206$	2.93098e119	2.00840
$207$	3.65567e119	1.95206
$208$	−1.06184e119	−0.442380
$209$	4.54112e118	0.147785
$210$	−1.28070e120	−3.25952
$211$	−9.06808e119	−1.80704	−0.903522	−	0.428541i	$-0.859028\pi$
$211$	−9.06808e119	−1.80704	−0.903522	+	0.428541i	$0.859028\pi$
$212$	1.75605e120	2.74309
$213$	6.70469e118	0.0821920
$214$	2.16000e120	2.08039
$215$	7.58087e119	0.574299
$216$	−2.24661e120	−1.34017
$217$	2.87400e120	1.35148
$218$	4.66745e120	1.73209
$219$	−1.00534e121	−2.94741
$220$	−4.35782e120	−1.01042
$221$	−2.40533e120	−0.441542
$222$	−6.84705e120	−0.996151
$223$	1.09411e121	1.26288	0.631438	−	0.775427i	$-0.282465\pi$
$223$	1.09411e121	1.26288	0.631438	+	0.775427i	$0.282465\pi$
$224$	−3.78641e120	−0.347100
$225$	−1.27344e121	−0.928066
$226$	1.66536e121	0.965879
$227$	−3.83836e120	−0.177343	−0.0886714	−	0.996061i	$-0.528262\pi$
$227$	−3.83836e120	−0.177343	−0.0886714	+	0.996061i	$0.528262\pi$
$228$	1.48901e121	0.548596
$229$	−3.29523e121	−0.969077	−0.484538	−	0.874770i	$-0.661012\pi$
$229$	−3.29523e121	−0.969077	−0.484538	+	0.874770i	$0.661012\pi$
$230$	5.85390e121	1.37550
$231$	1.34746e122	2.53221
$232$	2.82427e121	0.424889
$233$	−7.31322e121	−0.881614	−0.440807	−	0.897602i	$-0.645308\pi$
$233$	−7.31322e121	−0.881614	−0.440807	+	0.897602i	$0.645308\pi$
$234$	−1.42053e122	−1.37351
$235$	1.07789e121	0.0836717
$236$	−4.00713e122	−2.49957
$237$	−2.70550e121	−0.135740
$238$	6.83177e122	2.75943
$239$	6.15769e121	0.200413	0.100207	−	0.994967i	$-0.468050\pi$
$239$	6.15769e121	0.200413	0.100207	+	0.994967i	$0.468050\pi$
$240$	−3.17134e122	−0.832460
$241$	−4.32197e122	−0.915807	−0.457904	−	0.889002i	$-0.651399\pi$
$241$	−4.32197e122	−0.915807	−0.457904	+	0.889002i	$0.651399\pi$
$242$	−3.08379e122	−0.527952
$243$	8.36510e122	1.15811
$244$	−4.65231e122	−0.521306
$245$	1.83896e123	1.66924
$246$	−3.87885e123	−2.85460
$247$	1.56572e122	0.0935020
$248$	2.35965e123	1.14442
$249$	2.60718e123	1.02779
$250$	−5.37914e123	−1.72505
$251$	−1.94705e123	−0.508372	−0.254186	−	0.967155i	$-0.581808\pi$
$251$	−1.94705e123	−0.508372	−0.254186	+	0.967155i	$0.581808\pi$
$252$	2.66503e124	5.66988
$253$	−6.15906e123	−1.06858
$254$	9.04247e122	0.128041
$255$	−7.18389e123	−0.830884
$256$	−2.04021e124	−1.92893
$257$	−3.00208e123	−0.232202	−0.116101	−	0.993237i	$-0.537040\pi$
$257$	−3.00208e123	−0.232202	−0.116101	+	0.993237i	$0.537040\pi$
$258$	−3.95940e124	−2.50735
$259$	1.35074e124	0.700866
$260$	−1.50252e124	−0.639283
$261$	1.13955e124	0.397875
$262$	6.21853e124	1.78308
$263$	−5.66843e124	−1.33580	−0.667901	−	0.744250i	$-0.732807\pi$
$263$	−5.66843e124	−1.33580	−0.667901	+	0.744250i	$0.732807\pi$
$264$	1.10631e125	2.14425
$265$	5.51491e124	0.879784
$266$	−4.44706e124	−0.584344
$267$	2.92499e124	0.316807
$268$	−1.15064e125	−1.02801
$269$	−3.93115e124	−0.289919	−0.144960	−	0.989438i	$-0.546305\pi$
$269$	−3.93115e124	−0.289919	−0.144960	+	0.989438i	$0.546305\pi$
$270$	−1.45155e125	−0.884297
$271$	3.30250e125	1.66312	0.831561	−	0.555433i	$-0.187447\pi$
$271$	3.30250e125	1.66312	0.831561	+	0.555433i	$0.187447\pi$
$272$	1.69172e125	0.704743
$273$	4.64587e125	1.60210
$274$	−8.27881e125	−2.36491
$275$	2.14549e125	0.508033
$276$	−2.01952e126	−3.96672
$277$	1.15206e126	1.87830	0.939150	−	0.343506i	$-0.111615\pi$
$277$	1.15206e126	1.87830	0.939150	+	0.343506i	$0.111615\pi$
$278$	−1.13159e125	−0.153243
$279$	9.52083e125	1.07166
$280$	2.07432e126	1.94195
$281$	−2.15165e126	−1.67647	−0.838234	−	0.545310i	$-0.816412\pi$
$281$	−2.15165e126	−1.67647	−0.838234	+	0.545310i	$0.816412\pi$
$282$	−5.62968e125	−0.365304
$283$	−2.99134e126	−1.61757	−0.808787	−	0.588102i	$-0.799875\pi$
$283$	−2.99134e126	−1.61757	−0.808787	+	0.588102i	$0.799875\pi$
$284$	−2.23415e125	−0.100744
$285$	4.67627e125	0.175950
$286$	2.39330e126	0.751875
$287$	7.65196e126	2.00842
$288$	−1.25434e126	−0.275234
$289$	−1.61584e126	−0.296592
$290$	1.82478e126	0.280359
$291$	1.65370e126	0.212798
$292$	3.35000e127	3.61267
$293$	1.40475e127	1.27033	0.635164	−	0.772377i	$-0.280932\pi$
$293$	1.40475e127	1.27033	0.635164	+	0.772377i	$0.280932\pi$
$294$	−9.60469e127	−7.28779
$295$	−1.25845e127	−0.801681
$296$	1.10900e127	0.593486
$297$	1.52722e127	0.686980
$298$	−2.86908e127	−1.08544
$299$	−2.12356e127	−0.676082
$300$	7.03494e127	1.88589
$301$	7.81085e127	1.76410
$302$	−1.35286e128	−2.57571
$303$	1.14550e128	1.83950
$304$	−1.10121e127	−0.149238
$305$	−1.46107e127	−0.167197
$306$	2.26319e128	2.18810
$307$	2.10008e128	1.71637	0.858183	−	0.513344i	$-0.171593\pi$
$307$	2.10008e128	1.71637	0.858183	+	0.513344i	$0.171593\pi$
$308$	−4.49003e128	−3.10375
$309$	−3.17554e128	−1.85762
$310$	1.52459e128	0.755137
$311$	−1.65679e128	−0.695195	−0.347598	−	0.937644i	$-0.613002\pi$
$311$	−1.65679e128	−0.695195	−0.347598	+	0.937644i	$0.613002\pi$
$312$	3.81441e128	1.35664
$313$	5.41792e127	0.163418	0.0817089	−	0.996656i	$-0.473962\pi$
$313$	5.41792e127	0.163418	0.0817089	+	0.996656i	$0.473962\pi$
$314$	−2.21741e128	−0.567505
$315$	8.36958e128	1.81849
$316$	9.01532e127	0.166378
$317$	4.88808e128	0.766630	0.383315	−	0.923618i	$-0.374782\pi$
$317$	4.88808e128	0.766630	0.383315	+	0.923618i	$0.374782\pi$
$318$	−2.88037e129	−3.84107
$319$	−1.91991e128	−0.217801
$320$	−7.43962e128	−0.718334
$321$	−2.34024e129	−1.92420
$322$	6.03149e129	4.22520
$323$	−2.49451e128	−0.148955
$324$	−8.00314e128	−0.407561
$325$	7.39736e128	0.321428
$326$	2.56582e129	0.951744
$327$	−5.05692e129	−1.60205
$328$	6.28251e129	1.70071
$329$	1.11059e129	0.257018
$330$	7.14796e129	1.41486
$331$	−7.05139e129	−1.19435	−0.597177	−	0.802109i	$-0.703711\pi$
$331$	−7.05139e129	−1.19435	−0.597177	+	0.802109i	$0.703711\pi$
$332$	−8.68768e129	−1.25977
$333$	4.47466e129	0.555753
$334$	1.31012e130	1.39434
$335$	−3.61362e129	−0.329713
$336$	−3.26755e130	−2.55711
$337$	1.99757e129	0.134141	0.0670705	−	0.997748i	$-0.478635\pi$
$337$	1.99757e129	0.134141	0.0670705	+	0.997748i	$0.478635\pi$
$338$	−2.15204e130	−1.24062
$339$	−1.80432e130	−0.893364
$340$	2.39383e130	1.01842
$341$	−1.60407e130	−0.586640
$342$	−1.47320e130	−0.463357
$343$	1.18638e131	3.21052
$344$	6.41296e130	1.49382
$345$	−6.34236e130	−1.27224
$346$	1.30122e131	2.24870
$347$	−2.46045e130	−0.366477	−0.183238	−	0.983068i	$-0.558658\pi$
$347$	−2.46045e130	−0.366477	−0.183238	+	0.983068i	$0.558658\pi$
$348$	−6.29528e130	−0.808508
$349$	−1.20918e131	−1.33962	−0.669812	−	0.742530i	$-0.733625\pi$
$349$	−1.20918e131	−1.33962	−0.669812	+	0.742530i	$0.733625\pi$
$350$	−2.10105e131	−2.00878
$351$	5.26566e130	0.434646
$352$	2.11331e130	0.150666
$353$	−1.23149e130	−0.0758635	−0.0379317	−	0.999280i	$-0.512077\pi$
$353$	−1.23149e130	−0.0758635	−0.0379317	+	0.999280i	$0.512077\pi$
$354$	6.57273e131	3.50008
$355$	−7.01639e129	−0.0323112
$356$	−9.74669e130	−0.388313
$357$	−7.40183e131	−2.55227
$358$	−1.28728e131	−0.384323
$359$	1.31777e131	0.340781	0.170391	−	0.985377i	$-0.445497\pi$
$359$	1.31777e131	0.340781	0.170391	+	0.985377i	$0.445497\pi$
$360$	6.87170e131	1.53987
$361$	−4.98541e131	−0.968457
$362$	−6.82076e131	−1.14906
$363$	3.34111e131	0.488315
$364$	−1.54810e132	−1.96372
$365$	1.05208e132	1.15868
$366$	7.63100e131	0.729970
$367$	−6.40615e131	−0.532470	−0.266235	−	0.963908i	$-0.585780\pi$
$367$	−6.40615e131	−0.532470	−0.266235	+	0.963908i	$0.585780\pi$
$368$	1.49355e132	1.07909
$369$	2.53490e132	1.59258
$370$	7.16537e131	0.391606
$371$	5.68222e132	2.70248
$372$	−5.25965e132	−2.17769
$373$	−3.80510e132	−1.37202	−0.686011	−	0.727591i	$-0.740640\pi$
$373$	−3.80510e132	−1.37202	−0.686011	+	0.727591i	$0.740640\pi$
$374$	−3.81301e132	−1.19779
$375$	5.82799e132	1.59554
$376$	9.11829e131	0.217640
$377$	−6.61960e131	−0.137801
$378$	−1.49559e133	−2.71634
$379$	−5.26510e132	−0.834617	−0.417308	−	0.908765i	$-0.637027\pi$
$379$	−5.26510e132	−0.834617	−0.417308	+	0.908765i	$0.637027\pi$
$380$	−1.55823e132	−0.215664
$381$	−9.79699e131	−0.118429
$382$	4.71636e132	0.498131
$383$	1.46375e133	1.35124	0.675618	−	0.737252i	$-0.263877\pi$
$383$	1.46375e133	1.35124	0.675618	+	0.737252i	$0.263877\pi$
$384$	3.52950e133	2.84875
$385$	−1.41010e133	−0.995459
$386$	−3.79635e133	−2.34487
$387$	2.58753e133	1.39885
$388$	−5.51047e132	−0.260828
$389$	−3.22076e133	−1.33522	−0.667612	−	0.744509i	$-0.732683\pi$
$389$	−3.22076e133	−1.33522	−0.667612	+	0.744509i	$0.732683\pi$
$390$	2.46452e133	0.895170
$391$	3.38327e133	1.07705
$392$	1.55565e134	4.34191
$393$	−6.73741e133	−1.64921
$394$	−1.23824e134	−2.65919
$395$	2.83128e132	0.0533621
$396$	−1.48743e134	−2.46113
$397$	−2.68348e133	−0.389930	−0.194965	−	0.980810i	$-0.562459\pi$
$397$	−2.68348e133	−0.389930	−0.194965	+	0.980810i	$0.562459\pi$
$398$	1.14918e134	1.46693
$399$	4.81813e133	0.540474
$400$	−5.20273e133	−0.513029
$401$	1.39476e134	1.20939	0.604694	−	0.796458i	$-0.293295\pi$
$401$	1.39476e134	1.20939	0.604694	+	0.796458i	$0.293295\pi$
$402$	1.88735e134	1.43950
$403$	−5.53061e133	−0.371162
$404$	−3.81705e134	−2.25469
$405$	−2.51340e133	−0.130716
$406$	1.88014e134	0.861192
$407$	−7.53890e133	−0.304226
$408$	−6.07715e134	−2.16123
$409$	−4.04437e134	−1.26795	−0.633973	−	0.773355i	$-0.718577\pi$
$409$	−4.04437e134	−1.26795	−0.633973	+	0.773355i	$0.718577\pi$
$410$	4.05918e134	1.12220
$411$	8.96961e134	2.18736
$412$	1.05816e135	2.27690
$413$	−1.29663e135	−2.46256
$414$	1.99808e135	3.35038
$415$	−2.72839e134	−0.404044
$416$	7.28641e133	0.0953250
$417$	1.22601e134	0.141738
$418$	2.48204e134	0.253647
$419$	−2.74924e134	−0.248422	−0.124211	−	0.992256i	$-0.539640\pi$
$419$	−2.74924e134	−0.248422	−0.124211	+	0.992256i	$0.539640\pi$
$420$	−4.62366e135	−3.69528
$421$	1.15484e135	0.816568	0.408284	−	0.912855i	$-0.366127\pi$
$421$	1.15484e135	0.816568	0.408284	+	0.912855i	$0.366127\pi$
$422$	−4.95633e135	−3.10148
$423$	3.67909e134	0.203803
$424$	4.66529e135	2.28843
$425$	−1.17855e135	−0.512058
$426$	3.66458e134	0.141068
$427$	−1.50539e135	−0.513588
$428$	7.79817e135	2.35852
$429$	−2.59300e135	−0.695427
$430$	4.14347e135	0.985686
$431$	−4.81180e135	−1.01561	−0.507806	−	0.861471i	$-0.669543\pi$
$431$	−4.81180e135	−1.01561	−0.507806	+	0.861471i	$0.669543\pi$
$432$	−3.70346e135	−0.693736
$433$	6.41557e134	0.106686	0.0533432	−	0.998576i	$-0.483012\pi$
$433$	6.41557e134	0.106686	0.0533432	+	0.998576i	$0.483012\pi$
$434$	1.57084e136	2.31959
$435$	−1.97705e135	−0.259311
$436$	1.68507e136	1.96365
$437$	−2.20230e135	−0.228078
$438$	−5.49487e136	−5.05872
$439$	1.00426e136	0.822098	0.411049	−	0.911613i	$-0.365163\pi$
$439$	1.00426e136	0.822098	0.411049	+	0.911613i	$0.365163\pi$
$440$	−1.15774e136	−0.842944
$441$	6.27682e136	4.06586
$442$	−1.31468e136	−0.757831
$443$	−2.40052e136	−1.23172	−0.615861	−	0.787855i	$-0.711192\pi$
$443$	−2.40052e136	−1.23172	−0.615861	+	0.787855i	$0.711192\pi$
$444$	−2.47196e136	−1.12933
$445$	−3.06097e135	−0.124543
$446$	5.98007e136	2.16751
$447$	3.10848e136	1.00395
$448$	−7.66531e136	−2.20654
$449$	−9.47948e135	−0.243275	−0.121638	−	0.992575i	$-0.538815\pi$
$449$	−9.47948e135	−0.243275	−0.121638	+	0.992575i	$0.538815\pi$
$450$	−6.96023e136	−1.59286
$451$	−4.27078e136	−0.871797
$452$	6.01237e136	1.09501
$453$	1.46575e137	2.38233
$454$	−2.09793e136	−0.304379
$455$	−4.86186e136	−0.629818
$456$	3.95585e136	0.457667
$457$	1.10926e137	1.14643	0.573217	−	0.819404i	$-0.305695\pi$
$457$	1.10926e137	1.14643	0.573217	+	0.819404i	$0.305695\pi$
$458$	−1.80107e137	−1.66325
$459$	−8.38928e136	−0.692422
$460$	2.11341e137	1.55939
$461$	−1.18544e137	−0.782133	−0.391066	−	0.920362i	$-0.627894\pi$
$461$	−1.18544e137	−0.782133	−0.391066	+	0.920362i	$0.627894\pi$
$462$	7.36480e137	4.34610
$463$	−3.53347e137	−1.86544	−0.932719	−	0.360605i	$-0.882570\pi$
$463$	−3.53347e137	−1.86544	−0.932719	+	0.360605i	$0.882570\pi$
$464$	4.65572e136	0.219943
$465$	−1.65180e137	−0.698444
$466$	−3.99718e137	−1.51314
$467$	3.17223e137	1.07534	0.537669	−	0.843156i	$-0.319305\pi$
$467$	3.17223e137	1.07534	0.537669	+	0.843156i	$0.319305\pi$
$468$	−5.12847e137	−1.55713
$469$	−3.72325e137	−1.01279
$470$	5.89140e136	0.143608
$471$	2.40244e137	0.524899
$472$	−1.06457e138	−2.08527
$473$	−4.35946e137	−0.765745
$474$	−1.47875e137	−0.232975
$475$	7.67164e136	0.108435
$476$	2.46645e138	3.12834
$477$	1.88237e138	2.14294
$478$	3.36560e137	0.343975
$479$	1.95693e138	1.79596	0.897978	−	0.440040i	$-0.145036\pi$
$479$	1.95693e138	1.79596	0.897978	+	0.440040i	$0.145036\pi$
$480$	2.17620e137	0.179380
$481$	−2.59931e137	−0.192481
$482$	−2.36225e138	−1.57183
$483$	−6.53477e138	−3.90799
$484$	−1.11333e138	−0.598533
$485$	−1.73058e137	−0.0836548
$486$	4.57211e138	1.98769
$487$	3.20001e138	1.25144	0.625721	−	0.780047i	$-0.284805\pi$
$487$	3.20001e138	1.25144	0.625721	+	0.780047i	$0.284805\pi$
$488$	−1.23598e138	−0.434901
$489$	−2.77992e138	−0.880291
$490$	1.00512e139	2.86497
$491$	−3.24959e137	−0.0833934	−0.0416967	−	0.999130i	$-0.513276\pi$
$491$	−3.24959e137	−0.0833934	−0.0416967	+	0.999130i	$0.513276\pi$
$492$	−1.40037e139	−3.23623
$493$	1.05464e138	0.219527
$494$	8.55774e137	0.160480
$495$	−4.67131e138	−0.789352
$496$	3.88981e138	0.592409
$497$	−7.22925e137	−0.0992520
$498$	1.42500e139	1.76403
$499$	−1.01921e138	−0.113785	−0.0568925	−	0.998380i	$-0.518119\pi$
$499$	−1.01921e138	−0.113785	−0.0568925	+	0.998380i	$0.518119\pi$
$500$	−1.94201e139	−1.95567
$501$	−1.41944e139	−1.28966
$502$	−1.06420e139	−0.872533
$503$	1.93830e139	1.43440	0.717201	−	0.696867i	$-0.245423\pi$
$503$	1.93830e139	1.43440	0.717201	+	0.696867i	$0.245423\pi$
$504$	7.08017e139	4.73011
$505$	−1.19875e139	−0.723143
$506$	−3.36635e139	−1.83404
$507$	2.33161e139	1.14748
$508$	3.26457e138	0.145159
$509$	−2.32735e139	−0.935181	−0.467590	−	0.883945i	$-0.654878\pi$
$509$	−2.32735e139	−0.935181	−0.467590	+	0.883945i	$0.654878\pi$
$510$	−3.92649e139	−1.42607
$511$	1.08399e140	3.55918
$512$	−5.10679e139	−1.51616
$513$	5.46090e138	0.146629
$514$	−1.64084e139	−0.398535
$515$	3.32317e139	0.730265
$516$	−1.42945e140	−2.84255
$517$	−6.19852e138	−0.111564
$518$	7.38274e139	1.20292
$519$	−1.40979e140	−2.07987
$520$	−3.99174e139	−0.533323
$521$	−3.97205e139	−0.480697	−0.240349	−	0.970687i	$-0.577262\pi$
$521$	−3.97205e139	−0.480697	−0.240349	+	0.970687i	$0.577262\pi$
$522$	6.22843e139	0.682885
$523$	3.44897e139	0.342651	0.171326	−	0.985214i	$-0.445195\pi$
$523$	3.44897e139	0.342651	0.171326	+	0.985214i	$0.445195\pi$
$524$	2.24505e140	2.02146
$525$	2.27636e140	1.85797
$526$	−3.09819e140	−2.29267
$527$	8.81140e139	0.591287
$528$	1.82371e140	1.10997
$529$	1.17575e140	0.649154
$530$	3.01428e140	1.51000
$531$	−4.29539e140	−1.95270
$532$	−1.60550e140	−0.662464
$533$	−1.47251e140	−0.551579
$534$	1.59871e140	0.543744
$535$	2.44903e140	0.756441
$536$	−3.05691e140	−0.857623
$537$	1.39469e140	0.355469
$538$	−2.14864e140	−0.497596
$539$	−1.05752e141	−2.22570
$540$	−5.24048e140	−1.00252
$541$	−6.95481e140	−1.20956	−0.604778	−	0.796394i	$-0.706738\pi$
$541$	−6.95481e140	−1.20956	−0.604778	+	0.796394i	$0.706738\pi$
$542$	1.80504e141	2.85446
$543$	7.38990e140	1.06279
$544$	−1.16087e140	−0.151860
$545$	5.29201e140	0.629797
$546$	2.53929e141	2.74974
$547$	−1.02308e141	−1.00824	−0.504119	−	0.863634i	$-0.668183\pi$
$547$	−1.02308e141	−1.00824	−0.504119	+	0.863634i	$0.668183\pi$
$548$	−2.98887e141	−2.68107
$549$	−4.98698e140	−0.407251
$550$	1.17266e141	0.871952
$551$	−6.86505e139	−0.0464875
$552$	−5.36526e141	−3.30924
$553$	2.91718e140	0.163915
$554$	6.29678e141	3.22378
$555$	−7.76326e140	−0.362206
$556$	−4.08532e140	−0.173730
$557$	3.38589e141	1.31260	0.656298	−	0.754502i	$-0.272122\pi$
$557$	3.38589e141	1.31260	0.656298	+	0.754502i	$0.272122\pi$
$558$	5.20379e141	1.83932
$559$	−1.50309e141	−0.484480
$560$	3.41945e141	1.00525
$561$	4.13118e141	1.10786
$562$	−1.17602e142	−2.87737
$563$	−2.18776e141	−0.488447	−0.244223	−	0.969719i	$-0.578533\pi$
$563$	−2.18776e141	−0.488447	−0.244223	+	0.969719i	$0.578533\pi$
$564$	−2.03246e141	−0.414141
$565$	1.88820e141	0.351199
$566$	−1.63497e142	−2.77629
$567$	−2.58965e141	−0.401527
$568$	−5.93545e140	−0.0840455
$569$	−4.89513e140	−0.0633115	−0.0316557	−	0.999499i	$-0.510078\pi$
$569$	−4.89513e140	−0.0633115	−0.0316557	+	0.999499i	$0.510078\pi$
$570$	2.55590e141	0.301988
$571$	2.61141e141	0.281913	0.140957	−	0.990016i	$-0.454982\pi$
$571$	2.61141e141	0.281913	0.140957	+	0.990016i	$0.454982\pi$
$572$	8.64043e141	0.852393
$573$	−5.10991e141	−0.460734
$574$	4.18232e142	3.44711
$575$	−1.04049e142	−0.784054
$576$	−2.53932e142	−1.74968
$577$	6.21134e141	0.391409	0.195704	−	0.980663i	$-0.437301\pi$
$577$	6.21134e141	0.391409	0.195704	+	0.980663i	$0.437301\pi$
$578$	−8.83168e141	−0.509049
$579$	4.11312e142	2.16883
$580$	6.58795e141	0.317840
$581$	−2.81116e142	−1.24112
$582$	9.03859e141	0.365231
$583$	−3.17142e142	−1.17307
$584$	8.89994e142	3.01388
$585$	−1.61061e142	−0.499416
$586$	7.67792e142	2.18030
$587$	2.75624e142	0.716894	0.358447	−	0.933550i	$-0.383306\pi$
$587$	2.75624e142	0.716894	0.358447	+	0.933550i	$0.383306\pi$
$588$	−3.46754e143	−8.26208
$589$	−5.73568e141	−0.125212
$590$	−6.87829e142	−1.37595
$591$	1.34156e143	2.45954
$592$	1.82816e142	0.307217
$593$	1.00808e143	1.55302	0.776511	−	0.630103i	$-0.216987\pi$
$593$	1.00808e143	1.55302	0.776511	+	0.630103i	$0.216987\pi$
$594$	8.34731e142	1.17908
$595$	7.74594e142	1.00335
$596$	−1.03581e143	−1.23055
$597$	−1.24506e143	−1.35679
$598$	−1.16067e143	−1.16038
$599$	2.92686e142	0.268485	0.134242	−	0.990949i	$-0.457140\pi$
$599$	2.92686e142	0.268485	0.134242	+	0.990949i	$0.457140\pi$
$600$	1.86897e143	1.57330
$601$	−5.29667e142	−0.409230	−0.204615	−	0.978843i	$-0.565594\pi$
$601$	−5.29667e142	−0.409230	−0.204615	+	0.978843i	$0.565594\pi$
$602$	4.26917e143	3.02778
$603$	−1.23342e143	−0.803098
$604$	−4.88420e143	−2.92005
$605$	−3.49644e142	−0.191966
$606$	6.26095e143	3.15718
$607$	−3.80314e143	−1.76167	−0.880836	−	0.473422i	$-0.843019\pi$
$607$	−3.80314e143	−1.76167	−0.880836	+	0.473422i	$0.843019\pi$
$608$	7.55658e141	0.0321581
$609$	−2.03703e143	−0.796537
$610$	−7.98576e142	−0.286965
$611$	−2.13717e142	−0.0705857
$612$	8.17070e143	2.48063
$613$	6.11504e142	0.170681	0.0853405	−	0.996352i	$-0.472802\pi$
$613$	6.11504e142	0.170681	0.0853405	+	0.996352i	$0.472802\pi$
$614$	1.14784e144	2.94585
$615$	−4.39789e143	−1.03795
$616$	−1.19286e144	−2.58931
$617$	−1.36805e143	−0.273159	−0.136579	−	0.990629i	$-0.543611\pi$
$617$	−1.36805e143	−0.273159	−0.136579	+	0.990629i	$0.543611\pi$
$618$	−1.73565e144	−3.18828
$619$	1.10561e144	1.86867	0.934336	−	0.356392i	$-0.115993\pi$
$619$	1.10561e144	1.86867	0.934336	+	0.356392i	$0.115993\pi$
$620$	5.50417e143	0.856090
$621$	−7.40654e143	−1.06023
$622$	−9.05549e143	−1.19318
$623$	−3.15383e143	−0.382564
$624$	6.28794e143	0.702266
$625$	−1.62356e142	−0.0166973
$626$	2.96127e143	0.280478
$627$	−2.68914e143	−0.234604
$628$	−8.00544e143	−0.643374
$629$	4.14124e143	0.306636
$630$	4.57455e144	3.12112
$631$	4.05438e143	0.254925	0.127463	−	0.991843i	$-0.459317\pi$
$631$	4.05438e143	0.254925	0.127463	+	0.991843i	$0.459317\pi$
$632$	2.39510e143	0.138801
$633$	5.36990e144	2.86863
$634$	2.67167e144	1.31579
$635$	1.02524e143	0.0465565
$636$	−1.03989e145	−4.35458
$637$	−3.64618e144	−1.40818
$638$	−1.04936e144	−0.373819
$639$	−2.39486e143	−0.0787021
$640$	−3.69358e144	−1.11990
$641$	5.08331e144	1.42219	0.711096	−	0.703095i	$-0.248199\pi$
$641$	5.08331e144	1.42219	0.711096	+	0.703095i	$0.248199\pi$
$642$	−1.27910e145	−3.30256
$643$	−1.25760e143	−0.0299694	−0.0149847	−	0.999888i	$-0.504770\pi$
$643$	−1.25760e143	−0.0299694	−0.0149847	+	0.999888i	$0.504770\pi$
$644$	2.17752e145	4.79006
$645$	−4.48921e144	−0.911684
$646$	−1.36342e144	−0.255656
$647$	−2.02257e144	−0.350214	−0.175107	−	0.984549i	$-0.556027\pi$
$647$	−2.02257e144	−0.350214	−0.175107	+	0.984549i	$0.556027\pi$
$648$	−2.12619e144	−0.340008
$649$	7.23685e144	1.06893
$650$	4.04317e144	0.551676
$651$	−1.70192e145	−2.14544
$652$	9.26329e144	1.07898
$653$	7.57644e143	0.0815523	0.0407762	−	0.999168i	$-0.487017\pi$
$653$	7.57644e143	0.0815523	0.0407762	+	0.999168i	$0.487017\pi$
$654$	−2.76395e145	−2.74965
$655$	7.05063e144	0.648337
$656$	1.03565e145	0.880371
$657$	3.59099e145	2.82226
$658$	6.07013e144	0.441128
$659$	−1.16386e145	−0.782170	−0.391085	−	0.920355i	$-0.627900\pi$
$659$	−1.16386e145	−0.782170	−0.391085	+	0.920355i	$0.627900\pi$
$660$	2.58060e145	1.60401
$661$	−1.78883e145	−1.02847	−0.514236	−	0.857648i	$-0.671925\pi$
$661$	−1.78883e145	−1.02847	−0.514236	+	0.857648i	$0.671925\pi$
$662$	−3.85407e145	−2.04990
$663$	1.42438e145	0.700936
$664$	−2.30805e145	−1.05097
$665$	−5.04213e144	−0.212471
$666$	2.44571e145	0.953855
$667$	9.31097e144	0.336135
$668$	4.72987e145	1.58074
$669$	−6.47906e145	−2.00478
$670$	−1.97510e145	−0.565895
$671$	8.40205e144	0.222934
$672$	2.24222e145	0.551012
$673$	2.26250e144	0.0515007	0.0257504	−	0.999668i	$-0.491802\pi$
$673$	2.26250e144	0.0515007	0.0257504	+	0.999668i	$0.491802\pi$
$674$	1.09181e145	0.230230
$675$	2.58004e145	0.504061
$676$	−7.76942e145	−1.40648
$677$	−2.76550e145	−0.463934	−0.231967	−	0.972724i	$-0.574516\pi$
$677$	−2.76550e145	−0.463934	−0.231967	+	0.972724i	$0.574516\pi$
$678$	−9.86184e145	−1.53331
$679$	−1.78308e145	−0.256967
$680$	6.35967e145	0.849622
$681$	2.27298e145	0.281527
$682$	−8.76733e145	−1.00687
$683$	8.88576e145	0.946299	0.473150	−	0.880982i	$-0.343117\pi$
$683$	8.88576e145	0.946299	0.473150	+	0.880982i	$0.343117\pi$
$684$	−5.31862e145	−0.525303
$685$	−9.38660e145	−0.859892
$686$	6.48437e146	5.51031
$687$	1.95136e146	1.53838
$688$	1.05716e146	0.773276
$689$	−1.09346e146	−0.742189
$690$	−3.46654e146	−2.18357
$691$	−2.41484e146	−1.41179	−0.705894	−	0.708317i	$-0.749455\pi$
$691$	−2.41484e146	−1.41179	−0.705894	+	0.708317i	$0.749455\pi$
$692$	4.69773e146	2.54932
$693$	−4.81302e146	−2.42469
$694$	−1.34481e146	−0.628995
$695$	−1.28300e145	−0.0557199
$696$	−1.67247e146	−0.674499
$697$	2.34601e146	0.878704
$698$	−6.60903e146	−2.29924
$699$	4.33071e146	1.39954
$700$	−7.58533e146	−2.27733
$701$	2.26703e146	0.632381	0.316191	−	0.948696i	$-0.397596\pi$
$701$	2.26703e146	0.632381	0.316191	+	0.948696i	$0.397596\pi$
$702$	2.87805e146	0.745996
$703$	−2.69569e145	−0.0649338
$704$	4.27824e146	0.957796
$705$	−6.38299e145	−0.132826
$706$	−6.73093e145	−0.130207
$707$	−1.23512e147	−2.22131
$708$	2.37293e147	3.96800
$709$	1.10202e147	1.71359	0.856797	−	0.515653i	$-0.172451\pi$
$709$	1.10202e147	1.71359	0.856797	+	0.515653i	$0.172451\pi$
$710$	−3.83494e145	−0.0554567
$711$	9.66385e145	0.129977
$712$	−2.58940e146	−0.323951
$713$	7.77922e146	0.905368
$714$	−4.04561e147	−4.38053
$715$	2.71355e146	0.273386
$716$	−4.64741e146	−0.435703
$717$	−3.64644e146	−0.318150
$718$	7.20253e146	0.584893
$719$	6.75590e146	0.510676	0.255338	−	0.966852i	$-0.417813\pi$
$719$	6.75590e146	0.510676	0.255338	+	0.966852i	$0.417813\pi$
$720$	1.13278e147	0.797115
$721$	3.42399e147	2.24319
$722$	−2.72487e147	−1.66219
$723$	2.55937e147	1.45382
$724$	−2.46247e147	−1.30267
$725$	−3.24344e146	−0.159808
$726$	1.82615e147	0.838109
$727$	−2.29340e147	−0.980524	−0.490262	−	0.871575i	$-0.663099\pi$
$727$	−2.29340e147	−0.980524	−0.490262	+	0.871575i	$0.663099\pi$
$728$	−4.11284e147	−1.63823
$729$	−4.38924e147	−1.62900
$730$	5.75032e147	1.98868
$731$	2.39473e147	0.771812
$732$	2.75499e147	0.827559
$733$	−3.45294e147	−0.966795	−0.483398	−	0.875401i	$-0.660597\pi$
$733$	−3.45294e147	−0.966795	−0.483398	+	0.875401i	$0.660597\pi$
$734$	−3.50140e147	−0.913893
$735$	−1.08899e148	−2.64988
$736$	−1.02489e147	−0.232525
$737$	2.07806e147	0.439624
$738$	1.38550e148	2.73340
$739$	7.06279e146	0.129953	0.0649767	−	0.997887i	$-0.479303\pi$
$739$	7.06279e146	0.129953	0.0649767	+	0.997887i	$0.479303\pi$
$740$	2.58688e147	0.443960
$741$	−9.27182e146	−0.148432
$742$	3.10573e148	4.63833
$743$	−2.95242e146	−0.0411391	−0.0205696	−	0.999788i	$-0.506548\pi$
$743$	−2.95242e146	−0.0411391	−0.0205696	+	0.999788i	$0.506548\pi$
$744$	−1.39733e148	−1.81674
$745$	−3.25299e147	−0.394671
$746$	−2.07975e148	−2.35484
$747$	−9.31264e147	−0.984151
$748$	−1.37660e148	−1.35792
$749$	2.52333e148	2.32360
$750$	3.18540e148	2.73848
$751$	−9.39668e147	−0.754254	−0.377127	−	0.926161i	$-0.623088\pi$
$751$	−9.39668e147	−0.754254	−0.377127	+	0.926161i	$0.623088\pi$
$752$	1.50312e147	0.112661
$753$	1.15300e148	0.807026
$754$	−3.61807e147	−0.236512
$755$	−1.53389e148	−0.936542
$756$	−5.39946e148	−3.07948
$757$	−1.19425e148	−0.636293	−0.318146	−	0.948042i	$-0.603060\pi$
$757$	−1.19425e148	−0.636293	−0.318146	+	0.948042i	$0.603060\pi$
$758$	−2.87774e148	−1.43248
$759$	3.64725e148	1.69634
$760$	−4.13975e147	−0.179918
$761$	−4.71353e148	−1.91441	−0.957207	−	0.289403i	$-0.906543\pi$
$761$	−4.71353e148	−1.91441	−0.957207	+	0.289403i	$0.906543\pi$
$762$	−5.35473e147	−0.203262
$763$	5.45256e148	1.93458
$764$	1.70273e148	0.564726
$765$	2.56603e148	0.795605
$766$	8.00043e148	2.31916
$767$	2.49517e148	0.676301
$768$	1.20816e149	3.06213
$769$	−6.97797e148	−1.65395	−0.826975	−	0.562238i	$-0.809941\pi$
$769$	−6.97797e148	−1.65395	−0.826975	+	0.562238i	$0.809941\pi$
$770$	−7.70719e148	−1.70853
$771$	1.77776e148	0.368615
$772$	−1.37058e149	−2.65836
$773$	−3.33756e147	−0.0605598	−0.0302799	−	0.999541i	$-0.509640\pi$
$773$	−3.33756e147	−0.0605598	−0.0302799	+	0.999541i	$0.509640\pi$
$774$	1.41426e149	2.40088
$775$	−2.70987e148	−0.430437
$776$	−1.46396e148	−0.217596
$777$	−7.99878e148	−1.11261
$778$	−1.76037e149	−2.29168
$779$	−1.52711e148	−0.186076
$780$	8.89757e148	1.01484
$781$	4.03486e147	0.0430824
$782$	1.84919e149	1.84856
$783$	−2.30878e148	−0.216098
$784$	2.56444e149	2.24758
$785$	−2.51413e148	−0.206348
$786$	−3.68246e149	−2.83059
$787$	1.77419e149	1.27732	0.638662	−	0.769487i	$-0.279488\pi$
$787$	1.77419e149	1.27732	0.638662	+	0.769487i	$0.279488\pi$
$788$	−4.47036e149	−3.01469
$789$	3.35671e149	2.12055
$790$	1.54749e148	0.0915868
$791$	1.94548e149	1.07879
$792$	−3.95165e149	−2.05320
$793$	2.89692e148	0.141048
$794$	−1.46671e149	−0.669249
$795$	−3.26580e149	−1.39663
$796$	4.14882e149	1.66304
$797$	−1.62408e147	−0.00610243	−0.00305122	−	0.999995i	$-0.500971\pi$
$797$	−1.62408e147	−0.00610243	−0.00305122	+	0.999995i	$0.500971\pi$
$798$	2.63344e149	0.927630
$799$	3.40495e148	0.112448
$800$	3.57016e148	0.110549
$801$	−1.04478e149	−0.303355
$802$	7.62335e149	2.07571
$803$	−6.05009e149	−1.54494
$804$	6.81384e149	1.63194
$805$	6.83857e149	1.53630
$806$	−3.02286e149	−0.637036
$807$	2.32793e149	0.460239
$808$	−1.01407e150	−1.88098
$809$	−1.30934e149	−0.227879	−0.113940	−	0.993488i	$-0.536347\pi$
$809$	−1.30934e149	−0.227879	−0.113940	+	0.993488i	$0.536347\pi$
$810$	−1.37375e149	−0.224352
$811$	3.22566e149	0.494361	0.247180	−	0.968969i	$-0.420496\pi$
$811$	3.22566e149	0.494361	0.247180	+	0.968969i	$0.420496\pi$
$812$	6.78781e149	0.976324
$813$	−1.95566e150	−2.64016
$814$	−4.12053e149	−0.522151
$815$	2.90916e149	0.346059
$816$	−1.00180e150	−1.11876
$817$	−1.55882e149	−0.163441
$818$	−2.21053e150	−2.17621
$819$	−1.65947e150	−1.53408
$820$	1.46547e150	1.27222
$821$	2.32957e150	1.89935	0.949673	−	0.313244i	$-0.101416\pi$
$821$	2.32957e150	1.89935	0.949673	+	0.313244i	$0.101416\pi$
$822$	4.90251e150	3.75422
$823$	7.76145e148	0.0558279	0.0279140	−	0.999610i	$-0.491114\pi$
$823$	7.76145e148	0.0558279	0.0279140	+	0.999610i	$0.491114\pi$
$824$	2.81121e150	1.89951
$825$	−1.27051e150	−0.806489
$826$	−7.08696e150	−4.22656
$827$	−3.93407e149	−0.220449	−0.110225	−	0.993907i	$-0.535157\pi$
$827$	−3.93407e149	−0.220449	−0.110225	+	0.993907i	$0.535157\pi$
$828$	7.21357e150	3.79829
$829$	9.35889e149	0.463091	0.231545	−	0.972824i	$-0.425622\pi$
$829$	9.35889e149	0.463091	0.231545	+	0.972824i	$0.425622\pi$
$830$	−1.49125e150	−0.693472
$831$	−6.82219e150	−2.98175
$832$	1.47508e150	0.605989
$833$	5.80912e150	2.24333
$834$	6.70098e149	0.243269
$835$	1.48543e150	0.506988
$836$	8.96080e149	0.287557
$837$	−1.92896e150	−0.582053
$838$	−1.50265e150	−0.426374
$839$	9.21861e148	0.0245994	0.0122997	−	0.999924i	$-0.496085\pi$
$839$	9.21861e148	0.0245994	0.0122997	+	0.999924i	$0.496085\pi$
$840$	−1.22836e151	−3.08279
$841$	−3.94613e150	−0.931488
$842$	6.31198e150	1.40150
$843$	1.27415e151	2.66135
$844$	−1.78937e151	−3.51611
$845$	−2.44000e150	−0.451097
$846$	2.01088e150	0.349793
$847$	−3.60251e150	−0.589671
$848$	7.69058e150	1.18460
$849$	1.77140e151	2.56785
$850$	−6.44160e150	−0.878859
$851$	3.65613e150	0.469515
$852$	1.32301e150	0.159928
$853$	−4.27610e150	−0.486600	−0.243300	−	0.969951i	$-0.578230\pi$
$853$	−4.27610e150	−0.486600	−0.243300	+	0.969951i	$0.578230\pi$
$854$	−8.22802e150	−0.881485
$855$	−1.67033e150	−0.168479
$856$	2.07174e151	1.96760
$857$	−1.01859e151	−0.910936	−0.455468	−	0.890252i	$-0.650528\pi$
$857$	−1.01859e151	−0.910936	−0.455468	+	0.890252i	$0.650528\pi$
$858$	−1.41725e151	−1.19358
$859$	2.16488e151	1.71706	0.858531	−	0.512761i	$-0.171377\pi$
$859$	2.16488e151	1.71706	0.858531	+	0.512761i	$0.171377\pi$
$860$	1.49590e151	1.11746
$861$	−4.53131e151	−3.18831
$862$	−2.62998e151	−1.74312
$863$	2.52627e151	1.57734	0.788668	−	0.614819i	$-0.210771\pi$
$863$	2.52627e151	1.57734	0.788668	+	0.614819i	$0.210771\pi$
$864$	2.54134e150	0.149488
$865$	1.47533e151	0.817638
$866$	3.50655e150	0.183109
$867$	9.56861e150	0.470831
$868$	5.67115e151	2.62969
$869$	−1.62816e150	−0.0711507
$870$	−1.08059e151	−0.445062
$871$	7.16487e150	0.278146
$872$	4.47673e151	1.63818
$873$	−5.90687e150	−0.203762
$874$	−1.20371e151	−0.391456
$875$	−6.28396e151	−1.92672
$876$	−1.98379e152	−5.73502
$877$	−3.80409e151	−1.03698	−0.518492	−	0.855082i	$-0.673506\pi$
$877$	−3.80409e151	−1.03698	−0.518492	+	0.855082i	$0.673506\pi$
$878$	5.48898e151	1.41099
$879$	−8.31858e151	−2.01661
$880$	−1.90850e151	−0.436349
$881$	6.81368e150	0.146934	0.0734670	−	0.997298i	$-0.476594\pi$
$881$	6.81368e150	0.146934	0.0734670	+	0.997298i	$0.476594\pi$
$882$	3.43072e152	6.97835
$883$	5.85536e150	0.112351	0.0561755	−	0.998421i	$-0.482109\pi$
$883$	5.85536e150	0.112351	0.0561755	+	0.998421i	$0.482109\pi$
$884$	−4.74633e151	−0.859145
$885$	7.45223e151	1.27265
$886$	−1.31205e152	−2.11404
$887$	7.83937e151	1.19183	0.595916	−	0.803047i	$-0.296789\pi$
$887$	7.83937e151	1.19183	0.595916	+	0.803047i	$0.296789\pi$
$888$	−6.56726e151	−0.942142
$889$	1.05635e151	0.143010
$890$	−1.67303e151	−0.213756
$891$	1.44536e151	0.174291
$892$	2.15896e152	2.45728
$893$	−2.21641e150	−0.0238122
$894$	1.69900e152	1.72310
$895$	−1.45953e151	−0.139742
$896$	−3.80564e152	−3.44005
$897$	1.25752e152	1.07326
$898$	−5.18119e151	−0.417540
$899$	2.42495e151	0.184535
$900$	−2.51282e152	−1.80581
$901$	1.74211e152	1.18236
$902$	−2.33428e152	−1.49629
$903$	−4.62540e152	−2.80046
$904$	1.59730e152	0.913511
$905$	−7.73345e151	−0.417803
$906$	8.01134e152	4.08887
$907$	6.35683e151	0.306524	0.153262	−	0.988186i	$-0.451022\pi$
$907$	6.35683e151	0.306524	0.153262	+	0.988186i	$0.451022\pi$
$908$	−7.57407e151	−0.345071
$909$	−4.09163e152	−1.76140
$910$	−2.65734e152	−1.08097
$911$	2.37237e151	0.0911981	0.0455991	−	0.998960i	$-0.485480\pi$
$911$	2.37237e151	0.0911981	0.0455991	+	0.998960i	$0.485480\pi$
$912$	6.52108e151	0.236911
$913$	1.56899e152	0.538735
$914$	6.06287e152	1.96766
$915$	8.65211e151	0.265421
$916$	−6.50233e152	−1.88561
$917$	7.26453e152	1.99153
$918$	−4.58532e152	−1.18842
$919$	1.19403e152	0.292596	0.146298	−	0.989241i	$-0.453264\pi$
$919$	1.19403e152	0.292596	0.146298	+	0.989241i	$0.453264\pi$
$920$	5.61469e152	1.30093
$921$	−1.24362e153	−2.72468
$922$	−6.47923e152	−1.34240
$923$	1.39117e151	0.0272579
$924$	2.65889e153	4.92712
$925$	−1.27360e152	−0.223220
$926$	−1.93129e153	−3.20170
$927$	1.13428e153	1.77874
$928$	−3.19479e151	−0.0473939
$929$	1.09422e153	1.53566	0.767831	−	0.640653i	$-0.221336\pi$
$929$	1.09422e153	1.53566	0.767831	+	0.640653i	$0.221336\pi$
$930$	−9.02825e152	−1.19876
$931$	−3.78138e152	−0.475052
$932$	−1.44309e153	−1.71543
$933$	9.81110e152	1.10360
$934$	1.73384e153	1.84563
$935$	−4.32324e152	−0.435523
$936$	−1.36248e153	−1.29904
$937$	2.56796e152	0.231739	0.115870	−	0.993264i	$-0.463034\pi$
$937$	2.56796e152	0.231739	0.115870	+	0.993264i	$0.463034\pi$
$938$	−2.03501e153	−1.73829
$939$	−3.20836e152	−0.259421
$940$	2.12695e152	0.162807
$941$	3.66198e152	0.265369	0.132685	−	0.991158i	$-0.457640\pi$
$941$	3.66198e152	0.265369	0.132685	+	0.991158i	$0.457640\pi$
$942$	1.31310e153	0.900899
$943$	2.07120e153	1.34546
$944$	−1.75491e153	−1.07944
$945$	−1.69571e153	−0.987675
$946$	−2.38275e153	−1.31427
$947$	2.25802e153	1.17952	0.589759	−	0.807579i	$-0.299223\pi$
$947$	2.25802e153	1.17952	0.589759	+	0.807579i	$0.299223\pi$
$948$	−5.33866e152	−0.264121
$949$	−2.08599e153	−0.977469
$950$	4.19308e152	0.186109
$951$	−2.89460e153	−1.21700
$952$	6.55260e153	2.60982
$953$	−4.64132e153	−1.75129	−0.875643	−	0.482959i	$-0.839562\pi$
$953$	−4.64132e153	−1.75129	−0.875643	+	0.482959i	$0.839562\pi$
$954$	1.02885e154	3.67798
$955$	5.34746e152	0.181123
$956$	1.21507e153	0.389960
$957$	1.13692e153	0.345754
$958$	1.06960e154	3.08245
$959$	−9.67137e153	−2.64137
$960$	4.40556e153	1.14034
$961$	−2.05017e153	−0.502962
$962$	−1.42071e153	−0.330360
$963$	8.35914e153	1.84250
$964$	−8.52836e153	−1.78196
$965$	−4.30434e153	−0.852609
$966$	−3.57170e154	−6.70738
$967$	4.61379e153	0.821476	0.410738	−	0.911753i	$-0.365271\pi$
$967$	4.61379e153	0.821476	0.410738	+	0.911753i	$0.365271\pi$
$968$	−2.95778e153	−0.499327
$969$	1.47719e153	0.236462
$970$	−9.45879e152	−0.143579
$971$	7.27672e153	1.04748	0.523740	−	0.851878i	$-0.324536\pi$
$971$	7.27672e153	1.04748	0.523740	+	0.851878i	$0.324536\pi$
$972$	1.65065e154	2.25342
$973$	−1.32193e153	−0.171158
$974$	1.74903e154	2.14788
$975$	−4.38054e153	−0.510258
$976$	−2.03747e153	−0.225126
$977$	−7.44751e153	−0.780623	−0.390311	−	0.920683i	$-0.627633\pi$
$977$	−7.44751e153	−0.780623	−0.390311	+	0.920683i	$0.627633\pi$
$978$	−1.51942e154	−1.51087
$979$	1.76025e153	0.166060
$980$	3.62875e154	3.24798
$981$	1.80629e154	1.53403
$982$	−1.77613e153	−0.143130
$983$	6.26048e152	0.0478742	0.0239371	−	0.999713i	$-0.492380\pi$
$983$	6.26048e152	0.0478742	0.0239371	+	0.999713i	$0.492380\pi$
$984$	−3.72035e154	−2.69983
$985$	−1.40393e154	−0.966894
$986$	5.76433e153	0.376780
$987$	−6.57663e153	−0.408009
$988$	3.08957e153	0.181935
$989$	2.11421e154	1.18178
$990$	−2.55319e154	−1.35479
$991$	−2.68132e153	−0.135069	−0.0675344	−	0.997717i	$-0.521513\pi$
$991$	−2.68132e153	−0.135069	−0.0675344	+	0.997717i	$0.521513\pi$
$992$	−2.66922e153	−0.127654
$993$	4.17567e154	1.89601
$994$	−3.95128e153	−0.170349
$995$	1.30295e154	0.533382
$996$	5.14464e154	1.99986
$997$	−2.68784e154	−0.992206	−0.496103	−	0.868264i	$-0.665236\pi$
$997$	−2.68784e154	−0.992206	−0.496103	+	0.868264i	$0.665236\pi$
$998$	−5.57068e153	−0.195293
$999$	−9.06586e153	−0.301847

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+5.46569e15 q^{2} -5.92176e24 q^{3} +1.97326e31 q^{4} +6.19706e35 q^{5} -3.23665e40 q^{6} +6.38506e43 q^{7} +5.24235e46 q^{8} +2.11521e49 q^{9} +O(q^{10})\)	\(q+5.46569e15 q^{2} -5.92176e24 q^{3} +1.97326e31 q^{4} +6.19706e35 q^{5} -3.23665e40 q^{6} +6.38506e43 q^{7} +5.24235e46 q^{8} +2.11521e49 q^{9} +3.38712e51 q^{10} -3.56369e53 q^{11} -1.16852e56 q^{12} -1.22872e57 q^{13} +3.48988e59 q^{14} -3.66975e60 q^{15} +8.64183e61 q^{16} +1.95760e63 q^{17} +1.15611e65 q^{18} -1.27427e65 q^{19} +1.22284e67 q^{20} -3.78108e68 q^{21} -1.94780e69 q^{22} +1.72828e70 q^{23} -3.10439e71 q^{24} -6.02041e71 q^{25} -6.71578e72 q^{26} -4.28550e73 q^{27} +1.25994e75 q^{28} +5.38742e74 q^{29} -2.00577e76 q^{30} +4.50113e76 q^{31} -5.93010e76 q^{32} +2.11033e78 q^{33} +1.06996e79 q^{34} +3.95686e79 q^{35} +4.17385e80 q^{36} +2.11547e80 q^{37} -6.96479e80 q^{38} +7.27616e81 q^{39} +3.24871e82 q^{40} +1.19842e83 q^{41} -2.06662e84 q^{42} +1.22330e84 q^{43} -7.03208e84 q^{44} +1.31081e85 q^{45} +9.44625e85 q^{46} +1.73935e85 q^{47} -5.11749e86 q^{48} +2.96748e87 q^{49} -3.29057e87 q^{50} -1.15924e88 q^{51} -2.42457e88 q^{52} +8.89924e88 q^{53} -2.34232e89 q^{54} -2.20844e89 q^{55} +3.34727e90 q^{56} +7.54594e89 q^{57} +2.94460e90 q^{58} -2.03072e91 q^{59} -7.24136e91 q^{60} -2.35768e91 q^{61} +2.46018e92 q^{62} +1.35057e93 q^{63} -1.20051e93 q^{64} -7.61442e92 q^{65} +1.15344e94 q^{66} -5.83119e93 q^{67} +3.86284e94 q^{68} -1.02345e95 q^{69} +2.16270e95 q^{70} -1.13221e94 q^{71} +1.10886e96 q^{72} +1.69770e96 q^{73} +1.15625e96 q^{74} +3.56514e96 q^{75} -2.51447e96 q^{76} -2.27544e97 q^{77} +3.97692e97 q^{78} +4.56875e96 q^{79} +5.35540e97 q^{80} -4.05580e97 q^{81} +6.55017e98 q^{82} -4.40271e98 q^{83} -7.46105e99 q^{84} +1.21313e99 q^{85} +6.68618e99 q^{86} -3.19030e99 q^{87} -1.86821e100 q^{88} -4.93939e99 q^{89} +7.16446e100 q^{90} -7.84542e100 q^{91} +3.41034e101 q^{92} -2.66546e101 q^{93} +9.50676e100 q^{94} -7.89675e100 q^{95} +3.51167e101 q^{96} -2.79258e101 q^{97} +1.62193e103 q^{98} -7.53794e102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 43\!\cdots\!40 q^{2}+ \cdots + 35\!\cdots\!16 q^{9}+O(q^{10}) \) 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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