LMFDB - Embedded newform 891.2.k.a.161.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(161,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("891.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.k (of order $10$, degree $4$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.8
Character	$\chi$	$=$	891.161
Dual form			891.2.k.a.404.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.505702 - 0.367414i) q^{2} +(-0.497292 - 1.53051i) q^{4} +(0.749839 + 1.03206i) q^{5} +(4.60560 - 1.49645i) q^{7} +(-0.697171 + 2.14567i) q^{8} -0.797419i q^{10} +(0.591134 - 3.26352i) q^{11} +(0.490794 - 0.675520i) q^{13} +(-2.87888 - 0.935406i) q^{14} +(-1.46295 + 1.06289i) q^{16} +(0.199958 - 0.145278i) q^{17} +(2.08556 + 0.677640i) q^{19} +(1.20669 - 1.66087i) q^{20} +(-1.49800 + 1.43318i) q^{22} +4.84746i q^{23} +(1.04219 - 3.20752i) q^{25} +(-0.496392 + 0.161287i) q^{26} +(-4.58066 - 6.30474i) q^{28} +(2.40128 + 7.39039i) q^{29} +(-1.41927 - 1.03116i) q^{31} +5.64252 q^{32} -0.154496 q^{34} +(4.99790 + 3.63118i) q^{35} +(0.106959 + 0.329187i) q^{37} +(-0.805699 - 1.10895i) q^{38} +(-2.73724 + 0.889382i) q^{40} +(1.50228 - 4.62355i) q^{41} -0.423369i q^{43} +(-5.28881 + 0.718188i) q^{44} +(1.78103 - 2.45137i) q^{46} +(-7.07320 - 2.29822i) q^{47} +(13.3091 - 9.66963i) q^{49} +(-1.70552 + 1.23914i) q^{50} +(-1.27796 - 0.415234i) q^{52} +(6.95271 - 9.56959i) q^{53} +(3.81142 - 1.83703i) q^{55} +10.9254i q^{56} +(1.50100 - 4.61960i) q^{58} +(-4.99606 + 1.62332i) q^{59} +(-8.19100 - 11.2739i) q^{61} +(0.338865 + 1.04292i) q^{62} +(0.0724543 + 0.0526411i) q^{64} +1.06520 q^{65} +0.504907 q^{67} +(-0.321787 - 0.233792i) q^{68} +(-1.19330 - 3.67260i) q^{70} +(-6.95402 - 9.57138i) q^{71} +(3.85174 - 1.25150i) q^{73} +(0.0668585 - 0.205769i) q^{74} -3.52895i q^{76} +(-2.16117 - 15.9151i) q^{77} +(-1.30074 + 1.79032i) q^{79} +(-2.19395 - 0.712856i) q^{80} +(-2.45847 + 1.78618i) q^{82} +(3.33901 - 2.42593i) q^{83} +(0.299872 + 0.0974345i) q^{85} +(-0.155552 + 0.214099i) q^{86} +(6.59032 + 3.54361i) q^{88} +13.5225i q^{89} +(1.24952 - 3.84563i) q^{91} +(7.41908 - 2.41061i) q^{92} +(2.73253 + 3.76101i) q^{94} +(0.864467 + 2.66055i) q^{95} +(6.43118 + 4.67252i) q^{97} -10.2832 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) $ 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.505702	−	0.367414i	−0.357586	−	0.259801i	0.394459	−	0.918914i	$-0.370932\pi$
$2$	−0.505702	−	0.367414i	−0.357586	−	0.259801i	−0.752044	+	0.659113i	$0.770932\pi$
$3$		0			0
$3$		0			0
$4$	−0.497292	−	1.53051i	−0.248646	−	0.765254i
$5$	0.749839	+	1.03206i	0.335338	+	0.461553i	0.943073	−	0.332587i	$-0.107922\pi$
$5$	0.749839	+	1.03206i	0.335338	+	0.461553i	−0.607734	+	0.794140i	$0.707922\pi$
$6$		0			0
$7$	4.60560	−	1.49645i	1.74075	−	0.565606i	0.745822	−	0.666146i	$-0.232057\pi$
$7$	4.60560	−	1.49645i	1.74075	−	0.565606i	0.994933	+	0.100540i	$0.0320570\pi$
$8$	−0.697171	+	2.14567i	−0.246487	+	0.758609i
$9$		0			0
$10$		−	0.797419i		−	0.252166i
$11$	0.591134	−	3.26352i	0.178234	−	0.983988i
$11$	0.591134	−	3.26352i	0.178234	−	0.983988i
$12$		0			0
$13$	0.490794	−	0.675520i	0.136122	−	0.187356i	−0.735514	−	0.677509i	$-0.763059\pi$
$13$	0.490794	−	0.675520i	0.136122	−	0.187356i	0.871636	+	0.490154i	$0.163059\pi$
$14$	−2.87888	−	0.935406i	−0.769414	−	0.249998i
$15$		0			0
$16$	−1.46295	+	1.06289i	−0.365736	+	0.265723i
$17$	0.199958	−	0.145278i	0.0484969	−	0.0352351i	−0.563273	−	0.826271i	$-0.690458\pi$
$17$	0.199958	−	0.145278i	0.0484969	−	0.0352351i	0.611770	+	0.791036i	$0.290458\pi$
$18$		0			0
$19$	2.08556	+	0.677640i	0.478461	+	0.155461i	0.538311	−	0.842746i	$-0.319062\pi$
$19$	2.08556	+	0.677640i	0.478461	+	0.155461i	−0.0598507	+	0.998207i	$0.519062\pi$
$20$	1.20669	−	1.66087i	0.269825	−	0.371382i
$21$		0			0
$22$	−1.49800	+	1.43318i	−0.319375	+	0.305555i
$23$			4.84746i			1.01077i	0.862895	+	0.505383i	$0.168649\pi$
$23$			4.84746i			1.01077i	−0.862895	+	0.505383i	$0.831351\pi$
$24$		0			0
$25$	1.04219	−	3.20752i	0.208437	−	0.641504i
$26$	−0.496392	+	0.161287i	−0.0973504	+	0.0316311i
$27$		0			0
$28$	−4.58066	−	6.30474i	−0.865664	−	1.19148i
$29$	2.40128	+	7.39039i	0.445907	+	1.37236i	0.881486	+	0.472210i	$0.156544\pi$
$29$	2.40128	+	7.39039i	0.445907	+	1.37236i	−0.435579	+	0.900151i	$0.643456\pi$
$30$		0			0
$31$	−1.41927	−	1.03116i	−0.254908	−	0.185202i	0.452991	−	0.891515i	$-0.350357\pi$
$31$	−1.41927	−	1.03116i	−0.254908	−	0.185202i	−0.707899	+	0.706313i	$0.750357\pi$
$32$	5.64252			0.997466
$33$		0			0
$34$	−0.154496			−0.0264959
$35$	4.99790	+	3.63118i	0.844799	+	0.613782i
$36$		0			0
$37$	0.106959	+	0.329187i	0.0175840	+	0.0541180i	0.959464	−	0.281833i	$-0.0909424\pi$
$37$	0.106959	+	0.329187i	0.0175840	+	0.0541180i	−0.941879	+	0.335951i	$0.890942\pi$
$38$	−0.805699	−	1.10895i	−0.130702	−	0.179895i
$39$		0			0
$40$	−2.73724	+	0.889382i	−0.432795	+	0.140624i
$41$	1.50228	−	4.62355i	0.234617	−	0.722078i	−0.762555	−	0.646924i	$-0.776055\pi$
$41$	1.50228	−	4.62355i	0.234617	−	0.722078i	0.997172	−	0.0751541i	$-0.0239449\pi$
$42$		0			0
$43$		−	0.423369i		−	0.0645632i	−0.999479	−	0.0322816i	$-0.989723\pi$
$43$		−	0.423369i		−	0.0645632i	0.999479	−	0.0322816i	$-0.0102773\pi$
$44$	−5.28881	+	0.718188i	−0.797318	+	0.108271i
$45$		0			0
$46$	1.78103	−	2.45137i	0.262598	−	0.361435i
$47$	−7.07320	−	2.29822i	−1.03173	−	0.335230i	−0.256257	−	0.966609i	$-0.582489\pi$
$47$	−7.07320	−	2.29822i	−1.03173	−	0.335230i	−0.775475	+	0.631379i	$0.782489\pi$
$48$		0			0
$49$	13.3091	−	9.66963i	1.90130	−	1.38138i
$50$	−1.70552	+	1.23914i	−0.241197	+	0.175240i
$51$		0			0
$52$	−1.27796	−	0.415234i	−0.177221	−	0.0575825i
$53$	6.95271	−	9.56959i	0.955029	−	1.31448i	0.00577155	−	0.999983i	$-0.498163\pi$
$53$	6.95271	−	9.56959i	0.955029	−	1.31448i	0.949257	−	0.314501i	$-0.101837\pi$
$54$		0			0
$55$	3.81142	−	1.83703i	0.513932	−	0.247704i
$56$			10.9254i			1.45997i
$57$		0			0
$58$	1.50100	−	4.61960i	0.197091	−	0.606584i
$59$	−4.99606	+	1.62332i	−0.650432	+	0.211338i	−0.615604	−	0.788055i	$-0.711088\pi$
$59$	−4.99606	+	1.62332i	−0.650432	+	0.211338i	−0.0348272	+	0.999393i	$0.511088\pi$
$60$		0			0
$61$	−8.19100	−	11.2739i	−1.04875	−	1.44348i	−0.889888	−	0.456179i	$-0.849218\pi$
$61$	−8.19100	−	11.2739i	−1.04875	−	1.44348i	−0.158861	−	0.987301i	$-0.550782\pi$
$62$	0.338865	+	1.04292i	0.0430359	+	0.132451i
$63$		0			0
$64$	0.0724543	+	0.0526411i	0.00905678	+	0.00658014i
$65$	1.06520			0.132121
$66$		0			0
$67$	0.504907			0.0616842			0.0308421	−	0.999524i	$-0.490181\pi$
$67$	0.504907			0.0616842			0.0308421	+	0.999524i	$0.490181\pi$
$68$	−0.321787	−	0.233792i	−0.0390224	−	0.0283514i
$69$		0			0
$70$	−1.19330	−	3.67260i	−0.142626	−	0.438959i
$71$	−6.95402	−	9.57138i	−0.825290	−	1.13591i	−0.988781	−	0.149370i	$-0.952276\pi$
$71$	−6.95402	−	9.57138i	−0.825290	−	1.13591i	0.163491	−	0.986545i	$-0.447724\pi$
$72$		0			0
$73$	3.85174	−	1.25150i	0.450812	−	0.146478i	−0.0748068	−	0.997198i	$-0.523834\pi$
$73$	3.85174	−	1.25150i	0.450812	−	0.146478i	0.525618	+	0.850720i	$0.323834\pi$
$74$	0.0668585	−	0.205769i	0.00777214	−	0.0239202i
$75$		0			0
$76$		−	3.52895i		−	0.404799i
$77$	−2.16117	−	15.9151i	−0.246288	−	1.81369i
$78$		0			0
$79$	−1.30074	+	1.79032i	−0.146345	+	0.201426i	−0.875896	−	0.482500i	$-0.839729\pi$
$79$	−1.30074	+	1.79032i	−0.146345	+	0.201426i	0.729551	+	0.683926i	$0.239729\pi$
$80$	−2.19395	−	0.712856i	−0.245291	−	0.0796998i
$81$		0			0
$82$	−2.45847	+	1.78618i	−0.271492	+	0.197251i
$83$	3.33901	−	2.42593i	0.366503	−	0.266280i	−0.389256	−	0.921130i	$-0.627268\pi$
$83$	3.33901	−	2.42593i	0.366503	−	0.266280i	0.755760	+	0.654849i	$0.227268\pi$
$84$		0			0
$85$	0.299872	+	0.0974345i	0.0325257	+	0.0105683i
$86$	−0.155552	+	0.214099i	−0.0167736	+	0.0230869i
$87$		0			0
$88$	6.59032	+	3.54361i	0.702530	+	0.377750i
$89$			13.5225i			1.43338i	0.697393	+	0.716689i	$0.254343\pi$
$89$			13.5225i			1.43338i	−0.697393	+	0.716689i	$0.745657\pi$
$90$		0			0
$91$	1.24952	−	3.84563i	0.130985	−	0.403131i
$92$	7.41908	−	2.41061i	0.773493	−	0.251323i
$93$		0			0
$94$	2.73253	+	3.76101i	0.281839	+	0.387918i
$95$	0.864467	+	2.66055i	0.0886924	+	0.272967i
$96$		0			0
$97$	6.43118	+	4.67252i	0.652987	+	0.474423i	0.864287	−	0.502998i	$-0.167770\pi$
$97$	6.43118	+	4.67252i	0.652987	+	0.474423i	−0.211300	+	0.977421i	$0.567770\pi$
$98$	−10.2832			−1.03876
$99$		0			0
$100$	−5.42741			−0.542741
$101$	−4.36445	−	3.17096i	−0.434279	−	0.315522i	0.349079	−	0.937093i	$-0.386495\pi$
$101$	−4.36445	−	3.17096i	−0.434279	−	0.315522i	−0.783358	+	0.621571i	$0.786495\pi$
$102$		0			0
$103$	5.08550	+	15.6516i	0.501089	+	1.54219i	0.807247	+	0.590214i	$0.200957\pi$
$103$	5.08550	+	15.6516i	0.501089	+	1.54219i	−0.306157	+	0.951981i	$0.599043\pi$
$104$	1.10728	+	1.52404i	0.108577	+	0.149444i
$105$		0			0
$106$	−7.03201	+	2.28484i	−0.683009	+	0.221923i
$107$	0.705070	−	2.16998i	0.0681617	−	0.209780i	−0.911174	−	0.412022i	$-0.864823\pi$
$107$	0.705070	−	2.16998i	0.0681617	−	0.209780i	0.979336	+	0.202242i	$0.0648227\pi$
$108$		0			0
$109$			8.89941i			0.852409i	0.904627	+	0.426205i	$0.140150\pi$
$109$			8.89941i			0.852409i	−0.904627	+	0.426205i	$0.859850\pi$
$110$	−2.60239	−	0.471381i	−0.248128	−	0.0449445i
$111$		0			0
$112$	−5.14718	+	7.08449i	−0.486363	+	0.669421i
$113$	6.88671	+	2.23763i	0.647847	+	0.210498i	0.614465	−	0.788944i	$-0.289372\pi$
$113$	6.88671	+	2.23763i	0.647847	+	0.210498i	0.0333823	+	0.999443i	$0.489372\pi$
$114$		0			0
$115$	−5.00289	+	3.63482i	−0.466522	+	0.338948i
$116$	10.1169	−	7.35037i	0.939332	−	0.682465i
$117$		0			0
$118$	3.12295	+	1.01471i	0.287491	+	0.0934114i
$119$	0.703526	−	0.968320i	0.0644921	−	0.0887658i
$120$		0			0
$121$	−10.3011	−	3.85836i	−0.936466	−	0.350760i
$122$			8.71074i			0.788634i
$123$		0			0
$124$	−0.872407	+	2.68499i	−0.0783445	+	0.241119i
$125$	10.1582	−	3.30059i	0.908574	−	0.295213i
$126$		0			0
$127$	1.69280	+	2.32994i	0.150212	+	0.206749i	0.877491	−	0.479593i	$-0.159216\pi$
$127$	1.69280	+	2.32994i	0.150212	+	0.206749i	−0.727279	+	0.686341i	$0.759216\pi$
$128$	−3.50457	−	10.7860i	−0.309763	−	0.953353i
$129$		0			0
$130$	−0.538673	−	0.391369i	−0.0472447	−	0.0343253i
$131$	0.563363			0.0492213			0.0246106	−	0.999697i	$-0.492165\pi$
$131$	0.563363			0.0492213			0.0246106	+	0.999697i	$0.492165\pi$
$132$		0			0
$133$	10.6193			0.920812
$134$	−0.255333	−	0.185510i	−0.0220574	−	0.0160256i
$135$		0			0
$136$	0.172314	+	0.530328i	0.0147758	+	0.0454752i
$137$	2.72868	+	3.75570i	0.233127	+	0.320871i	0.909513	−	0.415676i	$-0.136455\pi$
$137$	2.72868	+	3.75570i	0.233127	+	0.320871i	−0.676386	+	0.736547i	$0.736455\pi$
$138$		0			0
$139$	−9.99398	+	3.24724i	−0.847678	+	0.275427i	−0.700473	−	0.713679i	$-0.747028\pi$
$139$	−9.99398	+	3.24724i	−0.847678	+	0.275427i	−0.147205	+	0.989106i	$0.547028\pi$
$140$	3.07214	−	9.45508i	0.259643	−	0.799100i
$141$		0			0
$142$			7.39528i			0.620598i
$143$	−1.91445	−	2.00104i	−0.160094	−	0.167335i
$144$		0			0
$145$	−5.82678	+	8.01988i	−0.483888	+	0.666015i
$146$	−2.40765	−	0.782294i	−0.199259	−	0.0647431i
$147$		0			0
$148$	0.450634	−	0.327405i	0.0370419	−	0.0269125i
$149$	−12.3170	+	8.94886i	−1.00905	+	0.733119i	−0.964010	−	0.265866i	$-0.914342\pi$
$149$	−12.3170	+	8.94886i	−1.00905	+	0.733119i	−0.0450420	+	0.998985i	$0.514342\pi$
$150$		0			0
$151$	7.26733	+	2.36130i	0.591407	+	0.192160i	0.589404	−	0.807838i	$-0.299363\pi$
$151$	7.26733	+	2.36130i	0.591407	+	0.192160i	0.00200261	+	0.999998i	$0.499363\pi$
$152$	−2.90799	+	4.00250i	−0.235869	+	0.324646i
$153$		0			0
$154$	−4.75452	+	8.84234i	−0.383130	+	0.712536i
$155$		−	2.23798i		−	0.179759i
$156$		0			0
$157$	−1.33807	+	4.11814i	−0.106789	+	0.328663i	−0.990146	−	0.140037i	$-0.955278\pi$
$157$	−1.33807	+	4.11814i	−0.106789	+	0.328663i	0.883357	+	0.468701i	$0.155278\pi$
$158$	1.31557	−	0.427456i	0.104662	−	0.0340066i
$159$		0			0
$160$	4.23098	+	5.82345i	0.334488	+	0.460384i
$161$	7.25399	+	22.3255i	0.571695	+	1.75950i
$162$		0			0
$163$	−5.76502	−	4.18853i	−0.451551	−	0.328071i	0.338657	−	0.940910i	$-0.390027\pi$
$163$	−5.76502	−	4.18853i	−0.451551	−	0.328071i	−0.790208	+	0.612839i	$0.790027\pi$
$164$	−7.82346			−0.610910
$165$		0			0
$166$	−2.57986			−0.200236
$167$	−6.61623	−	4.80697i	−0.511979	−	0.371975i	0.301595	−	0.953436i	$-0.402481\pi$
$167$	−6.61623	−	4.80697i	−0.511979	−	0.371975i	−0.813574	+	0.581462i	$0.802481\pi$
$168$		0			0
$169$	3.80177	+	11.7007i	0.292444	+	0.900050i
$170$	−0.115847	−	0.159450i	−0.00888509	−	0.0122293i
$171$		0			0
$172$	−0.647970	+	0.210538i	−0.0494072	+	0.0160534i
$173$	2.09058	−	6.43416i	0.158944	−	0.489180i	−0.839595	−	0.543213i	$-0.817208\pi$
$173$	2.09058	−	6.43416i	0.158944	−	0.489180i	0.998539	+	0.0540330i	$0.0172076\pi$
$174$		0			0
$175$		−	16.3321i		−	1.23459i
$176$	2.60397	+	5.40266i	0.196282	+	0.407241i
$177$		0			0
$178$	4.96834	−	6.83834i	0.372393	−	0.512555i
$179$	−6.85049	−	2.22586i	−0.512030	−	0.166369i	0.0415954	−	0.999135i	$-0.486756\pi$
$179$	−6.85049	−	2.22586i	−0.512030	−	0.166369i	−0.553625	+	0.832766i	$0.686756\pi$
$180$		0			0
$181$	0.383330	−	0.278506i	0.0284927	−	0.0207012i	−0.573448	−	0.819242i	$-0.694394\pi$
$181$	0.383330	−	0.278506i	0.0284927	−	0.0207012i	0.601940	+	0.798541i	$0.294394\pi$
$182$	−2.04482	+	1.48565i	−0.151572	+	0.110124i
$183$		0			0
$184$	−10.4011	−	3.37951i	−0.766777	−	0.249141i
$185$	−0.259540	+	0.357226i	−0.0190818	+	0.0262638i
$186$		0			0
$187$	−0.355915	−	0.738445i	−0.0260271	−	0.0540005i
$188$			11.9685i			0.872891i
$189$		0			0
$190$	0.540363	−	1.66307i	0.0392020	−	0.120651i
$191$	−0.0386108	+	0.0125454i	−0.00279378	+	0.000907754i	−0.310414	−	0.950602i	$-0.600468\pi$
$191$	−0.0386108	+	0.0125454i	−0.00279378	+	0.000907754i	0.307620	+	0.951509i	$0.400468\pi$
$192$		0			0
$193$	6.60502	+	9.09103i	0.475440	+	0.654387i	0.977621	−	0.210376i	$-0.0674688\pi$
$193$	6.60502	+	9.09103i	0.475440	+	0.654387i	−0.502181	+	0.864763i	$0.667469\pi$
$194$	−1.53551	−	4.72581i	−0.110243	−	0.339294i
$195$		0			0
$196$	−21.4180	−	15.5611i	−1.52985	−	1.11150i
$197$	−20.8150			−1.48301			−0.741504	−	0.670948i	$-0.765887\pi$
$197$	−20.8150			−1.48301			−0.741504	+	0.670948i	$0.765887\pi$
$198$		0			0
$199$	14.4111			1.02158			0.510788	−	0.859707i	$-0.329354\pi$
$199$	14.4111			1.02158			0.510788	+	0.859707i	$0.329354\pi$
$200$	6.15570	+	4.47238i	0.435274	+	0.316245i
$201$		0			0
$202$	1.04206	+	3.20712i	0.0733189	+	0.225652i
$203$	22.1187	+	30.4438i	1.55243	+	2.13674i
$204$		0			0
$205$	5.89828	−	1.91647i	0.411954	−	0.133852i
$206$	3.17886	−	9.78352i	0.221482	−	0.681650i
$207$		0			0
$208$			1.50991i			0.104693i
$209$	3.44434	−	6.40569i	0.238250	−	0.443091i
$210$		0			0
$211$	−10.6840	+	14.7053i	−0.735518	+	1.01235i	0.263346	+	0.964701i	$0.415174\pi$
$211$	−10.6840	+	14.7053i	−0.735518	+	1.01235i	−0.998864	+	0.0476521i	$0.984826\pi$
$212$	−18.1039	−	5.88230i	−1.24338	−	0.403998i
$213$		0			0
$214$	−1.15384	+	0.838313i	−0.0788748	+	0.0573059i
$215$	0.436944	−	0.317458i	0.0297993	−	0.0216505i
$216$		0			0
$217$	−8.07968	−	2.62525i	−0.548484	−	0.178213i
$218$	3.26977	−	4.50045i	0.221457	−	0.304809i
$219$		0			0
$220$	−4.70697	−	4.91987i	−0.317344	−	0.331698i
$221$		−	0.206377i		−	0.0138824i
$222$		0			0
$223$	0.233145	−	0.717545i	0.0156125	−	0.0480504i	−0.942947	−	0.332944i	$-0.891958\pi$
$223$	0.233145	−	0.717545i	0.0156125	−	0.0480504i	0.958559	+	0.284893i	$0.0919581\pi$
$224$	25.9872	−	8.44376i	1.73634	−	0.564172i
$225$		0			0
$226$	−2.66049	−	3.66185i	−0.176973	−	0.243582i
$227$	5.13526	+	15.8047i	0.340839	+	1.04900i	0.963774	+	0.266721i	$0.0859403\pi$
$227$	5.13526	+	15.8047i	0.340839	+	1.04900i	−0.622935	+	0.782274i	$0.714060\pi$
$228$		0			0
$229$	17.7967	+	12.9300i	1.17604	+	0.854441i	0.991719	−	0.128426i	$-0.0409923\pi$
$229$	17.7967	+	12.9300i	1.17604	+	0.854441i	0.184318	+	0.982867i	$0.440992\pi$
$230$	3.86546			0.254881
$231$		0			0
$232$	−17.5315			−1.15100
$233$	−12.5102	−	9.08916i	−0.819568	−	0.595451i	0.0970210	−	0.995282i	$-0.469069\pi$
$233$	−12.5102	−	9.08916i	−0.819568	−	0.595451i	−0.916589	+	0.399832i	$0.869069\pi$
$234$		0			0
$235$	−2.93185	−	9.02329i	−0.191252	−	0.588615i
$236$	4.96900	+	6.83925i	0.323455	+	0.445197i
$237$		0			0
$238$	−0.711549	+	0.231196i	−0.0461229	+	0.0149862i
$239$	5.81253	−	17.8891i	0.375981	−	1.15715i	−0.566833	−	0.823833i	$-0.691831\pi$
$239$	5.81253	−	17.8891i	0.375981	−	1.15715i	0.942814	−	0.333319i	$-0.108169\pi$
$240$		0			0
$241$			15.5682i			1.00284i	0.865205	+	0.501419i	$0.167189\pi$
$241$			15.5682i			1.00284i	−0.865205	+	0.501419i	$0.832811\pi$
$242$	3.79169	+	5.73596i	0.243739	+	0.368721i
$243$		0			0
$244$	−13.1815	+	18.1428i	−0.843862	+	1.16148i
$245$	19.9594	+	6.48519i	1.27516	+	0.414324i
$246$		0			0
$247$	1.48134	−	1.07626i	0.0942555	−	0.0684806i
$248$	3.20200	−	2.32639i	0.203327	−	0.147726i
$249$		0			0
$250$	−6.34969	−	2.06314i	−0.401590	−	0.130484i
$251$	−8.32155	+	11.4536i	−0.525252	+	0.722947i	−0.986397	−	0.164378i	$-0.947438\pi$
$251$	−8.32155	+	11.4536i	−0.525252	+	0.722947i	0.461146	+	0.887324i	$0.347438\pi$
$252$		0			0
$253$	15.8198	+	2.86550i	0.994582	+	0.180152i
$254$		−	1.80021i		−	0.112956i
$255$		0			0
$256$	−2.13529	+	6.57176i	−0.133456	+	0.410735i
$257$	14.1564	−	4.59968i	0.883050	−	0.286920i	0.167827	−	0.985817i	$-0.446325\pi$
$257$	14.1564	−	4.59968i	0.883050	−	0.286920i	0.715223	+	0.698896i	$0.246325\pi$
$258$		0			0
$259$	0.985226	+	1.35605i	0.0612189	+	0.0842606i
$260$	−0.529714	−	1.63029i	−0.0328515	−	0.101106i
$261$		0			0
$262$	−0.284894	−	0.206988i	−0.0176008	−	0.0127877i
$263$	−23.9012			−1.47381			−0.736906	−	0.675995i	$-0.763714\pi$
$263$	−23.9012			−1.47381			−0.736906	+	0.675995i	$0.763714\pi$
$264$		0			0
$265$	15.0898			0.926962
$266$	−5.37022	−	3.90169i	−0.329269	−	0.239228i
$267$		0			0
$268$	−0.251087	−	0.772765i	−0.0153376	−	0.0472041i
$269$	4.62668	+	6.36807i	0.282093	+	0.388268i	0.926426	−	0.376477i	$-0.122865\pi$
$269$	4.62668	+	6.36807i	0.282093	+	0.388268i	−0.644332	+	0.764745i	$0.722865\pi$
$270$		0			0
$271$	−4.67871	+	1.52020i	−0.284211	+	0.0923458i	−0.447654	−	0.894207i	$-0.647740\pi$
$271$	−4.67871	+	1.52020i	−0.284211	+	0.0923458i	0.163442	+	0.986553i	$0.447740\pi$
$272$	−0.138113	+	0.425067i	−0.00837432	+	0.0257735i
$273$		0			0
$274$		−	2.90182i		−	0.175305i
$275$	−9.85173	−	5.29727i	−0.594082	−	0.319437i
$276$		0			0
$277$	−15.5227	+	21.3651i	−0.932666	+	1.28371i	0.0261441	+	0.999658i	$0.491677\pi$
$277$	−15.5227	+	21.3651i	−0.932666	+	1.28371i	−0.958810	+	0.284047i	$0.908323\pi$
$278$	6.24706	+	2.02979i	0.374674	+	0.121739i
$279$		0			0
$280$	−11.2757	+	8.19229i	−0.673853	+	0.489583i
$281$	−12.8582	+	9.34205i	−0.767057	+	0.557300i	−0.901067	−	0.433680i	$-0.857215\pi$
$281$	−12.8582	+	9.34205i	−0.767057	+	0.557300i	0.134009	+	0.990980i	$0.457215\pi$
$282$		0			0
$283$	−10.4717	−	3.40245i	−0.622476	−	0.202255i	−0.0192367	−	0.999815i	$-0.506124\pi$
$283$	−10.4717	−	3.40245i	−0.622476	−	0.202255i	−0.603239	+	0.797560i	$0.706124\pi$
$284$	−11.1909	+	15.4030i	−0.664058	+	0.913997i
$285$		0			0
$286$	0.232931	+	1.71533i	0.0137735	+	0.101429i
$287$		−	23.5424i		−	1.38966i
$288$		0			0
$289$	−5.23441	+	16.1099i	−0.307907	+	0.947639i
$290$	5.89324	−	1.91483i	0.346063	−	0.112443i
$291$		0			0
$292$	−3.83088	−	5.27275i	−0.224185	−	0.308564i
$293$	−4.37823	−	13.4748i	−0.255779	−	0.787207i	−0.993675	−	0.112293i	$-0.964181\pi$
$293$	−4.37823	−	13.4748i	−0.255779	−	0.787207i	0.737896	−	0.674914i	$-0.235819\pi$
$294$		0			0
$295$	−5.42161	−	3.93903i	−0.315658	−	0.229339i
$296$	−0.780897			−0.0453887
$297$		0			0
$298$	9.51670			0.551288
$299$	3.27456	+	2.37911i	0.189373	+	0.137587i
$300$		0			0
$301$	−0.633551	−	1.94987i	−0.0365173	−	0.112389i
$302$	−2.80753	−	3.86423i	−0.161555	−	0.222362i
$303$		0			0
$304$	−3.77132	+	1.22538i	−0.216300	+	0.0702801i
$305$	5.49351	−	16.9073i	0.314557	−	0.968108i
$306$		0			0
$307$			11.5389i			0.658559i	0.944233	+	0.329279i	$0.106806\pi$
$307$			11.5389i			0.658559i	−0.944233	+	0.329279i	$0.893194\pi$
$308$	−23.2834	+	11.2221i	−1.32670	+	0.639441i
$309$		0			0
$310$	−0.822266	+	1.13175i	−0.0467016	+	0.0642792i
$311$	26.0233	+	8.45547i	1.47564	+	0.479466i	0.932808	−	0.360373i	$-0.117351\pi$
$311$	26.0233	+	8.45547i	1.47564	+	0.479466i	0.542836	+	0.839839i	$0.317351\pi$
$312$		0			0
$313$	−6.72263	+	4.88428i	−0.379986	+	0.276076i	−0.761340	−	0.648353i	$-0.775458\pi$
$313$	−6.72263	+	4.88428i	−0.379986	+	0.276076i	0.381354	+	0.924429i	$0.375458\pi$
$314$	2.18973	−	1.59093i	0.123573	−	0.0897814i
$315$		0			0
$316$	3.38694	+	1.10048i	0.190530	+	0.0619071i
$317$	−8.93083	+	12.2922i	−0.501605	+	0.690401i	−0.982476	−	0.186391i	$-0.940321\pi$
$317$	−8.93083	+	12.2922i	−0.501605	+	0.690401i	0.480870	+	0.876792i	$0.340321\pi$
$318$		0			0
$319$	25.5382	−	3.46792i	1.42986	−	0.194166i
$320$			0.114250i			0.00638676i
$321$		0			0
$322$	4.53434	−	13.9553i	0.252689	−	0.777697i
$323$	0.515471	−	0.167487i	0.0286816	−	0.00931920i
$324$		0			0
$325$	−1.65524	−	2.27825i	−0.0918165	−	0.126375i
$326$	1.37646	+	4.23630i	0.0762350	+	0.234627i
$327$		0			0
$328$	8.87328	+	6.44682i	0.489945	+	0.355966i
$329$	−36.0155			−1.98560
$330$		0			0
$331$	14.4144			0.792289			0.396145	−	0.918188i	$-0.370348\pi$
$331$	14.4144			0.792289			0.396145	+	0.918188i	$0.370348\pi$
$332$	−5.37337	−	3.90398i	−0.294902	−	0.214259i
$333$		0			0
$334$	1.57969	+	4.86179i	0.0864369	+	0.266025i
$335$	0.378599	+	0.521097i	0.0206851	+	0.0284706i
$336$		0			0
$337$	7.36396	−	2.39269i	0.401140	−	0.130338i	−0.101497	−	0.994836i	$-0.532363\pi$
$337$	7.36396	−	2.39269i	0.401140	−	0.130338i	0.502637	+	0.864497i	$0.332363\pi$
$338$	2.37642	−	7.31387i	0.129260	−	0.397822i
$339$		0			0
$340$		−	0.507411i		−	0.0275182i
$341$	−4.20419	+	4.02226i	−0.227670	+	0.217818i
$342$		0			0
$343$	26.9014	−	37.0266i	1.45254	−	1.99925i
$344$	0.908411	+	0.295161i	0.0489782	+	0.0159140i
$345$		0			0
$346$	−3.42121	+	2.48566i	−0.183926	+	0.133630i
$347$	−7.00708	+	5.09094i	−0.376160	+	0.273296i	−0.759761	−	0.650203i	$-0.774684\pi$
$347$	−7.00708	+	5.09094i	−0.376160	+	0.273296i	0.383601	+	0.923499i	$0.374684\pi$
$348$		0			0
$349$	15.9435	+	5.18035i	0.853434	+	0.277298i	0.702884	−	0.711305i	$-0.251895\pi$
$349$	15.9435	+	5.18035i	0.853434	+	0.277298i	0.150551	+	0.988602i	$0.451895\pi$
$350$	−6.00066	+	8.25920i	−0.320749	+	0.441473i
$351$		0			0
$352$	3.33549	−	18.4145i	0.177782	−	0.981495i
$353$			11.7069i			0.623096i	0.950230	+	0.311548i	$0.100847\pi$
$353$			11.7069i			0.623096i	−0.950230	+	0.311548i	$0.899153\pi$
$354$		0			0
$355$	4.66389	−	14.3540i	0.247534	−	0.761831i
$356$	20.6962	−	6.72461i	1.09690	−	0.356404i
$357$		0			0
$358$	2.64650	+	3.64259i	0.139872	+	0.192517i
$359$	5.55436	+	17.0946i	0.293148	+	0.902217i	0.983837	+	0.179065i	$0.0573073\pi$
$359$	5.55436	+	17.0946i	0.293148	+	0.902217i	−0.690689	+	0.723152i	$0.742693\pi$
$360$		0			0
$361$	−11.4810	−	8.34140i	−0.604261	−	0.439021i
$362$	−0.296178			−0.0155668
$363$		0			0
$364$	−6.50714			−0.341067
$365$	4.17981	+	3.03681i	0.218781	+	0.158954i
$366$		0			0
$367$	−8.48814	−	26.1238i	−0.443077	−	1.36365i	−0.884579	−	0.466391i	$-0.845554\pi$
$367$	−8.48814	−	26.1238i	−0.443077	−	1.36365i	0.441501	−	0.897261i	$-0.354446\pi$
$368$	−5.15233	−	7.09157i	−0.268584	−	0.369674i
$369$		0			0
$370$	0.262500	−	0.0852915i	0.0136467	−	0.00443409i
$371$	17.7010	−	54.4781i	0.918991	−	2.82836i
$372$		0			0
$373$			16.9714i			0.878744i	0.898305	+	0.439372i	$0.144799\pi$
$373$			16.9714i			0.878744i	−0.898305	+	0.439372i	$0.855201\pi$
$374$	−0.0913281	+	0.504202i	−0.00472246	+	0.0260717i
$375$		0			0
$376$	9.86246	−	13.5745i	0.508617	−	0.700052i
$377$	6.17089	+	2.00505i	0.317817	+	0.103265i
$378$		0			0
$379$	12.4374	−	9.03634i	0.638869	−	0.464165i	−0.220593	−	0.975366i	$-0.570799\pi$
$379$	12.4374	−	9.03634i	0.638869	−	0.464165i	0.859461	+	0.511201i	$0.170799\pi$
$380$	3.64211	−	2.64615i	0.186836	−	0.135744i
$381$		0			0
$382$	0.0241349	+	0.00784191i	0.00123485	+	0.000401227i
$383$	4.87293	−	6.70702i	0.248995	−	0.342713i	−0.666164	−	0.745805i	$-0.732065\pi$
$383$	4.87293	−	6.70702i	0.248995	−	0.342713i	0.915159	+	0.403093i	$0.132065\pi$
$384$		0			0
$385$	14.8049	−	14.1642i	0.754526	−	0.721875i
$386$		−	7.02414i		−	0.357519i
$387$		0			0
$388$	3.95316	−	12.1666i	0.200691	−	0.617665i
$389$	23.9516	−	7.78233i	1.21439	−	0.394580i	0.369355	−	0.929288i	$-0.379578\pi$
$389$	23.9516	−	7.78233i	1.21439	−	0.394580i	0.845037	+	0.534708i	$0.179578\pi$
$390$		0			0
$391$	0.704229	+	0.969289i	0.0356144	+	0.0490190i
$392$	11.4691	+	35.2984i	0.579279	+	1.78284i
$393$		0			0
$394$	10.5262	+	7.64773i	0.530302	+	0.385287i
$395$	−2.82307			−0.142044
$396$		0			0
$397$	−26.0948			−1.30966			−0.654830	−	0.755776i	$-0.727260\pi$
$397$	−26.0948			−1.30966			−0.654830	+	0.755776i	$0.727260\pi$
$398$	−7.28772	−	5.29484i	−0.365301	−	0.265406i
$399$		0			0
$400$	1.88458	+	5.80016i	0.0942292	+	0.290008i
$401$	−2.48443	−	3.41953i	−0.124067	−	0.170763i	0.742466	−	0.669884i	$-0.233656\pi$
$401$	−2.48443	−	3.41953i	−0.124067	−	0.170763i	−0.866532	+	0.499121i	$0.833656\pi$
$402$		0			0
$403$	−1.39314	+	0.452658i	−0.0693972	+	0.0225485i
$404$	−2.68277	+	8.25672i	−0.133473	+	0.410787i
$405$		0			0
$406$		−	23.5222i		−	1.16739i
$407$	1.13754	−	0.154470i	0.0563856	−	0.00765681i
$408$		0			0
$409$	14.8682	−	20.4643i	0.735183	−	1.01189i	−0.263698	−	0.964605i	$-0.584942\pi$
$409$	14.8682	−	20.4643i	0.735183	−	1.01189i	0.998881	−	0.0472876i	$-0.0150577\pi$
$410$	−3.68691	−	1.19795i	−0.182084	−	0.0591625i
$411$		0			0
$412$	21.4259	−	15.5668i	1.05558	−	0.766922i
$413$	−20.5807	+	14.9527i	−1.01271	+	0.735775i
$414$		0			0
$415$	5.00743	+	1.62701i	0.245805	+	0.0798669i
$416$	2.76932	−	3.81164i	0.135777	−	0.186881i
$417$		0			0
$418$	−4.09535	+	1.97388i	−0.200310	+	0.0965454i
$419$		−	15.4907i		−	0.756769i	−0.925649	−	0.378384i	$-0.876480\pi$
$419$		−	15.4907i		−	0.756769i	0.925649	−	0.378384i	$-0.123520\pi$
$420$		0			0
$421$	−8.97090	+	27.6096i	−0.437215	+	1.34561i	0.453585	+	0.891213i	$0.350145\pi$
$421$	−8.97090	+	27.6096i	−0.437215	+	1.34561i	−0.890800	+	0.454396i	$0.849855\pi$
$422$	10.8059	−	3.51104i	0.526021	−	0.170915i
$423$		0			0
$424$	15.6860	+	21.5899i	0.761778	+	1.04850i
$425$	−0.257588	−	0.792775i	−0.0124949	−	0.0384553i
$426$		0			0
$427$	−54.5954	−	39.6659i	−2.64206	−	1.91957i
$428$	−3.67180			−0.177483
$429$		0			0
$430$	−0.337602			−0.0162806
$431$	−3.88324	−	2.82134i	−0.187049	−	0.135899i	0.490320	−	0.871542i	$-0.336880\pi$
$431$	−3.88324	−	2.82134i	−0.187049	−	0.135899i	−0.677369	+	0.735643i	$0.736880\pi$
$432$		0			0
$433$	8.34981	+	25.6981i	0.401266	+	1.23497i	0.923973	+	0.382458i	$0.124922\pi$
$433$	8.34981	+	25.6981i	0.401266	+	1.23497i	−0.522706	+	0.852513i	$0.675078\pi$
$434$	3.12136	+	4.29618i	0.149830	+	0.206223i
$435$		0			0
$436$	13.6206	−	4.42561i	0.652310	−	0.211948i
$437$	−3.28483	+	10.1097i	−0.157135	+	0.483612i
$438$		0			0
$439$		−	31.8920i		−	1.52212i	−0.648681	−	0.761061i	$-0.724679\pi$
$439$		−	31.8920i		−	1.52212i	0.648681	−	0.761061i	$-0.275321\pi$
$440$	1.28444	+	9.45877i	0.0612334	+	0.450929i
$441$		0			0
$442$	−0.0758259	+	0.104365i	−0.00360667	+	0.00496416i
$443$	−10.6407	−	3.45736i	−0.505553	−	0.164264i	0.0451259	−	0.998981i	$-0.485631\pi$
$443$	−10.6407	−	3.45736i	−0.505553	−	0.164264i	−0.550679	+	0.834717i	$0.685631\pi$
$444$		0			0
$445$	−13.9560	+	10.1397i	−0.661580	+	0.480666i
$446$	−0.381538	+	0.277204i	−0.0180664	+	0.0131260i
$447$		0			0
$448$	0.412471	+	0.134020i	0.0194874	+	0.00633184i
$449$	14.9366	−	20.5585i	0.704903	−	0.970216i	−0.294989	−	0.955501i	$-0.595316\pi$
$449$	14.9366	−	20.5585i	0.704903	−	0.970216i	0.999892	−	0.0147150i	$-0.00468409\pi$
$450$		0			0
$451$	−14.2010	−	7.63587i	−0.668699	−	0.359559i
$452$		−	11.6529i		−	0.548107i
$453$		0			0
$454$	3.20996	−	9.87925i	0.150651	−	0.463656i
$455$	4.90588	−	1.59402i	0.229991	−	0.0747286i
$456$		0			0
$457$	−8.77479	−	12.0775i	−0.410467	−	0.564960i	0.552865	−	0.833271i	$-0.313535\pi$
$457$	−8.77479	−	12.0775i	−0.410467	−	0.564960i	−0.963332	+	0.268311i	$0.913535\pi$
$458$	−4.24914	−	13.0775i	−0.198549	−	0.611072i
$459$		0			0
$460$	8.05102	+	5.84941i	0.375381	+	0.272730i
$461$	13.0164			0.606233			0.303117	−	0.952953i	$-0.401973\pi$
$461$	13.0164			0.606233			0.303117	+	0.952953i	$0.401973\pi$
$462$		0			0
$463$	−4.03263			−0.187412			−0.0937062	−	0.995600i	$-0.529871\pi$
$463$	−4.03263			−0.187412			−0.0937062	+	0.995600i	$0.529871\pi$
$464$	−11.3681	−	8.25943i	−0.527752	−	0.383434i
$465$		0			0
$466$	2.98693	+	9.19282i	0.138367	+	0.425849i
$467$	24.7492	+	34.0643i	1.14525	+	1.57631i	0.755170	+	0.655529i	$0.227554\pi$
$467$	24.7492	+	34.0643i	1.14525	+	1.57631i	0.390085	+	0.920779i	$0.372446\pi$
$468$		0			0
$469$	2.32540	−	0.755569i	0.107377	−	0.0348889i
$470$	−1.83265	+	5.64030i	−0.0845336	+	0.260168i
$471$		0			0
$472$		−	11.8516i		−	0.545516i
$473$	−1.38167	−	0.250268i	−0.0635294	−	0.0115073i
$474$		0			0
$475$	4.34709	−	5.98325i	0.199458	−	0.274530i
$476$	−1.83188	−	0.595214i	−0.0839641	−	0.0272816i
$477$		0			0
$478$	−9.51213	+	6.91097i	−0.435075	+	0.316100i
$479$	−6.01551	+	4.37052i	−0.274856	+	0.199694i	−0.716670	−	0.697412i	$-0.754335\pi$
$479$	−6.01551	+	4.37052i	−0.274856	+	0.199694i	0.441815	+	0.897106i	$0.354335\pi$
$480$		0			0
$481$	0.274868	+	0.0893099i	0.0125329	+	0.00407218i
$482$	5.71999	−	7.87289i	0.260538	−	0.358600i
$483$		0			0
$484$	−0.782577	+	17.6847i	−0.0355717	+	0.803849i
$485$			10.1410i			0.460480i
$486$		0			0
$487$	4.00699	−	12.3322i	0.181574	−	0.558827i	−0.818299	−	0.574793i	$-0.805082\pi$
$487$	4.00699	−	12.3322i	0.181574	−	0.558827i	0.999873	+	0.0159664i	$0.00508249\pi$
$488$	29.9007	−	9.71532i	1.35354	−	0.439792i
$489$		0			0
$490$	−7.71075	−	10.6129i	−0.348336	−	0.479443i
$491$	9.95139	+	30.6272i	0.449100	+	1.38219i	0.877924	+	0.478799i	$0.158928\pi$
$491$	9.95139	+	30.6272i	0.449100	+	1.38219i	−0.428825	+	0.903388i	$0.641072\pi$
$492$		0			0
$493$	1.55382	+	1.12891i	0.0699804	+	0.0508437i
$494$	−1.14455			−0.0514957
$495$		0			0
$496$	3.17233			0.142442
$497$	−46.3506	−	33.6757i	−2.07911	−	1.51056i
$498$		0			0
$499$	−7.99350	−	24.6015i	−0.357838	−	1.10131i	−0.954346	−	0.298705i	$-0.903445\pi$
$499$	−7.99350	−	24.6015i	−0.357838	−	1.10131i	0.596507	−	0.802608i	$-0.296555\pi$
$500$	−10.1032	−	13.9058i	−0.451827	−	0.621886i
$501$		0			0
$502$	8.41645	−	2.73467i	0.375645	−	0.122054i
$503$	−0.339066	+	1.04354i	−0.0151182	+	0.0465290i	−0.958331	−	0.285660i	$-0.907787\pi$
$503$	−0.339066	+	1.04354i	−0.0151182	+	0.0465290i	0.943213	+	0.332189i	$0.107787\pi$
$504$		0			0
$505$		−	6.88210i		−	0.306250i
$506$	−6.94728	−	7.26151i	−0.308844	−	0.322813i
$507$		0			0
$508$	2.72418	−	3.74951i	0.120866	−	0.166357i
$509$	−6.65980	−	2.16390i	−0.295190	−	0.0959132i	0.157678	−	0.987491i	$-0.449599\pi$
$509$	−6.65980	−	2.16390i	−0.295190	−	0.0959132i	−0.452868	+	0.891577i	$0.649599\pi$
$510$		0			0
$511$	15.8668	−	11.5279i	0.701904	−	0.509963i
$512$	−14.8558	+	10.7934i	−0.656539	+	0.477003i
$513$		0			0
$514$	−8.84890	−	2.87518i	−0.390308	−	0.126819i
$515$	−12.3401	+	16.9847i	−0.543771	+	0.748436i
$516$		0			0
$517$	−11.6815	+	21.7250i	−0.513752	+	0.955463i
$518$		−	1.04774i		−	0.0460351i
$519$		0			0
$520$	−0.742624	+	2.28556i	−0.0325662	+	0.100229i
$521$	−7.27467	+	2.36368i	−0.318709	+	0.103555i	−0.464003	−	0.885834i	$-0.653587\pi$
$521$	−7.27467	+	2.36368i	−0.318709	+	0.103555i	0.145294	+	0.989389i	$0.453587\pi$
$522$		0			0
$523$	−18.3418	−	25.2453i	−0.802029	−	1.10390i	−0.992505	−	0.122206i	$-0.961003\pi$
$523$	−18.3418	−	25.2453i	−0.802029	−	1.10390i	0.190476	−	0.981692i	$-0.438997\pi$
$524$	−0.280156	−	0.862233i	−0.0122387	−	0.0376668i
$525$		0			0
$526$	12.0869	+	8.78164i	0.527014	+	0.382898i
$527$	−0.433599			−0.0188879
$528$		0			0
$529$	−0.497894			−0.0216476
$530$	−7.63097	−	5.54423i	−0.331468	−	0.240826i
$531$		0			0
$532$	−5.28091	−	16.2530i	−0.228956	−	0.704656i
$533$	−2.38599	−	3.28404i	−0.103349	−	0.142247i
$534$		0			0
$535$	2.76825	−	0.899460i	0.119682	−	0.0388870i
$536$	−0.352007	+	1.08337i	−0.0152044	+	0.0467943i
$537$		0			0
$538$		−	4.92026i		−	0.212127i
$539$	−23.6896	−	49.1506i	−1.02038	−	2.11707i
$540$		0			0
$541$	−16.7402	+	23.0409i	−0.719717	+	0.990605i	0.279817	+	0.960053i	$0.409726\pi$
$541$	−16.7402	+	23.0409i	−0.719717	+	0.990605i	−0.999533	+	0.0305514i	$0.990274\pi$
$542$	2.92458	+	0.950253i	0.125621	+	0.0408169i
$543$		0			0
$544$	1.12827	−	0.819734i	0.0483740	−	0.0351458i
$545$	−9.18477	+	6.67313i	−0.393432	+	0.285845i
$546$		0			0
$547$	−38.3795	−	12.4703i	−1.64099	−	0.533189i	−0.664229	−	0.747529i	$-0.731240\pi$
$547$	−38.3795	−	12.4703i	−1.64099	−	0.533189i	−0.976759	+	0.214340i	$0.931240\pi$
$548$	4.39118	−	6.04394i	0.187582	−	0.258185i
$549$		0			0
$550$	3.03575	+	6.29851i	0.129445	+	0.268569i
$551$			17.0403i			0.725942i
$552$		0			0
$553$	−3.31157	+	10.1920i	−0.140822	+	0.433407i
$554$	15.6997	−	5.10114i	0.667016	−	0.216727i
$555$		0			0
$556$	9.93986	+	13.6810i	0.421544	+	0.580206i
$557$	−5.23145	−	16.1007i	−0.221664	−	0.682211i	−0.998613	−	0.0526476i	$-0.983234\pi$
$557$	−5.23145	−	16.1007i	−0.221664	−	0.682211i	0.776950	−	0.629563i	$-0.216766\pi$
$558$		0			0
$559$	−0.285994	−	0.207787i	−0.0120963	−	0.00878845i
$560$	−11.1712			−0.472070
$561$		0			0
$562$	9.93484			0.419076
$563$	−18.8334	−	13.6833i	−0.793734	−	0.576682i	0.115335	−	0.993327i	$-0.463206\pi$
$563$	−18.8334	−	13.6833i	−0.793734	−	0.576682i	−0.909069	+	0.416645i	$0.863206\pi$
$564$		0			0
$565$	2.85454	+	8.78539i	0.120092	+	0.369604i
$566$	4.04544	+	5.56807i	0.170042	+	0.234043i
$567$		0			0
$568$	25.3852	−	8.24815i	1.06514	−	0.346085i
$569$	−7.03113	+	21.6396i	−0.294760	+	0.907179i	0.688542	+	0.725197i	$0.258251\pi$
$569$	−7.03113	+	21.6396i	−0.294760	+	0.907179i	−0.983302	+	0.181982i	$0.941749\pi$
$570$		0			0
$571$			28.8962i			1.20927i	0.796503	+	0.604634i	$0.206681\pi$
$571$			28.8962i			1.20927i	−0.796503	+	0.604634i	$0.793319\pi$
$572$	−2.11057	+	3.92518i	−0.0882473	+	0.164120i
$573$		0			0
$574$	−8.64980	+	11.9054i	−0.361036	+	0.496923i
$575$	15.5483	+	5.05196i	0.648410	+	0.210681i
$576$		0			0
$577$	25.9942	−	18.8859i	1.08215	−	0.786229i	0.104094	−	0.994567i	$-0.466806\pi$
$577$	25.9942	−	18.8859i	1.08215	−	0.786229i	0.978057	+	0.208339i	$0.0668056\pi$
$578$	8.56605	−	6.22360i	0.356301	−	0.258868i
$579$		0			0
$580$	15.1721	+	4.92972i	0.629988	+	0.204695i
$581$	11.7479	−	16.1695i	0.487383	−	0.670825i
$582$		0			0
$583$	−27.1206	−	28.3472i	−1.12322	−	1.17402i
$584$			9.13707i			0.378095i
$585$		0			0
$586$	−2.73676	+	8.42287i	−0.113054	+	0.347945i
$587$	−3.52838	+	1.14644i	−0.145632	+	0.0473187i	−0.380926	−	0.924606i	$-0.624395\pi$
$587$	−3.52838	+	1.14644i	−0.145632	+	0.0473187i	0.235294	+	0.971924i	$0.424395\pi$
$588$		0			0
$589$	−2.26122	−	3.11230i	−0.0931719	−	0.128240i
$590$	1.29446	+	3.98395i	0.0532923	+	0.164017i
$591$		0			0
$592$	−0.506366	−	0.367897i	−0.0208115	−	0.0151205i
$593$	38.2706			1.57159			0.785793	−	0.618490i	$-0.212255\pi$
$593$	38.2706			1.57159			0.785793	+	0.618490i	$0.212255\pi$
$594$		0			0
$595$	1.52690			0.0625968
$596$	19.8215	+	14.4011i	0.811919	+	0.589894i
$597$		0			0
$598$	−0.781835	−	2.40624i	−0.0319716	−	0.0983985i
$599$	−7.34752	−	10.1130i	−0.300212	−	0.413206i	0.632086	−	0.774898i	$-0.282199\pi$
$599$	−7.34752	−	10.1130i	−0.300212	−	0.413206i	−0.932297	+	0.361692i	$0.882199\pi$
$600$		0			0
$601$	21.7428	−	7.06468i	0.886909	−	0.288174i	0.170086	−	0.985429i	$-0.445596\pi$
$601$	21.7428	−	7.06468i	0.886909	−	0.288174i	0.716823	+	0.697255i	$0.245596\pi$
$602$	−0.396022	+	1.21883i	−0.0161406	+	0.0496758i
$603$		0			0
$604$		−	12.2970i		−	0.500356i
$605$	−3.74211	−	13.5246i	−0.152138	−	0.549852i
$606$		0			0
$607$	17.8663	−	24.5908i	0.725171	−	0.998112i	−0.274166	−	0.961682i	$-0.588402\pi$
$607$	17.8663	−	24.5908i	0.725171	−	0.998112i	0.999336	−	0.0364291i	$-0.0115983\pi$
$608$	11.7678	+	3.82360i	0.477248	+	0.155067i
$609$		0			0
$610$	−8.99005	+	6.53165i	−0.363997	+	0.264459i
$611$	−5.02398	+	3.65013i	−0.203248	+	0.147669i
$612$		0			0
$613$	1.41405	+	0.459451i	0.0571128	+	0.0185571i	0.337434	−	0.941349i	$-0.390441\pi$
$613$	1.41405	+	0.459451i	0.0571128	+	0.0185571i	−0.280321	+	0.959906i	$0.590441\pi$
$614$	4.23955	−	5.83524i	0.171094	−	0.235491i
$615$		0			0
$616$	35.6552	+	6.45837i	1.43659	+	0.260215i
$617$			33.6261i			1.35373i	0.736105	+	0.676867i	$0.236663\pi$
$617$			33.6261i			1.35373i	−0.736105	+	0.676867i	$0.763337\pi$
$618$		0			0
$619$	0.873090	−	2.68710i	0.0350925	−	0.108004i	−0.931976	−	0.362520i	$-0.881916\pi$
$619$	0.873090	−	2.68710i	0.0350925	−	0.108004i	0.967068	+	0.254517i	$0.0819164\pi$
$620$	−3.42525	+	1.11293i	−0.137561	+	0.0446964i
$621$		0			0
$622$	−10.0534	−	13.8373i	−0.403103	−	0.554824i
$623$	20.2357	+	62.2791i	0.810726	+	2.49516i
$624$		0			0
$625$	−2.61899	−	1.90281i	−0.104760	−	0.0761123i
$626$	5.19420			0.207602
$627$		0			0
$628$	6.96826			0.278064
$629$	0.0692110	+	0.0502848i	0.00275962	+	0.00200498i
$630$		0			0
$631$	2.32895	+	7.16777i	0.0927140	+	0.285344i	0.986651	−	0.162848i	$-0.0520680\pi$
$631$	2.32895	+	7.16777i	0.0927140	+	0.285344i	−0.893937	+	0.448192i	$0.852068\pi$
$632$	−2.93459	−	4.03912i	−0.116732	−	0.160667i
$633$		0			0
$634$	9.03268	−	2.93490i	0.358734	−	0.116560i
$635$	−1.13532	+	3.49416i	−0.0450538	+	0.138661i
$636$		0			0
$637$		−	13.7364i		−	0.544255i
$638$	−14.1889	−	7.62935i	−0.561743	−	0.302049i
$639$		0			0
$640$	8.50394	−	11.7047i	0.336148	−	0.462668i
$641$	18.3222	+	5.95325i	0.723685	+	0.235139i	0.647620	−	0.761963i	$-0.275764\pi$
$641$	18.3222	+	5.95325i	0.723685	+	0.235139i	0.0760647	+	0.997103i	$0.475764\pi$
$642$		0			0
$643$	15.1868	−	11.0339i	0.598909	−	0.435133i	−0.246583	−	0.969122i	$-0.579308\pi$
$643$	15.1868	−	11.0339i	0.598909	−	0.435133i	0.845491	+	0.533989i	$0.179308\pi$
$644$	30.5620	−	22.2046i	1.20431	−	0.874984i
$645$		0			0
$646$	−0.322212	−	0.104693i	−0.0126772	−	0.00411909i
$647$	−1.43599	+	1.97647i	−0.0564545	+	0.0777030i	−0.836311	−	0.548256i	$-0.815292\pi$
$647$	−1.43599	+	1.97647i	−0.0564545	+	0.0777030i	0.779856	+	0.625959i	$0.215292\pi$
$648$		0			0
$649$	2.34439	+	17.2643i	0.0920254	+	0.677685i
$650$			1.76028i			0.0690437i
$651$		0			0
$652$	−3.54368	+	10.9063i	−0.138781	+	0.427125i
$653$	18.9913	−	6.17063i	0.743185	−	0.241476i	0.0871389	−	0.996196i	$-0.472228\pi$
$653$	18.9913	−	6.17063i	0.743185	−	0.241476i	0.656046	+	0.754721i	$0.272228\pi$
$654$		0			0
$655$	0.422432	+	0.581427i	0.0165058	+	0.0227182i
$656$	2.71658	+	8.36077i	0.106065	+	0.326433i
$657$		0			0
$658$	18.2131	+	13.2326i	0.710022	+	0.515861i
$659$	35.6839			1.39005			0.695024	−	0.718986i	$-0.255394\pi$
$659$	35.6839			1.39005			0.695024	+	0.718986i	$0.255394\pi$
$660$		0			0
$661$	−8.91749			−0.346850			−0.173425	−	0.984847i	$-0.555483\pi$
$661$	−8.91749			−0.346850			−0.173425	+	0.984847i	$0.555483\pi$
$662$	−7.28941	−	5.29607i	−0.283311	−	0.205838i
$663$		0			0
$664$	2.87739	+	8.85570i	0.111664	+	0.343668i
$665$	7.96278	+	10.9598i	0.308783	+	0.425004i
$666$		0			0
$667$	−35.8246	+	11.6401i	−1.38714	+	0.450708i
$668$	−4.06691	+	12.5167i	−0.157353	+	0.484284i
$669$		0			0
$670$		−	0.402623i		−	0.0155547i
$671$	−41.6347	+	20.0671i	−1.60729	+	0.774680i
$672$		0			0
$673$	−6.42648	+	8.84529i	−0.247723	+	0.340961i	−0.914712	−	0.404106i	$-0.867583\pi$
$673$	−6.42648	+	8.84529i	−0.247723	+	0.340961i	0.666989	+	0.745067i	$0.267583\pi$
$674$	−4.60308	−	1.49563i	−0.177304	−	0.0576096i
$675$		0			0
$676$	16.0174	−	11.6373i	0.616052	−	0.447588i
$677$	−19.2277	+	13.9698i	−0.738981	+	0.536901i	−0.892392	−	0.451261i	$-0.850974\pi$
$677$	−19.2277	+	13.9698i	−0.738981	+	0.536901i	0.153411	+	0.988163i	$0.450974\pi$
$678$		0			0
$679$	36.6117	+	11.8958i	1.40503	+	0.456521i
$680$	−0.418125	+	0.575499i	−0.0160343	+	0.0220694i
$681$		0			0
$682$	3.60390	−	0.489388i	0.138001	−	0.0187396i
$683$			24.2759i			0.928892i	0.885602	+	0.464446i	$0.153746\pi$
$683$			24.2759i			0.928892i	−0.885602	+	0.464446i	$0.846254\pi$
$684$		0			0
$685$	−1.83006	+	5.63234i	−0.0699229	+	0.215201i
$686$	−27.2082	+	8.84048i	−1.03881	+	0.337531i
$687$		0			0
$688$	0.449995	+	0.619366i	0.0171559	+	0.0236131i
$689$	−3.05210	−	9.39340i	−0.116276	−	0.357860i
$690$		0			0
$691$	26.3977	+	19.1791i	1.00422	+	0.729606i	0.962988	−	0.269544i	$-0.0868728\pi$
$691$	26.3977	+	19.1791i	1.00422	+	0.729606i	0.0412285	+	0.999150i	$0.486873\pi$
$692$	−10.8872			−0.413868
$693$		0			0
$694$	5.41398			0.205512
$695$	−10.8452	−	7.87953i	−0.411383	−	0.298887i
$696$		0			0
$697$	−0.371307	−	1.14277i	−0.0140643	−	0.0432853i
$698$	−6.15932	−	8.47757i	−0.233134	−	0.320881i
$699$		0			0
$700$	−24.9965	+	8.12185i	−0.944778	+	0.306977i
$701$	11.0658	−	34.0571i	0.417951	−	1.28632i	−0.491634	−	0.870802i	$-0.663600\pi$
$701$	11.0658	−	34.0571i	0.417951	−	1.28632i	0.909585	−	0.415518i	$-0.136400\pi$
$702$		0			0
$703$			0.759020i			0.0286270i
$704$	0.214625	−	0.205338i	0.00808900	−	0.00773897i
$705$		0			0
$706$	4.30129	−	5.92021i	0.161881	−	0.222810i
$707$	−24.8461	−	8.07299i	−0.934434	−	0.303616i
$708$		0			0
$709$	−2.97546	+	2.16180i	−0.111746	+	0.0811882i	−0.642255	−	0.766491i	$-0.722001\pi$
$709$	−2.97546	+	2.16180i	−0.111746	+	0.0811882i	0.530509	+	0.847679i	$0.322001\pi$
$710$	−7.63240	+	5.54527i	−0.286439	+	0.208110i
$711$		0			0
$712$	−29.0147	−	9.42746i	−1.08737	−	0.353309i
$713$	4.99851	−	6.87986i	0.187196	−	0.257653i
$714$		0			0
$715$	0.629674	−	3.47629i	0.0235485	−	0.130006i
$716$			11.5916i			0.433200i
$717$		0			0
$718$	3.47193	−	10.6855i	0.129571	−	0.398780i
$719$	12.2052	−	3.96571i	0.455177	−	0.147896i	−0.0724502	−	0.997372i	$-0.523082\pi$
$719$	12.2052	−	3.96571i	0.455177	−	0.147896i	0.527627	+	0.849476i	$0.323082\pi$
$720$		0			0
$721$	46.8436	+	64.4747i	1.74455	+	2.40116i
$722$	2.74120	+	8.43653i	0.102017	+	0.313975i
$723$		0			0
$724$	−0.616883	−	0.448192i	−0.0229263	−	0.0166569i
$725$	26.2074			0.973318
$726$		0			0
$727$	−41.9125			−1.55445			−0.777224	−	0.629224i	$-0.783373\pi$
$727$	−41.9125			−1.55445			−0.777224	+	0.629224i	$0.783373\pi$
$728$	7.38033	+	5.36212i	0.273533	+	0.198733i
$729$		0			0
$730$	−0.997974	−	3.07145i	−0.0369367	−	0.113679i
$731$	−0.0615062	−	0.0846560i	−0.00227489	−	0.00313111i
$732$		0			0
$733$	−24.7362	+	8.03729i	−0.913653	+	0.296864i	−0.727861	−	0.685725i	$-0.759485\pi$
$733$	−24.7362	+	8.03729i	−0.913653	+	0.296864i	−0.185793	+	0.982589i	$0.559485\pi$
$734$	−5.30579	+	16.3295i	−0.195840	+	0.602734i
$735$		0			0
$736$			27.3519i			1.00820i
$737$	0.298468	−	1.64777i	0.0109942	−	0.0606966i
$738$		0			0
$739$	−17.3756	+	23.9154i	−0.639171	+	0.879744i	−0.998571	−	0.0534398i	$-0.982981\pi$
$739$	−17.3756	+	23.9154i	−0.639171	+	0.879744i	0.359400	+	0.933184i	$0.382981\pi$
$740$	0.675805	+	0.219582i	0.0248431	+	0.00807201i
$741$		0			0
$742$	−28.9675	+	21.0461i	−1.06343	+	0.772627i
$743$	12.0744	−	8.77259i	0.442968	−	0.321835i	−0.343845	−	0.939026i	$-0.611730\pi$
$743$	12.0744	−	8.77259i	0.442968	−	0.321835i	0.786813	+	0.617191i	$0.211730\pi$
$744$		0			0
$745$	−18.4716	−	6.00179i	−0.676747	−	0.219888i
$746$	6.23552	−	8.58246i	0.228299	−	0.314226i
$747$		0			0
$748$	−0.953203	+	0.911955i	−0.0348525	+	0.0333444i
$749$		−	11.0492i		−	0.403729i
$750$		0			0
$751$	−5.59944	+	17.2333i	−0.204327	+	0.628853i	0.795414	+	0.606067i	$0.207254\pi$
$751$	−5.59944	+	17.2333i	−0.204327	+	0.628853i	−0.999740	+	0.0227859i	$0.992746\pi$
$752$	12.7905	−	4.15587i	0.466420	−	0.151549i
$753$		0			0
$754$	−2.38395	−	3.28123i	−0.0868185	−	0.119495i
$755$	3.01231	+	9.27095i	0.109629	+	0.337404i
$756$		0			0
$757$	5.28836	+	3.84222i	0.192209	+	0.139648i	0.679728	−	0.733465i	$-0.262098\pi$
$757$	5.28836	+	3.84222i	0.192209	+	0.139648i	−0.487519	+	0.873112i	$0.662098\pi$
$758$	−9.60973			−0.349041
$759$		0			0
$760$	−6.31136			−0.228937
$761$	26.3742	+	19.1620i	0.956064	+	0.694621i	0.952233	−	0.305372i	$-0.0987806\pi$
$761$	26.3742	+	19.1620i	0.956064	+	0.694621i	0.00383069	+	0.999993i	$0.498781\pi$
$762$		0			0
$763$	13.3175	+	40.9872i	0.482127	+	1.48384i
$764$	0.0384017	+	0.0528554i	0.00138932	+	0.00191224i
$765$		0			0
$766$	−4.92851	+	1.60137i	−0.178074	+	0.0578598i
$767$	−1.35545	+	4.17165i	−0.0489426	+	0.150630i
$768$		0			0
$769$			40.3044i			1.45341i	0.686948	+	0.726707i	$0.258950\pi$
$769$			40.3044i			1.45341i	−0.686948	+	0.726707i	$0.741050\pi$
$770$	−12.6910	+	1.72336i	−0.457352	+	0.0621055i
$771$		0			0
$772$	10.6293	−	14.6299i	0.382556	−	0.526543i
$773$	−9.02009	−	2.93080i	−0.324430	−	0.105414i	0.142274	−	0.989827i	$-0.454559\pi$
$773$	−9.02009	−	2.93080i	−0.324430	−	0.105414i	−0.466704	+	0.884414i	$0.654559\pi$
$774$		0			0
$775$	−4.78661	+	3.47767i	−0.171940	+	0.124922i
$776$	−14.5093	+	10.5416i	−0.520855	+	0.378423i
$777$		0			0
$778$	−14.9717	−	4.86460i	−0.536761	−	0.174404i
$779$	6.26621	−	8.62470i	0.224510	−	0.309012i
$780$		0			0
$781$	−35.3472	+	17.0366i	−1.26482	+	0.609618i
$782$		−	0.748915i		−	0.0267812i
$783$		0			0
$784$	−9.19272	+	28.2923i	−0.328311	+	1.01044i
$785$	−5.25352	+	1.70697i	−0.187506	+	0.0609245i
$786$		0			0
$787$	−24.2354	−	33.3572i	−0.863899	−	1.18905i	−0.980626	−	0.195891i	$-0.937240\pi$
$787$	−24.2354	−	33.3572i	−0.863899	−	1.18905i	0.116727	−	0.993164i	$-0.462760\pi$
$788$	10.3511	+	31.8576i	0.368744	+	1.13488i
$789$		0			0
$790$	1.42763	+	1.03723i	0.0507928	+	0.0369032i
$791$	35.0659			1.24680
$792$		0			0
$793$	−11.6359			−0.413202
$794$	13.1962	+	9.58760i	0.468316	+	0.340251i
$795$		0			0
$796$	−7.16653	−	22.0563i	−0.254011	−	0.781765i
$797$	−7.50605	−	10.3312i	−0.265878	−	0.365950i	0.655115	−	0.755529i	$-0.272620\pi$
$797$	−7.50605	−	10.3312i	−0.265878	−	0.365950i	−0.920993	+	0.389580i	$0.872620\pi$
$798$		0			0
$799$	−1.74822	+	0.568032i	−0.0618477	+	0.0200955i
$800$	5.88056	−	18.0985i	0.207909	−	0.639878i
$801$		0			0
$802$			2.64208i			0.0932950i
$803$	−1.80742	−	13.3100i	−0.0637824	−	0.469700i
$804$		0			0
$805$	−17.6020	+	24.2271i	−0.620390	+	0.853893i
$806$	0.870827	+	0.282949i	0.0306736	+	0.00996644i
$807$		0			0
$808$	9.84660	−	7.15398i	0.346402	−	0.251676i
$809$	−33.5935	+	24.4071i	−1.18108	+	0.858107i	−0.992293	−	0.123910i	$-0.960457\pi$
$809$	−33.5935	+	24.4071i	−1.18108	+	0.858107i	−0.188790	+	0.982017i	$0.560457\pi$
$810$		0			0
$811$	5.10222	+	1.65781i	0.179163	+	0.0582137i	0.397225	−	0.917721i	$-0.369973\pi$
$811$	5.10222	+	1.65781i	0.179163	+	0.0582137i	−0.218061	+	0.975935i	$0.569973\pi$
$812$	35.5950	−	48.9924i	1.24914	−	1.71929i
$813$		0			0
$814$	−0.632009	−	0.339831i	−0.0221519	−	0.0119111i
$815$		−	9.09060i		−	0.318430i
$816$		0			0
$817$	0.286892	−	0.882962i	0.0100371	−	0.0308909i
$818$	−15.0377	+	4.88605i	−0.525782	+	0.170837i
$819$		0			0
$820$	−5.86634	−	8.07432i	−0.204861	−	0.281968i
$821$	−9.85555	−	30.3323i	−0.343961	−	1.05860i	−0.962138	−	0.272564i	$-0.912128\pi$
$821$	−9.85555	−	30.3323i	−0.343961	−	1.05860i	0.618177	−	0.786039i	$-0.287872\pi$
$822$		0			0
$823$	21.1304	+	15.3521i	0.736560	+	0.535142i	0.891632	−	0.452761i	$-0.149561\pi$
$823$	21.1304	+	15.3521i	0.736560	+	0.535142i	−0.155072	+	0.987903i	$0.549561\pi$
$824$	−37.1286			−1.29344
$825$		0			0
$826$	15.9015			0.553285
$827$	−31.8832	−	23.1645i	−1.10869	−	0.805508i	−0.126231	−	0.992001i	$-0.540288\pi$
$827$	−31.8832	−	23.1645i	−1.10869	−	0.805508i	−0.982456	+	0.186493i	$0.940288\pi$
$828$		0			0
$829$	−10.5153	−	32.3627i	−0.365211	−	1.12400i	−0.949849	−	0.312710i	$-0.898763\pi$
$829$	−10.5153	−	32.3627i	−0.365211	−	1.12400i	0.584638	−	0.811294i	$-0.301237\pi$
$830$	−1.93448	−	2.66259i	−0.0671469	−	0.0924197i
$831$		0			0
$832$	0.0711203	−	0.0231084i	0.00246565	−	0.000801139i
$833$	1.25648	−	3.86704i	0.0435343	−	0.133985i
$834$		0			0
$835$		−	10.4328i		−	0.361043i
$836$	−11.5168	−	2.08609i	−0.398317	−	0.0721488i
$837$		0			0
$838$	−5.69149	+	7.83367i	−0.196609	+	0.270610i
$839$	−54.2126	−	17.6148i	−1.87163	−	0.608129i	−0.990917	−	0.134474i	$-0.957065\pi$
$839$	−54.2126	−	17.6148i	−1.87163	−	0.608129i	−0.880711	−	0.473655i	$-0.842935\pi$
$840$		0			0
$841$	−25.3902	+	18.4471i	−0.875524	+	0.636106i
$842$	14.6808	−	10.6662i	0.505933	−	0.367582i
$843$		0			0
$844$	27.8196	+	9.03915i	0.957592	+	0.311140i
$845$	−9.22511	+	12.6973i	−0.317353	+	0.436800i
$846$		0			0
$847$	−53.2167	−	2.35493i	−1.82855	−	0.0809163i
$848$			21.3898i			0.734528i
$849$		0			0
$850$	−0.161014	+	0.495550i	−0.00552273	+	0.0169972i
$851$	−1.59572	+	0.518482i	−0.0547007	+	0.0177733i
$852$		0			0
$853$	19.0102	+	26.1653i	0.650898	+	0.895884i	0.999138	−	0.0415213i	$-0.0132204\pi$
$853$	19.0102	+	26.1653i	0.650898	+	0.895884i	−0.348240	+	0.937406i	$0.613220\pi$
$854$	13.0352	+	40.1182i	0.446056	+	1.37282i
$855$		0			0
$856$	4.16452	+	3.02570i	0.142340	+	0.103416i
$857$	33.6573			1.14971			0.574855	−	0.818255i	$-0.305058\pi$
$857$	33.6573			1.14971			0.574855	+	0.818255i	$0.305058\pi$
$858$		0			0
$859$	−38.0426			−1.29800			−0.648998	−	0.760790i	$-0.724812\pi$
$859$	−38.0426			−1.29800			−0.648998	+	0.760790i	$0.724812\pi$
$860$	−0.703162	−	0.510877i	−0.0239776	−	0.0174208i
$861$		0			0
$862$	0.927162	+	2.85351i	0.0315793	+	0.0971910i
$863$	9.20216	+	12.6657i	0.313245	+	0.431145i	0.936390	−	0.350962i	$-0.114145\pi$
$863$	9.20216	+	12.6657i	0.313245	+	0.431145i	−0.623145	+	0.782107i	$0.714145\pi$
$864$		0			0
$865$	8.20807	−	2.66696i	0.279083	−	0.0906795i
$866$	5.21932	−	16.0634i	0.177360	−	0.545857i
$867$		0			0
$868$			13.6715i			0.464042i
$869$	5.07382	+	5.30331i	0.172117	+	0.179902i
$870$		0			0
$871$	0.247806	−	0.341075i	0.00839657	−	0.0115569i
$872$	−19.0952	−	6.20441i	−0.646646	−	0.210108i
$873$		0			0
$874$	5.37559	−	3.90559i	0.181832	−	0.132109i
$875$	41.8453	−	30.4024i	1.41463	−	1.02779i
$876$		0			0
$877$	14.0197	+	4.55529i	0.473413	+	0.153821i	0.536000	−	0.844218i	$-0.319935\pi$
$877$	14.0197	+	4.55529i	0.473413	+	0.153821i	−0.0625864	+	0.998040i	$0.519935\pi$
$878$	−11.7176	+	16.1279i	−0.395449	+	0.544289i
$879$		0			0
$880$	−3.62334	+	6.73859i	−0.122143	+	0.227158i
$881$			29.1468i			0.981981i	0.871165	+	0.490990i	$0.163365\pi$
$881$			29.1468i			0.981981i	−0.871165	+	0.490990i	$0.836635\pi$
$882$		0			0
$883$	0.109578	−	0.337245i	0.00368758	−	0.0113492i	−0.949196	−	0.314686i	$-0.898101\pi$
$883$	0.109578	−	0.337245i	0.00368758	−	0.0113492i	0.952883	+	0.303337i	$0.0981008\pi$
$884$	−0.315862	+	0.102630i	−0.0106236	+	0.00345181i
$885$		0			0
$886$	4.11072	+	5.65792i	0.138102	+	0.190082i
$887$	0.796860	+	2.45248i	0.0267560	+	0.0823464i	0.963543	−	0.267554i	$-0.0862154\pi$
$887$	0.796860	+	2.45248i	0.0267560	+	0.0823464i	−0.936787	+	0.349900i	$0.886215\pi$
$888$		0			0
$889$	11.2830	+	8.19759i	0.378420	+	0.274938i
$890$	10.7831			0.361449
$891$		0			0
$892$	−1.21415			−0.0406528
$893$	−13.1942	−	9.58616i	−0.441528	−	0.320789i
$894$		0			0
$895$	−2.83953	−	8.73919i	−0.0949151	−	0.292119i
$896$	−32.2813	−	44.4314i	−1.07844	−	1.48435i
$897$		0			0
$898$	−15.1070	+	4.90855i	−0.504126	+	0.163801i
$899$	4.21260	−	12.9651i	0.140498	−	0.432409i
$900$		0			0
$901$		−	2.92359i		−	0.0973989i
$902$	4.37596	+	9.07913i	0.145703	+	0.302302i
$903$		0			0
$904$	−9.60242	+	13.2166i	−0.319372	+	0.439578i
$905$	0.574872	+	0.186787i	0.0191094	+	0.00620902i
$906$		0			0
$907$	−15.1705	+	11.0220i	−0.503728	+	0.365980i	−0.810439	−	0.585823i	$-0.800771\pi$
$907$	−15.1705	+	11.0220i	−0.503728	+	0.365980i	0.306711	+	0.951803i	$0.400771\pi$
$908$	21.6355	−	15.7191i	0.718000	−	0.521657i
$909$		0			0
$910$	−3.06658	−	0.996391i	−0.101656	−	0.0330301i
$911$	−7.20004	+	9.91000i	−0.238548	+	0.328333i	−0.911459	−	0.411390i	$-0.865043\pi$
$911$	−7.20004	+	9.91000i	−0.238548	+	0.328333i	0.672912	+	0.739723i	$0.265043\pi$
$912$		0			0
$913$	−5.94327	−	12.3310i	−0.196694	−	0.408095i
$914$			9.33158i			0.308661i
$915$		0			0
$916$	10.9394	−	33.6680i	0.361448	−	1.11242i
$917$	2.59463	−	0.843046i	0.0856822	−	0.0278398i
$918$		0			0
$919$	−14.4656	−	19.9102i	−0.477175	−	0.656775i	0.500784	−	0.865572i	$-0.333045\pi$
$919$	−14.4656	−	19.9102i	−0.477175	−	0.656775i	−0.977959	+	0.208797i	$0.933045\pi$
$920$	−4.31125	−	13.2687i	−0.142138	−	0.437455i
$921$		0			0
$922$	−6.58241	−	4.78240i	−0.216780	−	0.157500i
$923$	−9.87866			−0.325160
$924$		0			0
$925$	1.16735			0.0383821
$926$	2.03931	+	1.48165i	0.0670160	+	0.0486899i
$927$		0			0
$928$	13.5493	+	41.7004i	0.444777	+	1.36888i
$929$	11.3549	+	15.6287i	0.372543	+	0.512761i	0.953590	−	0.301109i	$-0.0973568\pi$
$929$	11.3549	+	15.6287i	0.372543	+	0.512761i	−0.581047	+	0.813870i	$0.697357\pi$
$930$		0			0
$931$	34.3095	−	11.1478i	1.12445	−	0.365355i
$932$	−7.68983	+	23.6669i	−0.251889	+	0.775234i
$933$		0			0
$934$		−	26.3196i		−	0.861203i
$935$	0.495244	−	0.921043i	0.0161962	−	0.0301213i
$936$		0			0
$937$	29.8196	−	41.0432i	0.974165	−	1.34082i	0.0342499	−	0.999413i	$-0.489096\pi$
$937$	29.8196	−	41.0432i	0.974165	−	1.34082i	0.939915	−	0.341409i	$-0.110904\pi$
$938$	−1.45357	−	0.472293i	−0.0474607	−	0.0154209i
$939$		0			0
$940$	−12.3522	+	8.97443i	−0.402886	+	0.292714i
$941$	−24.4499	+	17.7639i	−0.797043	+	0.579085i	−0.910045	−	0.414509i	$-0.863953\pi$
$941$	−24.4499	+	17.7639i	−0.797043	+	0.579085i	0.113002	+	0.993595i	$0.463953\pi$
$942$		0			0
$943$	22.4125	+	7.28227i	0.729852	+	0.237143i
$944$	5.58355	−	7.68510i	0.181729	−	0.250129i
$945$		0			0
$946$	0.606763	+	0.634207i	0.0197276	+	0.0206199i
$947$		−	11.3912i		−	0.370165i	−0.982723	−	0.185083i	$-0.940745\pi$
$947$		−	11.3912i		−	0.370165i	0.982723	−	0.185083i	$-0.0592553\pi$
$948$		0			0
$949$	1.04499	−	3.21616i	0.0339219	−	0.104401i
$950$	−4.39666	+	1.42856i	−0.142647	+	0.0463487i
$951$		0			0
$952$	1.58722	+	2.18462i	0.0514421	+	0.0708039i
$953$	−14.8543	−	45.7168i	−0.481178	−	1.48091i	−0.837441	−	0.546527i	$-0.815949\pi$
$953$	−14.8543	−	45.7168i	−0.481178	−	1.48091i	0.356263	−	0.934386i	$-0.384051\pi$
$954$		0			0
$955$	−0.0418995	−	0.0304418i	−0.00135584	−	0.000985073i
$956$	−30.2700			−0.979002
$957$		0			0
$958$	4.64785			0.150165
$959$	18.1874	+	13.2139i	0.587303	+	0.426700i
$960$		0			0
$961$	−8.62849	−	26.5558i	−0.278338	−	0.856638i
$962$	−0.106188	−	0.146155i	−0.00342362	−	0.00471221i
$963$		0			0
$964$	23.8273	−	7.74196i	0.767426	−	0.249352i
$965$	−4.42983	+	13.6336i	−0.142601	+	0.438882i
$966$		0			0
$967$		−	13.2274i		−	0.425363i	−0.977122	−	0.212681i	$-0.931780\pi$
$967$		−	13.2274i		−	0.425363i	0.977122	−	0.212681i	$-0.0682197\pi$
$968$	15.4604	−	19.4129i	0.496916	−	0.623954i
$969$		0			0
$970$	3.72596	−	5.12834i	0.119633	−	0.164661i
$971$	25.6742	+	8.34206i	0.823925	+	0.267710i	0.690484	−	0.723347i	$-0.257397\pi$
$971$	25.6742	+	8.34206i	0.823925	+	0.267710i	0.133441	+	0.991057i	$0.457397\pi$
$972$		0			0
$973$	−41.1690	+	29.9110i	−1.31982	+	0.958903i
$974$	−6.55738	+	4.76422i	−0.210112	+	0.152655i
$975$		0			0
$976$	23.9660	+	7.78701i	0.767132	+	0.249256i
$977$	23.2218	−	31.9621i	0.742931	−	1.02256i	−0.255513	−	0.966806i	$-0.582244\pi$
$977$	23.2218	−	31.9621i	0.742931	−	1.02256i	0.998445	−	0.0557519i	$-0.0177556\pi$
$978$		0			0
$979$	44.1308	+	7.99358i	1.41043	+	0.255476i
$980$		−	33.7730i		−	1.07884i
$981$		0			0
$982$	6.22044	−	19.1445i	0.198502	−	0.610927i
$983$	31.7553	−	10.3179i	1.01284	−	0.329091i	0.244853	−	0.969560i	$-0.421260\pi$
$983$	31.7553	−	10.3179i	1.01284	−	0.329091i	0.767984	+	0.640469i	$0.221260\pi$
$984$		0			0
$985$	−15.6079	−	21.4824i	−0.497309	−	0.684487i
$986$	−0.370990	−	1.14179i	−0.0118147	−	0.0363620i
$987$		0			0
$988$	−2.38388	−	1.73199i	−0.0758413	−	0.0551020i
$989$	2.05226			0.0652582
$990$		0			0
$991$	0.780068			0.0247797			0.0123898	−	0.999923i	$-0.496056\pi$
$991$	0.780068			0.0247797			0.0123898	+	0.999923i	$0.496056\pi$
$992$	−8.00826	−	5.81834i	−0.254263	−	0.184733i
$993$		0			0
$994$	11.0667	+	34.0597i	0.351014	+	1.08031i
$995$	10.8060	+	14.8732i	0.342573	+	0.471512i
$996$		0			0
$997$	−41.7246	+	13.5571i	−1.32143	+	0.429359i	−0.882986	−	0.469399i	$-0.844471\pi$
$997$	−41.7246	+	13.5571i	−1.32143	+	0.429359i	−0.438445	+	0.898758i	$0.644471\pi$
$998$	−4.99660	+	15.3779i	−0.158164	+	0.486780i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.161.8		80
3.2	odd	2	inner	891.2.k.a.161.13		80
9.2	odd	6		297.2.t.a.260.6		80
9.4	even	3		297.2.t.a.62.6		80
9.5	odd	6		99.2.p.a.29.5	✓	80
9.7	even	3		99.2.p.a.95.5	yes	80
11.8	odd	10	inner	891.2.k.a.404.13		80
33.8	even	10	inner	891.2.k.a.404.8		80
99.41	even	30		99.2.p.a.74.5	yes	80
99.52	odd	30		99.2.p.a.41.5	yes	80
99.74	even	30		297.2.t.a.206.6		80
99.85	odd	30		297.2.t.a.8.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.5	✓	80	9.5	odd	6
99.2.p.a.41.5	yes	80	99.52	odd	30
99.2.p.a.74.5	yes	80	99.41	even	30
99.2.p.a.95.5	yes	80	9.7	even	3
297.2.t.a.8.6		80	99.85	odd	30
297.2.t.a.62.6		80	9.4	even	3
297.2.t.a.206.6		80	99.74	even	30
297.2.t.a.260.6		80	9.2	odd	6
891.2.k.a.161.8		80	1.1	even	1	trivial
891.2.k.a.161.13		80	3.2	odd	2	inner
891.2.k.a.404.8		80	33.8	even	10	inner
891.2.k.a.404.13		80	11.8	odd	10	inner

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.505702 - 0.367414i) q^{2} +(-0.497292 - 1.53051i) q^{4} +(0.749839 + 1.03206i) q^{5} +(4.60560 - 1.49645i) q^{7} +(-0.697171 + 2.14567i) q^{8} -0.797419i q^{10} +(0.591134 - 3.26352i) q^{11} +(0.490794 - 0.675520i) q^{13} +(-2.87888 - 0.935406i) q^{14} +(-1.46295 + 1.06289i) q^{16} +(0.199958 - 0.145278i) q^{17} +(2.08556 + 0.677640i) q^{19} +(1.20669 - 1.66087i) q^{20} +(-1.49800 + 1.43318i) q^{22} +4.84746i q^{23} +(1.04219 - 3.20752i) q^{25} +(-0.496392 + 0.161287i) q^{26} +(-4.58066 - 6.30474i) q^{28} +(2.40128 + 7.39039i) q^{29} +(-1.41927 - 1.03116i) q^{31} +5.64252 q^{32} -0.154496 q^{34} +(4.99790 + 3.63118i) q^{35} +(0.106959 + 0.329187i) q^{37} +(-0.805699 - 1.10895i) q^{38} +(-2.73724 + 0.889382i) q^{40} +(1.50228 - 4.62355i) q^{41} -0.423369i q^{43} +(-5.28881 + 0.718188i) q^{44} +(1.78103 - 2.45137i) q^{46} +(-7.07320 - 2.29822i) q^{47} +(13.3091 - 9.66963i) q^{49} +(-1.70552 + 1.23914i) q^{50} +(-1.27796 - 0.415234i) q^{52} +(6.95271 - 9.56959i) q^{53} +(3.81142 - 1.83703i) q^{55} +10.9254i q^{56} +(1.50100 - 4.61960i) q^{58} +(-4.99606 + 1.62332i) q^{59} +(-8.19100 - 11.2739i) q^{61} +(0.338865 + 1.04292i) q^{62} +(0.0724543 + 0.0526411i) q^{64} +1.06520 q^{65} +0.504907 q^{67} +(-0.321787 - 0.233792i) q^{68} +(-1.19330 - 3.67260i) q^{70} +(-6.95402 - 9.57138i) q^{71} +(3.85174 - 1.25150i) q^{73} +(0.0668585 - 0.205769i) q^{74} -3.52895i q^{76} +(-2.16117 - 15.9151i) q^{77} +(-1.30074 + 1.79032i) q^{79} +(-2.19395 - 0.712856i) q^{80} +(-2.45847 + 1.78618i) q^{82} +(3.33901 - 2.42593i) q^{83} +(0.299872 + 0.0974345i) q^{85} +(-0.155552 + 0.214099i) q^{86} +(6.59032 + 3.54361i) q^{88} +13.5225i q^{89} +(1.24952 - 3.84563i) q^{91} +(7.41908 - 2.41061i) q^{92} +(2.73253 + 3.76101i) q^{94} +(0.864467 + 2.66055i) q^{95} +(6.43118 + 4.67252i) q^{97} -10.2832 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

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