LMFDB - Embedded newform 1224.2.l.d.1189.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1224,2,Mod(1189,1224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1224, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1224.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1224.l (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.77368920740$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{16} - 2x^{14} + 2x^{12} - 4x^{11} + 4x^{10} + 8x^{8} - 16x^{7} + 16x^{6} - 64x^{4} - 128x^{2} + 512 $ x^18 - x^16 - 2x^14 + 2x^12 - 4x^11 + 4x^10 + 8x^8 - 16x^7 + 16x^6 - 64x^4 - 128*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 408)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1189.12
Root			$0.480188 - 1.33020i$ of defining polynomial
Character	$\chi$	$=$	1224.1189
Dual form			1224.2.l.d.1189.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.480188 + 1.33020i) q^{2} +(-1.53884 + 1.27749i) q^{4} +1.12134 q^{5} +0.430012i q^{7} +(-2.43824 - 1.43352i) q^{8} +(0.538452 + 1.49159i) q^{10} -5.39665 q^{11} -6.00518i q^{13} +(-0.572000 + 0.206487i) q^{14} +(0.736050 - 3.93170i) q^{16} +(-2.88488 - 2.94575i) q^{17} -3.84246i q^{19} +(-1.72555 + 1.43249i) q^{20} +(-2.59141 - 7.17860i) q^{22} +4.07163i q^{23} -3.74261 q^{25} +(7.98806 - 2.88361i) q^{26} +(-0.549335 - 0.661719i) q^{28} -8.82509 q^{29} +4.48705i q^{31} +(5.58337 - 0.908863i) q^{32} +(2.53314 - 5.25197i) q^{34} +0.482188i q^{35} +0.669738 q^{37} +(5.11123 - 1.84510i) q^{38} +(-2.73408 - 1.60746i) q^{40} -5.53535i q^{41} +2.67318i q^{43} +(8.30458 - 6.89415i) q^{44} +(-5.41606 + 1.95515i) q^{46} +5.24991 q^{47} +6.81509 q^{49} +(-1.79716 - 4.97840i) q^{50} +(7.67154 + 9.24100i) q^{52} -5.51013i q^{53} -6.05145 q^{55} +(0.616432 - 1.04847i) q^{56} +(-4.23770 - 11.7391i) q^{58} +12.9148i q^{59} -15.3735 q^{61} +(-5.96865 + 2.15463i) q^{62} +(3.89003 + 6.99054i) q^{64} -6.73381i q^{65} -8.01924i q^{67} +(8.20253 + 0.847642i) q^{68} +(-0.641404 + 0.231541i) q^{70} -2.86065i q^{71} +7.42698i q^{73} +(0.321600 + 0.890882i) q^{74} +(4.90870 + 5.91293i) q^{76} -2.32062i q^{77} -9.20928i q^{79} +(0.825359 - 4.40875i) q^{80} +(7.36310 - 2.65801i) q^{82} -9.97903i q^{83} +(-3.23492 - 3.30318i) q^{85} +(-3.55585 + 1.28363i) q^{86} +(13.1583 + 7.73622i) q^{88} -5.26826 q^{89} +2.58230 q^{91} +(-5.20145 - 6.26558i) q^{92} +(2.52094 + 6.98341i) q^{94} -4.30869i q^{95} +14.5674i q^{97} +(3.27252 + 9.06540i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{4} + 4 q^{5} - 8 q^{10} + 6 q^{14} + 10 q^{16} + 2 q^{17} + 2 q^{20} + 2 q^{22} + 22 q^{25} - 2 q^{26} - 10 q^{28} - 12 q^{29} + 6 q^{34} - 16 q^{37} + 34 q^{38} - 10 q^{40} - 12 q^{44} + 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) $ 18 * q + 2 * q^4 + 4 * q^5 - 8 * q^10 + 6 * q^14 + 10 * q^16 + 2 * q^17 + 2 * q^20 + 2 * q^22 + 22 * q^25 - 2 * q^26 - 10 * q^28 - 12 * q^29 + 6 * q^34 - 16 * q^37 + 34 * q^38 - 10 * q^40 - 12 * q^44 + 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 + 14 * q^56 - 6 * q^58 - 16 * q^61 + 6 * q^62 + 2 * q^64 + 36 * q^68 - 32 * q^70 + 6 * q^74 + 62 * q^80 + 34 * q^82 + 16 * q^85 - 14 * q^86 + 16 * q^88 - 20 * q^89 + 2 * q^92 + 12 * q^94 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.480188	+	1.33020i	0.339544	+	0.940590i
$2$	0.480188	+	1.33020i	0.339544	+	0.940590i
$3$		0			0
$3$		0			0
$4$	−1.53884	+	1.27749i	−0.769419	+	0.638744i
$5$	1.12134			0.501476			0.250738	−	0.968055i	$-0.419327\pi$
$5$	1.12134			0.501476			0.250738	+	0.968055i	$0.419327\pi$
$6$		0			0
$7$			0.430012i			0.162529i	0.996693	+	0.0812646i	$0.0258959\pi$
$7$			0.430012i			0.162529i	−0.996693	+	0.0812646i	$0.974104\pi$
$8$	−2.43824	−	1.43352i	−0.862048	−	0.506827i
$9$		0			0
$10$	0.538452	+	1.49159i	0.170273	+	0.471684i
$11$	−5.39665			−1.62715			−0.813576	−	0.581459i	$-0.802482\pi$
$11$	−5.39665			−1.62715			−0.813576	+	0.581459i	$0.802482\pi$
$12$		0			0
$13$		−	6.00518i		−	1.66554i	−0.553622	−	0.832768i	$-0.686755\pi$
$13$		−	6.00518i		−	1.66554i	0.553622	−	0.832768i	$-0.313245\pi$
$14$	−0.572000	+	0.206487i	−0.152873	+	0.0551859i
$15$		0			0
$16$	0.736050	−	3.93170i	0.184013	−	0.982924i
$17$	−2.88488	−	2.94575i	−0.699686	−	0.714450i
$17$	−2.88488	−	2.94575i	−0.699686	−	0.714450i
$18$		0			0
$19$		−	3.84246i		−	0.881521i	−0.897625	−	0.440761i	$-0.854709\pi$
$19$		−	3.84246i		−	0.881521i	0.897625	−	0.440761i	$-0.145291\pi$
$20$	−1.72555	+	1.43249i	−0.385846	+	0.320315i
$21$		0			0
$22$	−2.59141	−	7.17860i	−0.552490	−	1.53048i
$23$			4.07163i			0.848993i	0.905430	+	0.424496i	$0.139549\pi$
$23$			4.07163i			0.848993i	−0.905430	+	0.424496i	$0.860451\pi$
$24$		0			0
$25$	−3.74261			−0.748522
$26$	7.98806	−	2.88361i	1.56659	−	0.565523i
$27$		0			0
$28$	−0.549335	−	0.661719i	−0.103815	−	0.125053i
$29$	−8.82509			−1.63878			−0.819389	−	0.573237i	$-0.805687\pi$
$29$	−8.82509			−1.63878			−0.819389	+	0.573237i	$0.805687\pi$
$30$		0			0
$31$			4.48705i			0.805898i	0.915223	+	0.402949i	$0.132015\pi$
$31$			4.48705i			0.805898i	−0.915223	+	0.402949i	$0.867985\pi$
$32$	5.58337	−	0.908863i	0.987009	−	0.160666i
$33$		0			0
$34$	2.53314	−	5.25197i	0.434430	−	0.900705i
$35$			0.482188i			0.0815046i
$36$		0			0
$37$	0.669738			0.110104			0.0550521	−	0.998483i	$-0.482468\pi$
$37$	0.669738			0.110104			0.0550521	+	0.998483i	$0.482468\pi$
$38$	5.11123	−	1.84510i	0.829150	−	0.299316i
$39$		0			0
$40$	−2.73408	−	1.60746i	−0.432297	−	0.254161i
$41$		−	5.53535i		−	0.864477i	−0.901759	−	0.432239i	$-0.857724\pi$
$41$		−	5.53535i		−	0.864477i	0.901759	−	0.432239i	$-0.142276\pi$
$42$		0			0
$43$			2.67318i			0.407656i	0.979007	+	0.203828i	$0.0653384\pi$
$43$			2.67318i			0.407656i	−0.979007	+	0.203828i	$0.934662\pi$
$44$	8.30458	−	6.89415i	1.25196	−	1.03933i
$45$		0			0
$46$	−5.41606	+	1.95515i	−0.798554	+	0.288271i
$47$	5.24991			0.765778			0.382889	−	0.923794i	$-0.374929\pi$
$47$	5.24991			0.765778			0.382889	+	0.923794i	$0.374929\pi$
$48$		0			0
$49$	6.81509			0.973584
$50$	−1.79716	−	4.97840i	−0.254156	−	0.704052i
$51$		0			0
$52$	7.67154	+	9.24100i	1.06385	+	1.28150i
$53$		−	5.51013i		−	0.756875i	−0.925627	−	0.378438i	$-0.876461\pi$
$53$		−	5.51013i		−	0.756875i	0.925627	−	0.378438i	$-0.123539\pi$
$54$		0			0
$55$	−6.05145			−0.815978
$56$	0.616432	−	1.04847i	0.0823741	−	0.140108i
$57$		0			0
$58$	−4.23770	−	11.7391i	−0.556438	−	1.54142i
$59$			12.9148i			1.68136i	0.541533	+	0.840680i	$0.317844\pi$
$59$			12.9148i			1.68136i	−0.541533	+	0.840680i	$0.682156\pi$
$60$		0			0
$61$	−15.3735			−1.96837			−0.984186	−	0.177139i	$-0.943316\pi$
$61$	−15.3735			−1.96837			−0.984186	+	0.177139i	$0.943316\pi$
$62$	−5.96865	+	2.15463i	−0.758019	+	0.273638i
$63$		0			0
$64$	3.89003	+	6.99054i	0.486254	+	0.873818i
$65$		−	6.73381i		−	0.835227i
$66$		0			0
$67$		−	8.01924i		−	0.979706i	−0.871805	−	0.489853i	$-0.837050\pi$
$67$		−	8.01924i		−	0.979706i	0.871805	−	0.489853i	$-0.162950\pi$
$68$	8.20253	+	0.847642i	0.994703	+	0.102792i
$69$		0			0
$70$	−0.641404	+	0.231541i	−0.0766624	+	0.0276744i
$71$		−	2.86065i		−	0.339497i	−0.985487	−	0.169749i	$-0.945704\pi$
$71$		−	2.86065i		−	0.339497i	0.985487	−	0.169749i	$-0.0542956\pi$
$72$		0			0
$73$			7.42698i			0.869262i	0.900609	+	0.434631i	$0.143121\pi$
$73$			7.42698i			0.869262i	−0.900609	+	0.434631i	$0.856879\pi$
$74$	0.321600	+	0.890882i	0.0373852	+	0.103563i
$75$		0			0
$76$	4.90870	+	5.91293i	0.563066	+	0.678260i
$77$		−	2.32062i		−	0.264460i
$78$		0			0
$79$		−	9.20928i		−	1.03612i	−0.855343	−	0.518062i	$-0.826654\pi$
$79$		−	9.20928i		−	1.03612i	0.855343	−	0.518062i	$-0.173346\pi$
$80$	0.825359	−	4.40875i	0.0922779	−	0.492913i
$81$		0			0
$82$	7.36310	−	2.65801i	0.813119	−	0.293528i
$83$		−	9.97903i		−	1.09534i	−0.836694	−	0.547670i	$-0.815515\pi$
$83$		−	9.97903i		−	1.09534i	0.836694	−	0.547670i	$-0.184485\pi$
$84$		0			0
$85$	−3.23492	−	3.30318i	−0.350876	−	0.358280i
$86$	−3.55585	+	1.28363i	−0.383438	+	0.138417i
$87$		0			0
$88$	13.1583	+	7.73622i	1.40268	+	0.824683i
$89$	−5.26826			−0.558434			−0.279217	−	0.960228i	$-0.590075\pi$
$89$	−5.26826			−0.558434			−0.279217	+	0.960228i	$0.590075\pi$
$90$		0			0
$91$	2.58230			0.270698
$92$	−5.20145	−	6.26558i	−0.542289	−	0.653231i
$93$		0			0
$94$	2.52094	+	6.98341i	0.260016	+	0.720283i
$95$		−	4.30869i		−	0.442062i
$96$		0			0
$97$			14.5674i			1.47909i	0.673105	+	0.739547i	$0.264960\pi$
$97$			14.5674i			1.47909i	−0.673105	+	0.739547i	$0.735040\pi$
$98$	3.27252	+	9.06540i	0.330575	+	0.915744i
$99$		0			0
$100$	5.75927	−	4.78114i	0.575927	−	0.478114i
$101$		−	16.7076i		−	1.66247i	−0.555924	−	0.831233i	$-0.687635\pi$
$101$		−	16.7076i		−	1.66247i	0.555924	−	0.831233i	$-0.312365\pi$
$102$		0			0
$103$	−3.41351			−0.336343			−0.168171	−	0.985758i	$-0.553786\pi$
$103$	−3.41351			−0.336343			−0.168171	+	0.985758i	$0.553786\pi$
$104$	−8.60855	+	14.6421i	−0.844138	+	1.43577i
$105$		0			0
$106$	7.32955	−	2.64590i	0.711909	−	0.256993i
$107$	15.8511			1.53239			0.766194	−	0.642610i	$-0.222148\pi$
$107$	15.8511			1.53239			0.766194	+	0.642610i	$0.222148\pi$
$108$		0			0
$109$	8.41308			0.805827			0.402914	−	0.915238i	$-0.367998\pi$
$109$	8.41308			0.805827			0.402914	+	0.915238i	$0.367998\pi$
$110$	−2.90584	−	8.04961i	−0.277061	−	0.767501i
$111$		0			0
$112$	1.69068	+	0.316510i	0.159754	+	0.0299074i
$113$			8.21141i			0.772465i	0.922402	+	0.386232i	$0.126224\pi$
$113$			8.21141i			0.772465i	−0.922402	+	0.386232i	$0.873776\pi$
$114$		0			0
$115$			4.56566i			0.425750i
$116$	13.5804	−	11.2739i	1.26091	−	1.04676i
$117$		0			0
$118$	−17.1792	+	6.20152i	−1.58147	+	0.570896i
$119$	1.26671	−	1.24053i	0.116119	−	0.113719i
$120$		0			0
$121$	18.1238			1.64762
$122$	−7.38216	−	20.4497i	−0.668349	−	1.85143i
$123$		0			0
$124$	−5.73215	−	6.90484i	−0.514762	−	0.620073i
$125$	−9.80339			−0.876842
$126$		0			0
$127$	−6.50879			−0.577562			−0.288781	−	0.957395i	$-0.593250\pi$
$127$	−6.50879			−0.577562			−0.288781	+	0.957395i	$0.593250\pi$
$128$	−7.43084	+	8.53127i	−0.656800	+	0.754065i
$129$		0			0
$130$	8.95729	−	3.23350i	0.785606	−	0.283596i
$131$	6.75159			0.589889			0.294944	−	0.955514i	$-0.404699\pi$
$131$	6.75159			0.589889			0.294944	+	0.955514i	$0.404699\pi$
$132$		0			0
$133$	1.65231			0.143273
$134$	10.6672	−	3.85074i	0.921502	−	0.332654i
$135$		0			0
$136$	2.81123	+	11.3180i	0.241061	+	0.970510i
$137$	7.11420			0.607807			0.303903	−	0.952703i	$-0.401710\pi$
$137$	7.11420			0.607807			0.303903	+	0.952703i	$0.401710\pi$
$138$		0			0
$139$	−0.583527			−0.0494941			−0.0247471	−	0.999694i	$-0.507878\pi$
$139$	−0.583527			−0.0494941			−0.0247471	+	0.999694i	$0.507878\pi$
$140$	−0.615989	−	0.742009i	−0.0520605	−	0.0627112i
$141$		0			0
$142$	3.80523	−	1.37365i	0.319328	−	0.115274i
$143$			32.4078i			2.71008i
$144$		0			0
$145$	−9.89589			−0.821809
$146$	−9.87933	+	3.56635i	−0.817619	+	0.295153i
$147$		0			0
$148$	−1.03062	+	0.855582i	−0.0847163	+	0.0703284i
$149$		−	9.11649i		−	0.746852i	−0.927660	−	0.373426i	$-0.878183\pi$
$149$		−	9.11649i		−	0.746852i	0.927660	−	0.373426i	$-0.121817\pi$
$150$		0			0
$151$	−6.07456			−0.494341			−0.247170	−	0.968972i	$-0.579501\pi$
$151$	−6.07456			−0.494341			−0.247170	+	0.968972i	$0.579501\pi$
$152$	−5.50825	+	9.36885i	−0.446778	+	0.759914i
$153$		0			0
$154$	3.08688	−	1.11434i	0.248748	−	0.0897958i
$155$			5.03148i			0.404139i
$156$		0			0
$157$			10.6193i			0.847510i	0.905777	+	0.423755i	$0.139288\pi$
$157$			10.6193i			0.847510i	−0.905777	+	0.423755i	$0.860712\pi$
$158$	12.2501	−	4.42218i	0.974568	−	0.351810i
$159$		0			0
$160$	6.26082	−	1.01914i	0.494962	−	0.0805701i
$161$	−1.75085			−0.137986
$162$		0			0
$163$	−13.6656			−1.07038			−0.535188	−	0.844733i	$-0.679759\pi$
$163$	−13.6656			−1.07038			−0.535188	+	0.844733i	$0.679759\pi$
$164$	7.07135	+	8.51802i	0.552179	+	0.665145i
$165$		0			0
$166$	13.2741	−	4.79181i	1.03027	−	0.371916i
$167$			2.20168i			0.170371i	0.996365	+	0.0851857i	$0.0271484\pi$
$167$			2.20168i			0.170371i	−0.996365	+	0.0851857i	$0.972852\pi$
$168$		0			0
$169$	−23.0621			−1.77401
$170$	2.84050	−	5.88922i	0.217857	−	0.451682i
$171$		0			0
$172$	−3.41496	−	4.11360i	−0.260388	−	0.313659i
$173$	−1.76714			−0.134353			−0.0671767	−	0.997741i	$-0.521399\pi$
$173$	−1.76714			−0.134353			−0.0671767	+	0.997741i	$0.521399\pi$
$174$		0			0
$175$		−	1.60937i		−	0.121657i
$176$	−3.97221	+	21.2180i	−0.299416	+	1.59937i
$177$		0			0
$178$	−2.52975	−	7.00781i	−0.189613	−	0.525258i
$179$			13.1303i			0.981408i	0.871326	+	0.490704i	$0.163260\pi$
$179$			13.1303i			0.981408i	−0.871326	+	0.490704i	$0.836740\pi$
$180$		0			0
$181$	−17.8616			−1.32764			−0.663820	−	0.747893i	$-0.731066\pi$
$181$	−17.8616			−1.32764			−0.663820	+	0.747893i	$0.731066\pi$
$182$	1.23999	+	3.43496i	0.0919141	+	0.254616i
$183$		0			0
$184$	5.83676	−	9.92760i	0.430292	−	0.731872i
$185$	0.751000			0.0552146
$186$		0			0
$187$	15.5687	+	15.8972i	1.13850	+	1.16252i
$188$	−8.07877	+	6.70670i	−0.589205	+	0.489136i
$189$		0			0
$190$	5.73140	−	2.06898i	0.415799	−	0.150100i
$191$	−22.4316			−1.62310			−0.811548	−	0.584286i	$-0.801374\pi$
$191$	−22.4316			−1.62310			−0.811548	+	0.584286i	$0.801374\pi$
$192$		0			0
$193$		−	24.1361i		−	1.73735i	−0.495380	−	0.868676i	$-0.664971\pi$
$193$		−	24.1361i		−	1.73735i	0.495380	−	0.868676i	$-0.335029\pi$
$194$	−19.3775	+	6.99509i	−1.39122	+	0.502218i
$195$		0			0
$196$	−10.4873	+	8.70619i	−0.749095	+	0.621871i
$197$	10.7417			0.765311			0.382655	−	0.923891i	$-0.375010\pi$
$197$	10.7417			0.765311			0.382655	+	0.923891i	$0.375010\pi$
$198$		0			0
$199$			19.2404i			1.36392i	0.731391	+	0.681958i	$0.238871\pi$
$199$			19.2404i			1.36392i	−0.731391	+	0.681958i	$0.761129\pi$
$200$	9.12538	+	5.36511i	0.645262	+	0.379371i
$201$		0			0
$202$	22.2243	−	8.02278i	1.56370	−	0.564481i
$203$		−	3.79490i		−	0.266349i
$204$		0			0
$205$		−	6.20699i		−	0.433515i
$206$	−1.63913	−	4.54063i	−0.114203	−	0.316361i
$207$		0			0
$208$	−23.6105	−	4.42011i	−1.63710	−	0.306480i
$209$			20.7364i			1.43437i
$210$		0			0
$211$	5.19644			0.357738			0.178869	−	0.983873i	$-0.442756\pi$
$211$	5.19644			0.357738			0.178869	+	0.983873i	$0.442756\pi$
$212$	7.03913	+	8.47921i	0.483449	+	0.582354i
$213$		0			0
$214$	7.61153	+	21.0851i	0.520313	+	1.44135i
$215$			2.99753i			0.204430i
$216$		0			0
$217$	−1.92948			−0.130982
$218$	4.03986	+	11.1910i	0.273614	+	0.757953i
$219$		0			0
$220$	9.31221	−	7.73066i	0.627829	−	0.521201i
$221$	−17.6898	+	17.3242i	−1.18994	+	1.16535i
$222$		0			0
$223$	−7.53829			−0.504801			−0.252401	−	0.967623i	$-0.581220\pi$
$223$	−7.53829			−0.504801			−0.252401	+	0.967623i	$0.581220\pi$
$224$	0.390822	+	2.40091i	0.0261129	+	0.160418i
$225$		0			0
$226$	−10.9228	+	3.94302i	−0.726572	+	0.262286i
$227$	−4.47282			−0.296872			−0.148436	−	0.988922i	$-0.547424\pi$
$227$	−4.47282			−0.296872			−0.148436	+	0.988922i	$0.547424\pi$
$228$		0			0
$229$		−	3.32290i		−	0.219583i	−0.993955	−	0.109792i	$-0.964982\pi$
$229$		−	3.32290i		−	0.219583i	0.993955	−	0.109792i	$-0.0350184\pi$
$230$	−6.07321	+	2.19237i	−0.400456	+	0.144561i
$231$		0			0
$232$	21.5177	+	12.6510i	1.41271	+	0.830576i
$233$		−	18.9254i		−	1.23984i	−0.784664	−	0.619922i	$-0.787164\pi$
$233$		−	18.9254i		−	1.23984i	0.784664	−	0.619922i	$-0.212836\pi$
$234$		0			0
$235$	5.88691			0.384020
$236$	−16.4985	−	19.8737i	−1.07396	−	1.29367i
$237$		0			0
$238$	2.25841	+	1.08928i	0.146391	+	0.0706077i
$239$	2.31610			0.149816			0.0749081	−	0.997190i	$-0.476134\pi$
$239$	2.31610			0.149816			0.0749081	+	0.997190i	$0.476134\pi$
$240$		0			0
$241$		−	4.26774i		−	0.274909i	−0.990508	−	0.137455i	$-0.956108\pi$
$241$		−	4.26774i		−	0.274909i	0.990508	−	0.137455i	$-0.0438921\pi$
$242$	8.70285	+	24.1082i	0.559440	+	1.54974i
$243$		0			0
$244$	23.6573	−	19.6394i	1.51450	−	1.25729i
$245$	7.64200			0.488229
$246$		0			0
$247$	−23.0747			−1.46821
$248$	6.43228	−	10.9405i	0.408450	−	0.694723i
$249$		0			0
$250$	−4.70747	−	13.0404i	−0.297727	−	0.824749i
$251$			7.72635i			0.487683i	0.969815	+	0.243841i	$0.0784076\pi$
$251$			7.72635i			0.487683i	−0.969815	+	0.243841i	$0.921592\pi$
$252$		0			0
$253$		−	21.9731i		−	1.38144i
$254$	−3.12544	−	8.65797i	−0.196108	−	0.543249i
$255$		0			0
$256$	−14.9165	−	5.78785i	−0.932279	−	0.361741i
$257$	28.3167			1.76634			0.883172	−	0.469049i	$-0.155403\pi$
$257$	28.3167			1.76634			0.883172	+	0.469049i	$0.155403\pi$
$258$		0			0
$259$			0.287995i			0.0178952i
$260$	8.60237	+	10.3623i	0.533496	+	0.642640i
$261$		0			0
$262$	3.24203	+	8.98093i	0.200293	+	0.554844i
$263$	−8.87100			−0.547009			−0.273505	−	0.961871i	$-0.588183\pi$
$263$	−8.87100			−0.547009			−0.273505	+	0.961871i	$0.588183\pi$
$264$		0			0
$265$		−	6.17871i		−	0.379555i
$266$	0.793417	+	2.19789i	0.0486475	+	0.134761i
$267$		0			0
$268$	10.2445	+	12.3403i	0.625781	+	0.753805i
$269$	−10.3713			−0.632351			−0.316176	−	0.948701i	$-0.602399\pi$
$269$	−10.3713			−0.632351			−0.316176	+	0.948701i	$0.602399\pi$
$270$		0			0
$271$	14.0483			0.853374			0.426687	−	0.904399i	$-0.359681\pi$
$271$	14.0483			0.853374			0.426687	+	0.904399i	$0.359681\pi$
$272$	−13.7052	+	9.17425i	−0.831001	+	0.556270i
$273$		0			0
$274$	3.41615	+	9.46327i	0.206377	+	0.571697i
$275$	20.1975			1.21796
$276$		0			0
$277$	−5.84445			−0.351159			−0.175579	−	0.984465i	$-0.556180\pi$
$277$	−5.84445			−0.351159			−0.175579	+	0.984465i	$0.556180\pi$
$278$	−0.280203	−	0.776205i	−0.0168054	−	0.0465537i
$279$		0			0
$280$	0.691226	−	1.17569i	0.0413087	−	0.0702609i
$281$	−2.55711			−0.152545			−0.0762723	−	0.997087i	$-0.524302\pi$
$281$	−2.55711			−0.152545			−0.0762723	+	0.997087i	$0.524302\pi$
$282$		0			0
$283$	−16.0967			−0.956848			−0.478424	−	0.878129i	$-0.658792\pi$
$283$	−16.0967			−0.956848			−0.478424	+	0.878129i	$0.658792\pi$
$284$	3.65445	+	4.40209i	0.216852	+	0.261216i
$285$		0			0
$286$	−43.1088	+	15.5619i	−2.54907	+	0.920192i
$287$	2.38027			0.140503
$288$		0			0
$289$	−0.354935	+	16.9963i	−0.0208785	+	0.999782i
$290$	−4.75189	−	13.1635i	−0.279040	−	0.772985i
$291$		0			0
$292$	−9.48787	−	11.4289i	−0.555236	−	0.668827i
$293$		−	6.66413i		−	0.389323i	−0.980871	−	0.194661i	$-0.937639\pi$
$293$		−	6.66413i		−	0.389323i	0.980871	−	0.194661i	$-0.0623608\pi$
$294$		0			0
$295$			14.4818i			0.843162i
$296$	−1.63298	−	0.960084i	−0.0949151	−	0.0558037i
$297$		0			0
$298$	12.1267	−	4.37763i	0.702481	−	0.253589i
$299$	24.4508			1.41403
$300$		0			0
$301$	−1.14950			−0.0662561
$302$	−2.91693	−	8.08035i	−0.167850	−	0.464972i
$303$		0			0
$304$	−15.1074	−	2.82825i	−0.866469	−	0.162211i
$305$	−17.2388			−0.987092
$306$		0			0
$307$		−	0.758629i		−	0.0432972i	−0.999766	−	0.0216486i	$-0.993108\pi$
$307$		−	0.758629i		−	0.0432972i	0.999766	−	0.0216486i	$-0.00689151\pi$
$308$	2.96457	+	3.57107i	0.168922	+	0.203480i
$309$		0			0
$310$	−6.69286	+	2.41606i	−0.380129	+	0.137223i
$311$		−	20.9587i		−	1.18846i	−0.804295	−	0.594231i	$-0.797457\pi$
$311$		−	20.9587i		−	1.18846i	0.804295	−	0.594231i	$-0.202543\pi$
$312$		0			0
$313$		−	4.04868i		−	0.228845i	−0.993432	−	0.114423i	$-0.963498\pi$
$313$		−	4.04868i		−	0.228845i	0.993432	−	0.114423i	$-0.0365018\pi$
$314$	−14.1257	+	5.09925i	−0.797160	+	0.287767i
$315$		0			0
$316$	11.7647	+	14.1716i	0.661818	+	0.797214i
$317$	−14.6008			−0.820063			−0.410032	−	0.912071i	$-0.634482\pi$
$317$	−14.6008			−0.820063			−0.410032	+	0.912071i	$0.634482\pi$
$318$		0			0
$319$	47.6259			2.66654
$320$	4.36203	+	7.83874i	0.243845	+	0.438199i
$321$		0			0
$322$	−0.840736	−	2.32897i	−0.0468524	−	0.129788i
$323$	−11.3190	+	11.0850i	−0.629803	+	0.616788i
$324$		0			0
$325$			22.4750i			1.24669i
$326$	−6.56208	−	18.1780i	−0.363440	−	1.00679i
$327$		0			0
$328$	−7.93505	+	13.4965i	−0.438140	+	0.745221i
$329$			2.25752i			0.124461i
$330$		0			0
$331$			9.20497i			0.505951i	0.967473	+	0.252975i	$0.0814092\pi$
$331$			9.20497i			0.505951i	−0.967473	+	0.252975i	$0.918591\pi$
$332$	12.7481	+	15.3561i	0.699642	+	0.842776i
$333$		0			0
$334$	−2.92867	+	1.05722i	−0.160250	+	0.0578486i
$335$		−	8.99226i		−	0.491299i
$336$		0			0
$337$		−	4.74226i		−	0.258328i	−0.991623	−	0.129164i	$-0.958771\pi$
$337$		−	4.74226i		−	0.258328i	0.991623	−	0.129164i	$-0.0412293\pi$
$338$	−11.0742	−	30.6772i	−0.602355	−	1.66862i
$339$		0			0
$340$	9.19778	+	0.950491i	0.498820	+	0.0515476i
$341$		−	24.2150i		−	1.31132i
$342$		0			0
$343$			5.94065i			0.320765i
$344$	3.83206	−	6.51786i	0.206611	−	0.351419i
$345$		0			0
$346$	−0.848562	−	2.35065i	−0.0456189	−	0.126372i
$347$	−13.0862			−0.702504			−0.351252	−	0.936281i	$-0.614244\pi$
$347$	−13.0862			−0.702504			−0.351252	+	0.936281i	$0.614244\pi$
$348$		0			0
$349$		−	26.8162i		−	1.43544i	−0.696333	−	0.717719i	$-0.745186\pi$
$349$		−	26.8162i		−	1.43544i	0.696333	−	0.717719i	$-0.254814\pi$
$350$	2.14077	−	0.772798i	0.114429	−	0.0413078i
$351$		0			0
$352$	−30.1315	+	4.90481i	−1.60601	+	0.261428i
$353$	−2.05561			−0.109409			−0.0547046	−	0.998503i	$-0.517422\pi$
$353$	−2.05561			−0.109409			−0.0547046	+	0.998503i	$0.517422\pi$
$354$		0			0
$355$		−	3.20775i		−	0.170250i
$356$	8.10700	−	6.73014i	0.429670	−	0.356696i
$357$		0			0
$358$	−17.4659	+	6.30504i	−0.923103	+	0.333231i
$359$	−9.53525			−0.503251			−0.251626	−	0.967825i	$-0.580965\pi$
$359$	−9.53525			−0.503251			−0.251626	+	0.967825i	$0.580965\pi$
$360$		0			0
$361$	4.23548			0.222920
$362$	−8.57691	−	23.7594i	−0.450792	−	1.24876i
$363$		0			0
$364$	−3.97374	+	3.29885i	−0.208281	+	0.172907i
$365$			8.32813i			0.435914i
$366$		0			0
$367$		−	4.51146i		−	0.235497i	−0.993043	−	0.117748i	$-0.962432\pi$
$367$		−	4.51146i		−	0.235497i	0.993043	−	0.117748i	$-0.0375676\pi$
$368$	16.0084	+	2.99692i	0.834495	+	0.156225i
$369$		0			0
$370$	0.360621	+	0.998977i	0.0187478	+	0.0519344i
$371$	2.36942			0.123014
$372$		0			0
$373$		−	6.52623i		−	0.337915i	−0.985623	−	0.168958i	$-0.945960\pi$
$373$		−	6.52623i		−	0.337915i	0.985623	−	0.168958i	$-0.0540401\pi$
$374$	−13.6705	+	28.3430i	−0.706884	+	1.46558i
$375$		0			0
$376$	−12.8005	−	7.52586i	−0.660138	−	0.388117i
$377$			52.9962i			2.72945i
$378$		0			0
$379$	4.45304			0.228738			0.114369	−	0.993438i	$-0.463515\pi$
$379$	4.45304			0.228738			0.114369	+	0.993438i	$0.463515\pi$
$380$	5.50430	+	6.63038i	0.282364	+	0.340131i
$381$		0			0
$382$	−10.7714	−	29.8384i	−0.551113	−	1.52667i
$383$	−20.5625			−1.05069			−0.525346	−	0.850889i	$-0.676064\pi$
$383$	−20.5625			−1.05069			−0.525346	+	0.850889i	$0.676064\pi$
$384$		0			0
$385$		−	2.60220i		−	0.132620i
$386$	32.1057	−	11.5899i	1.63414	−	0.589908i
$387$		0			0
$388$	−18.6097	−	22.4169i	−0.944762	−	1.13804i
$389$		−	6.79829i		−	0.344687i	−0.985037	−	0.172343i	$-0.944866\pi$
$389$		−	6.79829i		−	0.344687i	0.985037	−	0.172343i	$-0.0551339\pi$
$390$		0			0
$391$	11.9940	−	11.7462i	0.606563	−	0.594028i
$392$	−16.6168	−	9.76958i	−0.839276	−	0.493438i
$393$		0			0
$394$	5.15801	+	14.2885i	0.259857	+	0.719844i
$395$		−	10.3267i		−	0.519592i
$396$		0			0
$397$	30.3053			1.52098			0.760489	−	0.649351i	$-0.224960\pi$
$397$	30.3053			1.52098			0.760489	+	0.649351i	$0.224960\pi$
$398$	−25.5935	+	9.23901i	−1.28289	+	0.463110i
$399$		0			0
$400$	−2.75475	+	14.7148i	−0.137737	+	0.735740i
$401$		−	18.4318i		−	0.920438i	−0.887805	−	0.460219i	$-0.847771\pi$
$401$		−	18.4318i		−	0.920438i	0.887805	−	0.460219i	$-0.152229\pi$
$402$		0			0
$403$	26.9455			1.34225
$404$	21.3437	+	25.7103i	1.06189	+	1.27913i
$405$		0			0
$406$	5.04795	−	1.82226i	0.250526	−	0.0904374i
$407$	−3.61434			−0.179156
$408$		0			0
$409$	−17.9406			−0.887104			−0.443552	−	0.896249i	$-0.646282\pi$
$409$	−17.9406			−0.887104			−0.443552	+	0.896249i	$0.646282\pi$
$410$	8.25650	−	2.98052i	0.407760	−	0.147197i
$411$		0			0
$412$	5.25284	−	4.36071i	0.258789	−	0.214837i
$413$	−5.55350			−0.273270
$414$		0			0
$415$		−	11.1898i		−	0.549287i
$416$	−5.45788	−	33.5291i	−0.267595	−	1.64390i
$417$		0			0
$418$	−27.5835	+	9.95739i	−1.34915	+	0.487032i
$419$	28.9251			1.41308			0.706541	−	0.707672i	$-0.250255\pi$
$419$	28.9251			1.41308			0.706541	+	0.707672i	$0.250255\pi$
$420$		0			0
$421$			5.93424i			0.289217i	0.989489	+	0.144609i	$0.0461923\pi$
$421$			5.93424i			0.289217i	−0.989489	+	0.144609i	$0.953808\pi$
$422$	2.49527	+	6.91228i	0.121468	+	0.336484i
$423$		0			0
$424$	−7.89890	+	13.4350i	−0.383604	+	0.652463i
$425$	10.7970	+	11.0248i	0.523730	+	0.534781i
$426$		0			0
$427$		−	6.61078i		−	0.319918i
$428$	−24.3924	+	20.2496i	−1.17905	+	0.978803i
$429$		0			0
$430$	−3.98730	+	1.43938i	−0.192285	+	0.0694130i
$431$		−	28.4152i		−	1.36871i	−0.729149	−	0.684355i	$-0.760084\pi$
$431$		−	28.4152i		−	1.36871i	0.729149	−	0.684355i	$-0.239916\pi$
$432$		0			0
$433$	3.71311			0.178441			0.0892204	−	0.996012i	$-0.471562\pi$
$433$	3.71311			0.178441			0.0892204	+	0.996012i	$0.471562\pi$
$434$	−0.926515	−	2.56659i	−0.0444742	−	0.123200i
$435$		0			0
$436$	−12.9464	+	10.7476i	−0.620019	+	0.514717i
$437$	15.6451			0.748405
$438$		0			0
$439$			40.2651i			1.92175i	0.276988	+	0.960873i	$0.410664\pi$
$439$			40.2651i			1.92175i	−0.276988	+	0.960873i	$0.589336\pi$
$440$	14.7549	+	8.67489i	0.703412	+	0.413559i
$441$		0			0
$442$	−31.5390	−	15.2120i	−1.50016	−	0.723560i
$443$			30.4325i			1.44589i	0.690904	+	0.722947i	$0.257213\pi$
$443$			30.4325i			1.44589i	−0.690904	+	0.722947i	$0.742787\pi$
$444$		0			0
$445$	−5.90748			−0.280042
$446$	−3.61980	−	10.0274i	−0.171402	−	0.474811i
$447$		0			0
$448$	−3.00602	+	1.67276i	−0.142021	+	0.0790305i
$449$		−	22.5604i		−	1.06469i	−0.846527	−	0.532345i	$-0.821311\pi$
$449$		−	22.5604i		−	1.06469i	0.846527	−	0.532345i	$-0.178689\pi$
$450$		0			0
$451$			29.8724i			1.40664i
$452$	−10.4900	−	12.6360i	−0.493407	−	0.594349i
$453$		0			0
$454$	−2.14780	−	5.94973i	−0.100801	−	0.279234i
$455$	2.89562			0.135749
$456$		0			0
$457$	32.8689			1.53754			0.768770	−	0.639525i	$-0.220869\pi$
$457$	32.8689			1.53754			0.768770	+	0.639525i	$0.220869\pi$
$458$	4.42010	−	1.59562i	0.206538	−	0.0745583i
$459$		0			0
$460$	−5.83257	−	7.02581i	−0.271945	−	0.327580i
$461$			22.9549i			1.06911i	0.845132	+	0.534557i	$0.179522\pi$
$461$			22.9549i			1.06911i	−0.845132	+	0.534557i	$0.820478\pi$
$462$		0			0
$463$	−10.8137			−0.502554			−0.251277	−	0.967915i	$-0.580851\pi$
$463$	−10.8137			−0.502554			−0.251277	+	0.967915i	$0.580851\pi$
$464$	−6.49571	+	34.6976i	−0.301556	+	1.61079i
$465$		0			0
$466$	25.1745	−	9.08774i	1.16618	−	0.420982i
$467$		−	16.2589i		−	0.752372i	−0.926544	−	0.376186i	$-0.877235\pi$
$467$		−	16.2589i		−	0.752372i	0.926544	−	0.376186i	$-0.122765\pi$
$468$		0			0
$469$	3.44837			0.159231
$470$	2.82682	+	7.83074i	0.130392	+	0.361205i
$471$		0			0
$472$	18.5136	−	31.4893i	0.852157	−	1.44941i
$473$		−	14.4262i		−	0.663319i
$474$		0			0
$475$			14.3808i			0.659838i
$476$	−0.364496	+	3.52719i	−0.0167067	+	0.161668i
$477$		0			0
$478$	1.11216	+	3.08087i	0.0508692	+	0.140916i
$479$		−	17.6947i		−	0.808491i	−0.914651	−	0.404245i	$-0.867534\pi$
$479$		−	17.6947i		−	0.808491i	0.914651	−	0.404245i	$-0.132466\pi$
$480$		0			0
$481$		−	4.02189i		−	0.183383i
$482$	5.67692	−	2.04932i	0.258577	−	0.0933438i
$483$		0			0
$484$	−27.8897	+	23.1530i	−1.26771	+	1.05241i
$485$			16.3349i			0.741731i
$486$		0			0
$487$		−	37.5879i		−	1.70327i	−0.524136	−	0.851635i	$-0.675612\pi$
$487$		−	37.5879i		−	1.70327i	0.524136	−	0.851635i	$-0.324388\pi$
$488$	37.4842	+	22.0382i	1.69683	+	0.997623i
$489$		0			0
$490$	3.66960	+	10.1654i	0.165775	+	0.459224i
$491$		−	5.12711i		−	0.231383i	−0.993285	−	0.115692i	$-0.963092\pi$
$491$		−	5.12711i		−	0.231383i	0.993285	−	0.115692i	$-0.0369085\pi$
$492$		0			0
$493$	25.4593	+	25.9966i	1.14663	+	1.17083i
$494$	−11.0802	−	30.6938i	−0.498521	−	1.38098i
$495$		0			0
$496$	17.6417	+	3.30269i	0.792136	+	0.148295i
$497$	1.23012			0.0551782
$498$		0			0
$499$	14.1030			0.631336			0.315668	−	0.948870i	$-0.397771\pi$
$499$	14.1030			0.631336			0.315668	+	0.948870i	$0.397771\pi$
$500$	15.0858	−	12.5237i	0.674659	−	0.560077i
$501$		0			0
$502$	−10.2776	+	3.71010i	−0.458710	+	0.165590i
$503$			28.4331i			1.26777i	0.773428	+	0.633884i	$0.218540\pi$
$503$			28.4331i			1.26777i	−0.773428	+	0.633884i	$0.781460\pi$
$504$		0			0
$505$		−	18.7348i		−	0.833687i
$506$	29.2286	−	10.5512i	1.29937	−	0.469060i
$507$		0			0
$508$	10.0160	−	8.31490i	0.444387	−	0.368914i
$509$			5.52807i			0.245027i	0.992467	+	0.122514i	$0.0390956\pi$
$509$			5.52807i			0.245027i	−0.992467	+	0.122514i	$0.960904\pi$
$510$		0			0
$511$	−3.19369			−0.141281
$512$	0.536265	−	22.6211i	0.0236998	−	0.999719i
$513$		0			0
$514$	13.5973	+	37.6667i	0.599752	+	1.66141i
$515$	−3.82769			−0.168668
$516$		0			0
$517$	−28.3319			−1.24604
$518$	−0.383090	+	0.138292i	−0.0168320	+	0.00607620i
$519$		0			0
$520$	−9.65307	+	16.4187i	−0.423315	+	0.720006i
$521$		−	12.6317i		−	0.553404i	−0.960956	−	0.276702i	$-0.910759\pi$
$521$		−	12.6317i		−	0.553404i	0.960956	−	0.276702i	$-0.0892415\pi$
$522$		0			0
$523$		−	28.9269i		−	1.26489i	−0.774607	−	0.632443i	$-0.782052\pi$
$523$		−	28.9269i		−	1.26489i	0.774607	−	0.632443i	$-0.217948\pi$
$524$	−10.3896	+	8.62507i	−0.453872	+	0.376788i
$525$		0			0
$526$	−4.25975	−	11.8002i	−0.185734	−	0.514511i
$527$	13.2177	−	12.9446i	0.575774	−	0.563875i
$528$		0			0
$529$	6.42186			0.279211
$530$	8.21889	−	2.96694i	0.357006	−	0.128876i
$531$		0			0
$532$	−2.54263	+	2.11080i	−0.110237	+	0.0915148i
$533$	−33.2408			−1.43982
$534$		0			0
$535$	17.7744			0.768456
$536$	−11.4958	+	19.5528i	−0.496541	+	0.844554i
$537$		0			0
$538$	−4.98019	−	13.7959i	−0.214711	−	0.594783i
$539$	−36.7787			−1.58417
$540$		0			0
$541$	23.5358			1.01188			0.505942	−	0.862568i	$-0.331145\pi$
$541$	23.5358			1.01188			0.505942	+	0.862568i	$0.331145\pi$
$542$	6.74583	+	18.6870i	0.289758	+	0.802675i
$543$		0			0
$544$	−18.7846	−	13.8253i	−0.805384	−	0.592753i
$545$	9.43388			0.404103
$546$		0			0
$547$	−13.9646			−0.597083			−0.298542	−	0.954397i	$-0.596500\pi$
$547$	−13.9646			−0.597083			−0.298542	+	0.954397i	$0.596500\pi$
$548$	−10.9476	+	9.08830i	−0.467658	+	0.388233i
$549$		0			0
$550$	9.69862	+	26.8667i	0.413551	+	1.14560i
$551$			33.9101i			1.44462i
$552$		0			0
$553$	3.96010			0.168401
$554$	−2.80643	−	7.77426i	−0.119234	−	0.330297i
$555$		0			0
$556$	0.897954	−	0.745449i	0.0380817	−	0.0316141i
$557$		−	8.46728i		−	0.358770i	−0.983779	−	0.179385i	$-0.942589\pi$
$557$		−	8.46728i		−	0.358770i	0.983779	−	0.179385i	$-0.0574108\pi$
$558$		0			0
$559$	16.0529			0.678967
$560$	1.89581	+	0.354914i	0.0801128	+	0.0149979i
$561$		0			0
$562$	−1.22789	−	3.40146i	−0.0517956	−	0.143482i
$563$			44.6126i			1.88020i	0.340904	+	0.940098i	$0.389267\pi$
$563$			44.6126i			1.88020i	−0.340904	+	0.940098i	$0.610733\pi$
$564$		0			0
$565$			9.20774i			0.387373i
$566$	−7.72943	−	21.4117i	−0.324892	−	0.900002i
$567$		0			0
$568$	−4.10081	+	6.97496i	−0.172066	+	0.292663i
$569$	26.7831			1.12281			0.561403	−	0.827542i	$-0.310262\pi$
$569$	26.7831			1.12281			0.561403	+	0.827542i	$0.310262\pi$
$570$		0			0
$571$	−23.0894			−0.966260			−0.483130	−	0.875549i	$-0.660500\pi$
$571$	−23.0894			−0.966260			−0.483130	+	0.875549i	$0.660500\pi$
$572$	−41.4006	−	49.8704i	−1.73105	−	2.08519i
$573$		0			0
$574$	1.14298	+	3.16622i	0.0477069	+	0.132156i
$575$		−	15.2385i		−	0.635489i
$576$		0			0
$577$	3.58583			0.149280			0.0746401	−	0.997211i	$-0.476219\pi$
$577$	3.58583			0.149280			0.0746401	+	0.997211i	$0.476219\pi$
$578$	−22.7788	+	7.68928i	−0.947474	+	0.319832i
$579$		0			0
$580$	15.2282	−	12.6419i	0.632316	−	0.524925i
$581$	4.29110			0.178025
$582$		0			0
$583$			29.7363i			1.23155i
$584$	10.6467	−	18.1088i	0.440565	−	0.749346i
$585$		0			0
$586$	8.86459	−	3.20004i	0.366193	−	0.132192i
$587$		−	14.1022i		−	0.582060i	−0.956714	−	0.291030i	$-0.906002\pi$
$587$		−	14.1022i		−	0.582060i	0.956714	−	0.291030i	$-0.0939980\pi$
$588$		0			0
$589$	17.2413			0.710416
$590$	−19.2636	+	6.95398i	−0.793070	+	0.286291i
$591$		0			0
$592$	0.492961	−	2.63321i	0.0202606	−	0.108224i
$593$	25.0512			1.02873			0.514364	−	0.857572i	$-0.328028\pi$
$593$	25.0512			1.02873			0.514364	+	0.857572i	$0.328028\pi$
$594$		0			0
$595$	1.42041	−	1.39105i	0.0582310	−	0.0570276i
$596$	11.6462	+	14.0288i	0.477047	+	0.574642i
$597$		0			0
$598$	11.7410	+	32.5244i	0.480125	+	1.33002i
$599$	18.0576			0.737813			0.368906	−	0.929467i	$-0.379732\pi$
$599$	18.0576			0.737813			0.368906	+	0.929467i	$0.379732\pi$
$600$		0			0
$601$			3.41581i			0.139334i	0.997570	+	0.0696669i	$0.0221937\pi$
$601$			3.41581i			0.139334i	−0.997570	+	0.0696669i	$0.977806\pi$
$602$	−0.551976	−	1.52906i	−0.0224969	−	0.0623198i
$603$		0			0
$604$	9.34777	−	7.76017i	0.380355	−	0.315757i
$605$	20.3229			0.826243
$606$		0			0
$607$		−	34.7517i		−	1.41053i	−0.708944	−	0.705265i	$-0.750828\pi$
$607$		−	34.7517i		−	1.41053i	0.708944	−	0.705265i	$-0.249172\pi$
$608$	−3.49227	−	21.4539i	−0.141630	−	0.870069i
$609$		0			0
$610$	−8.27787	−	22.9310i	−0.335161	−	0.928449i
$611$		−	31.5266i		−	1.27543i
$612$		0			0
$613$			25.3171i			1.02255i	0.859417	+	0.511275i	$0.170827\pi$
$613$			25.3171i			1.02255i	−0.859417	+	0.511275i	$0.829173\pi$
$614$	1.00912	−	0.364285i	0.0407250	−	0.0147013i
$615$		0			0
$616$	−3.32667	+	5.65824i	−0.134035	+	0.227977i
$617$		−	36.3715i		−	1.46426i	−0.681164	−	0.732131i	$-0.738526\pi$
$617$		−	36.3715i		−	1.46426i	0.681164	−	0.732131i	$-0.261474\pi$
$618$		0			0
$619$	11.8607			0.476723			0.238362	−	0.971176i	$-0.423390\pi$
$619$	11.8607			0.476723			0.238362	+	0.971176i	$0.423390\pi$
$620$	−6.42766	−	7.74264i	−0.258141	−	0.310952i
$621$		0			0
$622$	27.8792	−	10.0641i	1.11785	−	0.403535i
$623$		−	2.26541i		−	0.0907619i
$624$		0			0
$625$	7.72015			0.308806
$626$	5.38554	−	1.94413i	0.215249	−	0.0777030i
$627$		0			0
$628$	−13.5660	−	16.3413i	−0.541342	−	0.652091i
$629$	−1.93211	−	1.97288i	−0.0770384	−	0.0786640i
$630$		0			0
$631$	32.5807			1.29702			0.648509	−	0.761207i	$-0.275393\pi$
$631$	32.5807			1.29702			0.648509	+	0.761207i	$0.275393\pi$
$632$	−13.2017	+	22.4544i	−0.525135	+	0.893189i
$633$		0			0
$634$	−7.01113	−	19.4219i	−0.278448	−	0.771343i
$635$	−7.29854			−0.289634
$636$		0			0
$637$		−	40.9258i		−	1.62154i
$638$	22.8694	+	63.3518i	0.905409	+	2.50812i
$639$		0			0
$640$	−8.33246	+	9.56642i	−0.329369	+	0.378146i
$641$		−	41.4702i		−	1.63797i	−0.573812	−	0.818987i	$-0.694536\pi$
$641$		−	41.4702i		−	1.63797i	0.573812	−	0.818987i	$-0.305464\pi$
$642$		0			0
$643$	−2.52348			−0.0995164			−0.0497582	−	0.998761i	$-0.515845\pi$
$643$	−2.52348			−0.0995164			−0.0497582	+	0.998761i	$0.515845\pi$
$644$	2.69427	−	2.23669i	0.106169	−	0.0881378i
$645$		0			0
$646$	−20.1805	−	9.73351i	−0.793991	−	0.382960i
$647$	−24.8614			−0.977403			−0.488702	−	0.872451i	$-0.662529\pi$
$647$	−24.8614			−0.977403			−0.488702	+	0.872451i	$0.662529\pi$
$648$		0			0
$649$		−	69.6965i		−	2.73583i
$650$	−29.8962	+	10.7922i	−1.17262	+	0.423306i
$651$		0			0
$652$	21.0292	−	17.4577i	0.823568	−	0.683696i
$653$	27.1912			1.06408			0.532038	−	0.846721i	$-0.321426\pi$
$653$	27.1912			1.06408			0.532038	+	0.846721i	$0.321426\pi$
$654$		0			0
$655$	7.57079			0.295815
$656$	−21.7633	−	4.07430i	−0.849715	−	0.159075i
$657$		0			0
$658$	−3.00295	+	1.08404i	−0.117067	+	0.0422601i
$659$			1.37987i			0.0537522i	0.999639	+	0.0268761i	$0.00855596\pi$
$659$			1.37987i			0.0537522i	−0.999639	+	0.0268761i	$0.991444\pi$
$660$		0			0
$661$		−	4.51858i		−	0.175753i	−0.996131	−	0.0878763i	$-0.971992\pi$
$661$		−	4.51858i		−	0.175753i	0.996131	−	0.0878763i	$-0.0280080\pi$
$662$	−12.2444	+	4.42012i	−0.475892	+	0.171793i
$663$		0			0
$664$	−14.3052	+	24.3313i	−0.555147	+	0.944236i
$665$	1.85279			0.0718480
$666$		0			0
$667$		−	35.9325i		−	1.39131i
$668$	−2.81262	−	3.38804i	−0.108824	−	0.131087i
$669$		0			0
$670$	11.9615	−	4.31797i	0.462111	−	0.166818i
$671$	82.9653			3.20284
$672$		0			0
$673$		−	12.8841i		−	0.496644i	−0.968678	−	0.248322i	$-0.920121\pi$
$673$		−	12.8841i		−	0.496644i	0.968678	−	0.248322i	$-0.0798791\pi$
$674$	6.30814	−	2.27718i	0.242980	−	0.0877136i
$675$		0			0
$676$	35.4889	−	29.4616i	1.36496	−	1.13314i
$677$	−4.05563			−0.155870			−0.0779352	−	0.996958i	$-0.524833\pi$
$677$	−4.05563			−0.155870			−0.0779352	+	0.996958i	$0.524833\pi$
$678$		0			0
$679$	−6.26415			−0.240396
$680$	3.15233	+	12.6913i	0.120886	+	0.486688i
$681$		0			0
$682$	32.2107	−	11.6278i	1.23341	−	0.445250i
$683$	18.7934			0.719111			0.359555	−	0.933124i	$-0.382928\pi$
$683$	18.7934			0.719111			0.359555	+	0.933124i	$0.382928\pi$
$684$		0			0
$685$	7.97740			0.304801
$686$	−7.90223	+	2.85263i	−0.301709	+	0.108914i
$687$		0			0
$688$	10.5101	+	1.96760i	0.400695	+	0.0750139i
$689$	−33.0893			−1.26060
$690$		0			0
$691$	47.9864			1.82549			0.912744	−	0.408532i	$-0.133959\pi$
$691$	47.9864			1.82549			0.912744	+	0.408532i	$0.133959\pi$
$692$	2.71935	−	2.25750i	0.103374	−	0.0858175i
$693$		0			0
$694$	−6.28384	−	17.4072i	−0.238531	−	0.660768i
$695$	−0.654329			−0.0248201
$696$		0			0
$697$	−16.3058	+	15.9688i	−0.617626	+	0.604863i
$698$	35.6708	−	12.8768i	1.35016	−	0.487395i
$699$		0			0
$700$	2.05595	+	2.47656i	0.0777074	+	0.0936050i
$701$			4.82240i			0.182140i	0.995845	+	0.0910698i	$0.0290286\pi$
$701$			4.82240i			0.182140i	−0.995845	+	0.0910698i	$0.970971\pi$
$702$		0			0
$703$		−	2.57344i		−	0.0970592i
$704$	−20.9931	−	37.7255i	−0.791208	−	1.42183i
$705$		0			0
$706$	−0.987080	−	2.73436i	−0.0371492	−	0.102909i
$707$	7.18446			0.270199
$708$		0			0
$709$	−4.48466			−0.168425			−0.0842125	−	0.996448i	$-0.526837\pi$
$709$	−4.48466			−0.168425			−0.0842125	+	0.996448i	$0.526837\pi$
$710$	4.26694	−	1.54032i	0.160135	−	0.0578073i
$711$		0			0
$712$	12.8453	+	7.55216i	0.481397	+	0.283029i
$713$	−18.2696			−0.684201
$714$		0			0
$715$			36.3400i			1.35904i
$716$	−16.7739	−	20.2055i	−0.626868	−	0.755115i
$717$		0			0
$718$	−4.57871	−	12.6837i	−0.170876	−	0.473353i
$719$		−	9.47496i		−	0.353356i	−0.984269	−	0.176678i	$-0.943465\pi$
$719$		−	9.47496i		−	0.353356i	0.984269	−	0.176678i	$-0.0565352\pi$
$720$		0			0
$721$		−	1.46785i		−	0.0546656i
$722$	2.03383	+	5.63401i	0.0756912	+	0.209676i
$723$		0			0
$724$	27.4861	−	22.8179i	1.02151	−	0.848022i
$725$	33.0289			1.22666
$726$		0			0
$727$	−36.9867			−1.37176			−0.685881	−	0.727714i	$-0.740583\pi$
$727$	−36.9867			−1.37176			−0.685881	+	0.727714i	$0.740583\pi$
$728$	−6.29626	−	3.70178i	−0.233355	−	0.137197i
$729$		0			0
$730$	−11.0780	+	3.99907i	−0.410017	+	0.148012i
$731$	7.87454	−	7.71181i	0.291250	−	0.285232i
$732$		0			0
$733$			17.6843i			0.653183i	0.945166	+	0.326591i	$0.105900\pi$
$733$			17.6843i			0.653183i	−0.945166	+	0.326591i	$0.894100\pi$
$734$	6.00113	−	2.16635i	0.221506	−	0.0799615i
$735$		0			0
$736$	3.70055	+	22.7334i	0.136404	+	0.837963i
$737$			43.2770i			1.59413i
$738$		0			0
$739$			38.7609i			1.42584i	0.701245	+	0.712921i	$0.252628\pi$
$739$			38.7609i			1.42584i	−0.701245	+	0.712921i	$0.747372\pi$
$740$	−1.15567	+	0.959394i	−0.0424832	+	0.0352680i
$741$		0			0
$742$	1.13777	+	3.15180i	0.0417688	+	0.115706i
$743$			20.7522i			0.761325i	0.924714	+	0.380663i	$0.124304\pi$
$743$			20.7522i			0.761325i	−0.924714	+	0.380663i	$0.875696\pi$
$744$		0			0
$745$		−	10.2226i		−	0.374528i
$746$	8.68116	−	3.13382i	0.317840	−	0.114737i
$747$		0			0
$748$	−44.2662	−	4.57443i	−1.61853	−	0.167258i
$749$			6.81618i			0.249058i
$750$		0			0
$751$		−	31.4975i		−	1.14936i	−0.818379	−	0.574679i	$-0.805127\pi$
$751$		−	31.4975i		−	1.14936i	0.818379	−	0.574679i	$-0.194873\pi$
$752$	3.86420	−	20.6410i	0.140913	−	0.752702i
$753$		0			0
$754$	−70.4954	+	25.4482i	−2.56729	+	0.926767i
$755$	−6.81162			−0.247900
$756$		0			0
$757$			39.5780i			1.43849i	0.694758	+	0.719243i	$0.255511\pi$
$757$			39.5780i			1.43849i	−0.694758	+	0.719243i	$0.744489\pi$
$758$	2.13830	+	5.92342i	0.0776665	+	0.215148i
$759$		0			0
$760$	−6.17660	+	10.5056i	−0.224049	+	0.381079i
$761$	−8.78157			−0.318332			−0.159166	−	0.987252i	$-0.550880\pi$
$761$	−8.78157			−0.318332			−0.159166	+	0.987252i	$0.550880\pi$
$762$		0			0
$763$			3.61773i			0.130971i
$764$	34.5187	−	28.6561i	1.24884	−	1.03674i
$765$		0			0
$766$	−9.87384	−	27.3521i	−0.356756	−	0.988271i
$767$	77.5554			2.80036
$768$		0			0
$769$	−27.4565			−0.990106			−0.495053	−	0.868863i	$-0.664851\pi$
$769$	−27.4565			−0.990106			−0.495053	+	0.868863i	$0.664851\pi$
$770$	3.46143	−	1.24954i	0.124741	−	0.0450304i
$771$		0			0
$772$	30.8335	+	37.1415i	1.10972	+	1.33675i
$773$		−	3.38405i		−	0.121716i	−0.998146	−	0.0608579i	$-0.980616\pi$
$773$		−	3.38405i		−	0.121716i	0.998146	−	0.0608579i	$-0.0193837\pi$
$774$		0			0
$775$		−	16.7933i		−	0.603232i
$776$	20.8827	−	35.5188i	0.749644	−	1.27505i
$777$		0			0
$778$	9.04305	−	3.26446i	0.324209	−	0.117036i
$779$	−21.2694			−0.762055
$780$		0			0
$781$			15.4379i			0.552413i
$782$	21.3841	+	10.3140i	0.764692	+	0.368828i
$783$		0			0
$784$	5.01625	−	26.7949i	0.179152	−	0.956959i
$785$			11.9078i			0.425006i
$786$		0			0
$787$	−27.3267			−0.974093			−0.487047	−	0.873376i	$-0.661926\pi$
$787$	−27.3267			−0.974093			−0.487047	+	0.873376i	$0.661926\pi$
$788$	−16.5297	+	13.7223i	−0.588845	+	0.488838i
$789$		0			0
$790$	13.7365	−	4.95875i	0.488723	−	0.176424i
$791$	−3.53101			−0.125548
$792$		0			0
$793$			92.3204i			3.27839i
$794$	14.5522	+	40.3119i	0.516439	+	1.43062i
$795$		0			0
$796$	−24.5794	−	29.6079i	−0.871193	−	1.04942i
$797$		−	25.8482i		−	0.915589i	−0.889058	−	0.457794i	$-0.848640\pi$
$797$		−	25.8482i		−	0.915589i	0.889058	−	0.457794i	$-0.151360\pi$
$798$		0			0
$799$	−15.1454	−	15.4649i	−0.535804	−	0.547110i
$800$	−20.8963	+	3.40152i	−0.738797	+	0.120262i
$801$		0			0
$802$	24.5178	−	8.85071i	0.865755	−	0.312529i
$803$		−	40.0808i		−	1.41442i
$804$		0			0
$805$	−1.96329			−0.0691968
$806$	12.9389	+	35.8428i	0.455754	+	1.26251i
$807$		0			0
$808$	−23.9507	+	40.7371i	−0.842582	+	1.43313i
$809$			38.7127i			1.36107i	0.732718	+	0.680533i	$0.238251\pi$
$809$			38.7127i			1.36107i	−0.732718	+	0.680533i	$0.761749\pi$
$810$		0			0
$811$	−35.1040			−1.23267			−0.616335	−	0.787484i	$-0.711383\pi$
$811$	−35.1040			−1.23267			−0.616335	+	0.787484i	$0.711383\pi$
$812$	4.84793	+	5.83973i	0.170129	+	0.204934i
$813$		0			0
$814$	−1.73556	−	4.80778i	−0.0608315	−	0.168513i
$815$	−15.3238			−0.536768
$816$		0			0
$817$	10.2716			0.359358
$818$	−8.61485	−	23.8645i	−0.301211	−	0.834401i
$819$		0			0
$820$	7.92935	+	9.55155i	0.276905	+	0.333555i
$821$	32.7883			1.14432			0.572160	−	0.820142i	$-0.306105\pi$
$821$	32.7883			1.14432			0.572160	+	0.820142i	$0.306105\pi$
$822$		0			0
$823$		−	43.1571i		−	1.50436i	−0.658957	−	0.752181i	$-0.729002\pi$
$823$		−	43.1571i		−	1.50436i	0.658957	−	0.752181i	$-0.270998\pi$
$824$	8.32295	+	4.89334i	0.289944	+	0.170468i
$825$		0			0
$826$	−2.66673	−	7.38725i	−0.0927873	−	0.257035i
$827$	−32.5472			−1.13178			−0.565889	−	0.824481i	$-0.691467\pi$
$827$	−32.5472			−1.13178			−0.565889	+	0.824481i	$0.691467\pi$
$828$		0			0
$829$		−	10.6856i		−	0.371128i	−0.982632	−	0.185564i	$-0.940589\pi$
$829$		−	10.6856i		−	0.371128i	0.982632	−	0.185564i	$-0.0594112\pi$
$830$	14.8847	−	5.37322i	0.516654	−	0.186507i
$831$		0			0
$832$	41.9794	−	23.3603i	1.45537	−	0.809873i
$833$	−19.6607	−	20.0756i	−0.681203	−	0.695578i
$834$		0			0
$835$			2.46883i			0.0854372i
$836$	−26.4905	−	31.9100i	−0.916194	−	1.10363i
$837$		0			0
$838$	13.8895	+	38.4760i	0.479804	+	1.32913i
$839$		−	42.7547i		−	1.47606i	−0.674770	−	0.738028i	$-0.735757\pi$
$839$		−	42.7547i		−	1.47606i	0.674770	−	0.738028i	$-0.264243\pi$
$840$		0			0
$841$	48.8823			1.68560
$842$	−7.89369	+	2.84955i	−0.272035	+	0.0982020i
$843$		0			0
$844$	−7.99648	+	6.63839i	−0.275250	+	0.228503i
$845$	−25.8604			−0.889624
$846$		0			0
$847$			7.79347i			0.267787i
$848$	−21.6642	−	4.05573i	−0.743951	−	0.139275i
$849$		0			0
$850$	−9.48056	+	19.6561i	−0.325181	+	0.674197i
$851$			2.72692i			0.0934777i
$852$		0			0
$853$	−52.4844			−1.79703			−0.898516	−	0.438941i	$-0.855354\pi$
$853$	−52.4844			−1.79703			−0.898516	+	0.438941i	$0.855354\pi$
$854$	8.79363	−	3.17442i	0.300912	−	0.108626i
$855$		0			0
$856$	−38.6489	−	22.7230i	−1.32099	−	0.776655i
$857$		−	31.5551i		−	1.07790i	−0.842337	−	0.538952i	$-0.818821\pi$
$857$		−	31.5551i		−	1.07790i	0.842337	−	0.538952i	$-0.181179\pi$
$858$		0			0
$859$		−	6.11248i		−	0.208555i	−0.994548	−	0.104278i	$-0.966747\pi$
$859$		−	6.11248i		−	0.208555i	0.994548	−	0.104278i	$-0.0332530\pi$
$860$	−3.82931	−	4.61272i	−0.130578	−	0.157292i
$861$		0			0
$862$	37.7977	−	13.6446i	1.28740	−	0.464738i
$863$	−44.8687			−1.52735			−0.763675	−	0.645601i	$-0.776607\pi$
$863$	−44.8687			−1.52735			−0.763675	+	0.645601i	$0.776607\pi$
$864$		0			0
$865$	−1.98156			−0.0673751
$866$	1.78299	+	4.93916i	0.0605885	+	0.167840i
$867$		0			0
$868$	2.96917	−	2.46489i	0.100780	−	0.0836639i
$869$			49.6992i			1.68593i
$870$		0			0
$871$	−48.1570			−1.63174
$872$	−20.5131	−	12.0603i	−0.694662	−	0.408415i
$873$		0			0
$874$	7.51258	+	20.8110i	0.254117	+	0.703943i
$875$		−	4.21558i		−	0.142512i
$876$		0			0
$877$	−34.6654			−1.17057			−0.585283	−	0.810829i	$-0.699017\pi$
$877$	−34.6654			−1.17057			−0.585283	+	0.810829i	$0.699017\pi$
$878$	−53.5604	+	19.3348i	−1.80758	+	0.652518i
$879$		0			0
$880$	−4.45417	+	23.7925i	−0.150150	+	0.802044i
$881$			39.0374i			1.31520i	0.753365	+	0.657602i	$0.228429\pi$
$881$			39.0374i			1.31520i	−0.753365	+	0.657602i	$0.771571\pi$
$882$		0			0
$883$		−	56.0176i		−	1.88514i	−0.334006	−	0.942571i	$-0.608401\pi$
$883$		−	56.0176i		−	1.88514i	0.334006	−	0.942571i	$-0.391599\pi$
$884$	5.09024	−	49.2576i	0.171203	−	1.65671i
$885$		0			0
$886$	−40.4812	+	14.6133i	−1.35999	+	0.490945i
$887$			13.9005i			0.466734i	0.972389	+	0.233367i	$0.0749744\pi$
$887$			13.9005i			0.466734i	−0.972389	+	0.233367i	$0.925026\pi$
$888$		0			0
$889$		−	2.79886i		−	0.0938707i
$890$	−2.83670	−	7.85811i	−0.0950865	−	0.263404i
$891$		0			0
$892$	11.6002	−	9.63007i	0.388404	−	0.322439i
$893$		−	20.1726i		−	0.675050i
$894$		0			0
$895$			14.7235i			0.492153i
$896$	−3.66855	−	3.19535i	−0.122558	−	0.106749i
$897$		0			0
$898$	30.0097	−	10.8332i	1.00144	−	0.361509i
$899$		−	39.5986i		−	1.32069i
$900$		0			0
$901$	−16.2315	+	15.8961i	−0.540750	+	0.529575i
$902$	−39.7361	+	14.3444i	−1.32307	+	0.477615i
$903$		0			0
$904$	11.7712	−	20.0214i	0.391505	−	0.665902i
$905$	−20.0288			−0.665780
$906$		0			0
$907$	−43.8898			−1.45734			−0.728668	−	0.684867i	$-0.759860\pi$
$907$	−43.8898			−1.45734			−0.728668	+	0.684867i	$0.759860\pi$
$908$	6.88295	−	5.71397i	0.228419	−	0.189625i
$909$		0			0
$910$	1.39044	+	3.85174i	0.0460927	+	0.127684i
$911$			15.3016i			0.506964i	0.967340	+	0.253482i	$0.0815758\pi$
$911$			15.3016i			0.506964i	−0.967340	+	0.253482i	$0.918424\pi$
$912$		0			0
$913$			53.8533i			1.78228i
$914$	15.7832	+	43.7220i	0.522063	+	1.44619i
$915$		0			0
$916$	4.24496	+	5.11341i	0.140258	+	0.168952i
$917$			2.90326i			0.0958742i
$918$		0			0
$919$	−42.3778			−1.39792			−0.698958	−	0.715163i	$-0.746353\pi$
$919$	−42.3778			−1.39792			−0.698958	+	0.715163i	$0.746353\pi$
$920$	6.54497	−	11.1322i	0.215781	−	0.367017i
$921$		0			0
$922$	−30.5345	+	11.0227i	−1.00560	+	0.363012i
$923$	−17.1787			−0.565445
$924$		0			0
$925$	−2.50657			−0.0824154
$926$	−5.19260	−	14.3843i	−0.170639	−	0.472697i
$927$		0			0
$928$	−49.2737	+	8.02080i	−1.61749	+	0.263296i
$929$		−	10.6062i		−	0.347979i	−0.984747	−	0.173990i	$-0.944334\pi$
$929$		−	10.6062i		−	0.347979i	0.984747	−	0.173990i	$-0.0556660\pi$
$930$		0			0
$931$		−	26.1867i		−	0.858235i
$932$	24.1770	+	29.1231i	0.791942	+	0.953960i
$933$		0			0
$934$	21.6275	−	7.80733i	0.707674	−	0.255464i
$935$	17.4577	+	17.8261i	0.570928	+	0.582976i
$936$		0			0
$937$	−8.71851			−0.284821			−0.142411	−	0.989808i	$-0.545485\pi$
$937$	−8.71851			−0.284821			−0.142411	+	0.989808i	$0.545485\pi$
$938$	1.65587	+	4.58701i	0.0540660	+	0.149771i
$939$		0			0
$940$	−9.05900	+	7.52045i	−0.295472	+	0.245290i
$941$	32.1897			1.04936			0.524678	−	0.851301i	$-0.324186\pi$
$941$	32.1897			1.04936			0.524678	+	0.851301i	$0.324186\pi$
$942$		0			0
$943$	22.5379			0.733935
$944$	50.7769	+	9.50592i	1.65265	+	0.309391i
$945$		0			0
$946$	19.1897	−	6.92730i	0.623911	−	0.225226i
$947$	−36.5026			−1.18618			−0.593088	−	0.805137i	$-0.702091\pi$
$947$	−36.5026			−1.18618			−0.593088	+	0.805137i	$0.702091\pi$
$948$		0			0
$949$	44.6003			1.44779
$950$	−19.1293	+	6.90550i	−0.620637	+	0.224044i
$951$		0			0
$952$	−4.86687	+	1.20886i	−0.157736	+	0.0391794i
$953$	−42.1408			−1.36507			−0.682537	−	0.730851i	$-0.739123\pi$
$953$	−42.1408			−1.36507			−0.682537	+	0.730851i	$0.739123\pi$
$954$		0			0
$955$	−25.1534			−0.813944
$956$	−3.56411	+	2.95879i	−0.115271	+	0.0956942i
$957$		0			0
$958$	23.5374	−	8.49678i	0.760458	−	0.274518i
$959$			3.05919i			0.0987864i
$960$		0			0
$961$	10.8664			0.350529
$962$	5.34990	−	1.93127i	0.172488	−	0.0622665i
$963$		0			0
$964$	5.45198	+	6.56736i	0.175597	+	0.211520i
$965$		−	27.0646i		−	0.871241i
$966$		0			0
$967$	11.8445			0.380893			0.190447	−	0.981698i	$-0.439006\pi$
$967$	11.8445			0.380893			0.190447	+	0.981698i	$0.439006\pi$
$968$	−44.1903	−	25.9809i	−1.42033	−	0.835058i
$969$		0			0
$970$	−21.7286	+	7.84383i	−0.697664	+	0.251850i
$971$		−	20.6928i		−	0.664062i	−0.943268	−	0.332031i	$-0.892266\pi$
$971$		−	20.6928i		−	0.664062i	0.943268	−	0.332031i	$-0.107734\pi$
$972$		0			0
$973$		−	0.250924i		−	0.00804424i
$974$	49.9992	−	18.0492i	1.60208	−	0.578335i
$975$		0			0
$976$	−11.3156	+	60.4438i	−0.362205	+	1.93476i
$977$	12.1171			0.387662			0.193831	−	0.981035i	$-0.437909\pi$
$977$	12.1171			0.387662			0.193831	+	0.981035i	$0.437909\pi$
$978$		0			0
$979$	28.4309			0.908657
$980$	−11.7598	+	9.76256i	−0.375653	+	0.311854i
$981$		0			0
$982$	6.82006	−	2.46198i	0.217637	−	0.0785649i
$983$		−	26.6673i		−	0.850556i	−0.905063	−	0.425278i	$-0.860176\pi$
$983$		−	26.6673i		−	0.850556i	0.905063	−	0.425278i	$-0.139824\pi$
$984$		0			0
$985$	12.0450			0.383785
$986$	−22.3552	+	46.3491i	−0.711935	+	1.47606i
$987$		0			0
$988$	35.5082	−	29.4776i	1.12967	−	0.937808i
$989$	−10.8842			−0.346097
$990$		0			0
$991$		−	12.1539i		−	0.386082i	−0.981191	−	0.193041i	$-0.938165\pi$
$991$		−	12.1539i		−	0.386082i	0.981191	−	0.193041i	$-0.0618350\pi$
$992$	4.07811	+	25.0528i	0.129480	+	0.795428i
$993$		0			0
$994$	0.590687	+	1.63629i	0.0187354	+	0.0519001i
$995$			21.5749i			0.683972i
$996$		0			0
$997$	−20.0983			−0.636520			−0.318260	−	0.948004i	$-0.603098\pi$
$997$	−20.0983			−0.636520			−0.318260	+	0.948004i	$0.603098\pi$
$998$	6.77208	+	18.7597i	0.214367	+	0.593828i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.2.l.d.1189.12		18
3.2	odd	2		408.2.l.b.373.7	yes	18
4.3	odd	2		4896.2.l.d.3025.11		18
8.3	odd	2		4896.2.l.c.3025.7		18
8.5	even	2		1224.2.l.c.1189.11		18
12.11	even	2		1632.2.l.a.1393.7		18
17.16	even	2		1224.2.l.c.1189.12		18
24.5	odd	2		408.2.l.a.373.8	yes	18
24.11	even	2		1632.2.l.b.1393.11		18
51.50	odd	2		408.2.l.a.373.7	✓	18
68.67	odd	2		4896.2.l.c.3025.8		18
136.67	odd	2		4896.2.l.d.3025.12		18
136.101	even	2	inner	1224.2.l.d.1189.11		18
204.203	even	2		1632.2.l.b.1393.12		18
408.101	odd	2		408.2.l.b.373.8	yes	18
408.203	even	2		1632.2.l.a.1393.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
408.2.l.a.373.7	✓	18	51.50	odd	2
408.2.l.a.373.8	yes	18	24.5	odd	2
408.2.l.b.373.7	yes	18	3.2	odd	2
408.2.l.b.373.8	yes	18	408.101	odd	2
1224.2.l.c.1189.11		18	8.5	even	2
1224.2.l.c.1189.12		18	17.16	even	2
1224.2.l.d.1189.11		18	136.101	even	2	inner
1224.2.l.d.1189.12		18	1.1	even	1	trivial
1632.2.l.a.1393.7		18	12.11	even	2
1632.2.l.a.1393.8		18	408.203	even	2
1632.2.l.b.1393.11		18	24.11	even	2
1632.2.l.b.1393.12		18	204.203	even	2
4896.2.l.c.3025.7		18	8.3	odd	2
4896.2.l.c.3025.8		18	68.67	odd	2
4896.2.l.d.3025.11		18	4.3	odd	2
4896.2.l.d.3025.12		18	136.67	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.480188 + 1.33020i) q^{2} +(-1.53884 + 1.27749i) q^{4} +1.12134 q^{5} +0.430012i q^{7} +(-2.43824 - 1.43352i) q^{8} +(0.538452 + 1.49159i) q^{10} -5.39665 q^{11} -6.00518i q^{13} +(-0.572000 + 0.206487i) q^{14} +(0.736050 - 3.93170i) q^{16} +(-2.88488 - 2.94575i) q^{17} -3.84246i q^{19} +(-1.72555 + 1.43249i) q^{20} +(-2.59141 - 7.17860i) q^{22} +4.07163i q^{23} -3.74261 q^{25} +(7.98806 - 2.88361i) q^{26} +(-0.549335 - 0.661719i) q^{28} -8.82509 q^{29} +4.48705i q^{31} +(5.58337 - 0.908863i) q^{32} +(2.53314 - 5.25197i) q^{34} +0.482188i q^{35} +0.669738 q^{37} +(5.11123 - 1.84510i) q^{38} +(-2.73408 - 1.60746i) q^{40} -5.53535i q^{41} +2.67318i q^{43} +(8.30458 - 6.89415i) q^{44} +(-5.41606 + 1.95515i) q^{46} +5.24991 q^{47} +6.81509 q^{49} +(-1.79716 - 4.97840i) q^{50} +(7.67154 + 9.24100i) q^{52} -5.51013i q^{53} -6.05145 q^{55} +(0.616432 - 1.04847i) q^{56} +(-4.23770 - 11.7391i) q^{58} +12.9148i q^{59} -15.3735 q^{61} +(-5.96865 + 2.15463i) q^{62} +(3.89003 + 6.99054i) q^{64} -6.73381i q^{65} -8.01924i q^{67} +(8.20253 + 0.847642i) q^{68} +(-0.641404 + 0.231541i) q^{70} -2.86065i q^{71} +7.42698i q^{73} +(0.321600 + 0.890882i) q^{74} +(4.90870 + 5.91293i) q^{76} -2.32062i q^{77} -9.20928i q^{79} +(0.825359 - 4.40875i) q^{80} +(7.36310 - 2.65801i) q^{82} -9.97903i q^{83} +(-3.23492 - 3.30318i) q^{85} +(-3.55585 + 1.28363i) q^{86} +(13.1583 + 7.73622i) q^{88} -5.26826 q^{89} +2.58230 q^{91} +(-5.20145 - 6.26558i) q^{92} +(2.52094 + 6.98341i) q^{94} -4.30869i q^{95} +14.5674i q^{97} +(3.27252 + 9.06540i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{4} + 4 q^{5} - 8 q^{10} + 6 q^{14} + 10 q^{16} + 2 q^{17} + 2 q^{20} + 2 q^{22} + 22 q^{25} - 2 q^{26} - 10 q^{28} - 12 q^{29} + 6 q^{34} - 16 q^{37} + 34 q^{38} - 10 q^{40} - 12 q^{44} + 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) \) 18 * q + 2 * q^4 + 4 * q^5 - 8 * q^10 + 6 * q^14 + 10 * q^16 + 2 * q^17 + 2 * q^20 + 2 * q^22 + 22 * q^25 - 2 * q^26 - 10 * q^28 - 12 * q^29 + 6 * q^34 - 16 * q^37 + 34 * q^38 - 10 * q^40 - 12 * q^44 + 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 + 14 * q^56 - 6 * q^58 - 16 * q^61 + 6 * q^62 + 2 * q^64 + 36 * q^68 - 32 * q^70 + 6 * q^74 + 62 * q^80 + 34 * q^82 + 16 * q^85 - 14 * q^86 + 16 * q^88 - 20 * q^89 + 2 * q^92 + 12 * q^94 + 60 * q^98

Introduction

L-functions

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