LMFDB - Embedded newform 675.2.y.a.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(19,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 27]))

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

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

chi := DirichletCharacter("675.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.y (of order $30$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	675.19
Dual form			675.2.y.a.604.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.264379 + 1.24380i) q^{2} +(0.349937 + 0.155802i) q^{4} +(-1.55641 - 1.60548i) q^{5} +(1.19020 + 0.687160i) q^{7} +(-1.78115 + 2.45154i) q^{8} +O(q^{10})$	\(q+(-0.264379 + 1.24380i) q^{2} +(0.349937 + 0.155802i) q^{4} +(-1.55641 - 1.60548i) q^{5} +(1.19020 + 0.687160i) q^{7} +(-1.78115 + 2.45154i) q^{8} +(2.40839 - 1.51142i) q^{10} +(2.38060 + 0.506011i) q^{11} +(1.09193 + 5.13715i) q^{13} +(-1.16936 + 1.29870i) q^{14} +(-2.06572 - 2.29421i) q^{16} +(2.53652 - 3.49123i) q^{17} +(-5.13239 - 3.72890i) q^{19} +(-0.294509 - 0.804310i) q^{20} +(-1.25876 + 2.82722i) q^{22} +(6.31314 + 5.68438i) q^{23} +(-0.155149 + 4.99759i) q^{25} -6.67830 q^{26} +(0.309433 + 0.425898i) q^{28} +(0.637748 + 6.06776i) q^{29} +(-0.796049 + 7.57390i) q^{31} +(-1.84891 + 1.06747i) q^{32} +(3.67180 + 4.07795i) q^{34} +(-0.749215 - 2.98035i) q^{35} +(5.78803 + 1.88065i) q^{37} +(5.99492 - 5.39785i) q^{38} +(6.70811 - 0.956010i) q^{40} +(-3.58329 + 0.761651i) q^{41} +(2.77141 + 1.60008i) q^{43} +(0.754221 + 0.547974i) q^{44} +(-8.73932 + 6.34949i) q^{46} +(-8.10470 + 0.851838i) q^{47} +(-2.55562 - 4.42647i) q^{49} +(-6.17501 - 1.51423i) q^{50} +(-0.418269 + 1.96780i) q^{52} +(-2.04788 - 2.81866i) q^{53} +(-2.89280 - 4.60957i) q^{55} +(-3.80452 + 1.69388i) q^{56} +(-7.71572 - 0.810955i) q^{58} +(6.84612 - 1.45519i) q^{59} +(2.39447 + 0.508959i) q^{61} +(-9.20999 - 2.99251i) q^{62} +(-2.74688 - 8.45403i) q^{64} +(6.54810 - 9.74862i) q^{65} +(3.89026 + 0.408883i) q^{67} +(1.43156 - 0.826513i) q^{68} +(3.90505 - 0.143937i) q^{70} +(-3.77547 + 2.74304i) q^{71} +(7.02114 - 2.28131i) q^{73} +(-3.86939 + 6.70198i) q^{74} +(-1.21504 - 2.10452i) q^{76} +(2.48567 + 2.23811i) q^{77} +(-0.609652 - 5.80045i) q^{79} +(-0.468204 + 6.88721i) q^{80} -4.65827i q^{82} +(3.51026 + 7.88417i) q^{83} +(-9.55299 + 1.36145i) q^{85} +(-2.72288 + 3.02407i) q^{86} +(-5.48071 + 4.93485i) q^{88} +(-3.14673 - 9.68464i) q^{89} +(-2.23043 + 6.86455i) q^{91} +(1.32356 + 2.97277i) q^{92} +(1.08319 - 10.3059i) q^{94} +(2.00144 + 14.0437i) q^{95} +(-8.01337 + 0.842239i) q^{97} +(6.18131 - 2.00843i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	−0.264379	+	1.24380i	−0.186944	+	0.879503i	0.780251	+	0.625467i	$0.215091\pi$
$2$	−0.264379	+	1.24380i	−0.186944	+	0.879503i	−0.967195	+	0.254036i	$0.918242\pi$
$3$		0			0
$3$		0			0
$4$	0.349937	+	0.155802i	0.174968	+	0.0779010i
$5$	−1.55641	−	1.60548i	−0.696050	−	0.717994i
$5$	−1.55641	−	1.60548i	−0.696050	−	0.717994i
$6$		0			0
$7$	1.19020	+	0.687160i	0.449852	+	0.259722i	0.707768	−	0.706445i	$-0.249702\pi$
$7$	1.19020	+	0.687160i	0.449852	+	0.259722i	−0.257916	+	0.966167i	$0.583036\pi$
$8$	−1.78115	+	2.45154i	−0.629731	+	0.866751i
$9$		0			0
$10$	2.40839	−	1.51142i	0.761600	−	0.477953i
$11$	2.38060	+	0.506011i	0.717777	+	0.152568i	0.552300	−	0.833645i	$-0.313750\pi$
$11$	2.38060	+	0.506011i	0.717777	+	0.152568i	0.165477	+	0.986214i	$0.447084\pi$
$12$		0			0
$13$	1.09193	+	5.13715i	0.302848	+	1.42479i	0.821698	+	0.569923i	$0.193027\pi$
$13$	1.09193	+	5.13715i	0.302848	+	1.42479i	−0.518850	+	0.854866i	$0.673640\pi$
$14$	−1.16936	+	1.29870i	−0.312524	+	0.347093i
$15$		0			0
$16$	−2.06572	−	2.29421i	−0.516429	−	0.573552i
$17$	2.53652	−	3.49123i	0.615198	−	0.846747i	−0.381795	−	0.924247i	$-0.624694\pi$
$17$	2.53652	−	3.49123i	0.615198	−	0.846747i	0.996992	+	0.0775004i	$0.0246939\pi$
$18$		0			0
$19$	−5.13239	−	3.72890i	−1.17745	−	0.855469i	−0.185570	−	0.982631i	$-0.559413\pi$
$19$	−5.13239	−	3.72890i	−1.17745	−	0.855469i	−0.991882	+	0.127162i	$0.959413\pi$
$20$	−0.294509	−	0.804310i	−0.0658543	−	0.179849i
$21$		0			0
$22$	−1.25876	+	2.82722i	−0.268368	+	0.602765i
$23$	6.31314	+	5.68438i	1.31638	+	1.18528i	0.968862	+	0.247603i	$0.0796427\pi$
$23$	6.31314	+	5.68438i	1.31638	+	1.18528i	0.347520	+	0.937673i	$0.387024\pi$
$24$		0			0
$25$	−0.155149	+	4.99759i	−0.0310298	+	0.999518i
$26$	−6.67830			−1.30972
$27$		0			0
$28$	0.309433	+	0.425898i	0.0584773	+	0.0804871i
$29$	0.637748	+	6.06776i	0.118427	+	1.12676i	0.878774	+	0.477239i	$0.158362\pi$
$29$	0.637748	+	6.06776i	0.118427	+	1.12676i	−0.760347	+	0.649517i	$0.774971\pi$
$30$		0			0
$31$	−0.796049	+	7.57390i	−0.142975	+	1.36031i	0.654089	+	0.756417i	$0.273052\pi$
$31$	−0.796049	+	7.57390i	−0.142975	+	1.36031i	−0.797064	+	0.603895i	$0.793615\pi$
$32$	−1.84891	+	1.06747i	−0.326843	+	0.188703i
$33$		0			0
$34$	3.67180	+	4.07795i	0.629709	+	0.699362i
$35$	−0.749215	−	2.98035i	−0.126640	−	0.503771i
$36$		0			0
$37$	5.78803	+	1.88065i	0.951547	+	0.309176i	0.743344	−	0.668909i	$-0.233239\pi$
$37$	5.78803	+	1.88065i	0.951547	+	0.309176i	0.208203	+	0.978086i	$0.433239\pi$
$38$	5.99492	−	5.39785i	0.972505	−	0.875647i
$39$		0			0
$40$	6.70811	−	0.956010i	1.06065	−	0.151158i
$41$	−3.58329	+	0.761651i	−0.559615	+	0.118950i	−0.479031	−	0.877798i	$-0.659012\pi$
$41$	−3.58329	+	0.761651i	−0.559615	+	0.118950i	−0.0805841	+	0.996748i	$0.525679\pi$
$42$		0			0
$43$	2.77141	+	1.60008i	0.422636	+	0.244009i	0.696205	−	0.717843i	$-0.254871\pi$
$43$	2.77141	+	1.60008i	0.422636	+	0.244009i	−0.273568	+	0.961853i	$0.588204\pi$
$44$	0.754221	+	0.547974i	0.113703	+	0.0826101i
$45$		0			0
$46$	−8.73932	+	6.34949i	−1.28854	+	0.936181i
$47$	−8.10470	+	0.851838i	−1.18219	+	0.124253i	−0.675158	−	0.737673i	$-0.735925\pi$
$47$	−8.10470	+	0.851838i	−1.18219	+	0.124253i	−0.507033	+	0.861926i	$0.669258\pi$
$48$		0			0
$49$	−2.55562	−	4.42647i	−0.365089	−	0.632352i
$50$	−6.17501	−	1.51423i	−0.873278	−	0.214145i
$51$		0			0
$52$	−0.418269	+	1.96780i	−0.0580035	+	0.272885i
$53$	−2.04788	−	2.81866i	−0.281297	−	0.387173i	0.644866	−	0.764296i	$-0.276913\pi$
$53$	−2.04788	−	2.81866i	−0.281297	−	0.387173i	−0.926163	+	0.377123i	$0.876913\pi$
$54$		0			0
$55$	−2.89280	−	4.60957i	−0.390065	−	0.621554i
$56$	−3.80452	+	1.69388i	−0.508400	+	0.226354i
$57$		0			0
$58$	−7.71572	−	0.810955i	−1.01312	−	0.106484i
$59$	6.84612	−	1.45519i	0.891289	−	0.189449i	0.260565	−	0.965456i	$-0.416091\pi$
$59$	6.84612	−	1.45519i	0.891289	−	0.189449i	0.630724	+	0.776007i	$0.282758\pi$
$60$		0			0
$61$	2.39447	+	0.508959i	0.306580	+	0.0651656i	0.358633	−	0.933479i	$-0.383243\pi$
$61$	2.39447	+	0.508959i	0.306580	+	0.0651656i	−0.0520528	+	0.998644i	$0.516576\pi$
$62$	−9.20999	−	2.99251i	−1.16967	−	0.380049i
$63$		0			0
$64$	−2.74688	−	8.45403i	−0.343360	−	1.05675i
$65$	6.54810	−	9.74862i	0.812192	−	1.20917i
$66$		0			0
$67$	3.89026	+	0.408883i	0.475271	+	0.0499530i	0.339136	−	0.940737i	$-0.389865\pi$
$67$	3.89026	+	0.408883i	0.475271	+	0.0499530i	0.136135	+	0.990690i	$0.456532\pi$
$68$	1.43156	−	0.826513i	0.173603	−	0.100229i
$69$		0			0
$70$	3.90505	−	0.143937i	0.466742	−	0.0172037i
$71$	−3.77547	+	2.74304i	−0.448066	+	0.325539i	−0.788832	−	0.614609i	$-0.789314\pi$
$71$	−3.77547	+	2.74304i	−0.448066	+	0.325539i	0.340766	+	0.940148i	$0.389314\pi$
$72$		0			0
$73$	7.02114	−	2.28131i	0.821762	−	0.267007i	0.132191	−	0.991224i	$-0.457799\pi$
$73$	7.02114	−	2.28131i	0.821762	−	0.267007i	0.689572	+	0.724218i	$0.257799\pi$
$74$	−3.86939	+	6.70198i	−0.449808	+	0.779090i
$75$		0			0
$76$	−1.21504	−	2.10452i	−0.139375	−	0.241405i
$77$	2.48567	+	2.23811i	0.283268	+	0.255056i
$78$		0			0
$79$	−0.609652	−	5.80045i	−0.0685912	−	0.652602i	−0.973764	−	0.227559i	$-0.926926\pi$
$79$	−0.609652	−	5.80045i	−0.0685912	−	0.652602i	0.905173	−	0.425043i	$-0.139741\pi$
$80$	−0.468204	+	6.88721i	−0.0523468	+	0.770013i
$81$		0			0
$82$		−	4.65827i		−	0.514420i
$83$	3.51026	+	7.88417i	0.385301	+	0.865400i	0.997222	+	0.0744816i	$0.0237302\pi$
$83$	3.51026	+	7.88417i	0.385301	+	0.865400i	−0.611921	+	0.790919i	$0.709603\pi$
$84$		0			0
$85$	−9.55299	+	1.36145i	−1.03617	+	0.147670i
$86$	−2.72288	+	3.02407i	−0.293616	+	0.326094i
$87$		0			0
$88$	−5.48071	+	4.93485i	−0.584245	+	0.526057i
$89$	−3.14673	−	9.68464i	−0.333553	−	1.02657i	−0.967431	−	0.253137i	$-0.918538\pi$
$89$	−3.14673	−	9.68464i	−0.333553	−	1.02657i	0.633878	−	0.773433i	$-0.281462\pi$
$90$		0			0
$91$	−2.23043	+	6.86455i	−0.233812	+	0.719601i
$92$	1.32356	+	2.97277i	0.137991	+	0.309933i
$93$		0			0
$94$	1.08319	−	10.3059i	0.111723	−	1.06297i
$95$	2.00144	+	14.0437i	0.205344	+	1.44085i
$96$		0			0
$97$	−8.01337	+	0.842239i	−0.813634	+	0.0855164i	−0.502200	−	0.864751i	$-0.667476\pi$
$97$	−8.01337	+	0.842239i	−0.813634	+	0.0855164i	−0.311434	+	0.950268i	$0.600809\pi$
$98$	6.18131	−	2.00843i	0.624407	−	0.202882i
$99$		0			0
$100$	−0.832927	+	1.72467i	−0.0832927	+	0.172467i
$101$	4.04713	−	7.00984i	0.402705	−	0.697505i	−0.591347	−	0.806417i	$-0.701403\pi$
$101$	4.04713	−	7.00984i	0.402705	−	0.697505i	0.994051	+	0.108912i	$0.0347368\pi$
$102$		0			0
$103$	2.22908	−	5.00659i	0.219637	−	0.493314i	−0.769798	−	0.638288i	$-0.779643\pi$
$103$	2.22908	−	5.00659i	0.219637	−	0.493314i	0.989436	+	0.144974i	$0.0463098\pi$
$104$	−14.5388	−	6.47311i	−1.42565	−	0.634740i
$105$		0			0
$106$	4.04728	−	1.80196i	0.393106	−	0.175022i
$107$		−	12.3572i		−	1.19462i	−0.802012	−	0.597308i	$-0.796237\pi$
$107$		−	12.3572i		−	1.19462i	0.802012	−	0.597308i	$-0.203763\pi$
$108$		0			0
$109$	0.282724	−	0.870134i	0.0270800	−	0.0833438i	−0.936603	−	0.350392i	$-0.886048\pi$
$109$	0.282724	−	0.870134i	0.0270800	−	0.0833438i	0.963683	+	0.267048i	$0.0860483\pi$
$110$	6.49820	−	2.37941i	0.619579	−	0.226868i
$111$		0			0
$112$	−0.882118	−	4.15004i	−0.0833523	−	0.392142i
$113$	1.18177	+	5.55978i	0.111171	+	0.523020i	0.998128	+	0.0611664i	$0.0194820\pi$
$113$	1.18177	+	5.55978i	0.111171	+	0.523020i	−0.886956	+	0.461853i	$0.847185\pi$
$114$		0			0
$115$	−0.699693	−	18.9829i	−0.0652467	−	1.77016i
$116$	−0.722198	+	2.22270i	−0.0670544	+	0.206372i
$117$		0			0
$118$			8.89996i			0.819308i
$119$	5.41800	−	2.41225i	0.496667	−	0.221130i
$120$		0			0
$121$	−4.63781	−	2.06488i	−0.421619	−	0.187717i
$122$	−1.26609	+	2.84369i	−0.114627	+	0.257455i
$123$		0			0
$124$	−1.45859	+	2.52636i	−0.130986	+	0.226874i
$125$	8.26502	−	7.52923i	0.739246	−	0.673435i
$126$		0			0
$127$	−0.138339	+	0.0449491i	−0.0122756	+	0.00398859i	−0.315148	−	0.949042i	$-0.602054\pi$
$127$	−0.138339	+	0.0449491i	−0.0122756	+	0.00398859i	0.302873	+	0.953031i	$0.402054\pi$
$128$	6.99490	−	0.735194i	0.618268	−	0.0649826i
$129$		0			0
$130$	10.3942	+	10.7219i	0.911631	+	0.940372i
$131$	−0.0493783	+	0.469803i	−0.00431420	+	0.0410469i	−0.996467	−	0.0839827i	$-0.973236\pi$
$131$	−0.0493783	+	0.469803i	−0.00431420	+	0.0410469i	0.992153	+	0.125030i	$0.0399026\pi$
$132$		0			0
$133$	−3.54620	−	7.96490i	−0.307495	−	0.690645i
$134$	−1.53707	+	4.73062i	−0.132783	+	0.408664i
$135$		0			0
$136$	4.04096	+	12.4368i	0.346509	+	1.06645i
$137$	9.69387	−	8.72840i	0.828203	−	0.745718i	−0.141517	−	0.989936i	$-0.545198\pi$
$137$	9.69387	−	8.72840i	0.828203	−	0.745718i	0.969720	+	0.244218i	$0.0785313\pi$
$138$		0			0
$139$	9.43806	−	10.4820i	0.800525	−	0.889074i	−0.195263	−	0.980751i	$-0.562556\pi$
$139$	9.43806	−	10.4820i	0.800525	−	0.889074i	0.995789	+	0.0916772i	$0.0292228\pi$
$140$	0.202166	−	1.15966i	0.0170861	−	0.0980093i
$141$		0			0
$142$	−2.41365	−	5.42115i	−0.202549	−	0.454933i
$143$			12.7820i			1.06889i
$144$		0			0
$145$	8.74909	−	10.4678i	0.726573	−	0.869308i
$146$	0.981259	+	9.33606i	0.0812096	+	0.772658i
$147$		0			0
$148$	1.73244	+	1.55989i	0.142406	+	0.128223i
$149$	5.23260	+	9.06313i	0.428671	+	0.742480i	0.996755	−	0.0804902i	$-0.0256486\pi$
$149$	5.23260	+	9.06313i	0.428671	+	0.742480i	−0.568084	+	0.822970i	$0.692315\pi$
$150$		0			0
$151$	1.88333	−	3.26203i	0.153263	−	0.265460i	−0.779162	−	0.626823i	$-0.784355\pi$
$151$	1.88333	−	3.26203i	0.153263	−	0.265460i	0.932425	+	0.361363i	$0.117688\pi$
$152$	18.2831	−	5.94054i	1.48296	−	0.481842i
$153$		0			0
$154$	−3.44092	+	2.49998i	−0.277278	+	0.201454i
$155$	13.3987	−	10.5101i	1.07621	−	0.844190i
$156$		0			0
$157$	14.7847	−	8.53592i	1.17994	−	0.681241i	0.223942	−	0.974602i	$-0.428107\pi$
$157$	14.7847	−	8.53592i	1.17994	−	0.681241i	0.956002	+	0.293361i	$0.0947739\pi$
$158$	7.37581	+	0.775229i	0.586788	+	0.0616739i
$159$		0			0
$160$	4.59146	+	1.30697i	0.362987	+	0.103325i
$161$	3.60780	+	11.1037i	0.284335	+	0.875092i
$162$		0			0
$163$	15.2411	+	4.95212i	1.19377	+	0.387880i	0.837466	−	0.546489i	$-0.184036\pi$
$163$	15.2411	+	4.95212i	1.19377	+	0.387880i	0.356306	+	0.934369i	$0.384036\pi$
$164$	−1.37259	−	0.291753i	−0.107181	−	0.0227821i
$165$		0			0
$166$	−10.7344	+	2.28167i	−0.833152	+	0.177092i
$167$	−13.3750	−	1.40576i	−1.03498	−	0.108781i	−0.428229	−	0.903670i	$-0.640863\pi$
$167$	−13.3750	−	1.40576i	−1.03498	−	0.108781i	−0.606755	+	0.794889i	$0.707529\pi$
$168$		0			0
$169$	−13.3219	+	5.93129i	−1.02476	+	0.456253i
$170$	0.832231	−	12.2420i	0.0638292	−	0.938918i
$171$		0			0
$172$	0.720524	+	0.991717i	0.0549395	+	0.0756177i
$173$	1.90872	−	8.97983i	0.145117	−	0.682724i	−0.844090	−	0.536202i	$-0.819859\pi$
$173$	1.90872	−	8.97983i	0.145117	−	0.682724i	0.989207	−	0.146522i	$-0.0468080\pi$
$174$		0			0
$175$	−3.61881	+	5.84151i	−0.273556	+	0.441576i
$176$	−3.75674	−	6.50686i	−0.283175	−	0.490473i
$177$		0			0
$178$	12.8777	−	1.35350i	0.965227	−	0.101449i
$179$	−0.326301	+	0.237071i	−0.0243889	+	0.0177195i	−0.599913	−	0.800065i	$-0.704798\pi$
$179$	−0.326301	+	0.237071i	−0.0243889	+	0.0177195i	0.575524	+	0.817785i	$0.304798\pi$
$180$		0			0
$181$	−11.3643	−	8.25667i	−0.844704	−	0.613714i	0.0789764	−	0.996876i	$-0.474835\pi$
$181$	−11.3643	−	8.25667i	−0.844704	−	0.613714i	−0.923681	+	0.383163i	$0.874835\pi$
$182$	−7.94849	−	4.58906i	−0.589181	−	0.340164i
$183$		0			0
$184$	−25.1801	+	5.35221i	−1.85630	+	0.394570i
$185$	−5.98923	−	12.2197i	−0.440337	−	0.898407i
$186$		0			0
$187$	7.80504	−	7.02769i	0.570761	−	0.513916i
$188$	−2.96885	−	0.964638i	−0.216526	−	0.0703534i
$189$		0			0
$190$	−17.9967	−	1.22345i	−1.30562	−	0.0887583i
$191$	−1.47993	−	1.64363i	−0.107084	−	0.118929i	0.687220	−	0.726449i	$-0.258831\pi$
$191$	−1.47993	−	1.64363i	−0.107084	−	0.118929i	−0.794304	+	0.607521i	$0.792164\pi$
$192$		0			0
$193$	−7.27044	+	4.19759i	−0.523338	+	0.302149i	−0.738299	−	0.674473i	$-0.764371\pi$
$193$	−7.27044	+	4.19759i	−0.523338	+	0.302149i	0.214961	+	0.976623i	$0.431037\pi$
$194$	1.07098	−	10.1897i	0.0768922	−	0.731580i
$195$		0			0
$196$	−0.204654	−	1.94715i	−0.0146182	−	0.139082i
$197$	1.26330	+	1.73878i	0.0900063	+	0.123883i	0.851645	−	0.524118i	$-0.175605\pi$
$197$	1.26330	+	1.73878i	0.0900063	+	0.123883i	−0.761639	+	0.648001i	$0.775605\pi$
$198$		0			0
$199$	4.93840			0.350074			0.175037	−	0.984562i	$-0.443996\pi$
$199$	4.93840			0.350074			0.175037	+	0.984562i	$0.443996\pi$
$200$	−11.9755	−	9.28181i	−0.846793	−	0.656323i
$201$		0			0
$202$	7.64889	+	6.88710i	0.538174	+	0.484574i
$203$	−3.41048	+	7.66007i	−0.239369	+	0.537631i
$204$		0			0
$205$	6.79989	+	4.56746i	0.474925	+	0.319005i
$206$	5.63790	+	4.09617i	0.392811	+	0.285394i
$207$		0			0
$208$	9.53007	−	13.1170i	0.660791	−	0.909501i
$209$	−10.3313	−	11.4741i	−0.714630	−	0.793678i
$210$		0			0
$211$	7.06487	−	7.84633i	0.486365	−	0.540164i	−0.449147	−	0.893458i	$-0.648272\pi$
$211$	7.06487	−	7.84633i	0.486365	−	0.540164i	0.935512	+	0.353294i	$0.114939\pi$
$212$	−0.277475	−	1.30542i	−0.0190570	−	0.0896563i
$213$		0			0
$214$	15.3699	+	3.26698i	1.05067	+	0.223326i
$215$	−1.74457	−	6.93983i	−0.118979	−	0.473293i
$216$		0			0
$217$	−6.15194	+	8.46742i	−0.417621	+	0.574806i
$218$	1.00753	+	0.581698i	0.0682386	+	0.0393976i
$219$		0			0
$220$	−0.294118	−	2.06376i	−0.0198294	−	0.139139i
$221$	20.7047	+	9.21831i	1.39275	+	0.620091i
$222$		0			0
$223$	−4.10941	+	19.3332i	−0.275186	+	1.29465i	0.595717	+	0.803194i	$0.296868\pi$
$223$	−4.10941	+	19.3332i	−0.275186	+	1.29465i	−0.870903	+	0.491455i	$0.836465\pi$
$224$	−2.93408			−0.196042
$225$		0			0
$226$	−7.22771			−0.480780
$227$	−2.26265	+	10.6449i	−0.150177	+	0.706529i	0.837039	+	0.547143i	$0.184285\pi$
$227$	−2.26265	+	10.6449i	−0.150177	+	0.706529i	−0.987216	+	0.159386i	$0.949049\pi$
$228$		0			0
$229$	−8.71960	−	3.88222i	−0.576207	−	0.256544i	0.0978769	−	0.995199i	$-0.468795\pi$
$229$	−8.71960	−	3.88222i	−0.576207	−	0.256544i	−0.674084	+	0.738655i	$0.735462\pi$
$230$	23.7960	+	4.14839i	1.56906	+	0.273537i
$231$		0			0
$232$	−16.0113	−	9.24413i	−1.05119	−	0.606907i
$233$	−3.65074	+	5.02481i	−0.239168	+	0.329186i	−0.911681	−	0.410899i	$-0.865215\pi$
$233$	−3.65074	+	5.02481i	−0.239168	+	0.329186i	0.672513	+	0.740085i	$0.265215\pi$
$234$		0			0
$235$	13.9819	+	11.6861i	0.912077	+	0.762319i
$236$	2.62243	+	0.557415i	0.170706	+	0.0362846i
$237$		0			0
$238$	1.56796	+	7.37668i	0.101636	+	0.478159i
$239$	8.54663	−	9.49199i	0.552835	−	0.613986i	−0.400354	−	0.916361i	$-0.631113\pi$
$239$	8.54663	−	9.49199i	0.552835	−	0.613986i	0.953189	+	0.302375i	$0.0977795\pi$
$240$		0			0
$241$	−8.93241	−	9.92045i	−0.575387	−	0.639032i	0.383256	−	0.923642i	$-0.374803\pi$
$241$	−8.93241	−	9.92045i	−0.575387	−	0.639032i	−0.958643	+	0.284610i	$0.908136\pi$
$242$	3.79445	−	5.22261i	0.243917	−	0.335722i
$243$		0			0
$244$	0.758615	+	0.551166i	0.0485653	+	0.0352848i
$245$	−3.12901	+	10.9924i	−0.199905	+	0.702280i
$246$		0			0
$247$	13.5517	−	30.4376i	0.862273	−	1.93670i
$248$	−17.1498	−	15.4418i	−1.08902	−	0.980555i
$249$		0			0
$250$	7.17980	+	12.2706i	0.454090	+	0.776064i
$251$	9.25226			0.583998			0.291999	−	0.956419i	$-0.405680\pi$
$251$	9.25226			0.583998			0.291999	+	0.956419i	$0.405680\pi$
$252$		0			0
$253$	12.1527	+	16.7267i	0.764033	+	1.05160i
$254$	−0.0193340	−	0.183950i	−0.00121312	−	0.0115421i
$255$		0			0
$256$	0.923459	−	8.78613i	0.0577162	−	0.549133i
$257$	−17.3590	+	10.0222i	−1.08283	+	0.625170i	−0.931658	−	0.363338i	$-0.881637\pi$
$257$	−17.3590	+	10.0222i	−1.08283	+	0.625170i	−0.151169	+	0.988508i	$0.548304\pi$
$258$		0			0
$259$	5.59659	+	6.21565i	0.347755	+	0.386222i
$260$	3.81027	−	2.39119i	0.236303	−	0.148295i
$261$		0			0
$262$	−0.571289	−	0.185623i	−0.0352944	−	0.0114678i
$263$	18.7958	−	16.9238i	1.15900	−	1.04357i	0.160601	−	0.987019i	$-0.448657\pi$
$263$	18.7958	−	16.9238i	1.15900	−	1.04357i	0.998400	−	0.0565495i	$-0.0180099\pi$
$264$		0			0
$265$	−1.33797	+	7.67483i	−0.0821906	+	0.471461i
$266$	10.8443	−	2.30503i	0.664908	−	0.141331i
$267$		0			0
$268$	1.29764	+	0.749193i	0.0792660	+	0.0457643i
$269$	−15.0118	−	10.9067i	−0.915288	−	0.664996i	0.0270585	−	0.999634i	$-0.491386\pi$
$269$	−15.0118	−	10.9067i	−0.915288	−	0.664996i	−0.942347	+	0.334638i	$0.891386\pi$
$270$		0			0
$271$	−7.65497	+	5.56166i	−0.465006	+	0.337847i	−0.795492	−	0.605964i	$-0.792787\pi$
$271$	−7.65497	+	5.56166i	−0.465006	+	0.337847i	0.330486	+	0.943811i	$0.392787\pi$
$272$	−13.2493	+	1.39256i	−0.803359	+	0.0844365i
$273$		0			0
$274$	8.29357	+	14.3649i	0.501033	+	0.867815i
$275$	−2.89819	+	11.8187i	−0.174767	+	0.712697i
$276$		0			0
$277$	−0.314336	+	1.47884i	−0.0188866	+	0.0888547i	−0.986581	−	0.163270i	$-0.947796\pi$
$277$	−0.314336	+	1.47884i	−0.0188866	+	0.0888547i	0.967695	+	0.252124i	$0.0811292\pi$
$278$	10.5424	+	14.5103i	0.632289	+	0.870271i
$279$		0			0
$280$	8.64091	+	3.47171i	0.516393	+	0.207474i
$281$	−10.0915	+	4.49302i	−0.602007	+	0.268031i	−0.685028	−	0.728517i	$-0.740210\pi$
$281$	−10.0915	+	4.49302i	−0.602007	+	0.268031i	0.0830206	+	0.996548i	$0.473543\pi$
$282$		0			0
$283$	−12.9320	−	1.35920i	−0.768726	−	0.0807963i	−0.287957	−	0.957643i	$-0.592976\pi$
$283$	−12.9320	−	1.35920i	−0.768726	−	0.0807963i	−0.480769	+	0.876847i	$0.659643\pi$
$284$	−1.74855	+	0.371665i	−0.103757	+	0.0220543i
$285$		0			0
$286$	−15.8983	−	3.37929i	−0.940088	−	0.199822i
$287$	−4.78819	−	1.55578i	−0.282638	−	0.0918347i
$288$		0			0
$289$	−0.501416	−	1.54320i	−0.0294951	−	0.0907765i
$290$	10.7069	+	13.6496i	0.628730	+	0.801534i
$291$		0			0
$292$	2.81239	+	0.295594i	0.164583	+	0.0172983i
$293$	−10.4176	+	6.01458i	−0.608600	+	0.351376i	−0.772417	−	0.635115i	$-0.780953\pi$
$293$	−10.4176	+	6.01458i	−0.608600	+	0.351376i	0.163817	+	0.986491i	$0.447619\pi$
$294$		0			0
$295$	−12.9917	−	8.72645i	−0.756405	−	0.508074i
$296$	−14.9198	+	10.8399i	−0.867198	+	0.630056i
$297$		0			0
$298$	−12.6561	+	4.11223i	−0.733151	+	0.238215i
$299$	−22.3080	+	38.6385i	−1.29010	+	2.23452i
$300$		0			0
$301$	2.19902	+	3.80881i	0.126749	+	0.219536i
$302$	3.55941	+	3.20491i	0.204821	+	0.184422i
$303$		0			0
$304$	2.04718	+	19.4776i	0.117414	+	1.11712i
$305$	−2.90965	−	4.63642i	−0.166606	−	0.265481i
$306$		0			0
$307$		−	33.1002i		−	1.88913i	−0.328325	−	0.944565i	$-0.606484\pi$
$307$		−	33.1002i		−	1.88913i	0.328325	−	0.944565i	$-0.393516\pi$
$308$	0.521126	+	1.17047i	0.0296939	+	0.0666936i
$309$		0			0
$310$	9.53015	+	19.4441i	0.541276	+	1.10435i
$311$	21.5709	−	23.9569i	1.22318	−	1.35847i	0.310089	−	0.950707i	$-0.399641\pi$
$311$	21.5709	−	23.9569i	1.22318	−	1.35847i	0.913086	−	0.407766i	$-0.133692\pi$
$312$		0			0
$313$	−16.6489	+	14.9908i	−0.941052	+	0.847327i	−0.988450	−	0.151549i	$-0.951574\pi$
$313$	−16.6489	+	14.9908i	−0.941052	+	0.847327i	0.0473975	+	0.998876i	$0.484907\pi$
$314$	6.70827	+	20.6459i	0.378570	+	1.16512i
$315$		0			0
$316$	0.690382	−	2.12478i	0.0388370	−	0.119528i
$317$	4.68669	+	10.5265i	0.263231	+	0.591226i	0.996010	−	0.0892400i	$-0.0284438\pi$
$317$	4.68669	+	10.5265i	0.263231	+	0.591226i	−0.732779	+	0.680467i	$0.761777\pi$
$318$		0			0
$319$	−1.55214	+	14.7676i	−0.0869031	+	0.826827i
$320$	−9.29751	+	17.5680i	−0.519747	+	0.982083i
$321$		0			0
$322$	−14.7646	+	1.55183i	−0.822801	+	0.0864798i
$323$	−26.0369	+	8.45990i	−1.44873	+	0.470721i
$324$		0			0
$325$	−25.8428	+	4.66002i	−1.43350	+	0.258491i
$326$	−10.1889	+	17.6477i	−0.564310	+	0.977414i
$327$		0			0
$328$	4.51515	−	10.1412i	0.249307	−	0.559953i
$329$	−10.2315	−	4.55537i	−0.564083	−	0.251146i
$330$		0			0
$331$	−1.97082	+	0.877464i	−0.108326	+	0.0482298i	−0.460184	−	0.887824i	$-0.652217\pi$
$331$	−1.97082	+	0.877464i	−0.108326	+	0.0482298i	0.351858	+	0.936053i	$0.385550\pi$
$332$			3.30587i			0.181433i
$333$		0			0
$334$	5.28455	−	16.2642i	0.289158	−	0.889936i
$335$	−5.39840	−	6.88214i	−0.294946	−	0.376011i
$336$		0			0
$337$	−2.56048	−	12.0461i	−0.139478	−	0.656194i	−0.991219	−	0.132231i	$-0.957786\pi$
$337$	−2.56048	−	12.0461i	−0.139478	−	0.656194i	0.851741	−	0.523964i	$-0.175547\pi$
$338$	−3.85534	−	18.1379i	−0.209703	−	0.986574i
$339$		0			0
$340$	−3.55506	−	1.01195i	−0.192800	−	0.0548808i
$341$	−5.72755	+	17.6276i	−0.310164	+	0.954588i
$342$		0			0
$343$		−	16.6447i		−	0.898731i
$344$	−8.85895	+	3.94426i	−0.477643	+	0.212660i
$345$		0			0
$346$	10.6645	+	4.74815i	0.573329	+	0.255262i
$347$	2.84731	−	6.39516i	0.152852	−	0.343310i	−0.820848	−	0.571147i	$-0.806499\pi$
$347$	2.84731	−	6.39516i	0.152852	−	0.343310i	0.973699	+	0.227837i	$0.0731652\pi$
$348$		0			0
$349$	14.4921	−	25.1011i	0.775745	−	1.34363i	−0.158629	−	0.987338i	$-0.550707\pi$
$349$	14.4921	−	25.1011i	0.775745	−	1.34363i	0.934375	−	0.356292i	$-0.115959\pi$
$350$	−6.30896	−	6.04546i	−0.337228	−	0.323143i
$351$		0			0
$352$	−4.94165	+	1.60564i	−0.263391	+	0.0855808i
$353$	−31.1182	+	3.27066i	−1.65626	+	0.174079i	−0.886009	−	0.463667i	$-0.846533\pi$
$353$	−31.1182	+	3.27066i	−1.65626	+	0.174079i	−0.770246	+	0.637747i	$0.779867\pi$
$354$		0			0
$355$	10.2801	+	1.79215i	0.545611	+	0.0951172i
$356$	0.407729	−	3.87928i	0.0216096	−	0.205601i
$357$		0			0
$358$	−0.208603	−	0.468531i	−0.0110250	−	0.0247626i
$359$	0.478803	−	1.47360i	0.0252702	−	0.0777738i	−0.937626	−	0.347645i	$-0.886981\pi$
$359$	0.478803	−	1.47360i	0.0252702	−	0.0777738i	0.962896	+	0.269872i	$0.0869813\pi$
$360$		0			0
$361$	6.56543	+	20.2063i	0.345549	+	1.06349i
$362$	13.2742	−	11.9521i	0.697675	−	0.628190i
$363$		0			0
$364$	−1.85002	+	2.05465i	−0.0969674	+	0.107693i
$365$	−14.5904	−	7.72166i	−0.763697	−	0.404170i
$366$		0			0
$367$	10.5658	+	23.7312i	0.551531	+	1.23876i	0.947282	+	0.320401i	$0.103817\pi$
$367$	10.5658	+	23.7312i	0.551531	+	1.23876i	−0.395751	+	0.918358i	$0.629516\pi$
$368$		−	26.2260i		−	1.36712i
$369$		0			0
$370$	16.7823	−	4.21882i	0.872470	−	0.219326i
$371$	−0.500504	−	4.76198i	−0.0259849	−	0.247230i
$372$		0			0
$373$	−7.38161	−	6.64643i	−0.382205	−	0.344139i	0.455526	−	0.890223i	$-0.349451\pi$
$373$	−7.38161	−	6.64643i	−0.382205	−	0.344139i	−0.837731	+	0.546084i	$0.816118\pi$
$374$	6.67759	+	11.5659i	0.345290	+	0.598060i
$375$		0			0
$376$	12.3474	−	21.3862i	0.636766	−	1.10291i
$377$	−30.4746	+	9.90181i	−1.56952	+	0.509969i
$378$		0			0
$379$	−1.77633	+	1.29058i	−0.0912441	+	0.0662927i	−0.632472	−	0.774583i	$-0.717960\pi$
$379$	−1.77633	+	1.29058i	−0.0912441	+	0.0662927i	0.541228	+	0.840876i	$0.317960\pi$
$380$	−1.48765	+	5.22623i	−0.0763151	+	0.268100i
$381$		0			0
$382$	2.43561	−	1.40620i	0.124617	−	0.0719476i
$383$	21.4526	+	2.25476i	1.09618	+	0.115213i	0.635311	−	0.772256i	$-0.280872\pi$
$383$	21.4526	+	2.25476i	1.09618	+	0.115213i	0.460867	+	0.887469i	$0.347538\pi$
$384$		0			0
$385$	−0.275490	−	7.47412i	−0.0140402	−	0.380916i
$386$	−3.29883	−	10.1528i	−0.167906	−	0.516762i
$387$		0			0
$388$	−2.93539	−	0.953768i	−0.149022	−	0.0484202i
$389$	−5.50357	−	1.16982i	−0.279042	−	0.0593122i	0.0662648	−	0.997802i	$-0.478892\pi$
$389$	−5.50357	−	1.16982i	−0.279042	−	0.0593122i	−0.345307	+	0.938490i	$0.612225\pi$
$390$		0			0
$391$	35.8589	−	7.62204i	1.81346	−	0.385463i
$392$	15.4036	+	1.61898i	0.778000	+	0.0817711i
$393$		0			0
$394$	−2.49670	+	1.11160i	−0.125782	+	0.0560016i
$395$	−8.36366	+	10.0067i	−0.420821	+	0.503492i
$396$		0			0
$397$	20.5753	+	28.3195i	1.03264	+	1.42131i	0.902943	+	0.429760i	$0.141402\pi$
$397$	20.5753	+	28.3195i	1.03264	+	1.42131i	0.129701	+	0.991553i	$0.458598\pi$
$398$	−1.30561	+	6.14240i	−0.0654442	+	0.307891i
$399$		0			0
$400$	11.7860	−	9.96766i	0.589301	−	0.498383i
$401$	5.37358	+	9.30732i	0.268344	+	0.464785i	0.968434	−	0.249269i	$-0.0801903\pi$
$401$	5.37358	+	9.30732i	0.268344	+	0.464785i	−0.700090	+	0.714054i	$0.746857\pi$
$402$		0			0
$403$	−39.7775	+	4.18078i	−1.98146	+	0.208260i
$404$	2.50839	−	1.82245i	0.124797	−	0.0906703i
$405$		0			0
$406$	−8.62597	−	6.26714i	−0.428100	−	0.311033i
$407$	12.8273	+	7.40587i	0.635828	+	0.367095i
$408$		0			0
$409$	−37.5119	+	7.97340i	−1.85485	+	0.394259i	−0.993507	−	0.113772i	$-0.963707\pi$
$409$	−37.5119	+	7.97340i	−1.85485	+	0.394259i	−0.861338	+	0.508032i	$0.830373\pi$
$410$	−7.47878	+	7.25020i	−0.369350	+	0.358062i
$411$		0			0
$412$	1.56007	−	1.40470i	0.0768592	−	0.0692044i
$413$	9.14818	+	2.97242i	0.450152	+	0.146263i
$414$		0			0
$415$	7.19448	−	17.9067i	0.353163	−	0.879005i
$416$	−7.50262	−	8.33250i	−0.367846	−	0.408534i
$417$		0			0
$418$	17.0029	−	9.81661i	0.831638	−	0.480146i
$419$	0.100706	−	0.958156i	0.00491982	−	0.0468090i	−0.991787	−	0.127904i	$-0.959175\pi$
$419$	0.100706	−	0.958156i	0.00491982	−	0.0468090i	0.996706	+	0.0810950i	$0.0258417\pi$
$420$		0			0
$421$	3.20028	+	30.4486i	0.155972	+	1.48397i	0.740201	+	0.672386i	$0.234730\pi$
$421$	3.20028	+	30.4486i	0.155972	+	1.48397i	−0.584229	+	0.811589i	$0.698603\pi$
$422$	7.89150	+	10.8617i	0.384152	+	0.528740i
$423$		0			0
$424$	10.5576			0.512724
$425$	17.0542	+	13.2182i	0.827250	+	0.641176i
$426$		0			0
$427$	2.50015	+	2.25114i	0.120991	+	0.108940i
$428$	1.92528	−	4.32424i	0.0930617	−	0.209020i
$429$		0			0
$430$	9.09303	−	0.335161i	0.438505	−	0.0161629i
$431$	13.7962	+	10.0236i	0.664542	+	0.482818i	0.868194	−	0.496226i	$-0.165281\pi$
$431$	13.7962	+	10.0236i	0.664542	+	0.482818i	−0.203652	+	0.979043i	$0.565281\pi$
$432$		0			0
$433$	−21.0699	+	29.0002i	−1.01255	+	1.39366i	−0.0952578	+	0.995453i	$0.530368\pi$
$433$	−21.0699	+	29.0002i	−1.01255	+	1.39366i	−0.917295	+	0.398207i	$0.869632\pi$
$434$	−8.90537	−	9.89042i	−0.427472	−	0.474755i
$435$		0			0
$436$	0.234504	−	0.260443i	0.0112307	−	0.0124730i
$437$	−11.2050	−	52.7156i	−0.536010	−	2.52173i
$438$		0			0
$439$	2.78036	+	0.590983i	0.132699	+	0.0282061i	0.273782	−	0.961792i	$-0.411725\pi$
$439$	2.78036	+	0.590983i	0.132699	+	0.0282061i	−0.141083	+	0.989998i	$0.545059\pi$
$440$	16.4531	+	1.11851i	0.784369	+	0.0533228i
$441$		0			0
$442$	−16.9397	+	23.3154i	−0.805737	+	1.10900i
$443$	−7.95124	−	4.59065i	−0.377775	−	0.218108i	0.299075	−	0.954230i	$-0.403322\pi$
$443$	−7.95124	−	4.59065i	−0.377775	−	0.218108i	−0.676850	+	0.736121i	$0.736655\pi$
$444$		0			0
$445$	−10.6509	+	20.1253i	−0.504901	+	0.954032i
$446$	−22.9603	−	10.2226i	−1.08720	−	0.484054i
$447$		0			0
$448$	2.53994	−	11.9495i	0.120001	−	0.564561i
$449$	14.3342			0.676474			0.338237	−	0.941061i	$-0.390169\pi$
$449$	14.3342			0.676474			0.338237	+	0.941061i	$0.390169\pi$
$450$		0			0
$451$	−8.91576			−0.419827
$452$	−0.452680	+	2.12969i	−0.0212923	+	0.100172i
$453$		0			0
$454$	−12.6420	−	5.62859i	−0.593319	−	0.264163i
$455$	14.4924	−	7.10317i	0.679414	−	0.333002i
$456$		0			0
$457$	−5.84075	−	3.37216i	−0.273219	−	0.157743i	0.357131	−	0.934054i	$-0.383755\pi$
$457$	−5.84075	−	3.37216i	−0.273219	−	0.157743i	−0.630350	+	0.776311i	$0.717088\pi$
$458$	7.13400	−	9.81910i	0.333350	−	0.458817i
$459$		0			0
$460$	2.71272	−	6.75183i	0.126481	−	0.314806i
$461$	13.9280	+	2.96049i	0.648691	+	0.137884i	0.520494	−	0.853865i	$-0.325748\pi$
$461$	13.9280	+	2.96049i	0.648691	+	0.137884i	0.128197	+	0.991749i	$0.459081\pi$
$462$		0			0
$463$	−4.63289	−	21.7961i	−0.215309	−	1.01295i	−0.944468	−	0.328604i	$-0.893422\pi$
$463$	−4.63289	−	21.7961i	−0.215309	−	1.01295i	0.729159	−	0.684344i	$-0.239912\pi$
$464$	12.6033	−	13.9974i	0.585094	−	0.649813i
$465$		0			0
$466$	−5.28470	−	5.86926i	−0.244809	−	0.271888i
$467$	5.52790	−	7.60850i	0.255801	−	0.352079i	−0.661732	−	0.749741i	$-0.730178\pi$
$467$	5.52790	−	7.60850i	0.255801	−	0.352079i	0.917532	+	0.397661i	$0.130178\pi$
$468$		0			0
$469$	4.34921	+	3.15988i	0.200828	+	0.145910i
$470$	−18.2318	+	14.3012i	−0.840969	+	0.659663i
$471$		0			0
$472$	−8.62651	+	19.3755i	−0.397067	+	0.891828i
$473$	5.78796	+	5.21150i	0.266131	+	0.239625i
$474$		0			0
$475$	19.4318	−	25.0711i	0.891593	−	1.15034i
$476$	2.27179			0.104127
$477$		0			0
$478$	9.54663	+	13.1398i	0.436653	+	0.601001i
$479$	−3.50429	−	33.3411i	−0.160115	−	1.52340i	−0.719503	−	0.694489i	$-0.755630\pi$
$479$	−3.50429	−	33.3411i	−0.160115	−	1.52340i	0.559388	−	0.828906i	$-0.311036\pi$
$480$		0			0
$481$	−3.34101	+	31.7875i	−0.152337	+	1.44939i
$482$	14.7006	−	8.48742i	0.669596	−	0.386591i
$483$		0			0
$484$	−1.30123	−	1.44516i	−0.0591466	−	0.0656890i
$485$	13.8243	+	11.5544i	0.627730	+	0.524661i
$486$		0			0
$487$	−18.8406	−	6.12169i	−0.853750	−	0.277400i	−0.150734	−	0.988574i	$-0.548164\pi$
$487$	−18.8406	−	6.12169i	−0.853750	−	0.277400i	−0.703016	+	0.711174i	$0.748164\pi$
$488$	−5.51263	+	4.96360i	−0.249545	+	0.224692i
$489$		0			0
$490$	−12.8452	−	6.79804i	−0.580286	−	0.307104i
$491$	−4.13166	+	0.878212i	−0.186459	+	0.0396331i	−0.300195	−	0.953878i	$-0.597052\pi$
$491$	−4.13166	+	0.878212i	−0.186459	+	0.0396331i	0.113736	+	0.993511i	$0.463718\pi$
$492$		0			0
$493$	22.8016	+	13.1645i	1.02693	+	0.592900i
$494$	34.2756	+	24.9027i	1.54213	+	1.12043i
$495$		0			0
$496$	19.0205	−	13.8192i	0.854047	−	0.620501i
$497$	−6.37846	+	0.670403i	−0.286113	+	0.0300717i
$498$		0			0
$499$	17.3240	+	30.0060i	0.775527	+	1.34325i	0.934498	+	0.355969i	$0.115849\pi$
$499$	17.3240	+	30.0060i	0.775527	+	1.34325i	−0.158970	+	0.987283i	$0.550817\pi$
$500$	4.06531	−	1.34705i	0.181806	−	0.0602419i
$501$		0			0
$502$	−2.44610	+	11.5080i	−0.109175	+	0.513627i
$503$	1.07095	+	1.47404i	0.0477515	+	0.0657243i	0.832225	−	0.554438i	$-0.187067\pi$
$503$	1.07095	+	1.47404i	0.0477515	+	0.0657243i	−0.784474	+	0.620162i	$0.787067\pi$
$504$		0			0
$505$	−17.5532	+	4.41261i	−0.781107	+	0.196359i
$506$	−24.0177	+	10.6934i	−1.06772	+	0.475379i
$507$		0			0
$508$	−0.0554131	−	0.00582415i	−0.00245856	−	0.000258405i
$509$	−32.5482	+	6.91833i	−1.44267	+	0.306650i	−0.861760	−	0.507316i	$-0.830638\pi$
$509$	−32.5482	+	6.91833i	−1.44267	+	0.306650i	−0.580913	+	0.813965i	$0.697305\pi$
$510$		0			0
$511$	9.92416	+	2.10945i	0.439019	+	0.0933164i
$512$	24.0625	+	7.81837i	1.06342	+	0.345526i
$513$		0			0
$514$	−7.87635	−	24.2409i	−0.347411	−	1.06922i
$515$	−11.5074	+	4.21358i	−0.507075	+	0.185673i
$516$		0			0
$517$	−19.7251	−	2.07319i	−0.867507	−	0.0911786i
$518$	−9.21067	+	5.31778i	−0.404694	+	0.233650i
$519$		0			0
$520$	12.2360	+	33.4167i	0.536584	+	1.46542i
$521$	24.1306	−	17.5319i	1.05718	−	0.768087i	0.0836160	−	0.996498i	$-0.473353\pi$
$521$	24.1306	−	17.5319i	1.05718	−	0.768087i	0.973565	+	0.228411i	$0.0733531\pi$
$522$		0			0
$523$	42.7727	−	13.8977i	1.87032	−	0.607703i	0.878895	−	0.477015i	$-0.158281\pi$
$523$	42.7727	−	13.8977i	1.87032	−	0.607703i	0.991423	−	0.130688i	$-0.0417188\pi$
$524$	−0.0904756	+	0.156708i	−0.00395244	+	0.00684583i
$525$		0			0
$526$	16.0807	+	27.8527i	0.701153	+	1.21443i
$527$	24.4230	+	21.9906i	1.06388	+	0.957924i
$528$		0			0
$529$	5.13945	+	48.8986i	0.223454	+	2.12603i
$530$	−9.19226	−	3.69323i	−0.399286	−	0.160424i
$531$		0			0
$532$		−	3.33972i		−	0.144795i
$533$	−7.82543	−	17.5762i	−0.338957	−	0.761310i
$534$		0			0
$535$	−19.8393	+	19.2329i	−0.857727	+	0.831512i
$536$	−7.93153	+	8.80885i	−0.342590	+	0.380485i
$537$		0			0
$538$	17.5347	−	15.7883i	0.755973	−	0.680682i
$539$	−3.84406	−	11.8308i	−0.165575	−	0.509589i
$540$		0			0
$541$	9.82187	−	30.2286i	0.422275	−	1.29963i	−0.483304	−	0.875453i	$-0.660563\pi$
$541$	9.82187	−	30.2286i	0.422275	−	1.29963i	0.905579	−	0.424177i	$-0.139437\pi$
$542$	−4.89381	−	10.9917i	−0.210207	−	0.472133i
$543$		0			0
$544$	−0.963028	+	9.16260i	−0.0412895	+	0.392843i
$545$	−1.83702	+	0.900381i	−0.0786893	+	0.0385681i
$546$		0			0
$547$	−11.4091	+	1.19915i	−0.487818	+	0.0512718i	−0.345245	−	0.938512i	$-0.612204\pi$
$547$	−11.4091	+	1.19915i	−0.487818	+	0.0512718i	−0.142573	+	0.989784i	$0.545538\pi$
$548$	4.75214	−	1.54407i	0.203002	−	0.0659592i
$549$		0			0
$550$	−13.9340	−	6.72940i	−0.594147	−	0.286943i
$551$	19.3529	−	33.5203i	0.824462	−	1.42801i
$552$		0			0
$553$	3.26024	−	7.32261i	0.138639	−	0.311389i
$554$	−1.75628	−	0.781946i	−0.0746172	−	0.0332217i
$555$		0			0
$556$	4.93584	−	2.19758i	0.209326	−	0.0931981i
$557$		−	11.6357i		−	0.493021i	−0.969140	−	0.246510i	$-0.920716\pi$
$557$		−	11.6357i		−	0.493021i	0.969140	−	0.246510i	$-0.0792839\pi$
$558$		0			0
$559$	−5.19363	+	15.9843i	−0.219667	+	0.676065i
$560$	−5.28987	+	7.87540i	−0.223538	+	0.332797i
$561$		0			0
$562$	−2.92046	−	13.7397i	−0.123192	−	0.579574i
$563$	−0.383647	−	1.80492i	−0.0161688	−	0.0760682i	0.969323	−	0.245789i	$-0.0790469\pi$
$563$	−0.383647	−	1.80492i	−0.0161688	−	0.0760682i	−0.985492	+	0.169720i	$0.945714\pi$
$564$		0			0
$565$	7.08680	−	10.5506i	0.298144	−	0.443868i
$566$	5.10952	−	15.7255i	0.214769	−	0.660992i
$567$		0			0
$568$		−	14.1415i		−	0.593364i
$569$	22.3370	−	9.94506i	0.936415	−	0.416919i	0.118952	−	0.992900i	$-0.462047\pi$
$569$	22.3370	−	9.94506i	0.936415	−	0.416919i	0.817463	+	0.575981i	$0.195380\pi$
$570$		0			0
$571$	3.27406	+	1.45771i	0.137015	+	0.0610031i	0.474099	−	0.880472i	$-0.342774\pi$
$571$	3.27406	+	1.45771i	0.137015	+	0.0610031i	−0.337084	+	0.941475i	$0.609441\pi$
$572$	−1.99146	+	4.47290i	−0.0832672	+	0.187021i
$573$		0			0
$574$	3.20098	−	5.54426i	0.133606	−	0.231413i
$575$	−29.3877	+	30.6686i	−1.22555	+	1.27897i
$576$		0			0
$577$	34.6052	−	11.2439i	1.44063	−	0.468091i	0.518539	−	0.855054i	$-0.326476\pi$
$577$	34.6052	−	11.2439i	1.44063	−	0.468091i	0.922095	+	0.386963i	$0.126476\pi$
$578$	2.05200	−	0.215674i	0.0853521	−	0.00897087i
$579$		0			0
$580$	4.69254	−	2.29996i	0.194847	−	0.0955007i
$581$	−1.23979	+	11.7958i	−0.0514352	+	0.489373i
$582$		0			0
$583$	−3.44889	−	7.74634i	−0.142839	−	0.320821i
$584$	−6.91298	+	21.2760i	−0.286061	+	0.880406i
$585$		0			0
$586$	−4.72678	−	14.5475i	−0.195262	−	0.600953i
$587$	26.1176	−	23.5164i	1.07799	−	0.970625i	0.0783341	−	0.996927i	$-0.475040\pi$
$587$	26.1176	−	23.5164i	1.07799	−	0.970625i	0.999654	+	0.0263023i	$0.00837325\pi$
$588$		0			0
$589$	32.3280	−	35.9038i	1.33205	−	1.47939i
$590$	14.2887	−	13.8520i	0.588258	−	0.570279i
$591$		0			0
$592$	−7.64183	−	17.1638i	−0.314077	−	0.705430i
$593$			16.8457i			0.691772i	0.938277	+	0.345886i	$0.112422\pi$
$593$			16.8457i			0.691772i	−0.938277	+	0.345886i	$0.887578\pi$
$594$		0			0
$595$	−12.3055	−	4.94404i	−0.504475	−	0.202686i
$596$	0.419026	+	3.98677i	0.0171640	+	0.163304i
$597$		0			0
$598$	−42.1610	−	37.9620i	−1.72409	−	1.55238i
$599$	7.43241	+	12.8733i	0.303680	+	0.525989i	0.976967	−	0.213393i	$-0.0684513\pi$
$599$	7.43241	+	12.8733i	0.303680	+	0.525989i	−0.673287	+	0.739382i	$0.735118\pi$
$600$		0			0
$601$	14.5760	−	25.2463i	0.594566	−	1.02982i	−0.399042	−	0.916933i	$-0.630657\pi$
$601$	14.5760	−	25.2463i	0.594566	−	1.02982i	0.993608	−	0.112886i	$-0.0360094\pi$
$602$	−5.31879	+	1.72818i	−0.216778	+	0.0704353i
$603$		0			0
$604$	1.16728	−	0.848076i	0.0474958	−	0.0345077i
$605$	3.90321	+	10.6597i	0.158688	+	0.433380i
$606$		0			0
$607$	−19.2603	+	11.1199i	−0.781751	+	0.451344i	−0.837051	−	0.547126i	$-0.815722\pi$
$607$	−19.2603	+	11.1199i	−0.781751	+	0.451344i	0.0552994	+	0.998470i	$0.482389\pi$
$608$	13.4698	+	1.41573i	0.546272	+	0.0574155i
$609$		0			0
$610$	6.53606	−	2.39327i	0.264637	−	0.0969007i
$611$	−13.2258	−	40.7049i	−0.535059	−	1.64674i
$612$		0			0
$613$	−36.6080	−	11.8947i	−1.47858	−	0.480421i	−0.544894	−	0.838505i	$-0.683430\pi$
$613$	−36.6080	−	11.8947i	−1.47858	−	0.480421i	−0.933689	+	0.358084i	$0.883430\pi$
$614$	41.1702	+	8.75100i	1.66149	+	0.353162i
$615$		0			0
$616$	−9.91415	+	2.10732i	−0.399453	+	0.0849063i
$617$	−24.0076	−	2.52330i	−0.966511	−	0.101584i	−0.391897	−	0.920009i	$-0.628181\pi$
$617$	−24.0076	−	2.52330i	−0.966511	−	0.101584i	−0.574614	+	0.818425i	$0.694848\pi$
$618$		0			0
$619$	30.8132	−	13.7189i	1.23849	−	0.551409i	0.320208	−	0.947347i	$-0.396247\pi$
$619$	30.8132	−	13.7189i	1.23849	−	0.551409i	0.918277	+	0.395938i	$0.129580\pi$
$620$	6.32621	−	1.59031i	0.254067	−	0.0638686i
$621$		0			0
$622$	24.0949	+	33.1637i	0.966116	+	1.32974i
$623$	2.90967	−	13.6889i	0.116574	−	0.548436i
$624$		0			0
$625$	−24.9519	−	1.55074i	−0.998074	−	0.0620298i
$626$	−14.2439	−	24.6712i	−0.569303	−	0.986061i
$627$		0			0
$628$	6.50361	−	0.683557i	0.259522	−	0.0272769i
$629$	21.2473	−	15.4370i	0.847183	−	0.615515i
$630$		0			0
$631$	−5.48744	−	3.98686i	−0.218452	−	0.158714i	0.473178	−	0.880967i	$-0.343107\pi$
$631$	−5.48744	−	3.98686i	−0.218452	−	0.158714i	−0.691629	+	0.722253i	$0.743107\pi$
$632$	15.3059	+	8.83689i	0.608837	+	0.351512i
$633$		0			0
$634$	−14.3320	+	3.04635i	−0.569195	+	0.120986i
$635$	0.287478	+	0.152142i	0.0114082	+	0.00603756i
$636$		0			0
$637$	19.9488	−	17.9620i	0.790402	−	0.711681i
$638$	−17.9577	−	5.83480i	−0.710951	−	0.231002i
$639$		0			0
$640$	−12.0673	−	10.0859i	−0.477002	−	0.398681i
$641$	−11.4878	−	12.7584i	−0.453739	−	0.503928i	0.472257	−	0.881461i	$-0.343439\pi$
$641$	−11.4878	−	12.7584i	−0.453739	−	0.503928i	−0.925996	+	0.377532i	$0.876773\pi$
$642$		0			0
$643$	−21.3557	+	12.3297i	−0.842188	+	0.486237i	−0.858007	−	0.513637i	$-0.828298\pi$
$643$	−21.3557	+	12.3297i	−0.842188	+	0.486237i	0.0158194	+	0.999875i	$0.494964\pi$
$644$	−0.467471	+	4.44769i	−0.0184209	+	0.175263i
$645$		0			0
$646$	−3.63886	−	34.6214i	−0.143169	−	1.36216i
$647$	9.52040	+	13.1037i	0.374286	+	0.515160i	0.954059	−	0.299618i	$-0.0968591\pi$
$647$	9.52040	+	13.1037i	0.374286	+	0.515160i	−0.579774	+	0.814778i	$0.696859\pi$
$648$		0			0
$649$	17.0342			0.668651
$650$	1.03613	−	33.3754i	0.0406404	−	1.30909i
$651$		0			0
$652$	4.56186	+	4.10752i	0.178656	+	0.160863i
$653$	3.05097	−	6.85258i	0.119394	−	0.268162i	−0.843956	−	0.536413i	$-0.819779\pi$
$653$	3.05097	−	6.85258i	0.119394	−	0.268162i	0.963349	+	0.268251i	$0.0864456\pi$
$654$		0			0
$655$	0.831114	−	0.651933i	0.0324743	−	0.0254731i
$656$	9.14943	+	6.64745i	0.357225	+	0.259539i
$657$		0			0
$658$	8.37099	−	11.5217i	0.326335	−	0.449162i
$659$	15.1828	+	16.8623i	0.591439	+	0.656860i	0.962352	−	0.271808i	$-0.0876215\pi$
$659$	15.1828	+	16.8623i	0.591439	+	0.656860i	−0.370912	+	0.928668i	$0.620955\pi$
$660$		0			0
$661$	16.8042	−	18.6629i	0.653606	−	0.725903i	−0.321680	−	0.946848i	$-0.604248\pi$
$661$	16.8042	−	18.6629i	0.653606	−	0.725903i	0.975286	+	0.220945i	$0.0709142\pi$
$662$	−0.570352	−	2.68329i	−0.0221673	−	0.104289i
$663$		0			0
$664$	−25.5807	−	5.43734i	−0.992722	−	0.211010i
$665$	−7.26815	+	18.0901i	−0.281847	+	0.701502i
$666$		0			0
$667$	−30.4653	+	41.9319i	−1.17962	+	1.62361i
$668$	−4.46137	−	2.57577i	−0.172615	−	0.0996596i
$669$		0			0
$670$	9.98726	−	4.89507i	0.385841	−	0.189113i
$671$	5.44272	+	2.42325i	0.210114	+	0.0935487i
$672$		0			0
$673$	−5.34541	+	25.1482i	−0.206050	+	0.969391i	0.746588	+	0.665286i	$0.231691\pi$
$673$	−5.34541	+	25.1482i	−0.206050	+	0.969391i	−0.952639	+	0.304104i	$0.901643\pi$
$674$	15.6600			0.603200
$675$		0			0
$676$	−5.58593			−0.214843
$677$	−6.39153	+	30.0698i	−0.245646	+	1.15568i	0.666402	+	0.745593i	$0.267833\pi$
$677$	−6.39153	+	30.0698i	−0.245646	+	1.15568i	−0.912048	+	0.410083i	$0.865500\pi$
$678$		0			0
$679$	−10.1162	−	4.50404i	−0.388226	−	0.172849i
$680$	13.6776	−	25.8445i	0.524514	−	0.991091i
$681$		0			0
$682$	−20.4110	−	11.7843i	−0.781579	−	0.451245i
$683$	−7.99855	+	11.0091i	−0.306056	+	0.421250i	−0.934146	−	0.356890i	$-0.883837\pi$
$683$	−7.99855	+	11.0091i	−0.306056	+	0.421250i	0.628090	+	0.778141i	$0.283837\pi$
$684$		0			0
$685$	−29.1010	−	1.97833i	−1.11189	−	0.0755883i
$686$	20.7028	+	4.40052i	0.790437	+	0.168012i
$687$		0			0
$688$	−2.05404	−	9.66350i	−0.0783095	−	0.368417i
$689$	12.2437	−	13.5980i	0.466449	−	0.518044i
$690$		0			0
$691$	6.42143	+	7.13172i	0.244283	+	0.271303i	0.852800	−	0.522237i	$-0.174902\pi$
$691$	6.42143	+	7.13172i	0.244283	+	0.271303i	−0.608518	+	0.793540i	$0.708236\pi$
$692$	2.06701	−	2.84499i	0.0785758	−	0.108150i
$693$		0			0
$694$	7.20157	+	5.23224i	0.273368	+	0.198613i
$695$	−31.5182	+	1.16174i	−1.19555	+	0.0440671i
$696$		0			0
$697$	−6.43000	+	14.4420i	−0.243553	+	0.547030i
$698$	27.3894	+	24.6616i	1.03671	+	0.933454i
$699$		0			0
$700$	−2.17647	+	1.48034i	−0.0822629	+	0.0559516i
$701$	−41.0188			−1.54926			−0.774630	−	0.632415i	$-0.782064\pi$
$701$	−41.0188			−1.54926			−0.774630	+	0.632415i	$0.782064\pi$
$702$		0			0
$703$	−22.6937	−	31.2352i	−0.855910	−	1.17806i
$704$	−2.26138	−	21.5156i	−0.0852289	−	0.810899i
$705$		0			0
$706$	4.15894	−	39.5697i	0.156524	−	1.48922i
$707$	9.63377	−	5.56206i	0.362315	−	0.209183i
$708$		0			0
$709$	5.97729	+	6.63845i	0.224482	+	0.249312i	0.844856	−	0.534994i	$-0.179686\pi$
$709$	5.97729	+	6.63845i	0.224482	+	0.249312i	−0.620374	+	0.784306i	$0.713019\pi$
$710$	−4.94692	+	12.3126i	−0.185655	+	0.462085i
$711$		0			0
$712$	29.3471	+	9.53545i	1.09983	+	0.357356i
$713$	−48.0785	+	43.2901i	−1.80055	+	1.62123i
$714$		0			0
$715$	20.5213	−	19.8941i	0.767453	−	0.743997i
$716$	−0.151121	+	0.0321217i	−0.00564765	+	0.00120044i
$717$		0			0
$718$	1.70629	+	0.985126i	0.0636781	+	0.0367646i
$719$	1.23693	+	0.898681i	0.0461297	+	0.0335152i	0.610611	−	0.791931i	$-0.290924\pi$
$719$	1.23693	+	0.898681i	0.0461297	+	0.0335152i	−0.564482	+	0.825446i	$0.690924\pi$
$720$		0			0
$721$	6.09337	−	4.42709i	0.226929	−	0.164874i
$722$	−26.8685	+	2.82399i	−0.999941	+	0.105098i
$723$		0			0
$724$	−2.69039	−	4.65990i	−0.0999877	−	0.173184i
$725$	−30.4232	+	2.24579i	−1.12989	+	0.0834067i
$726$		0			0
$727$	−0.750020	+	3.52857i	−0.0278167	+	0.130867i	−0.989865	−	0.142012i	$-0.954643\pi$
$727$	−0.750020	+	3.52857i	−0.0278167	+	0.130867i	0.962048	+	0.272880i	$0.0879761\pi$
$728$	−12.8560	−	17.6948i	−0.476475	−	0.655812i
$729$		0			0
$730$	13.4616	−	16.1062i	0.498237	−	0.596116i
$731$	12.6160	−	5.61700i	0.466619	−	0.207752i
$732$		0			0
$733$	33.9163	+	3.56475i	1.25273	+	0.131667i	0.707556	−	0.706657i	$-0.249798\pi$
$733$	33.9163	+	3.56475i	1.25273	+	0.131667i	0.545172	+	0.838324i	$0.316464\pi$
$734$	−32.3103	+	6.86778i	−1.19260	+	0.253494i
$735$		0			0
$736$	−17.7403	−	3.77081i	−0.653916	−	0.138994i
$737$	9.05424	+	2.94190i	0.333517	+	0.108366i
$738$		0			0
$739$	−12.7212	−	39.1520i	−0.467959	−	1.44023i	−0.855223	−	0.518260i	$-0.826580\pi$
$739$	−12.7212	−	39.1520i	−0.467959	−	1.44023i	0.387265	−	0.921969i	$-0.373420\pi$
$740$	−0.192008	−	5.20924i	−0.00705836	−	0.191495i
$741$		0			0
$742$	6.05529	+	0.636437i	0.222297	+	0.0233643i
$743$	−1.57204	+	0.907620i	−0.0576727	+	0.0332974i	−0.528559	−	0.848897i	$-0.677268\pi$
$743$	−1.57204	+	0.907620i	−0.0576727	+	0.0332974i	0.470886	+	0.882194i	$0.343934\pi$
$744$		0			0
$745$	6.40660	−	22.5068i	0.234720	−	0.824586i
$746$	10.2184	−	7.42410i	0.374122	−	0.271816i
$747$		0			0
$748$	3.82620	−	1.24321i	0.139900	−	0.0454562i
$749$	8.49138	−	14.7075i	0.310268	−	0.537401i
$750$		0			0
$751$	15.0131	+	26.0035i	0.547836	+	0.948879i	0.998423	+	0.0561468i	$0.0178815\pi$
$751$	15.0131	+	26.0035i	0.547836	+	0.948879i	−0.450587	+	0.892733i	$0.648785\pi$
$752$	18.6963	+	16.8342i	0.681783	+	0.613881i
$753$		0			0
$754$	−4.25907	−	40.5223i	−0.155106	−	1.47574i
$755$	−8.16837	+	2.05341i	−0.297277	+	0.0747312i
$756$		0			0
$757$			33.1683i			1.20552i	0.797922	+	0.602761i	$0.205933\pi$
$757$			33.1683i			1.20552i	−0.797922	+	0.602761i	$0.794067\pi$
$758$	−1.13561	−	2.55061i	−0.0412471	−	0.0926425i
$759$		0			0
$760$	−37.9935	−	20.1073i	−1.37817	−	0.729368i
$761$	−30.6454	+	34.0351i	−1.11089	+	1.23377i	−0.141061	+	0.990001i	$0.545051\pi$
$761$	−30.6454	+	34.0351i	−1.11089	+	1.23377i	−0.969833	+	0.243771i	$0.921615\pi$
$762$		0			0
$763$	0.934419	−	0.841354i	0.0338282	−	0.0304591i
$764$	−0.261801	−	0.805742i	−0.00947164	−	0.0291507i
$765$		0			0
$766$	−8.47611	+	26.0868i	−0.306254	+	0.942554i
$767$	14.9510	+	33.5806i	0.539851	+	1.21252i
$768$		0			0
$769$	0.0670905	−	0.638324i	0.00241935	−	0.0230185i	−0.993246	−	0.116031i	$-0.962983\pi$
$769$	0.0670905	−	0.638324i	0.00241935	−	0.0230185i	0.995665	+	0.0930122i	$0.0296496\pi$
$770$	9.36917	+	1.63334i	0.337642	+	0.0588616i
$771$		0			0
$772$	−3.19819	+	0.336143i	−0.115105	+	0.0120981i
$773$	40.2576	−	13.0805i	1.44796	−	0.470472i	0.523594	−	0.851968i	$-0.324591\pi$
$773$	40.2576	−	13.0805i	1.44796	−	0.470472i	0.924371	+	0.381496i	$0.124591\pi$
$774$		0			0
$775$	−37.7278	−	5.15341i	−1.35522	−	0.185116i
$776$	12.2082	−	21.1453i	0.438250	−	0.759070i
$777$		0			0
$778$	2.91005	−	6.53609i	0.104330	−	0.234330i
$779$	21.2310	+	9.45263i	0.760678	+	0.338676i
$780$		0			0
$781$	−10.3759	+	4.61964i	−0.371278	+	0.165304i
$782$			46.6166i			1.66701i
$783$		0			0
$784$	−4.87605	+	15.0069i	−0.174145	+	0.535962i
$785$	−36.7153	−	10.4511i	−1.31043	−	0.373015i
$786$		0			0
$787$	−0.193102	−	0.908474i	−0.00688335	−	0.0323836i	0.974572	−	0.224075i	$-0.0719361\pi$
$787$	−0.193102	−	0.908474i	−0.00688335	−	0.0323836i	−0.981455	+	0.191691i	$0.938603\pi$
$788$	0.171169	+	0.805288i	0.00609765	+	0.0286872i
$789$		0			0
$790$	−10.2352	−	13.0483i	−0.364152	−	0.464238i
$791$	−2.41392	+	7.42929i	−0.0858292	+	0.264155i
$792$		0			0
$793$			12.8565i			0.456547i
$794$	−40.6635	+	18.1046i	−1.44310	+	0.642507i
$795$		0			0
$796$	1.72813	+	0.769412i	0.0612519	+	0.0272711i
$797$	−0.0425251	+	0.0955130i	−0.00150632	+	0.00338324i	−0.914297	−	0.405044i	$-0.867256\pi$
$797$	−0.0425251	+	0.0955130i	−0.00150632	+	0.00338324i	0.912791	+	0.408428i	$0.133923\pi$
$798$		0			0
$799$	−17.5838	+	30.4560i	−0.622070	+	1.07746i
$800$	−5.04790	−	9.40569i	−0.178470	−	0.332541i
$801$		0			0
$802$	−12.9971	+	4.22303i	−0.458945	+	0.149120i
$803$	17.8689	−	1.87809i	0.630579	−	0.0662765i
$804$		0			0
$805$	12.2115	−	23.0742i	0.430400	−	0.813258i
$806$	5.31625	−	50.5807i	0.187257	−	1.78163i
$807$		0			0
$808$	9.97636	+	22.4073i	0.350967	+	0.788285i
$809$	9.65384	−	29.7115i	0.339411	−	1.04460i	−0.625098	−	0.780547i	$-0.714941\pi$
$809$	9.65384	−	29.7115i	0.339411	−	1.04460i	0.964508	−	0.264052i	$-0.0850592\pi$
$810$		0			0
$811$	14.3004	+	44.0120i	0.502154	+	1.54547i	0.805504	+	0.592591i	$0.201895\pi$
$811$	14.3004	+	44.0120i	0.502154	+	1.54547i	−0.303350	+	0.952879i	$0.598105\pi$
$812$	−2.38691	+	2.14918i	−0.0837640	+	0.0754215i
$813$		0			0
$814$	−12.6027	+	13.9968i	−0.441726	+	0.490586i
$815$	−15.7709	−	32.1768i	−0.552429	−	1.12710i
$816$		0			0
$817$	−8.25745	−	18.5465i	−0.288892	−	0.648861i
$818$		−	48.7655i		−	1.70505i
$819$		0			0
$820$	1.66791	+	2.65776i	0.0582461	+	0.0928130i
$821$	−1.40413	−	13.3594i	−0.0490045	−	0.466247i	−0.991315	−	0.131507i	$-0.958018\pi$
$821$	−1.40413	−	13.3594i	−0.0490045	−	0.466247i	0.942311	−	0.334740i	$-0.108648\pi$
$822$		0			0
$823$	20.1367	+	18.1312i	0.701921	+	0.632013i	0.940771	−	0.339044i	$-0.110103\pi$
$823$	20.1367	+	18.1312i	0.701921	+	0.632013i	−0.238849	+	0.971057i	$0.576770\pi$
$824$	8.30354	+	14.3822i	0.289268	+	0.501026i
$825$		0			0
$826$	−6.11570	+	10.5927i	−0.212792	+	0.368567i
$827$	−22.8204	+	7.41480i	−0.793543	+	0.257838i	−0.677612	−	0.735419i	$-0.736985\pi$
$827$	−22.8204	+	7.41480i	−0.793543	+	0.257838i	−0.115931	+	0.993257i	$0.536985\pi$
$828$		0			0
$829$	15.1912	−	11.0370i	0.527611	−	0.383332i	−0.291852	−	0.956463i	$-0.594272\pi$
$829$	15.1912	−	11.0370i	0.527611	−	0.383332i	0.819463	+	0.573131i	$0.194272\pi$
$830$	20.3704	+	13.6827i	0.707066	+	0.474933i
$831$		0			0
$832$	40.4302	−	23.3424i	1.40166	−	0.809251i
$833$	−21.9362	−	2.30559i	−0.760044	−	0.0798838i
$834$		0			0
$835$	18.5600	+	23.6612i	0.642296	+	0.818830i
$836$	−1.82762	−	5.62483i	−0.0632095	−	0.194539i
$837$		0			0
$838$	1.16513	+	0.378575i	0.0402489	+	0.0130777i
$839$	53.7655	+	11.4282i	1.85619	+	0.394546i	0.993752	−	0.111614i	$-0.0356020\pi$
$839$	53.7655	+	11.4282i	1.85619	+	0.394546i	0.862440	+	0.506160i	$0.168935\pi$
$840$		0			0
$841$	−8.04477	+	1.70997i	−0.277406	+	0.0589644i
$842$	−38.7182	−	4.06945i	−1.33432	−	0.140242i
$843$		0			0
$844$	3.69473	−	1.64500i	0.127178	−	0.0566232i
$845$	30.2570	+	12.1565i	1.04087	+	0.418197i
$846$		0			0
$847$	−4.10100	−	5.64454i	−0.140912	−	0.193949i
$848$	−2.23627	+	10.5208i	−0.0767937	+	0.361286i
$849$		0			0
$850$	−20.9496	+	17.7175i	−0.718565	+	0.607704i
$851$	25.8504	+	44.7742i	0.886140	+	1.53484i
$852$		0			0
$853$	−18.8356	+	1.97970i	−0.644919	+	0.0677837i	−0.421341	−	0.906902i	$-0.638440\pi$
$853$	−18.8356	+	1.97970i	−0.644919	+	0.0677837i	−0.223578	+	0.974686i	$0.571774\pi$
$854$	−3.46097	+	2.51454i	−0.118432	+	0.0860458i
$855$		0			0
$856$	30.2942	+	22.0100i	1.03543	+	0.752287i
$857$	−18.6942	−	10.7931i	−0.638582	−	0.368685i	0.145486	−	0.989360i	$-0.453525\pi$
$857$	−18.6942	−	10.7931i	−0.638582	−	0.368685i	−0.784068	+	0.620675i	$0.786859\pi$
$858$		0			0
$859$	42.3468	−	9.00108i	1.44485	−	0.307113i	0.582256	−	0.813005i	$-0.302170\pi$
$859$	42.3468	−	9.00108i	1.44485	−	0.307113i	0.862597	+	0.505892i	$0.168837\pi$
$860$	0.470749	−	2.70031i	0.0160524	−	0.0920798i
$861$		0			0
$862$	−16.1148	+	14.5098i	−0.548872	+	0.494206i
$863$	23.8143	+	7.73774i	0.810648	+	0.263396i	0.684872	−	0.728663i	$-0.259858\pi$
$863$	23.8143	+	7.73774i	0.810648	+	0.263396i	0.125776	+	0.992059i	$0.459858\pi$
$864$		0			0
$865$	−17.3877	+	10.9119i	−0.591200	+	0.371016i
$866$	−30.5001	−	33.8738i	−1.03644	−	1.15108i
$867$		0			0
$868$	−3.47203	+	2.00458i	−0.117848	+	0.0680398i
$869$	1.48376	−	14.1170i	0.0503331	−	0.478888i
$870$		0			0
$871$	2.14742	+	20.4313i	0.0727625	+	0.692289i
$872$	1.62960	+	2.24295i	0.0551851	+	0.0759558i
$873$		0			0
$874$	68.5303			2.31807
$875$	15.0108	−	3.28187i	0.507458	−	0.110948i
$876$		0			0
$877$	−12.0562	−	10.8555i	−0.407110	−	0.366563i	0.439985	−	0.898005i	$-0.354984\pi$
$877$	−12.0562	−	10.8555i	−0.407110	−	0.366563i	−0.847095	+	0.531442i	$0.821650\pi$
$878$	−1.47013	+	3.30198i	−0.0496146	+	0.111436i
$879$		0			0
$880$	−4.59961	+	16.1588i	−0.155053	+	0.544711i
$881$	−16.6839	−	12.1216i	−0.562095	−	0.408386i	0.270130	−	0.962824i	$-0.412933\pi$
$881$	−16.6839	−	12.1216i	−0.562095	−	0.408386i	−0.832225	+	0.554438i	$0.812933\pi$
$882$		0			0
$883$	6.90327	−	9.50153i	0.232313	−	0.319752i	−0.676906	−	0.736070i	$-0.736680\pi$
$883$	6.90327	−	9.50153i	0.232313	−	0.319752i	0.909219	+	0.416318i	$0.136680\pi$
$884$	5.80910	+	6.45165i	0.195381	+	0.216993i
$885$		0			0
$886$	7.81201	−	8.67612i	0.262450	−	0.291480i
$887$	4.85150	+	22.8245i	0.162898	+	0.766373i	0.981416	+	0.191893i	$0.0614625\pi$
$887$	4.85150	+	22.8245i	0.162898	+	0.766373i	−0.818518	+	0.574480i	$0.805204\pi$
$888$		0			0
$889$	−0.195538	−	0.0415629i	−0.00655813	−	0.00139397i
$890$	−22.2161	−	18.5684i	−0.744686	−	0.622413i
$891$		0			0
$892$	−4.45019	+	6.12516i	−0.149003	+	0.205085i
$893$	44.7729	+	25.8496i	1.49827	+	0.865026i
$894$		0			0
$895$	0.888473	+	0.154889i	0.0296984	+	0.00517736i
$896$	8.83050	+	3.93159i	0.295006	+	0.131345i
$897$		0			0
$898$	−3.78967	+	17.8290i	−0.126463	+	0.594961i
$899$	−46.4643			−1.54967
$900$		0			0
$901$	−15.0351			−0.500891
$902$	2.35714	−	11.0895i	0.0784842	−	0.369239i
$903$		0			0
$904$	−15.7349	−	7.00564i	−0.523336	−	0.233004i
$905$	4.43167	+	31.0960i	0.147314	+	1.03367i
$906$		0			0
$907$	−6.31172	−	3.64408i	−0.209577	−	0.121000i	0.391538	−	0.920162i	$-0.371943\pi$
$907$	−6.31172	−	3.64408i	−0.209577	−	0.121000i	−0.601115	+	0.799163i	$0.705277\pi$
$908$	−2.45029	+	3.37253i	−0.0813156	+	0.111921i
$909$		0			0
$910$	5.00348	+	19.9036i	0.165864	+	0.659799i
$911$	−26.6795	−	5.67090i	−0.883931	−	0.187885i	−0.256488	−	0.966548i	$-0.582565\pi$
$911$	−26.6795	−	5.67090i	−0.883931	−	0.187885i	−0.627443	+	0.778662i	$0.715899\pi$
$912$		0			0
$913$	4.36703	+	20.5453i	0.144528	+	0.679949i
$914$	5.73848	−	6.37323i	0.189812	−	0.210808i
$915$		0			0
$916$	−2.44645	−	2.71706i	−0.0808331	−	0.0897742i
$917$	−0.381600	+	0.525228i	−0.0126015	+	0.0173445i
$918$		0			0
$919$	7.69986	+	5.59428i	0.253995	+	0.184538i	0.707496	−	0.706718i	$-0.249825\pi$
$919$	7.69986	+	5.59428i	0.253995	+	0.184538i	−0.453500	+	0.891256i	$0.649825\pi$
$920$	47.7836	+	32.0960i	1.57538	+	1.05818i
$921$		0			0
$922$	−7.36453	+	16.5410i	−0.242538	+	0.544749i
$923$	−18.2140	−	16.3999i	−0.599520	−	0.539810i
$924$		0			0
$925$	−10.2967	+	28.6345i	−0.338554	+	0.941495i
$926$	28.3349			0.931142
$927$		0			0
$928$	−7.65627	−	10.5379i	−0.251329	−	0.345925i
$929$	−2.83843	−	27.0058i	−0.0931258	−	0.886032i	−0.936962	−	0.349431i	$-0.886375\pi$
$929$	−2.83843	−	27.0058i	−0.0931258	−	0.886032i	0.843836	−	0.536601i	$-0.180292\pi$
$930$		0			0
$931$	−3.38940	+	32.2480i	−0.111083	+	1.05689i
$932$	−2.06040	+	1.18957i	−0.0674907	+	0.0389658i
$933$		0			0
$934$	8.00203	+	8.88715i	0.261834	+	0.290797i
$935$	−23.4307	−	1.59286i	−0.766266	−	0.0520921i
$936$		0			0
$937$	3.39434	+	1.10289i	0.110888	+	0.0360297i	0.363935	−	0.931424i	$-0.381433\pi$
$937$	3.39434	+	1.10289i	0.110888	+	0.0360297i	−0.253047	+	0.967454i	$0.581433\pi$
$938$	−5.08012	+	4.57416i	−0.165872	+	0.149352i
$939$		0			0
$940$	3.07205	+	6.26781i	0.100199	+	0.204433i
$941$	−19.6443	+	4.17553i	−0.640386	+	0.136118i	−0.516650	−	0.856197i	$-0.672821\pi$
$941$	−19.6443	+	4.17553i	−0.640386	+	0.136118i	−0.123736	+	0.992315i	$0.539488\pi$
$942$		0			0
$943$	−26.9513	−	15.5603i	−0.877656	−	0.506715i
$944$	−17.4806	−	12.7004i	−0.568946	−	0.413364i
$945$		0			0
$946$	−8.01230	+	5.82128i	−0.260502	+	0.189266i
$947$	−16.0698	+	1.68901i	−0.522199	+	0.0548854i	−0.361961	−	0.932193i	$-0.617893\pi$
$947$	−16.0698	+	1.68901i	−0.522199	+	0.0548854i	−0.160238	+	0.987078i	$0.551226\pi$
$948$		0			0
$949$	19.3860	+	33.5776i	0.629298	+	1.08998i
$950$	26.0462	+	30.7977i	0.845049	+	0.999208i
$951$		0			0
$952$	−3.73653	+	17.5790i	−0.121102	+	0.569739i
$953$	−30.7863	−	42.3737i	−0.997266	−	1.37262i	−0.926988	−	0.375091i	$-0.877611\pi$
$953$	−30.7863	−	42.3737i	−0.997266	−	1.37262i	−0.0702776	−	0.997527i	$-0.522389\pi$
$954$		0			0
$955$	−0.335433	+	4.93417i	−0.0108544	+	0.159666i
$956$	4.46965	−	1.99002i	0.144559	−	0.0643617i
$957$		0			0
$958$	42.3963	+	4.45603i	1.36976	+	0.143968i
$959$	17.5354	−	3.72727i	0.566249	−	0.120360i
$960$		0			0
$961$	−26.4077	−	5.61313i	−0.851861	−	0.181069i
$962$	−38.6542	−	12.5595i	−1.24626	−	0.404935i
$963$		0			0
$964$	−1.58015	−	4.86322i	−0.0508934	−	0.156634i
$965$	18.0550	+	5.13938i	0.581210	+	0.165442i
$966$		0			0
$967$	−14.6411	−	1.53884i	−0.470826	−	0.0494858i	−0.133855	−	0.991001i	$-0.542736\pi$
$967$	−14.6411	−	1.53884i	−0.470826	−	0.0494858i	−0.336971	+	0.941515i	$0.609402\pi$
$968$	13.3228	−	7.69191i	0.428210	−	0.247227i
$969$		0			0
$970$	−18.0263	+	14.1400i	−0.578791	+	0.454008i
$971$	40.7593	−	29.6133i	1.30803	−	0.950337i	0.308028	−	0.951377i	$-0.400331\pi$
$971$	40.7593	−	29.6133i	1.30803	−	0.950337i	0.999999	+	0.00103991i	$0.000331013\pi$
$972$		0			0
$973$	18.4360	−	5.99021i	0.591030	−	0.192037i
$974$	12.5952	−	21.8156i	0.403578	−	0.699017i
$975$		0			0
$976$	−3.77862	−	6.54477i	−0.120951	−	0.209493i
$977$	17.1534	+	15.4450i	0.548786	+	0.494129i	0.896241	−	0.443567i	$-0.146287\pi$
$977$	17.1534	+	15.4450i	0.548786	+	0.494129i	−0.347455	+	0.937697i	$0.612954\pi$
$978$		0			0
$979$	−2.59056	−	24.6475i	−0.0827946	−	0.787738i
$980$	−2.80760	+	3.35915i	−0.0896853	+	0.107304i
$981$		0			0
$982$		−	5.37116i		−	0.171401i
$983$	2.58073	+	5.79641i	0.0823125	+	0.184877i	0.950013	−	0.312211i	$-0.101069\pi$
$983$	2.58073	+	5.79641i	0.0823125	+	0.184877i	−0.867700	+	0.497087i	$0.834403\pi$
$984$		0			0
$985$	0.825368	−	4.73447i	0.0262984	−	0.150853i
$986$	−22.4023	+	24.8803i	−0.713436	+	0.792351i
$987$		0			0
$988$	9.48447	−	8.53985i	0.301741	−	0.271689i
$989$	8.40088	+	25.8553i	0.267133	+	0.822150i
$990$		0			0
$991$	9.17859	−	28.2488i	0.291568	−	0.897353i	−0.692785	−	0.721144i	$-0.743617\pi$
$991$	9.17859	−	28.2488i	0.291568	−	0.897353i	0.984353	−	0.176209i	$-0.0563834\pi$
$992$	−6.61306	−	14.8532i	−0.209965	−	0.471589i
$993$		0			0
$994$	0.852480	−	8.11080i	0.0270390	−	0.257259i
$995$	−7.68619	−	7.92851i	−0.243669	−	0.251351i
$996$		0			0
$997$	41.4588	−	4.35750i	1.31301	−	0.138003i	0.577989	−	0.816044i	$-0.303837\pi$
$997$	41.4588	−	4.35750i	1.31301	−	0.138003i	0.735024	+	0.678041i	$0.237171\pi$
$998$	−41.9017	+	13.6147i	−1.32637	+	0.430965i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.y.a.19.8		224
3.2	odd	2		225.2.u.a.169.21	yes	224
9.4	even	3	inner	675.2.y.a.469.8		224
9.5	odd	6		225.2.u.a.94.21	yes	224
25.4	even	10	inner	675.2.y.a.154.8		224
75.29	odd	10		225.2.u.a.79.21	yes	224
225.4	even	30	inner	675.2.y.a.604.8		224
225.104	odd	30		225.2.u.a.4.21	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.21	✓	224	225.104	odd	30
225.2.u.a.79.21	yes	224	75.29	odd	10
225.2.u.a.94.21	yes	224	9.5	odd	6
225.2.u.a.169.21	yes	224	3.2	odd	2
675.2.y.a.19.8		224	1.1	even	1	trivial
675.2.y.a.154.8		224	25.4	even	10	inner
675.2.y.a.469.8		224	9.4	even	3	inner
675.2.y.a.604.8		224	225.4	even	30	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.y (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.264379 + 1.24380i) q^{2} +(0.349937 + 0.155802i) q^{4} +(-1.55641 - 1.60548i) q^{5} +(1.19020 + 0.687160i) q^{7} +(-1.78115 + 2.45154i) q^{8} +O(q^{10})\)	\(q+(-0.264379 + 1.24380i) q^{2} +(0.349937 + 0.155802i) q^{4} +(-1.55641 - 1.60548i) q^{5} +(1.19020 + 0.687160i) q^{7} +(-1.78115 + 2.45154i) q^{8} +(2.40839 - 1.51142i) q^{10} +(2.38060 + 0.506011i) q^{11} +(1.09193 + 5.13715i) q^{13} +(-1.16936 + 1.29870i) q^{14} +(-2.06572 - 2.29421i) q^{16} +(2.53652 - 3.49123i) q^{17} +(-5.13239 - 3.72890i) q^{19} +(-0.294509 - 0.804310i) q^{20} +(-1.25876 + 2.82722i) q^{22} +(6.31314 + 5.68438i) q^{23} +(-0.155149 + 4.99759i) q^{25} -6.67830 q^{26} +(0.309433 + 0.425898i) q^{28} +(0.637748 + 6.06776i) q^{29} +(-0.796049 + 7.57390i) q^{31} +(-1.84891 + 1.06747i) q^{32} +(3.67180 + 4.07795i) q^{34} +(-0.749215 - 2.98035i) q^{35} +(5.78803 + 1.88065i) q^{37} +(5.99492 - 5.39785i) q^{38} +(6.70811 - 0.956010i) q^{40} +(-3.58329 + 0.761651i) q^{41} +(2.77141 + 1.60008i) q^{43} +(0.754221 + 0.547974i) q^{44} +(-8.73932 + 6.34949i) q^{46} +(-8.10470 + 0.851838i) q^{47} +(-2.55562 - 4.42647i) q^{49} +(-6.17501 - 1.51423i) q^{50} +(-0.418269 + 1.96780i) q^{52} +(-2.04788 - 2.81866i) q^{53} +(-2.89280 - 4.60957i) q^{55} +(-3.80452 + 1.69388i) q^{56} +(-7.71572 - 0.810955i) q^{58} +(6.84612 - 1.45519i) q^{59} +(2.39447 + 0.508959i) q^{61} +(-9.20999 - 2.99251i) q^{62} +(-2.74688 - 8.45403i) q^{64} +(6.54810 - 9.74862i) q^{65} +(3.89026 + 0.408883i) q^{67} +(1.43156 - 0.826513i) q^{68} +(3.90505 - 0.143937i) q^{70} +(-3.77547 + 2.74304i) q^{71} +(7.02114 - 2.28131i) q^{73} +(-3.86939 + 6.70198i) q^{74} +(-1.21504 - 2.10452i) q^{76} +(2.48567 + 2.23811i) q^{77} +(-0.609652 - 5.80045i) q^{79} +(-0.468204 + 6.88721i) q^{80} -4.65827i q^{82} +(3.51026 + 7.88417i) q^{83} +(-9.55299 + 1.36145i) q^{85} +(-2.72288 + 3.02407i) q^{86} +(-5.48071 + 4.93485i) q^{88} +(-3.14673 - 9.68464i) q^{89} +(-2.23043 + 6.86455i) q^{91} +(1.32356 + 2.97277i) q^{92} +(1.08319 - 10.3059i) q^{94} +(2.00144 + 14.0437i) q^{95} +(-8.01337 + 0.842239i) q^{97} +(6.18131 - 2.00843i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

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