LMFDB - Embedded newform 1161.2.f.d.775.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1161,2,Mod(388,1161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1161, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1161.388");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1161 = 3^{3} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1161.f (of order $3$, degree $2$, not 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:	$9.27063167467$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 387)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			775.17
Character	$\chi$	$=$	1161.775
Dual form			1161.2.f.d.388.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.911404 - 1.57860i) q^{2} +(-0.661315 - 1.14543i) q^{4} +(-0.216442 - 0.374888i) q^{5} +(0.345529 - 0.598473i) q^{7} +1.23472 q^{8} +O(q^{10})$	\(q+(0.911404 - 1.57860i) q^{2} +(-0.661315 - 1.14543i) q^{4} +(-0.216442 - 0.374888i) q^{5} +(0.345529 - 0.598473i) q^{7} +1.23472 q^{8} -0.789063 q^{10} +(1.26780 - 2.19589i) q^{11} +(3.60136 + 6.23773i) q^{13} +(-0.629833 - 1.09090i) q^{14} +(2.44795 - 4.23998i) q^{16} -4.46895 q^{17} +6.05843 q^{19} +(-0.286272 + 0.495838i) q^{20} +(-2.31095 - 4.00268i) q^{22} +(-2.05578 - 3.56072i) q^{23} +(2.40631 - 4.16784i) q^{25} +13.1292 q^{26} -0.914014 q^{28} +(3.23074 - 5.59581i) q^{29} +(1.26948 + 2.19881i) q^{31} +(-3.22744 - 5.59009i) q^{32} +(-4.07302 + 7.05468i) q^{34} -0.299147 q^{35} -9.14340 q^{37} +(5.52168 - 9.56383i) q^{38} +(-0.267244 - 0.462880i) q^{40} +(0.455380 + 0.788741i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.35365 q^{44} -7.49459 q^{46} +(-4.79713 + 8.30887i) q^{47} +(3.26122 + 5.64860i) q^{49} +(-4.38623 - 7.59718i) q^{50} +(4.76326 - 8.25022i) q^{52} +8.85806 q^{53} -1.09761 q^{55} +(0.426630 - 0.738944i) q^{56} +(-5.88902 - 10.2001i) q^{58} +(-6.51130 - 11.2779i) q^{59} +(-0.396746 + 0.687184i) q^{61} +4.62805 q^{62} -1.97418 q^{64} +(1.55897 - 2.70021i) q^{65} +(-5.69986 - 9.87245i) q^{67} +(2.95539 + 5.11888i) q^{68} +(-0.272644 + 0.472233i) q^{70} +13.2707 q^{71} -4.01445 q^{73} +(-8.33334 + 14.4338i) q^{74} +(-4.00653 - 6.93952i) q^{76} +(-0.876120 - 1.51748i) q^{77} +(5.94290 - 10.2934i) q^{79} -2.11936 q^{80} +1.66014 q^{82} +(-4.88090 + 8.45396i) q^{83} +(0.967268 + 1.67536i) q^{85} +(-0.911404 - 1.57860i) q^{86} +(1.56537 - 2.71129i) q^{88} -8.04947 q^{89} +4.97749 q^{91} +(-2.71904 + 4.70951i) q^{92} +(8.74425 + 15.1455i) q^{94} +(-1.31130 - 2.27123i) q^{95} +(-7.49445 + 12.9808i) q^{97} +11.8892 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8}+O(q^{10}) $ 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8	$ 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8} - 4 q^{10} - 10 q^{11} + q^{13} - 10 q^{14} - 22 q^{16} + 40 q^{17} + 16 q^{19} - 30 q^{20} - 15 q^{22} - 19 q^{23} - 19 q^{25} + 50 q^{26} - 6 q^{28} - 25 q^{29} + 11 q^{31} - 36 q^{32} - 9 q^{34} + 18 q^{37} - 28 q^{38} - 12 q^{40} - 12 q^{41} + 20 q^{43} + 10 q^{44} + 8 q^{46} - 38 q^{47} - 37 q^{49} - 36 q^{50} + 8 q^{52} + 138 q^{53} - 18 q^{55} - 30 q^{56} + 27 q^{58} - 31 q^{59} - 19 q^{61} + 64 q^{62} + 22 q^{64} - 47 q^{65} - 9 q^{67} - 68 q^{68} + 6 q^{70} + 42 q^{71} - 4 q^{73} + 16 q^{74} - 37 q^{76} - 85 q^{77} + 4 q^{79} + 122 q^{80} + 2 q^{82} - 19 q^{83} + 6 q^{85} + 6 q^{86} - 60 q^{88} + 108 q^{89} - 6 q^{91} - 85 q^{92} + 19 q^{94} + 11 q^{95} - 2 q^{97} + 10 q^{98}+O(q^{100}) $ 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8 - 4 * q^10 - 10 * q^11 + q^13 - 10 * q^14 - 22 * q^16 + 40 * q^17 + 16 * q^19 - 30 * q^20 - 15 * q^22 - 19 * q^23 - 19 * q^25 + 50 * q^26 - 6 * q^28 - 25 * q^29 + 11 * q^31 - 36 * q^32 - 9 * q^34 + 18 * q^37 - 28 * q^38 - 12 * q^40 - 12 * q^41 + 20 * q^43 + 10 * q^44 + 8 * q^46 - 38 * q^47 - 37 * q^49 - 36 * q^50 + 8 * q^52 + 138 * q^53 - 18 * q^55 - 30 * q^56 + 27 * q^58 - 31 * q^59 - 19 * q^61 + 64 * q^62 + 22 * q^64 - 47 * q^65 - 9 * q^67 - 68 * q^68 + 6 * q^70 + 42 * q^71 - 4 * q^73 + 16 * q^74 - 37 * q^76 - 85 * q^77 + 4 * q^79 + 122 * q^80 + 2 * q^82 - 19 * q^83 + 6 * q^85 + 6 * q^86 - 60 * q^88 + 108 * q^89 - 6 * q^91 - 85 * q^92 + 19 * q^94 + 11 * q^95 - 2 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1161\mathbb{Z}\right)^\times$.

$n$	$433$	$947$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.911404	−	1.57860i	0.644460	−	1.11624i	−0.339966	−	0.940438i	$-0.610416\pi$
$2$	0.911404	−	1.57860i	0.644460	−	1.11624i	0.984426	−	0.175800i	$-0.0562511\pi$
$3$		0			0
$3$		0			0
$4$	−0.661315	−	1.14543i	−0.330658	−	0.572716i
$5$	−0.216442	−	0.374888i	−0.0967957	−	0.167655i	0.813561	−	0.581480i	$-0.197526\pi$
$5$	−0.216442	−	0.374888i	−0.0967957	−	0.167655i	−0.910357	+	0.413825i	$0.864193\pi$
$6$		0			0
$7$	0.345529	−	0.598473i	0.130598	−	0.226202i	−0.793309	−	0.608819i	$-0.791644\pi$
$7$	0.345529	−	0.598473i	0.130598	−	0.226202i	0.923907	+	0.382617i	$0.124977\pi$
$8$	1.23472			0.436538
$9$		0			0
$10$	−0.789063			−0.249524
$11$	1.26780	−	2.19589i	0.382255	−	0.662084i	−0.609130	−	0.793071i	$-0.708481\pi$
$11$	1.26780	−	2.19589i	0.382255	−	0.662084i	0.991384	+	0.130986i	$0.0418144\pi$
$12$		0			0
$13$	3.60136	+	6.23773i	0.998837	+	1.73004i	0.541176	+	0.840909i	$0.317979\pi$
$13$	3.60136	+	6.23773i	0.998837	+	1.73004i	0.457661	+	0.889127i	$0.348687\pi$
$14$	−0.629833	−	1.09090i	−0.168330	−	0.291556i
$15$		0			0
$16$	2.44795	−	4.23998i	0.611989	−	1.06000i
$17$	−4.46895			−1.08388			−0.541940	−	0.840417i	$-0.682310\pi$
$17$	−4.46895			−1.08388			−0.541940	+	0.840417i	$0.682310\pi$
$18$		0			0
$19$	6.05843			1.38990			0.694950	−	0.719058i	$-0.255427\pi$
$19$	6.05843			1.38990			0.694950	+	0.719058i	$0.255427\pi$
$20$	−0.286272	+	0.495838i	−0.0640124	+	0.110873i
$21$		0			0
$22$	−2.31095	−	4.00268i	−0.492696	−	0.853374i
$23$	−2.05578	−	3.56072i	−0.428660	−	0.742460i	0.568095	−	0.822963i	$-0.307681\pi$
$23$	−2.05578	−	3.56072i	−0.428660	−	0.742460i	−0.996754	+	0.0805028i	$0.974347\pi$
$24$		0			0
$25$	2.40631	−	4.16784i	0.481261	−	0.833569i
$26$	13.1292			2.57484
$27$		0			0
$28$	−0.914014			−0.172732
$29$	3.23074	−	5.59581i	0.599933	−	1.03912i	−0.392897	−	0.919583i	$-0.628527\pi$
$29$	3.23074	−	5.59581i	0.599933	−	1.03912i	0.992830	−	0.119533i	$-0.0381396\pi$
$30$		0			0
$31$	1.26948	+	2.19881i	0.228006	+	0.394918i	0.957217	−	0.289371i	$-0.0934461\pi$
$31$	1.26948	+	2.19881i	0.228006	+	0.394918i	−0.729211	+	0.684289i	$0.760113\pi$
$32$	−3.22744	−	5.59009i	−0.570536	−	0.988197i
$33$		0			0
$34$	−4.07302	+	7.05468i	−0.698518	+	1.20987i
$35$	−0.299147			−0.0505651
$36$		0			0
$37$	−9.14340			−1.50317			−0.751583	−	0.659638i	$-0.770709\pi$
$37$	−9.14340			−1.50317			−0.751583	+	0.659638i	$0.770709\pi$
$38$	5.52168	−	9.56383i	0.895735	−	1.55146i
$39$		0			0
$40$	−0.267244	−	0.462880i	−0.0422550	−	0.0731877i
$41$	0.455380	+	0.788741i	0.0711184	+	0.123181i	0.899392	−	0.437144i	$-0.144010\pi$
$41$	0.455380	+	0.788741i	0.0711184	+	0.123181i	−0.828273	+	0.560324i	$0.810677\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i
$44$	−3.35365			−0.505582
$45$		0			0
$46$	−7.49459			−1.10502
$47$	−4.79713	+	8.30887i	−0.699733	+	1.21197i	0.268826	+	0.963189i	$0.413364\pi$
$47$	−4.79713	+	8.30887i	−0.699733	+	1.21197i	−0.968559	+	0.248785i	$0.919969\pi$
$48$		0			0
$49$	3.26122	+	5.64860i	0.465889	+	0.806943i
$50$	−4.38623	−	7.59718i	−0.620307	−	1.07440i
$51$		0			0
$52$	4.76326	−	8.25022i	0.660546	−	1.14410i
$53$	8.85806			1.21675			0.608374	−	0.793650i	$-0.291822\pi$
$53$	8.85806			1.21675			0.608374	+	0.793650i	$0.291822\pi$
$54$		0			0
$55$	−1.09761			−0.148002
$56$	0.426630	−	0.738944i	0.0570108	−	0.0987456i
$57$		0			0
$58$	−5.88902	−	10.2001i	−0.773266	−	1.33934i
$59$	−6.51130	−	11.2779i	−0.847699	−	1.46826i	−0.883257	−	0.468890i	$-0.844654\pi$
$59$	−6.51130	−	11.2779i	−0.847699	−	1.46826i	0.0355576	−	0.999368i	$-0.488679\pi$
$60$		0			0
$61$	−0.396746	+	0.687184i	−0.0507981	+	0.0879849i	−0.890306	−	0.455362i	$-0.849510\pi$
$61$	−0.396746	+	0.687184i	−0.0507981	+	0.0879849i	0.839508	+	0.543347i	$0.182843\pi$
$62$	4.62805			0.587763
$63$		0			0
$64$	−1.97418			−0.246772
$65$	1.55897	−	2.70021i	0.193366	−	0.334920i
$66$		0			0
$67$	−5.69986	−	9.87245i	−0.696349	−	1.20611i	−0.969724	−	0.244204i	$-0.921473\pi$
$67$	−5.69986	−	9.87245i	−0.696349	−	1.20611i	0.273375	−	0.961908i	$-0.411860\pi$
$68$	2.95539	+	5.11888i	0.358393	+	0.620755i
$69$		0			0
$70$	−0.272644	+	0.472233i	−0.0325872	+	0.0564427i
$71$	13.2707			1.57495			0.787473	−	0.616349i	$-0.211389\pi$
$71$	13.2707			1.57495			0.787473	+	0.616349i	$0.211389\pi$
$72$		0			0
$73$	−4.01445			−0.469856			−0.234928	−	0.972013i	$-0.575485\pi$
$73$	−4.01445			−0.469856			−0.234928	+	0.972013i	$0.575485\pi$
$74$	−8.33334	+	14.4338i	−0.968731	+	1.67789i
$75$		0			0
$76$	−4.00653	−	6.93952i	−0.459581	−	0.796017i
$77$	−0.876120	−	1.51748i	−0.0998431	−	0.172933i
$78$		0			0
$79$	5.94290	−	10.2934i	0.668628	−	1.15810i	−0.309659	−	0.950848i	$-0.600215\pi$
$79$	5.94290	−	10.2934i	0.668628	−	1.15810i	0.978288	−	0.207251i	$-0.0664516\pi$
$80$	−2.11936			−0.236951
$81$		0			0
$82$	1.66014			0.183332
$83$	−4.88090	+	8.45396i	−0.535748	+	0.927943i	0.463379	+	0.886160i	$0.346637\pi$
$83$	−4.88090	+	8.45396i	−0.535748	+	0.927943i	−0.999127	+	0.0417825i	$0.986696\pi$
$84$		0			0
$85$	0.967268	+	1.67536i	0.104915	+	0.181718i
$86$	−0.911404	−	1.57860i	−0.0982792	−	0.170225i
$87$		0			0
$88$	1.56537	−	2.71129i	0.166869	−	0.289025i
$89$	−8.04947			−0.853242			−0.426621	−	0.904431i	$-0.640296\pi$
$89$	−8.04947			−0.853242			−0.426621	+	0.904431i	$0.640296\pi$
$90$		0			0
$91$	4.97749			0.521783
$92$	−2.71904	+	4.70951i	−0.283479	+	0.491000i
$93$		0			0
$94$	8.74425	+	15.1455i	0.901900	+	1.56214i
$95$	−1.31130	−	2.27123i	−0.134536	−	0.233024i
$96$		0			0
$97$	−7.49445	+	12.9808i	−0.760947	+	1.31800i	0.181417	+	0.983406i	$0.441932\pi$
$97$	−7.49445	+	12.9808i	−0.760947	+	1.31800i	−0.942363	+	0.334592i	$0.891402\pi$
$98$	11.8892			1.20099
$99$		0			0
$100$	−6.36531			−0.636531
$101$	−1.55310	+	2.69005i	−0.154539	+	0.267670i	−0.932891	−	0.360159i	$-0.882723\pi$
$101$	−1.55310	+	2.69005i	−0.154539	+	0.267670i	0.778352	+	0.627828i	$0.216056\pi$
$102$		0			0
$103$	−3.48129	−	6.02977i	−0.343022	−	0.594131i	0.641970	−	0.766729i	$-0.278117\pi$
$103$	−3.48129	−	6.02977i	−0.343022	−	0.594131i	−0.984992	+	0.172598i	$0.944784\pi$
$104$	4.44665	+	7.70183i	0.436030	+	0.755226i
$105$		0			0
$106$	8.07328	−	13.9833i	0.784146	−	1.35818i
$107$	−8.10561			−0.783599			−0.391800	−	0.920051i	$-0.628147\pi$
$107$	−8.10561			−0.783599			−0.391800	+	0.920051i	$0.628147\pi$
$108$		0			0
$109$	−0.0751888			−0.00720178			−0.00360089	−	0.999994i	$-0.501146\pi$
$109$	−0.0751888			−0.00720178			−0.00360089	+	0.999994i	$0.501146\pi$
$110$	−1.00037	+	1.73269i	−0.0953816	+	0.165206i
$111$		0			0
$112$	−1.69168	−	2.93007i	−0.159849	−	0.276866i
$113$	3.84430	+	6.65852i	0.361641	+	0.626380i	0.988231	−	0.152969i	$-0.0488833\pi$
$113$	3.84430	+	6.65852i	0.361641	+	0.626380i	−0.626590	+	0.779349i	$0.715550\pi$
$114$		0			0
$115$	−0.889913	+	1.54137i	−0.0829848	+	0.143734i
$116$	−8.54615			−0.793490
$117$		0			0
$118$	−23.7377			−2.18523
$119$	−1.54415	+	2.67455i	−0.141552	+	0.245176i
$120$		0			0
$121$	2.28539	+	3.95841i	0.207763	+	0.359856i
$122$	0.723192	+	1.25260i	0.0654747	+	0.113405i
$123$		0			0
$124$	1.67906	−	2.90821i	0.150784	−	0.261165i
$125$	−4.24772			−0.379927
$126$		0			0
$127$	0.411999			0.0365590			0.0182795	−	0.999833i	$-0.494181\pi$
$127$	0.411999			0.0365590			0.0182795	+	0.999833i	$0.494181\pi$
$128$	4.65560	−	8.06373i	0.411501	−	0.712740i
$129$		0			0
$130$	−2.84170	−	4.92197i	−0.249234	−	0.431685i
$131$	1.51555	+	2.62501i	0.132414	+	0.229348i	0.924607	−	0.380923i	$-0.124394\pi$
$131$	1.51555	+	2.62501i	0.132414	+	0.229348i	−0.792193	+	0.610271i	$0.791060\pi$
$132$		0			0
$133$	2.09336	−	3.62581i	0.181518	−	0.314398i
$134$	−20.7795			−1.79508
$135$		0			0
$136$	−5.51788			−0.473155
$137$	−5.34442	+	9.25680i	−0.456604	+	0.790862i	−0.998779	−	0.0494039i	$-0.984268\pi$
$137$	−5.34442	+	9.25680i	−0.456604	+	0.790862i	0.542174	+	0.840266i	$0.317601\pi$
$138$		0			0
$139$	11.3648	+	19.6844i	0.963951	+	1.66961i	0.712408	+	0.701766i	$0.247605\pi$
$139$	11.3648	+	19.6844i	0.963951	+	1.66961i	0.251543	+	0.967846i	$0.419062\pi$
$140$	0.197831	+	0.342653i	0.0167197	+	0.0289594i
$141$		0			0
$142$	12.0950	−	20.9492i	1.01499	−	1.75801i
$143$	18.2631			1.52724
$144$		0			0
$145$	−2.79707			−0.232284
$146$	−3.65879	+	6.33720i	−0.302803	+	0.524471i
$147$		0			0
$148$	6.04667	+	10.4731i	0.497033	+	0.860887i
$149$	7.49268	+	12.9777i	0.613824	+	1.06317i	0.990590	+	0.136866i	$0.0437028\pi$
$149$	7.49268	+	12.9777i	0.613824	+	1.06317i	−0.376766	+	0.926309i	$0.622964\pi$
$150$		0			0
$151$	−4.01750	+	6.95851i	−0.326939	+	0.566276i	−0.981903	−	0.189385i	$-0.939351\pi$
$151$	−4.01750	+	6.95851i	−0.326939	+	0.566276i	0.654964	+	0.755660i	$0.272684\pi$
$152$	7.48044			0.606744
$153$		0			0
$154$	−3.19400			−0.257380
$155$	0.549538	−	0.951828i	0.0441399	−	0.0764526i
$156$		0			0
$157$	−3.44630	−	5.96916i	−0.275045	−	0.476391i	0.695102	−	0.718911i	$-0.255359\pi$
$157$	−3.44630	−	5.96916i	−0.275045	−	0.476391i	−0.970146	+	0.242520i	$0.922026\pi$
$158$	−10.8328	−	18.7629i	−0.861809	−	1.49270i
$159$		0			0
$160$	−1.39710	+	2.41985i	−0.110451	+	0.191306i
$161$	−2.84132			−0.223928
$162$		0			0
$163$	6.87193			0.538251			0.269125	−	0.963105i	$-0.413265\pi$
$163$	6.87193			0.538251			0.269125	+	0.963105i	$0.413265\pi$
$164$	0.602299	−	1.04321i	0.0470317	−	0.0814613i
$165$		0			0
$166$	8.89694	+	15.4100i	0.690536	+	1.19604i
$167$	7.79562	+	13.5024i	0.603243	+	1.04485i	0.992327	+	0.123645i	$0.0394584\pi$
$167$	7.79562	+	13.5024i	0.603243	+	1.04485i	−0.389083	+	0.921203i	$0.627208\pi$
$168$		0			0
$169$	−19.4396	+	33.6703i	−1.49535	+	2.59002i
$170$	3.52629			0.270454
$171$		0			0
$172$	−1.32263			−0.100850
$173$	−1.53573	+	2.65997i	−0.116760	+	0.202234i	−0.918482	−	0.395463i	$-0.870584\pi$
$173$	−1.53573	+	2.65997i	−0.116760	+	0.202234i	0.801722	+	0.597697i	$0.203917\pi$
$174$		0			0
$175$	−1.66290	−	2.88022i	−0.125703	−	0.217724i
$176$	−6.20701	−	10.7509i	−0.467871	−	0.810376i
$177$		0			0
$178$	−7.33632	+	12.7069i	−0.549880	+	0.952420i
$179$	−6.81694			−0.509522			−0.254761	−	0.967004i	$-0.581997\pi$
$179$	−6.81694			−0.509522			−0.254761	+	0.967004i	$0.581997\pi$
$180$		0			0
$181$	−6.26156			−0.465418			−0.232709	−	0.972546i	$-0.574759\pi$
$181$	−6.26156			−0.465418			−0.232709	+	0.972546i	$0.574759\pi$
$182$	4.53651	−	7.85746i	0.336268	−	0.582434i
$183$		0			0
$184$	−2.53830	−	4.39647i	−0.187126	−	0.324112i
$185$	1.97901	+	3.42775i	0.145500	+	0.252013i
$186$		0			0
$187$	−5.66572	+	9.81331i	−0.414318	+	0.717620i
$188$	12.6897			0.925488
$189$		0			0
$190$	−4.78049			−0.346813
$191$	−4.89485	+	8.47813i	−0.354179	+	0.613456i	−0.986977	−	0.160861i	$-0.948573\pi$
$191$	−4.89485	+	8.47813i	−0.354179	+	0.613456i	0.632798	+	0.774317i	$0.281906\pi$
$192$		0			0
$193$	−3.22778	−	5.59068i	−0.232341	−	0.402426i	0.726156	−	0.687530i	$-0.241305\pi$
$193$	−3.22778	−	5.59068i	−0.232341	−	0.402426i	−0.958496	+	0.285104i	$0.907972\pi$
$194$	13.6610	+	23.6615i	0.980799	+	1.69879i
$195$		0			0
$196$	4.31339	−	7.47101i	0.308099	−	0.533643i
$197$	9.52049			0.678307			0.339154	−	0.940731i	$-0.389859\pi$
$197$	9.52049			0.678307			0.339154	+	0.940731i	$0.389859\pi$
$198$		0			0
$199$	16.8531			1.19469			0.597344	−	0.801985i	$-0.296223\pi$
$199$	16.8531			1.19469			0.597344	+	0.801985i	$0.296223\pi$
$200$	2.97110	−	5.14610i	0.210089	−	0.363884i
$201$		0			0
$202$	2.83100	+	4.90344i	0.199189	+	0.345005i
$203$	−2.23263	−	3.86702i	−0.156700	−	0.271412i
$204$		0			0
$205$	0.197126	−	0.341433i	0.0137679	−	0.0238467i
$206$	−12.6915			−0.884256
$207$		0			0
$208$	35.2638			2.44511
$209$	7.68085	−	13.3036i	0.531296	−	0.920231i
$210$		0			0
$211$	−0.656265	−	1.13668i	−0.0451792	−	0.0782526i	0.842552	−	0.538616i	$-0.181053\pi$
$211$	−0.656265	−	1.13668i	−0.0451792	−	0.0782526i	−0.887731	+	0.460363i	$0.847719\pi$
$212$	−5.85797	−	10.1463i	−0.402327	−	0.696851i
$213$		0			0
$214$	−7.38749	+	12.7955i	−0.504998	+	0.874683i
$215$	−0.432883			−0.0295224
$216$		0			0
$217$	1.75457			0.119108
$218$	−0.0685274	+	0.118693i	−0.00464126	+	0.00803890i
$219$		0			0
$220$	0.725869	+	1.25724i	0.0489381	+	0.0847633i
$221$	−16.0943	−	27.8761i	−1.08262	−	1.87515i
$222$		0			0
$223$	0.949986	−	1.64542i	0.0636157	−	0.110186i	−0.832463	−	0.554080i	$-0.813070\pi$
$223$	0.949986	−	1.64542i	0.0636157	−	0.110186i	0.896079	+	0.443894i	$0.146403\pi$
$224$	−4.46069			−0.298042
$225$		0			0
$226$	14.0148			0.932252
$227$	−6.36963	+	11.0325i	−0.422767	+	0.732254i	−0.996209	−	0.0869919i	$-0.972275\pi$
$227$	−6.36963	+	11.0325i	−0.422767	+	0.732254i	0.573442	+	0.819246i	$0.305608\pi$
$228$		0			0
$229$	−11.8720	−	20.5630i	−0.784526	−	1.35884i	−0.929282	−	0.369371i	$-0.879573\pi$
$229$	−11.8720	−	20.5630i	−0.784526	−	1.35884i	0.144756	−	0.989467i	$-0.453760\pi$
$230$	1.62214	+	2.80963i	0.106961	+	0.185262i
$231$		0			0
$232$	3.98904	−	6.90923i	0.261894	−	0.453613i
$233$	7.78814			0.510218			0.255109	−	0.966912i	$-0.417889\pi$
$233$	7.78814			0.510218			0.255109	+	0.966912i	$0.417889\pi$
$234$		0			0
$235$	4.15319			0.270925
$236$	−8.61204	+	14.9165i	−0.560596	+	0.970981i
$237$		0			0
$238$	2.81469	+	4.87519i	0.182449	+	0.316012i
$239$	−1.70650	−	2.95575i	−0.110385	−	0.191192i	0.805541	−	0.592540i	$-0.201875\pi$
$239$	−1.70650	−	2.95575i	−0.110385	−	0.191192i	−0.915925	+	0.401349i	$0.868542\pi$
$240$		0			0
$241$	6.16770	−	10.6828i	0.397296	−	0.688137i	−0.596095	−	0.802914i	$-0.703282\pi$
$241$	6.16770	−	10.6828i	0.397296	−	0.688137i	0.993391	+	0.114777i	$0.0366152\pi$
$242$	8.33166			0.535579
$243$		0			0
$244$	1.04950			0.0671871
$245$	1.41173	−	2.44518i	0.0901920	−	0.156217i
$246$		0			0
$247$	21.8186	+	37.7909i	1.38828	+	2.40458i
$248$	1.56745	+	2.71490i	0.0995331	+	0.172396i
$249$		0			0
$250$	−3.87139	+	6.70544i	−0.244848	+	0.424089i
$251$	−7.32241			−0.462186			−0.231093	−	0.972932i	$-0.574230\pi$
$251$	−7.32241			−0.462186			−0.231093	+	0.972932i	$0.574230\pi$
$252$		0			0
$253$	−10.4252			−0.655429
$254$	0.375498	−	0.650381i	0.0235608	−	0.0408086i
$255$		0			0
$256$	−10.4604	−	18.1180i	−0.653778	−	1.13238i
$257$	2.49747	+	4.32575i	0.155788	+	0.269833i	0.933346	−	0.358979i	$-0.116875\pi$
$257$	2.49747	+	4.32575i	0.155788	+	0.269833i	−0.777558	+	0.628812i	$0.783542\pi$
$258$		0			0
$259$	−3.15931	+	5.47208i	−0.196310	+	0.340019i
$260$	−4.12388			−0.255752
$261$		0			0
$262$	5.52511			0.341342
$263$	−9.05500	+	15.6837i	−0.558355	+	0.967099i	0.439279	+	0.898351i	$0.355234\pi$
$263$	−9.05500	+	15.6837i	−0.558355	+	0.967099i	−0.997634	+	0.0687485i	$0.978099\pi$
$264$		0			0
$265$	−1.91725	−	3.32078i	−0.117776	−	0.203994i
$266$	−3.81580	−	6.60916i	−0.233962	−	0.405234i
$267$		0			0
$268$	−7.53881	+	13.0576i	−0.460506	+	0.797620i
$269$	−12.3502			−0.753004			−0.376502	−	0.926416i	$-0.622873\pi$
$269$	−12.3502			−0.753004			−0.376502	+	0.926416i	$0.622873\pi$
$270$		0			0
$271$	−11.1352			−0.676418			−0.338209	−	0.941071i	$-0.609821\pi$
$271$	−11.1352			−0.676418			−0.338209	+	0.941071i	$0.609821\pi$
$272$	−10.9398	+	18.9483i	−0.663322	+	1.14891i
$273$		0			0
$274$	9.74185	+	16.8734i	0.588527	+	1.01936i
$275$	−6.10141	−	10.5679i	−0.367929	−	0.637271i
$276$		0			0
$277$	−7.92554	+	13.7274i	−0.476200	+	0.824802i	−0.999628	−	0.0272677i	$-0.991319\pi$
$277$	−7.92554	+	13.7274i	−0.476200	+	0.824802i	0.523429	+	0.852070i	$0.324653\pi$
$278$	41.4318			2.48491
$279$		0			0
$280$	−0.369362			−0.0220736
$281$	−4.44576	+	7.70028i	−0.265212	+	0.459360i	−0.967619	−	0.252415i	$-0.918775\pi$
$281$	−4.44576	+	7.70028i	−0.265212	+	0.459360i	0.702407	+	0.711775i	$0.252109\pi$
$282$		0			0
$283$	3.93496	+	6.81556i	0.233909	+	0.405143i	0.958955	−	0.283558i	$-0.0915148\pi$
$283$	3.93496	+	6.81556i	0.233909	+	0.405143i	−0.725046	+	0.688701i	$0.758181\pi$
$284$	−8.77614	−	15.2007i	−0.520768	−	0.901997i
$285$		0			0
$286$	16.6451	−	28.8302i	0.984245	−	1.70476i
$287$	0.629388			0.0371516
$288$		0			0
$289$	2.97154			0.174796
$290$	−2.54926	+	4.41545i	−0.149698	+	0.259284i
$291$		0			0
$292$	2.65482	+	4.59828i	0.155361	+	0.269094i
$293$	−16.7554	−	29.0212i	−0.978859	−	1.69543i	−0.666561	−	0.745450i	$-0.732235\pi$
$293$	−16.7554	−	29.0212i	−0.978859	−	1.69543i	−0.312298	−	0.949984i	$-0.601099\pi$
$294$		0			0
$295$	−2.81863	+	4.88202i	−0.164107	+	0.284242i
$296$	−11.2895			−0.656189
$297$		0			0
$298$	27.3154			1.58234
$299$	14.8072	−	25.6468i	0.856322	−	1.48319i
$300$		0			0
$301$	−0.345529	−	0.598473i	−0.0199160	−	0.0344954i
$302$	7.32313	+	12.6840i	0.421399	+	0.729884i
$303$		0			0
$304$	14.8308	−	25.6876i	0.850603	−	1.47329i
$305$	0.343489			0.0196681
$306$		0			0
$307$	12.9225			0.737524			0.368762	−	0.929524i	$-0.379782\pi$
$307$	12.9225			0.737524			0.368762	+	0.929524i	$0.379782\pi$
$308$	−1.15878	+	2.00707i	−0.0660277	+	0.114363i
$309$		0			0
$310$	−1.00170	−	1.73500i	−0.0568929	−	0.0985413i
$311$	−6.78105	−	11.7451i	−0.384518	−	0.666005i	0.607184	−	0.794561i	$-0.292299\pi$
$311$	−6.78105	−	11.7451i	−0.384518	−	0.666005i	−0.991702	+	0.128556i	$0.958966\pi$
$312$		0			0
$313$	11.6910	−	20.2493i	0.660812	−	1.14456i	−0.319591	−	0.947556i	$-0.603546\pi$
$313$	11.6910	−	20.2493i	0.660812	−	1.14456i	0.980403	−	0.197004i	$-0.0631211\pi$
$314$	−12.5639			−0.709021
$315$		0			0
$316$	−15.7205			−0.884348
$317$	0.805713	−	1.39554i	0.0452533	−	0.0783811i	−0.842512	−	0.538678i	$-0.818924\pi$
$317$	0.805713	−	1.39554i	0.0452533	−	0.0783811i	0.887765	+	0.460297i	$0.152257\pi$
$318$		0			0
$319$	−8.19183	−	14.1887i	−0.458655	−	0.794413i
$320$	0.427295	+	0.740096i	0.0238865	+	0.0413726i
$321$		0			0
$322$	−2.58960	+	4.48531i	−0.144312	+	0.249957i
$323$	−27.0748			−1.50648
$324$		0			0
$325$	34.6639			1.92281
$326$	6.26310	−	10.8480i	0.346881	−	0.600816i
$327$		0			0
$328$	0.562265	+	0.973871i	0.0310459	+	0.0537730i
$329$	3.31509	+	5.74191i	0.182767	+	0.316562i
$330$		0			0
$331$	−17.1277	+	29.6660i	−0.941422	+	1.63059i	−0.178660	+	0.983911i	$0.557176\pi$
$331$	−17.1277	+	29.6660i	−0.941422	+	1.63059i	−0.762762	+	0.646679i	$0.776157\pi$
$332$	12.9112			0.708597
$333$		0			0
$334$	28.4198			1.55506
$335$	−2.46737	+	4.27362i	−0.134807	+	0.233493i
$336$		0			0
$337$	−7.67840	−	13.2994i	−0.418269	−	0.724464i	0.577496	−	0.816393i	$-0.304030\pi$
$337$	−7.67840	−	13.2994i	−0.418269	−	0.724464i	−0.995766	+	0.0919297i	$0.970697\pi$
$338$	35.4346	+	61.3745i	1.92739	+	3.33833i
$339$		0			0
$340$	1.27934	−	2.21588i	0.0693818	−	0.120173i
$341$	6.43778			0.348625
$342$		0			0
$343$	9.34478			0.504571
$344$	0.617358	−	1.06929i	0.0332857	−	0.0576525i
$345$		0			0
$346$	2.79935	+	4.84861i	0.150494	+	0.260663i
$347$	−0.967222	−	1.67528i	−0.0519232	−	0.0899336i	0.838896	−	0.544292i	$-0.183202\pi$
$347$	−0.967222	−	1.67528i	−0.0519232	−	0.0899336i	−0.890819	+	0.454359i	$0.849868\pi$
$348$		0			0
$349$	−2.79439	+	4.84003i	−0.149580	+	0.259081i	−0.931072	−	0.364834i	$-0.881126\pi$
$349$	−2.79439	+	4.84003i	−0.149580	+	0.259081i	0.781492	+	0.623915i	$0.214459\pi$
$350$	−6.06228			−0.324043
$351$		0			0
$352$	−16.3669			−0.872360
$353$	−2.26919	+	3.93036i	−0.120777	+	0.209192i	−0.920074	−	0.391744i	$-0.871872\pi$
$353$	−2.26919	+	3.93036i	−0.120777	+	0.209192i	0.799297	+	0.600936i	$0.205205\pi$
$354$		0			0
$355$	−2.87234	−	4.97504i	−0.152448	−	0.264048i
$356$	5.32323	+	9.22011i	0.282131	+	0.488665i
$357$		0			0
$358$	−6.21298	+	10.7612i	−0.328366	+	0.568747i
$359$	11.5921			0.611809			0.305904	−	0.952062i	$-0.401041\pi$
$359$	11.5921			0.611809			0.305904	+	0.952062i	$0.401041\pi$
$360$		0			0
$361$	17.7046			0.931821
$362$	−5.70681	+	9.88449i	−0.299943	+	0.519517i
$363$		0			0
$364$	−3.29169	−	5.70137i	−0.172531	−	0.298833i
$365$	0.868894	+	1.50497i	0.0454800	+	0.0787737i
$366$		0			0
$367$	3.61750	−	6.26569i	0.188832	−	0.327066i	−0.756029	−	0.654538i	$-0.772863\pi$
$367$	3.61750	−	6.26569i	0.188832	−	0.327066i	0.944861	+	0.327472i	$0.106197\pi$
$368$	−20.1298			−1.04934
$369$		0			0
$370$	7.21472			0.375076
$371$	3.06072	−	5.30132i	0.158904	−	0.275231i
$372$		0			0
$373$	−5.87996	−	10.1844i	−0.304453	−	0.527328i	0.672686	−	0.739928i	$-0.265140\pi$
$373$	−5.87996	−	10.1844i	−0.304453	−	0.527328i	−0.977139	+	0.212600i	$0.931807\pi$
$374$	10.3275	+	17.8878i	0.534023	+	0.924955i
$375$		0			0
$376$	−5.92309	+	10.2591i	−0.305460	+	0.529072i
$377$	46.5402			2.39694
$378$		0			0
$379$	−5.11108			−0.262539			−0.131269	−	0.991347i	$-0.541905\pi$
$379$	−5.11108			−0.262539			−0.131269	+	0.991347i	$0.541905\pi$
$380$	−1.73436	+	3.00400i	−0.0889709	+	0.154102i
$381$		0			0
$382$	8.92237	+	15.4540i	0.456508	+	0.790696i
$383$	8.07593	+	13.9879i	0.412661	+	0.714749i	0.995180	−	0.0980678i	$-0.0312662\pi$
$383$	8.07593	+	13.9879i	0.412661	+	0.714749i	−0.582519	+	0.812817i	$0.697933\pi$
$384$		0			0
$385$	−0.379258	+	0.656893i	−0.0193288	+	0.0334784i
$386$	−11.7672			−0.598937
$387$		0			0
$388$	19.8248			1.00645
$389$	8.61616	−	14.9236i	0.436857	−	0.756658i	−0.560588	−	0.828095i	$-0.689425\pi$
$389$	8.61616	−	14.9236i	0.436857	−	0.756658i	0.997445	+	0.0714365i	$0.0227583\pi$
$390$		0			0
$391$	9.18718	+	15.9127i	0.464616	+	0.804738i
$392$	4.02668	+	6.97441i	0.203378	+	0.352261i
$393$		0			0
$394$	8.67702	−	15.0290i	0.437142	−	0.757152i
$395$	−5.14516			−0.258881
$396$		0			0
$397$	−29.6151			−1.48634			−0.743170	−	0.669103i	$-0.766679\pi$
$397$	−29.6151			−1.48634			−0.743170	+	0.669103i	$0.766679\pi$
$398$	15.3600	−	26.6043i	0.769929	−	1.33356i
$399$		0			0
$400$	−11.7811	−	20.4054i	−0.589053	−	1.02027i
$401$	−7.15251	−	12.3885i	−0.357179	−	0.618653i	0.630309	−	0.776344i	$-0.282928\pi$
$401$	−7.15251	−	12.3885i	−0.357179	−	0.618653i	−0.987488	+	0.157692i	$0.949595\pi$
$402$		0			0
$403$	−9.14372	+	15.8374i	−0.455481	+	0.788917i
$404$	4.10835			0.204398
$405$		0			0
$406$	−8.13931			−0.403947
$407$	−11.5920	+	20.0779i	−0.574592	+	0.995223i
$408$		0			0
$409$	−8.43314	−	14.6066i	−0.416992	−	0.722251i	0.578644	−	0.815581i	$-0.303582\pi$
$409$	−8.43314	−	14.6066i	−0.416992	−	0.722251i	−0.995635	+	0.0933297i	$0.970249\pi$
$410$	−0.359324	−	0.622367i	−0.0177457	−	0.0307365i
$411$		0			0
$412$	−4.60446	+	7.97516i	−0.226846	+	0.392908i
$413$	−8.99937			−0.442830
$414$		0			0
$415$	4.22572			0.207432
$416$	23.2463	−	40.2638i	1.13974	−	1.97409i
$417$		0			0
$418$	−14.0007	−	24.2500i	−0.684798	−	1.18610i
$419$	−0.720706	−	1.24830i	−0.0352088	−	0.0609835i	0.847884	−	0.530182i	$-0.177876\pi$
$419$	−0.720706	−	1.24830i	−0.0352088	−	0.0609835i	−0.883093	+	0.469198i	$0.844543\pi$
$420$		0			0
$421$	0.693490	−	1.20116i	0.0337986	−	0.0585409i	−0.848631	−	0.528985i	$-0.822573\pi$
$421$	0.693490	−	1.20116i	0.0337986	−	0.0585409i	0.882430	+	0.470444i	$0.155906\pi$
$422$	−2.39249			−0.116465
$423$		0			0
$424$	10.9372			0.531157
$425$	−10.7537	+	18.6259i	−0.521630	+	0.903489i
$426$		0			0
$427$	0.274174	+	0.474884i	0.0132682	+	0.0229812i
$428$	5.36036	+	9.28442i	0.259103	+	0.448780i
$429$		0			0
$430$	−0.394532	+	0.683349i	−0.0190260	+	0.0329540i
$431$	19.8758			0.957383			0.478692	−	0.877983i	$-0.341111\pi$
$431$	19.8758			0.957383			0.478692	+	0.877983i	$0.341111\pi$
$432$		0			0
$433$	−3.09155			−0.148570			−0.0742851	−	0.997237i	$-0.523667\pi$
$433$	−3.09155			−0.148570			−0.0742851	+	0.997237i	$0.523667\pi$
$434$	1.59912	−	2.76976i	0.0767604	−	0.132953i
$435$		0			0
$436$	0.0497235	+	0.0861236i	0.00238132	+	0.00412457i
$437$	−12.4548	−	21.5724i	−0.595794	−	1.03195i
$438$		0			0
$439$	−4.45099	+	7.70933i	−0.212434	+	0.367946i	−0.952476	−	0.304614i	$-0.901472\pi$
$439$	−4.45099	+	7.70933i	−0.212434	+	0.367946i	0.740042	+	0.672561i	$0.234806\pi$
$440$	−1.35524			−0.0646086
$441$		0			0
$442$	−58.6736			−2.79082
$443$	−5.48826	+	9.50594i	−0.260755	+	0.451641i	−0.966443	−	0.256882i	$-0.917305\pi$
$443$	−5.48826	+	9.50594i	−0.260755	+	0.451641i	0.705688	+	0.708523i	$0.250638\pi$
$444$		0			0
$445$	1.74224	+	3.01765i	0.0825901	+	0.143050i
$446$	−1.73164	−	2.99929i	−0.0819956	−	0.142021i
$447$		0			0
$448$	−0.682136	+	1.18149i	−0.0322279	+	0.0558204i
$449$	−18.7937			−0.886931			−0.443465	−	0.896292i	$-0.646251\pi$
$449$	−18.7937			−0.886931			−0.443465	+	0.896292i	$0.646251\pi$
$450$		0			0
$451$	2.30931			0.108741
$452$	5.08458	−	8.80675i	0.239159	−	0.414235i
$453$		0			0
$454$	11.6106	+	20.1102i	0.544913	+	0.943818i
$455$	−1.07734	−	1.86600i	−0.0505063	−	0.0874795i
$456$		0			0
$457$	−9.85804	+	17.0746i	−0.461140	+	0.798717i	−0.999018	−	0.0443053i	$-0.985893\pi$
$457$	−9.85804	+	17.0746i	−0.461140	+	0.798717i	0.537879	+	0.843022i	$0.319226\pi$
$458$	−43.2809			−2.02238
$459$		0			0
$460$	2.35405			0.109758
$461$	−20.0872	+	34.7921i	−0.935556	+	1.62043i	−0.161918	+	0.986804i	$0.551768\pi$
$461$	−20.0872	+	34.7921i	−0.935556	+	1.62043i	−0.773639	+	0.633627i	$0.781565\pi$
$462$		0			0
$463$	−11.1465	−	19.3064i	−0.518024	−	0.897243i	−0.999781	−	0.0209385i	$-0.993335\pi$
$463$	−11.1465	−	19.3064i	−0.518024	−	0.897243i	0.481757	−	0.876305i	$-0.339999\pi$
$464$	−15.8174	−	27.3966i	−0.734305	−	1.27185i
$465$		0			0
$466$	7.09814	−	12.2943i	0.328815	−	0.569524i
$467$	−2.81433			−0.130232			−0.0651158	−	0.997878i	$-0.520742\pi$
$467$	−2.81433			−0.130232			−0.0651158	+	0.997878i	$0.520742\pi$
$468$		0			0
$469$	−7.87786			−0.363766
$470$	3.78524	−	6.55623i	0.174600	−	0.302416i
$471$		0			0
$472$	−8.03960	−	13.9250i	−0.370053	−	0.640950i
$473$	−1.26780	−	2.19589i	−0.0582933	−	0.100967i
$474$		0			0
$475$	14.5784	−	25.2506i	0.668905	−	1.15858i
$476$	4.08468			0.187221
$477$		0			0
$478$	−6.22126			−0.284554
$479$	7.84457	−	13.5872i	0.358428	−	0.620815i	−0.629271	−	0.777186i	$-0.716646\pi$
$479$	7.84457	−	13.5872i	0.358428	−	0.620815i	0.987698	+	0.156371i	$0.0499797\pi$
$480$		0			0
$481$	−32.9287	−	57.0341i	−1.50142	−	2.60053i
$482$	−11.2425	−	19.4726i	−0.512083	−	0.886954i
$483$		0			0
$484$	3.02273	−	5.23552i	0.137397	−	0.237978i
$485$	6.48845			0.294625
$486$		0			0
$487$	−8.31905			−0.376972			−0.188486	−	0.982076i	$-0.560358\pi$
$487$	−8.31905			−0.376972			−0.188486	+	0.982076i	$0.560358\pi$
$488$	−0.489868	+	0.848476i	−0.0221753	+	0.0384087i
$489$		0			0
$490$	−2.57331	−	4.45710i	−0.116250	−	0.201351i
$491$	10.7300	+	18.5849i	0.484237	+	0.838723i	0.999836	−	0.0181071i	$-0.00576397\pi$
$491$	10.7300	+	18.5849i	0.484237	+	0.838723i	−0.515599	+	0.856830i	$0.672431\pi$
$492$		0			0
$493$	−14.4380	+	25.0074i	−0.650256	+	1.12628i
$494$	79.5422			3.57877
$495$		0			0
$496$	12.4305			0.558148
$497$	4.58542	−	7.94218i	0.205684	−	0.356256i
$498$		0			0
$499$	4.43186	+	7.67620i	0.198397	+	0.343634i	0.948009	−	0.318244i	$-0.103093\pi$
$499$	4.43186	+	7.67620i	0.198397	+	0.343634i	−0.749612	+	0.661878i	$0.769760\pi$
$500$	2.80908	+	4.86547i	0.125626	+	0.217590i
$501$		0			0
$502$	−6.67367	+	11.5591i	−0.297861	+	0.515910i
$503$	18.4384			0.822126			0.411063	−	0.911607i	$-0.365158\pi$
$503$	18.4384			0.822126			0.411063	+	0.911607i	$0.365158\pi$
$504$		0			0
$505$	1.34462			0.0598349
$506$	−9.50160	+	16.4573i	−0.422398	+	0.731614i
$507$		0			0
$508$	−0.272461	−	0.471917i	−0.0120885	−	0.0209379i
$509$	−2.69763	−	4.67243i	−0.119570	−	0.207102i	0.800027	−	0.599964i	$-0.204818\pi$
$509$	−2.69763	−	4.67243i	−0.119570	−	0.207102i	−0.919597	+	0.392862i	$0.871485\pi$
$510$		0			0
$511$	−1.38711	+	2.40254i	−0.0613621	+	0.106282i
$512$	−19.5124			−0.862333
$513$		0			0
$514$	9.10483			0.401597
$515$	−1.50699	+	2.61019i	−0.0664061	+	0.115019i
$516$		0			0
$517$	12.1636	+	21.0679i	0.534953	+	0.926565i
$518$	5.75881	+	9.97456i	0.253028	+	0.438257i
$519$		0			0
$520$	1.92488	−	3.33399i	0.0844116	−	0.146205i
$521$	−34.0231			−1.49058			−0.745290	−	0.666741i	$-0.767689\pi$
$521$	−34.0231			−1.49058			−0.745290	+	0.666741i	$0.767689\pi$
$522$		0			0
$523$	17.5996			0.769576			0.384788	−	0.923005i	$-0.374275\pi$
$523$	17.5996			0.769576			0.384788	+	0.923005i	$0.374275\pi$
$524$	2.00451	−	3.47191i	0.0875674	−	0.151671i
$525$		0			0
$526$	16.5055	+	28.5884i	0.719675	+	1.24651i
$527$	−5.67326	−	9.82637i	−0.247131	−	0.428043i
$528$		0			0
$529$	3.04754	−	5.27849i	0.132502	−	0.229500i
$530$	−6.98957			−0.303608
$531$		0			0
$532$	−5.53749			−0.240081
$533$	−3.27997	+	5.68108i	−0.142071	+	0.246075i
$534$		0			0
$535$	1.75439	+	3.03870i	0.0758490	+	0.131374i
$536$	−7.03770	−	12.1897i	−0.303983	−	0.526513i
$537$		0			0
$538$	−11.2560	+	19.4960i	−0.485281	+	0.840531i
$539$	16.5382			0.712352
$540$		0			0
$541$	19.6744			0.845868			0.422934	−	0.906160i	$-0.361000\pi$
$541$	19.6744			0.845868			0.422934	+	0.906160i	$0.361000\pi$
$542$	−10.1487	+	17.5781i	−0.435924	+	0.755043i
$543$		0			0
$544$	14.4233	+	24.9818i	0.618392	+	1.07109i
$545$	0.0162740	+	0.0281874i	0.000697101	+	0.00120741i
$546$		0			0
$547$	7.16166	−	12.4044i	0.306211	−	0.530372i	−0.671320	−	0.741168i	$-0.734272\pi$
$547$	7.16166	−	12.4044i	0.306211	−	0.530372i	0.977530	+	0.210796i	$0.0676055\pi$
$548$	14.1374			0.603919
$549$		0			0
$550$	−22.2434			−0.948461
$551$	19.5732	−	33.9018i	0.833847	−	1.44427i
$552$		0			0
$553$	−4.10689	−	7.11333i	−0.174643	−	0.302490i
$554$	14.4467	+	25.0225i	0.613783	+	1.06310i
$555$		0			0
$556$	15.0314	−	26.0352i	0.637475	−	1.10414i
$557$	−1.21426			−0.0514499			−0.0257250	−	0.999669i	$-0.508189\pi$
$557$	−1.21426			−0.0514499			−0.0257250	+	0.999669i	$0.508189\pi$
$558$		0			0
$559$	7.20272			0.304642
$560$	−0.732299	+	1.26838i	−0.0309453	+	0.0535988i
$561$		0			0
$562$	8.10377	+	14.0361i	0.341837	+	0.592079i
$563$	15.8136	+	27.3900i	0.666464	+	1.15435i	0.978886	+	0.204406i	$0.0655264\pi$
$563$	15.8136	+	27.3900i	0.666464	+	1.15435i	−0.312422	+	0.949943i	$0.601140\pi$
$564$		0			0
$565$	1.66413	−	2.88236i	0.0700105	−	0.121262i
$566$	14.3454			0.602981
$567$		0			0
$568$	16.3856			0.687524
$569$	−23.5071	+	40.7155i	−0.985468	+	1.70688i	−0.345632	+	0.938370i	$0.612336\pi$
$569$	−23.5071	+	40.7155i	−0.985468	+	1.70688i	−0.639836	+	0.768511i	$0.720998\pi$
$570$		0			0
$571$	−15.8025	−	27.3707i	−0.661314	−	1.14543i	−0.980271	−	0.197661i	$-0.936666\pi$
$571$	−15.8025	−	27.3707i	−0.661314	−	1.14543i	0.318956	−	0.947769i	$-0.396668\pi$
$572$	−12.0777	−	20.9192i	−0.504993	−	0.874674i
$573$		0			0
$574$	0.573627	−	0.993550i	0.0239427	−	0.0414700i
$575$	−19.7873			−0.825189
$576$		0			0
$577$	−35.2559			−1.46772			−0.733860	−	0.679300i	$-0.762283\pi$
$577$	−35.2559			−1.46772			−0.733860	+	0.679300i	$0.762283\pi$
$578$	2.70827	−	4.69087i	0.112649	−	0.195114i
$579$		0			0
$580$	1.84974	+	3.20385i	0.0768064	+	0.133033i
$581$	3.37298	+	5.84217i	0.139935	+	0.242374i
$582$		0			0
$583$	11.2302	−	19.4513i	0.465108	−	0.805590i
$584$	−4.95670			−0.205110
$585$		0			0
$586$	−61.0837			−2.52334
$587$	−14.2400	+	24.6645i	−0.587749	+	1.01801i	0.406777	+	0.913527i	$0.366652\pi$
$587$	−14.2400	+	24.6645i	−0.587749	+	1.01801i	−0.994527	+	0.104484i	$0.966681\pi$
$588$		0			0
$589$	7.69107	+	13.3213i	0.316905	+	0.548896i
$590$	5.13783	+	8.89898i	0.211521	+	0.366365i
$591$		0			0
$592$	−22.3826	+	38.7679i	−0.919921	+	1.59335i
$593$	4.79696			0.196987			0.0984937	−	0.995138i	$-0.468598\pi$
$593$	4.79696			0.196987			0.0984937	+	0.995138i	$0.468598\pi$
$594$		0			0
$595$	1.33688			0.0548065
$596$	9.91004	−	17.1647i	0.405931	−	0.703093i
$597$		0			0
$598$	−26.9907	−	46.7492i	−1.10373	−	1.91172i
$599$	2.53206	+	4.38566i	0.103457	+	0.179193i	0.913107	−	0.407720i	$-0.133676\pi$
$599$	2.53206	+	4.38566i	0.103457	+	0.179193i	−0.809650	+	0.586914i	$0.800343\pi$
$600$		0			0
$601$	17.9645	−	31.1154i	0.732785	−	1.26922i	−0.222903	−	0.974841i	$-0.571553\pi$
$601$	17.9645	−	31.1154i	0.732785	−	1.26922i	0.955688	−	0.294381i	$-0.0951134\pi$
$602$	−1.25967			−0.0513401
$603$		0			0
$604$	10.6273			0.432420
$605$	0.989308	−	1.71353i	0.0402211	−	0.0696649i
$606$		0			0
$607$	2.62783	+	4.55154i	0.106660	+	0.184741i	0.914415	−	0.404777i	$-0.132651\pi$
$607$	2.62783	+	4.55154i	0.106660	+	0.184741i	−0.807755	+	0.589518i	$0.799318\pi$
$608$	−19.5532	−	33.8672i	−0.792987	−	1.37349i
$609$		0			0
$610$	0.313058	−	0.542232i	0.0126753	−	0.0219543i
$611$	−69.1047			−2.79568
$612$		0			0
$613$	−21.9713			−0.887412			−0.443706	−	0.896172i	$-0.646337\pi$
$613$	−21.9713			−0.887412			−0.443706	+	0.896172i	$0.646337\pi$
$614$	11.7776	−	20.3994i	0.475305	−	0.823252i
$615$		0			0
$616$	−1.08176	−	1.87366i	−0.0435853	−	0.0754919i
$617$	−15.8691	−	27.4860i	−0.638864	−	1.10654i	−0.985682	−	0.168613i	$-0.946071\pi$
$617$	−15.8691	−	27.4860i	−0.638864	−	1.10654i	0.346818	−	0.937932i	$-0.387262\pi$
$618$		0			0
$619$	18.2257	−	31.5679i	0.732554	−	1.26882i	−0.223235	−	0.974765i	$-0.571662\pi$
$619$	18.2257	−	31.5679i	0.732554	−	1.26882i	0.955788	−	0.294055i	$-0.0950050\pi$
$620$	−1.45367			−0.0583808
$621$		0			0
$622$	−24.7211			−0.991226
$623$	−2.78132	+	4.81739i	−0.111431	+	0.193005i
$624$		0			0
$625$	−11.1121	−	19.2468i	−0.444486	−	0.769872i
$626$	−21.3104	−	36.9106i	−0.851734	−	1.47525i
$627$		0			0
$628$	−4.55818	+	7.89500i	−0.181891	+	0.315045i
$629$	40.8614			1.62925
$630$		0			0
$631$	−6.25533			−0.249021			−0.124510	−	0.992218i	$-0.539736\pi$
$631$	−6.25533			−0.249021			−0.124510	+	0.992218i	$0.539736\pi$
$632$	7.33779	−	12.7094i	0.291882	−	0.505554i
$633$		0			0
$634$	−1.46866	−	2.54379i	−0.0583279	−	0.101027i
$635$	−0.0891738	−	0.154454i	−0.00353876	−	0.00612930i
$636$		0			0
$637$	−23.4896	+	40.6852i	−0.930693	+	1.61201i
$638$	−29.8643			−1.18234
$639$		0			0
$640$	−4.03066			−0.159326
$641$	19.6607	−	34.0533i	0.776550	−	1.34502i	−0.157370	−	0.987540i	$-0.550301\pi$
$641$	19.6607	−	34.0533i	0.776550	−	1.34502i	0.933919	−	0.357484i	$-0.116365\pi$
$642$		0			0
$643$	−4.50051	−	7.79512i	−0.177483	−	0.307410i	0.763535	−	0.645767i	$-0.223462\pi$
$643$	−4.50051	−	7.79512i	−0.177483	−	0.307410i	−0.941018	+	0.338357i	$0.890129\pi$
$644$	1.87901	+	3.25454i	0.0740434	+	0.128247i
$645$		0			0
$646$	−24.6761	+	42.7403i	−0.970869	+	1.68160i
$647$	−49.7161			−1.95454			−0.977271	−	0.211996i	$-0.932004\pi$
$647$	−49.7161			−1.95454			−0.977271	+	0.211996i	$0.932004\pi$
$648$		0			0
$649$	−33.0200			−1.29615
$650$	31.5928	−	54.7203i	1.23917	−	2.14631i
$651$		0			0
$652$	−4.54451	−	7.87132i	−0.177977	−	0.308265i
$653$	−13.9053	−	24.0846i	−0.544155	−	0.942504i	−0.998660	−	0.0517595i	$-0.983517\pi$
$653$	−13.9053	−	24.0846i	−0.544155	−	0.942504i	0.454505	−	0.890744i	$-0.349816\pi$
$654$		0			0
$655$	0.656055	−	1.13632i	0.0256342	−	0.0443998i
$656$	4.45900			0.174095
$657$		0			0
$658$	12.0856			0.471144
$659$	4.38026	−	7.58682i	0.170631	−	0.295541i	−0.768010	−	0.640438i	$-0.778753\pi$
$659$	4.38026	−	7.58682i	0.170631	−	0.295541i	0.938640	+	0.344897i	$0.112086\pi$
$660$		0			0
$661$	2.31545	+	4.01048i	0.0900606	+	0.155990i	0.907536	−	0.419973i	$-0.137961\pi$
$661$	2.31545	+	4.01048i	0.0900606	+	0.155990i	−0.817476	+	0.575963i	$0.804627\pi$
$662$	31.2205	+	54.0754i	1.21342	+	2.10170i
$663$		0			0
$664$	−6.02652	+	10.4382i	−0.233874	+	0.405082i
$665$	−1.81236			−0.0702805
$666$		0			0
$667$	−26.5668			−1.02867
$668$	10.3107	−	17.8587i	0.398934	−	0.690974i
$669$		0			0
$670$	4.49755	+	7.78999i	0.173756	+	0.300953i
$671$	1.00598	+	1.74242i	0.0388356	+	0.0672653i
$672$		0			0
$673$	−5.26726	+	9.12317i	−0.203038	+	0.351672i	−0.949506	−	0.313749i	$-0.898415\pi$
$673$	−5.26726	+	9.12317i	−0.203038	+	0.351672i	0.746468	+	0.665422i	$0.231748\pi$
$674$	−27.9925			−1.07823
$675$		0			0
$676$	51.4227			1.97780
$677$	−1.01209	+	1.75299i	−0.0388978	+	0.0673730i	−0.884819	−	0.465935i	$-0.845718\pi$
$677$	−1.01209	+	1.75299i	−0.0388978	+	0.0673730i	0.845921	+	0.533308i	$0.179051\pi$
$678$		0			0
$679$	5.17910	+	8.97046i	0.198756	+	0.344255i
$680$	1.19430	+	2.06859i	0.0457993	+	0.0793267i
$681$		0			0
$682$	5.86742	−	10.1627i	0.224675	−	0.389148i
$683$	30.3719			1.16215			0.581075	−	0.813850i	$-0.302632\pi$
$683$	30.3719			1.16215			0.581075	+	0.813850i	$0.302632\pi$
$684$		0			0
$685$	4.62702			0.176789
$686$	8.51688	−	14.7517i	0.325176	−	0.563221i
$687$		0			0
$688$	−2.44795	−	4.23998i	−0.0933274	−	0.161648i
$689$	31.9011	+	55.2543i	1.21533	+	2.10502i
$690$		0			0
$691$	9.17681	−	15.8947i	0.349102	−	0.604663i	−0.636988	−	0.770874i	$-0.719820\pi$
$691$	9.17681	−	15.8947i	0.349102	−	0.604663i	0.986090	+	0.166211i	$0.0531532\pi$
$692$	4.06241			0.154430
$693$		0			0
$694$	−3.52612			−0.133850
$695$	4.91964	−	8.52106i	0.186613	−	0.323222i
$696$		0			0
$697$	−2.03507	−	3.52485i	−0.0770838	−	0.133513i
$698$	5.09364	+	8.82245i	0.192797	+	0.333935i
$699$		0			0
$700$	−2.19940	+	3.80947i	−0.0831294	+	0.143984i
$701$	4.98491			0.188277			0.0941387	−	0.995559i	$-0.469990\pi$
$701$	4.98491			0.188277			0.0941387	+	0.995559i	$0.469990\pi$
$702$		0			0
$703$	−55.3947			−2.08925
$704$	−2.50286	+	4.33507i	−0.0943299	+	0.163384i
$705$		0			0
$706$	4.13630	+	7.16429i	0.155672	+	0.269632i
$707$	1.07328	+	1.85898i	0.0403649	+	0.0699140i
$708$		0			0
$709$	−13.9418	+	24.1480i	−0.523597	+	0.906896i	0.476026	+	0.879431i	$0.342077\pi$
$709$	−13.9418	+	24.1480i	−0.523597	+	0.906896i	−0.999623	+	0.0274647i	$0.991257\pi$
$710$	−10.4715			−0.392987
$711$		0			0
$712$	−9.93880			−0.372472
$713$	5.21955	−	9.04053i	0.195474	−	0.338571i
$714$		0			0
$715$	−3.95290	−	6.84663i	−0.147830	−	0.256049i
$716$	4.50814	+	7.80833i	0.168477	+	0.291811i
$717$		0			0
$718$	10.5651	−	18.2993i	0.394286	−	0.682924i
$719$	10.7704			0.401668			0.200834	−	0.979625i	$-0.435635\pi$
$719$	10.7704			0.401668			0.200834	+	0.979625i	$0.435635\pi$
$720$		0			0
$721$	−4.81155			−0.179191
$722$	16.1361	−	27.9485i	0.600522	−	1.04013i
$723$		0			0
$724$	4.14087	+	7.17219i	0.153894	+	0.266552i
$725$	−15.5483	−	26.9304i	−0.577449	−	1.00017i
$726$		0			0
$727$	−1.23443	+	2.13810i	−0.0457826	+	0.0792977i	−0.888009	−	0.459827i	$-0.847911\pi$
$727$	−1.23443	+	2.13810i	−0.0457826	+	0.0792977i	0.842226	+	0.539125i	$0.181245\pi$
$728$	6.14578			0.227778
$729$		0			0
$730$	3.16766			0.117240
$731$	−2.23448	+	3.87023i	−0.0826451	+	0.143146i
$732$		0			0
$733$	6.20513	+	10.7476i	0.229192	+	0.396972i	0.957569	−	0.288205i	$-0.0930584\pi$
$733$	6.20513	+	10.7476i	0.229192	+	0.396972i	−0.728377	+	0.685177i	$0.759725\pi$
$734$	−6.59400	−	11.4211i	−0.243389	−	0.421562i
$735$		0			0
$736$	−13.2698	+	22.9840i	−0.489131	+	0.847200i
$737$	−28.9050			−1.06473
$738$		0			0
$739$	38.5237			1.41712			0.708559	−	0.705651i	$-0.249346\pi$
$739$	38.5237			1.41712			0.708559	+	0.705651i	$0.249346\pi$
$740$	2.61750	−	4.53365i	0.0962213	−	0.166660i
$741$		0			0
$742$	−5.57910	−	9.66328i	−0.204815	−	0.354750i
$743$	18.4038	+	31.8762i	0.675168	+	1.16943i	0.976420	+	0.215881i	$0.0692624\pi$
$743$	18.4038	+	31.8762i	0.675168	+	1.16943i	−0.301251	+	0.953545i	$0.597404\pi$
$744$		0			0
$745$	3.24345	−	5.61783i	0.118831	−	0.205821i
$746$	−21.4361			−0.784831
$747$		0			0
$748$	14.9873			0.547990
$749$	−2.80072	+	4.85099i	−0.102336	+	0.177251i
$750$		0			0
$751$	−7.09925	−	12.2963i	−0.259055	−	0.448697i	0.706934	−	0.707280i	$-0.250078\pi$
$751$	−7.09925	−	12.2963i	−0.259055	−	0.448697i	−0.965989	+	0.258583i	$0.916745\pi$
$752$	23.4863	+	40.6795i	0.856458	+	1.48343i
$753$		0			0
$754$	42.4169	−	73.4683i	1.54473	−	2.67556i
$755$	3.47822			0.126585
$756$		0			0
$757$	10.5676			0.384085			0.192042	−	0.981387i	$-0.438489\pi$
$757$	10.5676			0.384085			0.192042	+	0.981387i	$0.438489\pi$
$758$	−4.65826	+	8.06835i	−0.169196	+	0.293056i
$759$		0			0
$760$	−1.61908	−	2.80433i	−0.0587302	−	0.101724i
$761$	13.7421	+	23.8020i	0.498151	+	0.862823i	0.999998	−	0.00213360i	$-0.000679147\pi$
$761$	13.7421	+	23.8020i	0.498151	+	0.862823i	−0.501847	+	0.864957i	$0.667346\pi$
$762$		0			0
$763$	−0.0259799	+	0.0449985i	−0.000940535	+	0.00162906i
$764$	12.9482			0.468448
$765$		0			0
$766$	29.4417			1.06377
$767$	46.8990	−	81.2315i	1.69343	−	2.93310i
$768$		0			0
$769$	5.50415	+	9.53346i	0.198485	+	0.343785i	0.948037	−	0.318159i	$-0.103065\pi$
$769$	5.50415	+	9.53346i	0.198485	+	0.343785i	−0.749553	+	0.661945i	$0.769731\pi$
$770$	0.691314	+	1.19739i	0.0249132	+	0.0431510i
$771$		0			0
$772$	−4.26916	+	7.39440i	−0.153650	+	0.266130i
$773$	40.1139			1.44280			0.721398	−	0.692521i	$-0.243500\pi$
$773$	40.1139			1.44280			0.721398	+	0.692521i	$0.243500\pi$
$774$		0			0
$775$	12.2191			0.438921
$776$	−9.25352	+	16.0276i	−0.332182	+	0.575356i
$777$		0			0
$778$	−15.7056	−	27.2029i	−0.563073	−	0.975272i
$779$	2.75889	+	4.77854i	0.0988475	+	0.171209i
$780$		0			0
$781$	16.8246	−	29.1410i	0.602031	−	1.04275i
$782$	33.4929			1.19771
$783$		0			0
$784$	31.9333			1.14047
$785$	−1.49185	+	2.58395i	−0.0532462	+	0.0922252i
$786$		0			0
$787$	7.84526	+	13.5884i	0.279653	+	0.484374i	0.971299	−	0.237864i	$-0.0764472\pi$
$787$	7.84526	+	13.5884i	0.279653	+	0.484374i	−0.691645	+	0.722237i	$0.743114\pi$
$788$	−6.29605	−	10.9051i	−0.224287	−	0.388477i
$789$		0			0
$790$	−4.68932	+	8.12215i	−0.166839	+	0.288973i
$791$	5.31326			0.188918
$792$		0			0
$793$	−5.71529			−0.202956
$794$	−26.9913	+	46.7504i	−0.957887	+	1.65911i
$795$		0			0
$796$	−11.1452	−	19.3041i	−0.395033	−	0.684216i
$797$	−21.3861	−	37.0417i	−0.757533	−	1.31209i	−0.944105	−	0.329645i	$-0.893071\pi$
$797$	−21.3861	−	37.0417i	−0.757533	−	1.31209i	0.186572	−	0.982441i	$-0.440262\pi$
$798$		0			0
$799$	21.4381	−	37.1320i	0.758427	−	1.31363i
$800$	−31.0648			−1.09831
$801$		0			0
$802$	−26.0753			−0.920751
$803$	−5.08950	+	8.81527i	−0.179605	+	0.311084i
$804$		0			0
$805$	0.614981	+	1.06518i	0.0216752	+	0.0375426i
$806$	16.6673	+	28.8685i	0.587079	+	1.01685i
$807$		0			0
$808$	−1.91764	+	3.32144i	−0.0674622	+	0.116848i
$809$	−45.5750			−1.60233			−0.801166	−	0.598442i	$-0.795787\pi$
$809$	−45.5750			−1.60233			−0.801166	+	0.598442i	$0.795787\pi$
$810$		0			0
$811$	19.9527			0.700634			0.350317	−	0.936631i	$-0.386074\pi$
$811$	19.9527			0.700634			0.350317	+	0.936631i	$0.386074\pi$
$812$	−2.95294	+	5.11464i	−0.103628	+	0.179489i
$813$		0			0
$814$	21.1299	+	36.5981i	0.740603	+	1.28276i
$815$	−1.48737	−	2.57620i	−0.0521003	−	0.0902404i
$816$		0			0
$817$	3.02922	−	5.24676i	0.105979	−	0.183561i
$818$	−30.7440			−1.07494
$819$		0			0
$820$	−0.521451			−0.0182098
$821$	23.5697	−	40.8238i	0.822587	−	1.42476i	−0.0811632	−	0.996701i	$-0.525864\pi$
$821$	23.5697	−	40.8238i	0.822587	−	1.42476i	0.903750	−	0.428061i	$-0.140803\pi$
$822$		0			0
$823$	−11.1261	−	19.2710i	−0.387831	−	0.671744i	0.604326	−	0.796737i	$-0.293442\pi$
$823$	−11.1261	−	19.2710i	−0.387831	−	0.671744i	−0.992158	+	0.124993i	$0.960109\pi$
$824$	−4.29840	−	7.44505i	−0.149742	−	0.259361i
$825$		0			0
$826$	−8.20206	+	14.2064i	−0.285386	+	0.494303i
$827$	46.9285			1.63186			0.815931	−	0.578149i	$-0.196225\pi$
$827$	46.9285			1.63186			0.815931	+	0.578149i	$0.196225\pi$
$828$		0			0
$829$	48.4646			1.68324			0.841622	−	0.540067i	$-0.181601\pi$
$829$	48.4646			1.68324			0.841622	+	0.540067i	$0.181601\pi$
$830$	3.85134	−	6.67071i	0.133682	−	0.231544i
$831$		0			0
$832$	−7.10973	−	12.3144i	−0.246485	−	0.426925i
$833$	−14.5742	−	25.2433i	−0.504967	−	0.874629i
$834$		0			0
$835$	3.37459	−	5.84497i	0.116783	−	0.202273i
$836$	−20.3179			−0.702708
$837$		0			0
$838$	−2.62742			−0.0907627
$839$	4.63098	−	8.02109i	0.159879	−	0.276919i	−0.774946	−	0.632028i	$-0.782223\pi$
$839$	4.63098	−	8.02109i	0.159879	−	0.276919i	0.934825	+	0.355109i	$0.115556\pi$
$840$		0			0
$841$	−6.37537	−	11.0425i	−0.219840	−	0.380775i
$842$	−1.26410	−	2.18948i	−0.0435637	−	0.0754546i
$843$		0			0
$844$	−0.867996	+	1.50341i	−0.0298777	+	0.0517496i
$845$	16.8301			0.578974
$846$		0			0
$847$	3.15867			0.108533
$848$	21.6841	−	37.5580i	0.744636	−	1.28975i
$849$		0			0
$850$	19.6019	+	33.9514i	0.672339	+	1.16452i
$851$	18.7968	+	32.5571i	0.644347	+	1.11604i
$852$		0			0
$853$	15.3881	−	26.6529i	0.526877	−	0.912578i	−0.472632	−	0.881260i	$-0.656696\pi$
$853$	15.3881	−	26.6529i	0.526877	−	0.912578i	0.999509	−	0.0313185i	$-0.00997062\pi$
$854$	0.999534			0.0342034
$855$		0			0
$856$	−10.0081			−0.342071
$857$	−10.2118	+	17.6873i	−0.348828	+	0.604188i	−0.986042	−	0.166499i	$-0.946754\pi$
$857$	−10.2118	+	17.6873i	−0.348828	+	0.604188i	0.637213	+	0.770687i	$0.280087\pi$
$858$		0			0
$859$	17.8263	+	30.8761i	0.608226	+	1.05348i	0.991533	+	0.129858i	$0.0414521\pi$
$859$	17.8263	+	30.8761i	0.608226	+	1.05348i	−0.383306	+	0.923621i	$0.625215\pi$
$860$	0.286272	+	0.495838i	0.00976180	+	0.0169079i
$861$		0			0
$862$	18.1149	−	31.3759i	0.616995	−	1.06867i
$863$	−9.21342			−0.313628			−0.156814	−	0.987628i	$-0.550122\pi$
$863$	−9.21342			−0.313628			−0.156814	+	0.987628i	$0.550122\pi$
$864$		0			0
$865$	1.32959			0.0452073
$866$	−2.81765	+	4.88031i	−0.0957476	+	0.165840i
$867$		0			0
$868$	−1.16032	−	2.00974i	−0.0393840	−	0.0682151i
$869$	−15.0688	−	26.0999i	−0.511173	−	0.885377i
$870$		0			0
$871$	41.0545	−	71.1084i	1.39108	−	2.40942i
$872$	−0.0928368			−0.00314385
$873$		0			0
$874$	−45.4054			−1.53586
$875$	−1.46771	+	2.54215i	−0.0496176	+	0.0859402i
$876$		0			0
$877$	28.9184	+	50.0881i	0.976504	+	1.69135i	0.674881	+	0.737926i	$0.264195\pi$
$877$	28.9184	+	50.0881i	0.976504	+	1.69135i	0.301622	+	0.953428i	$0.402472\pi$
$878$	8.11330	+	14.0526i	0.273810	+	0.474254i
$879$		0			0
$880$	−2.68691	+	4.65387i	−0.0905758	+	0.156882i
$881$	28.9309			0.974706			0.487353	−	0.873205i	$-0.337962\pi$
$881$	28.9309			0.974706			0.487353	+	0.873205i	$0.337962\pi$
$882$		0			0
$883$	43.7957			1.47384			0.736922	−	0.675978i	$-0.236278\pi$
$883$	43.7957			1.47384			0.736922	+	0.675978i	$0.236278\pi$
$884$	−21.2868	+	36.8698i	−0.715953	+	1.24007i
$885$		0			0
$886$	10.0040	+	17.3275i	0.336092	+	0.582129i
$887$	−15.0762	−	26.1128i	−0.506210	−	0.876781i	−0.999974	−	0.00718527i	$-0.997713\pi$
$887$	−15.0762	−	26.1128i	−0.506210	−	0.876781i	0.493764	−	0.869596i	$-0.335620\pi$
$888$		0			0
$889$	0.142358	−	0.246571i	0.00477452	−	0.00826971i
$890$	6.35154			0.212904
$891$		0			0
$892$	−2.51296			−0.0841401
$893$	−29.0631	+	50.3387i	−0.972559	+	1.68452i
$894$		0			0
$895$	1.47547	+	2.55559i	0.0493195	+	0.0854239i
$896$	−3.21729	−	5.57250i	−0.107482	−	0.186164i
$897$		0			0
$898$	−17.1287	+	29.6677i	−0.571591	+	0.990025i
$899$	16.4055			0.547153
$900$		0			0
$901$	−39.5863			−1.31881
$902$	2.10472	−	3.64548i	0.0700795	−	0.121381i
$903$		0			0
$904$	4.74661	+	8.22137i	0.157870	+	0.273439i
$905$	1.35526	+	2.34738i	0.0450505	+	0.0780297i
$906$		0			0
$907$	20.8491	−	36.1118i	0.692284	−	1.19907i	−0.278803	−	0.960348i	$-0.589938\pi$
$907$	20.8491	−	36.1118i	0.692284	−	1.19907i	0.971088	−	0.238723i	$-0.0767289\pi$
$908$	16.8493			0.559165
$909$		0			0
$910$	−3.92756			−0.130197
$911$	4.40486	−	7.62944i	0.145939	−	0.252775i	−0.783784	−	0.621034i	$-0.786713\pi$
$911$	4.40486	−	7.62944i	0.145939	−	0.252775i	0.929723	+	0.368260i	$0.120046\pi$
$912$		0			0
$913$	12.3760	+	21.4358i	0.409584	+	0.709421i
$914$	17.9693	+	31.1238i	0.594372	+	1.02948i
$915$		0			0
$916$	−15.7023	+	27.1972i	−0.518819	+	0.898621i
$917$	2.09466			0.0691718
$918$		0			0
$919$	−10.9520			−0.361273			−0.180636	−	0.983550i	$-0.557816\pi$
$919$	−10.9520			−0.361273			−0.180636	+	0.983550i	$0.557816\pi$
$920$	−1.09879	+	1.90316i	−0.0362260	+	0.0627453i
$921$		0			0
$922$	36.6152	+	63.4194i	1.20586	+	2.08861i
$923$	47.7927	+	82.7793i	1.57312	+	2.72472i
$924$		0			0
$925$	−22.0018	+	38.1083i	−0.723416	+	1.25299i
$926$	−40.6360			−1.33538
$927$		0			0
$928$	−41.7080			−1.36913
$929$	14.1039	−	24.4287i	0.462735	−	0.801481i	−0.536361	−	0.843989i	$-0.680201\pi$
$929$	14.1039	−	24.4287i	0.462735	−	0.801481i	0.999096	+	0.0425081i	$0.0135348\pi$
$930$		0			0
$931$	19.7579	+	34.2217i	0.647538	+	1.12157i
$932$	−5.15041	−	8.92078i	−0.168707	−	0.292210i
$933$		0			0
$934$	−2.56499	+	4.44270i	−0.0839291	+	0.145369i
$935$	4.90519			0.160417
$936$		0			0
$937$	−32.3092			−1.05550			−0.527748	−	0.849401i	$-0.676963\pi$
$937$	−32.3092			−1.05550			−0.527748	+	0.849401i	$0.676963\pi$
$938$	−7.17992	+	12.4360i	−0.234433	+	0.406049i
$939$		0			0
$940$	−2.74657	−	4.75720i	−0.0895833	−	0.155163i
$941$	11.5701	+	20.0400i	0.377175	+	0.653286i	0.990650	−	0.136428i	$-0.0435623\pi$
$941$	11.5701	+	20.0400i	0.377175	+	0.653286i	−0.613475	+	0.789714i	$0.710229\pi$
$942$		0			0
$943$	1.87232	−	3.24296i	0.0609712	−	0.105605i
$944$	−63.7575			−2.07513
$945$		0			0
$946$	−4.62190			−0.150271
$947$	13.1368	−	22.7537i	0.426890	−	0.739396i	−0.569705	−	0.821850i	$-0.692942\pi$
$947$	13.1368	−	22.7537i	0.426890	−	0.739396i	0.996595	+	0.0824539i	$0.0262757\pi$
$948$		0			0
$949$	−14.4575	−	25.0411i	−0.469309	−	0.812868i
$950$	−26.5737	−	46.0270i	−0.862165	−	1.49331i
$951$		0			0
$952$	−1.90659	+	3.30231i	−0.0617929	+	0.107028i
$953$	8.01441			0.259612			0.129806	−	0.991539i	$-0.458565\pi$
$953$	8.01441			0.259612			0.129806	+	0.991539i	$0.458565\pi$
$954$		0			0
$955$	4.23780			0.137132
$956$	−2.25707	+	3.90936i	−0.0729989	+	0.126438i
$957$		0			0
$958$	−14.2991	−	24.7669i	−0.461985	−	0.800181i
$959$	3.69330	+	6.39698i	0.119263	+	0.206569i
$960$		0			0
$961$	12.2768	−	21.2641i	0.396027	−	0.685938i
$962$	−120.045			−3.87042
$963$		0			0
$964$	−16.3152			−0.525476
$965$	−1.39725	+	2.42011i	−0.0449791	+	0.0779061i
$966$		0			0
$967$	−12.2344	−	21.1906i	−0.393432	−	0.681445i	0.599467	−	0.800399i	$-0.295379\pi$
$967$	−12.2344	−	21.1906i	−0.393432	−	0.681445i	−0.992900	+	0.118954i	$0.962046\pi$
$968$	2.82181	+	4.88751i	0.0906963	+	0.157091i
$969$		0			0
$970$	5.91360	−	10.2427i	0.189874	−	0.328872i
$971$	20.7426			0.665662			0.332831	−	0.942987i	$-0.391996\pi$
$971$	20.7426			0.665662			0.332831	+	0.942987i	$0.391996\pi$
$972$		0			0
$973$	15.7075			0.503559
$974$	−7.58202	+	13.1324i	−0.242943	+	0.420790i
$975$		0			0
$976$	1.94243	+	3.36439i	0.0621757	+	0.107692i
$977$	−2.31165	−	4.00389i	−0.0739562	−	0.128096i	0.826676	−	0.562679i	$-0.190229\pi$
$977$	−2.31165	−	4.00389i	−0.0739562	−	0.128096i	−0.900632	+	0.434583i	$0.856896\pi$
$978$		0			0
$979$	−10.2051	+	17.6757i	−0.326156	+	0.564918i
$980$	−3.73439			−0.119291
$981$		0			0
$982$	39.1174			1.24829
$983$	−21.9604	+	38.0364i	−0.700427	+	1.21317i	0.267890	+	0.963449i	$0.413674\pi$
$983$	−21.9604	+	38.0364i	−0.700427	+	1.21317i	−0.968317	+	0.249725i	$0.919660\pi$
$984$		0			0
$985$	−2.06063	−	3.56912i	−0.0656572	−	0.113722i
$986$	26.3178	+	45.5837i	0.838128	+	1.45168i
$987$		0			0
$988$	28.8579	−	49.9834i	0.918093	−	1.59018i
$989$	−4.11156			−0.130740
$990$		0			0
$991$	30.0775			0.955442			0.477721	−	0.878511i	$-0.341463\pi$
$991$	30.0775			0.955442			0.477721	+	0.878511i	$0.341463\pi$
$992$	8.19435	−	14.1930i	0.260171	−	0.450629i
$993$		0			0
$994$	−8.35835	−	14.4771i	−0.265111	−	0.459185i
$995$	−3.64772	−	6.31804i	−0.115641	−	0.200295i
$996$		0			0
$997$	12.7130	−	22.0196i	0.402625	−	0.697367i	−0.591417	−	0.806366i	$-0.701431\pi$
$997$	12.7130	−	22.0196i	0.402625	−	0.697367i	0.994042	+	0.108999i	$0.0347646\pi$
$998$	16.1568			0.511436
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1161.2.f.d.775.17		40
3.2	odd	2		387.2.f.d.259.4	yes	40
9.2	odd	6		3483.2.a.t.1.17		20
9.4	even	3	inner	1161.2.f.d.388.17		40
9.5	odd	6		387.2.f.d.130.4	✓	40
9.7	even	3		3483.2.a.u.1.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.d.130.4	✓	40	9.5	odd	6
387.2.f.d.259.4	yes	40	3.2	odd	2
1161.2.f.d.388.17		40	9.4	even	3	inner
1161.2.f.d.775.17		40	1.1	even	1	trivial
3483.2.a.t.1.17		20	9.2	odd	6
3483.2.a.u.1.4		20	9.7	even	3

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:	\( N \)	\(=\)	\( 1161 = 3^{3} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1161.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.911404 - 1.57860i) q^{2} +(-0.661315 - 1.14543i) q^{4} +(-0.216442 - 0.374888i) q^{5} +(0.345529 - 0.598473i) q^{7} +1.23472 q^{8} +O(q^{10})\)	\(q+(0.911404 - 1.57860i) q^{2} +(-0.661315 - 1.14543i) q^{4} +(-0.216442 - 0.374888i) q^{5} +(0.345529 - 0.598473i) q^{7} +1.23472 q^{8} -0.789063 q^{10} +(1.26780 - 2.19589i) q^{11} +(3.60136 + 6.23773i) q^{13} +(-0.629833 - 1.09090i) q^{14} +(2.44795 - 4.23998i) q^{16} -4.46895 q^{17} +6.05843 q^{19} +(-0.286272 + 0.495838i) q^{20} +(-2.31095 - 4.00268i) q^{22} +(-2.05578 - 3.56072i) q^{23} +(2.40631 - 4.16784i) q^{25} +13.1292 q^{26} -0.914014 q^{28} +(3.23074 - 5.59581i) q^{29} +(1.26948 + 2.19881i) q^{31} +(-3.22744 - 5.59009i) q^{32} +(-4.07302 + 7.05468i) q^{34} -0.299147 q^{35} -9.14340 q^{37} +(5.52168 - 9.56383i) q^{38} +(-0.267244 - 0.462880i) q^{40} +(0.455380 + 0.788741i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.35365 q^{44} -7.49459 q^{46} +(-4.79713 + 8.30887i) q^{47} +(3.26122 + 5.64860i) q^{49} +(-4.38623 - 7.59718i) q^{50} +(4.76326 - 8.25022i) q^{52} +8.85806 q^{53} -1.09761 q^{55} +(0.426630 - 0.738944i) q^{56} +(-5.88902 - 10.2001i) q^{58} +(-6.51130 - 11.2779i) q^{59} +(-0.396746 + 0.687184i) q^{61} +4.62805 q^{62} -1.97418 q^{64} +(1.55897 - 2.70021i) q^{65} +(-5.69986 - 9.87245i) q^{67} +(2.95539 + 5.11888i) q^{68} +(-0.272644 + 0.472233i) q^{70} +13.2707 q^{71} -4.01445 q^{73} +(-8.33334 + 14.4338i) q^{74} +(-4.00653 - 6.93952i) q^{76} +(-0.876120 - 1.51748i) q^{77} +(5.94290 - 10.2934i) q^{79} -2.11936 q^{80} +1.66014 q^{82} +(-4.88090 + 8.45396i) q^{83} +(0.967268 + 1.67536i) q^{85} +(-0.911404 - 1.57860i) q^{86} +(1.56537 - 2.71129i) q^{88} -8.04947 q^{89} +4.97749 q^{91} +(-2.71904 + 4.70951i) q^{92} +(8.74425 + 15.1455i) q^{94} +(-1.31130 - 2.27123i) q^{95} +(-7.49445 + 12.9808i) q^{97} +11.8892 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8}+O(q^{10}) \) 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8	\( 40 q - 6 q^{2} - 22 q^{4} - 17 q^{5} - 3 q^{7} + 30 q^{8} - 4 q^{10} - 10 q^{11} + q^{13} - 10 q^{14} - 22 q^{16} + 40 q^{17} + 16 q^{19} - 30 q^{20} - 15 q^{22} - 19 q^{23} - 19 q^{25} + 50 q^{26} - 6 q^{28} - 25 q^{29} + 11 q^{31} - 36 q^{32} - 9 q^{34} + 18 q^{37} - 28 q^{38} - 12 q^{40} - 12 q^{41} + 20 q^{43} + 10 q^{44} + 8 q^{46} - 38 q^{47} - 37 q^{49} - 36 q^{50} + 8 q^{52} + 138 q^{53} - 18 q^{55} - 30 q^{56} + 27 q^{58} - 31 q^{59} - 19 q^{61} + 64 q^{62} + 22 q^{64} - 47 q^{65} - 9 q^{67} - 68 q^{68} + 6 q^{70} + 42 q^{71} - 4 q^{73} + 16 q^{74} - 37 q^{76} - 85 q^{77} + 4 q^{79} + 122 q^{80} + 2 q^{82} - 19 q^{83} + 6 q^{85} + 6 q^{86} - 60 q^{88} + 108 q^{89} - 6 q^{91} - 85 q^{92} + 19 q^{94} + 11 q^{95} - 2 q^{97} + 10 q^{98}+O(q^{100}) \) 40 * q - 6 * q^2 - 22 * q^4 - 17 * q^5 - 3 * q^7 + 30 * q^8 - 4 * q^10 - 10 * q^11 + q^13 - 10 * q^14 - 22 * q^16 + 40 * q^17 + 16 * q^19 - 30 * q^20 - 15 * q^22 - 19 * q^23 - 19 * q^25 + 50 * q^26 - 6 * q^28 - 25 * q^29 + 11 * q^31 - 36 * q^32 - 9 * q^34 + 18 * q^37 - 28 * q^38 - 12 * q^40 - 12 * q^41 + 20 * q^43 + 10 * q^44 + 8 * q^46 - 38 * q^47 - 37 * q^49 - 36 * q^50 + 8 * q^52 + 138 * q^53 - 18 * q^55 - 30 * q^56 + 27 * q^58 - 31 * q^59 - 19 * q^61 + 64 * q^62 + 22 * q^64 - 47 * q^65 - 9 * q^67 - 68 * q^68 + 6 * q^70 + 42 * q^71 - 4 * q^73 + 16 * q^74 - 37 * q^76 - 85 * q^77 + 4 * q^79 + 122 * q^80 + 2 * q^82 - 19 * q^83 + 6 * q^85 + 6 * q^86 - 60 * q^88 + 108 * q^89 - 6 * q^91 - 85 * q^92 + 19 * q^94 + 11 * q^95 - 2 * q^97 + 10 * q^98

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