LMFDB - Embedded newform 1368.2.p.a.341.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(341,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1368.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.p (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			341.2
Character	$\chi$	$=$	1368.341
Dual form			1368.2.p.a.341.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41138 - 0.0894099i) q^{2} +(1.98401 + 0.252383i) q^{4} +1.64947 q^{5} -2.97899 q^{7} +(-2.77764 - 0.533600i) q^{8} +O(q^{10})$	\(q+(-1.41138 - 0.0894099i) q^{2} +(1.98401 + 0.252383i) q^{4} +1.64947 q^{5} -2.97899 q^{7} +(-2.77764 - 0.533600i) q^{8} +(-2.32804 - 0.147479i) q^{10} +2.43029 q^{11} -4.57864 q^{13} +(4.20450 + 0.266351i) q^{14} +(3.87261 + 1.00146i) q^{16} -0.746594i q^{17} +(1.01655 + 4.23871i) q^{19} +(3.27257 + 0.416299i) q^{20} +(-3.43007 - 0.217292i) q^{22} -6.97482i q^{23} -2.27924 q^{25} +(6.46222 + 0.409375i) q^{26} +(-5.91036 - 0.751848i) q^{28} -6.73090i q^{29} +1.79093i q^{31} +(-5.37619 - 1.75970i) q^{32} +(-0.0667528 + 1.05373i) q^{34} -4.91376 q^{35} -10.0699 q^{37} +(-1.05576 - 6.07333i) q^{38} +(-4.58163 - 0.880158i) q^{40} -1.48683 q^{41} -7.95894i q^{43} +(4.82172 + 0.613364i) q^{44} +(-0.623618 + 9.84416i) q^{46} +9.17522i q^{47} +1.87440 q^{49} +(3.21689 + 0.203787i) q^{50} +(-9.08407 - 1.15557i) q^{52} -10.0354i q^{53} +4.00869 q^{55} +(8.27456 + 1.58959i) q^{56} +(-0.601809 + 9.49989i) q^{58} +6.89777i q^{59} -12.1920i q^{61} +(0.160127 - 2.52769i) q^{62} +(7.43054 + 2.96430i) q^{64} -7.55233 q^{65} +2.52529 q^{67} +(0.188428 - 1.48125i) q^{68} +(6.93521 + 0.439339i) q^{70} +8.76160 q^{71} -1.97358 q^{73} +(14.2125 + 0.900346i) q^{74} +(0.947065 + 8.66620i) q^{76} -7.23981 q^{77} -7.02559i q^{79} +(6.38775 + 1.65188i) q^{80} +(2.09849 + 0.132937i) q^{82} -12.6320 q^{83} -1.23148i q^{85} +(-0.711607 + 11.2331i) q^{86} +(-6.75046 - 1.29680i) q^{88} -7.99416 q^{89} +13.6397 q^{91} +(1.76033 - 13.8381i) q^{92} +(0.820355 - 12.9498i) q^{94} +(1.67677 + 6.99162i) q^{95} -0.170738i q^{97} +(-2.64549 - 0.167589i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{4}+O(q^{10}) $ 80 * q + 8 * q^4	$ 80 q + 8 q^{4} + 8 q^{16} + 80 q^{25} + 48 q^{49} - 16 q^{58} + 8 q^{64} + 32 q^{73} + 72 q^{76} - 16 q^{82}+O(q^{100}) $ 80 * q + 8 * q^4 + 8 * q^16 + 80 * q^25 + 48 * q^49 - 16 * q^58 + 8 * q^64 + 32 * q^73 + 72 * q^76 - 16 * q^82

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.41138	−	0.0894099i	−0.997999	−	0.0632223i
$2$	−1.41138	−	0.0894099i	−0.997999	−	0.0632223i
$3$		0			0
$3$		0			0
$4$	1.98401	+	0.252383i	0.992006	+	0.126192i
$5$	1.64947			0.737666			0.368833	−	0.929496i	$-0.379757\pi$
$5$	1.64947			0.737666			0.368833	+	0.929496i	$0.379757\pi$
$6$		0			0
$7$	−2.97899			−1.12595			−0.562977	−	0.826473i	$-0.690344\pi$
$7$	−2.97899			−1.12595			−0.562977	+	0.826473i	$0.690344\pi$
$8$	−2.77764	−	0.533600i	−0.982043	−	0.188656i
$9$		0			0
$10$	−2.32804	−	0.147479i	−0.736190	−	0.0466370i
$11$	2.43029			0.732759			0.366380	−	0.930465i	$-0.380597\pi$
$11$	2.43029			0.732759			0.366380	+	0.930465i	$0.380597\pi$
$12$		0			0
$13$	−4.57864			−1.26989			−0.634943	−	0.772559i	$-0.718976\pi$
$13$	−4.57864			−1.26989			−0.634943	+	0.772559i	$0.718976\pi$
$14$	4.20450	+	0.266351i	1.12370	+	0.0711854i
$15$		0			0
$16$	3.87261	+	1.00146i	0.968151	+	0.250366i
$17$		−	0.746594i		−	0.181076i	−0.995893	−	0.0905378i	$-0.971141\pi$
$17$		−	0.746594i		−	0.181076i	0.995893	−	0.0905378i	$-0.0288586\pi$
$18$		0			0
$19$	1.01655	+	4.23871i	0.233212	+	0.972426i
$19$	1.01655	+	4.23871i	0.233212	+	0.972426i
$20$	3.27257	+	0.416299i	0.731769	+	0.0930873i
$21$		0			0
$22$	−3.43007	−	0.217292i	−0.731293	−	0.0463267i
$23$		−	6.97482i		−	1.45435i	−0.686451	−	0.727176i	$-0.740833\pi$
$23$		−	6.97482i		−	1.45435i	0.686451	−	0.727176i	$-0.259167\pi$
$24$		0			0
$25$	−2.27924			−0.455849
$26$	6.46222	+	0.409375i	1.26735	+	0.0802851i
$27$		0			0
$28$	−5.91036	−	0.751848i	−1.11695	−	0.142086i
$29$		−	6.73090i		−	1.24990i	−0.780666	−	0.624948i	$-0.785120\pi$
$29$		−	6.73090i		−	1.24990i	0.780666	−	0.624948i	$-0.214880\pi$
$30$		0			0
$31$			1.79093i			0.321661i	0.986982	+	0.160830i	$0.0514172\pi$
$31$			1.79093i			0.321661i	−0.986982	+	0.160830i	$0.948583\pi$
$32$	−5.37619	−	1.75970i	−0.950386	−	0.311074i
$33$		0			0
$34$	−0.0667528	+	1.05373i	−0.0114480	+	0.180713i
$35$	−4.91376			−0.830577
$36$		0			0
$37$	−10.0699			−1.65548			−0.827738	−	0.561114i	$-0.810373\pi$
$37$	−10.0699			−1.65548			−0.827738	+	0.561114i	$0.810373\pi$
$38$	−1.05576	−	6.07333i	−0.171267	−	0.985225i
$39$		0			0
$40$	−4.58163	−	0.880158i	−0.724420	−	0.139165i
$41$	−1.48683			−0.232204			−0.116102	−	0.993237i	$-0.537040\pi$
$41$	−1.48683			−0.232204			−0.116102	+	0.993237i	$0.537040\pi$
$42$		0			0
$43$		−	7.95894i		−	1.21373i	−0.794806	−	0.606863i	$-0.792428\pi$
$43$		−	7.95894i		−	1.21373i	0.794806	−	0.606863i	$-0.207572\pi$
$44$	4.82172	+	0.613364i	0.726901	+	0.0924681i
$45$		0			0
$46$	−0.623618	+	9.84416i	−0.0919475	+	1.45144i
$47$			9.17522i			1.33834i	0.743108	+	0.669172i	$0.233351\pi$
$47$			9.17522i			1.33834i	−0.743108	+	0.669172i	$0.766649\pi$
$48$		0			0
$49$	1.87440			0.267771
$50$	3.21689	+	0.203787i	0.454937	+	0.0288198i
$51$		0			0
$52$	−9.08407	−	1.15557i	−1.25973	−	0.160249i
$53$		−	10.0354i		−	1.37846i	−0.724541	−	0.689232i	$-0.757948\pi$
$53$		−	10.0354i		−	1.37846i	0.724541	−	0.689232i	$-0.242052\pi$
$54$		0			0
$55$	4.00869			0.540532
$56$	8.27456	+	1.58959i	1.10573	+	0.212418i
$57$		0			0
$58$	−0.601809	+	9.49989i	−0.0790214	+	1.24740i
$59$			6.89777i			0.898014i	0.893528	+	0.449007i	$0.148222\pi$
$59$			6.89777i			0.898014i	−0.893528	+	0.449007i	$0.851778\pi$
$60$		0			0
$61$		−	12.1920i		−	1.56102i	−0.625141	−	0.780512i	$-0.714959\pi$
$61$		−	12.1920i		−	1.56102i	0.625141	−	0.780512i	$-0.285041\pi$
$62$	0.160127	−	2.52769i	0.0203361	−	0.321017i
$63$		0			0
$64$	7.43054	+	2.96430i	0.928818	+	0.370537i
$65$	−7.55233			−0.936751
$66$		0			0
$67$	2.52529			0.308513			0.154256	−	0.988031i	$-0.450702\pi$
$67$	2.52529			0.308513			0.154256	+	0.988031i	$0.450702\pi$
$68$	0.188428	−	1.48125i	0.0228502	−	0.179628i
$69$		0			0
$70$	6.93521	+	0.439339i	0.828916	+	0.0525110i
$71$	8.76160			1.03981			0.519905	−	0.854224i	$-0.325967\pi$
$71$	8.76160			1.03981			0.519905	+	0.854224i	$0.325967\pi$
$72$		0			0
$73$	−1.97358			−0.230990			−0.115495	−	0.993308i	$-0.536845\pi$
$73$	−1.97358			−0.230990			−0.115495	+	0.993308i	$0.536845\pi$
$74$	14.2125	+	0.900346i	1.65216	+	0.104663i
$75$		0			0
$76$	0.947065	+	8.66620i	0.108636	+	0.994082i
$77$	−7.23981			−0.825053
$78$		0			0
$79$		−	7.02559i		−	0.790441i	−0.918586	−	0.395220i	$-0.870668\pi$
$79$		−	7.02559i		−	0.790441i	0.918586	−	0.395220i	$-0.129332\pi$
$80$	6.38775	+	1.65188i	0.714172	+	0.184686i
$81$		0			0
$82$	2.09849	+	0.132937i	0.231740	+	0.0146805i
$83$	−12.6320			−1.38655			−0.693274	−	0.720675i	$-0.743832\pi$
$83$	−12.6320			−1.38655			−0.693274	+	0.720675i	$0.743832\pi$
$84$		0			0
$85$		−	1.23148i		−	0.133573i
$86$	−0.711607	+	11.2331i	−0.0767346	+	1.21130i
$87$		0			0
$88$	−6.75046	−	1.29680i	−0.719601	−	0.138240i
$89$	−7.99416			−0.847379			−0.423690	−	0.905807i	$-0.639265\pi$
$89$	−7.99416			−0.847379			−0.423690	+	0.905807i	$0.639265\pi$
$90$		0			0
$91$	13.6397			1.42983
$92$	1.76033	−	13.8381i	0.183527	−	1.44272i
$93$		0			0
$94$	0.820355	−	12.9498i	0.0846132	−	1.33567i
$95$	1.67677	+	6.99162i	0.172033	+	0.717325i
$96$		0			0
$97$		−	0.170738i		−	0.0173358i	−0.999962	−	0.00866790i	$-0.997241\pi$
$97$		−	0.170738i		−	0.0173358i	0.999962	−	0.00866790i	$-0.00275911\pi$
$98$	−2.64549	−	0.167589i	−0.267235	−	0.0169291i
$99$		0			0
$100$	−4.52205	−	0.575243i	−0.452205	−	0.0575243i
$101$	−5.91277			−0.588343			−0.294171	−	0.955753i	$-0.595044\pi$
$101$	−5.91277			−0.588343			−0.294171	+	0.955753i	$0.595044\pi$
$102$		0			0
$103$			16.8856i			1.66379i	0.554933	+	0.831895i	$0.312744\pi$
$103$			16.8856i			1.66379i	−0.554933	+	0.831895i	$0.687256\pi$
$104$	12.7178	+	2.44316i	1.24708	+	0.239572i
$105$		0			0
$106$	−0.897260	+	14.1638i	−0.0871496	+	1.37571i
$107$		−	11.8408i		−	1.14469i	−0.820011	−	0.572347i	$-0.806033\pi$
$107$		−	11.8408i		−	1.14469i	0.820011	−	0.572347i	$-0.193967\pi$
$108$		0			0
$109$	−8.04657			−0.770721			−0.385361	−	0.922766i	$-0.625923\pi$
$109$	−8.04657			−0.770721			−0.385361	+	0.922766i	$0.625923\pi$
$110$	−5.65780	−	0.358416i	−0.539450	−	0.0341737i
$111$		0			0
$112$	−11.5365	−	2.98335i	−1.09009	−	0.281900i
$113$	17.3103			1.62842			0.814208	−	0.580574i	$-0.197172\pi$
$113$	17.3103			1.62842			0.814208	+	0.580574i	$0.197172\pi$
$114$		0			0
$115$		−	11.5048i		−	1.07283i
$116$	1.69877	−	13.3542i	0.157727	−	1.23990i
$117$		0			0
$118$	0.616729	−	9.73541i	0.0567745	−	0.896217i
$119$			2.22410i			0.203883i
$120$		0			0
$121$	−5.09370			−0.463064
$122$	−1.09008	+	17.2076i	−0.0986915	+	1.55790i
$123$		0			0
$124$	−0.452001	+	3.55323i	−0.0405909	+	0.319089i
$125$	−12.0069			−1.07393
$126$		0			0
$127$			9.26771i			0.822376i	0.911551	+	0.411188i	$0.134886\pi$
$127$			9.26771i			0.822376i	−0.911551	+	0.411188i	$0.865114\pi$
$128$	−10.2223	−	4.84812i	−0.903533	−	0.428518i
$129$		0			0
$130$	10.6592	+	0.675253i	0.934877	+	0.0592236i
$131$	−17.5536			−1.53367			−0.766834	−	0.641845i	$-0.778169\pi$
$131$	−17.5536			−1.53367			−0.766834	+	0.641845i	$0.778169\pi$
$132$		0			0
$133$	−3.02829	−	12.6271i	−0.262586	−	1.09491i
$134$	−3.56415	−	0.225785i	−0.307896	−	0.0195049i
$135$		0			0
$136$	−0.398383	+	2.07377i	−0.0341610	+	0.177824i
$137$		−	11.7575i		−	1.00451i	−0.864720	−	0.502255i	$-0.832504\pi$
$137$		−	11.7575i		−	1.00451i	0.864720	−	0.502255i	$-0.167496\pi$
$138$		0			0
$139$			3.19586i			0.271069i	0.990773	+	0.135535i	$0.0432752\pi$
$139$			3.19586i			0.271069i	−0.990773	+	0.135535i	$0.956725\pi$
$140$	−9.74896	−	1.24015i	−0.823938	−	0.104812i
$141$		0			0
$142$	−12.3660	−	0.783373i	−1.03773	−	0.0657392i
$143$	−11.1274			−0.930520
$144$		0			0
$145$		−	11.1024i		−	0.922006i
$146$	2.78548	+	0.176458i	0.230528	+	0.0146037i
$147$		0			0
$148$	−19.9787	−	2.54147i	−1.64224	−	0.208907i
$149$	−7.47962			−0.612754			−0.306377	−	0.951910i	$-0.599117\pi$
$149$	−7.47962			−0.612754			−0.306377	+	0.951910i	$0.599117\pi$
$150$		0			0
$151$		−	22.1041i		−	1.79881i	−0.437119	−	0.899404i	$-0.644001\pi$
$151$		−	22.1041i		−	1.79881i	0.437119	−	0.899404i	$-0.355999\pi$
$152$	−0.561829	−	12.3160i	−0.0455703	−	0.998961i
$153$		0			0
$154$	10.2182	+	0.647310i	0.823402	+	0.0521617i
$155$			2.95409i			0.237278i
$156$		0			0
$157$		−	8.27782i		−	0.660642i	−0.943869	−	0.330321i	$-0.892843\pi$
$157$		−	8.27782i		−	0.660642i	0.943869	−	0.330321i	$-0.107157\pi$
$158$	−0.628157	+	9.91581i	−0.0499735	+	0.788859i
$159$		0			0
$160$	−8.86788	−	2.90257i	−0.701067	−	0.229468i
$161$			20.7779i			1.63753i
$162$		0			0
$163$		−	10.6737i		−	0.836031i	−0.908440	−	0.418015i	$-0.862726\pi$
$163$		−	10.6737i		−	0.836031i	0.908440	−	0.418015i	$-0.137274\pi$
$164$	−2.94989	−	0.375252i	−0.230348	−	0.0293022i
$165$		0			0
$166$	17.8287	+	1.12943i	1.38377	+	0.0876607i
$167$	−8.16879			−0.632120			−0.316060	−	0.948739i	$-0.602360\pi$
$167$	−8.16879			−0.632120			−0.316060	+	0.948739i	$0.602360\pi$
$168$		0			0
$169$	7.96392			0.612609
$170$	−0.110107	+	1.73810i	−0.00844481	+	0.133306i
$171$		0			0
$172$	2.00870	−	15.7906i	0.153162	−	1.20402i
$173$		−	22.4235i		−	1.70483i	−0.522869	−	0.852413i	$-0.675138\pi$
$173$		−	22.4235i		−	1.70483i	0.522869	−	0.852413i	$-0.324862\pi$
$174$		0			0
$175$	6.78985			0.513265
$176$	9.41154	+	2.43384i	0.709422	+	0.183458i
$177$		0			0
$178$	11.2828	+	0.714757i	0.845684	+	0.0535733i
$179$		−	1.45991i		−	0.109119i	−0.998511	−	0.0545594i	$-0.982625\pi$
$179$		−	1.45991i		−	0.109119i	0.998511	−	0.0545594i	$-0.0173754\pi$
$180$		0			0
$181$	−2.13358			−0.158588			−0.0792940	−	0.996851i	$-0.525267\pi$
$181$	−2.13358			−0.158588			−0.0792940	+	0.996851i	$0.525267\pi$
$182$	−19.2509	−	1.21953i	−1.42697	−	0.0903973i
$183$		0			0
$184$	−3.72177	+	19.3735i	−0.274372	+	1.42824i
$185$	−16.6100			−1.22119
$186$		0			0
$187$		−	1.81444i		−	0.132685i
$188$	−2.31567	+	18.2037i	−0.168888	+	1.32764i
$189$		0			0
$190$	−1.74144	−	10.0178i	−0.126338	−	0.726767i
$191$		−	8.60268i		−	0.622468i	−0.950333	−	0.311234i	$-0.899258\pi$
$191$		−	8.60268i		−	0.622468i	0.950333	−	0.311234i	$-0.100742\pi$
$192$		0			0
$193$			19.1276i			1.37683i	0.725316	+	0.688416i	$0.241694\pi$
$193$			19.1276i			1.37683i	−0.725316	+	0.688416i	$0.758306\pi$
$194$	−0.0152656	+	0.240977i	−0.00109601	+	0.0173011i
$195$		0			0
$196$	3.71882	+	0.473066i	0.265630	+	0.0337904i
$197$	12.2365			0.871815			0.435908	−	0.899991i	$-0.356427\pi$
$197$	12.2365			0.871815			0.435908	+	0.899991i	$0.356427\pi$
$198$		0			0
$199$	−13.4297			−0.952009			−0.476005	−	0.879443i	$-0.657915\pi$
$199$	−13.4297			−0.952009			−0.476005	+	0.879443i	$0.657915\pi$
$200$	6.33092	+	1.21621i	0.447663	+	0.0859987i
$201$		0			0
$202$	8.34519	+	0.528660i	0.587166	+	0.0371964i
$203$			20.0513i			1.40733i
$204$		0			0
$205$	−2.45249			−0.171289
$206$	1.50974	−	23.8321i	0.105189	−	1.66046i
$207$		0			0
$208$	−17.7313	−	4.58534i	−1.22944	−	0.317936i
$209$	2.47050	+	10.3013i	0.170888	+	0.712554i
$210$		0			0
$211$	7.90829			0.544429			0.272214	−	0.962237i	$-0.412244\pi$
$211$	7.90829			0.544429			0.272214	+	0.962237i	$0.412244\pi$
$212$	2.53276	−	19.9103i	0.173951	−	1.36744i
$213$		0			0
$214$	−1.05869	+	16.7119i	−0.0723702	+	1.14240i
$215$		−	13.1280i		−	0.895325i
$216$		0			0
$217$		−	5.33517i		−	0.362175i
$218$	11.3568	+	0.719442i	0.769180	+	0.0487268i
$219$		0			0
$220$	7.95329	+	1.01173i	0.536210	+	0.0682106i
$221$			3.41838i			0.229945i
$222$		0			0
$223$		−	1.85770i		−	0.124400i	−0.998064	−	0.0622002i	$-0.980188\pi$
$223$		−	1.85770i		−	0.124400i	0.998064	−	0.0622002i	$-0.0198117\pi$
$224$	16.0156	+	5.24213i	1.07009	+	0.350254i
$225$		0			0
$226$	−24.4315	−	1.54771i	−1.62516	−	0.102952i
$227$			8.00287i			0.531169i	0.964088	+	0.265585i	$0.0855650\pi$
$227$			8.00287i			0.531169i	−0.964088	+	0.265585i	$0.914435\pi$
$228$		0			0
$229$			18.3440i			1.21221i	0.795386	+	0.606103i	$0.207268\pi$
$229$			18.3440i			1.21221i	−0.795386	+	0.606103i	$0.792732\pi$
$230$	−1.02864	+	16.2377i	−0.0678265	+	1.07068i
$231$		0			0
$232$	−3.59161	+	18.6960i	−0.235801	+	1.22745i
$233$			0.594597i			0.0389534i	0.999810	+	0.0194767i	$0.00620001\pi$
$233$			0.594597i			0.0389534i	−0.999810	+	0.0194767i	$0.993800\pi$
$234$		0			0
$235$			15.1343i			0.987250i
$236$	−1.74088	+	13.6853i	−0.113322	+	0.890835i
$237$		0			0
$238$	0.198856	−	3.13906i	0.0128899	−	0.203475i
$239$		−	3.89453i		−	0.251916i	−0.992036	−	0.125958i	$-0.959799\pi$
$239$		−	3.89453i		−	0.251916i	0.992036	−	0.125958i	$-0.0402005\pi$
$240$		0			0
$241$			23.9755i			1.54440i	0.635382	+	0.772198i	$0.280843\pi$
$241$			23.9755i			1.54440i	−0.635382	+	0.772198i	$0.719157\pi$
$242$	7.18917	+	0.455427i	0.462138	+	0.0292760i
$243$		0			0
$244$	3.07705	−	24.1890i	0.196988	−	1.54854i
$245$	3.09176			0.197525
$246$		0			0
$247$	−4.65441	−	19.4075i	−0.296153	−	1.23487i
$248$	0.955641	−	4.97456i	0.0606833	−	0.315885i
$249$		0			0
$250$	16.9464	+	1.07354i	1.07178	+	0.0678964i
$251$	−1.81498			−0.114560			−0.0572802	−	0.998358i	$-0.518243\pi$
$251$	−1.81498			−0.114560			−0.0572802	+	0.998358i	$0.518243\pi$
$252$		0			0
$253$		−	16.9508i		−	1.06569i
$254$	0.828624	−	13.0803i	0.0519925	−	0.820731i
$255$		0			0
$256$	13.9941	+	7.75654i	0.874634	+	0.484784i
$257$	24.5922			1.53402			0.767010	−	0.641635i	$-0.221744\pi$
$257$	24.5922			1.53402			0.767010	+	0.641635i	$0.221744\pi$
$258$		0			0
$259$	29.9981			1.86399
$260$	−14.9839	−	1.90608i	−0.929263	−	0.118210i
$261$		0			0
$262$	24.7749	+	1.56947i	1.53060	+	0.0969621i
$263$			14.7000i			0.906444i	0.891398	+	0.453222i	$0.149725\pi$
$263$			14.7000i			0.906444i	−0.891398	+	0.453222i	$0.850275\pi$
$264$		0			0
$265$		−	16.5530i		−	1.01685i
$266$	3.14510	+	18.0924i	0.192838	+	1.10932i
$267$		0			0
$268$	5.01020	+	0.637340i	0.306046	+	0.0389317i
$269$			3.83007i			0.233523i	0.993160	+	0.116762i	$0.0372514\pi$
$269$			3.83007i			0.233523i	−0.993160	+	0.116762i	$0.962749\pi$
$270$		0			0
$271$	−3.62738			−0.220348			−0.110174	−	0.993912i	$-0.535141\pi$
$271$	−3.62738			−0.220348			−0.110174	+	0.993912i	$0.535141\pi$
$272$	0.747686	−	2.89126i	0.0453351	−	0.175309i
$273$		0			0
$274$	−1.05124	+	16.5943i	−0.0635074	+	1.00250i
$275$	−5.53922			−0.334028
$276$		0			0
$277$		−	0.168443i		−	0.0101208i	−0.999987	−	0.00506038i	$-0.998389\pi$
$277$		−	0.168443i		−	0.0101208i	0.999987	−	0.00506038i	$-0.00161078\pi$
$278$	0.285741	−	4.51058i	0.0171376	−	0.270527i
$279$		0			0
$280$	13.6487	+	2.62198i	0.815663	+	0.156694i
$281$	19.9619			1.19083			0.595414	−	0.803419i	$-0.296988\pi$
$281$	19.9619			1.19083			0.595414	+	0.803419i	$0.296988\pi$
$282$		0			0
$283$			21.2677i			1.26423i	0.774874	+	0.632116i	$0.217814\pi$
$283$			21.2677i			1.26423i	−0.774874	+	0.632116i	$0.782186\pi$
$284$	17.3831	+	2.21128i	1.03150	+	0.131215i
$285$		0			0
$286$	15.7050	+	0.994900i	0.928659	+	0.0588297i
$287$	4.42926			0.261451
$288$		0			0
$289$	16.4426			0.967212
$290$	−0.992666	+	15.6698i	−0.0582914	+	0.920162i
$291$		0			0
$292$	−3.91561	−	0.498099i	−0.229144	−	0.0291490i
$293$		−	9.95018i		−	0.581296i	−0.956830	−	0.290648i	$-0.906129\pi$
$293$		−	9.95018i		−	0.581296i	0.956830	−	0.290648i	$-0.0938708\pi$
$294$		0			0
$295$			11.3777i			0.662434i
$296$	27.9705	+	5.37328i	1.62575	+	0.312316i
$297$		0			0
$298$	10.5566	+	0.668751i	0.611528	+	0.0387397i
$299$			31.9352i			1.84686i
$300$		0			0
$301$			23.7096i			1.36660i
$302$	−1.97633	+	31.1974i	−0.113725	+	1.79521i
$303$		0			0
$304$	−0.308217	+	17.4329i	−0.0176775	+	0.999844i
$305$		−	20.1103i		−	1.15151i
$306$		0			0
$307$	17.4039			0.993292			0.496646	−	0.867953i	$-0.334565\pi$
$307$	17.4039			0.993292			0.496646	+	0.867953i	$0.334565\pi$
$308$	−14.3639	−	1.82721i	−0.818457	−	0.104115i
$309$		0			0
$310$	0.264125	−	4.16936i	0.0150013	−	0.236803i
$311$			4.41009i			0.250073i	0.992152	+	0.125037i	$0.0399048\pi$
$311$			4.41009i			0.250073i	−0.992152	+	0.125037i	$0.960095\pi$
$312$		0			0
$313$	−24.8414			−1.40412			−0.702060	−	0.712117i	$-0.747736\pi$
$313$	−24.8414			−1.40412			−0.702060	+	0.712117i	$0.747736\pi$
$314$	−0.740118	+	11.6832i	−0.0417673	+	0.659320i
$315$		0			0
$316$	1.77314	−	13.9389i	0.0997470	−	0.784122i
$317$			13.0987i			0.735696i	0.929886	+	0.367848i	$0.119905\pi$
$317$			13.0987i			0.735696i	−0.929886	+	0.367848i	$0.880095\pi$
$318$		0			0
$319$		−	16.3580i		−	0.915873i
$320$	12.2565	+	4.88952i	0.685157	+	0.273332i
$321$		0			0
$322$	1.85775	−	29.3257i	0.103529	−	1.63426i
$323$	3.16459	−	0.758949i	0.176083	−	0.0422290i
$324$		0			0
$325$	10.4358			0.578876
$326$	−0.954336	+	15.0647i	−0.0528558	+	0.834358i
$327$		0			0
$328$	4.12988	+	0.793374i	0.228035	+	0.0438067i
$329$		−	27.3329i		−	1.50691i
$330$		0			0
$331$	31.7178			1.74337			0.871684	−	0.490068i	$-0.163028\pi$
$331$	31.7178			1.74337			0.871684	+	0.490068i	$0.163028\pi$
$332$	−25.0621	−	3.18812i	−1.37546	−	0.174971i
$333$		0			0
$334$	11.5293	+	0.730370i	0.630855	+	0.0399641i
$335$	4.16539			0.227579
$336$		0			0
$337$			14.5535i			0.792782i	0.918082	+	0.396391i	$0.129737\pi$
$337$			14.5535i			0.792782i	−0.918082	+	0.396391i	$0.870263\pi$
$338$	−11.2402	−	0.712053i	−0.611384	−	0.0387306i
$339$		0			0
$340$	0.310806	−	2.44328i	0.0168558	−	0.132505i
$341$			4.35248i			0.235700i
$342$		0			0
$343$	15.2691			0.824456
$344$	−4.24689	+	22.1070i	−0.228977	+	1.19193i
$345$		0			0
$346$	−2.00488	+	31.6482i	−0.107783	+	1.70142i
$347$	16.5335			0.887564			0.443782	−	0.896135i	$-0.353636\pi$
$347$	16.5335			0.887564			0.443782	+	0.896135i	$0.353636\pi$
$348$		0			0
$349$		−	23.5408i		−	1.26011i	−0.776550	−	0.630056i	$-0.783032\pi$
$349$		−	23.5408i		−	1.26011i	0.776550	−	0.630056i	$-0.216968\pi$
$350$	−9.58309	−	0.607080i	−0.512238	−	0.0324498i
$351$		0			0
$352$	−13.0657	−	4.27657i	−0.696404	−	0.227942i
$353$			2.47540i			0.131752i	0.997828	+	0.0658761i	$0.0209842\pi$
$353$			2.47540i			0.131752i	−0.997828	+	0.0658761i	$0.979016\pi$
$354$		0			0
$355$	14.4520			0.767033
$356$	−15.8605	−	2.01759i	−0.840605	−	0.106932i
$357$		0			0
$358$	−0.130530	+	2.06049i	−0.00689874	+	0.108900i
$359$		−	11.7581i		−	0.620569i	−0.950644	−	0.310285i	$-0.899576\pi$
$359$		−	11.7581i		−	0.620569i	0.950644	−	0.310285i	$-0.100424\pi$
$360$		0			0
$361$	−16.9333	+	8.61770i	−0.891224	+	0.453563i
$362$	3.01131	+	0.190763i	0.158271	+	0.0100263i
$363$		0			0
$364$	27.0614	+	3.44244i	1.41840	+	0.180433i
$365$	−3.25537			−0.170394
$366$		0			0
$367$	21.5144			1.12304			0.561520	−	0.827463i	$-0.310217\pi$
$367$	21.5144			1.12304			0.561520	+	0.827463i	$0.310217\pi$
$368$	6.98503	−	27.0107i	0.364120	−	1.40803i
$369$		0			0
$370$	23.4430	+	1.48509i	1.21875	+	0.0772064i
$371$			29.8953i			1.55209i
$372$		0			0
$373$	−34.6286			−1.79300			−0.896500	−	0.443043i	$-0.853899\pi$
$373$	−34.6286			−1.79300			−0.896500	+	0.443043i	$0.853899\pi$
$374$	−0.162229	+	2.56087i	−0.00838864	+	0.132419i
$375$		0			0
$376$	4.89590	−	25.4854i	0.252487	−	1.31431i
$377$			30.8184i			1.58723i
$378$		0			0
$379$	1.97134			0.101261			0.0506304	−	0.998717i	$-0.483877\pi$
$379$	1.97134			0.101261			0.0506304	+	0.998717i	$0.483877\pi$
$380$	1.56216	+	14.2947i	0.0801369	+	0.733300i
$381$		0			0
$382$	−0.769164	+	12.1417i	−0.0393539	+	0.621223i
$383$	8.85996			0.452723			0.226361	−	0.974043i	$-0.427317\pi$
$383$	8.85996			0.452723			0.226361	+	0.974043i	$0.427317\pi$
$384$		0			0
$385$	−11.9419			−0.608613
$386$	1.71019	−	26.9964i	0.0870465	−	1.37408i
$387$		0			0
$388$	0.0430914	−	0.338746i	0.00218763	−	0.0171972i
$389$	20.6015			1.04454			0.522269	−	0.852781i	$-0.325086\pi$
$389$	20.6015			1.04454			0.522269	+	0.852781i	$0.325086\pi$
$390$		0			0
$391$	−5.20736			−0.263347
$392$	−5.20639	−	1.00018i	−0.262963	−	0.0505166i
$393$		0			0
$394$	−17.2704	−	1.09406i	−0.870071	−	0.0551182i
$395$		−	11.5885i		−	0.583081i
$396$		0			0
$397$			20.6164i			1.03471i	0.855771	+	0.517354i	$0.173083\pi$
$397$			20.6164i			1.03471i	−0.855771	+	0.517354i	$0.826917\pi$
$398$	18.9545	+	1.20075i	0.950105	+	0.0601882i
$399$		0			0
$400$	−8.82661	−	2.28258i	−0.441331	−	0.114129i
$401$	−28.9010			−1.44325			−0.721624	−	0.692285i	$-0.756604\pi$
$401$	−28.9010			−1.44325			−0.721624	+	0.692285i	$0.756604\pi$
$402$		0			0
$403$		−	8.20002i		−	0.408472i
$404$	−11.7310	−	1.49228i	−0.583639	−	0.0742439i
$405$		0			0
$406$	1.79278	−	28.3001i	0.0889744	−	1.40451i
$407$	−24.4727			−1.21307
$408$		0			0
$409$		−	36.1755i		−	1.78876i	−0.447305	−	0.894382i	$-0.647616\pi$
$409$		−	36.1755i		−	1.78876i	0.447305	−	0.894382i	$-0.352384\pi$
$410$	3.46140	+	0.219276i	0.170946	+	0.0108293i
$411$		0			0
$412$	−4.26165	+	33.5013i	−0.209956	+	1.65049i
$413$		−	20.5484i		−	1.01112i
$414$		0			0
$415$	−20.8362			−1.02281
$416$	24.6156	+	8.05702i	1.20688	+	0.395028i
$417$		0			0
$418$	−2.56580	−	14.7599i	−0.125497	−	0.721933i
$419$	−13.2900			−0.649260			−0.324630	−	0.945841i	$-0.605240\pi$
$419$	−13.2900			−0.649260			−0.324630	+	0.945841i	$0.605240\pi$
$420$		0			0
$421$	−22.6477			−1.10378			−0.551892	−	0.833916i	$-0.686094\pi$
$421$	−22.6477			−1.10378			−0.551892	+	0.833916i	$0.686094\pi$
$422$	−11.1616	−	0.707079i	−0.543340	−	0.0344201i
$423$		0			0
$424$	−5.35487	+	27.8746i	−0.260056	+	1.35371i
$425$			1.70167i			0.0825431i
$426$		0			0
$427$			36.3198i			1.75764i
$428$	2.98842	−	23.4923i	0.144451	−	1.13554i
$429$		0			0
$430$	−1.17378	+	18.5287i	−0.0566045	+	0.893534i
$431$	−5.33265			−0.256865			−0.128432	−	0.991718i	$-0.540994\pi$
$431$	−5.33265			−0.256865			−0.128432	+	0.991718i	$0.540994\pi$
$432$		0			0
$433$		−	24.4969i		−	1.17725i	−0.808408	−	0.588623i	$-0.799670\pi$
$433$		−	24.4969i		−	1.17725i	0.808408	−	0.588623i	$-0.200330\pi$
$434$	−0.477017	+	7.52997i	−0.0228975	+	0.361450i
$435$		0			0
$436$	−15.9645	−	2.03082i	−0.764560	−	0.0972586i
$437$	29.5642	−	7.09025i	1.41425	−	0.339172i
$438$		0			0
$439$			17.8987i			0.854259i	0.904190	+	0.427130i	$0.140475\pi$
$439$			17.8987i			0.854259i	−0.904190	+	0.427130i	$0.859525\pi$
$440$	−11.1347	−	2.13904i	−0.530825	−	0.101975i
$441$		0			0
$442$	0.305637	−	4.82465i	0.0145377	−	0.229485i
$443$	−13.4274			−0.637956			−0.318978	−	0.947762i	$-0.603340\pi$
$443$	−13.4274			−0.637956			−0.318978	+	0.947762i	$0.603340\pi$
$444$		0			0
$445$	−13.1861			−0.625083
$446$	−0.166096	+	2.62192i	−0.00786489	+	0.124152i
$447$		0			0
$448$	−22.1355	−	8.83061i	−1.04581	−	0.417207i
$449$	−12.1635			−0.574030			−0.287015	−	0.957926i	$-0.592663\pi$
$449$	−12.1635			−0.574030			−0.287015	+	0.957926i	$0.592663\pi$
$450$		0			0
$451$	−3.61343			−0.170150
$452$	34.3438	+	4.36883i	1.61540	+	0.205492i
$453$		0			0
$454$	0.715536	−	11.2951i	0.0335818	−	0.530107i
$455$	22.4983			1.05474
$456$		0			0
$457$	27.0173			1.26382			0.631908	−	0.775043i	$-0.282272\pi$
$457$	27.0173			1.26382			0.631908	+	0.775043i	$0.282272\pi$
$458$	1.64014	−	25.8905i	0.0766385	−	1.20978i
$459$		0			0
$460$	2.90361	−	22.8256i	0.135382	−	1.06425i
$461$	−10.0923			−0.470047			−0.235024	−	0.971990i	$-0.575517\pi$
$461$	−10.0923			−0.470047			−0.235024	+	0.971990i	$0.575517\pi$
$462$		0			0
$463$	14.4435			0.671248			0.335624	−	0.941996i	$-0.391053\pi$
$463$	14.4435			0.671248			0.335624	+	0.941996i	$0.391053\pi$
$464$	6.74075	−	26.0661i	0.312931	−	1.21009i
$465$		0			0
$466$	0.0531628	−	0.839205i	0.00246272	−	0.0388754i
$467$	34.4659			1.59489			0.797445	−	0.603392i	$-0.206184\pi$
$467$	34.4659			1.59489			0.797445	+	0.603392i	$0.206184\pi$
$468$		0			0
$469$	−7.52281			−0.347371
$470$	1.35315	−	21.3603i	0.0624162	−	0.985275i
$471$		0			0
$472$	3.68065	−	19.1595i	0.169416	−	0.881888i
$473$		−	19.3425i		−	0.889369i
$474$		0			0
$475$	−2.31696	−	9.66105i	−0.106310	−	0.443279i
$476$	−0.561325	+	4.41263i	−0.0257283	+	0.202253i
$477$		0			0
$478$	−0.348210	+	5.49668i	−0.0159267	+	0.251412i
$479$		−	10.5450i		−	0.481815i	−0.970548	−	0.240908i	$-0.922555\pi$
$479$		−	10.5450i		−	0.481815i	0.970548	−	0.240908i	$-0.0774451\pi$
$480$		0			0
$481$	46.1063			2.10227
$482$	2.14364	−	33.8386i	0.0976403	−	1.54131i
$483$		0			0
$484$	−10.1060	−	1.28557i	−0.459362	−	0.0584348i
$485$		−	0.281627i		−	0.0127880i
$486$		0			0
$487$			28.3899i			1.28647i	0.765669	+	0.643234i	$0.222408\pi$
$487$			28.3899i			1.28647i	−0.765669	+	0.643234i	$0.777592\pi$
$488$	−6.50564	+	33.8649i	−0.294497	+	1.53299i
$489$		0			0
$490$	−4.36366	−	0.276434i	−0.197130	−	0.0124880i
$491$	26.8461			1.21155			0.605773	−	0.795638i	$-0.292864\pi$
$491$	26.8461			1.21155			0.605773	+	0.795638i	$0.292864\pi$
$492$		0			0
$493$	−5.02525			−0.226326
$494$	4.83394	+	27.8076i	0.217489	+	1.25112i
$495$		0			0
$496$	−1.79355	+	6.93557i	−0.0805328	+	0.311416i
$497$	−26.1007			−1.17078
$498$		0			0
$499$			14.2028i			0.635804i	0.948124	+	0.317902i	$0.102978\pi$
$499$			14.2028i			0.635804i	−0.948124	+	0.317902i	$0.897022\pi$
$500$	−23.8218	−	3.03034i	−1.06535	−	0.135521i
$501$		0			0
$502$	2.56163	+	0.162277i	0.114331	+	0.00724277i
$503$			35.5971i			1.58720i	0.608442	+	0.793599i	$0.291795\pi$
$503$			35.5971i			1.58720i	−0.608442	+	0.793599i	$0.708205\pi$
$504$		0			0
$505$	−9.75294			−0.434000
$506$	−1.51557	+	23.9241i	−0.0673753	+	1.06356i
$507$		0			0
$508$	−2.33902	+	18.3872i	−0.103777	+	0.815802i
$509$		−	16.4385i		−	0.728625i	−0.931277	−	0.364312i	$-0.881304\pi$
$509$		−	16.4385i		−	0.728625i	0.931277	−	0.364312i	$-0.118696\pi$
$510$		0			0
$511$	5.87928			0.260084
$512$	−19.0576	−	12.1987i	−0.842235	−	0.539110i
$513$		0			0
$514$	−34.7091	−	2.19879i	−1.53095	−	0.0969843i
$515$			27.8523i			1.22732i
$516$		0			0
$517$			22.2984i			0.980683i
$518$	−42.3388	−	2.68212i	−1.86026	−	0.117846i
$519$		0			0
$520$	20.9776	+	4.02992i	0.919930	+	0.176724i
$521$	21.2264			0.929947			0.464973	−	0.885325i	$-0.346064\pi$
$521$	21.2264			0.929947			0.464973	+	0.885325i	$0.346064\pi$
$522$		0			0
$523$	−1.86129			−0.0813886			−0.0406943	−	0.999172i	$-0.512957\pi$
$523$	−1.86129			−0.0813886			−0.0406943	+	0.999172i	$0.512957\pi$
$524$	−34.8266	−	4.43025i	−1.52141	−	0.193536i
$525$		0			0
$526$	1.31433	−	20.7474i	0.0573075	−	0.904630i
$527$	1.33710			0.0582449
$528$		0			0
$529$	−25.6482			−1.11514
$530$	−1.48001	+	23.3627i	−0.0642873	+	1.01481i
$531$		0			0
$532$	−2.82130	−	25.8166i	−0.122319	−	1.11929i
$533$	6.80767			0.294873
$534$		0			0
$535$		−	19.5311i		−	0.844402i
$536$	−7.01433	−	1.34749i	−0.302973	−	0.0582028i
$537$		0			0
$538$	0.342446	−	5.40570i	0.0147639	−	0.233056i
$539$	4.55532			0.196212
$540$		0			0
$541$		−	18.1869i		−	0.781914i	−0.920409	−	0.390957i	$-0.872144\pi$
$541$		−	18.1869i		−	0.781914i	0.920409	−	0.390957i	$-0.127856\pi$
$542$	5.11962	+	0.324323i	0.219907	+	0.0139309i
$543$		0			0
$544$	−1.31378	+	4.01383i	−0.0563278	+	0.172092i
$545$	−13.2726			−0.568535
$546$		0			0
$547$	−40.6762			−1.73919			−0.869593	−	0.493769i	$-0.835619\pi$
$547$	−40.6762			−1.73919			−0.869593	+	0.493769i	$0.835619\pi$
$548$	2.96739	−	23.3270i	0.126761	−	0.996480i
$549$		0			0
$550$	7.81797	+	0.495261i	0.333359	+	0.0211180i
$551$	28.5303	−	6.84229i	1.21543	−	0.291491i
$552$		0			0
$553$			20.9292i			0.889999i
$554$	−0.0150605	+	0.237738i	−0.000639858	+	0.0101005i
$555$		0			0
$556$	−0.806581	+	6.34062i	−0.0342067	+	0.268902i
$557$	33.3325			1.41234			0.706171	−	0.708041i	$-0.250421\pi$
$557$	33.3325			1.41234			0.706171	+	0.708041i	$0.250421\pi$
$558$		0			0
$559$			36.4411i			1.54129i
$560$	−19.0291	−	4.92095i	−0.804125	−	0.207948i
$561$		0			0
$562$	−28.1740	−	1.78479i	−1.18845	−	0.0752869i
$563$			3.33778i			0.140671i	0.997523	+	0.0703353i	$0.0224069\pi$
$563$			3.33778i			0.140671i	−0.997523	+	0.0703353i	$0.977593\pi$
$564$		0			0
$565$	28.5528			1.20123
$566$	1.90154	−	30.0169i	0.0799277	−	1.26170i
$567$		0			0
$568$	−24.3365	−	4.67519i	−1.02114	−	0.196167i
$569$	9.69455			0.406417			0.203208	−	0.979136i	$-0.434863\pi$
$569$	9.69455			0.406417			0.203208	+	0.979136i	$0.434863\pi$
$570$		0			0
$571$			21.6272i			0.905070i	0.891747	+	0.452535i	$0.149480\pi$
$571$			21.6272i			0.905070i	−0.891747	+	0.452535i	$0.850520\pi$
$572$	−22.0769	−	2.80837i	−0.923082	−	0.117424i
$573$		0			0
$574$	−6.25139	−	0.396020i	−0.260928	−	0.0165295i
$575$			15.8973i			0.662964i
$576$		0			0
$577$	29.6177			1.23300			0.616500	−	0.787355i	$-0.288550\pi$
$577$	29.6177			1.23300			0.616500	+	0.787355i	$0.288550\pi$
$578$	−23.2068	−	1.47013i	−0.965277	−	0.0611494i
$579$		0			0
$580$	2.80207	−	22.0273i	0.116350	−	0.914636i
$581$	37.6308			1.56119
$582$		0			0
$583$		−	24.3888i		−	1.01008i
$584$	5.48189	+	1.05310i	0.226842	+	0.0435777i
$585$		0			0
$586$	−0.889644	+	14.0435i	−0.0367509	+	0.580133i
$587$	19.0897			0.787915			0.393958	−	0.919129i	$-0.371106\pi$
$587$	19.0897			0.787915			0.393958	+	0.919129i	$0.371106\pi$
$588$		0			0
$589$	−7.59123	+	1.82057i	−0.312791	+	0.0750152i
$590$	1.01728	−	16.0583i	0.0418806	−	0.661109i
$591$		0			0
$592$	−38.9966	−	10.0846i	−1.60275	−	0.414475i
$593$		−	5.44767i		−	0.223709i	−0.993725	−	0.111855i	$-0.964321\pi$
$593$		−	5.44767i		−	0.223709i	0.993725	−	0.111855i	$-0.0356791\pi$
$594$		0			0
$595$			3.66858i			0.150397i
$596$	−14.8396	−	1.88773i	−0.607856	−	0.0773245i
$597$		0			0
$598$	2.85532	−	45.0728i	0.116763	−	1.84316i
$599$	−10.2875			−0.420335			−0.210168	−	0.977665i	$-0.567401\pi$
$599$	−10.2875			−0.420335			−0.210168	+	0.977665i	$0.567401\pi$
$600$		0			0
$601$			32.4022i			1.32171i	0.750512	+	0.660856i	$0.229807\pi$
$601$			32.4022i			1.32171i	−0.750512	+	0.660856i	$0.770193\pi$
$602$	2.11987	−	33.4634i	0.0863996	−	1.36387i
$603$		0			0
$604$	5.57871	−	43.8548i	0.226994	−	1.78443i
$605$	−8.40192			−0.341586
$606$		0			0
$607$			10.5492i			0.428181i	0.976814	+	0.214090i	$0.0686787\pi$
$607$			10.5492i			0.428181i	−0.976814	+	0.214090i	$0.931321\pi$
$608$	1.99368	−	24.5769i	0.0808545	−	0.996726i
$609$		0			0
$610$	−1.79806	+	28.3834i	−0.0728014	+	1.14921i
$611$		−	42.0100i		−	1.69954i
$612$		0			0
$613$			36.5980i			1.47818i	0.673607	+	0.739090i	$0.264744\pi$
$613$			36.5980i			1.47818i	−0.673607	+	0.739090i	$0.735256\pi$
$614$	−24.5636	−	1.55608i	−0.991305	−	0.0627982i
$615$		0			0
$616$	20.1096	+	3.86316i	0.810237	+	0.155651i
$617$			15.3512i			0.618017i	0.951059	+	0.309009i	$0.0999972\pi$
$617$			15.3512i			0.618017i	−0.951059	+	0.309009i	$0.900003\pi$
$618$		0			0
$619$		−	27.2625i		−	1.09577i	−0.836553	−	0.547886i	$-0.815433\pi$
$619$		−	27.2625i		−	1.09577i	0.836553	−	0.547886i	$-0.184567\pi$
$620$	−0.745563	+	5.86095i	−0.0299425	+	0.235381i
$621$		0			0
$622$	0.394305	−	6.22433i	0.0158102	−	0.249573i
$623$	23.8145			0.954110
$624$		0			0
$625$	−8.40882			−0.336353
$626$	35.0608	+	2.22107i	1.40131	+	0.0887718i
$627$		0			0
$628$	2.08918	−	16.4233i	0.0833675	−	0.655360i
$629$			7.51810i			0.299766i
$630$		0			0
$631$	12.7290			0.506732			0.253366	−	0.967371i	$-0.418462\pi$
$631$	12.7290			0.506732			0.253366	+	0.967371i	$0.418462\pi$
$632$	−3.74886	+	19.5145i	−0.149121	+	0.776247i
$633$		0			0
$634$	1.17115	−	18.4873i	0.0465124	−	0.734224i
$635$			15.2868i			0.606639i
$636$		0			0
$637$	−8.58218			−0.340038
$638$	−1.46257	+	23.0875i	−0.0579036	+	0.914041i
$639$		0			0
$640$	−16.8614	−	7.99684i	−0.666506	−	0.316103i
$641$	−8.11642			−0.320579			−0.160290	−	0.987070i	$-0.551243\pi$
$641$	−8.11642			−0.320579			−0.160290	+	0.987070i	$0.551243\pi$
$642$		0			0
$643$		−	14.2945i		−	0.563721i	−0.959455	−	0.281861i	$-0.909048\pi$
$643$		−	14.2945i		−	0.563721i	0.959455	−	0.281861i	$-0.0909516\pi$
$644$	−5.24401	+	41.2237i	−0.206643	+	1.62444i
$645$		0			0
$646$	−4.53431	+	0.788223i	−0.178400	+	0.0310122i
$647$		−	22.7305i		−	0.893628i	−0.894627	−	0.446814i	$-0.852559\pi$
$647$		−	22.7305i		−	0.893628i	0.894627	−	0.446814i	$-0.147441\pi$
$648$		0			0
$649$			16.7636i			0.658028i
$650$	−14.7290	−	0.933066i	−0.577718	−	0.0365979i
$651$		0			0
$652$	2.69387	−	21.1768i	0.105500	−	0.829347i
$653$	−25.2711			−0.988935			−0.494468	−	0.869196i	$-0.664637\pi$
$653$	−25.2711			−0.988935			−0.494468	+	0.869196i	$0.664637\pi$
$654$		0			0
$655$	−28.9542			−1.13134
$656$	−5.75791	−	1.48901i	−0.224809	−	0.0581360i
$657$		0			0
$658$	−2.44383	+	38.5772i	−0.0952705	+	1.50390i
$659$		−	44.1809i		−	1.72104i	−0.509415	−	0.860521i	$-0.670138\pi$
$659$		−	44.1809i		−	1.72104i	0.509415	−	0.860521i	$-0.329862\pi$
$660$		0			0
$661$	11.1053			0.431947			0.215973	−	0.976399i	$-0.430708\pi$
$661$	11.1053			0.431947			0.215973	+	0.976399i	$0.430708\pi$
$662$	−44.7660	−	2.83588i	−1.73988	−	0.110220i
$663$		0			0
$664$	35.0872	+	6.74046i	1.36165	+	0.261581i
$665$	−4.99508	−	20.8280i	−0.193701	−	0.807675i
$666$		0			0
$667$	−46.9468			−1.81779
$668$	−16.2070	−	2.06167i	−0.627067	−	0.0797683i
$669$		0			0
$670$	−5.87896	−	0.372427i	−0.227124	−	0.0143881i
$671$		−	29.6300i		−	1.14385i
$672$		0			0
$673$		−	18.3290i		−	0.706531i	−0.935523	−	0.353266i	$-0.885071\pi$
$673$		−	18.3290i		−	0.706531i	0.935523	−	0.353266i	$-0.114929\pi$
$674$	1.30123	−	20.5406i	0.0501215	−	0.791196i
$675$		0			0
$676$	15.8005	+	2.00996i	0.607712	+	0.0773062i
$677$			35.6834i			1.37142i	0.727874	+	0.685711i	$0.240509\pi$
$677$			35.6834i			1.37142i	−0.727874	+	0.685711i	$0.759491\pi$
$678$		0			0
$679$			0.508627i			0.0195193i
$680$	−0.657121	+	3.42062i	−0.0251994	+	0.131175i
$681$		0			0
$682$	0.389154	−	6.14302i	0.0149015	−	0.235228i
$683$		−	20.9162i		−	0.800337i	−0.916442	−	0.400169i	$-0.868952\pi$
$683$		−	20.9162i		−	0.800337i	0.916442	−	0.400169i	$-0.131048\pi$
$684$		0			0
$685$		−	19.3936i		−	0.740993i
$686$	−21.5506	−	1.36521i	−0.822807	−	0.0521240i
$687$		0			0
$688$	7.97058	−	30.8218i	0.303876	−	1.17507i
$689$			45.9483i			1.75049i
$690$		0			0
$691$			16.5019i			0.627763i	0.949462	+	0.313881i	$0.101629\pi$
$691$			16.5019i			0.627763i	−0.949462	+	0.313881i	$0.898371\pi$
$692$	5.65932	−	44.4885i	0.215135	−	1.69120i
$693$		0			0
$694$	−23.3351	−	1.47826i	−0.885788	−	0.0561138i
$695$			5.27148i			0.199958i
$696$		0			0
$697$			1.11006i			0.0420465i
$698$	−2.10478	+	33.2252i	−0.0796672	+	1.25759i
$699$		0			0
$700$	13.4711	+	1.71365i	0.509161	+	0.0647697i
$701$	−32.3479			−1.22176			−0.610881	−	0.791722i	$-0.709185\pi$
$701$	−32.3479			−1.22176			−0.610881	+	0.791722i	$0.709185\pi$
$702$		0			0
$703$	−10.2365	−	42.6832i	−0.386077	−	1.60983i
$704$	18.0584	+	7.20409i	0.680600	+	0.271514i
$705$		0			0
$706$	0.221325	−	3.49374i	0.00832968	−	0.131489i
$707$	17.6141			0.662446
$708$		0			0
$709$		−	13.2883i		−	0.499052i	−0.968368	−	0.249526i	$-0.919725\pi$
$709$		−	13.2883i		−	0.499052i	0.968368	−	0.249526i	$-0.0802748\pi$
$710$	−20.3973	−	1.29215i	−0.765498	−	0.0484936i
$711$		0			0
$712$	22.2049	+	4.26569i	0.832163	+	0.159863i
$713$	12.4914			0.467808
$714$		0			0
$715$	−18.3543			−0.686413
$716$	0.368457	−	2.89648i	0.0137699	−	0.108246i
$717$		0			0
$718$	−1.05129	+	16.5952i	−0.0392338	+	0.619328i
$719$			32.9134i			1.22746i	0.789514	+	0.613732i	$0.210333\pi$
$719$			32.9134i			1.22746i	−0.789514	+	0.613732i	$0.789667\pi$
$720$		0			0
$721$		−	50.3021i		−	1.87335i
$722$	24.6698	−	10.6489i	0.918117	−	0.396311i
$723$		0			0
$724$	−4.23305	−	0.538481i	−0.157320	−	0.0200125i
$725$			15.3414i			0.569764i
$726$		0			0
$727$	−30.5725			−1.13387			−0.566936	−	0.823762i	$-0.691871\pi$
$727$	−30.5725			−1.13387			−0.566936	+	0.823762i	$0.691871\pi$
$728$	−37.8862	−	7.27816i	−1.40416	−	0.269747i
$729$		0			0
$730$	4.59457	+	0.291062i	0.170053	+	0.0107727i
$731$	−5.94209			−0.219776
$732$		0			0
$733$			0.0739768i			0.00273240i	0.999999	+	0.00136620i	$0.000434875\pi$
$733$			0.0739768i			0.00273240i	−0.999999	+	0.00136620i	$0.999565\pi$
$734$	−30.3650	−	1.92360i	−1.12079	−	0.0710012i
$735$		0			0
$736$	−12.2736	+	37.4980i	−0.452410	+	1.38219i
$737$	6.13717			0.226066
$738$		0			0
$739$		−	6.01384i		−	0.221223i	−0.993864	−	0.110611i	$-0.964719\pi$
$739$		−	6.01384i		−	0.221223i	0.993864	−	0.110611i	$-0.0352809\pi$
$740$	−32.9544	−	4.19208i	−1.21143	−	0.154104i
$741$		0			0
$742$	2.67293	−	42.1937i	0.0981264	−	1.54898i
$743$	−11.5289			−0.422956			−0.211478	−	0.977383i	$-0.567828\pi$
$743$	−11.5289			−0.422956			−0.211478	+	0.977383i	$0.567828\pi$
$744$		0			0
$745$	−12.3374			−0.452008
$746$	48.8743	+	3.09614i	1.78941	+	0.113358i
$747$		0			0
$748$	0.457934	−	3.59987i	0.0167437	−	0.131624i
$749$			35.2737i			1.28887i
$750$		0			0
$751$			31.0952i			1.13468i	0.823484	+	0.567339i	$0.192027\pi$
$751$			31.0952i			1.13468i	−0.823484	+	0.567339i	$0.807973\pi$
$752$	−9.18864	+	35.5320i	−0.335075	+	1.29572i
$753$		0			0
$754$	2.75546	−	43.4965i	0.100348	−	1.58405i
$755$		−	36.4601i		−	1.32692i
$756$		0			0
$757$			21.5505i			0.783265i	0.920122	+	0.391633i	$0.128090\pi$
$757$			21.5505i			0.783265i	−0.920122	+	0.391633i	$0.871910\pi$
$758$	−2.78232	−	0.176257i	−0.101058	−	0.00640194i
$759$		0			0
$760$	−0.926721	−	20.3149i	−0.0336157	−	0.736900i
$761$			12.5821i			0.456101i	0.973649	+	0.228050i	$0.0732351\pi$
$761$			12.5821i			0.456101i	−0.973649	+	0.228050i	$0.926765\pi$
$762$		0			0
$763$	23.9707			0.867796
$764$	2.17117	−	17.0678i	0.0785503	−	0.617492i
$765$		0			0
$766$	−12.5048	−	0.792168i	−0.451817	−	0.0286222i
$767$		−	31.5824i		−	1.14037i
$768$		0			0
$769$	−24.3454			−0.877916			−0.438958	−	0.898508i	$-0.644652\pi$
$769$	−24.3454			−0.877916			−0.438958	+	0.898508i	$0.644652\pi$
$770$	16.8545	+	1.06772i	0.607396	+	0.0384779i
$771$		0			0
$772$	−4.82748	+	37.9493i	−0.173745	+	1.36583i
$773$		−	4.76641i		−	0.171436i	−0.996319	−	0.0857180i	$-0.972682\pi$
$773$		−	4.76641i		−	0.171436i	0.996319	−	0.0857180i	$-0.0273184\pi$
$774$		0			0
$775$		−	4.08197i		−	0.146629i
$776$	−0.0911057	+	0.474248i	−0.00327050	+	0.0170245i
$777$		0			0
$778$	−29.0766	−	1.84198i	−1.04245	−	0.0660381i
$779$	−1.51144	−	6.30224i	−0.0541528	−	0.225801i
$780$		0			0
$781$	21.2932			0.761931
$782$	7.34959	+	0.465589i	0.262821	+	0.0166494i
$783$		0			0
$784$	7.25879	+	1.87714i	0.259243	+	0.0670406i
$785$		−	13.6540i		−	0.487333i
$786$		0			0
$787$	−53.5279			−1.90806			−0.954031	−	0.299707i	$-0.903111\pi$
$787$	−53.5279			−1.90806			−0.954031	+	0.299707i	$0.903111\pi$
$788$	24.2774	+	3.08829i	0.864846	+	0.110016i
$789$		0			0
$790$	−1.03613	+	16.3558i	−0.0368637	+	0.581915i
$791$	−51.5672			−1.83352
$792$		0			0
$793$			55.8227i			1.98232i
$794$	1.84331	−	29.0977i	0.0654167	−	1.03264i
$795$		0			0
$796$	−26.6448	−	3.38944i	−0.944399	−	0.120136i
$797$		−	24.7198i		−	0.875619i	−0.899068	−	0.437810i	$-0.855754\pi$
$797$		−	24.7198i		−	0.875619i	0.899068	−	0.437810i	$-0.144246\pi$
$798$		0			0
$799$	6.85016			0.242341
$800$	12.2537	+	4.01078i	0.433232	+	0.141803i
$801$		0			0
$802$	40.7905	+	2.58404i	1.44036	+	0.0912455i
$803$	−4.79637			−0.169260
$804$		0			0
$805$			34.2726i			1.20795i
$806$	−0.733163	+	11.5734i	−0.0258246	+	0.407655i
$807$		0			0
$808$	16.4235	+	3.15505i	0.577778	+	0.110994i
$809$		−	23.2380i		−	0.817003i	−0.912758	−	0.408501i	$-0.866051\pi$
$809$		−	23.2380i		−	0.817003i	0.912758	−	0.408501i	$-0.133949\pi$
$810$		0			0
$811$	−20.5201			−0.720557			−0.360278	−	0.932845i	$-0.617318\pi$
$811$	−20.5201			−0.720557			−0.360278	+	0.932845i	$0.617318\pi$
$812$	−5.06061	+	39.7820i	−0.177593	+	1.39608i
$813$		0			0
$814$	34.5404	+	2.18810i	1.21064	+	0.0766928i
$815$		−	17.6060i		−	0.616711i
$816$		0			0
$817$	33.7356	−	8.09064i	1.18026	−	0.283056i
$818$	−3.23445	+	51.0575i	−0.113090	+	1.78518i
$819$		0			0
$820$	−4.86576	−	0.618967i	−0.169920	−	0.0216153i
$821$	25.3720			0.885488			0.442744	−	0.896648i	$-0.354005\pi$
$821$	25.3720			0.885488			0.442744	+	0.896648i	$0.354005\pi$
$822$		0			0
$823$	18.2321			0.635529			0.317765	−	0.948170i	$-0.397068\pi$
$823$	18.2321			0.635529			0.317765	+	0.948170i	$0.397068\pi$
$824$	9.01017	−	46.9021i	0.313884	−	1.63391i
$825$		0			0
$826$	−1.83723	+	29.0017i	−0.0639254	+	1.00910i
$827$		−	49.3209i		−	1.71506i	−0.514437	−	0.857528i	$-0.671999\pi$
$827$		−	49.3209i		−	1.71506i	0.514437	−	0.857528i	$-0.328001\pi$
$828$		0			0
$829$	23.6567			0.821631			0.410815	−	0.911719i	$-0.365244\pi$
$829$	23.6567			0.821631			0.410815	+	0.911719i	$0.365244\pi$
$830$	29.4079	+	1.86296i	1.02076	+	0.0646643i
$831$		0			0
$832$	−34.0218	−	13.5724i	−1.17949	−	0.470540i
$833$		−	1.39941i		−	0.0484868i
$834$		0			0
$835$	−13.4742			−0.466293
$836$	2.30164	+	21.0614i	0.0796039	+	0.728422i
$837$		0			0
$838$	18.7573	+	1.18826i	0.647961	+	0.0410477i
$839$	25.3598			0.875517			0.437758	−	0.899093i	$-0.355773\pi$
$839$	25.3598			0.875517			0.437758	+	0.899093i	$0.355773\pi$
$840$		0			0
$841$	−16.3050			−0.562242
$842$	31.9647	+	2.02493i	1.10158	+	0.0697838i
$843$		0			0
$844$	15.6901	+	1.99592i	0.540077	+	0.0687024i
$845$	13.1363			0.451901
$846$		0			0
$847$	15.1741			0.521388
$848$	10.0500	−	38.8630i	0.345120	−	1.33456i
$849$		0			0
$850$	0.152146	−	2.40171i	0.00521857	−	0.0823780i
$851$			70.2356i			2.40764i
$852$		0			0
$853$		−	28.4959i		−	0.975682i	−0.872933	−	0.487841i	$-0.837785\pi$
$853$		−	28.4959i		−	0.975682i	0.872933	−	0.487841i	$-0.162215\pi$
$854$	3.24735	−	51.2612i	0.111122	−	1.75412i
$855$		0			0
$856$	−6.31826	+	32.8895i	−0.215954	+	1.12414i
$857$	3.20130			0.109354			0.0546772	−	0.998504i	$-0.482587\pi$
$857$	3.20130			0.109354			0.0546772	+	0.998504i	$0.482587\pi$
$858$		0			0
$859$		−	22.5083i		−	0.767974i	−0.923339	−	0.383987i	$-0.874551\pi$
$859$		−	22.5083i		−	0.767974i	0.923339	−	0.383987i	$-0.125449\pi$
$860$	3.31330	−	26.0462i	0.112983	−	0.888167i
$861$		0			0
$862$	7.52642	+	0.476791i	0.256351	+	0.0162396i
$863$	−49.8505			−1.69693			−0.848465	−	0.529252i	$-0.822473\pi$
$863$	−49.8505			−1.69693			−0.848465	+	0.529252i	$0.822473\pi$
$864$		0			0
$865$		−	36.9869i		−	1.25759i
$866$	−2.19027	+	34.5746i	−0.0744282	+	1.17489i
$867$		0			0
$868$	1.34651	−	10.5850i	0.0457035	−	0.359280i
$869$		−	17.0742i		−	0.579203i
$870$		0			0
$871$	−11.5624			−0.391776
$872$	22.3504	+	4.29365i	0.756882	+	0.145401i
$873$		0			0
$874$	−42.3604	+	7.36373i	−1.43286	+	0.249082i
$875$	35.7685			1.20920
$876$		0			0
$877$	9.97659			0.336885			0.168443	−	0.985711i	$-0.446126\pi$
$877$	9.97659			0.336885			0.168443	+	0.985711i	$0.446126\pi$
$878$	1.60032	−	25.2620i	0.0540082	−	0.852550i
$879$		0			0
$880$	15.5241	+	4.01455i	0.523316	+	0.135331i
$881$		−	44.7298i		−	1.50698i	−0.657457	−	0.753492i	$-0.728368\pi$
$881$		−	44.7298i		−	1.50698i	0.657457	−	0.753492i	$-0.271632\pi$
$882$		0			0
$883$		−	2.15295i		−	0.0724525i	−0.999344	−	0.0362262i	$-0.988466\pi$
$883$		−	2.15295i		−	0.0724525i	0.999344	−	0.0362262i	$-0.0115337\pi$
$884$	−0.862743	+	6.78211i	−0.0290172	+	0.228107i
$885$		0			0
$886$	18.9513	+	1.20054i	0.636680	+	0.0403331i
$887$	25.9273			0.870553			0.435277	−	0.900297i	$-0.356651\pi$
$887$	25.9273			0.870553			0.435277	+	0.900297i	$0.356651\pi$
$888$		0			0
$889$		−	27.6084i		−	0.925957i
$890$	18.6107	+	1.17897i	0.623832	+	0.0395192i
$891$		0			0
$892$	0.468851	−	3.68569i	0.0156983	−	0.123406i
$893$	−38.8911	+	9.32705i	−1.30144	+	0.312118i
$894$		0			0
$895$		−	2.40808i		−	0.0804932i
$896$	30.4522	+	14.4425i	1.01734	+	0.482491i
$897$		0			0
$898$	17.1674	+	1.08754i	0.572882	+	0.0362915i
$899$	12.0546			0.402043
$900$		0			0
$901$	−7.49234			−0.249606
$902$	5.09994	+	0.323076i	0.169809	+	0.0107573i
$903$		0			0
$904$	−48.0817	−	9.23677i	−1.59917	−	0.307211i
$905$	−3.51928			−0.116985
$906$		0			0
$907$	−39.9517			−1.32657			−0.663287	−	0.748365i	$-0.730839\pi$
$907$	−39.9517			−1.32657			−0.663287	+	0.748365i	$0.730839\pi$
$908$	−2.01979	+	15.8778i	−0.0670292	+	0.526923i
$909$		0			0
$910$	−31.7538	−	2.01157i	−1.05263	−	0.0666830i
$911$	−15.9066			−0.527010			−0.263505	−	0.964658i	$-0.584879\pi$
$911$	−15.9066			−0.527010			−0.263505	+	0.964658i	$0.584879\pi$
$912$		0			0
$913$	−30.6995			−1.01601
$914$	−38.1318	−	2.41561i	−1.26129	−	0.0799014i
$915$		0			0
$916$	−4.62972	+	36.3947i	−0.152970	+	1.20252i
$917$	52.2922			1.72684
$918$		0			0
$919$	24.6685			0.813739			0.406870	−	0.913486i	$-0.366620\pi$
$919$	24.6685			0.813739			0.406870	+	0.913486i	$0.366620\pi$
$920$	−6.13895	+	31.9561i	−0.202395	+	1.05356i
$921$		0			0
$922$	14.2442	+	0.902355i	0.469107	+	0.0297175i
$923$	−40.1162			−1.32044
$924$		0			0
$925$	22.9517			0.754647
$926$	−20.3854	−	1.29139i	−0.669905	−	0.0424378i
$927$		0			0
$928$	−11.8444	+	36.1866i	−0.388810	+	1.18788i
$929$		−	7.99237i		−	0.262221i	−0.991368	−	0.131111i	$-0.958146\pi$
$929$		−	7.99237i		−	0.262221i	0.991368	−	0.131111i	$-0.0418543\pi$
$930$		0			0
$931$	1.90541	+	7.94501i	0.0624474	+	0.260387i
$932$	−0.150066	+	1.17969i	−0.00491559	+	0.0386420i
$933$		0			0
$934$	−48.6446	−	3.08159i	−1.59170	−	0.100833i
$935$		−	2.99286i		−	0.0978771i
$936$		0			0
$937$	−47.0029			−1.53552			−0.767759	−	0.640738i	$-0.778628\pi$
$937$	−47.0029			−1.53552			−0.767759	+	0.640738i	$0.778628\pi$
$938$	10.6176	+	0.672613i	0.346676	+	0.0219616i
$939$		0			0
$940$	−3.81964	+	30.0265i	−0.124583	+	0.979358i
$941$		−	0.0556189i		−	0.00181312i	−1.00000		0.000906562i	$-0.999711\pi$
$941$		−	0.0556189i		−	0.00181312i	1.00000		0.000906562i	$-0.000288568\pi$
$942$		0			0
$943$			10.3704i			0.337706i
$944$	−6.90786	+	26.7124i	−0.224832	+	0.869413i
$945$		0			0
$946$	−1.72941	+	27.2997i	−0.0562280	+	0.887590i
$947$	16.4564			0.534760			0.267380	−	0.963591i	$-0.413842\pi$
$947$	16.4564			0.534760			0.267380	+	0.963591i	$0.413842\pi$
$948$		0			0
$949$	9.03632			0.293331
$950$	2.40633	+	13.8426i	0.0780717	+	0.449114i
$951$		0			0
$952$	1.18678	−	6.17774i	0.0384637	−	0.200222i
$953$	−0.871117			−0.0282183			−0.0141091	−	0.999900i	$-0.504491\pi$
$953$	−0.871117			−0.0282183			−0.0141091	+	0.999900i	$0.504491\pi$
$954$		0			0
$955$		−	14.1899i		−	0.459173i
$956$	0.982915	−	7.72680i	0.0317897	−	0.249903i
$957$		0			0
$958$	−0.942831	+	14.8831i	−0.0304615	+	0.480851i
$959$			35.0255i			1.13103i
$960$		0			0
$961$	27.7926			0.896534
$962$	−65.0737	−	4.12236i	−2.09806	−	0.132910i
$963$		0			0
$964$	−6.05101	+	47.5676i	−0.194890	+	1.53205i
$965$			31.5504i			1.01564i
$966$		0			0
$967$	13.5154			0.434626			0.217313	−	0.976102i	$-0.430271\pi$
$967$	13.5154			0.434626			0.217313	+	0.976102i	$0.430271\pi$
$968$	14.1485	+	2.71800i	0.454749	+	0.0873598i
$969$		0			0
$970$	−0.0251802	+	0.397484i	−0.000808489	+	0.0127624i
$971$			1.13624i			0.0364637i	0.999834	+	0.0182319i	$0.00580370\pi$
$971$			1.13624i			0.0364637i	−0.999834	+	0.0182319i	$0.994196\pi$
$972$		0			0
$973$		−	9.52044i		−	0.305211i
$974$	2.53834	−	40.0691i	0.0813335	−	1.28390i
$975$		0			0
$976$	12.2098	−	47.2147i	0.390827	−	1.51131i
$977$	41.5063			1.32790			0.663952	−	0.747775i	$-0.268878\pi$
$977$	41.5063			1.32790			0.663952	+	0.747775i	$0.268878\pi$
$978$		0			0
$979$	−19.4281			−0.620925
$980$	6.13409	+	0.780309i	0.195946	+	0.0249261i
$981$		0			0
$982$	−37.8901	−	2.40030i	−1.20912	−	0.0765967i
$983$	−53.3934			−1.70298			−0.851492	−	0.524368i	$-0.824302\pi$
$983$	−53.3934			−1.70298			−0.851492	+	0.524368i	$0.824302\pi$
$984$		0			0
$985$	20.1838			0.643108
$986$	7.09256	+	0.449307i	0.225873	+	0.0143088i
$987$		0			0
$988$	−4.33627	−	39.6794i	−0.137955	−	1.26237i
$989$	−55.5122			−1.76518
$990$		0			0
$991$		−	45.2236i		−	1.43657i	−0.695747	−	0.718287i	$-0.744926\pi$
$991$		−	45.2236i		−	1.43657i	0.695747	−	0.718287i	$-0.255074\pi$
$992$	3.15150	−	9.62839i	0.100060	−	0.305702i
$993$		0			0
$994$	36.8382	+	2.33366i	1.16844	+	0.0740193i
$995$	−22.1520			−0.702265
$996$		0			0
$997$			42.8940i			1.35847i	0.733922	+	0.679233i	$0.237688\pi$
$997$			42.8940i			1.35847i	−0.733922	+	0.679233i	$0.762312\pi$
$998$	1.26987	−	20.0456i	0.0401970	−	0.634532i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.p.a.341.2	yes	80
3.2	odd	2	inner	1368.2.p.a.341.79	yes	80
4.3	odd	2		5472.2.p.a.3761.53		80
8.3	odd	2		5472.2.p.a.3761.27		80
8.5	even	2	inner	1368.2.p.a.341.3	yes	80
12.11	even	2		5472.2.p.a.3761.25		80
19.18	odd	2	inner	1368.2.p.a.341.80	yes	80
24.5	odd	2	inner	1368.2.p.a.341.78	yes	80
24.11	even	2		5472.2.p.a.3761.55		80
57.56	even	2	inner	1368.2.p.a.341.1	✓	80
76.75	even	2		5472.2.p.a.3761.54		80
152.37	odd	2	inner	1368.2.p.a.341.77	yes	80
152.75	even	2		5472.2.p.a.3761.28		80
228.227	odd	2		5472.2.p.a.3761.26		80
456.227	odd	2		5472.2.p.a.3761.56		80
456.341	even	2	inner	1368.2.p.a.341.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.p.a.341.1	✓	80	57.56	even	2	inner
1368.2.p.a.341.2	yes	80	1.1	even	1	trivial
1368.2.p.a.341.3	yes	80	8.5	even	2	inner
1368.2.p.a.341.4	yes	80	456.341	even	2	inner
1368.2.p.a.341.77	yes	80	152.37	odd	2	inner
1368.2.p.a.341.78	yes	80	24.5	odd	2	inner
1368.2.p.a.341.79	yes	80	3.2	odd	2	inner
1368.2.p.a.341.80	yes	80	19.18	odd	2	inner
5472.2.p.a.3761.25		80	12.11	even	2
5472.2.p.a.3761.26		80	228.227	odd	2
5472.2.p.a.3761.27		80	8.3	odd	2
5472.2.p.a.3761.28		80	152.75	even	2
5472.2.p.a.3761.53		80	4.3	odd	2
5472.2.p.a.3761.54		80	76.75	even	2
5472.2.p.a.3761.55		80	24.11	even	2
5472.2.p.a.3761.56		80	456.227	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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41138 - 0.0894099i) q^{2} +(1.98401 + 0.252383i) q^{4} +1.64947 q^{5} -2.97899 q^{7} +(-2.77764 - 0.533600i) q^{8} +O(q^{10})\)	\(q+(-1.41138 - 0.0894099i) q^{2} +(1.98401 + 0.252383i) q^{4} +1.64947 q^{5} -2.97899 q^{7} +(-2.77764 - 0.533600i) q^{8} +(-2.32804 - 0.147479i) q^{10} +2.43029 q^{11} -4.57864 q^{13} +(4.20450 + 0.266351i) q^{14} +(3.87261 + 1.00146i) q^{16} -0.746594i q^{17} +(1.01655 + 4.23871i) q^{19} +(3.27257 + 0.416299i) q^{20} +(-3.43007 - 0.217292i) q^{22} -6.97482i q^{23} -2.27924 q^{25} +(6.46222 + 0.409375i) q^{26} +(-5.91036 - 0.751848i) q^{28} -6.73090i q^{29} +1.79093i q^{31} +(-5.37619 - 1.75970i) q^{32} +(-0.0667528 + 1.05373i) q^{34} -4.91376 q^{35} -10.0699 q^{37} +(-1.05576 - 6.07333i) q^{38} +(-4.58163 - 0.880158i) q^{40} -1.48683 q^{41} -7.95894i q^{43} +(4.82172 + 0.613364i) q^{44} +(-0.623618 + 9.84416i) q^{46} +9.17522i q^{47} +1.87440 q^{49} +(3.21689 + 0.203787i) q^{50} +(-9.08407 - 1.15557i) q^{52} -10.0354i q^{53} +4.00869 q^{55} +(8.27456 + 1.58959i) q^{56} +(-0.601809 + 9.49989i) q^{58} +6.89777i q^{59} -12.1920i q^{61} +(0.160127 - 2.52769i) q^{62} +(7.43054 + 2.96430i) q^{64} -7.55233 q^{65} +2.52529 q^{67} +(0.188428 - 1.48125i) q^{68} +(6.93521 + 0.439339i) q^{70} +8.76160 q^{71} -1.97358 q^{73} +(14.2125 + 0.900346i) q^{74} +(0.947065 + 8.66620i) q^{76} -7.23981 q^{77} -7.02559i q^{79} +(6.38775 + 1.65188i) q^{80} +(2.09849 + 0.132937i) q^{82} -12.6320 q^{83} -1.23148i q^{85} +(-0.711607 + 11.2331i) q^{86} +(-6.75046 - 1.29680i) q^{88} -7.99416 q^{89} +13.6397 q^{91} +(1.76033 - 13.8381i) q^{92} +(0.820355 - 12.9498i) q^{94} +(1.67677 + 6.99162i) q^{95} -0.170738i q^{97} +(-2.64549 - 0.167589i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{4}+O(q^{10}) \) 80 * q + 8 * q^4	\( 80 q + 8 q^{4} + 8 q^{16} + 80 q^{25} + 48 q^{49} - 16 q^{58} + 8 q^{64} + 32 q^{73} + 72 q^{76} - 16 q^{82}+O(q^{100}) \) 80 * q + 8 * q^4 + 8 * q^16 + 80 * q^25 + 48 * q^49 - 16 * q^58 + 8 * q^64 + 32 * q^73 + 72 * q^76 - 16 * q^82

Introduction

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